%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : PRO024^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:28:08 AM UTC 2026
% Result : Theorem 6.44s 2.14s
% Output : Refutation 6.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : PRO024^1 : TPTP v9.2.1. Released v7.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n014.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 11:29:42 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.19/0.46 ---- Original DTF file ---
% 0.19/0.46 thf(spec,logic,$$dhol).
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 % File : PRO024^1 : TPTP v9.2.1. Released v7.0.0.
% 0.19/0.46 % Domain : Processes
% 0.19/0.46 % Problem : Process algebra 193
% 0.19/0.46 % Version : [Bla16] axioms : Especial.
% 0.19/0.46 % English :
% 0.19/0.46
% 0.19/0.46 % Refs : [BH+14] Blanchette et al. (2014), Truly Modular (Co)datatypes
% 0.19/0.46 % : [RB15] Reynolds & Blanchette (2015), A Decision Procedure for
% 0.19/0.46 % : [Bla16] Blanchette (2016), Email to Geoff Sutcliffe
% 0.19/0.46 % Source : [Bla16]
% 0.19/0.46 % Names : process__193.p [Bla16]
% 0.19/0.46
% 0.19/0.46 % Status : Theorem
% 0.19/0.46 % Rating : 0.33 v9.1.0, 0.00 v7.2.0, 0.25 v7.1.0
% 0.19/0.46 % Syntax : Number of formulae : 324 ( 145 unt; 65 typ; 0 def)
% 0.19/0.46 % Number of atoms : 878 ( 371 equ; 0 cnn)
% 0.19/0.46 % Maximal formula atoms : 31 ( 3 avg)
% 0.19/0.46 % Number of connectives : 8492 ( 171 ~; 11 |; 49 &;7881 @)
% 0.19/0.46 % ( 0 <=>; 380 =>; 0 <=; 0 <~>)
% 0.19/0.46 % Maximal formula depth : 31 ( 11 avg)
% 0.19/0.46 % Number of types : 3 ( 2 usr)
% 0.19/0.46 % Number of type conns : 1364 (1364 >; 0 *; 0 +; 0 <<)
% 0.19/0.46 % Number of symbols : 66 ( 63 usr; 6 con; 0-14 aty)
% 0.19/0.46 % Number of variables : 2027 ( 252 ^;1648 !; 23 ?;2027 :)
% 0.19/0.46 % ( 104 !>; 0 ?*; 0 @-; 0 @+)
% 0.19/0.46 % SPC : TH1_THM_EQU_NAR
% 0.19/0.46
% 0.19/0.46 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.19/0.46 % 2016-07-13 14:40:02.087
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 %----Could-be-implicit typings (7)
% 0.19/0.46 thf(ty_t_Process__Mirabelle__xovoopgpgi_Oprocess__term,type,
% 0.19/0.46 proces554692349s_term: $tType > $tType > $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_t_Process__Mirabelle__xovoopgpgi_Oprocess,type,
% 0.19/0.46 proces634752977rocess: $tType > $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_t_Product__Type_Oprod,type,
% 0.19/0.46 product_prod: $tType > $tType > $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_t_Set_Oset,type,
% 0.19/0.46 set: $tType > $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_t_itself,type,
% 0.19/0.46 itself: $tType > $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_tf_b,type,
% 0.19/0.46 b: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_tf_a,type,
% 0.19/0.46 a: $tType ).
% 0.19/0.46
% 0.19/0.46 %----Explicit typings (58)
% 0.19/0.46 thf(sy_c_BNF__Def_Orel__fun,type,
% 0.19/0.46 bNF_rel_fun:
% 0.19/0.46 !>[A: $tType,C: $tType,B: $tType,D: $tType] : ( ( A > C > $o ) > ( B > D > $o ) > ( A > B ) > ( C > D ) > $o ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_HOL_Oundefined,type,
% 0.19/0.46 undefined:
% 0.19/0.46 !>[A: $tType] : A ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_If,type,
% 0.19/0.46 if:
% 0.19/0.46 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Order__Relation_Oabove,type,
% 0.19/0.46 order_above:
% 0.19/0.46 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > A > ( set @ A ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Order__Relation_OaboveS,type,
% 0.19/0.46 order_aboveS:
% 0.19/0.46 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > A > ( set @ A ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Process__Mirabelle__xovoopgpgi_OCH1,type,
% 0.19/0.46 proces1239275103le_CH1:
% 0.19/0.46 !>[A: $tType,B: $tType] : ( ( A > ( proces554692349s_term @ B @ A ) ) > ( proces554692349s_term @ B @ A ) > ( proces554692349s_term @ B @ A ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Process__Mirabelle__xovoopgpgi_OCH1__rel,type,
% 0.19/0.46 proces1869379930H1_rel:
% 0.19/0.46 !>[A: $tType,B: $tType] : ( ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) > ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) > $o ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Process__Mirabelle__xovoopgpgi_OCH2,type,
% 0.19/0.46 proces1239275104le_CH2:
% 0.19/0.46 !>[A: $tType,B: $tType] : ( ( A > ( proces554692349s_term @ B @ A ) ) > ( proces554692349s_term @ B @ A ) > ( proces554692349s_term @ B @ A ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Process__Mirabelle__xovoopgpgi_OCH2__rel,type,
% 0.19/0.46 proces93903513H2_rel:
% 0.19/0.46 !>[A: $tType,B: $tType] : ( ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) > ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) > $o ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Process__Mirabelle__xovoopgpgi_OCONT,type,
% 0.19/0.46 proces126235999e_CONT:
% 0.19/0.46 !>[A: $tType,B: $tType] : ( ( A > ( proces554692349s_term @ B @ A ) ) > ( proces554692349s_term @ B @ A ) > ( proces554692349s_term @ B @ A ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Process__Mirabelle__xovoopgpgi_OCONT__rel,type,
% 0.19/0.46 proces1004198490NT_rel:
% 0.19/0.46 !>[A: $tType,B: $tType] : ( ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) > ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) > $o ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Process__Mirabelle__xovoopgpgi_OPREF,type,
% 0.19/0.46 proces1708129104e_PREF:
% 0.19/0.46 !>[A: $tType,B: $tType,C: $tType] : ( ( A > ( proces554692349s_term @ B @ C ) ) > ( proces554692349s_term @ B @ A ) > B ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Process__Mirabelle__xovoopgpgi_OPREF__rel,type,
% 0.19/0.46 proces527360425EF_rel:
% 0.19/0.46 !>[A: $tType,B: $tType,C: $tType] : ( ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) ) > ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) ) > $o ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oguarded,type,
% 0.19/0.46 proces1121166967uarded:
% 0.19/0.46 !>[A: $tType,B: $tType,C: $tType] : ( ( A > ( proces554692349s_term @ B @ C ) ) > $o ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Process__Mirabelle__xovoopgpgi_OisACT,type,
% 0.19/0.46 proces687458811_isACT:
% 0.19/0.46 !>[A: $tType,B: $tType,C: $tType,D: $tType] : ( ( A > ( proces554692349s_term @ B @ C ) ) > ( proces554692349s_term @ D @ A ) > $o ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Process__Mirabelle__xovoopgpgi_OisACT__rel,type,
% 0.19/0.46 proces896239806CT_rel:
% 0.19/0.46 !>[A: $tType,B: $tType,C: $tType,D: $tType] : ( ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) > ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) > $o ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OAction,type,
% 0.19/0.46 proces1525233512Action:
% 0.19/0.46 !>[A: $tType] : ( A > ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OChoice,type,
% 0.19/0.46 proces1915862579Choice:
% 0.19/0.46 !>[A: $tType] : ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Ocase__process,type,
% 0.19/0.46 proces1406508781rocess:
% 0.19/0.46 !>[A: $tType,B: $tType] : ( ( A > ( proces634752977rocess @ A ) > B ) > ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B ) > ( proces634752977rocess @ A ) > B ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Och1Of,type,
% 0.19/0.46 proces979765041_ch1Of:
% 0.19/0.46 !>[A: $tType] : ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Och2Of,type,
% 0.19/0.46 proces988026546_ch2Of:
% 0.19/0.46 !>[A: $tType] : ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OcontOf,type,
% 0.19/0.46 proces1778668539contOf:
% 0.19/0.46 !>[A: $tType] : ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Ocorec__process,type,
% 0.19/0.46 proces894737309rocess:
% 0.19/0.46 !>[C: $tType,A: $tType] : ( ( C > $o ) > ( C > A ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > C > ( proces634752977rocess @ A ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OisAction,type,
% 0.19/0.46 proces10484146Action:
% 0.19/0.46 !>[A: $tType] : ( ( proces634752977rocess @ A ) > $o ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OisChoice,type,
% 0.19/0.46 proces401113213Choice:
% 0.19/0.46 !>[A: $tType] : ( ( proces634752977rocess @ A ) > $o ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Opred__process,type,
% 0.19/0.46 proces1205983068rocess:
% 0.19/0.46 !>[A: $tType] : ( ( A > $o ) > ( proces634752977rocess @ A ) > $o ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OprefOf,type,
% 0.19/0.46 proces745025900prefOf:
% 0.19/0.46 !>[A: $tType] : ( ( proces634752977rocess @ A ) > A ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Orel__process,type,
% 0.19/0.46 proces749077512rocess:
% 0.19/0.46 !>[A: $tType,B: $tType] : ( ( A > B > $o ) > ( proces634752977rocess @ A ) > ( proces634752977rocess @ B ) > $o ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_OACT,type,
% 0.19/0.46 proces1454156180ss_ACT:
% 0.19/0.46 !>[A: $tType,Pvar: $tType] : ( A > ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_OCH,type,
% 0.19/0.46 proces89589571ess_CH:
% 0.19/0.46 !>[A: $tType,Pvar: $tType] : ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_OPROC,type,
% 0.19/0.46 proces1062592052s_PROC:
% 0.19/0.46 !>[A: $tType,Pvar: $tType] : ( ( proces634752977rocess @ A ) > ( proces554692349s_term @ A @ Pvar ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_OVAR,type,
% 0.19/0.46 proces1627516585ss_VAR:
% 0.19/0.46 !>[Pvar: $tType,A: $tType] : ( Pvar > ( proces554692349s_term @ A @ Pvar ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Ocase__process__term,type,
% 0.19/0.46 proces460752237s_term:
% 0.19/0.46 !>[Pvar: $tType,B: $tType,A: $tType] : ( ( Pvar > B ) > ( ( proces634752977rocess @ A ) > B ) > ( A > ( proces554692349s_term @ A @ Pvar ) > B ) > ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > B ) > ( proces554692349s_term @ A @ Pvar ) > B ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Opred__process__term,type,
% 0.19/0.46 proces2118920028s_term:
% 0.19/0.46 !>[A: $tType,B: $tType] : ( ( A > $o ) > ( B > $o ) > ( proces554692349s_term @ A @ B ) > $o ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Orec__process__term,type,
% 0.19/0.46 proces2117273769s_term:
% 0.19/0.46 !>[Pvar: $tType,D: $tType,A: $tType] : ( ( Pvar > D ) > ( ( proces634752977rocess @ A ) > D ) > ( A > ( proces554692349s_term @ A @ Pvar ) > D > D ) > ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D > D > D ) > ( proces554692349s_term @ A @ Pvar ) > D ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Orel__process__term,type,
% 0.19/0.46 proces2029722208s_term:
% 0.19/0.46 !>[A: $tType,C: $tType,B: $tType,D: $tType] : ( ( A > C > $o ) > ( B > D > $o ) > ( proces554692349s_term @ A @ B ) > ( proces554692349s_term @ C @ D ) > $o ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Oset2__process__term,type,
% 0.19/0.46 proces1493547885s_term:
% 0.19/0.46 !>[A: $tType,Pvar: $tType] : ( ( proces554692349s_term @ A @ Pvar ) > ( set @ Pvar ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Process__Mirabelle__xovoopgpgi_Osolution,type,
% 0.19/0.46 proces1652378886lution:
% 0.19/0.46 !>[A: $tType,B: $tType] : ( ( A > ( proces554692349s_term @ B @ A ) ) > ( proces554692349s_term @ B @ A ) > ( proces634752977rocess @ B ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Product__Type_OPair,type,
% 0.19/0.46 product_Pair:
% 0.19/0.46 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Product__Type_Ocurry,type,
% 0.19/0.46 product_curry:
% 0.19/0.46 !>[A: $tType,B: $tType,C: $tType] : ( ( ( product_prod @ A @ B ) > C ) > A > B > C ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Product__Type_Ointernal__case__prod,type,
% 0.19/0.46 produc2004651681e_prod:
% 0.19/0.46 !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > ( product_prod @ A @ B ) > C ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod,type,
% 0.19/0.46 product_rec_prod:
% 0.19/0.46 !>[A: $tType,B: $tType,T: $tType] : ( ( A > B > T ) > ( product_prod @ A @ B ) > T ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Pure_Otype,type,
% 0.19/0.46 type:
% 0.19/0.46 !>[A: $tType] : ( itself @ A ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Relation_Oinv__image,type,
% 0.19/0.46 inv_image:
% 0.19/0.46 !>[B: $tType,A: $tType] : ( ( set @ ( product_prod @ B @ B ) ) > ( A > B ) > ( set @ ( product_prod @ A @ A ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Relation_Oinv__imagep,type,
% 0.19/0.46 inv_imagep:
% 0.19/0.46 !>[B: $tType,A: $tType] : ( ( B > B > $o ) > ( A > B ) > A > A > $o ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Set_OCollect,type,
% 0.19/0.46 collect:
% 0.19/0.46 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Wellfounded_Oacc,type,
% 0.19/0.46 acc:
% 0.19/0.46 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > ( set @ A ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Wellfounded_Oaccp,type,
% 0.19/0.46 accp:
% 0.19/0.46 !>[A: $tType] : ( ( A > A > $o ) > A > $o ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Wellfounded_Olex__prod,type,
% 0.19/0.46 lex_prod:
% 0.19/0.46 !>[A: $tType,B: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > ( set @ ( product_prod @ B @ B ) ) > ( set @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Wfrec_Oadm__wf,type,
% 0.19/0.46 adm_wf:
% 0.19/0.46 !>[A: $tType,B: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > ( ( A > B ) > A > B ) > $o ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Wfrec_Ocut,type,
% 0.19/0.46 cut:
% 0.19/0.46 !>[A: $tType,B: $tType] : ( ( A > B ) > ( set @ ( product_prod @ A @ A ) ) > A > A > B ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Wfrec_Osame__fst,type,
% 0.19/0.46 same_fst:
% 0.19/0.46 !>[A: $tType,B: $tType] : ( ( A > $o ) > ( A > ( set @ ( product_prod @ B @ B ) ) ) > ( set @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_member,type,
% 0.19/0.46 member:
% 0.19/0.46 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_v_p,type,
% 0.19/0.46 p: proces634752977rocess @ a ).
% 0.19/0.46
% 0.19/0.46 thf(sy_v_p_H____,type,
% 0.19/0.46 p2: proces634752977rocess @ a ).
% 0.19/0.46
% 0.19/0.46 thf(sy_v_pa____,type,
% 0.19/0.46 pa: proces634752977rocess @ a ).
% 0.19/0.46
% 0.19/0.46 thf(sy_v_q____,type,
% 0.19/0.46 q: proces634752977rocess @ a ).
% 0.19/0.46
% 0.19/0.46 thf(sy_v_sys,type,
% 0.19/0.46 sys: b > ( proces554692349s_term @ a @ b ) ).
% 0.19/0.46
% 0.19/0.46 %----Relevant facts (255)
% 0.19/0.46 thf(fact_0__092_060open_062isChoice_Ap_092_060close_062,axiom,
% 0.19/0.46 proces401113213Choice @ a @ pa ).
% 0.19/0.46
% 0.19/0.46 % \<open>isChoice p\<close>
% 0.19/0.46 thf(fact_1_process__term_Oinject_I2_J,axiom,
% 0.19/0.46 ! [Pvar: $tType,A: $tType,X2: proces634752977rocess @ A,Y2: proces634752977rocess @ A] :
% 0.19/0.46 ( ( ( proces1062592052s_PROC @ A @ Pvar @ X2 )
% 0.19/0.46 = ( proces1062592052s_PROC @ A @ Pvar @ Y2 ) )
% 0.19/0.46 = ( X2 = Y2 ) ) ).
% 0.19/0.46
% 0.19/0.46 % process_term.inject(2)
% 0.19/0.46 thf(fact_2__092_060open_062q_A_061_Asolution_Asys_A_IPROC_Ap_J_092_060close_062,axiom,
% 0.19/0.46 ( q
% 0.19/0.46 = ( proces1652378886lution @ b @ a @ sys @ ( proces1062592052s_PROC @ a @ b @ p ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % \<open>q = solution sys (PROC p)\<close>
% 0.19/0.46 thf(fact_3_isACT_Osimps_I2_J,axiom,
% 0.19/0.46 ! [A: $tType,C: $tType,B: $tType,D: $tType,Sys: A > ( proces554692349s_term @ B @ C ),P: proces634752977rocess @ D] :
% 0.19/0.46 ( ( proces687458811_isACT @ A @ B @ C @ D @ Sys @ ( proces1062592052s_PROC @ D @ A @ P ) )
% 0.19/0.46 = ( proces10484146Action @ D @ P ) ) ).
% 0.19/0.46
% 0.19/0.46 % isACT.simps(2)
% 0.19/0.46 thf(fact_4__092_060open_062isAction_Ap_A_092_060or_062_AisChoice_Ap_092_060close_062,axiom,
% 0.19/0.46 ( ( proces10484146Action @ a @ pa )
% 0.19/0.46 | ( proces401113213Choice @ a @ pa ) ) ).
% 0.19/0.46
% 0.19/0.46 % \<open>isAction p \<or> isChoice p\<close>
% 0.19/0.46 thf(fact_5_iss,axiom,
% 0.19/0.46 ( p2
% 0.19/0.46 = ( proces1652378886lution @ b @ a @ sys @ ( proces1062592052s_PROC @ a @ b @ pa ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % iss
% 0.19/0.46 thf(fact_6_process__term_Osimps_I22_J,axiom,
% 0.19/0.46 ! [Pvar: $tType,D: $tType,A: $tType,F1: Pvar > D,F2: ( proces634752977rocess @ A ) > D,F3: A > ( proces554692349s_term @ A @ Pvar ) > D > D,F4: ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D > D > D,X2: proces634752977rocess @ A] :
% 0.19/0.46 ( ( proces2117273769s_term @ Pvar @ D @ A @ F1 @ F2 @ F3 @ F4 @ ( proces1062592052s_PROC @ A @ Pvar @ X2 ) )
% 0.19/0.46 = ( F2 @ X2 ) ) ).
% 0.19/0.46
% 0.19/0.46 % process_term.simps(22)
% 0.19/0.46 thf(fact_7_process__term_Osimps_I18_J,axiom,
% 0.19/0.46 ! [Pvar: $tType,B: $tType,A: $tType,F1: Pvar > B,F2: ( proces634752977rocess @ A ) > B,F3: A > ( proces554692349s_term @ A @ Pvar ) > B,F4: ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > B,X2: proces634752977rocess @ A] :
% 0.19/0.46 ( ( proces460752237s_term @ Pvar @ B @ A @ F1 @ F2 @ F3 @ F4 @ ( proces1062592052s_PROC @ A @ Pvar @ X2 ) )
% 0.19/0.46 = ( F2 @ X2 ) ) ).
% 0.19/0.46
% 0.19/0.46 % process_term.simps(18)
% 0.19/0.46 thf(fact_8_solution_Odisc__iff_I2_J,axiom,
% 0.19/0.46 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 0.19/0.46 ( ( proces401113213Choice @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) )
% 0.19/0.46 = ( ~ ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % solution.disc_iff(2)
% 0.19/0.46 thf(fact_9_solution_Odisc__iff_I1_J,axiom,
% 0.19/0.46 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 0.19/0.46 ( ( proces10484146Action @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) )
% 0.19/0.46 = ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 ) ) ).
% 0.19/0.46
% 0.19/0.46 % solution.disc_iff(1)
% 0.19/0.46 thf(fact_10_solution_Odisc_I2_J,axiom,
% 0.19/0.46 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 0.19/0.46 ( ~ ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
% 0.19/0.46 => ( proces401113213Choice @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % solution.disc(2)
% 0.19/0.46 thf(fact_11_isACT_Osimps_I3_J,axiom,
% 0.19/0.46 ! [B: $tType,C: $tType,A: $tType,D: $tType,Sys: A > ( proces554692349s_term @ B @ C ),A2: D,T2: proces554692349s_term @ D @ A] : ( proces687458811_isACT @ A @ B @ C @ D @ Sys @ ( proces1454156180ss_ACT @ D @ A @ A2 @ T2 ) ) ).
% 0.19/0.46
% 0.19/0.46 % isACT.simps(3)
% 0.19/0.46 thf(fact_12_isACT_Osimps_I4_J,axiom,
% 0.19/0.46 ! [B: $tType,C: $tType,A: $tType,D: $tType,Sys: A > ( proces554692349s_term @ B @ C ),T1: proces554692349s_term @ D @ A,T22: proces554692349s_term @ D @ A] :
% 0.19/0.46 ~ ( proces687458811_isACT @ A @ B @ C @ D @ Sys @ ( proces89589571ess_CH @ D @ A @ T1 @ T22 ) ) ).
% 0.19/0.46
% 0.19/0.46 % isACT.simps(4)
% 0.19/0.46 thf(fact_13_solution_Odisc_I1_J,axiom,
% 0.19/0.46 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 0.19/0.46 ( ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
% 0.19/0.46 => ( proces10484146Action @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % solution.disc(1)
% 0.19/0.46 thf(fact_14_not__isAction__isChoice,axiom,
% 0.19/0.46 ! [A: $tType,P: proces634752977rocess @ A] :
% 0.19/0.46 ~ ( ( proces10484146Action @ A @ P )
% 0.19/0.46 & ( proces401113213Choice @ A @ P ) ) ).
% 0.19/0.46
% 0.19/0.46 % not_isAction_isChoice
% 0.19/0.46 thf(fact_15_process__term_Oinject_I4_J,axiom,
% 0.19/0.46 ! [Pvar: $tType,A: $tType,X41: proces554692349s_term @ A @ Pvar,X42: proces554692349s_term @ A @ Pvar,Y41: proces554692349s_term @ A @ Pvar,Y42: proces554692349s_term @ A @ Pvar] :
% 0.19/0.46 ( ( ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 )
% 0.19/0.46 = ( proces89589571ess_CH @ A @ Pvar @ Y41 @ Y42 ) )
% 0.19/0.46 = ( ( X41 = Y41 )
% 0.19/0.46 & ( X42 = Y42 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % process_term.inject(4)
% 0.19/0.46 thf(fact_16_process__term_Oinject_I3_J,axiom,
% 0.19/0.46 ! [Pvar: $tType,A: $tType,X31: A,X32: proces554692349s_term @ A @ Pvar,Y31: A,Y32: proces554692349s_term @ A @ Pvar] :
% 0.19/0.46 ( ( ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 )
% 0.19/0.46 = ( proces1454156180ss_ACT @ A @ Pvar @ Y31 @ Y32 ) )
% 0.19/0.46 = ( ( X31 = Y31 )
% 0.19/0.46 & ( X32 = Y32 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % process_term.inject(3)
% 0.19/0.46 thf(fact_17_process__term_Osimps_I24_J,axiom,
% 0.19/0.46 ! [D: $tType,Pvar: $tType,A: $tType,F1: Pvar > D,F2: ( proces634752977rocess @ A ) > D,F3: A > ( proces554692349s_term @ A @ Pvar ) > D > D,F4: ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D > D > D,X41: proces554692349s_term @ A @ Pvar,X42: proces554692349s_term @ A @ Pvar] :
% 0.19/0.46 ( ( proces2117273769s_term @ Pvar @ D @ A @ F1 @ F2 @ F3 @ F4 @ ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 ) )
% 0.19/0.46 = ( F4 @ X41 @ X42 @ ( proces2117273769s_term @ Pvar @ D @ A @ F1 @ F2 @ F3 @ F4 @ X41 ) @ ( proces2117273769s_term @ Pvar @ D @ A @ F1 @ F2 @ F3 @ F4 @ X42 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % process_term.simps(24)
% 0.19/0.46 thf(fact_18_process__term_Osimps_I23_J,axiom,
% 0.19/0.46 ! [D: $tType,Pvar: $tType,A: $tType,F1: Pvar > D,F2: ( proces634752977rocess @ A ) > D,F3: A > ( proces554692349s_term @ A @ Pvar ) > D > D,F4: ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D > D > D,X31: A,X32: proces554692349s_term @ A @ Pvar] :
% 0.19/0.46 ( ( proces2117273769s_term @ Pvar @ D @ A @ F1 @ F2 @ F3 @ F4 @ ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) )
% 0.19/0.46 = ( F3 @ X31 @ X32 @ ( proces2117273769s_term @ Pvar @ D @ A @ F1 @ F2 @ F3 @ F4 @ X32 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % process_term.simps(23)
% 0.19/0.46 thf(fact_19_process__term_Osimps_I20_J,axiom,
% 0.19/0.46 ! [B: $tType,Pvar: $tType,A: $tType,F1: Pvar > B,F2: ( proces634752977rocess @ A ) > B,F3: A > ( proces554692349s_term @ A @ Pvar ) > B,F4: ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > B,X41: proces554692349s_term @ A @ Pvar,X42: proces554692349s_term @ A @ Pvar] :
% 0.19/0.46 ( ( proces460752237s_term @ Pvar @ B @ A @ F1 @ F2 @ F3 @ F4 @ ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 ) )
% 0.19/0.46 = ( F4 @ X41 @ X42 ) ) ).
% 0.19/0.46
% 0.19/0.46 % process_term.simps(20)
% 0.19/0.46 thf(fact_20_process__term_Osimps_I19_J,axiom,
% 0.19/0.46 ! [B: $tType,Pvar: $tType,A: $tType,F1: Pvar > B,F2: ( proces634752977rocess @ A ) > B,F3: A > ( proces554692349s_term @ A @ Pvar ) > B,F4: ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > B,X31: A,X32: proces554692349s_term @ A @ Pvar] :
% 0.19/0.46 ( ( proces460752237s_term @ Pvar @ B @ A @ F1 @ F2 @ F3 @ F4 @ ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) )
% 0.19/0.46 = ( F3 @ X31 @ X32 ) ) ).
% 0.19/0.46
% 0.19/0.46 % process_term.simps(19)
% 0.19/0.46 thf(fact_21_process__term_Odistinct_I11_J,axiom,
% 0.19/0.46 ! [Pvar: $tType,A: $tType,X31: A,X32: proces554692349s_term @ A @ Pvar,X41: proces554692349s_term @ A @ Pvar,X42: proces554692349s_term @ A @ Pvar] :
% 0.19/0.46 ( ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 )
% 0.19/0.46 != ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 ) ) ).
% 0.19/0.46
% 0.19/0.46 % process_term.distinct(11)
% 0.19/0.46 thf(fact_22_process__term_Ocase__distrib,axiom,
% 0.19/0.46 ! [B: $tType,C: $tType,Pvar: $tType,A: $tType,H: B > C,F1: Pvar > B,F2: ( proces634752977rocess @ A ) > B,F3: A > ( proces554692349s_term @ A @ Pvar ) > B,F4: ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > B,Process_term: proces554692349s_term @ A @ Pvar] :
% 0.19/0.46 ( ( H @ ( proces460752237s_term @ Pvar @ B @ A @ F1 @ F2 @ F3 @ F4 @ Process_term ) )
% 0.19/0.46 = ( proces460752237s_term @ Pvar @ C @ A
% 0.19/0.46 @ ^ [X: Pvar] : ( H @ ( F1 @ X ) )
% 0.19/0.46 @ ^ [X: proces634752977rocess @ A] : ( H @ ( F2 @ X ) )
% 0.19/0.46 @ ^ [X1: A,X22: proces554692349s_term @ A @ Pvar] : ( H @ ( F3 @ X1 @ X22 ) )
% 0.19/0.46 @ ^ [X1: proces554692349s_term @ A @ Pvar,X22: proces554692349s_term @ A @ Pvar] : ( H @ ( F4 @ X1 @ X22 ) )
% 0.19/0.46 @ Process_term ) ) ).
% 0.19/0.46
% 0.19/0.46 % process_term.case_distrib
% 0.19/0.46 thf(fact_23_process_Oexhaust__disc,axiom,
% 0.19/0.46 ! [A: $tType,Process: proces634752977rocess @ A] :
% 0.19/0.46 ( ~ ( proces10484146Action @ A @ Process )
% 0.19/0.46 => ( proces401113213Choice @ A @ Process ) ) ).
% 0.19/0.46
% 0.19/0.46 % process.exhaust_disc
% 0.19/0.46 thf(fact_24_isAction__isChoice,axiom,
% 0.19/0.46 ! [A: $tType,P: proces634752977rocess @ A] :
% 0.19/0.46 ( ( proces10484146Action @ A @ P )
% 0.19/0.46 | ( proces401113213Choice @ A @ P ) ) ).
% 0.19/0.46
% 0.19/0.46 % isAction_isChoice
% 0.19/0.46 thf(fact_25_process_Odistinct__disc_I1_J,axiom,
% 0.19/0.46 ! [A: $tType,Process: proces634752977rocess @ A] :
% 0.19/0.46 ( ( proces10484146Action @ A @ Process )
% 0.19/0.46 => ~ ( proces401113213Choice @ A @ Process ) ) ).
% 0.19/0.46
% 0.19/0.46 % process.distinct_disc(1)
% 0.19/0.46 thf(fact_26_process_Odistinct__disc_I2_J,axiom,
% 0.19/0.46 ! [A: $tType,Process: proces634752977rocess @ A] :
% 0.19/0.46 ( ( proces401113213Choice @ A @ Process )
% 0.19/0.46 => ~ ( proces10484146Action @ A @ Process ) ) ).
% 0.19/0.46
% 0.19/0.46 % process.distinct_disc(2)
% 0.19/0.46 thf(fact_27_process__term_Odistinct_I9_J,axiom,
% 0.19/0.46 ! [Pvar: $tType,A: $tType,X2: proces634752977rocess @ A,X41: proces554692349s_term @ A @ Pvar,X42: proces554692349s_term @ A @ Pvar] :
% 0.19/0.46 ( ( proces1062592052s_PROC @ A @ Pvar @ X2 )
% 0.19/0.46 != ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 ) ) ).
% 0.19/0.46
% 0.19/0.46 % process_term.distinct(9)
% 0.19/0.46 thf(fact_28_process__term_Odistinct_I7_J,axiom,
% 0.19/0.46 ! [Pvar: $tType,A: $tType,X2: proces634752977rocess @ A,X31: A,X32: proces554692349s_term @ A @ Pvar] :
% 0.19/0.46 ( ( proces1062592052s_PROC @ A @ Pvar @ X2 )
% 0.19/0.46 != ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) ) ).
% 0.19/0.46
% 0.19/0.46 % process_term.distinct(7)
% 0.19/0.46 thf(fact_29_isACT_Oelims_I1_J,axiom,
% 0.19/0.46 ! [D: $tType,A: $tType,B: $tType,C: $tType,X3: A > ( proces554692349s_term @ B @ C ),Xa: proces554692349s_term @ D @ A,Y: $o] :
% 0.19/0.46 ( ( ( proces687458811_isACT @ A @ B @ C @ D @ X3 @ Xa )
% 0.19/0.46 = Y )
% 0.19/0.46 => ( ! [X4: A] :
% 0.19/0.46 ( ( Xa
% 0.19/0.46 = ( proces1627516585ss_VAR @ A @ D @ X4 ) )
% 0.19/0.46 => ( Y
% 0.19/0.46 = ( ~ ( proces460752237s_term @ C @ $o @ B
% 0.19/0.46 @ ^ [Pvar2: C] : $false
% 0.19/0.46 @ ( proces10484146Action @ B )
% 0.19/0.46 @ ^ [A3: B,T3: proces554692349s_term @ B @ C] : $true
% 0.19/0.46 @ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
% 0.19/0.46 @ ( X3 @ X4 ) ) ) ) )
% 0.19/0.46 => ( ! [P2: proces634752977rocess @ D] :
% 0.19/0.46 ( ( Xa
% 0.19/0.46 = ( proces1062592052s_PROC @ D @ A @ P2 ) )
% 0.19/0.46 => ( Y
% 0.19/0.46 = ( ~ ( proces10484146Action @ D @ P2 ) ) ) )
% 0.19/0.46 => ( ( ? [A4: D,T4: proces554692349s_term @ D @ A] :
% 0.19/0.46 ( Xa
% 0.19/0.46 = ( proces1454156180ss_ACT @ D @ A @ A4 @ T4 ) )
% 0.19/0.46 => ~ Y )
% 0.19/0.46 => ~ ( ? [T12: proces554692349s_term @ D @ A,T23: proces554692349s_term @ D @ A] :
% 0.19/0.46 ( Xa
% 0.19/0.46 = ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) )
% 0.19/0.46 => Y ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % isACT.elims(1)
% 0.19/0.46 thf(fact_30_isACT_Oelims_I2_J,axiom,
% 0.19/0.46 ! [C: $tType,B: $tType,A: $tType,D: $tType,X3: A > ( proces554692349s_term @ B @ C ),Xa: proces554692349s_term @ D @ A] :
% 0.19/0.46 ( ( proces687458811_isACT @ A @ B @ C @ D @ X3 @ Xa )
% 0.19/0.46 => ( ! [X4: A] :
% 0.19/0.46 ( ( Xa
% 0.19/0.46 = ( proces1627516585ss_VAR @ A @ D @ X4 ) )
% 0.19/0.46 => ~ ( proces460752237s_term @ C @ $o @ B
% 0.19/0.46 @ ^ [Pvar2: C] : $false
% 0.19/0.46 @ ( proces10484146Action @ B )
% 0.19/0.46 @ ^ [A3: B,T3: proces554692349s_term @ B @ C] : $true
% 0.19/0.46 @ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
% 0.19/0.46 @ ( X3 @ X4 ) ) )
% 0.19/0.46 => ( ! [P2: proces634752977rocess @ D] :
% 0.19/0.46 ( ( Xa
% 0.19/0.46 = ( proces1062592052s_PROC @ D @ A @ P2 ) )
% 0.19/0.46 => ~ ( proces10484146Action @ D @ P2 ) )
% 0.19/0.46 => ~ ! [A4: D,T4: proces554692349s_term @ D @ A] :
% 0.19/0.46 ( Xa
% 0.19/0.46 != ( proces1454156180ss_ACT @ D @ A @ A4 @ T4 ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % isACT.elims(2)
% 0.19/0.46 thf(fact_31_isACT_Oelims_I3_J,axiom,
% 0.19/0.46 ! [C: $tType,B: $tType,A: $tType,D: $tType,X3: A > ( proces554692349s_term @ B @ C ),Xa: proces554692349s_term @ D @ A] :
% 0.19/0.46 ( ~ ( proces687458811_isACT @ A @ B @ C @ D @ X3 @ Xa )
% 0.19/0.46 => ( ! [X4: A] :
% 0.19/0.46 ( ( Xa
% 0.19/0.46 = ( proces1627516585ss_VAR @ A @ D @ X4 ) )
% 0.19/0.46 => ( proces460752237s_term @ C @ $o @ B
% 0.19/0.46 @ ^ [Pvar2: C] : $false
% 0.19/0.46 @ ( proces10484146Action @ B )
% 0.19/0.46 @ ^ [A3: B,T3: proces554692349s_term @ B @ C] : $true
% 0.19/0.46 @ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
% 0.19/0.46 @ ( X3 @ X4 ) ) )
% 0.19/0.46 => ( ! [P2: proces634752977rocess @ D] :
% 0.19/0.46 ( ( Xa
% 0.19/0.46 = ( proces1062592052s_PROC @ D @ A @ P2 ) )
% 0.19/0.46 => ( proces10484146Action @ D @ P2 ) )
% 0.19/0.46 => ~ ! [T12: proces554692349s_term @ D @ A,T23: proces554692349s_term @ D @ A] :
% 0.19/0.46 ( Xa
% 0.19/0.46 != ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % isACT.elims(3)
% 0.19/0.46 thf(fact_32_CH2_Oinduct,axiom,
% 0.19/0.46 ! [A: $tType,B: $tType,P3: ( A > ( proces554692349s_term @ B @ A ) ) > ( proces554692349s_term @ B @ A ) > $o,A0: A > ( proces554692349s_term @ B @ A ),A1: proces554692349s_term @ B @ A] :
% 0.19/0.46 ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),X4: A] : ( P3 @ Sys2 @ ( proces1627516585ss_VAR @ A @ B @ X4 ) )
% 0.19/0.46 => ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),P2: proces634752977rocess @ B] : ( P3 @ Sys2 @ ( proces1062592052s_PROC @ B @ A @ P2 ) )
% 0.19/0.46 => ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),T12: proces554692349s_term @ B @ A,T23: proces554692349s_term @ B @ A] : ( P3 @ Sys2 @ ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) )
% 0.19/0.46 => ( ! [A4: A > ( proces554692349s_term @ B @ A ),V: B,Va: proces554692349s_term @ B @ A] : ( P3 @ A4 @ ( proces1454156180ss_ACT @ B @ A @ V @ Va ) )
% 0.19/0.46 => ( P3 @ A0 @ A1 ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % CH2.induct
% 0.19/0.46 thf(fact_33_CONT_Oinduct,axiom,
% 0.19/0.46 ! [A: $tType,B: $tType,P3: ( A > ( proces554692349s_term @ B @ A ) ) > ( proces554692349s_term @ B @ A ) > $o,A0: A > ( proces554692349s_term @ B @ A ),A1: proces554692349s_term @ B @ A] :
% 0.19/0.46 ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),X4: A] : ( P3 @ Sys2 @ ( proces1627516585ss_VAR @ A @ B @ X4 ) )
% 0.19/0.46 => ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),P2: proces634752977rocess @ B] : ( P3 @ Sys2 @ ( proces1062592052s_PROC @ B @ A @ P2 ) )
% 0.19/0.46 => ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),A4: B,T4: proces554692349s_term @ B @ A] : ( P3 @ Sys2 @ ( proces1454156180ss_ACT @ B @ A @ A4 @ T4 ) )
% 0.19/0.46 => ( ! [A4: A > ( proces554692349s_term @ B @ A ),V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] : ( P3 @ A4 @ ( proces89589571ess_CH @ B @ A @ V @ Va ) )
% 0.19/0.46 => ( P3 @ A0 @ A1 ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % CONT.induct
% 0.19/0.46 thf(fact_34_PREF_Oinduct,axiom,
% 0.19/0.46 ! [C: $tType,A: $tType,B: $tType,P3: ( A > ( proces554692349s_term @ B @ C ) ) > ( proces554692349s_term @ B @ A ) > $o,A0: A > ( proces554692349s_term @ B @ C ),A1: proces554692349s_term @ B @ A] :
% 0.19/0.46 ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),X4: A] : ( P3 @ Sys2 @ ( proces1627516585ss_VAR @ A @ B @ X4 ) )
% 0.19/0.46 => ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),P2: proces634752977rocess @ B] : ( P3 @ Sys2 @ ( proces1062592052s_PROC @ B @ A @ P2 ) )
% 0.19/0.46 => ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),A4: B,T4: proces554692349s_term @ B @ A] : ( P3 @ Sys2 @ ( proces1454156180ss_ACT @ B @ A @ A4 @ T4 ) )
% 0.19/0.46 => ( ! [A4: A > ( proces554692349s_term @ B @ C ),V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] : ( P3 @ A4 @ ( proces89589571ess_CH @ B @ A @ V @ Va ) )
% 0.19/0.46 => ( P3 @ A0 @ A1 ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % PREF.induct
% 0.19/0.46 thf(fact_35_isACT_Oinduct,axiom,
% 0.19/0.46 ! [B: $tType,C: $tType,A: $tType,D: $tType,P3: ( A > ( proces554692349s_term @ B @ C ) ) > ( proces554692349s_term @ D @ A ) > $o,A0: A > ( proces554692349s_term @ B @ C ),A1: proces554692349s_term @ D @ A] :
% 0.19/0.46 ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),X4: A] : ( P3 @ Sys2 @ ( proces1627516585ss_VAR @ A @ D @ X4 ) )
% 0.19/0.46 => ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),P2: proces634752977rocess @ D] : ( P3 @ Sys2 @ ( proces1062592052s_PROC @ D @ A @ P2 ) )
% 0.19/0.46 => ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),A4: D,T4: proces554692349s_term @ D @ A] : ( P3 @ Sys2 @ ( proces1454156180ss_ACT @ D @ A @ A4 @ T4 ) )
% 0.19/0.46 => ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),T12: proces554692349s_term @ D @ A,T23: proces554692349s_term @ D @ A] : ( P3 @ Sys2 @ ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) )
% 0.19/0.46 => ( P3 @ A0 @ A1 ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % isACT.induct
% 0.19/0.46 thf(fact_36_process__term_Oinduct,axiom,
% 0.19/0.46 ! [Pvar: $tType,A: $tType,P3: ( proces554692349s_term @ A @ Pvar ) > $o,Process_term: proces554692349s_term @ A @ Pvar] :
% 0.19/0.46 ( ! [X5: Pvar] : ( P3 @ ( proces1627516585ss_VAR @ Pvar @ A @ X5 ) )
% 0.19/0.46 => ( ! [X5: proces634752977rocess @ A] : ( P3 @ ( proces1062592052s_PROC @ A @ Pvar @ X5 ) )
% 0.19/0.46 => ( ! [X1a: A,X2a: proces554692349s_term @ A @ Pvar] :
% 0.19/0.46 ( ( P3 @ X2a )
% 0.19/0.46 => ( P3 @ ( proces1454156180ss_ACT @ A @ Pvar @ X1a @ X2a ) ) )
% 0.19/0.46 => ( ! [X1a: proces554692349s_term @ A @ Pvar,X2a: proces554692349s_term @ A @ Pvar] :
% 0.19/0.46 ( ( P3 @ X1a )
% 0.19/0.46 => ( ( P3 @ X2a )
% 0.19/0.46 => ( P3 @ ( proces89589571ess_CH @ A @ Pvar @ X1a @ X2a ) ) ) )
% 0.19/0.46 => ( P3 @ Process_term ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % process_term.induct
% 0.19/0.46 thf(fact_37_process__term_Oexhaust,axiom,
% 0.19/0.46 ! [Pvar: $tType,A: $tType,Y: proces554692349s_term @ A @ Pvar] :
% 0.19/0.46 ( ! [X12: Pvar] :
% 0.19/0.46 ( Y
% 0.19/0.46 != ( proces1627516585ss_VAR @ Pvar @ A @ X12 ) )
% 0.19/0.46 => ( ! [X23: proces634752977rocess @ A] :
% 0.19/0.46 ( Y
% 0.19/0.46 != ( proces1062592052s_PROC @ A @ Pvar @ X23 ) )
% 0.19/0.46 => ( ! [X312: A,X322: proces554692349s_term @ A @ Pvar] :
% 0.19/0.46 ( Y
% 0.19/0.46 != ( proces1454156180ss_ACT @ A @ Pvar @ X312 @ X322 ) )
% 0.19/0.46 => ~ ! [X412: proces554692349s_term @ A @ Pvar,X422: proces554692349s_term @ A @ Pvar] :
% 0.19/0.46 ( Y
% 0.19/0.46 != ( proces89589571ess_CH @ A @ Pvar @ X412 @ X422 ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % process_term.exhaust
% 0.19/0.46 thf(fact_38_isACT_Osimps_I1_J,axiom,
% 0.19/0.46 ! [D: $tType,B: $tType,C: $tType,A: $tType,Sys: A > ( proces554692349s_term @ B @ C ),X6: A] :
% 0.19/0.46 ( ( proces687458811_isACT @ A @ B @ C @ D @ Sys @ ( proces1627516585ss_VAR @ A @ D @ X6 ) )
% 0.19/0.46 = ( proces460752237s_term @ C @ $o @ B
% 0.19/0.46 @ ^ [Pvar2: C] : $false
% 0.19/0.46 @ ( proces10484146Action @ B )
% 0.19/0.46 @ ^ [A3: B,T3: proces554692349s_term @ B @ C] : $true
% 0.19/0.46 @ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
% 0.19/0.46 @ ( Sys @ X6 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % isACT.simps(1)
% 0.19/0.46 thf(fact_39_process__term_Oinject_I1_J,axiom,
% 0.19/0.46 ! [A: $tType,Pvar: $tType,X13: Pvar,Y1: Pvar] :
% 0.19/0.46 ( ( ( proces1627516585ss_VAR @ Pvar @ A @ X13 )
% 0.19/0.46 = ( proces1627516585ss_VAR @ Pvar @ A @ Y1 ) )
% 0.19/0.46 = ( X13 = Y1 ) ) ).
% 0.19/0.46
% 0.19/0.46 % process_term.inject(1)
% 0.19/0.46 thf(fact_40_process__term_Odistinct_I1_J,axiom,
% 0.19/0.46 ! [Pvar: $tType,A: $tType,X13: Pvar,X2: proces634752977rocess @ A] :
% 0.19/0.46 ( ( proces1627516585ss_VAR @ Pvar @ A @ X13 )
% 0.19/0.46 != ( proces1062592052s_PROC @ A @ Pvar @ X2 ) ) ).
% 0.19/0.46
% 0.19/0.46 % process_term.distinct(1)
% 0.19/0.46 thf(fact_41_process__term_Odistinct_I5_J,axiom,
% 0.19/0.46 ! [Pvar: $tType,A: $tType,X13: Pvar,X41: proces554692349s_term @ A @ Pvar,X42: proces554692349s_term @ A @ Pvar] :
% 0.19/0.46 ( ( proces1627516585ss_VAR @ Pvar @ A @ X13 )
% 0.19/0.46 != ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 ) ) ).
% 0.19/0.46
% 0.19/0.46 % process_term.distinct(5)
% 0.19/0.46 thf(fact_42_process__term_Odistinct_I3_J,axiom,
% 0.19/0.46 ! [Pvar: $tType,A: $tType,X13: Pvar,X31: A,X32: proces554692349s_term @ A @ Pvar] :
% 0.19/0.46 ( ( proces1627516585ss_VAR @ Pvar @ A @ X13 )
% 0.19/0.46 != ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) ) ).
% 0.19/0.46
% 0.19/0.46 % process_term.distinct(3)
% 0.19/0.46 thf(fact_43_process__term_Osimps_I17_J,axiom,
% 0.19/0.46 ! [A: $tType,B: $tType,Pvar: $tType,F1: Pvar > B,F2: ( proces634752977rocess @ A ) > B,F3: A > ( proces554692349s_term @ A @ Pvar ) > B,F4: ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > B,X13: Pvar] :
% 0.19/0.46 ( ( proces460752237s_term @ Pvar @ B @ A @ F1 @ F2 @ F3 @ F4 @ ( proces1627516585ss_VAR @ Pvar @ A @ X13 ) )
% 0.19/0.46 = ( F1 @ X13 ) ) ).
% 0.19/0.46
% 0.19/0.46 % process_term.simps(17)
% 0.19/0.46 thf(fact_44_mem__Collect__eq,axiom,
% 0.19/0.46 ! [A: $tType,A2: A,P3: A > $o] :
% 0.19/0.46 ( ( member @ A @ A2 @ ( collect @ A @ P3 ) )
% 0.19/0.46 = ( P3 @ A2 ) ) ).
% 0.19/0.46
% 0.19/0.46 % mem_Collect_eq
% 0.19/0.46 thf(fact_45_Collect__mem__eq,axiom,
% 0.19/0.46 ! [A: $tType,A5: set @ A] :
% 0.19/0.46 ( ( collect @ A
% 0.19/0.46 @ ^ [X: A] : ( member @ A @ X @ A5 ) )
% 0.19/0.46 = A5 ) ).
% 0.19/0.46
% 0.19/0.46 % Collect_mem_eq
% 0.19/0.46 thf(fact_46_Collect__cong,axiom,
% 0.19/0.46 ! [A: $tType,P3: A > $o,Q: A > $o] :
% 0.19/0.46 ( ! [X5: A] :
% 0.19/0.46 ( ( P3 @ X5 )
% 0.19/0.46 = ( Q @ X5 ) )
% 0.19/0.46 => ( ( collect @ A @ P3 )
% 0.19/0.46 = ( collect @ A @ Q ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % Collect_cong
% 0.19/0.46 thf(fact_47_ext,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.19/0.46 ( ! [X5: A] :
% 0.19/0.46 ( ( F @ X5 )
% 0.19/0.46 = ( G @ X5 ) )
% 0.19/0.46 => ( F = G ) ) ).
% 0.19/0.46
% 0.19/0.46 % ext
% 0.19/0.46 thf(fact_48_process__term_Osimps_I21_J,axiom,
% 0.19/0.46 ! [A: $tType,D: $tType,Pvar: $tType,F1: Pvar > D,F2: ( proces634752977rocess @ A ) > D,F3: A > ( proces554692349s_term @ A @ Pvar ) > D > D,F4: ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D > D > D,X13: Pvar] :
% 0.19/0.46 ( ( proces2117273769s_term @ Pvar @ D @ A @ F1 @ F2 @ F3 @ F4 @ ( proces1627516585ss_VAR @ Pvar @ A @ X13 ) )
% 0.19/0.46 = ( F1 @ X13 ) ) ).
% 0.19/0.46
% 0.19/0.46 % process_term.simps(21)
% 0.19/0.46 thf(fact_49_solution__VAR,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,Sys: A > ( proces554692349s_term @ B @ A ),X6: A] :
% 0.19/0.46 ( ( proces1121166967uarded @ A @ B @ A @ Sys )
% 0.19/0.46 => ( ( proces1652378886lution @ A @ B @ Sys @ ( proces1627516585ss_VAR @ A @ B @ X6 ) )
% 0.19/0.46 = ( proces1652378886lution @ A @ B @ Sys @ ( Sys @ X6 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % solution_VAR
% 0.19/0.46 thf(fact_50_isACT__VAR,axiom,
% 0.19/0.46 ! [C: $tType,B: $tType,A: $tType,Sys: A > ( proces554692349s_term @ B @ A ),X6: A] :
% 0.19/0.46 ( ( proces1121166967uarded @ A @ B @ A @ Sys )
% 0.19/0.46 => ( ( proces687458811_isACT @ A @ B @ A @ C @ Sys @ ( proces1627516585ss_VAR @ A @ C @ X6 ) )
% 0.19/0.46 = ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ ( Sys @ X6 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % isACT_VAR
% 0.19/0.46 thf(fact_51_isACT_Ocases,axiom,
% 0.19/0.46 ! [B: $tType,C: $tType,A: $tType,D: $tType,X3: product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A )] :
% 0.19/0.46 ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),X4: A] :
% 0.19/0.46 ( X3
% 0.19/0.46 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ Sys2 @ ( proces1627516585ss_VAR @ A @ D @ X4 ) ) )
% 0.19/0.46 => ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),P2: proces634752977rocess @ D] :
% 0.19/0.46 ( X3
% 0.19/0.46 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ Sys2 @ ( proces1062592052s_PROC @ D @ A @ P2 ) ) )
% 0.19/0.47 => ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),A4: D,T4: proces554692349s_term @ D @ A] :
% 0.19/0.47 ( X3
% 0.19/0.47 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ Sys2 @ ( proces1454156180ss_ACT @ D @ A @ A4 @ T4 ) ) )
% 0.19/0.47 => ~ ! [Sys2: A > ( proces554692349s_term @ B @ C ),T12: proces554692349s_term @ D @ A,T23: proces554692349s_term @ D @ A] :
% 0.19/0.47 ( X3
% 0.19/0.47 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ Sys2 @ ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % isACT.cases
% 0.19/0.47 thf(fact_52_PREF_Ocases,axiom,
% 0.19/0.47 ! [C: $tType,A: $tType,B: $tType,X3: product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A )] :
% 0.19/0.47 ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),X4: A] :
% 0.19/0.47 ( X3
% 0.19/0.47 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ Sys2 @ ( proces1627516585ss_VAR @ A @ B @ X4 ) ) )
% 0.19/0.47 => ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),P2: proces634752977rocess @ B] :
% 0.19/0.47 ( X3
% 0.19/0.47 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ Sys2 @ ( proces1062592052s_PROC @ B @ A @ P2 ) ) )
% 0.19/0.47 => ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),A4: B,T4: proces554692349s_term @ B @ A] :
% 0.19/0.47 ( X3
% 0.19/0.47 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ Sys2 @ ( proces1454156180ss_ACT @ B @ A @ A4 @ T4 ) ) )
% 0.19/0.47 => ~ ! [A4: A > ( proces554692349s_term @ B @ C ),V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] :
% 0.19/0.47 ( X3
% 0.19/0.47 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ A4 @ ( proces89589571ess_CH @ B @ A @ V @ Va ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % PREF.cases
% 0.19/0.47 thf(fact_53_CONT_Ocases,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,X3: product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A )] :
% 0.19/0.47 ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),X4: A] :
% 0.19/0.47 ( X3
% 0.19/0.47 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ Sys2 @ ( proces1627516585ss_VAR @ A @ B @ X4 ) ) )
% 0.19/0.47 => ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),P2: proces634752977rocess @ B] :
% 0.19/0.47 ( X3
% 0.19/0.47 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ Sys2 @ ( proces1062592052s_PROC @ B @ A @ P2 ) ) )
% 0.19/0.47 => ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),A4: B,T4: proces554692349s_term @ B @ A] :
% 0.19/0.47 ( X3
% 0.19/0.47 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ Sys2 @ ( proces1454156180ss_ACT @ B @ A @ A4 @ T4 ) ) )
% 0.19/0.47 => ~ ! [A4: A > ( proces554692349s_term @ B @ A ),V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] :
% 0.19/0.47 ( X3
% 0.19/0.47 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ A4 @ ( proces89589571ess_CH @ B @ A @ V @ Va ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % CONT.cases
% 0.19/0.47 thf(fact_54_CH2_Ocases,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,X3: product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A )] :
% 0.19/0.47 ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),X4: A] :
% 0.19/0.47 ( X3
% 0.19/0.47 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ Sys2 @ ( proces1627516585ss_VAR @ A @ B @ X4 ) ) )
% 0.19/0.47 => ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),P2: proces634752977rocess @ B] :
% 0.19/0.47 ( X3
% 0.19/0.47 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ Sys2 @ ( proces1062592052s_PROC @ B @ A @ P2 ) ) )
% 0.19/0.47 => ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),T12: proces554692349s_term @ B @ A,T23: proces554692349s_term @ B @ A] :
% 0.19/0.47 ( X3
% 0.19/0.47 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ Sys2 @ ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) ) )
% 0.19/0.47 => ~ ! [A4: A > ( proces554692349s_term @ B @ A ),V: B,Va: proces554692349s_term @ B @ A] :
% 0.19/0.47 ( X3
% 0.19/0.47 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ A4 @ ( proces1454156180ss_ACT @ B @ A @ V @ Va ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % CH2.cases
% 0.19/0.47 thf(fact_55_process__term_Oset__cases_I2_J,axiom,
% 0.19/0.47 ! [Pvar: $tType,A: $tType,E: Pvar,A2: proces554692349s_term @ A @ Pvar] :
% 0.19/0.47 ( ( member @ Pvar @ E @ ( proces1493547885s_term @ A @ Pvar @ A2 ) )
% 0.19/0.47 => ( ( A2
% 0.19/0.47 != ( proces1627516585ss_VAR @ Pvar @ A @ E ) )
% 0.19/0.47 => ( ! [Z1: A,Z2: proces554692349s_term @ A @ Pvar] :
% 0.19/0.47 ( ( A2
% 0.19/0.47 = ( proces1454156180ss_ACT @ A @ Pvar @ Z1 @ Z2 ) )
% 0.19/0.47 => ~ ( member @ Pvar @ E @ ( proces1493547885s_term @ A @ Pvar @ Z2 ) ) )
% 0.19/0.47 => ( ! [Z1: proces554692349s_term @ A @ Pvar] :
% 0.19/0.47 ( ? [Z2: proces554692349s_term @ A @ Pvar] :
% 0.19/0.47 ( A2
% 0.19/0.47 = ( proces89589571ess_CH @ A @ Pvar @ Z1 @ Z2 ) )
% 0.19/0.47 => ~ ( member @ Pvar @ E @ ( proces1493547885s_term @ A @ Pvar @ Z1 ) ) )
% 0.19/0.47 => ~ ! [Z1: proces554692349s_term @ A @ Pvar,Z2: proces554692349s_term @ A @ Pvar] :
% 0.19/0.47 ( ( A2
% 0.19/0.47 = ( proces89589571ess_CH @ A @ Pvar @ Z1 @ Z2 ) )
% 0.19/0.47 => ~ ( member @ Pvar @ E @ ( proces1493547885s_term @ A @ Pvar @ Z2 ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process_term.set_cases(2)
% 0.19/0.47 thf(fact_56_guarded__def,axiom,
% 0.19/0.47 ! [C: $tType,B: $tType,A: $tType] :
% 0.19/0.47 ( ( proces1121166967uarded @ A @ B @ C )
% 0.19/0.47 = ( ^ [Sys3: A > ( proces554692349s_term @ B @ C )] :
% 0.19/0.47 ! [X7: A,Y3: C] :
% 0.19/0.47 ( ( Sys3 @ X7 )
% 0.19/0.47 != ( proces1627516585ss_VAR @ C @ B @ Y3 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % guarded_def
% 0.19/0.47 thf(fact_57_process__term_Oset__intros_I6_J,axiom,
% 0.19/0.47 ! [A: $tType,Pvar: $tType,Ab: Pvar] : ( member @ Pvar @ Ab @ ( proces1493547885s_term @ A @ Pvar @ ( proces1627516585ss_VAR @ Pvar @ A @ Ab ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process_term.set_intros(6)
% 0.19/0.47 thf(fact_58_process__term_Oset__intros_I9_J,axiom,
% 0.19/0.47 ! [Pvar: $tType,A: $tType,Xm: Pvar,A2c: proces554692349s_term @ A @ Pvar,A1c: proces554692349s_term @ A @ Pvar] :
% 0.19/0.47 ( ( member @ Pvar @ Xm @ ( proces1493547885s_term @ A @ Pvar @ A2c ) )
% 0.19/0.47 => ( member @ Pvar @ Xm @ ( proces1493547885s_term @ A @ Pvar @ ( proces89589571ess_CH @ A @ Pvar @ A1c @ A2c ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process_term.set_intros(9)
% 0.19/0.47 thf(fact_59_process__term_Oset__intros_I8_J,axiom,
% 0.19/0.47 ! [Pvar: $tType,A: $tType,Xk: Pvar,A1c: proces554692349s_term @ A @ Pvar,A2c: proces554692349s_term @ A @ Pvar] :
% 0.19/0.47 ( ( member @ Pvar @ Xk @ ( proces1493547885s_term @ A @ Pvar @ A1c ) )
% 0.19/0.47 => ( member @ Pvar @ Xk @ ( proces1493547885s_term @ A @ Pvar @ ( proces89589571ess_CH @ A @ Pvar @ A1c @ A2c ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process_term.set_intros(8)
% 0.19/0.47 thf(fact_60_process__term_Osimps_I51_J,axiom,
% 0.19/0.47 ! [Pvar: $tType,A: $tType,X31: A,X32: proces554692349s_term @ A @ Pvar] :
% 0.19/0.47 ( ( proces1493547885s_term @ A @ Pvar @ ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) )
% 0.19/0.47 = ( proces1493547885s_term @ A @ Pvar @ X32 ) ) ).
% 0.19/0.47
% 0.19/0.47 % process_term.simps(51)
% 0.19/0.47 thf(fact_61_process__term_Oset__intros_I7_J,axiom,
% 0.19/0.47 ! [Pvar: $tType,A: $tType,Xi: Pvar,A2b: proces554692349s_term @ A @ Pvar,A1b: A] :
% 0.19/0.47 ( ( member @ Pvar @ Xi @ ( proces1493547885s_term @ A @ Pvar @ A2b ) )
% 0.19/0.47 => ( member @ Pvar @ Xi @ ( proces1493547885s_term @ A @ Pvar @ ( proces1454156180ss_ACT @ A @ Pvar @ A1b @ A2b ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process_term.set_intros(7)
% 0.19/0.47 thf(fact_62_prod_Oinject,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,X13: A,X2: B,Y1: A,Y2: B] :
% 0.19/0.47 ( ( ( product_Pair @ A @ B @ X13 @ X2 )
% 0.19/0.47 = ( product_Pair @ A @ B @ Y1 @ Y2 ) )
% 0.19/0.47 = ( ( X13 = Y1 )
% 0.19/0.47 & ( X2 = Y2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % prod.inject
% 0.19/0.47 thf(fact_63_old_Oprod_Oinject,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,A2: A,B2: B,A6: A,B3: B] :
% 0.19/0.47 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 0.19/0.47 = ( product_Pair @ A @ B @ A6 @ B3 ) )
% 0.19/0.47 = ( ( A2 = A6 )
% 0.19/0.47 & ( B2 = B3 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % old.prod.inject
% 0.19/0.47 thf(fact_64_isACT_Opelims_I1_J,axiom,
% 0.19/0.47 ! [B: $tType,C: $tType,A: $tType,D: $tType,X3: A > ( proces554692349s_term @ B @ C ),Xa: proces554692349s_term @ D @ A,Y: $o] :
% 0.19/0.47 ( ( ( proces687458811_isACT @ A @ B @ C @ D @ X3 @ Xa )
% 0.19/0.47 = Y )
% 0.19/0.47 => ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X3 @ Xa ) )
% 0.19/0.47 => ( ! [X4: A] :
% 0.19/0.47 ( ( Xa
% 0.19/0.47 = ( proces1627516585ss_VAR @ A @ D @ X4 ) )
% 0.19/0.47 => ( ( Y
% 0.19/0.47 = ( proces460752237s_term @ C @ $o @ B
% 0.19/0.47 @ ^ [Pvar2: C] : $false
% 0.19/0.47 @ ( proces10484146Action @ B )
% 0.19/0.47 @ ^ [A3: B,T3: proces554692349s_term @ B @ C] : $true
% 0.19/0.47 @ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
% 0.19/0.47 @ ( X3 @ X4 ) ) )
% 0.19/0.47 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X3 @ ( proces1627516585ss_VAR @ A @ D @ X4 ) ) ) ) )
% 0.19/0.47 => ( ! [P2: proces634752977rocess @ D] :
% 0.19/0.47 ( ( Xa
% 0.19/0.47 = ( proces1062592052s_PROC @ D @ A @ P2 ) )
% 0.19/0.47 => ( ( Y
% 0.19/0.47 = ( proces10484146Action @ D @ P2 ) )
% 0.19/0.47 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X3 @ ( proces1062592052s_PROC @ D @ A @ P2 ) ) ) ) )
% 0.19/0.47 => ( ! [A4: D,T4: proces554692349s_term @ D @ A] :
% 0.19/0.47 ( ( Xa
% 0.19/0.47 = ( proces1454156180ss_ACT @ D @ A @ A4 @ T4 ) )
% 0.19/0.47 => ( Y
% 0.19/0.47 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X3 @ ( proces1454156180ss_ACT @ D @ A @ A4 @ T4 ) ) ) ) )
% 0.19/0.47 => ~ ! [T12: proces554692349s_term @ D @ A,T23: proces554692349s_term @ D @ A] :
% 0.19/0.47 ( ( Xa
% 0.19/0.47 = ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) )
% 0.19/0.47 => ( ~ Y
% 0.19/0.47 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X3 @ ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % isACT.pelims(1)
% 0.19/0.47 thf(fact_65_isACT_Opelims_I2_J,axiom,
% 0.19/0.47 ! [B: $tType,C: $tType,A: $tType,D: $tType,X3: A > ( proces554692349s_term @ B @ C ),Xa: proces554692349s_term @ D @ A] :
% 0.19/0.47 ( ( proces687458811_isACT @ A @ B @ C @ D @ X3 @ Xa )
% 0.19/0.47 => ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X3 @ Xa ) )
% 0.19/0.47 => ( ! [X4: A] :
% 0.19/0.47 ( ( Xa
% 0.19/0.47 = ( proces1627516585ss_VAR @ A @ D @ X4 ) )
% 0.19/0.47 => ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X3 @ ( proces1627516585ss_VAR @ A @ D @ X4 ) ) )
% 0.19/0.47 => ~ ( proces460752237s_term @ C @ $o @ B
% 0.19/0.47 @ ^ [Pvar2: C] : $false
% 0.19/0.47 @ ( proces10484146Action @ B )
% 0.19/0.47 @ ^ [A3: B,T3: proces554692349s_term @ B @ C] : $true
% 0.19/0.47 @ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
% 0.19/0.47 @ ( X3 @ X4 ) ) ) )
% 0.19/0.47 => ( ! [P2: proces634752977rocess @ D] :
% 0.19/0.47 ( ( Xa
% 0.19/0.47 = ( proces1062592052s_PROC @ D @ A @ P2 ) )
% 0.19/0.47 => ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X3 @ ( proces1062592052s_PROC @ D @ A @ P2 ) ) )
% 0.19/0.47 => ~ ( proces10484146Action @ D @ P2 ) ) )
% 0.19/0.47 => ~ ! [A4: D,T4: proces554692349s_term @ D @ A] :
% 0.19/0.47 ( ( Xa
% 0.19/0.47 = ( proces1454156180ss_ACT @ D @ A @ A4 @ T4 ) )
% 0.19/0.47 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X3 @ ( proces1454156180ss_ACT @ D @ A @ A4 @ T4 ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % isACT.pelims(2)
% 0.19/0.47 thf(fact_66_isACT_Opelims_I3_J,axiom,
% 0.19/0.47 ! [B: $tType,C: $tType,A: $tType,D: $tType,X3: A > ( proces554692349s_term @ B @ C ),Xa: proces554692349s_term @ D @ A] :
% 0.19/0.47 ( ~ ( proces687458811_isACT @ A @ B @ C @ D @ X3 @ Xa )
% 0.19/0.47 => ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X3 @ Xa ) )
% 0.19/0.47 => ( ! [X4: A] :
% 0.19/0.47 ( ( Xa
% 0.19/0.47 = ( proces1627516585ss_VAR @ A @ D @ X4 ) )
% 0.19/0.47 => ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X3 @ ( proces1627516585ss_VAR @ A @ D @ X4 ) ) )
% 0.19/0.47 => ( proces460752237s_term @ C @ $o @ B
% 0.19/0.47 @ ^ [Pvar2: C] : $false
% 0.19/0.47 @ ( proces10484146Action @ B )
% 0.19/0.47 @ ^ [A3: B,T3: proces554692349s_term @ B @ C] : $true
% 0.19/0.47 @ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
% 0.19/0.47 @ ( X3 @ X4 ) ) ) )
% 0.19/0.47 => ( ! [P2: proces634752977rocess @ D] :
% 0.19/0.47 ( ( Xa
% 0.19/0.47 = ( proces1062592052s_PROC @ D @ A @ P2 ) )
% 0.19/0.47 => ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X3 @ ( proces1062592052s_PROC @ D @ A @ P2 ) ) )
% 0.19/0.47 => ( proces10484146Action @ D @ P2 ) ) )
% 0.19/0.47 => ~ ! [T12: proces554692349s_term @ D @ A,T23: proces554692349s_term @ D @ A] :
% 0.19/0.47 ( ( Xa
% 0.19/0.47 = ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) )
% 0.19/0.47 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X3 @ ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % isACT.pelims(3)
% 0.19/0.47 thf(fact_67_pred__equals__eq2,axiom,
% 0.19/0.47 ! [B: $tType,A: $tType,R: set @ ( product_prod @ A @ B ),S: set @ ( product_prod @ A @ B )] :
% 0.19/0.47 ( ( ( ^ [X: A,Y4: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X @ Y4 ) @ R ) )
% 0.19/0.47 = ( ^ [X: A,Y4: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X @ Y4 ) @ S ) ) )
% 0.19/0.47 = ( R = S ) ) ).
% 0.19/0.47
% 0.19/0.47 % pred_equals_eq2
% 0.19/0.47 thf(fact_68_surj__pair,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,P: product_prod @ A @ B] :
% 0.19/0.47 ? [X5: A,Y5: B] :
% 0.19/0.47 ( P
% 0.19/0.47 = ( product_Pair @ A @ B @ X5 @ Y5 ) ) ).
% 0.19/0.47
% 0.19/0.47 % surj_pair
% 0.19/0.47 thf(fact_69_old_Oprod_Oinducts,axiom,
% 0.19/0.47 ! [B: $tType,A: $tType,P3: ( product_prod @ A @ B ) > $o,Prod: product_prod @ A @ B] :
% 0.19/0.47 ( ! [A4: A,B4: B] : ( P3 @ ( product_Pair @ A @ B @ A4 @ B4 ) )
% 0.19/0.47 => ( P3 @ Prod ) ) ).
% 0.19/0.47
% 0.19/0.47 % old.prod.inducts
% 0.19/0.47 thf(fact_70_old_Oprod_Oexhaust,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,Y: product_prod @ A @ B] :
% 0.19/0.47 ~ ! [A4: A,B4: B] :
% 0.19/0.47 ( Y
% 0.19/0.47 != ( product_Pair @ A @ B @ A4 @ B4 ) ) ).
% 0.19/0.47
% 0.19/0.47 % old.prod.exhaust
% 0.19/0.47 thf(fact_71_prod__induct7,axiom,
% 0.19/0.47 ! [G2: $tType,F5: $tType,E2: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P3: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ ( product_prod @ F5 @ G2 ) ) ) ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ ( product_prod @ F5 @ G2 ) ) ) ) )] :
% 0.19/0.47 ( ! [A4: A,B4: B,C2: C,D2: D,E3: E2,F6: F5,G3: G2] : ( P3 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ ( product_prod @ F5 @ G2 ) ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ ( product_prod @ F5 @ G2 ) ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E2 @ ( product_prod @ F5 @ G2 ) ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E2 @ ( product_prod @ F5 @ G2 ) ) @ D2 @ ( product_Pair @ E2 @ ( product_prod @ F5 @ G2 ) @ E3 @ ( product_Pair @ F5 @ G2 @ F6 @ G3 ) ) ) ) ) ) )
% 0.19/0.47 => ( P3 @ X3 ) ) ).
% 0.19/0.47
% 0.19/0.47 % prod_induct7
% 0.19/0.47 thf(fact_72_prod__induct6,axiom,
% 0.19/0.47 ! [F5: $tType,E2: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P3: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ F5 ) ) ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ F5 ) ) ) )] :
% 0.19/0.47 ( ! [A4: A,B4: B,C2: C,D2: D,E3: E2,F6: F5] : ( P3 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ F5 ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ F5 ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E2 @ F5 ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E2 @ F5 ) @ D2 @ ( product_Pair @ E2 @ F5 @ E3 @ F6 ) ) ) ) ) )
% 0.19/0.47 => ( P3 @ X3 ) ) ).
% 0.19/0.47
% 0.19/0.47 % prod_induct6
% 0.19/0.47 thf(fact_73_prod__induct5,axiom,
% 0.19/0.47 ! [E2: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P3: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E2 ) ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E2 ) ) )] :
% 0.19/0.47 ( ! [A4: A,B4: B,C2: C,D2: D,E3: E2] : ( P3 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E2 ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E2 ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ E2 ) @ C2 @ ( product_Pair @ D @ E2 @ D2 @ E3 ) ) ) ) )
% 0.19/0.47 => ( P3 @ X3 ) ) ).
% 0.19/0.47
% 0.19/0.47 % prod_induct5
% 0.19/0.47 thf(fact_74_prod__induct4,axiom,
% 0.19/0.47 ! [D: $tType,C: $tType,B: $tType,A: $tType,P3: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 0.19/0.47 ( ! [A4: A,B4: B,C2: C,D2: D] : ( P3 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B4 @ ( product_Pair @ C @ D @ C2 @ D2 ) ) ) )
% 0.19/0.47 => ( P3 @ X3 ) ) ).
% 0.19/0.47
% 0.19/0.47 % prod_induct4
% 0.19/0.47 thf(fact_75_prod__induct3,axiom,
% 0.19/0.47 ! [C: $tType,B: $tType,A: $tType,P3: ( product_prod @ A @ ( product_prod @ B @ C ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ C )] :
% 0.19/0.47 ( ! [A4: A,B4: B,C2: C] : ( P3 @ ( product_Pair @ A @ ( product_prod @ B @ C ) @ A4 @ ( product_Pair @ B @ C @ B4 @ C2 ) ) )
% 0.19/0.47 => ( P3 @ X3 ) ) ).
% 0.19/0.47
% 0.19/0.47 % prod_induct3
% 0.19/0.47 thf(fact_76_prod__cases7,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,C: $tType,D: $tType,E2: $tType,F5: $tType,G2: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ ( product_prod @ F5 @ G2 ) ) ) ) )] :
% 0.19/0.47 ~ ! [A4: A,B4: B,C2: C,D2: D,E3: E2,F6: F5,G3: G2] :
% 0.19/0.47 ( Y
% 0.19/0.47 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ ( product_prod @ F5 @ G2 ) ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ ( product_prod @ F5 @ G2 ) ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E2 @ ( product_prod @ F5 @ G2 ) ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E2 @ ( product_prod @ F5 @ G2 ) ) @ D2 @ ( product_Pair @ E2 @ ( product_prod @ F5 @ G2 ) @ E3 @ ( product_Pair @ F5 @ G2 @ F6 @ G3 ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % prod_cases7
% 0.19/0.47 thf(fact_77_prod__cases6,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,C: $tType,D: $tType,E2: $tType,F5: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ F5 ) ) ) )] :
% 0.19/0.47 ~ ! [A4: A,B4: B,C2: C,D2: D,E3: E2,F6: F5] :
% 0.19/0.47 ( Y
% 0.19/0.47 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ F5 ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ F5 ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E2 @ F5 ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E2 @ F5 ) @ D2 @ ( product_Pair @ E2 @ F5 @ E3 @ F6 ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % prod_cases6
% 0.19/0.47 thf(fact_78_prod__cases5,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,C: $tType,D: $tType,E2: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E2 ) ) )] :
% 0.19/0.47 ~ ! [A4: A,B4: B,C2: C,D2: D,E3: E2] :
% 0.19/0.47 ( Y
% 0.19/0.47 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E2 ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E2 ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ E2 ) @ C2 @ ( product_Pair @ D @ E2 @ D2 @ E3 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % prod_cases5
% 0.19/0.47 thf(fact_79_prod__cases4,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,C: $tType,D: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 0.19/0.47 ~ ! [A4: A,B4: B,C2: C,D2: D] :
% 0.19/0.47 ( Y
% 0.19/0.47 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B4 @ ( product_Pair @ C @ D @ C2 @ D2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % prod_cases4
% 0.19/0.47 thf(fact_80_prod__cases3,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,C: $tType,Y: product_prod @ A @ ( product_prod @ B @ C )] :
% 0.19/0.47 ~ ! [A4: A,B4: B,C2: C] :
% 0.19/0.47 ( Y
% 0.19/0.47 != ( product_Pair @ A @ ( product_prod @ B @ C ) @ A4 @ ( product_Pair @ B @ C @ B4 @ C2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % prod_cases3
% 0.19/0.47 thf(fact_81_Pair__inject,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,A2: A,B2: B,A6: A,B3: B] :
% 0.19/0.47 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 0.19/0.47 = ( product_Pair @ A @ B @ A6 @ B3 ) )
% 0.19/0.47 => ~ ( ( A2 = A6 )
% 0.19/0.47 => ( B2 != B3 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Pair_inject
% 0.19/0.47 thf(fact_82_prod__cases,axiom,
% 0.19/0.47 ! [B: $tType,A: $tType,P3: ( product_prod @ A @ B ) > $o,P: product_prod @ A @ B] :
% 0.19/0.47 ( ! [A4: A,B4: B] : ( P3 @ ( product_Pair @ A @ B @ A4 @ B4 ) )
% 0.19/0.47 => ( P3 @ P ) ) ).
% 0.19/0.47
% 0.19/0.47 % prod_cases
% 0.19/0.47 thf(fact_83_old_Oprod_Orec,axiom,
% 0.19/0.47 ! [A: $tType,T: $tType,B: $tType,F1: A > B > T,A2: A,B2: B] :
% 0.19/0.47 ( ( product_rec_prod @ A @ B @ T @ F1 @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 0.19/0.47 = ( F1 @ A2 @ B2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % old.prod.rec
% 0.19/0.47 thf(fact_84_internal__case__prod__conv,axiom,
% 0.19/0.47 ! [B: $tType,A: $tType,C: $tType,C3: B > C > A,A2: B,B2: C] :
% 0.19/0.47 ( ( produc2004651681e_prod @ B @ C @ A @ C3 @ ( product_Pair @ B @ C @ A2 @ B2 ) )
% 0.19/0.47 = ( C3 @ A2 @ B2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % internal_case_prod_conv
% 0.19/0.47 thf(fact_85_accp__induct__rule,axiom,
% 0.19/0.47 ! [A: $tType,R2: A > A > $o,A2: A,P3: A > $o] :
% 0.19/0.47 ( ( accp @ A @ R2 @ A2 )
% 0.19/0.47 => ( ! [X5: A] :
% 0.19/0.47 ( ( accp @ A @ R2 @ X5 )
% 0.19/0.47 => ( ! [Y6: A] :
% 0.19/0.47 ( ( R2 @ Y6 @ X5 )
% 0.19/0.47 => ( P3 @ Y6 ) )
% 0.19/0.47 => ( P3 @ X5 ) ) )
% 0.19/0.47 => ( P3 @ A2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % accp_induct_rule
% 0.19/0.47 thf(fact_86_not__accp__down,axiom,
% 0.19/0.47 ! [A: $tType,R: A > A > $o,X3: A] :
% 0.19/0.47 ( ~ ( accp @ A @ R @ X3 )
% 0.19/0.47 => ~ ! [Z: A] :
% 0.19/0.47 ( ( R @ Z @ X3 )
% 0.19/0.47 => ( accp @ A @ R @ Z ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % not_accp_down
% 0.19/0.47 thf(fact_87_accp__downward,axiom,
% 0.19/0.47 ! [A: $tType,R2: A > A > $o,B2: A,A2: A] :
% 0.19/0.47 ( ( accp @ A @ R2 @ B2 )
% 0.19/0.47 => ( ( R2 @ A2 @ B2 )
% 0.19/0.47 => ( accp @ A @ R2 @ A2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % accp_downward
% 0.19/0.47 thf(fact_88_accp_Oinducts,axiom,
% 0.19/0.47 ! [A: $tType,R2: A > A > $o,X3: A,P3: A > $o] :
% 0.19/0.47 ( ( accp @ A @ R2 @ X3 )
% 0.19/0.47 => ( ! [X5: A] :
% 0.19/0.47 ( ! [Y6: A] :
% 0.19/0.47 ( ( R2 @ Y6 @ X5 )
% 0.19/0.47 => ( accp @ A @ R2 @ Y6 ) )
% 0.19/0.47 => ( ! [Y6: A] :
% 0.19/0.47 ( ( R2 @ Y6 @ X5 )
% 0.19/0.47 => ( P3 @ Y6 ) )
% 0.19/0.47 => ( P3 @ X5 ) ) )
% 0.19/0.47 => ( P3 @ X3 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % accp.inducts
% 0.19/0.47 thf(fact_89_accp__induct,axiom,
% 0.19/0.47 ! [A: $tType,R2: A > A > $o,A2: A,P3: A > $o] :
% 0.19/0.47 ( ( accp @ A @ R2 @ A2 )
% 0.19/0.47 => ( ! [X5: A] :
% 0.19/0.47 ( ( accp @ A @ R2 @ X5 )
% 0.19/0.47 => ( ! [Y6: A] :
% 0.19/0.47 ( ( R2 @ Y6 @ X5 )
% 0.19/0.47 => ( P3 @ Y6 ) )
% 0.19/0.47 => ( P3 @ X5 ) ) )
% 0.19/0.47 => ( P3 @ A2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % accp_induct
% 0.19/0.47 thf(fact_90_accp_Ocases,axiom,
% 0.19/0.47 ! [A: $tType,R2: A > A > $o,A2: A] :
% 0.19/0.47 ( ( accp @ A @ R2 @ A2 )
% 0.19/0.47 => ! [Y6: A] :
% 0.19/0.47 ( ( R2 @ Y6 @ A2 )
% 0.19/0.47 => ( accp @ A @ R2 @ Y6 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % accp.cases
% 0.19/0.47 thf(fact_91_accp_Osimps,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( accp @ A )
% 0.19/0.47 = ( ^ [R3: A > A > $o,A3: A] :
% 0.19/0.47 ? [X: A] :
% 0.19/0.47 ( ( A3 = X )
% 0.19/0.47 & ! [Y4: A] :
% 0.19/0.47 ( ( R3 @ Y4 @ X )
% 0.19/0.47 => ( accp @ A @ R3 @ Y4 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % accp.simps
% 0.19/0.47 thf(fact_92_accp_Ointros,axiom,
% 0.19/0.47 ! [A: $tType,R2: A > A > $o,X3: A] :
% 0.19/0.47 ( ! [Y5: A] :
% 0.19/0.47 ( ( R2 @ Y5 @ X3 )
% 0.19/0.47 => ( accp @ A @ R2 @ Y5 ) )
% 0.19/0.47 => ( accp @ A @ R2 @ X3 ) ) ).
% 0.19/0.47
% 0.19/0.47 % accp.intros
% 0.19/0.47 thf(fact_93_in__lex__prod,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,A2: A,B2: B,A6: A,B3: B,R2: set @ ( product_prod @ A @ A ),S2: set @ ( product_prod @ B @ B )] :
% 0.19/0.47 ( ( member @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ) @ ( product_Pair @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ A2 @ B2 ) @ ( product_Pair @ A @ B @ A6 @ B3 ) ) @ ( lex_prod @ A @ B @ R2 @ S2 ) )
% 0.19/0.47 = ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ A6 ) @ R2 )
% 0.19/0.47 | ( ( A2 = A6 )
% 0.19/0.47 & ( member @ ( product_prod @ B @ B ) @ ( product_Pair @ B @ B @ B2 @ B3 ) @ S2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % in_lex_prod
% 0.19/0.47 thf(fact_94_ssubst__Pair__rhs,axiom,
% 0.19/0.47 ! [B: $tType,A: $tType,R2: A,S2: B,R: set @ ( product_prod @ A @ B ),S3: B] :
% 0.19/0.47 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ R2 @ S2 ) @ R )
% 0.19/0.47 => ( ( S3 = S2 )
% 0.19/0.47 => ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ R2 @ S3 ) @ R ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % ssubst_Pair_rhs
% 0.19/0.47 thf(fact_95_curry__conv,axiom,
% 0.19/0.47 ! [A: $tType,C: $tType,B: $tType] :
% 0.19/0.47 ( ( product_curry @ B @ C @ A )
% 0.19/0.47 = ( ^ [F7: ( product_prod @ B @ C ) > A,A3: B,B5: C] : ( F7 @ ( product_Pair @ B @ C @ A3 @ B5 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % curry_conv
% 0.19/0.47 thf(fact_96_in__inv__imagep,axiom,
% 0.19/0.47 ! [B: $tType,A: $tType] :
% 0.19/0.47 ( ( inv_imagep @ A @ B )
% 0.19/0.47 = ( ^ [R3: A > A > $o,F7: B > A,X: B,Y4: B] : ( R3 @ ( F7 @ X ) @ ( F7 @ Y4 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % in_inv_imagep
% 0.19/0.47 thf(fact_97_acc__def,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( acc @ A )
% 0.19/0.47 = ( ^ [R3: set @ ( product_prod @ A @ A )] :
% 0.19/0.47 ( collect @ A
% 0.19/0.47 @ ( accp @ A
% 0.19/0.47 @ ^ [X: A,Y4: A] : ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y4 ) @ R3 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % acc_def
% 0.19/0.47 thf(fact_98_accp__acc__eq,axiom,
% 0.19/0.47 ! [A: $tType,R2: set @ ( product_prod @ A @ A )] :
% 0.19/0.47 ( ( accp @ A
% 0.19/0.47 @ ^ [X: A,Y4: A] : ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y4 ) @ R2 ) )
% 0.19/0.47 = ( ^ [X: A] : ( member @ A @ X @ ( acc @ A @ R2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % accp_acc_eq
% 0.19/0.47 thf(fact_99_curryI,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,F: ( product_prod @ A @ B ) > $o,A2: A,B2: B] :
% 0.19/0.47 ( ( F @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 0.19/0.47 => ( product_curry @ A @ B @ $o @ F @ A2 @ B2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % curryI
% 0.19/0.47 thf(fact_100_curry__K,axiom,
% 0.19/0.47 ! [B: $tType,C: $tType,A: $tType,C3: C] :
% 0.19/0.47 ( ( product_curry @ A @ B @ C
% 0.19/0.47 @ ^ [X: product_prod @ A @ B] : C3 )
% 0.19/0.47 = ( ^ [X: A,Y4: B] : C3 ) ) ).
% 0.19/0.47
% 0.19/0.47 % curry_K
% 0.19/0.47 thf(fact_101_acc__induct__rule,axiom,
% 0.19/0.47 ! [A: $tType,A2: A,R2: set @ ( product_prod @ A @ A ),P3: A > $o] :
% 0.19/0.47 ( ( member @ A @ A2 @ ( acc @ A @ R2 ) )
% 0.19/0.47 => ( ! [X5: A] :
% 0.19/0.47 ( ( member @ A @ X5 @ ( acc @ A @ R2 ) )
% 0.19/0.47 => ( ! [Y6: A] :
% 0.19/0.47 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y6 @ X5 ) @ R2 )
% 0.19/0.47 => ( P3 @ Y6 ) )
% 0.19/0.47 => ( P3 @ X5 ) ) )
% 0.19/0.47 => ( P3 @ A2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % acc_induct_rule
% 0.19/0.47 thf(fact_102_not__acc__down,axiom,
% 0.19/0.47 ! [A: $tType,X3: A,R: set @ ( product_prod @ A @ A )] :
% 0.19/0.47 ( ~ ( member @ A @ X3 @ ( acc @ A @ R ) )
% 0.19/0.47 => ~ ! [Z: A] :
% 0.19/0.47 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Z @ X3 ) @ R )
% 0.19/0.47 => ( member @ A @ Z @ ( acc @ A @ R ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % not_acc_down
% 0.19/0.47 thf(fact_103_acc__downward,axiom,
% 0.19/0.47 ! [A: $tType,B2: A,R2: set @ ( product_prod @ A @ A ),A2: A] :
% 0.19/0.47 ( ( member @ A @ B2 @ ( acc @ A @ R2 ) )
% 0.19/0.47 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ R2 )
% 0.19/0.47 => ( member @ A @ A2 @ ( acc @ A @ R2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % acc_downward
% 0.19/0.47 thf(fact_104_acc_Oinducts,axiom,
% 0.19/0.47 ! [A: $tType,X3: A,R2: set @ ( product_prod @ A @ A ),P3: A > $o] :
% 0.19/0.47 ( ( member @ A @ X3 @ ( acc @ A @ R2 ) )
% 0.19/0.47 => ( ! [X5: A] :
% 0.19/0.47 ( ! [Y6: A] :
% 0.19/0.47 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y6 @ X5 ) @ R2 )
% 0.19/0.47 => ( member @ A @ Y6 @ ( acc @ A @ R2 ) ) )
% 0.19/0.47 => ( ! [Y6: A] :
% 0.19/0.47 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y6 @ X5 ) @ R2 )
% 0.19/0.47 => ( P3 @ Y6 ) )
% 0.19/0.47 => ( P3 @ X5 ) ) )
% 0.19/0.47 => ( P3 @ X3 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % acc.inducts
% 0.19/0.47 thf(fact_105_acc__induct,axiom,
% 0.19/0.47 ! [A: $tType,A2: A,R2: set @ ( product_prod @ A @ A ),P3: A > $o] :
% 0.19/0.47 ( ( member @ A @ A2 @ ( acc @ A @ R2 ) )
% 0.19/0.47 => ( ! [X5: A] :
% 0.19/0.47 ( ( member @ A @ X5 @ ( acc @ A @ R2 ) )
% 0.19/0.47 => ( ! [Y6: A] :
% 0.19/0.47 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y6 @ X5 ) @ R2 )
% 0.19/0.47 => ( P3 @ Y6 ) )
% 0.19/0.47 => ( P3 @ X5 ) ) )
% 0.19/0.47 => ( P3 @ A2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % acc_induct
% 0.19/0.47 thf(fact_106_acc_Ointros,axiom,
% 0.19/0.47 ! [A: $tType,X3: A,R2: set @ ( product_prod @ A @ A )] :
% 0.19/0.47 ( ! [Y5: A] :
% 0.19/0.47 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y5 @ X3 ) @ R2 )
% 0.19/0.47 => ( member @ A @ Y5 @ ( acc @ A @ R2 ) ) )
% 0.19/0.47 => ( member @ A @ X3 @ ( acc @ A @ R2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % acc.intros
% 0.19/0.47 thf(fact_107_acc_Osimps,axiom,
% 0.19/0.47 ! [A: $tType,A2: A,R2: set @ ( product_prod @ A @ A )] :
% 0.19/0.47 ( ( member @ A @ A2 @ ( acc @ A @ R2 ) )
% 0.19/0.47 = ( ? [X: A] :
% 0.19/0.47 ( ( A2 = X )
% 0.19/0.47 & ! [Y4: A] :
% 0.19/0.47 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y4 @ X ) @ R2 )
% 0.19/0.47 => ( member @ A @ Y4 @ ( acc @ A @ R2 ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % acc.simps
% 0.19/0.47 thf(fact_108_acc_Ocases,axiom,
% 0.19/0.47 ! [A: $tType,A2: A,R2: set @ ( product_prod @ A @ A )] :
% 0.19/0.47 ( ( member @ A @ A2 @ ( acc @ A @ R2 ) )
% 0.19/0.47 => ! [Y6: A] :
% 0.19/0.47 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y6 @ A2 ) @ R2 )
% 0.19/0.47 => ( member @ A @ Y6 @ ( acc @ A @ R2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % acc.cases
% 0.19/0.47 thf(fact_109_curryE,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,F: ( product_prod @ A @ B ) > $o,A2: A,B2: B] :
% 0.19/0.47 ( ( product_curry @ A @ B @ $o @ F @ A2 @ B2 )
% 0.19/0.47 => ( F @ ( product_Pair @ A @ B @ A2 @ B2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % curryE
% 0.19/0.47 thf(fact_110_curryD,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,F: ( product_prod @ A @ B ) > $o,A2: A,B2: B] :
% 0.19/0.47 ( ( product_curry @ A @ B @ $o @ F @ A2 @ B2 )
% 0.19/0.47 => ( F @ ( product_Pair @ A @ B @ A2 @ B2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % curryD
% 0.19/0.47 thf(fact_111_inv__imagep__def,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType] :
% 0.19/0.47 ( ( inv_imagep @ B @ A )
% 0.19/0.47 = ( ^ [R3: B > B > $o,F7: A > B,X: A,Y4: A] : ( R3 @ ( F7 @ X ) @ ( F7 @ Y4 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % inv_imagep_def
% 0.19/0.47 thf(fact_112_curry__def,axiom,
% 0.19/0.47 ! [C: $tType,B: $tType,A: $tType] :
% 0.19/0.47 ( ( product_curry @ A @ B @ C )
% 0.19/0.47 = ( ^ [C4: ( product_prod @ A @ B ) > C,X: A,Y4: B] : ( C4 @ ( product_Pair @ A @ B @ X @ Y4 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % curry_def
% 0.19/0.47 thf(fact_113_same__fstI,axiom,
% 0.19/0.47 ! [B: $tType,A: $tType,P3: A > $o,X3: A,Y7: B,Y: B,R: A > ( set @ ( product_prod @ B @ B ) )] :
% 0.19/0.47 ( ( P3 @ X3 )
% 0.19/0.47 => ( ( member @ ( product_prod @ B @ B ) @ ( product_Pair @ B @ B @ Y7 @ Y ) @ ( R @ X3 ) )
% 0.19/0.47 => ( member @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ) @ ( product_Pair @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X3 @ Y7 ) @ ( product_Pair @ A @ B @ X3 @ Y ) ) @ ( same_fst @ A @ B @ P3 @ R ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % same_fstI
% 0.19/0.47 thf(fact_114_in__inv__image,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,X3: A,Y: A,R2: set @ ( product_prod @ B @ B ),F: A > B] :
% 0.19/0.47 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X3 @ Y ) @ ( inv_image @ B @ A @ R2 @ F ) )
% 0.19/0.47 = ( member @ ( product_prod @ B @ B ) @ ( product_Pair @ B @ B @ ( F @ X3 ) @ ( F @ Y ) ) @ R2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % in_inv_image
% 0.19/0.47 thf(fact_115_PREF_Opelims,axiom,
% 0.19/0.47 ! [C: $tType,A: $tType,B: $tType,X3: A > ( proces554692349s_term @ B @ C ),Xa: proces554692349s_term @ B @ A,Y: B] :
% 0.19/0.47 ( ( ( proces1708129104e_PREF @ A @ B @ C @ X3 @ Xa )
% 0.19/0.47 = Y )
% 0.19/0.47 => ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces527360425EF_rel @ A @ B @ C ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ X3 @ Xa ) )
% 0.19/0.47 => ( ! [X4: A] :
% 0.19/0.47 ( ( Xa
% 0.19/0.47 = ( proces1627516585ss_VAR @ A @ B @ X4 ) )
% 0.19/0.47 => ( ( Y
% 0.19/0.47 = ( proces460752237s_term @ C @ B @ B
% 0.19/0.47 @ ^ [Aa: C] : ( undefined @ B )
% 0.19/0.47 @ ( proces745025900prefOf @ B )
% 0.19/0.47 @ ^ [A3: B,T3: proces554692349s_term @ B @ C] : A3
% 0.19/0.47 @ ^ [Aa: proces554692349s_term @ B @ C,Ab2: proces554692349s_term @ B @ C] : ( undefined @ B )
% 0.19/0.47 @ ( X3 @ X4 ) ) )
% 0.19/0.47 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces527360425EF_rel @ A @ B @ C ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ X3 @ ( proces1627516585ss_VAR @ A @ B @ X4 ) ) ) ) )
% 0.19/0.47 => ( ! [P2: proces634752977rocess @ B] :
% 0.19/0.47 ( ( Xa
% 0.19/0.47 = ( proces1062592052s_PROC @ B @ A @ P2 ) )
% 0.19/0.47 => ( ( Y
% 0.19/0.47 = ( proces745025900prefOf @ B @ P2 ) )
% 0.19/0.47 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces527360425EF_rel @ A @ B @ C ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ X3 @ ( proces1062592052s_PROC @ B @ A @ P2 ) ) ) ) )
% 0.19/0.47 => ( ! [A4: B,T4: proces554692349s_term @ B @ A] :
% 0.19/0.47 ( ( Xa
% 0.19/0.47 = ( proces1454156180ss_ACT @ B @ A @ A4 @ T4 ) )
% 0.19/0.47 => ( ( Y = A4 )
% 0.19/0.47 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces527360425EF_rel @ A @ B @ C ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ X3 @ ( proces1454156180ss_ACT @ B @ A @ A4 @ T4 ) ) ) ) )
% 0.19/0.47 => ~ ! [V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] :
% 0.19/0.47 ( ( Xa
% 0.19/0.47 = ( proces89589571ess_CH @ B @ A @ V @ Va ) )
% 0.19/0.47 => ( ( Y
% 0.19/0.47 = ( undefined @ B ) )
% 0.19/0.47 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces527360425EF_rel @ A @ B @ C ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ X3 @ ( proces89589571ess_CH @ B @ A @ V @ Va ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % PREF.pelims
% 0.19/0.47 thf(fact_116_above__def,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( order_above @ A )
% 0.19/0.47 = ( ^ [R3: set @ ( product_prod @ A @ A ),A3: A] :
% 0.19/0.47 ( collect @ A
% 0.19/0.47 @ ^ [B5: A] : ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A3 @ B5 ) @ R3 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % above_def
% 0.19/0.47 thf(fact_117_aboveS__def,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( order_aboveS @ A )
% 0.19/0.47 = ( ^ [R3: set @ ( product_prod @ A @ A ),A3: A] :
% 0.19/0.47 ( collect @ A
% 0.19/0.47 @ ^ [B5: A] :
% 0.19/0.47 ( ( B5 != A3 )
% 0.19/0.47 & ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A3 @ B5 ) @ R3 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % aboveS_def
% 0.19/0.47 thf(fact_118_PREF_Osimps_I2_J,axiom,
% 0.19/0.47 ! [A: $tType,C: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ C ),P: proces634752977rocess @ B] :
% 0.19/0.47 ( ( proces1708129104e_PREF @ A @ B @ C @ Sys @ ( proces1062592052s_PROC @ B @ A @ P ) )
% 0.19/0.47 = ( proces745025900prefOf @ B @ P ) ) ).
% 0.19/0.47
% 0.19/0.47 % PREF.simps(2)
% 0.19/0.47 thf(fact_119_PREF_Osimps_I1_J,axiom,
% 0.19/0.47 ! [B: $tType,C: $tType,A: $tType,Sys: A > ( proces554692349s_term @ B @ C ),X6: A] :
% 0.19/0.47 ( ( proces1708129104e_PREF @ A @ B @ C @ Sys @ ( proces1627516585ss_VAR @ A @ B @ X6 ) )
% 0.19/0.47 = ( proces460752237s_term @ C @ B @ B
% 0.19/0.47 @ ^ [Aa: C] : ( undefined @ B )
% 0.19/0.47 @ ( proces745025900prefOf @ B )
% 0.19/0.47 @ ^ [A3: B,T3: proces554692349s_term @ B @ C] : A3
% 0.19/0.47 @ ^ [Aa: proces554692349s_term @ B @ C,Ab2: proces554692349s_term @ B @ C] : ( undefined @ B )
% 0.19/0.47 @ ( Sys @ X6 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % PREF.simps(1)
% 0.19/0.47 thf(fact_120_solution_Osimps_I3_J,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 0.19/0.47 ( ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
% 0.19/0.47 => ( ( proces745025900prefOf @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) )
% 0.19/0.47 = ( proces1708129104e_PREF @ A @ B @ A @ Sys @ T2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % solution.simps(3)
% 0.19/0.47 thf(fact_121_PREF_Osimps_I3_J,axiom,
% 0.19/0.47 ! [A: $tType,C: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ C ),A2: B,T2: proces554692349s_term @ B @ A] :
% 0.19/0.47 ( ( proces1708129104e_PREF @ A @ B @ C @ Sys @ ( proces1454156180ss_ACT @ B @ A @ A2 @ T2 ) )
% 0.19/0.47 = A2 ) ).
% 0.19/0.47
% 0.19/0.47 % PREF.simps(3)
% 0.19/0.47 thf(fact_122_PREF_Oelims,axiom,
% 0.19/0.47 ! [A: $tType,C: $tType,B: $tType,X3: A > ( proces554692349s_term @ B @ C ),Xa: proces554692349s_term @ B @ A,Y: B] :
% 0.19/0.47 ( ( ( proces1708129104e_PREF @ A @ B @ C @ X3 @ Xa )
% 0.19/0.47 = Y )
% 0.19/0.47 => ( ! [X4: A] :
% 0.19/0.47 ( ( Xa
% 0.19/0.47 = ( proces1627516585ss_VAR @ A @ B @ X4 ) )
% 0.19/0.47 => ( Y
% 0.19/0.47 != ( proces460752237s_term @ C @ B @ B
% 0.19/0.47 @ ^ [Aa: C] : ( undefined @ B )
% 0.19/0.47 @ ( proces745025900prefOf @ B )
% 0.19/0.47 @ ^ [A3: B,T3: proces554692349s_term @ B @ C] : A3
% 0.19/0.47 @ ^ [Aa: proces554692349s_term @ B @ C,Ab2: proces554692349s_term @ B @ C] : ( undefined @ B )
% 0.19/0.47 @ ( X3 @ X4 ) ) ) )
% 0.19/0.47 => ( ! [P2: proces634752977rocess @ B] :
% 0.19/0.47 ( ( Xa
% 0.19/0.47 = ( proces1062592052s_PROC @ B @ A @ P2 ) )
% 0.19/0.47 => ( Y
% 0.19/0.47 != ( proces745025900prefOf @ B @ P2 ) ) )
% 0.19/0.47 => ( ! [A4: B] :
% 0.19/0.47 ( ? [T4: proces554692349s_term @ B @ A] :
% 0.19/0.47 ( Xa
% 0.19/0.47 = ( proces1454156180ss_ACT @ B @ A @ A4 @ T4 ) )
% 0.19/0.47 => ( Y != A4 ) )
% 0.19/0.47 => ~ ( ? [V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] :
% 0.19/0.47 ( Xa
% 0.19/0.47 = ( proces89589571ess_CH @ B @ A @ V @ Va ) )
% 0.19/0.47 => ( Y
% 0.19/0.47 != ( undefined @ B ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % PREF.elims
% 0.19/0.47 thf(fact_123_prefOf__def,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( proces745025900prefOf @ A )
% 0.19/0.47 = ( proces1406508781rocess @ A @ A
% 0.19/0.47 @ ^ [X11: A,X122: proces634752977rocess @ A] : X11
% 0.19/0.47 @ ^ [Uu: proces634752977rocess @ A,Uv: proces634752977rocess @ A] : ( undefined @ A ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % prefOf_def
% 0.19/0.47 thf(fact_124_cut__def,axiom,
% 0.19/0.47 ! [B: $tType,A: $tType] :
% 0.19/0.47 ( ( cut @ A @ B )
% 0.19/0.47 = ( ^ [F7: A > B,R4: set @ ( product_prod @ A @ A ),X: A,Y4: A] : ( if @ B @ ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y4 @ X ) @ R4 ) @ ( F7 @ Y4 ) @ ( undefined @ B ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % cut_def
% 0.19/0.47 thf(fact_125_CH1_Opelims,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,X3: A > ( proces554692349s_term @ B @ A ),Xa: proces554692349s_term @ B @ A,Y: proces554692349s_term @ B @ A] :
% 0.19/0.47 ( ( ( proces1239275103le_CH1 @ A @ B @ X3 @ Xa )
% 0.19/0.47 = Y )
% 0.19/0.47 => ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1869379930H1_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X3 @ Xa ) )
% 0.19/0.47 => ( ! [X4: A] :
% 0.19/0.47 ( ( Xa
% 0.19/0.47 = ( proces1627516585ss_VAR @ A @ B @ X4 ) )
% 0.19/0.47 => ( ( Y
% 0.19/0.47 = ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 0.19/0.47 @ ^ [A3: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.19/0.47 @ ^ [P4: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces979765041_ch1Of @ B @ P4 ) )
% 0.19/0.47 @ ^ [A3: B,B5: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.19/0.47 @ ^ [T13: proces554692349s_term @ B @ A,T24: proces554692349s_term @ B @ A] : T13
% 0.19/0.47 @ ( X3 @ X4 ) ) )
% 0.19/0.47 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1869379930H1_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X3 @ ( proces1627516585ss_VAR @ A @ B @ X4 ) ) ) ) )
% 0.19/0.47 => ( ! [P2: proces634752977rocess @ B] :
% 0.19/0.47 ( ( Xa
% 0.19/0.47 = ( proces1062592052s_PROC @ B @ A @ P2 ) )
% 0.19/0.47 => ( ( Y
% 0.19/0.47 = ( proces1062592052s_PROC @ B @ A @ ( proces979765041_ch1Of @ B @ P2 ) ) )
% 0.19/0.47 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1869379930H1_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X3 @ ( proces1062592052s_PROC @ B @ A @ P2 ) ) ) ) )
% 0.19/0.47 => ( ! [T12: proces554692349s_term @ B @ A,T23: proces554692349s_term @ B @ A] :
% 0.19/0.47 ( ( Xa
% 0.19/0.47 = ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) )
% 0.19/0.47 => ( ( Y = T12 )
% 0.19/0.47 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1869379930H1_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X3 @ ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) ) ) ) )
% 0.19/0.47 => ~ ! [V: B,Va: proces554692349s_term @ B @ A] :
% 0.19/0.47 ( ( Xa
% 0.19/0.47 = ( proces1454156180ss_ACT @ B @ A @ V @ Va ) )
% 0.19/0.47 => ( ( Y
% 0.19/0.47 = ( undefined @ ( proces554692349s_term @ B @ A ) ) )
% 0.19/0.47 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1869379930H1_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X3 @ ( proces1454156180ss_ACT @ B @ A @ V @ Va ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % CH1.pelims
% 0.19/0.47 thf(fact_126_CH2_Opelims,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,X3: A > ( proces554692349s_term @ B @ A ),Xa: proces554692349s_term @ B @ A,Y: proces554692349s_term @ B @ A] :
% 0.19/0.47 ( ( ( proces1239275104le_CH2 @ A @ B @ X3 @ Xa )
% 0.19/0.47 = Y )
% 0.19/0.47 => ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces93903513H2_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X3 @ Xa ) )
% 0.19/0.47 => ( ! [X4: A] :
% 0.19/0.47 ( ( Xa
% 0.19/0.47 = ( proces1627516585ss_VAR @ A @ B @ X4 ) )
% 0.19/0.47 => ( ( Y
% 0.19/0.47 = ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 0.19/0.47 @ ^ [A3: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.19/0.47 @ ^ [P4: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces988026546_ch2Of @ B @ P4 ) )
% 0.19/0.47 @ ^ [A3: B,B5: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.19/0.47 @ ^ [T13: proces554692349s_term @ B @ A,T24: proces554692349s_term @ B @ A] : T24
% 0.19/0.47 @ ( X3 @ X4 ) ) )
% 0.19/0.47 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces93903513H2_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X3 @ ( proces1627516585ss_VAR @ A @ B @ X4 ) ) ) ) )
% 0.19/0.47 => ( ! [P2: proces634752977rocess @ B] :
% 0.19/0.47 ( ( Xa
% 0.19/0.47 = ( proces1062592052s_PROC @ B @ A @ P2 ) )
% 0.19/0.47 => ( ( Y
% 0.19/0.47 = ( proces1062592052s_PROC @ B @ A @ ( proces988026546_ch2Of @ B @ P2 ) ) )
% 0.19/0.47 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces93903513H2_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X3 @ ( proces1062592052s_PROC @ B @ A @ P2 ) ) ) ) )
% 0.19/0.47 => ( ! [T12: proces554692349s_term @ B @ A,T23: proces554692349s_term @ B @ A] :
% 0.19/0.47 ( ( Xa
% 0.19/0.47 = ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) )
% 0.19/0.47 => ( ( Y = T23 )
% 0.19/0.47 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces93903513H2_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X3 @ ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) ) ) ) )
% 0.19/0.47 => ~ ! [V: B,Va: proces554692349s_term @ B @ A] :
% 0.19/0.47 ( ( Xa
% 0.19/0.47 = ( proces1454156180ss_ACT @ B @ A @ V @ Va ) )
% 0.19/0.47 => ( ( Y
% 0.19/0.47 = ( undefined @ ( proces554692349s_term @ B @ A ) ) )
% 0.19/0.47 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces93903513H2_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X3 @ ( proces1454156180ss_ACT @ B @ A @ V @ Va ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % CH2.pelims
% 0.19/0.47 thf(fact_127_ch2Of__def,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( proces988026546_ch2Of @ A )
% 0.19/0.47 = ( proces1406508781rocess @ A @ ( proces634752977rocess @ A )
% 0.19/0.47 @ ^ [Uu: A,Uv: proces634752977rocess @ A] : ( undefined @ ( proces634752977rocess @ A ) )
% 0.19/0.47 @ ^ [X21: proces634752977rocess @ A,X222: proces634752977rocess @ A] : X222 ) ) ).
% 0.19/0.47
% 0.19/0.47 % ch2Of_def
% 0.19/0.47 thf(fact_128_ch1Of__def,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( proces979765041_ch1Of @ A )
% 0.19/0.47 = ( proces1406508781rocess @ A @ ( proces634752977rocess @ A )
% 0.19/0.47 @ ^ [Uu: A,Uv: proces634752977rocess @ A] : ( undefined @ ( proces634752977rocess @ A ) )
% 0.19/0.47 @ ^ [X21: proces634752977rocess @ A,X222: proces634752977rocess @ A] : X21 ) ) ).
% 0.19/0.47
% 0.19/0.47 % ch1Of_def
% 0.19/0.47 thf(fact_129_CH2_Osimps_I2_J,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),P: proces634752977rocess @ B] :
% 0.19/0.47 ( ( proces1239275104le_CH2 @ A @ B @ Sys @ ( proces1062592052s_PROC @ B @ A @ P ) )
% 0.19/0.47 = ( proces1062592052s_PROC @ B @ A @ ( proces988026546_ch2Of @ B @ P ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % CH2.simps(2)
% 0.19/0.47 thf(fact_130_CH1_Osimps_I2_J,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),P: proces634752977rocess @ B] :
% 0.19/0.47 ( ( proces1239275103le_CH1 @ A @ B @ Sys @ ( proces1062592052s_PROC @ B @ A @ P ) )
% 0.19/0.47 = ( proces1062592052s_PROC @ B @ A @ ( proces979765041_ch1Of @ B @ P ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % CH1.simps(2)
% 0.19/0.47 thf(fact_131_process_Ocase__distrib,axiom,
% 0.19/0.47 ! [B: $tType,C: $tType,A: $tType,H: B > C,F1: A > ( proces634752977rocess @ A ) > B,F2: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B,Process: proces634752977rocess @ A] :
% 0.19/0.47 ( ( H @ ( proces1406508781rocess @ A @ B @ F1 @ F2 @ Process ) )
% 0.19/0.47 = ( proces1406508781rocess @ A @ C
% 0.19/0.47 @ ^ [X1: A,X22: proces634752977rocess @ A] : ( H @ ( F1 @ X1 @ X22 ) )
% 0.19/0.47 @ ^ [X1: proces634752977rocess @ A,X22: proces634752977rocess @ A] : ( H @ ( F2 @ X1 @ X22 ) )
% 0.19/0.47 @ Process ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.case_distrib
% 0.19/0.47 thf(fact_132_solution_Osimps_I6_J,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 0.19/0.47 ( ~ ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
% 0.19/0.47 => ( ( proces988026546_ch2Of @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) )
% 0.19/0.47 = ( proces1652378886lution @ A @ B @ Sys @ ( proces1239275104le_CH2 @ A @ B @ Sys @ T2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % solution.simps(6)
% 0.19/0.47 thf(fact_133_solution_Osimps_I5_J,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 0.19/0.47 ( ~ ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
% 0.19/0.47 => ( ( proces979765041_ch1Of @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) )
% 0.19/0.47 = ( proces1652378886lution @ A @ B @ Sys @ ( proces1239275103le_CH1 @ A @ B @ Sys @ T2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % solution.simps(5)
% 0.19/0.47 thf(fact_134_CH2_Osimps_I1_J,axiom,
% 0.19/0.47 ! [B: $tType,A: $tType,Sys: A > ( proces554692349s_term @ B @ A ),X6: A] :
% 0.19/0.47 ( ( proces1239275104le_CH2 @ A @ B @ Sys @ ( proces1627516585ss_VAR @ A @ B @ X6 ) )
% 0.19/0.47 = ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 0.19/0.47 @ ^ [A3: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.19/0.47 @ ^ [P4: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces988026546_ch2Of @ B @ P4 ) )
% 0.19/0.47 @ ^ [A3: B,B5: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.19/0.47 @ ^ [T13: proces554692349s_term @ B @ A,T24: proces554692349s_term @ B @ A] : T24
% 0.19/0.47 @ ( Sys @ X6 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % CH2.simps(1)
% 0.19/0.47 thf(fact_135_CH1_Osimps_I1_J,axiom,
% 0.19/0.47 ! [B: $tType,A: $tType,Sys: A > ( proces554692349s_term @ B @ A ),X6: A] :
% 0.19/0.47 ( ( proces1239275103le_CH1 @ A @ B @ Sys @ ( proces1627516585ss_VAR @ A @ B @ X6 ) )
% 0.19/0.47 = ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 0.19/0.47 @ ^ [A3: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.19/0.47 @ ^ [P4: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces979765041_ch1Of @ B @ P4 ) )
% 0.19/0.47 @ ^ [A3: B,B5: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.19/0.47 @ ^ [T13: proces554692349s_term @ B @ A,T24: proces554692349s_term @ B @ A] : T13
% 0.19/0.47 @ ( Sys @ X6 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % CH1.simps(1)
% 0.19/0.47 thf(fact_136_cut__apply,axiom,
% 0.19/0.47 ! [B: $tType,A: $tType,X3: A,A2: A,R: set @ ( product_prod @ A @ A ),F: A > B] :
% 0.19/0.47 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X3 @ A2 ) @ R )
% 0.19/0.47 => ( ( cut @ A @ B @ F @ R @ A2 @ X3 )
% 0.19/0.47 = ( F @ X3 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % cut_apply
% 0.19/0.47 thf(fact_137_cuts__eq,axiom,
% 0.19/0.47 ! [B: $tType,A: $tType,F: A > B,R: set @ ( product_prod @ A @ A ),X3: A,G: A > B] :
% 0.19/0.47 ( ( ( cut @ A @ B @ F @ R @ X3 )
% 0.19/0.47 = ( cut @ A @ B @ G @ R @ X3 ) )
% 0.19/0.47 = ( ! [Y4: A] :
% 0.19/0.47 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y4 @ X3 ) @ R )
% 0.19/0.47 => ( ( F @ Y4 )
% 0.19/0.47 = ( G @ Y4 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % cuts_eq
% 0.19/0.47 thf(fact_138_CH2_Osimps_I3_J,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T1: proces554692349s_term @ B @ A,T22: proces554692349s_term @ B @ A] :
% 0.19/0.47 ( ( proces1239275104le_CH2 @ A @ B @ Sys @ ( proces89589571ess_CH @ B @ A @ T1 @ T22 ) )
% 0.19/0.47 = T22 ) ).
% 0.19/0.47
% 0.19/0.47 % CH2.simps(3)
% 0.19/0.47 thf(fact_139_CH1_Osimps_I3_J,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T1: proces554692349s_term @ B @ A,T22: proces554692349s_term @ B @ A] :
% 0.19/0.47 ( ( proces1239275103le_CH1 @ A @ B @ Sys @ ( proces89589571ess_CH @ B @ A @ T1 @ T22 ) )
% 0.19/0.47 = T1 ) ).
% 0.19/0.47
% 0.19/0.47 % CH1.simps(3)
% 0.19/0.47 thf(fact_140_process_Odisc__eq__case_I1_J,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( proces10484146Action @ A )
% 0.19/0.47 = ( proces1406508781rocess @ A @ $o
% 0.19/0.47 @ ^ [Uu2: A,Uv2: proces634752977rocess @ A] : $true
% 0.19/0.47 @ ^ [Uu2: proces634752977rocess @ A,Uv2: proces634752977rocess @ A] : $false ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.disc_eq_case(1)
% 0.19/0.47 thf(fact_141_process_Odisc__eq__case_I2_J,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( proces401113213Choice @ A )
% 0.19/0.47 = ( proces1406508781rocess @ A @ $o
% 0.19/0.47 @ ^ [Uu2: A,Uv2: proces634752977rocess @ A] : $false
% 0.19/0.47 @ ^ [Uu2: proces634752977rocess @ A,Uv2: proces634752977rocess @ A] : $true ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.disc_eq_case(2)
% 0.19/0.47 thf(fact_142_CH2_Oelims,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,X3: A > ( proces554692349s_term @ B @ A ),Xa: proces554692349s_term @ B @ A,Y: proces554692349s_term @ B @ A] :
% 0.19/0.47 ( ( ( proces1239275104le_CH2 @ A @ B @ X3 @ Xa )
% 0.19/0.47 = Y )
% 0.19/0.47 => ( ! [X4: A] :
% 0.19/0.47 ( ( Xa
% 0.19/0.47 = ( proces1627516585ss_VAR @ A @ B @ X4 ) )
% 0.19/0.47 => ( Y
% 0.19/0.47 != ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 0.19/0.47 @ ^ [A3: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.19/0.47 @ ^ [P4: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces988026546_ch2Of @ B @ P4 ) )
% 0.19/0.47 @ ^ [A3: B,B5: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.19/0.47 @ ^ [T13: proces554692349s_term @ B @ A,T24: proces554692349s_term @ B @ A] : T24
% 0.19/0.47 @ ( X3 @ X4 ) ) ) )
% 0.19/0.47 => ( ! [P2: proces634752977rocess @ B] :
% 0.19/0.47 ( ( Xa
% 0.19/0.47 = ( proces1062592052s_PROC @ B @ A @ P2 ) )
% 0.19/0.47 => ( Y
% 0.19/0.47 != ( proces1062592052s_PROC @ B @ A @ ( proces988026546_ch2Of @ B @ P2 ) ) ) )
% 0.19/0.47 => ( ! [T12: proces554692349s_term @ B @ A,T23: proces554692349s_term @ B @ A] :
% 0.19/0.47 ( ( Xa
% 0.19/0.47 = ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) )
% 0.19/0.47 => ( Y != T23 ) )
% 0.19/0.47 => ~ ( ? [V: B,Va: proces554692349s_term @ B @ A] :
% 0.19/0.47 ( Xa
% 0.19/0.47 = ( proces1454156180ss_ACT @ B @ A @ V @ Va ) )
% 0.19/0.47 => ( Y
% 0.19/0.47 != ( undefined @ ( proces554692349s_term @ B @ A ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % CH2.elims
% 0.19/0.47 thf(fact_143_CH1_Oelims,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,X3: A > ( proces554692349s_term @ B @ A ),Xa: proces554692349s_term @ B @ A,Y: proces554692349s_term @ B @ A] :
% 0.19/0.47 ( ( ( proces1239275103le_CH1 @ A @ B @ X3 @ Xa )
% 0.19/0.47 = Y )
% 0.19/0.47 => ( ! [X4: A] :
% 0.19/0.47 ( ( Xa
% 0.19/0.47 = ( proces1627516585ss_VAR @ A @ B @ X4 ) )
% 0.19/0.47 => ( Y
% 0.19/0.47 != ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 0.19/0.47 @ ^ [A3: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.19/0.47 @ ^ [P4: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces979765041_ch1Of @ B @ P4 ) )
% 0.19/0.47 @ ^ [A3: B,B5: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.19/0.47 @ ^ [T13: proces554692349s_term @ B @ A,T24: proces554692349s_term @ B @ A] : T13
% 0.19/0.47 @ ( X3 @ X4 ) ) ) )
% 0.19/0.47 => ( ! [P2: proces634752977rocess @ B] :
% 0.19/0.47 ( ( Xa
% 0.19/0.47 = ( proces1062592052s_PROC @ B @ A @ P2 ) )
% 0.19/0.47 => ( Y
% 0.19/0.47 != ( proces1062592052s_PROC @ B @ A @ ( proces979765041_ch1Of @ B @ P2 ) ) ) )
% 0.19/0.47 => ( ! [T12: proces554692349s_term @ B @ A] :
% 0.19/0.47 ( ? [T23: proces554692349s_term @ B @ A] :
% 0.19/0.47 ( Xa
% 0.19/0.47 = ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) )
% 0.19/0.47 => ( Y != T12 ) )
% 0.19/0.47 => ~ ( ? [V: B,Va: proces554692349s_term @ B @ A] :
% 0.19/0.47 ( Xa
% 0.19/0.47 = ( proces1454156180ss_ACT @ B @ A @ V @ Va ) )
% 0.19/0.47 => ( Y
% 0.19/0.47 != ( undefined @ ( proces554692349s_term @ B @ A ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % CH1.elims
% 0.19/0.47 thf(fact_144_process_Ocase__eq__if,axiom,
% 0.19/0.47 ! [B: $tType,A: $tType] :
% 0.19/0.47 ( ( proces1406508781rocess @ A @ B )
% 0.19/0.47 = ( ^ [F12: A > ( proces634752977rocess @ A ) > B,F22: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B,Process2: proces634752977rocess @ A] : ( if @ B @ ( proces10484146Action @ A @ Process2 ) @ ( F12 @ ( proces745025900prefOf @ A @ Process2 ) @ ( proces1778668539contOf @ A @ Process2 ) ) @ ( F22 @ ( proces979765041_ch1Of @ A @ Process2 ) @ ( proces988026546_ch2Of @ A @ Process2 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.case_eq_if
% 0.19/0.47 thf(fact_145_process_Ocoinduct__strong,axiom,
% 0.19/0.47 ! [A: $tType,R: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > $o,Process: proces634752977rocess @ A,Process3: proces634752977rocess @ A] :
% 0.19/0.47 ( ( R @ Process @ Process3 )
% 0.19/0.47 => ( ! [Process4: proces634752977rocess @ A,Process5: proces634752977rocess @ A] :
% 0.19/0.47 ( ( R @ Process4 @ Process5 )
% 0.19/0.47 => ( ( ( proces10484146Action @ A @ Process4 )
% 0.19/0.47 = ( proces10484146Action @ A @ Process5 ) )
% 0.19/0.47 & ( ( proces10484146Action @ A @ Process4 )
% 0.19/0.47 => ( ( proces10484146Action @ A @ Process5 )
% 0.19/0.47 => ( ( ( proces745025900prefOf @ A @ Process4 )
% 0.19/0.47 = ( proces745025900prefOf @ A @ Process5 ) )
% 0.19/0.47 & ( ( R @ ( proces1778668539contOf @ A @ Process4 ) @ ( proces1778668539contOf @ A @ Process5 ) )
% 0.19/0.47 | ( ( proces1778668539contOf @ A @ Process4 )
% 0.19/0.47 = ( proces1778668539contOf @ A @ Process5 ) ) ) ) ) )
% 0.19/0.47 & ( ( proces401113213Choice @ A @ Process4 )
% 0.19/0.47 => ( ( proces401113213Choice @ A @ Process5 )
% 0.19/0.47 => ( ( ( R @ ( proces979765041_ch1Of @ A @ Process4 ) @ ( proces979765041_ch1Of @ A @ Process5 ) )
% 0.19/0.47 | ( ( proces979765041_ch1Of @ A @ Process4 )
% 0.19/0.47 = ( proces979765041_ch1Of @ A @ Process5 ) ) )
% 0.19/0.47 & ( ( R @ ( proces988026546_ch2Of @ A @ Process4 ) @ ( proces988026546_ch2Of @ A @ Process5 ) )
% 0.19/0.47 | ( ( proces988026546_ch2Of @ A @ Process4 )
% 0.19/0.47 = ( proces988026546_ch2Of @ A @ Process5 ) ) ) ) ) ) ) )
% 0.19/0.47 => ( Process = Process3 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.coinduct_strong
% 0.19/0.47 thf(fact_146_process_Ocoinduct,axiom,
% 0.19/0.47 ! [A: $tType,R: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > $o,Process: proces634752977rocess @ A,Process3: proces634752977rocess @ A] :
% 0.19/0.47 ( ( R @ Process @ Process3 )
% 0.19/0.47 => ( ! [Process4: proces634752977rocess @ A,Process5: proces634752977rocess @ A] :
% 0.19/0.47 ( ( R @ Process4 @ Process5 )
% 0.19/0.47 => ( ( ( proces10484146Action @ A @ Process4 )
% 0.19/0.47 = ( proces10484146Action @ A @ Process5 ) )
% 0.19/0.47 & ( ( proces10484146Action @ A @ Process4 )
% 0.19/0.47 => ( ( proces10484146Action @ A @ Process5 )
% 0.19/0.47 => ( ( ( proces745025900prefOf @ A @ Process4 )
% 0.19/0.47 = ( proces745025900prefOf @ A @ Process5 ) )
% 0.19/0.47 & ( R @ ( proces1778668539contOf @ A @ Process4 ) @ ( proces1778668539contOf @ A @ Process5 ) ) ) ) )
% 0.19/0.47 & ( ( proces401113213Choice @ A @ Process4 )
% 0.19/0.47 => ( ( proces401113213Choice @ A @ Process5 )
% 0.19/0.47 => ( ( R @ ( proces979765041_ch1Of @ A @ Process4 ) @ ( proces979765041_ch1Of @ A @ Process5 ) )
% 0.19/0.47 & ( R @ ( proces988026546_ch2Of @ A @ Process4 ) @ ( proces988026546_ch2Of @ A @ Process5 ) ) ) ) ) ) )
% 0.19/0.47 => ( Process = Process3 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.coinduct
% 0.19/0.47 thf(fact_147_process_Oexpand,axiom,
% 0.19/0.47 ! [A: $tType,Process: proces634752977rocess @ A,Process3: proces634752977rocess @ A] :
% 0.19/0.47 ( ( ( proces10484146Action @ A @ Process )
% 0.19/0.47 = ( proces10484146Action @ A @ Process3 ) )
% 0.19/0.47 => ( ( ( proces10484146Action @ A @ Process )
% 0.19/0.47 => ( ( proces10484146Action @ A @ Process3 )
% 0.19/0.47 => ( ( ( proces745025900prefOf @ A @ Process )
% 0.19/0.47 = ( proces745025900prefOf @ A @ Process3 ) )
% 0.19/0.47 & ( ( proces1778668539contOf @ A @ Process )
% 0.19/0.47 = ( proces1778668539contOf @ A @ Process3 ) ) ) ) )
% 0.19/0.47 => ( ( ( proces401113213Choice @ A @ Process )
% 0.19/0.47 => ( ( proces401113213Choice @ A @ Process3 )
% 0.19/0.47 => ( ( ( proces979765041_ch1Of @ A @ Process )
% 0.19/0.47 = ( proces979765041_ch1Of @ A @ Process3 ) )
% 0.19/0.47 & ( ( proces988026546_ch2Of @ A @ Process )
% 0.19/0.47 = ( proces988026546_ch2Of @ A @ Process3 ) ) ) ) )
% 0.19/0.47 => ( Process = Process3 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.expand
% 0.19/0.47 thf(fact_148_contOf__def,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( proces1778668539contOf @ A )
% 0.19/0.47 = ( proces1406508781rocess @ A @ ( proces634752977rocess @ A )
% 0.19/0.47 @ ^ [X11: A,X122: proces634752977rocess @ A] : X122
% 0.19/0.47 @ ^ [Uu: proces634752977rocess @ A,Uv: proces634752977rocess @ A] : ( undefined @ ( proces634752977rocess @ A ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % contOf_def
% 0.19/0.47 thf(fact_149_CONT_Oelims,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,X3: A > ( proces554692349s_term @ B @ A ),Xa: proces554692349s_term @ B @ A,Y: proces554692349s_term @ B @ A] :
% 0.19/0.47 ( ( ( proces126235999e_CONT @ A @ B @ X3 @ Xa )
% 0.19/0.47 = Y )
% 0.19/0.47 => ( ! [X4: A] :
% 0.19/0.47 ( ( Xa
% 0.19/0.47 = ( proces1627516585ss_VAR @ A @ B @ X4 ) )
% 0.19/0.47 => ( Y
% 0.19/0.47 != ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 0.19/0.47 @ ^ [Aa: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.19/0.47 @ ^ [P4: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces1778668539contOf @ B @ P4 ) )
% 0.19/0.47 @ ^ [A3: B,T3: proces554692349s_term @ B @ A] : T3
% 0.19/0.47 @ ^ [Aa: proces554692349s_term @ B @ A,Ab2: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.19/0.47 @ ( X3 @ X4 ) ) ) )
% 0.19/0.47 => ( ! [P2: proces634752977rocess @ B] :
% 0.19/0.47 ( ( Xa
% 0.19/0.47 = ( proces1062592052s_PROC @ B @ A @ P2 ) )
% 0.19/0.47 => ( Y
% 0.19/0.47 != ( proces1062592052s_PROC @ B @ A @ ( proces1778668539contOf @ B @ P2 ) ) ) )
% 0.19/0.47 => ( ! [A4: B,T4: proces554692349s_term @ B @ A] :
% 0.19/0.47 ( ( Xa
% 0.19/0.47 = ( proces1454156180ss_ACT @ B @ A @ A4 @ T4 ) )
% 0.19/0.47 => ( Y != T4 ) )
% 0.19/0.47 => ~ ( ? [V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] :
% 0.19/0.47 ( Xa
% 0.19/0.47 = ( proces89589571ess_CH @ B @ A @ V @ Va ) )
% 0.19/0.47 => ( Y
% 0.19/0.47 != ( undefined @ ( proces554692349s_term @ B @ A ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % CONT.elims
% 0.19/0.47 thf(fact_150_CONT_Osimps_I1_J,axiom,
% 0.19/0.47 ! [B: $tType,A: $tType,Sys: A > ( proces554692349s_term @ B @ A ),X6: A] :
% 0.19/0.47 ( ( proces126235999e_CONT @ A @ B @ Sys @ ( proces1627516585ss_VAR @ A @ B @ X6 ) )
% 0.19/0.47 = ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 0.19/0.47 @ ^ [Aa: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.19/0.47 @ ^ [P4: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces1778668539contOf @ B @ P4 ) )
% 0.19/0.47 @ ^ [A3: B,T3: proces554692349s_term @ B @ A] : T3
% 0.19/0.47 @ ^ [Aa: proces554692349s_term @ B @ A,Ab2: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.19/0.47 @ ( Sys @ X6 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % CONT.simps(1)
% 0.19/0.47 thf(fact_151_CONT_Opelims,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,X3: A > ( proces554692349s_term @ B @ A ),Xa: proces554692349s_term @ B @ A,Y: proces554692349s_term @ B @ A] :
% 0.19/0.47 ( ( ( proces126235999e_CONT @ A @ B @ X3 @ Xa )
% 0.19/0.47 = Y )
% 0.19/0.47 => ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1004198490NT_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X3 @ Xa ) )
% 0.19/0.47 => ( ! [X4: A] :
% 0.19/0.47 ( ( Xa
% 0.19/0.47 = ( proces1627516585ss_VAR @ A @ B @ X4 ) )
% 0.19/0.47 => ( ( Y
% 0.19/0.47 = ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 0.19/0.47 @ ^ [Aa: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.19/0.47 @ ^ [P4: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces1778668539contOf @ B @ P4 ) )
% 0.19/0.47 @ ^ [A3: B,T3: proces554692349s_term @ B @ A] : T3
% 0.19/0.47 @ ^ [Aa: proces554692349s_term @ B @ A,Ab2: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.19/0.47 @ ( X3 @ X4 ) ) )
% 0.19/0.47 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1004198490NT_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X3 @ ( proces1627516585ss_VAR @ A @ B @ X4 ) ) ) ) )
% 0.19/0.47 => ( ! [P2: proces634752977rocess @ B] :
% 0.19/0.47 ( ( Xa
% 0.19/0.47 = ( proces1062592052s_PROC @ B @ A @ P2 ) )
% 0.19/0.47 => ( ( Y
% 0.19/0.47 = ( proces1062592052s_PROC @ B @ A @ ( proces1778668539contOf @ B @ P2 ) ) )
% 0.19/0.47 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1004198490NT_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X3 @ ( proces1062592052s_PROC @ B @ A @ P2 ) ) ) ) )
% 0.19/0.47 => ( ! [A4: B,T4: proces554692349s_term @ B @ A] :
% 0.19/0.47 ( ( Xa
% 0.19/0.47 = ( proces1454156180ss_ACT @ B @ A @ A4 @ T4 ) )
% 0.19/0.47 => ( ( Y = T4 )
% 0.19/0.47 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1004198490NT_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X3 @ ( proces1454156180ss_ACT @ B @ A @ A4 @ T4 ) ) ) ) )
% 0.19/0.47 => ~ ! [V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] :
% 0.19/0.47 ( ( Xa
% 0.19/0.47 = ( proces89589571ess_CH @ B @ A @ V @ Va ) )
% 0.19/0.47 => ( ( Y
% 0.19/0.47 = ( undefined @ ( proces554692349s_term @ B @ A ) ) )
% 0.19/0.47 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1004198490NT_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X3 @ ( proces89589571ess_CH @ B @ A @ V @ Va ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % CONT.pelims
% 0.19/0.47 thf(fact_152_CONT_Osimps_I3_J,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),A2: B,T2: proces554692349s_term @ B @ A] :
% 0.19/0.47 ( ( proces126235999e_CONT @ A @ B @ Sys @ ( proces1454156180ss_ACT @ B @ A @ A2 @ T2 ) )
% 0.19/0.47 = T2 ) ).
% 0.19/0.47
% 0.19/0.47 % CONT.simps(3)
% 0.19/0.47 thf(fact_153_CONT_Osimps_I2_J,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),P: proces634752977rocess @ B] :
% 0.19/0.47 ( ( proces126235999e_CONT @ A @ B @ Sys @ ( proces1062592052s_PROC @ B @ A @ P ) )
% 0.19/0.47 = ( proces1062592052s_PROC @ B @ A @ ( proces1778668539contOf @ B @ P ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % CONT.simps(2)
% 0.19/0.47 thf(fact_154_solution_Osimps_I4_J,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 0.19/0.47 ( ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
% 0.19/0.47 => ( ( proces1778668539contOf @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) )
% 0.19/0.47 = ( proces1652378886lution @ A @ B @ Sys @ ( proces126235999e_CONT @ A @ B @ Sys @ T2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % solution.simps(4)
% 0.19/0.47 thf(fact_155_process_Orel__coinduct,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,P3: ( proces634752977rocess @ A ) > ( proces634752977rocess @ B ) > $o,X3: proces634752977rocess @ A,Y: proces634752977rocess @ B,R: A > B > $o] :
% 0.19/0.47 ( ( P3 @ X3 @ Y )
% 0.19/0.47 => ( ! [Process4: proces634752977rocess @ A,Process5: proces634752977rocess @ B] :
% 0.19/0.47 ( ( P3 @ Process4 @ Process5 )
% 0.19/0.47 => ( ( ( proces10484146Action @ A @ Process4 )
% 0.19/0.47 = ( proces10484146Action @ B @ Process5 ) )
% 0.19/0.47 & ( ( proces10484146Action @ A @ Process4 )
% 0.19/0.47 => ( ( proces10484146Action @ B @ Process5 )
% 0.19/0.47 => ( ( R @ ( proces745025900prefOf @ A @ Process4 ) @ ( proces745025900prefOf @ B @ Process5 ) )
% 0.19/0.47 & ( P3 @ ( proces1778668539contOf @ A @ Process4 ) @ ( proces1778668539contOf @ B @ Process5 ) ) ) ) )
% 0.19/0.47 & ( ( proces401113213Choice @ A @ Process4 )
% 0.19/0.47 => ( ( proces401113213Choice @ B @ Process5 )
% 0.19/0.47 => ( ( P3 @ ( proces979765041_ch1Of @ A @ Process4 ) @ ( proces979765041_ch1Of @ B @ Process5 ) )
% 0.19/0.47 & ( P3 @ ( proces988026546_ch2Of @ A @ Process4 ) @ ( proces988026546_ch2Of @ B @ Process5 ) ) ) ) ) ) )
% 0.19/0.47 => ( proces749077512rocess @ A @ B @ R @ X3 @ Y ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.rel_coinduct
% 0.19/0.47 thf(fact_156_process_Orel__sel,axiom,
% 0.19/0.47 ! [B: $tType,A: $tType] :
% 0.19/0.47 ( ( proces749077512rocess @ A @ B )
% 0.19/0.47 = ( ^ [R4: A > B > $o,A3: proces634752977rocess @ A,B5: proces634752977rocess @ B] :
% 0.19/0.47 ( ( ( proces10484146Action @ A @ A3 )
% 0.19/0.47 = ( proces10484146Action @ B @ B5 ) )
% 0.19/0.47 & ( ( proces10484146Action @ A @ A3 )
% 0.19/0.47 => ( ( proces10484146Action @ B @ B5 )
% 0.19/0.47 => ( ( R4 @ ( proces745025900prefOf @ A @ A3 ) @ ( proces745025900prefOf @ B @ B5 ) )
% 0.19/0.47 & ( proces749077512rocess @ A @ B @ R4 @ ( proces1778668539contOf @ A @ A3 ) @ ( proces1778668539contOf @ B @ B5 ) ) ) ) )
% 0.19/0.47 & ( ( proces401113213Choice @ A @ A3 )
% 0.19/0.47 => ( ( proces401113213Choice @ B @ B5 )
% 0.19/0.47 => ( ( proces749077512rocess @ A @ B @ R4 @ ( proces979765041_ch1Of @ A @ A3 ) @ ( proces979765041_ch1Of @ B @ B5 ) )
% 0.19/0.47 & ( proces749077512rocess @ A @ B @ R4 @ ( proces988026546_ch2Of @ A @ A3 ) @ ( proces988026546_ch2Of @ B @ B5 ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.rel_sel
% 0.19/0.47 thf(fact_157_solution_Octr_I1_J,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 0.19/0.47 ( ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
% 0.19/0.47 => ( ( proces1652378886lution @ A @ B @ Sys @ T2 )
% 0.19/0.47 = ( proces1525233512Action @ B @ ( proces1708129104e_PREF @ A @ B @ A @ Sys @ T2 ) @ ( proces1652378886lution @ A @ B @ Sys @ ( proces126235999e_CONT @ A @ B @ Sys @ T2 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % solution.ctr(1)
% 0.19/0.47 thf(fact_158_process_Oinject_I1_J,axiom,
% 0.19/0.47 ! [A: $tType,X112: A,X123: proces634752977rocess @ A,Y11: A,Y12: proces634752977rocess @ A] :
% 0.19/0.47 ( ( ( proces1525233512Action @ A @ X112 @ X123 )
% 0.19/0.47 = ( proces1525233512Action @ A @ Y11 @ Y12 ) )
% 0.19/0.47 = ( ( X112 = Y11 )
% 0.19/0.47 & ( X123 = Y12 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.inject(1)
% 0.19/0.47 thf(fact_159_process_Orel__inject_I1_J,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,R: A > B > $o,X112: A,X123: proces634752977rocess @ A,Y11: B,Y12: proces634752977rocess @ B] :
% 0.19/0.47 ( ( proces749077512rocess @ A @ B @ R @ ( proces1525233512Action @ A @ X112 @ X123 ) @ ( proces1525233512Action @ B @ Y11 @ Y12 ) )
% 0.19/0.47 = ( ( R @ X112 @ Y11 )
% 0.19/0.47 & ( proces749077512rocess @ A @ B @ R @ X123 @ Y12 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.rel_inject(1)
% 0.19/0.47 thf(fact_160_process_Ocollapse_I1_J,axiom,
% 0.19/0.47 ! [A: $tType,Process: proces634752977rocess @ A] :
% 0.19/0.47 ( ( proces10484146Action @ A @ Process )
% 0.19/0.47 => ( ( proces1525233512Action @ A @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) )
% 0.19/0.47 = Process ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.collapse(1)
% 0.19/0.47 thf(fact_161_isAction__def,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( proces10484146Action @ A )
% 0.19/0.47 = ( ^ [Process2: proces634752977rocess @ A] :
% 0.19/0.47 ? [X11: A,X122: proces634752977rocess @ A] :
% 0.19/0.47 ( Process2
% 0.19/0.47 = ( proces1525233512Action @ A @ X11 @ X122 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % isAction_def
% 0.19/0.47 thf(fact_162_process_OdiscI_I1_J,axiom,
% 0.19/0.47 ! [A: $tType,Process: proces634752977rocess @ A,X112: A,X123: proces634752977rocess @ A] :
% 0.19/0.47 ( ( Process
% 0.19/0.47 = ( proces1525233512Action @ A @ X112 @ X123 ) )
% 0.19/0.47 => ( proces10484146Action @ A @ Process ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.discI(1)
% 0.19/0.47 thf(fact_163_process_Odisc_I1_J,axiom,
% 0.19/0.47 ! [A: $tType,X112: A,X123: proces634752977rocess @ A] : ( proces10484146Action @ A @ ( proces1525233512Action @ A @ X112 @ X123 ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.disc(1)
% 0.19/0.47 thf(fact_164_process_Orel__intros_I1_J,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,R: A > B > $o,X112: A,Y11: B,X123: proces634752977rocess @ A,Y12: proces634752977rocess @ B] :
% 0.19/0.47 ( ( R @ X112 @ Y11 )
% 0.19/0.47 => ( ( proces749077512rocess @ A @ B @ R @ X123 @ Y12 )
% 0.19/0.47 => ( proces749077512rocess @ A @ B @ R @ ( proces1525233512Action @ A @ X112 @ X123 ) @ ( proces1525233512Action @ B @ Y11 @ Y12 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.rel_intros(1)
% 0.19/0.47 thf(fact_165_process_Orel__eq,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( proces749077512rocess @ A @ A
% 0.19/0.47 @ ^ [Y8: A,Z3: A] : ( Y8 = Z3 ) )
% 0.19/0.47 = ( ^ [Y8: proces634752977rocess @ A,Z3: proces634752977rocess @ A] : ( Y8 = Z3 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.rel_eq
% 0.19/0.47 thf(fact_166_process_Orel__refl,axiom,
% 0.19/0.47 ! [B: $tType,Ra: B > B > $o,X3: proces634752977rocess @ B] :
% 0.19/0.47 ( ! [X5: B] : ( Ra @ X5 @ X5 )
% 0.19/0.47 => ( proces749077512rocess @ B @ B @ Ra @ X3 @ X3 ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.rel_refl
% 0.19/0.47 thf(fact_167_process_Osimps_I5_J,axiom,
% 0.19/0.47 ! [B: $tType,A: $tType,F1: A > ( proces634752977rocess @ A ) > B,F2: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B,X112: A,X123: proces634752977rocess @ A] :
% 0.19/0.47 ( ( proces1406508781rocess @ A @ B @ F1 @ F2 @ ( proces1525233512Action @ A @ X112 @ X123 ) )
% 0.19/0.47 = ( F1 @ X112 @ X123 ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.simps(5)
% 0.19/0.47 thf(fact_168_process_Osel_I1_J,axiom,
% 0.19/0.47 ! [A: $tType,X112: A,X123: proces634752977rocess @ A] :
% 0.19/0.47 ( ( proces745025900prefOf @ A @ ( proces1525233512Action @ A @ X112 @ X123 ) )
% 0.19/0.47 = X112 ) ).
% 0.19/0.47
% 0.19/0.47 % process.sel(1)
% 0.19/0.47 thf(fact_169_process_Odisc_I3_J,axiom,
% 0.19/0.47 ! [A: $tType,X112: A,X123: proces634752977rocess @ A] :
% 0.19/0.47 ~ ( proces401113213Choice @ A @ ( proces1525233512Action @ A @ X112 @ X123 ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.disc(3)
% 0.19/0.47 thf(fact_170_process_Osel_I2_J,axiom,
% 0.19/0.47 ! [A: $tType,X112: A,X123: proces634752977rocess @ A] :
% 0.19/0.47 ( ( proces1778668539contOf @ A @ ( proces1525233512Action @ A @ X112 @ X123 ) )
% 0.19/0.47 = X123 ) ).
% 0.19/0.47
% 0.19/0.47 % process.sel(2)
% 0.19/0.47 thf(fact_171_solution_Ocode,axiom,
% 0.19/0.47 ! [B: $tType,A: $tType] :
% 0.19/0.47 ( ( proces1652378886lution @ A @ B )
% 0.19/0.47 = ( ^ [Sys3: A > ( proces554692349s_term @ B @ A ),T3: proces554692349s_term @ B @ A] : ( if @ ( proces634752977rocess @ B ) @ ( proces687458811_isACT @ A @ B @ A @ B @ Sys3 @ T3 ) @ ( proces1525233512Action @ B @ ( proces1708129104e_PREF @ A @ B @ A @ Sys3 @ T3 ) @ ( proces1652378886lution @ A @ B @ Sys3 @ ( proces126235999e_CONT @ A @ B @ Sys3 @ T3 ) ) ) @ ( proces1915862579Choice @ B @ ( proces1652378886lution @ A @ B @ Sys3 @ ( proces1239275103le_CH1 @ A @ B @ Sys3 @ T3 ) ) @ ( proces1652378886lution @ A @ B @ Sys3 @ ( proces1239275104le_CH2 @ A @ B @ Sys3 @ T3 ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % solution.code
% 0.19/0.47 thf(fact_172_process_Osplit__sel__asm,axiom,
% 0.19/0.47 ! [B: $tType,A: $tType,P3: B > $o,F1: A > ( proces634752977rocess @ A ) > B,F2: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B,Process: proces634752977rocess @ A] :
% 0.19/0.47 ( ( P3 @ ( proces1406508781rocess @ A @ B @ F1 @ F2 @ Process ) )
% 0.19/0.47 = ( ~ ( ( ( Process
% 0.19/0.47 = ( proces1525233512Action @ A @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) ) )
% 0.19/0.47 & ~ ( P3 @ ( F1 @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) ) ) )
% 0.19/0.47 | ( ( Process
% 0.19/0.47 = ( proces1915862579Choice @ A @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) ) )
% 0.19/0.47 & ~ ( P3 @ ( F2 @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.split_sel_asm
% 0.19/0.47 thf(fact_173_process_Osplit__sel,axiom,
% 0.19/0.47 ! [B: $tType,A: $tType,P3: B > $o,F1: A > ( proces634752977rocess @ A ) > B,F2: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B,Process: proces634752977rocess @ A] :
% 0.19/0.47 ( ( P3 @ ( proces1406508781rocess @ A @ B @ F1 @ F2 @ Process ) )
% 0.19/0.47 = ( ( ( Process
% 0.19/0.47 = ( proces1525233512Action @ A @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) ) )
% 0.19/0.47 => ( P3 @ ( F1 @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) ) ) )
% 0.19/0.47 & ( ( Process
% 0.19/0.47 = ( proces1915862579Choice @ A @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) ) )
% 0.19/0.47 => ( P3 @ ( F2 @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.split_sel
% 0.19/0.47 thf(fact_174_process_Oinject_I2_J,axiom,
% 0.19/0.47 ! [A: $tType,X212: proces634752977rocess @ A,X223: proces634752977rocess @ A,Y21: proces634752977rocess @ A,Y22: proces634752977rocess @ A] :
% 0.19/0.47 ( ( ( proces1915862579Choice @ A @ X212 @ X223 )
% 0.19/0.47 = ( proces1915862579Choice @ A @ Y21 @ Y22 ) )
% 0.19/0.47 = ( ( X212 = Y21 )
% 0.19/0.47 & ( X223 = Y22 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.inject(2)
% 0.19/0.47 thf(fact_175_process_Orel__inject_I2_J,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,R: A > B > $o,X212: proces634752977rocess @ A,X223: proces634752977rocess @ A,Y21: proces634752977rocess @ B,Y22: proces634752977rocess @ B] :
% 0.19/0.47 ( ( proces749077512rocess @ A @ B @ R @ ( proces1915862579Choice @ A @ X212 @ X223 ) @ ( proces1915862579Choice @ B @ Y21 @ Y22 ) )
% 0.19/0.47 = ( ( proces749077512rocess @ A @ B @ R @ X212 @ Y21 )
% 0.19/0.47 & ( proces749077512rocess @ A @ B @ R @ X223 @ Y22 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.rel_inject(2)
% 0.19/0.47 thf(fact_176_process_Ocollapse_I2_J,axiom,
% 0.19/0.47 ! [A: $tType,Process: proces634752977rocess @ A] :
% 0.19/0.47 ( ( proces401113213Choice @ A @ Process )
% 0.19/0.47 => ( ( proces1915862579Choice @ A @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) )
% 0.19/0.47 = Process ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.collapse(2)
% 0.19/0.47 thf(fact_177_process_Odistinct_I1_J,axiom,
% 0.19/0.47 ! [A: $tType,X112: A,X123: proces634752977rocess @ A,X212: proces634752977rocess @ A,X223: proces634752977rocess @ A] :
% 0.19/0.47 ( ( proces1525233512Action @ A @ X112 @ X123 )
% 0.19/0.47 != ( proces1915862579Choice @ A @ X212 @ X223 ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.distinct(1)
% 0.19/0.47 thf(fact_178_process_Orel__intros_I2_J,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,R: A > B > $o,X212: proces634752977rocess @ A,Y21: proces634752977rocess @ B,X223: proces634752977rocess @ A,Y22: proces634752977rocess @ B] :
% 0.19/0.47 ( ( proces749077512rocess @ A @ B @ R @ X212 @ Y21 )
% 0.19/0.47 => ( ( proces749077512rocess @ A @ B @ R @ X223 @ Y22 )
% 0.19/0.47 => ( proces749077512rocess @ A @ B @ R @ ( proces1915862579Choice @ A @ X212 @ X223 ) @ ( proces1915862579Choice @ B @ Y21 @ Y22 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.rel_intros(2)
% 0.19/0.47 thf(fact_179_process_Oexhaust,axiom,
% 0.19/0.47 ! [A: $tType,Y: proces634752977rocess @ A] :
% 0.19/0.47 ( ! [X113: A,X124: proces634752977rocess @ A] :
% 0.19/0.47 ( Y
% 0.19/0.47 != ( proces1525233512Action @ A @ X113 @ X124 ) )
% 0.19/0.47 => ~ ! [X213: proces634752977rocess @ A,X224: proces634752977rocess @ A] :
% 0.19/0.47 ( Y
% 0.19/0.47 != ( proces1915862579Choice @ A @ X213 @ X224 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.exhaust
% 0.19/0.47 thf(fact_180_process_Odisc_I4_J,axiom,
% 0.19/0.47 ! [A: $tType,X212: proces634752977rocess @ A,X223: proces634752977rocess @ A] : ( proces401113213Choice @ A @ ( proces1915862579Choice @ A @ X212 @ X223 ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.disc(4)
% 0.19/0.47 thf(fact_181_process_OdiscI_I2_J,axiom,
% 0.19/0.47 ! [A: $tType,Process: proces634752977rocess @ A,X212: proces634752977rocess @ A,X223: proces634752977rocess @ A] :
% 0.19/0.47 ( ( Process
% 0.19/0.47 = ( proces1915862579Choice @ A @ X212 @ X223 ) )
% 0.19/0.47 => ( proces401113213Choice @ A @ Process ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.discI(2)
% 0.19/0.47 thf(fact_182_isChoice__def,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( proces401113213Choice @ A )
% 0.19/0.47 = ( ^ [Process2: proces634752977rocess @ A] :
% 0.19/0.47 ? [X21: proces634752977rocess @ A,X222: proces634752977rocess @ A] :
% 0.19/0.47 ( Process2
% 0.19/0.47 = ( proces1915862579Choice @ A @ X21 @ X222 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % isChoice_def
% 0.19/0.47 thf(fact_183_process_Osel_I4_J,axiom,
% 0.19/0.47 ! [A: $tType,X212: proces634752977rocess @ A,X223: proces634752977rocess @ A] :
% 0.19/0.47 ( ( proces988026546_ch2Of @ A @ ( proces1915862579Choice @ A @ X212 @ X223 ) )
% 0.19/0.47 = X223 ) ).
% 0.19/0.47
% 0.19/0.47 % process.sel(4)
% 0.19/0.47 thf(fact_184_process_Osel_I3_J,axiom,
% 0.19/0.47 ! [A: $tType,X212: proces634752977rocess @ A,X223: proces634752977rocess @ A] :
% 0.19/0.47 ( ( proces979765041_ch1Of @ A @ ( proces1915862579Choice @ A @ X212 @ X223 ) )
% 0.19/0.47 = X212 ) ).
% 0.19/0.47
% 0.19/0.47 % process.sel(3)
% 0.19/0.47 thf(fact_185_process_Osimps_I6_J,axiom,
% 0.19/0.47 ! [B: $tType,A: $tType,F1: A > ( proces634752977rocess @ A ) > B,F2: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B,X212: proces634752977rocess @ A,X223: proces634752977rocess @ A] :
% 0.19/0.47 ( ( proces1406508781rocess @ A @ B @ F1 @ F2 @ ( proces1915862579Choice @ A @ X212 @ X223 ) )
% 0.19/0.47 = ( F2 @ X212 @ X223 ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.simps(6)
% 0.19/0.47 thf(fact_186_process_Odisc_I2_J,axiom,
% 0.19/0.47 ! [A: $tType,X212: proces634752977rocess @ A,X223: proces634752977rocess @ A] :
% 0.19/0.47 ~ ( proces10484146Action @ A @ ( proces1915862579Choice @ A @ X212 @ X223 ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.disc(2)
% 0.19/0.47 thf(fact_187_process_Orel__cases,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,R: A > B > $o,A2: proces634752977rocess @ A,B2: proces634752977rocess @ B] :
% 0.19/0.47 ( ( proces749077512rocess @ A @ B @ R @ A2 @ B2 )
% 0.19/0.47 => ( ! [X12: A,X23: proces634752977rocess @ A] :
% 0.19/0.47 ( ( A2
% 0.19/0.47 = ( proces1525233512Action @ A @ X12 @ X23 ) )
% 0.19/0.47 => ! [Y13: B,Y23: proces634752977rocess @ B] :
% 0.19/0.47 ( ( B2
% 0.19/0.47 = ( proces1525233512Action @ B @ Y13 @ Y23 ) )
% 0.19/0.47 => ( ( R @ X12 @ Y13 )
% 0.19/0.47 => ~ ( proces749077512rocess @ A @ B @ R @ X23 @ Y23 ) ) ) )
% 0.19/0.47 => ~ ! [X1a: proces634752977rocess @ A,X2a: proces634752977rocess @ A] :
% 0.19/0.47 ( ( A2
% 0.19/0.47 = ( proces1915862579Choice @ A @ X1a @ X2a ) )
% 0.19/0.47 => ! [Y1a: proces634752977rocess @ B,Y2a: proces634752977rocess @ B] :
% 0.19/0.47 ( ( B2
% 0.19/0.47 = ( proces1915862579Choice @ B @ Y1a @ Y2a ) )
% 0.19/0.47 => ( ( proces749077512rocess @ A @ B @ R @ X1a @ Y1a )
% 0.19/0.47 => ~ ( proces749077512rocess @ A @ B @ R @ X2a @ Y2a ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.rel_cases
% 0.19/0.47 thf(fact_188_process_Orel__distinct_I1_J,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,R: A > B > $o,X112: A,X123: proces634752977rocess @ A,Y21: proces634752977rocess @ B,Y22: proces634752977rocess @ B] :
% 0.19/0.47 ~ ( proces749077512rocess @ A @ B @ R @ ( proces1525233512Action @ A @ X112 @ X123 ) @ ( proces1915862579Choice @ B @ Y21 @ Y22 ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.rel_distinct(1)
% 0.19/0.47 thf(fact_189_process_Orel__distinct_I2_J,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,R: A > B > $o,Y21: proces634752977rocess @ A,Y22: proces634752977rocess @ A,X112: B,X123: proces634752977rocess @ B] :
% 0.19/0.47 ~ ( proces749077512rocess @ A @ B @ R @ ( proces1915862579Choice @ A @ Y21 @ Y22 ) @ ( proces1525233512Action @ B @ X112 @ X123 ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.rel_distinct(2)
% 0.19/0.47 thf(fact_190_process__coind,axiom,
% 0.19/0.47 ! [A: $tType,Phi: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > $o,P: proces634752977rocess @ A,P5: proces634752977rocess @ A] :
% 0.19/0.47 ( ( Phi @ P @ P5 )
% 0.19/0.47 => ( ! [P2: proces634752977rocess @ A,P6: proces634752977rocess @ A] :
% 0.19/0.47 ( ( Phi @ P2 @ P6 )
% 0.19/0.47 => ( ( ( proces10484146Action @ A @ P2 )
% 0.19/0.47 = ( proces10484146Action @ A @ P6 ) )
% 0.19/0.47 & ( ( proces401113213Choice @ A @ P2 )
% 0.19/0.47 = ( proces401113213Choice @ A @ P6 ) ) ) )
% 0.19/0.47 => ( ! [A4: A,A7: A,P2: proces634752977rocess @ A,P6: proces634752977rocess @ A] :
% 0.19/0.47 ( ( Phi @ ( proces1525233512Action @ A @ A4 @ P2 ) @ ( proces1525233512Action @ A @ A7 @ P6 ) )
% 0.19/0.47 => ( ( A4 = A7 )
% 0.19/0.47 & ( Phi @ P2 @ P6 ) ) )
% 0.19/0.47 => ( ! [P2: proces634752977rocess @ A,Q2: proces634752977rocess @ A,P6: proces634752977rocess @ A,Q3: proces634752977rocess @ A] :
% 0.19/0.47 ( ( Phi @ ( proces1915862579Choice @ A @ P2 @ Q2 ) @ ( proces1915862579Choice @ A @ P6 @ Q3 ) )
% 0.19/0.47 => ( ( Phi @ P2 @ P6 )
% 0.19/0.47 & ( Phi @ Q2 @ Q3 ) ) )
% 0.19/0.47 => ( P = P5 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process_coind
% 0.19/0.47 thf(fact_191_process__strong__coind,axiom,
% 0.19/0.47 ! [A: $tType,Phi: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > $o,P: proces634752977rocess @ A,P5: proces634752977rocess @ A] :
% 0.19/0.47 ( ( Phi @ P @ P5 )
% 0.19/0.47 => ( ! [P2: proces634752977rocess @ A,P6: proces634752977rocess @ A] :
% 0.19/0.47 ( ( Phi @ P2 @ P6 )
% 0.19/0.47 => ( ( ( proces10484146Action @ A @ P2 )
% 0.19/0.47 = ( proces10484146Action @ A @ P6 ) )
% 0.19/0.47 & ( ( proces401113213Choice @ A @ P2 )
% 0.19/0.47 = ( proces401113213Choice @ A @ P6 ) ) ) )
% 0.19/0.47 => ( ! [A4: A,A7: A,P2: proces634752977rocess @ A,P6: proces634752977rocess @ A] :
% 0.19/0.47 ( ( Phi @ ( proces1525233512Action @ A @ A4 @ P2 ) @ ( proces1525233512Action @ A @ A7 @ P6 ) )
% 0.19/0.47 => ( ( A4 = A7 )
% 0.19/0.47 & ( ( Phi @ P2 @ P6 )
% 0.19/0.47 | ( P2 = P6 ) ) ) )
% 0.19/0.47 => ( ! [P2: proces634752977rocess @ A,Q2: proces634752977rocess @ A,P6: proces634752977rocess @ A,Q3: proces634752977rocess @ A] :
% 0.19/0.47 ( ( Phi @ ( proces1915862579Choice @ A @ P2 @ Q2 ) @ ( proces1915862579Choice @ A @ P6 @ Q3 ) )
% 0.19/0.47 => ( ( ( Phi @ P2 @ P6 )
% 0.19/0.47 | ( P2 = P6 ) )
% 0.19/0.47 & ( ( Phi @ Q2 @ Q3 )
% 0.19/0.47 | ( Q2 = Q3 ) ) ) )
% 0.19/0.47 => ( P = P5 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process_strong_coind
% 0.19/0.47 thf(fact_192_solution_Octr_I2_J,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 0.19/0.47 ( ~ ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
% 0.19/0.47 => ( ( proces1652378886lution @ A @ B @ Sys @ T2 )
% 0.19/0.47 = ( proces1915862579Choice @ B @ ( proces1652378886lution @ A @ B @ Sys @ ( proces1239275103le_CH1 @ A @ B @ Sys @ T2 ) ) @ ( proces1652378886lution @ A @ B @ Sys @ ( proces1239275104le_CH2 @ A @ B @ Sys @ T2 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % solution.ctr(2)
% 0.19/0.47 thf(fact_193_process_Oexhaust__sel,axiom,
% 0.19/0.47 ! [A: $tType,Process: proces634752977rocess @ A] :
% 0.19/0.47 ( ( Process
% 0.19/0.47 != ( proces1525233512Action @ A @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) ) )
% 0.19/0.47 => ( Process
% 0.19/0.47 = ( proces1915862579Choice @ A @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.exhaust_sel
% 0.19/0.47 thf(fact_194_adm__lemma,axiom,
% 0.19/0.47 ! [B: $tType,A: $tType,R: set @ ( product_prod @ A @ A ),F8: ( A > B ) > A > B] :
% 0.19/0.47 ( adm_wf @ A @ B @ R
% 0.19/0.47 @ ^ [F7: A > B,X: A] : ( F8 @ ( cut @ A @ B @ F7 @ R @ X ) @ X ) ) ).
% 0.19/0.47
% 0.19/0.47 % adm_lemma
% 0.19/0.47 thf(fact_195_process__term_Orel__induct,axiom,
% 0.19/0.47 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X3: proces554692349s_term @ A @ Pvar,Y: proces554692349s_term @ B @ C,Q: ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ B @ C ) > $o] :
% 0.19/0.47 ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X3 @ Y )
% 0.19/0.47 => ( ! [A12: Pvar,B1: C] :
% 0.19/0.47 ( ( R22 @ A12 @ B1 )
% 0.19/0.47 => ( Q @ ( proces1627516585ss_VAR @ Pvar @ A @ A12 ) @ ( proces1627516585ss_VAR @ C @ B @ B1 ) ) )
% 0.19/0.47 => ( ! [A22: proces634752977rocess @ A,B22: proces634752977rocess @ B] :
% 0.19/0.47 ( ( proces749077512rocess @ A @ B @ R1 @ A22 @ B22 )
% 0.19/0.47 => ( Q @ ( proces1062592052s_PROC @ A @ Pvar @ A22 ) @ ( proces1062592052s_PROC @ B @ C @ B22 ) ) )
% 0.19/0.47 => ( ! [A31: A,A32: proces554692349s_term @ A @ Pvar,B31: B,B32: proces554692349s_term @ B @ C] :
% 0.19/0.47 ( ( R1 @ A31 @ B31 )
% 0.19/0.47 => ( ( Q @ A32 @ B32 )
% 0.19/0.47 => ( Q @ ( proces1454156180ss_ACT @ A @ Pvar @ A31 @ A32 ) @ ( proces1454156180ss_ACT @ B @ C @ B31 @ B32 ) ) ) )
% 0.19/0.47 => ( ! [A41: proces554692349s_term @ A @ Pvar,A42: proces554692349s_term @ A @ Pvar,B41: proces554692349s_term @ B @ C,B42: proces554692349s_term @ B @ C] :
% 0.19/0.47 ( ( Q @ A41 @ B41 )
% 0.19/0.47 => ( ( Q @ A42 @ B42 )
% 0.19/0.47 => ( Q @ ( proces89589571ess_CH @ A @ Pvar @ A41 @ A42 ) @ ( proces89589571ess_CH @ B @ C @ B41 @ B42 ) ) ) )
% 0.19/0.47 => ( Q @ X3 @ Y ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process_term.rel_induct
% 0.19/0.47 thf(fact_196_process__term_Orel__cases,axiom,
% 0.19/0.47 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,A2: proces554692349s_term @ A @ Pvar,B2: proces554692349s_term @ B @ C] :
% 0.19/0.47 ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ A2 @ B2 )
% 0.19/0.47 => ( ! [X5: Pvar] :
% 0.19/0.47 ( ( A2
% 0.19/0.47 = ( proces1627516585ss_VAR @ Pvar @ A @ X5 ) )
% 0.19/0.47 => ! [Y5: C] :
% 0.19/0.47 ( ( B2
% 0.19/0.47 = ( proces1627516585ss_VAR @ C @ B @ Y5 ) )
% 0.19/0.47 => ~ ( R22 @ X5 @ Y5 ) ) )
% 0.19/0.47 => ( ! [Xa2: proces634752977rocess @ A] :
% 0.19/0.47 ( ( A2
% 0.19/0.47 = ( proces1062592052s_PROC @ A @ Pvar @ Xa2 ) )
% 0.19/0.47 => ! [Ya: proces634752977rocess @ B] :
% 0.19/0.47 ( ( B2
% 0.19/0.47 = ( proces1062592052s_PROC @ B @ C @ Ya ) )
% 0.19/0.47 => ~ ( proces749077512rocess @ A @ B @ R1 @ Xa2 @ Ya ) ) )
% 0.19/0.47 => ( ! [X1a: A,X2a: proces554692349s_term @ A @ Pvar] :
% 0.19/0.47 ( ( A2
% 0.19/0.47 = ( proces1454156180ss_ACT @ A @ Pvar @ X1a @ X2a ) )
% 0.19/0.47 => ! [Y1a: B,Y2a: proces554692349s_term @ B @ C] :
% 0.19/0.47 ( ( B2
% 0.19/0.47 = ( proces1454156180ss_ACT @ B @ C @ Y1a @ Y2a ) )
% 0.19/0.47 => ( ( R1 @ X1a @ Y1a )
% 0.19/0.47 => ~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X2a @ Y2a ) ) ) )
% 0.19/0.47 => ~ ! [X1b: proces554692349s_term @ A @ Pvar,X2b: proces554692349s_term @ A @ Pvar] :
% 0.19/0.47 ( ( A2
% 0.19/0.47 = ( proces89589571ess_CH @ A @ Pvar @ X1b @ X2b ) )
% 0.19/0.47 => ! [Y1b: proces554692349s_term @ B @ C,Y2b: proces554692349s_term @ B @ C] :
% 0.19/0.47 ( ( B2
% 0.19/0.47 = ( proces89589571ess_CH @ B @ C @ Y1b @ Y2b ) )
% 0.19/0.47 => ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X1b @ Y1b )
% 0.19/0.47 => ~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X2b @ Y2b ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process_term.rel_cases
% 0.19/0.47 thf(fact_197_process__term_Orel__intros_I2_J,axiom,
% 0.19/0.47 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,X2: proces634752977rocess @ A,Y2: proces634752977rocess @ B,R22: Pvar > C > $o] :
% 0.19/0.47 ( ( proces749077512rocess @ A @ B @ R1 @ X2 @ Y2 )
% 0.19/0.47 => ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1062592052s_PROC @ A @ Pvar @ X2 ) @ ( proces1062592052s_PROC @ B @ C @ Y2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process_term.rel_intros(2)
% 0.19/0.47 thf(fact_198_process__term_Orel__inject_I2_J,axiom,
% 0.19/0.47 ! [C: $tType,Pvar: $tType,A: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X2: proces634752977rocess @ A,Y2: proces634752977rocess @ B] :
% 0.19/0.47 ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1062592052s_PROC @ A @ Pvar @ X2 ) @ ( proces1062592052s_PROC @ B @ C @ Y2 ) )
% 0.19/0.47 = ( proces749077512rocess @ A @ B @ R1 @ X2 @ Y2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % process_term.rel_inject(2)
% 0.19/0.47 thf(fact_199_process__term_Orel__distinct_I2_J,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,C: $tType,D: $tType,R1: A > C > $o,R22: B > D > $o,Y2: proces634752977rocess @ A,X13: D] :
% 0.19/0.47 ~ ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R22 @ ( proces1062592052s_PROC @ A @ B @ Y2 ) @ ( proces1627516585ss_VAR @ D @ C @ X13 ) ) ).
% 0.19/0.47
% 0.19/0.47 % process_term.rel_distinct(2)
% 0.19/0.47 thf(fact_200_process__term_Orel__distinct_I1_J,axiom,
% 0.19/0.47 ! [Pvar: $tType,A: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X13: Pvar,Y2: proces634752977rocess @ B] :
% 0.19/0.47 ~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1627516585ss_VAR @ Pvar @ A @ X13 ) @ ( proces1062592052s_PROC @ B @ C @ Y2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % process_term.rel_distinct(1)
% 0.19/0.47 thf(fact_201_process__term_Orel__distinct_I10_J,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,D: $tType,C: $tType,R1: A > C > $o,R22: B > D > $o,Y41: proces554692349s_term @ A @ B,Y42: proces554692349s_term @ A @ B,X2: proces634752977rocess @ C] :
% 0.19/0.47 ~ ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R22 @ ( proces89589571ess_CH @ A @ B @ Y41 @ Y42 ) @ ( proces1062592052s_PROC @ C @ D @ X2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % process_term.rel_distinct(10)
% 0.19/0.47 thf(fact_202_process__term_Orel__distinct_I9_J,axiom,
% 0.19/0.47 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X2: proces634752977rocess @ A,Y41: proces554692349s_term @ B @ C,Y42: proces554692349s_term @ B @ C] :
% 0.19/0.47 ~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1062592052s_PROC @ A @ Pvar @ X2 ) @ ( proces89589571ess_CH @ B @ C @ Y41 @ Y42 ) ) ).
% 0.19/0.47
% 0.19/0.47 % process_term.rel_distinct(9)
% 0.19/0.47 thf(fact_203_process__term_Orel__distinct_I8_J,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,D: $tType,C: $tType,R1: A > C > $o,R22: B > D > $o,Y31: A,Y32: proces554692349s_term @ A @ B,X2: proces634752977rocess @ C] :
% 0.19/0.47 ~ ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R22 @ ( proces1454156180ss_ACT @ A @ B @ Y31 @ Y32 ) @ ( proces1062592052s_PROC @ C @ D @ X2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % process_term.rel_distinct(8)
% 0.19/0.47 thf(fact_204_process__term_Orel__distinct_I7_J,axiom,
% 0.19/0.47 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X2: proces634752977rocess @ A,Y31: B,Y32: proces554692349s_term @ B @ C] :
% 0.19/0.47 ~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1062592052s_PROC @ A @ Pvar @ X2 ) @ ( proces1454156180ss_ACT @ B @ C @ Y31 @ Y32 ) ) ).
% 0.19/0.47
% 0.19/0.47 % process_term.rel_distinct(7)
% 0.19/0.47 thf(fact_205_process__term_Orel__intros_I1_J,axiom,
% 0.19/0.47 ! [Pvar: $tType,A: $tType,B: $tType,C: $tType,R22: Pvar > C > $o,X13: Pvar,Y1: C,R1: A > B > $o] :
% 0.19/0.47 ( ( R22 @ X13 @ Y1 )
% 0.19/0.47 => ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1627516585ss_VAR @ Pvar @ A @ X13 ) @ ( proces1627516585ss_VAR @ C @ B @ Y1 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process_term.rel_intros(1)
% 0.19/0.47 thf(fact_206_process__term_Orel__inject_I1_J,axiom,
% 0.19/0.47 ! [B: $tType,A: $tType,Pvar: $tType,C: $tType,R1: A > B > $o,R22: Pvar > C > $o,X13: Pvar,Y1: C] :
% 0.19/0.47 ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1627516585ss_VAR @ Pvar @ A @ X13 ) @ ( proces1627516585ss_VAR @ C @ B @ Y1 ) )
% 0.19/0.47 = ( R22 @ X13 @ Y1 ) ) ).
% 0.19/0.47
% 0.19/0.47 % process_term.rel_inject(1)
% 0.19/0.47 thf(fact_207_process__term_Orel__intros_I4_J,axiom,
% 0.19/0.47 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X41: proces554692349s_term @ A @ Pvar,Y41: proces554692349s_term @ B @ C,X42: proces554692349s_term @ A @ Pvar,Y42: proces554692349s_term @ B @ C] :
% 0.19/0.47 ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X41 @ Y41 )
% 0.19/0.47 => ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X42 @ Y42 )
% 0.19/0.47 => ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 ) @ ( proces89589571ess_CH @ B @ C @ Y41 @ Y42 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process_term.rel_intros(4)
% 0.19/0.47 thf(fact_208_process__term_Orel__inject_I4_J,axiom,
% 0.19/0.47 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X41: proces554692349s_term @ A @ Pvar,X42: proces554692349s_term @ A @ Pvar,Y41: proces554692349s_term @ B @ C,Y42: proces554692349s_term @ B @ C] :
% 0.19/0.47 ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 ) @ ( proces89589571ess_CH @ B @ C @ Y41 @ Y42 ) )
% 0.19/0.47 = ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X41 @ Y41 )
% 0.19/0.47 & ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X42 @ Y42 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process_term.rel_inject(4)
% 0.19/0.47 thf(fact_209_process__term_Orel__intros_I3_J,axiom,
% 0.19/0.47 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,X31: A,Y31: B,R22: Pvar > C > $o,X32: proces554692349s_term @ A @ Pvar,Y32: proces554692349s_term @ B @ C] :
% 0.19/0.47 ( ( R1 @ X31 @ Y31 )
% 0.19/0.47 => ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X32 @ Y32 )
% 0.19/0.47 => ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) @ ( proces1454156180ss_ACT @ B @ C @ Y31 @ Y32 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process_term.rel_intros(3)
% 0.19/0.47 thf(fact_210_process__term_Orel__inject_I3_J,axiom,
% 0.19/0.47 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X31: A,X32: proces554692349s_term @ A @ Pvar,Y31: B,Y32: proces554692349s_term @ B @ C] :
% 0.19/0.47 ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) @ ( proces1454156180ss_ACT @ B @ C @ Y31 @ Y32 ) )
% 0.19/0.47 = ( ( R1 @ X31 @ Y31 )
% 0.19/0.47 & ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X32 @ Y32 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process_term.rel_inject(3)
% 0.19/0.47 thf(fact_211_process__term_Orel__eq,axiom,
% 0.19/0.47 ! [B: $tType,A: $tType] :
% 0.19/0.47 ( ( proces2029722208s_term @ A @ A @ B @ B
% 0.19/0.47 @ ^ [Y8: A,Z3: A] : ( Y8 = Z3 )
% 0.19/0.47 @ ^ [Y8: B,Z3: B] : ( Y8 = Z3 ) )
% 0.19/0.47 = ( ^ [Y8: proces554692349s_term @ A @ B,Z3: proces554692349s_term @ A @ B] : ( Y8 = Z3 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process_term.rel_eq
% 0.19/0.47 thf(fact_212_process__term_Orel__refl,axiom,
% 0.19/0.47 ! [D: $tType,C: $tType,R1a: C > C > $o,R2a: D > D > $o,X3: proces554692349s_term @ C @ D] :
% 0.19/0.47 ( ! [X5: C] : ( R1a @ X5 @ X5 )
% 0.19/0.47 => ( ! [X5: D] : ( R2a @ X5 @ X5 )
% 0.19/0.47 => ( proces2029722208s_term @ C @ C @ D @ D @ R1a @ R2a @ X3 @ X3 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process_term.rel_refl
% 0.19/0.47 thf(fact_213_process__term_Orel__distinct_I6_J,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,C: $tType,D: $tType,R1: A > C > $o,R22: B > D > $o,Y41: proces554692349s_term @ A @ B,Y42: proces554692349s_term @ A @ B,X13: D] :
% 0.19/0.47 ~ ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R22 @ ( proces89589571ess_CH @ A @ B @ Y41 @ Y42 ) @ ( proces1627516585ss_VAR @ D @ C @ X13 ) ) ).
% 0.19/0.47
% 0.19/0.47 % process_term.rel_distinct(6)
% 0.19/0.47 thf(fact_214_process__term_Orel__distinct_I5_J,axiom,
% 0.19/0.47 ! [Pvar: $tType,A: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X13: Pvar,Y41: proces554692349s_term @ B @ C,Y42: proces554692349s_term @ B @ C] :
% 0.19/0.47 ~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1627516585ss_VAR @ Pvar @ A @ X13 ) @ ( proces89589571ess_CH @ B @ C @ Y41 @ Y42 ) ) ).
% 0.19/0.47
% 0.19/0.47 % process_term.rel_distinct(5)
% 0.19/0.47 thf(fact_215_process__term_Orel__distinct_I4_J,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,C: $tType,D: $tType,R1: A > C > $o,R22: B > D > $o,Y31: A,Y32: proces554692349s_term @ A @ B,X13: D] :
% 0.19/0.47 ~ ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R22 @ ( proces1454156180ss_ACT @ A @ B @ Y31 @ Y32 ) @ ( proces1627516585ss_VAR @ D @ C @ X13 ) ) ).
% 0.19/0.47
% 0.19/0.47 % process_term.rel_distinct(4)
% 0.19/0.47 thf(fact_216_process__term_Orel__distinct_I3_J,axiom,
% 0.19/0.47 ! [Pvar: $tType,A: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X13: Pvar,Y31: B,Y32: proces554692349s_term @ B @ C] :
% 0.19/0.47 ~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1627516585ss_VAR @ Pvar @ A @ X13 ) @ ( proces1454156180ss_ACT @ B @ C @ Y31 @ Y32 ) ) ).
% 0.19/0.47
% 0.19/0.47 % process_term.rel_distinct(3)
% 0.19/0.47 thf(fact_217_process__term_Orel__distinct_I12_J,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,D: $tType,C: $tType,R1: A > C > $o,R22: B > D > $o,Y41: proces554692349s_term @ A @ B,Y42: proces554692349s_term @ A @ B,X31: C,X32: proces554692349s_term @ C @ D] :
% 0.19/0.47 ~ ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R22 @ ( proces89589571ess_CH @ A @ B @ Y41 @ Y42 ) @ ( proces1454156180ss_ACT @ C @ D @ X31 @ X32 ) ) ).
% 0.19/0.47
% 0.19/0.47 % process_term.rel_distinct(12)
% 0.19/0.47 thf(fact_218_process__term_Orel__distinct_I11_J,axiom,
% 0.19/0.47 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X31: A,X32: proces554692349s_term @ A @ Pvar,Y41: proces554692349s_term @ B @ C,Y42: proces554692349s_term @ B @ C] :
% 0.19/0.47 ~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) @ ( proces89589571ess_CH @ B @ C @ Y41 @ Y42 ) ) ).
% 0.19/0.47
% 0.19/0.47 % process_term.rel_distinct(11)
% 0.19/0.47 thf(fact_219_adm__wf__def,axiom,
% 0.19/0.47 ! [B: $tType,A: $tType] :
% 0.19/0.47 ( ( adm_wf @ A @ B )
% 0.19/0.47 = ( ^ [R4: set @ ( product_prod @ A @ A ),F9: ( A > B ) > A > B] :
% 0.19/0.47 ! [F7: A > B,G4: A > B,X: A] :
% 0.19/0.47 ( ! [Z4: A] :
% 0.19/0.47 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Z4 @ X ) @ R4 )
% 0.19/0.47 => ( ( F7 @ Z4 )
% 0.19/0.47 = ( G4 @ Z4 ) ) )
% 0.19/0.47 => ( ( F9 @ F7 @ X )
% 0.19/0.47 = ( F9 @ G4 @ X ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % adm_wf_def
% 0.19/0.47 thf(fact_220_process_Ocorec__code,axiom,
% 0.19/0.47 ! [A: $tType,C: $tType] :
% 0.19/0.47 ( ( proces894737309rocess @ C @ A )
% 0.19/0.47 = ( ^ [P4: C > $o,G11: C > A,Q12: C > $o,G121: C > ( proces634752977rocess @ A ),G122: C > C,Q21: C > $o,G211: C > ( proces634752977rocess @ A ),G212: C > C,Q22: C > $o,G221: C > ( proces634752977rocess @ A ),G222: C > C,A3: C] : ( if @ ( proces634752977rocess @ A ) @ ( P4 @ A3 ) @ ( proces1525233512Action @ A @ ( G11 @ A3 ) @ ( if @ ( proces634752977rocess @ A ) @ ( Q12 @ A3 ) @ ( G121 @ A3 ) @ ( proces894737309rocess @ C @ A @ P4 @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ ( G122 @ A3 ) ) ) ) @ ( proces1915862579Choice @ A @ ( if @ ( proces634752977rocess @ A ) @ ( Q21 @ A3 ) @ ( G211 @ A3 ) @ ( proces894737309rocess @ C @ A @ P4 @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ ( G212 @ A3 ) ) ) @ ( if @ ( proces634752977rocess @ A ) @ ( Q22 @ A3 ) @ ( G221 @ A3 ) @ ( proces894737309rocess @ C @ A @ P4 @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ ( G222 @ A3 ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.corec_code
% 0.19/0.47 thf(fact_221_process__term_Octr__transfer_I2_J,axiom,
% 0.19/0.47 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o] : ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ ( proces749077512rocess @ A @ B @ R1 ) @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ ( proces1062592052s_PROC @ A @ Pvar ) @ ( proces1062592052s_PROC @ B @ C ) ) ).
% 0.19/0.47
% 0.19/0.47 % process_term.ctr_transfer(2)
% 0.19/0.47 thf(fact_222_process_Ocorec__disc__iff_I1_J,axiom,
% 0.19/0.47 ! [A: $tType,C: $tType,P: C > $o,G112: C > A,Q122: C > $o,G1212: C > ( proces634752977rocess @ A ),G1222: C > C,Q212: C > $o,G2112: C > ( proces634752977rocess @ A ),G2122: C > C,Q222: C > $o,G2212: C > ( proces634752977rocess @ A ),G2222: C > C,A2: C] :
% 0.19/0.47 ( ( proces10484146Action @ A @ ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ A2 ) )
% 0.19/0.47 = ( P @ A2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.corec_disc_iff(1)
% 0.19/0.47 thf(fact_223_process_Ocorec__disc__iff_I2_J,axiom,
% 0.19/0.47 ! [A: $tType,C: $tType,P: C > $o,G112: C > A,Q122: C > $o,G1212: C > ( proces634752977rocess @ A ),G1222: C > C,Q212: C > $o,G2112: C > ( proces634752977rocess @ A ),G2122: C > C,Q222: C > $o,G2212: C > ( proces634752977rocess @ A ),G2222: C > C,A2: C] :
% 0.19/0.47 ( ( proces401113213Choice @ A @ ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ A2 ) )
% 0.19/0.47 = ( ~ ( P @ A2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.corec_disc_iff(2)
% 0.19/0.47 thf(fact_224_process__term_Octr__transfer_I1_J,axiom,
% 0.19/0.47 ! [Pvar: $tType,A: $tType,B: $tType,C: $tType,R22: Pvar > C > $o,R1: A > B > $o] : ( bNF_rel_fun @ Pvar @ C @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ R22 @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ ( proces1627516585ss_VAR @ Pvar @ A ) @ ( proces1627516585ss_VAR @ C @ B ) ) ).
% 0.19/0.47
% 0.19/0.47 % process_term.ctr_transfer(1)
% 0.19/0.47 thf(fact_225_process__term_Orec__transfer,axiom,
% 0.19/0.47 ! [Pvar: $tType,D: $tType,A: $tType,B: $tType,E2: $tType,C: $tType,R22: Pvar > C > $o,S: D > E2 > $o,R1: A > B > $o] : ( bNF_rel_fun @ ( Pvar > D ) @ ( C > E2 ) @ ( ( ( proces634752977rocess @ A ) > D ) > ( A > ( proces554692349s_term @ A @ Pvar ) > D > D ) > ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D > D > D ) > ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( ( proces634752977rocess @ B ) > E2 ) > ( B > ( proces554692349s_term @ B @ C ) > E2 > E2 ) > ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) > E2 > E2 > E2 ) > ( proces554692349s_term @ B @ C ) > E2 ) @ ( bNF_rel_fun @ Pvar @ C @ D @ E2 @ R22 @ S ) @ ( bNF_rel_fun @ ( ( proces634752977rocess @ A ) > D ) @ ( ( proces634752977rocess @ B ) > E2 ) @ ( ( A > ( proces554692349s_term @ A @ Pvar ) > D > D ) > ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D > D > D ) > ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( B > ( proces554692349s_term @ B @ C ) > E2 > E2 ) > ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) > E2 > E2 > E2 ) > ( proces554692349s_term @ B @ C ) > E2 ) @ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ D @ E2 @ ( proces749077512rocess @ A @ B @ R1 ) @ S ) @ ( bNF_rel_fun @ ( A > ( proces554692349s_term @ A @ Pvar ) > D > D ) @ ( B > ( proces554692349s_term @ B @ C ) > E2 > E2 ) @ ( ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D > D > D ) > ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) > E2 > E2 > E2 ) > ( proces554692349s_term @ B @ C ) > E2 ) @ ( bNF_rel_fun @ A @ B @ ( ( proces554692349s_term @ A @ Pvar ) > D > D ) @ ( ( proces554692349s_term @ B @ C ) > E2 > E2 ) @ R1 @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ ( D > D ) @ ( E2 > E2 ) @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ ( bNF_rel_fun @ D @ E2 @ D @ E2 @ S @ S ) ) ) @ ( bNF_rel_fun @ ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D > D > D ) @ ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) > E2 > E2 > E2 ) @ ( ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( proces554692349s_term @ B @ C ) > E2 ) @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ ( ( proces554692349s_term @ A @ Pvar ) > D > D > D ) @ ( ( proces554692349s_term @ B @ C ) > E2 > E2 > E2 ) @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ ( D > D > D ) @ ( E2 > E2 > E2 ) @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ ( bNF_rel_fun @ D @ E2 @ ( D > D ) @ ( E2 > E2 ) @ S @ ( bNF_rel_fun @ D @ E2 @ D @ E2 @ S @ S ) ) ) ) @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ D @ E2 @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ S ) ) ) ) @ ( proces2117273769s_term @ Pvar @ D @ A ) @ ( proces2117273769s_term @ C @ E2 @ B ) ) ).
% 0.19/0.47
% 0.19/0.47 % process_term.rec_transfer
% 0.19/0.47 thf(fact_226_process__term_Ocase__transfer,axiom,
% 0.19/0.47 ! [Pvar: $tType,D: $tType,A: $tType,B: $tType,E2: $tType,C: $tType,R22: Pvar > C > $o,S: D > E2 > $o,R1: A > B > $o] : ( bNF_rel_fun @ ( Pvar > D ) @ ( C > E2 ) @ ( ( ( proces634752977rocess @ A ) > D ) > ( A > ( proces554692349s_term @ A @ Pvar ) > D ) > ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D ) > ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( ( proces634752977rocess @ B ) > E2 ) > ( B > ( proces554692349s_term @ B @ C ) > E2 ) > ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) > E2 ) > ( proces554692349s_term @ B @ C ) > E2 ) @ ( bNF_rel_fun @ Pvar @ C @ D @ E2 @ R22 @ S ) @ ( bNF_rel_fun @ ( ( proces634752977rocess @ A ) > D ) @ ( ( proces634752977rocess @ B ) > E2 ) @ ( ( A > ( proces554692349s_term @ A @ Pvar ) > D ) > ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D ) > ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( B > ( proces554692349s_term @ B @ C ) > E2 ) > ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) > E2 ) > ( proces554692349s_term @ B @ C ) > E2 ) @ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ D @ E2 @ ( proces749077512rocess @ A @ B @ R1 ) @ S ) @ ( bNF_rel_fun @ ( A > ( proces554692349s_term @ A @ Pvar ) > D ) @ ( B > ( proces554692349s_term @ B @ C ) > E2 ) @ ( ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D ) > ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) > E2 ) > ( proces554692349s_term @ B @ C ) > E2 ) @ ( bNF_rel_fun @ A @ B @ ( ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( proces554692349s_term @ B @ C ) > E2 ) @ R1 @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ D @ E2 @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ S ) ) @ ( bNF_rel_fun @ ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) > E2 ) @ ( ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( proces554692349s_term @ B @ C ) > E2 ) @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ ( ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( proces554692349s_term @ B @ C ) > E2 ) @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ D @ E2 @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ S ) ) @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ D @ E2 @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ S ) ) ) ) @ ( proces460752237s_term @ Pvar @ D @ A ) @ ( proces460752237s_term @ C @ E2 @ B ) ) ).
% 0.19/0.47
% 0.19/0.47 % process_term.case_transfer
% 0.19/0.47 thf(fact_227_process_Ocorec_I1_J,axiom,
% 0.19/0.47 ! [A: $tType,C: $tType,P: C > $o,A2: C,G112: C > A,Q122: C > $o,G1212: C > ( proces634752977rocess @ A ),G1222: C > C,Q212: C > $o,G2112: C > ( proces634752977rocess @ A ),G2122: C > C,Q222: C > $o,G2212: C > ( proces634752977rocess @ A ),G2222: C > C] :
% 0.19/0.47 ( ( P @ A2 )
% 0.19/0.47 => ( ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ A2 )
% 0.19/0.47 = ( proces1525233512Action @ A @ ( G112 @ A2 ) @ ( if @ ( proces634752977rocess @ A ) @ ( Q122 @ A2 ) @ ( G1212 @ A2 ) @ ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ ( G1222 @ A2 ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.corec(1)
% 0.19/0.47 thf(fact_228_process_Ocorec__transfer,axiom,
% 0.19/0.47 ! [C: $tType,A: $tType,B: $tType,D: $tType,S: C > D > $o,R: A > B > $o] :
% 0.19/0.47 ( bNF_rel_fun @ ( C > $o ) @ ( D > $o ) @ ( ( C > A ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > C > ( proces634752977rocess @ A ) ) @ ( ( D > B ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > D > ( proces634752977rocess @ B ) )
% 0.19/0.47 @ ( bNF_rel_fun @ C @ D @ $o @ $o @ S
% 0.19/0.47 @ ^ [Y8: $o,Z3: $o] : ( Y8 = Z3 ) )
% 0.19/0.47 @ ( bNF_rel_fun @ ( C > A ) @ ( D > B ) @ ( ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > C > ( proces634752977rocess @ A ) ) @ ( ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > D > ( proces634752977rocess @ B ) ) @ ( bNF_rel_fun @ C @ D @ A @ B @ S @ R )
% 0.19/0.47 @ ( bNF_rel_fun @ ( C > $o ) @ ( D > $o ) @ ( ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > C > ( proces634752977rocess @ A ) ) @ ( ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > D > ( proces634752977rocess @ B ) )
% 0.19/0.47 @ ( bNF_rel_fun @ C @ D @ $o @ $o @ S
% 0.19/0.47 @ ^ [Y8: $o,Z3: $o] : ( Y8 = Z3 ) )
% 0.19/0.47 @ ( bNF_rel_fun @ ( C > ( proces634752977rocess @ A ) ) @ ( D > ( proces634752977rocess @ B ) ) @ ( ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > C > ( proces634752977rocess @ A ) ) @ ( ( D > D ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > D > ( proces634752977rocess @ B ) ) @ ( bNF_rel_fun @ C @ D @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ S @ ( proces749077512rocess @ A @ B @ R ) )
% 0.19/0.47 @ ( bNF_rel_fun @ ( C > C ) @ ( D > D ) @ ( ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > C > ( proces634752977rocess @ A ) ) @ ( ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > D > ( proces634752977rocess @ B ) ) @ ( bNF_rel_fun @ C @ D @ C @ D @ S @ S )
% 0.19/0.47 @ ( bNF_rel_fun @ ( C > $o ) @ ( D > $o ) @ ( ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > C > ( proces634752977rocess @ A ) ) @ ( ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > D > ( proces634752977rocess @ B ) )
% 0.19/0.47 @ ( bNF_rel_fun @ C @ D @ $o @ $o @ S
% 0.19/0.47 @ ^ [Y8: $o,Z3: $o] : ( Y8 = Z3 ) )
% 0.19/0.47 @ ( bNF_rel_fun @ ( C > ( proces634752977rocess @ A ) ) @ ( D > ( proces634752977rocess @ B ) ) @ ( ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > C > ( proces634752977rocess @ A ) ) @ ( ( D > D ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > D > ( proces634752977rocess @ B ) ) @ ( bNF_rel_fun @ C @ D @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ S @ ( proces749077512rocess @ A @ B @ R ) )
% 0.19/0.47 @ ( bNF_rel_fun @ ( C > C ) @ ( D > D ) @ ( ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > C > ( proces634752977rocess @ A ) ) @ ( ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > D > ( proces634752977rocess @ B ) ) @ ( bNF_rel_fun @ C @ D @ C @ D @ S @ S )
% 0.19/0.47 @ ( bNF_rel_fun @ ( C > $o ) @ ( D > $o ) @ ( ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > C > ( proces634752977rocess @ A ) ) @ ( ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > D > ( proces634752977rocess @ B ) )
% 0.19/0.47 @ ( bNF_rel_fun @ C @ D @ $o @ $o @ S
% 0.19/0.47 @ ^ [Y8: $o,Z3: $o] : ( Y8 = Z3 ) )
% 0.19/0.47 @ ( bNF_rel_fun @ ( C > ( proces634752977rocess @ A ) ) @ ( D > ( proces634752977rocess @ B ) ) @ ( ( C > C ) > C > ( proces634752977rocess @ A ) ) @ ( ( D > D ) > D > ( proces634752977rocess @ B ) ) @ ( bNF_rel_fun @ C @ D @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ S @ ( proces749077512rocess @ A @ B @ R ) ) @ ( bNF_rel_fun @ ( C > C ) @ ( D > D ) @ ( C > ( proces634752977rocess @ A ) ) @ ( D > ( proces634752977rocess @ B ) ) @ ( bNF_rel_fun @ C @ D @ C @ D @ S @ S ) @ ( bNF_rel_fun @ C @ D @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ S @ ( proces749077512rocess @ A @ B @ R ) ) ) ) ) ) ) ) ) ) ) )
% 0.19/0.47 @ ( proces894737309rocess @ C @ A )
% 0.19/0.47 @ ( proces894737309rocess @ D @ B ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.corec_transfer
% 0.19/0.47 thf(fact_229_process_Ocorec__disc_I1_J,axiom,
% 0.19/0.47 ! [A: $tType,C: $tType,P: C > $o,A2: C,G112: C > A,Q122: C > $o,G1212: C > ( proces634752977rocess @ A ),G1222: C > C,Q212: C > $o,G2112: C > ( proces634752977rocess @ A ),G2122: C > C,Q222: C > $o,G2212: C > ( proces634752977rocess @ A ),G2222: C > C] :
% 0.19/0.47 ( ( P @ A2 )
% 0.19/0.47 => ( proces10484146Action @ A @ ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ A2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.corec_disc(1)
% 0.19/0.47 thf(fact_230_process_Ocorec__disc_I2_J,axiom,
% 0.19/0.47 ! [A: $tType,C: $tType,P: C > $o,A2: C,G112: C > A,Q122: C > $o,G1212: C > ( proces634752977rocess @ A ),G1222: C > C,Q212: C > $o,G2112: C > ( proces634752977rocess @ A ),G2122: C > C,Q222: C > $o,G2212: C > ( proces634752977rocess @ A ),G2222: C > C] :
% 0.19/0.47 ( ~ ( P @ A2 )
% 0.19/0.47 => ( proces401113213Choice @ A @ ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ A2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.corec_disc(2)
% 0.19/0.47 thf(fact_231_process_Ocorec__sel_I1_J,axiom,
% 0.19/0.47 ! [A: $tType,C: $tType,P: C > $o,A2: C,G112: C > A,Q122: C > $o,G1212: C > ( proces634752977rocess @ A ),G1222: C > C,Q212: C > $o,G2112: C > ( proces634752977rocess @ A ),G2122: C > C,Q222: C > $o,G2212: C > ( proces634752977rocess @ A ),G2222: C > C] :
% 0.19/0.47 ( ( P @ A2 )
% 0.19/0.47 => ( ( proces745025900prefOf @ A @ ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ A2 ) )
% 0.19/0.47 = ( G112 @ A2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.corec_sel(1)
% 0.19/0.47 thf(fact_232_process_Ocorec__sel_I4_J,axiom,
% 0.19/0.47 ! [A: $tType,C: $tType,P: C > $o,A2: C,Q222: C > $o,G112: C > A,Q122: C > $o,G1212: C > ( proces634752977rocess @ A ),G1222: C > C,Q212: C > $o,G2112: C > ( proces634752977rocess @ A ),G2122: C > C,G2212: C > ( proces634752977rocess @ A ),G2222: C > C] :
% 0.19/0.47 ( ~ ( P @ A2 )
% 0.19/0.47 => ( ( ( Q222 @ A2 )
% 0.19/0.47 => ( ( proces988026546_ch2Of @ A @ ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ A2 ) )
% 0.19/0.47 = ( G2212 @ A2 ) ) )
% 0.19/0.47 & ( ~ ( Q222 @ A2 )
% 0.19/0.47 => ( ( proces988026546_ch2Of @ A @ ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ A2 ) )
% 0.19/0.47 = ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ ( G2222 @ A2 ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.corec_sel(4)
% 0.19/0.47 thf(fact_233_process_Ocorec__sel_I3_J,axiom,
% 0.19/0.47 ! [A: $tType,C: $tType,P: C > $o,A2: C,Q212: C > $o,G112: C > A,Q122: C > $o,G1212: C > ( proces634752977rocess @ A ),G1222: C > C,G2112: C > ( proces634752977rocess @ A ),G2122: C > C,Q222: C > $o,G2212: C > ( proces634752977rocess @ A ),G2222: C > C] :
% 0.19/0.47 ( ~ ( P @ A2 )
% 0.19/0.47 => ( ( ( Q212 @ A2 )
% 0.19/0.47 => ( ( proces979765041_ch1Of @ A @ ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ A2 ) )
% 0.19/0.47 = ( G2112 @ A2 ) ) )
% 0.19/0.47 & ( ~ ( Q212 @ A2 )
% 0.19/0.47 => ( ( proces979765041_ch1Of @ A @ ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ A2 ) )
% 0.19/0.47 = ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ ( G2122 @ A2 ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.corec_sel(3)
% 0.19/0.47 thf(fact_234_process_Ocorec__sel_I2_J,axiom,
% 0.19/0.47 ! [A: $tType,C: $tType,P: C > $o,A2: C,Q122: C > $o,G112: C > A,G1212: C > ( proces634752977rocess @ A ),G1222: C > C,Q212: C > $o,G2112: C > ( proces634752977rocess @ A ),G2122: C > C,Q222: C > $o,G2212: C > ( proces634752977rocess @ A ),G2222: C > C] :
% 0.19/0.47 ( ( P @ A2 )
% 0.19/0.47 => ( ( ( Q122 @ A2 )
% 0.19/0.47 => ( ( proces1778668539contOf @ A @ ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ A2 ) )
% 0.19/0.47 = ( G1212 @ A2 ) ) )
% 0.19/0.47 & ( ~ ( Q122 @ A2 )
% 0.19/0.47 => ( ( proces1778668539contOf @ A @ ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ A2 ) )
% 0.19/0.47 = ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ ( G1222 @ A2 ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.corec_sel(2)
% 0.19/0.47 thf(fact_235_process_Ocorec_I2_J,axiom,
% 0.19/0.47 ! [A: $tType,C: $tType,P: C > $o,A2: C,G112: C > A,Q122: C > $o,G1212: C > ( proces634752977rocess @ A ),G1222: C > C,Q212: C > $o,G2112: C > ( proces634752977rocess @ A ),G2122: C > C,Q222: C > $o,G2212: C > ( proces634752977rocess @ A ),G2222: C > C] :
% 0.19/0.47 ( ~ ( P @ A2 )
% 0.19/0.47 => ( ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ A2 )
% 0.19/0.47 = ( proces1915862579Choice @ A @ ( if @ ( proces634752977rocess @ A ) @ ( Q212 @ A2 ) @ ( G2112 @ A2 ) @ ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ ( G2122 @ A2 ) ) ) @ ( if @ ( proces634752977rocess @ A ) @ ( Q222 @ A2 ) @ ( G2212 @ A2 ) @ ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ ( G2222 @ A2 ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.corec(2)
% 0.19/0.47 thf(fact_236_process__term_Orel__transfer,axiom,
% 0.19/0.47 ! [A: $tType,C: $tType,B: $tType,D: $tType,H2: $tType,F5: $tType,G2: $tType,E2: $tType,S1a: A > E2 > $o,S1c: C > G2 > $o,S2a: B > F5 > $o,S2c: D > H2 > $o] :
% 0.19/0.47 ( bNF_rel_fun @ ( A > C > $o ) @ ( E2 > G2 > $o ) @ ( ( B > D > $o ) > ( proces554692349s_term @ A @ B ) > ( proces554692349s_term @ C @ D ) > $o ) @ ( ( F5 > H2 > $o ) > ( proces554692349s_term @ E2 @ F5 ) > ( proces554692349s_term @ G2 @ H2 ) > $o )
% 0.19/0.47 @ ( bNF_rel_fun @ A @ E2 @ ( C > $o ) @ ( G2 > $o ) @ S1a
% 0.19/0.47 @ ( bNF_rel_fun @ C @ G2 @ $o @ $o @ S1c
% 0.19/0.47 @ ^ [Y8: $o,Z3: $o] : ( Y8 = Z3 ) ) )
% 0.19/0.47 @ ( bNF_rel_fun @ ( B > D > $o ) @ ( F5 > H2 > $o ) @ ( ( proces554692349s_term @ A @ B ) > ( proces554692349s_term @ C @ D ) > $o ) @ ( ( proces554692349s_term @ E2 @ F5 ) > ( proces554692349s_term @ G2 @ H2 ) > $o )
% 0.19/0.47 @ ( bNF_rel_fun @ B @ F5 @ ( D > $o ) @ ( H2 > $o ) @ S2a
% 0.19/0.47 @ ( bNF_rel_fun @ D @ H2 @ $o @ $o @ S2c
% 0.19/0.47 @ ^ [Y8: $o,Z3: $o] : ( Y8 = Z3 ) ) )
% 0.19/0.47 @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ B ) @ ( proces554692349s_term @ E2 @ F5 ) @ ( ( proces554692349s_term @ C @ D ) > $o ) @ ( ( proces554692349s_term @ G2 @ H2 ) > $o ) @ ( proces2029722208s_term @ A @ E2 @ B @ F5 @ S1a @ S2a )
% 0.19/0.47 @ ( bNF_rel_fun @ ( proces554692349s_term @ C @ D ) @ ( proces554692349s_term @ G2 @ H2 ) @ $o @ $o @ ( proces2029722208s_term @ C @ G2 @ D @ H2 @ S1c @ S2c )
% 0.19/0.47 @ ^ [Y8: $o,Z3: $o] : ( Y8 = Z3 ) ) ) )
% 0.19/0.47 @ ( proces2029722208s_term @ A @ C @ B @ D )
% 0.19/0.47 @ ( proces2029722208s_term @ E2 @ G2 @ F5 @ H2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % process_term.rel_transfer
% 0.19/0.47 thf(fact_237_process__term_Octr__transfer_I3_J,axiom,
% 0.19/0.47 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o] : ( bNF_rel_fun @ A @ B @ ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) ) @ ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) ) @ R1 @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) ) @ ( proces1454156180ss_ACT @ A @ Pvar ) @ ( proces1454156180ss_ACT @ B @ C ) ) ).
% 0.19/0.47
% 0.19/0.47 % process_term.ctr_transfer(3)
% 0.19/0.47 thf(fact_238_process__term_Octr__transfer_I4_J,axiom,
% 0.19/0.47 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o] : ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) ) @ ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) ) @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) ) @ ( proces89589571ess_CH @ A @ Pvar ) @ ( proces89589571ess_CH @ B @ C ) ) ).
% 0.19/0.47
% 0.19/0.47 % process_term.ctr_transfer(4)
% 0.19/0.47 thf(fact_239_process_Odisc__transfer_I1_J,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,R: A > B > $o] :
% 0.19/0.47 ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ $o @ $o @ ( proces749077512rocess @ A @ B @ R )
% 0.19/0.47 @ ^ [Y8: $o,Z3: $o] : ( Y8 = Z3 )
% 0.19/0.47 @ ( proces10484146Action @ A )
% 0.19/0.47 @ ( proces10484146Action @ B ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.disc_transfer(1)
% 0.19/0.47 thf(fact_240_process_Odisc__transfer_I2_J,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,R: A > B > $o] :
% 0.19/0.47 ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ $o @ $o @ ( proces749077512rocess @ A @ B @ R )
% 0.19/0.47 @ ^ [Y8: $o,Z3: $o] : ( Y8 = Z3 )
% 0.19/0.47 @ ( proces401113213Choice @ A )
% 0.19/0.47 @ ( proces401113213Choice @ B ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.disc_transfer(2)
% 0.19/0.47 thf(fact_241_process_Octr__transfer_I1_J,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,R: A > B > $o] : ( bNF_rel_fun @ A @ B @ ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) @ ( ( proces634752977rocess @ B ) > ( proces634752977rocess @ B ) ) @ R @ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ ( proces749077512rocess @ A @ B @ R ) @ ( proces749077512rocess @ A @ B @ R ) ) @ ( proces1525233512Action @ A ) @ ( proces1525233512Action @ B ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.ctr_transfer(1)
% 0.19/0.47 thf(fact_242_process_Orel__transfer,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,D: $tType,C: $tType,Sa: A > C > $o,Sc: B > D > $o] :
% 0.19/0.47 ( bNF_rel_fun @ ( A > B > $o ) @ ( C > D > $o ) @ ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ B ) > $o ) @ ( ( proces634752977rocess @ C ) > ( proces634752977rocess @ D ) > $o )
% 0.19/0.47 @ ( bNF_rel_fun @ A @ C @ ( B > $o ) @ ( D > $o ) @ Sa
% 0.19/0.47 @ ( bNF_rel_fun @ B @ D @ $o @ $o @ Sc
% 0.19/0.47 @ ^ [Y8: $o,Z3: $o] : ( Y8 = Z3 ) ) )
% 0.19/0.47 @ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ C ) @ ( ( proces634752977rocess @ B ) > $o ) @ ( ( proces634752977rocess @ D ) > $o ) @ ( proces749077512rocess @ A @ C @ Sa )
% 0.19/0.47 @ ( bNF_rel_fun @ ( proces634752977rocess @ B ) @ ( proces634752977rocess @ D ) @ $o @ $o @ ( proces749077512rocess @ B @ D @ Sc )
% 0.19/0.47 @ ^ [Y8: $o,Z3: $o] : ( Y8 = Z3 ) ) )
% 0.19/0.47 @ ( proces749077512rocess @ A @ B )
% 0.19/0.47 @ ( proces749077512rocess @ C @ D ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.rel_transfer
% 0.19/0.47 thf(fact_243_process_Ocase__transfer,axiom,
% 0.19/0.47 ! [A: $tType,C: $tType,D: $tType,B: $tType,R: A > B > $o,S: C > D > $o] : ( bNF_rel_fun @ ( A > ( proces634752977rocess @ A ) > C ) @ ( B > ( proces634752977rocess @ B ) > D ) @ ( ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > C ) > ( proces634752977rocess @ A ) > C ) @ ( ( ( proces634752977rocess @ B ) > ( proces634752977rocess @ B ) > D ) > ( proces634752977rocess @ B ) > D ) @ ( bNF_rel_fun @ A @ B @ ( ( proces634752977rocess @ A ) > C ) @ ( ( proces634752977rocess @ B ) > D ) @ R @ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ C @ D @ ( proces749077512rocess @ A @ B @ R ) @ S ) ) @ ( bNF_rel_fun @ ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > C ) @ ( ( proces634752977rocess @ B ) > ( proces634752977rocess @ B ) > D ) @ ( ( proces634752977rocess @ A ) > C ) @ ( ( proces634752977rocess @ B ) > D ) @ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ ( ( proces634752977rocess @ A ) > C ) @ ( ( proces634752977rocess @ B ) > D ) @ ( proces749077512rocess @ A @ B @ R ) @ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ C @ D @ ( proces749077512rocess @ A @ B @ R ) @ S ) ) @ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ C @ D @ ( proces749077512rocess @ A @ B @ R ) @ S ) ) @ ( proces1406508781rocess @ A @ C ) @ ( proces1406508781rocess @ B @ D ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.case_transfer
% 0.19/0.47 thf(fact_244_process_Octr__transfer_I2_J,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,R: A > B > $o] : ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) @ ( ( proces634752977rocess @ B ) > ( proces634752977rocess @ B ) ) @ ( proces749077512rocess @ A @ B @ R ) @ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ ( proces749077512rocess @ A @ B @ R ) @ ( proces749077512rocess @ A @ B @ R ) ) @ ( proces1915862579Choice @ A ) @ ( proces1915862579Choice @ B ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.ctr_transfer(2)
% 0.19/0.47 thf(fact_245_process__term_Opred__transfer,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,D: $tType,C: $tType,R1: A > C > $o,R22: B > D > $o] :
% 0.19/0.47 ( bNF_rel_fun @ ( A > $o ) @ ( C > $o ) @ ( ( B > $o ) > ( proces554692349s_term @ A @ B ) > $o ) @ ( ( D > $o ) > ( proces554692349s_term @ C @ D ) > $o )
% 0.19/0.47 @ ( bNF_rel_fun @ A @ C @ $o @ $o @ R1
% 0.19/0.47 @ ^ [Y8: $o,Z3: $o] : ( Y8 = Z3 ) )
% 0.19/0.47 @ ( bNF_rel_fun @ ( B > $o ) @ ( D > $o ) @ ( ( proces554692349s_term @ A @ B ) > $o ) @ ( ( proces554692349s_term @ C @ D ) > $o )
% 0.19/0.47 @ ( bNF_rel_fun @ B @ D @ $o @ $o @ R22
% 0.19/0.47 @ ^ [Y8: $o,Z3: $o] : ( Y8 = Z3 ) )
% 0.19/0.47 @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ B ) @ ( proces554692349s_term @ C @ D ) @ $o @ $o @ ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R22 )
% 0.19/0.47 @ ^ [Y8: $o,Z3: $o] : ( Y8 = Z3 ) ) )
% 0.19/0.48 @ ( proces2118920028s_term @ A @ B )
% 0.19/0.48 @ ( proces2118920028s_term @ C @ D ) ) ).
% 0.19/0.48
% 0.19/0.48 % process_term.pred_transfer
% 0.19/0.48 thf(fact_246_process_Opred__transfer,axiom,
% 0.19/0.48 ! [A: $tType,B: $tType,R: A > B > $o] :
% 0.19/0.48 ( bNF_rel_fun @ ( A > $o ) @ ( B > $o ) @ ( ( proces634752977rocess @ A ) > $o ) @ ( ( proces634752977rocess @ B ) > $o )
% 0.19/0.48 @ ( bNF_rel_fun @ A @ B @ $o @ $o @ R
% 0.19/0.48 @ ^ [Y8: $o,Z3: $o] : ( Y8 = Z3 ) )
% 0.19/0.48 @ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ $o @ $o @ ( proces749077512rocess @ A @ B @ R )
% 0.19/0.48 @ ^ [Y8: $o,Z3: $o] : ( Y8 = Z3 ) )
% 0.19/0.48 @ ( proces1205983068rocess @ A )
% 0.19/0.48 @ ( proces1205983068rocess @ B ) ) ).
% 0.19/0.48
% 0.19/0.48 % process.pred_transfer
% 0.19/0.48 thf(fact_247_process__term_Opred__inject_I1_J,axiom,
% 0.19/0.48 ! [A: $tType,Pvar: $tType,P1: A > $o,P22: Pvar > $o,A2: Pvar] :
% 0.19/0.48 ( ( proces2118920028s_term @ A @ Pvar @ P1 @ P22 @ ( proces1627516585ss_VAR @ Pvar @ A @ A2 ) )
% 0.19/0.48 = ( P22 @ A2 ) ) ).
% 0.19/0.48
% 0.19/0.48 % process_term.pred_inject(1)
% 0.19/0.48 thf(fact_248_process__term_Opred__inject_I4_J,axiom,
% 0.19/0.48 ! [Pvar: $tType,A: $tType,P1: A > $o,P22: Pvar > $o,A2: proces554692349s_term @ A @ Pvar,Aa2: proces554692349s_term @ A @ Pvar] :
% 0.19/0.48 ( ( proces2118920028s_term @ A @ Pvar @ P1 @ P22 @ ( proces89589571ess_CH @ A @ Pvar @ A2 @ Aa2 ) )
% 0.19/0.48 = ( ( proces2118920028s_term @ A @ Pvar @ P1 @ P22 @ A2 )
% 0.19/0.48 & ( proces2118920028s_term @ A @ Pvar @ P1 @ P22 @ Aa2 ) ) ) ).
% 0.19/0.48
% 0.19/0.48 % process_term.pred_inject(4)
% 0.19/0.48 thf(fact_249_process__term_Opred__inject_I3_J,axiom,
% 0.19/0.48 ! [Pvar: $tType,A: $tType,P1: A > $o,P22: Pvar > $o,A2: A,Aa2: proces554692349s_term @ A @ Pvar] :
% 0.19/0.48 ( ( proces2118920028s_term @ A @ Pvar @ P1 @ P22 @ ( proces1454156180ss_ACT @ A @ Pvar @ A2 @ Aa2 ) )
% 0.19/0.48 = ( ( P1 @ A2 )
% 0.19/0.48 & ( proces2118920028s_term @ A @ Pvar @ P1 @ P22 @ Aa2 ) ) ) ).
% 0.19/0.48
% 0.19/0.48 % process_term.pred_inject(3)
% 0.19/0.48 thf(fact_250_process_Opred__inject_I1_J,axiom,
% 0.19/0.48 ! [A: $tType,P3: A > $o,A2: A,Aa2: proces634752977rocess @ A] :
% 0.19/0.48 ( ( proces1205983068rocess @ A @ P3 @ ( proces1525233512Action @ A @ A2 @ Aa2 ) )
% 0.19/0.48 = ( ( P3 @ A2 )
% 0.19/0.48 & ( proces1205983068rocess @ A @ P3 @ Aa2 ) ) ) ).
% 0.19/0.48
% 0.19/0.48 % process.pred_inject(1)
% 0.19/0.48 thf(fact_251_process_Opred__inject_I2_J,axiom,
% 0.19/0.48 ! [A: $tType,P3: A > $o,A2: proces634752977rocess @ A,Aa2: proces634752977rocess @ A] :
% 0.19/0.48 ( ( proces1205983068rocess @ A @ P3 @ ( proces1915862579Choice @ A @ A2 @ Aa2 ) )
% 0.19/0.48 = ( ( proces1205983068rocess @ A @ P3 @ A2 )
% 0.19/0.48 & ( proces1205983068rocess @ A @ P3 @ Aa2 ) ) ) ).
% 0.19/0.48
% 0.19/0.48 % process.pred_inject(2)
% 0.19/0.48 thf(fact_252_process__term_Opred__inject_I2_J,axiom,
% 0.19/0.48 ! [Pvar: $tType,A: $tType,P1: A > $o,P22: Pvar > $o,A2: proces634752977rocess @ A] :
% 0.19/0.48 ( ( proces2118920028s_term @ A @ Pvar @ P1 @ P22 @ ( proces1062592052s_PROC @ A @ Pvar @ A2 ) )
% 0.19/0.48 = ( proces1205983068rocess @ A @ P1 @ A2 ) ) ).
% 0.19/0.48
% 0.19/0.48 % process_term.pred_inject(2)
% 0.19/0.48 thf(fact_253_process_Opred__True,axiom,
% 0.19/0.48 ! [A: $tType] :
% 0.19/0.48 ( ( proces1205983068rocess @ A
% 0.19/0.48 @ ^ [Uu2: A] : $true )
% 0.19/0.48 = ( ^ [Uu2: proces634752977rocess @ A] : $true ) ) ).
% 0.19/0.48
% 0.19/0.48 % process.pred_True
% 0.19/0.48 thf(fact_254_process__term_Opred__True,axiom,
% 0.19/0.48 ! [B: $tType,A: $tType] :
% 0.19/0.48 ( ( proces2118920028s_term @ A @ B
% 0.19/0.48 @ ^ [Uu2: A] : $true
% 0.19/0.48 @ ^ [Uu2: B] : $true )
% 0.19/0.48 = ( ^ [Uu2: proces554692349s_term @ A @ B] : $true ) ) ).
% 0.19/0.48
% 0.19/0.48 % process_term.pred_True
% 0.19/0.48
% 0.19/0.48 %----Helper facts (3)
% 0.19/0.48 thf(help_If_3_1_T,axiom,
% 0.19/0.48 ! [P3: $o] :
% 0.19/0.48 ( ( P3 = $true )
% 0.19/0.48 | ( P3 = $false ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(help_If_2_1_T,axiom,
% 0.19/0.48 ! [A: $tType,X3: A,Y: A] :
% 0.19/0.48 ( ( if @ A @ $false @ X3 @ Y )
% 0.19/0.48 = Y ) ).
% 0.19/0.48
% 0.19/0.48 thf(help_If_1_1_T,axiom,
% 0.19/0.48 ! [A: $tType,X3: A,Y: A] :
% 0.19/0.48 ( ( if @ A @ $true @ X3 @ Y )
% 0.19/0.48 = X3 ) ).
% 0.19/0.48
% 0.19/0.48 %----Conjectures (1)
% 0.19/0.48 thf(conj_0,conjecture,
% 0.19/0.48 ~ ( proces687458811_isACT @ b @ a @ b @ a @ sys @ ( proces1062592052s_PROC @ a @ b @ pa ) ) ).
% 0.19/0.48
% 0.19/0.48 %------------------------------------------------------------------------------
% 0.19/0.48 ------------------------
% 2.99/1.55 ---- Embedded in THF ---
% 2.99/1.55 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.99/1.55 %%% Generated on Tue Feb 24 11:29:43 EST 2026
% 2.99/1.55 %%% using '$$dhol' embedding, version 1.3.0.
% 2.99/1.55 %%% Logic specification used:
% 2.99/1.55 %%% thf(spec, logic, $$dhol).
% 2.99/1.55
% 2.99/1.55 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.lDpXRCP47Y/DTF2DTF10445.p
% 2.99/1.55 thf(ty_t_Process__Mirabelle__xovoopgpgi_Oprocess__term, type, proces554692349s_term: ($tType > ($tType > $tType))).
% 2.99/1.55 thf(ty_t_Process__Mirabelle__xovoopgpgi_Oprocess, type, proces634752977rocess: ($tType > $tType)).
% 2.99/1.55 thf(ty_t_Product__Type_Oprod, type, product_prod: ($tType > ($tType > $tType))).
% 2.99/1.55 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 2.99/1.55 thf(ty_t_itself, type, itself: ($tType > $tType)).
% 2.99/1.55 thf(ty_tf_b, type, b: $tType).
% 2.99/1.55 thf(ty_tf_a, type, a: $tType).
% 2.99/1.55 thf(sy_c_BNF__Def_Orel__fun, type, bNF_rel_fun: (!> [A:$tType,C:$tType,B:$tType,D:$tType]: (((A > (C > $o)) > ((B > (D > $o)) > ((A > B) > ((C > D) > $o))))))).
% 2.99/1.55 thf(sy_c_HOL_Oundefined, type, undefined: (!> [A:$tType]: (A))).
% 2.99/1.55 thf(sy_c_If, type, if: (!> [A:$tType]: (($o > (A > (A > A)))))).
% 2.99/1.55 thf(sy_c_Order__Relation_Oabove, type, order_above: (!> [A:$tType]: (((set @ ((product_prod @ A) @ A)) > (A > (set @ A)))))).
% 2.99/1.55 thf(sy_c_Order__Relation_OaboveS, type, order_aboveS: (!> [A:$tType]: (((set @ ((product_prod @ A) @ A)) > (A > (set @ A)))))).
% 2.99/1.55 thf(sy_c_Process__Mirabelle__xovoopgpgi_OCH1, type, proces1239275103le_CH1: (!> [A:$tType,B:$tType]: (((A > ((proces554692349s_term @ B) @ A)) > (((proces554692349s_term @ B) @ A) > ((proces554692349s_term @ B) @ A)))))).
% 2.99/1.55 thf(sy_c_Process__Mirabelle__xovoopgpgi_OCH1__rel, type, proces1869379930H1_rel: (!> [A:$tType,B:$tType]: ((((product_prod @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) > (((product_prod @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) > $o))))).
% 2.99/1.55 thf(sy_c_Process__Mirabelle__xovoopgpgi_OCH2, type, proces1239275104le_CH2: (!> [A:$tType,B:$tType]: (((A > ((proces554692349s_term @ B) @ A)) > (((proces554692349s_term @ B) @ A) > ((proces554692349s_term @ B) @ A)))))).
% 2.99/1.55 thf(sy_c_Process__Mirabelle__xovoopgpgi_OCH2__rel, type, proces93903513H2_rel: (!> [A:$tType,B:$tType]: ((((product_prod @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) > (((product_prod @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) > $o))))).
% 2.99/1.55 thf(sy_c_Process__Mirabelle__xovoopgpgi_OCONT, type, proces126235999e_CONT: (!> [A:$tType,B:$tType]: (((A > ((proces554692349s_term @ B) @ A)) > (((proces554692349s_term @ B) @ A) > ((proces554692349s_term @ B) @ A)))))).
% 2.99/1.55 thf(sy_c_Process__Mirabelle__xovoopgpgi_OCONT__rel, type, proces1004198490NT_rel: (!> [A:$tType,B:$tType]: ((((product_prod @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) > (((product_prod @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) > $o))))).
% 2.99/1.55 thf(sy_c_Process__Mirabelle__xovoopgpgi_OPREF, type, proces1708129104e_PREF: (!> [A:$tType,B:$tType,C:$tType]: (((A > ((proces554692349s_term @ B) @ C)) > (((proces554692349s_term @ B) @ A) > B))))).
% 2.99/1.55 thf(sy_c_Process__Mirabelle__xovoopgpgi_OPREF__rel, type, proces527360425EF_rel: (!> [A:$tType,B:$tType,C:$tType]: ((((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ B) @ A)) > (((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ B) @ A)) > $o))))).
% 2.99/1.55 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oguarded, type, proces1121166967uarded: (!> [A:$tType,B:$tType,C:$tType]: (((A > ((proces554692349s_term @ B) @ C)) > $o)))).
% 2.99/1.55 thf(sy_c_Process__Mirabelle__xovoopgpgi_OisACT, type, proces687458811_isACT: (!> [A:$tType,B:$tType,C:$tType,D:$tType]: (((A > ((proces554692349s_term @ B) @ C)) > (((proces554692349s_term @ D) @ A) > $o))))).
% 2.99/1.55 thf(sy_c_Process__Mirabelle__xovoopgpgi_OisACT__rel, type, proces896239806CT_rel: (!> [A:$tType,B:$tType,C:$tType,D:$tType]: ((((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A)) > (((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A)) > $o))))).
% 2.99/1.55 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OAction, type, proces1525233512Action: (!> [A:$tType]: ((A > ((proces634752977rocess @ A) > (proces634752977rocess @ A)))))).
% 2.99/1.55 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OChoice, type, proces1915862579Choice: (!> [A:$tType]: (((proces634752977rocess @ A) > ((proces634752977rocess @ A) > (proces634752977rocess @ A)))))).
% 2.99/1.55 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Ocase__process, type, proces1406508781rocess: (!> [A:$tType,B:$tType]: (((A > ((proces634752977rocess @ A) > B)) > (((proces634752977rocess @ A) > ((proces634752977rocess @ A) > B)) > ((proces634752977rocess @ A) > B)))))).
% 2.99/1.55 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Och1Of, type, proces979765041_ch1Of: (!> [A:$tType]: (((proces634752977rocess @ A) > (proces634752977rocess @ A))))).
% 2.99/1.55 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Och2Of, type, proces988026546_ch2Of: (!> [A:$tType]: (((proces634752977rocess @ A) > (proces634752977rocess @ A))))).
% 2.99/1.55 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OcontOf, type, proces1778668539contOf: (!> [A:$tType]: (((proces634752977rocess @ A) > (proces634752977rocess @ A))))).
% 2.99/1.55 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Ocorec__process, type, proces894737309rocess: (!> [C:$tType,A:$tType]: (((C > $o) > ((C > A) > ((C > $o) > ((C > (proces634752977rocess @ A)) > ((C > C) > ((C > $o) > ((C > (proces634752977rocess @ A)) > ((C > C) > ((C > $o) > ((C > (proces634752977rocess @ A)) > ((C > C) > (C > (proces634752977rocess @ A)))))))))))))))).
% 2.99/1.55 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OisAction, type, proces10484146Action: (!> [A:$tType]: (((proces634752977rocess @ A) > $o)))).
% 2.99/1.55 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OisChoice, type, proces401113213Choice: (!> [A:$tType]: (((proces634752977rocess @ A) > $o)))).
% 2.99/1.55 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Opred__process, type, proces1205983068rocess: (!> [A:$tType]: (((A > $o) > ((proces634752977rocess @ A) > $o))))).
% 2.99/1.55 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OprefOf, type, proces745025900prefOf: (!> [A:$tType]: (((proces634752977rocess @ A) > A)))).
% 2.99/1.55 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Orel__process, type, proces749077512rocess: (!> [A:$tType,B:$tType]: (((A > (B > $o)) > ((proces634752977rocess @ A) > ((proces634752977rocess @ B) > $o)))))).
% 2.99/1.55 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_OACT, type, proces1454156180ss_ACT: (!> [A:$tType,Pvar:$tType]: ((A > (((proces554692349s_term @ A) @ Pvar) > ((proces554692349s_term @ A) @ Pvar)))))).
% 2.99/1.55 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_OCH, type, proces89589571ess_CH: (!> [A:$tType,Pvar:$tType]: ((((proces554692349s_term @ A) @ Pvar) > (((proces554692349s_term @ A) @ Pvar) > ((proces554692349s_term @ A) @ Pvar)))))).
% 2.99/1.55 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_OPROC, type, proces1062592052s_PROC: (!> [A:$tType,Pvar:$tType]: (((proces634752977rocess @ A) > ((proces554692349s_term @ A) @ Pvar))))).
% 2.99/1.55 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_OVAR, type, proces1627516585ss_VAR: (!> [Pvar:$tType,A:$tType]: ((Pvar > ((proces554692349s_term @ A) @ Pvar))))).
% 2.99/1.55 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Ocase__process__term, type, proces460752237s_term: (!> [Pvar:$tType,B:$tType,A:$tType]: (((Pvar > B) > (((proces634752977rocess @ A) > B) > ((A > (((proces554692349s_term @ A) @ Pvar) > B)) > ((((proces554692349s_term @ A) @ Pvar) > (((proces554692349s_term @ A) @ Pvar) > B)) > (((proces554692349s_term @ A) @ Pvar) > B)))))))).
% 2.99/1.55 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Opred__process__term, type, proces2118920028s_term: (!> [A:$tType,B:$tType]: (((A > $o) > ((B > $o) > (((proces554692349s_term @ A) @ B) > $o)))))).
% 2.99/1.55 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Orec__process__term, type, proces2117273769s_term: (!> [Pvar:$tType,D:$tType,A:$tType]: (((Pvar > D) > (((proces634752977rocess @ A) > D) > ((A > (((proces554692349s_term @ A) @ Pvar) > (D > D))) > ((((proces554692349s_term @ A) @ Pvar) > (((proces554692349s_term @ A) @ Pvar) > (D > (D > D)))) > (((proces554692349s_term @ A) @ Pvar) > D)))))))).
% 2.99/1.55 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Orel__process__term, type, proces2029722208s_term: (!> [A:$tType,C:$tType,B:$tType,D:$tType]: (((A > (C > $o)) > ((B > (D > $o)) > (((proces554692349s_term @ A) @ B) > (((proces554692349s_term @ C) @ D) > $o))))))).
% 2.99/1.55 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Oset2__process__term, type, proces1493547885s_term: (!> [A:$tType,Pvar:$tType]: ((((proces554692349s_term @ A) @ Pvar) > (set @ Pvar))))).
% 2.99/1.55 thf(sy_c_Process__Mirabelle__xovoopgpgi_Osolution, type, proces1652378886lution: (!> [A:$tType,B:$tType]: (((A > ((proces554692349s_term @ B) @ A)) > (((proces554692349s_term @ B) @ A) > (proces634752977rocess @ B)))))).
% 2.99/1.55 thf(sy_c_Product__Type_OPair, type, product_Pair: (!> [A:$tType,B:$tType]: ((A > (B > ((product_prod @ A) @ B)))))).
% 2.99/1.55 thf(sy_c_Product__Type_Ocurry, type, product_curry: (!> [A:$tType,B:$tType,C:$tType]: (((((product_prod @ A) @ B) > C) > (A > (B > C)))))).
% 2.99/1.55 thf(sy_c_Product__Type_Ointernal__case__prod, type, produc2004651681e_prod: (!> [A:$tType,B:$tType,C:$tType]: (((A > (B > C)) > (((product_prod @ A) @ B) > C))))).
% 2.99/1.55 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod, type, product_rec_prod: (!> [A:$tType,B:$tType,T:$tType]: (((A > (B > T)) > (((product_prod @ A) @ B) > T))))).
% 2.99/1.55 thf(sy_c_Pure_Otype, type, type: (!> [A:$tType]: ((itself @ A)))).
% 2.99/1.55 thf(sy_c_Relation_Oinv__image, type, inv_image: (!> [B:$tType,A:$tType]: (((set @ ((product_prod @ B) @ B)) > ((A > B) > (set @ ((product_prod @ A) @ A))))))).
% 2.99/1.55 thf(sy_c_Relation_Oinv__imagep, type, inv_imagep: (!> [B:$tType,A:$tType]: (((B > (B > $o)) > ((A > B) > (A > (A > $o))))))).
% 2.99/1.55 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 2.99/1.55 thf(sy_c_Wellfounded_Oacc, type, acc: (!> [A:$tType]: (((set @ ((product_prod @ A) @ A)) > (set @ A))))).
% 2.99/1.55 thf(sy_c_Wellfounded_Oaccp, type, accp: (!> [A:$tType]: (((A > (A > $o)) > (A > $o))))).
% 2.99/1.55 thf(sy_c_Wellfounded_Olex__prod, type, lex_prod: (!> [A:$tType,B:$tType]: (((set @ ((product_prod @ A) @ A)) > ((set @ ((product_prod @ B) @ B)) > (set @ ((product_prod @ ((product_prod @ A) @ B)) @ ((product_prod @ A) @ B)))))))).
% 2.99/1.55 thf(sy_c_Wfrec_Oadm__wf, type, adm_wf: (!> [A:$tType,B:$tType]: (((set @ ((product_prod @ A) @ A)) > (((A > B) > (A > B)) > $o))))).
% 2.99/1.55 thf(sy_c_Wfrec_Ocut, type, cut: (!> [A:$tType,B:$tType]: (((A > B) > ((set @ ((product_prod @ A) @ A)) > (A > (A > B))))))).
% 2.99/1.55 thf(sy_c_Wfrec_Osame__fst, type, same_fst: (!> [A:$tType,B:$tType]: (((A > $o) > ((A > (set @ ((product_prod @ B) @ B))) > (set @ ((product_prod @ ((product_prod @ A) @ B)) @ ((product_prod @ A) @ B)))))))).
% 2.99/1.55 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 2.99/1.55 thf(sy_v_p, type, p: (proces634752977rocess @ a)).
% 2.99/1.55 thf(sy_v_p_H____, type, p2: (proces634752977rocess @ a)).
% 2.99/1.55 thf(sy_v_pa____, type, pa: (proces634752977rocess @ a)).
% 2.99/1.55 thf(sy_v_q____, type, q: (proces634752977rocess @ a)).
% 2.99/1.55 thf(sy_v_sys, type, sys: (b > ((proces554692349s_term @ a) @ b))).
% 2.99/1.55 thf(fact_0__092_060open_062isChoice_Ap_092_060close_062, axiom, ((proces401113213Choice @ a) @ pa)).
% 2.99/1.55 thf(fact_1_process__term_Oinject_I2_J, axiom, (! [Pvar:$tType,A:$tType,X2:(proces634752977rocess @ A),Y2:(proces634752977rocess @ A)]: ((((((proces1062592052s_PROC @ A) @ Pvar) @ X2) = (((proces1062592052s_PROC @ A) @ Pvar) @ Y2)) = (X2 = Y2))))).
% 2.99/1.55 thf(fact_2__092_060open_062q_A_061_Asolution_Asys_A_IPROC_Ap_J_092_060close_062, axiom, (q = ((((proces1652378886lution @ b) @ a) @ sys) @ (((proces1062592052s_PROC @ a) @ b) @ p)))).
% 2.99/1.55 thf(fact_3_isACT_Osimps_I2_J, axiom, (! [A:$tType,C:$tType,B:$tType,D:$tType,Sys:(A > ((proces554692349s_term @ B) @ C)),P:(proces634752977rocess @ D)]: ((((((((proces687458811_isACT @ A) @ B) @ C) @ D) @ Sys) @ (((proces1062592052s_PROC @ D) @ A) @ P)) = ((proces10484146Action @ D) @ P))))).
% 2.99/1.55 thf(fact_4__092_060open_062isAction_Ap_A_092_060or_062_AisChoice_Ap_092_060close_062, axiom, (((proces10484146Action @ a) @ pa) | ((proces401113213Choice @ a) @ pa))).
% 2.99/1.55 thf(fact_5_iss, axiom, (p2 = ((((proces1652378886lution @ b) @ a) @ sys) @ (((proces1062592052s_PROC @ a) @ b) @ pa)))).
% 2.99/1.55 thf(fact_6_process__term_Osimps_I22_J, axiom, (! [Pvar:$tType,D:$tType,A:$tType,F1:(Pvar > D),F2:((proces634752977rocess @ A) > D),F3:(A > (((proces554692349s_term @ A) @ Pvar) > (D > D))),F4:(((proces554692349s_term @ A) @ Pvar) > (((proces554692349s_term @ A) @ Pvar) > (D > (D > D)))),X2:(proces634752977rocess @ A)]: ((((((((((proces2117273769s_term @ Pvar) @ D) @ A) @ F1) @ F2) @ F3) @ F4) @ (((proces1062592052s_PROC @ A) @ Pvar) @ X2)) = (F2 @ X2))))).
% 2.99/1.55 thf(fact_7_process__term_Osimps_I18_J, axiom, (! [Pvar:$tType,B:$tType,A:$tType,F1:(Pvar > B),F2:((proces634752977rocess @ A) > B),F3:(A > (((proces554692349s_term @ A) @ Pvar) > B)),F4:(((proces554692349s_term @ A) @ Pvar) > (((proces554692349s_term @ A) @ Pvar) > B)),X2:(proces634752977rocess @ A)]: ((((((((((proces460752237s_term @ Pvar) @ B) @ A) @ F1) @ F2) @ F3) @ F4) @ (((proces1062592052s_PROC @ A) @ Pvar) @ X2)) = (F2 @ X2))))).
% 2.99/1.55 thf(fact_8_solution_Odisc__iff_I2_J, axiom, (! [A:$tType,B:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),T2:((proces554692349s_term @ B) @ A)]: ((((proces401113213Choice @ B) @ ((((proces1652378886lution @ A) @ B) @ Sys) @ T2)) = (~ (((((((proces687458811_isACT @ A) @ B) @ A) @ B) @ Sys) @ T2))))))).
% 2.99/1.55 thf(fact_9_solution_Odisc__iff_I1_J, axiom, (! [A:$tType,B:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),T2:((proces554692349s_term @ B) @ A)]: ((((proces10484146Action @ B) @ ((((proces1652378886lution @ A) @ B) @ Sys) @ T2)) = ((((((proces687458811_isACT @ A) @ B) @ A) @ B) @ Sys) @ T2))))).
% 2.99/1.55 thf(fact_10_solution_Odisc_I2_J, axiom, (! [A:$tType,B:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),T2:((proces554692349s_term @ B) @ A)]: (((~ (((((((proces687458811_isACT @ A) @ B) @ A) @ B) @ Sys) @ T2))) => ((proces401113213Choice @ B) @ ((((proces1652378886lution @ A) @ B) @ Sys) @ T2)))))).
% 2.99/1.55 thf(fact_11_isACT_Osimps_I3_J, axiom, (! [B:$tType,C:$tType,A:$tType,D:$tType,Sys:(A > ((proces554692349s_term @ B) @ C)),A2:D,T2:((proces554692349s_term @ D) @ A)]: (((((((proces687458811_isACT @ A) @ B) @ C) @ D) @ Sys) @ ((((proces1454156180ss_ACT @ D) @ A) @ A2) @ T2))))).
% 2.99/1.55 thf(fact_12_isACT_Osimps_I4_J, axiom, (! [B:$tType,C:$tType,A:$tType,D:$tType,Sys:(A > ((proces554692349s_term @ B) @ C)),T1:((proces554692349s_term @ D) @ A),T22:((proces554692349s_term @ D) @ A)]: ((~ (((((((proces687458811_isACT @ A) @ B) @ C) @ D) @ Sys) @ ((((proces89589571ess_CH @ D) @ A) @ T1) @ T22))))))).
% 2.99/1.55 thf(fact_13_solution_Odisc_I1_J, axiom, (! [A:$tType,B:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),T2:((proces554692349s_term @ B) @ A)]: ((((((((proces687458811_isACT @ A) @ B) @ A) @ B) @ Sys) @ T2) => ((proces10484146Action @ B) @ ((((proces1652378886lution @ A) @ B) @ Sys) @ T2)))))).
% 2.99/1.55 thf(fact_14_not__isAction__isChoice, axiom, (! [A:$tType,P:(proces634752977rocess @ A)]: ((~ ((((proces10484146Action @ A) @ P) & ((proces401113213Choice @ A) @ P))))))).
% 2.99/1.55 thf(fact_15_process__term_Oinject_I4_J, axiom, (! [Pvar:$tType,A:$tType,X41:((proces554692349s_term @ A) @ Pvar),X42:((proces554692349s_term @ A) @ Pvar),Y41:((proces554692349s_term @ A) @ Pvar),Y42:((proces554692349s_term @ A) @ Pvar)]: (((((((proces89589571ess_CH @ A) @ Pvar) @ X41) @ X42) = ((((proces89589571ess_CH @ A) @ Pvar) @ Y41) @ Y42)) = ((X41 = Y41) & (X42 = Y42)))))).
% 2.99/1.55 thf(fact_16_process__term_Oinject_I3_J, axiom, (! [Pvar:$tType,A:$tType,X31:A,X32:((proces554692349s_term @ A) @ Pvar),Y31:A,Y32:((proces554692349s_term @ A) @ Pvar)]: (((((((proces1454156180ss_ACT @ A) @ Pvar) @ X31) @ X32) = ((((proces1454156180ss_ACT @ A) @ Pvar) @ Y31) @ Y32)) = ((X31 = Y31) & (X32 = Y32)))))).
% 2.99/1.55 thf(fact_17_process__term_Osimps_I24_J, axiom, (! [D:$tType,Pvar:$tType,A:$tType,F1:(Pvar > D),F2:((proces634752977rocess @ A) > D),F3:(A > (((proces554692349s_term @ A) @ Pvar) > (D > D))),F4:(((proces554692349s_term @ A) @ Pvar) > (((proces554692349s_term @ A) @ Pvar) > (D > (D > D)))),X41:((proces554692349s_term @ A) @ Pvar),X42:((proces554692349s_term @ A) @ Pvar)]: ((((((((((proces2117273769s_term @ Pvar) @ D) @ A) @ F1) @ F2) @ F3) @ F4) @ ((((proces89589571ess_CH @ A) @ Pvar) @ X41) @ X42)) = ((((F4 @ X41) @ X42) @ ((((((((proces2117273769s_term @ Pvar) @ D) @ A) @ F1) @ F2) @ F3) @ F4) @ X41)) @ ((((((((proces2117273769s_term @ Pvar) @ D) @ A) @ F1) @ F2) @ F3) @ F4) @ X42)))))).
% 2.99/1.55 thf(fact_18_process__term_Osimps_I23_J, axiom, (! [D:$tType,Pvar:$tType,A:$tType,F1:(Pvar > D),F2:((proces634752977rocess @ A) > D),F3:(A > (((proces554692349s_term @ A) @ Pvar) > (D > D))),F4:(((proces554692349s_term @ A) @ Pvar) > (((proces554692349s_term @ A) @ Pvar) > (D > (D > D)))),X31:A,X32:((proces554692349s_term @ A) @ Pvar)]: ((((((((((proces2117273769s_term @ Pvar) @ D) @ A) @ F1) @ F2) @ F3) @ F4) @ ((((proces1454156180ss_ACT @ A) @ Pvar) @ X31) @ X32)) = (((F3 @ X31) @ X32) @ ((((((((proces2117273769s_term @ Pvar) @ D) @ A) @ F1) @ F2) @ F3) @ F4) @ X32)))))).
% 2.99/1.55 thf(fact_19_process__term_Osimps_I20_J, axiom, (! [B:$tType,Pvar:$tType,A:$tType,F1:(Pvar > B),F2:((proces634752977rocess @ A) > B),F3:(A > (((proces554692349s_term @ A) @ Pvar) > B)),F4:(((proces554692349s_term @ A) @ Pvar) > (((proces554692349s_term @ A) @ Pvar) > B)),X41:((proces554692349s_term @ A) @ Pvar),X42:((proces554692349s_term @ A) @ Pvar)]: ((((((((((proces460752237s_term @ Pvar) @ B) @ A) @ F1) @ F2) @ F3) @ F4) @ ((((proces89589571ess_CH @ A) @ Pvar) @ X41) @ X42)) = ((F4 @ X41) @ X42))))).
% 2.99/1.55 thf(fact_20_process__term_Osimps_I19_J, axiom, (! [B:$tType,Pvar:$tType,A:$tType,F1:(Pvar > B),F2:((proces634752977rocess @ A) > B),F3:(A > (((proces554692349s_term @ A) @ Pvar) > B)),F4:(((proces554692349s_term @ A) @ Pvar) > (((proces554692349s_term @ A) @ Pvar) > B)),X31:A,X32:((proces554692349s_term @ A) @ Pvar)]: ((((((((((proces460752237s_term @ Pvar) @ B) @ A) @ F1) @ F2) @ F3) @ F4) @ ((((proces1454156180ss_ACT @ A) @ Pvar) @ X31) @ X32)) = ((F3 @ X31) @ X32))))).
% 2.99/1.55 thf(fact_21_process__term_Odistinct_I11_J, axiom, (! [Pvar:$tType,A:$tType,X31:A,X32:((proces554692349s_term @ A) @ Pvar),X41:((proces554692349s_term @ A) @ Pvar),X42:((proces554692349s_term @ A) @ Pvar)]: ((((((proces1454156180ss_ACT @ A) @ Pvar) @ X31) @ X32) != ((((proces89589571ess_CH @ A) @ Pvar) @ X41) @ X42))))).
% 2.99/1.55 thf(fact_22_process__term_Ocase__distrib, axiom, (! [B:$tType,C:$tType,Pvar:$tType,A:$tType,H:(B > C),F1:(Pvar > B),F2:((proces634752977rocess @ A) > B),F3:(A > (((proces554692349s_term @ A) @ Pvar) > B)),F4:(((proces554692349s_term @ A) @ Pvar) > (((proces554692349s_term @ A) @ Pvar) > B)),Process_term:((proces554692349s_term @ A) @ Pvar)]: (((H @ ((((((((proces460752237s_term @ Pvar) @ B) @ A) @ F1) @ F2) @ F3) @ F4) @ Process_term)) = ((((((((proces460752237s_term @ Pvar) @ C) @ A) @ (^ [X:Pvar]: ((H @ (F1 @ X))))) @ (^ [X:(proces634752977rocess @ A)]: ((H @ (F2 @ X))))) @ (^ [X1:A,X22:((proces554692349s_term @ A) @ Pvar)]: ((H @ ((F3 @ X1) @ X22))))) @ (^ [X1:((proces554692349s_term @ A) @ Pvar),X22:((proces554692349s_term @ A) @ Pvar)]: ((H @ ((F4 @ X1) @ X22))))) @ Process_term))))).
% 2.99/1.55 thf(fact_23_process_Oexhaust__disc, axiom, (! [A:$tType,Process:(proces634752977rocess @ A)]: (((~ (((proces10484146Action @ A) @ Process))) => ((proces401113213Choice @ A) @ Process))))).
% 2.99/1.55 thf(fact_24_isAction__isChoice, axiom, (! [A:$tType,P:(proces634752977rocess @ A)]: ((((proces10484146Action @ A) @ P) | ((proces401113213Choice @ A) @ P))))).
% 2.99/1.55 thf(fact_25_process_Odistinct__disc_I1_J, axiom, (! [A:$tType,Process:(proces634752977rocess @ A)]: ((((proces10484146Action @ A) @ Process) => (~ (((proces401113213Choice @ A) @ Process))))))).
% 2.99/1.55 thf(fact_26_process_Odistinct__disc_I2_J, axiom, (! [A:$tType,Process:(proces634752977rocess @ A)]: ((((proces401113213Choice @ A) @ Process) => (~ (((proces10484146Action @ A) @ Process))))))).
% 2.99/1.55 thf(fact_27_process__term_Odistinct_I9_J, axiom, (! [Pvar:$tType,A:$tType,X2:(proces634752977rocess @ A),X41:((proces554692349s_term @ A) @ Pvar),X42:((proces554692349s_term @ A) @ Pvar)]: (((((proces1062592052s_PROC @ A) @ Pvar) @ X2) != ((((proces89589571ess_CH @ A) @ Pvar) @ X41) @ X42))))).
% 2.99/1.55 thf(fact_28_process__term_Odistinct_I7_J, axiom, (! [Pvar:$tType,A:$tType,X2:(proces634752977rocess @ A),X31:A,X32:((proces554692349s_term @ A) @ Pvar)]: (((((proces1062592052s_PROC @ A) @ Pvar) @ X2) != ((((proces1454156180ss_ACT @ A) @ Pvar) @ X31) @ X32))))).
% 2.99/1.55 thf(fact_29_isACT_Oelims_I1_J, axiom, (! [D:$tType,A:$tType,B:$tType,C:$tType,X3:(A > ((proces554692349s_term @ B) @ C)),Xa:((proces554692349s_term @ D) @ A),Y:$o]: (((((((((proces687458811_isACT @ A) @ B) @ C) @ D) @ X3) @ Xa) = Y) => ((! [X4:A]: (((Xa = (((proces1627516585ss_VAR @ A) @ D) @ X4)) => (Y = (~ (((((((((proces460752237s_term @ C) @ $o) @ B) @ (^ [Pvar2:C]: ($false))) @ (proces10484146Action @ B)) @ (^ [A3:B,T3:((proces554692349s_term @ B) @ C)]: ($true))) @ (^ [Process_term1:((proces554692349s_term @ B) @ C),Process_term2:((proces554692349s_term @ B) @ C)]: ($false))) @ (X3 @ X4)))))))) => ((! [P2:(proces634752977rocess @ D)]: (((Xa = (((proces1062592052s_PROC @ D) @ A) @ P2)) => (Y = (~ (((proces10484146Action @ D) @ P2))))))) => (((? [A4:D,T4:((proces554692349s_term @ D) @ A)]: ((Xa = ((((proces1454156180ss_ACT @ D) @ A) @ A4) @ T4)))) => (~ (Y))) => (~ (((? [T12:((proces554692349s_term @ D) @ A),T23:((proces554692349s_term @ D) @ A)]: ((Xa = ((((proces89589571ess_CH @ D) @ A) @ T12) @ T23)))) => Y)))))))))).
% 2.99/1.55 thf(fact_30_isACT_Oelims_I2_J, axiom, (! [C:$tType,B:$tType,A:$tType,D:$tType,X3:(A > ((proces554692349s_term @ B) @ C)),Xa:((proces554692349s_term @ D) @ A)]: ((((((((proces687458811_isACT @ A) @ B) @ C) @ D) @ X3) @ Xa) => ((! [X4:A]: (((Xa = (((proces1627516585ss_VAR @ A) @ D) @ X4)) => (~ (((((((((proces460752237s_term @ C) @ $o) @ B) @ (^ [Pvar2:C]: ($false))) @ (proces10484146Action @ B)) @ (^ [A3:B,T3:((proces554692349s_term @ B) @ C)]: ($true))) @ (^ [Process_term1:((proces554692349s_term @ B) @ C),Process_term2:((proces554692349s_term @ B) @ C)]: ($false))) @ (X3 @ X4))))))) => ((! [P2:(proces634752977rocess @ D)]: (((Xa = (((proces1062592052s_PROC @ D) @ A) @ P2)) => (~ (((proces10484146Action @ D) @ P2)))))) => (~ ((! [A4:D,T4:((proces554692349s_term @ D) @ A)]: ((Xa != ((((proces1454156180ss_ACT @ D) @ A) @ A4) @ T4)))))))))))).
% 2.99/1.55 thf(fact_31_isACT_Oelims_I3_J, axiom, (! [C:$tType,B:$tType,A:$tType,D:$tType,X3:(A > ((proces554692349s_term @ B) @ C)),Xa:((proces554692349s_term @ D) @ A)]: (((~ (((((((proces687458811_isACT @ A) @ B) @ C) @ D) @ X3) @ Xa))) => ((! [X4:A]: (((Xa = (((proces1627516585ss_VAR @ A) @ D) @ X4)) => ((((((((proces460752237s_term @ C) @ $o) @ B) @ (^ [Pvar2:C]: ($false))) @ (proces10484146Action @ B)) @ (^ [A3:B,T3:((proces554692349s_term @ B) @ C)]: ($true))) @ (^ [Process_term1:((proces554692349s_term @ B) @ C),Process_term2:((proces554692349s_term @ B) @ C)]: ($false))) @ (X3 @ X4))))) => ((! [P2:(proces634752977rocess @ D)]: (((Xa = (((proces1062592052s_PROC @ D) @ A) @ P2)) => ((proces10484146Action @ D) @ P2)))) => (~ ((! [T12:((proces554692349s_term @ D) @ A),T23:((proces554692349s_term @ D) @ A)]: ((Xa != ((((proces89589571ess_CH @ D) @ A) @ T12) @ T23)))))))))))).
% 2.99/1.55 thf(fact_32_CH2_Oinduct, axiom, (! [A:$tType,B:$tType,P3:((A > ((proces554692349s_term @ B) @ A)) > (((proces554692349s_term @ B) @ A) > $o)),A0:(A > ((proces554692349s_term @ B) @ A)),A1:((proces554692349s_term @ B) @ A)]: (((! [Sys2:(A > ((proces554692349s_term @ B) @ A)),X4:A]: (((P3 @ Sys2) @ (((proces1627516585ss_VAR @ A) @ B) @ X4)))) => ((! [Sys2:(A > ((proces554692349s_term @ B) @ A)),P2:(proces634752977rocess @ B)]: (((P3 @ Sys2) @ (((proces1062592052s_PROC @ B) @ A) @ P2)))) => ((! [Sys2:(A > ((proces554692349s_term @ B) @ A)),T12:((proces554692349s_term @ B) @ A),T23:((proces554692349s_term @ B) @ A)]: (((P3 @ Sys2) @ ((((proces89589571ess_CH @ B) @ A) @ T12) @ T23)))) => ((! [A4:(A > ((proces554692349s_term @ B) @ A)),V:B,Va:((proces554692349s_term @ B) @ A)]: (((P3 @ A4) @ ((((proces1454156180ss_ACT @ B) @ A) @ V) @ Va)))) => ((P3 @ A0) @ A1)))))))).
% 2.99/1.55 thf(fact_33_CONT_Oinduct, axiom, (! [A:$tType,B:$tType,P3:((A > ((proces554692349s_term @ B) @ A)) > (((proces554692349s_term @ B) @ A) > $o)),A0:(A > ((proces554692349s_term @ B) @ A)),A1:((proces554692349s_term @ B) @ A)]: (((! [Sys2:(A > ((proces554692349s_term @ B) @ A)),X4:A]: (((P3 @ Sys2) @ (((proces1627516585ss_VAR @ A) @ B) @ X4)))) => ((! [Sys2:(A > ((proces554692349s_term @ B) @ A)),P2:(proces634752977rocess @ B)]: (((P3 @ Sys2) @ (((proces1062592052s_PROC @ B) @ A) @ P2)))) => ((! [Sys2:(A > ((proces554692349s_term @ B) @ A)),A4:B,T4:((proces554692349s_term @ B) @ A)]: (((P3 @ Sys2) @ ((((proces1454156180ss_ACT @ B) @ A) @ A4) @ T4)))) => ((! [A4:(A > ((proces554692349s_term @ B) @ A)),V:((proces554692349s_term @ B) @ A),Va:((proces554692349s_term @ B) @ A)]: (((P3 @ A4) @ ((((proces89589571ess_CH @ B) @ A) @ V) @ Va)))) => ((P3 @ A0) @ A1)))))))).
% 2.99/1.55 thf(fact_34_PREF_Oinduct, axiom, (! [C:$tType,A:$tType,B:$tType,P3:((A > ((proces554692349s_term @ B) @ C)) > (((proces554692349s_term @ B) @ A) > $o)),A0:(A > ((proces554692349s_term @ B) @ C)),A1:((proces554692349s_term @ B) @ A)]: (((! [Sys2:(A > ((proces554692349s_term @ B) @ C)),X4:A]: (((P3 @ Sys2) @ (((proces1627516585ss_VAR @ A) @ B) @ X4)))) => ((! [Sys2:(A > ((proces554692349s_term @ B) @ C)),P2:(proces634752977rocess @ B)]: (((P3 @ Sys2) @ (((proces1062592052s_PROC @ B) @ A) @ P2)))) => ((! [Sys2:(A > ((proces554692349s_term @ B) @ C)),A4:B,T4:((proces554692349s_term @ B) @ A)]: (((P3 @ Sys2) @ ((((proces1454156180ss_ACT @ B) @ A) @ A4) @ T4)))) => ((! [A4:(A > ((proces554692349s_term @ B) @ C)),V:((proces554692349s_term @ B) @ A),Va:((proces554692349s_term @ B) @ A)]: (((P3 @ A4) @ ((((proces89589571ess_CH @ B) @ A) @ V) @ Va)))) => ((P3 @ A0) @ A1)))))))).
% 2.99/1.55 thf(fact_35_isACT_Oinduct, axiom, (! [B:$tType,C:$tType,A:$tType,D:$tType,P3:((A > ((proces554692349s_term @ B) @ C)) > (((proces554692349s_term @ D) @ A) > $o)),A0:(A > ((proces554692349s_term @ B) @ C)),A1:((proces554692349s_term @ D) @ A)]: (((! [Sys2:(A > ((proces554692349s_term @ B) @ C)),X4:A]: (((P3 @ Sys2) @ (((proces1627516585ss_VAR @ A) @ D) @ X4)))) => ((! [Sys2:(A > ((proces554692349s_term @ B) @ C)),P2:(proces634752977rocess @ D)]: (((P3 @ Sys2) @ (((proces1062592052s_PROC @ D) @ A) @ P2)))) => ((! [Sys2:(A > ((proces554692349s_term @ B) @ C)),A4:D,T4:((proces554692349s_term @ D) @ A)]: (((P3 @ Sys2) @ ((((proces1454156180ss_ACT @ D) @ A) @ A4) @ T4)))) => ((! [Sys2:(A > ((proces554692349s_term @ B) @ C)),T12:((proces554692349s_term @ D) @ A),T23:((proces554692349s_term @ D) @ A)]: (((P3 @ Sys2) @ ((((proces89589571ess_CH @ D) @ A) @ T12) @ T23)))) => ((P3 @ A0) @ A1)))))))).
% 2.99/1.55 thf(fact_36_process__term_Oinduct, axiom, (! [Pvar:$tType,A:$tType,P3:(((proces554692349s_term @ A) @ Pvar) > $o),Process_term:((proces554692349s_term @ A) @ Pvar)]: (((! [X5:Pvar]: ((P3 @ (((proces1627516585ss_VAR @ Pvar) @ A) @ X5)))) => ((! [X5:(proces634752977rocess @ A)]: ((P3 @ (((proces1062592052s_PROC @ A) @ Pvar) @ X5)))) => ((! [X1a:A,X2a:((proces554692349s_term @ A) @ Pvar)]: (((P3 @ X2a) => (P3 @ ((((proces1454156180ss_ACT @ A) @ Pvar) @ X1a) @ X2a))))) => ((! [X1a:((proces554692349s_term @ A) @ Pvar),X2a:((proces554692349s_term @ A) @ Pvar)]: (((P3 @ X1a) => ((P3 @ X2a) => (P3 @ ((((proces89589571ess_CH @ A) @ Pvar) @ X1a) @ X2a)))))) => (P3 @ Process_term)))))))).
% 2.99/1.55 thf(fact_37_process__term_Oexhaust, axiom, (! [Pvar:$tType,A:$tType,Y:((proces554692349s_term @ A) @ Pvar)]: (((! [X12:Pvar]: ((Y != (((proces1627516585ss_VAR @ Pvar) @ A) @ X12)))) => ((! [X23:(proces634752977rocess @ A)]: ((Y != (((proces1062592052s_PROC @ A) @ Pvar) @ X23)))) => ((! [X312:A,X322:((proces554692349s_term @ A) @ Pvar)]: ((Y != ((((proces1454156180ss_ACT @ A) @ Pvar) @ X312) @ X322)))) => (~ ((! [X412:((proces554692349s_term @ A) @ Pvar),X422:((proces554692349s_term @ A) @ Pvar)]: ((Y != ((((proces89589571ess_CH @ A) @ Pvar) @ X412) @ X422)))))))))))).
% 2.99/1.55 thf(fact_38_isACT_Osimps_I1_J, axiom, (! [D:$tType,B:$tType,C:$tType,A:$tType,Sys:(A > ((proces554692349s_term @ B) @ C)),X6:A]: ((((((((proces687458811_isACT @ A) @ B) @ C) @ D) @ Sys) @ (((proces1627516585ss_VAR @ A) @ D) @ X6)) = ((((((((proces460752237s_term @ C) @ $o) @ B) @ (^ [Pvar2:C]: ($false))) @ (proces10484146Action @ B)) @ (^ [A3:B,T3:((proces554692349s_term @ B) @ C)]: ($true))) @ (^ [Process_term1:((proces554692349s_term @ B) @ C),Process_term2:((proces554692349s_term @ B) @ C)]: ($false))) @ (Sys @ X6)))))).
% 2.99/1.55 thf(fact_39_process__term_Oinject_I1_J, axiom, (! [A:$tType,Pvar:$tType,X13:Pvar,Y1:Pvar]: ((((((proces1627516585ss_VAR @ Pvar) @ A) @ X13) = (((proces1627516585ss_VAR @ Pvar) @ A) @ Y1)) = (X13 = Y1))))).
% 2.99/1.55 thf(fact_40_process__term_Odistinct_I1_J, axiom, (! [Pvar:$tType,A:$tType,X13:Pvar,X2:(proces634752977rocess @ A)]: (((((proces1627516585ss_VAR @ Pvar) @ A) @ X13) != (((proces1062592052s_PROC @ A) @ Pvar) @ X2))))).
% 2.99/1.55 thf(fact_41_process__term_Odistinct_I5_J, axiom, (! [Pvar:$tType,A:$tType,X13:Pvar,X41:((proces554692349s_term @ A) @ Pvar),X42:((proces554692349s_term @ A) @ Pvar)]: (((((proces1627516585ss_VAR @ Pvar) @ A) @ X13) != ((((proces89589571ess_CH @ A) @ Pvar) @ X41) @ X42))))).
% 2.99/1.55 thf(fact_42_process__term_Odistinct_I3_J, axiom, (! [Pvar:$tType,A:$tType,X13:Pvar,X31:A,X32:((proces554692349s_term @ A) @ Pvar)]: (((((proces1627516585ss_VAR @ Pvar) @ A) @ X13) != ((((proces1454156180ss_ACT @ A) @ Pvar) @ X31) @ X32))))).
% 2.99/1.55 thf(fact_43_process__term_Osimps_I17_J, axiom, (! [A:$tType,B:$tType,Pvar:$tType,F1:(Pvar > B),F2:((proces634752977rocess @ A) > B),F3:(A > (((proces554692349s_term @ A) @ Pvar) > B)),F4:(((proces554692349s_term @ A) @ Pvar) > (((proces554692349s_term @ A) @ Pvar) > B)),X13:Pvar]: ((((((((((proces460752237s_term @ Pvar) @ B) @ A) @ F1) @ F2) @ F3) @ F4) @ (((proces1627516585ss_VAR @ Pvar) @ A) @ X13)) = (F1 @ X13))))).
% 2.99/1.55 thf(fact_44_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P3:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P3)) = (P3 @ A2))))).
% 2.99/1.55 thf(fact_45_Collect__mem__eq, axiom, (! [A:$tType,A5:(set @ A)]: ((((collect @ A) @ (^ [X:A]: ((((member @ A) @ X) @ A5)))) = A5)))).
% 2.99/1.55 thf(fact_46_Collect__cong, axiom, (! [A:$tType,P3:(A > $o),Q:(A > $o)]: (((! [X5:A]: (((P3 @ X5) = (Q @ X5)))) => (((collect @ A) @ P3) = ((collect @ A) @ Q)))))).
% 2.99/1.55 thf(fact_47_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G:(A > B)]: (((! [X5:A]: (((F @ X5) = (G @ X5)))) => (F = G))))).
% 2.99/1.55 thf(fact_48_process__term_Osimps_I21_J, axiom, (! [A:$tType,D:$tType,Pvar:$tType,F1:(Pvar > D),F2:((proces634752977rocess @ A) > D),F3:(A > (((proces554692349s_term @ A) @ Pvar) > (D > D))),F4:(((proces554692349s_term @ A) @ Pvar) > (((proces554692349s_term @ A) @ Pvar) > (D > (D > D)))),X13:Pvar]: ((((((((((proces2117273769s_term @ Pvar) @ D) @ A) @ F1) @ F2) @ F3) @ F4) @ (((proces1627516585ss_VAR @ Pvar) @ A) @ X13)) = (F1 @ X13))))).
% 2.99/1.55 thf(fact_49_solution__VAR, axiom, (! [B:$tType,A:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),X6:A]: ((((((proces1121166967uarded @ A) @ B) @ A) @ Sys) => (((((proces1652378886lution @ A) @ B) @ Sys) @ (((proces1627516585ss_VAR @ A) @ B) @ X6)) = ((((proces1652378886lution @ A) @ B) @ Sys) @ (Sys @ X6))))))).
% 2.99/1.55 thf(fact_50_isACT__VAR, axiom, (! [C:$tType,B:$tType,A:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),X6:A]: ((((((proces1121166967uarded @ A) @ B) @ A) @ Sys) => (((((((proces687458811_isACT @ A) @ B) @ A) @ C) @ Sys) @ (((proces1627516585ss_VAR @ A) @ C) @ X6)) = ((((((proces687458811_isACT @ A) @ B) @ A) @ B) @ Sys) @ (Sys @ X6))))))).
% 2.99/1.55 thf(fact_51_isACT_Ocases, axiom, (! [B:$tType,C:$tType,A:$tType,D:$tType,X3:((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A))]: (((! [Sys2:(A > ((proces554692349s_term @ B) @ C)),X4:A]: ((X3 != ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A)) @ Sys2) @ (((proces1627516585ss_VAR @ A) @ D) @ X4))))) => ((! [Sys2:(A > ((proces554692349s_term @ B) @ C)),P2:(proces634752977rocess @ D)]: ((X3 != ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A)) @ Sys2) @ (((proces1062592052s_PROC @ D) @ A) @ P2))))) => ((! [Sys2:(A > ((proces554692349s_term @ B) @ C)),A4:D,T4:((proces554692349s_term @ D) @ A)]: ((X3 != ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A)) @ Sys2) @ ((((proces1454156180ss_ACT @ D) @ A) @ A4) @ T4))))) => (~ ((! [Sys2:(A > ((proces554692349s_term @ B) @ C)),T12:((proces554692349s_term @ D) @ A),T23:((proces554692349s_term @ D) @ A)]: ((X3 != ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A)) @ Sys2) @ ((((proces89589571ess_CH @ D) @ A) @ T12) @ T23))))))))))))).
% 2.99/1.55 thf(fact_52_PREF_Ocases, axiom, (! [C:$tType,A:$tType,B:$tType,X3:((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ B) @ A))]: (((! [Sys2:(A > ((proces554692349s_term @ B) @ C)),X4:A]: ((X3 != ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ B) @ A)) @ Sys2) @ (((proces1627516585ss_VAR @ A) @ B) @ X4))))) => ((! [Sys2:(A > ((proces554692349s_term @ B) @ C)),P2:(proces634752977rocess @ B)]: ((X3 != ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ B) @ A)) @ Sys2) @ (((proces1062592052s_PROC @ B) @ A) @ P2))))) => ((! [Sys2:(A > ((proces554692349s_term @ B) @ C)),A4:B,T4:((proces554692349s_term @ B) @ A)]: ((X3 != ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ B) @ A)) @ Sys2) @ ((((proces1454156180ss_ACT @ B) @ A) @ A4) @ T4))))) => (~ ((! [A4:(A > ((proces554692349s_term @ B) @ C)),V:((proces554692349s_term @ B) @ A),Va:((proces554692349s_term @ B) @ A)]: ((X3 != ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ B) @ A)) @ A4) @ ((((proces89589571ess_CH @ B) @ A) @ V) @ Va))))))))))))).
% 2.99/1.55 thf(fact_53_CONT_Ocases, axiom, (! [A:$tType,B:$tType,X3:((product_prod @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A))]: (((! [Sys2:(A > ((proces554692349s_term @ B) @ A)),X4:A]: ((X3 != ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ Sys2) @ (((proces1627516585ss_VAR @ A) @ B) @ X4))))) => ((! [Sys2:(A > ((proces554692349s_term @ B) @ A)),P2:(proces634752977rocess @ B)]: ((X3 != ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ Sys2) @ (((proces1062592052s_PROC @ B) @ A) @ P2))))) => ((! [Sys2:(A > ((proces554692349s_term @ B) @ A)),A4:B,T4:((proces554692349s_term @ B) @ A)]: ((X3 != ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ Sys2) @ ((((proces1454156180ss_ACT @ B) @ A) @ A4) @ T4))))) => (~ ((! [A4:(A > ((proces554692349s_term @ B) @ A)),V:((proces554692349s_term @ B) @ A),Va:((proces554692349s_term @ B) @ A)]: ((X3 != ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ A4) @ ((((proces89589571ess_CH @ B) @ A) @ V) @ Va))))))))))))).
% 2.99/1.55 thf(fact_54_CH2_Ocases, axiom, (! [A:$tType,B:$tType,X3:((product_prod @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A))]: (((! [Sys2:(A > ((proces554692349s_term @ B) @ A)),X4:A]: ((X3 != ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ Sys2) @ (((proces1627516585ss_VAR @ A) @ B) @ X4))))) => ((! [Sys2:(A > ((proces554692349s_term @ B) @ A)),P2:(proces634752977rocess @ B)]: ((X3 != ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ Sys2) @ (((proces1062592052s_PROC @ B) @ A) @ P2))))) => ((! [Sys2:(A > ((proces554692349s_term @ B) @ A)),T12:((proces554692349s_term @ B) @ A),T23:((proces554692349s_term @ B) @ A)]: ((X3 != ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ Sys2) @ ((((proces89589571ess_CH @ B) @ A) @ T12) @ T23))))) => (~ ((! [A4:(A > ((proces554692349s_term @ B) @ A)),V:B,Va:((proces554692349s_term @ B) @ A)]: ((X3 != ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ A4) @ ((((proces1454156180ss_ACT @ B) @ A) @ V) @ Va))))))))))))).
% 2.99/1.55 thf(fact_55_process__term_Oset__cases_I2_J, axiom, (! [Pvar:$tType,A:$tType,E:Pvar,A2:((proces554692349s_term @ A) @ Pvar)]: (((((member @ Pvar) @ E) @ (((proces1493547885s_term @ A) @ Pvar) @ A2)) => ((A2 != (((proces1627516585ss_VAR @ Pvar) @ A) @ E)) => ((! [Z1:A,Z2:((proces554692349s_term @ A) @ Pvar)]: (((A2 = ((((proces1454156180ss_ACT @ A) @ Pvar) @ Z1) @ Z2)) => (~ ((((member @ Pvar) @ E) @ (((proces1493547885s_term @ A) @ Pvar) @ Z2))))))) => ((! [Z1:((proces554692349s_term @ A) @ Pvar)]: (((? [Z2:((proces554692349s_term @ A) @ Pvar)]: ((A2 = ((((proces89589571ess_CH @ A) @ Pvar) @ Z1) @ Z2)))) => (~ ((((member @ Pvar) @ E) @ (((proces1493547885s_term @ A) @ Pvar) @ Z1))))))) => (~ ((! [Z1:((proces554692349s_term @ A) @ Pvar),Z2:((proces554692349s_term @ A) @ Pvar)]: (((A2 = ((((proces89589571ess_CH @ A) @ Pvar) @ Z1) @ Z2)) => (~ ((((member @ Pvar) @ E) @ (((proces1493547885s_term @ A) @ Pvar) @ Z2)))))))))))))))).
% 2.99/1.55 thf(fact_56_guarded__def, axiom, (! [C:$tType,B:$tType,A:$tType]: (((((proces1121166967uarded @ A) @ B) @ C) = (^ [Sys3:(A > ((proces554692349s_term @ B) @ C))]: ((! [X7:A,Y3:C]: (((Sys3 @ X7) != (((proces1627516585ss_VAR @ C) @ B) @ Y3)))))))))).
% 2.99/1.55 thf(fact_57_process__term_Oset__intros_I6_J, axiom, (! [A:$tType,Pvar:$tType,Ab:Pvar]: ((((member @ Pvar) @ Ab) @ (((proces1493547885s_term @ A) @ Pvar) @ (((proces1627516585ss_VAR @ Pvar) @ A) @ Ab)))))).
% 2.99/1.55 thf(fact_58_process__term_Oset__intros_I9_J, axiom, (! [Pvar:$tType,A:$tType,Xm:Pvar,A2c:((proces554692349s_term @ A) @ Pvar),A1c:((proces554692349s_term @ A) @ Pvar)]: (((((member @ Pvar) @ Xm) @ (((proces1493547885s_term @ A) @ Pvar) @ A2c)) => (((member @ Pvar) @ Xm) @ (((proces1493547885s_term @ A) @ Pvar) @ ((((proces89589571ess_CH @ A) @ Pvar) @ A1c) @ A2c))))))).
% 2.99/1.55 thf(fact_59_process__term_Oset__intros_I8_J, axiom, (! [Pvar:$tType,A:$tType,Xk:Pvar,A1c:((proces554692349s_term @ A) @ Pvar),A2c:((proces554692349s_term @ A) @ Pvar)]: (((((member @ Pvar) @ Xk) @ (((proces1493547885s_term @ A) @ Pvar) @ A1c)) => (((member @ Pvar) @ Xk) @ (((proces1493547885s_term @ A) @ Pvar) @ ((((proces89589571ess_CH @ A) @ Pvar) @ A1c) @ A2c))))))).
% 2.99/1.55 thf(fact_60_process__term_Osimps_I51_J, axiom, (! [Pvar:$tType,A:$tType,X31:A,X32:((proces554692349s_term @ A) @ Pvar)]: (((((proces1493547885s_term @ A) @ Pvar) @ ((((proces1454156180ss_ACT @ A) @ Pvar) @ X31) @ X32)) = (((proces1493547885s_term @ A) @ Pvar) @ X32))))).
% 2.99/1.55 thf(fact_61_process__term_Oset__intros_I7_J, axiom, (! [Pvar:$tType,A:$tType,Xi:Pvar,A2b:((proces554692349s_term @ A) @ Pvar),A1b:A]: (((((member @ Pvar) @ Xi) @ (((proces1493547885s_term @ A) @ Pvar) @ A2b)) => (((member @ Pvar) @ Xi) @ (((proces1493547885s_term @ A) @ Pvar) @ ((((proces1454156180ss_ACT @ A) @ Pvar) @ A1b) @ A2b))))))).
% 2.99/1.55 thf(fact_62_prod_Oinject, axiom, (! [A:$tType,B:$tType,X13:A,X2:B,Y1:A,Y2:B]: (((((((product_Pair @ A) @ B) @ X13) @ X2) = ((((product_Pair @ A) @ B) @ Y1) @ Y2)) = ((X13 = Y1) & (X2 = Y2)))))).
% 2.99/1.55 thf(fact_63_old_Oprod_Oinject, axiom, (! [A:$tType,B:$tType,A2:A,B2:B,A6:A,B3:B]: (((((((product_Pair @ A) @ B) @ A2) @ B2) = ((((product_Pair @ A) @ B) @ A6) @ B3)) = ((A2 = A6) & (B2 = B3)))))).
% 2.99/1.55 thf(fact_64_isACT_Opelims_I1_J, axiom, (! [B:$tType,C:$tType,A:$tType,D:$tType,X3:(A > ((proces554692349s_term @ B) @ C)),Xa:((proces554692349s_term @ D) @ A),Y:$o]: (((((((((proces687458811_isACT @ A) @ B) @ C) @ D) @ X3) @ Xa) = Y) => ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A))) @ ((((proces896239806CT_rel @ A) @ B) @ C) @ D)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A)) @ X3) @ Xa)) => ((! [X4:A]: (((Xa = (((proces1627516585ss_VAR @ A) @ D) @ X4)) => ((Y = ((((((((proces460752237s_term @ C) @ $o) @ B) @ (^ [Pvar2:C]: ($false))) @ (proces10484146Action @ B)) @ (^ [A3:B,T3:((proces554692349s_term @ B) @ C)]: ($true))) @ (^ [Process_term1:((proces554692349s_term @ B) @ C),Process_term2:((proces554692349s_term @ B) @ C)]: ($false))) @ (X3 @ X4))) => (~ ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A))) @ ((((proces896239806CT_rel @ A) @ B) @ C) @ D)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A)) @ X3) @ (((proces1627516585ss_VAR @ A) @ D) @ X4))))))))) => ((! [P2:(proces634752977rocess @ D)]: (((Xa = (((proces1062592052s_PROC @ D) @ A) @ P2)) => ((Y = ((proces10484146Action @ D) @ P2)) => (~ ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A))) @ ((((proces896239806CT_rel @ A) @ B) @ C) @ D)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A)) @ X3) @ (((proces1062592052s_PROC @ D) @ A) @ P2))))))))) => ((! [A4:D,T4:((proces554692349s_term @ D) @ A)]: (((Xa = ((((proces1454156180ss_ACT @ D) @ A) @ A4) @ T4)) => (Y => (~ ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A))) @ ((((proces896239806CT_rel @ A) @ B) @ C) @ D)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A)) @ X3) @ ((((proces1454156180ss_ACT @ D) @ A) @ A4) @ T4))))))))) => (~ ((! [T12:((proces554692349s_term @ D) @ A),T23:((proces554692349s_term @ D) @ A)]: (((Xa = ((((proces89589571ess_CH @ D) @ A) @ T12) @ T23)) => ((~ (Y)) => (~ ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A))) @ ((((proces896239806CT_rel @ A) @ B) @ C) @ D)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A)) @ X3) @ ((((proces89589571ess_CH @ D) @ A) @ T12) @ T23))))))))))))))))))).
% 2.99/1.55 thf(fact_65_isACT_Opelims_I2_J, axiom, (! [B:$tType,C:$tType,A:$tType,D:$tType,X3:(A > ((proces554692349s_term @ B) @ C)),Xa:((proces554692349s_term @ D) @ A)]: ((((((((proces687458811_isACT @ A) @ B) @ C) @ D) @ X3) @ Xa) => ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A))) @ ((((proces896239806CT_rel @ A) @ B) @ C) @ D)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A)) @ X3) @ Xa)) => ((! [X4:A]: (((Xa = (((proces1627516585ss_VAR @ A) @ D) @ X4)) => ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A))) @ ((((proces896239806CT_rel @ A) @ B) @ C) @ D)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A)) @ X3) @ (((proces1627516585ss_VAR @ A) @ D) @ X4))) => (~ (((((((((proces460752237s_term @ C) @ $o) @ B) @ (^ [Pvar2:C]: ($false))) @ (proces10484146Action @ B)) @ (^ [A3:B,T3:((proces554692349s_term @ B) @ C)]: ($true))) @ (^ [Process_term1:((proces554692349s_term @ B) @ C),Process_term2:((proces554692349s_term @ B) @ C)]: ($false))) @ (X3 @ X4)))))))) => ((! [P2:(proces634752977rocess @ D)]: (((Xa = (((proces1062592052s_PROC @ D) @ A) @ P2)) => ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A))) @ ((((proces896239806CT_rel @ A) @ B) @ C) @ D)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A)) @ X3) @ (((proces1062592052s_PROC @ D) @ A) @ P2))) => (~ (((proces10484146Action @ D) @ P2))))))) => (~ ((! [A4:D,T4:((proces554692349s_term @ D) @ A)]: (((Xa = ((((proces1454156180ss_ACT @ D) @ A) @ A4) @ T4)) => (~ ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A))) @ ((((proces896239806CT_rel @ A) @ B) @ C) @ D)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A)) @ X3) @ ((((proces1454156180ss_ACT @ D) @ A) @ A4) @ T4))))))))))))))))).
% 2.99/1.55 thf(fact_66_isACT_Opelims_I3_J, axiom, (! [B:$tType,C:$tType,A:$tType,D:$tType,X3:(A > ((proces554692349s_term @ B) @ C)),Xa:((proces554692349s_term @ D) @ A)]: (((~ (((((((proces687458811_isACT @ A) @ B) @ C) @ D) @ X3) @ Xa))) => ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A))) @ ((((proces896239806CT_rel @ A) @ B) @ C) @ D)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A)) @ X3) @ Xa)) => ((! [X4:A]: (((Xa = (((proces1627516585ss_VAR @ A) @ D) @ X4)) => ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A))) @ ((((proces896239806CT_rel @ A) @ B) @ C) @ D)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A)) @ X3) @ (((proces1627516585ss_VAR @ A) @ D) @ X4))) => ((((((((proces460752237s_term @ C) @ $o) @ B) @ (^ [Pvar2:C]: ($false))) @ (proces10484146Action @ B)) @ (^ [A3:B,T3:((proces554692349s_term @ B) @ C)]: ($true))) @ (^ [Process_term1:((proces554692349s_term @ B) @ C),Process_term2:((proces554692349s_term @ B) @ C)]: ($false))) @ (X3 @ X4)))))) => ((! [P2:(proces634752977rocess @ D)]: (((Xa = (((proces1062592052s_PROC @ D) @ A) @ P2)) => ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A))) @ ((((proces896239806CT_rel @ A) @ B) @ C) @ D)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A)) @ X3) @ (((proces1062592052s_PROC @ D) @ A) @ P2))) => ((proces10484146Action @ D) @ P2))))) => (~ ((! [T12:((proces554692349s_term @ D) @ A),T23:((proces554692349s_term @ D) @ A)]: (((Xa = ((((proces89589571ess_CH @ D) @ A) @ T12) @ T23)) => (~ ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A))) @ ((((proces896239806CT_rel @ A) @ B) @ C) @ D)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A)) @ X3) @ ((((proces89589571ess_CH @ D) @ A) @ T12) @ T23))))))))))))))))).
% 2.99/1.55 thf(fact_67_pred__equals__eq2, axiom, (! [B:$tType,A:$tType,R:(set @ ((product_prod @ A) @ B)),S:(set @ ((product_prod @ A) @ B))]: ((((^ [X:A,Y4:B]: ((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X) @ Y4)) @ R))) = (^ [X:A,Y4:B]: ((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X) @ Y4)) @ S)))) = (R = S))))).
% 2.99/1.55 thf(fact_68_surj__pair, axiom, (! [A:$tType,B:$tType,P:((product_prod @ A) @ B)]: ((? [X5:A,Y5:B]: ((P = ((((product_Pair @ A) @ B) @ X5) @ Y5))))))).
% 2.99/1.55 thf(fact_69_old_Oprod_Oinducts, axiom, (! [B:$tType,A:$tType,P3:(((product_prod @ A) @ B) > $o),Prod:((product_prod @ A) @ B)]: (((! [A4:A,B4:B]: ((P3 @ ((((product_Pair @ A) @ B) @ A4) @ B4)))) => (P3 @ Prod))))).
% 2.99/1.55 thf(fact_70_old_Oprod_Oexhaust, axiom, (! [A:$tType,B:$tType,Y:((product_prod @ A) @ B)]: ((~ ((! [A4:A,B4:B]: ((Y != ((((product_Pair @ A) @ B) @ A4) @ B4))))))))).
% 2.99/1.55 thf(fact_71_prod__induct7, axiom, (! [G2:$tType,F5:$tType,E2:$tType,D:$tType,C:$tType,B:$tType,A:$tType,P3:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E2) @ ((product_prod @ F5) @ G2)))))) > $o),X3:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E2) @ ((product_prod @ F5) @ G2))))))]: (((! [A4:A,B4:B,C2:C,D2:D,E3:E2,F6:F5,G3:G2]: ((P3 @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E2) @ ((product_prod @ F5) @ G2)))))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E2) @ ((product_prod @ F5) @ G2))))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E2) @ ((product_prod @ F5) @ G2)))) @ C2) @ ((((product_Pair @ D) @ ((product_prod @ E2) @ ((product_prod @ F5) @ G2))) @ D2) @ ((((product_Pair @ E2) @ ((product_prod @ F5) @ G2)) @ E3) @ ((((product_Pair @ F5) @ G2) @ F6) @ G3))))))))) => (P3 @ X3))))).
% 2.99/1.55 thf(fact_72_prod__induct6, axiom, (! [F5:$tType,E2:$tType,D:$tType,C:$tType,B:$tType,A:$tType,P3:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E2) @ F5))))) > $o),X3:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E2) @ F5)))))]: (((! [A4:A,B4:B,C2:C,D2:D,E3:E2,F6:F5]: ((P3 @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E2) @ F5))))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E2) @ F5)))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E2) @ F5))) @ C2) @ ((((product_Pair @ D) @ ((product_prod @ E2) @ F5)) @ D2) @ ((((product_Pair @ E2) @ F5) @ E3) @ F6)))))))) => (P3 @ X3))))).
% 2.99/1.55 thf(fact_73_prod__induct5, axiom, (! [E2:$tType,D:$tType,C:$tType,B:$tType,A:$tType,P3:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E2)))) > $o),X3:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E2))))]: (((! [A4:A,B4:B,C2:C,D2:D,E3:E2]: ((P3 @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E2)))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E2))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ E2)) @ C2) @ ((((product_Pair @ D) @ E2) @ D2) @ E3))))))) => (P3 @ X3))))).
% 2.99/1.55 thf(fact_74_prod__induct4, axiom, (! [D:$tType,C:$tType,B:$tType,A:$tType,P3:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D))) > $o),X3:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D)))]: (((! [A4:A,B4:B,C2:C,D2:D]: ((P3 @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C) @ D)) @ B4) @ ((((product_Pair @ C) @ D) @ C2) @ D2)))))) => (P3 @ X3))))).
% 2.99/1.55 thf(fact_75_prod__induct3, axiom, (! [C:$tType,B:$tType,A:$tType,P3:(((product_prod @ A) @ ((product_prod @ B) @ C)) > $o),X3:((product_prod @ A) @ ((product_prod @ B) @ C))]: (((! [A4:A,B4:B,C2:C]: ((P3 @ ((((product_Pair @ A) @ ((product_prod @ B) @ C)) @ A4) @ ((((product_Pair @ B) @ C) @ B4) @ C2))))) => (P3 @ X3))))).
% 2.99/1.55 thf(fact_76_prod__cases7, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,E2:$tType,F5:$tType,G2:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E2) @ ((product_prod @ F5) @ G2))))))]: ((~ ((! [A4:A,B4:B,C2:C,D2:D,E3:E2,F6:F5,G3:G2]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E2) @ ((product_prod @ F5) @ G2)))))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E2) @ ((product_prod @ F5) @ G2))))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E2) @ ((product_prod @ F5) @ G2)))) @ C2) @ ((((product_Pair @ D) @ ((product_prod @ E2) @ ((product_prod @ F5) @ G2))) @ D2) @ ((((product_Pair @ E2) @ ((product_prod @ F5) @ G2)) @ E3) @ ((((product_Pair @ F5) @ G2) @ F6) @ G3)))))))))))))).
% 2.99/1.55 thf(fact_77_prod__cases6, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,E2:$tType,F5:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E2) @ F5)))))]: ((~ ((! [A4:A,B4:B,C2:C,D2:D,E3:E2,F6:F5]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E2) @ F5))))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E2) @ F5)))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E2) @ F5))) @ C2) @ ((((product_Pair @ D) @ ((product_prod @ E2) @ F5)) @ D2) @ ((((product_Pair @ E2) @ F5) @ E3) @ F6))))))))))))).
% 2.99/1.55 thf(fact_78_prod__cases5, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,E2:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E2))))]: ((~ ((! [A4:A,B4:B,C2:C,D2:D,E3:E2]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E2)))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E2))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ E2)) @ C2) @ ((((product_Pair @ D) @ E2) @ D2) @ E3)))))))))))).
% 2.99/1.55 thf(fact_79_prod__cases4, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D)))]: ((~ ((! [A4:A,B4:B,C2:C,D2:D]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C) @ D)) @ B4) @ ((((product_Pair @ C) @ D) @ C2) @ D2))))))))))).
% 2.99/1.55 thf(fact_80_prod__cases3, axiom, (! [A:$tType,B:$tType,C:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ C))]: ((~ ((! [A4:A,B4:B,C2:C]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ C)) @ A4) @ ((((product_Pair @ B) @ C) @ B4) @ C2)))))))))).
% 2.99/1.55 thf(fact_81_Pair__inject, axiom, (! [A:$tType,B:$tType,A2:A,B2:B,A6:A,B3:B]: (((((((product_Pair @ A) @ B) @ A2) @ B2) = ((((product_Pair @ A) @ B) @ A6) @ B3)) => (~ (((A2 = A6) => (B2 != B3)))))))).
% 2.99/1.55 thf(fact_82_prod__cases, axiom, (! [B:$tType,A:$tType,P3:(((product_prod @ A) @ B) > $o),P:((product_prod @ A) @ B)]: (((! [A4:A,B4:B]: ((P3 @ ((((product_Pair @ A) @ B) @ A4) @ B4)))) => (P3 @ P))))).
% 2.99/1.55 thf(fact_83_old_Oprod_Orec, axiom, (! [A:$tType,T:$tType,B:$tType,F1:(A > (B > T)),A2:A,B2:B]: (((((((product_rec_prod @ A) @ B) @ T) @ F1) @ ((((product_Pair @ A) @ B) @ A2) @ B2)) = ((F1 @ A2) @ B2))))).
% 2.99/1.55 thf(fact_84_internal__case__prod__conv, axiom, (! [B:$tType,A:$tType,C:$tType,C3:(B > (C > A)),A2:B,B2:C]: (((((((produc2004651681e_prod @ B) @ C) @ A) @ C3) @ ((((product_Pair @ B) @ C) @ A2) @ B2)) = ((C3 @ A2) @ B2))))).
% 2.99/1.55 thf(fact_85_accp__induct__rule, axiom, (! [A:$tType,R2:(A > (A > $o)),A2:A,P3:(A > $o)]: (((((accp @ A) @ R2) @ A2) => ((! [X5:A]: (((((accp @ A) @ R2) @ X5) => ((! [Y6:A]: ((((R2 @ Y6) @ X5) => (P3 @ Y6)))) => (P3 @ X5))))) => (P3 @ A2)))))).
% 2.99/1.55 thf(fact_86_not__accp__down, axiom, (! [A:$tType,R:(A > (A > $o)),X3:A]: (((~ ((((accp @ A) @ R) @ X3))) => (~ ((! [Z:A]: ((((R @ Z) @ X3) => (((accp @ A) @ R) @ Z)))))))))).
% 2.99/1.55 thf(fact_87_accp__downward, axiom, (! [A:$tType,R2:(A > (A > $o)),B2:A,A2:A]: (((((accp @ A) @ R2) @ B2) => (((R2 @ A2) @ B2) => (((accp @ A) @ R2) @ A2)))))).
% 2.99/1.55 thf(fact_88_accp_Oinducts, axiom, (! [A:$tType,R2:(A > (A > $o)),X3:A,P3:(A > $o)]: (((((accp @ A) @ R2) @ X3) => ((! [X5:A]: (((! [Y6:A]: ((((R2 @ Y6) @ X5) => (((accp @ A) @ R2) @ Y6)))) => ((! [Y6:A]: ((((R2 @ Y6) @ X5) => (P3 @ Y6)))) => (P3 @ X5))))) => (P3 @ X3)))))).
% 2.99/1.55 thf(fact_89_accp__induct, axiom, (! [A:$tType,R2:(A > (A > $o)),A2:A,P3:(A > $o)]: (((((accp @ A) @ R2) @ A2) => ((! [X5:A]: (((((accp @ A) @ R2) @ X5) => ((! [Y6:A]: ((((R2 @ Y6) @ X5) => (P3 @ Y6)))) => (P3 @ X5))))) => (P3 @ A2)))))).
% 2.99/1.55 thf(fact_90_accp_Ocases, axiom, (! [A:$tType,R2:(A > (A > $o)),A2:A]: (((((accp @ A) @ R2) @ A2) => (! [Y6:A]: ((((R2 @ Y6) @ A2) => (((accp @ A) @ R2) @ Y6)))))))).
% 2.99/1.55 thf(fact_91_accp_Osimps, axiom, (! [A:$tType]: (((accp @ A) = (^ [R3:(A > (A > $o)),A3:A]: ((? [X:A]: (((A3 = X) & (! [Y4:A]: ((((R3 @ Y4) @ X) => (((accp @ A) @ R3) @ Y4))))))))))))).
% 2.99/1.55 thf(fact_92_accp_Ointros, axiom, (! [A:$tType,R2:(A > (A > $o)),X3:A]: (((! [Y5:A]: ((((R2 @ Y5) @ X3) => (((accp @ A) @ R2) @ Y5)))) => (((accp @ A) @ R2) @ X3))))).
% 2.99/1.55 thf(fact_93_in__lex__prod, axiom, (! [A:$tType,B:$tType,A2:A,B2:B,A6:A,B3:B,R2:(set @ ((product_prod @ A) @ A)),S2:(set @ ((product_prod @ B) @ B))]: (((((member @ ((product_prod @ ((product_prod @ A) @ B)) @ ((product_prod @ A) @ B))) @ ((((product_Pair @ ((product_prod @ A) @ B)) @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ A2) @ B2)) @ ((((product_Pair @ A) @ B) @ A6) @ B3))) @ ((((lex_prod @ A) @ B) @ R2) @ S2)) = ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A2) @ A6)) @ R2) | ((A2 = A6) & (((member @ ((product_prod @ B) @ B)) @ ((((product_Pair @ B) @ B) @ B2) @ B3)) @ S2))))))).
% 2.99/1.55 thf(fact_94_ssubst__Pair__rhs, axiom, (! [B:$tType,A:$tType,R2:A,S2:B,R:(set @ ((product_prod @ A) @ B)),S3:B]: (((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ R2) @ S2)) @ R) => ((S3 = S2) => (((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ R2) @ S3)) @ R)))))).
% 2.99/1.55 thf(fact_95_curry__conv, axiom, (! [A:$tType,C:$tType,B:$tType]: (((((product_curry @ B) @ C) @ A) = (^ [F7:(((product_prod @ B) @ C) > A),A3:B,B5:C]: ((F7 @ ((((product_Pair @ B) @ C) @ A3) @ B5)))))))).
% 2.99/1.55 thf(fact_96_in__inv__imagep, axiom, (! [B:$tType,A:$tType]: ((((inv_imagep @ A) @ B) = (^ [R3:(A > (A > $o)),F7:(B > A),X:B,Y4:B]: (((R3 @ (F7 @ X)) @ (F7 @ Y4)))))))).
% 2.99/1.55 thf(fact_97_acc__def, axiom, (! [A:$tType]: (((acc @ A) = (^ [R3:(set @ ((product_prod @ A) @ A))]: (((collect @ A) @ ((accp @ A) @ (^ [X:A,Y4:A]: ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X) @ Y4)) @ R3))))))))))).
% 2.99/1.55 thf(fact_98_accp__acc__eq, axiom, (! [A:$tType,R2:(set @ ((product_prod @ A) @ A))]: ((((accp @ A) @ (^ [X:A,Y4:A]: ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X) @ Y4)) @ R2)))) = (^ [X:A]: ((((member @ A) @ X) @ ((acc @ A) @ R2)))))))).
% 2.99/1.55 thf(fact_99_curryI, axiom, (! [A:$tType,B:$tType,F:(((product_prod @ A) @ B) > $o),A2:A,B2:B]: (((F @ ((((product_Pair @ A) @ B) @ A2) @ B2)) => ((((((product_curry @ A) @ B) @ $o) @ F) @ A2) @ B2))))).
% 2.99/1.55 thf(fact_100_curry__K, axiom, (! [B:$tType,C:$tType,A:$tType,C3:C]: ((((((product_curry @ A) @ B) @ C) @ (^ [X:((product_prod @ A) @ B)]: (C3))) = (^ [X:A,Y4:B]: (C3)))))).
% 2.99/1.55 thf(fact_101_acc__induct__rule, axiom, (! [A:$tType,A2:A,R2:(set @ ((product_prod @ A) @ A)),P3:(A > $o)]: (((((member @ A) @ A2) @ ((acc @ A) @ R2)) => ((! [X5:A]: (((((member @ A) @ X5) @ ((acc @ A) @ R2)) => ((! [Y6:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Y6) @ X5)) @ R2) => (P3 @ Y6)))) => (P3 @ X5))))) => (P3 @ A2)))))).
% 2.99/1.55 thf(fact_102_not__acc__down, axiom, (! [A:$tType,X3:A,R:(set @ ((product_prod @ A) @ A))]: (((~ ((((member @ A) @ X3) @ ((acc @ A) @ R)))) => (~ ((! [Z:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Z) @ X3)) @ R) => (((member @ A) @ Z) @ ((acc @ A) @ R))))))))))).
% 2.99/1.55 thf(fact_103_acc__downward, axiom, (! [A:$tType,B2:A,R2:(set @ ((product_prod @ A) @ A)),A2:A]: (((((member @ A) @ B2) @ ((acc @ A) @ R2)) => ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A2) @ B2)) @ R2) => (((member @ A) @ A2) @ ((acc @ A) @ R2))))))).
% 2.99/1.55 thf(fact_104_acc_Oinducts, axiom, (! [A:$tType,X3:A,R2:(set @ ((product_prod @ A) @ A)),P3:(A > $o)]: (((((member @ A) @ X3) @ ((acc @ A) @ R2)) => ((! [X5:A]: (((! [Y6:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Y6) @ X5)) @ R2) => (((member @ A) @ Y6) @ ((acc @ A) @ R2))))) => ((! [Y6:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Y6) @ X5)) @ R2) => (P3 @ Y6)))) => (P3 @ X5))))) => (P3 @ X3)))))).
% 2.99/1.55 thf(fact_105_acc__induct, axiom, (! [A:$tType,A2:A,R2:(set @ ((product_prod @ A) @ A)),P3:(A > $o)]: (((((member @ A) @ A2) @ ((acc @ A) @ R2)) => ((! [X5:A]: (((((member @ A) @ X5) @ ((acc @ A) @ R2)) => ((! [Y6:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Y6) @ X5)) @ R2) => (P3 @ Y6)))) => (P3 @ X5))))) => (P3 @ A2)))))).
% 2.99/1.55 thf(fact_106_acc_Ointros, axiom, (! [A:$tType,X3:A,R2:(set @ ((product_prod @ A) @ A))]: (((! [Y5:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Y5) @ X3)) @ R2) => (((member @ A) @ Y5) @ ((acc @ A) @ R2))))) => (((member @ A) @ X3) @ ((acc @ A) @ R2)))))).
% 2.99/1.55 thf(fact_107_acc_Osimps, axiom, (! [A:$tType,A2:A,R2:(set @ ((product_prod @ A) @ A))]: (((((member @ A) @ A2) @ ((acc @ A) @ R2)) = (? [X:A]: (((A2 = X) & (! [Y4:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Y4) @ X)) @ R2) => (((member @ A) @ Y4) @ ((acc @ A) @ R2)))))))))))).
% 2.99/1.55 thf(fact_108_acc_Ocases, axiom, (! [A:$tType,A2:A,R2:(set @ ((product_prod @ A) @ A))]: (((((member @ A) @ A2) @ ((acc @ A) @ R2)) => (! [Y6:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Y6) @ A2)) @ R2) => (((member @ A) @ Y6) @ ((acc @ A) @ R2))))))))).
% 2.99/1.55 thf(fact_109_curryE, axiom, (! [A:$tType,B:$tType,F:(((product_prod @ A) @ B) > $o),A2:A,B2:B]: ((((((((product_curry @ A) @ B) @ $o) @ F) @ A2) @ B2) => (F @ ((((product_Pair @ A) @ B) @ A2) @ B2)))))).
% 2.99/1.55 thf(fact_110_curryD, axiom, (! [A:$tType,B:$tType,F:(((product_prod @ A) @ B) > $o),A2:A,B2:B]: ((((((((product_curry @ A) @ B) @ $o) @ F) @ A2) @ B2) => (F @ ((((product_Pair @ A) @ B) @ A2) @ B2)))))).
% 2.99/1.55 thf(fact_111_inv__imagep__def, axiom, (! [A:$tType,B:$tType]: ((((inv_imagep @ B) @ A) = (^ [R3:(B > (B > $o)),F7:(A > B),X:A,Y4:A]: (((R3 @ (F7 @ X)) @ (F7 @ Y4)))))))).
% 2.99/1.55 thf(fact_112_curry__def, axiom, (! [C:$tType,B:$tType,A:$tType]: (((((product_curry @ A) @ B) @ C) = (^ [C4:(((product_prod @ A) @ B) > C),X:A,Y4:B]: ((C4 @ ((((product_Pair @ A) @ B) @ X) @ Y4)))))))).
% 2.99/1.55 thf(fact_113_same__fstI, axiom, (! [B:$tType,A:$tType,P3:(A > $o),X3:A,Y7:B,Y:B,R:(A > (set @ ((product_prod @ B) @ B)))]: (((P3 @ X3) => ((((member @ ((product_prod @ B) @ B)) @ ((((product_Pair @ B) @ B) @ Y7) @ Y)) @ (R @ X3)) => (((member @ ((product_prod @ ((product_prod @ A) @ B)) @ ((product_prod @ A) @ B))) @ ((((product_Pair @ ((product_prod @ A) @ B)) @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X3) @ Y7)) @ ((((product_Pair @ A) @ B) @ X3) @ Y))) @ ((((same_fst @ A) @ B) @ P3) @ R))))))).
% 2.99/1.55 thf(fact_114_in__inv__image, axiom, (! [A:$tType,B:$tType,X3:A,Y:A,R2:(set @ ((product_prod @ B) @ B)),F:(A > B)]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X3) @ Y)) @ ((((inv_image @ B) @ A) @ R2) @ F)) = (((member @ ((product_prod @ B) @ B)) @ ((((product_Pair @ B) @ B) @ (F @ X3)) @ (F @ Y))) @ R2))))).
% 2.99/1.55 thf(fact_115_PREF_Opelims, axiom, (! [C:$tType,A:$tType,B:$tType,X3:(A > ((proces554692349s_term @ B) @ C)),Xa:((proces554692349s_term @ B) @ A),Y:B]: ((((((((proces1708129104e_PREF @ A) @ B) @ C) @ X3) @ Xa) = Y) => ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ B) @ A))) @ (((proces527360425EF_rel @ A) @ B) @ C)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ B) @ A)) @ X3) @ Xa)) => ((! [X4:A]: (((Xa = (((proces1627516585ss_VAR @ A) @ B) @ X4)) => ((Y = ((((((((proces460752237s_term @ C) @ B) @ B) @ (^ [Aa:C]: ((undefined @ B)))) @ (proces745025900prefOf @ B)) @ (^ [A3:B,T3:((proces554692349s_term @ B) @ C)]: (A3))) @ (^ [Aa:((proces554692349s_term @ B) @ C),Ab2:((proces554692349s_term @ B) @ C)]: ((undefined @ B)))) @ (X3 @ X4))) => (~ ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ B) @ A))) @ (((proces527360425EF_rel @ A) @ B) @ C)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ B) @ A)) @ X3) @ (((proces1627516585ss_VAR @ A) @ B) @ X4))))))))) => ((! [P2:(proces634752977rocess @ B)]: (((Xa = (((proces1062592052s_PROC @ B) @ A) @ P2)) => ((Y = ((proces745025900prefOf @ B) @ P2)) => (~ ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ B) @ A))) @ (((proces527360425EF_rel @ A) @ B) @ C)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ B) @ A)) @ X3) @ (((proces1062592052s_PROC @ B) @ A) @ P2))))))))) => ((! [A4:B,T4:((proces554692349s_term @ B) @ A)]: (((Xa = ((((proces1454156180ss_ACT @ B) @ A) @ A4) @ T4)) => ((Y = A4) => (~ ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ B) @ A))) @ (((proces527360425EF_rel @ A) @ B) @ C)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ B) @ A)) @ X3) @ ((((proces1454156180ss_ACT @ B) @ A) @ A4) @ T4))))))))) => (~ ((! [V:((proces554692349s_term @ B) @ A),Va:((proces554692349s_term @ B) @ A)]: (((Xa = ((((proces89589571ess_CH @ B) @ A) @ V) @ Va)) => ((Y = (undefined @ B)) => (~ ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ B) @ A))) @ (((proces527360425EF_rel @ A) @ B) @ C)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ B) @ A)) @ X3) @ ((((proces89589571ess_CH @ B) @ A) @ V) @ Va))))))))))))))))))).
% 2.99/1.55 thf(fact_116_above__def, axiom, (! [A:$tType]: (((order_above @ A) = (^ [R3:(set @ ((product_prod @ A) @ A)),A3:A]: (((collect @ A) @ (^ [B5:A]: ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A3) @ B5)) @ R3)))))))))).
% 2.99/1.55 thf(fact_117_aboveS__def, axiom, (! [A:$tType]: (((order_aboveS @ A) = (^ [R3:(set @ ((product_prod @ A) @ A)),A3:A]: (((collect @ A) @ (^ [B5:A]: (((B5 != A3) & (((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A3) @ B5)) @ R3))))))))))).
% 2.99/1.55 thf(fact_118_PREF_Osimps_I2_J, axiom, (! [A:$tType,C:$tType,B:$tType,Sys:(A > ((proces554692349s_term @ B) @ C)),P:(proces634752977rocess @ B)]: (((((((proces1708129104e_PREF @ A) @ B) @ C) @ Sys) @ (((proces1062592052s_PROC @ B) @ A) @ P)) = ((proces745025900prefOf @ B) @ P))))).
% 2.99/1.55 thf(fact_119_PREF_Osimps_I1_J, axiom, (! [B:$tType,C:$tType,A:$tType,Sys:(A > ((proces554692349s_term @ B) @ C)),X6:A]: (((((((proces1708129104e_PREF @ A) @ B) @ C) @ Sys) @ (((proces1627516585ss_VAR @ A) @ B) @ X6)) = ((((((((proces460752237s_term @ C) @ B) @ B) @ (^ [Aa:C]: ((undefined @ B)))) @ (proces745025900prefOf @ B)) @ (^ [A3:B,T3:((proces554692349s_term @ B) @ C)]: (A3))) @ (^ [Aa:((proces554692349s_term @ B) @ C),Ab2:((proces554692349s_term @ B) @ C)]: ((undefined @ B)))) @ (Sys @ X6)))))).
% 2.99/1.55 thf(fact_120_solution_Osimps_I3_J, axiom, (! [A:$tType,B:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),T2:((proces554692349s_term @ B) @ A)]: ((((((((proces687458811_isACT @ A) @ B) @ A) @ B) @ Sys) @ T2) => (((proces745025900prefOf @ B) @ ((((proces1652378886lution @ A) @ B) @ Sys) @ T2)) = (((((proces1708129104e_PREF @ A) @ B) @ A) @ Sys) @ T2)))))).
% 2.99/1.55 thf(fact_121_PREF_Osimps_I3_J, axiom, (! [A:$tType,C:$tType,B:$tType,Sys:(A > ((proces554692349s_term @ B) @ C)),A2:B,T2:((proces554692349s_term @ B) @ A)]: (((((((proces1708129104e_PREF @ A) @ B) @ C) @ Sys) @ ((((proces1454156180ss_ACT @ B) @ A) @ A2) @ T2)) = A2)))).
% 2.99/1.55 thf(fact_122_PREF_Oelims, axiom, (! [A:$tType,C:$tType,B:$tType,X3:(A > ((proces554692349s_term @ B) @ C)),Xa:((proces554692349s_term @ B) @ A),Y:B]: ((((((((proces1708129104e_PREF @ A) @ B) @ C) @ X3) @ Xa) = Y) => ((! [X4:A]: (((Xa = (((proces1627516585ss_VAR @ A) @ B) @ X4)) => (Y != ((((((((proces460752237s_term @ C) @ B) @ B) @ (^ [Aa:C]: ((undefined @ B)))) @ (proces745025900prefOf @ B)) @ (^ [A3:B,T3:((proces554692349s_term @ B) @ C)]: (A3))) @ (^ [Aa:((proces554692349s_term @ B) @ C),Ab2:((proces554692349s_term @ B) @ C)]: ((undefined @ B)))) @ (X3 @ X4)))))) => ((! [P2:(proces634752977rocess @ B)]: (((Xa = (((proces1062592052s_PROC @ B) @ A) @ P2)) => (Y != ((proces745025900prefOf @ B) @ P2))))) => ((! [A4:B]: (((? [T4:((proces554692349s_term @ B) @ A)]: ((Xa = ((((proces1454156180ss_ACT @ B) @ A) @ A4) @ T4)))) => (Y != A4)))) => (~ (((? [V:((proces554692349s_term @ B) @ A),Va:((proces554692349s_term @ B) @ A)]: ((Xa = ((((proces89589571ess_CH @ B) @ A) @ V) @ Va)))) => (Y != (undefined @ B)))))))))))).
% 2.99/1.55 thf(fact_123_prefOf__def, axiom, (! [A:$tType]: (((proces745025900prefOf @ A) = ((((proces1406508781rocess @ A) @ A) @ (^ [X11:A,X122:(proces634752977rocess @ A)]: (X11))) @ (^ [Uu:(proces634752977rocess @ A),Uv:(proces634752977rocess @ A)]: ((undefined @ A)))))))).
% 2.99/1.55 thf(fact_124_cut__def, axiom, (! [B:$tType,A:$tType]: ((((cut @ A) @ B) = (^ [F7:(A > B),R4:(set @ ((product_prod @ A) @ A)),X:A,Y4:A]: (((((if @ B) @ (((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Y4) @ X)) @ R4)) @ (F7 @ Y4)) @ (undefined @ B)))))))).
% 2.99/1.55 thf(fact_125_CH1_Opelims, axiom, (! [A:$tType,B:$tType,X3:(A > ((proces554692349s_term @ B) @ A)),Xa:((proces554692349s_term @ B) @ A),Y:((proces554692349s_term @ B) @ A)]: (((((((proces1239275103le_CH1 @ A) @ B) @ X3) @ Xa) = Y) => ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A))) @ ((proces1869379930H1_rel @ A) @ B)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ X3) @ Xa)) => ((! [X4:A]: (((Xa = (((proces1627516585ss_VAR @ A) @ B) @ X4)) => ((Y = ((((((((proces460752237s_term @ A) @ ((proces554692349s_term @ B) @ A)) @ B) @ (^ [A3:A]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (^ [P4:(proces634752977rocess @ B)]: ((((proces1062592052s_PROC @ B) @ A) @ ((proces979765041_ch1Of @ B) @ P4))))) @ (^ [A3:B,B5:((proces554692349s_term @ B) @ A)]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (^ [T13:((proces554692349s_term @ B) @ A),T24:((proces554692349s_term @ B) @ A)]: (T13))) @ (X3 @ X4))) => (~ ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A))) @ ((proces1869379930H1_rel @ A) @ B)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ X3) @ (((proces1627516585ss_VAR @ A) @ B) @ X4))))))))) => ((! [P2:(proces634752977rocess @ B)]: (((Xa = (((proces1062592052s_PROC @ B) @ A) @ P2)) => ((Y = (((proces1062592052s_PROC @ B) @ A) @ ((proces979765041_ch1Of @ B) @ P2))) => (~ ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A))) @ ((proces1869379930H1_rel @ A) @ B)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ X3) @ (((proces1062592052s_PROC @ B) @ A) @ P2))))))))) => ((! [T12:((proces554692349s_term @ B) @ A),T23:((proces554692349s_term @ B) @ A)]: (((Xa = ((((proces89589571ess_CH @ B) @ A) @ T12) @ T23)) => ((Y = T12) => (~ ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A))) @ ((proces1869379930H1_rel @ A) @ B)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ X3) @ ((((proces89589571ess_CH @ B) @ A) @ T12) @ T23))))))))) => (~ ((! [V:B,Va:((proces554692349s_term @ B) @ A)]: (((Xa = ((((proces1454156180ss_ACT @ B) @ A) @ V) @ Va)) => ((Y = (undefined @ ((proces554692349s_term @ B) @ A))) => (~ ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A))) @ ((proces1869379930H1_rel @ A) @ B)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ X3) @ ((((proces1454156180ss_ACT @ B) @ A) @ V) @ Va))))))))))))))))))).
% 2.99/1.55 thf(fact_126_CH2_Opelims, axiom, (! [A:$tType,B:$tType,X3:(A > ((proces554692349s_term @ B) @ A)),Xa:((proces554692349s_term @ B) @ A),Y:((proces554692349s_term @ B) @ A)]: (((((((proces1239275104le_CH2 @ A) @ B) @ X3) @ Xa) = Y) => ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A))) @ ((proces93903513H2_rel @ A) @ B)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ X3) @ Xa)) => ((! [X4:A]: (((Xa = (((proces1627516585ss_VAR @ A) @ B) @ X4)) => ((Y = ((((((((proces460752237s_term @ A) @ ((proces554692349s_term @ B) @ A)) @ B) @ (^ [A3:A]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (^ [P4:(proces634752977rocess @ B)]: ((((proces1062592052s_PROC @ B) @ A) @ ((proces988026546_ch2Of @ B) @ P4))))) @ (^ [A3:B,B5:((proces554692349s_term @ B) @ A)]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (^ [T13:((proces554692349s_term @ B) @ A),T24:((proces554692349s_term @ B) @ A)]: (T24))) @ (X3 @ X4))) => (~ ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A))) @ ((proces93903513H2_rel @ A) @ B)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ X3) @ (((proces1627516585ss_VAR @ A) @ B) @ X4))))))))) => ((! [P2:(proces634752977rocess @ B)]: (((Xa = (((proces1062592052s_PROC @ B) @ A) @ P2)) => ((Y = (((proces1062592052s_PROC @ B) @ A) @ ((proces988026546_ch2Of @ B) @ P2))) => (~ ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A))) @ ((proces93903513H2_rel @ A) @ B)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ X3) @ (((proces1062592052s_PROC @ B) @ A) @ P2))))))))) => ((! [T12:((proces554692349s_term @ B) @ A),T23:((proces554692349s_term @ B) @ A)]: (((Xa = ((((proces89589571ess_CH @ B) @ A) @ T12) @ T23)) => ((Y = T23) => (~ ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A))) @ ((proces93903513H2_rel @ A) @ B)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ X3) @ ((((proces89589571ess_CH @ B) @ A) @ T12) @ T23))))))))) => (~ ((! [V:B,Va:((proces554692349s_term @ B) @ A)]: (((Xa = ((((proces1454156180ss_ACT @ B) @ A) @ V) @ Va)) => ((Y = (undefined @ ((proces554692349s_term @ B) @ A))) => (~ ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A))) @ ((proces93903513H2_rel @ A) @ B)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ X3) @ ((((proces1454156180ss_ACT @ B) @ A) @ V) @ Va))))))))))))))))))).
% 2.99/1.55 thf(fact_127_ch2Of__def, axiom, (! [A:$tType]: (((proces988026546_ch2Of @ A) = ((((proces1406508781rocess @ A) @ (proces634752977rocess @ A)) @ (^ [Uu:A,Uv:(proces634752977rocess @ A)]: ((undefined @ (proces634752977rocess @ A))))) @ (^ [X21:(proces634752977rocess @ A),X222:(proces634752977rocess @ A)]: (X222))))))).
% 2.99/1.55 thf(fact_128_ch1Of__def, axiom, (! [A:$tType]: (((proces979765041_ch1Of @ A) = ((((proces1406508781rocess @ A) @ (proces634752977rocess @ A)) @ (^ [Uu:A,Uv:(proces634752977rocess @ A)]: ((undefined @ (proces634752977rocess @ A))))) @ (^ [X21:(proces634752977rocess @ A),X222:(proces634752977rocess @ A)]: (X21))))))).
% 2.99/1.55 thf(fact_129_CH2_Osimps_I2_J, axiom, (! [A:$tType,B:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),P:(proces634752977rocess @ B)]: ((((((proces1239275104le_CH2 @ A) @ B) @ Sys) @ (((proces1062592052s_PROC @ B) @ A) @ P)) = (((proces1062592052s_PROC @ B) @ A) @ ((proces988026546_ch2Of @ B) @ P)))))).
% 2.99/1.55 thf(fact_130_CH1_Osimps_I2_J, axiom, (! [A:$tType,B:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),P:(proces634752977rocess @ B)]: ((((((proces1239275103le_CH1 @ A) @ B) @ Sys) @ (((proces1062592052s_PROC @ B) @ A) @ P)) = (((proces1062592052s_PROC @ B) @ A) @ ((proces979765041_ch1Of @ B) @ P)))))).
% 2.99/1.55 thf(fact_131_process_Ocase__distrib, axiom, (! [B:$tType,C:$tType,A:$tType,H:(B > C),F1:(A > ((proces634752977rocess @ A) > B)),F2:((proces634752977rocess @ A) > ((proces634752977rocess @ A) > B)),Process:(proces634752977rocess @ A)]: (((H @ (((((proces1406508781rocess @ A) @ B) @ F1) @ F2) @ Process)) = (((((proces1406508781rocess @ A) @ C) @ (^ [X1:A,X22:(proces634752977rocess @ A)]: ((H @ ((F1 @ X1) @ X22))))) @ (^ [X1:(proces634752977rocess @ A),X22:(proces634752977rocess @ A)]: ((H @ ((F2 @ X1) @ X22))))) @ Process))))).
% 2.99/1.55 thf(fact_132_solution_Osimps_I6_J, axiom, (! [A:$tType,B:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),T2:((proces554692349s_term @ B) @ A)]: (((~ (((((((proces687458811_isACT @ A) @ B) @ A) @ B) @ Sys) @ T2))) => (((proces988026546_ch2Of @ B) @ ((((proces1652378886lution @ A) @ B) @ Sys) @ T2)) = ((((proces1652378886lution @ A) @ B) @ Sys) @ ((((proces1239275104le_CH2 @ A) @ B) @ Sys) @ T2))))))).
% 2.99/1.55 thf(fact_133_solution_Osimps_I5_J, axiom, (! [A:$tType,B:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),T2:((proces554692349s_term @ B) @ A)]: (((~ (((((((proces687458811_isACT @ A) @ B) @ A) @ B) @ Sys) @ T2))) => (((proces979765041_ch1Of @ B) @ ((((proces1652378886lution @ A) @ B) @ Sys) @ T2)) = ((((proces1652378886lution @ A) @ B) @ Sys) @ ((((proces1239275103le_CH1 @ A) @ B) @ Sys) @ T2))))))).
% 2.99/1.55 thf(fact_134_CH2_Osimps_I1_J, axiom, (! [B:$tType,A:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),X6:A]: ((((((proces1239275104le_CH2 @ A) @ B) @ Sys) @ (((proces1627516585ss_VAR @ A) @ B) @ X6)) = ((((((((proces460752237s_term @ A) @ ((proces554692349s_term @ B) @ A)) @ B) @ (^ [A3:A]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (^ [P4:(proces634752977rocess @ B)]: ((((proces1062592052s_PROC @ B) @ A) @ ((proces988026546_ch2Of @ B) @ P4))))) @ (^ [A3:B,B5:((proces554692349s_term @ B) @ A)]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (^ [T13:((proces554692349s_term @ B) @ A),T24:((proces554692349s_term @ B) @ A)]: (T24))) @ (Sys @ X6)))))).
% 2.99/1.55 thf(fact_135_CH1_Osimps_I1_J, axiom, (! [B:$tType,A:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),X6:A]: ((((((proces1239275103le_CH1 @ A) @ B) @ Sys) @ (((proces1627516585ss_VAR @ A) @ B) @ X6)) = ((((((((proces460752237s_term @ A) @ ((proces554692349s_term @ B) @ A)) @ B) @ (^ [A3:A]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (^ [P4:(proces634752977rocess @ B)]: ((((proces1062592052s_PROC @ B) @ A) @ ((proces979765041_ch1Of @ B) @ P4))))) @ (^ [A3:B,B5:((proces554692349s_term @ B) @ A)]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (^ [T13:((proces554692349s_term @ B) @ A),T24:((proces554692349s_term @ B) @ A)]: (T13))) @ (Sys @ X6)))))).
% 2.99/1.55 thf(fact_136_cut__apply, axiom, (! [B:$tType,A:$tType,X3:A,A2:A,R:(set @ ((product_prod @ A) @ A)),F:(A > B)]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X3) @ A2)) @ R) => (((((((cut @ A) @ B) @ F) @ R) @ A2) @ X3) = (F @ X3)))))).
% 2.99/1.55 thf(fact_137_cuts__eq, axiom, (! [B:$tType,A:$tType,F:(A > B),R:(set @ ((product_prod @ A) @ A)),X3:A,G:(A > B)]: ((((((((cut @ A) @ B) @ F) @ R) @ X3) = (((((cut @ A) @ B) @ G) @ R) @ X3)) = (! [Y4:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Y4) @ X3)) @ R) => ((F @ Y4) = (G @ Y4))))))))).
% 2.99/1.55 thf(fact_138_CH2_Osimps_I3_J, axiom, (! [A:$tType,B:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),T1:((proces554692349s_term @ B) @ A),T22:((proces554692349s_term @ B) @ A)]: ((((((proces1239275104le_CH2 @ A) @ B) @ Sys) @ ((((proces89589571ess_CH @ B) @ A) @ T1) @ T22)) = T22)))).
% 2.99/1.55 thf(fact_139_CH1_Osimps_I3_J, axiom, (! [A:$tType,B:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),T1:((proces554692349s_term @ B) @ A),T22:((proces554692349s_term @ B) @ A)]: ((((((proces1239275103le_CH1 @ A) @ B) @ Sys) @ ((((proces89589571ess_CH @ B) @ A) @ T1) @ T22)) = T1)))).
% 2.99/1.55 thf(fact_140_process_Odisc__eq__case_I1_J, axiom, (! [A:$tType]: (((proces10484146Action @ A) = ((((proces1406508781rocess @ A) @ $o) @ (^ [Uu2:A,Uv2:(proces634752977rocess @ A)]: ($true))) @ (^ [Uu2:(proces634752977rocess @ A),Uv2:(proces634752977rocess @ A)]: ($false))))))).
% 2.99/1.55 thf(fact_141_process_Odisc__eq__case_I2_J, axiom, (! [A:$tType]: (((proces401113213Choice @ A) = ((((proces1406508781rocess @ A) @ $o) @ (^ [Uu2:A,Uv2:(proces634752977rocess @ A)]: ($false))) @ (^ [Uu2:(proces634752977rocess @ A),Uv2:(proces634752977rocess @ A)]: ($true))))))).
% 2.99/1.55 thf(fact_142_CH2_Oelims, axiom, (! [A:$tType,B:$tType,X3:(A > ((proces554692349s_term @ B) @ A)),Xa:((proces554692349s_term @ B) @ A),Y:((proces554692349s_term @ B) @ A)]: (((((((proces1239275104le_CH2 @ A) @ B) @ X3) @ Xa) = Y) => ((! [X4:A]: (((Xa = (((proces1627516585ss_VAR @ A) @ B) @ X4)) => (Y != ((((((((proces460752237s_term @ A) @ ((proces554692349s_term @ B) @ A)) @ B) @ (^ [A3:A]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (^ [P4:(proces634752977rocess @ B)]: ((((proces1062592052s_PROC @ B) @ A) @ ((proces988026546_ch2Of @ B) @ P4))))) @ (^ [A3:B,B5:((proces554692349s_term @ B) @ A)]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (^ [T13:((proces554692349s_term @ B) @ A),T24:((proces554692349s_term @ B) @ A)]: (T24))) @ (X3 @ X4)))))) => ((! [P2:(proces634752977rocess @ B)]: (((Xa = (((proces1062592052s_PROC @ B) @ A) @ P2)) => (Y != (((proces1062592052s_PROC @ B) @ A) @ ((proces988026546_ch2Of @ B) @ P2)))))) => ((! [T12:((proces554692349s_term @ B) @ A),T23:((proces554692349s_term @ B) @ A)]: (((Xa = ((((proces89589571ess_CH @ B) @ A) @ T12) @ T23)) => (Y != T23)))) => (~ (((? [V:B,Va:((proces554692349s_term @ B) @ A)]: ((Xa = ((((proces1454156180ss_ACT @ B) @ A) @ V) @ Va)))) => (Y != (undefined @ ((proces554692349s_term @ B) @ A))))))))))))).
% 2.99/1.55 thf(fact_143_CH1_Oelims, axiom, (! [A:$tType,B:$tType,X3:(A > ((proces554692349s_term @ B) @ A)),Xa:((proces554692349s_term @ B) @ A),Y:((proces554692349s_term @ B) @ A)]: (((((((proces1239275103le_CH1 @ A) @ B) @ X3) @ Xa) = Y) => ((! [X4:A]: (((Xa = (((proces1627516585ss_VAR @ A) @ B) @ X4)) => (Y != ((((((((proces460752237s_term @ A) @ ((proces554692349s_term @ B) @ A)) @ B) @ (^ [A3:A]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (^ [P4:(proces634752977rocess @ B)]: ((((proces1062592052s_PROC @ B) @ A) @ ((proces979765041_ch1Of @ B) @ P4))))) @ (^ [A3:B,B5:((proces554692349s_term @ B) @ A)]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (^ [T13:((proces554692349s_term @ B) @ A),T24:((proces554692349s_term @ B) @ A)]: (T13))) @ (X3 @ X4)))))) => ((! [P2:(proces634752977rocess @ B)]: (((Xa = (((proces1062592052s_PROC @ B) @ A) @ P2)) => (Y != (((proces1062592052s_PROC @ B) @ A) @ ((proces979765041_ch1Of @ B) @ P2)))))) => ((! [T12:((proces554692349s_term @ B) @ A)]: (((? [T23:((proces554692349s_term @ B) @ A)]: ((Xa = ((((proces89589571ess_CH @ B) @ A) @ T12) @ T23)))) => (Y != T12)))) => (~ (((? [V:B,Va:((proces554692349s_term @ B) @ A)]: ((Xa = ((((proces1454156180ss_ACT @ B) @ A) @ V) @ Va)))) => (Y != (undefined @ ((proces554692349s_term @ B) @ A))))))))))))).
% 2.99/1.55 thf(fact_144_process_Ocase__eq__if, axiom, (! [B:$tType,A:$tType]: ((((proces1406508781rocess @ A) @ B) = (^ [F12:(A > ((proces634752977rocess @ A) > B)),F22:((proces634752977rocess @ A) > ((proces634752977rocess @ A) > B)),Process2:(proces634752977rocess @ A)]: (((((if @ B) @ ((proces10484146Action @ A) @ Process2)) @ ((F12 @ ((proces745025900prefOf @ A) @ Process2)) @ ((proces1778668539contOf @ A) @ Process2))) @ ((F22 @ ((proces979765041_ch1Of @ A) @ Process2)) @ ((proces988026546_ch2Of @ A) @ Process2))))))))).
% 2.99/1.55 thf(fact_145_process_Ocoinduct__strong, axiom, (! [A:$tType,R:((proces634752977rocess @ A) > ((proces634752977rocess @ A) > $o)),Process:(proces634752977rocess @ A),Process3:(proces634752977rocess @ A)]: ((((R @ Process) @ Process3) => ((! [Process4:(proces634752977rocess @ A),Process5:(proces634752977rocess @ A)]: ((((R @ Process4) @ Process5) => ((((proces10484146Action @ A) @ Process4) = ((proces10484146Action @ A) @ Process5)) & ((((proces10484146Action @ A) @ Process4) => (((proces10484146Action @ A) @ Process5) => ((((proces745025900prefOf @ A) @ Process4) = ((proces745025900prefOf @ A) @ Process5)) & (((R @ ((proces1778668539contOf @ A) @ Process4)) @ ((proces1778668539contOf @ A) @ Process5)) | (((proces1778668539contOf @ A) @ Process4) = ((proces1778668539contOf @ A) @ Process5)))))) & (((proces401113213Choice @ A) @ Process4) => (((proces401113213Choice @ A) @ Process5) => ((((R @ ((proces979765041_ch1Of @ A) @ Process4)) @ ((proces979765041_ch1Of @ A) @ Process5)) | (((proces979765041_ch1Of @ A) @ Process4) = ((proces979765041_ch1Of @ A) @ Process5))) & (((R @ ((proces988026546_ch2Of @ A) @ Process4)) @ ((proces988026546_ch2Of @ A) @ Process5)) | (((proces988026546_ch2Of @ A) @ Process4) = ((proces988026546_ch2Of @ A) @ Process5))))))))))) => (Process = Process3)))))).
% 2.99/1.55 thf(fact_146_process_Ocoinduct, axiom, (! [A:$tType,R:((proces634752977rocess @ A) > ((proces634752977rocess @ A) > $o)),Process:(proces634752977rocess @ A),Process3:(proces634752977rocess @ A)]: ((((R @ Process) @ Process3) => ((! [Process4:(proces634752977rocess @ A),Process5:(proces634752977rocess @ A)]: ((((R @ Process4) @ Process5) => ((((proces10484146Action @ A) @ Process4) = ((proces10484146Action @ A) @ Process5)) & ((((proces10484146Action @ A) @ Process4) => (((proces10484146Action @ A) @ Process5) => ((((proces745025900prefOf @ A) @ Process4) = ((proces745025900prefOf @ A) @ Process5)) & ((R @ ((proces1778668539contOf @ A) @ Process4)) @ ((proces1778668539contOf @ A) @ Process5))))) & (((proces401113213Choice @ A) @ Process4) => (((proces401113213Choice @ A) @ Process5) => (((R @ ((proces979765041_ch1Of @ A) @ Process4)) @ ((proces979765041_ch1Of @ A) @ Process5)) & ((R @ ((proces988026546_ch2Of @ A) @ Process4)) @ ((proces988026546_ch2Of @ A) @ Process5)))))))))) => (Process = Process3)))))).
% 2.99/1.55 thf(fact_147_process_Oexpand, axiom, (! [A:$tType,Process:(proces634752977rocess @ A),Process3:(proces634752977rocess @ A)]: (((((proces10484146Action @ A) @ Process) = ((proces10484146Action @ A) @ Process3)) => ((((proces10484146Action @ A) @ Process) => (((proces10484146Action @ A) @ Process3) => ((((proces745025900prefOf @ A) @ Process) = ((proces745025900prefOf @ A) @ Process3)) & (((proces1778668539contOf @ A) @ Process) = ((proces1778668539contOf @ A) @ Process3))))) => ((((proces401113213Choice @ A) @ Process) => (((proces401113213Choice @ A) @ Process3) => ((((proces979765041_ch1Of @ A) @ Process) = ((proces979765041_ch1Of @ A) @ Process3)) & (((proces988026546_ch2Of @ A) @ Process) = ((proces988026546_ch2Of @ A) @ Process3))))) => (Process = Process3))))))).
% 2.99/1.55 thf(fact_148_contOf__def, axiom, (! [A:$tType]: (((proces1778668539contOf @ A) = ((((proces1406508781rocess @ A) @ (proces634752977rocess @ A)) @ (^ [X11:A,X122:(proces634752977rocess @ A)]: (X122))) @ (^ [Uu:(proces634752977rocess @ A),Uv:(proces634752977rocess @ A)]: ((undefined @ (proces634752977rocess @ A))))))))).
% 2.99/1.55 thf(fact_149_CONT_Oelims, axiom, (! [A:$tType,B:$tType,X3:(A > ((proces554692349s_term @ B) @ A)),Xa:((proces554692349s_term @ B) @ A),Y:((proces554692349s_term @ B) @ A)]: (((((((proces126235999e_CONT @ A) @ B) @ X3) @ Xa) = Y) => ((! [X4:A]: (((Xa = (((proces1627516585ss_VAR @ A) @ B) @ X4)) => (Y != ((((((((proces460752237s_term @ A) @ ((proces554692349s_term @ B) @ A)) @ B) @ (^ [Aa:A]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (^ [P4:(proces634752977rocess @ B)]: ((((proces1062592052s_PROC @ B) @ A) @ ((proces1778668539contOf @ B) @ P4))))) @ (^ [A3:B,T3:((proces554692349s_term @ B) @ A)]: (T3))) @ (^ [Aa:((proces554692349s_term @ B) @ A),Ab2:((proces554692349s_term @ B) @ A)]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (X3 @ X4)))))) => ((! [P2:(proces634752977rocess @ B)]: (((Xa = (((proces1062592052s_PROC @ B) @ A) @ P2)) => (Y != (((proces1062592052s_PROC @ B) @ A) @ ((proces1778668539contOf @ B) @ P2)))))) => ((! [A4:B,T4:((proces554692349s_term @ B) @ A)]: (((Xa = ((((proces1454156180ss_ACT @ B) @ A) @ A4) @ T4)) => (Y != T4)))) => (~ (((? [V:((proces554692349s_term @ B) @ A),Va:((proces554692349s_term @ B) @ A)]: ((Xa = ((((proces89589571ess_CH @ B) @ A) @ V) @ Va)))) => (Y != (undefined @ ((proces554692349s_term @ B) @ A))))))))))))).
% 2.99/1.55 thf(fact_150_CONT_Osimps_I1_J, axiom, (! [B:$tType,A:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),X6:A]: ((((((proces126235999e_CONT @ A) @ B) @ Sys) @ (((proces1627516585ss_VAR @ A) @ B) @ X6)) = ((((((((proces460752237s_term @ A) @ ((proces554692349s_term @ B) @ A)) @ B) @ (^ [Aa:A]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (^ [P4:(proces634752977rocess @ B)]: ((((proces1062592052s_PROC @ B) @ A) @ ((proces1778668539contOf @ B) @ P4))))) @ (^ [A3:B,T3:((proces554692349s_term @ B) @ A)]: (T3))) @ (^ [Aa:((proces554692349s_term @ B) @ A),Ab2:((proces554692349s_term @ B) @ A)]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (Sys @ X6)))))).
% 2.99/1.55 thf(fact_151_CONT_Opelims, axiom, (! [A:$tType,B:$tType,X3:(A > ((proces554692349s_term @ B) @ A)),Xa:((proces554692349s_term @ B) @ A),Y:((proces554692349s_term @ B) @ A)]: (((((((proces126235999e_CONT @ A) @ B) @ X3) @ Xa) = Y) => ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A))) @ ((proces1004198490NT_rel @ A) @ B)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ X3) @ Xa)) => ((! [X4:A]: (((Xa = (((proces1627516585ss_VAR @ A) @ B) @ X4)) => ((Y = ((((((((proces460752237s_term @ A) @ ((proces554692349s_term @ B) @ A)) @ B) @ (^ [Aa:A]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (^ [P4:(proces634752977rocess @ B)]: ((((proces1062592052s_PROC @ B) @ A) @ ((proces1778668539contOf @ B) @ P4))))) @ (^ [A3:B,T3:((proces554692349s_term @ B) @ A)]: (T3))) @ (^ [Aa:((proces554692349s_term @ B) @ A),Ab2:((proces554692349s_term @ B) @ A)]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (X3 @ X4))) => (~ ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A))) @ ((proces1004198490NT_rel @ A) @ B)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ X3) @ (((proces1627516585ss_VAR @ A) @ B) @ X4))))))))) => ((! [P2:(proces634752977rocess @ B)]: (((Xa = (((proces1062592052s_PROC @ B) @ A) @ P2)) => ((Y = (((proces1062592052s_PROC @ B) @ A) @ ((proces1778668539contOf @ B) @ P2))) => (~ ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A))) @ ((proces1004198490NT_rel @ A) @ B)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ X3) @ (((proces1062592052s_PROC @ B) @ A) @ P2))))))))) => ((! [A4:B,T4:((proces554692349s_term @ B) @ A)]: (((Xa = ((((proces1454156180ss_ACT @ B) @ A) @ A4) @ T4)) => ((Y = T4) => (~ ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A))) @ ((proces1004198490NT_rel @ A) @ B)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ X3) @ ((((proces1454156180ss_ACT @ B) @ A) @ A4) @ T4))))))))) => (~ ((! [V:((proces554692349s_term @ B) @ A),Va:((proces554692349s_term @ B) @ A)]: (((Xa = ((((proces89589571ess_CH @ B) @ A) @ V) @ Va)) => ((Y = (undefined @ ((proces554692349s_term @ B) @ A))) => (~ ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A))) @ ((proces1004198490NT_rel @ A) @ B)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ X3) @ ((((proces89589571ess_CH @ B) @ A) @ V) @ Va))))))))))))))))))).
% 2.99/1.55 thf(fact_152_CONT_Osimps_I3_J, axiom, (! [A:$tType,B:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),A2:B,T2:((proces554692349s_term @ B) @ A)]: ((((((proces126235999e_CONT @ A) @ B) @ Sys) @ ((((proces1454156180ss_ACT @ B) @ A) @ A2) @ T2)) = T2)))).
% 2.99/1.55 thf(fact_153_CONT_Osimps_I2_J, axiom, (! [A:$tType,B:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),P:(proces634752977rocess @ B)]: ((((((proces126235999e_CONT @ A) @ B) @ Sys) @ (((proces1062592052s_PROC @ B) @ A) @ P)) = (((proces1062592052s_PROC @ B) @ A) @ ((proces1778668539contOf @ B) @ P)))))).
% 2.99/1.55 thf(fact_154_solution_Osimps_I4_J, axiom, (! [A:$tType,B:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),T2:((proces554692349s_term @ B) @ A)]: ((((((((proces687458811_isACT @ A) @ B) @ A) @ B) @ Sys) @ T2) => (((proces1778668539contOf @ B) @ ((((proces1652378886lution @ A) @ B) @ Sys) @ T2)) = ((((proces1652378886lution @ A) @ B) @ Sys) @ ((((proces126235999e_CONT @ A) @ B) @ Sys) @ T2))))))).
% 2.99/1.55 thf(fact_155_process_Orel__coinduct, axiom, (! [A:$tType,B:$tType,P3:((proces634752977rocess @ A) > ((proces634752977rocess @ B) > $o)),X3:(proces634752977rocess @ A),Y:(proces634752977rocess @ B),R:(A > (B > $o))]: ((((P3 @ X3) @ Y) => ((! [Process4:(proces634752977rocess @ A),Process5:(proces634752977rocess @ B)]: ((((P3 @ Process4) @ Process5) => ((((proces10484146Action @ A) @ Process4) = ((proces10484146Action @ B) @ Process5)) & ((((proces10484146Action @ A) @ Process4) => (((proces10484146Action @ B) @ Process5) => (((R @ ((proces745025900prefOf @ A) @ Process4)) @ ((proces745025900prefOf @ B) @ Process5)) & ((P3 @ ((proces1778668539contOf @ A) @ Process4)) @ ((proces1778668539contOf @ B) @ Process5))))) & (((proces401113213Choice @ A) @ Process4) => (((proces401113213Choice @ B) @ Process5) => (((P3 @ ((proces979765041_ch1Of @ A) @ Process4)) @ ((proces979765041_ch1Of @ B) @ Process5)) & ((P3 @ ((proces988026546_ch2Of @ A) @ Process4)) @ ((proces988026546_ch2Of @ B) @ Process5)))))))))) => (((((proces749077512rocess @ A) @ B) @ R) @ X3) @ Y)))))).
% 2.99/1.55 thf(fact_156_process_Orel__sel, axiom, (! [B:$tType,A:$tType]: ((((proces749077512rocess @ A) @ B) = (^ [R4:(A > (B > $o)),A3:(proces634752977rocess @ A),B5:(proces634752977rocess @ B)]: (((((proces10484146Action @ A) @ A3) = ((proces10484146Action @ B) @ B5)) & ((((proces10484146Action @ A) @ A3) => (((proces10484146Action @ B) @ B5) => (((R4 @ ((proces745025900prefOf @ A) @ A3)) @ ((proces745025900prefOf @ B) @ B5)) & (((((proces749077512rocess @ A) @ B) @ R4) @ ((proces1778668539contOf @ A) @ A3)) @ ((proces1778668539contOf @ B) @ B5))))) & (((proces401113213Choice @ A) @ A3) => (((proces401113213Choice @ B) @ B5) => ((((((proces749077512rocess @ A) @ B) @ R4) @ ((proces979765041_ch1Of @ A) @ A3)) @ ((proces979765041_ch1Of @ B) @ B5)) & (((((proces749077512rocess @ A) @ B) @ R4) @ ((proces988026546_ch2Of @ A) @ A3)) @ ((proces988026546_ch2Of @ B) @ B5))))))))))))).
% 2.99/1.55 thf(fact_157_solution_Octr_I1_J, axiom, (! [A:$tType,B:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),T2:((proces554692349s_term @ B) @ A)]: ((((((((proces687458811_isACT @ A) @ B) @ A) @ B) @ Sys) @ T2) => (((((proces1652378886lution @ A) @ B) @ Sys) @ T2) = (((proces1525233512Action @ B) @ (((((proces1708129104e_PREF @ A) @ B) @ A) @ Sys) @ T2)) @ ((((proces1652378886lution @ A) @ B) @ Sys) @ ((((proces126235999e_CONT @ A) @ B) @ Sys) @ T2)))))))).
% 2.99/1.55 thf(fact_158_process_Oinject_I1_J, axiom, (! [A:$tType,X112:A,X123:(proces634752977rocess @ A),Y11:A,Y12:(proces634752977rocess @ A)]: ((((((proces1525233512Action @ A) @ X112) @ X123) = (((proces1525233512Action @ A) @ Y11) @ Y12)) = ((X112 = Y11) & (X123 = Y12)))))).
% 2.99/1.55 thf(fact_159_process_Orel__inject_I1_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),X112:A,X123:(proces634752977rocess @ A),Y11:B,Y12:(proces634752977rocess @ B)]: (((((((proces749077512rocess @ A) @ B) @ R) @ (((proces1525233512Action @ A) @ X112) @ X123)) @ (((proces1525233512Action @ B) @ Y11) @ Y12)) = (((R @ X112) @ Y11) & (((((proces749077512rocess @ A) @ B) @ R) @ X123) @ Y12)))))).
% 2.99/1.55 thf(fact_160_process_Ocollapse_I1_J, axiom, (! [A:$tType,Process:(proces634752977rocess @ A)]: ((((proces10484146Action @ A) @ Process) => ((((proces1525233512Action @ A) @ ((proces745025900prefOf @ A) @ Process)) @ ((proces1778668539contOf @ A) @ Process)) = Process))))).
% 2.99/1.55 thf(fact_161_isAction__def, axiom, (! [A:$tType]: (((proces10484146Action @ A) = (^ [Process2:(proces634752977rocess @ A)]: ((? [X11:A,X122:(proces634752977rocess @ A)]: ((Process2 = (((proces1525233512Action @ A) @ X11) @ X122)))))))))).
% 2.99/1.55 thf(fact_162_process_OdiscI_I1_J, axiom, (! [A:$tType,Process:(proces634752977rocess @ A),X112:A,X123:(proces634752977rocess @ A)]: (((Process = (((proces1525233512Action @ A) @ X112) @ X123)) => ((proces10484146Action @ A) @ Process))))).
% 2.99/1.55 thf(fact_163_process_Odisc_I1_J, axiom, (! [A:$tType,X112:A,X123:(proces634752977rocess @ A)]: (((proces10484146Action @ A) @ (((proces1525233512Action @ A) @ X112) @ X123))))).
% 2.99/1.55 thf(fact_164_process_Orel__intros_I1_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),X112:A,Y11:B,X123:(proces634752977rocess @ A),Y12:(proces634752977rocess @ B)]: ((((R @ X112) @ Y11) => ((((((proces749077512rocess @ A) @ B) @ R) @ X123) @ Y12) => (((((proces749077512rocess @ A) @ B) @ R) @ (((proces1525233512Action @ A) @ X112) @ X123)) @ (((proces1525233512Action @ B) @ Y11) @ Y12))))))).
% 2.99/1.55 thf(fact_165_process_Orel__eq, axiom, (! [A:$tType]: (((((proces749077512rocess @ A) @ A) @ (^ [Y8:A,Z3:A]: ((Y8 = Z3)))) = (^ [Y8:(proces634752977rocess @ A),Z3:(proces634752977rocess @ A)]: ((Y8 = Z3))))))).
% 2.99/1.55 thf(fact_166_process_Orel__refl, axiom, (! [B:$tType,Ra:(B > (B > $o)),X3:(proces634752977rocess @ B)]: (((! [X5:B]: (((Ra @ X5) @ X5))) => (((((proces749077512rocess @ B) @ B) @ Ra) @ X3) @ X3))))).
% 2.99/1.55 thf(fact_167_process_Osimps_I5_J, axiom, (! [B:$tType,A:$tType,F1:(A > ((proces634752977rocess @ A) > B)),F2:((proces634752977rocess @ A) > ((proces634752977rocess @ A) > B)),X112:A,X123:(proces634752977rocess @ A)]: (((((((proces1406508781rocess @ A) @ B) @ F1) @ F2) @ (((proces1525233512Action @ A) @ X112) @ X123)) = ((F1 @ X112) @ X123))))).
% 2.99/1.55 thf(fact_168_process_Osel_I1_J, axiom, (! [A:$tType,X112:A,X123:(proces634752977rocess @ A)]: ((((proces745025900prefOf @ A) @ (((proces1525233512Action @ A) @ X112) @ X123)) = X112)))).
% 2.99/1.55 thf(fact_169_process_Odisc_I3_J, axiom, (! [A:$tType,X112:A,X123:(proces634752977rocess @ A)]: ((~ (((proces401113213Choice @ A) @ (((proces1525233512Action @ A) @ X112) @ X123))))))).
% 2.99/1.55 thf(fact_170_process_Osel_I2_J, axiom, (! [A:$tType,X112:A,X123:(proces634752977rocess @ A)]: ((((proces1778668539contOf @ A) @ (((proces1525233512Action @ A) @ X112) @ X123)) = X123)))).
% 2.99/1.55 thf(fact_171_solution_Ocode, axiom, (! [B:$tType,A:$tType]: ((((proces1652378886lution @ A) @ B) = (^ [Sys3:(A > ((proces554692349s_term @ B) @ A)),T3:((proces554692349s_term @ B) @ A)]: (((((if @ (proces634752977rocess @ B)) @ ((((((proces687458811_isACT @ A) @ B) @ A) @ B) @ Sys3) @ T3)) @ (((proces1525233512Action @ B) @ (((((proces1708129104e_PREF @ A) @ B) @ A) @ Sys3) @ T3)) @ ((((proces1652378886lution @ A) @ B) @ Sys3) @ ((((proces126235999e_CONT @ A) @ B) @ Sys3) @ T3)))) @ (((proces1915862579Choice @ B) @ ((((proces1652378886lution @ A) @ B) @ Sys3) @ ((((proces1239275103le_CH1 @ A) @ B) @ Sys3) @ T3))) @ ((((proces1652378886lution @ A) @ B) @ Sys3) @ ((((proces1239275104le_CH2 @ A) @ B) @ Sys3) @ T3)))))))))).
% 2.99/1.55 thf(fact_172_process_Osplit__sel__asm, axiom, (! [B:$tType,A:$tType,P3:(B > $o),F1:(A > ((proces634752977rocess @ A) > B)),F2:((proces634752977rocess @ A) > ((proces634752977rocess @ A) > B)),Process:(proces634752977rocess @ A)]: (((P3 @ (((((proces1406508781rocess @ A) @ B) @ F1) @ F2) @ Process)) = (~ ((((Process = (((proces1525233512Action @ A) @ ((proces745025900prefOf @ A) @ Process)) @ ((proces1778668539contOf @ A) @ Process))) & (~ ((P3 @ ((F1 @ ((proces745025900prefOf @ A) @ Process)) @ ((proces1778668539contOf @ A) @ Process)))))) | ((Process = (((proces1915862579Choice @ A) @ ((proces979765041_ch1Of @ A) @ Process)) @ ((proces988026546_ch2Of @ A) @ Process))) & (~ ((P3 @ ((F2 @ ((proces979765041_ch1Of @ A) @ Process)) @ ((proces988026546_ch2Of @ A) @ Process))))))))))))).
% 2.99/1.55 thf(fact_173_process_Osplit__sel, axiom, (! [B:$tType,A:$tType,P3:(B > $o),F1:(A > ((proces634752977rocess @ A) > B)),F2:((proces634752977rocess @ A) > ((proces634752977rocess @ A) > B)),Process:(proces634752977rocess @ A)]: (((P3 @ (((((proces1406508781rocess @ A) @ B) @ F1) @ F2) @ Process)) = (((Process = (((proces1525233512Action @ A) @ ((proces745025900prefOf @ A) @ Process)) @ ((proces1778668539contOf @ A) @ Process))) => (P3 @ ((F1 @ ((proces745025900prefOf @ A) @ Process)) @ ((proces1778668539contOf @ A) @ Process)))) & ((Process = (((proces1915862579Choice @ A) @ ((proces979765041_ch1Of @ A) @ Process)) @ ((proces988026546_ch2Of @ A) @ Process))) => (P3 @ ((F2 @ ((proces979765041_ch1Of @ A) @ Process)) @ ((proces988026546_ch2Of @ A) @ Process))))))))).
% 2.99/1.55 thf(fact_174_process_Oinject_I2_J, axiom, (! [A:$tType,X212:(proces634752977rocess @ A),X223:(proces634752977rocess @ A),Y21:(proces634752977rocess @ A),Y22:(proces634752977rocess @ A)]: ((((((proces1915862579Choice @ A) @ X212) @ X223) = (((proces1915862579Choice @ A) @ Y21) @ Y22)) = ((X212 = Y21) & (X223 = Y22)))))).
% 2.99/1.55 thf(fact_175_process_Orel__inject_I2_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),X212:(proces634752977rocess @ A),X223:(proces634752977rocess @ A),Y21:(proces634752977rocess @ B),Y22:(proces634752977rocess @ B)]: (((((((proces749077512rocess @ A) @ B) @ R) @ (((proces1915862579Choice @ A) @ X212) @ X223)) @ (((proces1915862579Choice @ B) @ Y21) @ Y22)) = ((((((proces749077512rocess @ A) @ B) @ R) @ X212) @ Y21) & (((((proces749077512rocess @ A) @ B) @ R) @ X223) @ Y22)))))).
% 2.99/1.55 thf(fact_176_process_Ocollapse_I2_J, axiom, (! [A:$tType,Process:(proces634752977rocess @ A)]: ((((proces401113213Choice @ A) @ Process) => ((((proces1915862579Choice @ A) @ ((proces979765041_ch1Of @ A) @ Process)) @ ((proces988026546_ch2Of @ A) @ Process)) = Process))))).
% 2.99/1.55 thf(fact_177_process_Odistinct_I1_J, axiom, (! [A:$tType,X112:A,X123:(proces634752977rocess @ A),X212:(proces634752977rocess @ A),X223:(proces634752977rocess @ A)]: (((((proces1525233512Action @ A) @ X112) @ X123) != (((proces1915862579Choice @ A) @ X212) @ X223))))).
% 2.99/1.55 thf(fact_178_process_Orel__intros_I2_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),X212:(proces634752977rocess @ A),Y21:(proces634752977rocess @ B),X223:(proces634752977rocess @ A),Y22:(proces634752977rocess @ B)]: (((((((proces749077512rocess @ A) @ B) @ R) @ X212) @ Y21) => ((((((proces749077512rocess @ A) @ B) @ R) @ X223) @ Y22) => (((((proces749077512rocess @ A) @ B) @ R) @ (((proces1915862579Choice @ A) @ X212) @ X223)) @ (((proces1915862579Choice @ B) @ Y21) @ Y22))))))).
% 2.99/1.55 thf(fact_179_process_Oexhaust, axiom, (! [A:$tType,Y:(proces634752977rocess @ A)]: (((! [X113:A,X124:(proces634752977rocess @ A)]: ((Y != (((proces1525233512Action @ A) @ X113) @ X124)))) => (~ ((! [X213:(proces634752977rocess @ A),X224:(proces634752977rocess @ A)]: ((Y != (((proces1915862579Choice @ A) @ X213) @ X224)))))))))).
% 2.99/1.55 thf(fact_180_process_Odisc_I4_J, axiom, (! [A:$tType,X212:(proces634752977rocess @ A),X223:(proces634752977rocess @ A)]: (((proces401113213Choice @ A) @ (((proces1915862579Choice @ A) @ X212) @ X223))))).
% 2.99/1.55 thf(fact_181_process_OdiscI_I2_J, axiom, (! [A:$tType,Process:(proces634752977rocess @ A),X212:(proces634752977rocess @ A),X223:(proces634752977rocess @ A)]: (((Process = (((proces1915862579Choice @ A) @ X212) @ X223)) => ((proces401113213Choice @ A) @ Process))))).
% 2.99/1.55 thf(fact_182_isChoice__def, axiom, (! [A:$tType]: (((proces401113213Choice @ A) = (^ [Process2:(proces634752977rocess @ A)]: ((? [X21:(proces634752977rocess @ A),X222:(proces634752977rocess @ A)]: ((Process2 = (((proces1915862579Choice @ A) @ X21) @ X222)))))))))).
% 2.99/1.55 thf(fact_183_process_Osel_I4_J, axiom, (! [A:$tType,X212:(proces634752977rocess @ A),X223:(proces634752977rocess @ A)]: ((((proces988026546_ch2Of @ A) @ (((proces1915862579Choice @ A) @ X212) @ X223)) = X223)))).
% 2.99/1.55 thf(fact_184_process_Osel_I3_J, axiom, (! [A:$tType,X212:(proces634752977rocess @ A),X223:(proces634752977rocess @ A)]: ((((proces979765041_ch1Of @ A) @ (((proces1915862579Choice @ A) @ X212) @ X223)) = X212)))).
% 2.99/1.55 thf(fact_185_process_Osimps_I6_J, axiom, (! [B:$tType,A:$tType,F1:(A > ((proces634752977rocess @ A) > B)),F2:((proces634752977rocess @ A) > ((proces634752977rocess @ A) > B)),X212:(proces634752977rocess @ A),X223:(proces634752977rocess @ A)]: (((((((proces1406508781rocess @ A) @ B) @ F1) @ F2) @ (((proces1915862579Choice @ A) @ X212) @ X223)) = ((F2 @ X212) @ X223))))).
% 2.99/1.55 thf(fact_186_process_Odisc_I2_J, axiom, (! [A:$tType,X212:(proces634752977rocess @ A),X223:(proces634752977rocess @ A)]: ((~ (((proces10484146Action @ A) @ (((proces1915862579Choice @ A) @ X212) @ X223))))))).
% 2.99/1.55 thf(fact_187_process_Orel__cases, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),A2:(proces634752977rocess @ A),B2:(proces634752977rocess @ B)]: (((((((proces749077512rocess @ A) @ B) @ R) @ A2) @ B2) => ((! [X12:A,X23:(proces634752977rocess @ A)]: (((A2 = (((proces1525233512Action @ A) @ X12) @ X23)) => (! [Y13:B,Y23:(proces634752977rocess @ B)]: (((B2 = (((proces1525233512Action @ B) @ Y13) @ Y23)) => (((R @ X12) @ Y13) => (~ ((((((proces749077512rocess @ A) @ B) @ R) @ X23) @ Y23)))))))))) => (~ ((! [X1a:(proces634752977rocess @ A),X2a:(proces634752977rocess @ A)]: (((A2 = (((proces1915862579Choice @ A) @ X1a) @ X2a)) => (! [Y1a:(proces634752977rocess @ B),Y2a:(proces634752977rocess @ B)]: (((B2 = (((proces1915862579Choice @ B) @ Y1a) @ Y2a)) => ((((((proces749077512rocess @ A) @ B) @ R) @ X1a) @ Y1a) => (~ ((((((proces749077512rocess @ A) @ B) @ R) @ X2a) @ Y2a))))))))))))))))).
% 2.99/1.55 thf(fact_188_process_Orel__distinct_I1_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),X112:A,X123:(proces634752977rocess @ A),Y21:(proces634752977rocess @ B),Y22:(proces634752977rocess @ B)]: ((~ ((((((proces749077512rocess @ A) @ B) @ R) @ (((proces1525233512Action @ A) @ X112) @ X123)) @ (((proces1915862579Choice @ B) @ Y21) @ Y22))))))).
% 2.99/1.55 thf(fact_189_process_Orel__distinct_I2_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),Y21:(proces634752977rocess @ A),Y22:(proces634752977rocess @ A),X112:B,X123:(proces634752977rocess @ B)]: ((~ ((((((proces749077512rocess @ A) @ B) @ R) @ (((proces1915862579Choice @ A) @ Y21) @ Y22)) @ (((proces1525233512Action @ B) @ X112) @ X123))))))).
% 2.99/1.55 thf(fact_190_process__coind, axiom, (! [A:$tType,Phi:((proces634752977rocess @ A) > ((proces634752977rocess @ A) > $o)),P:(proces634752977rocess @ A),P5:(proces634752977rocess @ A)]: ((((Phi @ P) @ P5) => ((! [P2:(proces634752977rocess @ A),P6:(proces634752977rocess @ A)]: ((((Phi @ P2) @ P6) => ((((proces10484146Action @ A) @ P2) = ((proces10484146Action @ A) @ P6)) & (((proces401113213Choice @ A) @ P2) = ((proces401113213Choice @ A) @ P6)))))) => ((! [A4:A,A7:A,P2:(proces634752977rocess @ A),P6:(proces634752977rocess @ A)]: ((((Phi @ (((proces1525233512Action @ A) @ A4) @ P2)) @ (((proces1525233512Action @ A) @ A7) @ P6)) => ((A4 = A7) & ((Phi @ P2) @ P6))))) => ((! [P2:(proces634752977rocess @ A),Q2:(proces634752977rocess @ A),P6:(proces634752977rocess @ A),Q3:(proces634752977rocess @ A)]: ((((Phi @ (((proces1915862579Choice @ A) @ P2) @ Q2)) @ (((proces1915862579Choice @ A) @ P6) @ Q3)) => (((Phi @ P2) @ P6) & ((Phi @ Q2) @ Q3))))) => (P = P5)))))))).
% 2.99/1.55 thf(fact_191_process__strong__coind, axiom, (! [A:$tType,Phi:((proces634752977rocess @ A) > ((proces634752977rocess @ A) > $o)),P:(proces634752977rocess @ A),P5:(proces634752977rocess @ A)]: ((((Phi @ P) @ P5) => ((! [P2:(proces634752977rocess @ A),P6:(proces634752977rocess @ A)]: ((((Phi @ P2) @ P6) => ((((proces10484146Action @ A) @ P2) = ((proces10484146Action @ A) @ P6)) & (((proces401113213Choice @ A) @ P2) = ((proces401113213Choice @ A) @ P6)))))) => ((! [A4:A,A7:A,P2:(proces634752977rocess @ A),P6:(proces634752977rocess @ A)]: ((((Phi @ (((proces1525233512Action @ A) @ A4) @ P2)) @ (((proces1525233512Action @ A) @ A7) @ P6)) => ((A4 = A7) & (((Phi @ P2) @ P6) | (P2 = P6)))))) => ((! [P2:(proces634752977rocess @ A),Q2:(proces634752977rocess @ A),P6:(proces634752977rocess @ A),Q3:(proces634752977rocess @ A)]: ((((Phi @ (((proces1915862579Choice @ A) @ P2) @ Q2)) @ (((proces1915862579Choice @ A) @ P6) @ Q3)) => ((((Phi @ P2) @ P6) | (P2 = P6)) & (((Phi @ Q2) @ Q3) | (Q2 = Q3)))))) => (P = P5)))))))).
% 2.99/1.55 thf(fact_192_solution_Octr_I2_J, axiom, (! [A:$tType,B:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),T2:((proces554692349s_term @ B) @ A)]: (((~ (((((((proces687458811_isACT @ A) @ B) @ A) @ B) @ Sys) @ T2))) => (((((proces1652378886lution @ A) @ B) @ Sys) @ T2) = (((proces1915862579Choice @ B) @ ((((proces1652378886lution @ A) @ B) @ Sys) @ ((((proces1239275103le_CH1 @ A) @ B) @ Sys) @ T2))) @ ((((proces1652378886lution @ A) @ B) @ Sys) @ ((((proces1239275104le_CH2 @ A) @ B) @ Sys) @ T2)))))))).
% 2.99/1.55 thf(fact_193_process_Oexhaust__sel, axiom, (! [A:$tType,Process:(proces634752977rocess @ A)]: (((Process != (((proces1525233512Action @ A) @ ((proces745025900prefOf @ A) @ Process)) @ ((proces1778668539contOf @ A) @ Process))) => (Process = (((proces1915862579Choice @ A) @ ((proces979765041_ch1Of @ A) @ Process)) @ ((proces988026546_ch2Of @ A) @ Process))))))).
% 2.99/1.55 thf(fact_194_adm__lemma, axiom, (! [B:$tType,A:$tType,R:(set @ ((product_prod @ A) @ A)),F8:((A > B) > (A > B))]: (((((adm_wf @ A) @ B) @ R) @ (^ [F7:(A > B),X:A]: (((F8 @ (((((cut @ A) @ B) @ F7) @ R) @ X)) @ X))))))).
% 2.99/1.55 thf(fact_195_process__term_Orel__induct, axiom, (! [A:$tType,Pvar:$tType,C:$tType,B:$tType,R1:(A > (B > $o)),R22:(Pvar > (C > $o)),X3:((proces554692349s_term @ A) @ Pvar),Y:((proces554692349s_term @ B) @ C),Q:(((proces554692349s_term @ A) @ Pvar) > (((proces554692349s_term @ B) @ C) > $o))]: ((((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ X3) @ Y) => ((! [A12:Pvar,B1:C]: ((((R22 @ A12) @ B1) => ((Q @ (((proces1627516585ss_VAR @ Pvar) @ A) @ A12)) @ (((proces1627516585ss_VAR @ C) @ B) @ B1))))) => ((! [A22:(proces634752977rocess @ A),B22:(proces634752977rocess @ B)]: (((((((proces749077512rocess @ A) @ B) @ R1) @ A22) @ B22) => ((Q @ (((proces1062592052s_PROC @ A) @ Pvar) @ A22)) @ (((proces1062592052s_PROC @ B) @ C) @ B22))))) => ((! [A31:A,A32:((proces554692349s_term @ A) @ Pvar),B31:B,B32:((proces554692349s_term @ B) @ C)]: ((((R1 @ A31) @ B31) => (((Q @ A32) @ B32) => ((Q @ ((((proces1454156180ss_ACT @ A) @ Pvar) @ A31) @ A32)) @ ((((proces1454156180ss_ACT @ B) @ C) @ B31) @ B32)))))) => ((! [A41:((proces554692349s_term @ A) @ Pvar),A42:((proces554692349s_term @ A) @ Pvar),B41:((proces554692349s_term @ B) @ C),B42:((proces554692349s_term @ B) @ C)]: ((((Q @ A41) @ B41) => (((Q @ A42) @ B42) => ((Q @ ((((proces89589571ess_CH @ A) @ Pvar) @ A41) @ A42)) @ ((((proces89589571ess_CH @ B) @ C) @ B41) @ B42)))))) => ((Q @ X3) @ Y))))))))).
% 2.99/1.55 thf(fact_196_process__term_Orel__cases, axiom, (! [A:$tType,Pvar:$tType,C:$tType,B:$tType,R1:(A > (B > $o)),R22:(Pvar > (C > $o)),A2:((proces554692349s_term @ A) @ Pvar),B2:((proces554692349s_term @ B) @ C)]: ((((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ A2) @ B2) => ((! [X5:Pvar]: (((A2 = (((proces1627516585ss_VAR @ Pvar) @ A) @ X5)) => (! [Y5:C]: (((B2 = (((proces1627516585ss_VAR @ C) @ B) @ Y5)) => (~ (((R22 @ X5) @ Y5))))))))) => ((! [Xa2:(proces634752977rocess @ A)]: (((A2 = (((proces1062592052s_PROC @ A) @ Pvar) @ Xa2)) => (! [Ya:(proces634752977rocess @ B)]: (((B2 = (((proces1062592052s_PROC @ B) @ C) @ Ya)) => (~ ((((((proces749077512rocess @ A) @ B) @ R1) @ Xa2) @ Ya))))))))) => ((! [X1a:A,X2a:((proces554692349s_term @ A) @ Pvar)]: (((A2 = ((((proces1454156180ss_ACT @ A) @ Pvar) @ X1a) @ X2a)) => (! [Y1a:B,Y2a:((proces554692349s_term @ B) @ C)]: (((B2 = ((((proces1454156180ss_ACT @ B) @ C) @ Y1a) @ Y2a)) => (((R1 @ X1a) @ Y1a) => (~ (((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ X2a) @ Y2a)))))))))) => (~ ((! [X1b:((proces554692349s_term @ A) @ Pvar),X2b:((proces554692349s_term @ A) @ Pvar)]: (((A2 = ((((proces89589571ess_CH @ A) @ Pvar) @ X1b) @ X2b)) => (! [Y1b:((proces554692349s_term @ B) @ C),Y2b:((proces554692349s_term @ B) @ C)]: (((B2 = ((((proces89589571ess_CH @ B) @ C) @ Y1b) @ Y2b)) => (((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ X1b) @ Y1b) => (~ (((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ X2b) @ Y2b))))))))))))))))))).
% 2.99/1.55 thf(fact_197_process__term_Orel__intros_I2_J, axiom, (! [A:$tType,Pvar:$tType,C:$tType,B:$tType,R1:(A > (B > $o)),X2:(proces634752977rocess @ A),Y2:(proces634752977rocess @ B),R22:(Pvar > (C > $o))]: (((((((proces749077512rocess @ A) @ B) @ R1) @ X2) @ Y2) => ((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ (((proces1062592052s_PROC @ A) @ Pvar) @ X2)) @ (((proces1062592052s_PROC @ B) @ C) @ Y2)))))).
% 2.99/1.55 thf(fact_198_process__term_Orel__inject_I2_J, axiom, (! [C:$tType,Pvar:$tType,A:$tType,B:$tType,R1:(A > (B > $o)),R22:(Pvar > (C > $o)),X2:(proces634752977rocess @ A),Y2:(proces634752977rocess @ B)]: ((((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ (((proces1062592052s_PROC @ A) @ Pvar) @ X2)) @ (((proces1062592052s_PROC @ B) @ C) @ Y2)) = (((((proces749077512rocess @ A) @ B) @ R1) @ X2) @ Y2))))).
% 2.99/1.55 thf(fact_199_process__term_Orel__distinct_I2_J, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,R1:(A > (C > $o)),R22:(B > (D > $o)),Y2:(proces634752977rocess @ A),X13:D]: ((~ (((((((((proces2029722208s_term @ A) @ C) @ B) @ D) @ R1) @ R22) @ (((proces1062592052s_PROC @ A) @ B) @ Y2)) @ (((proces1627516585ss_VAR @ D) @ C) @ X13))))))).
% 2.99/1.55 thf(fact_200_process__term_Orel__distinct_I1_J, axiom, (! [Pvar:$tType,A:$tType,C:$tType,B:$tType,R1:(A > (B > $o)),R22:(Pvar > (C > $o)),X13:Pvar,Y2:(proces634752977rocess @ B)]: ((~ (((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ (((proces1627516585ss_VAR @ Pvar) @ A) @ X13)) @ (((proces1062592052s_PROC @ B) @ C) @ Y2))))))).
% 2.99/1.55 thf(fact_201_process__term_Orel__distinct_I10_J, axiom, (! [A:$tType,B:$tType,D:$tType,C:$tType,R1:(A > (C > $o)),R22:(B > (D > $o)),Y41:((proces554692349s_term @ A) @ B),Y42:((proces554692349s_term @ A) @ B),X2:(proces634752977rocess @ C)]: ((~ (((((((((proces2029722208s_term @ A) @ C) @ B) @ D) @ R1) @ R22) @ ((((proces89589571ess_CH @ A) @ B) @ Y41) @ Y42)) @ (((proces1062592052s_PROC @ C) @ D) @ X2))))))).
% 2.99/1.55 thf(fact_202_process__term_Orel__distinct_I9_J, axiom, (! [A:$tType,Pvar:$tType,C:$tType,B:$tType,R1:(A > (B > $o)),R22:(Pvar > (C > $o)),X2:(proces634752977rocess @ A),Y41:((proces554692349s_term @ B) @ C),Y42:((proces554692349s_term @ B) @ C)]: ((~ (((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ (((proces1062592052s_PROC @ A) @ Pvar) @ X2)) @ ((((proces89589571ess_CH @ B) @ C) @ Y41) @ Y42))))))).
% 2.99/1.55 thf(fact_203_process__term_Orel__distinct_I8_J, axiom, (! [A:$tType,B:$tType,D:$tType,C:$tType,R1:(A > (C > $o)),R22:(B > (D > $o)),Y31:A,Y32:((proces554692349s_term @ A) @ B),X2:(proces634752977rocess @ C)]: ((~ (((((((((proces2029722208s_term @ A) @ C) @ B) @ D) @ R1) @ R22) @ ((((proces1454156180ss_ACT @ A) @ B) @ Y31) @ Y32)) @ (((proces1062592052s_PROC @ C) @ D) @ X2))))))).
% 2.99/1.55 thf(fact_204_process__term_Orel__distinct_I7_J, axiom, (! [A:$tType,Pvar:$tType,C:$tType,B:$tType,R1:(A > (B > $o)),R22:(Pvar > (C > $o)),X2:(proces634752977rocess @ A),Y31:B,Y32:((proces554692349s_term @ B) @ C)]: ((~ (((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ (((proces1062592052s_PROC @ A) @ Pvar) @ X2)) @ ((((proces1454156180ss_ACT @ B) @ C) @ Y31) @ Y32))))))).
% 2.99/1.55 thf(fact_205_process__term_Orel__intros_I1_J, axiom, (! [Pvar:$tType,A:$tType,B:$tType,C:$tType,R22:(Pvar > (C > $o)),X13:Pvar,Y1:C,R1:(A > (B > $o))]: ((((R22 @ X13) @ Y1) => ((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ (((proces1627516585ss_VAR @ Pvar) @ A) @ X13)) @ (((proces1627516585ss_VAR @ C) @ B) @ Y1)))))).
% 2.99/1.55 thf(fact_206_process__term_Orel__inject_I1_J, axiom, (! [B:$tType,A:$tType,Pvar:$tType,C:$tType,R1:(A > (B > $o)),R22:(Pvar > (C > $o)),X13:Pvar,Y1:C]: ((((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ (((proces1627516585ss_VAR @ Pvar) @ A) @ X13)) @ (((proces1627516585ss_VAR @ C) @ B) @ Y1)) = ((R22 @ X13) @ Y1))))).
% 2.99/1.55 thf(fact_207_process__term_Orel__intros_I4_J, axiom, (! [A:$tType,Pvar:$tType,C:$tType,B:$tType,R1:(A > (B > $o)),R22:(Pvar > (C > $o)),X41:((proces554692349s_term @ A) @ Pvar),Y41:((proces554692349s_term @ B) @ C),X42:((proces554692349s_term @ A) @ Pvar),Y42:((proces554692349s_term @ B) @ C)]: ((((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ X41) @ Y41) => (((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ X42) @ Y42) => ((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ ((((proces89589571ess_CH @ A) @ Pvar) @ X41) @ X42)) @ ((((proces89589571ess_CH @ B) @ C) @ Y41) @ Y42))))))).
% 2.99/1.55 thf(fact_208_process__term_Orel__inject_I4_J, axiom, (! [A:$tType,Pvar:$tType,C:$tType,B:$tType,R1:(A > (B > $o)),R22:(Pvar > (C > $o)),X41:((proces554692349s_term @ A) @ Pvar),X42:((proces554692349s_term @ A) @ Pvar),Y41:((proces554692349s_term @ B) @ C),Y42:((proces554692349s_term @ B) @ C)]: ((((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ ((((proces89589571ess_CH @ A) @ Pvar) @ X41) @ X42)) @ ((((proces89589571ess_CH @ B) @ C) @ Y41) @ Y42)) = (((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ X41) @ Y41) & ((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ X42) @ Y42)))))).
% 2.99/1.55 thf(fact_209_process__term_Orel__intros_I3_J, axiom, (! [A:$tType,Pvar:$tType,C:$tType,B:$tType,R1:(A > (B > $o)),X31:A,Y31:B,R22:(Pvar > (C > $o)),X32:((proces554692349s_term @ A) @ Pvar),Y32:((proces554692349s_term @ B) @ C)]: ((((R1 @ X31) @ Y31) => (((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ X32) @ Y32) => ((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ ((((proces1454156180ss_ACT @ A) @ Pvar) @ X31) @ X32)) @ ((((proces1454156180ss_ACT @ B) @ C) @ Y31) @ Y32))))))).
% 2.99/1.55 thf(fact_210_process__term_Orel__inject_I3_J, axiom, (! [A:$tType,Pvar:$tType,C:$tType,B:$tType,R1:(A > (B > $o)),R22:(Pvar > (C > $o)),X31:A,X32:((proces554692349s_term @ A) @ Pvar),Y31:B,Y32:((proces554692349s_term @ B) @ C)]: ((((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ ((((proces1454156180ss_ACT @ A) @ Pvar) @ X31) @ X32)) @ ((((proces1454156180ss_ACT @ B) @ C) @ Y31) @ Y32)) = (((R1 @ X31) @ Y31) & ((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ X32) @ Y32)))))).
% 2.99/1.55 thf(fact_211_process__term_Orel__eq, axiom, (! [B:$tType,A:$tType]: ((((((((proces2029722208s_term @ A) @ A) @ B) @ B) @ (^ [Y8:A,Z3:A]: ((Y8 = Z3)))) @ (^ [Y8:B,Z3:B]: ((Y8 = Z3)))) = (^ [Y8:((proces554692349s_term @ A) @ B),Z3:((proces554692349s_term @ A) @ B)]: ((Y8 = Z3))))))).
% 2.99/1.55 thf(fact_212_process__term_Orel__refl, axiom, (! [D:$tType,C:$tType,R1a:(C > (C > $o)),R2a:(D > (D > $o)),X3:((proces554692349s_term @ C) @ D)]: (((! [X5:C]: (((R1a @ X5) @ X5))) => ((! [X5:D]: (((R2a @ X5) @ X5))) => ((((((((proces2029722208s_term @ C) @ C) @ D) @ D) @ R1a) @ R2a) @ X3) @ X3)))))).
% 2.99/1.55 thf(fact_213_process__term_Orel__distinct_I6_J, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,R1:(A > (C > $o)),R22:(B > (D > $o)),Y41:((proces554692349s_term @ A) @ B),Y42:((proces554692349s_term @ A) @ B),X13:D]: ((~ (((((((((proces2029722208s_term @ A) @ C) @ B) @ D) @ R1) @ R22) @ ((((proces89589571ess_CH @ A) @ B) @ Y41) @ Y42)) @ (((proces1627516585ss_VAR @ D) @ C) @ X13))))))).
% 2.99/1.55 thf(fact_214_process__term_Orel__distinct_I5_J, axiom, (! [Pvar:$tType,A:$tType,C:$tType,B:$tType,R1:(A > (B > $o)),R22:(Pvar > (C > $o)),X13:Pvar,Y41:((proces554692349s_term @ B) @ C),Y42:((proces554692349s_term @ B) @ C)]: ((~ (((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ (((proces1627516585ss_VAR @ Pvar) @ A) @ X13)) @ ((((proces89589571ess_CH @ B) @ C) @ Y41) @ Y42))))))).
% 2.99/1.55 thf(fact_215_process__term_Orel__distinct_I4_J, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,R1:(A > (C > $o)),R22:(B > (D > $o)),Y31:A,Y32:((proces554692349s_term @ A) @ B),X13:D]: ((~ (((((((((proces2029722208s_term @ A) @ C) @ B) @ D) @ R1) @ R22) @ ((((proces1454156180ss_ACT @ A) @ B) @ Y31) @ Y32)) @ (((proces1627516585ss_VAR @ D) @ C) @ X13))))))).
% 2.99/1.55 thf(fact_216_process__term_Orel__distinct_I3_J, axiom, (! [Pvar:$tType,A:$tType,C:$tType,B:$tType,R1:(A > (B > $o)),R22:(Pvar > (C > $o)),X13:Pvar,Y31:B,Y32:((proces554692349s_term @ B) @ C)]: ((~ (((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ (((proces1627516585ss_VAR @ Pvar) @ A) @ X13)) @ ((((proces1454156180ss_ACT @ B) @ C) @ Y31) @ Y32))))))).
% 2.99/1.55 thf(fact_217_process__term_Orel__distinct_I12_J, axiom, (! [A:$tType,B:$tType,D:$tType,C:$tType,R1:(A > (C > $o)),R22:(B > (D > $o)),Y41:((proces554692349s_term @ A) @ B),Y42:((proces554692349s_term @ A) @ B),X31:C,X32:((proces554692349s_term @ C) @ D)]: ((~ (((((((((proces2029722208s_term @ A) @ C) @ B) @ D) @ R1) @ R22) @ ((((proces89589571ess_CH @ A) @ B) @ Y41) @ Y42)) @ ((((proces1454156180ss_ACT @ C) @ D) @ X31) @ X32))))))).
% 2.99/1.55 thf(fact_218_process__term_Orel__distinct_I11_J, axiom, (! [A:$tType,Pvar:$tType,C:$tType,B:$tType,R1:(A > (B > $o)),R22:(Pvar > (C > $o)),X31:A,X32:((proces554692349s_term @ A) @ Pvar),Y41:((proces554692349s_term @ B) @ C),Y42:((proces554692349s_term @ B) @ C)]: ((~ (((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ ((((proces1454156180ss_ACT @ A) @ Pvar) @ X31) @ X32)) @ ((((proces89589571ess_CH @ B) @ C) @ Y41) @ Y42))))))).
% 2.99/1.55 thf(fact_219_adm__wf__def, axiom, (! [B:$tType,A:$tType]: ((((adm_wf @ A) @ B) = (^ [R4:(set @ ((product_prod @ A) @ A)),F9:((A > B) > (A > B))]: ((! [F7:(A > B),G4:(A > B),X:A]: (((! [Z4:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Z4) @ X)) @ R4) => ((F7 @ Z4) = (G4 @ Z4))))) => (((F9 @ F7) @ X) = ((F9 @ G4) @ X))))))))))).
% 2.99/1.55 thf(fact_220_process_Ocorec__code, axiom, (! [A:$tType,C:$tType]: ((((proces894737309rocess @ C) @ A) = (^ [P4:(C > $o),G11:(C > A),Q12:(C > $o),G121:(C > (proces634752977rocess @ A)),G122:(C > C),Q21:(C > $o),G211:(C > (proces634752977rocess @ A)),G212:(C > C),Q22:(C > $o),G221:(C > (proces634752977rocess @ A)),G222:(C > C),A3:C]: (((((if @ (proces634752977rocess @ A)) @ (P4 @ A3)) @ (((proces1525233512Action @ A) @ (G11 @ A3)) @ ((((if @ (proces634752977rocess @ A)) @ (Q12 @ A3)) @ (G121 @ A3)) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P4) @ G11) @ Q12) @ G121) @ G122) @ Q21) @ G211) @ G212) @ Q22) @ G221) @ G222) @ (G122 @ A3))))) @ (((proces1915862579Choice @ A) @ ((((if @ (proces634752977rocess @ A)) @ (Q21 @ A3)) @ (G211 @ A3)) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P4) @ G11) @ Q12) @ G121) @ G122) @ Q21) @ G211) @ G212) @ Q22) @ G221) @ G222) @ (G212 @ A3)))) @ ((((if @ (proces634752977rocess @ A)) @ (Q22 @ A3)) @ (G221 @ A3)) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P4) @ G11) @ Q12) @ G121) @ G122) @ Q21) @ G211) @ G212) @ Q22) @ G221) @ G222) @ (G222 @ A3))))))))))).
% 2.99/1.55 thf(fact_221_process__term_Octr__transfer_I2_J, axiom, (! [A:$tType,Pvar:$tType,C:$tType,B:$tType,R1:(A > (B > $o)),R22:(Pvar > (C > $o))]: (((((((((bNF_rel_fun @ (proces634752977rocess @ A)) @ (proces634752977rocess @ B)) @ ((proces554692349s_term @ A) @ Pvar)) @ ((proces554692349s_term @ B) @ C)) @ (((proces749077512rocess @ A) @ B) @ R1)) @ ((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22)) @ ((proces1062592052s_PROC @ A) @ Pvar)) @ ((proces1062592052s_PROC @ B) @ C))))).
% 2.99/1.55 thf(fact_222_process_Ocorec__disc__iff_I1_J, axiom, (! [A:$tType,C:$tType,P:(C > $o),G112:(C > A),Q122:(C > $o),G1212:(C > (proces634752977rocess @ A)),G1222:(C > C),Q212:(C > $o),G2112:(C > (proces634752977rocess @ A)),G2122:(C > C),Q222:(C > $o),G2212:(C > (proces634752977rocess @ A)),G2222:(C > C),A2:C]: ((((proces10484146Action @ A) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G112) @ Q122) @ G1212) @ G1222) @ Q212) @ G2112) @ G2122) @ Q222) @ G2212) @ G2222) @ A2)) = (P @ A2))))).
% 2.99/1.55 thf(fact_223_process_Ocorec__disc__iff_I2_J, axiom, (! [A:$tType,C:$tType,P:(C > $o),G112:(C > A),Q122:(C > $o),G1212:(C > (proces634752977rocess @ A)),G1222:(C > C),Q212:(C > $o),G2112:(C > (proces634752977rocess @ A)),G2122:(C > C),Q222:(C > $o),G2212:(C > (proces634752977rocess @ A)),G2222:(C > C),A2:C]: ((((proces401113213Choice @ A) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G112) @ Q122) @ G1212) @ G1222) @ Q212) @ G2112) @ G2122) @ Q222) @ G2212) @ G2222) @ A2)) = (~ ((P @ A2))))))).
% 2.99/1.55 thf(fact_224_process__term_Octr__transfer_I1_J, axiom, (! [Pvar:$tType,A:$tType,B:$tType,C:$tType,R22:(Pvar > (C > $o)),R1:(A > (B > $o))]: (((((((((bNF_rel_fun @ Pvar) @ C) @ ((proces554692349s_term @ A) @ Pvar)) @ ((proces554692349s_term @ B) @ C)) @ R22) @ ((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22)) @ ((proces1627516585ss_VAR @ Pvar) @ A)) @ ((proces1627516585ss_VAR @ C) @ B))))).
% 2.99/1.55 thf(fact_225_process__term_Orec__transfer, axiom, (! [Pvar:$tType,D:$tType,A:$tType,B:$tType,E2:$tType,C:$tType,R22:(Pvar > (C > $o)),S:(D > (E2 > $o)),R1:(A > (B > $o))]: (((((((((bNF_rel_fun @ (Pvar > D)) @ (C > E2)) @ (((proces634752977rocess @ A) > D) > ((A > (((proces554692349s_term @ A) @ Pvar) > (D > D))) > ((((proces554692349s_term @ A) @ Pvar) > (((proces554692349s_term @ A) @ Pvar) > (D > (D > D)))) > (((proces554692349s_term @ A) @ Pvar) > D))))) @ (((proces634752977rocess @ B) > E2) > ((B > (((proces554692349s_term @ B) @ C) > (E2 > E2))) > ((((proces554692349s_term @ B) @ C) > (((proces554692349s_term @ B) @ C) > (E2 > (E2 > E2)))) > (((proces554692349s_term @ B) @ C) > E2))))) @ ((((((bNF_rel_fun @ Pvar) @ C) @ D) @ E2) @ R22) @ S)) @ ((((((bNF_rel_fun @ ((proces634752977rocess @ A) > D)) @ ((proces634752977rocess @ B) > E2)) @ ((A > (((proces554692349s_term @ A) @ Pvar) > (D > D))) > ((((proces554692349s_term @ A) @ Pvar) > (((proces554692349s_term @ A) @ Pvar) > (D > (D > D)))) > (((proces554692349s_term @ A) @ Pvar) > D)))) @ ((B > (((proces554692349s_term @ B) @ C) > (E2 > E2))) > ((((proces554692349s_term @ B) @ C) > (((proces554692349s_term @ B) @ C) > (E2 > (E2 > E2)))) > (((proces554692349s_term @ B) @ C) > E2)))) @ ((((((bNF_rel_fun @ (proces634752977rocess @ A)) @ (proces634752977rocess @ B)) @ D) @ E2) @ (((proces749077512rocess @ A) @ B) @ R1)) @ S)) @ ((((((bNF_rel_fun @ (A > (((proces554692349s_term @ A) @ Pvar) > (D > D)))) @ (B > (((proces554692349s_term @ B) @ C) > (E2 > E2)))) @ ((((proces554692349s_term @ A) @ Pvar) > (((proces554692349s_term @ A) @ Pvar) > (D > (D > D)))) > (((proces554692349s_term @ A) @ Pvar) > D))) @ ((((proces554692349s_term @ B) @ C) > (((proces554692349s_term @ B) @ C) > (E2 > (E2 > E2)))) > (((proces554692349s_term @ B) @ C) > E2))) @ ((((((bNF_rel_fun @ A) @ B) @ (((proces554692349s_term @ A) @ Pvar) > (D > D))) @ (((proces554692349s_term @ B) @ C) > (E2 > E2))) @ R1) @ ((((((bNF_rel_fun @ ((proces554692349s_term @ A) @ Pvar)) @ ((proces554692349s_term @ B) @ C)) @ (D > D)) @ (E2 > E2)) @ ((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22)) @ ((((((bNF_rel_fun @ D) @ E2) @ D) @ E2) @ S) @ S)))) @ ((((((bNF_rel_fun @ (((proces554692349s_term @ A) @ Pvar) > (((proces554692349s_term @ A) @ Pvar) > (D > (D > D))))) @ (((proces554692349s_term @ B) @ C) > (((proces554692349s_term @ B) @ C) > (E2 > (E2 > E2))))) @ (((proces554692349s_term @ A) @ Pvar) > D)) @ (((proces554692349s_term @ B) @ C) > E2)) @ ((((((bNF_rel_fun @ ((proces554692349s_term @ A) @ Pvar)) @ ((proces554692349s_term @ B) @ C)) @ (((proces554692349s_term @ A) @ Pvar) > (D > (D > D)))) @ (((proces554692349s_term @ B) @ C) > (E2 > (E2 > E2)))) @ ((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22)) @ ((((((bNF_rel_fun @ ((proces554692349s_term @ A) @ Pvar)) @ ((proces554692349s_term @ B) @ C)) @ (D > (D > D))) @ (E2 > (E2 > E2))) @ ((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22)) @ ((((((bNF_rel_fun @ D) @ E2) @ (D > D)) @ (E2 > E2)) @ S) @ ((((((bNF_rel_fun @ D) @ E2) @ D) @ E2) @ S) @ S))))) @ ((((((bNF_rel_fun @ ((proces554692349s_term @ A) @ Pvar)) @ ((proces554692349s_term @ B) @ C)) @ D) @ E2) @ ((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22)) @ S))))) @ (((proces2117273769s_term @ Pvar) @ D) @ A)) @ (((proces2117273769s_term @ C) @ E2) @ B))))).
% 2.99/1.55 thf(fact_226_process__term_Ocase__transfer, axiom, (! [Pvar:$tType,D:$tType,A:$tType,B:$tType,E2:$tType,C:$tType,R22:(Pvar > (C > $o)),S:(D > (E2 > $o)),R1:(A > (B > $o))]: (((((((((bNF_rel_fun @ (Pvar > D)) @ (C > E2)) @ (((proces634752977rocess @ A) > D) > ((A > (((proces554692349s_term @ A) @ Pvar) > D)) > ((((proces554692349s_term @ A) @ Pvar) > (((proces554692349s_term @ A) @ Pvar) > D)) > (((proces554692349s_term @ A) @ Pvar) > D))))) @ (((proces634752977rocess @ B) > E2) > ((B > (((proces554692349s_term @ B) @ C) > E2)) > ((((proces554692349s_term @ B) @ C) > (((proces554692349s_term @ B) @ C) > E2)) > (((proces554692349s_term @ B) @ C) > E2))))) @ ((((((bNF_rel_fun @ Pvar) @ C) @ D) @ E2) @ R22) @ S)) @ ((((((bNF_rel_fun @ ((proces634752977rocess @ A) > D)) @ ((proces634752977rocess @ B) > E2)) @ ((A > (((proces554692349s_term @ A) @ Pvar) > D)) > ((((proces554692349s_term @ A) @ Pvar) > (((proces554692349s_term @ A) @ Pvar) > D)) > (((proces554692349s_term @ A) @ Pvar) > D)))) @ ((B > (((proces554692349s_term @ B) @ C) > E2)) > ((((proces554692349s_term @ B) @ C) > (((proces554692349s_term @ B) @ C) > E2)) > (((proces554692349s_term @ B) @ C) > E2)))) @ ((((((bNF_rel_fun @ (proces634752977rocess @ A)) @ (proces634752977rocess @ B)) @ D) @ E2) @ (((proces749077512rocess @ A) @ B) @ R1)) @ S)) @ ((((((bNF_rel_fun @ (A > (((proces554692349s_term @ A) @ Pvar) > D))) @ (B > (((proces554692349s_term @ B) @ C) > E2))) @ ((((proces554692349s_term @ A) @ Pvar) > (((proces554692349s_term @ A) @ Pvar) > D)) > (((proces554692349s_term @ A) @ Pvar) > D))) @ ((((proces554692349s_term @ B) @ C) > (((proces554692349s_term @ B) @ C) > E2)) > (((proces554692349s_term @ B) @ C) > E2))) @ ((((((bNF_rel_fun @ A) @ B) @ (((proces554692349s_term @ A) @ Pvar) > D)) @ (((proces554692349s_term @ B) @ C) > E2)) @ R1) @ ((((((bNF_rel_fun @ ((proces554692349s_term @ A) @ Pvar)) @ ((proces554692349s_term @ B) @ C)) @ D) @ E2) @ ((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22)) @ S))) @ ((((((bNF_rel_fun @ (((proces554692349s_term @ A) @ Pvar) > (((proces554692349s_term @ A) @ Pvar) > D))) @ (((proces554692349s_term @ B) @ C) > (((proces554692349s_term @ B) @ C) > E2))) @ (((proces554692349s_term @ A) @ Pvar) > D)) @ (((proces554692349s_term @ B) @ C) > E2)) @ ((((((bNF_rel_fun @ ((proces554692349s_term @ A) @ Pvar)) @ ((proces554692349s_term @ B) @ C)) @ (((proces554692349s_term @ A) @ Pvar) > D)) @ (((proces554692349s_term @ B) @ C) > E2)) @ ((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22)) @ ((((((bNF_rel_fun @ ((proces554692349s_term @ A) @ Pvar)) @ ((proces554692349s_term @ B) @ C)) @ D) @ E2) @ ((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22)) @ S))) @ ((((((bNF_rel_fun @ ((proces554692349s_term @ A) @ Pvar)) @ ((proces554692349s_term @ B) @ C)) @ D) @ E2) @ ((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22)) @ S))))) @ (((proces460752237s_term @ Pvar) @ D) @ A)) @ (((proces460752237s_term @ C) @ E2) @ B))))).
% 2.99/1.55 thf(fact_227_process_Ocorec_I1_J, axiom, (! [A:$tType,C:$tType,P:(C > $o),A2:C,G112:(C > A),Q122:(C > $o),G1212:(C > (proces634752977rocess @ A)),G1222:(C > C),Q212:(C > $o),G2112:(C > (proces634752977rocess @ A)),G2122:(C > C),Q222:(C > $o),G2212:(C > (proces634752977rocess @ A)),G2222:(C > C)]: (((P @ A2) => (((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G112) @ Q122) @ G1212) @ G1222) @ Q212) @ G2112) @ G2122) @ Q222) @ G2212) @ G2222) @ A2) = (((proces1525233512Action @ A) @ (G112 @ A2)) @ ((((if @ (proces634752977rocess @ A)) @ (Q122 @ A2)) @ (G1212 @ A2)) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G112) @ Q122) @ G1212) @ G1222) @ Q212) @ G2112) @ G2122) @ Q222) @ G2212) @ G2222) @ (G1222 @ A2))))))))).
% 2.99/1.55 thf(fact_228_process_Ocorec__transfer, axiom, (! [C:$tType,A:$tType,B:$tType,D:$tType,S:(C > (D > $o)),R:(A > (B > $o))]: (((((((((bNF_rel_fun @ (C > $o)) @ (D > $o)) @ ((C > A) > ((C > $o) > ((C > (proces634752977rocess @ A)) > ((C > C) > ((C > $o) > ((C > (proces634752977rocess @ A)) > ((C > C) > ((C > $o) > ((C > (proces634752977rocess @ A)) > ((C > C) > (C > (proces634752977rocess @ A))))))))))))) @ ((D > B) > ((D > $o) > ((D > (proces634752977rocess @ B)) > ((D > D) > ((D > $o) > ((D > (proces634752977rocess @ B)) > ((D > D) > ((D > $o) > ((D > (proces634752977rocess @ B)) > ((D > D) > (D > (proces634752977rocess @ B))))))))))))) @ ((((((bNF_rel_fun @ C) @ D) @ $o) @ $o) @ S) @ (^ [Y8:$o,Z3:$o]: ((Y8 = Z3))))) @ ((((((bNF_rel_fun @ (C > A)) @ (D > B)) @ ((C > $o) > ((C > (proces634752977rocess @ A)) > ((C > C) > ((C > $o) > ((C > (proces634752977rocess @ A)) > ((C > C) > ((C > $o) > ((C > (proces634752977rocess @ A)) > ((C > C) > (C > (proces634752977rocess @ A)))))))))))) @ ((D > $o) > ((D > (proces634752977rocess @ B)) > ((D > D) > ((D > $o) > ((D > (proces634752977rocess @ B)) > ((D > D) > ((D > $o) > ((D > (proces634752977rocess @ B)) > ((D > D) > (D > (proces634752977rocess @ B)))))))))))) @ ((((((bNF_rel_fun @ C) @ D) @ A) @ B) @ S) @ R)) @ ((((((bNF_rel_fun @ (C > $o)) @ (D > $o)) @ ((C > (proces634752977rocess @ A)) > ((C > C) > ((C > $o) > ((C > (proces634752977rocess @ A)) > ((C > C) > ((C > $o) > ((C > (proces634752977rocess @ A)) > ((C > C) > (C > (proces634752977rocess @ A))))))))))) @ ((D > (proces634752977rocess @ B)) > ((D > D) > ((D > $o) > ((D > (proces634752977rocess @ B)) > ((D > D) > ((D > $o) > ((D > (proces634752977rocess @ B)) > ((D > D) > (D > (proces634752977rocess @ B))))))))))) @ ((((((bNF_rel_fun @ C) @ D) @ $o) @ $o) @ S) @ (^ [Y8:$o,Z3:$o]: ((Y8 = Z3))))) @ ((((((bNF_rel_fun @ (C > (proces634752977rocess @ A))) @ (D > (proces634752977rocess @ B))) @ ((C > C) > ((C > $o) > ((C > (proces634752977rocess @ A)) > ((C > C) > ((C > $o) > ((C > (proces634752977rocess @ A)) > ((C > C) > (C > (proces634752977rocess @ A)))))))))) @ ((D > D) > ((D > $o) > ((D > (proces634752977rocess @ B)) > ((D > D) > ((D > $o) > ((D > (proces634752977rocess @ B)) > ((D > D) > (D > (proces634752977rocess @ B)))))))))) @ ((((((bNF_rel_fun @ C) @ D) @ (proces634752977rocess @ A)) @ (proces634752977rocess @ B)) @ S) @ (((proces749077512rocess @ A) @ B) @ R))) @ ((((((bNF_rel_fun @ (C > C)) @ (D > D)) @ ((C > $o) > ((C > (proces634752977rocess @ A)) > ((C > C) > ((C > $o) > ((C > (proces634752977rocess @ A)) > ((C > C) > (C > (proces634752977rocess @ A))))))))) @ ((D > $o) > ((D > (proces634752977rocess @ B)) > ((D > D) > ((D > $o) > ((D > (proces634752977rocess @ B)) > ((D > D) > (D > (proces634752977rocess @ B))))))))) @ ((((((bNF_rel_fun @ C) @ D) @ C) @ D) @ S) @ S)) @ ((((((bNF_rel_fun @ (C > $o)) @ (D > $o)) @ ((C > (proces634752977rocess @ A)) > ((C > C) > ((C > $o) > ((C > (proces634752977rocess @ A)) > ((C > C) > (C > (proces634752977rocess @ A)))))))) @ ((D > (proces634752977rocess @ B)) > ((D > D) > ((D > $o) > ((D > (proces634752977rocess @ B)) > ((D > D) > (D > (proces634752977rocess @ B)))))))) @ ((((((bNF_rel_fun @ C) @ D) @ $o) @ $o) @ S) @ (^ [Y8:$o,Z3:$o]: ((Y8 = Z3))))) @ ((((((bNF_rel_fun @ (C > (proces634752977rocess @ A))) @ (D > (proces634752977rocess @ B))) @ ((C > C) > ((C > $o) > ((C > (proces634752977rocess @ A)) > ((C > C) > (C > (proces634752977rocess @ A))))))) @ ((D > D) > ((D > $o) > ((D > (proces634752977rocess @ B)) > ((D > D) > (D > (proces634752977rocess @ B))))))) @ ((((((bNF_rel_fun @ C) @ D) @ (proces634752977rocess @ A)) @ (proces634752977rocess @ B)) @ S) @ (((proces749077512rocess @ A) @ B) @ R))) @ ((((((bNF_rel_fun @ (C > C)) @ (D > D)) @ ((C > $o) > ((C > (proces634752977rocess @ A)) > ((C > C) > (C > (proces634752977rocess @ A)))))) @ ((D > $o) > ((D > (proces634752977rocess @ B)) > ((D > D) > (D > (proces634752977rocess @ B)))))) @ ((((((bNF_rel_fun @ C) @ D) @ C) @ D) @ S) @ S)) @ ((((((bNF_rel_fun @ (C > $o)) @ (D > $o)) @ ((C > (proces634752977rocess @ A)) > ((C > C) > (C > (proces634752977rocess @ A))))) @ ((D > (proces634752977rocess @ B)) > ((D > D) > (D > (proces634752977rocess @ B))))) @ ((((((bNF_rel_fun @ C) @ D) @ $o) @ $o) @ S) @ (^ [Y8:$o,Z3:$o]: ((Y8 = Z3))))) @ ((((((bNF_rel_fun @ (C > (proces634752977rocess @ A))) @ (D > (proces634752977rocess @ B))) @ ((C > C) > (C > (proces634752977rocess @ A)))) @ ((D > D) > (D > (proces634752977rocess @ B)))) @ ((((((bNF_rel_fun @ C) @ D) @ (proces634752977rocess @ A)) @ (proces634752977rocess @ B)) @ S) @ (((proces749077512rocess @ A) @ B) @ R))) @ ((((((bNF_rel_fun @ (C > C)) @ (D > D)) @ (C > (proces634752977rocess @ A))) @ (D > (proces634752977rocess @ B))) @ ((((((bNF_rel_fun @ C) @ D) @ C) @ D) @ S) @ S)) @ ((((((bNF_rel_fun @ C) @ D) @ (proces634752977rocess @ A)) @ (proces634752977rocess @ B)) @ S) @ (((proces749077512rocess @ A) @ B) @ R))))))))))))) @ ((proces894737309rocess @ C) @ A)) @ ((proces894737309rocess @ D) @ B))))).
% 2.99/1.55 thf(fact_229_process_Ocorec__disc_I1_J, axiom, (! [A:$tType,C:$tType,P:(C > $o),A2:C,G112:(C > A),Q122:(C > $o),G1212:(C > (proces634752977rocess @ A)),G1222:(C > C),Q212:(C > $o),G2112:(C > (proces634752977rocess @ A)),G2122:(C > C),Q222:(C > $o),G2212:(C > (proces634752977rocess @ A)),G2222:(C > C)]: (((P @ A2) => ((proces10484146Action @ A) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G112) @ Q122) @ G1212) @ G1222) @ Q212) @ G2112) @ G2122) @ Q222) @ G2212) @ G2222) @ A2)))))).
% 2.99/1.55 thf(fact_230_process_Ocorec__disc_I2_J, axiom, (! [A:$tType,C:$tType,P:(C > $o),A2:C,G112:(C > A),Q122:(C > $o),G1212:(C > (proces634752977rocess @ A)),G1222:(C > C),Q212:(C > $o),G2112:(C > (proces634752977rocess @ A)),G2122:(C > C),Q222:(C > $o),G2212:(C > (proces634752977rocess @ A)),G2222:(C > C)]: (((~ ((P @ A2))) => ((proces401113213Choice @ A) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G112) @ Q122) @ G1212) @ G1222) @ Q212) @ G2112) @ G2122) @ Q222) @ G2212) @ G2222) @ A2)))))).
% 2.99/1.55 thf(fact_231_process_Ocorec__sel_I1_J, axiom, (! [A:$tType,C:$tType,P:(C > $o),A2:C,G112:(C > A),Q122:(C > $o),G1212:(C > (proces634752977rocess @ A)),G1222:(C > C),Q212:(C > $o),G2112:(C > (proces634752977rocess @ A)),G2122:(C > C),Q222:(C > $o),G2212:(C > (proces634752977rocess @ A)),G2222:(C > C)]: (((P @ A2) => (((proces745025900prefOf @ A) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G112) @ Q122) @ G1212) @ G1222) @ Q212) @ G2112) @ G2122) @ Q222) @ G2212) @ G2222) @ A2)) = (G112 @ A2)))))).
% 2.99/1.55 thf(fact_232_process_Ocorec__sel_I4_J, axiom, (! [A:$tType,C:$tType,P:(C > $o),A2:C,Q222:(C > $o),G112:(C > A),Q122:(C > $o),G1212:(C > (proces634752977rocess @ A)),G1222:(C > C),Q212:(C > $o),G2112:(C > (proces634752977rocess @ A)),G2122:(C > C),G2212:(C > (proces634752977rocess @ A)),G2222:(C > C)]: (((~ ((P @ A2))) => (((Q222 @ A2) => (((proces988026546_ch2Of @ A) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G112) @ Q122) @ G1212) @ G1222) @ Q212) @ G2112) @ G2122) @ Q222) @ G2212) @ G2222) @ A2)) = (G2212 @ A2))) & ((~ ((Q222 @ A2))) => (((proces988026546_ch2Of @ A) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G112) @ Q122) @ G1212) @ G1222) @ Q212) @ G2112) @ G2122) @ Q222) @ G2212) @ G2222) @ A2)) = ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G112) @ Q122) @ G1212) @ G1222) @ Q212) @ G2112) @ G2122) @ Q222) @ G2212) @ G2222) @ (G2222 @ A2))))))))).
% 2.99/1.55 thf(fact_233_process_Ocorec__sel_I3_J, axiom, (! [A:$tType,C:$tType,P:(C > $o),A2:C,Q212:(C > $o),G112:(C > A),Q122:(C > $o),G1212:(C > (proces634752977rocess @ A)),G1222:(C > C),G2112:(C > (proces634752977rocess @ A)),G2122:(C > C),Q222:(C > $o),G2212:(C > (proces634752977rocess @ A)),G2222:(C > C)]: (((~ ((P @ A2))) => (((Q212 @ A2) => (((proces979765041_ch1Of @ A) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G112) @ Q122) @ G1212) @ G1222) @ Q212) @ G2112) @ G2122) @ Q222) @ G2212) @ G2222) @ A2)) = (G2112 @ A2))) & ((~ ((Q212 @ A2))) => (((proces979765041_ch1Of @ A) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G112) @ Q122) @ G1212) @ G1222) @ Q212) @ G2112) @ G2122) @ Q222) @ G2212) @ G2222) @ A2)) = ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G112) @ Q122) @ G1212) @ G1222) @ Q212) @ G2112) @ G2122) @ Q222) @ G2212) @ G2222) @ (G2122 @ A2))))))))).
% 2.99/1.55 thf(fact_234_process_Ocorec__sel_I2_J, axiom, (! [A:$tType,C:$tType,P:(C > $o),A2:C,Q122:(C > $o),G112:(C > A),G1212:(C > (proces634752977rocess @ A)),G1222:(C > C),Q212:(C > $o),G2112:(C > (proces634752977rocess @ A)),G2122:(C > C),Q222:(C > $o),G2212:(C > (proces634752977rocess @ A)),G2222:(C > C)]: (((P @ A2) => (((Q122 @ A2) => (((proces1778668539contOf @ A) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G112) @ Q122) @ G1212) @ G1222) @ Q212) @ G2112) @ G2122) @ Q222) @ G2212) @ G2222) @ A2)) = (G1212 @ A2))) & ((~ ((Q122 @ A2))) => (((proces1778668539contOf @ A) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G112) @ Q122) @ G1212) @ G1222) @ Q212) @ G2112) @ G2122) @ Q222) @ G2212) @ G2222) @ A2)) = ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G112) @ Q122) @ G1212) @ G1222) @ Q212) @ G2112) @ G2122) @ Q222) @ G2212) @ G2222) @ (G1222 @ A2))))))))).
% 2.99/1.55 thf(fact_235_process_Ocorec_I2_J, axiom, (! [A:$tType,C:$tType,P:(C > $o),A2:C,G112:(C > A),Q122:(C > $o),G1212:(C > (proces634752977rocess @ A)),G1222:(C > C),Q212:(C > $o),G2112:(C > (proces634752977rocess @ A)),G2122:(C > C),Q222:(C > $o),G2212:(C > (proces634752977rocess @ A)),G2222:(C > C)]: (((~ ((P @ A2))) => (((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G112) @ Q122) @ G1212) @ G1222) @ Q212) @ G2112) @ G2122) @ Q222) @ G2212) @ G2222) @ A2) = (((proces1915862579Choice @ A) @ ((((if @ (proces634752977rocess @ A)) @ (Q212 @ A2)) @ (G2112 @ A2)) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G112) @ Q122) @ G1212) @ G1222) @ Q212) @ G2112) @ G2122) @ Q222) @ G2212) @ G2222) @ (G2122 @ A2)))) @ ((((if @ (proces634752977rocess @ A)) @ (Q222 @ A2)) @ (G2212 @ A2)) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G112) @ Q122) @ G1212) @ G1222) @ Q212) @ G2112) @ G2122) @ Q222) @ G2212) @ G2222) @ (G2222 @ A2))))))))).
% 2.99/1.55 thf(fact_236_process__term_Orel__transfer, axiom, (! [A:$tType,C:$tType,B:$tType,D:$tType,H2:$tType,F5:$tType,G2:$tType,E2:$tType,S1a:(A > (E2 > $o)),S1c:(C > (G2 > $o)),S2a:(B > (F5 > $o)),S2c:(D > (H2 > $o))]: (((((((((bNF_rel_fun @ (A > (C > $o))) @ (E2 > (G2 > $o))) @ ((B > (D > $o)) > (((proces554692349s_term @ A) @ B) > (((proces554692349s_term @ C) @ D) > $o)))) @ ((F5 > (H2 > $o)) > (((proces554692349s_term @ E2) @ F5) > (((proces554692349s_term @ G2) @ H2) > $o)))) @ ((((((bNF_rel_fun @ A) @ E2) @ (C > $o)) @ (G2 > $o)) @ S1a) @ ((((((bNF_rel_fun @ C) @ G2) @ $o) @ $o) @ S1c) @ (^ [Y8:$o,Z3:$o]: ((Y8 = Z3)))))) @ ((((((bNF_rel_fun @ (B > (D > $o))) @ (F5 > (H2 > $o))) @ (((proces554692349s_term @ A) @ B) > (((proces554692349s_term @ C) @ D) > $o))) @ (((proces554692349s_term @ E2) @ F5) > (((proces554692349s_term @ G2) @ H2) > $o))) @ ((((((bNF_rel_fun @ B) @ F5) @ (D > $o)) @ (H2 > $o)) @ S2a) @ ((((((bNF_rel_fun @ D) @ H2) @ $o) @ $o) @ S2c) @ (^ [Y8:$o,Z3:$o]: ((Y8 = Z3)))))) @ ((((((bNF_rel_fun @ ((proces554692349s_term @ A) @ B)) @ ((proces554692349s_term @ E2) @ F5)) @ (((proces554692349s_term @ C) @ D) > $o)) @ (((proces554692349s_term @ G2) @ H2) > $o)) @ ((((((proces2029722208s_term @ A) @ E2) @ B) @ F5) @ S1a) @ S2a)) @ ((((((bNF_rel_fun @ ((proces554692349s_term @ C) @ D)) @ ((proces554692349s_term @ G2) @ H2)) @ $o) @ $o) @ ((((((proces2029722208s_term @ C) @ G2) @ D) @ H2) @ S1c) @ S2c)) @ (^ [Y8:$o,Z3:$o]: ((Y8 = Z3))))))) @ ((((proces2029722208s_term @ A) @ C) @ B) @ D)) @ ((((proces2029722208s_term @ E2) @ G2) @ F5) @ H2))))).
% 2.99/1.55 thf(fact_237_process__term_Octr__transfer_I3_J, axiom, (! [A:$tType,Pvar:$tType,C:$tType,B:$tType,R1:(A > (B > $o)),R22:(Pvar > (C > $o))]: (((((((((bNF_rel_fun @ A) @ B) @ (((proces554692349s_term @ A) @ Pvar) > ((proces554692349s_term @ A) @ Pvar))) @ (((proces554692349s_term @ B) @ C) > ((proces554692349s_term @ B) @ C))) @ R1) @ ((((((bNF_rel_fun @ ((proces554692349s_term @ A) @ Pvar)) @ ((proces554692349s_term @ B) @ C)) @ ((proces554692349s_term @ A) @ Pvar)) @ ((proces554692349s_term @ B) @ C)) @ ((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22)) @ ((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22))) @ ((proces1454156180ss_ACT @ A) @ Pvar)) @ ((proces1454156180ss_ACT @ B) @ C))))).
% 2.99/1.55 thf(fact_238_process__term_Octr__transfer_I4_J, axiom, (! [A:$tType,Pvar:$tType,C:$tType,B:$tType,R1:(A > (B > $o)),R22:(Pvar > (C > $o))]: (((((((((bNF_rel_fun @ ((proces554692349s_term @ A) @ Pvar)) @ ((proces554692349s_term @ B) @ C)) @ (((proces554692349s_term @ A) @ Pvar) > ((proces554692349s_term @ A) @ Pvar))) @ (((proces554692349s_term @ B) @ C) > ((proces554692349s_term @ B) @ C))) @ ((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22)) @ ((((((bNF_rel_fun @ ((proces554692349s_term @ A) @ Pvar)) @ ((proces554692349s_term @ B) @ C)) @ ((proces554692349s_term @ A) @ Pvar)) @ ((proces554692349s_term @ B) @ C)) @ ((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22)) @ ((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22))) @ ((proces89589571ess_CH @ A) @ Pvar)) @ ((proces89589571ess_CH @ B) @ C))))).
% 2.99/1.55 thf(fact_239_process_Odisc__transfer_I1_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o))]: (((((((((bNF_rel_fun @ (proces634752977rocess @ A)) @ (proces634752977rocess @ B)) @ $o) @ $o) @ (((proces749077512rocess @ A) @ B) @ R)) @ (^ [Y8:$o,Z3:$o]: ((Y8 = Z3)))) @ (proces10484146Action @ A)) @ (proces10484146Action @ B))))).
% 2.99/1.55 thf(fact_240_process_Odisc__transfer_I2_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o))]: (((((((((bNF_rel_fun @ (proces634752977rocess @ A)) @ (proces634752977rocess @ B)) @ $o) @ $o) @ (((proces749077512rocess @ A) @ B) @ R)) @ (^ [Y8:$o,Z3:$o]: ((Y8 = Z3)))) @ (proces401113213Choice @ A)) @ (proces401113213Choice @ B))))).
% 2.99/1.55 thf(fact_241_process_Octr__transfer_I1_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o))]: (((((((((bNF_rel_fun @ A) @ B) @ ((proces634752977rocess @ A) > (proces634752977rocess @ A))) @ ((proces634752977rocess @ B) > (proces634752977rocess @ B))) @ R) @ ((((((bNF_rel_fun @ (proces634752977rocess @ A)) @ (proces634752977rocess @ B)) @ (proces634752977rocess @ A)) @ (proces634752977rocess @ B)) @ (((proces749077512rocess @ A) @ B) @ R)) @ (((proces749077512rocess @ A) @ B) @ R))) @ (proces1525233512Action @ A)) @ (proces1525233512Action @ B))))).
% 2.99/1.55 thf(fact_242_process_Orel__transfer, axiom, (! [A:$tType,B:$tType,D:$tType,C:$tType,Sa:(A > (C > $o)),Sc:(B > (D > $o))]: (((((((((bNF_rel_fun @ (A > (B > $o))) @ (C > (D > $o))) @ ((proces634752977rocess @ A) > ((proces634752977rocess @ B) > $o))) @ ((proces634752977rocess @ C) > ((proces634752977rocess @ D) > $o))) @ ((((((bNF_rel_fun @ A) @ C) @ (B > $o)) @ (D > $o)) @ Sa) @ ((((((bNF_rel_fun @ B) @ D) @ $o) @ $o) @ Sc) @ (^ [Y8:$o,Z3:$o]: ((Y8 = Z3)))))) @ ((((((bNF_rel_fun @ (proces634752977rocess @ A)) @ (proces634752977rocess @ C)) @ ((proces634752977rocess @ B) > $o)) @ ((proces634752977rocess @ D) > $o)) @ (((proces749077512rocess @ A) @ C) @ Sa)) @ ((((((bNF_rel_fun @ (proces634752977rocess @ B)) @ (proces634752977rocess @ D)) @ $o) @ $o) @ (((proces749077512rocess @ B) @ D) @ Sc)) @ (^ [Y8:$o,Z3:$o]: ((Y8 = Z3)))))) @ ((proces749077512rocess @ A) @ B)) @ ((proces749077512rocess @ C) @ D))))).
% 2.99/1.55 thf(fact_243_process_Ocase__transfer, axiom, (! [A:$tType,C:$tType,D:$tType,B:$tType,R:(A > (B > $o)),S:(C > (D > $o))]: (((((((((bNF_rel_fun @ (A > ((proces634752977rocess @ A) > C))) @ (B > ((proces634752977rocess @ B) > D))) @ (((proces634752977rocess @ A) > ((proces634752977rocess @ A) > C)) > ((proces634752977rocess @ A) > C))) @ (((proces634752977rocess @ B) > ((proces634752977rocess @ B) > D)) > ((proces634752977rocess @ B) > D))) @ ((((((bNF_rel_fun @ A) @ B) @ ((proces634752977rocess @ A) > C)) @ ((proces634752977rocess @ B) > D)) @ R) @ ((((((bNF_rel_fun @ (proces634752977rocess @ A)) @ (proces634752977rocess @ B)) @ C) @ D) @ (((proces749077512rocess @ A) @ B) @ R)) @ S))) @ ((((((bNF_rel_fun @ ((proces634752977rocess @ A) > ((proces634752977rocess @ A) > C))) @ ((proces634752977rocess @ B) > ((proces634752977rocess @ B) > D))) @ ((proces634752977rocess @ A) > C)) @ ((proces634752977rocess @ B) > D)) @ ((((((bNF_rel_fun @ (proces634752977rocess @ A)) @ (proces634752977rocess @ B)) @ ((proces634752977rocess @ A) > C)) @ ((proces634752977rocess @ B) > D)) @ (((proces749077512rocess @ A) @ B) @ R)) @ ((((((bNF_rel_fun @ (proces634752977rocess @ A)) @ (proces634752977rocess @ B)) @ C) @ D) @ (((proces749077512rocess @ A) @ B) @ R)) @ S))) @ ((((((bNF_rel_fun @ (proces634752977rocess @ A)) @ (proces634752977rocess @ B)) @ C) @ D) @ (((proces749077512rocess @ A) @ B) @ R)) @ S))) @ ((proces1406508781rocess @ A) @ C)) @ ((proces1406508781rocess @ B) @ D))))).
% 2.99/1.55 thf(fact_244_process_Octr__transfer_I2_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o))]: (((((((((bNF_rel_fun @ (proces634752977rocess @ A)) @ (proces634752977rocess @ B)) @ ((proces634752977rocess @ A) > (proces634752977rocess @ A))) @ ((proces634752977rocess @ B) > (proces634752977rocess @ B))) @ (((proces749077512rocess @ A) @ B) @ R)) @ ((((((bNF_rel_fun @ (proces634752977rocess @ A)) @ (proces634752977rocess @ B)) @ (proces634752977rocess @ A)) @ (proces634752977rocess @ B)) @ (((proces749077512rocess @ A) @ B) @ R)) @ (((proces749077512rocess @ A) @ B) @ R))) @ (proces1915862579Choice @ A)) @ (proces1915862579Choice @ B))))).
% 2.99/1.55 thf(fact_245_process__term_Opred__transfer, axiom, (! [A:$tType,B:$tType,D:$tType,C:$tType,R1:(A > (C > $o)),R22:(B > (D > $o))]: (((((((((bNF_rel_fun @ (A > $o)) @ (C > $o)) @ ((B > $o) > (((proces554692349s_term @ A) @ B) > $o))) @ ((D > $o) > (((proces554692349s_term @ C) @ D) > $o))) @ ((((((bNF_rel_fun @ A) @ C) @ $o) @ $o) @ R1) @ (^ [Y8:$o,Z3:$o]: ((Y8 = Z3))))) @ ((((((bNF_rel_fun @ (B > $o)) @ (D > $o)) @ (((proces554692349s_term @ A) @ B) > $o)) @ (((proces554692349s_term @ C) @ D) > $o)) @ ((((((bNF_rel_fun @ B) @ D) @ $o) @ $o) @ R22) @ (^ [Y8:$o,Z3:$o]: ((Y8 = Z3))))) @ ((((((bNF_rel_fun @ ((proces554692349s_term @ A) @ B)) @ ((proces554692349s_term @ C) @ D)) @ $o) @ $o) @ ((((((proces2029722208s_term @ A) @ C) @ B) @ D) @ R1) @ R22)) @ (^ [Y8:$o,Z3:$o]: ((Y8 = Z3)))))) @ ((proces2118920028s_term @ A) @ B)) @ ((proces2118920028s_term @ C) @ D))))).
% 2.99/1.55 thf(fact_246_process_Opred__transfer, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o))]: (((((((((bNF_rel_fun @ (A > $o)) @ (B > $o)) @ ((proces634752977rocess @ A) > $o)) @ ((proces634752977rocess @ B) > $o)) @ ((((((bNF_rel_fun @ A) @ B) @ $o) @ $o) @ R) @ (^ [Y8:$o,Z3:$o]: ((Y8 = Z3))))) @ ((((((bNF_rel_fun @ (proces634752977rocess @ A)) @ (proces634752977rocess @ B)) @ $o) @ $o) @ (((proces749077512rocess @ A) @ B) @ R)) @ (^ [Y8:$o,Z3:$o]: ((Y8 = Z3))))) @ (proces1205983068rocess @ A)) @ (proces1205983068rocess @ B))))).
% 2.99/1.55 thf(fact_247_process__term_Opred__inject_I1_J, axiom, (! [A:$tType,Pvar:$tType,P1:(A > $o),P22:(Pvar > $o),A2:Pvar]: (((((((proces2118920028s_term @ A) @ Pvar) @ P1) @ P22) @ (((proces1627516585ss_VAR @ Pvar) @ A) @ A2)) = (P22 @ A2))))).
% 2.99/1.55 thf(fact_248_process__term_Opred__inject_I4_J, axiom, (! [Pvar:$tType,A:$tType,P1:(A > $o),P22:(Pvar > $o),A2:((proces554692349s_term @ A) @ Pvar),Aa2:((proces554692349s_term @ A) @ Pvar)]: (((((((proces2118920028s_term @ A) @ Pvar) @ P1) @ P22) @ ((((proces89589571ess_CH @ A) @ Pvar) @ A2) @ Aa2)) = ((((((proces2118920028s_term @ A) @ Pvar) @ P1) @ P22) @ A2) & (((((proces2118920028s_term @ A) @ Pvar) @ P1) @ P22) @ Aa2)))))).
% 2.99/1.55 thf(fact_249_process__term_Opred__inject_I3_J, axiom, (! [Pvar:$tType,A:$tType,P1:(A > $o),P22:(Pvar > $o),A2:A,Aa2:((proces554692349s_term @ A) @ Pvar)]: (((((((proces2118920028s_term @ A) @ Pvar) @ P1) @ P22) @ ((((proces1454156180ss_ACT @ A) @ Pvar) @ A2) @ Aa2)) = ((P1 @ A2) & (((((proces2118920028s_term @ A) @ Pvar) @ P1) @ P22) @ Aa2)))))).
% 2.99/1.55 thf(fact_250_process_Opred__inject_I1_J, axiom, (! [A:$tType,P3:(A > $o),A2:A,Aa2:(proces634752977rocess @ A)]: (((((proces1205983068rocess @ A) @ P3) @ (((proces1525233512Action @ A) @ A2) @ Aa2)) = ((P3 @ A2) & (((proces1205983068rocess @ A) @ P3) @ Aa2)))))).
% 2.99/1.55 thf(fact_251_process_Opred__inject_I2_J, axiom, (! [A:$tType,P3:(A > $o),A2:(proces634752977rocess @ A),Aa2:(proces634752977rocess @ A)]: (((((proces1205983068rocess @ A) @ P3) @ (((proces1915862579Choice @ A) @ A2) @ Aa2)) = ((((proces1205983068rocess @ A) @ P3) @ A2) & (((proces1205983068rocess @ A) @ P3) @ Aa2)))))).
% 2.99/1.55 thf(fact_252_process__term_Opred__inject_I2_J, axiom, (! [Pvar:$tType,A:$tType,P1:(A > $o),P22:(Pvar > $o),A2:(proces634752977rocess @ A)]: (((((((proces2118920028s_term @ A) @ Pvar) @ P1) @ P22) @ (((proces1062592052s_PROC @ A) @ Pvar) @ A2)) = (((proces1205983068rocess @ A) @ P1) @ A2))))).
% 2.99/1.55 thf(fact_253_process_Opred__True, axiom, (! [A:$tType]: ((((proces1205983068rocess @ A) @ (^ [Uu2:A]: ($true))) = (^ [Uu2:(proces634752977rocess @ A)]: ($true)))))).
% 2.99/1.55 thf(fact_254_process__term_Opred__True, axiom, (! [B:$tType,A:$tType]: ((((((proces2118920028s_term @ A) @ B) @ (^ [Uu2:A]: ($true))) @ (^ [Uu2:B]: ($true))) = (^ [Uu2:((proces554692349s_term @ A) @ B)]: ($true)))))).
% 2.99/1.55 thf(help_If_3_1_T, axiom, (! [P3:$o]: (((P3 = $true) | (P3 = $false))))).
% 2.99/1.55 thf(help_If_2_1_T, axiom, (! [A:$tType,X3:A,Y:A]: ((((((if @ A) @ $false) @ X3) @ Y) = Y)))).
% 2.99/1.55 thf(help_If_1_1_T, axiom, (! [A:$tType,X3:A,Y:A]: ((((((if @ A) @ $true) @ X3) @ Y) = X3)))).
% 2.99/1.55 thf(conj_0, conjecture, (~ (((((((proces687458811_isACT @ b) @ a) @ b) @ a) @ sys) @ (((proces1062592052s_PROC @ a) @ b) @ pa))))).
% 2.99/1.55 % SZS output end ListOfTHF for /export/starexec/sandbox2/tmp/tmp.lDpXRCP47Y/DTF2DTF10445.p
% 2.99/1.55 ------------------------
% 2.99/1.59 ---- Cleaned THF ---
% 2.99/1.59 thf(ty_t_Process__Mirabelle__xovoopgpgi_Oprocess__term,type,
% 2.99/1.59 proces554692349s_term: $tType > $tType > $tType ).
% 2.99/1.59
% 2.99/1.59 thf(ty_t_Process__Mirabelle__xovoopgpgi_Oprocess,type,
% 2.99/1.59 proces634752977rocess: $tType > $tType ).
% 2.99/1.59
% 2.99/1.59 thf(ty_t_Product__Type_Oprod,type,
% 2.99/1.59 product_prod: $tType > $tType > $tType ).
% 2.99/1.59
% 2.99/1.59 thf(ty_t_Set_Oset,type,
% 2.99/1.59 set: $tType > $tType ).
% 2.99/1.59
% 2.99/1.59 thf(ty_t_itself,type,
% 2.99/1.59 itself: $tType > $tType ).
% 2.99/1.59
% 2.99/1.59 thf(ty_tf_b,type,
% 2.99/1.59 b: $tType ).
% 2.99/1.59
% 2.99/1.59 thf(ty_tf_a,type,
% 2.99/1.59 a: $tType ).
% 2.99/1.59
% 2.99/1.59 thf(sy_c_BNF__Def_Orel__fun,type,
% 2.99/1.59 bNF_rel_fun:
% 2.99/1.59 !>[A: $tType,C: $tType,B: $tType,D: $tType] : ( ( A > C > $o ) > ( B > D > $o ) > ( A > B ) > ( C > D ) > $o ) ).
% 2.99/1.59
% 2.99/1.59 thf(sy_c_HOL_Oundefined,type,
% 2.99/1.59 undefined:
% 2.99/1.59 !>[A: $tType] : A ).
% 2.99/1.59
% 2.99/1.59 thf(sy_c_If,type,
% 2.99/1.59 if:
% 2.99/1.59 !>[A: $tType] : ( $o > A > A > A ) ).
% 2.99/1.59
% 2.99/1.59 thf(sy_c_Order__Relation_Oabove,type,
% 2.99/1.59 order_above:
% 2.99/1.59 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > A > ( set @ A ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(sy_c_Order__Relation_OaboveS,type,
% 2.99/1.59 order_aboveS:
% 2.99/1.59 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > A > ( set @ A ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(sy_c_Process__Mirabelle__xovoopgpgi_OCH1,type,
% 2.99/1.59 proces1239275103le_CH1:
% 2.99/1.59 !>[A: $tType,B: $tType] : ( ( A > ( proces554692349s_term @ B @ A ) ) > ( proces554692349s_term @ B @ A ) > ( proces554692349s_term @ B @ A ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(sy_c_Process__Mirabelle__xovoopgpgi_OCH1__rel,type,
% 2.99/1.59 proces1869379930H1_rel:
% 2.99/1.59 !>[A: $tType,B: $tType] : ( ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) > ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) > $o ) ).
% 2.99/1.59
% 2.99/1.59 thf(sy_c_Process__Mirabelle__xovoopgpgi_OCH2,type,
% 2.99/1.59 proces1239275104le_CH2:
% 2.99/1.59 !>[A: $tType,B: $tType] : ( ( A > ( proces554692349s_term @ B @ A ) ) > ( proces554692349s_term @ B @ A ) > ( proces554692349s_term @ B @ A ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(sy_c_Process__Mirabelle__xovoopgpgi_OCH2__rel,type,
% 2.99/1.59 proces93903513H2_rel:
% 2.99/1.59 !>[A: $tType,B: $tType] : ( ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) > ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) > $o ) ).
% 2.99/1.59
% 2.99/1.59 thf(sy_c_Process__Mirabelle__xovoopgpgi_OCONT,type,
% 2.99/1.59 proces126235999e_CONT:
% 2.99/1.59 !>[A: $tType,B: $tType] : ( ( A > ( proces554692349s_term @ B @ A ) ) > ( proces554692349s_term @ B @ A ) > ( proces554692349s_term @ B @ A ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(sy_c_Process__Mirabelle__xovoopgpgi_OCONT__rel,type,
% 2.99/1.59 proces1004198490NT_rel:
% 2.99/1.59 !>[A: $tType,B: $tType] : ( ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) > ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) > $o ) ).
% 2.99/1.59
% 2.99/1.59 thf(sy_c_Process__Mirabelle__xovoopgpgi_OPREF,type,
% 2.99/1.59 proces1708129104e_PREF:
% 2.99/1.59 !>[A: $tType,B: $tType,C: $tType] : ( ( A > ( proces554692349s_term @ B @ C ) ) > ( proces554692349s_term @ B @ A ) > B ) ).
% 2.99/1.59
% 2.99/1.59 thf(sy_c_Process__Mirabelle__xovoopgpgi_OPREF__rel,type,
% 2.99/1.59 proces527360425EF_rel:
% 2.99/1.59 !>[A: $tType,B: $tType,C: $tType] : ( ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) ) > ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) ) > $o ) ).
% 2.99/1.59
% 2.99/1.59 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oguarded,type,
% 2.99/1.59 proces1121166967uarded:
% 2.99/1.59 !>[A: $tType,B: $tType,C: $tType] : ( ( A > ( proces554692349s_term @ B @ C ) ) > $o ) ).
% 2.99/1.59
% 2.99/1.59 thf(sy_c_Process__Mirabelle__xovoopgpgi_OisACT,type,
% 2.99/1.59 proces687458811_isACT:
% 2.99/1.59 !>[A: $tType,B: $tType,C: $tType,D: $tType] : ( ( A > ( proces554692349s_term @ B @ C ) ) > ( proces554692349s_term @ D @ A ) > $o ) ).
% 2.99/1.59
% 2.99/1.59 thf(sy_c_Process__Mirabelle__xovoopgpgi_OisACT__rel,type,
% 2.99/1.59 proces896239806CT_rel:
% 2.99/1.59 !>[A: $tType,B: $tType,C: $tType,D: $tType] : ( ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) > ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) > $o ) ).
% 2.99/1.59
% 2.99/1.59 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OAction,type,
% 2.99/1.59 proces1525233512Action:
% 2.99/1.59 !>[A: $tType] : ( A > ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OChoice,type,
% 2.99/1.59 proces1915862579Choice:
% 2.99/1.59 !>[A: $tType] : ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Ocase__process,type,
% 2.99/1.59 proces1406508781rocess:
% 2.99/1.59 !>[A: $tType,B: $tType] : ( ( A > ( proces634752977rocess @ A ) > B ) > ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B ) > ( proces634752977rocess @ A ) > B ) ).
% 2.99/1.59
% 2.99/1.59 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Och1Of,type,
% 2.99/1.59 proces979765041_ch1Of:
% 2.99/1.59 !>[A: $tType] : ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Och2Of,type,
% 2.99/1.59 proces988026546_ch2Of:
% 2.99/1.59 !>[A: $tType] : ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OcontOf,type,
% 2.99/1.59 proces1778668539contOf:
% 2.99/1.59 !>[A: $tType] : ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Ocorec__process,type,
% 2.99/1.59 proces894737309rocess:
% 2.99/1.59 !>[C: $tType,A: $tType] : ( ( C > $o ) > ( C > A ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > C > ( proces634752977rocess @ A ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OisAction,type,
% 2.99/1.59 proces10484146Action:
% 2.99/1.59 !>[A: $tType] : ( ( proces634752977rocess @ A ) > $o ) ).
% 2.99/1.59
% 2.99/1.59 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OisChoice,type,
% 2.99/1.59 proces401113213Choice:
% 2.99/1.59 !>[A: $tType] : ( ( proces634752977rocess @ A ) > $o ) ).
% 2.99/1.59
% 2.99/1.59 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Opred__process,type,
% 2.99/1.59 proces1205983068rocess:
% 2.99/1.59 !>[A: $tType] : ( ( A > $o ) > ( proces634752977rocess @ A ) > $o ) ).
% 2.99/1.59
% 2.99/1.59 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OprefOf,type,
% 2.99/1.59 proces745025900prefOf:
% 2.99/1.59 !>[A: $tType] : ( ( proces634752977rocess @ A ) > A ) ).
% 2.99/1.59
% 2.99/1.59 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Orel__process,type,
% 2.99/1.59 proces749077512rocess:
% 2.99/1.59 !>[A: $tType,B: $tType] : ( ( A > B > $o ) > ( proces634752977rocess @ A ) > ( proces634752977rocess @ B ) > $o ) ).
% 2.99/1.59
% 2.99/1.59 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_OACT,type,
% 2.99/1.59 proces1454156180ss_ACT:
% 2.99/1.59 !>[A: $tType,Pvar: $tType] : ( A > ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_OCH,type,
% 2.99/1.59 proces89589571ess_CH:
% 2.99/1.59 !>[A: $tType,Pvar: $tType] : ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_OPROC,type,
% 2.99/1.59 proces1062592052s_PROC:
% 2.99/1.59 !>[A: $tType,Pvar: $tType] : ( ( proces634752977rocess @ A ) > ( proces554692349s_term @ A @ Pvar ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_OVAR,type,
% 2.99/1.59 proces1627516585ss_VAR:
% 2.99/1.59 !>[Pvar: $tType,A: $tType] : ( Pvar > ( proces554692349s_term @ A @ Pvar ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Ocase__process__term,type,
% 2.99/1.59 proces460752237s_term:
% 2.99/1.59 !>[Pvar: $tType,B: $tType,A: $tType] : ( ( Pvar > B ) > ( ( proces634752977rocess @ A ) > B ) > ( A > ( proces554692349s_term @ A @ Pvar ) > B ) > ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > B ) > ( proces554692349s_term @ A @ Pvar ) > B ) ).
% 2.99/1.59
% 2.99/1.59 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Opred__process__term,type,
% 2.99/1.59 proces2118920028s_term:
% 2.99/1.59 !>[A: $tType,B: $tType] : ( ( A > $o ) > ( B > $o ) > ( proces554692349s_term @ A @ B ) > $o ) ).
% 2.99/1.59
% 2.99/1.59 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Orec__process__term,type,
% 2.99/1.59 proces2117273769s_term:
% 2.99/1.59 !>[Pvar: $tType,D: $tType,A: $tType] : ( ( Pvar > D ) > ( ( proces634752977rocess @ A ) > D ) > ( A > ( proces554692349s_term @ A @ Pvar ) > D > D ) > ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D > D > D ) > ( proces554692349s_term @ A @ Pvar ) > D ) ).
% 2.99/1.59
% 2.99/1.59 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Orel__process__term,type,
% 2.99/1.59 proces2029722208s_term:
% 2.99/1.59 !>[A: $tType,C: $tType,B: $tType,D: $tType] : ( ( A > C > $o ) > ( B > D > $o ) > ( proces554692349s_term @ A @ B ) > ( proces554692349s_term @ C @ D ) > $o ) ).
% 2.99/1.59
% 2.99/1.59 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Oset2__process__term,type,
% 2.99/1.59 proces1493547885s_term:
% 2.99/1.59 !>[A: $tType,Pvar: $tType] : ( ( proces554692349s_term @ A @ Pvar ) > ( set @ Pvar ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(sy_c_Process__Mirabelle__xovoopgpgi_Osolution,type,
% 2.99/1.59 proces1652378886lution:
% 2.99/1.59 !>[A: $tType,B: $tType] : ( ( A > ( proces554692349s_term @ B @ A ) ) > ( proces554692349s_term @ B @ A ) > ( proces634752977rocess @ B ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(sy_c_Product__Type_OPair,type,
% 2.99/1.59 product_Pair:
% 2.99/1.59 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(sy_c_Product__Type_Ocurry,type,
% 2.99/1.59 product_curry:
% 2.99/1.59 !>[A: $tType,B: $tType,C: $tType] : ( ( ( product_prod @ A @ B ) > C ) > A > B > C ) ).
% 2.99/1.59
% 2.99/1.59 thf(sy_c_Product__Type_Ointernal__case__prod,type,
% 2.99/1.59 produc2004651681e_prod:
% 2.99/1.59 !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > ( product_prod @ A @ B ) > C ) ).
% 2.99/1.59
% 2.99/1.59 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod,type,
% 2.99/1.59 product_rec_prod:
% 2.99/1.59 !>[A: $tType,B: $tType,T: $tType] : ( ( A > B > T ) > ( product_prod @ A @ B ) > T ) ).
% 2.99/1.59
% 2.99/1.59 thf(sy_c_Pure_Otype,type,
% 2.99/1.59 type:
% 2.99/1.59 !>[A: $tType] : ( itself @ A ) ).
% 2.99/1.59
% 2.99/1.59 thf(sy_c_Relation_Oinv__image,type,
% 2.99/1.59 inv_image:
% 2.99/1.59 !>[B: $tType,A: $tType] : ( ( set @ ( product_prod @ B @ B ) ) > ( A > B ) > ( set @ ( product_prod @ A @ A ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(sy_c_Relation_Oinv__imagep,type,
% 2.99/1.59 inv_imagep:
% 2.99/1.59 !>[B: $tType,A: $tType] : ( ( B > B > $o ) > ( A > B ) > A > A > $o ) ).
% 2.99/1.59
% 2.99/1.59 thf(sy_c_Set_OCollect,type,
% 2.99/1.59 collect:
% 2.99/1.59 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(sy_c_Wellfounded_Oacc,type,
% 2.99/1.59 acc:
% 2.99/1.59 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > ( set @ A ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(sy_c_Wellfounded_Oaccp,type,
% 2.99/1.59 accp:
% 2.99/1.59 !>[A: $tType] : ( ( A > A > $o ) > A > $o ) ).
% 2.99/1.59
% 2.99/1.59 thf(sy_c_Wellfounded_Olex__prod,type,
% 2.99/1.59 lex_prod:
% 2.99/1.59 !>[A: $tType,B: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > ( set @ ( product_prod @ B @ B ) ) > ( set @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(sy_c_Wfrec_Oadm__wf,type,
% 2.99/1.59 adm_wf:
% 2.99/1.59 !>[A: $tType,B: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > ( ( A > B ) > A > B ) > $o ) ).
% 2.99/1.59
% 2.99/1.59 thf(sy_c_Wfrec_Ocut,type,
% 2.99/1.59 cut:
% 2.99/1.59 !>[A: $tType,B: $tType] : ( ( A > B ) > ( set @ ( product_prod @ A @ A ) ) > A > A > B ) ).
% 2.99/1.59
% 2.99/1.59 thf(sy_c_Wfrec_Osame__fst,type,
% 2.99/1.59 same_fst:
% 2.99/1.59 !>[A: $tType,B: $tType] : ( ( A > $o ) > ( A > ( set @ ( product_prod @ B @ B ) ) ) > ( set @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(sy_c_member,type,
% 2.99/1.59 member:
% 2.99/1.59 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 2.99/1.59
% 2.99/1.59 thf(sy_v_p,type,
% 2.99/1.59 p: proces634752977rocess @ a ).
% 2.99/1.59
% 2.99/1.59 thf(sy_v_p_H____,type,
% 2.99/1.59 p2: proces634752977rocess @ a ).
% 2.99/1.59
% 2.99/1.59 thf(sy_v_pa____,type,
% 2.99/1.59 pa: proces634752977rocess @ a ).
% 2.99/1.59
% 2.99/1.59 thf(sy_v_q____,type,
% 2.99/1.59 q: proces634752977rocess @ a ).
% 2.99/1.59
% 2.99/1.59 thf(sy_v_sys,type,
% 2.99/1.59 sys: b > ( proces554692349s_term @ a @ b ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_0__092_060open_062isChoice_Ap_092_060close_062,axiom,
% 2.99/1.59 proces401113213Choice @ a @ pa ).
% 2.99/1.59
% 2.99/1.59 thf(fact_1_process__term_Oinject_I2_J,axiom,
% 2.99/1.59 ! [Pvar: $tType,A: $tType,X2: proces634752977rocess @ A,Y2: proces634752977rocess @ A] :
% 2.99/1.59 ( ( ( proces1062592052s_PROC @ A @ Pvar @ X2 )
% 2.99/1.59 = ( proces1062592052s_PROC @ A @ Pvar @ Y2 ) )
% 2.99/1.59 = ( X2 = Y2 ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_2__092_060open_062q_A_061_Asolution_Asys_A_IPROC_Ap_J_092_060close_062,axiom,
% 2.99/1.59 ( q
% 2.99/1.59 = ( proces1652378886lution @ b @ a @ sys @ ( proces1062592052s_PROC @ a @ b @ p ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_3_isACT_Osimps_I2_J,axiom,
% 2.99/1.59 ! [A: $tType,C: $tType,B: $tType,D: $tType,Sys: A > ( proces554692349s_term @ B @ C ),P: proces634752977rocess @ D] :
% 2.99/1.59 ( ( proces687458811_isACT @ A @ B @ C @ D @ Sys @ ( proces1062592052s_PROC @ D @ A @ P ) )
% 2.99/1.59 = ( proces10484146Action @ D @ P ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_4__092_060open_062isAction_Ap_A_092_060or_062_AisChoice_Ap_092_060close_062,axiom,
% 2.99/1.59 ( ( proces10484146Action @ a @ pa )
% 2.99/1.59 | ( proces401113213Choice @ a @ pa ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_5_iss,axiom,
% 2.99/1.59 ( p2
% 2.99/1.59 = ( proces1652378886lution @ b @ a @ sys @ ( proces1062592052s_PROC @ a @ b @ pa ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_6_process__term_Osimps_I22_J,axiom,
% 2.99/1.59 ! [Pvar: $tType,D: $tType,A: $tType,F1: Pvar > D,F2: ( proces634752977rocess @ A ) > D,F3: A > ( proces554692349s_term @ A @ Pvar ) > D > D,F4: ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D > D > D,X2: proces634752977rocess @ A] :
% 2.99/1.59 ( ( proces2117273769s_term @ Pvar @ D @ A @ F1 @ F2 @ F3 @ F4 @ ( proces1062592052s_PROC @ A @ Pvar @ X2 ) )
% 2.99/1.59 = ( F2 @ X2 ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_7_process__term_Osimps_I18_J,axiom,
% 2.99/1.59 ! [Pvar: $tType,B: $tType,A: $tType,F1: Pvar > B,F2: ( proces634752977rocess @ A ) > B,F3: A > ( proces554692349s_term @ A @ Pvar ) > B,F4: ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > B,X2: proces634752977rocess @ A] :
% 2.99/1.59 ( ( proces460752237s_term @ Pvar @ B @ A @ F1 @ F2 @ F3 @ F4 @ ( proces1062592052s_PROC @ A @ Pvar @ X2 ) )
% 2.99/1.59 = ( F2 @ X2 ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_8_solution_Odisc__iff_I2_J,axiom,
% 2.99/1.59 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 2.99/1.59 ( ( proces401113213Choice @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) )
% 2.99/1.59 = ( ~ ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_9_solution_Odisc__iff_I1_J,axiom,
% 2.99/1.59 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 2.99/1.59 ( ( proces10484146Action @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) )
% 2.99/1.59 = ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_10_solution_Odisc_I2_J,axiom,
% 2.99/1.59 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 2.99/1.59 ( ~ ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
% 2.99/1.59 => ( proces401113213Choice @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_11_isACT_Osimps_I3_J,axiom,
% 2.99/1.59 ! [B: $tType,C: $tType,A: $tType,D: $tType,Sys: A > ( proces554692349s_term @ B @ C ),A2: D,T2: proces554692349s_term @ D @ A] : ( proces687458811_isACT @ A @ B @ C @ D @ Sys @ ( proces1454156180ss_ACT @ D @ A @ A2 @ T2 ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_12_isACT_Osimps_I4_J,axiom,
% 2.99/1.59 ! [B: $tType,C: $tType,A: $tType,D: $tType,Sys: A > ( proces554692349s_term @ B @ C ),T1: proces554692349s_term @ D @ A,T22: proces554692349s_term @ D @ A] :
% 2.99/1.59 ~ ( proces687458811_isACT @ A @ B @ C @ D @ Sys @ ( proces89589571ess_CH @ D @ A @ T1 @ T22 ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_13_solution_Odisc_I1_J,axiom,
% 2.99/1.59 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 2.99/1.59 ( ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
% 2.99/1.59 => ( proces10484146Action @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_14_not__isAction__isChoice,axiom,
% 2.99/1.59 ! [A: $tType,P: proces634752977rocess @ A] :
% 2.99/1.59 ~ ( ( proces10484146Action @ A @ P )
% 2.99/1.59 & ( proces401113213Choice @ A @ P ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_15_process__term_Oinject_I4_J,axiom,
% 2.99/1.59 ! [Pvar: $tType,A: $tType,X41: proces554692349s_term @ A @ Pvar,X42: proces554692349s_term @ A @ Pvar,Y41: proces554692349s_term @ A @ Pvar,Y42: proces554692349s_term @ A @ Pvar] :
% 2.99/1.59 ( ( ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 )
% 2.99/1.59 = ( proces89589571ess_CH @ A @ Pvar @ Y41 @ Y42 ) )
% 2.99/1.59 = ( ( X41 = Y41 )
% 2.99/1.59 & ( X42 = Y42 ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_16_process__term_Oinject_I3_J,axiom,
% 2.99/1.59 ! [Pvar: $tType,A: $tType,X31: A,X32: proces554692349s_term @ A @ Pvar,Y31: A,Y32: proces554692349s_term @ A @ Pvar] :
% 2.99/1.59 ( ( ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 )
% 2.99/1.59 = ( proces1454156180ss_ACT @ A @ Pvar @ Y31 @ Y32 ) )
% 2.99/1.59 = ( ( X31 = Y31 )
% 2.99/1.59 & ( X32 = Y32 ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_17_process__term_Osimps_I24_J,axiom,
% 2.99/1.59 ! [D: $tType,Pvar: $tType,A: $tType,F1: Pvar > D,F2: ( proces634752977rocess @ A ) > D,F3: A > ( proces554692349s_term @ A @ Pvar ) > D > D,F4: ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D > D > D,X41: proces554692349s_term @ A @ Pvar,X42: proces554692349s_term @ A @ Pvar] :
% 2.99/1.59 ( ( proces2117273769s_term @ Pvar @ D @ A @ F1 @ F2 @ F3 @ F4 @ ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 ) )
% 2.99/1.59 = ( F4 @ X41 @ X42 @ ( proces2117273769s_term @ Pvar @ D @ A @ F1 @ F2 @ F3 @ F4 @ X41 ) @ ( proces2117273769s_term @ Pvar @ D @ A @ F1 @ F2 @ F3 @ F4 @ X42 ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_18_process__term_Osimps_I23_J,axiom,
% 2.99/1.59 ! [D: $tType,Pvar: $tType,A: $tType,F1: Pvar > D,F2: ( proces634752977rocess @ A ) > D,F3: A > ( proces554692349s_term @ A @ Pvar ) > D > D,F4: ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D > D > D,X31: A,X32: proces554692349s_term @ A @ Pvar] :
% 2.99/1.59 ( ( proces2117273769s_term @ Pvar @ D @ A @ F1 @ F2 @ F3 @ F4 @ ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) )
% 2.99/1.59 = ( F3 @ X31 @ X32 @ ( proces2117273769s_term @ Pvar @ D @ A @ F1 @ F2 @ F3 @ F4 @ X32 ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_19_process__term_Osimps_I20_J,axiom,
% 2.99/1.59 ! [B: $tType,Pvar: $tType,A: $tType,F1: Pvar > B,F2: ( proces634752977rocess @ A ) > B,F3: A > ( proces554692349s_term @ A @ Pvar ) > B,F4: ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > B,X41: proces554692349s_term @ A @ Pvar,X42: proces554692349s_term @ A @ Pvar] :
% 2.99/1.59 ( ( proces460752237s_term @ Pvar @ B @ A @ F1 @ F2 @ F3 @ F4 @ ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 ) )
% 2.99/1.59 = ( F4 @ X41 @ X42 ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_20_process__term_Osimps_I19_J,axiom,
% 2.99/1.59 ! [B: $tType,Pvar: $tType,A: $tType,F1: Pvar > B,F2: ( proces634752977rocess @ A ) > B,F3: A > ( proces554692349s_term @ A @ Pvar ) > B,F4: ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > B,X31: A,X32: proces554692349s_term @ A @ Pvar] :
% 2.99/1.59 ( ( proces460752237s_term @ Pvar @ B @ A @ F1 @ F2 @ F3 @ F4 @ ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) )
% 2.99/1.59 = ( F3 @ X31 @ X32 ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_21_process__term_Odistinct_I11_J,axiom,
% 2.99/1.59 ! [Pvar: $tType,A: $tType,X31: A,X32: proces554692349s_term @ A @ Pvar,X41: proces554692349s_term @ A @ Pvar,X42: proces554692349s_term @ A @ Pvar] :
% 2.99/1.59 ( ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 )
% 2.99/1.59 != ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_22_process__term_Ocase__distrib,axiom,
% 2.99/1.59 ! [B: $tType,C: $tType,Pvar: $tType,A: $tType,H: B > C,F1: Pvar > B,F2: ( proces634752977rocess @ A ) > B,F3: A > ( proces554692349s_term @ A @ Pvar ) > B,F4: ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > B,Process_term: proces554692349s_term @ A @ Pvar] :
% 2.99/1.59 ( ( H @ ( proces460752237s_term @ Pvar @ B @ A @ F1 @ F2 @ F3 @ F4 @ Process_term ) )
% 2.99/1.59 = ( proces460752237s_term @ Pvar @ C @ A
% 2.99/1.59 @ ^ [X: Pvar] : ( H @ ( F1 @ X ) )
% 2.99/1.59 @ ^ [X: proces634752977rocess @ A] : ( H @ ( F2 @ X ) )
% 2.99/1.59 @ ^ [X1: A,X22: proces554692349s_term @ A @ Pvar] : ( H @ ( F3 @ X1 @ X22 ) )
% 2.99/1.59 @ ^ [X1: proces554692349s_term @ A @ Pvar,X22: proces554692349s_term @ A @ Pvar] : ( H @ ( F4 @ X1 @ X22 ) )
% 2.99/1.59 @ Process_term ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_23_process_Oexhaust__disc,axiom,
% 2.99/1.59 ! [A: $tType,Process: proces634752977rocess @ A] :
% 2.99/1.59 ( ~ ( proces10484146Action @ A @ Process )
% 2.99/1.59 => ( proces401113213Choice @ A @ Process ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_24_isAction__isChoice,axiom,
% 2.99/1.59 ! [A: $tType,P: proces634752977rocess @ A] :
% 2.99/1.59 ( ( proces10484146Action @ A @ P )
% 2.99/1.59 | ( proces401113213Choice @ A @ P ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_25_process_Odistinct__disc_I1_J,axiom,
% 2.99/1.59 ! [A: $tType,Process: proces634752977rocess @ A] :
% 2.99/1.59 ( ( proces10484146Action @ A @ Process )
% 2.99/1.59 => ~ ( proces401113213Choice @ A @ Process ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_26_process_Odistinct__disc_I2_J,axiom,
% 2.99/1.59 ! [A: $tType,Process: proces634752977rocess @ A] :
% 2.99/1.59 ( ( proces401113213Choice @ A @ Process )
% 2.99/1.59 => ~ ( proces10484146Action @ A @ Process ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_27_process__term_Odistinct_I9_J,axiom,
% 2.99/1.59 ! [Pvar: $tType,A: $tType,X2: proces634752977rocess @ A,X41: proces554692349s_term @ A @ Pvar,X42: proces554692349s_term @ A @ Pvar] :
% 2.99/1.59 ( ( proces1062592052s_PROC @ A @ Pvar @ X2 )
% 2.99/1.59 != ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_28_process__term_Odistinct_I7_J,axiom,
% 2.99/1.59 ! [Pvar: $tType,A: $tType,X2: proces634752977rocess @ A,X31: A,X32: proces554692349s_term @ A @ Pvar] :
% 2.99/1.59 ( ( proces1062592052s_PROC @ A @ Pvar @ X2 )
% 2.99/1.59 != ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_29_isACT_Oelims_I1_J,axiom,
% 2.99/1.59 ! [D: $tType,A: $tType,B: $tType,C: $tType,X3: A > ( proces554692349s_term @ B @ C ),Xa: proces554692349s_term @ D @ A,Y: $o] :
% 2.99/1.59 ( ( ( proces687458811_isACT @ A @ B @ C @ D @ X3 @ Xa )
% 2.99/1.59 = Y )
% 2.99/1.59 => ( ! [X4: A] :
% 2.99/1.59 ( ( Xa
% 2.99/1.59 = ( proces1627516585ss_VAR @ A @ D @ X4 ) )
% 2.99/1.59 => ( Y
% 2.99/1.59 = ( ~ ( proces460752237s_term @ C @ $o @ B
% 2.99/1.59 @ ^ [Pvar2: C] : $false
% 2.99/1.59 @ ( proces10484146Action @ B )
% 2.99/1.59 @ ^ [A3: B,T3: proces554692349s_term @ B @ C] : $true
% 2.99/1.59 @ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
% 2.99/1.59 @ ( X3 @ X4 ) ) ) ) )
% 2.99/1.59 => ( ! [P2: proces634752977rocess @ D] :
% 2.99/1.59 ( ( Xa
% 2.99/1.59 = ( proces1062592052s_PROC @ D @ A @ P2 ) )
% 2.99/1.59 => ( Y
% 2.99/1.59 = ( ~ ( proces10484146Action @ D @ P2 ) ) ) )
% 2.99/1.59 => ( ( ? [A4: D,T4: proces554692349s_term @ D @ A] :
% 2.99/1.59 ( Xa
% 2.99/1.59 = ( proces1454156180ss_ACT @ D @ A @ A4 @ T4 ) )
% 2.99/1.59 => ~ Y )
% 2.99/1.59 => ~ ( ? [T12: proces554692349s_term @ D @ A,T23: proces554692349s_term @ D @ A] :
% 2.99/1.59 ( Xa
% 2.99/1.59 = ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) )
% 2.99/1.59 => Y ) ) ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_30_isACT_Oelims_I2_J,axiom,
% 2.99/1.59 ! [C: $tType,B: $tType,A: $tType,D: $tType,X3: A > ( proces554692349s_term @ B @ C ),Xa: proces554692349s_term @ D @ A] :
% 2.99/1.59 ( ( proces687458811_isACT @ A @ B @ C @ D @ X3 @ Xa )
% 2.99/1.59 => ( ! [X4: A] :
% 2.99/1.59 ( ( Xa
% 2.99/1.59 = ( proces1627516585ss_VAR @ A @ D @ X4 ) )
% 2.99/1.59 => ~ ( proces460752237s_term @ C @ $o @ B
% 2.99/1.59 @ ^ [Pvar2: C] : $false
% 2.99/1.59 @ ( proces10484146Action @ B )
% 2.99/1.59 @ ^ [A3: B,T3: proces554692349s_term @ B @ C] : $true
% 2.99/1.59 @ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
% 2.99/1.59 @ ( X3 @ X4 ) ) )
% 2.99/1.59 => ( ! [P2: proces634752977rocess @ D] :
% 2.99/1.59 ( ( Xa
% 2.99/1.59 = ( proces1062592052s_PROC @ D @ A @ P2 ) )
% 2.99/1.59 => ~ ( proces10484146Action @ D @ P2 ) )
% 2.99/1.59 => ~ ! [A4: D,T4: proces554692349s_term @ D @ A] :
% 2.99/1.59 ( Xa
% 2.99/1.59 != ( proces1454156180ss_ACT @ D @ A @ A4 @ T4 ) ) ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_31_isACT_Oelims_I3_J,axiom,
% 2.99/1.59 ! [C: $tType,B: $tType,A: $tType,D: $tType,X3: A > ( proces554692349s_term @ B @ C ),Xa: proces554692349s_term @ D @ A] :
% 2.99/1.59 ( ~ ( proces687458811_isACT @ A @ B @ C @ D @ X3 @ Xa )
% 2.99/1.59 => ( ! [X4: A] :
% 2.99/1.59 ( ( Xa
% 2.99/1.59 = ( proces1627516585ss_VAR @ A @ D @ X4 ) )
% 2.99/1.59 => ( proces460752237s_term @ C @ $o @ B
% 2.99/1.59 @ ^ [Pvar2: C] : $false
% 2.99/1.59 @ ( proces10484146Action @ B )
% 2.99/1.59 @ ^ [A3: B,T3: proces554692349s_term @ B @ C] : $true
% 2.99/1.59 @ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
% 2.99/1.59 @ ( X3 @ X4 ) ) )
% 2.99/1.59 => ( ! [P2: proces634752977rocess @ D] :
% 2.99/1.59 ( ( Xa
% 2.99/1.59 = ( proces1062592052s_PROC @ D @ A @ P2 ) )
% 2.99/1.59 => ( proces10484146Action @ D @ P2 ) )
% 2.99/1.59 => ~ ! [T12: proces554692349s_term @ D @ A,T23: proces554692349s_term @ D @ A] :
% 2.99/1.59 ( Xa
% 2.99/1.59 != ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) ) ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_32_CH2_Oinduct,axiom,
% 2.99/1.59 ! [A: $tType,B: $tType,P3: ( A > ( proces554692349s_term @ B @ A ) ) > ( proces554692349s_term @ B @ A ) > $o,A0: A > ( proces554692349s_term @ B @ A ),A1: proces554692349s_term @ B @ A] :
% 2.99/1.59 ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),X4: A] : ( P3 @ Sys2 @ ( proces1627516585ss_VAR @ A @ B @ X4 ) )
% 2.99/1.59 => ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),P2: proces634752977rocess @ B] : ( P3 @ Sys2 @ ( proces1062592052s_PROC @ B @ A @ P2 ) )
% 2.99/1.59 => ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),T12: proces554692349s_term @ B @ A,T23: proces554692349s_term @ B @ A] : ( P3 @ Sys2 @ ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) )
% 2.99/1.59 => ( ! [A4: A > ( proces554692349s_term @ B @ A ),V: B,Va: proces554692349s_term @ B @ A] : ( P3 @ A4 @ ( proces1454156180ss_ACT @ B @ A @ V @ Va ) )
% 2.99/1.59 => ( P3 @ A0 @ A1 ) ) ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_33_CONT_Oinduct,axiom,
% 2.99/1.59 ! [A: $tType,B: $tType,P3: ( A > ( proces554692349s_term @ B @ A ) ) > ( proces554692349s_term @ B @ A ) > $o,A0: A > ( proces554692349s_term @ B @ A ),A1: proces554692349s_term @ B @ A] :
% 2.99/1.59 ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),X4: A] : ( P3 @ Sys2 @ ( proces1627516585ss_VAR @ A @ B @ X4 ) )
% 2.99/1.59 => ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),P2: proces634752977rocess @ B] : ( P3 @ Sys2 @ ( proces1062592052s_PROC @ B @ A @ P2 ) )
% 2.99/1.59 => ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),A4: B,T4: proces554692349s_term @ B @ A] : ( P3 @ Sys2 @ ( proces1454156180ss_ACT @ B @ A @ A4 @ T4 ) )
% 2.99/1.59 => ( ! [A4: A > ( proces554692349s_term @ B @ A ),V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] : ( P3 @ A4 @ ( proces89589571ess_CH @ B @ A @ V @ Va ) )
% 2.99/1.59 => ( P3 @ A0 @ A1 ) ) ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_34_PREF_Oinduct,axiom,
% 2.99/1.59 ! [C: $tType,A: $tType,B: $tType,P3: ( A > ( proces554692349s_term @ B @ C ) ) > ( proces554692349s_term @ B @ A ) > $o,A0: A > ( proces554692349s_term @ B @ C ),A1: proces554692349s_term @ B @ A] :
% 2.99/1.59 ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),X4: A] : ( P3 @ Sys2 @ ( proces1627516585ss_VAR @ A @ B @ X4 ) )
% 2.99/1.59 => ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),P2: proces634752977rocess @ B] : ( P3 @ Sys2 @ ( proces1062592052s_PROC @ B @ A @ P2 ) )
% 2.99/1.59 => ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),A4: B,T4: proces554692349s_term @ B @ A] : ( P3 @ Sys2 @ ( proces1454156180ss_ACT @ B @ A @ A4 @ T4 ) )
% 2.99/1.59 => ( ! [A4: A > ( proces554692349s_term @ B @ C ),V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] : ( P3 @ A4 @ ( proces89589571ess_CH @ B @ A @ V @ Va ) )
% 2.99/1.59 => ( P3 @ A0 @ A1 ) ) ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_35_isACT_Oinduct,axiom,
% 2.99/1.59 ! [B: $tType,C: $tType,A: $tType,D: $tType,P3: ( A > ( proces554692349s_term @ B @ C ) ) > ( proces554692349s_term @ D @ A ) > $o,A0: A > ( proces554692349s_term @ B @ C ),A1: proces554692349s_term @ D @ A] :
% 2.99/1.59 ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),X4: A] : ( P3 @ Sys2 @ ( proces1627516585ss_VAR @ A @ D @ X4 ) )
% 2.99/1.59 => ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),P2: proces634752977rocess @ D] : ( P3 @ Sys2 @ ( proces1062592052s_PROC @ D @ A @ P2 ) )
% 2.99/1.59 => ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),A4: D,T4: proces554692349s_term @ D @ A] : ( P3 @ Sys2 @ ( proces1454156180ss_ACT @ D @ A @ A4 @ T4 ) )
% 2.99/1.59 => ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),T12: proces554692349s_term @ D @ A,T23: proces554692349s_term @ D @ A] : ( P3 @ Sys2 @ ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) )
% 2.99/1.59 => ( P3 @ A0 @ A1 ) ) ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_36_process__term_Oinduct,axiom,
% 2.99/1.59 ! [Pvar: $tType,A: $tType,P3: ( proces554692349s_term @ A @ Pvar ) > $o,Process_term: proces554692349s_term @ A @ Pvar] :
% 2.99/1.59 ( ! [X5: Pvar] : ( P3 @ ( proces1627516585ss_VAR @ Pvar @ A @ X5 ) )
% 2.99/1.59 => ( ! [X5: proces634752977rocess @ A] : ( P3 @ ( proces1062592052s_PROC @ A @ Pvar @ X5 ) )
% 2.99/1.59 => ( ! [X1a: A,X2a: proces554692349s_term @ A @ Pvar] :
% 2.99/1.59 ( ( P3 @ X2a )
% 2.99/1.59 => ( P3 @ ( proces1454156180ss_ACT @ A @ Pvar @ X1a @ X2a ) ) )
% 2.99/1.59 => ( ! [X1a: proces554692349s_term @ A @ Pvar,X2a: proces554692349s_term @ A @ Pvar] :
% 2.99/1.59 ( ( P3 @ X1a )
% 2.99/1.59 => ( ( P3 @ X2a )
% 2.99/1.59 => ( P3 @ ( proces89589571ess_CH @ A @ Pvar @ X1a @ X2a ) ) ) )
% 2.99/1.59 => ( P3 @ Process_term ) ) ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_37_process__term_Oexhaust,axiom,
% 2.99/1.59 ! [Pvar: $tType,A: $tType,Y: proces554692349s_term @ A @ Pvar] :
% 2.99/1.59 ( ! [X12: Pvar] :
% 2.99/1.59 ( Y
% 2.99/1.59 != ( proces1627516585ss_VAR @ Pvar @ A @ X12 ) )
% 2.99/1.59 => ( ! [X23: proces634752977rocess @ A] :
% 2.99/1.59 ( Y
% 2.99/1.59 != ( proces1062592052s_PROC @ A @ Pvar @ X23 ) )
% 2.99/1.59 => ( ! [X312: A,X322: proces554692349s_term @ A @ Pvar] :
% 2.99/1.59 ( Y
% 2.99/1.59 != ( proces1454156180ss_ACT @ A @ Pvar @ X312 @ X322 ) )
% 2.99/1.59 => ~ ! [X412: proces554692349s_term @ A @ Pvar,X422: proces554692349s_term @ A @ Pvar] :
% 2.99/1.59 ( Y
% 2.99/1.59 != ( proces89589571ess_CH @ A @ Pvar @ X412 @ X422 ) ) ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_38_isACT_Osimps_I1_J,axiom,
% 2.99/1.59 ! [D: $tType,B: $tType,C: $tType,A: $tType,Sys: A > ( proces554692349s_term @ B @ C ),X6: A] :
% 2.99/1.59 ( ( proces687458811_isACT @ A @ B @ C @ D @ Sys @ ( proces1627516585ss_VAR @ A @ D @ X6 ) )
% 2.99/1.59 = ( proces460752237s_term @ C @ $o @ B
% 2.99/1.59 @ ^ [Pvar2: C] : $false
% 2.99/1.59 @ ( proces10484146Action @ B )
% 2.99/1.59 @ ^ [A3: B,T3: proces554692349s_term @ B @ C] : $true
% 2.99/1.59 @ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
% 2.99/1.59 @ ( Sys @ X6 ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_39_process__term_Oinject_I1_J,axiom,
% 2.99/1.59 ! [A: $tType,Pvar: $tType,X13: Pvar,Y1: Pvar] :
% 2.99/1.59 ( ( ( proces1627516585ss_VAR @ Pvar @ A @ X13 )
% 2.99/1.59 = ( proces1627516585ss_VAR @ Pvar @ A @ Y1 ) )
% 2.99/1.59 = ( X13 = Y1 ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_40_process__term_Odistinct_I1_J,axiom,
% 2.99/1.59 ! [Pvar: $tType,A: $tType,X13: Pvar,X2: proces634752977rocess @ A] :
% 2.99/1.59 ( ( proces1627516585ss_VAR @ Pvar @ A @ X13 )
% 2.99/1.59 != ( proces1062592052s_PROC @ A @ Pvar @ X2 ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_41_process__term_Odistinct_I5_J,axiom,
% 2.99/1.59 ! [Pvar: $tType,A: $tType,X13: Pvar,X41: proces554692349s_term @ A @ Pvar,X42: proces554692349s_term @ A @ Pvar] :
% 2.99/1.59 ( ( proces1627516585ss_VAR @ Pvar @ A @ X13 )
% 2.99/1.59 != ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_42_process__term_Odistinct_I3_J,axiom,
% 2.99/1.59 ! [Pvar: $tType,A: $tType,X13: Pvar,X31: A,X32: proces554692349s_term @ A @ Pvar] :
% 2.99/1.59 ( ( proces1627516585ss_VAR @ Pvar @ A @ X13 )
% 2.99/1.59 != ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_43_process__term_Osimps_I17_J,axiom,
% 2.99/1.59 ! [A: $tType,B: $tType,Pvar: $tType,F1: Pvar > B,F2: ( proces634752977rocess @ A ) > B,F3: A > ( proces554692349s_term @ A @ Pvar ) > B,F4: ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > B,X13: Pvar] :
% 2.99/1.59 ( ( proces460752237s_term @ Pvar @ B @ A @ F1 @ F2 @ F3 @ F4 @ ( proces1627516585ss_VAR @ Pvar @ A @ X13 ) )
% 2.99/1.59 = ( F1 @ X13 ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_44_mem__Collect__eq,axiom,
% 2.99/1.59 ! [A: $tType,A2: A,P3: A > $o] :
% 2.99/1.59 ( ( member @ A @ A2 @ ( collect @ A @ P3 ) )
% 2.99/1.59 = ( P3 @ A2 ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_45_Collect__mem__eq,axiom,
% 2.99/1.59 ! [A: $tType,A5: set @ A] :
% 2.99/1.59 ( ( collect @ A
% 2.99/1.59 @ ^ [X: A] : ( member @ A @ X @ A5 ) )
% 2.99/1.59 = A5 ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_46_Collect__cong,axiom,
% 2.99/1.59 ! [A: $tType,P3: A > $o,Q: A > $o] :
% 2.99/1.59 ( ! [X5: A] :
% 2.99/1.59 ( ( P3 @ X5 )
% 2.99/1.59 = ( Q @ X5 ) )
% 2.99/1.59 => ( ( collect @ A @ P3 )
% 2.99/1.59 = ( collect @ A @ Q ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_47_ext,axiom,
% 2.99/1.59 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 2.99/1.59 ( ! [X5: A] :
% 2.99/1.59 ( ( F @ X5 )
% 2.99/1.59 = ( G @ X5 ) )
% 2.99/1.59 => ( F = G ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_48_process__term_Osimps_I21_J,axiom,
% 2.99/1.59 ! [A: $tType,D: $tType,Pvar: $tType,F1: Pvar > D,F2: ( proces634752977rocess @ A ) > D,F3: A > ( proces554692349s_term @ A @ Pvar ) > D > D,F4: ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D > D > D,X13: Pvar] :
% 2.99/1.59 ( ( proces2117273769s_term @ Pvar @ D @ A @ F1 @ F2 @ F3 @ F4 @ ( proces1627516585ss_VAR @ Pvar @ A @ X13 ) )
% 2.99/1.59 = ( F1 @ X13 ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_49_solution__VAR,axiom,
% 2.99/1.59 ! [B: $tType,A: $tType,Sys: A > ( proces554692349s_term @ B @ A ),X6: A] :
% 2.99/1.59 ( ( proces1121166967uarded @ A @ B @ A @ Sys )
% 2.99/1.59 => ( ( proces1652378886lution @ A @ B @ Sys @ ( proces1627516585ss_VAR @ A @ B @ X6 ) )
% 2.99/1.59 = ( proces1652378886lution @ A @ B @ Sys @ ( Sys @ X6 ) ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_50_isACT__VAR,axiom,
% 2.99/1.59 ! [C: $tType,B: $tType,A: $tType,Sys: A > ( proces554692349s_term @ B @ A ),X6: A] :
% 2.99/1.59 ( ( proces1121166967uarded @ A @ B @ A @ Sys )
% 2.99/1.59 => ( ( proces687458811_isACT @ A @ B @ A @ C @ Sys @ ( proces1627516585ss_VAR @ A @ C @ X6 ) )
% 2.99/1.59 = ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ ( Sys @ X6 ) ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_51_isACT_Ocases,axiom,
% 2.99/1.59 ! [B: $tType,C: $tType,A: $tType,D: $tType,X3: product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A )] :
% 2.99/1.59 ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),X4: A] :
% 2.99/1.59 ( X3
% 2.99/1.59 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ Sys2 @ ( proces1627516585ss_VAR @ A @ D @ X4 ) ) )
% 2.99/1.59 => ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),P2: proces634752977rocess @ D] :
% 2.99/1.59 ( X3
% 2.99/1.59 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ Sys2 @ ( proces1062592052s_PROC @ D @ A @ P2 ) ) )
% 2.99/1.59 => ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),A4: D,T4: proces554692349s_term @ D @ A] :
% 2.99/1.59 ( X3
% 2.99/1.59 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ Sys2 @ ( proces1454156180ss_ACT @ D @ A @ A4 @ T4 ) ) )
% 2.99/1.59 => ~ ! [Sys2: A > ( proces554692349s_term @ B @ C ),T12: proces554692349s_term @ D @ A,T23: proces554692349s_term @ D @ A] :
% 2.99/1.59 ( X3
% 2.99/1.59 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ Sys2 @ ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) ) ) ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_52_PREF_Ocases,axiom,
% 2.99/1.59 ! [C: $tType,A: $tType,B: $tType,X3: product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A )] :
% 2.99/1.59 ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),X4: A] :
% 2.99/1.59 ( X3
% 2.99/1.59 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ Sys2 @ ( proces1627516585ss_VAR @ A @ B @ X4 ) ) )
% 2.99/1.59 => ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),P2: proces634752977rocess @ B] :
% 2.99/1.59 ( X3
% 2.99/1.59 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ Sys2 @ ( proces1062592052s_PROC @ B @ A @ P2 ) ) )
% 2.99/1.59 => ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),A4: B,T4: proces554692349s_term @ B @ A] :
% 2.99/1.59 ( X3
% 2.99/1.59 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ Sys2 @ ( proces1454156180ss_ACT @ B @ A @ A4 @ T4 ) ) )
% 2.99/1.59 => ~ ! [A4: A > ( proces554692349s_term @ B @ C ),V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] :
% 2.99/1.59 ( X3
% 2.99/1.59 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ A4 @ ( proces89589571ess_CH @ B @ A @ V @ Va ) ) ) ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_53_CONT_Ocases,axiom,
% 2.99/1.59 ! [A: $tType,B: $tType,X3: product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A )] :
% 2.99/1.59 ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),X4: A] :
% 2.99/1.59 ( X3
% 2.99/1.59 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ Sys2 @ ( proces1627516585ss_VAR @ A @ B @ X4 ) ) )
% 2.99/1.59 => ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),P2: proces634752977rocess @ B] :
% 2.99/1.59 ( X3
% 2.99/1.59 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ Sys2 @ ( proces1062592052s_PROC @ B @ A @ P2 ) ) )
% 2.99/1.59 => ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),A4: B,T4: proces554692349s_term @ B @ A] :
% 2.99/1.59 ( X3
% 2.99/1.59 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ Sys2 @ ( proces1454156180ss_ACT @ B @ A @ A4 @ T4 ) ) )
% 2.99/1.59 => ~ ! [A4: A > ( proces554692349s_term @ B @ A ),V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] :
% 2.99/1.59 ( X3
% 2.99/1.59 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ A4 @ ( proces89589571ess_CH @ B @ A @ V @ Va ) ) ) ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_54_CH2_Ocases,axiom,
% 2.99/1.59 ! [A: $tType,B: $tType,X3: product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A )] :
% 2.99/1.59 ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),X4: A] :
% 2.99/1.59 ( X3
% 2.99/1.59 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ Sys2 @ ( proces1627516585ss_VAR @ A @ B @ X4 ) ) )
% 2.99/1.59 => ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),P2: proces634752977rocess @ B] :
% 2.99/1.59 ( X3
% 2.99/1.59 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ Sys2 @ ( proces1062592052s_PROC @ B @ A @ P2 ) ) )
% 2.99/1.59 => ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),T12: proces554692349s_term @ B @ A,T23: proces554692349s_term @ B @ A] :
% 2.99/1.59 ( X3
% 2.99/1.59 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ Sys2 @ ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) ) )
% 2.99/1.59 => ~ ! [A4: A > ( proces554692349s_term @ B @ A ),V: B,Va: proces554692349s_term @ B @ A] :
% 2.99/1.59 ( X3
% 2.99/1.59 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ A4 @ ( proces1454156180ss_ACT @ B @ A @ V @ Va ) ) ) ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_55_process__term_Oset__cases_I2_J,axiom,
% 2.99/1.59 ! [Pvar: $tType,A: $tType,E: Pvar,A2: proces554692349s_term @ A @ Pvar] :
% 2.99/1.59 ( ( member @ Pvar @ E @ ( proces1493547885s_term @ A @ Pvar @ A2 ) )
% 2.99/1.59 => ( ( A2
% 2.99/1.59 != ( proces1627516585ss_VAR @ Pvar @ A @ E ) )
% 2.99/1.59 => ( ! [Z1: A,Z2: proces554692349s_term @ A @ Pvar] :
% 2.99/1.59 ( ( A2
% 2.99/1.59 = ( proces1454156180ss_ACT @ A @ Pvar @ Z1 @ Z2 ) )
% 2.99/1.59 => ~ ( member @ Pvar @ E @ ( proces1493547885s_term @ A @ Pvar @ Z2 ) ) )
% 2.99/1.59 => ( ! [Z1: proces554692349s_term @ A @ Pvar] :
% 2.99/1.59 ( ? [Z2: proces554692349s_term @ A @ Pvar] :
% 2.99/1.59 ( A2
% 2.99/1.59 = ( proces89589571ess_CH @ A @ Pvar @ Z1 @ Z2 ) )
% 2.99/1.59 => ~ ( member @ Pvar @ E @ ( proces1493547885s_term @ A @ Pvar @ Z1 ) ) )
% 2.99/1.59 => ~ ! [Z1: proces554692349s_term @ A @ Pvar,Z2: proces554692349s_term @ A @ Pvar] :
% 2.99/1.59 ( ( A2
% 2.99/1.59 = ( proces89589571ess_CH @ A @ Pvar @ Z1 @ Z2 ) )
% 2.99/1.59 => ~ ( member @ Pvar @ E @ ( proces1493547885s_term @ A @ Pvar @ Z2 ) ) ) ) ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_56_guarded__def,axiom,
% 2.99/1.59 ! [C: $tType,B: $tType,A: $tType] :
% 2.99/1.59 ( ( proces1121166967uarded @ A @ B @ C )
% 2.99/1.59 = ( ^ [Sys3: A > ( proces554692349s_term @ B @ C )] :
% 2.99/1.59 ! [X7: A,Y3: C] :
% 2.99/1.59 ( ( Sys3 @ X7 )
% 2.99/1.59 != ( proces1627516585ss_VAR @ C @ B @ Y3 ) ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_57_process__term_Oset__intros_I6_J,axiom,
% 2.99/1.59 ! [A: $tType,Pvar: $tType,Ab: Pvar] : ( member @ Pvar @ Ab @ ( proces1493547885s_term @ A @ Pvar @ ( proces1627516585ss_VAR @ Pvar @ A @ Ab ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_58_process__term_Oset__intros_I9_J,axiom,
% 2.99/1.59 ! [Pvar: $tType,A: $tType,Xm: Pvar,A2c: proces554692349s_term @ A @ Pvar,A1c: proces554692349s_term @ A @ Pvar] :
% 2.99/1.59 ( ( member @ Pvar @ Xm @ ( proces1493547885s_term @ A @ Pvar @ A2c ) )
% 2.99/1.59 => ( member @ Pvar @ Xm @ ( proces1493547885s_term @ A @ Pvar @ ( proces89589571ess_CH @ A @ Pvar @ A1c @ A2c ) ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_59_process__term_Oset__intros_I8_J,axiom,
% 2.99/1.59 ! [Pvar: $tType,A: $tType,Xk: Pvar,A1c: proces554692349s_term @ A @ Pvar,A2c: proces554692349s_term @ A @ Pvar] :
% 2.99/1.59 ( ( member @ Pvar @ Xk @ ( proces1493547885s_term @ A @ Pvar @ A1c ) )
% 2.99/1.59 => ( member @ Pvar @ Xk @ ( proces1493547885s_term @ A @ Pvar @ ( proces89589571ess_CH @ A @ Pvar @ A1c @ A2c ) ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_60_process__term_Osimps_I51_J,axiom,
% 2.99/1.59 ! [Pvar: $tType,A: $tType,X31: A,X32: proces554692349s_term @ A @ Pvar] :
% 2.99/1.59 ( ( proces1493547885s_term @ A @ Pvar @ ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) )
% 2.99/1.59 = ( proces1493547885s_term @ A @ Pvar @ X32 ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_61_process__term_Oset__intros_I7_J,axiom,
% 2.99/1.59 ! [Pvar: $tType,A: $tType,Xi: Pvar,A2b: proces554692349s_term @ A @ Pvar,A1b: A] :
% 2.99/1.59 ( ( member @ Pvar @ Xi @ ( proces1493547885s_term @ A @ Pvar @ A2b ) )
% 2.99/1.59 => ( member @ Pvar @ Xi @ ( proces1493547885s_term @ A @ Pvar @ ( proces1454156180ss_ACT @ A @ Pvar @ A1b @ A2b ) ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_62_prod_Oinject,axiom,
% 2.99/1.59 ! [A: $tType,B: $tType,X13: A,X2: B,Y1: A,Y2: B] :
% 2.99/1.59 ( ( ( product_Pair @ A @ B @ X13 @ X2 )
% 2.99/1.59 = ( product_Pair @ A @ B @ Y1 @ Y2 ) )
% 2.99/1.59 = ( ( X13 = Y1 )
% 2.99/1.59 & ( X2 = Y2 ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_63_old_Oprod_Oinject,axiom,
% 2.99/1.59 ! [A: $tType,B: $tType,A2: A,B2: B,A6: A,B3: B] :
% 2.99/1.59 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 2.99/1.59 = ( product_Pair @ A @ B @ A6 @ B3 ) )
% 2.99/1.59 = ( ( A2 = A6 )
% 2.99/1.59 & ( B2 = B3 ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_64_isACT_Opelims_I1_J,axiom,
% 2.99/1.59 ! [B: $tType,C: $tType,A: $tType,D: $tType,X3: A > ( proces554692349s_term @ B @ C ),Xa: proces554692349s_term @ D @ A,Y: $o] :
% 2.99/1.59 ( ( ( proces687458811_isACT @ A @ B @ C @ D @ X3 @ Xa )
% 2.99/1.59 = Y )
% 2.99/1.59 => ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X3 @ Xa ) )
% 2.99/1.59 => ( ! [X4: A] :
% 2.99/1.59 ( ( Xa
% 2.99/1.59 = ( proces1627516585ss_VAR @ A @ D @ X4 ) )
% 2.99/1.59 => ( ( Y
% 2.99/1.59 = ( proces460752237s_term @ C @ $o @ B
% 2.99/1.59 @ ^ [Pvar2: C] : $false
% 2.99/1.59 @ ( proces10484146Action @ B )
% 2.99/1.59 @ ^ [A3: B,T3: proces554692349s_term @ B @ C] : $true
% 2.99/1.59 @ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
% 2.99/1.59 @ ( X3 @ X4 ) ) )
% 2.99/1.59 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X3 @ ( proces1627516585ss_VAR @ A @ D @ X4 ) ) ) ) )
% 2.99/1.59 => ( ! [P2: proces634752977rocess @ D] :
% 2.99/1.59 ( ( Xa
% 2.99/1.59 = ( proces1062592052s_PROC @ D @ A @ P2 ) )
% 2.99/1.59 => ( ( Y
% 2.99/1.59 = ( proces10484146Action @ D @ P2 ) )
% 2.99/1.59 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X3 @ ( proces1062592052s_PROC @ D @ A @ P2 ) ) ) ) )
% 2.99/1.59 => ( ! [A4: D,T4: proces554692349s_term @ D @ A] :
% 2.99/1.59 ( ( Xa
% 2.99/1.59 = ( proces1454156180ss_ACT @ D @ A @ A4 @ T4 ) )
% 2.99/1.59 => ( Y
% 2.99/1.59 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X3 @ ( proces1454156180ss_ACT @ D @ A @ A4 @ T4 ) ) ) ) )
% 2.99/1.59 => ~ ! [T12: proces554692349s_term @ D @ A,T23: proces554692349s_term @ D @ A] :
% 2.99/1.59 ( ( Xa
% 2.99/1.59 = ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) )
% 2.99/1.59 => ( ~ Y
% 2.99/1.59 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X3 @ ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) ) ) ) ) ) ) ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_65_isACT_Opelims_I2_J,axiom,
% 2.99/1.59 ! [B: $tType,C: $tType,A: $tType,D: $tType,X3: A > ( proces554692349s_term @ B @ C ),Xa: proces554692349s_term @ D @ A] :
% 2.99/1.59 ( ( proces687458811_isACT @ A @ B @ C @ D @ X3 @ Xa )
% 2.99/1.59 => ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X3 @ Xa ) )
% 2.99/1.59 => ( ! [X4: A] :
% 2.99/1.59 ( ( Xa
% 2.99/1.59 = ( proces1627516585ss_VAR @ A @ D @ X4 ) )
% 2.99/1.59 => ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X3 @ ( proces1627516585ss_VAR @ A @ D @ X4 ) ) )
% 2.99/1.59 => ~ ( proces460752237s_term @ C @ $o @ B
% 2.99/1.59 @ ^ [Pvar2: C] : $false
% 2.99/1.59 @ ( proces10484146Action @ B )
% 2.99/1.59 @ ^ [A3: B,T3: proces554692349s_term @ B @ C] : $true
% 2.99/1.59 @ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
% 2.99/1.59 @ ( X3 @ X4 ) ) ) )
% 2.99/1.59 => ( ! [P2: proces634752977rocess @ D] :
% 2.99/1.59 ( ( Xa
% 2.99/1.59 = ( proces1062592052s_PROC @ D @ A @ P2 ) )
% 2.99/1.59 => ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X3 @ ( proces1062592052s_PROC @ D @ A @ P2 ) ) )
% 2.99/1.59 => ~ ( proces10484146Action @ D @ P2 ) ) )
% 2.99/1.59 => ~ ! [A4: D,T4: proces554692349s_term @ D @ A] :
% 2.99/1.59 ( ( Xa
% 2.99/1.59 = ( proces1454156180ss_ACT @ D @ A @ A4 @ T4 ) )
% 2.99/1.59 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X3 @ ( proces1454156180ss_ACT @ D @ A @ A4 @ T4 ) ) ) ) ) ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_66_isACT_Opelims_I3_J,axiom,
% 2.99/1.59 ! [B: $tType,C: $tType,A: $tType,D: $tType,X3: A > ( proces554692349s_term @ B @ C ),Xa: proces554692349s_term @ D @ A] :
% 2.99/1.59 ( ~ ( proces687458811_isACT @ A @ B @ C @ D @ X3 @ Xa )
% 2.99/1.59 => ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X3 @ Xa ) )
% 2.99/1.59 => ( ! [X4: A] :
% 2.99/1.59 ( ( Xa
% 2.99/1.59 = ( proces1627516585ss_VAR @ A @ D @ X4 ) )
% 2.99/1.59 => ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X3 @ ( proces1627516585ss_VAR @ A @ D @ X4 ) ) )
% 2.99/1.59 => ( proces460752237s_term @ C @ $o @ B
% 2.99/1.59 @ ^ [Pvar2: C] : $false
% 2.99/1.59 @ ( proces10484146Action @ B )
% 2.99/1.59 @ ^ [A3: B,T3: proces554692349s_term @ B @ C] : $true
% 2.99/1.59 @ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
% 2.99/1.59 @ ( X3 @ X4 ) ) ) )
% 2.99/1.59 => ( ! [P2: proces634752977rocess @ D] :
% 2.99/1.59 ( ( Xa
% 2.99/1.59 = ( proces1062592052s_PROC @ D @ A @ P2 ) )
% 2.99/1.59 => ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X3 @ ( proces1062592052s_PROC @ D @ A @ P2 ) ) )
% 2.99/1.59 => ( proces10484146Action @ D @ P2 ) ) )
% 2.99/1.59 => ~ ! [T12: proces554692349s_term @ D @ A,T23: proces554692349s_term @ D @ A] :
% 2.99/1.59 ( ( Xa
% 2.99/1.59 = ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) )
% 2.99/1.59 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X3 @ ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) ) ) ) ) ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_67_pred__equals__eq2,axiom,
% 2.99/1.59 ! [B: $tType,A: $tType,R: set @ ( product_prod @ A @ B ),S: set @ ( product_prod @ A @ B )] :
% 2.99/1.59 ( ( ( ^ [X: A,Y4: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X @ Y4 ) @ R ) )
% 2.99/1.59 = ( ^ [X: A,Y4: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X @ Y4 ) @ S ) ) )
% 2.99/1.59 = ( R = S ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_68_surj__pair,axiom,
% 2.99/1.59 ! [A: $tType,B: $tType,P: product_prod @ A @ B] :
% 2.99/1.59 ? [X5: A,Y5: B] :
% 2.99/1.59 ( P
% 2.99/1.59 = ( product_Pair @ A @ B @ X5 @ Y5 ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_69_old_Oprod_Oinducts,axiom,
% 2.99/1.59 ! [B: $tType,A: $tType,P3: ( product_prod @ A @ B ) > $o,Prod: product_prod @ A @ B] :
% 2.99/1.59 ( ! [A4: A,B4: B] : ( P3 @ ( product_Pair @ A @ B @ A4 @ B4 ) )
% 2.99/1.59 => ( P3 @ Prod ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_70_old_Oprod_Oexhaust,axiom,
% 2.99/1.59 ! [A: $tType,B: $tType,Y: product_prod @ A @ B] :
% 2.99/1.59 ~ ! [A4: A,B4: B] :
% 2.99/1.59 ( Y
% 2.99/1.59 != ( product_Pair @ A @ B @ A4 @ B4 ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_71_prod__induct7,axiom,
% 2.99/1.59 ! [G2: $tType,F5: $tType,E2: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P3: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ ( product_prod @ F5 @ G2 ) ) ) ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ ( product_prod @ F5 @ G2 ) ) ) ) )] :
% 2.99/1.59 ( ! [A4: A,B4: B,C2: C,D2: D,E3: E2,F6: F5,G3: G2] : ( P3 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ ( product_prod @ F5 @ G2 ) ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ ( product_prod @ F5 @ G2 ) ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E2 @ ( product_prod @ F5 @ G2 ) ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E2 @ ( product_prod @ F5 @ G2 ) ) @ D2 @ ( product_Pair @ E2 @ ( product_prod @ F5 @ G2 ) @ E3 @ ( product_Pair @ F5 @ G2 @ F6 @ G3 ) ) ) ) ) ) )
% 2.99/1.59 => ( P3 @ X3 ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_72_prod__induct6,axiom,
% 2.99/1.59 ! [F5: $tType,E2: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P3: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ F5 ) ) ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ F5 ) ) ) )] :
% 2.99/1.59 ( ! [A4: A,B4: B,C2: C,D2: D,E3: E2,F6: F5] : ( P3 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ F5 ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ F5 ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E2 @ F5 ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E2 @ F5 ) @ D2 @ ( product_Pair @ E2 @ F5 @ E3 @ F6 ) ) ) ) ) )
% 2.99/1.59 => ( P3 @ X3 ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_73_prod__induct5,axiom,
% 2.99/1.59 ! [E2: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P3: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E2 ) ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E2 ) ) )] :
% 2.99/1.59 ( ! [A4: A,B4: B,C2: C,D2: D,E3: E2] : ( P3 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E2 ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E2 ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ E2 ) @ C2 @ ( product_Pair @ D @ E2 @ D2 @ E3 ) ) ) ) )
% 2.99/1.59 => ( P3 @ X3 ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_74_prod__induct4,axiom,
% 2.99/1.59 ! [D: $tType,C: $tType,B: $tType,A: $tType,P3: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 2.99/1.59 ( ! [A4: A,B4: B,C2: C,D2: D] : ( P3 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B4 @ ( product_Pair @ C @ D @ C2 @ D2 ) ) ) )
% 2.99/1.59 => ( P3 @ X3 ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_75_prod__induct3,axiom,
% 2.99/1.59 ! [C: $tType,B: $tType,A: $tType,P3: ( product_prod @ A @ ( product_prod @ B @ C ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ C )] :
% 2.99/1.59 ( ! [A4: A,B4: B,C2: C] : ( P3 @ ( product_Pair @ A @ ( product_prod @ B @ C ) @ A4 @ ( product_Pair @ B @ C @ B4 @ C2 ) ) )
% 2.99/1.59 => ( P3 @ X3 ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_76_prod__cases7,axiom,
% 2.99/1.59 ! [A: $tType,B: $tType,C: $tType,D: $tType,E2: $tType,F5: $tType,G2: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ ( product_prod @ F5 @ G2 ) ) ) ) )] :
% 2.99/1.59 ~ ! [A4: A,B4: B,C2: C,D2: D,E3: E2,F6: F5,G3: G2] :
% 2.99/1.59 ( Y
% 2.99/1.59 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ ( product_prod @ F5 @ G2 ) ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ ( product_prod @ F5 @ G2 ) ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E2 @ ( product_prod @ F5 @ G2 ) ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E2 @ ( product_prod @ F5 @ G2 ) ) @ D2 @ ( product_Pair @ E2 @ ( product_prod @ F5 @ G2 ) @ E3 @ ( product_Pair @ F5 @ G2 @ F6 @ G3 ) ) ) ) ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_77_prod__cases6,axiom,
% 2.99/1.59 ! [A: $tType,B: $tType,C: $tType,D: $tType,E2: $tType,F5: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ F5 ) ) ) )] :
% 2.99/1.59 ~ ! [A4: A,B4: B,C2: C,D2: D,E3: E2,F6: F5] :
% 2.99/1.59 ( Y
% 2.99/1.59 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ F5 ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ F5 ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E2 @ F5 ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E2 @ F5 ) @ D2 @ ( product_Pair @ E2 @ F5 @ E3 @ F6 ) ) ) ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_78_prod__cases5,axiom,
% 2.99/1.59 ! [A: $tType,B: $tType,C: $tType,D: $tType,E2: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E2 ) ) )] :
% 2.99/1.59 ~ ! [A4: A,B4: B,C2: C,D2: D,E3: E2] :
% 2.99/1.59 ( Y
% 2.99/1.59 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E2 ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E2 ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ E2 ) @ C2 @ ( product_Pair @ D @ E2 @ D2 @ E3 ) ) ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_79_prod__cases4,axiom,
% 2.99/1.59 ! [A: $tType,B: $tType,C: $tType,D: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 2.99/1.59 ~ ! [A4: A,B4: B,C2: C,D2: D] :
% 2.99/1.59 ( Y
% 2.99/1.59 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B4 @ ( product_Pair @ C @ D @ C2 @ D2 ) ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_80_prod__cases3,axiom,
% 2.99/1.59 ! [A: $tType,B: $tType,C: $tType,Y: product_prod @ A @ ( product_prod @ B @ C )] :
% 2.99/1.59 ~ ! [A4: A,B4: B,C2: C] :
% 2.99/1.59 ( Y
% 2.99/1.59 != ( product_Pair @ A @ ( product_prod @ B @ C ) @ A4 @ ( product_Pair @ B @ C @ B4 @ C2 ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_81_Pair__inject,axiom,
% 2.99/1.59 ! [A: $tType,B: $tType,A2: A,B2: B,A6: A,B3: B] :
% 2.99/1.59 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 2.99/1.59 = ( product_Pair @ A @ B @ A6 @ B3 ) )
% 2.99/1.59 => ~ ( ( A2 = A6 )
% 2.99/1.59 => ( B2 != B3 ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_82_prod__cases,axiom,
% 2.99/1.59 ! [B: $tType,A: $tType,P3: ( product_prod @ A @ B ) > $o,P: product_prod @ A @ B] :
% 2.99/1.59 ( ! [A4: A,B4: B] : ( P3 @ ( product_Pair @ A @ B @ A4 @ B4 ) )
% 2.99/1.59 => ( P3 @ P ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_83_old_Oprod_Orec,axiom,
% 2.99/1.59 ! [A: $tType,T: $tType,B: $tType,F1: A > B > T,A2: A,B2: B] :
% 2.99/1.59 ( ( product_rec_prod @ A @ B @ T @ F1 @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 2.99/1.59 = ( F1 @ A2 @ B2 ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_84_internal__case__prod__conv,axiom,
% 2.99/1.59 ! [B: $tType,A: $tType,C: $tType,C3: B > C > A,A2: B,B2: C] :
% 2.99/1.59 ( ( produc2004651681e_prod @ B @ C @ A @ C3 @ ( product_Pair @ B @ C @ A2 @ B2 ) )
% 2.99/1.59 = ( C3 @ A2 @ B2 ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_85_accp__induct__rule,axiom,
% 2.99/1.59 ! [A: $tType,R2: A > A > $o,A2: A,P3: A > $o] :
% 2.99/1.59 ( ( accp @ A @ R2 @ A2 )
% 2.99/1.59 => ( ! [X5: A] :
% 2.99/1.59 ( ( accp @ A @ R2 @ X5 )
% 2.99/1.59 => ( ! [Y6: A] :
% 2.99/1.59 ( ( R2 @ Y6 @ X5 )
% 2.99/1.59 => ( P3 @ Y6 ) )
% 2.99/1.59 => ( P3 @ X5 ) ) )
% 2.99/1.59 => ( P3 @ A2 ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_86_not__accp__down,axiom,
% 2.99/1.59 ! [A: $tType,R: A > A > $o,X3: A] :
% 2.99/1.59 ( ~ ( accp @ A @ R @ X3 )
% 2.99/1.59 => ~ ! [Z: A] :
% 2.99/1.59 ( ( R @ Z @ X3 )
% 2.99/1.59 => ( accp @ A @ R @ Z ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_87_accp__downward,axiom,
% 2.99/1.59 ! [A: $tType,R2: A > A > $o,B2: A,A2: A] :
% 2.99/1.59 ( ( accp @ A @ R2 @ B2 )
% 2.99/1.59 => ( ( R2 @ A2 @ B2 )
% 2.99/1.59 => ( accp @ A @ R2 @ A2 ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_88_accp_Oinducts,axiom,
% 2.99/1.59 ! [A: $tType,R2: A > A > $o,X3: A,P3: A > $o] :
% 2.99/1.59 ( ( accp @ A @ R2 @ X3 )
% 2.99/1.59 => ( ! [X5: A] :
% 2.99/1.59 ( ! [Y6: A] :
% 2.99/1.59 ( ( R2 @ Y6 @ X5 )
% 2.99/1.59 => ( accp @ A @ R2 @ Y6 ) )
% 2.99/1.59 => ( ! [Y6: A] :
% 2.99/1.59 ( ( R2 @ Y6 @ X5 )
% 2.99/1.59 => ( P3 @ Y6 ) )
% 2.99/1.59 => ( P3 @ X5 ) ) )
% 2.99/1.59 => ( P3 @ X3 ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_89_accp__induct,axiom,
% 2.99/1.59 ! [A: $tType,R2: A > A > $o,A2: A,P3: A > $o] :
% 2.99/1.59 ( ( accp @ A @ R2 @ A2 )
% 2.99/1.59 => ( ! [X5: A] :
% 2.99/1.59 ( ( accp @ A @ R2 @ X5 )
% 2.99/1.59 => ( ! [Y6: A] :
% 2.99/1.59 ( ( R2 @ Y6 @ X5 )
% 2.99/1.59 => ( P3 @ Y6 ) )
% 2.99/1.59 => ( P3 @ X5 ) ) )
% 2.99/1.59 => ( P3 @ A2 ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_90_accp_Ocases,axiom,
% 2.99/1.59 ! [A: $tType,R2: A > A > $o,A2: A] :
% 2.99/1.59 ( ( accp @ A @ R2 @ A2 )
% 2.99/1.59 => ! [Y6: A] :
% 2.99/1.59 ( ( R2 @ Y6 @ A2 )
% 2.99/1.59 => ( accp @ A @ R2 @ Y6 ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_91_accp_Osimps,axiom,
% 2.99/1.59 ! [A: $tType] :
% 2.99/1.59 ( ( accp @ A )
% 2.99/1.59 = ( ^ [R3: A > A > $o,A3: A] :
% 2.99/1.59 ? [X: A] :
% 2.99/1.59 ( ( A3 = X )
% 2.99/1.59 & ! [Y4: A] :
% 2.99/1.59 ( ( R3 @ Y4 @ X )
% 2.99/1.59 => ( accp @ A @ R3 @ Y4 ) ) ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_92_accp_Ointros,axiom,
% 2.99/1.59 ! [A: $tType,R2: A > A > $o,X3: A] :
% 2.99/1.59 ( ! [Y5: A] :
% 2.99/1.59 ( ( R2 @ Y5 @ X3 )
% 2.99/1.59 => ( accp @ A @ R2 @ Y5 ) )
% 2.99/1.59 => ( accp @ A @ R2 @ X3 ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_93_in__lex__prod,axiom,
% 2.99/1.59 ! [A: $tType,B: $tType,A2: A,B2: B,A6: A,B3: B,R2: set @ ( product_prod @ A @ A ),S2: set @ ( product_prod @ B @ B )] :
% 2.99/1.59 ( ( member @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ) @ ( product_Pair @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ A2 @ B2 ) @ ( product_Pair @ A @ B @ A6 @ B3 ) ) @ ( lex_prod @ A @ B @ R2 @ S2 ) )
% 2.99/1.59 = ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ A6 ) @ R2 )
% 2.99/1.59 | ( ( A2 = A6 )
% 2.99/1.59 & ( member @ ( product_prod @ B @ B ) @ ( product_Pair @ B @ B @ B2 @ B3 ) @ S2 ) ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_94_ssubst__Pair__rhs,axiom,
% 2.99/1.59 ! [B: $tType,A: $tType,R2: A,S2: B,R: set @ ( product_prod @ A @ B ),S3: B] :
% 2.99/1.59 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ R2 @ S2 ) @ R )
% 2.99/1.59 => ( ( S3 = S2 )
% 2.99/1.59 => ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ R2 @ S3 ) @ R ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_95_curry__conv,axiom,
% 2.99/1.59 ! [A: $tType,C: $tType,B: $tType] :
% 2.99/1.59 ( ( product_curry @ B @ C @ A )
% 2.99/1.59 = ( ^ [F7: ( product_prod @ B @ C ) > A,A3: B,B5: C] : ( F7 @ ( product_Pair @ B @ C @ A3 @ B5 ) ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_96_in__inv__imagep,axiom,
% 2.99/1.59 ! [B: $tType,A: $tType] :
% 2.99/1.59 ( ( inv_imagep @ A @ B )
% 2.99/1.59 = ( ^ [R3: A > A > $o,F7: B > A,X: B,Y4: B] : ( R3 @ ( F7 @ X ) @ ( F7 @ Y4 ) ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_97_acc__def,axiom,
% 2.99/1.59 ! [A: $tType] :
% 2.99/1.59 ( ( acc @ A )
% 2.99/1.59 = ( ^ [R3: set @ ( product_prod @ A @ A )] :
% 2.99/1.59 ( collect @ A
% 2.99/1.59 @ ( accp @ A
% 2.99/1.59 @ ^ [X: A,Y4: A] : ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y4 ) @ R3 ) ) ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_98_accp__acc__eq,axiom,
% 2.99/1.59 ! [A: $tType,R2: set @ ( product_prod @ A @ A )] :
% 2.99/1.59 ( ( accp @ A
% 2.99/1.59 @ ^ [X: A,Y4: A] : ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y4 ) @ R2 ) )
% 2.99/1.59 = ( ^ [X: A] : ( member @ A @ X @ ( acc @ A @ R2 ) ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_99_curryI,axiom,
% 2.99/1.59 ! [A: $tType,B: $tType,F: ( product_prod @ A @ B ) > $o,A2: A,B2: B] :
% 2.99/1.59 ( ( F @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 2.99/1.59 => ( product_curry @ A @ B @ $o @ F @ A2 @ B2 ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_100_curry__K,axiom,
% 2.99/1.59 ! [B: $tType,C: $tType,A: $tType,C3: C] :
% 2.99/1.59 ( ( product_curry @ A @ B @ C
% 2.99/1.59 @ ^ [X: product_prod @ A @ B] : C3 )
% 2.99/1.59 = ( ^ [X: A,Y4: B] : C3 ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_101_acc__induct__rule,axiom,
% 2.99/1.59 ! [A: $tType,A2: A,R2: set @ ( product_prod @ A @ A ),P3: A > $o] :
% 2.99/1.59 ( ( member @ A @ A2 @ ( acc @ A @ R2 ) )
% 2.99/1.59 => ( ! [X5: A] :
% 2.99/1.59 ( ( member @ A @ X5 @ ( acc @ A @ R2 ) )
% 2.99/1.59 => ( ! [Y6: A] :
% 2.99/1.59 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y6 @ X5 ) @ R2 )
% 2.99/1.59 => ( P3 @ Y6 ) )
% 2.99/1.59 => ( P3 @ X5 ) ) )
% 2.99/1.59 => ( P3 @ A2 ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_102_not__acc__down,axiom,
% 2.99/1.59 ! [A: $tType,X3: A,R: set @ ( product_prod @ A @ A )] :
% 2.99/1.59 ( ~ ( member @ A @ X3 @ ( acc @ A @ R ) )
% 2.99/1.59 => ~ ! [Z: A] :
% 2.99/1.59 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Z @ X3 ) @ R )
% 2.99/1.59 => ( member @ A @ Z @ ( acc @ A @ R ) ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_103_acc__downward,axiom,
% 2.99/1.59 ! [A: $tType,B2: A,R2: set @ ( product_prod @ A @ A ),A2: A] :
% 2.99/1.59 ( ( member @ A @ B2 @ ( acc @ A @ R2 ) )
% 2.99/1.59 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ R2 )
% 2.99/1.59 => ( member @ A @ A2 @ ( acc @ A @ R2 ) ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_104_acc_Oinducts,axiom,
% 2.99/1.59 ! [A: $tType,X3: A,R2: set @ ( product_prod @ A @ A ),P3: A > $o] :
% 2.99/1.59 ( ( member @ A @ X3 @ ( acc @ A @ R2 ) )
% 2.99/1.59 => ( ! [X5: A] :
% 2.99/1.59 ( ! [Y6: A] :
% 2.99/1.59 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y6 @ X5 ) @ R2 )
% 2.99/1.59 => ( member @ A @ Y6 @ ( acc @ A @ R2 ) ) )
% 2.99/1.59 => ( ! [Y6: A] :
% 2.99/1.59 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y6 @ X5 ) @ R2 )
% 2.99/1.59 => ( P3 @ Y6 ) )
% 2.99/1.59 => ( P3 @ X5 ) ) )
% 2.99/1.59 => ( P3 @ X3 ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_105_acc__induct,axiom,
% 2.99/1.59 ! [A: $tType,A2: A,R2: set @ ( product_prod @ A @ A ),P3: A > $o] :
% 2.99/1.59 ( ( member @ A @ A2 @ ( acc @ A @ R2 ) )
% 2.99/1.59 => ( ! [X5: A] :
% 2.99/1.59 ( ( member @ A @ X5 @ ( acc @ A @ R2 ) )
% 2.99/1.59 => ( ! [Y6: A] :
% 2.99/1.59 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y6 @ X5 ) @ R2 )
% 2.99/1.59 => ( P3 @ Y6 ) )
% 2.99/1.59 => ( P3 @ X5 ) ) )
% 2.99/1.59 => ( P3 @ A2 ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_106_acc_Ointros,axiom,
% 2.99/1.59 ! [A: $tType,X3: A,R2: set @ ( product_prod @ A @ A )] :
% 2.99/1.59 ( ! [Y5: A] :
% 2.99/1.59 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y5 @ X3 ) @ R2 )
% 2.99/1.59 => ( member @ A @ Y5 @ ( acc @ A @ R2 ) ) )
% 2.99/1.59 => ( member @ A @ X3 @ ( acc @ A @ R2 ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_107_acc_Osimps,axiom,
% 2.99/1.59 ! [A: $tType,A2: A,R2: set @ ( product_prod @ A @ A )] :
% 2.99/1.59 ( ( member @ A @ A2 @ ( acc @ A @ R2 ) )
% 2.99/1.59 = ( ? [X: A] :
% 2.99/1.59 ( ( A2 = X )
% 2.99/1.59 & ! [Y4: A] :
% 2.99/1.59 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y4 @ X ) @ R2 )
% 2.99/1.59 => ( member @ A @ Y4 @ ( acc @ A @ R2 ) ) ) ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_108_acc_Ocases,axiom,
% 2.99/1.59 ! [A: $tType,A2: A,R2: set @ ( product_prod @ A @ A )] :
% 2.99/1.59 ( ( member @ A @ A2 @ ( acc @ A @ R2 ) )
% 2.99/1.59 => ! [Y6: A] :
% 2.99/1.59 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y6 @ A2 ) @ R2 )
% 2.99/1.59 => ( member @ A @ Y6 @ ( acc @ A @ R2 ) ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_109_curryE,axiom,
% 2.99/1.59 ! [A: $tType,B: $tType,F: ( product_prod @ A @ B ) > $o,A2: A,B2: B] :
% 2.99/1.59 ( ( product_curry @ A @ B @ $o @ F @ A2 @ B2 )
% 2.99/1.59 => ( F @ ( product_Pair @ A @ B @ A2 @ B2 ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_110_curryD,axiom,
% 2.99/1.59 ! [A: $tType,B: $tType,F: ( product_prod @ A @ B ) > $o,A2: A,B2: B] :
% 2.99/1.59 ( ( product_curry @ A @ B @ $o @ F @ A2 @ B2 )
% 2.99/1.59 => ( F @ ( product_Pair @ A @ B @ A2 @ B2 ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_111_inv__imagep__def,axiom,
% 2.99/1.59 ! [A: $tType,B: $tType] :
% 2.99/1.59 ( ( inv_imagep @ B @ A )
% 2.99/1.59 = ( ^ [R3: B > B > $o,F7: A > B,X: A,Y4: A] : ( R3 @ ( F7 @ X ) @ ( F7 @ Y4 ) ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_112_curry__def,axiom,
% 2.99/1.59 ! [C: $tType,B: $tType,A: $tType] :
% 2.99/1.59 ( ( product_curry @ A @ B @ C )
% 2.99/1.59 = ( ^ [C4: ( product_prod @ A @ B ) > C,X: A,Y4: B] : ( C4 @ ( product_Pair @ A @ B @ X @ Y4 ) ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_113_same__fstI,axiom,
% 2.99/1.59 ! [B: $tType,A: $tType,P3: A > $o,X3: A,Y7: B,Y: B,R: A > ( set @ ( product_prod @ B @ B ) )] :
% 2.99/1.59 ( ( P3 @ X3 )
% 2.99/1.59 => ( ( member @ ( product_prod @ B @ B ) @ ( product_Pair @ B @ B @ Y7 @ Y ) @ ( R @ X3 ) )
% 2.99/1.59 => ( member @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ) @ ( product_Pair @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X3 @ Y7 ) @ ( product_Pair @ A @ B @ X3 @ Y ) ) @ ( same_fst @ A @ B @ P3 @ R ) ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_114_in__inv__image,axiom,
% 2.99/1.59 ! [A: $tType,B: $tType,X3: A,Y: A,R2: set @ ( product_prod @ B @ B ),F: A > B] :
% 2.99/1.59 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X3 @ Y ) @ ( inv_image @ B @ A @ R2 @ F ) )
% 2.99/1.59 = ( member @ ( product_prod @ B @ B ) @ ( product_Pair @ B @ B @ ( F @ X3 ) @ ( F @ Y ) ) @ R2 ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_115_PREF_Opelims,axiom,
% 2.99/1.59 ! [C: $tType,A: $tType,B: $tType,X3: A > ( proces554692349s_term @ B @ C ),Xa: proces554692349s_term @ B @ A,Y: B] :
% 2.99/1.59 ( ( ( proces1708129104e_PREF @ A @ B @ C @ X3 @ Xa )
% 2.99/1.59 = Y )
% 2.99/1.59 => ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces527360425EF_rel @ A @ B @ C ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ X3 @ Xa ) )
% 2.99/1.59 => ( ! [X4: A] :
% 2.99/1.59 ( ( Xa
% 2.99/1.59 = ( proces1627516585ss_VAR @ A @ B @ X4 ) )
% 2.99/1.59 => ( ( Y
% 2.99/1.59 = ( proces460752237s_term @ C @ B @ B
% 2.99/1.59 @ ^ [Aa: C] : ( undefined @ B )
% 2.99/1.59 @ ( proces745025900prefOf @ B )
% 2.99/1.59 @ ^ [A3: B,T3: proces554692349s_term @ B @ C] : A3
% 2.99/1.59 @ ^ [Aa: proces554692349s_term @ B @ C,Ab2: proces554692349s_term @ B @ C] : ( undefined @ B )
% 2.99/1.59 @ ( X3 @ X4 ) ) )
% 2.99/1.59 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces527360425EF_rel @ A @ B @ C ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ X3 @ ( proces1627516585ss_VAR @ A @ B @ X4 ) ) ) ) )
% 2.99/1.59 => ( ! [P2: proces634752977rocess @ B] :
% 2.99/1.59 ( ( Xa
% 2.99/1.59 = ( proces1062592052s_PROC @ B @ A @ P2 ) )
% 2.99/1.59 => ( ( Y
% 2.99/1.59 = ( proces745025900prefOf @ B @ P2 ) )
% 2.99/1.59 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces527360425EF_rel @ A @ B @ C ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ X3 @ ( proces1062592052s_PROC @ B @ A @ P2 ) ) ) ) )
% 2.99/1.59 => ( ! [A4: B,T4: proces554692349s_term @ B @ A] :
% 2.99/1.59 ( ( Xa
% 2.99/1.59 = ( proces1454156180ss_ACT @ B @ A @ A4 @ T4 ) )
% 2.99/1.59 => ( ( Y = A4 )
% 2.99/1.59 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces527360425EF_rel @ A @ B @ C ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ X3 @ ( proces1454156180ss_ACT @ B @ A @ A4 @ T4 ) ) ) ) )
% 2.99/1.59 => ~ ! [V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] :
% 2.99/1.59 ( ( Xa
% 2.99/1.59 = ( proces89589571ess_CH @ B @ A @ V @ Va ) )
% 2.99/1.59 => ( ( Y
% 2.99/1.59 = ( undefined @ B ) )
% 2.99/1.59 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces527360425EF_rel @ A @ B @ C ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ X3 @ ( proces89589571ess_CH @ B @ A @ V @ Va ) ) ) ) ) ) ) ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_116_above__def,axiom,
% 2.99/1.59 ! [A: $tType] :
% 2.99/1.59 ( ( order_above @ A )
% 2.99/1.59 = ( ^ [R3: set @ ( product_prod @ A @ A ),A3: A] :
% 2.99/1.59 ( collect @ A
% 2.99/1.59 @ ^ [B5: A] : ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A3 @ B5 ) @ R3 ) ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_117_aboveS__def,axiom,
% 2.99/1.59 ! [A: $tType] :
% 2.99/1.59 ( ( order_aboveS @ A )
% 2.99/1.59 = ( ^ [R3: set @ ( product_prod @ A @ A ),A3: A] :
% 2.99/1.59 ( collect @ A
% 2.99/1.59 @ ^ [B5: A] :
% 2.99/1.59 ( ( B5 != A3 )
% 2.99/1.59 & ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A3 @ B5 ) @ R3 ) ) ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_118_PREF_Osimps_I2_J,axiom,
% 2.99/1.59 ! [A: $tType,C: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ C ),P: proces634752977rocess @ B] :
% 2.99/1.59 ( ( proces1708129104e_PREF @ A @ B @ C @ Sys @ ( proces1062592052s_PROC @ B @ A @ P ) )
% 2.99/1.59 = ( proces745025900prefOf @ B @ P ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_119_PREF_Osimps_I1_J,axiom,
% 2.99/1.59 ! [B: $tType,C: $tType,A: $tType,Sys: A > ( proces554692349s_term @ B @ C ),X6: A] :
% 2.99/1.59 ( ( proces1708129104e_PREF @ A @ B @ C @ Sys @ ( proces1627516585ss_VAR @ A @ B @ X6 ) )
% 2.99/1.59 = ( proces460752237s_term @ C @ B @ B
% 2.99/1.59 @ ^ [Aa: C] : ( undefined @ B )
% 2.99/1.59 @ ( proces745025900prefOf @ B )
% 2.99/1.59 @ ^ [A3: B,T3: proces554692349s_term @ B @ C] : A3
% 2.99/1.59 @ ^ [Aa: proces554692349s_term @ B @ C,Ab2: proces554692349s_term @ B @ C] : ( undefined @ B )
% 2.99/1.59 @ ( Sys @ X6 ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_120_solution_Osimps_I3_J,axiom,
% 2.99/1.59 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 2.99/1.59 ( ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
% 2.99/1.59 => ( ( proces745025900prefOf @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) )
% 2.99/1.59 = ( proces1708129104e_PREF @ A @ B @ A @ Sys @ T2 ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_121_PREF_Osimps_I3_J,axiom,
% 2.99/1.59 ! [A: $tType,C: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ C ),A2: B,T2: proces554692349s_term @ B @ A] :
% 2.99/1.59 ( ( proces1708129104e_PREF @ A @ B @ C @ Sys @ ( proces1454156180ss_ACT @ B @ A @ A2 @ T2 ) )
% 2.99/1.59 = A2 ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_122_PREF_Oelims,axiom,
% 2.99/1.59 ! [A: $tType,C: $tType,B: $tType,X3: A > ( proces554692349s_term @ B @ C ),Xa: proces554692349s_term @ B @ A,Y: B] :
% 2.99/1.59 ( ( ( proces1708129104e_PREF @ A @ B @ C @ X3 @ Xa )
% 2.99/1.59 = Y )
% 2.99/1.59 => ( ! [X4: A] :
% 2.99/1.59 ( ( Xa
% 2.99/1.59 = ( proces1627516585ss_VAR @ A @ B @ X4 ) )
% 2.99/1.59 => ( Y
% 2.99/1.59 != ( proces460752237s_term @ C @ B @ B
% 2.99/1.59 @ ^ [Aa: C] : ( undefined @ B )
% 2.99/1.59 @ ( proces745025900prefOf @ B )
% 2.99/1.59 @ ^ [A3: B,T3: proces554692349s_term @ B @ C] : A3
% 2.99/1.59 @ ^ [Aa: proces554692349s_term @ B @ C,Ab2: proces554692349s_term @ B @ C] : ( undefined @ B )
% 2.99/1.59 @ ( X3 @ X4 ) ) ) )
% 2.99/1.59 => ( ! [P2: proces634752977rocess @ B] :
% 2.99/1.59 ( ( Xa
% 2.99/1.59 = ( proces1062592052s_PROC @ B @ A @ P2 ) )
% 2.99/1.59 => ( Y
% 2.99/1.59 != ( proces745025900prefOf @ B @ P2 ) ) )
% 2.99/1.59 => ( ! [A4: B] :
% 2.99/1.59 ( ? [T4: proces554692349s_term @ B @ A] :
% 2.99/1.59 ( Xa
% 2.99/1.59 = ( proces1454156180ss_ACT @ B @ A @ A4 @ T4 ) )
% 2.99/1.59 => ( Y != A4 ) )
% 2.99/1.59 => ~ ( ? [V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] :
% 2.99/1.59 ( Xa
% 2.99/1.59 = ( proces89589571ess_CH @ B @ A @ V @ Va ) )
% 2.99/1.59 => ( Y
% 2.99/1.59 != ( undefined @ B ) ) ) ) ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_123_prefOf__def,axiom,
% 2.99/1.59 ! [A: $tType] :
% 2.99/1.59 ( ( proces745025900prefOf @ A )
% 2.99/1.59 = ( proces1406508781rocess @ A @ A
% 2.99/1.59 @ ^ [X11: A,X122: proces634752977rocess @ A] : X11
% 2.99/1.59 @ ^ [Uu: proces634752977rocess @ A,Uv: proces634752977rocess @ A] : ( undefined @ A ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_124_cut__def,axiom,
% 2.99/1.59 ! [B: $tType,A: $tType] :
% 2.99/1.59 ( ( cut @ A @ B )
% 2.99/1.59 = ( ^ [F7: A > B,R4: set @ ( product_prod @ A @ A ),X: A,Y4: A] : ( if @ B @ ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y4 @ X ) @ R4 ) @ ( F7 @ Y4 ) @ ( undefined @ B ) ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_125_CH1_Opelims,axiom,
% 2.99/1.59 ! [A: $tType,B: $tType,X3: A > ( proces554692349s_term @ B @ A ),Xa: proces554692349s_term @ B @ A,Y: proces554692349s_term @ B @ A] :
% 2.99/1.59 ( ( ( proces1239275103le_CH1 @ A @ B @ X3 @ Xa )
% 2.99/1.59 = Y )
% 2.99/1.59 => ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1869379930H1_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X3 @ Xa ) )
% 2.99/1.59 => ( ! [X4: A] :
% 2.99/1.59 ( ( Xa
% 2.99/1.59 = ( proces1627516585ss_VAR @ A @ B @ X4 ) )
% 2.99/1.59 => ( ( Y
% 2.99/1.59 = ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 2.99/1.59 @ ^ [A3: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 2.99/1.59 @ ^ [P4: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces979765041_ch1Of @ B @ P4 ) )
% 2.99/1.59 @ ^ [A3: B,B5: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 2.99/1.59 @ ^ [T13: proces554692349s_term @ B @ A,T24: proces554692349s_term @ B @ A] : T13
% 2.99/1.59 @ ( X3 @ X4 ) ) )
% 2.99/1.59 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1869379930H1_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X3 @ ( proces1627516585ss_VAR @ A @ B @ X4 ) ) ) ) )
% 2.99/1.59 => ( ! [P2: proces634752977rocess @ B] :
% 2.99/1.59 ( ( Xa
% 2.99/1.59 = ( proces1062592052s_PROC @ B @ A @ P2 ) )
% 2.99/1.59 => ( ( Y
% 2.99/1.59 = ( proces1062592052s_PROC @ B @ A @ ( proces979765041_ch1Of @ B @ P2 ) ) )
% 2.99/1.59 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1869379930H1_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X3 @ ( proces1062592052s_PROC @ B @ A @ P2 ) ) ) ) )
% 2.99/1.59 => ( ! [T12: proces554692349s_term @ B @ A,T23: proces554692349s_term @ B @ A] :
% 2.99/1.59 ( ( Xa
% 2.99/1.59 = ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) )
% 2.99/1.59 => ( ( Y = T12 )
% 2.99/1.59 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1869379930H1_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X3 @ ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) ) ) ) )
% 2.99/1.59 => ~ ! [V: B,Va: proces554692349s_term @ B @ A] :
% 2.99/1.59 ( ( Xa
% 2.99/1.59 = ( proces1454156180ss_ACT @ B @ A @ V @ Va ) )
% 2.99/1.59 => ( ( Y
% 2.99/1.59 = ( undefined @ ( proces554692349s_term @ B @ A ) ) )
% 2.99/1.59 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1869379930H1_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X3 @ ( proces1454156180ss_ACT @ B @ A @ V @ Va ) ) ) ) ) ) ) ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_126_CH2_Opelims,axiom,
% 2.99/1.59 ! [A: $tType,B: $tType,X3: A > ( proces554692349s_term @ B @ A ),Xa: proces554692349s_term @ B @ A,Y: proces554692349s_term @ B @ A] :
% 2.99/1.59 ( ( ( proces1239275104le_CH2 @ A @ B @ X3 @ Xa )
% 2.99/1.59 = Y )
% 2.99/1.59 => ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces93903513H2_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X3 @ Xa ) )
% 2.99/1.59 => ( ! [X4: A] :
% 2.99/1.59 ( ( Xa
% 2.99/1.59 = ( proces1627516585ss_VAR @ A @ B @ X4 ) )
% 2.99/1.59 => ( ( Y
% 2.99/1.59 = ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 2.99/1.59 @ ^ [A3: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 2.99/1.59 @ ^ [P4: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces988026546_ch2Of @ B @ P4 ) )
% 2.99/1.59 @ ^ [A3: B,B5: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 2.99/1.59 @ ^ [T13: proces554692349s_term @ B @ A,T24: proces554692349s_term @ B @ A] : T24
% 2.99/1.59 @ ( X3 @ X4 ) ) )
% 2.99/1.59 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces93903513H2_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X3 @ ( proces1627516585ss_VAR @ A @ B @ X4 ) ) ) ) )
% 2.99/1.59 => ( ! [P2: proces634752977rocess @ B] :
% 2.99/1.59 ( ( Xa
% 2.99/1.59 = ( proces1062592052s_PROC @ B @ A @ P2 ) )
% 2.99/1.59 => ( ( Y
% 2.99/1.59 = ( proces1062592052s_PROC @ B @ A @ ( proces988026546_ch2Of @ B @ P2 ) ) )
% 2.99/1.59 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces93903513H2_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X3 @ ( proces1062592052s_PROC @ B @ A @ P2 ) ) ) ) )
% 2.99/1.59 => ( ! [T12: proces554692349s_term @ B @ A,T23: proces554692349s_term @ B @ A] :
% 2.99/1.59 ( ( Xa
% 2.99/1.59 = ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) )
% 2.99/1.59 => ( ( Y = T23 )
% 2.99/1.59 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces93903513H2_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X3 @ ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) ) ) ) )
% 2.99/1.59 => ~ ! [V: B,Va: proces554692349s_term @ B @ A] :
% 2.99/1.59 ( ( Xa
% 2.99/1.59 = ( proces1454156180ss_ACT @ B @ A @ V @ Va ) )
% 2.99/1.59 => ( ( Y
% 2.99/1.59 = ( undefined @ ( proces554692349s_term @ B @ A ) ) )
% 2.99/1.59 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces93903513H2_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X3 @ ( proces1454156180ss_ACT @ B @ A @ V @ Va ) ) ) ) ) ) ) ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_127_ch2Of__def,axiom,
% 2.99/1.59 ! [A: $tType] :
% 2.99/1.59 ( ( proces988026546_ch2Of @ A )
% 2.99/1.59 = ( proces1406508781rocess @ A @ ( proces634752977rocess @ A )
% 2.99/1.59 @ ^ [Uu: A,Uv: proces634752977rocess @ A] : ( undefined @ ( proces634752977rocess @ A ) )
% 2.99/1.59 @ ^ [X21: proces634752977rocess @ A,X222: proces634752977rocess @ A] : X222 ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_128_ch1Of__def,axiom,
% 2.99/1.59 ! [A: $tType] :
% 2.99/1.59 ( ( proces979765041_ch1Of @ A )
% 2.99/1.59 = ( proces1406508781rocess @ A @ ( proces634752977rocess @ A )
% 2.99/1.59 @ ^ [Uu: A,Uv: proces634752977rocess @ A] : ( undefined @ ( proces634752977rocess @ A ) )
% 2.99/1.59 @ ^ [X21: proces634752977rocess @ A,X222: proces634752977rocess @ A] : X21 ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_129_CH2_Osimps_I2_J,axiom,
% 2.99/1.59 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),P: proces634752977rocess @ B] :
% 2.99/1.59 ( ( proces1239275104le_CH2 @ A @ B @ Sys @ ( proces1062592052s_PROC @ B @ A @ P ) )
% 2.99/1.59 = ( proces1062592052s_PROC @ B @ A @ ( proces988026546_ch2Of @ B @ P ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_130_CH1_Osimps_I2_J,axiom,
% 2.99/1.59 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),P: proces634752977rocess @ B] :
% 2.99/1.59 ( ( proces1239275103le_CH1 @ A @ B @ Sys @ ( proces1062592052s_PROC @ B @ A @ P ) )
% 2.99/1.59 = ( proces1062592052s_PROC @ B @ A @ ( proces979765041_ch1Of @ B @ P ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_131_process_Ocase__distrib,axiom,
% 2.99/1.59 ! [B: $tType,C: $tType,A: $tType,H: B > C,F1: A > ( proces634752977rocess @ A ) > B,F2: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B,Process: proces634752977rocess @ A] :
% 2.99/1.59 ( ( H @ ( proces1406508781rocess @ A @ B @ F1 @ F2 @ Process ) )
% 2.99/1.59 = ( proces1406508781rocess @ A @ C
% 2.99/1.59 @ ^ [X1: A,X22: proces634752977rocess @ A] : ( H @ ( F1 @ X1 @ X22 ) )
% 2.99/1.59 @ ^ [X1: proces634752977rocess @ A,X22: proces634752977rocess @ A] : ( H @ ( F2 @ X1 @ X22 ) )
% 2.99/1.59 @ Process ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_132_solution_Osimps_I6_J,axiom,
% 2.99/1.59 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 2.99/1.59 ( ~ ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
% 2.99/1.59 => ( ( proces988026546_ch2Of @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) )
% 2.99/1.59 = ( proces1652378886lution @ A @ B @ Sys @ ( proces1239275104le_CH2 @ A @ B @ Sys @ T2 ) ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_133_solution_Osimps_I5_J,axiom,
% 2.99/1.59 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 2.99/1.59 ( ~ ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
% 2.99/1.59 => ( ( proces979765041_ch1Of @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) )
% 2.99/1.59 = ( proces1652378886lution @ A @ B @ Sys @ ( proces1239275103le_CH1 @ A @ B @ Sys @ T2 ) ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_134_CH2_Osimps_I1_J,axiom,
% 2.99/1.59 ! [B: $tType,A: $tType,Sys: A > ( proces554692349s_term @ B @ A ),X6: A] :
% 2.99/1.59 ( ( proces1239275104le_CH2 @ A @ B @ Sys @ ( proces1627516585ss_VAR @ A @ B @ X6 ) )
% 2.99/1.59 = ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 2.99/1.59 @ ^ [A3: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 2.99/1.59 @ ^ [P4: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces988026546_ch2Of @ B @ P4 ) )
% 2.99/1.59 @ ^ [A3: B,B5: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 2.99/1.59 @ ^ [T13: proces554692349s_term @ B @ A,T24: proces554692349s_term @ B @ A] : T24
% 2.99/1.59 @ ( Sys @ X6 ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_135_CH1_Osimps_I1_J,axiom,
% 2.99/1.59 ! [B: $tType,A: $tType,Sys: A > ( proces554692349s_term @ B @ A ),X6: A] :
% 2.99/1.59 ( ( proces1239275103le_CH1 @ A @ B @ Sys @ ( proces1627516585ss_VAR @ A @ B @ X6 ) )
% 2.99/1.59 = ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 2.99/1.59 @ ^ [A3: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 2.99/1.59 @ ^ [P4: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces979765041_ch1Of @ B @ P4 ) )
% 2.99/1.59 @ ^ [A3: B,B5: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 2.99/1.59 @ ^ [T13: proces554692349s_term @ B @ A,T24: proces554692349s_term @ B @ A] : T13
% 2.99/1.59 @ ( Sys @ X6 ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_136_cut__apply,axiom,
% 2.99/1.59 ! [B: $tType,A: $tType,X3: A,A2: A,R: set @ ( product_prod @ A @ A ),F: A > B] :
% 2.99/1.59 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X3 @ A2 ) @ R )
% 2.99/1.59 => ( ( cut @ A @ B @ F @ R @ A2 @ X3 )
% 2.99/1.59 = ( F @ X3 ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_137_cuts__eq,axiom,
% 2.99/1.59 ! [B: $tType,A: $tType,F: A > B,R: set @ ( product_prod @ A @ A ),X3: A,G: A > B] :
% 2.99/1.59 ( ( ( cut @ A @ B @ F @ R @ X3 )
% 2.99/1.59 = ( cut @ A @ B @ G @ R @ X3 ) )
% 2.99/1.59 = ( ! [Y4: A] :
% 2.99/1.59 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y4 @ X3 ) @ R )
% 2.99/1.59 => ( ( F @ Y4 )
% 2.99/1.59 = ( G @ Y4 ) ) ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_138_CH2_Osimps_I3_J,axiom,
% 2.99/1.59 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T1: proces554692349s_term @ B @ A,T22: proces554692349s_term @ B @ A] :
% 2.99/1.59 ( ( proces1239275104le_CH2 @ A @ B @ Sys @ ( proces89589571ess_CH @ B @ A @ T1 @ T22 ) )
% 2.99/1.59 = T22 ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_139_CH1_Osimps_I3_J,axiom,
% 2.99/1.59 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T1: proces554692349s_term @ B @ A,T22: proces554692349s_term @ B @ A] :
% 2.99/1.59 ( ( proces1239275103le_CH1 @ A @ B @ Sys @ ( proces89589571ess_CH @ B @ A @ T1 @ T22 ) )
% 2.99/1.59 = T1 ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_140_process_Odisc__eq__case_I1_J,axiom,
% 2.99/1.59 ! [A: $tType] :
% 2.99/1.59 ( ( proces10484146Action @ A )
% 2.99/1.59 = ( proces1406508781rocess @ A @ $o
% 2.99/1.59 @ ^ [Uu2: A,Uv2: proces634752977rocess @ A] : $true
% 2.99/1.59 @ ^ [Uu2: proces634752977rocess @ A,Uv2: proces634752977rocess @ A] : $false ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_141_process_Odisc__eq__case_I2_J,axiom,
% 2.99/1.59 ! [A: $tType] :
% 2.99/1.59 ( ( proces401113213Choice @ A )
% 2.99/1.59 = ( proces1406508781rocess @ A @ $o
% 2.99/1.59 @ ^ [Uu2: A,Uv2: proces634752977rocess @ A] : $false
% 2.99/1.59 @ ^ [Uu2: proces634752977rocess @ A,Uv2: proces634752977rocess @ A] : $true ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_142_CH2_Oelims,axiom,
% 2.99/1.59 ! [A: $tType,B: $tType,X3: A > ( proces554692349s_term @ B @ A ),Xa: proces554692349s_term @ B @ A,Y: proces554692349s_term @ B @ A] :
% 2.99/1.59 ( ( ( proces1239275104le_CH2 @ A @ B @ X3 @ Xa )
% 2.99/1.59 = Y )
% 2.99/1.59 => ( ! [X4: A] :
% 2.99/1.59 ( ( Xa
% 2.99/1.59 = ( proces1627516585ss_VAR @ A @ B @ X4 ) )
% 2.99/1.59 => ( Y
% 2.99/1.59 != ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 2.99/1.59 @ ^ [A3: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 2.99/1.59 @ ^ [P4: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces988026546_ch2Of @ B @ P4 ) )
% 2.99/1.59 @ ^ [A3: B,B5: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 2.99/1.59 @ ^ [T13: proces554692349s_term @ B @ A,T24: proces554692349s_term @ B @ A] : T24
% 2.99/1.59 @ ( X3 @ X4 ) ) ) )
% 2.99/1.59 => ( ! [P2: proces634752977rocess @ B] :
% 2.99/1.59 ( ( Xa
% 2.99/1.59 = ( proces1062592052s_PROC @ B @ A @ P2 ) )
% 2.99/1.59 => ( Y
% 2.99/1.59 != ( proces1062592052s_PROC @ B @ A @ ( proces988026546_ch2Of @ B @ P2 ) ) ) )
% 2.99/1.59 => ( ! [T12: proces554692349s_term @ B @ A,T23: proces554692349s_term @ B @ A] :
% 2.99/1.59 ( ( Xa
% 2.99/1.59 = ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) )
% 2.99/1.59 => ( Y != T23 ) )
% 2.99/1.59 => ~ ( ? [V: B,Va: proces554692349s_term @ B @ A] :
% 2.99/1.59 ( Xa
% 2.99/1.59 = ( proces1454156180ss_ACT @ B @ A @ V @ Va ) )
% 2.99/1.59 => ( Y
% 2.99/1.59 != ( undefined @ ( proces554692349s_term @ B @ A ) ) ) ) ) ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_143_CH1_Oelims,axiom,
% 2.99/1.59 ! [A: $tType,B: $tType,X3: A > ( proces554692349s_term @ B @ A ),Xa: proces554692349s_term @ B @ A,Y: proces554692349s_term @ B @ A] :
% 2.99/1.59 ( ( ( proces1239275103le_CH1 @ A @ B @ X3 @ Xa )
% 2.99/1.59 = Y )
% 2.99/1.59 => ( ! [X4: A] :
% 2.99/1.59 ( ( Xa
% 2.99/1.59 = ( proces1627516585ss_VAR @ A @ B @ X4 ) )
% 2.99/1.59 => ( Y
% 2.99/1.59 != ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 2.99/1.59 @ ^ [A3: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 2.99/1.59 @ ^ [P4: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces979765041_ch1Of @ B @ P4 ) )
% 2.99/1.59 @ ^ [A3: B,B5: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 2.99/1.59 @ ^ [T13: proces554692349s_term @ B @ A,T24: proces554692349s_term @ B @ A] : T13
% 2.99/1.59 @ ( X3 @ X4 ) ) ) )
% 2.99/1.59 => ( ! [P2: proces634752977rocess @ B] :
% 2.99/1.59 ( ( Xa
% 2.99/1.59 = ( proces1062592052s_PROC @ B @ A @ P2 ) )
% 2.99/1.59 => ( Y
% 2.99/1.59 != ( proces1062592052s_PROC @ B @ A @ ( proces979765041_ch1Of @ B @ P2 ) ) ) )
% 2.99/1.59 => ( ! [T12: proces554692349s_term @ B @ A] :
% 2.99/1.59 ( ? [T23: proces554692349s_term @ B @ A] :
% 2.99/1.59 ( Xa
% 2.99/1.59 = ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) )
% 2.99/1.59 => ( Y != T12 ) )
% 2.99/1.59 => ~ ( ? [V: B,Va: proces554692349s_term @ B @ A] :
% 2.99/1.59 ( Xa
% 2.99/1.59 = ( proces1454156180ss_ACT @ B @ A @ V @ Va ) )
% 2.99/1.59 => ( Y
% 2.99/1.59 != ( undefined @ ( proces554692349s_term @ B @ A ) ) ) ) ) ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_144_process_Ocase__eq__if,axiom,
% 2.99/1.59 ! [B: $tType,A: $tType] :
% 2.99/1.59 ( ( proces1406508781rocess @ A @ B )
% 2.99/1.59 = ( ^ [F12: A > ( proces634752977rocess @ A ) > B,F22: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B,Process2: proces634752977rocess @ A] : ( if @ B @ ( proces10484146Action @ A @ Process2 ) @ ( F12 @ ( proces745025900prefOf @ A @ Process2 ) @ ( proces1778668539contOf @ A @ Process2 ) ) @ ( F22 @ ( proces979765041_ch1Of @ A @ Process2 ) @ ( proces988026546_ch2Of @ A @ Process2 ) ) ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_145_process_Ocoinduct__strong,axiom,
% 2.99/1.59 ! [A: $tType,R: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > $o,Process: proces634752977rocess @ A,Process3: proces634752977rocess @ A] :
% 2.99/1.59 ( ( R @ Process @ Process3 )
% 2.99/1.59 => ( ! [Process4: proces634752977rocess @ A,Process5: proces634752977rocess @ A] :
% 2.99/1.59 ( ( R @ Process4 @ Process5 )
% 2.99/1.59 => ( ( ( proces10484146Action @ A @ Process4 )
% 2.99/1.59 = ( proces10484146Action @ A @ Process5 ) )
% 2.99/1.59 & ( ( proces10484146Action @ A @ Process4 )
% 2.99/1.59 => ( ( proces10484146Action @ A @ Process5 )
% 2.99/1.59 => ( ( ( proces745025900prefOf @ A @ Process4 )
% 2.99/1.59 = ( proces745025900prefOf @ A @ Process5 ) )
% 2.99/1.59 & ( ( R @ ( proces1778668539contOf @ A @ Process4 ) @ ( proces1778668539contOf @ A @ Process5 ) )
% 2.99/1.59 | ( ( proces1778668539contOf @ A @ Process4 )
% 2.99/1.59 = ( proces1778668539contOf @ A @ Process5 ) ) ) ) ) )
% 2.99/1.59 & ( ( proces401113213Choice @ A @ Process4 )
% 2.99/1.59 => ( ( proces401113213Choice @ A @ Process5 )
% 2.99/1.59 => ( ( ( R @ ( proces979765041_ch1Of @ A @ Process4 ) @ ( proces979765041_ch1Of @ A @ Process5 ) )
% 2.99/1.59 | ( ( proces979765041_ch1Of @ A @ Process4 )
% 2.99/1.59 = ( proces979765041_ch1Of @ A @ Process5 ) ) )
% 2.99/1.59 & ( ( R @ ( proces988026546_ch2Of @ A @ Process4 ) @ ( proces988026546_ch2Of @ A @ Process5 ) )
% 2.99/1.59 | ( ( proces988026546_ch2Of @ A @ Process4 )
% 2.99/1.59 = ( proces988026546_ch2Of @ A @ Process5 ) ) ) ) ) ) ) )
% 2.99/1.59 => ( Process = Process3 ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_146_process_Ocoinduct,axiom,
% 2.99/1.59 ! [A: $tType,R: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > $o,Process: proces634752977rocess @ A,Process3: proces634752977rocess @ A] :
% 2.99/1.59 ( ( R @ Process @ Process3 )
% 2.99/1.59 => ( ! [Process4: proces634752977rocess @ A,Process5: proces634752977rocess @ A] :
% 2.99/1.59 ( ( R @ Process4 @ Process5 )
% 2.99/1.59 => ( ( ( proces10484146Action @ A @ Process4 )
% 2.99/1.59 = ( proces10484146Action @ A @ Process5 ) )
% 2.99/1.59 & ( ( proces10484146Action @ A @ Process4 )
% 2.99/1.59 => ( ( proces10484146Action @ A @ Process5 )
% 2.99/1.59 => ( ( ( proces745025900prefOf @ A @ Process4 )
% 2.99/1.59 = ( proces745025900prefOf @ A @ Process5 ) )
% 2.99/1.59 & ( R @ ( proces1778668539contOf @ A @ Process4 ) @ ( proces1778668539contOf @ A @ Process5 ) ) ) ) )
% 2.99/1.59 & ( ( proces401113213Choice @ A @ Process4 )
% 2.99/1.59 => ( ( proces401113213Choice @ A @ Process5 )
% 2.99/1.59 => ( ( R @ ( proces979765041_ch1Of @ A @ Process4 ) @ ( proces979765041_ch1Of @ A @ Process5 ) )
% 2.99/1.59 & ( R @ ( proces988026546_ch2Of @ A @ Process4 ) @ ( proces988026546_ch2Of @ A @ Process5 ) ) ) ) ) ) )
% 2.99/1.59 => ( Process = Process3 ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_147_process_Oexpand,axiom,
% 2.99/1.59 ! [A: $tType,Process: proces634752977rocess @ A,Process3: proces634752977rocess @ A] :
% 2.99/1.59 ( ( ( proces10484146Action @ A @ Process )
% 2.99/1.59 = ( proces10484146Action @ A @ Process3 ) )
% 2.99/1.59 => ( ( ( proces10484146Action @ A @ Process )
% 2.99/1.59 => ( ( proces10484146Action @ A @ Process3 )
% 2.99/1.59 => ( ( ( proces745025900prefOf @ A @ Process )
% 2.99/1.59 = ( proces745025900prefOf @ A @ Process3 ) )
% 2.99/1.59 & ( ( proces1778668539contOf @ A @ Process )
% 2.99/1.59 = ( proces1778668539contOf @ A @ Process3 ) ) ) ) )
% 2.99/1.59 => ( ( ( proces401113213Choice @ A @ Process )
% 2.99/1.59 => ( ( proces401113213Choice @ A @ Process3 )
% 2.99/1.59 => ( ( ( proces979765041_ch1Of @ A @ Process )
% 2.99/1.59 = ( proces979765041_ch1Of @ A @ Process3 ) )
% 2.99/1.59 & ( ( proces988026546_ch2Of @ A @ Process )
% 2.99/1.59 = ( proces988026546_ch2Of @ A @ Process3 ) ) ) ) )
% 2.99/1.59 => ( Process = Process3 ) ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_148_contOf__def,axiom,
% 2.99/1.59 ! [A: $tType] :
% 2.99/1.59 ( ( proces1778668539contOf @ A )
% 2.99/1.59 = ( proces1406508781rocess @ A @ ( proces634752977rocess @ A )
% 2.99/1.59 @ ^ [X11: A,X122: proces634752977rocess @ A] : X122
% 2.99/1.59 @ ^ [Uu: proces634752977rocess @ A,Uv: proces634752977rocess @ A] : ( undefined @ ( proces634752977rocess @ A ) ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_149_CONT_Oelims,axiom,
% 2.99/1.59 ! [A: $tType,B: $tType,X3: A > ( proces554692349s_term @ B @ A ),Xa: proces554692349s_term @ B @ A,Y: proces554692349s_term @ B @ A] :
% 2.99/1.59 ( ( ( proces126235999e_CONT @ A @ B @ X3 @ Xa )
% 2.99/1.59 = Y )
% 2.99/1.59 => ( ! [X4: A] :
% 2.99/1.59 ( ( Xa
% 2.99/1.59 = ( proces1627516585ss_VAR @ A @ B @ X4 ) )
% 2.99/1.59 => ( Y
% 2.99/1.59 != ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 2.99/1.59 @ ^ [Aa: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 2.99/1.59 @ ^ [P4: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces1778668539contOf @ B @ P4 ) )
% 2.99/1.59 @ ^ [A3: B,T3: proces554692349s_term @ B @ A] : T3
% 2.99/1.59 @ ^ [Aa: proces554692349s_term @ B @ A,Ab2: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 2.99/1.59 @ ( X3 @ X4 ) ) ) )
% 2.99/1.59 => ( ! [P2: proces634752977rocess @ B] :
% 2.99/1.59 ( ( Xa
% 2.99/1.59 = ( proces1062592052s_PROC @ B @ A @ P2 ) )
% 2.99/1.59 => ( Y
% 2.99/1.59 != ( proces1062592052s_PROC @ B @ A @ ( proces1778668539contOf @ B @ P2 ) ) ) )
% 2.99/1.59 => ( ! [A4: B,T4: proces554692349s_term @ B @ A] :
% 2.99/1.59 ( ( Xa
% 2.99/1.59 = ( proces1454156180ss_ACT @ B @ A @ A4 @ T4 ) )
% 2.99/1.59 => ( Y != T4 ) )
% 2.99/1.59 => ~ ( ? [V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] :
% 2.99/1.59 ( Xa
% 2.99/1.59 = ( proces89589571ess_CH @ B @ A @ V @ Va ) )
% 2.99/1.59 => ( Y
% 2.99/1.59 != ( undefined @ ( proces554692349s_term @ B @ A ) ) ) ) ) ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_150_CONT_Osimps_I1_J,axiom,
% 2.99/1.59 ! [B: $tType,A: $tType,Sys: A > ( proces554692349s_term @ B @ A ),X6: A] :
% 2.99/1.59 ( ( proces126235999e_CONT @ A @ B @ Sys @ ( proces1627516585ss_VAR @ A @ B @ X6 ) )
% 2.99/1.59 = ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 2.99/1.59 @ ^ [Aa: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 2.99/1.59 @ ^ [P4: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces1778668539contOf @ B @ P4 ) )
% 2.99/1.59 @ ^ [A3: B,T3: proces554692349s_term @ B @ A] : T3
% 2.99/1.59 @ ^ [Aa: proces554692349s_term @ B @ A,Ab2: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 2.99/1.59 @ ( Sys @ X6 ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_151_CONT_Opelims,axiom,
% 2.99/1.59 ! [A: $tType,B: $tType,X3: A > ( proces554692349s_term @ B @ A ),Xa: proces554692349s_term @ B @ A,Y: proces554692349s_term @ B @ A] :
% 2.99/1.59 ( ( ( proces126235999e_CONT @ A @ B @ X3 @ Xa )
% 2.99/1.59 = Y )
% 2.99/1.59 => ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1004198490NT_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X3 @ Xa ) )
% 2.99/1.59 => ( ! [X4: A] :
% 2.99/1.59 ( ( Xa
% 2.99/1.59 = ( proces1627516585ss_VAR @ A @ B @ X4 ) )
% 2.99/1.59 => ( ( Y
% 2.99/1.59 = ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 2.99/1.59 @ ^ [Aa: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 2.99/1.59 @ ^ [P4: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces1778668539contOf @ B @ P4 ) )
% 2.99/1.59 @ ^ [A3: B,T3: proces554692349s_term @ B @ A] : T3
% 2.99/1.59 @ ^ [Aa: proces554692349s_term @ B @ A,Ab2: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 2.99/1.59 @ ( X3 @ X4 ) ) )
% 2.99/1.59 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1004198490NT_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X3 @ ( proces1627516585ss_VAR @ A @ B @ X4 ) ) ) ) )
% 2.99/1.59 => ( ! [P2: proces634752977rocess @ B] :
% 2.99/1.59 ( ( Xa
% 2.99/1.59 = ( proces1062592052s_PROC @ B @ A @ P2 ) )
% 2.99/1.59 => ( ( Y
% 2.99/1.59 = ( proces1062592052s_PROC @ B @ A @ ( proces1778668539contOf @ B @ P2 ) ) )
% 2.99/1.59 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1004198490NT_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X3 @ ( proces1062592052s_PROC @ B @ A @ P2 ) ) ) ) )
% 2.99/1.59 => ( ! [A4: B,T4: proces554692349s_term @ B @ A] :
% 2.99/1.59 ( ( Xa
% 2.99/1.59 = ( proces1454156180ss_ACT @ B @ A @ A4 @ T4 ) )
% 2.99/1.59 => ( ( Y = T4 )
% 2.99/1.59 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1004198490NT_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X3 @ ( proces1454156180ss_ACT @ B @ A @ A4 @ T4 ) ) ) ) )
% 2.99/1.59 => ~ ! [V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] :
% 2.99/1.59 ( ( Xa
% 2.99/1.59 = ( proces89589571ess_CH @ B @ A @ V @ Va ) )
% 2.99/1.59 => ( ( Y
% 2.99/1.59 = ( undefined @ ( proces554692349s_term @ B @ A ) ) )
% 2.99/1.59 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1004198490NT_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X3 @ ( proces89589571ess_CH @ B @ A @ V @ Va ) ) ) ) ) ) ) ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_152_CONT_Osimps_I3_J,axiom,
% 2.99/1.59 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),A2: B,T2: proces554692349s_term @ B @ A] :
% 2.99/1.59 ( ( proces126235999e_CONT @ A @ B @ Sys @ ( proces1454156180ss_ACT @ B @ A @ A2 @ T2 ) )
% 2.99/1.59 = T2 ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_153_CONT_Osimps_I2_J,axiom,
% 2.99/1.59 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),P: proces634752977rocess @ B] :
% 2.99/1.59 ( ( proces126235999e_CONT @ A @ B @ Sys @ ( proces1062592052s_PROC @ B @ A @ P ) )
% 2.99/1.59 = ( proces1062592052s_PROC @ B @ A @ ( proces1778668539contOf @ B @ P ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_154_solution_Osimps_I4_J,axiom,
% 2.99/1.59 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 2.99/1.59 ( ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
% 2.99/1.59 => ( ( proces1778668539contOf @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) )
% 2.99/1.59 = ( proces1652378886lution @ A @ B @ Sys @ ( proces126235999e_CONT @ A @ B @ Sys @ T2 ) ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_155_process_Orel__coinduct,axiom,
% 2.99/1.59 ! [A: $tType,B: $tType,P3: ( proces634752977rocess @ A ) > ( proces634752977rocess @ B ) > $o,X3: proces634752977rocess @ A,Y: proces634752977rocess @ B,R: A > B > $o] :
% 2.99/1.59 ( ( P3 @ X3 @ Y )
% 2.99/1.59 => ( ! [Process4: proces634752977rocess @ A,Process5: proces634752977rocess @ B] :
% 2.99/1.59 ( ( P3 @ Process4 @ Process5 )
% 2.99/1.59 => ( ( ( proces10484146Action @ A @ Process4 )
% 2.99/1.59 = ( proces10484146Action @ B @ Process5 ) )
% 2.99/1.59 & ( ( proces10484146Action @ A @ Process4 )
% 2.99/1.59 => ( ( proces10484146Action @ B @ Process5 )
% 2.99/1.59 => ( ( R @ ( proces745025900prefOf @ A @ Process4 ) @ ( proces745025900prefOf @ B @ Process5 ) )
% 2.99/1.59 & ( P3 @ ( proces1778668539contOf @ A @ Process4 ) @ ( proces1778668539contOf @ B @ Process5 ) ) ) ) )
% 2.99/1.59 & ( ( proces401113213Choice @ A @ Process4 )
% 2.99/1.59 => ( ( proces401113213Choice @ B @ Process5 )
% 2.99/1.59 => ( ( P3 @ ( proces979765041_ch1Of @ A @ Process4 ) @ ( proces979765041_ch1Of @ B @ Process5 ) )
% 2.99/1.59 & ( P3 @ ( proces988026546_ch2Of @ A @ Process4 ) @ ( proces988026546_ch2Of @ B @ Process5 ) ) ) ) ) ) )
% 2.99/1.59 => ( proces749077512rocess @ A @ B @ R @ X3 @ Y ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_156_process_Orel__sel,axiom,
% 2.99/1.59 ! [B: $tType,A: $tType] :
% 2.99/1.59 ( ( proces749077512rocess @ A @ B )
% 2.99/1.59 = ( ^ [R4: A > B > $o,A3: proces634752977rocess @ A,B5: proces634752977rocess @ B] :
% 2.99/1.59 ( ( ( proces10484146Action @ A @ A3 )
% 2.99/1.59 = ( proces10484146Action @ B @ B5 ) )
% 2.99/1.59 & ( ( proces10484146Action @ A @ A3 )
% 2.99/1.59 => ( ( proces10484146Action @ B @ B5 )
% 2.99/1.59 => ( ( R4 @ ( proces745025900prefOf @ A @ A3 ) @ ( proces745025900prefOf @ B @ B5 ) )
% 2.99/1.59 & ( proces749077512rocess @ A @ B @ R4 @ ( proces1778668539contOf @ A @ A3 ) @ ( proces1778668539contOf @ B @ B5 ) ) ) ) )
% 2.99/1.59 & ( ( proces401113213Choice @ A @ A3 )
% 2.99/1.59 => ( ( proces401113213Choice @ B @ B5 )
% 2.99/1.59 => ( ( proces749077512rocess @ A @ B @ R4 @ ( proces979765041_ch1Of @ A @ A3 ) @ ( proces979765041_ch1Of @ B @ B5 ) )
% 2.99/1.59 & ( proces749077512rocess @ A @ B @ R4 @ ( proces988026546_ch2Of @ A @ A3 ) @ ( proces988026546_ch2Of @ B @ B5 ) ) ) ) ) ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_157_solution_Octr_I1_J,axiom,
% 2.99/1.59 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 2.99/1.59 ( ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
% 2.99/1.59 => ( ( proces1652378886lution @ A @ B @ Sys @ T2 )
% 2.99/1.59 = ( proces1525233512Action @ B @ ( proces1708129104e_PREF @ A @ B @ A @ Sys @ T2 ) @ ( proces1652378886lution @ A @ B @ Sys @ ( proces126235999e_CONT @ A @ B @ Sys @ T2 ) ) ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_158_process_Oinject_I1_J,axiom,
% 2.99/1.59 ! [A: $tType,X112: A,X123: proces634752977rocess @ A,Y11: A,Y12: proces634752977rocess @ A] :
% 2.99/1.59 ( ( ( proces1525233512Action @ A @ X112 @ X123 )
% 2.99/1.59 = ( proces1525233512Action @ A @ Y11 @ Y12 ) )
% 2.99/1.59 = ( ( X112 = Y11 )
% 2.99/1.59 & ( X123 = Y12 ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_159_process_Orel__inject_I1_J,axiom,
% 2.99/1.59 ! [A: $tType,B: $tType,R: A > B > $o,X112: A,X123: proces634752977rocess @ A,Y11: B,Y12: proces634752977rocess @ B] :
% 2.99/1.59 ( ( proces749077512rocess @ A @ B @ R @ ( proces1525233512Action @ A @ X112 @ X123 ) @ ( proces1525233512Action @ B @ Y11 @ Y12 ) )
% 2.99/1.59 = ( ( R @ X112 @ Y11 )
% 2.99/1.59 & ( proces749077512rocess @ A @ B @ R @ X123 @ Y12 ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_160_process_Ocollapse_I1_J,axiom,
% 2.99/1.59 ! [A: $tType,Process: proces634752977rocess @ A] :
% 2.99/1.59 ( ( proces10484146Action @ A @ Process )
% 2.99/1.59 => ( ( proces1525233512Action @ A @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) )
% 2.99/1.59 = Process ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_161_isAction__def,axiom,
% 2.99/1.59 ! [A: $tType] :
% 2.99/1.59 ( ( proces10484146Action @ A )
% 2.99/1.59 = ( ^ [Process2: proces634752977rocess @ A] :
% 2.99/1.59 ? [X11: A,X122: proces634752977rocess @ A] :
% 2.99/1.59 ( Process2
% 2.99/1.59 = ( proces1525233512Action @ A @ X11 @ X122 ) ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_162_process_OdiscI_I1_J,axiom,
% 2.99/1.59 ! [A: $tType,Process: proces634752977rocess @ A,X112: A,X123: proces634752977rocess @ A] :
% 2.99/1.59 ( ( Process
% 2.99/1.59 = ( proces1525233512Action @ A @ X112 @ X123 ) )
% 2.99/1.59 => ( proces10484146Action @ A @ Process ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_163_process_Odisc_I1_J,axiom,
% 2.99/1.59 ! [A: $tType,X112: A,X123: proces634752977rocess @ A] : ( proces10484146Action @ A @ ( proces1525233512Action @ A @ X112 @ X123 ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_164_process_Orel__intros_I1_J,axiom,
% 2.99/1.59 ! [A: $tType,B: $tType,R: A > B > $o,X112: A,Y11: B,X123: proces634752977rocess @ A,Y12: proces634752977rocess @ B] :
% 2.99/1.59 ( ( R @ X112 @ Y11 )
% 2.99/1.59 => ( ( proces749077512rocess @ A @ B @ R @ X123 @ Y12 )
% 2.99/1.59 => ( proces749077512rocess @ A @ B @ R @ ( proces1525233512Action @ A @ X112 @ X123 ) @ ( proces1525233512Action @ B @ Y11 @ Y12 ) ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_165_process_Orel__eq,axiom,
% 2.99/1.59 ! [A: $tType] :
% 2.99/1.59 ( ( proces749077512rocess @ A @ A
% 2.99/1.59 @ ^ [Y8: A,Z3: A] : ( Y8 = Z3 ) )
% 2.99/1.59 = ( ^ [Y8: proces634752977rocess @ A,Z3: proces634752977rocess @ A] : ( Y8 = Z3 ) ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_166_process_Orel__refl,axiom,
% 2.99/1.59 ! [B: $tType,Ra: B > B > $o,X3: proces634752977rocess @ B] :
% 2.99/1.59 ( ! [X5: B] : ( Ra @ X5 @ X5 )
% 2.99/1.59 => ( proces749077512rocess @ B @ B @ Ra @ X3 @ X3 ) ) ).
% 2.99/1.59
% 2.99/1.59 thf(fact_167_process_Osimps_I5_J,axiom,
% 2.99/1.59 ! [B: $tType,A: $tType,F1: A > ( proces634752977rocess @ A ) > B,F2: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B,X112: A,X123: proces634752977rocess @ A] :
% 2.99/1.59 ( ( proces1406508781rocess @ A @ B @ F1 @ F2 @ ( proces1525233512Action @ A @ X112 @ X123 ) )
% 2.99/1.60 = ( F1 @ X112 @ X123 ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_168_process_Osel_I1_J,axiom,
% 2.99/1.60 ! [A: $tType,X112: A,X123: proces634752977rocess @ A] :
% 2.99/1.60 ( ( proces745025900prefOf @ A @ ( proces1525233512Action @ A @ X112 @ X123 ) )
% 2.99/1.60 = X112 ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_169_process_Odisc_I3_J,axiom,
% 2.99/1.60 ! [A: $tType,X112: A,X123: proces634752977rocess @ A] :
% 2.99/1.60 ~ ( proces401113213Choice @ A @ ( proces1525233512Action @ A @ X112 @ X123 ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_170_process_Osel_I2_J,axiom,
% 2.99/1.60 ! [A: $tType,X112: A,X123: proces634752977rocess @ A] :
% 2.99/1.60 ( ( proces1778668539contOf @ A @ ( proces1525233512Action @ A @ X112 @ X123 ) )
% 2.99/1.60 = X123 ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_171_solution_Ocode,axiom,
% 2.99/1.60 ! [B: $tType,A: $tType] :
% 2.99/1.60 ( ( proces1652378886lution @ A @ B )
% 2.99/1.60 = ( ^ [Sys3: A > ( proces554692349s_term @ B @ A ),T3: proces554692349s_term @ B @ A] : ( if @ ( proces634752977rocess @ B ) @ ( proces687458811_isACT @ A @ B @ A @ B @ Sys3 @ T3 ) @ ( proces1525233512Action @ B @ ( proces1708129104e_PREF @ A @ B @ A @ Sys3 @ T3 ) @ ( proces1652378886lution @ A @ B @ Sys3 @ ( proces126235999e_CONT @ A @ B @ Sys3 @ T3 ) ) ) @ ( proces1915862579Choice @ B @ ( proces1652378886lution @ A @ B @ Sys3 @ ( proces1239275103le_CH1 @ A @ B @ Sys3 @ T3 ) ) @ ( proces1652378886lution @ A @ B @ Sys3 @ ( proces1239275104le_CH2 @ A @ B @ Sys3 @ T3 ) ) ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_172_process_Osplit__sel__asm,axiom,
% 2.99/1.60 ! [B: $tType,A: $tType,P3: B > $o,F1: A > ( proces634752977rocess @ A ) > B,F2: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B,Process: proces634752977rocess @ A] :
% 2.99/1.60 ( ( P3 @ ( proces1406508781rocess @ A @ B @ F1 @ F2 @ Process ) )
% 2.99/1.60 = ( ~ ( ( ( Process
% 2.99/1.60 = ( proces1525233512Action @ A @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) ) )
% 2.99/1.60 & ~ ( P3 @ ( F1 @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) ) ) )
% 2.99/1.60 | ( ( Process
% 2.99/1.60 = ( proces1915862579Choice @ A @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) ) )
% 2.99/1.60 & ~ ( P3 @ ( F2 @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) ) ) ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_173_process_Osplit__sel,axiom,
% 2.99/1.60 ! [B: $tType,A: $tType,P3: B > $o,F1: A > ( proces634752977rocess @ A ) > B,F2: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B,Process: proces634752977rocess @ A] :
% 2.99/1.60 ( ( P3 @ ( proces1406508781rocess @ A @ B @ F1 @ F2 @ Process ) )
% 2.99/1.60 = ( ( ( Process
% 2.99/1.60 = ( proces1525233512Action @ A @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) ) )
% 2.99/1.60 => ( P3 @ ( F1 @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) ) ) )
% 2.99/1.60 & ( ( Process
% 2.99/1.60 = ( proces1915862579Choice @ A @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) ) )
% 2.99/1.60 => ( P3 @ ( F2 @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) ) ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_174_process_Oinject_I2_J,axiom,
% 2.99/1.60 ! [A: $tType,X212: proces634752977rocess @ A,X223: proces634752977rocess @ A,Y21: proces634752977rocess @ A,Y22: proces634752977rocess @ A] :
% 2.99/1.60 ( ( ( proces1915862579Choice @ A @ X212 @ X223 )
% 2.99/1.60 = ( proces1915862579Choice @ A @ Y21 @ Y22 ) )
% 2.99/1.60 = ( ( X212 = Y21 )
% 2.99/1.60 & ( X223 = Y22 ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_175_process_Orel__inject_I2_J,axiom,
% 2.99/1.60 ! [A: $tType,B: $tType,R: A > B > $o,X212: proces634752977rocess @ A,X223: proces634752977rocess @ A,Y21: proces634752977rocess @ B,Y22: proces634752977rocess @ B] :
% 2.99/1.60 ( ( proces749077512rocess @ A @ B @ R @ ( proces1915862579Choice @ A @ X212 @ X223 ) @ ( proces1915862579Choice @ B @ Y21 @ Y22 ) )
% 2.99/1.60 = ( ( proces749077512rocess @ A @ B @ R @ X212 @ Y21 )
% 2.99/1.60 & ( proces749077512rocess @ A @ B @ R @ X223 @ Y22 ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_176_process_Ocollapse_I2_J,axiom,
% 2.99/1.60 ! [A: $tType,Process: proces634752977rocess @ A] :
% 2.99/1.60 ( ( proces401113213Choice @ A @ Process )
% 2.99/1.60 => ( ( proces1915862579Choice @ A @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) )
% 2.99/1.60 = Process ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_177_process_Odistinct_I1_J,axiom,
% 2.99/1.60 ! [A: $tType,X112: A,X123: proces634752977rocess @ A,X212: proces634752977rocess @ A,X223: proces634752977rocess @ A] :
% 2.99/1.60 ( ( proces1525233512Action @ A @ X112 @ X123 )
% 2.99/1.60 != ( proces1915862579Choice @ A @ X212 @ X223 ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_178_process_Orel__intros_I2_J,axiom,
% 2.99/1.60 ! [A: $tType,B: $tType,R: A > B > $o,X212: proces634752977rocess @ A,Y21: proces634752977rocess @ B,X223: proces634752977rocess @ A,Y22: proces634752977rocess @ B] :
% 2.99/1.60 ( ( proces749077512rocess @ A @ B @ R @ X212 @ Y21 )
% 2.99/1.60 => ( ( proces749077512rocess @ A @ B @ R @ X223 @ Y22 )
% 2.99/1.60 => ( proces749077512rocess @ A @ B @ R @ ( proces1915862579Choice @ A @ X212 @ X223 ) @ ( proces1915862579Choice @ B @ Y21 @ Y22 ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_179_process_Oexhaust,axiom,
% 2.99/1.60 ! [A: $tType,Y: proces634752977rocess @ A] :
% 2.99/1.60 ( ! [X113: A,X124: proces634752977rocess @ A] :
% 2.99/1.60 ( Y
% 2.99/1.60 != ( proces1525233512Action @ A @ X113 @ X124 ) )
% 2.99/1.60 => ~ ! [X213: proces634752977rocess @ A,X224: proces634752977rocess @ A] :
% 2.99/1.60 ( Y
% 2.99/1.60 != ( proces1915862579Choice @ A @ X213 @ X224 ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_180_process_Odisc_I4_J,axiom,
% 2.99/1.60 ! [A: $tType,X212: proces634752977rocess @ A,X223: proces634752977rocess @ A] : ( proces401113213Choice @ A @ ( proces1915862579Choice @ A @ X212 @ X223 ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_181_process_OdiscI_I2_J,axiom,
% 2.99/1.60 ! [A: $tType,Process: proces634752977rocess @ A,X212: proces634752977rocess @ A,X223: proces634752977rocess @ A] :
% 2.99/1.60 ( ( Process
% 2.99/1.60 = ( proces1915862579Choice @ A @ X212 @ X223 ) )
% 2.99/1.60 => ( proces401113213Choice @ A @ Process ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_182_isChoice__def,axiom,
% 2.99/1.60 ! [A: $tType] :
% 2.99/1.60 ( ( proces401113213Choice @ A )
% 2.99/1.60 = ( ^ [Process2: proces634752977rocess @ A] :
% 2.99/1.60 ? [X21: proces634752977rocess @ A,X222: proces634752977rocess @ A] :
% 2.99/1.60 ( Process2
% 2.99/1.60 = ( proces1915862579Choice @ A @ X21 @ X222 ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_183_process_Osel_I4_J,axiom,
% 2.99/1.60 ! [A: $tType,X212: proces634752977rocess @ A,X223: proces634752977rocess @ A] :
% 2.99/1.60 ( ( proces988026546_ch2Of @ A @ ( proces1915862579Choice @ A @ X212 @ X223 ) )
% 2.99/1.60 = X223 ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_184_process_Osel_I3_J,axiom,
% 2.99/1.60 ! [A: $tType,X212: proces634752977rocess @ A,X223: proces634752977rocess @ A] :
% 2.99/1.60 ( ( proces979765041_ch1Of @ A @ ( proces1915862579Choice @ A @ X212 @ X223 ) )
% 2.99/1.60 = X212 ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_185_process_Osimps_I6_J,axiom,
% 2.99/1.60 ! [B: $tType,A: $tType,F1: A > ( proces634752977rocess @ A ) > B,F2: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B,X212: proces634752977rocess @ A,X223: proces634752977rocess @ A] :
% 2.99/1.60 ( ( proces1406508781rocess @ A @ B @ F1 @ F2 @ ( proces1915862579Choice @ A @ X212 @ X223 ) )
% 2.99/1.60 = ( F2 @ X212 @ X223 ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_186_process_Odisc_I2_J,axiom,
% 2.99/1.60 ! [A: $tType,X212: proces634752977rocess @ A,X223: proces634752977rocess @ A] :
% 2.99/1.60 ~ ( proces10484146Action @ A @ ( proces1915862579Choice @ A @ X212 @ X223 ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_187_process_Orel__cases,axiom,
% 2.99/1.60 ! [A: $tType,B: $tType,R: A > B > $o,A2: proces634752977rocess @ A,B2: proces634752977rocess @ B] :
% 2.99/1.60 ( ( proces749077512rocess @ A @ B @ R @ A2 @ B2 )
% 2.99/1.60 => ( ! [X12: A,X23: proces634752977rocess @ A] :
% 2.99/1.60 ( ( A2
% 2.99/1.60 = ( proces1525233512Action @ A @ X12 @ X23 ) )
% 2.99/1.60 => ! [Y13: B,Y23: proces634752977rocess @ B] :
% 2.99/1.60 ( ( B2
% 2.99/1.60 = ( proces1525233512Action @ B @ Y13 @ Y23 ) )
% 2.99/1.60 => ( ( R @ X12 @ Y13 )
% 2.99/1.60 => ~ ( proces749077512rocess @ A @ B @ R @ X23 @ Y23 ) ) ) )
% 2.99/1.60 => ~ ! [X1a: proces634752977rocess @ A,X2a: proces634752977rocess @ A] :
% 2.99/1.60 ( ( A2
% 2.99/1.60 = ( proces1915862579Choice @ A @ X1a @ X2a ) )
% 2.99/1.60 => ! [Y1a: proces634752977rocess @ B,Y2a: proces634752977rocess @ B] :
% 2.99/1.60 ( ( B2
% 2.99/1.60 = ( proces1915862579Choice @ B @ Y1a @ Y2a ) )
% 2.99/1.60 => ( ( proces749077512rocess @ A @ B @ R @ X1a @ Y1a )
% 2.99/1.60 => ~ ( proces749077512rocess @ A @ B @ R @ X2a @ Y2a ) ) ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_188_process_Orel__distinct_I1_J,axiom,
% 2.99/1.60 ! [A: $tType,B: $tType,R: A > B > $o,X112: A,X123: proces634752977rocess @ A,Y21: proces634752977rocess @ B,Y22: proces634752977rocess @ B] :
% 2.99/1.60 ~ ( proces749077512rocess @ A @ B @ R @ ( proces1525233512Action @ A @ X112 @ X123 ) @ ( proces1915862579Choice @ B @ Y21 @ Y22 ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_189_process_Orel__distinct_I2_J,axiom,
% 2.99/1.60 ! [A: $tType,B: $tType,R: A > B > $o,Y21: proces634752977rocess @ A,Y22: proces634752977rocess @ A,X112: B,X123: proces634752977rocess @ B] :
% 2.99/1.60 ~ ( proces749077512rocess @ A @ B @ R @ ( proces1915862579Choice @ A @ Y21 @ Y22 ) @ ( proces1525233512Action @ B @ X112 @ X123 ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_190_process__coind,axiom,
% 2.99/1.60 ! [A: $tType,Phi: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > $o,P: proces634752977rocess @ A,P5: proces634752977rocess @ A] :
% 2.99/1.60 ( ( Phi @ P @ P5 )
% 2.99/1.60 => ( ! [P2: proces634752977rocess @ A,P6: proces634752977rocess @ A] :
% 2.99/1.60 ( ( Phi @ P2 @ P6 )
% 2.99/1.60 => ( ( ( proces10484146Action @ A @ P2 )
% 2.99/1.60 = ( proces10484146Action @ A @ P6 ) )
% 2.99/1.60 & ( ( proces401113213Choice @ A @ P2 )
% 2.99/1.60 = ( proces401113213Choice @ A @ P6 ) ) ) )
% 2.99/1.60 => ( ! [A4: A,A7: A,P2: proces634752977rocess @ A,P6: proces634752977rocess @ A] :
% 2.99/1.60 ( ( Phi @ ( proces1525233512Action @ A @ A4 @ P2 ) @ ( proces1525233512Action @ A @ A7 @ P6 ) )
% 2.99/1.60 => ( ( A4 = A7 )
% 2.99/1.60 & ( Phi @ P2 @ P6 ) ) )
% 2.99/1.60 => ( ! [P2: proces634752977rocess @ A,Q2: proces634752977rocess @ A,P6: proces634752977rocess @ A,Q3: proces634752977rocess @ A] :
% 2.99/1.60 ( ( Phi @ ( proces1915862579Choice @ A @ P2 @ Q2 ) @ ( proces1915862579Choice @ A @ P6 @ Q3 ) )
% 2.99/1.60 => ( ( Phi @ P2 @ P6 )
% 2.99/1.60 & ( Phi @ Q2 @ Q3 ) ) )
% 2.99/1.60 => ( P = P5 ) ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_191_process__strong__coind,axiom,
% 2.99/1.60 ! [A: $tType,Phi: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > $o,P: proces634752977rocess @ A,P5: proces634752977rocess @ A] :
% 2.99/1.60 ( ( Phi @ P @ P5 )
% 2.99/1.60 => ( ! [P2: proces634752977rocess @ A,P6: proces634752977rocess @ A] :
% 2.99/1.60 ( ( Phi @ P2 @ P6 )
% 2.99/1.60 => ( ( ( proces10484146Action @ A @ P2 )
% 2.99/1.60 = ( proces10484146Action @ A @ P6 ) )
% 2.99/1.60 & ( ( proces401113213Choice @ A @ P2 )
% 2.99/1.60 = ( proces401113213Choice @ A @ P6 ) ) ) )
% 2.99/1.60 => ( ! [A4: A,A7: A,P2: proces634752977rocess @ A,P6: proces634752977rocess @ A] :
% 2.99/1.60 ( ( Phi @ ( proces1525233512Action @ A @ A4 @ P2 ) @ ( proces1525233512Action @ A @ A7 @ P6 ) )
% 2.99/1.60 => ( ( A4 = A7 )
% 2.99/1.60 & ( ( Phi @ P2 @ P6 )
% 2.99/1.60 | ( P2 = P6 ) ) ) )
% 2.99/1.60 => ( ! [P2: proces634752977rocess @ A,Q2: proces634752977rocess @ A,P6: proces634752977rocess @ A,Q3: proces634752977rocess @ A] :
% 2.99/1.60 ( ( Phi @ ( proces1915862579Choice @ A @ P2 @ Q2 ) @ ( proces1915862579Choice @ A @ P6 @ Q3 ) )
% 2.99/1.60 => ( ( ( Phi @ P2 @ P6 )
% 2.99/1.60 | ( P2 = P6 ) )
% 2.99/1.60 & ( ( Phi @ Q2 @ Q3 )
% 2.99/1.60 | ( Q2 = Q3 ) ) ) )
% 2.99/1.60 => ( P = P5 ) ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_192_solution_Octr_I2_J,axiom,
% 2.99/1.60 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 2.99/1.60 ( ~ ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
% 2.99/1.60 => ( ( proces1652378886lution @ A @ B @ Sys @ T2 )
% 2.99/1.60 = ( proces1915862579Choice @ B @ ( proces1652378886lution @ A @ B @ Sys @ ( proces1239275103le_CH1 @ A @ B @ Sys @ T2 ) ) @ ( proces1652378886lution @ A @ B @ Sys @ ( proces1239275104le_CH2 @ A @ B @ Sys @ T2 ) ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_193_process_Oexhaust__sel,axiom,
% 2.99/1.60 ! [A: $tType,Process: proces634752977rocess @ A] :
% 2.99/1.60 ( ( Process
% 2.99/1.60 != ( proces1525233512Action @ A @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) ) )
% 2.99/1.60 => ( Process
% 2.99/1.60 = ( proces1915862579Choice @ A @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_194_adm__lemma,axiom,
% 2.99/1.60 ! [B: $tType,A: $tType,R: set @ ( product_prod @ A @ A ),F8: ( A > B ) > A > B] :
% 2.99/1.60 ( adm_wf @ A @ B @ R
% 2.99/1.60 @ ^ [F7: A > B,X: A] : ( F8 @ ( cut @ A @ B @ F7 @ R @ X ) @ X ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_195_process__term_Orel__induct,axiom,
% 2.99/1.60 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X3: proces554692349s_term @ A @ Pvar,Y: proces554692349s_term @ B @ C,Q: ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ B @ C ) > $o] :
% 2.99/1.60 ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X3 @ Y )
% 2.99/1.60 => ( ! [A12: Pvar,B1: C] :
% 2.99/1.60 ( ( R22 @ A12 @ B1 )
% 2.99/1.60 => ( Q @ ( proces1627516585ss_VAR @ Pvar @ A @ A12 ) @ ( proces1627516585ss_VAR @ C @ B @ B1 ) ) )
% 2.99/1.60 => ( ! [A22: proces634752977rocess @ A,B22: proces634752977rocess @ B] :
% 2.99/1.60 ( ( proces749077512rocess @ A @ B @ R1 @ A22 @ B22 )
% 2.99/1.60 => ( Q @ ( proces1062592052s_PROC @ A @ Pvar @ A22 ) @ ( proces1062592052s_PROC @ B @ C @ B22 ) ) )
% 2.99/1.60 => ( ! [A31: A,A32: proces554692349s_term @ A @ Pvar,B31: B,B32: proces554692349s_term @ B @ C] :
% 2.99/1.60 ( ( R1 @ A31 @ B31 )
% 2.99/1.60 => ( ( Q @ A32 @ B32 )
% 2.99/1.60 => ( Q @ ( proces1454156180ss_ACT @ A @ Pvar @ A31 @ A32 ) @ ( proces1454156180ss_ACT @ B @ C @ B31 @ B32 ) ) ) )
% 2.99/1.60 => ( ! [A41: proces554692349s_term @ A @ Pvar,A42: proces554692349s_term @ A @ Pvar,B41: proces554692349s_term @ B @ C,B42: proces554692349s_term @ B @ C] :
% 2.99/1.60 ( ( Q @ A41 @ B41 )
% 2.99/1.60 => ( ( Q @ A42 @ B42 )
% 2.99/1.60 => ( Q @ ( proces89589571ess_CH @ A @ Pvar @ A41 @ A42 ) @ ( proces89589571ess_CH @ B @ C @ B41 @ B42 ) ) ) )
% 2.99/1.60 => ( Q @ X3 @ Y ) ) ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_196_process__term_Orel__cases,axiom,
% 2.99/1.60 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,A2: proces554692349s_term @ A @ Pvar,B2: proces554692349s_term @ B @ C] :
% 2.99/1.60 ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ A2 @ B2 )
% 2.99/1.60 => ( ! [X5: Pvar] :
% 2.99/1.60 ( ( A2
% 2.99/1.60 = ( proces1627516585ss_VAR @ Pvar @ A @ X5 ) )
% 2.99/1.60 => ! [Y5: C] :
% 2.99/1.60 ( ( B2
% 2.99/1.60 = ( proces1627516585ss_VAR @ C @ B @ Y5 ) )
% 2.99/1.60 => ~ ( R22 @ X5 @ Y5 ) ) )
% 2.99/1.60 => ( ! [Xa2: proces634752977rocess @ A] :
% 2.99/1.60 ( ( A2
% 2.99/1.60 = ( proces1062592052s_PROC @ A @ Pvar @ Xa2 ) )
% 2.99/1.60 => ! [Ya: proces634752977rocess @ B] :
% 2.99/1.60 ( ( B2
% 2.99/1.60 = ( proces1062592052s_PROC @ B @ C @ Ya ) )
% 2.99/1.60 => ~ ( proces749077512rocess @ A @ B @ R1 @ Xa2 @ Ya ) ) )
% 2.99/1.60 => ( ! [X1a: A,X2a: proces554692349s_term @ A @ Pvar] :
% 2.99/1.60 ( ( A2
% 2.99/1.60 = ( proces1454156180ss_ACT @ A @ Pvar @ X1a @ X2a ) )
% 2.99/1.60 => ! [Y1a: B,Y2a: proces554692349s_term @ B @ C] :
% 2.99/1.60 ( ( B2
% 2.99/1.60 = ( proces1454156180ss_ACT @ B @ C @ Y1a @ Y2a ) )
% 2.99/1.60 => ( ( R1 @ X1a @ Y1a )
% 2.99/1.60 => ~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X2a @ Y2a ) ) ) )
% 2.99/1.60 => ~ ! [X1b: proces554692349s_term @ A @ Pvar,X2b: proces554692349s_term @ A @ Pvar] :
% 2.99/1.60 ( ( A2
% 2.99/1.60 = ( proces89589571ess_CH @ A @ Pvar @ X1b @ X2b ) )
% 2.99/1.60 => ! [Y1b: proces554692349s_term @ B @ C,Y2b: proces554692349s_term @ B @ C] :
% 2.99/1.60 ( ( B2
% 2.99/1.60 = ( proces89589571ess_CH @ B @ C @ Y1b @ Y2b ) )
% 2.99/1.60 => ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X1b @ Y1b )
% 2.99/1.60 => ~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X2b @ Y2b ) ) ) ) ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_197_process__term_Orel__intros_I2_J,axiom,
% 2.99/1.60 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,X2: proces634752977rocess @ A,Y2: proces634752977rocess @ B,R22: Pvar > C > $o] :
% 2.99/1.60 ( ( proces749077512rocess @ A @ B @ R1 @ X2 @ Y2 )
% 2.99/1.60 => ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1062592052s_PROC @ A @ Pvar @ X2 ) @ ( proces1062592052s_PROC @ B @ C @ Y2 ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_198_process__term_Orel__inject_I2_J,axiom,
% 2.99/1.60 ! [C: $tType,Pvar: $tType,A: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X2: proces634752977rocess @ A,Y2: proces634752977rocess @ B] :
% 2.99/1.60 ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1062592052s_PROC @ A @ Pvar @ X2 ) @ ( proces1062592052s_PROC @ B @ C @ Y2 ) )
% 2.99/1.60 = ( proces749077512rocess @ A @ B @ R1 @ X2 @ Y2 ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_199_process__term_Orel__distinct_I2_J,axiom,
% 2.99/1.60 ! [A: $tType,B: $tType,C: $tType,D: $tType,R1: A > C > $o,R22: B > D > $o,Y2: proces634752977rocess @ A,X13: D] :
% 2.99/1.60 ~ ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R22 @ ( proces1062592052s_PROC @ A @ B @ Y2 ) @ ( proces1627516585ss_VAR @ D @ C @ X13 ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_200_process__term_Orel__distinct_I1_J,axiom,
% 2.99/1.60 ! [Pvar: $tType,A: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X13: Pvar,Y2: proces634752977rocess @ B] :
% 2.99/1.60 ~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1627516585ss_VAR @ Pvar @ A @ X13 ) @ ( proces1062592052s_PROC @ B @ C @ Y2 ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_201_process__term_Orel__distinct_I10_J,axiom,
% 2.99/1.60 ! [A: $tType,B: $tType,D: $tType,C: $tType,R1: A > C > $o,R22: B > D > $o,Y41: proces554692349s_term @ A @ B,Y42: proces554692349s_term @ A @ B,X2: proces634752977rocess @ C] :
% 2.99/1.60 ~ ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R22 @ ( proces89589571ess_CH @ A @ B @ Y41 @ Y42 ) @ ( proces1062592052s_PROC @ C @ D @ X2 ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_202_process__term_Orel__distinct_I9_J,axiom,
% 2.99/1.60 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X2: proces634752977rocess @ A,Y41: proces554692349s_term @ B @ C,Y42: proces554692349s_term @ B @ C] :
% 2.99/1.60 ~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1062592052s_PROC @ A @ Pvar @ X2 ) @ ( proces89589571ess_CH @ B @ C @ Y41 @ Y42 ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_203_process__term_Orel__distinct_I8_J,axiom,
% 2.99/1.60 ! [A: $tType,B: $tType,D: $tType,C: $tType,R1: A > C > $o,R22: B > D > $o,Y31: A,Y32: proces554692349s_term @ A @ B,X2: proces634752977rocess @ C] :
% 2.99/1.60 ~ ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R22 @ ( proces1454156180ss_ACT @ A @ B @ Y31 @ Y32 ) @ ( proces1062592052s_PROC @ C @ D @ X2 ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_204_process__term_Orel__distinct_I7_J,axiom,
% 2.99/1.60 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X2: proces634752977rocess @ A,Y31: B,Y32: proces554692349s_term @ B @ C] :
% 2.99/1.60 ~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1062592052s_PROC @ A @ Pvar @ X2 ) @ ( proces1454156180ss_ACT @ B @ C @ Y31 @ Y32 ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_205_process__term_Orel__intros_I1_J,axiom,
% 2.99/1.60 ! [Pvar: $tType,A: $tType,B: $tType,C: $tType,R22: Pvar > C > $o,X13: Pvar,Y1: C,R1: A > B > $o] :
% 2.99/1.60 ( ( R22 @ X13 @ Y1 )
% 2.99/1.60 => ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1627516585ss_VAR @ Pvar @ A @ X13 ) @ ( proces1627516585ss_VAR @ C @ B @ Y1 ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_206_process__term_Orel__inject_I1_J,axiom,
% 2.99/1.60 ! [B: $tType,A: $tType,Pvar: $tType,C: $tType,R1: A > B > $o,R22: Pvar > C > $o,X13: Pvar,Y1: C] :
% 2.99/1.60 ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1627516585ss_VAR @ Pvar @ A @ X13 ) @ ( proces1627516585ss_VAR @ C @ B @ Y1 ) )
% 2.99/1.60 = ( R22 @ X13 @ Y1 ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_207_process__term_Orel__intros_I4_J,axiom,
% 2.99/1.60 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X41: proces554692349s_term @ A @ Pvar,Y41: proces554692349s_term @ B @ C,X42: proces554692349s_term @ A @ Pvar,Y42: proces554692349s_term @ B @ C] :
% 2.99/1.60 ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X41 @ Y41 )
% 2.99/1.60 => ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X42 @ Y42 )
% 2.99/1.60 => ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 ) @ ( proces89589571ess_CH @ B @ C @ Y41 @ Y42 ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_208_process__term_Orel__inject_I4_J,axiom,
% 2.99/1.60 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X41: proces554692349s_term @ A @ Pvar,X42: proces554692349s_term @ A @ Pvar,Y41: proces554692349s_term @ B @ C,Y42: proces554692349s_term @ B @ C] :
% 2.99/1.60 ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 ) @ ( proces89589571ess_CH @ B @ C @ Y41 @ Y42 ) )
% 2.99/1.60 = ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X41 @ Y41 )
% 2.99/1.60 & ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X42 @ Y42 ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_209_process__term_Orel__intros_I3_J,axiom,
% 2.99/1.60 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,X31: A,Y31: B,R22: Pvar > C > $o,X32: proces554692349s_term @ A @ Pvar,Y32: proces554692349s_term @ B @ C] :
% 2.99/1.60 ( ( R1 @ X31 @ Y31 )
% 2.99/1.60 => ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X32 @ Y32 )
% 2.99/1.60 => ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) @ ( proces1454156180ss_ACT @ B @ C @ Y31 @ Y32 ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_210_process__term_Orel__inject_I3_J,axiom,
% 2.99/1.60 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X31: A,X32: proces554692349s_term @ A @ Pvar,Y31: B,Y32: proces554692349s_term @ B @ C] :
% 2.99/1.60 ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) @ ( proces1454156180ss_ACT @ B @ C @ Y31 @ Y32 ) )
% 2.99/1.60 = ( ( R1 @ X31 @ Y31 )
% 2.99/1.60 & ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X32 @ Y32 ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_211_process__term_Orel__eq,axiom,
% 2.99/1.60 ! [B: $tType,A: $tType] :
% 2.99/1.60 ( ( proces2029722208s_term @ A @ A @ B @ B
% 2.99/1.60 @ ^ [Y8: A,Z3: A] : ( Y8 = Z3 )
% 2.99/1.60 @ ^ [Y8: B,Z3: B] : ( Y8 = Z3 ) )
% 2.99/1.60 = ( ^ [Y8: proces554692349s_term @ A @ B,Z3: proces554692349s_term @ A @ B] : ( Y8 = Z3 ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_212_process__term_Orel__refl,axiom,
% 2.99/1.60 ! [D: $tType,C: $tType,R1a: C > C > $o,R2a: D > D > $o,X3: proces554692349s_term @ C @ D] :
% 2.99/1.60 ( ! [X5: C] : ( R1a @ X5 @ X5 )
% 2.99/1.60 => ( ! [X5: D] : ( R2a @ X5 @ X5 )
% 2.99/1.60 => ( proces2029722208s_term @ C @ C @ D @ D @ R1a @ R2a @ X3 @ X3 ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_213_process__term_Orel__distinct_I6_J,axiom,
% 2.99/1.60 ! [A: $tType,B: $tType,C: $tType,D: $tType,R1: A > C > $o,R22: B > D > $o,Y41: proces554692349s_term @ A @ B,Y42: proces554692349s_term @ A @ B,X13: D] :
% 2.99/1.60 ~ ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R22 @ ( proces89589571ess_CH @ A @ B @ Y41 @ Y42 ) @ ( proces1627516585ss_VAR @ D @ C @ X13 ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_214_process__term_Orel__distinct_I5_J,axiom,
% 2.99/1.60 ! [Pvar: $tType,A: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X13: Pvar,Y41: proces554692349s_term @ B @ C,Y42: proces554692349s_term @ B @ C] :
% 2.99/1.60 ~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1627516585ss_VAR @ Pvar @ A @ X13 ) @ ( proces89589571ess_CH @ B @ C @ Y41 @ Y42 ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_215_process__term_Orel__distinct_I4_J,axiom,
% 2.99/1.60 ! [A: $tType,B: $tType,C: $tType,D: $tType,R1: A > C > $o,R22: B > D > $o,Y31: A,Y32: proces554692349s_term @ A @ B,X13: D] :
% 2.99/1.60 ~ ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R22 @ ( proces1454156180ss_ACT @ A @ B @ Y31 @ Y32 ) @ ( proces1627516585ss_VAR @ D @ C @ X13 ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_216_process__term_Orel__distinct_I3_J,axiom,
% 2.99/1.60 ! [Pvar: $tType,A: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X13: Pvar,Y31: B,Y32: proces554692349s_term @ B @ C] :
% 2.99/1.60 ~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1627516585ss_VAR @ Pvar @ A @ X13 ) @ ( proces1454156180ss_ACT @ B @ C @ Y31 @ Y32 ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_217_process__term_Orel__distinct_I12_J,axiom,
% 2.99/1.60 ! [A: $tType,B: $tType,D: $tType,C: $tType,R1: A > C > $o,R22: B > D > $o,Y41: proces554692349s_term @ A @ B,Y42: proces554692349s_term @ A @ B,X31: C,X32: proces554692349s_term @ C @ D] :
% 2.99/1.60 ~ ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R22 @ ( proces89589571ess_CH @ A @ B @ Y41 @ Y42 ) @ ( proces1454156180ss_ACT @ C @ D @ X31 @ X32 ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_218_process__term_Orel__distinct_I11_J,axiom,
% 2.99/1.60 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X31: A,X32: proces554692349s_term @ A @ Pvar,Y41: proces554692349s_term @ B @ C,Y42: proces554692349s_term @ B @ C] :
% 2.99/1.60 ~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) @ ( proces89589571ess_CH @ B @ C @ Y41 @ Y42 ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_219_adm__wf__def,axiom,
% 2.99/1.60 ! [B: $tType,A: $tType] :
% 2.99/1.60 ( ( adm_wf @ A @ B )
% 2.99/1.60 = ( ^ [R4: set @ ( product_prod @ A @ A ),F9: ( A > B ) > A > B] :
% 2.99/1.60 ! [F7: A > B,G4: A > B,X: A] :
% 2.99/1.60 ( ! [Z4: A] :
% 2.99/1.60 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Z4 @ X ) @ R4 )
% 2.99/1.60 => ( ( F7 @ Z4 )
% 2.99/1.60 = ( G4 @ Z4 ) ) )
% 2.99/1.60 => ( ( F9 @ F7 @ X )
% 2.99/1.60 = ( F9 @ G4 @ X ) ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_220_process_Ocorec__code,axiom,
% 2.99/1.60 ! [A: $tType,C: $tType] :
% 2.99/1.60 ( ( proces894737309rocess @ C @ A )
% 2.99/1.60 = ( ^ [P4: C > $o,G11: C > A,Q12: C > $o,G121: C > ( proces634752977rocess @ A ),G122: C > C,Q21: C > $o,G211: C > ( proces634752977rocess @ A ),G212: C > C,Q22: C > $o,G221: C > ( proces634752977rocess @ A ),G222: C > C,A3: C] : ( if @ ( proces634752977rocess @ A ) @ ( P4 @ A3 ) @ ( proces1525233512Action @ A @ ( G11 @ A3 ) @ ( if @ ( proces634752977rocess @ A ) @ ( Q12 @ A3 ) @ ( G121 @ A3 ) @ ( proces894737309rocess @ C @ A @ P4 @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ ( G122 @ A3 ) ) ) ) @ ( proces1915862579Choice @ A @ ( if @ ( proces634752977rocess @ A ) @ ( Q21 @ A3 ) @ ( G211 @ A3 ) @ ( proces894737309rocess @ C @ A @ P4 @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ ( G212 @ A3 ) ) ) @ ( if @ ( proces634752977rocess @ A ) @ ( Q22 @ A3 ) @ ( G221 @ A3 ) @ ( proces894737309rocess @ C @ A @ P4 @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ ( G222 @ A3 ) ) ) ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_221_process__term_Octr__transfer_I2_J,axiom,
% 2.99/1.60 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o] : ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ ( proces749077512rocess @ A @ B @ R1 ) @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ ( proces1062592052s_PROC @ A @ Pvar ) @ ( proces1062592052s_PROC @ B @ C ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_222_process_Ocorec__disc__iff_I1_J,axiom,
% 2.99/1.60 ! [A: $tType,C: $tType,P: C > $o,G112: C > A,Q122: C > $o,G1212: C > ( proces634752977rocess @ A ),G1222: C > C,Q212: C > $o,G2112: C > ( proces634752977rocess @ A ),G2122: C > C,Q222: C > $o,G2212: C > ( proces634752977rocess @ A ),G2222: C > C,A2: C] :
% 2.99/1.60 ( ( proces10484146Action @ A @ ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ A2 ) )
% 2.99/1.60 = ( P @ A2 ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_223_process_Ocorec__disc__iff_I2_J,axiom,
% 2.99/1.60 ! [A: $tType,C: $tType,P: C > $o,G112: C > A,Q122: C > $o,G1212: C > ( proces634752977rocess @ A ),G1222: C > C,Q212: C > $o,G2112: C > ( proces634752977rocess @ A ),G2122: C > C,Q222: C > $o,G2212: C > ( proces634752977rocess @ A ),G2222: C > C,A2: C] :
% 2.99/1.60 ( ( proces401113213Choice @ A @ ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ A2 ) )
% 2.99/1.60 = ( ~ ( P @ A2 ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_224_process__term_Octr__transfer_I1_J,axiom,
% 2.99/1.60 ! [Pvar: $tType,A: $tType,B: $tType,C: $tType,R22: Pvar > C > $o,R1: A > B > $o] : ( bNF_rel_fun @ Pvar @ C @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ R22 @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ ( proces1627516585ss_VAR @ Pvar @ A ) @ ( proces1627516585ss_VAR @ C @ B ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_225_process__term_Orec__transfer,axiom,
% 2.99/1.60 ! [Pvar: $tType,D: $tType,A: $tType,B: $tType,E2: $tType,C: $tType,R22: Pvar > C > $o,S: D > E2 > $o,R1: A > B > $o] : ( bNF_rel_fun @ ( Pvar > D ) @ ( C > E2 ) @ ( ( ( proces634752977rocess @ A ) > D ) > ( A > ( proces554692349s_term @ A @ Pvar ) > D > D ) > ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D > D > D ) > ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( ( proces634752977rocess @ B ) > E2 ) > ( B > ( proces554692349s_term @ B @ C ) > E2 > E2 ) > ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) > E2 > E2 > E2 ) > ( proces554692349s_term @ B @ C ) > E2 ) @ ( bNF_rel_fun @ Pvar @ C @ D @ E2 @ R22 @ S ) @ ( bNF_rel_fun @ ( ( proces634752977rocess @ A ) > D ) @ ( ( proces634752977rocess @ B ) > E2 ) @ ( ( A > ( proces554692349s_term @ A @ Pvar ) > D > D ) > ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D > D > D ) > ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( B > ( proces554692349s_term @ B @ C ) > E2 > E2 ) > ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) > E2 > E2 > E2 ) > ( proces554692349s_term @ B @ C ) > E2 ) @ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ D @ E2 @ ( proces749077512rocess @ A @ B @ R1 ) @ S ) @ ( bNF_rel_fun @ ( A > ( proces554692349s_term @ A @ Pvar ) > D > D ) @ ( B > ( proces554692349s_term @ B @ C ) > E2 > E2 ) @ ( ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D > D > D ) > ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) > E2 > E2 > E2 ) > ( proces554692349s_term @ B @ C ) > E2 ) @ ( bNF_rel_fun @ A @ B @ ( ( proces554692349s_term @ A @ Pvar ) > D > D ) @ ( ( proces554692349s_term @ B @ C ) > E2 > E2 ) @ R1 @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ ( D > D ) @ ( E2 > E2 ) @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ ( bNF_rel_fun @ D @ E2 @ D @ E2 @ S @ S ) ) ) @ ( bNF_rel_fun @ ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D > D > D ) @ ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) > E2 > E2 > E2 ) @ ( ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( proces554692349s_term @ B @ C ) > E2 ) @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ ( ( proces554692349s_term @ A @ Pvar ) > D > D > D ) @ ( ( proces554692349s_term @ B @ C ) > E2 > E2 > E2 ) @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ ( D > D > D ) @ ( E2 > E2 > E2 ) @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ ( bNF_rel_fun @ D @ E2 @ ( D > D ) @ ( E2 > E2 ) @ S @ ( bNF_rel_fun @ D @ E2 @ D @ E2 @ S @ S ) ) ) ) @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ D @ E2 @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ S ) ) ) ) @ ( proces2117273769s_term @ Pvar @ D @ A ) @ ( proces2117273769s_term @ C @ E2 @ B ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_226_process__term_Ocase__transfer,axiom,
% 2.99/1.60 ! [Pvar: $tType,D: $tType,A: $tType,B: $tType,E2: $tType,C: $tType,R22: Pvar > C > $o,S: D > E2 > $o,R1: A > B > $o] : ( bNF_rel_fun @ ( Pvar > D ) @ ( C > E2 ) @ ( ( ( proces634752977rocess @ A ) > D ) > ( A > ( proces554692349s_term @ A @ Pvar ) > D ) > ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D ) > ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( ( proces634752977rocess @ B ) > E2 ) > ( B > ( proces554692349s_term @ B @ C ) > E2 ) > ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) > E2 ) > ( proces554692349s_term @ B @ C ) > E2 ) @ ( bNF_rel_fun @ Pvar @ C @ D @ E2 @ R22 @ S ) @ ( bNF_rel_fun @ ( ( proces634752977rocess @ A ) > D ) @ ( ( proces634752977rocess @ B ) > E2 ) @ ( ( A > ( proces554692349s_term @ A @ Pvar ) > D ) > ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D ) > ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( B > ( proces554692349s_term @ B @ C ) > E2 ) > ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) > E2 ) > ( proces554692349s_term @ B @ C ) > E2 ) @ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ D @ E2 @ ( proces749077512rocess @ A @ B @ R1 ) @ S ) @ ( bNF_rel_fun @ ( A > ( proces554692349s_term @ A @ Pvar ) > D ) @ ( B > ( proces554692349s_term @ B @ C ) > E2 ) @ ( ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D ) > ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) > E2 ) > ( proces554692349s_term @ B @ C ) > E2 ) @ ( bNF_rel_fun @ A @ B @ ( ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( proces554692349s_term @ B @ C ) > E2 ) @ R1 @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ D @ E2 @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ S ) ) @ ( bNF_rel_fun @ ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) > E2 ) @ ( ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( proces554692349s_term @ B @ C ) > E2 ) @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ ( ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( proces554692349s_term @ B @ C ) > E2 ) @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ D @ E2 @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ S ) ) @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ D @ E2 @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ S ) ) ) ) @ ( proces460752237s_term @ Pvar @ D @ A ) @ ( proces460752237s_term @ C @ E2 @ B ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_227_process_Ocorec_I1_J,axiom,
% 2.99/1.60 ! [A: $tType,C: $tType,P: C > $o,A2: C,G112: C > A,Q122: C > $o,G1212: C > ( proces634752977rocess @ A ),G1222: C > C,Q212: C > $o,G2112: C > ( proces634752977rocess @ A ),G2122: C > C,Q222: C > $o,G2212: C > ( proces634752977rocess @ A ),G2222: C > C] :
% 2.99/1.60 ( ( P @ A2 )
% 2.99/1.60 => ( ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ A2 )
% 2.99/1.60 = ( proces1525233512Action @ A @ ( G112 @ A2 ) @ ( if @ ( proces634752977rocess @ A ) @ ( Q122 @ A2 ) @ ( G1212 @ A2 ) @ ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ ( G1222 @ A2 ) ) ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_228_process_Ocorec__transfer,axiom,
% 2.99/1.60 ! [C: $tType,A: $tType,B: $tType,D: $tType,S: C > D > $o,R: A > B > $o] :
% 2.99/1.60 ( bNF_rel_fun @ ( C > $o ) @ ( D > $o ) @ ( ( C > A ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > C > ( proces634752977rocess @ A ) ) @ ( ( D > B ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > D > ( proces634752977rocess @ B ) )
% 2.99/1.60 @ ( bNF_rel_fun @ C @ D @ $o @ $o @ S
% 2.99/1.60 @ ^ [Y8: $o,Z3: $o] : ( Y8 = Z3 ) )
% 2.99/1.60 @ ( bNF_rel_fun @ ( C > A ) @ ( D > B ) @ ( ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > C > ( proces634752977rocess @ A ) ) @ ( ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > D > ( proces634752977rocess @ B ) ) @ ( bNF_rel_fun @ C @ D @ A @ B @ S @ R )
% 2.99/1.60 @ ( bNF_rel_fun @ ( C > $o ) @ ( D > $o ) @ ( ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > C > ( proces634752977rocess @ A ) ) @ ( ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > D > ( proces634752977rocess @ B ) )
% 2.99/1.60 @ ( bNF_rel_fun @ C @ D @ $o @ $o @ S
% 2.99/1.60 @ ^ [Y8: $o,Z3: $o] : ( Y8 = Z3 ) )
% 2.99/1.60 @ ( bNF_rel_fun @ ( C > ( proces634752977rocess @ A ) ) @ ( D > ( proces634752977rocess @ B ) ) @ ( ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > C > ( proces634752977rocess @ A ) ) @ ( ( D > D ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > D > ( proces634752977rocess @ B ) ) @ ( bNF_rel_fun @ C @ D @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ S @ ( proces749077512rocess @ A @ B @ R ) )
% 2.99/1.60 @ ( bNF_rel_fun @ ( C > C ) @ ( D > D ) @ ( ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > C > ( proces634752977rocess @ A ) ) @ ( ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > D > ( proces634752977rocess @ B ) ) @ ( bNF_rel_fun @ C @ D @ C @ D @ S @ S )
% 2.99/1.60 @ ( bNF_rel_fun @ ( C > $o ) @ ( D > $o ) @ ( ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > C > ( proces634752977rocess @ A ) ) @ ( ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > D > ( proces634752977rocess @ B ) )
% 2.99/1.60 @ ( bNF_rel_fun @ C @ D @ $o @ $o @ S
% 2.99/1.60 @ ^ [Y8: $o,Z3: $o] : ( Y8 = Z3 ) )
% 2.99/1.60 @ ( bNF_rel_fun @ ( C > ( proces634752977rocess @ A ) ) @ ( D > ( proces634752977rocess @ B ) ) @ ( ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > C > ( proces634752977rocess @ A ) ) @ ( ( D > D ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > D > ( proces634752977rocess @ B ) ) @ ( bNF_rel_fun @ C @ D @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ S @ ( proces749077512rocess @ A @ B @ R ) )
% 2.99/1.60 @ ( bNF_rel_fun @ ( C > C ) @ ( D > D ) @ ( ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > C > ( proces634752977rocess @ A ) ) @ ( ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > D > ( proces634752977rocess @ B ) ) @ ( bNF_rel_fun @ C @ D @ C @ D @ S @ S )
% 2.99/1.60 @ ( bNF_rel_fun @ ( C > $o ) @ ( D > $o ) @ ( ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > C > ( proces634752977rocess @ A ) ) @ ( ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > D > ( proces634752977rocess @ B ) )
% 2.99/1.60 @ ( bNF_rel_fun @ C @ D @ $o @ $o @ S
% 2.99/1.60 @ ^ [Y8: $o,Z3: $o] : ( Y8 = Z3 ) )
% 2.99/1.60 @ ( bNF_rel_fun @ ( C > ( proces634752977rocess @ A ) ) @ ( D > ( proces634752977rocess @ B ) ) @ ( ( C > C ) > C > ( proces634752977rocess @ A ) ) @ ( ( D > D ) > D > ( proces634752977rocess @ B ) ) @ ( bNF_rel_fun @ C @ D @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ S @ ( proces749077512rocess @ A @ B @ R ) ) @ ( bNF_rel_fun @ ( C > C ) @ ( D > D ) @ ( C > ( proces634752977rocess @ A ) ) @ ( D > ( proces634752977rocess @ B ) ) @ ( bNF_rel_fun @ C @ D @ C @ D @ S @ S ) @ ( bNF_rel_fun @ C @ D @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ S @ ( proces749077512rocess @ A @ B @ R ) ) ) ) ) ) ) ) ) ) ) )
% 2.99/1.60 @ ( proces894737309rocess @ C @ A )
% 2.99/1.60 @ ( proces894737309rocess @ D @ B ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_229_process_Ocorec__disc_I1_J,axiom,
% 2.99/1.60 ! [A: $tType,C: $tType,P: C > $o,A2: C,G112: C > A,Q122: C > $o,G1212: C > ( proces634752977rocess @ A ),G1222: C > C,Q212: C > $o,G2112: C > ( proces634752977rocess @ A ),G2122: C > C,Q222: C > $o,G2212: C > ( proces634752977rocess @ A ),G2222: C > C] :
% 2.99/1.60 ( ( P @ A2 )
% 2.99/1.60 => ( proces10484146Action @ A @ ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ A2 ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_230_process_Ocorec__disc_I2_J,axiom,
% 2.99/1.60 ! [A: $tType,C: $tType,P: C > $o,A2: C,G112: C > A,Q122: C > $o,G1212: C > ( proces634752977rocess @ A ),G1222: C > C,Q212: C > $o,G2112: C > ( proces634752977rocess @ A ),G2122: C > C,Q222: C > $o,G2212: C > ( proces634752977rocess @ A ),G2222: C > C] :
% 2.99/1.60 ( ~ ( P @ A2 )
% 2.99/1.60 => ( proces401113213Choice @ A @ ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ A2 ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_231_process_Ocorec__sel_I1_J,axiom,
% 2.99/1.60 ! [A: $tType,C: $tType,P: C > $o,A2: C,G112: C > A,Q122: C > $o,G1212: C > ( proces634752977rocess @ A ),G1222: C > C,Q212: C > $o,G2112: C > ( proces634752977rocess @ A ),G2122: C > C,Q222: C > $o,G2212: C > ( proces634752977rocess @ A ),G2222: C > C] :
% 2.99/1.60 ( ( P @ A2 )
% 2.99/1.60 => ( ( proces745025900prefOf @ A @ ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ A2 ) )
% 2.99/1.60 = ( G112 @ A2 ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_232_process_Ocorec__sel_I4_J,axiom,
% 2.99/1.60 ! [A: $tType,C: $tType,P: C > $o,A2: C,Q222: C > $o,G112: C > A,Q122: C > $o,G1212: C > ( proces634752977rocess @ A ),G1222: C > C,Q212: C > $o,G2112: C > ( proces634752977rocess @ A ),G2122: C > C,G2212: C > ( proces634752977rocess @ A ),G2222: C > C] :
% 2.99/1.60 ( ~ ( P @ A2 )
% 2.99/1.60 => ( ( ( Q222 @ A2 )
% 2.99/1.60 => ( ( proces988026546_ch2Of @ A @ ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ A2 ) )
% 2.99/1.60 = ( G2212 @ A2 ) ) )
% 2.99/1.60 & ( ~ ( Q222 @ A2 )
% 2.99/1.60 => ( ( proces988026546_ch2Of @ A @ ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ A2 ) )
% 2.99/1.60 = ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ ( G2222 @ A2 ) ) ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_233_process_Ocorec__sel_I3_J,axiom,
% 2.99/1.60 ! [A: $tType,C: $tType,P: C > $o,A2: C,Q212: C > $o,G112: C > A,Q122: C > $o,G1212: C > ( proces634752977rocess @ A ),G1222: C > C,G2112: C > ( proces634752977rocess @ A ),G2122: C > C,Q222: C > $o,G2212: C > ( proces634752977rocess @ A ),G2222: C > C] :
% 2.99/1.60 ( ~ ( P @ A2 )
% 2.99/1.60 => ( ( ( Q212 @ A2 )
% 2.99/1.60 => ( ( proces979765041_ch1Of @ A @ ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ A2 ) )
% 2.99/1.60 = ( G2112 @ A2 ) ) )
% 2.99/1.60 & ( ~ ( Q212 @ A2 )
% 2.99/1.60 => ( ( proces979765041_ch1Of @ A @ ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ A2 ) )
% 2.99/1.60 = ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ ( G2122 @ A2 ) ) ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_234_process_Ocorec__sel_I2_J,axiom,
% 2.99/1.60 ! [A: $tType,C: $tType,P: C > $o,A2: C,Q122: C > $o,G112: C > A,G1212: C > ( proces634752977rocess @ A ),G1222: C > C,Q212: C > $o,G2112: C > ( proces634752977rocess @ A ),G2122: C > C,Q222: C > $o,G2212: C > ( proces634752977rocess @ A ),G2222: C > C] :
% 2.99/1.60 ( ( P @ A2 )
% 2.99/1.60 => ( ( ( Q122 @ A2 )
% 2.99/1.60 => ( ( proces1778668539contOf @ A @ ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ A2 ) )
% 2.99/1.60 = ( G1212 @ A2 ) ) )
% 2.99/1.60 & ( ~ ( Q122 @ A2 )
% 2.99/1.60 => ( ( proces1778668539contOf @ A @ ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ A2 ) )
% 2.99/1.60 = ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ ( G1222 @ A2 ) ) ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_235_process_Ocorec_I2_J,axiom,
% 2.99/1.60 ! [A: $tType,C: $tType,P: C > $o,A2: C,G112: C > A,Q122: C > $o,G1212: C > ( proces634752977rocess @ A ),G1222: C > C,Q212: C > $o,G2112: C > ( proces634752977rocess @ A ),G2122: C > C,Q222: C > $o,G2212: C > ( proces634752977rocess @ A ),G2222: C > C] :
% 2.99/1.60 ( ~ ( P @ A2 )
% 2.99/1.60 => ( ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ A2 )
% 2.99/1.60 = ( proces1915862579Choice @ A @ ( if @ ( proces634752977rocess @ A ) @ ( Q212 @ A2 ) @ ( G2112 @ A2 ) @ ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ ( G2122 @ A2 ) ) ) @ ( if @ ( proces634752977rocess @ A ) @ ( Q222 @ A2 ) @ ( G2212 @ A2 ) @ ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ ( G2222 @ A2 ) ) ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_236_process__term_Orel__transfer,axiom,
% 2.99/1.60 ! [A: $tType,C: $tType,B: $tType,D: $tType,H2: $tType,F5: $tType,G2: $tType,E2: $tType,S1a: A > E2 > $o,S1c: C > G2 > $o,S2a: B > F5 > $o,S2c: D > H2 > $o] :
% 2.99/1.60 ( bNF_rel_fun @ ( A > C > $o ) @ ( E2 > G2 > $o ) @ ( ( B > D > $o ) > ( proces554692349s_term @ A @ B ) > ( proces554692349s_term @ C @ D ) > $o ) @ ( ( F5 > H2 > $o ) > ( proces554692349s_term @ E2 @ F5 ) > ( proces554692349s_term @ G2 @ H2 ) > $o )
% 2.99/1.60 @ ( bNF_rel_fun @ A @ E2 @ ( C > $o ) @ ( G2 > $o ) @ S1a
% 2.99/1.60 @ ( bNF_rel_fun @ C @ G2 @ $o @ $o @ S1c
% 2.99/1.60 @ ^ [Y8: $o,Z3: $o] : ( Y8 = Z3 ) ) )
% 2.99/1.60 @ ( bNF_rel_fun @ ( B > D > $o ) @ ( F5 > H2 > $o ) @ ( ( proces554692349s_term @ A @ B ) > ( proces554692349s_term @ C @ D ) > $o ) @ ( ( proces554692349s_term @ E2 @ F5 ) > ( proces554692349s_term @ G2 @ H2 ) > $o )
% 2.99/1.60 @ ( bNF_rel_fun @ B @ F5 @ ( D > $o ) @ ( H2 > $o ) @ S2a
% 2.99/1.60 @ ( bNF_rel_fun @ D @ H2 @ $o @ $o @ S2c
% 2.99/1.60 @ ^ [Y8: $o,Z3: $o] : ( Y8 = Z3 ) ) )
% 2.99/1.60 @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ B ) @ ( proces554692349s_term @ E2 @ F5 ) @ ( ( proces554692349s_term @ C @ D ) > $o ) @ ( ( proces554692349s_term @ G2 @ H2 ) > $o ) @ ( proces2029722208s_term @ A @ E2 @ B @ F5 @ S1a @ S2a )
% 2.99/1.60 @ ( bNF_rel_fun @ ( proces554692349s_term @ C @ D ) @ ( proces554692349s_term @ G2 @ H2 ) @ $o @ $o @ ( proces2029722208s_term @ C @ G2 @ D @ H2 @ S1c @ S2c )
% 2.99/1.60 @ ^ [Y8: $o,Z3: $o] : ( Y8 = Z3 ) ) ) )
% 2.99/1.60 @ ( proces2029722208s_term @ A @ C @ B @ D )
% 2.99/1.60 @ ( proces2029722208s_term @ E2 @ G2 @ F5 @ H2 ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_237_process__term_Octr__transfer_I3_J,axiom,
% 2.99/1.60 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o] : ( bNF_rel_fun @ A @ B @ ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) ) @ ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) ) @ R1 @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) ) @ ( proces1454156180ss_ACT @ A @ Pvar ) @ ( proces1454156180ss_ACT @ B @ C ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_238_process__term_Octr__transfer_I4_J,axiom,
% 2.99/1.60 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o] : ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) ) @ ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) ) @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) ) @ ( proces89589571ess_CH @ A @ Pvar ) @ ( proces89589571ess_CH @ B @ C ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_239_process_Odisc__transfer_I1_J,axiom,
% 2.99/1.60 ! [A: $tType,B: $tType,R: A > B > $o] :
% 2.99/1.60 ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ $o @ $o @ ( proces749077512rocess @ A @ B @ R )
% 2.99/1.60 @ ^ [Y8: $o,Z3: $o] : ( Y8 = Z3 )
% 2.99/1.60 @ ( proces10484146Action @ A )
% 2.99/1.60 @ ( proces10484146Action @ B ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_240_process_Odisc__transfer_I2_J,axiom,
% 2.99/1.60 ! [A: $tType,B: $tType,R: A > B > $o] :
% 2.99/1.60 ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ $o @ $o @ ( proces749077512rocess @ A @ B @ R )
% 2.99/1.60 @ ^ [Y8: $o,Z3: $o] : ( Y8 = Z3 )
% 2.99/1.60 @ ( proces401113213Choice @ A )
% 2.99/1.60 @ ( proces401113213Choice @ B ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_241_process_Octr__transfer_I1_J,axiom,
% 2.99/1.60 ! [A: $tType,B: $tType,R: A > B > $o] : ( bNF_rel_fun @ A @ B @ ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) @ ( ( proces634752977rocess @ B ) > ( proces634752977rocess @ B ) ) @ R @ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ ( proces749077512rocess @ A @ B @ R ) @ ( proces749077512rocess @ A @ B @ R ) ) @ ( proces1525233512Action @ A ) @ ( proces1525233512Action @ B ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_242_process_Orel__transfer,axiom,
% 2.99/1.60 ! [A: $tType,B: $tType,D: $tType,C: $tType,Sa: A > C > $o,Sc: B > D > $o] :
% 2.99/1.60 ( bNF_rel_fun @ ( A > B > $o ) @ ( C > D > $o ) @ ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ B ) > $o ) @ ( ( proces634752977rocess @ C ) > ( proces634752977rocess @ D ) > $o )
% 2.99/1.60 @ ( bNF_rel_fun @ A @ C @ ( B > $o ) @ ( D > $o ) @ Sa
% 2.99/1.60 @ ( bNF_rel_fun @ B @ D @ $o @ $o @ Sc
% 2.99/1.60 @ ^ [Y8: $o,Z3: $o] : ( Y8 = Z3 ) ) )
% 2.99/1.60 @ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ C ) @ ( ( proces634752977rocess @ B ) > $o ) @ ( ( proces634752977rocess @ D ) > $o ) @ ( proces749077512rocess @ A @ C @ Sa )
% 2.99/1.60 @ ( bNF_rel_fun @ ( proces634752977rocess @ B ) @ ( proces634752977rocess @ D ) @ $o @ $o @ ( proces749077512rocess @ B @ D @ Sc )
% 2.99/1.60 @ ^ [Y8: $o,Z3: $o] : ( Y8 = Z3 ) ) )
% 2.99/1.60 @ ( proces749077512rocess @ A @ B )
% 2.99/1.60 @ ( proces749077512rocess @ C @ D ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_243_process_Ocase__transfer,axiom,
% 2.99/1.60 ! [A: $tType,C: $tType,D: $tType,B: $tType,R: A > B > $o,S: C > D > $o] : ( bNF_rel_fun @ ( A > ( proces634752977rocess @ A ) > C ) @ ( B > ( proces634752977rocess @ B ) > D ) @ ( ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > C ) > ( proces634752977rocess @ A ) > C ) @ ( ( ( proces634752977rocess @ B ) > ( proces634752977rocess @ B ) > D ) > ( proces634752977rocess @ B ) > D ) @ ( bNF_rel_fun @ A @ B @ ( ( proces634752977rocess @ A ) > C ) @ ( ( proces634752977rocess @ B ) > D ) @ R @ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ C @ D @ ( proces749077512rocess @ A @ B @ R ) @ S ) ) @ ( bNF_rel_fun @ ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > C ) @ ( ( proces634752977rocess @ B ) > ( proces634752977rocess @ B ) > D ) @ ( ( proces634752977rocess @ A ) > C ) @ ( ( proces634752977rocess @ B ) > D ) @ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ ( ( proces634752977rocess @ A ) > C ) @ ( ( proces634752977rocess @ B ) > D ) @ ( proces749077512rocess @ A @ B @ R ) @ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ C @ D @ ( proces749077512rocess @ A @ B @ R ) @ S ) ) @ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ C @ D @ ( proces749077512rocess @ A @ B @ R ) @ S ) ) @ ( proces1406508781rocess @ A @ C ) @ ( proces1406508781rocess @ B @ D ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_244_process_Octr__transfer_I2_J,axiom,
% 2.99/1.60 ! [A: $tType,B: $tType,R: A > B > $o] : ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) @ ( ( proces634752977rocess @ B ) > ( proces634752977rocess @ B ) ) @ ( proces749077512rocess @ A @ B @ R ) @ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ ( proces749077512rocess @ A @ B @ R ) @ ( proces749077512rocess @ A @ B @ R ) ) @ ( proces1915862579Choice @ A ) @ ( proces1915862579Choice @ B ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_245_process__term_Opred__transfer,axiom,
% 2.99/1.60 ! [A: $tType,B: $tType,D: $tType,C: $tType,R1: A > C > $o,R22: B > D > $o] :
% 2.99/1.60 ( bNF_rel_fun @ ( A > $o ) @ ( C > $o ) @ ( ( B > $o ) > ( proces554692349s_term @ A @ B ) > $o ) @ ( ( D > $o ) > ( proces554692349s_term @ C @ D ) > $o )
% 2.99/1.60 @ ( bNF_rel_fun @ A @ C @ $o @ $o @ R1
% 2.99/1.60 @ ^ [Y8: $o,Z3: $o] : ( Y8 = Z3 ) )
% 2.99/1.60 @ ( bNF_rel_fun @ ( B > $o ) @ ( D > $o ) @ ( ( proces554692349s_term @ A @ B ) > $o ) @ ( ( proces554692349s_term @ C @ D ) > $o )
% 2.99/1.60 @ ( bNF_rel_fun @ B @ D @ $o @ $o @ R22
% 2.99/1.60 @ ^ [Y8: $o,Z3: $o] : ( Y8 = Z3 ) )
% 2.99/1.60 @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ B ) @ ( proces554692349s_term @ C @ D ) @ $o @ $o @ ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R22 )
% 2.99/1.60 @ ^ [Y8: $o,Z3: $o] : ( Y8 = Z3 ) ) )
% 2.99/1.60 @ ( proces2118920028s_term @ A @ B )
% 2.99/1.60 @ ( proces2118920028s_term @ C @ D ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_246_process_Opred__transfer,axiom,
% 2.99/1.60 ! [A: $tType,B: $tType,R: A > B > $o] :
% 2.99/1.60 ( bNF_rel_fun @ ( A > $o ) @ ( B > $o ) @ ( ( proces634752977rocess @ A ) > $o ) @ ( ( proces634752977rocess @ B ) > $o )
% 2.99/1.60 @ ( bNF_rel_fun @ A @ B @ $o @ $o @ R
% 2.99/1.60 @ ^ [Y8: $o,Z3: $o] : ( Y8 = Z3 ) )
% 2.99/1.60 @ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ $o @ $o @ ( proces749077512rocess @ A @ B @ R )
% 2.99/1.60 @ ^ [Y8: $o,Z3: $o] : ( Y8 = Z3 ) )
% 2.99/1.60 @ ( proces1205983068rocess @ A )
% 2.99/1.60 @ ( proces1205983068rocess @ B ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_247_process__term_Opred__inject_I1_J,axiom,
% 2.99/1.60 ! [A: $tType,Pvar: $tType,P1: A > $o,P22: Pvar > $o,A2: Pvar] :
% 2.99/1.60 ( ( proces2118920028s_term @ A @ Pvar @ P1 @ P22 @ ( proces1627516585ss_VAR @ Pvar @ A @ A2 ) )
% 2.99/1.60 = ( P22 @ A2 ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_248_process__term_Opred__inject_I4_J,axiom,
% 2.99/1.60 ! [Pvar: $tType,A: $tType,P1: A > $o,P22: Pvar > $o,A2: proces554692349s_term @ A @ Pvar,Aa2: proces554692349s_term @ A @ Pvar] :
% 2.99/1.60 ( ( proces2118920028s_term @ A @ Pvar @ P1 @ P22 @ ( proces89589571ess_CH @ A @ Pvar @ A2 @ Aa2 ) )
% 2.99/1.60 = ( ( proces2118920028s_term @ A @ Pvar @ P1 @ P22 @ A2 )
% 2.99/1.60 & ( proces2118920028s_term @ A @ Pvar @ P1 @ P22 @ Aa2 ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_249_process__term_Opred__inject_I3_J,axiom,
% 2.99/1.60 ! [Pvar: $tType,A: $tType,P1: A > $o,P22: Pvar > $o,A2: A,Aa2: proces554692349s_term @ A @ Pvar] :
% 2.99/1.60 ( ( proces2118920028s_term @ A @ Pvar @ P1 @ P22 @ ( proces1454156180ss_ACT @ A @ Pvar @ A2 @ Aa2 ) )
% 2.99/1.60 = ( ( P1 @ A2 )
% 2.99/1.60 & ( proces2118920028s_term @ A @ Pvar @ P1 @ P22 @ Aa2 ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_250_process_Opred__inject_I1_J,axiom,
% 2.99/1.60 ! [A: $tType,P3: A > $o,A2: A,Aa2: proces634752977rocess @ A] :
% 2.99/1.60 ( ( proces1205983068rocess @ A @ P3 @ ( proces1525233512Action @ A @ A2 @ Aa2 ) )
% 2.99/1.60 = ( ( P3 @ A2 )
% 2.99/1.60 & ( proces1205983068rocess @ A @ P3 @ Aa2 ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_251_process_Opred__inject_I2_J,axiom,
% 2.99/1.60 ! [A: $tType,P3: A > $o,A2: proces634752977rocess @ A,Aa2: proces634752977rocess @ A] :
% 2.99/1.60 ( ( proces1205983068rocess @ A @ P3 @ ( proces1915862579Choice @ A @ A2 @ Aa2 ) )
% 2.99/1.60 = ( ( proces1205983068rocess @ A @ P3 @ A2 )
% 2.99/1.60 & ( proces1205983068rocess @ A @ P3 @ Aa2 ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_252_process__term_Opred__inject_I2_J,axiom,
% 2.99/1.60 ! [Pvar: $tType,A: $tType,P1: A > $o,P22: Pvar > $o,A2: proces634752977rocess @ A] :
% 2.99/1.60 ( ( proces2118920028s_term @ A @ Pvar @ P1 @ P22 @ ( proces1062592052s_PROC @ A @ Pvar @ A2 ) )
% 2.99/1.60 = ( proces1205983068rocess @ A @ P1 @ A2 ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_253_process_Opred__True,axiom,
% 2.99/1.60 ! [A: $tType] :
% 2.99/1.60 ( ( proces1205983068rocess @ A
% 2.99/1.60 @ ^ [Uu2: A] : $true )
% 2.99/1.60 = ( ^ [Uu2: proces634752977rocess @ A] : $true ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(fact_254_process__term_Opred__True,axiom,
% 2.99/1.60 ! [B: $tType,A: $tType] :
% 2.99/1.60 ( ( proces2118920028s_term @ A @ B
% 2.99/1.60 @ ^ [Uu2: A] : $true
% 2.99/1.60 @ ^ [Uu2: B] : $true )
% 2.99/1.60 = ( ^ [Uu2: proces554692349s_term @ A @ B] : $true ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(help_If_3_1_T,axiom,
% 2.99/1.60 ! [P3: $o] :
% 2.99/1.60 ( ( P3 = $true )
% 2.99/1.60 | ( P3 = $false ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(help_If_2_1_T,axiom,
% 2.99/1.60 ! [A: $tType,X3: A,Y: A] :
% 2.99/1.60 ( ( if @ A @ $false @ X3 @ Y )
% 2.99/1.60 = Y ) ).
% 2.99/1.60
% 2.99/1.60 thf(help_If_1_1_T,axiom,
% 2.99/1.60 ! [A: $tType,X3: A,Y: A] :
% 2.99/1.60 ( ( if @ A @ $true @ X3 @ Y )
% 2.99/1.60 = X3 ) ).
% 2.99/1.60
% 2.99/1.60 thf(conj_0,conjecture,
% 2.99/1.60 ~ ( proces687458811_isACT @ b @ a @ b @ a @ sys @ ( proces1062592052s_PROC @ a @ b @ pa ) ) ).
% 2.99/1.60 ------------------------
% 3.17/1.62 % (10613)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_10445 for (2999ds/183Mi)
% 3.17/1.62 % (10614)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_10445 for (2999ds/4Mi)
% 3.17/1.62 % (10616)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_10445 for (2999ds/2Mi)
% 3.17/1.62 % (10618)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_10445 for (2999ds/275Mi)
% 3.17/1.62 % (10616)Instruction limit reached!
% 3.17/1.62 % (10616)------------------------------
% 3.17/1.62 % (10616)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.62 % (10616)Termination reason: Unknown
% 3.17/1.62 % (10616)Termination phase: shuffling
% 3.17/1.62
% 3.17/1.62 % (10616)Memory used [KB]: 1663
% 3.17/1.62 % (10616)Time elapsed: 0.002 s
% 3.17/1.62 % (10616)Instructions burned: 2 (million)
% 3.17/1.62 % (10616)------------------------------
% 3.17/1.62 % (10616)------------------------------
% 3.17/1.62 % (10619)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_10445 for (2999ds/18Mi)
% 3.17/1.62 % (10614)Instruction limit reached!
% 3.17/1.62 % (10614)------------------------------
% 3.17/1.62 % (10614)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.62 % (10614)Termination reason: Unknown
% 3.17/1.62 % (10614)Termination phase: shuffling
% 3.17/1.62
% 3.17/1.62 % (10614)Memory used [KB]: 1663
% 3.17/1.62 % (10614)Time elapsed: 0.003 s
% 3.17/1.62 % (10614)Instructions burned: 6 (million)
% 3.17/1.62 % (10614)------------------------------
% 3.17/1.62 % (10614)------------------------------
% 3.17/1.63 % (10619)Instruction limit reached!
% 3.17/1.63 % (10619)------------------------------
% 3.17/1.63 % (10619)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.63 % (10619)Termination reason: Unknown
% 3.17/1.63 % (10619)Termination phase: shuffling
% 3.17/1.63
% 3.17/1.63 % (10619)Memory used [KB]: 2046
% 3.17/1.63 % (10619)Time elapsed: 0.007 s
% 3.17/1.63 % (10619)Instructions burned: 19 (million)
% 3.17/1.63 % (10619)------------------------------
% 3.17/1.63 % (10619)------------------------------
% 3.17/1.63 % (10617)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_10445 for (2999ds/2Mi)
% 3.17/1.63 % (10615)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_10445 for (2999ds/27Mi)
% 3.17/1.63 % (10617)Instruction limit reached!
% 3.17/1.63 % (10617)------------------------------
% 3.17/1.63 % (10617)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.63 % (10617)Termination reason: Unknown
% 3.17/1.63 % (10617)Termination phase: shuffling
% 3.17/1.63
% 3.17/1.63 % (10617)Memory used [KB]: 1663
% 3.17/1.63 % (10617)Time elapsed: 0.003 s
% 3.17/1.63 % (10617)Instructions burned: 2 (million)
% 3.17/1.63 % (10617)------------------------------
% 3.17/1.63 % (10617)------------------------------
% 3.17/1.63 % (10620)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_10445 for (2999ds/3Mi)
% 3.17/1.63 % (10621)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_10445 for (2999ds/37Mi)
% 3.17/1.63 % (10620)Instruction limit reached!
% 3.17/1.63 % (10620)------------------------------
% 3.17/1.63 % (10620)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.63 % (10620)Termination reason: Unknown
% 3.17/1.63 % (10620)Termination phase: shuffling
% 3.17/1.63
% 3.17/1.63 % (10620)Memory used [KB]: 1663
% 3.17/1.63 % (10620)Time elapsed: 0.002 s
% 3.17/1.63 % (10620)Instructions burned: 3 (million)
% 3.17/1.63 % (10620)------------------------------
% 3.17/1.63 % (10620)------------------------------
% 3.17/1.64 % (10622)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_10445 for (2999ds/15Mi)
% 3.17/1.64 % (10624)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_10445 for (2999ds/1041Mi)
% 3.17/1.64 % (10622)Instruction limit reached!
% 3.17/1.64 % (10622)------------------------------
% 3.17/1.64 % (10622)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.64 % (10622)Termination reason: Unknown
% 3.17/1.64 % (10622)Termination phase: shuffling
% 3.17/1.64
% 3.17/1.64 % (10622)Memory used [KB]: 1791
% 3.17/1.64 % (10622)Time elapsed: 0.006 s
% 3.17/1.64 % (10622)Instructions burned: 16 (million)
% 3.17/1.64 % (10622)------------------------------
% 3.17/1.64 % (10622)------------------------------
% 3.17/1.65 % (10621)Instruction limit reached!
% 3.17/1.65 % (10621)------------------------------
% 3.17/1.65 % (10621)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.65 % (10621)Termination reason: Unknown
% 3.17/1.65 % (10621)Termination phase: shuffling
% 3.17/1.65
% 3.17/1.65 % (10621)Memory used [KB]: 2302
% 3.17/1.65 % (10621)Time elapsed: 0.012 s
% 3.17/1.65 % (10621)Instructions burned: 39 (million)
% 3.17/1.65 % (10621)------------------------------
% 3.17/1.65 % (10621)------------------------------
% 3.17/1.65 % (10615)Instruction limit reached!
% 3.17/1.65 % (10615)------------------------------
% 3.17/1.65 % (10615)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.65 % (10615)Termination reason: Unknown
% 3.17/1.65 % (10615)Termination phase: shuffling
% 3.17/1.65
% 3.17/1.65 % (10615)Memory used [KB]: 2046
% 3.17/1.65 % (10615)Time elapsed: 0.018 s
% 3.17/1.65 % (10615)Instructions burned: 27 (million)
% 3.17/1.65 % (10615)------------------------------
% 3.17/1.65 % (10615)------------------------------
% 3.17/1.65 % (10623)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_10445 for (2999ds/3Mi)
% 3.17/1.65 % (10623)Instruction limit reached!
% 3.17/1.65 % (10623)------------------------------
% 3.17/1.65 % (10623)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.65 % (10623)Termination reason: Unknown
% 3.17/1.65 % (10623)Termination phase: shuffling
% 3.17/1.65
% 3.17/1.65 % (10623)Memory used [KB]: 1663
% 3.17/1.65 % (10623)Time elapsed: 0.004 s
% 3.17/1.65 % (10623)Instructions burned: 4 (million)
% 3.17/1.65 % (10623)------------------------------
% 3.17/1.65 % (10623)------------------------------
% 3.17/1.65 % (10625)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_10445 for (2999ds/7Mi)
% 3.17/1.65 % (10626)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_10445 for (2999ds/16Mi)
% 3.17/1.66 % (10625)Instruction limit reached!
% 3.17/1.66 % (10625)------------------------------
% 3.17/1.66 % (10625)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.66 % (10625)Termination reason: Unknown
% 3.17/1.66 % (10625)Termination phase: shuffling
% 3.17/1.66
% 3.17/1.66 % (10625)Memory used [KB]: 1663
% 3.17/1.66 % (10625)Time elapsed: 0.003 s
% 3.17/1.66 % (10625)Instructions burned: 7 (million)
% 3.17/1.66 % (10625)------------------------------
% 3.17/1.66 % (10625)------------------------------
% 3.17/1.66 % (10626)Instruction limit reached!
% 3.17/1.66 % (10626)------------------------------
% 3.17/1.66 % (10626)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.66 % (10626)Termination reason: Unknown
% 3.17/1.66 % (10626)Termination phase: shuffling
% 3.17/1.66
% 3.17/1.66 % (10626)Memory used [KB]: 1918
% 3.17/1.66 % (10626)Time elapsed: 0.006 s
% 3.17/1.66 % (10626)Instructions burned: 16 (million)
% 3.17/1.66 % (10626)------------------------------
% 3.17/1.66 % (10626)------------------------------
% 3.17/1.66 % (10627)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_10445 for (2999ds/3Mi)
% 3.17/1.67 % (10618)Refutation not found, incomplete strategy
% 3.17/1.67 % (10618)------------------------------
% 3.17/1.67 % (10618)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.67 % (10618)Termination reason: Refutation not found, incomplete strategy
% 3.17/1.67
% 3.17/1.67
% 3.17/1.67 % (10618)Memory used [KB]: 7803
% 3.17/1.67 % (10618)Time elapsed: 0.042 s
% 3.17/1.67 % (10618)Instructions burned: 135 (million)
% 3.17/1.67 % (10618)------------------------------
% 3.17/1.67 % (10618)------------------------------
% 3.17/1.67 % (10629)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_10445 for (2999ds/7Mi)
% 3.17/1.67 % (10628)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_10445 for (2999ds/3Mi)
% 3.17/1.67 % (10627)Instruction limit reached!
% 3.17/1.67 % (10627)------------------------------
% 3.17/1.67 % (10627)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.67 % (10627)Termination reason: Unknown
% 3.17/1.67 % (10627)Termination phase: shuffling
% 3.17/1.67
% 3.17/1.67 % (10627)Memory used [KB]: 1663
% 3.17/1.67 % (10627)Time elapsed: 0.004 s
% 3.17/1.67 % (10627)Instructions burned: 4 (million)
% 3.17/1.67 % (10627)------------------------------
% 3.17/1.67 % (10627)------------------------------
% 3.17/1.67 % (10628)Instruction limit reached!
% 3.17/1.67 % (10628)------------------------------
% 3.17/1.67 % (10628)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.67 % (10628)Termination reason: Unknown
% 3.17/1.67 % (10628)Termination phase: shuffling
% 3.17/1.67
% 3.17/1.67 % (10628)Memory used [KB]: 1663
% 3.17/1.67 % (10628)Time elapsed: 0.002 s
% 3.17/1.67 % (10628)Instructions burned: 3 (million)
% 3.17/1.67 % (10628)------------------------------
% 3.17/1.67 % (10628)------------------------------
% 3.17/1.67 % (10629)Instruction limit reached!
% 3.17/1.67 % (10629)------------------------------
% 3.17/1.67 % (10629)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.67 % (10629)Termination reason: Unknown
% 3.17/1.67 % (10629)Termination phase: shuffling
% 3.17/1.67
% 3.17/1.67 % (10629)Memory used [KB]: 1791
% 3.17/1.67 % (10629)Time elapsed: 0.004 s
% 3.17/1.67 % (10629)Instructions burned: 9 (million)
% 3.17/1.67 % (10629)------------------------------
% 3.17/1.67 % (10629)------------------------------
% 3.17/1.67 % (10632)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_10445 for (2999ds/3Mi)
% 3.17/1.67 % (10632)Instruction limit reached!
% 3.17/1.67 % (10632)------------------------------
% 3.17/1.67 % (10632)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.67 % (10632)Termination reason: Unknown
% 3.17/1.67 % (10632)Termination phase: shuffling
% 3.17/1.67
% 3.17/1.67 % (10632)Memory used [KB]: 1663
% 3.17/1.67 % (10632)Time elapsed: 0.002 s
% 3.17/1.67 % (10632)Instructions burned: 3 (million)
% 3.17/1.67 % (10632)------------------------------
% 3.17/1.67 % (10632)------------------------------
% 3.17/1.68 % (10637)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_10445 for (2999ds/710Mi)
% 3.17/1.68 % (10634)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_10445 for (2999ds/4Mi)
% 3.17/1.68 % (10613)Instruction limit reached!
% 3.17/1.68 % (10613)------------------------------
% 3.17/1.68 % (10613)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.68 % (10613)Termination reason: Unknown
% 3.17/1.68 % (10613)Termination phase: Property scanning
% 3.17/1.68
% 3.17/1.68 % (10613)Memory used [KB]: 3709
% 3.17/1.68 % (10613)Time elapsed: 0.056 s
% 3.17/1.68 % (10613)Instructions burned: 185 (million)
% 3.17/1.68 % (10613)------------------------------
% 3.17/1.68 % (10613)------------------------------
% 3.17/1.68 % (10638)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_10445 for (2999ds/6Mi)
% 3.17/1.68 % (10636)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_10445 for (2999ds/18Mi)
% 3.17/1.68 % (10634)Instruction limit reached!
% 3.17/1.68 % (10634)------------------------------
% 3.17/1.68 % (10634)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.68 % (10634)Termination reason: Unknown
% 3.17/1.68 % (10634)Termination phase: shuffling
% 3.17/1.68
% 3.17/1.68 % (10634)Memory used [KB]: 1663
% 3.17/1.68 % (10634)Time elapsed: 0.003 s
% 3.17/1.68 % (10634)Instructions burned: 6 (million)
% 3.17/1.68 % (10634)------------------------------
% 3.17/1.68 % (10634)------------------------------
% 3.17/1.68 % (10640)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_10445 for (2999ds/902Mi)
% 3.17/1.68 % (10638)Instruction limit reached!
% 3.17/1.68 % (10638)------------------------------
% 3.17/1.68 % (10638)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.68 % (10638)Termination reason: Unknown
% 3.17/1.68 % (10638)Termination phase: shuffling
% 3.17/1.68
% 3.17/1.68 % (10638)Memory used [KB]: 1663
% 3.17/1.68 % (10638)Time elapsed: 0.003 s
% 3.17/1.68 % (10638)Instructions burned: 6 (million)
% 3.17/1.68 % (10638)------------------------------
% 3.17/1.68 % (10638)------------------------------
% 3.17/1.69 % (10636)Instruction limit reached!
% 3.17/1.69 % (10636)------------------------------
% 3.17/1.69 % (10636)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.69 % (10636)Termination reason: Unknown
% 3.17/1.69 % (10636)Termination phase: shuffling
% 3.17/1.69
% 3.17/1.69 % (10636)Memory used [KB]: 1918
% 3.17/1.69 % (10636)Time elapsed: 0.008 s
% 3.17/1.69 % (10636)Instructions burned: 19 (million)
% 3.17/1.69 % (10636)------------------------------
% 3.17/1.69 % (10636)------------------------------
% 3.17/1.69 % (10644)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_10445 for (2999ds/21Mi)
% 3.17/1.69 % (10646)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_10445 for (2999ds/5Mi)
% 3.17/1.69 % (10647)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_10445 for (2999ds/6Mi)
% 3.17/1.69 % (10646)Instruction limit reached!
% 3.17/1.69 % (10646)------------------------------
% 3.17/1.69 % (10646)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.69 % (10646)Termination reason: Unknown
% 3.17/1.69 % (10646)Termination phase: shuffling
% 3.17/1.69
% 3.17/1.69 % (10646)Memory used [KB]: 1791
% 3.17/1.69 % (10646)Time elapsed: 0.003 s
% 3.17/1.69 % (10646)Instructions burned: 6 (million)
% 3.17/1.69 % (10646)------------------------------
% 3.17/1.69 % (10646)------------------------------
% 3.17/1.69 % (10647)Instruction limit reached!
% 3.17/1.69 % (10647)------------------------------
% 3.17/1.69 % (10647)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.69 % (10647)Termination reason: Unknown
% 3.17/1.69 % (10647)Termination phase: shuffling
% 3.17/1.69
% 3.17/1.69 % (10647)Memory used [KB]: 1791
% 3.17/1.69 % (10647)Time elapsed: 0.003 s
% 3.17/1.69 % (10647)Instructions burned: 6 (million)
% 3.17/1.69 % (10647)------------------------------
% 3.17/1.69 % (10647)------------------------------
% 3.17/1.69 % (10644)Instruction limit reached!
% 3.17/1.69 % (10644)------------------------------
% 3.17/1.69 % (10644)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.69 % (10644)Termination reason: Unknown
% 3.17/1.69 % (10644)Termination phase: shuffling
% 3.17/1.69
% 3.17/1.69 % (10644)Memory used [KB]: 2046
% 3.17/1.69 % (10644)Time elapsed: 0.008 s
% 3.17/1.69 % (10644)Instructions burned: 22 (million)
% 3.17/1.69 % (10644)------------------------------
% 3.17/1.69 % (10644)------------------------------
% 3.17/1.69 % (10650)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_10445 for (2999ds/377Mi)
% 3.17/1.70 % (10653)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_10445 for (2999ds/779Mi)
% 3.17/1.70 % (10654)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_10445 for (2999ds/19Mi)
% 3.17/1.70 % (10657)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_10445 for (2999ds/879Mi)
% 3.17/1.71 % (10654)Instruction limit reached!
% 3.17/1.71 % (10654)------------------------------
% 3.17/1.71 % (10654)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.71 % (10654)Termination reason: Unknown
% 3.17/1.71 % (10654)Termination phase: shuffling
% 3.17/1.71
% 3.17/1.71 % (10654)Memory used [KB]: 2046
% 3.17/1.71 % (10654)Time elapsed: 0.007 s
% 3.17/1.71 % (10654)Instructions burned: 20 (million)
% 3.17/1.71 % (10654)------------------------------
% 3.17/1.71 % (10654)------------------------------
% 3.17/1.72 % (10663)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_10445 for (2998ds/17Mi)
% 3.17/1.72 % (10663)Instruction limit reached!
% 3.17/1.72 % (10663)------------------------------
% 3.17/1.72 % (10663)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.72 % (10663)Termination reason: Unknown
% 3.17/1.72 % (10663)Termination phase: shuffling
% 3.17/1.72
% 3.17/1.72 % (10663)Memory used [KB]: 1918
% 3.17/1.72 % (10663)Time elapsed: 0.007 s
% 3.17/1.72 % (10663)Instructions burned: 17 (million)
% 3.17/1.72 % (10663)------------------------------
% 3.17/1.72 % (10663)------------------------------
% 3.17/1.73 % (10669)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_10445 for (2998ds/3Mi)
% 3.17/1.73 % (10669)Instruction limit reached!
% 3.17/1.73 % (10669)------------------------------
% 3.17/1.73 % (10669)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.73 % (10669)Termination reason: Unknown
% 3.17/1.73 % (10669)Termination phase: shuffling
% 3.17/1.73
% 3.17/1.73 % (10669)Memory used [KB]: 1663
% 3.17/1.73 % (10669)Time elapsed: 0.002 s
% 3.17/1.73 % (10669)Instructions burned: 3 (million)
% 3.17/1.73 % (10669)------------------------------
% 3.17/1.73 % (10669)------------------------------
% 3.17/1.74 % (10674)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_10445 for (2998ds/30Mi)
% 3.17/1.75 % (10674)Instruction limit reached!
% 3.17/1.75 % (10674)------------------------------
% 3.17/1.75 % (10674)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.75 % (10674)Termination reason: Unknown
% 3.17/1.75 % (10674)Termination phase: shuffling
% 3.17/1.75
% 3.17/1.75 % (10674)Memory used [KB]: 2174
% 3.17/1.75 % (10674)Time elapsed: 0.011 s
% 3.17/1.75 % (10674)Instructions burned: 31 (million)
% 3.17/1.75 % (10674)------------------------------
% 3.17/1.75 % (10674)------------------------------
% 3.17/1.76 % (10685)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_10445 for (2998ds/127Mi)
% 3.17/1.80 % (10685)Instruction limit reached!
% 3.17/1.80 % (10685)------------------------------
% 3.17/1.80 % (10685)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.80 % (10685)Termination reason: Unknown
% 3.17/1.80 % (10685)Termination phase: Preprocessing 3
% 3.17/1.80
% 3.17/1.80 % (10685)Memory used [KB]: 3326
% 3.17/1.80 % (10685)Time elapsed: 0.042 s
% 3.17/1.80 % (10685)Instructions burned: 128 (million)
% 3.17/1.80 % (10685)------------------------------
% 3.17/1.80 % (10685)------------------------------
% 3.17/1.81 % (10650)Instruction limit reached!
% 3.17/1.81 % (10650)------------------------------
% 3.17/1.81 % (10650)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.81 % (10650)Termination reason: Unknown
% 3.17/1.81 % (10650)Termination phase: Saturation
% 3.17/1.81
% 3.17/1.81 % (10650)Memory used [KB]: 9210
% 3.17/1.81 % (10650)Time elapsed: 0.113 s
% 3.17/1.81 % (10650)Instructions burned: 378 (million)
% 3.17/1.81 % (10650)------------------------------
% 3.17/1.81 % (10650)------------------------------
% 3.17/1.81 % (10703)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_10445 for (2997ds/100Mi)
% 3.17/1.82 % (10705)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_10445 for (2997ds/3Mi)
% 3.17/1.82 % (10705)Instruction limit reached!
% 3.17/1.82 % (10705)------------------------------
% 3.17/1.82 % (10705)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.82 % (10705)Termination reason: Unknown
% 3.17/1.82 % (10705)Termination phase: shuffling
% 3.17/1.82
% 3.17/1.82 % (10705)Memory used [KB]: 1663
% 3.17/1.82 % (10705)Time elapsed: 0.002 s
% 3.17/1.82 % (10705)Instructions burned: 3 (million)
% 3.17/1.82 % (10705)------------------------------
% 3.17/1.82 % (10705)------------------------------
% 3.17/1.83 % (10708)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_10445 for (2997ds/20Mi)
% 3.17/1.83 % (10708)Instruction limit reached!
% 3.17/1.83 % (10708)------------------------------
% 3.17/1.83 % (10708)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.83 % (10708)Termination reason: Unknown
% 3.17/1.83 % (10708)Termination phase: shuffling
% 3.17/1.83
% 3.17/1.83 % (10708)Memory used [KB]: 2046
% 3.17/1.83 % (10708)Time elapsed: 0.008 s
% 3.17/1.83 % (10708)Instructions burned: 22 (million)
% 3.17/1.83 % (10708)------------------------------
% 3.17/1.83 % (10708)------------------------------
% 3.17/1.84 % (10703)Instruction limit reached!
% 3.17/1.84 % (10703)------------------------------
% 3.17/1.84 % (10703)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.84 % (10703)Termination reason: Unknown
% 3.17/1.84 % (10703)Termination phase: Property scanning
% 3.17/1.84
% 3.17/1.84 % (10703)Memory used [KB]: 2942
% 3.17/1.84 % (10703)Time elapsed: 0.029 s
% 3.17/1.84 % (10703)Instructions burned: 101 (million)
% 3.17/1.84 % (10703)------------------------------
% 3.17/1.84 % (10703)------------------------------
% 3.17/1.84 % (10716)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_10445 for (2997ds/86Mi)
% 3.17/1.85 % (10717)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_10445 for (2997ds/107Mi)
% 3.17/1.87 % (10716)Instruction limit reached!
% 3.17/1.87 % (10716)------------------------------
% 3.17/1.87 % (10716)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.87 % (10716)Termination reason: Unknown
% 3.17/1.87 % (10716)Termination phase: Property scanning
% 3.17/1.87
% 3.17/1.87 % (10716)Memory used [KB]: 2942
% 3.17/1.87 % (10716)Time elapsed: 0.029 s
% 3.17/1.87 % (10716)Instructions burned: 86 (million)
% 3.17/1.87 % (10716)------------------------------
% 3.17/1.87 % (10716)------------------------------
% 3.17/1.88 % (10738)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_10445 for (2997ds/39Mi)
% 3.17/1.88 % (10717)Instruction limit reached!
% 3.17/1.88 % (10717)------------------------------
% 3.17/1.88 % (10717)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.88 % (10717)Termination reason: Unknown
% 3.17/1.88 % (10717)Termination phase: SInE selection
% 3.17/1.88
% 3.17/1.88 % (10717)Memory used [KB]: 2942
% 3.17/1.88 % (10717)Time elapsed: 0.035 s
% 3.17/1.88 % (10717)Instructions burned: 109 (million)
% 3.17/1.88 % (10717)------------------------------
% 3.17/1.88 % (10717)------------------------------
% 3.17/1.89 % (10738)Instruction limit reached!
% 3.17/1.89 % (10738)------------------------------
% 3.17/1.89 % (10738)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.89 % (10738)Termination reason: Unknown
% 3.17/1.89 % (10738)Termination phase: shuffling
% 3.17/1.89
% 3.17/1.89 % (10738)Memory used [KB]: 2302
% 3.17/1.89 % (10738)Time elapsed: 0.012 s
% 3.17/1.89 % (10738)Instructions burned: 39 (million)
% 3.17/1.89 % (10738)------------------------------
% 3.17/1.89 % (10738)------------------------------
% 3.17/1.89 % (10739)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_10445 for (2997ds/448Mi)
% 3.17/1.90 % (10637)Instruction limit reached!
% 3.17/1.90 % (10637)------------------------------
% 3.17/1.90 % (10637)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.90 % (10637)Termination reason: Unknown
% 3.17/1.90 % (10637)Termination phase: Saturation
% 3.17/1.90
% 3.17/1.90 % (10637)Memory used [KB]: 9722
% 3.17/1.90 % (10637)Time elapsed: 0.222 s
% 3.17/1.90 % (10637)Instructions burned: 713 (million)
% 3.17/1.90 % (10637)------------------------------
% 3.17/1.90 % (10637)------------------------------
% 3.17/1.90 % (10745)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_10445 for (2997ds/46Mi)
% 3.17/1.91 % (10751)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_10445 for (2997ds/98Mi)
% 3.17/1.92 % (10745)Instruction limit reached!
% 3.17/1.92 % (10745)------------------------------
% 3.17/1.92 % (10745)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.92 % (10745)Termination reason: Unknown
% 3.17/1.92 % (10745)Termination phase: shuffling
% 3.17/1.92
% 3.17/1.92 % (10745)Memory used [KB]: 2430
% 3.17/1.92 % (10745)Time elapsed: 0.016 s
% 3.17/1.92 % (10745)Instructions burned: 47 (million)
% 3.17/1.92 % (10745)------------------------------
% 3.17/1.92 % (10745)------------------------------
% 3.17/1.92 % (10653)Instruction limit reached!
% 3.17/1.92 % (10653)------------------------------
% 3.17/1.92 % (10653)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.92 % (10653)Termination reason: Unknown
% 3.17/1.92 % (10653)Termination phase: Saturation
% 3.17/1.92
% 3.17/1.92 % (10653)Memory used [KB]: 9978
% 3.17/1.92 % (10653)Time elapsed: 0.222 s
% 3.17/1.92 % (10653)Instructions burned: 779 (million)
% 3.17/1.92 % (10653)------------------------------
% 3.17/1.92 % (10653)------------------------------
% 3.17/1.93 % (10764)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_10445 for (2996ds/507Mi)
% 3.17/1.93 % (10767)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_10445 for (2996ds/149Mi)
% 3.17/1.93 % (10751)Instruction limit reached!
% 3.17/1.93 % (10751)------------------------------
% 3.17/1.93 % (10751)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.93 % (10751)Termination reason: Unknown
% 3.17/1.93 % (10751)Termination phase: Property scanning
% 3.17/1.93
% 3.17/1.93 % (10751)Memory used [KB]: 2942
% 3.17/1.93 % (10751)Time elapsed: 0.028 s
% 3.17/1.93 % (10751)Instructions burned: 99 (million)
% 3.17/1.93 % (10751)------------------------------
% 3.17/1.93 % (10751)------------------------------
% 3.17/1.94 % (10640)Instruction limit reached!
% 3.17/1.94 % (10640)------------------------------
% 3.17/1.94 % (10640)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.94 % (10640)Termination reason: Unknown
% 3.17/1.94 % (10640)Termination phase: Saturation
% 3.17/1.94
% 3.17/1.94 % (10640)Memory used [KB]: 11129
% 3.17/1.94 % (10640)Time elapsed: 0.263 s
% 3.17/1.94 % (10640)Instructions burned: 902 (million)
% 3.17/1.94 % (10640)------------------------------
% 3.17/1.94 % (10640)------------------------------
% 3.17/1.94 % (10768)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_10445 for (2996ds/39Mi)
% 3.17/1.95 % (10624)Instruction limit reached!
% 3.17/1.95 % (10624)------------------------------
% 3.17/1.95 % (10624)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.95 % (10624)Termination reason: Unknown
% 3.17/1.95 % (10624)Termination phase: Saturation
% 3.17/1.95
% 3.17/1.95 % (10624)Memory used [KB]: 11513
% 3.17/1.95 % (10624)Time elapsed: 0.306 s
% 3.17/1.95 % (10624)Instructions burned: 1043 (million)
% 3.17/1.95 % (10624)------------------------------
% 3.17/1.95 % (10624)------------------------------
% 3.17/1.95 % (10774)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_10445 for (2996ds/6Mi)
% 3.17/1.95 % (10774)Instruction limit reached!
% 3.17/1.95 % (10774)------------------------------
% 3.17/1.95 % (10774)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.95 % (10774)Termination reason: Unknown
% 3.17/1.95 % (10774)Termination phase: shuffling
% 3.17/1.95
% 3.17/1.95 % (10774)Memory used [KB]: 1791
% 3.17/1.95 % (10774)Time elapsed: 0.003 s
% 3.17/1.95 % (10774)Instructions burned: 6 (million)
% 3.17/1.95 % (10774)------------------------------
% 3.17/1.95 % (10774)------------------------------
% 3.17/1.96 % (10768)Instruction limit reached!
% 3.17/1.96 % (10768)------------------------------
% 3.17/1.96 % (10768)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.96 % (10768)Termination reason: Unknown
% 3.17/1.96 % (10768)Termination phase: shuffling
% 3.17/1.96
% 3.17/1.96 % (10768)Memory used [KB]: 2302
% 3.17/1.96 % (10768)Time elapsed: 0.014 s
% 3.17/1.96 % (10768)Instructions burned: 40 (million)
% 3.17/1.96 % (10768)------------------------------
% 3.17/1.96 % (10768)------------------------------
% 3.17/1.96 % (10781)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_10445 for (2996ds/1087Mi)
% 3.17/1.96 % (10786)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_10445 for (2996ds/47Mi)
% 3.17/1.97 % (10787)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_10445 for (2996ds/44Mi)
% 3.17/1.98 % (10657)Instruction limit reached!
% 3.17/1.98 % (10657)------------------------------
% 3.17/1.98 % (10657)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.98 % (10657)Termination reason: Unknown
% 3.17/1.98 % (10657)Termination phase: Saturation
% 3.17/1.98
% 3.17/1.98 % (10657)Memory used [KB]: 8827
% 3.17/1.98 % (10657)Time elapsed: 0.273 s
% 3.17/1.98 % (10657)Instructions burned: 880 (million)
% 3.17/1.98 % (10657)------------------------------
% 3.17/1.98 % (10657)------------------------------
% 3.17/1.98 % (10767)Instruction limit reached!
% 3.17/1.98 % (10767)------------------------------
% 3.17/1.98 % (10767)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.98 % (10767)Termination reason: Unknown
% 3.17/1.98 % (10767)Termination phase: Property scanning
% 3.17/1.98
% 3.17/1.98 % (10767)Memory used [KB]: 3709
% 3.17/1.98 % (10767)Time elapsed: 0.047 s
% 3.17/1.98 % (10767)Instructions burned: 150 (million)
% 3.17/1.98 % (10767)------------------------------
% 3.17/1.98 % (10767)------------------------------
% 3.17/1.98 % (10786)Instruction limit reached!
% 3.17/1.98 % (10786)------------------------------
% 3.17/1.98 % (10786)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.98 % (10786)Termination reason: Unknown
% 3.17/1.98 % (10786)Termination phase: shuffling
% 3.17/1.98
% 3.17/1.98 % (10786)Memory used [KB]: 2430
% 3.17/1.98 % (10786)Time elapsed: 0.016 s
% 3.17/1.98 % (10786)Instructions burned: 47 (million)
% 3.17/1.98 % (10786)------------------------------
% 3.17/1.98 % (10786)------------------------------
% 3.17/1.98 % (10787)Instruction limit reached!
% 3.17/1.98 % (10787)------------------------------
% 3.17/1.98 % (10787)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.98 % (10787)Termination reason: Unknown
% 3.17/1.98 % (10787)Termination phase: shuffling
% 3.17/1.98
% 3.17/1.98 % (10787)Memory used [KB]: 2430
% 3.17/1.98 % (10787)Time elapsed: 0.014 s
% 3.17/1.98 % (10787)Instructions burned: 46 (million)
% 3.17/1.98 % (10787)------------------------------
% 3.17/1.98 % (10787)------------------------------
% 3.17/1.99 % (10794)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_10445 for (2996ds/432Mi)
% 3.17/1.99 % (10796)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_10445 for (2996ds/62Mi)
% 3.17/1.99 % (10797)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_10445 for (2996ds/31Mi)
% 3.17/1.99 % (10799)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_10445 for (2996ds/96Mi)
% 3.17/2.00 % (10797)Instruction limit reached!
% 3.17/2.00 % (10797)------------------------------
% 3.17/2.00 % (10797)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/2.00 % (10797)Termination reason: Unknown
% 3.17/2.00 % (10797)Termination phase: shuffling
% 3.17/2.00
% 3.17/2.00 % (10797)Memory used [KB]: 2174
% 3.17/2.00 % (10797)Time elapsed: 0.011 s
% 3.17/2.00 % (10797)Instructions burned: 31 (million)
% 3.17/2.00 % (10797)------------------------------
% 3.17/2.00 % (10797)------------------------------
% 3.17/2.00 % (10796)Instruction limit reached!
% 3.17/2.00 % (10796)------------------------------
% 3.17/2.00 % (10796)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/2.00 % (10796)Termination reason: Unknown
% 3.17/2.00 % (10796)Termination phase: shuffling
% 3.17/2.00
% 3.17/2.00 % (10796)Memory used [KB]: 2814
% 3.17/2.00 % (10796)Time elapsed: 0.019 s
% 3.17/2.00 % (10796)Instructions burned: 64 (million)
% 3.17/2.00 % (10796)------------------------------
% 3.17/2.00 % (10796)------------------------------
% 3.17/2.02 % (10739)Instruction limit reached!
% 3.17/2.02 % (10739)------------------------------
% 3.17/2.02 % (10739)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/2.02 % (10739)Termination reason: Unknown
% 3.17/2.02 % (10739)Termination phase: Saturation
% 3.17/2.02
% 3.17/2.02 % (10739)Memory used [KB]: 9466
% 3.17/2.02 % (10739)Time elapsed: 0.125 s
% 3.17/2.02 % (10739)Instructions burned: 450 (million)
% 3.17/2.02 % (10739)------------------------------
% 3.17/2.02 % (10739)------------------------------
% 3.17/2.02 % (10799)Instruction limit reached!
% 3.17/2.02 % (10799)------------------------------
% 3.17/2.02 % (10799)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/2.02 % (10799)Termination reason: Unknown
% 3.17/2.02 % (10799)Termination phase: Property scanning
% 3.17/2.02
% 3.17/2.02 % (10799)Memory used [KB]: 2942
% 3.17/2.02 % (10799)Time elapsed: 0.030 s
% 3.17/2.02 % (10799)Instructions burned: 96 (million)
% 3.17/2.02 % (10799)------------------------------
% 3.17/2.02 % (10799)------------------------------
% 3.17/2.02 % (10812)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_10445 for (2995ds/453Mi)
% 3.17/2.02 % (10813)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_10445 for (2995ds/71Mi)
% 3.17/2.03 % (10816)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_10445 for (2995ds/83Mi)
% 3.17/2.03 % (10817)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_10445 for (2995ds/11Mi)
% 5.98/2.03 % (10817)Instruction limit reached!
% 5.98/2.03 % (10817)------------------------------
% 5.98/2.03 % (10817)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.98/2.03 % (10817)Termination reason: Unknown
% 5.98/2.03 % (10817)Termination phase: shuffling
% 5.98/2.03
% 5.98/2.03 % (10817)Memory used [KB]: 1918
% 5.98/2.03 % (10817)Time elapsed: 0.005 s
% 5.98/2.03 % (10817)Instructions burned: 14 (million)
% 5.98/2.03 % (10817)------------------------------
% 5.98/2.03 % (10817)------------------------------
% 5.98/2.04 % (10822)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_10445 for (2995ds/41Mi)
% 5.98/2.04 % (10813)Instruction limit reached!
% 5.98/2.04 % (10813)------------------------------
% 5.98/2.04 % (10813)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.98/2.04 % (10813)Termination reason: Unknown
% 5.98/2.04 % (10813)Termination phase: shuffling
% 5.98/2.04
% 5.98/2.04 % (10813)Memory used [KB]: 2942
% 5.98/2.04 % (10813)Time elapsed: 0.024 s
% 5.98/2.04 % (10813)Instructions burned: 73 (million)
% 5.98/2.04 % (10813)------------------------------
% 5.98/2.04 % (10813)------------------------------
% 5.98/2.05 % (10826)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_10445 for (2995ds/6Mi)
% 5.98/2.05 % (10822)Instruction limit reached!
% 5.98/2.05 % (10822)------------------------------
% 5.98/2.05 % (10822)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.98/2.05 % (10822)Termination reason: Unknown
% 5.98/2.05 % (10822)Termination phase: shuffling
% 5.98/2.05
% 5.98/2.05 % (10822)Memory used [KB]: 2430
% 5.98/2.05 % (10822)Time elapsed: 0.013 s
% 5.98/2.05 % (10822)Instructions burned: 42 (million)
% 5.98/2.05 % (10822)------------------------------
% 5.98/2.05 % (10822)------------------------------
% 5.98/2.05 % (10816)Instruction limit reached!
% 5.98/2.05 % (10816)------------------------------
% 5.98/2.05 % (10816)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.98/2.05 % (10816)Termination reason: Unknown
% 5.98/2.05 % (10816)Termination phase: Property scanning
% 5.98/2.05
% 5.98/2.05 % (10816)Memory used [KB]: 2942
% 5.98/2.05 % (10816)Time elapsed: 0.028 s
% 5.98/2.05 % (10816)Instructions burned: 86 (million)
% 5.98/2.05 % (10816)------------------------------
% 5.98/2.05 % (10816)------------------------------
% 5.98/2.05 % (10826)Instruction limit reached!
% 5.98/2.05 % (10826)------------------------------
% 5.98/2.05 % (10826)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.98/2.05 % (10826)Termination reason: Unknown
% 5.98/2.05 % (10826)Termination phase: shuffling
% 5.98/2.05
% 5.98/2.05 % (10826)Memory used [KB]: 1791
% 5.98/2.05 % (10826)Time elapsed: 0.004 s
% 5.98/2.05 % (10826)Instructions burned: 8 (million)
% 5.98/2.05 % (10826)------------------------------
% 5.98/2.05 % (10826)------------------------------
% 5.98/2.06 % (10830)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_10445 for (2995ds/150Mi)
% 5.98/2.06 % (10831)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_10445 for (2995ds/343Mi)
% 5.98/2.06 % (10833)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_10445 for (2995ds/109Mi)
% 5.98/2.07 % (10764)Instruction limit reached!
% 5.98/2.07 % (10764)------------------------------
% 5.98/2.07 % (10764)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.98/2.07 % (10764)Termination reason: Unknown
% 5.98/2.07 % (10764)Termination phase: Saturation
% 5.98/2.07
% 5.98/2.07 % (10764)Memory used [KB]: 11385
% 5.98/2.07 % (10764)Time elapsed: 0.150 s
% 5.98/2.07 % (10764)Instructions burned: 510 (million)
% 5.98/2.07 % (10764)------------------------------
% 5.98/2.07 % (10764)------------------------------
% 5.98/2.08 % (10842)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_10445 for (2995ds/253Mi)
% 5.98/2.10 % (10833)Instruction limit reached!
% 5.98/2.10 % (10833)------------------------------
% 5.98/2.10 % (10833)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.98/2.10 % (10833)Termination reason: Unknown
% 5.98/2.10 % (10833)Termination phase: SInE selection
% 5.98/2.10
% 5.98/2.10 % (10833)Memory used [KB]: 2942
% 5.98/2.10 % (10833)Time elapsed: 0.034 s
% 5.98/2.10 % (10833)Instructions burned: 111 (million)
% 5.98/2.10 % (10833)------------------------------
% 5.98/2.10 % (10833)------------------------------
% 5.98/2.11 % (10849)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_10445 for (2995ds/140Mi)
% 5.98/2.11 % (10794)Instruction limit reached!
% 5.98/2.11 % (10794)------------------------------
% 5.98/2.11 % (10794)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.98/2.11 % (10794)Termination reason: Unknown
% 5.98/2.11 % (10794)Termination phase: Saturation
% 5.98/2.11
% 5.98/2.11 % (10794)Memory used [KB]: 4477
% 5.98/2.11 % (10794)Time elapsed: 0.124 s
% 5.98/2.11 % (10794)Instructions burned: 432 (million)
% 5.98/2.11 % (10794)------------------------------
% 5.98/2.11 % (10794)------------------------------
% 5.98/2.11 % (10830)Instruction limit reached!
% 5.98/2.11 % (10830)------------------------------
% 5.98/2.11 % (10830)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.98/2.11 % (10830)Termination reason: Unknown
% 5.98/2.11 % (10830)Termination phase: Preprocessing 3
% 5.98/2.11
% 5.98/2.11 % (10830)Memory used [KB]: 3709
% 5.98/2.11 % (10830)Time elapsed: 0.048 s
% 5.98/2.11 % (10830)Instructions burned: 153 (million)
% 5.98/2.11 % (10830)------------------------------
% 5.98/2.11 % (10830)------------------------------
% 5.98/2.12 % (10853)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_10445 for (2994ds/614Mi)
% 5.98/2.12 % (10854)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_10445 for (2994ds/202Mi)
% 6.44/2.14 % (10842)First to succeed.
% 6.44/2.14 % (10842)Refutation found. Thanks to Tanya!
% 6.44/2.14 % SZS status Theorem for DTF2THF_10445
% 6.44/2.14 % SZS output start Proof for DTF2THF_10445
% 6.44/2.14 thf(type_def_6, type, product_prod: ($tType * $tType) > $tType).
% 6.44/2.14 thf(type_def_7, type, set: ($tType) > $tType).
% 6.44/2.14 thf(type_def_8, type, proces554692349s_term: ($tType * $tType) > $tType).
% 6.44/2.14 thf(type_def_9, type, proces634752977rocess: ($tType) > $tType).
% 6.44/2.14 thf(type_def_10, type, itself: ($tType) > $tType).
% 6.44/2.14 thf(type_def_11, type, a: $tType).
% 6.44/2.14 thf(type_def_12, type, b: $tType).
% 6.44/2.14 thf(func_def_0, type, proces554692349s_term: ($tType * $tType) > $tType).
% 6.44/2.14 thf(func_def_1, type, proces634752977rocess: ($tType) > $tType).
% 6.44/2.14 thf(func_def_2, type, product_prod: ($tType * $tType) > $tType).
% 6.44/2.14 thf(func_def_3, type, set: ($tType) > $tType).
% 6.44/2.14 thf(func_def_4, type, itself: ($tType) > $tType).
% 6.44/2.14 thf(func_def_5, type, b: $tType).
% 6.44/2.14 thf(func_def_6, type, a: $tType).
% 6.44/2.14 thf(func_def_7, type, bNF_rel_fun: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((X0 > X1 > $o) > (X2 > X3 > $o) > (X0 > X2) > (X1 > X3) > $o)).
% 6.44/2.14 thf(func_def_8, type, undefined: !>[X0: $tType]:(X0)).
% 6.44/2.14 thf(func_def_9, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 6.44/2.14 thf(func_def_10, type, order_above: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0 > set @ X0)).
% 6.44/2.14 thf(func_def_11, type, order_aboveS: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0 > set @ X0)).
% 6.44/2.14 thf(func_def_12, type, proces1239275103le_CH1: !>[X0: $tType, X1: $tType]:((X0 > proces554692349s_term @ X1 @ X0) > proces554692349s_term @ X1 @ X0 > proces554692349s_term @ X1 @ X0)).
% 6.44/2.14 thf(func_def_13, type, proces1869379930H1_rel: !>[X0: $tType, X1: $tType]:(product_prod @ (X0 > proces554692349s_term @ X1 @ X0) @ proces554692349s_term @ X1 @ X0 > product_prod @ (X0 > proces554692349s_term @ X1 @ X0) @ proces554692349s_term @ X1 @ X0 > $o)).
% 6.44/2.14 thf(func_def_14, type, proces1239275104le_CH2: !>[X0: $tType, X1: $tType]:((X0 > proces554692349s_term @ X1 @ X0) > proces554692349s_term @ X1 @ X0 > proces554692349s_term @ X1 @ X0)).
% 6.44/2.14 thf(func_def_15, type, proces93903513H2_rel: !>[X0: $tType, X1: $tType]:(product_prod @ (X0 > proces554692349s_term @ X1 @ X0) @ proces554692349s_term @ X1 @ X0 > product_prod @ (X0 > proces554692349s_term @ X1 @ X0) @ proces554692349s_term @ X1 @ X0 > $o)).
% 6.44/2.14 thf(func_def_16, type, proces126235999e_CONT: !>[X0: $tType, X1: $tType]:((X0 > proces554692349s_term @ X1 @ X0) > proces554692349s_term @ X1 @ X0 > proces554692349s_term @ X1 @ X0)).
% 6.44/2.14 thf(func_def_17, type, proces1004198490NT_rel: !>[X0: $tType, X1: $tType]:(product_prod @ (X0 > proces554692349s_term @ X1 @ X0) @ proces554692349s_term @ X1 @ X0 > product_prod @ (X0 > proces554692349s_term @ X1 @ X0) @ proces554692349s_term @ X1 @ X0 > $o)).
% 6.44/2.14 thf(func_def_18, type, proces1708129104e_PREF: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > proces554692349s_term @ X1 @ X2) > proces554692349s_term @ X1 @ X0 > X1)).
% 6.44/2.14 thf(func_def_19, type, proces527360425EF_rel: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ (X0 > proces554692349s_term @ X1 @ X2) @ proces554692349s_term @ X1 @ X0 > product_prod @ (X0 > proces554692349s_term @ X1 @ X2) @ proces554692349s_term @ X1 @ X0 > $o)).
% 6.44/2.14 thf(func_def_20, type, proces1121166967uarded: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > proces554692349s_term @ X1 @ X2) > $o)).
% 6.44/2.14 thf(func_def_21, type, proces687458811_isACT: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((X0 > proces554692349s_term @ X1 @ X2) > proces554692349s_term @ X3 @ X0 > $o)).
% 6.44/2.14 thf(func_def_22, type, proces896239806CT_rel: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ (X0 > proces554692349s_term @ X1 @ X2) @ proces554692349s_term @ X3 @ X0 > product_prod @ (X0 > proces554692349s_term @ X1 @ X2) @ proces554692349s_term @ X3 @ X0 > $o)).
% 6.44/2.14 thf(func_def_23, type, proces1525233512Action: !>[X0: $tType]:(X0 > proces634752977rocess @ X0 > proces634752977rocess @ X0)).
% 6.44/2.14 thf(func_def_24, type, proces1915862579Choice: !>[X0: $tType]:(proces634752977rocess @ X0 > proces634752977rocess @ X0 > proces634752977rocess @ X0)).
% 6.44/2.14 thf(func_def_25, type, proces1406508781rocess: !>[X0: $tType, X1: $tType]:((X0 > proces634752977rocess @ X0 > X1) > (proces634752977rocess @ X0 > proces634752977rocess @ X0 > X1) > proces634752977rocess @ X0 > X1)).
% 6.44/2.14 thf(func_def_26, type, proces979765041_ch1Of: !>[X0: $tType]:(proces634752977rocess @ X0 > proces634752977rocess @ X0)).
% 6.44/2.14 thf(func_def_27, type, proces988026546_ch2Of: !>[X0: $tType]:(proces634752977rocess @ X0 > proces634752977rocess @ X0)).
% 6.44/2.14 thf(func_def_28, type, proces1778668539contOf: !>[X0: $tType]:(proces634752977rocess @ X0 > proces634752977rocess @ X0)).
% 6.44/2.14 thf(func_def_29, type, proces894737309rocess: !>[X0: $tType, X1: $tType]:((X0 > $o) > (X0 > X1) > (X0 > $o) > (X0 > proces634752977rocess @ X1) > (X0 > X0) > (X0 > $o) > (X0 > proces634752977rocess @ X1) > (X0 > X0) > (X0 > $o) > (X0 > proces634752977rocess @ X1) > (X0 > X0) > X0 > proces634752977rocess @ X1)).
% 6.44/2.14 thf(func_def_30, type, proces10484146Action: !>[X0: $tType]:(proces634752977rocess @ X0 > $o)).
% 6.44/2.14 thf(func_def_31, type, proces401113213Choice: !>[X0: $tType]:(proces634752977rocess @ X0 > $o)).
% 6.44/2.14 thf(func_def_32, type, proces1205983068rocess: !>[X0: $tType]:((X0 > $o) > proces634752977rocess @ X0 > $o)).
% 6.44/2.14 thf(func_def_33, type, proces745025900prefOf: !>[X0: $tType]:(proces634752977rocess @ X0 > X0)).
% 6.44/2.14 thf(func_def_34, type, proces749077512rocess: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > proces634752977rocess @ X0 > proces634752977rocess @ X1 > $o)).
% 6.44/2.14 thf(func_def_35, type, proces1454156180ss_ACT: !>[X0: $tType, X1: $tType]:(X0 > proces554692349s_term @ X0 @ X1 > proces554692349s_term @ X0 @ X1)).
% 6.44/2.14 thf(func_def_36, type, proces89589571ess_CH: !>[X0: $tType, X1: $tType]:(proces554692349s_term @ X0 @ X1 > proces554692349s_term @ X0 @ X1 > proces554692349s_term @ X0 @ X1)).
% 6.44/2.14 thf(func_def_37, type, proces1062592052s_PROC: !>[X0: $tType, X1: $tType]:(proces634752977rocess @ X0 > proces554692349s_term @ X0 @ X1)).
% 6.44/2.14 thf(func_def_38, type, proces1627516585ss_VAR: !>[X0: $tType, X1: $tType]:(X0 > proces554692349s_term @ X1 @ X0)).
% 6.44/2.14 thf(func_def_39, type, proces460752237s_term: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1) > (proces634752977rocess @ X2 > X1) > (X2 > proces554692349s_term @ X2 @ X0 > X1) > (proces554692349s_term @ X2 @ X0 > proces554692349s_term @ X2 @ X0 > X1) > proces554692349s_term @ X2 @ X0 > X1)).
% 6.44/2.14 thf(func_def_40, type, proces2118920028s_term: !>[X0: $tType, X1: $tType]:((X0 > $o) > (X1 > $o) > proces554692349s_term @ X0 @ X1 > $o)).
% 6.44/2.14 thf(func_def_41, type, proces2117273769s_term: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1) > (proces634752977rocess @ X2 > X1) > (X2 > proces554692349s_term @ X2 @ X0 > X1 > X1) > (proces554692349s_term @ X2 @ X0 > proces554692349s_term @ X2 @ X0 > X1 > X1 > X1) > proces554692349s_term @ X2 @ X0 > X1)).
% 6.44/2.14 thf(func_def_42, type, proces2029722208s_term: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((X0 > X1 > $o) > (X2 > X3 > $o) > proces554692349s_term @ X0 @ X2 > proces554692349s_term @ X1 @ X3 > $o)).
% 6.44/2.14 thf(func_def_43, type, proces1493547885s_term: !>[X0: $tType, X1: $tType]:(proces554692349s_term @ X0 @ X1 > set @ X1)).
% 6.44/2.14 thf(func_def_44, type, proces1652378886lution: !>[X0: $tType, X1: $tType]:((X0 > proces554692349s_term @ X1 @ X0) > proces554692349s_term @ X1 @ X0 > proces634752977rocess @ X1)).
% 6.44/2.14 thf(func_def_45, type, product_Pair: !>[X0: $tType, X1: $tType]:(X0 > X1 > product_prod @ X0 @ X1)).
% 6.44/2.14 thf(func_def_46, type, product_curry: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ X1 > X2) > X0 > X1 > X2)).
% 6.44/2.14 thf(func_def_47, type, produc2004651681e_prod: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2)).
% 6.44/2.14 thf(func_def_48, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2)).
% 6.44/2.14 thf(func_def_49, type, type: !>[X0: $tType]:(itself @ X0)).
% 6.44/2.14 thf(func_def_50, type, inv_image: !>[X0: $tType, X1: $tType]:(set @ product_prod @ X0 @ X0 > (X1 > X0) > set @ product_prod @ X1 @ X1)).
% 6.44/2.14 thf(func_def_51, type, inv_imagep: !>[X0: $tType, X1: $tType]:((X0 > X0 > $o) > (X1 > X0) > X1 > X1 > $o)).
% 6.44/2.14 thf(func_def_52, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 6.44/2.14 thf(func_def_53, type, acc: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > set @ X0)).
% 6.44/2.14 thf(func_def_54, type, accp: !>[X0: $tType]:((X0 > X0 > $o) > X0 > $o)).
% 6.44/2.14 thf(func_def_55, type, lex_prod: !>[X0: $tType, X1: $tType]:(set @ product_prod @ X0 @ X0 > set @ product_prod @ X1 @ X1 > set @ product_prod @ product_prod @ X0 @ X1 @ product_prod @ X0 @ X1)).
% 6.44/2.14 thf(func_def_56, type, adm_wf: !>[X0: $tType, X1: $tType]:(set @ product_prod @ X0 @ X0 > ((X0 > X1) > X0 > X1) > $o)).
% 6.44/2.14 thf(func_def_57, type, cut: !>[X0: $tType, X1: $tType]:((X0 > X1) > set @ product_prod @ X0 @ X0 > X0 > X0 > X1)).
% 6.44/2.14 thf(func_def_58, type, same_fst: !>[X0: $tType, X1: $tType]:((X0 > $o) > (X0 > set @ product_prod @ X1 @ X1) > set @ product_prod @ product_prod @ X0 @ X1 @ product_prod @ X0 @ X1)).
% 6.44/2.14 thf(func_def_59, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 6.44/2.14 thf(func_def_60, type, p: proces634752977rocess @ a).
% 6.44/2.14 thf(func_def_61, type, p2: proces634752977rocess @ a).
% 6.44/2.14 thf(func_def_62, type, pa: proces634752977rocess @ a).
% 6.44/2.14 thf(func_def_63, type, q: proces634752977rocess @ a).
% 6.44/2.14 thf(func_def_64, type, sys: b > proces554692349s_term @ a @ b).
% 6.44/2.14 thf(func_def_87, type, sP0: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > $o)).
% 6.44/2.14 thf(func_def_88, type, sK1: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3)).
% 6.44/2.14 thf(func_def_89, type, sK2: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 6.44/2.14 thf(func_def_90, type, sK3: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 6.44/2.14 thf(func_def_91, type, sK4: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 6.44/2.14 thf(func_def_92, type, sK5: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X5)).
% 6.44/2.14 thf(func_def_93, type, sK6: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4)).
% 6.44/2.14 thf(func_def_94, type, sK7: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3)).
% 6.44/2.14 thf(func_def_95, type, sK8: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 6.44/2.14 thf(func_def_96, type, sK9: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 6.44/2.14 thf(func_def_97, type, sK10: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 6.44/2.14 thf(func_def_98, type, sK11: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X0)).
% 6.44/2.14 thf(func_def_99, type, sK12: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X1)).
% 6.44/2.14 thf(func_def_100, type, sK13: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X2)).
% 6.44/2.14 thf(func_def_101, type, sK14: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X3)).
% 6.44/2.14 thf(func_def_102, type, sK15: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X4)).
% 6.44/2.14 thf(func_def_103, type, sK16: !>[X0: $tType, X1: $tType]:(product_prod @ (X0 > proces554692349s_term @ X1 @ X0) @ proces554692349s_term @ X1 @ X0 > X0 > proces554692349s_term @ X1 @ X0)).
% 6.44/2.14 thf(func_def_104, type, sK17: !>[X0: $tType, X1: $tType]:(product_prod @ (X0 > proces554692349s_term @ X1 @ X0) @ proces554692349s_term @ X1 @ X0 > X0)).
% 6.44/2.14 thf(func_def_105, type, sK18: !>[X0: $tType, X1: $tType]:(product_prod @ (X0 > proces554692349s_term @ X1 @ X0) @ proces554692349s_term @ X1 @ X0 > X0 > proces554692349s_term @ X1 @ X0)).
% 6.44/2.14 thf(func_def_106, type, sK19: !>[X0: $tType, X1: $tType]:(product_prod @ (X0 > proces554692349s_term @ X1 @ X0) @ proces554692349s_term @ X1 @ X0 > proces634752977rocess @ X1)).
% 6.44/2.14 thf(func_def_107, type, sK20: !>[X0: $tType, X1: $tType]:(product_prod @ (X0 > proces554692349s_term @ X1 @ X0) @ proces554692349s_term @ X1 @ X0 > X0 > proces554692349s_term @ X1 @ X0)).
% 6.44/2.14 thf(func_def_108, type, sK21: !>[X0: $tType, X1: $tType]:(product_prod @ (X0 > proces554692349s_term @ X1 @ X0) @ proces554692349s_term @ X1 @ X0 > X1)).
% 6.44/2.14 thf(func_def_109, type, sK22: !>[X0: $tType, X1: $tType]:(product_prod @ (X0 > proces554692349s_term @ X1 @ X0) @ proces554692349s_term @ X1 @ X0 > proces554692349s_term @ X1 @ X0)).
% 6.44/2.14 thf(func_def_110, type, sK23: !>[X0: $tType, X1: $tType]:(product_prod @ (X0 > proces554692349s_term @ X1 @ X0) @ proces554692349s_term @ X1 @ X0 > X0 > proces554692349s_term @ X1 @ X0)).
% 6.44/2.14 thf(func_def_111, type, sK24: !>[X0: $tType, X1: $tType]:(product_prod @ (X0 > proces554692349s_term @ X1 @ X0) @ proces554692349s_term @ X1 @ X0 > proces554692349s_term @ X1 @ X0)).
% 6.44/2.14 thf(func_def_112, type, sK25: !>[X0: $tType, X1: $tType]:(product_prod @ (X0 > proces554692349s_term @ X1 @ X0) @ proces554692349s_term @ X1 @ X0 > proces554692349s_term @ X1 @ X0)).
% 6.44/2.14 thf(func_def_113, type, sK26: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 6.44/2.14 thf(func_def_114, type, sK27: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ (X1 > proces554692349s_term @ X2 @ X0) @ proces554692349s_term @ X2 @ X1 > X1 > proces554692349s_term @ X2 @ X0)).
% 6.44/2.14 thf(func_def_115, type, sK28: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ (X1 > proces554692349s_term @ X2 @ X0) @ proces554692349s_term @ X2 @ X1 > X2)).
% 6.44/2.14 thf(func_def_116, type, sK29: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ (X1 > proces554692349s_term @ X2 @ X0) @ proces554692349s_term @ X2 @ X1 > proces554692349s_term @ X2 @ X1)).
% 6.44/2.14 thf(func_def_117, type, sK30: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ (X1 > proces554692349s_term @ X2 @ X0) @ proces554692349s_term @ X2 @ X1 > X1 > proces554692349s_term @ X2 @ X0)).
% 6.44/2.14 thf(func_def_118, type, sK31: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ (X1 > proces554692349s_term @ X2 @ X0) @ proces554692349s_term @ X2 @ X1 > proces554692349s_term @ X2 @ X1)).
% 6.44/2.14 thf(func_def_119, type, sK32: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ (X1 > proces554692349s_term @ X2 @ X0) @ proces554692349s_term @ X2 @ X1 > proces554692349s_term @ X2 @ X1)).
% 6.44/2.14 thf(func_def_120, type, sK33: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ (X1 > proces554692349s_term @ X2 @ X0) @ proces554692349s_term @ X2 @ X1 > X1 > proces554692349s_term @ X2 @ X0)).
% 6.44/2.14 thf(func_def_121, type, sK34: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ (X1 > proces554692349s_term @ X2 @ X0) @ proces554692349s_term @ X2 @ X1 > X1)).
% 6.44/2.14 thf(func_def_122, type, sK35: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ (X1 > proces554692349s_term @ X2 @ X0) @ proces554692349s_term @ X2 @ X1 > X1 > proces554692349s_term @ X2 @ X0)).
% 6.44/2.14 thf(func_def_123, type, sK36: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ (X1 > proces554692349s_term @ X2 @ X0) @ proces554692349s_term @ X2 @ X1 > proces634752977rocess @ X2)).
% 6.44/2.14 thf(func_def_124, type, sK37: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ product_prod @ X1 @ X2 > X0)).
% 6.44/2.14 thf(func_def_125, type, sK38: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ product_prod @ X1 @ X2 > X1)).
% 6.44/2.14 thf(func_def_126, type, sK39: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ product_prod @ X1 @ X2 > X2)).
% 6.44/2.14 thf(func_def_127, type, sK40: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 6.44/2.14 thf(func_def_128, type, sK41: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 6.44/2.14 thf(func_def_129, type, sK42: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 6.44/2.14 thf(func_def_130, type, sK43: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > proces634752977rocess @ X0)).
% 6.44/2.14 thf(func_def_131, type, sK44: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > proces634752977rocess @ X0)).
% 6.44/2.14 thf(func_def_132, type, sK45: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > X0)).
% 6.44/2.14 thf(func_def_133, type, sK46: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > X0)).
% 6.44/2.14 thf(func_def_134, type, sK47: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > proces634752977rocess @ X0)).
% 6.44/2.14 thf(func_def_135, type, sK48: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > proces634752977rocess @ X0)).
% 6.44/2.14 thf(func_def_136, type, sK49: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > proces634752977rocess @ X0)).
% 6.44/2.14 thf(func_def_137, type, sK50: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > proces634752977rocess @ X0)).
% 6.44/2.14 thf(func_def_138, type, sK51: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > proces634752977rocess @ X0)).
% 6.44/2.14 thf(func_def_139, type, sK52: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > proces634752977rocess @ X0)).
% 6.44/2.14 thf(func_def_140, type, sK53: !>[X0: $tType]:(proces634752977rocess @ X0 > X0)).
% 6.44/2.14 thf(func_def_141, type, sK54: !>[X0: $tType]:(proces634752977rocess @ X0 > proces634752977rocess @ X0)).
% 6.44/2.14 thf(func_def_142, type, sK55: !>[X0: $tType]:(proces634752977rocess @ X0 > proces634752977rocess @ X0)).
% 6.44/2.14 thf(func_def_143, type, sK56: !>[X0: $tType]:(proces634752977rocess @ X0 > proces634752977rocess @ X0)).
% 6.44/2.14 thf(func_def_144, type, sK57: !>[X0: $tType, X1: $tType]:(product_prod @ (X0 > proces554692349s_term @ X1 @ X0) @ proces554692349s_term @ X1 @ X0 > X0 > proces554692349s_term @ X1 @ X0)).
% 6.44/2.14 thf(func_def_145, type, sK58: !>[X0: $tType, X1: $tType]:(product_prod @ (X0 > proces554692349s_term @ X1 @ X0) @ proces554692349s_term @ X1 @ X0 > X0)).
% 6.44/2.14 thf(func_def_146, type, sK59: !>[X0: $tType, X1: $tType]:(product_prod @ (X0 > proces554692349s_term @ X1 @ X0) @ proces554692349s_term @ X1 @ X0 > X0 > proces554692349s_term @ X1 @ X0)).
% 6.44/2.14 thf(func_def_147, type, sK60: !>[X0: $tType, X1: $tType]:(product_prod @ (X0 > proces554692349s_term @ X1 @ X0) @ proces554692349s_term @ X1 @ X0 > proces554692349s_term @ X1 @ X0)).
% 6.44/2.14 thf(func_def_148, type, sK61: !>[X0: $tType, X1: $tType]:(product_prod @ (X0 > proces554692349s_term @ X1 @ X0) @ proces554692349s_term @ X1 @ X0 > proces554692349s_term @ X1 @ X0)).
% 6.44/2.14 thf(func_def_149, type, sK62: !>[X0: $tType, X1: $tType]:(product_prod @ (X0 > proces554692349s_term @ X1 @ X0) @ proces554692349s_term @ X1 @ X0 > X0 > proces554692349s_term @ X1 @ X0)).
% 6.44/2.14 thf(func_def_150, type, sK63: !>[X0: $tType, X1: $tType]:(product_prod @ (X0 > proces554692349s_term @ X1 @ X0) @ proces554692349s_term @ X1 @ X0 > proces634752977rocess @ X1)).
% 6.44/2.14 thf(func_def_151, type, sK64: !>[X0: $tType, X1: $tType]:(product_prod @ (X0 > proces554692349s_term @ X1 @ X0) @ proces554692349s_term @ X1 @ X0 > X0 > proces554692349s_term @ X1 @ X0)).
% 6.44/2.14 thf(func_def_152, type, sK65: !>[X0: $tType, X1: $tType]:(product_prod @ (X0 > proces554692349s_term @ X1 @ X0) @ proces554692349s_term @ X1 @ X0 > X1)).
% 6.44/2.14 thf(func_def_153, type, sK66: !>[X0: $tType, X1: $tType]:(product_prod @ (X0 > proces554692349s_term @ X1 @ X0) @ proces554692349s_term @ X1 @ X0 > proces554692349s_term @ X1 @ X0)).
% 6.44/2.14 thf(func_def_154, type, sK67: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X1)).
% 6.44/2.14 thf(func_def_155, type, sK68: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X0)).
% 6.44/2.14 thf(func_def_156, type, sK69: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((X2 > proces554692349s_term @ X0 @ X1) > proces554692349s_term @ X3 @ X2 > $o) > X2 > proces554692349s_term @ X0 @ X1)).
% 6.44/2.14 thf(func_def_157, type, sK70: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((X2 > proces554692349s_term @ X0 @ X1) > proces554692349s_term @ X3 @ X2 > $o) > X3)).
% 6.44/2.14 thf(func_def_158, type, sK71: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((X2 > proces554692349s_term @ X0 @ X1) > proces554692349s_term @ X3 @ X2 > $o) > proces554692349s_term @ X3 @ X2)).
% 6.44/2.14 thf(func_def_159, type, sK72: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((X2 > proces554692349s_term @ X0 @ X1) > proces554692349s_term @ X3 @ X2 > $o) > X2 > proces554692349s_term @ X0 @ X1)).
% 6.44/2.14 thf(func_def_160, type, sK73: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((X2 > proces554692349s_term @ X0 @ X1) > proces554692349s_term @ X3 @ X2 > $o) > proces634752977rocess @ X3)).
% 6.44/2.14 thf(func_def_161, type, sK74: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((X2 > proces554692349s_term @ X0 @ X1) > proces554692349s_term @ X3 @ X2 > $o) > X2 > proces554692349s_term @ X0 @ X1)).
% 6.44/2.14 thf(func_def_162, type, sK75: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((X2 > proces554692349s_term @ X0 @ X1) > proces554692349s_term @ X3 @ X2 > $o) > proces554692349s_term @ X3 @ X2)).
% 6.44/2.14 thf(func_def_163, type, sK76: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((X2 > proces554692349s_term @ X0 @ X1) > proces554692349s_term @ X3 @ X2 > $o) > proces554692349s_term @ X3 @ X2)).
% 6.44/2.14 thf(func_def_164, type, sK77: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((X2 > proces554692349s_term @ X0 @ X1) > proces554692349s_term @ X3 @ X2 > $o) > X2 > proces554692349s_term @ X0 @ X1)).
% 6.44/2.14 thf(func_def_165, type, sK78: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((X2 > proces554692349s_term @ X0 @ X1) > proces554692349s_term @ X3 @ X2 > $o) > X2)).
% 6.44/2.14 thf(func_def_166, type, sK79: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X6)).
% 6.44/2.14 thf(func_def_167, type, sK80: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X5)).
% 6.44/2.14 thf(func_def_168, type, sK81: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4)).
% 6.44/2.14 thf(func_def_169, type, sK82: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3)).
% 6.44/2.14 thf(func_def_170, type, sK83: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 6.44/2.14 thf(func_def_171, type, sK84: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 6.44/2.14 thf(func_def_172, type, sK85: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 6.44/2.14 thf(func_def_173, type, sK86: !>[X0: $tType, X1: $tType]:(proces554692349s_term @ X1 @ X0 > proces554692349s_term @ X1 @ X0)).
% 6.44/2.14 thf(func_def_174, type, sK87: !>[X0: $tType, X1: $tType]:(proces554692349s_term @ X1 @ X0 > proces554692349s_term @ X1 @ X0)).
% 6.44/2.14 thf(func_def_175, type, sK88: !>[X0: $tType, X1: $tType]:(proces554692349s_term @ X1 @ X0 > X0)).
% 6.44/2.14 thf(func_def_176, type, sK89: !>[X0: $tType, X1: $tType]:(proces554692349s_term @ X1 @ X0 > X1)).
% 6.44/2.14 thf(func_def_177, type, sK90: !>[X0: $tType, X1: $tType]:(proces554692349s_term @ X1 @ X0 > proces554692349s_term @ X1 @ X0)).
% 6.44/2.14 thf(func_def_178, type, sK91: !>[X0: $tType, X1: $tType]:(proces554692349s_term @ X1 @ X0 > proces634752977rocess @ X1)).
% 6.44/2.14 thf(func_def_179, type, sK92: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4)).
% 6.44/2.14 thf(func_def_180, type, sK93: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3)).
% 6.44/2.14 thf(func_def_181, type, sK94: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 6.44/2.14 thf(func_def_182, type, sK95: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 6.44/2.14 thf(func_def_183, type, sK96: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 6.44/2.14 thf(func_def_184, type, sK97: !>[X0: $tType, X1: $tType, X2: $tType]:(((X1 > proces554692349s_term @ X2 @ X0) > proces554692349s_term @ X2 @ X1 > $o) > X1 > proces554692349s_term @ X2 @ X0)).
% 6.44/2.14 thf(func_def_185, type, sK98: !>[X0: $tType, X1: $tType, X2: $tType]:(((X1 > proces554692349s_term @ X2 @ X0) > proces554692349s_term @ X2 @ X1 > $o) > X2)).
% 6.44/2.14 thf(func_def_186, type, sK99: !>[X0: $tType, X1: $tType, X2: $tType]:(((X1 > proces554692349s_term @ X2 @ X0) > proces554692349s_term @ X2 @ X1 > $o) > proces554692349s_term @ X2 @ X1)).
% 6.44/2.14 thf(func_def_187, type, sK100: !>[X0: $tType, X1: $tType, X2: $tType]:(((X1 > proces554692349s_term @ X2 @ X0) > proces554692349s_term @ X2 @ X1 > $o) > X1 > proces554692349s_term @ X2 @ X0)).
% 6.44/2.14 thf(func_def_188, type, sK101: !>[X0: $tType, X1: $tType, X2: $tType]:(((X1 > proces554692349s_term @ X2 @ X0) > proces554692349s_term @ X2 @ X1 > $o) > proces554692349s_term @ X2 @ X1)).
% 6.44/2.14 thf(func_def_189, type, sK102: !>[X0: $tType, X1: $tType, X2: $tType]:(((X1 > proces554692349s_term @ X2 @ X0) > proces554692349s_term @ X2 @ X1 > $o) > proces554692349s_term @ X2 @ X1)).
% 6.44/2.14 thf(func_def_190, type, sK103: !>[X0: $tType, X1: $tType, X2: $tType]:(((X1 > proces554692349s_term @ X2 @ X0) > proces554692349s_term @ X2 @ X1 > $o) > X1 > proces554692349s_term @ X2 @ X0)).
% 6.44/2.14 thf(func_def_191, type, sK104: !>[X0: $tType, X1: $tType, X2: $tType]:(((X1 > proces554692349s_term @ X2 @ X0) > proces554692349s_term @ X2 @ X1 > $o) > proces634752977rocess @ X2)).
% 6.44/2.14 thf(func_def_192, type, sK105: !>[X0: $tType, X1: $tType, X2: $tType]:(((X1 > proces554692349s_term @ X2 @ X0) > proces554692349s_term @ X2 @ X1 > $o) > X1 > proces554692349s_term @ X2 @ X0)).
% 6.44/2.14 thf(func_def_193, type, sK106: !>[X0: $tType, X1: $tType, X2: $tType]:(((X1 > proces554692349s_term @ X2 @ X0) > proces554692349s_term @ X2 @ X1 > $o) > X1)).
% 6.44/2.14 thf(func_def_194, type, sK107: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X0)).
% 6.44/2.14 thf(func_def_195, type, sK108: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X1)).
% 6.44/2.14 thf(func_def_196, type, sK109: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X0)).
% 6.44/2.14 thf(func_def_197, type, sK110: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X1)).
% 6.44/2.14 thf(func_def_198, type, sK111: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X2)).
% 6.44/2.14 thf(func_def_199, type, sK112: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X3)).
% 6.44/2.14 thf(func_def_200, type, sK113: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X4)).
% 6.44/2.14 thf(func_def_201, type, sK114: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X5)).
% 6.44/2.14 thf(func_def_202, type, sK115: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X6)).
% 6.44/2.14 thf(func_def_203, type, sK116: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ (X2 > proces554692349s_term @ X0 @ X1) @ proces554692349s_term @ X3 @ X2 > X2 > proces554692349s_term @ X0 @ X1)).
% 6.44/2.14 thf(func_def_204, type, sK117: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ (X2 > proces554692349s_term @ X0 @ X1) @ proces554692349s_term @ X3 @ X2 > X3)).
% 6.44/2.14 thf(func_def_205, type, sK118: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ (X2 > proces554692349s_term @ X0 @ X1) @ proces554692349s_term @ X3 @ X2 > proces554692349s_term @ X3 @ X2)).
% 6.44/2.14 thf(func_def_206, type, sK119: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ (X2 > proces554692349s_term @ X0 @ X1) @ proces554692349s_term @ X3 @ X2 > X2 > proces554692349s_term @ X0 @ X1)).
% 6.44/2.14 thf(func_def_207, type, sK120: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ (X2 > proces554692349s_term @ X0 @ X1) @ proces554692349s_term @ X3 @ X2 > proces634752977rocess @ X3)).
% 6.44/2.14 thf(func_def_208, type, sK121: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ (X2 > proces554692349s_term @ X0 @ X1) @ proces554692349s_term @ X3 @ X2 > X2 > proces554692349s_term @ X0 @ X1)).
% 6.44/2.14 thf(func_def_209, type, sK122: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ (X2 > proces554692349s_term @ X0 @ X1) @ proces554692349s_term @ X3 @ X2 > X2)).
% 6.44/2.14 thf(func_def_210, type, sK123: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ (X2 > proces554692349s_term @ X0 @ X1) @ proces554692349s_term @ X3 @ X2 > X2 > proces554692349s_term @ X0 @ X1)).
% 6.44/2.14 thf(func_def_211, type, sK124: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ (X2 > proces554692349s_term @ X0 @ X1) @ proces554692349s_term @ X3 @ X2 > proces554692349s_term @ X3 @ X2)).
% 6.44/2.14 thf(func_def_212, type, sK125: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ (X2 > proces554692349s_term @ X0 @ X1) @ proces554692349s_term @ X3 @ X2 > proces554692349s_term @ X3 @ X2)).
% 6.44/2.14 thf(func_def_213, type, sK126: !>[X0: $tType, X1: $tType]:((proces554692349s_term @ X1 @ X0 > $o) > proces634752977rocess @ X1)).
% 6.44/2.14 thf(func_def_214, type, sK127: !>[X0: $tType, X1: $tType]:((proces554692349s_term @ X1 @ X0 > $o) > X0)).
% 6.44/2.14 thf(func_def_215, type, sK128: !>[X0: $tType, X1: $tType]:((proces554692349s_term @ X1 @ X0 > $o) > X1)).
% 6.44/2.14 thf(func_def_216, type, sK129: !>[X0: $tType, X1: $tType]:((proces554692349s_term @ X1 @ X0 > $o) > proces554692349s_term @ X1 @ X0)).
% 6.44/2.14 thf(func_def_217, type, sK130: !>[X0: $tType, X1: $tType]:((proces554692349s_term @ X1 @ X0 > $o) > proces554692349s_term @ X1 @ X0)).
% 6.44/2.14 thf(func_def_218, type, sK131: !>[X0: $tType, X1: $tType]:((proces554692349s_term @ X1 @ X0 > $o) > proces554692349s_term @ X1 @ X0)).
% 6.44/2.14 thf(func_def_219, type, sK132: !>[X0: $tType, X1: $tType]:(((X0 > proces554692349s_term @ X1 @ X0) > proces554692349s_term @ X1 @ X0 > $o) > X0 > proces554692349s_term @ X1 @ X0)).
% 6.44/2.14 thf(func_def_220, type, sK133: !>[X0: $tType, X1: $tType]:(((X0 > proces554692349s_term @ X1 @ X0) > proces554692349s_term @ X1 @ X0 > $o) > X0)).
% 6.44/2.14 thf(func_def_221, type, sK134: !>[X0: $tType, X1: $tType]:(((X0 > proces554692349s_term @ X1 @ X0) > proces554692349s_term @ X1 @ X0 > $o) > X0 > proces554692349s_term @ X1 @ X0)).
% 6.44/2.14 thf(func_def_222, type, sK135: !>[X0: $tType, X1: $tType]:(((X0 > proces554692349s_term @ X1 @ X0) > proces554692349s_term @ X1 @ X0 > $o) > proces634752977rocess @ X1)).
% 6.44/2.14 thf(func_def_223, type, sK136: !>[X0: $tType, X1: $tType]:(((X0 > proces554692349s_term @ X1 @ X0) > proces554692349s_term @ X1 @ X0 > $o) > X0 > proces554692349s_term @ X1 @ X0)).
% 6.44/2.14 thf(func_def_224, type, sK137: !>[X0: $tType, X1: $tType]:(((X0 > proces554692349s_term @ X1 @ X0) > proces554692349s_term @ X1 @ X0 > $o) > proces554692349s_term @ X1 @ X0)).
% 6.44/2.14 thf(func_def_225, type, sK138: !>[X0: $tType, X1: $tType]:(((X0 > proces554692349s_term @ X1 @ X0) > proces554692349s_term @ X1 @ X0 > $o) > proces554692349s_term @ X1 @ X0)).
% 6.44/2.14 thf(func_def_226, type, sK139: !>[X0: $tType, X1: $tType]:(((X0 > proces554692349s_term @ X1 @ X0) > proces554692349s_term @ X1 @ X0 > $o) > X0 > proces554692349s_term @ X1 @ X0)).
% 6.44/2.14 thf(func_def_227, type, sK140: !>[X0: $tType, X1: $tType]:(((X0 > proces554692349s_term @ X1 @ X0) > proces554692349s_term @ X1 @ X0 > $o) > X1)).
% 6.44/2.14 thf(func_def_228, type, sK141: !>[X0: $tType, X1: $tType]:(((X0 > proces554692349s_term @ X1 @ X0) > proces554692349s_term @ X1 @ X0 > $o) > proces554692349s_term @ X1 @ X0)).
% 6.44/2.14 thf(func_def_229, type, sK142: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X0)).
% 6.44/2.14 thf(func_def_230, type, sK143: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X1)).
% 6.44/2.14 thf(func_def_231, type, sK144: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X2)).
% 6.44/2.14 thf(func_def_232, type, sK145: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X3)).
% 6.44/2.14 thf(func_def_233, type, sK146: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X4)).
% 6.44/2.14 thf(func_def_234, type, sK147: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X5)).
% 6.44/2.14 thf(func_def_235, type, sK148: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > proces634752977rocess @ X0)).
% 6.44/2.14 thf(func_def_236, type, sK149: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > proces634752977rocess @ X0)).
% 6.44/2.14 thf(func_def_237, type, sK150: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > proces634752977rocess @ X0)).
% 6.44/2.14 thf(func_def_238, type, sK151: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > proces634752977rocess @ X0)).
% 6.44/2.14 thf(func_def_239, type, sK152: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > X0)).
% 6.44/2.14 thf(func_def_240, type, sK153: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > X0)).
% 6.44/2.14 thf(func_def_241, type, sK154: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > proces634752977rocess @ X0)).
% 6.44/2.14 thf(func_def_242, type, sK155: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > proces634752977rocess @ X0)).
% 6.44/2.14 thf(func_def_243, type, sK156: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > proces634752977rocess @ X0)).
% 6.44/2.14 thf(func_def_244, type, sK157: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > proces634752977rocess @ X0)).
% 6.44/2.14 thf(func_def_245, type, sK158: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X0)).
% 6.44/2.14 thf(func_def_246, type, sK159: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X1)).
% 6.44/2.14 thf(func_def_247, type, sK160: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X0)).
% 6.44/2.14 thf(func_def_248, type, sK161: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X1)).
% 6.44/2.14 thf(func_def_249, type, sK162: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X2)).
% 6.44/2.14 thf(func_def_250, type, sK163: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X3)).
% 6.44/2.14 thf(func_def_251, type, sK164: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X1)).
% 6.44/2.14 thf(func_def_252, type, sK165: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X0)).
% 6.44/2.14 thf(func_def_253, type, sK166: !>[X0: $tType, X1: $tType]:(((X0 > proces554692349s_term @ X1 @ X0) > proces554692349s_term @ X1 @ X0 > $o) > X0 > proces554692349s_term @ X1 @ X0)).
% 6.44/2.14 thf(func_def_254, type, sK167: !>[X0: $tType, X1: $tType]:(((X0 > proces554692349s_term @ X1 @ X0) > proces554692349s_term @ X1 @ X0 > $o) > proces634752977rocess @ X1)).
% 6.44/2.14 thf(func_def_255, type, sK168: !>[X0: $tType, X1: $tType]:(((X0 > proces554692349s_term @ X1 @ X0) > proces554692349s_term @ X1 @ X0 > $o) > X0 > proces554692349s_term @ X1 @ X0)).
% 6.44/2.14 thf(func_def_256, type, sK169: !>[X0: $tType, X1: $tType]:(((X0 > proces554692349s_term @ X1 @ X0) > proces554692349s_term @ X1 @ X0 > $o) > X1)).
% 6.44/2.14 thf(func_def_257, type, sK170: !>[X0: $tType, X1: $tType]:(((X0 > proces554692349s_term @ X1 @ X0) > proces554692349s_term @ X1 @ X0 > $o) > proces554692349s_term @ X1 @ X0)).
% 6.44/2.14 thf(func_def_258, type, sK171: !>[X0: $tType, X1: $tType]:(((X0 > proces554692349s_term @ X1 @ X0) > proces554692349s_term @ X1 @ X0 > $o) > X0 > proces554692349s_term @ X1 @ X0)).
% 6.44/2.14 thf(func_def_259, type, sK172: !>[X0: $tType, X1: $tType]:(((X0 > proces554692349s_term @ X1 @ X0) > proces554692349s_term @ X1 @ X0 > $o) > X0)).
% 6.44/2.14 thf(func_def_260, type, sK173: !>[X0: $tType, X1: $tType]:(((X0 > proces554692349s_term @ X1 @ X0) > proces554692349s_term @ X1 @ X0 > $o) > X0 > proces554692349s_term @ X1 @ X0)).
% 6.44/2.14 thf(func_def_261, type, sK174: !>[X0: $tType, X1: $tType]:(((X0 > proces554692349s_term @ X1 @ X0) > proces554692349s_term @ X1 @ X0 > $o) > proces554692349s_term @ X1 @ X0)).
% 6.44/2.14 thf(func_def_262, type, sK175: !>[X0: $tType, X1: $tType]:(((X0 > proces554692349s_term @ X1 @ X0) > proces554692349s_term @ X1 @ X0 > $o) > proces554692349s_term @ X1 @ X0)).
% 6.44/2.14 thf(func_def_264, type, ph177: !>[X0: $tType]:(X0)).
% 6.44/2.14 thf(f990,plain,(
% 6.44/2.14 $false),
% 6.44/2.14 inference(trivial_inequality_removal,[status(thm)],[f985])).
% 6.44/2.14 thf(f985,plain,(
% 6.44/2.14 ($true != $true)),
% 6.44/2.14 inference(superposition,[status(thm)],[f981,f956])).
% 6.44/2.14 thf(f956,plain,(
% 6.44/2.14 ((proces401113213Choice @ a @ pa) = $true)),
% 6.44/2.14 inference(cnf_transformation,[status(thm)],[f457])).
% 6.44/2.14 thf(f457,plain,(
% 6.44/2.14 ((proces401113213Choice @ a @ pa) = $true)),
% 6.44/2.14 inference(fool_elimination,[status(thm)],[f456])).
% 6.44/2.14 thf(f456,plain,(
% 6.44/2.14 (proces401113213Choice @ a @ pa)),
% 6.44/2.14 inference(rectify,[status(thm)],[f1])).
% 6.44/2.14 thf(f1,axiom,(
% 6.44/2.14 (proces401113213Choice @ a @ pa)),
% 6.44/2.14 file('/export/starexec/sandbox2/tmp/tmp.lDpXRCP47Y/DTF2THF_10445.p',fact_0__092_060open_062isChoice_Ap_092_060close_062)).
% 6.44/2.14 thf(f981,plain,(
% 6.44/2.14 ((proces401113213Choice @ a @ pa) != $true)),
% 6.44/2.14 inference(trivial_inequality_removal,[status(thm)],[f978])).
% 6.44/2.14 thf(f978,plain,(
% 6.44/2.14 ((proces401113213Choice @ a @ pa) != $true) | ($true != $true)),
% 6.44/2.14 inference(superposition,[status(thm)],[f859,f975])).
% 6.44/2.14 thf(f975,plain,(
% 6.44/2.14 ((proces10484146Action @ a @ pa) = $true)),
% 6.44/2.14 inference(superposition,[status(thm)],[f952,f909])).
% 6.44/2.14 thf(f909,plain,(
% 6.44/2.14 ( ! [X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X4 : X0 > proces554692349s_term @ X2 @ X1,X5 : proces634752977rocess @ X3] : (((proces10484146Action @ X3 @ X5) = (proces687458811_isACT @ X0 @ X2 @ X1 @ X3 @ X4 @ (proces1062592052s_PROC @ X3 @ X0 @ X5)))) )),
% 6.44/2.15 inference(cnf_transformation,[status(thm)],[f662])).
% 6.44/2.15 thf(f662,plain,(
% 6.44/2.15 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : $tType,X4 : X0 > proces554692349s_term @ X2 @ X1,X5 : proces634752977rocess @ X3] : ((proces10484146Action @ X3 @ X5) = (proces687458811_isACT @ X0 @ X2 @ X1 @ X3 @ X4 @ (proces1062592052s_PROC @ X3 @ X0 @ X5)))),
% 6.44/2.15 inference(rectify,[status(thm)],[f4])).
% 6.44/2.15 thf(f4,axiom,(
% 6.44/2.15 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : $tType,X8 : X0 > proces554692349s_term @ X2 @ X1,X9 : proces634752977rocess @ X3] : ((proces687458811_isACT @ X0 @ X2 @ X1 @ X3 @ X8 @ (proces1062592052s_PROC @ X3 @ X0 @ X9)) = (proces10484146Action @ X3 @ X9))),
% 6.44/2.15 file('/export/starexec/sandbox2/tmp/tmp.lDpXRCP47Y/DTF2THF_10445.p',fact_3_isACT_Osimps_I2_J)).
% 6.44/2.15 thf(f952,plain,(
% 6.44/2.15 ((proces687458811_isACT @ b @ a @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ pa)) = $true)),
% 6.44/2.15 inference(cnf_transformation,[status(thm)],[f660])).
% 6.44/2.15 thf(f660,plain,(
% 6.44/2.15 ((proces687458811_isACT @ b @ a @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ pa)) = $true)),
% 6.44/2.15 inference(flattening,[status(thm)],[f317])).
% 6.44/2.15 thf(f317,plain,(
% 6.44/2.15 ~~((proces687458811_isACT @ b @ a @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ pa)) = $true)),
% 6.44/2.15 inference(fool_elimination,[status(thm)],[f316])).
% 6.44/2.15 thf(f316,plain,(
% 6.44/2.15 ~~(proces687458811_isACT @ b @ a @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ pa))),
% 6.44/2.15 inference(rectify,[status(thm)],[f260])).
% 6.44/2.15 thf(f260,negated_conjecture,(
% 6.44/2.15 ~~(proces687458811_isACT @ b @ a @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ pa))),
% 6.44/2.15 inference(negated_conjecture,[status(cth)],[f259])).
% 6.44/2.15 thf(f259,conjecture,(
% 6.44/2.15 ~(proces687458811_isACT @ b @ a @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ pa))),
% 6.44/2.15 file('/export/starexec/sandbox2/tmp/tmp.lDpXRCP47Y/DTF2THF_10445.p',conj_0)).
% 6.44/2.15 thf(f859,plain,(
% 6.44/2.15 ( ! [X0 : $tType,X1 : proces634752977rocess @ X0] : (($true != (proces401113213Choice @ X0 @ X1)) | ($true != (proces10484146Action @ X0 @ X1))) )),
% 6.44/2.15 inference(cnf_transformation,[status(thm)],[f699])).
% 6.44/2.15 thf(f699,plain,(
% 6.44/2.15 ! [X0 : $tType,X1 : proces634752977rocess @ X0] : (($true != (proces401113213Choice @ X0 @ X1)) | ($true != (proces10484146Action @ X0 @ X1)))),
% 6.44/2.15 inference(ennf_transformation,[status(thm)],[f431])).
% 6.44/2.15 thf(f431,plain,(
% 6.44/2.15 ! [X0 : $tType,X1 : proces634752977rocess @ X0] : ~(($true = (proces10484146Action @ X0 @ X1)) & ($true = (proces401113213Choice @ X0 @ X1)))),
% 6.44/2.15 inference(fool_elimination,[status(thm)],[f430])).
% 6.44/2.15 thf(f430,plain,(
% 6.44/2.15 ! [X0 : $tType,X1 : proces634752977rocess @ X0] : ~((proces401113213Choice @ X0 @ X1) & (proces10484146Action @ X0 @ X1))),
% 6.44/2.15 inference(rectify,[status(thm)],[f15])).
% 6.44/2.15 thf(f15,axiom,(
% 6.44/2.15 ! [X0 : $tType,X9 : proces634752977rocess @ X0] : ~((proces401113213Choice @ X0 @ X9) & (proces10484146Action @ X0 @ X9))),
% 6.44/2.15 file('/export/starexec/sandbox2/tmp/tmp.lDpXRCP47Y/DTF2THF_10445.p',fact_14_not__isAction__isChoice)).
% 6.44/2.15 % SZS output end Proof for DTF2THF_10445
% 6.44/2.15 % (10842)------------------------------
% 6.44/2.15 % (10842)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.44/2.15 % (10842)Termination reason: Refutation
% 6.44/2.15
% 6.44/2.15 % (10842)Memory used [KB]: 8443
% 6.44/2.15 % (10842)Time elapsed: 0.060 s
% 6.44/2.15 % (10842)Instructions burned: 188 (million)
% 6.44/2.15 % (10842)------------------------------
% 6.44/2.15 % (10842)------------------------------
% 6.44/2.15 % (10612)Success in time 0.537 s
%------------------------------------------------------------------------------