%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : PRO026^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n029.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 3.29s 1.81s
% Output : Refutation 3.29s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : PRO026^1 : TPTP v9.2.1. Released v7.0.0.
% 0.00/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n029.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 11:29:44 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.31/0.46 ---- Original DTF file ---
% 0.31/0.46 thf(spec,logic,$$dhol).
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 % File : PRO026^1 : TPTP v9.2.1. Released v7.0.0.
% 0.31/0.46 % Domain : Processes
% 0.31/0.46 % Problem : Process algebra 206
% 0.31/0.46 % Version : [Bla16] axioms : Especial.
% 0.31/0.46 % English :
% 0.31/0.46
% 0.31/0.46 % Refs : [BH+14] Blanchette et al. (2014), Truly Modular (Co)datatypes
% 0.31/0.46 % : [RB15] Reynolds & Blanchette (2015), A Decision Procedure for
% 0.31/0.46 % : [Bla16] Blanchette (2016), Email to Geoff Sutcliffe
% 0.31/0.46 % Source : [Bla16]
% 0.31/0.46 % Names : process__206.p [Bla16]
% 0.31/0.46
% 0.31/0.46 % Status : Theorem
% 0.31/0.46 % Rating : 0.00 v7.2.0, 0.25 v7.1.0
% 0.31/0.46 % Syntax : Number of formulae : 316 ( 146 unt; 57 typ; 0 def)
% 0.31/0.46 % Number of atoms : 901 ( 387 equ; 0 cnn)
% 0.31/0.46 % Maximal formula atoms : 31 ( 3 avg)
% 0.31/0.46 % Number of connectives : 8558 ( 165 ~; 9 |; 45 &;7988 @)
% 0.31/0.46 % ( 0 <=>; 351 =>; 0 <=; 0 <~>)
% 0.31/0.46 % Maximal formula depth : 31 ( 12 avg)
% 0.31/0.46 % Number of types : 3 ( 2 usr)
% 0.31/0.46 % Number of type conns : 1526 (1526 >; 0 *; 0 +; 0 <<)
% 0.31/0.46 % Number of symbols : 58 ( 55 usr; 3 con; 0-14 aty)
% 0.31/0.46 % Number of variables : 2144 ( 271 ^;1751 !; 21 ?;2144 :)
% 0.31/0.46 % ( 101 !>; 0 ?*; 0 @-; 0 @+)
% 0.31/0.46 % SPC : TH1_THM_EQU_NAR
% 0.31/0.46
% 0.31/0.46 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.31/0.46 % 2016-07-13 14:40:09.955
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 %----Could-be-implicit typings (7)
% 0.31/0.46 thf(ty_t_Process__Mirabelle__xovoopgpgi_Oprocess__term,type,
% 0.31/0.46 proces554692349s_term: $tType > $tType > $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_t_Process__Mirabelle__xovoopgpgi_Oprocess,type,
% 0.31/0.46 proces634752977rocess: $tType > $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_t_Product__Type_Oprod,type,
% 0.31/0.46 product_prod: $tType > $tType > $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_t_Set_Oset,type,
% 0.31/0.46 set: $tType > $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_t_itself,type,
% 0.31/0.46 itself: $tType > $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_tf_b,type,
% 0.31/0.46 b: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_tf_a,type,
% 0.31/0.46 a: $tType ).
% 0.31/0.46
% 0.31/0.46 %----Explicit typings (50)
% 0.31/0.46 thf(sy_c_BNF__Def_Orel__fun,type,
% 0.31/0.46 bNF_rel_fun:
% 0.31/0.46 !>[A: $tType,C: $tType,B: $tType,D: $tType] : ( ( A > C > $o ) > ( B > D > $o ) > ( A > B ) > ( C > D ) > $o ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Basic__BNFs_Opred__fun,type,
% 0.31/0.46 basic_pred_fun:
% 0.31/0.46 !>[A: $tType,B: $tType] : ( ( A > $o ) > ( B > $o ) > ( A > B ) > $o ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Fun_Omap__fun,type,
% 0.31/0.46 map_fun:
% 0.31/0.46 !>[C: $tType,A: $tType,B: $tType,D: $tType] : ( ( C > A ) > ( B > D ) > ( A > B ) > C > D ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_HOL_Oundefined,type,
% 0.31/0.46 undefined:
% 0.31/0.46 !>[A: $tType] : A ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_If,type,
% 0.31/0.46 if:
% 0.31/0.46 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Process__Mirabelle__xovoopgpgi_OCH1,type,
% 0.31/0.46 proces1239275103le_CH1:
% 0.31/0.46 !>[A: $tType,B: $tType] : ( ( A > ( proces554692349s_term @ B @ A ) ) > ( proces554692349s_term @ B @ A ) > ( proces554692349s_term @ B @ A ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Process__Mirabelle__xovoopgpgi_OCH1__rel,type,
% 0.31/0.46 proces1869379930H1_rel:
% 0.31/0.46 !>[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 ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Process__Mirabelle__xovoopgpgi_OCH2,type,
% 0.31/0.46 proces1239275104le_CH2:
% 0.31/0.46 !>[A: $tType,B: $tType] : ( ( A > ( proces554692349s_term @ B @ A ) ) > ( proces554692349s_term @ B @ A ) > ( proces554692349s_term @ B @ A ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Process__Mirabelle__xovoopgpgi_OCH2__rel,type,
% 0.31/0.46 proces93903513H2_rel:
% 0.31/0.46 !>[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 ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Process__Mirabelle__xovoopgpgi_OCONT,type,
% 0.31/0.46 proces126235999e_CONT:
% 0.31/0.46 !>[A: $tType,B: $tType] : ( ( A > ( proces554692349s_term @ B @ A ) ) > ( proces554692349s_term @ B @ A ) > ( proces554692349s_term @ B @ A ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Process__Mirabelle__xovoopgpgi_OCONT__rel,type,
% 0.31/0.46 proces1004198490NT_rel:
% 0.31/0.46 !>[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 ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Process__Mirabelle__xovoopgpgi_OPREF,type,
% 0.31/0.46 proces1708129104e_PREF:
% 0.31/0.46 !>[A: $tType,B: $tType,C: $tType] : ( ( A > ( proces554692349s_term @ B @ C ) ) > ( proces554692349s_term @ B @ A ) > B ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Process__Mirabelle__xovoopgpgi_OPREF__rel,type,
% 0.31/0.46 proces527360425EF_rel:
% 0.31/0.46 !>[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 ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oguarded,type,
% 0.31/0.46 proces1121166967uarded:
% 0.31/0.46 !>[A: $tType,B: $tType,C: $tType] : ( ( A > ( proces554692349s_term @ B @ C ) ) > $o ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Process__Mirabelle__xovoopgpgi_OisACT,type,
% 0.31/0.46 proces687458811_isACT:
% 0.31/0.46 !>[A: $tType,B: $tType,C: $tType,D: $tType] : ( ( A > ( proces554692349s_term @ B @ C ) ) > ( proces554692349s_term @ D @ A ) > $o ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Process__Mirabelle__xovoopgpgi_OisACT__rel,type,
% 0.31/0.46 proces896239806CT_rel:
% 0.31/0.46 !>[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 ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OAction,type,
% 0.31/0.46 proces1525233512Action:
% 0.31/0.46 !>[A: $tType] : ( A > ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OChoice,type,
% 0.31/0.46 proces1915862579Choice:
% 0.31/0.46 !>[A: $tType] : ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Ocase__process,type,
% 0.31/0.47 proces1406508781rocess:
% 0.31/0.47 !>[A: $tType,B: $tType] : ( ( A > ( proces634752977rocess @ A ) > B ) > ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B ) > ( proces634752977rocess @ A ) > B ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Och1Of,type,
% 0.31/0.47 proces979765041_ch1Of:
% 0.31/0.47 !>[A: $tType] : ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Och2Of,type,
% 0.31/0.47 proces988026546_ch2Of:
% 0.31/0.47 !>[A: $tType] : ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OcontOf,type,
% 0.31/0.47 proces1778668539contOf:
% 0.31/0.47 !>[A: $tType] : ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Ocorec__process,type,
% 0.31/0.47 proces894737309rocess:
% 0.31/0.47 !>[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 ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OisAction,type,
% 0.31/0.47 proces10484146Action:
% 0.31/0.47 !>[A: $tType] : ( ( proces634752977rocess @ A ) > $o ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OisChoice,type,
% 0.31/0.47 proces401113213Choice:
% 0.31/0.47 !>[A: $tType] : ( ( proces634752977rocess @ A ) > $o ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Omap__process,type,
% 0.31/0.47 proces370407749rocess:
% 0.31/0.47 !>[A: $tType,Aa: $tType] : ( ( A > Aa ) > ( proces634752977rocess @ A ) > ( proces634752977rocess @ Aa ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Opred__process,type,
% 0.31/0.47 proces1205983068rocess:
% 0.31/0.47 !>[A: $tType] : ( ( A > $o ) > ( proces634752977rocess @ A ) > $o ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OprefOf,type,
% 0.31/0.47 proces745025900prefOf:
% 0.31/0.47 !>[A: $tType] : ( ( proces634752977rocess @ A ) > A ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Orel__process,type,
% 0.31/0.47 proces749077512rocess:
% 0.31/0.47 !>[A: $tType,B: $tType] : ( ( A > B > $o ) > ( proces634752977rocess @ A ) > ( proces634752977rocess @ B ) > $o ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_OACT,type,
% 0.31/0.47 proces1454156180ss_ACT:
% 0.31/0.47 !>[A: $tType,Pvar: $tType] : ( A > ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_OCH,type,
% 0.31/0.47 proces89589571ess_CH:
% 0.31/0.47 !>[A: $tType,Pvar: $tType] : ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_OPROC,type,
% 0.31/0.47 proces1062592052s_PROC:
% 0.31/0.47 !>[A: $tType,Pvar: $tType] : ( ( proces634752977rocess @ A ) > ( proces554692349s_term @ A @ Pvar ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_OVAR,type,
% 0.31/0.47 proces1627516585ss_VAR:
% 0.31/0.47 !>[Pvar: $tType,A: $tType] : ( Pvar > ( proces554692349s_term @ A @ Pvar ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Ocase__process__term,type,
% 0.31/0.47 proces460752237s_term:
% 0.31/0.47 !>[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 ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Omap__process__term,type,
% 0.31/0.47 proces224683037s_term:
% 0.31/0.47 !>[A: $tType,Aa: $tType,Pvar: $tType,Pvara: $tType] : ( ( A > Aa ) > ( Pvar > Pvara ) > ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ Aa @ Pvara ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Opred__process__term,type,
% 0.31/0.47 proces2118920028s_term:
% 0.31/0.47 !>[A: $tType,B: $tType] : ( ( A > $o ) > ( B > $o ) > ( proces554692349s_term @ A @ B ) > $o ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Orec__process__term,type,
% 0.31/0.47 proces2117273769s_term:
% 0.31/0.47 !>[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 ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Orel__process__term,type,
% 0.31/0.47 proces2029722208s_term:
% 0.31/0.47 !>[A: $tType,C: $tType,B: $tType,D: $tType] : ( ( A > C > $o ) > ( B > D > $o ) > ( proces554692349s_term @ A @ B ) > ( proces554692349s_term @ C @ D ) > $o ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Oset2__process__term,type,
% 0.31/0.47 proces1493547885s_term:
% 0.31/0.47 !>[A: $tType,Pvar: $tType] : ( ( proces554692349s_term @ A @ Pvar ) > ( set @ Pvar ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Process__Mirabelle__xovoopgpgi_Osolution,type,
% 0.31/0.47 proces1652378886lution:
% 0.31/0.47 !>[A: $tType,B: $tType] : ( ( A > ( proces554692349s_term @ B @ A ) ) > ( proces554692349s_term @ B @ A ) > ( proces634752977rocess @ B ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Product__Type_OPair,type,
% 0.31/0.47 product_Pair:
% 0.31/0.47 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Product__Type_Ocurry,type,
% 0.31/0.47 product_curry:
% 0.31/0.47 !>[A: $tType,B: $tType,C: $tType] : ( ( ( product_prod @ A @ B ) > C ) > A > B > C ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Product__Type_Ointernal__case__prod,type,
% 0.31/0.47 produc2004651681e_prod:
% 0.31/0.47 !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > ( product_prod @ A @ B ) > C ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod,type,
% 0.31/0.47 product_rec_prod:
% 0.31/0.47 !>[A: $tType,B: $tType,T: $tType] : ( ( A > B > T ) > ( product_prod @ A @ B ) > T ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Pure_Otype,type,
% 0.31/0.47 type:
% 0.31/0.47 !>[A: $tType] : ( itself @ A ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Set_OCollect,type,
% 0.31/0.47 collect:
% 0.31/0.47 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Wellfounded_Oaccp,type,
% 0.31/0.47 accp:
% 0.31/0.47 !>[A: $tType] : ( ( A > A > $o ) > A > $o ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_member,type,
% 0.31/0.47 member:
% 0.31/0.47 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_v_p,type,
% 0.31/0.47 p: proces634752977rocess @ a ).
% 0.31/0.47
% 0.31/0.47 thf(sy_v_sys,type,
% 0.31/0.47 sys: b > ( proces554692349s_term @ a @ b ) ).
% 0.31/0.47
% 0.31/0.47 %----Relevant facts (255)
% 0.31/0.47 thf(fact_0__092_060open_062_092_060And_062q_O_Aq_A_061_Asolution_Asys_A_IPROC_Ap_J_A_092_060Longrightarrow_062_Ap_A_061_Aq_092_060close_062,axiom,
% 0.31/0.47 ! [Q: proces634752977rocess @ a] :
% 0.31/0.47 ( ( Q
% 0.31/0.47 = ( proces1652378886lution @ b @ a @ sys @ ( proces1062592052s_PROC @ a @ b @ p ) ) )
% 0.31/0.47 => ( p = Q ) ) ).
% 0.31/0.47
% 0.31/0.47 % \<open>\<And>q. q = solution sys (PROC p) \<Longrightarrow> p = q\<close>
% 0.31/0.47 thf(fact_1_process__term_Oinject_I2_J,axiom,
% 0.31/0.47 ! [Pvar: $tType,A: $tType,X2: proces634752977rocess @ A,Y2: proces634752977rocess @ A] :
% 0.31/0.47 ( ( ( proces1062592052s_PROC @ A @ Pvar @ X2 )
% 0.31/0.47 = ( proces1062592052s_PROC @ A @ Pvar @ Y2 ) )
% 0.31/0.47 = ( X2 = Y2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_term.inject(2)
% 0.31/0.47 thf(fact_2_process__term_Osimps_I22_J,axiom,
% 0.31/0.47 ! [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] :
% 0.31/0.47 ( ( proces2117273769s_term @ Pvar @ D @ A @ F1 @ F2 @ F3 @ F4 @ ( proces1062592052s_PROC @ A @ Pvar @ X2 ) )
% 0.31/0.47 = ( F2 @ X2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_term.simps(22)
% 0.31/0.47 thf(fact_3_process__term_Osimps_I18_J,axiom,
% 0.31/0.47 ! [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] :
% 0.31/0.47 ( ( proces460752237s_term @ Pvar @ B @ A @ F1 @ F2 @ F3 @ F4 @ ( proces1062592052s_PROC @ A @ Pvar @ X2 ) )
% 0.31/0.47 = ( F2 @ X2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_term.simps(18)
% 0.31/0.47 thf(fact_4_process__term_Odistinct_I7_J,axiom,
% 0.31/0.47 ! [Pvar: $tType,A: $tType,X2: proces634752977rocess @ A,X31: A,X32: proces554692349s_term @ A @ Pvar] :
% 0.31/0.47 ( ( proces1062592052s_PROC @ A @ Pvar @ X2 )
% 0.31/0.47 != ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_term.distinct(7)
% 0.31/0.47 thf(fact_5_process__term_Odistinct_I9_J,axiom,
% 0.31/0.47 ! [Pvar: $tType,A: $tType,X2: proces634752977rocess @ A,X41: proces554692349s_term @ A @ Pvar,X42: proces554692349s_term @ A @ Pvar] :
% 0.31/0.47 ( ( proces1062592052s_PROC @ A @ Pvar @ X2 )
% 0.31/0.47 != ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_term.distinct(9)
% 0.31/0.47 thf(fact_6_process__term_Odistinct_I1_J,axiom,
% 0.31/0.47 ! [Pvar: $tType,A: $tType,X1: Pvar,X2: proces634752977rocess @ A] :
% 0.31/0.47 ( ( proces1627516585ss_VAR @ Pvar @ A @ X1 )
% 0.31/0.47 != ( proces1062592052s_PROC @ A @ Pvar @ X2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_term.distinct(1)
% 0.31/0.47 thf(fact_7_solution__VAR,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType,Sys: A > ( proces554692349s_term @ B @ A ),X: A] :
% 0.31/0.47 ( ( proces1121166967uarded @ A @ B @ A @ Sys )
% 0.31/0.47 => ( ( proces1652378886lution @ A @ B @ Sys @ ( proces1627516585ss_VAR @ A @ B @ X ) )
% 0.31/0.47 = ( proces1652378886lution @ A @ B @ Sys @ ( Sys @ X ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % solution_VAR
% 0.31/0.47 thf(fact_8_PREF_Osimps_I2_J,axiom,
% 0.31/0.47 ! [A: $tType,C: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ C ),P: proces634752977rocess @ B] :
% 0.31/0.47 ( ( proces1708129104e_PREF @ A @ B @ C @ Sys @ ( proces1062592052s_PROC @ B @ A @ P ) )
% 0.31/0.47 = ( proces745025900prefOf @ B @ P ) ) ).
% 0.31/0.47
% 0.31/0.47 % PREF.simps(2)
% 0.31/0.47 thf(fact_9_process__term_Opred__inject_I2_J,axiom,
% 0.31/0.47 ! [Pvar: $tType,A: $tType,P1: A > $o,P2: Pvar > $o,A2: proces634752977rocess @ A] :
% 0.31/0.47 ( ( proces2118920028s_term @ A @ Pvar @ P1 @ P2 @ ( proces1062592052s_PROC @ A @ Pvar @ A2 ) )
% 0.31/0.47 = ( proces1205983068rocess @ A @ P1 @ A2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_term.pred_inject(2)
% 0.31/0.47 thf(fact_10_CH1_Osimps_I2_J,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),P: proces634752977rocess @ B] :
% 0.31/0.47 ( ( proces1239275103le_CH1 @ A @ B @ Sys @ ( proces1062592052s_PROC @ B @ A @ P ) )
% 0.31/0.47 = ( proces1062592052s_PROC @ B @ A @ ( proces979765041_ch1Of @ B @ P ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % CH1.simps(2)
% 0.31/0.47 thf(fact_11_CH2_Osimps_I2_J,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),P: proces634752977rocess @ B] :
% 0.31/0.47 ( ( proces1239275104le_CH2 @ A @ B @ Sys @ ( proces1062592052s_PROC @ B @ A @ P ) )
% 0.31/0.47 = ( proces1062592052s_PROC @ B @ A @ ( proces988026546_ch2Of @ B @ P ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % CH2.simps(2)
% 0.31/0.47 thf(fact_12_CONT_Osimps_I2_J,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),P: proces634752977rocess @ B] :
% 0.31/0.47 ( ( proces126235999e_CONT @ A @ B @ Sys @ ( proces1062592052s_PROC @ B @ A @ P ) )
% 0.31/0.47 = ( proces1062592052s_PROC @ B @ A @ ( proces1778668539contOf @ B @ P ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % CONT.simps(2)
% 0.31/0.47 thf(fact_13_solution_Odisc__iff_I2_J,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 0.31/0.47 ( ( proces401113213Choice @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) )
% 0.31/0.47 = ( ~ ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % solution.disc_iff(2)
% 0.31/0.47 thf(fact_14_process__term_Oinject_I1_J,axiom,
% 0.31/0.47 ! [A: $tType,Pvar: $tType,X1: Pvar,Y1: Pvar] :
% 0.31/0.47 ( ( ( proces1627516585ss_VAR @ Pvar @ A @ X1 )
% 0.31/0.47 = ( proces1627516585ss_VAR @ Pvar @ A @ Y1 ) )
% 0.31/0.47 = ( X1 = Y1 ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_term.inject(1)
% 0.31/0.47 thf(fact_15_process__term_Oinject_I4_J,axiom,
% 0.31/0.47 ! [Pvar: $tType,A: $tType,X41: proces554692349s_term @ A @ Pvar,X42: proces554692349s_term @ A @ Pvar,Y41: proces554692349s_term @ A @ Pvar,Y42: proces554692349s_term @ A @ Pvar] :
% 0.31/0.47 ( ( ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 )
% 0.31/0.47 = ( proces89589571ess_CH @ A @ Pvar @ Y41 @ Y42 ) )
% 0.31/0.47 = ( ( X41 = Y41 )
% 0.31/0.47 & ( X42 = Y42 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_term.inject(4)
% 0.31/0.47 thf(fact_16_process__term_Oinject_I3_J,axiom,
% 0.31/0.47 ! [Pvar: $tType,A: $tType,X31: A,X32: proces554692349s_term @ A @ Pvar,Y31: A,Y32: proces554692349s_term @ A @ Pvar] :
% 0.31/0.47 ( ( ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 )
% 0.31/0.47 = ( proces1454156180ss_ACT @ A @ Pvar @ Y31 @ Y32 ) )
% 0.31/0.47 = ( ( X31 = Y31 )
% 0.31/0.47 & ( X32 = Y32 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_term.inject(3)
% 0.31/0.47 thf(fact_17_process__term_Opred__inject_I1_J,axiom,
% 0.31/0.47 ! [A: $tType,Pvar: $tType,P1: A > $o,P2: Pvar > $o,A2: Pvar] :
% 0.31/0.47 ( ( proces2118920028s_term @ A @ Pvar @ P1 @ P2 @ ( proces1627516585ss_VAR @ Pvar @ A @ A2 ) )
% 0.31/0.47 = ( P2 @ A2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_term.pred_inject(1)
% 0.31/0.47 thf(fact_18_process__term_Opred__inject_I4_J,axiom,
% 0.31/0.47 ! [Pvar: $tType,A: $tType,P1: A > $o,P2: Pvar > $o,A2: proces554692349s_term @ A @ Pvar,Aa2: proces554692349s_term @ A @ Pvar] :
% 0.31/0.47 ( ( proces2118920028s_term @ A @ Pvar @ P1 @ P2 @ ( proces89589571ess_CH @ A @ Pvar @ A2 @ Aa2 ) )
% 0.31/0.47 = ( ( proces2118920028s_term @ A @ Pvar @ P1 @ P2 @ A2 )
% 0.31/0.47 & ( proces2118920028s_term @ A @ Pvar @ P1 @ P2 @ Aa2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_term.pred_inject(4)
% 0.31/0.47 thf(fact_19_process__term_Opred__inject_I3_J,axiom,
% 0.31/0.47 ! [Pvar: $tType,A: $tType,P1: A > $o,P2: Pvar > $o,A2: A,Aa2: proces554692349s_term @ A @ Pvar] :
% 0.31/0.47 ( ( proces2118920028s_term @ A @ Pvar @ P1 @ P2 @ ( proces1454156180ss_ACT @ A @ Pvar @ A2 @ Aa2 ) )
% 0.31/0.47 = ( ( P1 @ A2 )
% 0.31/0.47 & ( proces2118920028s_term @ A @ Pvar @ P1 @ P2 @ Aa2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_term.pred_inject(3)
% 0.31/0.47 thf(fact_20_CH1_Osimps_I3_J,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T1: proces554692349s_term @ B @ A,T22: proces554692349s_term @ B @ A] :
% 0.31/0.47 ( ( proces1239275103le_CH1 @ A @ B @ Sys @ ( proces89589571ess_CH @ B @ A @ T1 @ T22 ) )
% 0.31/0.47 = T1 ) ).
% 0.31/0.47
% 0.31/0.47 % CH1.simps(3)
% 0.31/0.47 thf(fact_21_CH2_Osimps_I3_J,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T1: proces554692349s_term @ B @ A,T22: proces554692349s_term @ B @ A] :
% 0.31/0.47 ( ( proces1239275104le_CH2 @ A @ B @ Sys @ ( proces89589571ess_CH @ B @ A @ T1 @ T22 ) )
% 0.31/0.47 = T22 ) ).
% 0.31/0.47
% 0.31/0.47 % CH2.simps(3)
% 0.31/0.47 thf(fact_22_CONT_Osimps_I3_J,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),A2: B,T2: proces554692349s_term @ B @ A] :
% 0.31/0.47 ( ( proces126235999e_CONT @ A @ B @ Sys @ ( proces1454156180ss_ACT @ B @ A @ A2 @ T2 ) )
% 0.31/0.47 = T2 ) ).
% 0.31/0.47
% 0.31/0.47 % CONT.simps(3)
% 0.31/0.47 thf(fact_23_PREF_Osimps_I3_J,axiom,
% 0.31/0.47 ! [A: $tType,C: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ C ),A2: B,T2: proces554692349s_term @ B @ A] :
% 0.31/0.47 ( ( proces1708129104e_PREF @ A @ B @ C @ Sys @ ( proces1454156180ss_ACT @ B @ A @ A2 @ T2 ) )
% 0.31/0.47 = A2 ) ).
% 0.31/0.47
% 0.31/0.47 % PREF.simps(3)
% 0.31/0.47 thf(fact_24_isACT_Osimps_I4_J,axiom,
% 0.31/0.47 ! [B: $tType,C: $tType,A: $tType,D: $tType,Sys: A > ( proces554692349s_term @ B @ C ),T1: proces554692349s_term @ D @ A,T22: proces554692349s_term @ D @ A] :
% 0.31/0.47 ~ ( proces687458811_isACT @ A @ B @ C @ D @ Sys @ ( proces89589571ess_CH @ D @ A @ T1 @ T22 ) ) ).
% 0.31/0.47
% 0.31/0.47 % isACT.simps(4)
% 0.31/0.47 thf(fact_25_isACT_Osimps_I3_J,axiom,
% 0.31/0.47 ! [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 ) ) ).
% 0.31/0.47
% 0.31/0.47 % isACT.simps(3)
% 0.31/0.47 thf(fact_26_process__term_Osimps_I24_J,axiom,
% 0.31/0.47 ! [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] :
% 0.31/0.47 ( ( proces2117273769s_term @ Pvar @ D @ A @ F1 @ F2 @ F3 @ F4 @ ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 ) )
% 0.31/0.47 = ( F4 @ X41 @ X42 @ ( proces2117273769s_term @ Pvar @ D @ A @ F1 @ F2 @ F3 @ F4 @ X41 ) @ ( proces2117273769s_term @ Pvar @ D @ A @ F1 @ F2 @ F3 @ F4 @ X42 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_term.simps(24)
% 0.31/0.47 thf(fact_27_process__term_Osimps_I23_J,axiom,
% 0.31/0.47 ! [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] :
% 0.31/0.47 ( ( proces2117273769s_term @ Pvar @ D @ A @ F1 @ F2 @ F3 @ F4 @ ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) )
% 0.31/0.47 = ( F3 @ X31 @ X32 @ ( proces2117273769s_term @ Pvar @ D @ A @ F1 @ F2 @ F3 @ F4 @ X32 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_term.simps(23)
% 0.31/0.47 thf(fact_28_process__term_Osimps_I21_J,axiom,
% 0.31/0.47 ! [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,X1: Pvar] :
% 0.31/0.47 ( ( proces2117273769s_term @ Pvar @ D @ A @ F1 @ F2 @ F3 @ F4 @ ( proces1627516585ss_VAR @ Pvar @ A @ X1 ) )
% 0.31/0.47 = ( F1 @ X1 ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_term.simps(21)
% 0.31/0.47 thf(fact_29_process__term_Osimps_I20_J,axiom,
% 0.31/0.47 ! [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] :
% 0.31/0.47 ( ( proces460752237s_term @ Pvar @ B @ A @ F1 @ F2 @ F3 @ F4 @ ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 ) )
% 0.31/0.47 = ( F4 @ X41 @ X42 ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_term.simps(20)
% 0.31/0.47 thf(fact_30_process__term_Osimps_I19_J,axiom,
% 0.31/0.47 ! [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] :
% 0.31/0.47 ( ( proces460752237s_term @ Pvar @ B @ A @ F1 @ F2 @ F3 @ F4 @ ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) )
% 0.31/0.47 = ( F3 @ X31 @ X32 ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_term.simps(19)
% 0.31/0.47 thf(fact_31_process__term_Osimps_I17_J,axiom,
% 0.31/0.47 ! [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,X1: Pvar] :
% 0.31/0.47 ( ( proces460752237s_term @ Pvar @ B @ A @ F1 @ F2 @ F3 @ F4 @ ( proces1627516585ss_VAR @ Pvar @ A @ X1 ) )
% 0.31/0.47 = ( F1 @ X1 ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_term.simps(17)
% 0.31/0.47 thf(fact_32_process__term_Odistinct_I11_J,axiom,
% 0.31/0.47 ! [Pvar: $tType,A: $tType,X31: A,X32: proces554692349s_term @ A @ Pvar,X41: proces554692349s_term @ A @ Pvar,X42: proces554692349s_term @ A @ Pvar] :
% 0.31/0.47 ( ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 )
% 0.31/0.47 != ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_term.distinct(11)
% 0.31/0.47 thf(fact_33_process__term_Odistinct_I5_J,axiom,
% 0.31/0.47 ! [Pvar: $tType,A: $tType,X1: Pvar,X41: proces554692349s_term @ A @ Pvar,X42: proces554692349s_term @ A @ Pvar] :
% 0.31/0.47 ( ( proces1627516585ss_VAR @ Pvar @ A @ X1 )
% 0.31/0.47 != ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_term.distinct(5)
% 0.31/0.47 thf(fact_34_process__term_Odistinct_I3_J,axiom,
% 0.31/0.47 ! [Pvar: $tType,A: $tType,X1: Pvar,X31: A,X32: proces554692349s_term @ A @ Pvar] :
% 0.31/0.47 ( ( proces1627516585ss_VAR @ Pvar @ A @ X1 )
% 0.31/0.47 != ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_term.distinct(3)
% 0.31/0.47 thf(fact_35_isACT__VAR,axiom,
% 0.31/0.47 ! [C: $tType,B: $tType,A: $tType,Sys: A > ( proces554692349s_term @ B @ A ),X: A] :
% 0.31/0.47 ( ( proces1121166967uarded @ A @ B @ A @ Sys )
% 0.31/0.47 => ( ( proces687458811_isACT @ A @ B @ A @ C @ Sys @ ( proces1627516585ss_VAR @ A @ C @ X ) )
% 0.31/0.47 = ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ ( Sys @ X ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % isACT_VAR
% 0.31/0.47 thf(fact_36_CH2_Oinduct,axiom,
% 0.31/0.47 ! [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] :
% 0.31/0.47 ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),X3: A] : ( P3 @ Sys2 @ ( proces1627516585ss_VAR @ A @ B @ X3 ) )
% 0.31/0.47 => ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),P4: proces634752977rocess @ B] : ( P3 @ Sys2 @ ( proces1062592052s_PROC @ B @ A @ P4 ) )
% 0.31/0.47 => ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),T12: proces554692349s_term @ B @ A,T23: proces554692349s_term @ B @ A] : ( P3 @ Sys2 @ ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) )
% 0.31/0.47 => ( ! [A3: A > ( proces554692349s_term @ B @ A ),V: B,Va: proces554692349s_term @ B @ A] : ( P3 @ A3 @ ( proces1454156180ss_ACT @ B @ A @ V @ Va ) )
% 0.31/0.47 => ( P3 @ A0 @ A1 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % CH2.induct
% 0.31/0.47 thf(fact_37_CONT_Oinduct,axiom,
% 0.31/0.47 ! [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] :
% 0.31/0.47 ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),X3: A] : ( P3 @ Sys2 @ ( proces1627516585ss_VAR @ A @ B @ X3 ) )
% 0.31/0.47 => ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),P4: proces634752977rocess @ B] : ( P3 @ Sys2 @ ( proces1062592052s_PROC @ B @ A @ P4 ) )
% 0.31/0.47 => ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),A3: B,T3: proces554692349s_term @ B @ A] : ( P3 @ Sys2 @ ( proces1454156180ss_ACT @ B @ A @ A3 @ T3 ) )
% 0.31/0.47 => ( ! [A3: A > ( proces554692349s_term @ B @ A ),V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] : ( P3 @ A3 @ ( proces89589571ess_CH @ B @ A @ V @ Va ) )
% 0.31/0.47 => ( P3 @ A0 @ A1 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % CONT.induct
% 0.31/0.47 thf(fact_38_PREF_Oinduct,axiom,
% 0.31/0.47 ! [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] :
% 0.31/0.47 ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),X3: A] : ( P3 @ Sys2 @ ( proces1627516585ss_VAR @ A @ B @ X3 ) )
% 0.31/0.47 => ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),P4: proces634752977rocess @ B] : ( P3 @ Sys2 @ ( proces1062592052s_PROC @ B @ A @ P4 ) )
% 0.31/0.47 => ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),A3: B,T3: proces554692349s_term @ B @ A] : ( P3 @ Sys2 @ ( proces1454156180ss_ACT @ B @ A @ A3 @ T3 ) )
% 0.31/0.47 => ( ! [A3: A > ( proces554692349s_term @ B @ C ),V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] : ( P3 @ A3 @ ( proces89589571ess_CH @ B @ A @ V @ Va ) )
% 0.31/0.47 => ( P3 @ A0 @ A1 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % PREF.induct
% 0.31/0.47 thf(fact_39_guarded__def,axiom,
% 0.31/0.47 ! [C: $tType,B: $tType,A: $tType] :
% 0.31/0.47 ( ( proces1121166967uarded @ A @ B @ C )
% 0.31/0.47 = ( ^ [Sys3: A > ( proces554692349s_term @ B @ C )] :
% 0.31/0.47 ! [X4: A,Y: C] :
% 0.31/0.47 ( ( Sys3 @ X4 )
% 0.31/0.47 != ( proces1627516585ss_VAR @ C @ B @ Y ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % guarded_def
% 0.31/0.47 thf(fact_40_isACT_Oinduct,axiom,
% 0.31/0.47 ! [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] :
% 0.31/0.47 ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),X3: A] : ( P3 @ Sys2 @ ( proces1627516585ss_VAR @ A @ D @ X3 ) )
% 0.31/0.47 => ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),P4: proces634752977rocess @ D] : ( P3 @ Sys2 @ ( proces1062592052s_PROC @ D @ A @ P4 ) )
% 0.31/0.47 => ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),A3: D,T3: proces554692349s_term @ D @ A] : ( P3 @ Sys2 @ ( proces1454156180ss_ACT @ D @ A @ A3 @ T3 ) )
% 0.31/0.47 => ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),T12: proces554692349s_term @ D @ A,T23: proces554692349s_term @ D @ A] : ( P3 @ Sys2 @ ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) )
% 0.31/0.47 => ( P3 @ A0 @ A1 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % isACT.induct
% 0.31/0.47 thf(fact_41_process__term_Oinduct,axiom,
% 0.31/0.47 ! [Pvar: $tType,A: $tType,P3: ( proces554692349s_term @ A @ Pvar ) > $o,Process_term: proces554692349s_term @ A @ Pvar] :
% 0.31/0.47 ( ! [X5: Pvar] : ( P3 @ ( proces1627516585ss_VAR @ Pvar @ A @ X5 ) )
% 0.31/0.47 => ( ! [X5: proces634752977rocess @ A] : ( P3 @ ( proces1062592052s_PROC @ A @ Pvar @ X5 ) )
% 0.31/0.47 => ( ! [X1a: A,X2a: proces554692349s_term @ A @ Pvar] :
% 0.31/0.47 ( ( P3 @ X2a )
% 0.31/0.47 => ( P3 @ ( proces1454156180ss_ACT @ A @ Pvar @ X1a @ X2a ) ) )
% 0.31/0.47 => ( ! [X1a: proces554692349s_term @ A @ Pvar,X2a: proces554692349s_term @ A @ Pvar] :
% 0.31/0.47 ( ( P3 @ X1a )
% 0.31/0.47 => ( ( P3 @ X2a )
% 0.31/0.47 => ( P3 @ ( proces89589571ess_CH @ A @ Pvar @ X1a @ X2a ) ) ) )
% 0.31/0.47 => ( P3 @ Process_term ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_term.induct
% 0.31/0.47 thf(fact_42_process__term_Oexhaust,axiom,
% 0.31/0.47 ! [Pvar: $tType,A: $tType,Y3: proces554692349s_term @ A @ Pvar] :
% 0.31/0.47 ( ! [X12: Pvar] :
% 0.31/0.47 ( Y3
% 0.31/0.47 != ( proces1627516585ss_VAR @ Pvar @ A @ X12 ) )
% 0.31/0.47 => ( ! [X22: proces634752977rocess @ A] :
% 0.31/0.47 ( Y3
% 0.31/0.47 != ( proces1062592052s_PROC @ A @ Pvar @ X22 ) )
% 0.31/0.47 => ( ! [X312: A,X322: proces554692349s_term @ A @ Pvar] :
% 0.31/0.47 ( Y3
% 0.31/0.47 != ( proces1454156180ss_ACT @ A @ Pvar @ X312 @ X322 ) )
% 0.31/0.47 => ~ ! [X412: proces554692349s_term @ A @ Pvar,X422: proces554692349s_term @ A @ Pvar] :
% 0.31/0.47 ( Y3
% 0.31/0.47 != ( proces89589571ess_CH @ A @ Pvar @ X412 @ X422 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_term.exhaust
% 0.31/0.47 thf(fact_43_solution_Osimps_I4_J,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 0.31/0.47 ( ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
% 0.31/0.47 => ( ( proces1778668539contOf @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) )
% 0.31/0.47 = ( proces1652378886lution @ A @ B @ Sys @ ( proces126235999e_CONT @ A @ B @ Sys @ T2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % solution.simps(4)
% 0.31/0.47 thf(fact_44_mem__Collect__eq,axiom,
% 0.31/0.47 ! [A: $tType,A2: A,P3: A > $o] :
% 0.31/0.47 ( ( member @ A @ A2 @ ( collect @ A @ P3 ) )
% 0.31/0.47 = ( P3 @ A2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % mem_Collect_eq
% 0.31/0.47 thf(fact_45_Collect__mem__eq,axiom,
% 0.31/0.47 ! [A: $tType,A4: set @ A] :
% 0.31/0.47 ( ( collect @ A
% 0.31/0.47 @ ^ [X6: A] : ( member @ A @ X6 @ A4 ) )
% 0.31/0.47 = A4 ) ).
% 0.31/0.47
% 0.31/0.47 % Collect_mem_eq
% 0.31/0.47 thf(fact_46_Collect__cong,axiom,
% 0.31/0.47 ! [A: $tType,P3: A > $o,Q2: A > $o] :
% 0.31/0.47 ( ! [X5: A] :
% 0.31/0.47 ( ( P3 @ X5 )
% 0.31/0.47 = ( Q2 @ X5 ) )
% 0.31/0.47 => ( ( collect @ A @ P3 )
% 0.31/0.47 = ( collect @ A @ Q2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Collect_cong
% 0.31/0.47 thf(fact_47_ext,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.31/0.47 ( ! [X5: A] :
% 0.31/0.47 ( ( F @ X5 )
% 0.31/0.47 = ( G @ X5 ) )
% 0.31/0.47 => ( F = G ) ) ).
% 0.31/0.47
% 0.31/0.47 % ext
% 0.31/0.47 thf(fact_48_solution_Osimps_I5_J,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 0.31/0.47 ( ~ ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
% 0.31/0.47 => ( ( proces979765041_ch1Of @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) )
% 0.31/0.47 = ( proces1652378886lution @ A @ B @ Sys @ ( proces1239275103le_CH1 @ A @ B @ Sys @ T2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % solution.simps(5)
% 0.31/0.47 thf(fact_49_solution_Osimps_I6_J,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 0.31/0.47 ( ~ ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
% 0.31/0.47 => ( ( proces988026546_ch2Of @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) )
% 0.31/0.47 = ( proces1652378886lution @ A @ B @ Sys @ ( proces1239275104le_CH2 @ A @ B @ Sys @ T2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % solution.simps(6)
% 0.31/0.47 thf(fact_50_solution_Osimps_I3_J,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 0.31/0.47 ( ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
% 0.31/0.47 => ( ( proces745025900prefOf @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) )
% 0.31/0.47 = ( proces1708129104e_PREF @ A @ B @ A @ Sys @ T2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % solution.simps(3)
% 0.31/0.47 thf(fact_51_solution_Odisc_I2_J,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 0.31/0.47 ( ~ ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
% 0.31/0.47 => ( proces401113213Choice @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % solution.disc(2)
% 0.31/0.47 thf(fact_52_process_Oexpand,axiom,
% 0.31/0.47 ! [A: $tType,Process: proces634752977rocess @ A,Process2: proces634752977rocess @ A] :
% 0.31/0.47 ( ( ( proces10484146Action @ A @ Process )
% 0.31/0.47 = ( proces10484146Action @ A @ Process2 ) )
% 0.31/0.47 => ( ( ( proces10484146Action @ A @ Process )
% 0.31/0.47 => ( ( proces10484146Action @ A @ Process2 )
% 0.31/0.47 => ( ( ( proces745025900prefOf @ A @ Process )
% 0.31/0.47 = ( proces745025900prefOf @ A @ Process2 ) )
% 0.31/0.47 & ( ( proces1778668539contOf @ A @ Process )
% 0.31/0.47 = ( proces1778668539contOf @ A @ Process2 ) ) ) ) )
% 0.31/0.47 => ( ( ( proces401113213Choice @ A @ Process )
% 0.31/0.47 => ( ( proces401113213Choice @ A @ Process2 )
% 0.31/0.47 => ( ( ( proces979765041_ch1Of @ A @ Process )
% 0.31/0.47 = ( proces979765041_ch1Of @ A @ Process2 ) )
% 0.31/0.47 & ( ( proces988026546_ch2Of @ A @ Process )
% 0.31/0.47 = ( proces988026546_ch2Of @ A @ Process2 ) ) ) ) )
% 0.31/0.47 => ( Process = Process2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % process.expand
% 0.31/0.47 thf(fact_53_process_Ocoinduct,axiom,
% 0.31/0.47 ! [A: $tType,R: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > $o,Process: proces634752977rocess @ A,Process2: proces634752977rocess @ A] :
% 0.31/0.47 ( ( R @ Process @ Process2 )
% 0.31/0.47 => ( ! [Process3: proces634752977rocess @ A,Process4: proces634752977rocess @ A] :
% 0.31/0.47 ( ( R @ Process3 @ Process4 )
% 0.31/0.47 => ( ( ( proces10484146Action @ A @ Process3 )
% 0.31/0.47 = ( proces10484146Action @ A @ Process4 ) )
% 0.31/0.47 & ( ( proces10484146Action @ A @ Process3 )
% 0.31/0.47 => ( ( proces10484146Action @ A @ Process4 )
% 0.31/0.47 => ( ( ( proces745025900prefOf @ A @ Process3 )
% 0.31/0.47 = ( proces745025900prefOf @ A @ Process4 ) )
% 0.31/0.47 & ( R @ ( proces1778668539contOf @ A @ Process3 ) @ ( proces1778668539contOf @ A @ Process4 ) ) ) ) )
% 0.31/0.47 & ( ( proces401113213Choice @ A @ Process3 )
% 0.31/0.47 => ( ( proces401113213Choice @ A @ Process4 )
% 0.31/0.47 => ( ( R @ ( proces979765041_ch1Of @ A @ Process3 ) @ ( proces979765041_ch1Of @ A @ Process4 ) )
% 0.31/0.47 & ( R @ ( proces988026546_ch2Of @ A @ Process3 ) @ ( proces988026546_ch2Of @ A @ Process4 ) ) ) ) ) ) )
% 0.31/0.47 => ( Process = Process2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % process.coinduct
% 0.31/0.47 thf(fact_54_process_Ocoinduct__strong,axiom,
% 0.31/0.47 ! [A: $tType,R: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > $o,Process: proces634752977rocess @ A,Process2: proces634752977rocess @ A] :
% 0.31/0.47 ( ( R @ Process @ Process2 )
% 0.31/0.47 => ( ! [Process3: proces634752977rocess @ A,Process4: proces634752977rocess @ A] :
% 0.31/0.47 ( ( R @ Process3 @ Process4 )
% 0.31/0.47 => ( ( ( proces10484146Action @ A @ Process3 )
% 0.31/0.47 = ( proces10484146Action @ A @ Process4 ) )
% 0.31/0.47 & ( ( proces10484146Action @ A @ Process3 )
% 0.31/0.47 => ( ( proces10484146Action @ A @ Process4 )
% 0.31/0.47 => ( ( ( proces745025900prefOf @ A @ Process3 )
% 0.31/0.47 = ( proces745025900prefOf @ A @ Process4 ) )
% 0.31/0.47 & ( ( R @ ( proces1778668539contOf @ A @ Process3 ) @ ( proces1778668539contOf @ A @ Process4 ) )
% 0.31/0.47 | ( ( proces1778668539contOf @ A @ Process3 )
% 0.31/0.47 = ( proces1778668539contOf @ A @ Process4 ) ) ) ) ) )
% 0.31/0.47 & ( ( proces401113213Choice @ A @ Process3 )
% 0.31/0.47 => ( ( proces401113213Choice @ A @ Process4 )
% 0.31/0.47 => ( ( ( R @ ( proces979765041_ch1Of @ A @ Process3 ) @ ( proces979765041_ch1Of @ A @ Process4 ) )
% 0.31/0.47 | ( ( proces979765041_ch1Of @ A @ Process3 )
% 0.31/0.47 = ( proces979765041_ch1Of @ A @ Process4 ) ) )
% 0.31/0.47 & ( ( R @ ( proces988026546_ch2Of @ A @ Process3 ) @ ( proces988026546_ch2Of @ A @ Process4 ) )
% 0.31/0.47 | ( ( proces988026546_ch2Of @ A @ Process3 )
% 0.31/0.47 = ( proces988026546_ch2Of @ A @ Process4 ) ) ) ) ) ) ) )
% 0.31/0.47 => ( Process = Process2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % process.coinduct_strong
% 0.31/0.47 thf(fact_55_solution_Octr_I1_J,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 0.31/0.47 ( ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
% 0.31/0.47 => ( ( proces1652378886lution @ A @ B @ Sys @ T2 )
% 0.31/0.47 = ( proces1525233512Action @ B @ ( proces1708129104e_PREF @ A @ B @ A @ Sys @ T2 ) @ ( proces1652378886lution @ A @ B @ Sys @ ( proces126235999e_CONT @ A @ B @ Sys @ T2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % solution.ctr(1)
% 0.31/0.47 thf(fact_56_solution_Octr_I2_J,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 0.31/0.47 ( ~ ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
% 0.31/0.47 => ( ( proces1652378886lution @ A @ B @ Sys @ T2 )
% 0.31/0.47 = ( proces1915862579Choice @ B @ ( proces1652378886lution @ A @ B @ Sys @ ( proces1239275103le_CH1 @ A @ B @ Sys @ T2 ) ) @ ( proces1652378886lution @ A @ B @ Sys @ ( proces1239275104le_CH2 @ A @ B @ Sys @ T2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % solution.ctr(2)
% 0.31/0.47 thf(fact_57_process_Ocollapse_I2_J,axiom,
% 0.31/0.47 ! [A: $tType,Process: proces634752977rocess @ A] :
% 0.31/0.47 ( ( proces401113213Choice @ A @ Process )
% 0.31/0.47 => ( ( proces1915862579Choice @ A @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) )
% 0.31/0.47 = Process ) ) ).
% 0.31/0.47
% 0.31/0.47 % process.collapse(2)
% 0.31/0.47 thf(fact_58_solution_Ocode,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType] :
% 0.31/0.47 ( ( proces1652378886lution @ A @ B )
% 0.31/0.47 = ( ^ [Sys3: A > ( proces554692349s_term @ B @ A ),T4: proces554692349s_term @ B @ A] : ( if @ ( proces634752977rocess @ B ) @ ( proces687458811_isACT @ A @ B @ A @ B @ Sys3 @ T4 ) @ ( proces1525233512Action @ B @ ( proces1708129104e_PREF @ A @ B @ A @ Sys3 @ T4 ) @ ( proces1652378886lution @ A @ B @ Sys3 @ ( proces126235999e_CONT @ A @ B @ Sys3 @ T4 ) ) ) @ ( proces1915862579Choice @ B @ ( proces1652378886lution @ A @ B @ Sys3 @ ( proces1239275103le_CH1 @ A @ B @ Sys3 @ T4 ) ) @ ( proces1652378886lution @ A @ B @ Sys3 @ ( proces1239275104le_CH2 @ A @ B @ Sys3 @ T4 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % solution.code
% 0.31/0.47 thf(fact_59_CH2_Ocases,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType,X7: product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A )] :
% 0.31/0.47 ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),X3: A] :
% 0.31/0.47 ( X7
% 0.31/0.47 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ Sys2 @ ( proces1627516585ss_VAR @ A @ B @ X3 ) ) )
% 0.31/0.47 => ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),P4: proces634752977rocess @ B] :
% 0.31/0.47 ( X7
% 0.31/0.47 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ Sys2 @ ( proces1062592052s_PROC @ B @ A @ P4 ) ) )
% 0.31/0.47 => ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),T12: proces554692349s_term @ B @ A,T23: proces554692349s_term @ B @ A] :
% 0.31/0.47 ( X7
% 0.31/0.47 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ Sys2 @ ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) ) )
% 0.31/0.47 => ~ ! [A3: A > ( proces554692349s_term @ B @ A ),V: B,Va: proces554692349s_term @ B @ A] :
% 0.31/0.47 ( X7
% 0.31/0.47 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ A3 @ ( proces1454156180ss_ACT @ B @ A @ V @ Va ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % CH2.cases
% 0.31/0.47 thf(fact_60_CONT_Ocases,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType,X7: product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A )] :
% 0.31/0.47 ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),X3: A] :
% 0.31/0.47 ( X7
% 0.31/0.47 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ Sys2 @ ( proces1627516585ss_VAR @ A @ B @ X3 ) ) )
% 0.31/0.47 => ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),P4: proces634752977rocess @ B] :
% 0.31/0.47 ( X7
% 0.31/0.47 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ Sys2 @ ( proces1062592052s_PROC @ B @ A @ P4 ) ) )
% 0.31/0.47 => ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),A3: B,T3: proces554692349s_term @ B @ A] :
% 0.31/0.47 ( X7
% 0.31/0.47 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ Sys2 @ ( proces1454156180ss_ACT @ B @ A @ A3 @ T3 ) ) )
% 0.31/0.47 => ~ ! [A3: A > ( proces554692349s_term @ B @ A ),V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] :
% 0.31/0.47 ( X7
% 0.31/0.47 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ A3 @ ( proces89589571ess_CH @ B @ A @ V @ Va ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % CONT.cases
% 0.31/0.47 thf(fact_61_PREF_Ocases,axiom,
% 0.31/0.47 ! [C: $tType,A: $tType,B: $tType,X7: product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A )] :
% 0.31/0.47 ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),X3: A] :
% 0.31/0.47 ( X7
% 0.31/0.47 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ Sys2 @ ( proces1627516585ss_VAR @ A @ B @ X3 ) ) )
% 0.31/0.47 => ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),P4: proces634752977rocess @ B] :
% 0.31/0.47 ( X7
% 0.31/0.47 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ Sys2 @ ( proces1062592052s_PROC @ B @ A @ P4 ) ) )
% 0.31/0.47 => ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),A3: B,T3: proces554692349s_term @ B @ A] :
% 0.31/0.47 ( X7
% 0.31/0.47 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ Sys2 @ ( proces1454156180ss_ACT @ B @ A @ A3 @ T3 ) ) )
% 0.31/0.47 => ~ ! [A3: A > ( proces554692349s_term @ B @ C ),V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] :
% 0.31/0.47 ( X7
% 0.31/0.47 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ A3 @ ( proces89589571ess_CH @ B @ A @ V @ Va ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % PREF.cases
% 0.31/0.47 thf(fact_62_isACT_Ocases,axiom,
% 0.31/0.47 ! [B: $tType,C: $tType,A: $tType,D: $tType,X7: product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A )] :
% 0.31/0.47 ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),X3: A] :
% 0.31/0.47 ( X7
% 0.31/0.47 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ Sys2 @ ( proces1627516585ss_VAR @ A @ D @ X3 ) ) )
% 0.31/0.47 => ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),P4: proces634752977rocess @ D] :
% 0.31/0.47 ( X7
% 0.31/0.47 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ Sys2 @ ( proces1062592052s_PROC @ D @ A @ P4 ) ) )
% 0.31/0.47 => ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),A3: D,T3: proces554692349s_term @ D @ A] :
% 0.31/0.47 ( X7
% 0.31/0.47 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ Sys2 @ ( proces1454156180ss_ACT @ D @ A @ A3 @ T3 ) ) )
% 0.31/0.47 => ~ ! [Sys2: A > ( proces554692349s_term @ B @ C ),T12: proces554692349s_term @ D @ A,T23: proces554692349s_term @ D @ A] :
% 0.31/0.47 ( X7
% 0.31/0.47 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ Sys2 @ ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % isACT.cases
% 0.31/0.47 thf(fact_63_process_Oinject_I1_J,axiom,
% 0.31/0.47 ! [A: $tType,X11: A,X122: proces634752977rocess @ A,Y11: A,Y12: proces634752977rocess @ A] :
% 0.31/0.47 ( ( ( proces1525233512Action @ A @ X11 @ X122 )
% 0.31/0.47 = ( proces1525233512Action @ A @ Y11 @ Y12 ) )
% 0.31/0.47 = ( ( X11 = Y11 )
% 0.31/0.47 & ( X122 = Y12 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % process.inject(1)
% 0.31/0.47 thf(fact_64_process_Oinject_I2_J,axiom,
% 0.31/0.47 ! [A: $tType,X21: proces634752977rocess @ A,X222: proces634752977rocess @ A,Y21: proces634752977rocess @ A,Y22: proces634752977rocess @ A] :
% 0.31/0.47 ( ( ( proces1915862579Choice @ A @ X21 @ X222 )
% 0.31/0.47 = ( proces1915862579Choice @ A @ Y21 @ Y22 ) )
% 0.31/0.47 = ( ( X21 = Y21 )
% 0.31/0.47 & ( X222 = Y22 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % process.inject(2)
% 0.31/0.47 thf(fact_65_process_Opred__inject_I1_J,axiom,
% 0.31/0.47 ! [A: $tType,P3: A > $o,A2: A,Aa2: proces634752977rocess @ A] :
% 0.31/0.47 ( ( proces1205983068rocess @ A @ P3 @ ( proces1525233512Action @ A @ A2 @ Aa2 ) )
% 0.31/0.47 = ( ( P3 @ A2 )
% 0.31/0.47 & ( proces1205983068rocess @ A @ P3 @ Aa2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % process.pred_inject(1)
% 0.31/0.47 thf(fact_66_process_Opred__inject_I2_J,axiom,
% 0.31/0.47 ! [A: $tType,P3: A > $o,A2: proces634752977rocess @ A,Aa2: proces634752977rocess @ A] :
% 0.31/0.47 ( ( proces1205983068rocess @ A @ P3 @ ( proces1915862579Choice @ A @ A2 @ Aa2 ) )
% 0.31/0.47 = ( ( proces1205983068rocess @ A @ P3 @ A2 )
% 0.31/0.47 & ( proces1205983068rocess @ A @ P3 @ Aa2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % process.pred_inject(2)
% 0.31/0.47 thf(fact_67_solution_Odisc__iff_I1_J,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 0.31/0.47 ( ( proces10484146Action @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) )
% 0.31/0.47 = ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % solution.disc_iff(1)
% 0.31/0.47 thf(fact_68_process_Ocollapse_I1_J,axiom,
% 0.31/0.47 ! [A: $tType,Process: proces634752977rocess @ A] :
% 0.31/0.47 ( ( proces10484146Action @ A @ Process )
% 0.31/0.47 => ( ( proces1525233512Action @ A @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) )
% 0.31/0.47 = Process ) ) ).
% 0.31/0.47
% 0.31/0.47 % process.collapse(1)
% 0.31/0.47 thf(fact_69_process__coind,axiom,
% 0.31/0.47 ! [A: $tType,Phi: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > $o,P: proces634752977rocess @ A,P5: proces634752977rocess @ A] :
% 0.31/0.47 ( ( Phi @ P @ P5 )
% 0.31/0.47 => ( ! [P4: proces634752977rocess @ A,P6: proces634752977rocess @ A] :
% 0.31/0.47 ( ( Phi @ P4 @ P6 )
% 0.31/0.47 => ( ( ( proces10484146Action @ A @ P4 )
% 0.31/0.47 = ( proces10484146Action @ A @ P6 ) )
% 0.31/0.47 & ( ( proces401113213Choice @ A @ P4 )
% 0.31/0.47 = ( proces401113213Choice @ A @ P6 ) ) ) )
% 0.31/0.47 => ( ! [A3: A,A5: A,P4: proces634752977rocess @ A,P6: proces634752977rocess @ A] :
% 0.31/0.47 ( ( Phi @ ( proces1525233512Action @ A @ A3 @ P4 ) @ ( proces1525233512Action @ A @ A5 @ P6 ) )
% 0.31/0.47 => ( ( A3 = A5 )
% 0.31/0.47 & ( Phi @ P4 @ P6 ) ) )
% 0.31/0.47 => ( ! [P4: proces634752977rocess @ A,Q3: proces634752977rocess @ A,P6: proces634752977rocess @ A,Q4: proces634752977rocess @ A] :
% 0.31/0.47 ( ( Phi @ ( proces1915862579Choice @ A @ P4 @ Q3 ) @ ( proces1915862579Choice @ A @ P6 @ Q4 ) )
% 0.31/0.47 => ( ( Phi @ P4 @ P6 )
% 0.31/0.47 & ( Phi @ Q3 @ Q4 ) ) )
% 0.31/0.47 => ( P = P5 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_coind
% 0.31/0.47 thf(fact_70_process__strong__coind,axiom,
% 0.31/0.47 ! [A: $tType,Phi: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > $o,P: proces634752977rocess @ A,P5: proces634752977rocess @ A] :
% 0.31/0.47 ( ( Phi @ P @ P5 )
% 0.31/0.47 => ( ! [P4: proces634752977rocess @ A,P6: proces634752977rocess @ A] :
% 0.31/0.47 ( ( Phi @ P4 @ P6 )
% 0.31/0.47 => ( ( ( proces10484146Action @ A @ P4 )
% 0.31/0.47 = ( proces10484146Action @ A @ P6 ) )
% 0.31/0.47 & ( ( proces401113213Choice @ A @ P4 )
% 0.31/0.47 = ( proces401113213Choice @ A @ P6 ) ) ) )
% 0.31/0.47 => ( ! [A3: A,A5: A,P4: proces634752977rocess @ A,P6: proces634752977rocess @ A] :
% 0.31/0.47 ( ( Phi @ ( proces1525233512Action @ A @ A3 @ P4 ) @ ( proces1525233512Action @ A @ A5 @ P6 ) )
% 0.31/0.47 => ( ( A3 = A5 )
% 0.31/0.47 & ( ( Phi @ P4 @ P6 )
% 0.31/0.47 | ( P4 = P6 ) ) ) )
% 0.31/0.47 => ( ! [P4: proces634752977rocess @ A,Q3: proces634752977rocess @ A,P6: proces634752977rocess @ A,Q4: proces634752977rocess @ A] :
% 0.31/0.47 ( ( Phi @ ( proces1915862579Choice @ A @ P4 @ Q3 ) @ ( proces1915862579Choice @ A @ P6 @ Q4 ) )
% 0.31/0.47 => ( ( ( Phi @ P4 @ P6 )
% 0.31/0.47 | ( P4 = P6 ) )
% 0.31/0.47 & ( ( Phi @ Q3 @ Q4 )
% 0.31/0.47 | ( Q3 = Q4 ) ) ) )
% 0.31/0.47 => ( P = P5 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_strong_coind
% 0.31/0.47 thf(fact_71_isAction__def,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( proces10484146Action @ A )
% 0.31/0.47 = ( ^ [Process5: proces634752977rocess @ A] :
% 0.31/0.47 ? [X112: A,X123: proces634752977rocess @ A] :
% 0.31/0.47 ( Process5
% 0.31/0.47 = ( proces1525233512Action @ A @ X112 @ X123 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % isAction_def
% 0.31/0.47 thf(fact_72_process_Oexhaust,axiom,
% 0.31/0.47 ! [A: $tType,Y3: proces634752977rocess @ A] :
% 0.31/0.47 ( ! [X113: A,X124: proces634752977rocess @ A] :
% 0.31/0.47 ( Y3
% 0.31/0.47 != ( proces1525233512Action @ A @ X113 @ X124 ) )
% 0.31/0.47 => ~ ! [X212: proces634752977rocess @ A,X223: proces634752977rocess @ A] :
% 0.31/0.47 ( Y3
% 0.31/0.47 != ( proces1915862579Choice @ A @ X212 @ X223 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % process.exhaust
% 0.31/0.47 thf(fact_73_process_Odistinct_I1_J,axiom,
% 0.31/0.47 ! [A: $tType,X11: A,X122: proces634752977rocess @ A,X21: proces634752977rocess @ A,X222: proces634752977rocess @ A] :
% 0.31/0.47 ( ( proces1525233512Action @ A @ X11 @ X122 )
% 0.31/0.47 != ( proces1915862579Choice @ A @ X21 @ X222 ) ) ).
% 0.31/0.47
% 0.31/0.47 % process.distinct(1)
% 0.31/0.47 thf(fact_74_process_OdiscI_I1_J,axiom,
% 0.31/0.47 ! [A: $tType,Process: proces634752977rocess @ A,X11: A,X122: proces634752977rocess @ A] :
% 0.31/0.47 ( ( Process
% 0.31/0.47 = ( proces1525233512Action @ A @ X11 @ X122 ) )
% 0.31/0.47 => ( proces10484146Action @ A @ Process ) ) ).
% 0.31/0.47
% 0.31/0.47 % process.discI(1)
% 0.31/0.47 thf(fact_75_process_Odisc_I1_J,axiom,
% 0.31/0.47 ! [A: $tType,X11: A,X122: proces634752977rocess @ A] : ( proces10484146Action @ A @ ( proces1525233512Action @ A @ X11 @ X122 ) ) ).
% 0.31/0.47
% 0.31/0.47 % process.disc(1)
% 0.31/0.47 thf(fact_76_process_Odisc_I2_J,axiom,
% 0.31/0.47 ! [A: $tType,X21: proces634752977rocess @ A,X222: proces634752977rocess @ A] :
% 0.31/0.47 ~ ( proces10484146Action @ A @ ( proces1915862579Choice @ A @ X21 @ X222 ) ) ).
% 0.31/0.47
% 0.31/0.47 % process.disc(2)
% 0.31/0.47 thf(fact_77_not__isAction__isChoice,axiom,
% 0.31/0.47 ! [A: $tType,P: proces634752977rocess @ A] :
% 0.31/0.47 ~ ( ( proces10484146Action @ A @ P )
% 0.31/0.47 & ( proces401113213Choice @ A @ P ) ) ).
% 0.31/0.47
% 0.31/0.47 % not_isAction_isChoice
% 0.31/0.47 thf(fact_78_process_Oexhaust__disc,axiom,
% 0.31/0.47 ! [A: $tType,Process: proces634752977rocess @ A] :
% 0.31/0.47 ( ~ ( proces10484146Action @ A @ Process )
% 0.31/0.47 => ( proces401113213Choice @ A @ Process ) ) ).
% 0.31/0.47
% 0.31/0.47 % process.exhaust_disc
% 0.31/0.47 thf(fact_79_isAction__isChoice,axiom,
% 0.31/0.47 ! [A: $tType,P: proces634752977rocess @ A] :
% 0.31/0.47 ( ( proces10484146Action @ A @ P )
% 0.31/0.47 | ( proces401113213Choice @ A @ P ) ) ).
% 0.31/0.47
% 0.31/0.47 % isAction_isChoice
% 0.31/0.47 thf(fact_80_process_Odistinct__disc_I1_J,axiom,
% 0.31/0.47 ! [A: $tType,Process: proces634752977rocess @ A] :
% 0.31/0.47 ( ( proces10484146Action @ A @ Process )
% 0.31/0.47 => ~ ( proces401113213Choice @ A @ Process ) ) ).
% 0.31/0.47
% 0.31/0.47 % process.distinct_disc(1)
% 0.31/0.47 thf(fact_81_process_Odistinct__disc_I2_J,axiom,
% 0.31/0.47 ! [A: $tType,Process: proces634752977rocess @ A] :
% 0.31/0.47 ( ( proces401113213Choice @ A @ Process )
% 0.31/0.47 => ~ ( proces10484146Action @ A @ Process ) ) ).
% 0.31/0.47
% 0.31/0.47 % process.distinct_disc(2)
% 0.31/0.47 thf(fact_82_isChoice__def,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( proces401113213Choice @ A )
% 0.31/0.47 = ( ^ [Process5: proces634752977rocess @ A] :
% 0.31/0.47 ? [X213: proces634752977rocess @ A,X224: proces634752977rocess @ A] :
% 0.31/0.47 ( Process5
% 0.31/0.47 = ( proces1915862579Choice @ A @ X213 @ X224 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % isChoice_def
% 0.31/0.47 thf(fact_83_process_OdiscI_I2_J,axiom,
% 0.31/0.47 ! [A: $tType,Process: proces634752977rocess @ A,X21: proces634752977rocess @ A,X222: proces634752977rocess @ A] :
% 0.31/0.47 ( ( Process
% 0.31/0.47 = ( proces1915862579Choice @ A @ X21 @ X222 ) )
% 0.31/0.47 => ( proces401113213Choice @ A @ Process ) ) ).
% 0.31/0.47
% 0.31/0.47 % process.discI(2)
% 0.31/0.47 thf(fact_84_process_Odisc_I3_J,axiom,
% 0.31/0.47 ! [A: $tType,X11: A,X122: proces634752977rocess @ A] :
% 0.31/0.47 ~ ( proces401113213Choice @ A @ ( proces1525233512Action @ A @ X11 @ X122 ) ) ).
% 0.31/0.47
% 0.31/0.47 % process.disc(3)
% 0.31/0.47 thf(fact_85_process_Odisc_I4_J,axiom,
% 0.31/0.47 ! [A: $tType,X21: proces634752977rocess @ A,X222: proces634752977rocess @ A] : ( proces401113213Choice @ A @ ( proces1915862579Choice @ A @ X21 @ X222 ) ) ).
% 0.31/0.47
% 0.31/0.47 % process.disc(4)
% 0.31/0.47 thf(fact_86_process_Osel_I2_J,axiom,
% 0.31/0.47 ! [A: $tType,X11: A,X122: proces634752977rocess @ A] :
% 0.31/0.47 ( ( proces1778668539contOf @ A @ ( proces1525233512Action @ A @ X11 @ X122 ) )
% 0.31/0.47 = X122 ) ).
% 0.31/0.47
% 0.31/0.47 % process.sel(2)
% 0.31/0.47 thf(fact_87_process_Osel_I3_J,axiom,
% 0.31/0.47 ! [A: $tType,X21: proces634752977rocess @ A,X222: proces634752977rocess @ A] :
% 0.31/0.47 ( ( proces979765041_ch1Of @ A @ ( proces1915862579Choice @ A @ X21 @ X222 ) )
% 0.31/0.47 = X21 ) ).
% 0.31/0.47
% 0.31/0.47 % process.sel(3)
% 0.31/0.47 thf(fact_88_process_Osel_I4_J,axiom,
% 0.31/0.47 ! [A: $tType,X21: proces634752977rocess @ A,X222: proces634752977rocess @ A] :
% 0.31/0.47 ( ( proces988026546_ch2Of @ A @ ( proces1915862579Choice @ A @ X21 @ X222 ) )
% 0.31/0.47 = X222 ) ).
% 0.31/0.47
% 0.31/0.47 % process.sel(4)
% 0.31/0.47 thf(fact_89_process_Osel_I1_J,axiom,
% 0.31/0.47 ! [A: $tType,X11: A,X122: proces634752977rocess @ A] :
% 0.31/0.47 ( ( proces745025900prefOf @ A @ ( proces1525233512Action @ A @ X11 @ X122 ) )
% 0.31/0.47 = X11 ) ).
% 0.31/0.47
% 0.31/0.47 % process.sel(1)
% 0.31/0.47 thf(fact_90_isACT_Osimps_I2_J,axiom,
% 0.31/0.47 ! [A: $tType,C: $tType,B: $tType,D: $tType,Sys: A > ( proces554692349s_term @ B @ C ),P: proces634752977rocess @ D] :
% 0.31/0.47 ( ( proces687458811_isACT @ A @ B @ C @ D @ Sys @ ( proces1062592052s_PROC @ D @ A @ P ) )
% 0.31/0.47 = ( proces10484146Action @ D @ P ) ) ).
% 0.31/0.47
% 0.31/0.47 % isACT.simps(2)
% 0.31/0.47 thf(fact_91_process_Oexhaust__sel,axiom,
% 0.31/0.47 ! [A: $tType,Process: proces634752977rocess @ A] :
% 0.31/0.47 ( ( Process
% 0.31/0.47 != ( proces1525233512Action @ A @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) ) )
% 0.31/0.47 => ( Process
% 0.31/0.47 = ( proces1915862579Choice @ A @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % process.exhaust_sel
% 0.31/0.47 thf(fact_92_solution_Odisc_I1_J,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 0.31/0.47 ( ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
% 0.31/0.47 => ( proces10484146Action @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % solution.disc(1)
% 0.31/0.47 thf(fact_93_process_Osplit__sel__asm,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType,P3: B > $o,F1: A > ( proces634752977rocess @ A ) > B,F2: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B,Process: proces634752977rocess @ A] :
% 0.31/0.47 ( ( P3 @ ( proces1406508781rocess @ A @ B @ F1 @ F2 @ Process ) )
% 0.31/0.47 = ( ~ ( ( ( Process
% 0.31/0.47 = ( proces1525233512Action @ A @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) ) )
% 0.31/0.47 & ~ ( P3 @ ( F1 @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) ) ) )
% 0.31/0.47 | ( ( Process
% 0.31/0.47 = ( proces1915862579Choice @ A @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) ) )
% 0.31/0.47 & ~ ( P3 @ ( F2 @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % process.split_sel_asm
% 0.31/0.47 thf(fact_94_process_Osplit__sel,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType,P3: B > $o,F1: A > ( proces634752977rocess @ A ) > B,F2: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B,Process: proces634752977rocess @ A] :
% 0.31/0.47 ( ( P3 @ ( proces1406508781rocess @ A @ B @ F1 @ F2 @ Process ) )
% 0.31/0.47 = ( ( ( Process
% 0.31/0.47 = ( proces1525233512Action @ A @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) ) )
% 0.31/0.47 => ( P3 @ ( F1 @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) ) ) )
% 0.31/0.47 & ( ( Process
% 0.31/0.47 = ( proces1915862579Choice @ A @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) ) )
% 0.31/0.47 => ( P3 @ ( F2 @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % process.split_sel
% 0.31/0.47 thf(fact_95_process_Ocase__eq__if,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType] :
% 0.31/0.47 ( ( proces1406508781rocess @ A @ B )
% 0.31/0.47 = ( ^ [F12: A > ( proces634752977rocess @ A ) > B,F22: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B,Process5: proces634752977rocess @ A] : ( if @ B @ ( proces10484146Action @ A @ Process5 ) @ ( F12 @ ( proces745025900prefOf @ A @ Process5 ) @ ( proces1778668539contOf @ A @ Process5 ) ) @ ( F22 @ ( proces979765041_ch1Of @ A @ Process5 ) @ ( proces988026546_ch2Of @ A @ Process5 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % process.case_eq_if
% 0.31/0.47 thf(fact_96_old_Oprod_Oinject,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType,A2: A,B2: B,A6: A,B3: B] :
% 0.31/0.47 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 0.31/0.47 = ( product_Pair @ A @ B @ A6 @ B3 ) )
% 0.31/0.47 = ( ( A2 = A6 )
% 0.31/0.47 & ( B2 = B3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % old.prod.inject
% 0.31/0.47 thf(fact_97_prod_Oinject,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType,X1: A,X2: B,Y1: A,Y2: B] :
% 0.31/0.47 ( ( ( product_Pair @ A @ B @ X1 @ X2 )
% 0.31/0.47 = ( product_Pair @ A @ B @ Y1 @ Y2 ) )
% 0.31/0.47 = ( ( X1 = Y1 )
% 0.31/0.47 & ( X2 = Y2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % prod.inject
% 0.31/0.47 thf(fact_98_process_Orel__coinduct,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType,P3: ( proces634752977rocess @ A ) > ( proces634752977rocess @ B ) > $o,X7: proces634752977rocess @ A,Y3: proces634752977rocess @ B,R: A > B > $o] :
% 0.31/0.47 ( ( P3 @ X7 @ Y3 )
% 0.31/0.47 => ( ! [Process3: proces634752977rocess @ A,Process4: proces634752977rocess @ B] :
% 0.31/0.47 ( ( P3 @ Process3 @ Process4 )
% 0.31/0.47 => ( ( ( proces10484146Action @ A @ Process3 )
% 0.31/0.47 = ( proces10484146Action @ B @ Process4 ) )
% 0.31/0.47 & ( ( proces10484146Action @ A @ Process3 )
% 0.31/0.47 => ( ( proces10484146Action @ B @ Process4 )
% 0.31/0.47 => ( ( R @ ( proces745025900prefOf @ A @ Process3 ) @ ( proces745025900prefOf @ B @ Process4 ) )
% 0.31/0.47 & ( P3 @ ( proces1778668539contOf @ A @ Process3 ) @ ( proces1778668539contOf @ B @ Process4 ) ) ) ) )
% 0.31/0.47 & ( ( proces401113213Choice @ A @ Process3 )
% 0.31/0.47 => ( ( proces401113213Choice @ B @ Process4 )
% 0.31/0.47 => ( ( P3 @ ( proces979765041_ch1Of @ A @ Process3 ) @ ( proces979765041_ch1Of @ B @ Process4 ) )
% 0.31/0.47 & ( P3 @ ( proces988026546_ch2Of @ A @ Process3 ) @ ( proces988026546_ch2Of @ B @ Process4 ) ) ) ) ) ) )
% 0.31/0.47 => ( proces749077512rocess @ A @ B @ R @ X7 @ Y3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % process.rel_coinduct
% 0.31/0.47 thf(fact_99_process_Orel__sel,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType] :
% 0.31/0.47 ( ( proces749077512rocess @ A @ B )
% 0.31/0.47 = ( ^ [R2: A > B > $o,A7: proces634752977rocess @ A,B4: proces634752977rocess @ B] :
% 0.31/0.47 ( ( ( proces10484146Action @ A @ A7 )
% 0.31/0.47 = ( proces10484146Action @ B @ B4 ) )
% 0.31/0.47 & ( ( proces10484146Action @ A @ A7 )
% 0.31/0.47 => ( ( proces10484146Action @ B @ B4 )
% 0.31/0.47 => ( ( R2 @ ( proces745025900prefOf @ A @ A7 ) @ ( proces745025900prefOf @ B @ B4 ) )
% 0.31/0.47 & ( proces749077512rocess @ A @ B @ R2 @ ( proces1778668539contOf @ A @ A7 ) @ ( proces1778668539contOf @ B @ B4 ) ) ) ) )
% 0.31/0.47 & ( ( proces401113213Choice @ A @ A7 )
% 0.31/0.47 => ( ( proces401113213Choice @ B @ B4 )
% 0.31/0.47 => ( ( proces749077512rocess @ A @ B @ R2 @ ( proces979765041_ch1Of @ A @ A7 ) @ ( proces979765041_ch1Of @ B @ B4 ) )
% 0.31/0.47 & ( proces749077512rocess @ A @ B @ R2 @ ( proces988026546_ch2Of @ A @ A7 ) @ ( proces988026546_ch2Of @ B @ B4 ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % process.rel_sel
% 0.31/0.47 thf(fact_100_process_Orel__inject_I1_J,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType,R: A > B > $o,X11: A,X122: proces634752977rocess @ A,Y11: B,Y12: proces634752977rocess @ B] :
% 0.31/0.47 ( ( proces749077512rocess @ A @ B @ R @ ( proces1525233512Action @ A @ X11 @ X122 ) @ ( proces1525233512Action @ B @ Y11 @ Y12 ) )
% 0.31/0.47 = ( ( R @ X11 @ Y11 )
% 0.31/0.47 & ( proces749077512rocess @ A @ B @ R @ X122 @ Y12 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % process.rel_inject(1)
% 0.31/0.47 thf(fact_101_process_Orel__inject_I2_J,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType,R: A > B > $o,X21: proces634752977rocess @ A,X222: proces634752977rocess @ A,Y21: proces634752977rocess @ B,Y22: proces634752977rocess @ B] :
% 0.31/0.47 ( ( proces749077512rocess @ A @ B @ R @ ( proces1915862579Choice @ A @ X21 @ X222 ) @ ( proces1915862579Choice @ B @ Y21 @ Y22 ) )
% 0.31/0.47 = ( ( proces749077512rocess @ A @ B @ R @ X21 @ Y21 )
% 0.31/0.47 & ( proces749077512rocess @ A @ B @ R @ X222 @ Y22 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % process.rel_inject(2)
% 0.31/0.47 thf(fact_102_process_Orel__eq,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( proces749077512rocess @ A @ A
% 0.31/0.47 @ ^ [Y4: A,Z: A] : ( Y4 = Z ) )
% 0.31/0.47 = ( ^ [Y4: proces634752977rocess @ A,Z: proces634752977rocess @ A] : ( Y4 = Z ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % process.rel_eq
% 0.31/0.47 thf(fact_103_process_Orel__refl,axiom,
% 0.31/0.47 ! [B: $tType,Ra: B > B > $o,X7: proces634752977rocess @ B] :
% 0.31/0.47 ( ! [X5: B] : ( Ra @ X5 @ X5 )
% 0.31/0.47 => ( proces749077512rocess @ B @ B @ Ra @ X7 @ X7 ) ) ).
% 0.31/0.47
% 0.31/0.47 % process.rel_refl
% 0.31/0.47 thf(fact_104_process_Orel__intros_I1_J,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType,R: A > B > $o,X11: A,Y11: B,X122: proces634752977rocess @ A,Y12: proces634752977rocess @ B] :
% 0.31/0.47 ( ( R @ X11 @ Y11 )
% 0.31/0.47 => ( ( proces749077512rocess @ A @ B @ R @ X122 @ Y12 )
% 0.31/0.47 => ( proces749077512rocess @ A @ B @ R @ ( proces1525233512Action @ A @ X11 @ X122 ) @ ( proces1525233512Action @ B @ Y11 @ Y12 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % process.rel_intros(1)
% 0.31/0.47 thf(fact_105_process_Orel__intros_I2_J,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType,R: A > B > $o,X21: proces634752977rocess @ A,Y21: proces634752977rocess @ B,X222: proces634752977rocess @ A,Y22: proces634752977rocess @ B] :
% 0.31/0.47 ( ( proces749077512rocess @ A @ B @ R @ X21 @ Y21 )
% 0.31/0.47 => ( ( proces749077512rocess @ A @ B @ R @ X222 @ Y22 )
% 0.31/0.47 => ( proces749077512rocess @ A @ B @ R @ ( proces1915862579Choice @ A @ X21 @ X222 ) @ ( proces1915862579Choice @ B @ Y21 @ Y22 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % process.rel_intros(2)
% 0.31/0.47 thf(fact_106_process_Orel__distinct_I2_J,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType,R: A > B > $o,Y21: proces634752977rocess @ A,Y22: proces634752977rocess @ A,X11: B,X122: proces634752977rocess @ B] :
% 0.31/0.47 ~ ( proces749077512rocess @ A @ B @ R @ ( proces1915862579Choice @ A @ Y21 @ Y22 ) @ ( proces1525233512Action @ B @ X11 @ X122 ) ) ).
% 0.31/0.47
% 0.31/0.47 % process.rel_distinct(2)
% 0.31/0.47 thf(fact_107_process_Orel__distinct_I1_J,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType,R: A > B > $o,X11: A,X122: proces634752977rocess @ A,Y21: proces634752977rocess @ B,Y22: proces634752977rocess @ B] :
% 0.31/0.47 ~ ( proces749077512rocess @ A @ B @ R @ ( proces1525233512Action @ A @ X11 @ X122 ) @ ( proces1915862579Choice @ B @ Y21 @ Y22 ) ) ).
% 0.31/0.47
% 0.31/0.47 % process.rel_distinct(1)
% 0.31/0.47 thf(fact_108_process_Orel__cases,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType,R: A > B > $o,A2: proces634752977rocess @ A,B2: proces634752977rocess @ B] :
% 0.31/0.47 ( ( proces749077512rocess @ A @ B @ R @ A2 @ B2 )
% 0.31/0.47 => ( ! [X12: A,X22: proces634752977rocess @ A] :
% 0.31/0.47 ( ( A2
% 0.31/0.47 = ( proces1525233512Action @ A @ X12 @ X22 ) )
% 0.31/0.47 => ! [Y13: B,Y23: proces634752977rocess @ B] :
% 0.31/0.47 ( ( B2
% 0.31/0.47 = ( proces1525233512Action @ B @ Y13 @ Y23 ) )
% 0.31/0.47 => ( ( R @ X12 @ Y13 )
% 0.31/0.47 => ~ ( proces749077512rocess @ A @ B @ R @ X22 @ Y23 ) ) ) )
% 0.31/0.47 => ~ ! [X1a: proces634752977rocess @ A,X2a: proces634752977rocess @ A] :
% 0.31/0.47 ( ( A2
% 0.31/0.47 = ( proces1915862579Choice @ A @ X1a @ X2a ) )
% 0.31/0.47 => ! [Y1a: proces634752977rocess @ B,Y2a: proces634752977rocess @ B] :
% 0.31/0.47 ( ( B2
% 0.31/0.47 = ( proces1915862579Choice @ B @ Y1a @ Y2a ) )
% 0.31/0.47 => ( ( proces749077512rocess @ A @ B @ R @ X1a @ Y1a )
% 0.31/0.47 => ~ ( proces749077512rocess @ A @ B @ R @ X2a @ Y2a ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % process.rel_cases
% 0.31/0.47 thf(fact_109_process_Osimps_I5_J,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType,F1: A > ( proces634752977rocess @ A ) > B,F2: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B,X11: A,X122: proces634752977rocess @ A] :
% 0.31/0.47 ( ( proces1406508781rocess @ A @ B @ F1 @ F2 @ ( proces1525233512Action @ A @ X11 @ X122 ) )
% 0.31/0.47 = ( F1 @ X11 @ X122 ) ) ).
% 0.31/0.47
% 0.31/0.47 % process.simps(5)
% 0.31/0.47 thf(fact_110_process_Osimps_I6_J,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType,F1: A > ( proces634752977rocess @ A ) > B,F2: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B,X21: proces634752977rocess @ A,X222: proces634752977rocess @ A] :
% 0.31/0.47 ( ( proces1406508781rocess @ A @ B @ F1 @ F2 @ ( proces1915862579Choice @ A @ X21 @ X222 ) )
% 0.31/0.47 = ( F2 @ X21 @ X222 ) ) ).
% 0.31/0.47
% 0.31/0.47 % process.simps(6)
% 0.31/0.47 thf(fact_111_surj__pair,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType,P: product_prod @ A @ B] :
% 0.31/0.47 ? [X5: A,Y5: B] :
% 0.31/0.47 ( P
% 0.31/0.47 = ( product_Pair @ A @ B @ X5 @ Y5 ) ) ).
% 0.31/0.47
% 0.31/0.47 % surj_pair
% 0.31/0.47 thf(fact_112_prod__cases,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType,P3: ( product_prod @ A @ B ) > $o,P: product_prod @ A @ B] :
% 0.31/0.47 ( ! [A3: A,B5: B] : ( P3 @ ( product_Pair @ A @ B @ A3 @ B5 ) )
% 0.31/0.47 => ( P3 @ P ) ) ).
% 0.31/0.47
% 0.31/0.47 % prod_cases
% 0.31/0.47 thf(fact_113_Pair__inject,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType,A2: A,B2: B,A6: A,B3: B] :
% 0.31/0.47 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 0.31/0.47 = ( product_Pair @ A @ B @ A6 @ B3 ) )
% 0.31/0.47 => ~ ( ( A2 = A6 )
% 0.31/0.47 => ( B2 != B3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Pair_inject
% 0.31/0.47 thf(fact_114_prod__cases3,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType,C: $tType,Y3: product_prod @ A @ ( product_prod @ B @ C )] :
% 0.31/0.47 ~ ! [A3: A,B5: B,C2: C] :
% 0.31/0.47 ( Y3
% 0.31/0.47 != ( product_Pair @ A @ ( product_prod @ B @ C ) @ A3 @ ( product_Pair @ B @ C @ B5 @ C2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % prod_cases3
% 0.31/0.47 thf(fact_115_prod__cases4,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType,C: $tType,D: $tType,Y3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 0.31/0.47 ~ ! [A3: A,B5: B,C2: C,D2: D] :
% 0.31/0.47 ( Y3
% 0.31/0.47 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B5 @ ( product_Pair @ C @ D @ C2 @ D2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % prod_cases4
% 0.31/0.47 thf(fact_116_prod__cases5,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,Y3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) )] :
% 0.31/0.47 ~ ! [A3: A,B5: B,C2: C,D2: D,E2: E] :
% 0.31/0.47 ( Y3
% 0.31/0.47 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D @ E ) @ C2 @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % prod_cases5
% 0.31/0.47 thf(fact_117_prod__cases6,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,F5: $tType,Y3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F5 ) ) ) )] :
% 0.31/0.47 ~ ! [A3: A,B5: B,C2: C,D2: D,E2: E,F6: F5] :
% 0.31/0.47 ( Y3
% 0.31/0.47 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F5 ) ) ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F5 ) ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ F5 ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E @ F5 ) @ D2 @ ( product_Pair @ E @ F5 @ E2 @ F6 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % prod_cases6
% 0.31/0.47 thf(fact_118_prod__cases7,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,F5: $tType,G2: $tType,Y3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G2 ) ) ) ) )] :
% 0.31/0.47 ~ ! [A3: A,B5: B,C2: C,D2: D,E2: E,F6: F5,G3: G2] :
% 0.31/0.47 ( Y3
% 0.31/0.47 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G2 ) ) ) ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G2 ) ) ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G2 ) ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G2 ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F5 @ G2 ) @ E2 @ ( product_Pair @ F5 @ G2 @ F6 @ G3 ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % prod_cases7
% 0.31/0.47 thf(fact_119_prod__induct3,axiom,
% 0.31/0.47 ! [C: $tType,B: $tType,A: $tType,P3: ( product_prod @ A @ ( product_prod @ B @ C ) ) > $o,X7: product_prod @ A @ ( product_prod @ B @ C )] :
% 0.31/0.47 ( ! [A3: A,B5: B,C2: C] : ( P3 @ ( product_Pair @ A @ ( product_prod @ B @ C ) @ A3 @ ( product_Pair @ B @ C @ B5 @ C2 ) ) )
% 0.31/0.47 => ( P3 @ X7 ) ) ).
% 0.31/0.47
% 0.31/0.47 % prod_induct3
% 0.31/0.47 thf(fact_120_prod__induct4,axiom,
% 0.31/0.47 ! [D: $tType,C: $tType,B: $tType,A: $tType,P3: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) ) > $o,X7: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 0.31/0.47 ( ! [A3: A,B5: B,C2: C,D2: D] : ( P3 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B5 @ ( product_Pair @ C @ D @ C2 @ D2 ) ) ) )
% 0.31/0.47 => ( P3 @ X7 ) ) ).
% 0.31/0.47
% 0.31/0.47 % prod_induct4
% 0.31/0.47 thf(fact_121_prod__induct5,axiom,
% 0.31/0.47 ! [E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P3: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) ) > $o,X7: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) )] :
% 0.31/0.47 ( ! [A3: A,B5: B,C2: C,D2: D,E2: E] : ( P3 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D @ E ) @ C2 @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) )
% 0.31/0.47 => ( P3 @ X7 ) ) ).
% 0.31/0.47
% 0.31/0.47 % prod_induct5
% 0.31/0.47 thf(fact_122_prod__induct6,axiom,
% 0.31/0.47 ! [F5: $tType,E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P3: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F5 ) ) ) ) ) > $o,X7: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F5 ) ) ) )] :
% 0.31/0.47 ( ! [A3: A,B5: B,C2: C,D2: D,E2: E,F6: F5] : ( P3 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F5 ) ) ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F5 ) ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ F5 ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E @ F5 ) @ D2 @ ( product_Pair @ E @ F5 @ E2 @ F6 ) ) ) ) ) )
% 0.31/0.47 => ( P3 @ X7 ) ) ).
% 0.31/0.47
% 0.31/0.47 % prod_induct6
% 0.31/0.47 thf(fact_123_prod__induct7,axiom,
% 0.31/0.47 ! [G2: $tType,F5: $tType,E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P3: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G2 ) ) ) ) ) ) > $o,X7: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G2 ) ) ) ) )] :
% 0.31/0.47 ( ! [A3: A,B5: B,C2: C,D2: D,E2: E,F6: F5,G3: G2] : ( P3 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G2 ) ) ) ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G2 ) ) ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G2 ) ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G2 ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F5 @ G2 ) @ E2 @ ( product_Pair @ F5 @ G2 @ F6 @ G3 ) ) ) ) ) ) )
% 0.31/0.47 => ( P3 @ X7 ) ) ).
% 0.31/0.47
% 0.31/0.47 % prod_induct7
% 0.31/0.47 thf(fact_124_old_Oprod_Oexhaust,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType,Y3: product_prod @ A @ B] :
% 0.31/0.47 ~ ! [A3: A,B5: B] :
% 0.31/0.47 ( Y3
% 0.31/0.47 != ( product_Pair @ A @ B @ A3 @ B5 ) ) ).
% 0.31/0.47
% 0.31/0.47 % old.prod.exhaust
% 0.31/0.47 thf(fact_125_old_Oprod_Oinducts,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType,P3: ( product_prod @ A @ B ) > $o,Prod: product_prod @ A @ B] :
% 0.31/0.47 ( ! [A3: A,B5: B] : ( P3 @ ( product_Pair @ A @ B @ A3 @ B5 ) )
% 0.31/0.47 => ( P3 @ Prod ) ) ).
% 0.31/0.47
% 0.31/0.47 % old.prod.inducts
% 0.31/0.47 thf(fact_126_old_Oprod_Orec,axiom,
% 0.31/0.47 ! [A: $tType,T: $tType,B: $tType,F1: A > B > T,A2: A,B2: B] :
% 0.31/0.47 ( ( product_rec_prod @ A @ B @ T @ F1 @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 0.31/0.47 = ( F1 @ A2 @ B2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % old.prod.rec
% 0.31/0.47 thf(fact_127_process__term_Orel__cases,axiom,
% 0.31/0.47 ! [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] :
% 0.31/0.47 ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ A2 @ B2 )
% 0.31/0.47 => ( ! [X5: Pvar] :
% 0.31/0.47 ( ( A2
% 0.31/0.47 = ( proces1627516585ss_VAR @ Pvar @ A @ X5 ) )
% 0.31/0.47 => ! [Y5: C] :
% 0.31/0.47 ( ( B2
% 0.31/0.47 = ( proces1627516585ss_VAR @ C @ B @ Y5 ) )
% 0.31/0.47 => ~ ( R22 @ X5 @ Y5 ) ) )
% 0.31/0.47 => ( ! [Xa: proces634752977rocess @ A] :
% 0.31/0.47 ( ( A2
% 0.31/0.47 = ( proces1062592052s_PROC @ A @ Pvar @ Xa ) )
% 0.31/0.47 => ! [Ya: proces634752977rocess @ B] :
% 0.31/0.47 ( ( B2
% 0.31/0.47 = ( proces1062592052s_PROC @ B @ C @ Ya ) )
% 0.31/0.47 => ~ ( proces749077512rocess @ A @ B @ R1 @ Xa @ Ya ) ) )
% 0.31/0.47 => ( ! [X1a: A,X2a: proces554692349s_term @ A @ Pvar] :
% 0.31/0.47 ( ( A2
% 0.31/0.47 = ( proces1454156180ss_ACT @ A @ Pvar @ X1a @ X2a ) )
% 0.31/0.47 => ! [Y1a: B,Y2a: proces554692349s_term @ B @ C] :
% 0.31/0.47 ( ( B2
% 0.31/0.47 = ( proces1454156180ss_ACT @ B @ C @ Y1a @ Y2a ) )
% 0.31/0.47 => ( ( R1 @ X1a @ Y1a )
% 0.31/0.47 => ~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X2a @ Y2a ) ) ) )
% 0.31/0.47 => ~ ! [X1b: proces554692349s_term @ A @ Pvar,X2b: proces554692349s_term @ A @ Pvar] :
% 0.31/0.47 ( ( A2
% 0.31/0.47 = ( proces89589571ess_CH @ A @ Pvar @ X1b @ X2b ) )
% 0.31/0.47 => ! [Y1b: proces554692349s_term @ B @ C,Y2b: proces554692349s_term @ B @ C] :
% 0.31/0.47 ( ( B2
% 0.31/0.47 = ( proces89589571ess_CH @ B @ C @ Y1b @ Y2b ) )
% 0.31/0.47 => ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X1b @ Y1b )
% 0.31/0.47 => ~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X2b @ Y2b ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_term.rel_cases
% 0.31/0.47 thf(fact_128_process__term_Orel__induct,axiom,
% 0.31/0.47 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X7: proces554692349s_term @ A @ Pvar,Y3: proces554692349s_term @ B @ C,Q2: ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ B @ C ) > $o] :
% 0.31/0.47 ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X7 @ Y3 )
% 0.31/0.47 => ( ! [A12: Pvar,B1: C] :
% 0.31/0.47 ( ( R22 @ A12 @ B1 )
% 0.31/0.47 => ( Q2 @ ( proces1627516585ss_VAR @ Pvar @ A @ A12 ) @ ( proces1627516585ss_VAR @ C @ B @ B1 ) ) )
% 0.31/0.47 => ( ! [A22: proces634752977rocess @ A,B22: proces634752977rocess @ B] :
% 0.31/0.47 ( ( proces749077512rocess @ A @ B @ R1 @ A22 @ B22 )
% 0.31/0.47 => ( Q2 @ ( proces1062592052s_PROC @ A @ Pvar @ A22 ) @ ( proces1062592052s_PROC @ B @ C @ B22 ) ) )
% 0.31/0.47 => ( ! [A31: A,A32: proces554692349s_term @ A @ Pvar,B31: B,B32: proces554692349s_term @ B @ C] :
% 0.31/0.47 ( ( R1 @ A31 @ B31 )
% 0.31/0.47 => ( ( Q2 @ A32 @ B32 )
% 0.31/0.47 => ( Q2 @ ( proces1454156180ss_ACT @ A @ Pvar @ A31 @ A32 ) @ ( proces1454156180ss_ACT @ B @ C @ B31 @ B32 ) ) ) )
% 0.31/0.47 => ( ! [A41: proces554692349s_term @ A @ Pvar,A42: proces554692349s_term @ A @ Pvar,B41: proces554692349s_term @ B @ C,B42: proces554692349s_term @ B @ C] :
% 0.31/0.47 ( ( Q2 @ A41 @ B41 )
% 0.31/0.47 => ( ( Q2 @ A42 @ B42 )
% 0.31/0.47 => ( Q2 @ ( proces89589571ess_CH @ A @ Pvar @ A41 @ A42 ) @ ( proces89589571ess_CH @ B @ C @ B41 @ B42 ) ) ) )
% 0.31/0.47 => ( Q2 @ X7 @ Y3 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_term.rel_induct
% 0.31/0.47 thf(fact_129_internal__case__prod__conv,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType,C: $tType,C3: B > C > A,A2: B,B2: C] :
% 0.31/0.47 ( ( produc2004651681e_prod @ B @ C @ A @ C3 @ ( product_Pair @ B @ C @ A2 @ B2 ) )
% 0.31/0.47 = ( C3 @ A2 @ B2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % internal_case_prod_conv
% 0.31/0.47 thf(fact_130_process__term_Oset__cases_I2_J,axiom,
% 0.31/0.47 ! [Pvar: $tType,A: $tType,E3: Pvar,A2: proces554692349s_term @ A @ Pvar] :
% 0.31/0.47 ( ( member @ Pvar @ E3 @ ( proces1493547885s_term @ A @ Pvar @ A2 ) )
% 0.31/0.47 => ( ( A2
% 0.31/0.47 != ( proces1627516585ss_VAR @ Pvar @ A @ E3 ) )
% 0.31/0.47 => ( ! [Z1: A,Z2: proces554692349s_term @ A @ Pvar] :
% 0.31/0.47 ( ( A2
% 0.31/0.47 = ( proces1454156180ss_ACT @ A @ Pvar @ Z1 @ Z2 ) )
% 0.31/0.47 => ~ ( member @ Pvar @ E3 @ ( proces1493547885s_term @ A @ Pvar @ Z2 ) ) )
% 0.31/0.47 => ( ! [Z1: proces554692349s_term @ A @ Pvar] :
% 0.31/0.47 ( ? [Z2: proces554692349s_term @ A @ Pvar] :
% 0.31/0.47 ( A2
% 0.31/0.47 = ( proces89589571ess_CH @ A @ Pvar @ Z1 @ Z2 ) )
% 0.31/0.47 => ~ ( member @ Pvar @ E3 @ ( proces1493547885s_term @ A @ Pvar @ Z1 ) ) )
% 0.31/0.47 => ~ ! [Z1: proces554692349s_term @ A @ Pvar,Z2: proces554692349s_term @ A @ Pvar] :
% 0.31/0.47 ( ( A2
% 0.31/0.47 = ( proces89589571ess_CH @ A @ Pvar @ Z1 @ Z2 ) )
% 0.31/0.47 => ~ ( member @ Pvar @ E3 @ ( proces1493547885s_term @ A @ Pvar @ Z2 ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_term.set_cases(2)
% 0.31/0.47 thf(fact_131_process__term_Orel__inject_I1_J,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType,Pvar: $tType,C: $tType,R1: A > B > $o,R22: Pvar > C > $o,X1: Pvar,Y1: C] :
% 0.31/0.47 ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1627516585ss_VAR @ Pvar @ A @ X1 ) @ ( proces1627516585ss_VAR @ C @ B @ Y1 ) )
% 0.31/0.47 = ( R22 @ X1 @ Y1 ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_term.rel_inject(1)
% 0.31/0.47 thf(fact_132_process__term_Orel__intros_I1_J,axiom,
% 0.31/0.47 ! [Pvar: $tType,A: $tType,B: $tType,C: $tType,R22: Pvar > C > $o,X1: Pvar,Y1: C,R1: A > B > $o] :
% 0.31/0.47 ( ( R22 @ X1 @ Y1 )
% 0.31/0.47 => ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1627516585ss_VAR @ Pvar @ A @ X1 ) @ ( proces1627516585ss_VAR @ C @ B @ Y1 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_term.rel_intros(1)
% 0.31/0.47 thf(fact_133_process__term_Orel__inject_I4_J,axiom,
% 0.31/0.47 ! [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] :
% 0.31/0.47 ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 ) @ ( proces89589571ess_CH @ B @ C @ Y41 @ Y42 ) )
% 0.31/0.47 = ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X41 @ Y41 )
% 0.31/0.47 & ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X42 @ Y42 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_term.rel_inject(4)
% 0.31/0.47 thf(fact_134_process__term_Orel__intros_I4_J,axiom,
% 0.31/0.47 ! [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] :
% 0.31/0.47 ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X41 @ Y41 )
% 0.31/0.47 => ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X42 @ Y42 )
% 0.31/0.47 => ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 ) @ ( proces89589571ess_CH @ B @ C @ Y41 @ Y42 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_term.rel_intros(4)
% 0.31/0.47 thf(fact_135_process__term_Orel__inject_I3_J,axiom,
% 0.31/0.47 ! [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] :
% 0.31/0.47 ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) @ ( proces1454156180ss_ACT @ B @ C @ Y31 @ Y32 ) )
% 0.31/0.47 = ( ( R1 @ X31 @ Y31 )
% 0.31/0.47 & ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X32 @ Y32 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_term.rel_inject(3)
% 0.31/0.47 thf(fact_136_process__term_Orel__intros_I3_J,axiom,
% 0.31/0.47 ! [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] :
% 0.31/0.47 ( ( R1 @ X31 @ Y31 )
% 0.31/0.47 => ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X32 @ Y32 )
% 0.31/0.47 => ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) @ ( proces1454156180ss_ACT @ B @ C @ Y31 @ Y32 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_term.rel_intros(3)
% 0.31/0.47 thf(fact_137_process__term_Orel__refl,axiom,
% 0.31/0.47 ! [D: $tType,C: $tType,R1a: C > C > $o,R2a: D > D > $o,X7: proces554692349s_term @ C @ D] :
% 0.31/0.47 ( ! [X5: C] : ( R1a @ X5 @ X5 )
% 0.31/0.47 => ( ! [X5: D] : ( R2a @ X5 @ X5 )
% 0.31/0.47 => ( proces2029722208s_term @ C @ C @ D @ D @ R1a @ R2a @ X7 @ X7 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_term.rel_refl
% 0.31/0.47 thf(fact_138_process__term_Orel__eq,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType] :
% 0.31/0.47 ( ( proces2029722208s_term @ A @ A @ B @ B
% 0.31/0.47 @ ^ [Y4: A,Z: A] : ( Y4 = Z )
% 0.31/0.47 @ ^ [Y4: B,Z: B] : ( Y4 = Z ) )
% 0.31/0.47 = ( ^ [Y4: proces554692349s_term @ A @ B,Z: proces554692349s_term @ A @ B] : ( Y4 = Z ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_term.rel_eq
% 0.31/0.47 thf(fact_139_process__term_Oset__intros_I6_J,axiom,
% 0.31/0.47 ! [A: $tType,Pvar: $tType,Ab: Pvar] : ( member @ Pvar @ Ab @ ( proces1493547885s_term @ A @ Pvar @ ( proces1627516585ss_VAR @ Pvar @ A @ Ab ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_term.set_intros(6)
% 0.31/0.47 thf(fact_140_process__term_Oset__intros_I8_J,axiom,
% 0.31/0.47 ! [Pvar: $tType,A: $tType,Xk: Pvar,A1c: proces554692349s_term @ A @ Pvar,A2c: proces554692349s_term @ A @ Pvar] :
% 0.31/0.47 ( ( member @ Pvar @ Xk @ ( proces1493547885s_term @ A @ Pvar @ A1c ) )
% 0.31/0.47 => ( member @ Pvar @ Xk @ ( proces1493547885s_term @ A @ Pvar @ ( proces89589571ess_CH @ A @ Pvar @ A1c @ A2c ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_term.set_intros(8)
% 0.31/0.47 thf(fact_141_process__term_Oset__intros_I9_J,axiom,
% 0.31/0.47 ! [Pvar: $tType,A: $tType,Xm: Pvar,A2c: proces554692349s_term @ A @ Pvar,A1c: proces554692349s_term @ A @ Pvar] :
% 0.31/0.47 ( ( member @ Pvar @ Xm @ ( proces1493547885s_term @ A @ Pvar @ A2c ) )
% 0.31/0.47 => ( member @ Pvar @ Xm @ ( proces1493547885s_term @ A @ Pvar @ ( proces89589571ess_CH @ A @ Pvar @ A1c @ A2c ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_term.set_intros(9)
% 0.31/0.47 thf(fact_142_process__term_Oset__intros_I7_J,axiom,
% 0.31/0.47 ! [Pvar: $tType,A: $tType,Xi: Pvar,A2b: proces554692349s_term @ A @ Pvar,A1b: A] :
% 0.31/0.47 ( ( member @ Pvar @ Xi @ ( proces1493547885s_term @ A @ Pvar @ A2b ) )
% 0.31/0.47 => ( member @ Pvar @ Xi @ ( proces1493547885s_term @ A @ Pvar @ ( proces1454156180ss_ACT @ A @ Pvar @ A1b @ A2b ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_term.set_intros(7)
% 0.31/0.47 thf(fact_143_process__term_Osimps_I51_J,axiom,
% 0.31/0.47 ! [Pvar: $tType,A: $tType,X31: A,X32: proces554692349s_term @ A @ Pvar] :
% 0.31/0.47 ( ( proces1493547885s_term @ A @ Pvar @ ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) )
% 0.31/0.47 = ( proces1493547885s_term @ A @ Pvar @ X32 ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_term.simps(51)
% 0.31/0.47 thf(fact_144_process__term_Orel__intros_I2_J,axiom,
% 0.31/0.47 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,X2: proces634752977rocess @ A,Y2: proces634752977rocess @ B,R22: Pvar > C > $o] :
% 0.31/0.47 ( ( proces749077512rocess @ A @ B @ R1 @ X2 @ Y2 )
% 0.31/0.47 => ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1062592052s_PROC @ A @ Pvar @ X2 ) @ ( proces1062592052s_PROC @ B @ C @ Y2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_term.rel_intros(2)
% 0.31/0.47 thf(fact_145_process__term_Orel__inject_I2_J,axiom,
% 0.31/0.47 ! [C: $tType,Pvar: $tType,A: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X2: proces634752977rocess @ A,Y2: proces634752977rocess @ B] :
% 0.31/0.47 ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1062592052s_PROC @ A @ Pvar @ X2 ) @ ( proces1062592052s_PROC @ B @ C @ Y2 ) )
% 0.31/0.47 = ( proces749077512rocess @ A @ B @ R1 @ X2 @ Y2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_term.rel_inject(2)
% 0.31/0.47 thf(fact_146_process__term_Orel__distinct_I2_J,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType,C: $tType,D: $tType,R1: A > C > $o,R22: B > D > $o,Y2: proces634752977rocess @ A,X1: D] :
% 0.31/0.47 ~ ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R22 @ ( proces1062592052s_PROC @ A @ B @ Y2 ) @ ( proces1627516585ss_VAR @ D @ C @ X1 ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_term.rel_distinct(2)
% 0.31/0.47 thf(fact_147_process__term_Orel__distinct_I1_J,axiom,
% 0.31/0.47 ! [Pvar: $tType,A: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X1: Pvar,Y2: proces634752977rocess @ B] :
% 0.31/0.47 ~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1627516585ss_VAR @ Pvar @ A @ X1 ) @ ( proces1062592052s_PROC @ B @ C @ Y2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_term.rel_distinct(1)
% 0.31/0.47 thf(fact_148_process__term_Orel__distinct_I10_J,axiom,
% 0.31/0.47 ! [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] :
% 0.31/0.47 ~ ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R22 @ ( proces89589571ess_CH @ A @ B @ Y41 @ Y42 ) @ ( proces1062592052s_PROC @ C @ D @ X2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_term.rel_distinct(10)
% 0.31/0.47 thf(fact_149_process__term_Orel__distinct_I9_J,axiom,
% 0.31/0.47 ! [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] :
% 0.31/0.47 ~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1062592052s_PROC @ A @ Pvar @ X2 ) @ ( proces89589571ess_CH @ B @ C @ Y41 @ Y42 ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_term.rel_distinct(9)
% 0.31/0.47 thf(fact_150_process__term_Orel__distinct_I8_J,axiom,
% 0.31/0.47 ! [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] :
% 0.31/0.47 ~ ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R22 @ ( proces1454156180ss_ACT @ A @ B @ Y31 @ Y32 ) @ ( proces1062592052s_PROC @ C @ D @ X2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_term.rel_distinct(8)
% 0.31/0.47 thf(fact_151_process__term_Orel__distinct_I7_J,axiom,
% 0.31/0.47 ! [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] :
% 0.31/0.47 ~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1062592052s_PROC @ A @ Pvar @ X2 ) @ ( proces1454156180ss_ACT @ B @ C @ Y31 @ Y32 ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_term.rel_distinct(7)
% 0.31/0.47 thf(fact_152_process__term_Orel__distinct_I5_J,axiom,
% 0.31/0.47 ! [Pvar: $tType,A: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X1: Pvar,Y41: proces554692349s_term @ B @ C,Y42: proces554692349s_term @ B @ C] :
% 0.31/0.47 ~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1627516585ss_VAR @ Pvar @ A @ X1 ) @ ( proces89589571ess_CH @ B @ C @ Y41 @ Y42 ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_term.rel_distinct(5)
% 0.31/0.47 thf(fact_153_process__term_Orel__distinct_I6_J,axiom,
% 0.31/0.47 ! [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,X1: D] :
% 0.31/0.47 ~ ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R22 @ ( proces89589571ess_CH @ A @ B @ Y41 @ Y42 ) @ ( proces1627516585ss_VAR @ D @ C @ X1 ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_term.rel_distinct(6)
% 0.31/0.47 thf(fact_154_process__term_Orel__distinct_I3_J,axiom,
% 0.31/0.47 ! [Pvar: $tType,A: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X1: Pvar,Y31: B,Y32: proces554692349s_term @ B @ C] :
% 0.31/0.47 ~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1627516585ss_VAR @ Pvar @ A @ X1 ) @ ( proces1454156180ss_ACT @ B @ C @ Y31 @ Y32 ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_term.rel_distinct(3)
% 0.31/0.47 thf(fact_155_process__term_Orel__distinct_I4_J,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType,C: $tType,D: $tType,R1: A > C > $o,R22: B > D > $o,Y31: A,Y32: proces554692349s_term @ A @ B,X1: D] :
% 0.31/0.47 ~ ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R22 @ ( proces1454156180ss_ACT @ A @ B @ Y31 @ Y32 ) @ ( proces1627516585ss_VAR @ D @ C @ X1 ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_term.rel_distinct(4)
% 0.31/0.47 thf(fact_156_process__term_Orel__distinct_I11_J,axiom,
% 0.31/0.47 ! [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] :
% 0.31/0.47 ~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) @ ( proces89589571ess_CH @ B @ C @ Y41 @ Y42 ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_term.rel_distinct(11)
% 0.31/0.47 thf(fact_157_process__term_Orel__distinct_I12_J,axiom,
% 0.31/0.47 ! [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] :
% 0.31/0.47 ~ ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R22 @ ( proces89589571ess_CH @ A @ B @ Y41 @ Y42 ) @ ( proces1454156180ss_ACT @ C @ D @ X31 @ X32 ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_term.rel_distinct(12)
% 0.31/0.47 thf(fact_158_ssubst__Pair__rhs,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType,R3: A,S: B,R: set @ ( product_prod @ A @ B ),S2: B] :
% 0.31/0.47 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ R3 @ S ) @ R )
% 0.31/0.47 => ( ( S2 = S )
% 0.31/0.47 => ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ R3 @ S2 ) @ R ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ssubst_Pair_rhs
% 0.31/0.47 thf(fact_159_curry__conv,axiom,
% 0.31/0.47 ! [A: $tType,C: $tType,B: $tType] :
% 0.31/0.47 ( ( product_curry @ B @ C @ A )
% 0.31/0.47 = ( ^ [F7: ( product_prod @ B @ C ) > A,A7: B,B4: C] : ( F7 @ ( product_Pair @ B @ C @ A7 @ B4 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % curry_conv
% 0.31/0.47 thf(fact_160_process__term_Octr__transfer_I2_J,axiom,
% 0.31/0.47 ! [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 ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_term.ctr_transfer(2)
% 0.31/0.47 thf(fact_161_isACT_Oelims_I1_J,axiom,
% 0.31/0.47 ! [D: $tType,A: $tType,B: $tType,C: $tType,X7: A > ( proces554692349s_term @ B @ C ),Xa2: proces554692349s_term @ D @ A,Y3: $o] :
% 0.31/0.47 ( ( ( proces687458811_isACT @ A @ B @ C @ D @ X7 @ Xa2 )
% 0.31/0.47 = Y3 )
% 0.31/0.47 => ( ! [X3: A] :
% 0.31/0.47 ( ( Xa2
% 0.31/0.47 = ( proces1627516585ss_VAR @ A @ D @ X3 ) )
% 0.31/0.47 => ( Y3
% 0.31/0.47 = ( ~ ( proces460752237s_term @ C @ $o @ B
% 0.31/0.47 @ ^ [Pvar2: C] : $false
% 0.31/0.47 @ ( proces10484146Action @ B )
% 0.31/0.47 @ ^ [A7: B,T4: proces554692349s_term @ B @ C] : $true
% 0.31/0.47 @ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
% 0.31/0.47 @ ( X7 @ X3 ) ) ) ) )
% 0.31/0.47 => ( ! [P4: proces634752977rocess @ D] :
% 0.31/0.47 ( ( Xa2
% 0.31/0.47 = ( proces1062592052s_PROC @ D @ A @ P4 ) )
% 0.31/0.47 => ( Y3
% 0.31/0.47 = ( ~ ( proces10484146Action @ D @ P4 ) ) ) )
% 0.31/0.47 => ( ( ? [A3: D,T3: proces554692349s_term @ D @ A] :
% 0.31/0.47 ( Xa2
% 0.31/0.47 = ( proces1454156180ss_ACT @ D @ A @ A3 @ T3 ) )
% 0.31/0.47 => ~ Y3 )
% 0.31/0.47 => ~ ( ? [T12: proces554692349s_term @ D @ A,T23: proces554692349s_term @ D @ A] :
% 0.31/0.47 ( Xa2
% 0.31/0.47 = ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) )
% 0.31/0.47 => Y3 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % isACT.elims(1)
% 0.31/0.47 thf(fact_162_curryI,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType,F: ( product_prod @ A @ B ) > $o,A2: A,B2: B] :
% 0.31/0.47 ( ( F @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 0.31/0.47 => ( product_curry @ A @ B @ $o @ F @ A2 @ B2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % curryI
% 0.31/0.47 thf(fact_163_curry__def,axiom,
% 0.31/0.47 ! [C: $tType,B: $tType,A: $tType] :
% 0.31/0.47 ( ( product_curry @ A @ B @ C )
% 0.31/0.47 = ( ^ [C4: ( product_prod @ A @ B ) > C,X6: A,Y6: B] : ( C4 @ ( product_Pair @ A @ B @ X6 @ Y6 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % curry_def
% 0.31/0.47 thf(fact_164_process__term_Ocase__transfer,axiom,
% 0.31/0.47 ! [Pvar: $tType,D: $tType,A: $tType,B: $tType,E: $tType,C: $tType,R22: Pvar > C > $o,S3: D > E > $o,R1: A > B > $o] : ( bNF_rel_fun @ ( Pvar > D ) @ ( C > E ) @ ( ( ( 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 ) > E ) > ( B > ( proces554692349s_term @ B @ C ) > E ) > ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) > E ) > ( proces554692349s_term @ B @ C ) > E ) @ ( bNF_rel_fun @ Pvar @ C @ D @ E @ R22 @ S3 ) @ ( bNF_rel_fun @ ( ( proces634752977rocess @ A ) > D ) @ ( ( proces634752977rocess @ B ) > E ) @ ( ( 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 ) > E ) > ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) > E ) > ( proces554692349s_term @ B @ C ) > E ) @ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ D @ E @ ( proces749077512rocess @ A @ B @ R1 ) @ S3 ) @ ( bNF_rel_fun @ ( A > ( proces554692349s_term @ A @ Pvar ) > D ) @ ( B > ( proces554692349s_term @ B @ C ) > E ) @ ( ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D ) > ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) > E ) > ( proces554692349s_term @ B @ C ) > E ) @ ( bNF_rel_fun @ A @ B @ ( ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( proces554692349s_term @ B @ C ) > E ) @ R1 @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ D @ E @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ S3 ) ) @ ( bNF_rel_fun @ ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) > E ) @ ( ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( proces554692349s_term @ B @ C ) > E ) @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ ( ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( proces554692349s_term @ B @ C ) > E ) @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ D @ E @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ S3 ) ) @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ D @ E @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ S3 ) ) ) ) @ ( proces460752237s_term @ Pvar @ D @ A ) @ ( proces460752237s_term @ C @ E @ B ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_term.case_transfer
% 0.31/0.47 thf(fact_165_process__term_Orec__transfer,axiom,
% 0.31/0.47 ! [Pvar: $tType,D: $tType,A: $tType,B: $tType,E: $tType,C: $tType,R22: Pvar > C > $o,S3: D > E > $o,R1: A > B > $o] : ( bNF_rel_fun @ ( Pvar > D ) @ ( C > E ) @ ( ( ( 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 ) > E ) > ( B > ( proces554692349s_term @ B @ C ) > E > E ) > ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) > E > E > E ) > ( proces554692349s_term @ B @ C ) > E ) @ ( bNF_rel_fun @ Pvar @ C @ D @ E @ R22 @ S3 ) @ ( bNF_rel_fun @ ( ( proces634752977rocess @ A ) > D ) @ ( ( proces634752977rocess @ B ) > E ) @ ( ( 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 ) > E > E ) > ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) > E > E > E ) > ( proces554692349s_term @ B @ C ) > E ) @ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ D @ E @ ( proces749077512rocess @ A @ B @ R1 ) @ S3 ) @ ( bNF_rel_fun @ ( A > ( proces554692349s_term @ A @ Pvar ) > D > D ) @ ( B > ( proces554692349s_term @ B @ C ) > E > E ) @ ( ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D > D > D ) > ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) > E > E > E ) > ( proces554692349s_term @ B @ C ) > E ) @ ( bNF_rel_fun @ A @ B @ ( ( proces554692349s_term @ A @ Pvar ) > D > D ) @ ( ( proces554692349s_term @ B @ C ) > E > E ) @ R1 @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ ( D > D ) @ ( E > E ) @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ ( bNF_rel_fun @ D @ E @ D @ E @ S3 @ S3 ) ) ) @ ( bNF_rel_fun @ ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D > D > D ) @ ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) > E > E > E ) @ ( ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( proces554692349s_term @ B @ C ) > E ) @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ ( ( proces554692349s_term @ A @ Pvar ) > D > D > D ) @ ( ( proces554692349s_term @ B @ C ) > E > E > E ) @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ ( D > D > D ) @ ( E > E > E ) @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ ( bNF_rel_fun @ D @ E @ ( D > D ) @ ( E > E ) @ S3 @ ( bNF_rel_fun @ D @ E @ D @ E @ S3 @ S3 ) ) ) ) @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ D @ E @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ S3 ) ) ) ) @ ( proces2117273769s_term @ Pvar @ D @ A ) @ ( proces2117273769s_term @ C @ E @ B ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_term.rec_transfer
% 0.31/0.47 thf(fact_166_process__term_Ocase__distrib,axiom,
% 0.31/0.47 ! [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] :
% 0.31/0.47 ( ( H @ ( proces460752237s_term @ Pvar @ B @ A @ F1 @ F2 @ F3 @ F4 @ Process_term ) )
% 0.31/0.47 = ( proces460752237s_term @ Pvar @ C @ A
% 0.31/0.47 @ ^ [X6: Pvar] : ( H @ ( F1 @ X6 ) )
% 0.31/0.47 @ ^ [X6: proces634752977rocess @ A] : ( H @ ( F2 @ X6 ) )
% 0.31/0.47 @ ^ [X13: A,X23: proces554692349s_term @ A @ Pvar] : ( H @ ( F3 @ X13 @ X23 ) )
% 0.31/0.47 @ ^ [X13: proces554692349s_term @ A @ Pvar,X23: proces554692349s_term @ A @ Pvar] : ( H @ ( F4 @ X13 @ X23 ) )
% 0.31/0.47 @ Process_term ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_term.case_distrib
% 0.31/0.47 thf(fact_167_process__term_Opred__True,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType] :
% 0.31/0.47 ( ( proces2118920028s_term @ A @ B
% 0.31/0.47 @ ^ [Uu: A] : $true
% 0.31/0.47 @ ^ [Uu: B] : $true )
% 0.31/0.47 = ( ^ [Uu: proces554692349s_term @ A @ B] : $true ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_term.pred_True
% 0.31/0.47 thf(fact_168_process_Opred__True,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( proces1205983068rocess @ A
% 0.31/0.47 @ ^ [Uu: A] : $true )
% 0.31/0.47 = ( ^ [Uu: proces634752977rocess @ A] : $true ) ) ).
% 0.31/0.47
% 0.31/0.47 % process.pred_True
% 0.31/0.47 thf(fact_169_process_Odisc__eq__case_I2_J,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( proces401113213Choice @ A )
% 0.31/0.47 = ( proces1406508781rocess @ A @ $o
% 0.31/0.47 @ ^ [Uu: A,Uv: proces634752977rocess @ A] : $false
% 0.31/0.47 @ ^ [Uu: proces634752977rocess @ A,Uv: proces634752977rocess @ A] : $true ) ) ).
% 0.31/0.47
% 0.31/0.47 % process.disc_eq_case(2)
% 0.31/0.47 thf(fact_170_process_Ocase__distrib,axiom,
% 0.31/0.47 ! [B: $tType,C: $tType,A: $tType,H: B > C,F1: A > ( proces634752977rocess @ A ) > B,F2: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B,Process: proces634752977rocess @ A] :
% 0.31/0.47 ( ( H @ ( proces1406508781rocess @ A @ B @ F1 @ F2 @ Process ) )
% 0.31/0.47 = ( proces1406508781rocess @ A @ C
% 0.31/0.47 @ ^ [X13: A,X23: proces634752977rocess @ A] : ( H @ ( F1 @ X13 @ X23 ) )
% 0.31/0.47 @ ^ [X13: proces634752977rocess @ A,X23: proces634752977rocess @ A] : ( H @ ( F2 @ X13 @ X23 ) )
% 0.31/0.47 @ Process ) ) ).
% 0.31/0.47
% 0.31/0.47 % process.case_distrib
% 0.31/0.47 thf(fact_171_curry__K,axiom,
% 0.31/0.47 ! [B: $tType,C: $tType,A: $tType,C3: C] :
% 0.31/0.47 ( ( product_curry @ A @ B @ C
% 0.31/0.47 @ ^ [X6: product_prod @ A @ B] : C3 )
% 0.31/0.47 = ( ^ [X6: A,Y6: B] : C3 ) ) ).
% 0.31/0.47
% 0.31/0.47 % curry_K
% 0.31/0.47 thf(fact_172_process_Odisc__eq__case_I1_J,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( proces10484146Action @ A )
% 0.31/0.47 = ( proces1406508781rocess @ A @ $o
% 0.31/0.47 @ ^ [Uu: A,Uv: proces634752977rocess @ A] : $true
% 0.31/0.47 @ ^ [Uu: proces634752977rocess @ A,Uv: proces634752977rocess @ A] : $false ) ) ).
% 0.31/0.47
% 0.31/0.47 % process.disc_eq_case(1)
% 0.31/0.47 thf(fact_173_isACT_Osimps_I1_J,axiom,
% 0.31/0.47 ! [D: $tType,B: $tType,C: $tType,A: $tType,Sys: A > ( proces554692349s_term @ B @ C ),X: A] :
% 0.31/0.47 ( ( proces687458811_isACT @ A @ B @ C @ D @ Sys @ ( proces1627516585ss_VAR @ A @ D @ X ) )
% 0.31/0.47 = ( proces460752237s_term @ C @ $o @ B
% 0.31/0.47 @ ^ [Pvar2: C] : $false
% 0.31/0.47 @ ( proces10484146Action @ B )
% 0.31/0.47 @ ^ [A7: B,T4: proces554692349s_term @ B @ C] : $true
% 0.31/0.47 @ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
% 0.31/0.47 @ ( Sys @ X ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % isACT.simps(1)
% 0.31/0.47 thf(fact_174_curryD,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType,F: ( product_prod @ A @ B ) > $o,A2: A,B2: B] :
% 0.31/0.47 ( ( product_curry @ A @ B @ $o @ F @ A2 @ B2 )
% 0.31/0.47 => ( F @ ( product_Pair @ A @ B @ A2 @ B2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % curryD
% 0.31/0.47 thf(fact_175_curryE,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType,F: ( product_prod @ A @ B ) > $o,A2: A,B2: B] :
% 0.31/0.47 ( ( product_curry @ A @ B @ $o @ F @ A2 @ B2 )
% 0.31/0.47 => ( F @ ( product_Pair @ A @ B @ A2 @ B2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % curryE
% 0.31/0.47 thf(fact_176_process__term_Octr__transfer_I1_J,axiom,
% 0.31/0.47 ! [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 ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_term.ctr_transfer(1)
% 0.31/0.47 thf(fact_177_isACT_Oelims_I3_J,axiom,
% 0.31/0.47 ! [C: $tType,B: $tType,A: $tType,D: $tType,X7: A > ( proces554692349s_term @ B @ C ),Xa2: proces554692349s_term @ D @ A] :
% 0.31/0.47 ( ~ ( proces687458811_isACT @ A @ B @ C @ D @ X7 @ Xa2 )
% 0.31/0.47 => ( ! [X3: A] :
% 0.31/0.47 ( ( Xa2
% 0.31/0.47 = ( proces1627516585ss_VAR @ A @ D @ X3 ) )
% 0.31/0.47 => ( proces460752237s_term @ C @ $o @ B
% 0.31/0.47 @ ^ [Pvar2: C] : $false
% 0.31/0.47 @ ( proces10484146Action @ B )
% 0.31/0.47 @ ^ [A7: B,T4: proces554692349s_term @ B @ C] : $true
% 0.31/0.47 @ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
% 0.31/0.47 @ ( X7 @ X3 ) ) )
% 0.31/0.47 => ( ! [P4: proces634752977rocess @ D] :
% 0.31/0.47 ( ( Xa2
% 0.31/0.47 = ( proces1062592052s_PROC @ D @ A @ P4 ) )
% 0.31/0.47 => ( proces10484146Action @ D @ P4 ) )
% 0.31/0.47 => ~ ! [T12: proces554692349s_term @ D @ A,T23: proces554692349s_term @ D @ A] :
% 0.31/0.47 ( Xa2
% 0.31/0.47 != ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % isACT.elims(3)
% 0.31/0.47 thf(fact_178_isACT_Oelims_I2_J,axiom,
% 0.31/0.47 ! [C: $tType,B: $tType,A: $tType,D: $tType,X7: A > ( proces554692349s_term @ B @ C ),Xa2: proces554692349s_term @ D @ A] :
% 0.31/0.47 ( ( proces687458811_isACT @ A @ B @ C @ D @ X7 @ Xa2 )
% 0.31/0.47 => ( ! [X3: A] :
% 0.31/0.47 ( ( Xa2
% 0.31/0.47 = ( proces1627516585ss_VAR @ A @ D @ X3 ) )
% 0.31/0.47 => ~ ( proces460752237s_term @ C @ $o @ B
% 0.31/0.47 @ ^ [Pvar2: C] : $false
% 0.31/0.47 @ ( proces10484146Action @ B )
% 0.31/0.47 @ ^ [A7: B,T4: proces554692349s_term @ B @ C] : $true
% 0.31/0.47 @ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
% 0.31/0.47 @ ( X7 @ X3 ) ) )
% 0.31/0.47 => ( ! [P4: proces634752977rocess @ D] :
% 0.31/0.47 ( ( Xa2
% 0.31/0.47 = ( proces1062592052s_PROC @ D @ A @ P4 ) )
% 0.31/0.47 => ~ ( proces10484146Action @ D @ P4 ) )
% 0.31/0.47 => ~ ! [A3: D,T3: proces554692349s_term @ D @ A] :
% 0.31/0.47 ( Xa2
% 0.31/0.47 != ( proces1454156180ss_ACT @ D @ A @ A3 @ T3 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % isACT.elims(2)
% 0.31/0.47 thf(fact_179_PREF_Oelims,axiom,
% 0.31/0.47 ! [A: $tType,C: $tType,B: $tType,X7: A > ( proces554692349s_term @ B @ C ),Xa2: proces554692349s_term @ B @ A,Y3: B] :
% 0.31/0.47 ( ( ( proces1708129104e_PREF @ A @ B @ C @ X7 @ Xa2 )
% 0.31/0.47 = Y3 )
% 0.31/0.47 => ( ! [X3: A] :
% 0.31/0.47 ( ( Xa2
% 0.31/0.47 = ( proces1627516585ss_VAR @ A @ B @ X3 ) )
% 0.31/0.47 => ( Y3
% 0.31/0.47 != ( proces460752237s_term @ C @ B @ B
% 0.31/0.47 @ ^ [Aa3: C] : ( undefined @ B )
% 0.31/0.47 @ ( proces745025900prefOf @ B )
% 0.31/0.47 @ ^ [A7: B,T4: proces554692349s_term @ B @ C] : A7
% 0.31/0.47 @ ^ [Aa3: proces554692349s_term @ B @ C,Ab2: proces554692349s_term @ B @ C] : ( undefined @ B )
% 0.31/0.47 @ ( X7 @ X3 ) ) ) )
% 0.31/0.47 => ( ! [P4: proces634752977rocess @ B] :
% 0.31/0.47 ( ( Xa2
% 0.31/0.47 = ( proces1062592052s_PROC @ B @ A @ P4 ) )
% 0.31/0.47 => ( Y3
% 0.31/0.47 != ( proces745025900prefOf @ B @ P4 ) ) )
% 0.31/0.47 => ( ! [A3: B] :
% 0.31/0.47 ( ? [T3: proces554692349s_term @ B @ A] :
% 0.31/0.47 ( Xa2
% 0.31/0.47 = ( proces1454156180ss_ACT @ B @ A @ A3 @ T3 ) )
% 0.31/0.47 => ( Y3 != A3 ) )
% 0.31/0.47 => ~ ( ? [V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] :
% 0.31/0.47 ( Xa2
% 0.31/0.47 = ( proces89589571ess_CH @ B @ A @ V @ Va ) )
% 0.31/0.47 => ( Y3
% 0.31/0.47 != ( undefined @ B ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % PREF.elims
% 0.31/0.47 thf(fact_180_rel__funI,axiom,
% 0.31/0.47 ! [A: $tType,C: $tType,D: $tType,B: $tType,A4: A > B > $o,B6: C > D > $o,F: A > C,G: B > D] :
% 0.31/0.47 ( ! [X5: A,Y5: B] :
% 0.31/0.47 ( ( A4 @ X5 @ Y5 )
% 0.31/0.47 => ( B6 @ ( F @ X5 ) @ ( G @ Y5 ) ) )
% 0.31/0.47 => ( bNF_rel_fun @ A @ B @ C @ D @ A4 @ B6 @ F @ G ) ) ).
% 0.31/0.47
% 0.31/0.47 % rel_funI
% 0.31/0.47 thf(fact_181_CH1_Oelims,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType,X7: A > ( proces554692349s_term @ B @ A ),Xa2: proces554692349s_term @ B @ A,Y3: proces554692349s_term @ B @ A] :
% 0.31/0.47 ( ( ( proces1239275103le_CH1 @ A @ B @ X7 @ Xa2 )
% 0.31/0.47 = Y3 )
% 0.31/0.47 => ( ! [X3: A] :
% 0.31/0.47 ( ( Xa2
% 0.31/0.47 = ( proces1627516585ss_VAR @ A @ B @ X3 ) )
% 0.31/0.47 => ( Y3
% 0.31/0.47 != ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 0.31/0.47 @ ^ [A7: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.31/0.47 @ ^ [P7: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces979765041_ch1Of @ B @ P7 ) )
% 0.31/0.47 @ ^ [A7: B,B4: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.31/0.47 @ ^ [T13: proces554692349s_term @ B @ A,T24: proces554692349s_term @ B @ A] : T13
% 0.31/0.47 @ ( X7 @ X3 ) ) ) )
% 0.31/0.47 => ( ! [P4: proces634752977rocess @ B] :
% 0.31/0.47 ( ( Xa2
% 0.31/0.47 = ( proces1062592052s_PROC @ B @ A @ P4 ) )
% 0.31/0.47 => ( Y3
% 0.31/0.47 != ( proces1062592052s_PROC @ B @ A @ ( proces979765041_ch1Of @ B @ P4 ) ) ) )
% 0.31/0.47 => ( ! [T12: proces554692349s_term @ B @ A] :
% 0.31/0.47 ( ? [T23: proces554692349s_term @ B @ A] :
% 0.31/0.47 ( Xa2
% 0.31/0.47 = ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) )
% 0.31/0.47 => ( Y3 != T12 ) )
% 0.31/0.47 => ~ ( ? [V: B,Va: proces554692349s_term @ B @ A] :
% 0.31/0.47 ( Xa2
% 0.31/0.47 = ( proces1454156180ss_ACT @ B @ A @ V @ Va ) )
% 0.31/0.47 => ( Y3
% 0.31/0.47 != ( undefined @ ( proces554692349s_term @ B @ A ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % CH1.elims
% 0.31/0.47 thf(fact_182_process__term_Octr__transfer_I4_J,axiom,
% 0.31/0.47 ! [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 ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_term.ctr_transfer(4)
% 0.31/0.47 thf(fact_183_process__term_Octr__transfer_I3_J,axiom,
% 0.31/0.47 ! [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 ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_term.ctr_transfer(3)
% 0.31/0.47 thf(fact_184_process__term_Opred__transfer,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType,D: $tType,C: $tType,R1: A > C > $o,R22: B > D > $o] :
% 0.31/0.47 ( bNF_rel_fun @ ( A > $o ) @ ( C > $o ) @ ( ( B > $o ) > ( proces554692349s_term @ A @ B ) > $o ) @ ( ( D > $o ) > ( proces554692349s_term @ C @ D ) > $o )
% 0.31/0.47 @ ( bNF_rel_fun @ A @ C @ $o @ $o @ R1
% 0.31/0.47 @ ^ [Y4: $o,Z: $o] : ( Y4 = Z ) )
% 0.31/0.47 @ ( bNF_rel_fun @ ( B > $o ) @ ( D > $o ) @ ( ( proces554692349s_term @ A @ B ) > $o ) @ ( ( proces554692349s_term @ C @ D ) > $o )
% 0.31/0.47 @ ( bNF_rel_fun @ B @ D @ $o @ $o @ R22
% 0.31/0.47 @ ^ [Y4: $o,Z: $o] : ( Y4 = Z ) )
% 0.31/0.47 @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ B ) @ ( proces554692349s_term @ C @ D ) @ $o @ $o @ ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R22 )
% 0.31/0.47 @ ^ [Y4: $o,Z: $o] : ( Y4 = Z ) ) )
% 0.31/0.47 @ ( proces2118920028s_term @ A @ B )
% 0.31/0.47 @ ( proces2118920028s_term @ C @ D ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_term.pred_transfer
% 0.31/0.47 thf(fact_185_process__term_Orel__transfer,axiom,
% 0.31/0.47 ! [A: $tType,C: $tType,B: $tType,D: $tType,H2: $tType,F5: $tType,G2: $tType,E: $tType,S1a: A > E > $o,S1c: C > G2 > $o,S2a: B > F5 > $o,S2c: D > H2 > $o] :
% 0.31/0.47 ( bNF_rel_fun @ ( A > C > $o ) @ ( E > G2 > $o ) @ ( ( B > D > $o ) > ( proces554692349s_term @ A @ B ) > ( proces554692349s_term @ C @ D ) > $o ) @ ( ( F5 > H2 > $o ) > ( proces554692349s_term @ E @ F5 ) > ( proces554692349s_term @ G2 @ H2 ) > $o )
% 0.31/0.47 @ ( bNF_rel_fun @ A @ E @ ( C > $o ) @ ( G2 > $o ) @ S1a
% 0.31/0.47 @ ( bNF_rel_fun @ C @ G2 @ $o @ $o @ S1c
% 0.31/0.47 @ ^ [Y4: $o,Z: $o] : ( Y4 = Z ) ) )
% 0.31/0.47 @ ( bNF_rel_fun @ ( B > D > $o ) @ ( F5 > H2 > $o ) @ ( ( proces554692349s_term @ A @ B ) > ( proces554692349s_term @ C @ D ) > $o ) @ ( ( proces554692349s_term @ E @ F5 ) > ( proces554692349s_term @ G2 @ H2 ) > $o )
% 0.31/0.47 @ ( bNF_rel_fun @ B @ F5 @ ( D > $o ) @ ( H2 > $o ) @ S2a
% 0.31/0.47 @ ( bNF_rel_fun @ D @ H2 @ $o @ $o @ S2c
% 0.31/0.47 @ ^ [Y4: $o,Z: $o] : ( Y4 = Z ) ) )
% 0.31/0.47 @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ B ) @ ( proces554692349s_term @ E @ F5 ) @ ( ( proces554692349s_term @ C @ D ) > $o ) @ ( ( proces554692349s_term @ G2 @ H2 ) > $o ) @ ( proces2029722208s_term @ A @ E @ B @ F5 @ S1a @ S2a )
% 0.31/0.47 @ ( bNF_rel_fun @ ( proces554692349s_term @ C @ D ) @ ( proces554692349s_term @ G2 @ H2 ) @ $o @ $o @ ( proces2029722208s_term @ C @ G2 @ D @ H2 @ S1c @ S2c )
% 0.31/0.47 @ ^ [Y4: $o,Z: $o] : ( Y4 = Z ) ) ) )
% 0.31/0.47 @ ( proces2029722208s_term @ A @ C @ B @ D )
% 0.31/0.47 @ ( proces2029722208s_term @ E @ G2 @ F5 @ H2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_term.rel_transfer
% 0.31/0.47 thf(fact_186_process_Opred__transfer,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType,R: A > B > $o] :
% 0.31/0.47 ( bNF_rel_fun @ ( A > $o ) @ ( B > $o ) @ ( ( proces634752977rocess @ A ) > $o ) @ ( ( proces634752977rocess @ B ) > $o )
% 0.31/0.47 @ ( bNF_rel_fun @ A @ B @ $o @ $o @ R
% 0.31/0.47 @ ^ [Y4: $o,Z: $o] : ( Y4 = Z ) )
% 0.31/0.47 @ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ $o @ $o @ ( proces749077512rocess @ A @ B @ R )
% 0.31/0.47 @ ^ [Y4: $o,Z: $o] : ( Y4 = Z ) )
% 0.31/0.47 @ ( proces1205983068rocess @ A )
% 0.31/0.47 @ ( proces1205983068rocess @ B ) ) ).
% 0.31/0.47
% 0.31/0.47 % process.pred_transfer
% 0.31/0.47 thf(fact_187_process_Orel__transfer,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType,D: $tType,C: $tType,Sa: A > C > $o,Sc: B > D > $o] :
% 0.31/0.47 ( bNF_rel_fun @ ( A > B > $o ) @ ( C > D > $o ) @ ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ B ) > $o ) @ ( ( proces634752977rocess @ C ) > ( proces634752977rocess @ D ) > $o )
% 0.31/0.47 @ ( bNF_rel_fun @ A @ C @ ( B > $o ) @ ( D > $o ) @ Sa
% 0.31/0.47 @ ( bNF_rel_fun @ B @ D @ $o @ $o @ Sc
% 0.31/0.47 @ ^ [Y4: $o,Z: $o] : ( Y4 = Z ) ) )
% 0.31/0.47 @ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ C ) @ ( ( proces634752977rocess @ B ) > $o ) @ ( ( proces634752977rocess @ D ) > $o ) @ ( proces749077512rocess @ A @ C @ Sa )
% 0.31/0.47 @ ( bNF_rel_fun @ ( proces634752977rocess @ B ) @ ( proces634752977rocess @ D ) @ $o @ $o @ ( proces749077512rocess @ B @ D @ Sc )
% 0.31/0.47 @ ^ [Y4: $o,Z: $o] : ( Y4 = Z ) ) )
% 0.31/0.47 @ ( proces749077512rocess @ A @ B )
% 0.31/0.47 @ ( proces749077512rocess @ C @ D ) ) ).
% 0.31/0.47
% 0.31/0.47 % process.rel_transfer
% 0.31/0.47 thf(fact_188_process_Ocase__transfer,axiom,
% 0.31/0.47 ! [A: $tType,C: $tType,D: $tType,B: $tType,R: A > B > $o,S3: 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 ) @ S3 ) ) @ ( 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 ) @ S3 ) ) @ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ C @ D @ ( proces749077512rocess @ A @ B @ R ) @ S3 ) ) @ ( proces1406508781rocess @ A @ C ) @ ( proces1406508781rocess @ B @ D ) ) ).
% 0.31/0.47
% 0.31/0.47 % process.case_transfer
% 0.31/0.47 thf(fact_189_process_Octr__transfer_I2_J,axiom,
% 0.31/0.47 ! [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 ) ) ).
% 0.31/0.47
% 0.31/0.47 % process.ctr_transfer(2)
% 0.31/0.47 thf(fact_190_process_Octr__transfer_I1_J,axiom,
% 0.31/0.47 ! [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 ) ) ).
% 0.31/0.47
% 0.31/0.47 % process.ctr_transfer(1)
% 0.31/0.47 thf(fact_191_contOf__def,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( proces1778668539contOf @ A )
% 0.31/0.47 = ( proces1406508781rocess @ A @ ( proces634752977rocess @ A )
% 0.31/0.47 @ ^ [X112: A,X123: proces634752977rocess @ A] : X123
% 0.31/0.47 @ ^ [Uu2: proces634752977rocess @ A,Uv2: proces634752977rocess @ A] : ( undefined @ ( proces634752977rocess @ A ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % contOf_def
% 0.31/0.47 thf(fact_192_ch2Of__def,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( proces988026546_ch2Of @ A )
% 0.31/0.47 = ( proces1406508781rocess @ A @ ( proces634752977rocess @ A )
% 0.31/0.47 @ ^ [Uu2: A,Uv2: proces634752977rocess @ A] : ( undefined @ ( proces634752977rocess @ A ) )
% 0.31/0.47 @ ^ [X213: proces634752977rocess @ A,X224: proces634752977rocess @ A] : X224 ) ) ).
% 0.31/0.47
% 0.31/0.47 % ch2Of_def
% 0.31/0.47 thf(fact_193_ch1Of__def,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( proces979765041_ch1Of @ A )
% 0.31/0.47 = ( proces1406508781rocess @ A @ ( proces634752977rocess @ A )
% 0.31/0.47 @ ^ [Uu2: A,Uv2: proces634752977rocess @ A] : ( undefined @ ( proces634752977rocess @ A ) )
% 0.31/0.47 @ ^ [X213: proces634752977rocess @ A,X224: proces634752977rocess @ A] : X213 ) ) ).
% 0.31/0.47
% 0.31/0.47 % ch1Of_def
% 0.31/0.47 thf(fact_194_process_Odisc__transfer_I1_J,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType,R: A > B > $o] :
% 0.31/0.47 ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ $o @ $o @ ( proces749077512rocess @ A @ B @ R )
% 0.31/0.47 @ ^ [Y4: $o,Z: $o] : ( Y4 = Z )
% 0.31/0.47 @ ( proces10484146Action @ A )
% 0.31/0.47 @ ( proces10484146Action @ B ) ) ).
% 0.31/0.47
% 0.31/0.47 % process.disc_transfer(1)
% 0.31/0.47 thf(fact_195_process_Odisc__transfer_I2_J,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType,R: A > B > $o] :
% 0.31/0.47 ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ $o @ $o @ ( proces749077512rocess @ A @ B @ R )
% 0.31/0.47 @ ^ [Y4: $o,Z: $o] : ( Y4 = Z )
% 0.31/0.47 @ ( proces401113213Choice @ A )
% 0.31/0.47 @ ( proces401113213Choice @ B ) ) ).
% 0.31/0.47
% 0.31/0.47 % process.disc_transfer(2)
% 0.31/0.47 thf(fact_196_rel__fun__mono_H,axiom,
% 0.31/0.47 ! [A: $tType,C: $tType,D: $tType,B: $tType,Y7: A > B > $o,X: A > B > $o,A4: C > D > $o,B6: C > D > $o,F: A > C,G: B > D] :
% 0.31/0.47 ( ! [X5: A,Y5: B] :
% 0.31/0.47 ( ( Y7 @ X5 @ Y5 )
% 0.31/0.47 => ( X @ X5 @ Y5 ) )
% 0.31/0.47 => ( ! [X5: C,Y5: D] :
% 0.31/0.47 ( ( A4 @ X5 @ Y5 )
% 0.31/0.47 => ( B6 @ X5 @ Y5 ) )
% 0.31/0.47 => ( ( bNF_rel_fun @ A @ B @ C @ D @ X @ A4 @ F @ G )
% 0.31/0.47 => ( bNF_rel_fun @ A @ B @ C @ D @ Y7 @ B6 @ F @ G ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % rel_fun_mono'
% 0.31/0.47 thf(fact_197_rel__fun__mono,axiom,
% 0.31/0.47 ! [A: $tType,C: $tType,D: $tType,B: $tType,X: A > B > $o,A4: C > D > $o,F: A > C,G: B > D,Y7: A > B > $o,B6: C > D > $o] :
% 0.31/0.47 ( ( bNF_rel_fun @ A @ B @ C @ D @ X @ A4 @ F @ G )
% 0.31/0.47 => ( ! [X5: A,Y5: B] :
% 0.31/0.47 ( ( Y7 @ X5 @ Y5 )
% 0.31/0.47 => ( X @ X5 @ Y5 ) )
% 0.31/0.47 => ( ! [X5: C,Y5: D] :
% 0.31/0.47 ( ( A4 @ X5 @ Y5 )
% 0.31/0.47 => ( B6 @ X5 @ Y5 ) )
% 0.31/0.47 => ( bNF_rel_fun @ A @ B @ C @ D @ Y7 @ B6 @ F @ G ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % rel_fun_mono
% 0.31/0.47 thf(fact_198_rel__funD,axiom,
% 0.31/0.47 ! [A: $tType,C: $tType,D: $tType,B: $tType,A4: A > B > $o,B6: C > D > $o,F: A > C,G: B > D,X7: A,Y3: B] :
% 0.31/0.47 ( ( bNF_rel_fun @ A @ B @ C @ D @ A4 @ B6 @ F @ G )
% 0.31/0.47 => ( ( A4 @ X7 @ Y3 )
% 0.31/0.47 => ( B6 @ ( F @ X7 ) @ ( G @ Y3 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % rel_funD
% 0.31/0.47 thf(fact_199_prefOf__def,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( proces745025900prefOf @ A )
% 0.31/0.47 = ( proces1406508781rocess @ A @ A
% 0.31/0.47 @ ^ [X112: A,X123: proces634752977rocess @ A] : X112
% 0.31/0.47 @ ^ [Uu2: proces634752977rocess @ A,Uv2: proces634752977rocess @ A] : ( undefined @ A ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % prefOf_def
% 0.31/0.47 thf(fact_200_CONT_Osimps_I1_J,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType,Sys: A > ( proces554692349s_term @ B @ A ),X: A] :
% 0.31/0.47 ( ( proces126235999e_CONT @ A @ B @ Sys @ ( proces1627516585ss_VAR @ A @ B @ X ) )
% 0.31/0.47 = ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 0.31/0.47 @ ^ [Aa3: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.31/0.47 @ ^ [P7: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces1778668539contOf @ B @ P7 ) )
% 0.31/0.47 @ ^ [A7: B,T4: proces554692349s_term @ B @ A] : T4
% 0.31/0.47 @ ^ [Aa3: proces554692349s_term @ B @ A,Ab2: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.31/0.47 @ ( Sys @ X ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % CONT.simps(1)
% 0.31/0.47 thf(fact_201_CH1_Osimps_I1_J,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType,Sys: A > ( proces554692349s_term @ B @ A ),X: A] :
% 0.31/0.47 ( ( proces1239275103le_CH1 @ A @ B @ Sys @ ( proces1627516585ss_VAR @ A @ B @ X ) )
% 0.31/0.47 = ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 0.31/0.47 @ ^ [A7: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.31/0.47 @ ^ [P7: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces979765041_ch1Of @ B @ P7 ) )
% 0.31/0.47 @ ^ [A7: B,B4: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.31/0.47 @ ^ [T13: proces554692349s_term @ B @ A,T24: proces554692349s_term @ B @ A] : T13
% 0.31/0.47 @ ( Sys @ X ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % CH1.simps(1)
% 0.31/0.47 thf(fact_202_CH2_Osimps_I1_J,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType,Sys: A > ( proces554692349s_term @ B @ A ),X: A] :
% 0.31/0.47 ( ( proces1239275104le_CH2 @ A @ B @ Sys @ ( proces1627516585ss_VAR @ A @ B @ X ) )
% 0.31/0.47 = ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 0.31/0.47 @ ^ [A7: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.31/0.47 @ ^ [P7: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces988026546_ch2Of @ B @ P7 ) )
% 0.31/0.47 @ ^ [A7: B,B4: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.31/0.47 @ ^ [T13: proces554692349s_term @ B @ A,T24: proces554692349s_term @ B @ A] : T24
% 0.31/0.47 @ ( Sys @ X ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % CH2.simps(1)
% 0.31/0.47 thf(fact_203_PREF_Osimps_I1_J,axiom,
% 0.31/0.47 ! [B: $tType,C: $tType,A: $tType,Sys: A > ( proces554692349s_term @ B @ C ),X: A] :
% 0.31/0.47 ( ( proces1708129104e_PREF @ A @ B @ C @ Sys @ ( proces1627516585ss_VAR @ A @ B @ X ) )
% 0.31/0.47 = ( proces460752237s_term @ C @ B @ B
% 0.31/0.47 @ ^ [Aa3: C] : ( undefined @ B )
% 0.31/0.47 @ ( proces745025900prefOf @ B )
% 0.31/0.47 @ ^ [A7: B,T4: proces554692349s_term @ B @ C] : A7
% 0.31/0.47 @ ^ [Aa3: proces554692349s_term @ B @ C,Ab2: proces554692349s_term @ B @ C] : ( undefined @ B )
% 0.31/0.47 @ ( Sys @ X ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % PREF.simps(1)
% 0.31/0.47 thf(fact_204_CONT_Oelims,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType,X7: A > ( proces554692349s_term @ B @ A ),Xa2: proces554692349s_term @ B @ A,Y3: proces554692349s_term @ B @ A] :
% 0.31/0.47 ( ( ( proces126235999e_CONT @ A @ B @ X7 @ Xa2 )
% 0.31/0.47 = Y3 )
% 0.31/0.47 => ( ! [X3: A] :
% 0.31/0.47 ( ( Xa2
% 0.31/0.47 = ( proces1627516585ss_VAR @ A @ B @ X3 ) )
% 0.31/0.47 => ( Y3
% 0.31/0.47 != ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 0.31/0.47 @ ^ [Aa3: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.31/0.47 @ ^ [P7: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces1778668539contOf @ B @ P7 ) )
% 0.31/0.47 @ ^ [A7: B,T4: proces554692349s_term @ B @ A] : T4
% 0.31/0.47 @ ^ [Aa3: proces554692349s_term @ B @ A,Ab2: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.31/0.47 @ ( X7 @ X3 ) ) ) )
% 0.31/0.47 => ( ! [P4: proces634752977rocess @ B] :
% 0.31/0.47 ( ( Xa2
% 0.31/0.47 = ( proces1062592052s_PROC @ B @ A @ P4 ) )
% 0.31/0.47 => ( Y3
% 0.31/0.47 != ( proces1062592052s_PROC @ B @ A @ ( proces1778668539contOf @ B @ P4 ) ) ) )
% 0.31/0.47 => ( ! [A3: B,T3: proces554692349s_term @ B @ A] :
% 0.31/0.47 ( ( Xa2
% 0.31/0.47 = ( proces1454156180ss_ACT @ B @ A @ A3 @ T3 ) )
% 0.31/0.47 => ( Y3 != T3 ) )
% 0.31/0.47 => ~ ( ? [V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] :
% 0.31/0.47 ( Xa2
% 0.31/0.47 = ( proces89589571ess_CH @ B @ A @ V @ Va ) )
% 0.31/0.47 => ( Y3
% 0.31/0.47 != ( undefined @ ( proces554692349s_term @ B @ A ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % CONT.elims
% 0.31/0.47 thf(fact_205_CH2_Oelims,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType,X7: A > ( proces554692349s_term @ B @ A ),Xa2: proces554692349s_term @ B @ A,Y3: proces554692349s_term @ B @ A] :
% 0.31/0.47 ( ( ( proces1239275104le_CH2 @ A @ B @ X7 @ Xa2 )
% 0.31/0.47 = Y3 )
% 0.31/0.47 => ( ! [X3: A] :
% 0.31/0.47 ( ( Xa2
% 0.31/0.47 = ( proces1627516585ss_VAR @ A @ B @ X3 ) )
% 0.31/0.47 => ( Y3
% 0.31/0.47 != ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 0.31/0.47 @ ^ [A7: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.31/0.47 @ ^ [P7: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces988026546_ch2Of @ B @ P7 ) )
% 0.31/0.47 @ ^ [A7: B,B4: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.31/0.47 @ ^ [T13: proces554692349s_term @ B @ A,T24: proces554692349s_term @ B @ A] : T24
% 0.31/0.47 @ ( X7 @ X3 ) ) ) )
% 0.31/0.47 => ( ! [P4: proces634752977rocess @ B] :
% 0.31/0.47 ( ( Xa2
% 0.31/0.47 = ( proces1062592052s_PROC @ B @ A @ P4 ) )
% 0.31/0.47 => ( Y3
% 0.31/0.47 != ( proces1062592052s_PROC @ B @ A @ ( proces988026546_ch2Of @ B @ P4 ) ) ) )
% 0.31/0.47 => ( ! [T12: proces554692349s_term @ B @ A,T23: proces554692349s_term @ B @ A] :
% 0.31/0.47 ( ( Xa2
% 0.31/0.47 = ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) )
% 0.31/0.47 => ( Y3 != T23 ) )
% 0.31/0.47 => ~ ( ? [V: B,Va: proces554692349s_term @ B @ A] :
% 0.31/0.47 ( Xa2
% 0.31/0.47 = ( proces1454156180ss_ACT @ B @ A @ V @ Va ) )
% 0.31/0.47 => ( Y3
% 0.31/0.47 != ( undefined @ ( proces554692349s_term @ B @ A ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % CH2.elims
% 0.31/0.47 thf(fact_206_Let__transfer,axiom,
% 0.31/0.47 ! [A: $tType,C: $tType,D: $tType,B: $tType,A4: A > B > $o,B6: C > D > $o] :
% 0.31/0.47 ( bNF_rel_fun @ A @ B @ ( ( A > C ) > C ) @ ( ( B > D ) > D ) @ A4 @ ( bNF_rel_fun @ ( A > C ) @ ( B > D ) @ C @ D @ ( bNF_rel_fun @ A @ B @ C @ D @ A4 @ B6 ) @ B6 )
% 0.31/0.47 @ ^ [S4: A,F7: A > C] : ( F7 @ S4 )
% 0.31/0.47 @ ^ [S4: B,F7: B > D] : ( F7 @ S4 ) ) ).
% 0.31/0.47
% 0.31/0.47 % Let_transfer
% 0.31/0.47 thf(fact_207_let__rsp,axiom,
% 0.31/0.47 ! [A: $tType,C: $tType,D: $tType,B: $tType,R1: A > B > $o,R22: C > D > $o] :
% 0.31/0.47 ( bNF_rel_fun @ A @ B @ ( ( A > C ) > C ) @ ( ( B > D ) > D ) @ R1 @ ( bNF_rel_fun @ ( A > C ) @ ( B > D ) @ C @ D @ ( bNF_rel_fun @ A @ B @ C @ D @ R1 @ R22 ) @ R22 )
% 0.31/0.47 @ ^ [S4: A,F7: A > C] : ( F7 @ S4 )
% 0.31/0.47 @ ^ [S4: B,F7: B > D] : ( F7 @ S4 ) ) ).
% 0.31/0.47
% 0.31/0.47 % let_rsp
% 0.31/0.47 thf(fact_208_CH2_Opelims,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType,X7: A > ( proces554692349s_term @ B @ A ),Xa2: proces554692349s_term @ B @ A,Y3: proces554692349s_term @ B @ A] :
% 0.31/0.47 ( ( ( proces1239275104le_CH2 @ A @ B @ X7 @ Xa2 )
% 0.31/0.47 = Y3 )
% 0.31/0.47 => ( ( 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 ) @ X7 @ Xa2 ) )
% 0.31/0.47 => ( ! [X3: A] :
% 0.31/0.47 ( ( Xa2
% 0.31/0.47 = ( proces1627516585ss_VAR @ A @ B @ X3 ) )
% 0.31/0.47 => ( ( Y3
% 0.31/0.47 = ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 0.31/0.47 @ ^ [A7: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.31/0.47 @ ^ [P7: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces988026546_ch2Of @ B @ P7 ) )
% 0.31/0.47 @ ^ [A7: B,B4: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.31/0.47 @ ^ [T13: proces554692349s_term @ B @ A,T24: proces554692349s_term @ B @ A] : T24
% 0.31/0.47 @ ( X7 @ X3 ) ) )
% 0.31/0.47 => ~ ( 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 ) @ X7 @ ( proces1627516585ss_VAR @ A @ B @ X3 ) ) ) ) )
% 0.31/0.47 => ( ! [P4: proces634752977rocess @ B] :
% 0.31/0.47 ( ( Xa2
% 0.31/0.47 = ( proces1062592052s_PROC @ B @ A @ P4 ) )
% 0.31/0.47 => ( ( Y3
% 0.31/0.47 = ( proces1062592052s_PROC @ B @ A @ ( proces988026546_ch2Of @ B @ P4 ) ) )
% 0.31/0.47 => ~ ( 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 ) @ X7 @ ( proces1062592052s_PROC @ B @ A @ P4 ) ) ) ) )
% 0.31/0.47 => ( ! [T12: proces554692349s_term @ B @ A,T23: proces554692349s_term @ B @ A] :
% 0.31/0.47 ( ( Xa2
% 0.31/0.47 = ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) )
% 0.31/0.47 => ( ( Y3 = T23 )
% 0.31/0.47 => ~ ( 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 ) @ X7 @ ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) ) ) ) )
% 0.31/0.47 => ~ ! [V: B,Va: proces554692349s_term @ B @ A] :
% 0.31/0.47 ( ( Xa2
% 0.31/0.47 = ( proces1454156180ss_ACT @ B @ A @ V @ Va ) )
% 0.31/0.47 => ( ( Y3
% 0.31/0.47 = ( undefined @ ( proces554692349s_term @ B @ A ) ) )
% 0.31/0.47 => ~ ( 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 ) @ X7 @ ( proces1454156180ss_ACT @ B @ A @ V @ Va ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % CH2.pelims
% 0.31/0.47 thf(fact_209_rel__funE,axiom,
% 0.31/0.47 ! [A: $tType,C: $tType,D: $tType,B: $tType,A4: A > B > $o,B6: C > D > $o,F: A > C,G: B > D,X7: A,Y3: B] :
% 0.31/0.47 ( ( bNF_rel_fun @ A @ B @ C @ D @ A4 @ B6 @ F @ G )
% 0.31/0.47 => ( ( A4 @ X7 @ Y3 )
% 0.31/0.47 => ( B6 @ ( F @ X7 ) @ ( G @ Y3 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % rel_funE
% 0.31/0.47 thf(fact_210_rel__funD2,axiom,
% 0.31/0.47 ! [B: $tType,C: $tType,A: $tType,A4: A > A > $o,B6: B > C > $o,F: A > B,G: A > C,X7: A] :
% 0.31/0.47 ( ( bNF_rel_fun @ A @ A @ B @ C @ A4 @ B6 @ F @ G )
% 0.31/0.47 => ( ( A4 @ X7 @ X7 )
% 0.31/0.47 => ( B6 @ ( F @ X7 ) @ ( G @ X7 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % rel_funD2
% 0.31/0.47 thf(fact_211_CH1_Opelims,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType,X7: A > ( proces554692349s_term @ B @ A ),Xa2: proces554692349s_term @ B @ A,Y3: proces554692349s_term @ B @ A] :
% 0.31/0.47 ( ( ( proces1239275103le_CH1 @ A @ B @ X7 @ Xa2 )
% 0.31/0.47 = Y3 )
% 0.31/0.47 => ( ( 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 ) @ X7 @ Xa2 ) )
% 0.31/0.47 => ( ! [X3: A] :
% 0.31/0.47 ( ( Xa2
% 0.31/0.47 = ( proces1627516585ss_VAR @ A @ B @ X3 ) )
% 0.31/0.47 => ( ( Y3
% 0.31/0.47 = ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 0.31/0.47 @ ^ [A7: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.31/0.47 @ ^ [P7: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces979765041_ch1Of @ B @ P7 ) )
% 0.31/0.47 @ ^ [A7: B,B4: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.31/0.47 @ ^ [T13: proces554692349s_term @ B @ A,T24: proces554692349s_term @ B @ A] : T13
% 0.31/0.47 @ ( X7 @ X3 ) ) )
% 0.31/0.47 => ~ ( 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 ) @ X7 @ ( proces1627516585ss_VAR @ A @ B @ X3 ) ) ) ) )
% 0.31/0.47 => ( ! [P4: proces634752977rocess @ B] :
% 0.31/0.47 ( ( Xa2
% 0.31/0.47 = ( proces1062592052s_PROC @ B @ A @ P4 ) )
% 0.31/0.47 => ( ( Y3
% 0.31/0.47 = ( proces1062592052s_PROC @ B @ A @ ( proces979765041_ch1Of @ B @ P4 ) ) )
% 0.31/0.47 => ~ ( 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 ) @ X7 @ ( proces1062592052s_PROC @ B @ A @ P4 ) ) ) ) )
% 0.31/0.47 => ( ! [T12: proces554692349s_term @ B @ A,T23: proces554692349s_term @ B @ A] :
% 0.31/0.47 ( ( Xa2
% 0.31/0.47 = ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) )
% 0.31/0.47 => ( ( Y3 = T12 )
% 0.31/0.47 => ~ ( 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 ) @ X7 @ ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) ) ) ) )
% 0.31/0.47 => ~ ! [V: B,Va: proces554692349s_term @ B @ A] :
% 0.31/0.47 ( ( Xa2
% 0.31/0.47 = ( proces1454156180ss_ACT @ B @ A @ V @ Va ) )
% 0.31/0.47 => ( ( Y3
% 0.31/0.47 = ( undefined @ ( proces554692349s_term @ B @ A ) ) )
% 0.31/0.47 => ~ ( 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 ) @ X7 @ ( proces1454156180ss_ACT @ B @ A @ V @ Va ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % CH1.pelims
% 0.31/0.47 thf(fact_212_CONT_Opelims,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType,X7: A > ( proces554692349s_term @ B @ A ),Xa2: proces554692349s_term @ B @ A,Y3: proces554692349s_term @ B @ A] :
% 0.31/0.47 ( ( ( proces126235999e_CONT @ A @ B @ X7 @ Xa2 )
% 0.31/0.47 = Y3 )
% 0.31/0.47 => ( ( 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 ) @ X7 @ Xa2 ) )
% 0.31/0.47 => ( ! [X3: A] :
% 0.31/0.47 ( ( Xa2
% 0.31/0.47 = ( proces1627516585ss_VAR @ A @ B @ X3 ) )
% 0.31/0.47 => ( ( Y3
% 0.31/0.47 = ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 0.31/0.47 @ ^ [Aa3: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.31/0.47 @ ^ [P7: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces1778668539contOf @ B @ P7 ) )
% 0.31/0.47 @ ^ [A7: B,T4: proces554692349s_term @ B @ A] : T4
% 0.31/0.47 @ ^ [Aa3: proces554692349s_term @ B @ A,Ab2: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.31/0.47 @ ( X7 @ X3 ) ) )
% 0.31/0.47 => ~ ( 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 ) @ X7 @ ( proces1627516585ss_VAR @ A @ B @ X3 ) ) ) ) )
% 0.31/0.47 => ( ! [P4: proces634752977rocess @ B] :
% 0.31/0.47 ( ( Xa2
% 0.31/0.47 = ( proces1062592052s_PROC @ B @ A @ P4 ) )
% 0.31/0.47 => ( ( Y3
% 0.31/0.47 = ( proces1062592052s_PROC @ B @ A @ ( proces1778668539contOf @ B @ P4 ) ) )
% 0.31/0.47 => ~ ( 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 ) @ X7 @ ( proces1062592052s_PROC @ B @ A @ P4 ) ) ) ) )
% 0.31/0.47 => ( ! [A3: B,T3: proces554692349s_term @ B @ A] :
% 0.31/0.47 ( ( Xa2
% 0.31/0.47 = ( proces1454156180ss_ACT @ B @ A @ A3 @ T3 ) )
% 0.31/0.47 => ( ( Y3 = T3 )
% 0.31/0.47 => ~ ( 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 ) @ X7 @ ( proces1454156180ss_ACT @ B @ A @ A3 @ T3 ) ) ) ) )
% 0.31/0.47 => ~ ! [V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] :
% 0.31/0.47 ( ( Xa2
% 0.31/0.47 = ( proces89589571ess_CH @ B @ A @ V @ Va ) )
% 0.31/0.47 => ( ( Y3
% 0.31/0.47 = ( undefined @ ( proces554692349s_term @ B @ A ) ) )
% 0.31/0.47 => ~ ( 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 ) @ X7 @ ( proces89589571ess_CH @ B @ A @ V @ Va ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % CONT.pelims
% 0.31/0.47 thf(fact_213_PREF_Opelims,axiom,
% 0.31/0.47 ! [C: $tType,A: $tType,B: $tType,X7: A > ( proces554692349s_term @ B @ C ),Xa2: proces554692349s_term @ B @ A,Y3: B] :
% 0.31/0.47 ( ( ( proces1708129104e_PREF @ A @ B @ C @ X7 @ Xa2 )
% 0.31/0.47 = Y3 )
% 0.31/0.47 => ( ( 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 ) @ X7 @ Xa2 ) )
% 0.31/0.47 => ( ! [X3: A] :
% 0.31/0.47 ( ( Xa2
% 0.31/0.47 = ( proces1627516585ss_VAR @ A @ B @ X3 ) )
% 0.31/0.47 => ( ( Y3
% 0.31/0.47 = ( proces460752237s_term @ C @ B @ B
% 0.31/0.47 @ ^ [Aa3: C] : ( undefined @ B )
% 0.31/0.47 @ ( proces745025900prefOf @ B )
% 0.31/0.47 @ ^ [A7: B,T4: proces554692349s_term @ B @ C] : A7
% 0.31/0.47 @ ^ [Aa3: proces554692349s_term @ B @ C,Ab2: proces554692349s_term @ B @ C] : ( undefined @ B )
% 0.31/0.47 @ ( X7 @ X3 ) ) )
% 0.31/0.47 => ~ ( 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 ) @ X7 @ ( proces1627516585ss_VAR @ A @ B @ X3 ) ) ) ) )
% 0.31/0.47 => ( ! [P4: proces634752977rocess @ B] :
% 0.31/0.47 ( ( Xa2
% 0.31/0.47 = ( proces1062592052s_PROC @ B @ A @ P4 ) )
% 0.31/0.47 => ( ( Y3
% 0.31/0.47 = ( proces745025900prefOf @ B @ P4 ) )
% 0.31/0.47 => ~ ( 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 ) @ X7 @ ( proces1062592052s_PROC @ B @ A @ P4 ) ) ) ) )
% 0.31/0.47 => ( ! [A3: B,T3: proces554692349s_term @ B @ A] :
% 0.31/0.47 ( ( Xa2
% 0.31/0.47 = ( proces1454156180ss_ACT @ B @ A @ A3 @ T3 ) )
% 0.31/0.47 => ( ( Y3 = A3 )
% 0.31/0.47 => ~ ( 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 ) @ X7 @ ( proces1454156180ss_ACT @ B @ A @ A3 @ T3 ) ) ) ) )
% 0.31/0.47 => ~ ! [V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] :
% 0.31/0.47 ( ( Xa2
% 0.31/0.47 = ( proces89589571ess_CH @ B @ A @ V @ Va ) )
% 0.31/0.47 => ( ( Y3
% 0.31/0.47 = ( undefined @ B ) )
% 0.31/0.47 => ~ ( 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 ) @ X7 @ ( proces89589571ess_CH @ B @ A @ V @ Va ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % PREF.pelims
% 0.31/0.47 thf(fact_214_isACT_Opelims_I1_J,axiom,
% 0.31/0.47 ! [B: $tType,C: $tType,A: $tType,D: $tType,X7: A > ( proces554692349s_term @ B @ C ),Xa2: proces554692349s_term @ D @ A,Y3: $o] :
% 0.31/0.47 ( ( ( proces687458811_isACT @ A @ B @ C @ D @ X7 @ Xa2 )
% 0.31/0.47 = Y3 )
% 0.31/0.47 => ( ( 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 ) @ X7 @ Xa2 ) )
% 0.31/0.47 => ( ! [X3: A] :
% 0.31/0.47 ( ( Xa2
% 0.31/0.47 = ( proces1627516585ss_VAR @ A @ D @ X3 ) )
% 0.31/0.47 => ( ( Y3
% 0.31/0.47 = ( proces460752237s_term @ C @ $o @ B
% 0.31/0.47 @ ^ [Pvar2: C] : $false
% 0.31/0.47 @ ( proces10484146Action @ B )
% 0.31/0.47 @ ^ [A7: B,T4: proces554692349s_term @ B @ C] : $true
% 0.31/0.47 @ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
% 0.31/0.47 @ ( X7 @ X3 ) ) )
% 0.31/0.47 => ~ ( 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 ) @ X7 @ ( proces1627516585ss_VAR @ A @ D @ X3 ) ) ) ) )
% 0.31/0.47 => ( ! [P4: proces634752977rocess @ D] :
% 0.31/0.47 ( ( Xa2
% 0.31/0.47 = ( proces1062592052s_PROC @ D @ A @ P4 ) )
% 0.31/0.47 => ( ( Y3
% 0.31/0.47 = ( proces10484146Action @ D @ P4 ) )
% 0.31/0.47 => ~ ( 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 ) @ X7 @ ( proces1062592052s_PROC @ D @ A @ P4 ) ) ) ) )
% 0.31/0.47 => ( ! [A3: D,T3: proces554692349s_term @ D @ A] :
% 0.31/0.47 ( ( Xa2
% 0.31/0.47 = ( proces1454156180ss_ACT @ D @ A @ A3 @ T3 ) )
% 0.31/0.47 => ( Y3
% 0.31/0.47 => ~ ( 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 ) @ X7 @ ( proces1454156180ss_ACT @ D @ A @ A3 @ T3 ) ) ) ) )
% 0.31/0.47 => ~ ! [T12: proces554692349s_term @ D @ A,T23: proces554692349s_term @ D @ A] :
% 0.31/0.47 ( ( Xa2
% 0.31/0.47 = ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) )
% 0.31/0.47 => ( ~ Y3
% 0.31/0.47 => ~ ( 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 ) @ X7 @ ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % isACT.pelims(1)
% 0.31/0.47 thf(fact_215_isACT_Opelims_I3_J,axiom,
% 0.31/0.47 ! [B: $tType,C: $tType,A: $tType,D: $tType,X7: A > ( proces554692349s_term @ B @ C ),Xa2: proces554692349s_term @ D @ A] :
% 0.31/0.47 ( ~ ( proces687458811_isACT @ A @ B @ C @ D @ X7 @ Xa2 )
% 0.31/0.47 => ( ( 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 ) @ X7 @ Xa2 ) )
% 0.31/0.47 => ( ! [X3: A] :
% 0.31/0.47 ( ( Xa2
% 0.31/0.47 = ( proces1627516585ss_VAR @ A @ D @ X3 ) )
% 0.31/0.47 => ( ( 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 ) @ X7 @ ( proces1627516585ss_VAR @ A @ D @ X3 ) ) )
% 0.31/0.47 => ( proces460752237s_term @ C @ $o @ B
% 0.31/0.47 @ ^ [Pvar2: C] : $false
% 0.31/0.47 @ ( proces10484146Action @ B )
% 0.31/0.47 @ ^ [A7: B,T4: proces554692349s_term @ B @ C] : $true
% 0.31/0.47 @ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
% 0.31/0.47 @ ( X7 @ X3 ) ) ) )
% 0.31/0.47 => ( ! [P4: proces634752977rocess @ D] :
% 0.31/0.47 ( ( Xa2
% 0.31/0.47 = ( proces1062592052s_PROC @ D @ A @ P4 ) )
% 0.31/0.47 => ( ( 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 ) @ X7 @ ( proces1062592052s_PROC @ D @ A @ P4 ) ) )
% 0.31/0.47 => ( proces10484146Action @ D @ P4 ) ) )
% 0.31/0.47 => ~ ! [T12: proces554692349s_term @ D @ A,T23: proces554692349s_term @ D @ A] :
% 0.31/0.47 ( ( Xa2
% 0.31/0.47 = ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) )
% 0.31/0.47 => ~ ( 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 ) @ X7 @ ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % isACT.pelims(3)
% 0.31/0.47 thf(fact_216_isACT_Opelims_I2_J,axiom,
% 0.31/0.47 ! [B: $tType,C: $tType,A: $tType,D: $tType,X7: A > ( proces554692349s_term @ B @ C ),Xa2: proces554692349s_term @ D @ A] :
% 0.31/0.47 ( ( proces687458811_isACT @ A @ B @ C @ D @ X7 @ Xa2 )
% 0.31/0.47 => ( ( 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 ) @ X7 @ Xa2 ) )
% 0.31/0.47 => ( ! [X3: A] :
% 0.31/0.47 ( ( Xa2
% 0.31/0.47 = ( proces1627516585ss_VAR @ A @ D @ X3 ) )
% 0.31/0.47 => ( ( 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 ) @ X7 @ ( proces1627516585ss_VAR @ A @ D @ X3 ) ) )
% 0.31/0.47 => ~ ( proces460752237s_term @ C @ $o @ B
% 0.31/0.47 @ ^ [Pvar2: C] : $false
% 0.31/0.47 @ ( proces10484146Action @ B )
% 0.31/0.47 @ ^ [A7: B,T4: proces554692349s_term @ B @ C] : $true
% 0.31/0.47 @ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
% 0.31/0.47 @ ( X7 @ X3 ) ) ) )
% 0.31/0.47 => ( ! [P4: proces634752977rocess @ D] :
% 0.31/0.47 ( ( Xa2
% 0.31/0.47 = ( proces1062592052s_PROC @ D @ A @ P4 ) )
% 0.31/0.47 => ( ( 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 ) @ X7 @ ( proces1062592052s_PROC @ D @ A @ P4 ) ) )
% 0.31/0.47 => ~ ( proces10484146Action @ D @ P4 ) ) )
% 0.31/0.47 => ~ ! [A3: D,T3: proces554692349s_term @ D @ A] :
% 0.31/0.47 ( ( Xa2
% 0.31/0.47 = ( proces1454156180ss_ACT @ D @ A @ A3 @ T3 ) )
% 0.31/0.47 => ~ ( 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 ) @ X7 @ ( proces1454156180ss_ACT @ D @ A @ A3 @ T3 ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % isACT.pelims(2)
% 0.31/0.47 thf(fact_217_fun_Orel__transfer,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType,C: $tType,E: $tType,D: $tType,Sa: A > C > $o,Sc: B > E > $o] :
% 0.31/0.47 ( bNF_rel_fun @ ( A > B > $o ) @ ( C > E > $o ) @ ( ( D > A ) > ( D > B ) > $o ) @ ( ( D > C ) > ( D > E ) > $o )
% 0.31/0.47 @ ( bNF_rel_fun @ A @ C @ ( B > $o ) @ ( E > $o ) @ Sa
% 0.31/0.47 @ ( bNF_rel_fun @ B @ E @ $o @ $o @ Sc
% 0.31/0.47 @ ^ [Y4: $o,Z: $o] : ( Y4 = Z ) ) )
% 0.31/0.47 @ ( bNF_rel_fun @ ( D > A ) @ ( D > C ) @ ( ( D > B ) > $o ) @ ( ( D > E ) > $o )
% 0.31/0.47 @ ( bNF_rel_fun @ D @ D @ A @ C
% 0.31/0.47 @ ^ [Y4: D,Z: D] : ( Y4 = Z )
% 0.31/0.47 @ Sa )
% 0.31/0.47 @ ( bNF_rel_fun @ ( D > B ) @ ( D > E ) @ $o @ $o
% 0.31/0.47 @ ( bNF_rel_fun @ D @ D @ B @ E
% 0.31/0.47 @ ^ [Y4: D,Z: D] : ( Y4 = Z )
% 0.31/0.47 @ Sc )
% 0.31/0.47 @ ^ [Y4: $o,Z: $o] : ( Y4 = Z ) ) )
% 0.31/0.47 @ ( bNF_rel_fun @ D @ D @ A @ B
% 0.31/0.47 @ ^ [Y4: D,Z: D] : ( Y4 = Z ) )
% 0.31/0.47 @ ( bNF_rel_fun @ D @ D @ C @ E
% 0.31/0.47 @ ^ [Y4: D,Z: D] : ( Y4 = Z ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % fun.rel_transfer
% 0.31/0.47 thf(fact_218_If__transfer,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType,A4: A > B > $o] :
% 0.31/0.47 ( bNF_rel_fun @ $o @ $o @ ( A > A > A ) @ ( B > B > B )
% 0.31/0.47 @ ^ [Y4: $o,Z: $o] : ( Y4 = Z )
% 0.31/0.47 @ ( bNF_rel_fun @ A @ B @ ( A > A ) @ ( B > B ) @ A4 @ ( bNF_rel_fun @ A @ B @ A @ B @ A4 @ A4 ) )
% 0.31/0.47 @ ( if @ A )
% 0.31/0.47 @ ( if @ B ) ) ).
% 0.31/0.47
% 0.31/0.47 % If_transfer
% 0.31/0.47 thf(fact_219_fun_Orel__refl,axiom,
% 0.31/0.47 ! [B: $tType,D: $tType,Ra: B > B > $o,X7: D > B] :
% 0.31/0.47 ( ! [X5: B] : ( Ra @ X5 @ X5 )
% 0.31/0.47 => ( bNF_rel_fun @ D @ D @ B @ B
% 0.31/0.47 @ ^ [Y4: D,Z: D] : ( Y4 = Z )
% 0.31/0.47 @ Ra
% 0.31/0.47 @ X7
% 0.31/0.47 @ X7 ) ) ).
% 0.31/0.47
% 0.31/0.47 % fun.rel_refl
% 0.31/0.47 thf(fact_220_fun_Orel__eq,axiom,
% 0.31/0.47 ! [A: $tType,D: $tType] :
% 0.31/0.47 ( ( bNF_rel_fun @ D @ D @ A @ A
% 0.31/0.47 @ ^ [Y4: D,Z: D] : ( Y4 = Z )
% 0.31/0.47 @ ^ [Y4: A,Z: A] : ( Y4 = Z ) )
% 0.31/0.47 = ( ^ [Y4: D > A,Z: D > A] : ( Y4 = Z ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % fun.rel_eq
% 0.31/0.47 thf(fact_221_rel__fun__def__butlast,axiom,
% 0.31/0.47 ! [B: $tType,D: $tType,C: $tType,E: $tType,F5: $tType,A: $tType,R: A > B > $o,S3: C > E > $o,T2: D > F5 > $o,F: A > C > D,G: B > E > F5] :
% 0.31/0.47 ( ( bNF_rel_fun @ A @ B @ ( C > D ) @ ( E > F5 ) @ R @ ( bNF_rel_fun @ C @ E @ D @ F5 @ S3 @ T2 ) @ F @ G )
% 0.31/0.47 = ( ! [X6: A,Y6: B] :
% 0.31/0.47 ( ( R @ X6 @ Y6 )
% 0.31/0.47 => ( bNF_rel_fun @ C @ E @ D @ F5 @ S3 @ T2 @ ( F @ X6 ) @ ( G @ Y6 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % rel_fun_def_butlast
% 0.31/0.47 thf(fact_222_process_Ocorec__transfer,axiom,
% 0.31/0.47 ! [C: $tType,A: $tType,B: $tType,D: $tType,S3: C > D > $o,R: A > B > $o] :
% 0.31/0.47 ( 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 ) )
% 0.31/0.47 @ ( bNF_rel_fun @ C @ D @ $o @ $o @ S3
% 0.31/0.47 @ ^ [Y4: $o,Z: $o] : ( Y4 = Z ) )
% 0.31/0.47 @ ( 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 @ S3 @ R )
% 0.31/0.47 @ ( 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 ) )
% 0.31/0.47 @ ( bNF_rel_fun @ C @ D @ $o @ $o @ S3
% 0.31/0.47 @ ^ [Y4: $o,Z: $o] : ( Y4 = Z ) )
% 0.31/0.47 @ ( 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 ) @ S3 @ ( proces749077512rocess @ A @ B @ R ) )
% 0.31/0.47 @ ( 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 @ S3 @ S3 )
% 0.31/0.47 @ ( 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 ) )
% 0.31/0.47 @ ( bNF_rel_fun @ C @ D @ $o @ $o @ S3
% 0.31/0.47 @ ^ [Y4: $o,Z: $o] : ( Y4 = Z ) )
% 0.31/0.47 @ ( 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 ) @ S3 @ ( proces749077512rocess @ A @ B @ R ) )
% 0.31/0.47 @ ( 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 @ S3 @ S3 )
% 0.31/0.47 @ ( bNF_rel_fun @ ( C > $o ) @ ( D > $o ) @ ( ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > C > ( proces634752977rocess @ A ) ) @ ( ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > D > ( proces634752977rocess @ B ) )
% 0.31/0.47 @ ( bNF_rel_fun @ C @ D @ $o @ $o @ S3
% 0.31/0.47 @ ^ [Y4: $o,Z: $o] : ( Y4 = Z ) )
% 0.31/0.47 @ ( 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 ) @ S3 @ ( proces749077512rocess @ A @ B @ R ) ) @ ( bNF_rel_fun @ ( C > C ) @ ( D > D ) @ ( C > ( proces634752977rocess @ A ) ) @ ( D > ( proces634752977rocess @ B ) ) @ ( bNF_rel_fun @ C @ D @ C @ D @ S3 @ S3 ) @ ( bNF_rel_fun @ C @ D @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ S3 @ ( proces749077512rocess @ A @ B @ R ) ) ) ) ) ) ) ) ) ) ) )
% 0.31/0.47 @ ( proces894737309rocess @ C @ A )
% 0.31/0.47 @ ( proces894737309rocess @ D @ B ) ) ).
% 0.31/0.47
% 0.31/0.47 % process.corec_transfer
% 0.31/0.47 thf(fact_223_map__fun__parametric,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType,E: $tType,F5: $tType,H2: $tType,G2: $tType,D: $tType,C: $tType,A4: A > C > $o,B6: B > D > $o,C5: E > G2 > $o,D3: F5 > H2 > $o] : ( bNF_rel_fun @ ( A > B ) @ ( C > D ) @ ( ( E > F5 ) > ( B > E ) > A > F5 ) @ ( ( G2 > H2 ) > ( D > G2 ) > C > H2 ) @ ( bNF_rel_fun @ A @ C @ B @ D @ A4 @ B6 ) @ ( bNF_rel_fun @ ( E > F5 ) @ ( G2 > H2 ) @ ( ( B > E ) > A > F5 ) @ ( ( D > G2 ) > C > H2 ) @ ( bNF_rel_fun @ E @ G2 @ F5 @ H2 @ C5 @ D3 ) @ ( bNF_rel_fun @ ( B > E ) @ ( D > G2 ) @ ( A > F5 ) @ ( C > H2 ) @ ( bNF_rel_fun @ B @ D @ E @ G2 @ B6 @ C5 ) @ ( bNF_rel_fun @ A @ C @ F5 @ H2 @ A4 @ D3 ) ) ) @ ( map_fun @ A @ B @ E @ F5 ) @ ( map_fun @ C @ D @ G2 @ H2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % map_fun_parametric
% 0.31/0.47 thf(fact_224_process_Ocorec__disc__iff_I1_J,axiom,
% 0.31/0.47 ! [A: $tType,C: $tType,P: 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,A2: C] :
% 0.31/0.47 ( ( proces10484146Action @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) )
% 0.31/0.47 = ( P @ A2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % process.corec_disc_iff(1)
% 0.31/0.47 thf(fact_225_process_Ocorec__disc__iff_I2_J,axiom,
% 0.31/0.47 ! [A: $tType,C: $tType,P: 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,A2: C] :
% 0.31/0.47 ( ( proces401113213Choice @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) )
% 0.31/0.47 = ( ~ ( P @ A2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % process.corec_disc_iff(2)
% 0.31/0.47 thf(fact_226_process_Ocorec__sel_I1_J,axiom,
% 0.31/0.47 ! [A: $tType,C: $tType,P: C > $o,A2: C,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] :
% 0.31/0.47 ( ( P @ A2 )
% 0.31/0.47 => ( ( proces745025900prefOf @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) )
% 0.31/0.47 = ( G11 @ A2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % process.corec_sel(1)
% 0.31/0.47 thf(fact_227_process_Ocorec__sel_I3_J,axiom,
% 0.31/0.47 ! [A: $tType,C: $tType,P: C > $o,A2: C,Q21: C > $o,G11: C > A,Q12: C > $o,G121: C > ( proces634752977rocess @ A ),G122: C > C,G211: C > ( proces634752977rocess @ A ),G212: C > C,Q22: C > $o,G221: C > ( proces634752977rocess @ A ),G222: C > C] :
% 0.31/0.47 ( ~ ( P @ A2 )
% 0.31/0.47 => ( ( ( Q21 @ A2 )
% 0.31/0.47 => ( ( proces979765041_ch1Of @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) )
% 0.31/0.47 = ( G211 @ A2 ) ) )
% 0.31/0.47 & ( ~ ( Q21 @ A2 )
% 0.31/0.47 => ( ( proces979765041_ch1Of @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) )
% 0.31/0.47 = ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ ( G212 @ A2 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % process.corec_sel(3)
% 0.31/0.47 thf(fact_228_process_Ocorec__sel_I4_J,axiom,
% 0.31/0.47 ! [A: $tType,C: $tType,P: C > $o,A2: C,Q22: 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,G221: C > ( proces634752977rocess @ A ),G222: C > C] :
% 0.31/0.47 ( ~ ( P @ A2 )
% 0.31/0.47 => ( ( ( Q22 @ A2 )
% 0.31/0.47 => ( ( proces988026546_ch2Of @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) )
% 0.31/0.47 = ( G221 @ A2 ) ) )
% 0.31/0.47 & ( ~ ( Q22 @ A2 )
% 0.31/0.47 => ( ( proces988026546_ch2Of @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) )
% 0.31/0.47 = ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ ( G222 @ A2 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % process.corec_sel(4)
% 0.31/0.47 thf(fact_229_process_Ocorec__sel_I2_J,axiom,
% 0.31/0.47 ! [A: $tType,C: $tType,P: C > $o,A2: C,Q12: C > $o,G11: C > A,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] :
% 0.31/0.47 ( ( P @ A2 )
% 0.31/0.47 => ( ( ( Q12 @ A2 )
% 0.31/0.47 => ( ( proces1778668539contOf @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) )
% 0.31/0.47 = ( G121 @ A2 ) ) )
% 0.31/0.47 & ( ~ ( Q12 @ A2 )
% 0.31/0.47 => ( ( proces1778668539contOf @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) )
% 0.31/0.47 = ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ ( G122 @ A2 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % process.corec_sel(2)
% 0.31/0.47 thf(fact_230_process_Ocorec__disc_I2_J,axiom,
% 0.31/0.47 ! [A: $tType,C: $tType,P: C > $o,A2: C,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] :
% 0.31/0.47 ( ~ ( P @ A2 )
% 0.31/0.47 => ( proces401113213Choice @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % process.corec_disc(2)
% 0.31/0.47 thf(fact_231_process_Ocorec_I2_J,axiom,
% 0.31/0.47 ! [A: $tType,C: $tType,P: C > $o,A2: C,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] :
% 0.31/0.47 ( ~ ( P @ A2 )
% 0.31/0.47 => ( ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 )
% 0.31/0.47 = ( proces1915862579Choice @ A @ ( if @ ( proces634752977rocess @ A ) @ ( Q21 @ A2 ) @ ( G211 @ A2 ) @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ ( G212 @ A2 ) ) ) @ ( if @ ( proces634752977rocess @ A ) @ ( Q22 @ A2 ) @ ( G221 @ A2 ) @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ ( G222 @ A2 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % process.corec(2)
% 0.31/0.47 thf(fact_232_process_Ocorec_I1_J,axiom,
% 0.31/0.47 ! [A: $tType,C: $tType,P: C > $o,A2: C,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] :
% 0.31/0.47 ( ( P @ A2 )
% 0.31/0.47 => ( ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 )
% 0.31/0.47 = ( proces1525233512Action @ A @ ( G11 @ A2 ) @ ( if @ ( proces634752977rocess @ A ) @ ( Q12 @ A2 ) @ ( G121 @ A2 ) @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ ( G122 @ A2 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % process.corec(1)
% 0.31/0.47 thf(fact_233_process_Ocorec__disc_I1_J,axiom,
% 0.31/0.47 ! [A: $tType,C: $tType,P: C > $o,A2: C,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] :
% 0.31/0.47 ( ( P @ A2 )
% 0.31/0.47 => ( proces10484146Action @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % process.corec_disc(1)
% 0.31/0.47 thf(fact_234_process_Ocorec__code,axiom,
% 0.31/0.47 ! [A: $tType,C: $tType] :
% 0.31/0.47 ( ( proces894737309rocess @ C @ A )
% 0.31/0.47 = ( ^ [P7: 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,A7: C] : ( if @ ( proces634752977rocess @ A ) @ ( P7 @ A7 ) @ ( proces1525233512Action @ A @ ( G112 @ A7 ) @ ( if @ ( proces634752977rocess @ A ) @ ( Q122 @ A7 ) @ ( G1212 @ A7 ) @ ( proces894737309rocess @ C @ A @ P7 @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ ( G1222 @ A7 ) ) ) ) @ ( proces1915862579Choice @ A @ ( if @ ( proces634752977rocess @ A ) @ ( Q212 @ A7 ) @ ( G2112 @ A7 ) @ ( proces894737309rocess @ C @ A @ P7 @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ ( G2122 @ A7 ) ) ) @ ( if @ ( proces634752977rocess @ A ) @ ( Q222 @ A7 ) @ ( G2212 @ A7 ) @ ( proces894737309rocess @ C @ A @ P7 @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ ( G2222 @ A7 ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % process.corec_code
% 0.31/0.47 thf(fact_235_fun_Opred__transfer,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType,D: $tType,R: A > B > $o] :
% 0.31/0.47 ( bNF_rel_fun @ ( A > $o ) @ ( B > $o ) @ ( ( D > A ) > $o ) @ ( ( D > B ) > $o )
% 0.31/0.47 @ ( bNF_rel_fun @ A @ B @ $o @ $o @ R
% 0.31/0.47 @ ^ [Y4: $o,Z: $o] : ( Y4 = Z ) )
% 0.31/0.47 @ ( bNF_rel_fun @ ( D > A ) @ ( D > B ) @ $o @ $o
% 0.31/0.47 @ ( bNF_rel_fun @ D @ D @ A @ B
% 0.31/0.47 @ ^ [Y4: D,Z: D] : ( Y4 = Z )
% 0.31/0.47 @ R )
% 0.31/0.47 @ ^ [Y4: $o,Z: $o] : ( Y4 = Z ) )
% 0.31/0.47 @ ( basic_pred_fun @ D @ A
% 0.31/0.47 @ ^ [Uu: D] : $true )
% 0.31/0.47 @ ( basic_pred_fun @ D @ B
% 0.31/0.47 @ ^ [Uu: D] : $true ) ) ).
% 0.31/0.47
% 0.31/0.47 % fun.pred_transfer
% 0.31/0.47 thf(fact_236_pred__equals__eq2,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType,R: set @ ( product_prod @ A @ B ),S3: set @ ( product_prod @ A @ B )] :
% 0.31/0.47 ( ( ( ^ [X6: A,Y6: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X6 @ Y6 ) @ R ) )
% 0.31/0.47 = ( ^ [X6: A,Y6: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X6 @ Y6 ) @ S3 ) ) )
% 0.31/0.47 = ( R = S3 ) ) ).
% 0.31/0.47
% 0.31/0.47 % pred_equals_eq2
% 0.31/0.47 thf(fact_237_fun_Opred__True,axiom,
% 0.31/0.47 ! [A: $tType,D: $tType] :
% 0.31/0.47 ( ( basic_pred_fun @ D @ A
% 0.31/0.47 @ ^ [Uu: D] : $true
% 0.31/0.47 @ ^ [Uu: A] : $true )
% 0.31/0.47 = ( ^ [Uu: D > A] : $true ) ) ).
% 0.31/0.47
% 0.31/0.47 % fun.pred_True
% 0.31/0.47 thf(fact_238_process__term_Omap__transfer,axiom,
% 0.31/0.47 ! [A: $tType,C: $tType,B: $tType,D: $tType,L: $tType,J: $tType,K: $tType,I: $tType,R1b: A > I > $o,S1d: C > K > $o,R2b: B > J > $o,S2d: D > L > $o] : ( bNF_rel_fun @ ( A > C ) @ ( I > K ) @ ( ( B > D ) > ( proces554692349s_term @ A @ B ) > ( proces554692349s_term @ C @ D ) ) @ ( ( J > L ) > ( proces554692349s_term @ I @ J ) > ( proces554692349s_term @ K @ L ) ) @ ( bNF_rel_fun @ A @ I @ C @ K @ R1b @ S1d ) @ ( bNF_rel_fun @ ( B > D ) @ ( J > L ) @ ( ( proces554692349s_term @ A @ B ) > ( proces554692349s_term @ C @ D ) ) @ ( ( proces554692349s_term @ I @ J ) > ( proces554692349s_term @ K @ L ) ) @ ( bNF_rel_fun @ B @ J @ D @ L @ R2b @ S2d ) @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ B ) @ ( proces554692349s_term @ I @ J ) @ ( proces554692349s_term @ C @ D ) @ ( proces554692349s_term @ K @ L ) @ ( proces2029722208s_term @ A @ I @ B @ J @ R1b @ R2b ) @ ( proces2029722208s_term @ C @ K @ D @ L @ S1d @ S2d ) ) ) @ ( proces224683037s_term @ A @ C @ B @ D ) @ ( proces224683037s_term @ I @ K @ J @ L ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_term.map_transfer
% 0.31/0.47 thf(fact_239_process_Omap__transfer,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType,F5: $tType,E: $tType,Rb: A > E > $o,Sd: B > F5 > $o] : ( bNF_rel_fun @ ( A > B ) @ ( E > F5 ) @ ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ B ) ) @ ( ( proces634752977rocess @ E ) > ( proces634752977rocess @ F5 ) ) @ ( bNF_rel_fun @ A @ E @ B @ F5 @ Rb @ Sd ) @ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ E ) @ ( proces634752977rocess @ B ) @ ( proces634752977rocess @ F5 ) @ ( proces749077512rocess @ A @ E @ Rb ) @ ( proces749077512rocess @ B @ F5 @ Sd ) ) @ ( proces370407749rocess @ A @ B ) @ ( proces370407749rocess @ E @ F5 ) ) ).
% 0.31/0.47
% 0.31/0.47 % process.map_transfer
% 0.31/0.47 thf(fact_240_process_Omap__disc__iff_I1_J,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType,F: A > B,A2: proces634752977rocess @ A] :
% 0.31/0.47 ( ( proces10484146Action @ B @ ( proces370407749rocess @ A @ B @ F @ A2 ) )
% 0.31/0.47 = ( proces10484146Action @ A @ A2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % process.map_disc_iff(1)
% 0.31/0.47 thf(fact_241_process_Omap__disc__iff_I2_J,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType,F: A > B,A2: proces634752977rocess @ A] :
% 0.31/0.47 ( ( proces401113213Choice @ B @ ( proces370407749rocess @ A @ B @ F @ A2 ) )
% 0.31/0.47 = ( proces401113213Choice @ A @ A2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % process.map_disc_iff(2)
% 0.31/0.47 thf(fact_242_process_Omap__sel_I3_J,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType,A2: proces634752977rocess @ A,F: A > B] :
% 0.31/0.47 ( ( proces401113213Choice @ A @ A2 )
% 0.31/0.47 => ( ( proces979765041_ch1Of @ B @ ( proces370407749rocess @ A @ B @ F @ A2 ) )
% 0.31/0.47 = ( proces370407749rocess @ A @ B @ F @ ( proces979765041_ch1Of @ A @ A2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % process.map_sel(3)
% 0.31/0.47 thf(fact_243_process_Omap__sel_I4_J,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType,A2: proces634752977rocess @ A,F: A > B] :
% 0.31/0.47 ( ( proces401113213Choice @ A @ A2 )
% 0.31/0.47 => ( ( proces988026546_ch2Of @ B @ ( proces370407749rocess @ A @ B @ F @ A2 ) )
% 0.31/0.47 = ( proces370407749rocess @ A @ B @ F @ ( proces988026546_ch2Of @ A @ A2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % process.map_sel(4)
% 0.31/0.47 thf(fact_244_process__term_Omap__cong__pred,axiom,
% 0.31/0.47 ! [D: $tType,C: $tType,B: $tType,A: $tType,X7: proces554692349s_term @ A @ B,Ya2: proces554692349s_term @ A @ B,F1: A > C,G1: A > C,F2: B > D,G22: B > D] :
% 0.31/0.47 ( ( X7 = Ya2 )
% 0.31/0.47 => ( ( proces2118920028s_term @ A @ B
% 0.31/0.47 @ ^ [Z12: A] :
% 0.31/0.47 ( ( F1 @ Z12 )
% 0.31/0.47 = ( G1 @ Z12 ) )
% 0.31/0.47 @ ^ [Z22: B] :
% 0.31/0.47 ( ( F2 @ Z22 )
% 0.31/0.47 = ( G22 @ Z22 ) )
% 0.31/0.47 @ Ya2 )
% 0.31/0.47 => ( ( proces224683037s_term @ A @ C @ B @ D @ F1 @ F2 @ X7 )
% 0.31/0.47 = ( proces224683037s_term @ A @ C @ B @ D @ G1 @ G22 @ Ya2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_term.map_cong_pred
% 0.31/0.47 thf(fact_245_process_Osimps_I15_J,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType,F: A > B,X11: A,X122: proces634752977rocess @ A] :
% 0.31/0.47 ( ( proces370407749rocess @ A @ B @ F @ ( proces1525233512Action @ A @ X11 @ X122 ) )
% 0.31/0.47 = ( proces1525233512Action @ B @ ( F @ X11 ) @ ( proces370407749rocess @ A @ B @ F @ X122 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % process.simps(15)
% 0.31/0.47 thf(fact_246_process_Osimps_I16_J,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType,F: A > B,X21: proces634752977rocess @ A,X222: proces634752977rocess @ A] :
% 0.31/0.47 ( ( proces370407749rocess @ A @ B @ F @ ( proces1915862579Choice @ A @ X21 @ X222 ) )
% 0.31/0.47 = ( proces1915862579Choice @ B @ ( proces370407749rocess @ A @ B @ F @ X21 ) @ ( proces370407749rocess @ A @ B @ F @ X222 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % process.simps(16)
% 0.31/0.47 thf(fact_247_process__term_Osimps_I25_J,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType,C: $tType,Pvar: $tType,F1: A > B,F2: Pvar > C,X1: Pvar] :
% 0.31/0.47 ( ( proces224683037s_term @ A @ B @ Pvar @ C @ F1 @ F2 @ ( proces1627516585ss_VAR @ Pvar @ A @ X1 ) )
% 0.31/0.47 = ( proces1627516585ss_VAR @ C @ B @ ( F2 @ X1 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_term.simps(25)
% 0.31/0.47 thf(fact_248_process__term_Osimps_I28_J,axiom,
% 0.31/0.47 ! [C: $tType,B: $tType,Pvar: $tType,A: $tType,F1: A > B,F2: Pvar > C,X41: proces554692349s_term @ A @ Pvar,X42: proces554692349s_term @ A @ Pvar] :
% 0.31/0.47 ( ( proces224683037s_term @ A @ B @ Pvar @ C @ F1 @ F2 @ ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 ) )
% 0.31/0.47 = ( proces89589571ess_CH @ B @ C @ ( proces224683037s_term @ A @ B @ Pvar @ C @ F1 @ F2 @ X41 ) @ ( proces224683037s_term @ A @ B @ Pvar @ C @ F1 @ F2 @ X42 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_term.simps(28)
% 0.31/0.47 thf(fact_249_process__term_Osimps_I27_J,axiom,
% 0.31/0.47 ! [C: $tType,B: $tType,Pvar: $tType,A: $tType,F1: A > B,F2: Pvar > C,X31: A,X32: proces554692349s_term @ A @ Pvar] :
% 0.31/0.47 ( ( proces224683037s_term @ A @ B @ Pvar @ C @ F1 @ F2 @ ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) )
% 0.31/0.47 = ( proces1454156180ss_ACT @ B @ C @ ( F1 @ X31 ) @ ( proces224683037s_term @ A @ B @ Pvar @ C @ F1 @ F2 @ X32 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_term.simps(27)
% 0.31/0.47 thf(fact_250_process__term_Osimps_I26_J,axiom,
% 0.31/0.47 ! [Pvar: $tType,C: $tType,B: $tType,A: $tType,F1: A > B,F2: Pvar > C,X2: proces634752977rocess @ A] :
% 0.31/0.47 ( ( proces224683037s_term @ A @ B @ Pvar @ C @ F1 @ F2 @ ( proces1062592052s_PROC @ A @ Pvar @ X2 ) )
% 0.31/0.47 = ( proces1062592052s_PROC @ B @ C @ ( proces370407749rocess @ A @ B @ F1 @ X2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % process_term.simps(26)
% 0.31/0.47 thf(fact_251_process_Orel__map_I2_J,axiom,
% 0.31/0.47 ! [A: $tType,C: $tType,B: $tType,Sa: A > C > $o,X7: proces634752977rocess @ A,G: B > C,Y3: proces634752977rocess @ B] :
% 0.31/0.47 ( ( proces749077512rocess @ A @ C @ Sa @ X7 @ ( proces370407749rocess @ B @ C @ G @ Y3 ) )
% 0.31/0.47 = ( proces749077512rocess @ A @ B
% 0.31/0.47 @ ^ [X6: A,Y6: B] : ( Sa @ X6 @ ( G @ Y6 ) )
% 0.31/0.47 @ X7
% 0.31/0.47 @ Y3 ) ) ).
% 0.31/0.47
% 0.31/0.47 % process.rel_map(2)
% 0.31/0.47 thf(fact_252_process_Orel__map_I1_J,axiom,
% 0.31/0.47 ! [A: $tType,C: $tType,B: $tType,Sb: C > B > $o,I2: A > C,X7: proces634752977rocess @ A,Y3: proces634752977rocess @ B] :
% 0.31/0.47 ( ( proces749077512rocess @ C @ B @ Sb @ ( proces370407749rocess @ A @ C @ I2 @ X7 ) @ Y3 )
% 0.31/0.47 = ( proces749077512rocess @ A @ B
% 0.31/0.47 @ ^ [X6: A] : ( Sb @ ( I2 @ X6 ) )
% 0.31/0.47 @ X7
% 0.31/0.47 @ Y3 ) ) ).
% 0.31/0.47
% 0.31/0.47 % process.rel_map(1)
% 0.31/0.47 thf(fact_253_process_Omap__cong__pred,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType,X7: proces634752977rocess @ A,Ya2: proces634752977rocess @ A,F: A > B,G: A > B] :
% 0.31/0.47 ( ( X7 = Ya2 )
% 0.31/0.47 => ( ( proces1205983068rocess @ A
% 0.31/0.47 @ ^ [Z3: A] :
% 0.31/0.47 ( ( F @ Z3 )
% 0.31/0.47 = ( G @ Z3 ) )
% 0.31/0.47 @ Ya2 )
% 0.31/0.47 => ( ( proces370407749rocess @ A @ B @ F @ X7 )
% 0.31/0.47 = ( proces370407749rocess @ A @ B @ G @ Ya2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % process.map_cong_pred
% 0.31/0.47 thf(fact_254_process__term_Omap__ident,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType,T5: proces554692349s_term @ A @ B] :
% 0.31/0.47 ( ( proces224683037s_term @ A @ A @ B @ B
% 0.31/0.47 @ ^ [X6: A] : X6
% 0.31/0.47 @ ^ [X6: B] : X6
% 0.31/0.47 @ T5 )
% 0.31/0.47 = T5 ) ).
% 0.31/0.47
% 0.31/0.47 % process_term.map_ident
% 0.31/0.47
% 0.31/0.47 %----Helper facts (3)
% 0.31/0.47 thf(help_If_3_1_T,axiom,
% 0.31/0.47 ! [P3: $o] :
% 0.31/0.47 ( ( P3 = $true )
% 0.31/0.47 | ( P3 = $false ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(help_If_2_1_T,axiom,
% 0.31/0.47 ! [A: $tType,X7: A,Y3: A] :
% 0.31/0.47 ( ( if @ A @ $false @ X7 @ Y3 )
% 0.31/0.47 = Y3 ) ).
% 0.31/0.47
% 0.31/0.47 thf(help_If_1_1_T,axiom,
% 0.31/0.47 ! [A: $tType,X7: A,Y3: A] :
% 0.31/0.47 ( ( if @ A @ $true @ X7 @ Y3 )
% 0.31/0.47 = X7 ) ).
% 0.31/0.47
% 0.31/0.47 %----Conjectures (1)
% 0.31/0.47 thf(conj_0,conjecture,
% 0.31/0.47 ( ( proces1652378886lution @ b @ a @ sys @ ( proces1062592052s_PROC @ a @ b @ p ) )
% 0.31/0.47 = p ) ).
% 0.31/0.47
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 ------------------------
% 3.19/1.61 ---- Embedded in THF ---
% 3.19/1.62 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 3.19/1.62 %%% Generated on Tue Feb 24 11:29:45 EST 2026
% 3.19/1.62 %%% using '$$dhol' embedding, version 1.3.0.
% 3.19/1.62 %%% Logic specification used:
% 3.19/1.62 %%% thf(spec, logic, $$dhol).
% 3.19/1.62
% 3.19/1.62 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.509jbUU17G/DTF2DTF31439.p
% 3.19/1.62 thf(ty_t_Process__Mirabelle__xovoopgpgi_Oprocess__term, type, proces554692349s_term: ($tType > ($tType > $tType))).
% 3.19/1.62 thf(ty_t_Process__Mirabelle__xovoopgpgi_Oprocess, type, proces634752977rocess: ($tType > $tType)).
% 3.19/1.62 thf(ty_t_Product__Type_Oprod, type, product_prod: ($tType > ($tType > $tType))).
% 3.19/1.62 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 3.19/1.62 thf(ty_t_itself, type, itself: ($tType > $tType)).
% 3.19/1.62 thf(ty_tf_b, type, b: $tType).
% 3.19/1.62 thf(ty_tf_a, type, a: $tType).
% 3.19/1.62 thf(sy_c_BNF__Def_Orel__fun, type, bNF_rel_fun: (!> [A:$tType,C:$tType,B:$tType,D:$tType]: (((A > (C > $o)) > ((B > (D > $o)) > ((A > B) > ((C > D) > $o))))))).
% 3.19/1.62 thf(sy_c_Basic__BNFs_Opred__fun, type, basic_pred_fun: (!> [A:$tType,B:$tType]: (((A > $o) > ((B > $o) > ((A > B) > $o)))))).
% 3.19/1.62 thf(sy_c_Fun_Omap__fun, type, map_fun: (!> [C:$tType,A:$tType,B:$tType,D:$tType]: (((C > A) > ((B > D) > ((A > B) > (C > D))))))).
% 3.19/1.62 thf(sy_c_HOL_Oundefined, type, undefined: (!> [A:$tType]: (A))).
% 3.19/1.62 thf(sy_c_If, type, if: (!> [A:$tType]: (($o > (A > (A > A)))))).
% 3.19/1.62 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)))))).
% 3.19/1.62 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)) > $o))))).
% 3.19/1.62 thf(sy_c_Process__Mirabelle__xovoopgpgi_OCH2, type, proces1239275104le_CH2: (!> [A:$tType,B:$tType]: (((A > ((proces554692349s_term @ B) @ A)) > (((proces554692349s_term @ B) @ A) > ((proces554692349s_term @ B) @ A)))))).
% 3.19/1.62 thf(sy_c_Process__Mirabelle__xovoopgpgi_OCH2__rel, type, proces93903513H2_rel: (!> [A:$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)) > $o))))).
% 3.19/1.62 thf(sy_c_Process__Mirabelle__xovoopgpgi_OCONT, type, proces126235999e_CONT: (!> [A:$tType,B:$tType]: (((A > ((proces554692349s_term @ B) @ A)) > (((proces554692349s_term @ B) @ A) > ((proces554692349s_term @ B) @ A)))))).
% 3.19/1.62 thf(sy_c_Process__Mirabelle__xovoopgpgi_OCONT__rel, type, proces1004198490NT_rel: (!> [A:$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)) > $o))))).
% 3.19/1.62 thf(sy_c_Process__Mirabelle__xovoopgpgi_OPREF, type, proces1708129104e_PREF: (!> [A:$tType,B:$tType,C:$tType]: (((A > ((proces554692349s_term @ B) @ C)) > (((proces554692349s_term @ B) @ A) > B))))).
% 3.19/1.62 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)) > $o))))).
% 3.19/1.62 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oguarded, type, proces1121166967uarded: (!> [A:$tType,B:$tType,C:$tType]: (((A > ((proces554692349s_term @ B) @ C)) > $o)))).
% 3.19/1.62 thf(sy_c_Process__Mirabelle__xovoopgpgi_OisACT, type, proces687458811_isACT: (!> [A:$tType,B:$tType,C:$tType,D:$tType]: (((A > ((proces554692349s_term @ B) @ C)) > (((proces554692349s_term @ D) @ A) > $o))))).
% 3.19/1.62 thf(sy_c_Process__Mirabelle__xovoopgpgi_OisACT__rel, type, proces896239806CT_rel: (!> [A:$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)) > $o))))).
% 3.19/1.62 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OAction, type, proces1525233512Action: (!> [A:$tType]: ((A > ((proces634752977rocess @ A) > (proces634752977rocess @ A)))))).
% 3.19/1.62 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OChoice, type, proces1915862579Choice: (!> [A:$tType]: (((proces634752977rocess @ A) > ((proces634752977rocess @ A) > (proces634752977rocess @ A)))))).
% 3.19/1.62 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Ocase__process, type, proces1406508781rocess: (!> [A:$tType,B:$tType]: (((A > ((proces634752977rocess @ A) > B)) > (((proces634752977rocess @ A) > ((proces634752977rocess @ A) > B)) > ((proces634752977rocess @ A) > B)))))).
% 3.19/1.62 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Och1Of, type, proces979765041_ch1Of: (!> [A:$tType]: (((proces634752977rocess @ A) > (proces634752977rocess @ A))))).
% 3.19/1.62 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Och2Of, type, proces988026546_ch2Of: (!> [A:$tType]: (((proces634752977rocess @ A) > (proces634752977rocess @ A))))).
% 3.19/1.62 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OcontOf, type, proces1778668539contOf: (!> [A:$tType]: (((proces634752977rocess @ A) > (proces634752977rocess @ A))))).
% 3.19/1.62 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 > $o) > ((C > (proces634752977rocess @ A)) > ((C > C) > (C > (proces634752977rocess @ A)))))))))))))))).
% 3.19/1.62 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OisAction, type, proces10484146Action: (!> [A:$tType]: (((proces634752977rocess @ A) > $o)))).
% 3.19/1.62 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OisChoice, type, proces401113213Choice: (!> [A:$tType]: (((proces634752977rocess @ A) > $o)))).
% 3.19/1.62 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Omap__process, type, proces370407749rocess: (!> [A:$tType,Aa:$tType]: (((A > Aa) > ((proces634752977rocess @ A) > (proces634752977rocess @ Aa)))))).
% 3.19/1.62 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Opred__process, type, proces1205983068rocess: (!> [A:$tType]: (((A > $o) > ((proces634752977rocess @ A) > $o))))).
% 3.19/1.62 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OprefOf, type, proces745025900prefOf: (!> [A:$tType]: (((proces634752977rocess @ A) > A)))).
% 3.19/1.62 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Orel__process, type, proces749077512rocess: (!> [A:$tType,B:$tType]: (((A > (B > $o)) > ((proces634752977rocess @ A) > ((proces634752977rocess @ B) > $o)))))).
% 3.19/1.62 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_OACT, type, proces1454156180ss_ACT: (!> [A:$tType,Pvar:$tType]: ((A > (((proces554692349s_term @ A) @ Pvar) > ((proces554692349s_term @ A) @ Pvar)))))).
% 3.19/1.62 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_OCH, type, proces89589571ess_CH: (!> [A:$tType,Pvar:$tType]: ((((proces554692349s_term @ A) @ Pvar) > (((proces554692349s_term @ A) @ Pvar) > ((proces554692349s_term @ A) @ Pvar)))))).
% 3.19/1.62 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_OPROC, type, proces1062592052s_PROC: (!> [A:$tType,Pvar:$tType]: (((proces634752977rocess @ A) > ((proces554692349s_term @ A) @ Pvar))))).
% 3.19/1.62 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_OVAR, type, proces1627516585ss_VAR: (!> [Pvar:$tType,A:$tType]: ((Pvar > ((proces554692349s_term @ A) @ Pvar))))).
% 3.19/1.62 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Ocase__process__term, type, proces460752237s_term: (!> [Pvar:$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)))))))).
% 3.19/1.62 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Omap__process__term, type, proces224683037s_term: (!> [A:$tType,Aa:$tType,Pvar:$tType,Pvara:$tType]: (((A > Aa) > ((Pvar > Pvara) > (((proces554692349s_term @ A) @ Pvar) > ((proces554692349s_term @ Aa) @ Pvara))))))).
% 3.19/1.62 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) > $o)))))).
% 3.19/1.62 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Orec__process__term, type, proces2117273769s_term: (!> [Pvar:$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)))))))).
% 3.19/1.62 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) > $o))))))).
% 3.19/1.62 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Oset2__process__term, type, proces1493547885s_term: (!> [A:$tType,Pvar:$tType]: ((((proces554692349s_term @ A) @ Pvar) > (set @ Pvar))))).
% 3.19/1.62 thf(sy_c_Process__Mirabelle__xovoopgpgi_Osolution, type, proces1652378886lution: (!> [A:$tType,B:$tType]: (((A > ((proces554692349s_term @ B) @ A)) > (((proces554692349s_term @ B) @ A) > (proces634752977rocess @ B)))))).
% 3.19/1.62 thf(sy_c_Product__Type_OPair, type, product_Pair: (!> [A:$tType,B:$tType]: ((A > (B > ((product_prod @ A) @ B)))))).
% 3.19/1.62 thf(sy_c_Product__Type_Ocurry, type, product_curry: (!> [A:$tType,B:$tType,C:$tType]: (((((product_prod @ A) @ B) > C) > (A > (B > C)))))).
% 3.19/1.62 thf(sy_c_Product__Type_Ointernal__case__prod, type, produc2004651681e_prod: (!> [A:$tType,B:$tType,C:$tType]: (((A > (B > C)) > (((product_prod @ A) @ B) > C))))).
% 3.19/1.62 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod, type, product_rec_prod: (!> [A:$tType,B:$tType,T:$tType]: (((A > (B > T)) > (((product_prod @ A) @ B) > T))))).
% 3.19/1.62 thf(sy_c_Pure_Otype, type, type: (!> [A:$tType]: ((itself @ A)))).
% 3.19/1.62 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 3.19/1.62 thf(sy_c_Wellfounded_Oaccp, type, accp: (!> [A:$tType]: (((A > (A > $o)) > (A > $o))))).
% 3.19/1.62 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 3.19/1.62 thf(sy_v_p, type, p: (proces634752977rocess @ a)).
% 3.19/1.62 thf(sy_v_sys, type, sys: (b > ((proces554692349s_term @ a) @ b))).
% 3.19/1.62 thf(fact_0__092_060open_062_092_060And_062q_O_Aq_A_061_Asolution_Asys_A_IPROC_Ap_J_A_092_060Longrightarrow_062_Ap_A_061_Aq_092_060close_062, axiom, (! [Q:(proces634752977rocess @ a)]: (((Q = ((((proces1652378886lution @ b) @ a) @ sys) @ (((proces1062592052s_PROC @ a) @ b) @ p))) => (p = Q))))).
% 3.19/1.62 thf(fact_1_process__term_Oinject_I2_J, axiom, (! [Pvar:$tType,A:$tType,X2:(proces634752977rocess @ A),Y2:(proces634752977rocess @ A)]: ((((((proces1062592052s_PROC @ A) @ Pvar) @ X2) = (((proces1062592052s_PROC @ A) @ Pvar) @ Y2)) = (X2 = Y2))))).
% 3.19/1.62 thf(fact_2_process__term_Osimps_I22_J, axiom, (! [Pvar:$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))))).
% 3.19/1.62 thf(fact_3_process__term_Osimps_I18_J, axiom, (! [Pvar:$tType,B:$tType,A:$tType,F1:(Pvar > B),F2:((proces634752977rocess @ A) > B),F3:(A > (((proces554692349s_term @ A) @ Pvar) > B)),F4:(((proces554692349s_term @ A) @ Pvar) > (((proces554692349s_term @ A) @ Pvar) > B)),X2:(proces634752977rocess @ A)]: ((((((((((proces460752237s_term @ Pvar) @ B) @ A) @ F1) @ F2) @ F3) @ F4) @ (((proces1062592052s_PROC @ A) @ Pvar) @ X2)) = (F2 @ X2))))).
% 3.19/1.62 thf(fact_4_process__term_Odistinct_I7_J, axiom, (! [Pvar:$tType,A:$tType,X2:(proces634752977rocess @ A),X31:A,X32:((proces554692349s_term @ A) @ Pvar)]: (((((proces1062592052s_PROC @ A) @ Pvar) @ X2) != ((((proces1454156180ss_ACT @ A) @ Pvar) @ X31) @ X32))))).
% 3.19/1.62 thf(fact_5_process__term_Odistinct_I9_J, axiom, (! [Pvar:$tType,A:$tType,X2:(proces634752977rocess @ A),X41:((proces554692349s_term @ A) @ Pvar),X42:((proces554692349s_term @ A) @ Pvar)]: (((((proces1062592052s_PROC @ A) @ Pvar) @ X2) != ((((proces89589571ess_CH @ A) @ Pvar) @ X41) @ X42))))).
% 3.19/1.62 thf(fact_6_process__term_Odistinct_I1_J, axiom, (! [Pvar:$tType,A:$tType,X1:Pvar,X2:(proces634752977rocess @ A)]: (((((proces1627516585ss_VAR @ Pvar) @ A) @ X1) != (((proces1062592052s_PROC @ A) @ Pvar) @ X2))))).
% 3.19/1.62 thf(fact_7_solution__VAR, axiom, (! [B:$tType,A:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),X:A]: ((((((proces1121166967uarded @ A) @ B) @ A) @ Sys) => (((((proces1652378886lution @ A) @ B) @ Sys) @ (((proces1627516585ss_VAR @ A) @ B) @ X)) = ((((proces1652378886lution @ A) @ B) @ Sys) @ (Sys @ X))))))).
% 3.19/1.62 thf(fact_8_PREF_Osimps_I2_J, axiom, (! [A:$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))))).
% 3.19/1.62 thf(fact_9_process__term_Opred__inject_I2_J, axiom, (! [Pvar:$tType,A:$tType,P1:(A > $o),P2:(Pvar > $o),A2:(proces634752977rocess @ A)]: (((((((proces2118920028s_term @ A) @ Pvar) @ P1) @ P2) @ (((proces1062592052s_PROC @ A) @ Pvar) @ A2)) = (((proces1205983068rocess @ A) @ P1) @ A2))))).
% 3.19/1.62 thf(fact_10_CH1_Osimps_I2_J, axiom, (! [A:$tType,B:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),P:(proces634752977rocess @ B)]: ((((((proces1239275103le_CH1 @ A) @ B) @ Sys) @ (((proces1062592052s_PROC @ B) @ A) @ P)) = (((proces1062592052s_PROC @ B) @ A) @ ((proces979765041_ch1Of @ B) @ P)))))).
% 3.19/1.62 thf(fact_11_CH2_Osimps_I2_J, axiom, (! [A:$tType,B:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),P:(proces634752977rocess @ B)]: ((((((proces1239275104le_CH2 @ A) @ B) @ Sys) @ (((proces1062592052s_PROC @ B) @ A) @ P)) = (((proces1062592052s_PROC @ B) @ A) @ ((proces988026546_ch2Of @ B) @ P)))))).
% 3.19/1.62 thf(fact_12_CONT_Osimps_I2_J, axiom, (! [A:$tType,B:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),P:(proces634752977rocess @ B)]: ((((((proces126235999e_CONT @ A) @ B) @ Sys) @ (((proces1062592052s_PROC @ B) @ A) @ P)) = (((proces1062592052s_PROC @ B) @ A) @ ((proces1778668539contOf @ B) @ P)))))).
% 3.19/1.62 thf(fact_13_solution_Odisc__iff_I2_J, axiom, (! [A:$tType,B:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),T2:((proces554692349s_term @ B) @ A)]: ((((proces401113213Choice @ B) @ ((((proces1652378886lution @ A) @ B) @ Sys) @ T2)) = (~ (((((((proces687458811_isACT @ A) @ B) @ A) @ B) @ Sys) @ T2))))))).
% 3.19/1.62 thf(fact_14_process__term_Oinject_I1_J, axiom, (! [A:$tType,Pvar:$tType,X1:Pvar,Y1:Pvar]: ((((((proces1627516585ss_VAR @ Pvar) @ A) @ X1) = (((proces1627516585ss_VAR @ Pvar) @ A) @ Y1)) = (X1 = Y1))))).
% 3.19/1.62 thf(fact_15_process__term_Oinject_I4_J, axiom, (! [Pvar:$tType,A:$tType,X41:((proces554692349s_term @ A) @ Pvar),X42:((proces554692349s_term @ A) @ Pvar),Y41:((proces554692349s_term @ A) @ Pvar),Y42:((proces554692349s_term @ A) @ Pvar)]: (((((((proces89589571ess_CH @ A) @ Pvar) @ X41) @ X42) = ((((proces89589571ess_CH @ A) @ Pvar) @ Y41) @ Y42)) = ((X41 = Y41) & (X42 = Y42)))))).
% 3.19/1.62 thf(fact_16_process__term_Oinject_I3_J, axiom, (! [Pvar:$tType,A:$tType,X31:A,X32:((proces554692349s_term @ A) @ Pvar),Y31:A,Y32:((proces554692349s_term @ A) @ Pvar)]: (((((((proces1454156180ss_ACT @ A) @ Pvar) @ X31) @ X32) = ((((proces1454156180ss_ACT @ A) @ Pvar) @ Y31) @ Y32)) = ((X31 = Y31) & (X32 = Y32)))))).
% 3.19/1.62 thf(fact_17_process__term_Opred__inject_I1_J, axiom, (! [A:$tType,Pvar:$tType,P1:(A > $o),P2:(Pvar > $o),A2:Pvar]: (((((((proces2118920028s_term @ A) @ Pvar) @ P1) @ P2) @ (((proces1627516585ss_VAR @ Pvar) @ A) @ A2)) = (P2 @ A2))))).
% 3.19/1.62 thf(fact_18_process__term_Opred__inject_I4_J, axiom, (! [Pvar:$tType,A:$tType,P1:(A > $o),P2:(Pvar > $o),A2:((proces554692349s_term @ A) @ Pvar),Aa2:((proces554692349s_term @ A) @ Pvar)]: (((((((proces2118920028s_term @ A) @ Pvar) @ P1) @ P2) @ ((((proces89589571ess_CH @ A) @ Pvar) @ A2) @ Aa2)) = ((((((proces2118920028s_term @ A) @ Pvar) @ P1) @ P2) @ A2) & (((((proces2118920028s_term @ A) @ Pvar) @ P1) @ P2) @ Aa2)))))).
% 3.19/1.62 thf(fact_19_process__term_Opred__inject_I3_J, axiom, (! [Pvar:$tType,A:$tType,P1:(A > $o),P2:(Pvar > $o),A2:A,Aa2:((proces554692349s_term @ A) @ Pvar)]: (((((((proces2118920028s_term @ A) @ Pvar) @ P1) @ P2) @ ((((proces1454156180ss_ACT @ A) @ Pvar) @ A2) @ Aa2)) = ((P1 @ A2) & (((((proces2118920028s_term @ A) @ Pvar) @ P1) @ P2) @ Aa2)))))).
% 3.19/1.62 thf(fact_20_CH1_Osimps_I3_J, axiom, (! [A:$tType,B:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),T1:((proces554692349s_term @ B) @ A),T22:((proces554692349s_term @ B) @ A)]: ((((((proces1239275103le_CH1 @ A) @ B) @ Sys) @ ((((proces89589571ess_CH @ B) @ A) @ T1) @ T22)) = T1)))).
% 3.19/1.62 thf(fact_21_CH2_Osimps_I3_J, axiom, (! [A:$tType,B:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),T1:((proces554692349s_term @ B) @ A),T22:((proces554692349s_term @ B) @ A)]: ((((((proces1239275104le_CH2 @ A) @ B) @ Sys) @ ((((proces89589571ess_CH @ B) @ A) @ T1) @ T22)) = T22)))).
% 3.19/1.62 thf(fact_22_CONT_Osimps_I3_J, axiom, (! [A:$tType,B:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),A2:B,T2:((proces554692349s_term @ B) @ A)]: ((((((proces126235999e_CONT @ A) @ B) @ Sys) @ ((((proces1454156180ss_ACT @ B) @ A) @ A2) @ T2)) = T2)))).
% 3.19/1.62 thf(fact_23_PREF_Osimps_I3_J, axiom, (! [A:$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)))).
% 3.19/1.62 thf(fact_24_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))))))).
% 3.19/1.62 thf(fact_25_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))))).
% 3.19/1.62 thf(fact_26_process__term_Osimps_I24_J, axiom, (! [D:$tType,Pvar:$tType,A:$tType,F1:(Pvar > D),F2:((proces634752977rocess @ A) > D),F3:(A > (((proces554692349s_term @ A) @ Pvar) > (D > D))),F4:(((proces554692349s_term @ A) @ Pvar) > (((proces554692349s_term @ A) @ Pvar) > (D > (D > D)))),X41:((proces554692349s_term @ A) @ Pvar),X42:((proces554692349s_term @ A) @ Pvar)]: ((((((((((proces2117273769s_term @ Pvar) @ D) @ A) @ F1) @ F2) @ F3) @ F4) @ ((((proces89589571ess_CH @ A) @ Pvar) @ X41) @ X42)) = ((((F4 @ X41) @ X42) @ ((((((((proces2117273769s_term @ Pvar) @ D) @ A) @ F1) @ F2) @ F3) @ F4) @ X41)) @ ((((((((proces2117273769s_term @ Pvar) @ D) @ A) @ F1) @ F2) @ F3) @ F4) @ X42)))))).
% 3.19/1.62 thf(fact_27_process__term_Osimps_I23_J, axiom, (! [D:$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)))))).
% 3.19/1.62 thf(fact_28_process__term_Osimps_I21_J, axiom, (! [A:$tType,D:$tType,Pvar:$tType,F1:(Pvar > D),F2:((proces634752977rocess @ A) > D),F3:(A > (((proces554692349s_term @ A) @ Pvar) > (D > D))),F4:(((proces554692349s_term @ A) @ Pvar) > (((proces554692349s_term @ A) @ Pvar) > (D > (D > D)))),X1:Pvar]: ((((((((((proces2117273769s_term @ Pvar) @ D) @ A) @ F1) @ F2) @ F3) @ F4) @ (((proces1627516585ss_VAR @ Pvar) @ A) @ X1)) = (F1 @ X1))))).
% 3.19/1.62 thf(fact_29_process__term_Osimps_I20_J, axiom, (! [B:$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))))).
% 3.19/1.62 thf(fact_30_process__term_Osimps_I19_J, axiom, (! [B:$tType,Pvar:$tType,A:$tType,F1:(Pvar > B),F2:((proces634752977rocess @ A) > B),F3:(A > (((proces554692349s_term @ A) @ Pvar) > B)),F4:(((proces554692349s_term @ A) @ Pvar) > (((proces554692349s_term @ A) @ Pvar) > B)),X31:A,X32:((proces554692349s_term @ A) @ Pvar)]: ((((((((((proces460752237s_term @ Pvar) @ B) @ A) @ F1) @ F2) @ F3) @ F4) @ ((((proces1454156180ss_ACT @ A) @ Pvar) @ X31) @ X32)) = ((F3 @ X31) @ X32))))).
% 3.19/1.62 thf(fact_31_process__term_Osimps_I17_J, axiom, (! [A:$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)),X1:Pvar]: ((((((((((proces460752237s_term @ Pvar) @ B) @ A) @ F1) @ F2) @ F3) @ F4) @ (((proces1627516585ss_VAR @ Pvar) @ A) @ X1)) = (F1 @ X1))))).
% 3.19/1.62 thf(fact_32_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))))).
% 3.19/1.62 thf(fact_33_process__term_Odistinct_I5_J, axiom, (! [Pvar:$tType,A:$tType,X1:Pvar,X41:((proces554692349s_term @ A) @ Pvar),X42:((proces554692349s_term @ A) @ Pvar)]: (((((proces1627516585ss_VAR @ Pvar) @ A) @ X1) != ((((proces89589571ess_CH @ A) @ Pvar) @ X41) @ X42))))).
% 3.19/1.62 thf(fact_34_process__term_Odistinct_I3_J, axiom, (! [Pvar:$tType,A:$tType,X1:Pvar,X31:A,X32:((proces554692349s_term @ A) @ Pvar)]: (((((proces1627516585ss_VAR @ Pvar) @ A) @ X1) != ((((proces1454156180ss_ACT @ A) @ Pvar) @ X31) @ X32))))).
% 3.19/1.62 thf(fact_35_isACT__VAR, axiom, (! [C:$tType,B:$tType,A:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),X:A]: ((((((proces1121166967uarded @ A) @ B) @ A) @ Sys) => (((((((proces687458811_isACT @ A) @ B) @ A) @ C) @ Sys) @ (((proces1627516585ss_VAR @ A) @ C) @ X)) = ((((((proces687458811_isACT @ A) @ B) @ A) @ B) @ Sys) @ (Sys @ X))))))).
% 3.19/1.62 thf(fact_36_CH2_Oinduct, axiom, (! [A:$tType,B:$tType,P3:((A > ((proces554692349s_term @ B) @ A)) > (((proces554692349s_term @ B) @ A) > $o)),A0:(A > ((proces554692349s_term @ B) @ A)),A1:((proces554692349s_term @ B) @ A)]: (((! [Sys2:(A > ((proces554692349s_term @ B) @ A)),X3:A]: (((P3 @ Sys2) @ (((proces1627516585ss_VAR @ A) @ B) @ X3)))) => ((! [Sys2:(A > ((proces554692349s_term @ B) @ A)),P4:(proces634752977rocess @ B)]: (((P3 @ Sys2) @ (((proces1062592052s_PROC @ B) @ A) @ P4)))) => ((! [Sys2:(A > ((proces554692349s_term @ B) @ A)),T12:((proces554692349s_term @ B) @ A),T23:((proces554692349s_term @ B) @ A)]: (((P3 @ Sys2) @ ((((proces89589571ess_CH @ B) @ A) @ T12) @ T23)))) => ((! [A3:(A > ((proces554692349s_term @ B) @ A)),V:B,Va:((proces554692349s_term @ B) @ A)]: (((P3 @ A3) @ ((((proces1454156180ss_ACT @ B) @ A) @ V) @ Va)))) => ((P3 @ A0) @ A1)))))))).
% 3.19/1.62 thf(fact_37_CONT_Oinduct, axiom, (! [A:$tType,B:$tType,P3:((A > ((proces554692349s_term @ B) @ A)) > (((proces554692349s_term @ B) @ A) > $o)),A0:(A > ((proces554692349s_term @ B) @ A)),A1:((proces554692349s_term @ B) @ A)]: (((! [Sys2:(A > ((proces554692349s_term @ B) @ A)),X3:A]: (((P3 @ Sys2) @ (((proces1627516585ss_VAR @ A) @ B) @ X3)))) => ((! [Sys2:(A > ((proces554692349s_term @ B) @ A)),P4:(proces634752977rocess @ B)]: (((P3 @ Sys2) @ (((proces1062592052s_PROC @ B) @ A) @ P4)))) => ((! [Sys2:(A > ((proces554692349s_term @ B) @ A)),A3:B,T3:((proces554692349s_term @ B) @ A)]: (((P3 @ Sys2) @ ((((proces1454156180ss_ACT @ B) @ A) @ A3) @ T3)))) => ((! [A3:(A > ((proces554692349s_term @ B) @ A)),V:((proces554692349s_term @ B) @ A),Va:((proces554692349s_term @ B) @ A)]: (((P3 @ A3) @ ((((proces89589571ess_CH @ B) @ A) @ V) @ Va)))) => ((P3 @ A0) @ A1)))))))).
% 3.19/1.62 thf(fact_38_PREF_Oinduct, axiom, (! [C:$tType,A:$tType,B:$tType,P3:((A > ((proces554692349s_term @ B) @ C)) > (((proces554692349s_term @ B) @ A) > $o)),A0:(A > ((proces554692349s_term @ B) @ C)),A1:((proces554692349s_term @ B) @ A)]: (((! [Sys2:(A > ((proces554692349s_term @ B) @ C)),X3:A]: (((P3 @ Sys2) @ (((proces1627516585ss_VAR @ A) @ B) @ X3)))) => ((! [Sys2:(A > ((proces554692349s_term @ B) @ C)),P4:(proces634752977rocess @ B)]: (((P3 @ Sys2) @ (((proces1062592052s_PROC @ B) @ A) @ P4)))) => ((! [Sys2:(A > ((proces554692349s_term @ B) @ C)),A3:B,T3:((proces554692349s_term @ B) @ A)]: (((P3 @ Sys2) @ ((((proces1454156180ss_ACT @ B) @ A) @ A3) @ T3)))) => ((! [A3:(A > ((proces554692349s_term @ B) @ C)),V:((proces554692349s_term @ B) @ A),Va:((proces554692349s_term @ B) @ A)]: (((P3 @ A3) @ ((((proces89589571ess_CH @ B) @ A) @ V) @ Va)))) => ((P3 @ A0) @ A1)))))))).
% 3.19/1.62 thf(fact_39_guarded__def, axiom, (! [C:$tType,B:$tType,A:$tType]: (((((proces1121166967uarded @ A) @ B) @ C) = (^ [Sys3:(A > ((proces554692349s_term @ B) @ C))]: ((! [X4:A,Y:C]: (((Sys3 @ X4) != (((proces1627516585ss_VAR @ C) @ B) @ Y)))))))))).
% 3.19/1.62 thf(fact_40_isACT_Oinduct, axiom, (! [B:$tType,C:$tType,A:$tType,D:$tType,P3:((A > ((proces554692349s_term @ B) @ C)) > (((proces554692349s_term @ D) @ A) > $o)),A0:(A > ((proces554692349s_term @ B) @ C)),A1:((proces554692349s_term @ D) @ A)]: (((! [Sys2:(A > ((proces554692349s_term @ B) @ C)),X3:A]: (((P3 @ Sys2) @ (((proces1627516585ss_VAR @ A) @ D) @ X3)))) => ((! [Sys2:(A > ((proces554692349s_term @ B) @ C)),P4:(proces634752977rocess @ D)]: (((P3 @ Sys2) @ (((proces1062592052s_PROC @ D) @ A) @ P4)))) => ((! [Sys2:(A > ((proces554692349s_term @ B) @ C)),A3:D,T3:((proces554692349s_term @ D) @ A)]: (((P3 @ Sys2) @ ((((proces1454156180ss_ACT @ D) @ A) @ A3) @ T3)))) => ((! [Sys2:(A > ((proces554692349s_term @ B) @ C)),T12:((proces554692349s_term @ D) @ A),T23:((proces554692349s_term @ D) @ A)]: (((P3 @ Sys2) @ ((((proces89589571ess_CH @ D) @ A) @ T12) @ T23)))) => ((P3 @ A0) @ A1)))))))).
% 3.19/1.62 thf(fact_41_process__term_Oinduct, axiom, (! [Pvar:$tType,A:$tType,P3:(((proces554692349s_term @ A) @ Pvar) > $o),Process_term:((proces554692349s_term @ A) @ Pvar)]: (((! [X5:Pvar]: ((P3 @ (((proces1627516585ss_VAR @ Pvar) @ A) @ X5)))) => ((! [X5:(proces634752977rocess @ A)]: ((P3 @ (((proces1062592052s_PROC @ A) @ Pvar) @ X5)))) => ((! [X1a:A,X2a:((proces554692349s_term @ A) @ Pvar)]: (((P3 @ X2a) => (P3 @ ((((proces1454156180ss_ACT @ A) @ Pvar) @ X1a) @ X2a))))) => ((! [X1a:((proces554692349s_term @ A) @ Pvar),X2a:((proces554692349s_term @ A) @ Pvar)]: (((P3 @ X1a) => ((P3 @ X2a) => (P3 @ ((((proces89589571ess_CH @ A) @ Pvar) @ X1a) @ X2a)))))) => (P3 @ Process_term)))))))).
% 3.19/1.62 thf(fact_42_process__term_Oexhaust, axiom, (! [Pvar:$tType,A:$tType,Y3:((proces554692349s_term @ A) @ Pvar)]: (((! [X12:Pvar]: ((Y3 != (((proces1627516585ss_VAR @ Pvar) @ A) @ X12)))) => ((! [X22:(proces634752977rocess @ A)]: ((Y3 != (((proces1062592052s_PROC @ A) @ Pvar) @ X22)))) => ((! [X312:A,X322:((proces554692349s_term @ A) @ Pvar)]: ((Y3 != ((((proces1454156180ss_ACT @ A) @ Pvar) @ X312) @ X322)))) => (~ ((! [X412:((proces554692349s_term @ A) @ Pvar),X422:((proces554692349s_term @ A) @ Pvar)]: ((Y3 != ((((proces89589571ess_CH @ A) @ Pvar) @ X412) @ X422)))))))))))).
% 3.19/1.62 thf(fact_43_solution_Osimps_I4_J, axiom, (! [A:$tType,B:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),T2:((proces554692349s_term @ B) @ A)]: ((((((((proces687458811_isACT @ A) @ B) @ A) @ B) @ Sys) @ T2) => (((proces1778668539contOf @ B) @ ((((proces1652378886lution @ A) @ B) @ Sys) @ T2)) = ((((proces1652378886lution @ A) @ B) @ Sys) @ ((((proces126235999e_CONT @ A) @ B) @ Sys) @ T2))))))).
% 3.19/1.62 thf(fact_44_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P3:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P3)) = (P3 @ A2))))).
% 3.19/1.62 thf(fact_45_Collect__mem__eq, axiom, (! [A:$tType,A4:(set @ A)]: ((((collect @ A) @ (^ [X6:A]: ((((member @ A) @ X6) @ A4)))) = A4)))).
% 3.19/1.62 thf(fact_46_Collect__cong, axiom, (! [A:$tType,P3:(A > $o),Q2:(A > $o)]: (((! [X5:A]: (((P3 @ X5) = (Q2 @ X5)))) => (((collect @ A) @ P3) = ((collect @ A) @ Q2)))))).
% 3.19/1.62 thf(fact_47_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G:(A > B)]: (((! [X5:A]: (((F @ X5) = (G @ X5)))) => (F = G))))).
% 3.19/1.62 thf(fact_48_solution_Osimps_I5_J, axiom, (! [A:$tType,B:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),T2:((proces554692349s_term @ B) @ A)]: (((~ (((((((proces687458811_isACT @ A) @ B) @ A) @ B) @ Sys) @ T2))) => (((proces979765041_ch1Of @ B) @ ((((proces1652378886lution @ A) @ B) @ Sys) @ T2)) = ((((proces1652378886lution @ A) @ B) @ Sys) @ ((((proces1239275103le_CH1 @ A) @ B) @ Sys) @ T2))))))).
% 3.19/1.62 thf(fact_49_solution_Osimps_I6_J, axiom, (! [A:$tType,B:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),T2:((proces554692349s_term @ B) @ A)]: (((~ (((((((proces687458811_isACT @ A) @ B) @ A) @ B) @ Sys) @ T2))) => (((proces988026546_ch2Of @ B) @ ((((proces1652378886lution @ A) @ B) @ Sys) @ T2)) = ((((proces1652378886lution @ A) @ B) @ Sys) @ ((((proces1239275104le_CH2 @ A) @ B) @ Sys) @ T2))))))).
% 3.19/1.62 thf(fact_50_solution_Osimps_I3_J, axiom, (! [A:$tType,B:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),T2:((proces554692349s_term @ B) @ A)]: ((((((((proces687458811_isACT @ A) @ B) @ A) @ B) @ Sys) @ T2) => (((proces745025900prefOf @ B) @ ((((proces1652378886lution @ A) @ B) @ Sys) @ T2)) = (((((proces1708129104e_PREF @ A) @ B) @ A) @ Sys) @ T2)))))).
% 3.19/1.62 thf(fact_51_solution_Odisc_I2_J, axiom, (! [A:$tType,B:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),T2:((proces554692349s_term @ B) @ A)]: (((~ (((((((proces687458811_isACT @ A) @ B) @ A) @ B) @ Sys) @ T2))) => ((proces401113213Choice @ B) @ ((((proces1652378886lution @ A) @ B) @ Sys) @ T2)))))).
% 3.19/1.62 thf(fact_52_process_Oexpand, axiom, (! [A:$tType,Process:(proces634752977rocess @ A),Process2:(proces634752977rocess @ A)]: (((((proces10484146Action @ A) @ Process) = ((proces10484146Action @ A) @ Process2)) => ((((proces10484146Action @ A) @ Process) => (((proces10484146Action @ A) @ Process2) => ((((proces745025900prefOf @ A) @ Process) = ((proces745025900prefOf @ A) @ Process2)) & (((proces1778668539contOf @ A) @ Process) = ((proces1778668539contOf @ A) @ Process2))))) => ((((proces401113213Choice @ A) @ Process) => (((proces401113213Choice @ A) @ Process2) => ((((proces979765041_ch1Of @ A) @ Process) = ((proces979765041_ch1Of @ A) @ Process2)) & (((proces988026546_ch2Of @ A) @ Process) = ((proces988026546_ch2Of @ A) @ Process2))))) => (Process = Process2))))))).
% 3.19/1.62 thf(fact_53_process_Ocoinduct, axiom, (! [A:$tType,R:((proces634752977rocess @ A) > ((proces634752977rocess @ A) > $o)),Process:(proces634752977rocess @ A),Process2:(proces634752977rocess @ A)]: ((((R @ Process) @ Process2) => ((! [Process3:(proces634752977rocess @ A),Process4:(proces634752977rocess @ A)]: ((((R @ Process3) @ Process4) => ((((proces10484146Action @ A) @ Process3) = ((proces10484146Action @ A) @ Process4)) & ((((proces10484146Action @ A) @ Process3) => (((proces10484146Action @ A) @ Process4) => ((((proces745025900prefOf @ A) @ Process3) = ((proces745025900prefOf @ A) @ Process4)) & ((R @ ((proces1778668539contOf @ A) @ Process3)) @ ((proces1778668539contOf @ A) @ Process4))))) & (((proces401113213Choice @ A) @ Process3) => (((proces401113213Choice @ A) @ Process4) => (((R @ ((proces979765041_ch1Of @ A) @ Process3)) @ ((proces979765041_ch1Of @ A) @ Process4)) & ((R @ ((proces988026546_ch2Of @ A) @ Process3)) @ ((proces988026546_ch2Of @ A) @ Process4)))))))))) => (Process = Process2)))))).
% 3.19/1.62 thf(fact_54_process_Ocoinduct__strong, axiom, (! [A:$tType,R:((proces634752977rocess @ A) > ((proces634752977rocess @ A) > $o)),Process:(proces634752977rocess @ A),Process2:(proces634752977rocess @ A)]: ((((R @ Process) @ Process2) => ((! [Process3:(proces634752977rocess @ A),Process4:(proces634752977rocess @ A)]: ((((R @ Process3) @ Process4) => ((((proces10484146Action @ A) @ Process3) = ((proces10484146Action @ A) @ Process4)) & ((((proces10484146Action @ A) @ Process3) => (((proces10484146Action @ A) @ Process4) => ((((proces745025900prefOf @ A) @ Process3) = ((proces745025900prefOf @ A) @ Process4)) & (((R @ ((proces1778668539contOf @ A) @ Process3)) @ ((proces1778668539contOf @ A) @ Process4)) | (((proces1778668539contOf @ A) @ Process3) = ((proces1778668539contOf @ A) @ Process4)))))) & (((proces401113213Choice @ A) @ Process3) => (((proces401113213Choice @ A) @ Process4) => ((((R @ ((proces979765041_ch1Of @ A) @ Process3)) @ ((proces979765041_ch1Of @ A) @ Process4)) | (((proces979765041_ch1Of @ A) @ Process3) = ((proces979765041_ch1Of @ A) @ Process4))) & (((R @ ((proces988026546_ch2Of @ A) @ Process3)) @ ((proces988026546_ch2Of @ A) @ Process4)) | (((proces988026546_ch2Of @ A) @ Process3) = ((proces988026546_ch2Of @ A) @ Process4))))))))))) => (Process = Process2)))))).
% 3.19/1.62 thf(fact_55_solution_Octr_I1_J, axiom, (! [A:$tType,B:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),T2:((proces554692349s_term @ B) @ A)]: ((((((((proces687458811_isACT @ A) @ B) @ A) @ B) @ Sys) @ T2) => (((((proces1652378886lution @ A) @ B) @ Sys) @ T2) = (((proces1525233512Action @ B) @ (((((proces1708129104e_PREF @ A) @ B) @ A) @ Sys) @ T2)) @ ((((proces1652378886lution @ A) @ B) @ Sys) @ ((((proces126235999e_CONT @ A) @ B) @ Sys) @ T2)))))))).
% 3.19/1.62 thf(fact_56_solution_Octr_I2_J, axiom, (! [A:$tType,B:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),T2:((proces554692349s_term @ B) @ A)]: (((~ (((((((proces687458811_isACT @ A) @ B) @ A) @ B) @ Sys) @ T2))) => (((((proces1652378886lution @ A) @ B) @ Sys) @ T2) = (((proces1915862579Choice @ B) @ ((((proces1652378886lution @ A) @ B) @ Sys) @ ((((proces1239275103le_CH1 @ A) @ B) @ Sys) @ T2))) @ ((((proces1652378886lution @ A) @ B) @ Sys) @ ((((proces1239275104le_CH2 @ A) @ B) @ Sys) @ T2)))))))).
% 3.19/1.62 thf(fact_57_process_Ocollapse_I2_J, axiom, (! [A:$tType,Process:(proces634752977rocess @ A)]: ((((proces401113213Choice @ A) @ Process) => ((((proces1915862579Choice @ A) @ ((proces979765041_ch1Of @ A) @ Process)) @ ((proces988026546_ch2Of @ A) @ Process)) = Process))))).
% 3.19/1.62 thf(fact_58_solution_Ocode, axiom, (! [B:$tType,A:$tType]: ((((proces1652378886lution @ A) @ B) = (^ [Sys3:(A > ((proces554692349s_term @ B) @ A)),T4:((proces554692349s_term @ B) @ A)]: (((((if @ (proces634752977rocess @ B)) @ ((((((proces687458811_isACT @ A) @ B) @ A) @ B) @ Sys3) @ T4)) @ (((proces1525233512Action @ B) @ (((((proces1708129104e_PREF @ A) @ B) @ A) @ Sys3) @ T4)) @ ((((proces1652378886lution @ A) @ B) @ Sys3) @ ((((proces126235999e_CONT @ A) @ B) @ Sys3) @ T4)))) @ (((proces1915862579Choice @ B) @ ((((proces1652378886lution @ A) @ B) @ Sys3) @ ((((proces1239275103le_CH1 @ A) @ B) @ Sys3) @ T4))) @ ((((proces1652378886lution @ A) @ B) @ Sys3) @ ((((proces1239275104le_CH2 @ A) @ B) @ Sys3) @ T4)))))))))).
% 3.19/1.62 thf(fact_59_CH2_Ocases, axiom, (! [A:$tType,B:$tType,X7:((product_prod @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A))]: (((! [Sys2:(A > ((proces554692349s_term @ B) @ A)),X3:A]: ((X7 != ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ Sys2) @ (((proces1627516585ss_VAR @ A) @ B) @ X3))))) => ((! [Sys2:(A > ((proces554692349s_term @ B) @ A)),P4:(proces634752977rocess @ B)]: ((X7 != ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ Sys2) @ (((proces1062592052s_PROC @ B) @ A) @ P4))))) => ((! [Sys2:(A > ((proces554692349s_term @ B) @ A)),T12:((proces554692349s_term @ B) @ A),T23:((proces554692349s_term @ B) @ A)]: ((X7 != ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ Sys2) @ ((((proces89589571ess_CH @ B) @ A) @ T12) @ T23))))) => (~ ((! [A3:(A > ((proces554692349s_term @ B) @ A)),V:B,Va:((proces554692349s_term @ B) @ A)]: ((X7 != ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ A3) @ ((((proces1454156180ss_ACT @ B) @ A) @ V) @ Va))))))))))))).
% 3.19/1.62 thf(fact_60_CONT_Ocases, axiom, (! [A:$tType,B:$tType,X7:((product_prod @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A))]: (((! [Sys2:(A > ((proces554692349s_term @ B) @ A)),X3:A]: ((X7 != ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ Sys2) @ (((proces1627516585ss_VAR @ A) @ B) @ X3))))) => ((! [Sys2:(A > ((proces554692349s_term @ B) @ A)),P4:(proces634752977rocess @ B)]: ((X7 != ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ Sys2) @ (((proces1062592052s_PROC @ B) @ A) @ P4))))) => ((! [Sys2:(A > ((proces554692349s_term @ B) @ A)),A3:B,T3:((proces554692349s_term @ B) @ A)]: ((X7 != ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ Sys2) @ ((((proces1454156180ss_ACT @ B) @ A) @ A3) @ T3))))) => (~ ((! [A3:(A > ((proces554692349s_term @ B) @ A)),V:((proces554692349s_term @ B) @ A),Va:((proces554692349s_term @ B) @ A)]: ((X7 != ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ A3) @ ((((proces89589571ess_CH @ B) @ A) @ V) @ Va))))))))))))).
% 3.19/1.62 thf(fact_61_PREF_Ocases, axiom, (! [C:$tType,A:$tType,B:$tType,X7:((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ B) @ A))]: (((! [Sys2:(A > ((proces554692349s_term @ B) @ C)),X3:A]: ((X7 != ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ B) @ A)) @ Sys2) @ (((proces1627516585ss_VAR @ A) @ B) @ X3))))) => ((! [Sys2:(A > ((proces554692349s_term @ B) @ C)),P4:(proces634752977rocess @ B)]: ((X7 != ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ B) @ A)) @ Sys2) @ (((proces1062592052s_PROC @ B) @ A) @ P4))))) => ((! [Sys2:(A > ((proces554692349s_term @ B) @ C)),A3:B,T3:((proces554692349s_term @ B) @ A)]: ((X7 != ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ B) @ A)) @ Sys2) @ ((((proces1454156180ss_ACT @ B) @ A) @ A3) @ T3))))) => (~ ((! [A3:(A > ((proces554692349s_term @ B) @ C)),V:((proces554692349s_term @ B) @ A),Va:((proces554692349s_term @ B) @ A)]: ((X7 != ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ B) @ A)) @ A3) @ ((((proces89589571ess_CH @ B) @ A) @ V) @ Va))))))))))))).
% 3.19/1.62 thf(fact_62_isACT_Ocases, axiom, (! [B:$tType,C:$tType,A:$tType,D:$tType,X7:((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A))]: (((! [Sys2:(A > ((proces554692349s_term @ B) @ C)),X3:A]: ((X7 != ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A)) @ Sys2) @ (((proces1627516585ss_VAR @ A) @ D) @ X3))))) => ((! [Sys2:(A > ((proces554692349s_term @ B) @ C)),P4:(proces634752977rocess @ D)]: ((X7 != ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A)) @ Sys2) @ (((proces1062592052s_PROC @ D) @ A) @ P4))))) => ((! [Sys2:(A > ((proces554692349s_term @ B) @ C)),A3:D,T3:((proces554692349s_term @ D) @ A)]: ((X7 != ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A)) @ Sys2) @ ((((proces1454156180ss_ACT @ D) @ A) @ A3) @ T3))))) => (~ ((! [Sys2:(A > ((proces554692349s_term @ B) @ C)),T12:((proces554692349s_term @ D) @ A),T23:((proces554692349s_term @ D) @ A)]: ((X7 != ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A)) @ Sys2) @ ((((proces89589571ess_CH @ D) @ A) @ T12) @ T23))))))))))))).
% 3.19/1.62 thf(fact_63_process_Oinject_I1_J, axiom, (! [A:$tType,X11:A,X122:(proces634752977rocess @ A),Y11:A,Y12:(proces634752977rocess @ A)]: ((((((proces1525233512Action @ A) @ X11) @ X122) = (((proces1525233512Action @ A) @ Y11) @ Y12)) = ((X11 = Y11) & (X122 = Y12)))))).
% 3.19/1.62 thf(fact_64_process_Oinject_I2_J, axiom, (! [A:$tType,X21:(proces634752977rocess @ A),X222:(proces634752977rocess @ A),Y21:(proces634752977rocess @ A),Y22:(proces634752977rocess @ A)]: ((((((proces1915862579Choice @ A) @ X21) @ X222) = (((proces1915862579Choice @ A) @ Y21) @ Y22)) = ((X21 = Y21) & (X222 = Y22)))))).
% 3.19/1.62 thf(fact_65_process_Opred__inject_I1_J, axiom, (! [A:$tType,P3:(A > $o),A2:A,Aa2:(proces634752977rocess @ A)]: (((((proces1205983068rocess @ A) @ P3) @ (((proces1525233512Action @ A) @ A2) @ Aa2)) = ((P3 @ A2) & (((proces1205983068rocess @ A) @ P3) @ Aa2)))))).
% 3.19/1.62 thf(fact_66_process_Opred__inject_I2_J, axiom, (! [A:$tType,P3:(A > $o),A2:(proces634752977rocess @ A),Aa2:(proces634752977rocess @ A)]: (((((proces1205983068rocess @ A) @ P3) @ (((proces1915862579Choice @ A) @ A2) @ Aa2)) = ((((proces1205983068rocess @ A) @ P3) @ A2) & (((proces1205983068rocess @ A) @ P3) @ Aa2)))))).
% 3.19/1.62 thf(fact_67_solution_Odisc__iff_I1_J, axiom, (! [A:$tType,B:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),T2:((proces554692349s_term @ B) @ A)]: ((((proces10484146Action @ B) @ ((((proces1652378886lution @ A) @ B) @ Sys) @ T2)) = ((((((proces687458811_isACT @ A) @ B) @ A) @ B) @ Sys) @ T2))))).
% 3.19/1.62 thf(fact_68_process_Ocollapse_I1_J, axiom, (! [A:$tType,Process:(proces634752977rocess @ A)]: ((((proces10484146Action @ A) @ Process) => ((((proces1525233512Action @ A) @ ((proces745025900prefOf @ A) @ Process)) @ ((proces1778668539contOf @ A) @ Process)) = Process))))).
% 3.19/1.62 thf(fact_69_process__coind, axiom, (! [A:$tType,Phi:((proces634752977rocess @ A) > ((proces634752977rocess @ A) > $o)),P:(proces634752977rocess @ A),P5:(proces634752977rocess @ A)]: ((((Phi @ P) @ P5) => ((! [P4:(proces634752977rocess @ A),P6:(proces634752977rocess @ A)]: ((((Phi @ P4) @ P6) => ((((proces10484146Action @ A) @ P4) = ((proces10484146Action @ A) @ P6)) & (((proces401113213Choice @ A) @ P4) = ((proces401113213Choice @ A) @ P6)))))) => ((! [A3:A,A5:A,P4:(proces634752977rocess @ A),P6:(proces634752977rocess @ A)]: ((((Phi @ (((proces1525233512Action @ A) @ A3) @ P4)) @ (((proces1525233512Action @ A) @ A5) @ P6)) => ((A3 = A5) & ((Phi @ P4) @ P6))))) => ((! [P4:(proces634752977rocess @ A),Q3:(proces634752977rocess @ A),P6:(proces634752977rocess @ A),Q4:(proces634752977rocess @ A)]: ((((Phi @ (((proces1915862579Choice @ A) @ P4) @ Q3)) @ (((proces1915862579Choice @ A) @ P6) @ Q4)) => (((Phi @ P4) @ P6) & ((Phi @ Q3) @ Q4))))) => (P = P5)))))))).
% 3.19/1.62 thf(fact_70_process__strong__coind, axiom, (! [A:$tType,Phi:((proces634752977rocess @ A) > ((proces634752977rocess @ A) > $o)),P:(proces634752977rocess @ A),P5:(proces634752977rocess @ A)]: ((((Phi @ P) @ P5) => ((! [P4:(proces634752977rocess @ A),P6:(proces634752977rocess @ A)]: ((((Phi @ P4) @ P6) => ((((proces10484146Action @ A) @ P4) = ((proces10484146Action @ A) @ P6)) & (((proces401113213Choice @ A) @ P4) = ((proces401113213Choice @ A) @ P6)))))) => ((! [A3:A,A5:A,P4:(proces634752977rocess @ A),P6:(proces634752977rocess @ A)]: ((((Phi @ (((proces1525233512Action @ A) @ A3) @ P4)) @ (((proces1525233512Action @ A) @ A5) @ P6)) => ((A3 = A5) & (((Phi @ P4) @ P6) | (P4 = P6)))))) => ((! [P4:(proces634752977rocess @ A),Q3:(proces634752977rocess @ A),P6:(proces634752977rocess @ A),Q4:(proces634752977rocess @ A)]: ((((Phi @ (((proces1915862579Choice @ A) @ P4) @ Q3)) @ (((proces1915862579Choice @ A) @ P6) @ Q4)) => ((((Phi @ P4) @ P6) | (P4 = P6)) & (((Phi @ Q3) @ Q4) | (Q3 = Q4)))))) => (P = P5)))))))).
% 3.19/1.62 thf(fact_71_isAction__def, axiom, (! [A:$tType]: (((proces10484146Action @ A) = (^ [Process5:(proces634752977rocess @ A)]: ((? [X112:A,X123:(proces634752977rocess @ A)]: ((Process5 = (((proces1525233512Action @ A) @ X112) @ X123)))))))))).
% 3.19/1.62 thf(fact_72_process_Oexhaust, axiom, (! [A:$tType,Y3:(proces634752977rocess @ A)]: (((! [X113:A,X124:(proces634752977rocess @ A)]: ((Y3 != (((proces1525233512Action @ A) @ X113) @ X124)))) => (~ ((! [X212:(proces634752977rocess @ A),X223:(proces634752977rocess @ A)]: ((Y3 != (((proces1915862579Choice @ A) @ X212) @ X223)))))))))).
% 3.19/1.62 thf(fact_73_process_Odistinct_I1_J, axiom, (! [A:$tType,X11:A,X122:(proces634752977rocess @ A),X21:(proces634752977rocess @ A),X222:(proces634752977rocess @ A)]: (((((proces1525233512Action @ A) @ X11) @ X122) != (((proces1915862579Choice @ A) @ X21) @ X222))))).
% 3.19/1.62 thf(fact_74_process_OdiscI_I1_J, axiom, (! [A:$tType,Process:(proces634752977rocess @ A),X11:A,X122:(proces634752977rocess @ A)]: (((Process = (((proces1525233512Action @ A) @ X11) @ X122)) => ((proces10484146Action @ A) @ Process))))).
% 3.19/1.62 thf(fact_75_process_Odisc_I1_J, axiom, (! [A:$tType,X11:A,X122:(proces634752977rocess @ A)]: (((proces10484146Action @ A) @ (((proces1525233512Action @ A) @ X11) @ X122))))).
% 3.19/1.62 thf(fact_76_process_Odisc_I2_J, axiom, (! [A:$tType,X21:(proces634752977rocess @ A),X222:(proces634752977rocess @ A)]: ((~ (((proces10484146Action @ A) @ (((proces1915862579Choice @ A) @ X21) @ X222))))))).
% 3.19/1.62 thf(fact_77_not__isAction__isChoice, axiom, (! [A:$tType,P:(proces634752977rocess @ A)]: ((~ ((((proces10484146Action @ A) @ P) & ((proces401113213Choice @ A) @ P))))))).
% 3.19/1.62 thf(fact_78_process_Oexhaust__disc, axiom, (! [A:$tType,Process:(proces634752977rocess @ A)]: (((~ (((proces10484146Action @ A) @ Process))) => ((proces401113213Choice @ A) @ Process))))).
% 3.19/1.62 thf(fact_79_isAction__isChoice, axiom, (! [A:$tType,P:(proces634752977rocess @ A)]: ((((proces10484146Action @ A) @ P) | ((proces401113213Choice @ A) @ P))))).
% 3.19/1.62 thf(fact_80_process_Odistinct__disc_I1_J, axiom, (! [A:$tType,Process:(proces634752977rocess @ A)]: ((((proces10484146Action @ A) @ Process) => (~ (((proces401113213Choice @ A) @ Process))))))).
% 3.19/1.62 thf(fact_81_process_Odistinct__disc_I2_J, axiom, (! [A:$tType,Process:(proces634752977rocess @ A)]: ((((proces401113213Choice @ A) @ Process) => (~ (((proces10484146Action @ A) @ Process))))))).
% 3.19/1.62 thf(fact_82_isChoice__def, axiom, (! [A:$tType]: (((proces401113213Choice @ A) = (^ [Process5:(proces634752977rocess @ A)]: ((? [X213:(proces634752977rocess @ A),X224:(proces634752977rocess @ A)]: ((Process5 = (((proces1915862579Choice @ A) @ X213) @ X224)))))))))).
% 3.19/1.62 thf(fact_83_process_OdiscI_I2_J, axiom, (! [A:$tType,Process:(proces634752977rocess @ A),X21:(proces634752977rocess @ A),X222:(proces634752977rocess @ A)]: (((Process = (((proces1915862579Choice @ A) @ X21) @ X222)) => ((proces401113213Choice @ A) @ Process))))).
% 3.19/1.62 thf(fact_84_process_Odisc_I3_J, axiom, (! [A:$tType,X11:A,X122:(proces634752977rocess @ A)]: ((~ (((proces401113213Choice @ A) @ (((proces1525233512Action @ A) @ X11) @ X122))))))).
% 3.19/1.62 thf(fact_85_process_Odisc_I4_J, axiom, (! [A:$tType,X21:(proces634752977rocess @ A),X222:(proces634752977rocess @ A)]: (((proces401113213Choice @ A) @ (((proces1915862579Choice @ A) @ X21) @ X222))))).
% 3.19/1.62 thf(fact_86_process_Osel_I2_J, axiom, (! [A:$tType,X11:A,X122:(proces634752977rocess @ A)]: ((((proces1778668539contOf @ A) @ (((proces1525233512Action @ A) @ X11) @ X122)) = X122)))).
% 3.19/1.62 thf(fact_87_process_Osel_I3_J, axiom, (! [A:$tType,X21:(proces634752977rocess @ A),X222:(proces634752977rocess @ A)]: ((((proces979765041_ch1Of @ A) @ (((proces1915862579Choice @ A) @ X21) @ X222)) = X21)))).
% 3.19/1.62 thf(fact_88_process_Osel_I4_J, axiom, (! [A:$tType,X21:(proces634752977rocess @ A),X222:(proces634752977rocess @ A)]: ((((proces988026546_ch2Of @ A) @ (((proces1915862579Choice @ A) @ X21) @ X222)) = X222)))).
% 3.19/1.62 thf(fact_89_process_Osel_I1_J, axiom, (! [A:$tType,X11:A,X122:(proces634752977rocess @ A)]: ((((proces745025900prefOf @ A) @ (((proces1525233512Action @ A) @ X11) @ X122)) = X11)))).
% 3.19/1.62 thf(fact_90_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))))).
% 3.19/1.62 thf(fact_91_process_Oexhaust__sel, axiom, (! [A:$tType,Process:(proces634752977rocess @ A)]: (((Process != (((proces1525233512Action @ A) @ ((proces745025900prefOf @ A) @ Process)) @ ((proces1778668539contOf @ A) @ Process))) => (Process = (((proces1915862579Choice @ A) @ ((proces979765041_ch1Of @ A) @ Process)) @ ((proces988026546_ch2Of @ A) @ Process))))))).
% 3.19/1.62 thf(fact_92_solution_Odisc_I1_J, axiom, (! [A:$tType,B:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),T2:((proces554692349s_term @ B) @ A)]: ((((((((proces687458811_isACT @ A) @ B) @ A) @ B) @ Sys) @ T2) => ((proces10484146Action @ B) @ ((((proces1652378886lution @ A) @ B) @ Sys) @ T2)))))).
% 3.19/1.62 thf(fact_93_process_Osplit__sel__asm, axiom, (! [B:$tType,A:$tType,P3:(B > $o),F1:(A > ((proces634752977rocess @ A) > B)),F2:((proces634752977rocess @ A) > ((proces634752977rocess @ A) > B)),Process:(proces634752977rocess @ A)]: (((P3 @ (((((proces1406508781rocess @ A) @ B) @ F1) @ F2) @ Process)) = (~ ((((Process = (((proces1525233512Action @ A) @ ((proces745025900prefOf @ A) @ Process)) @ ((proces1778668539contOf @ A) @ Process))) & (~ ((P3 @ ((F1 @ ((proces745025900prefOf @ A) @ Process)) @ ((proces1778668539contOf @ A) @ Process)))))) | ((Process = (((proces1915862579Choice @ A) @ ((proces979765041_ch1Of @ A) @ Process)) @ ((proces988026546_ch2Of @ A) @ Process))) & (~ ((P3 @ ((F2 @ ((proces979765041_ch1Of @ A) @ Process)) @ ((proces988026546_ch2Of @ A) @ Process))))))))))))).
% 3.19/1.62 thf(fact_94_process_Osplit__sel, axiom, (! [B:$tType,A:$tType,P3:(B > $o),F1:(A > ((proces634752977rocess @ A) > B)),F2:((proces634752977rocess @ A) > ((proces634752977rocess @ A) > B)),Process:(proces634752977rocess @ A)]: (((P3 @ (((((proces1406508781rocess @ A) @ B) @ F1) @ F2) @ Process)) = (((Process = (((proces1525233512Action @ A) @ ((proces745025900prefOf @ A) @ Process)) @ ((proces1778668539contOf @ A) @ Process))) => (P3 @ ((F1 @ ((proces745025900prefOf @ A) @ Process)) @ ((proces1778668539contOf @ A) @ Process)))) & ((Process = (((proces1915862579Choice @ A) @ ((proces979765041_ch1Of @ A) @ Process)) @ ((proces988026546_ch2Of @ A) @ Process))) => (P3 @ ((F2 @ ((proces979765041_ch1Of @ A) @ Process)) @ ((proces988026546_ch2Of @ A) @ Process))))))))).
% 3.19/1.62 thf(fact_95_process_Ocase__eq__if, axiom, (! [B:$tType,A:$tType]: ((((proces1406508781rocess @ A) @ B) = (^ [F12:(A > ((proces634752977rocess @ A) > B)),F22:((proces634752977rocess @ A) > ((proces634752977rocess @ A) > B)),Process5:(proces634752977rocess @ A)]: (((((if @ B) @ ((proces10484146Action @ A) @ Process5)) @ ((F12 @ ((proces745025900prefOf @ A) @ Process5)) @ ((proces1778668539contOf @ A) @ Process5))) @ ((F22 @ ((proces979765041_ch1Of @ A) @ Process5)) @ ((proces988026546_ch2Of @ A) @ Process5))))))))).
% 3.19/1.62 thf(fact_96_old_Oprod_Oinject, axiom, (! [A:$tType,B:$tType,A2:A,B2:B,A6:A,B3:B]: (((((((product_Pair @ A) @ B) @ A2) @ B2) = ((((product_Pair @ A) @ B) @ A6) @ B3)) = ((A2 = A6) & (B2 = B3)))))).
% 3.19/1.62 thf(fact_97_prod_Oinject, axiom, (! [A:$tType,B:$tType,X1:A,X2:B,Y1:A,Y2:B]: (((((((product_Pair @ A) @ B) @ X1) @ X2) = ((((product_Pair @ A) @ B) @ Y1) @ Y2)) = ((X1 = Y1) & (X2 = Y2)))))).
% 3.19/1.62 thf(fact_98_process_Orel__coinduct, axiom, (! [A:$tType,B:$tType,P3:((proces634752977rocess @ A) > ((proces634752977rocess @ B) > $o)),X7:(proces634752977rocess @ A),Y3:(proces634752977rocess @ B),R:(A > (B > $o))]: ((((P3 @ X7) @ Y3) => ((! [Process3:(proces634752977rocess @ A),Process4:(proces634752977rocess @ B)]: ((((P3 @ Process3) @ Process4) => ((((proces10484146Action @ A) @ Process3) = ((proces10484146Action @ B) @ Process4)) & ((((proces10484146Action @ A) @ Process3) => (((proces10484146Action @ B) @ Process4) => (((R @ ((proces745025900prefOf @ A) @ Process3)) @ ((proces745025900prefOf @ B) @ Process4)) & ((P3 @ ((proces1778668539contOf @ A) @ Process3)) @ ((proces1778668539contOf @ B) @ Process4))))) & (((proces401113213Choice @ A) @ Process3) => (((proces401113213Choice @ B) @ Process4) => (((P3 @ ((proces979765041_ch1Of @ A) @ Process3)) @ ((proces979765041_ch1Of @ B) @ Process4)) & ((P3 @ ((proces988026546_ch2Of @ A) @ Process3)) @ ((proces988026546_ch2Of @ B) @ Process4)))))))))) => (((((proces749077512rocess @ A) @ B) @ R) @ X7) @ Y3)))))).
% 3.19/1.62 thf(fact_99_process_Orel__sel, axiom, (! [B:$tType,A:$tType]: ((((proces749077512rocess @ A) @ B) = (^ [R2:(A > (B > $o)),A7:(proces634752977rocess @ A),B4:(proces634752977rocess @ B)]: (((((proces10484146Action @ A) @ A7) = ((proces10484146Action @ B) @ B4)) & ((((proces10484146Action @ A) @ A7) => (((proces10484146Action @ B) @ B4) => (((R2 @ ((proces745025900prefOf @ A) @ A7)) @ ((proces745025900prefOf @ B) @ B4)) & (((((proces749077512rocess @ A) @ B) @ R2) @ ((proces1778668539contOf @ A) @ A7)) @ ((proces1778668539contOf @ B) @ B4))))) & (((proces401113213Choice @ A) @ A7) => (((proces401113213Choice @ B) @ B4) => ((((((proces749077512rocess @ A) @ B) @ R2) @ ((proces979765041_ch1Of @ A) @ A7)) @ ((proces979765041_ch1Of @ B) @ B4)) & (((((proces749077512rocess @ A) @ B) @ R2) @ ((proces988026546_ch2Of @ A) @ A7)) @ ((proces988026546_ch2Of @ B) @ B4))))))))))))).
% 3.19/1.62 thf(fact_100_process_Orel__inject_I1_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),X11:A,X122:(proces634752977rocess @ A),Y11:B,Y12:(proces634752977rocess @ B)]: (((((((proces749077512rocess @ A) @ B) @ R) @ (((proces1525233512Action @ A) @ X11) @ X122)) @ (((proces1525233512Action @ B) @ Y11) @ Y12)) = (((R @ X11) @ Y11) & (((((proces749077512rocess @ A) @ B) @ R) @ X122) @ Y12)))))).
% 3.19/1.62 thf(fact_101_process_Orel__inject_I2_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),X21:(proces634752977rocess @ A),X222:(proces634752977rocess @ A),Y21:(proces634752977rocess @ B),Y22:(proces634752977rocess @ B)]: (((((((proces749077512rocess @ A) @ B) @ R) @ (((proces1915862579Choice @ A) @ X21) @ X222)) @ (((proces1915862579Choice @ B) @ Y21) @ Y22)) = ((((((proces749077512rocess @ A) @ B) @ R) @ X21) @ Y21) & (((((proces749077512rocess @ A) @ B) @ R) @ X222) @ Y22)))))).
% 3.19/1.62 thf(fact_102_process_Orel__eq, axiom, (! [A:$tType]: (((((proces749077512rocess @ A) @ A) @ (^ [Y4:A,Z:A]: ((Y4 = Z)))) = (^ [Y4:(proces634752977rocess @ A),Z:(proces634752977rocess @ A)]: ((Y4 = Z))))))).
% 3.19/1.62 thf(fact_103_process_Orel__refl, axiom, (! [B:$tType,Ra:(B > (B > $o)),X7:(proces634752977rocess @ B)]: (((! [X5:B]: (((Ra @ X5) @ X5))) => (((((proces749077512rocess @ B) @ B) @ Ra) @ X7) @ X7))))).
% 3.19/1.62 thf(fact_104_process_Orel__intros_I1_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),X11:A,Y11:B,X122:(proces634752977rocess @ A),Y12:(proces634752977rocess @ B)]: ((((R @ X11) @ Y11) => ((((((proces749077512rocess @ A) @ B) @ R) @ X122) @ Y12) => (((((proces749077512rocess @ A) @ B) @ R) @ (((proces1525233512Action @ A) @ X11) @ X122)) @ (((proces1525233512Action @ B) @ Y11) @ Y12))))))).
% 3.19/1.62 thf(fact_105_process_Orel__intros_I2_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),X21:(proces634752977rocess @ A),Y21:(proces634752977rocess @ B),X222:(proces634752977rocess @ A),Y22:(proces634752977rocess @ B)]: (((((((proces749077512rocess @ A) @ B) @ R) @ X21) @ Y21) => ((((((proces749077512rocess @ A) @ B) @ R) @ X222) @ Y22) => (((((proces749077512rocess @ A) @ B) @ R) @ (((proces1915862579Choice @ A) @ X21) @ X222)) @ (((proces1915862579Choice @ B) @ Y21) @ Y22))))))).
% 3.19/1.62 thf(fact_106_process_Orel__distinct_I2_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),Y21:(proces634752977rocess @ A),Y22:(proces634752977rocess @ A),X11:B,X122:(proces634752977rocess @ B)]: ((~ ((((((proces749077512rocess @ A) @ B) @ R) @ (((proces1915862579Choice @ A) @ Y21) @ Y22)) @ (((proces1525233512Action @ B) @ X11) @ X122))))))).
% 3.19/1.62 thf(fact_107_process_Orel__distinct_I1_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),X11:A,X122:(proces634752977rocess @ A),Y21:(proces634752977rocess @ B),Y22:(proces634752977rocess @ B)]: ((~ ((((((proces749077512rocess @ A) @ B) @ R) @ (((proces1525233512Action @ A) @ X11) @ X122)) @ (((proces1915862579Choice @ B) @ Y21) @ Y22))))))).
% 3.19/1.62 thf(fact_108_process_Orel__cases, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),A2:(proces634752977rocess @ A),B2:(proces634752977rocess @ B)]: (((((((proces749077512rocess @ A) @ B) @ R) @ A2) @ B2) => ((! [X12:A,X22:(proces634752977rocess @ A)]: (((A2 = (((proces1525233512Action @ A) @ X12) @ X22)) => (! [Y13:B,Y23:(proces634752977rocess @ B)]: (((B2 = (((proces1525233512Action @ B) @ Y13) @ Y23)) => (((R @ X12) @ Y13) => (~ ((((((proces749077512rocess @ A) @ B) @ R) @ X22) @ Y23)))))))))) => (~ ((! [X1a:(proces634752977rocess @ A),X2a:(proces634752977rocess @ A)]: (((A2 = (((proces1915862579Choice @ A) @ X1a) @ X2a)) => (! [Y1a:(proces634752977rocess @ B),Y2a:(proces634752977rocess @ B)]: (((B2 = (((proces1915862579Choice @ B) @ Y1a) @ Y2a)) => ((((((proces749077512rocess @ A) @ B) @ R) @ X1a) @ Y1a) => (~ ((((((proces749077512rocess @ A) @ B) @ R) @ X2a) @ Y2a))))))))))))))))).
% 3.19/1.62 thf(fact_109_process_Osimps_I5_J, axiom, (! [B:$tType,A:$tType,F1:(A > ((proces634752977rocess @ A) > B)),F2:((proces634752977rocess @ A) > ((proces634752977rocess @ A) > B)),X11:A,X122:(proces634752977rocess @ A)]: (((((((proces1406508781rocess @ A) @ B) @ F1) @ F2) @ (((proces1525233512Action @ A) @ X11) @ X122)) = ((F1 @ X11) @ X122))))).
% 3.19/1.62 thf(fact_110_process_Osimps_I6_J, axiom, (! [B:$tType,A:$tType,F1:(A > ((proces634752977rocess @ A) > B)),F2:((proces634752977rocess @ A) > ((proces634752977rocess @ A) > B)),X21:(proces634752977rocess @ A),X222:(proces634752977rocess @ A)]: (((((((proces1406508781rocess @ A) @ B) @ F1) @ F2) @ (((proces1915862579Choice @ A) @ X21) @ X222)) = ((F2 @ X21) @ X222))))).
% 3.19/1.62 thf(fact_111_surj__pair, axiom, (! [A:$tType,B:$tType,P:((product_prod @ A) @ B)]: ((? [X5:A,Y5:B]: ((P = ((((product_Pair @ A) @ B) @ X5) @ Y5))))))).
% 3.19/1.62 thf(fact_112_prod__cases, axiom, (! [B:$tType,A:$tType,P3:(((product_prod @ A) @ B) > $o),P:((product_prod @ A) @ B)]: (((! [A3:A,B5:B]: ((P3 @ ((((product_Pair @ A) @ B) @ A3) @ B5)))) => (P3 @ P))))).
% 3.19/1.62 thf(fact_113_Pair__inject, axiom, (! [A:$tType,B:$tType,A2:A,B2:B,A6:A,B3:B]: (((((((product_Pair @ A) @ B) @ A2) @ B2) = ((((product_Pair @ A) @ B) @ A6) @ B3)) => (~ (((A2 = A6) => (B2 != B3)))))))).
% 3.19/1.62 thf(fact_114_prod__cases3, axiom, (! [A:$tType,B:$tType,C:$tType,Y3:((product_prod @ A) @ ((product_prod @ B) @ C))]: ((~ ((! [A3:A,B5:B,C2:C]: ((Y3 != ((((product_Pair @ A) @ ((product_prod @ B) @ C)) @ A3) @ ((((product_Pair @ B) @ C) @ B5) @ C2)))))))))).
% 3.19/1.62 thf(fact_115_prod__cases4, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,Y3:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D)))]: ((~ ((! [A3:A,B5:B,C2:C,D2:D]: ((Y3 != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D))) @ A3) @ ((((product_Pair @ B) @ ((product_prod @ C) @ D)) @ B5) @ ((((product_Pair @ C) @ D) @ C2) @ D2))))))))))).
% 3.19/1.62 thf(fact_116_prod__cases5, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,E:$tType,Y3:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E))))]: ((~ ((! [A3:A,B5:B,C2:C,D2:D,E2:E]: ((Y3 != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E)))) @ A3) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E))) @ B5) @ ((((product_Pair @ C) @ ((product_prod @ D) @ E)) @ C2) @ ((((product_Pair @ D) @ E) @ D2) @ E2)))))))))))).
% 3.19/1.62 thf(fact_117_prod__cases6, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,E:$tType,F5:$tType,Y3:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F5)))))]: ((~ ((! [A3:A,B5:B,C2:C,D2:D,E2:E,F6:F5]: ((Y3 != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F5))))) @ A3) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F5)))) @ B5) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F5))) @ C2) @ ((((product_Pair @ D) @ ((product_prod @ E) @ F5)) @ D2) @ ((((product_Pair @ E) @ F5) @ E2) @ F6))))))))))))).
% 3.19/1.62 thf(fact_118_prod__cases7, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,E:$tType,F5:$tType,G2:$tType,Y3:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F5) @ G2))))))]: ((~ ((! [A3:A,B5:B,C2:C,D2:D,E2:E,F6:F5,G3:G2]: ((Y3 != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F5) @ G2)))))) @ A3) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F5) @ G2))))) @ B5) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F5) @ G2)))) @ C2) @ ((((product_Pair @ D) @ ((product_prod @ E) @ ((product_prod @ F5) @ G2))) @ D2) @ ((((product_Pair @ E) @ ((product_prod @ F5) @ G2)) @ E2) @ ((((product_Pair @ F5) @ G2) @ F6) @ G3)))))))))))))).
% 3.19/1.62 thf(fact_119_prod__induct3, axiom, (! [C:$tType,B:$tType,A:$tType,P3:(((product_prod @ A) @ ((product_prod @ B) @ C)) > $o),X7:((product_prod @ A) @ ((product_prod @ B) @ C))]: (((! [A3:A,B5:B,C2:C]: ((P3 @ ((((product_Pair @ A) @ ((product_prod @ B) @ C)) @ A3) @ ((((product_Pair @ B) @ C) @ B5) @ C2))))) => (P3 @ X7))))).
% 3.19/1.62 thf(fact_120_prod__induct4, axiom, (! [D:$tType,C:$tType,B:$tType,A:$tType,P3:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D))) > $o),X7:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D)))]: (((! [A3:A,B5:B,C2:C,D2:D]: ((P3 @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D))) @ A3) @ ((((product_Pair @ B) @ ((product_prod @ C) @ D)) @ B5) @ ((((product_Pair @ C) @ D) @ C2) @ D2)))))) => (P3 @ X7))))).
% 3.19/1.62 thf(fact_121_prod__induct5, axiom, (! [E:$tType,D:$tType,C:$tType,B:$tType,A:$tType,P3:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E)))) > $o),X7:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E))))]: (((! [A3:A,B5:B,C2:C,D2:D,E2:E]: ((P3 @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E)))) @ A3) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E))) @ B5) @ ((((product_Pair @ C) @ ((product_prod @ D) @ E)) @ C2) @ ((((product_Pair @ D) @ E) @ D2) @ E2))))))) => (P3 @ X7))))).
% 3.19/1.62 thf(fact_122_prod__induct6, axiom, (! [F5:$tType,E:$tType,D:$tType,C:$tType,B:$tType,A:$tType,P3:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F5))))) > $o),X7:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F5)))))]: (((! [A3:A,B5:B,C2:C,D2:D,E2:E,F6:F5]: ((P3 @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F5))))) @ A3) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F5)))) @ B5) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F5))) @ C2) @ ((((product_Pair @ D) @ ((product_prod @ E) @ F5)) @ D2) @ ((((product_Pair @ E) @ F5) @ E2) @ F6)))))))) => (P3 @ X7))))).
% 3.19/1.62 thf(fact_123_prod__induct7, axiom, (! [G2:$tType,F5:$tType,E:$tType,D:$tType,C:$tType,B:$tType,A:$tType,P3:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F5) @ G2)))))) > $o),X7:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F5) @ G2))))))]: (((! [A3:A,B5:B,C2:C,D2:D,E2:E,F6:F5,G3:G2]: ((P3 @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F5) @ G2)))))) @ A3) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F5) @ G2))))) @ B5) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F5) @ G2)))) @ C2) @ ((((product_Pair @ D) @ ((product_prod @ E) @ ((product_prod @ F5) @ G2))) @ D2) @ ((((product_Pair @ E) @ ((product_prod @ F5) @ G2)) @ E2) @ ((((product_Pair @ F5) @ G2) @ F6) @ G3))))))))) => (P3 @ X7))))).
% 3.19/1.62 thf(fact_124_old_Oprod_Oexhaust, axiom, (! [A:$tType,B:$tType,Y3:((product_prod @ A) @ B)]: ((~ ((! [A3:A,B5:B]: ((Y3 != ((((product_Pair @ A) @ B) @ A3) @ B5))))))))).
% 3.19/1.62 thf(fact_125_old_Oprod_Oinducts, axiom, (! [B:$tType,A:$tType,P3:(((product_prod @ A) @ B) > $o),Prod:((product_prod @ A) @ B)]: (((! [A3:A,B5:B]: ((P3 @ ((((product_Pair @ A) @ B) @ A3) @ B5)))) => (P3 @ Prod))))).
% 3.19/1.62 thf(fact_126_old_Oprod_Orec, axiom, (! [A:$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))))).
% 3.19/1.62 thf(fact_127_process__term_Orel__cases, axiom, (! [A:$tType,Pvar:$tType,C:$tType,B:$tType,R1:(A > (B > $o)),R22:(Pvar > (C > $o)),A2:((proces554692349s_term @ A) @ Pvar),B2:((proces554692349s_term @ B) @ C)]: ((((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ A2) @ B2) => ((! [X5:Pvar]: (((A2 = (((proces1627516585ss_VAR @ Pvar) @ A) @ X5)) => (! [Y5:C]: (((B2 = (((proces1627516585ss_VAR @ C) @ B) @ Y5)) => (~ (((R22 @ X5) @ Y5))))))))) => ((! [Xa:(proces634752977rocess @ A)]: (((A2 = (((proces1062592052s_PROC @ A) @ Pvar) @ Xa)) => (! [Ya:(proces634752977rocess @ B)]: (((B2 = (((proces1062592052s_PROC @ B) @ C) @ Ya)) => (~ ((((((proces749077512rocess @ A) @ B) @ R1) @ Xa) @ Ya))))))))) => ((! [X1a:A,X2a:((proces554692349s_term @ A) @ Pvar)]: (((A2 = ((((proces1454156180ss_ACT @ A) @ Pvar) @ X1a) @ X2a)) => (! [Y1a:B,Y2a:((proces554692349s_term @ B) @ C)]: (((B2 = ((((proces1454156180ss_ACT @ B) @ C) @ Y1a) @ Y2a)) => (((R1 @ X1a) @ Y1a) => (~ (((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ X2a) @ Y2a)))))))))) => (~ ((! [X1b:((proces554692349s_term @ A) @ Pvar),X2b:((proces554692349s_term @ A) @ Pvar)]: (((A2 = ((((proces89589571ess_CH @ A) @ Pvar) @ X1b) @ X2b)) => (! [Y1b:((proces554692349s_term @ B) @ C),Y2b:((proces554692349s_term @ B) @ C)]: (((B2 = ((((proces89589571ess_CH @ B) @ C) @ Y1b) @ Y2b)) => (((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ X1b) @ Y1b) => (~ (((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ X2b) @ Y2b))))))))))))))))))).
% 3.19/1.62 thf(fact_128_process__term_Orel__induct, axiom, (! [A:$tType,Pvar:$tType,C:$tType,B:$tType,R1:(A > (B > $o)),R22:(Pvar > (C > $o)),X7:((proces554692349s_term @ A) @ Pvar),Y3:((proces554692349s_term @ B) @ C),Q2:(((proces554692349s_term @ A) @ Pvar) > (((proces554692349s_term @ B) @ C) > $o))]: ((((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ X7) @ Y3) => ((! [A12:Pvar,B1:C]: ((((R22 @ A12) @ B1) => ((Q2 @ (((proces1627516585ss_VAR @ Pvar) @ A) @ A12)) @ (((proces1627516585ss_VAR @ C) @ B) @ B1))))) => ((! [A22:(proces634752977rocess @ A),B22:(proces634752977rocess @ B)]: (((((((proces749077512rocess @ A) @ B) @ R1) @ A22) @ B22) => ((Q2 @ (((proces1062592052s_PROC @ A) @ Pvar) @ A22)) @ (((proces1062592052s_PROC @ B) @ C) @ B22))))) => ((! [A31:A,A32:((proces554692349s_term @ A) @ Pvar),B31:B,B32:((proces554692349s_term @ B) @ C)]: ((((R1 @ A31) @ B31) => (((Q2 @ A32) @ B32) => ((Q2 @ ((((proces1454156180ss_ACT @ A) @ Pvar) @ A31) @ A32)) @ ((((proces1454156180ss_ACT @ B) @ C) @ B31) @ B32)))))) => ((! [A41:((proces554692349s_term @ A) @ Pvar),A42:((proces554692349s_term @ A) @ Pvar),B41:((proces554692349s_term @ B) @ C),B42:((proces554692349s_term @ B) @ C)]: ((((Q2 @ A41) @ B41) => (((Q2 @ A42) @ B42) => ((Q2 @ ((((proces89589571ess_CH @ A) @ Pvar) @ A41) @ A42)) @ ((((proces89589571ess_CH @ B) @ C) @ B41) @ B42)))))) => ((Q2 @ X7) @ Y3))))))))).
% 3.19/1.62 thf(fact_129_internal__case__prod__conv, axiom, (! [B:$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))))).
% 3.19/1.62 thf(fact_130_process__term_Oset__cases_I2_J, axiom, (! [Pvar:$tType,A:$tType,E3:Pvar,A2:((proces554692349s_term @ A) @ Pvar)]: (((((member @ Pvar) @ E3) @ (((proces1493547885s_term @ A) @ Pvar) @ A2)) => ((A2 != (((proces1627516585ss_VAR @ Pvar) @ A) @ E3)) => ((! [Z1:A,Z2:((proces554692349s_term @ A) @ Pvar)]: (((A2 = ((((proces1454156180ss_ACT @ A) @ Pvar) @ Z1) @ Z2)) => (~ ((((member @ Pvar) @ E3) @ (((proces1493547885s_term @ A) @ Pvar) @ Z2))))))) => ((! [Z1:((proces554692349s_term @ A) @ Pvar)]: (((? [Z2:((proces554692349s_term @ A) @ Pvar)]: ((A2 = ((((proces89589571ess_CH @ A) @ Pvar) @ Z1) @ Z2)))) => (~ ((((member @ Pvar) @ E3) @ (((proces1493547885s_term @ A) @ Pvar) @ Z1))))))) => (~ ((! [Z1:((proces554692349s_term @ A) @ Pvar),Z2:((proces554692349s_term @ A) @ Pvar)]: (((A2 = ((((proces89589571ess_CH @ A) @ Pvar) @ Z1) @ Z2)) => (~ ((((member @ Pvar) @ E3) @ (((proces1493547885s_term @ A) @ Pvar) @ Z2)))))))))))))))).
% 3.19/1.62 thf(fact_131_process__term_Orel__inject_I1_J, axiom, (! [B:$tType,A:$tType,Pvar:$tType,C:$tType,R1:(A > (B > $o)),R22:(Pvar > (C > $o)),X1:Pvar,Y1:C]: ((((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ (((proces1627516585ss_VAR @ Pvar) @ A) @ X1)) @ (((proces1627516585ss_VAR @ C) @ B) @ Y1)) = ((R22 @ X1) @ Y1))))).
% 3.19/1.62 thf(fact_132_process__term_Orel__intros_I1_J, axiom, (! [Pvar:$tType,A:$tType,B:$tType,C:$tType,R22:(Pvar > (C > $o)),X1:Pvar,Y1:C,R1:(A > (B > $o))]: ((((R22 @ X1) @ Y1) => ((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ (((proces1627516585ss_VAR @ Pvar) @ A) @ X1)) @ (((proces1627516585ss_VAR @ C) @ B) @ Y1)))))).
% 3.19/1.62 thf(fact_133_process__term_Orel__inject_I4_J, axiom, (! [A:$tType,Pvar:$tType,C:$tType,B:$tType,R1:(A > (B > $o)),R22:(Pvar > (C > $o)),X41:((proces554692349s_term @ A) @ Pvar),X42:((proces554692349s_term @ A) @ Pvar),Y41:((proces554692349s_term @ B) @ C),Y42:((proces554692349s_term @ B) @ C)]: ((((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ ((((proces89589571ess_CH @ A) @ Pvar) @ X41) @ X42)) @ ((((proces89589571ess_CH @ B) @ C) @ Y41) @ Y42)) = (((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ X41) @ Y41) & ((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ X42) @ Y42)))))).
% 3.19/1.62 thf(fact_134_process__term_Orel__intros_I4_J, axiom, (! [A:$tType,Pvar:$tType,C:$tType,B:$tType,R1:(A > (B > $o)),R22:(Pvar > (C > $o)),X41:((proces554692349s_term @ A) @ Pvar),Y41:((proces554692349s_term @ B) @ C),X42:((proces554692349s_term @ A) @ Pvar),Y42:((proces554692349s_term @ B) @ C)]: ((((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ X41) @ Y41) => (((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ X42) @ Y42) => ((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ ((((proces89589571ess_CH @ A) @ Pvar) @ X41) @ X42)) @ ((((proces89589571ess_CH @ B) @ C) @ Y41) @ Y42))))))).
% 3.19/1.62 thf(fact_135_process__term_Orel__inject_I3_J, axiom, (! [A:$tType,Pvar:$tType,C:$tType,B:$tType,R1:(A > (B > $o)),R22:(Pvar > (C > $o)),X31:A,X32:((proces554692349s_term @ A) @ Pvar),Y31:B,Y32:((proces554692349s_term @ B) @ C)]: ((((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ ((((proces1454156180ss_ACT @ A) @ Pvar) @ X31) @ X32)) @ ((((proces1454156180ss_ACT @ B) @ C) @ Y31) @ Y32)) = (((R1 @ X31) @ Y31) & ((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ X32) @ Y32)))))).
% 3.19/1.62 thf(fact_136_process__term_Orel__intros_I3_J, axiom, (! [A:$tType,Pvar:$tType,C:$tType,B:$tType,R1:(A > (B > $o)),X31:A,Y31:B,R22:(Pvar > (C > $o)),X32:((proces554692349s_term @ A) @ Pvar),Y32:((proces554692349s_term @ B) @ C)]: ((((R1 @ X31) @ Y31) => (((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ X32) @ Y32) => ((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ ((((proces1454156180ss_ACT @ A) @ Pvar) @ X31) @ X32)) @ ((((proces1454156180ss_ACT @ B) @ C) @ Y31) @ Y32))))))).
% 3.19/1.62 thf(fact_137_process__term_Orel__refl, axiom, (! [D:$tType,C:$tType,R1a:(C > (C > $o)),R2a:(D > (D > $o)),X7:((proces554692349s_term @ C) @ D)]: (((! [X5:C]: (((R1a @ X5) @ X5))) => ((! [X5:D]: (((R2a @ X5) @ X5))) => ((((((((proces2029722208s_term @ C) @ C) @ D) @ D) @ R1a) @ R2a) @ X7) @ X7)))))).
% 3.19/1.62 thf(fact_138_process__term_Orel__eq, axiom, (! [B:$tType,A:$tType]: ((((((((proces2029722208s_term @ A) @ A) @ B) @ B) @ (^ [Y4:A,Z:A]: ((Y4 = Z)))) @ (^ [Y4:B,Z:B]: ((Y4 = Z)))) = (^ [Y4:((proces554692349s_term @ A) @ B),Z:((proces554692349s_term @ A) @ B)]: ((Y4 = Z))))))).
% 3.19/1.62 thf(fact_139_process__term_Oset__intros_I6_J, axiom, (! [A:$tType,Pvar:$tType,Ab:Pvar]: ((((member @ Pvar) @ Ab) @ (((proces1493547885s_term @ A) @ Pvar) @ (((proces1627516585ss_VAR @ Pvar) @ A) @ Ab)))))).
% 3.19/1.62 thf(fact_140_process__term_Oset__intros_I8_J, axiom, (! [Pvar:$tType,A:$tType,Xk:Pvar,A1c:((proces554692349s_term @ A) @ Pvar),A2c:((proces554692349s_term @ A) @ Pvar)]: (((((member @ Pvar) @ Xk) @ (((proces1493547885s_term @ A) @ Pvar) @ A1c)) => (((member @ Pvar) @ Xk) @ (((proces1493547885s_term @ A) @ Pvar) @ ((((proces89589571ess_CH @ A) @ Pvar) @ A1c) @ A2c))))))).
% 3.19/1.62 thf(fact_141_process__term_Oset__intros_I9_J, axiom, (! [Pvar:$tType,A:$tType,Xm:Pvar,A2c:((proces554692349s_term @ A) @ Pvar),A1c:((proces554692349s_term @ A) @ Pvar)]: (((((member @ Pvar) @ Xm) @ (((proces1493547885s_term @ A) @ Pvar) @ A2c)) => (((member @ Pvar) @ Xm) @ (((proces1493547885s_term @ A) @ Pvar) @ ((((proces89589571ess_CH @ A) @ Pvar) @ A1c) @ A2c))))))).
% 3.19/1.62 thf(fact_142_process__term_Oset__intros_I7_J, axiom, (! [Pvar:$tType,A:$tType,Xi:Pvar,A2b:((proces554692349s_term @ A) @ Pvar),A1b:A]: (((((member @ Pvar) @ Xi) @ (((proces1493547885s_term @ A) @ Pvar) @ A2b)) => (((member @ Pvar) @ Xi) @ (((proces1493547885s_term @ A) @ Pvar) @ ((((proces1454156180ss_ACT @ A) @ Pvar) @ A1b) @ A2b))))))).
% 3.19/1.62 thf(fact_143_process__term_Osimps_I51_J, axiom, (! [Pvar:$tType,A:$tType,X31:A,X32:((proces554692349s_term @ A) @ Pvar)]: (((((proces1493547885s_term @ A) @ Pvar) @ ((((proces1454156180ss_ACT @ A) @ Pvar) @ X31) @ X32)) = (((proces1493547885s_term @ A) @ Pvar) @ X32))))).
% 3.19/1.62 thf(fact_144_process__term_Orel__intros_I2_J, axiom, (! [A:$tType,Pvar:$tType,C:$tType,B:$tType,R1:(A > (B > $o)),X2:(proces634752977rocess @ A),Y2:(proces634752977rocess @ B),R22:(Pvar > (C > $o))]: (((((((proces749077512rocess @ A) @ B) @ R1) @ X2) @ Y2) => ((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ (((proces1062592052s_PROC @ A) @ Pvar) @ X2)) @ (((proces1062592052s_PROC @ B) @ C) @ Y2)))))).
% 3.19/1.62 thf(fact_145_process__term_Orel__inject_I2_J, axiom, (! [C:$tType,Pvar:$tType,A:$tType,B:$tType,R1:(A > (B > $o)),R22:(Pvar > (C > $o)),X2:(proces634752977rocess @ A),Y2:(proces634752977rocess @ B)]: ((((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ (((proces1062592052s_PROC @ A) @ Pvar) @ X2)) @ (((proces1062592052s_PROC @ B) @ C) @ Y2)) = (((((proces749077512rocess @ A) @ B) @ R1) @ X2) @ Y2))))).
% 3.19/1.62 thf(fact_146_process__term_Orel__distinct_I2_J, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,R1:(A > (C > $o)),R22:(B > (D > $o)),Y2:(proces634752977rocess @ A),X1:D]: ((~ (((((((((proces2029722208s_term @ A) @ C) @ B) @ D) @ R1) @ R22) @ (((proces1062592052s_PROC @ A) @ B) @ Y2)) @ (((proces1627516585ss_VAR @ D) @ C) @ X1))))))).
% 3.19/1.62 thf(fact_147_process__term_Orel__distinct_I1_J, axiom, (! [Pvar:$tType,A:$tType,C:$tType,B:$tType,R1:(A > (B > $o)),R22:(Pvar > (C > $o)),X1:Pvar,Y2:(proces634752977rocess @ B)]: ((~ (((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ (((proces1627516585ss_VAR @ Pvar) @ A) @ X1)) @ (((proces1062592052s_PROC @ B) @ C) @ Y2))))))).
% 3.19/1.62 thf(fact_148_process__term_Orel__distinct_I10_J, axiom, (! [A:$tType,B:$tType,D:$tType,C:$tType,R1:(A > (C > $o)),R22:(B > (D > $o)),Y41:((proces554692349s_term @ A) @ B),Y42:((proces554692349s_term @ A) @ B),X2:(proces634752977rocess @ C)]: ((~ (((((((((proces2029722208s_term @ A) @ C) @ B) @ D) @ R1) @ R22) @ ((((proces89589571ess_CH @ A) @ B) @ Y41) @ Y42)) @ (((proces1062592052s_PROC @ C) @ D) @ X2))))))).
% 3.19/1.62 thf(fact_149_process__term_Orel__distinct_I9_J, axiom, (! [A:$tType,Pvar:$tType,C:$tType,B:$tType,R1:(A > (B > $o)),R22:(Pvar > (C > $o)),X2:(proces634752977rocess @ A),Y41:((proces554692349s_term @ B) @ C),Y42:((proces554692349s_term @ B) @ C)]: ((~ (((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ (((proces1062592052s_PROC @ A) @ Pvar) @ X2)) @ ((((proces89589571ess_CH @ B) @ C) @ Y41) @ Y42))))))).
% 3.19/1.62 thf(fact_150_process__term_Orel__distinct_I8_J, axiom, (! [A:$tType,B:$tType,D:$tType,C:$tType,R1:(A > (C > $o)),R22:(B > (D > $o)),Y31:A,Y32:((proces554692349s_term @ A) @ B),X2:(proces634752977rocess @ C)]: ((~ (((((((((proces2029722208s_term @ A) @ C) @ B) @ D) @ R1) @ R22) @ ((((proces1454156180ss_ACT @ A) @ B) @ Y31) @ Y32)) @ (((proces1062592052s_PROC @ C) @ D) @ X2))))))).
% 3.19/1.62 thf(fact_151_process__term_Orel__distinct_I7_J, axiom, (! [A:$tType,Pvar:$tType,C:$tType,B:$tType,R1:(A > (B > $o)),R22:(Pvar > (C > $o)),X2:(proces634752977rocess @ A),Y31:B,Y32:((proces554692349s_term @ B) @ C)]: ((~ (((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ (((proces1062592052s_PROC @ A) @ Pvar) @ X2)) @ ((((proces1454156180ss_ACT @ B) @ C) @ Y31) @ Y32))))))).
% 3.19/1.62 thf(fact_152_process__term_Orel__distinct_I5_J, axiom, (! [Pvar:$tType,A:$tType,C:$tType,B:$tType,R1:(A > (B > $o)),R22:(Pvar > (C > $o)),X1:Pvar,Y41:((proces554692349s_term @ B) @ C),Y42:((proces554692349s_term @ B) @ C)]: ((~ (((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ (((proces1627516585ss_VAR @ Pvar) @ A) @ X1)) @ ((((proces89589571ess_CH @ B) @ C) @ Y41) @ Y42))))))).
% 3.19/1.62 thf(fact_153_process__term_Orel__distinct_I6_J, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,R1:(A > (C > $o)),R22:(B > (D > $o)),Y41:((proces554692349s_term @ A) @ B),Y42:((proces554692349s_term @ A) @ B),X1:D]: ((~ (((((((((proces2029722208s_term @ A) @ C) @ B) @ D) @ R1) @ R22) @ ((((proces89589571ess_CH @ A) @ B) @ Y41) @ Y42)) @ (((proces1627516585ss_VAR @ D) @ C) @ X1))))))).
% 3.19/1.62 thf(fact_154_process__term_Orel__distinct_I3_J, axiom, (! [Pvar:$tType,A:$tType,C:$tType,B:$tType,R1:(A > (B > $o)),R22:(Pvar > (C > $o)),X1:Pvar,Y31:B,Y32:((proces554692349s_term @ B) @ C)]: ((~ (((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ (((proces1627516585ss_VAR @ Pvar) @ A) @ X1)) @ ((((proces1454156180ss_ACT @ B) @ C) @ Y31) @ Y32))))))).
% 3.19/1.62 thf(fact_155_process__term_Orel__distinct_I4_J, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,R1:(A > (C > $o)),R22:(B > (D > $o)),Y31:A,Y32:((proces554692349s_term @ A) @ B),X1:D]: ((~ (((((((((proces2029722208s_term @ A) @ C) @ B) @ D) @ R1) @ R22) @ ((((proces1454156180ss_ACT @ A) @ B) @ Y31) @ Y32)) @ (((proces1627516585ss_VAR @ D) @ C) @ X1))))))).
% 3.19/1.62 thf(fact_156_process__term_Orel__distinct_I11_J, axiom, (! [A:$tType,Pvar:$tType,C:$tType,B:$tType,R1:(A > (B > $o)),R22:(Pvar > (C > $o)),X31:A,X32:((proces554692349s_term @ A) @ Pvar),Y41:((proces554692349s_term @ B) @ C),Y42:((proces554692349s_term @ B) @ C)]: ((~ (((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ ((((proces1454156180ss_ACT @ A) @ Pvar) @ X31) @ X32)) @ ((((proces89589571ess_CH @ B) @ C) @ Y41) @ Y42))))))).
% 3.19/1.62 thf(fact_157_process__term_Orel__distinct_I12_J, axiom, (! [A:$tType,B:$tType,D:$tType,C:$tType,R1:(A > (C > $o)),R22:(B > (D > $o)),Y41:((proces554692349s_term @ A) @ B),Y42:((proces554692349s_term @ A) @ B),X31:C,X32:((proces554692349s_term @ C) @ D)]: ((~ (((((((((proces2029722208s_term @ A) @ C) @ B) @ D) @ R1) @ R22) @ ((((proces89589571ess_CH @ A) @ B) @ Y41) @ Y42)) @ ((((proces1454156180ss_ACT @ C) @ D) @ X31) @ X32))))))).
% 3.19/1.62 thf(fact_158_ssubst__Pair__rhs, axiom, (! [B:$tType,A:$tType,R3:A,S:B,R:(set @ ((product_prod @ A) @ B)),S2:B]: (((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ R3) @ S)) @ R) => ((S2 = S) => (((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ R3) @ S2)) @ R)))))).
% 3.19/1.62 thf(fact_159_curry__conv, axiom, (! [A:$tType,C:$tType,B:$tType]: (((((product_curry @ B) @ C) @ A) = (^ [F7:(((product_prod @ B) @ C) > A),A7:B,B4:C]: ((F7 @ ((((product_Pair @ B) @ C) @ A7) @ B4)))))))).
% 3.19/1.62 thf(fact_160_process__term_Octr__transfer_I2_J, axiom, (! [A:$tType,Pvar:$tType,C:$tType,B:$tType,R1:(A > (B > $o)),R22:(Pvar > (C > $o))]: (((((((((bNF_rel_fun @ (proces634752977rocess @ A)) @ (proces634752977rocess @ B)) @ ((proces554692349s_term @ A) @ Pvar)) @ ((proces554692349s_term @ B) @ C)) @ (((proces749077512rocess @ A) @ B) @ R1)) @ ((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22)) @ ((proces1062592052s_PROC @ A) @ Pvar)) @ ((proces1062592052s_PROC @ B) @ C))))).
% 3.19/1.62 thf(fact_161_isACT_Oelims_I1_J, axiom, (! [D:$tType,A:$tType,B:$tType,C:$tType,X7:(A > ((proces554692349s_term @ B) @ C)),Xa2:((proces554692349s_term @ D) @ A),Y3:$o]: (((((((((proces687458811_isACT @ A) @ B) @ C) @ D) @ X7) @ Xa2) = Y3) => ((! [X3:A]: (((Xa2 = (((proces1627516585ss_VAR @ A) @ D) @ X3)) => (Y3 = (~ (((((((((proces460752237s_term @ C) @ $o) @ B) @ (^ [Pvar2:C]: ($false))) @ (proces10484146Action @ B)) @ (^ [A7:B,T4:((proces554692349s_term @ B) @ C)]: ($true))) @ (^ [Process_term1:((proces554692349s_term @ B) @ C),Process_term2:((proces554692349s_term @ B) @ C)]: ($false))) @ (X7 @ X3)))))))) => ((! [P4:(proces634752977rocess @ D)]: (((Xa2 = (((proces1062592052s_PROC @ D) @ A) @ P4)) => (Y3 = (~ (((proces10484146Action @ D) @ P4))))))) => (((? [A3:D,T3:((proces554692349s_term @ D) @ A)]: ((Xa2 = ((((proces1454156180ss_ACT @ D) @ A) @ A3) @ T3)))) => (~ (Y3))) => (~ (((? [T12:((proces554692349s_term @ D) @ A),T23:((proces554692349s_term @ D) @ A)]: ((Xa2 = ((((proces89589571ess_CH @ D) @ A) @ T12) @ T23)))) => Y3)))))))))).
% 3.19/1.62 thf(fact_162_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) @ $o) @ F) @ A2) @ B2))))).
% 3.19/1.62 thf(fact_163_curry__def, axiom, (! [C:$tType,B:$tType,A:$tType]: (((((product_curry @ A) @ B) @ C) = (^ [C4:(((product_prod @ A) @ B) > C),X6:A,Y6:B]: ((C4 @ ((((product_Pair @ A) @ B) @ X6) @ Y6)))))))).
% 3.19/1.62 thf(fact_164_process__term_Ocase__transfer, axiom, (! [Pvar:$tType,D:$tType,A:$tType,B:$tType,E:$tType,C:$tType,R22:(Pvar > (C > $o)),S3:(D > (E > $o)),R1:(A > (B > $o))]: (((((((((bNF_rel_fun @ (Pvar > D)) @ (C > E)) @ (((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) > E) > ((B > (((proces554692349s_term @ B) @ C) > E)) > ((((proces554692349s_term @ B) @ C) > (((proces554692349s_term @ B) @ C) > E)) > (((proces554692349s_term @ B) @ C) > E))))) @ ((((((bNF_rel_fun @ Pvar) @ C) @ D) @ E) @ R22) @ S3)) @ ((((((bNF_rel_fun @ ((proces634752977rocess @ A) > D)) @ ((proces634752977rocess @ B) > E)) @ ((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) > E)) > ((((proces554692349s_term @ B) @ C) > (((proces554692349s_term @ B) @ C) > E)) > (((proces554692349s_term @ B) @ C) > E)))) @ ((((((bNF_rel_fun @ (proces634752977rocess @ A)) @ (proces634752977rocess @ B)) @ D) @ E) @ (((proces749077512rocess @ A) @ B) @ R1)) @ S3)) @ ((((((bNF_rel_fun @ (A > (((proces554692349s_term @ A) @ Pvar) > D))) @ (B > (((proces554692349s_term @ B) @ C) > E))) @ ((((proces554692349s_term @ A) @ Pvar) > (((proces554692349s_term @ A) @ Pvar) > D)) > (((proces554692349s_term @ A) @ Pvar) > D))) @ ((((proces554692349s_term @ B) @ C) > (((proces554692349s_term @ B) @ C) > E)) > (((proces554692349s_term @ B) @ C) > E))) @ ((((((bNF_rel_fun @ A) @ B) @ (((proces554692349s_term @ A) @ Pvar) > D)) @ (((proces554692349s_term @ B) @ C) > E)) @ R1) @ ((((((bNF_rel_fun @ ((proces554692349s_term @ A) @ Pvar)) @ ((proces554692349s_term @ B) @ C)) @ D) @ E) @ ((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22)) @ S3))) @ ((((((bNF_rel_fun @ (((proces554692349s_term @ A) @ Pvar) > (((proces554692349s_term @ A) @ Pvar) > D))) @ (((proces554692349s_term @ B) @ C) > (((proces554692349s_term @ B) @ C) > E))) @ (((proces554692349s_term @ A) @ Pvar) > D)) @ (((proces554692349s_term @ B) @ C) > E)) @ ((((((bNF_rel_fun @ ((proces554692349s_term @ A) @ Pvar)) @ ((proces554692349s_term @ B) @ C)) @ (((proces554692349s_term @ A) @ Pvar) > D)) @ (((proces554692349s_term @ B) @ C) > E)) @ ((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22)) @ ((((((bNF_rel_fun @ ((proces554692349s_term @ A) @ Pvar)) @ ((proces554692349s_term @ B) @ C)) @ D) @ E) @ ((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22)) @ S3))) @ ((((((bNF_rel_fun @ ((proces554692349s_term @ A) @ Pvar)) @ ((proces554692349s_term @ B) @ C)) @ D) @ E) @ ((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22)) @ S3))))) @ (((proces460752237s_term @ Pvar) @ D) @ A)) @ (((proces460752237s_term @ C) @ E) @ B))))).
% 3.19/1.62 thf(fact_165_process__term_Orec__transfer, axiom, (! [Pvar:$tType,D:$tType,A:$tType,B:$tType,E:$tType,C:$tType,R22:(Pvar > (C > $o)),S3:(D > (E > $o)),R1:(A > (B > $o))]: (((((((((bNF_rel_fun @ (Pvar > D)) @ (C > E)) @ (((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) > E) > ((B > (((proces554692349s_term @ B) @ C) > (E > E))) > ((((proces554692349s_term @ B) @ C) > (((proces554692349s_term @ B) @ C) > (E > (E > E)))) > (((proces554692349s_term @ B) @ C) > E))))) @ ((((((bNF_rel_fun @ Pvar) @ C) @ D) @ E) @ R22) @ S3)) @ ((((((bNF_rel_fun @ ((proces634752977rocess @ A) > D)) @ ((proces634752977rocess @ B) > E)) @ ((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) > (E > E))) > ((((proces554692349s_term @ B) @ C) > (((proces554692349s_term @ B) @ C) > (E > (E > E)))) > (((proces554692349s_term @ B) @ C) > E)))) @ ((((((bNF_rel_fun @ (proces634752977rocess @ A)) @ (proces634752977rocess @ B)) @ D) @ E) @ (((proces749077512rocess @ A) @ B) @ R1)) @ S3)) @ ((((((bNF_rel_fun @ (A > (((proces554692349s_term @ A) @ Pvar) > (D > D)))) @ (B > (((proces554692349s_term @ B) @ C) > (E > E)))) @ ((((proces554692349s_term @ A) @ Pvar) > (((proces554692349s_term @ A) @ Pvar) > (D > (D > D)))) > (((proces554692349s_term @ A) @ Pvar) > D))) @ ((((proces554692349s_term @ B) @ C) > (((proces554692349s_term @ B) @ C) > (E > (E > E)))) > (((proces554692349s_term @ B) @ C) > E))) @ ((((((bNF_rel_fun @ A) @ B) @ (((proces554692349s_term @ A) @ Pvar) > (D > D))) @ (((proces554692349s_term @ B) @ C) > (E > E))) @ R1) @ ((((((bNF_rel_fun @ ((proces554692349s_term @ A) @ Pvar)) @ ((proces554692349s_term @ B) @ C)) @ (D > D)) @ (E > E)) @ ((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22)) @ ((((((bNF_rel_fun @ D) @ E) @ D) @ E) @ S3) @ S3)))) @ ((((((bNF_rel_fun @ (((proces554692349s_term @ A) @ Pvar) > (((proces554692349s_term @ A) @ Pvar) > (D > (D > D))))) @ (((proces554692349s_term @ B) @ C) > (((proces554692349s_term @ B) @ C) > (E > (E > E))))) @ (((proces554692349s_term @ A) @ Pvar) > D)) @ (((proces554692349s_term @ B) @ C) > E)) @ ((((((bNF_rel_fun @ ((proces554692349s_term @ A) @ Pvar)) @ ((proces554692349s_term @ B) @ C)) @ (((proces554692349s_term @ A) @ Pvar) > (D > (D > D)))) @ (((proces554692349s_term @ B) @ C) > (E > (E > E)))) @ ((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22)) @ ((((((bNF_rel_fun @ ((proces554692349s_term @ A) @ Pvar)) @ ((proces554692349s_term @ B) @ C)) @ (D > (D > D))) @ (E > (E > E))) @ ((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22)) @ ((((((bNF_rel_fun @ D) @ E) @ (D > D)) @ (E > E)) @ S3) @ ((((((bNF_rel_fun @ D) @ E) @ D) @ E) @ S3) @ S3))))) @ ((((((bNF_rel_fun @ ((proces554692349s_term @ A) @ Pvar)) @ ((proces554692349s_term @ B) @ C)) @ D) @ E) @ ((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22)) @ S3))))) @ (((proces2117273769s_term @ Pvar) @ D) @ A)) @ (((proces2117273769s_term @ C) @ E) @ B))))).
% 3.19/1.62 thf(fact_166_process__term_Ocase__distrib, axiom, (! [B:$tType,C:$tType,Pvar:$tType,A:$tType,H:(B > C),F1:(Pvar > B),F2:((proces634752977rocess @ A) > B),F3:(A > (((proces554692349s_term @ A) @ Pvar) > B)),F4:(((proces554692349s_term @ A) @ Pvar) > (((proces554692349s_term @ A) @ Pvar) > B)),Process_term:((proces554692349s_term @ A) @ Pvar)]: (((H @ ((((((((proces460752237s_term @ Pvar) @ B) @ A) @ F1) @ F2) @ F3) @ F4) @ Process_term)) = ((((((((proces460752237s_term @ Pvar) @ C) @ A) @ (^ [X6:Pvar]: ((H @ (F1 @ X6))))) @ (^ [X6:(proces634752977rocess @ A)]: ((H @ (F2 @ X6))))) @ (^ [X13:A,X23:((proces554692349s_term @ A) @ Pvar)]: ((H @ ((F3 @ X13) @ X23))))) @ (^ [X13:((proces554692349s_term @ A) @ Pvar),X23:((proces554692349s_term @ A) @ Pvar)]: ((H @ ((F4 @ X13) @ X23))))) @ Process_term))))).
% 3.19/1.62 thf(fact_167_process__term_Opred__True, axiom, (! [B:$tType,A:$tType]: ((((((proces2118920028s_term @ A) @ B) @ (^ [Uu:A]: ($true))) @ (^ [Uu:B]: ($true))) = (^ [Uu:((proces554692349s_term @ A) @ B)]: ($true)))))).
% 3.19/1.62 thf(fact_168_process_Opred__True, axiom, (! [A:$tType]: ((((proces1205983068rocess @ A) @ (^ [Uu:A]: ($true))) = (^ [Uu:(proces634752977rocess @ A)]: ($true)))))).
% 3.19/1.62 thf(fact_169_process_Odisc__eq__case_I2_J, axiom, (! [A:$tType]: (((proces401113213Choice @ A) = ((((proces1406508781rocess @ A) @ $o) @ (^ [Uu:A,Uv:(proces634752977rocess @ A)]: ($false))) @ (^ [Uu:(proces634752977rocess @ A),Uv:(proces634752977rocess @ A)]: ($true))))))).
% 3.19/1.62 thf(fact_170_process_Ocase__distrib, axiom, (! [B:$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) @ (^ [X13:A,X23:(proces634752977rocess @ A)]: ((H @ ((F1 @ X13) @ X23))))) @ (^ [X13:(proces634752977rocess @ A),X23:(proces634752977rocess @ A)]: ((H @ ((F2 @ X13) @ X23))))) @ Process))))).
% 3.19/1.62 thf(fact_171_curry__K, axiom, (! [B:$tType,C:$tType,A:$tType,C3:C]: ((((((product_curry @ A) @ B) @ C) @ (^ [X6:((product_prod @ A) @ B)]: (C3))) = (^ [X6:A,Y6:B]: (C3)))))).
% 3.19/1.62 thf(fact_172_process_Odisc__eq__case_I1_J, axiom, (! [A:$tType]: (((proces10484146Action @ A) = ((((proces1406508781rocess @ A) @ $o) @ (^ [Uu:A,Uv:(proces634752977rocess @ A)]: ($true))) @ (^ [Uu:(proces634752977rocess @ A),Uv:(proces634752977rocess @ A)]: ($false))))))).
% 3.19/1.62 thf(fact_173_isACT_Osimps_I1_J, axiom, (! [D:$tType,B:$tType,C:$tType,A:$tType,Sys:(A > ((proces554692349s_term @ B) @ C)),X:A]: ((((((((proces687458811_isACT @ A) @ B) @ C) @ D) @ Sys) @ (((proces1627516585ss_VAR @ A) @ D) @ X)) = ((((((((proces460752237s_term @ C) @ $o) @ B) @ (^ [Pvar2:C]: ($false))) @ (proces10484146Action @ B)) @ (^ [A7:B,T4:((proces554692349s_term @ B) @ C)]: ($true))) @ (^ [Process_term1:((proces554692349s_term @ B) @ C),Process_term2:((proces554692349s_term @ B) @ C)]: ($false))) @ (Sys @ X)))))).
% 3.19/1.62 thf(fact_174_curryD, axiom, (! [A:$tType,B:$tType,F:(((product_prod @ A) @ B) > $o),A2:A,B2:B]: ((((((((product_curry @ A) @ B) @ $o) @ F) @ A2) @ B2) => (F @ ((((product_Pair @ A) @ B) @ A2) @ B2)))))).
% 3.19/1.62 thf(fact_175_curryE, axiom, (! [A:$tType,B:$tType,F:(((product_prod @ A) @ B) > $o),A2:A,B2:B]: ((((((((product_curry @ A) @ B) @ $o) @ F) @ A2) @ B2) => (F @ ((((product_Pair @ A) @ B) @ A2) @ B2)))))).
% 3.19/1.62 thf(fact_176_process__term_Octr__transfer_I1_J, axiom, (! [Pvar:$tType,A:$tType,B:$tType,C:$tType,R22:(Pvar > (C > $o)),R1:(A > (B > $o))]: (((((((((bNF_rel_fun @ Pvar) @ C) @ ((proces554692349s_term @ A) @ Pvar)) @ ((proces554692349s_term @ B) @ C)) @ R22) @ ((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22)) @ ((proces1627516585ss_VAR @ Pvar) @ A)) @ ((proces1627516585ss_VAR @ C) @ B))))).
% 3.19/1.62 thf(fact_177_isACT_Oelims_I3_J, axiom, (! [C:$tType,B:$tType,A:$tType,D:$tType,X7:(A > ((proces554692349s_term @ B) @ C)),Xa2:((proces554692349s_term @ D) @ A)]: (((~ (((((((proces687458811_isACT @ A) @ B) @ C) @ D) @ X7) @ Xa2))) => ((! [X3:A]: (((Xa2 = (((proces1627516585ss_VAR @ A) @ D) @ X3)) => ((((((((proces460752237s_term @ C) @ $o) @ B) @ (^ [Pvar2:C]: ($false))) @ (proces10484146Action @ B)) @ (^ [A7:B,T4:((proces554692349s_term @ B) @ C)]: ($true))) @ (^ [Process_term1:((proces554692349s_term @ B) @ C),Process_term2:((proces554692349s_term @ B) @ C)]: ($false))) @ (X7 @ X3))))) => ((! [P4:(proces634752977rocess @ D)]: (((Xa2 = (((proces1062592052s_PROC @ D) @ A) @ P4)) => ((proces10484146Action @ D) @ P4)))) => (~ ((! [T12:((proces554692349s_term @ D) @ A),T23:((proces554692349s_term @ D) @ A)]: ((Xa2 != ((((proces89589571ess_CH @ D) @ A) @ T12) @ T23)))))))))))).
% 3.19/1.62 thf(fact_178_isACT_Oelims_I2_J, axiom, (! [C:$tType,B:$tType,A:$tType,D:$tType,X7:(A > ((proces554692349s_term @ B) @ C)),Xa2:((proces554692349s_term @ D) @ A)]: ((((((((proces687458811_isACT @ A) @ B) @ C) @ D) @ X7) @ Xa2) => ((! [X3:A]: (((Xa2 = (((proces1627516585ss_VAR @ A) @ D) @ X3)) => (~ (((((((((proces460752237s_term @ C) @ $o) @ B) @ (^ [Pvar2:C]: ($false))) @ (proces10484146Action @ B)) @ (^ [A7:B,T4:((proces554692349s_term @ B) @ C)]: ($true))) @ (^ [Process_term1:((proces554692349s_term @ B) @ C),Process_term2:((proces554692349s_term @ B) @ C)]: ($false))) @ (X7 @ X3))))))) => ((! [P4:(proces634752977rocess @ D)]: (((Xa2 = (((proces1062592052s_PROC @ D) @ A) @ P4)) => (~ (((proces10484146Action @ D) @ P4)))))) => (~ ((! [A3:D,T3:((proces554692349s_term @ D) @ A)]: ((Xa2 != ((((proces1454156180ss_ACT @ D) @ A) @ A3) @ T3)))))))))))).
% 3.19/1.62 thf(fact_179_PREF_Oelims, axiom, (! [A:$tType,C:$tType,B:$tType,X7:(A > ((proces554692349s_term @ B) @ C)),Xa2:((proces554692349s_term @ B) @ A),Y3:B]: ((((((((proces1708129104e_PREF @ A) @ B) @ C) @ X7) @ Xa2) = Y3) => ((! [X3:A]: (((Xa2 = (((proces1627516585ss_VAR @ A) @ B) @ X3)) => (Y3 != ((((((((proces460752237s_term @ C) @ B) @ B) @ (^ [Aa3:C]: ((undefined @ B)))) @ (proces745025900prefOf @ B)) @ (^ [A7:B,T4:((proces554692349s_term @ B) @ C)]: (A7))) @ (^ [Aa3:((proces554692349s_term @ B) @ C),Ab2:((proces554692349s_term @ B) @ C)]: ((undefined @ B)))) @ (X7 @ X3)))))) => ((! [P4:(proces634752977rocess @ B)]: (((Xa2 = (((proces1062592052s_PROC @ B) @ A) @ P4)) => (Y3 != ((proces745025900prefOf @ B) @ P4))))) => ((! [A3:B]: (((? [T3:((proces554692349s_term @ B) @ A)]: ((Xa2 = ((((proces1454156180ss_ACT @ B) @ A) @ A3) @ T3)))) => (Y3 != A3)))) => (~ (((? [V:((proces554692349s_term @ B) @ A),Va:((proces554692349s_term @ B) @ A)]: ((Xa2 = ((((proces89589571ess_CH @ B) @ A) @ V) @ Va)))) => (Y3 != (undefined @ B)))))))))))).
% 3.19/1.62 thf(fact_180_rel__funI, axiom, (! [A:$tType,C:$tType,D:$tType,B:$tType,A4:(A > (B > $o)),B6:(C > (D > $o)),F:(A > C),G:(B > D)]: (((! [X5:A,Y5:B]: ((((A4 @ X5) @ Y5) => ((B6 @ (F @ X5)) @ (G @ Y5))))) => ((((((((bNF_rel_fun @ A) @ B) @ C) @ D) @ A4) @ B6) @ F) @ G))))).
% 3.19/1.62 thf(fact_181_CH1_Oelims, axiom, (! [A:$tType,B:$tType,X7:(A > ((proces554692349s_term @ B) @ A)),Xa2:((proces554692349s_term @ B) @ A),Y3:((proces554692349s_term @ B) @ A)]: (((((((proces1239275103le_CH1 @ A) @ B) @ X7) @ Xa2) = Y3) => ((! [X3:A]: (((Xa2 = (((proces1627516585ss_VAR @ A) @ B) @ X3)) => (Y3 != ((((((((proces460752237s_term @ A) @ ((proces554692349s_term @ B) @ A)) @ B) @ (^ [A7:A]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (^ [P7:(proces634752977rocess @ B)]: ((((proces1062592052s_PROC @ B) @ A) @ ((proces979765041_ch1Of @ B) @ P7))))) @ (^ [A7:B,B4:((proces554692349s_term @ B) @ A)]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (^ [T13:((proces554692349s_term @ B) @ A),T24:((proces554692349s_term @ B) @ A)]: (T13))) @ (X7 @ X3)))))) => ((! [P4:(proces634752977rocess @ B)]: (((Xa2 = (((proces1062592052s_PROC @ B) @ A) @ P4)) => (Y3 != (((proces1062592052s_PROC @ B) @ A) @ ((proces979765041_ch1Of @ B) @ P4)))))) => ((! [T12:((proces554692349s_term @ B) @ A)]: (((? [T23:((proces554692349s_term @ B) @ A)]: ((Xa2 = ((((proces89589571ess_CH @ B) @ A) @ T12) @ T23)))) => (Y3 != T12)))) => (~ (((? [V:B,Va:((proces554692349s_term @ B) @ A)]: ((Xa2 = ((((proces1454156180ss_ACT @ B) @ A) @ V) @ Va)))) => (Y3 != (undefined @ ((proces554692349s_term @ B) @ A))))))))))))).
% 3.19/1.62 thf(fact_182_process__term_Octr__transfer_I4_J, axiom, (! [A:$tType,Pvar:$tType,C:$tType,B:$tType,R1:(A > (B > $o)),R22:(Pvar > (C > $o))]: (((((((((bNF_rel_fun @ ((proces554692349s_term @ A) @ Pvar)) @ ((proces554692349s_term @ B) @ C)) @ (((proces554692349s_term @ A) @ Pvar) > ((proces554692349s_term @ A) @ Pvar))) @ (((proces554692349s_term @ B) @ C) > ((proces554692349s_term @ B) @ C))) @ ((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22)) @ ((((((bNF_rel_fun @ ((proces554692349s_term @ A) @ Pvar)) @ ((proces554692349s_term @ B) @ C)) @ ((proces554692349s_term @ A) @ Pvar)) @ ((proces554692349s_term @ B) @ C)) @ ((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22)) @ ((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22))) @ ((proces89589571ess_CH @ A) @ Pvar)) @ ((proces89589571ess_CH @ B) @ C))))).
% 3.19/1.62 thf(fact_183_process__term_Octr__transfer_I3_J, axiom, (! [A:$tType,Pvar:$tType,C:$tType,B:$tType,R1:(A > (B > $o)),R22:(Pvar > (C > $o))]: (((((((((bNF_rel_fun @ A) @ B) @ (((proces554692349s_term @ A) @ Pvar) > ((proces554692349s_term @ A) @ Pvar))) @ (((proces554692349s_term @ B) @ C) > ((proces554692349s_term @ B) @ C))) @ R1) @ ((((((bNF_rel_fun @ ((proces554692349s_term @ A) @ Pvar)) @ ((proces554692349s_term @ B) @ C)) @ ((proces554692349s_term @ A) @ Pvar)) @ ((proces554692349s_term @ B) @ C)) @ ((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22)) @ ((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22))) @ ((proces1454156180ss_ACT @ A) @ Pvar)) @ ((proces1454156180ss_ACT @ B) @ C))))).
% 3.19/1.62 thf(fact_184_process__term_Opred__transfer, axiom, (! [A:$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) @ $o) @ R1) @ (^ [Y4:$o,Z:$o]: ((Y4 = Z))))) @ ((((((bNF_rel_fun @ (B > $o)) @ (D > $o)) @ (((proces554692349s_term @ A) @ B) > $o)) @ (((proces554692349s_term @ C) @ D) > $o)) @ ((((((bNF_rel_fun @ B) @ D) @ $o) @ $o) @ R22) @ (^ [Y4:$o,Z:$o]: ((Y4 = Z))))) @ ((((((bNF_rel_fun @ ((proces554692349s_term @ A) @ B)) @ ((proces554692349s_term @ C) @ D)) @ $o) @ $o) @ ((((((proces2029722208s_term @ A) @ C) @ B) @ D) @ R1) @ R22)) @ (^ [Y4:$o,Z:$o]: ((Y4 = Z)))))) @ ((proces2118920028s_term @ A) @ B)) @ ((proces2118920028s_term @ C) @ D))))).
% 3.19/1.62 thf(fact_185_process__term_Orel__transfer, axiom, (! [A:$tType,C:$tType,B:$tType,D:$tType,H2:$tType,F5:$tType,G2:$tType,E:$tType,S1a:(A > (E > $o)),S1c:(C > (G2 > $o)),S2a:(B > (F5 > $o)),S2c:(D > (H2 > $o))]: (((((((((bNF_rel_fun @ (A > (C > $o))) @ (E > (G2 > $o))) @ ((B > (D > $o)) > (((proces554692349s_term @ A) @ B) > (((proces554692349s_term @ C) @ D) > $o)))) @ ((F5 > (H2 > $o)) > (((proces554692349s_term @ E) @ F5) > (((proces554692349s_term @ G2) @ H2) > $o)))) @ ((((((bNF_rel_fun @ A) @ E) @ (C > $o)) @ (G2 > $o)) @ S1a) @ ((((((bNF_rel_fun @ C) @ G2) @ $o) @ $o) @ S1c) @ (^ [Y4:$o,Z:$o]: ((Y4 = Z)))))) @ ((((((bNF_rel_fun @ (B > (D > $o))) @ (F5 > (H2 > $o))) @ (((proces554692349s_term @ A) @ B) > (((proces554692349s_term @ C) @ D) > $o))) @ (((proces554692349s_term @ E) @ F5) > (((proces554692349s_term @ G2) @ H2) > $o))) @ ((((((bNF_rel_fun @ B) @ F5) @ (D > $o)) @ (H2 > $o)) @ S2a) @ ((((((bNF_rel_fun @ D) @ H2) @ $o) @ $o) @ S2c) @ (^ [Y4:$o,Z:$o]: ((Y4 = Z)))))) @ ((((((bNF_rel_fun @ ((proces554692349s_term @ A) @ B)) @ ((proces554692349s_term @ E) @ F5)) @ (((proces554692349s_term @ C) @ D) > $o)) @ (((proces554692349s_term @ G2) @ H2) > $o)) @ ((((((proces2029722208s_term @ A) @ E) @ B) @ F5) @ S1a) @ S2a)) @ ((((((bNF_rel_fun @ ((proces554692349s_term @ C) @ D)) @ ((proces554692349s_term @ G2) @ H2)) @ $o) @ $o) @ ((((((proces2029722208s_term @ C) @ G2) @ D) @ H2) @ S1c) @ S2c)) @ (^ [Y4:$o,Z:$o]: ((Y4 = Z))))))) @ ((((proces2029722208s_term @ A) @ C) @ B) @ D)) @ ((((proces2029722208s_term @ E) @ G2) @ F5) @ H2))))).
% 3.19/1.62 thf(fact_186_process_Opred__transfer, axiom, (! [A:$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) @ $o) @ R) @ (^ [Y4:$o,Z:$o]: ((Y4 = Z))))) @ ((((((bNF_rel_fun @ (proces634752977rocess @ A)) @ (proces634752977rocess @ B)) @ $o) @ $o) @ (((proces749077512rocess @ A) @ B) @ R)) @ (^ [Y4:$o,Z:$o]: ((Y4 = Z))))) @ (proces1205983068rocess @ A)) @ (proces1205983068rocess @ B))))).
% 3.19/1.62 thf(fact_187_process_Orel__transfer, axiom, (! [A:$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) @ $o) @ Sc) @ (^ [Y4:$o,Z:$o]: ((Y4 = Z)))))) @ ((((((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) @ $o) @ (((proces749077512rocess @ B) @ D) @ Sc)) @ (^ [Y4:$o,Z:$o]: ((Y4 = Z)))))) @ ((proces749077512rocess @ A) @ B)) @ ((proces749077512rocess @ C) @ D))))).
% 3.19/1.62 thf(fact_188_process_Ocase__transfer, axiom, (! [A:$tType,C:$tType,D:$tType,B:$tType,R:(A > (B > $o)),S3:(C > (D > $o))]: (((((((((bNF_rel_fun @ (A > ((proces634752977rocess @ A) > C))) @ (B > ((proces634752977rocess @ B) > D))) @ (((proces634752977rocess @ A) > ((proces634752977rocess @ A) > C)) > ((proces634752977rocess @ A) > C))) @ (((proces634752977rocess @ B) > ((proces634752977rocess @ B) > D)) > ((proces634752977rocess @ B) > D))) @ ((((((bNF_rel_fun @ A) @ B) @ ((proces634752977rocess @ A) > C)) @ ((proces634752977rocess @ B) > D)) @ R) @ ((((((bNF_rel_fun @ (proces634752977rocess @ A)) @ (proces634752977rocess @ B)) @ C) @ D) @ (((proces749077512rocess @ A) @ B) @ R)) @ S3))) @ ((((((bNF_rel_fun @ ((proces634752977rocess @ A) > ((proces634752977rocess @ A) > C))) @ ((proces634752977rocess @ B) > ((proces634752977rocess @ B) > D))) @ ((proces634752977rocess @ A) > C)) @ ((proces634752977rocess @ B) > D)) @ ((((((bNF_rel_fun @ (proces634752977rocess @ A)) @ (proces634752977rocess @ B)) @ ((proces634752977rocess @ A) > C)) @ ((proces634752977rocess @ B) > D)) @ (((proces749077512rocess @ A) @ B) @ R)) @ ((((((bNF_rel_fun @ (proces634752977rocess @ A)) @ (proces634752977rocess @ B)) @ C) @ D) @ (((proces749077512rocess @ A) @ B) @ R)) @ S3))) @ ((((((bNF_rel_fun @ (proces634752977rocess @ A)) @ (proces634752977rocess @ B)) @ C) @ D) @ (((proces749077512rocess @ A) @ B) @ R)) @ S3))) @ ((proces1406508781rocess @ A) @ C)) @ ((proces1406508781rocess @ B) @ D))))).
% 3.19/1.62 thf(fact_189_process_Octr__transfer_I2_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o))]: (((((((((bNF_rel_fun @ (proces634752977rocess @ A)) @ (proces634752977rocess @ B)) @ ((proces634752977rocess @ A) > (proces634752977rocess @ A))) @ ((proces634752977rocess @ B) > (proces634752977rocess @ B))) @ (((proces749077512rocess @ A) @ B) @ R)) @ ((((((bNF_rel_fun @ (proces634752977rocess @ A)) @ (proces634752977rocess @ B)) @ (proces634752977rocess @ A)) @ (proces634752977rocess @ B)) @ (((proces749077512rocess @ A) @ B) @ R)) @ (((proces749077512rocess @ A) @ B) @ R))) @ (proces1915862579Choice @ A)) @ (proces1915862579Choice @ B))))).
% 3.19/1.62 thf(fact_190_process_Octr__transfer_I1_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o))]: (((((((((bNF_rel_fun @ A) @ B) @ ((proces634752977rocess @ A) > (proces634752977rocess @ A))) @ ((proces634752977rocess @ B) > (proces634752977rocess @ B))) @ R) @ ((((((bNF_rel_fun @ (proces634752977rocess @ A)) @ (proces634752977rocess @ B)) @ (proces634752977rocess @ A)) @ (proces634752977rocess @ B)) @ (((proces749077512rocess @ A) @ B) @ R)) @ (((proces749077512rocess @ A) @ B) @ R))) @ (proces1525233512Action @ A)) @ (proces1525233512Action @ B))))).
% 3.19/1.62 thf(fact_191_contOf__def, axiom, (! [A:$tType]: (((proces1778668539contOf @ A) = ((((proces1406508781rocess @ A) @ (proces634752977rocess @ A)) @ (^ [X112:A,X123:(proces634752977rocess @ A)]: (X123))) @ (^ [Uu2:(proces634752977rocess @ A),Uv2:(proces634752977rocess @ A)]: ((undefined @ (proces634752977rocess @ A))))))))).
% 3.19/1.62 thf(fact_192_ch2Of__def, axiom, (! [A:$tType]: (((proces988026546_ch2Of @ A) = ((((proces1406508781rocess @ A) @ (proces634752977rocess @ A)) @ (^ [Uu2:A,Uv2:(proces634752977rocess @ A)]: ((undefined @ (proces634752977rocess @ A))))) @ (^ [X213:(proces634752977rocess @ A),X224:(proces634752977rocess @ A)]: (X224))))))).
% 3.19/1.62 thf(fact_193_ch1Of__def, axiom, (! [A:$tType]: (((proces979765041_ch1Of @ A) = ((((proces1406508781rocess @ A) @ (proces634752977rocess @ A)) @ (^ [Uu2:A,Uv2:(proces634752977rocess @ A)]: ((undefined @ (proces634752977rocess @ A))))) @ (^ [X213:(proces634752977rocess @ A),X224:(proces634752977rocess @ A)]: (X213))))))).
% 3.19/1.62 thf(fact_194_process_Odisc__transfer_I1_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o))]: (((((((((bNF_rel_fun @ (proces634752977rocess @ A)) @ (proces634752977rocess @ B)) @ $o) @ $o) @ (((proces749077512rocess @ A) @ B) @ R)) @ (^ [Y4:$o,Z:$o]: ((Y4 = Z)))) @ (proces10484146Action @ A)) @ (proces10484146Action @ B))))).
% 3.19/1.62 thf(fact_195_process_Odisc__transfer_I2_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o))]: (((((((((bNF_rel_fun @ (proces634752977rocess @ A)) @ (proces634752977rocess @ B)) @ $o) @ $o) @ (((proces749077512rocess @ A) @ B) @ R)) @ (^ [Y4:$o,Z:$o]: ((Y4 = Z)))) @ (proces401113213Choice @ A)) @ (proces401113213Choice @ B))))).
% 3.19/1.62 thf(fact_196_rel__fun__mono_H, axiom, (! [A:$tType,C:$tType,D:$tType,B:$tType,Y7:(A > (B > $o)),X:(A > (B > $o)),A4:(C > (D > $o)),B6:(C > (D > $o)),F:(A > C),G:(B > D)]: (((! [X5:A,Y5:B]: ((((Y7 @ X5) @ Y5) => ((X @ X5) @ Y5)))) => ((! [X5:C,Y5:D]: ((((A4 @ X5) @ Y5) => ((B6 @ X5) @ Y5)))) => (((((((((bNF_rel_fun @ A) @ B) @ C) @ D) @ X) @ A4) @ F) @ G) => ((((((((bNF_rel_fun @ A) @ B) @ C) @ D) @ Y7) @ B6) @ F) @ G))))))).
% 3.19/1.62 thf(fact_197_rel__fun__mono, axiom, (! [A:$tType,C:$tType,D:$tType,B:$tType,X:(A > (B > $o)),A4:(C > (D > $o)),F:(A > C),G:(B > D),Y7:(A > (B > $o)),B6:(C > (D > $o))]: ((((((((((bNF_rel_fun @ A) @ B) @ C) @ D) @ X) @ A4) @ F) @ G) => ((! [X5:A,Y5:B]: ((((Y7 @ X5) @ Y5) => ((X @ X5) @ Y5)))) => ((! [X5:C,Y5:D]: ((((A4 @ X5) @ Y5) => ((B6 @ X5) @ Y5)))) => ((((((((bNF_rel_fun @ A) @ B) @ C) @ D) @ Y7) @ B6) @ F) @ G))))))).
% 3.19/1.62 thf(fact_198_rel__funD, axiom, (! [A:$tType,C:$tType,D:$tType,B:$tType,A4:(A > (B > $o)),B6:(C > (D > $o)),F:(A > C),G:(B > D),X7:A,Y3:B]: ((((((((((bNF_rel_fun @ A) @ B) @ C) @ D) @ A4) @ B6) @ F) @ G) => (((A4 @ X7) @ Y3) => ((B6 @ (F @ X7)) @ (G @ Y3))))))).
% 3.19/1.62 thf(fact_199_prefOf__def, axiom, (! [A:$tType]: (((proces745025900prefOf @ A) = ((((proces1406508781rocess @ A) @ A) @ (^ [X112:A,X123:(proces634752977rocess @ A)]: (X112))) @ (^ [Uu2:(proces634752977rocess @ A),Uv2:(proces634752977rocess @ A)]: ((undefined @ A)))))))).
% 3.19/1.62 thf(fact_200_CONT_Osimps_I1_J, axiom, (! [B:$tType,A:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),X:A]: ((((((proces126235999e_CONT @ A) @ B) @ Sys) @ (((proces1627516585ss_VAR @ A) @ B) @ X)) = ((((((((proces460752237s_term @ A) @ ((proces554692349s_term @ B) @ A)) @ B) @ (^ [Aa3:A]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (^ [P7:(proces634752977rocess @ B)]: ((((proces1062592052s_PROC @ B) @ A) @ ((proces1778668539contOf @ B) @ P7))))) @ (^ [A7:B,T4:((proces554692349s_term @ B) @ A)]: (T4))) @ (^ [Aa3:((proces554692349s_term @ B) @ A),Ab2:((proces554692349s_term @ B) @ A)]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (Sys @ X)))))).
% 3.19/1.62 thf(fact_201_CH1_Osimps_I1_J, axiom, (! [B:$tType,A:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),X:A]: ((((((proces1239275103le_CH1 @ A) @ B) @ Sys) @ (((proces1627516585ss_VAR @ A) @ B) @ X)) = ((((((((proces460752237s_term @ A) @ ((proces554692349s_term @ B) @ A)) @ B) @ (^ [A7:A]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (^ [P7:(proces634752977rocess @ B)]: ((((proces1062592052s_PROC @ B) @ A) @ ((proces979765041_ch1Of @ B) @ P7))))) @ (^ [A7:B,B4:((proces554692349s_term @ B) @ A)]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (^ [T13:((proces554692349s_term @ B) @ A),T24:((proces554692349s_term @ B) @ A)]: (T13))) @ (Sys @ X)))))).
% 3.19/1.62 thf(fact_202_CH2_Osimps_I1_J, axiom, (! [B:$tType,A:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),X:A]: ((((((proces1239275104le_CH2 @ A) @ B) @ Sys) @ (((proces1627516585ss_VAR @ A) @ B) @ X)) = ((((((((proces460752237s_term @ A) @ ((proces554692349s_term @ B) @ A)) @ B) @ (^ [A7:A]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (^ [P7:(proces634752977rocess @ B)]: ((((proces1062592052s_PROC @ B) @ A) @ ((proces988026546_ch2Of @ B) @ P7))))) @ (^ [A7:B,B4:((proces554692349s_term @ B) @ A)]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (^ [T13:((proces554692349s_term @ B) @ A),T24:((proces554692349s_term @ B) @ A)]: (T24))) @ (Sys @ X)))))).
% 3.19/1.62 thf(fact_203_PREF_Osimps_I1_J, axiom, (! [B:$tType,C:$tType,A:$tType,Sys:(A > ((proces554692349s_term @ B) @ C)),X:A]: (((((((proces1708129104e_PREF @ A) @ B) @ C) @ Sys) @ (((proces1627516585ss_VAR @ A) @ B) @ X)) = ((((((((proces460752237s_term @ C) @ B) @ B) @ (^ [Aa3:C]: ((undefined @ B)))) @ (proces745025900prefOf @ B)) @ (^ [A7:B,T4:((proces554692349s_term @ B) @ C)]: (A7))) @ (^ [Aa3:((proces554692349s_term @ B) @ C),Ab2:((proces554692349s_term @ B) @ C)]: ((undefined @ B)))) @ (Sys @ X)))))).
% 3.19/1.62 thf(fact_204_CONT_Oelims, axiom, (! [A:$tType,B:$tType,X7:(A > ((proces554692349s_term @ B) @ A)),Xa2:((proces554692349s_term @ B) @ A),Y3:((proces554692349s_term @ B) @ A)]: (((((((proces126235999e_CONT @ A) @ B) @ X7) @ Xa2) = Y3) => ((! [X3:A]: (((Xa2 = (((proces1627516585ss_VAR @ A) @ B) @ X3)) => (Y3 != ((((((((proces460752237s_term @ A) @ ((proces554692349s_term @ B) @ A)) @ B) @ (^ [Aa3:A]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (^ [P7:(proces634752977rocess @ B)]: ((((proces1062592052s_PROC @ B) @ A) @ ((proces1778668539contOf @ B) @ P7))))) @ (^ [A7:B,T4:((proces554692349s_term @ B) @ A)]: (T4))) @ (^ [Aa3:((proces554692349s_term @ B) @ A),Ab2:((proces554692349s_term @ B) @ A)]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (X7 @ X3)))))) => ((! [P4:(proces634752977rocess @ B)]: (((Xa2 = (((proces1062592052s_PROC @ B) @ A) @ P4)) => (Y3 != (((proces1062592052s_PROC @ B) @ A) @ ((proces1778668539contOf @ B) @ P4)))))) => ((! [A3:B,T3:((proces554692349s_term @ B) @ A)]: (((Xa2 = ((((proces1454156180ss_ACT @ B) @ A) @ A3) @ T3)) => (Y3 != T3)))) => (~ (((? [V:((proces554692349s_term @ B) @ A),Va:((proces554692349s_term @ B) @ A)]: ((Xa2 = ((((proces89589571ess_CH @ B) @ A) @ V) @ Va)))) => (Y3 != (undefined @ ((proces554692349s_term @ B) @ A))))))))))))).
% 3.19/1.62 thf(fact_205_CH2_Oelims, axiom, (! [A:$tType,B:$tType,X7:(A > ((proces554692349s_term @ B) @ A)),Xa2:((proces554692349s_term @ B) @ A),Y3:((proces554692349s_term @ B) @ A)]: (((((((proces1239275104le_CH2 @ A) @ B) @ X7) @ Xa2) = Y3) => ((! [X3:A]: (((Xa2 = (((proces1627516585ss_VAR @ A) @ B) @ X3)) => (Y3 != ((((((((proces460752237s_term @ A) @ ((proces554692349s_term @ B) @ A)) @ B) @ (^ [A7:A]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (^ [P7:(proces634752977rocess @ B)]: ((((proces1062592052s_PROC @ B) @ A) @ ((proces988026546_ch2Of @ B) @ P7))))) @ (^ [A7:B,B4:((proces554692349s_term @ B) @ A)]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (^ [T13:((proces554692349s_term @ B) @ A),T24:((proces554692349s_term @ B) @ A)]: (T24))) @ (X7 @ X3)))))) => ((! [P4:(proces634752977rocess @ B)]: (((Xa2 = (((proces1062592052s_PROC @ B) @ A) @ P4)) => (Y3 != (((proces1062592052s_PROC @ B) @ A) @ ((proces988026546_ch2Of @ B) @ P4)))))) => ((! [T12:((proces554692349s_term @ B) @ A),T23:((proces554692349s_term @ B) @ A)]: (((Xa2 = ((((proces89589571ess_CH @ B) @ A) @ T12) @ T23)) => (Y3 != T23)))) => (~ (((? [V:B,Va:((proces554692349s_term @ B) @ A)]: ((Xa2 = ((((proces1454156180ss_ACT @ B) @ A) @ V) @ Va)))) => (Y3 != (undefined @ ((proces554692349s_term @ B) @ A))))))))))))).
% 3.19/1.62 thf(fact_206_Let__transfer, axiom, (! [A:$tType,C:$tType,D:$tType,B:$tType,A4:(A > (B > $o)),B6:(C > (D > $o))]: (((((((((bNF_rel_fun @ A) @ B) @ ((A > C) > C)) @ ((B > D) > D)) @ A4) @ ((((((bNF_rel_fun @ (A > C)) @ (B > D)) @ C) @ D) @ ((((((bNF_rel_fun @ A) @ B) @ C) @ D) @ A4) @ B6)) @ B6)) @ (^ [S4:A,F7:(A > C)]: ((F7 @ S4)))) @ (^ [S4:B,F7:(B > D)]: ((F7 @ S4))))))).
% 3.19/1.62 thf(fact_207_let__rsp, axiom, (! [A:$tType,C:$tType,D:$tType,B:$tType,R1:(A > (B > $o)),R22:(C > (D > $o))]: (((((((((bNF_rel_fun @ A) @ B) @ ((A > C) > C)) @ ((B > D) > D)) @ R1) @ ((((((bNF_rel_fun @ (A > C)) @ (B > D)) @ C) @ D) @ ((((((bNF_rel_fun @ A) @ B) @ C) @ D) @ R1) @ R22)) @ R22)) @ (^ [S4:A,F7:(A > C)]: ((F7 @ S4)))) @ (^ [S4:B,F7:(B > D)]: ((F7 @ S4))))))).
% 3.19/1.62 thf(fact_208_CH2_Opelims, axiom, (! [A:$tType,B:$tType,X7:(A > ((proces554692349s_term @ B) @ A)),Xa2:((proces554692349s_term @ B) @ A),Y3:((proces554692349s_term @ B) @ A)]: (((((((proces1239275104le_CH2 @ A) @ B) @ X7) @ Xa2) = Y3) => ((((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)) @ X7) @ Xa2)) => ((! [X3:A]: (((Xa2 = (((proces1627516585ss_VAR @ A) @ B) @ X3)) => ((Y3 = ((((((((proces460752237s_term @ A) @ ((proces554692349s_term @ B) @ A)) @ B) @ (^ [A7:A]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (^ [P7:(proces634752977rocess @ B)]: ((((proces1062592052s_PROC @ B) @ A) @ ((proces988026546_ch2Of @ B) @ P7))))) @ (^ [A7:B,B4:((proces554692349s_term @ B) @ A)]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (^ [T13:((proces554692349s_term @ B) @ A),T24:((proces554692349s_term @ B) @ A)]: (T24))) @ (X7 @ X3))) => (~ ((((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)) @ X7) @ (((proces1627516585ss_VAR @ A) @ B) @ X3))))))))) => ((! [P4:(proces634752977rocess @ B)]: (((Xa2 = (((proces1062592052s_PROC @ B) @ A) @ P4)) => ((Y3 = (((proces1062592052s_PROC @ B) @ A) @ ((proces988026546_ch2Of @ B) @ P4))) => (~ ((((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)) @ X7) @ (((proces1062592052s_PROC @ B) @ A) @ P4))))))))) => ((! [T12:((proces554692349s_term @ B) @ A),T23:((proces554692349s_term @ B) @ A)]: (((Xa2 = ((((proces89589571ess_CH @ B) @ A) @ T12) @ T23)) => ((Y3 = 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)) @ X7) @ ((((proces89589571ess_CH @ B) @ A) @ T12) @ T23))))))))) => (~ ((! [V:B,Va:((proces554692349s_term @ B) @ A)]: (((Xa2 = ((((proces1454156180ss_ACT @ B) @ A) @ V) @ Va)) => ((Y3 = (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)) @ X7) @ ((((proces1454156180ss_ACT @ B) @ A) @ V) @ Va))))))))))))))))))).
% 3.19/1.62 thf(fact_209_rel__funE, axiom, (! [A:$tType,C:$tType,D:$tType,B:$tType,A4:(A > (B > $o)),B6:(C > (D > $o)),F:(A > C),G:(B > D),X7:A,Y3:B]: ((((((((((bNF_rel_fun @ A) @ B) @ C) @ D) @ A4) @ B6) @ F) @ G) => (((A4 @ X7) @ Y3) => ((B6 @ (F @ X7)) @ (G @ Y3))))))).
% 3.19/1.62 thf(fact_210_rel__funD2, axiom, (! [B:$tType,C:$tType,A:$tType,A4:(A > (A > $o)),B6:(B > (C > $o)),F:(A > B),G:(A > C),X7:A]: ((((((((((bNF_rel_fun @ A) @ A) @ B) @ C) @ A4) @ B6) @ F) @ G) => (((A4 @ X7) @ X7) => ((B6 @ (F @ X7)) @ (G @ X7))))))).
% 3.19/1.62 thf(fact_211_CH1_Opelims, axiom, (! [A:$tType,B:$tType,X7:(A > ((proces554692349s_term @ B) @ A)),Xa2:((proces554692349s_term @ B) @ A),Y3:((proces554692349s_term @ B) @ A)]: (((((((proces1239275103le_CH1 @ A) @ B) @ X7) @ Xa2) = Y3) => ((((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)) @ X7) @ Xa2)) => ((! [X3:A]: (((Xa2 = (((proces1627516585ss_VAR @ A) @ B) @ X3)) => ((Y3 = ((((((((proces460752237s_term @ A) @ ((proces554692349s_term @ B) @ A)) @ B) @ (^ [A7:A]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (^ [P7:(proces634752977rocess @ B)]: ((((proces1062592052s_PROC @ B) @ A) @ ((proces979765041_ch1Of @ B) @ P7))))) @ (^ [A7:B,B4:((proces554692349s_term @ B) @ A)]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (^ [T13:((proces554692349s_term @ B) @ A),T24:((proces554692349s_term @ B) @ A)]: (T13))) @ (X7 @ X3))) => (~ ((((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)) @ X7) @ (((proces1627516585ss_VAR @ A) @ B) @ X3))))))))) => ((! [P4:(proces634752977rocess @ B)]: (((Xa2 = (((proces1062592052s_PROC @ B) @ A) @ P4)) => ((Y3 = (((proces1062592052s_PROC @ B) @ A) @ ((proces979765041_ch1Of @ B) @ P4))) => (~ ((((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)) @ X7) @ (((proces1062592052s_PROC @ B) @ A) @ P4))))))))) => ((! [T12:((proces554692349s_term @ B) @ A),T23:((proces554692349s_term @ B) @ A)]: (((Xa2 = ((((proces89589571ess_CH @ B) @ A) @ T12) @ T23)) => ((Y3 = 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)) @ X7) @ ((((proces89589571ess_CH @ B) @ A) @ T12) @ T23))))))))) => (~ ((! [V:B,Va:((proces554692349s_term @ B) @ A)]: (((Xa2 = ((((proces1454156180ss_ACT @ B) @ A) @ V) @ Va)) => ((Y3 = (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)) @ X7) @ ((((proces1454156180ss_ACT @ B) @ A) @ V) @ Va))))))))))))))))))).
% 3.19/1.62 thf(fact_212_CONT_Opelims, axiom, (! [A:$tType,B:$tType,X7:(A > ((proces554692349s_term @ B) @ A)),Xa2:((proces554692349s_term @ B) @ A),Y3:((proces554692349s_term @ B) @ A)]: (((((((proces126235999e_CONT @ A) @ B) @ X7) @ Xa2) = Y3) => ((((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)) @ X7) @ Xa2)) => ((! [X3:A]: (((Xa2 = (((proces1627516585ss_VAR @ A) @ B) @ X3)) => ((Y3 = ((((((((proces460752237s_term @ A) @ ((proces554692349s_term @ B) @ A)) @ B) @ (^ [Aa3:A]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (^ [P7:(proces634752977rocess @ B)]: ((((proces1062592052s_PROC @ B) @ A) @ ((proces1778668539contOf @ B) @ P7))))) @ (^ [A7:B,T4:((proces554692349s_term @ B) @ A)]: (T4))) @ (^ [Aa3:((proces554692349s_term @ B) @ A),Ab2:((proces554692349s_term @ B) @ A)]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (X7 @ X3))) => (~ ((((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)) @ X7) @ (((proces1627516585ss_VAR @ A) @ B) @ X3))))))))) => ((! [P4:(proces634752977rocess @ B)]: (((Xa2 = (((proces1062592052s_PROC @ B) @ A) @ P4)) => ((Y3 = (((proces1062592052s_PROC @ B) @ A) @ ((proces1778668539contOf @ B) @ P4))) => (~ ((((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)) @ X7) @ (((proces1062592052s_PROC @ B) @ A) @ P4))))))))) => ((! [A3:B,T3:((proces554692349s_term @ B) @ A)]: (((Xa2 = ((((proces1454156180ss_ACT @ B) @ A) @ A3) @ T3)) => ((Y3 = T3) => (~ ((((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)) @ X7) @ ((((proces1454156180ss_ACT @ B) @ A) @ A3) @ T3))))))))) => (~ ((! [V:((proces554692349s_term @ B) @ A),Va:((proces554692349s_term @ B) @ A)]: (((Xa2 = ((((proces89589571ess_CH @ B) @ A) @ V) @ Va)) => ((Y3 = (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)) @ X7) @ ((((proces89589571ess_CH @ B) @ A) @ V) @ Va))))))))))))))))))).
% 3.19/1.62 thf(fact_213_PREF_Opelims, axiom, (! [C:$tType,A:$tType,B:$tType,X7:(A > ((proces554692349s_term @ B) @ C)),Xa2:((proces554692349s_term @ B) @ A),Y3:B]: ((((((((proces1708129104e_PREF @ A) @ B) @ C) @ X7) @ Xa2) = Y3) => ((((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)) @ X7) @ Xa2)) => ((! [X3:A]: (((Xa2 = (((proces1627516585ss_VAR @ A) @ B) @ X3)) => ((Y3 = ((((((((proces460752237s_term @ C) @ B) @ B) @ (^ [Aa3:C]: ((undefined @ B)))) @ (proces745025900prefOf @ B)) @ (^ [A7:B,T4:((proces554692349s_term @ B) @ C)]: (A7))) @ (^ [Aa3:((proces554692349s_term @ B) @ C),Ab2:((proces554692349s_term @ B) @ C)]: ((undefined @ B)))) @ (X7 @ X3))) => (~ ((((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)) @ X7) @ (((proces1627516585ss_VAR @ A) @ B) @ X3))))))))) => ((! [P4:(proces634752977rocess @ B)]: (((Xa2 = (((proces1062592052s_PROC @ B) @ A) @ P4)) => ((Y3 = ((proces745025900prefOf @ B) @ P4)) => (~ ((((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)) @ X7) @ (((proces1062592052s_PROC @ B) @ A) @ P4))))))))) => ((! [A3:B,T3:((proces554692349s_term @ B) @ A)]: (((Xa2 = ((((proces1454156180ss_ACT @ B) @ A) @ A3) @ T3)) => ((Y3 = A3) => (~ ((((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)) @ X7) @ ((((proces1454156180ss_ACT @ B) @ A) @ A3) @ T3))))))))) => (~ ((! [V:((proces554692349s_term @ B) @ A),Va:((proces554692349s_term @ B) @ A)]: (((Xa2 = ((((proces89589571ess_CH @ B) @ A) @ V) @ Va)) => ((Y3 = (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)) @ X7) @ ((((proces89589571ess_CH @ B) @ A) @ V) @ Va))))))))))))))))))).
% 3.19/1.62 thf(fact_214_isACT_Opelims_I1_J, axiom, (! [B:$tType,C:$tType,A:$tType,D:$tType,X7:(A > ((proces554692349s_term @ B) @ C)),Xa2:((proces554692349s_term @ D) @ A),Y3:$o]: (((((((((proces687458811_isACT @ A) @ B) @ C) @ D) @ X7) @ Xa2) = Y3) => ((((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)) @ X7) @ Xa2)) => ((! [X3:A]: (((Xa2 = (((proces1627516585ss_VAR @ A) @ D) @ X3)) => ((Y3 = ((((((((proces460752237s_term @ C) @ $o) @ B) @ (^ [Pvar2:C]: ($false))) @ (proces10484146Action @ B)) @ (^ [A7:B,T4:((proces554692349s_term @ B) @ C)]: ($true))) @ (^ [Process_term1:((proces554692349s_term @ B) @ C),Process_term2:((proces554692349s_term @ B) @ C)]: ($false))) @ (X7 @ X3))) => (~ ((((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)) @ X7) @ (((proces1627516585ss_VAR @ A) @ D) @ X3))))))))) => ((! [P4:(proces634752977rocess @ D)]: (((Xa2 = (((proces1062592052s_PROC @ D) @ A) @ P4)) => ((Y3 = ((proces10484146Action @ D) @ P4)) => (~ ((((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)) @ X7) @ (((proces1062592052s_PROC @ D) @ A) @ P4))))))))) => ((! [A3:D,T3:((proces554692349s_term @ D) @ A)]: (((Xa2 = ((((proces1454156180ss_ACT @ D) @ A) @ A3) @ T3)) => (Y3 => (~ ((((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)) @ X7) @ ((((proces1454156180ss_ACT @ D) @ A) @ A3) @ T3))))))))) => (~ ((! [T12:((proces554692349s_term @ D) @ A),T23:((proces554692349s_term @ D) @ A)]: (((Xa2 = ((((proces89589571ess_CH @ D) @ A) @ T12) @ T23)) => ((~ (Y3)) => (~ ((((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)) @ X7) @ ((((proces89589571ess_CH @ D) @ A) @ T12) @ T23))))))))))))))))))).
% 3.19/1.62 thf(fact_215_isACT_Opelims_I3_J, axiom, (! [B:$tType,C:$tType,A:$tType,D:$tType,X7:(A > ((proces554692349s_term @ B) @ C)),Xa2:((proces554692349s_term @ D) @ A)]: (((~ (((((((proces687458811_isACT @ A) @ B) @ C) @ D) @ X7) @ Xa2))) => ((((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)) @ X7) @ Xa2)) => ((! [X3:A]: (((Xa2 = (((proces1627516585ss_VAR @ A) @ D) @ X3)) => ((((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)) @ X7) @ (((proces1627516585ss_VAR @ A) @ D) @ X3))) => ((((((((proces460752237s_term @ C) @ $o) @ B) @ (^ [Pvar2:C]: ($false))) @ (proces10484146Action @ B)) @ (^ [A7:B,T4:((proces554692349s_term @ B) @ C)]: ($true))) @ (^ [Process_term1:((proces554692349s_term @ B) @ C),Process_term2:((proces554692349s_term @ B) @ C)]: ($false))) @ (X7 @ X3)))))) => ((! [P4:(proces634752977rocess @ D)]: (((Xa2 = (((proces1062592052s_PROC @ D) @ A) @ P4)) => ((((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)) @ X7) @ (((proces1062592052s_PROC @ D) @ A) @ P4))) => ((proces10484146Action @ D) @ P4))))) => (~ ((! [T12:((proces554692349s_term @ D) @ A),T23:((proces554692349s_term @ D) @ A)]: (((Xa2 = ((((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)) @ X7) @ ((((proces89589571ess_CH @ D) @ A) @ T12) @ T23))))))))))))))))).
% 3.19/1.62 thf(fact_216_isACT_Opelims_I2_J, axiom, (! [B:$tType,C:$tType,A:$tType,D:$tType,X7:(A > ((proces554692349s_term @ B) @ C)),Xa2:((proces554692349s_term @ D) @ A)]: ((((((((proces687458811_isACT @ A) @ B) @ C) @ D) @ X7) @ Xa2) => ((((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)) @ X7) @ Xa2)) => ((! [X3:A]: (((Xa2 = (((proces1627516585ss_VAR @ A) @ D) @ X3)) => ((((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)) @ X7) @ (((proces1627516585ss_VAR @ A) @ D) @ X3))) => (~ (((((((((proces460752237s_term @ C) @ $o) @ B) @ (^ [Pvar2:C]: ($false))) @ (proces10484146Action @ B)) @ (^ [A7:B,T4:((proces554692349s_term @ B) @ C)]: ($true))) @ (^ [Process_term1:((proces554692349s_term @ B) @ C),Process_term2:((proces554692349s_term @ B) @ C)]: ($false))) @ (X7 @ X3)))))))) => ((! [P4:(proces634752977rocess @ D)]: (((Xa2 = (((proces1062592052s_PROC @ D) @ A) @ P4)) => ((((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)) @ X7) @ (((proces1062592052s_PROC @ D) @ A) @ P4))) => (~ (((proces10484146Action @ D) @ P4))))))) => (~ ((! [A3:D,T3:((proces554692349s_term @ D) @ A)]: (((Xa2 = ((((proces1454156180ss_ACT @ D) @ A) @ A3) @ T3)) => (~ ((((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)) @ X7) @ ((((proces1454156180ss_ACT @ D) @ A) @ A3) @ T3))))))))))))))))).
% 3.19/1.62 thf(fact_217_fun_Orel__transfer, axiom, (! [B:$tType,A:$tType,C:$tType,E:$tType,D:$tType,Sa:(A > (C > $o)),Sc:(B > (E > $o))]: (((((((((bNF_rel_fun @ (A > (B > $o))) @ (C > (E > $o))) @ ((D > A) > ((D > B) > $o))) @ ((D > C) > ((D > E) > $o))) @ ((((((bNF_rel_fun @ A) @ C) @ (B > $o)) @ (E > $o)) @ Sa) @ ((((((bNF_rel_fun @ B) @ E) @ $o) @ $o) @ Sc) @ (^ [Y4:$o,Z:$o]: ((Y4 = Z)))))) @ ((((((bNF_rel_fun @ (D > A)) @ (D > C)) @ ((D > B) > $o)) @ ((D > E) > $o)) @ ((((((bNF_rel_fun @ D) @ D) @ A) @ C) @ (^ [Y4:D,Z:D]: ((Y4 = Z)))) @ Sa)) @ ((((((bNF_rel_fun @ (D > B)) @ (D > E)) @ $o) @ $o) @ ((((((bNF_rel_fun @ D) @ D) @ B) @ E) @ (^ [Y4:D,Z:D]: ((Y4 = Z)))) @ Sc)) @ (^ [Y4:$o,Z:$o]: ((Y4 = Z)))))) @ (((((bNF_rel_fun @ D) @ D) @ A) @ B) @ (^ [Y4:D,Z:D]: ((Y4 = Z))))) @ (((((bNF_rel_fun @ D) @ D) @ C) @ E) @ (^ [Y4:D,Z:D]: ((Y4 = Z)))))))).
% 3.19/1.62 thf(fact_218_If__transfer, axiom, (! [A:$tType,B:$tType,A4:(A > (B > $o))]: (((((((((bNF_rel_fun @ $o) @ $o) @ (A > (A > A))) @ (B > (B > B))) @ (^ [Y4:$o,Z:$o]: ((Y4 = Z)))) @ ((((((bNF_rel_fun @ A) @ B) @ (A > A)) @ (B > B)) @ A4) @ ((((((bNF_rel_fun @ A) @ B) @ A) @ B) @ A4) @ A4))) @ (if @ A)) @ (if @ B))))).
% 3.19/1.62 thf(fact_219_fun_Orel__refl, axiom, (! [B:$tType,D:$tType,Ra:(B > (B > $o)),X7:(D > B)]: (((! [X5:B]: (((Ra @ X5) @ X5))) => ((((((((bNF_rel_fun @ D) @ D) @ B) @ B) @ (^ [Y4:D,Z:D]: ((Y4 = Z)))) @ Ra) @ X7) @ X7))))).
% 3.19/1.62 thf(fact_220_fun_Orel__eq, axiom, (! [A:$tType,D:$tType]: ((((((((bNF_rel_fun @ D) @ D) @ A) @ A) @ (^ [Y4:D,Z:D]: ((Y4 = Z)))) @ (^ [Y4:A,Z:A]: ((Y4 = Z)))) = (^ [Y4:(D > A),Z:(D > A)]: ((Y4 = Z))))))).
% 3.19/1.62 thf(fact_221_rel__fun__def__butlast, axiom, (! [B:$tType,D:$tType,C:$tType,E:$tType,F5:$tType,A:$tType,R:(A > (B > $o)),S3:(C > (E > $o)),T2:(D > (F5 > $o)),F:(A > (C > D)),G:(B > (E > F5))]: ((((((((((bNF_rel_fun @ A) @ B) @ (C > D)) @ (E > F5)) @ R) @ ((((((bNF_rel_fun @ C) @ E) @ D) @ F5) @ S3) @ T2)) @ F) @ G) = (! [X6:A,Y6:B]: ((((R @ X6) @ Y6) => ((((((((bNF_rel_fun @ C) @ E) @ D) @ F5) @ S3) @ T2) @ (F @ X6)) @ (G @ Y6))))))))).
% 3.19/1.62 thf(fact_222_process_Ocorec__transfer, axiom, (! [C:$tType,A:$tType,B:$tType,D:$tType,S3:(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) @ $o) @ S3) @ (^ [Y4:$o,Z:$o]: ((Y4 = Z))))) @ ((((((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) @ S3) @ 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) @ $o) @ S3) @ (^ [Y4:$o,Z:$o]: ((Y4 = Z))))) @ ((((((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)) @ S3) @ (((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) @ S3) @ S3)) @ ((((((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) @ $o) @ S3) @ (^ [Y4:$o,Z:$o]: ((Y4 = Z))))) @ ((((((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)) @ S3) @ (((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) @ S3) @ S3)) @ ((((((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) @ $o) @ S3) @ (^ [Y4:$o,Z:$o]: ((Y4 = Z))))) @ ((((((bNF_rel_fun @ (C > (proces634752977rocess @ A))) @ (D > (proces634752977rocess @ B))) @ ((C > C) > (C > (proces634752977rocess @ A)))) @ ((D > D) > (D > (proces634752977rocess @ B)))) @ ((((((bNF_rel_fun @ C) @ D) @ (proces634752977rocess @ A)) @ (proces634752977rocess @ B)) @ S3) @ (((proces749077512rocess @ A) @ B) @ R))) @ ((((((bNF_rel_fun @ (C > C)) @ (D > D)) @ (C > (proces634752977rocess @ A))) @ (D > (proces634752977rocess @ B))) @ ((((((bNF_rel_fun @ C) @ D) @ C) @ D) @ S3) @ S3)) @ ((((((bNF_rel_fun @ C) @ D) @ (proces634752977rocess @ A)) @ (proces634752977rocess @ B)) @ S3) @ (((proces749077512rocess @ A) @ B) @ R))))))))))))) @ ((proces894737309rocess @ C) @ A)) @ ((proces894737309rocess @ D) @ B))))).
% 3.19/1.62 thf(fact_223_map__fun__parametric, axiom, (! [A:$tType,B:$tType,E:$tType,F5:$tType,H2:$tType,G2:$tType,D:$tType,C:$tType,A4:(A > (C > $o)),B6:(B > (D > $o)),C5:(E > (G2 > $o)),D3:(F5 > (H2 > $o))]: (((((((((bNF_rel_fun @ (A > B)) @ (C > D)) @ ((E > F5) > ((B > E) > (A > F5)))) @ ((G2 > H2) > ((D > G2) > (C > H2)))) @ ((((((bNF_rel_fun @ A) @ C) @ B) @ D) @ A4) @ B6)) @ ((((((bNF_rel_fun @ (E > F5)) @ (G2 > H2)) @ ((B > E) > (A > F5))) @ ((D > G2) > (C > H2))) @ ((((((bNF_rel_fun @ E) @ G2) @ F5) @ H2) @ C5) @ D3)) @ ((((((bNF_rel_fun @ (B > E)) @ (D > G2)) @ (A > F5)) @ (C > H2)) @ ((((((bNF_rel_fun @ B) @ D) @ E) @ G2) @ B6) @ C5)) @ ((((((bNF_rel_fun @ A) @ C) @ F5) @ H2) @ A4) @ D3)))) @ ((((map_fun @ A) @ B) @ E) @ F5)) @ ((((map_fun @ C) @ D) @ G2) @ H2))))).
% 3.19/1.62 thf(fact_224_process_Ocorec__disc__iff_I1_J, axiom, (! [A:$tType,C:$tType,P:(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 > $o),G221:(C > (proces634752977rocess @ A)),G222:(C > C),A2:C]: ((((proces10484146Action @ A) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G11) @ Q12) @ G121) @ G122) @ Q21) @ G211) @ G212) @ Q22) @ G221) @ G222) @ A2)) = (P @ A2))))).
% 3.19/1.62 thf(fact_225_process_Ocorec__disc__iff_I2_J, axiom, (! [A:$tType,C:$tType,P:(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 > $o),G221:(C > (proces634752977rocess @ A)),G222:(C > C),A2:C]: ((((proces401113213Choice @ A) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G11) @ Q12) @ G121) @ G122) @ Q21) @ G211) @ G212) @ Q22) @ G221) @ G222) @ A2)) = (~ ((P @ A2))))))).
% 3.19/1.62 thf(fact_226_process_Ocorec__sel_I1_J, axiom, (! [A:$tType,C:$tType,P:(C > $o),A2:C,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 > $o),G221:(C > (proces634752977rocess @ A)),G222:(C > C)]: (((P @ A2) => (((proces745025900prefOf @ A) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G11) @ Q12) @ G121) @ G122) @ Q21) @ G211) @ G212) @ Q22) @ G221) @ G222) @ A2)) = (G11 @ A2)))))).
% 3.19/1.62 thf(fact_227_process_Ocorec__sel_I3_J, axiom, (! [A:$tType,C:$tType,P:(C > $o),A2:C,Q21:(C > $o),G11:(C > A),Q12:(C > $o),G121:(C > (proces634752977rocess @ A)),G122:(C > C),G211:(C > (proces634752977rocess @ A)),G212:(C > C),Q22:(C > $o),G221:(C > (proces634752977rocess @ A)),G222:(C > C)]: (((~ ((P @ A2))) => (((Q21 @ A2) => (((proces979765041_ch1Of @ A) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G11) @ Q12) @ G121) @ G122) @ Q21) @ G211) @ G212) @ Q22) @ G221) @ G222) @ A2)) = (G211 @ A2))) & ((~ ((Q21 @ A2))) => (((proces979765041_ch1Of @ A) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G11) @ Q12) @ G121) @ G122) @ Q21) @ G211) @ G212) @ Q22) @ G221) @ G222) @ A2)) = ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G11) @ Q12) @ G121) @ G122) @ Q21) @ G211) @ G212) @ Q22) @ G221) @ G222) @ (G212 @ A2))))))))).
% 3.19/1.62 thf(fact_228_process_Ocorec__sel_I4_J, axiom, (! [A:$tType,C:$tType,P:(C > $o),A2:C,Q22:(C > $o),G11:(C > A),Q12:(C > $o),G121:(C > (proces634752977rocess @ A)),G122:(C > C),Q21:(C > $o),G211:(C > (proces634752977rocess @ A)),G212:(C > C),G221:(C > (proces634752977rocess @ A)),G222:(C > C)]: (((~ ((P @ A2))) => (((Q22 @ A2) => (((proces988026546_ch2Of @ A) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G11) @ Q12) @ G121) @ G122) @ Q21) @ G211) @ G212) @ Q22) @ G221) @ G222) @ A2)) = (G221 @ A2))) & ((~ ((Q22 @ A2))) => (((proces988026546_ch2Of @ A) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G11) @ Q12) @ G121) @ G122) @ Q21) @ G211) @ G212) @ Q22) @ G221) @ G222) @ A2)) = ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G11) @ Q12) @ G121) @ G122) @ Q21) @ G211) @ G212) @ Q22) @ G221) @ G222) @ (G222 @ A2))))))))).
% 3.19/1.62 thf(fact_229_process_Ocorec__sel_I2_J, axiom, (! [A:$tType,C:$tType,P:(C > $o),A2:C,Q12:(C > $o),G11:(C > A),G121:(C > (proces634752977rocess @ A)),G122:(C > C),Q21:(C > $o),G211:(C > (proces634752977rocess @ A)),G212:(C > C),Q22:(C > $o),G221:(C > (proces634752977rocess @ A)),G222:(C > C)]: (((P @ A2) => (((Q12 @ A2) => (((proces1778668539contOf @ A) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G11) @ Q12) @ G121) @ G122) @ Q21) @ G211) @ G212) @ Q22) @ G221) @ G222) @ A2)) = (G121 @ A2))) & ((~ ((Q12 @ A2))) => (((proces1778668539contOf @ A) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G11) @ Q12) @ G121) @ G122) @ Q21) @ G211) @ G212) @ Q22) @ G221) @ G222) @ A2)) = ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G11) @ Q12) @ G121) @ G122) @ Q21) @ G211) @ G212) @ Q22) @ G221) @ G222) @ (G122 @ A2))))))))).
% 3.19/1.62 thf(fact_230_process_Ocorec__disc_I2_J, axiom, (! [A:$tType,C:$tType,P:(C > $o),A2:C,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 > $o),G221:(C > (proces634752977rocess @ A)),G222:(C > C)]: (((~ ((P @ A2))) => ((proces401113213Choice @ A) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G11) @ Q12) @ G121) @ G122) @ Q21) @ G211) @ G212) @ Q22) @ G221) @ G222) @ A2)))))).
% 3.19/1.62 thf(fact_231_process_Ocorec_I2_J, axiom, (! [A:$tType,C:$tType,P:(C > $o),A2:C,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 > $o),G221:(C > (proces634752977rocess @ A)),G222:(C > C)]: (((~ ((P @ A2))) => (((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G11) @ Q12) @ G121) @ G122) @ Q21) @ G211) @ G212) @ Q22) @ G221) @ G222) @ A2) = (((proces1915862579Choice @ A) @ ((((if @ (proces634752977rocess @ A)) @ (Q21 @ A2)) @ (G211 @ A2)) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G11) @ Q12) @ G121) @ G122) @ Q21) @ G211) @ G212) @ Q22) @ G221) @ G222) @ (G212 @ A2)))) @ ((((if @ (proces634752977rocess @ A)) @ (Q22 @ A2)) @ (G221 @ A2)) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G11) @ Q12) @ G121) @ G122) @ Q21) @ G211) @ G212) @ Q22) @ G221) @ G222) @ (G222 @ A2))))))))).
% 3.19/1.62 thf(fact_232_process_Ocorec_I1_J, axiom, (! [A:$tType,C:$tType,P:(C > $o),A2:C,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 > $o),G221:(C > (proces634752977rocess @ A)),G222:(C > C)]: (((P @ A2) => (((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G11) @ Q12) @ G121) @ G122) @ Q21) @ G211) @ G212) @ Q22) @ G221) @ G222) @ A2) = (((proces1525233512Action @ A) @ (G11 @ A2)) @ ((((if @ (proces634752977rocess @ A)) @ (Q12 @ A2)) @ (G121 @ A2)) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G11) @ Q12) @ G121) @ G122) @ Q21) @ G211) @ G212) @ Q22) @ G221) @ G222) @ (G122 @ A2))))))))).
% 3.19/1.62 thf(fact_233_process_Ocorec__disc_I1_J, axiom, (! [A:$tType,C:$tType,P:(C > $o),A2:C,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 > $o),G221:(C > (proces634752977rocess @ A)),G222:(C > C)]: (((P @ A2) => ((proces10484146Action @ A) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G11) @ Q12) @ G121) @ G122) @ Q21) @ G211) @ G212) @ Q22) @ G221) @ G222) @ A2)))))).
% 3.19/1.62 thf(fact_234_process_Ocorec__code, axiom, (! [A:$tType,C:$tType]: ((((proces894737309rocess @ C) @ A) = (^ [P7:(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 > $o),G2212:(C > (proces634752977rocess @ A)),G2222:(C > C),A7:C]: (((((if @ (proces634752977rocess @ A)) @ (P7 @ A7)) @ (((proces1525233512Action @ A) @ (G112 @ A7)) @ ((((if @ (proces634752977rocess @ A)) @ (Q122 @ A7)) @ (G1212 @ A7)) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P7) @ G112) @ Q122) @ G1212) @ G1222) @ Q212) @ G2112) @ G2122) @ Q222) @ G2212) @ G2222) @ (G1222 @ A7))))) @ (((proces1915862579Choice @ A) @ ((((if @ (proces634752977rocess @ A)) @ (Q212 @ A7)) @ (G2112 @ A7)) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P7) @ G112) @ Q122) @ G1212) @ G1222) @ Q212) @ G2112) @ G2122) @ Q222) @ G2212) @ G2222) @ (G2122 @ A7)))) @ ((((if @ (proces634752977rocess @ A)) @ (Q222 @ A7)) @ (G2212 @ A7)) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P7) @ G112) @ Q122) @ G1212) @ G1222) @ Q212) @ G2112) @ G2122) @ Q222) @ G2212) @ G2222) @ (G2222 @ A7))))))))))).
% 3.19/1.62 thf(fact_235_fun_Opred__transfer, axiom, (! [A:$tType,B:$tType,D:$tType,R:(A > (B > $o))]: (((((((((bNF_rel_fun @ (A > $o)) @ (B > $o)) @ ((D > A) > $o)) @ ((D > B) > $o)) @ ((((((bNF_rel_fun @ A) @ B) @ $o) @ $o) @ R) @ (^ [Y4:$o,Z:$o]: ((Y4 = Z))))) @ ((((((bNF_rel_fun @ (D > A)) @ (D > B)) @ $o) @ $o) @ ((((((bNF_rel_fun @ D) @ D) @ A) @ B) @ (^ [Y4:D,Z:D]: ((Y4 = Z)))) @ R)) @ (^ [Y4:$o,Z:$o]: ((Y4 = Z))))) @ (((basic_pred_fun @ D) @ A) @ (^ [Uu:D]: ($true)))) @ (((basic_pred_fun @ D) @ B) @ (^ [Uu:D]: ($true))))))).
% 3.19/1.62 thf(fact_236_pred__equals__eq2, axiom, (! [B:$tType,A:$tType,R:(set @ ((product_prod @ A) @ B)),S3:(set @ ((product_prod @ A) @ B))]: ((((^ [X6:A,Y6:B]: ((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X6) @ Y6)) @ R))) = (^ [X6:A,Y6:B]: ((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X6) @ Y6)) @ S3)))) = (R = S3))))).
% 3.19/1.62 thf(fact_237_fun_Opred__True, axiom, (! [A:$tType,D:$tType]: ((((((basic_pred_fun @ D) @ A) @ (^ [Uu:D]: ($true))) @ (^ [Uu:A]: ($true))) = (^ [Uu:(D > A)]: ($true)))))).
% 3.19/1.62 thf(fact_238_process__term_Omap__transfer, axiom, (! [A:$tType,C:$tType,B:$tType,D:$tType,L:$tType,J:$tType,K:$tType,I:$tType,R1b:(A > (I > $o)),S1d:(C > (K > $o)),R2b:(B > (J > $o)),S2d:(D > (L > $o))]: (((((((((bNF_rel_fun @ (A > C)) @ (I > K)) @ ((B > D) > (((proces554692349s_term @ A) @ B) > ((proces554692349s_term @ C) @ D)))) @ ((J > L) > (((proces554692349s_term @ I) @ J) > ((proces554692349s_term @ K) @ L)))) @ ((((((bNF_rel_fun @ A) @ I) @ C) @ K) @ R1b) @ S1d)) @ ((((((bNF_rel_fun @ (B > D)) @ (J > L)) @ (((proces554692349s_term @ A) @ B) > ((proces554692349s_term @ C) @ D))) @ (((proces554692349s_term @ I) @ J) > ((proces554692349s_term @ K) @ L))) @ ((((((bNF_rel_fun @ B) @ J) @ D) @ L) @ R2b) @ S2d)) @ ((((((bNF_rel_fun @ ((proces554692349s_term @ A) @ B)) @ ((proces554692349s_term @ I) @ J)) @ ((proces554692349s_term @ C) @ D)) @ ((proces554692349s_term @ K) @ L)) @ ((((((proces2029722208s_term @ A) @ I) @ B) @ J) @ R1b) @ R2b)) @ ((((((proces2029722208s_term @ C) @ K) @ D) @ L) @ S1d) @ S2d)))) @ ((((proces224683037s_term @ A) @ C) @ B) @ D)) @ ((((proces224683037s_term @ I) @ K) @ J) @ L))))).
% 3.19/1.62 thf(fact_239_process_Omap__transfer, axiom, (! [A:$tType,B:$tType,F5:$tType,E:$tType,Rb:(A > (E > $o)),Sd:(B > (F5 > $o))]: (((((((((bNF_rel_fun @ (A > B)) @ (E > F5)) @ ((proces634752977rocess @ A) > (proces634752977rocess @ B))) @ ((proces634752977rocess @ E) > (proces634752977rocess @ F5))) @ ((((((bNF_rel_fun @ A) @ E) @ B) @ F5) @ Rb) @ Sd)) @ ((((((bNF_rel_fun @ (proces634752977rocess @ A)) @ (proces634752977rocess @ E)) @ (proces634752977rocess @ B)) @ (proces634752977rocess @ F5)) @ (((proces749077512rocess @ A) @ E) @ Rb)) @ (((proces749077512rocess @ B) @ F5) @ Sd))) @ ((proces370407749rocess @ A) @ B)) @ ((proces370407749rocess @ E) @ F5))))).
% 3.19/1.62 thf(fact_240_process_Omap__disc__iff_I1_J, axiom, (! [B:$tType,A:$tType,F:(A > B),A2:(proces634752977rocess @ A)]: ((((proces10484146Action @ B) @ ((((proces370407749rocess @ A) @ B) @ F) @ A2)) = ((proces10484146Action @ A) @ A2))))).
% 3.19/1.62 thf(fact_241_process_Omap__disc__iff_I2_J, axiom, (! [B:$tType,A:$tType,F:(A > B),A2:(proces634752977rocess @ A)]: ((((proces401113213Choice @ B) @ ((((proces370407749rocess @ A) @ B) @ F) @ A2)) = ((proces401113213Choice @ A) @ A2))))).
% 3.19/1.62 thf(fact_242_process_Omap__sel_I3_J, axiom, (! [B:$tType,A:$tType,A2:(proces634752977rocess @ A),F:(A > B)]: ((((proces401113213Choice @ A) @ A2) => (((proces979765041_ch1Of @ B) @ ((((proces370407749rocess @ A) @ B) @ F) @ A2)) = ((((proces370407749rocess @ A) @ B) @ F) @ ((proces979765041_ch1Of @ A) @ A2))))))).
% 3.19/1.62 thf(fact_243_process_Omap__sel_I4_J, axiom, (! [B:$tType,A:$tType,A2:(proces634752977rocess @ A),F:(A > B)]: ((((proces401113213Choice @ A) @ A2) => (((proces988026546_ch2Of @ B) @ ((((proces370407749rocess @ A) @ B) @ F) @ A2)) = ((((proces370407749rocess @ A) @ B) @ F) @ ((proces988026546_ch2Of @ A) @ A2))))))).
% 3.19/1.62 thf(fact_244_process__term_Omap__cong__pred, axiom, (! [D:$tType,C:$tType,B:$tType,A:$tType,X7:((proces554692349s_term @ A) @ B),Ya2:((proces554692349s_term @ A) @ B),F1:(A > C),G1:(A > C),F2:(B > D),G22:(B > D)]: (((X7 = Ya2) => ((((((proces2118920028s_term @ A) @ B) @ (^ [Z12:A]: (((F1 @ Z12) = (G1 @ Z12))))) @ (^ [Z22:B]: (((F2 @ Z22) = (G22 @ Z22))))) @ Ya2) => ((((((((proces224683037s_term @ A) @ C) @ B) @ D) @ F1) @ F2) @ X7) = (((((((proces224683037s_term @ A) @ C) @ B) @ D) @ G1) @ G22) @ Ya2))))))).
% 3.19/1.62 thf(fact_245_process_Osimps_I15_J, axiom, (! [B:$tType,A:$tType,F:(A > B),X11:A,X122:(proces634752977rocess @ A)]: ((((((proces370407749rocess @ A) @ B) @ F) @ (((proces1525233512Action @ A) @ X11) @ X122)) = (((proces1525233512Action @ B) @ (F @ X11)) @ ((((proces370407749rocess @ A) @ B) @ F) @ X122)))))).
% 3.19/1.62 thf(fact_246_process_Osimps_I16_J, axiom, (! [B:$tType,A:$tType,F:(A > B),X21:(proces634752977rocess @ A),X222:(proces634752977rocess @ A)]: ((((((proces370407749rocess @ A) @ B) @ F) @ (((proces1915862579Choice @ A) @ X21) @ X222)) = (((proces1915862579Choice @ B) @ ((((proces370407749rocess @ A) @ B) @ F) @ X21)) @ ((((proces370407749rocess @ A) @ B) @ F) @ X222)))))).
% 3.19/1.62 thf(fact_247_process__term_Osimps_I25_J, axiom, (! [A:$tType,B:$tType,C:$tType,Pvar:$tType,F1:(A > B),F2:(Pvar > C),X1:Pvar]: (((((((((proces224683037s_term @ A) @ B) @ Pvar) @ C) @ F1) @ F2) @ (((proces1627516585ss_VAR @ Pvar) @ A) @ X1)) = (((proces1627516585ss_VAR @ C) @ B) @ (F2 @ X1)))))).
% 3.19/1.62 thf(fact_248_process__term_Osimps_I28_J, axiom, (! [C:$tType,B:$tType,Pvar:$tType,A:$tType,F1:(A > B),F2:(Pvar > C),X41:((proces554692349s_term @ A) @ Pvar),X42:((proces554692349s_term @ A) @ Pvar)]: (((((((((proces224683037s_term @ A) @ B) @ Pvar) @ C) @ F1) @ F2) @ ((((proces89589571ess_CH @ A) @ Pvar) @ X41) @ X42)) = ((((proces89589571ess_CH @ B) @ C) @ (((((((proces224683037s_term @ A) @ B) @ Pvar) @ C) @ F1) @ F2) @ X41)) @ (((((((proces224683037s_term @ A) @ B) @ Pvar) @ C) @ F1) @ F2) @ X42)))))).
% 3.19/1.62 thf(fact_249_process__term_Osimps_I27_J, axiom, (! [C:$tType,B:$tType,Pvar:$tType,A:$tType,F1:(A > B),F2:(Pvar > C),X31:A,X32:((proces554692349s_term @ A) @ Pvar)]: (((((((((proces224683037s_term @ A) @ B) @ Pvar) @ C) @ F1) @ F2) @ ((((proces1454156180ss_ACT @ A) @ Pvar) @ X31) @ X32)) = ((((proces1454156180ss_ACT @ B) @ C) @ (F1 @ X31)) @ (((((((proces224683037s_term @ A) @ B) @ Pvar) @ C) @ F1) @ F2) @ X32)))))).
% 3.19/1.62 thf(fact_250_process__term_Osimps_I26_J, axiom, (! [Pvar:$tType,C:$tType,B:$tType,A:$tType,F1:(A > B),F2:(Pvar > C),X2:(proces634752977rocess @ A)]: (((((((((proces224683037s_term @ A) @ B) @ Pvar) @ C) @ F1) @ F2) @ (((proces1062592052s_PROC @ A) @ Pvar) @ X2)) = (((proces1062592052s_PROC @ B) @ C) @ ((((proces370407749rocess @ A) @ B) @ F1) @ X2)))))).
% 3.19/1.62 thf(fact_251_process_Orel__map_I2_J, axiom, (! [A:$tType,C:$tType,B:$tType,Sa:(A > (C > $o)),X7:(proces634752977rocess @ A),G:(B > C),Y3:(proces634752977rocess @ B)]: (((((((proces749077512rocess @ A) @ C) @ Sa) @ X7) @ ((((proces370407749rocess @ B) @ C) @ G) @ Y3)) = (((((proces749077512rocess @ A) @ B) @ (^ [X6:A,Y6:B]: (((Sa @ X6) @ (G @ Y6))))) @ X7) @ Y3))))).
% 3.19/1.62 thf(fact_252_process_Orel__map_I1_J, axiom, (! [A:$tType,C:$tType,B:$tType,Sb:(C > (B > $o)),I2:(A > C),X7:(proces634752977rocess @ A),Y3:(proces634752977rocess @ B)]: (((((((proces749077512rocess @ C) @ B) @ Sb) @ ((((proces370407749rocess @ A) @ C) @ I2) @ X7)) @ Y3) = (((((proces749077512rocess @ A) @ B) @ (^ [X6:A]: ((Sb @ (I2 @ X6))))) @ X7) @ Y3))))).
% 3.19/1.62 thf(fact_253_process_Omap__cong__pred, axiom, (! [B:$tType,A:$tType,X7:(proces634752977rocess @ A),Ya2:(proces634752977rocess @ A),F:(A > B),G:(A > B)]: (((X7 = Ya2) => ((((proces1205983068rocess @ A) @ (^ [Z3:A]: (((F @ Z3) = (G @ Z3))))) @ Ya2) => (((((proces370407749rocess @ A) @ B) @ F) @ X7) = ((((proces370407749rocess @ A) @ B) @ G) @ Ya2))))))).
% 3.19/1.62 thf(fact_254_process__term_Omap__ident, axiom, (! [B:$tType,A:$tType,T5:((proces554692349s_term @ A) @ B)]: (((((((((proces224683037s_term @ A) @ A) @ B) @ B) @ (^ [X6:A]: (X6))) @ (^ [X6:B]: (X6))) @ T5) = T5)))).
% 3.19/1.62 thf(help_If_3_1_T, axiom, (! [P3:$o]: (((P3 = $true) | (P3 = $false))))).
% 3.19/1.62 thf(help_If_2_1_T, axiom, (! [A:$tType,X7:A,Y3:A]: ((((((if @ A) @ $false) @ X7) @ Y3) = Y3)))).
% 3.19/1.62 thf(help_If_1_1_T, axiom, (! [A:$tType,X7:A,Y3:A]: ((((((if @ A) @ $true) @ X7) @ Y3) = X7)))).
% 3.19/1.62 thf(conj_0, conjecture, (((((proces1652378886lution @ b) @ a) @ sys) @ (((proces1062592052s_PROC @ a) @ b) @ p)) = p)).
% 3.19/1.62 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.509jbUU17G/DTF2DTF31439.p
% 3.19/1.62 ------------------------
% 3.19/1.69 ---- Cleaned THF ---
% 3.19/1.69 thf(ty_t_Process__Mirabelle__xovoopgpgi_Oprocess__term,type,
% 3.19/1.69 proces554692349s_term: $tType > $tType > $tType ).
% 3.19/1.69
% 3.19/1.69 thf(ty_t_Process__Mirabelle__xovoopgpgi_Oprocess,type,
% 3.19/1.69 proces634752977rocess: $tType > $tType ).
% 3.19/1.69
% 3.19/1.69 thf(ty_t_Product__Type_Oprod,type,
% 3.19/1.69 product_prod: $tType > $tType > $tType ).
% 3.19/1.69
% 3.19/1.69 thf(ty_t_Set_Oset,type,
% 3.19/1.69 set: $tType > $tType ).
% 3.19/1.69
% 3.19/1.69 thf(ty_t_itself,type,
% 3.19/1.69 itself: $tType > $tType ).
% 3.19/1.69
% 3.19/1.69 thf(ty_tf_b,type,
% 3.19/1.69 b: $tType ).
% 3.19/1.69
% 3.19/1.69 thf(ty_tf_a,type,
% 3.19/1.69 a: $tType ).
% 3.19/1.69
% 3.19/1.69 thf(sy_c_BNF__Def_Orel__fun,type,
% 3.19/1.69 bNF_rel_fun:
% 3.19/1.69 !>[A: $tType,C: $tType,B: $tType,D: $tType] : ( ( A > C > $o ) > ( B > D > $o ) > ( A > B ) > ( C > D ) > $o ) ).
% 3.19/1.69
% 3.19/1.69 thf(sy_c_Basic__BNFs_Opred__fun,type,
% 3.19/1.69 basic_pred_fun:
% 3.19/1.69 !>[A: $tType,B: $tType] : ( ( A > $o ) > ( B > $o ) > ( A > B ) > $o ) ).
% 3.19/1.69
% 3.19/1.69 thf(sy_c_Fun_Omap__fun,type,
% 3.19/1.69 map_fun:
% 3.19/1.69 !>[C: $tType,A: $tType,B: $tType,D: $tType] : ( ( C > A ) > ( B > D ) > ( A > B ) > C > D ) ).
% 3.19/1.69
% 3.19/1.69 thf(sy_c_HOL_Oundefined,type,
% 3.19/1.69 undefined:
% 3.19/1.69 !>[A: $tType] : A ).
% 3.19/1.69
% 3.19/1.69 thf(sy_c_If,type,
% 3.19/1.69 if:
% 3.19/1.69 !>[A: $tType] : ( $o > A > A > A ) ).
% 3.19/1.69
% 3.19/1.69 thf(sy_c_Process__Mirabelle__xovoopgpgi_OCH1,type,
% 3.19/1.69 proces1239275103le_CH1:
% 3.19/1.69 !>[A: $tType,B: $tType] : ( ( A > ( proces554692349s_term @ B @ A ) ) > ( proces554692349s_term @ B @ A ) > ( proces554692349s_term @ B @ A ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(sy_c_Process__Mirabelle__xovoopgpgi_OCH1__rel,type,
% 3.19/1.69 proces1869379930H1_rel:
% 3.19/1.69 !>[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 ) ).
% 3.19/1.69
% 3.19/1.69 thf(sy_c_Process__Mirabelle__xovoopgpgi_OCH2,type,
% 3.19/1.69 proces1239275104le_CH2:
% 3.19/1.69 !>[A: $tType,B: $tType] : ( ( A > ( proces554692349s_term @ B @ A ) ) > ( proces554692349s_term @ B @ A ) > ( proces554692349s_term @ B @ A ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(sy_c_Process__Mirabelle__xovoopgpgi_OCH2__rel,type,
% 3.19/1.69 proces93903513H2_rel:
% 3.19/1.69 !>[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 ) ).
% 3.19/1.69
% 3.19/1.69 thf(sy_c_Process__Mirabelle__xovoopgpgi_OCONT,type,
% 3.19/1.69 proces126235999e_CONT:
% 3.19/1.69 !>[A: $tType,B: $tType] : ( ( A > ( proces554692349s_term @ B @ A ) ) > ( proces554692349s_term @ B @ A ) > ( proces554692349s_term @ B @ A ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(sy_c_Process__Mirabelle__xovoopgpgi_OCONT__rel,type,
% 3.19/1.69 proces1004198490NT_rel:
% 3.19/1.69 !>[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 ) ).
% 3.19/1.69
% 3.19/1.69 thf(sy_c_Process__Mirabelle__xovoopgpgi_OPREF,type,
% 3.19/1.69 proces1708129104e_PREF:
% 3.19/1.69 !>[A: $tType,B: $tType,C: $tType] : ( ( A > ( proces554692349s_term @ B @ C ) ) > ( proces554692349s_term @ B @ A ) > B ) ).
% 3.19/1.69
% 3.19/1.69 thf(sy_c_Process__Mirabelle__xovoopgpgi_OPREF__rel,type,
% 3.19/1.69 proces527360425EF_rel:
% 3.19/1.69 !>[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 ) ).
% 3.19/1.69
% 3.19/1.69 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oguarded,type,
% 3.19/1.69 proces1121166967uarded:
% 3.19/1.69 !>[A: $tType,B: $tType,C: $tType] : ( ( A > ( proces554692349s_term @ B @ C ) ) > $o ) ).
% 3.19/1.69
% 3.19/1.69 thf(sy_c_Process__Mirabelle__xovoopgpgi_OisACT,type,
% 3.19/1.69 proces687458811_isACT:
% 3.19/1.69 !>[A: $tType,B: $tType,C: $tType,D: $tType] : ( ( A > ( proces554692349s_term @ B @ C ) ) > ( proces554692349s_term @ D @ A ) > $o ) ).
% 3.19/1.69
% 3.19/1.69 thf(sy_c_Process__Mirabelle__xovoopgpgi_OisACT__rel,type,
% 3.19/1.69 proces896239806CT_rel:
% 3.19/1.69 !>[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 ) ).
% 3.19/1.69
% 3.19/1.69 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OAction,type,
% 3.19/1.69 proces1525233512Action:
% 3.19/1.69 !>[A: $tType] : ( A > ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OChoice,type,
% 3.19/1.69 proces1915862579Choice:
% 3.19/1.69 !>[A: $tType] : ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Ocase__process,type,
% 3.19/1.69 proces1406508781rocess:
% 3.19/1.69 !>[A: $tType,B: $tType] : ( ( A > ( proces634752977rocess @ A ) > B ) > ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B ) > ( proces634752977rocess @ A ) > B ) ).
% 3.19/1.69
% 3.19/1.69 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Och1Of,type,
% 3.19/1.69 proces979765041_ch1Of:
% 3.19/1.69 !>[A: $tType] : ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Och2Of,type,
% 3.19/1.69 proces988026546_ch2Of:
% 3.19/1.69 !>[A: $tType] : ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OcontOf,type,
% 3.19/1.69 proces1778668539contOf:
% 3.19/1.69 !>[A: $tType] : ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Ocorec__process,type,
% 3.19/1.69 proces894737309rocess:
% 3.19/1.69 !>[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 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OisAction,type,
% 3.19/1.69 proces10484146Action:
% 3.19/1.69 !>[A: $tType] : ( ( proces634752977rocess @ A ) > $o ) ).
% 3.19/1.69
% 3.19/1.69 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OisChoice,type,
% 3.19/1.69 proces401113213Choice:
% 3.19/1.69 !>[A: $tType] : ( ( proces634752977rocess @ A ) > $o ) ).
% 3.19/1.69
% 3.19/1.69 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Omap__process,type,
% 3.19/1.69 proces370407749rocess:
% 3.19/1.69 !>[A: $tType,Aa: $tType] : ( ( A > Aa ) > ( proces634752977rocess @ A ) > ( proces634752977rocess @ Aa ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Opred__process,type,
% 3.19/1.69 proces1205983068rocess:
% 3.19/1.69 !>[A: $tType] : ( ( A > $o ) > ( proces634752977rocess @ A ) > $o ) ).
% 3.19/1.69
% 3.19/1.69 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OprefOf,type,
% 3.19/1.69 proces745025900prefOf:
% 3.19/1.69 !>[A: $tType] : ( ( proces634752977rocess @ A ) > A ) ).
% 3.19/1.69
% 3.19/1.69 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Orel__process,type,
% 3.19/1.69 proces749077512rocess:
% 3.19/1.69 !>[A: $tType,B: $tType] : ( ( A > B > $o ) > ( proces634752977rocess @ A ) > ( proces634752977rocess @ B ) > $o ) ).
% 3.19/1.69
% 3.19/1.69 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_OACT,type,
% 3.19/1.69 proces1454156180ss_ACT:
% 3.19/1.69 !>[A: $tType,Pvar: $tType] : ( A > ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_OCH,type,
% 3.19/1.69 proces89589571ess_CH:
% 3.19/1.69 !>[A: $tType,Pvar: $tType] : ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_OPROC,type,
% 3.19/1.69 proces1062592052s_PROC:
% 3.19/1.69 !>[A: $tType,Pvar: $tType] : ( ( proces634752977rocess @ A ) > ( proces554692349s_term @ A @ Pvar ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_OVAR,type,
% 3.19/1.69 proces1627516585ss_VAR:
% 3.19/1.69 !>[Pvar: $tType,A: $tType] : ( Pvar > ( proces554692349s_term @ A @ Pvar ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Ocase__process__term,type,
% 3.19/1.69 proces460752237s_term:
% 3.19/1.69 !>[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 ) ).
% 3.19/1.69
% 3.19/1.69 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Omap__process__term,type,
% 3.19/1.69 proces224683037s_term:
% 3.19/1.69 !>[A: $tType,Aa: $tType,Pvar: $tType,Pvara: $tType] : ( ( A > Aa ) > ( Pvar > Pvara ) > ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ Aa @ Pvara ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Opred__process__term,type,
% 3.19/1.69 proces2118920028s_term:
% 3.19/1.69 !>[A: $tType,B: $tType] : ( ( A > $o ) > ( B > $o ) > ( proces554692349s_term @ A @ B ) > $o ) ).
% 3.19/1.69
% 3.19/1.69 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Orec__process__term,type,
% 3.19/1.69 proces2117273769s_term:
% 3.19/1.69 !>[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 ) ).
% 3.19/1.69
% 3.19/1.69 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Orel__process__term,type,
% 3.19/1.69 proces2029722208s_term:
% 3.19/1.69 !>[A: $tType,C: $tType,B: $tType,D: $tType] : ( ( A > C > $o ) > ( B > D > $o ) > ( proces554692349s_term @ A @ B ) > ( proces554692349s_term @ C @ D ) > $o ) ).
% 3.19/1.69
% 3.19/1.69 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Oset2__process__term,type,
% 3.19/1.69 proces1493547885s_term:
% 3.19/1.69 !>[A: $tType,Pvar: $tType] : ( ( proces554692349s_term @ A @ Pvar ) > ( set @ Pvar ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(sy_c_Process__Mirabelle__xovoopgpgi_Osolution,type,
% 3.19/1.69 proces1652378886lution:
% 3.19/1.69 !>[A: $tType,B: $tType] : ( ( A > ( proces554692349s_term @ B @ A ) ) > ( proces554692349s_term @ B @ A ) > ( proces634752977rocess @ B ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(sy_c_Product__Type_OPair,type,
% 3.19/1.69 product_Pair:
% 3.19/1.69 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(sy_c_Product__Type_Ocurry,type,
% 3.19/1.69 product_curry:
% 3.19/1.69 !>[A: $tType,B: $tType,C: $tType] : ( ( ( product_prod @ A @ B ) > C ) > A > B > C ) ).
% 3.19/1.69
% 3.19/1.69 thf(sy_c_Product__Type_Ointernal__case__prod,type,
% 3.19/1.69 produc2004651681e_prod:
% 3.19/1.69 !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > ( product_prod @ A @ B ) > C ) ).
% 3.19/1.69
% 3.19/1.69 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod,type,
% 3.19/1.69 product_rec_prod:
% 3.19/1.69 !>[A: $tType,B: $tType,T: $tType] : ( ( A > B > T ) > ( product_prod @ A @ B ) > T ) ).
% 3.19/1.69
% 3.19/1.69 thf(sy_c_Pure_Otype,type,
% 3.19/1.69 type:
% 3.19/1.69 !>[A: $tType] : ( itself @ A ) ).
% 3.19/1.69
% 3.19/1.69 thf(sy_c_Set_OCollect,type,
% 3.19/1.69 collect:
% 3.19/1.69 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(sy_c_Wellfounded_Oaccp,type,
% 3.19/1.69 accp:
% 3.19/1.69 !>[A: $tType] : ( ( A > A > $o ) > A > $o ) ).
% 3.19/1.69
% 3.19/1.69 thf(sy_c_member,type,
% 3.19/1.69 member:
% 3.19/1.69 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 3.19/1.69
% 3.19/1.69 thf(sy_v_p,type,
% 3.19/1.69 p: proces634752977rocess @ a ).
% 3.19/1.69
% 3.19/1.69 thf(sy_v_sys,type,
% 3.19/1.69 sys: b > ( proces554692349s_term @ a @ b ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_0__092_060open_062_092_060And_062q_O_Aq_A_061_Asolution_Asys_A_IPROC_Ap_J_A_092_060Longrightarrow_062_Ap_A_061_Aq_092_060close_062,axiom,
% 3.19/1.69 ! [Q: proces634752977rocess @ a] :
% 3.19/1.69 ( ( Q
% 3.19/1.69 = ( proces1652378886lution @ b @ a @ sys @ ( proces1062592052s_PROC @ a @ b @ p ) ) )
% 3.19/1.69 => ( p = Q ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_1_process__term_Oinject_I2_J,axiom,
% 3.19/1.69 ! [Pvar: $tType,A: $tType,X2: proces634752977rocess @ A,Y2: proces634752977rocess @ A] :
% 3.19/1.69 ( ( ( proces1062592052s_PROC @ A @ Pvar @ X2 )
% 3.19/1.69 = ( proces1062592052s_PROC @ A @ Pvar @ Y2 ) )
% 3.19/1.69 = ( X2 = Y2 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_2_process__term_Osimps_I22_J,axiom,
% 3.19/1.69 ! [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] :
% 3.19/1.69 ( ( proces2117273769s_term @ Pvar @ D @ A @ F1 @ F2 @ F3 @ F4 @ ( proces1062592052s_PROC @ A @ Pvar @ X2 ) )
% 3.19/1.69 = ( F2 @ X2 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_3_process__term_Osimps_I18_J,axiom,
% 3.19/1.69 ! [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] :
% 3.19/1.69 ( ( proces460752237s_term @ Pvar @ B @ A @ F1 @ F2 @ F3 @ F4 @ ( proces1062592052s_PROC @ A @ Pvar @ X2 ) )
% 3.19/1.69 = ( F2 @ X2 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_4_process__term_Odistinct_I7_J,axiom,
% 3.19/1.69 ! [Pvar: $tType,A: $tType,X2: proces634752977rocess @ A,X31: A,X32: proces554692349s_term @ A @ Pvar] :
% 3.19/1.69 ( ( proces1062592052s_PROC @ A @ Pvar @ X2 )
% 3.19/1.69 != ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_5_process__term_Odistinct_I9_J,axiom,
% 3.19/1.69 ! [Pvar: $tType,A: $tType,X2: proces634752977rocess @ A,X41: proces554692349s_term @ A @ Pvar,X42: proces554692349s_term @ A @ Pvar] :
% 3.19/1.69 ( ( proces1062592052s_PROC @ A @ Pvar @ X2 )
% 3.19/1.69 != ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_6_process__term_Odistinct_I1_J,axiom,
% 3.19/1.69 ! [Pvar: $tType,A: $tType,X1: Pvar,X2: proces634752977rocess @ A] :
% 3.19/1.69 ( ( proces1627516585ss_VAR @ Pvar @ A @ X1 )
% 3.19/1.69 != ( proces1062592052s_PROC @ A @ Pvar @ X2 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_7_solution__VAR,axiom,
% 3.19/1.69 ! [B: $tType,A: $tType,Sys: A > ( proces554692349s_term @ B @ A ),X: A] :
% 3.19/1.69 ( ( proces1121166967uarded @ A @ B @ A @ Sys )
% 3.19/1.69 => ( ( proces1652378886lution @ A @ B @ Sys @ ( proces1627516585ss_VAR @ A @ B @ X ) )
% 3.19/1.69 = ( proces1652378886lution @ A @ B @ Sys @ ( Sys @ X ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_8_PREF_Osimps_I2_J,axiom,
% 3.19/1.69 ! [A: $tType,C: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ C ),P: proces634752977rocess @ B] :
% 3.19/1.69 ( ( proces1708129104e_PREF @ A @ B @ C @ Sys @ ( proces1062592052s_PROC @ B @ A @ P ) )
% 3.19/1.69 = ( proces745025900prefOf @ B @ P ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_9_process__term_Opred__inject_I2_J,axiom,
% 3.19/1.69 ! [Pvar: $tType,A: $tType,P1: A > $o,P2: Pvar > $o,A2: proces634752977rocess @ A] :
% 3.19/1.69 ( ( proces2118920028s_term @ A @ Pvar @ P1 @ P2 @ ( proces1062592052s_PROC @ A @ Pvar @ A2 ) )
% 3.19/1.69 = ( proces1205983068rocess @ A @ P1 @ A2 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_10_CH1_Osimps_I2_J,axiom,
% 3.19/1.69 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),P: proces634752977rocess @ B] :
% 3.19/1.69 ( ( proces1239275103le_CH1 @ A @ B @ Sys @ ( proces1062592052s_PROC @ B @ A @ P ) )
% 3.19/1.69 = ( proces1062592052s_PROC @ B @ A @ ( proces979765041_ch1Of @ B @ P ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_11_CH2_Osimps_I2_J,axiom,
% 3.19/1.69 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),P: proces634752977rocess @ B] :
% 3.19/1.69 ( ( proces1239275104le_CH2 @ A @ B @ Sys @ ( proces1062592052s_PROC @ B @ A @ P ) )
% 3.19/1.69 = ( proces1062592052s_PROC @ B @ A @ ( proces988026546_ch2Of @ B @ P ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_12_CONT_Osimps_I2_J,axiom,
% 3.19/1.69 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),P: proces634752977rocess @ B] :
% 3.19/1.69 ( ( proces126235999e_CONT @ A @ B @ Sys @ ( proces1062592052s_PROC @ B @ A @ P ) )
% 3.19/1.69 = ( proces1062592052s_PROC @ B @ A @ ( proces1778668539contOf @ B @ P ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_13_solution_Odisc__iff_I2_J,axiom,
% 3.19/1.69 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 3.19/1.69 ( ( proces401113213Choice @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) )
% 3.19/1.69 = ( ~ ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_14_process__term_Oinject_I1_J,axiom,
% 3.19/1.69 ! [A: $tType,Pvar: $tType,X1: Pvar,Y1: Pvar] :
% 3.19/1.69 ( ( ( proces1627516585ss_VAR @ Pvar @ A @ X1 )
% 3.19/1.69 = ( proces1627516585ss_VAR @ Pvar @ A @ Y1 ) )
% 3.19/1.69 = ( X1 = Y1 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_15_process__term_Oinject_I4_J,axiom,
% 3.19/1.69 ! [Pvar: $tType,A: $tType,X41: proces554692349s_term @ A @ Pvar,X42: proces554692349s_term @ A @ Pvar,Y41: proces554692349s_term @ A @ Pvar,Y42: proces554692349s_term @ A @ Pvar] :
% 3.19/1.69 ( ( ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 )
% 3.19/1.69 = ( proces89589571ess_CH @ A @ Pvar @ Y41 @ Y42 ) )
% 3.19/1.69 = ( ( X41 = Y41 )
% 3.19/1.69 & ( X42 = Y42 ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_16_process__term_Oinject_I3_J,axiom,
% 3.19/1.69 ! [Pvar: $tType,A: $tType,X31: A,X32: proces554692349s_term @ A @ Pvar,Y31: A,Y32: proces554692349s_term @ A @ Pvar] :
% 3.19/1.69 ( ( ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 )
% 3.19/1.69 = ( proces1454156180ss_ACT @ A @ Pvar @ Y31 @ Y32 ) )
% 3.19/1.69 = ( ( X31 = Y31 )
% 3.19/1.69 & ( X32 = Y32 ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_17_process__term_Opred__inject_I1_J,axiom,
% 3.19/1.69 ! [A: $tType,Pvar: $tType,P1: A > $o,P2: Pvar > $o,A2: Pvar] :
% 3.19/1.69 ( ( proces2118920028s_term @ A @ Pvar @ P1 @ P2 @ ( proces1627516585ss_VAR @ Pvar @ A @ A2 ) )
% 3.19/1.69 = ( P2 @ A2 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_18_process__term_Opred__inject_I4_J,axiom,
% 3.19/1.69 ! [Pvar: $tType,A: $tType,P1: A > $o,P2: Pvar > $o,A2: proces554692349s_term @ A @ Pvar,Aa2: proces554692349s_term @ A @ Pvar] :
% 3.19/1.69 ( ( proces2118920028s_term @ A @ Pvar @ P1 @ P2 @ ( proces89589571ess_CH @ A @ Pvar @ A2 @ Aa2 ) )
% 3.19/1.69 = ( ( proces2118920028s_term @ A @ Pvar @ P1 @ P2 @ A2 )
% 3.19/1.69 & ( proces2118920028s_term @ A @ Pvar @ P1 @ P2 @ Aa2 ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_19_process__term_Opred__inject_I3_J,axiom,
% 3.19/1.69 ! [Pvar: $tType,A: $tType,P1: A > $o,P2: Pvar > $o,A2: A,Aa2: proces554692349s_term @ A @ Pvar] :
% 3.19/1.69 ( ( proces2118920028s_term @ A @ Pvar @ P1 @ P2 @ ( proces1454156180ss_ACT @ A @ Pvar @ A2 @ Aa2 ) )
% 3.19/1.69 = ( ( P1 @ A2 )
% 3.19/1.69 & ( proces2118920028s_term @ A @ Pvar @ P1 @ P2 @ Aa2 ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_20_CH1_Osimps_I3_J,axiom,
% 3.19/1.69 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T1: proces554692349s_term @ B @ A,T22: proces554692349s_term @ B @ A] :
% 3.19/1.69 ( ( proces1239275103le_CH1 @ A @ B @ Sys @ ( proces89589571ess_CH @ B @ A @ T1 @ T22 ) )
% 3.19/1.69 = T1 ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_21_CH2_Osimps_I3_J,axiom,
% 3.19/1.69 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T1: proces554692349s_term @ B @ A,T22: proces554692349s_term @ B @ A] :
% 3.19/1.69 ( ( proces1239275104le_CH2 @ A @ B @ Sys @ ( proces89589571ess_CH @ B @ A @ T1 @ T22 ) )
% 3.19/1.69 = T22 ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_22_CONT_Osimps_I3_J,axiom,
% 3.19/1.69 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),A2: B,T2: proces554692349s_term @ B @ A] :
% 3.19/1.69 ( ( proces126235999e_CONT @ A @ B @ Sys @ ( proces1454156180ss_ACT @ B @ A @ A2 @ T2 ) )
% 3.19/1.69 = T2 ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_23_PREF_Osimps_I3_J,axiom,
% 3.19/1.69 ! [A: $tType,C: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ C ),A2: B,T2: proces554692349s_term @ B @ A] :
% 3.19/1.69 ( ( proces1708129104e_PREF @ A @ B @ C @ Sys @ ( proces1454156180ss_ACT @ B @ A @ A2 @ T2 ) )
% 3.19/1.69 = A2 ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_24_isACT_Osimps_I4_J,axiom,
% 3.19/1.69 ! [B: $tType,C: $tType,A: $tType,D: $tType,Sys: A > ( proces554692349s_term @ B @ C ),T1: proces554692349s_term @ D @ A,T22: proces554692349s_term @ D @ A] :
% 3.19/1.69 ~ ( proces687458811_isACT @ A @ B @ C @ D @ Sys @ ( proces89589571ess_CH @ D @ A @ T1 @ T22 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_25_isACT_Osimps_I3_J,axiom,
% 3.19/1.69 ! [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 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_26_process__term_Osimps_I24_J,axiom,
% 3.19/1.69 ! [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] :
% 3.19/1.69 ( ( proces2117273769s_term @ Pvar @ D @ A @ F1 @ F2 @ F3 @ F4 @ ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 ) )
% 3.19/1.69 = ( F4 @ X41 @ X42 @ ( proces2117273769s_term @ Pvar @ D @ A @ F1 @ F2 @ F3 @ F4 @ X41 ) @ ( proces2117273769s_term @ Pvar @ D @ A @ F1 @ F2 @ F3 @ F4 @ X42 ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_27_process__term_Osimps_I23_J,axiom,
% 3.19/1.69 ! [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] :
% 3.19/1.69 ( ( proces2117273769s_term @ Pvar @ D @ A @ F1 @ F2 @ F3 @ F4 @ ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) )
% 3.19/1.69 = ( F3 @ X31 @ X32 @ ( proces2117273769s_term @ Pvar @ D @ A @ F1 @ F2 @ F3 @ F4 @ X32 ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_28_process__term_Osimps_I21_J,axiom,
% 3.19/1.69 ! [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,X1: Pvar] :
% 3.19/1.69 ( ( proces2117273769s_term @ Pvar @ D @ A @ F1 @ F2 @ F3 @ F4 @ ( proces1627516585ss_VAR @ Pvar @ A @ X1 ) )
% 3.19/1.69 = ( F1 @ X1 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_29_process__term_Osimps_I20_J,axiom,
% 3.19/1.69 ! [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] :
% 3.19/1.69 ( ( proces460752237s_term @ Pvar @ B @ A @ F1 @ F2 @ F3 @ F4 @ ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 ) )
% 3.19/1.69 = ( F4 @ X41 @ X42 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_30_process__term_Osimps_I19_J,axiom,
% 3.19/1.69 ! [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] :
% 3.19/1.69 ( ( proces460752237s_term @ Pvar @ B @ A @ F1 @ F2 @ F3 @ F4 @ ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) )
% 3.19/1.69 = ( F3 @ X31 @ X32 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_31_process__term_Osimps_I17_J,axiom,
% 3.19/1.69 ! [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,X1: Pvar] :
% 3.19/1.69 ( ( proces460752237s_term @ Pvar @ B @ A @ F1 @ F2 @ F3 @ F4 @ ( proces1627516585ss_VAR @ Pvar @ A @ X1 ) )
% 3.19/1.69 = ( F1 @ X1 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_32_process__term_Odistinct_I11_J,axiom,
% 3.19/1.69 ! [Pvar: $tType,A: $tType,X31: A,X32: proces554692349s_term @ A @ Pvar,X41: proces554692349s_term @ A @ Pvar,X42: proces554692349s_term @ A @ Pvar] :
% 3.19/1.69 ( ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 )
% 3.19/1.69 != ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_33_process__term_Odistinct_I5_J,axiom,
% 3.19/1.69 ! [Pvar: $tType,A: $tType,X1: Pvar,X41: proces554692349s_term @ A @ Pvar,X42: proces554692349s_term @ A @ Pvar] :
% 3.19/1.69 ( ( proces1627516585ss_VAR @ Pvar @ A @ X1 )
% 3.19/1.69 != ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_34_process__term_Odistinct_I3_J,axiom,
% 3.19/1.69 ! [Pvar: $tType,A: $tType,X1: Pvar,X31: A,X32: proces554692349s_term @ A @ Pvar] :
% 3.19/1.69 ( ( proces1627516585ss_VAR @ Pvar @ A @ X1 )
% 3.19/1.69 != ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_35_isACT__VAR,axiom,
% 3.19/1.69 ! [C: $tType,B: $tType,A: $tType,Sys: A > ( proces554692349s_term @ B @ A ),X: A] :
% 3.19/1.69 ( ( proces1121166967uarded @ A @ B @ A @ Sys )
% 3.19/1.69 => ( ( proces687458811_isACT @ A @ B @ A @ C @ Sys @ ( proces1627516585ss_VAR @ A @ C @ X ) )
% 3.19/1.69 = ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ ( Sys @ X ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_36_CH2_Oinduct,axiom,
% 3.19/1.69 ! [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] :
% 3.19/1.69 ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),X3: A] : ( P3 @ Sys2 @ ( proces1627516585ss_VAR @ A @ B @ X3 ) )
% 3.19/1.69 => ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),P4: proces634752977rocess @ B] : ( P3 @ Sys2 @ ( proces1062592052s_PROC @ B @ A @ P4 ) )
% 3.19/1.69 => ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),T12: proces554692349s_term @ B @ A,T23: proces554692349s_term @ B @ A] : ( P3 @ Sys2 @ ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) )
% 3.19/1.69 => ( ! [A3: A > ( proces554692349s_term @ B @ A ),V: B,Va: proces554692349s_term @ B @ A] : ( P3 @ A3 @ ( proces1454156180ss_ACT @ B @ A @ V @ Va ) )
% 3.19/1.69 => ( P3 @ A0 @ A1 ) ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_37_CONT_Oinduct,axiom,
% 3.19/1.69 ! [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] :
% 3.19/1.69 ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),X3: A] : ( P3 @ Sys2 @ ( proces1627516585ss_VAR @ A @ B @ X3 ) )
% 3.19/1.69 => ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),P4: proces634752977rocess @ B] : ( P3 @ Sys2 @ ( proces1062592052s_PROC @ B @ A @ P4 ) )
% 3.19/1.69 => ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),A3: B,T3: proces554692349s_term @ B @ A] : ( P3 @ Sys2 @ ( proces1454156180ss_ACT @ B @ A @ A3 @ T3 ) )
% 3.19/1.69 => ( ! [A3: A > ( proces554692349s_term @ B @ A ),V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] : ( P3 @ A3 @ ( proces89589571ess_CH @ B @ A @ V @ Va ) )
% 3.19/1.69 => ( P3 @ A0 @ A1 ) ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_38_PREF_Oinduct,axiom,
% 3.19/1.69 ! [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] :
% 3.19/1.69 ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),X3: A] : ( P3 @ Sys2 @ ( proces1627516585ss_VAR @ A @ B @ X3 ) )
% 3.19/1.69 => ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),P4: proces634752977rocess @ B] : ( P3 @ Sys2 @ ( proces1062592052s_PROC @ B @ A @ P4 ) )
% 3.19/1.69 => ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),A3: B,T3: proces554692349s_term @ B @ A] : ( P3 @ Sys2 @ ( proces1454156180ss_ACT @ B @ A @ A3 @ T3 ) )
% 3.19/1.69 => ( ! [A3: A > ( proces554692349s_term @ B @ C ),V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] : ( P3 @ A3 @ ( proces89589571ess_CH @ B @ A @ V @ Va ) )
% 3.19/1.69 => ( P3 @ A0 @ A1 ) ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_39_guarded__def,axiom,
% 3.19/1.69 ! [C: $tType,B: $tType,A: $tType] :
% 3.19/1.69 ( ( proces1121166967uarded @ A @ B @ C )
% 3.19/1.69 = ( ^ [Sys3: A > ( proces554692349s_term @ B @ C )] :
% 3.19/1.69 ! [X4: A,Y: C] :
% 3.19/1.69 ( ( Sys3 @ X4 )
% 3.19/1.69 != ( proces1627516585ss_VAR @ C @ B @ Y ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_40_isACT_Oinduct,axiom,
% 3.19/1.69 ! [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] :
% 3.19/1.69 ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),X3: A] : ( P3 @ Sys2 @ ( proces1627516585ss_VAR @ A @ D @ X3 ) )
% 3.19/1.69 => ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),P4: proces634752977rocess @ D] : ( P3 @ Sys2 @ ( proces1062592052s_PROC @ D @ A @ P4 ) )
% 3.19/1.69 => ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),A3: D,T3: proces554692349s_term @ D @ A] : ( P3 @ Sys2 @ ( proces1454156180ss_ACT @ D @ A @ A3 @ T3 ) )
% 3.19/1.69 => ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),T12: proces554692349s_term @ D @ A,T23: proces554692349s_term @ D @ A] : ( P3 @ Sys2 @ ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) )
% 3.19/1.69 => ( P3 @ A0 @ A1 ) ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_41_process__term_Oinduct,axiom,
% 3.19/1.69 ! [Pvar: $tType,A: $tType,P3: ( proces554692349s_term @ A @ Pvar ) > $o,Process_term: proces554692349s_term @ A @ Pvar] :
% 3.19/1.69 ( ! [X5: Pvar] : ( P3 @ ( proces1627516585ss_VAR @ Pvar @ A @ X5 ) )
% 3.19/1.69 => ( ! [X5: proces634752977rocess @ A] : ( P3 @ ( proces1062592052s_PROC @ A @ Pvar @ X5 ) )
% 3.19/1.69 => ( ! [X1a: A,X2a: proces554692349s_term @ A @ Pvar] :
% 3.19/1.69 ( ( P3 @ X2a )
% 3.19/1.69 => ( P3 @ ( proces1454156180ss_ACT @ A @ Pvar @ X1a @ X2a ) ) )
% 3.19/1.69 => ( ! [X1a: proces554692349s_term @ A @ Pvar,X2a: proces554692349s_term @ A @ Pvar] :
% 3.19/1.69 ( ( P3 @ X1a )
% 3.19/1.69 => ( ( P3 @ X2a )
% 3.19/1.69 => ( P3 @ ( proces89589571ess_CH @ A @ Pvar @ X1a @ X2a ) ) ) )
% 3.19/1.69 => ( P3 @ Process_term ) ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_42_process__term_Oexhaust,axiom,
% 3.19/1.69 ! [Pvar: $tType,A: $tType,Y3: proces554692349s_term @ A @ Pvar] :
% 3.19/1.69 ( ! [X12: Pvar] :
% 3.19/1.69 ( Y3
% 3.19/1.69 != ( proces1627516585ss_VAR @ Pvar @ A @ X12 ) )
% 3.19/1.69 => ( ! [X22: proces634752977rocess @ A] :
% 3.19/1.69 ( Y3
% 3.19/1.69 != ( proces1062592052s_PROC @ A @ Pvar @ X22 ) )
% 3.19/1.69 => ( ! [X312: A,X322: proces554692349s_term @ A @ Pvar] :
% 3.19/1.69 ( Y3
% 3.19/1.69 != ( proces1454156180ss_ACT @ A @ Pvar @ X312 @ X322 ) )
% 3.19/1.69 => ~ ! [X412: proces554692349s_term @ A @ Pvar,X422: proces554692349s_term @ A @ Pvar] :
% 3.19/1.69 ( Y3
% 3.19/1.69 != ( proces89589571ess_CH @ A @ Pvar @ X412 @ X422 ) ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_43_solution_Osimps_I4_J,axiom,
% 3.19/1.69 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 3.19/1.69 ( ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
% 3.19/1.69 => ( ( proces1778668539contOf @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) )
% 3.19/1.69 = ( proces1652378886lution @ A @ B @ Sys @ ( proces126235999e_CONT @ A @ B @ Sys @ T2 ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_44_mem__Collect__eq,axiom,
% 3.19/1.69 ! [A: $tType,A2: A,P3: A > $o] :
% 3.19/1.69 ( ( member @ A @ A2 @ ( collect @ A @ P3 ) )
% 3.19/1.69 = ( P3 @ A2 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_45_Collect__mem__eq,axiom,
% 3.19/1.69 ! [A: $tType,A4: set @ A] :
% 3.19/1.69 ( ( collect @ A
% 3.19/1.69 @ ^ [X6: A] : ( member @ A @ X6 @ A4 ) )
% 3.19/1.69 = A4 ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_46_Collect__cong,axiom,
% 3.19/1.69 ! [A: $tType,P3: A > $o,Q2: A > $o] :
% 3.19/1.69 ( ! [X5: A] :
% 3.19/1.69 ( ( P3 @ X5 )
% 3.19/1.69 = ( Q2 @ X5 ) )
% 3.19/1.69 => ( ( collect @ A @ P3 )
% 3.19/1.69 = ( collect @ A @ Q2 ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_47_ext,axiom,
% 3.19/1.69 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 3.19/1.69 ( ! [X5: A] :
% 3.19/1.69 ( ( F @ X5 )
% 3.19/1.69 = ( G @ X5 ) )
% 3.19/1.69 => ( F = G ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_48_solution_Osimps_I5_J,axiom,
% 3.19/1.69 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 3.19/1.69 ( ~ ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
% 3.19/1.69 => ( ( proces979765041_ch1Of @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) )
% 3.19/1.69 = ( proces1652378886lution @ A @ B @ Sys @ ( proces1239275103le_CH1 @ A @ B @ Sys @ T2 ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_49_solution_Osimps_I6_J,axiom,
% 3.19/1.69 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 3.19/1.69 ( ~ ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
% 3.19/1.69 => ( ( proces988026546_ch2Of @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) )
% 3.19/1.69 = ( proces1652378886lution @ A @ B @ Sys @ ( proces1239275104le_CH2 @ A @ B @ Sys @ T2 ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_50_solution_Osimps_I3_J,axiom,
% 3.19/1.69 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 3.19/1.69 ( ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
% 3.19/1.69 => ( ( proces745025900prefOf @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) )
% 3.19/1.69 = ( proces1708129104e_PREF @ A @ B @ A @ Sys @ T2 ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_51_solution_Odisc_I2_J,axiom,
% 3.19/1.69 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 3.19/1.69 ( ~ ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
% 3.19/1.69 => ( proces401113213Choice @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_52_process_Oexpand,axiom,
% 3.19/1.69 ! [A: $tType,Process: proces634752977rocess @ A,Process2: proces634752977rocess @ A] :
% 3.19/1.69 ( ( ( proces10484146Action @ A @ Process )
% 3.19/1.69 = ( proces10484146Action @ A @ Process2 ) )
% 3.19/1.69 => ( ( ( proces10484146Action @ A @ Process )
% 3.19/1.69 => ( ( proces10484146Action @ A @ Process2 )
% 3.19/1.69 => ( ( ( proces745025900prefOf @ A @ Process )
% 3.19/1.69 = ( proces745025900prefOf @ A @ Process2 ) )
% 3.19/1.69 & ( ( proces1778668539contOf @ A @ Process )
% 3.19/1.69 = ( proces1778668539contOf @ A @ Process2 ) ) ) ) )
% 3.19/1.69 => ( ( ( proces401113213Choice @ A @ Process )
% 3.19/1.69 => ( ( proces401113213Choice @ A @ Process2 )
% 3.19/1.69 => ( ( ( proces979765041_ch1Of @ A @ Process )
% 3.19/1.69 = ( proces979765041_ch1Of @ A @ Process2 ) )
% 3.19/1.69 & ( ( proces988026546_ch2Of @ A @ Process )
% 3.19/1.69 = ( proces988026546_ch2Of @ A @ Process2 ) ) ) ) )
% 3.19/1.69 => ( Process = Process2 ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_53_process_Ocoinduct,axiom,
% 3.19/1.69 ! [A: $tType,R: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > $o,Process: proces634752977rocess @ A,Process2: proces634752977rocess @ A] :
% 3.19/1.69 ( ( R @ Process @ Process2 )
% 3.19/1.69 => ( ! [Process3: proces634752977rocess @ A,Process4: proces634752977rocess @ A] :
% 3.19/1.69 ( ( R @ Process3 @ Process4 )
% 3.19/1.69 => ( ( ( proces10484146Action @ A @ Process3 )
% 3.19/1.69 = ( proces10484146Action @ A @ Process4 ) )
% 3.19/1.69 & ( ( proces10484146Action @ A @ Process3 )
% 3.19/1.69 => ( ( proces10484146Action @ A @ Process4 )
% 3.19/1.69 => ( ( ( proces745025900prefOf @ A @ Process3 )
% 3.19/1.69 = ( proces745025900prefOf @ A @ Process4 ) )
% 3.19/1.69 & ( R @ ( proces1778668539contOf @ A @ Process3 ) @ ( proces1778668539contOf @ A @ Process4 ) ) ) ) )
% 3.19/1.69 & ( ( proces401113213Choice @ A @ Process3 )
% 3.19/1.69 => ( ( proces401113213Choice @ A @ Process4 )
% 3.19/1.69 => ( ( R @ ( proces979765041_ch1Of @ A @ Process3 ) @ ( proces979765041_ch1Of @ A @ Process4 ) )
% 3.19/1.69 & ( R @ ( proces988026546_ch2Of @ A @ Process3 ) @ ( proces988026546_ch2Of @ A @ Process4 ) ) ) ) ) ) )
% 3.19/1.69 => ( Process = Process2 ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_54_process_Ocoinduct__strong,axiom,
% 3.19/1.69 ! [A: $tType,R: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > $o,Process: proces634752977rocess @ A,Process2: proces634752977rocess @ A] :
% 3.19/1.69 ( ( R @ Process @ Process2 )
% 3.19/1.69 => ( ! [Process3: proces634752977rocess @ A,Process4: proces634752977rocess @ A] :
% 3.19/1.69 ( ( R @ Process3 @ Process4 )
% 3.19/1.69 => ( ( ( proces10484146Action @ A @ Process3 )
% 3.19/1.69 = ( proces10484146Action @ A @ Process4 ) )
% 3.19/1.69 & ( ( proces10484146Action @ A @ Process3 )
% 3.19/1.69 => ( ( proces10484146Action @ A @ Process4 )
% 3.19/1.69 => ( ( ( proces745025900prefOf @ A @ Process3 )
% 3.19/1.69 = ( proces745025900prefOf @ A @ Process4 ) )
% 3.19/1.69 & ( ( R @ ( proces1778668539contOf @ A @ Process3 ) @ ( proces1778668539contOf @ A @ Process4 ) )
% 3.19/1.69 | ( ( proces1778668539contOf @ A @ Process3 )
% 3.19/1.69 = ( proces1778668539contOf @ A @ Process4 ) ) ) ) ) )
% 3.19/1.69 & ( ( proces401113213Choice @ A @ Process3 )
% 3.19/1.69 => ( ( proces401113213Choice @ A @ Process4 )
% 3.19/1.69 => ( ( ( R @ ( proces979765041_ch1Of @ A @ Process3 ) @ ( proces979765041_ch1Of @ A @ Process4 ) )
% 3.19/1.69 | ( ( proces979765041_ch1Of @ A @ Process3 )
% 3.19/1.69 = ( proces979765041_ch1Of @ A @ Process4 ) ) )
% 3.19/1.69 & ( ( R @ ( proces988026546_ch2Of @ A @ Process3 ) @ ( proces988026546_ch2Of @ A @ Process4 ) )
% 3.19/1.69 | ( ( proces988026546_ch2Of @ A @ Process3 )
% 3.19/1.69 = ( proces988026546_ch2Of @ A @ Process4 ) ) ) ) ) ) ) )
% 3.19/1.69 => ( Process = Process2 ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_55_solution_Octr_I1_J,axiom,
% 3.19/1.69 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 3.19/1.69 ( ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
% 3.19/1.69 => ( ( proces1652378886lution @ A @ B @ Sys @ T2 )
% 3.19/1.69 = ( proces1525233512Action @ B @ ( proces1708129104e_PREF @ A @ B @ A @ Sys @ T2 ) @ ( proces1652378886lution @ A @ B @ Sys @ ( proces126235999e_CONT @ A @ B @ Sys @ T2 ) ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_56_solution_Octr_I2_J,axiom,
% 3.19/1.69 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 3.19/1.69 ( ~ ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
% 3.19/1.69 => ( ( proces1652378886lution @ A @ B @ Sys @ T2 )
% 3.19/1.69 = ( proces1915862579Choice @ B @ ( proces1652378886lution @ A @ B @ Sys @ ( proces1239275103le_CH1 @ A @ B @ Sys @ T2 ) ) @ ( proces1652378886lution @ A @ B @ Sys @ ( proces1239275104le_CH2 @ A @ B @ Sys @ T2 ) ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_57_process_Ocollapse_I2_J,axiom,
% 3.19/1.69 ! [A: $tType,Process: proces634752977rocess @ A] :
% 3.19/1.69 ( ( proces401113213Choice @ A @ Process )
% 3.19/1.69 => ( ( proces1915862579Choice @ A @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) )
% 3.19/1.69 = Process ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_58_solution_Ocode,axiom,
% 3.19/1.69 ! [B: $tType,A: $tType] :
% 3.19/1.69 ( ( proces1652378886lution @ A @ B )
% 3.19/1.69 = ( ^ [Sys3: A > ( proces554692349s_term @ B @ A ),T4: proces554692349s_term @ B @ A] : ( if @ ( proces634752977rocess @ B ) @ ( proces687458811_isACT @ A @ B @ A @ B @ Sys3 @ T4 ) @ ( proces1525233512Action @ B @ ( proces1708129104e_PREF @ A @ B @ A @ Sys3 @ T4 ) @ ( proces1652378886lution @ A @ B @ Sys3 @ ( proces126235999e_CONT @ A @ B @ Sys3 @ T4 ) ) ) @ ( proces1915862579Choice @ B @ ( proces1652378886lution @ A @ B @ Sys3 @ ( proces1239275103le_CH1 @ A @ B @ Sys3 @ T4 ) ) @ ( proces1652378886lution @ A @ B @ Sys3 @ ( proces1239275104le_CH2 @ A @ B @ Sys3 @ T4 ) ) ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_59_CH2_Ocases,axiom,
% 3.19/1.69 ! [A: $tType,B: $tType,X7: product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A )] :
% 3.19/1.69 ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),X3: A] :
% 3.19/1.69 ( X7
% 3.19/1.69 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ Sys2 @ ( proces1627516585ss_VAR @ A @ B @ X3 ) ) )
% 3.19/1.69 => ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),P4: proces634752977rocess @ B] :
% 3.19/1.69 ( X7
% 3.19/1.69 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ Sys2 @ ( proces1062592052s_PROC @ B @ A @ P4 ) ) )
% 3.19/1.69 => ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),T12: proces554692349s_term @ B @ A,T23: proces554692349s_term @ B @ A] :
% 3.19/1.69 ( X7
% 3.19/1.69 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ Sys2 @ ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) ) )
% 3.19/1.69 => ~ ! [A3: A > ( proces554692349s_term @ B @ A ),V: B,Va: proces554692349s_term @ B @ A] :
% 3.19/1.69 ( X7
% 3.19/1.69 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ A3 @ ( proces1454156180ss_ACT @ B @ A @ V @ Va ) ) ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_60_CONT_Ocases,axiom,
% 3.19/1.69 ! [A: $tType,B: $tType,X7: product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A )] :
% 3.19/1.69 ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),X3: A] :
% 3.19/1.69 ( X7
% 3.19/1.69 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ Sys2 @ ( proces1627516585ss_VAR @ A @ B @ X3 ) ) )
% 3.19/1.69 => ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),P4: proces634752977rocess @ B] :
% 3.19/1.69 ( X7
% 3.19/1.69 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ Sys2 @ ( proces1062592052s_PROC @ B @ A @ P4 ) ) )
% 3.19/1.69 => ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),A3: B,T3: proces554692349s_term @ B @ A] :
% 3.19/1.69 ( X7
% 3.19/1.69 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ Sys2 @ ( proces1454156180ss_ACT @ B @ A @ A3 @ T3 ) ) )
% 3.19/1.69 => ~ ! [A3: A > ( proces554692349s_term @ B @ A ),V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] :
% 3.19/1.69 ( X7
% 3.19/1.69 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ A3 @ ( proces89589571ess_CH @ B @ A @ V @ Va ) ) ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_61_PREF_Ocases,axiom,
% 3.19/1.69 ! [C: $tType,A: $tType,B: $tType,X7: product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A )] :
% 3.19/1.69 ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),X3: A] :
% 3.19/1.69 ( X7
% 3.19/1.69 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ Sys2 @ ( proces1627516585ss_VAR @ A @ B @ X3 ) ) )
% 3.19/1.69 => ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),P4: proces634752977rocess @ B] :
% 3.19/1.69 ( X7
% 3.19/1.69 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ Sys2 @ ( proces1062592052s_PROC @ B @ A @ P4 ) ) )
% 3.19/1.69 => ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),A3: B,T3: proces554692349s_term @ B @ A] :
% 3.19/1.69 ( X7
% 3.19/1.69 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ Sys2 @ ( proces1454156180ss_ACT @ B @ A @ A3 @ T3 ) ) )
% 3.19/1.69 => ~ ! [A3: A > ( proces554692349s_term @ B @ C ),V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] :
% 3.19/1.69 ( X7
% 3.19/1.69 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ A3 @ ( proces89589571ess_CH @ B @ A @ V @ Va ) ) ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_62_isACT_Ocases,axiom,
% 3.19/1.69 ! [B: $tType,C: $tType,A: $tType,D: $tType,X7: product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A )] :
% 3.19/1.69 ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),X3: A] :
% 3.19/1.69 ( X7
% 3.19/1.69 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ Sys2 @ ( proces1627516585ss_VAR @ A @ D @ X3 ) ) )
% 3.19/1.69 => ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),P4: proces634752977rocess @ D] :
% 3.19/1.69 ( X7
% 3.19/1.69 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ Sys2 @ ( proces1062592052s_PROC @ D @ A @ P4 ) ) )
% 3.19/1.69 => ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),A3: D,T3: proces554692349s_term @ D @ A] :
% 3.19/1.69 ( X7
% 3.19/1.69 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ Sys2 @ ( proces1454156180ss_ACT @ D @ A @ A3 @ T3 ) ) )
% 3.19/1.69 => ~ ! [Sys2: A > ( proces554692349s_term @ B @ C ),T12: proces554692349s_term @ D @ A,T23: proces554692349s_term @ D @ A] :
% 3.19/1.69 ( X7
% 3.19/1.69 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ Sys2 @ ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) ) ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_63_process_Oinject_I1_J,axiom,
% 3.19/1.69 ! [A: $tType,X11: A,X122: proces634752977rocess @ A,Y11: A,Y12: proces634752977rocess @ A] :
% 3.19/1.69 ( ( ( proces1525233512Action @ A @ X11 @ X122 )
% 3.19/1.69 = ( proces1525233512Action @ A @ Y11 @ Y12 ) )
% 3.19/1.69 = ( ( X11 = Y11 )
% 3.19/1.69 & ( X122 = Y12 ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_64_process_Oinject_I2_J,axiom,
% 3.19/1.69 ! [A: $tType,X21: proces634752977rocess @ A,X222: proces634752977rocess @ A,Y21: proces634752977rocess @ A,Y22: proces634752977rocess @ A] :
% 3.19/1.69 ( ( ( proces1915862579Choice @ A @ X21 @ X222 )
% 3.19/1.69 = ( proces1915862579Choice @ A @ Y21 @ Y22 ) )
% 3.19/1.69 = ( ( X21 = Y21 )
% 3.19/1.69 & ( X222 = Y22 ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_65_process_Opred__inject_I1_J,axiom,
% 3.19/1.69 ! [A: $tType,P3: A > $o,A2: A,Aa2: proces634752977rocess @ A] :
% 3.19/1.69 ( ( proces1205983068rocess @ A @ P3 @ ( proces1525233512Action @ A @ A2 @ Aa2 ) )
% 3.19/1.69 = ( ( P3 @ A2 )
% 3.19/1.69 & ( proces1205983068rocess @ A @ P3 @ Aa2 ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_66_process_Opred__inject_I2_J,axiom,
% 3.19/1.69 ! [A: $tType,P3: A > $o,A2: proces634752977rocess @ A,Aa2: proces634752977rocess @ A] :
% 3.19/1.69 ( ( proces1205983068rocess @ A @ P3 @ ( proces1915862579Choice @ A @ A2 @ Aa2 ) )
% 3.19/1.69 = ( ( proces1205983068rocess @ A @ P3 @ A2 )
% 3.19/1.69 & ( proces1205983068rocess @ A @ P3 @ Aa2 ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_67_solution_Odisc__iff_I1_J,axiom,
% 3.19/1.69 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 3.19/1.69 ( ( proces10484146Action @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) )
% 3.19/1.69 = ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_68_process_Ocollapse_I1_J,axiom,
% 3.19/1.69 ! [A: $tType,Process: proces634752977rocess @ A] :
% 3.19/1.69 ( ( proces10484146Action @ A @ Process )
% 3.19/1.69 => ( ( proces1525233512Action @ A @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) )
% 3.19/1.69 = Process ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_69_process__coind,axiom,
% 3.19/1.69 ! [A: $tType,Phi: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > $o,P: proces634752977rocess @ A,P5: proces634752977rocess @ A] :
% 3.19/1.69 ( ( Phi @ P @ P5 )
% 3.19/1.69 => ( ! [P4: proces634752977rocess @ A,P6: proces634752977rocess @ A] :
% 3.19/1.69 ( ( Phi @ P4 @ P6 )
% 3.19/1.69 => ( ( ( proces10484146Action @ A @ P4 )
% 3.19/1.69 = ( proces10484146Action @ A @ P6 ) )
% 3.19/1.69 & ( ( proces401113213Choice @ A @ P4 )
% 3.19/1.69 = ( proces401113213Choice @ A @ P6 ) ) ) )
% 3.19/1.69 => ( ! [A3: A,A5: A,P4: proces634752977rocess @ A,P6: proces634752977rocess @ A] :
% 3.19/1.69 ( ( Phi @ ( proces1525233512Action @ A @ A3 @ P4 ) @ ( proces1525233512Action @ A @ A5 @ P6 ) )
% 3.19/1.69 => ( ( A3 = A5 )
% 3.19/1.69 & ( Phi @ P4 @ P6 ) ) )
% 3.19/1.69 => ( ! [P4: proces634752977rocess @ A,Q3: proces634752977rocess @ A,P6: proces634752977rocess @ A,Q4: proces634752977rocess @ A] :
% 3.19/1.69 ( ( Phi @ ( proces1915862579Choice @ A @ P4 @ Q3 ) @ ( proces1915862579Choice @ A @ P6 @ Q4 ) )
% 3.19/1.69 => ( ( Phi @ P4 @ P6 )
% 3.19/1.69 & ( Phi @ Q3 @ Q4 ) ) )
% 3.19/1.69 => ( P = P5 ) ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_70_process__strong__coind,axiom,
% 3.19/1.69 ! [A: $tType,Phi: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > $o,P: proces634752977rocess @ A,P5: proces634752977rocess @ A] :
% 3.19/1.69 ( ( Phi @ P @ P5 )
% 3.19/1.69 => ( ! [P4: proces634752977rocess @ A,P6: proces634752977rocess @ A] :
% 3.19/1.69 ( ( Phi @ P4 @ P6 )
% 3.19/1.69 => ( ( ( proces10484146Action @ A @ P4 )
% 3.19/1.69 = ( proces10484146Action @ A @ P6 ) )
% 3.19/1.69 & ( ( proces401113213Choice @ A @ P4 )
% 3.19/1.69 = ( proces401113213Choice @ A @ P6 ) ) ) )
% 3.19/1.69 => ( ! [A3: A,A5: A,P4: proces634752977rocess @ A,P6: proces634752977rocess @ A] :
% 3.19/1.69 ( ( Phi @ ( proces1525233512Action @ A @ A3 @ P4 ) @ ( proces1525233512Action @ A @ A5 @ P6 ) )
% 3.19/1.69 => ( ( A3 = A5 )
% 3.19/1.69 & ( ( Phi @ P4 @ P6 )
% 3.19/1.69 | ( P4 = P6 ) ) ) )
% 3.19/1.69 => ( ! [P4: proces634752977rocess @ A,Q3: proces634752977rocess @ A,P6: proces634752977rocess @ A,Q4: proces634752977rocess @ A] :
% 3.19/1.69 ( ( Phi @ ( proces1915862579Choice @ A @ P4 @ Q3 ) @ ( proces1915862579Choice @ A @ P6 @ Q4 ) )
% 3.19/1.69 => ( ( ( Phi @ P4 @ P6 )
% 3.19/1.69 | ( P4 = P6 ) )
% 3.19/1.69 & ( ( Phi @ Q3 @ Q4 )
% 3.19/1.69 | ( Q3 = Q4 ) ) ) )
% 3.19/1.69 => ( P = P5 ) ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_71_isAction__def,axiom,
% 3.19/1.69 ! [A: $tType] :
% 3.19/1.69 ( ( proces10484146Action @ A )
% 3.19/1.69 = ( ^ [Process5: proces634752977rocess @ A] :
% 3.19/1.69 ? [X112: A,X123: proces634752977rocess @ A] :
% 3.19/1.69 ( Process5
% 3.19/1.69 = ( proces1525233512Action @ A @ X112 @ X123 ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_72_process_Oexhaust,axiom,
% 3.19/1.69 ! [A: $tType,Y3: proces634752977rocess @ A] :
% 3.19/1.69 ( ! [X113: A,X124: proces634752977rocess @ A] :
% 3.19/1.69 ( Y3
% 3.19/1.69 != ( proces1525233512Action @ A @ X113 @ X124 ) )
% 3.19/1.69 => ~ ! [X212: proces634752977rocess @ A,X223: proces634752977rocess @ A] :
% 3.19/1.69 ( Y3
% 3.19/1.69 != ( proces1915862579Choice @ A @ X212 @ X223 ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_73_process_Odistinct_I1_J,axiom,
% 3.19/1.69 ! [A: $tType,X11: A,X122: proces634752977rocess @ A,X21: proces634752977rocess @ A,X222: proces634752977rocess @ A] :
% 3.19/1.69 ( ( proces1525233512Action @ A @ X11 @ X122 )
% 3.19/1.69 != ( proces1915862579Choice @ A @ X21 @ X222 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_74_process_OdiscI_I1_J,axiom,
% 3.19/1.69 ! [A: $tType,Process: proces634752977rocess @ A,X11: A,X122: proces634752977rocess @ A] :
% 3.19/1.69 ( ( Process
% 3.19/1.69 = ( proces1525233512Action @ A @ X11 @ X122 ) )
% 3.19/1.69 => ( proces10484146Action @ A @ Process ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_75_process_Odisc_I1_J,axiom,
% 3.19/1.69 ! [A: $tType,X11: A,X122: proces634752977rocess @ A] : ( proces10484146Action @ A @ ( proces1525233512Action @ A @ X11 @ X122 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_76_process_Odisc_I2_J,axiom,
% 3.19/1.69 ! [A: $tType,X21: proces634752977rocess @ A,X222: proces634752977rocess @ A] :
% 3.19/1.69 ~ ( proces10484146Action @ A @ ( proces1915862579Choice @ A @ X21 @ X222 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_77_not__isAction__isChoice,axiom,
% 3.19/1.69 ! [A: $tType,P: proces634752977rocess @ A] :
% 3.19/1.69 ~ ( ( proces10484146Action @ A @ P )
% 3.19/1.69 & ( proces401113213Choice @ A @ P ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_78_process_Oexhaust__disc,axiom,
% 3.19/1.69 ! [A: $tType,Process: proces634752977rocess @ A] :
% 3.19/1.69 ( ~ ( proces10484146Action @ A @ Process )
% 3.19/1.69 => ( proces401113213Choice @ A @ Process ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_79_isAction__isChoice,axiom,
% 3.19/1.69 ! [A: $tType,P: proces634752977rocess @ A] :
% 3.19/1.69 ( ( proces10484146Action @ A @ P )
% 3.19/1.69 | ( proces401113213Choice @ A @ P ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_80_process_Odistinct__disc_I1_J,axiom,
% 3.19/1.69 ! [A: $tType,Process: proces634752977rocess @ A] :
% 3.19/1.69 ( ( proces10484146Action @ A @ Process )
% 3.19/1.69 => ~ ( proces401113213Choice @ A @ Process ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_81_process_Odistinct__disc_I2_J,axiom,
% 3.19/1.69 ! [A: $tType,Process: proces634752977rocess @ A] :
% 3.19/1.69 ( ( proces401113213Choice @ A @ Process )
% 3.19/1.69 => ~ ( proces10484146Action @ A @ Process ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_82_isChoice__def,axiom,
% 3.19/1.69 ! [A: $tType] :
% 3.19/1.69 ( ( proces401113213Choice @ A )
% 3.19/1.69 = ( ^ [Process5: proces634752977rocess @ A] :
% 3.19/1.69 ? [X213: proces634752977rocess @ A,X224: proces634752977rocess @ A] :
% 3.19/1.69 ( Process5
% 3.19/1.69 = ( proces1915862579Choice @ A @ X213 @ X224 ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_83_process_OdiscI_I2_J,axiom,
% 3.19/1.69 ! [A: $tType,Process: proces634752977rocess @ A,X21: proces634752977rocess @ A,X222: proces634752977rocess @ A] :
% 3.19/1.69 ( ( Process
% 3.19/1.69 = ( proces1915862579Choice @ A @ X21 @ X222 ) )
% 3.19/1.69 => ( proces401113213Choice @ A @ Process ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_84_process_Odisc_I3_J,axiom,
% 3.19/1.69 ! [A: $tType,X11: A,X122: proces634752977rocess @ A] :
% 3.19/1.69 ~ ( proces401113213Choice @ A @ ( proces1525233512Action @ A @ X11 @ X122 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_85_process_Odisc_I4_J,axiom,
% 3.19/1.69 ! [A: $tType,X21: proces634752977rocess @ A,X222: proces634752977rocess @ A] : ( proces401113213Choice @ A @ ( proces1915862579Choice @ A @ X21 @ X222 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_86_process_Osel_I2_J,axiom,
% 3.19/1.69 ! [A: $tType,X11: A,X122: proces634752977rocess @ A] :
% 3.19/1.69 ( ( proces1778668539contOf @ A @ ( proces1525233512Action @ A @ X11 @ X122 ) )
% 3.19/1.69 = X122 ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_87_process_Osel_I3_J,axiom,
% 3.19/1.69 ! [A: $tType,X21: proces634752977rocess @ A,X222: proces634752977rocess @ A] :
% 3.19/1.69 ( ( proces979765041_ch1Of @ A @ ( proces1915862579Choice @ A @ X21 @ X222 ) )
% 3.19/1.69 = X21 ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_88_process_Osel_I4_J,axiom,
% 3.19/1.69 ! [A: $tType,X21: proces634752977rocess @ A,X222: proces634752977rocess @ A] :
% 3.19/1.69 ( ( proces988026546_ch2Of @ A @ ( proces1915862579Choice @ A @ X21 @ X222 ) )
% 3.19/1.69 = X222 ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_89_process_Osel_I1_J,axiom,
% 3.19/1.69 ! [A: $tType,X11: A,X122: proces634752977rocess @ A] :
% 3.19/1.69 ( ( proces745025900prefOf @ A @ ( proces1525233512Action @ A @ X11 @ X122 ) )
% 3.19/1.69 = X11 ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_90_isACT_Osimps_I2_J,axiom,
% 3.19/1.69 ! [A: $tType,C: $tType,B: $tType,D: $tType,Sys: A > ( proces554692349s_term @ B @ C ),P: proces634752977rocess @ D] :
% 3.19/1.69 ( ( proces687458811_isACT @ A @ B @ C @ D @ Sys @ ( proces1062592052s_PROC @ D @ A @ P ) )
% 3.19/1.69 = ( proces10484146Action @ D @ P ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_91_process_Oexhaust__sel,axiom,
% 3.19/1.69 ! [A: $tType,Process: proces634752977rocess @ A] :
% 3.19/1.69 ( ( Process
% 3.19/1.69 != ( proces1525233512Action @ A @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) ) )
% 3.19/1.69 => ( Process
% 3.19/1.69 = ( proces1915862579Choice @ A @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_92_solution_Odisc_I1_J,axiom,
% 3.19/1.69 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 3.19/1.69 ( ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
% 3.19/1.69 => ( proces10484146Action @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_93_process_Osplit__sel__asm,axiom,
% 3.19/1.69 ! [B: $tType,A: $tType,P3: B > $o,F1: A > ( proces634752977rocess @ A ) > B,F2: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B,Process: proces634752977rocess @ A] :
% 3.19/1.69 ( ( P3 @ ( proces1406508781rocess @ A @ B @ F1 @ F2 @ Process ) )
% 3.19/1.69 = ( ~ ( ( ( Process
% 3.19/1.69 = ( proces1525233512Action @ A @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) ) )
% 3.19/1.69 & ~ ( P3 @ ( F1 @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) ) ) )
% 3.19/1.69 | ( ( Process
% 3.19/1.69 = ( proces1915862579Choice @ A @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) ) )
% 3.19/1.69 & ~ ( P3 @ ( F2 @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) ) ) ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_94_process_Osplit__sel,axiom,
% 3.19/1.69 ! [B: $tType,A: $tType,P3: B > $o,F1: A > ( proces634752977rocess @ A ) > B,F2: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B,Process: proces634752977rocess @ A] :
% 3.19/1.69 ( ( P3 @ ( proces1406508781rocess @ A @ B @ F1 @ F2 @ Process ) )
% 3.19/1.69 = ( ( ( Process
% 3.19/1.69 = ( proces1525233512Action @ A @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) ) )
% 3.19/1.69 => ( P3 @ ( F1 @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) ) ) )
% 3.19/1.69 & ( ( Process
% 3.19/1.69 = ( proces1915862579Choice @ A @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) ) )
% 3.19/1.69 => ( P3 @ ( F2 @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) ) ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_95_process_Ocase__eq__if,axiom,
% 3.19/1.69 ! [B: $tType,A: $tType] :
% 3.19/1.69 ( ( proces1406508781rocess @ A @ B )
% 3.19/1.69 = ( ^ [F12: A > ( proces634752977rocess @ A ) > B,F22: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B,Process5: proces634752977rocess @ A] : ( if @ B @ ( proces10484146Action @ A @ Process5 ) @ ( F12 @ ( proces745025900prefOf @ A @ Process5 ) @ ( proces1778668539contOf @ A @ Process5 ) ) @ ( F22 @ ( proces979765041_ch1Of @ A @ Process5 ) @ ( proces988026546_ch2Of @ A @ Process5 ) ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_96_old_Oprod_Oinject,axiom,
% 3.19/1.69 ! [A: $tType,B: $tType,A2: A,B2: B,A6: A,B3: B] :
% 3.19/1.69 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 3.19/1.69 = ( product_Pair @ A @ B @ A6 @ B3 ) )
% 3.19/1.69 = ( ( A2 = A6 )
% 3.19/1.69 & ( B2 = B3 ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_97_prod_Oinject,axiom,
% 3.19/1.69 ! [A: $tType,B: $tType,X1: A,X2: B,Y1: A,Y2: B] :
% 3.19/1.69 ( ( ( product_Pair @ A @ B @ X1 @ X2 )
% 3.19/1.69 = ( product_Pair @ A @ B @ Y1 @ Y2 ) )
% 3.19/1.69 = ( ( X1 = Y1 )
% 3.19/1.69 & ( X2 = Y2 ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_98_process_Orel__coinduct,axiom,
% 3.19/1.69 ! [A: $tType,B: $tType,P3: ( proces634752977rocess @ A ) > ( proces634752977rocess @ B ) > $o,X7: proces634752977rocess @ A,Y3: proces634752977rocess @ B,R: A > B > $o] :
% 3.19/1.69 ( ( P3 @ X7 @ Y3 )
% 3.19/1.69 => ( ! [Process3: proces634752977rocess @ A,Process4: proces634752977rocess @ B] :
% 3.19/1.69 ( ( P3 @ Process3 @ Process4 )
% 3.19/1.69 => ( ( ( proces10484146Action @ A @ Process3 )
% 3.19/1.69 = ( proces10484146Action @ B @ Process4 ) )
% 3.19/1.69 & ( ( proces10484146Action @ A @ Process3 )
% 3.19/1.69 => ( ( proces10484146Action @ B @ Process4 )
% 3.19/1.69 => ( ( R @ ( proces745025900prefOf @ A @ Process3 ) @ ( proces745025900prefOf @ B @ Process4 ) )
% 3.19/1.69 & ( P3 @ ( proces1778668539contOf @ A @ Process3 ) @ ( proces1778668539contOf @ B @ Process4 ) ) ) ) )
% 3.19/1.69 & ( ( proces401113213Choice @ A @ Process3 )
% 3.19/1.69 => ( ( proces401113213Choice @ B @ Process4 )
% 3.19/1.69 => ( ( P3 @ ( proces979765041_ch1Of @ A @ Process3 ) @ ( proces979765041_ch1Of @ B @ Process4 ) )
% 3.19/1.69 & ( P3 @ ( proces988026546_ch2Of @ A @ Process3 ) @ ( proces988026546_ch2Of @ B @ Process4 ) ) ) ) ) ) )
% 3.19/1.69 => ( proces749077512rocess @ A @ B @ R @ X7 @ Y3 ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_99_process_Orel__sel,axiom,
% 3.19/1.69 ! [B: $tType,A: $tType] :
% 3.19/1.69 ( ( proces749077512rocess @ A @ B )
% 3.19/1.69 = ( ^ [R2: A > B > $o,A7: proces634752977rocess @ A,B4: proces634752977rocess @ B] :
% 3.19/1.69 ( ( ( proces10484146Action @ A @ A7 )
% 3.19/1.69 = ( proces10484146Action @ B @ B4 ) )
% 3.19/1.69 & ( ( proces10484146Action @ A @ A7 )
% 3.19/1.69 => ( ( proces10484146Action @ B @ B4 )
% 3.19/1.69 => ( ( R2 @ ( proces745025900prefOf @ A @ A7 ) @ ( proces745025900prefOf @ B @ B4 ) )
% 3.19/1.69 & ( proces749077512rocess @ A @ B @ R2 @ ( proces1778668539contOf @ A @ A7 ) @ ( proces1778668539contOf @ B @ B4 ) ) ) ) )
% 3.19/1.69 & ( ( proces401113213Choice @ A @ A7 )
% 3.19/1.69 => ( ( proces401113213Choice @ B @ B4 )
% 3.19/1.69 => ( ( proces749077512rocess @ A @ B @ R2 @ ( proces979765041_ch1Of @ A @ A7 ) @ ( proces979765041_ch1Of @ B @ B4 ) )
% 3.19/1.69 & ( proces749077512rocess @ A @ B @ R2 @ ( proces988026546_ch2Of @ A @ A7 ) @ ( proces988026546_ch2Of @ B @ B4 ) ) ) ) ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_100_process_Orel__inject_I1_J,axiom,
% 3.19/1.69 ! [A: $tType,B: $tType,R: A > B > $o,X11: A,X122: proces634752977rocess @ A,Y11: B,Y12: proces634752977rocess @ B] :
% 3.19/1.69 ( ( proces749077512rocess @ A @ B @ R @ ( proces1525233512Action @ A @ X11 @ X122 ) @ ( proces1525233512Action @ B @ Y11 @ Y12 ) )
% 3.19/1.69 = ( ( R @ X11 @ Y11 )
% 3.19/1.69 & ( proces749077512rocess @ A @ B @ R @ X122 @ Y12 ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_101_process_Orel__inject_I2_J,axiom,
% 3.19/1.69 ! [A: $tType,B: $tType,R: A > B > $o,X21: proces634752977rocess @ A,X222: proces634752977rocess @ A,Y21: proces634752977rocess @ B,Y22: proces634752977rocess @ B] :
% 3.19/1.69 ( ( proces749077512rocess @ A @ B @ R @ ( proces1915862579Choice @ A @ X21 @ X222 ) @ ( proces1915862579Choice @ B @ Y21 @ Y22 ) )
% 3.19/1.69 = ( ( proces749077512rocess @ A @ B @ R @ X21 @ Y21 )
% 3.19/1.69 & ( proces749077512rocess @ A @ B @ R @ X222 @ Y22 ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_102_process_Orel__eq,axiom,
% 3.19/1.69 ! [A: $tType] :
% 3.19/1.69 ( ( proces749077512rocess @ A @ A
% 3.19/1.69 @ ^ [Y4: A,Z: A] : ( Y4 = Z ) )
% 3.19/1.69 = ( ^ [Y4: proces634752977rocess @ A,Z: proces634752977rocess @ A] : ( Y4 = Z ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_103_process_Orel__refl,axiom,
% 3.19/1.69 ! [B: $tType,Ra: B > B > $o,X7: proces634752977rocess @ B] :
% 3.19/1.69 ( ! [X5: B] : ( Ra @ X5 @ X5 )
% 3.19/1.69 => ( proces749077512rocess @ B @ B @ Ra @ X7 @ X7 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_104_process_Orel__intros_I1_J,axiom,
% 3.19/1.69 ! [A: $tType,B: $tType,R: A > B > $o,X11: A,Y11: B,X122: proces634752977rocess @ A,Y12: proces634752977rocess @ B] :
% 3.19/1.69 ( ( R @ X11 @ Y11 )
% 3.19/1.69 => ( ( proces749077512rocess @ A @ B @ R @ X122 @ Y12 )
% 3.19/1.69 => ( proces749077512rocess @ A @ B @ R @ ( proces1525233512Action @ A @ X11 @ X122 ) @ ( proces1525233512Action @ B @ Y11 @ Y12 ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_105_process_Orel__intros_I2_J,axiom,
% 3.19/1.69 ! [A: $tType,B: $tType,R: A > B > $o,X21: proces634752977rocess @ A,Y21: proces634752977rocess @ B,X222: proces634752977rocess @ A,Y22: proces634752977rocess @ B] :
% 3.19/1.69 ( ( proces749077512rocess @ A @ B @ R @ X21 @ Y21 )
% 3.19/1.69 => ( ( proces749077512rocess @ A @ B @ R @ X222 @ Y22 )
% 3.19/1.69 => ( proces749077512rocess @ A @ B @ R @ ( proces1915862579Choice @ A @ X21 @ X222 ) @ ( proces1915862579Choice @ B @ Y21 @ Y22 ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_106_process_Orel__distinct_I2_J,axiom,
% 3.19/1.69 ! [A: $tType,B: $tType,R: A > B > $o,Y21: proces634752977rocess @ A,Y22: proces634752977rocess @ A,X11: B,X122: proces634752977rocess @ B] :
% 3.19/1.69 ~ ( proces749077512rocess @ A @ B @ R @ ( proces1915862579Choice @ A @ Y21 @ Y22 ) @ ( proces1525233512Action @ B @ X11 @ X122 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_107_process_Orel__distinct_I1_J,axiom,
% 3.19/1.69 ! [A: $tType,B: $tType,R: A > B > $o,X11: A,X122: proces634752977rocess @ A,Y21: proces634752977rocess @ B,Y22: proces634752977rocess @ B] :
% 3.19/1.69 ~ ( proces749077512rocess @ A @ B @ R @ ( proces1525233512Action @ A @ X11 @ X122 ) @ ( proces1915862579Choice @ B @ Y21 @ Y22 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_108_process_Orel__cases,axiom,
% 3.19/1.69 ! [A: $tType,B: $tType,R: A > B > $o,A2: proces634752977rocess @ A,B2: proces634752977rocess @ B] :
% 3.19/1.69 ( ( proces749077512rocess @ A @ B @ R @ A2 @ B2 )
% 3.19/1.69 => ( ! [X12: A,X22: proces634752977rocess @ A] :
% 3.19/1.69 ( ( A2
% 3.19/1.69 = ( proces1525233512Action @ A @ X12 @ X22 ) )
% 3.19/1.69 => ! [Y13: B,Y23: proces634752977rocess @ B] :
% 3.19/1.69 ( ( B2
% 3.19/1.69 = ( proces1525233512Action @ B @ Y13 @ Y23 ) )
% 3.19/1.69 => ( ( R @ X12 @ Y13 )
% 3.19/1.69 => ~ ( proces749077512rocess @ A @ B @ R @ X22 @ Y23 ) ) ) )
% 3.19/1.69 => ~ ! [X1a: proces634752977rocess @ A,X2a: proces634752977rocess @ A] :
% 3.19/1.69 ( ( A2
% 3.19/1.69 = ( proces1915862579Choice @ A @ X1a @ X2a ) )
% 3.19/1.69 => ! [Y1a: proces634752977rocess @ B,Y2a: proces634752977rocess @ B] :
% 3.19/1.69 ( ( B2
% 3.19/1.69 = ( proces1915862579Choice @ B @ Y1a @ Y2a ) )
% 3.19/1.69 => ( ( proces749077512rocess @ A @ B @ R @ X1a @ Y1a )
% 3.19/1.69 => ~ ( proces749077512rocess @ A @ B @ R @ X2a @ Y2a ) ) ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_109_process_Osimps_I5_J,axiom,
% 3.19/1.69 ! [B: $tType,A: $tType,F1: A > ( proces634752977rocess @ A ) > B,F2: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B,X11: A,X122: proces634752977rocess @ A] :
% 3.19/1.69 ( ( proces1406508781rocess @ A @ B @ F1 @ F2 @ ( proces1525233512Action @ A @ X11 @ X122 ) )
% 3.19/1.69 = ( F1 @ X11 @ X122 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_110_process_Osimps_I6_J,axiom,
% 3.19/1.69 ! [B: $tType,A: $tType,F1: A > ( proces634752977rocess @ A ) > B,F2: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B,X21: proces634752977rocess @ A,X222: proces634752977rocess @ A] :
% 3.19/1.69 ( ( proces1406508781rocess @ A @ B @ F1 @ F2 @ ( proces1915862579Choice @ A @ X21 @ X222 ) )
% 3.19/1.69 = ( F2 @ X21 @ X222 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_111_surj__pair,axiom,
% 3.19/1.69 ! [A: $tType,B: $tType,P: product_prod @ A @ B] :
% 3.19/1.69 ? [X5: A,Y5: B] :
% 3.19/1.69 ( P
% 3.19/1.69 = ( product_Pair @ A @ B @ X5 @ Y5 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_112_prod__cases,axiom,
% 3.19/1.69 ! [B: $tType,A: $tType,P3: ( product_prod @ A @ B ) > $o,P: product_prod @ A @ B] :
% 3.19/1.69 ( ! [A3: A,B5: B] : ( P3 @ ( product_Pair @ A @ B @ A3 @ B5 ) )
% 3.19/1.69 => ( P3 @ P ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_113_Pair__inject,axiom,
% 3.19/1.69 ! [A: $tType,B: $tType,A2: A,B2: B,A6: A,B3: B] :
% 3.19/1.69 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 3.19/1.69 = ( product_Pair @ A @ B @ A6 @ B3 ) )
% 3.19/1.69 => ~ ( ( A2 = A6 )
% 3.19/1.69 => ( B2 != B3 ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_114_prod__cases3,axiom,
% 3.19/1.69 ! [A: $tType,B: $tType,C: $tType,Y3: product_prod @ A @ ( product_prod @ B @ C )] :
% 3.19/1.69 ~ ! [A3: A,B5: B,C2: C] :
% 3.19/1.69 ( Y3
% 3.19/1.69 != ( product_Pair @ A @ ( product_prod @ B @ C ) @ A3 @ ( product_Pair @ B @ C @ B5 @ C2 ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_115_prod__cases4,axiom,
% 3.19/1.69 ! [A: $tType,B: $tType,C: $tType,D: $tType,Y3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 3.19/1.69 ~ ! [A3: A,B5: B,C2: C,D2: D] :
% 3.19/1.69 ( Y3
% 3.19/1.69 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B5 @ ( product_Pair @ C @ D @ C2 @ D2 ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_116_prod__cases5,axiom,
% 3.19/1.69 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,Y3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) )] :
% 3.19/1.69 ~ ! [A3: A,B5: B,C2: C,D2: D,E2: E] :
% 3.19/1.69 ( Y3
% 3.19/1.69 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D @ E ) @ C2 @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_117_prod__cases6,axiom,
% 3.19/1.69 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,F5: $tType,Y3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F5 ) ) ) )] :
% 3.19/1.69 ~ ! [A3: A,B5: B,C2: C,D2: D,E2: E,F6: F5] :
% 3.19/1.69 ( Y3
% 3.19/1.69 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F5 ) ) ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F5 ) ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ F5 ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E @ F5 ) @ D2 @ ( product_Pair @ E @ F5 @ E2 @ F6 ) ) ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_118_prod__cases7,axiom,
% 3.19/1.69 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,F5: $tType,G2: $tType,Y3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G2 ) ) ) ) )] :
% 3.19/1.69 ~ ! [A3: A,B5: B,C2: C,D2: D,E2: E,F6: F5,G3: G2] :
% 3.19/1.69 ( Y3
% 3.19/1.69 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G2 ) ) ) ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G2 ) ) ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G2 ) ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G2 ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F5 @ G2 ) @ E2 @ ( product_Pair @ F5 @ G2 @ F6 @ G3 ) ) ) ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_119_prod__induct3,axiom,
% 3.19/1.69 ! [C: $tType,B: $tType,A: $tType,P3: ( product_prod @ A @ ( product_prod @ B @ C ) ) > $o,X7: product_prod @ A @ ( product_prod @ B @ C )] :
% 3.19/1.69 ( ! [A3: A,B5: B,C2: C] : ( P3 @ ( product_Pair @ A @ ( product_prod @ B @ C ) @ A3 @ ( product_Pair @ B @ C @ B5 @ C2 ) ) )
% 3.19/1.69 => ( P3 @ X7 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_120_prod__induct4,axiom,
% 3.19/1.69 ! [D: $tType,C: $tType,B: $tType,A: $tType,P3: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) ) > $o,X7: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 3.19/1.69 ( ! [A3: A,B5: B,C2: C,D2: D] : ( P3 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B5 @ ( product_Pair @ C @ D @ C2 @ D2 ) ) ) )
% 3.19/1.69 => ( P3 @ X7 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_121_prod__induct5,axiom,
% 3.19/1.69 ! [E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P3: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) ) > $o,X7: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) )] :
% 3.19/1.69 ( ! [A3: A,B5: B,C2: C,D2: D,E2: E] : ( P3 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D @ E ) @ C2 @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) )
% 3.19/1.69 => ( P3 @ X7 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_122_prod__induct6,axiom,
% 3.19/1.69 ! [F5: $tType,E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P3: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F5 ) ) ) ) ) > $o,X7: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F5 ) ) ) )] :
% 3.19/1.69 ( ! [A3: A,B5: B,C2: C,D2: D,E2: E,F6: F5] : ( P3 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F5 ) ) ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F5 ) ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ F5 ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E @ F5 ) @ D2 @ ( product_Pair @ E @ F5 @ E2 @ F6 ) ) ) ) ) )
% 3.19/1.69 => ( P3 @ X7 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_123_prod__induct7,axiom,
% 3.19/1.69 ! [G2: $tType,F5: $tType,E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P3: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G2 ) ) ) ) ) ) > $o,X7: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G2 ) ) ) ) )] :
% 3.19/1.69 ( ! [A3: A,B5: B,C2: C,D2: D,E2: E,F6: F5,G3: G2] : ( P3 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G2 ) ) ) ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G2 ) ) ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G2 ) ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G2 ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F5 @ G2 ) @ E2 @ ( product_Pair @ F5 @ G2 @ F6 @ G3 ) ) ) ) ) ) )
% 3.19/1.69 => ( P3 @ X7 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_124_old_Oprod_Oexhaust,axiom,
% 3.19/1.69 ! [A: $tType,B: $tType,Y3: product_prod @ A @ B] :
% 3.19/1.69 ~ ! [A3: A,B5: B] :
% 3.19/1.69 ( Y3
% 3.19/1.69 != ( product_Pair @ A @ B @ A3 @ B5 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_125_old_Oprod_Oinducts,axiom,
% 3.19/1.69 ! [B: $tType,A: $tType,P3: ( product_prod @ A @ B ) > $o,Prod: product_prod @ A @ B] :
% 3.19/1.69 ( ! [A3: A,B5: B] : ( P3 @ ( product_Pair @ A @ B @ A3 @ B5 ) )
% 3.19/1.69 => ( P3 @ Prod ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_126_old_Oprod_Orec,axiom,
% 3.19/1.69 ! [A: $tType,T: $tType,B: $tType,F1: A > B > T,A2: A,B2: B] :
% 3.19/1.69 ( ( product_rec_prod @ A @ B @ T @ F1 @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 3.19/1.69 = ( F1 @ A2 @ B2 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_127_process__term_Orel__cases,axiom,
% 3.19/1.69 ! [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] :
% 3.19/1.69 ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ A2 @ B2 )
% 3.19/1.69 => ( ! [X5: Pvar] :
% 3.19/1.69 ( ( A2
% 3.19/1.69 = ( proces1627516585ss_VAR @ Pvar @ A @ X5 ) )
% 3.19/1.69 => ! [Y5: C] :
% 3.19/1.69 ( ( B2
% 3.19/1.69 = ( proces1627516585ss_VAR @ C @ B @ Y5 ) )
% 3.19/1.69 => ~ ( R22 @ X5 @ Y5 ) ) )
% 3.19/1.69 => ( ! [Xa: proces634752977rocess @ A] :
% 3.19/1.69 ( ( A2
% 3.19/1.69 = ( proces1062592052s_PROC @ A @ Pvar @ Xa ) )
% 3.19/1.69 => ! [Ya: proces634752977rocess @ B] :
% 3.19/1.69 ( ( B2
% 3.19/1.69 = ( proces1062592052s_PROC @ B @ C @ Ya ) )
% 3.19/1.69 => ~ ( proces749077512rocess @ A @ B @ R1 @ Xa @ Ya ) ) )
% 3.19/1.69 => ( ! [X1a: A,X2a: proces554692349s_term @ A @ Pvar] :
% 3.19/1.69 ( ( A2
% 3.19/1.69 = ( proces1454156180ss_ACT @ A @ Pvar @ X1a @ X2a ) )
% 3.19/1.69 => ! [Y1a: B,Y2a: proces554692349s_term @ B @ C] :
% 3.19/1.69 ( ( B2
% 3.19/1.69 = ( proces1454156180ss_ACT @ B @ C @ Y1a @ Y2a ) )
% 3.19/1.69 => ( ( R1 @ X1a @ Y1a )
% 3.19/1.69 => ~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X2a @ Y2a ) ) ) )
% 3.19/1.69 => ~ ! [X1b: proces554692349s_term @ A @ Pvar,X2b: proces554692349s_term @ A @ Pvar] :
% 3.19/1.69 ( ( A2
% 3.19/1.69 = ( proces89589571ess_CH @ A @ Pvar @ X1b @ X2b ) )
% 3.19/1.69 => ! [Y1b: proces554692349s_term @ B @ C,Y2b: proces554692349s_term @ B @ C] :
% 3.19/1.69 ( ( B2
% 3.19/1.69 = ( proces89589571ess_CH @ B @ C @ Y1b @ Y2b ) )
% 3.19/1.69 => ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X1b @ Y1b )
% 3.19/1.69 => ~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X2b @ Y2b ) ) ) ) ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_128_process__term_Orel__induct,axiom,
% 3.19/1.69 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X7: proces554692349s_term @ A @ Pvar,Y3: proces554692349s_term @ B @ C,Q2: ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ B @ C ) > $o] :
% 3.19/1.69 ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X7 @ Y3 )
% 3.19/1.69 => ( ! [A12: Pvar,B1: C] :
% 3.19/1.69 ( ( R22 @ A12 @ B1 )
% 3.19/1.69 => ( Q2 @ ( proces1627516585ss_VAR @ Pvar @ A @ A12 ) @ ( proces1627516585ss_VAR @ C @ B @ B1 ) ) )
% 3.19/1.69 => ( ! [A22: proces634752977rocess @ A,B22: proces634752977rocess @ B] :
% 3.19/1.69 ( ( proces749077512rocess @ A @ B @ R1 @ A22 @ B22 )
% 3.19/1.69 => ( Q2 @ ( proces1062592052s_PROC @ A @ Pvar @ A22 ) @ ( proces1062592052s_PROC @ B @ C @ B22 ) ) )
% 3.19/1.69 => ( ! [A31: A,A32: proces554692349s_term @ A @ Pvar,B31: B,B32: proces554692349s_term @ B @ C] :
% 3.19/1.69 ( ( R1 @ A31 @ B31 )
% 3.19/1.69 => ( ( Q2 @ A32 @ B32 )
% 3.19/1.69 => ( Q2 @ ( proces1454156180ss_ACT @ A @ Pvar @ A31 @ A32 ) @ ( proces1454156180ss_ACT @ B @ C @ B31 @ B32 ) ) ) )
% 3.19/1.69 => ( ! [A41: proces554692349s_term @ A @ Pvar,A42: proces554692349s_term @ A @ Pvar,B41: proces554692349s_term @ B @ C,B42: proces554692349s_term @ B @ C] :
% 3.19/1.69 ( ( Q2 @ A41 @ B41 )
% 3.19/1.69 => ( ( Q2 @ A42 @ B42 )
% 3.19/1.69 => ( Q2 @ ( proces89589571ess_CH @ A @ Pvar @ A41 @ A42 ) @ ( proces89589571ess_CH @ B @ C @ B41 @ B42 ) ) ) )
% 3.19/1.69 => ( Q2 @ X7 @ Y3 ) ) ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_129_internal__case__prod__conv,axiom,
% 3.19/1.69 ! [B: $tType,A: $tType,C: $tType,C3: B > C > A,A2: B,B2: C] :
% 3.19/1.69 ( ( produc2004651681e_prod @ B @ C @ A @ C3 @ ( product_Pair @ B @ C @ A2 @ B2 ) )
% 3.19/1.69 = ( C3 @ A2 @ B2 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_130_process__term_Oset__cases_I2_J,axiom,
% 3.19/1.69 ! [Pvar: $tType,A: $tType,E3: Pvar,A2: proces554692349s_term @ A @ Pvar] :
% 3.19/1.69 ( ( member @ Pvar @ E3 @ ( proces1493547885s_term @ A @ Pvar @ A2 ) )
% 3.19/1.69 => ( ( A2
% 3.19/1.69 != ( proces1627516585ss_VAR @ Pvar @ A @ E3 ) )
% 3.19/1.69 => ( ! [Z1: A,Z2: proces554692349s_term @ A @ Pvar] :
% 3.19/1.69 ( ( A2
% 3.19/1.69 = ( proces1454156180ss_ACT @ A @ Pvar @ Z1 @ Z2 ) )
% 3.19/1.69 => ~ ( member @ Pvar @ E3 @ ( proces1493547885s_term @ A @ Pvar @ Z2 ) ) )
% 3.19/1.69 => ( ! [Z1: proces554692349s_term @ A @ Pvar] :
% 3.19/1.69 ( ? [Z2: proces554692349s_term @ A @ Pvar] :
% 3.19/1.69 ( A2
% 3.19/1.69 = ( proces89589571ess_CH @ A @ Pvar @ Z1 @ Z2 ) )
% 3.19/1.69 => ~ ( member @ Pvar @ E3 @ ( proces1493547885s_term @ A @ Pvar @ Z1 ) ) )
% 3.19/1.69 => ~ ! [Z1: proces554692349s_term @ A @ Pvar,Z2: proces554692349s_term @ A @ Pvar] :
% 3.19/1.69 ( ( A2
% 3.19/1.69 = ( proces89589571ess_CH @ A @ Pvar @ Z1 @ Z2 ) )
% 3.19/1.69 => ~ ( member @ Pvar @ E3 @ ( proces1493547885s_term @ A @ Pvar @ Z2 ) ) ) ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_131_process__term_Orel__inject_I1_J,axiom,
% 3.19/1.69 ! [B: $tType,A: $tType,Pvar: $tType,C: $tType,R1: A > B > $o,R22: Pvar > C > $o,X1: Pvar,Y1: C] :
% 3.19/1.69 ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1627516585ss_VAR @ Pvar @ A @ X1 ) @ ( proces1627516585ss_VAR @ C @ B @ Y1 ) )
% 3.19/1.69 = ( R22 @ X1 @ Y1 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_132_process__term_Orel__intros_I1_J,axiom,
% 3.19/1.69 ! [Pvar: $tType,A: $tType,B: $tType,C: $tType,R22: Pvar > C > $o,X1: Pvar,Y1: C,R1: A > B > $o] :
% 3.19/1.69 ( ( R22 @ X1 @ Y1 )
% 3.19/1.69 => ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1627516585ss_VAR @ Pvar @ A @ X1 ) @ ( proces1627516585ss_VAR @ C @ B @ Y1 ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_133_process__term_Orel__inject_I4_J,axiom,
% 3.19/1.69 ! [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] :
% 3.19/1.69 ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 ) @ ( proces89589571ess_CH @ B @ C @ Y41 @ Y42 ) )
% 3.19/1.69 = ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X41 @ Y41 )
% 3.19/1.69 & ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X42 @ Y42 ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_134_process__term_Orel__intros_I4_J,axiom,
% 3.19/1.69 ! [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] :
% 3.19/1.69 ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X41 @ Y41 )
% 3.19/1.69 => ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X42 @ Y42 )
% 3.19/1.69 => ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 ) @ ( proces89589571ess_CH @ B @ C @ Y41 @ Y42 ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_135_process__term_Orel__inject_I3_J,axiom,
% 3.19/1.69 ! [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] :
% 3.19/1.69 ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) @ ( proces1454156180ss_ACT @ B @ C @ Y31 @ Y32 ) )
% 3.19/1.69 = ( ( R1 @ X31 @ Y31 )
% 3.19/1.69 & ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X32 @ Y32 ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_136_process__term_Orel__intros_I3_J,axiom,
% 3.19/1.69 ! [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] :
% 3.19/1.69 ( ( R1 @ X31 @ Y31 )
% 3.19/1.69 => ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X32 @ Y32 )
% 3.19/1.69 => ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) @ ( proces1454156180ss_ACT @ B @ C @ Y31 @ Y32 ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_137_process__term_Orel__refl,axiom,
% 3.19/1.69 ! [D: $tType,C: $tType,R1a: C > C > $o,R2a: D > D > $o,X7: proces554692349s_term @ C @ D] :
% 3.19/1.69 ( ! [X5: C] : ( R1a @ X5 @ X5 )
% 3.19/1.69 => ( ! [X5: D] : ( R2a @ X5 @ X5 )
% 3.19/1.69 => ( proces2029722208s_term @ C @ C @ D @ D @ R1a @ R2a @ X7 @ X7 ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_138_process__term_Orel__eq,axiom,
% 3.19/1.69 ! [B: $tType,A: $tType] :
% 3.19/1.69 ( ( proces2029722208s_term @ A @ A @ B @ B
% 3.19/1.69 @ ^ [Y4: A,Z: A] : ( Y4 = Z )
% 3.19/1.69 @ ^ [Y4: B,Z: B] : ( Y4 = Z ) )
% 3.19/1.69 = ( ^ [Y4: proces554692349s_term @ A @ B,Z: proces554692349s_term @ A @ B] : ( Y4 = Z ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_139_process__term_Oset__intros_I6_J,axiom,
% 3.19/1.69 ! [A: $tType,Pvar: $tType,Ab: Pvar] : ( member @ Pvar @ Ab @ ( proces1493547885s_term @ A @ Pvar @ ( proces1627516585ss_VAR @ Pvar @ A @ Ab ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_140_process__term_Oset__intros_I8_J,axiom,
% 3.19/1.69 ! [Pvar: $tType,A: $tType,Xk: Pvar,A1c: proces554692349s_term @ A @ Pvar,A2c: proces554692349s_term @ A @ Pvar] :
% 3.19/1.69 ( ( member @ Pvar @ Xk @ ( proces1493547885s_term @ A @ Pvar @ A1c ) )
% 3.19/1.69 => ( member @ Pvar @ Xk @ ( proces1493547885s_term @ A @ Pvar @ ( proces89589571ess_CH @ A @ Pvar @ A1c @ A2c ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_141_process__term_Oset__intros_I9_J,axiom,
% 3.19/1.69 ! [Pvar: $tType,A: $tType,Xm: Pvar,A2c: proces554692349s_term @ A @ Pvar,A1c: proces554692349s_term @ A @ Pvar] :
% 3.19/1.69 ( ( member @ Pvar @ Xm @ ( proces1493547885s_term @ A @ Pvar @ A2c ) )
% 3.19/1.69 => ( member @ Pvar @ Xm @ ( proces1493547885s_term @ A @ Pvar @ ( proces89589571ess_CH @ A @ Pvar @ A1c @ A2c ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_142_process__term_Oset__intros_I7_J,axiom,
% 3.19/1.69 ! [Pvar: $tType,A: $tType,Xi: Pvar,A2b: proces554692349s_term @ A @ Pvar,A1b: A] :
% 3.19/1.69 ( ( member @ Pvar @ Xi @ ( proces1493547885s_term @ A @ Pvar @ A2b ) )
% 3.19/1.69 => ( member @ Pvar @ Xi @ ( proces1493547885s_term @ A @ Pvar @ ( proces1454156180ss_ACT @ A @ Pvar @ A1b @ A2b ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_143_process__term_Osimps_I51_J,axiom,
% 3.19/1.69 ! [Pvar: $tType,A: $tType,X31: A,X32: proces554692349s_term @ A @ Pvar] :
% 3.19/1.69 ( ( proces1493547885s_term @ A @ Pvar @ ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) )
% 3.19/1.69 = ( proces1493547885s_term @ A @ Pvar @ X32 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_144_process__term_Orel__intros_I2_J,axiom,
% 3.19/1.69 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,X2: proces634752977rocess @ A,Y2: proces634752977rocess @ B,R22: Pvar > C > $o] :
% 3.19/1.69 ( ( proces749077512rocess @ A @ B @ R1 @ X2 @ Y2 )
% 3.19/1.69 => ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1062592052s_PROC @ A @ Pvar @ X2 ) @ ( proces1062592052s_PROC @ B @ C @ Y2 ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_145_process__term_Orel__inject_I2_J,axiom,
% 3.19/1.69 ! [C: $tType,Pvar: $tType,A: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X2: proces634752977rocess @ A,Y2: proces634752977rocess @ B] :
% 3.19/1.69 ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1062592052s_PROC @ A @ Pvar @ X2 ) @ ( proces1062592052s_PROC @ B @ C @ Y2 ) )
% 3.19/1.69 = ( proces749077512rocess @ A @ B @ R1 @ X2 @ Y2 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_146_process__term_Orel__distinct_I2_J,axiom,
% 3.19/1.69 ! [A: $tType,B: $tType,C: $tType,D: $tType,R1: A > C > $o,R22: B > D > $o,Y2: proces634752977rocess @ A,X1: D] :
% 3.19/1.69 ~ ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R22 @ ( proces1062592052s_PROC @ A @ B @ Y2 ) @ ( proces1627516585ss_VAR @ D @ C @ X1 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_147_process__term_Orel__distinct_I1_J,axiom,
% 3.19/1.69 ! [Pvar: $tType,A: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X1: Pvar,Y2: proces634752977rocess @ B] :
% 3.19/1.69 ~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1627516585ss_VAR @ Pvar @ A @ X1 ) @ ( proces1062592052s_PROC @ B @ C @ Y2 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_148_process__term_Orel__distinct_I10_J,axiom,
% 3.19/1.69 ! [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] :
% 3.19/1.69 ~ ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R22 @ ( proces89589571ess_CH @ A @ B @ Y41 @ Y42 ) @ ( proces1062592052s_PROC @ C @ D @ X2 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_149_process__term_Orel__distinct_I9_J,axiom,
% 3.19/1.69 ! [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] :
% 3.19/1.69 ~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1062592052s_PROC @ A @ Pvar @ X2 ) @ ( proces89589571ess_CH @ B @ C @ Y41 @ Y42 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_150_process__term_Orel__distinct_I8_J,axiom,
% 3.19/1.69 ! [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] :
% 3.19/1.69 ~ ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R22 @ ( proces1454156180ss_ACT @ A @ B @ Y31 @ Y32 ) @ ( proces1062592052s_PROC @ C @ D @ X2 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_151_process__term_Orel__distinct_I7_J,axiom,
% 3.19/1.69 ! [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] :
% 3.19/1.69 ~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1062592052s_PROC @ A @ Pvar @ X2 ) @ ( proces1454156180ss_ACT @ B @ C @ Y31 @ Y32 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_152_process__term_Orel__distinct_I5_J,axiom,
% 3.19/1.69 ! [Pvar: $tType,A: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X1: Pvar,Y41: proces554692349s_term @ B @ C,Y42: proces554692349s_term @ B @ C] :
% 3.19/1.69 ~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1627516585ss_VAR @ Pvar @ A @ X1 ) @ ( proces89589571ess_CH @ B @ C @ Y41 @ Y42 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_153_process__term_Orel__distinct_I6_J,axiom,
% 3.19/1.69 ! [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,X1: D] :
% 3.19/1.69 ~ ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R22 @ ( proces89589571ess_CH @ A @ B @ Y41 @ Y42 ) @ ( proces1627516585ss_VAR @ D @ C @ X1 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_154_process__term_Orel__distinct_I3_J,axiom,
% 3.19/1.69 ! [Pvar: $tType,A: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X1: Pvar,Y31: B,Y32: proces554692349s_term @ B @ C] :
% 3.19/1.69 ~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1627516585ss_VAR @ Pvar @ A @ X1 ) @ ( proces1454156180ss_ACT @ B @ C @ Y31 @ Y32 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_155_process__term_Orel__distinct_I4_J,axiom,
% 3.19/1.69 ! [A: $tType,B: $tType,C: $tType,D: $tType,R1: A > C > $o,R22: B > D > $o,Y31: A,Y32: proces554692349s_term @ A @ B,X1: D] :
% 3.19/1.69 ~ ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R22 @ ( proces1454156180ss_ACT @ A @ B @ Y31 @ Y32 ) @ ( proces1627516585ss_VAR @ D @ C @ X1 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_156_process__term_Orel__distinct_I11_J,axiom,
% 3.19/1.69 ! [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] :
% 3.19/1.69 ~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) @ ( proces89589571ess_CH @ B @ C @ Y41 @ Y42 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_157_process__term_Orel__distinct_I12_J,axiom,
% 3.19/1.69 ! [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] :
% 3.19/1.69 ~ ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R22 @ ( proces89589571ess_CH @ A @ B @ Y41 @ Y42 ) @ ( proces1454156180ss_ACT @ C @ D @ X31 @ X32 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_158_ssubst__Pair__rhs,axiom,
% 3.19/1.69 ! [B: $tType,A: $tType,R3: A,S: B,R: set @ ( product_prod @ A @ B ),S2: B] :
% 3.19/1.69 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ R3 @ S ) @ R )
% 3.19/1.69 => ( ( S2 = S )
% 3.19/1.69 => ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ R3 @ S2 ) @ R ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_159_curry__conv,axiom,
% 3.19/1.69 ! [A: $tType,C: $tType,B: $tType] :
% 3.19/1.69 ( ( product_curry @ B @ C @ A )
% 3.19/1.69 = ( ^ [F7: ( product_prod @ B @ C ) > A,A7: B,B4: C] : ( F7 @ ( product_Pair @ B @ C @ A7 @ B4 ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_160_process__term_Octr__transfer_I2_J,axiom,
% 3.19/1.69 ! [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 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_161_isACT_Oelims_I1_J,axiom,
% 3.19/1.69 ! [D: $tType,A: $tType,B: $tType,C: $tType,X7: A > ( proces554692349s_term @ B @ C ),Xa2: proces554692349s_term @ D @ A,Y3: $o] :
% 3.19/1.69 ( ( ( proces687458811_isACT @ A @ B @ C @ D @ X7 @ Xa2 )
% 3.19/1.69 = Y3 )
% 3.19/1.69 => ( ! [X3: A] :
% 3.19/1.69 ( ( Xa2
% 3.19/1.69 = ( proces1627516585ss_VAR @ A @ D @ X3 ) )
% 3.19/1.69 => ( Y3
% 3.19/1.69 = ( ~ ( proces460752237s_term @ C @ $o @ B
% 3.19/1.69 @ ^ [Pvar2: C] : $false
% 3.19/1.69 @ ( proces10484146Action @ B )
% 3.19/1.69 @ ^ [A7: B,T4: proces554692349s_term @ B @ C] : $true
% 3.19/1.69 @ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
% 3.19/1.69 @ ( X7 @ X3 ) ) ) ) )
% 3.19/1.69 => ( ! [P4: proces634752977rocess @ D] :
% 3.19/1.69 ( ( Xa2
% 3.19/1.69 = ( proces1062592052s_PROC @ D @ A @ P4 ) )
% 3.19/1.69 => ( Y3
% 3.19/1.69 = ( ~ ( proces10484146Action @ D @ P4 ) ) ) )
% 3.19/1.69 => ( ( ? [A3: D,T3: proces554692349s_term @ D @ A] :
% 3.19/1.69 ( Xa2
% 3.19/1.69 = ( proces1454156180ss_ACT @ D @ A @ A3 @ T3 ) )
% 3.19/1.69 => ~ Y3 )
% 3.19/1.69 => ~ ( ? [T12: proces554692349s_term @ D @ A,T23: proces554692349s_term @ D @ A] :
% 3.19/1.69 ( Xa2
% 3.19/1.69 = ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) )
% 3.19/1.69 => Y3 ) ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_162_curryI,axiom,
% 3.19/1.69 ! [A: $tType,B: $tType,F: ( product_prod @ A @ B ) > $o,A2: A,B2: B] :
% 3.19/1.69 ( ( F @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 3.19/1.69 => ( product_curry @ A @ B @ $o @ F @ A2 @ B2 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_163_curry__def,axiom,
% 3.19/1.69 ! [C: $tType,B: $tType,A: $tType] :
% 3.19/1.69 ( ( product_curry @ A @ B @ C )
% 3.19/1.69 = ( ^ [C4: ( product_prod @ A @ B ) > C,X6: A,Y6: B] : ( C4 @ ( product_Pair @ A @ B @ X6 @ Y6 ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_164_process__term_Ocase__transfer,axiom,
% 3.19/1.69 ! [Pvar: $tType,D: $tType,A: $tType,B: $tType,E: $tType,C: $tType,R22: Pvar > C > $o,S3: D > E > $o,R1: A > B > $o] : ( bNF_rel_fun @ ( Pvar > D ) @ ( C > E ) @ ( ( ( 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 ) > E ) > ( B > ( proces554692349s_term @ B @ C ) > E ) > ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) > E ) > ( proces554692349s_term @ B @ C ) > E ) @ ( bNF_rel_fun @ Pvar @ C @ D @ E @ R22 @ S3 ) @ ( bNF_rel_fun @ ( ( proces634752977rocess @ A ) > D ) @ ( ( proces634752977rocess @ B ) > E ) @ ( ( 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 ) > E ) > ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) > E ) > ( proces554692349s_term @ B @ C ) > E ) @ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ D @ E @ ( proces749077512rocess @ A @ B @ R1 ) @ S3 ) @ ( bNF_rel_fun @ ( A > ( proces554692349s_term @ A @ Pvar ) > D ) @ ( B > ( proces554692349s_term @ B @ C ) > E ) @ ( ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D ) > ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) > E ) > ( proces554692349s_term @ B @ C ) > E ) @ ( bNF_rel_fun @ A @ B @ ( ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( proces554692349s_term @ B @ C ) > E ) @ R1 @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ D @ E @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ S3 ) ) @ ( bNF_rel_fun @ ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) > E ) @ ( ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( proces554692349s_term @ B @ C ) > E ) @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ ( ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( proces554692349s_term @ B @ C ) > E ) @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ D @ E @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ S3 ) ) @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ D @ E @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ S3 ) ) ) ) @ ( proces460752237s_term @ Pvar @ D @ A ) @ ( proces460752237s_term @ C @ E @ B ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_165_process__term_Orec__transfer,axiom,
% 3.19/1.69 ! [Pvar: $tType,D: $tType,A: $tType,B: $tType,E: $tType,C: $tType,R22: Pvar > C > $o,S3: D > E > $o,R1: A > B > $o] : ( bNF_rel_fun @ ( Pvar > D ) @ ( C > E ) @ ( ( ( 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 ) > E ) > ( B > ( proces554692349s_term @ B @ C ) > E > E ) > ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) > E > E > E ) > ( proces554692349s_term @ B @ C ) > E ) @ ( bNF_rel_fun @ Pvar @ C @ D @ E @ R22 @ S3 ) @ ( bNF_rel_fun @ ( ( proces634752977rocess @ A ) > D ) @ ( ( proces634752977rocess @ B ) > E ) @ ( ( 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 ) > E > E ) > ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) > E > E > E ) > ( proces554692349s_term @ B @ C ) > E ) @ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ D @ E @ ( proces749077512rocess @ A @ B @ R1 ) @ S3 ) @ ( bNF_rel_fun @ ( A > ( proces554692349s_term @ A @ Pvar ) > D > D ) @ ( B > ( proces554692349s_term @ B @ C ) > E > E ) @ ( ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D > D > D ) > ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) > E > E > E ) > ( proces554692349s_term @ B @ C ) > E ) @ ( bNF_rel_fun @ A @ B @ ( ( proces554692349s_term @ A @ Pvar ) > D > D ) @ ( ( proces554692349s_term @ B @ C ) > E > E ) @ R1 @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ ( D > D ) @ ( E > E ) @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ ( bNF_rel_fun @ D @ E @ D @ E @ S3 @ S3 ) ) ) @ ( bNF_rel_fun @ ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D > D > D ) @ ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) > E > E > E ) @ ( ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( proces554692349s_term @ B @ C ) > E ) @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ ( ( proces554692349s_term @ A @ Pvar ) > D > D > D ) @ ( ( proces554692349s_term @ B @ C ) > E > E > E ) @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ ( D > D > D ) @ ( E > E > E ) @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ ( bNF_rel_fun @ D @ E @ ( D > D ) @ ( E > E ) @ S3 @ ( bNF_rel_fun @ D @ E @ D @ E @ S3 @ S3 ) ) ) ) @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ D @ E @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ S3 ) ) ) ) @ ( proces2117273769s_term @ Pvar @ D @ A ) @ ( proces2117273769s_term @ C @ E @ B ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_166_process__term_Ocase__distrib,axiom,
% 3.19/1.69 ! [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] :
% 3.19/1.69 ( ( H @ ( proces460752237s_term @ Pvar @ B @ A @ F1 @ F2 @ F3 @ F4 @ Process_term ) )
% 3.19/1.69 = ( proces460752237s_term @ Pvar @ C @ A
% 3.19/1.69 @ ^ [X6: Pvar] : ( H @ ( F1 @ X6 ) )
% 3.19/1.69 @ ^ [X6: proces634752977rocess @ A] : ( H @ ( F2 @ X6 ) )
% 3.19/1.69 @ ^ [X13: A,X23: proces554692349s_term @ A @ Pvar] : ( H @ ( F3 @ X13 @ X23 ) )
% 3.19/1.69 @ ^ [X13: proces554692349s_term @ A @ Pvar,X23: proces554692349s_term @ A @ Pvar] : ( H @ ( F4 @ X13 @ X23 ) )
% 3.19/1.69 @ Process_term ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_167_process__term_Opred__True,axiom,
% 3.19/1.69 ! [B: $tType,A: $tType] :
% 3.19/1.69 ( ( proces2118920028s_term @ A @ B
% 3.19/1.69 @ ^ [Uu: A] : $true
% 3.19/1.69 @ ^ [Uu: B] : $true )
% 3.19/1.69 = ( ^ [Uu: proces554692349s_term @ A @ B] : $true ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_168_process_Opred__True,axiom,
% 3.19/1.69 ! [A: $tType] :
% 3.19/1.69 ( ( proces1205983068rocess @ A
% 3.19/1.69 @ ^ [Uu: A] : $true )
% 3.19/1.69 = ( ^ [Uu: proces634752977rocess @ A] : $true ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_169_process_Odisc__eq__case_I2_J,axiom,
% 3.19/1.69 ! [A: $tType] :
% 3.19/1.69 ( ( proces401113213Choice @ A )
% 3.19/1.69 = ( proces1406508781rocess @ A @ $o
% 3.19/1.69 @ ^ [Uu: A,Uv: proces634752977rocess @ A] : $false
% 3.19/1.69 @ ^ [Uu: proces634752977rocess @ A,Uv: proces634752977rocess @ A] : $true ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_170_process_Ocase__distrib,axiom,
% 3.19/1.69 ! [B: $tType,C: $tType,A: $tType,H: B > C,F1: A > ( proces634752977rocess @ A ) > B,F2: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B,Process: proces634752977rocess @ A] :
% 3.19/1.69 ( ( H @ ( proces1406508781rocess @ A @ B @ F1 @ F2 @ Process ) )
% 3.19/1.69 = ( proces1406508781rocess @ A @ C
% 3.19/1.69 @ ^ [X13: A,X23: proces634752977rocess @ A] : ( H @ ( F1 @ X13 @ X23 ) )
% 3.19/1.69 @ ^ [X13: proces634752977rocess @ A,X23: proces634752977rocess @ A] : ( H @ ( F2 @ X13 @ X23 ) )
% 3.19/1.69 @ Process ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_171_curry__K,axiom,
% 3.19/1.69 ! [B: $tType,C: $tType,A: $tType,C3: C] :
% 3.19/1.69 ( ( product_curry @ A @ B @ C
% 3.19/1.69 @ ^ [X6: product_prod @ A @ B] : C3 )
% 3.19/1.69 = ( ^ [X6: A,Y6: B] : C3 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_172_process_Odisc__eq__case_I1_J,axiom,
% 3.19/1.69 ! [A: $tType] :
% 3.19/1.69 ( ( proces10484146Action @ A )
% 3.19/1.69 = ( proces1406508781rocess @ A @ $o
% 3.19/1.69 @ ^ [Uu: A,Uv: proces634752977rocess @ A] : $true
% 3.19/1.69 @ ^ [Uu: proces634752977rocess @ A,Uv: proces634752977rocess @ A] : $false ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_173_isACT_Osimps_I1_J,axiom,
% 3.19/1.69 ! [D: $tType,B: $tType,C: $tType,A: $tType,Sys: A > ( proces554692349s_term @ B @ C ),X: A] :
% 3.19/1.69 ( ( proces687458811_isACT @ A @ B @ C @ D @ Sys @ ( proces1627516585ss_VAR @ A @ D @ X ) )
% 3.19/1.69 = ( proces460752237s_term @ C @ $o @ B
% 3.19/1.69 @ ^ [Pvar2: C] : $false
% 3.19/1.69 @ ( proces10484146Action @ B )
% 3.19/1.69 @ ^ [A7: B,T4: proces554692349s_term @ B @ C] : $true
% 3.19/1.69 @ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
% 3.19/1.69 @ ( Sys @ X ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_174_curryD,axiom,
% 3.19/1.69 ! [A: $tType,B: $tType,F: ( product_prod @ A @ B ) > $o,A2: A,B2: B] :
% 3.19/1.69 ( ( product_curry @ A @ B @ $o @ F @ A2 @ B2 )
% 3.19/1.69 => ( F @ ( product_Pair @ A @ B @ A2 @ B2 ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_175_curryE,axiom,
% 3.19/1.69 ! [A: $tType,B: $tType,F: ( product_prod @ A @ B ) > $o,A2: A,B2: B] :
% 3.19/1.69 ( ( product_curry @ A @ B @ $o @ F @ A2 @ B2 )
% 3.19/1.69 => ( F @ ( product_Pair @ A @ B @ A2 @ B2 ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_176_process__term_Octr__transfer_I1_J,axiom,
% 3.19/1.69 ! [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 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_177_isACT_Oelims_I3_J,axiom,
% 3.19/1.69 ! [C: $tType,B: $tType,A: $tType,D: $tType,X7: A > ( proces554692349s_term @ B @ C ),Xa2: proces554692349s_term @ D @ A] :
% 3.19/1.69 ( ~ ( proces687458811_isACT @ A @ B @ C @ D @ X7 @ Xa2 )
% 3.19/1.69 => ( ! [X3: A] :
% 3.19/1.69 ( ( Xa2
% 3.19/1.69 = ( proces1627516585ss_VAR @ A @ D @ X3 ) )
% 3.19/1.69 => ( proces460752237s_term @ C @ $o @ B
% 3.19/1.69 @ ^ [Pvar2: C] : $false
% 3.19/1.69 @ ( proces10484146Action @ B )
% 3.19/1.69 @ ^ [A7: B,T4: proces554692349s_term @ B @ C] : $true
% 3.19/1.69 @ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
% 3.19/1.69 @ ( X7 @ X3 ) ) )
% 3.19/1.69 => ( ! [P4: proces634752977rocess @ D] :
% 3.19/1.69 ( ( Xa2
% 3.19/1.69 = ( proces1062592052s_PROC @ D @ A @ P4 ) )
% 3.19/1.69 => ( proces10484146Action @ D @ P4 ) )
% 3.19/1.69 => ~ ! [T12: proces554692349s_term @ D @ A,T23: proces554692349s_term @ D @ A] :
% 3.19/1.69 ( Xa2
% 3.19/1.69 != ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_178_isACT_Oelims_I2_J,axiom,
% 3.19/1.69 ! [C: $tType,B: $tType,A: $tType,D: $tType,X7: A > ( proces554692349s_term @ B @ C ),Xa2: proces554692349s_term @ D @ A] :
% 3.19/1.69 ( ( proces687458811_isACT @ A @ B @ C @ D @ X7 @ Xa2 )
% 3.19/1.69 => ( ! [X3: A] :
% 3.19/1.69 ( ( Xa2
% 3.19/1.69 = ( proces1627516585ss_VAR @ A @ D @ X3 ) )
% 3.19/1.69 => ~ ( proces460752237s_term @ C @ $o @ B
% 3.19/1.69 @ ^ [Pvar2: C] : $false
% 3.19/1.69 @ ( proces10484146Action @ B )
% 3.19/1.69 @ ^ [A7: B,T4: proces554692349s_term @ B @ C] : $true
% 3.19/1.69 @ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
% 3.19/1.69 @ ( X7 @ X3 ) ) )
% 3.19/1.69 => ( ! [P4: proces634752977rocess @ D] :
% 3.19/1.69 ( ( Xa2
% 3.19/1.69 = ( proces1062592052s_PROC @ D @ A @ P4 ) )
% 3.19/1.69 => ~ ( proces10484146Action @ D @ P4 ) )
% 3.19/1.69 => ~ ! [A3: D,T3: proces554692349s_term @ D @ A] :
% 3.19/1.69 ( Xa2
% 3.19/1.69 != ( proces1454156180ss_ACT @ D @ A @ A3 @ T3 ) ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_179_PREF_Oelims,axiom,
% 3.19/1.69 ! [A: $tType,C: $tType,B: $tType,X7: A > ( proces554692349s_term @ B @ C ),Xa2: proces554692349s_term @ B @ A,Y3: B] :
% 3.19/1.69 ( ( ( proces1708129104e_PREF @ A @ B @ C @ X7 @ Xa2 )
% 3.19/1.69 = Y3 )
% 3.19/1.69 => ( ! [X3: A] :
% 3.19/1.69 ( ( Xa2
% 3.19/1.69 = ( proces1627516585ss_VAR @ A @ B @ X3 ) )
% 3.19/1.69 => ( Y3
% 3.19/1.69 != ( proces460752237s_term @ C @ B @ B
% 3.19/1.69 @ ^ [Aa3: C] : ( undefined @ B )
% 3.19/1.69 @ ( proces745025900prefOf @ B )
% 3.19/1.69 @ ^ [A7: B,T4: proces554692349s_term @ B @ C] : A7
% 3.19/1.69 @ ^ [Aa3: proces554692349s_term @ B @ C,Ab2: proces554692349s_term @ B @ C] : ( undefined @ B )
% 3.19/1.69 @ ( X7 @ X3 ) ) ) )
% 3.19/1.69 => ( ! [P4: proces634752977rocess @ B] :
% 3.19/1.69 ( ( Xa2
% 3.19/1.69 = ( proces1062592052s_PROC @ B @ A @ P4 ) )
% 3.19/1.69 => ( Y3
% 3.19/1.69 != ( proces745025900prefOf @ B @ P4 ) ) )
% 3.19/1.69 => ( ! [A3: B] :
% 3.19/1.69 ( ? [T3: proces554692349s_term @ B @ A] :
% 3.19/1.69 ( Xa2
% 3.19/1.69 = ( proces1454156180ss_ACT @ B @ A @ A3 @ T3 ) )
% 3.19/1.69 => ( Y3 != A3 ) )
% 3.19/1.69 => ~ ( ? [V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] :
% 3.19/1.69 ( Xa2
% 3.19/1.69 = ( proces89589571ess_CH @ B @ A @ V @ Va ) )
% 3.19/1.69 => ( Y3
% 3.19/1.69 != ( undefined @ B ) ) ) ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_180_rel__funI,axiom,
% 3.19/1.69 ! [A: $tType,C: $tType,D: $tType,B: $tType,A4: A > B > $o,B6: C > D > $o,F: A > C,G: B > D] :
% 3.19/1.69 ( ! [X5: A,Y5: B] :
% 3.19/1.69 ( ( A4 @ X5 @ Y5 )
% 3.19/1.69 => ( B6 @ ( F @ X5 ) @ ( G @ Y5 ) ) )
% 3.19/1.69 => ( bNF_rel_fun @ A @ B @ C @ D @ A4 @ B6 @ F @ G ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_181_CH1_Oelims,axiom,
% 3.19/1.69 ! [A: $tType,B: $tType,X7: A > ( proces554692349s_term @ B @ A ),Xa2: proces554692349s_term @ B @ A,Y3: proces554692349s_term @ B @ A] :
% 3.19/1.69 ( ( ( proces1239275103le_CH1 @ A @ B @ X7 @ Xa2 )
% 3.19/1.69 = Y3 )
% 3.19/1.69 => ( ! [X3: A] :
% 3.19/1.69 ( ( Xa2
% 3.19/1.69 = ( proces1627516585ss_VAR @ A @ B @ X3 ) )
% 3.19/1.69 => ( Y3
% 3.19/1.69 != ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 3.19/1.69 @ ^ [A7: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 3.19/1.69 @ ^ [P7: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces979765041_ch1Of @ B @ P7 ) )
% 3.19/1.69 @ ^ [A7: B,B4: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 3.19/1.69 @ ^ [T13: proces554692349s_term @ B @ A,T24: proces554692349s_term @ B @ A] : T13
% 3.19/1.69 @ ( X7 @ X3 ) ) ) )
% 3.19/1.69 => ( ! [P4: proces634752977rocess @ B] :
% 3.19/1.69 ( ( Xa2
% 3.19/1.69 = ( proces1062592052s_PROC @ B @ A @ P4 ) )
% 3.19/1.69 => ( Y3
% 3.19/1.69 != ( proces1062592052s_PROC @ B @ A @ ( proces979765041_ch1Of @ B @ P4 ) ) ) )
% 3.19/1.69 => ( ! [T12: proces554692349s_term @ B @ A] :
% 3.19/1.69 ( ? [T23: proces554692349s_term @ B @ A] :
% 3.19/1.69 ( Xa2
% 3.19/1.69 = ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) )
% 3.19/1.69 => ( Y3 != T12 ) )
% 3.19/1.69 => ~ ( ? [V: B,Va: proces554692349s_term @ B @ A] :
% 3.19/1.69 ( Xa2
% 3.19/1.69 = ( proces1454156180ss_ACT @ B @ A @ V @ Va ) )
% 3.19/1.69 => ( Y3
% 3.19/1.69 != ( undefined @ ( proces554692349s_term @ B @ A ) ) ) ) ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_182_process__term_Octr__transfer_I4_J,axiom,
% 3.19/1.69 ! [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 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_183_process__term_Octr__transfer_I3_J,axiom,
% 3.19/1.69 ! [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 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_184_process__term_Opred__transfer,axiom,
% 3.19/1.69 ! [A: $tType,B: $tType,D: $tType,C: $tType,R1: A > C > $o,R22: B > D > $o] :
% 3.19/1.69 ( bNF_rel_fun @ ( A > $o ) @ ( C > $o ) @ ( ( B > $o ) > ( proces554692349s_term @ A @ B ) > $o ) @ ( ( D > $o ) > ( proces554692349s_term @ C @ D ) > $o )
% 3.19/1.69 @ ( bNF_rel_fun @ A @ C @ $o @ $o @ R1
% 3.19/1.69 @ ^ [Y4: $o,Z: $o] : ( Y4 = Z ) )
% 3.19/1.69 @ ( bNF_rel_fun @ ( B > $o ) @ ( D > $o ) @ ( ( proces554692349s_term @ A @ B ) > $o ) @ ( ( proces554692349s_term @ C @ D ) > $o )
% 3.19/1.69 @ ( bNF_rel_fun @ B @ D @ $o @ $o @ R22
% 3.19/1.69 @ ^ [Y4: $o,Z: $o] : ( Y4 = Z ) )
% 3.19/1.69 @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ B ) @ ( proces554692349s_term @ C @ D ) @ $o @ $o @ ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R22 )
% 3.19/1.69 @ ^ [Y4: $o,Z: $o] : ( Y4 = Z ) ) )
% 3.19/1.69 @ ( proces2118920028s_term @ A @ B )
% 3.19/1.69 @ ( proces2118920028s_term @ C @ D ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_185_process__term_Orel__transfer,axiom,
% 3.19/1.69 ! [A: $tType,C: $tType,B: $tType,D: $tType,H2: $tType,F5: $tType,G2: $tType,E: $tType,S1a: A > E > $o,S1c: C > G2 > $o,S2a: B > F5 > $o,S2c: D > H2 > $o] :
% 3.19/1.69 ( bNF_rel_fun @ ( A > C > $o ) @ ( E > G2 > $o ) @ ( ( B > D > $o ) > ( proces554692349s_term @ A @ B ) > ( proces554692349s_term @ C @ D ) > $o ) @ ( ( F5 > H2 > $o ) > ( proces554692349s_term @ E @ F5 ) > ( proces554692349s_term @ G2 @ H2 ) > $o )
% 3.19/1.69 @ ( bNF_rel_fun @ A @ E @ ( C > $o ) @ ( G2 > $o ) @ S1a
% 3.19/1.69 @ ( bNF_rel_fun @ C @ G2 @ $o @ $o @ S1c
% 3.19/1.69 @ ^ [Y4: $o,Z: $o] : ( Y4 = Z ) ) )
% 3.19/1.69 @ ( bNF_rel_fun @ ( B > D > $o ) @ ( F5 > H2 > $o ) @ ( ( proces554692349s_term @ A @ B ) > ( proces554692349s_term @ C @ D ) > $o ) @ ( ( proces554692349s_term @ E @ F5 ) > ( proces554692349s_term @ G2 @ H2 ) > $o )
% 3.19/1.69 @ ( bNF_rel_fun @ B @ F5 @ ( D > $o ) @ ( H2 > $o ) @ S2a
% 3.19/1.69 @ ( bNF_rel_fun @ D @ H2 @ $o @ $o @ S2c
% 3.19/1.69 @ ^ [Y4: $o,Z: $o] : ( Y4 = Z ) ) )
% 3.19/1.69 @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ B ) @ ( proces554692349s_term @ E @ F5 ) @ ( ( proces554692349s_term @ C @ D ) > $o ) @ ( ( proces554692349s_term @ G2 @ H2 ) > $o ) @ ( proces2029722208s_term @ A @ E @ B @ F5 @ S1a @ S2a )
% 3.19/1.69 @ ( bNF_rel_fun @ ( proces554692349s_term @ C @ D ) @ ( proces554692349s_term @ G2 @ H2 ) @ $o @ $o @ ( proces2029722208s_term @ C @ G2 @ D @ H2 @ S1c @ S2c )
% 3.19/1.69 @ ^ [Y4: $o,Z: $o] : ( Y4 = Z ) ) ) )
% 3.19/1.69 @ ( proces2029722208s_term @ A @ C @ B @ D )
% 3.19/1.69 @ ( proces2029722208s_term @ E @ G2 @ F5 @ H2 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_186_process_Opred__transfer,axiom,
% 3.19/1.69 ! [A: $tType,B: $tType,R: A > B > $o] :
% 3.19/1.69 ( bNF_rel_fun @ ( A > $o ) @ ( B > $o ) @ ( ( proces634752977rocess @ A ) > $o ) @ ( ( proces634752977rocess @ B ) > $o )
% 3.19/1.69 @ ( bNF_rel_fun @ A @ B @ $o @ $o @ R
% 3.19/1.69 @ ^ [Y4: $o,Z: $o] : ( Y4 = Z ) )
% 3.19/1.69 @ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ $o @ $o @ ( proces749077512rocess @ A @ B @ R )
% 3.19/1.69 @ ^ [Y4: $o,Z: $o] : ( Y4 = Z ) )
% 3.19/1.69 @ ( proces1205983068rocess @ A )
% 3.19/1.69 @ ( proces1205983068rocess @ B ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_187_process_Orel__transfer,axiom,
% 3.19/1.69 ! [A: $tType,B: $tType,D: $tType,C: $tType,Sa: A > C > $o,Sc: B > D > $o] :
% 3.19/1.69 ( bNF_rel_fun @ ( A > B > $o ) @ ( C > D > $o ) @ ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ B ) > $o ) @ ( ( proces634752977rocess @ C ) > ( proces634752977rocess @ D ) > $o )
% 3.19/1.69 @ ( bNF_rel_fun @ A @ C @ ( B > $o ) @ ( D > $o ) @ Sa
% 3.19/1.69 @ ( bNF_rel_fun @ B @ D @ $o @ $o @ Sc
% 3.19/1.69 @ ^ [Y4: $o,Z: $o] : ( Y4 = Z ) ) )
% 3.19/1.69 @ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ C ) @ ( ( proces634752977rocess @ B ) > $o ) @ ( ( proces634752977rocess @ D ) > $o ) @ ( proces749077512rocess @ A @ C @ Sa )
% 3.19/1.69 @ ( bNF_rel_fun @ ( proces634752977rocess @ B ) @ ( proces634752977rocess @ D ) @ $o @ $o @ ( proces749077512rocess @ B @ D @ Sc )
% 3.19/1.69 @ ^ [Y4: $o,Z: $o] : ( Y4 = Z ) ) )
% 3.19/1.69 @ ( proces749077512rocess @ A @ B )
% 3.19/1.69 @ ( proces749077512rocess @ C @ D ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_188_process_Ocase__transfer,axiom,
% 3.19/1.69 ! [A: $tType,C: $tType,D: $tType,B: $tType,R: A > B > $o,S3: 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 ) @ S3 ) ) @ ( 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 ) @ S3 ) ) @ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ C @ D @ ( proces749077512rocess @ A @ B @ R ) @ S3 ) ) @ ( proces1406508781rocess @ A @ C ) @ ( proces1406508781rocess @ B @ D ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_189_process_Octr__transfer_I2_J,axiom,
% 3.19/1.69 ! [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 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_190_process_Octr__transfer_I1_J,axiom,
% 3.19/1.69 ! [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 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_191_contOf__def,axiom,
% 3.19/1.69 ! [A: $tType] :
% 3.19/1.69 ( ( proces1778668539contOf @ A )
% 3.19/1.69 = ( proces1406508781rocess @ A @ ( proces634752977rocess @ A )
% 3.19/1.69 @ ^ [X112: A,X123: proces634752977rocess @ A] : X123
% 3.19/1.69 @ ^ [Uu2: proces634752977rocess @ A,Uv2: proces634752977rocess @ A] : ( undefined @ ( proces634752977rocess @ A ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_192_ch2Of__def,axiom,
% 3.19/1.69 ! [A: $tType] :
% 3.19/1.69 ( ( proces988026546_ch2Of @ A )
% 3.19/1.69 = ( proces1406508781rocess @ A @ ( proces634752977rocess @ A )
% 3.19/1.69 @ ^ [Uu2: A,Uv2: proces634752977rocess @ A] : ( undefined @ ( proces634752977rocess @ A ) )
% 3.19/1.69 @ ^ [X213: proces634752977rocess @ A,X224: proces634752977rocess @ A] : X224 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_193_ch1Of__def,axiom,
% 3.19/1.69 ! [A: $tType] :
% 3.19/1.69 ( ( proces979765041_ch1Of @ A )
% 3.19/1.69 = ( proces1406508781rocess @ A @ ( proces634752977rocess @ A )
% 3.19/1.69 @ ^ [Uu2: A,Uv2: proces634752977rocess @ A] : ( undefined @ ( proces634752977rocess @ A ) )
% 3.19/1.69 @ ^ [X213: proces634752977rocess @ A,X224: proces634752977rocess @ A] : X213 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_194_process_Odisc__transfer_I1_J,axiom,
% 3.19/1.69 ! [A: $tType,B: $tType,R: A > B > $o] :
% 3.19/1.69 ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ $o @ $o @ ( proces749077512rocess @ A @ B @ R )
% 3.19/1.69 @ ^ [Y4: $o,Z: $o] : ( Y4 = Z )
% 3.19/1.69 @ ( proces10484146Action @ A )
% 3.19/1.69 @ ( proces10484146Action @ B ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_195_process_Odisc__transfer_I2_J,axiom,
% 3.19/1.69 ! [A: $tType,B: $tType,R: A > B > $o] :
% 3.19/1.69 ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ $o @ $o @ ( proces749077512rocess @ A @ B @ R )
% 3.19/1.69 @ ^ [Y4: $o,Z: $o] : ( Y4 = Z )
% 3.19/1.69 @ ( proces401113213Choice @ A )
% 3.19/1.69 @ ( proces401113213Choice @ B ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_196_rel__fun__mono_H,axiom,
% 3.19/1.69 ! [A: $tType,C: $tType,D: $tType,B: $tType,Y7: A > B > $o,X: A > B > $o,A4: C > D > $o,B6: C > D > $o,F: A > C,G: B > D] :
% 3.19/1.69 ( ! [X5: A,Y5: B] :
% 3.19/1.69 ( ( Y7 @ X5 @ Y5 )
% 3.19/1.69 => ( X @ X5 @ Y5 ) )
% 3.19/1.69 => ( ! [X5: C,Y5: D] :
% 3.19/1.69 ( ( A4 @ X5 @ Y5 )
% 3.19/1.69 => ( B6 @ X5 @ Y5 ) )
% 3.19/1.69 => ( ( bNF_rel_fun @ A @ B @ C @ D @ X @ A4 @ F @ G )
% 3.19/1.69 => ( bNF_rel_fun @ A @ B @ C @ D @ Y7 @ B6 @ F @ G ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_197_rel__fun__mono,axiom,
% 3.19/1.69 ! [A: $tType,C: $tType,D: $tType,B: $tType,X: A > B > $o,A4: C > D > $o,F: A > C,G: B > D,Y7: A > B > $o,B6: C > D > $o] :
% 3.19/1.69 ( ( bNF_rel_fun @ A @ B @ C @ D @ X @ A4 @ F @ G )
% 3.19/1.69 => ( ! [X5: A,Y5: B] :
% 3.19/1.69 ( ( Y7 @ X5 @ Y5 )
% 3.19/1.69 => ( X @ X5 @ Y5 ) )
% 3.19/1.69 => ( ! [X5: C,Y5: D] :
% 3.19/1.69 ( ( A4 @ X5 @ Y5 )
% 3.19/1.69 => ( B6 @ X5 @ Y5 ) )
% 3.19/1.69 => ( bNF_rel_fun @ A @ B @ C @ D @ Y7 @ B6 @ F @ G ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_198_rel__funD,axiom,
% 3.19/1.69 ! [A: $tType,C: $tType,D: $tType,B: $tType,A4: A > B > $o,B6: C > D > $o,F: A > C,G: B > D,X7: A,Y3: B] :
% 3.19/1.69 ( ( bNF_rel_fun @ A @ B @ C @ D @ A4 @ B6 @ F @ G )
% 3.19/1.69 => ( ( A4 @ X7 @ Y3 )
% 3.19/1.69 => ( B6 @ ( F @ X7 ) @ ( G @ Y3 ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_199_prefOf__def,axiom,
% 3.19/1.69 ! [A: $tType] :
% 3.19/1.69 ( ( proces745025900prefOf @ A )
% 3.19/1.69 = ( proces1406508781rocess @ A @ A
% 3.19/1.69 @ ^ [X112: A,X123: proces634752977rocess @ A] : X112
% 3.19/1.69 @ ^ [Uu2: proces634752977rocess @ A,Uv2: proces634752977rocess @ A] : ( undefined @ A ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_200_CONT_Osimps_I1_J,axiom,
% 3.19/1.69 ! [B: $tType,A: $tType,Sys: A > ( proces554692349s_term @ B @ A ),X: A] :
% 3.19/1.69 ( ( proces126235999e_CONT @ A @ B @ Sys @ ( proces1627516585ss_VAR @ A @ B @ X ) )
% 3.19/1.69 = ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 3.19/1.69 @ ^ [Aa3: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 3.19/1.69 @ ^ [P7: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces1778668539contOf @ B @ P7 ) )
% 3.19/1.69 @ ^ [A7: B,T4: proces554692349s_term @ B @ A] : T4
% 3.19/1.69 @ ^ [Aa3: proces554692349s_term @ B @ A,Ab2: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 3.19/1.69 @ ( Sys @ X ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_201_CH1_Osimps_I1_J,axiom,
% 3.19/1.69 ! [B: $tType,A: $tType,Sys: A > ( proces554692349s_term @ B @ A ),X: A] :
% 3.19/1.69 ( ( proces1239275103le_CH1 @ A @ B @ Sys @ ( proces1627516585ss_VAR @ A @ B @ X ) )
% 3.19/1.69 = ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 3.19/1.69 @ ^ [A7: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 3.19/1.69 @ ^ [P7: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces979765041_ch1Of @ B @ P7 ) )
% 3.19/1.69 @ ^ [A7: B,B4: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 3.19/1.69 @ ^ [T13: proces554692349s_term @ B @ A,T24: proces554692349s_term @ B @ A] : T13
% 3.19/1.69 @ ( Sys @ X ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_202_CH2_Osimps_I1_J,axiom,
% 3.19/1.69 ! [B: $tType,A: $tType,Sys: A > ( proces554692349s_term @ B @ A ),X: A] :
% 3.19/1.69 ( ( proces1239275104le_CH2 @ A @ B @ Sys @ ( proces1627516585ss_VAR @ A @ B @ X ) )
% 3.19/1.69 = ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 3.19/1.69 @ ^ [A7: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 3.19/1.69 @ ^ [P7: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces988026546_ch2Of @ B @ P7 ) )
% 3.19/1.69 @ ^ [A7: B,B4: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 3.19/1.69 @ ^ [T13: proces554692349s_term @ B @ A,T24: proces554692349s_term @ B @ A] : T24
% 3.19/1.69 @ ( Sys @ X ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_203_PREF_Osimps_I1_J,axiom,
% 3.19/1.69 ! [B: $tType,C: $tType,A: $tType,Sys: A > ( proces554692349s_term @ B @ C ),X: A] :
% 3.19/1.69 ( ( proces1708129104e_PREF @ A @ B @ C @ Sys @ ( proces1627516585ss_VAR @ A @ B @ X ) )
% 3.19/1.69 = ( proces460752237s_term @ C @ B @ B
% 3.19/1.69 @ ^ [Aa3: C] : ( undefined @ B )
% 3.19/1.69 @ ( proces745025900prefOf @ B )
% 3.19/1.69 @ ^ [A7: B,T4: proces554692349s_term @ B @ C] : A7
% 3.19/1.69 @ ^ [Aa3: proces554692349s_term @ B @ C,Ab2: proces554692349s_term @ B @ C] : ( undefined @ B )
% 3.19/1.69 @ ( Sys @ X ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_204_CONT_Oelims,axiom,
% 3.19/1.69 ! [A: $tType,B: $tType,X7: A > ( proces554692349s_term @ B @ A ),Xa2: proces554692349s_term @ B @ A,Y3: proces554692349s_term @ B @ A] :
% 3.19/1.69 ( ( ( proces126235999e_CONT @ A @ B @ X7 @ Xa2 )
% 3.19/1.69 = Y3 )
% 3.19/1.69 => ( ! [X3: A] :
% 3.19/1.69 ( ( Xa2
% 3.19/1.69 = ( proces1627516585ss_VAR @ A @ B @ X3 ) )
% 3.19/1.69 => ( Y3
% 3.19/1.69 != ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 3.19/1.69 @ ^ [Aa3: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 3.19/1.69 @ ^ [P7: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces1778668539contOf @ B @ P7 ) )
% 3.19/1.69 @ ^ [A7: B,T4: proces554692349s_term @ B @ A] : T4
% 3.19/1.69 @ ^ [Aa3: proces554692349s_term @ B @ A,Ab2: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 3.19/1.69 @ ( X7 @ X3 ) ) ) )
% 3.19/1.69 => ( ! [P4: proces634752977rocess @ B] :
% 3.19/1.69 ( ( Xa2
% 3.19/1.69 = ( proces1062592052s_PROC @ B @ A @ P4 ) )
% 3.19/1.69 => ( Y3
% 3.19/1.69 != ( proces1062592052s_PROC @ B @ A @ ( proces1778668539contOf @ B @ P4 ) ) ) )
% 3.19/1.69 => ( ! [A3: B,T3: proces554692349s_term @ B @ A] :
% 3.19/1.69 ( ( Xa2
% 3.19/1.69 = ( proces1454156180ss_ACT @ B @ A @ A3 @ T3 ) )
% 3.19/1.69 => ( Y3 != T3 ) )
% 3.19/1.69 => ~ ( ? [V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] :
% 3.19/1.69 ( Xa2
% 3.19/1.69 = ( proces89589571ess_CH @ B @ A @ V @ Va ) )
% 3.19/1.69 => ( Y3
% 3.19/1.69 != ( undefined @ ( proces554692349s_term @ B @ A ) ) ) ) ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_205_CH2_Oelims,axiom,
% 3.19/1.69 ! [A: $tType,B: $tType,X7: A > ( proces554692349s_term @ B @ A ),Xa2: proces554692349s_term @ B @ A,Y3: proces554692349s_term @ B @ A] :
% 3.19/1.69 ( ( ( proces1239275104le_CH2 @ A @ B @ X7 @ Xa2 )
% 3.19/1.69 = Y3 )
% 3.19/1.69 => ( ! [X3: A] :
% 3.19/1.69 ( ( Xa2
% 3.19/1.69 = ( proces1627516585ss_VAR @ A @ B @ X3 ) )
% 3.19/1.69 => ( Y3
% 3.19/1.69 != ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 3.19/1.69 @ ^ [A7: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 3.19/1.69 @ ^ [P7: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces988026546_ch2Of @ B @ P7 ) )
% 3.19/1.69 @ ^ [A7: B,B4: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 3.19/1.69 @ ^ [T13: proces554692349s_term @ B @ A,T24: proces554692349s_term @ B @ A] : T24
% 3.19/1.69 @ ( X7 @ X3 ) ) ) )
% 3.19/1.69 => ( ! [P4: proces634752977rocess @ B] :
% 3.19/1.69 ( ( Xa2
% 3.19/1.69 = ( proces1062592052s_PROC @ B @ A @ P4 ) )
% 3.19/1.69 => ( Y3
% 3.19/1.69 != ( proces1062592052s_PROC @ B @ A @ ( proces988026546_ch2Of @ B @ P4 ) ) ) )
% 3.19/1.69 => ( ! [T12: proces554692349s_term @ B @ A,T23: proces554692349s_term @ B @ A] :
% 3.19/1.69 ( ( Xa2
% 3.19/1.69 = ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) )
% 3.19/1.69 => ( Y3 != T23 ) )
% 3.19/1.69 => ~ ( ? [V: B,Va: proces554692349s_term @ B @ A] :
% 3.19/1.69 ( Xa2
% 3.19/1.69 = ( proces1454156180ss_ACT @ B @ A @ V @ Va ) )
% 3.19/1.69 => ( Y3
% 3.19/1.69 != ( undefined @ ( proces554692349s_term @ B @ A ) ) ) ) ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_206_Let__transfer,axiom,
% 3.19/1.69 ! [A: $tType,C: $tType,D: $tType,B: $tType,A4: A > B > $o,B6: C > D > $o] :
% 3.19/1.69 ( bNF_rel_fun @ A @ B @ ( ( A > C ) > C ) @ ( ( B > D ) > D ) @ A4 @ ( bNF_rel_fun @ ( A > C ) @ ( B > D ) @ C @ D @ ( bNF_rel_fun @ A @ B @ C @ D @ A4 @ B6 ) @ B6 )
% 3.19/1.69 @ ^ [S4: A,F7: A > C] : ( F7 @ S4 )
% 3.19/1.69 @ ^ [S4: B,F7: B > D] : ( F7 @ S4 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_207_let__rsp,axiom,
% 3.19/1.69 ! [A: $tType,C: $tType,D: $tType,B: $tType,R1: A > B > $o,R22: C > D > $o] :
% 3.19/1.69 ( bNF_rel_fun @ A @ B @ ( ( A > C ) > C ) @ ( ( B > D ) > D ) @ R1 @ ( bNF_rel_fun @ ( A > C ) @ ( B > D ) @ C @ D @ ( bNF_rel_fun @ A @ B @ C @ D @ R1 @ R22 ) @ R22 )
% 3.19/1.69 @ ^ [S4: A,F7: A > C] : ( F7 @ S4 )
% 3.19/1.69 @ ^ [S4: B,F7: B > D] : ( F7 @ S4 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_208_CH2_Opelims,axiom,
% 3.19/1.69 ! [A: $tType,B: $tType,X7: A > ( proces554692349s_term @ B @ A ),Xa2: proces554692349s_term @ B @ A,Y3: proces554692349s_term @ B @ A] :
% 3.19/1.69 ( ( ( proces1239275104le_CH2 @ A @ B @ X7 @ Xa2 )
% 3.19/1.69 = Y3 )
% 3.19/1.69 => ( ( 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 ) @ X7 @ Xa2 ) )
% 3.19/1.69 => ( ! [X3: A] :
% 3.19/1.69 ( ( Xa2
% 3.19/1.69 = ( proces1627516585ss_VAR @ A @ B @ X3 ) )
% 3.19/1.69 => ( ( Y3
% 3.19/1.69 = ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 3.19/1.69 @ ^ [A7: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 3.19/1.69 @ ^ [P7: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces988026546_ch2Of @ B @ P7 ) )
% 3.19/1.69 @ ^ [A7: B,B4: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 3.19/1.69 @ ^ [T13: proces554692349s_term @ B @ A,T24: proces554692349s_term @ B @ A] : T24
% 3.19/1.69 @ ( X7 @ X3 ) ) )
% 3.19/1.69 => ~ ( 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 ) @ X7 @ ( proces1627516585ss_VAR @ A @ B @ X3 ) ) ) ) )
% 3.19/1.69 => ( ! [P4: proces634752977rocess @ B] :
% 3.19/1.69 ( ( Xa2
% 3.19/1.69 = ( proces1062592052s_PROC @ B @ A @ P4 ) )
% 3.19/1.69 => ( ( Y3
% 3.19/1.69 = ( proces1062592052s_PROC @ B @ A @ ( proces988026546_ch2Of @ B @ P4 ) ) )
% 3.19/1.69 => ~ ( 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 ) @ X7 @ ( proces1062592052s_PROC @ B @ A @ P4 ) ) ) ) )
% 3.19/1.69 => ( ! [T12: proces554692349s_term @ B @ A,T23: proces554692349s_term @ B @ A] :
% 3.19/1.69 ( ( Xa2
% 3.19/1.69 = ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) )
% 3.19/1.69 => ( ( Y3 = T23 )
% 3.19/1.69 => ~ ( 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 ) @ X7 @ ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) ) ) ) )
% 3.19/1.69 => ~ ! [V: B,Va: proces554692349s_term @ B @ A] :
% 3.19/1.69 ( ( Xa2
% 3.19/1.69 = ( proces1454156180ss_ACT @ B @ A @ V @ Va ) )
% 3.19/1.69 => ( ( Y3
% 3.19/1.69 = ( undefined @ ( proces554692349s_term @ B @ A ) ) )
% 3.19/1.69 => ~ ( 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 ) @ X7 @ ( proces1454156180ss_ACT @ B @ A @ V @ Va ) ) ) ) ) ) ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_209_rel__funE,axiom,
% 3.19/1.69 ! [A: $tType,C: $tType,D: $tType,B: $tType,A4: A > B > $o,B6: C > D > $o,F: A > C,G: B > D,X7: A,Y3: B] :
% 3.19/1.69 ( ( bNF_rel_fun @ A @ B @ C @ D @ A4 @ B6 @ F @ G )
% 3.19/1.69 => ( ( A4 @ X7 @ Y3 )
% 3.19/1.69 => ( B6 @ ( F @ X7 ) @ ( G @ Y3 ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_210_rel__funD2,axiom,
% 3.19/1.69 ! [B: $tType,C: $tType,A: $tType,A4: A > A > $o,B6: B > C > $o,F: A > B,G: A > C,X7: A] :
% 3.19/1.69 ( ( bNF_rel_fun @ A @ A @ B @ C @ A4 @ B6 @ F @ G )
% 3.19/1.69 => ( ( A4 @ X7 @ X7 )
% 3.19/1.69 => ( B6 @ ( F @ X7 ) @ ( G @ X7 ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_211_CH1_Opelims,axiom,
% 3.19/1.69 ! [A: $tType,B: $tType,X7: A > ( proces554692349s_term @ B @ A ),Xa2: proces554692349s_term @ B @ A,Y3: proces554692349s_term @ B @ A] :
% 3.19/1.69 ( ( ( proces1239275103le_CH1 @ A @ B @ X7 @ Xa2 )
% 3.19/1.69 = Y3 )
% 3.19/1.69 => ( ( 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 ) @ X7 @ Xa2 ) )
% 3.19/1.69 => ( ! [X3: A] :
% 3.19/1.69 ( ( Xa2
% 3.19/1.69 = ( proces1627516585ss_VAR @ A @ B @ X3 ) )
% 3.19/1.69 => ( ( Y3
% 3.19/1.69 = ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 3.19/1.69 @ ^ [A7: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 3.19/1.69 @ ^ [P7: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces979765041_ch1Of @ B @ P7 ) )
% 3.19/1.69 @ ^ [A7: B,B4: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 3.19/1.69 @ ^ [T13: proces554692349s_term @ B @ A,T24: proces554692349s_term @ B @ A] : T13
% 3.19/1.69 @ ( X7 @ X3 ) ) )
% 3.19/1.69 => ~ ( 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 ) @ X7 @ ( proces1627516585ss_VAR @ A @ B @ X3 ) ) ) ) )
% 3.19/1.69 => ( ! [P4: proces634752977rocess @ B] :
% 3.19/1.69 ( ( Xa2
% 3.19/1.69 = ( proces1062592052s_PROC @ B @ A @ P4 ) )
% 3.19/1.69 => ( ( Y3
% 3.19/1.69 = ( proces1062592052s_PROC @ B @ A @ ( proces979765041_ch1Of @ B @ P4 ) ) )
% 3.19/1.69 => ~ ( 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 ) @ X7 @ ( proces1062592052s_PROC @ B @ A @ P4 ) ) ) ) )
% 3.19/1.69 => ( ! [T12: proces554692349s_term @ B @ A,T23: proces554692349s_term @ B @ A] :
% 3.19/1.69 ( ( Xa2
% 3.19/1.69 = ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) )
% 3.19/1.69 => ( ( Y3 = T12 )
% 3.19/1.69 => ~ ( 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 ) @ X7 @ ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) ) ) ) )
% 3.19/1.69 => ~ ! [V: B,Va: proces554692349s_term @ B @ A] :
% 3.19/1.69 ( ( Xa2
% 3.19/1.69 = ( proces1454156180ss_ACT @ B @ A @ V @ Va ) )
% 3.19/1.69 => ( ( Y3
% 3.19/1.69 = ( undefined @ ( proces554692349s_term @ B @ A ) ) )
% 3.19/1.69 => ~ ( 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 ) @ X7 @ ( proces1454156180ss_ACT @ B @ A @ V @ Va ) ) ) ) ) ) ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_212_CONT_Opelims,axiom,
% 3.19/1.69 ! [A: $tType,B: $tType,X7: A > ( proces554692349s_term @ B @ A ),Xa2: proces554692349s_term @ B @ A,Y3: proces554692349s_term @ B @ A] :
% 3.19/1.69 ( ( ( proces126235999e_CONT @ A @ B @ X7 @ Xa2 )
% 3.19/1.69 = Y3 )
% 3.19/1.69 => ( ( 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 ) @ X7 @ Xa2 ) )
% 3.19/1.69 => ( ! [X3: A] :
% 3.19/1.69 ( ( Xa2
% 3.19/1.69 = ( proces1627516585ss_VAR @ A @ B @ X3 ) )
% 3.19/1.69 => ( ( Y3
% 3.19/1.69 = ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 3.19/1.69 @ ^ [Aa3: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 3.19/1.69 @ ^ [P7: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces1778668539contOf @ B @ P7 ) )
% 3.19/1.69 @ ^ [A7: B,T4: proces554692349s_term @ B @ A] : T4
% 3.19/1.69 @ ^ [Aa3: proces554692349s_term @ B @ A,Ab2: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 3.19/1.69 @ ( X7 @ X3 ) ) )
% 3.19/1.69 => ~ ( 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 ) @ X7 @ ( proces1627516585ss_VAR @ A @ B @ X3 ) ) ) ) )
% 3.19/1.69 => ( ! [P4: proces634752977rocess @ B] :
% 3.19/1.69 ( ( Xa2
% 3.19/1.69 = ( proces1062592052s_PROC @ B @ A @ P4 ) )
% 3.19/1.69 => ( ( Y3
% 3.19/1.69 = ( proces1062592052s_PROC @ B @ A @ ( proces1778668539contOf @ B @ P4 ) ) )
% 3.19/1.69 => ~ ( 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 ) @ X7 @ ( proces1062592052s_PROC @ B @ A @ P4 ) ) ) ) )
% 3.19/1.69 => ( ! [A3: B,T3: proces554692349s_term @ B @ A] :
% 3.19/1.69 ( ( Xa2
% 3.19/1.69 = ( proces1454156180ss_ACT @ B @ A @ A3 @ T3 ) )
% 3.19/1.69 => ( ( Y3 = T3 )
% 3.19/1.69 => ~ ( 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 ) @ X7 @ ( proces1454156180ss_ACT @ B @ A @ A3 @ T3 ) ) ) ) )
% 3.19/1.69 => ~ ! [V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] :
% 3.19/1.69 ( ( Xa2
% 3.19/1.69 = ( proces89589571ess_CH @ B @ A @ V @ Va ) )
% 3.19/1.69 => ( ( Y3
% 3.19/1.69 = ( undefined @ ( proces554692349s_term @ B @ A ) ) )
% 3.19/1.69 => ~ ( 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 ) @ X7 @ ( proces89589571ess_CH @ B @ A @ V @ Va ) ) ) ) ) ) ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_213_PREF_Opelims,axiom,
% 3.19/1.69 ! [C: $tType,A: $tType,B: $tType,X7: A > ( proces554692349s_term @ B @ C ),Xa2: proces554692349s_term @ B @ A,Y3: B] :
% 3.19/1.69 ( ( ( proces1708129104e_PREF @ A @ B @ C @ X7 @ Xa2 )
% 3.19/1.69 = Y3 )
% 3.19/1.69 => ( ( 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 ) @ X7 @ Xa2 ) )
% 3.19/1.69 => ( ! [X3: A] :
% 3.19/1.69 ( ( Xa2
% 3.19/1.69 = ( proces1627516585ss_VAR @ A @ B @ X3 ) )
% 3.19/1.69 => ( ( Y3
% 3.19/1.69 = ( proces460752237s_term @ C @ B @ B
% 3.19/1.69 @ ^ [Aa3: C] : ( undefined @ B )
% 3.19/1.69 @ ( proces745025900prefOf @ B )
% 3.19/1.69 @ ^ [A7: B,T4: proces554692349s_term @ B @ C] : A7
% 3.19/1.69 @ ^ [Aa3: proces554692349s_term @ B @ C,Ab2: proces554692349s_term @ B @ C] : ( undefined @ B )
% 3.19/1.69 @ ( X7 @ X3 ) ) )
% 3.19/1.69 => ~ ( 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 ) @ X7 @ ( proces1627516585ss_VAR @ A @ B @ X3 ) ) ) ) )
% 3.19/1.69 => ( ! [P4: proces634752977rocess @ B] :
% 3.19/1.69 ( ( Xa2
% 3.19/1.69 = ( proces1062592052s_PROC @ B @ A @ P4 ) )
% 3.19/1.69 => ( ( Y3
% 3.19/1.69 = ( proces745025900prefOf @ B @ P4 ) )
% 3.19/1.69 => ~ ( 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 ) @ X7 @ ( proces1062592052s_PROC @ B @ A @ P4 ) ) ) ) )
% 3.19/1.69 => ( ! [A3: B,T3: proces554692349s_term @ B @ A] :
% 3.19/1.69 ( ( Xa2
% 3.19/1.69 = ( proces1454156180ss_ACT @ B @ A @ A3 @ T3 ) )
% 3.19/1.69 => ( ( Y3 = A3 )
% 3.19/1.69 => ~ ( 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 ) @ X7 @ ( proces1454156180ss_ACT @ B @ A @ A3 @ T3 ) ) ) ) )
% 3.19/1.69 => ~ ! [V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] :
% 3.19/1.69 ( ( Xa2
% 3.19/1.69 = ( proces89589571ess_CH @ B @ A @ V @ Va ) )
% 3.19/1.69 => ( ( Y3
% 3.19/1.69 = ( undefined @ B ) )
% 3.19/1.69 => ~ ( 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 ) @ X7 @ ( proces89589571ess_CH @ B @ A @ V @ Va ) ) ) ) ) ) ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_214_isACT_Opelims_I1_J,axiom,
% 3.19/1.69 ! [B: $tType,C: $tType,A: $tType,D: $tType,X7: A > ( proces554692349s_term @ B @ C ),Xa2: proces554692349s_term @ D @ A,Y3: $o] :
% 3.19/1.69 ( ( ( proces687458811_isACT @ A @ B @ C @ D @ X7 @ Xa2 )
% 3.19/1.69 = Y3 )
% 3.19/1.69 => ( ( 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 ) @ X7 @ Xa2 ) )
% 3.19/1.69 => ( ! [X3: A] :
% 3.19/1.69 ( ( Xa2
% 3.19/1.69 = ( proces1627516585ss_VAR @ A @ D @ X3 ) )
% 3.19/1.69 => ( ( Y3
% 3.19/1.69 = ( proces460752237s_term @ C @ $o @ B
% 3.19/1.69 @ ^ [Pvar2: C] : $false
% 3.19/1.69 @ ( proces10484146Action @ B )
% 3.19/1.69 @ ^ [A7: B,T4: proces554692349s_term @ B @ C] : $true
% 3.19/1.69 @ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
% 3.19/1.69 @ ( X7 @ X3 ) ) )
% 3.19/1.69 => ~ ( 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 ) @ X7 @ ( proces1627516585ss_VAR @ A @ D @ X3 ) ) ) ) )
% 3.19/1.69 => ( ! [P4: proces634752977rocess @ D] :
% 3.19/1.69 ( ( Xa2
% 3.19/1.69 = ( proces1062592052s_PROC @ D @ A @ P4 ) )
% 3.19/1.69 => ( ( Y3
% 3.19/1.69 = ( proces10484146Action @ D @ P4 ) )
% 3.19/1.69 => ~ ( 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 ) @ X7 @ ( proces1062592052s_PROC @ D @ A @ P4 ) ) ) ) )
% 3.19/1.69 => ( ! [A3: D,T3: proces554692349s_term @ D @ A] :
% 3.19/1.69 ( ( Xa2
% 3.19/1.69 = ( proces1454156180ss_ACT @ D @ A @ A3 @ T3 ) )
% 3.19/1.69 => ( Y3
% 3.19/1.69 => ~ ( 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 ) @ X7 @ ( proces1454156180ss_ACT @ D @ A @ A3 @ T3 ) ) ) ) )
% 3.19/1.69 => ~ ! [T12: proces554692349s_term @ D @ A,T23: proces554692349s_term @ D @ A] :
% 3.19/1.69 ( ( Xa2
% 3.19/1.69 = ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) )
% 3.19/1.69 => ( ~ Y3
% 3.19/1.69 => ~ ( 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 ) @ X7 @ ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) ) ) ) ) ) ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_215_isACT_Opelims_I3_J,axiom,
% 3.19/1.69 ! [B: $tType,C: $tType,A: $tType,D: $tType,X7: A > ( proces554692349s_term @ B @ C ),Xa2: proces554692349s_term @ D @ A] :
% 3.19/1.69 ( ~ ( proces687458811_isACT @ A @ B @ C @ D @ X7 @ Xa2 )
% 3.19/1.69 => ( ( 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 ) @ X7 @ Xa2 ) )
% 3.19/1.69 => ( ! [X3: A] :
% 3.19/1.69 ( ( Xa2
% 3.19/1.69 = ( proces1627516585ss_VAR @ A @ D @ X3 ) )
% 3.19/1.69 => ( ( 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 ) @ X7 @ ( proces1627516585ss_VAR @ A @ D @ X3 ) ) )
% 3.19/1.69 => ( proces460752237s_term @ C @ $o @ B
% 3.19/1.69 @ ^ [Pvar2: C] : $false
% 3.19/1.69 @ ( proces10484146Action @ B )
% 3.19/1.69 @ ^ [A7: B,T4: proces554692349s_term @ B @ C] : $true
% 3.19/1.69 @ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
% 3.19/1.69 @ ( X7 @ X3 ) ) ) )
% 3.19/1.69 => ( ! [P4: proces634752977rocess @ D] :
% 3.19/1.69 ( ( Xa2
% 3.19/1.69 = ( proces1062592052s_PROC @ D @ A @ P4 ) )
% 3.19/1.69 => ( ( 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 ) @ X7 @ ( proces1062592052s_PROC @ D @ A @ P4 ) ) )
% 3.19/1.69 => ( proces10484146Action @ D @ P4 ) ) )
% 3.19/1.69 => ~ ! [T12: proces554692349s_term @ D @ A,T23: proces554692349s_term @ D @ A] :
% 3.19/1.69 ( ( Xa2
% 3.19/1.69 = ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) )
% 3.19/1.69 => ~ ( 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 ) @ X7 @ ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) ) ) ) ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_216_isACT_Opelims_I2_J,axiom,
% 3.19/1.69 ! [B: $tType,C: $tType,A: $tType,D: $tType,X7: A > ( proces554692349s_term @ B @ C ),Xa2: proces554692349s_term @ D @ A] :
% 3.19/1.69 ( ( proces687458811_isACT @ A @ B @ C @ D @ X7 @ Xa2 )
% 3.19/1.69 => ( ( 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 ) @ X7 @ Xa2 ) )
% 3.19/1.69 => ( ! [X3: A] :
% 3.19/1.69 ( ( Xa2
% 3.19/1.69 = ( proces1627516585ss_VAR @ A @ D @ X3 ) )
% 3.19/1.69 => ( ( 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 ) @ X7 @ ( proces1627516585ss_VAR @ A @ D @ X3 ) ) )
% 3.19/1.69 => ~ ( proces460752237s_term @ C @ $o @ B
% 3.19/1.69 @ ^ [Pvar2: C] : $false
% 3.19/1.69 @ ( proces10484146Action @ B )
% 3.19/1.69 @ ^ [A7: B,T4: proces554692349s_term @ B @ C] : $true
% 3.19/1.69 @ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
% 3.19/1.69 @ ( X7 @ X3 ) ) ) )
% 3.19/1.69 => ( ! [P4: proces634752977rocess @ D] :
% 3.19/1.69 ( ( Xa2
% 3.19/1.69 = ( proces1062592052s_PROC @ D @ A @ P4 ) )
% 3.19/1.69 => ( ( 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 ) @ X7 @ ( proces1062592052s_PROC @ D @ A @ P4 ) ) )
% 3.19/1.69 => ~ ( proces10484146Action @ D @ P4 ) ) )
% 3.19/1.69 => ~ ! [A3: D,T3: proces554692349s_term @ D @ A] :
% 3.19/1.69 ( ( Xa2
% 3.19/1.69 = ( proces1454156180ss_ACT @ D @ A @ A3 @ T3 ) )
% 3.19/1.69 => ~ ( 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 ) @ X7 @ ( proces1454156180ss_ACT @ D @ A @ A3 @ T3 ) ) ) ) ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_217_fun_Orel__transfer,axiom,
% 3.19/1.69 ! [B: $tType,A: $tType,C: $tType,E: $tType,D: $tType,Sa: A > C > $o,Sc: B > E > $o] :
% 3.19/1.69 ( bNF_rel_fun @ ( A > B > $o ) @ ( C > E > $o ) @ ( ( D > A ) > ( D > B ) > $o ) @ ( ( D > C ) > ( D > E ) > $o )
% 3.19/1.69 @ ( bNF_rel_fun @ A @ C @ ( B > $o ) @ ( E > $o ) @ Sa
% 3.19/1.69 @ ( bNF_rel_fun @ B @ E @ $o @ $o @ Sc
% 3.19/1.69 @ ^ [Y4: $o,Z: $o] : ( Y4 = Z ) ) )
% 3.19/1.69 @ ( bNF_rel_fun @ ( D > A ) @ ( D > C ) @ ( ( D > B ) > $o ) @ ( ( D > E ) > $o )
% 3.19/1.69 @ ( bNF_rel_fun @ D @ D @ A @ C
% 3.19/1.69 @ ^ [Y4: D,Z: D] : ( Y4 = Z )
% 3.19/1.69 @ Sa )
% 3.19/1.69 @ ( bNF_rel_fun @ ( D > B ) @ ( D > E ) @ $o @ $o
% 3.19/1.69 @ ( bNF_rel_fun @ D @ D @ B @ E
% 3.19/1.69 @ ^ [Y4: D,Z: D] : ( Y4 = Z )
% 3.19/1.69 @ Sc )
% 3.19/1.69 @ ^ [Y4: $o,Z: $o] : ( Y4 = Z ) ) )
% 3.19/1.69 @ ( bNF_rel_fun @ D @ D @ A @ B
% 3.19/1.69 @ ^ [Y4: D,Z: D] : ( Y4 = Z ) )
% 3.19/1.69 @ ( bNF_rel_fun @ D @ D @ C @ E
% 3.19/1.69 @ ^ [Y4: D,Z: D] : ( Y4 = Z ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_218_If__transfer,axiom,
% 3.19/1.69 ! [A: $tType,B: $tType,A4: A > B > $o] :
% 3.19/1.69 ( bNF_rel_fun @ $o @ $o @ ( A > A > A ) @ ( B > B > B )
% 3.19/1.69 @ ^ [Y4: $o,Z: $o] : ( Y4 = Z )
% 3.19/1.69 @ ( bNF_rel_fun @ A @ B @ ( A > A ) @ ( B > B ) @ A4 @ ( bNF_rel_fun @ A @ B @ A @ B @ A4 @ A4 ) )
% 3.19/1.69 @ ( if @ A )
% 3.19/1.69 @ ( if @ B ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_219_fun_Orel__refl,axiom,
% 3.19/1.69 ! [B: $tType,D: $tType,Ra: B > B > $o,X7: D > B] :
% 3.19/1.69 ( ! [X5: B] : ( Ra @ X5 @ X5 )
% 3.19/1.69 => ( bNF_rel_fun @ D @ D @ B @ B
% 3.19/1.69 @ ^ [Y4: D,Z: D] : ( Y4 = Z )
% 3.19/1.69 @ Ra
% 3.19/1.69 @ X7
% 3.19/1.69 @ X7 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_220_fun_Orel__eq,axiom,
% 3.19/1.69 ! [A: $tType,D: $tType] :
% 3.19/1.69 ( ( bNF_rel_fun @ D @ D @ A @ A
% 3.19/1.69 @ ^ [Y4: D,Z: D] : ( Y4 = Z )
% 3.19/1.69 @ ^ [Y4: A,Z: A] : ( Y4 = Z ) )
% 3.19/1.69 = ( ^ [Y4: D > A,Z: D > A] : ( Y4 = Z ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_221_rel__fun__def__butlast,axiom,
% 3.19/1.69 ! [B: $tType,D: $tType,C: $tType,E: $tType,F5: $tType,A: $tType,R: A > B > $o,S3: C > E > $o,T2: D > F5 > $o,F: A > C > D,G: B > E > F5] :
% 3.19/1.69 ( ( bNF_rel_fun @ A @ B @ ( C > D ) @ ( E > F5 ) @ R @ ( bNF_rel_fun @ C @ E @ D @ F5 @ S3 @ T2 ) @ F @ G )
% 3.19/1.69 = ( ! [X6: A,Y6: B] :
% 3.19/1.69 ( ( R @ X6 @ Y6 )
% 3.19/1.69 => ( bNF_rel_fun @ C @ E @ D @ F5 @ S3 @ T2 @ ( F @ X6 ) @ ( G @ Y6 ) ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_222_process_Ocorec__transfer,axiom,
% 3.19/1.69 ! [C: $tType,A: $tType,B: $tType,D: $tType,S3: C > D > $o,R: A > B > $o] :
% 3.19/1.69 ( 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 ) )
% 3.19/1.69 @ ( bNF_rel_fun @ C @ D @ $o @ $o @ S3
% 3.19/1.69 @ ^ [Y4: $o,Z: $o] : ( Y4 = Z ) )
% 3.19/1.69 @ ( 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 @ S3 @ R )
% 3.19/1.69 @ ( 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 ) )
% 3.19/1.69 @ ( bNF_rel_fun @ C @ D @ $o @ $o @ S3
% 3.19/1.69 @ ^ [Y4: $o,Z: $o] : ( Y4 = Z ) )
% 3.19/1.69 @ ( 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 ) @ S3 @ ( proces749077512rocess @ A @ B @ R ) )
% 3.19/1.69 @ ( 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 @ S3 @ S3 )
% 3.19/1.69 @ ( 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 ) )
% 3.19/1.69 @ ( bNF_rel_fun @ C @ D @ $o @ $o @ S3
% 3.19/1.69 @ ^ [Y4: $o,Z: $o] : ( Y4 = Z ) )
% 3.19/1.69 @ ( 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 ) @ S3 @ ( proces749077512rocess @ A @ B @ R ) )
% 3.19/1.69 @ ( 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 @ S3 @ S3 )
% 3.19/1.69 @ ( bNF_rel_fun @ ( C > $o ) @ ( D > $o ) @ ( ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > C > ( proces634752977rocess @ A ) ) @ ( ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > D > ( proces634752977rocess @ B ) )
% 3.19/1.69 @ ( bNF_rel_fun @ C @ D @ $o @ $o @ S3
% 3.19/1.69 @ ^ [Y4: $o,Z: $o] : ( Y4 = Z ) )
% 3.19/1.69 @ ( 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 ) @ S3 @ ( proces749077512rocess @ A @ B @ R ) ) @ ( bNF_rel_fun @ ( C > C ) @ ( D > D ) @ ( C > ( proces634752977rocess @ A ) ) @ ( D > ( proces634752977rocess @ B ) ) @ ( bNF_rel_fun @ C @ D @ C @ D @ S3 @ S3 ) @ ( bNF_rel_fun @ C @ D @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ S3 @ ( proces749077512rocess @ A @ B @ R ) ) ) ) ) ) ) ) ) ) ) )
% 3.19/1.69 @ ( proces894737309rocess @ C @ A )
% 3.19/1.69 @ ( proces894737309rocess @ D @ B ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_223_map__fun__parametric,axiom,
% 3.19/1.69 ! [A: $tType,B: $tType,E: $tType,F5: $tType,H2: $tType,G2: $tType,D: $tType,C: $tType,A4: A > C > $o,B6: B > D > $o,C5: E > G2 > $o,D3: F5 > H2 > $o] : ( bNF_rel_fun @ ( A > B ) @ ( C > D ) @ ( ( E > F5 ) > ( B > E ) > A > F5 ) @ ( ( G2 > H2 ) > ( D > G2 ) > C > H2 ) @ ( bNF_rel_fun @ A @ C @ B @ D @ A4 @ B6 ) @ ( bNF_rel_fun @ ( E > F5 ) @ ( G2 > H2 ) @ ( ( B > E ) > A > F5 ) @ ( ( D > G2 ) > C > H2 ) @ ( bNF_rel_fun @ E @ G2 @ F5 @ H2 @ C5 @ D3 ) @ ( bNF_rel_fun @ ( B > E ) @ ( D > G2 ) @ ( A > F5 ) @ ( C > H2 ) @ ( bNF_rel_fun @ B @ D @ E @ G2 @ B6 @ C5 ) @ ( bNF_rel_fun @ A @ C @ F5 @ H2 @ A4 @ D3 ) ) ) @ ( map_fun @ A @ B @ E @ F5 ) @ ( map_fun @ C @ D @ G2 @ H2 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_224_process_Ocorec__disc__iff_I1_J,axiom,
% 3.19/1.69 ! [A: $tType,C: $tType,P: 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,A2: C] :
% 3.19/1.69 ( ( proces10484146Action @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) )
% 3.19/1.69 = ( P @ A2 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_225_process_Ocorec__disc__iff_I2_J,axiom,
% 3.19/1.69 ! [A: $tType,C: $tType,P: 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,A2: C] :
% 3.19/1.69 ( ( proces401113213Choice @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) )
% 3.19/1.69 = ( ~ ( P @ A2 ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_226_process_Ocorec__sel_I1_J,axiom,
% 3.19/1.69 ! [A: $tType,C: $tType,P: C > $o,A2: C,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] :
% 3.19/1.69 ( ( P @ A2 )
% 3.19/1.69 => ( ( proces745025900prefOf @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) )
% 3.19/1.69 = ( G11 @ A2 ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_227_process_Ocorec__sel_I3_J,axiom,
% 3.19/1.69 ! [A: $tType,C: $tType,P: C > $o,A2: C,Q21: C > $o,G11: C > A,Q12: C > $o,G121: C > ( proces634752977rocess @ A ),G122: C > C,G211: C > ( proces634752977rocess @ A ),G212: C > C,Q22: C > $o,G221: C > ( proces634752977rocess @ A ),G222: C > C] :
% 3.19/1.69 ( ~ ( P @ A2 )
% 3.19/1.69 => ( ( ( Q21 @ A2 )
% 3.19/1.69 => ( ( proces979765041_ch1Of @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) )
% 3.19/1.69 = ( G211 @ A2 ) ) )
% 3.19/1.69 & ( ~ ( Q21 @ A2 )
% 3.19/1.69 => ( ( proces979765041_ch1Of @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) )
% 3.19/1.69 = ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ ( G212 @ A2 ) ) ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_228_process_Ocorec__sel_I4_J,axiom,
% 3.19/1.69 ! [A: $tType,C: $tType,P: C > $o,A2: C,Q22: 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,G221: C > ( proces634752977rocess @ A ),G222: C > C] :
% 3.19/1.69 ( ~ ( P @ A2 )
% 3.19/1.69 => ( ( ( Q22 @ A2 )
% 3.19/1.69 => ( ( proces988026546_ch2Of @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) )
% 3.19/1.69 = ( G221 @ A2 ) ) )
% 3.19/1.69 & ( ~ ( Q22 @ A2 )
% 3.19/1.69 => ( ( proces988026546_ch2Of @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) )
% 3.19/1.69 = ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ ( G222 @ A2 ) ) ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_229_process_Ocorec__sel_I2_J,axiom,
% 3.19/1.69 ! [A: $tType,C: $tType,P: C > $o,A2: C,Q12: C > $o,G11: C > A,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] :
% 3.19/1.69 ( ( P @ A2 )
% 3.19/1.69 => ( ( ( Q12 @ A2 )
% 3.19/1.69 => ( ( proces1778668539contOf @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) )
% 3.19/1.69 = ( G121 @ A2 ) ) )
% 3.19/1.69 & ( ~ ( Q12 @ A2 )
% 3.19/1.69 => ( ( proces1778668539contOf @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) )
% 3.19/1.69 = ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ ( G122 @ A2 ) ) ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_230_process_Ocorec__disc_I2_J,axiom,
% 3.19/1.69 ! [A: $tType,C: $tType,P: C > $o,A2: C,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] :
% 3.19/1.69 ( ~ ( P @ A2 )
% 3.19/1.69 => ( proces401113213Choice @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_231_process_Ocorec_I2_J,axiom,
% 3.19/1.69 ! [A: $tType,C: $tType,P: C > $o,A2: C,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] :
% 3.19/1.69 ( ~ ( P @ A2 )
% 3.19/1.69 => ( ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 )
% 3.19/1.69 = ( proces1915862579Choice @ A @ ( if @ ( proces634752977rocess @ A ) @ ( Q21 @ A2 ) @ ( G211 @ A2 ) @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ ( G212 @ A2 ) ) ) @ ( if @ ( proces634752977rocess @ A ) @ ( Q22 @ A2 ) @ ( G221 @ A2 ) @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ ( G222 @ A2 ) ) ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_232_process_Ocorec_I1_J,axiom,
% 3.19/1.69 ! [A: $tType,C: $tType,P: C > $o,A2: C,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] :
% 3.19/1.69 ( ( P @ A2 )
% 3.19/1.69 => ( ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 )
% 3.19/1.69 = ( proces1525233512Action @ A @ ( G11 @ A2 ) @ ( if @ ( proces634752977rocess @ A ) @ ( Q12 @ A2 ) @ ( G121 @ A2 ) @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ ( G122 @ A2 ) ) ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_233_process_Ocorec__disc_I1_J,axiom,
% 3.19/1.69 ! [A: $tType,C: $tType,P: C > $o,A2: C,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] :
% 3.19/1.69 ( ( P @ A2 )
% 3.19/1.69 => ( proces10484146Action @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_234_process_Ocorec__code,axiom,
% 3.19/1.69 ! [A: $tType,C: $tType] :
% 3.19/1.69 ( ( proces894737309rocess @ C @ A )
% 3.19/1.69 = ( ^ [P7: 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,A7: C] : ( if @ ( proces634752977rocess @ A ) @ ( P7 @ A7 ) @ ( proces1525233512Action @ A @ ( G112 @ A7 ) @ ( if @ ( proces634752977rocess @ A ) @ ( Q122 @ A7 ) @ ( G1212 @ A7 ) @ ( proces894737309rocess @ C @ A @ P7 @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ ( G1222 @ A7 ) ) ) ) @ ( proces1915862579Choice @ A @ ( if @ ( proces634752977rocess @ A ) @ ( Q212 @ A7 ) @ ( G2112 @ A7 ) @ ( proces894737309rocess @ C @ A @ P7 @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ ( G2122 @ A7 ) ) ) @ ( if @ ( proces634752977rocess @ A ) @ ( Q222 @ A7 ) @ ( G2212 @ A7 ) @ ( proces894737309rocess @ C @ A @ P7 @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ ( G2222 @ A7 ) ) ) ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_235_fun_Opred__transfer,axiom,
% 3.19/1.69 ! [A: $tType,B: $tType,D: $tType,R: A > B > $o] :
% 3.19/1.69 ( bNF_rel_fun @ ( A > $o ) @ ( B > $o ) @ ( ( D > A ) > $o ) @ ( ( D > B ) > $o )
% 3.19/1.69 @ ( bNF_rel_fun @ A @ B @ $o @ $o @ R
% 3.19/1.69 @ ^ [Y4: $o,Z: $o] : ( Y4 = Z ) )
% 3.19/1.69 @ ( bNF_rel_fun @ ( D > A ) @ ( D > B ) @ $o @ $o
% 3.19/1.69 @ ( bNF_rel_fun @ D @ D @ A @ B
% 3.19/1.69 @ ^ [Y4: D,Z: D] : ( Y4 = Z )
% 3.19/1.69 @ R )
% 3.19/1.69 @ ^ [Y4: $o,Z: $o] : ( Y4 = Z ) )
% 3.19/1.69 @ ( basic_pred_fun @ D @ A
% 3.19/1.69 @ ^ [Uu: D] : $true )
% 3.19/1.69 @ ( basic_pred_fun @ D @ B
% 3.19/1.69 @ ^ [Uu: D] : $true ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_236_pred__equals__eq2,axiom,
% 3.19/1.69 ! [B: $tType,A: $tType,R: set @ ( product_prod @ A @ B ),S3: set @ ( product_prod @ A @ B )] :
% 3.19/1.69 ( ( ( ^ [X6: A,Y6: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X6 @ Y6 ) @ R ) )
% 3.19/1.69 = ( ^ [X6: A,Y6: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X6 @ Y6 ) @ S3 ) ) )
% 3.19/1.69 = ( R = S3 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_237_fun_Opred__True,axiom,
% 3.19/1.69 ! [A: $tType,D: $tType] :
% 3.19/1.69 ( ( basic_pred_fun @ D @ A
% 3.19/1.69 @ ^ [Uu: D] : $true
% 3.19/1.69 @ ^ [Uu: A] : $true )
% 3.19/1.69 = ( ^ [Uu: D > A] : $true ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_238_process__term_Omap__transfer,axiom,
% 3.19/1.69 ! [A: $tType,C: $tType,B: $tType,D: $tType,L: $tType,J: $tType,K: $tType,I: $tType,R1b: A > I > $o,S1d: C > K > $o,R2b: B > J > $o,S2d: D > L > $o] : ( bNF_rel_fun @ ( A > C ) @ ( I > K ) @ ( ( B > D ) > ( proces554692349s_term @ A @ B ) > ( proces554692349s_term @ C @ D ) ) @ ( ( J > L ) > ( proces554692349s_term @ I @ J ) > ( proces554692349s_term @ K @ L ) ) @ ( bNF_rel_fun @ A @ I @ C @ K @ R1b @ S1d ) @ ( bNF_rel_fun @ ( B > D ) @ ( J > L ) @ ( ( proces554692349s_term @ A @ B ) > ( proces554692349s_term @ C @ D ) ) @ ( ( proces554692349s_term @ I @ J ) > ( proces554692349s_term @ K @ L ) ) @ ( bNF_rel_fun @ B @ J @ D @ L @ R2b @ S2d ) @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ B ) @ ( proces554692349s_term @ I @ J ) @ ( proces554692349s_term @ C @ D ) @ ( proces554692349s_term @ K @ L ) @ ( proces2029722208s_term @ A @ I @ B @ J @ R1b @ R2b ) @ ( proces2029722208s_term @ C @ K @ D @ L @ S1d @ S2d ) ) ) @ ( proces224683037s_term @ A @ C @ B @ D ) @ ( proces224683037s_term @ I @ K @ J @ L ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_239_process_Omap__transfer,axiom,
% 3.19/1.69 ! [A: $tType,B: $tType,F5: $tType,E: $tType,Rb: A > E > $o,Sd: B > F5 > $o] : ( bNF_rel_fun @ ( A > B ) @ ( E > F5 ) @ ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ B ) ) @ ( ( proces634752977rocess @ E ) > ( proces634752977rocess @ F5 ) ) @ ( bNF_rel_fun @ A @ E @ B @ F5 @ Rb @ Sd ) @ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ E ) @ ( proces634752977rocess @ B ) @ ( proces634752977rocess @ F5 ) @ ( proces749077512rocess @ A @ E @ Rb ) @ ( proces749077512rocess @ B @ F5 @ Sd ) ) @ ( proces370407749rocess @ A @ B ) @ ( proces370407749rocess @ E @ F5 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_240_process_Omap__disc__iff_I1_J,axiom,
% 3.19/1.69 ! [B: $tType,A: $tType,F: A > B,A2: proces634752977rocess @ A] :
% 3.19/1.69 ( ( proces10484146Action @ B @ ( proces370407749rocess @ A @ B @ F @ A2 ) )
% 3.19/1.69 = ( proces10484146Action @ A @ A2 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_241_process_Omap__disc__iff_I2_J,axiom,
% 3.19/1.69 ! [B: $tType,A: $tType,F: A > B,A2: proces634752977rocess @ A] :
% 3.19/1.69 ( ( proces401113213Choice @ B @ ( proces370407749rocess @ A @ B @ F @ A2 ) )
% 3.19/1.69 = ( proces401113213Choice @ A @ A2 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_242_process_Omap__sel_I3_J,axiom,
% 3.19/1.69 ! [B: $tType,A: $tType,A2: proces634752977rocess @ A,F: A > B] :
% 3.19/1.69 ( ( proces401113213Choice @ A @ A2 )
% 3.19/1.69 => ( ( proces979765041_ch1Of @ B @ ( proces370407749rocess @ A @ B @ F @ A2 ) )
% 3.19/1.69 = ( proces370407749rocess @ A @ B @ F @ ( proces979765041_ch1Of @ A @ A2 ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_243_process_Omap__sel_I4_J,axiom,
% 3.19/1.69 ! [B: $tType,A: $tType,A2: proces634752977rocess @ A,F: A > B] :
% 3.19/1.69 ( ( proces401113213Choice @ A @ A2 )
% 3.19/1.69 => ( ( proces988026546_ch2Of @ B @ ( proces370407749rocess @ A @ B @ F @ A2 ) )
% 3.19/1.69 = ( proces370407749rocess @ A @ B @ F @ ( proces988026546_ch2Of @ A @ A2 ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_244_process__term_Omap__cong__pred,axiom,
% 3.19/1.69 ! [D: $tType,C: $tType,B: $tType,A: $tType,X7: proces554692349s_term @ A @ B,Ya2: proces554692349s_term @ A @ B,F1: A > C,G1: A > C,F2: B > D,G22: B > D] :
% 3.19/1.69 ( ( X7 = Ya2 )
% 3.19/1.69 => ( ( proces2118920028s_term @ A @ B
% 3.19/1.69 @ ^ [Z12: A] :
% 3.19/1.69 ( ( F1 @ Z12 )
% 3.19/1.69 = ( G1 @ Z12 ) )
% 3.19/1.69 @ ^ [Z22: B] :
% 3.19/1.69 ( ( F2 @ Z22 )
% 3.19/1.69 = ( G22 @ Z22 ) )
% 3.19/1.69 @ Ya2 )
% 3.19/1.69 => ( ( proces224683037s_term @ A @ C @ B @ D @ F1 @ F2 @ X7 )
% 3.19/1.69 = ( proces224683037s_term @ A @ C @ B @ D @ G1 @ G22 @ Ya2 ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_245_process_Osimps_I15_J,axiom,
% 3.19/1.69 ! [B: $tType,A: $tType,F: A > B,X11: A,X122: proces634752977rocess @ A] :
% 3.19/1.69 ( ( proces370407749rocess @ A @ B @ F @ ( proces1525233512Action @ A @ X11 @ X122 ) )
% 3.19/1.69 = ( proces1525233512Action @ B @ ( F @ X11 ) @ ( proces370407749rocess @ A @ B @ F @ X122 ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_246_process_Osimps_I16_J,axiom,
% 3.19/1.69 ! [B: $tType,A: $tType,F: A > B,X21: proces634752977rocess @ A,X222: proces634752977rocess @ A] :
% 3.19/1.69 ( ( proces370407749rocess @ A @ B @ F @ ( proces1915862579Choice @ A @ X21 @ X222 ) )
% 3.19/1.69 = ( proces1915862579Choice @ B @ ( proces370407749rocess @ A @ B @ F @ X21 ) @ ( proces370407749rocess @ A @ B @ F @ X222 ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_247_process__term_Osimps_I25_J,axiom,
% 3.19/1.69 ! [A: $tType,B: $tType,C: $tType,Pvar: $tType,F1: A > B,F2: Pvar > C,X1: Pvar] :
% 3.19/1.69 ( ( proces224683037s_term @ A @ B @ Pvar @ C @ F1 @ F2 @ ( proces1627516585ss_VAR @ Pvar @ A @ X1 ) )
% 3.19/1.69 = ( proces1627516585ss_VAR @ C @ B @ ( F2 @ X1 ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_248_process__term_Osimps_I28_J,axiom,
% 3.19/1.69 ! [C: $tType,B: $tType,Pvar: $tType,A: $tType,F1: A > B,F2: Pvar > C,X41: proces554692349s_term @ A @ Pvar,X42: proces554692349s_term @ A @ Pvar] :
% 3.19/1.69 ( ( proces224683037s_term @ A @ B @ Pvar @ C @ F1 @ F2 @ ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 ) )
% 3.19/1.69 = ( proces89589571ess_CH @ B @ C @ ( proces224683037s_term @ A @ B @ Pvar @ C @ F1 @ F2 @ X41 ) @ ( proces224683037s_term @ A @ B @ Pvar @ C @ F1 @ F2 @ X42 ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_249_process__term_Osimps_I27_J,axiom,
% 3.19/1.69 ! [C: $tType,B: $tType,Pvar: $tType,A: $tType,F1: A > B,F2: Pvar > C,X31: A,X32: proces554692349s_term @ A @ Pvar] :
% 3.19/1.69 ( ( proces224683037s_term @ A @ B @ Pvar @ C @ F1 @ F2 @ ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) )
% 3.19/1.69 = ( proces1454156180ss_ACT @ B @ C @ ( F1 @ X31 ) @ ( proces224683037s_term @ A @ B @ Pvar @ C @ F1 @ F2 @ X32 ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_250_process__term_Osimps_I26_J,axiom,
% 3.19/1.69 ! [Pvar: $tType,C: $tType,B: $tType,A: $tType,F1: A > B,F2: Pvar > C,X2: proces634752977rocess @ A] :
% 3.19/1.69 ( ( proces224683037s_term @ A @ B @ Pvar @ C @ F1 @ F2 @ ( proces1062592052s_PROC @ A @ Pvar @ X2 ) )
% 3.19/1.69 = ( proces1062592052s_PROC @ B @ C @ ( proces370407749rocess @ A @ B @ F1 @ X2 ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_251_process_Orel__map_I2_J,axiom,
% 3.19/1.69 ! [A: $tType,C: $tType,B: $tType,Sa: A > C > $o,X7: proces634752977rocess @ A,G: B > C,Y3: proces634752977rocess @ B] :
% 3.19/1.69 ( ( proces749077512rocess @ A @ C @ Sa @ X7 @ ( proces370407749rocess @ B @ C @ G @ Y3 ) )
% 3.19/1.69 = ( proces749077512rocess @ A @ B
% 3.19/1.69 @ ^ [X6: A,Y6: B] : ( Sa @ X6 @ ( G @ Y6 ) )
% 3.19/1.69 @ X7
% 3.19/1.69 @ Y3 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_252_process_Orel__map_I1_J,axiom,
% 3.19/1.69 ! [A: $tType,C: $tType,B: $tType,Sb: C > B > $o,I2: A > C,X7: proces634752977rocess @ A,Y3: proces634752977rocess @ B] :
% 3.19/1.69 ( ( proces749077512rocess @ C @ B @ Sb @ ( proces370407749rocess @ A @ C @ I2 @ X7 ) @ Y3 )
% 3.19/1.69 = ( proces749077512rocess @ A @ B
% 3.19/1.69 @ ^ [X6: A] : ( Sb @ ( I2 @ X6 ) )
% 3.19/1.69 @ X7
% 3.19/1.69 @ Y3 ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_253_process_Omap__cong__pred,axiom,
% 3.19/1.69 ! [B: $tType,A: $tType,X7: proces634752977rocess @ A,Ya2: proces634752977rocess @ A,F: A > B,G: A > B] :
% 3.19/1.69 ( ( X7 = Ya2 )
% 3.19/1.69 => ( ( proces1205983068rocess @ A
% 3.19/1.69 @ ^ [Z3: A] :
% 3.19/1.69 ( ( F @ Z3 )
% 3.19/1.69 = ( G @ Z3 ) )
% 3.19/1.69 @ Ya2 )
% 3.19/1.69 => ( ( proces370407749rocess @ A @ B @ F @ X7 )
% 3.19/1.69 = ( proces370407749rocess @ A @ B @ G @ Ya2 ) ) ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(fact_254_process__term_Omap__ident,axiom,
% 3.19/1.69 ! [B: $tType,A: $tType,T5: proces554692349s_term @ A @ B] :
% 3.19/1.69 ( ( proces224683037s_term @ A @ A @ B @ B
% 3.19/1.69 @ ^ [X6: A] : X6
% 3.19/1.69 @ ^ [X6: B] : X6
% 3.19/1.69 @ T5 )
% 3.19/1.69 = T5 ) ).
% 3.19/1.69
% 3.19/1.69 thf(help_If_3_1_T,axiom,
% 3.19/1.69 ! [P3: $o] :
% 3.19/1.69 ( ( P3 = $true )
% 3.19/1.69 | ( P3 = $false ) ) ).
% 3.19/1.69
% 3.19/1.69 thf(help_If_2_1_T,axiom,
% 3.19/1.69 ! [A: $tType,X7: A,Y3: A] :
% 3.19/1.69 ( ( if @ A @ $false @ X7 @ Y3 )
% 3.19/1.69 = Y3 ) ).
% 3.19/1.69
% 3.19/1.69 thf(help_If_1_1_T,axiom,
% 3.19/1.69 ! [A: $tType,X7: A,Y3: A] :
% 3.19/1.69 ( ( if @ A @ $true @ X7 @ Y3 )
% 3.19/1.69 = X7 ) ).
% 3.19/1.69
% 3.19/1.69 thf(conj_0,conjecture,
% 3.19/1.69 ( ( proces1652378886lution @ b @ a @ sys @ ( proces1062592052s_PROC @ a @ b @ p ) )
% 3.19/1.69 = p ) ).
% 3.19/1.69 ------------------------
% 3.29/1.75 % (31572)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_31439 for (2999ds/183Mi)
% 3.29/1.75 % (31574)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_31439 for (2999ds/27Mi)
% 3.29/1.75 % (31573)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_31439 for (2999ds/4Mi)
% 3.29/1.75 % (31575)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_31439 for (2999ds/2Mi)
% 3.29/1.75 % (31576)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_31439 for (2999ds/2Mi)
% 3.29/1.75 % (31578)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_31439 for (2999ds/18Mi)
% 3.29/1.75 % (31573)Instruction limit reached!
% 3.29/1.75 % (31573)------------------------------
% 3.29/1.75 % (31573)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.29/1.75 % (31573)Termination reason: Unknown
% 3.29/1.75 % (31573)Termination phase: shuffling
% 3.29/1.75
% 3.29/1.75 % (31573)Memory used [KB]: 1663
% 3.29/1.75 % (31573)Time elapsed: 0.004 s
% 3.29/1.75 % (31573)Instructions burned: 4 (million)
% 3.29/1.75 % (31573)------------------------------
% 3.29/1.75 % (31573)------------------------------
% 3.29/1.76 % (31575)Instruction limit reached!
% 3.29/1.76 % (31575)------------------------------
% 3.29/1.76 % (31575)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.29/1.76 % (31575)Termination reason: Unknown
% 3.29/1.76 % (31575)Termination phase: shuffling
% 3.29/1.76
% 3.29/1.76 % (31576)Instruction limit reached!
% 3.29/1.76 % (31576)------------------------------
% 3.29/1.76 % (31576)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.29/1.76 % (31575)Memory used [KB]: 1535
% 3.29/1.76 % (31575)Time elapsed: 0.004 s
% 3.29/1.76 % (31575)Instructions burned: 3 (million)
% 3.29/1.76 % (31575)------------------------------
% 3.29/1.76 % (31575)------------------------------
% 3.29/1.76 % (31576)Termination reason: Unknown
% 3.29/1.76 % (31576)Termination phase: shuffling
% 3.29/1.76
% 3.29/1.76 % (31576)Memory used [KB]: 1663
% 3.29/1.76 % (31576)Time elapsed: 0.004 s
% 3.29/1.76 % (31576)Instructions burned: 3 (million)
% 3.29/1.76 % (31576)------------------------------
% 3.29/1.76 % (31576)------------------------------
% 3.29/1.76 % (31577)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_31439 for (2999ds/275Mi)
% 3.29/1.76 % (31578)Instruction limit reached!
% 3.29/1.76 % (31578)------------------------------
% 3.29/1.76 % (31578)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.29/1.77 % (31578)Termination reason: Unknown
% 3.29/1.77 % (31578)Termination phase: shuffling
% 3.29/1.77
% 3.29/1.77 % (31578)Memory used [KB]: 1918
% 3.29/1.77 % (31578)Time elapsed: 0.013 s
% 3.29/1.77 % (31578)Instructions burned: 18 (million)
% 3.29/1.77 % (31578)------------------------------
% 3.29/1.77 % (31578)------------------------------
% 3.29/1.77 % (31574)Instruction limit reached!
% 3.29/1.77 % (31574)------------------------------
% 3.29/1.77 % (31574)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.29/1.77 % (31574)Termination reason: Unknown
% 3.29/1.77 % (31574)Termination phase: shuffling
% 3.29/1.77
% 3.29/1.77 % (31574)Memory used [KB]: 2174
% 3.29/1.77 % (31574)Time elapsed: 0.019 s
% 3.29/1.77 % (31574)Instructions burned: 28 (million)
% 3.29/1.77 % (31574)------------------------------
% 3.29/1.77 % (31574)------------------------------
% 3.29/1.77 % (31579)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_31439 for (2999ds/3Mi)
% 3.29/1.77 % (31580)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_31439 for (2999ds/37Mi)
% 3.29/1.77 % (31581)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_31439 for (2999ds/15Mi)
% 3.29/1.77 % (31579)Instruction limit reached!
% 3.29/1.77 % (31579)------------------------------
% 3.29/1.77 % (31579)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.29/1.77 % (31579)Termination reason: Unknown
% 3.29/1.77 % (31579)Termination phase: shuffling
% 3.29/1.77
% 3.29/1.77 % (31579)Memory used [KB]: 1663
% 3.29/1.77 % (31579)Time elapsed: 0.004 s
% 3.29/1.77 % (31579)Instructions burned: 3 (million)
% 3.29/1.77 % (31579)------------------------------
% 3.29/1.77 % (31579)------------------------------
% 3.29/1.78 % (31582)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_31439 for (2999ds/3Mi)
% 3.29/1.78 % (31581)Instruction limit reached!
% 3.29/1.78 % (31581)------------------------------
% 3.29/1.78 % (31581)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.29/1.78 % (31581)Termination reason: Unknown
% 3.29/1.78 % (31581)Termination phase: shuffling
% 3.29/1.78
% 3.29/1.78 % (31581)Memory used [KB]: 1918
% 3.29/1.78 % (31581)Time elapsed: 0.012 s
% 3.29/1.78 % (31581)Instructions burned: 16 (million)
% 3.29/1.78 % (31581)------------------------------
% 3.29/1.78 % (31581)------------------------------
% 3.29/1.78 % (31583)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_31439 for (2999ds/1041Mi)
% 3.29/1.79 % (31582)Instruction limit reached!
% 3.29/1.79 % (31582)------------------------------
% 3.29/1.79 % (31582)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.29/1.79 % (31582)Termination reason: Unknown
% 3.29/1.79 % (31582)Termination phase: shuffling
% 3.29/1.79
% 3.29/1.79 % (31582)Memory used [KB]: 1663
% 3.29/1.79 % (31582)Time elapsed: 0.005 s
% 3.29/1.79 % (31582)Instructions burned: 4 (million)
% 3.29/1.79 % (31582)------------------------------
% 3.29/1.79 % (31582)------------------------------
% 3.29/1.79 % (31584)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_31439 for (2999ds/7Mi)
% 3.29/1.79 % (31584)Instruction limit reached!
% 3.29/1.79 % (31584)------------------------------
% 3.29/1.79 % (31584)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.29/1.79 % (31584)Termination reason: Unknown
% 3.29/1.79 % (31584)Termination phase: shuffling
% 3.29/1.79
% 3.29/1.79 % (31584)Memory used [KB]: 1791
% 3.29/1.79 % (31584)Time elapsed: 0.005 s
% 3.29/1.79 % (31584)Instructions burned: 7 (million)
% 3.29/1.79 % (31584)------------------------------
% 3.29/1.79 % (31584)------------------------------
% 3.29/1.79 % (31580)Instruction limit reached!
% 3.29/1.79 % (31580)------------------------------
% 3.29/1.79 % (31580)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.29/1.79 % (31580)Termination reason: Unknown
% 3.29/1.79 % (31580)Termination phase: shuffling
% 3.29/1.79
% 3.29/1.79 % (31580)Memory used [KB]: 2302
% 3.29/1.79 % (31580)Time elapsed: 0.021 s
% 3.29/1.79 % (31580)Instructions burned: 37 (million)
% 3.29/1.79 % (31580)------------------------------
% 3.29/1.79 % (31580)------------------------------
% 3.29/1.80 % (31585)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_31439 for (2999ds/16Mi)
% 3.29/1.80 % (31587)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_31439 for (2998ds/3Mi)
% 3.29/1.80 % (31586)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_31439 for (2999ds/3Mi)
% 3.29/1.81 % (31587)Instruction limit reached!
% 3.29/1.81 % (31587)------------------------------
% 3.29/1.81 % (31587)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.29/1.81 % (31587)Termination reason: Unknown
% 3.29/1.81 % (31587)Termination phase: shuffling
% 3.29/1.81
% 3.29/1.81 % (31587)Memory used [KB]: 1663
% 3.29/1.81 % (31587)Time elapsed: 0.003 s
% 3.29/1.81 % (31587)Instructions burned: 5 (million)
% 3.29/1.81 % (31587)------------------------------
% 3.29/1.81 % (31587)------------------------------
% 3.29/1.81 % (31586)Instruction limit reached!
% 3.29/1.81 % (31586)------------------------------
% 3.29/1.81 % (31586)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.29/1.81 % (31586)Termination reason: Unknown
% 3.29/1.81 % (31586)Termination phase: shuffling
% 3.29/1.81 % (31588)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_31439 for (2998ds/7Mi)
% 3.29/1.81
% 3.29/1.81 % (31586)Memory used [KB]: 1663
% 3.29/1.81 % (31586)Time elapsed: 0.004 s
% 3.29/1.81 % (31586)Instructions burned: 3 (million)
% 3.29/1.81 % (31586)------------------------------
% 3.29/1.81 % (31586)------------------------------
% 3.29/1.81 % (31577)First to succeed.
% 3.29/1.81 % (31572)Instruction limit reached!
% 3.29/1.81 % (31572)------------------------------
% 3.29/1.81 % (31572)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.29/1.81 % (31572)Termination reason: Unknown
% 3.29/1.81 % (31572)Termination phase: Property scanning
% 3.29/1.81
% 3.29/1.81 % (31572)Memory used [KB]: 3837
% 3.29/1.81 % (31572)Time elapsed: 0.062 s
% 3.29/1.81 % (31572)Instructions burned: 184 (million)
% 3.29/1.81 % (31572)------------------------------
% 3.29/1.81 % (31572)------------------------------
% 3.29/1.81 % (31577)Refutation found. Thanks to Tanya!
% 3.29/1.81 % SZS status Theorem for DTF2THF_31439
% 3.29/1.81 % SZS output start Proof for DTF2THF_31439
% 3.29/1.81 thf(type_def_6, type, proces554692349s_term: ($tType * $tType) > $tType).
% 3.29/1.81 thf(type_def_7, type, product_prod: ($tType * $tType) > $tType).
% 3.29/1.81 thf(type_def_8, type, proces634752977rocess: ($tType) > $tType).
% 3.29/1.81 thf(type_def_9, type, set: ($tType) > $tType).
% 3.29/1.81 thf(type_def_10, type, itself: ($tType) > $tType).
% 3.29/1.81 thf(type_def_11, type, a: $tType).
% 3.29/1.81 thf(type_def_12, type, b: $tType).
% 3.29/1.81 thf(func_def_0, type, proces554692349s_term: ($tType * $tType) > $tType).
% 3.29/1.81 thf(func_def_1, type, proces634752977rocess: ($tType) > $tType).
% 3.29/1.81 thf(func_def_2, type, product_prod: ($tType * $tType) > $tType).
% 3.29/1.81 thf(func_def_3, type, set: ($tType) > $tType).
% 3.29/1.81 thf(func_def_4, type, itself: ($tType) > $tType).
% 3.29/1.81 thf(func_def_5, type, b: $tType).
% 3.29/1.81 thf(func_def_6, type, a: $tType).
% 3.29/1.81 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)).
% 3.29/1.81 thf(func_def_8, type, basic_pred_fun: !>[X0: $tType, X1: $tType]:((X0 > $o) > (X1 > $o) > (X0 > X1) > $o)).
% 3.29/1.81 thf(func_def_9, type, map_fun: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((X0 > X1) > (X2 > X3) > (X1 > X2) > X0 > X3)).
% 3.29/1.81 thf(func_def_10, type, undefined: !>[X0: $tType]:(X0)).
% 3.29/1.81 thf(func_def_11, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 3.29/1.81 thf(func_def_12, type, proces1239275103le_CH1: !>[X0: $tType, X1: $tType]:((X0 > proces554692349s_term @ X1 @ X0) > proces554692349s_term @ X1 @ X0 > proces554692349s_term @ X1 @ X0)).
% 3.29/1.81 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)).
% 3.29/1.81 thf(func_def_14, type, proces1239275104le_CH2: !>[X0: $tType, X1: $tType]:((X0 > proces554692349s_term @ X1 @ X0) > proces554692349s_term @ X1 @ X0 > proces554692349s_term @ X1 @ X0)).
% 3.29/1.81 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)).
% 3.29/1.81 thf(func_def_16, type, proces126235999e_CONT: !>[X0: $tType, X1: $tType]:((X0 > proces554692349s_term @ X1 @ X0) > proces554692349s_term @ X1 @ X0 > proces554692349s_term @ X1 @ X0)).
% 3.29/1.81 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)).
% 3.29/1.81 thf(func_def_18, type, proces1708129104e_PREF: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > proces554692349s_term @ X1 @ X2) > proces554692349s_term @ X1 @ X0 > X1)).
% 3.29/1.81 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)).
% 3.29/1.81 thf(func_def_20, type, proces1121166967uarded: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > proces554692349s_term @ X1 @ X2) > $o)).
% 3.29/1.81 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)).
% 3.29/1.81 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)).
% 3.29/1.81 thf(func_def_23, type, proces1525233512Action: !>[X0: $tType]:(X0 > proces634752977rocess @ X0 > proces634752977rocess @ X0)).
% 3.29/1.81 thf(func_def_24, type, proces1915862579Choice: !>[X0: $tType]:(proces634752977rocess @ X0 > proces634752977rocess @ X0 > proces634752977rocess @ X0)).
% 3.29/1.81 thf(func_def_25, type, proces1406508781rocess: !>[X0: $tType, X1: $tType]:((X0 > proces634752977rocess @ X0 > X1) > (proces634752977rocess @ X0 > proces634752977rocess @ X0 > X1) > proces634752977rocess @ X0 > X1)).
% 3.29/1.81 thf(func_def_26, type, proces979765041_ch1Of: !>[X0: $tType]:(proces634752977rocess @ X0 > proces634752977rocess @ X0)).
% 3.29/1.81 thf(func_def_27, type, proces988026546_ch2Of: !>[X0: $tType]:(proces634752977rocess @ X0 > proces634752977rocess @ X0)).
% 3.29/1.81 thf(func_def_28, type, proces1778668539contOf: !>[X0: $tType]:(proces634752977rocess @ X0 > proces634752977rocess @ X0)).
% 3.29/1.81 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)).
% 3.29/1.81 thf(func_def_30, type, proces10484146Action: !>[X0: $tType]:(proces634752977rocess @ X0 > $o)).
% 3.29/1.81 thf(func_def_31, type, proces401113213Choice: !>[X0: $tType]:(proces634752977rocess @ X0 > $o)).
% 3.29/1.81 thf(func_def_32, type, proces370407749rocess: !>[X0: $tType, X1: $tType]:((X0 > X1) > proces634752977rocess @ X0 > proces634752977rocess @ X1)).
% 3.29/1.81 thf(func_def_33, type, proces1205983068rocess: !>[X0: $tType]:((X0 > $o) > proces634752977rocess @ X0 > $o)).
% 3.29/1.81 thf(func_def_34, type, proces745025900prefOf: !>[X0: $tType]:(proces634752977rocess @ X0 > X0)).
% 3.29/1.81 thf(func_def_35, type, proces749077512rocess: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > proces634752977rocess @ X0 > proces634752977rocess @ X1 > $o)).
% 3.29/1.81 thf(func_def_36, type, proces1454156180ss_ACT: !>[X0: $tType, X1: $tType]:(X0 > proces554692349s_term @ X0 @ X1 > proces554692349s_term @ X0 @ X1)).
% 3.29/1.81 thf(func_def_37, type, proces89589571ess_CH: !>[X0: $tType, X1: $tType]:(proces554692349s_term @ X0 @ X1 > proces554692349s_term @ X0 @ X1 > proces554692349s_term @ X0 @ X1)).
% 3.29/1.81 thf(func_def_38, type, proces1062592052s_PROC: !>[X0: $tType, X1: $tType]:(proces634752977rocess @ X0 > proces554692349s_term @ X0 @ X1)).
% 3.29/1.81 thf(func_def_39, type, proces1627516585ss_VAR: !>[X0: $tType, X1: $tType]:(X0 > proces554692349s_term @ X1 @ X0)).
% 3.29/1.81 thf(func_def_40, 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)).
% 3.29/1.81 thf(func_def_41, type, proces224683037s_term: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((X0 > X1) > (X2 > X3) > proces554692349s_term @ X0 @ X2 > proces554692349s_term @ X1 @ X3)).
% 3.29/1.81 thf(func_def_42, type, proces2118920028s_term: !>[X0: $tType, X1: $tType]:((X0 > $o) > (X1 > $o) > proces554692349s_term @ X0 @ X1 > $o)).
% 3.29/1.81 thf(func_def_43, 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)).
% 3.29/1.81 thf(func_def_44, 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)).
% 3.29/1.81 thf(func_def_45, type, proces1493547885s_term: !>[X0: $tType, X1: $tType]:(proces554692349s_term @ X0 @ X1 > set @ X1)).
% 3.29/1.81 thf(func_def_46, type, proces1652378886lution: !>[X0: $tType, X1: $tType]:((X0 > proces554692349s_term @ X1 @ X0) > proces554692349s_term @ X1 @ X0 > proces634752977rocess @ X1)).
% 3.29/1.81 thf(func_def_47, type, product_Pair: !>[X0: $tType, X1: $tType]:(X0 > X1 > product_prod @ X0 @ X1)).
% 3.29/1.81 thf(func_def_48, type, product_curry: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ X1 > X2) > X0 > X1 > X2)).
% 3.29/1.81 thf(func_def_49, type, produc2004651681e_prod: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2)).
% 3.29/1.81 thf(func_def_50, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2)).
% 3.29/1.81 thf(func_def_51, type, type: !>[X0: $tType]:(itself @ X0)).
% 3.29/1.81 thf(func_def_52, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 3.29/1.81 thf(func_def_53, type, accp: !>[X0: $tType]:((X0 > X0 > $o) > X0 > $o)).
% 3.29/1.81 thf(func_def_54, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 3.29/1.81 thf(func_def_55, type, p: proces634752977rocess @ a).
% 3.29/1.81 thf(func_def_56, type, sys: b > proces554692349s_term @ a @ b).
% 3.29/1.81 thf(func_def_79, type, sP0: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > $o)).
% 3.29/1.81 thf(func_def_80, type, sK1: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > proces634752977rocess @ X0)).
% 3.29/1.81 thf(func_def_81, type, sK2: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > proces634752977rocess @ X0)).
% 3.29/1.81 thf(func_def_82, type, sK3: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > proces634752977rocess @ X0)).
% 3.29/1.81 thf(func_def_83, type, sK4: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > proces634752977rocess @ X0)).
% 3.29/1.81 thf(func_def_84, type, sK5: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > X0)).
% 3.29/1.81 thf(func_def_85, type, sK6: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > X0)).
% 3.29/1.81 thf(func_def_86, type, sK7: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > proces634752977rocess @ X0)).
% 3.29/1.81 thf(func_def_87, type, sK8: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > proces634752977rocess @ X0)).
% 3.29/1.81 thf(func_def_88, type, sK9: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > proces634752977rocess @ X0)).
% 3.29/1.81 thf(func_def_89, type, sK10: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > proces634752977rocess @ X0)).
% 3.29/1.81 thf(func_def_90, type, sK11: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > proces634752977rocess @ X0)).
% 3.29/1.81 thf(func_def_91, type, sK12: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > proces634752977rocess @ X0)).
% 3.29/1.81 thf(func_def_92, type, sK13: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > proces634752977rocess @ X0)).
% 3.29/1.81 thf(func_def_93, type, sK14: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > proces634752977rocess @ X0)).
% 3.29/1.81 thf(func_def_94, type, sK15: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > X0)).
% 3.29/1.81 thf(func_def_95, type, sK16: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > X0)).
% 3.29/1.81 thf(func_def_96, type, sK17: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > proces634752977rocess @ X0)).
% 3.29/1.81 thf(func_def_97, type, sK18: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > proces634752977rocess @ X0)).
% 3.29/1.81 thf(func_def_98, type, sK19: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > proces634752977rocess @ X0)).
% 3.29/1.81 thf(func_def_99, type, sK20: !>[X0: $tType]:((proces634752977rocess @ X0 > proces634752977rocess @ X0 > $o) > proces634752977rocess @ X0)).
% 3.29/1.81 thf(func_def_100, type, sK21: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 3.29/1.81 thf(func_def_102, type, ph23: !>[X0: $tType]:(X0)).
% 3.29/1.81 thf(f743,plain,(
% 3.29/1.81 $false),
% 3.29/1.81 inference(subsumption_resolution,[status(thm)],[f717,f738])).
% 3.29/1.81 thf(f738,plain,(
% 3.29/1.81 (p = (proces1652378886lution @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ p)))),
% 3.29/1.81 inference(equality_resolution,[status(thm)],[f715])).
% 3.29/1.81 thf(f715,plain,(
% 3.29/1.81 ( ! [X0 : proces634752977rocess @ a] : (((proces1652378886lution @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ p)) != X0) | (p = X0)) )),
% 3.29/1.81 inference(cnf_transformation,[status(thm)],[f669])).
% 3.29/1.81 thf(f669,plain,(
% 3.29/1.81 ! [X0 : proces634752977rocess @ a] : (((proces1652378886lution @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ p)) != X0) | (p = X0))),
% 3.29/1.81 inference(ennf_transformation,[status(thm)],[f647])).
% 3.29/1.81 thf(f647,plain,(
% 3.29/1.81 ! [X0 : proces634752977rocess @ a] : (((proces1652378886lution @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ p)) = X0) => (p = X0))),
% 3.29/1.81 inference(rectify,[status(thm)],[f1])).
% 3.29/1.81 thf(f1,axiom,(
% 3.29/1.81 ! [X8 : proces634752977rocess @ a] : (((proces1652378886lution @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ p)) = X8) => (p = X8))),
% 3.29/1.81 file('/export/starexec/sandbox/tmp/tmp.509jbUU17G/DTF2THF_31439.p',fact_0__092_060open_062_092_060And_062q_O_Aq_A_061_Asolution_Asys_A_IPROC_Ap_J_A_092_060Longrightarrow_062_Ap_A_061_Aq_092_060close_062)).
% 3.29/1.81 thf(f717,plain,(
% 3.29/1.81 (p != (proces1652378886lution @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ p)))),
% 3.29/1.81 inference(cnf_transformation,[status(thm)],[f646])).
% 3.29/1.81 thf(f646,plain,(
% 3.29/1.81 (p != (proces1652378886lution @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ p)))),
% 3.29/1.81 inference(flattening,[status(thm)],[f260])).
% 3.29/1.81 thf(f260,negated_conjecture,(
% 3.29/1.81 ~(p = (proces1652378886lution @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ p)))),
% 3.29/1.81 inference(negated_conjecture,[status(cth)],[f259])).
% 3.29/1.81 thf(f259,conjecture,(
% 3.29/1.81 (p = (proces1652378886lution @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ p)))),
% 3.29/1.81 file('/export/starexec/sandbox/tmp/tmp.509jbUU17G/DTF2THF_31439.p',conj_0)).
% 3.29/1.81 % SZS output end Proof for DTF2THF_31439
% 3.29/1.81 % (31577)------------------------------
% 3.29/1.81 % (31577)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.29/1.81 % (31577)Termination reason: Refutation
% 3.29/1.81
% 3.29/1.81 % (31577)Memory used [KB]: 7675
% 3.29/1.81 % (31577)Time elapsed: 0.054 s
% 3.29/1.81 % (31577)Instructions burned: 125 (million)
% 3.29/1.81 % (31577)------------------------------
% 3.29/1.81 % (31577)------------------------------
% 3.29/1.81 % (31571)Success in time 0.115 s
%------------------------------------------------------------------------------