DT2H2X---1.9.5.THM-Ref.s

%------------------------------------------------------------------------------
% File     : DT2H2X---1.9.5
% Problem  : ITP189^2 : TPTP v9.2.1. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300

% Computer : n006.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 08:56:16 AM UTC 2026

% Result   : Theorem 3.33s 1.86s
% Output   : Refutation 3.33s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : ITP189^2 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.13  % Command  : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34  % Computer : n006.cluster.edu
% 0.17/0.34  % Model    : x86_64 x86_64
% 0.17/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34  % Memory   : 8042.1875MB
% 0.17/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34  % CPULimit : 300
% 0.17/0.34  % WCLimit  : 300
% 0.17/0.34  % DateTime : Tue Feb 24 08:29:15 EST 2026
% 0.17/0.34  % CPUTime  : 
% 0.17/0.34  Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.29/0.47  ---- Original DTF file ---
% 0.29/0.47  thf(spec,logic,$$dhol).
% 0.29/0.47  %------------------------------------------------------------------------------
% 0.29/0.47  % File     : ITP189^2 : TPTP v9.2.1. Released v7.5.0.
% 0.29/0.47  % Domain   : Interactive Theorem Proving
% 0.29/0.47  % Problem  : Sledgehammer Strong_Late_Sim_SC problem prob_754__3415948_1
% 0.29/0.47  % Version  : Especial.
% 0.29/0.47  % English  :
% 0.29/0.47  
% 0.29/0.47  % Refs     : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.29/0.47  %          : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.29/0.47  % Source   : [Des21]
% 0.29/0.47  % Names    : Strong_Late_Sim_SC/prob_754__3415948_1 [Des21]
% 0.29/0.47  
% 0.29/0.47  % Status   : Theorem
% 0.29/0.47  % Rating   : 0.00 v7.5.0
% 0.29/0.47  % Syntax   : Number of formulae    :  324 ( 134 unt;  50 typ;   0 def)
% 0.29/0.47  %            Number of atoms       :  736 ( 225 equ;   0 cnn)
% 0.29/0.47  %            Maximal formula atoms :   17 (   2 avg)
% 0.29/0.47  %            Number of connectives : 4189 ( 125   ~;   5   |;  45   &;3622   @)
% 0.29/0.47  %                                         (   0 <=>; 392  =>;   0  <=;   0 <~>)
% 0.29/0.47  %            Maximal formula depth :   28 (  10 avg)
% 0.29/0.47  %            Number of types       :    6 (   5 usr)
% 0.29/0.47  %            Number of type conns  :  145 ( 145   >;   0   *;   0   +;   0  <<)
% 0.29/0.47  %            Number of symbols     :   46 (  45 usr;   9 con; 0-5 aty)
% 0.29/0.47  %            Number of variables   : 1250 (  28   ^;1187   !;  13   ?;1250   :)
% 0.29/0.47  %                                         (  22  !>;   0  ?*;   0  @-;   0  @+)
% 0.29/0.47  % SPC      : TH1_THM_EQU_NAR
% 0.29/0.47  
% 0.29/0.47  % Comments : This file was generated by Sledgehammer 2021-02-23 16:17:28.408
% 0.29/0.47  %------------------------------------------------------------------------------
% 0.29/0.47  % Could-be-implicit typings (8)
% 0.29/0.47  thf(ty_t_Late__Semantics_Oresidual,type,
% 0.29/0.47      late_residual: $tType ).
% 0.29/0.47  
% 0.29/0.47  thf(ty_t_Late__Semantics_Osubject,type,
% 0.29/0.47      late_subject: $tType ).
% 0.29/0.47  
% 0.29/0.47  thf(ty_t_Late__Semantics_OfreeRes,type,
% 0.29/0.47      late_freeRes: $tType ).
% 0.29/0.47  
% 0.29/0.47  thf(ty_t_Product__Type_Oprod,type,
% 0.29/0.47      product_prod: $tType > $tType > $tType ).
% 0.29/0.47  
% 0.29/0.47  thf(ty_t_Nominal_Onoption,type,
% 0.29/0.47      noption: $tType > $tType ).
% 0.29/0.47  
% 0.29/0.47  thf(ty_t_Agent_Oname,type,
% 0.29/0.47      name: $tType ).
% 0.29/0.47  
% 0.29/0.47  thf(ty_t_Agent_Opi,type,
% 0.29/0.47      pi: $tType ).
% 0.29/0.47  
% 0.29/0.47  thf(ty_t_Set_Oset,type,
% 0.29/0.47      set: $tType > $tType ).
% 0.29/0.47  
% 0.29/0.47  % Explicit typings (42)
% 0.29/0.47  thf(sy_cl_HOL_Otype,type,
% 0.29/0.47      type: 
% 0.29/0.47        !>[A: $tType] : $o ).
% 0.29/0.47  
% 0.29/0.47  thf(sy_cl_Agent_Ofs__name,type,
% 0.29/0.47      fs_name: 
% 0.29/0.47        !>[A: $tType] : $o ).
% 0.29/0.47  
% 0.29/0.47  thf(sy_cl_Orderings_Oord,type,
% 0.29/0.47      ord: 
% 0.29/0.47        !>[A: $tType] : $o ).
% 0.29/0.47  
% 0.29/0.47  thf(sy_cl_Orderings_Oorder,type,
% 0.29/0.47      order: 
% 0.29/0.47        !>[A: $tType] : $o ).
% 0.29/0.47  
% 0.29/0.47  thf(sy_cl_Orderings_Olinorder,type,
% 0.29/0.47      linorder: 
% 0.29/0.47        !>[A: $tType] : $o ).
% 0.29/0.47  
% 0.29/0.47  thf(sy_cl_Orderings_Opreorder,type,
% 0.29/0.47      preorder: 
% 0.29/0.47        !>[A: $tType] : $o ).
% 0.29/0.47  
% 0.29/0.47  thf(sy_c_Agent_Opi_OInput,type,
% 0.29/0.47      input: name > name > pi > pi ).
% 0.29/0.47  
% 0.29/0.47  thf(sy_c_Agent_Opi_OOutput,type,
% 0.29/0.47      output: name > name > pi > pi ).
% 0.29/0.47  
% 0.29/0.47  thf(sy_c_Agent_Opi_OPar,type,
% 0.29/0.47      par: pi > pi > pi ).
% 0.29/0.47  
% 0.29/0.47  thf(sy_c_Agent_Opi_OPiNil,type,
% 0.29/0.47      piNil: pi ).
% 0.29/0.47  
% 0.29/0.47  thf(sy_c_Agent_Opi_ORes,type,
% 0.29/0.47      res: name > pi > pi ).
% 0.29/0.47  
% 0.29/0.47  thf(sy_c_Agent_Opi_OSum,type,
% 0.29/0.47      sum: pi > pi > pi ).
% 0.29/0.47  
% 0.29/0.47  thf(sy_c_Agent_Opi_OTau,type,
% 0.29/0.47      tau: pi > pi ).
% 0.29/0.47  
% 0.29/0.47  thf(sy_c_Agent_Osubs,type,
% 0.29/0.47      subs: pi > name > name > pi ).
% 0.29/0.47  
% 0.29/0.47  thf(sy_c_Agent_Osubst__name,type,
% 0.29/0.47      subst_name: name > name > name > name ).
% 0.29/0.47  
% 0.29/0.47  thf(sy_c_Late__Semantics_OfreeRes_OOutputR,type,
% 0.29/0.47      late_OutputR: name > name > late_freeRes ).
% 0.29/0.47  
% 0.29/0.47  thf(sy_c_Late__Semantics_OfreeRes_OTauR,type,
% 0.29/0.47      late_TauR: late_freeRes ).
% 0.29/0.47  
% 0.29/0.47  thf(sy_c_Late__Semantics_OfreeRes_OfreeRes__rec,type,
% 0.29/0.47      late_freeRes_rec: 
% 0.29/0.47        !>[T: $tType] : ( ( name > name > T ) > T > late_freeRes > T ) ).
% 0.29/0.47  
% 0.29/0.47  thf(sy_c_Late__Semantics_Oresidual_OBoundR,type,
% 0.29/0.47      late_BoundR: late_subject > name > pi > late_residual ).
% 0.29/0.47  
% 0.29/0.47  thf(sy_c_Late__Semantics_Oresidual_OFreeR,type,
% 0.29/0.47      late_FreeR: late_freeRes > pi > late_residual ).
% 0.29/0.47  
% 0.29/0.47  thf(sy_c_Late__Semantics_Osubject_OBoundOutputS,type,
% 0.29/0.47      late_BoundOutputS: name > late_subject ).
% 0.29/0.47  
% 0.29/0.47  thf(sy_c_Late__Semantics_Osubject_OInputS,type,
% 0.29/0.47      late_InputS: name > late_subject ).
% 0.29/0.47  
% 0.29/0.47  thf(sy_c_Late__Semantics_Osubject_Osubject__rec,type,
% 0.29/0.47      late_subject_rec: 
% 0.29/0.47        !>[T: $tType] : ( ( name > T ) > ( name > T ) > late_subject > T ) ).
% 0.29/0.47  
% 0.29/0.47  thf(sy_c_Late__Semantics_Otransitions,type,
% 0.29/0.47      late_transitions: pi > late_residual > $o ).
% 0.29/0.47  
% 0.29/0.47  thf(sy_c_Nominal_Oabs__fun,type,
% 0.29/0.47      abs_fun: 
% 0.29/0.47        !>[X: $tType,A: $tType] : ( X > A > X > ( noption @ A ) ) ).
% 0.29/0.47  
% 0.29/0.47  thf(sy_c_Nominal_Ofresh,type,
% 0.29/0.47      fresh: 
% 0.29/0.47        !>[X: $tType,A: $tType] : ( X > A > $o ) ).
% 0.29/0.47  
% 0.29/0.47  thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.29/0.47      ord_less_eq: 
% 0.29/0.47        !>[A: $tType] : ( A > A > $o ) ).
% 0.29/0.47  
% 0.29/0.47  thf(sy_c_Product__Type_OPair,type,
% 0.29/0.47      product_Pair: 
% 0.29/0.47        !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 0.29/0.47  
% 0.29/0.47  thf(sy_c_Product__Type_Oold_Oprod_Orec__prod,type,
% 0.29/0.47      product_rec_prod: 
% 0.29/0.47        !>[A: $tType,B: $tType,T: $tType] : ( ( A > B > T ) > ( product_prod @ A @ B ) > T ) ).
% 0.29/0.47  
% 0.29/0.47  thf(sy_c_Rel_Oeqvt,type,
% 0.29/0.47      eqvt: 
% 0.29/0.47        !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > $o ) ).
% 0.29/0.47  
% 0.29/0.47  thf(sy_c_Relation_OId,type,
% 0.29/0.47      id: 
% 0.29/0.47        !>[A: $tType] : ( set @ ( product_prod @ A @ A ) ) ).
% 0.29/0.47  
% 0.29/0.47  thf(sy_c_Set_OCollect,type,
% 0.29/0.47      collect: 
% 0.29/0.47        !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.29/0.47  
% 0.29/0.47  thf(sy_c_Strong__Late__Sim_Oderivative,type,
% 0.29/0.47      strong2129052853vative: pi > pi > late_subject > name > ( set @ ( product_prod @ pi @ pi ) ) > $o ).
% 0.29/0.47  
% 0.29/0.47  thf(sy_c_Strong__Late__Sim_Osimulation,type,
% 0.29/0.47      strong743114133lation: pi > ( set @ ( product_prod @ pi @ pi ) ) > pi > $o ).
% 0.29/0.47  
% 0.29/0.47  thf(sy_c_member,type,
% 0.29/0.47      member: 
% 0.29/0.47        !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.29/0.47  
% 0.29/0.47  thf(sy_v_P,type,
% 0.29/0.47      p: pi ).
% 0.29/0.47  
% 0.29/0.47  thf(sy_v_P_H____,type,
% 0.29/0.47      p2: pi ).
% 0.29/0.47  
% 0.29/0.47  thf(sy_v_PxQ____,type,
% 0.29/0.47      pxQ: pi ).
% 0.29/0.47  
% 0.29/0.47  thf(sy_v_Q,type,
% 0.29/0.47      q: pi ).
% 0.29/0.47  
% 0.29/0.47  thf(sy_v_Rel,type,
% 0.29/0.47      rel: set @ ( product_prod @ pi @ pi ) ).
% 0.29/0.47  
% 0.29/0.47  thf(sy_v__092_060alpha_062____,type,
% 0.29/0.47      alpha: late_freeRes ).
% 0.29/0.47  
% 0.29/0.47  thf(sy_v_x,type,
% 0.29/0.47      x: name ).
% 0.29/0.47  
% 0.29/0.47  % Relevant facts (256)
% 0.29/0.47  thf(fact_0__092_060open_062x_A_092_060sharp_062_A_092_060alpha_062_092_060close_062,axiom,
% 0.29/0.47      fresh @ name @ late_freeRes @ x @ alpha ).
% 0.29/0.47  
% 0.29/0.47  % \<open>x \<sharp> \<alpha>\<close>
% 0.29/0.47  thf(fact_1__092_060open_062P_A_092_060parallel_062_AQ_A_092_060longmapsto_062_A_092_060alpha_062_A_092_060prec_062_AP_H_A_092_060parallel_062_AQ_092_060close_062,axiom,
% 0.29/0.47      late_transitions @ ( par @ p @ q ) @ ( late_FreeR @ alpha @ ( par @ p2 @ q ) ) ).
% 0.29/0.47  
% 0.29/0.47  % \<open>P \<parallel> Q \<longmapsto> \<alpha> \<prec> P' \<parallel> Q\<close>
% 0.29/0.47  thf(fact_2_cPar1_Ohyps,axiom,
% 0.29/0.47      late_transitions @ p @ ( late_FreeR @ alpha @ p2 ) ).
% 0.29/0.47  
% 0.29/0.47  % cPar1.hyps
% 0.29/0.47  thf(fact_3_Free_Ohyps,axiom,
% 0.29/0.47      late_transitions @ ( par @ p @ ( res @ x @ q ) ) @ ( late_FreeR @ alpha @ pxQ ) ).
% 0.29/0.47  
% 0.29/0.47  % Free.hyps
% 0.29/0.47  thf(fact_4_assms_I1_J,axiom,
% 0.29/0.47      fresh @ name @ pi @ x @ p ).
% 0.29/0.47  
% 0.29/0.47  % assms(1)
% 0.29/0.47  thf(fact_5__092_060open_062x_A_092_060sharp_062_AP_H_092_060close_062,axiom,
% 0.29/0.47      fresh @ name @ pi @ x @ p2 ).
% 0.29/0.47  
% 0.29/0.47  % \<open>x \<sharp> P'\<close>
% 0.29/0.47  thf(fact_6_Par1F,axiom,
% 0.29/0.47      ! [P: pi,Alpha: late_freeRes,P2: pi,Q: pi] :
% 0.29/0.47        ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 0.29/0.47       => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha @ ( par @ P2 @ Q ) ) ) ) ).
% 0.29/0.47  
% 0.29/0.47  % Par1F
% 0.29/0.47  thf(fact_7_Par2F,axiom,
% 0.29/0.47      ! [Q: pi,Alpha: late_freeRes,Q2: pi,P: pi] :
% 0.29/0.47        ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 0.29/0.47       => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha @ ( par @ P @ Q2 ) ) ) ) ).
% 0.29/0.47  
% 0.29/0.47  % Par2F
% 0.29/0.47  thf(fact_8_pi_Odistinct_I85_J,axiom,
% 0.29/0.47      ! [Pi1: pi,Pi2: pi,Name: name,Pi: pi] :
% 0.29/0.47        ( ( par @ Pi1 @ Pi2 )
% 0.29/0.47       != ( res @ Name @ Pi ) ) ).
% 0.29/0.47  
% 0.29/0.47  % pi.distinct(85)
% 0.29/0.47  thf(fact_9_resCasesF,axiom,
% 0.29/0.47      ! [X2: name,P: pi,Alpha: late_freeRes,XP: pi,F: pi > $o] :
% 0.29/0.47        ( ( late_transitions @ ( res @ X2 @ P ) @ ( late_FreeR @ Alpha @ XP ) )
% 0.29/0.47       => ( ! [P3: pi] :
% 0.29/0.47              ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P3 ) )
% 0.29/0.47             => ( ( fresh @ name @ late_freeRes @ X2 @ Alpha )
% 0.29/0.47               => ( F @ ( res @ X2 @ P3 ) ) ) )
% 0.29/0.47         => ( F @ XP ) ) ) ).
% 0.29/0.47  
% 0.29/0.47  % resCasesF
% 0.29/0.47  thf(fact_10_resCasesF_H,axiom,
% 0.29/0.47      ! [X2: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 0.29/0.47        ( ( late_transitions @ ( res @ X2 @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 0.29/0.47       => ~ ! [P4: pi,Alpha2: late_freeRes,P3: pi,Y: name] :
% 0.29/0.47              ( ( ( res @ X2 @ P )
% 0.29/0.47                = ( res @ Y @ P4 ) )
% 0.29/0.47             => ( ( ( late_FreeR @ Alpha @ P2 )
% 0.29/0.47                  = ( late_FreeR @ Alpha2 @ ( res @ Y @ P3 ) ) )
% 0.29/0.47               => ( ( late_transitions @ P4 @ ( late_FreeR @ Alpha2 @ P3 ) )
% 0.29/0.47                 => ~ ( fresh @ name @ late_freeRes @ Y @ Alpha2 ) ) ) ) ) ).
% 0.29/0.47  
% 0.29/0.47  % resCasesF'
% 0.29/0.47  thf(fact_11_ResF,axiom,
% 0.29/0.47      ! [P: pi,Alpha: late_freeRes,P2: pi,Y2: name] :
% 0.29/0.47        ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 0.29/0.47       => ( ( fresh @ name @ late_freeRes @ Y2 @ Alpha )
% 0.29/0.47         => ( late_transitions @ ( res @ Y2 @ P ) @ ( late_FreeR @ Alpha @ ( res @ Y2 @ P2 ) ) ) ) ) ).
% 0.29/0.47  
% 0.29/0.47  % ResF
% 0.29/0.47  thf(fact_12_residual_Oinject_I2_J,axiom,
% 0.29/0.47      ! [X22: late_freeRes,X1: pi,Y22: late_freeRes,Y1: pi] :
% 0.29/0.47        ( ( ( late_FreeR @ X22 @ X1 )
% 0.29/0.47          = ( late_FreeR @ Y22 @ Y1 ) )
% 0.29/0.47        = ( ( X22 = Y22 )
% 0.29/0.47          & ( X1 = Y1 ) ) ) ).
% 0.29/0.47  
% 0.29/0.47  % residual.inject(2)
% 0.29/0.47  thf(fact_13_pi_Oinject_I7_J,axiom,
% 0.29/0.47      ! [X22: pi,X1: pi,Y22: pi,Y1: pi] :
% 0.29/0.47        ( ( ( par @ X22 @ X1 )
% 0.29/0.47          = ( par @ Y22 @ Y1 ) )
% 0.29/0.47        = ( ( X22 = Y22 )
% 0.29/0.47          & ( X1 = Y1 ) ) ) ).
% 0.29/0.47  
% 0.29/0.47  % pi.inject(7)
% 0.29/0.47  thf(fact_14_resInputFreeTrans,axiom,
% 0.29/0.47      ! [X2: name,A2: name,Y2: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 0.29/0.47        ~ ( late_transitions @ ( res @ X2 @ ( input @ A2 @ Y2 @ P ) ) @ ( late_FreeR @ Alpha @ P2 ) ) ).
% 0.29/0.47  
% 0.29/0.47  % resInputFreeTrans
% 0.29/0.47  thf(fact_15_EqvtRel,axiom,
% 0.29/0.47      eqvt @ pi @ rel ).
% 0.29/0.47  
% 0.29/0.47  % EqvtRel
% 0.29/0.47  thf(fact_16_resZeroTrans,axiom,
% 0.29/0.47      ! [X2: name,Rs: late_residual] :
% 0.29/0.47        ~ ( late_transitions @ ( res @ X2 @ piNil ) @ Rs ) ).
% 0.29/0.47  
% 0.29/0.47  % resZeroTrans
% 0.29/0.47  thf(fact_17_pi_Ofresh_I8_J,axiom,
% 0.29/0.47      ! [A2: name,X22: pi,X1: pi] :
% 0.29/0.47        ( ( fresh @ name @ pi @ A2 @ ( par @ X22 @ X1 ) )
% 0.29/0.47        = ( ( fresh @ name @ pi @ A2 @ X22 )
% 0.29/0.47          & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 0.29/0.47  
% 0.29/0.47  % pi.fresh(8)
% 0.29/0.47  thf(fact_18_pi_Ofresh_I1_J,axiom,
% 0.29/0.47      ! [A2: name] : ( fresh @ name @ pi @ A2 @ piNil ) ).
% 0.29/0.47  
% 0.29/0.47  % pi.fresh(1)
% 0.29/0.47  thf(fact_19_pi_Odistinct_I5_J,axiom,
% 0.29/0.47      ! [Name1: name,Name2: name,Pi: pi] :
% 0.29/0.47        ( piNil
% 0.29/0.47       != ( input @ Name1 @ Name2 @ Pi ) ) ).
% 0.29/0.47  
% 0.29/0.47  % pi.distinct(5)
% 0.29/0.47  thf(fact_20_name__exists__fresh,axiom,
% 0.29/0.47      ! [A: $tType] :
% 0.29/0.47        ( ( fs_name @ A )
% 0.29/0.47       => ! [X2: A] :
% 0.29/0.47            ~ ! [C: name] :
% 0.29/0.47                ~ ( fresh @ name @ A @ C @ X2 ) ) ).
% 0.29/0.47  
% 0.29/0.47  % name_exists_fresh
% 0.29/0.47  thf(fact_21_freshRes,axiom,
% 0.29/0.47      ! [A2: name,P: pi] : ( fresh @ name @ pi @ A2 @ ( res @ A2 @ P ) ) ).
% 0.29/0.47  
% 0.29/0.47  % freshRes
% 0.29/0.47  thf(fact_22_pi_Odistinct_I57_J,axiom,
% 0.29/0.47      ! [Name12: name,Name22: name,Pi3: pi,Name: name,Pi: pi] :
% 0.29/0.47        ( ( input @ Name12 @ Name22 @ Pi3 )
% 0.29/0.47       != ( res @ Name @ Pi ) ) ).
% 0.29/0.47  
% 0.29/0.47  % pi.distinct(57)
% 0.29/0.47  thf(fact_23_pi_Odistinct_I55_J,axiom,
% 0.29/0.47      ! [Name12: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 0.29/0.47        ( ( input @ Name12 @ Name22 @ Pi3 )
% 0.29/0.47       != ( par @ Pi12 @ Pi22 ) ) ).
% 0.29/0.47  
% 0.29/0.47  % pi.distinct(55)
% 0.29/0.47  thf(fact_24_zeroTrans,axiom,
% 0.29/0.47      ! [Rs: late_residual] :
% 0.29/0.47        ~ ( late_transitions @ piNil @ Rs ) ).
% 0.29/0.47  
% 0.29/0.47  % zeroTrans
% 0.29/0.47  thf(fact_25_nilCases_H,axiom,
% 0.29/0.47      ! [Rs: late_residual] :
% 0.29/0.47        ~ ( late_transitions @ piNil @ Rs ) ).
% 0.29/0.47  
% 0.29/0.47  % nilCases'
% 0.29/0.47  thf(fact_26_pi_Odistinct_I15_J,axiom,
% 0.29/0.47      ! [Name: name,Pi: pi] :
% 0.29/0.47        ( piNil
% 0.29/0.47       != ( res @ Name @ Pi ) ) ).
% 0.29/0.47  
% 0.29/0.47  % pi.distinct(15)
% 0.29/0.47  thf(fact_27_pi_Odistinct_I13_J,axiom,
% 0.29/0.47      ! [Pi12: pi,Pi22: pi] :
% 0.29/0.47        ( piNil
% 0.29/0.47       != ( par @ Pi12 @ Pi22 ) ) ).
% 0.29/0.47  
% 0.29/0.47  % pi.distinct(13)
% 0.29/0.47  thf(fact_28_freshFreeDerivative_I1_J,axiom,
% 0.29/0.47      ! [P: pi,Alpha: late_freeRes,P2: pi,Y2: name] :
% 0.29/0.47        ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 0.29/0.47       => ( ( fresh @ name @ pi @ Y2 @ P )
% 0.29/0.47         => ( fresh @ name @ late_freeRes @ Y2 @ Alpha ) ) ) ).
% 0.29/0.47  
% 0.29/0.47  % freshFreeDerivative(1)
% 0.29/0.47  thf(fact_29_freshFreeDerivative_I2_J,axiom,
% 0.29/0.47      ! [P: pi,Alpha: late_freeRes,P2: pi,Y2: name] :
% 0.29/0.47        ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 0.29/0.47       => ( ( fresh @ name @ pi @ Y2 @ P )
% 0.29/0.47         => ( fresh @ name @ pi @ Y2 @ P2 ) ) ) ).
% 0.29/0.47  
% 0.29/0.47  % freshFreeDerivative(2)
% 0.29/0.47  thf(fact_30_resTrans_I2_J,axiom,
% 0.29/0.47      ! [X2: name,Y2: name,P: pi,Rs: late_residual] :
% 0.29/0.47        ~ ( late_transitions @ ( res @ X2 @ ( input @ X2 @ Y2 @ P ) ) @ Rs ) ).
% 0.29/0.47  
% 0.29/0.47  % resTrans(2)
% 0.29/0.47  thf(fact_31_inputFreeTrans,axiom,
% 0.29/0.47      ! [A2: name,X2: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 0.29/0.47        ~ ( late_transitions @ ( input @ A2 @ X2 @ P ) @ ( late_FreeR @ Alpha @ P2 ) ) ).
% 0.29/0.47  
% 0.29/0.47  % inputFreeTrans
% 0.29/0.47  thf(fact_32_ScopeExt,axiom,
% 0.29/0.47      ! [Y2: name,R: pi,Z: name,S: pi] :
% 0.29/0.47        ( ( fresh @ name @ pi @ Y2 @ R )
% 0.29/0.47       => ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( res @ Y2 @ ( res @ Z @ ( par @ R @ S ) ) ) @ ( res @ Z @ ( par @ R @ ( res @ Y2 @ S ) ) ) ) @ rel ) ) ).
% 0.29/0.47  
% 0.29/0.47  % ScopeExt
% 0.29/0.47  thf(fact_33_Res,axiom,
% 0.29/0.47      ! [Y2: name,R: pi,S: pi] :
% 0.29/0.47        ( ( fresh @ name @ pi @ Y2 @ R )
% 0.29/0.47       => ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( res @ Y2 @ ( par @ R @ S ) ) @ ( par @ R @ ( res @ Y2 @ S ) ) ) @ rel ) ) ).
% 0.29/0.47  
% 0.29/0.47  % Res
% 0.29/0.47  thf(fact_34_outputFreshTrans,axiom,
% 0.29/0.47      ! [A2: name,B2: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 0.29/0.47        ( ( late_transitions @ ( output @ A2 @ B2 @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 0.29/0.47       => ~ ( ( fresh @ name @ late_freeRes @ A2 @ Alpha )
% 0.29/0.47            | ( fresh @ name @ late_freeRes @ B2 @ Alpha ) ) ) ).
% 0.29/0.47  
% 0.29/0.47  % outputFreshTrans
% 0.29/0.47  thf(fact_35_residual_Ofresh_I2_J,axiom,
% 0.29/0.47      ! [A2: name,X22: late_freeRes,X1: pi] :
% 0.29/0.47        ( ( fresh @ name @ late_residual @ A2 @ ( late_FreeR @ X22 @ X1 ) )
% 0.29/0.47        = ( ( fresh @ name @ late_freeRes @ A2 @ X22 )
% 0.29/0.47          & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 0.29/0.47  
% 0.29/0.47  % residual.fresh(2)
% 0.29/0.47  thf(fact_36_Id,axiom,
% 0.29/0.47      ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ rel ).
% 0.29/0.48  
% 0.29/0.48  % Id
% 0.29/0.48  thf(fact_37_parCasesB,axiom,
% 0.29/0.48      ! [P: pi,Q: pi,A2: late_subject,X2: name,PQ: pi,Prop: pi > $o] :
% 0.29/0.48        ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X2 @ PQ ) )
% 0.29/0.48       => ( ( fresh @ name @ pi @ X2 @ P )
% 0.29/0.48         => ( ( fresh @ name @ pi @ X2 @ Q )
% 0.29/0.48           => ( ! [P3: pi] :
% 0.29/0.48                  ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P3 ) )
% 0.29/0.48                 => ( Prop @ ( par @ P3 @ Q ) ) )
% 0.29/0.48             => ( ! [Q3: pi] :
% 0.29/0.48                    ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X2 @ Q3 ) )
% 0.29/0.48                   => ( Prop @ ( par @ P @ Q3 ) ) )
% 0.29/0.48               => ( Prop @ PQ ) ) ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % parCasesB
% 0.29/0.48  thf(fact_38_Late__Semantics_OPar2B,axiom,
% 0.29/0.48      ! [Q: pi,A2: late_subject,X2: name,Q2: pi,P: pi] :
% 0.29/0.48        ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X2 @ Q2 ) )
% 0.29/0.48       => ( ( fresh @ name @ pi @ X2 @ P )
% 0.29/0.48         => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X2 @ ( par @ P @ Q2 ) ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % Late_Semantics.Par2B
% 0.29/0.48  thf(fact_39_Late__Semantics_OPar1B,axiom,
% 0.29/0.48      ! [P: pi,A2: late_subject,X2: name,P2: pi,Q: pi] :
% 0.29/0.48        ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P2 ) )
% 0.29/0.48       => ( ( fresh @ name @ pi @ X2 @ Q )
% 0.29/0.48         => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X2 @ ( par @ P2 @ Q ) ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % Late_Semantics.Par1B
% 0.29/0.48  thf(fact_40_nilSim_I2_J,axiom,
% 0.29/0.48      ! [Rel: set @ ( product_prod @ pi @ pi ),A2: name,X2: name,P: pi] :
% 0.29/0.48        ~ ( strong743114133lation @ piNil @ Rel @ ( input @ A2 @ X2 @ P ) ) ).
% 0.29/0.48  
% 0.29/0.48  % nilSim(2)
% 0.29/0.48  thf(fact_41_freeRes_Ofresh_I2_J,axiom,
% 0.29/0.48      ! [A2: name] : ( fresh @ name @ late_freeRes @ A2 @ late_TauR ) ).
% 0.29/0.48  
% 0.29/0.48  % freeRes.fresh(2)
% 0.29/0.48  thf(fact_42_pi_Ofresh_I2_J,axiom,
% 0.29/0.48      ! [A2: name,X3: name,X22: name,X1: pi] :
% 0.29/0.48        ( ( fresh @ name @ pi @ A2 @ ( output @ X3 @ X22 @ X1 ) )
% 0.29/0.48        = ( ( fresh @ name @ name @ A2 @ X3 )
% 0.29/0.48          & ( fresh @ name @ name @ A2 @ X22 )
% 0.29/0.48          & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % pi.fresh(2)
% 0.29/0.48  thf(fact_43_pi_Oinject_I1_J,axiom,
% 0.29/0.48      ! [X3: name,X22: name,X1: pi,Y3: name,Y22: name,Y1: pi] :
% 0.29/0.48        ( ( ( output @ X3 @ X22 @ X1 )
% 0.29/0.48          = ( output @ Y3 @ Y22 @ Y1 ) )
% 0.29/0.48        = ( ( X3 = Y3 )
% 0.29/0.48          & ( X22 = Y22 )
% 0.29/0.48          & ( X1 = Y1 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % pi.inject(1)
% 0.29/0.48  thf(fact_44_outputBoundTrans,axiom,
% 0.29/0.48      ! [A2: name,B2: name,P: pi,C2: late_subject,X2: name,P2: pi] :
% 0.29/0.48        ~ ( late_transitions @ ( output @ A2 @ B2 @ P ) @ ( late_BoundR @ C2 @ X2 @ P2 ) ) ).
% 0.29/0.48  
% 0.29/0.48  % outputBoundTrans
% 0.29/0.48  thf(fact_45_mem__Collect__eq,axiom,
% 0.29/0.48      ! [A: $tType,A2: A,P: A > $o] :
% 0.29/0.48        ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 0.29/0.48        = ( P @ A2 ) ) ).
% 0.29/0.48  
% 0.29/0.48  % mem_Collect_eq
% 0.29/0.48  thf(fact_46_Collect__mem__eq,axiom,
% 0.29/0.48      ! [A: $tType,A3: set @ A] :
% 0.29/0.48        ( ( collect @ A
% 0.29/0.48          @ ^ [X4: A] : ( member @ A @ X4 @ A3 ) )
% 0.29/0.48        = A3 ) ).
% 0.29/0.48  
% 0.29/0.48  % Collect_mem_eq
% 0.29/0.48  thf(fact_47_Collect__cong,axiom,
% 0.29/0.48      ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.29/0.48        ( ! [X5: A] :
% 0.29/0.48            ( ( P @ X5 )
% 0.29/0.48            = ( Q @ X5 ) )
% 0.29/0.48       => ( ( collect @ A @ P )
% 0.29/0.48          = ( collect @ A @ Q ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % Collect_cong
% 0.29/0.48  thf(fact_48_nilSim_I3_J,axiom,
% 0.29/0.48      ! [Rel: set @ ( product_prod @ pi @ pi ),A2: name,B2: name,P: pi] :
% 0.29/0.48        ~ ( strong743114133lation @ piNil @ Rel @ ( output @ A2 @ B2 @ P ) ) ).
% 0.29/0.48  
% 0.29/0.48  % nilSim(3)
% 0.29/0.48  thf(fact_49_Late__Semantics_OResB,axiom,
% 0.29/0.48      ! [P: pi,A2: late_subject,X2: name,P2: pi,Y2: name] :
% 0.29/0.48        ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P2 ) )
% 0.29/0.48       => ( ( fresh @ name @ late_subject @ Y2 @ A2 )
% 0.29/0.48         => ( ( Y2 != X2 )
% 0.29/0.48           => ( late_transitions @ ( res @ Y2 @ P ) @ ( late_BoundR @ A2 @ X2 @ ( res @ Y2 @ P2 ) ) ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % Late_Semantics.ResB
% 0.29/0.48  thf(fact_50_freshBoundDerivative_I1_J,axiom,
% 0.29/0.48      ! [P: pi,A2: late_subject,X2: name,P2: pi,Y2: name] :
% 0.29/0.48        ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P2 ) )
% 0.29/0.48       => ( ( fresh @ name @ pi @ Y2 @ P )
% 0.29/0.48         => ( fresh @ name @ late_subject @ Y2 @ A2 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % freshBoundDerivative(1)
% 0.29/0.48  thf(fact_51_inputIneqTrans,axiom,
% 0.29/0.48      ! [A2: name,X2: name,P: pi,B2: late_subject,Y2: name,P2: pi] :
% 0.29/0.48        ( ( late_transitions @ ( input @ A2 @ X2 @ P ) @ ( late_BoundR @ B2 @ Y2 @ P2 ) )
% 0.29/0.48       => ~ ( fresh @ name @ late_subject @ A2 @ B2 ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inputIneqTrans
% 0.29/0.48  thf(fact_52_parSym,axiom,
% 0.29/0.48      ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi,Q: pi] :
% 0.29/0.48        ( ! [R2: pi,S2: pi] : ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( par @ R2 @ S2 ) @ ( par @ S2 @ R2 ) ) @ Rel )
% 0.29/0.48       => ( ! [R2: pi,S2: pi,X5: name] :
% 0.29/0.48              ( ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ R2 @ S2 ) @ Rel )
% 0.29/0.48             => ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( res @ X5 @ R2 ) @ ( res @ X5 @ S2 ) ) @ Rel ) )
% 0.29/0.48         => ( strong743114133lation @ ( par @ P @ Q ) @ Rel @ ( par @ Q @ P ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % parSym
% 0.29/0.48  thf(fact_53_residual_Odistinct_I1_J,axiom,
% 0.29/0.48      ! [Subject: late_subject,Name3: name,Pi3: pi,FreeRes: late_freeRes,Pi: pi] :
% 0.29/0.48        ( ( late_BoundR @ Subject @ Name3 @ Pi3 )
% 0.29/0.48       != ( late_FreeR @ FreeRes @ Pi ) ) ).
% 0.29/0.48  
% 0.29/0.48  % residual.distinct(1)
% 0.29/0.48  thf(fact_54_residual_Oinducts,axiom,
% 0.29/0.48      ! [P: late_residual > $o,Residual: late_residual] :
% 0.29/0.48        ( ! [Subject2: late_subject,Name4: name,Pi4: pi] : ( P @ ( late_BoundR @ Subject2 @ Name4 @ Pi4 ) )
% 0.29/0.48       => ( ! [FreeRes2: late_freeRes,Pi4: pi] : ( P @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 0.29/0.48         => ( P @ Residual ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % residual.inducts
% 0.29/0.48  thf(fact_55_parZeroRight,axiom,
% 0.29/0.48      ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi] :
% 0.29/0.48        ( ! [Q4: pi] : ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ Q4 @ ( par @ Q4 @ piNil ) ) @ Rel )
% 0.29/0.48       => ( strong743114133lation @ P @ Rel @ ( par @ P @ piNil ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % parZeroRight
% 0.29/0.48  thf(fact_56_parZeroLeft,axiom,
% 0.29/0.48      ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi] :
% 0.29/0.48        ( ! [Q4: pi] : ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( par @ Q4 @ piNil ) @ Q4 ) @ Rel )
% 0.29/0.48       => ( strong743114133lation @ ( par @ P @ piNil ) @ Rel @ P ) ) ).
% 0.29/0.48  
% 0.29/0.48  % parZeroLeft
% 0.29/0.48  thf(fact_57_outputTauTrans,axiom,
% 0.29/0.48      ! [A2: name,B2: name,P: pi,P2: pi] :
% 0.29/0.48        ~ ( late_transitions @ ( output @ A2 @ B2 @ P ) @ ( late_FreeR @ late_TauR @ P2 ) ) ).
% 0.29/0.48  
% 0.29/0.48  % outputTauTrans
% 0.29/0.48  thf(fact_58_pi_Odistinct_I31_J,axiom,
% 0.29/0.48      ! [Name12: name,Name22: name,Pi3: pi,Name: name,Pi: pi] :
% 0.29/0.48        ( ( output @ Name12 @ Name22 @ Pi3 )
% 0.29/0.48       != ( res @ Name @ Pi ) ) ).
% 0.29/0.48  
% 0.29/0.48  % pi.distinct(31)
% 0.29/0.48  thf(fact_59_pi_Odistinct_I29_J,axiom,
% 0.29/0.48      ! [Name12: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 0.29/0.48        ( ( output @ Name12 @ Name22 @ Pi3 )
% 0.29/0.48       != ( par @ Pi12 @ Pi22 ) ) ).
% 0.29/0.48  
% 0.29/0.48  % pi.distinct(29)
% 0.29/0.48  thf(fact_60_transitions_OResB,axiom,
% 0.29/0.48      ! [P: pi,A2: late_subject,X2: name,P2: pi,Y2: name] :
% 0.29/0.48        ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P2 ) )
% 0.29/0.48       => ( ( fresh @ name @ late_subject @ Y2 @ A2 )
% 0.29/0.48         => ( ( Y2 != X2 )
% 0.29/0.48           => ( ( fresh @ name @ pi @ X2 @ P )
% 0.29/0.48             => ( ( fresh @ name @ late_subject @ X2 @ A2 )
% 0.29/0.48               => ( late_transitions @ ( res @ Y2 @ P ) @ ( late_BoundR @ A2 @ X2 @ ( res @ Y2 @ P2 ) ) ) ) ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % transitions.ResB
% 0.29/0.48  thf(fact_61_parCasesB_H,axiom,
% 0.29/0.48      ! [P: pi,Q: pi,B2: late_subject,Y2: name,P2: pi] :
% 0.29/0.48        ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ B2 @ Y2 @ P2 ) )
% 0.29/0.48       => ( ! [P4: pi,A4: late_subject,X5: name,P3: pi,Q4: pi] :
% 0.29/0.48              ( ( ( par @ P @ Q )
% 0.29/0.48                = ( par @ P4 @ Q4 ) )
% 0.29/0.48             => ( ( ( late_BoundR @ B2 @ Y2 @ P2 )
% 0.29/0.48                  = ( late_BoundR @ A4 @ X5 @ ( par @ P3 @ Q4 ) ) )
% 0.29/0.48               => ( ( late_transitions @ P4 @ ( late_BoundR @ A4 @ X5 @ P3 ) )
% 0.29/0.48                 => ( ( fresh @ name @ pi @ X5 @ P4 )
% 0.29/0.48                   => ( ( fresh @ name @ pi @ X5 @ Q4 )
% 0.29/0.48                     => ~ ( fresh @ name @ late_subject @ X5 @ A4 ) ) ) ) ) )
% 0.29/0.48         => ~ ! [Q4: pi,A4: late_subject,X5: name,Q3: pi,P4: pi] :
% 0.29/0.48                ( ( ( par @ P @ Q )
% 0.29/0.48                  = ( par @ P4 @ Q4 ) )
% 0.29/0.48               => ( ( ( late_BoundR @ B2 @ Y2 @ P2 )
% 0.29/0.48                    = ( late_BoundR @ A4 @ X5 @ ( par @ P4 @ Q3 ) ) )
% 0.29/0.48                 => ( ( late_transitions @ Q4 @ ( late_BoundR @ A4 @ X5 @ Q3 ) )
% 0.29/0.48                   => ( ( fresh @ name @ pi @ X5 @ P4 )
% 0.29/0.48                     => ( ( fresh @ name @ pi @ X5 @ Q4 )
% 0.29/0.48                       => ~ ( fresh @ name @ late_subject @ X5 @ A4 ) ) ) ) ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % parCasesB'
% 0.29/0.48  thf(fact_62_transitions_OPar1B,axiom,
% 0.29/0.48      ! [P: pi,A2: late_subject,X2: name,P2: pi,Q: pi] :
% 0.29/0.48        ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P2 ) )
% 0.29/0.48       => ( ( fresh @ name @ pi @ X2 @ P )
% 0.29/0.48         => ( ( fresh @ name @ pi @ X2 @ Q )
% 0.29/0.48           => ( ( fresh @ name @ late_subject @ X2 @ A2 )
% 0.29/0.48             => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X2 @ ( par @ P2 @ Q ) ) ) ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % transitions.Par1B
% 0.29/0.48  thf(fact_63_transitions_OPar2B,axiom,
% 0.29/0.48      ! [Q: pi,A2: late_subject,X2: name,Q2: pi,P: pi] :
% 0.29/0.48        ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X2 @ Q2 ) )
% 0.29/0.48       => ( ( fresh @ name @ pi @ X2 @ P )
% 0.29/0.48         => ( ( fresh @ name @ pi @ X2 @ Q )
% 0.29/0.48           => ( ( fresh @ name @ late_subject @ X2 @ A2 )
% 0.29/0.48             => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X2 @ ( par @ P @ Q2 ) ) ) ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % transitions.Par2B
% 0.29/0.48  thf(fact_64_pi_Odistinct_I21_J,axiom,
% 0.29/0.48      ! [Name12: name,Name22: name,Pi3: pi,Name1: name,Name2: name,Pi: pi] :
% 0.29/0.48        ( ( output @ Name12 @ Name22 @ Pi3 )
% 0.29/0.48       != ( input @ Name1 @ Name2 @ Pi ) ) ).
% 0.29/0.48  
% 0.29/0.48  % pi.distinct(21)
% 0.29/0.48  thf(fact_65_pi_Odistinct_I1_J,axiom,
% 0.29/0.48      ! [Name1: name,Name2: name,Pi: pi] :
% 0.29/0.48        ( piNil
% 0.29/0.48       != ( output @ Name1 @ Name2 @ Pi ) ) ).
% 0.29/0.48  
% 0.29/0.48  % pi.distinct(1)
% 0.29/0.48  thf(fact_66_nilSimRight,axiom,
% 0.29/0.48      ! [P: pi,Rel: set @ ( product_prod @ pi @ pi )] : ( strong743114133lation @ P @ Rel @ piNil ) ).
% 0.29/0.48  
% 0.29/0.48  % nilSimRight
% 0.29/0.48  thf(fact_67_parAssocLeft,axiom,
% 0.29/0.48      ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi,Q: pi,R: pi] :
% 0.29/0.48        ( ! [S2: pi,T2: pi,U: pi] : ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( par @ ( par @ S2 @ T2 ) @ U ) @ ( par @ S2 @ ( par @ T2 @ U ) ) ) @ Rel )
% 0.29/0.48       => ( ! [S2: pi,T2: pi,X5: name] :
% 0.29/0.48              ( ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ S2 @ T2 ) @ Rel )
% 0.29/0.48             => ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( res @ X5 @ S2 ) @ ( res @ X5 @ T2 ) ) @ Rel ) )
% 0.29/0.48         => ( ! [S2: pi,T2: pi,U: pi,X5: name] :
% 0.29/0.48                ( ( fresh @ name @ pi @ X5 @ S2 )
% 0.29/0.48               => ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( res @ X5 @ ( par @ ( par @ S2 @ T2 ) @ U ) ) @ ( par @ S2 @ ( res @ X5 @ ( par @ T2 @ U ) ) ) ) @ Rel ) )
% 0.29/0.48           => ( ! [S2: pi,T2: pi,U: pi,X5: name] :
% 0.29/0.48                  ( ( fresh @ name @ pi @ X5 @ U )
% 0.29/0.48                 => ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( par @ ( res @ X5 @ ( par @ S2 @ T2 ) ) @ U ) @ ( res @ X5 @ ( par @ S2 @ ( par @ T2 @ U ) ) ) ) @ Rel ) )
% 0.29/0.48             => ( strong743114133lation @ ( par @ ( par @ P @ Q ) @ R ) @ Rel @ ( par @ P @ ( par @ Q @ R ) ) ) ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % parAssocLeft
% 0.29/0.48  thf(fact_68_resOutputTauTrans,axiom,
% 0.29/0.48      ! [X2: name,A2: name,B2: name,P: pi,P2: pi] :
% 0.29/0.48        ~ ( late_transitions @ ( res @ X2 @ ( output @ A2 @ B2 @ P ) ) @ ( late_FreeR @ late_TauR @ P2 ) ) ).
% 0.29/0.48  
% 0.29/0.48  % resOutputTauTrans
% 0.29/0.48  thf(fact_69_freshResidual,axiom,
% 0.29/0.48      ! [P: pi,Rs: late_residual,X2: name] :
% 0.29/0.48        ( ( late_transitions @ P @ Rs )
% 0.29/0.48       => ( ( fresh @ name @ pi @ X2 @ P )
% 0.29/0.48         => ( fresh @ name @ late_residual @ X2 @ Rs ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % freshResidual
% 0.29/0.48  thf(fact_70_residual_Ostrong__inducts,axiom,
% 0.29/0.48      ! [A: $tType] :
% 0.29/0.48        ( ( fs_name @ A )
% 0.29/0.48       => ! [P: A > late_residual > $o,Z: A,Residual: late_residual] :
% 0.29/0.48            ( ! [Subject2: late_subject,Name4: name,Pi4: pi,Z2: A] :
% 0.29/0.48                ( ( fresh @ name @ A @ Name4 @ Z2 )
% 0.29/0.48               => ( ( fresh @ name @ late_subject @ Name4 @ Subject2 )
% 0.29/0.48                 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name4 @ Pi4 ) ) ) )
% 0.29/0.48           => ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: A] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 0.29/0.48             => ( P @ Z @ Residual ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % residual.strong_inducts
% 0.29/0.48  thf(fact_71_residual_Ostrong__induct,axiom,
% 0.29/0.48      ! [N: $tType] :
% 0.29/0.48        ( ( fs_name @ N )
% 0.29/0.48       => ! [P: N > late_residual > $o,Z: N,Residual: late_residual] :
% 0.29/0.48            ( ! [Subject2: late_subject,Name4: name,Pi4: pi,Z2: N] :
% 0.29/0.48                ( ( fresh @ name @ N @ Name4 @ Z2 )
% 0.29/0.48               => ( ( fresh @ name @ late_subject @ Name4 @ Subject2 )
% 0.29/0.48                 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name4 @ Pi4 ) ) ) )
% 0.29/0.48           => ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: N] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 0.29/0.48             => ( P @ Z @ Residual ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % residual.strong_induct
% 0.29/0.48  thf(fact_72_freshBoundDerivative_I2_J,axiom,
% 0.29/0.48      ! [P: pi,A2: late_subject,X2: name,P2: pi,Y2: name] :
% 0.29/0.48        ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P2 ) )
% 0.29/0.48       => ( ( fresh @ name @ pi @ Y2 @ P )
% 0.29/0.48         => ( ( Y2 != X2 )
% 0.29/0.48           => ( fresh @ name @ pi @ Y2 @ P2 ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % freshBoundDerivative(2)
% 0.29/0.48  thf(fact_73_resTrans_I1_J,axiom,
% 0.29/0.48      ! [X2: name,B2: name,P: pi,Rs: late_residual] :
% 0.29/0.48        ~ ( late_transitions @ ( res @ X2 @ ( output @ X2 @ B2 @ P ) ) @ Rs ) ).
% 0.29/0.48  
% 0.29/0.48  % resTrans(1)
% 0.29/0.48  thf(fact_74_pair__in__Id__conv,axiom,
% 0.29/0.48      ! [A: $tType,A2: A,B2: A] :
% 0.29/0.48        ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ ( id @ A ) )
% 0.29/0.48        = ( A2 = B2 ) ) ).
% 0.29/0.48  
% 0.29/0.48  % pair_in_Id_conv
% 0.29/0.48  thf(fact_75_IdI,axiom,
% 0.29/0.48      ! [A: $tType,A2: A] : ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ A2 ) @ ( id @ A ) ) ).
% 0.29/0.48  
% 0.29/0.48  % IdI
% 0.29/0.48  thf(fact_76_fresh__prod,axiom,
% 0.29/0.48      ! [A: $tType,X: $tType,B: $tType,A2: X,X2: A,Y2: B] :
% 0.29/0.48        ( ( fresh @ X @ ( product_prod @ A @ B ) @ A2 @ ( product_Pair @ A @ B @ X2 @ Y2 ) )
% 0.29/0.48        = ( ( fresh @ X @ A @ A2 @ X2 )
% 0.29/0.48          & ( fresh @ X @ B @ A2 @ Y2 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % fresh_prod
% 0.29/0.48  thf(fact_77_simE_I2_J,axiom,
% 0.29/0.48      ! [P: pi,Rel: set @ ( product_prod @ pi @ pi ),Q: pi,Alpha: late_freeRes,Q2: pi] :
% 0.29/0.48        ( ( strong743114133lation @ P @ Rel @ Q )
% 0.29/0.48       => ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 0.29/0.48         => ? [P3: pi] :
% 0.29/0.48              ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P3 ) )
% 0.29/0.48              & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P3 @ Q2 ) @ Rel ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % simE(2)
% 0.29/0.48  thf(fact_78_Strong__Late__Sim_Oreflexive,axiom,
% 0.29/0.48      ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi] :
% 0.29/0.48        ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 0.29/0.48       => ( strong743114133lation @ P @ Rel @ P ) ) ).
% 0.29/0.48  
% 0.29/0.48  % Strong_Late_Sim.reflexive
% 0.29/0.48  thf(fact_79_simCasesCont,axiom,
% 0.29/0.48      ! [A: $tType] :
% 0.29/0.48        ( ( fs_name @ A )
% 0.29/0.48       => ! [Rel: set @ ( product_prod @ pi @ pi ),Q: pi,P: pi,C3: A] :
% 0.29/0.48            ( ( eqvt @ pi @ Rel )
% 0.29/0.48           => ( ! [A4: late_subject,X5: name,Q3: pi] :
% 0.29/0.48                  ( ( late_transitions @ Q @ ( late_BoundR @ A4 @ X5 @ Q3 ) )
% 0.29/0.48                 => ( ( fresh @ name @ pi @ X5 @ P )
% 0.29/0.48                   => ( ( fresh @ name @ pi @ X5 @ Q )
% 0.29/0.48                     => ( ( fresh @ name @ late_subject @ X5 @ A4 )
% 0.29/0.48                       => ( ( fresh @ name @ A @ X5 @ C3 )
% 0.29/0.48                         => ? [P5: pi] :
% 0.29/0.48                              ( ( late_transitions @ P @ ( late_BoundR @ A4 @ X5 @ P5 ) )
% 0.29/0.48                              & ( strong2129052853vative @ P5 @ Q3 @ A4 @ X5 @ Rel ) ) ) ) ) ) )
% 0.29/0.48             => ( ! [Alpha2: late_freeRes,Q3: pi] :
% 0.29/0.48                    ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 0.29/0.48                   => ? [P5: pi] :
% 0.29/0.48                        ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P5 ) )
% 0.29/0.48                        & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P5 @ Q3 ) @ Rel ) ) )
% 0.29/0.48               => ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % simCasesCont
% 0.29/0.48  thf(fact_80_subset__antisym,axiom,
% 0.29/0.48      ! [A: $tType,A3: set @ A,B3: set @ A] :
% 0.29/0.48        ( ( ord_less_eq @ ( set @ A ) @ A3 @ B3 )
% 0.29/0.48       => ( ( ord_less_eq @ ( set @ A ) @ B3 @ A3 )
% 0.29/0.48         => ( A3 = B3 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % subset_antisym
% 0.29/0.48  thf(fact_81_subsetI,axiom,
% 0.29/0.48      ! [A: $tType,A3: set @ A,B3: set @ A] :
% 0.29/0.48        ( ! [X5: A] :
% 0.29/0.48            ( ( member @ A @ X5 @ A3 )
% 0.29/0.48           => ( member @ A @ X5 @ B3 ) )
% 0.29/0.48       => ( ord_less_eq @ ( set @ A ) @ A3 @ B3 ) ) ).
% 0.29/0.48  
% 0.29/0.48  % subsetI
% 0.29/0.48  thf(fact_82_name__fresh,axiom,
% 0.29/0.48      ( ( fresh @ name @ name )
% 0.29/0.48      = ( ^ [A5: name,B4: name] : ( A5 != B4 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % name_fresh
% 0.29/0.48  thf(fact_83_derivativeMonotonic,axiom,
% 0.29/0.48      ! [P: pi,Q: pi,A2: late_subject,X2: name,A3: set @ ( product_prod @ pi @ pi ),B3: set @ ( product_prod @ pi @ pi )] :
% 0.29/0.48        ( ( strong2129052853vative @ P @ Q @ A2 @ X2 @ A3 )
% 0.29/0.48       => ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ A3 @ B3 )
% 0.29/0.48         => ( strong2129052853vative @ P @ Q @ A2 @ X2 @ B3 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % derivativeMonotonic
% 0.29/0.48  thf(fact_84_derivativeReflexive,axiom,
% 0.29/0.48      ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi,A2: late_subject,X2: name] :
% 0.29/0.48        ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 0.29/0.48       => ( strong2129052853vative @ P @ P @ A2 @ X2 @ Rel ) ) ).
% 0.29/0.48  
% 0.29/0.48  % derivativeReflexive
% 0.29/0.48  thf(fact_85_in__mono,axiom,
% 0.29/0.48      ! [A: $tType,A3: set @ A,B3: set @ A,X2: A] :
% 0.29/0.48        ( ( ord_less_eq @ ( set @ A ) @ A3 @ B3 )
% 0.29/0.48       => ( ( member @ A @ X2 @ A3 )
% 0.29/0.48         => ( member @ A @ X2 @ B3 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % in_mono
% 0.29/0.48  thf(fact_86_subsetD,axiom,
% 0.29/0.48      ! [A: $tType,A3: set @ A,B3: set @ A,C2: A] :
% 0.29/0.48        ( ( ord_less_eq @ ( set @ A ) @ A3 @ B3 )
% 0.29/0.48       => ( ( member @ A @ C2 @ A3 )
% 0.29/0.48         => ( member @ A @ C2 @ B3 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % subsetD
% 0.29/0.48  thf(fact_87_equalityE,axiom,
% 0.29/0.48      ! [A: $tType,A3: set @ A,B3: set @ A] :
% 0.29/0.48        ( ( A3 = B3 )
% 0.29/0.48       => ~ ( ( ord_less_eq @ ( set @ A ) @ A3 @ B3 )
% 0.29/0.48           => ~ ( ord_less_eq @ ( set @ A ) @ B3 @ A3 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % equalityE
% 0.29/0.48  thf(fact_88_subset__eq,axiom,
% 0.29/0.48      ! [A: $tType] :
% 0.29/0.48        ( ( ord_less_eq @ ( set @ A ) )
% 0.29/0.48        = ( ^ [A6: set @ A,B5: set @ A] :
% 0.29/0.48            ! [X4: A] :
% 0.29/0.48              ( ( member @ A @ X4 @ A6 )
% 0.29/0.48             => ( member @ A @ X4 @ B5 ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % subset_eq
% 0.29/0.48  thf(fact_89_equalityD1,axiom,
% 0.29/0.48      ! [A: $tType,A3: set @ A,B3: set @ A] :
% 0.29/0.48        ( ( A3 = B3 )
% 0.29/0.48       => ( ord_less_eq @ ( set @ A ) @ A3 @ B3 ) ) ).
% 0.29/0.48  
% 0.29/0.48  % equalityD1
% 0.29/0.48  thf(fact_90_equalityD2,axiom,
% 0.29/0.48      ! [A: $tType,A3: set @ A,B3: set @ A] :
% 0.29/0.48        ( ( A3 = B3 )
% 0.29/0.48       => ( ord_less_eq @ ( set @ A ) @ B3 @ A3 ) ) ).
% 0.29/0.48  
% 0.29/0.48  % equalityD2
% 0.29/0.48  thf(fact_91_subset__iff,axiom,
% 0.29/0.48      ! [A: $tType] :
% 0.29/0.48        ( ( ord_less_eq @ ( set @ A ) )
% 0.29/0.48        = ( ^ [A6: set @ A,B5: set @ A] :
% 0.29/0.48            ! [T3: A] :
% 0.29/0.48              ( ( member @ A @ T3 @ A6 )
% 0.29/0.48             => ( member @ A @ T3 @ B5 ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % subset_iff
% 0.29/0.48  thf(fact_92_subset__refl,axiom,
% 0.29/0.48      ! [A: $tType,A3: set @ A] : ( ord_less_eq @ ( set @ A ) @ A3 @ A3 ) ).
% 0.29/0.48  
% 0.29/0.48  % subset_refl
% 0.29/0.48  thf(fact_93_Collect__mono,axiom,
% 0.29/0.48      ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.29/0.48        ( ! [X5: A] :
% 0.29/0.48            ( ( P @ X5 )
% 0.29/0.48           => ( Q @ X5 ) )
% 0.29/0.48       => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % Collect_mono
% 0.29/0.48  thf(fact_94_subset__trans,axiom,
% 0.29/0.48      ! [A: $tType,A3: set @ A,B3: set @ A,C3: set @ A] :
% 0.29/0.48        ( ( ord_less_eq @ ( set @ A ) @ A3 @ B3 )
% 0.29/0.48       => ( ( ord_less_eq @ ( set @ A ) @ B3 @ C3 )
% 0.29/0.48         => ( ord_less_eq @ ( set @ A ) @ A3 @ C3 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % subset_trans
% 0.29/0.48  thf(fact_95_set__eq__subset,axiom,
% 0.29/0.48      ! [A: $tType] :
% 0.29/0.48        ( ( ^ [Y4: set @ A,Z3: set @ A] : ( Y4 = Z3 ) )
% 0.29/0.48        = ( ^ [A6: set @ A,B5: set @ A] :
% 0.29/0.48              ( ( ord_less_eq @ ( set @ A ) @ A6 @ B5 )
% 0.29/0.48              & ( ord_less_eq @ ( set @ A ) @ B5 @ A6 ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % set_eq_subset
% 0.29/0.48  thf(fact_96_Collect__mono__iff,axiom,
% 0.29/0.48      ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.29/0.48        ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) )
% 0.29/0.48        = ( ! [X4: A] :
% 0.29/0.48              ( ( P @ X4 )
% 0.29/0.48             => ( Q @ X4 ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % Collect_mono_iff
% 0.29/0.48  thf(fact_97_simE_I1_J,axiom,
% 0.29/0.48      ! [P: pi,Rel: set @ ( product_prod @ pi @ pi ),Q: pi,A2: late_subject,X2: name,Q2: pi] :
% 0.29/0.48        ( ( strong743114133lation @ P @ Rel @ Q )
% 0.29/0.48       => ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X2 @ Q2 ) )
% 0.29/0.48         => ( ( fresh @ name @ pi @ X2 @ P )
% 0.29/0.48           => ? [P3: pi] :
% 0.29/0.48                ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P3 ) )
% 0.29/0.48                & ( strong2129052853vative @ P3 @ Q2 @ A2 @ X2 @ Rel ) ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % simE(1)
% 0.29/0.48  thf(fact_98_fresh__prodD_I2_J,axiom,
% 0.29/0.48      ! [B: $tType,A: $tType,C4: $tType,A2: A,X2: B,Y2: C4] :
% 0.29/0.48        ( ( fresh @ A @ ( product_prod @ B @ C4 ) @ A2 @ ( product_Pair @ B @ C4 @ X2 @ Y2 ) )
% 0.29/0.48       => ( fresh @ A @ C4 @ A2 @ Y2 ) ) ).
% 0.29/0.48  
% 0.29/0.48  % fresh_prodD(2)
% 0.29/0.48  thf(fact_99_fresh__prodD_I1_J,axiom,
% 0.29/0.48      ! [C4: $tType,A: $tType,B: $tType,A2: A,X2: B,Y2: C4] :
% 0.29/0.48        ( ( fresh @ A @ ( product_prod @ B @ C4 ) @ A2 @ ( product_Pair @ B @ C4 @ X2 @ Y2 ) )
% 0.29/0.48       => ( fresh @ A @ B @ A2 @ X2 ) ) ).
% 0.29/0.48  
% 0.29/0.48  % fresh_prodD(1)
% 0.29/0.48  thf(fact_100_subrelI,axiom,
% 0.29/0.48      ! [B: $tType,A: $tType,R3: set @ ( product_prod @ A @ B ),S3: set @ ( product_prod @ A @ B )] :
% 0.29/0.48        ( ! [X5: A,Y: B] :
% 0.29/0.48            ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X5 @ Y ) @ R3 )
% 0.29/0.48           => ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X5 @ Y ) @ S3 ) )
% 0.29/0.48       => ( ord_less_eq @ ( set @ ( product_prod @ A @ B ) ) @ R3 @ S3 ) ) ).
% 0.29/0.48  
% 0.29/0.48  % subrelI
% 0.29/0.48  thf(fact_101_simCases,axiom,
% 0.29/0.48      ! [Q: pi,P: pi,Rel: set @ ( product_prod @ pi @ pi )] :
% 0.29/0.48        ( ! [A4: late_subject,Y: name,Q3: pi] :
% 0.29/0.48            ( ( late_transitions @ Q @ ( late_BoundR @ A4 @ Y @ Q3 ) )
% 0.29/0.48           => ( ( fresh @ name @ pi @ Y @ P )
% 0.29/0.48             => ? [P5: pi] :
% 0.29/0.48                  ( ( late_transitions @ P @ ( late_BoundR @ A4 @ Y @ P5 ) )
% 0.29/0.48                  & ( strong2129052853vative @ P5 @ Q3 @ A4 @ Y @ Rel ) ) ) )
% 0.29/0.48       => ( ! [Alpha2: late_freeRes,Q3: pi] :
% 0.29/0.48              ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 0.29/0.48             => ? [P5: pi] :
% 0.29/0.48                  ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P5 ) )
% 0.29/0.48                  & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P5 @ Q3 ) @ Rel ) ) )
% 0.29/0.48         => ( strong743114133lation @ P @ Rel @ Q ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % simCases
% 0.29/0.48  thf(fact_102_simulation__def,axiom,
% 0.29/0.48      ( strong743114133lation
% 0.29/0.48      = ( ^ [P6: pi,Rel2: set @ ( product_prod @ pi @ pi ),Q5: pi] :
% 0.29/0.48            ( ! [A5: late_subject,X4: name,Q6: pi] :
% 0.29/0.48                ( ( ( late_transitions @ Q5 @ ( late_BoundR @ A5 @ X4 @ Q6 ) )
% 0.29/0.48                  & ( fresh @ name @ pi @ X4 @ P6 ) )
% 0.29/0.48               => ? [P7: pi] :
% 0.29/0.48                    ( ( late_transitions @ P6 @ ( late_BoundR @ A5 @ X4 @ P7 ) )
% 0.29/0.48                    & ( strong2129052853vative @ P7 @ Q6 @ A5 @ X4 @ Rel2 ) ) )
% 0.29/0.48            & ! [Alpha3: late_freeRes,Q6: pi] :
% 0.29/0.48                ( ( late_transitions @ Q5 @ ( late_FreeR @ Alpha3 @ Q6 ) )
% 0.29/0.48               => ? [P7: pi] :
% 0.29/0.48                    ( ( late_transitions @ P6 @ ( late_FreeR @ Alpha3 @ P7 ) )
% 0.29/0.48                    & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P7 @ Q6 ) @ Rel2 ) ) ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % simulation_def
% 0.29/0.48  thf(fact_103_IdE,axiom,
% 0.29/0.48      ! [A: $tType,P8: product_prod @ A @ A] :
% 0.29/0.48        ( ( member @ ( product_prod @ A @ A ) @ P8 @ ( id @ A ) )
% 0.29/0.48       => ~ ! [X5: A] :
% 0.29/0.48              ( P8
% 0.29/0.48             != ( product_Pair @ A @ A @ X5 @ X5 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % IdE
% 0.29/0.48  thf(fact_104_monotonic,axiom,
% 0.29/0.48      ! [P: pi,A3: set @ ( product_prod @ pi @ pi ),P2: pi,B3: set @ ( product_prod @ pi @ pi )] :
% 0.29/0.48        ( ( strong743114133lation @ P @ A3 @ P2 )
% 0.29/0.48       => ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ A3 @ B3 )
% 0.29/0.48         => ( strong743114133lation @ P @ B3 @ P2 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % monotonic
% 0.29/0.48  thf(fact_105_prod_Oinject,axiom,
% 0.29/0.48      ! [A: $tType,B: $tType,X1: A,X22: B,Y1: A,Y22: B] :
% 0.29/0.48        ( ( ( product_Pair @ A @ B @ X1 @ X22 )
% 0.29/0.48          = ( product_Pair @ A @ B @ Y1 @ Y22 ) )
% 0.29/0.48        = ( ( X1 = Y1 )
% 0.29/0.48          & ( X22 = Y22 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % prod.inject
% 0.29/0.48  thf(fact_106_old_Oprod_Oinject,axiom,
% 0.29/0.48      ! [A: $tType,B: $tType,A2: A,B2: B,A7: A,B6: B] :
% 0.29/0.48        ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 0.29/0.48          = ( product_Pair @ A @ B @ A7 @ B6 ) )
% 0.29/0.48        = ( ( A2 = A7 )
% 0.29/0.48          & ( B2 = B6 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % old.prod.inject
% 0.29/0.48  thf(fact_107_order__refl,axiom,
% 0.29/0.48      ! [A: $tType] :
% 0.29/0.48        ( ( preorder @ A )
% 0.29/0.48       => ! [X2: A] : ( ord_less_eq @ A @ X2 @ X2 ) ) ).
% 0.29/0.48  
% 0.29/0.48  % order_refl
% 0.29/0.48  thf(fact_108_resSimCases,axiom,
% 0.29/0.48      ! [A: $tType] :
% 0.29/0.48        ( ( fs_name @ A )
% 0.29/0.48       => ! [Rel: set @ ( product_prod @ pi @ pi ),Q: pi,X2: name,P: pi,C3: A] :
% 0.29/0.48            ( ( eqvt @ pi @ Rel )
% 0.29/0.48           => ( ! [Q3: pi,A4: name] :
% 0.29/0.48                  ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A4 @ X2 ) @ Q3 ) )
% 0.29/0.48                 => ( ( A4 != X2 )
% 0.29/0.48                   => ? [P5: pi] :
% 0.29/0.48                        ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A4 ) @ X2 @ P5 ) )
% 0.29/0.48                        & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P5 @ Q3 ) @ Rel ) ) ) )
% 0.29/0.48             => ( ! [Q3: pi,A4: late_subject,Y: name] :
% 0.29/0.48                    ( ( late_transitions @ Q @ ( late_BoundR @ A4 @ Y @ Q3 ) )
% 0.29/0.48                   => ( ( fresh @ name @ late_subject @ X2 @ A4 )
% 0.29/0.48                     => ( ( X2 != Y )
% 0.29/0.48                       => ( ( fresh @ name @ A @ Y @ C3 )
% 0.29/0.48                         => ? [P5: pi] :
% 0.29/0.48                              ( ( late_transitions @ P @ ( late_BoundR @ A4 @ Y @ P5 ) )
% 0.29/0.48                              & ( strong2129052853vative @ P5 @ ( res @ X2 @ Q3 ) @ A4 @ Y @ Rel ) ) ) ) ) )
% 0.29/0.48               => ( ! [Q3: pi,Alpha2: late_freeRes] :
% 0.29/0.48                      ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 0.29/0.48                     => ( ( fresh @ name @ late_freeRes @ X2 @ Alpha2 )
% 0.29/0.48                       => ? [P5: pi] :
% 0.29/0.48                            ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P5 ) )
% 0.29/0.48                            & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P5 @ ( res @ X2 @ Q3 ) ) @ Rel ) ) ) )
% 0.29/0.48                 => ( strong743114133lation @ P @ Rel @ ( res @ X2 @ Q ) ) ) ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % resSimCases
% 0.29/0.48  thf(fact_109_IdD,axiom,
% 0.29/0.48      ! [A: $tType,A2: A,B2: A] :
% 0.29/0.48        ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ ( id @ A ) )
% 0.29/0.48       => ( A2 = B2 ) ) ).
% 0.29/0.48  
% 0.29/0.48  % IdD
% 0.29/0.48  thf(fact_110_sumResLeft,axiom,
% 0.29/0.48      ! [Rel: set @ ( product_prod @ pi @ pi ),X2: name,P: pi,Q: pi] :
% 0.29/0.48        ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 0.29/0.48       => ( ( eqvt @ pi @ Rel )
% 0.29/0.48         => ( strong743114133lation @ ( sum @ ( res @ X2 @ P ) @ ( res @ X2 @ Q ) ) @ Rel @ ( res @ X2 @ ( sum @ P @ Q ) ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sumResLeft
% 0.29/0.48  thf(fact_111_Late__Semantics_OfreeRes_Oinject,axiom,
% 0.29/0.48      ! [X22: name,X1: name,Y22: name,Y1: name] :
% 0.29/0.48        ( ( ( late_OutputR @ X22 @ X1 )
% 0.29/0.48          = ( late_OutputR @ Y22 @ Y1 ) )
% 0.29/0.48        = ( ( X22 = Y22 )
% 0.29/0.48          & ( X1 = Y1 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % Late_Semantics.freeRes.inject
% 0.29/0.48  thf(fact_112_Late__Semantics_Osubject_Oinject_I2_J,axiom,
% 0.29/0.48      ! [X1: name,Y1: name] :
% 0.29/0.48        ( ( ( late_BoundOutputS @ X1 )
% 0.29/0.48          = ( late_BoundOutputS @ Y1 ) )
% 0.29/0.48        = ( X1 = Y1 ) ) ).
% 0.29/0.48  
% 0.29/0.48  % Late_Semantics.subject.inject(2)
% 0.29/0.48  thf(fact_113_pi_Ofresh_I7_J,axiom,
% 0.29/0.48      ! [A2: name,X22: pi,X1: pi] :
% 0.29/0.48        ( ( fresh @ name @ pi @ A2 @ ( sum @ X22 @ X1 ) )
% 0.29/0.48        = ( ( fresh @ name @ pi @ A2 @ X22 )
% 0.29/0.48          & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % pi.fresh(7)
% 0.29/0.48  thf(fact_114_subject_Ofresh_I2_J,axiom,
% 0.29/0.48      ! [A2: name,X1: name] :
% 0.29/0.48        ( ( fresh @ name @ late_subject @ A2 @ ( late_BoundOutputS @ X1 ) )
% 0.29/0.48        = ( fresh @ name @ name @ A2 @ X1 ) ) ).
% 0.29/0.48  
% 0.29/0.48  % subject.fresh(2)
% 0.29/0.48  thf(fact_115_freeRes_Ofresh_I1_J,axiom,
% 0.29/0.48      ! [A2: name,X22: name,X1: name] :
% 0.29/0.48        ( ( fresh @ name @ late_freeRes @ A2 @ ( late_OutputR @ X22 @ X1 ) )
% 0.29/0.48        = ( ( fresh @ name @ name @ A2 @ X22 )
% 0.29/0.48          & ( fresh @ name @ name @ A2 @ X1 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % freeRes.fresh(1)
% 0.29/0.48  thf(fact_116_pi_Oinject_I6_J,axiom,
% 0.29/0.48      ! [X22: pi,X1: pi,Y22: pi,Y1: pi] :
% 0.29/0.48        ( ( ( sum @ X22 @ X1 )
% 0.29/0.48          = ( sum @ Y22 @ Y1 ) )
% 0.29/0.48        = ( ( X22 = Y22 )
% 0.29/0.48          & ( X1 = Y1 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % pi.inject(6)
% 0.29/0.48  thf(fact_117_sumCases,axiom,
% 0.29/0.48      ! [P: pi,Q: pi,Rs: late_residual] :
% 0.29/0.48        ( ( late_transitions @ ( sum @ P @ Q ) @ Rs )
% 0.29/0.48       => ( ~ ( late_transitions @ P @ Rs )
% 0.29/0.48         => ( late_transitions @ Q @ Rs ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sumCases
% 0.29/0.48  thf(fact_118_sumCases_H,axiom,
% 0.29/0.48      ! [P: pi,Q: pi,Rs: late_residual] :
% 0.29/0.48        ( ( late_transitions @ ( sum @ P @ Q ) @ Rs )
% 0.29/0.48       => ( ~ ( late_transitions @ P @ Rs )
% 0.29/0.48         => ( late_transitions @ Q @ Rs ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sumCases'
% 0.29/0.48  thf(fact_119_Sum1,axiom,
% 0.29/0.48      ! [P: pi,Rs: late_residual,Q: pi] :
% 0.29/0.48        ( ( late_transitions @ P @ Rs )
% 0.29/0.48       => ( late_transitions @ ( sum @ P @ Q ) @ Rs ) ) ).
% 0.29/0.48  
% 0.29/0.48  % Sum1
% 0.29/0.48  thf(fact_120_Sum2,axiom,
% 0.29/0.48      ! [Q: pi,Rs: late_residual,P: pi] :
% 0.29/0.48        ( ( late_transitions @ Q @ Rs )
% 0.29/0.48       => ( late_transitions @ ( sum @ P @ Q ) @ Rs ) ) ).
% 0.29/0.48  
% 0.29/0.48  % Sum2
% 0.29/0.48  thf(fact_121_pi_Odistinct_I81_J,axiom,
% 0.29/0.48      ! [Pi1: pi,Pi2: pi,Name: name,Pi: pi] :
% 0.29/0.48        ( ( sum @ Pi1 @ Pi2 )
% 0.29/0.48       != ( res @ Name @ Pi ) ) ).
% 0.29/0.48  
% 0.29/0.48  % pi.distinct(81)
% 0.29/0.48  thf(fact_122_pi_Odistinct_I79_J,axiom,
% 0.29/0.48      ! [Pi1: pi,Pi2: pi,Pi12: pi,Pi22: pi] :
% 0.29/0.48        ( ( sum @ Pi1 @ Pi2 )
% 0.29/0.48       != ( par @ Pi12 @ Pi22 ) ) ).
% 0.29/0.48  
% 0.29/0.48  % pi.distinct(79)
% 0.29/0.48  thf(fact_123_pi_Odistinct_I53_J,axiom,
% 0.29/0.48      ! [Name12: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 0.29/0.48        ( ( input @ Name12 @ Name22 @ Pi3 )
% 0.29/0.48       != ( sum @ Pi12 @ Pi22 ) ) ).
% 0.29/0.48  
% 0.29/0.48  % pi.distinct(53)
% 0.29/0.48  thf(fact_124_pi_Odistinct_I11_J,axiom,
% 0.29/0.48      ! [Pi12: pi,Pi22: pi] :
% 0.29/0.48        ( piNil
% 0.29/0.48       != ( sum @ Pi12 @ Pi22 ) ) ).
% 0.29/0.48  
% 0.29/0.48  % pi.distinct(11)
% 0.29/0.48  thf(fact_125_pi_Odistinct_I27_J,axiom,
% 0.29/0.48      ! [Name12: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 0.29/0.48        ( ( output @ Name12 @ Name22 @ Pi3 )
% 0.29/0.48       != ( sum @ Pi12 @ Pi22 ) ) ).
% 0.29/0.48  
% 0.29/0.48  % pi.distinct(27)
% 0.29/0.48  thf(fact_126_Late__Semantics_OfreeRes_Odistinct_I1_J,axiom,
% 0.29/0.48      ! [Name12: name,Name22: name] :
% 0.29/0.48        ( ( late_OutputR @ Name12 @ Name22 )
% 0.29/0.48       != late_TauR ) ).
% 0.29/0.48  
% 0.29/0.48  % Late_Semantics.freeRes.distinct(1)
% 0.29/0.48  thf(fact_127_freeRes_Oinducts,axiom,
% 0.29/0.48      ! [P: late_freeRes > $o,FreeRes3: late_freeRes] :
% 0.29/0.48        ( ! [Name13: name,Name23: name] : ( P @ ( late_OutputR @ Name13 @ Name23 ) )
% 0.29/0.48       => ( ( P @ late_TauR )
% 0.29/0.48         => ( P @ FreeRes3 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % freeRes.inducts
% 0.29/0.48  thf(fact_128_freeRes_Ostrong__induct_H,axiom,
% 0.29/0.48      ! [N: $tType,P: N > late_freeRes > $o,Z: N,FreeRes3: late_freeRes] :
% 0.29/0.48        ( ! [Name13: name,Name23: name,Z2: N] : ( P @ Z2 @ ( late_OutputR @ Name13 @ Name23 ) )
% 0.29/0.48       => ( ! [Z2: N] : ( P @ Z2 @ late_TauR )
% 0.29/0.48         => ( P @ Z @ FreeRes3 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % freeRes.strong_induct'
% 0.29/0.48  thf(fact_129_freeRes_Ostrong__inducts,axiom,
% 0.29/0.48      ! [A: $tType,P: A > late_freeRes > $o,Z: A,FreeRes3: late_freeRes] :
% 0.29/0.48        ( ! [Name13: name,Name23: name,Z2: A] : ( P @ Z2 @ ( late_OutputR @ Name13 @ Name23 ) )
% 0.29/0.48       => ( ! [Z2: A] : ( P @ Z2 @ late_TauR )
% 0.29/0.48         => ( P @ Z @ FreeRes3 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % freeRes.strong_inducts
% 0.29/0.48  thf(fact_130_Open,axiom,
% 0.29/0.48      ! [P: pi,A2: name,B2: name,P2: pi] :
% 0.29/0.48        ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P2 ) )
% 0.29/0.48       => ( ( A2 != B2 )
% 0.29/0.48         => ( late_transitions @ ( res @ B2 @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ B2 @ P2 ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % Open
% 0.29/0.48  thf(fact_131_dual__order_Oantisym,axiom,
% 0.29/0.48      ! [A: $tType] :
% 0.29/0.48        ( ( order @ A )
% 0.29/0.48       => ! [B2: A,A2: A] :
% 0.29/0.48            ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.29/0.48           => ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.29/0.48             => ( A2 = B2 ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % dual_order.antisym
% 0.29/0.48  thf(fact_132_dual__order_Oeq__iff,axiom,
% 0.29/0.48      ! [A: $tType] :
% 0.29/0.48        ( ( order @ A )
% 0.29/0.48       => ( ( ^ [Y4: A,Z3: A] : ( Y4 = Z3 ) )
% 0.29/0.48          = ( ^ [A5: A,B4: A] :
% 0.29/0.48                ( ( ord_less_eq @ A @ B4 @ A5 )
% 0.29/0.48                & ( ord_less_eq @ A @ A5 @ B4 ) ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % dual_order.eq_iff
% 0.29/0.48  thf(fact_133_dual__order_Otrans,axiom,
% 0.29/0.48      ! [A: $tType] :
% 0.29/0.48        ( ( order @ A )
% 0.29/0.48       => ! [B2: A,A2: A,C2: A] :
% 0.29/0.48            ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.29/0.48           => ( ( ord_less_eq @ A @ C2 @ B2 )
% 0.29/0.48             => ( ord_less_eq @ A @ C2 @ A2 ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % dual_order.trans
% 0.29/0.48  thf(fact_134_linorder__wlog,axiom,
% 0.29/0.48      ! [A: $tType] :
% 0.29/0.48        ( ( linorder @ A )
% 0.29/0.48       => ! [P: A > A > $o,A2: A,B2: A] :
% 0.29/0.48            ( ! [A4: A,B7: A] :
% 0.29/0.48                ( ( ord_less_eq @ A @ A4 @ B7 )
% 0.29/0.48               => ( P @ A4 @ B7 ) )
% 0.29/0.48           => ( ! [A4: A,B7: A] :
% 0.29/0.48                  ( ( P @ B7 @ A4 )
% 0.29/0.48                 => ( P @ A4 @ B7 ) )
% 0.29/0.48             => ( P @ A2 @ B2 ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % linorder_wlog
% 0.29/0.48  thf(fact_135_dual__order_Orefl,axiom,
% 0.29/0.48      ! [A: $tType] :
% 0.29/0.48        ( ( order @ A )
% 0.29/0.48       => ! [A2: A] : ( ord_less_eq @ A @ A2 @ A2 ) ) ).
% 0.29/0.48  
% 0.29/0.48  % dual_order.refl
% 0.29/0.48  thf(fact_136_order__trans,axiom,
% 0.29/0.48      ! [A: $tType] :
% 0.29/0.48        ( ( preorder @ A )
% 0.29/0.48       => ! [X2: A,Y2: A,Z: A] :
% 0.29/0.48            ( ( ord_less_eq @ A @ X2 @ Y2 )
% 0.29/0.48           => ( ( ord_less_eq @ A @ Y2 @ Z )
% 0.29/0.48             => ( ord_less_eq @ A @ X2 @ Z ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % order_trans
% 0.29/0.48  thf(fact_137_order__class_Oorder_Oantisym,axiom,
% 0.29/0.48      ! [A: $tType] :
% 0.29/0.48        ( ( order @ A )
% 0.29/0.48       => ! [A2: A,B2: A] :
% 0.29/0.48            ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.29/0.48           => ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.29/0.48             => ( A2 = B2 ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % order_class.order.antisym
% 0.29/0.48  thf(fact_138_ord__le__eq__trans,axiom,
% 0.29/0.48      ! [A: $tType] :
% 0.29/0.48        ( ( ord @ A )
% 0.29/0.48       => ! [A2: A,B2: A,C2: A] :
% 0.29/0.48            ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.29/0.48           => ( ( B2 = C2 )
% 0.29/0.48             => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % ord_le_eq_trans
% 0.29/0.48  thf(fact_139_ord__eq__le__trans,axiom,
% 0.29/0.48      ! [A: $tType] :
% 0.29/0.48        ( ( ord @ A )
% 0.29/0.48       => ! [A2: A,B2: A,C2: A] :
% 0.29/0.48            ( ( A2 = B2 )
% 0.29/0.48           => ( ( ord_less_eq @ A @ B2 @ C2 )
% 0.29/0.48             => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % ord_eq_le_trans
% 0.29/0.48  thf(fact_140_order__class_Oorder_Oeq__iff,axiom,
% 0.29/0.48      ! [A: $tType] :
% 0.29/0.48        ( ( order @ A )
% 0.29/0.48       => ( ( ^ [Y4: A,Z3: A] : ( Y4 = Z3 ) )
% 0.29/0.48          = ( ^ [A5: A,B4: A] :
% 0.29/0.48                ( ( ord_less_eq @ A @ A5 @ B4 )
% 0.29/0.48                & ( ord_less_eq @ A @ B4 @ A5 ) ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % order_class.order.eq_iff
% 0.29/0.48  thf(fact_141_antisym__conv,axiom,
% 0.29/0.48      ! [A: $tType] :
% 0.29/0.48        ( ( order @ A )
% 0.29/0.48       => ! [Y2: A,X2: A] :
% 0.29/0.48            ( ( ord_less_eq @ A @ Y2 @ X2 )
% 0.29/0.48           => ( ( ord_less_eq @ A @ X2 @ Y2 )
% 0.29/0.48              = ( X2 = Y2 ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % antisym_conv
% 0.29/0.48  thf(fact_142_le__cases3,axiom,
% 0.29/0.48      ! [A: $tType] :
% 0.29/0.48        ( ( linorder @ A )
% 0.29/0.48       => ! [X2: A,Y2: A,Z: A] :
% 0.29/0.48            ( ( ( ord_less_eq @ A @ X2 @ Y2 )
% 0.29/0.48             => ~ ( ord_less_eq @ A @ Y2 @ Z ) )
% 0.29/0.48           => ( ( ( ord_less_eq @ A @ Y2 @ X2 )
% 0.29/0.48               => ~ ( ord_less_eq @ A @ X2 @ Z ) )
% 0.29/0.48             => ( ( ( ord_less_eq @ A @ X2 @ Z )
% 0.29/0.48                 => ~ ( ord_less_eq @ A @ Z @ Y2 ) )
% 0.29/0.48               => ( ( ( ord_less_eq @ A @ Z @ Y2 )
% 0.29/0.48                   => ~ ( ord_less_eq @ A @ Y2 @ X2 ) )
% 0.29/0.48                 => ( ( ( ord_less_eq @ A @ Y2 @ Z )
% 0.29/0.48                     => ~ ( ord_less_eq @ A @ Z @ X2 ) )
% 0.29/0.48                   => ~ ( ( ord_less_eq @ A @ Z @ X2 )
% 0.29/0.48                       => ~ ( ord_less_eq @ A @ X2 @ Y2 ) ) ) ) ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % le_cases3
% 0.29/0.48  thf(fact_143_order_Otrans,axiom,
% 0.29/0.48      ! [A: $tType] :
% 0.29/0.48        ( ( order @ A )
% 0.29/0.48       => ! [A2: A,B2: A,C2: A] :
% 0.29/0.48            ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.29/0.48           => ( ( ord_less_eq @ A @ B2 @ C2 )
% 0.29/0.48             => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % order.trans
% 0.29/0.48  thf(fact_144_le__cases,axiom,
% 0.29/0.48      ! [A: $tType] :
% 0.29/0.48        ( ( linorder @ A )
% 0.29/0.48       => ! [X2: A,Y2: A] :
% 0.29/0.48            ( ~ ( ord_less_eq @ A @ X2 @ Y2 )
% 0.29/0.48           => ( ord_less_eq @ A @ Y2 @ X2 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % le_cases
% 0.29/0.48  thf(fact_145_eq__refl,axiom,
% 0.29/0.48      ! [A: $tType] :
% 0.29/0.48        ( ( preorder @ A )
% 0.29/0.48       => ! [X2: A,Y2: A] :
% 0.29/0.48            ( ( X2 = Y2 )
% 0.29/0.48           => ( ord_less_eq @ A @ X2 @ Y2 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % eq_refl
% 0.29/0.48  thf(fact_146_linear,axiom,
% 0.29/0.48      ! [A: $tType] :
% 0.29/0.48        ( ( linorder @ A )
% 0.29/0.48       => ! [X2: A,Y2: A] :
% 0.29/0.48            ( ( ord_less_eq @ A @ X2 @ Y2 )
% 0.29/0.48            | ( ord_less_eq @ A @ Y2 @ X2 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % linear
% 0.29/0.48  thf(fact_147_antisym,axiom,
% 0.29/0.48      ! [A: $tType] :
% 0.29/0.48        ( ( order @ A )
% 0.29/0.48       => ! [X2: A,Y2: A] :
% 0.29/0.48            ( ( ord_less_eq @ A @ X2 @ Y2 )
% 0.29/0.48           => ( ( ord_less_eq @ A @ Y2 @ X2 )
% 0.29/0.48             => ( X2 = Y2 ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % antisym
% 0.29/0.48  thf(fact_148_eq__iff,axiom,
% 0.29/0.48      ! [A: $tType] :
% 0.29/0.48        ( ( order @ A )
% 0.29/0.48       => ( ( ^ [Y4: A,Z3: A] : ( Y4 = Z3 ) )
% 0.29/0.48          = ( ^ [X4: A,Y5: A] :
% 0.29/0.48                ( ( ord_less_eq @ A @ X4 @ Y5 )
% 0.29/0.48                & ( ord_less_eq @ A @ Y5 @ X4 ) ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % eq_iff
% 0.29/0.48  thf(fact_149_ord__le__eq__subst,axiom,
% 0.29/0.48      ! [A: $tType,B: $tType] :
% 0.29/0.48        ( ( ( ord @ B )
% 0.29/0.48          & ( ord @ A ) )
% 0.29/0.48       => ! [A2: A,B2: A,F2: A > B,C2: B] :
% 0.29/0.48            ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.29/0.48           => ( ( ( F2 @ B2 )
% 0.29/0.48                = C2 )
% 0.29/0.48             => ( ! [X5: A,Y: A] :
% 0.29/0.48                    ( ( ord_less_eq @ A @ X5 @ Y )
% 0.29/0.48                   => ( ord_less_eq @ B @ ( F2 @ X5 ) @ ( F2 @ Y ) ) )
% 0.29/0.48               => ( ord_less_eq @ B @ ( F2 @ A2 ) @ C2 ) ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % ord_le_eq_subst
% 0.29/0.48  thf(fact_150_ord__eq__le__subst,axiom,
% 0.29/0.48      ! [A: $tType,B: $tType] :
% 0.29/0.48        ( ( ( ord @ B )
% 0.29/0.48          & ( ord @ A ) )
% 0.29/0.48       => ! [A2: A,F2: B > A,B2: B,C2: B] :
% 0.29/0.48            ( ( A2
% 0.29/0.48              = ( F2 @ B2 ) )
% 0.29/0.48           => ( ( ord_less_eq @ B @ B2 @ C2 )
% 0.29/0.48             => ( ! [X5: B,Y: B] :
% 0.29/0.48                    ( ( ord_less_eq @ B @ X5 @ Y )
% 0.29/0.48                   => ( ord_less_eq @ A @ ( F2 @ X5 ) @ ( F2 @ Y ) ) )
% 0.29/0.48               => ( ord_less_eq @ A @ A2 @ ( F2 @ C2 ) ) ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % ord_eq_le_subst
% 0.29/0.48  thf(fact_151_order__subst2,axiom,
% 0.29/0.48      ! [A: $tType,C4: $tType] :
% 0.29/0.48        ( ( ( order @ C4 )
% 0.29/0.48          & ( order @ A ) )
% 0.29/0.48       => ! [A2: A,B2: A,F2: A > C4,C2: C4] :
% 0.29/0.48            ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.29/0.48           => ( ( ord_less_eq @ C4 @ ( F2 @ B2 ) @ C2 )
% 0.29/0.48             => ( ! [X5: A,Y: A] :
% 0.29/0.48                    ( ( ord_less_eq @ A @ X5 @ Y )
% 0.29/0.48                   => ( ord_less_eq @ C4 @ ( F2 @ X5 ) @ ( F2 @ Y ) ) )
% 0.29/0.48               => ( ord_less_eq @ C4 @ ( F2 @ A2 ) @ C2 ) ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % order_subst2
% 0.29/0.48  thf(fact_152_order__subst1,axiom,
% 0.29/0.48      ! [A: $tType,B: $tType] :
% 0.29/0.48        ( ( ( order @ B )
% 0.29/0.48          & ( order @ A ) )
% 0.29/0.48       => ! [A2: A,F2: B > A,B2: B,C2: B] :
% 0.29/0.48            ( ( ord_less_eq @ A @ A2 @ ( F2 @ B2 ) )
% 0.29/0.48           => ( ( ord_less_eq @ B @ B2 @ C2 )
% 0.29/0.48             => ( ! [X5: B,Y: B] :
% 0.29/0.48                    ( ( ord_less_eq @ B @ X5 @ Y )
% 0.29/0.48                   => ( ord_less_eq @ A @ ( F2 @ X5 ) @ ( F2 @ Y ) ) )
% 0.29/0.48               => ( ord_less_eq @ A @ A2 @ ( F2 @ C2 ) ) ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % order_subst1
% 0.29/0.48  thf(fact_153_le__fun__def,axiom,
% 0.29/0.48      ! [B: $tType,A: $tType] :
% 0.29/0.48        ( ( ord @ B )
% 0.29/0.48       => ( ( ord_less_eq @ ( A > B ) )
% 0.29/0.48          = ( ^ [F3: A > B,G: A > B] :
% 0.29/0.48              ! [X4: A] : ( ord_less_eq @ B @ ( F3 @ X4 ) @ ( G @ X4 ) ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % le_fun_def
% 0.29/0.48  thf(fact_154_le__funI,axiom,
% 0.29/0.48      ! [B: $tType,A: $tType] :
% 0.29/0.48        ( ( ord @ B )
% 0.29/0.48       => ! [F2: A > B,G2: A > B] :
% 0.29/0.48            ( ! [X5: A] : ( ord_less_eq @ B @ ( F2 @ X5 ) @ ( G2 @ X5 ) )
% 0.29/0.48           => ( ord_less_eq @ ( A > B ) @ F2 @ G2 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % le_funI
% 0.29/0.48  thf(fact_155_le__funE,axiom,
% 0.29/0.48      ! [B: $tType,A: $tType] :
% 0.29/0.48        ( ( ord @ B )
% 0.29/0.48       => ! [F2: A > B,G2: A > B,X2: A] :
% 0.29/0.48            ( ( ord_less_eq @ ( A > B ) @ F2 @ G2 )
% 0.29/0.48           => ( ord_less_eq @ B @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % le_funE
% 0.29/0.48  thf(fact_156_le__funD,axiom,
% 0.29/0.48      ! [B: $tType,A: $tType] :
% 0.29/0.48        ( ( ord @ B )
% 0.29/0.48       => ! [F2: A > B,G2: A > B,X2: A] :
% 0.29/0.48            ( ( ord_less_eq @ ( A > B ) @ F2 @ G2 )
% 0.29/0.48           => ( ord_less_eq @ B @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % le_funD
% 0.29/0.48  thf(fact_157_old_Oprod_Oinducts,axiom,
% 0.29/0.48      ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,Prod: product_prod @ A @ B] :
% 0.29/0.48        ( ! [A4: A,B7: B] : ( P @ ( product_Pair @ A @ B @ A4 @ B7 ) )
% 0.29/0.48       => ( P @ Prod ) ) ).
% 0.29/0.48  
% 0.29/0.48  % old.prod.inducts
% 0.29/0.48  thf(fact_158_old_Oprod_Oexhaust,axiom,
% 0.29/0.48      ! [A: $tType,B: $tType,Y2: product_prod @ A @ B] :
% 0.29/0.48        ~ ! [A4: A,B7: B] :
% 0.29/0.48            ( Y2
% 0.29/0.48           != ( product_Pair @ A @ B @ A4 @ B7 ) ) ).
% 0.29/0.48  
% 0.29/0.48  % old.prod.exhaust
% 0.29/0.48  thf(fact_159_prod__induct7,axiom,
% 0.29/0.48      ! [G3: $tType,F4: $tType,E: $tType,D: $tType,C4: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C4 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G3 ) ) ) ) ) ) > $o,X2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C4 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G3 ) ) ) ) )] :
% 0.29/0.48        ( ! [A4: A,B7: B,C: C4,D2: D,E2: E,F5: F4,G4: G3] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C4 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G3 ) ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C4 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G3 ) ) ) ) @ B7 @ ( product_Pair @ C4 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G3 ) ) ) @ C @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G3 ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F4 @ G3 ) @ E2 @ ( product_Pair @ F4 @ G3 @ F5 @ G4 ) ) ) ) ) ) )
% 0.29/0.48       => ( P @ X2 ) ) ).
% 0.29/0.48  
% 0.29/0.48  % prod_induct7
% 0.29/0.48  thf(fact_160_prod__induct6,axiom,
% 0.29/0.48      ! [F4: $tType,E: $tType,D: $tType,C4: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C4 @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) ) ) ) > $o,X2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C4 @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) ) )] :
% 0.29/0.48        ( ! [A4: A,B7: B,C: C4,D2: D,E2: E,F5: F4] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C4 @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C4 @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) ) @ B7 @ ( product_Pair @ C4 @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) @ C @ ( product_Pair @ D @ ( product_prod @ E @ F4 ) @ D2 @ ( product_Pair @ E @ F4 @ E2 @ F5 ) ) ) ) ) )
% 0.29/0.48       => ( P @ X2 ) ) ).
% 0.29/0.48  
% 0.29/0.48  % prod_induct6
% 0.29/0.48  thf(fact_161_prod__induct5,axiom,
% 0.29/0.48      ! [E: $tType,D: $tType,C4: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C4 @ ( product_prod @ D @ E ) ) ) ) > $o,X2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C4 @ ( product_prod @ D @ E ) ) )] :
% 0.29/0.48        ( ! [A4: A,B7: B,C: C4,D2: D,E2: E] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C4 @ ( product_prod @ D @ E ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C4 @ ( product_prod @ D @ E ) ) @ B7 @ ( product_Pair @ C4 @ ( product_prod @ D @ E ) @ C @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) )
% 0.29/0.48       => ( P @ X2 ) ) ).
% 0.29/0.48  
% 0.29/0.48  % prod_induct5
% 0.29/0.48  thf(fact_162_prod__induct4,axiom,
% 0.29/0.48      ! [D: $tType,C4: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C4 @ D ) ) ) > $o,X2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C4 @ D ) )] :
% 0.29/0.48        ( ! [A4: A,B7: B,C: C4,D2: D] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C4 @ D ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C4 @ D ) @ B7 @ ( product_Pair @ C4 @ D @ C @ D2 ) ) ) )
% 0.29/0.48       => ( P @ X2 ) ) ).
% 0.29/0.48  
% 0.29/0.48  % prod_induct4
% 0.29/0.48  thf(fact_163_prod__induct3,axiom,
% 0.29/0.48      ! [C4: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ C4 ) ) > $o,X2: product_prod @ A @ ( product_prod @ B @ C4 )] :
% 0.29/0.48        ( ! [A4: A,B7: B,C: C4] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ C4 ) @ A4 @ ( product_Pair @ B @ C4 @ B7 @ C ) ) )
% 0.29/0.48       => ( P @ X2 ) ) ).
% 0.29/0.48  
% 0.29/0.48  % prod_induct3
% 0.29/0.48  thf(fact_164_prod__cases7,axiom,
% 0.29/0.48      ! [A: $tType,B: $tType,C4: $tType,D: $tType,E: $tType,F4: $tType,G3: $tType,Y2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C4 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G3 ) ) ) ) )] :
% 0.29/0.48        ~ ! [A4: A,B7: B,C: C4,D2: D,E2: E,F5: F4,G4: G3] :
% 0.29/0.48            ( Y2
% 0.29/0.48           != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C4 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G3 ) ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C4 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G3 ) ) ) ) @ B7 @ ( product_Pair @ C4 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G3 ) ) ) @ C @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G3 ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F4 @ G3 ) @ E2 @ ( product_Pair @ F4 @ G3 @ F5 @ G4 ) ) ) ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % prod_cases7
% 0.29/0.48  thf(fact_165_prod__cases6,axiom,
% 0.29/0.48      ! [A: $tType,B: $tType,C4: $tType,D: $tType,E: $tType,F4: $tType,Y2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C4 @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) ) )] :
% 0.29/0.48        ~ ! [A4: A,B7: B,C: C4,D2: D,E2: E,F5: F4] :
% 0.29/0.48            ( Y2
% 0.29/0.48           != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C4 @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C4 @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) ) @ B7 @ ( product_Pair @ C4 @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) @ C @ ( product_Pair @ D @ ( product_prod @ E @ F4 ) @ D2 @ ( product_Pair @ E @ F4 @ E2 @ F5 ) ) ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % prod_cases6
% 0.29/0.48  thf(fact_166_prod__cases5,axiom,
% 0.29/0.48      ! [A: $tType,B: $tType,C4: $tType,D: $tType,E: $tType,Y2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C4 @ ( product_prod @ D @ E ) ) )] :
% 0.29/0.48        ~ ! [A4: A,B7: B,C: C4,D2: D,E2: E] :
% 0.29/0.48            ( Y2
% 0.29/0.48           != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C4 @ ( product_prod @ D @ E ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C4 @ ( product_prod @ D @ E ) ) @ B7 @ ( product_Pair @ C4 @ ( product_prod @ D @ E ) @ C @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % prod_cases5
% 0.29/0.48  thf(fact_167_prod__cases4,axiom,
% 0.29/0.48      ! [A: $tType,B: $tType,C4: $tType,D: $tType,Y2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C4 @ D ) )] :
% 0.29/0.48        ~ ! [A4: A,B7: B,C: C4,D2: D] :
% 0.29/0.48            ( Y2
% 0.29/0.48           != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C4 @ D ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C4 @ D ) @ B7 @ ( product_Pair @ C4 @ D @ C @ D2 ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % prod_cases4
% 0.29/0.48  thf(fact_168_prod__cases3,axiom,
% 0.29/0.48      ! [A: $tType,B: $tType,C4: $tType,Y2: product_prod @ A @ ( product_prod @ B @ C4 )] :
% 0.29/0.48        ~ ! [A4: A,B7: B,C: C4] :
% 0.29/0.48            ( Y2
% 0.29/0.48           != ( product_Pair @ A @ ( product_prod @ B @ C4 ) @ A4 @ ( product_Pair @ B @ C4 @ B7 @ C ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % prod_cases3
% 0.29/0.48  thf(fact_169_Pair__inject,axiom,
% 0.29/0.48      ! [A: $tType,B: $tType,A2: A,B2: B,A7: A,B6: B] :
% 0.29/0.48        ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 0.29/0.48          = ( product_Pair @ A @ B @ A7 @ B6 ) )
% 0.29/0.48       => ~ ( ( A2 = A7 )
% 0.29/0.48           => ( B2 != B6 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % Pair_inject
% 0.29/0.48  thf(fact_170_prod__cases,axiom,
% 0.29/0.48      ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,P8: product_prod @ A @ B] :
% 0.29/0.48        ( ! [A4: A,B7: B] : ( P @ ( product_Pair @ A @ B @ A4 @ B7 ) )
% 0.29/0.48       => ( P @ P8 ) ) ).
% 0.29/0.48  
% 0.29/0.48  % prod_cases
% 0.29/0.48  thf(fact_171_surj__pair,axiom,
% 0.29/0.48      ! [A: $tType,B: $tType,P8: product_prod @ A @ B] :
% 0.29/0.48      ? [X5: A,Y: B] :
% 0.29/0.48        ( P8
% 0.29/0.48        = ( product_Pair @ A @ B @ X5 @ Y ) ) ).
% 0.29/0.48  
% 0.29/0.48  % surj_pair
% 0.29/0.48  thf(fact_172_resCasesB_H,axiom,
% 0.29/0.48      ! [X6: name,P: pi,A2: late_subject,Y6: name,P2: pi] :
% 0.29/0.48        ( ( late_transitions @ ( res @ X6 @ P ) @ ( late_BoundR @ A2 @ Y6 @ P2 ) )
% 0.29/0.48       => ( ! [P4: pi,A4: name,B7: name] :
% 0.29/0.48              ( ( ( res @ X6 @ P )
% 0.29/0.48                = ( res @ B7 @ P4 ) )
% 0.29/0.48             => ! [P3: pi] :
% 0.29/0.48                  ( ( ( late_BoundR @ A2 @ Y6 @ P2 )
% 0.29/0.48                    = ( late_BoundR @ ( late_BoundOutputS @ A4 ) @ B7 @ P3 ) )
% 0.29/0.48                 => ( ( late_transitions @ P4 @ ( late_FreeR @ ( late_OutputR @ A4 @ B7 ) @ P3 ) )
% 0.29/0.48                   => ( A4 = B7 ) ) ) )
% 0.29/0.48         => ~ ! [P4: pi,A4: late_subject,X5: name,P3: pi,Y: name] :
% 0.29/0.48                ( ( ( res @ X6 @ P )
% 0.29/0.48                  = ( res @ Y @ P4 ) )
% 0.29/0.48               => ( ( ( late_BoundR @ A2 @ Y6 @ P2 )
% 0.29/0.48                    = ( late_BoundR @ A4 @ X5 @ ( res @ Y @ P3 ) ) )
% 0.29/0.48                 => ( ( late_transitions @ P4 @ ( late_BoundR @ A4 @ X5 @ P3 ) )
% 0.29/0.48                   => ( ( fresh @ name @ late_subject @ Y @ A4 )
% 0.29/0.48                     => ( ( Y != X5 )
% 0.29/0.48                       => ( ( fresh @ name @ pi @ X5 @ P4 )
% 0.29/0.48                         => ~ ( fresh @ name @ late_subject @ X5 @ A4 ) ) ) ) ) ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % resCasesB'
% 0.29/0.48  thf(fact_173_outputCases,axiom,
% 0.29/0.48      ! [A2: name,B2: name,P: pi,Alpha: late_freeRes,P2: pi,Prop: late_freeRes > pi > $o] :
% 0.29/0.48        ( ( late_transitions @ ( output @ A2 @ B2 @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 0.29/0.48       => ( ( ( Alpha
% 0.29/0.48              = ( late_OutputR @ A2 @ B2 ) )
% 0.29/0.48           => ( ( P = P2 )
% 0.29/0.48             => ( Prop @ ( late_OutputR @ A2 @ B2 ) @ P ) ) )
% 0.29/0.48         => ( Prop @ Alpha @ P2 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % outputCases
% 0.29/0.48  thf(fact_174_outputCases_H,axiom,
% 0.29/0.48      ! [A2: name,B2: name,P: pi,Rs: late_residual] :
% 0.29/0.48        ( ( late_transitions @ ( output @ A2 @ B2 @ P ) @ Rs )
% 0.29/0.48       => ~ ! [A4: name,B7: name,P4: pi] :
% 0.29/0.48              ( ( ( A2 = A4 )
% 0.29/0.48                & ( B2 = B7 )
% 0.29/0.48                & ( P = P4 ) )
% 0.29/0.48             => ( Rs
% 0.29/0.48               != ( late_FreeR @ ( late_OutputR @ A4 @ B7 ) @ P4 ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % outputCases'
% 0.29/0.48  thf(fact_175_outputIneqTrans,axiom,
% 0.29/0.48      ! [A2: name,B2: name,P: pi,C2: name,D3: name,P2: pi] :
% 0.29/0.48        ( ( late_transitions @ ( output @ A2 @ B2 @ P ) @ ( late_FreeR @ ( late_OutputR @ C2 @ D3 ) @ P2 ) )
% 0.29/0.48       => ~ ( ( A2 != C2 )
% 0.29/0.48            | ( B2 != D3 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % outputIneqTrans
% 0.29/0.48  thf(fact_176_Output,axiom,
% 0.29/0.48      ! [A2: name,B2: name,P: pi] : ( late_transitions @ ( output @ A2 @ B2 @ P ) @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P ) ) ).
% 0.29/0.48  
% 0.29/0.48  % Output
% 0.29/0.48  thf(fact_177_sumIdempRight,axiom,
% 0.29/0.48      ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi] :
% 0.29/0.48        ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 0.29/0.48       => ( strong743114133lation @ ( sum @ P @ P ) @ Rel @ P ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sumIdempRight
% 0.29/0.48  thf(fact_178_sumAssocRight,axiom,
% 0.29/0.48      ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi,Q: pi,R: pi] :
% 0.29/0.48        ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 0.29/0.48       => ( strong743114133lation @ ( sum @ P @ ( sum @ Q @ R ) ) @ Rel @ ( sum @ ( sum @ P @ Q ) @ R ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sumAssocRight
% 0.29/0.48  thf(fact_179_sumIdempLeft,axiom,
% 0.29/0.48      ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi] :
% 0.29/0.48        ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 0.29/0.48       => ( strong743114133lation @ P @ Rel @ ( sum @ P @ P ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sumIdempLeft
% 0.29/0.48  thf(fact_180_sumAssocLeft,axiom,
% 0.29/0.48      ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi,Q: pi,R: pi] :
% 0.29/0.48        ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 0.29/0.48       => ( strong743114133lation @ ( sum @ ( sum @ P @ Q ) @ R ) @ Rel @ ( sum @ P @ ( sum @ Q @ R ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sumAssocLeft
% 0.29/0.48  thf(fact_181_sumSym,axiom,
% 0.29/0.48      ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi,Q: pi] :
% 0.29/0.48        ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 0.29/0.48       => ( strong743114133lation @ ( sum @ P @ Q ) @ Rel @ ( sum @ Q @ P ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sumSym
% 0.29/0.48  thf(fact_182_inputBoundOutputTrans,axiom,
% 0.29/0.48      ! [A2: name,X2: name,P: pi,B2: name,Y2: name,P2: pi] :
% 0.29/0.48        ~ ( late_transitions @ ( input @ A2 @ X2 @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ B2 ) @ Y2 @ P2 ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inputBoundOutputTrans
% 0.29/0.48  thf(fact_183_resCases_H,axiom,
% 0.29/0.48      ! [X2: name,P: pi,Rs: late_residual] :
% 0.29/0.48        ( ( late_transitions @ ( res @ X2 @ P ) @ Rs )
% 0.29/0.48       => ( ! [P4: pi,A4: name,B7: name] :
% 0.29/0.48              ( ( ( res @ X2 @ P )
% 0.29/0.48                = ( res @ B7 @ P4 ) )
% 0.29/0.48             => ! [P3: pi] :
% 0.29/0.48                  ( ( Rs
% 0.29/0.48                    = ( late_BoundR @ ( late_BoundOutputS @ A4 ) @ B7 @ P3 ) )
% 0.29/0.48                 => ( ( late_transitions @ P4 @ ( late_FreeR @ ( late_OutputR @ A4 @ B7 ) @ P3 ) )
% 0.29/0.48                   => ( A4 = B7 ) ) ) )
% 0.29/0.48         => ( ! [P4: pi,A4: late_subject,X5: name,P3: pi,Y: name] :
% 0.29/0.48                ( ( ( res @ X2 @ P )
% 0.29/0.48                  = ( res @ Y @ P4 ) )
% 0.29/0.48               => ( ( Rs
% 0.29/0.48                    = ( late_BoundR @ A4 @ X5 @ ( res @ Y @ P3 ) ) )
% 0.29/0.48                 => ( ( late_transitions @ P4 @ ( late_BoundR @ A4 @ X5 @ P3 ) )
% 0.29/0.48                   => ( ( fresh @ name @ late_subject @ Y @ A4 )
% 0.29/0.48                     => ( ( Y != X5 )
% 0.29/0.48                       => ( ( fresh @ name @ pi @ X5 @ P4 )
% 0.29/0.48                         => ~ ( fresh @ name @ late_subject @ X5 @ A4 ) ) ) ) ) ) )
% 0.29/0.48           => ~ ! [P4: pi,Alpha2: late_freeRes,P3: pi,Y: name] :
% 0.29/0.48                  ( ( ( res @ X2 @ P )
% 0.29/0.48                    = ( res @ Y @ P4 ) )
% 0.29/0.48                 => ( ( Rs
% 0.29/0.48                      = ( late_FreeR @ Alpha2 @ ( res @ Y @ P3 ) ) )
% 0.29/0.48                   => ( ( late_transitions @ P4 @ ( late_FreeR @ Alpha2 @ P3 ) )
% 0.29/0.48                     => ~ ( fresh @ name @ late_freeRes @ Y @ Alpha2 ) ) ) ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % resCases'
% 0.29/0.48  thf(fact_184_resOutputOutputTrans,axiom,
% 0.29/0.48      ! [X2: name,A2: name,P: pi,B2: name,Y2: name,P2: pi] :
% 0.29/0.48        ~ ( late_transitions @ ( res @ X2 @ ( output @ A2 @ X2 @ P ) ) @ ( late_FreeR @ ( late_OutputR @ B2 @ Y2 ) @ P2 ) ) ).
% 0.29/0.48  
% 0.29/0.48  % resOutputOutputTrans
% 0.29/0.48  thf(fact_185_sumZeroLeft,axiom,
% 0.29/0.48      ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi] :
% 0.29/0.48        ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 0.29/0.48       => ( strong743114133lation @ ( sum @ P @ piNil ) @ Rel @ P ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sumZeroLeft
% 0.29/0.48  thf(fact_186_sumZeroRight,axiom,
% 0.29/0.48      ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi] :
% 0.29/0.48        ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 0.29/0.48       => ( strong743114133lation @ P @ Rel @ ( sum @ P @ piNil ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sumZeroRight
% 0.29/0.48  thf(fact_187_resInputBoundOutputTrans,axiom,
% 0.29/0.48      ! [X2: name,A2: name,Y2: name,P: pi,B2: name,Z: name,P2: pi] :
% 0.29/0.48        ~ ( late_transitions @ ( res @ X2 @ ( input @ A2 @ Y2 @ P ) ) @ ( late_BoundR @ ( late_BoundOutputS @ B2 ) @ Z @ P2 ) ) ).
% 0.29/0.48  
% 0.29/0.48  % resInputBoundOutputTrans
% 0.29/0.48  thf(fact_188_sumResRight,axiom,
% 0.29/0.48      ! [Rel: set @ ( product_prod @ pi @ pi ),X2: name,P: pi,Q: pi] :
% 0.29/0.48        ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 0.29/0.48       => ( ( eqvt @ pi @ Rel )
% 0.29/0.48         => ( strong743114133lation @ ( res @ X2 @ ( sum @ P @ Q ) ) @ Rel @ ( sum @ ( res @ X2 @ P ) @ ( res @ X2 @ Q ) ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sumResRight
% 0.29/0.48  thf(fact_189_old_Oprod_Orec,axiom,
% 0.29/0.48      ! [A: $tType,T: $tType,B: $tType,F1: A > B > T,A2: A,B2: B] :
% 0.29/0.48        ( ( product_rec_prod @ A @ B @ T @ F1 @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 0.29/0.48        = ( F1 @ A2 @ B2 ) ) ).
% 0.29/0.48  
% 0.29/0.48  % old.prod.rec
% 0.29/0.48  thf(fact_190_Late__Semantics1_Osubject_Oinject_I2_J,axiom,
% 0.29/0.48      ! [X22: name,Y22: name] :
% 0.29/0.48        ( ( ( late_BoundOutputS @ X22 )
% 0.29/0.48          = ( late_BoundOutputS @ Y22 ) )
% 0.29/0.48        = ( X22 = Y22 ) ) ).
% 0.29/0.48  
% 0.29/0.48  % Late_Semantics1.subject.inject(2)
% 0.29/0.48  thf(fact_191_Late__Semantics1_OfreeRes_Oinject,axiom,
% 0.29/0.48      ! [X11: name,X12: name,Y11: name,Y12: name] :
% 0.29/0.48        ( ( ( late_OutputR @ X11 @ X12 )
% 0.29/0.48          = ( late_OutputR @ Y11 @ Y12 ) )
% 0.29/0.48        = ( ( X11 = Y11 )
% 0.29/0.48          & ( X12 = Y12 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % Late_Semantics1.freeRes.inject
% 0.29/0.48  thf(fact_192_Late__Semantics1_OfreeRes_Odistinct_I1_J,axiom,
% 0.29/0.48      ! [X11: name,X12: name] :
% 0.29/0.48        ( ( late_OutputR @ X11 @ X12 )
% 0.29/0.48       != late_TauR ) ).
% 0.29/0.48  
% 0.29/0.48  % Late_Semantics1.freeRes.distinct(1)
% 0.29/0.48  thf(fact_193_freeRes_Oexhaust,axiom,
% 0.29/0.48      ! [Y2: late_freeRes] :
% 0.29/0.48        ( ! [X112: name,X122: name] :
% 0.29/0.48            ( Y2
% 0.29/0.48           != ( late_OutputR @ X112 @ X122 ) )
% 0.29/0.48       => ( Y2 = late_TauR ) ) ).
% 0.29/0.48  
% 0.29/0.48  % freeRes.exhaust
% 0.29/0.48  thf(fact_194_resOutputInputTrans,axiom,
% 0.29/0.48      ! [X2: name,A2: name,B2: name,P: pi,C2: name,Y2: name,P2: pi] :
% 0.29/0.48        ~ ( late_transitions @ ( res @ X2 @ ( output @ A2 @ B2 @ P ) ) @ ( late_BoundR @ ( late_InputS @ C2 ) @ Y2 @ P2 ) ) ).
% 0.29/0.48  
% 0.29/0.48  % resOutputInputTrans
% 0.29/0.48  thf(fact_195_freeRes_Orecs_I2_J,axiom,
% 0.29/0.48      ! [T: $tType,P: T > $o,F1: name > name > T,F22: T] :
% 0.29/0.48        ( ! [X13: name,X23: name] : ( P @ ( F1 @ X13 @ X23 ) )
% 0.29/0.48       => ( ( P @ F22 )
% 0.29/0.48         => ( ( late_freeRes_rec @ T @ F1 @ F22 @ late_TauR )
% 0.29/0.48            = F22 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % freeRes.recs(2)
% 0.29/0.48  thf(fact_196_Late__Semantics1_Osubject_Oinject_I1_J,axiom,
% 0.29/0.48      ! [X1: name,Y1: name] :
% 0.29/0.48        ( ( ( late_InputS @ X1 )
% 0.29/0.48          = ( late_InputS @ Y1 ) )
% 0.29/0.48        = ( X1 = Y1 ) ) ).
% 0.29/0.48  
% 0.29/0.48  % Late_Semantics1.subject.inject(1)
% 0.29/0.48  thf(fact_197_subject_Ofresh_I1_J,axiom,
% 0.29/0.48      ! [A2: name,X1: name] :
% 0.29/0.48        ( ( fresh @ name @ late_subject @ A2 @ ( late_InputS @ X1 ) )
% 0.29/0.48        = ( fresh @ name @ name @ A2 @ X1 ) ) ).
% 0.29/0.48  
% 0.29/0.48  % subject.fresh(1)
% 0.29/0.48  thf(fact_198_subject_Oexhaust,axiom,
% 0.29/0.48      ! [Y2: late_subject] :
% 0.29/0.48        ( ! [X13: name] :
% 0.29/0.48            ( Y2
% 0.29/0.48           != ( late_InputS @ X13 ) )
% 0.29/0.48       => ~ ! [X23: name] :
% 0.29/0.48              ( Y2
% 0.29/0.48             != ( late_BoundOutputS @ X23 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % subject.exhaust
% 0.29/0.48  thf(fact_199_Late__Semantics1_Osubject_Odistinct_I1_J,axiom,
% 0.29/0.48      ! [X1: name,X22: name] :
% 0.29/0.48        ( ( late_InputS @ X1 )
% 0.29/0.48       != ( late_BoundOutputS @ X22 ) ) ).
% 0.29/0.48  
% 0.29/0.48  % Late_Semantics1.subject.distinct(1)
% 0.29/0.48  thf(fact_200_subject_Ostrong__inducts,axiom,
% 0.29/0.48      ! [A: $tType,P: A > late_subject > $o,Z: A,Subject: late_subject] :
% 0.29/0.48        ( ! [Name4: name,Z2: A] : ( P @ Z2 @ ( late_InputS @ Name4 ) )
% 0.29/0.48       => ( ! [Name4: name,Z2: A] : ( P @ Z2 @ ( late_BoundOutputS @ Name4 ) )
% 0.29/0.48         => ( P @ Z @ Subject ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % subject.strong_inducts
% 0.29/0.48  thf(fact_201_subject_Ostrong__induct_H,axiom,
% 0.29/0.48      ! [N: $tType,P: N > late_subject > $o,Z: N,Subject: late_subject] :
% 0.29/0.48        ( ! [Name4: name,Z2: N] : ( P @ Z2 @ ( late_InputS @ Name4 ) )
% 0.29/0.48       => ( ! [Name4: name,Z2: N] : ( P @ Z2 @ ( late_BoundOutputS @ Name4 ) )
% 0.29/0.48         => ( P @ Z @ Subject ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % subject.strong_induct'
% 0.29/0.48  thf(fact_202_subject_Oinducts,axiom,
% 0.29/0.48      ! [P: late_subject > $o,Subject: late_subject] :
% 0.29/0.48        ( ! [Name4: name] : ( P @ ( late_InputS @ Name4 ) )
% 0.29/0.48       => ( ! [Name4: name] : ( P @ ( late_BoundOutputS @ Name4 ) )
% 0.29/0.48         => ( P @ Subject ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % subject.inducts
% 0.29/0.48  thf(fact_203_Late__Semantics_Osubject_Odistinct_I1_J,axiom,
% 0.29/0.48      ! [Name3: name,Name: name] :
% 0.29/0.48        ( ( late_InputS @ Name3 )
% 0.29/0.48       != ( late_BoundOutputS @ Name ) ) ).
% 0.29/0.48  
% 0.29/0.48  % Late_Semantics.subject.distinct(1)
% 0.29/0.48  thf(fact_204_transitions_OInput,axiom,
% 0.29/0.48      ! [X2: name,A2: name,P: pi] :
% 0.29/0.48        ( ( X2 != A2 )
% 0.29/0.48       => ( late_transitions @ ( input @ A2 @ X2 @ P ) @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % transitions.Input
% 0.29/0.48  thf(fact_205_Late__Semantics_OInput,axiom,
% 0.29/0.48      ! [A2: name,X2: name,P: pi] : ( late_transitions @ ( input @ A2 @ X2 @ P ) @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P ) ) ).
% 0.29/0.48  
% 0.29/0.48  % Late_Semantics.Input
% 0.29/0.48  thf(fact_206_freeRes_Orecs_I1_J,axiom,
% 0.29/0.48      ! [T: $tType,P: T > $o,F1: name > name > T,F22: T,Name12: name,Name22: name] :
% 0.29/0.48        ( ! [X13: name,X23: name] : ( P @ ( F1 @ X13 @ X23 ) )
% 0.29/0.48       => ( ( P @ F22 )
% 0.29/0.48         => ( ( late_freeRes_rec @ T @ F1 @ F22 @ ( late_OutputR @ Name12 @ Name22 ) )
% 0.29/0.48            = ( F1 @ Name12 @ Name22 ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % freeRes.recs(1)
% 0.29/0.48  thf(fact_207_Late__Semantics_OClose1,axiom,
% 0.29/0.48      ! [P: pi,A2: name,X2: name,P2: pi,Q: pi,Y2: name,Q2: pi] :
% 0.29/0.48        ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P2 ) )
% 0.29/0.48       => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y2 @ Q2 ) )
% 0.29/0.48         => ( ( fresh @ name @ pi @ Y2 @ P )
% 0.29/0.48           => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y2 @ ( par @ ( subs @ P2 @ X2 @ Y2 ) @ Q2 ) ) ) ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % Late_Semantics.Close1
% 0.29/0.48  thf(fact_208_Late__Semantics_OClose2,axiom,
% 0.29/0.48      ! [P: pi,A2: name,Y2: name,P2: pi,Q: pi,X2: name,Q2: pi] :
% 0.29/0.48        ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y2 @ P2 ) )
% 0.29/0.48       => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ Q2 ) )
% 0.29/0.48         => ( ( fresh @ name @ pi @ Y2 @ Q )
% 0.29/0.48           => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y2 @ ( par @ P2 @ ( subs @ Q2 @ X2 @ Y2 ) ) ) ) ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % Late_Semantics.Close2
% 0.29/0.48  thf(fact_209_subst__identity,axiom,
% 0.29/0.48      ! [P: pi,A2: name] :
% 0.29/0.48        ( ( subs @ P @ A2 @ A2 )
% 0.29/0.48        = P ) ).
% 0.29/0.48  
% 0.29/0.48  % subst_identity
% 0.29/0.48  thf(fact_210_simps_I9_J,axiom,
% 0.29/0.48      ! [X2: name,C2: name,D3: name,P: pi] :
% 0.29/0.48        ( ( X2 != C2 )
% 0.29/0.48       => ( ( X2 != D3 )
% 0.29/0.48         => ( ( subs @ ( res @ X2 @ P ) @ C2 @ D3 )
% 0.29/0.48            = ( res @ X2 @ ( subs @ P @ C2 @ D3 ) ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % simps(9)
% 0.29/0.48  thf(fact_211_simps_I8_J,axiom,
% 0.29/0.48      ! [P: pi,Q: pi,C2: name,D3: name] :
% 0.29/0.48        ( ( subs @ ( par @ P @ Q ) @ C2 @ D3 )
% 0.29/0.48        = ( par @ ( subs @ P @ C2 @ D3 ) @ ( subs @ Q @ C2 @ D3 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % simps(8)
% 0.29/0.48  thf(fact_212_substTrans,axiom,
% 0.29/0.48      ! [B2: name,P: pi,A2: name,C2: name] :
% 0.29/0.48        ( ( fresh @ name @ pi @ B2 @ P )
% 0.29/0.48       => ( ( subs @ ( subs @ P @ A2 @ B2 ) @ B2 @ C2 )
% 0.29/0.48          = ( subs @ P @ A2 @ C2 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % substTrans
% 0.29/0.48  thf(fact_213_simps_I7_J,axiom,
% 0.29/0.48      ! [P: pi,Q: pi,C2: name,D3: name] :
% 0.29/0.48        ( ( subs @ ( sum @ P @ Q ) @ C2 @ D3 )
% 0.29/0.48        = ( sum @ ( subs @ P @ C2 @ D3 ) @ ( subs @ Q @ C2 @ D3 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % simps(7)
% 0.29/0.48  thf(fact_214_simps_I1_J,axiom,
% 0.29/0.48      ! [C2: name,D3: name] :
% 0.29/0.48        ( ( subs @ piNil @ C2 @ D3 )
% 0.29/0.48        = piNil ) ).
% 0.29/0.48  
% 0.29/0.48  % simps(1)
% 0.29/0.48  thf(fact_215_fresh__fact2,axiom,
% 0.29/0.48      ! [A2: name,B2: name,P: pi] :
% 0.29/0.48        ( ( A2 != B2 )
% 0.29/0.48       => ( fresh @ name @ pi @ A2 @ ( subs @ P @ A2 @ B2 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % fresh_fact2
% 0.29/0.48  thf(fact_216_fresh__fact1,axiom,
% 0.29/0.48      ! [A2: name,P: pi,C2: name,B2: name] :
% 0.29/0.48        ( ( fresh @ name @ pi @ A2 @ P )
% 0.29/0.48       => ( ( A2 != C2 )
% 0.29/0.48         => ( fresh @ name @ pi @ A2 @ ( subs @ P @ B2 @ C2 ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % fresh_fact1
% 0.29/0.48  thf(fact_217_forget,axiom,
% 0.29/0.48      ! [A2: name,P: pi,B2: name] :
% 0.29/0.48        ( ( fresh @ name @ pi @ A2 @ P )
% 0.29/0.48       => ( ( subs @ P @ A2 @ B2 )
% 0.29/0.48          = P ) ) ).
% 0.29/0.48  
% 0.29/0.48  % forget
% 0.29/0.48  thf(fact_218_substRes2,axiom,
% 0.29/0.48      ! [B2: name,P: pi,A2: name] :
% 0.29/0.48        ( ( fresh @ name @ pi @ B2 @ P )
% 0.29/0.48       => ( ( res @ A2 @ P )
% 0.29/0.48          = ( res @ B2 @ ( subs @ P @ A2 @ B2 ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % substRes2
% 0.29/0.48  thf(fact_219_Agent_OsubstRes3,axiom,
% 0.29/0.48      ! [B2: name,P: pi,A2: name] :
% 0.29/0.48        ( ( fresh @ name @ pi @ B2 @ P )
% 0.29/0.48       => ( ( subs @ ( res @ A2 @ P ) @ A2 @ B2 )
% 0.29/0.48          = ( res @ B2 @ ( subs @ P @ A2 @ B2 ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % Agent.substRes3
% 0.29/0.48  thf(fact_220_Late__Semantics_OComm2,axiom,
% 0.29/0.48      ! [P: pi,A2: name,B2: name,P2: pi,Q: pi,X2: name,Q2: pi] :
% 0.29/0.48        ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P2 ) )
% 0.29/0.48       => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ Q2 ) )
% 0.29/0.48         => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P2 @ ( subs @ Q2 @ X2 @ B2 ) ) ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % Late_Semantics.Comm2
% 0.29/0.48  thf(fact_221_Late__Semantics_OComm1,axiom,
% 0.29/0.48      ! [P: pi,A2: name,X2: name,P2: pi,Q: pi,B2: name,Q2: pi] :
% 0.29/0.48        ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P2 ) )
% 0.29/0.48       => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ Q2 ) )
% 0.29/0.48         => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P2 @ X2 @ B2 ) @ Q2 ) ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % Late_Semantics.Comm1
% 0.29/0.48  thf(fact_222_transitions_OComm1,axiom,
% 0.29/0.48      ! [P: pi,A2: name,X2: name,P2: pi,Q: pi,B2: name,Q2: pi] :
% 0.29/0.48        ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P2 ) )
% 0.29/0.48       => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ Q2 ) )
% 0.29/0.48         => ( ( fresh @ name @ pi @ X2 @ P )
% 0.29/0.48           => ( ( fresh @ name @ pi @ X2 @ Q )
% 0.29/0.48             => ( ( X2 != A2 )
% 0.29/0.48               => ( ( X2 != B2 )
% 0.29/0.48                 => ( ( fresh @ name @ pi @ X2 @ Q2 )
% 0.29/0.48                   => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P2 @ X2 @ B2 ) @ Q2 ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % transitions.Comm1
% 0.29/0.48  thf(fact_223_transitions_OComm2,axiom,
% 0.29/0.48      ! [P: pi,A2: name,B2: name,P2: pi,Q: pi,X2: name,Q2: pi] :
% 0.29/0.48        ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P2 ) )
% 0.29/0.48       => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ Q2 ) )
% 0.29/0.48         => ( ( fresh @ name @ pi @ X2 @ P )
% 0.29/0.48           => ( ( fresh @ name @ pi @ X2 @ Q )
% 0.29/0.48             => ( ( X2 != A2 )
% 0.29/0.48               => ( ( X2 != B2 )
% 0.29/0.48                 => ( ( fresh @ name @ pi @ X2 @ P2 )
% 0.29/0.48                   => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P2 @ ( subs @ Q2 @ X2 @ B2 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % transitions.Comm2
% 0.29/0.48  thf(fact_224_transitions_OClose2,axiom,
% 0.29/0.48      ! [P: pi,A2: name,Y2: name,P2: pi,Q: pi,X2: name,Q2: pi] :
% 0.29/0.48        ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y2 @ P2 ) )
% 0.29/0.48       => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ Q2 ) )
% 0.29/0.48         => ( ( fresh @ name @ pi @ X2 @ P )
% 0.29/0.48           => ( ( fresh @ name @ pi @ X2 @ Q )
% 0.29/0.48             => ( ( fresh @ name @ pi @ Y2 @ P )
% 0.29/0.48               => ( ( fresh @ name @ pi @ Y2 @ Q )
% 0.29/0.48                 => ( ( X2 != A2 )
% 0.29/0.48                   => ( ( fresh @ name @ pi @ X2 @ P2 )
% 0.29/0.48                     => ( ( Y2 != A2 )
% 0.29/0.48                       => ( ( fresh @ name @ pi @ Y2 @ Q2 )
% 0.29/0.48                         => ( ( X2 != Y2 )
% 0.29/0.48                           => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y2 @ ( par @ P2 @ ( subs @ Q2 @ X2 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % transitions.Close2
% 0.29/0.48  thf(fact_225_transitions_OClose1,axiom,
% 0.29/0.48      ! [P: pi,A2: name,X2: name,P2: pi,Q: pi,Y2: name,Q2: pi] :
% 0.29/0.48        ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P2 ) )
% 0.29/0.48       => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y2 @ Q2 ) )
% 0.29/0.48         => ( ( fresh @ name @ pi @ X2 @ P )
% 0.29/0.48           => ( ( fresh @ name @ pi @ X2 @ Q )
% 0.29/0.48             => ( ( fresh @ name @ pi @ Y2 @ P )
% 0.29/0.48               => ( ( fresh @ name @ pi @ Y2 @ Q )
% 0.29/0.48                 => ( ( X2 != A2 )
% 0.29/0.48                   => ( ( fresh @ name @ pi @ X2 @ Q2 )
% 0.29/0.48                     => ( ( Y2 != A2 )
% 0.29/0.48                       => ( ( fresh @ name @ pi @ Y2 @ P2 )
% 0.29/0.48                         => ( ( X2 != Y2 )
% 0.29/0.48                           => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y2 @ ( par @ ( subs @ P2 @ X2 @ Y2 ) @ Q2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % transitions.Close1
% 0.29/0.48  thf(fact_226_subject_Orecs_I2_J,axiom,
% 0.29/0.48      ! [T: $tType,P: T > $o,F1: name > T,F22: name > T,Name3: name] :
% 0.29/0.48        ( ! [X13: name] : ( P @ ( F1 @ X13 ) )
% 0.29/0.48       => ( ! [X13: name] : ( P @ ( F22 @ X13 ) )
% 0.29/0.48         => ( ( late_subject_rec @ T @ F1 @ F22 @ ( late_BoundOutputS @ Name3 ) )
% 0.29/0.48            = ( F22 @ Name3 ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % subject.recs(2)
% 0.29/0.48  thf(fact_227_subject_Orecs_I1_J,axiom,
% 0.29/0.48      ! [T: $tType,P: T > $o,F1: name > T,F22: name > T,Name3: name] :
% 0.29/0.48        ( ! [X13: name] : ( P @ ( F1 @ X13 ) )
% 0.29/0.48       => ( ! [X13: name] : ( P @ ( F22 @ X13 ) )
% 0.29/0.48         => ( ( late_subject_rec @ T @ F1 @ F22 @ ( late_InputS @ Name3 ) )
% 0.29/0.48            = ( F1 @ Name3 ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % subject.recs(1)
% 0.29/0.48  thf(fact_228_resTauOutputTrans,axiom,
% 0.29/0.48      ! [X2: name,P: pi,A2: name,B2: name,P2: pi] :
% 0.29/0.48        ~ ( late_transitions @ ( res @ X2 @ ( tau @ P ) ) @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P2 ) ) ).
% 0.29/0.48  
% 0.29/0.48  % resTauOutputTrans
% 0.29/0.48  thf(fact_229_residual_Ofresh_I1_J,axiom,
% 0.29/0.48      ! [A2: name,X3: late_subject,X1: name,X22: pi] :
% 0.29/0.48        ( ( fresh @ name @ late_residual @ A2 @ ( late_BoundR @ X3 @ X1 @ X22 ) )
% 0.29/0.48        = ( ( fresh @ name @ late_subject @ A2 @ X3 )
% 0.29/0.48          & ( fresh @ name @ ( name > ( noption @ pi ) ) @ A2 @ ( abs_fun @ name @ pi @ X1 @ X22 ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % residual.fresh(1)
% 0.29/0.48  thf(fact_230_pi_Ofresh_I3_J,axiom,
% 0.29/0.48      ! [A2: name,X1: pi] :
% 0.29/0.48        ( ( fresh @ name @ pi @ A2 @ ( tau @ X1 ) )
% 0.29/0.48        = ( fresh @ name @ pi @ A2 @ X1 ) ) ).
% 0.29/0.48  
% 0.29/0.48  % pi.fresh(3)
% 0.29/0.48  thf(fact_231_simps_I2_J,axiom,
% 0.29/0.48      ! [P: pi,C2: name,D3: name] :
% 0.29/0.48        ( ( subs @ ( tau @ P ) @ C2 @ D3 )
% 0.29/0.48        = ( tau @ ( subs @ P @ C2 @ D3 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % simps(2)
% 0.29/0.48  thf(fact_232_pi_Ofresh_I9_J,axiom,
% 0.29/0.48      ! [A2: name,X1: name,X22: pi] :
% 0.29/0.48        ( ( fresh @ name @ pi @ A2 @ ( res @ X1 @ X22 ) )
% 0.29/0.48        = ( fresh @ name @ ( name > ( noption @ pi ) ) @ A2 @ ( abs_fun @ name @ pi @ X1 @ X22 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % pi.fresh(9)
% 0.29/0.48  thf(fact_233_pi_Ofresh_I4_J,axiom,
% 0.29/0.48      ! [A2: name,X3: name,X1: name,X22: pi] :
% 0.29/0.48        ( ( fresh @ name @ pi @ A2 @ ( input @ X3 @ X1 @ X22 ) )
% 0.29/0.48        = ( ( fresh @ name @ name @ A2 @ X3 )
% 0.29/0.48          & ( fresh @ name @ ( name > ( noption @ pi ) ) @ A2 @ ( abs_fun @ name @ pi @ X1 @ X22 ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % pi.fresh(4)
% 0.29/0.48  thf(fact_234_tauBoundTrans,axiom,
% 0.29/0.48      ! [P: pi,A2: late_subject,X2: name,P2: pi] :
% 0.29/0.48        ~ ( late_transitions @ ( tau @ P ) @ ( late_BoundR @ A2 @ X2 @ P2 ) ) ).
% 0.29/0.48  
% 0.29/0.48  % tauBoundTrans
% 0.29/0.48  thf(fact_235_nilSim_I1_J,axiom,
% 0.29/0.48      ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi] :
% 0.29/0.48        ~ ( strong743114133lation @ piNil @ Rel @ ( tau @ P ) ) ).
% 0.29/0.48  
% 0.29/0.48  % nilSim(1)
% 0.29/0.48  thf(fact_236_pi_Oinject_I8_J,axiom,
% 0.29/0.48      ! [X1: name,X22: pi,Y1: name,Y22: pi] :
% 0.29/0.48        ( ( ( res @ X1 @ X22 )
% 0.29/0.48          = ( res @ Y1 @ Y22 ) )
% 0.29/0.48        = ( ( abs_fun @ name @ pi @ X1 @ X22 )
% 0.29/0.48          = ( abs_fun @ name @ pi @ Y1 @ Y22 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % pi.inject(8)
% 0.29/0.48  thf(fact_237_residual_Oinject_I1_J,axiom,
% 0.29/0.48      ! [X3: late_subject,X1: name,X22: pi,Y3: late_subject,Y1: name,Y22: pi] :
% 0.29/0.48        ( ( ( late_BoundR @ X3 @ X1 @ X22 )
% 0.29/0.48          = ( late_BoundR @ Y3 @ Y1 @ Y22 ) )
% 0.29/0.48        = ( ( X3 = Y3 )
% 0.29/0.48          & ( ( abs_fun @ name @ pi @ X1 @ X22 )
% 0.29/0.48            = ( abs_fun @ name @ pi @ Y1 @ Y22 ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % residual.inject(1)
% 0.29/0.48  thf(fact_238_pi_Oinject_I2_J,axiom,
% 0.29/0.48      ! [X1: pi,Y1: pi] :
% 0.29/0.48        ( ( ( tau @ X1 )
% 0.29/0.48          = ( tau @ Y1 ) )
% 0.29/0.48        = ( X1 = Y1 ) ) ).
% 0.29/0.48  
% 0.29/0.48  % pi.inject(2)
% 0.29/0.48  thf(fact_239_abs__fun__eq1,axiom,
% 0.29/0.48      ! [X: $tType,A: $tType,A2: X,X2: A,Y2: A] :
% 0.29/0.48        ( ( ( abs_fun @ X @ A @ A2 @ X2 )
% 0.29/0.48          = ( abs_fun @ X @ A @ A2 @ Y2 ) )
% 0.29/0.48        = ( X2 = Y2 ) ) ).
% 0.29/0.48  
% 0.29/0.48  % abs_fun_eq1
% 0.29/0.48  thf(fact_240_pi_Odistinct_I19_J,axiom,
% 0.29/0.48      ! [Name12: name,Name22: name,Pi3: pi,Pi: pi] :
% 0.29/0.48        ( ( output @ Name12 @ Name22 @ Pi3 )
% 0.29/0.48       != ( tau @ Pi ) ) ).
% 0.29/0.48  
% 0.29/0.48  % pi.distinct(19)
% 0.29/0.48  thf(fact_241_pi_Odistinct_I3_J,axiom,
% 0.29/0.48      ! [Pi: pi] :
% 0.29/0.48        ( piNil
% 0.29/0.48       != ( tau @ Pi ) ) ).
% 0.29/0.48  
% 0.29/0.48  % pi.distinct(3)
% 0.29/0.48  thf(fact_242_pi_Odistinct_I35_J,axiom,
% 0.29/0.48      ! [Pi3: pi,Name1: name,Name2: name,Pi: pi] :
% 0.29/0.48        ( ( tau @ Pi3 )
% 0.29/0.48       != ( input @ Name1 @ Name2 @ Pi ) ) ).
% 0.29/0.48  
% 0.29/0.48  % pi.distinct(35)
% 0.29/0.48  thf(fact_243_pi_Odistinct_I41_J,axiom,
% 0.29/0.48      ! [Pi3: pi,Pi12: pi,Pi22: pi] :
% 0.29/0.48        ( ( tau @ Pi3 )
% 0.29/0.48       != ( sum @ Pi12 @ Pi22 ) ) ).
% 0.29/0.48  
% 0.29/0.48  % pi.distinct(41)
% 0.29/0.48  thf(fact_244_pi_Odistinct_I43_J,axiom,
% 0.29/0.48      ! [Pi3: pi,Pi12: pi,Pi22: pi] :
% 0.29/0.48        ( ( tau @ Pi3 )
% 0.29/0.48       != ( par @ Pi12 @ Pi22 ) ) ).
% 0.29/0.48  
% 0.29/0.48  % pi.distinct(43)
% 0.29/0.48  thf(fact_245_pi_Odistinct_I45_J,axiom,
% 0.29/0.48      ! [Pi3: pi,Name: name,Pi: pi] :
% 0.29/0.48        ( ( tau @ Pi3 )
% 0.29/0.48       != ( res @ Name @ Pi ) ) ).
% 0.29/0.48  
% 0.29/0.48  % pi.distinct(45)
% 0.29/0.48  thf(fact_246_pi_Oinject_I3_J,axiom,
% 0.29/0.48      ! [X3: name,X1: name,X22: pi,Y3: name,Y1: name,Y22: pi] :
% 0.29/0.48        ( ( ( input @ X3 @ X1 @ X22 )
% 0.29/0.48          = ( input @ Y3 @ Y1 @ Y22 ) )
% 0.29/0.48        = ( ( X3 = Y3 )
% 0.29/0.48          & ( ( abs_fun @ name @ pi @ X1 @ X22 )
% 0.29/0.48            = ( abs_fun @ name @ pi @ Y1 @ Y22 ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % pi.inject(3)
% 0.29/0.48  thf(fact_247_name__fresh__abs,axiom,
% 0.29/0.48      ! [A: $tType] :
% 0.29/0.48        ( ( fs_name @ A )
% 0.29/0.48       => ! [B2: name,A2: name,X2: A] :
% 0.29/0.48            ( ( fresh @ name @ ( name > ( noption @ A ) ) @ B2 @ ( abs_fun @ name @ A @ A2 @ X2 ) )
% 0.29/0.48            = ( ( B2 = A2 )
% 0.29/0.48              | ( fresh @ name @ A @ B2 @ X2 ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % name_fresh_abs
% 0.29/0.48  thf(fact_248_abs__fresh_I1_J,axiom,
% 0.29/0.48      ! [X7: $tType] :
% 0.29/0.48        ( ( fs_name @ X7 )
% 0.29/0.48       => ! [B2: name,A2: name,X2: X7] :
% 0.29/0.48            ( ( fresh @ name @ ( name > ( noption @ X7 ) ) @ B2 @ ( abs_fun @ name @ X7 @ A2 @ X2 ) )
% 0.29/0.48            = ( ( B2 = A2 )
% 0.29/0.48              | ( fresh @ name @ X7 @ B2 @ X2 ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % abs_fresh(1)
% 0.29/0.48  thf(fact_249_resTauBoundTrans,axiom,
% 0.29/0.48      ! [X2: name,P: pi,A2: late_subject,Y2: name,P2: pi] :
% 0.29/0.48        ~ ( late_transitions @ ( res @ X2 @ ( tau @ P ) ) @ ( late_BoundR @ A2 @ Y2 @ P2 ) ) ).
% 0.29/0.48  
% 0.29/0.48  % resTauBoundTrans
% 0.29/0.48  thf(fact_250_tauOutputTrans,axiom,
% 0.29/0.48      ! [P: pi,A2: name,B2: name,P2: pi] :
% 0.29/0.48        ~ ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P2 ) ) ).
% 0.29/0.48  
% 0.29/0.48  % tauOutputTrans
% 0.29/0.48  thf(fact_251_Tau,axiom,
% 0.29/0.48      ! [P: pi] : ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ late_TauR @ P ) ) ).
% 0.29/0.48  
% 0.29/0.48  % Tau
% 0.29/0.48  thf(fact_252_tauCases_H,axiom,
% 0.29/0.48      ! [P: pi,Rs: late_residual] :
% 0.29/0.48        ( ( late_transitions @ ( tau @ P ) @ Rs )
% 0.29/0.48       => ~ ! [P4: pi] :
% 0.29/0.48              ( ( ( tau @ P )
% 0.29/0.48                = ( tau @ P4 ) )
% 0.29/0.48             => ( Rs
% 0.29/0.48               != ( late_FreeR @ late_TauR @ P4 ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % tauCases'
% 0.29/0.48  thf(fact_253_tauCases,axiom,
% 0.29/0.48      ! [P: pi,Alpha: late_freeRes,P2: pi,Prop: late_freeRes > pi > $o] :
% 0.29/0.48        ( ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 0.29/0.48       => ( ( ( Alpha = late_TauR )
% 0.29/0.48           => ( ( P = P2 )
% 0.29/0.48             => ( Prop @ late_TauR @ P ) ) )
% 0.29/0.48         => ( Prop @ Alpha @ P2 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % tauCases
% 0.29/0.48  thf(fact_254_inputCases_H,axiom,
% 0.29/0.48      ! [A2: name,B2: name,P: pi,Rs: late_residual] :
% 0.29/0.48        ( ( late_transitions @ ( input @ A2 @ B2 @ P ) @ Rs )
% 0.29/0.48       => ~ ! [X5: name,A4: name,P4: pi] :
% 0.29/0.48              ( ( ( A2 = A4 )
% 0.29/0.48                & ( ( abs_fun @ name @ pi @ B2 @ P )
% 0.29/0.48                  = ( abs_fun @ name @ pi @ X5 @ P4 ) ) )
% 0.29/0.48             => ( ( Rs
% 0.29/0.48                  = ( late_BoundR @ ( late_InputS @ A4 ) @ X5 @ P4 ) )
% 0.29/0.48               => ( X5 = A4 ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inputCases'
% 0.29/0.48  thf(fact_255_simps_I3_J,axiom,
% 0.29/0.48      ! [A2: name,B2: name,P: pi,C2: name,D3: name] :
% 0.29/0.48        ( ( subs @ ( output @ A2 @ B2 @ P ) @ C2 @ D3 )
% 0.29/0.48        = ( output @ ( subst_name @ A2 @ C2 @ D3 ) @ ( subst_name @ B2 @ C2 @ D3 ) @ ( subs @ P @ C2 @ D3 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % simps(3)
% 0.29/0.48  
% 0.29/0.48  % Type constructors (17)
% 0.29/0.48  thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.29/0.48      ! [A8: $tType,A9: $tType] :
% 0.29/0.48        ( ( preorder @ A9 )
% 0.29/0.48       => ( preorder @ ( A8 > A9 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  thf(tcon_fun___Orderings_Oorder,axiom,
% 0.29/0.48      ! [A8: $tType,A9: $tType] :
% 0.29/0.48        ( ( order @ A9 )
% 0.29/0.48       => ( order @ ( A8 > A9 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  thf(tcon_fun___Orderings_Oord,axiom,
% 0.29/0.48      ! [A8: $tType,A9: $tType] :
% 0.29/0.48        ( ( ord @ A9 )
% 0.29/0.48       => ( ord @ ( A8 > A9 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  thf(tcon_Set_Oset___Orderings_Opreorder_1,axiom,
% 0.29/0.48      ! [A8: $tType] : ( preorder @ ( set @ A8 ) ) ).
% 0.29/0.48  
% 0.29/0.48  thf(tcon_Set_Oset___Orderings_Oorder_2,axiom,
% 0.29/0.48      ! [A8: $tType] : ( order @ ( set @ A8 ) ) ).
% 0.29/0.48  
% 0.29/0.48  thf(tcon_Set_Oset___Orderings_Oord_3,axiom,
% 0.29/0.48      ! [A8: $tType] : ( ord @ ( set @ A8 ) ) ).
% 0.29/0.48  
% 0.29/0.48  thf(tcon_Agent_Opi___Agent_Ofs__name,axiom,
% 0.29/0.48      fs_name @ pi ).
% 0.29/0.48  
% 0.29/0.48  thf(tcon_HOL_Obool___Orderings_Opreorder_4,axiom,
% 0.29/0.48      preorder @ $o ).
% 0.29/0.48  
% 0.29/0.48  thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 0.29/0.48      linorder @ $o ).
% 0.29/0.48  
% 0.29/0.48  thf(tcon_HOL_Obool___Orderings_Oorder_5,axiom,
% 0.29/0.48      order @ $o ).
% 0.29/0.48  
% 0.29/0.48  thf(tcon_HOL_Obool___Orderings_Oord_6,axiom,
% 0.29/0.48      ord @ $o ).
% 0.29/0.48  
% 0.29/0.48  thf(tcon_HOL_Obool___Agent_Ofs__name_7,axiom,
% 0.29/0.48      fs_name @ $o ).
% 0.29/0.48  
% 0.29/0.48  thf(tcon_Agent_Oname___Agent_Ofs__name_8,axiom,
% 0.29/0.48      fs_name @ name ).
% 0.29/0.48  
% 0.29/0.48  thf(tcon_Product__Type_Oprod___Agent_Ofs__name_9,axiom,
% 0.29/0.48      ! [A8: $tType,A9: $tType] :
% 0.29/0.48        ( ( ( fs_name @ A8 )
% 0.29/0.48          & ( fs_name @ A9 ) )
% 0.29/0.48       => ( fs_name @ ( product_prod @ A8 @ A9 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  thf(tcon_Late__Semantics_OfreeRes___Agent_Ofs__name_10,axiom,
% 0.29/0.48      fs_name @ late_freeRes ).
% 0.29/0.48  
% 0.29/0.48  thf(tcon_Late__Semantics_Osubject___Agent_Ofs__name_11,axiom,
% 0.29/0.48      fs_name @ late_subject ).
% 0.29/0.48  
% 0.29/0.48  thf(tcon_Late__Semantics_Oresidual___Agent_Ofs__name_12,axiom,
% 0.29/0.48      fs_name @ late_residual ).
% 0.29/0.48  
% 0.29/0.48  % Conjectures (1)
% 0.29/0.48  thf(conj_0,conjecture,
% 0.29/0.48      late_transitions @ ( res @ x @ ( par @ p @ q ) ) @ ( late_FreeR @ alpha @ ( res @ x @ ( par @ p2 @ q ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  %------------------------------------------------------------------------------
% 0.29/0.48  ------------------------
% 3.25/1.72  ---- Embedded in THF ---
% 3.25/1.72  %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 3.25/1.72  %%% Generated on Tue Feb 24 08:29:16 EST 2026
% 3.25/1.72  %%% using '$$dhol' embedding, version 1.3.0.
% 3.25/1.72  %%% Logic specification used:
% 3.25/1.72  %%% thf(spec, logic, $$dhol).
% 3.25/1.72  
% 3.25/1.72  % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.gpMSqBPIcZ/DTF2DTF18468.p
% 3.25/1.72  thf(ty_t_Late__Semantics_Oresidual, type, late_residual: $tType).
% 3.25/1.72  thf(ty_t_Late__Semantics_Osubject, type, late_subject: $tType).
% 3.25/1.72  thf(ty_t_Late__Semantics_OfreeRes, type, late_freeRes: $tType).
% 3.25/1.72  thf(ty_t_Product__Type_Oprod, type, product_prod: ($tType > ($tType > $tType))).
% 3.25/1.72  thf(ty_t_Nominal_Onoption, type, noption: ($tType > $tType)).
% 3.25/1.72  thf(ty_t_Agent_Oname, type, name: $tType).
% 3.25/1.72  thf(ty_t_Agent_Opi, type, pi: $tType).
% 3.25/1.72  thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 3.25/1.72  thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: ($o))).
% 3.25/1.72  thf(sy_cl_Agent_Ofs__name, type, fs_name: (!> [A:$tType]: ($o))).
% 3.25/1.72  thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: ($o))).
% 3.25/1.72  thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: ($o))).
% 3.25/1.72  thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: ($o))).
% 3.25/1.72  thf(sy_cl_Orderings_Opreorder, type, preorder: (!> [A:$tType]: ($o))).
% 3.25/1.72  thf(sy_c_Agent_Opi_OInput, type, input: (name > (name > (pi > pi)))).
% 3.25/1.72  thf(sy_c_Agent_Opi_OOutput, type, output: (name > (name > (pi > pi)))).
% 3.25/1.72  thf(sy_c_Agent_Opi_OPar, type, par: (pi > (pi > pi))).
% 3.25/1.72  thf(sy_c_Agent_Opi_OPiNil, type, piNil: pi).
% 3.25/1.72  thf(sy_c_Agent_Opi_ORes, type, res: (name > (pi > pi))).
% 3.25/1.72  thf(sy_c_Agent_Opi_OSum, type, sum: (pi > (pi > pi))).
% 3.25/1.72  thf(sy_c_Agent_Opi_OTau, type, tau: (pi > pi)).
% 3.25/1.72  thf(sy_c_Agent_Osubs, type, subs: (pi > (name > (name > pi)))).
% 3.25/1.72  thf(sy_c_Agent_Osubst__name, type, subst_name: (name > (name > (name > name)))).
% 3.25/1.72  thf(sy_c_Late__Semantics_OfreeRes_OOutputR, type, late_OutputR: (name > (name > late_freeRes))).
% 3.25/1.72  thf(sy_c_Late__Semantics_OfreeRes_OTauR, type, late_TauR: late_freeRes).
% 3.25/1.72  thf(sy_c_Late__Semantics_OfreeRes_OfreeRes__rec, type, late_freeRes_rec: (!> [T:$tType]: (((name > (name > T)) > (T > (late_freeRes > T)))))).
% 3.25/1.72  thf(sy_c_Late__Semantics_Oresidual_OBoundR, type, late_BoundR: (late_subject > (name > (pi > late_residual)))).
% 3.25/1.72  thf(sy_c_Late__Semantics_Oresidual_OFreeR, type, late_FreeR: (late_freeRes > (pi > late_residual))).
% 3.25/1.72  thf(sy_c_Late__Semantics_Osubject_OBoundOutputS, type, late_BoundOutputS: (name > late_subject)).
% 3.25/1.72  thf(sy_c_Late__Semantics_Osubject_OInputS, type, late_InputS: (name > late_subject)).
% 3.25/1.72  thf(sy_c_Late__Semantics_Osubject_Osubject__rec, type, late_subject_rec: (!> [T:$tType]: (((name > T) > ((name > T) > (late_subject > T)))))).
% 3.25/1.72  thf(sy_c_Late__Semantics_Otransitions, type, late_transitions: (pi > (late_residual > $o))).
% 3.25/1.72  thf(sy_c_Nominal_Oabs__fun, type, abs_fun: (!> [X:$tType,A:$tType]: ((X > (A > (X > (noption @ A))))))).
% 3.25/1.72  thf(sy_c_Nominal_Ofresh, type, fresh: (!> [X:$tType,A:$tType]: ((X > (A > $o))))).
% 3.25/1.72  thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 3.25/1.72  thf(sy_c_Product__Type_OPair, type, product_Pair: (!> [A:$tType,B:$tType]: ((A > (B > ((product_prod @ A) @ B)))))).
% 3.25/1.72  thf(sy_c_Product__Type_Oold_Oprod_Orec__prod, type, product_rec_prod: (!> [A:$tType,B:$tType,T:$tType]: (((A > (B > T)) > (((product_prod @ A) @ B) > T))))).
% 3.25/1.72  thf(sy_c_Rel_Oeqvt, type, eqvt: (!> [A:$tType]: (((set @ ((product_prod @ A) @ A)) > $o)))).
% 3.25/1.72  thf(sy_c_Relation_OId, type, id: (!> [A:$tType]: ((set @ ((product_prod @ A) @ A))))).
% 3.25/1.72  thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 3.25/1.72  thf(sy_c_Strong__Late__Sim_Oderivative, type, strong2129052853vative: (pi > (pi > (late_subject > (name > ((set @ ((product_prod @ pi) @ pi)) > $o)))))).
% 3.25/1.72  thf(sy_c_Strong__Late__Sim_Osimulation, type, strong743114133lation: (pi > ((set @ ((product_prod @ pi) @ pi)) > (pi > $o)))).
% 3.25/1.72  thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 3.25/1.72  thf(sy_v_P, type, p: pi).
% 3.25/1.72  thf(sy_v_P_H____, type, p2: pi).
% 3.25/1.72  thf(sy_v_PxQ____, type, pxQ: pi).
% 3.25/1.72  thf(sy_v_Q, type, q: pi).
% 3.25/1.72  thf(sy_v_Rel, type, rel: (set @ ((product_prod @ pi) @ pi))).
% 3.25/1.72  thf(sy_v__092_060alpha_062____, type, alpha: late_freeRes).
% 3.25/1.72  thf(sy_v_x, type, x: name).
% 3.25/1.72  thf(fact_0__092_060open_062x_A_092_060sharp_062_A_092_060alpha_062_092_060close_062, axiom, ((((fresh @ name) @ late_freeRes) @ x) @ alpha)).
% 3.25/1.72  thf(fact_1__092_060open_062P_A_092_060parallel_062_AQ_A_092_060longmapsto_062_A_092_060alpha_062_A_092_060prec_062_AP_H_A_092_060parallel_062_AQ_092_060close_062, axiom, ((late_transitions @ ((par @ p) @ q)) @ ((late_FreeR @ alpha) @ ((par @ p2) @ q)))).
% 3.25/1.72  thf(fact_2_cPar1_Ohyps, axiom, ((late_transitions @ p) @ ((late_FreeR @ alpha) @ p2))).
% 3.25/1.72  thf(fact_3_Free_Ohyps, axiom, ((late_transitions @ ((par @ p) @ ((res @ x) @ q))) @ ((late_FreeR @ alpha) @ pxQ))).
% 3.25/1.72  thf(fact_4_assms_I1_J, axiom, ((((fresh @ name) @ pi) @ x) @ p)).
% 3.25/1.72  thf(fact_5__092_060open_062x_A_092_060sharp_062_AP_H_092_060close_062, axiom, ((((fresh @ name) @ pi) @ x) @ p2)).
% 3.25/1.72  thf(fact_6_Par1F, axiom, (! [P:pi,Alpha:late_freeRes,P2:pi,Q:pi]: ((((late_transitions @ P) @ ((late_FreeR @ Alpha) @ P2)) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ Alpha) @ ((par @ P2) @ Q))))))).
% 3.25/1.72  thf(fact_7_Par2F, axiom, (! [Q:pi,Alpha:late_freeRes,Q2:pi,P:pi]: ((((late_transitions @ Q) @ ((late_FreeR @ Alpha) @ Q2)) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ Alpha) @ ((par @ P) @ Q2))))))).
% 3.25/1.72  thf(fact_8_pi_Odistinct_I85_J, axiom, (! [Pi1:pi,Pi2:pi,Name:name,Pi:pi]: ((((par @ Pi1) @ Pi2) != ((res @ Name) @ Pi))))).
% 3.25/1.72  thf(fact_9_resCasesF, axiom, (! [X2:name,P:pi,Alpha:late_freeRes,XP:pi,F:(pi > $o)]: ((((late_transitions @ ((res @ X2) @ P)) @ ((late_FreeR @ Alpha) @ XP)) => ((! [P3:pi]: ((((late_transitions @ P) @ ((late_FreeR @ Alpha) @ P3)) => (((((fresh @ name) @ late_freeRes) @ X2) @ Alpha) => (F @ ((res @ X2) @ P3)))))) => (F @ XP)))))).
% 3.25/1.72  thf(fact_10_resCasesF_H, axiom, (! [X2:name,P:pi,Alpha:late_freeRes,P2:pi]: ((((late_transitions @ ((res @ X2) @ P)) @ ((late_FreeR @ Alpha) @ P2)) => (~ ((! [P4:pi,Alpha2:late_freeRes,P3:pi,Y:name]: (((((res @ X2) @ P) = ((res @ Y) @ P4)) => ((((late_FreeR @ Alpha) @ P2) = ((late_FreeR @ Alpha2) @ ((res @ Y) @ P3))) => (((late_transitions @ P4) @ ((late_FreeR @ Alpha2) @ P3)) => (~ (((((fresh @ name) @ late_freeRes) @ Y) @ Alpha2)))))))))))))).
% 3.25/1.72  thf(fact_11_ResF, axiom, (! [P:pi,Alpha:late_freeRes,P2:pi,Y2:name]: ((((late_transitions @ P) @ ((late_FreeR @ Alpha) @ P2)) => (((((fresh @ name) @ late_freeRes) @ Y2) @ Alpha) => ((late_transitions @ ((res @ Y2) @ P)) @ ((late_FreeR @ Alpha) @ ((res @ Y2) @ P2)))))))).
% 3.25/1.72  thf(fact_12_residual_Oinject_I2_J, axiom, (! [X22:late_freeRes,X1:pi,Y22:late_freeRes,Y1:pi]: (((((late_FreeR @ X22) @ X1) = ((late_FreeR @ Y22) @ Y1)) = ((X22 = Y22) & (X1 = Y1)))))).
% 3.25/1.72  thf(fact_13_pi_Oinject_I7_J, axiom, (! [X22:pi,X1:pi,Y22:pi,Y1:pi]: (((((par @ X22) @ X1) = ((par @ Y22) @ Y1)) = ((X22 = Y22) & (X1 = Y1)))))).
% 3.25/1.72  thf(fact_14_resInputFreeTrans, axiom, (! [X2:name,A2:name,Y2:name,P:pi,Alpha:late_freeRes,P2:pi]: ((~ (((late_transitions @ ((res @ X2) @ (((input @ A2) @ Y2) @ P))) @ ((late_FreeR @ Alpha) @ P2))))))).
% 3.25/1.72  thf(fact_15_EqvtRel, axiom, ((eqvt @ pi) @ rel)).
% 3.25/1.72  thf(fact_16_resZeroTrans, axiom, (! [X2:name,Rs:late_residual]: ((~ (((late_transitions @ ((res @ X2) @ piNil)) @ Rs)))))).
% 3.25/1.72  thf(fact_17_pi_Ofresh_I8_J, axiom, (! [A2:name,X22:pi,X1:pi]: ((((((fresh @ name) @ pi) @ A2) @ ((par @ X22) @ X1)) = (((((fresh @ name) @ pi) @ A2) @ X22) & ((((fresh @ name) @ pi) @ A2) @ X1)))))).
% 3.25/1.72  thf(fact_18_pi_Ofresh_I1_J, axiom, (! [A2:name]: (((((fresh @ name) @ pi) @ A2) @ piNil)))).
% 3.25/1.72  thf(fact_19_pi_Odistinct_I5_J, axiom, (! [Name1:name,Name2:name,Pi:pi]: ((piNil != (((input @ Name1) @ Name2) @ Pi))))).
% 3.25/1.72  thf(fact_20_name__exists__fresh, axiom, (! [A:$tType]: (((fs_name @ A) => (! [X2:A]: ((~ ((! [C:name]: ((~ (((((fresh @ name) @ A) @ C) @ X2))))))))))))).
% 3.25/1.72  thf(fact_21_freshRes, axiom, (! [A2:name,P:pi]: (((((fresh @ name) @ pi) @ A2) @ ((res @ A2) @ P))))).
% 3.25/1.72  thf(fact_22_pi_Odistinct_I57_J, axiom, (! [Name12:name,Name22:name,Pi3:pi,Name:name,Pi:pi]: (((((input @ Name12) @ Name22) @ Pi3) != ((res @ Name) @ Pi))))).
% 3.25/1.72  thf(fact_23_pi_Odistinct_I55_J, axiom, (! [Name12:name,Name22:name,Pi3:pi,Pi12:pi,Pi22:pi]: (((((input @ Name12) @ Name22) @ Pi3) != ((par @ Pi12) @ Pi22))))).
% 3.25/1.72  thf(fact_24_zeroTrans, axiom, (! [Rs:late_residual]: ((~ (((late_transitions @ piNil) @ Rs)))))).
% 3.25/1.72  thf(fact_25_nilCases_H, axiom, (! [Rs:late_residual]: ((~ (((late_transitions @ piNil) @ Rs)))))).
% 3.25/1.72  thf(fact_26_pi_Odistinct_I15_J, axiom, (! [Name:name,Pi:pi]: ((piNil != ((res @ Name) @ Pi))))).
% 3.25/1.72  thf(fact_27_pi_Odistinct_I13_J, axiom, (! [Pi12:pi,Pi22:pi]: ((piNil != ((par @ Pi12) @ Pi22))))).
% 3.25/1.72  thf(fact_28_freshFreeDerivative_I1_J, axiom, (! [P:pi,Alpha:late_freeRes,P2:pi,Y2:name]: ((((late_transitions @ P) @ ((late_FreeR @ Alpha) @ P2)) => (((((fresh @ name) @ pi) @ Y2) @ P) => ((((fresh @ name) @ late_freeRes) @ Y2) @ Alpha)))))).
% 3.25/1.72  thf(fact_29_freshFreeDerivative_I2_J, axiom, (! [P:pi,Alpha:late_freeRes,P2:pi,Y2:name]: ((((late_transitions @ P) @ ((late_FreeR @ Alpha) @ P2)) => (((((fresh @ name) @ pi) @ Y2) @ P) => ((((fresh @ name) @ pi) @ Y2) @ P2)))))).
% 3.25/1.72  thf(fact_30_resTrans_I2_J, axiom, (! [X2:name,Y2:name,P:pi,Rs:late_residual]: ((~ (((late_transitions @ ((res @ X2) @ (((input @ X2) @ Y2) @ P))) @ Rs)))))).
% 3.25/1.72  thf(fact_31_inputFreeTrans, axiom, (! [A2:name,X2:name,P:pi,Alpha:late_freeRes,P2:pi]: ((~ (((late_transitions @ (((input @ A2) @ X2) @ P)) @ ((late_FreeR @ Alpha) @ P2))))))).
% 3.25/1.72  thf(fact_32_ScopeExt, axiom, (! [Y2:name,R:pi,Z:name,S:pi]: ((((((fresh @ name) @ pi) @ Y2) @ R) => (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ ((res @ Y2) @ ((res @ Z) @ ((par @ R) @ S)))) @ ((res @ Z) @ ((par @ R) @ ((res @ Y2) @ S))))) @ rel))))).
% 3.25/1.72  thf(fact_33_Res, axiom, (! [Y2:name,R:pi,S:pi]: ((((((fresh @ name) @ pi) @ Y2) @ R) => (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ ((res @ Y2) @ ((par @ R) @ S))) @ ((par @ R) @ ((res @ Y2) @ S)))) @ rel))))).
% 3.25/1.72  thf(fact_34_outputFreshTrans, axiom, (! [A2:name,B2:name,P:pi,Alpha:late_freeRes,P2:pi]: ((((late_transitions @ (((output @ A2) @ B2) @ P)) @ ((late_FreeR @ Alpha) @ P2)) => (~ ((((((fresh @ name) @ late_freeRes) @ A2) @ Alpha) | ((((fresh @ name) @ late_freeRes) @ B2) @ Alpha)))))))).
% 3.25/1.72  thf(fact_35_residual_Ofresh_I2_J, axiom, (! [A2:name,X22:late_freeRes,X1:pi]: ((((((fresh @ name) @ late_residual) @ A2) @ ((late_FreeR @ X22) @ X1)) = (((((fresh @ name) @ late_freeRes) @ A2) @ X22) & ((((fresh @ name) @ pi) @ A2) @ X1)))))).
% 3.25/1.72  thf(fact_36_Id, axiom, (((ord_less_eq @ (set @ ((product_prod @ pi) @ pi))) @ (id @ pi)) @ rel)).
% 3.25/1.72  thf(fact_37_parCasesB, axiom, (! [P:pi,Q:pi,A2:late_subject,X2:name,PQ:pi,Prop:(pi > $o)]: ((((late_transitions @ ((par @ P) @ Q)) @ (((late_BoundR @ A2) @ X2) @ PQ)) => (((((fresh @ name) @ pi) @ X2) @ P) => (((((fresh @ name) @ pi) @ X2) @ Q) => ((! [P3:pi]: ((((late_transitions @ P) @ (((late_BoundR @ A2) @ X2) @ P3)) => (Prop @ ((par @ P3) @ Q))))) => ((! [Q3:pi]: ((((late_transitions @ Q) @ (((late_BoundR @ A2) @ X2) @ Q3)) => (Prop @ ((par @ P) @ Q3))))) => (Prop @ PQ))))))))).
% 3.25/1.72  thf(fact_38_Late__Semantics_OPar2B, axiom, (! [Q:pi,A2:late_subject,X2:name,Q2:pi,P:pi]: ((((late_transitions @ Q) @ (((late_BoundR @ A2) @ X2) @ Q2)) => (((((fresh @ name) @ pi) @ X2) @ P) => ((late_transitions @ ((par @ P) @ Q)) @ (((late_BoundR @ A2) @ X2) @ ((par @ P) @ Q2)))))))).
% 3.25/1.72  thf(fact_39_Late__Semantics_OPar1B, axiom, (! [P:pi,A2:late_subject,X2:name,P2:pi,Q:pi]: ((((late_transitions @ P) @ (((late_BoundR @ A2) @ X2) @ P2)) => (((((fresh @ name) @ pi) @ X2) @ Q) => ((late_transitions @ ((par @ P) @ Q)) @ (((late_BoundR @ A2) @ X2) @ ((par @ P2) @ Q)))))))).
% 3.25/1.72  thf(fact_40_nilSim_I2_J, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),A2:name,X2:name,P:pi]: ((~ ((((strong743114133lation @ piNil) @ Rel) @ (((input @ A2) @ X2) @ P))))))).
% 3.25/1.72  thf(fact_41_freeRes_Ofresh_I2_J, axiom, (! [A2:name]: (((((fresh @ name) @ late_freeRes) @ A2) @ late_TauR)))).
% 3.25/1.72  thf(fact_42_pi_Ofresh_I2_J, axiom, (! [A2:name,X3:name,X22:name,X1:pi]: ((((((fresh @ name) @ pi) @ A2) @ (((output @ X3) @ X22) @ X1)) = (((((fresh @ name) @ name) @ A2) @ X3) & (((((fresh @ name) @ name) @ A2) @ X22) & ((((fresh @ name) @ pi) @ A2) @ X1))))))).
% 3.25/1.72  thf(fact_43_pi_Oinject_I1_J, axiom, (! [X3:name,X22:name,X1:pi,Y3:name,Y22:name,Y1:pi]: ((((((output @ X3) @ X22) @ X1) = (((output @ Y3) @ Y22) @ Y1)) = ((X3 = Y3) & ((X22 = Y22) & (X1 = Y1))))))).
% 3.25/1.72  thf(fact_44_outputBoundTrans, axiom, (! [A2:name,B2:name,P:pi,C2:late_subject,X2:name,P2:pi]: ((~ (((late_transitions @ (((output @ A2) @ B2) @ P)) @ (((late_BoundR @ C2) @ X2) @ P2))))))).
% 3.25/1.72  thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P)) = (P @ A2))))).
% 3.25/1.72  thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A3:(set @ A)]: ((((collect @ A) @ (^ [X4:A]: ((((member @ A) @ X4) @ A3)))) = A3)))).
% 3.25/1.72  thf(fact_47_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X5:A]: (((P @ X5) = (Q @ X5)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 3.25/1.72  thf(fact_48_nilSim_I3_J, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),A2:name,B2:name,P:pi]: ((~ ((((strong743114133lation @ piNil) @ Rel) @ (((output @ A2) @ B2) @ P))))))).
% 3.25/1.72  thf(fact_49_Late__Semantics_OResB, axiom, (! [P:pi,A2:late_subject,X2:name,P2:pi,Y2:name]: ((((late_transitions @ P) @ (((late_BoundR @ A2) @ X2) @ P2)) => (((((fresh @ name) @ late_subject) @ Y2) @ A2) => ((Y2 != X2) => ((late_transitions @ ((res @ Y2) @ P)) @ (((late_BoundR @ A2) @ X2) @ ((res @ Y2) @ P2))))))))).
% 3.25/1.72  thf(fact_50_freshBoundDerivative_I1_J, axiom, (! [P:pi,A2:late_subject,X2:name,P2:pi,Y2:name]: ((((late_transitions @ P) @ (((late_BoundR @ A2) @ X2) @ P2)) => (((((fresh @ name) @ pi) @ Y2) @ P) => ((((fresh @ name) @ late_subject) @ Y2) @ A2)))))).
% 3.25/1.72  thf(fact_51_inputIneqTrans, axiom, (! [A2:name,X2:name,P:pi,B2:late_subject,Y2:name,P2:pi]: ((((late_transitions @ (((input @ A2) @ X2) @ P)) @ (((late_BoundR @ B2) @ Y2) @ P2)) => (~ (((((fresh @ name) @ late_subject) @ A2) @ B2))))))).
% 3.25/1.72  thf(fact_52_parSym, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),P:pi,Q:pi]: (((! [R2:pi,S2:pi]: ((((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ ((par @ R2) @ S2)) @ ((par @ S2) @ R2))) @ Rel))) => ((! [R2:pi,S2:pi,X5:name]: (((((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ R2) @ S2)) @ Rel) => (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ ((res @ X5) @ R2)) @ ((res @ X5) @ S2))) @ Rel)))) => (((strong743114133lation @ ((par @ P) @ Q)) @ Rel) @ ((par @ Q) @ P))))))).
% 3.25/1.72  thf(fact_53_residual_Odistinct_I1_J, axiom, (! [Subject:late_subject,Name3:name,Pi3:pi,FreeRes:late_freeRes,Pi:pi]: (((((late_BoundR @ Subject) @ Name3) @ Pi3) != ((late_FreeR @ FreeRes) @ Pi))))).
% 3.25/1.72  thf(fact_54_residual_Oinducts, axiom, (! [P:(late_residual > $o),Residual:late_residual]: (((! [Subject2:late_subject,Name4:name,Pi4:pi]: ((P @ (((late_BoundR @ Subject2) @ Name4) @ Pi4)))) => ((! [FreeRes2:late_freeRes,Pi4:pi]: ((P @ ((late_FreeR @ FreeRes2) @ Pi4)))) => (P @ Residual)))))).
% 3.25/1.72  thf(fact_55_parZeroRight, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),P:pi]: (((! [Q4:pi]: ((((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ Q4) @ ((par @ Q4) @ piNil))) @ Rel))) => (((strong743114133lation @ P) @ Rel) @ ((par @ P) @ piNil)))))).
% 3.25/1.72  thf(fact_56_parZeroLeft, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),P:pi]: (((! [Q4:pi]: ((((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ ((par @ Q4) @ piNil)) @ Q4)) @ Rel))) => (((strong743114133lation @ ((par @ P) @ piNil)) @ Rel) @ P))))).
% 3.25/1.72  thf(fact_57_outputTauTrans, axiom, (! [A2:name,B2:name,P:pi,P2:pi]: ((~ (((late_transitions @ (((output @ A2) @ B2) @ P)) @ ((late_FreeR @ late_TauR) @ P2))))))).
% 3.25/1.72  thf(fact_58_pi_Odistinct_I31_J, axiom, (! [Name12:name,Name22:name,Pi3:pi,Name:name,Pi:pi]: (((((output @ Name12) @ Name22) @ Pi3) != ((res @ Name) @ Pi))))).
% 3.25/1.72  thf(fact_59_pi_Odistinct_I29_J, axiom, (! [Name12:name,Name22:name,Pi3:pi,Pi12:pi,Pi22:pi]: (((((output @ Name12) @ Name22) @ Pi3) != ((par @ Pi12) @ Pi22))))).
% 3.25/1.72  thf(fact_60_transitions_OResB, axiom, (! [P:pi,A2:late_subject,X2:name,P2:pi,Y2:name]: ((((late_transitions @ P) @ (((late_BoundR @ A2) @ X2) @ P2)) => (((((fresh @ name) @ late_subject) @ Y2) @ A2) => ((Y2 != X2) => (((((fresh @ name) @ pi) @ X2) @ P) => (((((fresh @ name) @ late_subject) @ X2) @ A2) => ((late_transitions @ ((res @ Y2) @ P)) @ (((late_BoundR @ A2) @ X2) @ ((res @ Y2) @ P2))))))))))).
% 3.25/1.72  thf(fact_61_parCasesB_H, axiom, (! [P:pi,Q:pi,B2:late_subject,Y2:name,P2:pi]: ((((late_transitions @ ((par @ P) @ Q)) @ (((late_BoundR @ B2) @ Y2) @ P2)) => ((! [P4:pi,A4:late_subject,X5:name,P3:pi,Q4:pi]: (((((par @ P) @ Q) = ((par @ P4) @ Q4)) => (((((late_BoundR @ B2) @ Y2) @ P2) = (((late_BoundR @ A4) @ X5) @ ((par @ P3) @ Q4))) => (((late_transitions @ P4) @ (((late_BoundR @ A4) @ X5) @ P3)) => (((((fresh @ name) @ pi) @ X5) @ P4) => (((((fresh @ name) @ pi) @ X5) @ Q4) => (~ (((((fresh @ name) @ late_subject) @ X5) @ A4)))))))))) => (~ ((! [Q4:pi,A4:late_subject,X5:name,Q3:pi,P4:pi]: (((((par @ P) @ Q) = ((par @ P4) @ Q4)) => (((((late_BoundR @ B2) @ Y2) @ P2) = (((late_BoundR @ A4) @ X5) @ ((par @ P4) @ Q3))) => (((late_transitions @ Q4) @ (((late_BoundR @ A4) @ X5) @ Q3)) => (((((fresh @ name) @ pi) @ X5) @ P4) => (((((fresh @ name) @ pi) @ X5) @ Q4) => (~ (((((fresh @ name) @ late_subject) @ X5) @ A4))))))))))))))))).
% 3.25/1.72  thf(fact_62_transitions_OPar1B, axiom, (! [P:pi,A2:late_subject,X2:name,P2:pi,Q:pi]: ((((late_transitions @ P) @ (((late_BoundR @ A2) @ X2) @ P2)) => (((((fresh @ name) @ pi) @ X2) @ P) => (((((fresh @ name) @ pi) @ X2) @ Q) => (((((fresh @ name) @ late_subject) @ X2) @ A2) => ((late_transitions @ ((par @ P) @ Q)) @ (((late_BoundR @ A2) @ X2) @ ((par @ P2) @ Q)))))))))).
% 3.25/1.72  thf(fact_63_transitions_OPar2B, axiom, (! [Q:pi,A2:late_subject,X2:name,Q2:pi,P:pi]: ((((late_transitions @ Q) @ (((late_BoundR @ A2) @ X2) @ Q2)) => (((((fresh @ name) @ pi) @ X2) @ P) => (((((fresh @ name) @ pi) @ X2) @ Q) => (((((fresh @ name) @ late_subject) @ X2) @ A2) => ((late_transitions @ ((par @ P) @ Q)) @ (((late_BoundR @ A2) @ X2) @ ((par @ P) @ Q2)))))))))).
% 3.25/1.72  thf(fact_64_pi_Odistinct_I21_J, axiom, (! [Name12:name,Name22:name,Pi3:pi,Name1:name,Name2:name,Pi:pi]: (((((output @ Name12) @ Name22) @ Pi3) != (((input @ Name1) @ Name2) @ Pi))))).
% 3.25/1.72  thf(fact_65_pi_Odistinct_I1_J, axiom, (! [Name1:name,Name2:name,Pi:pi]: ((piNil != (((output @ Name1) @ Name2) @ Pi))))).
% 3.25/1.72  thf(fact_66_nilSimRight, axiom, (! [P:pi,Rel:(set @ ((product_prod @ pi) @ pi))]: ((((strong743114133lation @ P) @ Rel) @ piNil)))).
% 3.25/1.72  thf(fact_67_parAssocLeft, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),P:pi,Q:pi,R:pi]: (((! [S2:pi,T2:pi,U:pi]: ((((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ ((par @ ((par @ S2) @ T2)) @ U)) @ ((par @ S2) @ ((par @ T2) @ U)))) @ Rel))) => ((! [S2:pi,T2:pi,X5:name]: (((((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ S2) @ T2)) @ Rel) => (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ ((res @ X5) @ S2)) @ ((res @ X5) @ T2))) @ Rel)))) => ((! [S2:pi,T2:pi,U:pi,X5:name]: ((((((fresh @ name) @ pi) @ X5) @ S2) => (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ ((res @ X5) @ ((par @ ((par @ S2) @ T2)) @ U))) @ ((par @ S2) @ ((res @ X5) @ ((par @ T2) @ U))))) @ Rel)))) => ((! [S2:pi,T2:pi,U:pi,X5:name]: ((((((fresh @ name) @ pi) @ X5) @ U) => (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ ((par @ ((res @ X5) @ ((par @ S2) @ T2))) @ U)) @ ((res @ X5) @ ((par @ S2) @ ((par @ T2) @ U))))) @ Rel)))) => (((strong743114133lation @ ((par @ ((par @ P) @ Q)) @ R)) @ Rel) @ ((par @ P) @ ((par @ Q) @ R)))))))))).
% 3.25/1.72  thf(fact_68_resOutputTauTrans, axiom, (! [X2:name,A2:name,B2:name,P:pi,P2:pi]: ((~ (((late_transitions @ ((res @ X2) @ (((output @ A2) @ B2) @ P))) @ ((late_FreeR @ late_TauR) @ P2))))))).
% 3.25/1.72  thf(fact_69_freshResidual, axiom, (! [P:pi,Rs:late_residual,X2:name]: ((((late_transitions @ P) @ Rs) => (((((fresh @ name) @ pi) @ X2) @ P) => ((((fresh @ name) @ late_residual) @ X2) @ Rs)))))).
% 3.25/1.72  thf(fact_70_residual_Ostrong__inducts, axiom, (! [A:$tType]: (((fs_name @ A) => (! [P:(A > (late_residual > $o)),Z:A,Residual:late_residual]: (((! [Subject2:late_subject,Name4:name,Pi4:pi,Z2:A]: ((((((fresh @ name) @ A) @ Name4) @ Z2) => (((((fresh @ name) @ late_subject) @ Name4) @ Subject2) => ((P @ Z2) @ (((late_BoundR @ Subject2) @ Name4) @ Pi4)))))) => ((! [FreeRes2:late_freeRes,Pi4:pi,Z2:A]: (((P @ Z2) @ ((late_FreeR @ FreeRes2) @ Pi4)))) => ((P @ Z) @ Residual))))))))).
% 3.25/1.72  thf(fact_71_residual_Ostrong__induct, axiom, (! [N:$tType]: (((fs_name @ N) => (! [P:(N > (late_residual > $o)),Z:N,Residual:late_residual]: (((! [Subject2:late_subject,Name4:name,Pi4:pi,Z2:N]: ((((((fresh @ name) @ N) @ Name4) @ Z2) => (((((fresh @ name) @ late_subject) @ Name4) @ Subject2) => ((P @ Z2) @ (((late_BoundR @ Subject2) @ Name4) @ Pi4)))))) => ((! [FreeRes2:late_freeRes,Pi4:pi,Z2:N]: (((P @ Z2) @ ((late_FreeR @ FreeRes2) @ Pi4)))) => ((P @ Z) @ Residual))))))))).
% 3.25/1.72  thf(fact_72_freshBoundDerivative_I2_J, axiom, (! [P:pi,A2:late_subject,X2:name,P2:pi,Y2:name]: ((((late_transitions @ P) @ (((late_BoundR @ A2) @ X2) @ P2)) => (((((fresh @ name) @ pi) @ Y2) @ P) => ((Y2 != X2) => ((((fresh @ name) @ pi) @ Y2) @ P2))))))).
% 3.25/1.72  thf(fact_73_resTrans_I1_J, axiom, (! [X2:name,B2:name,P:pi,Rs:late_residual]: ((~ (((late_transitions @ ((res @ X2) @ (((output @ X2) @ B2) @ P))) @ Rs)))))).
% 3.25/1.72  thf(fact_74_pair__in__Id__conv, axiom, (! [A:$tType,A2:A,B2:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A2) @ B2)) @ (id @ A)) = (A2 = B2))))).
% 3.25/1.72  thf(fact_75_IdI, axiom, (! [A:$tType,A2:A]: ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A2) @ A2)) @ (id @ A))))).
% 3.25/1.72  thf(fact_76_fresh__prod, axiom, (! [A:$tType,X:$tType,B:$tType,A2:X,X2:A,Y2:B]: ((((((fresh @ X) @ ((product_prod @ A) @ B)) @ A2) @ ((((product_Pair @ A) @ B) @ X2) @ Y2)) = (((((fresh @ X) @ A) @ A2) @ X2) & ((((fresh @ X) @ B) @ A2) @ Y2)))))).
% 3.25/1.72  thf(fact_77_simE_I2_J, axiom, (! [P:pi,Rel:(set @ ((product_prod @ pi) @ pi)),Q:pi,Alpha:late_freeRes,Q2:pi]: (((((strong743114133lation @ P) @ Rel) @ Q) => (((late_transitions @ Q) @ ((late_FreeR @ Alpha) @ Q2)) => (? [P3:pi]: ((((late_transitions @ P) @ ((late_FreeR @ Alpha) @ P3)) & (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ P3) @ Q2)) @ Rel))))))))).
% 3.25/1.72  thf(fact_78_Strong__Late__Sim_Oreflexive, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),P:pi]: (((((ord_less_eq @ (set @ ((product_prod @ pi) @ pi))) @ (id @ pi)) @ Rel) => (((strong743114133lation @ P) @ Rel) @ P))))).
% 3.25/1.72  thf(fact_79_simCasesCont, axiom, (! [A:$tType]: (((fs_name @ A) => (! [Rel:(set @ ((product_prod @ pi) @ pi)),Q:pi,P:pi,C3:A]: ((((eqvt @ pi) @ Rel) => ((! [A4:late_subject,X5:name,Q3:pi]: ((((late_transitions @ Q) @ (((late_BoundR @ A4) @ X5) @ Q3)) => (((((fresh @ name) @ pi) @ X5) @ P) => (((((fresh @ name) @ pi) @ X5) @ Q) => (((((fresh @ name) @ late_subject) @ X5) @ A4) => (((((fresh @ name) @ A) @ X5) @ C3) => (? [P5:pi]: ((((late_transitions @ P) @ (((late_BoundR @ A4) @ X5) @ P5)) & (((((strong2129052853vative @ P5) @ Q3) @ A4) @ X5) @ Rel))))))))))) => ((! [Alpha2:late_freeRes,Q3:pi]: ((((late_transitions @ Q) @ ((late_FreeR @ Alpha2) @ Q3)) => (? [P5:pi]: ((((late_transitions @ P) @ ((late_FreeR @ Alpha2) @ P5)) & (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ P5) @ Q3)) @ Rel))))))) => (((strong743114133lation @ P) @ Rel) @ Q)))))))))).
% 3.25/1.72  thf(fact_80_subset__antisym, axiom, (! [A:$tType,A3:(set @ A),B3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A3) @ B3) => ((((ord_less_eq @ (set @ A)) @ B3) @ A3) => (A3 = B3)))))).
% 3.25/1.72  thf(fact_81_subsetI, axiom, (! [A:$tType,A3:(set @ A),B3:(set @ A)]: (((! [X5:A]: (((((member @ A) @ X5) @ A3) => (((member @ A) @ X5) @ B3)))) => (((ord_less_eq @ (set @ A)) @ A3) @ B3))))).
% 3.25/1.72  thf(fact_82_name__fresh, axiom, (((fresh @ name) @ name) = (^ [A5:name,B4:name]: ((A5 != B4))))).
% 3.25/1.72  thf(fact_83_derivativeMonotonic, axiom, (! [P:pi,Q:pi,A2:late_subject,X2:name,A3:(set @ ((product_prod @ pi) @ pi)),B3:(set @ ((product_prod @ pi) @ pi))]: (((((((strong2129052853vative @ P) @ Q) @ A2) @ X2) @ A3) => ((((ord_less_eq @ (set @ ((product_prod @ pi) @ pi))) @ A3) @ B3) => (((((strong2129052853vative @ P) @ Q) @ A2) @ X2) @ B3)))))).
% 3.25/1.72  thf(fact_84_derivativeReflexive, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),P:pi,A2:late_subject,X2:name]: (((((ord_less_eq @ (set @ ((product_prod @ pi) @ pi))) @ (id @ pi)) @ Rel) => (((((strong2129052853vative @ P) @ P) @ A2) @ X2) @ Rel))))).
% 3.25/1.72  thf(fact_85_in__mono, axiom, (! [A:$tType,A3:(set @ A),B3:(set @ A),X2:A]: (((((ord_less_eq @ (set @ A)) @ A3) @ B3) => ((((member @ A) @ X2) @ A3) => (((member @ A) @ X2) @ B3)))))).
% 3.25/1.72  thf(fact_86_subsetD, axiom, (! [A:$tType,A3:(set @ A),B3:(set @ A),C2:A]: (((((ord_less_eq @ (set @ A)) @ A3) @ B3) => ((((member @ A) @ C2) @ A3) => (((member @ A) @ C2) @ B3)))))).
% 3.25/1.72  thf(fact_87_equalityE, axiom, (! [A:$tType,A3:(set @ A),B3:(set @ A)]: (((A3 = B3) => (~ (((((ord_less_eq @ (set @ A)) @ A3) @ B3) => (~ ((((ord_less_eq @ (set @ A)) @ B3) @ A3)))))))))).
% 3.25/1.72  thf(fact_88_subset__eq, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A6:(set @ A),B5:(set @ A)]: ((! [X4:A]: (((((member @ A) @ X4) @ A6) => (((member @ A) @ X4) @ B5)))))))))).
% 3.25/1.72  thf(fact_89_equalityD1, axiom, (! [A:$tType,A3:(set @ A),B3:(set @ A)]: (((A3 = B3) => (((ord_less_eq @ (set @ A)) @ A3) @ B3))))).
% 3.25/1.72  thf(fact_90_equalityD2, axiom, (! [A:$tType,A3:(set @ A),B3:(set @ A)]: (((A3 = B3) => (((ord_less_eq @ (set @ A)) @ B3) @ A3))))).
% 3.25/1.72  thf(fact_91_subset__iff, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A6:(set @ A),B5:(set @ A)]: ((! [T3:A]: (((((member @ A) @ T3) @ A6) => (((member @ A) @ T3) @ B5)))))))))).
% 3.25/1.72  thf(fact_92_subset__refl, axiom, (! [A:$tType,A3:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ A3) @ A3)))).
% 3.25/1.72  thf(fact_93_Collect__mono, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X5:A]: (((P @ X5) => (Q @ X5)))) => (((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P)) @ ((collect @ A) @ Q)))))).
% 3.25/1.72  thf(fact_94_subset__trans, axiom, (! [A:$tType,A3:(set @ A),B3:(set @ A),C3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A3) @ B3) => ((((ord_less_eq @ (set @ A)) @ B3) @ C3) => (((ord_less_eq @ (set @ A)) @ A3) @ C3)))))).
% 3.25/1.72  thf(fact_95_set__eq__subset, axiom, (! [A:$tType]: (((^ [Y4:(set @ A),Z3:(set @ A)]: ((Y4 = Z3))) = (^ [A6:(set @ A),B5:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A6) @ B5) & (((ord_less_eq @ (set @ A)) @ B5) @ A6)))))))).
% 3.25/1.72  thf(fact_96_Collect__mono__iff, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P)) @ ((collect @ A) @ Q)) = (! [X4:A]: (((P @ X4) => (Q @ X4)))))))).
% 3.25/1.72  thf(fact_97_simE_I1_J, axiom, (! [P:pi,Rel:(set @ ((product_prod @ pi) @ pi)),Q:pi,A2:late_subject,X2:name,Q2:pi]: (((((strong743114133lation @ P) @ Rel) @ Q) => (((late_transitions @ Q) @ (((late_BoundR @ A2) @ X2) @ Q2)) => (((((fresh @ name) @ pi) @ X2) @ P) => (? [P3:pi]: ((((late_transitions @ P) @ (((late_BoundR @ A2) @ X2) @ P3)) & (((((strong2129052853vative @ P3) @ Q2) @ A2) @ X2) @ Rel)))))))))).
% 3.25/1.72  thf(fact_98_fresh__prodD_I2_J, axiom, (! [B:$tType,A:$tType,C4:$tType,A2:A,X2:B,Y2:C4]: ((((((fresh @ A) @ ((product_prod @ B) @ C4)) @ A2) @ ((((product_Pair @ B) @ C4) @ X2) @ Y2)) => ((((fresh @ A) @ C4) @ A2) @ Y2))))).
% 3.25/1.72  thf(fact_99_fresh__prodD_I1_J, axiom, (! [C4:$tType,A:$tType,B:$tType,A2:A,X2:B,Y2:C4]: ((((((fresh @ A) @ ((product_prod @ B) @ C4)) @ A2) @ ((((product_Pair @ B) @ C4) @ X2) @ Y2)) => ((((fresh @ A) @ B) @ A2) @ X2))))).
% 3.25/1.72  thf(fact_100_subrelI, axiom, (! [B:$tType,A:$tType,R3:(set @ ((product_prod @ A) @ B)),S3:(set @ ((product_prod @ A) @ B))]: (((! [X5:A,Y:B]: (((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X5) @ Y)) @ R3) => (((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X5) @ Y)) @ S3)))) => (((ord_less_eq @ (set @ ((product_prod @ A) @ B))) @ R3) @ S3))))).
% 3.25/1.72  thf(fact_101_simCases, axiom, (! [Q:pi,P:pi,Rel:(set @ ((product_prod @ pi) @ pi))]: (((! [A4:late_subject,Y:name,Q3:pi]: ((((late_transitions @ Q) @ (((late_BoundR @ A4) @ Y) @ Q3)) => (((((fresh @ name) @ pi) @ Y) @ P) => (? [P5:pi]: ((((late_transitions @ P) @ (((late_BoundR @ A4) @ Y) @ P5)) & (((((strong2129052853vative @ P5) @ Q3) @ A4) @ Y) @ Rel)))))))) => ((! [Alpha2:late_freeRes,Q3:pi]: ((((late_transitions @ Q) @ ((late_FreeR @ Alpha2) @ Q3)) => (? [P5:pi]: ((((late_transitions @ P) @ ((late_FreeR @ Alpha2) @ P5)) & (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ P5) @ Q3)) @ Rel))))))) => (((strong743114133lation @ P) @ Rel) @ Q)))))).
% 3.25/1.72  thf(fact_102_simulation__def, axiom, (strong743114133lation = (^ [P6:pi,Rel2:(set @ ((product_prod @ pi) @ pi)),Q5:pi]: (((! [A5:late_subject,X4:name,Q6:pi]: (((((late_transitions @ Q5) @ (((late_BoundR @ A5) @ X4) @ Q6)) & ((((fresh @ name) @ pi) @ X4) @ P6)) => (? [P7:pi]: ((((late_transitions @ P6) @ (((late_BoundR @ A5) @ X4) @ P7)) & (((((strong2129052853vative @ P7) @ Q6) @ A5) @ X4) @ Rel2))))))) & (! [Alpha3:late_freeRes,Q6:pi]: ((((late_transitions @ Q5) @ ((late_FreeR @ Alpha3) @ Q6)) => (? [P7:pi]: ((((late_transitions @ P6) @ ((late_FreeR @ Alpha3) @ P7)) & (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ P7) @ Q6)) @ Rel2)))))))))))).
% 3.25/1.72  thf(fact_103_IdE, axiom, (! [A:$tType,P8:((product_prod @ A) @ A)]: (((((member @ ((product_prod @ A) @ A)) @ P8) @ (id @ A)) => (~ ((! [X5:A]: ((P8 != ((((product_Pair @ A) @ A) @ X5) @ X5)))))))))).
% 3.25/1.72  thf(fact_104_monotonic, axiom, (! [P:pi,A3:(set @ ((product_prod @ pi) @ pi)),P2:pi,B3:(set @ ((product_prod @ pi) @ pi))]: (((((strong743114133lation @ P) @ A3) @ P2) => ((((ord_less_eq @ (set @ ((product_prod @ pi) @ pi))) @ A3) @ B3) => (((strong743114133lation @ P) @ B3) @ P2)))))).
% 3.25/1.72  thf(fact_105_prod_Oinject, axiom, (! [A:$tType,B:$tType,X1:A,X22:B,Y1:A,Y22:B]: (((((((product_Pair @ A) @ B) @ X1) @ X22) = ((((product_Pair @ A) @ B) @ Y1) @ Y22)) = ((X1 = Y1) & (X22 = Y22)))))).
% 3.25/1.72  thf(fact_106_old_Oprod_Oinject, axiom, (! [A:$tType,B:$tType,A2:A,B2:B,A7:A,B6:B]: (((((((product_Pair @ A) @ B) @ A2) @ B2) = ((((product_Pair @ A) @ B) @ A7) @ B6)) = ((A2 = A7) & (B2 = B6)))))).
% 3.25/1.72  thf(fact_107_order__refl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X2:A]: ((((ord_less_eq @ A) @ X2) @ X2))))))).
% 3.25/1.72  thf(fact_108_resSimCases, axiom, (! [A:$tType]: (((fs_name @ A) => (! [Rel:(set @ ((product_prod @ pi) @ pi)),Q:pi,X2:name,P:pi,C3:A]: ((((eqvt @ pi) @ Rel) => ((! [Q3:pi,A4:name]: ((((late_transitions @ Q) @ ((late_FreeR @ ((late_OutputR @ A4) @ X2)) @ Q3)) => ((A4 != X2) => (? [P5:pi]: ((((late_transitions @ P) @ (((late_BoundR @ (late_BoundOutputS @ A4)) @ X2) @ P5)) & (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ P5) @ Q3)) @ Rel)))))))) => ((! [Q3:pi,A4:late_subject,Y:name]: ((((late_transitions @ Q) @ (((late_BoundR @ A4) @ Y) @ Q3)) => (((((fresh @ name) @ late_subject) @ X2) @ A4) => ((X2 != Y) => (((((fresh @ name) @ A) @ Y) @ C3) => (? [P5:pi]: ((((late_transitions @ P) @ (((late_BoundR @ A4) @ Y) @ P5)) & (((((strong2129052853vative @ P5) @ ((res @ X2) @ Q3)) @ A4) @ Y) @ Rel)))))))))) => ((! [Q3:pi,Alpha2:late_freeRes]: ((((late_transitions @ Q) @ ((late_FreeR @ Alpha2) @ Q3)) => (((((fresh @ name) @ late_freeRes) @ X2) @ Alpha2) => (? [P5:pi]: ((((late_transitions @ P) @ ((late_FreeR @ Alpha2) @ P5)) & (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ P5) @ ((res @ X2) @ Q3))) @ Rel)))))))) => (((strong743114133lation @ P) @ Rel) @ ((res @ X2) @ Q)))))))))))).
% 3.25/1.72  thf(fact_109_IdD, axiom, (! [A:$tType,A2:A,B2:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A2) @ B2)) @ (id @ A)) => (A2 = B2))))).
% 3.25/1.72  thf(fact_110_sumResLeft, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),X2:name,P:pi,Q:pi]: (((((ord_less_eq @ (set @ ((product_prod @ pi) @ pi))) @ (id @ pi)) @ Rel) => (((eqvt @ pi) @ Rel) => (((strong743114133lation @ ((sum @ ((res @ X2) @ P)) @ ((res @ X2) @ Q))) @ Rel) @ ((res @ X2) @ ((sum @ P) @ Q)))))))).
% 3.25/1.72  thf(fact_111_Late__Semantics_OfreeRes_Oinject, axiom, (! [X22:name,X1:name,Y22:name,Y1:name]: (((((late_OutputR @ X22) @ X1) = ((late_OutputR @ Y22) @ Y1)) = ((X22 = Y22) & (X1 = Y1)))))).
% 3.25/1.72  thf(fact_112_Late__Semantics_Osubject_Oinject_I2_J, axiom, (! [X1:name,Y1:name]: ((((late_BoundOutputS @ X1) = (late_BoundOutputS @ Y1)) = (X1 = Y1))))).
% 3.25/1.72  thf(fact_113_pi_Ofresh_I7_J, axiom, (! [A2:name,X22:pi,X1:pi]: ((((((fresh @ name) @ pi) @ A2) @ ((sum @ X22) @ X1)) = (((((fresh @ name) @ pi) @ A2) @ X22) & ((((fresh @ name) @ pi) @ A2) @ X1)))))).
% 3.25/1.72  thf(fact_114_subject_Ofresh_I2_J, axiom, (! [A2:name,X1:name]: ((((((fresh @ name) @ late_subject) @ A2) @ (late_BoundOutputS @ X1)) = ((((fresh @ name) @ name) @ A2) @ X1))))).
% 3.25/1.72  thf(fact_115_freeRes_Ofresh_I1_J, axiom, (! [A2:name,X22:name,X1:name]: ((((((fresh @ name) @ late_freeRes) @ A2) @ ((late_OutputR @ X22) @ X1)) = (((((fresh @ name) @ name) @ A2) @ X22) & ((((fresh @ name) @ name) @ A2) @ X1)))))).
% 3.25/1.72  thf(fact_116_pi_Oinject_I6_J, axiom, (! [X22:pi,X1:pi,Y22:pi,Y1:pi]: (((((sum @ X22) @ X1) = ((sum @ Y22) @ Y1)) = ((X22 = Y22) & (X1 = Y1)))))).
% 3.25/1.72  thf(fact_117_sumCases, axiom, (! [P:pi,Q:pi,Rs:late_residual]: ((((late_transitions @ ((sum @ P) @ Q)) @ Rs) => ((~ (((late_transitions @ P) @ Rs))) => ((late_transitions @ Q) @ Rs)))))).
% 3.25/1.72  thf(fact_118_sumCases_H, axiom, (! [P:pi,Q:pi,Rs:late_residual]: ((((late_transitions @ ((sum @ P) @ Q)) @ Rs) => ((~ (((late_transitions @ P) @ Rs))) => ((late_transitions @ Q) @ Rs)))))).
% 3.25/1.72  thf(fact_119_Sum1, axiom, (! [P:pi,Rs:late_residual,Q:pi]: ((((late_transitions @ P) @ Rs) => ((late_transitions @ ((sum @ P) @ Q)) @ Rs))))).
% 3.25/1.72  thf(fact_120_Sum2, axiom, (! [Q:pi,Rs:late_residual,P:pi]: ((((late_transitions @ Q) @ Rs) => ((late_transitions @ ((sum @ P) @ Q)) @ Rs))))).
% 3.25/1.72  thf(fact_121_pi_Odistinct_I81_J, axiom, (! [Pi1:pi,Pi2:pi,Name:name,Pi:pi]: ((((sum @ Pi1) @ Pi2) != ((res @ Name) @ Pi))))).
% 3.25/1.72  thf(fact_122_pi_Odistinct_I79_J, axiom, (! [Pi1:pi,Pi2:pi,Pi12:pi,Pi22:pi]: ((((sum @ Pi1) @ Pi2) != ((par @ Pi12) @ Pi22))))).
% 3.25/1.72  thf(fact_123_pi_Odistinct_I53_J, axiom, (! [Name12:name,Name22:name,Pi3:pi,Pi12:pi,Pi22:pi]: (((((input @ Name12) @ Name22) @ Pi3) != ((sum @ Pi12) @ Pi22))))).
% 3.25/1.72  thf(fact_124_pi_Odistinct_I11_J, axiom, (! [Pi12:pi,Pi22:pi]: ((piNil != ((sum @ Pi12) @ Pi22))))).
% 3.25/1.72  thf(fact_125_pi_Odistinct_I27_J, axiom, (! [Name12:name,Name22:name,Pi3:pi,Pi12:pi,Pi22:pi]: (((((output @ Name12) @ Name22) @ Pi3) != ((sum @ Pi12) @ Pi22))))).
% 3.25/1.72  thf(fact_126_Late__Semantics_OfreeRes_Odistinct_I1_J, axiom, (! [Name12:name,Name22:name]: ((((late_OutputR @ Name12) @ Name22) != late_TauR)))).
% 3.25/1.72  thf(fact_127_freeRes_Oinducts, axiom, (! [P:(late_freeRes > $o),FreeRes3:late_freeRes]: (((! [Name13:name,Name23:name]: ((P @ ((late_OutputR @ Name13) @ Name23)))) => ((P @ late_TauR) => (P @ FreeRes3)))))).
% 3.25/1.72  thf(fact_128_freeRes_Ostrong__induct_H, axiom, (! [N:$tType,P:(N > (late_freeRes > $o)),Z:N,FreeRes3:late_freeRes]: (((! [Name13:name,Name23:name,Z2:N]: (((P @ Z2) @ ((late_OutputR @ Name13) @ Name23)))) => ((! [Z2:N]: (((P @ Z2) @ late_TauR))) => ((P @ Z) @ FreeRes3)))))).
% 3.25/1.72  thf(fact_129_freeRes_Ostrong__inducts, axiom, (! [A:$tType,P:(A > (late_freeRes > $o)),Z:A,FreeRes3:late_freeRes]: (((! [Name13:name,Name23:name,Z2:A]: (((P @ Z2) @ ((late_OutputR @ Name13) @ Name23)))) => ((! [Z2:A]: (((P @ Z2) @ late_TauR))) => ((P @ Z) @ FreeRes3)))))).
% 3.25/1.72  thf(fact_130_Open, axiom, (! [P:pi,A2:name,B2:name,P2:pi]: ((((late_transitions @ P) @ ((late_FreeR @ ((late_OutputR @ A2) @ B2)) @ P2)) => ((A2 != B2) => ((late_transitions @ ((res @ B2) @ P)) @ (((late_BoundR @ (late_BoundOutputS @ A2)) @ B2) @ P2))))))).
% 3.25/1.72  thf(fact_131_dual__order_Oantisym, axiom, (! [A:$tType]: (((order @ A) => (! [B2:A,A2:A]: (((((ord_less_eq @ A) @ B2) @ A2) => ((((ord_less_eq @ A) @ A2) @ B2) => (A2 = B2))))))))).
% 3.25/1.72  thf(fact_132_dual__order_Oeq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y4:A,Z3:A]: ((Y4 = Z3))) = (^ [A5:A,B4:A]: (((((ord_less_eq @ A) @ B4) @ A5) & (((ord_less_eq @ A) @ A5) @ B4))))))))).
% 3.25/1.72  thf(fact_133_dual__order_Otrans, axiom, (! [A:$tType]: (((order @ A) => (! [B2:A,A2:A,C2:A]: (((((ord_less_eq @ A) @ B2) @ A2) => ((((ord_less_eq @ A) @ C2) @ B2) => (((ord_less_eq @ A) @ C2) @ A2))))))))).
% 3.25/1.72  thf(fact_134_linorder__wlog, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:(A > (A > $o)),A2:A,B2:A]: (((! [A4:A,B7:A]: (((((ord_less_eq @ A) @ A4) @ B7) => ((P @ A4) @ B7)))) => ((! [A4:A,B7:A]: ((((P @ B7) @ A4) => ((P @ A4) @ B7)))) => ((P @ A2) @ B2))))))))).
% 3.25/1.72  thf(fact_135_dual__order_Orefl, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A]: ((((ord_less_eq @ A) @ A2) @ A2))))))).
% 3.25/1.72  thf(fact_136_order__trans, axiom, (! [A:$tType]: (((preorder @ A) => (! [X2:A,Y2:A,Z:A]: (((((ord_less_eq @ A) @ X2) @ Y2) => ((((ord_less_eq @ A) @ Y2) @ Z) => (((ord_less_eq @ A) @ X2) @ Z))))))))).
% 3.25/1.72  thf(fact_137_order__class_Oorder_Oantisym, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ B2) @ A2) => (A2 = B2))))))))).
% 3.25/1.72  thf(fact_138_ord__le__eq__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A2:A,B2:A,C2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((B2 = C2) => (((ord_less_eq @ A) @ A2) @ C2))))))))).
% 3.25/1.72  thf(fact_139_ord__eq__le__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A2:A,B2:A,C2:A]: (((A2 = B2) => ((((ord_less_eq @ A) @ B2) @ C2) => (((ord_less_eq @ A) @ A2) @ C2))))))))).
% 3.25/1.72  thf(fact_140_order__class_Oorder_Oeq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y4:A,Z3:A]: ((Y4 = Z3))) = (^ [A5:A,B4:A]: (((((ord_less_eq @ A) @ A5) @ B4) & (((ord_less_eq @ A) @ B4) @ A5))))))))).
% 3.25/1.72  thf(fact_141_antisym__conv, axiom, (! [A:$tType]: (((order @ A) => (! [Y2:A,X2:A]: (((((ord_less_eq @ A) @ Y2) @ X2) => ((((ord_less_eq @ A) @ X2) @ Y2) = (X2 = Y2))))))))).
% 3.25/1.72  thf(fact_142_le__cases3, axiom, (! [A:$tType]: (((linorder @ A) => (! [X2:A,Y2:A,Z:A]: ((((((ord_less_eq @ A) @ X2) @ Y2) => (~ ((((ord_less_eq @ A) @ Y2) @ Z)))) => (((((ord_less_eq @ A) @ Y2) @ X2) => (~ ((((ord_less_eq @ A) @ X2) @ Z)))) => (((((ord_less_eq @ A) @ X2) @ Z) => (~ ((((ord_less_eq @ A) @ Z) @ Y2)))) => (((((ord_less_eq @ A) @ Z) @ Y2) => (~ ((((ord_less_eq @ A) @ Y2) @ X2)))) => (((((ord_less_eq @ A) @ Y2) @ Z) => (~ ((((ord_less_eq @ A) @ Z) @ X2)))) => (~ (((((ord_less_eq @ A) @ Z) @ X2) => (~ ((((ord_less_eq @ A) @ X2) @ Y2))))))))))))))))).
% 3.25/1.72  thf(fact_143_order_Otrans, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B2:A,C2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ B2) @ C2) => (((ord_less_eq @ A) @ A2) @ C2))))))))).
% 3.25/1.72  thf(fact_144_le__cases, axiom, (! [A:$tType]: (((linorder @ A) => (! [X2:A,Y2:A]: (((~ ((((ord_less_eq @ A) @ X2) @ Y2))) => (((ord_less_eq @ A) @ Y2) @ X2)))))))).
% 3.25/1.72  thf(fact_145_eq__refl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X2:A,Y2:A]: (((X2 = Y2) => (((ord_less_eq @ A) @ X2) @ Y2)))))))).
% 3.25/1.72  thf(fact_146_linear, axiom, (! [A:$tType]: (((linorder @ A) => (! [X2:A,Y2:A]: (((((ord_less_eq @ A) @ X2) @ Y2) | (((ord_less_eq @ A) @ Y2) @ X2)))))))).
% 3.25/1.72  thf(fact_147_antisym, axiom, (! [A:$tType]: (((order @ A) => (! [X2:A,Y2:A]: (((((ord_less_eq @ A) @ X2) @ Y2) => ((((ord_less_eq @ A) @ Y2) @ X2) => (X2 = Y2))))))))).
% 3.25/1.72  thf(fact_148_eq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y4:A,Z3:A]: ((Y4 = Z3))) = (^ [X4:A,Y5:A]: (((((ord_less_eq @ A) @ X4) @ Y5) & (((ord_less_eq @ A) @ Y5) @ X4))))))))).
% 3.25/1.72  thf(fact_149_ord__le__eq__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A2:A,B2:A,F2:(A > B),C2:B]: (((((ord_less_eq @ A) @ A2) @ B2) => (((F2 @ B2) = C2) => ((! [X5:A,Y:A]: (((((ord_less_eq @ A) @ X5) @ Y) => (((ord_less_eq @ B) @ (F2 @ X5)) @ (F2 @ Y))))) => (((ord_less_eq @ B) @ (F2 @ A2)) @ C2)))))))))).
% 3.25/1.72  thf(fact_150_ord__eq__le__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A2:A,F2:(B > A),B2:B,C2:B]: (((A2 = (F2 @ B2)) => ((((ord_less_eq @ B) @ B2) @ C2) => ((! [X5:B,Y:B]: (((((ord_less_eq @ B) @ X5) @ Y) => (((ord_less_eq @ A) @ (F2 @ X5)) @ (F2 @ Y))))) => (((ord_less_eq @ A) @ A2) @ (F2 @ C2))))))))))).
% 3.25/1.72  thf(fact_151_order__subst2, axiom, (! [A:$tType,C4:$tType]: ((((order @ C4) & (order @ A)) => (! [A2:A,B2:A,F2:(A > C4),C2:C4]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ C4) @ (F2 @ B2)) @ C2) => ((! [X5:A,Y:A]: (((((ord_less_eq @ A) @ X5) @ Y) => (((ord_less_eq @ C4) @ (F2 @ X5)) @ (F2 @ Y))))) => (((ord_less_eq @ C4) @ (F2 @ A2)) @ C2)))))))))).
% 3.25/1.72  thf(fact_152_order__subst1, axiom, (! [A:$tType,B:$tType]: ((((order @ B) & (order @ A)) => (! [A2:A,F2:(B > A),B2:B,C2:B]: (((((ord_less_eq @ A) @ A2) @ (F2 @ B2)) => ((((ord_less_eq @ B) @ B2) @ C2) => ((! [X5:B,Y:B]: (((((ord_less_eq @ B) @ X5) @ Y) => (((ord_less_eq @ A) @ (F2 @ X5)) @ (F2 @ Y))))) => (((ord_less_eq @ A) @ A2) @ (F2 @ C2))))))))))).
% 3.25/1.72  thf(fact_153_le__fun__def, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => ((ord_less_eq @ (A > B)) = (^ [F3:(A > B),G:(A > B)]: ((! [X4:A]: ((((ord_less_eq @ B) @ (F3 @ X4)) @ (G @ X4))))))))))).
% 3.25/1.72  thf(fact_154_le__funI, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F2:(A > B),G2:(A > B)]: (((! [X5:A]: ((((ord_less_eq @ B) @ (F2 @ X5)) @ (G2 @ X5)))) => (((ord_less_eq @ (A > B)) @ F2) @ G2)))))))).
% 3.25/1.72  thf(fact_155_le__funE, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F2:(A > B),G2:(A > B),X2:A]: (((((ord_less_eq @ (A > B)) @ F2) @ G2) => (((ord_less_eq @ B) @ (F2 @ X2)) @ (G2 @ X2))))))))).
% 3.25/1.72  thf(fact_156_le__funD, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F2:(A > B),G2:(A > B),X2:A]: (((((ord_less_eq @ (A > B)) @ F2) @ G2) => (((ord_less_eq @ B) @ (F2 @ X2)) @ (G2 @ X2))))))))).
% 3.25/1.72  thf(fact_157_old_Oprod_Oinducts, axiom, (! [B:$tType,A:$tType,P:(((product_prod @ A) @ B) > $o),Prod:((product_prod @ A) @ B)]: (((! [A4:A,B7:B]: ((P @ ((((product_Pair @ A) @ B) @ A4) @ B7)))) => (P @ Prod))))).
% 3.25/1.72  thf(fact_158_old_Oprod_Oexhaust, axiom, (! [A:$tType,B:$tType,Y2:((product_prod @ A) @ B)]: ((~ ((! [A4:A,B7:B]: ((Y2 != ((((product_Pair @ A) @ B) @ A4) @ B7))))))))).
% 3.25/1.72  thf(fact_159_prod__induct7, axiom, (! [G3:$tType,F4:$tType,E:$tType,D:$tType,C4:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C4) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F4) @ G3)))))) > $o),X2:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C4) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F4) @ G3))))))]: (((! [A4:A,B7:B,C:C4,D2:D,E2:E,F5:F4,G4:G3]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C4) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F4) @ G3)))))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C4) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F4) @ G3))))) @ B7) @ ((((product_Pair @ C4) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F4) @ G3)))) @ C) @ ((((product_Pair @ D) @ ((product_prod @ E) @ ((product_prod @ F4) @ G3))) @ D2) @ ((((product_Pair @ E) @ ((product_prod @ F4) @ G3)) @ E2) @ ((((product_Pair @ F4) @ G3) @ F5) @ G4))))))))) => (P @ X2))))).
% 3.25/1.72  thf(fact_160_prod__induct6, axiom, (! [F4:$tType,E:$tType,D:$tType,C4:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C4) @ ((product_prod @ D) @ ((product_prod @ E) @ F4))))) > $o),X2:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C4) @ ((product_prod @ D) @ ((product_prod @ E) @ F4)))))]: (((! [A4:A,B7:B,C:C4,D2:D,E2:E,F5:F4]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C4) @ ((product_prod @ D) @ ((product_prod @ E) @ F4))))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C4) @ ((product_prod @ D) @ ((product_prod @ E) @ F4)))) @ B7) @ ((((product_Pair @ C4) @ ((product_prod @ D) @ ((product_prod @ E) @ F4))) @ C) @ ((((product_Pair @ D) @ ((product_prod @ E) @ F4)) @ D2) @ ((((product_Pair @ E) @ F4) @ E2) @ F5)))))))) => (P @ X2))))).
% 3.25/1.72  thf(fact_161_prod__induct5, axiom, (! [E:$tType,D:$tType,C4:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C4) @ ((product_prod @ D) @ E)))) > $o),X2:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C4) @ ((product_prod @ D) @ E))))]: (((! [A4:A,B7:B,C:C4,D2:D,E2:E]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C4) @ ((product_prod @ D) @ E)))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C4) @ ((product_prod @ D) @ E))) @ B7) @ ((((product_Pair @ C4) @ ((product_prod @ D) @ E)) @ C) @ ((((product_Pair @ D) @ E) @ D2) @ E2))))))) => (P @ X2))))).
% 3.25/1.72  thf(fact_162_prod__induct4, axiom, (! [D:$tType,C4:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C4) @ D))) > $o),X2:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C4) @ D)))]: (((! [A4:A,B7:B,C:C4,D2:D]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C4) @ D))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C4) @ D)) @ B7) @ ((((product_Pair @ C4) @ D) @ C) @ D2)))))) => (P @ X2))))).
% 3.25/1.72  thf(fact_163_prod__induct3, axiom, (! [C4:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ C4)) > $o),X2:((product_prod @ A) @ ((product_prod @ B) @ C4))]: (((! [A4:A,B7:B,C:C4]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ C4)) @ A4) @ ((((product_Pair @ B) @ C4) @ B7) @ C))))) => (P @ X2))))).
% 3.25/1.72  thf(fact_164_prod__cases7, axiom, (! [A:$tType,B:$tType,C4:$tType,D:$tType,E:$tType,F4:$tType,G3:$tType,Y2:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C4) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F4) @ G3))))))]: ((~ ((! [A4:A,B7:B,C:C4,D2:D,E2:E,F5:F4,G4:G3]: ((Y2 != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C4) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F4) @ G3)))))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C4) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F4) @ G3))))) @ B7) @ ((((product_Pair @ C4) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F4) @ G3)))) @ C) @ ((((product_Pair @ D) @ ((product_prod @ E) @ ((product_prod @ F4) @ G3))) @ D2) @ ((((product_Pair @ E) @ ((product_prod @ F4) @ G3)) @ E2) @ ((((product_Pair @ F4) @ G3) @ F5) @ G4)))))))))))))).
% 3.25/1.72  thf(fact_165_prod__cases6, axiom, (! [A:$tType,B:$tType,C4:$tType,D:$tType,E:$tType,F4:$tType,Y2:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C4) @ ((product_prod @ D) @ ((product_prod @ E) @ F4)))))]: ((~ ((! [A4:A,B7:B,C:C4,D2:D,E2:E,F5:F4]: ((Y2 != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C4) @ ((product_prod @ D) @ ((product_prod @ E) @ F4))))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C4) @ ((product_prod @ D) @ ((product_prod @ E) @ F4)))) @ B7) @ ((((product_Pair @ C4) @ ((product_prod @ D) @ ((product_prod @ E) @ F4))) @ C) @ ((((product_Pair @ D) @ ((product_prod @ E) @ F4)) @ D2) @ ((((product_Pair @ E) @ F4) @ E2) @ F5))))))))))))).
% 3.25/1.72  thf(fact_166_prod__cases5, axiom, (! [A:$tType,B:$tType,C4:$tType,D:$tType,E:$tType,Y2:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C4) @ ((product_prod @ D) @ E))))]: ((~ ((! [A4:A,B7:B,C:C4,D2:D,E2:E]: ((Y2 != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C4) @ ((product_prod @ D) @ E)))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C4) @ ((product_prod @ D) @ E))) @ B7) @ ((((product_Pair @ C4) @ ((product_prod @ D) @ E)) @ C) @ ((((product_Pair @ D) @ E) @ D2) @ E2)))))))))))).
% 3.25/1.72  thf(fact_167_prod__cases4, axiom, (! [A:$tType,B:$tType,C4:$tType,D:$tType,Y2:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C4) @ D)))]: ((~ ((! [A4:A,B7:B,C:C4,D2:D]: ((Y2 != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C4) @ D))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C4) @ D)) @ B7) @ ((((product_Pair @ C4) @ D) @ C) @ D2))))))))))).
% 3.25/1.72  thf(fact_168_prod__cases3, axiom, (! [A:$tType,B:$tType,C4:$tType,Y2:((product_prod @ A) @ ((product_prod @ B) @ C4))]: ((~ ((! [A4:A,B7:B,C:C4]: ((Y2 != ((((product_Pair @ A) @ ((product_prod @ B) @ C4)) @ A4) @ ((((product_Pair @ B) @ C4) @ B7) @ C)))))))))).
% 3.25/1.72  thf(fact_169_Pair__inject, axiom, (! [A:$tType,B:$tType,A2:A,B2:B,A7:A,B6:B]: (((((((product_Pair @ A) @ B) @ A2) @ B2) = ((((product_Pair @ A) @ B) @ A7) @ B6)) => (~ (((A2 = A7) => (B2 != B6)))))))).
% 3.25/1.72  thf(fact_170_prod__cases, axiom, (! [B:$tType,A:$tType,P:(((product_prod @ A) @ B) > $o),P8:((product_prod @ A) @ B)]: (((! [A4:A,B7:B]: ((P @ ((((product_Pair @ A) @ B) @ A4) @ B7)))) => (P @ P8))))).
% 3.25/1.72  thf(fact_171_surj__pair, axiom, (! [A:$tType,B:$tType,P8:((product_prod @ A) @ B)]: ((? [X5:A,Y:B]: ((P8 = ((((product_Pair @ A) @ B) @ X5) @ Y))))))).
% 3.25/1.72  thf(fact_172_resCasesB_H, axiom, (! [X6:name,P:pi,A2:late_subject,Y6:name,P2:pi]: ((((late_transitions @ ((res @ X6) @ P)) @ (((late_BoundR @ A2) @ Y6) @ P2)) => ((! [P4:pi,A4:name,B7:name]: (((((res @ X6) @ P) = ((res @ B7) @ P4)) => (! [P3:pi]: ((((((late_BoundR @ A2) @ Y6) @ P2) = (((late_BoundR @ (late_BoundOutputS @ A4)) @ B7) @ P3)) => (((late_transitions @ P4) @ ((late_FreeR @ ((late_OutputR @ A4) @ B7)) @ P3)) => (A4 = B7)))))))) => (~ ((! [P4:pi,A4:late_subject,X5:name,P3:pi,Y:name]: (((((res @ X6) @ P) = ((res @ Y) @ P4)) => (((((late_BoundR @ A2) @ Y6) @ P2) = (((late_BoundR @ A4) @ X5) @ ((res @ Y) @ P3))) => (((late_transitions @ P4) @ (((late_BoundR @ A4) @ X5) @ P3)) => (((((fresh @ name) @ late_subject) @ Y) @ A4) => ((Y != X5) => (((((fresh @ name) @ pi) @ X5) @ P4) => (~ (((((fresh @ name) @ late_subject) @ X5) @ A4)))))))))))))))))).
% 3.25/1.72  thf(fact_173_outputCases, axiom, (! [A2:name,B2:name,P:pi,Alpha:late_freeRes,P2:pi,Prop:(late_freeRes > (pi > $o))]: ((((late_transitions @ (((output @ A2) @ B2) @ P)) @ ((late_FreeR @ Alpha) @ P2)) => (((Alpha = ((late_OutputR @ A2) @ B2)) => ((P = P2) => ((Prop @ ((late_OutputR @ A2) @ B2)) @ P))) => ((Prop @ Alpha) @ P2)))))).
% 3.25/1.72  thf(fact_174_outputCases_H, axiom, (! [A2:name,B2:name,P:pi,Rs:late_residual]: ((((late_transitions @ (((output @ A2) @ B2) @ P)) @ Rs) => (~ ((! [A4:name,B7:name,P4:pi]: ((((A2 = A4) & ((B2 = B7) & (P = P4))) => (Rs != ((late_FreeR @ ((late_OutputR @ A4) @ B7)) @ P4))))))))))).
% 3.25/1.72  thf(fact_175_outputIneqTrans, axiom, (! [A2:name,B2:name,P:pi,C2:name,D3:name,P2:pi]: ((((late_transitions @ (((output @ A2) @ B2) @ P)) @ ((late_FreeR @ ((late_OutputR @ C2) @ D3)) @ P2)) => (~ (((A2 != C2) | (B2 != D3)))))))).
% 3.25/1.72  thf(fact_176_Output, axiom, (! [A2:name,B2:name,P:pi]: (((late_transitions @ (((output @ A2) @ B2) @ P)) @ ((late_FreeR @ ((late_OutputR @ A2) @ B2)) @ P))))).
% 3.25/1.72  thf(fact_177_sumIdempRight, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),P:pi]: (((((ord_less_eq @ (set @ ((product_prod @ pi) @ pi))) @ (id @ pi)) @ Rel) => (((strong743114133lation @ ((sum @ P) @ P)) @ Rel) @ P))))).
% 3.25/1.72  thf(fact_178_sumAssocRight, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),P:pi,Q:pi,R:pi]: (((((ord_less_eq @ (set @ ((product_prod @ pi) @ pi))) @ (id @ pi)) @ Rel) => (((strong743114133lation @ ((sum @ P) @ ((sum @ Q) @ R))) @ Rel) @ ((sum @ ((sum @ P) @ Q)) @ R)))))).
% 3.25/1.72  thf(fact_179_sumIdempLeft, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),P:pi]: (((((ord_less_eq @ (set @ ((product_prod @ pi) @ pi))) @ (id @ pi)) @ Rel) => (((strong743114133lation @ P) @ Rel) @ ((sum @ P) @ P)))))).
% 3.25/1.72  thf(fact_180_sumAssocLeft, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),P:pi,Q:pi,R:pi]: (((((ord_less_eq @ (set @ ((product_prod @ pi) @ pi))) @ (id @ pi)) @ Rel) => (((strong743114133lation @ ((sum @ ((sum @ P) @ Q)) @ R)) @ Rel) @ ((sum @ P) @ ((sum @ Q) @ R))))))).
% 3.25/1.72  thf(fact_181_sumSym, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),P:pi,Q:pi]: (((((ord_less_eq @ (set @ ((product_prod @ pi) @ pi))) @ (id @ pi)) @ Rel) => (((strong743114133lation @ ((sum @ P) @ Q)) @ Rel) @ ((sum @ Q) @ P)))))).
% 3.25/1.72  thf(fact_182_inputBoundOutputTrans, axiom, (! [A2:name,X2:name,P:pi,B2:name,Y2:name,P2:pi]: ((~ (((late_transitions @ (((input @ A2) @ X2) @ P)) @ (((late_BoundR @ (late_BoundOutputS @ B2)) @ Y2) @ P2))))))).
% 3.25/1.72  thf(fact_183_resCases_H, axiom, (! [X2:name,P:pi,Rs:late_residual]: ((((late_transitions @ ((res @ X2) @ P)) @ Rs) => ((! [P4:pi,A4:name,B7:name]: (((((res @ X2) @ P) = ((res @ B7) @ P4)) => (! [P3:pi]: (((Rs = (((late_BoundR @ (late_BoundOutputS @ A4)) @ B7) @ P3)) => (((late_transitions @ P4) @ ((late_FreeR @ ((late_OutputR @ A4) @ B7)) @ P3)) => (A4 = B7)))))))) => ((! [P4:pi,A4:late_subject,X5:name,P3:pi,Y:name]: (((((res @ X2) @ P) = ((res @ Y) @ P4)) => ((Rs = (((late_BoundR @ A4) @ X5) @ ((res @ Y) @ P3))) => (((late_transitions @ P4) @ (((late_BoundR @ A4) @ X5) @ P3)) => (((((fresh @ name) @ late_subject) @ Y) @ A4) => ((Y != X5) => (((((fresh @ name) @ pi) @ X5) @ P4) => (~ (((((fresh @ name) @ late_subject) @ X5) @ A4))))))))))) => (~ ((! [P4:pi,Alpha2:late_freeRes,P3:pi,Y:name]: (((((res @ X2) @ P) = ((res @ Y) @ P4)) => ((Rs = ((late_FreeR @ Alpha2) @ ((res @ Y) @ P3))) => (((late_transitions @ P4) @ ((late_FreeR @ Alpha2) @ P3)) => (~ (((((fresh @ name) @ late_freeRes) @ Y) @ Alpha2)))))))))))))))).
% 3.25/1.72  thf(fact_184_resOutputOutputTrans, axiom, (! [X2:name,A2:name,P:pi,B2:name,Y2:name,P2:pi]: ((~ (((late_transitions @ ((res @ X2) @ (((output @ A2) @ X2) @ P))) @ ((late_FreeR @ ((late_OutputR @ B2) @ Y2)) @ P2))))))).
% 3.25/1.72  thf(fact_185_sumZeroLeft, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),P:pi]: (((((ord_less_eq @ (set @ ((product_prod @ pi) @ pi))) @ (id @ pi)) @ Rel) => (((strong743114133lation @ ((sum @ P) @ piNil)) @ Rel) @ P))))).
% 3.25/1.72  thf(fact_186_sumZeroRight, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),P:pi]: (((((ord_less_eq @ (set @ ((product_prod @ pi) @ pi))) @ (id @ pi)) @ Rel) => (((strong743114133lation @ P) @ Rel) @ ((sum @ P) @ piNil)))))).
% 3.25/1.72  thf(fact_187_resInputBoundOutputTrans, axiom, (! [X2:name,A2:name,Y2:name,P:pi,B2:name,Z:name,P2:pi]: ((~ (((late_transitions @ ((res @ X2) @ (((input @ A2) @ Y2) @ P))) @ (((late_BoundR @ (late_BoundOutputS @ B2)) @ Z) @ P2))))))).
% 3.25/1.72  thf(fact_188_sumResRight, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),X2:name,P:pi,Q:pi]: (((((ord_less_eq @ (set @ ((product_prod @ pi) @ pi))) @ (id @ pi)) @ Rel) => (((eqvt @ pi) @ Rel) => (((strong743114133lation @ ((res @ X2) @ ((sum @ P) @ Q))) @ Rel) @ ((sum @ ((res @ X2) @ P)) @ ((res @ X2) @ Q)))))))).
% 3.25/1.72  thf(fact_189_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))))).
% 3.25/1.72  thf(fact_190_Late__Semantics1_Osubject_Oinject_I2_J, axiom, (! [X22:name,Y22:name]: ((((late_BoundOutputS @ X22) = (late_BoundOutputS @ Y22)) = (X22 = Y22))))).
% 3.25/1.72  thf(fact_191_Late__Semantics1_OfreeRes_Oinject, axiom, (! [X11:name,X12:name,Y11:name,Y12:name]: (((((late_OutputR @ X11) @ X12) = ((late_OutputR @ Y11) @ Y12)) = ((X11 = Y11) & (X12 = Y12)))))).
% 3.25/1.72  thf(fact_192_Late__Semantics1_OfreeRes_Odistinct_I1_J, axiom, (! [X11:name,X12:name]: ((((late_OutputR @ X11) @ X12) != late_TauR)))).
% 3.25/1.72  thf(fact_193_freeRes_Oexhaust, axiom, (! [Y2:late_freeRes]: (((! [X112:name,X122:name]: ((Y2 != ((late_OutputR @ X112) @ X122)))) => (Y2 = late_TauR))))).
% 3.25/1.72  thf(fact_194_resOutputInputTrans, axiom, (! [X2:name,A2:name,B2:name,P:pi,C2:name,Y2:name,P2:pi]: ((~ (((late_transitions @ ((res @ X2) @ (((output @ A2) @ B2) @ P))) @ (((late_BoundR @ (late_InputS @ C2)) @ Y2) @ P2))))))).
% 3.25/1.72  thf(fact_195_freeRes_Orecs_I2_J, axiom, (! [T:$tType,P:(T > $o),F1:(name > (name > T)),F22:T]: (((! [X13:name,X23:name]: ((P @ ((F1 @ X13) @ X23)))) => ((P @ F22) => (((((late_freeRes_rec @ T) @ F1) @ F22) @ late_TauR) = F22)))))).
% 3.25/1.72  thf(fact_196_Late__Semantics1_Osubject_Oinject_I1_J, axiom, (! [X1:name,Y1:name]: ((((late_InputS @ X1) = (late_InputS @ Y1)) = (X1 = Y1))))).
% 3.25/1.72  thf(fact_197_subject_Ofresh_I1_J, axiom, (! [A2:name,X1:name]: ((((((fresh @ name) @ late_subject) @ A2) @ (late_InputS @ X1)) = ((((fresh @ name) @ name) @ A2) @ X1))))).
% 3.25/1.72  thf(fact_198_subject_Oexhaust, axiom, (! [Y2:late_subject]: (((! [X13:name]: ((Y2 != (late_InputS @ X13)))) => (~ ((! [X23:name]: ((Y2 != (late_BoundOutputS @ X23)))))))))).
% 3.25/1.72  thf(fact_199_Late__Semantics1_Osubject_Odistinct_I1_J, axiom, (! [X1:name,X22:name]: (((late_InputS @ X1) != (late_BoundOutputS @ X22))))).
% 3.25/1.72  thf(fact_200_subject_Ostrong__inducts, axiom, (! [A:$tType,P:(A > (late_subject > $o)),Z:A,Subject:late_subject]: (((! [Name4:name,Z2:A]: (((P @ Z2) @ (late_InputS @ Name4)))) => ((! [Name4:name,Z2:A]: (((P @ Z2) @ (late_BoundOutputS @ Name4)))) => ((P @ Z) @ Subject)))))).
% 3.25/1.72  thf(fact_201_subject_Ostrong__induct_H, axiom, (! [N:$tType,P:(N > (late_subject > $o)),Z:N,Subject:late_subject]: (((! [Name4:name,Z2:N]: (((P @ Z2) @ (late_InputS @ Name4)))) => ((! [Name4:name,Z2:N]: (((P @ Z2) @ (late_BoundOutputS @ Name4)))) => ((P @ Z) @ Subject)))))).
% 3.25/1.72  thf(fact_202_subject_Oinducts, axiom, (! [P:(late_subject > $o),Subject:late_subject]: (((! [Name4:name]: ((P @ (late_InputS @ Name4)))) => ((! [Name4:name]: ((P @ (late_BoundOutputS @ Name4)))) => (P @ Subject)))))).
% 3.25/1.72  thf(fact_203_Late__Semantics_Osubject_Odistinct_I1_J, axiom, (! [Name3:name,Name:name]: (((late_InputS @ Name3) != (late_BoundOutputS @ Name))))).
% 3.25/1.72  thf(fact_204_transitions_OInput, axiom, (! [X2:name,A2:name,P:pi]: (((X2 != A2) => ((late_transitions @ (((input @ A2) @ X2) @ P)) @ (((late_BoundR @ (late_InputS @ A2)) @ X2) @ P)))))).
% 3.25/1.72  thf(fact_205_Late__Semantics_OInput, axiom, (! [A2:name,X2:name,P:pi]: (((late_transitions @ (((input @ A2) @ X2) @ P)) @ (((late_BoundR @ (late_InputS @ A2)) @ X2) @ P))))).
% 3.25/1.72  thf(fact_206_freeRes_Orecs_I1_J, axiom, (! [T:$tType,P:(T > $o),F1:(name > (name > T)),F22:T,Name12:name,Name22:name]: (((! [X13:name,X23:name]: ((P @ ((F1 @ X13) @ X23)))) => ((P @ F22) => (((((late_freeRes_rec @ T) @ F1) @ F22) @ ((late_OutputR @ Name12) @ Name22)) = ((F1 @ Name12) @ Name22))))))).
% 3.25/1.72  thf(fact_207_Late__Semantics_OClose1, axiom, (! [P:pi,A2:name,X2:name,P2:pi,Q:pi,Y2:name,Q2:pi]: ((((late_transitions @ P) @ (((late_BoundR @ (late_InputS @ A2)) @ X2) @ P2)) => (((late_transitions @ Q) @ (((late_BoundR @ (late_BoundOutputS @ A2)) @ Y2) @ Q2)) => (((((fresh @ name) @ pi) @ Y2) @ P) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ late_TauR) @ ((res @ Y2) @ ((par @ (((subs @ P2) @ X2) @ Y2)) @ Q2)))))))))).
% 3.25/1.72  thf(fact_208_Late__Semantics_OClose2, axiom, (! [P:pi,A2:name,Y2:name,P2:pi,Q:pi,X2:name,Q2:pi]: ((((late_transitions @ P) @ (((late_BoundR @ (late_BoundOutputS @ A2)) @ Y2) @ P2)) => (((late_transitions @ Q) @ (((late_BoundR @ (late_InputS @ A2)) @ X2) @ Q2)) => (((((fresh @ name) @ pi) @ Y2) @ Q) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ late_TauR) @ ((res @ Y2) @ ((par @ P2) @ (((subs @ Q2) @ X2) @ Y2))))))))))).
% 3.25/1.72  thf(fact_209_subst__identity, axiom, (! [P:pi,A2:name]: (((((subs @ P) @ A2) @ A2) = P)))).
% 3.25/1.72  thf(fact_210_simps_I9_J, axiom, (! [X2:name,C2:name,D3:name,P:pi]: (((X2 != C2) => ((X2 != D3) => ((((subs @ ((res @ X2) @ P)) @ C2) @ D3) = ((res @ X2) @ (((subs @ P) @ C2) @ D3)))))))).
% 3.25/1.72  thf(fact_211_simps_I8_J, axiom, (! [P:pi,Q:pi,C2:name,D3:name]: (((((subs @ ((par @ P) @ Q)) @ C2) @ D3) = ((par @ (((subs @ P) @ C2) @ D3)) @ (((subs @ Q) @ C2) @ D3)))))).
% 3.25/1.72  thf(fact_212_substTrans, axiom, (! [B2:name,P:pi,A2:name,C2:name]: ((((((fresh @ name) @ pi) @ B2) @ P) => ((((subs @ (((subs @ P) @ A2) @ B2)) @ B2) @ C2) = (((subs @ P) @ A2) @ C2)))))).
% 3.25/1.72  thf(fact_213_simps_I7_J, axiom, (! [P:pi,Q:pi,C2:name,D3:name]: (((((subs @ ((sum @ P) @ Q)) @ C2) @ D3) = ((sum @ (((subs @ P) @ C2) @ D3)) @ (((subs @ Q) @ C2) @ D3)))))).
% 3.25/1.72  thf(fact_214_simps_I1_J, axiom, (! [C2:name,D3:name]: (((((subs @ piNil) @ C2) @ D3) = piNil)))).
% 3.25/1.72  thf(fact_215_fresh__fact2, axiom, (! [A2:name,B2:name,P:pi]: (((A2 != B2) => ((((fresh @ name) @ pi) @ A2) @ (((subs @ P) @ A2) @ B2)))))).
% 3.25/1.72  thf(fact_216_fresh__fact1, axiom, (! [A2:name,P:pi,C2:name,B2:name]: ((((((fresh @ name) @ pi) @ A2) @ P) => ((A2 != C2) => ((((fresh @ name) @ pi) @ A2) @ (((subs @ P) @ B2) @ C2))))))).
% 3.25/1.72  thf(fact_217_forget, axiom, (! [A2:name,P:pi,B2:name]: ((((((fresh @ name) @ pi) @ A2) @ P) => ((((subs @ P) @ A2) @ B2) = P))))).
% 3.25/1.72  thf(fact_218_substRes2, axiom, (! [B2:name,P:pi,A2:name]: ((((((fresh @ name) @ pi) @ B2) @ P) => (((res @ A2) @ P) = ((res @ B2) @ (((subs @ P) @ A2) @ B2))))))).
% 3.25/1.72  thf(fact_219_Agent_OsubstRes3, axiom, (! [B2:name,P:pi,A2:name]: ((((((fresh @ name) @ pi) @ B2) @ P) => ((((subs @ ((res @ A2) @ P)) @ A2) @ B2) = ((res @ B2) @ (((subs @ P) @ A2) @ B2))))))).
% 3.25/1.72  thf(fact_220_Late__Semantics_OComm2, axiom, (! [P:pi,A2:name,B2:name,P2:pi,Q:pi,X2:name,Q2:pi]: ((((late_transitions @ P) @ ((late_FreeR @ ((late_OutputR @ A2) @ B2)) @ P2)) => (((late_transitions @ Q) @ (((late_BoundR @ (late_InputS @ A2)) @ X2) @ Q2)) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ late_TauR) @ ((par @ P2) @ (((subs @ Q2) @ X2) @ B2))))))))).
% 3.25/1.72  thf(fact_221_Late__Semantics_OComm1, axiom, (! [P:pi,A2:name,X2:name,P2:pi,Q:pi,B2:name,Q2:pi]: ((((late_transitions @ P) @ (((late_BoundR @ (late_InputS @ A2)) @ X2) @ P2)) => (((late_transitions @ Q) @ ((late_FreeR @ ((late_OutputR @ A2) @ B2)) @ Q2)) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ late_TauR) @ ((par @ (((subs @ P2) @ X2) @ B2)) @ Q2)))))))).
% 3.25/1.72  thf(fact_222_transitions_OComm1, axiom, (! [P:pi,A2:name,X2:name,P2:pi,Q:pi,B2:name,Q2:pi]: ((((late_transitions @ P) @ (((late_BoundR @ (late_InputS @ A2)) @ X2) @ P2)) => (((late_transitions @ Q) @ ((late_FreeR @ ((late_OutputR @ A2) @ B2)) @ Q2)) => (((((fresh @ name) @ pi) @ X2) @ P) => (((((fresh @ name) @ pi) @ X2) @ Q) => ((X2 != A2) => ((X2 != B2) => (((((fresh @ name) @ pi) @ X2) @ Q2) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ late_TauR) @ ((par @ (((subs @ P2) @ X2) @ B2)) @ Q2))))))))))))).
% 3.25/1.72  thf(fact_223_transitions_OComm2, axiom, (! [P:pi,A2:name,B2:name,P2:pi,Q:pi,X2:name,Q2:pi]: ((((late_transitions @ P) @ ((late_FreeR @ ((late_OutputR @ A2) @ B2)) @ P2)) => (((late_transitions @ Q) @ (((late_BoundR @ (late_InputS @ A2)) @ X2) @ Q2)) => (((((fresh @ name) @ pi) @ X2) @ P) => (((((fresh @ name) @ pi) @ X2) @ Q) => ((X2 != A2) => ((X2 != B2) => (((((fresh @ name) @ pi) @ X2) @ P2) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ late_TauR) @ ((par @ P2) @ (((subs @ Q2) @ X2) @ B2)))))))))))))).
% 3.25/1.72  thf(fact_224_transitions_OClose2, axiom, (! [P:pi,A2:name,Y2:name,P2:pi,Q:pi,X2:name,Q2:pi]: ((((late_transitions @ P) @ (((late_BoundR @ (late_BoundOutputS @ A2)) @ Y2) @ P2)) => (((late_transitions @ Q) @ (((late_BoundR @ (late_InputS @ A2)) @ X2) @ Q2)) => (((((fresh @ name) @ pi) @ X2) @ P) => (((((fresh @ name) @ pi) @ X2) @ Q) => (((((fresh @ name) @ pi) @ Y2) @ P) => (((((fresh @ name) @ pi) @ Y2) @ Q) => ((X2 != A2) => (((((fresh @ name) @ pi) @ X2) @ P2) => ((Y2 != A2) => (((((fresh @ name) @ pi) @ Y2) @ Q2) => ((X2 != Y2) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ late_TauR) @ ((res @ Y2) @ ((par @ P2) @ (((subs @ Q2) @ X2) @ Y2))))))))))))))))))).
% 3.25/1.72  thf(fact_225_transitions_OClose1, axiom, (! [P:pi,A2:name,X2:name,P2:pi,Q:pi,Y2:name,Q2:pi]: ((((late_transitions @ P) @ (((late_BoundR @ (late_InputS @ A2)) @ X2) @ P2)) => (((late_transitions @ Q) @ (((late_BoundR @ (late_BoundOutputS @ A2)) @ Y2) @ Q2)) => (((((fresh @ name) @ pi) @ X2) @ P) => (((((fresh @ name) @ pi) @ X2) @ Q) => (((((fresh @ name) @ pi) @ Y2) @ P) => (((((fresh @ name) @ pi) @ Y2) @ Q) => ((X2 != A2) => (((((fresh @ name) @ pi) @ X2) @ Q2) => ((Y2 != A2) => (((((fresh @ name) @ pi) @ Y2) @ P2) => ((X2 != Y2) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ late_TauR) @ ((res @ Y2) @ ((par @ (((subs @ P2) @ X2) @ Y2)) @ Q2)))))))))))))))))).
% 3.25/1.72  thf(fact_226_subject_Orecs_I2_J, axiom, (! [T:$tType,P:(T > $o),F1:(name > T),F22:(name > T),Name3:name]: (((! [X13:name]: ((P @ (F1 @ X13)))) => ((! [X13:name]: ((P @ (F22 @ X13)))) => (((((late_subject_rec @ T) @ F1) @ F22) @ (late_BoundOutputS @ Name3)) = (F22 @ Name3))))))).
% 3.25/1.72  thf(fact_227_subject_Orecs_I1_J, axiom, (! [T:$tType,P:(T > $o),F1:(name > T),F22:(name > T),Name3:name]: (((! [X13:name]: ((P @ (F1 @ X13)))) => ((! [X13:name]: ((P @ (F22 @ X13)))) => (((((late_subject_rec @ T) @ F1) @ F22) @ (late_InputS @ Name3)) = (F1 @ Name3))))))).
% 3.25/1.72  thf(fact_228_resTauOutputTrans, axiom, (! [X2:name,P:pi,A2:name,B2:name,P2:pi]: ((~ (((late_transitions @ ((res @ X2) @ (tau @ P))) @ ((late_FreeR @ ((late_OutputR @ A2) @ B2)) @ P2))))))).
% 3.25/1.72  thf(fact_229_residual_Ofresh_I1_J, axiom, (! [A2:name,X3:late_subject,X1:name,X22:pi]: ((((((fresh @ name) @ late_residual) @ A2) @ (((late_BoundR @ X3) @ X1) @ X22)) = (((((fresh @ name) @ late_subject) @ A2) @ X3) & ((((fresh @ name) @ (name > (noption @ pi))) @ A2) @ ((((abs_fun @ name) @ pi) @ X1) @ X22))))))).
% 3.25/1.72  thf(fact_230_pi_Ofresh_I3_J, axiom, (! [A2:name,X1:pi]: ((((((fresh @ name) @ pi) @ A2) @ (tau @ X1)) = ((((fresh @ name) @ pi) @ A2) @ X1))))).
% 3.25/1.72  thf(fact_231_simps_I2_J, axiom, (! [P:pi,C2:name,D3:name]: (((((subs @ (tau @ P)) @ C2) @ D3) = (tau @ (((subs @ P) @ C2) @ D3)))))).
% 3.25/1.72  thf(fact_232_pi_Ofresh_I9_J, axiom, (! [A2:name,X1:name,X22:pi]: ((((((fresh @ name) @ pi) @ A2) @ ((res @ X1) @ X22)) = ((((fresh @ name) @ (name > (noption @ pi))) @ A2) @ ((((abs_fun @ name) @ pi) @ X1) @ X22)))))).
% 3.25/1.72  thf(fact_233_pi_Ofresh_I4_J, axiom, (! [A2:name,X3:name,X1:name,X22:pi]: ((((((fresh @ name) @ pi) @ A2) @ (((input @ X3) @ X1) @ X22)) = (((((fresh @ name) @ name) @ A2) @ X3) & ((((fresh @ name) @ (name > (noption @ pi))) @ A2) @ ((((abs_fun @ name) @ pi) @ X1) @ X22))))))).
% 3.25/1.72  thf(fact_234_tauBoundTrans, axiom, (! [P:pi,A2:late_subject,X2:name,P2:pi]: ((~ (((late_transitions @ (tau @ P)) @ (((late_BoundR @ A2) @ X2) @ P2))))))).
% 3.25/1.72  thf(fact_235_nilSim_I1_J, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),P:pi]: ((~ ((((strong743114133lation @ piNil) @ Rel) @ (tau @ P))))))).
% 3.25/1.72  thf(fact_236_pi_Oinject_I8_J, axiom, (! [X1:name,X22:pi,Y1:name,Y22:pi]: (((((res @ X1) @ X22) = ((res @ Y1) @ Y22)) = (((((abs_fun @ name) @ pi) @ X1) @ X22) = ((((abs_fun @ name) @ pi) @ Y1) @ Y22)))))).
% 3.25/1.72  thf(fact_237_residual_Oinject_I1_J, axiom, (! [X3:late_subject,X1:name,X22:pi,Y3:late_subject,Y1:name,Y22:pi]: ((((((late_BoundR @ X3) @ X1) @ X22) = (((late_BoundR @ Y3) @ Y1) @ Y22)) = ((X3 = Y3) & (((((abs_fun @ name) @ pi) @ X1) @ X22) = ((((abs_fun @ name) @ pi) @ Y1) @ Y22))))))).
% 3.25/1.72  thf(fact_238_pi_Oinject_I2_J, axiom, (! [X1:pi,Y1:pi]: ((((tau @ X1) = (tau @ Y1)) = (X1 = Y1))))).
% 3.25/1.72  thf(fact_239_abs__fun__eq1, axiom, (! [X:$tType,A:$tType,A2:X,X2:A,Y2:A]: (((((((abs_fun @ X) @ A) @ A2) @ X2) = ((((abs_fun @ X) @ A) @ A2) @ Y2)) = (X2 = Y2))))).
% 3.25/1.72  thf(fact_240_pi_Odistinct_I19_J, axiom, (! [Name12:name,Name22:name,Pi3:pi,Pi:pi]: (((((output @ Name12) @ Name22) @ Pi3) != (tau @ Pi))))).
% 3.25/1.72  thf(fact_241_pi_Odistinct_I3_J, axiom, (! [Pi:pi]: ((piNil != (tau @ Pi))))).
% 3.25/1.72  thf(fact_242_pi_Odistinct_I35_J, axiom, (! [Pi3:pi,Name1:name,Name2:name,Pi:pi]: (((tau @ Pi3) != (((input @ Name1) @ Name2) @ Pi))))).
% 3.25/1.72  thf(fact_243_pi_Odistinct_I41_J, axiom, (! [Pi3:pi,Pi12:pi,Pi22:pi]: (((tau @ Pi3) != ((sum @ Pi12) @ Pi22))))).
% 3.25/1.72  thf(fact_244_pi_Odistinct_I43_J, axiom, (! [Pi3:pi,Pi12:pi,Pi22:pi]: (((tau @ Pi3) != ((par @ Pi12) @ Pi22))))).
% 3.25/1.72  thf(fact_245_pi_Odistinct_I45_J, axiom, (! [Pi3:pi,Name:name,Pi:pi]: (((tau @ Pi3) != ((res @ Name) @ Pi))))).
% 3.25/1.72  thf(fact_246_pi_Oinject_I3_J, axiom, (! [X3:name,X1:name,X22:pi,Y3:name,Y1:name,Y22:pi]: ((((((input @ X3) @ X1) @ X22) = (((input @ Y3) @ Y1) @ Y22)) = ((X3 = Y3) & (((((abs_fun @ name) @ pi) @ X1) @ X22) = ((((abs_fun @ name) @ pi) @ Y1) @ Y22))))))).
% 3.25/1.72  thf(fact_247_name__fresh__abs, axiom, (! [A:$tType]: (((fs_name @ A) => (! [B2:name,A2:name,X2:A]: ((((((fresh @ name) @ (name > (noption @ A))) @ B2) @ ((((abs_fun @ name) @ A) @ A2) @ X2)) = ((B2 = A2) | ((((fresh @ name) @ A) @ B2) @ X2))))))))).
% 3.25/1.72  thf(fact_248_abs__fresh_I1_J, axiom, (! [X7:$tType]: (((fs_name @ X7) => (! [B2:name,A2:name,X2:X7]: ((((((fresh @ name) @ (name > (noption @ X7))) @ B2) @ ((((abs_fun @ name) @ X7) @ A2) @ X2)) = ((B2 = A2) | ((((fresh @ name) @ X7) @ B2) @ X2))))))))).
% 3.25/1.72  thf(fact_249_resTauBoundTrans, axiom, (! [X2:name,P:pi,A2:late_subject,Y2:name,P2:pi]: ((~ (((late_transitions @ ((res @ X2) @ (tau @ P))) @ (((late_BoundR @ A2) @ Y2) @ P2))))))).
% 3.25/1.72  thf(fact_250_tauOutputTrans, axiom, (! [P:pi,A2:name,B2:name,P2:pi]: ((~ (((late_transitions @ (tau @ P)) @ ((late_FreeR @ ((late_OutputR @ A2) @ B2)) @ P2))))))).
% 3.25/1.72  thf(fact_251_Tau, axiom, (! [P:pi]: (((late_transitions @ (tau @ P)) @ ((late_FreeR @ late_TauR) @ P))))).
% 3.25/1.72  thf(fact_252_tauCases_H, axiom, (! [P:pi,Rs:late_residual]: ((((late_transitions @ (tau @ P)) @ Rs) => (~ ((! [P4:pi]: ((((tau @ P) = (tau @ P4)) => (Rs != ((late_FreeR @ late_TauR) @ P4))))))))))).
% 3.25/1.72  thf(fact_253_tauCases, axiom, (! [P:pi,Alpha:late_freeRes,P2:pi,Prop:(late_freeRes > (pi > $o))]: ((((late_transitions @ (tau @ P)) @ ((late_FreeR @ Alpha) @ P2)) => (((Alpha = late_TauR) => ((P = P2) => ((Prop @ late_TauR) @ P))) => ((Prop @ Alpha) @ P2)))))).
% 3.25/1.72  thf(fact_254_inputCases_H, axiom, (! [A2:name,B2:name,P:pi,Rs:late_residual]: ((((late_transitions @ (((input @ A2) @ B2) @ P)) @ Rs) => (~ ((! [X5:name,A4:name,P4:pi]: ((((A2 = A4) & (((((abs_fun @ name) @ pi) @ B2) @ P) = ((((abs_fun @ name) @ pi) @ X5) @ P4))) => ((Rs = (((late_BoundR @ (late_InputS @ A4)) @ X5) @ P4)) => (X5 = A4))))))))))).
% 3.25/1.72  thf(fact_255_simps_I3_J, axiom, (! [A2:name,B2:name,P:pi,C2:name,D3:name]: (((((subs @ (((output @ A2) @ B2) @ P)) @ C2) @ D3) = (((output @ (((subst_name @ A2) @ C2) @ D3)) @ (((subst_name @ B2) @ C2) @ D3)) @ (((subs @ P) @ C2) @ D3)))))).
% 3.25/1.72  thf(tcon_fun___Orderings_Opreorder, axiom, (! [A8:$tType,A9:$tType]: (((preorder @ A9) => (preorder @ (A8 > A9)))))).
% 3.25/1.72  thf(tcon_fun___Orderings_Oorder, axiom, (! [A8:$tType,A9:$tType]: (((order @ A9) => (order @ (A8 > A9)))))).
% 3.25/1.72  thf(tcon_fun___Orderings_Oord, axiom, (! [A8:$tType,A9:$tType]: (((ord @ A9) => (ord @ (A8 > A9)))))).
% 3.25/1.72  thf(tcon_Set_Oset___Orderings_Opreorder_1, axiom, (! [A8:$tType]: ((preorder @ (set @ A8))))).
% 3.25/1.72  thf(tcon_Set_Oset___Orderings_Oorder_2, axiom, (! [A8:$tType]: ((order @ (set @ A8))))).
% 3.25/1.72  thf(tcon_Set_Oset___Orderings_Oord_3, axiom, (! [A8:$tType]: ((ord @ (set @ A8))))).
% 3.25/1.72  thf(tcon_Agent_Opi___Agent_Ofs__name, axiom, (fs_name @ pi)).
% 3.25/1.72  thf(tcon_HOL_Obool___Orderings_Opreorder_4, axiom, (preorder @ $o)).
% 3.25/1.72  thf(tcon_HOL_Obool___Orderings_Olinorder, axiom, (linorder @ $o)).
% 3.25/1.72  thf(tcon_HOL_Obool___Orderings_Oorder_5, axiom, (order @ $o)).
% 3.25/1.72  thf(tcon_HOL_Obool___Orderings_Oord_6, axiom, (ord @ $o)).
% 3.25/1.72  thf(tcon_HOL_Obool___Agent_Ofs__name_7, axiom, (fs_name @ $o)).
% 3.25/1.72  thf(tcon_Agent_Oname___Agent_Ofs__name_8, axiom, (fs_name @ name)).
% 3.25/1.72  thf(tcon_Product__Type_Oprod___Agent_Ofs__name_9, axiom, (! [A8:$tType,A9:$tType]: ((((fs_name @ A8) & (fs_name @ A9)) => (fs_name @ ((product_prod @ A8) @ A9)))))).
% 3.25/1.72  thf(tcon_Late__Semantics_OfreeRes___Agent_Ofs__name_10, axiom, (fs_name @ late_freeRes)).
% 3.25/1.72  thf(tcon_Late__Semantics_Osubject___Agent_Ofs__name_11, axiom, (fs_name @ late_subject)).
% 3.25/1.72  thf(tcon_Late__Semantics_Oresidual___Agent_Ofs__name_12, axiom, (fs_name @ late_residual)).
% 3.25/1.72  thf(conj_0, conjecture, ((late_transitions @ ((res @ x) @ ((par @ p) @ q))) @ ((late_FreeR @ alpha) @ ((res @ x) @ ((par @ p2) @ q))))).
% 3.25/1.72  % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.gpMSqBPIcZ/DTF2DTF18468.p
% 3.25/1.72  ------------------------
% 3.25/1.77  ---- Cleaned THF ---
% 3.25/1.78  thf(ty_t_Late__Semantics_Oresidual,type,
% 3.25/1.78      late_residual: $tType ).
% 3.25/1.78  
% 3.25/1.78  thf(ty_t_Late__Semantics_Osubject,type,
% 3.25/1.78      late_subject: $tType ).
% 3.25/1.78  
% 3.25/1.78  thf(ty_t_Late__Semantics_OfreeRes,type,
% 3.25/1.78      late_freeRes: $tType ).
% 3.25/1.78  
% 3.25/1.78  thf(ty_t_Product__Type_Oprod,type,
% 3.25/1.78      product_prod: $tType > $tType > $tType ).
% 3.25/1.78  
% 3.25/1.78  thf(ty_t_Nominal_Onoption,type,
% 3.25/1.78      noption: $tType > $tType ).
% 3.25/1.78  
% 3.25/1.78  thf(ty_t_Agent_Oname,type,
% 3.25/1.78      name: $tType ).
% 3.25/1.78  
% 3.25/1.78  thf(ty_t_Agent_Opi,type,
% 3.25/1.78      pi: $tType ).
% 3.25/1.78  
% 3.25/1.78  thf(ty_t_Set_Oset,type,
% 3.25/1.78      set: $tType > $tType ).
% 3.25/1.78  
% 3.25/1.78  thf(sy_cl_HOL_Otype,type,
% 3.25/1.78      type: 
% 3.25/1.78        !>[A: $tType] : $o ).
% 3.25/1.78  
% 3.25/1.78  thf(sy_cl_Agent_Ofs__name,type,
% 3.25/1.78      fs_name: 
% 3.25/1.78        !>[A: $tType] : $o ).
% 3.25/1.78  
% 3.25/1.78  thf(sy_cl_Orderings_Oord,type,
% 3.25/1.78      ord: 
% 3.25/1.78        !>[A: $tType] : $o ).
% 3.25/1.78  
% 3.25/1.78  thf(sy_cl_Orderings_Oorder,type,
% 3.25/1.78      order: 
% 3.25/1.78        !>[A: $tType] : $o ).
% 3.25/1.78  
% 3.25/1.78  thf(sy_cl_Orderings_Olinorder,type,
% 3.25/1.78      linorder: 
% 3.25/1.78        !>[A: $tType] : $o ).
% 3.25/1.78  
% 3.25/1.78  thf(sy_cl_Orderings_Opreorder,type,
% 3.25/1.78      preorder: 
% 3.25/1.78        !>[A: $tType] : $o ).
% 3.25/1.78  
% 3.25/1.78  thf(sy_c_Agent_Opi_OInput,type,
% 3.25/1.78      input: name > name > pi > pi ).
% 3.25/1.78  
% 3.25/1.78  thf(sy_c_Agent_Opi_OOutput,type,
% 3.25/1.78      output: name > name > pi > pi ).
% 3.25/1.78  
% 3.25/1.78  thf(sy_c_Agent_Opi_OPar,type,
% 3.25/1.78      par: pi > pi > pi ).
% 3.25/1.78  
% 3.25/1.78  thf(sy_c_Agent_Opi_OPiNil,type,
% 3.25/1.78      piNil: pi ).
% 3.25/1.78  
% 3.25/1.78  thf(sy_c_Agent_Opi_ORes,type,
% 3.25/1.78      res: name > pi > pi ).
% 3.25/1.78  
% 3.25/1.78  thf(sy_c_Agent_Opi_OSum,type,
% 3.25/1.78      sum: pi > pi > pi ).
% 3.25/1.78  
% 3.25/1.78  thf(sy_c_Agent_Opi_OTau,type,
% 3.25/1.78      tau: pi > pi ).
% 3.25/1.78  
% 3.25/1.78  thf(sy_c_Agent_Osubs,type,
% 3.25/1.78      subs: pi > name > name > pi ).
% 3.25/1.78  
% 3.25/1.78  thf(sy_c_Agent_Osubst__name,type,
% 3.25/1.78      subst_name: name > name > name > name ).
% 3.25/1.78  
% 3.25/1.78  thf(sy_c_Late__Semantics_OfreeRes_OOutputR,type,
% 3.25/1.78      late_OutputR: name > name > late_freeRes ).
% 3.25/1.78  
% 3.25/1.78  thf(sy_c_Late__Semantics_OfreeRes_OTauR,type,
% 3.25/1.78      late_TauR: late_freeRes ).
% 3.25/1.78  
% 3.25/1.78  thf(sy_c_Late__Semantics_OfreeRes_OfreeRes__rec,type,
% 3.25/1.78      late_freeRes_rec: 
% 3.25/1.78        !>[T: $tType] : ( ( name > name > T ) > T > late_freeRes > T ) ).
% 3.25/1.78  
% 3.25/1.78  thf(sy_c_Late__Semantics_Oresidual_OBoundR,type,
% 3.25/1.78      late_BoundR: late_subject > name > pi > late_residual ).
% 3.25/1.78  
% 3.25/1.78  thf(sy_c_Late__Semantics_Oresidual_OFreeR,type,
% 3.25/1.78      late_FreeR: late_freeRes > pi > late_residual ).
% 3.25/1.78  
% 3.25/1.78  thf(sy_c_Late__Semantics_Osubject_OBoundOutputS,type,
% 3.25/1.78      late_BoundOutputS: name > late_subject ).
% 3.25/1.78  
% 3.25/1.78  thf(sy_c_Late__Semantics_Osubject_OInputS,type,
% 3.25/1.78      late_InputS: name > late_subject ).
% 3.25/1.78  
% 3.25/1.78  thf(sy_c_Late__Semantics_Osubject_Osubject__rec,type,
% 3.25/1.78      late_subject_rec: 
% 3.25/1.78        !>[T: $tType] : ( ( name > T ) > ( name > T ) > late_subject > T ) ).
% 3.25/1.78  
% 3.25/1.78  thf(sy_c_Late__Semantics_Otransitions,type,
% 3.25/1.78      late_transitions: pi > late_residual > $o ).
% 3.25/1.78  
% 3.25/1.78  thf(sy_c_Nominal_Oabs__fun,type,
% 3.25/1.78      abs_fun: 
% 3.25/1.78        !>[X: $tType,A: $tType] : ( X > A > X > ( noption @ A ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(sy_c_Nominal_Ofresh,type,
% 3.25/1.78      fresh: 
% 3.25/1.78        !>[X: $tType,A: $tType] : ( X > A > $o ) ).
% 3.25/1.78  
% 3.25/1.78  thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 3.25/1.78      ord_less_eq: 
% 3.25/1.78        !>[A: $tType] : ( A > A > $o ) ).
% 3.25/1.78  
% 3.25/1.78  thf(sy_c_Product__Type_OPair,type,
% 3.25/1.78      product_Pair: 
% 3.25/1.78        !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(sy_c_Product__Type_Oold_Oprod_Orec__prod,type,
% 3.25/1.78      product_rec_prod: 
% 3.25/1.78        !>[A: $tType,B: $tType,T: $tType] : ( ( A > B > T ) > ( product_prod @ A @ B ) > T ) ).
% 3.25/1.78  
% 3.25/1.78  thf(sy_c_Rel_Oeqvt,type,
% 3.25/1.78      eqvt: 
% 3.25/1.78        !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > $o ) ).
% 3.25/1.78  
% 3.25/1.78  thf(sy_c_Relation_OId,type,
% 3.25/1.78      id: 
% 3.25/1.78        !>[A: $tType] : ( set @ ( product_prod @ A @ A ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(sy_c_Set_OCollect,type,
% 3.25/1.78      collect: 
% 3.25/1.78        !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(sy_c_Strong__Late__Sim_Oderivative,type,
% 3.25/1.78      strong2129052853vative: pi > pi > late_subject > name > ( set @ ( product_prod @ pi @ pi ) ) > $o ).
% 3.25/1.78  
% 3.25/1.78  thf(sy_c_Strong__Late__Sim_Osimulation,type,
% 3.25/1.78      strong743114133lation: pi > ( set @ ( product_prod @ pi @ pi ) ) > pi > $o ).
% 3.25/1.78  
% 3.25/1.78  thf(sy_c_member,type,
% 3.25/1.78      member: 
% 3.25/1.78        !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 3.25/1.78  
% 3.25/1.78  thf(sy_v_P,type,
% 3.25/1.78      p: pi ).
% 3.25/1.78  
% 3.25/1.78  thf(sy_v_P_H____,type,
% 3.25/1.78      p2: pi ).
% 3.25/1.78  
% 3.25/1.78  thf(sy_v_PxQ____,type,
% 3.25/1.78      pxQ: pi ).
% 3.25/1.78  
% 3.25/1.78  thf(sy_v_Q,type,
% 3.25/1.78      q: pi ).
% 3.25/1.78  
% 3.25/1.78  thf(sy_v_Rel,type,
% 3.25/1.78      rel: set @ ( product_prod @ pi @ pi ) ).
% 3.25/1.78  
% 3.25/1.78  thf(sy_v__092_060alpha_062____,type,
% 3.25/1.78      alpha: late_freeRes ).
% 3.25/1.78  
% 3.25/1.78  thf(sy_v_x,type,
% 3.25/1.78      x: name ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_0__092_060open_062x_A_092_060sharp_062_A_092_060alpha_062_092_060close_062,axiom,
% 3.25/1.78      fresh @ name @ late_freeRes @ x @ alpha ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_1__092_060open_062P_A_092_060parallel_062_AQ_A_092_060longmapsto_062_A_092_060alpha_062_A_092_060prec_062_AP_H_A_092_060parallel_062_AQ_092_060close_062,axiom,
% 3.25/1.78      late_transitions @ ( par @ p @ q ) @ ( late_FreeR @ alpha @ ( par @ p2 @ q ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_2_cPar1_Ohyps,axiom,
% 3.25/1.78      late_transitions @ p @ ( late_FreeR @ alpha @ p2 ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_3_Free_Ohyps,axiom,
% 3.25/1.78      late_transitions @ ( par @ p @ ( res @ x @ q ) ) @ ( late_FreeR @ alpha @ pxQ ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_4_assms_I1_J,axiom,
% 3.25/1.78      fresh @ name @ pi @ x @ p ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_5__092_060open_062x_A_092_060sharp_062_AP_H_092_060close_062,axiom,
% 3.25/1.78      fresh @ name @ pi @ x @ p2 ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_6_Par1F,axiom,
% 3.25/1.78      ! [P: pi,Alpha: late_freeRes,P2: pi,Q: pi] :
% 3.25/1.78        ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 3.25/1.78       => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha @ ( par @ P2 @ Q ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_7_Par2F,axiom,
% 3.25/1.78      ! [Q: pi,Alpha: late_freeRes,Q2: pi,P: pi] :
% 3.25/1.78        ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 3.25/1.78       => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha @ ( par @ P @ Q2 ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_8_pi_Odistinct_I85_J,axiom,
% 3.25/1.78      ! [Pi1: pi,Pi2: pi,Name: name,Pi: pi] :
% 3.25/1.78        ( ( par @ Pi1 @ Pi2 )
% 3.25/1.78       != ( res @ Name @ Pi ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_9_resCasesF,axiom,
% 3.25/1.78      ! [X2: name,P: pi,Alpha: late_freeRes,XP: pi,F: pi > $o] :
% 3.25/1.78        ( ( late_transitions @ ( res @ X2 @ P ) @ ( late_FreeR @ Alpha @ XP ) )
% 3.25/1.78       => ( ! [P3: pi] :
% 3.25/1.78              ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P3 ) )
% 3.25/1.78             => ( ( fresh @ name @ late_freeRes @ X2 @ Alpha )
% 3.25/1.78               => ( F @ ( res @ X2 @ P3 ) ) ) )
% 3.25/1.78         => ( F @ XP ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_10_resCasesF_H,axiom,
% 3.25/1.78      ! [X2: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 3.25/1.78        ( ( late_transitions @ ( res @ X2 @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 3.25/1.78       => ~ ! [P4: pi,Alpha2: late_freeRes,P3: pi,Y: name] :
% 3.25/1.78              ( ( ( res @ X2 @ P )
% 3.25/1.78                = ( res @ Y @ P4 ) )
% 3.25/1.78             => ( ( ( late_FreeR @ Alpha @ P2 )
% 3.25/1.78                  = ( late_FreeR @ Alpha2 @ ( res @ Y @ P3 ) ) )
% 3.25/1.78               => ( ( late_transitions @ P4 @ ( late_FreeR @ Alpha2 @ P3 ) )
% 3.25/1.78                 => ~ ( fresh @ name @ late_freeRes @ Y @ Alpha2 ) ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_11_ResF,axiom,
% 3.25/1.78      ! [P: pi,Alpha: late_freeRes,P2: pi,Y2: name] :
% 3.25/1.78        ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 3.25/1.78       => ( ( fresh @ name @ late_freeRes @ Y2 @ Alpha )
% 3.25/1.78         => ( late_transitions @ ( res @ Y2 @ P ) @ ( late_FreeR @ Alpha @ ( res @ Y2 @ P2 ) ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_12_residual_Oinject_I2_J,axiom,
% 3.25/1.78      ! [X22: late_freeRes,X1: pi,Y22: late_freeRes,Y1: pi] :
% 3.25/1.78        ( ( ( late_FreeR @ X22 @ X1 )
% 3.25/1.78          = ( late_FreeR @ Y22 @ Y1 ) )
% 3.25/1.78        = ( ( X22 = Y22 )
% 3.25/1.78          & ( X1 = Y1 ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_13_pi_Oinject_I7_J,axiom,
% 3.25/1.78      ! [X22: pi,X1: pi,Y22: pi,Y1: pi] :
% 3.25/1.78        ( ( ( par @ X22 @ X1 )
% 3.25/1.78          = ( par @ Y22 @ Y1 ) )
% 3.25/1.78        = ( ( X22 = Y22 )
% 3.25/1.78          & ( X1 = Y1 ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_14_resInputFreeTrans,axiom,
% 3.25/1.78      ! [X2: name,A2: name,Y2: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 3.25/1.78        ~ ( late_transitions @ ( res @ X2 @ ( input @ A2 @ Y2 @ P ) ) @ ( late_FreeR @ Alpha @ P2 ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_15_EqvtRel,axiom,
% 3.25/1.78      eqvt @ pi @ rel ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_16_resZeroTrans,axiom,
% 3.25/1.78      ! [X2: name,Rs: late_residual] :
% 3.25/1.78        ~ ( late_transitions @ ( res @ X2 @ piNil ) @ Rs ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_17_pi_Ofresh_I8_J,axiom,
% 3.25/1.78      ! [A2: name,X22: pi,X1: pi] :
% 3.25/1.78        ( ( fresh @ name @ pi @ A2 @ ( par @ X22 @ X1 ) )
% 3.25/1.78        = ( ( fresh @ name @ pi @ A2 @ X22 )
% 3.25/1.78          & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_18_pi_Ofresh_I1_J,axiom,
% 3.25/1.78      ! [A2: name] : ( fresh @ name @ pi @ A2 @ piNil ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_19_pi_Odistinct_I5_J,axiom,
% 3.25/1.78      ! [Name1: name,Name2: name,Pi: pi] :
% 3.25/1.78        ( piNil
% 3.25/1.78       != ( input @ Name1 @ Name2 @ Pi ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_20_name__exists__fresh,axiom,
% 3.25/1.78      ! [A: $tType] :
% 3.25/1.78        ( ( fs_name @ A )
% 3.25/1.78       => ! [X2: A] :
% 3.25/1.78            ~ ! [C: name] :
% 3.25/1.78                ~ ( fresh @ name @ A @ C @ X2 ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_21_freshRes,axiom,
% 3.25/1.78      ! [A2: name,P: pi] : ( fresh @ name @ pi @ A2 @ ( res @ A2 @ P ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_22_pi_Odistinct_I57_J,axiom,
% 3.25/1.78      ! [Name12: name,Name22: name,Pi3: pi,Name: name,Pi: pi] :
% 3.25/1.78        ( ( input @ Name12 @ Name22 @ Pi3 )
% 3.25/1.78       != ( res @ Name @ Pi ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_23_pi_Odistinct_I55_J,axiom,
% 3.25/1.78      ! [Name12: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 3.25/1.78        ( ( input @ Name12 @ Name22 @ Pi3 )
% 3.25/1.78       != ( par @ Pi12 @ Pi22 ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_24_zeroTrans,axiom,
% 3.25/1.78      ! [Rs: late_residual] :
% 3.25/1.78        ~ ( late_transitions @ piNil @ Rs ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_25_nilCases_H,axiom,
% 3.25/1.78      ! [Rs: late_residual] :
% 3.25/1.78        ~ ( late_transitions @ piNil @ Rs ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_26_pi_Odistinct_I15_J,axiom,
% 3.25/1.78      ! [Name: name,Pi: pi] :
% 3.25/1.78        ( piNil
% 3.25/1.78       != ( res @ Name @ Pi ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_27_pi_Odistinct_I13_J,axiom,
% 3.25/1.78      ! [Pi12: pi,Pi22: pi] :
% 3.25/1.78        ( piNil
% 3.25/1.78       != ( par @ Pi12 @ Pi22 ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_28_freshFreeDerivative_I1_J,axiom,
% 3.25/1.78      ! [P: pi,Alpha: late_freeRes,P2: pi,Y2: name] :
% 3.25/1.78        ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 3.25/1.78       => ( ( fresh @ name @ pi @ Y2 @ P )
% 3.25/1.78         => ( fresh @ name @ late_freeRes @ Y2 @ Alpha ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_29_freshFreeDerivative_I2_J,axiom,
% 3.25/1.78      ! [P: pi,Alpha: late_freeRes,P2: pi,Y2: name] :
% 3.25/1.78        ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 3.25/1.78       => ( ( fresh @ name @ pi @ Y2 @ P )
% 3.25/1.78         => ( fresh @ name @ pi @ Y2 @ P2 ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_30_resTrans_I2_J,axiom,
% 3.25/1.78      ! [X2: name,Y2: name,P: pi,Rs: late_residual] :
% 3.25/1.78        ~ ( late_transitions @ ( res @ X2 @ ( input @ X2 @ Y2 @ P ) ) @ Rs ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_31_inputFreeTrans,axiom,
% 3.25/1.78      ! [A2: name,X2: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 3.25/1.78        ~ ( late_transitions @ ( input @ A2 @ X2 @ P ) @ ( late_FreeR @ Alpha @ P2 ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_32_ScopeExt,axiom,
% 3.25/1.78      ! [Y2: name,R: pi,Z: name,S: pi] :
% 3.25/1.78        ( ( fresh @ name @ pi @ Y2 @ R )
% 3.25/1.78       => ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( res @ Y2 @ ( res @ Z @ ( par @ R @ S ) ) ) @ ( res @ Z @ ( par @ R @ ( res @ Y2 @ S ) ) ) ) @ rel ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_33_Res,axiom,
% 3.25/1.78      ! [Y2: name,R: pi,S: pi] :
% 3.25/1.78        ( ( fresh @ name @ pi @ Y2 @ R )
% 3.25/1.78       => ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( res @ Y2 @ ( par @ R @ S ) ) @ ( par @ R @ ( res @ Y2 @ S ) ) ) @ rel ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_34_outputFreshTrans,axiom,
% 3.25/1.78      ! [A2: name,B2: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 3.25/1.78        ( ( late_transitions @ ( output @ A2 @ B2 @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 3.25/1.78       => ~ ( ( fresh @ name @ late_freeRes @ A2 @ Alpha )
% 3.25/1.78            | ( fresh @ name @ late_freeRes @ B2 @ Alpha ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_35_residual_Ofresh_I2_J,axiom,
% 3.25/1.78      ! [A2: name,X22: late_freeRes,X1: pi] :
% 3.25/1.78        ( ( fresh @ name @ late_residual @ A2 @ ( late_FreeR @ X22 @ X1 ) )
% 3.25/1.78        = ( ( fresh @ name @ late_freeRes @ A2 @ X22 )
% 3.25/1.78          & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_36_Id,axiom,
% 3.25/1.78      ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ rel ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_37_parCasesB,axiom,
% 3.25/1.78      ! [P: pi,Q: pi,A2: late_subject,X2: name,PQ: pi,Prop: pi > $o] :
% 3.25/1.78        ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X2 @ PQ ) )
% 3.25/1.78       => ( ( fresh @ name @ pi @ X2 @ P )
% 3.25/1.78         => ( ( fresh @ name @ pi @ X2 @ Q )
% 3.25/1.78           => ( ! [P3: pi] :
% 3.25/1.78                  ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P3 ) )
% 3.25/1.78                 => ( Prop @ ( par @ P3 @ Q ) ) )
% 3.25/1.78             => ( ! [Q3: pi] :
% 3.25/1.78                    ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X2 @ Q3 ) )
% 3.25/1.78                   => ( Prop @ ( par @ P @ Q3 ) ) )
% 3.25/1.78               => ( Prop @ PQ ) ) ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_38_Late__Semantics_OPar2B,axiom,
% 3.25/1.78      ! [Q: pi,A2: late_subject,X2: name,Q2: pi,P: pi] :
% 3.25/1.78        ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X2 @ Q2 ) )
% 3.25/1.78       => ( ( fresh @ name @ pi @ X2 @ P )
% 3.25/1.78         => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X2 @ ( par @ P @ Q2 ) ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_39_Late__Semantics_OPar1B,axiom,
% 3.25/1.78      ! [P: pi,A2: late_subject,X2: name,P2: pi,Q: pi] :
% 3.25/1.78        ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P2 ) )
% 3.25/1.78       => ( ( fresh @ name @ pi @ X2 @ Q )
% 3.25/1.78         => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X2 @ ( par @ P2 @ Q ) ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_40_nilSim_I2_J,axiom,
% 3.25/1.78      ! [Rel: set @ ( product_prod @ pi @ pi ),A2: name,X2: name,P: pi] :
% 3.25/1.78        ~ ( strong743114133lation @ piNil @ Rel @ ( input @ A2 @ X2 @ P ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_41_freeRes_Ofresh_I2_J,axiom,
% 3.25/1.78      ! [A2: name] : ( fresh @ name @ late_freeRes @ A2 @ late_TauR ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_42_pi_Ofresh_I2_J,axiom,
% 3.25/1.78      ! [A2: name,X3: name,X22: name,X1: pi] :
% 3.25/1.78        ( ( fresh @ name @ pi @ A2 @ ( output @ X3 @ X22 @ X1 ) )
% 3.25/1.78        = ( ( fresh @ name @ name @ A2 @ X3 )
% 3.25/1.78          & ( fresh @ name @ name @ A2 @ X22 )
% 3.25/1.78          & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_43_pi_Oinject_I1_J,axiom,
% 3.25/1.78      ! [X3: name,X22: name,X1: pi,Y3: name,Y22: name,Y1: pi] :
% 3.25/1.78        ( ( ( output @ X3 @ X22 @ X1 )
% 3.25/1.78          = ( output @ Y3 @ Y22 @ Y1 ) )
% 3.25/1.78        = ( ( X3 = Y3 )
% 3.25/1.78          & ( X22 = Y22 )
% 3.25/1.78          & ( X1 = Y1 ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_44_outputBoundTrans,axiom,
% 3.25/1.78      ! [A2: name,B2: name,P: pi,C2: late_subject,X2: name,P2: pi] :
% 3.25/1.78        ~ ( late_transitions @ ( output @ A2 @ B2 @ P ) @ ( late_BoundR @ C2 @ X2 @ P2 ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_45_mem__Collect__eq,axiom,
% 3.25/1.78      ! [A: $tType,A2: A,P: A > $o] :
% 3.25/1.78        ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 3.25/1.78        = ( P @ A2 ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_46_Collect__mem__eq,axiom,
% 3.25/1.78      ! [A: $tType,A3: set @ A] :
% 3.25/1.78        ( ( collect @ A
% 3.25/1.78          @ ^ [X4: A] : ( member @ A @ X4 @ A3 ) )
% 3.25/1.78        = A3 ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_47_Collect__cong,axiom,
% 3.25/1.78      ! [A: $tType,P: A > $o,Q: A > $o] :
% 3.25/1.78        ( ! [X5: A] :
% 3.25/1.78            ( ( P @ X5 )
% 3.25/1.78            = ( Q @ X5 ) )
% 3.25/1.78       => ( ( collect @ A @ P )
% 3.25/1.78          = ( collect @ A @ Q ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_48_nilSim_I3_J,axiom,
% 3.25/1.78      ! [Rel: set @ ( product_prod @ pi @ pi ),A2: name,B2: name,P: pi] :
% 3.25/1.78        ~ ( strong743114133lation @ piNil @ Rel @ ( output @ A2 @ B2 @ P ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_49_Late__Semantics_OResB,axiom,
% 3.25/1.78      ! [P: pi,A2: late_subject,X2: name,P2: pi,Y2: name] :
% 3.25/1.78        ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P2 ) )
% 3.25/1.78       => ( ( fresh @ name @ late_subject @ Y2 @ A2 )
% 3.25/1.78         => ( ( Y2 != X2 )
% 3.25/1.78           => ( late_transitions @ ( res @ Y2 @ P ) @ ( late_BoundR @ A2 @ X2 @ ( res @ Y2 @ P2 ) ) ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_50_freshBoundDerivative_I1_J,axiom,
% 3.25/1.78      ! [P: pi,A2: late_subject,X2: name,P2: pi,Y2: name] :
% 3.25/1.78        ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P2 ) )
% 3.25/1.78       => ( ( fresh @ name @ pi @ Y2 @ P )
% 3.25/1.78         => ( fresh @ name @ late_subject @ Y2 @ A2 ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_51_inputIneqTrans,axiom,
% 3.25/1.78      ! [A2: name,X2: name,P: pi,B2: late_subject,Y2: name,P2: pi] :
% 3.25/1.78        ( ( late_transitions @ ( input @ A2 @ X2 @ P ) @ ( late_BoundR @ B2 @ Y2 @ P2 ) )
% 3.25/1.78       => ~ ( fresh @ name @ late_subject @ A2 @ B2 ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_52_parSym,axiom,
% 3.25/1.78      ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi,Q: pi] :
% 3.25/1.78        ( ! [R2: pi,S2: pi] : ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( par @ R2 @ S2 ) @ ( par @ S2 @ R2 ) ) @ Rel )
% 3.25/1.78       => ( ! [R2: pi,S2: pi,X5: name] :
% 3.25/1.78              ( ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ R2 @ S2 ) @ Rel )
% 3.25/1.78             => ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( res @ X5 @ R2 ) @ ( res @ X5 @ S2 ) ) @ Rel ) )
% 3.25/1.78         => ( strong743114133lation @ ( par @ P @ Q ) @ Rel @ ( par @ Q @ P ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_53_residual_Odistinct_I1_J,axiom,
% 3.25/1.78      ! [Subject: late_subject,Name3: name,Pi3: pi,FreeRes: late_freeRes,Pi: pi] :
% 3.25/1.78        ( ( late_BoundR @ Subject @ Name3 @ Pi3 )
% 3.25/1.78       != ( late_FreeR @ FreeRes @ Pi ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_54_residual_Oinducts,axiom,
% 3.25/1.78      ! [P: late_residual > $o,Residual: late_residual] :
% 3.25/1.78        ( ! [Subject2: late_subject,Name4: name,Pi4: pi] : ( P @ ( late_BoundR @ Subject2 @ Name4 @ Pi4 ) )
% 3.25/1.78       => ( ! [FreeRes2: late_freeRes,Pi4: pi] : ( P @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 3.25/1.78         => ( P @ Residual ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_55_parZeroRight,axiom,
% 3.25/1.78      ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi] :
% 3.25/1.78        ( ! [Q4: pi] : ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ Q4 @ ( par @ Q4 @ piNil ) ) @ Rel )
% 3.25/1.78       => ( strong743114133lation @ P @ Rel @ ( par @ P @ piNil ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_56_parZeroLeft,axiom,
% 3.25/1.78      ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi] :
% 3.25/1.78        ( ! [Q4: pi] : ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( par @ Q4 @ piNil ) @ Q4 ) @ Rel )
% 3.25/1.78       => ( strong743114133lation @ ( par @ P @ piNil ) @ Rel @ P ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_57_outputTauTrans,axiom,
% 3.25/1.78      ! [A2: name,B2: name,P: pi,P2: pi] :
% 3.25/1.78        ~ ( late_transitions @ ( output @ A2 @ B2 @ P ) @ ( late_FreeR @ late_TauR @ P2 ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_58_pi_Odistinct_I31_J,axiom,
% 3.25/1.78      ! [Name12: name,Name22: name,Pi3: pi,Name: name,Pi: pi] :
% 3.25/1.78        ( ( output @ Name12 @ Name22 @ Pi3 )
% 3.25/1.78       != ( res @ Name @ Pi ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_59_pi_Odistinct_I29_J,axiom,
% 3.25/1.78      ! [Name12: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 3.25/1.78        ( ( output @ Name12 @ Name22 @ Pi3 )
% 3.25/1.78       != ( par @ Pi12 @ Pi22 ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_60_transitions_OResB,axiom,
% 3.25/1.78      ! [P: pi,A2: late_subject,X2: name,P2: pi,Y2: name] :
% 3.25/1.78        ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P2 ) )
% 3.25/1.78       => ( ( fresh @ name @ late_subject @ Y2 @ A2 )
% 3.25/1.78         => ( ( Y2 != X2 )
% 3.25/1.78           => ( ( fresh @ name @ pi @ X2 @ P )
% 3.25/1.78             => ( ( fresh @ name @ late_subject @ X2 @ A2 )
% 3.25/1.78               => ( late_transitions @ ( res @ Y2 @ P ) @ ( late_BoundR @ A2 @ X2 @ ( res @ Y2 @ P2 ) ) ) ) ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_61_parCasesB_H,axiom,
% 3.25/1.78      ! [P: pi,Q: pi,B2: late_subject,Y2: name,P2: pi] :
% 3.25/1.78        ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ B2 @ Y2 @ P2 ) )
% 3.25/1.78       => ( ! [P4: pi,A4: late_subject,X5: name,P3: pi,Q4: pi] :
% 3.25/1.78              ( ( ( par @ P @ Q )
% 3.25/1.78                = ( par @ P4 @ Q4 ) )
% 3.25/1.78             => ( ( ( late_BoundR @ B2 @ Y2 @ P2 )
% 3.25/1.78                  = ( late_BoundR @ A4 @ X5 @ ( par @ P3 @ Q4 ) ) )
% 3.25/1.78               => ( ( late_transitions @ P4 @ ( late_BoundR @ A4 @ X5 @ P3 ) )
% 3.25/1.78                 => ( ( fresh @ name @ pi @ X5 @ P4 )
% 3.25/1.78                   => ( ( fresh @ name @ pi @ X5 @ Q4 )
% 3.25/1.78                     => ~ ( fresh @ name @ late_subject @ X5 @ A4 ) ) ) ) ) )
% 3.25/1.78         => ~ ! [Q4: pi,A4: late_subject,X5: name,Q3: pi,P4: pi] :
% 3.25/1.78                ( ( ( par @ P @ Q )
% 3.25/1.78                  = ( par @ P4 @ Q4 ) )
% 3.25/1.78               => ( ( ( late_BoundR @ B2 @ Y2 @ P2 )
% 3.25/1.78                    = ( late_BoundR @ A4 @ X5 @ ( par @ P4 @ Q3 ) ) )
% 3.25/1.78                 => ( ( late_transitions @ Q4 @ ( late_BoundR @ A4 @ X5 @ Q3 ) )
% 3.25/1.78                   => ( ( fresh @ name @ pi @ X5 @ P4 )
% 3.25/1.78                     => ( ( fresh @ name @ pi @ X5 @ Q4 )
% 3.25/1.78                       => ~ ( fresh @ name @ late_subject @ X5 @ A4 ) ) ) ) ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_62_transitions_OPar1B,axiom,
% 3.25/1.78      ! [P: pi,A2: late_subject,X2: name,P2: pi,Q: pi] :
% 3.25/1.78        ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P2 ) )
% 3.25/1.78       => ( ( fresh @ name @ pi @ X2 @ P )
% 3.25/1.78         => ( ( fresh @ name @ pi @ X2 @ Q )
% 3.25/1.78           => ( ( fresh @ name @ late_subject @ X2 @ A2 )
% 3.25/1.78             => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X2 @ ( par @ P2 @ Q ) ) ) ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_63_transitions_OPar2B,axiom,
% 3.25/1.78      ! [Q: pi,A2: late_subject,X2: name,Q2: pi,P: pi] :
% 3.25/1.78        ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X2 @ Q2 ) )
% 3.25/1.78       => ( ( fresh @ name @ pi @ X2 @ P )
% 3.25/1.78         => ( ( fresh @ name @ pi @ X2 @ Q )
% 3.25/1.78           => ( ( fresh @ name @ late_subject @ X2 @ A2 )
% 3.25/1.78             => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X2 @ ( par @ P @ Q2 ) ) ) ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_64_pi_Odistinct_I21_J,axiom,
% 3.25/1.78      ! [Name12: name,Name22: name,Pi3: pi,Name1: name,Name2: name,Pi: pi] :
% 3.25/1.78        ( ( output @ Name12 @ Name22 @ Pi3 )
% 3.25/1.78       != ( input @ Name1 @ Name2 @ Pi ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_65_pi_Odistinct_I1_J,axiom,
% 3.25/1.78      ! [Name1: name,Name2: name,Pi: pi] :
% 3.25/1.78        ( piNil
% 3.25/1.78       != ( output @ Name1 @ Name2 @ Pi ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_66_nilSimRight,axiom,
% 3.25/1.78      ! [P: pi,Rel: set @ ( product_prod @ pi @ pi )] : ( strong743114133lation @ P @ Rel @ piNil ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_67_parAssocLeft,axiom,
% 3.25/1.78      ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi,Q: pi,R: pi] :
% 3.25/1.78        ( ! [S2: pi,T2: pi,U: pi] : ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( par @ ( par @ S2 @ T2 ) @ U ) @ ( par @ S2 @ ( par @ T2 @ U ) ) ) @ Rel )
% 3.25/1.78       => ( ! [S2: pi,T2: pi,X5: name] :
% 3.25/1.78              ( ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ S2 @ T2 ) @ Rel )
% 3.25/1.78             => ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( res @ X5 @ S2 ) @ ( res @ X5 @ T2 ) ) @ Rel ) )
% 3.25/1.78         => ( ! [S2: pi,T2: pi,U: pi,X5: name] :
% 3.25/1.78                ( ( fresh @ name @ pi @ X5 @ S2 )
% 3.25/1.78               => ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( res @ X5 @ ( par @ ( par @ S2 @ T2 ) @ U ) ) @ ( par @ S2 @ ( res @ X5 @ ( par @ T2 @ U ) ) ) ) @ Rel ) )
% 3.25/1.78           => ( ! [S2: pi,T2: pi,U: pi,X5: name] :
% 3.25/1.78                  ( ( fresh @ name @ pi @ X5 @ U )
% 3.25/1.78                 => ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( par @ ( res @ X5 @ ( par @ S2 @ T2 ) ) @ U ) @ ( res @ X5 @ ( par @ S2 @ ( par @ T2 @ U ) ) ) ) @ Rel ) )
% 3.25/1.78             => ( strong743114133lation @ ( par @ ( par @ P @ Q ) @ R ) @ Rel @ ( par @ P @ ( par @ Q @ R ) ) ) ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_68_resOutputTauTrans,axiom,
% 3.25/1.78      ! [X2: name,A2: name,B2: name,P: pi,P2: pi] :
% 3.25/1.78        ~ ( late_transitions @ ( res @ X2 @ ( output @ A2 @ B2 @ P ) ) @ ( late_FreeR @ late_TauR @ P2 ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_69_freshResidual,axiom,
% 3.25/1.78      ! [P: pi,Rs: late_residual,X2: name] :
% 3.25/1.78        ( ( late_transitions @ P @ Rs )
% 3.25/1.78       => ( ( fresh @ name @ pi @ X2 @ P )
% 3.25/1.78         => ( fresh @ name @ late_residual @ X2 @ Rs ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_70_residual_Ostrong__inducts,axiom,
% 3.25/1.78      ! [A: $tType] :
% 3.25/1.78        ( ( fs_name @ A )
% 3.25/1.78       => ! [P: A > late_residual > $o,Z: A,Residual: late_residual] :
% 3.25/1.78            ( ! [Subject2: late_subject,Name4: name,Pi4: pi,Z2: A] :
% 3.25/1.78                ( ( fresh @ name @ A @ Name4 @ Z2 )
% 3.25/1.78               => ( ( fresh @ name @ late_subject @ Name4 @ Subject2 )
% 3.25/1.78                 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name4 @ Pi4 ) ) ) )
% 3.25/1.78           => ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: A] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 3.25/1.78             => ( P @ Z @ Residual ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_71_residual_Ostrong__induct,axiom,
% 3.25/1.78      ! [N: $tType] :
% 3.25/1.78        ( ( fs_name @ N )
% 3.25/1.78       => ! [P: N > late_residual > $o,Z: N,Residual: late_residual] :
% 3.25/1.78            ( ! [Subject2: late_subject,Name4: name,Pi4: pi,Z2: N] :
% 3.25/1.78                ( ( fresh @ name @ N @ Name4 @ Z2 )
% 3.25/1.78               => ( ( fresh @ name @ late_subject @ Name4 @ Subject2 )
% 3.25/1.78                 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name4 @ Pi4 ) ) ) )
% 3.25/1.78           => ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: N] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 3.25/1.78             => ( P @ Z @ Residual ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_72_freshBoundDerivative_I2_J,axiom,
% 3.25/1.78      ! [P: pi,A2: late_subject,X2: name,P2: pi,Y2: name] :
% 3.25/1.78        ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P2 ) )
% 3.25/1.78       => ( ( fresh @ name @ pi @ Y2 @ P )
% 3.25/1.78         => ( ( Y2 != X2 )
% 3.25/1.78           => ( fresh @ name @ pi @ Y2 @ P2 ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_73_resTrans_I1_J,axiom,
% 3.25/1.78      ! [X2: name,B2: name,P: pi,Rs: late_residual] :
% 3.25/1.78        ~ ( late_transitions @ ( res @ X2 @ ( output @ X2 @ B2 @ P ) ) @ Rs ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_74_pair__in__Id__conv,axiom,
% 3.25/1.78      ! [A: $tType,A2: A,B2: A] :
% 3.25/1.78        ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ ( id @ A ) )
% 3.25/1.78        = ( A2 = B2 ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_75_IdI,axiom,
% 3.25/1.78      ! [A: $tType,A2: A] : ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ A2 ) @ ( id @ A ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_76_fresh__prod,axiom,
% 3.25/1.78      ! [A: $tType,X: $tType,B: $tType,A2: X,X2: A,Y2: B] :
% 3.25/1.78        ( ( fresh @ X @ ( product_prod @ A @ B ) @ A2 @ ( product_Pair @ A @ B @ X2 @ Y2 ) )
% 3.25/1.78        = ( ( fresh @ X @ A @ A2 @ X2 )
% 3.25/1.78          & ( fresh @ X @ B @ A2 @ Y2 ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_77_simE_I2_J,axiom,
% 3.25/1.78      ! [P: pi,Rel: set @ ( product_prod @ pi @ pi ),Q: pi,Alpha: late_freeRes,Q2: pi] :
% 3.25/1.78        ( ( strong743114133lation @ P @ Rel @ Q )
% 3.25/1.78       => ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 3.25/1.78         => ? [P3: pi] :
% 3.25/1.78              ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P3 ) )
% 3.25/1.78              & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P3 @ Q2 ) @ Rel ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_78_Strong__Late__Sim_Oreflexive,axiom,
% 3.25/1.78      ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi] :
% 3.25/1.78        ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 3.25/1.78       => ( strong743114133lation @ P @ Rel @ P ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_79_simCasesCont,axiom,
% 3.25/1.78      ! [A: $tType] :
% 3.25/1.78        ( ( fs_name @ A )
% 3.25/1.78       => ! [Rel: set @ ( product_prod @ pi @ pi ),Q: pi,P: pi,C3: A] :
% 3.25/1.78            ( ( eqvt @ pi @ Rel )
% 3.25/1.78           => ( ! [A4: late_subject,X5: name,Q3: pi] :
% 3.25/1.78                  ( ( late_transitions @ Q @ ( late_BoundR @ A4 @ X5 @ Q3 ) )
% 3.25/1.78                 => ( ( fresh @ name @ pi @ X5 @ P )
% 3.25/1.78                   => ( ( fresh @ name @ pi @ X5 @ Q )
% 3.25/1.78                     => ( ( fresh @ name @ late_subject @ X5 @ A4 )
% 3.25/1.78                       => ( ( fresh @ name @ A @ X5 @ C3 )
% 3.25/1.78                         => ? [P5: pi] :
% 3.25/1.78                              ( ( late_transitions @ P @ ( late_BoundR @ A4 @ X5 @ P5 ) )
% 3.25/1.78                              & ( strong2129052853vative @ P5 @ Q3 @ A4 @ X5 @ Rel ) ) ) ) ) ) )
% 3.25/1.78             => ( ! [Alpha2: late_freeRes,Q3: pi] :
% 3.25/1.78                    ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 3.25/1.78                   => ? [P5: pi] :
% 3.25/1.78                        ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P5 ) )
% 3.25/1.78                        & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P5 @ Q3 ) @ Rel ) ) )
% 3.25/1.78               => ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_80_subset__antisym,axiom,
% 3.25/1.78      ! [A: $tType,A3: set @ A,B3: set @ A] :
% 3.25/1.78        ( ( ord_less_eq @ ( set @ A ) @ A3 @ B3 )
% 3.25/1.78       => ( ( ord_less_eq @ ( set @ A ) @ B3 @ A3 )
% 3.25/1.78         => ( A3 = B3 ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_81_subsetI,axiom,
% 3.25/1.78      ! [A: $tType,A3: set @ A,B3: set @ A] :
% 3.25/1.78        ( ! [X5: A] :
% 3.25/1.78            ( ( member @ A @ X5 @ A3 )
% 3.25/1.78           => ( member @ A @ X5 @ B3 ) )
% 3.25/1.78       => ( ord_less_eq @ ( set @ A ) @ A3 @ B3 ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_82_name__fresh,axiom,
% 3.25/1.78      ( ( fresh @ name @ name )
% 3.25/1.78      = ( ^ [A5: name,B4: name] : ( A5 != B4 ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_83_derivativeMonotonic,axiom,
% 3.25/1.78      ! [P: pi,Q: pi,A2: late_subject,X2: name,A3: set @ ( product_prod @ pi @ pi ),B3: set @ ( product_prod @ pi @ pi )] :
% 3.25/1.78        ( ( strong2129052853vative @ P @ Q @ A2 @ X2 @ A3 )
% 3.25/1.78       => ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ A3 @ B3 )
% 3.25/1.78         => ( strong2129052853vative @ P @ Q @ A2 @ X2 @ B3 ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_84_derivativeReflexive,axiom,
% 3.25/1.78      ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi,A2: late_subject,X2: name] :
% 3.25/1.78        ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 3.25/1.78       => ( strong2129052853vative @ P @ P @ A2 @ X2 @ Rel ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_85_in__mono,axiom,
% 3.25/1.78      ! [A: $tType,A3: set @ A,B3: set @ A,X2: A] :
% 3.25/1.78        ( ( ord_less_eq @ ( set @ A ) @ A3 @ B3 )
% 3.25/1.78       => ( ( member @ A @ X2 @ A3 )
% 3.25/1.78         => ( member @ A @ X2 @ B3 ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_86_subsetD,axiom,
% 3.25/1.78      ! [A: $tType,A3: set @ A,B3: set @ A,C2: A] :
% 3.25/1.78        ( ( ord_less_eq @ ( set @ A ) @ A3 @ B3 )
% 3.25/1.78       => ( ( member @ A @ C2 @ A3 )
% 3.25/1.78         => ( member @ A @ C2 @ B3 ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_87_equalityE,axiom,
% 3.25/1.78      ! [A: $tType,A3: set @ A,B3: set @ A] :
% 3.25/1.78        ( ( A3 = B3 )
% 3.25/1.78       => ~ ( ( ord_less_eq @ ( set @ A ) @ A3 @ B3 )
% 3.25/1.78           => ~ ( ord_less_eq @ ( set @ A ) @ B3 @ A3 ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_88_subset__eq,axiom,
% 3.25/1.78      ! [A: $tType] :
% 3.25/1.78        ( ( ord_less_eq @ ( set @ A ) )
% 3.25/1.78        = ( ^ [A6: set @ A,B5: set @ A] :
% 3.25/1.78            ! [X4: A] :
% 3.25/1.78              ( ( member @ A @ X4 @ A6 )
% 3.25/1.78             => ( member @ A @ X4 @ B5 ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_89_equalityD1,axiom,
% 3.25/1.78      ! [A: $tType,A3: set @ A,B3: set @ A] :
% 3.25/1.78        ( ( A3 = B3 )
% 3.25/1.78       => ( ord_less_eq @ ( set @ A ) @ A3 @ B3 ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_90_equalityD2,axiom,
% 3.25/1.78      ! [A: $tType,A3: set @ A,B3: set @ A] :
% 3.25/1.78        ( ( A3 = B3 )
% 3.25/1.78       => ( ord_less_eq @ ( set @ A ) @ B3 @ A3 ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_91_subset__iff,axiom,
% 3.25/1.78      ! [A: $tType] :
% 3.25/1.78        ( ( ord_less_eq @ ( set @ A ) )
% 3.25/1.78        = ( ^ [A6: set @ A,B5: set @ A] :
% 3.25/1.78            ! [T3: A] :
% 3.25/1.78              ( ( member @ A @ T3 @ A6 )
% 3.25/1.78             => ( member @ A @ T3 @ B5 ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_92_subset__refl,axiom,
% 3.25/1.78      ! [A: $tType,A3: set @ A] : ( ord_less_eq @ ( set @ A ) @ A3 @ A3 ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_93_Collect__mono,axiom,
% 3.25/1.78      ! [A: $tType,P: A > $o,Q: A > $o] :
% 3.25/1.78        ( ! [X5: A] :
% 3.25/1.78            ( ( P @ X5 )
% 3.25/1.78           => ( Q @ X5 ) )
% 3.25/1.78       => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_94_subset__trans,axiom,
% 3.25/1.78      ! [A: $tType,A3: set @ A,B3: set @ A,C3: set @ A] :
% 3.25/1.78        ( ( ord_less_eq @ ( set @ A ) @ A3 @ B3 )
% 3.25/1.78       => ( ( ord_less_eq @ ( set @ A ) @ B3 @ C3 )
% 3.25/1.78         => ( ord_less_eq @ ( set @ A ) @ A3 @ C3 ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_95_set__eq__subset,axiom,
% 3.25/1.78      ! [A: $tType] :
% 3.25/1.78        ( ( ^ [Y4: set @ A,Z3: set @ A] : ( Y4 = Z3 ) )
% 3.25/1.78        = ( ^ [A6: set @ A,B5: set @ A] :
% 3.25/1.78              ( ( ord_less_eq @ ( set @ A ) @ A6 @ B5 )
% 3.25/1.78              & ( ord_less_eq @ ( set @ A ) @ B5 @ A6 ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_96_Collect__mono__iff,axiom,
% 3.25/1.78      ! [A: $tType,P: A > $o,Q: A > $o] :
% 3.25/1.78        ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) )
% 3.25/1.78        = ( ! [X4: A] :
% 3.25/1.78              ( ( P @ X4 )
% 3.25/1.78             => ( Q @ X4 ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_97_simE_I1_J,axiom,
% 3.25/1.78      ! [P: pi,Rel: set @ ( product_prod @ pi @ pi ),Q: pi,A2: late_subject,X2: name,Q2: pi] :
% 3.25/1.78        ( ( strong743114133lation @ P @ Rel @ Q )
% 3.25/1.78       => ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X2 @ Q2 ) )
% 3.25/1.78         => ( ( fresh @ name @ pi @ X2 @ P )
% 3.25/1.78           => ? [P3: pi] :
% 3.25/1.78                ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P3 ) )
% 3.25/1.78                & ( strong2129052853vative @ P3 @ Q2 @ A2 @ X2 @ Rel ) ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_98_fresh__prodD_I2_J,axiom,
% 3.25/1.78      ! [B: $tType,A: $tType,C4: $tType,A2: A,X2: B,Y2: C4] :
% 3.25/1.78        ( ( fresh @ A @ ( product_prod @ B @ C4 ) @ A2 @ ( product_Pair @ B @ C4 @ X2 @ Y2 ) )
% 3.25/1.78       => ( fresh @ A @ C4 @ A2 @ Y2 ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_99_fresh__prodD_I1_J,axiom,
% 3.25/1.78      ! [C4: $tType,A: $tType,B: $tType,A2: A,X2: B,Y2: C4] :
% 3.25/1.78        ( ( fresh @ A @ ( product_prod @ B @ C4 ) @ A2 @ ( product_Pair @ B @ C4 @ X2 @ Y2 ) )
% 3.25/1.78       => ( fresh @ A @ B @ A2 @ X2 ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_100_subrelI,axiom,
% 3.25/1.78      ! [B: $tType,A: $tType,R3: set @ ( product_prod @ A @ B ),S3: set @ ( product_prod @ A @ B )] :
% 3.25/1.78        ( ! [X5: A,Y: B] :
% 3.25/1.78            ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X5 @ Y ) @ R3 )
% 3.25/1.78           => ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X5 @ Y ) @ S3 ) )
% 3.25/1.78       => ( ord_less_eq @ ( set @ ( product_prod @ A @ B ) ) @ R3 @ S3 ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_101_simCases,axiom,
% 3.25/1.78      ! [Q: pi,P: pi,Rel: set @ ( product_prod @ pi @ pi )] :
% 3.25/1.78        ( ! [A4: late_subject,Y: name,Q3: pi] :
% 3.25/1.78            ( ( late_transitions @ Q @ ( late_BoundR @ A4 @ Y @ Q3 ) )
% 3.25/1.78           => ( ( fresh @ name @ pi @ Y @ P )
% 3.25/1.78             => ? [P5: pi] :
% 3.25/1.78                  ( ( late_transitions @ P @ ( late_BoundR @ A4 @ Y @ P5 ) )
% 3.25/1.78                  & ( strong2129052853vative @ P5 @ Q3 @ A4 @ Y @ Rel ) ) ) )
% 3.25/1.78       => ( ! [Alpha2: late_freeRes,Q3: pi] :
% 3.25/1.78              ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 3.25/1.78             => ? [P5: pi] :
% 3.25/1.78                  ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P5 ) )
% 3.25/1.78                  & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P5 @ Q3 ) @ Rel ) ) )
% 3.25/1.78         => ( strong743114133lation @ P @ Rel @ Q ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_102_simulation__def,axiom,
% 3.25/1.78      ( strong743114133lation
% 3.25/1.78      = ( ^ [P6: pi,Rel2: set @ ( product_prod @ pi @ pi ),Q5: pi] :
% 3.25/1.78            ( ! [A5: late_subject,X4: name,Q6: pi] :
% 3.25/1.78                ( ( ( late_transitions @ Q5 @ ( late_BoundR @ A5 @ X4 @ Q6 ) )
% 3.25/1.78                  & ( fresh @ name @ pi @ X4 @ P6 ) )
% 3.25/1.78               => ? [P7: pi] :
% 3.25/1.78                    ( ( late_transitions @ P6 @ ( late_BoundR @ A5 @ X4 @ P7 ) )
% 3.25/1.78                    & ( strong2129052853vative @ P7 @ Q6 @ A5 @ X4 @ Rel2 ) ) )
% 3.25/1.78            & ! [Alpha3: late_freeRes,Q6: pi] :
% 3.25/1.78                ( ( late_transitions @ Q5 @ ( late_FreeR @ Alpha3 @ Q6 ) )
% 3.25/1.78               => ? [P7: pi] :
% 3.25/1.78                    ( ( late_transitions @ P6 @ ( late_FreeR @ Alpha3 @ P7 ) )
% 3.25/1.78                    & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P7 @ Q6 ) @ Rel2 ) ) ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_103_IdE,axiom,
% 3.25/1.78      ! [A: $tType,P8: product_prod @ A @ A] :
% 3.25/1.78        ( ( member @ ( product_prod @ A @ A ) @ P8 @ ( id @ A ) )
% 3.25/1.78       => ~ ! [X5: A] :
% 3.25/1.78              ( P8
% 3.25/1.78             != ( product_Pair @ A @ A @ X5 @ X5 ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_104_monotonic,axiom,
% 3.25/1.78      ! [P: pi,A3: set @ ( product_prod @ pi @ pi ),P2: pi,B3: set @ ( product_prod @ pi @ pi )] :
% 3.25/1.78        ( ( strong743114133lation @ P @ A3 @ P2 )
% 3.25/1.78       => ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ A3 @ B3 )
% 3.25/1.78         => ( strong743114133lation @ P @ B3 @ P2 ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_105_prod_Oinject,axiom,
% 3.25/1.78      ! [A: $tType,B: $tType,X1: A,X22: B,Y1: A,Y22: B] :
% 3.25/1.78        ( ( ( product_Pair @ A @ B @ X1 @ X22 )
% 3.25/1.78          = ( product_Pair @ A @ B @ Y1 @ Y22 ) )
% 3.25/1.78        = ( ( X1 = Y1 )
% 3.25/1.78          & ( X22 = Y22 ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_106_old_Oprod_Oinject,axiom,
% 3.25/1.78      ! [A: $tType,B: $tType,A2: A,B2: B,A7: A,B6: B] :
% 3.25/1.78        ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 3.25/1.78          = ( product_Pair @ A @ B @ A7 @ B6 ) )
% 3.25/1.78        = ( ( A2 = A7 )
% 3.25/1.78          & ( B2 = B6 ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_107_order__refl,axiom,
% 3.25/1.78      ! [A: $tType] :
% 3.25/1.78        ( ( preorder @ A )
% 3.25/1.78       => ! [X2: A] : ( ord_less_eq @ A @ X2 @ X2 ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_108_resSimCases,axiom,
% 3.25/1.78      ! [A: $tType] :
% 3.25/1.78        ( ( fs_name @ A )
% 3.25/1.78       => ! [Rel: set @ ( product_prod @ pi @ pi ),Q: pi,X2: name,P: pi,C3: A] :
% 3.25/1.78            ( ( eqvt @ pi @ Rel )
% 3.25/1.78           => ( ! [Q3: pi,A4: name] :
% 3.25/1.78                  ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A4 @ X2 ) @ Q3 ) )
% 3.25/1.78                 => ( ( A4 != X2 )
% 3.25/1.78                   => ? [P5: pi] :
% 3.25/1.78                        ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A4 ) @ X2 @ P5 ) )
% 3.25/1.78                        & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P5 @ Q3 ) @ Rel ) ) ) )
% 3.25/1.78             => ( ! [Q3: pi,A4: late_subject,Y: name] :
% 3.25/1.78                    ( ( late_transitions @ Q @ ( late_BoundR @ A4 @ Y @ Q3 ) )
% 3.25/1.78                   => ( ( fresh @ name @ late_subject @ X2 @ A4 )
% 3.25/1.78                     => ( ( X2 != Y )
% 3.25/1.78                       => ( ( fresh @ name @ A @ Y @ C3 )
% 3.25/1.78                         => ? [P5: pi] :
% 3.25/1.78                              ( ( late_transitions @ P @ ( late_BoundR @ A4 @ Y @ P5 ) )
% 3.25/1.78                              & ( strong2129052853vative @ P5 @ ( res @ X2 @ Q3 ) @ A4 @ Y @ Rel ) ) ) ) ) )
% 3.25/1.78               => ( ! [Q3: pi,Alpha2: late_freeRes] :
% 3.25/1.78                      ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 3.25/1.78                     => ( ( fresh @ name @ late_freeRes @ X2 @ Alpha2 )
% 3.25/1.78                       => ? [P5: pi] :
% 3.25/1.78                            ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P5 ) )
% 3.25/1.78                            & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P5 @ ( res @ X2 @ Q3 ) ) @ Rel ) ) ) )
% 3.25/1.78                 => ( strong743114133lation @ P @ Rel @ ( res @ X2 @ Q ) ) ) ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_109_IdD,axiom,
% 3.25/1.78      ! [A: $tType,A2: A,B2: A] :
% 3.25/1.78        ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ ( id @ A ) )
% 3.25/1.78       => ( A2 = B2 ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_110_sumResLeft,axiom,
% 3.25/1.78      ! [Rel: set @ ( product_prod @ pi @ pi ),X2: name,P: pi,Q: pi] :
% 3.25/1.78        ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 3.25/1.78       => ( ( eqvt @ pi @ Rel )
% 3.25/1.78         => ( strong743114133lation @ ( sum @ ( res @ X2 @ P ) @ ( res @ X2 @ Q ) ) @ Rel @ ( res @ X2 @ ( sum @ P @ Q ) ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_111_Late__Semantics_OfreeRes_Oinject,axiom,
% 3.25/1.78      ! [X22: name,X1: name,Y22: name,Y1: name] :
% 3.25/1.78        ( ( ( late_OutputR @ X22 @ X1 )
% 3.25/1.78          = ( late_OutputR @ Y22 @ Y1 ) )
% 3.25/1.78        = ( ( X22 = Y22 )
% 3.25/1.78          & ( X1 = Y1 ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_112_Late__Semantics_Osubject_Oinject_I2_J,axiom,
% 3.25/1.78      ! [X1: name,Y1: name] :
% 3.25/1.78        ( ( ( late_BoundOutputS @ X1 )
% 3.25/1.78          = ( late_BoundOutputS @ Y1 ) )
% 3.25/1.78        = ( X1 = Y1 ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_113_pi_Ofresh_I7_J,axiom,
% 3.25/1.78      ! [A2: name,X22: pi,X1: pi] :
% 3.25/1.78        ( ( fresh @ name @ pi @ A2 @ ( sum @ X22 @ X1 ) )
% 3.25/1.78        = ( ( fresh @ name @ pi @ A2 @ X22 )
% 3.25/1.78          & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_114_subject_Ofresh_I2_J,axiom,
% 3.25/1.78      ! [A2: name,X1: name] :
% 3.25/1.78        ( ( fresh @ name @ late_subject @ A2 @ ( late_BoundOutputS @ X1 ) )
% 3.25/1.78        = ( fresh @ name @ name @ A2 @ X1 ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_115_freeRes_Ofresh_I1_J,axiom,
% 3.25/1.78      ! [A2: name,X22: name,X1: name] :
% 3.25/1.78        ( ( fresh @ name @ late_freeRes @ A2 @ ( late_OutputR @ X22 @ X1 ) )
% 3.25/1.78        = ( ( fresh @ name @ name @ A2 @ X22 )
% 3.25/1.78          & ( fresh @ name @ name @ A2 @ X1 ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_116_pi_Oinject_I6_J,axiom,
% 3.25/1.78      ! [X22: pi,X1: pi,Y22: pi,Y1: pi] :
% 3.25/1.78        ( ( ( sum @ X22 @ X1 )
% 3.25/1.78          = ( sum @ Y22 @ Y1 ) )
% 3.25/1.78        = ( ( X22 = Y22 )
% 3.25/1.78          & ( X1 = Y1 ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_117_sumCases,axiom,
% 3.25/1.78      ! [P: pi,Q: pi,Rs: late_residual] :
% 3.25/1.78        ( ( late_transitions @ ( sum @ P @ Q ) @ Rs )
% 3.25/1.78       => ( ~ ( late_transitions @ P @ Rs )
% 3.25/1.78         => ( late_transitions @ Q @ Rs ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_118_sumCases_H,axiom,
% 3.25/1.78      ! [P: pi,Q: pi,Rs: late_residual] :
% 3.25/1.78        ( ( late_transitions @ ( sum @ P @ Q ) @ Rs )
% 3.25/1.78       => ( ~ ( late_transitions @ P @ Rs )
% 3.25/1.78         => ( late_transitions @ Q @ Rs ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_119_Sum1,axiom,
% 3.25/1.78      ! [P: pi,Rs: late_residual,Q: pi] :
% 3.25/1.78        ( ( late_transitions @ P @ Rs )
% 3.25/1.78       => ( late_transitions @ ( sum @ P @ Q ) @ Rs ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_120_Sum2,axiom,
% 3.25/1.78      ! [Q: pi,Rs: late_residual,P: pi] :
% 3.25/1.78        ( ( late_transitions @ Q @ Rs )
% 3.25/1.78       => ( late_transitions @ ( sum @ P @ Q ) @ Rs ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_121_pi_Odistinct_I81_J,axiom,
% 3.25/1.78      ! [Pi1: pi,Pi2: pi,Name: name,Pi: pi] :
% 3.25/1.78        ( ( sum @ Pi1 @ Pi2 )
% 3.25/1.78       != ( res @ Name @ Pi ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_122_pi_Odistinct_I79_J,axiom,
% 3.25/1.78      ! [Pi1: pi,Pi2: pi,Pi12: pi,Pi22: pi] :
% 3.25/1.78        ( ( sum @ Pi1 @ Pi2 )
% 3.25/1.78       != ( par @ Pi12 @ Pi22 ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_123_pi_Odistinct_I53_J,axiom,
% 3.25/1.78      ! [Name12: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 3.25/1.78        ( ( input @ Name12 @ Name22 @ Pi3 )
% 3.25/1.78       != ( sum @ Pi12 @ Pi22 ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_124_pi_Odistinct_I11_J,axiom,
% 3.25/1.78      ! [Pi12: pi,Pi22: pi] :
% 3.25/1.78        ( piNil
% 3.25/1.78       != ( sum @ Pi12 @ Pi22 ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_125_pi_Odistinct_I27_J,axiom,
% 3.25/1.78      ! [Name12: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 3.25/1.78        ( ( output @ Name12 @ Name22 @ Pi3 )
% 3.25/1.78       != ( sum @ Pi12 @ Pi22 ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_126_Late__Semantics_OfreeRes_Odistinct_I1_J,axiom,
% 3.25/1.78      ! [Name12: name,Name22: name] :
% 3.25/1.78        ( ( late_OutputR @ Name12 @ Name22 )
% 3.25/1.78       != late_TauR ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_127_freeRes_Oinducts,axiom,
% 3.25/1.78      ! [P: late_freeRes > $o,FreeRes3: late_freeRes] :
% 3.25/1.78        ( ! [Name13: name,Name23: name] : ( P @ ( late_OutputR @ Name13 @ Name23 ) )
% 3.25/1.78       => ( ( P @ late_TauR )
% 3.25/1.78         => ( P @ FreeRes3 ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_128_freeRes_Ostrong__induct_H,axiom,
% 3.25/1.78      ! [N: $tType,P: N > late_freeRes > $o,Z: N,FreeRes3: late_freeRes] :
% 3.25/1.78        ( ! [Name13: name,Name23: name,Z2: N] : ( P @ Z2 @ ( late_OutputR @ Name13 @ Name23 ) )
% 3.25/1.78       => ( ! [Z2: N] : ( P @ Z2 @ late_TauR )
% 3.25/1.78         => ( P @ Z @ FreeRes3 ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_129_freeRes_Ostrong__inducts,axiom,
% 3.25/1.78      ! [A: $tType,P: A > late_freeRes > $o,Z: A,FreeRes3: late_freeRes] :
% 3.25/1.78        ( ! [Name13: name,Name23: name,Z2: A] : ( P @ Z2 @ ( late_OutputR @ Name13 @ Name23 ) )
% 3.25/1.78       => ( ! [Z2: A] : ( P @ Z2 @ late_TauR )
% 3.25/1.78         => ( P @ Z @ FreeRes3 ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_130_Open,axiom,
% 3.25/1.78      ! [P: pi,A2: name,B2: name,P2: pi] :
% 3.25/1.78        ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P2 ) )
% 3.25/1.78       => ( ( A2 != B2 )
% 3.25/1.78         => ( late_transitions @ ( res @ B2 @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ B2 @ P2 ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_131_dual__order_Oantisym,axiom,
% 3.25/1.78      ! [A: $tType] :
% 3.25/1.78        ( ( order @ A )
% 3.25/1.78       => ! [B2: A,A2: A] :
% 3.25/1.78            ( ( ord_less_eq @ A @ B2 @ A2 )
% 3.25/1.78           => ( ( ord_less_eq @ A @ A2 @ B2 )
% 3.25/1.78             => ( A2 = B2 ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_132_dual__order_Oeq__iff,axiom,
% 3.25/1.78      ! [A: $tType] :
% 3.25/1.78        ( ( order @ A )
% 3.25/1.78       => ( ( ^ [Y4: A,Z3: A] : ( Y4 = Z3 ) )
% 3.25/1.78          = ( ^ [A5: A,B4: A] :
% 3.25/1.78                ( ( ord_less_eq @ A @ B4 @ A5 )
% 3.25/1.78                & ( ord_less_eq @ A @ A5 @ B4 ) ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_133_dual__order_Otrans,axiom,
% 3.25/1.78      ! [A: $tType] :
% 3.25/1.78        ( ( order @ A )
% 3.25/1.78       => ! [B2: A,A2: A,C2: A] :
% 3.25/1.78            ( ( ord_less_eq @ A @ B2 @ A2 )
% 3.25/1.78           => ( ( ord_less_eq @ A @ C2 @ B2 )
% 3.25/1.78             => ( ord_less_eq @ A @ C2 @ A2 ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_134_linorder__wlog,axiom,
% 3.25/1.78      ! [A: $tType] :
% 3.25/1.78        ( ( linorder @ A )
% 3.25/1.78       => ! [P: A > A > $o,A2: A,B2: A] :
% 3.25/1.78            ( ! [A4: A,B7: A] :
% 3.25/1.78                ( ( ord_less_eq @ A @ A4 @ B7 )
% 3.25/1.78               => ( P @ A4 @ B7 ) )
% 3.25/1.78           => ( ! [A4: A,B7: A] :
% 3.25/1.78                  ( ( P @ B7 @ A4 )
% 3.25/1.78                 => ( P @ A4 @ B7 ) )
% 3.25/1.78             => ( P @ A2 @ B2 ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_135_dual__order_Orefl,axiom,
% 3.25/1.78      ! [A: $tType] :
% 3.25/1.78        ( ( order @ A )
% 3.25/1.78       => ! [A2: A] : ( ord_less_eq @ A @ A2 @ A2 ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_136_order__trans,axiom,
% 3.25/1.78      ! [A: $tType] :
% 3.25/1.78        ( ( preorder @ A )
% 3.25/1.78       => ! [X2: A,Y2: A,Z: A] :
% 3.25/1.78            ( ( ord_less_eq @ A @ X2 @ Y2 )
% 3.25/1.78           => ( ( ord_less_eq @ A @ Y2 @ Z )
% 3.25/1.78             => ( ord_less_eq @ A @ X2 @ Z ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_137_order__class_Oorder_Oantisym,axiom,
% 3.25/1.78      ! [A: $tType] :
% 3.25/1.78        ( ( order @ A )
% 3.25/1.78       => ! [A2: A,B2: A] :
% 3.25/1.78            ( ( ord_less_eq @ A @ A2 @ B2 )
% 3.25/1.78           => ( ( ord_less_eq @ A @ B2 @ A2 )
% 3.25/1.78             => ( A2 = B2 ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_138_ord__le__eq__trans,axiom,
% 3.25/1.78      ! [A: $tType] :
% 3.25/1.78        ( ( ord @ A )
% 3.25/1.78       => ! [A2: A,B2: A,C2: A] :
% 3.25/1.78            ( ( ord_less_eq @ A @ A2 @ B2 )
% 3.25/1.78           => ( ( B2 = C2 )
% 3.25/1.78             => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_139_ord__eq__le__trans,axiom,
% 3.25/1.78      ! [A: $tType] :
% 3.25/1.78        ( ( ord @ A )
% 3.25/1.78       => ! [A2: A,B2: A,C2: A] :
% 3.25/1.78            ( ( A2 = B2 )
% 3.25/1.78           => ( ( ord_less_eq @ A @ B2 @ C2 )
% 3.25/1.78             => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_140_order__class_Oorder_Oeq__iff,axiom,
% 3.25/1.78      ! [A: $tType] :
% 3.25/1.78        ( ( order @ A )
% 3.25/1.78       => ( ( ^ [Y4: A,Z3: A] : ( Y4 = Z3 ) )
% 3.25/1.78          = ( ^ [A5: A,B4: A] :
% 3.25/1.78                ( ( ord_less_eq @ A @ A5 @ B4 )
% 3.25/1.78                & ( ord_less_eq @ A @ B4 @ A5 ) ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_141_antisym__conv,axiom,
% 3.25/1.78      ! [A: $tType] :
% 3.25/1.78        ( ( order @ A )
% 3.25/1.78       => ! [Y2: A,X2: A] :
% 3.25/1.78            ( ( ord_less_eq @ A @ Y2 @ X2 )
% 3.25/1.78           => ( ( ord_less_eq @ A @ X2 @ Y2 )
% 3.25/1.78              = ( X2 = Y2 ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_142_le__cases3,axiom,
% 3.25/1.78      ! [A: $tType] :
% 3.25/1.78        ( ( linorder @ A )
% 3.25/1.78       => ! [X2: A,Y2: A,Z: A] :
% 3.25/1.78            ( ( ( ord_less_eq @ A @ X2 @ Y2 )
% 3.25/1.78             => ~ ( ord_less_eq @ A @ Y2 @ Z ) )
% 3.25/1.78           => ( ( ( ord_less_eq @ A @ Y2 @ X2 )
% 3.25/1.78               => ~ ( ord_less_eq @ A @ X2 @ Z ) )
% 3.25/1.78             => ( ( ( ord_less_eq @ A @ X2 @ Z )
% 3.25/1.78                 => ~ ( ord_less_eq @ A @ Z @ Y2 ) )
% 3.25/1.78               => ( ( ( ord_less_eq @ A @ Z @ Y2 )
% 3.25/1.78                   => ~ ( ord_less_eq @ A @ Y2 @ X2 ) )
% 3.25/1.78                 => ( ( ( ord_less_eq @ A @ Y2 @ Z )
% 3.25/1.78                     => ~ ( ord_less_eq @ A @ Z @ X2 ) )
% 3.25/1.78                   => ~ ( ( ord_less_eq @ A @ Z @ X2 )
% 3.25/1.78                       => ~ ( ord_less_eq @ A @ X2 @ Y2 ) ) ) ) ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_143_order_Otrans,axiom,
% 3.25/1.78      ! [A: $tType] :
% 3.25/1.78        ( ( order @ A )
% 3.25/1.78       => ! [A2: A,B2: A,C2: A] :
% 3.25/1.78            ( ( ord_less_eq @ A @ A2 @ B2 )
% 3.25/1.78           => ( ( ord_less_eq @ A @ B2 @ C2 )
% 3.25/1.78             => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_144_le__cases,axiom,
% 3.25/1.78      ! [A: $tType] :
% 3.25/1.78        ( ( linorder @ A )
% 3.25/1.78       => ! [X2: A,Y2: A] :
% 3.25/1.78            ( ~ ( ord_less_eq @ A @ X2 @ Y2 )
% 3.25/1.78           => ( ord_less_eq @ A @ Y2 @ X2 ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_145_eq__refl,axiom,
% 3.25/1.78      ! [A: $tType] :
% 3.25/1.78        ( ( preorder @ A )
% 3.25/1.78       => ! [X2: A,Y2: A] :
% 3.25/1.78            ( ( X2 = Y2 )
% 3.25/1.78           => ( ord_less_eq @ A @ X2 @ Y2 ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_146_linear,axiom,
% 3.25/1.78      ! [A: $tType] :
% 3.25/1.78        ( ( linorder @ A )
% 3.25/1.78       => ! [X2: A,Y2: A] :
% 3.25/1.78            ( ( ord_less_eq @ A @ X2 @ Y2 )
% 3.25/1.78            | ( ord_less_eq @ A @ Y2 @ X2 ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_147_antisym,axiom,
% 3.25/1.78      ! [A: $tType] :
% 3.25/1.78        ( ( order @ A )
% 3.25/1.78       => ! [X2: A,Y2: A] :
% 3.25/1.78            ( ( ord_less_eq @ A @ X2 @ Y2 )
% 3.25/1.78           => ( ( ord_less_eq @ A @ Y2 @ X2 )
% 3.25/1.78             => ( X2 = Y2 ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_148_eq__iff,axiom,
% 3.25/1.78      ! [A: $tType] :
% 3.25/1.78        ( ( order @ A )
% 3.25/1.78       => ( ( ^ [Y4: A,Z3: A] : ( Y4 = Z3 ) )
% 3.25/1.78          = ( ^ [X4: A,Y5: A] :
% 3.25/1.78                ( ( ord_less_eq @ A @ X4 @ Y5 )
% 3.25/1.78                & ( ord_less_eq @ A @ Y5 @ X4 ) ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_149_ord__le__eq__subst,axiom,
% 3.25/1.78      ! [A: $tType,B: $tType] :
% 3.25/1.78        ( ( ( ord @ B )
% 3.25/1.78          & ( ord @ A ) )
% 3.25/1.78       => ! [A2: A,B2: A,F2: A > B,C2: B] :
% 3.25/1.78            ( ( ord_less_eq @ A @ A2 @ B2 )
% 3.25/1.78           => ( ( ( F2 @ B2 )
% 3.25/1.78                = C2 )
% 3.25/1.78             => ( ! [X5: A,Y: A] :
% 3.25/1.78                    ( ( ord_less_eq @ A @ X5 @ Y )
% 3.25/1.78                   => ( ord_less_eq @ B @ ( F2 @ X5 ) @ ( F2 @ Y ) ) )
% 3.25/1.78               => ( ord_less_eq @ B @ ( F2 @ A2 ) @ C2 ) ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_150_ord__eq__le__subst,axiom,
% 3.25/1.78      ! [A: $tType,B: $tType] :
% 3.25/1.78        ( ( ( ord @ B )
% 3.25/1.78          & ( ord @ A ) )
% 3.25/1.78       => ! [A2: A,F2: B > A,B2: B,C2: B] :
% 3.25/1.78            ( ( A2
% 3.25/1.78              = ( F2 @ B2 ) )
% 3.25/1.78           => ( ( ord_less_eq @ B @ B2 @ C2 )
% 3.25/1.78             => ( ! [X5: B,Y: B] :
% 3.25/1.78                    ( ( ord_less_eq @ B @ X5 @ Y )
% 3.25/1.78                   => ( ord_less_eq @ A @ ( F2 @ X5 ) @ ( F2 @ Y ) ) )
% 3.25/1.78               => ( ord_less_eq @ A @ A2 @ ( F2 @ C2 ) ) ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_151_order__subst2,axiom,
% 3.25/1.78      ! [A: $tType,C4: $tType] :
% 3.25/1.78        ( ( ( order @ C4 )
% 3.25/1.78          & ( order @ A ) )
% 3.25/1.78       => ! [A2: A,B2: A,F2: A > C4,C2: C4] :
% 3.25/1.78            ( ( ord_less_eq @ A @ A2 @ B2 )
% 3.25/1.78           => ( ( ord_less_eq @ C4 @ ( F2 @ B2 ) @ C2 )
% 3.25/1.78             => ( ! [X5: A,Y: A] :
% 3.25/1.78                    ( ( ord_less_eq @ A @ X5 @ Y )
% 3.25/1.78                   => ( ord_less_eq @ C4 @ ( F2 @ X5 ) @ ( F2 @ Y ) ) )
% 3.25/1.78               => ( ord_less_eq @ C4 @ ( F2 @ A2 ) @ C2 ) ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_152_order__subst1,axiom,
% 3.25/1.78      ! [A: $tType,B: $tType] :
% 3.25/1.78        ( ( ( order @ B )
% 3.25/1.78          & ( order @ A ) )
% 3.25/1.78       => ! [A2: A,F2: B > A,B2: B,C2: B] :
% 3.25/1.78            ( ( ord_less_eq @ A @ A2 @ ( F2 @ B2 ) )
% 3.25/1.78           => ( ( ord_less_eq @ B @ B2 @ C2 )
% 3.25/1.78             => ( ! [X5: B,Y: B] :
% 3.25/1.78                    ( ( ord_less_eq @ B @ X5 @ Y )
% 3.25/1.78                   => ( ord_less_eq @ A @ ( F2 @ X5 ) @ ( F2 @ Y ) ) )
% 3.25/1.78               => ( ord_less_eq @ A @ A2 @ ( F2 @ C2 ) ) ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_153_le__fun__def,axiom,
% 3.25/1.78      ! [B: $tType,A: $tType] :
% 3.25/1.78        ( ( ord @ B )
% 3.25/1.78       => ( ( ord_less_eq @ ( A > B ) )
% 3.25/1.78          = ( ^ [F3: A > B,G: A > B] :
% 3.25/1.78              ! [X4: A] : ( ord_less_eq @ B @ ( F3 @ X4 ) @ ( G @ X4 ) ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_154_le__funI,axiom,
% 3.25/1.78      ! [B: $tType,A: $tType] :
% 3.25/1.78        ( ( ord @ B )
% 3.25/1.78       => ! [F2: A > B,G2: A > B] :
% 3.25/1.78            ( ! [X5: A] : ( ord_less_eq @ B @ ( F2 @ X5 ) @ ( G2 @ X5 ) )
% 3.25/1.78           => ( ord_less_eq @ ( A > B ) @ F2 @ G2 ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_155_le__funE,axiom,
% 3.25/1.78      ! [B: $tType,A: $tType] :
% 3.25/1.78        ( ( ord @ B )
% 3.25/1.78       => ! [F2: A > B,G2: A > B,X2: A] :
% 3.25/1.78            ( ( ord_less_eq @ ( A > B ) @ F2 @ G2 )
% 3.25/1.78           => ( ord_less_eq @ B @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_156_le__funD,axiom,
% 3.25/1.78      ! [B: $tType,A: $tType] :
% 3.25/1.78        ( ( ord @ B )
% 3.25/1.78       => ! [F2: A > B,G2: A > B,X2: A] :
% 3.25/1.78            ( ( ord_less_eq @ ( A > B ) @ F2 @ G2 )
% 3.25/1.78           => ( ord_less_eq @ B @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_157_old_Oprod_Oinducts,axiom,
% 3.25/1.78      ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,Prod: product_prod @ A @ B] :
% 3.25/1.78        ( ! [A4: A,B7: B] : ( P @ ( product_Pair @ A @ B @ A4 @ B7 ) )
% 3.25/1.78       => ( P @ Prod ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_158_old_Oprod_Oexhaust,axiom,
% 3.25/1.78      ! [A: $tType,B: $tType,Y2: product_prod @ A @ B] :
% 3.25/1.78        ~ ! [A4: A,B7: B] :
% 3.25/1.78            ( Y2
% 3.25/1.78           != ( product_Pair @ A @ B @ A4 @ B7 ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_159_prod__induct7,axiom,
% 3.25/1.78      ! [G3: $tType,F4: $tType,E: $tType,D: $tType,C4: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C4 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G3 ) ) ) ) ) ) > $o,X2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C4 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G3 ) ) ) ) )] :
% 3.25/1.78        ( ! [A4: A,B7: B,C: C4,D2: D,E2: E,F5: F4,G4: G3] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C4 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G3 ) ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C4 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G3 ) ) ) ) @ B7 @ ( product_Pair @ C4 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G3 ) ) ) @ C @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G3 ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F4 @ G3 ) @ E2 @ ( product_Pair @ F4 @ G3 @ F5 @ G4 ) ) ) ) ) ) )
% 3.25/1.78       => ( P @ X2 ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_160_prod__induct6,axiom,
% 3.25/1.78      ! [F4: $tType,E: $tType,D: $tType,C4: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C4 @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) ) ) ) > $o,X2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C4 @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) ) )] :
% 3.25/1.78        ( ! [A4: A,B7: B,C: C4,D2: D,E2: E,F5: F4] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C4 @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C4 @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) ) @ B7 @ ( product_Pair @ C4 @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) @ C @ ( product_Pair @ D @ ( product_prod @ E @ F4 ) @ D2 @ ( product_Pair @ E @ F4 @ E2 @ F5 ) ) ) ) ) )
% 3.25/1.78       => ( P @ X2 ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_161_prod__induct5,axiom,
% 3.25/1.78      ! [E: $tType,D: $tType,C4: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C4 @ ( product_prod @ D @ E ) ) ) ) > $o,X2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C4 @ ( product_prod @ D @ E ) ) )] :
% 3.25/1.78        ( ! [A4: A,B7: B,C: C4,D2: D,E2: E] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C4 @ ( product_prod @ D @ E ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C4 @ ( product_prod @ D @ E ) ) @ B7 @ ( product_Pair @ C4 @ ( product_prod @ D @ E ) @ C @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) )
% 3.25/1.78       => ( P @ X2 ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_162_prod__induct4,axiom,
% 3.25/1.78      ! [D: $tType,C4: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C4 @ D ) ) ) > $o,X2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C4 @ D ) )] :
% 3.25/1.78        ( ! [A4: A,B7: B,C: C4,D2: D] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C4 @ D ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C4 @ D ) @ B7 @ ( product_Pair @ C4 @ D @ C @ D2 ) ) ) )
% 3.25/1.78       => ( P @ X2 ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_163_prod__induct3,axiom,
% 3.25/1.78      ! [C4: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ C4 ) ) > $o,X2: product_prod @ A @ ( product_prod @ B @ C4 )] :
% 3.25/1.78        ( ! [A4: A,B7: B,C: C4] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ C4 ) @ A4 @ ( product_Pair @ B @ C4 @ B7 @ C ) ) )
% 3.25/1.78       => ( P @ X2 ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_164_prod__cases7,axiom,
% 3.25/1.78      ! [A: $tType,B: $tType,C4: $tType,D: $tType,E: $tType,F4: $tType,G3: $tType,Y2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C4 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G3 ) ) ) ) )] :
% 3.25/1.78        ~ ! [A4: A,B7: B,C: C4,D2: D,E2: E,F5: F4,G4: G3] :
% 3.25/1.78            ( Y2
% 3.25/1.78           != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C4 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G3 ) ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C4 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G3 ) ) ) ) @ B7 @ ( product_Pair @ C4 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G3 ) ) ) @ C @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G3 ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F4 @ G3 ) @ E2 @ ( product_Pair @ F4 @ G3 @ F5 @ G4 ) ) ) ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_165_prod__cases6,axiom,
% 3.25/1.78      ! [A: $tType,B: $tType,C4: $tType,D: $tType,E: $tType,F4: $tType,Y2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C4 @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) ) )] :
% 3.25/1.78        ~ ! [A4: A,B7: B,C: C4,D2: D,E2: E,F5: F4] :
% 3.25/1.78            ( Y2
% 3.25/1.78           != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C4 @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C4 @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) ) @ B7 @ ( product_Pair @ C4 @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) @ C @ ( product_Pair @ D @ ( product_prod @ E @ F4 ) @ D2 @ ( product_Pair @ E @ F4 @ E2 @ F5 ) ) ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_166_prod__cases5,axiom,
% 3.25/1.78      ! [A: $tType,B: $tType,C4: $tType,D: $tType,E: $tType,Y2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C4 @ ( product_prod @ D @ E ) ) )] :
% 3.25/1.78        ~ ! [A4: A,B7: B,C: C4,D2: D,E2: E] :
% 3.25/1.78            ( Y2
% 3.25/1.78           != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C4 @ ( product_prod @ D @ E ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C4 @ ( product_prod @ D @ E ) ) @ B7 @ ( product_Pair @ C4 @ ( product_prod @ D @ E ) @ C @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_167_prod__cases4,axiom,
% 3.25/1.78      ! [A: $tType,B: $tType,C4: $tType,D: $tType,Y2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C4 @ D ) )] :
% 3.25/1.78        ~ ! [A4: A,B7: B,C: C4,D2: D] :
% 3.25/1.78            ( Y2
% 3.25/1.78           != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C4 @ D ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C4 @ D ) @ B7 @ ( product_Pair @ C4 @ D @ C @ D2 ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_168_prod__cases3,axiom,
% 3.25/1.78      ! [A: $tType,B: $tType,C4: $tType,Y2: product_prod @ A @ ( product_prod @ B @ C4 )] :
% 3.25/1.78        ~ ! [A4: A,B7: B,C: C4] :
% 3.25/1.78            ( Y2
% 3.25/1.78           != ( product_Pair @ A @ ( product_prod @ B @ C4 ) @ A4 @ ( product_Pair @ B @ C4 @ B7 @ C ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_169_Pair__inject,axiom,
% 3.25/1.78      ! [A: $tType,B: $tType,A2: A,B2: B,A7: A,B6: B] :
% 3.25/1.78        ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 3.25/1.78          = ( product_Pair @ A @ B @ A7 @ B6 ) )
% 3.25/1.78       => ~ ( ( A2 = A7 )
% 3.25/1.78           => ( B2 != B6 ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_170_prod__cases,axiom,
% 3.25/1.78      ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,P8: product_prod @ A @ B] :
% 3.25/1.78        ( ! [A4: A,B7: B] : ( P @ ( product_Pair @ A @ B @ A4 @ B7 ) )
% 3.25/1.78       => ( P @ P8 ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_171_surj__pair,axiom,
% 3.25/1.78      ! [A: $tType,B: $tType,P8: product_prod @ A @ B] :
% 3.25/1.78      ? [X5: A,Y: B] :
% 3.25/1.78        ( P8
% 3.25/1.78        = ( product_Pair @ A @ B @ X5 @ Y ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_172_resCasesB_H,axiom,
% 3.25/1.78      ! [X6: name,P: pi,A2: late_subject,Y6: name,P2: pi] :
% 3.25/1.78        ( ( late_transitions @ ( res @ X6 @ P ) @ ( late_BoundR @ A2 @ Y6 @ P2 ) )
% 3.25/1.78       => ( ! [P4: pi,A4: name,B7: name] :
% 3.25/1.78              ( ( ( res @ X6 @ P )
% 3.25/1.78                = ( res @ B7 @ P4 ) )
% 3.25/1.78             => ! [P3: pi] :
% 3.25/1.78                  ( ( ( late_BoundR @ A2 @ Y6 @ P2 )
% 3.25/1.78                    = ( late_BoundR @ ( late_BoundOutputS @ A4 ) @ B7 @ P3 ) )
% 3.25/1.78                 => ( ( late_transitions @ P4 @ ( late_FreeR @ ( late_OutputR @ A4 @ B7 ) @ P3 ) )
% 3.25/1.78                   => ( A4 = B7 ) ) ) )
% 3.25/1.78         => ~ ! [P4: pi,A4: late_subject,X5: name,P3: pi,Y: name] :
% 3.25/1.78                ( ( ( res @ X6 @ P )
% 3.25/1.78                  = ( res @ Y @ P4 ) )
% 3.25/1.78               => ( ( ( late_BoundR @ A2 @ Y6 @ P2 )
% 3.25/1.78                    = ( late_BoundR @ A4 @ X5 @ ( res @ Y @ P3 ) ) )
% 3.25/1.78                 => ( ( late_transitions @ P4 @ ( late_BoundR @ A4 @ X5 @ P3 ) )
% 3.25/1.78                   => ( ( fresh @ name @ late_subject @ Y @ A4 )
% 3.25/1.78                     => ( ( Y != X5 )
% 3.25/1.78                       => ( ( fresh @ name @ pi @ X5 @ P4 )
% 3.25/1.78                         => ~ ( fresh @ name @ late_subject @ X5 @ A4 ) ) ) ) ) ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_173_outputCases,axiom,
% 3.25/1.78      ! [A2: name,B2: name,P: pi,Alpha: late_freeRes,P2: pi,Prop: late_freeRes > pi > $o] :
% 3.25/1.78        ( ( late_transitions @ ( output @ A2 @ B2 @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 3.25/1.78       => ( ( ( Alpha
% 3.25/1.78              = ( late_OutputR @ A2 @ B2 ) )
% 3.25/1.78           => ( ( P = P2 )
% 3.25/1.78             => ( Prop @ ( late_OutputR @ A2 @ B2 ) @ P ) ) )
% 3.25/1.78         => ( Prop @ Alpha @ P2 ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_174_outputCases_H,axiom,
% 3.25/1.78      ! [A2: name,B2: name,P: pi,Rs: late_residual] :
% 3.25/1.78        ( ( late_transitions @ ( output @ A2 @ B2 @ P ) @ Rs )
% 3.25/1.78       => ~ ! [A4: name,B7: name,P4: pi] :
% 3.25/1.78              ( ( ( A2 = A4 )
% 3.25/1.78                & ( B2 = B7 )
% 3.25/1.78                & ( P = P4 ) )
% 3.25/1.78             => ( Rs
% 3.25/1.78               != ( late_FreeR @ ( late_OutputR @ A4 @ B7 ) @ P4 ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_175_outputIneqTrans,axiom,
% 3.25/1.78      ! [A2: name,B2: name,P: pi,C2: name,D3: name,P2: pi] :
% 3.25/1.78        ( ( late_transitions @ ( output @ A2 @ B2 @ P ) @ ( late_FreeR @ ( late_OutputR @ C2 @ D3 ) @ P2 ) )
% 3.25/1.78       => ~ ( ( A2 != C2 )
% 3.25/1.78            | ( B2 != D3 ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_176_Output,axiom,
% 3.25/1.78      ! [A2: name,B2: name,P: pi] : ( late_transitions @ ( output @ A2 @ B2 @ P ) @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_177_sumIdempRight,axiom,
% 3.25/1.78      ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi] :
% 3.25/1.78        ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 3.25/1.78       => ( strong743114133lation @ ( sum @ P @ P ) @ Rel @ P ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_178_sumAssocRight,axiom,
% 3.25/1.78      ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi,Q: pi,R: pi] :
% 3.25/1.78        ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 3.25/1.78       => ( strong743114133lation @ ( sum @ P @ ( sum @ Q @ R ) ) @ Rel @ ( sum @ ( sum @ P @ Q ) @ R ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_179_sumIdempLeft,axiom,
% 3.25/1.78      ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi] :
% 3.25/1.78        ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 3.25/1.78       => ( strong743114133lation @ P @ Rel @ ( sum @ P @ P ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_180_sumAssocLeft,axiom,
% 3.25/1.78      ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi,Q: pi,R: pi] :
% 3.25/1.78        ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 3.25/1.78       => ( strong743114133lation @ ( sum @ ( sum @ P @ Q ) @ R ) @ Rel @ ( sum @ P @ ( sum @ Q @ R ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_181_sumSym,axiom,
% 3.25/1.78      ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi,Q: pi] :
% 3.25/1.78        ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 3.25/1.78       => ( strong743114133lation @ ( sum @ P @ Q ) @ Rel @ ( sum @ Q @ P ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_182_inputBoundOutputTrans,axiom,
% 3.25/1.78      ! [A2: name,X2: name,P: pi,B2: name,Y2: name,P2: pi] :
% 3.25/1.78        ~ ( late_transitions @ ( input @ A2 @ X2 @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ B2 ) @ Y2 @ P2 ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_183_resCases_H,axiom,
% 3.25/1.78      ! [X2: name,P: pi,Rs: late_residual] :
% 3.25/1.78        ( ( late_transitions @ ( res @ X2 @ P ) @ Rs )
% 3.25/1.78       => ( ! [P4: pi,A4: name,B7: name] :
% 3.25/1.78              ( ( ( res @ X2 @ P )
% 3.25/1.78                = ( res @ B7 @ P4 ) )
% 3.25/1.78             => ! [P3: pi] :
% 3.25/1.78                  ( ( Rs
% 3.25/1.78                    = ( late_BoundR @ ( late_BoundOutputS @ A4 ) @ B7 @ P3 ) )
% 3.25/1.78                 => ( ( late_transitions @ P4 @ ( late_FreeR @ ( late_OutputR @ A4 @ B7 ) @ P3 ) )
% 3.25/1.78                   => ( A4 = B7 ) ) ) )
% 3.25/1.78         => ( ! [P4: pi,A4: late_subject,X5: name,P3: pi,Y: name] :
% 3.25/1.78                ( ( ( res @ X2 @ P )
% 3.25/1.78                  = ( res @ Y @ P4 ) )
% 3.25/1.78               => ( ( Rs
% 3.25/1.78                    = ( late_BoundR @ A4 @ X5 @ ( res @ Y @ P3 ) ) )
% 3.25/1.78                 => ( ( late_transitions @ P4 @ ( late_BoundR @ A4 @ X5 @ P3 ) )
% 3.25/1.78                   => ( ( fresh @ name @ late_subject @ Y @ A4 )
% 3.25/1.78                     => ( ( Y != X5 )
% 3.25/1.78                       => ( ( fresh @ name @ pi @ X5 @ P4 )
% 3.25/1.78                         => ~ ( fresh @ name @ late_subject @ X5 @ A4 ) ) ) ) ) ) )
% 3.25/1.78           => ~ ! [P4: pi,Alpha2: late_freeRes,P3: pi,Y: name] :
% 3.25/1.78                  ( ( ( res @ X2 @ P )
% 3.25/1.78                    = ( res @ Y @ P4 ) )
% 3.25/1.78                 => ( ( Rs
% 3.25/1.78                      = ( late_FreeR @ Alpha2 @ ( res @ Y @ P3 ) ) )
% 3.25/1.78                   => ( ( late_transitions @ P4 @ ( late_FreeR @ Alpha2 @ P3 ) )
% 3.25/1.78                     => ~ ( fresh @ name @ late_freeRes @ Y @ Alpha2 ) ) ) ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_184_resOutputOutputTrans,axiom,
% 3.25/1.78      ! [X2: name,A2: name,P: pi,B2: name,Y2: name,P2: pi] :
% 3.25/1.78        ~ ( late_transitions @ ( res @ X2 @ ( output @ A2 @ X2 @ P ) ) @ ( late_FreeR @ ( late_OutputR @ B2 @ Y2 ) @ P2 ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_185_sumZeroLeft,axiom,
% 3.25/1.78      ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi] :
% 3.25/1.78        ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 3.25/1.78       => ( strong743114133lation @ ( sum @ P @ piNil ) @ Rel @ P ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_186_sumZeroRight,axiom,
% 3.25/1.78      ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi] :
% 3.25/1.78        ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 3.25/1.78       => ( strong743114133lation @ P @ Rel @ ( sum @ P @ piNil ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_187_resInputBoundOutputTrans,axiom,
% 3.25/1.78      ! [X2: name,A2: name,Y2: name,P: pi,B2: name,Z: name,P2: pi] :
% 3.25/1.78        ~ ( late_transitions @ ( res @ X2 @ ( input @ A2 @ Y2 @ P ) ) @ ( late_BoundR @ ( late_BoundOutputS @ B2 ) @ Z @ P2 ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_188_sumResRight,axiom,
% 3.25/1.78      ! [Rel: set @ ( product_prod @ pi @ pi ),X2: name,P: pi,Q: pi] :
% 3.25/1.78        ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 3.25/1.78       => ( ( eqvt @ pi @ Rel )
% 3.25/1.78         => ( strong743114133lation @ ( res @ X2 @ ( sum @ P @ Q ) ) @ Rel @ ( sum @ ( res @ X2 @ P ) @ ( res @ X2 @ Q ) ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_189_old_Oprod_Orec,axiom,
% 3.25/1.78      ! [A: $tType,T: $tType,B: $tType,F1: A > B > T,A2: A,B2: B] :
% 3.25/1.78        ( ( product_rec_prod @ A @ B @ T @ F1 @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 3.25/1.78        = ( F1 @ A2 @ B2 ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_190_Late__Semantics1_Osubject_Oinject_I2_J,axiom,
% 3.25/1.78      ! [X22: name,Y22: name] :
% 3.25/1.78        ( ( ( late_BoundOutputS @ X22 )
% 3.25/1.78          = ( late_BoundOutputS @ Y22 ) )
% 3.25/1.78        = ( X22 = Y22 ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_191_Late__Semantics1_OfreeRes_Oinject,axiom,
% 3.25/1.78      ! [X11: name,X12: name,Y11: name,Y12: name] :
% 3.25/1.78        ( ( ( late_OutputR @ X11 @ X12 )
% 3.25/1.78          = ( late_OutputR @ Y11 @ Y12 ) )
% 3.25/1.78        = ( ( X11 = Y11 )
% 3.25/1.78          & ( X12 = Y12 ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_192_Late__Semantics1_OfreeRes_Odistinct_I1_J,axiom,
% 3.25/1.78      ! [X11: name,X12: name] :
% 3.25/1.78        ( ( late_OutputR @ X11 @ X12 )
% 3.25/1.78       != late_TauR ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_193_freeRes_Oexhaust,axiom,
% 3.25/1.78      ! [Y2: late_freeRes] :
% 3.25/1.78        ( ! [X112: name,X122: name] :
% 3.25/1.78            ( Y2
% 3.25/1.78           != ( late_OutputR @ X112 @ X122 ) )
% 3.25/1.78       => ( Y2 = late_TauR ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_194_resOutputInputTrans,axiom,
% 3.25/1.78      ! [X2: name,A2: name,B2: name,P: pi,C2: name,Y2: name,P2: pi] :
% 3.25/1.78        ~ ( late_transitions @ ( res @ X2 @ ( output @ A2 @ B2 @ P ) ) @ ( late_BoundR @ ( late_InputS @ C2 ) @ Y2 @ P2 ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_195_freeRes_Orecs_I2_J,axiom,
% 3.25/1.78      ! [T: $tType,P: T > $o,F1: name > name > T,F22: T] :
% 3.25/1.78        ( ! [X13: name,X23: name] : ( P @ ( F1 @ X13 @ X23 ) )
% 3.25/1.78       => ( ( P @ F22 )
% 3.25/1.78         => ( ( late_freeRes_rec @ T @ F1 @ F22 @ late_TauR )
% 3.25/1.78            = F22 ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_196_Late__Semantics1_Osubject_Oinject_I1_J,axiom,
% 3.25/1.78      ! [X1: name,Y1: name] :
% 3.25/1.78        ( ( ( late_InputS @ X1 )
% 3.25/1.78          = ( late_InputS @ Y1 ) )
% 3.25/1.78        = ( X1 = Y1 ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_197_subject_Ofresh_I1_J,axiom,
% 3.25/1.78      ! [A2: name,X1: name] :
% 3.25/1.78        ( ( fresh @ name @ late_subject @ A2 @ ( late_InputS @ X1 ) )
% 3.25/1.78        = ( fresh @ name @ name @ A2 @ X1 ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_198_subject_Oexhaust,axiom,
% 3.25/1.78      ! [Y2: late_subject] :
% 3.25/1.78        ( ! [X13: name] :
% 3.25/1.78            ( Y2
% 3.25/1.78           != ( late_InputS @ X13 ) )
% 3.25/1.78       => ~ ! [X23: name] :
% 3.25/1.78              ( Y2
% 3.25/1.78             != ( late_BoundOutputS @ X23 ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_199_Late__Semantics1_Osubject_Odistinct_I1_J,axiom,
% 3.25/1.78      ! [X1: name,X22: name] :
% 3.25/1.78        ( ( late_InputS @ X1 )
% 3.25/1.78       != ( late_BoundOutputS @ X22 ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_200_subject_Ostrong__inducts,axiom,
% 3.25/1.78      ! [A: $tType,P: A > late_subject > $o,Z: A,Subject: late_subject] :
% 3.25/1.78        ( ! [Name4: name,Z2: A] : ( P @ Z2 @ ( late_InputS @ Name4 ) )
% 3.25/1.78       => ( ! [Name4: name,Z2: A] : ( P @ Z2 @ ( late_BoundOutputS @ Name4 ) )
% 3.25/1.78         => ( P @ Z @ Subject ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_201_subject_Ostrong__induct_H,axiom,
% 3.25/1.78      ! [N: $tType,P: N > late_subject > $o,Z: N,Subject: late_subject] :
% 3.25/1.78        ( ! [Name4: name,Z2: N] : ( P @ Z2 @ ( late_InputS @ Name4 ) )
% 3.25/1.78       => ( ! [Name4: name,Z2: N] : ( P @ Z2 @ ( late_BoundOutputS @ Name4 ) )
% 3.25/1.78         => ( P @ Z @ Subject ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_202_subject_Oinducts,axiom,
% 3.25/1.78      ! [P: late_subject > $o,Subject: late_subject] :
% 3.25/1.78        ( ! [Name4: name] : ( P @ ( late_InputS @ Name4 ) )
% 3.25/1.78       => ( ! [Name4: name] : ( P @ ( late_BoundOutputS @ Name4 ) )
% 3.25/1.78         => ( P @ Subject ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_203_Late__Semantics_Osubject_Odistinct_I1_J,axiom,
% 3.25/1.78      ! [Name3: name,Name: name] :
% 3.25/1.78        ( ( late_InputS @ Name3 )
% 3.25/1.78       != ( late_BoundOutputS @ Name ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_204_transitions_OInput,axiom,
% 3.25/1.78      ! [X2: name,A2: name,P: pi] :
% 3.25/1.78        ( ( X2 != A2 )
% 3.25/1.78       => ( late_transitions @ ( input @ A2 @ X2 @ P ) @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_205_Late__Semantics_OInput,axiom,
% 3.25/1.78      ! [A2: name,X2: name,P: pi] : ( late_transitions @ ( input @ A2 @ X2 @ P ) @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_206_freeRes_Orecs_I1_J,axiom,
% 3.25/1.78      ! [T: $tType,P: T > $o,F1: name > name > T,F22: T,Name12: name,Name22: name] :
% 3.25/1.78        ( ! [X13: name,X23: name] : ( P @ ( F1 @ X13 @ X23 ) )
% 3.25/1.78       => ( ( P @ F22 )
% 3.25/1.78         => ( ( late_freeRes_rec @ T @ F1 @ F22 @ ( late_OutputR @ Name12 @ Name22 ) )
% 3.25/1.78            = ( F1 @ Name12 @ Name22 ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_207_Late__Semantics_OClose1,axiom,
% 3.25/1.78      ! [P: pi,A2: name,X2: name,P2: pi,Q: pi,Y2: name,Q2: pi] :
% 3.25/1.78        ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P2 ) )
% 3.25/1.78       => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y2 @ Q2 ) )
% 3.25/1.78         => ( ( fresh @ name @ pi @ Y2 @ P )
% 3.25/1.78           => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y2 @ ( par @ ( subs @ P2 @ X2 @ Y2 ) @ Q2 ) ) ) ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_208_Late__Semantics_OClose2,axiom,
% 3.25/1.78      ! [P: pi,A2: name,Y2: name,P2: pi,Q: pi,X2: name,Q2: pi] :
% 3.25/1.78        ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y2 @ P2 ) )
% 3.25/1.78       => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ Q2 ) )
% 3.25/1.78         => ( ( fresh @ name @ pi @ Y2 @ Q )
% 3.25/1.78           => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y2 @ ( par @ P2 @ ( subs @ Q2 @ X2 @ Y2 ) ) ) ) ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_209_subst__identity,axiom,
% 3.25/1.78      ! [P: pi,A2: name] :
% 3.25/1.78        ( ( subs @ P @ A2 @ A2 )
% 3.25/1.78        = P ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_210_simps_I9_J,axiom,
% 3.25/1.78      ! [X2: name,C2: name,D3: name,P: pi] :
% 3.25/1.78        ( ( X2 != C2 )
% 3.25/1.78       => ( ( X2 != D3 )
% 3.25/1.78         => ( ( subs @ ( res @ X2 @ P ) @ C2 @ D3 )
% 3.25/1.78            = ( res @ X2 @ ( subs @ P @ C2 @ D3 ) ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_211_simps_I8_J,axiom,
% 3.25/1.78      ! [P: pi,Q: pi,C2: name,D3: name] :
% 3.25/1.78        ( ( subs @ ( par @ P @ Q ) @ C2 @ D3 )
% 3.25/1.78        = ( par @ ( subs @ P @ C2 @ D3 ) @ ( subs @ Q @ C2 @ D3 ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_212_substTrans,axiom,
% 3.25/1.78      ! [B2: name,P: pi,A2: name,C2: name] :
% 3.25/1.78        ( ( fresh @ name @ pi @ B2 @ P )
% 3.25/1.78       => ( ( subs @ ( subs @ P @ A2 @ B2 ) @ B2 @ C2 )
% 3.25/1.78          = ( subs @ P @ A2 @ C2 ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_213_simps_I7_J,axiom,
% 3.25/1.78      ! [P: pi,Q: pi,C2: name,D3: name] :
% 3.25/1.78        ( ( subs @ ( sum @ P @ Q ) @ C2 @ D3 )
% 3.25/1.78        = ( sum @ ( subs @ P @ C2 @ D3 ) @ ( subs @ Q @ C2 @ D3 ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_214_simps_I1_J,axiom,
% 3.25/1.78      ! [C2: name,D3: name] :
% 3.25/1.78        ( ( subs @ piNil @ C2 @ D3 )
% 3.25/1.78        = piNil ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_215_fresh__fact2,axiom,
% 3.25/1.78      ! [A2: name,B2: name,P: pi] :
% 3.25/1.78        ( ( A2 != B2 )
% 3.25/1.78       => ( fresh @ name @ pi @ A2 @ ( subs @ P @ A2 @ B2 ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_216_fresh__fact1,axiom,
% 3.25/1.78      ! [A2: name,P: pi,C2: name,B2: name] :
% 3.25/1.78        ( ( fresh @ name @ pi @ A2 @ P )
% 3.25/1.78       => ( ( A2 != C2 )
% 3.25/1.78         => ( fresh @ name @ pi @ A2 @ ( subs @ P @ B2 @ C2 ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_217_forget,axiom,
% 3.25/1.78      ! [A2: name,P: pi,B2: name] :
% 3.25/1.78        ( ( fresh @ name @ pi @ A2 @ P )
% 3.25/1.78       => ( ( subs @ P @ A2 @ B2 )
% 3.25/1.78          = P ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_218_substRes2,axiom,
% 3.25/1.78      ! [B2: name,P: pi,A2: name] :
% 3.25/1.78        ( ( fresh @ name @ pi @ B2 @ P )
% 3.25/1.78       => ( ( res @ A2 @ P )
% 3.25/1.78          = ( res @ B2 @ ( subs @ P @ A2 @ B2 ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_219_Agent_OsubstRes3,axiom,
% 3.25/1.78      ! [B2: name,P: pi,A2: name] :
% 3.25/1.78        ( ( fresh @ name @ pi @ B2 @ P )
% 3.25/1.78       => ( ( subs @ ( res @ A2 @ P ) @ A2 @ B2 )
% 3.25/1.78          = ( res @ B2 @ ( subs @ P @ A2 @ B2 ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_220_Late__Semantics_OComm2,axiom,
% 3.25/1.78      ! [P: pi,A2: name,B2: name,P2: pi,Q: pi,X2: name,Q2: pi] :
% 3.25/1.78        ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P2 ) )
% 3.25/1.78       => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ Q2 ) )
% 3.25/1.78         => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P2 @ ( subs @ Q2 @ X2 @ B2 ) ) ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_221_Late__Semantics_OComm1,axiom,
% 3.25/1.78      ! [P: pi,A2: name,X2: name,P2: pi,Q: pi,B2: name,Q2: pi] :
% 3.25/1.78        ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P2 ) )
% 3.25/1.78       => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ Q2 ) )
% 3.25/1.78         => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P2 @ X2 @ B2 ) @ Q2 ) ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_222_transitions_OComm1,axiom,
% 3.25/1.78      ! [P: pi,A2: name,X2: name,P2: pi,Q: pi,B2: name,Q2: pi] :
% 3.25/1.78        ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P2 ) )
% 3.25/1.78       => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ Q2 ) )
% 3.25/1.78         => ( ( fresh @ name @ pi @ X2 @ P )
% 3.25/1.78           => ( ( fresh @ name @ pi @ X2 @ Q )
% 3.25/1.78             => ( ( X2 != A2 )
% 3.25/1.78               => ( ( X2 != B2 )
% 3.25/1.78                 => ( ( fresh @ name @ pi @ X2 @ Q2 )
% 3.25/1.78                   => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P2 @ X2 @ B2 ) @ Q2 ) ) ) ) ) ) ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_223_transitions_OComm2,axiom,
% 3.25/1.78      ! [P: pi,A2: name,B2: name,P2: pi,Q: pi,X2: name,Q2: pi] :
% 3.25/1.78        ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P2 ) )
% 3.25/1.78       => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ Q2 ) )
% 3.25/1.78         => ( ( fresh @ name @ pi @ X2 @ P )
% 3.25/1.78           => ( ( fresh @ name @ pi @ X2 @ Q )
% 3.25/1.78             => ( ( X2 != A2 )
% 3.25/1.78               => ( ( X2 != B2 )
% 3.25/1.78                 => ( ( fresh @ name @ pi @ X2 @ P2 )
% 3.25/1.78                   => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P2 @ ( subs @ Q2 @ X2 @ B2 ) ) ) ) ) ) ) ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_224_transitions_OClose2,axiom,
% 3.25/1.78      ! [P: pi,A2: name,Y2: name,P2: pi,Q: pi,X2: name,Q2: pi] :
% 3.25/1.78        ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y2 @ P2 ) )
% 3.25/1.78       => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ Q2 ) )
% 3.25/1.78         => ( ( fresh @ name @ pi @ X2 @ P )
% 3.25/1.78           => ( ( fresh @ name @ pi @ X2 @ Q )
% 3.25/1.78             => ( ( fresh @ name @ pi @ Y2 @ P )
% 3.25/1.78               => ( ( fresh @ name @ pi @ Y2 @ Q )
% 3.25/1.78                 => ( ( X2 != A2 )
% 3.25/1.78                   => ( ( fresh @ name @ pi @ X2 @ P2 )
% 3.25/1.78                     => ( ( Y2 != A2 )
% 3.25/1.78                       => ( ( fresh @ name @ pi @ Y2 @ Q2 )
% 3.25/1.78                         => ( ( X2 != Y2 )
% 3.25/1.78                           => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y2 @ ( par @ P2 @ ( subs @ Q2 @ X2 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_225_transitions_OClose1,axiom,
% 3.25/1.78      ! [P: pi,A2: name,X2: name,P2: pi,Q: pi,Y2: name,Q2: pi] :
% 3.25/1.78        ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P2 ) )
% 3.25/1.78       => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y2 @ Q2 ) )
% 3.25/1.78         => ( ( fresh @ name @ pi @ X2 @ P )
% 3.25/1.78           => ( ( fresh @ name @ pi @ X2 @ Q )
% 3.25/1.78             => ( ( fresh @ name @ pi @ Y2 @ P )
% 3.25/1.78               => ( ( fresh @ name @ pi @ Y2 @ Q )
% 3.25/1.78                 => ( ( X2 != A2 )
% 3.25/1.78                   => ( ( fresh @ name @ pi @ X2 @ Q2 )
% 3.25/1.78                     => ( ( Y2 != A2 )
% 3.25/1.78                       => ( ( fresh @ name @ pi @ Y2 @ P2 )
% 3.25/1.78                         => ( ( X2 != Y2 )
% 3.25/1.78                           => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y2 @ ( par @ ( subs @ P2 @ X2 @ Y2 ) @ Q2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_226_subject_Orecs_I2_J,axiom,
% 3.25/1.78      ! [T: $tType,P: T > $o,F1: name > T,F22: name > T,Name3: name] :
% 3.25/1.78        ( ! [X13: name] : ( P @ ( F1 @ X13 ) )
% 3.25/1.78       => ( ! [X13: name] : ( P @ ( F22 @ X13 ) )
% 3.25/1.78         => ( ( late_subject_rec @ T @ F1 @ F22 @ ( late_BoundOutputS @ Name3 ) )
% 3.25/1.78            = ( F22 @ Name3 ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_227_subject_Orecs_I1_J,axiom,
% 3.25/1.78      ! [T: $tType,P: T > $o,F1: name > T,F22: name > T,Name3: name] :
% 3.25/1.78        ( ! [X13: name] : ( P @ ( F1 @ X13 ) )
% 3.25/1.78       => ( ! [X13: name] : ( P @ ( F22 @ X13 ) )
% 3.25/1.78         => ( ( late_subject_rec @ T @ F1 @ F22 @ ( late_InputS @ Name3 ) )
% 3.25/1.78            = ( F1 @ Name3 ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_228_resTauOutputTrans,axiom,
% 3.25/1.78      ! [X2: name,P: pi,A2: name,B2: name,P2: pi] :
% 3.25/1.78        ~ ( late_transitions @ ( res @ X2 @ ( tau @ P ) ) @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P2 ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_229_residual_Ofresh_I1_J,axiom,
% 3.25/1.78      ! [A2: name,X3: late_subject,X1: name,X22: pi] :
% 3.25/1.78        ( ( fresh @ name @ late_residual @ A2 @ ( late_BoundR @ X3 @ X1 @ X22 ) )
% 3.25/1.78        = ( ( fresh @ name @ late_subject @ A2 @ X3 )
% 3.25/1.78          & ( fresh @ name @ ( name > ( noption @ pi ) ) @ A2 @ ( abs_fun @ name @ pi @ X1 @ X22 ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_230_pi_Ofresh_I3_J,axiom,
% 3.25/1.78      ! [A2: name,X1: pi] :
% 3.25/1.78        ( ( fresh @ name @ pi @ A2 @ ( tau @ X1 ) )
% 3.25/1.78        = ( fresh @ name @ pi @ A2 @ X1 ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_231_simps_I2_J,axiom,
% 3.25/1.78      ! [P: pi,C2: name,D3: name] :
% 3.25/1.78        ( ( subs @ ( tau @ P ) @ C2 @ D3 )
% 3.25/1.78        = ( tau @ ( subs @ P @ C2 @ D3 ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_232_pi_Ofresh_I9_J,axiom,
% 3.25/1.78      ! [A2: name,X1: name,X22: pi] :
% 3.25/1.78        ( ( fresh @ name @ pi @ A2 @ ( res @ X1 @ X22 ) )
% 3.25/1.78        = ( fresh @ name @ ( name > ( noption @ pi ) ) @ A2 @ ( abs_fun @ name @ pi @ X1 @ X22 ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_233_pi_Ofresh_I4_J,axiom,
% 3.25/1.78      ! [A2: name,X3: name,X1: name,X22: pi] :
% 3.25/1.78        ( ( fresh @ name @ pi @ A2 @ ( input @ X3 @ X1 @ X22 ) )
% 3.25/1.78        = ( ( fresh @ name @ name @ A2 @ X3 )
% 3.25/1.78          & ( fresh @ name @ ( name > ( noption @ pi ) ) @ A2 @ ( abs_fun @ name @ pi @ X1 @ X22 ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_234_tauBoundTrans,axiom,
% 3.25/1.78      ! [P: pi,A2: late_subject,X2: name,P2: pi] :
% 3.25/1.78        ~ ( late_transitions @ ( tau @ P ) @ ( late_BoundR @ A2 @ X2 @ P2 ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_235_nilSim_I1_J,axiom,
% 3.25/1.78      ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi] :
% 3.25/1.78        ~ ( strong743114133lation @ piNil @ Rel @ ( tau @ P ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_236_pi_Oinject_I8_J,axiom,
% 3.25/1.78      ! [X1: name,X22: pi,Y1: name,Y22: pi] :
% 3.25/1.78        ( ( ( res @ X1 @ X22 )
% 3.25/1.78          = ( res @ Y1 @ Y22 ) )
% 3.25/1.78        = ( ( abs_fun @ name @ pi @ X1 @ X22 )
% 3.25/1.78          = ( abs_fun @ name @ pi @ Y1 @ Y22 ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_237_residual_Oinject_I1_J,axiom,
% 3.25/1.78      ! [X3: late_subject,X1: name,X22: pi,Y3: late_subject,Y1: name,Y22: pi] :
% 3.25/1.78        ( ( ( late_BoundR @ X3 @ X1 @ X22 )
% 3.25/1.78          = ( late_BoundR @ Y3 @ Y1 @ Y22 ) )
% 3.25/1.78        = ( ( X3 = Y3 )
% 3.25/1.78          & ( ( abs_fun @ name @ pi @ X1 @ X22 )
% 3.25/1.78            = ( abs_fun @ name @ pi @ Y1 @ Y22 ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_238_pi_Oinject_I2_J,axiom,
% 3.25/1.78      ! [X1: pi,Y1: pi] :
% 3.25/1.78        ( ( ( tau @ X1 )
% 3.25/1.78          = ( tau @ Y1 ) )
% 3.25/1.78        = ( X1 = Y1 ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_239_abs__fun__eq1,axiom,
% 3.25/1.78      ! [X: $tType,A: $tType,A2: X,X2: A,Y2: A] :
% 3.25/1.78        ( ( ( abs_fun @ X @ A @ A2 @ X2 )
% 3.25/1.78          = ( abs_fun @ X @ A @ A2 @ Y2 ) )
% 3.25/1.78        = ( X2 = Y2 ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_240_pi_Odistinct_I19_J,axiom,
% 3.25/1.78      ! [Name12: name,Name22: name,Pi3: pi,Pi: pi] :
% 3.25/1.78        ( ( output @ Name12 @ Name22 @ Pi3 )
% 3.25/1.78       != ( tau @ Pi ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_241_pi_Odistinct_I3_J,axiom,
% 3.25/1.78      ! [Pi: pi] :
% 3.25/1.78        ( piNil
% 3.25/1.78       != ( tau @ Pi ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_242_pi_Odistinct_I35_J,axiom,
% 3.25/1.78      ! [Pi3: pi,Name1: name,Name2: name,Pi: pi] :
% 3.25/1.78        ( ( tau @ Pi3 )
% 3.25/1.78       != ( input @ Name1 @ Name2 @ Pi ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_243_pi_Odistinct_I41_J,axiom,
% 3.25/1.78      ! [Pi3: pi,Pi12: pi,Pi22: pi] :
% 3.25/1.78        ( ( tau @ Pi3 )
% 3.25/1.78       != ( sum @ Pi12 @ Pi22 ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_244_pi_Odistinct_I43_J,axiom,
% 3.25/1.78      ! [Pi3: pi,Pi12: pi,Pi22: pi] :
% 3.25/1.78        ( ( tau @ Pi3 )
% 3.25/1.78       != ( par @ Pi12 @ Pi22 ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_245_pi_Odistinct_I45_J,axiom,
% 3.25/1.78      ! [Pi3: pi,Name: name,Pi: pi] :
% 3.25/1.78        ( ( tau @ Pi3 )
% 3.25/1.78       != ( res @ Name @ Pi ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_246_pi_Oinject_I3_J,axiom,
% 3.25/1.78      ! [X3: name,X1: name,X22: pi,Y3: name,Y1: name,Y22: pi] :
% 3.25/1.78        ( ( ( input @ X3 @ X1 @ X22 )
% 3.25/1.78          = ( input @ Y3 @ Y1 @ Y22 ) )
% 3.25/1.78        = ( ( X3 = Y3 )
% 3.25/1.78          & ( ( abs_fun @ name @ pi @ X1 @ X22 )
% 3.25/1.78            = ( abs_fun @ name @ pi @ Y1 @ Y22 ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_247_name__fresh__abs,axiom,
% 3.25/1.78      ! [A: $tType] :
% 3.25/1.78        ( ( fs_name @ A )
% 3.25/1.78       => ! [B2: name,A2: name,X2: A] :
% 3.25/1.78            ( ( fresh @ name @ ( name > ( noption @ A ) ) @ B2 @ ( abs_fun @ name @ A @ A2 @ X2 ) )
% 3.25/1.78            = ( ( B2 = A2 )
% 3.25/1.78              | ( fresh @ name @ A @ B2 @ X2 ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_248_abs__fresh_I1_J,axiom,
% 3.25/1.78      ! [X7: $tType] :
% 3.25/1.78        ( ( fs_name @ X7 )
% 3.25/1.78       => ! [B2: name,A2: name,X2: X7] :
% 3.25/1.78            ( ( fresh @ name @ ( name > ( noption @ X7 ) ) @ B2 @ ( abs_fun @ name @ X7 @ A2 @ X2 ) )
% 3.25/1.78            = ( ( B2 = A2 )
% 3.25/1.78              | ( fresh @ name @ X7 @ B2 @ X2 ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_249_resTauBoundTrans,axiom,
% 3.25/1.78      ! [X2: name,P: pi,A2: late_subject,Y2: name,P2: pi] :
% 3.25/1.78        ~ ( late_transitions @ ( res @ X2 @ ( tau @ P ) ) @ ( late_BoundR @ A2 @ Y2 @ P2 ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_250_tauOutputTrans,axiom,
% 3.25/1.78      ! [P: pi,A2: name,B2: name,P2: pi] :
% 3.25/1.78        ~ ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P2 ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_251_Tau,axiom,
% 3.25/1.78      ! [P: pi] : ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ late_TauR @ P ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_252_tauCases_H,axiom,
% 3.25/1.78      ! [P: pi,Rs: late_residual] :
% 3.25/1.78        ( ( late_transitions @ ( tau @ P ) @ Rs )
% 3.25/1.78       => ~ ! [P4: pi] :
% 3.25/1.78              ( ( ( tau @ P )
% 3.25/1.78                = ( tau @ P4 ) )
% 3.25/1.78             => ( Rs
% 3.25/1.78               != ( late_FreeR @ late_TauR @ P4 ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_253_tauCases,axiom,
% 3.25/1.78      ! [P: pi,Alpha: late_freeRes,P2: pi,Prop: late_freeRes > pi > $o] :
% 3.25/1.78        ( ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 3.25/1.78       => ( ( ( Alpha = late_TauR )
% 3.25/1.78           => ( ( P = P2 )
% 3.25/1.78             => ( Prop @ late_TauR @ P ) ) )
% 3.25/1.78         => ( Prop @ Alpha @ P2 ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_254_inputCases_H,axiom,
% 3.25/1.78      ! [A2: name,B2: name,P: pi,Rs: late_residual] :
% 3.25/1.78        ( ( late_transitions @ ( input @ A2 @ B2 @ P ) @ Rs )
% 3.25/1.78       => ~ ! [X5: name,A4: name,P4: pi] :
% 3.25/1.78              ( ( ( A2 = A4 )
% 3.25/1.78                & ( ( abs_fun @ name @ pi @ B2 @ P )
% 3.25/1.78                  = ( abs_fun @ name @ pi @ X5 @ P4 ) ) )
% 3.25/1.78             => ( ( Rs
% 3.25/1.78                  = ( late_BoundR @ ( late_InputS @ A4 ) @ X5 @ P4 ) )
% 3.25/1.78               => ( X5 = A4 ) ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(fact_255_simps_I3_J,axiom,
% 3.25/1.78      ! [A2: name,B2: name,P: pi,C2: name,D3: name] :
% 3.25/1.78        ( ( subs @ ( output @ A2 @ B2 @ P ) @ C2 @ D3 )
% 3.25/1.78        = ( output @ ( subst_name @ A2 @ C2 @ D3 ) @ ( subst_name @ B2 @ C2 @ D3 ) @ ( subs @ P @ C2 @ D3 ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(tcon_fun___Orderings_Opreorder,axiom,
% 3.25/1.78      ! [A8: $tType,A9: $tType] :
% 3.25/1.78        ( ( preorder @ A9 )
% 3.25/1.78       => ( preorder @ ( A8 > A9 ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(tcon_fun___Orderings_Oorder,axiom,
% 3.25/1.78      ! [A8: $tType,A9: $tType] :
% 3.25/1.78        ( ( order @ A9 )
% 3.25/1.78       => ( order @ ( A8 > A9 ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(tcon_fun___Orderings_Oord,axiom,
% 3.25/1.78      ! [A8: $tType,A9: $tType] :
% 3.25/1.78        ( ( ord @ A9 )
% 3.25/1.78       => ( ord @ ( A8 > A9 ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(tcon_Set_Oset___Orderings_Opreorder_1,axiom,
% 3.25/1.78      ! [A8: $tType] : ( preorder @ ( set @ A8 ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(tcon_Set_Oset___Orderings_Oorder_2,axiom,
% 3.25/1.78      ! [A8: $tType] : ( order @ ( set @ A8 ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(tcon_Set_Oset___Orderings_Oord_3,axiom,
% 3.25/1.78      ! [A8: $tType] : ( ord @ ( set @ A8 ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(tcon_Agent_Opi___Agent_Ofs__name,axiom,
% 3.25/1.78      fs_name @ pi ).
% 3.25/1.78  
% 3.25/1.78  thf(tcon_HOL_Obool___Orderings_Opreorder_4,axiom,
% 3.25/1.78      preorder @ $o ).
% 3.25/1.78  
% 3.25/1.78  thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 3.25/1.78      linorder @ $o ).
% 3.25/1.78  
% 3.25/1.78  thf(tcon_HOL_Obool___Orderings_Oorder_5,axiom,
% 3.25/1.78      order @ $o ).
% 3.25/1.78  
% 3.25/1.78  thf(tcon_HOL_Obool___Orderings_Oord_6,axiom,
% 3.25/1.78      ord @ $o ).
% 3.25/1.78  
% 3.25/1.78  thf(tcon_HOL_Obool___Agent_Ofs__name_7,axiom,
% 3.25/1.78      fs_name @ $o ).
% 3.25/1.78  
% 3.25/1.78  thf(tcon_Agent_Oname___Agent_Ofs__name_8,axiom,
% 3.25/1.78      fs_name @ name ).
% 3.25/1.78  
% 3.25/1.78  thf(tcon_Product__Type_Oprod___Agent_Ofs__name_9,axiom,
% 3.25/1.78      ! [A8: $tType,A9: $tType] :
% 3.25/1.78        ( ( ( fs_name @ A8 )
% 3.25/1.78          & ( fs_name @ A9 ) )
% 3.25/1.78       => ( fs_name @ ( product_prod @ A8 @ A9 ) ) ) ).
% 3.25/1.78  
% 3.25/1.78  thf(tcon_Late__Semantics_OfreeRes___Agent_Ofs__name_10,axiom,
% 3.25/1.78      fs_name @ late_freeRes ).
% 3.25/1.78  
% 3.25/1.78  thf(tcon_Late__Semantics_Osubject___Agent_Ofs__name_11,axiom,
% 3.25/1.78      fs_name @ late_subject ).
% 3.25/1.78  
% 3.25/1.78  thf(tcon_Late__Semantics_Oresidual___Agent_Ofs__name_12,axiom,
% 3.25/1.78      fs_name @ late_residual ).
% 3.25/1.78  
% 3.25/1.78  thf(conj_0,conjecture,
% 3.25/1.78      late_transitions @ ( res @ x @ ( par @ p @ q ) ) @ ( late_FreeR @ alpha @ ( res @ x @ ( par @ p2 @ q ) ) ) ).
% 3.25/1.78  ------------------------
% 3.33/1.82  % (18627)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_18468 for (2999ds/4Mi)
% 3.33/1.82  % (18630)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_18468 for (2999ds/2Mi)
% 3.33/1.82  % (18628)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_18468 for (2999ds/27Mi)
% 3.33/1.82  % (18629)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_18468 for (2999ds/2Mi)
% 3.33/1.82  % (18626)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_18468 for (2999ds/183Mi)
% 3.33/1.82  % (18631)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_18468 for (2999ds/275Mi)
% 3.33/1.82  % (18632)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_18468 for (2999ds/18Mi)
% 3.33/1.82  % (18629)Instruction limit reached!
% 3.33/1.82  % (18629)------------------------------
% 3.33/1.82  % (18629)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.33/1.82  % (18629)Termination reason: Unknown
% 3.33/1.82  % (18630)Instruction limit reached!
% 3.33/1.82  % (18630)------------------------------
% 3.33/1.82  % (18630)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.33/1.82  % (18629)Termination phase: shuffling
% 3.33/1.82  
% 3.33/1.82  % (18629)Memory used [KB]: 1407
% 3.33/1.82  % (18629)Time elapsed: 0.003 s
% 3.33/1.82  % (18629)Instructions burned: 2 (million)
% 3.33/1.82  % (18629)------------------------------
% 3.33/1.82  % (18629)------------------------------
% 3.33/1.82  % (18630)Termination reason: Unknown
% 3.33/1.82  % (18630)Termination phase: shuffling
% 3.33/1.82  
% 3.33/1.82  % (18630)Memory used [KB]: 1407
% 3.33/1.82  % (18630)Time elapsed: 0.003 s
% 3.33/1.82  % (18630)Instructions burned: 2 (million)
% 3.33/1.82  % (18630)------------------------------
% 3.33/1.82  % (18630)------------------------------
% 3.33/1.82  % (18627)Instruction limit reached!
% 3.33/1.82  % (18627)------------------------------
% 3.33/1.82  % (18627)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.33/1.82  % (18627)Termination reason: Unknown
% 3.33/1.82  % (18627)Termination phase: shuffling
% 3.33/1.82  
% 3.33/1.82  % (18627)Memory used [KB]: 1407
% 3.33/1.82  % (18627)Time elapsed: 0.004 s
% 3.33/1.82  % (18627)Instructions burned: 4 (million)
% 3.33/1.82  % (18627)------------------------------
% 3.33/1.82  % (18627)------------------------------
% 3.33/1.83  % (18632)Instruction limit reached!
% 3.33/1.83  % (18632)------------------------------
% 3.33/1.83  % (18632)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.33/1.83  % (18632)Termination reason: Unknown
% 3.33/1.83  % (18632)Termination phase: shuffling
% 3.33/1.83  
% 3.33/1.83  % (18632)Memory used [KB]: 1791
% 3.33/1.83  % (18632)Time elapsed: 0.012 s
% 3.33/1.83  % (18632)Instructions burned: 19 (million)
% 3.33/1.83  % (18632)------------------------------
% 3.33/1.83  % (18632)------------------------------
% 3.33/1.84  % (18628)Instruction limit reached!
% 3.33/1.84  % (18628)------------------------------
% 3.33/1.84  % (18628)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.33/1.84  % (18628)Termination reason: Unknown
% 3.33/1.84  % (18628)Termination phase: shuffling
% 3.33/1.84  
% 3.33/1.84  % (18628)Memory used [KB]: 1918
% 3.33/1.84  % (18628)Time elapsed: 0.017 s
% 3.33/1.84  % (18628)Instructions burned: 28 (million)
% 3.33/1.84  % (18628)------------------------------
% 3.33/1.84  % (18628)------------------------------
% 3.33/1.84  % (18635)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_18468 for (2999ds/15Mi)
% 3.33/1.84  % (18634)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_18468 for (2999ds/37Mi)
% 3.33/1.84  % (18633)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_18468 for (2999ds/3Mi)
% 3.33/1.84  % (18633)Instruction limit reached!
% 3.33/1.84  % (18633)------------------------------
% 3.33/1.84  % (18633)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.33/1.84  % (18633)Termination reason: Unknown
% 3.33/1.84  % (18633)Termination phase: shuffling
% 3.33/1.84  
% 3.33/1.84  % (18633)Memory used [KB]: 1407
% 3.33/1.84  % (18633)Time elapsed: 0.003 s
% 3.33/1.84  % (18633)Instructions burned: 3 (million)
% 3.33/1.84  % (18633)------------------------------
% 3.33/1.84  % (18633)------------------------------
% 3.33/1.85  % (18635)Instruction limit reached!
% 3.33/1.85  % (18635)------------------------------
% 3.33/1.85  % (18635)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.33/1.85  % (18635)Termination reason: Unknown
% 3.33/1.85  % (18635)Termination phase: shuffling
% 3.33/1.85  
% 3.33/1.85  % (18635)Memory used [KB]: 1663
% 3.33/1.85  % (18635)Time elapsed: 0.010 s
% 3.33/1.85  % (18635)Instructions burned: 15 (million)
% 3.33/1.85  % (18635)------------------------------
% 3.33/1.85  % (18635)------------------------------
% 3.33/1.85  % (18636)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_18468 for (2999ds/3Mi)
% 3.33/1.86  % (18636)Instruction limit reached!
% 3.33/1.86  % (18636)------------------------------
% 3.33/1.86  % (18636)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.33/1.86  % (18636)Termination reason: Unknown
% 3.33/1.86  % (18636)Termination phase: shuffling
% 3.33/1.86  
% 3.33/1.86  % (18636)Memory used [KB]: 1407
% 3.33/1.86  % (18636)Time elapsed: 0.004 s
% 3.33/1.86  % (18636)Instructions burned: 4 (million)
% 3.33/1.86  % (18636)------------------------------
% 3.33/1.86  % (18636)------------------------------
% 3.33/1.86  % (18637)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_18468 for (2999ds/1041Mi)
% 3.33/1.86  % (18631)First to succeed.
% 3.33/1.86  % (18634)Instruction limit reached!
% 3.33/1.86  % (18634)------------------------------
% 3.33/1.86  % (18634)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.33/1.86  % (18634)Termination reason: Unknown
% 3.33/1.86  % (18634)Termination phase: shuffling
% 3.33/1.86  
% 3.33/1.86  % (18634)Memory used [KB]: 2174
% 3.33/1.86  % (18634)Time elapsed: 0.021 s
% 3.33/1.86  % (18634)Instructions burned: 37 (million)
% 3.33/1.86  % (18634)------------------------------
% 3.33/1.86  % (18634)------------------------------
% 3.33/1.86  % (18631)Refutation found. Thanks to Tanya!
% 3.33/1.86  % SZS status Theorem for DTF2THF_18468
% 3.33/1.86  % SZS output start Proof for DTF2THF_18468
% 3.33/1.86  thf(type_def_5, type, name: $tType).
% 3.33/1.86  thf(type_def_6, type, pi: $tType).
% 3.33/1.86  thf(type_def_8, type, late_freeRes: $tType).
% 3.33/1.86  thf(type_def_9, type, late_subject: $tType).
% 3.33/1.86  thf(type_def_10, type, late_residual: $tType).
% 3.33/1.86  thf(type_def_11, type, noption: ($tType) > $tType).
% 3.33/1.86  thf(type_def_12, type, product_prod: ($tType * $tType) > $tType).
% 3.33/1.86  thf(type_def_13, type, set: ($tType) > $tType).
% 3.33/1.86  thf(func_def_0, type, late_residual: $tType).
% 3.33/1.86  thf(func_def_1, type, late_subject: $tType).
% 3.33/1.86  thf(func_def_2, type, late_freeRes: $tType).
% 3.33/1.86  thf(func_def_3, type, product_prod: ($tType * $tType) > $tType).
% 3.33/1.86  thf(func_def_4, type, noption: ($tType) > $tType).
% 3.33/1.86  thf(func_def_5, type, name: $tType).
% 3.33/1.86  thf(func_def_6, type, pi: $tType).
% 3.33/1.86  thf(func_def_7, type, set: ($tType) > $tType).
% 3.33/1.86  thf(func_def_8, type, type: !>[X0: $tType]:($o)).
% 3.33/1.86  thf(func_def_9, type, fs_name: !>[X0: $tType]:($o)).
% 3.33/1.86  thf(func_def_10, type, ord: !>[X0: $tType]:($o)).
% 3.33/1.86  thf(func_def_11, type, order: !>[X0: $tType]:($o)).
% 3.33/1.86  thf(func_def_12, type, linorder: !>[X0: $tType]:($o)).
% 3.33/1.86  thf(func_def_13, type, preorder: !>[X0: $tType]:($o)).
% 3.33/1.86  thf(func_def_14, type, input: name > name > pi > pi).
% 3.33/1.86  thf(func_def_15, type, output: name > name > pi > pi).
% 3.33/1.86  thf(func_def_16, type, par: pi > pi > pi).
% 3.33/1.86  thf(func_def_17, type, piNil: pi).
% 3.33/1.86  thf(func_def_18, type, res: name > pi > pi).
% 3.33/1.86  thf(func_def_19, type, sum: pi > pi > pi).
% 3.33/1.86  thf(func_def_20, type, tau: pi > pi).
% 3.33/1.86  thf(func_def_21, type, subs: pi > name > name > pi).
% 3.33/1.86  thf(func_def_22, type, subst_name: name > name > name > name).
% 3.33/1.86  thf(func_def_23, type, late_OutputR: name > name > late_freeRes).
% 3.33/1.86  thf(func_def_24, type, late_TauR: late_freeRes).
% 3.33/1.86  thf(func_def_25, type, late_freeRes_rec: !>[X0: $tType]:((name > name > X0) > X0 > late_freeRes > X0)).
% 3.33/1.86  thf(func_def_26, type, late_BoundR: late_subject > name > pi > late_residual).
% 3.33/1.86  thf(func_def_27, type, late_FreeR: late_freeRes > pi > late_residual).
% 3.33/1.86  thf(func_def_28, type, late_BoundOutputS: name > late_subject).
% 3.33/1.86  thf(func_def_29, type, late_InputS: name > late_subject).
% 3.33/1.86  thf(func_def_30, type, late_subject_rec: !>[X0: $tType]:((name > X0) > (name > X0) > late_subject > X0)).
% 3.33/1.86  thf(func_def_31, type, late_transitions: pi > late_residual > $o).
% 3.33/1.86  thf(func_def_32, type, abs_fun: !>[X0: $tType, X1: $tType]:(X0 > X1 > X0 > noption @ X1)).
% 3.33/1.86  thf(func_def_33, type, fresh: !>[X0: $tType, X1: $tType]:(X0 > X1 > $o)).
% 3.33/1.86  thf(func_def_34, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 3.33/1.86  thf(func_def_35, type, product_Pair: !>[X0: $tType, X1: $tType]:(X0 > X1 > product_prod @ X0 @ X1)).
% 3.33/1.86  thf(func_def_36, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2)).
% 3.33/1.86  thf(func_def_37, type, eqvt: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > $o)).
% 3.33/1.86  thf(func_def_38, type, id: !>[X0: $tType]:(set @ product_prod @ X0 @ X0)).
% 3.33/1.86  thf(func_def_39, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 3.33/1.86  thf(func_def_40, type, strong2129052853vative: pi > pi > late_subject > name > set @ product_prod @ pi @ pi > $o).
% 3.33/1.86  thf(func_def_41, type, strong743114133lation: pi > set @ product_prod @ pi @ pi > pi > $o).
% 3.33/1.86  thf(func_def_42, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 3.33/1.86  thf(func_def_43, type, p: pi).
% 3.33/1.86  thf(func_def_44, type, p2: pi).
% 3.33/1.86  thf(func_def_45, type, pxQ: pi).
% 3.33/1.86  thf(func_def_46, type, q: pi).
% 3.33/1.86  thf(func_def_47, type, rel: set @ product_prod @ pi @ pi).
% 3.33/1.86  thf(func_def_48, type, alpha: late_freeRes).
% 3.33/1.86  thf(func_def_49, type, x: name).
% 3.33/1.86  thf(func_def_67, type, sP0: late_subject > name > pi > pi > pi > $o).
% 3.33/1.86  thf(func_def_68, type, sK1: (late_residual > $o) > late_freeRes).
% 3.33/1.86  thf(func_def_69, type, sK2: (late_residual > $o) > pi).
% 3.33/1.86  thf(func_def_70, type, sK3: (late_residual > $o) > late_subject).
% 3.33/1.86  thf(func_def_71, type, sK4: (late_residual > $o) > name).
% 3.33/1.86  thf(func_def_72, type, sK5: (late_residual > $o) > pi).
% 3.33/1.86  thf(func_def_73, type, sK6: (pi > $o) > late_freeRes > pi > name > pi).
% 3.33/1.86  thf(func_def_74, type, sK7: pi > late_freeRes > pi > name > pi).
% 3.33/1.86  thf(func_def_75, type, sK8: pi > late_freeRes > pi > name > late_freeRes).
% 3.33/1.86  thf(func_def_76, type, sK9: pi > late_freeRes > pi > name > pi).
% 3.33/1.86  thf(func_def_77, type, sK10: pi > late_freeRes > pi > name > name).
% 3.33/1.86  thf(func_def_78, type, sK11: late_subject > name > pi > pi > pi > pi).
% 3.33/1.86  thf(func_def_79, type, sK12: late_subject > name > pi > pi > pi > late_subject).
% 3.33/1.86  thf(func_def_80, type, sK13: late_subject > name > pi > pi > pi > name).
% 3.33/1.86  thf(func_def_81, type, sK14: late_subject > name > pi > pi > pi > pi).
% 3.33/1.86  thf(func_def_82, type, sK15: late_subject > name > pi > pi > pi > pi).
% 3.33/1.86  thf(func_def_83, type, sK16: pi > name > late_subject > pi > pi > pi).
% 3.33/1.86  thf(func_def_84, type, sK17: pi > name > late_subject > pi > pi > late_subject).
% 3.33/1.86  thf(func_def_85, type, sK18: pi > name > late_subject > pi > pi > name).
% 3.33/1.86  thf(func_def_86, type, sK19: pi > name > late_subject > pi > pi > pi).
% 3.33/1.86  thf(func_def_87, type, sK20: pi > name > late_subject > pi > pi > pi).
% 3.33/1.86  thf(func_def_88, type, sK21: (pi > $o) > name > late_subject > pi > pi > pi).
% 3.33/1.86  thf(func_def_89, type, sK22: (pi > $o) > name > late_subject > pi > pi > pi).
% 3.33/1.86  thf(func_def_91, type, ph24: !>[X0: $tType]:(X0)).
% 3.33/1.86  thf(f860,plain,(
% 3.33/1.86    $false),
% 3.33/1.86    inference(subsumption_resolution,[status(thm)],[f859,f814])).
% 3.33/1.86  thf(f814,plain,(
% 3.33/1.86    ((late_transitions @ (par @ p @ q) @ (late_FreeR @ alpha @ (par @ p2 @ q))) = $true)),
% 3.33/1.86    inference(cnf_transformation,[status(thm)],[f350])).
% 3.33/1.86  thf(f350,plain,(
% 3.33/1.86    ((late_transitions @ (par @ p @ q) @ (late_FreeR @ alpha @ (par @ p2 @ q))) = $true)),
% 3.33/1.86    inference(fool_elimination,[status(thm)],[f349])).
% 3.33/1.86  thf(f349,plain,(
% 3.33/1.86    (late_transitions @ (par @ p @ q) @ (late_FreeR @ alpha @ (par @ p2 @ q)))),
% 3.33/1.86    inference(rectify,[status(thm)],[f2])).
% 3.33/1.86  thf(f2,axiom,(
% 3.33/1.86    (late_transitions @ (par @ p @ q) @ (late_FreeR @ alpha @ (par @ p2 @ q)))),
% 3.33/1.86    file('/export/starexec/sandbox/tmp/tmp.gpMSqBPIcZ/DTF2THF_18468.p',fact_1__092_060open_062P_A_092_060parallel_062_AQ_A_092_060longmapsto_062_A_092_060alpha_062_A_092_060prec_062_AP_H_A_092_060parallel_062_AQ_092_060close_062)).
% 3.33/1.86  thf(f859,plain,(
% 3.33/1.86    ((late_transitions @ (par @ p @ q) @ (late_FreeR @ alpha @ (par @ p2 @ q))) != $true)),
% 3.33/1.86    inference(subsumption_resolution,[status(thm)],[f858,f802])).
% 3.33/1.86  thf(f802,plain,(
% 3.33/1.86    ((fresh @ name @ late_freeRes @ x @ alpha) = $true)),
% 3.33/1.86    inference(cnf_transformation,[status(thm)],[f548])).
% 3.33/1.86  thf(f548,plain,(
% 3.33/1.86    ((fresh @ name @ late_freeRes @ x @ alpha) = $true)),
% 3.33/1.86    inference(fool_elimination,[status(thm)],[f547])).
% 3.33/1.86  thf(f547,plain,(
% 3.33/1.86    (fresh @ name @ late_freeRes @ x @ alpha)),
% 3.33/1.86    inference(rectify,[status(thm)],[f1])).
% 3.33/1.86  thf(f1,axiom,(
% 3.33/1.86    (fresh @ name @ late_freeRes @ x @ alpha)),
% 3.33/1.86    file('/export/starexec/sandbox/tmp/tmp.gpMSqBPIcZ/DTF2THF_18468.p',fact_0__092_060open_062x_A_092_060sharp_062_A_092_060alpha_062_092_060close_062)).
% 3.33/1.86  thf(f858,plain,(
% 3.33/1.86    ((fresh @ name @ late_freeRes @ x @ alpha) != $true) | ((late_transitions @ (par @ p @ q) @ (late_FreeR @ alpha @ (par @ p2 @ q))) != $true)),
% 3.33/1.86    inference(trivial_inequality_removal,[status(thm)],[f857])).
% 3.33/1.86  thf(f857,plain,(
% 3.33/1.86    ((fresh @ name @ late_freeRes @ x @ alpha) != $true) | ($true != $true) | ((late_transitions @ (par @ p @ q) @ (late_FreeR @ alpha @ (par @ p2 @ q))) != $true)),
% 3.33/1.86    inference(superposition,[status(thm)],[f815,f810])).
% 3.33/1.86  thf(f810,plain,(
% 3.33/1.86    ( ! [X2 : pi,X3 : name,X0 : pi,X1 : late_freeRes] : (($true = (late_transitions @ (res @ X3 @ X0) @ (late_FreeR @ X1 @ (res @ X3 @ X2)))) | ((late_transitions @ X0 @ (late_FreeR @ X1 @ X2)) != $true) | ($true != (fresh @ name @ late_freeRes @ X3 @ X1))) )),
% 3.33/1.86    inference(cnf_transformation,[status(thm)],[f737])).
% 3.33/1.86  thf(f737,plain,(
% 3.33/1.86    ! [X0 : pi,X1 : late_freeRes,X2 : pi,X3 : name] : (((late_transitions @ X0 @ (late_FreeR @ X1 @ X2)) != $true) | ($true != (fresh @ name @ late_freeRes @ X3 @ X1)) | ($true = (late_transitions @ (res @ X3 @ X0) @ (late_FreeR @ X1 @ (res @ X3 @ X2)))))),
% 3.33/1.86    inference(flattening,[status(thm)],[f736])).
% 3.33/1.86  thf(f736,plain,(
% 3.33/1.86    ! [X0 : pi,X1 : late_freeRes,X2 : pi,X3 : name] : ((($true = (late_transitions @ (res @ X3 @ X0) @ (late_FreeR @ X1 @ (res @ X3 @ X2)))) | ($true != (fresh @ name @ late_freeRes @ X3 @ X1))) | ((late_transitions @ X0 @ (late_FreeR @ X1 @ X2)) != $true))),
% 3.33/1.86    inference(ennf_transformation,[status(thm)],[f648])).
% 3.33/1.86  thf(f648,plain,(
% 3.33/1.86    ! [X0 : pi,X1 : late_freeRes,X2 : pi,X3 : name] : (((late_transitions @ X0 @ (late_FreeR @ X1 @ X2)) = $true) => (($true = (fresh @ name @ late_freeRes @ X3 @ X1)) => ($true = (late_transitions @ (res @ X3 @ X0) @ (late_FreeR @ X1 @ (res @ X3 @ X2))))))),
% 3.33/1.86    inference(fool_elimination,[status(thm)],[f647])).
% 3.33/1.86  thf(f647,plain,(
% 3.33/1.86    ! [X0 : pi,X1 : late_freeRes,X2 : pi,X3 : name] : ((late_transitions @ X0 @ (late_FreeR @ X1 @ X2)) => ((fresh @ name @ late_freeRes @ X3 @ X1) => (late_transitions @ (res @ X3 @ X0) @ (late_FreeR @ X1 @ (res @ X3 @ X2)))))),
% 3.33/1.86    inference(rectify,[status(thm)],[f12])).
% 3.33/1.86  thf(f12,axiom,(
% 3.33/1.86    ! [X4 : pi,X5 : late_freeRes,X6 : pi,X20 : name] : ((late_transitions @ X4 @ (late_FreeR @ X5 @ X6)) => ((fresh @ name @ late_freeRes @ X20 @ X5) => (late_transitions @ (res @ X20 @ X4) @ (late_FreeR @ X5 @ (res @ X20 @ X6)))))),
% 3.33/1.86    file('/export/starexec/sandbox/tmp/tmp.gpMSqBPIcZ/DTF2THF_18468.p',fact_11_ResF)).
% 3.33/1.86  thf(f815,plain,(
% 3.33/1.86    ((late_transitions @ (res @ x @ (par @ p @ q)) @ (late_FreeR @ alpha @ (res @ x @ (par @ p2 @ q)))) != $true)),
% 3.33/1.86    inference(cnf_transformation,[status(thm)],[f725])).
% 3.33/1.86  thf(f725,plain,(
% 3.33/1.86    ((late_transitions @ (res @ x @ (par @ p @ q)) @ (late_FreeR @ alpha @ (res @ x @ (par @ p2 @ q)))) != $true)),
% 3.33/1.86    inference(flattening,[status(thm)],[f358])).
% 3.33/1.86  thf(f358,plain,(
% 3.33/1.86    ~((late_transitions @ (res @ x @ (par @ p @ q)) @ (late_FreeR @ alpha @ (res @ x @ (par @ p2 @ q)))) = $true)),
% 3.33/1.86    inference(fool_elimination,[status(thm)],[f357])).
% 3.33/1.86  thf(f357,plain,(
% 3.33/1.86    ~(late_transitions @ (res @ x @ (par @ p @ q)) @ (late_FreeR @ alpha @ (res @ x @ (par @ p2 @ q))))),
% 3.33/1.86    inference(rectify,[status(thm)],[f275])).
% 3.33/1.86  thf(f275,negated_conjecture,(
% 3.33/1.86    ~(late_transitions @ (res @ x @ (par @ p @ q)) @ (late_FreeR @ alpha @ (res @ x @ (par @ p2 @ q))))),
% 3.33/1.86    inference(negated_conjecture,[status(cth)],[f274])).
% 3.33/1.86  thf(f274,conjecture,(
% 3.33/1.86    (late_transitions @ (res @ x @ (par @ p @ q)) @ (late_FreeR @ alpha @ (res @ x @ (par @ p2 @ q))))),
% 3.33/1.86    file('/export/starexec/sandbox/tmp/tmp.gpMSqBPIcZ/DTF2THF_18468.p',conj_0)).
% 3.33/1.86  % SZS output end Proof for DTF2THF_18468
% 3.33/1.86  % (18631)------------------------------
% 3.33/1.86  % (18631)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.33/1.86  % (18631)Termination reason: Refutation
% 3.33/1.86  
% 3.33/1.86  % (18631)Memory used [KB]: 6652
% 3.33/1.86  % (18631)Time elapsed: 0.040 s
% 3.33/1.86  % (18631)Instructions burned: 68 (million)
% 3.33/1.86  % (18631)------------------------------
% 3.33/1.86  % (18631)------------------------------
% 3.33/1.86  % (18625)Success in time 0.072 s
%------------------------------------------------------------------------------