%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP186^2 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n016.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 08:56:15 AM UTC 2026
% Result : Theorem 2.87s 1.62s
% Output : Refutation 2.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ITP186^2 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n016.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 08:29:36 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.31/0.45 ---- Original DTF file ---
% 0.31/0.45 thf(spec,logic,$$dhol).
% 0.31/0.45 %------------------------------------------------------------------------------
% 0.31/0.45 % File : ITP186^2 : TPTP v9.2.1. Released v7.5.0.
% 0.31/0.45 % Domain : Interactive Theorem Proving
% 0.31/0.45 % Problem : Sledgehammer Strong_Late_Sim_SC problem prob_570__3414234_1
% 0.31/0.45 % Version : Especial.
% 0.31/0.45 % English :
% 0.31/0.45
% 0.31/0.45 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.31/0.45 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.31/0.45 % Source : [Des21]
% 0.31/0.45 % Names : Strong_Late_Sim_SC/prob_570__3414234_1 [Des21]
% 0.31/0.45
% 0.31/0.45 % Status : Theorem
% 0.31/0.45 % Rating : 0.33 v9.1.0, 0.00 v8.2.0, 0.33 v8.1.0, 0.00 v7.5.0
% 0.31/0.45 % Syntax : Number of formulae : 332 ( 178 unt; 57 typ; 0 def)
% 0.31/0.45 % Number of atoms : 661 ( 280 equ; 0 cnn)
% 0.31/0.45 % Maximal formula atoms : 16 ( 2 avg)
% 0.31/0.45 % Number of connectives : 3759 ( 142 ~; 7 |; 35 &;3162 @)
% 0.31/0.45 % ( 0 <=>; 413 =>; 0 <=; 0 <~>)
% 0.31/0.45 % Maximal formula depth : 39 ( 8 avg)
% 0.31/0.45 % Number of types : 6 ( 5 usr)
% 0.31/0.45 % Number of type conns : 394 ( 394 >; 0 *; 0 +; 0 <<)
% 0.31/0.45 % Number of symbols : 55 ( 52 usr; 15 con; 0-13 aty)
% 0.31/0.45 % Number of variables : 1292 ( 39 ^;1226 !; 4 ?;1292 :)
% 0.31/0.45 % ( 23 !>; 0 ?*; 0 @-; 0 @+)
% 0.31/0.45 % SPC : TH1_THM_EQU_NAR
% 0.31/0.45
% 0.31/0.45 % Comments : This file was generated by Sledgehammer 2021-02-23 16:16:57.508
% 0.31/0.45 %------------------------------------------------------------------------------
% 0.31/0.45 % Could-be-implicit typings (7)
% 0.31/0.45 thf(ty_t_Late__Semantics_Oresidual,type,
% 0.31/0.45 late_residual: $tType ).
% 0.31/0.45
% 0.31/0.45 thf(ty_t_Late__Semantics_Osubject,type,
% 0.31/0.45 late_subject: $tType ).
% 0.31/0.45
% 0.31/0.45 thf(ty_t_Late__Semantics_OfreeRes,type,
% 0.31/0.45 late_freeRes: $tType ).
% 0.31/0.45
% 0.31/0.45 thf(ty_t_Nominal_Onoption,type,
% 0.31/0.45 noption: $tType > $tType ).
% 0.31/0.45
% 0.31/0.45 thf(ty_t_Agent_Oname,type,
% 0.31/0.45 name: $tType ).
% 0.31/0.45
% 0.31/0.45 thf(ty_t_Agent_Opi,type,
% 0.31/0.45 pi: $tType ).
% 0.31/0.45
% 0.31/0.45 thf(ty_t_Set_Oset,type,
% 0.31/0.45 set: $tType > $tType ).
% 0.31/0.45
% 0.31/0.45 % Explicit typings (50)
% 0.31/0.45 thf(sy_cl_Agent_Ofs__name,type,
% 0.31/0.45 fs_name:
% 0.31/0.45 !>[A: $tType] : $o ).
% 0.31/0.45
% 0.31/0.45 thf(sy_cl_Agent_Opt__name,type,
% 0.31/0.45 pt_name:
% 0.31/0.45 !>[A: $tType] : $o ).
% 0.31/0.45
% 0.31/0.45 thf(sy_c_Agent_Opi_OBang,type,
% 0.31/0.45 bang: pi > pi ).
% 0.31/0.45
% 0.31/0.45 thf(sy_c_Agent_Opi_OInput,type,
% 0.31/0.45 input: name > name > pi > pi ).
% 0.31/0.45
% 0.31/0.45 thf(sy_c_Agent_Opi_OMatch,type,
% 0.31/0.45 match: name > name > pi > pi ).
% 0.31/0.45
% 0.31/0.45 thf(sy_c_Agent_Opi_OMismatch,type,
% 0.31/0.45 mismatch: name > name > pi > pi ).
% 0.31/0.45
% 0.31/0.45 thf(sy_c_Agent_Opi_OOutput,type,
% 0.31/0.45 output: name > name > pi > pi ).
% 0.31/0.45
% 0.31/0.45 thf(sy_c_Agent_Opi_OPar,type,
% 0.31/0.45 par: pi > pi > pi ).
% 0.31/0.45
% 0.31/0.45 thf(sy_c_Agent_Opi_OPiNil,type,
% 0.31/0.45 piNil: pi ).
% 0.31/0.45
% 0.31/0.45 thf(sy_c_Agent_Opi_ORes,type,
% 0.31/0.45 res: name > pi > pi ).
% 0.31/0.45
% 0.31/0.45 thf(sy_c_Agent_Opi_OSum,type,
% 0.31/0.45 sum: pi > pi > pi ).
% 0.31/0.45
% 0.31/0.45 thf(sy_c_Agent_Opi_OTau,type,
% 0.31/0.45 tau: pi > pi ).
% 0.31/0.45
% 0.31/0.45 thf(sy_c_Agent_Opi_Opi__rec,type,
% 0.31/0.45 pi_rec:
% 0.31/0.45 !>[T: $tType] : ( T > ( name > name > pi > T > T ) > ( pi > T > T ) > ( name > name > pi > T > T ) > ( name > name > pi > T > T ) > ( name > name > pi > T > T ) > ( pi > pi > T > T > T ) > ( pi > pi > T > T > T ) > ( name > pi > T > T ) > ( pi > T > T ) > pi > T ) ).
% 0.31/0.45
% 0.31/0.45 thf(sy_c_Agent_Opi_Opi__rec__set,type,
% 0.31/0.45 pi_rec_set:
% 0.31/0.45 !>[T: $tType] : ( T > ( name > name > pi > T > T ) > ( pi > T > T ) > ( name > name > pi > T > T ) > ( name > name > pi > T > T ) > ( name > name > pi > T > T ) > ( pi > pi > T > T > T ) > ( pi > pi > T > T > T ) > ( name > pi > T > T ) > ( pi > T > T ) > pi > T > $o ) ).
% 0.31/0.45
% 0.31/0.45 thf(sy_c_Agent_Osubs,type,
% 0.31/0.45 subs: pi > name > name > pi ).
% 0.31/0.45
% 0.31/0.45 thf(sy_c_Agent_Osubst__name,type,
% 0.31/0.45 subst_name: name > name > name > name ).
% 0.31/0.45
% 0.31/0.45 thf(sy_c_Finite__Set_Ofinite,type,
% 0.31/0.45 finite_finite:
% 0.31/0.45 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 0.31/0.45
% 0.31/0.45 thf(sy_c_If,type,
% 0.31/0.45 if:
% 0.31/0.45 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.31/0.45
% 0.31/0.45 thf(sy_c_Late__Semantics1_OfreeRes_Ocase__freeRes,type,
% 0.31/0.45 late_case_freeRes:
% 0.31/0.45 !>[A: $tType] : ( ( name > name > A ) > A > late_freeRes > A ) ).
% 0.31/0.45
% 0.31/0.45 thf(sy_c_Late__Semantics1_Osubject_Ocase__subject,type,
% 0.31/0.45 late_case_subject:
% 0.31/0.45 !>[A: $tType] : ( ( name > A ) > ( name > A ) > late_subject > A ) ).
% 0.31/0.45
% 0.31/0.45 thf(sy_c_Late__Semantics_ObangPred,type,
% 0.31/0.46 late_bangPred: pi > pi > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Late__Semantics_OfreeRes_OOutputR,type,
% 0.31/0.46 late_OutputR: name > name > late_freeRes ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Late__Semantics_OfreeRes_OTauR,type,
% 0.31/0.46 late_TauR: late_freeRes ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Late__Semantics_OfreeRes_OfreeRes__rec,type,
% 0.31/0.46 late_freeRes_rec:
% 0.31/0.46 !>[T: $tType] : ( ( name > name > T ) > T > late_freeRes > T ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Late__Semantics_Oresidual_OBoundR,type,
% 0.31/0.46 late_BoundR: late_subject > name > pi > late_residual ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Late__Semantics_Oresidual_OFreeR,type,
% 0.31/0.46 late_FreeR: late_freeRes > pi > late_residual ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Late__Semantics_Oresidual_Oresidual__rec,type,
% 0.31/0.46 late_residual_rec:
% 0.31/0.46 !>[T: $tType] : ( ( late_subject > name > pi > T ) > ( late_freeRes > pi > T ) > late_residual > T ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Late__Semantics_Oresidual_Oresidual__rec__set,type,
% 0.31/0.46 late_r582136743ec_set:
% 0.31/0.46 !>[T: $tType] : ( ( late_subject > name > pi > T ) > ( late_freeRes > pi > T ) > late_residual > T > $o ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Late__Semantics_Osubject_OBoundOutputS,type,
% 0.31/0.46 late_BoundOutputS: name > late_subject ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Late__Semantics_Osubject_OInputS,type,
% 0.31/0.46 late_InputS: name > late_subject ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Late__Semantics_Osubject_Osubject__rec,type,
% 0.31/0.46 late_subject_rec:
% 0.31/0.46 !>[T: $tType] : ( ( name > T ) > ( name > T ) > late_subject > T ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Late__Semantics_Otransitions,type,
% 0.31/0.46 late_transitions: pi > late_residual > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Lattices_Osup__class_Osup,type,
% 0.31/0.46 sup_sup:
% 0.31/0.46 !>[A: $tType] : ( A > A > A ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Nominal_Oabs__fun,type,
% 0.31/0.46 abs_fun:
% 0.31/0.46 !>[X: $tType,A: $tType] : ( X > A > X > ( noption @ A ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Nominal_Ofresh,type,
% 0.31/0.46 fresh:
% 0.31/0.46 !>[X: $tType,A: $tType] : ( X > A > $o ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Nominal_Osupp,type,
% 0.31/0.46 supp:
% 0.31/0.46 !>[A: $tType,X: $tType] : ( A > ( set @ X ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Nominal_Osupports,type,
% 0.31/0.46 supports:
% 0.31/0.46 !>[X: $tType,A: $tType] : ( ( set @ X ) > A > $o ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Set_OCollect,type,
% 0.31/0.46 collect:
% 0.31/0.46 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_member,type,
% 0.31/0.46 member:
% 0.31/0.46 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_v_P,type,
% 0.31/0.46 p: pi ).
% 0.31/0.46
% 0.31/0.46 thf(sy_v_PQR____,type,
% 0.31/0.46 pqr: pi ).
% 0.31/0.46
% 0.31/0.46 thf(sy_v_P_H____,type,
% 0.31/0.46 p2: pi ).
% 0.31/0.46
% 0.31/0.46 thf(sy_v_Q,type,
% 0.31/0.46 q: pi ).
% 0.31/0.46
% 0.31/0.46 thf(sy_v_QR____,type,
% 0.31/0.46 qr: pi ).
% 0.31/0.46
% 0.31/0.46 thf(sy_v_Q_H____,type,
% 0.31/0.46 q2: pi ).
% 0.31/0.46
% 0.31/0.46 thf(sy_v_R,type,
% 0.31/0.46 r: pi ).
% 0.31/0.46
% 0.31/0.46 thf(sy_v__092_060alpha_062____,type,
% 0.31/0.46 alpha: late_freeRes ).
% 0.31/0.46
% 0.31/0.46 thf(sy_v_a____,type,
% 0.31/0.46 a: name ).
% 0.31/0.46
% 0.31/0.46 thf(sy_v_b____,type,
% 0.31/0.46 b: name ).
% 0.31/0.46
% 0.31/0.46 thf(sy_v_x____,type,
% 0.31/0.46 x: name ).
% 0.31/0.46
% 0.31/0.46 % Relevant facts (256)
% 0.31/0.46 thf(fact_0_cComm2_Ohyps_I9_J,axiom,
% 0.31/0.46 alpha = late_TauR ).
% 0.31/0.46
% 0.31/0.46 % cComm2.hyps(9)
% 0.31/0.46 thf(fact_1_cComm2_Ohyps_I5_J,axiom,
% 0.31/0.46 x != a ).
% 0.31/0.46
% 0.31/0.46 % cComm2.hyps(5)
% 0.31/0.46 thf(fact_2_cComm2_Ohyps_I6_J,axiom,
% 0.31/0.46 x != b ).
% 0.31/0.46
% 0.31/0.46 % cComm2.hyps(6)
% 0.31/0.46 thf(fact_3__092_060open_062P_A_092_060parallel_062_AQ_A_092_060longmapsto_062_A_092_060tau_062_A_092_060prec_062_AP_H_A_092_060parallel_062_AQ_H_091x_058_058_061b_093_092_060close_062,axiom,
% 0.31/0.46 late_transitions @ ( par @ p @ q ) @ ( late_FreeR @ late_TauR @ ( par @ p2 @ ( subs @ q2 @ x @ b ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % \<open>P \<parallel> Q \<longmapsto> \<tau> \<prec> P' \<parallel> Q'[x::=b]\<close>
% 0.31/0.46 thf(fact_4_Free_Ohyps,axiom,
% 0.31/0.46 late_transitions @ ( par @ p @ ( par @ q @ r ) ) @ ( late_FreeR @ alpha @ pqr ) ).
% 0.31/0.46
% 0.31/0.46 % Free.hyps
% 0.31/0.46 thf(fact_5_cComm2_Ohyps_I8_J,axiom,
% 0.31/0.46 fresh @ name @ pi @ x @ q ).
% 0.31/0.46
% 0.31/0.46 % cComm2.hyps(8)
% 0.31/0.46 thf(fact_6_cComm2_Ohyps_I3_J,axiom,
% 0.31/0.46 fresh @ name @ pi @ x @ p ).
% 0.31/0.46
% 0.31/0.46 % cComm2.hyps(3)
% 0.31/0.46 thf(fact_7_cComm2_Ohyps_I7_J,axiom,
% 0.31/0.46 fresh @ name @ pi @ x @ p2 ).
% 0.31/0.46
% 0.31/0.46 % cComm2.hyps(7)
% 0.31/0.46 thf(fact_8_cComm2_Ohyps_I4_J,axiom,
% 0.31/0.46 fresh @ name @ pi @ x @ ( par @ q @ r ) ).
% 0.31/0.46
% 0.31/0.46 % cComm2.hyps(4)
% 0.31/0.46 thf(fact_9_cComm2_Ohyps_I1_J,axiom,
% 0.31/0.46 late_transitions @ p @ ( late_FreeR @ ( late_OutputR @ a @ b ) @ p2 ) ).
% 0.31/0.46
% 0.31/0.46 % cComm2.hyps(1)
% 0.31/0.46 thf(fact_10_simps_I8_J,axiom,
% 0.31/0.46 ! [P: pi,Q: pi,C: name,D: name] :
% 0.31/0.46 ( ( subs @ ( par @ P @ Q ) @ C @ D )
% 0.31/0.46 = ( par @ ( subs @ P @ C @ D ) @ ( subs @ Q @ C @ D ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % simps(8)
% 0.31/0.46 thf(fact_11_Par1F,axiom,
% 0.31/0.46 ! [P: pi,Alpha: late_freeRes,P2: pi,Q: pi] :
% 0.31/0.46 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 0.31/0.46 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha @ ( par @ P2 @ Q ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Par1F
% 0.31/0.46 thf(fact_12_Par2F,axiom,
% 0.31/0.46 ! [Q: pi,Alpha: late_freeRes,Q2: pi,P: pi] :
% 0.31/0.46 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 0.31/0.46 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha @ ( par @ P @ Q2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Par2F
% 0.31/0.46 thf(fact_13__092_060open_062x_A_092_060sharp_062_AR_092_060close_062,axiom,
% 0.31/0.46 fresh @ name @ pi @ x @ r ).
% 0.31/0.46
% 0.31/0.46 % \<open>x \<sharp> R\<close>
% 0.31/0.46 thf(fact_14_subst__identity,axiom,
% 0.31/0.46 ! [P: pi,A2: name] :
% 0.31/0.46 ( ( subs @ P @ A2 @ A2 )
% 0.31/0.46 = P ) ).
% 0.31/0.46
% 0.31/0.46 % subst_identity
% 0.31/0.46 thf(fact_15_cPar1_Ohyps,axiom,
% 0.31/0.46 late_transitions @ q @ ( late_BoundR @ ( late_InputS @ a ) @ x @ q2 ) ).
% 0.31/0.46
% 0.31/0.46 % cPar1.hyps
% 0.31/0.46 thf(fact_16_cComm2_Ohyps_I2_J,axiom,
% 0.31/0.46 late_transitions @ ( par @ q @ r ) @ ( late_BoundR @ ( late_InputS @ a ) @ x @ qr ) ).
% 0.31/0.46
% 0.31/0.46 % cComm2.hyps(2)
% 0.31/0.46 thf(fact_17_residual_Oinject_I2_J,axiom,
% 0.31/0.46 ! [X2: late_freeRes,X1: pi,Y2: late_freeRes,Y1: pi] :
% 0.31/0.46 ( ( ( late_FreeR @ X2 @ X1 )
% 0.31/0.46 = ( late_FreeR @ Y2 @ Y1 ) )
% 0.31/0.46 = ( ( X2 = Y2 )
% 0.31/0.46 & ( X1 = Y1 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % residual.inject(2)
% 0.31/0.46 thf(fact_18_pi_Oinject_I7_J,axiom,
% 0.31/0.46 ! [X2: pi,X1: pi,Y2: pi,Y1: pi] :
% 0.31/0.46 ( ( ( par @ X2 @ X1 )
% 0.31/0.46 = ( par @ Y2 @ Y1 ) )
% 0.31/0.46 = ( ( X2 = Y2 )
% 0.31/0.46 & ( X1 = Y1 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.inject(7)
% 0.31/0.46 thf(fact_19_tauCases,axiom,
% 0.31/0.46 ! [P: pi,Alpha: late_freeRes,P2: pi,Prop: late_freeRes > pi > $o] :
% 0.31/0.46 ( ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 0.31/0.46 => ( ( ( Alpha = late_TauR )
% 0.31/0.46 => ( ( P = P2 )
% 0.31/0.46 => ( Prop @ late_TauR @ P ) ) )
% 0.31/0.46 => ( Prop @ Alpha @ P2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % tauCases
% 0.31/0.46 thf(fact_20_tauCases_H,axiom,
% 0.31/0.46 ! [P: pi,Rs: late_residual] :
% 0.31/0.46 ( ( late_transitions @ ( tau @ P ) @ Rs )
% 0.31/0.46 => ~ ! [P3: pi] :
% 0.31/0.46 ( ( ( tau @ P )
% 0.31/0.46 = ( tau @ P3 ) )
% 0.31/0.46 => ( Rs
% 0.31/0.46 != ( late_FreeR @ late_TauR @ P3 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % tauCases'
% 0.31/0.46 thf(fact_21_Late__Semantics_OfreeRes_Oinject,axiom,
% 0.31/0.46 ! [X2: name,X1: name,Y2: name,Y1: name] :
% 0.31/0.46 ( ( ( late_OutputR @ X2 @ X1 )
% 0.31/0.46 = ( late_OutputR @ Y2 @ Y1 ) )
% 0.31/0.46 = ( ( X2 = Y2 )
% 0.31/0.46 & ( X1 = Y1 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Late_Semantics.freeRes.inject
% 0.31/0.46 thf(fact_22_pi_Ofresh_I8_J,axiom,
% 0.31/0.46 ! [A2: name,X2: pi,X1: pi] :
% 0.31/0.46 ( ( fresh @ name @ pi @ A2 @ ( par @ X2 @ X1 ) )
% 0.31/0.46 = ( ( fresh @ name @ pi @ A2 @ X2 )
% 0.31/0.46 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.fresh(8)
% 0.31/0.46 thf(fact_23_substTrans,axiom,
% 0.31/0.46 ! [B: name,P: pi,A2: name,C: name] :
% 0.31/0.46 ( ( fresh @ name @ pi @ B @ P )
% 0.31/0.46 => ( ( subs @ ( subs @ P @ A2 @ B ) @ B @ C )
% 0.31/0.46 = ( subs @ P @ A2 @ C ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % substTrans
% 0.31/0.46 thf(fact_24_pi_Ofresh_I3_J,axiom,
% 0.31/0.46 ! [A2: name,X1: pi] :
% 0.31/0.46 ( ( fresh @ name @ pi @ A2 @ ( tau @ X1 ) )
% 0.31/0.46 = ( fresh @ name @ pi @ A2 @ X1 ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.fresh(3)
% 0.31/0.46 thf(fact_25_simps_I2_J,axiom,
% 0.31/0.46 ! [P: pi,C: name,D: name] :
% 0.31/0.46 ( ( subs @ ( tau @ P ) @ C @ D )
% 0.31/0.46 = ( tau @ ( subs @ P @ C @ D ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % simps(2)
% 0.31/0.46 thf(fact_26_pi_Oinject_I2_J,axiom,
% 0.31/0.46 ! [X1: pi,Y1: pi] :
% 0.31/0.46 ( ( ( tau @ X1 )
% 0.31/0.46 = ( tau @ Y1 ) )
% 0.31/0.46 = ( X1 = Y1 ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.inject(2)
% 0.31/0.46 thf(fact_27_freshBoundDerivative_I2_J,axiom,
% 0.31/0.46 ! [P: pi,A2: late_subject,X3: name,P2: pi,Y: name] :
% 0.31/0.46 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X3 @ P2 ) )
% 0.31/0.46 => ( ( fresh @ name @ pi @ Y @ P )
% 0.31/0.46 => ( ( Y != X3 )
% 0.31/0.46 => ( fresh @ name @ pi @ Y @ P2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % freshBoundDerivative(2)
% 0.31/0.46 thf(fact_28_name__exists__fresh,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( fs_name @ A )
% 0.31/0.46 => ! [X3: A] :
% 0.31/0.46 ~ ! [C2: name] :
% 0.31/0.46 ~ ( fresh @ name @ A @ C2 @ X3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % name_exists_fresh
% 0.31/0.46 thf(fact_29_tauBoundTrans,axiom,
% 0.31/0.46 ! [P: pi,A2: late_subject,X3: name,P2: pi] :
% 0.31/0.46 ~ ( late_transitions @ ( tau @ P ) @ ( late_BoundR @ A2 @ X3 @ P2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % tauBoundTrans
% 0.31/0.46 thf(fact_30_residual_Ostrong__induct,axiom,
% 0.31/0.46 ! [N: $tType] :
% 0.31/0.46 ( ( fs_name @ N )
% 0.31/0.46 => ! [P: N > late_residual > $o,Z: N,Residual: late_residual] :
% 0.31/0.46 ( ! [Subject: late_subject,Name: name,Pi: pi,Z2: N] :
% 0.31/0.46 ( ( fresh @ name @ N @ Name @ Z2 )
% 0.31/0.46 => ( ( fresh @ name @ late_subject @ Name @ Subject )
% 0.31/0.46 => ( P @ Z2 @ ( late_BoundR @ Subject @ Name @ Pi ) ) ) )
% 0.31/0.46 => ( ! [FreeRes: late_freeRes,Pi: pi,Z2: N] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi ) )
% 0.31/0.46 => ( P @ Z @ Residual ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % residual.strong_induct
% 0.31/0.46 thf(fact_31_residual_Ostrong__inducts,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( fs_name @ A )
% 0.31/0.46 => ! [P: A > late_residual > $o,Z: A,Residual: late_residual] :
% 0.31/0.46 ( ! [Subject: late_subject,Name: name,Pi: pi,Z2: A] :
% 0.31/0.46 ( ( fresh @ name @ A @ Name @ Z2 )
% 0.31/0.46 => ( ( fresh @ name @ late_subject @ Name @ Subject )
% 0.31/0.46 => ( P @ Z2 @ ( late_BoundR @ Subject @ Name @ Pi ) ) ) )
% 0.31/0.46 => ( ! [FreeRes: late_freeRes,Pi: pi,Z2: A] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi ) )
% 0.31/0.46 => ( P @ Z @ Residual ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % residual.strong_inducts
% 0.31/0.46 thf(fact_32_residual_Oinducts,axiom,
% 0.31/0.46 ! [P: late_residual > $o,Residual: late_residual] :
% 0.31/0.46 ( ! [Subject: late_subject,Name: name,Pi: pi] : ( P @ ( late_BoundR @ Subject @ Name @ Pi ) )
% 0.31/0.46 => ( ! [FreeRes: late_freeRes,Pi: pi] : ( P @ ( late_FreeR @ FreeRes @ Pi ) )
% 0.31/0.46 => ( P @ Residual ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % residual.inducts
% 0.31/0.46 thf(fact_33_residual_Odistinct_I1_J,axiom,
% 0.31/0.46 ! [Subject2: late_subject,Name2: name,Pi2: pi,FreeRes2: late_freeRes,Pi3: pi] :
% 0.31/0.46 ( ( late_BoundR @ Subject2 @ Name2 @ Pi2 )
% 0.31/0.46 != ( late_FreeR @ FreeRes2 @ Pi3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % residual.distinct(1)
% 0.31/0.46 thf(fact_34_fresh__fact2,axiom,
% 0.31/0.46 ! [A2: name,B: name,P: pi] :
% 0.31/0.46 ( ( A2 != B )
% 0.31/0.46 => ( fresh @ name @ pi @ A2 @ ( subs @ P @ A2 @ B ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % fresh_fact2
% 0.31/0.46 thf(fact_35_fresh__fact1,axiom,
% 0.31/0.46 ! [A2: name,P: pi,C: name,B: name] :
% 0.31/0.46 ( ( fresh @ name @ pi @ A2 @ P )
% 0.31/0.46 => ( ( A2 != C )
% 0.31/0.46 => ( fresh @ name @ pi @ A2 @ ( subs @ P @ B @ C ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % fresh_fact1
% 0.31/0.46 thf(fact_36_forget,axiom,
% 0.31/0.46 ! [A2: name,P: pi,B: name] :
% 0.31/0.46 ( ( fresh @ name @ pi @ A2 @ P )
% 0.31/0.46 => ( ( subs @ P @ A2 @ B )
% 0.31/0.46 = P ) ) ).
% 0.31/0.46
% 0.31/0.46 % forget
% 0.31/0.46 thf(fact_37_parCasesB,axiom,
% 0.31/0.46 ! [P: pi,Q: pi,A2: late_subject,X3: name,PQ: pi,Prop: pi > $o] :
% 0.31/0.46 ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X3 @ PQ ) )
% 0.31/0.46 => ( ( fresh @ name @ pi @ X3 @ P )
% 0.31/0.46 => ( ( fresh @ name @ pi @ X3 @ Q )
% 0.31/0.46 => ( ! [P4: pi] :
% 0.31/0.46 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X3 @ P4 ) )
% 0.31/0.46 => ( Prop @ ( par @ P4 @ Q ) ) )
% 0.31/0.46 => ( ! [Q3: pi] :
% 0.31/0.46 ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X3 @ Q3 ) )
% 0.31/0.46 => ( Prop @ ( par @ P @ Q3 ) ) )
% 0.31/0.46 => ( Prop @ PQ ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % parCasesB
% 0.31/0.46 thf(fact_38_Late__Semantics_OPar2B,axiom,
% 0.31/0.46 ! [Q: pi,A2: late_subject,X3: name,Q2: pi,P: pi] :
% 0.31/0.46 ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X3 @ Q2 ) )
% 0.31/0.46 => ( ( fresh @ name @ pi @ X3 @ P )
% 0.31/0.46 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X3 @ ( par @ P @ Q2 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Late_Semantics.Par2B
% 0.31/0.46 thf(fact_39_Late__Semantics_OPar1B,axiom,
% 0.31/0.46 ! [P: pi,A2: late_subject,X3: name,P2: pi,Q: pi] :
% 0.31/0.46 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X3 @ P2 ) )
% 0.31/0.46 => ( ( fresh @ name @ pi @ X3 @ Q )
% 0.31/0.46 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X3 @ ( par @ P2 @ Q ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Late_Semantics.Par1B
% 0.31/0.46 thf(fact_40_pi_Odistinct_I43_J,axiom,
% 0.31/0.46 ! [Pi2: pi,Pi1: pi,Pi22: pi] :
% 0.31/0.46 ( ( tau @ Pi2 )
% 0.31/0.46 != ( par @ Pi1 @ Pi22 ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.distinct(43)
% 0.31/0.46 thf(fact_41_freeRes_Ostrong__inducts,axiom,
% 0.31/0.46 ! [A: $tType,P: A > late_freeRes > $o,Z: A,FreeRes3: late_freeRes] :
% 0.31/0.46 ( ! [Name1: name,Name22: name,Z2: A] : ( P @ Z2 @ ( late_OutputR @ Name1 @ Name22 ) )
% 0.31/0.46 => ( ! [Z2: A] : ( P @ Z2 @ late_TauR )
% 0.31/0.46 => ( P @ Z @ FreeRes3 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % freeRes.strong_inducts
% 0.31/0.46 thf(fact_42_freeRes_Ostrong__induct_H,axiom,
% 0.31/0.46 ! [N: $tType,P: N > late_freeRes > $o,Z: N,FreeRes3: late_freeRes] :
% 0.31/0.46 ( ! [Name1: name,Name22: name,Z2: N] : ( P @ Z2 @ ( late_OutputR @ Name1 @ Name22 ) )
% 0.31/0.46 => ( ! [Z2: N] : ( P @ Z2 @ late_TauR )
% 0.31/0.46 => ( P @ Z @ FreeRes3 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % freeRes.strong_induct'
% 0.31/0.46 thf(fact_43_freeRes_Oinducts,axiom,
% 0.31/0.46 ! [P: late_freeRes > $o,FreeRes3: late_freeRes] :
% 0.31/0.46 ( ! [Name1: name,Name22: name] : ( P @ ( late_OutputR @ Name1 @ Name22 ) )
% 0.31/0.46 => ( ( P @ late_TauR )
% 0.31/0.46 => ( P @ FreeRes3 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % freeRes.inducts
% 0.31/0.46 thf(fact_44_Late__Semantics_OfreeRes_Odistinct_I1_J,axiom,
% 0.31/0.46 ! [Name12: name,Name23: name] :
% 0.31/0.46 ( ( late_OutputR @ Name12 @ Name23 )
% 0.31/0.46 != late_TauR ) ).
% 0.31/0.46
% 0.31/0.46 % Late_Semantics.freeRes.distinct(1)
% 0.31/0.46 thf(fact_45_mem__Collect__eq,axiom,
% 0.31/0.46 ! [A: $tType,A2: A,P: A > $o] :
% 0.31/0.46 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 0.31/0.46 = ( P @ A2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % mem_Collect_eq
% 0.31/0.46 thf(fact_46_Collect__mem__eq,axiom,
% 0.31/0.46 ! [A: $tType,A3: set @ A] :
% 0.31/0.46 ( ( collect @ A
% 0.31/0.46 @ ^ [X4: A] : ( member @ A @ X4 @ A3 ) )
% 0.31/0.46 = A3 ) ).
% 0.31/0.46
% 0.31/0.46 % Collect_mem_eq
% 0.31/0.46 thf(fact_47_Collect__cong,axiom,
% 0.31/0.46 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.31/0.46 ( ! [X5: A] :
% 0.31/0.46 ( ( P @ X5 )
% 0.31/0.46 = ( Q @ X5 ) )
% 0.31/0.46 => ( ( collect @ A @ P )
% 0.31/0.46 = ( collect @ A @ Q ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Collect_cong
% 0.31/0.46 thf(fact_48_ext,axiom,
% 0.31/0.46 ! [B2: $tType,A: $tType,F: A > B2,G: A > B2] :
% 0.31/0.46 ( ! [X5: A] :
% 0.31/0.46 ( ( F @ X5 )
% 0.31/0.46 = ( G @ X5 ) )
% 0.31/0.46 => ( F = G ) ) ).
% 0.31/0.46
% 0.31/0.46 % ext
% 0.31/0.46 thf(fact_49_tauOutputTrans,axiom,
% 0.31/0.46 ! [P: pi,A2: name,B: name,P2: pi] :
% 0.31/0.46 ~ ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ ( late_OutputR @ A2 @ B ) @ P2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % tauOutputTrans
% 0.31/0.46 thf(fact_50_transitions_OComm2,axiom,
% 0.31/0.46 ! [P: pi,A2: name,B: name,P2: pi,Q: pi,X3: name,Q2: pi] :
% 0.31/0.46 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A2 @ B ) @ P2 ) )
% 0.31/0.46 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ Q2 ) )
% 0.31/0.46 => ( ( fresh @ name @ pi @ X3 @ P )
% 0.31/0.46 => ( ( fresh @ name @ pi @ X3 @ Q )
% 0.31/0.46 => ( ( X3 != A2 )
% 0.31/0.46 => ( ( X3 != B )
% 0.31/0.46 => ( ( fresh @ name @ pi @ X3 @ P2 )
% 0.31/0.46 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P2 @ ( subs @ Q2 @ X3 @ B ) ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % transitions.Comm2
% 0.31/0.46 thf(fact_51_transitions_OComm1,axiom,
% 0.31/0.46 ! [P: pi,A2: name,X3: name,P2: pi,Q: pi,B: name,Q2: pi] :
% 0.31/0.46 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ P2 ) )
% 0.31/0.46 => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A2 @ B ) @ Q2 ) )
% 0.31/0.46 => ( ( fresh @ name @ pi @ X3 @ P )
% 0.31/0.46 => ( ( fresh @ name @ pi @ X3 @ Q )
% 0.31/0.46 => ( ( X3 != A2 )
% 0.31/0.46 => ( ( X3 != B )
% 0.31/0.46 => ( ( fresh @ name @ pi @ X3 @ Q2 )
% 0.31/0.46 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P2 @ X3 @ B ) @ Q2 ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % transitions.Comm1
% 0.31/0.46 thf(fact_52_freshFreeDerivative_I2_J,axiom,
% 0.31/0.46 ! [P: pi,Alpha: late_freeRes,P2: pi,Y: name] :
% 0.31/0.46 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 0.31/0.46 => ( ( fresh @ name @ pi @ Y @ P )
% 0.31/0.46 => ( fresh @ name @ pi @ Y @ P2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % freshFreeDerivative(2)
% 0.31/0.46 thf(fact_53_Late__Semantics_OComm2,axiom,
% 0.31/0.46 ! [P: pi,A2: name,B: name,P2: pi,Q: pi,X3: name,Q2: pi] :
% 0.31/0.46 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A2 @ B ) @ P2 ) )
% 0.31/0.46 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ Q2 ) )
% 0.31/0.46 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P2 @ ( subs @ Q2 @ X3 @ B ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Late_Semantics.Comm2
% 0.31/0.46 thf(fact_54_Late__Semantics_OComm1,axiom,
% 0.31/0.46 ! [P: pi,A2: name,X3: name,P2: pi,Q: pi,B: name,Q2: pi] :
% 0.31/0.46 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ P2 ) )
% 0.31/0.46 => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A2 @ B ) @ Q2 ) )
% 0.31/0.46 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P2 @ X3 @ B ) @ Q2 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Late_Semantics.Comm1
% 0.31/0.46 thf(fact_55_Tau,axiom,
% 0.31/0.46 ! [P: pi] : ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ late_TauR @ P ) ) ).
% 0.31/0.46
% 0.31/0.46 % Tau
% 0.31/0.46 thf(fact_56_Late__Semantics1_Osubject_Oinject_I1_J,axiom,
% 0.31/0.46 ! [X1: name,Y1: name] :
% 0.31/0.46 ( ( ( late_InputS @ X1 )
% 0.31/0.46 = ( late_InputS @ Y1 ) )
% 0.31/0.46 = ( X1 = Y1 ) ) ).
% 0.31/0.46
% 0.31/0.46 % Late_Semantics1.subject.inject(1)
% 0.31/0.46 thf(fact_57_Late__Semantics1_OfreeRes_Oinject,axiom,
% 0.31/0.46 ! [X11: name,X12: name,Y11: name,Y12: name] :
% 0.31/0.46 ( ( ( late_OutputR @ X11 @ X12 )
% 0.31/0.46 = ( late_OutputR @ Y11 @ Y12 ) )
% 0.31/0.46 = ( ( X11 = Y11 )
% 0.31/0.46 & ( X12 = Y12 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Late_Semantics1.freeRes.inject
% 0.31/0.46 thf(fact_58_freeRes_Oexhaust,axiom,
% 0.31/0.46 ! [Y: late_freeRes] :
% 0.31/0.46 ( ! [X112: name,X122: name] :
% 0.31/0.46 ( Y
% 0.31/0.46 != ( late_OutputR @ X112 @ X122 ) )
% 0.31/0.46 => ( Y = late_TauR ) ) ).
% 0.31/0.46
% 0.31/0.46 % freeRes.exhaust
% 0.31/0.46 thf(fact_59_Late__Semantics1_OfreeRes_Odistinct_I1_J,axiom,
% 0.31/0.46 ! [X11: name,X12: name] :
% 0.31/0.46 ( ( late_OutputR @ X11 @ X12 )
% 0.31/0.46 != late_TauR ) ).
% 0.31/0.46
% 0.31/0.46 % Late_Semantics1.freeRes.distinct(1)
% 0.31/0.46 thf(fact_60_freeRes_Orecs_I2_J,axiom,
% 0.31/0.46 ! [T: $tType,P: T > $o,F1: name > name > T,F2: T] :
% 0.31/0.46 ( ! [X13: name,X22: name] : ( P @ ( F1 @ X13 @ X22 ) )
% 0.31/0.46 => ( ( P @ F2 )
% 0.31/0.46 => ( ( late_freeRes_rec @ T @ F1 @ F2 @ late_TauR )
% 0.31/0.46 = F2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % freeRes.recs(2)
% 0.31/0.46 thf(fact_61_subject_Orecs_I1_J,axiom,
% 0.31/0.46 ! [T: $tType,P: T > $o,F1: name > T,F2: name > T,Name2: name] :
% 0.31/0.46 ( ! [X13: name] : ( P @ ( F1 @ X13 ) )
% 0.31/0.46 => ( ! [X13: name] : ( P @ ( F2 @ X13 ) )
% 0.31/0.46 => ( ( late_subject_rec @ T @ F1 @ F2 @ ( late_InputS @ Name2 ) )
% 0.31/0.46 = ( F1 @ Name2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % subject.recs(1)
% 0.31/0.46 thf(fact_62_freeRes_Orecs_I1_J,axiom,
% 0.31/0.46 ! [T: $tType,P: T > $o,F1: name > name > T,F2: T,Name12: name,Name23: name] :
% 0.31/0.46 ( ! [X13: name,X22: name] : ( P @ ( F1 @ X13 @ X22 ) )
% 0.31/0.46 => ( ( P @ F2 )
% 0.31/0.46 => ( ( late_freeRes_rec @ T @ F1 @ F2 @ ( late_OutputR @ Name12 @ Name23 ) )
% 0.31/0.46 = ( F1 @ Name12 @ Name23 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % freeRes.recs(1)
% 0.31/0.46 thf(fact_63_transitions_OClose2,axiom,
% 0.31/0.46 ! [P: pi,A2: name,Y: name,P2: pi,Q: pi,X3: name,Q2: pi] :
% 0.31/0.46 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y @ P2 ) )
% 0.31/0.46 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ Q2 ) )
% 0.31/0.46 => ( ( fresh @ name @ pi @ X3 @ P )
% 0.31/0.46 => ( ( fresh @ name @ pi @ X3 @ Q )
% 0.31/0.46 => ( ( fresh @ name @ pi @ Y @ P )
% 0.31/0.46 => ( ( fresh @ name @ pi @ Y @ Q )
% 0.31/0.46 => ( ( X3 != A2 )
% 0.31/0.46 => ( ( fresh @ name @ pi @ X3 @ P2 )
% 0.31/0.46 => ( ( Y != A2 )
% 0.31/0.46 => ( ( fresh @ name @ pi @ Y @ Q2 )
% 0.31/0.46 => ( ( X3 != Y )
% 0.31/0.46 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ P2 @ ( subs @ Q2 @ X3 @ Y ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % transitions.Close2
% 0.31/0.46 thf(fact_64_transitions_OClose1,axiom,
% 0.31/0.46 ! [P: pi,A2: name,X3: name,P2: pi,Q: pi,Y: name,Q2: pi] :
% 0.31/0.46 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ P2 ) )
% 0.31/0.46 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y @ Q2 ) )
% 0.31/0.46 => ( ( fresh @ name @ pi @ X3 @ P )
% 0.31/0.46 => ( ( fresh @ name @ pi @ X3 @ Q )
% 0.31/0.46 => ( ( fresh @ name @ pi @ Y @ P )
% 0.31/0.46 => ( ( fresh @ name @ pi @ Y @ Q )
% 0.31/0.46 => ( ( X3 != A2 )
% 0.31/0.46 => ( ( fresh @ name @ pi @ X3 @ Q2 )
% 0.31/0.46 => ( ( Y != A2 )
% 0.31/0.46 => ( ( fresh @ name @ pi @ Y @ P2 )
% 0.31/0.46 => ( ( X3 != Y )
% 0.31/0.46 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ ( subs @ P2 @ X3 @ Y ) @ Q2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % transitions.Close1
% 0.31/0.46 thf(fact_65_Late__Semantics_OClose2,axiom,
% 0.31/0.46 ! [P: pi,A2: name,Y: name,P2: pi,Q: pi,X3: name,Q2: pi] :
% 0.31/0.46 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y @ P2 ) )
% 0.31/0.46 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ Q2 ) )
% 0.31/0.46 => ( ( fresh @ name @ pi @ Y @ Q )
% 0.31/0.46 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ P2 @ ( subs @ Q2 @ X3 @ Y ) ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Late_Semantics.Close2
% 0.31/0.46 thf(fact_66_freeRes_Ofresh_I1_J,axiom,
% 0.31/0.46 ! [A2: name,X2: name,X1: name] :
% 0.31/0.46 ( ( fresh @ name @ late_freeRes @ A2 @ ( late_OutputR @ X2 @ X1 ) )
% 0.31/0.46 = ( ( fresh @ name @ name @ A2 @ X2 )
% 0.31/0.46 & ( fresh @ name @ name @ A2 @ X1 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % freeRes.fresh(1)
% 0.31/0.46 thf(fact_67_Late__Semantics_Osubject_Oinject_I2_J,axiom,
% 0.31/0.46 ! [X1: name,Y1: name] :
% 0.31/0.46 ( ( ( late_BoundOutputS @ X1 )
% 0.31/0.46 = ( late_BoundOutputS @ Y1 ) )
% 0.31/0.46 = ( X1 = Y1 ) ) ).
% 0.31/0.46
% 0.31/0.46 % Late_Semantics.subject.inject(2)
% 0.31/0.46 thf(fact_68_Late__Semantics1_Osubject_Oinject_I2_J,axiom,
% 0.31/0.46 ! [X2: name,Y2: name] :
% 0.31/0.46 ( ( ( late_BoundOutputS @ X2 )
% 0.31/0.46 = ( late_BoundOutputS @ Y2 ) )
% 0.31/0.46 = ( X2 = Y2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % Late_Semantics1.subject.inject(2)
% 0.31/0.46 thf(fact_69_freeRes_Ofresh_I2_J,axiom,
% 0.31/0.46 ! [A2: name] : ( fresh @ name @ late_freeRes @ A2 @ late_TauR ) ).
% 0.31/0.46
% 0.31/0.46 % freeRes.fresh(2)
% 0.31/0.46 thf(fact_70_residual_Ofresh_I2_J,axiom,
% 0.31/0.46 ! [A2: name,X2: late_freeRes,X1: pi] :
% 0.31/0.46 ( ( fresh @ name @ late_residual @ A2 @ ( late_FreeR @ X2 @ X1 ) )
% 0.31/0.46 = ( ( fresh @ name @ late_freeRes @ A2 @ X2 )
% 0.31/0.46 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % residual.fresh(2)
% 0.31/0.46 thf(fact_71_simps_I9_J,axiom,
% 0.31/0.46 ! [X3: name,C: name,D: name,P: pi] :
% 0.31/0.46 ( ( X3 != C )
% 0.31/0.46 => ( ( X3 != D )
% 0.31/0.46 => ( ( subs @ ( res @ X3 @ P ) @ C @ D )
% 0.31/0.46 = ( res @ X3 @ ( subs @ P @ C @ D ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % simps(9)
% 0.31/0.46 thf(fact_72_subject_Ofresh_I1_J,axiom,
% 0.31/0.46 ! [A2: name,X1: name] :
% 0.31/0.46 ( ( fresh @ name @ late_subject @ A2 @ ( late_InputS @ X1 ) )
% 0.31/0.46 = ( fresh @ name @ name @ A2 @ X1 ) ) ).
% 0.31/0.46
% 0.31/0.46 % subject.fresh(1)
% 0.31/0.46 thf(fact_73_subject_Ofresh_I2_J,axiom,
% 0.31/0.46 ! [A2: name,X1: name] :
% 0.31/0.46 ( ( fresh @ name @ late_subject @ A2 @ ( late_BoundOutputS @ X1 ) )
% 0.31/0.46 = ( fresh @ name @ name @ A2 @ X1 ) ) ).
% 0.31/0.46
% 0.31/0.46 % subject.fresh(2)
% 0.31/0.46 thf(fact_74_subject_Orecs_I2_J,axiom,
% 0.31/0.46 ! [T: $tType,P: T > $o,F1: name > T,F2: name > T,Name2: name] :
% 0.31/0.46 ( ! [X13: name] : ( P @ ( F1 @ X13 ) )
% 0.31/0.46 => ( ! [X13: name] : ( P @ ( F2 @ X13 ) )
% 0.31/0.46 => ( ( late_subject_rec @ T @ F1 @ F2 @ ( late_BoundOutputS @ Name2 ) )
% 0.31/0.46 = ( F2 @ Name2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % subject.recs(2)
% 0.31/0.46 thf(fact_75_subject_Oexhaust,axiom,
% 0.31/0.46 ! [Y: late_subject] :
% 0.31/0.46 ( ! [X13: name] :
% 0.31/0.46 ( Y
% 0.31/0.46 != ( late_InputS @ X13 ) )
% 0.31/0.46 => ~ ! [X22: name] :
% 0.31/0.46 ( Y
% 0.31/0.46 != ( late_BoundOutputS @ X22 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % subject.exhaust
% 0.31/0.46 thf(fact_76_Late__Semantics1_Osubject_Odistinct_I1_J,axiom,
% 0.31/0.46 ! [X1: name,X2: name] :
% 0.31/0.46 ( ( late_InputS @ X1 )
% 0.31/0.46 != ( late_BoundOutputS @ X2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % Late_Semantics1.subject.distinct(1)
% 0.31/0.46 thf(fact_77_Late__Semantics_OResB,axiom,
% 0.31/0.46 ! [P: pi,A2: late_subject,X3: name,P2: pi,Y: name] :
% 0.31/0.46 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X3 @ P2 ) )
% 0.31/0.46 => ( ( fresh @ name @ late_subject @ Y @ A2 )
% 0.31/0.46 => ( ( Y != X3 )
% 0.31/0.46 => ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A2 @ X3 @ ( res @ Y @ P2 ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Late_Semantics.ResB
% 0.31/0.46 thf(fact_78_resCasesF,axiom,
% 0.31/0.46 ! [X3: name,P: pi,Alpha: late_freeRes,XP: pi,F3: pi > $o] :
% 0.31/0.46 ( ( late_transitions @ ( res @ X3 @ P ) @ ( late_FreeR @ Alpha @ XP ) )
% 0.31/0.46 => ( ! [P4: pi] :
% 0.31/0.46 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P4 ) )
% 0.31/0.46 => ( ( fresh @ name @ late_freeRes @ X3 @ Alpha )
% 0.31/0.46 => ( F3 @ ( res @ X3 @ P4 ) ) ) )
% 0.31/0.46 => ( F3 @ XP ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % resCasesF
% 0.31/0.46 thf(fact_79_resCasesF_H,axiom,
% 0.31/0.46 ! [X3: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 0.31/0.46 ( ( late_transitions @ ( res @ X3 @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 0.31/0.46 => ~ ! [P3: pi,Alpha2: late_freeRes,P4: pi,Y3: name] :
% 0.31/0.46 ( ( ( res @ X3 @ P )
% 0.31/0.46 = ( res @ Y3 @ P3 ) )
% 0.31/0.46 => ( ( ( late_FreeR @ Alpha @ P2 )
% 0.31/0.46 = ( late_FreeR @ Alpha2 @ ( res @ Y3 @ P4 ) ) )
% 0.31/0.46 => ( ( late_transitions @ P3 @ ( late_FreeR @ Alpha2 @ P4 ) )
% 0.31/0.46 => ~ ( fresh @ name @ late_freeRes @ Y3 @ Alpha2 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % resCasesF'
% 0.31/0.46 thf(fact_80_ResF,axiom,
% 0.31/0.46 ! [P: pi,Alpha: late_freeRes,P2: pi,Y: name] :
% 0.31/0.46 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 0.31/0.46 => ( ( fresh @ name @ late_freeRes @ Y @ Alpha )
% 0.31/0.46 => ( late_transitions @ ( res @ Y @ P ) @ ( late_FreeR @ Alpha @ ( res @ Y @ P2 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % ResF
% 0.31/0.46 thf(fact_81_pi_Odistinct_I85_J,axiom,
% 0.31/0.46 ! [Pi12: pi,Pi23: pi,Name3: name,Pi3: pi] :
% 0.31/0.46 ( ( par @ Pi12 @ Pi23 )
% 0.31/0.46 != ( res @ Name3 @ Pi3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.distinct(85)
% 0.31/0.46 thf(fact_82_freshRes,axiom,
% 0.31/0.46 ! [A2: name,P: pi] : ( fresh @ name @ pi @ A2 @ ( res @ A2 @ P ) ) ).
% 0.31/0.46
% 0.31/0.46 % freshRes
% 0.31/0.46 thf(fact_83_pi_Odistinct_I45_J,axiom,
% 0.31/0.46 ! [Pi2: pi,Name3: name,Pi3: pi] :
% 0.31/0.46 ( ( tau @ Pi2 )
% 0.31/0.46 != ( res @ Name3 @ Pi3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.distinct(45)
% 0.31/0.46 thf(fact_84_resCases_H,axiom,
% 0.31/0.46 ! [X3: name,P: pi,Rs: late_residual] :
% 0.31/0.46 ( ( late_transitions @ ( res @ X3 @ P ) @ Rs )
% 0.31/0.46 => ( ! [P3: pi,A4: name,B3: name] :
% 0.31/0.46 ( ( ( res @ X3 @ P )
% 0.31/0.46 = ( res @ B3 @ P3 ) )
% 0.31/0.46 => ! [P4: pi] :
% 0.31/0.46 ( ( Rs
% 0.31/0.46 = ( late_BoundR @ ( late_BoundOutputS @ A4 ) @ B3 @ P4 ) )
% 0.31/0.46 => ( ( late_transitions @ P3 @ ( late_FreeR @ ( late_OutputR @ A4 @ B3 ) @ P4 ) )
% 0.31/0.46 => ( A4 = B3 ) ) ) )
% 0.31/0.46 => ( ! [P3: pi,A4: late_subject,X5: name,P4: pi,Y3: name] :
% 0.31/0.46 ( ( ( res @ X3 @ P )
% 0.31/0.46 = ( res @ Y3 @ P3 ) )
% 0.31/0.46 => ( ( Rs
% 0.31/0.46 = ( late_BoundR @ A4 @ X5 @ ( res @ Y3 @ P4 ) ) )
% 0.31/0.46 => ( ( late_transitions @ P3 @ ( late_BoundR @ A4 @ X5 @ P4 ) )
% 0.31/0.46 => ( ( fresh @ name @ late_subject @ Y3 @ A4 )
% 0.31/0.46 => ( ( Y3 != X5 )
% 0.31/0.46 => ( ( fresh @ name @ pi @ X5 @ P3 )
% 0.31/0.46 => ~ ( fresh @ name @ late_subject @ X5 @ A4 ) ) ) ) ) ) )
% 0.31/0.46 => ~ ! [P3: pi,Alpha2: late_freeRes,P4: pi,Y3: name] :
% 0.31/0.46 ( ( ( res @ X3 @ P )
% 0.31/0.46 = ( res @ Y3 @ P3 ) )
% 0.31/0.46 => ( ( Rs
% 0.31/0.46 = ( late_FreeR @ Alpha2 @ ( res @ Y3 @ P4 ) ) )
% 0.31/0.46 => ( ( late_transitions @ P3 @ ( late_FreeR @ Alpha2 @ P4 ) )
% 0.31/0.46 => ~ ( fresh @ name @ late_freeRes @ Y3 @ Alpha2 ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % resCases'
% 0.31/0.46 thf(fact_85_transitions_OResB,axiom,
% 0.31/0.46 ! [P: pi,A2: late_subject,X3: name,P2: pi,Y: name] :
% 0.31/0.46 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X3 @ P2 ) )
% 0.31/0.46 => ( ( fresh @ name @ late_subject @ Y @ A2 )
% 0.31/0.46 => ( ( Y != X3 )
% 0.31/0.46 => ( ( fresh @ name @ pi @ X3 @ P )
% 0.31/0.46 => ( ( fresh @ name @ late_subject @ X3 @ A2 )
% 0.31/0.46 => ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A2 @ X3 @ ( res @ Y @ P2 ) ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % transitions.ResB
% 0.31/0.46 thf(fact_86_subject_Ostrong__inducts,axiom,
% 0.31/0.46 ! [A: $tType,P: A > late_subject > $o,Z: A,Subject2: late_subject] :
% 0.31/0.46 ( ! [Name: name,Z2: A] : ( P @ Z2 @ ( late_InputS @ Name ) )
% 0.31/0.46 => ( ! [Name: name,Z2: A] : ( P @ Z2 @ ( late_BoundOutputS @ Name ) )
% 0.31/0.46 => ( P @ Z @ Subject2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % subject.strong_inducts
% 0.31/0.46 thf(fact_87_subject_Ostrong__induct_H,axiom,
% 0.31/0.46 ! [N: $tType,P: N > late_subject > $o,Z: N,Subject2: late_subject] :
% 0.31/0.46 ( ! [Name: name,Z2: N] : ( P @ Z2 @ ( late_InputS @ Name ) )
% 0.31/0.46 => ( ! [Name: name,Z2: N] : ( P @ Z2 @ ( late_BoundOutputS @ Name ) )
% 0.31/0.46 => ( P @ Z @ Subject2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % subject.strong_induct'
% 0.31/0.46 thf(fact_88_subject_Oinducts,axiom,
% 0.31/0.46 ! [P: late_subject > $o,Subject2: late_subject] :
% 0.31/0.46 ( ! [Name: name] : ( P @ ( late_InputS @ Name ) )
% 0.31/0.46 => ( ! [Name: name] : ( P @ ( late_BoundOutputS @ Name ) )
% 0.31/0.46 => ( P @ Subject2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % subject.inducts
% 0.31/0.46 thf(fact_89_Late__Semantics_Osubject_Odistinct_I1_J,axiom,
% 0.31/0.46 ! [Name2: name,Name3: name] :
% 0.31/0.46 ( ( late_InputS @ Name2 )
% 0.31/0.46 != ( late_BoundOutputS @ Name3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % Late_Semantics.subject.distinct(1)
% 0.31/0.46 thf(fact_90_resCasesB_H,axiom,
% 0.31/0.46 ! [X6: name,P: pi,A2: late_subject,Y4: name,P2: pi] :
% 0.31/0.46 ( ( late_transitions @ ( res @ X6 @ P ) @ ( late_BoundR @ A2 @ Y4 @ P2 ) )
% 0.31/0.46 => ( ! [P3: pi,A4: name,B3: name] :
% 0.31/0.46 ( ( ( res @ X6 @ P )
% 0.31/0.46 = ( res @ B3 @ P3 ) )
% 0.31/0.46 => ! [P4: pi] :
% 0.31/0.46 ( ( ( late_BoundR @ A2 @ Y4 @ P2 )
% 0.31/0.46 = ( late_BoundR @ ( late_BoundOutputS @ A4 ) @ B3 @ P4 ) )
% 0.31/0.46 => ( ( late_transitions @ P3 @ ( late_FreeR @ ( late_OutputR @ A4 @ B3 ) @ P4 ) )
% 0.31/0.46 => ( A4 = B3 ) ) ) )
% 0.31/0.46 => ~ ! [P3: pi,A4: late_subject,X5: name,P4: pi,Y3: name] :
% 0.31/0.46 ( ( ( res @ X6 @ P )
% 0.31/0.46 = ( res @ Y3 @ P3 ) )
% 0.31/0.46 => ( ( ( late_BoundR @ A2 @ Y4 @ P2 )
% 0.31/0.46 = ( late_BoundR @ A4 @ X5 @ ( res @ Y3 @ P4 ) ) )
% 0.31/0.46 => ( ( late_transitions @ P3 @ ( late_BoundR @ A4 @ X5 @ P4 ) )
% 0.31/0.46 => ( ( fresh @ name @ late_subject @ Y3 @ A4 )
% 0.31/0.46 => ( ( Y3 != X5 )
% 0.31/0.46 => ( ( fresh @ name @ pi @ X5 @ P3 )
% 0.31/0.46 => ~ ( fresh @ name @ late_subject @ X5 @ A4 ) ) ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % resCasesB'
% 0.31/0.46 thf(fact_91_freshResidual,axiom,
% 0.31/0.46 ! [P: pi,Rs: late_residual,X3: name] :
% 0.31/0.46 ( ( late_transitions @ P @ Rs )
% 0.31/0.46 => ( ( fresh @ name @ pi @ X3 @ P )
% 0.31/0.46 => ( fresh @ name @ late_residual @ X3 @ Rs ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % freshResidual
% 0.31/0.46 thf(fact_92_substRes3,axiom,
% 0.31/0.46 ! [B: name,P: pi,A2: name] :
% 0.31/0.46 ( ( fresh @ name @ pi @ B @ P )
% 0.31/0.46 => ( ( subs @ ( res @ A2 @ P ) @ A2 @ B )
% 0.31/0.46 = ( res @ B @ ( subs @ P @ A2 @ B ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % substRes3
% 0.31/0.46 thf(fact_93_substRes2,axiom,
% 0.31/0.46 ! [B: name,P: pi,A2: name] :
% 0.31/0.46 ( ( fresh @ name @ pi @ B @ P )
% 0.31/0.46 => ( ( res @ A2 @ P )
% 0.31/0.46 = ( res @ B @ ( subs @ P @ A2 @ B ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % substRes2
% 0.31/0.46 thf(fact_94_Open,axiom,
% 0.31/0.46 ! [P: pi,A2: name,B: name,P2: pi] :
% 0.31/0.46 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A2 @ B ) @ P2 ) )
% 0.31/0.46 => ( ( A2 != B )
% 0.31/0.46 => ( late_transitions @ ( res @ B @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ B @ P2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Open
% 0.31/0.46 thf(fact_95_freshFreeDerivative_I1_J,axiom,
% 0.31/0.46 ! [P: pi,Alpha: late_freeRes,P2: pi,Y: name] :
% 0.31/0.46 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 0.31/0.46 => ( ( fresh @ name @ pi @ Y @ P )
% 0.31/0.46 => ( fresh @ name @ late_freeRes @ Y @ Alpha ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % freshFreeDerivative(1)
% 0.31/0.46 thf(fact_96_freshBoundDerivative_I1_J,axiom,
% 0.31/0.46 ! [P: pi,A2: late_subject,X3: name,P2: pi,Y: name] :
% 0.31/0.46 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X3 @ P2 ) )
% 0.31/0.46 => ( ( fresh @ name @ pi @ Y @ P )
% 0.31/0.46 => ( fresh @ name @ late_subject @ Y @ A2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % freshBoundDerivative(1)
% 0.31/0.46 thf(fact_97_resTauBoundTrans,axiom,
% 0.31/0.46 ! [X3: name,P: pi,A2: late_subject,Y: name,P2: pi] :
% 0.31/0.46 ~ ( late_transitions @ ( res @ X3 @ ( tau @ P ) ) @ ( late_BoundR @ A2 @ Y @ P2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % resTauBoundTrans
% 0.31/0.46 thf(fact_98_parCasesB_H,axiom,
% 0.31/0.46 ! [P: pi,Q: pi,B: late_subject,Y: name,P2: pi] :
% 0.31/0.46 ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ B @ Y @ P2 ) )
% 0.31/0.46 => ( ! [P3: pi,A4: late_subject,X5: name,P4: pi,Q4: pi] :
% 0.31/0.46 ( ( ( par @ P @ Q )
% 0.31/0.46 = ( par @ P3 @ Q4 ) )
% 0.31/0.46 => ( ( ( late_BoundR @ B @ Y @ P2 )
% 0.31/0.46 = ( late_BoundR @ A4 @ X5 @ ( par @ P4 @ Q4 ) ) )
% 0.31/0.46 => ( ( late_transitions @ P3 @ ( late_BoundR @ A4 @ X5 @ P4 ) )
% 0.31/0.46 => ( ( fresh @ name @ pi @ X5 @ P3 )
% 0.31/0.46 => ( ( fresh @ name @ pi @ X5 @ Q4 )
% 0.31/0.46 => ~ ( fresh @ name @ late_subject @ X5 @ A4 ) ) ) ) ) )
% 0.31/0.46 => ~ ! [Q4: pi,A4: late_subject,X5: name,Q3: pi,P3: pi] :
% 0.31/0.46 ( ( ( par @ P @ Q )
% 0.31/0.46 = ( par @ P3 @ Q4 ) )
% 0.31/0.46 => ( ( ( late_BoundR @ B @ Y @ P2 )
% 0.31/0.46 = ( late_BoundR @ A4 @ X5 @ ( par @ P3 @ Q3 ) ) )
% 0.31/0.46 => ( ( late_transitions @ Q4 @ ( late_BoundR @ A4 @ X5 @ Q3 ) )
% 0.31/0.46 => ( ( fresh @ name @ pi @ X5 @ P3 )
% 0.31/0.46 => ( ( fresh @ name @ pi @ X5 @ Q4 )
% 0.31/0.46 => ~ ( fresh @ name @ late_subject @ X5 @ A4 ) ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % parCasesB'
% 0.31/0.46 thf(fact_99_transitions_OPar1B,axiom,
% 0.31/0.46 ! [P: pi,A2: late_subject,X3: name,P2: pi,Q: pi] :
% 0.31/0.46 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X3 @ P2 ) )
% 0.31/0.46 => ( ( fresh @ name @ pi @ X3 @ P )
% 0.31/0.46 => ( ( fresh @ name @ pi @ X3 @ Q )
% 0.31/0.46 => ( ( fresh @ name @ late_subject @ X3 @ A2 )
% 0.31/0.46 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X3 @ ( par @ P2 @ Q ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % transitions.Par1B
% 0.31/0.46 thf(fact_100_transitions_OPar2B,axiom,
% 0.31/0.46 ! [Q: pi,A2: late_subject,X3: name,Q2: pi,P: pi] :
% 0.31/0.46 ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X3 @ Q2 ) )
% 0.31/0.46 => ( ( fresh @ name @ pi @ X3 @ P )
% 0.31/0.46 => ( ( fresh @ name @ pi @ X3 @ Q )
% 0.31/0.46 => ( ( fresh @ name @ late_subject @ X3 @ A2 )
% 0.31/0.46 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X3 @ ( par @ P @ Q2 ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % transitions.Par2B
% 0.31/0.46 thf(fact_101_resTauOutputTrans,axiom,
% 0.31/0.46 ! [X3: name,P: pi,A2: name,B: name,P2: pi] :
% 0.31/0.46 ~ ( late_transitions @ ( res @ X3 @ ( tau @ P ) ) @ ( late_FreeR @ ( late_OutputR @ A2 @ B ) @ P2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % resTauOutputTrans
% 0.31/0.46 thf(fact_102_Late__Semantics_OClose1,axiom,
% 0.31/0.46 ! [P: pi,A2: name,X3: name,P2: pi,Q: pi,Y: name,Q2: pi] :
% 0.31/0.46 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ P2 ) )
% 0.31/0.46 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y @ Q2 ) )
% 0.31/0.46 => ( ( fresh @ name @ pi @ Y @ P )
% 0.31/0.46 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ ( subs @ P2 @ X3 @ Y ) @ Q2 ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Late_Semantics.Close1
% 0.31/0.46 thf(fact_103_resOutputTauTrans,axiom,
% 0.31/0.46 ! [X3: name,A2: name,B: name,P: pi,P2: pi] :
% 0.31/0.46 ~ ( late_transitions @ ( res @ X3 @ ( output @ A2 @ B @ P ) ) @ ( late_FreeR @ late_TauR @ P2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % resOutputTauTrans
% 0.31/0.46 thf(fact_104_resOutputInputTrans,axiom,
% 0.31/0.46 ! [X3: name,A2: name,B: name,P: pi,C: name,Y: name,P2: pi] :
% 0.31/0.46 ~ ( late_transitions @ ( res @ X3 @ ( output @ A2 @ B @ P ) ) @ ( late_BoundR @ ( late_InputS @ C ) @ Y @ P2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % resOutputInputTrans
% 0.31/0.46 thf(fact_105_resOutputOutputTrans,axiom,
% 0.31/0.46 ! [X3: name,A2: name,P: pi,B: name,Y: name,P2: pi] :
% 0.31/0.46 ~ ( late_transitions @ ( res @ X3 @ ( output @ A2 @ X3 @ P ) ) @ ( late_FreeR @ ( late_OutputR @ B @ Y ) @ P2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % resOutputOutputTrans
% 0.31/0.46 thf(fact_106_resInputBoundOutputTrans,axiom,
% 0.31/0.46 ! [X3: name,A2: name,Y: name,P: pi,B: name,Z: name,P2: pi] :
% 0.31/0.46 ~ ( late_transitions @ ( res @ X3 @ ( input @ A2 @ Y @ P ) ) @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ Z @ P2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % resInputBoundOutputTrans
% 0.31/0.46 thf(fact_107_outputTauTrans,axiom,
% 0.31/0.46 ! [A2: name,B: name,P: pi,P2: pi] :
% 0.31/0.46 ~ ( late_transitions @ ( output @ A2 @ B @ P ) @ ( late_FreeR @ late_TauR @ P2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % outputTauTrans
% 0.31/0.46 thf(fact_108_outputCases,axiom,
% 0.31/0.46 ! [A2: name,B: name,P: pi,Alpha: late_freeRes,P2: pi,Prop: late_freeRes > pi > $o] :
% 0.31/0.46 ( ( late_transitions @ ( output @ A2 @ B @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 0.31/0.46 => ( ( ( Alpha
% 0.31/0.46 = ( late_OutputR @ A2 @ B ) )
% 0.31/0.46 => ( ( P = P2 )
% 0.31/0.46 => ( Prop @ ( late_OutputR @ A2 @ B ) @ P ) ) )
% 0.31/0.46 => ( Prop @ Alpha @ P2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % outputCases
% 0.31/0.46 thf(fact_109_outputCases_H,axiom,
% 0.31/0.46 ! [A2: name,B: name,P: pi,Rs: late_residual] :
% 0.31/0.46 ( ( late_transitions @ ( output @ A2 @ B @ P ) @ Rs )
% 0.31/0.46 => ~ ! [A4: name,B3: name,P3: pi] :
% 0.31/0.46 ( ( ( A2 = A4 )
% 0.31/0.46 & ( B = B3 )
% 0.31/0.46 & ( P = P3 ) )
% 0.31/0.46 => ( Rs
% 0.31/0.46 != ( late_FreeR @ ( late_OutputR @ A4 @ B3 ) @ P3 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % outputCases'
% 0.31/0.46 thf(fact_110_name__fresh,axiom,
% 0.31/0.46 ( ( fresh @ name @ name )
% 0.31/0.46 = ( ^ [A5: name,B4: name] : ( A5 != B4 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % name_fresh
% 0.31/0.46 thf(fact_111_pi_Ofresh_I2_J,axiom,
% 0.31/0.46 ! [A2: name,X32: name,X2: name,X1: pi] :
% 0.31/0.46 ( ( fresh @ name @ pi @ A2 @ ( output @ X32 @ X2 @ X1 ) )
% 0.31/0.46 = ( ( fresh @ name @ name @ A2 @ X32 )
% 0.31/0.46 & ( fresh @ name @ name @ A2 @ X2 )
% 0.31/0.46 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.fresh(2)
% 0.31/0.46 thf(fact_112_pi_Odistinct_I21_J,axiom,
% 0.31/0.46 ! [Name12: name,Name23: name,Pi2: pi,Name13: name,Name24: name,Pi3: pi] :
% 0.31/0.46 ( ( output @ Name12 @ Name23 @ Pi2 )
% 0.31/0.46 != ( input @ Name13 @ Name24 @ Pi3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.distinct(21)
% 0.31/0.46 thf(fact_113_pi_Oinject_I1_J,axiom,
% 0.31/0.46 ! [X32: name,X2: name,X1: pi,Y32: name,Y2: name,Y1: pi] :
% 0.31/0.46 ( ( ( output @ X32 @ X2 @ X1 )
% 0.31/0.46 = ( output @ Y32 @ Y2 @ Y1 ) )
% 0.31/0.46 = ( ( X32 = Y32 )
% 0.31/0.46 & ( X2 = Y2 )
% 0.31/0.46 & ( X1 = Y1 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.inject(1)
% 0.31/0.46 thf(fact_114_pi_Odistinct_I55_J,axiom,
% 0.31/0.46 ! [Name12: name,Name23: name,Pi2: pi,Pi1: pi,Pi22: pi] :
% 0.31/0.46 ( ( input @ Name12 @ Name23 @ Pi2 )
% 0.31/0.46 != ( par @ Pi1 @ Pi22 ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.distinct(55)
% 0.31/0.46 thf(fact_115_pi_Odistinct_I57_J,axiom,
% 0.31/0.46 ! [Name12: name,Name23: name,Pi2: pi,Name3: name,Pi3: pi] :
% 0.31/0.46 ( ( input @ Name12 @ Name23 @ Pi2 )
% 0.31/0.46 != ( res @ Name3 @ Pi3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.distinct(57)
% 0.31/0.46 thf(fact_116_pi_Odistinct_I29_J,axiom,
% 0.31/0.46 ! [Name12: name,Name23: name,Pi2: pi,Pi1: pi,Pi22: pi] :
% 0.31/0.46 ( ( output @ Name12 @ Name23 @ Pi2 )
% 0.31/0.46 != ( par @ Pi1 @ Pi22 ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.distinct(29)
% 0.31/0.46 thf(fact_117_pi_Odistinct_I31_J,axiom,
% 0.31/0.46 ! [Name12: name,Name23: name,Pi2: pi,Name3: name,Pi3: pi] :
% 0.31/0.46 ( ( output @ Name12 @ Name23 @ Pi2 )
% 0.31/0.46 != ( res @ Name3 @ Pi3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.distinct(31)
% 0.31/0.46 thf(fact_118_pi_Odistinct_I35_J,axiom,
% 0.31/0.46 ! [Pi2: pi,Name13: name,Name24: name,Pi3: pi] :
% 0.31/0.46 ( ( tau @ Pi2 )
% 0.31/0.46 != ( input @ Name13 @ Name24 @ Pi3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.distinct(35)
% 0.31/0.46 thf(fact_119_pi_Odistinct_I19_J,axiom,
% 0.31/0.46 ! [Name12: name,Name23: name,Pi2: pi,Pi3: pi] :
% 0.31/0.46 ( ( output @ Name12 @ Name23 @ Pi2 )
% 0.31/0.46 != ( tau @ Pi3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.distinct(19)
% 0.31/0.46 thf(fact_120_resTrans_I2_J,axiom,
% 0.31/0.46 ! [X3: name,Y: name,P: pi,Rs: late_residual] :
% 0.31/0.46 ~ ( late_transitions @ ( res @ X3 @ ( input @ X3 @ Y @ P ) ) @ Rs ) ).
% 0.31/0.46
% 0.31/0.46 % resTrans(2)
% 0.31/0.46 thf(fact_121_inputFreeTrans,axiom,
% 0.31/0.46 ! [A2: name,X3: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 0.31/0.46 ~ ( late_transitions @ ( input @ A2 @ X3 @ P ) @ ( late_FreeR @ Alpha @ P2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % inputFreeTrans
% 0.31/0.46 thf(fact_122_resTrans_I1_J,axiom,
% 0.31/0.46 ! [X3: name,B: name,P: pi,Rs: late_residual] :
% 0.31/0.46 ~ ( late_transitions @ ( res @ X3 @ ( output @ X3 @ B @ P ) ) @ Rs ) ).
% 0.31/0.46
% 0.31/0.46 % resTrans(1)
% 0.31/0.46 thf(fact_123_outputBoundTrans,axiom,
% 0.31/0.46 ! [A2: name,B: name,P: pi,C: late_subject,X3: name,P2: pi] :
% 0.31/0.46 ~ ( late_transitions @ ( output @ A2 @ B @ P ) @ ( late_BoundR @ C @ X3 @ P2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % outputBoundTrans
% 0.31/0.46 thf(fact_124_outputFreshTrans,axiom,
% 0.31/0.46 ! [A2: name,B: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 0.31/0.46 ( ( late_transitions @ ( output @ A2 @ B @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 0.31/0.46 => ~ ( ( fresh @ name @ late_freeRes @ A2 @ Alpha )
% 0.31/0.46 | ( fresh @ name @ late_freeRes @ B @ Alpha ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % outputFreshTrans
% 0.31/0.46 thf(fact_125_resInputFreeTrans,axiom,
% 0.31/0.46 ! [X3: name,A2: name,Y: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 0.31/0.46 ~ ( late_transitions @ ( res @ X3 @ ( input @ A2 @ Y @ P ) ) @ ( late_FreeR @ Alpha @ P2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % resInputFreeTrans
% 0.31/0.46 thf(fact_126_Late__Semantics_OInput,axiom,
% 0.31/0.46 ! [A2: name,X3: name,P: pi] : ( late_transitions @ ( input @ A2 @ X3 @ P ) @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ P ) ) ).
% 0.31/0.46
% 0.31/0.46 % Late_Semantics.Input
% 0.31/0.46 thf(fact_127_transitions_OInput,axiom,
% 0.31/0.46 ! [X3: name,A2: name,P: pi] :
% 0.31/0.46 ( ( X3 != A2 )
% 0.31/0.46 => ( late_transitions @ ( input @ A2 @ X3 @ P ) @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ P ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % transitions.Input
% 0.31/0.46 thf(fact_128_inputBoundOutputTrans,axiom,
% 0.31/0.46 ! [A2: name,X3: name,P: pi,B: name,Y: name,P2: pi] :
% 0.31/0.46 ~ ( late_transitions @ ( input @ A2 @ X3 @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ Y @ P2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % inputBoundOutputTrans
% 0.31/0.46 thf(fact_129_inputIneqTrans,axiom,
% 0.31/0.46 ! [A2: name,X3: name,P: pi,B: late_subject,Y: name,P2: pi] :
% 0.31/0.46 ( ( late_transitions @ ( input @ A2 @ X3 @ P ) @ ( late_BoundR @ B @ Y @ P2 ) )
% 0.31/0.46 => ~ ( fresh @ name @ late_subject @ A2 @ B ) ) ).
% 0.31/0.46
% 0.31/0.46 % inputIneqTrans
% 0.31/0.46 thf(fact_130_Output,axiom,
% 0.31/0.46 ! [A2: name,B: name,P: pi] : ( late_transitions @ ( output @ A2 @ B @ P ) @ ( late_FreeR @ ( late_OutputR @ A2 @ B ) @ P ) ) ).
% 0.31/0.46
% 0.31/0.46 % Output
% 0.31/0.46 thf(fact_131_outputIneqTrans,axiom,
% 0.31/0.46 ! [A2: name,B: name,P: pi,C: name,D: name,P2: pi] :
% 0.31/0.46 ( ( late_transitions @ ( output @ A2 @ B @ P ) @ ( late_FreeR @ ( late_OutputR @ C @ D ) @ P2 ) )
% 0.31/0.46 => ~ ( ( A2 != C )
% 0.31/0.46 | ( B != D ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % outputIneqTrans
% 0.31/0.46 thf(fact_132_residual_Ofresh_I1_J,axiom,
% 0.31/0.46 ! [A2: name,X32: late_subject,X1: name,X2: pi] :
% 0.31/0.46 ( ( fresh @ name @ late_residual @ A2 @ ( late_BoundR @ X32 @ X1 @ X2 ) )
% 0.31/0.46 = ( ( fresh @ name @ late_subject @ A2 @ X32 )
% 0.31/0.46 & ( fresh @ name @ ( name > ( noption @ pi ) ) @ A2 @ ( abs_fun @ name @ pi @ X1 @ X2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % residual.fresh(1)
% 0.31/0.46 thf(fact_133_simps_I3_J,axiom,
% 0.31/0.46 ! [A2: name,B: name,P: pi,C: name,D: name] :
% 0.31/0.46 ( ( subs @ ( output @ A2 @ B @ P ) @ C @ D )
% 0.31/0.46 = ( output @ ( subst_name @ A2 @ C @ D ) @ ( subst_name @ B @ C @ D ) @ ( subs @ P @ C @ D ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % simps(3)
% 0.31/0.46 thf(fact_134_substInput,axiom,
% 0.31/0.46 ! [X3: name,B: name,C: name,A2: name,P: pi] :
% 0.31/0.46 ( ( X3 != B )
% 0.31/0.46 => ( ( X3 != C )
% 0.31/0.46 => ( ( subs @ ( input @ A2 @ X3 @ P ) @ B @ C )
% 0.31/0.46 = ( input @ ( subst_name @ A2 @ B @ C ) @ X3 @ ( subs @ P @ B @ C ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % substInput
% 0.31/0.46 thf(fact_135_simps_I4_J,axiom,
% 0.31/0.46 ! [X3: name,A2: name,C: name,D: name,P: pi] :
% 0.31/0.46 ( ( X3 != A2 )
% 0.31/0.46 => ( ( X3 != C )
% 0.31/0.46 => ( ( X3 != D )
% 0.31/0.46 => ( ( subs @ ( input @ A2 @ X3 @ P ) @ C @ D )
% 0.31/0.46 = ( input @ ( subst_name @ A2 @ C @ D ) @ X3 @ ( subs @ P @ C @ D ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % simps(4)
% 0.31/0.46 thf(fact_136_inputCases_H,axiom,
% 0.31/0.46 ! [A2: name,B: name,P: pi,Rs: late_residual] :
% 0.31/0.46 ( ( late_transitions @ ( input @ A2 @ B @ P ) @ Rs )
% 0.31/0.46 => ~ ! [X5: name,A4: name,P3: pi] :
% 0.31/0.46 ( ( ( A2 = A4 )
% 0.31/0.46 & ( ( abs_fun @ name @ pi @ B @ P )
% 0.31/0.46 = ( abs_fun @ name @ pi @ X5 @ P3 ) ) )
% 0.31/0.46 => ( ( Rs
% 0.31/0.46 = ( late_BoundR @ ( late_InputS @ A4 ) @ X5 @ P3 ) )
% 0.31/0.46 => ( X5 = A4 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % inputCases'
% 0.31/0.46 thf(fact_137_pi_Ofresh_I9_J,axiom,
% 0.31/0.46 ! [A2: name,X1: name,X2: pi] :
% 0.31/0.46 ( ( fresh @ name @ pi @ A2 @ ( res @ X1 @ X2 ) )
% 0.31/0.46 = ( fresh @ name @ ( name > ( noption @ pi ) ) @ A2 @ ( abs_fun @ name @ pi @ X1 @ X2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.fresh(9)
% 0.31/0.46 thf(fact_138_pi_Ofresh_I4_J,axiom,
% 0.31/0.46 ! [A2: name,X32: name,X1: name,X2: pi] :
% 0.31/0.46 ( ( fresh @ name @ pi @ A2 @ ( input @ X32 @ X1 @ X2 ) )
% 0.31/0.46 = ( ( fresh @ name @ name @ A2 @ X32 )
% 0.31/0.46 & ( fresh @ name @ ( name > ( noption @ pi ) ) @ A2 @ ( abs_fun @ name @ pi @ X1 @ X2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.fresh(4)
% 0.31/0.46 thf(fact_139_pi_Oinject_I8_J,axiom,
% 0.31/0.46 ! [X1: name,X2: pi,Y1: name,Y2: pi] :
% 0.31/0.46 ( ( ( res @ X1 @ X2 )
% 0.31/0.46 = ( res @ Y1 @ Y2 ) )
% 0.31/0.46 = ( ( abs_fun @ name @ pi @ X1 @ X2 )
% 0.31/0.46 = ( abs_fun @ name @ pi @ Y1 @ Y2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.inject(8)
% 0.31/0.46 thf(fact_140_residual_Oinject_I1_J,axiom,
% 0.31/0.46 ! [X32: late_subject,X1: name,X2: pi,Y32: late_subject,Y1: name,Y2: pi] :
% 0.31/0.46 ( ( ( late_BoundR @ X32 @ X1 @ X2 )
% 0.31/0.46 = ( late_BoundR @ Y32 @ Y1 @ Y2 ) )
% 0.31/0.46 = ( ( X32 = Y32 )
% 0.31/0.46 & ( ( abs_fun @ name @ pi @ X1 @ X2 )
% 0.31/0.46 = ( abs_fun @ name @ pi @ Y1 @ Y2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % residual.inject(1)
% 0.31/0.46 thf(fact_141_subst__name__def,axiom,
% 0.31/0.46 ( subst_name
% 0.31/0.46 = ( ^ [A5: name,B4: name,C3: name] : ( if @ name @ ( A5 = B4 ) @ C3 @ A5 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % subst_name_def
% 0.31/0.46 thf(fact_142_name__fresh__abs,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( fs_name @ A )
% 0.31/0.46 => ! [B: name,A2: name,X3: A] :
% 0.31/0.46 ( ( fresh @ name @ ( name > ( noption @ A ) ) @ B @ ( abs_fun @ name @ A @ A2 @ X3 ) )
% 0.31/0.46 = ( ( B = A2 )
% 0.31/0.46 | ( fresh @ name @ A @ B @ X3 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % name_fresh_abs
% 0.31/0.46 thf(fact_143_abs__fresh_I1_J,axiom,
% 0.31/0.46 ! [X7: $tType] :
% 0.31/0.46 ( ( fs_name @ X7 )
% 0.31/0.46 => ! [B: name,A2: name,X3: X7] :
% 0.31/0.46 ( ( fresh @ name @ ( name > ( noption @ X7 ) ) @ B @ ( abs_fun @ name @ X7 @ A2 @ X3 ) )
% 0.31/0.46 = ( ( B = A2 )
% 0.31/0.46 | ( fresh @ name @ X7 @ B @ X3 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % abs_fresh(1)
% 0.31/0.46 thf(fact_144_pi_Oinject_I3_J,axiom,
% 0.31/0.46 ! [X32: name,X1: name,X2: pi,Y32: name,Y1: name,Y2: pi] :
% 0.31/0.46 ( ( ( input @ X32 @ X1 @ X2 )
% 0.31/0.46 = ( input @ Y32 @ Y1 @ Y2 ) )
% 0.31/0.46 = ( ( X32 = Y32 )
% 0.31/0.46 & ( ( abs_fun @ name @ pi @ X1 @ X2 )
% 0.31/0.46 = ( abs_fun @ name @ pi @ Y1 @ Y2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.inject(3)
% 0.31/0.46 thf(fact_145_simps_I5_J,axiom,
% 0.31/0.46 ! [A2: name,B: name,P: pi,C: name,D: name] :
% 0.31/0.46 ( ( subs @ ( match @ A2 @ B @ P ) @ C @ D )
% 0.31/0.46 = ( match @ ( subst_name @ A2 @ C @ D ) @ ( subst_name @ B @ C @ D ) @ ( subs @ P @ C @ D ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % simps(5)
% 0.31/0.46 thf(fact_146_simps_I6_J,axiom,
% 0.31/0.46 ! [A2: name,B: name,P: pi,C: name,D: name] :
% 0.31/0.46 ( ( subs @ ( mismatch @ A2 @ B @ P ) @ C @ D )
% 0.31/0.46 = ( mismatch @ ( subst_name @ A2 @ C @ D ) @ ( subst_name @ B @ C @ D ) @ ( subs @ P @ C @ D ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % simps(6)
% 0.31/0.46 thf(fact_147_pi_Ofresh_I5_J,axiom,
% 0.31/0.46 ! [A2: name,X32: name,X2: name,X1: pi] :
% 0.31/0.46 ( ( fresh @ name @ pi @ A2 @ ( match @ X32 @ X2 @ X1 ) )
% 0.31/0.46 = ( ( fresh @ name @ name @ A2 @ X32 )
% 0.31/0.46 & ( fresh @ name @ name @ A2 @ X2 )
% 0.31/0.46 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.fresh(5)
% 0.31/0.46 thf(fact_148_pi_Ofresh_I6_J,axiom,
% 0.31/0.46 ! [A2: name,X32: name,X2: name,X1: pi] :
% 0.31/0.46 ( ( fresh @ name @ pi @ A2 @ ( mismatch @ X32 @ X2 @ X1 ) )
% 0.31/0.46 = ( ( fresh @ name @ name @ A2 @ X32 )
% 0.31/0.46 & ( fresh @ name @ name @ A2 @ X2 )
% 0.31/0.46 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.fresh(6)
% 0.31/0.46 thf(fact_149_matchCases,axiom,
% 0.31/0.46 ! [A2: name,B: name,P: pi,Rs: late_residual,F3: name > name > $o] :
% 0.31/0.46 ( ( late_transitions @ ( match @ A2 @ B @ P ) @ Rs )
% 0.31/0.46 => ( ( ( late_transitions @ P @ Rs )
% 0.31/0.46 => ( ( A2 = B )
% 0.31/0.46 => ( F3 @ A2 @ A2 ) ) )
% 0.31/0.46 => ( F3 @ A2 @ B ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % matchCases
% 0.31/0.46 thf(fact_150_matchTrans,axiom,
% 0.31/0.46 ! [A2: name,B: name,P: pi,Rs: late_residual] :
% 0.31/0.46 ( ( late_transitions @ ( match @ A2 @ B @ P ) @ Rs )
% 0.31/0.46 => ( A2 = B ) ) ).
% 0.31/0.46
% 0.31/0.46 % matchTrans
% 0.31/0.46 thf(fact_151_matchCases_H,axiom,
% 0.31/0.46 ! [A2: name,B: name,P: pi,Rs: late_residual] :
% 0.31/0.46 ( ( late_transitions @ ( match @ A2 @ B @ P ) @ Rs )
% 0.31/0.46 => ~ ! [P3: pi] :
% 0.31/0.46 ( ( ( B = A2 )
% 0.31/0.46 & ( P = P3 ) )
% 0.31/0.46 => ~ ( late_transitions @ P3 @ Rs ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % matchCases'
% 0.31/0.46 thf(fact_152_mismatchCases,axiom,
% 0.31/0.46 ! [A2: name,B: name,P: pi,Rs: late_residual,F3: name > name > $o] :
% 0.31/0.46 ( ( late_transitions @ ( mismatch @ A2 @ B @ P ) @ Rs )
% 0.31/0.46 => ( ( ( late_transitions @ P @ Rs )
% 0.31/0.46 => ( ( A2 != B )
% 0.31/0.46 => ( F3 @ A2 @ B ) ) )
% 0.31/0.46 => ( F3 @ A2 @ B ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % mismatchCases
% 0.31/0.46 thf(fact_153_mismatchTrans,axiom,
% 0.31/0.46 ! [A2: name,P: pi,Rs: late_residual] :
% 0.31/0.46 ~ ( late_transitions @ ( mismatch @ A2 @ A2 @ P ) @ Rs ) ).
% 0.31/0.46
% 0.31/0.46 % mismatchTrans
% 0.31/0.46 thf(fact_154_mismatchCases_H,axiom,
% 0.31/0.46 ! [A2: name,B: name,P: pi,Rs: late_residual] :
% 0.31/0.46 ( ( late_transitions @ ( mismatch @ A2 @ B @ P ) @ Rs )
% 0.31/0.46 => ~ ! [P3: pi,A4: name,B3: name] :
% 0.31/0.46 ( ( ( A2 = A4 )
% 0.31/0.46 & ( B = B3 )
% 0.31/0.46 & ( P = P3 ) )
% 0.31/0.46 => ( ( late_transitions @ P3 @ Rs )
% 0.31/0.46 => ( A4 = B3 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % mismatchCases'
% 0.31/0.46 thf(fact_155_Match,axiom,
% 0.31/0.46 ! [P: pi,Rs: late_residual,B: name] :
% 0.31/0.46 ( ( late_transitions @ P @ Rs )
% 0.31/0.46 => ( late_transitions @ ( match @ B @ B @ P ) @ Rs ) ) ).
% 0.31/0.46
% 0.31/0.46 % Match
% 0.31/0.46 thf(fact_156_Mismatch,axiom,
% 0.31/0.46 ! [P: pi,Rs: late_residual,A2: name,B: name] :
% 0.31/0.46 ( ( late_transitions @ P @ Rs )
% 0.31/0.46 => ( ( A2 != B )
% 0.31/0.46 => ( late_transitions @ ( mismatch @ A2 @ B @ P ) @ Rs ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Mismatch
% 0.31/0.46 thf(fact_157_pi_Odistinct_I73_J,axiom,
% 0.31/0.46 ! [Name12: name,Name23: name,Pi2: pi,Pi1: pi,Pi22: pi] :
% 0.31/0.46 ( ( mismatch @ Name12 @ Name23 @ Pi2 )
% 0.31/0.46 != ( par @ Pi1 @ Pi22 ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.distinct(73)
% 0.31/0.46 thf(fact_158_pi_Odistinct_I65_J,axiom,
% 0.31/0.46 ! [Name12: name,Name23: name,Pi2: pi,Pi1: pi,Pi22: pi] :
% 0.31/0.46 ( ( match @ Name12 @ Name23 @ Pi2 )
% 0.31/0.46 != ( par @ Pi1 @ Pi22 ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.distinct(65)
% 0.31/0.46 thf(fact_159_pi_Odistinct_I75_J,axiom,
% 0.31/0.46 ! [Name12: name,Name23: name,Pi2: pi,Name3: name,Pi3: pi] :
% 0.31/0.46 ( ( mismatch @ Name12 @ Name23 @ Pi2 )
% 0.31/0.46 != ( res @ Name3 @ Pi3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.distinct(75)
% 0.31/0.46 thf(fact_160_pi_Odistinct_I67_J,axiom,
% 0.31/0.46 ! [Name12: name,Name23: name,Pi2: pi,Name3: name,Pi3: pi] :
% 0.31/0.46 ( ( match @ Name12 @ Name23 @ Pi2 )
% 0.31/0.46 != ( res @ Name3 @ Pi3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.distinct(67)
% 0.31/0.46 thf(fact_161_pi_Odistinct_I61_J,axiom,
% 0.31/0.46 ! [Name12: name,Name23: name,Pi2: pi,Name13: name,Name24: name,Pi3: pi] :
% 0.31/0.46 ( ( match @ Name12 @ Name23 @ Pi2 )
% 0.31/0.46 != ( mismatch @ Name13 @ Name24 @ Pi3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.distinct(61)
% 0.31/0.46 thf(fact_162_pi_Oinject_I4_J,axiom,
% 0.31/0.46 ! [X32: name,X2: name,X1: pi,Y32: name,Y2: name,Y1: pi] :
% 0.31/0.46 ( ( ( match @ X32 @ X2 @ X1 )
% 0.31/0.46 = ( match @ Y32 @ Y2 @ Y1 ) )
% 0.31/0.46 = ( ( X32 = Y32 )
% 0.31/0.46 & ( X2 = Y2 )
% 0.31/0.46 & ( X1 = Y1 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.inject(4)
% 0.31/0.46 thf(fact_163_pi_Oinject_I5_J,axiom,
% 0.31/0.46 ! [X32: name,X2: name,X1: pi,Y32: name,Y2: name,Y1: pi] :
% 0.31/0.46 ( ( ( mismatch @ X32 @ X2 @ X1 )
% 0.31/0.46 = ( mismatch @ Y32 @ Y2 @ Y1 ) )
% 0.31/0.46 = ( ( X32 = Y32 )
% 0.31/0.46 & ( X2 = Y2 )
% 0.31/0.46 & ( X1 = Y1 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.inject(5)
% 0.31/0.46 thf(fact_164_pi_Odistinct_I49_J,axiom,
% 0.31/0.46 ! [Name12: name,Name23: name,Pi2: pi,Name13: name,Name24: name,Pi3: pi] :
% 0.31/0.46 ( ( input @ Name12 @ Name23 @ Pi2 )
% 0.31/0.46 != ( match @ Name13 @ Name24 @ Pi3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.distinct(49)
% 0.31/0.46 thf(fact_165_pi_Odistinct_I51_J,axiom,
% 0.31/0.46 ! [Name12: name,Name23: name,Pi2: pi,Name13: name,Name24: name,Pi3: pi] :
% 0.31/0.46 ( ( input @ Name12 @ Name23 @ Pi2 )
% 0.31/0.46 != ( mismatch @ Name13 @ Name24 @ Pi3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.distinct(51)
% 0.31/0.46 thf(fact_166_pi_Odistinct_I23_J,axiom,
% 0.31/0.46 ! [Name12: name,Name23: name,Pi2: pi,Name13: name,Name24: name,Pi3: pi] :
% 0.31/0.46 ( ( output @ Name12 @ Name23 @ Pi2 )
% 0.31/0.46 != ( match @ Name13 @ Name24 @ Pi3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.distinct(23)
% 0.31/0.46 thf(fact_167_pi_Odistinct_I25_J,axiom,
% 0.31/0.46 ! [Name12: name,Name23: name,Pi2: pi,Name13: name,Name24: name,Pi3: pi] :
% 0.31/0.46 ( ( output @ Name12 @ Name23 @ Pi2 )
% 0.31/0.46 != ( mismatch @ Name13 @ Name24 @ Pi3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.distinct(25)
% 0.31/0.46 thf(fact_168_pi_Odistinct_I39_J,axiom,
% 0.31/0.46 ! [Pi2: pi,Name13: name,Name24: name,Pi3: pi] :
% 0.31/0.46 ( ( tau @ Pi2 )
% 0.31/0.46 != ( mismatch @ Name13 @ Name24 @ Pi3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.distinct(39)
% 0.31/0.46 thf(fact_169_pi_Odistinct_I37_J,axiom,
% 0.31/0.46 ! [Pi2: pi,Name13: name,Name24: name,Pi3: pi] :
% 0.31/0.46 ( ( tau @ Pi2 )
% 0.31/0.46 != ( match @ Name13 @ Name24 @ Pi3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.distinct(37)
% 0.31/0.46 thf(fact_170_abs__fun__eq1,axiom,
% 0.31/0.46 ! [X: $tType,A: $tType,A2: X,X3: A,Y: A] :
% 0.31/0.46 ( ( ( abs_fun @ X @ A @ A2 @ X3 )
% 0.31/0.46 = ( abs_fun @ X @ A @ A2 @ Y ) )
% 0.31/0.46 = ( X3 = Y ) ) ).
% 0.31/0.46
% 0.31/0.46 % abs_fun_eq1
% 0.31/0.46 thf(fact_171_freeRes_Ocase_I2_J,axiom,
% 0.31/0.46 ! [A: $tType,F1: name > name > A,F2: A] :
% 0.31/0.46 ( ( late_case_freeRes @ A @ F1 @ F2 @ late_TauR )
% 0.31/0.46 = F2 ) ).
% 0.31/0.46
% 0.31/0.46 % freeRes.case(2)
% 0.31/0.46 thf(fact_172_subject_Ocase_I2_J,axiom,
% 0.31/0.46 ! [A: $tType,F1: name > A,F2: name > A,X2: name] :
% 0.31/0.46 ( ( late_case_subject @ A @ F1 @ F2 @ ( late_BoundOutputS @ X2 ) )
% 0.31/0.46 = ( F2 @ X2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % subject.case(2)
% 0.31/0.46 thf(fact_173_freeRes_Ocase_I1_J,axiom,
% 0.31/0.46 ! [A: $tType,F1: name > name > A,F2: A,X11: name,X12: name] :
% 0.31/0.46 ( ( late_case_freeRes @ A @ F1 @ F2 @ ( late_OutputR @ X11 @ X12 ) )
% 0.31/0.46 = ( F1 @ X11 @ X12 ) ) ).
% 0.31/0.46
% 0.31/0.46 % freeRes.case(1)
% 0.31/0.46 thf(fact_174_subject_Ocase_I1_J,axiom,
% 0.31/0.46 ! [A: $tType,F1: name > A,F2: name > A,X1: name] :
% 0.31/0.46 ( ( late_case_subject @ A @ F1 @ F2 @ ( late_InputS @ X1 ) )
% 0.31/0.46 = ( F1 @ X1 ) ) ).
% 0.31/0.46
% 0.31/0.46 % subject.case(1)
% 0.31/0.46 thf(fact_175_pi_Ostrong__inducts,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( fs_name @ A )
% 0.31/0.46 => ! [P: A > pi > $o,Z: A,Pi2: pi] :
% 0.31/0.46 ( ! [Z2: A] : ( P @ Z2 @ piNil )
% 0.31/0.46 => ( ! [Name1: name,Name22: name,Pi: pi,Z2: A] :
% 0.31/0.46 ( ! [Za: A] : ( P @ Za @ Pi )
% 0.31/0.46 => ( P @ Z2 @ ( output @ Name1 @ Name22 @ Pi ) ) )
% 0.31/0.46 => ( ! [Pi: pi,Z2: A] :
% 0.31/0.46 ( ! [Za: A] : ( P @ Za @ Pi )
% 0.31/0.46 => ( P @ Z2 @ ( tau @ Pi ) ) )
% 0.31/0.46 => ( ! [Name1: name,Name22: name,Pi: pi,Z2: A] :
% 0.31/0.46 ( ( fresh @ name @ A @ Name22 @ Z2 )
% 0.31/0.46 => ( ( fresh @ name @ name @ Name22 @ Name1 )
% 0.31/0.46 => ( ! [Za: A] : ( P @ Za @ Pi )
% 0.31/0.46 => ( P @ Z2 @ ( input @ Name1 @ Name22 @ Pi ) ) ) ) )
% 0.31/0.46 => ( ! [Name1: name,Name22: name,Pi: pi,Z2: A] :
% 0.31/0.46 ( ! [Za: A] : ( P @ Za @ Pi )
% 0.31/0.46 => ( P @ Z2 @ ( match @ Name1 @ Name22 @ Pi ) ) )
% 0.31/0.46 => ( ! [Name1: name,Name22: name,Pi: pi,Z2: A] :
% 0.31/0.46 ( ! [Za: A] : ( P @ Za @ Pi )
% 0.31/0.46 => ( P @ Z2 @ ( mismatch @ Name1 @ Name22 @ Pi ) ) )
% 0.31/0.46 => ( ! [Pi13: pi,Pi24: pi,Z2: A] :
% 0.31/0.46 ( ! [Za: A] : ( P @ Za @ Pi13 )
% 0.31/0.46 => ( ! [Za: A] : ( P @ Za @ Pi24 )
% 0.31/0.46 => ( P @ Z2 @ ( sum @ Pi13 @ Pi24 ) ) ) )
% 0.31/0.46 => ( ! [Pi13: pi,Pi24: pi,Z2: A] :
% 0.31/0.46 ( ! [Za: A] : ( P @ Za @ Pi13 )
% 0.31/0.46 => ( ! [Za: A] : ( P @ Za @ Pi24 )
% 0.31/0.46 => ( P @ Z2 @ ( par @ Pi13 @ Pi24 ) ) ) )
% 0.31/0.46 => ( ! [Name: name,Pi: pi,Z2: A] :
% 0.31/0.46 ( ( fresh @ name @ A @ Name @ Z2 )
% 0.31/0.46 => ( ! [Za: A] : ( P @ Za @ Pi )
% 0.31/0.46 => ( P @ Z2 @ ( res @ Name @ Pi ) ) ) )
% 0.31/0.46 => ( ! [Pi: pi,Z2: A] :
% 0.31/0.46 ( ! [Za: A] : ( P @ Za @ Pi )
% 0.31/0.46 => ( P @ Z2 @ ( bang @ Pi ) ) )
% 0.31/0.46 => ( P @ Z @ Pi2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.strong_inducts
% 0.31/0.46 thf(fact_176_pi_Ostrong__induct,axiom,
% 0.31/0.46 ! [N: $tType] :
% 0.31/0.46 ( ( fs_name @ N )
% 0.31/0.46 => ! [P: N > pi > $o,Z: N,Pi2: pi] :
% 0.31/0.46 ( ! [Z2: N] : ( P @ Z2 @ piNil )
% 0.31/0.46 => ( ! [Name1: name,Name22: name,Pi: pi,Z2: N] :
% 0.31/0.46 ( ! [Za: N] : ( P @ Za @ Pi )
% 0.31/0.46 => ( P @ Z2 @ ( output @ Name1 @ Name22 @ Pi ) ) )
% 0.31/0.46 => ( ! [Pi: pi,Z2: N] :
% 0.31/0.46 ( ! [Za: N] : ( P @ Za @ Pi )
% 0.31/0.46 => ( P @ Z2 @ ( tau @ Pi ) ) )
% 0.31/0.46 => ( ! [Name1: name,Name22: name,Pi: pi,Z2: N] :
% 0.31/0.46 ( ( fresh @ name @ N @ Name22 @ Z2 )
% 0.31/0.46 => ( ( fresh @ name @ name @ Name22 @ Name1 )
% 0.31/0.46 => ( ! [Za: N] : ( P @ Za @ Pi )
% 0.31/0.46 => ( P @ Z2 @ ( input @ Name1 @ Name22 @ Pi ) ) ) ) )
% 0.31/0.46 => ( ! [Name1: name,Name22: name,Pi: pi,Z2: N] :
% 0.31/0.46 ( ! [Za: N] : ( P @ Za @ Pi )
% 0.31/0.46 => ( P @ Z2 @ ( match @ Name1 @ Name22 @ Pi ) ) )
% 0.31/0.46 => ( ! [Name1: name,Name22: name,Pi: pi,Z2: N] :
% 0.31/0.46 ( ! [Za: N] : ( P @ Za @ Pi )
% 0.31/0.46 => ( P @ Z2 @ ( mismatch @ Name1 @ Name22 @ Pi ) ) )
% 0.31/0.46 => ( ! [Pi13: pi,Pi24: pi,Z2: N] :
% 0.31/0.46 ( ! [Za: N] : ( P @ Za @ Pi13 )
% 0.31/0.46 => ( ! [Za: N] : ( P @ Za @ Pi24 )
% 0.31/0.46 => ( P @ Z2 @ ( sum @ Pi13 @ Pi24 ) ) ) )
% 0.31/0.46 => ( ! [Pi13: pi,Pi24: pi,Z2: N] :
% 0.31/0.46 ( ! [Za: N] : ( P @ Za @ Pi13 )
% 0.31/0.46 => ( ! [Za: N] : ( P @ Za @ Pi24 )
% 0.31/0.46 => ( P @ Z2 @ ( par @ Pi13 @ Pi24 ) ) ) )
% 0.31/0.46 => ( ! [Name: name,Pi: pi,Z2: N] :
% 0.31/0.46 ( ( fresh @ name @ N @ Name @ Z2 )
% 0.31/0.46 => ( ! [Za: N] : ( P @ Za @ Pi )
% 0.31/0.46 => ( P @ Z2 @ ( res @ Name @ Pi ) ) ) )
% 0.31/0.46 => ( ! [Pi: pi,Z2: N] :
% 0.31/0.46 ( ! [Za: N] : ( P @ Za @ Pi )
% 0.31/0.46 => ( P @ Z2 @ ( bang @ Pi ) ) )
% 0.31/0.46 => ( P @ Z @ Pi2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.strong_induct
% 0.31/0.46 thf(fact_177_residual_Ostrong__induct_H,axiom,
% 0.31/0.46 ! [N: $tType,F: N > ( set @ name ),P: N > late_residual > $o,Z: N,Residual: late_residual] :
% 0.31/0.46 ( ! [X5: N] : ( finite_finite @ name @ ( F @ X5 ) )
% 0.31/0.46 => ( ! [Subject: late_subject,Name: name,Pi: pi,Z2: N] :
% 0.31/0.46 ( ~ ( member @ name @ Name @ ( F @ Z2 ) )
% 0.31/0.46 => ( ( fresh @ name @ late_subject @ Name @ Subject )
% 0.31/0.46 => ( P @ Z2 @ ( late_BoundR @ Subject @ Name @ Pi ) ) ) )
% 0.31/0.46 => ( ! [FreeRes: late_freeRes,Pi: pi,Z2: N] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi ) )
% 0.31/0.46 => ( P @ Z @ Residual ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % residual.strong_induct'
% 0.31/0.46 thf(fact_178_pi_Ofresh_I10_J,axiom,
% 0.31/0.46 ! [A2: name,X1: pi] :
% 0.31/0.46 ( ( fresh @ name @ pi @ A2 @ ( bang @ X1 ) )
% 0.31/0.46 = ( fresh @ name @ pi @ A2 @ X1 ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.fresh(10)
% 0.31/0.46 thf(fact_179_pi_Ofresh_I7_J,axiom,
% 0.31/0.46 ! [A2: name,X2: pi,X1: pi] :
% 0.31/0.46 ( ( fresh @ name @ pi @ A2 @ ( sum @ X2 @ X1 ) )
% 0.31/0.46 = ( ( fresh @ name @ pi @ A2 @ X2 )
% 0.31/0.46 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.fresh(7)
% 0.31/0.46 thf(fact_180_simps_I10_J,axiom,
% 0.31/0.46 ! [P: pi,C: name,D: name] :
% 0.31/0.46 ( ( subs @ ( bang @ P ) @ C @ D )
% 0.31/0.46 = ( bang @ ( subs @ P @ C @ D ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % simps(10)
% 0.31/0.46 thf(fact_181_pi_Ofresh_I1_J,axiom,
% 0.31/0.46 ! [A2: name] : ( fresh @ name @ pi @ A2 @ piNil ) ).
% 0.31/0.46
% 0.31/0.46 % pi.fresh(1)
% 0.31/0.46 thf(fact_182_simps_I7_J,axiom,
% 0.31/0.46 ! [P: pi,Q: pi,C: name,D: name] :
% 0.31/0.46 ( ( subs @ ( sum @ P @ Q ) @ C @ D )
% 0.31/0.46 = ( sum @ ( subs @ P @ C @ D ) @ ( subs @ Q @ C @ D ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % simps(7)
% 0.31/0.46 thf(fact_183_simps_I1_J,axiom,
% 0.31/0.46 ! [C: name,D: name] :
% 0.31/0.46 ( ( subs @ piNil @ C @ D )
% 0.31/0.46 = piNil ) ).
% 0.31/0.46
% 0.31/0.46 % simps(1)
% 0.31/0.46 thf(fact_184_pi_Odistinct_I59_J,axiom,
% 0.31/0.46 ! [Name12: name,Name23: name,Pi2: pi,Pi3: pi] :
% 0.31/0.46 ( ( input @ Name12 @ Name23 @ Pi2 )
% 0.31/0.46 != ( bang @ Pi3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.distinct(59)
% 0.31/0.46 thf(fact_185_pi_Odistinct_I33_J,axiom,
% 0.31/0.46 ! [Name12: name,Name23: name,Pi2: pi,Pi3: pi] :
% 0.31/0.46 ( ( output @ Name12 @ Name23 @ Pi2 )
% 0.31/0.46 != ( bang @ Pi3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.distinct(33)
% 0.31/0.46 thf(fact_186_sumCases,axiom,
% 0.31/0.46 ! [P: pi,Q: pi,Rs: late_residual] :
% 0.31/0.46 ( ( late_transitions @ ( sum @ P @ Q ) @ Rs )
% 0.31/0.46 => ( ~ ( late_transitions @ P @ Rs )
% 0.31/0.46 => ( late_transitions @ Q @ Rs ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % sumCases
% 0.31/0.46 thf(fact_187_sumCases_H,axiom,
% 0.31/0.46 ! [P: pi,Q: pi,Rs: late_residual] :
% 0.31/0.46 ( ( late_transitions @ ( sum @ P @ Q ) @ Rs )
% 0.31/0.46 => ( ~ ( late_transitions @ P @ Rs )
% 0.31/0.46 => ( late_transitions @ Q @ Rs ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % sumCases'
% 0.31/0.46 thf(fact_188_Sum1,axiom,
% 0.31/0.46 ! [P: pi,Rs: late_residual,Q: pi] :
% 0.31/0.46 ( ( late_transitions @ P @ Rs )
% 0.31/0.46 => ( late_transitions @ ( sum @ P @ Q ) @ Rs ) ) ).
% 0.31/0.46
% 0.31/0.46 % Sum1
% 0.31/0.46 thf(fact_189_Sum2,axiom,
% 0.31/0.46 ! [Q: pi,Rs: late_residual,P: pi] :
% 0.31/0.46 ( ( late_transitions @ Q @ Rs )
% 0.31/0.46 => ( late_transitions @ ( sum @ P @ Q ) @ Rs ) ) ).
% 0.31/0.46
% 0.31/0.46 % Sum2
% 0.31/0.46 thf(fact_190_pi_Odistinct_I47_J,axiom,
% 0.31/0.46 ! [Pi2: pi,Pi3: pi] :
% 0.31/0.46 ( ( tau @ Pi2 )
% 0.31/0.46 != ( bang @ Pi3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.distinct(47)
% 0.31/0.46 thf(fact_191_pi_Odistinct_I79_J,axiom,
% 0.31/0.46 ! [Pi12: pi,Pi23: pi,Pi1: pi,Pi22: pi] :
% 0.31/0.46 ( ( sum @ Pi12 @ Pi23 )
% 0.31/0.46 != ( par @ Pi1 @ Pi22 ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.distinct(79)
% 0.31/0.46 thf(fact_192_pi_Odistinct_I81_J,axiom,
% 0.31/0.46 ! [Pi12: pi,Pi23: pi,Name3: name,Pi3: pi] :
% 0.31/0.46 ( ( sum @ Pi12 @ Pi23 )
% 0.31/0.46 != ( res @ Name3 @ Pi3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.distinct(81)
% 0.31/0.46 thf(fact_193_pi_Odistinct_I53_J,axiom,
% 0.31/0.46 ! [Name12: name,Name23: name,Pi2: pi,Pi1: pi,Pi22: pi] :
% 0.31/0.46 ( ( input @ Name12 @ Name23 @ Pi2 )
% 0.31/0.46 != ( sum @ Pi1 @ Pi22 ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.distinct(53)
% 0.31/0.46 thf(fact_194_pi_Odistinct_I27_J,axiom,
% 0.31/0.46 ! [Name12: name,Name23: name,Pi2: pi,Pi1: pi,Pi22: pi] :
% 0.31/0.46 ( ( output @ Name12 @ Name23 @ Pi2 )
% 0.31/0.46 != ( sum @ Pi1 @ Pi22 ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.distinct(27)
% 0.31/0.46 thf(fact_195_pi_Odistinct_I41_J,axiom,
% 0.31/0.46 ! [Pi2: pi,Pi1: pi,Pi22: pi] :
% 0.31/0.46 ( ( tau @ Pi2 )
% 0.31/0.46 != ( sum @ Pi1 @ Pi22 ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.distinct(41)
% 0.31/0.46 thf(fact_196_nilCases_H,axiom,
% 0.31/0.46 ! [Rs: late_residual] :
% 0.31/0.46 ~ ( late_transitions @ piNil @ Rs ) ).
% 0.31/0.46
% 0.31/0.46 % nilCases'
% 0.31/0.46 thf(fact_197_zeroTrans,axiom,
% 0.31/0.46 ! [Rs: late_residual] :
% 0.31/0.46 ~ ( late_transitions @ piNil @ Rs ) ).
% 0.31/0.46
% 0.31/0.46 % zeroTrans
% 0.31/0.46 thf(fact_198_pi_Odistinct_I13_J,axiom,
% 0.31/0.46 ! [Pi1: pi,Pi22: pi] :
% 0.31/0.46 ( piNil
% 0.31/0.46 != ( par @ Pi1 @ Pi22 ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.distinct(13)
% 0.31/0.46 thf(fact_199_pi_Odistinct_I15_J,axiom,
% 0.31/0.46 ! [Name3: name,Pi3: pi] :
% 0.31/0.46 ( piNil
% 0.31/0.46 != ( res @ Name3 @ Pi3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.distinct(15)
% 0.31/0.46 thf(fact_200_pi_Odistinct_I11_J,axiom,
% 0.31/0.46 ! [Pi1: pi,Pi22: pi] :
% 0.31/0.46 ( piNil
% 0.31/0.46 != ( sum @ Pi1 @ Pi22 ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.distinct(11)
% 0.31/0.46 thf(fact_201_pi_Odistinct_I17_J,axiom,
% 0.31/0.46 ! [Pi3: pi] :
% 0.31/0.46 ( piNil
% 0.31/0.46 != ( bang @ Pi3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.distinct(17)
% 0.31/0.46 thf(fact_202_pi_Odistinct_I83_J,axiom,
% 0.31/0.46 ! [Pi12: pi,Pi23: pi,Pi3: pi] :
% 0.31/0.46 ( ( sum @ Pi12 @ Pi23 )
% 0.31/0.46 != ( bang @ Pi3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.distinct(83)
% 0.31/0.46 thf(fact_203_pi_Oinject_I6_J,axiom,
% 0.31/0.46 ! [X2: pi,X1: pi,Y2: pi,Y1: pi] :
% 0.31/0.46 ( ( ( sum @ X2 @ X1 )
% 0.31/0.46 = ( sum @ Y2 @ Y1 ) )
% 0.31/0.46 = ( ( X2 = Y2 )
% 0.31/0.46 & ( X1 = Y1 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.inject(6)
% 0.31/0.46 thf(fact_204_pi_Oinject_I9_J,axiom,
% 0.31/0.46 ! [X1: pi,Y1: pi] :
% 0.31/0.46 ( ( ( bang @ X1 )
% 0.31/0.46 = ( bang @ Y1 ) )
% 0.31/0.46 = ( X1 = Y1 ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.inject(9)
% 0.31/0.46 thf(fact_205_pi_Odistinct_I89_J,axiom,
% 0.31/0.46 ! [Name2: name,Pi2: pi,Pi3: pi] :
% 0.31/0.46 ( ( res @ Name2 @ Pi2 )
% 0.31/0.46 != ( bang @ Pi3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.distinct(89)
% 0.31/0.46 thf(fact_206_pi_Odistinct_I87_J,axiom,
% 0.31/0.46 ! [Pi12: pi,Pi23: pi,Pi3: pi] :
% 0.31/0.46 ( ( par @ Pi12 @ Pi23 )
% 0.31/0.46 != ( bang @ Pi3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.distinct(87)
% 0.31/0.46 thf(fact_207_pi_Odistinct_I3_J,axiom,
% 0.31/0.46 ! [Pi3: pi] :
% 0.31/0.46 ( piNil
% 0.31/0.46 != ( tau @ Pi3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.distinct(3)
% 0.31/0.46 thf(fact_208_pi_Odistinct_I1_J,axiom,
% 0.31/0.46 ! [Name13: name,Name24: name,Pi3: pi] :
% 0.31/0.46 ( piNil
% 0.31/0.46 != ( output @ Name13 @ Name24 @ Pi3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.distinct(1)
% 0.31/0.46 thf(fact_209_pi_Odistinct_I5_J,axiom,
% 0.31/0.46 ! [Name13: name,Name24: name,Pi3: pi] :
% 0.31/0.46 ( piNil
% 0.31/0.46 != ( input @ Name13 @ Name24 @ Pi3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.distinct(5)
% 0.31/0.46 thf(fact_210_pi_Odistinct_I77_J,axiom,
% 0.31/0.46 ! [Name12: name,Name23: name,Pi2: pi,Pi3: pi] :
% 0.31/0.46 ( ( mismatch @ Name12 @ Name23 @ Pi2 )
% 0.31/0.46 != ( bang @ Pi3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.distinct(77)
% 0.31/0.46 thf(fact_211_pi_Odistinct_I71_J,axiom,
% 0.31/0.46 ! [Name12: name,Name23: name,Pi2: pi,Pi1: pi,Pi22: pi] :
% 0.31/0.46 ( ( mismatch @ Name12 @ Name23 @ Pi2 )
% 0.31/0.46 != ( sum @ Pi1 @ Pi22 ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.distinct(71)
% 0.31/0.46 thf(fact_212_pi_Odistinct_I69_J,axiom,
% 0.31/0.46 ! [Name12: name,Name23: name,Pi2: pi,Pi3: pi] :
% 0.31/0.46 ( ( match @ Name12 @ Name23 @ Pi2 )
% 0.31/0.46 != ( bang @ Pi3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.distinct(69)
% 0.31/0.46 thf(fact_213_pi_Odistinct_I63_J,axiom,
% 0.31/0.46 ! [Name12: name,Name23: name,Pi2: pi,Pi1: pi,Pi22: pi] :
% 0.31/0.46 ( ( match @ Name12 @ Name23 @ Pi2 )
% 0.31/0.46 != ( sum @ Pi1 @ Pi22 ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.distinct(63)
% 0.31/0.46 thf(fact_214_pi_Odistinct_I9_J,axiom,
% 0.31/0.46 ! [Name13: name,Name24: name,Pi3: pi] :
% 0.31/0.46 ( piNil
% 0.31/0.46 != ( mismatch @ Name13 @ Name24 @ Pi3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.distinct(9)
% 0.31/0.46 thf(fact_215_pi_Odistinct_I7_J,axiom,
% 0.31/0.46 ! [Name13: name,Name24: name,Pi3: pi] :
% 0.31/0.46 ( piNil
% 0.31/0.46 != ( match @ Name13 @ Name24 @ Pi3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.distinct(7)
% 0.31/0.46 thf(fact_216_Bang,axiom,
% 0.31/0.46 ! [P: pi,Rs: late_residual] :
% 0.31/0.46 ( ( late_transitions @ ( par @ P @ ( bang @ P ) ) @ Rs )
% 0.31/0.46 => ( late_transitions @ ( bang @ P ) @ Rs ) ) ).
% 0.31/0.46
% 0.31/0.46 % Bang
% 0.31/0.46 thf(fact_217_bangCases,axiom,
% 0.31/0.46 ! [P: pi,Rs: late_residual] :
% 0.31/0.46 ( ( late_transitions @ ( bang @ P ) @ Rs )
% 0.31/0.46 => ~ ! [P3: pi] :
% 0.31/0.46 ( ( ( bang @ P )
% 0.31/0.46 = ( bang @ P3 ) )
% 0.31/0.46 => ~ ( late_transitions @ ( par @ P3 @ ( bang @ P3 ) ) @ Rs ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % bangCases
% 0.31/0.46 thf(fact_218_pi_Ostrong__induct_H,axiom,
% 0.31/0.46 ! [N: $tType,F: N > ( set @ name ),P: N > pi > $o,Z: N,Pi2: pi] :
% 0.31/0.46 ( ! [X5: N] : ( finite_finite @ name @ ( F @ X5 ) )
% 0.31/0.46 => ( ! [Z2: N] : ( P @ Z2 @ piNil )
% 0.31/0.46 => ( ! [Name1: name,Name22: name,Pi: pi,Z2: N] :
% 0.31/0.46 ( ! [Za: N] : ( P @ Za @ Pi )
% 0.31/0.46 => ( P @ Z2 @ ( output @ Name1 @ Name22 @ Pi ) ) )
% 0.31/0.46 => ( ! [Pi: pi,Z2: N] :
% 0.31/0.46 ( ! [Za: N] : ( P @ Za @ Pi )
% 0.31/0.46 => ( P @ Z2 @ ( tau @ Pi ) ) )
% 0.31/0.46 => ( ! [Name1: name,Name22: name,Pi: pi,Z2: N] :
% 0.31/0.46 ( ~ ( member @ name @ Name22 @ ( F @ Z2 ) )
% 0.31/0.46 => ( ( fresh @ name @ name @ Name22 @ Name1 )
% 0.31/0.46 => ( ! [Za: N] : ( P @ Za @ Pi )
% 0.31/0.46 => ( P @ Z2 @ ( input @ Name1 @ Name22 @ Pi ) ) ) ) )
% 0.31/0.46 => ( ! [Name1: name,Name22: name,Pi: pi,Z2: N] :
% 0.31/0.46 ( ! [Za: N] : ( P @ Za @ Pi )
% 0.31/0.46 => ( P @ Z2 @ ( match @ Name1 @ Name22 @ Pi ) ) )
% 0.31/0.46 => ( ! [Name1: name,Name22: name,Pi: pi,Z2: N] :
% 0.31/0.46 ( ! [Za: N] : ( P @ Za @ Pi )
% 0.31/0.46 => ( P @ Z2 @ ( mismatch @ Name1 @ Name22 @ Pi ) ) )
% 0.31/0.46 => ( ! [Pi13: pi,Pi24: pi,Z2: N] :
% 0.31/0.46 ( ! [Za: N] : ( P @ Za @ Pi13 )
% 0.31/0.46 => ( ! [Za: N] : ( P @ Za @ Pi24 )
% 0.31/0.46 => ( P @ Z2 @ ( sum @ Pi13 @ Pi24 ) ) ) )
% 0.31/0.46 => ( ! [Pi13: pi,Pi24: pi,Z2: N] :
% 0.31/0.46 ( ! [Za: N] : ( P @ Za @ Pi13 )
% 0.31/0.46 => ( ! [Za: N] : ( P @ Za @ Pi24 )
% 0.31/0.46 => ( P @ Z2 @ ( par @ Pi13 @ Pi24 ) ) ) )
% 0.31/0.46 => ( ! [Name: name,Pi: pi,Z2: N] :
% 0.31/0.46 ( ~ ( member @ name @ Name @ ( F @ Z2 ) )
% 0.31/0.46 => ( ! [Za: N] : ( P @ Za @ Pi )
% 0.31/0.46 => ( P @ Z2 @ ( res @ Name @ Pi ) ) ) )
% 0.31/0.46 => ( ! [Pi: pi,Z2: N] :
% 0.31/0.46 ( ! [Za: N] : ( P @ Za @ Pi )
% 0.31/0.46 => ( P @ Z2 @ ( bang @ Pi ) ) )
% 0.31/0.46 => ( P @ Z @ Pi2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.strong_induct'
% 0.31/0.46 thf(fact_219_resZeroTrans,axiom,
% 0.31/0.46 ! [X3: name,Rs: late_residual] :
% 0.31/0.46 ~ ( late_transitions @ ( res @ X3 @ piNil ) @ Rs ) ).
% 0.31/0.46
% 0.31/0.46 % resZeroTrans
% 0.31/0.46 thf(fact_220_pi_Oinducts,axiom,
% 0.31/0.46 ! [P: pi > $o,Pi2: pi] :
% 0.31/0.46 ( ( P @ piNil )
% 0.31/0.46 => ( ! [Name1: name,Name22: name,Pi: pi] :
% 0.31/0.46 ( ( P @ Pi )
% 0.31/0.46 => ( P @ ( output @ Name1 @ Name22 @ Pi ) ) )
% 0.31/0.46 => ( ! [Pi: pi] :
% 0.31/0.46 ( ( P @ Pi )
% 0.31/0.46 => ( P @ ( tau @ Pi ) ) )
% 0.31/0.46 => ( ! [Name1: name,Name22: name,Pi: pi] :
% 0.31/0.46 ( ( P @ Pi )
% 0.31/0.46 => ( P @ ( input @ Name1 @ Name22 @ Pi ) ) )
% 0.31/0.46 => ( ! [Name1: name,Name22: name,Pi: pi] :
% 0.31/0.46 ( ( P @ Pi )
% 0.31/0.46 => ( P @ ( match @ Name1 @ Name22 @ Pi ) ) )
% 0.31/0.46 => ( ! [Name1: name,Name22: name,Pi: pi] :
% 0.31/0.46 ( ( P @ Pi )
% 0.31/0.46 => ( P @ ( mismatch @ Name1 @ Name22 @ Pi ) ) )
% 0.31/0.46 => ( ! [Pi13: pi,Pi24: pi] :
% 0.31/0.46 ( ( P @ Pi13 )
% 0.31/0.46 => ( ( P @ Pi24 )
% 0.31/0.46 => ( P @ ( sum @ Pi13 @ Pi24 ) ) ) )
% 0.31/0.46 => ( ! [Pi13: pi,Pi24: pi] :
% 0.31/0.46 ( ( P @ Pi13 )
% 0.31/0.46 => ( ( P @ Pi24 )
% 0.31/0.46 => ( P @ ( par @ Pi13 @ Pi24 ) ) ) )
% 0.31/0.46 => ( ! [Name: name,Pi: pi] :
% 0.31/0.46 ( ( P @ Pi )
% 0.31/0.46 => ( P @ ( res @ Name @ Pi ) ) )
% 0.31/0.46 => ( ! [Pi: pi] :
% 0.31/0.46 ( ( P @ Pi )
% 0.31/0.46 => ( P @ ( bang @ Pi ) ) )
% 0.31/0.46 => ( P @ Pi2 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.inducts
% 0.31/0.46 thf(fact_221_aux2,axiom,
% 0.31/0.46 ! [P: pi] : ( late_bangPred @ P @ ( par @ P @ ( bang @ P ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % aux2
% 0.31/0.46 thf(fact_222_bangPred_Ocases,axiom,
% 0.31/0.46 ! [A1: pi,A22: pi] :
% 0.31/0.46 ( ( late_bangPred @ A1 @ A22 )
% 0.31/0.46 => ( ( A22
% 0.31/0.46 != ( bang @ A1 ) )
% 0.31/0.46 => ( A22
% 0.31/0.46 = ( par @ A1 @ ( bang @ A1 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % bangPred.cases
% 0.31/0.46 thf(fact_223_bangPred_Osimps,axiom,
% 0.31/0.46 ( late_bangPred
% 0.31/0.46 = ( ^ [A12: pi,A23: pi] :
% 0.31/0.46 ( ? [P5: pi] :
% 0.31/0.46 ( ( A12 = P5 )
% 0.31/0.46 & ( A23
% 0.31/0.46 = ( bang @ P5 ) ) )
% 0.31/0.46 | ? [P5: pi] :
% 0.31/0.46 ( ( A12 = P5 )
% 0.31/0.46 & ( A23
% 0.31/0.46 = ( par @ P5 @ ( bang @ P5 ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % bangPred.simps
% 0.31/0.46 thf(fact_224_aux1,axiom,
% 0.31/0.46 ! [P: pi] : ( late_bangPred @ P @ ( bang @ P ) ) ).
% 0.31/0.46
% 0.31/0.46 % aux1
% 0.31/0.46 thf(fact_225_bangPred_Oinducts,axiom,
% 0.31/0.46 ! [X1: pi,X2: pi,P: pi > pi > $o] :
% 0.31/0.46 ( ( late_bangPred @ X1 @ X2 )
% 0.31/0.46 => ( ! [P3: pi] : ( P @ P3 @ ( bang @ P3 ) )
% 0.31/0.46 => ( ! [P3: pi] : ( P @ P3 @ ( par @ P3 @ ( bang @ P3 ) ) )
% 0.31/0.46 => ( P @ X1 @ X2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % bangPred.inducts
% 0.31/0.46 thf(fact_226_subs__def,axiom,
% 0.31/0.46 ( subs
% 0.31/0.46 = ( ^ [X4: pi,C3: name,D2: name] :
% 0.31/0.46 ( pi_rec @ pi @ piNil
% 0.31/0.46 @ ^ [A5: name,B4: name,P5: pi] : ( output @ ( subst_name @ A5 @ C3 @ D2 ) @ ( subst_name @ B4 @ C3 @ D2 ) )
% 0.31/0.46 @ ^ [P5: pi] : tau
% 0.31/0.46 @ ^ [A5: name,Y5: name,P5: pi] : ( input @ ( subst_name @ A5 @ C3 @ D2 ) @ Y5 )
% 0.31/0.46 @ ^ [A5: name,B4: name,P5: pi] : ( match @ ( subst_name @ A5 @ C3 @ D2 ) @ ( subst_name @ B4 @ C3 @ D2 ) )
% 0.31/0.46 @ ^ [A5: name,B4: name,P5: pi] : ( mismatch @ ( subst_name @ A5 @ C3 @ D2 ) @ ( subst_name @ B4 @ C3 @ D2 ) )
% 0.31/0.46 @ ^ [P5: pi,Q5: pi] : sum
% 0.31/0.46 @ ^ [P5: pi,Q5: pi] : par
% 0.31/0.46 @ ^ [Y5: name,P5: pi] : ( res @ Y5 )
% 0.31/0.46 @ ^ [P5: pi] : bang
% 0.31/0.46 @ X4 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % subs_def
% 0.31/0.46 thf(fact_227_abs__fresh_I2_J,axiom,
% 0.31/0.46 ! [X8: $tType] :
% 0.31/0.46 ( ( pt_name @ X8 )
% 0.31/0.46 => ! [X3: X8,B: name,A2: name] :
% 0.31/0.46 ( ( finite_finite @ name @ ( supp @ X8 @ name @ X3 ) )
% 0.31/0.46 => ( ( fresh @ name @ ( name > ( noption @ X8 ) ) @ B @ ( abs_fun @ name @ X8 @ A2 @ X3 ) )
% 0.31/0.46 = ( ( B = A2 )
% 0.31/0.46 | ( fresh @ name @ X8 @ B @ X3 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % abs_fresh(2)
% 0.31/0.46 thf(fact_228_exists__fresh_H,axiom,
% 0.31/0.46 ! [A: $tType,X3: A] :
% 0.31/0.46 ( ( finite_finite @ name @ ( supp @ A @ name @ X3 ) )
% 0.31/0.46 => ? [C2: name] : ( fresh @ name @ A @ C2 @ X3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % exists_fresh'
% 0.31/0.46 thf(fact_229_exists__fresh,axiom,
% 0.31/0.46 ! [A: $tType,X3: A] :
% 0.31/0.46 ( ( finite_finite @ name @ ( supp @ A @ name @ X3 ) )
% 0.31/0.46 => ~ ! [C2: name] :
% 0.31/0.46 ~ ( fresh @ name @ A @ C2 @ X3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % exists_fresh
% 0.31/0.46 thf(fact_230_supp__fresh__iff,axiom,
% 0.31/0.46 ! [X: $tType,A: $tType] :
% 0.31/0.46 ( ( supp @ A @ X )
% 0.31/0.46 = ( ^ [X4: A] :
% 0.31/0.46 ( collect @ X
% 0.31/0.46 @ ^ [A5: X] :
% 0.31/0.46 ~ ( fresh @ X @ A @ A5 @ X4 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % supp_fresh_iff
% 0.31/0.46 thf(fact_231_fresh__def,axiom,
% 0.31/0.46 ! [A: $tType,X: $tType] :
% 0.31/0.46 ( ( fresh @ X @ A )
% 0.31/0.46 = ( ^ [A5: X,X4: A] :
% 0.31/0.46 ~ ( member @ X @ A5 @ ( supp @ A @ X @ X4 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % fresh_def
% 0.31/0.46 thf(fact_232_pi_Osupp_I9_J,axiom,
% 0.31/0.46 ! [X1: name,X2: pi] :
% 0.31/0.46 ( ( supp @ pi @ name @ ( res @ X1 @ X2 ) )
% 0.31/0.46 = ( supp @ ( name > ( noption @ pi ) ) @ name @ ( abs_fun @ name @ pi @ X1 @ X2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.supp(9)
% 0.31/0.46 thf(fact_233_freeRes_Ocase__distrib,axiom,
% 0.31/0.46 ! [A: $tType,B2: $tType,H: A > B2,F1: name > name > A,F2: A,FreeRes3: late_freeRes] :
% 0.31/0.46 ( ( H @ ( late_case_freeRes @ A @ F1 @ F2 @ FreeRes3 ) )
% 0.31/0.46 = ( late_case_freeRes @ B2
% 0.31/0.46 @ ^ [X14: name,X23: name] : ( H @ ( F1 @ X14 @ X23 ) )
% 0.31/0.46 @ ( H @ F2 )
% 0.31/0.46 @ FreeRes3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % freeRes.case_distrib
% 0.31/0.46 thf(fact_234_subject_Ocase__distrib,axiom,
% 0.31/0.46 ! [B2: $tType,A: $tType,H: A > B2,F1: name > A,F2: name > A,Subject2: late_subject] :
% 0.31/0.46 ( ( H @ ( late_case_subject @ A @ F1 @ F2 @ Subject2 ) )
% 0.31/0.46 = ( late_case_subject @ B2
% 0.31/0.46 @ ^ [X4: name] : ( H @ ( F1 @ X4 ) )
% 0.31/0.46 @ ^ [X4: name] : ( H @ ( F2 @ X4 ) )
% 0.31/0.46 @ Subject2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % subject.case_distrib
% 0.31/0.46 thf(fact_235_pi_Osupp_I3_J,axiom,
% 0.31/0.46 ! [X1: pi] :
% 0.31/0.46 ( ( supp @ pi @ name @ ( tau @ X1 ) )
% 0.31/0.46 = ( supp @ pi @ name @ X1 ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.supp(3)
% 0.31/0.46 thf(fact_236_subject_Osupp_I2_J,axiom,
% 0.31/0.46 ! [X1: name] :
% 0.31/0.46 ( ( supp @ late_subject @ name @ ( late_BoundOutputS @ X1 ) )
% 0.31/0.46 = ( supp @ name @ name @ X1 ) ) ).
% 0.31/0.46
% 0.31/0.46 % subject.supp(2)
% 0.31/0.46 thf(fact_237_subject_Osupp_I1_J,axiom,
% 0.31/0.46 ! [X1: name] :
% 0.31/0.46 ( ( supp @ late_subject @ name @ ( late_InputS @ X1 ) )
% 0.31/0.46 = ( supp @ name @ name @ X1 ) ) ).
% 0.31/0.46
% 0.31/0.46 % subject.supp(1)
% 0.31/0.46 thf(fact_238_pi_Osupp_I10_J,axiom,
% 0.31/0.46 ! [X1: pi] :
% 0.31/0.46 ( ( supp @ pi @ name @ ( bang @ X1 ) )
% 0.31/0.46 = ( supp @ pi @ name @ X1 ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.supp(10)
% 0.31/0.46 thf(fact_239_fs__name1,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( fs_name @ A )
% 0.31/0.46 => ! [X3: A] : ( finite_finite @ name @ ( supp @ A @ name @ X3 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % fs_name1
% 0.31/0.46 thf(fact_240_residual_Orecs_I2_J,axiom,
% 0.31/0.46 ! [N: $tType,T: $tType] :
% 0.31/0.46 ( ( pt_name @ T )
% 0.31/0.46 => ! [F1: late_subject > name > pi > T,F2: late_freeRes > pi > T,Z: N,P: T > $o,FreeRes3: late_freeRes,Pi2: pi] :
% 0.31/0.46 ( ( finite_finite @ name @ ( supp @ ( late_subject > name > pi > T ) @ name @ F1 ) )
% 0.31/0.46 => ( ( finite_finite @ name @ ( supp @ ( late_freeRes > pi > T ) @ name @ F2 ) )
% 0.31/0.46 => ( ( finite_finite @ name @ ( supp @ N @ name @ Z ) )
% 0.31/0.46 => ( ! [X13: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X13 @ X22 @ X33 ) )
% 0.31/0.46 => ( ! [X13: late_freeRes,X22: pi] : ( P @ ( F2 @ X13 @ X22 ) )
% 0.31/0.46 => ( ! [X13: late_subject,X22: name,X33: pi] :
% 0.31/0.46 ( ( fresh @ name @ ( late_subject > name > pi > T ) @ X22 @ F1 )
% 0.31/0.46 => ( ( fresh @ name @ late_subject @ X22 @ X13 )
% 0.31/0.46 => ( ( fresh @ name @ N @ X22 @ Z )
% 0.31/0.46 => ( ( P @ ( F1 @ X13 @ X22 @ X33 ) )
% 0.31/0.46 => ( fresh @ name @ T @ X22 @ ( F1 @ X13 @ X22 @ X33 ) ) ) ) ) )
% 0.31/0.46 => ( ( late_residual_rec @ T @ F1 @ F2 @ ( late_FreeR @ FreeRes3 @ Pi2 ) )
% 0.31/0.46 = ( F2 @ FreeRes3 @ Pi2 ) ) ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % residual.recs(2)
% 0.31/0.46 thf(fact_241_residual_Orecs_I1_J,axiom,
% 0.31/0.46 ! [N: $tType,T: $tType] :
% 0.31/0.46 ( ( pt_name @ T )
% 0.31/0.46 => ! [F1: late_subject > name > pi > T,F2: late_freeRes > pi > T,Z: N,P: T > $o,Name2: name,Subject2: late_subject,Pi2: pi] :
% 0.31/0.46 ( ( finite_finite @ name @ ( supp @ ( late_subject > name > pi > T ) @ name @ F1 ) )
% 0.31/0.46 => ( ( finite_finite @ name @ ( supp @ ( late_freeRes > pi > T ) @ name @ F2 ) )
% 0.31/0.46 => ( ( finite_finite @ name @ ( supp @ N @ name @ Z ) )
% 0.31/0.46 => ( ! [X13: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X13 @ X22 @ X33 ) )
% 0.31/0.46 => ( ! [X13: late_freeRes,X22: pi] : ( P @ ( F2 @ X13 @ X22 ) )
% 0.31/0.46 => ( ! [X13: late_subject,X22: name,X33: pi] :
% 0.31/0.46 ( ( fresh @ name @ ( late_subject > name > pi > T ) @ X22 @ F1 )
% 0.31/0.46 => ( ( fresh @ name @ late_subject @ X22 @ X13 )
% 0.31/0.46 => ( ( fresh @ name @ N @ X22 @ Z )
% 0.31/0.46 => ( ( P @ ( F1 @ X13 @ X22 @ X33 ) )
% 0.31/0.46 => ( fresh @ name @ T @ X22 @ ( F1 @ X13 @ X22 @ X33 ) ) ) ) ) )
% 0.31/0.46 => ( ( fresh @ name @ ( late_subject > name > pi > T ) @ Name2 @ F1 )
% 0.31/0.46 => ( ( fresh @ name @ ( late_freeRes > pi > T ) @ Name2 @ F2 )
% 0.31/0.46 => ( ( fresh @ name @ late_subject @ Name2 @ Subject2 )
% 0.31/0.46 => ( ( late_residual_rec @ T @ F1 @ F2 @ ( late_BoundR @ Subject2 @ Name2 @ Pi2 ) )
% 0.31/0.46 = ( F1 @ Subject2 @ Name2 @ Pi2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % residual.recs(1)
% 0.31/0.46 thf(fact_242_residual_Orec__fresh,axiom,
% 0.31/0.46 ! [T: $tType] :
% 0.31/0.46 ( ( pt_name @ T )
% 0.31/0.46 => ! [F1: late_subject > name > pi > T,F2: late_freeRes > pi > T,X3: late_residual,Y: T,A2: name] :
% 0.31/0.46 ( ( finite_finite @ name @ ( supp @ ( late_subject > name > pi > T ) @ name @ F1 ) )
% 0.31/0.46 => ( ( finite_finite @ name @ ( supp @ ( late_freeRes > pi > T ) @ name @ F2 ) )
% 0.31/0.46 => ( ( late_r582136743ec_set @ T @ F1 @ F2 @ X3 @ Y )
% 0.31/0.46 => ( ! [Y6: T] :
% 0.31/0.46 ( ( late_r582136743ec_set @ T @ F1 @ F2 @ X3 @ Y6 )
% 0.31/0.46 => ( Y6 = Y ) )
% 0.31/0.46 => ( ( fresh @ name @ late_residual @ A2 @ X3 )
% 0.31/0.46 => ( ( fresh @ name @ ( late_subject > name > pi > T ) @ A2 @ F1 )
% 0.31/0.46 => ( ( fresh @ name @ ( late_freeRes > pi > T ) @ A2 @ F2 )
% 0.31/0.46 => ( fresh @ name @ T @ A2 @ Y ) ) ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % residual.rec_fresh
% 0.31/0.46 thf(fact_243_residual_Orec__unique,axiom,
% 0.31/0.46 ! [N: $tType,T: $tType] :
% 0.31/0.46 ( ( pt_name @ T )
% 0.31/0.46 => ! [F1: late_subject > name > pi > T,F2: late_freeRes > pi > T,Z: N,P: T > $o,X3: late_residual] :
% 0.31/0.46 ( ( finite_finite @ name @ ( supp @ ( late_subject > name > pi > T ) @ name @ F1 ) )
% 0.31/0.46 => ( ( finite_finite @ name @ ( supp @ ( late_freeRes > pi > T ) @ name @ F2 ) )
% 0.31/0.46 => ( ( finite_finite @ name @ ( supp @ N @ name @ Z ) )
% 0.31/0.46 => ( ! [X13: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X13 @ X22 @ X33 ) )
% 0.31/0.46 => ( ! [X13: late_freeRes,X22: pi] : ( P @ ( F2 @ X13 @ X22 ) )
% 0.31/0.46 => ( ! [X13: late_subject,X22: name] :
% 0.31/0.46 ( ( fresh @ name @ ( late_subject > name > pi > T ) @ X22 @ F1 )
% 0.31/0.46 => ( ( fresh @ name @ late_subject @ X22 @ X13 )
% 0.31/0.46 => ( ( fresh @ name @ N @ X22 @ Z )
% 0.31/0.46 => ! [X33: pi] :
% 0.31/0.46 ( ( P @ ( F1 @ X13 @ X22 @ X33 ) )
% 0.31/0.46 => ( fresh @ name @ T @ X22 @ ( F1 @ X13 @ X22 @ X33 ) ) ) ) ) )
% 0.31/0.46 => ? [X5: T] :
% 0.31/0.46 ( ( late_r582136743ec_set @ T @ F1 @ F2 @ X3 @ X5 )
% 0.31/0.46 & ! [Y7: T] :
% 0.31/0.46 ( ( late_r582136743ec_set @ T @ F1 @ F2 @ X3 @ Y7 )
% 0.31/0.46 => ( Y7 = X5 ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % residual.rec_unique
% 0.31/0.46 thf(fact_244_residual_Orec__fin__supp,axiom,
% 0.31/0.46 ! [T: $tType] :
% 0.31/0.46 ( ( pt_name @ T )
% 0.31/0.46 => ! [F1: late_subject > name > pi > T,F2: late_freeRes > pi > T,X1: late_residual,Y1: T] :
% 0.31/0.46 ( ( finite_finite @ name @ ( supp @ ( late_subject > name > pi > T ) @ name @ F1 ) )
% 0.31/0.46 => ( ( finite_finite @ name @ ( supp @ ( late_freeRes > pi > T ) @ name @ F2 ) )
% 0.31/0.46 => ( ( late_r582136743ec_set @ T @ F1 @ F2 @ X1 @ Y1 )
% 0.31/0.46 => ( finite_finite @ name @ ( supp @ T @ name @ Y1 ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % residual.rec_fin_supp
% 0.31/0.46 thf(fact_245_pi_Osupp_I4_J,axiom,
% 0.31/0.46 ! [X32: name,X1: name,X2: pi] :
% 0.31/0.46 ( ( supp @ pi @ name @ ( input @ X32 @ X1 @ X2 ) )
% 0.31/0.46 = ( sup_sup @ ( set @ name ) @ ( supp @ name @ name @ X32 ) @ ( supp @ ( name > ( noption @ pi ) ) @ name @ ( abs_fun @ name @ pi @ X1 @ X2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.supp(4)
% 0.31/0.46 thf(fact_246_residual_Osupp_I1_J,axiom,
% 0.31/0.46 ! [X32: late_subject,X1: name,X2: pi] :
% 0.31/0.46 ( ( supp @ late_residual @ name @ ( late_BoundR @ X32 @ X1 @ X2 ) )
% 0.31/0.46 = ( sup_sup @ ( set @ name ) @ ( supp @ late_subject @ name @ X32 ) @ ( supp @ ( name > ( noption @ pi ) ) @ name @ ( abs_fun @ name @ pi @ X1 @ X2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % residual.supp(1)
% 0.31/0.46 thf(fact_247_pi_Osupp_I7_J,axiom,
% 0.31/0.46 ! [X2: pi,X1: pi] :
% 0.31/0.46 ( ( supp @ pi @ name @ ( sum @ X2 @ X1 ) )
% 0.31/0.46 = ( sup_sup @ ( set @ name ) @ ( supp @ pi @ name @ X2 ) @ ( supp @ pi @ name @ X1 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.supp(7)
% 0.31/0.46 thf(fact_248_pi_Osupp_I8_J,axiom,
% 0.31/0.46 ! [X2: pi,X1: pi] :
% 0.31/0.46 ( ( supp @ pi @ name @ ( par @ X2 @ X1 ) )
% 0.31/0.46 = ( sup_sup @ ( set @ name ) @ ( supp @ pi @ name @ X2 ) @ ( supp @ pi @ name @ X1 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.supp(8)
% 0.31/0.46 thf(fact_249_freeRes_Osupp_I1_J,axiom,
% 0.31/0.46 ! [X2: name,X1: name] :
% 0.31/0.46 ( ( supp @ late_freeRes @ name @ ( late_OutputR @ X2 @ X1 ) )
% 0.31/0.46 = ( sup_sup @ ( set @ name ) @ ( supp @ name @ name @ X2 ) @ ( supp @ name @ name @ X1 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % freeRes.supp(1)
% 0.31/0.46 thf(fact_250_residual_Osupp_I2_J,axiom,
% 0.31/0.46 ! [X2: late_freeRes,X1: pi] :
% 0.31/0.46 ( ( supp @ late_residual @ name @ ( late_FreeR @ X2 @ X1 ) )
% 0.31/0.46 = ( sup_sup @ ( set @ name ) @ ( supp @ late_freeRes @ name @ X2 ) @ ( supp @ pi @ name @ X1 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % residual.supp(2)
% 0.31/0.46 thf(fact_251_pi_Osupp_I2_J,axiom,
% 0.31/0.46 ! [X32: name,X2: name,X1: pi] :
% 0.31/0.46 ( ( supp @ pi @ name @ ( output @ X32 @ X2 @ X1 ) )
% 0.31/0.46 = ( sup_sup @ ( set @ name ) @ ( supp @ name @ name @ X32 ) @ ( sup_sup @ ( set @ name ) @ ( supp @ name @ name @ X2 ) @ ( supp @ pi @ name @ X1 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.supp(2)
% 0.31/0.46 thf(fact_252_pi_Osupp_I6_J,axiom,
% 0.31/0.46 ! [X32: name,X2: name,X1: pi] :
% 0.31/0.46 ( ( supp @ pi @ name @ ( mismatch @ X32 @ X2 @ X1 ) )
% 0.31/0.46 = ( sup_sup @ ( set @ name ) @ ( supp @ name @ name @ X32 ) @ ( sup_sup @ ( set @ name ) @ ( supp @ name @ name @ X2 ) @ ( supp @ pi @ name @ X1 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.supp(6)
% 0.31/0.46 thf(fact_253_pi_Osupp_I5_J,axiom,
% 0.31/0.46 ! [X32: name,X2: name,X1: pi] :
% 0.31/0.46 ( ( supp @ pi @ name @ ( match @ X32 @ X2 @ X1 ) )
% 0.31/0.46 = ( sup_sup @ ( set @ name ) @ ( supp @ name @ name @ X32 ) @ ( sup_sup @ ( set @ name ) @ ( supp @ name @ name @ X2 ) @ ( supp @ pi @ name @ X1 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.supp(5)
% 0.31/0.46 thf(fact_254_pi_Orec__fin__supp,axiom,
% 0.31/0.46 ! [T: $tType] :
% 0.31/0.46 ( ( pt_name @ T )
% 0.31/0.46 => ! [F1: T,F2: name > name > pi > T > T,F32: pi > T > T,F4: name > name > pi > T > T,F5: name > name > pi > T > T,F6: name > name > pi > T > T,F7: pi > pi > T > T > T,F8: pi > pi > T > T > T,F9: name > pi > T > T,F10: pi > T > T,X1: pi,Y1: T] :
% 0.31/0.46 ( ( finite_finite @ name @ ( supp @ T @ name @ F1 ) )
% 0.31/0.46 => ( ( finite_finite @ name @ ( supp @ ( name > name > pi > T > T ) @ name @ F2 ) )
% 0.31/0.46 => ( ( finite_finite @ name @ ( supp @ ( pi > T > T ) @ name @ F32 ) )
% 0.31/0.46 => ( ( finite_finite @ name @ ( supp @ ( name > name > pi > T > T ) @ name @ F4 ) )
% 0.31/0.46 => ( ( finite_finite @ name @ ( supp @ ( name > name > pi > T > T ) @ name @ F5 ) )
% 0.31/0.46 => ( ( finite_finite @ name @ ( supp @ ( name > name > pi > T > T ) @ name @ F6 ) )
% 0.31/0.46 => ( ( finite_finite @ name @ ( supp @ ( pi > pi > T > T > T ) @ name @ F7 ) )
% 0.31/0.46 => ( ( finite_finite @ name @ ( supp @ ( pi > pi > T > T > T ) @ name @ F8 ) )
% 0.31/0.46 => ( ( finite_finite @ name @ ( supp @ ( name > pi > T > T ) @ name @ F9 ) )
% 0.31/0.46 => ( ( finite_finite @ name @ ( supp @ ( pi > T > T ) @ name @ F10 ) )
% 0.31/0.46 => ( ( pi_rec_set @ T @ F1 @ F2 @ F32 @ F4 @ F5 @ F6 @ F7 @ F8 @ F9 @ F10 @ X1 @ Y1 )
% 0.31/0.46 => ( finite_finite @ name @ ( supp @ T @ name @ Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % pi.rec_fin_supp
% 0.31/0.46 thf(fact_255_supports__fresh,axiom,
% 0.31/0.46 ! [X: $tType,A: $tType,S: set @ X,X3: A,A2: X] :
% 0.31/0.46 ( ( supports @ X @ A @ S @ X3 )
% 0.31/0.46 => ( ( finite_finite @ X @ S )
% 0.31/0.46 => ( ~ ( member @ X @ A2 @ S )
% 0.31/0.46 => ( fresh @ X @ A @ A2 @ X3 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % supports_fresh
% 0.31/0.46
% 0.31/0.46 % Type constructors (15)
% 0.31/0.46 thf(tcon_fun___Agent_Opt__name,axiom,
% 0.31/0.46 ! [A6: $tType,A7: $tType] :
% 0.31/0.46 ( ( ( pt_name @ A6 )
% 0.31/0.46 & ( pt_name @ A7 ) )
% 0.31/0.46 => ( pt_name @ ( A6 > A7 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(tcon_Set_Oset___Agent_Opt__name_1,axiom,
% 0.31/0.46 ! [A6: $tType] :
% 0.31/0.46 ( ( pt_name @ A6 )
% 0.31/0.46 => ( pt_name @ ( set @ A6 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(tcon_Agent_Opi___Agent_Opt__name_2,axiom,
% 0.31/0.46 pt_name @ pi ).
% 0.31/0.46
% 0.31/0.46 thf(tcon_Agent_Opi___Agent_Ofs__name,axiom,
% 0.31/0.46 fs_name @ pi ).
% 0.31/0.46
% 0.31/0.46 thf(tcon_HOL_Obool___Agent_Opt__name_3,axiom,
% 0.31/0.46 pt_name @ $o ).
% 0.31/0.46
% 0.31/0.46 thf(tcon_HOL_Obool___Agent_Ofs__name_4,axiom,
% 0.31/0.46 fs_name @ $o ).
% 0.31/0.46
% 0.31/0.46 thf(tcon_Agent_Oname___Agent_Opt__name_5,axiom,
% 0.31/0.46 pt_name @ name ).
% 0.31/0.46
% 0.31/0.46 thf(tcon_Agent_Oname___Agent_Ofs__name_6,axiom,
% 0.31/0.46 fs_name @ name ).
% 0.31/0.46
% 0.31/0.46 thf(tcon_Nominal_Onoption___Agent_Opt__name_7,axiom,
% 0.31/0.46 ! [A6: $tType] :
% 0.31/0.46 ( ( pt_name @ A6 )
% 0.31/0.46 => ( pt_name @ ( noption @ A6 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(tcon_Late__Semantics_OfreeRes___Agent_Opt__name_8,axiom,
% 0.31/0.46 pt_name @ late_freeRes ).
% 0.31/0.46
% 0.31/0.46 thf(tcon_Late__Semantics_OfreeRes___Agent_Ofs__name_9,axiom,
% 0.31/0.46 fs_name @ late_freeRes ).
% 0.31/0.46
% 0.31/0.46 thf(tcon_Late__Semantics_Osubject___Agent_Opt__name_10,axiom,
% 0.31/0.46 pt_name @ late_subject ).
% 0.31/0.46
% 0.31/0.46 thf(tcon_Late__Semantics_Osubject___Agent_Ofs__name_11,axiom,
% 0.31/0.46 fs_name @ late_subject ).
% 0.31/0.46
% 0.31/0.46 thf(tcon_Late__Semantics_Oresidual___Agent_Opt__name_12,axiom,
% 0.31/0.46 pt_name @ late_residual ).
% 0.31/0.46
% 0.31/0.46 thf(tcon_Late__Semantics_Oresidual___Agent_Ofs__name_13,axiom,
% 0.31/0.46 fs_name @ late_residual ).
% 0.31/0.46
% 0.31/0.46 % Helper facts (3)
% 0.31/0.46 thf(help_If_3_1_T,axiom,
% 0.31/0.46 ! [P: $o] :
% 0.31/0.46 ( ( P = $true )
% 0.31/0.46 | ( P = $false ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(help_If_2_1_T,axiom,
% 0.31/0.46 ! [A: $tType,X3: A,Y: A] :
% 0.31/0.46 ( ( if @ A @ $false @ X3 @ Y )
% 0.31/0.46 = Y ) ).
% 0.31/0.46
% 0.31/0.46 thf(help_If_1_1_T,axiom,
% 0.31/0.46 ! [A: $tType,X3: A,Y: A] :
% 0.31/0.46 ( ( if @ A @ $true @ X3 @ Y )
% 0.31/0.46 = X3 ) ).
% 0.31/0.46
% 0.31/0.46 % Conjectures (1)
% 0.31/0.46 thf(conj_0,conjecture,
% 0.31/0.46 late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_FreeR @ late_TauR @ ( par @ ( par @ p2 @ ( subs @ q2 @ x @ b ) ) @ r ) ) ).
% 0.31/0.46
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 ------------------------
% 2.59/1.49 ---- Embedded in THF ---
% 2.59/1.49 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.59/1.49 %%% Generated on Tue Feb 24 08:29:37 EST 2026
% 2.59/1.49 %%% using '$$dhol' embedding, version 1.3.0.
% 2.59/1.49 %%% Logic specification used:
% 2.59/1.49 %%% thf(spec, logic, $$dhol).
% 2.59/1.49
% 2.59/1.49 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.Is4Z84IKKq/DTF2DTF17420.p
% 2.59/1.49 thf(ty_t_Late__Semantics_Oresidual, type, late_residual: $tType).
% 2.59/1.49 thf(ty_t_Late__Semantics_Osubject, type, late_subject: $tType).
% 2.59/1.49 thf(ty_t_Late__Semantics_OfreeRes, type, late_freeRes: $tType).
% 2.59/1.49 thf(ty_t_Nominal_Onoption, type, noption: ($tType > $tType)).
% 2.59/1.49 thf(ty_t_Agent_Oname, type, name: $tType).
% 2.59/1.49 thf(ty_t_Agent_Opi, type, pi: $tType).
% 2.59/1.49 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 2.59/1.49 thf(sy_cl_Agent_Ofs__name, type, fs_name: (!> [A:$tType]: ($o))).
% 2.59/1.49 thf(sy_cl_Agent_Opt__name, type, pt_name: (!> [A:$tType]: ($o))).
% 2.59/1.49 thf(sy_c_Agent_Opi_OBang, type, bang: (pi > pi)).
% 2.59/1.49 thf(sy_c_Agent_Opi_OInput, type, input: (name > (name > (pi > pi)))).
% 2.59/1.49 thf(sy_c_Agent_Opi_OMatch, type, match: (name > (name > (pi > pi)))).
% 2.59/1.49 thf(sy_c_Agent_Opi_OMismatch, type, mismatch: (name > (name > (pi > pi)))).
% 2.59/1.49 thf(sy_c_Agent_Opi_OOutput, type, output: (name > (name > (pi > pi)))).
% 2.59/1.49 thf(sy_c_Agent_Opi_OPar, type, par: (pi > (pi > pi))).
% 2.59/1.49 thf(sy_c_Agent_Opi_OPiNil, type, piNil: pi).
% 2.59/1.49 thf(sy_c_Agent_Opi_ORes, type, res: (name > (pi > pi))).
% 2.59/1.49 thf(sy_c_Agent_Opi_OSum, type, sum: (pi > (pi > pi))).
% 2.59/1.49 thf(sy_c_Agent_Opi_OTau, type, tau: (pi > pi)).
% 2.59/1.49 thf(sy_c_Agent_Opi_Opi__rec, type, pi_rec: (!> [T:$tType]: ((T > ((name > (name > (pi > (T > T)))) > ((pi > (T > T)) > ((name > (name > (pi > (T > T)))) > ((name > (name > (pi > (T > T)))) > ((name > (name > (pi > (T > T)))) > ((pi > (pi > (T > (T > T)))) > ((pi > (pi > (T > (T > T)))) > ((name > (pi > (T > T))) > ((pi > (T > T)) > (pi > T)))))))))))))).
% 2.59/1.49 thf(sy_c_Agent_Opi_Opi__rec__set, type, pi_rec_set: (!> [T:$tType]: ((T > ((name > (name > (pi > (T > T)))) > ((pi > (T > T)) > ((name > (name > (pi > (T > T)))) > ((name > (name > (pi > (T > T)))) > ((name > (name > (pi > (T > T)))) > ((pi > (pi > (T > (T > T)))) > ((pi > (pi > (T > (T > T)))) > ((name > (pi > (T > T))) > ((pi > (T > T)) > (pi > (T > $o))))))))))))))).
% 2.59/1.49 thf(sy_c_Agent_Osubs, type, subs: (pi > (name > (name > pi)))).
% 2.59/1.49 thf(sy_c_Agent_Osubst__name, type, subst_name: (name > (name > (name > name)))).
% 2.59/1.49 thf(sy_c_Finite__Set_Ofinite, type, finite_finite: (!> [A:$tType]: (((set @ A) > $o)))).
% 2.59/1.49 thf(sy_c_If, type, if: (!> [A:$tType]: (($o > (A > (A > A)))))).
% 2.59/1.49 thf(sy_c_Late__Semantics1_OfreeRes_Ocase__freeRes, type, late_case_freeRes: (!> [A:$tType]: (((name > (name > A)) > (A > (late_freeRes > A)))))).
% 2.59/1.49 thf(sy_c_Late__Semantics1_Osubject_Ocase__subject, type, late_case_subject: (!> [A:$tType]: (((name > A) > ((name > A) > (late_subject > A)))))).
% 2.59/1.49 thf(sy_c_Late__Semantics_ObangPred, type, late_bangPred: (pi > (pi > $o))).
% 2.59/1.49 thf(sy_c_Late__Semantics_OfreeRes_OOutputR, type, late_OutputR: (name > (name > late_freeRes))).
% 2.59/1.49 thf(sy_c_Late__Semantics_OfreeRes_OTauR, type, late_TauR: late_freeRes).
% 2.59/1.49 thf(sy_c_Late__Semantics_OfreeRes_OfreeRes__rec, type, late_freeRes_rec: (!> [T:$tType]: (((name > (name > T)) > (T > (late_freeRes > T)))))).
% 2.59/1.49 thf(sy_c_Late__Semantics_Oresidual_OBoundR, type, late_BoundR: (late_subject > (name > (pi > late_residual)))).
% 2.59/1.49 thf(sy_c_Late__Semantics_Oresidual_OFreeR, type, late_FreeR: (late_freeRes > (pi > late_residual))).
% 2.59/1.49 thf(sy_c_Late__Semantics_Oresidual_Oresidual__rec, type, late_residual_rec: (!> [T:$tType]: (((late_subject > (name > (pi > T))) > ((late_freeRes > (pi > T)) > (late_residual > T)))))).
% 2.59/1.49 thf(sy_c_Late__Semantics_Oresidual_Oresidual__rec__set, type, late_r582136743ec_set: (!> [T:$tType]: (((late_subject > (name > (pi > T))) > ((late_freeRes > (pi > T)) > (late_residual > (T > $o))))))).
% 2.59/1.49 thf(sy_c_Late__Semantics_Osubject_OBoundOutputS, type, late_BoundOutputS: (name > late_subject)).
% 2.59/1.49 thf(sy_c_Late__Semantics_Osubject_OInputS, type, late_InputS: (name > late_subject)).
% 2.59/1.49 thf(sy_c_Late__Semantics_Osubject_Osubject__rec, type, late_subject_rec: (!> [T:$tType]: (((name > T) > ((name > T) > (late_subject > T)))))).
% 2.59/1.49 thf(sy_c_Late__Semantics_Otransitions, type, late_transitions: (pi > (late_residual > $o))).
% 2.59/1.49 thf(sy_c_Lattices_Osup__class_Osup, type, sup_sup: (!> [A:$tType]: ((A > (A > A))))).
% 2.59/1.49 thf(sy_c_Nominal_Oabs__fun, type, abs_fun: (!> [X:$tType,A:$tType]: ((X > (A > (X > (noption @ A))))))).
% 2.59/1.49 thf(sy_c_Nominal_Ofresh, type, fresh: (!> [X:$tType,A:$tType]: ((X > (A > $o))))).
% 2.59/1.49 thf(sy_c_Nominal_Osupp, type, supp: (!> [A:$tType,X:$tType]: ((A > (set @ X))))).
% 2.59/1.49 thf(sy_c_Nominal_Osupports, type, supports: (!> [X:$tType,A:$tType]: (((set @ X) > (A > $o))))).
% 2.59/1.49 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 2.59/1.49 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 2.59/1.49 thf(sy_v_P, type, p: pi).
% 2.59/1.49 thf(sy_v_PQR____, type, pqr: pi).
% 2.59/1.49 thf(sy_v_P_H____, type, p2: pi).
% 2.59/1.49 thf(sy_v_Q, type, q: pi).
% 2.59/1.49 thf(sy_v_QR____, type, qr: pi).
% 2.59/1.49 thf(sy_v_Q_H____, type, q2: pi).
% 2.59/1.49 thf(sy_v_R, type, r: pi).
% 2.59/1.49 thf(sy_v__092_060alpha_062____, type, alpha: late_freeRes).
% 2.59/1.49 thf(sy_v_a____, type, a: name).
% 2.59/1.49 thf(sy_v_b____, type, b: name).
% 2.59/1.49 thf(sy_v_x____, type, x: name).
% 2.59/1.49 thf(fact_0_cComm2_Ohyps_I9_J, axiom, (alpha = late_TauR)).
% 2.59/1.49 thf(fact_1_cComm2_Ohyps_I5_J, axiom, (x != a)).
% 2.59/1.49 thf(fact_2_cComm2_Ohyps_I6_J, axiom, (x != b)).
% 2.59/1.49 thf(fact_3__092_060open_062P_A_092_060parallel_062_AQ_A_092_060longmapsto_062_A_092_060tau_062_A_092_060prec_062_AP_H_A_092_060parallel_062_AQ_H_091x_058_058_061b_093_092_060close_062, axiom, ((late_transitions @ ((par @ p) @ q)) @ ((late_FreeR @ late_TauR) @ ((par @ p2) @ (((subs @ q2) @ x) @ b))))).
% 2.59/1.49 thf(fact_4_Free_Ohyps, axiom, ((late_transitions @ ((par @ p) @ ((par @ q) @ r))) @ ((late_FreeR @ alpha) @ pqr))).
% 2.59/1.49 thf(fact_5_cComm2_Ohyps_I8_J, axiom, ((((fresh @ name) @ pi) @ x) @ q)).
% 2.59/1.49 thf(fact_6_cComm2_Ohyps_I3_J, axiom, ((((fresh @ name) @ pi) @ x) @ p)).
% 2.59/1.49 thf(fact_7_cComm2_Ohyps_I7_J, axiom, ((((fresh @ name) @ pi) @ x) @ p2)).
% 2.59/1.49 thf(fact_8_cComm2_Ohyps_I4_J, axiom, ((((fresh @ name) @ pi) @ x) @ ((par @ q) @ r))).
% 2.59/1.49 thf(fact_9_cComm2_Ohyps_I1_J, axiom, ((late_transitions @ p) @ ((late_FreeR @ ((late_OutputR @ a) @ b)) @ p2))).
% 2.59/1.49 thf(fact_10_simps_I8_J, axiom, (! [P:pi,Q:pi,C:name,D:name]: (((((subs @ ((par @ P) @ Q)) @ C) @ D) = ((par @ (((subs @ P) @ C) @ D)) @ (((subs @ Q) @ C) @ D)))))).
% 2.59/1.49 thf(fact_11_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))))))).
% 2.59/1.49 thf(fact_12_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))))))).
% 2.59/1.49 thf(fact_13__092_060open_062x_A_092_060sharp_062_AR_092_060close_062, axiom, ((((fresh @ name) @ pi) @ x) @ r)).
% 2.59/1.49 thf(fact_14_subst__identity, axiom, (! [P:pi,A2:name]: (((((subs @ P) @ A2) @ A2) = P)))).
% 2.59/1.49 thf(fact_15_cPar1_Ohyps, axiom, ((late_transitions @ q) @ (((late_BoundR @ (late_InputS @ a)) @ x) @ q2))).
% 2.59/1.49 thf(fact_16_cComm2_Ohyps_I2_J, axiom, ((late_transitions @ ((par @ q) @ r)) @ (((late_BoundR @ (late_InputS @ a)) @ x) @ qr))).
% 2.59/1.49 thf(fact_17_residual_Oinject_I2_J, axiom, (! [X2:late_freeRes,X1:pi,Y2:late_freeRes,Y1:pi]: (((((late_FreeR @ X2) @ X1) = ((late_FreeR @ Y2) @ Y1)) = ((X2 = Y2) & (X1 = Y1)))))).
% 2.59/1.49 thf(fact_18_pi_Oinject_I7_J, axiom, (! [X2:pi,X1:pi,Y2:pi,Y1:pi]: (((((par @ X2) @ X1) = ((par @ Y2) @ Y1)) = ((X2 = Y2) & (X1 = Y1)))))).
% 2.59/1.49 thf(fact_19_tauCases, axiom, (! [P:pi,Alpha:late_freeRes,P2:pi,Prop:(late_freeRes > (pi > $o))]: ((((late_transitions @ (tau @ P)) @ ((late_FreeR @ Alpha) @ P2)) => (((Alpha = late_TauR) => ((P = P2) => ((Prop @ late_TauR) @ P))) => ((Prop @ Alpha) @ P2)))))).
% 2.59/1.49 thf(fact_20_tauCases_H, axiom, (! [P:pi,Rs:late_residual]: ((((late_transitions @ (tau @ P)) @ Rs) => (~ ((! [P3:pi]: ((((tau @ P) = (tau @ P3)) => (Rs != ((late_FreeR @ late_TauR) @ P3))))))))))).
% 2.59/1.49 thf(fact_21_Late__Semantics_OfreeRes_Oinject, axiom, (! [X2:name,X1:name,Y2:name,Y1:name]: (((((late_OutputR @ X2) @ X1) = ((late_OutputR @ Y2) @ Y1)) = ((X2 = Y2) & (X1 = Y1)))))).
% 2.59/1.49 thf(fact_22_pi_Ofresh_I8_J, axiom, (! [A2:name,X2:pi,X1:pi]: ((((((fresh @ name) @ pi) @ A2) @ ((par @ X2) @ X1)) = (((((fresh @ name) @ pi) @ A2) @ X2) & ((((fresh @ name) @ pi) @ A2) @ X1)))))).
% 2.59/1.49 thf(fact_23_substTrans, axiom, (! [B:name,P:pi,A2:name,C:name]: ((((((fresh @ name) @ pi) @ B) @ P) => ((((subs @ (((subs @ P) @ A2) @ B)) @ B) @ C) = (((subs @ P) @ A2) @ C)))))).
% 2.59/1.49 thf(fact_24_pi_Ofresh_I3_J, axiom, (! [A2:name,X1:pi]: ((((((fresh @ name) @ pi) @ A2) @ (tau @ X1)) = ((((fresh @ name) @ pi) @ A2) @ X1))))).
% 2.59/1.49 thf(fact_25_simps_I2_J, axiom, (! [P:pi,C:name,D:name]: (((((subs @ (tau @ P)) @ C) @ D) = (tau @ (((subs @ P) @ C) @ D)))))).
% 2.59/1.49 thf(fact_26_pi_Oinject_I2_J, axiom, (! [X1:pi,Y1:pi]: ((((tau @ X1) = (tau @ Y1)) = (X1 = Y1))))).
% 2.59/1.49 thf(fact_27_freshBoundDerivative_I2_J, axiom, (! [P:pi,A2:late_subject,X3:name,P2:pi,Y:name]: ((((late_transitions @ P) @ (((late_BoundR @ A2) @ X3) @ P2)) => (((((fresh @ name) @ pi) @ Y) @ P) => ((Y != X3) => ((((fresh @ name) @ pi) @ Y) @ P2))))))).
% 2.59/1.49 thf(fact_28_name__exists__fresh, axiom, (! [A:$tType]: (((fs_name @ A) => (! [X3:A]: ((~ ((! [C2:name]: ((~ (((((fresh @ name) @ A) @ C2) @ X3))))))))))))).
% 2.59/1.49 thf(fact_29_tauBoundTrans, axiom, (! [P:pi,A2:late_subject,X3:name,P2:pi]: ((~ (((late_transitions @ (tau @ P)) @ (((late_BoundR @ A2) @ X3) @ P2))))))).
% 2.59/1.49 thf(fact_30_residual_Ostrong__induct, axiom, (! [N:$tType]: (((fs_name @ N) => (! [P:(N > (late_residual > $o)),Z:N,Residual:late_residual]: (((! [Subject:late_subject,Name:name,Pi:pi,Z2:N]: ((((((fresh @ name) @ N) @ Name) @ Z2) => (((((fresh @ name) @ late_subject) @ Name) @ Subject) => ((P @ Z2) @ (((late_BoundR @ Subject) @ Name) @ Pi)))))) => ((! [FreeRes:late_freeRes,Pi:pi,Z2:N]: (((P @ Z2) @ ((late_FreeR @ FreeRes) @ Pi)))) => ((P @ Z) @ Residual))))))))).
% 2.59/1.49 thf(fact_31_residual_Ostrong__inducts, axiom, (! [A:$tType]: (((fs_name @ A) => (! [P:(A > (late_residual > $o)),Z:A,Residual:late_residual]: (((! [Subject:late_subject,Name:name,Pi:pi,Z2:A]: ((((((fresh @ name) @ A) @ Name) @ Z2) => (((((fresh @ name) @ late_subject) @ Name) @ Subject) => ((P @ Z2) @ (((late_BoundR @ Subject) @ Name) @ Pi)))))) => ((! [FreeRes:late_freeRes,Pi:pi,Z2:A]: (((P @ Z2) @ ((late_FreeR @ FreeRes) @ Pi)))) => ((P @ Z) @ Residual))))))))).
% 2.59/1.49 thf(fact_32_residual_Oinducts, axiom, (! [P:(late_residual > $o),Residual:late_residual]: (((! [Subject:late_subject,Name:name,Pi:pi]: ((P @ (((late_BoundR @ Subject) @ Name) @ Pi)))) => ((! [FreeRes:late_freeRes,Pi:pi]: ((P @ ((late_FreeR @ FreeRes) @ Pi)))) => (P @ Residual)))))).
% 2.59/1.49 thf(fact_33_residual_Odistinct_I1_J, axiom, (! [Subject2:late_subject,Name2:name,Pi2:pi,FreeRes2:late_freeRes,Pi3:pi]: (((((late_BoundR @ Subject2) @ Name2) @ Pi2) != ((late_FreeR @ FreeRes2) @ Pi3))))).
% 2.59/1.49 thf(fact_34_fresh__fact2, axiom, (! [A2:name,B:name,P:pi]: (((A2 != B) => ((((fresh @ name) @ pi) @ A2) @ (((subs @ P) @ A2) @ B)))))).
% 2.59/1.49 thf(fact_35_fresh__fact1, axiom, (! [A2:name,P:pi,C:name,B:name]: ((((((fresh @ name) @ pi) @ A2) @ P) => ((A2 != C) => ((((fresh @ name) @ pi) @ A2) @ (((subs @ P) @ B) @ C))))))).
% 2.59/1.49 thf(fact_36_forget, axiom, (! [A2:name,P:pi,B:name]: ((((((fresh @ name) @ pi) @ A2) @ P) => ((((subs @ P) @ A2) @ B) = P))))).
% 2.59/1.49 thf(fact_37_parCasesB, axiom, (! [P:pi,Q:pi,A2:late_subject,X3:name,PQ:pi,Prop:(pi > $o)]: ((((late_transitions @ ((par @ P) @ Q)) @ (((late_BoundR @ A2) @ X3) @ PQ)) => (((((fresh @ name) @ pi) @ X3) @ P) => (((((fresh @ name) @ pi) @ X3) @ Q) => ((! [P4:pi]: ((((late_transitions @ P) @ (((late_BoundR @ A2) @ X3) @ P4)) => (Prop @ ((par @ P4) @ Q))))) => ((! [Q3:pi]: ((((late_transitions @ Q) @ (((late_BoundR @ A2) @ X3) @ Q3)) => (Prop @ ((par @ P) @ Q3))))) => (Prop @ PQ))))))))).
% 2.59/1.49 thf(fact_38_Late__Semantics_OPar2B, axiom, (! [Q:pi,A2:late_subject,X3:name,Q2:pi,P:pi]: ((((late_transitions @ Q) @ (((late_BoundR @ A2) @ X3) @ Q2)) => (((((fresh @ name) @ pi) @ X3) @ P) => ((late_transitions @ ((par @ P) @ Q)) @ (((late_BoundR @ A2) @ X3) @ ((par @ P) @ Q2)))))))).
% 2.59/1.49 thf(fact_39_Late__Semantics_OPar1B, axiom, (! [P:pi,A2:late_subject,X3:name,P2:pi,Q:pi]: ((((late_transitions @ P) @ (((late_BoundR @ A2) @ X3) @ P2)) => (((((fresh @ name) @ pi) @ X3) @ Q) => ((late_transitions @ ((par @ P) @ Q)) @ (((late_BoundR @ A2) @ X3) @ ((par @ P2) @ Q)))))))).
% 2.59/1.49 thf(fact_40_pi_Odistinct_I43_J, axiom, (! [Pi2:pi,Pi1:pi,Pi22:pi]: (((tau @ Pi2) != ((par @ Pi1) @ Pi22))))).
% 2.59/1.49 thf(fact_41_freeRes_Ostrong__inducts, axiom, (! [A:$tType,P:(A > (late_freeRes > $o)),Z:A,FreeRes3:late_freeRes]: (((! [Name1:name,Name22:name,Z2:A]: (((P @ Z2) @ ((late_OutputR @ Name1) @ Name22)))) => ((! [Z2:A]: (((P @ Z2) @ late_TauR))) => ((P @ Z) @ FreeRes3)))))).
% 2.59/1.49 thf(fact_42_freeRes_Ostrong__induct_H, axiom, (! [N:$tType,P:(N > (late_freeRes > $o)),Z:N,FreeRes3:late_freeRes]: (((! [Name1:name,Name22:name,Z2:N]: (((P @ Z2) @ ((late_OutputR @ Name1) @ Name22)))) => ((! [Z2:N]: (((P @ Z2) @ late_TauR))) => ((P @ Z) @ FreeRes3)))))).
% 2.59/1.49 thf(fact_43_freeRes_Oinducts, axiom, (! [P:(late_freeRes > $o),FreeRes3:late_freeRes]: (((! [Name1:name,Name22:name]: ((P @ ((late_OutputR @ Name1) @ Name22)))) => ((P @ late_TauR) => (P @ FreeRes3)))))).
% 2.59/1.49 thf(fact_44_Late__Semantics_OfreeRes_Odistinct_I1_J, axiom, (! [Name12:name,Name23:name]: ((((late_OutputR @ Name12) @ Name23) != late_TauR)))).
% 2.59/1.49 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P)) = (P @ A2))))).
% 2.59/1.49 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A3:(set @ A)]: ((((collect @ A) @ (^ [X4:A]: ((((member @ A) @ X4) @ A3)))) = A3)))).
% 2.59/1.49 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X5:A]: (((P @ X5) = (Q @ X5)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 2.59/1.49 thf(fact_48_ext, axiom, (! [B2:$tType,A:$tType,F:(A > B2),G:(A > B2)]: (((! [X5:A]: (((F @ X5) = (G @ X5)))) => (F = G))))).
% 2.59/1.49 thf(fact_49_tauOutputTrans, axiom, (! [P:pi,A2:name,B:name,P2:pi]: ((~ (((late_transitions @ (tau @ P)) @ ((late_FreeR @ ((late_OutputR @ A2) @ B)) @ P2))))))).
% 2.59/1.49 thf(fact_50_transitions_OComm2, axiom, (! [P:pi,A2:name,B:name,P2:pi,Q:pi,X3:name,Q2:pi]: ((((late_transitions @ P) @ ((late_FreeR @ ((late_OutputR @ A2) @ B)) @ P2)) => (((late_transitions @ Q) @ (((late_BoundR @ (late_InputS @ A2)) @ X3) @ Q2)) => (((((fresh @ name) @ pi) @ X3) @ P) => (((((fresh @ name) @ pi) @ X3) @ Q) => ((X3 != A2) => ((X3 != B) => (((((fresh @ name) @ pi) @ X3) @ P2) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ late_TauR) @ ((par @ P2) @ (((subs @ Q2) @ X3) @ B)))))))))))))).
% 2.59/1.49 thf(fact_51_transitions_OComm1, axiom, (! [P:pi,A2:name,X3:name,P2:pi,Q:pi,B:name,Q2:pi]: ((((late_transitions @ P) @ (((late_BoundR @ (late_InputS @ A2)) @ X3) @ P2)) => (((late_transitions @ Q) @ ((late_FreeR @ ((late_OutputR @ A2) @ B)) @ Q2)) => (((((fresh @ name) @ pi) @ X3) @ P) => (((((fresh @ name) @ pi) @ X3) @ Q) => ((X3 != A2) => ((X3 != B) => (((((fresh @ name) @ pi) @ X3) @ Q2) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ late_TauR) @ ((par @ (((subs @ P2) @ X3) @ B)) @ Q2))))))))))))).
% 2.59/1.49 thf(fact_52_freshFreeDerivative_I2_J, axiom, (! [P:pi,Alpha:late_freeRes,P2:pi,Y:name]: ((((late_transitions @ P) @ ((late_FreeR @ Alpha) @ P2)) => (((((fresh @ name) @ pi) @ Y) @ P) => ((((fresh @ name) @ pi) @ Y) @ P2)))))).
% 2.59/1.49 thf(fact_53_Late__Semantics_OComm2, axiom, (! [P:pi,A2:name,B:name,P2:pi,Q:pi,X3:name,Q2:pi]: ((((late_transitions @ P) @ ((late_FreeR @ ((late_OutputR @ A2) @ B)) @ P2)) => (((late_transitions @ Q) @ (((late_BoundR @ (late_InputS @ A2)) @ X3) @ Q2)) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ late_TauR) @ ((par @ P2) @ (((subs @ Q2) @ X3) @ B))))))))).
% 2.59/1.49 thf(fact_54_Late__Semantics_OComm1, axiom, (! [P:pi,A2:name,X3:name,P2:pi,Q:pi,B:name,Q2:pi]: ((((late_transitions @ P) @ (((late_BoundR @ (late_InputS @ A2)) @ X3) @ P2)) => (((late_transitions @ Q) @ ((late_FreeR @ ((late_OutputR @ A2) @ B)) @ Q2)) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ late_TauR) @ ((par @ (((subs @ P2) @ X3) @ B)) @ Q2)))))))).
% 2.59/1.49 thf(fact_55_Tau, axiom, (! [P:pi]: (((late_transitions @ (tau @ P)) @ ((late_FreeR @ late_TauR) @ P))))).
% 2.59/1.49 thf(fact_56_Late__Semantics1_Osubject_Oinject_I1_J, axiom, (! [X1:name,Y1:name]: ((((late_InputS @ X1) = (late_InputS @ Y1)) = (X1 = Y1))))).
% 2.59/1.49 thf(fact_57_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)))))).
% 2.59/1.49 thf(fact_58_freeRes_Oexhaust, axiom, (! [Y:late_freeRes]: (((! [X112:name,X122:name]: ((Y != ((late_OutputR @ X112) @ X122)))) => (Y = late_TauR))))).
% 2.59/1.49 thf(fact_59_Late__Semantics1_OfreeRes_Odistinct_I1_J, axiom, (! [X11:name,X12:name]: ((((late_OutputR @ X11) @ X12) != late_TauR)))).
% 2.59/1.49 thf(fact_60_freeRes_Orecs_I2_J, axiom, (! [T:$tType,P:(T > $o),F1:(name > (name > T)),F2:T]: (((! [X13:name,X22:name]: ((P @ ((F1 @ X13) @ X22)))) => ((P @ F2) => (((((late_freeRes_rec @ T) @ F1) @ F2) @ late_TauR) = F2)))))).
% 2.59/1.49 thf(fact_61_subject_Orecs_I1_J, axiom, (! [T:$tType,P:(T > $o),F1:(name > T),F2:(name > T),Name2:name]: (((! [X13:name]: ((P @ (F1 @ X13)))) => ((! [X13:name]: ((P @ (F2 @ X13)))) => (((((late_subject_rec @ T) @ F1) @ F2) @ (late_InputS @ Name2)) = (F1 @ Name2))))))).
% 2.59/1.49 thf(fact_62_freeRes_Orecs_I1_J, axiom, (! [T:$tType,P:(T > $o),F1:(name > (name > T)),F2:T,Name12:name,Name23:name]: (((! [X13:name,X22:name]: ((P @ ((F1 @ X13) @ X22)))) => ((P @ F2) => (((((late_freeRes_rec @ T) @ F1) @ F2) @ ((late_OutputR @ Name12) @ Name23)) = ((F1 @ Name12) @ Name23))))))).
% 2.59/1.49 thf(fact_63_transitions_OClose2, axiom, (! [P:pi,A2:name,Y:name,P2:pi,Q:pi,X3:name,Q2:pi]: ((((late_transitions @ P) @ (((late_BoundR @ (late_BoundOutputS @ A2)) @ Y) @ P2)) => (((late_transitions @ Q) @ (((late_BoundR @ (late_InputS @ A2)) @ X3) @ Q2)) => (((((fresh @ name) @ pi) @ X3) @ P) => (((((fresh @ name) @ pi) @ X3) @ Q) => (((((fresh @ name) @ pi) @ Y) @ P) => (((((fresh @ name) @ pi) @ Y) @ Q) => ((X3 != A2) => (((((fresh @ name) @ pi) @ X3) @ P2) => ((Y != A2) => (((((fresh @ name) @ pi) @ Y) @ Q2) => ((X3 != Y) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ late_TauR) @ ((res @ Y) @ ((par @ P2) @ (((subs @ Q2) @ X3) @ Y))))))))))))))))))).
% 2.59/1.49 thf(fact_64_transitions_OClose1, axiom, (! [P:pi,A2:name,X3:name,P2:pi,Q:pi,Y:name,Q2:pi]: ((((late_transitions @ P) @ (((late_BoundR @ (late_InputS @ A2)) @ X3) @ P2)) => (((late_transitions @ Q) @ (((late_BoundR @ (late_BoundOutputS @ A2)) @ Y) @ Q2)) => (((((fresh @ name) @ pi) @ X3) @ P) => (((((fresh @ name) @ pi) @ X3) @ Q) => (((((fresh @ name) @ pi) @ Y) @ P) => (((((fresh @ name) @ pi) @ Y) @ Q) => ((X3 != A2) => (((((fresh @ name) @ pi) @ X3) @ Q2) => ((Y != A2) => (((((fresh @ name) @ pi) @ Y) @ P2) => ((X3 != Y) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ late_TauR) @ ((res @ Y) @ ((par @ (((subs @ P2) @ X3) @ Y)) @ Q2)))))))))))))))))).
% 2.59/1.49 thf(fact_65_Late__Semantics_OClose2, axiom, (! [P:pi,A2:name,Y:name,P2:pi,Q:pi,X3:name,Q2:pi]: ((((late_transitions @ P) @ (((late_BoundR @ (late_BoundOutputS @ A2)) @ Y) @ P2)) => (((late_transitions @ Q) @ (((late_BoundR @ (late_InputS @ A2)) @ X3) @ Q2)) => (((((fresh @ name) @ pi) @ Y) @ Q) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ late_TauR) @ ((res @ Y) @ ((par @ P2) @ (((subs @ Q2) @ X3) @ Y))))))))))).
% 2.59/1.49 thf(fact_66_freeRes_Ofresh_I1_J, axiom, (! [A2:name,X2:name,X1:name]: ((((((fresh @ name) @ late_freeRes) @ A2) @ ((late_OutputR @ X2) @ X1)) = (((((fresh @ name) @ name) @ A2) @ X2) & ((((fresh @ name) @ name) @ A2) @ X1)))))).
% 2.59/1.49 thf(fact_67_Late__Semantics_Osubject_Oinject_I2_J, axiom, (! [X1:name,Y1:name]: ((((late_BoundOutputS @ X1) = (late_BoundOutputS @ Y1)) = (X1 = Y1))))).
% 2.59/1.49 thf(fact_68_Late__Semantics1_Osubject_Oinject_I2_J, axiom, (! [X2:name,Y2:name]: ((((late_BoundOutputS @ X2) = (late_BoundOutputS @ Y2)) = (X2 = Y2))))).
% 2.59/1.49 thf(fact_69_freeRes_Ofresh_I2_J, axiom, (! [A2:name]: (((((fresh @ name) @ late_freeRes) @ A2) @ late_TauR)))).
% 2.59/1.49 thf(fact_70_residual_Ofresh_I2_J, axiom, (! [A2:name,X2:late_freeRes,X1:pi]: ((((((fresh @ name) @ late_residual) @ A2) @ ((late_FreeR @ X2) @ X1)) = (((((fresh @ name) @ late_freeRes) @ A2) @ X2) & ((((fresh @ name) @ pi) @ A2) @ X1)))))).
% 2.59/1.49 thf(fact_71_simps_I9_J, axiom, (! [X3:name,C:name,D:name,P:pi]: (((X3 != C) => ((X3 != D) => ((((subs @ ((res @ X3) @ P)) @ C) @ D) = ((res @ X3) @ (((subs @ P) @ C) @ D)))))))).
% 2.59/1.49 thf(fact_72_subject_Ofresh_I1_J, axiom, (! [A2:name,X1:name]: ((((((fresh @ name) @ late_subject) @ A2) @ (late_InputS @ X1)) = ((((fresh @ name) @ name) @ A2) @ X1))))).
% 2.59/1.49 thf(fact_73_subject_Ofresh_I2_J, axiom, (! [A2:name,X1:name]: ((((((fresh @ name) @ late_subject) @ A2) @ (late_BoundOutputS @ X1)) = ((((fresh @ name) @ name) @ A2) @ X1))))).
% 2.59/1.49 thf(fact_74_subject_Orecs_I2_J, axiom, (! [T:$tType,P:(T > $o),F1:(name > T),F2:(name > T),Name2:name]: (((! [X13:name]: ((P @ (F1 @ X13)))) => ((! [X13:name]: ((P @ (F2 @ X13)))) => (((((late_subject_rec @ T) @ F1) @ F2) @ (late_BoundOutputS @ Name2)) = (F2 @ Name2))))))).
% 2.59/1.49 thf(fact_75_subject_Oexhaust, axiom, (! [Y:late_subject]: (((! [X13:name]: ((Y != (late_InputS @ X13)))) => (~ ((! [X22:name]: ((Y != (late_BoundOutputS @ X22)))))))))).
% 2.59/1.49 thf(fact_76_Late__Semantics1_Osubject_Odistinct_I1_J, axiom, (! [X1:name,X2:name]: (((late_InputS @ X1) != (late_BoundOutputS @ X2))))).
% 2.59/1.49 thf(fact_77_Late__Semantics_OResB, axiom, (! [P:pi,A2:late_subject,X3:name,P2:pi,Y:name]: ((((late_transitions @ P) @ (((late_BoundR @ A2) @ X3) @ P2)) => (((((fresh @ name) @ late_subject) @ Y) @ A2) => ((Y != X3) => ((late_transitions @ ((res @ Y) @ P)) @ (((late_BoundR @ A2) @ X3) @ ((res @ Y) @ P2))))))))).
% 2.59/1.49 thf(fact_78_resCasesF, axiom, (! [X3:name,P:pi,Alpha:late_freeRes,XP:pi,F3:(pi > $o)]: ((((late_transitions @ ((res @ X3) @ P)) @ ((late_FreeR @ Alpha) @ XP)) => ((! [P4:pi]: ((((late_transitions @ P) @ ((late_FreeR @ Alpha) @ P4)) => (((((fresh @ name) @ late_freeRes) @ X3) @ Alpha) => (F3 @ ((res @ X3) @ P4)))))) => (F3 @ XP)))))).
% 2.59/1.49 thf(fact_79_resCasesF_H, axiom, (! [X3:name,P:pi,Alpha:late_freeRes,P2:pi]: ((((late_transitions @ ((res @ X3) @ P)) @ ((late_FreeR @ Alpha) @ P2)) => (~ ((! [P3:pi,Alpha2:late_freeRes,P4:pi,Y3:name]: (((((res @ X3) @ P) = ((res @ Y3) @ P3)) => ((((late_FreeR @ Alpha) @ P2) = ((late_FreeR @ Alpha2) @ ((res @ Y3) @ P4))) => (((late_transitions @ P3) @ ((late_FreeR @ Alpha2) @ P4)) => (~ (((((fresh @ name) @ late_freeRes) @ Y3) @ Alpha2)))))))))))))).
% 2.59/1.49 thf(fact_80_ResF, axiom, (! [P:pi,Alpha:late_freeRes,P2:pi,Y:name]: ((((late_transitions @ P) @ ((late_FreeR @ Alpha) @ P2)) => (((((fresh @ name) @ late_freeRes) @ Y) @ Alpha) => ((late_transitions @ ((res @ Y) @ P)) @ ((late_FreeR @ Alpha) @ ((res @ Y) @ P2)))))))).
% 2.59/1.49 thf(fact_81_pi_Odistinct_I85_J, axiom, (! [Pi12:pi,Pi23:pi,Name3:name,Pi3:pi]: ((((par @ Pi12) @ Pi23) != ((res @ Name3) @ Pi3))))).
% 2.59/1.49 thf(fact_82_freshRes, axiom, (! [A2:name,P:pi]: (((((fresh @ name) @ pi) @ A2) @ ((res @ A2) @ P))))).
% 2.59/1.49 thf(fact_83_pi_Odistinct_I45_J, axiom, (! [Pi2:pi,Name3:name,Pi3:pi]: (((tau @ Pi2) != ((res @ Name3) @ Pi3))))).
% 2.59/1.49 thf(fact_84_resCases_H, axiom, (! [X3:name,P:pi,Rs:late_residual]: ((((late_transitions @ ((res @ X3) @ P)) @ Rs) => ((! [P3:pi,A4:name,B3:name]: (((((res @ X3) @ P) = ((res @ B3) @ P3)) => (! [P4:pi]: (((Rs = (((late_BoundR @ (late_BoundOutputS @ A4)) @ B3) @ P4)) => (((late_transitions @ P3) @ ((late_FreeR @ ((late_OutputR @ A4) @ B3)) @ P4)) => (A4 = B3)))))))) => ((! [P3:pi,A4:late_subject,X5:name,P4:pi,Y3:name]: (((((res @ X3) @ P) = ((res @ Y3) @ P3)) => ((Rs = (((late_BoundR @ A4) @ X5) @ ((res @ Y3) @ P4))) => (((late_transitions @ P3) @ (((late_BoundR @ A4) @ X5) @ P4)) => (((((fresh @ name) @ late_subject) @ Y3) @ A4) => ((Y3 != X5) => (((((fresh @ name) @ pi) @ X5) @ P3) => (~ (((((fresh @ name) @ late_subject) @ X5) @ A4))))))))))) => (~ ((! [P3:pi,Alpha2:late_freeRes,P4:pi,Y3:name]: (((((res @ X3) @ P) = ((res @ Y3) @ P3)) => ((Rs = ((late_FreeR @ Alpha2) @ ((res @ Y3) @ P4))) => (((late_transitions @ P3) @ ((late_FreeR @ Alpha2) @ P4)) => (~ (((((fresh @ name) @ late_freeRes) @ Y3) @ Alpha2)))))))))))))))).
% 2.59/1.49 thf(fact_85_transitions_OResB, axiom, (! [P:pi,A2:late_subject,X3:name,P2:pi,Y:name]: ((((late_transitions @ P) @ (((late_BoundR @ A2) @ X3) @ P2)) => (((((fresh @ name) @ late_subject) @ Y) @ A2) => ((Y != X3) => (((((fresh @ name) @ pi) @ X3) @ P) => (((((fresh @ name) @ late_subject) @ X3) @ A2) => ((late_transitions @ ((res @ Y) @ P)) @ (((late_BoundR @ A2) @ X3) @ ((res @ Y) @ P2))))))))))).
% 2.59/1.49 thf(fact_86_subject_Ostrong__inducts, axiom, (! [A:$tType,P:(A > (late_subject > $o)),Z:A,Subject2:late_subject]: (((! [Name:name,Z2:A]: (((P @ Z2) @ (late_InputS @ Name)))) => ((! [Name:name,Z2:A]: (((P @ Z2) @ (late_BoundOutputS @ Name)))) => ((P @ Z) @ Subject2)))))).
% 2.59/1.49 thf(fact_87_subject_Ostrong__induct_H, axiom, (! [N:$tType,P:(N > (late_subject > $o)),Z:N,Subject2:late_subject]: (((! [Name:name,Z2:N]: (((P @ Z2) @ (late_InputS @ Name)))) => ((! [Name:name,Z2:N]: (((P @ Z2) @ (late_BoundOutputS @ Name)))) => ((P @ Z) @ Subject2)))))).
% 2.59/1.49 thf(fact_88_subject_Oinducts, axiom, (! [P:(late_subject > $o),Subject2:late_subject]: (((! [Name:name]: ((P @ (late_InputS @ Name)))) => ((! [Name:name]: ((P @ (late_BoundOutputS @ Name)))) => (P @ Subject2)))))).
% 2.59/1.49 thf(fact_89_Late__Semantics_Osubject_Odistinct_I1_J, axiom, (! [Name2:name,Name3:name]: (((late_InputS @ Name2) != (late_BoundOutputS @ Name3))))).
% 2.59/1.49 thf(fact_90_resCasesB_H, axiom, (! [X6:name,P:pi,A2:late_subject,Y4:name,P2:pi]: ((((late_transitions @ ((res @ X6) @ P)) @ (((late_BoundR @ A2) @ Y4) @ P2)) => ((! [P3:pi,A4:name,B3:name]: (((((res @ X6) @ P) = ((res @ B3) @ P3)) => (! [P4:pi]: ((((((late_BoundR @ A2) @ Y4) @ P2) = (((late_BoundR @ (late_BoundOutputS @ A4)) @ B3) @ P4)) => (((late_transitions @ P3) @ ((late_FreeR @ ((late_OutputR @ A4) @ B3)) @ P4)) => (A4 = B3)))))))) => (~ ((! [P3:pi,A4:late_subject,X5:name,P4:pi,Y3:name]: (((((res @ X6) @ P) = ((res @ Y3) @ P3)) => (((((late_BoundR @ A2) @ Y4) @ P2) = (((late_BoundR @ A4) @ X5) @ ((res @ Y3) @ P4))) => (((late_transitions @ P3) @ (((late_BoundR @ A4) @ X5) @ P4)) => (((((fresh @ name) @ late_subject) @ Y3) @ A4) => ((Y3 != X5) => (((((fresh @ name) @ pi) @ X5) @ P3) => (~ (((((fresh @ name) @ late_subject) @ X5) @ A4)))))))))))))))))).
% 2.59/1.49 thf(fact_91_freshResidual, axiom, (! [P:pi,Rs:late_residual,X3:name]: ((((late_transitions @ P) @ Rs) => (((((fresh @ name) @ pi) @ X3) @ P) => ((((fresh @ name) @ late_residual) @ X3) @ Rs)))))).
% 2.59/1.49 thf(fact_92_substRes3, axiom, (! [B:name,P:pi,A2:name]: ((((((fresh @ name) @ pi) @ B) @ P) => ((((subs @ ((res @ A2) @ P)) @ A2) @ B) = ((res @ B) @ (((subs @ P) @ A2) @ B))))))).
% 2.59/1.49 thf(fact_93_substRes2, axiom, (! [B:name,P:pi,A2:name]: ((((((fresh @ name) @ pi) @ B) @ P) => (((res @ A2) @ P) = ((res @ B) @ (((subs @ P) @ A2) @ B))))))).
% 2.59/1.49 thf(fact_94_Open, axiom, (! [P:pi,A2:name,B:name,P2:pi]: ((((late_transitions @ P) @ ((late_FreeR @ ((late_OutputR @ A2) @ B)) @ P2)) => ((A2 != B) => ((late_transitions @ ((res @ B) @ P)) @ (((late_BoundR @ (late_BoundOutputS @ A2)) @ B) @ P2))))))).
% 2.59/1.49 thf(fact_95_freshFreeDerivative_I1_J, axiom, (! [P:pi,Alpha:late_freeRes,P2:pi,Y:name]: ((((late_transitions @ P) @ ((late_FreeR @ Alpha) @ P2)) => (((((fresh @ name) @ pi) @ Y) @ P) => ((((fresh @ name) @ late_freeRes) @ Y) @ Alpha)))))).
% 2.59/1.49 thf(fact_96_freshBoundDerivative_I1_J, axiom, (! [P:pi,A2:late_subject,X3:name,P2:pi,Y:name]: ((((late_transitions @ P) @ (((late_BoundR @ A2) @ X3) @ P2)) => (((((fresh @ name) @ pi) @ Y) @ P) => ((((fresh @ name) @ late_subject) @ Y) @ A2)))))).
% 2.59/1.49 thf(fact_97_resTauBoundTrans, axiom, (! [X3:name,P:pi,A2:late_subject,Y:name,P2:pi]: ((~ (((late_transitions @ ((res @ X3) @ (tau @ P))) @ (((late_BoundR @ A2) @ Y) @ P2))))))).
% 2.59/1.49 thf(fact_98_parCasesB_H, axiom, (! [P:pi,Q:pi,B:late_subject,Y:name,P2:pi]: ((((late_transitions @ ((par @ P) @ Q)) @ (((late_BoundR @ B) @ Y) @ P2)) => ((! [P3:pi,A4:late_subject,X5:name,P4:pi,Q4:pi]: (((((par @ P) @ Q) = ((par @ P3) @ Q4)) => (((((late_BoundR @ B) @ Y) @ P2) = (((late_BoundR @ A4) @ X5) @ ((par @ P4) @ Q4))) => (((late_transitions @ P3) @ (((late_BoundR @ A4) @ X5) @ P4)) => (((((fresh @ name) @ pi) @ X5) @ P3) => (((((fresh @ name) @ pi) @ X5) @ Q4) => (~ (((((fresh @ name) @ late_subject) @ X5) @ A4)))))))))) => (~ ((! [Q4:pi,A4:late_subject,X5:name,Q3:pi,P3:pi]: (((((par @ P) @ Q) = ((par @ P3) @ Q4)) => (((((late_BoundR @ B) @ Y) @ P2) = (((late_BoundR @ A4) @ X5) @ ((par @ P3) @ Q3))) => (((late_transitions @ Q4) @ (((late_BoundR @ A4) @ X5) @ Q3)) => (((((fresh @ name) @ pi) @ X5) @ P3) => (((((fresh @ name) @ pi) @ X5) @ Q4) => (~ (((((fresh @ name) @ late_subject) @ X5) @ A4))))))))))))))))).
% 2.59/1.49 thf(fact_99_transitions_OPar1B, axiom, (! [P:pi,A2:late_subject,X3:name,P2:pi,Q:pi]: ((((late_transitions @ P) @ (((late_BoundR @ A2) @ X3) @ P2)) => (((((fresh @ name) @ pi) @ X3) @ P) => (((((fresh @ name) @ pi) @ X3) @ Q) => (((((fresh @ name) @ late_subject) @ X3) @ A2) => ((late_transitions @ ((par @ P) @ Q)) @ (((late_BoundR @ A2) @ X3) @ ((par @ P2) @ Q)))))))))).
% 2.59/1.49 thf(fact_100_transitions_OPar2B, axiom, (! [Q:pi,A2:late_subject,X3:name,Q2:pi,P:pi]: ((((late_transitions @ Q) @ (((late_BoundR @ A2) @ X3) @ Q2)) => (((((fresh @ name) @ pi) @ X3) @ P) => (((((fresh @ name) @ pi) @ X3) @ Q) => (((((fresh @ name) @ late_subject) @ X3) @ A2) => ((late_transitions @ ((par @ P) @ Q)) @ (((late_BoundR @ A2) @ X3) @ ((par @ P) @ Q2)))))))))).
% 2.59/1.49 thf(fact_101_resTauOutputTrans, axiom, (! [X3:name,P:pi,A2:name,B:name,P2:pi]: ((~ (((late_transitions @ ((res @ X3) @ (tau @ P))) @ ((late_FreeR @ ((late_OutputR @ A2) @ B)) @ P2))))))).
% 2.59/1.49 thf(fact_102_Late__Semantics_OClose1, axiom, (! [P:pi,A2:name,X3:name,P2:pi,Q:pi,Y:name,Q2:pi]: ((((late_transitions @ P) @ (((late_BoundR @ (late_InputS @ A2)) @ X3) @ P2)) => (((late_transitions @ Q) @ (((late_BoundR @ (late_BoundOutputS @ A2)) @ Y) @ Q2)) => (((((fresh @ name) @ pi) @ Y) @ P) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ late_TauR) @ ((res @ Y) @ ((par @ (((subs @ P2) @ X3) @ Y)) @ Q2)))))))))).
% 2.59/1.49 thf(fact_103_resOutputTauTrans, axiom, (! [X3:name,A2:name,B:name,P:pi,P2:pi]: ((~ (((late_transitions @ ((res @ X3) @ (((output @ A2) @ B) @ P))) @ ((late_FreeR @ late_TauR) @ P2))))))).
% 2.59/1.49 thf(fact_104_resOutputInputTrans, axiom, (! [X3:name,A2:name,B:name,P:pi,C:name,Y:name,P2:pi]: ((~ (((late_transitions @ ((res @ X3) @ (((output @ A2) @ B) @ P))) @ (((late_BoundR @ (late_InputS @ C)) @ Y) @ P2))))))).
% 2.59/1.49 thf(fact_105_resOutputOutputTrans, axiom, (! [X3:name,A2:name,P:pi,B:name,Y:name,P2:pi]: ((~ (((late_transitions @ ((res @ X3) @ (((output @ A2) @ X3) @ P))) @ ((late_FreeR @ ((late_OutputR @ B) @ Y)) @ P2))))))).
% 2.59/1.49 thf(fact_106_resInputBoundOutputTrans, axiom, (! [X3:name,A2:name,Y:name,P:pi,B:name,Z:name,P2:pi]: ((~ (((late_transitions @ ((res @ X3) @ (((input @ A2) @ Y) @ P))) @ (((late_BoundR @ (late_BoundOutputS @ B)) @ Z) @ P2))))))).
% 2.59/1.49 thf(fact_107_outputTauTrans, axiom, (! [A2:name,B:name,P:pi,P2:pi]: ((~ (((late_transitions @ (((output @ A2) @ B) @ P)) @ ((late_FreeR @ late_TauR) @ P2))))))).
% 2.59/1.49 thf(fact_108_outputCases, axiom, (! [A2:name,B:name,P:pi,Alpha:late_freeRes,P2:pi,Prop:(late_freeRes > (pi > $o))]: ((((late_transitions @ (((output @ A2) @ B) @ P)) @ ((late_FreeR @ Alpha) @ P2)) => (((Alpha = ((late_OutputR @ A2) @ B)) => ((P = P2) => ((Prop @ ((late_OutputR @ A2) @ B)) @ P))) => ((Prop @ Alpha) @ P2)))))).
% 2.59/1.49 thf(fact_109_outputCases_H, axiom, (! [A2:name,B:name,P:pi,Rs:late_residual]: ((((late_transitions @ (((output @ A2) @ B) @ P)) @ Rs) => (~ ((! [A4:name,B3:name,P3:pi]: ((((A2 = A4) & ((B = B3) & (P = P3))) => (Rs != ((late_FreeR @ ((late_OutputR @ A4) @ B3)) @ P3))))))))))).
% 2.59/1.49 thf(fact_110_name__fresh, axiom, (((fresh @ name) @ name) = (^ [A5:name,B4:name]: ((A5 != B4))))).
% 2.59/1.49 thf(fact_111_pi_Ofresh_I2_J, axiom, (! [A2:name,X32:name,X2:name,X1:pi]: ((((((fresh @ name) @ pi) @ A2) @ (((output @ X32) @ X2) @ X1)) = (((((fresh @ name) @ name) @ A2) @ X32) & (((((fresh @ name) @ name) @ A2) @ X2) & ((((fresh @ name) @ pi) @ A2) @ X1))))))).
% 2.59/1.49 thf(fact_112_pi_Odistinct_I21_J, axiom, (! [Name12:name,Name23:name,Pi2:pi,Name13:name,Name24:name,Pi3:pi]: (((((output @ Name12) @ Name23) @ Pi2) != (((input @ Name13) @ Name24) @ Pi3))))).
% 2.59/1.49 thf(fact_113_pi_Oinject_I1_J, axiom, (! [X32:name,X2:name,X1:pi,Y32:name,Y2:name,Y1:pi]: ((((((output @ X32) @ X2) @ X1) = (((output @ Y32) @ Y2) @ Y1)) = ((X32 = Y32) & ((X2 = Y2) & (X1 = Y1))))))).
% 2.59/1.49 thf(fact_114_pi_Odistinct_I55_J, axiom, (! [Name12:name,Name23:name,Pi2:pi,Pi1:pi,Pi22:pi]: (((((input @ Name12) @ Name23) @ Pi2) != ((par @ Pi1) @ Pi22))))).
% 2.59/1.49 thf(fact_115_pi_Odistinct_I57_J, axiom, (! [Name12:name,Name23:name,Pi2:pi,Name3:name,Pi3:pi]: (((((input @ Name12) @ Name23) @ Pi2) != ((res @ Name3) @ Pi3))))).
% 2.59/1.49 thf(fact_116_pi_Odistinct_I29_J, axiom, (! [Name12:name,Name23:name,Pi2:pi,Pi1:pi,Pi22:pi]: (((((output @ Name12) @ Name23) @ Pi2) != ((par @ Pi1) @ Pi22))))).
% 2.59/1.49 thf(fact_117_pi_Odistinct_I31_J, axiom, (! [Name12:name,Name23:name,Pi2:pi,Name3:name,Pi3:pi]: (((((output @ Name12) @ Name23) @ Pi2) != ((res @ Name3) @ Pi3))))).
% 2.59/1.49 thf(fact_118_pi_Odistinct_I35_J, axiom, (! [Pi2:pi,Name13:name,Name24:name,Pi3:pi]: (((tau @ Pi2) != (((input @ Name13) @ Name24) @ Pi3))))).
% 2.59/1.49 thf(fact_119_pi_Odistinct_I19_J, axiom, (! [Name12:name,Name23:name,Pi2:pi,Pi3:pi]: (((((output @ Name12) @ Name23) @ Pi2) != (tau @ Pi3))))).
% 2.59/1.49 thf(fact_120_resTrans_I2_J, axiom, (! [X3:name,Y:name,P:pi,Rs:late_residual]: ((~ (((late_transitions @ ((res @ X3) @ (((input @ X3) @ Y) @ P))) @ Rs)))))).
% 2.59/1.49 thf(fact_121_inputFreeTrans, axiom, (! [A2:name,X3:name,P:pi,Alpha:late_freeRes,P2:pi]: ((~ (((late_transitions @ (((input @ A2) @ X3) @ P)) @ ((late_FreeR @ Alpha) @ P2))))))).
% 2.59/1.49 thf(fact_122_resTrans_I1_J, axiom, (! [X3:name,B:name,P:pi,Rs:late_residual]: ((~ (((late_transitions @ ((res @ X3) @ (((output @ X3) @ B) @ P))) @ Rs)))))).
% 2.59/1.49 thf(fact_123_outputBoundTrans, axiom, (! [A2:name,B:name,P:pi,C:late_subject,X3:name,P2:pi]: ((~ (((late_transitions @ (((output @ A2) @ B) @ P)) @ (((late_BoundR @ C) @ X3) @ P2))))))).
% 2.59/1.49 thf(fact_124_outputFreshTrans, axiom, (! [A2:name,B:name,P:pi,Alpha:late_freeRes,P2:pi]: ((((late_transitions @ (((output @ A2) @ B) @ P)) @ ((late_FreeR @ Alpha) @ P2)) => (~ ((((((fresh @ name) @ late_freeRes) @ A2) @ Alpha) | ((((fresh @ name) @ late_freeRes) @ B) @ Alpha)))))))).
% 2.59/1.49 thf(fact_125_resInputFreeTrans, axiom, (! [X3:name,A2:name,Y:name,P:pi,Alpha:late_freeRes,P2:pi]: ((~ (((late_transitions @ ((res @ X3) @ (((input @ A2) @ Y) @ P))) @ ((late_FreeR @ Alpha) @ P2))))))).
% 2.59/1.49 thf(fact_126_Late__Semantics_OInput, axiom, (! [A2:name,X3:name,P:pi]: (((late_transitions @ (((input @ A2) @ X3) @ P)) @ (((late_BoundR @ (late_InputS @ A2)) @ X3) @ P))))).
% 2.59/1.49 thf(fact_127_transitions_OInput, axiom, (! [X3:name,A2:name,P:pi]: (((X3 != A2) => ((late_transitions @ (((input @ A2) @ X3) @ P)) @ (((late_BoundR @ (late_InputS @ A2)) @ X3) @ P)))))).
% 2.59/1.49 thf(fact_128_inputBoundOutputTrans, axiom, (! [A2:name,X3:name,P:pi,B:name,Y:name,P2:pi]: ((~ (((late_transitions @ (((input @ A2) @ X3) @ P)) @ (((late_BoundR @ (late_BoundOutputS @ B)) @ Y) @ P2))))))).
% 2.59/1.49 thf(fact_129_inputIneqTrans, axiom, (! [A2:name,X3:name,P:pi,B:late_subject,Y:name,P2:pi]: ((((late_transitions @ (((input @ A2) @ X3) @ P)) @ (((late_BoundR @ B) @ Y) @ P2)) => (~ (((((fresh @ name) @ late_subject) @ A2) @ B))))))).
% 2.59/1.49 thf(fact_130_Output, axiom, (! [A2:name,B:name,P:pi]: (((late_transitions @ (((output @ A2) @ B) @ P)) @ ((late_FreeR @ ((late_OutputR @ A2) @ B)) @ P))))).
% 2.59/1.49 thf(fact_131_outputIneqTrans, axiom, (! [A2:name,B:name,P:pi,C:name,D:name,P2:pi]: ((((late_transitions @ (((output @ A2) @ B) @ P)) @ ((late_FreeR @ ((late_OutputR @ C) @ D)) @ P2)) => (~ (((A2 != C) | (B != D)))))))).
% 2.59/1.49 thf(fact_132_residual_Ofresh_I1_J, axiom, (! [A2:name,X32:late_subject,X1:name,X2:pi]: ((((((fresh @ name) @ late_residual) @ A2) @ (((late_BoundR @ X32) @ X1) @ X2)) = (((((fresh @ name) @ late_subject) @ A2) @ X32) & ((((fresh @ name) @ (name > (noption @ pi))) @ A2) @ ((((abs_fun @ name) @ pi) @ X1) @ X2))))))).
% 2.59/1.49 thf(fact_133_simps_I3_J, axiom, (! [A2:name,B:name,P:pi,C:name,D:name]: (((((subs @ (((output @ A2) @ B) @ P)) @ C) @ D) = (((output @ (((subst_name @ A2) @ C) @ D)) @ (((subst_name @ B) @ C) @ D)) @ (((subs @ P) @ C) @ D)))))).
% 2.59/1.49 thf(fact_134_substInput, axiom, (! [X3:name,B:name,C:name,A2:name,P:pi]: (((X3 != B) => ((X3 != C) => ((((subs @ (((input @ A2) @ X3) @ P)) @ B) @ C) = (((input @ (((subst_name @ A2) @ B) @ C)) @ X3) @ (((subs @ P) @ B) @ C)))))))).
% 2.59/1.49 thf(fact_135_simps_I4_J, axiom, (! [X3:name,A2:name,C:name,D:name,P:pi]: (((X3 != A2) => ((X3 != C) => ((X3 != D) => ((((subs @ (((input @ A2) @ X3) @ P)) @ C) @ D) = (((input @ (((subst_name @ A2) @ C) @ D)) @ X3) @ (((subs @ P) @ C) @ D))))))))).
% 2.59/1.49 thf(fact_136_inputCases_H, axiom, (! [A2:name,B:name,P:pi,Rs:late_residual]: ((((late_transitions @ (((input @ A2) @ B) @ P)) @ Rs) => (~ ((! [X5:name,A4:name,P3:pi]: ((((A2 = A4) & (((((abs_fun @ name) @ pi) @ B) @ P) = ((((abs_fun @ name) @ pi) @ X5) @ P3))) => ((Rs = (((late_BoundR @ (late_InputS @ A4)) @ X5) @ P3)) => (X5 = A4))))))))))).
% 2.59/1.49 thf(fact_137_pi_Ofresh_I9_J, axiom, (! [A2:name,X1:name,X2:pi]: ((((((fresh @ name) @ pi) @ A2) @ ((res @ X1) @ X2)) = ((((fresh @ name) @ (name > (noption @ pi))) @ A2) @ ((((abs_fun @ name) @ pi) @ X1) @ X2)))))).
% 2.59/1.49 thf(fact_138_pi_Ofresh_I4_J, axiom, (! [A2:name,X32:name,X1:name,X2:pi]: ((((((fresh @ name) @ pi) @ A2) @ (((input @ X32) @ X1) @ X2)) = (((((fresh @ name) @ name) @ A2) @ X32) & ((((fresh @ name) @ (name > (noption @ pi))) @ A2) @ ((((abs_fun @ name) @ pi) @ X1) @ X2))))))).
% 2.59/1.49 thf(fact_139_pi_Oinject_I8_J, axiom, (! [X1:name,X2:pi,Y1:name,Y2:pi]: (((((res @ X1) @ X2) = ((res @ Y1) @ Y2)) = (((((abs_fun @ name) @ pi) @ X1) @ X2) = ((((abs_fun @ name) @ pi) @ Y1) @ Y2)))))).
% 2.59/1.49 thf(fact_140_residual_Oinject_I1_J, axiom, (! [X32:late_subject,X1:name,X2:pi,Y32:late_subject,Y1:name,Y2:pi]: ((((((late_BoundR @ X32) @ X1) @ X2) = (((late_BoundR @ Y32) @ Y1) @ Y2)) = ((X32 = Y32) & (((((abs_fun @ name) @ pi) @ X1) @ X2) = ((((abs_fun @ name) @ pi) @ Y1) @ Y2))))))).
% 2.59/1.49 thf(fact_141_subst__name__def, axiom, (subst_name = (^ [A5:name,B4:name,C3:name]: (((((if @ name) @ (A5 = B4)) @ C3) @ A5))))).
% 2.59/1.49 thf(fact_142_name__fresh__abs, axiom, (! [A:$tType]: (((fs_name @ A) => (! [B:name,A2:name,X3:A]: ((((((fresh @ name) @ (name > (noption @ A))) @ B) @ ((((abs_fun @ name) @ A) @ A2) @ X3)) = ((B = A2) | ((((fresh @ name) @ A) @ B) @ X3))))))))).
% 2.59/1.49 thf(fact_143_abs__fresh_I1_J, axiom, (! [X7:$tType]: (((fs_name @ X7) => (! [B:name,A2:name,X3:X7]: ((((((fresh @ name) @ (name > (noption @ X7))) @ B) @ ((((abs_fun @ name) @ X7) @ A2) @ X3)) = ((B = A2) | ((((fresh @ name) @ X7) @ B) @ X3))))))))).
% 2.59/1.49 thf(fact_144_pi_Oinject_I3_J, axiom, (! [X32:name,X1:name,X2:pi,Y32:name,Y1:name,Y2:pi]: ((((((input @ X32) @ X1) @ X2) = (((input @ Y32) @ Y1) @ Y2)) = ((X32 = Y32) & (((((abs_fun @ name) @ pi) @ X1) @ X2) = ((((abs_fun @ name) @ pi) @ Y1) @ Y2))))))).
% 2.59/1.49 thf(fact_145_simps_I5_J, axiom, (! [A2:name,B:name,P:pi,C:name,D:name]: (((((subs @ (((match @ A2) @ B) @ P)) @ C) @ D) = (((match @ (((subst_name @ A2) @ C) @ D)) @ (((subst_name @ B) @ C) @ D)) @ (((subs @ P) @ C) @ D)))))).
% 2.59/1.49 thf(fact_146_simps_I6_J, axiom, (! [A2:name,B:name,P:pi,C:name,D:name]: (((((subs @ (((mismatch @ A2) @ B) @ P)) @ C) @ D) = (((mismatch @ (((subst_name @ A2) @ C) @ D)) @ (((subst_name @ B) @ C) @ D)) @ (((subs @ P) @ C) @ D)))))).
% 2.59/1.49 thf(fact_147_pi_Ofresh_I5_J, axiom, (! [A2:name,X32:name,X2:name,X1:pi]: ((((((fresh @ name) @ pi) @ A2) @ (((match @ X32) @ X2) @ X1)) = (((((fresh @ name) @ name) @ A2) @ X32) & (((((fresh @ name) @ name) @ A2) @ X2) & ((((fresh @ name) @ pi) @ A2) @ X1))))))).
% 2.59/1.49 thf(fact_148_pi_Ofresh_I6_J, axiom, (! [A2:name,X32:name,X2:name,X1:pi]: ((((((fresh @ name) @ pi) @ A2) @ (((mismatch @ X32) @ X2) @ X1)) = (((((fresh @ name) @ name) @ A2) @ X32) & (((((fresh @ name) @ name) @ A2) @ X2) & ((((fresh @ name) @ pi) @ A2) @ X1))))))).
% 2.59/1.49 thf(fact_149_matchCases, axiom, (! [A2:name,B:name,P:pi,Rs:late_residual,F3:(name > (name > $o))]: ((((late_transitions @ (((match @ A2) @ B) @ P)) @ Rs) => ((((late_transitions @ P) @ Rs) => ((A2 = B) => ((F3 @ A2) @ A2))) => ((F3 @ A2) @ B)))))).
% 2.59/1.49 thf(fact_150_matchTrans, axiom, (! [A2:name,B:name,P:pi,Rs:late_residual]: ((((late_transitions @ (((match @ A2) @ B) @ P)) @ Rs) => (A2 = B))))).
% 2.59/1.49 thf(fact_151_matchCases_H, axiom, (! [A2:name,B:name,P:pi,Rs:late_residual]: ((((late_transitions @ (((match @ A2) @ B) @ P)) @ Rs) => (~ ((! [P3:pi]: ((((B = A2) & (P = P3)) => (~ (((late_transitions @ P3) @ Rs)))))))))))).
% 2.59/1.49 thf(fact_152_mismatchCases, axiom, (! [A2:name,B:name,P:pi,Rs:late_residual,F3:(name > (name > $o))]: ((((late_transitions @ (((mismatch @ A2) @ B) @ P)) @ Rs) => ((((late_transitions @ P) @ Rs) => ((A2 != B) => ((F3 @ A2) @ B))) => ((F3 @ A2) @ B)))))).
% 2.59/1.49 thf(fact_153_mismatchTrans, axiom, (! [A2:name,P:pi,Rs:late_residual]: ((~ (((late_transitions @ (((mismatch @ A2) @ A2) @ P)) @ Rs)))))).
% 2.59/1.49 thf(fact_154_mismatchCases_H, axiom, (! [A2:name,B:name,P:pi,Rs:late_residual]: ((((late_transitions @ (((mismatch @ A2) @ B) @ P)) @ Rs) => (~ ((! [P3:pi,A4:name,B3:name]: ((((A2 = A4) & ((B = B3) & (P = P3))) => (((late_transitions @ P3) @ Rs) => (A4 = B3))))))))))).
% 2.59/1.49 thf(fact_155_Match, axiom, (! [P:pi,Rs:late_residual,B:name]: ((((late_transitions @ P) @ Rs) => ((late_transitions @ (((match @ B) @ B) @ P)) @ Rs))))).
% 2.59/1.49 thf(fact_156_Mismatch, axiom, (! [P:pi,Rs:late_residual,A2:name,B:name]: ((((late_transitions @ P) @ Rs) => ((A2 != B) => ((late_transitions @ (((mismatch @ A2) @ B) @ P)) @ Rs)))))).
% 2.59/1.49 thf(fact_157_pi_Odistinct_I73_J, axiom, (! [Name12:name,Name23:name,Pi2:pi,Pi1:pi,Pi22:pi]: (((((mismatch @ Name12) @ Name23) @ Pi2) != ((par @ Pi1) @ Pi22))))).
% 2.59/1.49 thf(fact_158_pi_Odistinct_I65_J, axiom, (! [Name12:name,Name23:name,Pi2:pi,Pi1:pi,Pi22:pi]: (((((match @ Name12) @ Name23) @ Pi2) != ((par @ Pi1) @ Pi22))))).
% 2.59/1.49 thf(fact_159_pi_Odistinct_I75_J, axiom, (! [Name12:name,Name23:name,Pi2:pi,Name3:name,Pi3:pi]: (((((mismatch @ Name12) @ Name23) @ Pi2) != ((res @ Name3) @ Pi3))))).
% 2.59/1.49 thf(fact_160_pi_Odistinct_I67_J, axiom, (! [Name12:name,Name23:name,Pi2:pi,Name3:name,Pi3:pi]: (((((match @ Name12) @ Name23) @ Pi2) != ((res @ Name3) @ Pi3))))).
% 2.59/1.49 thf(fact_161_pi_Odistinct_I61_J, axiom, (! [Name12:name,Name23:name,Pi2:pi,Name13:name,Name24:name,Pi3:pi]: (((((match @ Name12) @ Name23) @ Pi2) != (((mismatch @ Name13) @ Name24) @ Pi3))))).
% 2.59/1.49 thf(fact_162_pi_Oinject_I4_J, axiom, (! [X32:name,X2:name,X1:pi,Y32:name,Y2:name,Y1:pi]: ((((((match @ X32) @ X2) @ X1) = (((match @ Y32) @ Y2) @ Y1)) = ((X32 = Y32) & ((X2 = Y2) & (X1 = Y1))))))).
% 2.59/1.49 thf(fact_163_pi_Oinject_I5_J, axiom, (! [X32:name,X2:name,X1:pi,Y32:name,Y2:name,Y1:pi]: ((((((mismatch @ X32) @ X2) @ X1) = (((mismatch @ Y32) @ Y2) @ Y1)) = ((X32 = Y32) & ((X2 = Y2) & (X1 = Y1))))))).
% 2.59/1.49 thf(fact_164_pi_Odistinct_I49_J, axiom, (! [Name12:name,Name23:name,Pi2:pi,Name13:name,Name24:name,Pi3:pi]: (((((input @ Name12) @ Name23) @ Pi2) != (((match @ Name13) @ Name24) @ Pi3))))).
% 2.59/1.49 thf(fact_165_pi_Odistinct_I51_J, axiom, (! [Name12:name,Name23:name,Pi2:pi,Name13:name,Name24:name,Pi3:pi]: (((((input @ Name12) @ Name23) @ Pi2) != (((mismatch @ Name13) @ Name24) @ Pi3))))).
% 2.59/1.49 thf(fact_166_pi_Odistinct_I23_J, axiom, (! [Name12:name,Name23:name,Pi2:pi,Name13:name,Name24:name,Pi3:pi]: (((((output @ Name12) @ Name23) @ Pi2) != (((match @ Name13) @ Name24) @ Pi3))))).
% 2.59/1.49 thf(fact_167_pi_Odistinct_I25_J, axiom, (! [Name12:name,Name23:name,Pi2:pi,Name13:name,Name24:name,Pi3:pi]: (((((output @ Name12) @ Name23) @ Pi2) != (((mismatch @ Name13) @ Name24) @ Pi3))))).
% 2.59/1.49 thf(fact_168_pi_Odistinct_I39_J, axiom, (! [Pi2:pi,Name13:name,Name24:name,Pi3:pi]: (((tau @ Pi2) != (((mismatch @ Name13) @ Name24) @ Pi3))))).
% 2.59/1.49 thf(fact_169_pi_Odistinct_I37_J, axiom, (! [Pi2:pi,Name13:name,Name24:name,Pi3:pi]: (((tau @ Pi2) != (((match @ Name13) @ Name24) @ Pi3))))).
% 2.59/1.49 thf(fact_170_abs__fun__eq1, axiom, (! [X:$tType,A:$tType,A2:X,X3:A,Y:A]: (((((((abs_fun @ X) @ A) @ A2) @ X3) = ((((abs_fun @ X) @ A) @ A2) @ Y)) = (X3 = Y))))).
% 2.59/1.49 thf(fact_171_freeRes_Ocase_I2_J, axiom, (! [A:$tType,F1:(name > (name > A)),F2:A]: ((((((late_case_freeRes @ A) @ F1) @ F2) @ late_TauR) = F2)))).
% 2.59/1.49 thf(fact_172_subject_Ocase_I2_J, axiom, (! [A:$tType,F1:(name > A),F2:(name > A),X2:name]: ((((((late_case_subject @ A) @ F1) @ F2) @ (late_BoundOutputS @ X2)) = (F2 @ X2))))).
% 2.59/1.49 thf(fact_173_freeRes_Ocase_I1_J, axiom, (! [A:$tType,F1:(name > (name > A)),F2:A,X11:name,X12:name]: ((((((late_case_freeRes @ A) @ F1) @ F2) @ ((late_OutputR @ X11) @ X12)) = ((F1 @ X11) @ X12))))).
% 2.59/1.49 thf(fact_174_subject_Ocase_I1_J, axiom, (! [A:$tType,F1:(name > A),F2:(name > A),X1:name]: ((((((late_case_subject @ A) @ F1) @ F2) @ (late_InputS @ X1)) = (F1 @ X1))))).
% 2.59/1.49 thf(fact_175_pi_Ostrong__inducts, axiom, (! [A:$tType]: (((fs_name @ A) => (! [P:(A > (pi > $o)),Z:A,Pi2:pi]: (((! [Z2:A]: (((P @ Z2) @ piNil))) => ((! [Name1:name,Name22:name,Pi:pi,Z2:A]: (((! [Za:A]: (((P @ Za) @ Pi))) => ((P @ Z2) @ (((output @ Name1) @ Name22) @ Pi))))) => ((! [Pi:pi,Z2:A]: (((! [Za:A]: (((P @ Za) @ Pi))) => ((P @ Z2) @ (tau @ Pi))))) => ((! [Name1:name,Name22:name,Pi:pi,Z2:A]: ((((((fresh @ name) @ A) @ Name22) @ Z2) => (((((fresh @ name) @ name) @ Name22) @ Name1) => ((! [Za:A]: (((P @ Za) @ Pi))) => ((P @ Z2) @ (((input @ Name1) @ Name22) @ Pi))))))) => ((! [Name1:name,Name22:name,Pi:pi,Z2:A]: (((! [Za:A]: (((P @ Za) @ Pi))) => ((P @ Z2) @ (((match @ Name1) @ Name22) @ Pi))))) => ((! [Name1:name,Name22:name,Pi:pi,Z2:A]: (((! [Za:A]: (((P @ Za) @ Pi))) => ((P @ Z2) @ (((mismatch @ Name1) @ Name22) @ Pi))))) => ((! [Pi13:pi,Pi24:pi,Z2:A]: (((! [Za:A]: (((P @ Za) @ Pi13))) => ((! [Za:A]: (((P @ Za) @ Pi24))) => ((P @ Z2) @ ((sum @ Pi13) @ Pi24)))))) => ((! [Pi13:pi,Pi24:pi,Z2:A]: (((! [Za:A]: (((P @ Za) @ Pi13))) => ((! [Za:A]: (((P @ Za) @ Pi24))) => ((P @ Z2) @ ((par @ Pi13) @ Pi24)))))) => ((! [Name:name,Pi:pi,Z2:A]: ((((((fresh @ name) @ A) @ Name) @ Z2) => ((! [Za:A]: (((P @ Za) @ Pi))) => ((P @ Z2) @ ((res @ Name) @ Pi)))))) => ((! [Pi:pi,Z2:A]: (((! [Za:A]: (((P @ Za) @ Pi))) => ((P @ Z2) @ (bang @ Pi))))) => ((P @ Z) @ Pi2))))))))))))))))).
% 2.59/1.49 thf(fact_176_pi_Ostrong__induct, axiom, (! [N:$tType]: (((fs_name @ N) => (! [P:(N > (pi > $o)),Z:N,Pi2:pi]: (((! [Z2:N]: (((P @ Z2) @ piNil))) => ((! [Name1:name,Name22:name,Pi:pi,Z2:N]: (((! [Za:N]: (((P @ Za) @ Pi))) => ((P @ Z2) @ (((output @ Name1) @ Name22) @ Pi))))) => ((! [Pi:pi,Z2:N]: (((! [Za:N]: (((P @ Za) @ Pi))) => ((P @ Z2) @ (tau @ Pi))))) => ((! [Name1:name,Name22:name,Pi:pi,Z2:N]: ((((((fresh @ name) @ N) @ Name22) @ Z2) => (((((fresh @ name) @ name) @ Name22) @ Name1) => ((! [Za:N]: (((P @ Za) @ Pi))) => ((P @ Z2) @ (((input @ Name1) @ Name22) @ Pi))))))) => ((! [Name1:name,Name22:name,Pi:pi,Z2:N]: (((! [Za:N]: (((P @ Za) @ Pi))) => ((P @ Z2) @ (((match @ Name1) @ Name22) @ Pi))))) => ((! [Name1:name,Name22:name,Pi:pi,Z2:N]: (((! [Za:N]: (((P @ Za) @ Pi))) => ((P @ Z2) @ (((mismatch @ Name1) @ Name22) @ Pi))))) => ((! [Pi13:pi,Pi24:pi,Z2:N]: (((! [Za:N]: (((P @ Za) @ Pi13))) => ((! [Za:N]: (((P @ Za) @ Pi24))) => ((P @ Z2) @ ((sum @ Pi13) @ Pi24)))))) => ((! [Pi13:pi,Pi24:pi,Z2:N]: (((! [Za:N]: (((P @ Za) @ Pi13))) => ((! [Za:N]: (((P @ Za) @ Pi24))) => ((P @ Z2) @ ((par @ Pi13) @ Pi24)))))) => ((! [Name:name,Pi:pi,Z2:N]: ((((((fresh @ name) @ N) @ Name) @ Z2) => ((! [Za:N]: (((P @ Za) @ Pi))) => ((P @ Z2) @ ((res @ Name) @ Pi)))))) => ((! [Pi:pi,Z2:N]: (((! [Za:N]: (((P @ Za) @ Pi))) => ((P @ Z2) @ (bang @ Pi))))) => ((P @ Z) @ Pi2))))))))))))))))).
% 2.59/1.49 thf(fact_177_residual_Ostrong__induct_H, axiom, (! [N:$tType,F:(N > (set @ name)),P:(N > (late_residual > $o)),Z:N,Residual:late_residual]: (((! [X5:N]: (((finite_finite @ name) @ (F @ X5)))) => ((! [Subject:late_subject,Name:name,Pi:pi,Z2:N]: (((~ ((((member @ name) @ Name) @ (F @ Z2)))) => (((((fresh @ name) @ late_subject) @ Name) @ Subject) => ((P @ Z2) @ (((late_BoundR @ Subject) @ Name) @ Pi)))))) => ((! [FreeRes:late_freeRes,Pi:pi,Z2:N]: (((P @ Z2) @ ((late_FreeR @ FreeRes) @ Pi)))) => ((P @ Z) @ Residual))))))).
% 2.59/1.49 thf(fact_178_pi_Ofresh_I10_J, axiom, (! [A2:name,X1:pi]: ((((((fresh @ name) @ pi) @ A2) @ (bang @ X1)) = ((((fresh @ name) @ pi) @ A2) @ X1))))).
% 2.59/1.49 thf(fact_179_pi_Ofresh_I7_J, axiom, (! [A2:name,X2:pi,X1:pi]: ((((((fresh @ name) @ pi) @ A2) @ ((sum @ X2) @ X1)) = (((((fresh @ name) @ pi) @ A2) @ X2) & ((((fresh @ name) @ pi) @ A2) @ X1)))))).
% 2.59/1.49 thf(fact_180_simps_I10_J, axiom, (! [P:pi,C:name,D:name]: (((((subs @ (bang @ P)) @ C) @ D) = (bang @ (((subs @ P) @ C) @ D)))))).
% 2.59/1.49 thf(fact_181_pi_Ofresh_I1_J, axiom, (! [A2:name]: (((((fresh @ name) @ pi) @ A2) @ piNil)))).
% 2.59/1.49 thf(fact_182_simps_I7_J, axiom, (! [P:pi,Q:pi,C:name,D:name]: (((((subs @ ((sum @ P) @ Q)) @ C) @ D) = ((sum @ (((subs @ P) @ C) @ D)) @ (((subs @ Q) @ C) @ D)))))).
% 2.59/1.49 thf(fact_183_simps_I1_J, axiom, (! [C:name,D:name]: (((((subs @ piNil) @ C) @ D) = piNil)))).
% 2.59/1.49 thf(fact_184_pi_Odistinct_I59_J, axiom, (! [Name12:name,Name23:name,Pi2:pi,Pi3:pi]: (((((input @ Name12) @ Name23) @ Pi2) != (bang @ Pi3))))).
% 2.59/1.49 thf(fact_185_pi_Odistinct_I33_J, axiom, (! [Name12:name,Name23:name,Pi2:pi,Pi3:pi]: (((((output @ Name12) @ Name23) @ Pi2) != (bang @ Pi3))))).
% 2.59/1.49 thf(fact_186_sumCases, axiom, (! [P:pi,Q:pi,Rs:late_residual]: ((((late_transitions @ ((sum @ P) @ Q)) @ Rs) => ((~ (((late_transitions @ P) @ Rs))) => ((late_transitions @ Q) @ Rs)))))).
% 2.59/1.49 thf(fact_187_sumCases_H, axiom, (! [P:pi,Q:pi,Rs:late_residual]: ((((late_transitions @ ((sum @ P) @ Q)) @ Rs) => ((~ (((late_transitions @ P) @ Rs))) => ((late_transitions @ Q) @ Rs)))))).
% 2.59/1.49 thf(fact_188_Sum1, axiom, (! [P:pi,Rs:late_residual,Q:pi]: ((((late_transitions @ P) @ Rs) => ((late_transitions @ ((sum @ P) @ Q)) @ Rs))))).
% 2.59/1.49 thf(fact_189_Sum2, axiom, (! [Q:pi,Rs:late_residual,P:pi]: ((((late_transitions @ Q) @ Rs) => ((late_transitions @ ((sum @ P) @ Q)) @ Rs))))).
% 2.59/1.49 thf(fact_190_pi_Odistinct_I47_J, axiom, (! [Pi2:pi,Pi3:pi]: (((tau @ Pi2) != (bang @ Pi3))))).
% 2.59/1.49 thf(fact_191_pi_Odistinct_I79_J, axiom, (! [Pi12:pi,Pi23:pi,Pi1:pi,Pi22:pi]: ((((sum @ Pi12) @ Pi23) != ((par @ Pi1) @ Pi22))))).
% 2.59/1.49 thf(fact_192_pi_Odistinct_I81_J, axiom, (! [Pi12:pi,Pi23:pi,Name3:name,Pi3:pi]: ((((sum @ Pi12) @ Pi23) != ((res @ Name3) @ Pi3))))).
% 2.59/1.49 thf(fact_193_pi_Odistinct_I53_J, axiom, (! [Name12:name,Name23:name,Pi2:pi,Pi1:pi,Pi22:pi]: (((((input @ Name12) @ Name23) @ Pi2) != ((sum @ Pi1) @ Pi22))))).
% 2.59/1.49 thf(fact_194_pi_Odistinct_I27_J, axiom, (! [Name12:name,Name23:name,Pi2:pi,Pi1:pi,Pi22:pi]: (((((output @ Name12) @ Name23) @ Pi2) != ((sum @ Pi1) @ Pi22))))).
% 2.59/1.49 thf(fact_195_pi_Odistinct_I41_J, axiom, (! [Pi2:pi,Pi1:pi,Pi22:pi]: (((tau @ Pi2) != ((sum @ Pi1) @ Pi22))))).
% 2.59/1.49 thf(fact_196_nilCases_H, axiom, (! [Rs:late_residual]: ((~ (((late_transitions @ piNil) @ Rs)))))).
% 2.59/1.49 thf(fact_197_zeroTrans, axiom, (! [Rs:late_residual]: ((~ (((late_transitions @ piNil) @ Rs)))))).
% 2.59/1.49 thf(fact_198_pi_Odistinct_I13_J, axiom, (! [Pi1:pi,Pi22:pi]: ((piNil != ((par @ Pi1) @ Pi22))))).
% 2.59/1.49 thf(fact_199_pi_Odistinct_I15_J, axiom, (! [Name3:name,Pi3:pi]: ((piNil != ((res @ Name3) @ Pi3))))).
% 2.59/1.49 thf(fact_200_pi_Odistinct_I11_J, axiom, (! [Pi1:pi,Pi22:pi]: ((piNil != ((sum @ Pi1) @ Pi22))))).
% 2.59/1.49 thf(fact_201_pi_Odistinct_I17_J, axiom, (! [Pi3:pi]: ((piNil != (bang @ Pi3))))).
% 2.59/1.49 thf(fact_202_pi_Odistinct_I83_J, axiom, (! [Pi12:pi,Pi23:pi,Pi3:pi]: ((((sum @ Pi12) @ Pi23) != (bang @ Pi3))))).
% 2.59/1.49 thf(fact_203_pi_Oinject_I6_J, axiom, (! [X2:pi,X1:pi,Y2:pi,Y1:pi]: (((((sum @ X2) @ X1) = ((sum @ Y2) @ Y1)) = ((X2 = Y2) & (X1 = Y1)))))).
% 2.59/1.49 thf(fact_204_pi_Oinject_I9_J, axiom, (! [X1:pi,Y1:pi]: ((((bang @ X1) = (bang @ Y1)) = (X1 = Y1))))).
% 2.59/1.49 thf(fact_205_pi_Odistinct_I89_J, axiom, (! [Name2:name,Pi2:pi,Pi3:pi]: ((((res @ Name2) @ Pi2) != (bang @ Pi3))))).
% 2.59/1.49 thf(fact_206_pi_Odistinct_I87_J, axiom, (! [Pi12:pi,Pi23:pi,Pi3:pi]: ((((par @ Pi12) @ Pi23) != (bang @ Pi3))))).
% 2.59/1.49 thf(fact_207_pi_Odistinct_I3_J, axiom, (! [Pi3:pi]: ((piNil != (tau @ Pi3))))).
% 2.59/1.49 thf(fact_208_pi_Odistinct_I1_J, axiom, (! [Name13:name,Name24:name,Pi3:pi]: ((piNil != (((output @ Name13) @ Name24) @ Pi3))))).
% 2.59/1.49 thf(fact_209_pi_Odistinct_I5_J, axiom, (! [Name13:name,Name24:name,Pi3:pi]: ((piNil != (((input @ Name13) @ Name24) @ Pi3))))).
% 2.59/1.49 thf(fact_210_pi_Odistinct_I77_J, axiom, (! [Name12:name,Name23:name,Pi2:pi,Pi3:pi]: (((((mismatch @ Name12) @ Name23) @ Pi2) != (bang @ Pi3))))).
% 2.59/1.49 thf(fact_211_pi_Odistinct_I71_J, axiom, (! [Name12:name,Name23:name,Pi2:pi,Pi1:pi,Pi22:pi]: (((((mismatch @ Name12) @ Name23) @ Pi2) != ((sum @ Pi1) @ Pi22))))).
% 2.59/1.49 thf(fact_212_pi_Odistinct_I69_J, axiom, (! [Name12:name,Name23:name,Pi2:pi,Pi3:pi]: (((((match @ Name12) @ Name23) @ Pi2) != (bang @ Pi3))))).
% 2.59/1.49 thf(fact_213_pi_Odistinct_I63_J, axiom, (! [Name12:name,Name23:name,Pi2:pi,Pi1:pi,Pi22:pi]: (((((match @ Name12) @ Name23) @ Pi2) != ((sum @ Pi1) @ Pi22))))).
% 2.59/1.49 thf(fact_214_pi_Odistinct_I9_J, axiom, (! [Name13:name,Name24:name,Pi3:pi]: ((piNil != (((mismatch @ Name13) @ Name24) @ Pi3))))).
% 2.59/1.49 thf(fact_215_pi_Odistinct_I7_J, axiom, (! [Name13:name,Name24:name,Pi3:pi]: ((piNil != (((match @ Name13) @ Name24) @ Pi3))))).
% 2.59/1.49 thf(fact_216_Bang, axiom, (! [P:pi,Rs:late_residual]: ((((late_transitions @ ((par @ P) @ (bang @ P))) @ Rs) => ((late_transitions @ (bang @ P)) @ Rs))))).
% 2.59/1.49 thf(fact_217_bangCases, axiom, (! [P:pi,Rs:late_residual]: ((((late_transitions @ (bang @ P)) @ Rs) => (~ ((! [P3:pi]: ((((bang @ P) = (bang @ P3)) => (~ (((late_transitions @ ((par @ P3) @ (bang @ P3))) @ Rs)))))))))))).
% 2.59/1.49 thf(fact_218_pi_Ostrong__induct_H, axiom, (! [N:$tType,F:(N > (set @ name)),P:(N > (pi > $o)),Z:N,Pi2:pi]: (((! [X5:N]: (((finite_finite @ name) @ (F @ X5)))) => ((! [Z2:N]: (((P @ Z2) @ piNil))) => ((! [Name1:name,Name22:name,Pi:pi,Z2:N]: (((! [Za:N]: (((P @ Za) @ Pi))) => ((P @ Z2) @ (((output @ Name1) @ Name22) @ Pi))))) => ((! [Pi:pi,Z2:N]: (((! [Za:N]: (((P @ Za) @ Pi))) => ((P @ Z2) @ (tau @ Pi))))) => ((! [Name1:name,Name22:name,Pi:pi,Z2:N]: (((~ ((((member @ name) @ Name22) @ (F @ Z2)))) => (((((fresh @ name) @ name) @ Name22) @ Name1) => ((! [Za:N]: (((P @ Za) @ Pi))) => ((P @ Z2) @ (((input @ Name1) @ Name22) @ Pi))))))) => ((! [Name1:name,Name22:name,Pi:pi,Z2:N]: (((! [Za:N]: (((P @ Za) @ Pi))) => ((P @ Z2) @ (((match @ Name1) @ Name22) @ Pi))))) => ((! [Name1:name,Name22:name,Pi:pi,Z2:N]: (((! [Za:N]: (((P @ Za) @ Pi))) => ((P @ Z2) @ (((mismatch @ Name1) @ Name22) @ Pi))))) => ((! [Pi13:pi,Pi24:pi,Z2:N]: (((! [Za:N]: (((P @ Za) @ Pi13))) => ((! [Za:N]: (((P @ Za) @ Pi24))) => ((P @ Z2) @ ((sum @ Pi13) @ Pi24)))))) => ((! [Pi13:pi,Pi24:pi,Z2:N]: (((! [Za:N]: (((P @ Za) @ Pi13))) => ((! [Za:N]: (((P @ Za) @ Pi24))) => ((P @ Z2) @ ((par @ Pi13) @ Pi24)))))) => ((! [Name:name,Pi:pi,Z2:N]: (((~ ((((member @ name) @ Name) @ (F @ Z2)))) => ((! [Za:N]: (((P @ Za) @ Pi))) => ((P @ Z2) @ ((res @ Name) @ Pi)))))) => ((! [Pi:pi,Z2:N]: (((! [Za:N]: (((P @ Za) @ Pi))) => ((P @ Z2) @ (bang @ Pi))))) => ((P @ Z) @ Pi2))))))))))))))).
% 2.59/1.49 thf(fact_219_resZeroTrans, axiom, (! [X3:name,Rs:late_residual]: ((~ (((late_transitions @ ((res @ X3) @ piNil)) @ Rs)))))).
% 2.59/1.49 thf(fact_220_pi_Oinducts, axiom, (! [P:(pi > $o),Pi2:pi]: (((P @ piNil) => ((! [Name1:name,Name22:name,Pi:pi]: (((P @ Pi) => (P @ (((output @ Name1) @ Name22) @ Pi))))) => ((! [Pi:pi]: (((P @ Pi) => (P @ (tau @ Pi))))) => ((! [Name1:name,Name22:name,Pi:pi]: (((P @ Pi) => (P @ (((input @ Name1) @ Name22) @ Pi))))) => ((! [Name1:name,Name22:name,Pi:pi]: (((P @ Pi) => (P @ (((match @ Name1) @ Name22) @ Pi))))) => ((! [Name1:name,Name22:name,Pi:pi]: (((P @ Pi) => (P @ (((mismatch @ Name1) @ Name22) @ Pi))))) => ((! [Pi13:pi,Pi24:pi]: (((P @ Pi13) => ((P @ Pi24) => (P @ ((sum @ Pi13) @ Pi24)))))) => ((! [Pi13:pi,Pi24:pi]: (((P @ Pi13) => ((P @ Pi24) => (P @ ((par @ Pi13) @ Pi24)))))) => ((! [Name:name,Pi:pi]: (((P @ Pi) => (P @ ((res @ Name) @ Pi))))) => ((! [Pi:pi]: (((P @ Pi) => (P @ (bang @ Pi))))) => (P @ Pi2)))))))))))))).
% 2.59/1.49 thf(fact_221_aux2, axiom, (! [P:pi]: (((late_bangPred @ P) @ ((par @ P) @ (bang @ P)))))).
% 2.59/1.49 thf(fact_222_bangPred_Ocases, axiom, (! [A1:pi,A22:pi]: ((((late_bangPred @ A1) @ A22) => ((A22 != (bang @ A1)) => (A22 = ((par @ A1) @ (bang @ A1)))))))).
% 2.59/1.49 thf(fact_223_bangPred_Osimps, axiom, (late_bangPred = (^ [A12:pi,A23:pi]: (((? [P5:pi]: (((A12 = P5) & (A23 = (bang @ P5))))) | (? [P5:pi]: (((A12 = P5) & (A23 = ((par @ P5) @ (bang @ P5))))))))))).
% 2.59/1.49 thf(fact_224_aux1, axiom, (! [P:pi]: (((late_bangPred @ P) @ (bang @ P))))).
% 2.59/1.49 thf(fact_225_bangPred_Oinducts, axiom, (! [X1:pi,X2:pi,P:(pi > (pi > $o))]: ((((late_bangPred @ X1) @ X2) => ((! [P3:pi]: (((P @ P3) @ (bang @ P3)))) => ((! [P3:pi]: (((P @ P3) @ ((par @ P3) @ (bang @ P3))))) => ((P @ X1) @ X2))))))).
% 2.59/1.49 thf(fact_226_subs__def, axiom, (subs = (^ [X4:pi,C3:name,D2:name]: (((((((((((((pi_rec @ pi) @ piNil) @ (^ [A5:name,B4:name,P5:pi]: (((output @ (((subst_name @ A5) @ C3) @ D2)) @ (((subst_name @ B4) @ C3) @ D2))))) @ (^ [P5:pi]: (tau))) @ (^ [A5:name,Y5:name,P5:pi]: (((input @ (((subst_name @ A5) @ C3) @ D2)) @ Y5)))) @ (^ [A5:name,B4:name,P5:pi]: (((match @ (((subst_name @ A5) @ C3) @ D2)) @ (((subst_name @ B4) @ C3) @ D2))))) @ (^ [A5:name,B4:name,P5:pi]: (((mismatch @ (((subst_name @ A5) @ C3) @ D2)) @ (((subst_name @ B4) @ C3) @ D2))))) @ (^ [P5:pi,Q5:pi]: (sum))) @ (^ [P5:pi,Q5:pi]: (par))) @ (^ [Y5:name,P5:pi]: ((res @ Y5)))) @ (^ [P5:pi]: (bang))) @ X4))))).
% 2.59/1.49 thf(fact_227_abs__fresh_I2_J, axiom, (! [X8:$tType]: (((pt_name @ X8) => (! [X3:X8,B:name,A2:name]: ((((finite_finite @ name) @ (((supp @ X8) @ name) @ X3)) => (((((fresh @ name) @ (name > (noption @ X8))) @ B) @ ((((abs_fun @ name) @ X8) @ A2) @ X3)) = ((B = A2) | ((((fresh @ name) @ X8) @ B) @ X3)))))))))).
% 2.59/1.49 thf(fact_228_exists__fresh_H, axiom, (! [A:$tType,X3:A]: ((((finite_finite @ name) @ (((supp @ A) @ name) @ X3)) => (? [C2:name]: (((((fresh @ name) @ A) @ C2) @ X3))))))).
% 2.59/1.49 thf(fact_229_exists__fresh, axiom, (! [A:$tType,X3:A]: ((((finite_finite @ name) @ (((supp @ A) @ name) @ X3)) => (~ ((! [C2:name]: ((~ (((((fresh @ name) @ A) @ C2) @ X3))))))))))).
% 2.59/1.49 thf(fact_230_supp__fresh__iff, axiom, (! [X:$tType,A:$tType]: ((((supp @ A) @ X) = (^ [X4:A]: (((collect @ X) @ (^ [A5:X]: ((~ (((((fresh @ X) @ A) @ A5) @ X4)))))))))))).
% 2.59/1.49 thf(fact_231_fresh__def, axiom, (! [A:$tType,X:$tType]: ((((fresh @ X) @ A) = (^ [A5:X,X4:A]: ((~ ((((member @ X) @ A5) @ (((supp @ A) @ X) @ X4)))))))))).
% 2.59/1.49 thf(fact_232_pi_Osupp_I9_J, axiom, (! [X1:name,X2:pi]: (((((supp @ pi) @ name) @ ((res @ X1) @ X2)) = (((supp @ (name > (noption @ pi))) @ name) @ ((((abs_fun @ name) @ pi) @ X1) @ X2)))))).
% 2.59/1.49 thf(fact_233_freeRes_Ocase__distrib, axiom, (! [A:$tType,B2:$tType,H:(A > B2),F1:(name > (name > A)),F2:A,FreeRes3:late_freeRes]: (((H @ ((((late_case_freeRes @ A) @ F1) @ F2) @ FreeRes3)) = ((((late_case_freeRes @ B2) @ (^ [X14:name,X23:name]: ((H @ ((F1 @ X14) @ X23))))) @ (H @ F2)) @ FreeRes3))))).
% 2.59/1.49 thf(fact_234_subject_Ocase__distrib, axiom, (! [B2:$tType,A:$tType,H:(A > B2),F1:(name > A),F2:(name > A),Subject2:late_subject]: (((H @ ((((late_case_subject @ A) @ F1) @ F2) @ Subject2)) = ((((late_case_subject @ B2) @ (^ [X4:name]: ((H @ (F1 @ X4))))) @ (^ [X4:name]: ((H @ (F2 @ X4))))) @ Subject2))))).
% 2.59/1.49 thf(fact_235_pi_Osupp_I3_J, axiom, (! [X1:pi]: (((((supp @ pi) @ name) @ (tau @ X1)) = (((supp @ pi) @ name) @ X1))))).
% 2.59/1.49 thf(fact_236_subject_Osupp_I2_J, axiom, (! [X1:name]: (((((supp @ late_subject) @ name) @ (late_BoundOutputS @ X1)) = (((supp @ name) @ name) @ X1))))).
% 2.59/1.49 thf(fact_237_subject_Osupp_I1_J, axiom, (! [X1:name]: (((((supp @ late_subject) @ name) @ (late_InputS @ X1)) = (((supp @ name) @ name) @ X1))))).
% 2.59/1.49 thf(fact_238_pi_Osupp_I10_J, axiom, (! [X1:pi]: (((((supp @ pi) @ name) @ (bang @ X1)) = (((supp @ pi) @ name) @ X1))))).
% 2.59/1.49 thf(fact_239_fs__name1, axiom, (! [A:$tType]: (((fs_name @ A) => (! [X3:A]: (((finite_finite @ name) @ (((supp @ A) @ name) @ X3)))))))).
% 2.59/1.49 thf(fact_240_residual_Orecs_I2_J, axiom, (! [N:$tType,T:$tType]: (((pt_name @ T) => (! [F1:(late_subject > (name > (pi > T))),F2:(late_freeRes > (pi > T)),Z:N,P:(T > $o),FreeRes3:late_freeRes,Pi2:pi]: ((((finite_finite @ name) @ (((supp @ (late_subject > (name > (pi > T)))) @ name) @ F1)) => (((finite_finite @ name) @ (((supp @ (late_freeRes > (pi > T))) @ name) @ F2)) => (((finite_finite @ name) @ (((supp @ N) @ name) @ Z)) => ((! [X13:late_subject,X22:name,X33:pi]: ((P @ (((F1 @ X13) @ X22) @ X33)))) => ((! [X13:late_freeRes,X22:pi]: ((P @ ((F2 @ X13) @ X22)))) => ((! [X13:late_subject,X22:name,X33:pi]: ((((((fresh @ name) @ (late_subject > (name > (pi > T)))) @ X22) @ F1) => (((((fresh @ name) @ late_subject) @ X22) @ X13) => (((((fresh @ name) @ N) @ X22) @ Z) => ((P @ (((F1 @ X13) @ X22) @ X33)) => ((((fresh @ name) @ T) @ X22) @ (((F1 @ X13) @ X22) @ X33)))))))) => (((((late_residual_rec @ T) @ F1) @ F2) @ ((late_FreeR @ FreeRes3) @ Pi2)) = ((F2 @ FreeRes3) @ Pi2)))))))))))))).
% 2.59/1.49 thf(fact_241_residual_Orecs_I1_J, axiom, (! [N:$tType,T:$tType]: (((pt_name @ T) => (! [F1:(late_subject > (name > (pi > T))),F2:(late_freeRes > (pi > T)),Z:N,P:(T > $o),Name2:name,Subject2:late_subject,Pi2:pi]: ((((finite_finite @ name) @ (((supp @ (late_subject > (name > (pi > T)))) @ name) @ F1)) => (((finite_finite @ name) @ (((supp @ (late_freeRes > (pi > T))) @ name) @ F2)) => (((finite_finite @ name) @ (((supp @ N) @ name) @ Z)) => ((! [X13:late_subject,X22:name,X33:pi]: ((P @ (((F1 @ X13) @ X22) @ X33)))) => ((! [X13:late_freeRes,X22:pi]: ((P @ ((F2 @ X13) @ X22)))) => ((! [X13:late_subject,X22:name,X33:pi]: ((((((fresh @ name) @ (late_subject > (name > (pi > T)))) @ X22) @ F1) => (((((fresh @ name) @ late_subject) @ X22) @ X13) => (((((fresh @ name) @ N) @ X22) @ Z) => ((P @ (((F1 @ X13) @ X22) @ X33)) => ((((fresh @ name) @ T) @ X22) @ (((F1 @ X13) @ X22) @ X33)))))))) => (((((fresh @ name) @ (late_subject > (name > (pi > T)))) @ Name2) @ F1) => (((((fresh @ name) @ (late_freeRes > (pi > T))) @ Name2) @ F2) => (((((fresh @ name) @ late_subject) @ Name2) @ Subject2) => (((((late_residual_rec @ T) @ F1) @ F2) @ (((late_BoundR @ Subject2) @ Name2) @ Pi2)) = (((F1 @ Subject2) @ Name2) @ Pi2))))))))))))))))).
% 2.59/1.49 thf(fact_242_residual_Orec__fresh, axiom, (! [T:$tType]: (((pt_name @ T) => (! [F1:(late_subject > (name > (pi > T))),F2:(late_freeRes > (pi > T)),X3:late_residual,Y:T,A2:name]: ((((finite_finite @ name) @ (((supp @ (late_subject > (name > (pi > T)))) @ name) @ F1)) => (((finite_finite @ name) @ (((supp @ (late_freeRes > (pi > T))) @ name) @ F2)) => ((((((late_r582136743ec_set @ T) @ F1) @ F2) @ X3) @ Y) => ((! [Y6:T]: (((((((late_r582136743ec_set @ T) @ F1) @ F2) @ X3) @ Y6) => (Y6 = Y)))) => (((((fresh @ name) @ late_residual) @ A2) @ X3) => (((((fresh @ name) @ (late_subject > (name > (pi > T)))) @ A2) @ F1) => (((((fresh @ name) @ (late_freeRes > (pi > T))) @ A2) @ F2) => ((((fresh @ name) @ T) @ A2) @ Y)))))))))))))).
% 2.59/1.49 thf(fact_243_residual_Orec__unique, axiom, (! [N:$tType,T:$tType]: (((pt_name @ T) => (! [F1:(late_subject > (name > (pi > T))),F2:(late_freeRes > (pi > T)),Z:N,P:(T > $o),X3:late_residual]: ((((finite_finite @ name) @ (((supp @ (late_subject > (name > (pi > T)))) @ name) @ F1)) => (((finite_finite @ name) @ (((supp @ (late_freeRes > (pi > T))) @ name) @ F2)) => (((finite_finite @ name) @ (((supp @ N) @ name) @ Z)) => ((! [X13:late_subject,X22:name,X33:pi]: ((P @ (((F1 @ X13) @ X22) @ X33)))) => ((! [X13:late_freeRes,X22:pi]: ((P @ ((F2 @ X13) @ X22)))) => ((! [X13:late_subject,X22:name]: ((((((fresh @ name) @ (late_subject > (name > (pi > T)))) @ X22) @ F1) => (((((fresh @ name) @ late_subject) @ X22) @ X13) => (((((fresh @ name) @ N) @ X22) @ Z) => (! [X33:pi]: (((P @ (((F1 @ X13) @ X22) @ X33)) => ((((fresh @ name) @ T) @ X22) @ (((F1 @ X13) @ X22) @ X33)))))))))) => (? [X5:T]: (((((((late_r582136743ec_set @ T) @ F1) @ F2) @ X3) @ X5) & (! [Y7:T]: (((((((late_r582136743ec_set @ T) @ F1) @ F2) @ X3) @ Y7) => (Y7 = X5))))))))))))))))))).
% 2.59/1.49 thf(fact_244_residual_Orec__fin__supp, axiom, (! [T:$tType]: (((pt_name @ T) => (! [F1:(late_subject > (name > (pi > T))),F2:(late_freeRes > (pi > T)),X1:late_residual,Y1:T]: ((((finite_finite @ name) @ (((supp @ (late_subject > (name > (pi > T)))) @ name) @ F1)) => (((finite_finite @ name) @ (((supp @ (late_freeRes > (pi > T))) @ name) @ F2)) => ((((((late_r582136743ec_set @ T) @ F1) @ F2) @ X1) @ Y1) => ((finite_finite @ name) @ (((supp @ T) @ name) @ Y1))))))))))).
% 2.59/1.49 thf(fact_245_pi_Osupp_I4_J, axiom, (! [X32:name,X1:name,X2:pi]: (((((supp @ pi) @ name) @ (((input @ X32) @ X1) @ X2)) = (((sup_sup @ (set @ name)) @ (((supp @ name) @ name) @ X32)) @ (((supp @ (name > (noption @ pi))) @ name) @ ((((abs_fun @ name) @ pi) @ X1) @ X2))))))).
% 2.59/1.49 thf(fact_246_residual_Osupp_I1_J, axiom, (! [X32:late_subject,X1:name,X2:pi]: (((((supp @ late_residual) @ name) @ (((late_BoundR @ X32) @ X1) @ X2)) = (((sup_sup @ (set @ name)) @ (((supp @ late_subject) @ name) @ X32)) @ (((supp @ (name > (noption @ pi))) @ name) @ ((((abs_fun @ name) @ pi) @ X1) @ X2))))))).
% 2.59/1.49 thf(fact_247_pi_Osupp_I7_J, axiom, (! [X2:pi,X1:pi]: (((((supp @ pi) @ name) @ ((sum @ X2) @ X1)) = (((sup_sup @ (set @ name)) @ (((supp @ pi) @ name) @ X2)) @ (((supp @ pi) @ name) @ X1)))))).
% 2.59/1.49 thf(fact_248_pi_Osupp_I8_J, axiom, (! [X2:pi,X1:pi]: (((((supp @ pi) @ name) @ ((par @ X2) @ X1)) = (((sup_sup @ (set @ name)) @ (((supp @ pi) @ name) @ X2)) @ (((supp @ pi) @ name) @ X1)))))).
% 2.59/1.49 thf(fact_249_freeRes_Osupp_I1_J, axiom, (! [X2:name,X1:name]: (((((supp @ late_freeRes) @ name) @ ((late_OutputR @ X2) @ X1)) = (((sup_sup @ (set @ name)) @ (((supp @ name) @ name) @ X2)) @ (((supp @ name) @ name) @ X1)))))).
% 2.59/1.49 thf(fact_250_residual_Osupp_I2_J, axiom, (! [X2:late_freeRes,X1:pi]: (((((supp @ late_residual) @ name) @ ((late_FreeR @ X2) @ X1)) = (((sup_sup @ (set @ name)) @ (((supp @ late_freeRes) @ name) @ X2)) @ (((supp @ pi) @ name) @ X1)))))).
% 2.59/1.49 thf(fact_251_pi_Osupp_I2_J, axiom, (! [X32:name,X2:name,X1:pi]: (((((supp @ pi) @ name) @ (((output @ X32) @ X2) @ X1)) = (((sup_sup @ (set @ name)) @ (((supp @ name) @ name) @ X32)) @ (((sup_sup @ (set @ name)) @ (((supp @ name) @ name) @ X2)) @ (((supp @ pi) @ name) @ X1))))))).
% 2.59/1.49 thf(fact_252_pi_Osupp_I6_J, axiom, (! [X32:name,X2:name,X1:pi]: (((((supp @ pi) @ name) @ (((mismatch @ X32) @ X2) @ X1)) = (((sup_sup @ (set @ name)) @ (((supp @ name) @ name) @ X32)) @ (((sup_sup @ (set @ name)) @ (((supp @ name) @ name) @ X2)) @ (((supp @ pi) @ name) @ X1))))))).
% 2.59/1.49 thf(fact_253_pi_Osupp_I5_J, axiom, (! [X32:name,X2:name,X1:pi]: (((((supp @ pi) @ name) @ (((match @ X32) @ X2) @ X1)) = (((sup_sup @ (set @ name)) @ (((supp @ name) @ name) @ X32)) @ (((sup_sup @ (set @ name)) @ (((supp @ name) @ name) @ X2)) @ (((supp @ pi) @ name) @ X1))))))).
% 2.59/1.49 thf(fact_254_pi_Orec__fin__supp, axiom, (! [T:$tType]: (((pt_name @ T) => (! [F1:T,F2:(name > (name > (pi > (T > T)))),F32:(pi > (T > T)),F4:(name > (name > (pi > (T > T)))),F5:(name > (name > (pi > (T > T)))),F6:(name > (name > (pi > (T > T)))),F7:(pi > (pi > (T > (T > T)))),F8:(pi > (pi > (T > (T > T)))),F9:(name > (pi > (T > T))),F10:(pi > (T > T)),X1:pi,Y1:T]: ((((finite_finite @ name) @ (((supp @ T) @ name) @ F1)) => (((finite_finite @ name) @ (((supp @ (name > (name > (pi > (T > T))))) @ name) @ F2)) => (((finite_finite @ name) @ (((supp @ (pi > (T > T))) @ name) @ F32)) => (((finite_finite @ name) @ (((supp @ (name > (name > (pi > (T > T))))) @ name) @ F4)) => (((finite_finite @ name) @ (((supp @ (name > (name > (pi > (T > T))))) @ name) @ F5)) => (((finite_finite @ name) @ (((supp @ (name > (name > (pi > (T > T))))) @ name) @ F6)) => (((finite_finite @ name) @ (((supp @ (pi > (pi > (T > (T > T))))) @ name) @ F7)) => (((finite_finite @ name) @ (((supp @ (pi > (pi > (T > (T > T))))) @ name) @ F8)) => (((finite_finite @ name) @ (((supp @ (name > (pi > (T > T)))) @ name) @ F9)) => (((finite_finite @ name) @ (((supp @ (pi > (T > T))) @ name) @ F10)) => ((((((((((((((pi_rec_set @ T) @ F1) @ F2) @ F32) @ F4) @ F5) @ F6) @ F7) @ F8) @ F9) @ F10) @ X1) @ Y1) => ((finite_finite @ name) @ (((supp @ T) @ name) @ Y1))))))))))))))))))).
% 2.59/1.49 thf(fact_255_supports__fresh, axiom, (! [X:$tType,A:$tType,S:(set @ X),X3:A,A2:X]: ((((((supports @ X) @ A) @ S) @ X3) => (((finite_finite @ X) @ S) => ((~ ((((member @ X) @ A2) @ S))) => ((((fresh @ X) @ A) @ A2) @ X3))))))).
% 2.59/1.49 thf(tcon_fun___Agent_Opt__name, axiom, (! [A6:$tType,A7:$tType]: ((((pt_name @ A6) & (pt_name @ A7)) => (pt_name @ (A6 > A7)))))).
% 2.59/1.49 thf(tcon_Set_Oset___Agent_Opt__name_1, axiom, (! [A6:$tType]: (((pt_name @ A6) => (pt_name @ (set @ A6)))))).
% 2.59/1.49 thf(tcon_Agent_Opi___Agent_Opt__name_2, axiom, (pt_name @ pi)).
% 2.59/1.49 thf(tcon_Agent_Opi___Agent_Ofs__name, axiom, (fs_name @ pi)).
% 2.59/1.49 thf(tcon_HOL_Obool___Agent_Opt__name_3, axiom, (pt_name @ $o)).
% 2.59/1.49 thf(tcon_HOL_Obool___Agent_Ofs__name_4, axiom, (fs_name @ $o)).
% 2.59/1.49 thf(tcon_Agent_Oname___Agent_Opt__name_5, axiom, (pt_name @ name)).
% 2.59/1.49 thf(tcon_Agent_Oname___Agent_Ofs__name_6, axiom, (fs_name @ name)).
% 2.59/1.49 thf(tcon_Nominal_Onoption___Agent_Opt__name_7, axiom, (! [A6:$tType]: (((pt_name @ A6) => (pt_name @ (noption @ A6)))))).
% 2.59/1.49 thf(tcon_Late__Semantics_OfreeRes___Agent_Opt__name_8, axiom, (pt_name @ late_freeRes)).
% 2.59/1.49 thf(tcon_Late__Semantics_OfreeRes___Agent_Ofs__name_9, axiom, (fs_name @ late_freeRes)).
% 2.59/1.49 thf(tcon_Late__Semantics_Osubject___Agent_Opt__name_10, axiom, (pt_name @ late_subject)).
% 2.59/1.49 thf(tcon_Late__Semantics_Osubject___Agent_Ofs__name_11, axiom, (fs_name @ late_subject)).
% 2.59/1.49 thf(tcon_Late__Semantics_Oresidual___Agent_Opt__name_12, axiom, (pt_name @ late_residual)).
% 2.59/1.49 thf(tcon_Late__Semantics_Oresidual___Agent_Ofs__name_13, axiom, (fs_name @ late_residual)).
% 2.59/1.49 thf(help_If_3_1_T, axiom, (! [P:$o]: (((P = $true) | (P = $false))))).
% 2.59/1.49 thf(help_If_2_1_T, axiom, (! [A:$tType,X3:A,Y:A]: ((((((if @ A) @ $false) @ X3) @ Y) = Y)))).
% 2.59/1.49 thf(help_If_1_1_T, axiom, (! [A:$tType,X3:A,Y:A]: ((((((if @ A) @ $true) @ X3) @ Y) = X3)))).
% 2.59/1.49 thf(conj_0, conjecture, ((late_transitions @ ((par @ ((par @ p) @ q)) @ r)) @ ((late_FreeR @ late_TauR) @ ((par @ ((par @ p2) @ (((subs @ q2) @ x) @ b))) @ r)))).
% 2.59/1.49 % SZS output end ListOfTHF for /export/starexec/sandbox2/tmp/tmp.Is4Z84IKKq/DTF2DTF17420.p
% 2.59/1.49 ------------------------
% 2.84/1.52 ---- Cleaned THF ---
% 2.84/1.52 thf(ty_t_Late__Semantics_Oresidual,type,
% 2.84/1.52 late_residual: $tType ).
% 2.84/1.52
% 2.84/1.52 thf(ty_t_Late__Semantics_Osubject,type,
% 2.84/1.52 late_subject: $tType ).
% 2.84/1.52
% 2.84/1.52 thf(ty_t_Late__Semantics_OfreeRes,type,
% 2.84/1.52 late_freeRes: $tType ).
% 2.84/1.52
% 2.84/1.52 thf(ty_t_Nominal_Onoption,type,
% 2.84/1.52 noption: $tType > $tType ).
% 2.84/1.52
% 2.84/1.52 thf(ty_t_Agent_Oname,type,
% 2.84/1.52 name: $tType ).
% 2.84/1.52
% 2.84/1.52 thf(ty_t_Agent_Opi,type,
% 2.84/1.52 pi: $tType ).
% 2.84/1.52
% 2.84/1.52 thf(ty_t_Set_Oset,type,
% 2.84/1.52 set: $tType > $tType ).
% 2.84/1.52
% 2.84/1.52 thf(sy_cl_Agent_Ofs__name,type,
% 2.84/1.52 fs_name:
% 2.84/1.52 !>[A: $tType] : $o ).
% 2.84/1.52
% 2.84/1.52 thf(sy_cl_Agent_Opt__name,type,
% 2.84/1.52 pt_name:
% 2.84/1.52 !>[A: $tType] : $o ).
% 2.84/1.52
% 2.84/1.52 thf(sy_c_Agent_Opi_OBang,type,
% 2.84/1.52 bang: pi > pi ).
% 2.84/1.52
% 2.84/1.52 thf(sy_c_Agent_Opi_OInput,type,
% 2.84/1.52 input: name > name > pi > pi ).
% 2.84/1.52
% 2.84/1.52 thf(sy_c_Agent_Opi_OMatch,type,
% 2.84/1.52 match: name > name > pi > pi ).
% 2.84/1.52
% 2.84/1.52 thf(sy_c_Agent_Opi_OMismatch,type,
% 2.84/1.52 mismatch: name > name > pi > pi ).
% 2.84/1.52
% 2.84/1.52 thf(sy_c_Agent_Opi_OOutput,type,
% 2.84/1.52 output: name > name > pi > pi ).
% 2.84/1.52
% 2.84/1.52 thf(sy_c_Agent_Opi_OPar,type,
% 2.84/1.52 par: pi > pi > pi ).
% 2.84/1.52
% 2.84/1.52 thf(sy_c_Agent_Opi_OPiNil,type,
% 2.84/1.52 piNil: pi ).
% 2.84/1.52
% 2.84/1.52 thf(sy_c_Agent_Opi_ORes,type,
% 2.84/1.52 res: name > pi > pi ).
% 2.84/1.52
% 2.84/1.52 thf(sy_c_Agent_Opi_OSum,type,
% 2.84/1.52 sum: pi > pi > pi ).
% 2.84/1.52
% 2.84/1.52 thf(sy_c_Agent_Opi_OTau,type,
% 2.84/1.52 tau: pi > pi ).
% 2.84/1.52
% 2.84/1.52 thf(sy_c_Agent_Opi_Opi__rec,type,
% 2.84/1.52 pi_rec:
% 2.84/1.52 !>[T: $tType] : ( T > ( name > name > pi > T > T ) > ( pi > T > T ) > ( name > name > pi > T > T ) > ( name > name > pi > T > T ) > ( name > name > pi > T > T ) > ( pi > pi > T > T > T ) > ( pi > pi > T > T > T ) > ( name > pi > T > T ) > ( pi > T > T ) > pi > T ) ).
% 2.84/1.52
% 2.84/1.52 thf(sy_c_Agent_Opi_Opi__rec__set,type,
% 2.84/1.52 pi_rec_set:
% 2.84/1.52 !>[T: $tType] : ( T > ( name > name > pi > T > T ) > ( pi > T > T ) > ( name > name > pi > T > T ) > ( name > name > pi > T > T ) > ( name > name > pi > T > T ) > ( pi > pi > T > T > T ) > ( pi > pi > T > T > T ) > ( name > pi > T > T ) > ( pi > T > T ) > pi > T > $o ) ).
% 2.84/1.52
% 2.84/1.52 thf(sy_c_Agent_Osubs,type,
% 2.84/1.52 subs: pi > name > name > pi ).
% 2.84/1.52
% 2.84/1.52 thf(sy_c_Agent_Osubst__name,type,
% 2.84/1.52 subst_name: name > name > name > name ).
% 2.84/1.52
% 2.84/1.52 thf(sy_c_Finite__Set_Ofinite,type,
% 2.84/1.52 finite_finite:
% 2.84/1.52 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 2.84/1.52
% 2.84/1.52 thf(sy_c_If,type,
% 2.84/1.52 if:
% 2.84/1.52 !>[A: $tType] : ( $o > A > A > A ) ).
% 2.84/1.52
% 2.84/1.52 thf(sy_c_Late__Semantics1_OfreeRes_Ocase__freeRes,type,
% 2.84/1.52 late_case_freeRes:
% 2.84/1.52 !>[A: $tType] : ( ( name > name > A ) > A > late_freeRes > A ) ).
% 2.84/1.52
% 2.84/1.52 thf(sy_c_Late__Semantics1_Osubject_Ocase__subject,type,
% 2.84/1.52 late_case_subject:
% 2.84/1.52 !>[A: $tType] : ( ( name > A ) > ( name > A ) > late_subject > A ) ).
% 2.84/1.52
% 2.84/1.52 thf(sy_c_Late__Semantics_ObangPred,type,
% 2.84/1.52 late_bangPred: pi > pi > $o ).
% 2.84/1.52
% 2.84/1.52 thf(sy_c_Late__Semantics_OfreeRes_OOutputR,type,
% 2.84/1.52 late_OutputR: name > name > late_freeRes ).
% 2.84/1.52
% 2.84/1.52 thf(sy_c_Late__Semantics_OfreeRes_OTauR,type,
% 2.84/1.52 late_TauR: late_freeRes ).
% 2.84/1.52
% 2.84/1.52 thf(sy_c_Late__Semantics_OfreeRes_OfreeRes__rec,type,
% 2.84/1.52 late_freeRes_rec:
% 2.84/1.52 !>[T: $tType] : ( ( name > name > T ) > T > late_freeRes > T ) ).
% 2.84/1.52
% 2.84/1.52 thf(sy_c_Late__Semantics_Oresidual_OBoundR,type,
% 2.84/1.52 late_BoundR: late_subject > name > pi > late_residual ).
% 2.84/1.52
% 2.84/1.52 thf(sy_c_Late__Semantics_Oresidual_OFreeR,type,
% 2.84/1.52 late_FreeR: late_freeRes > pi > late_residual ).
% 2.84/1.52
% 2.84/1.52 thf(sy_c_Late__Semantics_Oresidual_Oresidual__rec,type,
% 2.84/1.52 late_residual_rec:
% 2.84/1.52 !>[T: $tType] : ( ( late_subject > name > pi > T ) > ( late_freeRes > pi > T ) > late_residual > T ) ).
% 2.84/1.52
% 2.84/1.52 thf(sy_c_Late__Semantics_Oresidual_Oresidual__rec__set,type,
% 2.84/1.52 late_r582136743ec_set:
% 2.84/1.52 !>[T: $tType] : ( ( late_subject > name > pi > T ) > ( late_freeRes > pi > T ) > late_residual > T > $o ) ).
% 2.84/1.52
% 2.84/1.52 thf(sy_c_Late__Semantics_Osubject_OBoundOutputS,type,
% 2.84/1.52 late_BoundOutputS: name > late_subject ).
% 2.84/1.52
% 2.84/1.52 thf(sy_c_Late__Semantics_Osubject_OInputS,type,
% 2.84/1.52 late_InputS: name > late_subject ).
% 2.84/1.52
% 2.84/1.52 thf(sy_c_Late__Semantics_Osubject_Osubject__rec,type,
% 2.84/1.52 late_subject_rec:
% 2.84/1.52 !>[T: $tType] : ( ( name > T ) > ( name > T ) > late_subject > T ) ).
% 2.84/1.52
% 2.84/1.52 thf(sy_c_Late__Semantics_Otransitions,type,
% 2.84/1.52 late_transitions: pi > late_residual > $o ).
% 2.84/1.52
% 2.84/1.52 thf(sy_c_Lattices_Osup__class_Osup,type,
% 2.84/1.52 sup_sup:
% 2.84/1.52 !>[A: $tType] : ( A > A > A ) ).
% 2.84/1.52
% 2.84/1.52 thf(sy_c_Nominal_Oabs__fun,type,
% 2.84/1.52 abs_fun:
% 2.84/1.52 !>[X: $tType,A: $tType] : ( X > A > X > ( noption @ A ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(sy_c_Nominal_Ofresh,type,
% 2.84/1.52 fresh:
% 2.84/1.52 !>[X: $tType,A: $tType] : ( X > A > $o ) ).
% 2.84/1.52
% 2.84/1.52 thf(sy_c_Nominal_Osupp,type,
% 2.84/1.52 supp:
% 2.84/1.52 !>[A: $tType,X: $tType] : ( A > ( set @ X ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(sy_c_Nominal_Osupports,type,
% 2.84/1.52 supports:
% 2.84/1.52 !>[X: $tType,A: $tType] : ( ( set @ X ) > A > $o ) ).
% 2.84/1.52
% 2.84/1.52 thf(sy_c_Set_OCollect,type,
% 2.84/1.52 collect:
% 2.84/1.52 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(sy_c_member,type,
% 2.84/1.52 member:
% 2.84/1.52 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 2.84/1.52
% 2.84/1.52 thf(sy_v_P,type,
% 2.84/1.52 p: pi ).
% 2.84/1.52
% 2.84/1.52 thf(sy_v_PQR____,type,
% 2.84/1.52 pqr: pi ).
% 2.84/1.52
% 2.84/1.52 thf(sy_v_P_H____,type,
% 2.84/1.52 p2: pi ).
% 2.84/1.52
% 2.84/1.52 thf(sy_v_Q,type,
% 2.84/1.52 q: pi ).
% 2.84/1.52
% 2.84/1.52 thf(sy_v_QR____,type,
% 2.84/1.52 qr: pi ).
% 2.84/1.52
% 2.84/1.52 thf(sy_v_Q_H____,type,
% 2.84/1.52 q2: pi ).
% 2.84/1.52
% 2.84/1.52 thf(sy_v_R,type,
% 2.84/1.52 r: pi ).
% 2.84/1.52
% 2.84/1.52 thf(sy_v__092_060alpha_062____,type,
% 2.84/1.52 alpha: late_freeRes ).
% 2.84/1.52
% 2.84/1.52 thf(sy_v_a____,type,
% 2.84/1.52 a: name ).
% 2.84/1.52
% 2.84/1.52 thf(sy_v_b____,type,
% 2.84/1.52 b: name ).
% 2.84/1.52
% 2.84/1.52 thf(sy_v_x____,type,
% 2.84/1.52 x: name ).
% 2.84/1.52
% 2.84/1.52 thf(fact_0_cComm2_Ohyps_I9_J,axiom,
% 2.84/1.52 alpha = late_TauR ).
% 2.84/1.52
% 2.84/1.52 thf(fact_1_cComm2_Ohyps_I5_J,axiom,
% 2.84/1.52 x != a ).
% 2.84/1.52
% 2.84/1.52 thf(fact_2_cComm2_Ohyps_I6_J,axiom,
% 2.84/1.52 x != b ).
% 2.84/1.52
% 2.84/1.52 thf(fact_3__092_060open_062P_A_092_060parallel_062_AQ_A_092_060longmapsto_062_A_092_060tau_062_A_092_060prec_062_AP_H_A_092_060parallel_062_AQ_H_091x_058_058_061b_093_092_060close_062,axiom,
% 2.84/1.52 late_transitions @ ( par @ p @ q ) @ ( late_FreeR @ late_TauR @ ( par @ p2 @ ( subs @ q2 @ x @ b ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_4_Free_Ohyps,axiom,
% 2.84/1.52 late_transitions @ ( par @ p @ ( par @ q @ r ) ) @ ( late_FreeR @ alpha @ pqr ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_5_cComm2_Ohyps_I8_J,axiom,
% 2.84/1.52 fresh @ name @ pi @ x @ q ).
% 2.84/1.52
% 2.84/1.52 thf(fact_6_cComm2_Ohyps_I3_J,axiom,
% 2.84/1.52 fresh @ name @ pi @ x @ p ).
% 2.84/1.52
% 2.84/1.52 thf(fact_7_cComm2_Ohyps_I7_J,axiom,
% 2.84/1.52 fresh @ name @ pi @ x @ p2 ).
% 2.84/1.52
% 2.84/1.52 thf(fact_8_cComm2_Ohyps_I4_J,axiom,
% 2.84/1.52 fresh @ name @ pi @ x @ ( par @ q @ r ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_9_cComm2_Ohyps_I1_J,axiom,
% 2.84/1.52 late_transitions @ p @ ( late_FreeR @ ( late_OutputR @ a @ b ) @ p2 ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_10_simps_I8_J,axiom,
% 2.84/1.52 ! [P: pi,Q: pi,C: name,D: name] :
% 2.84/1.52 ( ( subs @ ( par @ P @ Q ) @ C @ D )
% 2.84/1.52 = ( par @ ( subs @ P @ C @ D ) @ ( subs @ Q @ C @ D ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_11_Par1F,axiom,
% 2.84/1.52 ! [P: pi,Alpha: late_freeRes,P2: pi,Q: pi] :
% 2.84/1.52 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 2.84/1.52 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha @ ( par @ P2 @ Q ) ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_12_Par2F,axiom,
% 2.84/1.52 ! [Q: pi,Alpha: late_freeRes,Q2: pi,P: pi] :
% 2.84/1.52 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 2.84/1.52 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha @ ( par @ P @ Q2 ) ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_13__092_060open_062x_A_092_060sharp_062_AR_092_060close_062,axiom,
% 2.84/1.52 fresh @ name @ pi @ x @ r ).
% 2.84/1.52
% 2.84/1.52 thf(fact_14_subst__identity,axiom,
% 2.84/1.52 ! [P: pi,A2: name] :
% 2.84/1.52 ( ( subs @ P @ A2 @ A2 )
% 2.84/1.52 = P ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_15_cPar1_Ohyps,axiom,
% 2.84/1.52 late_transitions @ q @ ( late_BoundR @ ( late_InputS @ a ) @ x @ q2 ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_16_cComm2_Ohyps_I2_J,axiom,
% 2.84/1.52 late_transitions @ ( par @ q @ r ) @ ( late_BoundR @ ( late_InputS @ a ) @ x @ qr ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_17_residual_Oinject_I2_J,axiom,
% 2.84/1.52 ! [X2: late_freeRes,X1: pi,Y2: late_freeRes,Y1: pi] :
% 2.84/1.52 ( ( ( late_FreeR @ X2 @ X1 )
% 2.84/1.52 = ( late_FreeR @ Y2 @ Y1 ) )
% 2.84/1.52 = ( ( X2 = Y2 )
% 2.84/1.52 & ( X1 = Y1 ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_18_pi_Oinject_I7_J,axiom,
% 2.84/1.52 ! [X2: pi,X1: pi,Y2: pi,Y1: pi] :
% 2.84/1.52 ( ( ( par @ X2 @ X1 )
% 2.84/1.52 = ( par @ Y2 @ Y1 ) )
% 2.84/1.52 = ( ( X2 = Y2 )
% 2.84/1.52 & ( X1 = Y1 ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_19_tauCases,axiom,
% 2.84/1.52 ! [P: pi,Alpha: late_freeRes,P2: pi,Prop: late_freeRes > pi > $o] :
% 2.84/1.52 ( ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 2.84/1.52 => ( ( ( Alpha = late_TauR )
% 2.84/1.52 => ( ( P = P2 )
% 2.84/1.52 => ( Prop @ late_TauR @ P ) ) )
% 2.84/1.52 => ( Prop @ Alpha @ P2 ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_20_tauCases_H,axiom,
% 2.84/1.52 ! [P: pi,Rs: late_residual] :
% 2.84/1.52 ( ( late_transitions @ ( tau @ P ) @ Rs )
% 2.84/1.52 => ~ ! [P3: pi] :
% 2.84/1.52 ( ( ( tau @ P )
% 2.84/1.52 = ( tau @ P3 ) )
% 2.84/1.52 => ( Rs
% 2.84/1.52 != ( late_FreeR @ late_TauR @ P3 ) ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_21_Late__Semantics_OfreeRes_Oinject,axiom,
% 2.84/1.52 ! [X2: name,X1: name,Y2: name,Y1: name] :
% 2.84/1.52 ( ( ( late_OutputR @ X2 @ X1 )
% 2.84/1.52 = ( late_OutputR @ Y2 @ Y1 ) )
% 2.84/1.52 = ( ( X2 = Y2 )
% 2.84/1.52 & ( X1 = Y1 ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_22_pi_Ofresh_I8_J,axiom,
% 2.84/1.52 ! [A2: name,X2: pi,X1: pi] :
% 2.84/1.52 ( ( fresh @ name @ pi @ A2 @ ( par @ X2 @ X1 ) )
% 2.84/1.52 = ( ( fresh @ name @ pi @ A2 @ X2 )
% 2.84/1.52 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_23_substTrans,axiom,
% 2.84/1.52 ! [B: name,P: pi,A2: name,C: name] :
% 2.84/1.52 ( ( fresh @ name @ pi @ B @ P )
% 2.84/1.52 => ( ( subs @ ( subs @ P @ A2 @ B ) @ B @ C )
% 2.84/1.52 = ( subs @ P @ A2 @ C ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_24_pi_Ofresh_I3_J,axiom,
% 2.84/1.52 ! [A2: name,X1: pi] :
% 2.84/1.52 ( ( fresh @ name @ pi @ A2 @ ( tau @ X1 ) )
% 2.84/1.52 = ( fresh @ name @ pi @ A2 @ X1 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_25_simps_I2_J,axiom,
% 2.84/1.52 ! [P: pi,C: name,D: name] :
% 2.84/1.52 ( ( subs @ ( tau @ P ) @ C @ D )
% 2.84/1.52 = ( tau @ ( subs @ P @ C @ D ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_26_pi_Oinject_I2_J,axiom,
% 2.84/1.52 ! [X1: pi,Y1: pi] :
% 2.84/1.52 ( ( ( tau @ X1 )
% 2.84/1.52 = ( tau @ Y1 ) )
% 2.84/1.52 = ( X1 = Y1 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_27_freshBoundDerivative_I2_J,axiom,
% 2.84/1.52 ! [P: pi,A2: late_subject,X3: name,P2: pi,Y: name] :
% 2.84/1.52 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X3 @ P2 ) )
% 2.84/1.52 => ( ( fresh @ name @ pi @ Y @ P )
% 2.84/1.52 => ( ( Y != X3 )
% 2.84/1.52 => ( fresh @ name @ pi @ Y @ P2 ) ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_28_name__exists__fresh,axiom,
% 2.84/1.52 ! [A: $tType] :
% 2.84/1.52 ( ( fs_name @ A )
% 2.84/1.52 => ! [X3: A] :
% 2.84/1.52 ~ ! [C2: name] :
% 2.84/1.52 ~ ( fresh @ name @ A @ C2 @ X3 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_29_tauBoundTrans,axiom,
% 2.84/1.52 ! [P: pi,A2: late_subject,X3: name,P2: pi] :
% 2.84/1.52 ~ ( late_transitions @ ( tau @ P ) @ ( late_BoundR @ A2 @ X3 @ P2 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_30_residual_Ostrong__induct,axiom,
% 2.84/1.52 ! [N: $tType] :
% 2.84/1.52 ( ( fs_name @ N )
% 2.84/1.52 => ! [P: N > late_residual > $o,Z: N,Residual: late_residual] :
% 2.84/1.52 ( ! [Subject: late_subject,Name: name,Pi: pi,Z2: N] :
% 2.84/1.52 ( ( fresh @ name @ N @ Name @ Z2 )
% 2.84/1.52 => ( ( fresh @ name @ late_subject @ Name @ Subject )
% 2.84/1.52 => ( P @ Z2 @ ( late_BoundR @ Subject @ Name @ Pi ) ) ) )
% 2.84/1.52 => ( ! [FreeRes: late_freeRes,Pi: pi,Z2: N] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi ) )
% 2.84/1.52 => ( P @ Z @ Residual ) ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_31_residual_Ostrong__inducts,axiom,
% 2.84/1.52 ! [A: $tType] :
% 2.84/1.52 ( ( fs_name @ A )
% 2.84/1.52 => ! [P: A > late_residual > $o,Z: A,Residual: late_residual] :
% 2.84/1.52 ( ! [Subject: late_subject,Name: name,Pi: pi,Z2: A] :
% 2.84/1.52 ( ( fresh @ name @ A @ Name @ Z2 )
% 2.84/1.52 => ( ( fresh @ name @ late_subject @ Name @ Subject )
% 2.84/1.52 => ( P @ Z2 @ ( late_BoundR @ Subject @ Name @ Pi ) ) ) )
% 2.84/1.52 => ( ! [FreeRes: late_freeRes,Pi: pi,Z2: A] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi ) )
% 2.84/1.52 => ( P @ Z @ Residual ) ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_32_residual_Oinducts,axiom,
% 2.84/1.52 ! [P: late_residual > $o,Residual: late_residual] :
% 2.84/1.52 ( ! [Subject: late_subject,Name: name,Pi: pi] : ( P @ ( late_BoundR @ Subject @ Name @ Pi ) )
% 2.84/1.52 => ( ! [FreeRes: late_freeRes,Pi: pi] : ( P @ ( late_FreeR @ FreeRes @ Pi ) )
% 2.84/1.52 => ( P @ Residual ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_33_residual_Odistinct_I1_J,axiom,
% 2.84/1.52 ! [Subject2: late_subject,Name2: name,Pi2: pi,FreeRes2: late_freeRes,Pi3: pi] :
% 2.84/1.52 ( ( late_BoundR @ Subject2 @ Name2 @ Pi2 )
% 2.84/1.52 != ( late_FreeR @ FreeRes2 @ Pi3 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_34_fresh__fact2,axiom,
% 2.84/1.52 ! [A2: name,B: name,P: pi] :
% 2.84/1.52 ( ( A2 != B )
% 2.84/1.52 => ( fresh @ name @ pi @ A2 @ ( subs @ P @ A2 @ B ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_35_fresh__fact1,axiom,
% 2.84/1.52 ! [A2: name,P: pi,C: name,B: name] :
% 2.84/1.52 ( ( fresh @ name @ pi @ A2 @ P )
% 2.84/1.52 => ( ( A2 != C )
% 2.84/1.52 => ( fresh @ name @ pi @ A2 @ ( subs @ P @ B @ C ) ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_36_forget,axiom,
% 2.84/1.52 ! [A2: name,P: pi,B: name] :
% 2.84/1.52 ( ( fresh @ name @ pi @ A2 @ P )
% 2.84/1.52 => ( ( subs @ P @ A2 @ B )
% 2.84/1.52 = P ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_37_parCasesB,axiom,
% 2.84/1.52 ! [P: pi,Q: pi,A2: late_subject,X3: name,PQ: pi,Prop: pi > $o] :
% 2.84/1.52 ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X3 @ PQ ) )
% 2.84/1.52 => ( ( fresh @ name @ pi @ X3 @ P )
% 2.84/1.52 => ( ( fresh @ name @ pi @ X3 @ Q )
% 2.84/1.52 => ( ! [P4: pi] :
% 2.84/1.52 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X3 @ P4 ) )
% 2.84/1.52 => ( Prop @ ( par @ P4 @ Q ) ) )
% 2.84/1.52 => ( ! [Q3: pi] :
% 2.84/1.52 ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X3 @ Q3 ) )
% 2.84/1.52 => ( Prop @ ( par @ P @ Q3 ) ) )
% 2.84/1.52 => ( Prop @ PQ ) ) ) ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_38_Late__Semantics_OPar2B,axiom,
% 2.84/1.52 ! [Q: pi,A2: late_subject,X3: name,Q2: pi,P: pi] :
% 2.84/1.52 ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X3 @ Q2 ) )
% 2.84/1.52 => ( ( fresh @ name @ pi @ X3 @ P )
% 2.84/1.52 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X3 @ ( par @ P @ Q2 ) ) ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_39_Late__Semantics_OPar1B,axiom,
% 2.84/1.52 ! [P: pi,A2: late_subject,X3: name,P2: pi,Q: pi] :
% 2.84/1.52 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X3 @ P2 ) )
% 2.84/1.52 => ( ( fresh @ name @ pi @ X3 @ Q )
% 2.84/1.52 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X3 @ ( par @ P2 @ Q ) ) ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_40_pi_Odistinct_I43_J,axiom,
% 2.84/1.52 ! [Pi2: pi,Pi1: pi,Pi22: pi] :
% 2.84/1.52 ( ( tau @ Pi2 )
% 2.84/1.52 != ( par @ Pi1 @ Pi22 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_41_freeRes_Ostrong__inducts,axiom,
% 2.84/1.52 ! [A: $tType,P: A > late_freeRes > $o,Z: A,FreeRes3: late_freeRes] :
% 2.84/1.52 ( ! [Name1: name,Name22: name,Z2: A] : ( P @ Z2 @ ( late_OutputR @ Name1 @ Name22 ) )
% 2.84/1.52 => ( ! [Z2: A] : ( P @ Z2 @ late_TauR )
% 2.84/1.52 => ( P @ Z @ FreeRes3 ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_42_freeRes_Ostrong__induct_H,axiom,
% 2.84/1.52 ! [N: $tType,P: N > late_freeRes > $o,Z: N,FreeRes3: late_freeRes] :
% 2.84/1.52 ( ! [Name1: name,Name22: name,Z2: N] : ( P @ Z2 @ ( late_OutputR @ Name1 @ Name22 ) )
% 2.84/1.52 => ( ! [Z2: N] : ( P @ Z2 @ late_TauR )
% 2.84/1.52 => ( P @ Z @ FreeRes3 ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_43_freeRes_Oinducts,axiom,
% 2.84/1.52 ! [P: late_freeRes > $o,FreeRes3: late_freeRes] :
% 2.84/1.52 ( ! [Name1: name,Name22: name] : ( P @ ( late_OutputR @ Name1 @ Name22 ) )
% 2.84/1.52 => ( ( P @ late_TauR )
% 2.84/1.52 => ( P @ FreeRes3 ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_44_Late__Semantics_OfreeRes_Odistinct_I1_J,axiom,
% 2.84/1.52 ! [Name12: name,Name23: name] :
% 2.84/1.52 ( ( late_OutputR @ Name12 @ Name23 )
% 2.84/1.52 != late_TauR ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_45_mem__Collect__eq,axiom,
% 2.84/1.52 ! [A: $tType,A2: A,P: A > $o] :
% 2.84/1.52 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 2.84/1.52 = ( P @ A2 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_46_Collect__mem__eq,axiom,
% 2.84/1.52 ! [A: $tType,A3: set @ A] :
% 2.84/1.52 ( ( collect @ A
% 2.84/1.52 @ ^ [X4: A] : ( member @ A @ X4 @ A3 ) )
% 2.84/1.52 = A3 ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_47_Collect__cong,axiom,
% 2.84/1.52 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.84/1.52 ( ! [X5: A] :
% 2.84/1.52 ( ( P @ X5 )
% 2.84/1.52 = ( Q @ X5 ) )
% 2.84/1.52 => ( ( collect @ A @ P )
% 2.84/1.52 = ( collect @ A @ Q ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_48_ext,axiom,
% 2.84/1.52 ! [B2: $tType,A: $tType,F: A > B2,G: A > B2] :
% 2.84/1.52 ( ! [X5: A] :
% 2.84/1.52 ( ( F @ X5 )
% 2.84/1.52 = ( G @ X5 ) )
% 2.84/1.52 => ( F = G ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_49_tauOutputTrans,axiom,
% 2.84/1.52 ! [P: pi,A2: name,B: name,P2: pi] :
% 2.84/1.52 ~ ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ ( late_OutputR @ A2 @ B ) @ P2 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_50_transitions_OComm2,axiom,
% 2.84/1.52 ! [P: pi,A2: name,B: name,P2: pi,Q: pi,X3: name,Q2: pi] :
% 2.84/1.52 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A2 @ B ) @ P2 ) )
% 2.84/1.52 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ Q2 ) )
% 2.84/1.52 => ( ( fresh @ name @ pi @ X3 @ P )
% 2.84/1.52 => ( ( fresh @ name @ pi @ X3 @ Q )
% 2.84/1.52 => ( ( X3 != A2 )
% 2.84/1.52 => ( ( X3 != B )
% 2.84/1.52 => ( ( fresh @ name @ pi @ X3 @ P2 )
% 2.84/1.52 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P2 @ ( subs @ Q2 @ X3 @ B ) ) ) ) ) ) ) ) ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_51_transitions_OComm1,axiom,
% 2.84/1.52 ! [P: pi,A2: name,X3: name,P2: pi,Q: pi,B: name,Q2: pi] :
% 2.84/1.52 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ P2 ) )
% 2.84/1.52 => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A2 @ B ) @ Q2 ) )
% 2.84/1.52 => ( ( fresh @ name @ pi @ X3 @ P )
% 2.84/1.52 => ( ( fresh @ name @ pi @ X3 @ Q )
% 2.84/1.52 => ( ( X3 != A2 )
% 2.84/1.52 => ( ( X3 != B )
% 2.84/1.52 => ( ( fresh @ name @ pi @ X3 @ Q2 )
% 2.84/1.52 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P2 @ X3 @ B ) @ Q2 ) ) ) ) ) ) ) ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_52_freshFreeDerivative_I2_J,axiom,
% 2.84/1.52 ! [P: pi,Alpha: late_freeRes,P2: pi,Y: name] :
% 2.84/1.52 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 2.84/1.52 => ( ( fresh @ name @ pi @ Y @ P )
% 2.84/1.52 => ( fresh @ name @ pi @ Y @ P2 ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_53_Late__Semantics_OComm2,axiom,
% 2.84/1.52 ! [P: pi,A2: name,B: name,P2: pi,Q: pi,X3: name,Q2: pi] :
% 2.84/1.52 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A2 @ B ) @ P2 ) )
% 2.84/1.52 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ Q2 ) )
% 2.84/1.52 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P2 @ ( subs @ Q2 @ X3 @ B ) ) ) ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_54_Late__Semantics_OComm1,axiom,
% 2.84/1.52 ! [P: pi,A2: name,X3: name,P2: pi,Q: pi,B: name,Q2: pi] :
% 2.84/1.52 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ P2 ) )
% 2.84/1.52 => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A2 @ B ) @ Q2 ) )
% 2.84/1.52 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P2 @ X3 @ B ) @ Q2 ) ) ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_55_Tau,axiom,
% 2.84/1.52 ! [P: pi] : ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ late_TauR @ P ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_56_Late__Semantics1_Osubject_Oinject_I1_J,axiom,
% 2.84/1.52 ! [X1: name,Y1: name] :
% 2.84/1.52 ( ( ( late_InputS @ X1 )
% 2.84/1.52 = ( late_InputS @ Y1 ) )
% 2.84/1.52 = ( X1 = Y1 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_57_Late__Semantics1_OfreeRes_Oinject,axiom,
% 2.84/1.52 ! [X11: name,X12: name,Y11: name,Y12: name] :
% 2.84/1.52 ( ( ( late_OutputR @ X11 @ X12 )
% 2.84/1.52 = ( late_OutputR @ Y11 @ Y12 ) )
% 2.84/1.52 = ( ( X11 = Y11 )
% 2.84/1.52 & ( X12 = Y12 ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_58_freeRes_Oexhaust,axiom,
% 2.84/1.52 ! [Y: late_freeRes] :
% 2.84/1.52 ( ! [X112: name,X122: name] :
% 2.84/1.52 ( Y
% 2.84/1.52 != ( late_OutputR @ X112 @ X122 ) )
% 2.84/1.52 => ( Y = late_TauR ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_59_Late__Semantics1_OfreeRes_Odistinct_I1_J,axiom,
% 2.84/1.52 ! [X11: name,X12: name] :
% 2.84/1.52 ( ( late_OutputR @ X11 @ X12 )
% 2.84/1.52 != late_TauR ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_60_freeRes_Orecs_I2_J,axiom,
% 2.84/1.52 ! [T: $tType,P: T > $o,F1: name > name > T,F2: T] :
% 2.84/1.52 ( ! [X13: name,X22: name] : ( P @ ( F1 @ X13 @ X22 ) )
% 2.84/1.52 => ( ( P @ F2 )
% 2.84/1.52 => ( ( late_freeRes_rec @ T @ F1 @ F2 @ late_TauR )
% 2.84/1.52 = F2 ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_61_subject_Orecs_I1_J,axiom,
% 2.84/1.52 ! [T: $tType,P: T > $o,F1: name > T,F2: name > T,Name2: name] :
% 2.84/1.52 ( ! [X13: name] : ( P @ ( F1 @ X13 ) )
% 2.84/1.52 => ( ! [X13: name] : ( P @ ( F2 @ X13 ) )
% 2.84/1.52 => ( ( late_subject_rec @ T @ F1 @ F2 @ ( late_InputS @ Name2 ) )
% 2.84/1.52 = ( F1 @ Name2 ) ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_62_freeRes_Orecs_I1_J,axiom,
% 2.84/1.52 ! [T: $tType,P: T > $o,F1: name > name > T,F2: T,Name12: name,Name23: name] :
% 2.84/1.52 ( ! [X13: name,X22: name] : ( P @ ( F1 @ X13 @ X22 ) )
% 2.84/1.52 => ( ( P @ F2 )
% 2.84/1.52 => ( ( late_freeRes_rec @ T @ F1 @ F2 @ ( late_OutputR @ Name12 @ Name23 ) )
% 2.84/1.52 = ( F1 @ Name12 @ Name23 ) ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_63_transitions_OClose2,axiom,
% 2.84/1.52 ! [P: pi,A2: name,Y: name,P2: pi,Q: pi,X3: name,Q2: pi] :
% 2.84/1.52 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y @ P2 ) )
% 2.84/1.52 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ Q2 ) )
% 2.84/1.52 => ( ( fresh @ name @ pi @ X3 @ P )
% 2.84/1.52 => ( ( fresh @ name @ pi @ X3 @ Q )
% 2.84/1.52 => ( ( fresh @ name @ pi @ Y @ P )
% 2.84/1.52 => ( ( fresh @ name @ pi @ Y @ Q )
% 2.84/1.52 => ( ( X3 != A2 )
% 2.84/1.52 => ( ( fresh @ name @ pi @ X3 @ P2 )
% 2.84/1.52 => ( ( Y != A2 )
% 2.84/1.52 => ( ( fresh @ name @ pi @ Y @ Q2 )
% 2.84/1.52 => ( ( X3 != Y )
% 2.84/1.52 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ P2 @ ( subs @ Q2 @ X3 @ Y ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_64_transitions_OClose1,axiom,
% 2.84/1.52 ! [P: pi,A2: name,X3: name,P2: pi,Q: pi,Y: name,Q2: pi] :
% 2.84/1.52 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ P2 ) )
% 2.84/1.52 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y @ Q2 ) )
% 2.84/1.52 => ( ( fresh @ name @ pi @ X3 @ P )
% 2.84/1.52 => ( ( fresh @ name @ pi @ X3 @ Q )
% 2.84/1.52 => ( ( fresh @ name @ pi @ Y @ P )
% 2.84/1.52 => ( ( fresh @ name @ pi @ Y @ Q )
% 2.84/1.52 => ( ( X3 != A2 )
% 2.84/1.52 => ( ( fresh @ name @ pi @ X3 @ Q2 )
% 2.84/1.52 => ( ( Y != A2 )
% 2.84/1.52 => ( ( fresh @ name @ pi @ Y @ P2 )
% 2.84/1.52 => ( ( X3 != Y )
% 2.84/1.52 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ ( subs @ P2 @ X3 @ Y ) @ Q2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_65_Late__Semantics_OClose2,axiom,
% 2.84/1.52 ! [P: pi,A2: name,Y: name,P2: pi,Q: pi,X3: name,Q2: pi] :
% 2.84/1.52 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y @ P2 ) )
% 2.84/1.52 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ Q2 ) )
% 2.84/1.52 => ( ( fresh @ name @ pi @ Y @ Q )
% 2.84/1.52 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ P2 @ ( subs @ Q2 @ X3 @ Y ) ) ) ) ) ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_66_freeRes_Ofresh_I1_J,axiom,
% 2.84/1.52 ! [A2: name,X2: name,X1: name] :
% 2.84/1.52 ( ( fresh @ name @ late_freeRes @ A2 @ ( late_OutputR @ X2 @ X1 ) )
% 2.84/1.52 = ( ( fresh @ name @ name @ A2 @ X2 )
% 2.84/1.52 & ( fresh @ name @ name @ A2 @ X1 ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_67_Late__Semantics_Osubject_Oinject_I2_J,axiom,
% 2.84/1.52 ! [X1: name,Y1: name] :
% 2.84/1.52 ( ( ( late_BoundOutputS @ X1 )
% 2.84/1.52 = ( late_BoundOutputS @ Y1 ) )
% 2.84/1.52 = ( X1 = Y1 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_68_Late__Semantics1_Osubject_Oinject_I2_J,axiom,
% 2.84/1.52 ! [X2: name,Y2: name] :
% 2.84/1.52 ( ( ( late_BoundOutputS @ X2 )
% 2.84/1.52 = ( late_BoundOutputS @ Y2 ) )
% 2.84/1.52 = ( X2 = Y2 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_69_freeRes_Ofresh_I2_J,axiom,
% 2.84/1.52 ! [A2: name] : ( fresh @ name @ late_freeRes @ A2 @ late_TauR ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_70_residual_Ofresh_I2_J,axiom,
% 2.84/1.52 ! [A2: name,X2: late_freeRes,X1: pi] :
% 2.84/1.52 ( ( fresh @ name @ late_residual @ A2 @ ( late_FreeR @ X2 @ X1 ) )
% 2.84/1.52 = ( ( fresh @ name @ late_freeRes @ A2 @ X2 )
% 2.84/1.52 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_71_simps_I9_J,axiom,
% 2.84/1.52 ! [X3: name,C: name,D: name,P: pi] :
% 2.84/1.52 ( ( X3 != C )
% 2.84/1.52 => ( ( X3 != D )
% 2.84/1.52 => ( ( subs @ ( res @ X3 @ P ) @ C @ D )
% 2.84/1.52 = ( res @ X3 @ ( subs @ P @ C @ D ) ) ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_72_subject_Ofresh_I1_J,axiom,
% 2.84/1.52 ! [A2: name,X1: name] :
% 2.84/1.52 ( ( fresh @ name @ late_subject @ A2 @ ( late_InputS @ X1 ) )
% 2.84/1.52 = ( fresh @ name @ name @ A2 @ X1 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_73_subject_Ofresh_I2_J,axiom,
% 2.84/1.52 ! [A2: name,X1: name] :
% 2.84/1.52 ( ( fresh @ name @ late_subject @ A2 @ ( late_BoundOutputS @ X1 ) )
% 2.84/1.52 = ( fresh @ name @ name @ A2 @ X1 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_74_subject_Orecs_I2_J,axiom,
% 2.84/1.52 ! [T: $tType,P: T > $o,F1: name > T,F2: name > T,Name2: name] :
% 2.84/1.52 ( ! [X13: name] : ( P @ ( F1 @ X13 ) )
% 2.84/1.52 => ( ! [X13: name] : ( P @ ( F2 @ X13 ) )
% 2.84/1.52 => ( ( late_subject_rec @ T @ F1 @ F2 @ ( late_BoundOutputS @ Name2 ) )
% 2.84/1.52 = ( F2 @ Name2 ) ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_75_subject_Oexhaust,axiom,
% 2.84/1.52 ! [Y: late_subject] :
% 2.84/1.52 ( ! [X13: name] :
% 2.84/1.52 ( Y
% 2.84/1.52 != ( late_InputS @ X13 ) )
% 2.84/1.52 => ~ ! [X22: name] :
% 2.84/1.52 ( Y
% 2.84/1.52 != ( late_BoundOutputS @ X22 ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_76_Late__Semantics1_Osubject_Odistinct_I1_J,axiom,
% 2.84/1.52 ! [X1: name,X2: name] :
% 2.84/1.52 ( ( late_InputS @ X1 )
% 2.84/1.52 != ( late_BoundOutputS @ X2 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_77_Late__Semantics_OResB,axiom,
% 2.84/1.52 ! [P: pi,A2: late_subject,X3: name,P2: pi,Y: name] :
% 2.84/1.52 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X3 @ P2 ) )
% 2.84/1.52 => ( ( fresh @ name @ late_subject @ Y @ A2 )
% 2.84/1.52 => ( ( Y != X3 )
% 2.84/1.52 => ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A2 @ X3 @ ( res @ Y @ P2 ) ) ) ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_78_resCasesF,axiom,
% 2.84/1.52 ! [X3: name,P: pi,Alpha: late_freeRes,XP: pi,F3: pi > $o] :
% 2.84/1.52 ( ( late_transitions @ ( res @ X3 @ P ) @ ( late_FreeR @ Alpha @ XP ) )
% 2.84/1.52 => ( ! [P4: pi] :
% 2.84/1.52 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P4 ) )
% 2.84/1.52 => ( ( fresh @ name @ late_freeRes @ X3 @ Alpha )
% 2.84/1.52 => ( F3 @ ( res @ X3 @ P4 ) ) ) )
% 2.84/1.52 => ( F3 @ XP ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_79_resCasesF_H,axiom,
% 2.84/1.52 ! [X3: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 2.84/1.52 ( ( late_transitions @ ( res @ X3 @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 2.84/1.52 => ~ ! [P3: pi,Alpha2: late_freeRes,P4: pi,Y3: name] :
% 2.84/1.52 ( ( ( res @ X3 @ P )
% 2.84/1.52 = ( res @ Y3 @ P3 ) )
% 2.84/1.52 => ( ( ( late_FreeR @ Alpha @ P2 )
% 2.84/1.52 = ( late_FreeR @ Alpha2 @ ( res @ Y3 @ P4 ) ) )
% 2.84/1.52 => ( ( late_transitions @ P3 @ ( late_FreeR @ Alpha2 @ P4 ) )
% 2.84/1.52 => ~ ( fresh @ name @ late_freeRes @ Y3 @ Alpha2 ) ) ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_80_ResF,axiom,
% 2.84/1.52 ! [P: pi,Alpha: late_freeRes,P2: pi,Y: name] :
% 2.84/1.52 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 2.84/1.52 => ( ( fresh @ name @ late_freeRes @ Y @ Alpha )
% 2.84/1.52 => ( late_transitions @ ( res @ Y @ P ) @ ( late_FreeR @ Alpha @ ( res @ Y @ P2 ) ) ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_81_pi_Odistinct_I85_J,axiom,
% 2.84/1.52 ! [Pi12: pi,Pi23: pi,Name3: name,Pi3: pi] :
% 2.84/1.52 ( ( par @ Pi12 @ Pi23 )
% 2.84/1.52 != ( res @ Name3 @ Pi3 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_82_freshRes,axiom,
% 2.84/1.52 ! [A2: name,P: pi] : ( fresh @ name @ pi @ A2 @ ( res @ A2 @ P ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_83_pi_Odistinct_I45_J,axiom,
% 2.84/1.52 ! [Pi2: pi,Name3: name,Pi3: pi] :
% 2.84/1.52 ( ( tau @ Pi2 )
% 2.84/1.52 != ( res @ Name3 @ Pi3 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_84_resCases_H,axiom,
% 2.84/1.52 ! [X3: name,P: pi,Rs: late_residual] :
% 2.84/1.52 ( ( late_transitions @ ( res @ X3 @ P ) @ Rs )
% 2.84/1.52 => ( ! [P3: pi,A4: name,B3: name] :
% 2.84/1.52 ( ( ( res @ X3 @ P )
% 2.84/1.52 = ( res @ B3 @ P3 ) )
% 2.84/1.52 => ! [P4: pi] :
% 2.84/1.52 ( ( Rs
% 2.84/1.52 = ( late_BoundR @ ( late_BoundOutputS @ A4 ) @ B3 @ P4 ) )
% 2.84/1.52 => ( ( late_transitions @ P3 @ ( late_FreeR @ ( late_OutputR @ A4 @ B3 ) @ P4 ) )
% 2.84/1.52 => ( A4 = B3 ) ) ) )
% 2.84/1.52 => ( ! [P3: pi,A4: late_subject,X5: name,P4: pi,Y3: name] :
% 2.84/1.52 ( ( ( res @ X3 @ P )
% 2.84/1.52 = ( res @ Y3 @ P3 ) )
% 2.84/1.52 => ( ( Rs
% 2.84/1.52 = ( late_BoundR @ A4 @ X5 @ ( res @ Y3 @ P4 ) ) )
% 2.84/1.52 => ( ( late_transitions @ P3 @ ( late_BoundR @ A4 @ X5 @ P4 ) )
% 2.84/1.52 => ( ( fresh @ name @ late_subject @ Y3 @ A4 )
% 2.84/1.52 => ( ( Y3 != X5 )
% 2.84/1.52 => ( ( fresh @ name @ pi @ X5 @ P3 )
% 2.84/1.52 => ~ ( fresh @ name @ late_subject @ X5 @ A4 ) ) ) ) ) ) )
% 2.84/1.52 => ~ ! [P3: pi,Alpha2: late_freeRes,P4: pi,Y3: name] :
% 2.84/1.52 ( ( ( res @ X3 @ P )
% 2.84/1.52 = ( res @ Y3 @ P3 ) )
% 2.84/1.52 => ( ( Rs
% 2.84/1.52 = ( late_FreeR @ Alpha2 @ ( res @ Y3 @ P4 ) ) )
% 2.84/1.52 => ( ( late_transitions @ P3 @ ( late_FreeR @ Alpha2 @ P4 ) )
% 2.84/1.52 => ~ ( fresh @ name @ late_freeRes @ Y3 @ Alpha2 ) ) ) ) ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_85_transitions_OResB,axiom,
% 2.84/1.52 ! [P: pi,A2: late_subject,X3: name,P2: pi,Y: name] :
% 2.84/1.52 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X3 @ P2 ) )
% 2.84/1.52 => ( ( fresh @ name @ late_subject @ Y @ A2 )
% 2.84/1.52 => ( ( Y != X3 )
% 2.84/1.52 => ( ( fresh @ name @ pi @ X3 @ P )
% 2.84/1.52 => ( ( fresh @ name @ late_subject @ X3 @ A2 )
% 2.84/1.52 => ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A2 @ X3 @ ( res @ Y @ P2 ) ) ) ) ) ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_86_subject_Ostrong__inducts,axiom,
% 2.84/1.52 ! [A: $tType,P: A > late_subject > $o,Z: A,Subject2: late_subject] :
% 2.84/1.52 ( ! [Name: name,Z2: A] : ( P @ Z2 @ ( late_InputS @ Name ) )
% 2.84/1.52 => ( ! [Name: name,Z2: A] : ( P @ Z2 @ ( late_BoundOutputS @ Name ) )
% 2.84/1.52 => ( P @ Z @ Subject2 ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_87_subject_Ostrong__induct_H,axiom,
% 2.84/1.52 ! [N: $tType,P: N > late_subject > $o,Z: N,Subject2: late_subject] :
% 2.84/1.52 ( ! [Name: name,Z2: N] : ( P @ Z2 @ ( late_InputS @ Name ) )
% 2.84/1.52 => ( ! [Name: name,Z2: N] : ( P @ Z2 @ ( late_BoundOutputS @ Name ) )
% 2.84/1.52 => ( P @ Z @ Subject2 ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_88_subject_Oinducts,axiom,
% 2.84/1.52 ! [P: late_subject > $o,Subject2: late_subject] :
% 2.84/1.52 ( ! [Name: name] : ( P @ ( late_InputS @ Name ) )
% 2.84/1.52 => ( ! [Name: name] : ( P @ ( late_BoundOutputS @ Name ) )
% 2.84/1.52 => ( P @ Subject2 ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_89_Late__Semantics_Osubject_Odistinct_I1_J,axiom,
% 2.84/1.52 ! [Name2: name,Name3: name] :
% 2.84/1.52 ( ( late_InputS @ Name2 )
% 2.84/1.52 != ( late_BoundOutputS @ Name3 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_90_resCasesB_H,axiom,
% 2.84/1.52 ! [X6: name,P: pi,A2: late_subject,Y4: name,P2: pi] :
% 2.84/1.52 ( ( late_transitions @ ( res @ X6 @ P ) @ ( late_BoundR @ A2 @ Y4 @ P2 ) )
% 2.84/1.52 => ( ! [P3: pi,A4: name,B3: name] :
% 2.84/1.52 ( ( ( res @ X6 @ P )
% 2.84/1.52 = ( res @ B3 @ P3 ) )
% 2.84/1.52 => ! [P4: pi] :
% 2.84/1.52 ( ( ( late_BoundR @ A2 @ Y4 @ P2 )
% 2.84/1.52 = ( late_BoundR @ ( late_BoundOutputS @ A4 ) @ B3 @ P4 ) )
% 2.84/1.52 => ( ( late_transitions @ P3 @ ( late_FreeR @ ( late_OutputR @ A4 @ B3 ) @ P4 ) )
% 2.84/1.52 => ( A4 = B3 ) ) ) )
% 2.84/1.52 => ~ ! [P3: pi,A4: late_subject,X5: name,P4: pi,Y3: name] :
% 2.84/1.52 ( ( ( res @ X6 @ P )
% 2.84/1.52 = ( res @ Y3 @ P3 ) )
% 2.84/1.52 => ( ( ( late_BoundR @ A2 @ Y4 @ P2 )
% 2.84/1.52 = ( late_BoundR @ A4 @ X5 @ ( res @ Y3 @ P4 ) ) )
% 2.84/1.52 => ( ( late_transitions @ P3 @ ( late_BoundR @ A4 @ X5 @ P4 ) )
% 2.84/1.52 => ( ( fresh @ name @ late_subject @ Y3 @ A4 )
% 2.84/1.52 => ( ( Y3 != X5 )
% 2.84/1.52 => ( ( fresh @ name @ pi @ X5 @ P3 )
% 2.84/1.52 => ~ ( fresh @ name @ late_subject @ X5 @ A4 ) ) ) ) ) ) ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_91_freshResidual,axiom,
% 2.84/1.52 ! [P: pi,Rs: late_residual,X3: name] :
% 2.84/1.52 ( ( late_transitions @ P @ Rs )
% 2.84/1.52 => ( ( fresh @ name @ pi @ X3 @ P )
% 2.84/1.52 => ( fresh @ name @ late_residual @ X3 @ Rs ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_92_substRes3,axiom,
% 2.84/1.52 ! [B: name,P: pi,A2: name] :
% 2.84/1.52 ( ( fresh @ name @ pi @ B @ P )
% 2.84/1.52 => ( ( subs @ ( res @ A2 @ P ) @ A2 @ B )
% 2.84/1.52 = ( res @ B @ ( subs @ P @ A2 @ B ) ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_93_substRes2,axiom,
% 2.84/1.52 ! [B: name,P: pi,A2: name] :
% 2.84/1.52 ( ( fresh @ name @ pi @ B @ P )
% 2.84/1.52 => ( ( res @ A2 @ P )
% 2.84/1.52 = ( res @ B @ ( subs @ P @ A2 @ B ) ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_94_Open,axiom,
% 2.84/1.52 ! [P: pi,A2: name,B: name,P2: pi] :
% 2.84/1.52 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A2 @ B ) @ P2 ) )
% 2.84/1.52 => ( ( A2 != B )
% 2.84/1.52 => ( late_transitions @ ( res @ B @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ B @ P2 ) ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_95_freshFreeDerivative_I1_J,axiom,
% 2.84/1.52 ! [P: pi,Alpha: late_freeRes,P2: pi,Y: name] :
% 2.84/1.52 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 2.84/1.52 => ( ( fresh @ name @ pi @ Y @ P )
% 2.84/1.52 => ( fresh @ name @ late_freeRes @ Y @ Alpha ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_96_freshBoundDerivative_I1_J,axiom,
% 2.84/1.52 ! [P: pi,A2: late_subject,X3: name,P2: pi,Y: name] :
% 2.84/1.52 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X3 @ P2 ) )
% 2.84/1.52 => ( ( fresh @ name @ pi @ Y @ P )
% 2.84/1.52 => ( fresh @ name @ late_subject @ Y @ A2 ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_97_resTauBoundTrans,axiom,
% 2.84/1.52 ! [X3: name,P: pi,A2: late_subject,Y: name,P2: pi] :
% 2.84/1.52 ~ ( late_transitions @ ( res @ X3 @ ( tau @ P ) ) @ ( late_BoundR @ A2 @ Y @ P2 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_98_parCasesB_H,axiom,
% 2.84/1.52 ! [P: pi,Q: pi,B: late_subject,Y: name,P2: pi] :
% 2.84/1.52 ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ B @ Y @ P2 ) )
% 2.84/1.52 => ( ! [P3: pi,A4: late_subject,X5: name,P4: pi,Q4: pi] :
% 2.84/1.52 ( ( ( par @ P @ Q )
% 2.84/1.52 = ( par @ P3 @ Q4 ) )
% 2.84/1.52 => ( ( ( late_BoundR @ B @ Y @ P2 )
% 2.84/1.52 = ( late_BoundR @ A4 @ X5 @ ( par @ P4 @ Q4 ) ) )
% 2.84/1.52 => ( ( late_transitions @ P3 @ ( late_BoundR @ A4 @ X5 @ P4 ) )
% 2.84/1.52 => ( ( fresh @ name @ pi @ X5 @ P3 )
% 2.84/1.52 => ( ( fresh @ name @ pi @ X5 @ Q4 )
% 2.84/1.52 => ~ ( fresh @ name @ late_subject @ X5 @ A4 ) ) ) ) ) )
% 2.84/1.52 => ~ ! [Q4: pi,A4: late_subject,X5: name,Q3: pi,P3: pi] :
% 2.84/1.52 ( ( ( par @ P @ Q )
% 2.84/1.52 = ( par @ P3 @ Q4 ) )
% 2.84/1.52 => ( ( ( late_BoundR @ B @ Y @ P2 )
% 2.84/1.52 = ( late_BoundR @ A4 @ X5 @ ( par @ P3 @ Q3 ) ) )
% 2.84/1.52 => ( ( late_transitions @ Q4 @ ( late_BoundR @ A4 @ X5 @ Q3 ) )
% 2.84/1.52 => ( ( fresh @ name @ pi @ X5 @ P3 )
% 2.84/1.52 => ( ( fresh @ name @ pi @ X5 @ Q4 )
% 2.84/1.52 => ~ ( fresh @ name @ late_subject @ X5 @ A4 ) ) ) ) ) ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_99_transitions_OPar1B,axiom,
% 2.84/1.52 ! [P: pi,A2: late_subject,X3: name,P2: pi,Q: pi] :
% 2.84/1.52 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X3 @ P2 ) )
% 2.84/1.52 => ( ( fresh @ name @ pi @ X3 @ P )
% 2.84/1.52 => ( ( fresh @ name @ pi @ X3 @ Q )
% 2.84/1.52 => ( ( fresh @ name @ late_subject @ X3 @ A2 )
% 2.84/1.52 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X3 @ ( par @ P2 @ Q ) ) ) ) ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_100_transitions_OPar2B,axiom,
% 2.84/1.52 ! [Q: pi,A2: late_subject,X3: name,Q2: pi,P: pi] :
% 2.84/1.52 ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X3 @ Q2 ) )
% 2.84/1.52 => ( ( fresh @ name @ pi @ X3 @ P )
% 2.84/1.52 => ( ( fresh @ name @ pi @ X3 @ Q )
% 2.84/1.52 => ( ( fresh @ name @ late_subject @ X3 @ A2 )
% 2.84/1.52 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X3 @ ( par @ P @ Q2 ) ) ) ) ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_101_resTauOutputTrans,axiom,
% 2.84/1.52 ! [X3: name,P: pi,A2: name,B: name,P2: pi] :
% 2.84/1.52 ~ ( late_transitions @ ( res @ X3 @ ( tau @ P ) ) @ ( late_FreeR @ ( late_OutputR @ A2 @ B ) @ P2 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_102_Late__Semantics_OClose1,axiom,
% 2.84/1.52 ! [P: pi,A2: name,X3: name,P2: pi,Q: pi,Y: name,Q2: pi] :
% 2.84/1.52 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ P2 ) )
% 2.84/1.52 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y @ Q2 ) )
% 2.84/1.52 => ( ( fresh @ name @ pi @ Y @ P )
% 2.84/1.52 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ ( subs @ P2 @ X3 @ Y ) @ Q2 ) ) ) ) ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_103_resOutputTauTrans,axiom,
% 2.84/1.52 ! [X3: name,A2: name,B: name,P: pi,P2: pi] :
% 2.84/1.52 ~ ( late_transitions @ ( res @ X3 @ ( output @ A2 @ B @ P ) ) @ ( late_FreeR @ late_TauR @ P2 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_104_resOutputInputTrans,axiom,
% 2.84/1.52 ! [X3: name,A2: name,B: name,P: pi,C: name,Y: name,P2: pi] :
% 2.84/1.52 ~ ( late_transitions @ ( res @ X3 @ ( output @ A2 @ B @ P ) ) @ ( late_BoundR @ ( late_InputS @ C ) @ Y @ P2 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_105_resOutputOutputTrans,axiom,
% 2.84/1.52 ! [X3: name,A2: name,P: pi,B: name,Y: name,P2: pi] :
% 2.84/1.52 ~ ( late_transitions @ ( res @ X3 @ ( output @ A2 @ X3 @ P ) ) @ ( late_FreeR @ ( late_OutputR @ B @ Y ) @ P2 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_106_resInputBoundOutputTrans,axiom,
% 2.84/1.52 ! [X3: name,A2: name,Y: name,P: pi,B: name,Z: name,P2: pi] :
% 2.84/1.52 ~ ( late_transitions @ ( res @ X3 @ ( input @ A2 @ Y @ P ) ) @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ Z @ P2 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_107_outputTauTrans,axiom,
% 2.84/1.52 ! [A2: name,B: name,P: pi,P2: pi] :
% 2.84/1.52 ~ ( late_transitions @ ( output @ A2 @ B @ P ) @ ( late_FreeR @ late_TauR @ P2 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_108_outputCases,axiom,
% 2.84/1.52 ! [A2: name,B: name,P: pi,Alpha: late_freeRes,P2: pi,Prop: late_freeRes > pi > $o] :
% 2.84/1.52 ( ( late_transitions @ ( output @ A2 @ B @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 2.84/1.52 => ( ( ( Alpha
% 2.84/1.52 = ( late_OutputR @ A2 @ B ) )
% 2.84/1.52 => ( ( P = P2 )
% 2.84/1.52 => ( Prop @ ( late_OutputR @ A2 @ B ) @ P ) ) )
% 2.84/1.52 => ( Prop @ Alpha @ P2 ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_109_outputCases_H,axiom,
% 2.84/1.52 ! [A2: name,B: name,P: pi,Rs: late_residual] :
% 2.84/1.52 ( ( late_transitions @ ( output @ A2 @ B @ P ) @ Rs )
% 2.84/1.52 => ~ ! [A4: name,B3: name,P3: pi] :
% 2.84/1.52 ( ( ( A2 = A4 )
% 2.84/1.52 & ( B = B3 )
% 2.84/1.52 & ( P = P3 ) )
% 2.84/1.52 => ( Rs
% 2.84/1.52 != ( late_FreeR @ ( late_OutputR @ A4 @ B3 ) @ P3 ) ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_110_name__fresh,axiom,
% 2.84/1.52 ( ( fresh @ name @ name )
% 2.84/1.52 = ( ^ [A5: name,B4: name] : ( A5 != B4 ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_111_pi_Ofresh_I2_J,axiom,
% 2.84/1.52 ! [A2: name,X32: name,X2: name,X1: pi] :
% 2.84/1.52 ( ( fresh @ name @ pi @ A2 @ ( output @ X32 @ X2 @ X1 ) )
% 2.84/1.52 = ( ( fresh @ name @ name @ A2 @ X32 )
% 2.84/1.52 & ( fresh @ name @ name @ A2 @ X2 )
% 2.84/1.52 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_112_pi_Odistinct_I21_J,axiom,
% 2.84/1.52 ! [Name12: name,Name23: name,Pi2: pi,Name13: name,Name24: name,Pi3: pi] :
% 2.84/1.52 ( ( output @ Name12 @ Name23 @ Pi2 )
% 2.84/1.52 != ( input @ Name13 @ Name24 @ Pi3 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_113_pi_Oinject_I1_J,axiom,
% 2.84/1.52 ! [X32: name,X2: name,X1: pi,Y32: name,Y2: name,Y1: pi] :
% 2.84/1.52 ( ( ( output @ X32 @ X2 @ X1 )
% 2.84/1.52 = ( output @ Y32 @ Y2 @ Y1 ) )
% 2.84/1.52 = ( ( X32 = Y32 )
% 2.84/1.52 & ( X2 = Y2 )
% 2.84/1.52 & ( X1 = Y1 ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_114_pi_Odistinct_I55_J,axiom,
% 2.84/1.52 ! [Name12: name,Name23: name,Pi2: pi,Pi1: pi,Pi22: pi] :
% 2.84/1.52 ( ( input @ Name12 @ Name23 @ Pi2 )
% 2.84/1.52 != ( par @ Pi1 @ Pi22 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_115_pi_Odistinct_I57_J,axiom,
% 2.84/1.52 ! [Name12: name,Name23: name,Pi2: pi,Name3: name,Pi3: pi] :
% 2.84/1.52 ( ( input @ Name12 @ Name23 @ Pi2 )
% 2.84/1.52 != ( res @ Name3 @ Pi3 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_116_pi_Odistinct_I29_J,axiom,
% 2.84/1.52 ! [Name12: name,Name23: name,Pi2: pi,Pi1: pi,Pi22: pi] :
% 2.84/1.52 ( ( output @ Name12 @ Name23 @ Pi2 )
% 2.84/1.52 != ( par @ Pi1 @ Pi22 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_117_pi_Odistinct_I31_J,axiom,
% 2.84/1.52 ! [Name12: name,Name23: name,Pi2: pi,Name3: name,Pi3: pi] :
% 2.84/1.52 ( ( output @ Name12 @ Name23 @ Pi2 )
% 2.84/1.52 != ( res @ Name3 @ Pi3 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_118_pi_Odistinct_I35_J,axiom,
% 2.84/1.52 ! [Pi2: pi,Name13: name,Name24: name,Pi3: pi] :
% 2.84/1.52 ( ( tau @ Pi2 )
% 2.84/1.52 != ( input @ Name13 @ Name24 @ Pi3 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_119_pi_Odistinct_I19_J,axiom,
% 2.84/1.52 ! [Name12: name,Name23: name,Pi2: pi,Pi3: pi] :
% 2.84/1.52 ( ( output @ Name12 @ Name23 @ Pi2 )
% 2.84/1.52 != ( tau @ Pi3 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_120_resTrans_I2_J,axiom,
% 2.84/1.52 ! [X3: name,Y: name,P: pi,Rs: late_residual] :
% 2.84/1.52 ~ ( late_transitions @ ( res @ X3 @ ( input @ X3 @ Y @ P ) ) @ Rs ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_121_inputFreeTrans,axiom,
% 2.84/1.52 ! [A2: name,X3: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 2.84/1.52 ~ ( late_transitions @ ( input @ A2 @ X3 @ P ) @ ( late_FreeR @ Alpha @ P2 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_122_resTrans_I1_J,axiom,
% 2.84/1.52 ! [X3: name,B: name,P: pi,Rs: late_residual] :
% 2.84/1.52 ~ ( late_transitions @ ( res @ X3 @ ( output @ X3 @ B @ P ) ) @ Rs ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_123_outputBoundTrans,axiom,
% 2.84/1.52 ! [A2: name,B: name,P: pi,C: late_subject,X3: name,P2: pi] :
% 2.84/1.52 ~ ( late_transitions @ ( output @ A2 @ B @ P ) @ ( late_BoundR @ C @ X3 @ P2 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_124_outputFreshTrans,axiom,
% 2.84/1.52 ! [A2: name,B: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 2.84/1.52 ( ( late_transitions @ ( output @ A2 @ B @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 2.84/1.52 => ~ ( ( fresh @ name @ late_freeRes @ A2 @ Alpha )
% 2.84/1.52 | ( fresh @ name @ late_freeRes @ B @ Alpha ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_125_resInputFreeTrans,axiom,
% 2.84/1.52 ! [X3: name,A2: name,Y: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 2.84/1.52 ~ ( late_transitions @ ( res @ X3 @ ( input @ A2 @ Y @ P ) ) @ ( late_FreeR @ Alpha @ P2 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_126_Late__Semantics_OInput,axiom,
% 2.84/1.52 ! [A2: name,X3: name,P: pi] : ( late_transitions @ ( input @ A2 @ X3 @ P ) @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ P ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_127_transitions_OInput,axiom,
% 2.84/1.52 ! [X3: name,A2: name,P: pi] :
% 2.84/1.52 ( ( X3 != A2 )
% 2.84/1.52 => ( late_transitions @ ( input @ A2 @ X3 @ P ) @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ P ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_128_inputBoundOutputTrans,axiom,
% 2.84/1.52 ! [A2: name,X3: name,P: pi,B: name,Y: name,P2: pi] :
% 2.84/1.52 ~ ( late_transitions @ ( input @ A2 @ X3 @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ Y @ P2 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_129_inputIneqTrans,axiom,
% 2.84/1.52 ! [A2: name,X3: name,P: pi,B: late_subject,Y: name,P2: pi] :
% 2.84/1.52 ( ( late_transitions @ ( input @ A2 @ X3 @ P ) @ ( late_BoundR @ B @ Y @ P2 ) )
% 2.84/1.52 => ~ ( fresh @ name @ late_subject @ A2 @ B ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_130_Output,axiom,
% 2.84/1.52 ! [A2: name,B: name,P: pi] : ( late_transitions @ ( output @ A2 @ B @ P ) @ ( late_FreeR @ ( late_OutputR @ A2 @ B ) @ P ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_131_outputIneqTrans,axiom,
% 2.84/1.52 ! [A2: name,B: name,P: pi,C: name,D: name,P2: pi] :
% 2.84/1.52 ( ( late_transitions @ ( output @ A2 @ B @ P ) @ ( late_FreeR @ ( late_OutputR @ C @ D ) @ P2 ) )
% 2.84/1.52 => ~ ( ( A2 != C )
% 2.84/1.52 | ( B != D ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_132_residual_Ofresh_I1_J,axiom,
% 2.84/1.52 ! [A2: name,X32: late_subject,X1: name,X2: pi] :
% 2.84/1.52 ( ( fresh @ name @ late_residual @ A2 @ ( late_BoundR @ X32 @ X1 @ X2 ) )
% 2.84/1.52 = ( ( fresh @ name @ late_subject @ A2 @ X32 )
% 2.84/1.52 & ( fresh @ name @ ( name > ( noption @ pi ) ) @ A2 @ ( abs_fun @ name @ pi @ X1 @ X2 ) ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_133_simps_I3_J,axiom,
% 2.84/1.52 ! [A2: name,B: name,P: pi,C: name,D: name] :
% 2.84/1.52 ( ( subs @ ( output @ A2 @ B @ P ) @ C @ D )
% 2.84/1.52 = ( output @ ( subst_name @ A2 @ C @ D ) @ ( subst_name @ B @ C @ D ) @ ( subs @ P @ C @ D ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_134_substInput,axiom,
% 2.84/1.52 ! [X3: name,B: name,C: name,A2: name,P: pi] :
% 2.84/1.52 ( ( X3 != B )
% 2.84/1.52 => ( ( X3 != C )
% 2.84/1.52 => ( ( subs @ ( input @ A2 @ X3 @ P ) @ B @ C )
% 2.84/1.52 = ( input @ ( subst_name @ A2 @ B @ C ) @ X3 @ ( subs @ P @ B @ C ) ) ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_135_simps_I4_J,axiom,
% 2.84/1.52 ! [X3: name,A2: name,C: name,D: name,P: pi] :
% 2.84/1.52 ( ( X3 != A2 )
% 2.84/1.52 => ( ( X3 != C )
% 2.84/1.52 => ( ( X3 != D )
% 2.84/1.52 => ( ( subs @ ( input @ A2 @ X3 @ P ) @ C @ D )
% 2.84/1.52 = ( input @ ( subst_name @ A2 @ C @ D ) @ X3 @ ( subs @ P @ C @ D ) ) ) ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_136_inputCases_H,axiom,
% 2.84/1.52 ! [A2: name,B: name,P: pi,Rs: late_residual] :
% 2.84/1.52 ( ( late_transitions @ ( input @ A2 @ B @ P ) @ Rs )
% 2.84/1.52 => ~ ! [X5: name,A4: name,P3: pi] :
% 2.84/1.52 ( ( ( A2 = A4 )
% 2.84/1.52 & ( ( abs_fun @ name @ pi @ B @ P )
% 2.84/1.52 = ( abs_fun @ name @ pi @ X5 @ P3 ) ) )
% 2.84/1.52 => ( ( Rs
% 2.84/1.52 = ( late_BoundR @ ( late_InputS @ A4 ) @ X5 @ P3 ) )
% 2.84/1.52 => ( X5 = A4 ) ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_137_pi_Ofresh_I9_J,axiom,
% 2.84/1.52 ! [A2: name,X1: name,X2: pi] :
% 2.84/1.52 ( ( fresh @ name @ pi @ A2 @ ( res @ X1 @ X2 ) )
% 2.84/1.52 = ( fresh @ name @ ( name > ( noption @ pi ) ) @ A2 @ ( abs_fun @ name @ pi @ X1 @ X2 ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_138_pi_Ofresh_I4_J,axiom,
% 2.84/1.52 ! [A2: name,X32: name,X1: name,X2: pi] :
% 2.84/1.52 ( ( fresh @ name @ pi @ A2 @ ( input @ X32 @ X1 @ X2 ) )
% 2.84/1.52 = ( ( fresh @ name @ name @ A2 @ X32 )
% 2.84/1.52 & ( fresh @ name @ ( name > ( noption @ pi ) ) @ A2 @ ( abs_fun @ name @ pi @ X1 @ X2 ) ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_139_pi_Oinject_I8_J,axiom,
% 2.84/1.52 ! [X1: name,X2: pi,Y1: name,Y2: pi] :
% 2.84/1.52 ( ( ( res @ X1 @ X2 )
% 2.84/1.52 = ( res @ Y1 @ Y2 ) )
% 2.84/1.52 = ( ( abs_fun @ name @ pi @ X1 @ X2 )
% 2.84/1.52 = ( abs_fun @ name @ pi @ Y1 @ Y2 ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_140_residual_Oinject_I1_J,axiom,
% 2.84/1.52 ! [X32: late_subject,X1: name,X2: pi,Y32: late_subject,Y1: name,Y2: pi] :
% 2.84/1.52 ( ( ( late_BoundR @ X32 @ X1 @ X2 )
% 2.84/1.52 = ( late_BoundR @ Y32 @ Y1 @ Y2 ) )
% 2.84/1.52 = ( ( X32 = Y32 )
% 2.84/1.52 & ( ( abs_fun @ name @ pi @ X1 @ X2 )
% 2.84/1.52 = ( abs_fun @ name @ pi @ Y1 @ Y2 ) ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_141_subst__name__def,axiom,
% 2.84/1.52 ( subst_name
% 2.84/1.52 = ( ^ [A5: name,B4: name,C3: name] : ( if @ name @ ( A5 = B4 ) @ C3 @ A5 ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_142_name__fresh__abs,axiom,
% 2.84/1.52 ! [A: $tType] :
% 2.84/1.52 ( ( fs_name @ A )
% 2.84/1.52 => ! [B: name,A2: name,X3: A] :
% 2.84/1.52 ( ( fresh @ name @ ( name > ( noption @ A ) ) @ B @ ( abs_fun @ name @ A @ A2 @ X3 ) )
% 2.84/1.52 = ( ( B = A2 )
% 2.84/1.52 | ( fresh @ name @ A @ B @ X3 ) ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_143_abs__fresh_I1_J,axiom,
% 2.84/1.52 ! [X7: $tType] :
% 2.84/1.52 ( ( fs_name @ X7 )
% 2.84/1.52 => ! [B: name,A2: name,X3: X7] :
% 2.84/1.52 ( ( fresh @ name @ ( name > ( noption @ X7 ) ) @ B @ ( abs_fun @ name @ X7 @ A2 @ X3 ) )
% 2.84/1.52 = ( ( B = A2 )
% 2.84/1.52 | ( fresh @ name @ X7 @ B @ X3 ) ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_144_pi_Oinject_I3_J,axiom,
% 2.84/1.52 ! [X32: name,X1: name,X2: pi,Y32: name,Y1: name,Y2: pi] :
% 2.84/1.52 ( ( ( input @ X32 @ X1 @ X2 )
% 2.84/1.52 = ( input @ Y32 @ Y1 @ Y2 ) )
% 2.84/1.52 = ( ( X32 = Y32 )
% 2.84/1.52 & ( ( abs_fun @ name @ pi @ X1 @ X2 )
% 2.84/1.52 = ( abs_fun @ name @ pi @ Y1 @ Y2 ) ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_145_simps_I5_J,axiom,
% 2.84/1.52 ! [A2: name,B: name,P: pi,C: name,D: name] :
% 2.84/1.52 ( ( subs @ ( match @ A2 @ B @ P ) @ C @ D )
% 2.84/1.52 = ( match @ ( subst_name @ A2 @ C @ D ) @ ( subst_name @ B @ C @ D ) @ ( subs @ P @ C @ D ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_146_simps_I6_J,axiom,
% 2.84/1.52 ! [A2: name,B: name,P: pi,C: name,D: name] :
% 2.84/1.52 ( ( subs @ ( mismatch @ A2 @ B @ P ) @ C @ D )
% 2.84/1.52 = ( mismatch @ ( subst_name @ A2 @ C @ D ) @ ( subst_name @ B @ C @ D ) @ ( subs @ P @ C @ D ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_147_pi_Ofresh_I5_J,axiom,
% 2.84/1.52 ! [A2: name,X32: name,X2: name,X1: pi] :
% 2.84/1.52 ( ( fresh @ name @ pi @ A2 @ ( match @ X32 @ X2 @ X1 ) )
% 2.84/1.52 = ( ( fresh @ name @ name @ A2 @ X32 )
% 2.84/1.52 & ( fresh @ name @ name @ A2 @ X2 )
% 2.84/1.52 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_148_pi_Ofresh_I6_J,axiom,
% 2.84/1.52 ! [A2: name,X32: name,X2: name,X1: pi] :
% 2.84/1.52 ( ( fresh @ name @ pi @ A2 @ ( mismatch @ X32 @ X2 @ X1 ) )
% 2.84/1.52 = ( ( fresh @ name @ name @ A2 @ X32 )
% 2.84/1.52 & ( fresh @ name @ name @ A2 @ X2 )
% 2.84/1.52 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_149_matchCases,axiom,
% 2.84/1.52 ! [A2: name,B: name,P: pi,Rs: late_residual,F3: name > name > $o] :
% 2.84/1.52 ( ( late_transitions @ ( match @ A2 @ B @ P ) @ Rs )
% 2.84/1.52 => ( ( ( late_transitions @ P @ Rs )
% 2.84/1.52 => ( ( A2 = B )
% 2.84/1.52 => ( F3 @ A2 @ A2 ) ) )
% 2.84/1.52 => ( F3 @ A2 @ B ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_150_matchTrans,axiom,
% 2.84/1.52 ! [A2: name,B: name,P: pi,Rs: late_residual] :
% 2.84/1.52 ( ( late_transitions @ ( match @ A2 @ B @ P ) @ Rs )
% 2.84/1.52 => ( A2 = B ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_151_matchCases_H,axiom,
% 2.84/1.52 ! [A2: name,B: name,P: pi,Rs: late_residual] :
% 2.84/1.52 ( ( late_transitions @ ( match @ A2 @ B @ P ) @ Rs )
% 2.84/1.52 => ~ ! [P3: pi] :
% 2.84/1.52 ( ( ( B = A2 )
% 2.84/1.52 & ( P = P3 ) )
% 2.84/1.52 => ~ ( late_transitions @ P3 @ Rs ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_152_mismatchCases,axiom,
% 2.84/1.52 ! [A2: name,B: name,P: pi,Rs: late_residual,F3: name > name > $o] :
% 2.84/1.52 ( ( late_transitions @ ( mismatch @ A2 @ B @ P ) @ Rs )
% 2.84/1.52 => ( ( ( late_transitions @ P @ Rs )
% 2.84/1.52 => ( ( A2 != B )
% 2.84/1.52 => ( F3 @ A2 @ B ) ) )
% 2.84/1.52 => ( F3 @ A2 @ B ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_153_mismatchTrans,axiom,
% 2.84/1.52 ! [A2: name,P: pi,Rs: late_residual] :
% 2.84/1.52 ~ ( late_transitions @ ( mismatch @ A2 @ A2 @ P ) @ Rs ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_154_mismatchCases_H,axiom,
% 2.84/1.52 ! [A2: name,B: name,P: pi,Rs: late_residual] :
% 2.84/1.52 ( ( late_transitions @ ( mismatch @ A2 @ B @ P ) @ Rs )
% 2.84/1.52 => ~ ! [P3: pi,A4: name,B3: name] :
% 2.84/1.52 ( ( ( A2 = A4 )
% 2.84/1.52 & ( B = B3 )
% 2.84/1.52 & ( P = P3 ) )
% 2.84/1.52 => ( ( late_transitions @ P3 @ Rs )
% 2.84/1.52 => ( A4 = B3 ) ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_155_Match,axiom,
% 2.84/1.52 ! [P: pi,Rs: late_residual,B: name] :
% 2.84/1.52 ( ( late_transitions @ P @ Rs )
% 2.84/1.52 => ( late_transitions @ ( match @ B @ B @ P ) @ Rs ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_156_Mismatch,axiom,
% 2.84/1.52 ! [P: pi,Rs: late_residual,A2: name,B: name] :
% 2.84/1.52 ( ( late_transitions @ P @ Rs )
% 2.84/1.52 => ( ( A2 != B )
% 2.84/1.52 => ( late_transitions @ ( mismatch @ A2 @ B @ P ) @ Rs ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_157_pi_Odistinct_I73_J,axiom,
% 2.84/1.52 ! [Name12: name,Name23: name,Pi2: pi,Pi1: pi,Pi22: pi] :
% 2.84/1.52 ( ( mismatch @ Name12 @ Name23 @ Pi2 )
% 2.84/1.52 != ( par @ Pi1 @ Pi22 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_158_pi_Odistinct_I65_J,axiom,
% 2.84/1.52 ! [Name12: name,Name23: name,Pi2: pi,Pi1: pi,Pi22: pi] :
% 2.84/1.52 ( ( match @ Name12 @ Name23 @ Pi2 )
% 2.84/1.52 != ( par @ Pi1 @ Pi22 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_159_pi_Odistinct_I75_J,axiom,
% 2.84/1.52 ! [Name12: name,Name23: name,Pi2: pi,Name3: name,Pi3: pi] :
% 2.84/1.52 ( ( mismatch @ Name12 @ Name23 @ Pi2 )
% 2.84/1.52 != ( res @ Name3 @ Pi3 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_160_pi_Odistinct_I67_J,axiom,
% 2.84/1.52 ! [Name12: name,Name23: name,Pi2: pi,Name3: name,Pi3: pi] :
% 2.84/1.52 ( ( match @ Name12 @ Name23 @ Pi2 )
% 2.84/1.52 != ( res @ Name3 @ Pi3 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_161_pi_Odistinct_I61_J,axiom,
% 2.84/1.52 ! [Name12: name,Name23: name,Pi2: pi,Name13: name,Name24: name,Pi3: pi] :
% 2.84/1.52 ( ( match @ Name12 @ Name23 @ Pi2 )
% 2.84/1.52 != ( mismatch @ Name13 @ Name24 @ Pi3 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_162_pi_Oinject_I4_J,axiom,
% 2.84/1.52 ! [X32: name,X2: name,X1: pi,Y32: name,Y2: name,Y1: pi] :
% 2.84/1.52 ( ( ( match @ X32 @ X2 @ X1 )
% 2.84/1.52 = ( match @ Y32 @ Y2 @ Y1 ) )
% 2.84/1.52 = ( ( X32 = Y32 )
% 2.84/1.52 & ( X2 = Y2 )
% 2.84/1.52 & ( X1 = Y1 ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_163_pi_Oinject_I5_J,axiom,
% 2.84/1.52 ! [X32: name,X2: name,X1: pi,Y32: name,Y2: name,Y1: pi] :
% 2.84/1.52 ( ( ( mismatch @ X32 @ X2 @ X1 )
% 2.84/1.52 = ( mismatch @ Y32 @ Y2 @ Y1 ) )
% 2.84/1.52 = ( ( X32 = Y32 )
% 2.84/1.52 & ( X2 = Y2 )
% 2.84/1.52 & ( X1 = Y1 ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_164_pi_Odistinct_I49_J,axiom,
% 2.84/1.52 ! [Name12: name,Name23: name,Pi2: pi,Name13: name,Name24: name,Pi3: pi] :
% 2.84/1.52 ( ( input @ Name12 @ Name23 @ Pi2 )
% 2.84/1.52 != ( match @ Name13 @ Name24 @ Pi3 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_165_pi_Odistinct_I51_J,axiom,
% 2.84/1.52 ! [Name12: name,Name23: name,Pi2: pi,Name13: name,Name24: name,Pi3: pi] :
% 2.84/1.52 ( ( input @ Name12 @ Name23 @ Pi2 )
% 2.84/1.52 != ( mismatch @ Name13 @ Name24 @ Pi3 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_166_pi_Odistinct_I23_J,axiom,
% 2.84/1.52 ! [Name12: name,Name23: name,Pi2: pi,Name13: name,Name24: name,Pi3: pi] :
% 2.84/1.52 ( ( output @ Name12 @ Name23 @ Pi2 )
% 2.84/1.52 != ( match @ Name13 @ Name24 @ Pi3 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_167_pi_Odistinct_I25_J,axiom,
% 2.84/1.52 ! [Name12: name,Name23: name,Pi2: pi,Name13: name,Name24: name,Pi3: pi] :
% 2.84/1.52 ( ( output @ Name12 @ Name23 @ Pi2 )
% 2.84/1.52 != ( mismatch @ Name13 @ Name24 @ Pi3 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_168_pi_Odistinct_I39_J,axiom,
% 2.84/1.52 ! [Pi2: pi,Name13: name,Name24: name,Pi3: pi] :
% 2.84/1.52 ( ( tau @ Pi2 )
% 2.84/1.52 != ( mismatch @ Name13 @ Name24 @ Pi3 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_169_pi_Odistinct_I37_J,axiom,
% 2.84/1.52 ! [Pi2: pi,Name13: name,Name24: name,Pi3: pi] :
% 2.84/1.52 ( ( tau @ Pi2 )
% 2.84/1.52 != ( match @ Name13 @ Name24 @ Pi3 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_170_abs__fun__eq1,axiom,
% 2.84/1.52 ! [X: $tType,A: $tType,A2: X,X3: A,Y: A] :
% 2.84/1.52 ( ( ( abs_fun @ X @ A @ A2 @ X3 )
% 2.84/1.52 = ( abs_fun @ X @ A @ A2 @ Y ) )
% 2.84/1.52 = ( X3 = Y ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_171_freeRes_Ocase_I2_J,axiom,
% 2.84/1.52 ! [A: $tType,F1: name > name > A,F2: A] :
% 2.84/1.52 ( ( late_case_freeRes @ A @ F1 @ F2 @ late_TauR )
% 2.84/1.52 = F2 ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_172_subject_Ocase_I2_J,axiom,
% 2.84/1.52 ! [A: $tType,F1: name > A,F2: name > A,X2: name] :
% 2.84/1.52 ( ( late_case_subject @ A @ F1 @ F2 @ ( late_BoundOutputS @ X2 ) )
% 2.84/1.52 = ( F2 @ X2 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_173_freeRes_Ocase_I1_J,axiom,
% 2.84/1.52 ! [A: $tType,F1: name > name > A,F2: A,X11: name,X12: name] :
% 2.84/1.52 ( ( late_case_freeRes @ A @ F1 @ F2 @ ( late_OutputR @ X11 @ X12 ) )
% 2.84/1.52 = ( F1 @ X11 @ X12 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_174_subject_Ocase_I1_J,axiom,
% 2.84/1.52 ! [A: $tType,F1: name > A,F2: name > A,X1: name] :
% 2.84/1.52 ( ( late_case_subject @ A @ F1 @ F2 @ ( late_InputS @ X1 ) )
% 2.84/1.52 = ( F1 @ X1 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_175_pi_Ostrong__inducts,axiom,
% 2.84/1.52 ! [A: $tType] :
% 2.84/1.52 ( ( fs_name @ A )
% 2.84/1.52 => ! [P: A > pi > $o,Z: A,Pi2: pi] :
% 2.84/1.52 ( ! [Z2: A] : ( P @ Z2 @ piNil )
% 2.84/1.52 => ( ! [Name1: name,Name22: name,Pi: pi,Z2: A] :
% 2.84/1.52 ( ! [Za: A] : ( P @ Za @ Pi )
% 2.84/1.52 => ( P @ Z2 @ ( output @ Name1 @ Name22 @ Pi ) ) )
% 2.84/1.52 => ( ! [Pi: pi,Z2: A] :
% 2.84/1.52 ( ! [Za: A] : ( P @ Za @ Pi )
% 2.84/1.52 => ( P @ Z2 @ ( tau @ Pi ) ) )
% 2.84/1.52 => ( ! [Name1: name,Name22: name,Pi: pi,Z2: A] :
% 2.84/1.52 ( ( fresh @ name @ A @ Name22 @ Z2 )
% 2.84/1.52 => ( ( fresh @ name @ name @ Name22 @ Name1 )
% 2.84/1.52 => ( ! [Za: A] : ( P @ Za @ Pi )
% 2.84/1.52 => ( P @ Z2 @ ( input @ Name1 @ Name22 @ Pi ) ) ) ) )
% 2.84/1.52 => ( ! [Name1: name,Name22: name,Pi: pi,Z2: A] :
% 2.84/1.52 ( ! [Za: A] : ( P @ Za @ Pi )
% 2.84/1.52 => ( P @ Z2 @ ( match @ Name1 @ Name22 @ Pi ) ) )
% 2.84/1.52 => ( ! [Name1: name,Name22: name,Pi: pi,Z2: A] :
% 2.84/1.52 ( ! [Za: A] : ( P @ Za @ Pi )
% 2.84/1.52 => ( P @ Z2 @ ( mismatch @ Name1 @ Name22 @ Pi ) ) )
% 2.84/1.52 => ( ! [Pi13: pi,Pi24: pi,Z2: A] :
% 2.84/1.52 ( ! [Za: A] : ( P @ Za @ Pi13 )
% 2.84/1.52 => ( ! [Za: A] : ( P @ Za @ Pi24 )
% 2.84/1.52 => ( P @ Z2 @ ( sum @ Pi13 @ Pi24 ) ) ) )
% 2.84/1.52 => ( ! [Pi13: pi,Pi24: pi,Z2: A] :
% 2.84/1.52 ( ! [Za: A] : ( P @ Za @ Pi13 )
% 2.84/1.52 => ( ! [Za: A] : ( P @ Za @ Pi24 )
% 2.84/1.52 => ( P @ Z2 @ ( par @ Pi13 @ Pi24 ) ) ) )
% 2.84/1.52 => ( ! [Name: name,Pi: pi,Z2: A] :
% 2.84/1.52 ( ( fresh @ name @ A @ Name @ Z2 )
% 2.84/1.52 => ( ! [Za: A] : ( P @ Za @ Pi )
% 2.84/1.52 => ( P @ Z2 @ ( res @ Name @ Pi ) ) ) )
% 2.84/1.52 => ( ! [Pi: pi,Z2: A] :
% 2.84/1.52 ( ! [Za: A] : ( P @ Za @ Pi )
% 2.84/1.52 => ( P @ Z2 @ ( bang @ Pi ) ) )
% 2.84/1.52 => ( P @ Z @ Pi2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_176_pi_Ostrong__induct,axiom,
% 2.84/1.52 ! [N: $tType] :
% 2.84/1.52 ( ( fs_name @ N )
% 2.84/1.52 => ! [P: N > pi > $o,Z: N,Pi2: pi] :
% 2.84/1.52 ( ! [Z2: N] : ( P @ Z2 @ piNil )
% 2.84/1.52 => ( ! [Name1: name,Name22: name,Pi: pi,Z2: N] :
% 2.84/1.52 ( ! [Za: N] : ( P @ Za @ Pi )
% 2.84/1.52 => ( P @ Z2 @ ( output @ Name1 @ Name22 @ Pi ) ) )
% 2.84/1.52 => ( ! [Pi: pi,Z2: N] :
% 2.84/1.52 ( ! [Za: N] : ( P @ Za @ Pi )
% 2.84/1.52 => ( P @ Z2 @ ( tau @ Pi ) ) )
% 2.84/1.52 => ( ! [Name1: name,Name22: name,Pi: pi,Z2: N] :
% 2.84/1.52 ( ( fresh @ name @ N @ Name22 @ Z2 )
% 2.84/1.52 => ( ( fresh @ name @ name @ Name22 @ Name1 )
% 2.84/1.52 => ( ! [Za: N] : ( P @ Za @ Pi )
% 2.84/1.52 => ( P @ Z2 @ ( input @ Name1 @ Name22 @ Pi ) ) ) ) )
% 2.84/1.52 => ( ! [Name1: name,Name22: name,Pi: pi,Z2: N] :
% 2.84/1.52 ( ! [Za: N] : ( P @ Za @ Pi )
% 2.84/1.52 => ( P @ Z2 @ ( match @ Name1 @ Name22 @ Pi ) ) )
% 2.84/1.52 => ( ! [Name1: name,Name22: name,Pi: pi,Z2: N] :
% 2.84/1.52 ( ! [Za: N] : ( P @ Za @ Pi )
% 2.84/1.52 => ( P @ Z2 @ ( mismatch @ Name1 @ Name22 @ Pi ) ) )
% 2.84/1.52 => ( ! [Pi13: pi,Pi24: pi,Z2: N] :
% 2.84/1.52 ( ! [Za: N] : ( P @ Za @ Pi13 )
% 2.84/1.52 => ( ! [Za: N] : ( P @ Za @ Pi24 )
% 2.84/1.52 => ( P @ Z2 @ ( sum @ Pi13 @ Pi24 ) ) ) )
% 2.84/1.52 => ( ! [Pi13: pi,Pi24: pi,Z2: N] :
% 2.84/1.52 ( ! [Za: N] : ( P @ Za @ Pi13 )
% 2.84/1.52 => ( ! [Za: N] : ( P @ Za @ Pi24 )
% 2.84/1.52 => ( P @ Z2 @ ( par @ Pi13 @ Pi24 ) ) ) )
% 2.84/1.52 => ( ! [Name: name,Pi: pi,Z2: N] :
% 2.84/1.52 ( ( fresh @ name @ N @ Name @ Z2 )
% 2.84/1.52 => ( ! [Za: N] : ( P @ Za @ Pi )
% 2.84/1.52 => ( P @ Z2 @ ( res @ Name @ Pi ) ) ) )
% 2.84/1.52 => ( ! [Pi: pi,Z2: N] :
% 2.84/1.52 ( ! [Za: N] : ( P @ Za @ Pi )
% 2.84/1.52 => ( P @ Z2 @ ( bang @ Pi ) ) )
% 2.84/1.52 => ( P @ Z @ Pi2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_177_residual_Ostrong__induct_H,axiom,
% 2.84/1.52 ! [N: $tType,F: N > ( set @ name ),P: N > late_residual > $o,Z: N,Residual: late_residual] :
% 2.84/1.52 ( ! [X5: N] : ( finite_finite @ name @ ( F @ X5 ) )
% 2.84/1.52 => ( ! [Subject: late_subject,Name: name,Pi: pi,Z2: N] :
% 2.84/1.52 ( ~ ( member @ name @ Name @ ( F @ Z2 ) )
% 2.84/1.52 => ( ( fresh @ name @ late_subject @ Name @ Subject )
% 2.84/1.52 => ( P @ Z2 @ ( late_BoundR @ Subject @ Name @ Pi ) ) ) )
% 2.84/1.52 => ( ! [FreeRes: late_freeRes,Pi: pi,Z2: N] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi ) )
% 2.84/1.52 => ( P @ Z @ Residual ) ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_178_pi_Ofresh_I10_J,axiom,
% 2.84/1.52 ! [A2: name,X1: pi] :
% 2.84/1.52 ( ( fresh @ name @ pi @ A2 @ ( bang @ X1 ) )
% 2.84/1.52 = ( fresh @ name @ pi @ A2 @ X1 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_179_pi_Ofresh_I7_J,axiom,
% 2.84/1.52 ! [A2: name,X2: pi,X1: pi] :
% 2.84/1.52 ( ( fresh @ name @ pi @ A2 @ ( sum @ X2 @ X1 ) )
% 2.84/1.52 = ( ( fresh @ name @ pi @ A2 @ X2 )
% 2.84/1.52 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_180_simps_I10_J,axiom,
% 2.84/1.52 ! [P: pi,C: name,D: name] :
% 2.84/1.52 ( ( subs @ ( bang @ P ) @ C @ D )
% 2.84/1.52 = ( bang @ ( subs @ P @ C @ D ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_181_pi_Ofresh_I1_J,axiom,
% 2.84/1.52 ! [A2: name] : ( fresh @ name @ pi @ A2 @ piNil ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_182_simps_I7_J,axiom,
% 2.84/1.52 ! [P: pi,Q: pi,C: name,D: name] :
% 2.84/1.52 ( ( subs @ ( sum @ P @ Q ) @ C @ D )
% 2.84/1.52 = ( sum @ ( subs @ P @ C @ D ) @ ( subs @ Q @ C @ D ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_183_simps_I1_J,axiom,
% 2.84/1.52 ! [C: name,D: name] :
% 2.84/1.52 ( ( subs @ piNil @ C @ D )
% 2.84/1.52 = piNil ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_184_pi_Odistinct_I59_J,axiom,
% 2.84/1.52 ! [Name12: name,Name23: name,Pi2: pi,Pi3: pi] :
% 2.84/1.52 ( ( input @ Name12 @ Name23 @ Pi2 )
% 2.84/1.52 != ( bang @ Pi3 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_185_pi_Odistinct_I33_J,axiom,
% 2.84/1.52 ! [Name12: name,Name23: name,Pi2: pi,Pi3: pi] :
% 2.84/1.52 ( ( output @ Name12 @ Name23 @ Pi2 )
% 2.84/1.52 != ( bang @ Pi3 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_186_sumCases,axiom,
% 2.84/1.52 ! [P: pi,Q: pi,Rs: late_residual] :
% 2.84/1.52 ( ( late_transitions @ ( sum @ P @ Q ) @ Rs )
% 2.84/1.52 => ( ~ ( late_transitions @ P @ Rs )
% 2.84/1.52 => ( late_transitions @ Q @ Rs ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_187_sumCases_H,axiom,
% 2.84/1.52 ! [P: pi,Q: pi,Rs: late_residual] :
% 2.84/1.52 ( ( late_transitions @ ( sum @ P @ Q ) @ Rs )
% 2.84/1.52 => ( ~ ( late_transitions @ P @ Rs )
% 2.84/1.52 => ( late_transitions @ Q @ Rs ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_188_Sum1,axiom,
% 2.84/1.52 ! [P: pi,Rs: late_residual,Q: pi] :
% 2.84/1.52 ( ( late_transitions @ P @ Rs )
% 2.84/1.52 => ( late_transitions @ ( sum @ P @ Q ) @ Rs ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_189_Sum2,axiom,
% 2.84/1.52 ! [Q: pi,Rs: late_residual,P: pi] :
% 2.84/1.52 ( ( late_transitions @ Q @ Rs )
% 2.84/1.52 => ( late_transitions @ ( sum @ P @ Q ) @ Rs ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_190_pi_Odistinct_I47_J,axiom,
% 2.84/1.52 ! [Pi2: pi,Pi3: pi] :
% 2.84/1.52 ( ( tau @ Pi2 )
% 2.84/1.52 != ( bang @ Pi3 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_191_pi_Odistinct_I79_J,axiom,
% 2.84/1.52 ! [Pi12: pi,Pi23: pi,Pi1: pi,Pi22: pi] :
% 2.84/1.52 ( ( sum @ Pi12 @ Pi23 )
% 2.84/1.52 != ( par @ Pi1 @ Pi22 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_192_pi_Odistinct_I81_J,axiom,
% 2.84/1.52 ! [Pi12: pi,Pi23: pi,Name3: name,Pi3: pi] :
% 2.84/1.52 ( ( sum @ Pi12 @ Pi23 )
% 2.84/1.52 != ( res @ Name3 @ Pi3 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_193_pi_Odistinct_I53_J,axiom,
% 2.84/1.52 ! [Name12: name,Name23: name,Pi2: pi,Pi1: pi,Pi22: pi] :
% 2.84/1.52 ( ( input @ Name12 @ Name23 @ Pi2 )
% 2.84/1.52 != ( sum @ Pi1 @ Pi22 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_194_pi_Odistinct_I27_J,axiom,
% 2.84/1.52 ! [Name12: name,Name23: name,Pi2: pi,Pi1: pi,Pi22: pi] :
% 2.84/1.52 ( ( output @ Name12 @ Name23 @ Pi2 )
% 2.84/1.52 != ( sum @ Pi1 @ Pi22 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_195_pi_Odistinct_I41_J,axiom,
% 2.84/1.52 ! [Pi2: pi,Pi1: pi,Pi22: pi] :
% 2.84/1.52 ( ( tau @ Pi2 )
% 2.84/1.52 != ( sum @ Pi1 @ Pi22 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_196_nilCases_H,axiom,
% 2.84/1.52 ! [Rs: late_residual] :
% 2.84/1.52 ~ ( late_transitions @ piNil @ Rs ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_197_zeroTrans,axiom,
% 2.84/1.52 ! [Rs: late_residual] :
% 2.84/1.52 ~ ( late_transitions @ piNil @ Rs ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_198_pi_Odistinct_I13_J,axiom,
% 2.84/1.52 ! [Pi1: pi,Pi22: pi] :
% 2.84/1.52 ( piNil
% 2.84/1.52 != ( par @ Pi1 @ Pi22 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_199_pi_Odistinct_I15_J,axiom,
% 2.84/1.52 ! [Name3: name,Pi3: pi] :
% 2.84/1.52 ( piNil
% 2.84/1.52 != ( res @ Name3 @ Pi3 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_200_pi_Odistinct_I11_J,axiom,
% 2.84/1.52 ! [Pi1: pi,Pi22: pi] :
% 2.84/1.52 ( piNil
% 2.84/1.52 != ( sum @ Pi1 @ Pi22 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_201_pi_Odistinct_I17_J,axiom,
% 2.84/1.52 ! [Pi3: pi] :
% 2.84/1.52 ( piNil
% 2.84/1.52 != ( bang @ Pi3 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_202_pi_Odistinct_I83_J,axiom,
% 2.84/1.52 ! [Pi12: pi,Pi23: pi,Pi3: pi] :
% 2.84/1.52 ( ( sum @ Pi12 @ Pi23 )
% 2.84/1.52 != ( bang @ Pi3 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_203_pi_Oinject_I6_J,axiom,
% 2.84/1.52 ! [X2: pi,X1: pi,Y2: pi,Y1: pi] :
% 2.84/1.52 ( ( ( sum @ X2 @ X1 )
% 2.84/1.52 = ( sum @ Y2 @ Y1 ) )
% 2.84/1.52 = ( ( X2 = Y2 )
% 2.84/1.52 & ( X1 = Y1 ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_204_pi_Oinject_I9_J,axiom,
% 2.84/1.52 ! [X1: pi,Y1: pi] :
% 2.84/1.52 ( ( ( bang @ X1 )
% 2.84/1.52 = ( bang @ Y1 ) )
% 2.84/1.52 = ( X1 = Y1 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_205_pi_Odistinct_I89_J,axiom,
% 2.84/1.52 ! [Name2: name,Pi2: pi,Pi3: pi] :
% 2.84/1.52 ( ( res @ Name2 @ Pi2 )
% 2.84/1.52 != ( bang @ Pi3 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_206_pi_Odistinct_I87_J,axiom,
% 2.84/1.52 ! [Pi12: pi,Pi23: pi,Pi3: pi] :
% 2.84/1.52 ( ( par @ Pi12 @ Pi23 )
% 2.84/1.52 != ( bang @ Pi3 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_207_pi_Odistinct_I3_J,axiom,
% 2.84/1.52 ! [Pi3: pi] :
% 2.84/1.52 ( piNil
% 2.84/1.52 != ( tau @ Pi3 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_208_pi_Odistinct_I1_J,axiom,
% 2.84/1.52 ! [Name13: name,Name24: name,Pi3: pi] :
% 2.84/1.52 ( piNil
% 2.84/1.52 != ( output @ Name13 @ Name24 @ Pi3 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_209_pi_Odistinct_I5_J,axiom,
% 2.84/1.52 ! [Name13: name,Name24: name,Pi3: pi] :
% 2.84/1.52 ( piNil
% 2.84/1.52 != ( input @ Name13 @ Name24 @ Pi3 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_210_pi_Odistinct_I77_J,axiom,
% 2.84/1.52 ! [Name12: name,Name23: name,Pi2: pi,Pi3: pi] :
% 2.84/1.52 ( ( mismatch @ Name12 @ Name23 @ Pi2 )
% 2.84/1.52 != ( bang @ Pi3 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_211_pi_Odistinct_I71_J,axiom,
% 2.84/1.52 ! [Name12: name,Name23: name,Pi2: pi,Pi1: pi,Pi22: pi] :
% 2.84/1.52 ( ( mismatch @ Name12 @ Name23 @ Pi2 )
% 2.84/1.52 != ( sum @ Pi1 @ Pi22 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_212_pi_Odistinct_I69_J,axiom,
% 2.84/1.52 ! [Name12: name,Name23: name,Pi2: pi,Pi3: pi] :
% 2.84/1.52 ( ( match @ Name12 @ Name23 @ Pi2 )
% 2.84/1.52 != ( bang @ Pi3 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_213_pi_Odistinct_I63_J,axiom,
% 2.84/1.52 ! [Name12: name,Name23: name,Pi2: pi,Pi1: pi,Pi22: pi] :
% 2.84/1.52 ( ( match @ Name12 @ Name23 @ Pi2 )
% 2.84/1.52 != ( sum @ Pi1 @ Pi22 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_214_pi_Odistinct_I9_J,axiom,
% 2.84/1.52 ! [Name13: name,Name24: name,Pi3: pi] :
% 2.84/1.52 ( piNil
% 2.84/1.52 != ( mismatch @ Name13 @ Name24 @ Pi3 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_215_pi_Odistinct_I7_J,axiom,
% 2.84/1.52 ! [Name13: name,Name24: name,Pi3: pi] :
% 2.84/1.52 ( piNil
% 2.84/1.52 != ( match @ Name13 @ Name24 @ Pi3 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_216_Bang,axiom,
% 2.84/1.52 ! [P: pi,Rs: late_residual] :
% 2.84/1.52 ( ( late_transitions @ ( par @ P @ ( bang @ P ) ) @ Rs )
% 2.84/1.52 => ( late_transitions @ ( bang @ P ) @ Rs ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_217_bangCases,axiom,
% 2.84/1.52 ! [P: pi,Rs: late_residual] :
% 2.84/1.52 ( ( late_transitions @ ( bang @ P ) @ Rs )
% 2.84/1.52 => ~ ! [P3: pi] :
% 2.84/1.52 ( ( ( bang @ P )
% 2.84/1.52 = ( bang @ P3 ) )
% 2.84/1.52 => ~ ( late_transitions @ ( par @ P3 @ ( bang @ P3 ) ) @ Rs ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_218_pi_Ostrong__induct_H,axiom,
% 2.84/1.52 ! [N: $tType,F: N > ( set @ name ),P: N > pi > $o,Z: N,Pi2: pi] :
% 2.84/1.52 ( ! [X5: N] : ( finite_finite @ name @ ( F @ X5 ) )
% 2.84/1.52 => ( ! [Z2: N] : ( P @ Z2 @ piNil )
% 2.84/1.52 => ( ! [Name1: name,Name22: name,Pi: pi,Z2: N] :
% 2.84/1.52 ( ! [Za: N] : ( P @ Za @ Pi )
% 2.84/1.52 => ( P @ Z2 @ ( output @ Name1 @ Name22 @ Pi ) ) )
% 2.84/1.52 => ( ! [Pi: pi,Z2: N] :
% 2.84/1.52 ( ! [Za: N] : ( P @ Za @ Pi )
% 2.84/1.52 => ( P @ Z2 @ ( tau @ Pi ) ) )
% 2.84/1.52 => ( ! [Name1: name,Name22: name,Pi: pi,Z2: N] :
% 2.84/1.52 ( ~ ( member @ name @ Name22 @ ( F @ Z2 ) )
% 2.84/1.52 => ( ( fresh @ name @ name @ Name22 @ Name1 )
% 2.84/1.52 => ( ! [Za: N] : ( P @ Za @ Pi )
% 2.84/1.52 => ( P @ Z2 @ ( input @ Name1 @ Name22 @ Pi ) ) ) ) )
% 2.84/1.52 => ( ! [Name1: name,Name22: name,Pi: pi,Z2: N] :
% 2.84/1.52 ( ! [Za: N] : ( P @ Za @ Pi )
% 2.84/1.52 => ( P @ Z2 @ ( match @ Name1 @ Name22 @ Pi ) ) )
% 2.84/1.52 => ( ! [Name1: name,Name22: name,Pi: pi,Z2: N] :
% 2.84/1.52 ( ! [Za: N] : ( P @ Za @ Pi )
% 2.84/1.52 => ( P @ Z2 @ ( mismatch @ Name1 @ Name22 @ Pi ) ) )
% 2.84/1.52 => ( ! [Pi13: pi,Pi24: pi,Z2: N] :
% 2.84/1.52 ( ! [Za: N] : ( P @ Za @ Pi13 )
% 2.84/1.52 => ( ! [Za: N] : ( P @ Za @ Pi24 )
% 2.84/1.52 => ( P @ Z2 @ ( sum @ Pi13 @ Pi24 ) ) ) )
% 2.84/1.52 => ( ! [Pi13: pi,Pi24: pi,Z2: N] :
% 2.84/1.52 ( ! [Za: N] : ( P @ Za @ Pi13 )
% 2.84/1.52 => ( ! [Za: N] : ( P @ Za @ Pi24 )
% 2.84/1.52 => ( P @ Z2 @ ( par @ Pi13 @ Pi24 ) ) ) )
% 2.84/1.52 => ( ! [Name: name,Pi: pi,Z2: N] :
% 2.84/1.52 ( ~ ( member @ name @ Name @ ( F @ Z2 ) )
% 2.84/1.52 => ( ! [Za: N] : ( P @ Za @ Pi )
% 2.84/1.52 => ( P @ Z2 @ ( res @ Name @ Pi ) ) ) )
% 2.84/1.52 => ( ! [Pi: pi,Z2: N] :
% 2.84/1.52 ( ! [Za: N] : ( P @ Za @ Pi )
% 2.84/1.52 => ( P @ Z2 @ ( bang @ Pi ) ) )
% 2.84/1.52 => ( P @ Z @ Pi2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_219_resZeroTrans,axiom,
% 2.84/1.52 ! [X3: name,Rs: late_residual] :
% 2.84/1.52 ~ ( late_transitions @ ( res @ X3 @ piNil ) @ Rs ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_220_pi_Oinducts,axiom,
% 2.84/1.52 ! [P: pi > $o,Pi2: pi] :
% 2.84/1.52 ( ( P @ piNil )
% 2.84/1.52 => ( ! [Name1: name,Name22: name,Pi: pi] :
% 2.84/1.52 ( ( P @ Pi )
% 2.84/1.52 => ( P @ ( output @ Name1 @ Name22 @ Pi ) ) )
% 2.84/1.52 => ( ! [Pi: pi] :
% 2.84/1.52 ( ( P @ Pi )
% 2.84/1.52 => ( P @ ( tau @ Pi ) ) )
% 2.84/1.52 => ( ! [Name1: name,Name22: name,Pi: pi] :
% 2.84/1.52 ( ( P @ Pi )
% 2.84/1.52 => ( P @ ( input @ Name1 @ Name22 @ Pi ) ) )
% 2.84/1.52 => ( ! [Name1: name,Name22: name,Pi: pi] :
% 2.84/1.52 ( ( P @ Pi )
% 2.84/1.52 => ( P @ ( match @ Name1 @ Name22 @ Pi ) ) )
% 2.84/1.52 => ( ! [Name1: name,Name22: name,Pi: pi] :
% 2.84/1.52 ( ( P @ Pi )
% 2.84/1.52 => ( P @ ( mismatch @ Name1 @ Name22 @ Pi ) ) )
% 2.84/1.52 => ( ! [Pi13: pi,Pi24: pi] :
% 2.84/1.52 ( ( P @ Pi13 )
% 2.84/1.52 => ( ( P @ Pi24 )
% 2.84/1.52 => ( P @ ( sum @ Pi13 @ Pi24 ) ) ) )
% 2.84/1.52 => ( ! [Pi13: pi,Pi24: pi] :
% 2.84/1.52 ( ( P @ Pi13 )
% 2.84/1.52 => ( ( P @ Pi24 )
% 2.84/1.52 => ( P @ ( par @ Pi13 @ Pi24 ) ) ) )
% 2.84/1.52 => ( ! [Name: name,Pi: pi] :
% 2.84/1.52 ( ( P @ Pi )
% 2.84/1.52 => ( P @ ( res @ Name @ Pi ) ) )
% 2.84/1.52 => ( ! [Pi: pi] :
% 2.84/1.52 ( ( P @ Pi )
% 2.84/1.52 => ( P @ ( bang @ Pi ) ) )
% 2.84/1.52 => ( P @ Pi2 ) ) ) ) ) ) ) ) ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_221_aux2,axiom,
% 2.84/1.52 ! [P: pi] : ( late_bangPred @ P @ ( par @ P @ ( bang @ P ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_222_bangPred_Ocases,axiom,
% 2.84/1.52 ! [A1: pi,A22: pi] :
% 2.84/1.52 ( ( late_bangPred @ A1 @ A22 )
% 2.84/1.52 => ( ( A22
% 2.84/1.52 != ( bang @ A1 ) )
% 2.84/1.52 => ( A22
% 2.84/1.52 = ( par @ A1 @ ( bang @ A1 ) ) ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_223_bangPred_Osimps,axiom,
% 2.84/1.52 ( late_bangPred
% 2.84/1.52 = ( ^ [A12: pi,A23: pi] :
% 2.84/1.52 ( ? [P5: pi] :
% 2.84/1.52 ( ( A12 = P5 )
% 2.84/1.52 & ( A23
% 2.84/1.52 = ( bang @ P5 ) ) )
% 2.84/1.52 | ? [P5: pi] :
% 2.84/1.52 ( ( A12 = P5 )
% 2.84/1.52 & ( A23
% 2.84/1.52 = ( par @ P5 @ ( bang @ P5 ) ) ) ) ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_224_aux1,axiom,
% 2.84/1.52 ! [P: pi] : ( late_bangPred @ P @ ( bang @ P ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_225_bangPred_Oinducts,axiom,
% 2.84/1.52 ! [X1: pi,X2: pi,P: pi > pi > $o] :
% 2.84/1.52 ( ( late_bangPred @ X1 @ X2 )
% 2.84/1.52 => ( ! [P3: pi] : ( P @ P3 @ ( bang @ P3 ) )
% 2.84/1.52 => ( ! [P3: pi] : ( P @ P3 @ ( par @ P3 @ ( bang @ P3 ) ) )
% 2.84/1.52 => ( P @ X1 @ X2 ) ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_226_subs__def,axiom,
% 2.84/1.52 ( subs
% 2.84/1.52 = ( ^ [X4: pi,C3: name,D2: name] :
% 2.84/1.52 ( pi_rec @ pi @ piNil
% 2.84/1.52 @ ^ [A5: name,B4: name,P5: pi] : ( output @ ( subst_name @ A5 @ C3 @ D2 ) @ ( subst_name @ B4 @ C3 @ D2 ) )
% 2.84/1.52 @ ^ [P5: pi] : tau
% 2.84/1.52 @ ^ [A5: name,Y5: name,P5: pi] : ( input @ ( subst_name @ A5 @ C3 @ D2 ) @ Y5 )
% 2.84/1.52 @ ^ [A5: name,B4: name,P5: pi] : ( match @ ( subst_name @ A5 @ C3 @ D2 ) @ ( subst_name @ B4 @ C3 @ D2 ) )
% 2.84/1.52 @ ^ [A5: name,B4: name,P5: pi] : ( mismatch @ ( subst_name @ A5 @ C3 @ D2 ) @ ( subst_name @ B4 @ C3 @ D2 ) )
% 2.84/1.52 @ ^ [P5: pi,Q5: pi] : sum
% 2.84/1.52 @ ^ [P5: pi,Q5: pi] : par
% 2.84/1.52 @ ^ [Y5: name,P5: pi] : ( res @ Y5 )
% 2.84/1.52 @ ^ [P5: pi] : bang
% 2.84/1.52 @ X4 ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_227_abs__fresh_I2_J,axiom,
% 2.84/1.52 ! [X8: $tType] :
% 2.84/1.52 ( ( pt_name @ X8 )
% 2.84/1.52 => ! [X3: X8,B: name,A2: name] :
% 2.84/1.52 ( ( finite_finite @ name @ ( supp @ X8 @ name @ X3 ) )
% 2.84/1.52 => ( ( fresh @ name @ ( name > ( noption @ X8 ) ) @ B @ ( abs_fun @ name @ X8 @ A2 @ X3 ) )
% 2.84/1.52 = ( ( B = A2 )
% 2.84/1.52 | ( fresh @ name @ X8 @ B @ X3 ) ) ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_228_exists__fresh_H,axiom,
% 2.84/1.52 ! [A: $tType,X3: A] :
% 2.84/1.52 ( ( finite_finite @ name @ ( supp @ A @ name @ X3 ) )
% 2.84/1.52 => ? [C2: name] : ( fresh @ name @ A @ C2 @ X3 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_229_exists__fresh,axiom,
% 2.84/1.52 ! [A: $tType,X3: A] :
% 2.84/1.52 ( ( finite_finite @ name @ ( supp @ A @ name @ X3 ) )
% 2.84/1.52 => ~ ! [C2: name] :
% 2.84/1.52 ~ ( fresh @ name @ A @ C2 @ X3 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_230_supp__fresh__iff,axiom,
% 2.84/1.52 ! [X: $tType,A: $tType] :
% 2.84/1.52 ( ( supp @ A @ X )
% 2.84/1.52 = ( ^ [X4: A] :
% 2.84/1.52 ( collect @ X
% 2.84/1.52 @ ^ [A5: X] :
% 2.84/1.52 ~ ( fresh @ X @ A @ A5 @ X4 ) ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_231_fresh__def,axiom,
% 2.84/1.52 ! [A: $tType,X: $tType] :
% 2.84/1.52 ( ( fresh @ X @ A )
% 2.84/1.52 = ( ^ [A5: X,X4: A] :
% 2.84/1.52 ~ ( member @ X @ A5 @ ( supp @ A @ X @ X4 ) ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_232_pi_Osupp_I9_J,axiom,
% 2.84/1.52 ! [X1: name,X2: pi] :
% 2.84/1.52 ( ( supp @ pi @ name @ ( res @ X1 @ X2 ) )
% 2.84/1.52 = ( supp @ ( name > ( noption @ pi ) ) @ name @ ( abs_fun @ name @ pi @ X1 @ X2 ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_233_freeRes_Ocase__distrib,axiom,
% 2.84/1.52 ! [A: $tType,B2: $tType,H: A > B2,F1: name > name > A,F2: A,FreeRes3: late_freeRes] :
% 2.84/1.52 ( ( H @ ( late_case_freeRes @ A @ F1 @ F2 @ FreeRes3 ) )
% 2.84/1.52 = ( late_case_freeRes @ B2
% 2.84/1.52 @ ^ [X14: name,X23: name] : ( H @ ( F1 @ X14 @ X23 ) )
% 2.84/1.52 @ ( H @ F2 )
% 2.84/1.52 @ FreeRes3 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_234_subject_Ocase__distrib,axiom,
% 2.84/1.52 ! [B2: $tType,A: $tType,H: A > B2,F1: name > A,F2: name > A,Subject2: late_subject] :
% 2.84/1.52 ( ( H @ ( late_case_subject @ A @ F1 @ F2 @ Subject2 ) )
% 2.84/1.52 = ( late_case_subject @ B2
% 2.84/1.52 @ ^ [X4: name] : ( H @ ( F1 @ X4 ) )
% 2.84/1.52 @ ^ [X4: name] : ( H @ ( F2 @ X4 ) )
% 2.84/1.52 @ Subject2 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_235_pi_Osupp_I3_J,axiom,
% 2.84/1.52 ! [X1: pi] :
% 2.84/1.52 ( ( supp @ pi @ name @ ( tau @ X1 ) )
% 2.84/1.52 = ( supp @ pi @ name @ X1 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_236_subject_Osupp_I2_J,axiom,
% 2.84/1.52 ! [X1: name] :
% 2.84/1.52 ( ( supp @ late_subject @ name @ ( late_BoundOutputS @ X1 ) )
% 2.84/1.52 = ( supp @ name @ name @ X1 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_237_subject_Osupp_I1_J,axiom,
% 2.84/1.52 ! [X1: name] :
% 2.84/1.52 ( ( supp @ late_subject @ name @ ( late_InputS @ X1 ) )
% 2.84/1.52 = ( supp @ name @ name @ X1 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_238_pi_Osupp_I10_J,axiom,
% 2.84/1.52 ! [X1: pi] :
% 2.84/1.52 ( ( supp @ pi @ name @ ( bang @ X1 ) )
% 2.84/1.52 = ( supp @ pi @ name @ X1 ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_239_fs__name1,axiom,
% 2.84/1.52 ! [A: $tType] :
% 2.84/1.52 ( ( fs_name @ A )
% 2.84/1.52 => ! [X3: A] : ( finite_finite @ name @ ( supp @ A @ name @ X3 ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_240_residual_Orecs_I2_J,axiom,
% 2.84/1.52 ! [N: $tType,T: $tType] :
% 2.84/1.52 ( ( pt_name @ T )
% 2.84/1.52 => ! [F1: late_subject > name > pi > T,F2: late_freeRes > pi > T,Z: N,P: T > $o,FreeRes3: late_freeRes,Pi2: pi] :
% 2.84/1.52 ( ( finite_finite @ name @ ( supp @ ( late_subject > name > pi > T ) @ name @ F1 ) )
% 2.84/1.52 => ( ( finite_finite @ name @ ( supp @ ( late_freeRes > pi > T ) @ name @ F2 ) )
% 2.84/1.52 => ( ( finite_finite @ name @ ( supp @ N @ name @ Z ) )
% 2.84/1.52 => ( ! [X13: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X13 @ X22 @ X33 ) )
% 2.84/1.52 => ( ! [X13: late_freeRes,X22: pi] : ( P @ ( F2 @ X13 @ X22 ) )
% 2.84/1.52 => ( ! [X13: late_subject,X22: name,X33: pi] :
% 2.84/1.52 ( ( fresh @ name @ ( late_subject > name > pi > T ) @ X22 @ F1 )
% 2.84/1.52 => ( ( fresh @ name @ late_subject @ X22 @ X13 )
% 2.84/1.52 => ( ( fresh @ name @ N @ X22 @ Z )
% 2.84/1.52 => ( ( P @ ( F1 @ X13 @ X22 @ X33 ) )
% 2.84/1.52 => ( fresh @ name @ T @ X22 @ ( F1 @ X13 @ X22 @ X33 ) ) ) ) ) )
% 2.84/1.52 => ( ( late_residual_rec @ T @ F1 @ F2 @ ( late_FreeR @ FreeRes3 @ Pi2 ) )
% 2.84/1.52 = ( F2 @ FreeRes3 @ Pi2 ) ) ) ) ) ) ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_241_residual_Orecs_I1_J,axiom,
% 2.84/1.52 ! [N: $tType,T: $tType] :
% 2.84/1.52 ( ( pt_name @ T )
% 2.84/1.52 => ! [F1: late_subject > name > pi > T,F2: late_freeRes > pi > T,Z: N,P: T > $o,Name2: name,Subject2: late_subject,Pi2: pi] :
% 2.84/1.52 ( ( finite_finite @ name @ ( supp @ ( late_subject > name > pi > T ) @ name @ F1 ) )
% 2.84/1.52 => ( ( finite_finite @ name @ ( supp @ ( late_freeRes > pi > T ) @ name @ F2 ) )
% 2.84/1.52 => ( ( finite_finite @ name @ ( supp @ N @ name @ Z ) )
% 2.84/1.52 => ( ! [X13: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X13 @ X22 @ X33 ) )
% 2.84/1.52 => ( ! [X13: late_freeRes,X22: pi] : ( P @ ( F2 @ X13 @ X22 ) )
% 2.84/1.52 => ( ! [X13: late_subject,X22: name,X33: pi] :
% 2.84/1.52 ( ( fresh @ name @ ( late_subject > name > pi > T ) @ X22 @ F1 )
% 2.84/1.52 => ( ( fresh @ name @ late_subject @ X22 @ X13 )
% 2.84/1.52 => ( ( fresh @ name @ N @ X22 @ Z )
% 2.84/1.52 => ( ( P @ ( F1 @ X13 @ X22 @ X33 ) )
% 2.84/1.52 => ( fresh @ name @ T @ X22 @ ( F1 @ X13 @ X22 @ X33 ) ) ) ) ) )
% 2.84/1.52 => ( ( fresh @ name @ ( late_subject > name > pi > T ) @ Name2 @ F1 )
% 2.84/1.52 => ( ( fresh @ name @ ( late_freeRes > pi > T ) @ Name2 @ F2 )
% 2.84/1.52 => ( ( fresh @ name @ late_subject @ Name2 @ Subject2 )
% 2.84/1.52 => ( ( late_residual_rec @ T @ F1 @ F2 @ ( late_BoundR @ Subject2 @ Name2 @ Pi2 ) )
% 2.84/1.52 = ( F1 @ Subject2 @ Name2 @ Pi2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_242_residual_Orec__fresh,axiom,
% 2.84/1.52 ! [T: $tType] :
% 2.84/1.52 ( ( pt_name @ T )
% 2.84/1.52 => ! [F1: late_subject > name > pi > T,F2: late_freeRes > pi > T,X3: late_residual,Y: T,A2: name] :
% 2.84/1.52 ( ( finite_finite @ name @ ( supp @ ( late_subject > name > pi > T ) @ name @ F1 ) )
% 2.84/1.52 => ( ( finite_finite @ name @ ( supp @ ( late_freeRes > pi > T ) @ name @ F2 ) )
% 2.84/1.52 => ( ( late_r582136743ec_set @ T @ F1 @ F2 @ X3 @ Y )
% 2.84/1.52 => ( ! [Y6: T] :
% 2.84/1.52 ( ( late_r582136743ec_set @ T @ F1 @ F2 @ X3 @ Y6 )
% 2.84/1.52 => ( Y6 = Y ) )
% 2.84/1.52 => ( ( fresh @ name @ late_residual @ A2 @ X3 )
% 2.84/1.52 => ( ( fresh @ name @ ( late_subject > name > pi > T ) @ A2 @ F1 )
% 2.84/1.52 => ( ( fresh @ name @ ( late_freeRes > pi > T ) @ A2 @ F2 )
% 2.84/1.52 => ( fresh @ name @ T @ A2 @ Y ) ) ) ) ) ) ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_243_residual_Orec__unique,axiom,
% 2.84/1.52 ! [N: $tType,T: $tType] :
% 2.84/1.52 ( ( pt_name @ T )
% 2.84/1.52 => ! [F1: late_subject > name > pi > T,F2: late_freeRes > pi > T,Z: N,P: T > $o,X3: late_residual] :
% 2.84/1.52 ( ( finite_finite @ name @ ( supp @ ( late_subject > name > pi > T ) @ name @ F1 ) )
% 2.84/1.52 => ( ( finite_finite @ name @ ( supp @ ( late_freeRes > pi > T ) @ name @ F2 ) )
% 2.84/1.52 => ( ( finite_finite @ name @ ( supp @ N @ name @ Z ) )
% 2.84/1.52 => ( ! [X13: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X13 @ X22 @ X33 ) )
% 2.84/1.52 => ( ! [X13: late_freeRes,X22: pi] : ( P @ ( F2 @ X13 @ X22 ) )
% 2.84/1.52 => ( ! [X13: late_subject,X22: name] :
% 2.84/1.52 ( ( fresh @ name @ ( late_subject > name > pi > T ) @ X22 @ F1 )
% 2.84/1.52 => ( ( fresh @ name @ late_subject @ X22 @ X13 )
% 2.84/1.52 => ( ( fresh @ name @ N @ X22 @ Z )
% 2.84/1.52 => ! [X33: pi] :
% 2.84/1.52 ( ( P @ ( F1 @ X13 @ X22 @ X33 ) )
% 2.84/1.52 => ( fresh @ name @ T @ X22 @ ( F1 @ X13 @ X22 @ X33 ) ) ) ) ) )
% 2.84/1.52 => ? [X5: T] :
% 2.84/1.52 ( ( late_r582136743ec_set @ T @ F1 @ F2 @ X3 @ X5 )
% 2.84/1.52 & ! [Y7: T] :
% 2.84/1.52 ( ( late_r582136743ec_set @ T @ F1 @ F2 @ X3 @ Y7 )
% 2.84/1.52 => ( Y7 = X5 ) ) ) ) ) ) ) ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_244_residual_Orec__fin__supp,axiom,
% 2.84/1.52 ! [T: $tType] :
% 2.84/1.52 ( ( pt_name @ T )
% 2.84/1.52 => ! [F1: late_subject > name > pi > T,F2: late_freeRes > pi > T,X1: late_residual,Y1: T] :
% 2.84/1.52 ( ( finite_finite @ name @ ( supp @ ( late_subject > name > pi > T ) @ name @ F1 ) )
% 2.84/1.52 => ( ( finite_finite @ name @ ( supp @ ( late_freeRes > pi > T ) @ name @ F2 ) )
% 2.84/1.52 => ( ( late_r582136743ec_set @ T @ F1 @ F2 @ X1 @ Y1 )
% 2.84/1.52 => ( finite_finite @ name @ ( supp @ T @ name @ Y1 ) ) ) ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_245_pi_Osupp_I4_J,axiom,
% 2.84/1.52 ! [X32: name,X1: name,X2: pi] :
% 2.84/1.52 ( ( supp @ pi @ name @ ( input @ X32 @ X1 @ X2 ) )
% 2.84/1.52 = ( sup_sup @ ( set @ name ) @ ( supp @ name @ name @ X32 ) @ ( supp @ ( name > ( noption @ pi ) ) @ name @ ( abs_fun @ name @ pi @ X1 @ X2 ) ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_246_residual_Osupp_I1_J,axiom,
% 2.84/1.52 ! [X32: late_subject,X1: name,X2: pi] :
% 2.84/1.52 ( ( supp @ late_residual @ name @ ( late_BoundR @ X32 @ X1 @ X2 ) )
% 2.84/1.52 = ( sup_sup @ ( set @ name ) @ ( supp @ late_subject @ name @ X32 ) @ ( supp @ ( name > ( noption @ pi ) ) @ name @ ( abs_fun @ name @ pi @ X1 @ X2 ) ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_247_pi_Osupp_I7_J,axiom,
% 2.84/1.52 ! [X2: pi,X1: pi] :
% 2.84/1.52 ( ( supp @ pi @ name @ ( sum @ X2 @ X1 ) )
% 2.84/1.52 = ( sup_sup @ ( set @ name ) @ ( supp @ pi @ name @ X2 ) @ ( supp @ pi @ name @ X1 ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_248_pi_Osupp_I8_J,axiom,
% 2.84/1.52 ! [X2: pi,X1: pi] :
% 2.84/1.52 ( ( supp @ pi @ name @ ( par @ X2 @ X1 ) )
% 2.84/1.52 = ( sup_sup @ ( set @ name ) @ ( supp @ pi @ name @ X2 ) @ ( supp @ pi @ name @ X1 ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_249_freeRes_Osupp_I1_J,axiom,
% 2.84/1.52 ! [X2: name,X1: name] :
% 2.84/1.52 ( ( supp @ late_freeRes @ name @ ( late_OutputR @ X2 @ X1 ) )
% 2.84/1.52 = ( sup_sup @ ( set @ name ) @ ( supp @ name @ name @ X2 ) @ ( supp @ name @ name @ X1 ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_250_residual_Osupp_I2_J,axiom,
% 2.84/1.52 ! [X2: late_freeRes,X1: pi] :
% 2.84/1.52 ( ( supp @ late_residual @ name @ ( late_FreeR @ X2 @ X1 ) )
% 2.84/1.52 = ( sup_sup @ ( set @ name ) @ ( supp @ late_freeRes @ name @ X2 ) @ ( supp @ pi @ name @ X1 ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_251_pi_Osupp_I2_J,axiom,
% 2.84/1.52 ! [X32: name,X2: name,X1: pi] :
% 2.84/1.52 ( ( supp @ pi @ name @ ( output @ X32 @ X2 @ X1 ) )
% 2.84/1.52 = ( sup_sup @ ( set @ name ) @ ( supp @ name @ name @ X32 ) @ ( sup_sup @ ( set @ name ) @ ( supp @ name @ name @ X2 ) @ ( supp @ pi @ name @ X1 ) ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_252_pi_Osupp_I6_J,axiom,
% 2.84/1.52 ! [X32: name,X2: name,X1: pi] :
% 2.84/1.52 ( ( supp @ pi @ name @ ( mismatch @ X32 @ X2 @ X1 ) )
% 2.84/1.52 = ( sup_sup @ ( set @ name ) @ ( supp @ name @ name @ X32 ) @ ( sup_sup @ ( set @ name ) @ ( supp @ name @ name @ X2 ) @ ( supp @ pi @ name @ X1 ) ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_253_pi_Osupp_I5_J,axiom,
% 2.84/1.52 ! [X32: name,X2: name,X1: pi] :
% 2.84/1.52 ( ( supp @ pi @ name @ ( match @ X32 @ X2 @ X1 ) )
% 2.84/1.52 = ( sup_sup @ ( set @ name ) @ ( supp @ name @ name @ X32 ) @ ( sup_sup @ ( set @ name ) @ ( supp @ name @ name @ X2 ) @ ( supp @ pi @ name @ X1 ) ) ) ) ).
% 2.84/1.52
% 2.84/1.52 thf(fact_254_pi_Orec__fin__supp,axiom,
% 2.84/1.52 ! [T: $tType] :
% 2.84/1.52 ( ( pt_name @ T )
% 2.84/1.52 => ! [F1: T,F2: name > name > pi > T > T,F32: pi > T > T,F4: name > name > pi > T > T,F5: name > name > pi > T > T,F6: name > name > pi > T > T,F7: pi > pi > T > T > T,F8: pi > pi > T > T > T,F9: name > pi > T > T,F10: pi > T > T,X1: pi,Y1: T] :
% 2.84/1.53 ( ( finite_finite @ name @ ( supp @ T @ name @ F1 ) )
% 2.84/1.53 => ( ( finite_finite @ name @ ( supp @ ( name > name > pi > T > T ) @ name @ F2 ) )
% 2.84/1.53 => ( ( finite_finite @ name @ ( supp @ ( pi > T > T ) @ name @ F32 ) )
% 2.84/1.53 => ( ( finite_finite @ name @ ( supp @ ( name > name > pi > T > T ) @ name @ F4 ) )
% 2.84/1.53 => ( ( finite_finite @ name @ ( supp @ ( name > name > pi > T > T ) @ name @ F5 ) )
% 2.84/1.53 => ( ( finite_finite @ name @ ( supp @ ( name > name > pi > T > T ) @ name @ F6 ) )
% 2.84/1.53 => ( ( finite_finite @ name @ ( supp @ ( pi > pi > T > T > T ) @ name @ F7 ) )
% 2.84/1.53 => ( ( finite_finite @ name @ ( supp @ ( pi > pi > T > T > T ) @ name @ F8 ) )
% 2.84/1.53 => ( ( finite_finite @ name @ ( supp @ ( name > pi > T > T ) @ name @ F9 ) )
% 2.84/1.53 => ( ( finite_finite @ name @ ( supp @ ( pi > T > T ) @ name @ F10 ) )
% 2.84/1.53 => ( ( pi_rec_set @ T @ F1 @ F2 @ F32 @ F4 @ F5 @ F6 @ F7 @ F8 @ F9 @ F10 @ X1 @ Y1 )
% 2.84/1.53 => ( finite_finite @ name @ ( supp @ T @ name @ Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.84/1.53
% 2.84/1.53 thf(fact_255_supports__fresh,axiom,
% 2.84/1.53 ! [X: $tType,A: $tType,S: set @ X,X3: A,A2: X] :
% 2.84/1.53 ( ( supports @ X @ A @ S @ X3 )
% 2.84/1.53 => ( ( finite_finite @ X @ S )
% 2.84/1.53 => ( ~ ( member @ X @ A2 @ S )
% 2.84/1.53 => ( fresh @ X @ A @ A2 @ X3 ) ) ) ) ).
% 2.84/1.53
% 2.84/1.53 thf(tcon_fun___Agent_Opt__name,axiom,
% 2.84/1.53 ! [A6: $tType,A7: $tType] :
% 2.84/1.53 ( ( ( pt_name @ A6 )
% 2.84/1.53 & ( pt_name @ A7 ) )
% 2.84/1.53 => ( pt_name @ ( A6 > A7 ) ) ) ).
% 2.84/1.53
% 2.84/1.53 thf(tcon_Set_Oset___Agent_Opt__name_1,axiom,
% 2.84/1.53 ! [A6: $tType] :
% 2.84/1.53 ( ( pt_name @ A6 )
% 2.84/1.53 => ( pt_name @ ( set @ A6 ) ) ) ).
% 2.84/1.53
% 2.84/1.53 thf(tcon_Agent_Opi___Agent_Opt__name_2,axiom,
% 2.84/1.53 pt_name @ pi ).
% 2.84/1.53
% 2.84/1.53 thf(tcon_Agent_Opi___Agent_Ofs__name,axiom,
% 2.84/1.53 fs_name @ pi ).
% 2.84/1.53
% 2.84/1.53 thf(tcon_HOL_Obool___Agent_Opt__name_3,axiom,
% 2.84/1.53 pt_name @ $o ).
% 2.84/1.53
% 2.84/1.53 thf(tcon_HOL_Obool___Agent_Ofs__name_4,axiom,
% 2.84/1.53 fs_name @ $o ).
% 2.84/1.53
% 2.84/1.53 thf(tcon_Agent_Oname___Agent_Opt__name_5,axiom,
% 2.84/1.53 pt_name @ name ).
% 2.84/1.53
% 2.84/1.53 thf(tcon_Agent_Oname___Agent_Ofs__name_6,axiom,
% 2.84/1.53 fs_name @ name ).
% 2.84/1.53
% 2.84/1.53 thf(tcon_Nominal_Onoption___Agent_Opt__name_7,axiom,
% 2.84/1.53 ! [A6: $tType] :
% 2.84/1.53 ( ( pt_name @ A6 )
% 2.84/1.53 => ( pt_name @ ( noption @ A6 ) ) ) ).
% 2.84/1.53
% 2.84/1.53 thf(tcon_Late__Semantics_OfreeRes___Agent_Opt__name_8,axiom,
% 2.84/1.53 pt_name @ late_freeRes ).
% 2.84/1.53
% 2.84/1.53 thf(tcon_Late__Semantics_OfreeRes___Agent_Ofs__name_9,axiom,
% 2.84/1.53 fs_name @ late_freeRes ).
% 2.84/1.53
% 2.84/1.53 thf(tcon_Late__Semantics_Osubject___Agent_Opt__name_10,axiom,
% 2.84/1.53 pt_name @ late_subject ).
% 2.84/1.53
% 2.84/1.53 thf(tcon_Late__Semantics_Osubject___Agent_Ofs__name_11,axiom,
% 2.84/1.53 fs_name @ late_subject ).
% 2.84/1.53
% 2.84/1.53 thf(tcon_Late__Semantics_Oresidual___Agent_Opt__name_12,axiom,
% 2.84/1.53 pt_name @ late_residual ).
% 2.84/1.53
% 2.84/1.53 thf(tcon_Late__Semantics_Oresidual___Agent_Ofs__name_13,axiom,
% 2.84/1.53 fs_name @ late_residual ).
% 2.84/1.53
% 2.84/1.53 thf(help_If_3_1_T,axiom,
% 2.84/1.53 ! [P: $o] :
% 2.84/1.53 ( ( P = $true )
% 2.84/1.53 | ( P = $false ) ) ).
% 2.84/1.53
% 2.84/1.53 thf(help_If_2_1_T,axiom,
% 2.84/1.53 ! [A: $tType,X3: A,Y: A] :
% 2.84/1.53 ( ( if @ A @ $false @ X3 @ Y )
% 2.84/1.53 = Y ) ).
% 2.84/1.53
% 2.84/1.53 thf(help_If_1_1_T,axiom,
% 2.84/1.53 ! [A: $tType,X3: A,Y: A] :
% 2.84/1.53 ( ( if @ A @ $true @ X3 @ Y )
% 2.84/1.53 = X3 ) ).
% 2.84/1.53
% 2.84/1.53 thf(conj_0,conjecture,
% 2.84/1.53 late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_FreeR @ late_TauR @ ( par @ ( par @ p2 @ ( subs @ q2 @ x @ b ) ) @ r ) ) ).
% 2.84/1.53 ------------------------
% 2.84/1.56 % (17633)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_17420 for (2999ds/4Mi)
% 2.84/1.56 % (17638)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_17420 for (2999ds/18Mi)
% 2.84/1.56 % (17633)Instruction limit reached!
% 2.84/1.56 % (17633)------------------------------
% 2.84/1.56 % (17633)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.56 % (17633)Termination reason: Unknown
% 2.84/1.56 % (17633)Termination phase: shuffling
% 2.84/1.56
% 2.84/1.56 % (17633)Memory used [KB]: 1535
% 2.84/1.56 % (17633)Time elapsed: 0.003 s
% 2.84/1.56 % (17633)Instructions burned: 5 (million)
% 2.84/1.56 % (17633)------------------------------
% 2.84/1.56 % (17633)------------------------------
% 2.84/1.56 % (17632)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_17420 for (2999ds/183Mi)
% 2.84/1.56 % (17638)Instruction limit reached!
% 2.84/1.56 % (17638)------------------------------
% 2.84/1.56 % (17638)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.56 % (17638)Termination reason: Unknown
% 2.84/1.56 % (17638)Termination phase: shuffling
% 2.84/1.56
% 2.84/1.56 % (17638)Memory used [KB]: 1663
% 2.84/1.56 % (17638)Time elapsed: 0.007 s
% 2.84/1.56 % (17638)Instructions burned: 18 (million)
% 2.84/1.56 % (17638)------------------------------
% 2.84/1.56 % (17638)------------------------------
% 2.84/1.57 % (17634)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_17420 for (2999ds/27Mi)
% 2.84/1.57 % (17635)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_17420 for (2999ds/2Mi)
% 2.84/1.57 % (17636)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_17420 for (2999ds/2Mi)
% 2.84/1.57 % (17637)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_17420 for (2999ds/275Mi)
% 2.84/1.57 % (17635)Instruction limit reached!
% 2.84/1.57 % (17635)------------------------------
% 2.84/1.57 % (17635)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.57 % (17635)Termination reason: Unknown
% 2.84/1.57 % (17635)Termination phase: shuffling
% 2.84/1.57
% 2.84/1.57 % (17635)Memory used [KB]: 1407
% 2.84/1.57 % (17635)Time elapsed: 0.004 s
% 2.84/1.57 % (17635)Instructions burned: 3 (million)
% 2.84/1.57 % (17635)------------------------------
% 2.84/1.57 % (17635)------------------------------
% 2.84/1.57 % (17636)Instruction limit reached!
% 2.84/1.57 % (17636)------------------------------
% 2.84/1.57 % (17636)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.57 % (17636)Termination reason: Unknown
% 2.84/1.57 % (17636)Termination phase: shuffling
% 2.84/1.57
% 2.84/1.57 % (17636)Memory used [KB]: 1407
% 2.84/1.57 % (17636)Time elapsed: 0.004 s
% 2.84/1.57 % (17636)Instructions burned: 3 (million)
% 2.84/1.57 % (17636)------------------------------
% 2.84/1.57 % (17636)------------------------------
% 2.84/1.57 % (17639)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_17420 for (2999ds/3Mi)
% 2.84/1.57 % (17639)Instruction limit reached!
% 2.84/1.57 % (17639)------------------------------
% 2.84/1.57 % (17639)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.57 % (17639)Termination reason: Unknown
% 2.84/1.57 % (17639)Termination phase: shuffling
% 2.84/1.57
% 2.84/1.57 % (17639)Memory used [KB]: 1407
% 2.84/1.57 % (17639)Time elapsed: 0.002 s
% 2.84/1.57 % (17639)Instructions burned: 3 (million)
% 2.84/1.57 % (17639)------------------------------
% 2.84/1.57 % (17639)------------------------------
% 2.84/1.57 % (17640)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_17420 for (2999ds/37Mi)
% 2.84/1.58 % (17643)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_17420 for (2999ds/1041Mi)
% 2.84/1.58 % (17634)Instruction limit reached!
% 2.84/1.58 % (17634)------------------------------
% 2.84/1.58 % (17634)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.58 % (17634)Termination reason: Unknown
% 2.84/1.58 % (17634)Termination phase: Property scanning
% 2.84/1.58
% 2.84/1.58 % (17634)Memory used [KB]: 1918
% 2.84/1.58 % (17634)Time elapsed: 0.019 s
% 2.84/1.58 % (17634)Instructions burned: 27 (million)
% 2.84/1.58 % (17634)------------------------------
% 2.84/1.58 % (17634)------------------------------
% 2.84/1.58 % (17640)Instruction limit reached!
% 2.84/1.58 % (17640)------------------------------
% 2.84/1.58 % (17640)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.58 % (17640)Termination reason: Unknown
% 2.84/1.58 % (17640)Termination phase: shuffling
% 2.84/1.58
% 2.84/1.58 % (17640)Memory used [KB]: 2174
% 2.84/1.58 % (17640)Time elapsed: 0.012 s
% 2.84/1.58 % (17640)Instructions burned: 39 (million)
% 2.84/1.58 % (17640)------------------------------
% 2.84/1.58 % (17640)------------------------------
% 2.84/1.59 % (17641)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_17420 for (2999ds/15Mi)
% 2.84/1.59 % (17642)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_17420 for (2999ds/3Mi)
% 2.84/1.59 % (17642)Instruction limit reached!
% 2.84/1.59 % (17642)------------------------------
% 2.84/1.59 % (17642)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.59 % (17642)Termination reason: Unknown
% 2.84/1.59 % (17642)Termination phase: shuffling
% 2.84/1.59
% 2.84/1.59 % (17642)Memory used [KB]: 1407
% 2.84/1.59 % (17642)Time elapsed: 0.004 s
% 2.84/1.59 % (17642)Instructions burned: 3 (million)
% 2.84/1.59 % (17642)------------------------------
% 2.84/1.59 % (17642)------------------------------
% 2.84/1.59 % (17645)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_17420 for (2999ds/16Mi)
% 2.84/1.59 % (17641)Instruction limit reached!
% 2.84/1.59 % (17641)------------------------------
% 2.84/1.59 % (17641)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.59 % (17641)Termination reason: Unknown
% 2.84/1.59 % (17641)Termination phase: shuffling
% 2.84/1.59
% 2.84/1.59 % (17641)Memory used [KB]: 1663
% 2.84/1.59 % (17641)Time elapsed: 0.011 s
% 2.84/1.59 % (17641)Instructions burned: 15 (million)
% 2.84/1.59 % (17641)------------------------------
% 2.84/1.59 % (17641)------------------------------
% 2.87/1.60 % (17645)Instruction limit reached!
% 2.87/1.60 % (17645)------------------------------
% 2.87/1.60 % (17645)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.60 % (17645)Termination reason: Unknown
% 2.87/1.60 % (17645)Termination phase: shuffling
% 2.87/1.60
% 2.87/1.60 % (17645)Memory used [KB]: 1663
% 2.87/1.60 % (17645)Time elapsed: 0.006 s
% 2.87/1.60 % (17645)Instructions burned: 16 (million)
% 2.87/1.60 % (17645)------------------------------
% 2.87/1.60 % (17645)------------------------------
% 2.87/1.60 % (17644)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_17420 for (2999ds/7Mi)
% 2.87/1.60 % (17644)Instruction limit reached!
% 2.87/1.60 % (17644)------------------------------
% 2.87/1.60 % (17644)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.60 % (17644)Termination reason: Unknown
% 2.87/1.60 % (17644)Termination phase: shuffling
% 2.87/1.60
% 2.87/1.60 % (17644)Memory used [KB]: 1535
% 2.87/1.60 % (17644)Time elapsed: 0.006 s
% 2.87/1.60 % (17644)Instructions burned: 8 (million)
% 2.87/1.60 % (17644)------------------------------
% 2.87/1.60 % (17644)------------------------------
% 2.87/1.60 % (17646)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_17420 for (2999ds/3Mi)
% 2.87/1.60 % (17646)Instruction limit reached!
% 2.87/1.60 % (17646)------------------------------
% 2.87/1.60 % (17646)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.60 % (17646)Termination reason: Unknown
% 2.87/1.61 % (17646)Termination phase: shuffling
% 2.87/1.61
% 2.87/1.61 % (17646)Memory used [KB]: 1407
% 2.87/1.61 % (17646)Time elapsed: 0.003 s
% 2.87/1.61 % (17646)Instructions burned: 3 (million)
% 2.87/1.61 % (17646)------------------------------
% 2.87/1.61 % (17646)------------------------------
% 2.87/1.61 % (17648)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_17420 for (2999ds/7Mi)
% 2.87/1.61 % (17648)Instruction limit reached!
% 2.87/1.61 % (17648)------------------------------
% 2.87/1.61 % (17648)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.61 % (17648)Termination reason: Unknown
% 2.87/1.61 % (17648)Termination phase: shuffling
% 2.87/1.61
% 2.87/1.61 % (17648)Memory used [KB]: 1535
% 2.87/1.61 % (17648)Time elapsed: 0.003 s
% 2.87/1.61 % (17648)Instructions burned: 7 (million)
% 2.87/1.61 % (17648)------------------------------
% 2.87/1.61 % (17648)------------------------------
% 2.87/1.61 % (17647)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_17420 for (2999ds/3Mi)
% 2.87/1.61 % (17647)Instruction limit reached!
% 2.87/1.61 % (17647)------------------------------
% 2.87/1.61 % (17647)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.61 % (17647)Termination reason: Unknown
% 2.87/1.61 % (17647)Termination phase: shuffling
% 2.87/1.61
% 2.87/1.61 % (17647)Memory used [KB]: 1407
% 2.87/1.61 % (17647)Time elapsed: 0.004 s
% 2.87/1.61 % (17647)Instructions burned: 3 (million)
% 2.87/1.61 % (17647)------------------------------
% 2.87/1.61 % (17647)------------------------------
% 2.87/1.61 % (17637)First to succeed.
% 2.87/1.62 % (17632)Instruction limit reached!
% 2.87/1.62 % (17632)------------------------------
% 2.87/1.62 % (17632)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.62 % (17632)Termination reason: Unknown
% 2.87/1.62 % (17632)Termination phase: Saturation
% 2.87/1.62
% 2.87/1.62 % (17632)Memory used [KB]: 7164
% 2.87/1.62 % (17632)Time elapsed: 0.055 s
% 2.87/1.62 % (17632)Instructions burned: 185 (million)
% 2.87/1.62 % (17632)------------------------------
% 2.87/1.62 % (17632)------------------------------
% 2.87/1.62 % (17649)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_17420 for (2999ds/3Mi)
% 2.87/1.62 % (17637)Refutation found. Thanks to Tanya!
% 2.87/1.62 % SZS status Theorem for DTF2THF_17420
% 2.87/1.62 % SZS output start Proof for DTF2THF_17420
% 2.87/1.62 thf(type_def_5, type, pi: $tType).
% 2.87/1.62 thf(type_def_7, type, name: $tType).
% 2.87/1.62 thf(type_def_8, type, set: ($tType) > $tType).
% 2.87/1.62 thf(type_def_9, type, late_freeRes: $tType).
% 2.87/1.62 thf(type_def_10, type, late_subject: $tType).
% 2.87/1.62 thf(type_def_11, type, late_residual: $tType).
% 2.87/1.62 thf(type_def_12, type, noption: ($tType) > $tType).
% 2.87/1.62 thf(func_def_0, type, late_residual: $tType).
% 2.87/1.62 thf(func_def_1, type, late_subject: $tType).
% 2.87/1.62 thf(func_def_2, type, late_freeRes: $tType).
% 2.87/1.62 thf(func_def_3, type, noption: ($tType) > $tType).
% 2.87/1.62 thf(func_def_4, type, name: $tType).
% 2.87/1.62 thf(func_def_5, type, pi: $tType).
% 2.87/1.62 thf(func_def_6, type, set: ($tType) > $tType).
% 2.87/1.62 thf(func_def_7, type, fs_name: !>[X0: $tType]:($o)).
% 2.87/1.62 thf(func_def_8, type, pt_name: !>[X0: $tType]:($o)).
% 2.87/1.62 thf(func_def_9, type, bang: pi > pi).
% 2.87/1.62 thf(func_def_10, type, input: name > name > pi > pi).
% 2.87/1.62 thf(func_def_11, type, match: name > name > pi > pi).
% 2.87/1.62 thf(func_def_12, type, mismatch: name > name > pi > pi).
% 2.87/1.62 thf(func_def_13, type, output: name > name > pi > pi).
% 2.87/1.62 thf(func_def_14, type, par: pi > pi > pi).
% 2.87/1.62 thf(func_def_15, type, piNil: pi).
% 2.87/1.62 thf(func_def_16, type, res: name > pi > pi).
% 2.87/1.62 thf(func_def_17, type, sum: pi > pi > pi).
% 2.87/1.62 thf(func_def_18, type, tau: pi > pi).
% 2.87/1.62 thf(func_def_19, type, pi_rec: !>[X0: $tType]:(X0 > (name > name > pi > X0 > X0) > (pi > X0 > X0) > (name > name > pi > X0 > X0) > (name > name > pi > X0 > X0) > (name > name > pi > X0 > X0) > (pi > pi > X0 > X0 > X0) > (pi > pi > X0 > X0 > X0) > (name > pi > X0 > X0) > (pi > X0 > X0) > pi > X0)).
% 2.87/1.62 thf(func_def_20, type, pi_rec_set: !>[X0: $tType]:(X0 > (name > name > pi > X0 > X0) > (pi > X0 > X0) > (name > name > pi > X0 > X0) > (name > name > pi > X0 > X0) > (name > name > pi > X0 > X0) > (pi > pi > X0 > X0 > X0) > (pi > pi > X0 > X0 > X0) > (name > pi > X0 > X0) > (pi > X0 > X0) > pi > X0 > $o)).
% 2.87/1.62 thf(func_def_21, type, subs: pi > name > name > pi).
% 2.87/1.62 thf(func_def_22, type, subst_name: name > name > name > name).
% 2.87/1.62 thf(func_def_23, type, finite_finite: !>[X0: $tType]:(set @ X0 > $o)).
% 2.87/1.62 thf(func_def_24, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 2.87/1.62 thf(func_def_25, type, late_case_freeRes: !>[X0: $tType]:((name > name > X0) > X0 > late_freeRes > X0)).
% 2.87/1.62 thf(func_def_26, type, late_case_subject: !>[X0: $tType]:((name > X0) > (name > X0) > late_subject > X0)).
% 2.87/1.62 thf(func_def_27, type, late_bangPred: pi > pi > $o).
% 2.87/1.62 thf(func_def_28, type, late_OutputR: name > name > late_freeRes).
% 2.87/1.62 thf(func_def_29, type, late_TauR: late_freeRes).
% 2.87/1.62 thf(func_def_30, type, late_freeRes_rec: !>[X0: $tType]:((name > name > X0) > X0 > late_freeRes > X0)).
% 2.87/1.62 thf(func_def_31, type, late_BoundR: late_subject > name > pi > late_residual).
% 2.87/1.62 thf(func_def_32, type, late_FreeR: late_freeRes > pi > late_residual).
% 2.87/1.62 thf(func_def_33, type, late_residual_rec: !>[X0: $tType]:((late_subject > name > pi > X0) > (late_freeRes > pi > X0) > late_residual > X0)).
% 2.87/1.62 thf(func_def_34, type, late_r582136743ec_set: !>[X0: $tType]:((late_subject > name > pi > X0) > (late_freeRes > pi > X0) > late_residual > X0 > $o)).
% 2.87/1.62 thf(func_def_35, type, late_BoundOutputS: name > late_subject).
% 2.87/1.62 thf(func_def_36, type, late_InputS: name > late_subject).
% 2.87/1.62 thf(func_def_37, type, late_subject_rec: !>[X0: $tType]:((name > X0) > (name > X0) > late_subject > X0)).
% 2.87/1.62 thf(func_def_38, type, late_transitions: pi > late_residual > $o).
% 2.87/1.62 thf(func_def_39, type, sup_sup: !>[X0: $tType]:(X0 > X0 > X0)).
% 2.87/1.62 thf(func_def_40, type, abs_fun: !>[X0: $tType, X1: $tType]:(X0 > X1 > X0 > noption @ X1)).
% 2.87/1.62 thf(func_def_41, type, fresh: !>[X0: $tType, X1: $tType]:(X0 > X1 > $o)).
% 2.87/1.62 thf(func_def_42, type, supp: !>[X0: $tType, X1: $tType]:(X0 > set @ X1)).
% 2.87/1.62 thf(func_def_43, type, supports: !>[X0: $tType, X1: $tType]:(set @ X0 > X1 > $o)).
% 2.87/1.62 thf(func_def_44, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 2.87/1.62 thf(func_def_45, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 2.87/1.62 thf(func_def_46, type, p: pi).
% 2.87/1.62 thf(func_def_47, type, pqr: pi).
% 2.87/1.62 thf(func_def_48, type, p2: pi).
% 2.87/1.62 thf(func_def_49, type, q: pi).
% 2.87/1.62 thf(func_def_50, type, qr: pi).
% 2.87/1.62 thf(func_def_51, type, q2: pi).
% 2.87/1.62 thf(func_def_52, type, r: pi).
% 2.87/1.62 thf(func_def_53, type, alpha: late_freeRes).
% 2.87/1.62 thf(func_def_54, type, a: name).
% 2.87/1.62 thf(func_def_55, type, b: name).
% 2.87/1.62 thf(func_def_56, type, x: name).
% 2.87/1.62 thf(func_def_71, type, sP0: late_subject > name > pi > pi > pi > $o).
% 2.87/1.62 thf(func_def_72, type, sK1: !>[X0: $tType]:((X0 > late_freeRes > $o) > name)).
% 2.87/1.62 thf(func_def_73, type, sK2: !>[X0: $tType]:((X0 > late_freeRes > $o) > name)).
% 2.87/1.62 thf(func_def_74, type, sK3: !>[X0: $tType]:((X0 > late_freeRes > $o) > X0)).
% 2.87/1.62 thf(func_def_75, type, sK4: !>[X0: $tType]:((X0 > late_freeRes > $o) > X0)).
% 2.87/1.62 thf(func_def_76, type, sK5: (pi > $o) > late_freeRes > pi > name > pi).
% 2.87/1.62 thf(func_def_77, type, sK6: (pi > $o) > name > late_subject > pi > pi > pi).
% 2.87/1.62 thf(func_def_78, type, sK7: (pi > $o) > name > late_subject > pi > pi > pi).
% 2.87/1.62 thf(func_def_79, type, sK8: (late_freeRes > $o) > name).
% 2.87/1.62 thf(func_def_80, type, sK9: (late_freeRes > $o) > name).
% 2.87/1.62 thf(func_def_81, type, sK10: !>[X0: $tType]:((X0 > late_freeRes > $o) > X0)).
% 2.87/1.62 thf(func_def_82, type, sK11: !>[X0: $tType]:((X0 > late_freeRes > $o) > name)).
% 2.87/1.62 thf(func_def_83, type, sK12: !>[X0: $tType]:((X0 > late_freeRes > $o) > name)).
% 2.87/1.62 thf(func_def_84, type, sK13: !>[X0: $tType]:((X0 > late_freeRes > $o) > X0)).
% 2.87/1.62 thf(func_def_85, type, sK14: (late_residual > $o) > late_subject).
% 2.87/1.62 thf(func_def_86, type, sK15: (late_residual > $o) > name).
% 2.87/1.62 thf(func_def_87, type, sK16: (late_residual > $o) > pi).
% 2.87/1.62 thf(func_def_88, type, sK17: (late_residual > $o) > late_freeRes).
% 2.87/1.62 thf(func_def_89, type, sK18: (late_residual > $o) > pi).
% 2.87/1.62 thf(func_def_90, type, sK19: pi > late_freeRes > pi > name > pi).
% 2.87/1.62 thf(func_def_91, type, sK20: pi > late_freeRes > pi > name > late_freeRes).
% 2.87/1.62 thf(func_def_92, type, sK21: pi > late_freeRes > pi > name > pi).
% 2.87/1.62 thf(func_def_93, type, sK22: pi > late_freeRes > pi > name > name).
% 2.87/1.62 thf(func_def_94, type, sK23: late_subject > name > pi > pi > pi > pi).
% 2.87/1.62 thf(func_def_95, type, sK24: late_subject > name > pi > pi > pi > late_subject).
% 2.87/1.62 thf(func_def_96, type, sK25: late_subject > name > pi > pi > pi > name).
% 2.87/1.62 thf(func_def_97, type, sK26: late_subject > name > pi > pi > pi > pi).
% 2.87/1.62 thf(func_def_98, type, sK27: late_subject > name > pi > pi > pi > pi).
% 2.87/1.62 thf(func_def_99, type, sK28: pi > name > late_subject > pi > pi > pi).
% 2.87/1.62 thf(func_def_100, type, sK29: pi > name > late_subject > pi > pi > late_subject).
% 2.87/1.62 thf(func_def_101, type, sK30: pi > name > late_subject > pi > pi > name).
% 2.87/1.62 thf(func_def_102, type, sK31: pi > name > late_subject > pi > pi > pi).
% 2.87/1.62 thf(func_def_103, type, sK32: pi > name > late_subject > pi > pi > pi).
% 2.87/1.62 thf(func_def_104, type, sK33: late_freeRes > name).
% 2.87/1.62 thf(func_def_105, type, sK34: late_freeRes > name).
% 2.87/1.62 thf(func_def_106, type, sK35: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 2.87/1.62 thf(func_def_107, type, sK36: late_residual > pi > name > name > name).
% 2.87/1.62 thf(func_def_108, type, sK37: late_residual > pi > name > name > name).
% 2.87/1.62 thf(func_def_109, type, sK38: late_residual > pi > name > name > pi).
% 2.87/1.62 thf(func_def_110, type, sK39: late_residual > pi > pi).
% 2.87/1.62 thf(func_def_112, type, ph41: !>[X0: $tType]:(X0)).
% 2.87/1.62 thf(f971,plain,(
% 2.87/1.62 $false),
% 2.87/1.62 inference(subsumption_resolution,[status(thm)],[f970,f875])).
% 2.87/1.62 thf(f875,plain,(
% 2.87/1.62 ((late_transitions @ (par @ p @ q) @ (late_FreeR @ late_TauR @ (par @ p2 @ (subs @ q2 @ x @ b)))) = $true)),
% 2.87/1.62 inference(cnf_transformation,[status(thm)],[f391])).
% 2.87/1.62 thf(f391,plain,(
% 2.87/1.62 ((late_transitions @ (par @ p @ q) @ (late_FreeR @ late_TauR @ (par @ p2 @ (subs @ q2 @ x @ b)))) = $true)),
% 2.87/1.62 inference(fool_elimination,[status(thm)],[f390])).
% 2.87/1.62 thf(f390,plain,(
% 2.87/1.62 (late_transitions @ (par @ p @ q) @ (late_FreeR @ late_TauR @ (par @ p2 @ (subs @ q2 @ x @ b))))),
% 2.87/1.62 inference(rectify,[status(thm)],[f4])).
% 2.87/1.62 thf(f4,axiom,(
% 2.87/1.62 (late_transitions @ (par @ p @ q) @ (late_FreeR @ late_TauR @ (par @ p2 @ (subs @ q2 @ x @ b))))),
% 2.87/1.62 file('/export/starexec/sandbox2/tmp/tmp.Is4Z84IKKq/DTF2THF_17420.p',fact_3__092_060open_062P_A_092_060parallel_062_AQ_A_092_060longmapsto_062_A_092_060tau_062_A_092_060prec_062_AP_H_A_092_060parallel_062_AQ_H_091x_058_058_061b_093_092_060close_062)).
% 2.87/1.62 thf(f970,plain,(
% 2.87/1.62 ((late_transitions @ (par @ p @ q) @ (late_FreeR @ late_TauR @ (par @ p2 @ (subs @ q2 @ x @ b)))) != $true)),
% 2.87/1.62 inference(trivial_inequality_removal,[status(thm)],[f969])).
% 2.87/1.62 thf(f969,plain,(
% 2.87/1.62 ($true != $true) | ((late_transitions @ (par @ p @ q) @ (late_FreeR @ late_TauR @ (par @ p2 @ (subs @ q2 @ x @ b)))) != $true)),
% 2.87/1.62 inference(superposition,[status(thm)],[f953,f848])).
% 2.87/1.62 thf(f848,plain,(
% 2.87/1.62 ( ! [X2 : pi,X3 : pi,X0 : pi,X1 : late_freeRes] : (((late_transitions @ (par @ X0 @ X3) @ (late_FreeR @ X1 @ (par @ X2 @ X3))) = $true) | ($true != (late_transitions @ X0 @ (late_FreeR @ X1 @ X2)))) )),
% 2.87/1.62 inference(cnf_transformation,[status(thm)],[f744])).
% 2.87/1.62 thf(f744,plain,(
% 2.87/1.62 ! [X0 : pi,X1 : late_freeRes,X2 : pi,X3 : pi] : (($true != (late_transitions @ X0 @ (late_FreeR @ X1 @ X2))) | ((late_transitions @ (par @ X0 @ X3) @ (late_FreeR @ X1 @ (par @ X2 @ X3))) = $true))),
% 2.87/1.62 inference(ennf_transformation,[status(thm)],[f467])).
% 2.87/1.62 thf(f467,plain,(
% 2.87/1.62 ! [X0 : pi,X1 : late_freeRes,X2 : pi,X3 : pi] : (($true = (late_transitions @ X0 @ (late_FreeR @ X1 @ X2))) => ((late_transitions @ (par @ X0 @ X3) @ (late_FreeR @ X1 @ (par @ X2 @ X3))) = $true))),
% 2.87/1.62 inference(fool_elimination,[status(thm)],[f466])).
% 2.87/1.62 thf(f466,plain,(
% 2.87/1.62 ! [X0 : pi,X1 : late_freeRes,X2 : pi,X3 : pi] : ((late_transitions @ X0 @ (late_FreeR @ X1 @ X2)) => (late_transitions @ (par @ X0 @ X3) @ (late_FreeR @ X1 @ (par @ X2 @ X3))))),
% 2.87/1.62 inference(rectify,[status(thm)],[f12])).
% 2.87/1.62 thf(f12,axiom,(
% 2.87/1.62 ! [X3 : pi,X7 : late_freeRes,X8 : pi,X4 : pi] : ((late_transitions @ X3 @ (late_FreeR @ X7 @ X8)) => (late_transitions @ (par @ X3 @ X4) @ (late_FreeR @ X7 @ (par @ X8 @ X4))))),
% 2.87/1.62 file('/export/starexec/sandbox2/tmp/tmp.Is4Z84IKKq/DTF2THF_17420.p',fact_11_Par1F)).
% 2.87/1.62 thf(f953,plain,(
% 2.87/1.62 ((late_transitions @ (par @ (par @ p @ q) @ r) @ (late_FreeR @ late_TauR @ (par @ (par @ p2 @ (subs @ q2 @ x @ b)) @ r))) != $true)),
% 2.87/1.62 inference(cnf_transformation,[status(thm)],[f642])).
% 2.87/1.62 thf(f642,plain,(
% 2.87/1.62 ((late_transitions @ (par @ (par @ p @ q) @ r) @ (late_FreeR @ late_TauR @ (par @ (par @ p2 @ (subs @ q2 @ x @ b)) @ r))) != $true)),
% 2.87/1.62 inference(flattening,[status(thm)],[f331])).
% 2.87/1.62 thf(f331,plain,(
% 2.87/1.62 ~((late_transitions @ (par @ (par @ p @ q) @ r) @ (late_FreeR @ late_TauR @ (par @ (par @ p2 @ (subs @ q2 @ x @ b)) @ r))) = $true)),
% 2.87/1.62 inference(fool_elimination,[status(thm)],[f330])).
% 2.87/1.62 thf(f330,plain,(
% 2.87/1.62 ~(late_transitions @ (par @ (par @ p @ q) @ r) @ (late_FreeR @ late_TauR @ (par @ (par @ p2 @ (subs @ q2 @ x @ b)) @ r)))),
% 2.87/1.62 inference(rectify,[status(thm)],[f276])).
% 2.87/1.62 thf(f276,negated_conjecture,(
% 2.87/1.62 ~(late_transitions @ (par @ (par @ p @ q) @ r) @ (late_FreeR @ late_TauR @ (par @ (par @ p2 @ (subs @ q2 @ x @ b)) @ r)))),
% 2.87/1.62 inference(negated_conjecture,[status(cth)],[f275])).
% 2.87/1.62 thf(f275,conjecture,(
% 2.87/1.62 (late_transitions @ (par @ (par @ p @ q) @ r) @ (late_FreeR @ late_TauR @ (par @ (par @ p2 @ (subs @ q2 @ x @ b)) @ r)))),
% 2.87/1.62 file('/export/starexec/sandbox2/tmp/tmp.Is4Z84IKKq/DTF2THF_17420.p',conj_0)).
% 2.87/1.62 % SZS output end Proof for DTF2THF_17420
% 2.87/1.62 % (17637)------------------------------
% 2.87/1.62 % (17637)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.62 % (17637)Termination reason: Refutation
% 2.87/1.62
% 2.87/1.62 % (17637)Memory used [KB]: 6908
% 2.87/1.62 % (17637)Time elapsed: 0.052 s
% 2.87/1.62 % (17637)Instructions burned: 85 (million)
% 2.87/1.62 % (17637)------------------------------
% 2.87/1.62 % (17637)------------------------------
% 2.87/1.62 % (17631)Success in time 0.08 s
%------------------------------------------------------------------------------