%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP185^2 : 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 : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:56:14 AM UTC 2026
% Result : Theorem 2.72s 1.61s
% Output : Refutation 2.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP185^2 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n029.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 08:29:14 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.28/0.46 ---- Original DTF file ---
% 0.28/0.47 thf(spec,logic,$$dhol).
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 % File : ITP185^2 : TPTP v9.2.1. Released v7.5.0.
% 0.28/0.47 % Domain : Interactive Theorem Proving
% 0.28/0.47 % Problem : Sledgehammer Strong_Late_Sim_SC problem prob_529__3413750_1
% 0.28/0.47 % Version : Especial.
% 0.28/0.47 % English :
% 0.28/0.47
% 0.28/0.47 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.28/0.47 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.28/0.47 % Source : [Des21]
% 0.28/0.47 % Names : Strong_Late_Sim_SC/prob_529__3413750_1 [Des21]
% 0.28/0.47
% 0.28/0.47 % Status : Theorem
% 0.28/0.47 % Rating : 0.67 v9.1.0, 0.33 v8.1.0, 0.25 v7.5.0
% 0.28/0.47 % Syntax : Number of formulae : 330 ( 180 unt; 55 typ; 0 def)
% 0.28/0.47 % Number of atoms : 646 ( 279 equ; 0 cnn)
% 0.28/0.47 % Maximal formula atoms : 16 ( 2 avg)
% 0.28/0.47 % Number of connectives : 3623 ( 142 ~; 7 |; 35 &;3041 @)
% 0.28/0.47 % ( 0 <=>; 398 =>; 0 <=; 0 <~>)
% 0.28/0.47 % Maximal formula depth : 28 ( 8 avg)
% 0.28/0.47 % Number of types : 6 ( 5 usr)
% 0.28/0.47 % Number of type conns : 287 ( 287 >; 0 *; 0 +; 0 <<)
% 0.28/0.47 % Number of symbols : 53 ( 50 usr; 15 con; 0-12 aty)
% 0.28/0.47 % Number of variables : 1265 ( 39 ^;1202 !; 4 ?;1265 :)
% 0.28/0.47 % ( 20 !>; 0 ?*; 0 @-; 0 @+)
% 0.28/0.47 % SPC : TH1_THM_EQU_NAR
% 0.28/0.47
% 0.28/0.47 % Comments : This file was generated by Sledgehammer 2021-02-23 16:16:49.259
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 % Could-be-implicit typings (7)
% 0.28/0.47 thf(ty_t_Late__Semantics_Oresidual,type,
% 0.28/0.47 late_residual: $tType ).
% 0.28/0.47
% 0.28/0.47 thf(ty_t_Late__Semantics_Osubject,type,
% 0.28/0.47 late_subject: $tType ).
% 0.28/0.47
% 0.28/0.47 thf(ty_t_Late__Semantics_OfreeRes,type,
% 0.28/0.47 late_freeRes: $tType ).
% 0.28/0.47
% 0.28/0.47 thf(ty_t_Nominal_Onoption,type,
% 0.28/0.47 noption: $tType > $tType ).
% 0.28/0.47
% 0.28/0.47 thf(ty_t_Agent_Oname,type,
% 0.28/0.47 name: $tType ).
% 0.28/0.47
% 0.28/0.47 thf(ty_t_Agent_Opi,type,
% 0.28/0.47 pi: $tType ).
% 0.28/0.47
% 0.28/0.47 thf(ty_t_Set_Oset,type,
% 0.28/0.47 set: $tType > $tType ).
% 0.28/0.47
% 0.28/0.47 % Explicit typings (48)
% 0.28/0.47 thf(sy_cl_Agent_Ofs__name,type,
% 0.28/0.47 fs_name:
% 0.28/0.47 !>[A: $tType] : $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_cl_Agent_Opt__name,type,
% 0.28/0.47 pt_name:
% 0.28/0.47 !>[A: $tType] : $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Agent_Opi_OBang,type,
% 0.28/0.47 bang: pi > pi ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Agent_Opi_OInput,type,
% 0.28/0.47 input: name > name > pi > pi ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Agent_Opi_OMatch,type,
% 0.28/0.47 match: name > name > pi > pi ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Agent_Opi_OMismatch,type,
% 0.28/0.47 mismatch: name > name > pi > pi ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Agent_Opi_OOutput,type,
% 0.28/0.47 output: name > name > pi > pi ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Agent_Opi_OPar,type,
% 0.28/0.47 par: pi > pi > pi ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Agent_Opi_OPiNil,type,
% 0.28/0.47 piNil: pi ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Agent_Opi_ORes,type,
% 0.28/0.47 res: name > pi > pi ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Agent_Opi_OSum,type,
% 0.28/0.47 sum: pi > pi > pi ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Agent_Opi_OTau,type,
% 0.28/0.47 tau: pi > pi ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Agent_Opi_Opi__rec,type,
% 0.28/0.47 pi_rec:
% 0.28/0.47 !>[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 ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Agent_Osubs,type,
% 0.28/0.47 subs: pi > name > name > pi ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Agent_Osubst__name,type,
% 0.28/0.47 subst_name: name > name > name > name ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Finite__Set_Ofinite,type,
% 0.28/0.47 finite_finite:
% 0.28/0.47 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_If,type,
% 0.28/0.47 if:
% 0.28/0.47 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Late__Semantics1_OfreeRes_Ocase__freeRes,type,
% 0.28/0.47 late_case_freeRes:
% 0.28/0.47 !>[A: $tType] : ( ( name > name > A ) > A > late_freeRes > A ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Late__Semantics1_Osubject_Ocase__subject,type,
% 0.28/0.47 late_case_subject:
% 0.28/0.47 !>[A: $tType] : ( ( name > A ) > ( name > A ) > late_subject > A ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Late__Semantics_ObangPred,type,
% 0.28/0.47 late_bangPred: pi > pi > $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Late__Semantics_OfreeRes_OOutputR,type,
% 0.28/0.47 late_OutputR: name > name > late_freeRes ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Late__Semantics_OfreeRes_OTauR,type,
% 0.28/0.47 late_TauR: late_freeRes ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Late__Semantics_OfreeRes_OfreeRes__rec,type,
% 0.28/0.47 late_freeRes_rec:
% 0.28/0.47 !>[T: $tType] : ( ( name > name > T ) > T > late_freeRes > T ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Late__Semantics_Oresidual_OBoundR,type,
% 0.28/0.47 late_BoundR: late_subject > name > pi > late_residual ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Late__Semantics_Oresidual_OFreeR,type,
% 0.28/0.47 late_FreeR: late_freeRes > pi > late_residual ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Late__Semantics_Oresidual_Oresidual__rec,type,
% 0.28/0.47 late_residual_rec:
% 0.28/0.47 !>[T: $tType] : ( ( late_subject > name > pi > T ) > ( late_freeRes > pi > T ) > late_residual > T ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Late__Semantics_Oresidual_Oresidual__rec__set,type,
% 0.28/0.47 late_r582136743ec_set:
% 0.28/0.47 !>[T: $tType] : ( ( late_subject > name > pi > T ) > ( late_freeRes > pi > T ) > late_residual > T > $o ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Late__Semantics_Osubject_OBoundOutputS,type,
% 0.28/0.47 late_BoundOutputS: name > late_subject ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Late__Semantics_Osubject_OInputS,type,
% 0.28/0.47 late_InputS: name > late_subject ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Late__Semantics_Osubject_Osubject__rec,type,
% 0.28/0.47 late_subject_rec:
% 0.28/0.47 !>[T: $tType] : ( ( name > T ) > ( name > T ) > late_subject > T ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Late__Semantics_Otransitions,type,
% 0.28/0.47 late_transitions: pi > late_residual > $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Lattices_Osup__class_Osup,type,
% 0.28/0.47 sup_sup:
% 0.28/0.47 !>[A: $tType] : ( A > A > A ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Nominal_Oabs__fun,type,
% 0.28/0.47 abs_fun:
% 0.28/0.47 !>[X: $tType,A: $tType] : ( X > A > X > ( noption @ A ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Nominal_Ofresh,type,
% 0.28/0.47 fresh:
% 0.28/0.47 !>[X: $tType,A: $tType] : ( X > A > $o ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Nominal_Osupp,type,
% 0.28/0.47 supp:
% 0.28/0.47 !>[A: $tType,X: $tType] : ( A > ( set @ X ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Set_OCollect,type,
% 0.28/0.47 collect:
% 0.28/0.47 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_member,type,
% 0.28/0.47 member:
% 0.28/0.47 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_v_P,type,
% 0.28/0.47 p: pi ).
% 0.28/0.47
% 0.28/0.47 thf(sy_v_PQR____,type,
% 0.28/0.47 pqr: pi ).
% 0.28/0.47
% 0.28/0.47 thf(sy_v_Q,type,
% 0.28/0.47 q: pi ).
% 0.28/0.47
% 0.28/0.47 thf(sy_v_QR____,type,
% 0.28/0.47 qr: pi ).
% 0.28/0.47
% 0.28/0.47 thf(sy_v_Q_H____,type,
% 0.28/0.47 q2: pi ).
% 0.28/0.47
% 0.28/0.47 thf(sy_v_R,type,
% 0.28/0.47 r: pi ).
% 0.28/0.47
% 0.28/0.47 thf(sy_v_R_H____,type,
% 0.28/0.47 r2: pi ).
% 0.28/0.47
% 0.28/0.47 thf(sy_v__092_060alpha_062____,type,
% 0.28/0.47 alpha: late_freeRes ).
% 0.28/0.47
% 0.28/0.47 thf(sy_v_a____,type,
% 0.28/0.47 a: name ).
% 0.28/0.47
% 0.28/0.47 thf(sy_v_x____,type,
% 0.28/0.47 x: name ).
% 0.28/0.47
% 0.28/0.47 thf(sy_v_y____,type,
% 0.28/0.47 y: name ).
% 0.28/0.47
% 0.28/0.47 % Relevant facts (256)
% 0.28/0.47 thf(fact_0_cClose2_Ohyps_I14_J,axiom,
% 0.28/0.47 alpha = late_TauR ).
% 0.28/0.47
% 0.28/0.47 % cClose2.hyps(14)
% 0.28/0.47 thf(fact_1_cClose2_Ohyps_I10_J,axiom,
% 0.28/0.47 y != a ).
% 0.28/0.47
% 0.28/0.47 % cClose2.hyps(10)
% 0.28/0.47 thf(fact_2_cClose2_Ohyps_I5_J,axiom,
% 0.28/0.47 x != a ).
% 0.28/0.47
% 0.28/0.47 % cClose2.hyps(5)
% 0.28/0.47 thf(fact_3_cClose2_Ohyps_I9_J,axiom,
% 0.28/0.47 fresh @ name @ pi @ y @ r ).
% 0.28/0.47
% 0.28/0.47 % cClose2.hyps(9)
% 0.28/0.47 thf(fact_4_cClose2_Ohyps_I6_J,axiom,
% 0.28/0.47 x != y ).
% 0.28/0.47
% 0.28/0.47 % cClose2.hyps(6)
% 0.28/0.47 thf(fact_5_cClose2_Ohyps_I8_J,axiom,
% 0.28/0.47 fresh @ name @ pi @ y @ q ).
% 0.28/0.47
% 0.28/0.47 % cClose2.hyps(8)
% 0.28/0.47 thf(fact_6_cClose2_Ohyps_I3_J,axiom,
% 0.28/0.47 fresh @ name @ pi @ x @ q ).
% 0.28/0.47
% 0.28/0.47 % cClose2.hyps(3)
% 0.28/0.47 thf(fact_7_cClose2_Ohyps_I13_J,axiom,
% 0.28/0.47 fresh @ name @ pi @ y @ p ).
% 0.28/0.47
% 0.28/0.47 % cClose2.hyps(13)
% 0.28/0.47 thf(fact_8_cClose2_Ohyps_I12_J,axiom,
% 0.28/0.47 fresh @ name @ pi @ x @ p ).
% 0.28/0.47
% 0.28/0.47 % cClose2.hyps(12)
% 0.28/0.47 thf(fact_9_cClose2_Ohyps_I4_J,axiom,
% 0.28/0.47 fresh @ name @ pi @ x @ r ).
% 0.28/0.47
% 0.28/0.47 % cClose2.hyps(4)
% 0.28/0.47 thf(fact_10_cClose2_Ohyps_I7_J,axiom,
% 0.28/0.47 fresh @ name @ pi @ x @ q2 ).
% 0.28/0.47
% 0.28/0.47 % cClose2.hyps(7)
% 0.28/0.47 thf(fact_11_cClose2_Ohyps_I11_J,axiom,
% 0.28/0.47 fresh @ name @ pi @ y @ r2 ).
% 0.28/0.47
% 0.28/0.47 % cClose2.hyps(11)
% 0.28/0.47 thf(fact_12_cClose2_Ohyps_I2_J,axiom,
% 0.28/0.47 late_transitions @ r @ ( late_BoundR @ ( late_InputS @ a ) @ x @ r2 ) ).
% 0.28/0.47
% 0.28/0.47 % cClose2.hyps(2)
% 0.28/0.47 thf(fact_13__092_060open_062P_A_092_060parallel_062_AQ_A_092_060longmapsto_062_Aa_060_092_060nu_062y_062_A_092_060prec_062_AP_A_092_060parallel_062_AQ_H_092_060close_062,axiom,
% 0.28/0.47 late_transitions @ ( par @ p @ q ) @ ( late_BoundR @ ( late_BoundOutputS @ a ) @ y @ ( par @ p @ q2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % \<open>P \<parallel> Q \<longmapsto> a<\<nu>y> \<prec> P \<parallel> Q'\<close>
% 0.28/0.47 thf(fact_14_cClose2_Ohyps_I1_J,axiom,
% 0.28/0.47 late_transitions @ q @ ( late_BoundR @ ( late_BoundOutputS @ a ) @ y @ q2 ) ).
% 0.28/0.47
% 0.28/0.47 % cClose2.hyps(1)
% 0.28/0.47 thf(fact_15_cPar2_Ohyps,axiom,
% 0.28/0.47 late_transitions @ ( par @ q @ r ) @ ( late_FreeR @ alpha @ qr ) ).
% 0.28/0.47
% 0.28/0.47 % cPar2.hyps
% 0.28/0.47 thf(fact_16_Free_Ohyps,axiom,
% 0.28/0.47 late_transitions @ ( par @ p @ ( par @ q @ r ) ) @ ( late_FreeR @ alpha @ pqr ) ).
% 0.28/0.47
% 0.28/0.47 % Free.hyps
% 0.28/0.47 thf(fact_17_simps_I9_J,axiom,
% 0.28/0.47 ! [X2: name,C: name,D: name,P: pi] :
% 0.28/0.47 ( ( X2 != C )
% 0.28/0.47 => ( ( X2 != D )
% 0.28/0.47 => ( ( subs @ ( res @ X2 @ P ) @ C @ D )
% 0.28/0.47 = ( res @ X2 @ ( subs @ P @ C @ D ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % simps(9)
% 0.28/0.47 thf(fact_18_simps_I8_J,axiom,
% 0.28/0.47 ! [P: pi,Q: pi,C: name,D: name] :
% 0.28/0.47 ( ( subs @ ( par @ P @ Q ) @ C @ D )
% 0.28/0.47 = ( par @ ( subs @ P @ C @ D ) @ ( subs @ Q @ C @ D ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % simps(8)
% 0.28/0.47 thf(fact_19_Par1F,axiom,
% 0.28/0.47 ! [P: pi,Alpha: late_freeRes,P2: pi,Q: pi] :
% 0.28/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 0.28/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha @ ( par @ P2 @ Q ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Par1F
% 0.28/0.47 thf(fact_20_Par2F,axiom,
% 0.28/0.47 ! [Q: pi,Alpha: late_freeRes,Q2: pi,P: pi] :
% 0.28/0.47 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 0.28/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha @ ( par @ P @ Q2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Par2F
% 0.28/0.47 thf(fact_21_subst__identity,axiom,
% 0.28/0.47 ! [P: pi,A2: name] :
% 0.28/0.47 ( ( subs @ P @ A2 @ A2 )
% 0.28/0.47 = P ) ).
% 0.28/0.47
% 0.28/0.47 % subst_identity
% 0.28/0.47 thf(fact_22_pi_Odistinct_I85_J,axiom,
% 0.28/0.47 ! [Pi1: pi,Pi2: pi,Name: name,Pi: pi] :
% 0.28/0.47 ( ( par @ Pi1 @ Pi2 )
% 0.28/0.47 != ( res @ Name @ Pi ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.distinct(85)
% 0.28/0.47 thf(fact_23_Late__Semantics_OClose1,axiom,
% 0.28/0.47 ! [P: pi,A2: name,X2: name,P2: pi,Q: pi,Y: name,Q2: pi] :
% 0.28/0.47 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P2 ) )
% 0.28/0.47 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y @ Q2 ) )
% 0.28/0.47 => ( ( fresh @ name @ pi @ Y @ P )
% 0.28/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ ( subs @ P2 @ X2 @ Y ) @ Q2 ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Late_Semantics.Close1
% 0.28/0.47 thf(fact_24_Late__Semantics_OClose2,axiom,
% 0.28/0.47 ! [P: pi,A2: name,Y: name,P2: pi,Q: pi,X2: name,Q2: pi] :
% 0.28/0.47 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y @ P2 ) )
% 0.28/0.47 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ Q2 ) )
% 0.28/0.47 => ( ( fresh @ name @ pi @ Y @ Q )
% 0.28/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ P2 @ ( subs @ Q2 @ X2 @ Y ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Late_Semantics.Close2
% 0.28/0.47 thf(fact_25_transitions_OClose1,axiom,
% 0.28/0.47 ! [P: pi,A2: name,X2: name,P2: pi,Q: pi,Y: name,Q2: pi] :
% 0.28/0.47 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P2 ) )
% 0.28/0.47 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y @ Q2 ) )
% 0.28/0.47 => ( ( fresh @ name @ pi @ X2 @ P )
% 0.28/0.47 => ( ( fresh @ name @ pi @ X2 @ Q )
% 0.28/0.47 => ( ( fresh @ name @ pi @ Y @ P )
% 0.28/0.47 => ( ( fresh @ name @ pi @ Y @ Q )
% 0.28/0.47 => ( ( X2 != A2 )
% 0.28/0.47 => ( ( fresh @ name @ pi @ X2 @ Q2 )
% 0.28/0.47 => ( ( Y != A2 )
% 0.28/0.47 => ( ( fresh @ name @ pi @ Y @ P2 )
% 0.28/0.47 => ( ( X2 != Y )
% 0.28/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ ( subs @ P2 @ X2 @ Y ) @ Q2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % transitions.Close1
% 0.28/0.47 thf(fact_26_transitions_OClose2,axiom,
% 0.28/0.47 ! [P: pi,A2: name,Y: name,P2: pi,Q: pi,X2: name,Q2: pi] :
% 0.28/0.47 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y @ P2 ) )
% 0.28/0.47 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ Q2 ) )
% 0.28/0.47 => ( ( fresh @ name @ pi @ X2 @ P )
% 0.28/0.47 => ( ( fresh @ name @ pi @ X2 @ Q )
% 0.28/0.47 => ( ( fresh @ name @ pi @ Y @ P )
% 0.28/0.47 => ( ( fresh @ name @ pi @ Y @ Q )
% 0.28/0.47 => ( ( X2 != A2 )
% 0.28/0.47 => ( ( fresh @ name @ pi @ X2 @ P2 )
% 0.28/0.47 => ( ( Y != A2 )
% 0.28/0.47 => ( ( fresh @ name @ pi @ Y @ Q2 )
% 0.28/0.47 => ( ( X2 != Y )
% 0.28/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ P2 @ ( subs @ Q2 @ X2 @ Y ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % transitions.Close2
% 0.28/0.47 thf(fact_27_substRes2,axiom,
% 0.28/0.47 ! [B: name,P: pi,A2: name] :
% 0.28/0.47 ( ( fresh @ name @ pi @ B @ P )
% 0.28/0.47 => ( ( res @ A2 @ P )
% 0.28/0.47 = ( res @ B @ ( subs @ P @ A2 @ B ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % substRes2
% 0.28/0.47 thf(fact_28_substRes3,axiom,
% 0.28/0.47 ! [B: name,P: pi,A2: name] :
% 0.28/0.47 ( ( fresh @ name @ pi @ B @ P )
% 0.28/0.47 => ( ( subs @ ( res @ A2 @ P ) @ A2 @ B )
% 0.28/0.47 = ( res @ B @ ( subs @ P @ A2 @ B ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % substRes3
% 0.28/0.47 thf(fact_29_Late__Semantics_Osubject_Oinject_I2_J,axiom,
% 0.28/0.47 ! [X1: name,Y1: name] :
% 0.28/0.47 ( ( ( late_BoundOutputS @ X1 )
% 0.28/0.47 = ( late_BoundOutputS @ Y1 ) )
% 0.28/0.47 = ( X1 = Y1 ) ) ).
% 0.28/0.47
% 0.28/0.47 % Late_Semantics.subject.inject(2)
% 0.28/0.47 thf(fact_30_pi_Ofresh_I8_J,axiom,
% 0.28/0.47 ! [A2: name,X22: pi,X1: pi] :
% 0.28/0.47 ( ( fresh @ name @ pi @ A2 @ ( par @ X22 @ X1 ) )
% 0.28/0.47 = ( ( fresh @ name @ pi @ A2 @ X22 )
% 0.28/0.47 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.fresh(8)
% 0.28/0.47 thf(fact_31_substTrans,axiom,
% 0.28/0.47 ! [B: name,P: pi,A2: name,C: name] :
% 0.28/0.47 ( ( fresh @ name @ pi @ B @ P )
% 0.28/0.47 => ( ( subs @ ( subs @ P @ A2 @ B ) @ B @ C )
% 0.28/0.47 = ( subs @ P @ A2 @ C ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % substTrans
% 0.28/0.47 thf(fact_32_Late__Semantics_Osubject_Odistinct_I1_J,axiom,
% 0.28/0.47 ! [Name2: name,Name: name] :
% 0.28/0.47 ( ( late_InputS @ Name2 )
% 0.28/0.47 != ( late_BoundOutputS @ Name ) ) ).
% 0.28/0.47
% 0.28/0.47 % Late_Semantics.subject.distinct(1)
% 0.28/0.47 thf(fact_33_name__exists__fresh,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( fs_name @ A )
% 0.28/0.47 => ! [X2: A] :
% 0.28/0.47 ~ ! [C2: name] :
% 0.28/0.47 ~ ( fresh @ name @ A @ C2 @ X2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % name_exists_fresh
% 0.28/0.47 thf(fact_34_subject_Oinducts,axiom,
% 0.28/0.47 ! [P: late_subject > $o,Subject: late_subject] :
% 0.28/0.47 ( ! [Name3: name] : ( P @ ( late_InputS @ Name3 ) )
% 0.28/0.47 => ( ! [Name3: name] : ( P @ ( late_BoundOutputS @ Name3 ) )
% 0.28/0.47 => ( P @ Subject ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subject.inducts
% 0.28/0.47 thf(fact_35_subject_Ostrong__induct_H,axiom,
% 0.28/0.47 ! [N: $tType,P: N > late_subject > $o,Z: N,Subject: late_subject] :
% 0.28/0.47 ( ! [Name3: name,Z2: N] : ( P @ Z2 @ ( late_InputS @ Name3 ) )
% 0.28/0.47 => ( ! [Name3: name,Z2: N] : ( P @ Z2 @ ( late_BoundOutputS @ Name3 ) )
% 0.28/0.47 => ( P @ Z @ Subject ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subject.strong_induct'
% 0.28/0.47 thf(fact_36_subject_Ostrong__inducts,axiom,
% 0.28/0.47 ! [A: $tType,P: A > late_subject > $o,Z: A,Subject: late_subject] :
% 0.28/0.47 ( ! [Name3: name,Z2: A] : ( P @ Z2 @ ( late_InputS @ Name3 ) )
% 0.28/0.47 => ( ! [Name3: name,Z2: A] : ( P @ Z2 @ ( late_BoundOutputS @ Name3 ) )
% 0.28/0.47 => ( P @ Z @ Subject ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subject.strong_inducts
% 0.28/0.47 thf(fact_37_residual_Ostrong__inducts,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( fs_name @ A )
% 0.28/0.47 => ! [P: A > late_residual > $o,Z: A,Residual: late_residual] :
% 0.28/0.47 ( ! [Subject2: late_subject,Name3: name,Pi3: pi,Z2: A] :
% 0.28/0.47 ( ( fresh @ name @ A @ Name3 @ Z2 )
% 0.28/0.47 => ( ( fresh @ name @ late_subject @ Name3 @ Subject2 )
% 0.28/0.47 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi3 ) ) ) )
% 0.28/0.47 => ( ! [FreeRes: late_freeRes,Pi3: pi,Z2: A] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi3 ) )
% 0.28/0.47 => ( P @ Z @ Residual ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % residual.strong_inducts
% 0.28/0.47 thf(fact_38_residual_Ostrong__induct,axiom,
% 0.28/0.47 ! [N: $tType] :
% 0.28/0.47 ( ( fs_name @ N )
% 0.28/0.47 => ! [P: N > late_residual > $o,Z: N,Residual: late_residual] :
% 0.28/0.47 ( ! [Subject2: late_subject,Name3: name,Pi3: pi,Z2: N] :
% 0.28/0.47 ( ( fresh @ name @ N @ Name3 @ Z2 )
% 0.28/0.47 => ( ( fresh @ name @ late_subject @ Name3 @ Subject2 )
% 0.28/0.47 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi3 ) ) ) )
% 0.28/0.47 => ( ! [FreeRes: late_freeRes,Pi3: pi,Z2: N] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi3 ) )
% 0.28/0.47 => ( P @ Z @ Residual ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % residual.strong_induct
% 0.28/0.47 thf(fact_39_freshBoundDerivative_I2_J,axiom,
% 0.28/0.47 ! [P: pi,A2: late_subject,X2: name,P2: pi,Y: name] :
% 0.28/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P2 ) )
% 0.28/0.47 => ( ( fresh @ name @ pi @ Y @ P )
% 0.28/0.47 => ( ( Y != X2 )
% 0.28/0.47 => ( fresh @ name @ pi @ Y @ P2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % freshBoundDerivative(2)
% 0.28/0.47 thf(fact_40_freshRes,axiom,
% 0.28/0.47 ! [A2: name,P: pi] : ( fresh @ name @ pi @ A2 @ ( res @ A2 @ P ) ) ).
% 0.28/0.47
% 0.28/0.47 % freshRes
% 0.28/0.47 thf(fact_41_residual_Oinducts,axiom,
% 0.28/0.47 ! [P: late_residual > $o,Residual: late_residual] :
% 0.28/0.47 ( ! [Subject2: late_subject,Name3: name,Pi3: pi] : ( P @ ( late_BoundR @ Subject2 @ Name3 @ Pi3 ) )
% 0.28/0.47 => ( ! [FreeRes: late_freeRes,Pi3: pi] : ( P @ ( late_FreeR @ FreeRes @ Pi3 ) )
% 0.28/0.47 => ( P @ Residual ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % residual.inducts
% 0.28/0.47 thf(fact_42_residual_Odistinct_I1_J,axiom,
% 0.28/0.47 ! [Subject: late_subject,Name2: name,Pi4: pi,FreeRes2: late_freeRes,Pi: pi] :
% 0.28/0.47 ( ( late_BoundR @ Subject @ Name2 @ Pi4 )
% 0.28/0.47 != ( late_FreeR @ FreeRes2 @ Pi ) ) ).
% 0.28/0.47
% 0.28/0.47 % residual.distinct(1)
% 0.28/0.47 thf(fact_43_fresh__fact2,axiom,
% 0.28/0.47 ! [A2: name,B: name,P: pi] :
% 0.28/0.47 ( ( A2 != B )
% 0.28/0.47 => ( fresh @ name @ pi @ A2 @ ( subs @ P @ A2 @ B ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % fresh_fact2
% 0.28/0.47 thf(fact_44_fresh__fact1,axiom,
% 0.28/0.47 ! [A2: name,P: pi,C: name,B: name] :
% 0.28/0.47 ( ( fresh @ name @ pi @ A2 @ P )
% 0.28/0.47 => ( ( A2 != C )
% 0.28/0.47 => ( fresh @ name @ pi @ A2 @ ( subs @ P @ B @ C ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % fresh_fact1
% 0.28/0.47 thf(fact_45_mem__Collect__eq,axiom,
% 0.28/0.47 ! [A: $tType,A2: A,P: A > $o] :
% 0.28/0.47 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 0.28/0.47 = ( P @ A2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % mem_Collect_eq
% 0.28/0.47 thf(fact_46_Collect__mem__eq,axiom,
% 0.28/0.47 ! [A: $tType,A3: set @ A] :
% 0.28/0.47 ( ( collect @ A
% 0.28/0.47 @ ^ [X3: A] : ( member @ A @ X3 @ A3 ) )
% 0.28/0.47 = A3 ) ).
% 0.28/0.47
% 0.28/0.47 % Collect_mem_eq
% 0.28/0.47 thf(fact_47_Collect__cong,axiom,
% 0.28/0.47 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.28/0.47 ( ! [X4: A] :
% 0.28/0.47 ( ( P @ X4 )
% 0.28/0.47 = ( Q @ X4 ) )
% 0.28/0.47 => ( ( collect @ A @ P )
% 0.28/0.47 = ( collect @ A @ Q ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Collect_cong
% 0.28/0.47 thf(fact_48_ext,axiom,
% 0.28/0.47 ! [B2: $tType,A: $tType,F: A > B2,G: A > B2] :
% 0.28/0.47 ( ! [X4: A] :
% 0.28/0.47 ( ( F @ X4 )
% 0.28/0.47 = ( G @ X4 ) )
% 0.28/0.47 => ( F = G ) ) ).
% 0.28/0.47
% 0.28/0.47 % ext
% 0.28/0.47 thf(fact_49_forget,axiom,
% 0.28/0.47 ! [A2: name,P: pi,B: name] :
% 0.28/0.47 ( ( fresh @ name @ pi @ A2 @ P )
% 0.28/0.47 => ( ( subs @ P @ A2 @ B )
% 0.28/0.47 = P ) ) ).
% 0.28/0.47
% 0.28/0.47 % forget
% 0.28/0.47 thf(fact_50_parCasesB,axiom,
% 0.28/0.47 ! [P: pi,Q: pi,A2: late_subject,X2: name,PQ: pi,Prop: pi > $o] :
% 0.28/0.47 ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X2 @ PQ ) )
% 0.28/0.47 => ( ( fresh @ name @ pi @ X2 @ P )
% 0.28/0.47 => ( ( fresh @ name @ pi @ X2 @ Q )
% 0.28/0.47 => ( ! [P3: pi] :
% 0.28/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P3 ) )
% 0.28/0.47 => ( Prop @ ( par @ P3 @ Q ) ) )
% 0.28/0.47 => ( ! [Q3: pi] :
% 0.28/0.47 ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X2 @ Q3 ) )
% 0.28/0.47 => ( Prop @ ( par @ P @ Q3 ) ) )
% 0.28/0.47 => ( Prop @ PQ ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % parCasesB
% 0.28/0.47 thf(fact_51_Late__Semantics_OPar2B,axiom,
% 0.28/0.47 ! [Q: pi,A2: late_subject,X2: name,Q2: pi,P: pi] :
% 0.28/0.47 ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X2 @ Q2 ) )
% 0.28/0.47 => ( ( fresh @ name @ pi @ X2 @ P )
% 0.28/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X2 @ ( par @ P @ Q2 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Late_Semantics.Par2B
% 0.28/0.47 thf(fact_52_Late__Semantics_OPar1B,axiom,
% 0.28/0.47 ! [P: pi,A2: late_subject,X2: name,P2: pi,Q: pi] :
% 0.28/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P2 ) )
% 0.28/0.47 => ( ( fresh @ name @ pi @ X2 @ Q )
% 0.28/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X2 @ ( par @ P2 @ Q ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Late_Semantics.Par1B
% 0.28/0.47 thf(fact_53_pi_Oinject_I7_J,axiom,
% 0.28/0.47 ! [X22: pi,X1: pi,Y2: pi,Y1: pi] :
% 0.28/0.47 ( ( ( par @ X22 @ X1 )
% 0.28/0.47 = ( par @ Y2 @ Y1 ) )
% 0.28/0.47 = ( ( X22 = Y2 )
% 0.28/0.47 & ( X1 = Y1 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.inject(7)
% 0.28/0.47 thf(fact_54_freshFreeDerivative_I2_J,axiom,
% 0.28/0.47 ! [P: pi,Alpha: late_freeRes,P2: pi,Y: name] :
% 0.28/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 0.28/0.47 => ( ( fresh @ name @ pi @ Y @ P )
% 0.28/0.47 => ( fresh @ name @ pi @ Y @ P2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % freshFreeDerivative(2)
% 0.28/0.47 thf(fact_55_residual_Oinject_I2_J,axiom,
% 0.28/0.47 ! [X22: late_freeRes,X1: pi,Y2: late_freeRes,Y1: pi] :
% 0.28/0.47 ( ( ( late_FreeR @ X22 @ X1 )
% 0.28/0.47 = ( late_FreeR @ Y2 @ Y1 ) )
% 0.28/0.47 = ( ( X22 = Y2 )
% 0.28/0.47 & ( X1 = Y1 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % residual.inject(2)
% 0.28/0.47 thf(fact_56_transitions_OComm2,axiom,
% 0.28/0.47 ! [P: pi,A2: name,B: name,P2: pi,Q: pi,X2: name,Q2: pi] :
% 0.28/0.47 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A2 @ B ) @ P2 ) )
% 0.28/0.47 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ Q2 ) )
% 0.28/0.47 => ( ( fresh @ name @ pi @ X2 @ P )
% 0.28/0.47 => ( ( fresh @ name @ pi @ X2 @ Q )
% 0.28/0.47 => ( ( X2 != A2 )
% 0.28/0.47 => ( ( X2 != B )
% 0.28/0.47 => ( ( fresh @ name @ pi @ X2 @ P2 )
% 0.28/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P2 @ ( subs @ Q2 @ X2 @ B ) ) ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % transitions.Comm2
% 0.28/0.47 thf(fact_57_transitions_OComm1,axiom,
% 0.28/0.47 ! [P: pi,A2: name,X2: name,P2: pi,Q: pi,B: name,Q2: pi] :
% 0.28/0.47 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P2 ) )
% 0.28/0.47 => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A2 @ B ) @ Q2 ) )
% 0.28/0.47 => ( ( fresh @ name @ pi @ X2 @ P )
% 0.28/0.47 => ( ( fresh @ name @ pi @ X2 @ Q )
% 0.28/0.47 => ( ( X2 != A2 )
% 0.28/0.47 => ( ( X2 != B )
% 0.28/0.47 => ( ( fresh @ name @ pi @ X2 @ Q2 )
% 0.28/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P2 @ X2 @ B ) @ Q2 ) ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % transitions.Comm1
% 0.28/0.47 thf(fact_58_Late__Semantics1_Osubject_Oinject_I1_J,axiom,
% 0.28/0.47 ! [X1: name,Y1: name] :
% 0.28/0.47 ( ( ( late_InputS @ X1 )
% 0.28/0.47 = ( late_InputS @ Y1 ) )
% 0.28/0.47 = ( X1 = Y1 ) ) ).
% 0.28/0.47
% 0.28/0.47 % Late_Semantics1.subject.inject(1)
% 0.28/0.47 thf(fact_59_Late__Semantics1_Osubject_Oinject_I2_J,axiom,
% 0.28/0.47 ! [X22: name,Y2: name] :
% 0.28/0.47 ( ( ( late_BoundOutputS @ X22 )
% 0.28/0.47 = ( late_BoundOutputS @ Y2 ) )
% 0.28/0.47 = ( X22 = Y2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % Late_Semantics1.subject.inject(2)
% 0.28/0.47 thf(fact_60_Late__Semantics_OComm2,axiom,
% 0.28/0.47 ! [P: pi,A2: name,B: name,P2: pi,Q: pi,X2: name,Q2: pi] :
% 0.28/0.47 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A2 @ B ) @ P2 ) )
% 0.28/0.47 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ Q2 ) )
% 0.28/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P2 @ ( subs @ Q2 @ X2 @ B ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Late_Semantics.Comm2
% 0.28/0.47 thf(fact_61_Late__Semantics_OComm1,axiom,
% 0.28/0.47 ! [P: pi,A2: name,X2: name,P2: pi,Q: pi,B: name,Q2: pi] :
% 0.28/0.47 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P2 ) )
% 0.28/0.47 => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A2 @ B ) @ Q2 ) )
% 0.28/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P2 @ X2 @ B ) @ Q2 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Late_Semantics.Comm1
% 0.28/0.47 thf(fact_62_Late__Semantics1_Osubject_Odistinct_I1_J,axiom,
% 0.28/0.47 ! [X1: name,X22: name] :
% 0.28/0.47 ( ( late_InputS @ X1 )
% 0.28/0.47 != ( late_BoundOutputS @ X22 ) ) ).
% 0.28/0.47
% 0.28/0.47 % Late_Semantics1.subject.distinct(1)
% 0.28/0.47 thf(fact_63_subject_Oexhaust,axiom,
% 0.28/0.47 ! [Y: late_subject] :
% 0.28/0.47 ( ! [X12: name] :
% 0.28/0.47 ( Y
% 0.28/0.47 != ( late_InputS @ X12 ) )
% 0.28/0.47 => ~ ! [X23: name] :
% 0.28/0.47 ( Y
% 0.28/0.47 != ( late_BoundOutputS @ X23 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subject.exhaust
% 0.28/0.47 thf(fact_64_Open,axiom,
% 0.28/0.47 ! [P: pi,A2: name,B: name,P2: pi] :
% 0.28/0.47 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A2 @ B ) @ P2 ) )
% 0.28/0.47 => ( ( A2 != B )
% 0.28/0.47 => ( late_transitions @ ( res @ B @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ B @ P2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Open
% 0.28/0.47 thf(fact_65_freeRes_Ofresh_I1_J,axiom,
% 0.28/0.47 ! [A2: name,X22: name,X1: name] :
% 0.28/0.47 ( ( fresh @ name @ late_freeRes @ A2 @ ( late_OutputR @ X22 @ X1 ) )
% 0.28/0.47 = ( ( fresh @ name @ name @ A2 @ X22 )
% 0.28/0.47 & ( fresh @ name @ name @ A2 @ X1 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % freeRes.fresh(1)
% 0.28/0.47 thf(fact_66_Late__Semantics_OfreeRes_Oinject,axiom,
% 0.28/0.47 ! [X22: name,X1: name,Y2: name,Y1: name] :
% 0.28/0.47 ( ( ( late_OutputR @ X22 @ X1 )
% 0.28/0.47 = ( late_OutputR @ Y2 @ Y1 ) )
% 0.28/0.47 = ( ( X22 = Y2 )
% 0.28/0.47 & ( X1 = Y1 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Late_Semantics.freeRes.inject
% 0.28/0.47 thf(fact_67_Late__Semantics1_OfreeRes_Oinject,axiom,
% 0.28/0.47 ! [X11: name,X122: name,Y11: name,Y12: name] :
% 0.28/0.47 ( ( ( late_OutputR @ X11 @ X122 )
% 0.28/0.47 = ( late_OutputR @ Y11 @ Y12 ) )
% 0.28/0.47 = ( ( X11 = Y11 )
% 0.28/0.47 & ( X122 = Y12 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Late_Semantics1.freeRes.inject
% 0.28/0.47 thf(fact_68_freeRes_Ofresh_I2_J,axiom,
% 0.28/0.47 ! [A2: name] : ( fresh @ name @ late_freeRes @ A2 @ late_TauR ) ).
% 0.28/0.47
% 0.28/0.47 % freeRes.fresh(2)
% 0.28/0.47 thf(fact_69_residual_Ofresh_I2_J,axiom,
% 0.28/0.47 ! [A2: name,X22: late_freeRes,X1: pi] :
% 0.28/0.47 ( ( fresh @ name @ late_residual @ A2 @ ( late_FreeR @ X22 @ X1 ) )
% 0.28/0.47 = ( ( fresh @ name @ late_freeRes @ A2 @ X22 )
% 0.28/0.47 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % residual.fresh(2)
% 0.28/0.47 thf(fact_70_subject_Ofresh_I2_J,axiom,
% 0.28/0.47 ! [A2: name,X1: name] :
% 0.28/0.47 ( ( fresh @ name @ late_subject @ A2 @ ( late_BoundOutputS @ X1 ) )
% 0.28/0.47 = ( fresh @ name @ name @ A2 @ X1 ) ) ).
% 0.28/0.47
% 0.28/0.47 % subject.fresh(2)
% 0.28/0.47 thf(fact_71_subject_Ofresh_I1_J,axiom,
% 0.28/0.47 ! [A2: name,X1: name] :
% 0.28/0.47 ( ( fresh @ name @ late_subject @ A2 @ ( late_InputS @ X1 ) )
% 0.28/0.47 = ( fresh @ name @ name @ A2 @ X1 ) ) ).
% 0.28/0.47
% 0.28/0.47 % subject.fresh(1)
% 0.28/0.47 thf(fact_72_Late__Semantics1_OfreeRes_Odistinct_I1_J,axiom,
% 0.28/0.47 ! [X11: name,X122: name] :
% 0.28/0.47 ( ( late_OutputR @ X11 @ X122 )
% 0.28/0.47 != late_TauR ) ).
% 0.28/0.47
% 0.28/0.47 % Late_Semantics1.freeRes.distinct(1)
% 0.28/0.47 thf(fact_73_freeRes_Oexhaust,axiom,
% 0.28/0.47 ! [Y: late_freeRes] :
% 0.28/0.47 ( ! [X112: name,X123: name] :
% 0.28/0.47 ( Y
% 0.28/0.47 != ( late_OutputR @ X112 @ X123 ) )
% 0.28/0.47 => ( Y = late_TauR ) ) ).
% 0.28/0.47
% 0.28/0.47 % freeRes.exhaust
% 0.28/0.47 thf(fact_74_Late__Semantics_OfreeRes_Odistinct_I1_J,axiom,
% 0.28/0.47 ! [Name1: name,Name22: name] :
% 0.28/0.47 ( ( late_OutputR @ Name1 @ Name22 )
% 0.28/0.47 != late_TauR ) ).
% 0.28/0.47
% 0.28/0.47 % Late_Semantics.freeRes.distinct(1)
% 0.28/0.47 thf(fact_75_freeRes_Oinducts,axiom,
% 0.28/0.47 ! [P: late_freeRes > $o,FreeRes3: late_freeRes] :
% 0.28/0.47 ( ! [Name12: name,Name23: name] : ( P @ ( late_OutputR @ Name12 @ Name23 ) )
% 0.28/0.47 => ( ( P @ late_TauR )
% 0.28/0.47 => ( P @ FreeRes3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % freeRes.inducts
% 0.28/0.47 thf(fact_76_freeRes_Ostrong__induct_H,axiom,
% 0.28/0.47 ! [N: $tType,P: N > late_freeRes > $o,Z: N,FreeRes3: late_freeRes] :
% 0.28/0.47 ( ! [Name12: name,Name23: name,Z2: N] : ( P @ Z2 @ ( late_OutputR @ Name12 @ Name23 ) )
% 0.28/0.47 => ( ! [Z2: N] : ( P @ Z2 @ late_TauR )
% 0.28/0.47 => ( P @ Z @ FreeRes3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % freeRes.strong_induct'
% 0.28/0.47 thf(fact_77_freeRes_Ostrong__inducts,axiom,
% 0.28/0.47 ! [A: $tType,P: A > late_freeRes > $o,Z: A,FreeRes3: late_freeRes] :
% 0.28/0.47 ( ! [Name12: name,Name23: name,Z2: A] : ( P @ Z2 @ ( late_OutputR @ Name12 @ Name23 ) )
% 0.28/0.47 => ( ! [Z2: A] : ( P @ Z2 @ late_TauR )
% 0.28/0.47 => ( P @ Z @ FreeRes3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % freeRes.strong_inducts
% 0.28/0.47 thf(fact_78_resCases_H,axiom,
% 0.28/0.47 ! [X2: name,P: pi,Rs: late_residual] :
% 0.28/0.47 ( ( late_transitions @ ( res @ X2 @ P ) @ Rs )
% 0.28/0.47 => ( ! [P4: pi,A4: name,B3: name] :
% 0.28/0.47 ( ( ( res @ X2 @ P )
% 0.28/0.47 = ( res @ B3 @ P4 ) )
% 0.28/0.47 => ! [P3: pi] :
% 0.28/0.47 ( ( Rs
% 0.28/0.47 = ( late_BoundR @ ( late_BoundOutputS @ A4 ) @ B3 @ P3 ) )
% 0.28/0.47 => ( ( late_transitions @ P4 @ ( late_FreeR @ ( late_OutputR @ A4 @ B3 ) @ P3 ) )
% 0.28/0.47 => ( A4 = B3 ) ) ) )
% 0.28/0.47 => ( ! [P4: pi,A4: late_subject,X4: name,P3: pi,Y3: name] :
% 0.28/0.47 ( ( ( res @ X2 @ P )
% 0.28/0.47 = ( res @ Y3 @ P4 ) )
% 0.28/0.47 => ( ( Rs
% 0.28/0.47 = ( late_BoundR @ A4 @ X4 @ ( res @ Y3 @ P3 ) ) )
% 0.28/0.47 => ( ( late_transitions @ P4 @ ( late_BoundR @ A4 @ X4 @ P3 ) )
% 0.28/0.47 => ( ( fresh @ name @ late_subject @ Y3 @ A4 )
% 0.28/0.47 => ( ( Y3 != X4 )
% 0.28/0.47 => ( ( fresh @ name @ pi @ X4 @ P4 )
% 0.28/0.47 => ~ ( fresh @ name @ late_subject @ X4 @ A4 ) ) ) ) ) ) )
% 0.28/0.47 => ~ ! [P4: pi,Alpha2: late_freeRes,P3: pi,Y3: name] :
% 0.28/0.47 ( ( ( res @ X2 @ P )
% 0.28/0.47 = ( res @ Y3 @ P4 ) )
% 0.28/0.47 => ( ( Rs
% 0.28/0.47 = ( late_FreeR @ Alpha2 @ ( res @ Y3 @ P3 ) ) )
% 0.28/0.47 => ( ( late_transitions @ P4 @ ( late_FreeR @ Alpha2 @ P3 ) )
% 0.28/0.47 => ~ ( fresh @ name @ late_freeRes @ Y3 @ Alpha2 ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % resCases'
% 0.28/0.47 thf(fact_79_freshResidual,axiom,
% 0.28/0.47 ! [P: pi,Rs: late_residual,X2: name] :
% 0.28/0.47 ( ( late_transitions @ P @ Rs )
% 0.28/0.47 => ( ( fresh @ name @ pi @ X2 @ P )
% 0.28/0.47 => ( fresh @ name @ late_residual @ X2 @ Rs ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % freshResidual
% 0.28/0.47 thf(fact_80_resCasesF,axiom,
% 0.28/0.47 ! [X2: name,P: pi,Alpha: late_freeRes,XP: pi,F2: pi > $o] :
% 0.28/0.47 ( ( late_transitions @ ( res @ X2 @ P ) @ ( late_FreeR @ Alpha @ XP ) )
% 0.28/0.47 => ( ! [P3: pi] :
% 0.28/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P3 ) )
% 0.28/0.47 => ( ( fresh @ name @ late_freeRes @ X2 @ Alpha )
% 0.28/0.47 => ( F2 @ ( res @ X2 @ P3 ) ) ) )
% 0.28/0.47 => ( F2 @ XP ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % resCasesF
% 0.28/0.47 thf(fact_81_resCasesF_H,axiom,
% 0.28/0.47 ! [X2: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 0.28/0.47 ( ( late_transitions @ ( res @ X2 @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 0.28/0.47 => ~ ! [P4: pi,Alpha2: late_freeRes,P3: pi,Y3: name] :
% 0.28/0.47 ( ( ( res @ X2 @ P )
% 0.28/0.47 = ( res @ Y3 @ P4 ) )
% 0.28/0.47 => ( ( ( late_FreeR @ Alpha @ P2 )
% 0.28/0.47 = ( late_FreeR @ Alpha2 @ ( res @ Y3 @ P3 ) ) )
% 0.28/0.47 => ( ( late_transitions @ P4 @ ( late_FreeR @ Alpha2 @ P3 ) )
% 0.28/0.47 => ~ ( fresh @ name @ late_freeRes @ Y3 @ Alpha2 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % resCasesF'
% 0.28/0.47 thf(fact_82_ResF,axiom,
% 0.28/0.47 ! [P: pi,Alpha: late_freeRes,P2: pi,Y: name] :
% 0.28/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 0.28/0.47 => ( ( fresh @ name @ late_freeRes @ Y @ Alpha )
% 0.28/0.47 => ( late_transitions @ ( res @ Y @ P ) @ ( late_FreeR @ Alpha @ ( res @ Y @ P2 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % ResF
% 0.28/0.47 thf(fact_83_Late__Semantics_OResB,axiom,
% 0.28/0.47 ! [P: pi,A2: late_subject,X2: name,P2: pi,Y: name] :
% 0.28/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P2 ) )
% 0.28/0.47 => ( ( fresh @ name @ late_subject @ Y @ A2 )
% 0.28/0.47 => ( ( Y != X2 )
% 0.28/0.47 => ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A2 @ X2 @ ( res @ Y @ P2 ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Late_Semantics.ResB
% 0.28/0.47 thf(fact_84_freshFreeDerivative_I1_J,axiom,
% 0.28/0.47 ! [P: pi,Alpha: late_freeRes,P2: pi,Y: name] :
% 0.28/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 0.28/0.47 => ( ( fresh @ name @ pi @ Y @ P )
% 0.28/0.47 => ( fresh @ name @ late_freeRes @ Y @ Alpha ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % freshFreeDerivative(1)
% 0.28/0.47 thf(fact_85_freshBoundDerivative_I1_J,axiom,
% 0.28/0.47 ! [P: pi,A2: late_subject,X2: name,P2: pi,Y: name] :
% 0.28/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P2 ) )
% 0.28/0.47 => ( ( fresh @ name @ pi @ Y @ P )
% 0.28/0.47 => ( fresh @ name @ late_subject @ Y @ A2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % freshBoundDerivative(1)
% 0.28/0.47 thf(fact_86_resCasesB_H,axiom,
% 0.28/0.47 ! [X5: name,P: pi,A2: late_subject,Y4: name,P2: pi] :
% 0.28/0.47 ( ( late_transitions @ ( res @ X5 @ P ) @ ( late_BoundR @ A2 @ Y4 @ P2 ) )
% 0.28/0.47 => ( ! [P4: pi,A4: name,B3: name] :
% 0.28/0.47 ( ( ( res @ X5 @ P )
% 0.28/0.47 = ( res @ B3 @ P4 ) )
% 0.28/0.47 => ! [P3: pi] :
% 0.28/0.47 ( ( ( late_BoundR @ A2 @ Y4 @ P2 )
% 0.28/0.47 = ( late_BoundR @ ( late_BoundOutputS @ A4 ) @ B3 @ P3 ) )
% 0.28/0.47 => ( ( late_transitions @ P4 @ ( late_FreeR @ ( late_OutputR @ A4 @ B3 ) @ P3 ) )
% 0.28/0.47 => ( A4 = B3 ) ) ) )
% 0.28/0.47 => ~ ! [P4: pi,A4: late_subject,X4: name,P3: pi,Y3: name] :
% 0.28/0.47 ( ( ( res @ X5 @ P )
% 0.28/0.47 = ( res @ Y3 @ P4 ) )
% 0.28/0.47 => ( ( ( late_BoundR @ A2 @ Y4 @ P2 )
% 0.28/0.47 = ( late_BoundR @ A4 @ X4 @ ( res @ Y3 @ P3 ) ) )
% 0.28/0.47 => ( ( late_transitions @ P4 @ ( late_BoundR @ A4 @ X4 @ P3 ) )
% 0.28/0.47 => ( ( fresh @ name @ late_subject @ Y3 @ A4 )
% 0.28/0.47 => ( ( Y3 != X4 )
% 0.28/0.47 => ( ( fresh @ name @ pi @ X4 @ P4 )
% 0.28/0.47 => ~ ( fresh @ name @ late_subject @ X4 @ A4 ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % resCasesB'
% 0.28/0.47 thf(fact_87_parCasesB_H,axiom,
% 0.28/0.47 ! [P: pi,Q: pi,B: late_subject,Y: name,P2: pi] :
% 0.28/0.47 ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ B @ Y @ P2 ) )
% 0.28/0.47 => ( ! [P4: pi,A4: late_subject,X4: name,P3: pi,Q4: pi] :
% 0.28/0.47 ( ( ( par @ P @ Q )
% 0.28/0.47 = ( par @ P4 @ Q4 ) )
% 0.28/0.47 => ( ( ( late_BoundR @ B @ Y @ P2 )
% 0.28/0.47 = ( late_BoundR @ A4 @ X4 @ ( par @ P3 @ Q4 ) ) )
% 0.28/0.47 => ( ( late_transitions @ P4 @ ( late_BoundR @ A4 @ X4 @ P3 ) )
% 0.28/0.47 => ( ( fresh @ name @ pi @ X4 @ P4 )
% 0.28/0.47 => ( ( fresh @ name @ pi @ X4 @ Q4 )
% 0.28/0.47 => ~ ( fresh @ name @ late_subject @ X4 @ A4 ) ) ) ) ) )
% 0.28/0.47 => ~ ! [Q4: pi,A4: late_subject,X4: name,Q3: pi,P4: pi] :
% 0.28/0.47 ( ( ( par @ P @ Q )
% 0.28/0.47 = ( par @ P4 @ Q4 ) )
% 0.28/0.47 => ( ( ( late_BoundR @ B @ Y @ P2 )
% 0.28/0.47 = ( late_BoundR @ A4 @ X4 @ ( par @ P4 @ Q3 ) ) )
% 0.28/0.47 => ( ( late_transitions @ Q4 @ ( late_BoundR @ A4 @ X4 @ Q3 ) )
% 0.28/0.47 => ( ( fresh @ name @ pi @ X4 @ P4 )
% 0.28/0.47 => ( ( fresh @ name @ pi @ X4 @ Q4 )
% 0.28/0.47 => ~ ( fresh @ name @ late_subject @ X4 @ A4 ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % parCasesB'
% 0.28/0.47 thf(fact_88_transitions_OPar1B,axiom,
% 0.28/0.47 ! [P: pi,A2: late_subject,X2: name,P2: pi,Q: pi] :
% 0.28/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P2 ) )
% 0.28/0.47 => ( ( fresh @ name @ pi @ X2 @ P )
% 0.28/0.47 => ( ( fresh @ name @ pi @ X2 @ Q )
% 0.28/0.47 => ( ( fresh @ name @ late_subject @ X2 @ A2 )
% 0.28/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X2 @ ( par @ P2 @ Q ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % transitions.Par1B
% 0.28/0.47 thf(fact_89_transitions_OPar2B,axiom,
% 0.28/0.47 ! [Q: pi,A2: late_subject,X2: name,Q2: pi,P: pi] :
% 0.28/0.47 ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X2 @ Q2 ) )
% 0.28/0.47 => ( ( fresh @ name @ pi @ X2 @ P )
% 0.28/0.47 => ( ( fresh @ name @ pi @ X2 @ Q )
% 0.28/0.47 => ( ( fresh @ name @ late_subject @ X2 @ A2 )
% 0.28/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X2 @ ( par @ P @ Q2 ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % transitions.Par2B
% 0.28/0.47 thf(fact_90_transitions_OResB,axiom,
% 0.28/0.47 ! [P: pi,A2: late_subject,X2: name,P2: pi,Y: name] :
% 0.28/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P2 ) )
% 0.28/0.47 => ( ( fresh @ name @ late_subject @ Y @ A2 )
% 0.28/0.47 => ( ( Y != X2 )
% 0.28/0.47 => ( ( fresh @ name @ pi @ X2 @ P )
% 0.28/0.47 => ( ( fresh @ name @ late_subject @ X2 @ A2 )
% 0.28/0.47 => ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A2 @ X2 @ ( res @ Y @ P2 ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % transitions.ResB
% 0.28/0.47 thf(fact_91_freeRes_Orecs_I2_J,axiom,
% 0.28/0.47 ! [T: $tType,P: T > $o,F1: name > name > T,F22: T] :
% 0.28/0.47 ( ! [X12: name,X23: name] : ( P @ ( F1 @ X12 @ X23 ) )
% 0.28/0.47 => ( ( P @ F22 )
% 0.28/0.47 => ( ( late_freeRes_rec @ T @ F1 @ F22 @ late_TauR )
% 0.28/0.47 = F22 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % freeRes.recs(2)
% 0.28/0.47 thf(fact_92_subject_Orecs_I1_J,axiom,
% 0.28/0.47 ! [T: $tType,P: T > $o,F1: name > T,F22: name > T,Name2: name] :
% 0.28/0.47 ( ! [X12: name] : ( P @ ( F1 @ X12 ) )
% 0.28/0.47 => ( ! [X12: name] : ( P @ ( F22 @ X12 ) )
% 0.28/0.47 => ( ( late_subject_rec @ T @ F1 @ F22 @ ( late_InputS @ Name2 ) )
% 0.28/0.47 = ( F1 @ Name2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subject.recs(1)
% 0.28/0.47 thf(fact_93_subject_Orecs_I2_J,axiom,
% 0.28/0.47 ! [T: $tType,P: T > $o,F1: name > T,F22: name > T,Name2: name] :
% 0.28/0.47 ( ! [X12: name] : ( P @ ( F1 @ X12 ) )
% 0.28/0.47 => ( ! [X12: name] : ( P @ ( F22 @ X12 ) )
% 0.28/0.47 => ( ( late_subject_rec @ T @ F1 @ F22 @ ( late_BoundOutputS @ Name2 ) )
% 0.28/0.47 = ( F22 @ Name2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subject.recs(2)
% 0.28/0.47 thf(fact_94_freeRes_Orecs_I1_J,axiom,
% 0.28/0.47 ! [T: $tType,P: T > $o,F1: name > name > T,F22: T,Name1: name,Name22: name] :
% 0.28/0.47 ( ! [X12: name,X23: name] : ( P @ ( F1 @ X12 @ X23 ) )
% 0.28/0.47 => ( ( P @ F22 )
% 0.28/0.47 => ( ( late_freeRes_rec @ T @ F1 @ F22 @ ( late_OutputR @ Name1 @ Name22 ) )
% 0.28/0.47 = ( F1 @ Name1 @ Name22 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % freeRes.recs(1)
% 0.28/0.47 thf(fact_95_resTauOutputTrans,axiom,
% 0.28/0.47 ! [X2: name,P: pi,A2: name,B: name,P2: pi] :
% 0.28/0.47 ~ ( late_transitions @ ( res @ X2 @ ( tau @ P ) ) @ ( late_FreeR @ ( late_OutputR @ A2 @ B ) @ P2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % resTauOutputTrans
% 0.28/0.47 thf(fact_96_resOutputTauTrans,axiom,
% 0.28/0.47 ! [X2: name,A2: name,B: name,P: pi,P2: pi] :
% 0.28/0.47 ~ ( late_transitions @ ( res @ X2 @ ( output @ A2 @ B @ P ) ) @ ( late_FreeR @ late_TauR @ P2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % resOutputTauTrans
% 0.28/0.47 thf(fact_97_resOutputInputTrans,axiom,
% 0.28/0.47 ! [X2: name,A2: name,B: name,P: pi,C: name,Y: name,P2: pi] :
% 0.28/0.47 ~ ( late_transitions @ ( res @ X2 @ ( output @ A2 @ B @ P ) ) @ ( late_BoundR @ ( late_InputS @ C ) @ Y @ P2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % resOutputInputTrans
% 0.28/0.47 thf(fact_98_name__fresh,axiom,
% 0.28/0.47 ( ( fresh @ name @ name )
% 0.28/0.47 = ( ^ [A5: name,B4: name] : ( A5 != B4 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % name_fresh
% 0.28/0.47 thf(fact_99_pi_Ofresh_I3_J,axiom,
% 0.28/0.47 ! [A2: name,X1: pi] :
% 0.28/0.47 ( ( fresh @ name @ pi @ A2 @ ( tau @ X1 ) )
% 0.28/0.47 = ( fresh @ name @ pi @ A2 @ X1 ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.fresh(3)
% 0.28/0.47 thf(fact_100_simps_I2_J,axiom,
% 0.28/0.47 ! [P: pi,C: name,D: name] :
% 0.28/0.47 ( ( subs @ ( tau @ P ) @ C @ D )
% 0.28/0.47 = ( tau @ ( subs @ P @ C @ D ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % simps(2)
% 0.28/0.47 thf(fact_101_pi_Ofresh_I2_J,axiom,
% 0.28/0.47 ! [A2: name,X32: name,X22: name,X1: pi] :
% 0.28/0.47 ( ( fresh @ name @ pi @ A2 @ ( output @ X32 @ X22 @ X1 ) )
% 0.28/0.47 = ( ( fresh @ name @ name @ A2 @ X32 )
% 0.28/0.47 & ( fresh @ name @ name @ A2 @ X22 )
% 0.28/0.47 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.fresh(2)
% 0.28/0.47 thf(fact_102_pi_Odistinct_I19_J,axiom,
% 0.28/0.47 ! [Name1: name,Name22: name,Pi4: pi,Pi: pi] :
% 0.28/0.47 ( ( output @ Name1 @ Name22 @ Pi4 )
% 0.28/0.47 != ( tau @ Pi ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.distinct(19)
% 0.28/0.47 thf(fact_103_pi_Oinject_I1_J,axiom,
% 0.28/0.47 ! [X32: name,X22: name,X1: pi,Y32: name,Y2: name,Y1: pi] :
% 0.28/0.47 ( ( ( output @ X32 @ X22 @ X1 )
% 0.28/0.47 = ( output @ Y32 @ Y2 @ Y1 ) )
% 0.28/0.47 = ( ( X32 = Y32 )
% 0.28/0.47 & ( X22 = Y2 )
% 0.28/0.47 & ( X1 = Y1 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.inject(1)
% 0.28/0.47 thf(fact_104_pi_Oinject_I2_J,axiom,
% 0.28/0.47 ! [X1: pi,Y1: pi] :
% 0.28/0.47 ( ( ( tau @ X1 )
% 0.28/0.47 = ( tau @ Y1 ) )
% 0.28/0.47 = ( X1 = Y1 ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.inject(2)
% 0.28/0.47 thf(fact_105_pi_Odistinct_I29_J,axiom,
% 0.28/0.47 ! [Name1: name,Name22: name,Pi4: pi,Pi12: pi,Pi22: pi] :
% 0.28/0.47 ( ( output @ Name1 @ Name22 @ Pi4 )
% 0.28/0.47 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.distinct(29)
% 0.28/0.47 thf(fact_106_pi_Odistinct_I31_J,axiom,
% 0.28/0.47 ! [Name1: name,Name22: name,Pi4: pi,Name: name,Pi: pi] :
% 0.28/0.47 ( ( output @ Name1 @ Name22 @ Pi4 )
% 0.28/0.47 != ( res @ Name @ Pi ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.distinct(31)
% 0.28/0.47 thf(fact_107_pi_Odistinct_I43_J,axiom,
% 0.28/0.47 ! [Pi4: pi,Pi12: pi,Pi22: pi] :
% 0.28/0.47 ( ( tau @ Pi4 )
% 0.28/0.47 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.distinct(43)
% 0.28/0.47 thf(fact_108_pi_Odistinct_I45_J,axiom,
% 0.28/0.47 ! [Pi4: pi,Name: name,Pi: pi] :
% 0.28/0.47 ( ( tau @ Pi4 )
% 0.28/0.47 != ( res @ Name @ Pi ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.distinct(45)
% 0.28/0.47 thf(fact_109_resTrans_I1_J,axiom,
% 0.28/0.47 ! [X2: name,B: name,P: pi,Rs: late_residual] :
% 0.28/0.47 ~ ( late_transitions @ ( res @ X2 @ ( output @ X2 @ B @ P ) ) @ Rs ) ).
% 0.28/0.47
% 0.28/0.47 % resTrans(1)
% 0.28/0.47 thf(fact_110_outputBoundTrans,axiom,
% 0.28/0.47 ! [A2: name,B: name,P: pi,C: late_subject,X2: name,P2: pi] :
% 0.28/0.47 ~ ( late_transitions @ ( output @ A2 @ B @ P ) @ ( late_BoundR @ C @ X2 @ P2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % outputBoundTrans
% 0.28/0.47 thf(fact_111_outputFreshTrans,axiom,
% 0.28/0.47 ! [A2: name,B: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 0.28/0.47 ( ( late_transitions @ ( output @ A2 @ B @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 0.28/0.47 => ~ ( ( fresh @ name @ late_freeRes @ A2 @ Alpha )
% 0.28/0.47 | ( fresh @ name @ late_freeRes @ B @ Alpha ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % outputFreshTrans
% 0.28/0.47 thf(fact_112_tauBoundTrans,axiom,
% 0.28/0.47 ! [P: pi,A2: late_subject,X2: name,P2: pi] :
% 0.28/0.47 ~ ( late_transitions @ ( tau @ P ) @ ( late_BoundR @ A2 @ X2 @ P2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % tauBoundTrans
% 0.28/0.47 thf(fact_113_resTauBoundTrans,axiom,
% 0.28/0.47 ! [X2: name,P: pi,A2: late_subject,Y: name,P2: pi] :
% 0.28/0.47 ~ ( late_transitions @ ( res @ X2 @ ( tau @ P ) ) @ ( late_BoundR @ A2 @ Y @ P2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % resTauBoundTrans
% 0.28/0.47 thf(fact_114_Output,axiom,
% 0.28/0.47 ! [A2: name,B: name,P: pi] : ( late_transitions @ ( output @ A2 @ B @ P ) @ ( late_FreeR @ ( late_OutputR @ A2 @ B ) @ P ) ) ).
% 0.28/0.47
% 0.28/0.47 % Output
% 0.28/0.47 thf(fact_115_outputIneqTrans,axiom,
% 0.28/0.47 ! [A2: name,B: name,P: pi,C: name,D: name,P2: pi] :
% 0.28/0.47 ( ( late_transitions @ ( output @ A2 @ B @ P ) @ ( late_FreeR @ ( late_OutputR @ C @ D ) @ P2 ) )
% 0.28/0.47 => ~ ( ( A2 != C )
% 0.28/0.47 | ( B != D ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % outputIneqTrans
% 0.28/0.47 thf(fact_116_outputCases_H,axiom,
% 0.28/0.47 ! [A2: name,B: name,P: pi,Rs: late_residual] :
% 0.28/0.47 ( ( late_transitions @ ( output @ A2 @ B @ P ) @ Rs )
% 0.28/0.47 => ~ ! [A4: name,B3: name,P4: pi] :
% 0.28/0.47 ( ( ( A2 = A4 )
% 0.28/0.47 & ( B = B3 )
% 0.28/0.47 & ( P = P4 ) )
% 0.28/0.47 => ( Rs
% 0.28/0.47 != ( late_FreeR @ ( late_OutputR @ A4 @ B3 ) @ P4 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % outputCases'
% 0.28/0.47 thf(fact_117_outputCases,axiom,
% 0.28/0.47 ! [A2: name,B: name,P: pi,Alpha: late_freeRes,P2: pi,Prop: late_freeRes > pi > $o] :
% 0.28/0.47 ( ( late_transitions @ ( output @ A2 @ B @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 0.28/0.47 => ( ( ( Alpha
% 0.28/0.47 = ( late_OutputR @ A2 @ B ) )
% 0.28/0.47 => ( ( P = P2 )
% 0.28/0.47 => ( Prop @ ( late_OutputR @ A2 @ B ) @ P ) ) )
% 0.28/0.47 => ( Prop @ Alpha @ P2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % outputCases
% 0.28/0.47 thf(fact_118_outputTauTrans,axiom,
% 0.28/0.47 ! [A2: name,B: name,P: pi,P2: pi] :
% 0.28/0.47 ~ ( late_transitions @ ( output @ A2 @ B @ P ) @ ( late_FreeR @ late_TauR @ P2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % outputTauTrans
% 0.28/0.47 thf(fact_119_tauOutputTrans,axiom,
% 0.28/0.47 ! [P: pi,A2: name,B: name,P2: pi] :
% 0.28/0.47 ~ ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ ( late_OutputR @ A2 @ B ) @ P2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % tauOutputTrans
% 0.28/0.47 thf(fact_120_Tau,axiom,
% 0.28/0.47 ! [P: pi] : ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ late_TauR @ P ) ) ).
% 0.28/0.47
% 0.28/0.47 % Tau
% 0.28/0.47 thf(fact_121_tauCases_H,axiom,
% 0.28/0.47 ! [P: pi,Rs: late_residual] :
% 0.28/0.47 ( ( late_transitions @ ( tau @ P ) @ Rs )
% 0.28/0.47 => ~ ! [P4: pi] :
% 0.28/0.47 ( ( ( tau @ P )
% 0.28/0.47 = ( tau @ P4 ) )
% 0.28/0.47 => ( Rs
% 0.28/0.47 != ( late_FreeR @ late_TauR @ P4 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % tauCases'
% 0.28/0.47 thf(fact_122_tauCases,axiom,
% 0.28/0.47 ! [P: pi,Alpha: late_freeRes,P2: pi,Prop: late_freeRes > pi > $o] :
% 0.28/0.47 ( ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 0.28/0.47 => ( ( ( Alpha = late_TauR )
% 0.28/0.47 => ( ( P = P2 )
% 0.28/0.47 => ( Prop @ late_TauR @ P ) ) )
% 0.28/0.47 => ( Prop @ Alpha @ P2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % tauCases
% 0.28/0.47 thf(fact_123_resOutputOutputTrans,axiom,
% 0.28/0.47 ! [X2: name,A2: name,P: pi,B: name,Y: name,P2: pi] :
% 0.28/0.47 ~ ( late_transitions @ ( res @ X2 @ ( output @ A2 @ X2 @ P ) ) @ ( late_FreeR @ ( late_OutputR @ B @ Y ) @ P2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % resOutputOutputTrans
% 0.28/0.47 thf(fact_124_resInputBoundOutputTrans,axiom,
% 0.28/0.47 ! [X2: name,A2: name,Y: name,P: pi,B: name,Z: name,P2: pi] :
% 0.28/0.47 ~ ( late_transitions @ ( res @ X2 @ ( input @ A2 @ Y @ P ) ) @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ Z @ P2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % resInputBoundOutputTrans
% 0.28/0.47 thf(fact_125_residual_Ofresh_I1_J,axiom,
% 0.28/0.47 ! [A2: name,X32: late_subject,X1: name,X22: pi] :
% 0.28/0.47 ( ( fresh @ name @ late_residual @ A2 @ ( late_BoundR @ X32 @ X1 @ X22 ) )
% 0.28/0.47 = ( ( fresh @ name @ late_subject @ A2 @ X32 )
% 0.28/0.47 & ( fresh @ name @ ( name > ( noption @ pi ) ) @ A2 @ ( abs_fun @ name @ pi @ X1 @ X22 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % residual.fresh(1)
% 0.28/0.47 thf(fact_126_simps_I3_J,axiom,
% 0.28/0.47 ! [A2: name,B: name,P: pi,C: name,D: name] :
% 0.28/0.47 ( ( subs @ ( output @ A2 @ B @ P ) @ C @ D )
% 0.28/0.47 = ( output @ ( subst_name @ A2 @ C @ D ) @ ( subst_name @ B @ C @ D ) @ ( subs @ P @ C @ D ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % simps(3)
% 0.28/0.47 thf(fact_127_inputIneqTrans,axiom,
% 0.28/0.47 ! [A2: name,X2: name,P: pi,B: late_subject,Y: name,P2: pi] :
% 0.28/0.47 ( ( late_transitions @ ( input @ A2 @ X2 @ P ) @ ( late_BoundR @ B @ Y @ P2 ) )
% 0.28/0.47 => ~ ( fresh @ name @ late_subject @ A2 @ B ) ) ).
% 0.28/0.47
% 0.28/0.47 % inputIneqTrans
% 0.28/0.47 thf(fact_128_transitions_OInput,axiom,
% 0.28/0.47 ! [X2: name,A2: name,P: pi] :
% 0.28/0.47 ( ( X2 != A2 )
% 0.28/0.47 => ( late_transitions @ ( input @ A2 @ X2 @ P ) @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % transitions.Input
% 0.28/0.47 thf(fact_129_substInput,axiom,
% 0.28/0.47 ! [X2: name,B: name,C: name,A2: name,P: pi] :
% 0.28/0.47 ( ( X2 != B )
% 0.28/0.47 => ( ( X2 != C )
% 0.28/0.47 => ( ( subs @ ( input @ A2 @ X2 @ P ) @ B @ C )
% 0.28/0.47 = ( input @ ( subst_name @ A2 @ B @ C ) @ X2 @ ( subs @ P @ B @ C ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % substInput
% 0.28/0.47 thf(fact_130_simps_I4_J,axiom,
% 0.28/0.47 ! [X2: name,A2: name,C: name,D: name,P: pi] :
% 0.28/0.47 ( ( X2 != A2 )
% 0.28/0.47 => ( ( X2 != C )
% 0.28/0.47 => ( ( X2 != D )
% 0.28/0.47 => ( ( subs @ ( input @ A2 @ X2 @ P ) @ C @ D )
% 0.28/0.47 = ( input @ ( subst_name @ A2 @ C @ D ) @ X2 @ ( subs @ P @ C @ D ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % simps(4)
% 0.28/0.47 thf(fact_131_pi_Ofresh_I9_J,axiom,
% 0.28/0.47 ! [A2: name,X1: name,X22: pi] :
% 0.28/0.47 ( ( fresh @ name @ pi @ A2 @ ( res @ X1 @ X22 ) )
% 0.28/0.47 = ( fresh @ name @ ( name > ( noption @ pi ) ) @ A2 @ ( abs_fun @ name @ pi @ X1 @ X22 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.fresh(9)
% 0.28/0.47 thf(fact_132_pi_Ofresh_I4_J,axiom,
% 0.28/0.47 ! [A2: name,X32: name,X1: name,X22: pi] :
% 0.28/0.47 ( ( fresh @ name @ pi @ A2 @ ( input @ X32 @ X1 @ X22 ) )
% 0.28/0.47 = ( ( fresh @ name @ name @ A2 @ X32 )
% 0.28/0.47 & ( fresh @ name @ ( name > ( noption @ pi ) ) @ A2 @ ( abs_fun @ name @ pi @ X1 @ X22 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.fresh(4)
% 0.28/0.47 thf(fact_133_pi_Oinject_I3_J,axiom,
% 0.28/0.47 ! [X32: name,X1: name,X22: pi,Y32: name,Y1: name,Y2: pi] :
% 0.28/0.47 ( ( ( input @ X32 @ X1 @ X22 )
% 0.28/0.47 = ( input @ Y32 @ Y1 @ Y2 ) )
% 0.28/0.47 = ( ( X32 = Y32 )
% 0.28/0.47 & ( ( abs_fun @ name @ pi @ X1 @ X22 )
% 0.28/0.47 = ( abs_fun @ name @ pi @ Y1 @ Y2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.inject(3)
% 0.28/0.47 thf(fact_134_subst__name__def,axiom,
% 0.28/0.47 ( subst_name
% 0.28/0.47 = ( ^ [A5: name,B4: name,C3: name] : ( if @ name @ ( A5 = B4 ) @ C3 @ A5 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subst_name_def
% 0.28/0.47 thf(fact_135_pi_Oinject_I8_J,axiom,
% 0.28/0.47 ! [X1: name,X22: pi,Y1: name,Y2: pi] :
% 0.28/0.47 ( ( ( res @ X1 @ X22 )
% 0.28/0.47 = ( res @ Y1 @ Y2 ) )
% 0.28/0.47 = ( ( abs_fun @ name @ pi @ X1 @ X22 )
% 0.28/0.47 = ( abs_fun @ name @ pi @ Y1 @ Y2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.inject(8)
% 0.28/0.47 thf(fact_136_residual_Oinject_I1_J,axiom,
% 0.28/0.47 ! [X32: late_subject,X1: name,X22: pi,Y32: late_subject,Y1: name,Y2: pi] :
% 0.28/0.47 ( ( ( late_BoundR @ X32 @ X1 @ X22 )
% 0.28/0.47 = ( late_BoundR @ Y32 @ Y1 @ Y2 ) )
% 0.28/0.47 = ( ( X32 = Y32 )
% 0.28/0.47 & ( ( abs_fun @ name @ pi @ X1 @ X22 )
% 0.28/0.47 = ( abs_fun @ name @ pi @ Y1 @ Y2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % residual.inject(1)
% 0.28/0.47 thf(fact_137_name__fresh__abs,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( fs_name @ A )
% 0.28/0.47 => ! [B: name,A2: name,X2: A] :
% 0.28/0.47 ( ( fresh @ name @ ( name > ( noption @ A ) ) @ B @ ( abs_fun @ name @ A @ A2 @ X2 ) )
% 0.28/0.47 = ( ( B = A2 )
% 0.28/0.47 | ( fresh @ name @ A @ B @ X2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % name_fresh_abs
% 0.28/0.47 thf(fact_138_abs__fresh_I1_J,axiom,
% 0.28/0.47 ! [X6: $tType] :
% 0.28/0.47 ( ( fs_name @ X6 )
% 0.28/0.47 => ! [B: name,A2: name,X2: X6] :
% 0.28/0.47 ( ( fresh @ name @ ( name > ( noption @ X6 ) ) @ B @ ( abs_fun @ name @ X6 @ A2 @ X2 ) )
% 0.28/0.47 = ( ( B = A2 )
% 0.28/0.47 | ( fresh @ name @ X6 @ B @ X2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % abs_fresh(1)
% 0.28/0.47 thf(fact_139_pi_Odistinct_I55_J,axiom,
% 0.28/0.47 ! [Name1: name,Name22: name,Pi4: pi,Pi12: pi,Pi22: pi] :
% 0.28/0.47 ( ( input @ Name1 @ Name22 @ Pi4 )
% 0.28/0.47 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.distinct(55)
% 0.28/0.47 thf(fact_140_pi_Odistinct_I57_J,axiom,
% 0.28/0.47 ! [Name1: name,Name22: name,Pi4: pi,Name: name,Pi: pi] :
% 0.28/0.47 ( ( input @ Name1 @ Name22 @ Pi4 )
% 0.28/0.47 != ( res @ Name @ Pi ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.distinct(57)
% 0.28/0.47 thf(fact_141_pi_Odistinct_I21_J,axiom,
% 0.28/0.47 ! [Name1: name,Name22: name,Pi4: pi,Name13: name,Name24: name,Pi: pi] :
% 0.28/0.47 ( ( output @ Name1 @ Name22 @ Pi4 )
% 0.28/0.47 != ( input @ Name13 @ Name24 @ Pi ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.distinct(21)
% 0.28/0.47 thf(fact_142_pi_Odistinct_I35_J,axiom,
% 0.28/0.47 ! [Pi4: pi,Name13: name,Name24: name,Pi: pi] :
% 0.28/0.47 ( ( tau @ Pi4 )
% 0.28/0.47 != ( input @ Name13 @ Name24 @ Pi ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.distinct(35)
% 0.28/0.47 thf(fact_143_inputCases_H,axiom,
% 0.28/0.47 ! [A2: name,B: name,P: pi,Rs: late_residual] :
% 0.28/0.47 ( ( late_transitions @ ( input @ A2 @ B @ P ) @ Rs )
% 0.28/0.47 => ~ ! [X4: name,A4: name,P4: pi] :
% 0.28/0.47 ( ( ( A2 = A4 )
% 0.28/0.47 & ( ( abs_fun @ name @ pi @ B @ P )
% 0.28/0.47 = ( abs_fun @ name @ pi @ X4 @ P4 ) ) )
% 0.28/0.47 => ( ( Rs
% 0.28/0.47 = ( late_BoundR @ ( late_InputS @ A4 ) @ X4 @ P4 ) )
% 0.28/0.47 => ( X4 = A4 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % inputCases'
% 0.28/0.47 thf(fact_144_resTrans_I2_J,axiom,
% 0.28/0.47 ! [X2: name,Y: name,P: pi,Rs: late_residual] :
% 0.28/0.47 ~ ( late_transitions @ ( res @ X2 @ ( input @ X2 @ Y @ P ) ) @ Rs ) ).
% 0.28/0.47
% 0.28/0.47 % resTrans(2)
% 0.28/0.47 thf(fact_145_inputFreeTrans,axiom,
% 0.28/0.47 ! [A2: name,X2: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 0.28/0.47 ~ ( late_transitions @ ( input @ A2 @ X2 @ P ) @ ( late_FreeR @ Alpha @ P2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % inputFreeTrans
% 0.28/0.47 thf(fact_146_resInputFreeTrans,axiom,
% 0.28/0.47 ! [X2: name,A2: name,Y: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 0.28/0.47 ~ ( late_transitions @ ( res @ X2 @ ( input @ A2 @ Y @ P ) ) @ ( late_FreeR @ Alpha @ P2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % resInputFreeTrans
% 0.28/0.47 thf(fact_147_inputBoundOutputTrans,axiom,
% 0.28/0.47 ! [A2: name,X2: name,P: pi,B: name,Y: name,P2: pi] :
% 0.28/0.47 ~ ( late_transitions @ ( input @ A2 @ X2 @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ Y @ P2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % inputBoundOutputTrans
% 0.28/0.47 thf(fact_148_Late__Semantics_OInput,axiom,
% 0.28/0.47 ! [A2: name,X2: name,P: pi] : ( late_transitions @ ( input @ A2 @ X2 @ P ) @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P ) ) ).
% 0.28/0.47
% 0.28/0.47 % Late_Semantics.Input
% 0.28/0.47 thf(fact_149_simps_I5_J,axiom,
% 0.28/0.47 ! [A2: name,B: name,P: pi,C: name,D: name] :
% 0.28/0.47 ( ( subs @ ( match @ A2 @ B @ P ) @ C @ D )
% 0.28/0.47 = ( match @ ( subst_name @ A2 @ C @ D ) @ ( subst_name @ B @ C @ D ) @ ( subs @ P @ C @ D ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % simps(5)
% 0.28/0.47 thf(fact_150_simps_I6_J,axiom,
% 0.28/0.47 ! [A2: name,B: name,P: pi,C: name,D: name] :
% 0.28/0.47 ( ( subs @ ( mismatch @ A2 @ B @ P ) @ C @ D )
% 0.28/0.47 = ( mismatch @ ( subst_name @ A2 @ C @ D ) @ ( subst_name @ B @ C @ D ) @ ( subs @ P @ C @ D ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % simps(6)
% 0.28/0.47 thf(fact_151_pi_Ofresh_I5_J,axiom,
% 0.28/0.47 ! [A2: name,X32: name,X22: name,X1: pi] :
% 0.28/0.47 ( ( fresh @ name @ pi @ A2 @ ( match @ X32 @ X22 @ X1 ) )
% 0.28/0.47 = ( ( fresh @ name @ name @ A2 @ X32 )
% 0.28/0.47 & ( fresh @ name @ name @ A2 @ X22 )
% 0.28/0.47 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.fresh(5)
% 0.28/0.47 thf(fact_152_pi_Ofresh_I6_J,axiom,
% 0.28/0.47 ! [A2: name,X32: name,X22: name,X1: pi] :
% 0.28/0.47 ( ( fresh @ name @ pi @ A2 @ ( mismatch @ X32 @ X22 @ X1 ) )
% 0.28/0.47 = ( ( fresh @ name @ name @ A2 @ X32 )
% 0.28/0.47 & ( fresh @ name @ name @ A2 @ X22 )
% 0.28/0.47 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.fresh(6)
% 0.28/0.47 thf(fact_153_pi_Odistinct_I61_J,axiom,
% 0.28/0.47 ! [Name1: name,Name22: name,Pi4: pi,Name13: name,Name24: name,Pi: pi] :
% 0.28/0.47 ( ( match @ Name1 @ Name22 @ Pi4 )
% 0.28/0.47 != ( mismatch @ Name13 @ Name24 @ Pi ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.distinct(61)
% 0.28/0.47 thf(fact_154_pi_Oinject_I4_J,axiom,
% 0.28/0.47 ! [X32: name,X22: name,X1: pi,Y32: name,Y2: name,Y1: pi] :
% 0.28/0.47 ( ( ( match @ X32 @ X22 @ X1 )
% 0.28/0.47 = ( match @ Y32 @ Y2 @ Y1 ) )
% 0.28/0.47 = ( ( X32 = Y32 )
% 0.28/0.47 & ( X22 = Y2 )
% 0.28/0.47 & ( X1 = Y1 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.inject(4)
% 0.28/0.47 thf(fact_155_pi_Oinject_I5_J,axiom,
% 0.28/0.47 ! [X32: name,X22: name,X1: pi,Y32: name,Y2: name,Y1: pi] :
% 0.28/0.47 ( ( ( mismatch @ X32 @ X22 @ X1 )
% 0.28/0.47 = ( mismatch @ Y32 @ Y2 @ Y1 ) )
% 0.28/0.47 = ( ( X32 = Y32 )
% 0.28/0.47 & ( X22 = Y2 )
% 0.28/0.47 & ( X1 = Y1 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.inject(5)
% 0.28/0.47 thf(fact_156_Mismatch,axiom,
% 0.28/0.47 ! [P: pi,Rs: late_residual,A2: name,B: name] :
% 0.28/0.47 ( ( late_transitions @ P @ Rs )
% 0.28/0.47 => ( ( A2 != B )
% 0.28/0.47 => ( late_transitions @ ( mismatch @ A2 @ B @ P ) @ Rs ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Mismatch
% 0.28/0.47 thf(fact_157_Match,axiom,
% 0.28/0.47 ! [P: pi,Rs: late_residual,B: name] :
% 0.28/0.47 ( ( late_transitions @ P @ Rs )
% 0.28/0.47 => ( late_transitions @ ( match @ B @ B @ P ) @ Rs ) ) ).
% 0.28/0.47
% 0.28/0.47 % Match
% 0.28/0.47 thf(fact_158_mismatchCases_H,axiom,
% 0.28/0.47 ! [A2: name,B: name,P: pi,Rs: late_residual] :
% 0.28/0.47 ( ( late_transitions @ ( mismatch @ A2 @ B @ P ) @ Rs )
% 0.28/0.47 => ~ ! [P4: pi,A4: name,B3: name] :
% 0.28/0.47 ( ( ( A2 = A4 )
% 0.28/0.47 & ( B = B3 )
% 0.28/0.47 & ( P = P4 ) )
% 0.28/0.47 => ( ( late_transitions @ P4 @ Rs )
% 0.28/0.47 => ( A4 = B3 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % mismatchCases'
% 0.28/0.47 thf(fact_159_mismatchTrans,axiom,
% 0.28/0.47 ! [A2: name,P: pi,Rs: late_residual] :
% 0.28/0.47 ~ ( late_transitions @ ( mismatch @ A2 @ A2 @ P ) @ Rs ) ).
% 0.28/0.47
% 0.28/0.47 % mismatchTrans
% 0.28/0.47 thf(fact_160_mismatchCases,axiom,
% 0.28/0.47 ! [A2: name,B: name,P: pi,Rs: late_residual,F2: name > name > $o] :
% 0.28/0.47 ( ( late_transitions @ ( mismatch @ A2 @ B @ P ) @ Rs )
% 0.28/0.47 => ( ( ( late_transitions @ P @ Rs )
% 0.28/0.47 => ( ( A2 != B )
% 0.28/0.47 => ( F2 @ A2 @ B ) ) )
% 0.28/0.47 => ( F2 @ A2 @ B ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % mismatchCases
% 0.28/0.47 thf(fact_161_matchCases_H,axiom,
% 0.28/0.47 ! [A2: name,B: name,P: pi,Rs: late_residual] :
% 0.28/0.47 ( ( late_transitions @ ( match @ A2 @ B @ P ) @ Rs )
% 0.28/0.47 => ~ ! [P4: pi] :
% 0.28/0.47 ( ( ( B = A2 )
% 0.28/0.47 & ( P = P4 ) )
% 0.28/0.47 => ~ ( late_transitions @ P4 @ Rs ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % matchCases'
% 0.28/0.47 thf(fact_162_matchTrans,axiom,
% 0.28/0.47 ! [A2: name,B: name,P: pi,Rs: late_residual] :
% 0.28/0.47 ( ( late_transitions @ ( match @ A2 @ B @ P ) @ Rs )
% 0.28/0.47 => ( A2 = B ) ) ).
% 0.28/0.47
% 0.28/0.47 % matchTrans
% 0.28/0.47 thf(fact_163_matchCases,axiom,
% 0.28/0.47 ! [A2: name,B: name,P: pi,Rs: late_residual,F2: name > name > $o] :
% 0.28/0.47 ( ( late_transitions @ ( match @ A2 @ B @ P ) @ Rs )
% 0.28/0.47 => ( ( ( late_transitions @ P @ Rs )
% 0.28/0.47 => ( ( A2 = B )
% 0.28/0.47 => ( F2 @ A2 @ A2 ) ) )
% 0.28/0.47 => ( F2 @ A2 @ B ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % matchCases
% 0.28/0.47 thf(fact_164_pi_Odistinct_I65_J,axiom,
% 0.28/0.47 ! [Name1: name,Name22: name,Pi4: pi,Pi12: pi,Pi22: pi] :
% 0.28/0.47 ( ( match @ Name1 @ Name22 @ Pi4 )
% 0.28/0.47 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.distinct(65)
% 0.28/0.47 thf(fact_165_pi_Odistinct_I73_J,axiom,
% 0.28/0.47 ! [Name1: name,Name22: name,Pi4: pi,Pi12: pi,Pi22: pi] :
% 0.28/0.47 ( ( mismatch @ Name1 @ Name22 @ Pi4 )
% 0.28/0.47 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.distinct(73)
% 0.28/0.47 thf(fact_166_pi_Odistinct_I67_J,axiom,
% 0.28/0.47 ! [Name1: name,Name22: name,Pi4: pi,Name: name,Pi: pi] :
% 0.28/0.47 ( ( match @ Name1 @ Name22 @ Pi4 )
% 0.28/0.47 != ( res @ Name @ Pi ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.distinct(67)
% 0.28/0.47 thf(fact_167_pi_Odistinct_I75_J,axiom,
% 0.28/0.47 ! [Name1: name,Name22: name,Pi4: pi,Name: name,Pi: pi] :
% 0.28/0.47 ( ( mismatch @ Name1 @ Name22 @ Pi4 )
% 0.28/0.47 != ( res @ Name @ Pi ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.distinct(75)
% 0.28/0.47 thf(fact_168_pi_Odistinct_I49_J,axiom,
% 0.28/0.47 ! [Name1: name,Name22: name,Pi4: pi,Name13: name,Name24: name,Pi: pi] :
% 0.28/0.47 ( ( input @ Name1 @ Name22 @ Pi4 )
% 0.28/0.47 != ( match @ Name13 @ Name24 @ Pi ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.distinct(49)
% 0.28/0.47 thf(fact_169_pi_Odistinct_I51_J,axiom,
% 0.28/0.47 ! [Name1: name,Name22: name,Pi4: pi,Name13: name,Name24: name,Pi: pi] :
% 0.28/0.47 ( ( input @ Name1 @ Name22 @ Pi4 )
% 0.28/0.47 != ( mismatch @ Name13 @ Name24 @ Pi ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.distinct(51)
% 0.28/0.47 thf(fact_170_pi_Odistinct_I23_J,axiom,
% 0.28/0.47 ! [Name1: name,Name22: name,Pi4: pi,Name13: name,Name24: name,Pi: pi] :
% 0.28/0.47 ( ( output @ Name1 @ Name22 @ Pi4 )
% 0.28/0.47 != ( match @ Name13 @ Name24 @ Pi ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.distinct(23)
% 0.28/0.47 thf(fact_171_pi_Odistinct_I25_J,axiom,
% 0.28/0.47 ! [Name1: name,Name22: name,Pi4: pi,Name13: name,Name24: name,Pi: pi] :
% 0.28/0.47 ( ( output @ Name1 @ Name22 @ Pi4 )
% 0.28/0.47 != ( mismatch @ Name13 @ Name24 @ Pi ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.distinct(25)
% 0.28/0.47 thf(fact_172_pi_Odistinct_I37_J,axiom,
% 0.28/0.47 ! [Pi4: pi,Name13: name,Name24: name,Pi: pi] :
% 0.28/0.47 ( ( tau @ Pi4 )
% 0.28/0.47 != ( match @ Name13 @ Name24 @ Pi ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.distinct(37)
% 0.28/0.47 thf(fact_173_pi_Odistinct_I39_J,axiom,
% 0.28/0.47 ! [Pi4: pi,Name13: name,Name24: name,Pi: pi] :
% 0.28/0.47 ( ( tau @ Pi4 )
% 0.28/0.47 != ( mismatch @ Name13 @ Name24 @ Pi ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.distinct(39)
% 0.28/0.47 thf(fact_174_abs__fun__eq1,axiom,
% 0.28/0.47 ! [X: $tType,A: $tType,A2: X,X2: A,Y: A] :
% 0.28/0.47 ( ( ( abs_fun @ X @ A @ A2 @ X2 )
% 0.28/0.47 = ( abs_fun @ X @ A @ A2 @ Y ) )
% 0.28/0.47 = ( X2 = Y ) ) ).
% 0.28/0.47
% 0.28/0.47 % abs_fun_eq1
% 0.28/0.47 thf(fact_175_freeRes_Ocase_I2_J,axiom,
% 0.28/0.47 ! [A: $tType,F1: name > name > A,F22: A] :
% 0.28/0.47 ( ( late_case_freeRes @ A @ F1 @ F22 @ late_TauR )
% 0.28/0.47 = F22 ) ).
% 0.28/0.47
% 0.28/0.47 % freeRes.case(2)
% 0.28/0.47 thf(fact_176_subject_Ocase_I1_J,axiom,
% 0.28/0.47 ! [A: $tType,F1: name > A,F22: name > A,X1: name] :
% 0.28/0.47 ( ( late_case_subject @ A @ F1 @ F22 @ ( late_InputS @ X1 ) )
% 0.28/0.47 = ( F1 @ X1 ) ) ).
% 0.28/0.47
% 0.28/0.47 % subject.case(1)
% 0.28/0.47 thf(fact_177_freeRes_Ocase_I1_J,axiom,
% 0.28/0.47 ! [A: $tType,F1: name > name > A,F22: A,X11: name,X122: name] :
% 0.28/0.47 ( ( late_case_freeRes @ A @ F1 @ F22 @ ( late_OutputR @ X11 @ X122 ) )
% 0.28/0.47 = ( F1 @ X11 @ X122 ) ) ).
% 0.28/0.47
% 0.28/0.47 % freeRes.case(1)
% 0.28/0.47 thf(fact_178_subject_Ocase_I2_J,axiom,
% 0.28/0.47 ! [A: $tType,F1: name > A,F22: name > A,X22: name] :
% 0.28/0.47 ( ( late_case_subject @ A @ F1 @ F22 @ ( late_BoundOutputS @ X22 ) )
% 0.28/0.47 = ( F22 @ X22 ) ) ).
% 0.28/0.47
% 0.28/0.47 % subject.case(2)
% 0.28/0.47 thf(fact_179_pi_Ostrong__inducts,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( fs_name @ A )
% 0.28/0.47 => ! [P: A > pi > $o,Z: A,Pi4: pi] :
% 0.28/0.47 ( ! [Z2: A] : ( P @ Z2 @ piNil )
% 0.28/0.47 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: A] :
% 0.28/0.47 ( ! [Za: A] : ( P @ Za @ Pi3 )
% 0.28/0.47 => ( P @ Z2 @ ( output @ Name12 @ Name23 @ Pi3 ) ) )
% 0.28/0.47 => ( ! [Pi3: pi,Z2: A] :
% 0.28/0.47 ( ! [Za: A] : ( P @ Za @ Pi3 )
% 0.28/0.47 => ( P @ Z2 @ ( tau @ Pi3 ) ) )
% 0.28/0.47 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: A] :
% 0.28/0.47 ( ( fresh @ name @ A @ Name23 @ Z2 )
% 0.28/0.47 => ( ( fresh @ name @ name @ Name23 @ Name12 )
% 0.28/0.47 => ( ! [Za: A] : ( P @ Za @ Pi3 )
% 0.28/0.47 => ( P @ Z2 @ ( input @ Name12 @ Name23 @ Pi3 ) ) ) ) )
% 0.28/0.47 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: A] :
% 0.28/0.47 ( ! [Za: A] : ( P @ Za @ Pi3 )
% 0.28/0.47 => ( P @ Z2 @ ( match @ Name12 @ Name23 @ Pi3 ) ) )
% 0.28/0.47 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: A] :
% 0.28/0.47 ( ! [Za: A] : ( P @ Za @ Pi3 )
% 0.28/0.47 => ( P @ Z2 @ ( mismatch @ Name12 @ Name23 @ Pi3 ) ) )
% 0.28/0.47 => ( ! [Pi13: pi,Pi23: pi,Z2: A] :
% 0.28/0.47 ( ! [Za: A] : ( P @ Za @ Pi13 )
% 0.28/0.47 => ( ! [Za: A] : ( P @ Za @ Pi23 )
% 0.28/0.47 => ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 0.28/0.47 => ( ! [Pi13: pi,Pi23: pi,Z2: A] :
% 0.28/0.47 ( ! [Za: A] : ( P @ Za @ Pi13 )
% 0.28/0.47 => ( ! [Za: A] : ( P @ Za @ Pi23 )
% 0.28/0.47 => ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
% 0.28/0.47 => ( ! [Name3: name,Pi3: pi,Z2: A] :
% 0.28/0.47 ( ( fresh @ name @ A @ Name3 @ Z2 )
% 0.28/0.47 => ( ! [Za: A] : ( P @ Za @ Pi3 )
% 0.28/0.47 => ( P @ Z2 @ ( res @ Name3 @ Pi3 ) ) ) )
% 0.28/0.47 => ( ! [Pi3: pi,Z2: A] :
% 0.28/0.47 ( ! [Za: A] : ( P @ Za @ Pi3 )
% 0.28/0.47 => ( P @ Z2 @ ( bang @ Pi3 ) ) )
% 0.28/0.47 => ( P @ Z @ Pi4 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.strong_inducts
% 0.28/0.47 thf(fact_180_pi_Ostrong__induct,axiom,
% 0.28/0.47 ! [N: $tType] :
% 0.28/0.47 ( ( fs_name @ N )
% 0.28/0.47 => ! [P: N > pi > $o,Z: N,Pi4: pi] :
% 0.28/0.47 ( ! [Z2: N] : ( P @ Z2 @ piNil )
% 0.28/0.47 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: N] :
% 0.28/0.47 ( ! [Za: N] : ( P @ Za @ Pi3 )
% 0.28/0.47 => ( P @ Z2 @ ( output @ Name12 @ Name23 @ Pi3 ) ) )
% 0.28/0.47 => ( ! [Pi3: pi,Z2: N] :
% 0.28/0.47 ( ! [Za: N] : ( P @ Za @ Pi3 )
% 0.28/0.47 => ( P @ Z2 @ ( tau @ Pi3 ) ) )
% 0.28/0.47 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: N] :
% 0.28/0.47 ( ( fresh @ name @ N @ Name23 @ Z2 )
% 0.28/0.47 => ( ( fresh @ name @ name @ Name23 @ Name12 )
% 0.28/0.47 => ( ! [Za: N] : ( P @ Za @ Pi3 )
% 0.28/0.47 => ( P @ Z2 @ ( input @ Name12 @ Name23 @ Pi3 ) ) ) ) )
% 0.28/0.47 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: N] :
% 0.28/0.47 ( ! [Za: N] : ( P @ Za @ Pi3 )
% 0.28/0.47 => ( P @ Z2 @ ( match @ Name12 @ Name23 @ Pi3 ) ) )
% 0.28/0.47 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: N] :
% 0.28/0.47 ( ! [Za: N] : ( P @ Za @ Pi3 )
% 0.28/0.47 => ( P @ Z2 @ ( mismatch @ Name12 @ Name23 @ Pi3 ) ) )
% 0.28/0.47 => ( ! [Pi13: pi,Pi23: pi,Z2: N] :
% 0.28/0.47 ( ! [Za: N] : ( P @ Za @ Pi13 )
% 0.28/0.47 => ( ! [Za: N] : ( P @ Za @ Pi23 )
% 0.28/0.47 => ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 0.28/0.47 => ( ! [Pi13: pi,Pi23: pi,Z2: N] :
% 0.28/0.47 ( ! [Za: N] : ( P @ Za @ Pi13 )
% 0.28/0.47 => ( ! [Za: N] : ( P @ Za @ Pi23 )
% 0.28/0.47 => ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
% 0.28/0.47 => ( ! [Name3: name,Pi3: pi,Z2: N] :
% 0.28/0.47 ( ( fresh @ name @ N @ Name3 @ Z2 )
% 0.28/0.47 => ( ! [Za: N] : ( P @ Za @ Pi3 )
% 0.28/0.47 => ( P @ Z2 @ ( res @ Name3 @ Pi3 ) ) ) )
% 0.28/0.47 => ( ! [Pi3: pi,Z2: N] :
% 0.28/0.47 ( ! [Za: N] : ( P @ Za @ Pi3 )
% 0.28/0.47 => ( P @ Z2 @ ( bang @ Pi3 ) ) )
% 0.28/0.47 => ( P @ Z @ Pi4 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.strong_induct
% 0.28/0.47 thf(fact_181_residual_Ostrong__induct_H,axiom,
% 0.28/0.47 ! [N: $tType,F: N > ( set @ name ),P: N > late_residual > $o,Z: N,Residual: late_residual] :
% 0.28/0.47 ( ! [X4: N] : ( finite_finite @ name @ ( F @ X4 ) )
% 0.28/0.47 => ( ! [Subject2: late_subject,Name3: name,Pi3: pi,Z2: N] :
% 0.28/0.47 ( ~ ( member @ name @ Name3 @ ( F @ Z2 ) )
% 0.28/0.47 => ( ( fresh @ name @ late_subject @ Name3 @ Subject2 )
% 0.28/0.47 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi3 ) ) ) )
% 0.28/0.47 => ( ! [FreeRes: late_freeRes,Pi3: pi,Z2: N] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi3 ) )
% 0.28/0.47 => ( P @ Z @ Residual ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % residual.strong_induct'
% 0.28/0.47 thf(fact_182_pi_Ofresh_I10_J,axiom,
% 0.28/0.47 ! [A2: name,X1: pi] :
% 0.28/0.47 ( ( fresh @ name @ pi @ A2 @ ( bang @ X1 ) )
% 0.28/0.47 = ( fresh @ name @ pi @ A2 @ X1 ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.fresh(10)
% 0.28/0.47 thf(fact_183_pi_Ofresh_I7_J,axiom,
% 0.28/0.47 ! [A2: name,X22: pi,X1: pi] :
% 0.28/0.47 ( ( fresh @ name @ pi @ A2 @ ( sum @ X22 @ X1 ) )
% 0.28/0.47 = ( ( fresh @ name @ pi @ A2 @ X22 )
% 0.28/0.47 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.fresh(7)
% 0.28/0.47 thf(fact_184_pi_Ofresh_I1_J,axiom,
% 0.28/0.47 ! [A2: name] : ( fresh @ name @ pi @ A2 @ piNil ) ).
% 0.28/0.47
% 0.28/0.47 % pi.fresh(1)
% 0.28/0.47 thf(fact_185_simps_I10_J,axiom,
% 0.28/0.47 ! [P: pi,C: name,D: name] :
% 0.28/0.47 ( ( subs @ ( bang @ P ) @ C @ D )
% 0.28/0.47 = ( bang @ ( subs @ P @ C @ D ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % simps(10)
% 0.28/0.47 thf(fact_186_simps_I7_J,axiom,
% 0.28/0.47 ! [P: pi,Q: pi,C: name,D: name] :
% 0.28/0.47 ( ( subs @ ( sum @ P @ Q ) @ C @ D )
% 0.28/0.47 = ( sum @ ( subs @ P @ C @ D ) @ ( subs @ Q @ C @ D ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % simps(7)
% 0.28/0.47 thf(fact_187_simps_I1_J,axiom,
% 0.28/0.47 ! [C: name,D: name] :
% 0.28/0.47 ( ( subs @ piNil @ C @ D )
% 0.28/0.47 = piNil ) ).
% 0.28/0.47
% 0.28/0.47 % simps(1)
% 0.28/0.47 thf(fact_188_pi_Odistinct_I59_J,axiom,
% 0.28/0.47 ! [Name1: name,Name22: name,Pi4: pi,Pi: pi] :
% 0.28/0.47 ( ( input @ Name1 @ Name22 @ Pi4 )
% 0.28/0.47 != ( bang @ Pi ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.distinct(59)
% 0.28/0.47 thf(fact_189_pi_Odistinct_I53_J,axiom,
% 0.28/0.47 ! [Name1: name,Name22: name,Pi4: pi,Pi12: pi,Pi22: pi] :
% 0.28/0.47 ( ( input @ Name1 @ Name22 @ Pi4 )
% 0.28/0.47 != ( sum @ Pi12 @ Pi22 ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.distinct(53)
% 0.28/0.47 thf(fact_190_pi_Odistinct_I87_J,axiom,
% 0.28/0.47 ! [Pi1: pi,Pi2: pi,Pi: pi] :
% 0.28/0.47 ( ( par @ Pi1 @ Pi2 )
% 0.28/0.47 != ( bang @ Pi ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.distinct(87)
% 0.28/0.47 thf(fact_191_pi_Odistinct_I89_J,axiom,
% 0.28/0.47 ! [Name2: name,Pi4: pi,Pi: pi] :
% 0.28/0.47 ( ( res @ Name2 @ Pi4 )
% 0.28/0.47 != ( bang @ Pi ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.distinct(89)
% 0.28/0.47 thf(fact_192_pi_Odistinct_I33_J,axiom,
% 0.28/0.47 ! [Name1: name,Name22: name,Pi4: pi,Pi: pi] :
% 0.28/0.47 ( ( output @ Name1 @ Name22 @ Pi4 )
% 0.28/0.47 != ( bang @ Pi ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.distinct(33)
% 0.28/0.47 thf(fact_193_sumCases,axiom,
% 0.28/0.47 ! [P: pi,Q: pi,Rs: late_residual] :
% 0.28/0.47 ( ( late_transitions @ ( sum @ P @ Q ) @ Rs )
% 0.28/0.47 => ( ~ ( late_transitions @ P @ Rs )
% 0.28/0.47 => ( late_transitions @ Q @ Rs ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sumCases
% 0.28/0.47 thf(fact_194_sumCases_H,axiom,
% 0.28/0.47 ! [P: pi,Q: pi,Rs: late_residual] :
% 0.28/0.47 ( ( late_transitions @ ( sum @ P @ Q ) @ Rs )
% 0.28/0.47 => ( ~ ( late_transitions @ P @ Rs )
% 0.28/0.47 => ( late_transitions @ Q @ Rs ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sumCases'
% 0.28/0.47 thf(fact_195_Sum1,axiom,
% 0.28/0.47 ! [P: pi,Rs: late_residual,Q: pi] :
% 0.28/0.47 ( ( late_transitions @ P @ Rs )
% 0.28/0.47 => ( late_transitions @ ( sum @ P @ Q ) @ Rs ) ) ).
% 0.28/0.47
% 0.28/0.47 % Sum1
% 0.28/0.47 thf(fact_196_Sum2,axiom,
% 0.28/0.47 ! [Q: pi,Rs: late_residual,P: pi] :
% 0.28/0.47 ( ( late_transitions @ Q @ Rs )
% 0.28/0.47 => ( late_transitions @ ( sum @ P @ Q ) @ Rs ) ) ).
% 0.28/0.47
% 0.28/0.47 % Sum2
% 0.28/0.47 thf(fact_197_pi_Odistinct_I47_J,axiom,
% 0.28/0.47 ! [Pi4: pi,Pi: pi] :
% 0.28/0.47 ( ( tau @ Pi4 )
% 0.28/0.47 != ( bang @ Pi ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.distinct(47)
% 0.28/0.47 thf(fact_198_pi_Odistinct_I79_J,axiom,
% 0.28/0.47 ! [Pi1: pi,Pi2: pi,Pi12: pi,Pi22: pi] :
% 0.28/0.47 ( ( sum @ Pi1 @ Pi2 )
% 0.28/0.47 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.distinct(79)
% 0.28/0.47 thf(fact_199_pi_Odistinct_I81_J,axiom,
% 0.28/0.47 ! [Pi1: pi,Pi2: pi,Name: name,Pi: pi] :
% 0.28/0.47 ( ( sum @ Pi1 @ Pi2 )
% 0.28/0.47 != ( res @ Name @ Pi ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.distinct(81)
% 0.28/0.47 thf(fact_200_pi_Odistinct_I11_J,axiom,
% 0.28/0.47 ! [Pi12: pi,Pi22: pi] :
% 0.28/0.47 ( piNil
% 0.28/0.47 != ( sum @ Pi12 @ Pi22 ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.distinct(11)
% 0.28/0.47 thf(fact_201_pi_Odistinct_I17_J,axiom,
% 0.28/0.47 ! [Pi: pi] :
% 0.28/0.47 ( piNil
% 0.28/0.47 != ( bang @ Pi ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.distinct(17)
% 0.28/0.47 thf(fact_202_pi_Odistinct_I83_J,axiom,
% 0.28/0.47 ! [Pi1: pi,Pi2: pi,Pi: pi] :
% 0.28/0.47 ( ( sum @ Pi1 @ Pi2 )
% 0.28/0.47 != ( bang @ Pi ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.distinct(83)
% 0.28/0.47 thf(fact_203_pi_Oinject_I6_J,axiom,
% 0.28/0.47 ! [X22: pi,X1: pi,Y2: pi,Y1: pi] :
% 0.28/0.47 ( ( ( sum @ X22 @ X1 )
% 0.28/0.47 = ( sum @ Y2 @ Y1 ) )
% 0.28/0.47 = ( ( X22 = Y2 )
% 0.28/0.47 & ( X1 = Y1 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.inject(6)
% 0.28/0.47 thf(fact_204_pi_Oinject_I9_J,axiom,
% 0.28/0.47 ! [X1: pi,Y1: pi] :
% 0.28/0.47 ( ( ( bang @ X1 )
% 0.28/0.47 = ( bang @ Y1 ) )
% 0.28/0.47 = ( X1 = Y1 ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.inject(9)
% 0.28/0.47 thf(fact_205_pi_Odistinct_I3_J,axiom,
% 0.28/0.47 ! [Pi: pi] :
% 0.28/0.47 ( piNil
% 0.28/0.47 != ( tau @ Pi ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.distinct(3)
% 0.28/0.47 thf(fact_206_pi_Odistinct_I1_J,axiom,
% 0.28/0.47 ! [Name13: name,Name24: name,Pi: pi] :
% 0.28/0.47 ( piNil
% 0.28/0.47 != ( output @ Name13 @ Name24 @ Pi ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.distinct(1)
% 0.28/0.47 thf(fact_207_pi_Odistinct_I5_J,axiom,
% 0.28/0.47 ! [Name13: name,Name24: name,Pi: pi] :
% 0.28/0.47 ( piNil
% 0.28/0.47 != ( input @ Name13 @ Name24 @ Pi ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.distinct(5)
% 0.28/0.47 thf(fact_208_pi_Odistinct_I15_J,axiom,
% 0.28/0.47 ! [Name: name,Pi: pi] :
% 0.28/0.47 ( piNil
% 0.28/0.47 != ( res @ Name @ Pi ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.distinct(15)
% 0.28/0.47 thf(fact_209_pi_Odistinct_I13_J,axiom,
% 0.28/0.47 ! [Pi12: pi,Pi22: pi] :
% 0.28/0.47 ( piNil
% 0.28/0.47 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.distinct(13)
% 0.28/0.47 thf(fact_210_nilCases_H,axiom,
% 0.28/0.47 ! [Rs: late_residual] :
% 0.28/0.47 ~ ( late_transitions @ piNil @ Rs ) ).
% 0.28/0.47
% 0.28/0.47 % nilCases'
% 0.28/0.47 thf(fact_211_zeroTrans,axiom,
% 0.28/0.47 ! [Rs: late_residual] :
% 0.28/0.47 ~ ( late_transitions @ piNil @ Rs ) ).
% 0.28/0.47
% 0.28/0.47 % zeroTrans
% 0.28/0.47 thf(fact_212_pi_Odistinct_I41_J,axiom,
% 0.28/0.47 ! [Pi4: pi,Pi12: pi,Pi22: pi] :
% 0.28/0.47 ( ( tau @ Pi4 )
% 0.28/0.47 != ( sum @ Pi12 @ Pi22 ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.distinct(41)
% 0.28/0.47 thf(fact_213_pi_Odistinct_I27_J,axiom,
% 0.28/0.47 ! [Name1: name,Name22: name,Pi4: pi,Pi12: pi,Pi22: pi] :
% 0.28/0.47 ( ( output @ Name1 @ Name22 @ Pi4 )
% 0.28/0.47 != ( sum @ Pi12 @ Pi22 ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.distinct(27)
% 0.28/0.47 thf(fact_214_pi_Odistinct_I77_J,axiom,
% 0.28/0.47 ! [Name1: name,Name22: name,Pi4: pi,Pi: pi] :
% 0.28/0.47 ( ( mismatch @ Name1 @ Name22 @ Pi4 )
% 0.28/0.47 != ( bang @ Pi ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.distinct(77)
% 0.28/0.47 thf(fact_215_pi_Odistinct_I71_J,axiom,
% 0.28/0.47 ! [Name1: name,Name22: name,Pi4: pi,Pi12: pi,Pi22: pi] :
% 0.28/0.47 ( ( mismatch @ Name1 @ Name22 @ Pi4 )
% 0.28/0.47 != ( sum @ Pi12 @ Pi22 ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.distinct(71)
% 0.28/0.47 thf(fact_216_pi_Odistinct_I69_J,axiom,
% 0.28/0.47 ! [Name1: name,Name22: name,Pi4: pi,Pi: pi] :
% 0.28/0.47 ( ( match @ Name1 @ Name22 @ Pi4 )
% 0.28/0.47 != ( bang @ Pi ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.distinct(69)
% 0.28/0.47 thf(fact_217_pi_Odistinct_I63_J,axiom,
% 0.28/0.47 ! [Name1: name,Name22: name,Pi4: pi,Pi12: pi,Pi22: pi] :
% 0.28/0.47 ( ( match @ Name1 @ Name22 @ Pi4 )
% 0.28/0.47 != ( sum @ Pi12 @ Pi22 ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.distinct(63)
% 0.28/0.47 thf(fact_218_pi_Odistinct_I9_J,axiom,
% 0.28/0.47 ! [Name13: name,Name24: name,Pi: pi] :
% 0.28/0.47 ( piNil
% 0.28/0.47 != ( mismatch @ Name13 @ Name24 @ Pi ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.distinct(9)
% 0.28/0.47 thf(fact_219_pi_Odistinct_I7_J,axiom,
% 0.28/0.47 ! [Name13: name,Name24: name,Pi: pi] :
% 0.28/0.47 ( piNil
% 0.28/0.47 != ( match @ Name13 @ Name24 @ Pi ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.distinct(7)
% 0.28/0.47 thf(fact_220_Bang,axiom,
% 0.28/0.47 ! [P: pi,Rs: late_residual] :
% 0.28/0.47 ( ( late_transitions @ ( par @ P @ ( bang @ P ) ) @ Rs )
% 0.28/0.47 => ( late_transitions @ ( bang @ P ) @ Rs ) ) ).
% 0.28/0.47
% 0.28/0.47 % Bang
% 0.28/0.47 thf(fact_221_bangCases,axiom,
% 0.28/0.47 ! [P: pi,Rs: late_residual] :
% 0.28/0.47 ( ( late_transitions @ ( bang @ P ) @ Rs )
% 0.28/0.47 => ~ ! [P4: pi] :
% 0.28/0.47 ( ( ( bang @ P )
% 0.28/0.47 = ( bang @ P4 ) )
% 0.28/0.47 => ~ ( late_transitions @ ( par @ P4 @ ( bang @ P4 ) ) @ Rs ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % bangCases
% 0.28/0.47 thf(fact_222_pi_Ostrong__induct_H,axiom,
% 0.28/0.47 ! [N: $tType,F: N > ( set @ name ),P: N > pi > $o,Z: N,Pi4: pi] :
% 0.28/0.47 ( ! [X4: N] : ( finite_finite @ name @ ( F @ X4 ) )
% 0.28/0.47 => ( ! [Z2: N] : ( P @ Z2 @ piNil )
% 0.28/0.47 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: N] :
% 0.28/0.47 ( ! [Za: N] : ( P @ Za @ Pi3 )
% 0.28/0.47 => ( P @ Z2 @ ( output @ Name12 @ Name23 @ Pi3 ) ) )
% 0.28/0.47 => ( ! [Pi3: pi,Z2: N] :
% 0.28/0.47 ( ! [Za: N] : ( P @ Za @ Pi3 )
% 0.28/0.47 => ( P @ Z2 @ ( tau @ Pi3 ) ) )
% 0.28/0.47 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: N] :
% 0.28/0.47 ( ~ ( member @ name @ Name23 @ ( F @ Z2 ) )
% 0.28/0.47 => ( ( fresh @ name @ name @ Name23 @ Name12 )
% 0.28/0.47 => ( ! [Za: N] : ( P @ Za @ Pi3 )
% 0.28/0.47 => ( P @ Z2 @ ( input @ Name12 @ Name23 @ Pi3 ) ) ) ) )
% 0.28/0.47 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: N] :
% 0.28/0.47 ( ! [Za: N] : ( P @ Za @ Pi3 )
% 0.28/0.47 => ( P @ Z2 @ ( match @ Name12 @ Name23 @ Pi3 ) ) )
% 0.28/0.47 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: N] :
% 0.28/0.47 ( ! [Za: N] : ( P @ Za @ Pi3 )
% 0.28/0.47 => ( P @ Z2 @ ( mismatch @ Name12 @ Name23 @ Pi3 ) ) )
% 0.28/0.47 => ( ! [Pi13: pi,Pi23: pi,Z2: N] :
% 0.28/0.47 ( ! [Za: N] : ( P @ Za @ Pi13 )
% 0.28/0.47 => ( ! [Za: N] : ( P @ Za @ Pi23 )
% 0.28/0.47 => ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 0.28/0.47 => ( ! [Pi13: pi,Pi23: pi,Z2: N] :
% 0.28/0.47 ( ! [Za: N] : ( P @ Za @ Pi13 )
% 0.28/0.47 => ( ! [Za: N] : ( P @ Za @ Pi23 )
% 0.28/0.47 => ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
% 0.28/0.47 => ( ! [Name3: name,Pi3: pi,Z2: N] :
% 0.28/0.47 ( ~ ( member @ name @ Name3 @ ( F @ Z2 ) )
% 0.28/0.47 => ( ! [Za: N] : ( P @ Za @ Pi3 )
% 0.28/0.47 => ( P @ Z2 @ ( res @ Name3 @ Pi3 ) ) ) )
% 0.28/0.47 => ( ! [Pi3: pi,Z2: N] :
% 0.28/0.47 ( ! [Za: N] : ( P @ Za @ Pi3 )
% 0.28/0.47 => ( P @ Z2 @ ( bang @ Pi3 ) ) )
% 0.28/0.47 => ( P @ Z @ Pi4 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.strong_induct'
% 0.28/0.47 thf(fact_223_resZeroTrans,axiom,
% 0.28/0.47 ! [X2: name,Rs: late_residual] :
% 0.28/0.47 ~ ( late_transitions @ ( res @ X2 @ piNil ) @ Rs ) ).
% 0.28/0.47
% 0.28/0.47 % resZeroTrans
% 0.28/0.47 thf(fact_224_pi_Oinducts,axiom,
% 0.28/0.47 ! [P: pi > $o,Pi4: pi] :
% 0.28/0.47 ( ( P @ piNil )
% 0.28/0.47 => ( ! [Name12: name,Name23: name,Pi3: pi] :
% 0.28/0.47 ( ( P @ Pi3 )
% 0.28/0.47 => ( P @ ( output @ Name12 @ Name23 @ Pi3 ) ) )
% 0.28/0.47 => ( ! [Pi3: pi] :
% 0.28/0.47 ( ( P @ Pi3 )
% 0.28/0.47 => ( P @ ( tau @ Pi3 ) ) )
% 0.28/0.47 => ( ! [Name12: name,Name23: name,Pi3: pi] :
% 0.28/0.47 ( ( P @ Pi3 )
% 0.28/0.47 => ( P @ ( input @ Name12 @ Name23 @ Pi3 ) ) )
% 0.28/0.47 => ( ! [Name12: name,Name23: name,Pi3: pi] :
% 0.28/0.47 ( ( P @ Pi3 )
% 0.28/0.47 => ( P @ ( match @ Name12 @ Name23 @ Pi3 ) ) )
% 0.28/0.47 => ( ! [Name12: name,Name23: name,Pi3: pi] :
% 0.28/0.47 ( ( P @ Pi3 )
% 0.28/0.47 => ( P @ ( mismatch @ Name12 @ Name23 @ Pi3 ) ) )
% 0.28/0.47 => ( ! [Pi13: pi,Pi23: pi] :
% 0.28/0.47 ( ( P @ Pi13 )
% 0.28/0.47 => ( ( P @ Pi23 )
% 0.28/0.47 => ( P @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 0.28/0.47 => ( ! [Pi13: pi,Pi23: pi] :
% 0.28/0.47 ( ( P @ Pi13 )
% 0.28/0.47 => ( ( P @ Pi23 )
% 0.28/0.47 => ( P @ ( par @ Pi13 @ Pi23 ) ) ) )
% 0.28/0.47 => ( ! [Name3: name,Pi3: pi] :
% 0.28/0.47 ( ( P @ Pi3 )
% 0.28/0.47 => ( P @ ( res @ Name3 @ Pi3 ) ) )
% 0.28/0.47 => ( ! [Pi3: pi] :
% 0.28/0.47 ( ( P @ Pi3 )
% 0.28/0.47 => ( P @ ( bang @ Pi3 ) ) )
% 0.28/0.47 => ( P @ Pi4 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.inducts
% 0.28/0.47 thf(fact_225_aux2,axiom,
% 0.28/0.47 ! [P: pi] : ( late_bangPred @ P @ ( par @ P @ ( bang @ P ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % aux2
% 0.28/0.47 thf(fact_226_bangPred_Ocases,axiom,
% 0.28/0.47 ! [A1: pi,A22: pi] :
% 0.28/0.47 ( ( late_bangPred @ A1 @ A22 )
% 0.28/0.47 => ( ( A22
% 0.28/0.47 != ( bang @ A1 ) )
% 0.28/0.47 => ( A22
% 0.28/0.47 = ( par @ A1 @ ( bang @ A1 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % bangPred.cases
% 0.28/0.47 thf(fact_227_bangPred_Osimps,axiom,
% 0.28/0.47 ( late_bangPred
% 0.28/0.47 = ( ^ [A12: pi,A23: pi] :
% 0.28/0.47 ( ? [P5: pi] :
% 0.28/0.47 ( ( A12 = P5 )
% 0.28/0.47 & ( A23
% 0.28/0.47 = ( bang @ P5 ) ) )
% 0.28/0.47 | ? [P5: pi] :
% 0.28/0.47 ( ( A12 = P5 )
% 0.28/0.47 & ( A23
% 0.28/0.47 = ( par @ P5 @ ( bang @ P5 ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % bangPred.simps
% 0.28/0.47 thf(fact_228_aux1,axiom,
% 0.28/0.47 ! [P: pi] : ( late_bangPred @ P @ ( bang @ P ) ) ).
% 0.28/0.47
% 0.28/0.47 % aux1
% 0.28/0.47 thf(fact_229_bangPred_Oinducts,axiom,
% 0.28/0.47 ! [X1: pi,X22: pi,P: pi > pi > $o] :
% 0.28/0.47 ( ( late_bangPred @ X1 @ X22 )
% 0.28/0.47 => ( ! [P4: pi] : ( P @ P4 @ ( bang @ P4 ) )
% 0.28/0.47 => ( ! [P4: pi] : ( P @ P4 @ ( par @ P4 @ ( bang @ P4 ) ) )
% 0.28/0.47 => ( P @ X1 @ X22 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % bangPred.inducts
% 0.28/0.47 thf(fact_230_subs__def,axiom,
% 0.28/0.47 ( subs
% 0.28/0.47 = ( ^ [X3: pi,C3: name,D2: name] :
% 0.28/0.47 ( pi_rec @ pi @ piNil
% 0.28/0.47 @ ^ [A5: name,B4: name,P5: pi] : ( output @ ( subst_name @ A5 @ C3 @ D2 ) @ ( subst_name @ B4 @ C3 @ D2 ) )
% 0.28/0.47 @ ^ [P5: pi] : tau
% 0.28/0.47 @ ^ [A5: name,Y5: name,P5: pi] : ( input @ ( subst_name @ A5 @ C3 @ D2 ) @ Y5 )
% 0.28/0.47 @ ^ [A5: name,B4: name,P5: pi] : ( match @ ( subst_name @ A5 @ C3 @ D2 ) @ ( subst_name @ B4 @ C3 @ D2 ) )
% 0.28/0.47 @ ^ [A5: name,B4: name,P5: pi] : ( mismatch @ ( subst_name @ A5 @ C3 @ D2 ) @ ( subst_name @ B4 @ C3 @ D2 ) )
% 0.28/0.47 @ ^ [P5: pi,Q5: pi] : sum
% 0.28/0.47 @ ^ [P5: pi,Q5: pi] : par
% 0.28/0.47 @ ^ [Y5: name,P5: pi] : ( res @ Y5 )
% 0.28/0.47 @ ^ [P5: pi] : bang
% 0.28/0.47 @ X3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subs_def
% 0.28/0.47 thf(fact_231_abs__fresh_I2_J,axiom,
% 0.28/0.47 ! [X7: $tType] :
% 0.28/0.47 ( ( pt_name @ X7 )
% 0.28/0.47 => ! [X2: X7,B: name,A2: name] :
% 0.28/0.47 ( ( finite_finite @ name @ ( supp @ X7 @ name @ X2 ) )
% 0.28/0.47 => ( ( fresh @ name @ ( name > ( noption @ X7 ) ) @ B @ ( abs_fun @ name @ X7 @ A2 @ X2 ) )
% 0.28/0.47 = ( ( B = A2 )
% 0.28/0.47 | ( fresh @ name @ X7 @ B @ X2 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % abs_fresh(2)
% 0.28/0.47 thf(fact_232_exists__fresh,axiom,
% 0.28/0.47 ! [A: $tType,X2: A] :
% 0.28/0.47 ( ( finite_finite @ name @ ( supp @ A @ name @ X2 ) )
% 0.28/0.47 => ~ ! [C2: name] :
% 0.28/0.47 ~ ( fresh @ name @ A @ C2 @ X2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % exists_fresh
% 0.28/0.47 thf(fact_233_exists__fresh_H,axiom,
% 0.28/0.47 ! [A: $tType,X2: A] :
% 0.28/0.47 ( ( finite_finite @ name @ ( supp @ A @ name @ X2 ) )
% 0.28/0.47 => ? [C2: name] : ( fresh @ name @ A @ C2 @ X2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % exists_fresh'
% 0.28/0.47 thf(fact_234_supp__fresh__iff,axiom,
% 0.28/0.47 ! [X: $tType,A: $tType] :
% 0.28/0.47 ( ( supp @ A @ X )
% 0.28/0.47 = ( ^ [X3: A] :
% 0.28/0.47 ( collect @ X
% 0.28/0.47 @ ^ [A5: X] :
% 0.28/0.47 ~ ( fresh @ X @ A @ A5 @ X3 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % supp_fresh_iff
% 0.28/0.47 thf(fact_235_fresh__def,axiom,
% 0.28/0.47 ! [A: $tType,X: $tType] :
% 0.28/0.47 ( ( fresh @ X @ A )
% 0.28/0.47 = ( ^ [A5: X,X3: A] :
% 0.28/0.47 ~ ( member @ X @ A5 @ ( supp @ A @ X @ X3 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % fresh_def
% 0.28/0.47 thf(fact_236_pi_Osupp_I9_J,axiom,
% 0.28/0.47 ! [X1: name,X22: pi] :
% 0.28/0.47 ( ( supp @ pi @ name @ ( res @ X1 @ X22 ) )
% 0.28/0.47 = ( supp @ ( name > ( noption @ pi ) ) @ name @ ( abs_fun @ name @ pi @ X1 @ X22 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.supp(9)
% 0.28/0.47 thf(fact_237_freeRes_Ocase__distrib,axiom,
% 0.28/0.47 ! [A: $tType,B2: $tType,H: A > B2,F1: name > name > A,F22: A,FreeRes3: late_freeRes] :
% 0.28/0.47 ( ( H @ ( late_case_freeRes @ A @ F1 @ F22 @ FreeRes3 ) )
% 0.28/0.47 = ( late_case_freeRes @ B2
% 0.28/0.47 @ ^ [X13: name,X24: name] : ( H @ ( F1 @ X13 @ X24 ) )
% 0.28/0.47 @ ( H @ F22 )
% 0.28/0.47 @ FreeRes3 ) ) ).
% 0.28/0.47
% 0.28/0.47 % freeRes.case_distrib
% 0.28/0.47 thf(fact_238_subject_Ocase__distrib,axiom,
% 0.28/0.47 ! [B2: $tType,A: $tType,H: A > B2,F1: name > A,F22: name > A,Subject: late_subject] :
% 0.28/0.47 ( ( H @ ( late_case_subject @ A @ F1 @ F22 @ Subject ) )
% 0.28/0.47 = ( late_case_subject @ B2
% 0.28/0.47 @ ^ [X3: name] : ( H @ ( F1 @ X3 ) )
% 0.28/0.47 @ ^ [X3: name] : ( H @ ( F22 @ X3 ) )
% 0.28/0.47 @ Subject ) ) ).
% 0.28/0.47
% 0.28/0.47 % subject.case_distrib
% 0.28/0.47 thf(fact_239_pi_Osupp_I3_J,axiom,
% 0.28/0.47 ! [X1: pi] :
% 0.28/0.47 ( ( supp @ pi @ name @ ( tau @ X1 ) )
% 0.28/0.47 = ( supp @ pi @ name @ X1 ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.supp(3)
% 0.28/0.47 thf(fact_240_subject_Osupp_I2_J,axiom,
% 0.28/0.47 ! [X1: name] :
% 0.28/0.47 ( ( supp @ late_subject @ name @ ( late_BoundOutputS @ X1 ) )
% 0.28/0.47 = ( supp @ name @ name @ X1 ) ) ).
% 0.28/0.47
% 0.28/0.47 % subject.supp(2)
% 0.28/0.47 thf(fact_241_subject_Osupp_I1_J,axiom,
% 0.28/0.47 ! [X1: name] :
% 0.28/0.47 ( ( supp @ late_subject @ name @ ( late_InputS @ X1 ) )
% 0.28/0.47 = ( supp @ name @ name @ X1 ) ) ).
% 0.28/0.47
% 0.28/0.47 % subject.supp(1)
% 0.28/0.47 thf(fact_242_pi_Osupp_I10_J,axiom,
% 0.28/0.47 ! [X1: pi] :
% 0.28/0.47 ( ( supp @ pi @ name @ ( bang @ X1 ) )
% 0.28/0.47 = ( supp @ pi @ name @ X1 ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.supp(10)
% 0.28/0.47 thf(fact_243_fs__name1,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( fs_name @ A )
% 0.28/0.47 => ! [X2: A] : ( finite_finite @ name @ ( supp @ A @ name @ X2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % fs_name1
% 0.28/0.47 thf(fact_244_residual_Orecs_I2_J,axiom,
% 0.28/0.47 ! [N: $tType,T: $tType] :
% 0.28/0.47 ( ( pt_name @ T )
% 0.28/0.47 => ! [F1: late_subject > name > pi > T,F22: late_freeRes > pi > T,Z: N,P: T > $o,FreeRes3: late_freeRes,Pi4: pi] :
% 0.28/0.47 ( ( finite_finite @ name @ ( supp @ ( late_subject > name > pi > T ) @ name @ F1 ) )
% 0.28/0.47 => ( ( finite_finite @ name @ ( supp @ ( late_freeRes > pi > T ) @ name @ F22 ) )
% 0.28/0.47 => ( ( finite_finite @ name @ ( supp @ N @ name @ Z ) )
% 0.28/0.47 => ( ! [X12: late_subject,X23: name,X33: pi] : ( P @ ( F1 @ X12 @ X23 @ X33 ) )
% 0.28/0.47 => ( ! [X12: late_freeRes,X23: pi] : ( P @ ( F22 @ X12 @ X23 ) )
% 0.28/0.47 => ( ! [X12: late_subject,X23: name,X33: pi] :
% 0.28/0.47 ( ( fresh @ name @ ( late_subject > name > pi > T ) @ X23 @ F1 )
% 0.28/0.47 => ( ( fresh @ name @ late_subject @ X23 @ X12 )
% 0.28/0.47 => ( ( fresh @ name @ N @ X23 @ Z )
% 0.28/0.47 => ( ( P @ ( F1 @ X12 @ X23 @ X33 ) )
% 0.28/0.47 => ( fresh @ name @ T @ X23 @ ( F1 @ X12 @ X23 @ X33 ) ) ) ) ) )
% 0.28/0.47 => ( ( late_residual_rec @ T @ F1 @ F22 @ ( late_FreeR @ FreeRes3 @ Pi4 ) )
% 0.28/0.47 = ( F22 @ FreeRes3 @ Pi4 ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % residual.recs(2)
% 0.28/0.47 thf(fact_245_residual_Orecs_I1_J,axiom,
% 0.28/0.47 ! [N: $tType,T: $tType] :
% 0.28/0.47 ( ( pt_name @ T )
% 0.28/0.47 => ! [F1: late_subject > name > pi > T,F22: late_freeRes > pi > T,Z: N,P: T > $o,Name2: name,Subject: late_subject,Pi4: pi] :
% 0.28/0.47 ( ( finite_finite @ name @ ( supp @ ( late_subject > name > pi > T ) @ name @ F1 ) )
% 0.28/0.47 => ( ( finite_finite @ name @ ( supp @ ( late_freeRes > pi > T ) @ name @ F22 ) )
% 0.28/0.47 => ( ( finite_finite @ name @ ( supp @ N @ name @ Z ) )
% 0.28/0.47 => ( ! [X12: late_subject,X23: name,X33: pi] : ( P @ ( F1 @ X12 @ X23 @ X33 ) )
% 0.28/0.47 => ( ! [X12: late_freeRes,X23: pi] : ( P @ ( F22 @ X12 @ X23 ) )
% 0.28/0.47 => ( ! [X12: late_subject,X23: name,X33: pi] :
% 0.28/0.47 ( ( fresh @ name @ ( late_subject > name > pi > T ) @ X23 @ F1 )
% 0.28/0.47 => ( ( fresh @ name @ late_subject @ X23 @ X12 )
% 0.28/0.47 => ( ( fresh @ name @ N @ X23 @ Z )
% 0.28/0.47 => ( ( P @ ( F1 @ X12 @ X23 @ X33 ) )
% 0.28/0.47 => ( fresh @ name @ T @ X23 @ ( F1 @ X12 @ X23 @ X33 ) ) ) ) ) )
% 0.28/0.47 => ( ( fresh @ name @ ( late_subject > name > pi > T ) @ Name2 @ F1 )
% 0.28/0.47 => ( ( fresh @ name @ ( late_freeRes > pi > T ) @ Name2 @ F22 )
% 0.28/0.47 => ( ( fresh @ name @ late_subject @ Name2 @ Subject )
% 0.28/0.47 => ( ( late_residual_rec @ T @ F1 @ F22 @ ( late_BoundR @ Subject @ Name2 @ Pi4 ) )
% 0.28/0.47 = ( F1 @ Subject @ Name2 @ Pi4 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % residual.recs(1)
% 0.28/0.47 thf(fact_246_residual_Orec__fresh,axiom,
% 0.28/0.47 ! [T: $tType] :
% 0.28/0.47 ( ( pt_name @ T )
% 0.28/0.47 => ! [F1: late_subject > name > pi > T,F22: late_freeRes > pi > T,X2: late_residual,Y: T,A2: name] :
% 0.28/0.47 ( ( finite_finite @ name @ ( supp @ ( late_subject > name > pi > T ) @ name @ F1 ) )
% 0.28/0.47 => ( ( finite_finite @ name @ ( supp @ ( late_freeRes > pi > T ) @ name @ F22 ) )
% 0.28/0.47 => ( ( late_r582136743ec_set @ T @ F1 @ F22 @ X2 @ Y )
% 0.28/0.47 => ( ! [Y6: T] :
% 0.28/0.47 ( ( late_r582136743ec_set @ T @ F1 @ F22 @ X2 @ Y6 )
% 0.28/0.47 => ( Y6 = Y ) )
% 0.28/0.47 => ( ( fresh @ name @ late_residual @ A2 @ X2 )
% 0.28/0.47 => ( ( fresh @ name @ ( late_subject > name > pi > T ) @ A2 @ F1 )
% 0.28/0.47 => ( ( fresh @ name @ ( late_freeRes > pi > T ) @ A2 @ F22 )
% 0.28/0.47 => ( fresh @ name @ T @ A2 @ Y ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % residual.rec_fresh
% 0.28/0.47 thf(fact_247_residual_Orec__unique,axiom,
% 0.28/0.47 ! [N: $tType,T: $tType] :
% 0.28/0.47 ( ( pt_name @ T )
% 0.28/0.47 => ! [F1: late_subject > name > pi > T,F22: late_freeRes > pi > T,Z: N,P: T > $o,X2: late_residual] :
% 0.28/0.47 ( ( finite_finite @ name @ ( supp @ ( late_subject > name > pi > T ) @ name @ F1 ) )
% 0.28/0.47 => ( ( finite_finite @ name @ ( supp @ ( late_freeRes > pi > T ) @ name @ F22 ) )
% 0.28/0.47 => ( ( finite_finite @ name @ ( supp @ N @ name @ Z ) )
% 0.28/0.47 => ( ! [X12: late_subject,X23: name,X33: pi] : ( P @ ( F1 @ X12 @ X23 @ X33 ) )
% 0.28/0.47 => ( ! [X12: late_freeRes,X23: pi] : ( P @ ( F22 @ X12 @ X23 ) )
% 0.28/0.47 => ( ! [X12: late_subject,X23: name] :
% 0.28/0.47 ( ( fresh @ name @ ( late_subject > name > pi > T ) @ X23 @ F1 )
% 0.28/0.47 => ( ( fresh @ name @ late_subject @ X23 @ X12 )
% 0.28/0.47 => ( ( fresh @ name @ N @ X23 @ Z )
% 0.28/0.47 => ! [X33: pi] :
% 0.28/0.47 ( ( P @ ( F1 @ X12 @ X23 @ X33 ) )
% 0.28/0.47 => ( fresh @ name @ T @ X23 @ ( F1 @ X12 @ X23 @ X33 ) ) ) ) ) )
% 0.28/0.47 => ? [X4: T] :
% 0.28/0.47 ( ( late_r582136743ec_set @ T @ F1 @ F22 @ X2 @ X4 )
% 0.28/0.47 & ! [Y7: T] :
% 0.28/0.47 ( ( late_r582136743ec_set @ T @ F1 @ F22 @ X2 @ Y7 )
% 0.28/0.47 => ( Y7 = X4 ) ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % residual.rec_unique
% 0.28/0.47 thf(fact_248_residual_Orec__fin__supp,axiom,
% 0.28/0.47 ! [T: $tType] :
% 0.28/0.47 ( ( pt_name @ T )
% 0.28/0.47 => ! [F1: late_subject > name > pi > T,F22: late_freeRes > pi > T,X1: late_residual,Y1: T] :
% 0.28/0.47 ( ( finite_finite @ name @ ( supp @ ( late_subject > name > pi > T ) @ name @ F1 ) )
% 0.28/0.47 => ( ( finite_finite @ name @ ( supp @ ( late_freeRes > pi > T ) @ name @ F22 ) )
% 0.28/0.47 => ( ( late_r582136743ec_set @ T @ F1 @ F22 @ X1 @ Y1 )
% 0.28/0.47 => ( finite_finite @ name @ ( supp @ T @ name @ Y1 ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % residual.rec_fin_supp
% 0.28/0.47 thf(fact_249_pi_Osupp_I4_J,axiom,
% 0.28/0.47 ! [X32: name,X1: name,X22: pi] :
% 0.28/0.47 ( ( supp @ pi @ name @ ( input @ X32 @ X1 @ X22 ) )
% 0.28/0.47 = ( sup_sup @ ( set @ name ) @ ( supp @ name @ name @ X32 ) @ ( supp @ ( name > ( noption @ pi ) ) @ name @ ( abs_fun @ name @ pi @ X1 @ X22 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.supp(4)
% 0.28/0.47 thf(fact_250_residual_Osupp_I1_J,axiom,
% 0.28/0.47 ! [X32: late_subject,X1: name,X22: pi] :
% 0.28/0.47 ( ( supp @ late_residual @ name @ ( late_BoundR @ X32 @ X1 @ X22 ) )
% 0.28/0.47 = ( sup_sup @ ( set @ name ) @ ( supp @ late_subject @ name @ X32 ) @ ( supp @ ( name > ( noption @ pi ) ) @ name @ ( abs_fun @ name @ pi @ X1 @ X22 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % residual.supp(1)
% 0.28/0.47 thf(fact_251_pi_Osupp_I7_J,axiom,
% 0.28/0.47 ! [X22: pi,X1: pi] :
% 0.28/0.47 ( ( supp @ pi @ name @ ( sum @ X22 @ X1 ) )
% 0.28/0.47 = ( sup_sup @ ( set @ name ) @ ( supp @ pi @ name @ X22 ) @ ( supp @ pi @ name @ X1 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.supp(7)
% 0.28/0.47 thf(fact_252_pi_Osupp_I8_J,axiom,
% 0.28/0.47 ! [X22: pi,X1: pi] :
% 0.28/0.47 ( ( supp @ pi @ name @ ( par @ X22 @ X1 ) )
% 0.28/0.47 = ( sup_sup @ ( set @ name ) @ ( supp @ pi @ name @ X22 ) @ ( supp @ pi @ name @ X1 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.supp(8)
% 0.28/0.47 thf(fact_253_residual_Osupp_I2_J,axiom,
% 0.28/0.47 ! [X22: late_freeRes,X1: pi] :
% 0.28/0.47 ( ( supp @ late_residual @ name @ ( late_FreeR @ X22 @ X1 ) )
% 0.28/0.47 = ( sup_sup @ ( set @ name ) @ ( supp @ late_freeRes @ name @ X22 ) @ ( supp @ pi @ name @ X1 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % residual.supp(2)
% 0.28/0.47 thf(fact_254_freeRes_Osupp_I1_J,axiom,
% 0.28/0.47 ! [X22: name,X1: name] :
% 0.28/0.47 ( ( supp @ late_freeRes @ name @ ( late_OutputR @ X22 @ X1 ) )
% 0.28/0.47 = ( sup_sup @ ( set @ name ) @ ( supp @ name @ name @ X22 ) @ ( supp @ name @ name @ X1 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % freeRes.supp(1)
% 0.28/0.47 thf(fact_255_pi_Osupp_I2_J,axiom,
% 0.28/0.47 ! [X32: name,X22: name,X1: pi] :
% 0.28/0.47 ( ( supp @ pi @ name @ ( output @ X32 @ X22 @ X1 ) )
% 0.28/0.47 = ( sup_sup @ ( set @ name ) @ ( supp @ name @ name @ X32 ) @ ( sup_sup @ ( set @ name ) @ ( supp @ name @ name @ X22 ) @ ( supp @ pi @ name @ X1 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % pi.supp(2)
% 0.28/0.47
% 0.28/0.47 % Type constructors (15)
% 0.28/0.47 thf(tcon_fun___Agent_Opt__name,axiom,
% 0.28/0.47 ! [A6: $tType,A7: $tType] :
% 0.28/0.47 ( ( ( pt_name @ A6 )
% 0.28/0.47 & ( pt_name @ A7 ) )
% 0.28/0.47 => ( pt_name @ ( A6 > A7 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Set_Oset___Agent_Opt__name_1,axiom,
% 0.28/0.47 ! [A6: $tType] :
% 0.28/0.47 ( ( pt_name @ A6 )
% 0.28/0.47 => ( pt_name @ ( set @ A6 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Agent_Opi___Agent_Opt__name_2,axiom,
% 0.28/0.47 pt_name @ pi ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Agent_Opi___Agent_Ofs__name,axiom,
% 0.28/0.47 fs_name @ pi ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_HOL_Obool___Agent_Opt__name_3,axiom,
% 0.28/0.47 pt_name @ $o ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_HOL_Obool___Agent_Ofs__name_4,axiom,
% 0.28/0.47 fs_name @ $o ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Agent_Oname___Agent_Opt__name_5,axiom,
% 0.28/0.47 pt_name @ name ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Agent_Oname___Agent_Ofs__name_6,axiom,
% 0.28/0.47 fs_name @ name ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Nominal_Onoption___Agent_Opt__name_7,axiom,
% 0.28/0.47 ! [A6: $tType] :
% 0.28/0.47 ( ( pt_name @ A6 )
% 0.28/0.47 => ( pt_name @ ( noption @ A6 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Late__Semantics_OfreeRes___Agent_Opt__name_8,axiom,
% 0.28/0.47 pt_name @ late_freeRes ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Late__Semantics_OfreeRes___Agent_Ofs__name_9,axiom,
% 0.28/0.47 fs_name @ late_freeRes ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Late__Semantics_Osubject___Agent_Opt__name_10,axiom,
% 0.28/0.47 pt_name @ late_subject ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Late__Semantics_Osubject___Agent_Ofs__name_11,axiom,
% 0.28/0.47 fs_name @ late_subject ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Late__Semantics_Oresidual___Agent_Opt__name_12,axiom,
% 0.28/0.47 pt_name @ late_residual ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Late__Semantics_Oresidual___Agent_Ofs__name_13,axiom,
% 0.28/0.47 fs_name @ late_residual ).
% 0.28/0.47
% 0.28/0.47 % Helper facts (3)
% 0.28/0.47 thf(help_If_3_1_T,axiom,
% 0.28/0.47 ! [P: $o] :
% 0.28/0.47 ( ( P = $true )
% 0.28/0.47 | ( P = $false ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(help_If_2_1_T,axiom,
% 0.28/0.47 ! [A: $tType,X2: A,Y: A] :
% 0.28/0.47 ( ( if @ A @ $false @ X2 @ Y )
% 0.28/0.47 = Y ) ).
% 0.28/0.47
% 0.28/0.47 thf(help_If_1_1_T,axiom,
% 0.28/0.47 ! [A: $tType,X2: A,Y: A] :
% 0.28/0.47 ( ( if @ A @ $true @ X2 @ Y )
% 0.28/0.47 = X2 ) ).
% 0.28/0.47
% 0.28/0.47 % Conjectures (1)
% 0.28/0.47 thf(conj_0,conjecture,
% 0.28/0.47 late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_FreeR @ late_TauR @ ( res @ y @ ( par @ ( par @ p @ q2 ) @ ( subs @ r2 @ x @ y ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 ------------------------
% 2.44/1.49 ---- Embedded in THF ---
% 2.44/1.49 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.44/1.49 %%% Generated on Tue Feb 24 08:29:15 EST 2026
% 2.44/1.49 %%% using '$$dhol' embedding, version 1.3.0.
% 2.44/1.49 %%% Logic specification used:
% 2.44/1.49 %%% thf(spec, logic, $$dhol).
% 2.44/1.49
% 2.44/1.49 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.pAINnnNPiL/DTF2DTF21913.p
% 2.44/1.49 thf(ty_t_Late__Semantics_Oresidual, type, late_residual: $tType).
% 2.44/1.49 thf(ty_t_Late__Semantics_Osubject, type, late_subject: $tType).
% 2.44/1.49 thf(ty_t_Late__Semantics_OfreeRes, type, late_freeRes: $tType).
% 2.44/1.49 thf(ty_t_Nominal_Onoption, type, noption: ($tType > $tType)).
% 2.44/1.49 thf(ty_t_Agent_Oname, type, name: $tType).
% 2.44/1.49 thf(ty_t_Agent_Opi, type, pi: $tType).
% 2.44/1.49 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 2.44/1.49 thf(sy_cl_Agent_Ofs__name, type, fs_name: (!> [A:$tType]: ($o))).
% 2.44/1.49 thf(sy_cl_Agent_Opt__name, type, pt_name: (!> [A:$tType]: ($o))).
% 2.44/1.49 thf(sy_c_Agent_Opi_OBang, type, bang: (pi > pi)).
% 2.44/1.49 thf(sy_c_Agent_Opi_OInput, type, input: (name > (name > (pi > pi)))).
% 2.44/1.49 thf(sy_c_Agent_Opi_OMatch, type, match: (name > (name > (pi > pi)))).
% 2.44/1.49 thf(sy_c_Agent_Opi_OMismatch, type, mismatch: (name > (name > (pi > pi)))).
% 2.44/1.49 thf(sy_c_Agent_Opi_OOutput, type, output: (name > (name > (pi > pi)))).
% 2.44/1.49 thf(sy_c_Agent_Opi_OPar, type, par: (pi > (pi > pi))).
% 2.44/1.49 thf(sy_c_Agent_Opi_OPiNil, type, piNil: pi).
% 2.44/1.49 thf(sy_c_Agent_Opi_ORes, type, res: (name > (pi > pi))).
% 2.44/1.49 thf(sy_c_Agent_Opi_OSum, type, sum: (pi > (pi > pi))).
% 2.44/1.49 thf(sy_c_Agent_Opi_OTau, type, tau: (pi > pi)).
% 2.44/1.49 thf(sy_c_Agent_Opi_Opi__rec, type, pi_rec: (!> [T:$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)))))))))))))).
% 2.44/1.49 thf(sy_c_Agent_Osubs, type, subs: (pi > (name > (name > pi)))).
% 2.44/1.49 thf(sy_c_Agent_Osubst__name, type, subst_name: (name > (name > (name > name)))).
% 2.44/1.49 thf(sy_c_Finite__Set_Ofinite, type, finite_finite: (!> [A:$tType]: (((set @ A) > $o)))).
% 2.44/1.49 thf(sy_c_If, type, if: (!> [A:$tType]: (($o > (A > (A > A)))))).
% 2.44/1.49 thf(sy_c_Late__Semantics1_OfreeRes_Ocase__freeRes, type, late_case_freeRes: (!> [A:$tType]: (((name > (name > A)) > (A > (late_freeRes > A)))))).
% 2.44/1.49 thf(sy_c_Late__Semantics1_Osubject_Ocase__subject, type, late_case_subject: (!> [A:$tType]: (((name > A) > ((name > A) > (late_subject > A)))))).
% 2.44/1.49 thf(sy_c_Late__Semantics_ObangPred, type, late_bangPred: (pi > (pi > $o))).
% 2.44/1.49 thf(sy_c_Late__Semantics_OfreeRes_OOutputR, type, late_OutputR: (name > (name > late_freeRes))).
% 2.44/1.49 thf(sy_c_Late__Semantics_OfreeRes_OTauR, type, late_TauR: late_freeRes).
% 2.44/1.49 thf(sy_c_Late__Semantics_OfreeRes_OfreeRes__rec, type, late_freeRes_rec: (!> [T:$tType]: (((name > (name > T)) > (T > (late_freeRes > T)))))).
% 2.44/1.49 thf(sy_c_Late__Semantics_Oresidual_OBoundR, type, late_BoundR: (late_subject > (name > (pi > late_residual)))).
% 2.44/1.49 thf(sy_c_Late__Semantics_Oresidual_OFreeR, type, late_FreeR: (late_freeRes > (pi > late_residual))).
% 2.44/1.49 thf(sy_c_Late__Semantics_Oresidual_Oresidual__rec, type, late_residual_rec: (!> [T:$tType]: (((late_subject > (name > (pi > T))) > ((late_freeRes > (pi > T)) > (late_residual > T)))))).
% 2.44/1.49 thf(sy_c_Late__Semantics_Oresidual_Oresidual__rec__set, type, late_r582136743ec_set: (!> [T:$tType]: (((late_subject > (name > (pi > T))) > ((late_freeRes > (pi > T)) > (late_residual > (T > $o))))))).
% 2.44/1.49 thf(sy_c_Late__Semantics_Osubject_OBoundOutputS, type, late_BoundOutputS: (name > late_subject)).
% 2.44/1.49 thf(sy_c_Late__Semantics_Osubject_OInputS, type, late_InputS: (name > late_subject)).
% 2.44/1.49 thf(sy_c_Late__Semantics_Osubject_Osubject__rec, type, late_subject_rec: (!> [T:$tType]: (((name > T) > ((name > T) > (late_subject > T)))))).
% 2.44/1.49 thf(sy_c_Late__Semantics_Otransitions, type, late_transitions: (pi > (late_residual > $o))).
% 2.44/1.49 thf(sy_c_Lattices_Osup__class_Osup, type, sup_sup: (!> [A:$tType]: ((A > (A > A))))).
% 2.44/1.49 thf(sy_c_Nominal_Oabs__fun, type, abs_fun: (!> [X:$tType,A:$tType]: ((X > (A > (X > (noption @ A))))))).
% 2.44/1.49 thf(sy_c_Nominal_Ofresh, type, fresh: (!> [X:$tType,A:$tType]: ((X > (A > $o))))).
% 2.44/1.49 thf(sy_c_Nominal_Osupp, type, supp: (!> [A:$tType,X:$tType]: ((A > (set @ X))))).
% 2.44/1.49 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 2.44/1.49 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 2.44/1.49 thf(sy_v_P, type, p: pi).
% 2.44/1.49 thf(sy_v_PQR____, type, pqr: pi).
% 2.44/1.49 thf(sy_v_Q, type, q: pi).
% 2.44/1.49 thf(sy_v_QR____, type, qr: pi).
% 2.44/1.49 thf(sy_v_Q_H____, type, q2: pi).
% 2.44/1.49 thf(sy_v_R, type, r: pi).
% 2.44/1.49 thf(sy_v_R_H____, type, r2: pi).
% 2.44/1.49 thf(sy_v__092_060alpha_062____, type, alpha: late_freeRes).
% 2.44/1.49 thf(sy_v_a____, type, a: name).
% 2.44/1.49 thf(sy_v_x____, type, x: name).
% 2.44/1.49 thf(sy_v_y____, type, y: name).
% 2.44/1.49 thf(fact_0_cClose2_Ohyps_I14_J, axiom, (alpha = late_TauR)).
% 2.44/1.49 thf(fact_1_cClose2_Ohyps_I10_J, axiom, (y != a)).
% 2.44/1.49 thf(fact_2_cClose2_Ohyps_I5_J, axiom, (x != a)).
% 2.44/1.49 thf(fact_3_cClose2_Ohyps_I9_J, axiom, ((((fresh @ name) @ pi) @ y) @ r)).
% 2.44/1.49 thf(fact_4_cClose2_Ohyps_I6_J, axiom, (x != y)).
% 2.44/1.49 thf(fact_5_cClose2_Ohyps_I8_J, axiom, ((((fresh @ name) @ pi) @ y) @ q)).
% 2.44/1.49 thf(fact_6_cClose2_Ohyps_I3_J, axiom, ((((fresh @ name) @ pi) @ x) @ q)).
% 2.44/1.49 thf(fact_7_cClose2_Ohyps_I13_J, axiom, ((((fresh @ name) @ pi) @ y) @ p)).
% 2.44/1.49 thf(fact_8_cClose2_Ohyps_I12_J, axiom, ((((fresh @ name) @ pi) @ x) @ p)).
% 2.44/1.49 thf(fact_9_cClose2_Ohyps_I4_J, axiom, ((((fresh @ name) @ pi) @ x) @ r)).
% 2.44/1.49 thf(fact_10_cClose2_Ohyps_I7_J, axiom, ((((fresh @ name) @ pi) @ x) @ q2)).
% 2.44/1.49 thf(fact_11_cClose2_Ohyps_I11_J, axiom, ((((fresh @ name) @ pi) @ y) @ r2)).
% 2.44/1.49 thf(fact_12_cClose2_Ohyps_I2_J, axiom, ((late_transitions @ r) @ (((late_BoundR @ (late_InputS @ a)) @ x) @ r2))).
% 2.44/1.49 thf(fact_13__092_060open_062P_A_092_060parallel_062_AQ_A_092_060longmapsto_062_Aa_060_092_060nu_062y_062_A_092_060prec_062_AP_A_092_060parallel_062_AQ_H_092_060close_062, axiom, ((late_transitions @ ((par @ p) @ q)) @ (((late_BoundR @ (late_BoundOutputS @ a)) @ y) @ ((par @ p) @ q2)))).
% 2.44/1.49 thf(fact_14_cClose2_Ohyps_I1_J, axiom, ((late_transitions @ q) @ (((late_BoundR @ (late_BoundOutputS @ a)) @ y) @ q2))).
% 2.44/1.49 thf(fact_15_cPar2_Ohyps, axiom, ((late_transitions @ ((par @ q) @ r)) @ ((late_FreeR @ alpha) @ qr))).
% 2.44/1.49 thf(fact_16_Free_Ohyps, axiom, ((late_transitions @ ((par @ p) @ ((par @ q) @ r))) @ ((late_FreeR @ alpha) @ pqr))).
% 2.44/1.49 thf(fact_17_simps_I9_J, axiom, (! [X2:name,C:name,D:name,P:pi]: (((X2 != C) => ((X2 != D) => ((((subs @ ((res @ X2) @ P)) @ C) @ D) = ((res @ X2) @ (((subs @ P) @ C) @ D)))))))).
% 2.44/1.49 thf(fact_18_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)))))).
% 2.44/1.49 thf(fact_19_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))))))).
% 2.44/1.49 thf(fact_20_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))))))).
% 2.44/1.49 thf(fact_21_subst__identity, axiom, (! [P:pi,A2:name]: (((((subs @ P) @ A2) @ A2) = P)))).
% 2.44/1.49 thf(fact_22_pi_Odistinct_I85_J, axiom, (! [Pi1:pi,Pi2:pi,Name:name,Pi:pi]: ((((par @ Pi1) @ Pi2) != ((res @ Name) @ Pi))))).
% 2.44/1.49 thf(fact_23_Late__Semantics_OClose1, axiom, (! [P:pi,A2:name,X2:name,P2:pi,Q:pi,Y:name,Q2:pi]: ((((late_transitions @ P) @ (((late_BoundR @ (late_InputS @ A2)) @ X2) @ 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) @ X2) @ Y)) @ Q2)))))))))).
% 2.44/1.49 thf(fact_24_Late__Semantics_OClose2, axiom, (! [P:pi,A2:name,Y:name,P2:pi,Q:pi,X2:name,Q2:pi]: ((((late_transitions @ P) @ (((late_BoundR @ (late_BoundOutputS @ A2)) @ Y) @ P2)) => (((late_transitions @ Q) @ (((late_BoundR @ (late_InputS @ A2)) @ X2) @ Q2)) => (((((fresh @ name) @ pi) @ Y) @ Q) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ late_TauR) @ ((res @ Y) @ ((par @ P2) @ (((subs @ Q2) @ X2) @ Y))))))))))).
% 2.44/1.49 thf(fact_25_transitions_OClose1, axiom, (! [P:pi,A2:name,X2:name,P2:pi,Q:pi,Y:name,Q2:pi]: ((((late_transitions @ P) @ (((late_BoundR @ (late_InputS @ A2)) @ X2) @ P2)) => (((late_transitions @ Q) @ (((late_BoundR @ (late_BoundOutputS @ A2)) @ Y) @ Q2)) => (((((fresh @ name) @ pi) @ X2) @ P) => (((((fresh @ name) @ pi) @ X2) @ Q) => (((((fresh @ name) @ pi) @ Y) @ P) => (((((fresh @ name) @ pi) @ Y) @ Q) => ((X2 != A2) => (((((fresh @ name) @ pi) @ X2) @ Q2) => ((Y != A2) => (((((fresh @ name) @ pi) @ Y) @ P2) => ((X2 != Y) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ late_TauR) @ ((res @ Y) @ ((par @ (((subs @ P2) @ X2) @ Y)) @ Q2)))))))))))))))))).
% 2.44/1.49 thf(fact_26_transitions_OClose2, axiom, (! [P:pi,A2:name,Y:name,P2:pi,Q:pi,X2:name,Q2:pi]: ((((late_transitions @ P) @ (((late_BoundR @ (late_BoundOutputS @ A2)) @ Y) @ P2)) => (((late_transitions @ Q) @ (((late_BoundR @ (late_InputS @ A2)) @ X2) @ Q2)) => (((((fresh @ name) @ pi) @ X2) @ P) => (((((fresh @ name) @ pi) @ X2) @ Q) => (((((fresh @ name) @ pi) @ Y) @ P) => (((((fresh @ name) @ pi) @ Y) @ Q) => ((X2 != A2) => (((((fresh @ name) @ pi) @ X2) @ P2) => ((Y != A2) => (((((fresh @ name) @ pi) @ Y) @ Q2) => ((X2 != Y) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ late_TauR) @ ((res @ Y) @ ((par @ P2) @ (((subs @ Q2) @ X2) @ Y))))))))))))))))))).
% 2.44/1.49 thf(fact_27_substRes2, axiom, (! [B:name,P:pi,A2:name]: ((((((fresh @ name) @ pi) @ B) @ P) => (((res @ A2) @ P) = ((res @ B) @ (((subs @ P) @ A2) @ B))))))).
% 2.44/1.49 thf(fact_28_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))))))).
% 2.44/1.49 thf(fact_29_Late__Semantics_Osubject_Oinject_I2_J, axiom, (! [X1:name,Y1:name]: ((((late_BoundOutputS @ X1) = (late_BoundOutputS @ Y1)) = (X1 = Y1))))).
% 2.44/1.49 thf(fact_30_pi_Ofresh_I8_J, axiom, (! [A2:name,X22:pi,X1:pi]: ((((((fresh @ name) @ pi) @ A2) @ ((par @ X22) @ X1)) = (((((fresh @ name) @ pi) @ A2) @ X22) & ((((fresh @ name) @ pi) @ A2) @ X1)))))).
% 2.44/1.49 thf(fact_31_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)))))).
% 2.44/1.49 thf(fact_32_Late__Semantics_Osubject_Odistinct_I1_J, axiom, (! [Name2:name,Name:name]: (((late_InputS @ Name2) != (late_BoundOutputS @ Name))))).
% 2.44/1.49 thf(fact_33_name__exists__fresh, axiom, (! [A:$tType]: (((fs_name @ A) => (! [X2:A]: ((~ ((! [C2:name]: ((~ (((((fresh @ name) @ A) @ C2) @ X2))))))))))))).
% 2.44/1.49 thf(fact_34_subject_Oinducts, axiom, (! [P:(late_subject > $o),Subject:late_subject]: (((! [Name3:name]: ((P @ (late_InputS @ Name3)))) => ((! [Name3:name]: ((P @ (late_BoundOutputS @ Name3)))) => (P @ Subject)))))).
% 2.44/1.49 thf(fact_35_subject_Ostrong__induct_H, axiom, (! [N:$tType,P:(N > (late_subject > $o)),Z:N,Subject:late_subject]: (((! [Name3:name,Z2:N]: (((P @ Z2) @ (late_InputS @ Name3)))) => ((! [Name3:name,Z2:N]: (((P @ Z2) @ (late_BoundOutputS @ Name3)))) => ((P @ Z) @ Subject)))))).
% 2.44/1.49 thf(fact_36_subject_Ostrong__inducts, axiom, (! [A:$tType,P:(A > (late_subject > $o)),Z:A,Subject:late_subject]: (((! [Name3:name,Z2:A]: (((P @ Z2) @ (late_InputS @ Name3)))) => ((! [Name3:name,Z2:A]: (((P @ Z2) @ (late_BoundOutputS @ Name3)))) => ((P @ Z) @ Subject)))))).
% 2.44/1.49 thf(fact_37_residual_Ostrong__inducts, axiom, (! [A:$tType]: (((fs_name @ A) => (! [P:(A > (late_residual > $o)),Z:A,Residual:late_residual]: (((! [Subject2:late_subject,Name3:name,Pi3:pi,Z2:A]: ((((((fresh @ name) @ A) @ Name3) @ Z2) => (((((fresh @ name) @ late_subject) @ Name3) @ Subject2) => ((P @ Z2) @ (((late_BoundR @ Subject2) @ Name3) @ Pi3)))))) => ((! [FreeRes:late_freeRes,Pi3:pi,Z2:A]: (((P @ Z2) @ ((late_FreeR @ FreeRes) @ Pi3)))) => ((P @ Z) @ Residual))))))))).
% 2.44/1.49 thf(fact_38_residual_Ostrong__induct, axiom, (! [N:$tType]: (((fs_name @ N) => (! [P:(N > (late_residual > $o)),Z:N,Residual:late_residual]: (((! [Subject2:late_subject,Name3:name,Pi3:pi,Z2:N]: ((((((fresh @ name) @ N) @ Name3) @ Z2) => (((((fresh @ name) @ late_subject) @ Name3) @ Subject2) => ((P @ Z2) @ (((late_BoundR @ Subject2) @ Name3) @ Pi3)))))) => ((! [FreeRes:late_freeRes,Pi3:pi,Z2:N]: (((P @ Z2) @ ((late_FreeR @ FreeRes) @ Pi3)))) => ((P @ Z) @ Residual))))))))).
% 2.44/1.49 thf(fact_39_freshBoundDerivative_I2_J, axiom, (! [P:pi,A2:late_subject,X2:name,P2:pi,Y:name]: ((((late_transitions @ P) @ (((late_BoundR @ A2) @ X2) @ P2)) => (((((fresh @ name) @ pi) @ Y) @ P) => ((Y != X2) => ((((fresh @ name) @ pi) @ Y) @ P2))))))).
% 2.44/1.49 thf(fact_40_freshRes, axiom, (! [A2:name,P:pi]: (((((fresh @ name) @ pi) @ A2) @ ((res @ A2) @ P))))).
% 2.44/1.49 thf(fact_41_residual_Oinducts, axiom, (! [P:(late_residual > $o),Residual:late_residual]: (((! [Subject2:late_subject,Name3:name,Pi3:pi]: ((P @ (((late_BoundR @ Subject2) @ Name3) @ Pi3)))) => ((! [FreeRes:late_freeRes,Pi3:pi]: ((P @ ((late_FreeR @ FreeRes) @ Pi3)))) => (P @ Residual)))))).
% 2.44/1.49 thf(fact_42_residual_Odistinct_I1_J, axiom, (! [Subject:late_subject,Name2:name,Pi4:pi,FreeRes2:late_freeRes,Pi:pi]: (((((late_BoundR @ Subject) @ Name2) @ Pi4) != ((late_FreeR @ FreeRes2) @ Pi))))).
% 2.44/1.49 thf(fact_43_fresh__fact2, axiom, (! [A2:name,B:name,P:pi]: (((A2 != B) => ((((fresh @ name) @ pi) @ A2) @ (((subs @ P) @ A2) @ B)))))).
% 2.44/1.49 thf(fact_44_fresh__fact1, axiom, (! [A2:name,P:pi,C:name,B:name]: ((((((fresh @ name) @ pi) @ A2) @ P) => ((A2 != C) => ((((fresh @ name) @ pi) @ A2) @ (((subs @ P) @ B) @ C))))))).
% 2.44/1.49 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P)) = (P @ A2))))).
% 2.44/1.49 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A3:(set @ A)]: ((((collect @ A) @ (^ [X3:A]: ((((member @ A) @ X3) @ A3)))) = A3)))).
% 2.44/1.49 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X4:A]: (((P @ X4) = (Q @ X4)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 2.44/1.49 thf(fact_48_ext, axiom, (! [B2:$tType,A:$tType,F:(A > B2),G:(A > B2)]: (((! [X4:A]: (((F @ X4) = (G @ X4)))) => (F = G))))).
% 2.44/1.49 thf(fact_49_forget, axiom, (! [A2:name,P:pi,B:name]: ((((((fresh @ name) @ pi) @ A2) @ P) => ((((subs @ P) @ A2) @ B) = P))))).
% 2.44/1.49 thf(fact_50_parCasesB, axiom, (! [P:pi,Q:pi,A2:late_subject,X2:name,PQ:pi,Prop:(pi > $o)]: ((((late_transitions @ ((par @ P) @ Q)) @ (((late_BoundR @ A2) @ X2) @ PQ)) => (((((fresh @ name) @ pi) @ X2) @ P) => (((((fresh @ name) @ pi) @ X2) @ Q) => ((! [P3:pi]: ((((late_transitions @ P) @ (((late_BoundR @ A2) @ X2) @ P3)) => (Prop @ ((par @ P3) @ Q))))) => ((! [Q3:pi]: ((((late_transitions @ Q) @ (((late_BoundR @ A2) @ X2) @ Q3)) => (Prop @ ((par @ P) @ Q3))))) => (Prop @ PQ))))))))).
% 2.44/1.49 thf(fact_51_Late__Semantics_OPar2B, axiom, (! [Q:pi,A2:late_subject,X2:name,Q2:pi,P:pi]: ((((late_transitions @ Q) @ (((late_BoundR @ A2) @ X2) @ Q2)) => (((((fresh @ name) @ pi) @ X2) @ P) => ((late_transitions @ ((par @ P) @ Q)) @ (((late_BoundR @ A2) @ X2) @ ((par @ P) @ Q2)))))))).
% 2.44/1.49 thf(fact_52_Late__Semantics_OPar1B, axiom, (! [P:pi,A2:late_subject,X2:name,P2:pi,Q:pi]: ((((late_transitions @ P) @ (((late_BoundR @ A2) @ X2) @ P2)) => (((((fresh @ name) @ pi) @ X2) @ Q) => ((late_transitions @ ((par @ P) @ Q)) @ (((late_BoundR @ A2) @ X2) @ ((par @ P2) @ Q)))))))).
% 2.44/1.49 thf(fact_53_pi_Oinject_I7_J, axiom, (! [X22:pi,X1:pi,Y2:pi,Y1:pi]: (((((par @ X22) @ X1) = ((par @ Y2) @ Y1)) = ((X22 = Y2) & (X1 = Y1)))))).
% 2.44/1.49 thf(fact_54_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)))))).
% 2.44/1.49 thf(fact_55_residual_Oinject_I2_J, axiom, (! [X22:late_freeRes,X1:pi,Y2:late_freeRes,Y1:pi]: (((((late_FreeR @ X22) @ X1) = ((late_FreeR @ Y2) @ Y1)) = ((X22 = Y2) & (X1 = Y1)))))).
% 2.44/1.49 thf(fact_56_transitions_OComm2, axiom, (! [P:pi,A2:name,B:name,P2:pi,Q:pi,X2:name,Q2:pi]: ((((late_transitions @ P) @ ((late_FreeR @ ((late_OutputR @ A2) @ B)) @ P2)) => (((late_transitions @ Q) @ (((late_BoundR @ (late_InputS @ A2)) @ X2) @ Q2)) => (((((fresh @ name) @ pi) @ X2) @ P) => (((((fresh @ name) @ pi) @ X2) @ Q) => ((X2 != A2) => ((X2 != B) => (((((fresh @ name) @ pi) @ X2) @ P2) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ late_TauR) @ ((par @ P2) @ (((subs @ Q2) @ X2) @ B)))))))))))))).
% 2.44/1.49 thf(fact_57_transitions_OComm1, axiom, (! [P:pi,A2:name,X2:name,P2:pi,Q:pi,B:name,Q2:pi]: ((((late_transitions @ P) @ (((late_BoundR @ (late_InputS @ A2)) @ X2) @ P2)) => (((late_transitions @ Q) @ ((late_FreeR @ ((late_OutputR @ A2) @ B)) @ Q2)) => (((((fresh @ name) @ pi) @ X2) @ P) => (((((fresh @ name) @ pi) @ X2) @ Q) => ((X2 != A2) => ((X2 != B) => (((((fresh @ name) @ pi) @ X2) @ Q2) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ late_TauR) @ ((par @ (((subs @ P2) @ X2) @ B)) @ Q2))))))))))))).
% 2.44/1.49 thf(fact_58_Late__Semantics1_Osubject_Oinject_I1_J, axiom, (! [X1:name,Y1:name]: ((((late_InputS @ X1) = (late_InputS @ Y1)) = (X1 = Y1))))).
% 2.44/1.49 thf(fact_59_Late__Semantics1_Osubject_Oinject_I2_J, axiom, (! [X22:name,Y2:name]: ((((late_BoundOutputS @ X22) = (late_BoundOutputS @ Y2)) = (X22 = Y2))))).
% 2.44/1.49 thf(fact_60_Late__Semantics_OComm2, axiom, (! [P:pi,A2:name,B:name,P2:pi,Q:pi,X2:name,Q2:pi]: ((((late_transitions @ P) @ ((late_FreeR @ ((late_OutputR @ A2) @ B)) @ P2)) => (((late_transitions @ Q) @ (((late_BoundR @ (late_InputS @ A2)) @ X2) @ Q2)) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ late_TauR) @ ((par @ P2) @ (((subs @ Q2) @ X2) @ B))))))))).
% 2.44/1.49 thf(fact_61_Late__Semantics_OComm1, axiom, (! [P:pi,A2:name,X2:name,P2:pi,Q:pi,B:name,Q2:pi]: ((((late_transitions @ P) @ (((late_BoundR @ (late_InputS @ A2)) @ X2) @ P2)) => (((late_transitions @ Q) @ ((late_FreeR @ ((late_OutputR @ A2) @ B)) @ Q2)) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ late_TauR) @ ((par @ (((subs @ P2) @ X2) @ B)) @ Q2)))))))).
% 2.44/1.49 thf(fact_62_Late__Semantics1_Osubject_Odistinct_I1_J, axiom, (! [X1:name,X22:name]: (((late_InputS @ X1) != (late_BoundOutputS @ X22))))).
% 2.44/1.49 thf(fact_63_subject_Oexhaust, axiom, (! [Y:late_subject]: (((! [X12:name]: ((Y != (late_InputS @ X12)))) => (~ ((! [X23:name]: ((Y != (late_BoundOutputS @ X23)))))))))).
% 2.44/1.49 thf(fact_64_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))))))).
% 2.44/1.49 thf(fact_65_freeRes_Ofresh_I1_J, axiom, (! [A2:name,X22:name,X1:name]: ((((((fresh @ name) @ late_freeRes) @ A2) @ ((late_OutputR @ X22) @ X1)) = (((((fresh @ name) @ name) @ A2) @ X22) & ((((fresh @ name) @ name) @ A2) @ X1)))))).
% 2.44/1.49 thf(fact_66_Late__Semantics_OfreeRes_Oinject, axiom, (! [X22:name,X1:name,Y2:name,Y1:name]: (((((late_OutputR @ X22) @ X1) = ((late_OutputR @ Y2) @ Y1)) = ((X22 = Y2) & (X1 = Y1)))))).
% 2.44/1.49 thf(fact_67_Late__Semantics1_OfreeRes_Oinject, axiom, (! [X11:name,X122:name,Y11:name,Y12:name]: (((((late_OutputR @ X11) @ X122) = ((late_OutputR @ Y11) @ Y12)) = ((X11 = Y11) & (X122 = Y12)))))).
% 2.44/1.49 thf(fact_68_freeRes_Ofresh_I2_J, axiom, (! [A2:name]: (((((fresh @ name) @ late_freeRes) @ A2) @ late_TauR)))).
% 2.44/1.49 thf(fact_69_residual_Ofresh_I2_J, axiom, (! [A2:name,X22:late_freeRes,X1:pi]: ((((((fresh @ name) @ late_residual) @ A2) @ ((late_FreeR @ X22) @ X1)) = (((((fresh @ name) @ late_freeRes) @ A2) @ X22) & ((((fresh @ name) @ pi) @ A2) @ X1)))))).
% 2.44/1.49 thf(fact_70_subject_Ofresh_I2_J, axiom, (! [A2:name,X1:name]: ((((((fresh @ name) @ late_subject) @ A2) @ (late_BoundOutputS @ X1)) = ((((fresh @ name) @ name) @ A2) @ X1))))).
% 2.44/1.49 thf(fact_71_subject_Ofresh_I1_J, axiom, (! [A2:name,X1:name]: ((((((fresh @ name) @ late_subject) @ A2) @ (late_InputS @ X1)) = ((((fresh @ name) @ name) @ A2) @ X1))))).
% 2.44/1.49 thf(fact_72_Late__Semantics1_OfreeRes_Odistinct_I1_J, axiom, (! [X11:name,X122:name]: ((((late_OutputR @ X11) @ X122) != late_TauR)))).
% 2.44/1.49 thf(fact_73_freeRes_Oexhaust, axiom, (! [Y:late_freeRes]: (((! [X112:name,X123:name]: ((Y != ((late_OutputR @ X112) @ X123)))) => (Y = late_TauR))))).
% 2.44/1.49 thf(fact_74_Late__Semantics_OfreeRes_Odistinct_I1_J, axiom, (! [Name1:name,Name22:name]: ((((late_OutputR @ Name1) @ Name22) != late_TauR)))).
% 2.44/1.49 thf(fact_75_freeRes_Oinducts, axiom, (! [P:(late_freeRes > $o),FreeRes3:late_freeRes]: (((! [Name12:name,Name23:name]: ((P @ ((late_OutputR @ Name12) @ Name23)))) => ((P @ late_TauR) => (P @ FreeRes3)))))).
% 2.44/1.49 thf(fact_76_freeRes_Ostrong__induct_H, axiom, (! [N:$tType,P:(N > (late_freeRes > $o)),Z:N,FreeRes3:late_freeRes]: (((! [Name12:name,Name23:name,Z2:N]: (((P @ Z2) @ ((late_OutputR @ Name12) @ Name23)))) => ((! [Z2:N]: (((P @ Z2) @ late_TauR))) => ((P @ Z) @ FreeRes3)))))).
% 2.44/1.49 thf(fact_77_freeRes_Ostrong__inducts, axiom, (! [A:$tType,P:(A > (late_freeRes > $o)),Z:A,FreeRes3:late_freeRes]: (((! [Name12:name,Name23:name,Z2:A]: (((P @ Z2) @ ((late_OutputR @ Name12) @ Name23)))) => ((! [Z2:A]: (((P @ Z2) @ late_TauR))) => ((P @ Z) @ FreeRes3)))))).
% 2.44/1.49 thf(fact_78_resCases_H, axiom, (! [X2:name,P:pi,Rs:late_residual]: ((((late_transitions @ ((res @ X2) @ P)) @ Rs) => ((! [P4:pi,A4:name,B3:name]: (((((res @ X2) @ P) = ((res @ B3) @ P4)) => (! [P3:pi]: (((Rs = (((late_BoundR @ (late_BoundOutputS @ A4)) @ B3) @ P3)) => (((late_transitions @ P4) @ ((late_FreeR @ ((late_OutputR @ A4) @ B3)) @ P3)) => (A4 = B3)))))))) => ((! [P4:pi,A4:late_subject,X4:name,P3:pi,Y3:name]: (((((res @ X2) @ P) = ((res @ Y3) @ P4)) => ((Rs = (((late_BoundR @ A4) @ X4) @ ((res @ Y3) @ P3))) => (((late_transitions @ P4) @ (((late_BoundR @ A4) @ X4) @ P3)) => (((((fresh @ name) @ late_subject) @ Y3) @ A4) => ((Y3 != X4) => (((((fresh @ name) @ pi) @ X4) @ P4) => (~ (((((fresh @ name) @ late_subject) @ X4) @ A4))))))))))) => (~ ((! [P4:pi,Alpha2:late_freeRes,P3:pi,Y3:name]: (((((res @ X2) @ P) = ((res @ Y3) @ P4)) => ((Rs = ((late_FreeR @ Alpha2) @ ((res @ Y3) @ P3))) => (((late_transitions @ P4) @ ((late_FreeR @ Alpha2) @ P3)) => (~ (((((fresh @ name) @ late_freeRes) @ Y3) @ Alpha2)))))))))))))))).
% 2.44/1.49 thf(fact_79_freshResidual, axiom, (! [P:pi,Rs:late_residual,X2:name]: ((((late_transitions @ P) @ Rs) => (((((fresh @ name) @ pi) @ X2) @ P) => ((((fresh @ name) @ late_residual) @ X2) @ Rs)))))).
% 2.44/1.49 thf(fact_80_resCasesF, axiom, (! [X2:name,P:pi,Alpha:late_freeRes,XP:pi,F2:(pi > $o)]: ((((late_transitions @ ((res @ X2) @ P)) @ ((late_FreeR @ Alpha) @ XP)) => ((! [P3:pi]: ((((late_transitions @ P) @ ((late_FreeR @ Alpha) @ P3)) => (((((fresh @ name) @ late_freeRes) @ X2) @ Alpha) => (F2 @ ((res @ X2) @ P3)))))) => (F2 @ XP)))))).
% 2.44/1.49 thf(fact_81_resCasesF_H, axiom, (! [X2:name,P:pi,Alpha:late_freeRes,P2:pi]: ((((late_transitions @ ((res @ X2) @ P)) @ ((late_FreeR @ Alpha) @ P2)) => (~ ((! [P4:pi,Alpha2:late_freeRes,P3:pi,Y3:name]: (((((res @ X2) @ P) = ((res @ Y3) @ P4)) => ((((late_FreeR @ Alpha) @ P2) = ((late_FreeR @ Alpha2) @ ((res @ Y3) @ P3))) => (((late_transitions @ P4) @ ((late_FreeR @ Alpha2) @ P3)) => (~ (((((fresh @ name) @ late_freeRes) @ Y3) @ Alpha2)))))))))))))).
% 2.44/1.49 thf(fact_82_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)))))))).
% 2.44/1.49 thf(fact_83_Late__Semantics_OResB, axiom, (! [P:pi,A2:late_subject,X2:name,P2:pi,Y:name]: ((((late_transitions @ P) @ (((late_BoundR @ A2) @ X2) @ P2)) => (((((fresh @ name) @ late_subject) @ Y) @ A2) => ((Y != X2) => ((late_transitions @ ((res @ Y) @ P)) @ (((late_BoundR @ A2) @ X2) @ ((res @ Y) @ P2))))))))).
% 2.44/1.49 thf(fact_84_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)))))).
% 2.44/1.49 thf(fact_85_freshBoundDerivative_I1_J, axiom, (! [P:pi,A2:late_subject,X2:name,P2:pi,Y:name]: ((((late_transitions @ P) @ (((late_BoundR @ A2) @ X2) @ P2)) => (((((fresh @ name) @ pi) @ Y) @ P) => ((((fresh @ name) @ late_subject) @ Y) @ A2)))))).
% 2.44/1.49 thf(fact_86_resCasesB_H, axiom, (! [X5:name,P:pi,A2:late_subject,Y4:name,P2:pi]: ((((late_transitions @ ((res @ X5) @ P)) @ (((late_BoundR @ A2) @ Y4) @ P2)) => ((! [P4:pi,A4:name,B3:name]: (((((res @ X5) @ P) = ((res @ B3) @ P4)) => (! [P3:pi]: ((((((late_BoundR @ A2) @ Y4) @ P2) = (((late_BoundR @ (late_BoundOutputS @ A4)) @ B3) @ P3)) => (((late_transitions @ P4) @ ((late_FreeR @ ((late_OutputR @ A4) @ B3)) @ P3)) => (A4 = B3)))))))) => (~ ((! [P4:pi,A4:late_subject,X4:name,P3:pi,Y3:name]: (((((res @ X5) @ P) = ((res @ Y3) @ P4)) => (((((late_BoundR @ A2) @ Y4) @ P2) = (((late_BoundR @ A4) @ X4) @ ((res @ Y3) @ P3))) => (((late_transitions @ P4) @ (((late_BoundR @ A4) @ X4) @ P3)) => (((((fresh @ name) @ late_subject) @ Y3) @ A4) => ((Y3 != X4) => (((((fresh @ name) @ pi) @ X4) @ P4) => (~ (((((fresh @ name) @ late_subject) @ X4) @ A4)))))))))))))))))).
% 2.44/1.49 thf(fact_87_parCasesB_H, axiom, (! [P:pi,Q:pi,B:late_subject,Y:name,P2:pi]: ((((late_transitions @ ((par @ P) @ Q)) @ (((late_BoundR @ B) @ Y) @ P2)) => ((! [P4:pi,A4:late_subject,X4:name,P3:pi,Q4:pi]: (((((par @ P) @ Q) = ((par @ P4) @ Q4)) => (((((late_BoundR @ B) @ Y) @ P2) = (((late_BoundR @ A4) @ X4) @ ((par @ P3) @ Q4))) => (((late_transitions @ P4) @ (((late_BoundR @ A4) @ X4) @ P3)) => (((((fresh @ name) @ pi) @ X4) @ P4) => (((((fresh @ name) @ pi) @ X4) @ Q4) => (~ (((((fresh @ name) @ late_subject) @ X4) @ A4)))))))))) => (~ ((! [Q4:pi,A4:late_subject,X4:name,Q3:pi,P4:pi]: (((((par @ P) @ Q) = ((par @ P4) @ Q4)) => (((((late_BoundR @ B) @ Y) @ P2) = (((late_BoundR @ A4) @ X4) @ ((par @ P4) @ Q3))) => (((late_transitions @ Q4) @ (((late_BoundR @ A4) @ X4) @ Q3)) => (((((fresh @ name) @ pi) @ X4) @ P4) => (((((fresh @ name) @ pi) @ X4) @ Q4) => (~ (((((fresh @ name) @ late_subject) @ X4) @ A4))))))))))))))))).
% 2.44/1.49 thf(fact_88_transitions_OPar1B, axiom, (! [P:pi,A2:late_subject,X2:name,P2:pi,Q:pi]: ((((late_transitions @ P) @ (((late_BoundR @ A2) @ X2) @ P2)) => (((((fresh @ name) @ pi) @ X2) @ P) => (((((fresh @ name) @ pi) @ X2) @ Q) => (((((fresh @ name) @ late_subject) @ X2) @ A2) => ((late_transitions @ ((par @ P) @ Q)) @ (((late_BoundR @ A2) @ X2) @ ((par @ P2) @ Q)))))))))).
% 2.44/1.49 thf(fact_89_transitions_OPar2B, axiom, (! [Q:pi,A2:late_subject,X2:name,Q2:pi,P:pi]: ((((late_transitions @ Q) @ (((late_BoundR @ A2) @ X2) @ Q2)) => (((((fresh @ name) @ pi) @ X2) @ P) => (((((fresh @ name) @ pi) @ X2) @ Q) => (((((fresh @ name) @ late_subject) @ X2) @ A2) => ((late_transitions @ ((par @ P) @ Q)) @ (((late_BoundR @ A2) @ X2) @ ((par @ P) @ Q2)))))))))).
% 2.44/1.49 thf(fact_90_transitions_OResB, axiom, (! [P:pi,A2:late_subject,X2:name,P2:pi,Y:name]: ((((late_transitions @ P) @ (((late_BoundR @ A2) @ X2) @ P2)) => (((((fresh @ name) @ late_subject) @ Y) @ A2) => ((Y != X2) => (((((fresh @ name) @ pi) @ X2) @ P) => (((((fresh @ name) @ late_subject) @ X2) @ A2) => ((late_transitions @ ((res @ Y) @ P)) @ (((late_BoundR @ A2) @ X2) @ ((res @ Y) @ P2))))))))))).
% 2.44/1.49 thf(fact_91_freeRes_Orecs_I2_J, axiom, (! [T:$tType,P:(T > $o),F1:(name > (name > T)),F22:T]: (((! [X12:name,X23:name]: ((P @ ((F1 @ X12) @ X23)))) => ((P @ F22) => (((((late_freeRes_rec @ T) @ F1) @ F22) @ late_TauR) = F22)))))).
% 2.44/1.49 thf(fact_92_subject_Orecs_I1_J, axiom, (! [T:$tType,P:(T > $o),F1:(name > T),F22:(name > T),Name2:name]: (((! [X12:name]: ((P @ (F1 @ X12)))) => ((! [X12:name]: ((P @ (F22 @ X12)))) => (((((late_subject_rec @ T) @ F1) @ F22) @ (late_InputS @ Name2)) = (F1 @ Name2))))))).
% 2.44/1.49 thf(fact_93_subject_Orecs_I2_J, axiom, (! [T:$tType,P:(T > $o),F1:(name > T),F22:(name > T),Name2:name]: (((! [X12:name]: ((P @ (F1 @ X12)))) => ((! [X12:name]: ((P @ (F22 @ X12)))) => (((((late_subject_rec @ T) @ F1) @ F22) @ (late_BoundOutputS @ Name2)) = (F22 @ Name2))))))).
% 2.44/1.49 thf(fact_94_freeRes_Orecs_I1_J, axiom, (! [T:$tType,P:(T > $o),F1:(name > (name > T)),F22:T,Name1:name,Name22:name]: (((! [X12:name,X23:name]: ((P @ ((F1 @ X12) @ X23)))) => ((P @ F22) => (((((late_freeRes_rec @ T) @ F1) @ F22) @ ((late_OutputR @ Name1) @ Name22)) = ((F1 @ Name1) @ Name22))))))).
% 2.44/1.49 thf(fact_95_resTauOutputTrans, axiom, (! [X2:name,P:pi,A2:name,B:name,P2:pi]: ((~ (((late_transitions @ ((res @ X2) @ (tau @ P))) @ ((late_FreeR @ ((late_OutputR @ A2) @ B)) @ P2))))))).
% 2.44/1.49 thf(fact_96_resOutputTauTrans, axiom, (! [X2:name,A2:name,B:name,P:pi,P2:pi]: ((~ (((late_transitions @ ((res @ X2) @ (((output @ A2) @ B) @ P))) @ ((late_FreeR @ late_TauR) @ P2))))))).
% 2.44/1.49 thf(fact_97_resOutputInputTrans, axiom, (! [X2:name,A2:name,B:name,P:pi,C:name,Y:name,P2:pi]: ((~ (((late_transitions @ ((res @ X2) @ (((output @ A2) @ B) @ P))) @ (((late_BoundR @ (late_InputS @ C)) @ Y) @ P2))))))).
% 2.44/1.49 thf(fact_98_name__fresh, axiom, (((fresh @ name) @ name) = (^ [A5:name,B4:name]: ((A5 != B4))))).
% 2.44/1.49 thf(fact_99_pi_Ofresh_I3_J, axiom, (! [A2:name,X1:pi]: ((((((fresh @ name) @ pi) @ A2) @ (tau @ X1)) = ((((fresh @ name) @ pi) @ A2) @ X1))))).
% 2.44/1.49 thf(fact_100_simps_I2_J, axiom, (! [P:pi,C:name,D:name]: (((((subs @ (tau @ P)) @ C) @ D) = (tau @ (((subs @ P) @ C) @ D)))))).
% 2.44/1.49 thf(fact_101_pi_Ofresh_I2_J, axiom, (! [A2:name,X32:name,X22:name,X1:pi]: ((((((fresh @ name) @ pi) @ A2) @ (((output @ X32) @ X22) @ X1)) = (((((fresh @ name) @ name) @ A2) @ X32) & (((((fresh @ name) @ name) @ A2) @ X22) & ((((fresh @ name) @ pi) @ A2) @ X1))))))).
% 2.44/1.49 thf(fact_102_pi_Odistinct_I19_J, axiom, (! [Name1:name,Name22:name,Pi4:pi,Pi:pi]: (((((output @ Name1) @ Name22) @ Pi4) != (tau @ Pi))))).
% 2.44/1.49 thf(fact_103_pi_Oinject_I1_J, axiom, (! [X32:name,X22:name,X1:pi,Y32:name,Y2:name,Y1:pi]: ((((((output @ X32) @ X22) @ X1) = (((output @ Y32) @ Y2) @ Y1)) = ((X32 = Y32) & ((X22 = Y2) & (X1 = Y1))))))).
% 2.44/1.49 thf(fact_104_pi_Oinject_I2_J, axiom, (! [X1:pi,Y1:pi]: ((((tau @ X1) = (tau @ Y1)) = (X1 = Y1))))).
% 2.44/1.49 thf(fact_105_pi_Odistinct_I29_J, axiom, (! [Name1:name,Name22:name,Pi4:pi,Pi12:pi,Pi22:pi]: (((((output @ Name1) @ Name22) @ Pi4) != ((par @ Pi12) @ Pi22))))).
% 2.44/1.49 thf(fact_106_pi_Odistinct_I31_J, axiom, (! [Name1:name,Name22:name,Pi4:pi,Name:name,Pi:pi]: (((((output @ Name1) @ Name22) @ Pi4) != ((res @ Name) @ Pi))))).
% 2.44/1.49 thf(fact_107_pi_Odistinct_I43_J, axiom, (! [Pi4:pi,Pi12:pi,Pi22:pi]: (((tau @ Pi4) != ((par @ Pi12) @ Pi22))))).
% 2.44/1.49 thf(fact_108_pi_Odistinct_I45_J, axiom, (! [Pi4:pi,Name:name,Pi:pi]: (((tau @ Pi4) != ((res @ Name) @ Pi))))).
% 2.44/1.49 thf(fact_109_resTrans_I1_J, axiom, (! [X2:name,B:name,P:pi,Rs:late_residual]: ((~ (((late_transitions @ ((res @ X2) @ (((output @ X2) @ B) @ P))) @ Rs)))))).
% 2.44/1.49 thf(fact_110_outputBoundTrans, axiom, (! [A2:name,B:name,P:pi,C:late_subject,X2:name,P2:pi]: ((~ (((late_transitions @ (((output @ A2) @ B) @ P)) @ (((late_BoundR @ C) @ X2) @ P2))))))).
% 2.44/1.49 thf(fact_111_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)))))))).
% 2.44/1.49 thf(fact_112_tauBoundTrans, axiom, (! [P:pi,A2:late_subject,X2:name,P2:pi]: ((~ (((late_transitions @ (tau @ P)) @ (((late_BoundR @ A2) @ X2) @ P2))))))).
% 2.44/1.49 thf(fact_113_resTauBoundTrans, axiom, (! [X2:name,P:pi,A2:late_subject,Y:name,P2:pi]: ((~ (((late_transitions @ ((res @ X2) @ (tau @ P))) @ (((late_BoundR @ A2) @ Y) @ P2))))))).
% 2.44/1.49 thf(fact_114_Output, axiom, (! [A2:name,B:name,P:pi]: (((late_transitions @ (((output @ A2) @ B) @ P)) @ ((late_FreeR @ ((late_OutputR @ A2) @ B)) @ P))))).
% 2.44/1.49 thf(fact_115_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)))))))).
% 2.44/1.49 thf(fact_116_outputCases_H, axiom, (! [A2:name,B:name,P:pi,Rs:late_residual]: ((((late_transitions @ (((output @ A2) @ B) @ P)) @ Rs) => (~ ((! [A4:name,B3:name,P4:pi]: ((((A2 = A4) & ((B = B3) & (P = P4))) => (Rs != ((late_FreeR @ ((late_OutputR @ A4) @ B3)) @ P4))))))))))).
% 2.44/1.49 thf(fact_117_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)))))).
% 2.44/1.49 thf(fact_118_outputTauTrans, axiom, (! [A2:name,B:name,P:pi,P2:pi]: ((~ (((late_transitions @ (((output @ A2) @ B) @ P)) @ ((late_FreeR @ late_TauR) @ P2))))))).
% 2.44/1.49 thf(fact_119_tauOutputTrans, axiom, (! [P:pi,A2:name,B:name,P2:pi]: ((~ (((late_transitions @ (tau @ P)) @ ((late_FreeR @ ((late_OutputR @ A2) @ B)) @ P2))))))).
% 2.44/1.49 thf(fact_120_Tau, axiom, (! [P:pi]: (((late_transitions @ (tau @ P)) @ ((late_FreeR @ late_TauR) @ P))))).
% 2.44/1.49 thf(fact_121_tauCases_H, axiom, (! [P:pi,Rs:late_residual]: ((((late_transitions @ (tau @ P)) @ Rs) => (~ ((! [P4:pi]: ((((tau @ P) = (tau @ P4)) => (Rs != ((late_FreeR @ late_TauR) @ P4))))))))))).
% 2.44/1.49 thf(fact_122_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)))))).
% 2.44/1.49 thf(fact_123_resOutputOutputTrans, axiom, (! [X2:name,A2:name,P:pi,B:name,Y:name,P2:pi]: ((~ (((late_transitions @ ((res @ X2) @ (((output @ A2) @ X2) @ P))) @ ((late_FreeR @ ((late_OutputR @ B) @ Y)) @ P2))))))).
% 2.44/1.49 thf(fact_124_resInputBoundOutputTrans, axiom, (! [X2:name,A2:name,Y:name,P:pi,B:name,Z:name,P2:pi]: ((~ (((late_transitions @ ((res @ X2) @ (((input @ A2) @ Y) @ P))) @ (((late_BoundR @ (late_BoundOutputS @ B)) @ Z) @ P2))))))).
% 2.44/1.49 thf(fact_125_residual_Ofresh_I1_J, axiom, (! [A2:name,X32:late_subject,X1:name,X22:pi]: ((((((fresh @ name) @ late_residual) @ A2) @ (((late_BoundR @ X32) @ X1) @ X22)) = (((((fresh @ name) @ late_subject) @ A2) @ X32) & ((((fresh @ name) @ (name > (noption @ pi))) @ A2) @ ((((abs_fun @ name) @ pi) @ X1) @ X22))))))).
% 2.44/1.49 thf(fact_126_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)))))).
% 2.44/1.49 thf(fact_127_inputIneqTrans, axiom, (! [A2:name,X2:name,P:pi,B:late_subject,Y:name,P2:pi]: ((((late_transitions @ (((input @ A2) @ X2) @ P)) @ (((late_BoundR @ B) @ Y) @ P2)) => (~ (((((fresh @ name) @ late_subject) @ A2) @ B))))))).
% 2.44/1.49 thf(fact_128_transitions_OInput, axiom, (! [X2:name,A2:name,P:pi]: (((X2 != A2) => ((late_transitions @ (((input @ A2) @ X2) @ P)) @ (((late_BoundR @ (late_InputS @ A2)) @ X2) @ P)))))).
% 2.44/1.49 thf(fact_129_substInput, axiom, (! [X2:name,B:name,C:name,A2:name,P:pi]: (((X2 != B) => ((X2 != C) => ((((subs @ (((input @ A2) @ X2) @ P)) @ B) @ C) = (((input @ (((subst_name @ A2) @ B) @ C)) @ X2) @ (((subs @ P) @ B) @ C)))))))).
% 2.44/1.49 thf(fact_130_simps_I4_J, axiom, (! [X2:name,A2:name,C:name,D:name,P:pi]: (((X2 != A2) => ((X2 != C) => ((X2 != D) => ((((subs @ (((input @ A2) @ X2) @ P)) @ C) @ D) = (((input @ (((subst_name @ A2) @ C) @ D)) @ X2) @ (((subs @ P) @ C) @ D))))))))).
% 2.44/1.49 thf(fact_131_pi_Ofresh_I9_J, axiom, (! [A2:name,X1:name,X22:pi]: ((((((fresh @ name) @ pi) @ A2) @ ((res @ X1) @ X22)) = ((((fresh @ name) @ (name > (noption @ pi))) @ A2) @ ((((abs_fun @ name) @ pi) @ X1) @ X22)))))).
% 2.44/1.49 thf(fact_132_pi_Ofresh_I4_J, axiom, (! [A2:name,X32:name,X1:name,X22:pi]: ((((((fresh @ name) @ pi) @ A2) @ (((input @ X32) @ X1) @ X22)) = (((((fresh @ name) @ name) @ A2) @ X32) & ((((fresh @ name) @ (name > (noption @ pi))) @ A2) @ ((((abs_fun @ name) @ pi) @ X1) @ X22))))))).
% 2.44/1.49 thf(fact_133_pi_Oinject_I3_J, axiom, (! [X32:name,X1:name,X22:pi,Y32:name,Y1:name,Y2:pi]: ((((((input @ X32) @ X1) @ X22) = (((input @ Y32) @ Y1) @ Y2)) = ((X32 = Y32) & (((((abs_fun @ name) @ pi) @ X1) @ X22) = ((((abs_fun @ name) @ pi) @ Y1) @ Y2))))))).
% 2.44/1.49 thf(fact_134_subst__name__def, axiom, (subst_name = (^ [A5:name,B4:name,C3:name]: (((((if @ name) @ (A5 = B4)) @ C3) @ A5))))).
% 2.44/1.49 thf(fact_135_pi_Oinject_I8_J, axiom, (! [X1:name,X22:pi,Y1:name,Y2:pi]: (((((res @ X1) @ X22) = ((res @ Y1) @ Y2)) = (((((abs_fun @ name) @ pi) @ X1) @ X22) = ((((abs_fun @ name) @ pi) @ Y1) @ Y2)))))).
% 2.44/1.49 thf(fact_136_residual_Oinject_I1_J, axiom, (! [X32:late_subject,X1:name,X22:pi,Y32:late_subject,Y1:name,Y2:pi]: ((((((late_BoundR @ X32) @ X1) @ X22) = (((late_BoundR @ Y32) @ Y1) @ Y2)) = ((X32 = Y32) & (((((abs_fun @ name) @ pi) @ X1) @ X22) = ((((abs_fun @ name) @ pi) @ Y1) @ Y2))))))).
% 2.44/1.49 thf(fact_137_name__fresh__abs, axiom, (! [A:$tType]: (((fs_name @ A) => (! [B:name,A2:name,X2:A]: ((((((fresh @ name) @ (name > (noption @ A))) @ B) @ ((((abs_fun @ name) @ A) @ A2) @ X2)) = ((B = A2) | ((((fresh @ name) @ A) @ B) @ X2))))))))).
% 2.44/1.49 thf(fact_138_abs__fresh_I1_J, axiom, (! [X6:$tType]: (((fs_name @ X6) => (! [B:name,A2:name,X2:X6]: ((((((fresh @ name) @ (name > (noption @ X6))) @ B) @ ((((abs_fun @ name) @ X6) @ A2) @ X2)) = ((B = A2) | ((((fresh @ name) @ X6) @ B) @ X2))))))))).
% 2.44/1.49 thf(fact_139_pi_Odistinct_I55_J, axiom, (! [Name1:name,Name22:name,Pi4:pi,Pi12:pi,Pi22:pi]: (((((input @ Name1) @ Name22) @ Pi4) != ((par @ Pi12) @ Pi22))))).
% 2.44/1.49 thf(fact_140_pi_Odistinct_I57_J, axiom, (! [Name1:name,Name22:name,Pi4:pi,Name:name,Pi:pi]: (((((input @ Name1) @ Name22) @ Pi4) != ((res @ Name) @ Pi))))).
% 2.44/1.49 thf(fact_141_pi_Odistinct_I21_J, axiom, (! [Name1:name,Name22:name,Pi4:pi,Name13:name,Name24:name,Pi:pi]: (((((output @ Name1) @ Name22) @ Pi4) != (((input @ Name13) @ Name24) @ Pi))))).
% 2.44/1.49 thf(fact_142_pi_Odistinct_I35_J, axiom, (! [Pi4:pi,Name13:name,Name24:name,Pi:pi]: (((tau @ Pi4) != (((input @ Name13) @ Name24) @ Pi))))).
% 2.44/1.49 thf(fact_143_inputCases_H, axiom, (! [A2:name,B:name,P:pi,Rs:late_residual]: ((((late_transitions @ (((input @ A2) @ B) @ P)) @ Rs) => (~ ((! [X4:name,A4:name,P4:pi]: ((((A2 = A4) & (((((abs_fun @ name) @ pi) @ B) @ P) = ((((abs_fun @ name) @ pi) @ X4) @ P4))) => ((Rs = (((late_BoundR @ (late_InputS @ A4)) @ X4) @ P4)) => (X4 = A4))))))))))).
% 2.44/1.49 thf(fact_144_resTrans_I2_J, axiom, (! [X2:name,Y:name,P:pi,Rs:late_residual]: ((~ (((late_transitions @ ((res @ X2) @ (((input @ X2) @ Y) @ P))) @ Rs)))))).
% 2.44/1.49 thf(fact_145_inputFreeTrans, axiom, (! [A2:name,X2:name,P:pi,Alpha:late_freeRes,P2:pi]: ((~ (((late_transitions @ (((input @ A2) @ X2) @ P)) @ ((late_FreeR @ Alpha) @ P2))))))).
% 2.44/1.49 thf(fact_146_resInputFreeTrans, axiom, (! [X2:name,A2:name,Y:name,P:pi,Alpha:late_freeRes,P2:pi]: ((~ (((late_transitions @ ((res @ X2) @ (((input @ A2) @ Y) @ P))) @ ((late_FreeR @ Alpha) @ P2))))))).
% 2.44/1.49 thf(fact_147_inputBoundOutputTrans, axiom, (! [A2:name,X2:name,P:pi,B:name,Y:name,P2:pi]: ((~ (((late_transitions @ (((input @ A2) @ X2) @ P)) @ (((late_BoundR @ (late_BoundOutputS @ B)) @ Y) @ P2))))))).
% 2.44/1.49 thf(fact_148_Late__Semantics_OInput, axiom, (! [A2:name,X2:name,P:pi]: (((late_transitions @ (((input @ A2) @ X2) @ P)) @ (((late_BoundR @ (late_InputS @ A2)) @ X2) @ P))))).
% 2.44/1.49 thf(fact_149_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)))))).
% 2.44/1.49 thf(fact_150_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)))))).
% 2.44/1.49 thf(fact_151_pi_Ofresh_I5_J, axiom, (! [A2:name,X32:name,X22:name,X1:pi]: ((((((fresh @ name) @ pi) @ A2) @ (((match @ X32) @ X22) @ X1)) = (((((fresh @ name) @ name) @ A2) @ X32) & (((((fresh @ name) @ name) @ A2) @ X22) & ((((fresh @ name) @ pi) @ A2) @ X1))))))).
% 2.44/1.49 thf(fact_152_pi_Ofresh_I6_J, axiom, (! [A2:name,X32:name,X22:name,X1:pi]: ((((((fresh @ name) @ pi) @ A2) @ (((mismatch @ X32) @ X22) @ X1)) = (((((fresh @ name) @ name) @ A2) @ X32) & (((((fresh @ name) @ name) @ A2) @ X22) & ((((fresh @ name) @ pi) @ A2) @ X1))))))).
% 2.44/1.49 thf(fact_153_pi_Odistinct_I61_J, axiom, (! [Name1:name,Name22:name,Pi4:pi,Name13:name,Name24:name,Pi:pi]: (((((match @ Name1) @ Name22) @ Pi4) != (((mismatch @ Name13) @ Name24) @ Pi))))).
% 2.44/1.49 thf(fact_154_pi_Oinject_I4_J, axiom, (! [X32:name,X22:name,X1:pi,Y32:name,Y2:name,Y1:pi]: ((((((match @ X32) @ X22) @ X1) = (((match @ Y32) @ Y2) @ Y1)) = ((X32 = Y32) & ((X22 = Y2) & (X1 = Y1))))))).
% 2.44/1.49 thf(fact_155_pi_Oinject_I5_J, axiom, (! [X32:name,X22:name,X1:pi,Y32:name,Y2:name,Y1:pi]: ((((((mismatch @ X32) @ X22) @ X1) = (((mismatch @ Y32) @ Y2) @ Y1)) = ((X32 = Y32) & ((X22 = Y2) & (X1 = Y1))))))).
% 2.44/1.49 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)))))).
% 2.44/1.49 thf(fact_157_Match, axiom, (! [P:pi,Rs:late_residual,B:name]: ((((late_transitions @ P) @ Rs) => ((late_transitions @ (((match @ B) @ B) @ P)) @ Rs))))).
% 2.44/1.49 thf(fact_158_mismatchCases_H, axiom, (! [A2:name,B:name,P:pi,Rs:late_residual]: ((((late_transitions @ (((mismatch @ A2) @ B) @ P)) @ Rs) => (~ ((! [P4:pi,A4:name,B3:name]: ((((A2 = A4) & ((B = B3) & (P = P4))) => (((late_transitions @ P4) @ Rs) => (A4 = B3))))))))))).
% 2.44/1.49 thf(fact_159_mismatchTrans, axiom, (! [A2:name,P:pi,Rs:late_residual]: ((~ (((late_transitions @ (((mismatch @ A2) @ A2) @ P)) @ Rs)))))).
% 2.44/1.49 thf(fact_160_mismatchCases, axiom, (! [A2:name,B:name,P:pi,Rs:late_residual,F2:(name > (name > $o))]: ((((late_transitions @ (((mismatch @ A2) @ B) @ P)) @ Rs) => ((((late_transitions @ P) @ Rs) => ((A2 != B) => ((F2 @ A2) @ B))) => ((F2 @ A2) @ B)))))).
% 2.44/1.49 thf(fact_161_matchCases_H, axiom, (! [A2:name,B:name,P:pi,Rs:late_residual]: ((((late_transitions @ (((match @ A2) @ B) @ P)) @ Rs) => (~ ((! [P4:pi]: ((((B = A2) & (P = P4)) => (~ (((late_transitions @ P4) @ Rs)))))))))))).
% 2.44/1.49 thf(fact_162_matchTrans, axiom, (! [A2:name,B:name,P:pi,Rs:late_residual]: ((((late_transitions @ (((match @ A2) @ B) @ P)) @ Rs) => (A2 = B))))).
% 2.44/1.49 thf(fact_163_matchCases, axiom, (! [A2:name,B:name,P:pi,Rs:late_residual,F2:(name > (name > $o))]: ((((late_transitions @ (((match @ A2) @ B) @ P)) @ Rs) => ((((late_transitions @ P) @ Rs) => ((A2 = B) => ((F2 @ A2) @ A2))) => ((F2 @ A2) @ B)))))).
% 2.44/1.49 thf(fact_164_pi_Odistinct_I65_J, axiom, (! [Name1:name,Name22:name,Pi4:pi,Pi12:pi,Pi22:pi]: (((((match @ Name1) @ Name22) @ Pi4) != ((par @ Pi12) @ Pi22))))).
% 2.44/1.49 thf(fact_165_pi_Odistinct_I73_J, axiom, (! [Name1:name,Name22:name,Pi4:pi,Pi12:pi,Pi22:pi]: (((((mismatch @ Name1) @ Name22) @ Pi4) != ((par @ Pi12) @ Pi22))))).
% 2.44/1.49 thf(fact_166_pi_Odistinct_I67_J, axiom, (! [Name1:name,Name22:name,Pi4:pi,Name:name,Pi:pi]: (((((match @ Name1) @ Name22) @ Pi4) != ((res @ Name) @ Pi))))).
% 2.44/1.49 thf(fact_167_pi_Odistinct_I75_J, axiom, (! [Name1:name,Name22:name,Pi4:pi,Name:name,Pi:pi]: (((((mismatch @ Name1) @ Name22) @ Pi4) != ((res @ Name) @ Pi))))).
% 2.44/1.49 thf(fact_168_pi_Odistinct_I49_J, axiom, (! [Name1:name,Name22:name,Pi4:pi,Name13:name,Name24:name,Pi:pi]: (((((input @ Name1) @ Name22) @ Pi4) != (((match @ Name13) @ Name24) @ Pi))))).
% 2.44/1.49 thf(fact_169_pi_Odistinct_I51_J, axiom, (! [Name1:name,Name22:name,Pi4:pi,Name13:name,Name24:name,Pi:pi]: (((((input @ Name1) @ Name22) @ Pi4) != (((mismatch @ Name13) @ Name24) @ Pi))))).
% 2.44/1.49 thf(fact_170_pi_Odistinct_I23_J, axiom, (! [Name1:name,Name22:name,Pi4:pi,Name13:name,Name24:name,Pi:pi]: (((((output @ Name1) @ Name22) @ Pi4) != (((match @ Name13) @ Name24) @ Pi))))).
% 2.44/1.49 thf(fact_171_pi_Odistinct_I25_J, axiom, (! [Name1:name,Name22:name,Pi4:pi,Name13:name,Name24:name,Pi:pi]: (((((output @ Name1) @ Name22) @ Pi4) != (((mismatch @ Name13) @ Name24) @ Pi))))).
% 2.44/1.49 thf(fact_172_pi_Odistinct_I37_J, axiom, (! [Pi4:pi,Name13:name,Name24:name,Pi:pi]: (((tau @ Pi4) != (((match @ Name13) @ Name24) @ Pi))))).
% 2.44/1.49 thf(fact_173_pi_Odistinct_I39_J, axiom, (! [Pi4:pi,Name13:name,Name24:name,Pi:pi]: (((tau @ Pi4) != (((mismatch @ Name13) @ Name24) @ Pi))))).
% 2.44/1.49 thf(fact_174_abs__fun__eq1, axiom, (! [X:$tType,A:$tType,A2:X,X2:A,Y:A]: (((((((abs_fun @ X) @ A) @ A2) @ X2) = ((((abs_fun @ X) @ A) @ A2) @ Y)) = (X2 = Y))))).
% 2.44/1.49 thf(fact_175_freeRes_Ocase_I2_J, axiom, (! [A:$tType,F1:(name > (name > A)),F22:A]: ((((((late_case_freeRes @ A) @ F1) @ F22) @ late_TauR) = F22)))).
% 2.44/1.49 thf(fact_176_subject_Ocase_I1_J, axiom, (! [A:$tType,F1:(name > A),F22:(name > A),X1:name]: ((((((late_case_subject @ A) @ F1) @ F22) @ (late_InputS @ X1)) = (F1 @ X1))))).
% 2.44/1.49 thf(fact_177_freeRes_Ocase_I1_J, axiom, (! [A:$tType,F1:(name > (name > A)),F22:A,X11:name,X122:name]: ((((((late_case_freeRes @ A) @ F1) @ F22) @ ((late_OutputR @ X11) @ X122)) = ((F1 @ X11) @ X122))))).
% 2.44/1.49 thf(fact_178_subject_Ocase_I2_J, axiom, (! [A:$tType,F1:(name > A),F22:(name > A),X22:name]: ((((((late_case_subject @ A) @ F1) @ F22) @ (late_BoundOutputS @ X22)) = (F22 @ X22))))).
% 2.44/1.49 thf(fact_179_pi_Ostrong__inducts, axiom, (! [A:$tType]: (((fs_name @ A) => (! [P:(A > (pi > $o)),Z:A,Pi4:pi]: (((! [Z2:A]: (((P @ Z2) @ piNil))) => ((! [Name12:name,Name23:name,Pi3:pi,Z2:A]: (((! [Za:A]: (((P @ Za) @ Pi3))) => ((P @ Z2) @ (((output @ Name12) @ Name23) @ Pi3))))) => ((! [Pi3:pi,Z2:A]: (((! [Za:A]: (((P @ Za) @ Pi3))) => ((P @ Z2) @ (tau @ Pi3))))) => ((! [Name12:name,Name23:name,Pi3:pi,Z2:A]: ((((((fresh @ name) @ A) @ Name23) @ Z2) => (((((fresh @ name) @ name) @ Name23) @ Name12) => ((! [Za:A]: (((P @ Za) @ Pi3))) => ((P @ Z2) @ (((input @ Name12) @ Name23) @ Pi3))))))) => ((! [Name12:name,Name23:name,Pi3:pi,Z2:A]: (((! [Za:A]: (((P @ Za) @ Pi3))) => ((P @ Z2) @ (((match @ Name12) @ Name23) @ Pi3))))) => ((! [Name12:name,Name23:name,Pi3:pi,Z2:A]: (((! [Za:A]: (((P @ Za) @ Pi3))) => ((P @ Z2) @ (((mismatch @ Name12) @ Name23) @ Pi3))))) => ((! [Pi13:pi,Pi23:pi,Z2:A]: (((! [Za:A]: (((P @ Za) @ Pi13))) => ((! [Za:A]: (((P @ Za) @ Pi23))) => ((P @ Z2) @ ((sum @ Pi13) @ Pi23)))))) => ((! [Pi13:pi,Pi23:pi,Z2:A]: (((! [Za:A]: (((P @ Za) @ Pi13))) => ((! [Za:A]: (((P @ Za) @ Pi23))) => ((P @ Z2) @ ((par @ Pi13) @ Pi23)))))) => ((! [Name3:name,Pi3:pi,Z2:A]: ((((((fresh @ name) @ A) @ Name3) @ Z2) => ((! [Za:A]: (((P @ Za) @ Pi3))) => ((P @ Z2) @ ((res @ Name3) @ Pi3)))))) => ((! [Pi3:pi,Z2:A]: (((! [Za:A]: (((P @ Za) @ Pi3))) => ((P @ Z2) @ (bang @ Pi3))))) => ((P @ Z) @ Pi4))))))))))))))))).
% 2.44/1.49 thf(fact_180_pi_Ostrong__induct, axiom, (! [N:$tType]: (((fs_name @ N) => (! [P:(N > (pi > $o)),Z:N,Pi4:pi]: (((! [Z2:N]: (((P @ Z2) @ piNil))) => ((! [Name12:name,Name23:name,Pi3:pi,Z2:N]: (((! [Za:N]: (((P @ Za) @ Pi3))) => ((P @ Z2) @ (((output @ Name12) @ Name23) @ Pi3))))) => ((! [Pi3:pi,Z2:N]: (((! [Za:N]: (((P @ Za) @ Pi3))) => ((P @ Z2) @ (tau @ Pi3))))) => ((! [Name12:name,Name23:name,Pi3:pi,Z2:N]: ((((((fresh @ name) @ N) @ Name23) @ Z2) => (((((fresh @ name) @ name) @ Name23) @ Name12) => ((! [Za:N]: (((P @ Za) @ Pi3))) => ((P @ Z2) @ (((input @ Name12) @ Name23) @ Pi3))))))) => ((! [Name12:name,Name23:name,Pi3:pi,Z2:N]: (((! [Za:N]: (((P @ Za) @ Pi3))) => ((P @ Z2) @ (((match @ Name12) @ Name23) @ Pi3))))) => ((! [Name12:name,Name23:name,Pi3:pi,Z2:N]: (((! [Za:N]: (((P @ Za) @ Pi3))) => ((P @ Z2) @ (((mismatch @ Name12) @ Name23) @ Pi3))))) => ((! [Pi13:pi,Pi23:pi,Z2:N]: (((! [Za:N]: (((P @ Za) @ Pi13))) => ((! [Za:N]: (((P @ Za) @ Pi23))) => ((P @ Z2) @ ((sum @ Pi13) @ Pi23)))))) => ((! [Pi13:pi,Pi23:pi,Z2:N]: (((! [Za:N]: (((P @ Za) @ Pi13))) => ((! [Za:N]: (((P @ Za) @ Pi23))) => ((P @ Z2) @ ((par @ Pi13) @ Pi23)))))) => ((! [Name3:name,Pi3:pi,Z2:N]: ((((((fresh @ name) @ N) @ Name3) @ Z2) => ((! [Za:N]: (((P @ Za) @ Pi3))) => ((P @ Z2) @ ((res @ Name3) @ Pi3)))))) => ((! [Pi3:pi,Z2:N]: (((! [Za:N]: (((P @ Za) @ Pi3))) => ((P @ Z2) @ (bang @ Pi3))))) => ((P @ Z) @ Pi4))))))))))))))))).
% 2.44/1.49 thf(fact_181_residual_Ostrong__induct_H, axiom, (! [N:$tType,F:(N > (set @ name)),P:(N > (late_residual > $o)),Z:N,Residual:late_residual]: (((! [X4:N]: (((finite_finite @ name) @ (F @ X4)))) => ((! [Subject2:late_subject,Name3:name,Pi3:pi,Z2:N]: (((~ ((((member @ name) @ Name3) @ (F @ Z2)))) => (((((fresh @ name) @ late_subject) @ Name3) @ Subject2) => ((P @ Z2) @ (((late_BoundR @ Subject2) @ Name3) @ Pi3)))))) => ((! [FreeRes:late_freeRes,Pi3:pi,Z2:N]: (((P @ Z2) @ ((late_FreeR @ FreeRes) @ Pi3)))) => ((P @ Z) @ Residual))))))).
% 2.44/1.49 thf(fact_182_pi_Ofresh_I10_J, axiom, (! [A2:name,X1:pi]: ((((((fresh @ name) @ pi) @ A2) @ (bang @ X1)) = ((((fresh @ name) @ pi) @ A2) @ X1))))).
% 2.44/1.49 thf(fact_183_pi_Ofresh_I7_J, axiom, (! [A2:name,X22:pi,X1:pi]: ((((((fresh @ name) @ pi) @ A2) @ ((sum @ X22) @ X1)) = (((((fresh @ name) @ pi) @ A2) @ X22) & ((((fresh @ name) @ pi) @ A2) @ X1)))))).
% 2.44/1.49 thf(fact_184_pi_Ofresh_I1_J, axiom, (! [A2:name]: (((((fresh @ name) @ pi) @ A2) @ piNil)))).
% 2.44/1.49 thf(fact_185_simps_I10_J, axiom, (! [P:pi,C:name,D:name]: (((((subs @ (bang @ P)) @ C) @ D) = (bang @ (((subs @ P) @ C) @ D)))))).
% 2.44/1.49 thf(fact_186_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)))))).
% 2.44/1.49 thf(fact_187_simps_I1_J, axiom, (! [C:name,D:name]: (((((subs @ piNil) @ C) @ D) = piNil)))).
% 2.44/1.49 thf(fact_188_pi_Odistinct_I59_J, axiom, (! [Name1:name,Name22:name,Pi4:pi,Pi:pi]: (((((input @ Name1) @ Name22) @ Pi4) != (bang @ Pi))))).
% 2.44/1.49 thf(fact_189_pi_Odistinct_I53_J, axiom, (! [Name1:name,Name22:name,Pi4:pi,Pi12:pi,Pi22:pi]: (((((input @ Name1) @ Name22) @ Pi4) != ((sum @ Pi12) @ Pi22))))).
% 2.44/1.49 thf(fact_190_pi_Odistinct_I87_J, axiom, (! [Pi1:pi,Pi2:pi,Pi:pi]: ((((par @ Pi1) @ Pi2) != (bang @ Pi))))).
% 2.44/1.49 thf(fact_191_pi_Odistinct_I89_J, axiom, (! [Name2:name,Pi4:pi,Pi:pi]: ((((res @ Name2) @ Pi4) != (bang @ Pi))))).
% 2.44/1.49 thf(fact_192_pi_Odistinct_I33_J, axiom, (! [Name1:name,Name22:name,Pi4:pi,Pi:pi]: (((((output @ Name1) @ Name22) @ Pi4) != (bang @ Pi))))).
% 2.44/1.49 thf(fact_193_sumCases, axiom, (! [P:pi,Q:pi,Rs:late_residual]: ((((late_transitions @ ((sum @ P) @ Q)) @ Rs) => ((~ (((late_transitions @ P) @ Rs))) => ((late_transitions @ Q) @ Rs)))))).
% 2.44/1.49 thf(fact_194_sumCases_H, axiom, (! [P:pi,Q:pi,Rs:late_residual]: ((((late_transitions @ ((sum @ P) @ Q)) @ Rs) => ((~ (((late_transitions @ P) @ Rs))) => ((late_transitions @ Q) @ Rs)))))).
% 2.44/1.49 thf(fact_195_Sum1, axiom, (! [P:pi,Rs:late_residual,Q:pi]: ((((late_transitions @ P) @ Rs) => ((late_transitions @ ((sum @ P) @ Q)) @ Rs))))).
% 2.44/1.49 thf(fact_196_Sum2, axiom, (! [Q:pi,Rs:late_residual,P:pi]: ((((late_transitions @ Q) @ Rs) => ((late_transitions @ ((sum @ P) @ Q)) @ Rs))))).
% 2.44/1.49 thf(fact_197_pi_Odistinct_I47_J, axiom, (! [Pi4:pi,Pi:pi]: (((tau @ Pi4) != (bang @ Pi))))).
% 2.44/1.49 thf(fact_198_pi_Odistinct_I79_J, axiom, (! [Pi1:pi,Pi2:pi,Pi12:pi,Pi22:pi]: ((((sum @ Pi1) @ Pi2) != ((par @ Pi12) @ Pi22))))).
% 2.44/1.49 thf(fact_199_pi_Odistinct_I81_J, axiom, (! [Pi1:pi,Pi2:pi,Name:name,Pi:pi]: ((((sum @ Pi1) @ Pi2) != ((res @ Name) @ Pi))))).
% 2.44/1.49 thf(fact_200_pi_Odistinct_I11_J, axiom, (! [Pi12:pi,Pi22:pi]: ((piNil != ((sum @ Pi12) @ Pi22))))).
% 2.44/1.49 thf(fact_201_pi_Odistinct_I17_J, axiom, (! [Pi:pi]: ((piNil != (bang @ Pi))))).
% 2.44/1.49 thf(fact_202_pi_Odistinct_I83_J, axiom, (! [Pi1:pi,Pi2:pi,Pi:pi]: ((((sum @ Pi1) @ Pi2) != (bang @ Pi))))).
% 2.44/1.49 thf(fact_203_pi_Oinject_I6_J, axiom, (! [X22:pi,X1:pi,Y2:pi,Y1:pi]: (((((sum @ X22) @ X1) = ((sum @ Y2) @ Y1)) = ((X22 = Y2) & (X1 = Y1)))))).
% 2.44/1.49 thf(fact_204_pi_Oinject_I9_J, axiom, (! [X1:pi,Y1:pi]: ((((bang @ X1) = (bang @ Y1)) = (X1 = Y1))))).
% 2.44/1.49 thf(fact_205_pi_Odistinct_I3_J, axiom, (! [Pi:pi]: ((piNil != (tau @ Pi))))).
% 2.44/1.49 thf(fact_206_pi_Odistinct_I1_J, axiom, (! [Name13:name,Name24:name,Pi:pi]: ((piNil != (((output @ Name13) @ Name24) @ Pi))))).
% 2.44/1.49 thf(fact_207_pi_Odistinct_I5_J, axiom, (! [Name13:name,Name24:name,Pi:pi]: ((piNil != (((input @ Name13) @ Name24) @ Pi))))).
% 2.44/1.49 thf(fact_208_pi_Odistinct_I15_J, axiom, (! [Name:name,Pi:pi]: ((piNil != ((res @ Name) @ Pi))))).
% 2.44/1.49 thf(fact_209_pi_Odistinct_I13_J, axiom, (! [Pi12:pi,Pi22:pi]: ((piNil != ((par @ Pi12) @ Pi22))))).
% 2.44/1.49 thf(fact_210_nilCases_H, axiom, (! [Rs:late_residual]: ((~ (((late_transitions @ piNil) @ Rs)))))).
% 2.44/1.49 thf(fact_211_zeroTrans, axiom, (! [Rs:late_residual]: ((~ (((late_transitions @ piNil) @ Rs)))))).
% 2.44/1.49 thf(fact_212_pi_Odistinct_I41_J, axiom, (! [Pi4:pi,Pi12:pi,Pi22:pi]: (((tau @ Pi4) != ((sum @ Pi12) @ Pi22))))).
% 2.44/1.49 thf(fact_213_pi_Odistinct_I27_J, axiom, (! [Name1:name,Name22:name,Pi4:pi,Pi12:pi,Pi22:pi]: (((((output @ Name1) @ Name22) @ Pi4) != ((sum @ Pi12) @ Pi22))))).
% 2.44/1.49 thf(fact_214_pi_Odistinct_I77_J, axiom, (! [Name1:name,Name22:name,Pi4:pi,Pi:pi]: (((((mismatch @ Name1) @ Name22) @ Pi4) != (bang @ Pi))))).
% 2.44/1.49 thf(fact_215_pi_Odistinct_I71_J, axiom, (! [Name1:name,Name22:name,Pi4:pi,Pi12:pi,Pi22:pi]: (((((mismatch @ Name1) @ Name22) @ Pi4) != ((sum @ Pi12) @ Pi22))))).
% 2.44/1.49 thf(fact_216_pi_Odistinct_I69_J, axiom, (! [Name1:name,Name22:name,Pi4:pi,Pi:pi]: (((((match @ Name1) @ Name22) @ Pi4) != (bang @ Pi))))).
% 2.44/1.49 thf(fact_217_pi_Odistinct_I63_J, axiom, (! [Name1:name,Name22:name,Pi4:pi,Pi12:pi,Pi22:pi]: (((((match @ Name1) @ Name22) @ Pi4) != ((sum @ Pi12) @ Pi22))))).
% 2.44/1.49 thf(fact_218_pi_Odistinct_I9_J, axiom, (! [Name13:name,Name24:name,Pi:pi]: ((piNil != (((mismatch @ Name13) @ Name24) @ Pi))))).
% 2.44/1.49 thf(fact_219_pi_Odistinct_I7_J, axiom, (! [Name13:name,Name24:name,Pi:pi]: ((piNil != (((match @ Name13) @ Name24) @ Pi))))).
% 2.44/1.49 thf(fact_220_Bang, axiom, (! [P:pi,Rs:late_residual]: ((((late_transitions @ ((par @ P) @ (bang @ P))) @ Rs) => ((late_transitions @ (bang @ P)) @ Rs))))).
% 2.44/1.49 thf(fact_221_bangCases, axiom, (! [P:pi,Rs:late_residual]: ((((late_transitions @ (bang @ P)) @ Rs) => (~ ((! [P4:pi]: ((((bang @ P) = (bang @ P4)) => (~ (((late_transitions @ ((par @ P4) @ (bang @ P4))) @ Rs)))))))))))).
% 2.44/1.49 thf(fact_222_pi_Ostrong__induct_H, axiom, (! [N:$tType,F:(N > (set @ name)),P:(N > (pi > $o)),Z:N,Pi4:pi]: (((! [X4:N]: (((finite_finite @ name) @ (F @ X4)))) => ((! [Z2:N]: (((P @ Z2) @ piNil))) => ((! [Name12:name,Name23:name,Pi3:pi,Z2:N]: (((! [Za:N]: (((P @ Za) @ Pi3))) => ((P @ Z2) @ (((output @ Name12) @ Name23) @ Pi3))))) => ((! [Pi3:pi,Z2:N]: (((! [Za:N]: (((P @ Za) @ Pi3))) => ((P @ Z2) @ (tau @ Pi3))))) => ((! [Name12:name,Name23:name,Pi3:pi,Z2:N]: (((~ ((((member @ name) @ Name23) @ (F @ Z2)))) => (((((fresh @ name) @ name) @ Name23) @ Name12) => ((! [Za:N]: (((P @ Za) @ Pi3))) => ((P @ Z2) @ (((input @ Name12) @ Name23) @ Pi3))))))) => ((! [Name12:name,Name23:name,Pi3:pi,Z2:N]: (((! [Za:N]: (((P @ Za) @ Pi3))) => ((P @ Z2) @ (((match @ Name12) @ Name23) @ Pi3))))) => ((! [Name12:name,Name23:name,Pi3:pi,Z2:N]: (((! [Za:N]: (((P @ Za) @ Pi3))) => ((P @ Z2) @ (((mismatch @ Name12) @ Name23) @ Pi3))))) => ((! [Pi13:pi,Pi23:pi,Z2:N]: (((! [Za:N]: (((P @ Za) @ Pi13))) => ((! [Za:N]: (((P @ Za) @ Pi23))) => ((P @ Z2) @ ((sum @ Pi13) @ Pi23)))))) => ((! [Pi13:pi,Pi23:pi,Z2:N]: (((! [Za:N]: (((P @ Za) @ Pi13))) => ((! [Za:N]: (((P @ Za) @ Pi23))) => ((P @ Z2) @ ((par @ Pi13) @ Pi23)))))) => ((! [Name3:name,Pi3:pi,Z2:N]: (((~ ((((member @ name) @ Name3) @ (F @ Z2)))) => ((! [Za:N]: (((P @ Za) @ Pi3))) => ((P @ Z2) @ ((res @ Name3) @ Pi3)))))) => ((! [Pi3:pi,Z2:N]: (((! [Za:N]: (((P @ Za) @ Pi3))) => ((P @ Z2) @ (bang @ Pi3))))) => ((P @ Z) @ Pi4))))))))))))))).
% 2.44/1.49 thf(fact_223_resZeroTrans, axiom, (! [X2:name,Rs:late_residual]: ((~ (((late_transitions @ ((res @ X2) @ piNil)) @ Rs)))))).
% 2.44/1.49 thf(fact_224_pi_Oinducts, axiom, (! [P:(pi > $o),Pi4:pi]: (((P @ piNil) => ((! [Name12:name,Name23:name,Pi3:pi]: (((P @ Pi3) => (P @ (((output @ Name12) @ Name23) @ Pi3))))) => ((! [Pi3:pi]: (((P @ Pi3) => (P @ (tau @ Pi3))))) => ((! [Name12:name,Name23:name,Pi3:pi]: (((P @ Pi3) => (P @ (((input @ Name12) @ Name23) @ Pi3))))) => ((! [Name12:name,Name23:name,Pi3:pi]: (((P @ Pi3) => (P @ (((match @ Name12) @ Name23) @ Pi3))))) => ((! [Name12:name,Name23:name,Pi3:pi]: (((P @ Pi3) => (P @ (((mismatch @ Name12) @ Name23) @ Pi3))))) => ((! [Pi13:pi,Pi23:pi]: (((P @ Pi13) => ((P @ Pi23) => (P @ ((sum @ Pi13) @ Pi23)))))) => ((! [Pi13:pi,Pi23:pi]: (((P @ Pi13) => ((P @ Pi23) => (P @ ((par @ Pi13) @ Pi23)))))) => ((! [Name3:name,Pi3:pi]: (((P @ Pi3) => (P @ ((res @ Name3) @ Pi3))))) => ((! [Pi3:pi]: (((P @ Pi3) => (P @ (bang @ Pi3))))) => (P @ Pi4)))))))))))))).
% 2.44/1.49 thf(fact_225_aux2, axiom, (! [P:pi]: (((late_bangPred @ P) @ ((par @ P) @ (bang @ P)))))).
% 2.44/1.49 thf(fact_226_bangPred_Ocases, axiom, (! [A1:pi,A22:pi]: ((((late_bangPred @ A1) @ A22) => ((A22 != (bang @ A1)) => (A22 = ((par @ A1) @ (bang @ A1)))))))).
% 2.44/1.49 thf(fact_227_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))))))))))).
% 2.44/1.49 thf(fact_228_aux1, axiom, (! [P:pi]: (((late_bangPred @ P) @ (bang @ P))))).
% 2.44/1.49 thf(fact_229_bangPred_Oinducts, axiom, (! [X1:pi,X22:pi,P:(pi > (pi > $o))]: ((((late_bangPred @ X1) @ X22) => ((! [P4:pi]: (((P @ P4) @ (bang @ P4)))) => ((! [P4:pi]: (((P @ P4) @ ((par @ P4) @ (bang @ P4))))) => ((P @ X1) @ X22))))))).
% 2.44/1.49 thf(fact_230_subs__def, axiom, (subs = (^ [X3:pi,C3:name,D2:name]: (((((((((((((pi_rec @ pi) @ piNil) @ (^ [A5:name,B4:name,P5:pi]: (((output @ (((subst_name @ A5) @ C3) @ D2)) @ (((subst_name @ B4) @ C3) @ D2))))) @ (^ [P5:pi]: (tau))) @ (^ [A5:name,Y5:name,P5:pi]: (((input @ (((subst_name @ A5) @ C3) @ D2)) @ Y5)))) @ (^ [A5:name,B4:name,P5:pi]: (((match @ (((subst_name @ A5) @ C3) @ D2)) @ (((subst_name @ B4) @ C3) @ D2))))) @ (^ [A5:name,B4:name,P5:pi]: (((mismatch @ (((subst_name @ A5) @ C3) @ D2)) @ (((subst_name @ B4) @ C3) @ D2))))) @ (^ [P5:pi,Q5:pi]: (sum))) @ (^ [P5:pi,Q5:pi]: (par))) @ (^ [Y5:name,P5:pi]: ((res @ Y5)))) @ (^ [P5:pi]: (bang))) @ X3))))).
% 2.44/1.49 thf(fact_231_abs__fresh_I2_J, axiom, (! [X7:$tType]: (((pt_name @ X7) => (! [X2:X7,B:name,A2:name]: ((((finite_finite @ name) @ (((supp @ X7) @ name) @ X2)) => (((((fresh @ name) @ (name > (noption @ X7))) @ B) @ ((((abs_fun @ name) @ X7) @ A2) @ X2)) = ((B = A2) | ((((fresh @ name) @ X7) @ B) @ X2)))))))))).
% 2.44/1.49 thf(fact_232_exists__fresh, axiom, (! [A:$tType,X2:A]: ((((finite_finite @ name) @ (((supp @ A) @ name) @ X2)) => (~ ((! [C2:name]: ((~ (((((fresh @ name) @ A) @ C2) @ X2))))))))))).
% 2.44/1.49 thf(fact_233_exists__fresh_H, axiom, (! [A:$tType,X2:A]: ((((finite_finite @ name) @ (((supp @ A) @ name) @ X2)) => (? [C2:name]: (((((fresh @ name) @ A) @ C2) @ X2))))))).
% 2.44/1.49 thf(fact_234_supp__fresh__iff, axiom, (! [X:$tType,A:$tType]: ((((supp @ A) @ X) = (^ [X3:A]: (((collect @ X) @ (^ [A5:X]: ((~ (((((fresh @ X) @ A) @ A5) @ X3)))))))))))).
% 2.44/1.49 thf(fact_235_fresh__def, axiom, (! [A:$tType,X:$tType]: ((((fresh @ X) @ A) = (^ [A5:X,X3:A]: ((~ ((((member @ X) @ A5) @ (((supp @ A) @ X) @ X3)))))))))).
% 2.44/1.49 thf(fact_236_pi_Osupp_I9_J, axiom, (! [X1:name,X22:pi]: (((((supp @ pi) @ name) @ ((res @ X1) @ X22)) = (((supp @ (name > (noption @ pi))) @ name) @ ((((abs_fun @ name) @ pi) @ X1) @ X22)))))).
% 2.44/1.49 thf(fact_237_freeRes_Ocase__distrib, axiom, (! [A:$tType,B2:$tType,H:(A > B2),F1:(name > (name > A)),F22:A,FreeRes3:late_freeRes]: (((H @ ((((late_case_freeRes @ A) @ F1) @ F22) @ FreeRes3)) = ((((late_case_freeRes @ B2) @ (^ [X13:name,X24:name]: ((H @ ((F1 @ X13) @ X24))))) @ (H @ F22)) @ FreeRes3))))).
% 2.44/1.49 thf(fact_238_subject_Ocase__distrib, axiom, (! [B2:$tType,A:$tType,H:(A > B2),F1:(name > A),F22:(name > A),Subject:late_subject]: (((H @ ((((late_case_subject @ A) @ F1) @ F22) @ Subject)) = ((((late_case_subject @ B2) @ (^ [X3:name]: ((H @ (F1 @ X3))))) @ (^ [X3:name]: ((H @ (F22 @ X3))))) @ Subject))))).
% 2.44/1.49 thf(fact_239_pi_Osupp_I3_J, axiom, (! [X1:pi]: (((((supp @ pi) @ name) @ (tau @ X1)) = (((supp @ pi) @ name) @ X1))))).
% 2.44/1.49 thf(fact_240_subject_Osupp_I2_J, axiom, (! [X1:name]: (((((supp @ late_subject) @ name) @ (late_BoundOutputS @ X1)) = (((supp @ name) @ name) @ X1))))).
% 2.44/1.49 thf(fact_241_subject_Osupp_I1_J, axiom, (! [X1:name]: (((((supp @ late_subject) @ name) @ (late_InputS @ X1)) = (((supp @ name) @ name) @ X1))))).
% 2.44/1.49 thf(fact_242_pi_Osupp_I10_J, axiom, (! [X1:pi]: (((((supp @ pi) @ name) @ (bang @ X1)) = (((supp @ pi) @ name) @ X1))))).
% 2.44/1.49 thf(fact_243_fs__name1, axiom, (! [A:$tType]: (((fs_name @ A) => (! [X2:A]: (((finite_finite @ name) @ (((supp @ A) @ name) @ X2)))))))).
% 2.44/1.49 thf(fact_244_residual_Orecs_I2_J, axiom, (! [N:$tType,T:$tType]: (((pt_name @ T) => (! [F1:(late_subject > (name > (pi > T))),F22:(late_freeRes > (pi > T)),Z:N,P:(T > $o),FreeRes3:late_freeRes,Pi4:pi]: ((((finite_finite @ name) @ (((supp @ (late_subject > (name > (pi > T)))) @ name) @ F1)) => (((finite_finite @ name) @ (((supp @ (late_freeRes > (pi > T))) @ name) @ F22)) => (((finite_finite @ name) @ (((supp @ N) @ name) @ Z)) => ((! [X12:late_subject,X23:name,X33:pi]: ((P @ (((F1 @ X12) @ X23) @ X33)))) => ((! [X12:late_freeRes,X23:pi]: ((P @ ((F22 @ X12) @ X23)))) => ((! [X12:late_subject,X23:name,X33:pi]: ((((((fresh @ name) @ (late_subject > (name > (pi > T)))) @ X23) @ F1) => (((((fresh @ name) @ late_subject) @ X23) @ X12) => (((((fresh @ name) @ N) @ X23) @ Z) => ((P @ (((F1 @ X12) @ X23) @ X33)) => ((((fresh @ name) @ T) @ X23) @ (((F1 @ X12) @ X23) @ X33)))))))) => (((((late_residual_rec @ T) @ F1) @ F22) @ ((late_FreeR @ FreeRes3) @ Pi4)) = ((F22 @ FreeRes3) @ Pi4)))))))))))))).
% 2.44/1.49 thf(fact_245_residual_Orecs_I1_J, axiom, (! [N:$tType,T:$tType]: (((pt_name @ T) => (! [F1:(late_subject > (name > (pi > T))),F22:(late_freeRes > (pi > T)),Z:N,P:(T > $o),Name2:name,Subject:late_subject,Pi4:pi]: ((((finite_finite @ name) @ (((supp @ (late_subject > (name > (pi > T)))) @ name) @ F1)) => (((finite_finite @ name) @ (((supp @ (late_freeRes > (pi > T))) @ name) @ F22)) => (((finite_finite @ name) @ (((supp @ N) @ name) @ Z)) => ((! [X12:late_subject,X23:name,X33:pi]: ((P @ (((F1 @ X12) @ X23) @ X33)))) => ((! [X12:late_freeRes,X23:pi]: ((P @ ((F22 @ X12) @ X23)))) => ((! [X12:late_subject,X23:name,X33:pi]: ((((((fresh @ name) @ (late_subject > (name > (pi > T)))) @ X23) @ F1) => (((((fresh @ name) @ late_subject) @ X23) @ X12) => (((((fresh @ name) @ N) @ X23) @ Z) => ((P @ (((F1 @ X12) @ X23) @ X33)) => ((((fresh @ name) @ T) @ X23) @ (((F1 @ X12) @ X23) @ X33)))))))) => (((((fresh @ name) @ (late_subject > (name > (pi > T)))) @ Name2) @ F1) => (((((fresh @ name) @ (late_freeRes > (pi > T))) @ Name2) @ F22) => (((((fresh @ name) @ late_subject) @ Name2) @ Subject) => (((((late_residual_rec @ T) @ F1) @ F22) @ (((late_BoundR @ Subject) @ Name2) @ Pi4)) = (((F1 @ Subject) @ Name2) @ Pi4))))))))))))))))).
% 2.44/1.49 thf(fact_246_residual_Orec__fresh, axiom, (! [T:$tType]: (((pt_name @ T) => (! [F1:(late_subject > (name > (pi > T))),F22:(late_freeRes > (pi > T)),X2: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) @ F22)) => ((((((late_r582136743ec_set @ T) @ F1) @ F22) @ X2) @ Y) => ((! [Y6:T]: (((((((late_r582136743ec_set @ T) @ F1) @ F22) @ X2) @ Y6) => (Y6 = Y)))) => (((((fresh @ name) @ late_residual) @ A2) @ X2) => (((((fresh @ name) @ (late_subject > (name > (pi > T)))) @ A2) @ F1) => (((((fresh @ name) @ (late_freeRes > (pi > T))) @ A2) @ F22) => ((((fresh @ name) @ T) @ A2) @ Y)))))))))))))).
% 2.44/1.49 thf(fact_247_residual_Orec__unique, axiom, (! [N:$tType,T:$tType]: (((pt_name @ T) => (! [F1:(late_subject > (name > (pi > T))),F22:(late_freeRes > (pi > T)),Z:N,P:(T > $o),X2:late_residual]: ((((finite_finite @ name) @ (((supp @ (late_subject > (name > (pi > T)))) @ name) @ F1)) => (((finite_finite @ name) @ (((supp @ (late_freeRes > (pi > T))) @ name) @ F22)) => (((finite_finite @ name) @ (((supp @ N) @ name) @ Z)) => ((! [X12:late_subject,X23:name,X33:pi]: ((P @ (((F1 @ X12) @ X23) @ X33)))) => ((! [X12:late_freeRes,X23:pi]: ((P @ ((F22 @ X12) @ X23)))) => ((! [X12:late_subject,X23:name]: ((((((fresh @ name) @ (late_subject > (name > (pi > T)))) @ X23) @ F1) => (((((fresh @ name) @ late_subject) @ X23) @ X12) => (((((fresh @ name) @ N) @ X23) @ Z) => (! [X33:pi]: (((P @ (((F1 @ X12) @ X23) @ X33)) => ((((fresh @ name) @ T) @ X23) @ (((F1 @ X12) @ X23) @ X33)))))))))) => (? [X4:T]: (((((((late_r582136743ec_set @ T) @ F1) @ F22) @ X2) @ X4) & (! [Y7:T]: (((((((late_r582136743ec_set @ T) @ F1) @ F22) @ X2) @ Y7) => (Y7 = X4))))))))))))))))))).
% 2.44/1.49 thf(fact_248_residual_Orec__fin__supp, axiom, (! [T:$tType]: (((pt_name @ T) => (! [F1:(late_subject > (name > (pi > T))),F22:(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) @ F22)) => ((((((late_r582136743ec_set @ T) @ F1) @ F22) @ X1) @ Y1) => ((finite_finite @ name) @ (((supp @ T) @ name) @ Y1))))))))))).
% 2.44/1.49 thf(fact_249_pi_Osupp_I4_J, axiom, (! [X32:name,X1:name,X22:pi]: (((((supp @ pi) @ name) @ (((input @ X32) @ X1) @ X22)) = (((sup_sup @ (set @ name)) @ (((supp @ name) @ name) @ X32)) @ (((supp @ (name > (noption @ pi))) @ name) @ ((((abs_fun @ name) @ pi) @ X1) @ X22))))))).
% 2.44/1.49 thf(fact_250_residual_Osupp_I1_J, axiom, (! [X32:late_subject,X1:name,X22:pi]: (((((supp @ late_residual) @ name) @ (((late_BoundR @ X32) @ X1) @ X22)) = (((sup_sup @ (set @ name)) @ (((supp @ late_subject) @ name) @ X32)) @ (((supp @ (name > (noption @ pi))) @ name) @ ((((abs_fun @ name) @ pi) @ X1) @ X22))))))).
% 2.44/1.49 thf(fact_251_pi_Osupp_I7_J, axiom, (! [X22:pi,X1:pi]: (((((supp @ pi) @ name) @ ((sum @ X22) @ X1)) = (((sup_sup @ (set @ name)) @ (((supp @ pi) @ name) @ X22)) @ (((supp @ pi) @ name) @ X1)))))).
% 2.44/1.49 thf(fact_252_pi_Osupp_I8_J, axiom, (! [X22:pi,X1:pi]: (((((supp @ pi) @ name) @ ((par @ X22) @ X1)) = (((sup_sup @ (set @ name)) @ (((supp @ pi) @ name) @ X22)) @ (((supp @ pi) @ name) @ X1)))))).
% 2.44/1.49 thf(fact_253_residual_Osupp_I2_J, axiom, (! [X22:late_freeRes,X1:pi]: (((((supp @ late_residual) @ name) @ ((late_FreeR @ X22) @ X1)) = (((sup_sup @ (set @ name)) @ (((supp @ late_freeRes) @ name) @ X22)) @ (((supp @ pi) @ name) @ X1)))))).
% 2.44/1.49 thf(fact_254_freeRes_Osupp_I1_J, axiom, (! [X22:name,X1:name]: (((((supp @ late_freeRes) @ name) @ ((late_OutputR @ X22) @ X1)) = (((sup_sup @ (set @ name)) @ (((supp @ name) @ name) @ X22)) @ (((supp @ name) @ name) @ X1)))))).
% 2.44/1.49 thf(fact_255_pi_Osupp_I2_J, axiom, (! [X32:name,X22:name,X1:pi]: (((((supp @ pi) @ name) @ (((output @ X32) @ X22) @ X1)) = (((sup_sup @ (set @ name)) @ (((supp @ name) @ name) @ X32)) @ (((sup_sup @ (set @ name)) @ (((supp @ name) @ name) @ X22)) @ (((supp @ pi) @ name) @ X1))))))).
% 2.44/1.49 thf(tcon_fun___Agent_Opt__name, axiom, (! [A6:$tType,A7:$tType]: ((((pt_name @ A6) & (pt_name @ A7)) => (pt_name @ (A6 > A7)))))).
% 2.44/1.49 thf(tcon_Set_Oset___Agent_Opt__name_1, axiom, (! [A6:$tType]: (((pt_name @ A6) => (pt_name @ (set @ A6)))))).
% 2.44/1.49 thf(tcon_Agent_Opi___Agent_Opt__name_2, axiom, (pt_name @ pi)).
% 2.44/1.49 thf(tcon_Agent_Opi___Agent_Ofs__name, axiom, (fs_name @ pi)).
% 2.44/1.49 thf(tcon_HOL_Obool___Agent_Opt__name_3, axiom, (pt_name @ $o)).
% 2.44/1.49 thf(tcon_HOL_Obool___Agent_Ofs__name_4, axiom, (fs_name @ $o)).
% 2.44/1.49 thf(tcon_Agent_Oname___Agent_Opt__name_5, axiom, (pt_name @ name)).
% 2.44/1.49 thf(tcon_Agent_Oname___Agent_Ofs__name_6, axiom, (fs_name @ name)).
% 2.44/1.49 thf(tcon_Nominal_Onoption___Agent_Opt__name_7, axiom, (! [A6:$tType]: (((pt_name @ A6) => (pt_name @ (noption @ A6)))))).
% 2.44/1.49 thf(tcon_Late__Semantics_OfreeRes___Agent_Opt__name_8, axiom, (pt_name @ late_freeRes)).
% 2.44/1.49 thf(tcon_Late__Semantics_OfreeRes___Agent_Ofs__name_9, axiom, (fs_name @ late_freeRes)).
% 2.44/1.49 thf(tcon_Late__Semantics_Osubject___Agent_Opt__name_10, axiom, (pt_name @ late_subject)).
% 2.44/1.49 thf(tcon_Late__Semantics_Osubject___Agent_Ofs__name_11, axiom, (fs_name @ late_subject)).
% 2.44/1.49 thf(tcon_Late__Semantics_Oresidual___Agent_Opt__name_12, axiom, (pt_name @ late_residual)).
% 2.44/1.49 thf(tcon_Late__Semantics_Oresidual___Agent_Ofs__name_13, axiom, (fs_name @ late_residual)).
% 2.44/1.49 thf(help_If_3_1_T, axiom, (! [P:$o]: (((P = $true) | (P = $false))))).
% 2.44/1.49 thf(help_If_2_1_T, axiom, (! [A:$tType,X2:A,Y:A]: ((((((if @ A) @ $false) @ X2) @ Y) = Y)))).
% 2.44/1.49 thf(help_If_1_1_T, axiom, (! [A:$tType,X2:A,Y:A]: ((((((if @ A) @ $true) @ X2) @ Y) = X2)))).
% 2.44/1.49 thf(conj_0, conjecture, ((late_transitions @ ((par @ ((par @ p) @ q)) @ r)) @ ((late_FreeR @ late_TauR) @ ((res @ y) @ ((par @ ((par @ p) @ q2)) @ (((subs @ r2) @ x) @ y)))))).
% 2.44/1.49 % SZS output end ListOfTHF for /export/starexec/sandbox2/tmp/tmp.pAINnnNPiL/DTF2DTF21913.p
% 2.44/1.49 ------------------------
% 2.69/1.52 ---- Cleaned THF ---
% 2.69/1.52 thf(ty_t_Late__Semantics_Oresidual,type,
% 2.69/1.52 late_residual: $tType ).
% 2.69/1.52
% 2.69/1.52 thf(ty_t_Late__Semantics_Osubject,type,
% 2.69/1.52 late_subject: $tType ).
% 2.69/1.52
% 2.69/1.52 thf(ty_t_Late__Semantics_OfreeRes,type,
% 2.69/1.52 late_freeRes: $tType ).
% 2.69/1.52
% 2.69/1.52 thf(ty_t_Nominal_Onoption,type,
% 2.69/1.52 noption: $tType > $tType ).
% 2.69/1.52
% 2.69/1.52 thf(ty_t_Agent_Oname,type,
% 2.69/1.52 name: $tType ).
% 2.69/1.52
% 2.69/1.52 thf(ty_t_Agent_Opi,type,
% 2.69/1.52 pi: $tType ).
% 2.69/1.52
% 2.69/1.52 thf(ty_t_Set_Oset,type,
% 2.69/1.52 set: $tType > $tType ).
% 2.69/1.52
% 2.69/1.52 thf(sy_cl_Agent_Ofs__name,type,
% 2.69/1.52 fs_name:
% 2.69/1.52 !>[A: $tType] : $o ).
% 2.69/1.52
% 2.69/1.52 thf(sy_cl_Agent_Opt__name,type,
% 2.69/1.52 pt_name:
% 2.69/1.52 !>[A: $tType] : $o ).
% 2.69/1.52
% 2.69/1.52 thf(sy_c_Agent_Opi_OBang,type,
% 2.69/1.52 bang: pi > pi ).
% 2.69/1.52
% 2.69/1.52 thf(sy_c_Agent_Opi_OInput,type,
% 2.69/1.52 input: name > name > pi > pi ).
% 2.69/1.52
% 2.69/1.52 thf(sy_c_Agent_Opi_OMatch,type,
% 2.69/1.52 match: name > name > pi > pi ).
% 2.69/1.52
% 2.69/1.52 thf(sy_c_Agent_Opi_OMismatch,type,
% 2.69/1.52 mismatch: name > name > pi > pi ).
% 2.69/1.52
% 2.69/1.52 thf(sy_c_Agent_Opi_OOutput,type,
% 2.69/1.52 output: name > name > pi > pi ).
% 2.69/1.52
% 2.69/1.52 thf(sy_c_Agent_Opi_OPar,type,
% 2.69/1.52 par: pi > pi > pi ).
% 2.69/1.52
% 2.69/1.52 thf(sy_c_Agent_Opi_OPiNil,type,
% 2.69/1.52 piNil: pi ).
% 2.69/1.52
% 2.69/1.52 thf(sy_c_Agent_Opi_ORes,type,
% 2.69/1.53 res: name > pi > pi ).
% 2.69/1.53
% 2.69/1.53 thf(sy_c_Agent_Opi_OSum,type,
% 2.69/1.53 sum: pi > pi > pi ).
% 2.69/1.53
% 2.69/1.53 thf(sy_c_Agent_Opi_OTau,type,
% 2.69/1.53 tau: pi > pi ).
% 2.69/1.53
% 2.69/1.53 thf(sy_c_Agent_Opi_Opi__rec,type,
% 2.69/1.53 pi_rec:
% 2.69/1.53 !>[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 ) ).
% 2.69/1.53
% 2.69/1.53 thf(sy_c_Agent_Osubs,type,
% 2.69/1.53 subs: pi > name > name > pi ).
% 2.69/1.53
% 2.69/1.53 thf(sy_c_Agent_Osubst__name,type,
% 2.69/1.53 subst_name: name > name > name > name ).
% 2.69/1.53
% 2.69/1.53 thf(sy_c_Finite__Set_Ofinite,type,
% 2.69/1.53 finite_finite:
% 2.69/1.53 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 2.69/1.53
% 2.69/1.53 thf(sy_c_If,type,
% 2.69/1.53 if:
% 2.69/1.53 !>[A: $tType] : ( $o > A > A > A ) ).
% 2.69/1.53
% 2.69/1.53 thf(sy_c_Late__Semantics1_OfreeRes_Ocase__freeRes,type,
% 2.69/1.53 late_case_freeRes:
% 2.69/1.53 !>[A: $tType] : ( ( name > name > A ) > A > late_freeRes > A ) ).
% 2.69/1.53
% 2.69/1.53 thf(sy_c_Late__Semantics1_Osubject_Ocase__subject,type,
% 2.69/1.53 late_case_subject:
% 2.69/1.53 !>[A: $tType] : ( ( name > A ) > ( name > A ) > late_subject > A ) ).
% 2.69/1.53
% 2.69/1.53 thf(sy_c_Late__Semantics_ObangPred,type,
% 2.69/1.53 late_bangPred: pi > pi > $o ).
% 2.69/1.53
% 2.69/1.53 thf(sy_c_Late__Semantics_OfreeRes_OOutputR,type,
% 2.69/1.53 late_OutputR: name > name > late_freeRes ).
% 2.69/1.53
% 2.69/1.53 thf(sy_c_Late__Semantics_OfreeRes_OTauR,type,
% 2.69/1.53 late_TauR: late_freeRes ).
% 2.69/1.53
% 2.69/1.53 thf(sy_c_Late__Semantics_OfreeRes_OfreeRes__rec,type,
% 2.69/1.53 late_freeRes_rec:
% 2.69/1.53 !>[T: $tType] : ( ( name > name > T ) > T > late_freeRes > T ) ).
% 2.69/1.53
% 2.69/1.53 thf(sy_c_Late__Semantics_Oresidual_OBoundR,type,
% 2.69/1.53 late_BoundR: late_subject > name > pi > late_residual ).
% 2.69/1.53
% 2.69/1.53 thf(sy_c_Late__Semantics_Oresidual_OFreeR,type,
% 2.69/1.53 late_FreeR: late_freeRes > pi > late_residual ).
% 2.69/1.53
% 2.69/1.53 thf(sy_c_Late__Semantics_Oresidual_Oresidual__rec,type,
% 2.69/1.53 late_residual_rec:
% 2.69/1.53 !>[T: $tType] : ( ( late_subject > name > pi > T ) > ( late_freeRes > pi > T ) > late_residual > T ) ).
% 2.69/1.53
% 2.69/1.53 thf(sy_c_Late__Semantics_Oresidual_Oresidual__rec__set,type,
% 2.69/1.53 late_r582136743ec_set:
% 2.69/1.53 !>[T: $tType] : ( ( late_subject > name > pi > T ) > ( late_freeRes > pi > T ) > late_residual > T > $o ) ).
% 2.69/1.53
% 2.69/1.53 thf(sy_c_Late__Semantics_Osubject_OBoundOutputS,type,
% 2.69/1.53 late_BoundOutputS: name > late_subject ).
% 2.69/1.53
% 2.69/1.53 thf(sy_c_Late__Semantics_Osubject_OInputS,type,
% 2.69/1.53 late_InputS: name > late_subject ).
% 2.69/1.53
% 2.69/1.53 thf(sy_c_Late__Semantics_Osubject_Osubject__rec,type,
% 2.69/1.53 late_subject_rec:
% 2.69/1.53 !>[T: $tType] : ( ( name > T ) > ( name > T ) > late_subject > T ) ).
% 2.69/1.53
% 2.69/1.53 thf(sy_c_Late__Semantics_Otransitions,type,
% 2.69/1.53 late_transitions: pi > late_residual > $o ).
% 2.69/1.53
% 2.69/1.53 thf(sy_c_Lattices_Osup__class_Osup,type,
% 2.69/1.53 sup_sup:
% 2.69/1.53 !>[A: $tType] : ( A > A > A ) ).
% 2.69/1.53
% 2.69/1.53 thf(sy_c_Nominal_Oabs__fun,type,
% 2.69/1.53 abs_fun:
% 2.69/1.53 !>[X: $tType,A: $tType] : ( X > A > X > ( noption @ A ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(sy_c_Nominal_Ofresh,type,
% 2.69/1.53 fresh:
% 2.69/1.53 !>[X: $tType,A: $tType] : ( X > A > $o ) ).
% 2.69/1.53
% 2.69/1.53 thf(sy_c_Nominal_Osupp,type,
% 2.69/1.53 supp:
% 2.69/1.53 !>[A: $tType,X: $tType] : ( A > ( set @ X ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(sy_c_Set_OCollect,type,
% 2.69/1.53 collect:
% 2.69/1.53 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(sy_c_member,type,
% 2.69/1.53 member:
% 2.69/1.53 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 2.69/1.53
% 2.69/1.53 thf(sy_v_P,type,
% 2.69/1.53 p: pi ).
% 2.69/1.53
% 2.69/1.53 thf(sy_v_PQR____,type,
% 2.69/1.53 pqr: pi ).
% 2.69/1.53
% 2.69/1.53 thf(sy_v_Q,type,
% 2.69/1.53 q: pi ).
% 2.69/1.53
% 2.69/1.53 thf(sy_v_QR____,type,
% 2.69/1.53 qr: pi ).
% 2.69/1.53
% 2.69/1.53 thf(sy_v_Q_H____,type,
% 2.69/1.53 q2: pi ).
% 2.69/1.53
% 2.69/1.53 thf(sy_v_R,type,
% 2.69/1.53 r: pi ).
% 2.69/1.53
% 2.69/1.53 thf(sy_v_R_H____,type,
% 2.69/1.53 r2: pi ).
% 2.69/1.53
% 2.69/1.53 thf(sy_v__092_060alpha_062____,type,
% 2.69/1.53 alpha: late_freeRes ).
% 2.69/1.53
% 2.69/1.53 thf(sy_v_a____,type,
% 2.69/1.53 a: name ).
% 2.69/1.53
% 2.69/1.53 thf(sy_v_x____,type,
% 2.69/1.53 x: name ).
% 2.69/1.53
% 2.69/1.53 thf(sy_v_y____,type,
% 2.69/1.53 y: name ).
% 2.69/1.53
% 2.69/1.53 thf(fact_0_cClose2_Ohyps_I14_J,axiom,
% 2.69/1.53 alpha = late_TauR ).
% 2.69/1.53
% 2.69/1.53 thf(fact_1_cClose2_Ohyps_I10_J,axiom,
% 2.69/1.53 y != a ).
% 2.69/1.53
% 2.69/1.53 thf(fact_2_cClose2_Ohyps_I5_J,axiom,
% 2.69/1.53 x != a ).
% 2.69/1.53
% 2.69/1.53 thf(fact_3_cClose2_Ohyps_I9_J,axiom,
% 2.69/1.53 fresh @ name @ pi @ y @ r ).
% 2.69/1.53
% 2.69/1.53 thf(fact_4_cClose2_Ohyps_I6_J,axiom,
% 2.69/1.53 x != y ).
% 2.69/1.53
% 2.69/1.53 thf(fact_5_cClose2_Ohyps_I8_J,axiom,
% 2.69/1.53 fresh @ name @ pi @ y @ q ).
% 2.69/1.53
% 2.69/1.53 thf(fact_6_cClose2_Ohyps_I3_J,axiom,
% 2.69/1.53 fresh @ name @ pi @ x @ q ).
% 2.69/1.53
% 2.69/1.53 thf(fact_7_cClose2_Ohyps_I13_J,axiom,
% 2.69/1.53 fresh @ name @ pi @ y @ p ).
% 2.69/1.53
% 2.69/1.53 thf(fact_8_cClose2_Ohyps_I12_J,axiom,
% 2.69/1.53 fresh @ name @ pi @ x @ p ).
% 2.69/1.53
% 2.69/1.53 thf(fact_9_cClose2_Ohyps_I4_J,axiom,
% 2.69/1.53 fresh @ name @ pi @ x @ r ).
% 2.69/1.53
% 2.69/1.53 thf(fact_10_cClose2_Ohyps_I7_J,axiom,
% 2.69/1.53 fresh @ name @ pi @ x @ q2 ).
% 2.69/1.53
% 2.69/1.53 thf(fact_11_cClose2_Ohyps_I11_J,axiom,
% 2.69/1.53 fresh @ name @ pi @ y @ r2 ).
% 2.69/1.53
% 2.69/1.53 thf(fact_12_cClose2_Ohyps_I2_J,axiom,
% 2.69/1.53 late_transitions @ r @ ( late_BoundR @ ( late_InputS @ a ) @ x @ r2 ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_13__092_060open_062P_A_092_060parallel_062_AQ_A_092_060longmapsto_062_Aa_060_092_060nu_062y_062_A_092_060prec_062_AP_A_092_060parallel_062_AQ_H_092_060close_062,axiom,
% 2.69/1.53 late_transitions @ ( par @ p @ q ) @ ( late_BoundR @ ( late_BoundOutputS @ a ) @ y @ ( par @ p @ q2 ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_14_cClose2_Ohyps_I1_J,axiom,
% 2.69/1.53 late_transitions @ q @ ( late_BoundR @ ( late_BoundOutputS @ a ) @ y @ q2 ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_15_cPar2_Ohyps,axiom,
% 2.69/1.53 late_transitions @ ( par @ q @ r ) @ ( late_FreeR @ alpha @ qr ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_16_Free_Ohyps,axiom,
% 2.69/1.53 late_transitions @ ( par @ p @ ( par @ q @ r ) ) @ ( late_FreeR @ alpha @ pqr ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_17_simps_I9_J,axiom,
% 2.69/1.53 ! [X2: name,C: name,D: name,P: pi] :
% 2.69/1.53 ( ( X2 != C )
% 2.69/1.53 => ( ( X2 != D )
% 2.69/1.53 => ( ( subs @ ( res @ X2 @ P ) @ C @ D )
% 2.69/1.53 = ( res @ X2 @ ( subs @ P @ C @ D ) ) ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_18_simps_I8_J,axiom,
% 2.69/1.53 ! [P: pi,Q: pi,C: name,D: name] :
% 2.69/1.53 ( ( subs @ ( par @ P @ Q ) @ C @ D )
% 2.69/1.53 = ( par @ ( subs @ P @ C @ D ) @ ( subs @ Q @ C @ D ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_19_Par1F,axiom,
% 2.69/1.53 ! [P: pi,Alpha: late_freeRes,P2: pi,Q: pi] :
% 2.69/1.53 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 2.69/1.53 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha @ ( par @ P2 @ Q ) ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_20_Par2F,axiom,
% 2.69/1.53 ! [Q: pi,Alpha: late_freeRes,Q2: pi,P: pi] :
% 2.69/1.53 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 2.69/1.53 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha @ ( par @ P @ Q2 ) ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_21_subst__identity,axiom,
% 2.69/1.53 ! [P: pi,A2: name] :
% 2.69/1.53 ( ( subs @ P @ A2 @ A2 )
% 2.69/1.53 = P ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_22_pi_Odistinct_I85_J,axiom,
% 2.69/1.53 ! [Pi1: pi,Pi2: pi,Name: name,Pi: pi] :
% 2.69/1.53 ( ( par @ Pi1 @ Pi2 )
% 2.69/1.53 != ( res @ Name @ Pi ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_23_Late__Semantics_OClose1,axiom,
% 2.69/1.53 ! [P: pi,A2: name,X2: name,P2: pi,Q: pi,Y: name,Q2: pi] :
% 2.69/1.53 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P2 ) )
% 2.69/1.53 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y @ Q2 ) )
% 2.69/1.53 => ( ( fresh @ name @ pi @ Y @ P )
% 2.69/1.53 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ ( subs @ P2 @ X2 @ Y ) @ Q2 ) ) ) ) ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_24_Late__Semantics_OClose2,axiom,
% 2.69/1.53 ! [P: pi,A2: name,Y: name,P2: pi,Q: pi,X2: name,Q2: pi] :
% 2.69/1.53 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y @ P2 ) )
% 2.69/1.53 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ Q2 ) )
% 2.69/1.53 => ( ( fresh @ name @ pi @ Y @ Q )
% 2.69/1.53 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ P2 @ ( subs @ Q2 @ X2 @ Y ) ) ) ) ) ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_25_transitions_OClose1,axiom,
% 2.69/1.53 ! [P: pi,A2: name,X2: name,P2: pi,Q: pi,Y: name,Q2: pi] :
% 2.69/1.53 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P2 ) )
% 2.69/1.53 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y @ Q2 ) )
% 2.69/1.53 => ( ( fresh @ name @ pi @ X2 @ P )
% 2.69/1.53 => ( ( fresh @ name @ pi @ X2 @ Q )
% 2.69/1.53 => ( ( fresh @ name @ pi @ Y @ P )
% 2.69/1.53 => ( ( fresh @ name @ pi @ Y @ Q )
% 2.69/1.53 => ( ( X2 != A2 )
% 2.69/1.53 => ( ( fresh @ name @ pi @ X2 @ Q2 )
% 2.69/1.53 => ( ( Y != A2 )
% 2.69/1.53 => ( ( fresh @ name @ pi @ Y @ P2 )
% 2.69/1.53 => ( ( X2 != Y )
% 2.69/1.53 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ ( subs @ P2 @ X2 @ Y ) @ Q2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_26_transitions_OClose2,axiom,
% 2.69/1.53 ! [P: pi,A2: name,Y: name,P2: pi,Q: pi,X2: name,Q2: pi] :
% 2.69/1.53 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y @ P2 ) )
% 2.69/1.53 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ Q2 ) )
% 2.69/1.53 => ( ( fresh @ name @ pi @ X2 @ P )
% 2.69/1.53 => ( ( fresh @ name @ pi @ X2 @ Q )
% 2.69/1.53 => ( ( fresh @ name @ pi @ Y @ P )
% 2.69/1.53 => ( ( fresh @ name @ pi @ Y @ Q )
% 2.69/1.53 => ( ( X2 != A2 )
% 2.69/1.53 => ( ( fresh @ name @ pi @ X2 @ P2 )
% 2.69/1.53 => ( ( Y != A2 )
% 2.69/1.53 => ( ( fresh @ name @ pi @ Y @ Q2 )
% 2.69/1.53 => ( ( X2 != Y )
% 2.69/1.53 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ P2 @ ( subs @ Q2 @ X2 @ Y ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_27_substRes2,axiom,
% 2.69/1.53 ! [B: name,P: pi,A2: name] :
% 2.69/1.53 ( ( fresh @ name @ pi @ B @ P )
% 2.69/1.53 => ( ( res @ A2 @ P )
% 2.69/1.53 = ( res @ B @ ( subs @ P @ A2 @ B ) ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_28_substRes3,axiom,
% 2.69/1.53 ! [B: name,P: pi,A2: name] :
% 2.69/1.53 ( ( fresh @ name @ pi @ B @ P )
% 2.69/1.53 => ( ( subs @ ( res @ A2 @ P ) @ A2 @ B )
% 2.69/1.53 = ( res @ B @ ( subs @ P @ A2 @ B ) ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_29_Late__Semantics_Osubject_Oinject_I2_J,axiom,
% 2.69/1.53 ! [X1: name,Y1: name] :
% 2.69/1.53 ( ( ( late_BoundOutputS @ X1 )
% 2.69/1.53 = ( late_BoundOutputS @ Y1 ) )
% 2.69/1.53 = ( X1 = Y1 ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_30_pi_Ofresh_I8_J,axiom,
% 2.69/1.53 ! [A2: name,X22: pi,X1: pi] :
% 2.69/1.53 ( ( fresh @ name @ pi @ A2 @ ( par @ X22 @ X1 ) )
% 2.69/1.53 = ( ( fresh @ name @ pi @ A2 @ X22 )
% 2.69/1.53 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_31_substTrans,axiom,
% 2.69/1.53 ! [B: name,P: pi,A2: name,C: name] :
% 2.69/1.53 ( ( fresh @ name @ pi @ B @ P )
% 2.69/1.53 => ( ( subs @ ( subs @ P @ A2 @ B ) @ B @ C )
% 2.69/1.53 = ( subs @ P @ A2 @ C ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_32_Late__Semantics_Osubject_Odistinct_I1_J,axiom,
% 2.69/1.53 ! [Name2: name,Name: name] :
% 2.69/1.53 ( ( late_InputS @ Name2 )
% 2.69/1.53 != ( late_BoundOutputS @ Name ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_33_name__exists__fresh,axiom,
% 2.69/1.53 ! [A: $tType] :
% 2.69/1.53 ( ( fs_name @ A )
% 2.69/1.53 => ! [X2: A] :
% 2.69/1.53 ~ ! [C2: name] :
% 2.69/1.53 ~ ( fresh @ name @ A @ C2 @ X2 ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_34_subject_Oinducts,axiom,
% 2.69/1.53 ! [P: late_subject > $o,Subject: late_subject] :
% 2.69/1.53 ( ! [Name3: name] : ( P @ ( late_InputS @ Name3 ) )
% 2.69/1.53 => ( ! [Name3: name] : ( P @ ( late_BoundOutputS @ Name3 ) )
% 2.69/1.53 => ( P @ Subject ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_35_subject_Ostrong__induct_H,axiom,
% 2.69/1.53 ! [N: $tType,P: N > late_subject > $o,Z: N,Subject: late_subject] :
% 2.69/1.53 ( ! [Name3: name,Z2: N] : ( P @ Z2 @ ( late_InputS @ Name3 ) )
% 2.69/1.53 => ( ! [Name3: name,Z2: N] : ( P @ Z2 @ ( late_BoundOutputS @ Name3 ) )
% 2.69/1.53 => ( P @ Z @ Subject ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_36_subject_Ostrong__inducts,axiom,
% 2.69/1.53 ! [A: $tType,P: A > late_subject > $o,Z: A,Subject: late_subject] :
% 2.69/1.53 ( ! [Name3: name,Z2: A] : ( P @ Z2 @ ( late_InputS @ Name3 ) )
% 2.69/1.53 => ( ! [Name3: name,Z2: A] : ( P @ Z2 @ ( late_BoundOutputS @ Name3 ) )
% 2.69/1.53 => ( P @ Z @ Subject ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_37_residual_Ostrong__inducts,axiom,
% 2.69/1.53 ! [A: $tType] :
% 2.69/1.53 ( ( fs_name @ A )
% 2.69/1.53 => ! [P: A > late_residual > $o,Z: A,Residual: late_residual] :
% 2.69/1.53 ( ! [Subject2: late_subject,Name3: name,Pi3: pi,Z2: A] :
% 2.69/1.53 ( ( fresh @ name @ A @ Name3 @ Z2 )
% 2.69/1.53 => ( ( fresh @ name @ late_subject @ Name3 @ Subject2 )
% 2.69/1.53 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi3 ) ) ) )
% 2.69/1.53 => ( ! [FreeRes: late_freeRes,Pi3: pi,Z2: A] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi3 ) )
% 2.69/1.53 => ( P @ Z @ Residual ) ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_38_residual_Ostrong__induct,axiom,
% 2.69/1.53 ! [N: $tType] :
% 2.69/1.53 ( ( fs_name @ N )
% 2.69/1.53 => ! [P: N > late_residual > $o,Z: N,Residual: late_residual] :
% 2.69/1.53 ( ! [Subject2: late_subject,Name3: name,Pi3: pi,Z2: N] :
% 2.69/1.53 ( ( fresh @ name @ N @ Name3 @ Z2 )
% 2.69/1.53 => ( ( fresh @ name @ late_subject @ Name3 @ Subject2 )
% 2.69/1.53 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi3 ) ) ) )
% 2.69/1.53 => ( ! [FreeRes: late_freeRes,Pi3: pi,Z2: N] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi3 ) )
% 2.69/1.53 => ( P @ Z @ Residual ) ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_39_freshBoundDerivative_I2_J,axiom,
% 2.69/1.53 ! [P: pi,A2: late_subject,X2: name,P2: pi,Y: name] :
% 2.69/1.53 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P2 ) )
% 2.69/1.53 => ( ( fresh @ name @ pi @ Y @ P )
% 2.69/1.53 => ( ( Y != X2 )
% 2.69/1.53 => ( fresh @ name @ pi @ Y @ P2 ) ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_40_freshRes,axiom,
% 2.69/1.53 ! [A2: name,P: pi] : ( fresh @ name @ pi @ A2 @ ( res @ A2 @ P ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_41_residual_Oinducts,axiom,
% 2.69/1.53 ! [P: late_residual > $o,Residual: late_residual] :
% 2.69/1.53 ( ! [Subject2: late_subject,Name3: name,Pi3: pi] : ( P @ ( late_BoundR @ Subject2 @ Name3 @ Pi3 ) )
% 2.69/1.53 => ( ! [FreeRes: late_freeRes,Pi3: pi] : ( P @ ( late_FreeR @ FreeRes @ Pi3 ) )
% 2.69/1.53 => ( P @ Residual ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_42_residual_Odistinct_I1_J,axiom,
% 2.69/1.53 ! [Subject: late_subject,Name2: name,Pi4: pi,FreeRes2: late_freeRes,Pi: pi] :
% 2.69/1.53 ( ( late_BoundR @ Subject @ Name2 @ Pi4 )
% 2.69/1.53 != ( late_FreeR @ FreeRes2 @ Pi ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_43_fresh__fact2,axiom,
% 2.69/1.53 ! [A2: name,B: name,P: pi] :
% 2.69/1.53 ( ( A2 != B )
% 2.69/1.53 => ( fresh @ name @ pi @ A2 @ ( subs @ P @ A2 @ B ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_44_fresh__fact1,axiom,
% 2.69/1.53 ! [A2: name,P: pi,C: name,B: name] :
% 2.69/1.53 ( ( fresh @ name @ pi @ A2 @ P )
% 2.69/1.53 => ( ( A2 != C )
% 2.69/1.53 => ( fresh @ name @ pi @ A2 @ ( subs @ P @ B @ C ) ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_45_mem__Collect__eq,axiom,
% 2.69/1.53 ! [A: $tType,A2: A,P: A > $o] :
% 2.69/1.53 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 2.69/1.53 = ( P @ A2 ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_46_Collect__mem__eq,axiom,
% 2.69/1.53 ! [A: $tType,A3: set @ A] :
% 2.69/1.53 ( ( collect @ A
% 2.69/1.53 @ ^ [X3: A] : ( member @ A @ X3 @ A3 ) )
% 2.69/1.53 = A3 ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_47_Collect__cong,axiom,
% 2.69/1.53 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.69/1.53 ( ! [X4: A] :
% 2.69/1.53 ( ( P @ X4 )
% 2.69/1.53 = ( Q @ X4 ) )
% 2.69/1.53 => ( ( collect @ A @ P )
% 2.69/1.53 = ( collect @ A @ Q ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_48_ext,axiom,
% 2.69/1.53 ! [B2: $tType,A: $tType,F: A > B2,G: A > B2] :
% 2.69/1.53 ( ! [X4: A] :
% 2.69/1.53 ( ( F @ X4 )
% 2.69/1.53 = ( G @ X4 ) )
% 2.69/1.53 => ( F = G ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_49_forget,axiom,
% 2.69/1.53 ! [A2: name,P: pi,B: name] :
% 2.69/1.53 ( ( fresh @ name @ pi @ A2 @ P )
% 2.69/1.53 => ( ( subs @ P @ A2 @ B )
% 2.69/1.53 = P ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_50_parCasesB,axiom,
% 2.69/1.53 ! [P: pi,Q: pi,A2: late_subject,X2: name,PQ: pi,Prop: pi > $o] :
% 2.69/1.53 ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X2 @ PQ ) )
% 2.69/1.53 => ( ( fresh @ name @ pi @ X2 @ P )
% 2.69/1.53 => ( ( fresh @ name @ pi @ X2 @ Q )
% 2.69/1.53 => ( ! [P3: pi] :
% 2.69/1.53 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P3 ) )
% 2.69/1.53 => ( Prop @ ( par @ P3 @ Q ) ) )
% 2.69/1.53 => ( ! [Q3: pi] :
% 2.69/1.53 ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X2 @ Q3 ) )
% 2.69/1.53 => ( Prop @ ( par @ P @ Q3 ) ) )
% 2.69/1.53 => ( Prop @ PQ ) ) ) ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_51_Late__Semantics_OPar2B,axiom,
% 2.69/1.53 ! [Q: pi,A2: late_subject,X2: name,Q2: pi,P: pi] :
% 2.69/1.53 ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X2 @ Q2 ) )
% 2.69/1.53 => ( ( fresh @ name @ pi @ X2 @ P )
% 2.69/1.53 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X2 @ ( par @ P @ Q2 ) ) ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_52_Late__Semantics_OPar1B,axiom,
% 2.69/1.53 ! [P: pi,A2: late_subject,X2: name,P2: pi,Q: pi] :
% 2.69/1.53 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P2 ) )
% 2.69/1.53 => ( ( fresh @ name @ pi @ X2 @ Q )
% 2.69/1.53 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X2 @ ( par @ P2 @ Q ) ) ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_53_pi_Oinject_I7_J,axiom,
% 2.69/1.53 ! [X22: pi,X1: pi,Y2: pi,Y1: pi] :
% 2.69/1.53 ( ( ( par @ X22 @ X1 )
% 2.69/1.53 = ( par @ Y2 @ Y1 ) )
% 2.69/1.53 = ( ( X22 = Y2 )
% 2.69/1.53 & ( X1 = Y1 ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_54_freshFreeDerivative_I2_J,axiom,
% 2.69/1.53 ! [P: pi,Alpha: late_freeRes,P2: pi,Y: name] :
% 2.69/1.53 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 2.69/1.53 => ( ( fresh @ name @ pi @ Y @ P )
% 2.69/1.53 => ( fresh @ name @ pi @ Y @ P2 ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_55_residual_Oinject_I2_J,axiom,
% 2.69/1.53 ! [X22: late_freeRes,X1: pi,Y2: late_freeRes,Y1: pi] :
% 2.69/1.53 ( ( ( late_FreeR @ X22 @ X1 )
% 2.69/1.53 = ( late_FreeR @ Y2 @ Y1 ) )
% 2.69/1.53 = ( ( X22 = Y2 )
% 2.69/1.53 & ( X1 = Y1 ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_56_transitions_OComm2,axiom,
% 2.69/1.53 ! [P: pi,A2: name,B: name,P2: pi,Q: pi,X2: name,Q2: pi] :
% 2.69/1.53 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A2 @ B ) @ P2 ) )
% 2.69/1.53 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ Q2 ) )
% 2.69/1.53 => ( ( fresh @ name @ pi @ X2 @ P )
% 2.69/1.53 => ( ( fresh @ name @ pi @ X2 @ Q )
% 2.69/1.53 => ( ( X2 != A2 )
% 2.69/1.53 => ( ( X2 != B )
% 2.69/1.53 => ( ( fresh @ name @ pi @ X2 @ P2 )
% 2.69/1.53 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P2 @ ( subs @ Q2 @ X2 @ B ) ) ) ) ) ) ) ) ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_57_transitions_OComm1,axiom,
% 2.69/1.53 ! [P: pi,A2: name,X2: name,P2: pi,Q: pi,B: name,Q2: pi] :
% 2.69/1.53 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P2 ) )
% 2.69/1.53 => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A2 @ B ) @ Q2 ) )
% 2.69/1.53 => ( ( fresh @ name @ pi @ X2 @ P )
% 2.69/1.53 => ( ( fresh @ name @ pi @ X2 @ Q )
% 2.69/1.53 => ( ( X2 != A2 )
% 2.69/1.53 => ( ( X2 != B )
% 2.69/1.53 => ( ( fresh @ name @ pi @ X2 @ Q2 )
% 2.69/1.53 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P2 @ X2 @ B ) @ Q2 ) ) ) ) ) ) ) ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_58_Late__Semantics1_Osubject_Oinject_I1_J,axiom,
% 2.69/1.53 ! [X1: name,Y1: name] :
% 2.69/1.53 ( ( ( late_InputS @ X1 )
% 2.69/1.53 = ( late_InputS @ Y1 ) )
% 2.69/1.53 = ( X1 = Y1 ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_59_Late__Semantics1_Osubject_Oinject_I2_J,axiom,
% 2.69/1.53 ! [X22: name,Y2: name] :
% 2.69/1.53 ( ( ( late_BoundOutputS @ X22 )
% 2.69/1.53 = ( late_BoundOutputS @ Y2 ) )
% 2.69/1.53 = ( X22 = Y2 ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_60_Late__Semantics_OComm2,axiom,
% 2.69/1.53 ! [P: pi,A2: name,B: name,P2: pi,Q: pi,X2: name,Q2: pi] :
% 2.69/1.53 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A2 @ B ) @ P2 ) )
% 2.69/1.53 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ Q2 ) )
% 2.69/1.53 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P2 @ ( subs @ Q2 @ X2 @ B ) ) ) ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_61_Late__Semantics_OComm1,axiom,
% 2.69/1.53 ! [P: pi,A2: name,X2: name,P2: pi,Q: pi,B: name,Q2: pi] :
% 2.69/1.53 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P2 ) )
% 2.69/1.53 => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A2 @ B ) @ Q2 ) )
% 2.69/1.53 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P2 @ X2 @ B ) @ Q2 ) ) ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_62_Late__Semantics1_Osubject_Odistinct_I1_J,axiom,
% 2.69/1.53 ! [X1: name,X22: name] :
% 2.69/1.53 ( ( late_InputS @ X1 )
% 2.69/1.53 != ( late_BoundOutputS @ X22 ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_63_subject_Oexhaust,axiom,
% 2.69/1.53 ! [Y: late_subject] :
% 2.69/1.53 ( ! [X12: name] :
% 2.69/1.53 ( Y
% 2.69/1.53 != ( late_InputS @ X12 ) )
% 2.69/1.53 => ~ ! [X23: name] :
% 2.69/1.53 ( Y
% 2.69/1.53 != ( late_BoundOutputS @ X23 ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_64_Open,axiom,
% 2.69/1.53 ! [P: pi,A2: name,B: name,P2: pi] :
% 2.69/1.53 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A2 @ B ) @ P2 ) )
% 2.69/1.53 => ( ( A2 != B )
% 2.69/1.53 => ( late_transitions @ ( res @ B @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ B @ P2 ) ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_65_freeRes_Ofresh_I1_J,axiom,
% 2.69/1.53 ! [A2: name,X22: name,X1: name] :
% 2.69/1.53 ( ( fresh @ name @ late_freeRes @ A2 @ ( late_OutputR @ X22 @ X1 ) )
% 2.69/1.53 = ( ( fresh @ name @ name @ A2 @ X22 )
% 2.69/1.53 & ( fresh @ name @ name @ A2 @ X1 ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_66_Late__Semantics_OfreeRes_Oinject,axiom,
% 2.69/1.53 ! [X22: name,X1: name,Y2: name,Y1: name] :
% 2.69/1.53 ( ( ( late_OutputR @ X22 @ X1 )
% 2.69/1.53 = ( late_OutputR @ Y2 @ Y1 ) )
% 2.69/1.53 = ( ( X22 = Y2 )
% 2.69/1.53 & ( X1 = Y1 ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_67_Late__Semantics1_OfreeRes_Oinject,axiom,
% 2.69/1.53 ! [X11: name,X122: name,Y11: name,Y12: name] :
% 2.69/1.53 ( ( ( late_OutputR @ X11 @ X122 )
% 2.69/1.53 = ( late_OutputR @ Y11 @ Y12 ) )
% 2.69/1.53 = ( ( X11 = Y11 )
% 2.69/1.53 & ( X122 = Y12 ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_68_freeRes_Ofresh_I2_J,axiom,
% 2.69/1.53 ! [A2: name] : ( fresh @ name @ late_freeRes @ A2 @ late_TauR ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_69_residual_Ofresh_I2_J,axiom,
% 2.69/1.53 ! [A2: name,X22: late_freeRes,X1: pi] :
% 2.69/1.53 ( ( fresh @ name @ late_residual @ A2 @ ( late_FreeR @ X22 @ X1 ) )
% 2.69/1.53 = ( ( fresh @ name @ late_freeRes @ A2 @ X22 )
% 2.69/1.53 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_70_subject_Ofresh_I2_J,axiom,
% 2.69/1.53 ! [A2: name,X1: name] :
% 2.69/1.53 ( ( fresh @ name @ late_subject @ A2 @ ( late_BoundOutputS @ X1 ) )
% 2.69/1.53 = ( fresh @ name @ name @ A2 @ X1 ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_71_subject_Ofresh_I1_J,axiom,
% 2.69/1.53 ! [A2: name,X1: name] :
% 2.69/1.53 ( ( fresh @ name @ late_subject @ A2 @ ( late_InputS @ X1 ) )
% 2.69/1.53 = ( fresh @ name @ name @ A2 @ X1 ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_72_Late__Semantics1_OfreeRes_Odistinct_I1_J,axiom,
% 2.69/1.53 ! [X11: name,X122: name] :
% 2.69/1.53 ( ( late_OutputR @ X11 @ X122 )
% 2.69/1.53 != late_TauR ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_73_freeRes_Oexhaust,axiom,
% 2.69/1.53 ! [Y: late_freeRes] :
% 2.69/1.53 ( ! [X112: name,X123: name] :
% 2.69/1.53 ( Y
% 2.69/1.53 != ( late_OutputR @ X112 @ X123 ) )
% 2.69/1.53 => ( Y = late_TauR ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_74_Late__Semantics_OfreeRes_Odistinct_I1_J,axiom,
% 2.69/1.53 ! [Name1: name,Name22: name] :
% 2.69/1.53 ( ( late_OutputR @ Name1 @ Name22 )
% 2.69/1.53 != late_TauR ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_75_freeRes_Oinducts,axiom,
% 2.69/1.53 ! [P: late_freeRes > $o,FreeRes3: late_freeRes] :
% 2.69/1.53 ( ! [Name12: name,Name23: name] : ( P @ ( late_OutputR @ Name12 @ Name23 ) )
% 2.69/1.53 => ( ( P @ late_TauR )
% 2.69/1.53 => ( P @ FreeRes3 ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_76_freeRes_Ostrong__induct_H,axiom,
% 2.69/1.53 ! [N: $tType,P: N > late_freeRes > $o,Z: N,FreeRes3: late_freeRes] :
% 2.69/1.53 ( ! [Name12: name,Name23: name,Z2: N] : ( P @ Z2 @ ( late_OutputR @ Name12 @ Name23 ) )
% 2.69/1.53 => ( ! [Z2: N] : ( P @ Z2 @ late_TauR )
% 2.69/1.53 => ( P @ Z @ FreeRes3 ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_77_freeRes_Ostrong__inducts,axiom,
% 2.69/1.53 ! [A: $tType,P: A > late_freeRes > $o,Z: A,FreeRes3: late_freeRes] :
% 2.69/1.53 ( ! [Name12: name,Name23: name,Z2: A] : ( P @ Z2 @ ( late_OutputR @ Name12 @ Name23 ) )
% 2.69/1.53 => ( ! [Z2: A] : ( P @ Z2 @ late_TauR )
% 2.69/1.53 => ( P @ Z @ FreeRes3 ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_78_resCases_H,axiom,
% 2.69/1.53 ! [X2: name,P: pi,Rs: late_residual] :
% 2.69/1.53 ( ( late_transitions @ ( res @ X2 @ P ) @ Rs )
% 2.69/1.53 => ( ! [P4: pi,A4: name,B3: name] :
% 2.69/1.53 ( ( ( res @ X2 @ P )
% 2.69/1.53 = ( res @ B3 @ P4 ) )
% 2.69/1.53 => ! [P3: pi] :
% 2.69/1.53 ( ( Rs
% 2.69/1.53 = ( late_BoundR @ ( late_BoundOutputS @ A4 ) @ B3 @ P3 ) )
% 2.69/1.53 => ( ( late_transitions @ P4 @ ( late_FreeR @ ( late_OutputR @ A4 @ B3 ) @ P3 ) )
% 2.69/1.53 => ( A4 = B3 ) ) ) )
% 2.69/1.53 => ( ! [P4: pi,A4: late_subject,X4: name,P3: pi,Y3: name] :
% 2.69/1.53 ( ( ( res @ X2 @ P )
% 2.69/1.53 = ( res @ Y3 @ P4 ) )
% 2.69/1.53 => ( ( Rs
% 2.69/1.53 = ( late_BoundR @ A4 @ X4 @ ( res @ Y3 @ P3 ) ) )
% 2.69/1.53 => ( ( late_transitions @ P4 @ ( late_BoundR @ A4 @ X4 @ P3 ) )
% 2.69/1.53 => ( ( fresh @ name @ late_subject @ Y3 @ A4 )
% 2.69/1.53 => ( ( Y3 != X4 )
% 2.69/1.53 => ( ( fresh @ name @ pi @ X4 @ P4 )
% 2.69/1.53 => ~ ( fresh @ name @ late_subject @ X4 @ A4 ) ) ) ) ) ) )
% 2.69/1.53 => ~ ! [P4: pi,Alpha2: late_freeRes,P3: pi,Y3: name] :
% 2.69/1.53 ( ( ( res @ X2 @ P )
% 2.69/1.53 = ( res @ Y3 @ P4 ) )
% 2.69/1.53 => ( ( Rs
% 2.69/1.53 = ( late_FreeR @ Alpha2 @ ( res @ Y3 @ P3 ) ) )
% 2.69/1.53 => ( ( late_transitions @ P4 @ ( late_FreeR @ Alpha2 @ P3 ) )
% 2.69/1.53 => ~ ( fresh @ name @ late_freeRes @ Y3 @ Alpha2 ) ) ) ) ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_79_freshResidual,axiom,
% 2.69/1.53 ! [P: pi,Rs: late_residual,X2: name] :
% 2.69/1.53 ( ( late_transitions @ P @ Rs )
% 2.69/1.53 => ( ( fresh @ name @ pi @ X2 @ P )
% 2.69/1.53 => ( fresh @ name @ late_residual @ X2 @ Rs ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_80_resCasesF,axiom,
% 2.69/1.53 ! [X2: name,P: pi,Alpha: late_freeRes,XP: pi,F2: pi > $o] :
% 2.69/1.53 ( ( late_transitions @ ( res @ X2 @ P ) @ ( late_FreeR @ Alpha @ XP ) )
% 2.69/1.53 => ( ! [P3: pi] :
% 2.69/1.53 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P3 ) )
% 2.69/1.53 => ( ( fresh @ name @ late_freeRes @ X2 @ Alpha )
% 2.69/1.53 => ( F2 @ ( res @ X2 @ P3 ) ) ) )
% 2.69/1.53 => ( F2 @ XP ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_81_resCasesF_H,axiom,
% 2.69/1.53 ! [X2: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 2.69/1.53 ( ( late_transitions @ ( res @ X2 @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 2.69/1.53 => ~ ! [P4: pi,Alpha2: late_freeRes,P3: pi,Y3: name] :
% 2.69/1.53 ( ( ( res @ X2 @ P )
% 2.69/1.53 = ( res @ Y3 @ P4 ) )
% 2.69/1.53 => ( ( ( late_FreeR @ Alpha @ P2 )
% 2.69/1.53 = ( late_FreeR @ Alpha2 @ ( res @ Y3 @ P3 ) ) )
% 2.69/1.53 => ( ( late_transitions @ P4 @ ( late_FreeR @ Alpha2 @ P3 ) )
% 2.69/1.53 => ~ ( fresh @ name @ late_freeRes @ Y3 @ Alpha2 ) ) ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_82_ResF,axiom,
% 2.69/1.53 ! [P: pi,Alpha: late_freeRes,P2: pi,Y: name] :
% 2.69/1.53 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 2.69/1.53 => ( ( fresh @ name @ late_freeRes @ Y @ Alpha )
% 2.69/1.53 => ( late_transitions @ ( res @ Y @ P ) @ ( late_FreeR @ Alpha @ ( res @ Y @ P2 ) ) ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_83_Late__Semantics_OResB,axiom,
% 2.69/1.53 ! [P: pi,A2: late_subject,X2: name,P2: pi,Y: name] :
% 2.69/1.53 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P2 ) )
% 2.69/1.53 => ( ( fresh @ name @ late_subject @ Y @ A2 )
% 2.69/1.53 => ( ( Y != X2 )
% 2.69/1.53 => ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A2 @ X2 @ ( res @ Y @ P2 ) ) ) ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_84_freshFreeDerivative_I1_J,axiom,
% 2.69/1.53 ! [P: pi,Alpha: late_freeRes,P2: pi,Y: name] :
% 2.69/1.53 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 2.69/1.53 => ( ( fresh @ name @ pi @ Y @ P )
% 2.69/1.53 => ( fresh @ name @ late_freeRes @ Y @ Alpha ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_85_freshBoundDerivative_I1_J,axiom,
% 2.69/1.53 ! [P: pi,A2: late_subject,X2: name,P2: pi,Y: name] :
% 2.69/1.53 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P2 ) )
% 2.69/1.53 => ( ( fresh @ name @ pi @ Y @ P )
% 2.69/1.53 => ( fresh @ name @ late_subject @ Y @ A2 ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_86_resCasesB_H,axiom,
% 2.69/1.53 ! [X5: name,P: pi,A2: late_subject,Y4: name,P2: pi] :
% 2.69/1.53 ( ( late_transitions @ ( res @ X5 @ P ) @ ( late_BoundR @ A2 @ Y4 @ P2 ) )
% 2.69/1.53 => ( ! [P4: pi,A4: name,B3: name] :
% 2.69/1.53 ( ( ( res @ X5 @ P )
% 2.69/1.53 = ( res @ B3 @ P4 ) )
% 2.69/1.53 => ! [P3: pi] :
% 2.69/1.53 ( ( ( late_BoundR @ A2 @ Y4 @ P2 )
% 2.69/1.53 = ( late_BoundR @ ( late_BoundOutputS @ A4 ) @ B3 @ P3 ) )
% 2.69/1.53 => ( ( late_transitions @ P4 @ ( late_FreeR @ ( late_OutputR @ A4 @ B3 ) @ P3 ) )
% 2.69/1.53 => ( A4 = B3 ) ) ) )
% 2.69/1.53 => ~ ! [P4: pi,A4: late_subject,X4: name,P3: pi,Y3: name] :
% 2.69/1.53 ( ( ( res @ X5 @ P )
% 2.69/1.53 = ( res @ Y3 @ P4 ) )
% 2.69/1.53 => ( ( ( late_BoundR @ A2 @ Y4 @ P2 )
% 2.69/1.53 = ( late_BoundR @ A4 @ X4 @ ( res @ Y3 @ P3 ) ) )
% 2.69/1.53 => ( ( late_transitions @ P4 @ ( late_BoundR @ A4 @ X4 @ P3 ) )
% 2.69/1.53 => ( ( fresh @ name @ late_subject @ Y3 @ A4 )
% 2.69/1.53 => ( ( Y3 != X4 )
% 2.69/1.53 => ( ( fresh @ name @ pi @ X4 @ P4 )
% 2.69/1.53 => ~ ( fresh @ name @ late_subject @ X4 @ A4 ) ) ) ) ) ) ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_87_parCasesB_H,axiom,
% 2.69/1.53 ! [P: pi,Q: pi,B: late_subject,Y: name,P2: pi] :
% 2.69/1.53 ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ B @ Y @ P2 ) )
% 2.69/1.53 => ( ! [P4: pi,A4: late_subject,X4: name,P3: pi,Q4: pi] :
% 2.69/1.53 ( ( ( par @ P @ Q )
% 2.69/1.53 = ( par @ P4 @ Q4 ) )
% 2.69/1.53 => ( ( ( late_BoundR @ B @ Y @ P2 )
% 2.69/1.53 = ( late_BoundR @ A4 @ X4 @ ( par @ P3 @ Q4 ) ) )
% 2.69/1.53 => ( ( late_transitions @ P4 @ ( late_BoundR @ A4 @ X4 @ P3 ) )
% 2.69/1.53 => ( ( fresh @ name @ pi @ X4 @ P4 )
% 2.69/1.53 => ( ( fresh @ name @ pi @ X4 @ Q4 )
% 2.69/1.53 => ~ ( fresh @ name @ late_subject @ X4 @ A4 ) ) ) ) ) )
% 2.69/1.53 => ~ ! [Q4: pi,A4: late_subject,X4: name,Q3: pi,P4: pi] :
% 2.69/1.53 ( ( ( par @ P @ Q )
% 2.69/1.53 = ( par @ P4 @ Q4 ) )
% 2.69/1.53 => ( ( ( late_BoundR @ B @ Y @ P2 )
% 2.69/1.53 = ( late_BoundR @ A4 @ X4 @ ( par @ P4 @ Q3 ) ) )
% 2.69/1.53 => ( ( late_transitions @ Q4 @ ( late_BoundR @ A4 @ X4 @ Q3 ) )
% 2.69/1.53 => ( ( fresh @ name @ pi @ X4 @ P4 )
% 2.69/1.53 => ( ( fresh @ name @ pi @ X4 @ Q4 )
% 2.69/1.53 => ~ ( fresh @ name @ late_subject @ X4 @ A4 ) ) ) ) ) ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_88_transitions_OPar1B,axiom,
% 2.69/1.53 ! [P: pi,A2: late_subject,X2: name,P2: pi,Q: pi] :
% 2.69/1.53 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P2 ) )
% 2.69/1.53 => ( ( fresh @ name @ pi @ X2 @ P )
% 2.69/1.53 => ( ( fresh @ name @ pi @ X2 @ Q )
% 2.69/1.53 => ( ( fresh @ name @ late_subject @ X2 @ A2 )
% 2.69/1.53 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X2 @ ( par @ P2 @ Q ) ) ) ) ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_89_transitions_OPar2B,axiom,
% 2.69/1.53 ! [Q: pi,A2: late_subject,X2: name,Q2: pi,P: pi] :
% 2.69/1.53 ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X2 @ Q2 ) )
% 2.69/1.53 => ( ( fresh @ name @ pi @ X2 @ P )
% 2.69/1.53 => ( ( fresh @ name @ pi @ X2 @ Q )
% 2.69/1.53 => ( ( fresh @ name @ late_subject @ X2 @ A2 )
% 2.69/1.53 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X2 @ ( par @ P @ Q2 ) ) ) ) ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_90_transitions_OResB,axiom,
% 2.69/1.53 ! [P: pi,A2: late_subject,X2: name,P2: pi,Y: name] :
% 2.69/1.53 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P2 ) )
% 2.69/1.53 => ( ( fresh @ name @ late_subject @ Y @ A2 )
% 2.69/1.53 => ( ( Y != X2 )
% 2.69/1.53 => ( ( fresh @ name @ pi @ X2 @ P )
% 2.69/1.53 => ( ( fresh @ name @ late_subject @ X2 @ A2 )
% 2.69/1.53 => ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A2 @ X2 @ ( res @ Y @ P2 ) ) ) ) ) ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_91_freeRes_Orecs_I2_J,axiom,
% 2.69/1.53 ! [T: $tType,P: T > $o,F1: name > name > T,F22: T] :
% 2.69/1.53 ( ! [X12: name,X23: name] : ( P @ ( F1 @ X12 @ X23 ) )
% 2.69/1.53 => ( ( P @ F22 )
% 2.69/1.53 => ( ( late_freeRes_rec @ T @ F1 @ F22 @ late_TauR )
% 2.69/1.53 = F22 ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_92_subject_Orecs_I1_J,axiom,
% 2.69/1.53 ! [T: $tType,P: T > $o,F1: name > T,F22: name > T,Name2: name] :
% 2.69/1.53 ( ! [X12: name] : ( P @ ( F1 @ X12 ) )
% 2.69/1.53 => ( ! [X12: name] : ( P @ ( F22 @ X12 ) )
% 2.69/1.53 => ( ( late_subject_rec @ T @ F1 @ F22 @ ( late_InputS @ Name2 ) )
% 2.69/1.53 = ( F1 @ Name2 ) ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_93_subject_Orecs_I2_J,axiom,
% 2.69/1.53 ! [T: $tType,P: T > $o,F1: name > T,F22: name > T,Name2: name] :
% 2.69/1.53 ( ! [X12: name] : ( P @ ( F1 @ X12 ) )
% 2.69/1.53 => ( ! [X12: name] : ( P @ ( F22 @ X12 ) )
% 2.69/1.53 => ( ( late_subject_rec @ T @ F1 @ F22 @ ( late_BoundOutputS @ Name2 ) )
% 2.69/1.53 = ( F22 @ Name2 ) ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_94_freeRes_Orecs_I1_J,axiom,
% 2.69/1.53 ! [T: $tType,P: T > $o,F1: name > name > T,F22: T,Name1: name,Name22: name] :
% 2.69/1.53 ( ! [X12: name,X23: name] : ( P @ ( F1 @ X12 @ X23 ) )
% 2.69/1.53 => ( ( P @ F22 )
% 2.69/1.53 => ( ( late_freeRes_rec @ T @ F1 @ F22 @ ( late_OutputR @ Name1 @ Name22 ) )
% 2.69/1.53 = ( F1 @ Name1 @ Name22 ) ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_95_resTauOutputTrans,axiom,
% 2.69/1.53 ! [X2: name,P: pi,A2: name,B: name,P2: pi] :
% 2.69/1.53 ~ ( late_transitions @ ( res @ X2 @ ( tau @ P ) ) @ ( late_FreeR @ ( late_OutputR @ A2 @ B ) @ P2 ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_96_resOutputTauTrans,axiom,
% 2.69/1.53 ! [X2: name,A2: name,B: name,P: pi,P2: pi] :
% 2.69/1.53 ~ ( late_transitions @ ( res @ X2 @ ( output @ A2 @ B @ P ) ) @ ( late_FreeR @ late_TauR @ P2 ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_97_resOutputInputTrans,axiom,
% 2.69/1.53 ! [X2: name,A2: name,B: name,P: pi,C: name,Y: name,P2: pi] :
% 2.69/1.53 ~ ( late_transitions @ ( res @ X2 @ ( output @ A2 @ B @ P ) ) @ ( late_BoundR @ ( late_InputS @ C ) @ Y @ P2 ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_98_name__fresh,axiom,
% 2.69/1.53 ( ( fresh @ name @ name )
% 2.69/1.53 = ( ^ [A5: name,B4: name] : ( A5 != B4 ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_99_pi_Ofresh_I3_J,axiom,
% 2.69/1.53 ! [A2: name,X1: pi] :
% 2.69/1.53 ( ( fresh @ name @ pi @ A2 @ ( tau @ X1 ) )
% 2.69/1.53 = ( fresh @ name @ pi @ A2 @ X1 ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_100_simps_I2_J,axiom,
% 2.69/1.53 ! [P: pi,C: name,D: name] :
% 2.69/1.53 ( ( subs @ ( tau @ P ) @ C @ D )
% 2.69/1.53 = ( tau @ ( subs @ P @ C @ D ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_101_pi_Ofresh_I2_J,axiom,
% 2.69/1.53 ! [A2: name,X32: name,X22: name,X1: pi] :
% 2.69/1.53 ( ( fresh @ name @ pi @ A2 @ ( output @ X32 @ X22 @ X1 ) )
% 2.69/1.53 = ( ( fresh @ name @ name @ A2 @ X32 )
% 2.69/1.53 & ( fresh @ name @ name @ A2 @ X22 )
% 2.69/1.53 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_102_pi_Odistinct_I19_J,axiom,
% 2.69/1.53 ! [Name1: name,Name22: name,Pi4: pi,Pi: pi] :
% 2.69/1.53 ( ( output @ Name1 @ Name22 @ Pi4 )
% 2.69/1.53 != ( tau @ Pi ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_103_pi_Oinject_I1_J,axiom,
% 2.69/1.53 ! [X32: name,X22: name,X1: pi,Y32: name,Y2: name,Y1: pi] :
% 2.69/1.53 ( ( ( output @ X32 @ X22 @ X1 )
% 2.69/1.53 = ( output @ Y32 @ Y2 @ Y1 ) )
% 2.69/1.53 = ( ( X32 = Y32 )
% 2.69/1.53 & ( X22 = Y2 )
% 2.69/1.53 & ( X1 = Y1 ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_104_pi_Oinject_I2_J,axiom,
% 2.69/1.53 ! [X1: pi,Y1: pi] :
% 2.69/1.53 ( ( ( tau @ X1 )
% 2.69/1.53 = ( tau @ Y1 ) )
% 2.69/1.53 = ( X1 = Y1 ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_105_pi_Odistinct_I29_J,axiom,
% 2.69/1.53 ! [Name1: name,Name22: name,Pi4: pi,Pi12: pi,Pi22: pi] :
% 2.69/1.53 ( ( output @ Name1 @ Name22 @ Pi4 )
% 2.69/1.53 != ( par @ Pi12 @ Pi22 ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_106_pi_Odistinct_I31_J,axiom,
% 2.69/1.53 ! [Name1: name,Name22: name,Pi4: pi,Name: name,Pi: pi] :
% 2.69/1.53 ( ( output @ Name1 @ Name22 @ Pi4 )
% 2.69/1.53 != ( res @ Name @ Pi ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_107_pi_Odistinct_I43_J,axiom,
% 2.69/1.53 ! [Pi4: pi,Pi12: pi,Pi22: pi] :
% 2.69/1.53 ( ( tau @ Pi4 )
% 2.69/1.53 != ( par @ Pi12 @ Pi22 ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_108_pi_Odistinct_I45_J,axiom,
% 2.69/1.53 ! [Pi4: pi,Name: name,Pi: pi] :
% 2.69/1.53 ( ( tau @ Pi4 )
% 2.69/1.53 != ( res @ Name @ Pi ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_109_resTrans_I1_J,axiom,
% 2.69/1.53 ! [X2: name,B: name,P: pi,Rs: late_residual] :
% 2.69/1.53 ~ ( late_transitions @ ( res @ X2 @ ( output @ X2 @ B @ P ) ) @ Rs ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_110_outputBoundTrans,axiom,
% 2.69/1.53 ! [A2: name,B: name,P: pi,C: late_subject,X2: name,P2: pi] :
% 2.69/1.53 ~ ( late_transitions @ ( output @ A2 @ B @ P ) @ ( late_BoundR @ C @ X2 @ P2 ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_111_outputFreshTrans,axiom,
% 2.69/1.53 ! [A2: name,B: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 2.69/1.53 ( ( late_transitions @ ( output @ A2 @ B @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 2.69/1.53 => ~ ( ( fresh @ name @ late_freeRes @ A2 @ Alpha )
% 2.69/1.53 | ( fresh @ name @ late_freeRes @ B @ Alpha ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_112_tauBoundTrans,axiom,
% 2.69/1.53 ! [P: pi,A2: late_subject,X2: name,P2: pi] :
% 2.69/1.53 ~ ( late_transitions @ ( tau @ P ) @ ( late_BoundR @ A2 @ X2 @ P2 ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_113_resTauBoundTrans,axiom,
% 2.69/1.53 ! [X2: name,P: pi,A2: late_subject,Y: name,P2: pi] :
% 2.69/1.53 ~ ( late_transitions @ ( res @ X2 @ ( tau @ P ) ) @ ( late_BoundR @ A2 @ Y @ P2 ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_114_Output,axiom,
% 2.69/1.53 ! [A2: name,B: name,P: pi] : ( late_transitions @ ( output @ A2 @ B @ P ) @ ( late_FreeR @ ( late_OutputR @ A2 @ B ) @ P ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_115_outputIneqTrans,axiom,
% 2.69/1.53 ! [A2: name,B: name,P: pi,C: name,D: name,P2: pi] :
% 2.69/1.53 ( ( late_transitions @ ( output @ A2 @ B @ P ) @ ( late_FreeR @ ( late_OutputR @ C @ D ) @ P2 ) )
% 2.69/1.53 => ~ ( ( A2 != C )
% 2.69/1.53 | ( B != D ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_116_outputCases_H,axiom,
% 2.69/1.53 ! [A2: name,B: name,P: pi,Rs: late_residual] :
% 2.69/1.53 ( ( late_transitions @ ( output @ A2 @ B @ P ) @ Rs )
% 2.69/1.53 => ~ ! [A4: name,B3: name,P4: pi] :
% 2.69/1.53 ( ( ( A2 = A4 )
% 2.69/1.53 & ( B = B3 )
% 2.69/1.53 & ( P = P4 ) )
% 2.69/1.53 => ( Rs
% 2.69/1.53 != ( late_FreeR @ ( late_OutputR @ A4 @ B3 ) @ P4 ) ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_117_outputCases,axiom,
% 2.69/1.53 ! [A2: name,B: name,P: pi,Alpha: late_freeRes,P2: pi,Prop: late_freeRes > pi > $o] :
% 2.69/1.53 ( ( late_transitions @ ( output @ A2 @ B @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 2.69/1.53 => ( ( ( Alpha
% 2.69/1.53 = ( late_OutputR @ A2 @ B ) )
% 2.69/1.53 => ( ( P = P2 )
% 2.69/1.53 => ( Prop @ ( late_OutputR @ A2 @ B ) @ P ) ) )
% 2.69/1.53 => ( Prop @ Alpha @ P2 ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_118_outputTauTrans,axiom,
% 2.69/1.53 ! [A2: name,B: name,P: pi,P2: pi] :
% 2.69/1.53 ~ ( late_transitions @ ( output @ A2 @ B @ P ) @ ( late_FreeR @ late_TauR @ P2 ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_119_tauOutputTrans,axiom,
% 2.69/1.53 ! [P: pi,A2: name,B: name,P2: pi] :
% 2.69/1.53 ~ ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ ( late_OutputR @ A2 @ B ) @ P2 ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_120_Tau,axiom,
% 2.69/1.53 ! [P: pi] : ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ late_TauR @ P ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_121_tauCases_H,axiom,
% 2.69/1.53 ! [P: pi,Rs: late_residual] :
% 2.69/1.53 ( ( late_transitions @ ( tau @ P ) @ Rs )
% 2.69/1.53 => ~ ! [P4: pi] :
% 2.69/1.53 ( ( ( tau @ P )
% 2.69/1.53 = ( tau @ P4 ) )
% 2.69/1.53 => ( Rs
% 2.69/1.53 != ( late_FreeR @ late_TauR @ P4 ) ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_122_tauCases,axiom,
% 2.69/1.53 ! [P: pi,Alpha: late_freeRes,P2: pi,Prop: late_freeRes > pi > $o] :
% 2.69/1.53 ( ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 2.69/1.53 => ( ( ( Alpha = late_TauR )
% 2.69/1.53 => ( ( P = P2 )
% 2.69/1.53 => ( Prop @ late_TauR @ P ) ) )
% 2.69/1.53 => ( Prop @ Alpha @ P2 ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_123_resOutputOutputTrans,axiom,
% 2.69/1.53 ! [X2: name,A2: name,P: pi,B: name,Y: name,P2: pi] :
% 2.69/1.53 ~ ( late_transitions @ ( res @ X2 @ ( output @ A2 @ X2 @ P ) ) @ ( late_FreeR @ ( late_OutputR @ B @ Y ) @ P2 ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_124_resInputBoundOutputTrans,axiom,
% 2.69/1.53 ! [X2: name,A2: name,Y: name,P: pi,B: name,Z: name,P2: pi] :
% 2.69/1.53 ~ ( late_transitions @ ( res @ X2 @ ( input @ A2 @ Y @ P ) ) @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ Z @ P2 ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_125_residual_Ofresh_I1_J,axiom,
% 2.69/1.53 ! [A2: name,X32: late_subject,X1: name,X22: pi] :
% 2.69/1.53 ( ( fresh @ name @ late_residual @ A2 @ ( late_BoundR @ X32 @ X1 @ X22 ) )
% 2.69/1.53 = ( ( fresh @ name @ late_subject @ A2 @ X32 )
% 2.69/1.53 & ( fresh @ name @ ( name > ( noption @ pi ) ) @ A2 @ ( abs_fun @ name @ pi @ X1 @ X22 ) ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_126_simps_I3_J,axiom,
% 2.69/1.53 ! [A2: name,B: name,P: pi,C: name,D: name] :
% 2.69/1.53 ( ( subs @ ( output @ A2 @ B @ P ) @ C @ D )
% 2.69/1.53 = ( output @ ( subst_name @ A2 @ C @ D ) @ ( subst_name @ B @ C @ D ) @ ( subs @ P @ C @ D ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_127_inputIneqTrans,axiom,
% 2.69/1.53 ! [A2: name,X2: name,P: pi,B: late_subject,Y: name,P2: pi] :
% 2.69/1.53 ( ( late_transitions @ ( input @ A2 @ X2 @ P ) @ ( late_BoundR @ B @ Y @ P2 ) )
% 2.69/1.53 => ~ ( fresh @ name @ late_subject @ A2 @ B ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_128_transitions_OInput,axiom,
% 2.69/1.53 ! [X2: name,A2: name,P: pi] :
% 2.69/1.53 ( ( X2 != A2 )
% 2.69/1.53 => ( late_transitions @ ( input @ A2 @ X2 @ P ) @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_129_substInput,axiom,
% 2.69/1.53 ! [X2: name,B: name,C: name,A2: name,P: pi] :
% 2.69/1.53 ( ( X2 != B )
% 2.69/1.53 => ( ( X2 != C )
% 2.69/1.53 => ( ( subs @ ( input @ A2 @ X2 @ P ) @ B @ C )
% 2.69/1.53 = ( input @ ( subst_name @ A2 @ B @ C ) @ X2 @ ( subs @ P @ B @ C ) ) ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_130_simps_I4_J,axiom,
% 2.69/1.53 ! [X2: name,A2: name,C: name,D: name,P: pi] :
% 2.69/1.53 ( ( X2 != A2 )
% 2.69/1.53 => ( ( X2 != C )
% 2.69/1.53 => ( ( X2 != D )
% 2.69/1.53 => ( ( subs @ ( input @ A2 @ X2 @ P ) @ C @ D )
% 2.69/1.53 = ( input @ ( subst_name @ A2 @ C @ D ) @ X2 @ ( subs @ P @ C @ D ) ) ) ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_131_pi_Ofresh_I9_J,axiom,
% 2.69/1.53 ! [A2: name,X1: name,X22: pi] :
% 2.69/1.53 ( ( fresh @ name @ pi @ A2 @ ( res @ X1 @ X22 ) )
% 2.69/1.53 = ( fresh @ name @ ( name > ( noption @ pi ) ) @ A2 @ ( abs_fun @ name @ pi @ X1 @ X22 ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_132_pi_Ofresh_I4_J,axiom,
% 2.69/1.53 ! [A2: name,X32: name,X1: name,X22: pi] :
% 2.69/1.53 ( ( fresh @ name @ pi @ A2 @ ( input @ X32 @ X1 @ X22 ) )
% 2.69/1.53 = ( ( fresh @ name @ name @ A2 @ X32 )
% 2.69/1.53 & ( fresh @ name @ ( name > ( noption @ pi ) ) @ A2 @ ( abs_fun @ name @ pi @ X1 @ X22 ) ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_133_pi_Oinject_I3_J,axiom,
% 2.69/1.53 ! [X32: name,X1: name,X22: pi,Y32: name,Y1: name,Y2: pi] :
% 2.69/1.53 ( ( ( input @ X32 @ X1 @ X22 )
% 2.69/1.53 = ( input @ Y32 @ Y1 @ Y2 ) )
% 2.69/1.53 = ( ( X32 = Y32 )
% 2.69/1.53 & ( ( abs_fun @ name @ pi @ X1 @ X22 )
% 2.69/1.53 = ( abs_fun @ name @ pi @ Y1 @ Y2 ) ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_134_subst__name__def,axiom,
% 2.69/1.53 ( subst_name
% 2.69/1.53 = ( ^ [A5: name,B4: name,C3: name] : ( if @ name @ ( A5 = B4 ) @ C3 @ A5 ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_135_pi_Oinject_I8_J,axiom,
% 2.69/1.53 ! [X1: name,X22: pi,Y1: name,Y2: pi] :
% 2.69/1.53 ( ( ( res @ X1 @ X22 )
% 2.69/1.53 = ( res @ Y1 @ Y2 ) )
% 2.69/1.53 = ( ( abs_fun @ name @ pi @ X1 @ X22 )
% 2.69/1.53 = ( abs_fun @ name @ pi @ Y1 @ Y2 ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_136_residual_Oinject_I1_J,axiom,
% 2.69/1.53 ! [X32: late_subject,X1: name,X22: pi,Y32: late_subject,Y1: name,Y2: pi] :
% 2.69/1.53 ( ( ( late_BoundR @ X32 @ X1 @ X22 )
% 2.69/1.53 = ( late_BoundR @ Y32 @ Y1 @ Y2 ) )
% 2.69/1.53 = ( ( X32 = Y32 )
% 2.69/1.53 & ( ( abs_fun @ name @ pi @ X1 @ X22 )
% 2.69/1.53 = ( abs_fun @ name @ pi @ Y1 @ Y2 ) ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_137_name__fresh__abs,axiom,
% 2.69/1.53 ! [A: $tType] :
% 2.69/1.53 ( ( fs_name @ A )
% 2.69/1.53 => ! [B: name,A2: name,X2: A] :
% 2.69/1.53 ( ( fresh @ name @ ( name > ( noption @ A ) ) @ B @ ( abs_fun @ name @ A @ A2 @ X2 ) )
% 2.69/1.53 = ( ( B = A2 )
% 2.69/1.53 | ( fresh @ name @ A @ B @ X2 ) ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_138_abs__fresh_I1_J,axiom,
% 2.69/1.53 ! [X6: $tType] :
% 2.69/1.53 ( ( fs_name @ X6 )
% 2.69/1.53 => ! [B: name,A2: name,X2: X6] :
% 2.69/1.53 ( ( fresh @ name @ ( name > ( noption @ X6 ) ) @ B @ ( abs_fun @ name @ X6 @ A2 @ X2 ) )
% 2.69/1.53 = ( ( B = A2 )
% 2.69/1.53 | ( fresh @ name @ X6 @ B @ X2 ) ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_139_pi_Odistinct_I55_J,axiom,
% 2.69/1.53 ! [Name1: name,Name22: name,Pi4: pi,Pi12: pi,Pi22: pi] :
% 2.69/1.53 ( ( input @ Name1 @ Name22 @ Pi4 )
% 2.69/1.53 != ( par @ Pi12 @ Pi22 ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_140_pi_Odistinct_I57_J,axiom,
% 2.69/1.53 ! [Name1: name,Name22: name,Pi4: pi,Name: name,Pi: pi] :
% 2.69/1.53 ( ( input @ Name1 @ Name22 @ Pi4 )
% 2.69/1.53 != ( res @ Name @ Pi ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_141_pi_Odistinct_I21_J,axiom,
% 2.69/1.53 ! [Name1: name,Name22: name,Pi4: pi,Name13: name,Name24: name,Pi: pi] :
% 2.69/1.53 ( ( output @ Name1 @ Name22 @ Pi4 )
% 2.69/1.53 != ( input @ Name13 @ Name24 @ Pi ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_142_pi_Odistinct_I35_J,axiom,
% 2.69/1.53 ! [Pi4: pi,Name13: name,Name24: name,Pi: pi] :
% 2.69/1.53 ( ( tau @ Pi4 )
% 2.69/1.53 != ( input @ Name13 @ Name24 @ Pi ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_143_inputCases_H,axiom,
% 2.69/1.53 ! [A2: name,B: name,P: pi,Rs: late_residual] :
% 2.69/1.53 ( ( late_transitions @ ( input @ A2 @ B @ P ) @ Rs )
% 2.69/1.53 => ~ ! [X4: name,A4: name,P4: pi] :
% 2.69/1.53 ( ( ( A2 = A4 )
% 2.69/1.53 & ( ( abs_fun @ name @ pi @ B @ P )
% 2.69/1.53 = ( abs_fun @ name @ pi @ X4 @ P4 ) ) )
% 2.69/1.53 => ( ( Rs
% 2.69/1.53 = ( late_BoundR @ ( late_InputS @ A4 ) @ X4 @ P4 ) )
% 2.69/1.53 => ( X4 = A4 ) ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_144_resTrans_I2_J,axiom,
% 2.69/1.53 ! [X2: name,Y: name,P: pi,Rs: late_residual] :
% 2.69/1.53 ~ ( late_transitions @ ( res @ X2 @ ( input @ X2 @ Y @ P ) ) @ Rs ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_145_inputFreeTrans,axiom,
% 2.69/1.53 ! [A2: name,X2: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 2.69/1.53 ~ ( late_transitions @ ( input @ A2 @ X2 @ P ) @ ( late_FreeR @ Alpha @ P2 ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_146_resInputFreeTrans,axiom,
% 2.69/1.53 ! [X2: name,A2: name,Y: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 2.69/1.53 ~ ( late_transitions @ ( res @ X2 @ ( input @ A2 @ Y @ P ) ) @ ( late_FreeR @ Alpha @ P2 ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_147_inputBoundOutputTrans,axiom,
% 2.69/1.53 ! [A2: name,X2: name,P: pi,B: name,Y: name,P2: pi] :
% 2.69/1.53 ~ ( late_transitions @ ( input @ A2 @ X2 @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ Y @ P2 ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_148_Late__Semantics_OInput,axiom,
% 2.69/1.53 ! [A2: name,X2: name,P: pi] : ( late_transitions @ ( input @ A2 @ X2 @ P ) @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_149_simps_I5_J,axiom,
% 2.69/1.53 ! [A2: name,B: name,P: pi,C: name,D: name] :
% 2.69/1.53 ( ( subs @ ( match @ A2 @ B @ P ) @ C @ D )
% 2.69/1.53 = ( match @ ( subst_name @ A2 @ C @ D ) @ ( subst_name @ B @ C @ D ) @ ( subs @ P @ C @ D ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_150_simps_I6_J,axiom,
% 2.69/1.53 ! [A2: name,B: name,P: pi,C: name,D: name] :
% 2.69/1.53 ( ( subs @ ( mismatch @ A2 @ B @ P ) @ C @ D )
% 2.69/1.53 = ( mismatch @ ( subst_name @ A2 @ C @ D ) @ ( subst_name @ B @ C @ D ) @ ( subs @ P @ C @ D ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_151_pi_Ofresh_I5_J,axiom,
% 2.69/1.53 ! [A2: name,X32: name,X22: name,X1: pi] :
% 2.69/1.53 ( ( fresh @ name @ pi @ A2 @ ( match @ X32 @ X22 @ X1 ) )
% 2.69/1.53 = ( ( fresh @ name @ name @ A2 @ X32 )
% 2.69/1.53 & ( fresh @ name @ name @ A2 @ X22 )
% 2.69/1.53 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_152_pi_Ofresh_I6_J,axiom,
% 2.69/1.53 ! [A2: name,X32: name,X22: name,X1: pi] :
% 2.69/1.53 ( ( fresh @ name @ pi @ A2 @ ( mismatch @ X32 @ X22 @ X1 ) )
% 2.69/1.53 = ( ( fresh @ name @ name @ A2 @ X32 )
% 2.69/1.53 & ( fresh @ name @ name @ A2 @ X22 )
% 2.69/1.53 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_153_pi_Odistinct_I61_J,axiom,
% 2.69/1.53 ! [Name1: name,Name22: name,Pi4: pi,Name13: name,Name24: name,Pi: pi] :
% 2.69/1.53 ( ( match @ Name1 @ Name22 @ Pi4 )
% 2.69/1.53 != ( mismatch @ Name13 @ Name24 @ Pi ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_154_pi_Oinject_I4_J,axiom,
% 2.69/1.53 ! [X32: name,X22: name,X1: pi,Y32: name,Y2: name,Y1: pi] :
% 2.69/1.53 ( ( ( match @ X32 @ X22 @ X1 )
% 2.69/1.53 = ( match @ Y32 @ Y2 @ Y1 ) )
% 2.69/1.53 = ( ( X32 = Y32 )
% 2.69/1.53 & ( X22 = Y2 )
% 2.69/1.53 & ( X1 = Y1 ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_155_pi_Oinject_I5_J,axiom,
% 2.69/1.53 ! [X32: name,X22: name,X1: pi,Y32: name,Y2: name,Y1: pi] :
% 2.69/1.53 ( ( ( mismatch @ X32 @ X22 @ X1 )
% 2.69/1.53 = ( mismatch @ Y32 @ Y2 @ Y1 ) )
% 2.69/1.53 = ( ( X32 = Y32 )
% 2.69/1.53 & ( X22 = Y2 )
% 2.69/1.53 & ( X1 = Y1 ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_156_Mismatch,axiom,
% 2.69/1.53 ! [P: pi,Rs: late_residual,A2: name,B: name] :
% 2.69/1.53 ( ( late_transitions @ P @ Rs )
% 2.69/1.53 => ( ( A2 != B )
% 2.69/1.53 => ( late_transitions @ ( mismatch @ A2 @ B @ P ) @ Rs ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_157_Match,axiom,
% 2.69/1.53 ! [P: pi,Rs: late_residual,B: name] :
% 2.69/1.53 ( ( late_transitions @ P @ Rs )
% 2.69/1.53 => ( late_transitions @ ( match @ B @ B @ P ) @ Rs ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_158_mismatchCases_H,axiom,
% 2.69/1.53 ! [A2: name,B: name,P: pi,Rs: late_residual] :
% 2.69/1.53 ( ( late_transitions @ ( mismatch @ A2 @ B @ P ) @ Rs )
% 2.69/1.53 => ~ ! [P4: pi,A4: name,B3: name] :
% 2.69/1.53 ( ( ( A2 = A4 )
% 2.69/1.53 & ( B = B3 )
% 2.69/1.53 & ( P = P4 ) )
% 2.69/1.53 => ( ( late_transitions @ P4 @ Rs )
% 2.69/1.53 => ( A4 = B3 ) ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_159_mismatchTrans,axiom,
% 2.69/1.53 ! [A2: name,P: pi,Rs: late_residual] :
% 2.69/1.53 ~ ( late_transitions @ ( mismatch @ A2 @ A2 @ P ) @ Rs ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_160_mismatchCases,axiom,
% 2.69/1.53 ! [A2: name,B: name,P: pi,Rs: late_residual,F2: name > name > $o] :
% 2.69/1.53 ( ( late_transitions @ ( mismatch @ A2 @ B @ P ) @ Rs )
% 2.69/1.53 => ( ( ( late_transitions @ P @ Rs )
% 2.69/1.53 => ( ( A2 != B )
% 2.69/1.53 => ( F2 @ A2 @ B ) ) )
% 2.69/1.53 => ( F2 @ A2 @ B ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_161_matchCases_H,axiom,
% 2.69/1.53 ! [A2: name,B: name,P: pi,Rs: late_residual] :
% 2.69/1.53 ( ( late_transitions @ ( match @ A2 @ B @ P ) @ Rs )
% 2.69/1.53 => ~ ! [P4: pi] :
% 2.69/1.53 ( ( ( B = A2 )
% 2.69/1.53 & ( P = P4 ) )
% 2.69/1.53 => ~ ( late_transitions @ P4 @ Rs ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_162_matchTrans,axiom,
% 2.69/1.53 ! [A2: name,B: name,P: pi,Rs: late_residual] :
% 2.69/1.53 ( ( late_transitions @ ( match @ A2 @ B @ P ) @ Rs )
% 2.69/1.53 => ( A2 = B ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_163_matchCases,axiom,
% 2.69/1.53 ! [A2: name,B: name,P: pi,Rs: late_residual,F2: name > name > $o] :
% 2.69/1.53 ( ( late_transitions @ ( match @ A2 @ B @ P ) @ Rs )
% 2.69/1.53 => ( ( ( late_transitions @ P @ Rs )
% 2.69/1.53 => ( ( A2 = B )
% 2.69/1.53 => ( F2 @ A2 @ A2 ) ) )
% 2.69/1.53 => ( F2 @ A2 @ B ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_164_pi_Odistinct_I65_J,axiom,
% 2.69/1.53 ! [Name1: name,Name22: name,Pi4: pi,Pi12: pi,Pi22: pi] :
% 2.69/1.53 ( ( match @ Name1 @ Name22 @ Pi4 )
% 2.69/1.53 != ( par @ Pi12 @ Pi22 ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_165_pi_Odistinct_I73_J,axiom,
% 2.69/1.53 ! [Name1: name,Name22: name,Pi4: pi,Pi12: pi,Pi22: pi] :
% 2.69/1.53 ( ( mismatch @ Name1 @ Name22 @ Pi4 )
% 2.69/1.53 != ( par @ Pi12 @ Pi22 ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_166_pi_Odistinct_I67_J,axiom,
% 2.69/1.53 ! [Name1: name,Name22: name,Pi4: pi,Name: name,Pi: pi] :
% 2.69/1.53 ( ( match @ Name1 @ Name22 @ Pi4 )
% 2.69/1.53 != ( res @ Name @ Pi ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_167_pi_Odistinct_I75_J,axiom,
% 2.69/1.53 ! [Name1: name,Name22: name,Pi4: pi,Name: name,Pi: pi] :
% 2.69/1.53 ( ( mismatch @ Name1 @ Name22 @ Pi4 )
% 2.69/1.53 != ( res @ Name @ Pi ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_168_pi_Odistinct_I49_J,axiom,
% 2.69/1.53 ! [Name1: name,Name22: name,Pi4: pi,Name13: name,Name24: name,Pi: pi] :
% 2.69/1.53 ( ( input @ Name1 @ Name22 @ Pi4 )
% 2.69/1.53 != ( match @ Name13 @ Name24 @ Pi ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_169_pi_Odistinct_I51_J,axiom,
% 2.69/1.53 ! [Name1: name,Name22: name,Pi4: pi,Name13: name,Name24: name,Pi: pi] :
% 2.69/1.53 ( ( input @ Name1 @ Name22 @ Pi4 )
% 2.69/1.53 != ( mismatch @ Name13 @ Name24 @ Pi ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_170_pi_Odistinct_I23_J,axiom,
% 2.69/1.53 ! [Name1: name,Name22: name,Pi4: pi,Name13: name,Name24: name,Pi: pi] :
% 2.69/1.53 ( ( output @ Name1 @ Name22 @ Pi4 )
% 2.69/1.53 != ( match @ Name13 @ Name24 @ Pi ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_171_pi_Odistinct_I25_J,axiom,
% 2.69/1.53 ! [Name1: name,Name22: name,Pi4: pi,Name13: name,Name24: name,Pi: pi] :
% 2.69/1.53 ( ( output @ Name1 @ Name22 @ Pi4 )
% 2.69/1.53 != ( mismatch @ Name13 @ Name24 @ Pi ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_172_pi_Odistinct_I37_J,axiom,
% 2.69/1.53 ! [Pi4: pi,Name13: name,Name24: name,Pi: pi] :
% 2.69/1.53 ( ( tau @ Pi4 )
% 2.69/1.53 != ( match @ Name13 @ Name24 @ Pi ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_173_pi_Odistinct_I39_J,axiom,
% 2.69/1.53 ! [Pi4: pi,Name13: name,Name24: name,Pi: pi] :
% 2.69/1.53 ( ( tau @ Pi4 )
% 2.69/1.53 != ( mismatch @ Name13 @ Name24 @ Pi ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_174_abs__fun__eq1,axiom,
% 2.69/1.53 ! [X: $tType,A: $tType,A2: X,X2: A,Y: A] :
% 2.69/1.53 ( ( ( abs_fun @ X @ A @ A2 @ X2 )
% 2.69/1.53 = ( abs_fun @ X @ A @ A2 @ Y ) )
% 2.69/1.53 = ( X2 = Y ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_175_freeRes_Ocase_I2_J,axiom,
% 2.69/1.53 ! [A: $tType,F1: name > name > A,F22: A] :
% 2.69/1.53 ( ( late_case_freeRes @ A @ F1 @ F22 @ late_TauR )
% 2.69/1.53 = F22 ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_176_subject_Ocase_I1_J,axiom,
% 2.69/1.53 ! [A: $tType,F1: name > A,F22: name > A,X1: name] :
% 2.69/1.53 ( ( late_case_subject @ A @ F1 @ F22 @ ( late_InputS @ X1 ) )
% 2.69/1.53 = ( F1 @ X1 ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_177_freeRes_Ocase_I1_J,axiom,
% 2.69/1.53 ! [A: $tType,F1: name > name > A,F22: A,X11: name,X122: name] :
% 2.69/1.53 ( ( late_case_freeRes @ A @ F1 @ F22 @ ( late_OutputR @ X11 @ X122 ) )
% 2.69/1.53 = ( F1 @ X11 @ X122 ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_178_subject_Ocase_I2_J,axiom,
% 2.69/1.53 ! [A: $tType,F1: name > A,F22: name > A,X22: name] :
% 2.69/1.53 ( ( late_case_subject @ A @ F1 @ F22 @ ( late_BoundOutputS @ X22 ) )
% 2.69/1.53 = ( F22 @ X22 ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_179_pi_Ostrong__inducts,axiom,
% 2.69/1.53 ! [A: $tType] :
% 2.69/1.53 ( ( fs_name @ A )
% 2.69/1.53 => ! [P: A > pi > $o,Z: A,Pi4: pi] :
% 2.69/1.53 ( ! [Z2: A] : ( P @ Z2 @ piNil )
% 2.69/1.53 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: A] :
% 2.69/1.53 ( ! [Za: A] : ( P @ Za @ Pi3 )
% 2.69/1.53 => ( P @ Z2 @ ( output @ Name12 @ Name23 @ Pi3 ) ) )
% 2.69/1.53 => ( ! [Pi3: pi,Z2: A] :
% 2.69/1.53 ( ! [Za: A] : ( P @ Za @ Pi3 )
% 2.69/1.53 => ( P @ Z2 @ ( tau @ Pi3 ) ) )
% 2.69/1.53 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: A] :
% 2.69/1.53 ( ( fresh @ name @ A @ Name23 @ Z2 )
% 2.69/1.53 => ( ( fresh @ name @ name @ Name23 @ Name12 )
% 2.69/1.53 => ( ! [Za: A] : ( P @ Za @ Pi3 )
% 2.69/1.53 => ( P @ Z2 @ ( input @ Name12 @ Name23 @ Pi3 ) ) ) ) )
% 2.69/1.53 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: A] :
% 2.69/1.53 ( ! [Za: A] : ( P @ Za @ Pi3 )
% 2.69/1.53 => ( P @ Z2 @ ( match @ Name12 @ Name23 @ Pi3 ) ) )
% 2.69/1.53 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: A] :
% 2.69/1.53 ( ! [Za: A] : ( P @ Za @ Pi3 )
% 2.69/1.53 => ( P @ Z2 @ ( mismatch @ Name12 @ Name23 @ Pi3 ) ) )
% 2.69/1.53 => ( ! [Pi13: pi,Pi23: pi,Z2: A] :
% 2.69/1.53 ( ! [Za: A] : ( P @ Za @ Pi13 )
% 2.69/1.53 => ( ! [Za: A] : ( P @ Za @ Pi23 )
% 2.69/1.53 => ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 2.69/1.53 => ( ! [Pi13: pi,Pi23: pi,Z2: A] :
% 2.69/1.53 ( ! [Za: A] : ( P @ Za @ Pi13 )
% 2.69/1.53 => ( ! [Za: A] : ( P @ Za @ Pi23 )
% 2.69/1.53 => ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
% 2.69/1.53 => ( ! [Name3: name,Pi3: pi,Z2: A] :
% 2.69/1.53 ( ( fresh @ name @ A @ Name3 @ Z2 )
% 2.69/1.53 => ( ! [Za: A] : ( P @ Za @ Pi3 )
% 2.69/1.53 => ( P @ Z2 @ ( res @ Name3 @ Pi3 ) ) ) )
% 2.69/1.53 => ( ! [Pi3: pi,Z2: A] :
% 2.69/1.53 ( ! [Za: A] : ( P @ Za @ Pi3 )
% 2.69/1.53 => ( P @ Z2 @ ( bang @ Pi3 ) ) )
% 2.69/1.53 => ( P @ Z @ Pi4 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_180_pi_Ostrong__induct,axiom,
% 2.69/1.53 ! [N: $tType] :
% 2.69/1.53 ( ( fs_name @ N )
% 2.69/1.53 => ! [P: N > pi > $o,Z: N,Pi4: pi] :
% 2.69/1.53 ( ! [Z2: N] : ( P @ Z2 @ piNil )
% 2.69/1.53 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: N] :
% 2.69/1.53 ( ! [Za: N] : ( P @ Za @ Pi3 )
% 2.69/1.53 => ( P @ Z2 @ ( output @ Name12 @ Name23 @ Pi3 ) ) )
% 2.69/1.53 => ( ! [Pi3: pi,Z2: N] :
% 2.69/1.53 ( ! [Za: N] : ( P @ Za @ Pi3 )
% 2.69/1.53 => ( P @ Z2 @ ( tau @ Pi3 ) ) )
% 2.69/1.53 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: N] :
% 2.69/1.53 ( ( fresh @ name @ N @ Name23 @ Z2 )
% 2.69/1.53 => ( ( fresh @ name @ name @ Name23 @ Name12 )
% 2.69/1.53 => ( ! [Za: N] : ( P @ Za @ Pi3 )
% 2.69/1.53 => ( P @ Z2 @ ( input @ Name12 @ Name23 @ Pi3 ) ) ) ) )
% 2.69/1.53 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: N] :
% 2.69/1.53 ( ! [Za: N] : ( P @ Za @ Pi3 )
% 2.69/1.53 => ( P @ Z2 @ ( match @ Name12 @ Name23 @ Pi3 ) ) )
% 2.69/1.53 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: N] :
% 2.69/1.53 ( ! [Za: N] : ( P @ Za @ Pi3 )
% 2.69/1.53 => ( P @ Z2 @ ( mismatch @ Name12 @ Name23 @ Pi3 ) ) )
% 2.69/1.53 => ( ! [Pi13: pi,Pi23: pi,Z2: N] :
% 2.69/1.53 ( ! [Za: N] : ( P @ Za @ Pi13 )
% 2.69/1.53 => ( ! [Za: N] : ( P @ Za @ Pi23 )
% 2.69/1.53 => ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 2.69/1.53 => ( ! [Pi13: pi,Pi23: pi,Z2: N] :
% 2.69/1.53 ( ! [Za: N] : ( P @ Za @ Pi13 )
% 2.69/1.53 => ( ! [Za: N] : ( P @ Za @ Pi23 )
% 2.69/1.53 => ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
% 2.69/1.53 => ( ! [Name3: name,Pi3: pi,Z2: N] :
% 2.69/1.53 ( ( fresh @ name @ N @ Name3 @ Z2 )
% 2.69/1.53 => ( ! [Za: N] : ( P @ Za @ Pi3 )
% 2.69/1.53 => ( P @ Z2 @ ( res @ Name3 @ Pi3 ) ) ) )
% 2.69/1.53 => ( ! [Pi3: pi,Z2: N] :
% 2.69/1.53 ( ! [Za: N] : ( P @ Za @ Pi3 )
% 2.69/1.53 => ( P @ Z2 @ ( bang @ Pi3 ) ) )
% 2.69/1.53 => ( P @ Z @ Pi4 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_181_residual_Ostrong__induct_H,axiom,
% 2.69/1.53 ! [N: $tType,F: N > ( set @ name ),P: N > late_residual > $o,Z: N,Residual: late_residual] :
% 2.69/1.53 ( ! [X4: N] : ( finite_finite @ name @ ( F @ X4 ) )
% 2.69/1.53 => ( ! [Subject2: late_subject,Name3: name,Pi3: pi,Z2: N] :
% 2.69/1.53 ( ~ ( member @ name @ Name3 @ ( F @ Z2 ) )
% 2.69/1.53 => ( ( fresh @ name @ late_subject @ Name3 @ Subject2 )
% 2.69/1.53 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi3 ) ) ) )
% 2.69/1.53 => ( ! [FreeRes: late_freeRes,Pi3: pi,Z2: N] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi3 ) )
% 2.69/1.53 => ( P @ Z @ Residual ) ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_182_pi_Ofresh_I10_J,axiom,
% 2.69/1.53 ! [A2: name,X1: pi] :
% 2.69/1.53 ( ( fresh @ name @ pi @ A2 @ ( bang @ X1 ) )
% 2.69/1.53 = ( fresh @ name @ pi @ A2 @ X1 ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_183_pi_Ofresh_I7_J,axiom,
% 2.69/1.53 ! [A2: name,X22: pi,X1: pi] :
% 2.69/1.53 ( ( fresh @ name @ pi @ A2 @ ( sum @ X22 @ X1 ) )
% 2.69/1.53 = ( ( fresh @ name @ pi @ A2 @ X22 )
% 2.69/1.53 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_184_pi_Ofresh_I1_J,axiom,
% 2.69/1.53 ! [A2: name] : ( fresh @ name @ pi @ A2 @ piNil ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_185_simps_I10_J,axiom,
% 2.69/1.53 ! [P: pi,C: name,D: name] :
% 2.69/1.53 ( ( subs @ ( bang @ P ) @ C @ D )
% 2.69/1.53 = ( bang @ ( subs @ P @ C @ D ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_186_simps_I7_J,axiom,
% 2.69/1.53 ! [P: pi,Q: pi,C: name,D: name] :
% 2.69/1.53 ( ( subs @ ( sum @ P @ Q ) @ C @ D )
% 2.69/1.53 = ( sum @ ( subs @ P @ C @ D ) @ ( subs @ Q @ C @ D ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_187_simps_I1_J,axiom,
% 2.69/1.53 ! [C: name,D: name] :
% 2.69/1.53 ( ( subs @ piNil @ C @ D )
% 2.69/1.53 = piNil ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_188_pi_Odistinct_I59_J,axiom,
% 2.69/1.53 ! [Name1: name,Name22: name,Pi4: pi,Pi: pi] :
% 2.69/1.53 ( ( input @ Name1 @ Name22 @ Pi4 )
% 2.69/1.53 != ( bang @ Pi ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_189_pi_Odistinct_I53_J,axiom,
% 2.69/1.53 ! [Name1: name,Name22: name,Pi4: pi,Pi12: pi,Pi22: pi] :
% 2.69/1.53 ( ( input @ Name1 @ Name22 @ Pi4 )
% 2.69/1.53 != ( sum @ Pi12 @ Pi22 ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_190_pi_Odistinct_I87_J,axiom,
% 2.69/1.53 ! [Pi1: pi,Pi2: pi,Pi: pi] :
% 2.69/1.53 ( ( par @ Pi1 @ Pi2 )
% 2.69/1.53 != ( bang @ Pi ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_191_pi_Odistinct_I89_J,axiom,
% 2.69/1.53 ! [Name2: name,Pi4: pi,Pi: pi] :
% 2.69/1.53 ( ( res @ Name2 @ Pi4 )
% 2.69/1.53 != ( bang @ Pi ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_192_pi_Odistinct_I33_J,axiom,
% 2.69/1.53 ! [Name1: name,Name22: name,Pi4: pi,Pi: pi] :
% 2.69/1.53 ( ( output @ Name1 @ Name22 @ Pi4 )
% 2.69/1.53 != ( bang @ Pi ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_193_sumCases,axiom,
% 2.69/1.53 ! [P: pi,Q: pi,Rs: late_residual] :
% 2.69/1.53 ( ( late_transitions @ ( sum @ P @ Q ) @ Rs )
% 2.69/1.53 => ( ~ ( late_transitions @ P @ Rs )
% 2.69/1.53 => ( late_transitions @ Q @ Rs ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_194_sumCases_H,axiom,
% 2.69/1.53 ! [P: pi,Q: pi,Rs: late_residual] :
% 2.69/1.53 ( ( late_transitions @ ( sum @ P @ Q ) @ Rs )
% 2.69/1.53 => ( ~ ( late_transitions @ P @ Rs )
% 2.69/1.53 => ( late_transitions @ Q @ Rs ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_195_Sum1,axiom,
% 2.69/1.53 ! [P: pi,Rs: late_residual,Q: pi] :
% 2.69/1.53 ( ( late_transitions @ P @ Rs )
% 2.69/1.53 => ( late_transitions @ ( sum @ P @ Q ) @ Rs ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_196_Sum2,axiom,
% 2.69/1.53 ! [Q: pi,Rs: late_residual,P: pi] :
% 2.69/1.53 ( ( late_transitions @ Q @ Rs )
% 2.69/1.53 => ( late_transitions @ ( sum @ P @ Q ) @ Rs ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_197_pi_Odistinct_I47_J,axiom,
% 2.69/1.53 ! [Pi4: pi,Pi: pi] :
% 2.69/1.53 ( ( tau @ Pi4 )
% 2.69/1.53 != ( bang @ Pi ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_198_pi_Odistinct_I79_J,axiom,
% 2.69/1.53 ! [Pi1: pi,Pi2: pi,Pi12: pi,Pi22: pi] :
% 2.69/1.53 ( ( sum @ Pi1 @ Pi2 )
% 2.69/1.53 != ( par @ Pi12 @ Pi22 ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_199_pi_Odistinct_I81_J,axiom,
% 2.69/1.53 ! [Pi1: pi,Pi2: pi,Name: name,Pi: pi] :
% 2.69/1.53 ( ( sum @ Pi1 @ Pi2 )
% 2.69/1.53 != ( res @ Name @ Pi ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_200_pi_Odistinct_I11_J,axiom,
% 2.69/1.53 ! [Pi12: pi,Pi22: pi] :
% 2.69/1.53 ( piNil
% 2.69/1.53 != ( sum @ Pi12 @ Pi22 ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_201_pi_Odistinct_I17_J,axiom,
% 2.69/1.53 ! [Pi: pi] :
% 2.69/1.53 ( piNil
% 2.69/1.53 != ( bang @ Pi ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_202_pi_Odistinct_I83_J,axiom,
% 2.69/1.53 ! [Pi1: pi,Pi2: pi,Pi: pi] :
% 2.69/1.53 ( ( sum @ Pi1 @ Pi2 )
% 2.69/1.53 != ( bang @ Pi ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_203_pi_Oinject_I6_J,axiom,
% 2.69/1.53 ! [X22: pi,X1: pi,Y2: pi,Y1: pi] :
% 2.69/1.53 ( ( ( sum @ X22 @ X1 )
% 2.69/1.53 = ( sum @ Y2 @ Y1 ) )
% 2.69/1.53 = ( ( X22 = Y2 )
% 2.69/1.53 & ( X1 = Y1 ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_204_pi_Oinject_I9_J,axiom,
% 2.69/1.53 ! [X1: pi,Y1: pi] :
% 2.69/1.53 ( ( ( bang @ X1 )
% 2.69/1.53 = ( bang @ Y1 ) )
% 2.69/1.53 = ( X1 = Y1 ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_205_pi_Odistinct_I3_J,axiom,
% 2.69/1.53 ! [Pi: pi] :
% 2.69/1.53 ( piNil
% 2.69/1.53 != ( tau @ Pi ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_206_pi_Odistinct_I1_J,axiom,
% 2.69/1.53 ! [Name13: name,Name24: name,Pi: pi] :
% 2.69/1.53 ( piNil
% 2.69/1.53 != ( output @ Name13 @ Name24 @ Pi ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_207_pi_Odistinct_I5_J,axiom,
% 2.69/1.53 ! [Name13: name,Name24: name,Pi: pi] :
% 2.69/1.53 ( piNil
% 2.69/1.53 != ( input @ Name13 @ Name24 @ Pi ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_208_pi_Odistinct_I15_J,axiom,
% 2.69/1.53 ! [Name: name,Pi: pi] :
% 2.69/1.53 ( piNil
% 2.69/1.53 != ( res @ Name @ Pi ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_209_pi_Odistinct_I13_J,axiom,
% 2.69/1.53 ! [Pi12: pi,Pi22: pi] :
% 2.69/1.53 ( piNil
% 2.69/1.53 != ( par @ Pi12 @ Pi22 ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_210_nilCases_H,axiom,
% 2.69/1.53 ! [Rs: late_residual] :
% 2.69/1.53 ~ ( late_transitions @ piNil @ Rs ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_211_zeroTrans,axiom,
% 2.69/1.53 ! [Rs: late_residual] :
% 2.69/1.53 ~ ( late_transitions @ piNil @ Rs ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_212_pi_Odistinct_I41_J,axiom,
% 2.69/1.53 ! [Pi4: pi,Pi12: pi,Pi22: pi] :
% 2.69/1.53 ( ( tau @ Pi4 )
% 2.69/1.53 != ( sum @ Pi12 @ Pi22 ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_213_pi_Odistinct_I27_J,axiom,
% 2.69/1.53 ! [Name1: name,Name22: name,Pi4: pi,Pi12: pi,Pi22: pi] :
% 2.69/1.53 ( ( output @ Name1 @ Name22 @ Pi4 )
% 2.69/1.53 != ( sum @ Pi12 @ Pi22 ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_214_pi_Odistinct_I77_J,axiom,
% 2.69/1.53 ! [Name1: name,Name22: name,Pi4: pi,Pi: pi] :
% 2.69/1.53 ( ( mismatch @ Name1 @ Name22 @ Pi4 )
% 2.69/1.53 != ( bang @ Pi ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_215_pi_Odistinct_I71_J,axiom,
% 2.69/1.53 ! [Name1: name,Name22: name,Pi4: pi,Pi12: pi,Pi22: pi] :
% 2.69/1.53 ( ( mismatch @ Name1 @ Name22 @ Pi4 )
% 2.69/1.53 != ( sum @ Pi12 @ Pi22 ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_216_pi_Odistinct_I69_J,axiom,
% 2.69/1.53 ! [Name1: name,Name22: name,Pi4: pi,Pi: pi] :
% 2.69/1.53 ( ( match @ Name1 @ Name22 @ Pi4 )
% 2.69/1.53 != ( bang @ Pi ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_217_pi_Odistinct_I63_J,axiom,
% 2.69/1.53 ! [Name1: name,Name22: name,Pi4: pi,Pi12: pi,Pi22: pi] :
% 2.69/1.53 ( ( match @ Name1 @ Name22 @ Pi4 )
% 2.69/1.53 != ( sum @ Pi12 @ Pi22 ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_218_pi_Odistinct_I9_J,axiom,
% 2.69/1.53 ! [Name13: name,Name24: name,Pi: pi] :
% 2.69/1.53 ( piNil
% 2.69/1.53 != ( mismatch @ Name13 @ Name24 @ Pi ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_219_pi_Odistinct_I7_J,axiom,
% 2.69/1.53 ! [Name13: name,Name24: name,Pi: pi] :
% 2.69/1.53 ( piNil
% 2.69/1.53 != ( match @ Name13 @ Name24 @ Pi ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_220_Bang,axiom,
% 2.69/1.53 ! [P: pi,Rs: late_residual] :
% 2.69/1.53 ( ( late_transitions @ ( par @ P @ ( bang @ P ) ) @ Rs )
% 2.69/1.53 => ( late_transitions @ ( bang @ P ) @ Rs ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_221_bangCases,axiom,
% 2.69/1.53 ! [P: pi,Rs: late_residual] :
% 2.69/1.53 ( ( late_transitions @ ( bang @ P ) @ Rs )
% 2.69/1.53 => ~ ! [P4: pi] :
% 2.69/1.53 ( ( ( bang @ P )
% 2.69/1.53 = ( bang @ P4 ) )
% 2.69/1.53 => ~ ( late_transitions @ ( par @ P4 @ ( bang @ P4 ) ) @ Rs ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_222_pi_Ostrong__induct_H,axiom,
% 2.69/1.53 ! [N: $tType,F: N > ( set @ name ),P: N > pi > $o,Z: N,Pi4: pi] :
% 2.69/1.53 ( ! [X4: N] : ( finite_finite @ name @ ( F @ X4 ) )
% 2.69/1.53 => ( ! [Z2: N] : ( P @ Z2 @ piNil )
% 2.69/1.53 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: N] :
% 2.69/1.53 ( ! [Za: N] : ( P @ Za @ Pi3 )
% 2.69/1.53 => ( P @ Z2 @ ( output @ Name12 @ Name23 @ Pi3 ) ) )
% 2.69/1.53 => ( ! [Pi3: pi,Z2: N] :
% 2.69/1.53 ( ! [Za: N] : ( P @ Za @ Pi3 )
% 2.69/1.53 => ( P @ Z2 @ ( tau @ Pi3 ) ) )
% 2.69/1.53 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: N] :
% 2.69/1.53 ( ~ ( member @ name @ Name23 @ ( F @ Z2 ) )
% 2.69/1.53 => ( ( fresh @ name @ name @ Name23 @ Name12 )
% 2.69/1.53 => ( ! [Za: N] : ( P @ Za @ Pi3 )
% 2.69/1.53 => ( P @ Z2 @ ( input @ Name12 @ Name23 @ Pi3 ) ) ) ) )
% 2.69/1.53 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: N] :
% 2.69/1.53 ( ! [Za: N] : ( P @ Za @ Pi3 )
% 2.69/1.53 => ( P @ Z2 @ ( match @ Name12 @ Name23 @ Pi3 ) ) )
% 2.69/1.53 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: N] :
% 2.69/1.53 ( ! [Za: N] : ( P @ Za @ Pi3 )
% 2.69/1.53 => ( P @ Z2 @ ( mismatch @ Name12 @ Name23 @ Pi3 ) ) )
% 2.69/1.53 => ( ! [Pi13: pi,Pi23: pi,Z2: N] :
% 2.69/1.53 ( ! [Za: N] : ( P @ Za @ Pi13 )
% 2.69/1.53 => ( ! [Za: N] : ( P @ Za @ Pi23 )
% 2.69/1.53 => ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 2.69/1.53 => ( ! [Pi13: pi,Pi23: pi,Z2: N] :
% 2.69/1.53 ( ! [Za: N] : ( P @ Za @ Pi13 )
% 2.69/1.53 => ( ! [Za: N] : ( P @ Za @ Pi23 )
% 2.69/1.53 => ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
% 2.69/1.53 => ( ! [Name3: name,Pi3: pi,Z2: N] :
% 2.69/1.53 ( ~ ( member @ name @ Name3 @ ( F @ Z2 ) )
% 2.69/1.53 => ( ! [Za: N] : ( P @ Za @ Pi3 )
% 2.69/1.53 => ( P @ Z2 @ ( res @ Name3 @ Pi3 ) ) ) )
% 2.69/1.53 => ( ! [Pi3: pi,Z2: N] :
% 2.69/1.53 ( ! [Za: N] : ( P @ Za @ Pi3 )
% 2.69/1.53 => ( P @ Z2 @ ( bang @ Pi3 ) ) )
% 2.69/1.53 => ( P @ Z @ Pi4 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_223_resZeroTrans,axiom,
% 2.69/1.53 ! [X2: name,Rs: late_residual] :
% 2.69/1.53 ~ ( late_transitions @ ( res @ X2 @ piNil ) @ Rs ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_224_pi_Oinducts,axiom,
% 2.69/1.53 ! [P: pi > $o,Pi4: pi] :
% 2.69/1.53 ( ( P @ piNil )
% 2.69/1.53 => ( ! [Name12: name,Name23: name,Pi3: pi] :
% 2.69/1.53 ( ( P @ Pi3 )
% 2.69/1.53 => ( P @ ( output @ Name12 @ Name23 @ Pi3 ) ) )
% 2.69/1.53 => ( ! [Pi3: pi] :
% 2.69/1.53 ( ( P @ Pi3 )
% 2.69/1.53 => ( P @ ( tau @ Pi3 ) ) )
% 2.69/1.53 => ( ! [Name12: name,Name23: name,Pi3: pi] :
% 2.69/1.53 ( ( P @ Pi3 )
% 2.69/1.53 => ( P @ ( input @ Name12 @ Name23 @ Pi3 ) ) )
% 2.69/1.53 => ( ! [Name12: name,Name23: name,Pi3: pi] :
% 2.69/1.53 ( ( P @ Pi3 )
% 2.69/1.53 => ( P @ ( match @ Name12 @ Name23 @ Pi3 ) ) )
% 2.69/1.53 => ( ! [Name12: name,Name23: name,Pi3: pi] :
% 2.69/1.53 ( ( P @ Pi3 )
% 2.69/1.53 => ( P @ ( mismatch @ Name12 @ Name23 @ Pi3 ) ) )
% 2.69/1.53 => ( ! [Pi13: pi,Pi23: pi] :
% 2.69/1.53 ( ( P @ Pi13 )
% 2.69/1.53 => ( ( P @ Pi23 )
% 2.69/1.53 => ( P @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 2.69/1.53 => ( ! [Pi13: pi,Pi23: pi] :
% 2.69/1.53 ( ( P @ Pi13 )
% 2.69/1.53 => ( ( P @ Pi23 )
% 2.69/1.53 => ( P @ ( par @ Pi13 @ Pi23 ) ) ) )
% 2.69/1.53 => ( ! [Name3: name,Pi3: pi] :
% 2.69/1.53 ( ( P @ Pi3 )
% 2.69/1.53 => ( P @ ( res @ Name3 @ Pi3 ) ) )
% 2.69/1.53 => ( ! [Pi3: pi] :
% 2.69/1.53 ( ( P @ Pi3 )
% 2.69/1.53 => ( P @ ( bang @ Pi3 ) ) )
% 2.69/1.53 => ( P @ Pi4 ) ) ) ) ) ) ) ) ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_225_aux2,axiom,
% 2.69/1.53 ! [P: pi] : ( late_bangPred @ P @ ( par @ P @ ( bang @ P ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_226_bangPred_Ocases,axiom,
% 2.69/1.53 ! [A1: pi,A22: pi] :
% 2.69/1.53 ( ( late_bangPred @ A1 @ A22 )
% 2.69/1.53 => ( ( A22
% 2.69/1.53 != ( bang @ A1 ) )
% 2.69/1.53 => ( A22
% 2.69/1.53 = ( par @ A1 @ ( bang @ A1 ) ) ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_227_bangPred_Osimps,axiom,
% 2.69/1.53 ( late_bangPred
% 2.69/1.53 = ( ^ [A12: pi,A23: pi] :
% 2.69/1.53 ( ? [P5: pi] :
% 2.69/1.53 ( ( A12 = P5 )
% 2.69/1.53 & ( A23
% 2.69/1.53 = ( bang @ P5 ) ) )
% 2.69/1.53 | ? [P5: pi] :
% 2.69/1.53 ( ( A12 = P5 )
% 2.69/1.53 & ( A23
% 2.69/1.53 = ( par @ P5 @ ( bang @ P5 ) ) ) ) ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_228_aux1,axiom,
% 2.69/1.53 ! [P: pi] : ( late_bangPred @ P @ ( bang @ P ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_229_bangPred_Oinducts,axiom,
% 2.69/1.53 ! [X1: pi,X22: pi,P: pi > pi > $o] :
% 2.69/1.53 ( ( late_bangPred @ X1 @ X22 )
% 2.69/1.53 => ( ! [P4: pi] : ( P @ P4 @ ( bang @ P4 ) )
% 2.69/1.53 => ( ! [P4: pi] : ( P @ P4 @ ( par @ P4 @ ( bang @ P4 ) ) )
% 2.69/1.53 => ( P @ X1 @ X22 ) ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_230_subs__def,axiom,
% 2.69/1.53 ( subs
% 2.69/1.53 = ( ^ [X3: pi,C3: name,D2: name] :
% 2.69/1.53 ( pi_rec @ pi @ piNil
% 2.69/1.53 @ ^ [A5: name,B4: name,P5: pi] : ( output @ ( subst_name @ A5 @ C3 @ D2 ) @ ( subst_name @ B4 @ C3 @ D2 ) )
% 2.69/1.53 @ ^ [P5: pi] : tau
% 2.69/1.53 @ ^ [A5: name,Y5: name,P5: pi] : ( input @ ( subst_name @ A5 @ C3 @ D2 ) @ Y5 )
% 2.69/1.53 @ ^ [A5: name,B4: name,P5: pi] : ( match @ ( subst_name @ A5 @ C3 @ D2 ) @ ( subst_name @ B4 @ C3 @ D2 ) )
% 2.69/1.53 @ ^ [A5: name,B4: name,P5: pi] : ( mismatch @ ( subst_name @ A5 @ C3 @ D2 ) @ ( subst_name @ B4 @ C3 @ D2 ) )
% 2.69/1.53 @ ^ [P5: pi,Q5: pi] : sum
% 2.69/1.53 @ ^ [P5: pi,Q5: pi] : par
% 2.69/1.53 @ ^ [Y5: name,P5: pi] : ( res @ Y5 )
% 2.69/1.53 @ ^ [P5: pi] : bang
% 2.69/1.53 @ X3 ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_231_abs__fresh_I2_J,axiom,
% 2.69/1.53 ! [X7: $tType] :
% 2.69/1.53 ( ( pt_name @ X7 )
% 2.69/1.53 => ! [X2: X7,B: name,A2: name] :
% 2.69/1.53 ( ( finite_finite @ name @ ( supp @ X7 @ name @ X2 ) )
% 2.69/1.53 => ( ( fresh @ name @ ( name > ( noption @ X7 ) ) @ B @ ( abs_fun @ name @ X7 @ A2 @ X2 ) )
% 2.69/1.53 = ( ( B = A2 )
% 2.69/1.53 | ( fresh @ name @ X7 @ B @ X2 ) ) ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_232_exists__fresh,axiom,
% 2.69/1.53 ! [A: $tType,X2: A] :
% 2.69/1.53 ( ( finite_finite @ name @ ( supp @ A @ name @ X2 ) )
% 2.69/1.53 => ~ ! [C2: name] :
% 2.69/1.53 ~ ( fresh @ name @ A @ C2 @ X2 ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_233_exists__fresh_H,axiom,
% 2.69/1.53 ! [A: $tType,X2: A] :
% 2.69/1.53 ( ( finite_finite @ name @ ( supp @ A @ name @ X2 ) )
% 2.69/1.53 => ? [C2: name] : ( fresh @ name @ A @ C2 @ X2 ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_234_supp__fresh__iff,axiom,
% 2.69/1.53 ! [X: $tType,A: $tType] :
% 2.69/1.53 ( ( supp @ A @ X )
% 2.69/1.53 = ( ^ [X3: A] :
% 2.69/1.53 ( collect @ X
% 2.69/1.53 @ ^ [A5: X] :
% 2.69/1.53 ~ ( fresh @ X @ A @ A5 @ X3 ) ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_235_fresh__def,axiom,
% 2.69/1.53 ! [A: $tType,X: $tType] :
% 2.69/1.53 ( ( fresh @ X @ A )
% 2.69/1.53 = ( ^ [A5: X,X3: A] :
% 2.69/1.53 ~ ( member @ X @ A5 @ ( supp @ A @ X @ X3 ) ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_236_pi_Osupp_I9_J,axiom,
% 2.69/1.53 ! [X1: name,X22: pi] :
% 2.69/1.53 ( ( supp @ pi @ name @ ( res @ X1 @ X22 ) )
% 2.69/1.53 = ( supp @ ( name > ( noption @ pi ) ) @ name @ ( abs_fun @ name @ pi @ X1 @ X22 ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_237_freeRes_Ocase__distrib,axiom,
% 2.69/1.53 ! [A: $tType,B2: $tType,H: A > B2,F1: name > name > A,F22: A,FreeRes3: late_freeRes] :
% 2.69/1.53 ( ( H @ ( late_case_freeRes @ A @ F1 @ F22 @ FreeRes3 ) )
% 2.69/1.53 = ( late_case_freeRes @ B2
% 2.69/1.53 @ ^ [X13: name,X24: name] : ( H @ ( F1 @ X13 @ X24 ) )
% 2.69/1.53 @ ( H @ F22 )
% 2.69/1.53 @ FreeRes3 ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_238_subject_Ocase__distrib,axiom,
% 2.69/1.53 ! [B2: $tType,A: $tType,H: A > B2,F1: name > A,F22: name > A,Subject: late_subject] :
% 2.69/1.53 ( ( H @ ( late_case_subject @ A @ F1 @ F22 @ Subject ) )
% 2.69/1.53 = ( late_case_subject @ B2
% 2.69/1.53 @ ^ [X3: name] : ( H @ ( F1 @ X3 ) )
% 2.69/1.53 @ ^ [X3: name] : ( H @ ( F22 @ X3 ) )
% 2.69/1.53 @ Subject ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_239_pi_Osupp_I3_J,axiom,
% 2.69/1.53 ! [X1: pi] :
% 2.69/1.53 ( ( supp @ pi @ name @ ( tau @ X1 ) )
% 2.69/1.53 = ( supp @ pi @ name @ X1 ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_240_subject_Osupp_I2_J,axiom,
% 2.69/1.53 ! [X1: name] :
% 2.69/1.53 ( ( supp @ late_subject @ name @ ( late_BoundOutputS @ X1 ) )
% 2.69/1.53 = ( supp @ name @ name @ X1 ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_241_subject_Osupp_I1_J,axiom,
% 2.69/1.53 ! [X1: name] :
% 2.69/1.53 ( ( supp @ late_subject @ name @ ( late_InputS @ X1 ) )
% 2.69/1.53 = ( supp @ name @ name @ X1 ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_242_pi_Osupp_I10_J,axiom,
% 2.69/1.53 ! [X1: pi] :
% 2.69/1.53 ( ( supp @ pi @ name @ ( bang @ X1 ) )
% 2.69/1.53 = ( supp @ pi @ name @ X1 ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_243_fs__name1,axiom,
% 2.69/1.53 ! [A: $tType] :
% 2.69/1.53 ( ( fs_name @ A )
% 2.69/1.53 => ! [X2: A] : ( finite_finite @ name @ ( supp @ A @ name @ X2 ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_244_residual_Orecs_I2_J,axiom,
% 2.69/1.53 ! [N: $tType,T: $tType] :
% 2.69/1.53 ( ( pt_name @ T )
% 2.69/1.53 => ! [F1: late_subject > name > pi > T,F22: late_freeRes > pi > T,Z: N,P: T > $o,FreeRes3: late_freeRes,Pi4: pi] :
% 2.69/1.53 ( ( finite_finite @ name @ ( supp @ ( late_subject > name > pi > T ) @ name @ F1 ) )
% 2.69/1.53 => ( ( finite_finite @ name @ ( supp @ ( late_freeRes > pi > T ) @ name @ F22 ) )
% 2.69/1.53 => ( ( finite_finite @ name @ ( supp @ N @ name @ Z ) )
% 2.69/1.53 => ( ! [X12: late_subject,X23: name,X33: pi] : ( P @ ( F1 @ X12 @ X23 @ X33 ) )
% 2.69/1.53 => ( ! [X12: late_freeRes,X23: pi] : ( P @ ( F22 @ X12 @ X23 ) )
% 2.69/1.53 => ( ! [X12: late_subject,X23: name,X33: pi] :
% 2.69/1.53 ( ( fresh @ name @ ( late_subject > name > pi > T ) @ X23 @ F1 )
% 2.69/1.53 => ( ( fresh @ name @ late_subject @ X23 @ X12 )
% 2.69/1.53 => ( ( fresh @ name @ N @ X23 @ Z )
% 2.69/1.53 => ( ( P @ ( F1 @ X12 @ X23 @ X33 ) )
% 2.69/1.53 => ( fresh @ name @ T @ X23 @ ( F1 @ X12 @ X23 @ X33 ) ) ) ) ) )
% 2.69/1.53 => ( ( late_residual_rec @ T @ F1 @ F22 @ ( late_FreeR @ FreeRes3 @ Pi4 ) )
% 2.69/1.53 = ( F22 @ FreeRes3 @ Pi4 ) ) ) ) ) ) ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_245_residual_Orecs_I1_J,axiom,
% 2.69/1.53 ! [N: $tType,T: $tType] :
% 2.69/1.53 ( ( pt_name @ T )
% 2.69/1.53 => ! [F1: late_subject > name > pi > T,F22: late_freeRes > pi > T,Z: N,P: T > $o,Name2: name,Subject: late_subject,Pi4: pi] :
% 2.69/1.53 ( ( finite_finite @ name @ ( supp @ ( late_subject > name > pi > T ) @ name @ F1 ) )
% 2.69/1.53 => ( ( finite_finite @ name @ ( supp @ ( late_freeRes > pi > T ) @ name @ F22 ) )
% 2.69/1.53 => ( ( finite_finite @ name @ ( supp @ N @ name @ Z ) )
% 2.69/1.53 => ( ! [X12: late_subject,X23: name,X33: pi] : ( P @ ( F1 @ X12 @ X23 @ X33 ) )
% 2.69/1.53 => ( ! [X12: late_freeRes,X23: pi] : ( P @ ( F22 @ X12 @ X23 ) )
% 2.69/1.53 => ( ! [X12: late_subject,X23: name,X33: pi] :
% 2.69/1.53 ( ( fresh @ name @ ( late_subject > name > pi > T ) @ X23 @ F1 )
% 2.69/1.53 => ( ( fresh @ name @ late_subject @ X23 @ X12 )
% 2.69/1.53 => ( ( fresh @ name @ N @ X23 @ Z )
% 2.69/1.53 => ( ( P @ ( F1 @ X12 @ X23 @ X33 ) )
% 2.69/1.53 => ( fresh @ name @ T @ X23 @ ( F1 @ X12 @ X23 @ X33 ) ) ) ) ) )
% 2.69/1.53 => ( ( fresh @ name @ ( late_subject > name > pi > T ) @ Name2 @ F1 )
% 2.69/1.53 => ( ( fresh @ name @ ( late_freeRes > pi > T ) @ Name2 @ F22 )
% 2.69/1.53 => ( ( fresh @ name @ late_subject @ Name2 @ Subject )
% 2.69/1.53 => ( ( late_residual_rec @ T @ F1 @ F22 @ ( late_BoundR @ Subject @ Name2 @ Pi4 ) )
% 2.69/1.53 = ( F1 @ Subject @ Name2 @ Pi4 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_246_residual_Orec__fresh,axiom,
% 2.69/1.53 ! [T: $tType] :
% 2.69/1.53 ( ( pt_name @ T )
% 2.69/1.53 => ! [F1: late_subject > name > pi > T,F22: late_freeRes > pi > T,X2: late_residual,Y: T,A2: name] :
% 2.69/1.53 ( ( finite_finite @ name @ ( supp @ ( late_subject > name > pi > T ) @ name @ F1 ) )
% 2.69/1.53 => ( ( finite_finite @ name @ ( supp @ ( late_freeRes > pi > T ) @ name @ F22 ) )
% 2.69/1.53 => ( ( late_r582136743ec_set @ T @ F1 @ F22 @ X2 @ Y )
% 2.69/1.53 => ( ! [Y6: T] :
% 2.69/1.53 ( ( late_r582136743ec_set @ T @ F1 @ F22 @ X2 @ Y6 )
% 2.69/1.53 => ( Y6 = Y ) )
% 2.69/1.53 => ( ( fresh @ name @ late_residual @ A2 @ X2 )
% 2.69/1.53 => ( ( fresh @ name @ ( late_subject > name > pi > T ) @ A2 @ F1 )
% 2.69/1.53 => ( ( fresh @ name @ ( late_freeRes > pi > T ) @ A2 @ F22 )
% 2.69/1.53 => ( fresh @ name @ T @ A2 @ Y ) ) ) ) ) ) ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_247_residual_Orec__unique,axiom,
% 2.69/1.53 ! [N: $tType,T: $tType] :
% 2.69/1.53 ( ( pt_name @ T )
% 2.69/1.53 => ! [F1: late_subject > name > pi > T,F22: late_freeRes > pi > T,Z: N,P: T > $o,X2: late_residual] :
% 2.69/1.53 ( ( finite_finite @ name @ ( supp @ ( late_subject > name > pi > T ) @ name @ F1 ) )
% 2.69/1.53 => ( ( finite_finite @ name @ ( supp @ ( late_freeRes > pi > T ) @ name @ F22 ) )
% 2.69/1.53 => ( ( finite_finite @ name @ ( supp @ N @ name @ Z ) )
% 2.69/1.53 => ( ! [X12: late_subject,X23: name,X33: pi] : ( P @ ( F1 @ X12 @ X23 @ X33 ) )
% 2.69/1.53 => ( ! [X12: late_freeRes,X23: pi] : ( P @ ( F22 @ X12 @ X23 ) )
% 2.69/1.53 => ( ! [X12: late_subject,X23: name] :
% 2.69/1.53 ( ( fresh @ name @ ( late_subject > name > pi > T ) @ X23 @ F1 )
% 2.69/1.53 => ( ( fresh @ name @ late_subject @ X23 @ X12 )
% 2.69/1.53 => ( ( fresh @ name @ N @ X23 @ Z )
% 2.69/1.53 => ! [X33: pi] :
% 2.69/1.53 ( ( P @ ( F1 @ X12 @ X23 @ X33 ) )
% 2.69/1.53 => ( fresh @ name @ T @ X23 @ ( F1 @ X12 @ X23 @ X33 ) ) ) ) ) )
% 2.69/1.53 => ? [X4: T] :
% 2.69/1.53 ( ( late_r582136743ec_set @ T @ F1 @ F22 @ X2 @ X4 )
% 2.69/1.53 & ! [Y7: T] :
% 2.69/1.53 ( ( late_r582136743ec_set @ T @ F1 @ F22 @ X2 @ Y7 )
% 2.69/1.53 => ( Y7 = X4 ) ) ) ) ) ) ) ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_248_residual_Orec__fin__supp,axiom,
% 2.69/1.53 ! [T: $tType] :
% 2.69/1.53 ( ( pt_name @ T )
% 2.69/1.53 => ! [F1: late_subject > name > pi > T,F22: late_freeRes > pi > T,X1: late_residual,Y1: T] :
% 2.69/1.53 ( ( finite_finite @ name @ ( supp @ ( late_subject > name > pi > T ) @ name @ F1 ) )
% 2.69/1.53 => ( ( finite_finite @ name @ ( supp @ ( late_freeRes > pi > T ) @ name @ F22 ) )
% 2.69/1.53 => ( ( late_r582136743ec_set @ T @ F1 @ F22 @ X1 @ Y1 )
% 2.69/1.53 => ( finite_finite @ name @ ( supp @ T @ name @ Y1 ) ) ) ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_249_pi_Osupp_I4_J,axiom,
% 2.69/1.53 ! [X32: name,X1: name,X22: pi] :
% 2.69/1.53 ( ( supp @ pi @ name @ ( input @ X32 @ X1 @ X22 ) )
% 2.69/1.53 = ( sup_sup @ ( set @ name ) @ ( supp @ name @ name @ X32 ) @ ( supp @ ( name > ( noption @ pi ) ) @ name @ ( abs_fun @ name @ pi @ X1 @ X22 ) ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_250_residual_Osupp_I1_J,axiom,
% 2.69/1.53 ! [X32: late_subject,X1: name,X22: pi] :
% 2.69/1.53 ( ( supp @ late_residual @ name @ ( late_BoundR @ X32 @ X1 @ X22 ) )
% 2.69/1.53 = ( sup_sup @ ( set @ name ) @ ( supp @ late_subject @ name @ X32 ) @ ( supp @ ( name > ( noption @ pi ) ) @ name @ ( abs_fun @ name @ pi @ X1 @ X22 ) ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_251_pi_Osupp_I7_J,axiom,
% 2.69/1.53 ! [X22: pi,X1: pi] :
% 2.69/1.53 ( ( supp @ pi @ name @ ( sum @ X22 @ X1 ) )
% 2.69/1.53 = ( sup_sup @ ( set @ name ) @ ( supp @ pi @ name @ X22 ) @ ( supp @ pi @ name @ X1 ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_252_pi_Osupp_I8_J,axiom,
% 2.69/1.53 ! [X22: pi,X1: pi] :
% 2.69/1.53 ( ( supp @ pi @ name @ ( par @ X22 @ X1 ) )
% 2.69/1.53 = ( sup_sup @ ( set @ name ) @ ( supp @ pi @ name @ X22 ) @ ( supp @ pi @ name @ X1 ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_253_residual_Osupp_I2_J,axiom,
% 2.69/1.53 ! [X22: late_freeRes,X1: pi] :
% 2.69/1.53 ( ( supp @ late_residual @ name @ ( late_FreeR @ X22 @ X1 ) )
% 2.69/1.53 = ( sup_sup @ ( set @ name ) @ ( supp @ late_freeRes @ name @ X22 ) @ ( supp @ pi @ name @ X1 ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_254_freeRes_Osupp_I1_J,axiom,
% 2.69/1.53 ! [X22: name,X1: name] :
% 2.69/1.53 ( ( supp @ late_freeRes @ name @ ( late_OutputR @ X22 @ X1 ) )
% 2.69/1.53 = ( sup_sup @ ( set @ name ) @ ( supp @ name @ name @ X22 ) @ ( supp @ name @ name @ X1 ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(fact_255_pi_Osupp_I2_J,axiom,
% 2.69/1.53 ! [X32: name,X22: name,X1: pi] :
% 2.69/1.53 ( ( supp @ pi @ name @ ( output @ X32 @ X22 @ X1 ) )
% 2.69/1.53 = ( sup_sup @ ( set @ name ) @ ( supp @ name @ name @ X32 ) @ ( sup_sup @ ( set @ name ) @ ( supp @ name @ name @ X22 ) @ ( supp @ pi @ name @ X1 ) ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(tcon_fun___Agent_Opt__name,axiom,
% 2.69/1.53 ! [A6: $tType,A7: $tType] :
% 2.69/1.53 ( ( ( pt_name @ A6 )
% 2.69/1.53 & ( pt_name @ A7 ) )
% 2.69/1.53 => ( pt_name @ ( A6 > A7 ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(tcon_Set_Oset___Agent_Opt__name_1,axiom,
% 2.69/1.53 ! [A6: $tType] :
% 2.69/1.53 ( ( pt_name @ A6 )
% 2.69/1.53 => ( pt_name @ ( set @ A6 ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(tcon_Agent_Opi___Agent_Opt__name_2,axiom,
% 2.69/1.53 pt_name @ pi ).
% 2.69/1.53
% 2.69/1.53 thf(tcon_Agent_Opi___Agent_Ofs__name,axiom,
% 2.69/1.53 fs_name @ pi ).
% 2.69/1.53
% 2.69/1.53 thf(tcon_HOL_Obool___Agent_Opt__name_3,axiom,
% 2.69/1.53 pt_name @ $o ).
% 2.69/1.53
% 2.69/1.53 thf(tcon_HOL_Obool___Agent_Ofs__name_4,axiom,
% 2.69/1.53 fs_name @ $o ).
% 2.69/1.53
% 2.69/1.53 thf(tcon_Agent_Oname___Agent_Opt__name_5,axiom,
% 2.69/1.53 pt_name @ name ).
% 2.69/1.53
% 2.69/1.53 thf(tcon_Agent_Oname___Agent_Ofs__name_6,axiom,
% 2.69/1.53 fs_name @ name ).
% 2.69/1.53
% 2.69/1.53 thf(tcon_Nominal_Onoption___Agent_Opt__name_7,axiom,
% 2.69/1.53 ! [A6: $tType] :
% 2.69/1.53 ( ( pt_name @ A6 )
% 2.69/1.53 => ( pt_name @ ( noption @ A6 ) ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(tcon_Late__Semantics_OfreeRes___Agent_Opt__name_8,axiom,
% 2.69/1.53 pt_name @ late_freeRes ).
% 2.69/1.53
% 2.69/1.53 thf(tcon_Late__Semantics_OfreeRes___Agent_Ofs__name_9,axiom,
% 2.69/1.53 fs_name @ late_freeRes ).
% 2.69/1.53
% 2.69/1.53 thf(tcon_Late__Semantics_Osubject___Agent_Opt__name_10,axiom,
% 2.69/1.53 pt_name @ late_subject ).
% 2.69/1.53
% 2.69/1.53 thf(tcon_Late__Semantics_Osubject___Agent_Ofs__name_11,axiom,
% 2.69/1.53 fs_name @ late_subject ).
% 2.69/1.53
% 2.69/1.53 thf(tcon_Late__Semantics_Oresidual___Agent_Opt__name_12,axiom,
% 2.69/1.53 pt_name @ late_residual ).
% 2.69/1.53
% 2.69/1.53 thf(tcon_Late__Semantics_Oresidual___Agent_Ofs__name_13,axiom,
% 2.69/1.53 fs_name @ late_residual ).
% 2.69/1.53
% 2.69/1.53 thf(help_If_3_1_T,axiom,
% 2.69/1.53 ! [P: $o] :
% 2.69/1.53 ( ( P = $true )
% 2.69/1.53 | ( P = $false ) ) ).
% 2.69/1.53
% 2.69/1.53 thf(help_If_2_1_T,axiom,
% 2.69/1.53 ! [A: $tType,X2: A,Y: A] :
% 2.69/1.53 ( ( if @ A @ $false @ X2 @ Y )
% 2.69/1.53 = Y ) ).
% 2.69/1.53
% 2.69/1.53 thf(help_If_1_1_T,axiom,
% 2.69/1.53 ! [A: $tType,X2: A,Y: A] :
% 2.69/1.53 ( ( if @ A @ $true @ X2 @ Y )
% 2.69/1.53 = X2 ) ).
% 2.69/1.53
% 2.69/1.53 thf(conj_0,conjecture,
% 2.69/1.53 late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_FreeR @ late_TauR @ ( res @ y @ ( par @ ( par @ p @ q2 ) @ ( subs @ r2 @ x @ y ) ) ) ) ).
% 2.69/1.53 ------------------------
% 2.69/1.55 % (22138)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_21913 for (2999ds/4Mi)
% 2.69/1.55 % (22139)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_21913 for (2999ds/27Mi)
% 2.69/1.55 % (22138)Instruction limit reached!
% 2.69/1.55 % (22138)------------------------------
% 2.69/1.55 % (22138)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.55 % (22138)Termination reason: Unknown
% 2.69/1.55 % (22138)Termination phase: shuffling
% 2.69/1.55
% 2.69/1.55 % (22138)Memory used [KB]: 1535
% 2.69/1.55 % (22138)Time elapsed: 0.003 s
% 2.69/1.55 % (22138)Instructions burned: 6 (million)
% 2.69/1.55 % (22138)------------------------------
% 2.69/1.55 % (22138)------------------------------
% 2.69/1.56 % (22137)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_21913 for (2999ds/183Mi)
% 2.69/1.56 % (22140)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_21913 for (2999ds/2Mi)
% 2.69/1.56 % (22141)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_21913 for (2999ds/2Mi)
% 2.69/1.56 % (22142)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_21913 for (2999ds/275Mi)
% 2.69/1.56 % (22143)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_21913 for (2999ds/18Mi)
% 2.69/1.56 % (22139)Instruction limit reached!
% 2.69/1.56 % (22139)------------------------------
% 2.69/1.56 % (22139)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.56 % (22139)Termination reason: Unknown
% 2.69/1.56 % (22139)Termination phase: Property scanning
% 2.69/1.56
% 2.69/1.56 % (22139)Memory used [KB]: 1791
% 2.69/1.56 % (22139)Time elapsed: 0.010 s
% 2.69/1.56 % (22139)Instructions burned: 28 (million)
% 2.69/1.56 % (22139)------------------------------
% 2.69/1.56 % (22139)------------------------------
% 2.69/1.56 % (22140)Instruction limit reached!
% 2.69/1.56 % (22140)------------------------------
% 2.69/1.56 % (22140)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.56 % (22140)Termination reason: Unknown
% 2.69/1.56 % (22140)Termination phase: shuffling
% 2.69/1.56
% 2.69/1.56 % (22140)Memory used [KB]: 1407
% 2.69/1.56 % (22140)Time elapsed: 0.004 s
% 2.69/1.56 % (22140)Instructions burned: 3 (million)
% 2.69/1.56 % (22140)------------------------------
% 2.69/1.56 % (22140)------------------------------
% 2.69/1.56 % (22141)Instruction limit reached!
% 2.69/1.56 % (22141)------------------------------
% 2.69/1.56 % (22141)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.56 % (22141)Termination reason: Unknown
% 2.69/1.56 % (22141)Termination phase: shuffling
% 2.69/1.56
% 2.69/1.56 % (22141)Memory used [KB]: 1407
% 2.69/1.56 % (22141)Time elapsed: 0.004 s
% 2.69/1.56 % (22141)Instructions burned: 3 (million)
% 2.69/1.56 % (22141)------------------------------
% 2.69/1.56 % (22141)------------------------------
% 2.69/1.56 % (22144)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_21913 for (2999ds/3Mi)
% 2.69/1.56 % (22144)Instruction limit reached!
% 2.69/1.56 % (22144)------------------------------
% 2.69/1.56 % (22144)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.56 % (22144)Termination reason: Unknown
% 2.69/1.56 % (22144)Termination phase: shuffling
% 2.69/1.56
% 2.69/1.56 % (22144)Memory used [KB]: 1407
% 2.69/1.56 % (22144)Time elapsed: 0.002 s
% 2.69/1.56 % (22144)Instructions burned: 3 (million)
% 2.69/1.56 % (22144)------------------------------
% 2.69/1.56 % (22144)------------------------------
% 2.69/1.57 % (22145)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_21913 for (2999ds/37Mi)
% 2.69/1.57 % (22143)Instruction limit reached!
% 2.69/1.57 % (22143)------------------------------
% 2.69/1.57 % (22143)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.57 % (22143)Termination reason: Unknown
% 2.69/1.57 % (22143)Termination phase: shuffling
% 2.69/1.57
% 2.69/1.57 % (22143)Memory used [KB]: 1791
% 2.69/1.57 % (22143)Time elapsed: 0.014 s
% 2.69/1.57 % (22143)Instructions burned: 19 (million)
% 2.69/1.57 % (22143)------------------------------
% 2.69/1.57 % (22143)------------------------------
% 2.69/1.57 % (22148)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_21913 for (2999ds/1041Mi)
% 2.69/1.58 % (22146)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_21913 for (2999ds/15Mi)
% 2.69/1.58 % (22147)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_21913 for (2999ds/3Mi)
% 2.69/1.58 % (22145)Instruction limit reached!
% 2.69/1.58 % (22145)------------------------------
% 2.69/1.58 % (22145)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.58 % (22145)Termination reason: Unknown
% 2.69/1.58 % (22145)Termination phase: shuffling
% 2.69/1.58
% 2.69/1.58 % (22145)Memory used [KB]: 2174
% 2.69/1.58 % (22145)Time elapsed: 0.012 s
% 2.69/1.58 % (22145)Instructions burned: 39 (million)
% 2.69/1.58 % (22145)------------------------------
% 2.69/1.58 % (22145)------------------------------
% 2.69/1.58 % (22147)Instruction limit reached!
% 2.69/1.58 % (22147)------------------------------
% 2.69/1.58 % (22147)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.58 % (22147)Termination reason: Unknown
% 2.69/1.58 % (22147)Termination phase: shuffling
% 2.69/1.58
% 2.69/1.58 % (22147)Memory used [KB]: 1407
% 2.69/1.58 % (22147)Time elapsed: 0.004 s
% 2.69/1.58 % (22147)Instructions burned: 3 (million)
% 2.69/1.58 % (22147)------------------------------
% 2.69/1.58 % (22147)------------------------------
% 2.69/1.59 % (22146)Instruction limit reached!
% 2.69/1.59 % (22146)------------------------------
% 2.69/1.59 % (22146)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.59 % (22146)Termination reason: Unknown
% 2.69/1.59 % (22146)Termination phase: shuffling
% 2.69/1.59
% 2.69/1.59 % (22146)Memory used [KB]: 1663
% 2.69/1.59 % (22146)Time elapsed: 0.012 s
% 2.69/1.59 % (22146)Instructions burned: 16 (million)
% 2.69/1.59 % (22146)------------------------------
% 2.69/1.59 % (22146)------------------------------
% 2.69/1.59 % (22149)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_21913 for (2999ds/7Mi)
% 2.69/1.59 % (22150)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_21913 for (2999ds/16Mi)
% 2.69/1.59 % (22149)Instruction limit reached!
% 2.69/1.59 % (22149)------------------------------
% 2.69/1.59 % (22149)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.59 % (22149)Termination reason: Unknown
% 2.69/1.59 % (22149)Termination phase: shuffling
% 2.69/1.59
% 2.69/1.59 % (22149)Memory used [KB]: 1535
% 2.69/1.59 % (22149)Time elapsed: 0.006 s
% 2.69/1.59 % (22149)Instructions burned: 7 (million)
% 2.69/1.59 % (22149)------------------------------
% 2.69/1.59 % (22149)------------------------------
% 2.69/1.59 % (22150)Instruction limit reached!
% 2.69/1.59 % (22150)------------------------------
% 2.69/1.59 % (22150)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.59 % (22150)Termination reason: Unknown
% 2.69/1.59 % (22150)Termination phase: shuffling
% 2.69/1.59
% 2.69/1.59 % (22150)Memory used [KB]: 1663
% 2.69/1.59 % (22150)Time elapsed: 0.006 s
% 2.69/1.59 % (22150)Instructions burned: 16 (million)
% 2.69/1.59 % (22150)------------------------------
% 2.69/1.59 % (22150)------------------------------
% 2.72/1.60 % (22151)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_21913 for (2999ds/3Mi)
% 2.72/1.60 % (22151)Instruction limit reached!
% 2.72/1.60 % (22151)------------------------------
% 2.72/1.60 % (22151)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.60 % (22151)Termination reason: Unknown
% 2.72/1.60 % (22151)Termination phase: shuffling
% 2.72/1.60
% 2.72/1.60 % (22151)Memory used [KB]: 1407
% 2.72/1.60 % (22151)Time elapsed: 0.003 s
% 2.72/1.60 % (22151)Instructions burned: 3 (million)
% 2.72/1.60 % (22151)------------------------------
% 2.72/1.60 % (22151)------------------------------
% 2.72/1.60 % (22152)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_21913 for (2999ds/3Mi)
% 2.72/1.60 % (22154)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_21913 for (2999ds/3Mi)
% 2.72/1.60 % (22152)Instruction limit reached!
% 2.72/1.60 % (22152)------------------------------
% 2.72/1.60 % (22152)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.60 % (22152)Termination reason: Unknown
% 2.72/1.60 % (22152)Termination phase: shuffling
% 2.72/1.60
% 2.72/1.60 % (22152)Memory used [KB]: 1407
% 2.72/1.60 % (22152)Time elapsed: 0.003 s
% 2.72/1.60 % (22152)Instructions burned: 4 (million)
% 2.72/1.60 % (22152)------------------------------
% 2.72/1.60 % (22152)------------------------------
% 2.72/1.60 % (22154)Instruction limit reached!
% 2.72/1.60 % (22154)------------------------------
% 2.72/1.60 % (22154)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.60 % (22154)Termination reason: Unknown
% 2.72/1.60 % (22154)Termination phase: shuffling
% 2.72/1.60
% 2.72/1.60 % (22154)Memory used [KB]: 1407
% 2.72/1.60 % (22154)Time elapsed: 0.002 s
% 2.72/1.60 % (22154)Instructions burned: 4 (million)
% 2.72/1.60 % (22154)------------------------------
% 2.72/1.60 % (22154)------------------------------
% 2.72/1.61 % (22142)First to succeed.
% 2.72/1.61 % (22142)Refutation found. Thanks to Tanya!
% 2.72/1.61 % SZS status Theorem for DTF2THF_21913
% 2.72/1.61 % SZS output start Proof for DTF2THF_21913
% 2.72/1.61 thf(type_def_5, type, pi: $tType).
% 2.72/1.61 thf(type_def_7, type, name: $tType).
% 2.72/1.61 thf(type_def_8, type, set: ($tType) > $tType).
% 2.72/1.61 thf(type_def_9, type, late_freeRes: $tType).
% 2.72/1.61 thf(type_def_10, type, late_subject: $tType).
% 2.72/1.61 thf(type_def_11, type, late_residual: $tType).
% 2.72/1.61 thf(type_def_12, type, noption: ($tType) > $tType).
% 2.72/1.61 thf(func_def_0, type, late_residual: $tType).
% 2.72/1.61 thf(func_def_1, type, late_subject: $tType).
% 2.72/1.61 thf(func_def_2, type, late_freeRes: $tType).
% 2.72/1.61 thf(func_def_3, type, noption: ($tType) > $tType).
% 2.72/1.61 thf(func_def_4, type, name: $tType).
% 2.72/1.61 thf(func_def_5, type, pi: $tType).
% 2.72/1.61 thf(func_def_6, type, set: ($tType) > $tType).
% 2.72/1.61 thf(func_def_7, type, fs_name: !>[X0: $tType]:($o)).
% 2.72/1.61 thf(func_def_8, type, pt_name: !>[X0: $tType]:($o)).
% 2.72/1.61 thf(func_def_9, type, bang: pi > pi).
% 2.72/1.61 thf(func_def_10, type, input: name > name > pi > pi).
% 2.72/1.61 thf(func_def_11, type, match: name > name > pi > pi).
% 2.72/1.61 thf(func_def_12, type, mismatch: name > name > pi > pi).
% 2.72/1.61 thf(func_def_13, type, output: name > name > pi > pi).
% 2.72/1.61 thf(func_def_14, type, par: pi > pi > pi).
% 2.72/1.61 thf(func_def_15, type, piNil: pi).
% 2.72/1.61 thf(func_def_16, type, res: name > pi > pi).
% 2.72/1.61 thf(func_def_17, type, sum: pi > pi > pi).
% 2.72/1.61 thf(func_def_18, type, tau: pi > pi).
% 2.72/1.61 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)).
% 2.72/1.61 thf(func_def_20, type, subs: pi > name > name > pi).
% 2.72/1.61 thf(func_def_21, type, subst_name: name > name > name > name).
% 2.72/1.61 thf(func_def_22, type, finite_finite: !>[X0: $tType]:(set @ X0 > $o)).
% 2.72/1.61 thf(func_def_23, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 2.72/1.61 thf(func_def_24, type, late_case_freeRes: !>[X0: $tType]:((name > name > X0) > X0 > late_freeRes > X0)).
% 2.72/1.61 thf(func_def_25, type, late_case_subject: !>[X0: $tType]:((name > X0) > (name > X0) > late_subject > X0)).
% 2.72/1.61 thf(func_def_26, type, late_bangPred: pi > pi > $o).
% 2.72/1.61 thf(func_def_27, type, late_OutputR: name > name > late_freeRes).
% 2.72/1.61 thf(func_def_28, type, late_TauR: late_freeRes).
% 2.72/1.61 thf(func_def_29, type, late_freeRes_rec: !>[X0: $tType]:((name > name > X0) > X0 > late_freeRes > X0)).
% 2.72/1.61 thf(func_def_30, type, late_BoundR: late_subject > name > pi > late_residual).
% 2.72/1.61 thf(func_def_31, type, late_FreeR: late_freeRes > pi > late_residual).
% 2.72/1.61 thf(func_def_32, type, late_residual_rec: !>[X0: $tType]:((late_subject > name > pi > X0) > (late_freeRes > pi > X0) > late_residual > X0)).
% 2.72/1.61 thf(func_def_33, type, late_r582136743ec_set: !>[X0: $tType]:((late_subject > name > pi > X0) > (late_freeRes > pi > X0) > late_residual > X0 > $o)).
% 2.72/1.61 thf(func_def_34, type, late_BoundOutputS: name > late_subject).
% 2.72/1.61 thf(func_def_35, type, late_InputS: name > late_subject).
% 2.72/1.61 thf(func_def_36, type, late_subject_rec: !>[X0: $tType]:((name > X0) > (name > X0) > late_subject > X0)).
% 2.72/1.61 thf(func_def_37, type, late_transitions: pi > late_residual > $o).
% 2.72/1.61 thf(func_def_38, type, sup_sup: !>[X0: $tType]:(X0 > X0 > X0)).
% 2.72/1.61 thf(func_def_39, type, abs_fun: !>[X0: $tType, X1: $tType]:(X0 > X1 > X0 > noption @ X1)).
% 2.72/1.61 thf(func_def_40, type, fresh: !>[X0: $tType, X1: $tType]:(X0 > X1 > $o)).
% 2.72/1.61 thf(func_def_41, type, supp: !>[X0: $tType, X1: $tType]:(X0 > set @ X1)).
% 2.72/1.61 thf(func_def_42, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 2.72/1.61 thf(func_def_43, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 2.72/1.61 thf(func_def_44, type, p: pi).
% 2.72/1.61 thf(func_def_45, type, pqr: pi).
% 2.72/1.61 thf(func_def_46, type, q: pi).
% 2.72/1.61 thf(func_def_47, type, qr: pi).
% 2.72/1.61 thf(func_def_48, type, q2: pi).
% 2.72/1.61 thf(func_def_49, type, r: pi).
% 2.72/1.61 thf(func_def_50, type, r2: pi).
% 2.72/1.61 thf(func_def_51, type, alpha: late_freeRes).
% 2.72/1.61 thf(func_def_52, type, a: name).
% 2.72/1.61 thf(func_def_53, type, x: name).
% 2.72/1.61 thf(func_def_54, type, y: name).
% 2.72/1.61 thf(func_def_69, type, sP0: late_subject > name > pi > name > pi > $o).
% 2.72/1.61 thf(func_def_70, type, sP1: late_residual > name > pi > $o).
% 2.72/1.61 thf(func_def_71, type, sP2: late_residual > name > pi > $o).
% 2.72/1.61 thf(func_def_72, type, sP3: late_subject > name > pi > pi > pi > $o).
% 2.72/1.61 thf(func_def_73, type, sK4: !>[X0: $tType]:((X0 > late_subject > $o) > name)).
% 2.72/1.61 thf(func_def_74, type, sK5: !>[X0: $tType]:((X0 > late_subject > $o) > X0)).
% 2.72/1.61 thf(func_def_75, type, sK6: !>[X0: $tType]:((X0 > late_subject > $o) > name)).
% 2.72/1.61 thf(func_def_76, type, sK7: !>[X0: $tType]:((X0 > late_subject > $o) > X0)).
% 2.72/1.61 thf(func_def_77, type, sK8: !>[X0: $tType]:((X0 > late_freeRes > $o) > X0)).
% 2.72/1.61 thf(func_def_78, type, sK9: !>[X0: $tType]:((X0 > late_freeRes > $o) > name)).
% 2.72/1.61 thf(func_def_79, type, sK10: !>[X0: $tType]:((X0 > late_freeRes > $o) > name)).
% 2.72/1.61 thf(func_def_80, type, sK11: !>[X0: $tType]:((X0 > late_freeRes > $o) > X0)).
% 2.72/1.61 thf(func_def_81, type, sK12: (late_residual > $o) > late_subject).
% 2.72/1.61 thf(func_def_82, type, sK13: (late_residual > $o) > name).
% 2.72/1.61 thf(func_def_83, type, sK14: (late_residual > $o) > pi).
% 2.72/1.61 thf(func_def_84, type, sK15: (late_residual > $o) > late_freeRes).
% 2.72/1.61 thf(func_def_85, type, sK16: (late_residual > $o) > pi).
% 2.72/1.61 thf(func_def_86, type, sK17: late_subject > name > pi > name > pi > pi).
% 2.72/1.61 thf(func_def_87, type, sK18: late_subject > name > pi > name > pi > late_subject).
% 2.72/1.61 thf(func_def_88, type, sK19: late_subject > name > pi > name > pi > name).
% 2.72/1.61 thf(func_def_89, type, sK20: late_subject > name > pi > name > pi > pi).
% 2.72/1.61 thf(func_def_90, type, sK21: late_subject > name > pi > name > pi > name).
% 2.72/1.61 thf(func_def_91, type, sK22: pi > name > late_subject > pi > name > pi).
% 2.72/1.61 thf(func_def_92, type, sK23: pi > name > late_subject > pi > name > name).
% 2.72/1.61 thf(func_def_93, type, sK24: pi > name > late_subject > pi > name > name).
% 2.72/1.61 thf(func_def_94, type, sK25: pi > name > late_subject > pi > name > pi).
% 2.72/1.61 thf(func_def_95, type, sK26: (pi > $o) > name > late_subject > pi > pi > pi).
% 2.72/1.61 thf(func_def_96, type, sK27: (pi > $o) > name > late_subject > pi > pi > pi).
% 2.72/1.61 thf(func_def_97, type, sK28: (late_freeRes > $o) > name).
% 2.72/1.61 thf(func_def_98, type, sK29: (late_freeRes > $o) > name).
% 2.72/1.61 thf(func_def_99, type, sK30: late_residual > pi > name > name > name).
% 2.72/1.61 thf(func_def_100, type, sK31: late_residual > pi > name > name > name).
% 2.72/1.61 thf(func_def_101, type, sK32: late_residual > pi > name > name > pi).
% 2.72/1.61 thf(func_def_102, type, sK33: pi > late_freeRes > pi > name > pi).
% 2.72/1.61 thf(func_def_103, type, sK34: pi > late_freeRes > pi > name > late_freeRes).
% 2.72/1.61 thf(func_def_104, type, sK35: pi > late_freeRes > pi > name > pi).
% 2.72/1.61 thf(func_def_105, type, sK36: pi > late_freeRes > pi > name > name).
% 2.72/1.61 thf(func_def_106, type, sK37: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 2.72/1.61 thf(func_def_107, type, sK38: late_residual > pi > pi).
% 2.72/1.61 thf(func_def_108, type, sK39: late_residual > name > pi > pi).
% 2.72/1.61 thf(func_def_109, type, sK40: late_residual > name > pi > late_freeRes).
% 2.72/1.61 thf(func_def_110, type, sK41: late_residual > name > pi > pi).
% 2.72/1.61 thf(func_def_111, type, sK42: late_residual > name > pi > name).
% 2.72/1.61 thf(func_def_112, type, sK43: late_residual > name > pi > pi).
% 2.72/1.61 thf(func_def_113, type, sK44: late_residual > name > pi > late_subject).
% 2.72/1.61 thf(func_def_114, type, sK45: late_residual > name > pi > name).
% 2.72/1.61 thf(func_def_115, type, sK46: late_residual > name > pi > pi).
% 2.72/1.61 thf(func_def_116, type, sK47: late_residual > name > pi > name).
% 2.72/1.61 thf(func_def_117, type, sK48: late_residual > pi > name > pi).
% 2.72/1.61 thf(func_def_118, type, sK49: late_residual > pi > name > name).
% 2.72/1.61 thf(func_def_119, type, sK50: late_residual > pi > name > name).
% 2.72/1.61 thf(func_def_120, type, sK51: late_residual > pi > name > pi).
% 2.72/1.61 thf(func_def_121, type, sK52: late_subject > name).
% 2.72/1.61 thf(func_def_122, type, sK53: late_subject > name).
% 2.72/1.61 thf(func_def_123, type, sK54: (late_subject > $o) > name).
% 2.72/1.61 thf(func_def_124, type, sK55: (late_subject > $o) > name).
% 2.72/1.61 thf(func_def_125, type, sK56: !>[X0: $tType]:((X0 > late_subject > $o) > name)).
% 2.72/1.61 thf(func_def_126, type, sK57: !>[X0: $tType]:((X0 > late_subject > $o) > X0)).
% 2.72/1.61 thf(func_def_127, type, sK58: !>[X0: $tType]:((X0 > late_subject > $o) > name)).
% 2.72/1.61 thf(func_def_128, type, sK59: !>[X0: $tType]:((X0 > late_subject > $o) > X0)).
% 2.72/1.61 thf(func_def_129, type, sK60: (pi > $o) > late_freeRes > pi > name > pi).
% 2.72/1.61 thf(func_def_130, type, sK61: late_subject > name > pi > pi > pi > pi).
% 2.72/1.61 thf(func_def_131, type, sK62: late_subject > name > pi > pi > pi > late_subject).
% 2.72/1.61 thf(func_def_132, type, sK63: late_subject > name > pi > pi > pi > name).
% 2.72/1.61 thf(func_def_133, type, sK64: late_subject > name > pi > pi > pi > pi).
% 2.72/1.61 thf(func_def_134, type, sK65: late_subject > name > pi > pi > pi > pi).
% 2.72/1.61 thf(func_def_135, type, sK66: pi > name > late_subject > pi > pi > pi).
% 2.72/1.61 thf(func_def_136, type, sK67: pi > name > late_subject > pi > pi > late_subject).
% 2.72/1.61 thf(func_def_137, type, sK68: pi > name > late_subject > pi > pi > name).
% 2.72/1.61 thf(func_def_138, type, sK69: pi > name > late_subject > pi > pi > pi).
% 2.72/1.61 thf(func_def_139, type, sK70: pi > name > late_subject > pi > pi > pi).
% 2.72/1.61 thf(func_def_140, type, sK71: late_freeRes > name).
% 2.72/1.61 thf(func_def_141, type, sK72: late_freeRes > name).
% 2.72/1.61 thf(func_def_142, type, sK73: !>[X0: $tType]:((X0 > late_freeRes > $o) > name)).
% 2.72/1.61 thf(func_def_143, type, sK74: !>[X0: $tType]:((X0 > late_freeRes > $o) > name)).
% 2.72/1.61 thf(func_def_144, type, sK75: !>[X0: $tType]:((X0 > late_freeRes > $o) > X0)).
% 2.72/1.61 thf(func_def_145, type, sK76: !>[X0: $tType]:((X0 > late_freeRes > $o) > X0)).
% 2.72/1.61 thf(func_def_147, type, ph78: !>[X0: $tType]:(X0)).
% 2.72/1.61 thf(f1108,plain,(
% 2.72/1.61 $false),
% 2.72/1.61 inference(subsumption_resolution,[status(thm)],[f1105,f936])).
% 2.72/1.61 thf(f936,plain,(
% 2.72/1.61 ((late_transitions @ r @ (late_BoundR @ (late_InputS @ a) @ x @ r2)) = $true)),
% 2.72/1.61 inference(cnf_transformation,[status(thm)],[f323])).
% 2.72/1.61 thf(f323,plain,(
% 2.72/1.61 ((late_transitions @ r @ (late_BoundR @ (late_InputS @ a) @ x @ r2)) = $true)),
% 2.72/1.61 inference(fool_elimination,[status(thm)],[f322])).
% 2.72/1.61 thf(f322,plain,(
% 2.72/1.61 (late_transitions @ r @ (late_BoundR @ (late_InputS @ a) @ x @ r2))),
% 2.72/1.61 inference(rectify,[status(thm)],[f13])).
% 2.72/1.61 thf(f13,axiom,(
% 2.72/1.61 (late_transitions @ r @ (late_BoundR @ (late_InputS @ a) @ x @ r2))),
% 2.72/1.61 file('/export/starexec/sandbox2/tmp/tmp.pAINnnNPiL/DTF2THF_21913.p',fact_12_cClose2_Ohyps_I2_J)).
% 2.72/1.61 thf(f1105,plain,(
% 2.72/1.61 ((late_transitions @ r @ (late_BoundR @ (late_InputS @ a) @ x @ r2)) != $true)),
% 2.72/1.61 inference(trivial_inequality_removal,[status(thm)],[f1101])).
% 2.72/1.61 thf(f1101,plain,(
% 2.72/1.61 ((late_transitions @ r @ (late_BoundR @ (late_InputS @ a) @ x @ r2)) != $true) | ($true != $true)),
% 2.72/1.61 inference(superposition,[status(thm)],[f1091,f922])).
% 2.72/1.61 thf(f922,plain,(
% 2.72/1.61 ((late_transitions @ (par @ p @ q) @ (late_BoundR @ (late_BoundOutputS @ a) @ y @ (par @ p @ q2))) = $true)),
% 2.72/1.61 inference(cnf_transformation,[status(thm)],[f409])).
% 2.72/1.61 thf(f409,plain,(
% 2.72/1.61 ((late_transitions @ (par @ p @ q) @ (late_BoundR @ (late_BoundOutputS @ a) @ y @ (par @ p @ q2))) = $true)),
% 2.72/1.61 inference(fool_elimination,[status(thm)],[f408])).
% 2.72/1.61 thf(f408,plain,(
% 2.72/1.61 (late_transitions @ (par @ p @ q) @ (late_BoundR @ (late_BoundOutputS @ a) @ y @ (par @ p @ q2)))),
% 2.72/1.61 inference(rectify,[status(thm)],[f14])).
% 2.72/1.61 thf(f14,axiom,(
% 2.72/1.61 (late_transitions @ (par @ p @ q) @ (late_BoundR @ (late_BoundOutputS @ a) @ y @ (par @ p @ q2)))),
% 2.72/1.61 file('/export/starexec/sandbox2/tmp/tmp.pAINnnNPiL/DTF2THF_21913.p',fact_13__092_060open_062P_A_092_060parallel_062_AQ_A_092_060longmapsto_062_Aa_060_092_060nu_062y_062_A_092_060prec_062_AP_A_092_060parallel_062_AQ_H_092_060close_062)).
% 2.72/1.61 thf(f1091,plain,(
% 2.72/1.61 ( ! [X0 : name] : (((late_transitions @ (par @ p @ q) @ (late_BoundR @ (late_BoundOutputS @ X0) @ y @ (par @ p @ q2))) != $true) | ((late_transitions @ r @ (late_BoundR @ (late_InputS @ X0) @ x @ r2)) != $true)) )),
% 2.72/1.61 inference(subsumption_resolution,[status(thm)],[f1090,f917])).
% 2.72/1.61 thf(f917,plain,(
% 2.72/1.61 ((fresh @ name @ pi @ y @ r) = $true)),
% 2.72/1.61 inference(cnf_transformation,[status(thm)],[f475])).
% 2.72/1.61 thf(f475,plain,(
% 2.72/1.61 ((fresh @ name @ pi @ y @ r) = $true)),
% 2.72/1.61 inference(fool_elimination,[status(thm)],[f474])).
% 2.72/1.61 thf(f474,plain,(
% 2.72/1.61 (fresh @ name @ pi @ y @ r)),
% 2.72/1.61 inference(rectify,[status(thm)],[f4])).
% 2.72/1.61 thf(f4,axiom,(
% 2.72/1.61 (fresh @ name @ pi @ y @ r)),
% 2.72/1.61 file('/export/starexec/sandbox2/tmp/tmp.pAINnnNPiL/DTF2THF_21913.p',fact_3_cClose2_Ohyps_I9_J)).
% 2.72/1.61 thf(f1090,plain,(
% 2.72/1.61 ( ! [X0 : name] : (((late_transitions @ (par @ p @ q) @ (late_BoundR @ (late_BoundOutputS @ X0) @ y @ (par @ p @ q2))) != $true) | ((late_transitions @ r @ (late_BoundR @ (late_InputS @ X0) @ x @ r2)) != $true) | ((fresh @ name @ pi @ y @ r) != $true)) )),
% 2.72/1.61 inference(trivial_inequality_removal,[status(thm)],[f1087])).
% 2.72/1.61 thf(f1087,plain,(
% 2.72/1.61 ( ! [X0 : name] : (((late_transitions @ (par @ p @ q) @ (late_BoundR @ (late_BoundOutputS @ X0) @ y @ (par @ p @ q2))) != $true) | ((fresh @ name @ pi @ y @ r) != $true) | ($true != $true) | ((late_transitions @ r @ (late_BoundR @ (late_InputS @ X0) @ x @ r2)) != $true)) )),
% 2.72/1.61 inference(superposition,[status(thm)],[f935,f927])).
% 2.72/1.61 thf(f927,plain,(
% 2.72/1.61 ( ! [X2 : name,X3 : pi,X0 : pi,X1 : name,X6 : pi,X4 : pi,X5 : name] : (((late_transitions @ (par @ X0 @ X4) @ (late_FreeR @ late_TauR @ (res @ X2 @ (par @ X3 @ (subs @ X6 @ X5 @ X2))))) = $true) | ((late_transitions @ X0 @ (late_BoundR @ (late_BoundOutputS @ X1) @ X2 @ X3)) != $true) | ((fresh @ name @ pi @ X2 @ X4) != $true) | ((late_transitions @ X4 @ (late_BoundR @ (late_InputS @ X1) @ X5 @ X6)) != $true)) )),
% 2.72/1.61 inference(cnf_transformation,[status(thm)],[f712])).
% 2.72/1.61 thf(f712,plain,(
% 2.72/1.61 ! [X0 : pi,X1 : name,X2 : name,X3 : pi,X4 : pi,X5 : name,X6 : pi] : (((late_transitions @ X4 @ (late_BoundR @ (late_InputS @ X1) @ X5 @ X6)) != $true) | ((late_transitions @ X0 @ (late_BoundR @ (late_BoundOutputS @ X1) @ X2 @ X3)) != $true) | ((fresh @ name @ pi @ X2 @ X4) != $true) | ((late_transitions @ (par @ X0 @ X4) @ (late_FreeR @ late_TauR @ (res @ X2 @ (par @ X3 @ (subs @ X6 @ X5 @ X2))))) = $true))),
% 2.72/1.61 inference(flattening,[status(thm)],[f711])).
% 2.72/1.61 thf(f711,plain,(
% 2.72/1.61 ! [X0 : pi,X1 : name,X2 : name,X3 : pi,X4 : pi,X5 : name,X6 : pi] : (((((late_transitions @ (par @ X0 @ X4) @ (late_FreeR @ late_TauR @ (res @ X2 @ (par @ X3 @ (subs @ X6 @ X5 @ X2))))) = $true) | ((fresh @ name @ pi @ X2 @ X4) != $true)) | ((late_transitions @ X4 @ (late_BoundR @ (late_InputS @ X1) @ X5 @ X6)) != $true)) | ((late_transitions @ X0 @ (late_BoundR @ (late_BoundOutputS @ X1) @ X2 @ X3)) != $true))),
% 2.72/1.61 inference(ennf_transformation,[status(thm)],[f531])).
% 2.72/1.61 thf(f531,plain,(
% 2.72/1.61 ! [X0 : pi,X1 : name,X2 : name,X3 : pi,X4 : pi,X5 : name,X6 : pi] : (((late_transitions @ X0 @ (late_BoundR @ (late_BoundOutputS @ X1) @ X2 @ X3)) = $true) => (((late_transitions @ X4 @ (late_BoundR @ (late_InputS @ X1) @ X5 @ X6)) = $true) => (((fresh @ name @ pi @ X2 @ X4) = $true) => ((late_transitions @ (par @ X0 @ X4) @ (late_FreeR @ late_TauR @ (res @ X2 @ (par @ X3 @ (subs @ X6 @ X5 @ X2))))) = $true))))),
% 2.72/1.61 inference(fool_elimination,[status(thm)],[f530])).
% 2.72/1.61 thf(f530,plain,(
% 2.72/1.61 ! [X0 : pi,X1 : name,X2 : name,X3 : pi,X4 : pi,X5 : name,X6 : pi] : ((late_transitions @ X0 @ (late_BoundR @ (late_BoundOutputS @ X1) @ X2 @ X3)) => ((late_transitions @ X4 @ (late_BoundR @ (late_InputS @ X1) @ X5 @ X6)) => ((fresh @ name @ pi @ X2 @ X4) => (late_transitions @ (par @ X0 @ X4) @ (late_FreeR @ late_TauR @ (res @ X2 @ (par @ X3 @ (subs @ X6 @ X5 @ X2))))))))),
% 2.72/1.61 inference(rectify,[status(thm)],[f25])).
% 2.72/1.61 thf(f25,axiom,(
% 2.72/1.61 ! [X6 : pi,X11 : name,X16 : name,X9 : pi,X7 : pi,X3 : name,X10 : pi] : ((late_transitions @ X6 @ (late_BoundR @ (late_BoundOutputS @ X11) @ X16 @ X9)) => ((late_transitions @ X7 @ (late_BoundR @ (late_InputS @ X11) @ X3 @ X10)) => ((fresh @ name @ pi @ X16 @ X7) => (late_transitions @ (par @ X6 @ X7) @ (late_FreeR @ late_TauR @ (res @ X16 @ (par @ X9 @ (subs @ X10 @ X3 @ X16))))))))),
% 2.72/1.61 file('/export/starexec/sandbox2/tmp/tmp.pAINnnNPiL/DTF2THF_21913.p',fact_24_Late__Semantics_OClose2)).
% 2.72/1.61 thf(f935,plain,(
% 2.72/1.61 ((late_transitions @ (par @ (par @ p @ q) @ r) @ (late_FreeR @ late_TauR @ (res @ y @ (par @ (par @ p @ q2) @ (subs @ r2 @ x @ y))))) != $true)),
% 2.72/1.61 inference(cnf_transformation,[status(thm)],[f644])).
% 2.72/1.61 thf(f644,plain,(
% 2.72/1.61 ((late_transitions @ (par @ (par @ p @ q) @ r) @ (late_FreeR @ late_TauR @ (res @ y @ (par @ (par @ p @ q2) @ (subs @ r2 @ x @ y))))) != $true)),
% 2.72/1.61 inference(flattening,[status(thm)],[f643])).
% 2.72/1.61 thf(f643,plain,(
% 2.72/1.61 ~((late_transitions @ (par @ (par @ p @ q) @ r) @ (late_FreeR @ late_TauR @ (res @ y @ (par @ (par @ p @ q2) @ (subs @ r2 @ x @ y))))) = $true)),
% 2.72/1.61 inference(fool_elimination,[status(thm)],[f642])).
% 2.72/1.61 thf(f642,plain,(
% 2.72/1.61 ~(late_transitions @ (par @ (par @ p @ q) @ r) @ (late_FreeR @ late_TauR @ (res @ y @ (par @ (par @ p @ q2) @ (subs @ r2 @ x @ y)))))),
% 2.72/1.61 inference(rectify,[status(thm)],[f276])).
% 2.72/1.61 thf(f276,negated_conjecture,(
% 2.72/1.61 ~(late_transitions @ (par @ (par @ p @ q) @ r) @ (late_FreeR @ late_TauR @ (res @ y @ (par @ (par @ p @ q2) @ (subs @ r2 @ x @ y)))))),
% 2.72/1.61 inference(negated_conjecture,[status(cth)],[f275])).
% 2.72/1.61 thf(f275,conjecture,(
% 2.72/1.61 (late_transitions @ (par @ (par @ p @ q) @ r) @ (late_FreeR @ late_TauR @ (res @ y @ (par @ (par @ p @ q2) @ (subs @ r2 @ x @ y)))))),
% 2.72/1.61 file('/export/starexec/sandbox2/tmp/tmp.pAINnnNPiL/DTF2THF_21913.p',conj_0)).
% 2.72/1.61 % SZS output end Proof for DTF2THF_21913
% 2.72/1.61 % (22142)------------------------------
% 2.72/1.61 % (22142)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.61 % (22142)Termination reason: Refutation
% 2.72/1.61
% 2.72/1.61 % (22142)Memory used [KB]: 7291
% 2.72/1.61 % (22142)Time elapsed: 0.050 s
% 2.72/1.61 % (22142)Instructions burned: 105 (million)
% 2.72/1.61 % (22142)------------------------------
% 2.72/1.61 % (22142)------------------------------
% 2.72/1.61 % (22136)Success in time 0.07 s
%------------------------------------------------------------------------------