%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP187^2 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:56:15 AM UTC 2026
% Result : Theorem 2.80s 1.68s
% Output : Refutation 2.80s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP187^2 : TPTP v9.2.1. Released v7.5.0.
% 0.13/0.14 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.35 % Computer : n001.cluster.edu
% 0.18/0.35 % Model : x86_64 x86_64
% 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.35 % Memory : 8042.1875MB
% 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.35 % CPULimit : 300
% 0.18/0.35 % WCLimit : 300
% 0.18/0.35 % DateTime : Tue Feb 24 08:30:05 EST 2026
% 0.18/0.35 % CPUTime :
% 0.18/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.33/0.48 ---- Original DTF file ---
% 0.33/0.48 thf(spec,logic,$$dhol).
% 0.33/0.48 %------------------------------------------------------------------------------
% 0.33/0.48 % File : ITP187^2 : TPTP v9.2.1. Released v7.5.0.
% 0.33/0.48 % Domain : Interactive Theorem Proving
% 0.33/0.48 % Problem : Sledgehammer Strong_Late_Sim_SC problem prob_617__3414780_1
% 0.33/0.48 % Version : Especial.
% 0.33/0.48 % English :
% 0.33/0.48
% 0.33/0.48 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.33/0.48 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.33/0.48 % Source : [Des21]
% 0.33/0.48 % Names : Strong_Late_Sim_SC/prob_617__3414780_1 [Des21]
% 0.33/0.48
% 0.33/0.48 % Status : Theorem
% 0.33/0.48 % Rating : 0.33 v8.1.0, 0.00 v7.5.0
% 0.33/0.48 % Syntax : Number of formulae : 320 ( 167 unt; 53 typ; 0 def)
% 0.33/0.48 % Number of atoms : 634 ( 262 equ; 0 cnn)
% 0.33/0.48 % Maximal formula atoms : 17 ( 2 avg)
% 0.33/0.48 % Number of connectives : 3959 ( 147 ~; 5 |; 49 &;3422 @)
% 0.33/0.48 % ( 0 <=>; 336 =>; 0 <=; 0 <~>)
% 0.33/0.48 % Maximal formula depth : 28 ( 9 avg)
% 0.33/0.48 % Number of types : 6 ( 5 usr)
% 0.33/0.48 % Number of type conns : 142 ( 142 >; 0 *; 0 +; 0 <<)
% 0.33/0.48 % Number of symbols : 51 ( 48 usr; 16 con; 0-5 aty)
% 0.33/0.48 % Number of variables : 1276 ( 9 ^;1234 !; 14 ?;1276 :)
% 0.33/0.48 % ( 19 !>; 0 ?*; 0 @-; 0 @+)
% 0.33/0.48 % SPC : TH1_THM_EQU_NAR
% 0.33/0.48
% 0.33/0.48 % Comments : This file was generated by Sledgehammer 2021-02-23 16:17:08.690
% 0.33/0.48 %------------------------------------------------------------------------------
% 0.33/0.48 % Could-be-implicit typings (8)
% 0.33/0.48 thf(ty_t_Late__Semantics_Oresidual,type,
% 0.33/0.48 late_residual: $tType ).
% 0.33/0.48
% 0.33/0.48 thf(ty_t_Late__Semantics_Osubject,type,
% 0.33/0.48 late_subject: $tType ).
% 0.33/0.48
% 0.33/0.48 thf(ty_t_Late__Semantics_OfreeRes,type,
% 0.33/0.48 late_freeRes: $tType ).
% 0.33/0.48
% 0.33/0.48 thf(ty_t_Product__Type_Oprod,type,
% 0.33/0.48 product_prod: $tType > $tType > $tType ).
% 0.33/0.48
% 0.33/0.48 thf(ty_t_Nominal_Onoption,type,
% 0.33/0.48 noption: $tType > $tType ).
% 0.33/0.48
% 0.33/0.48 thf(ty_t_Agent_Oname,type,
% 0.33/0.48 name: $tType ).
% 0.33/0.48
% 0.33/0.48 thf(ty_t_Agent_Opi,type,
% 0.33/0.48 pi: $tType ).
% 0.33/0.48
% 0.33/0.48 thf(ty_t_Set_Oset,type,
% 0.33/0.48 set: $tType > $tType ).
% 0.33/0.48
% 0.33/0.48 % Explicit typings (45)
% 0.33/0.48 thf(sy_cl_Agent_Ofs__name,type,
% 0.33/0.48 fs_name:
% 0.33/0.48 !>[A: $tType] : $o ).
% 0.33/0.48
% 0.33/0.48 thf(sy_c_Agent_Opi_OBang,type,
% 0.33/0.48 bang: pi > pi ).
% 0.33/0.48
% 0.33/0.48 thf(sy_c_Agent_Opi_OInput,type,
% 0.33/0.48 input: name > name > pi > pi ).
% 0.33/0.48
% 0.33/0.48 thf(sy_c_Agent_Opi_OMatch,type,
% 0.33/0.48 match: name > name > pi > pi ).
% 0.33/0.48
% 0.33/0.48 thf(sy_c_Agent_Opi_OMismatch,type,
% 0.33/0.48 mismatch: name > name > pi > pi ).
% 0.33/0.48
% 0.33/0.48 thf(sy_c_Agent_Opi_OOutput,type,
% 0.33/0.48 output: name > name > pi > pi ).
% 0.33/0.48
% 0.33/0.48 thf(sy_c_Agent_Opi_OPar,type,
% 0.33/0.48 par: pi > pi > pi ).
% 0.33/0.48
% 0.33/0.48 thf(sy_c_Agent_Opi_OPiNil,type,
% 0.33/0.48 piNil: pi ).
% 0.33/0.48
% 0.33/0.48 thf(sy_c_Agent_Opi_ORes,type,
% 0.33/0.48 res: name > pi > pi ).
% 0.33/0.48
% 0.33/0.48 thf(sy_c_Agent_Opi_OSum,type,
% 0.33/0.48 sum: pi > pi > pi ).
% 0.33/0.48
% 0.33/0.48 thf(sy_c_Agent_Opi_OTau,type,
% 0.33/0.48 tau: pi > pi ).
% 0.33/0.48
% 0.33/0.48 thf(sy_c_Agent_Osubs,type,
% 0.33/0.48 subs: pi > name > name > pi ).
% 0.33/0.48
% 0.33/0.48 thf(sy_c_Agent_Osubst__name,type,
% 0.33/0.48 subst_name: name > name > name > name ).
% 0.33/0.48
% 0.33/0.48 thf(sy_c_If,type,
% 0.33/0.48 if:
% 0.33/0.48 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.33/0.48
% 0.33/0.48 thf(sy_c_Late__Semantics_OfreeRes_OOutputR,type,
% 0.33/0.48 late_OutputR: name > name > late_freeRes ).
% 0.33/0.48
% 0.33/0.48 thf(sy_c_Late__Semantics_OfreeRes_OTauR,type,
% 0.33/0.48 late_TauR: late_freeRes ).
% 0.33/0.48
% 0.33/0.48 thf(sy_c_Late__Semantics_OfreeRes_OfreeRes__rec,type,
% 0.33/0.48 late_freeRes_rec:
% 0.33/0.48 !>[T: $tType] : ( ( name > name > T ) > T > late_freeRes > T ) ).
% 0.33/0.48
% 0.33/0.48 thf(sy_c_Late__Semantics_Oresidual_OBoundR,type,
% 0.33/0.48 late_BoundR: late_subject > name > pi > late_residual ).
% 0.33/0.48
% 0.33/0.48 thf(sy_c_Late__Semantics_Oresidual_OFreeR,type,
% 0.33/0.48 late_FreeR: late_freeRes > pi > late_residual ).
% 0.33/0.48
% 0.33/0.48 thf(sy_c_Late__Semantics_Osubject_OBoundOutputS,type,
% 0.33/0.48 late_BoundOutputS: name > late_subject ).
% 0.33/0.48
% 0.33/0.48 thf(sy_c_Late__Semantics_Osubject_OInputS,type,
% 0.33/0.48 late_InputS: name > late_subject ).
% 0.33/0.48
% 0.33/0.48 thf(sy_c_Late__Semantics_Osubject_Osubject__rec,type,
% 0.33/0.48 late_subject_rec:
% 0.33/0.48 !>[T: $tType] : ( ( name > T ) > ( name > T ) > late_subject > T ) ).
% 0.33/0.48
% 0.33/0.48 thf(sy_c_Late__Semantics_Otransitions,type,
% 0.33/0.48 late_transitions: pi > late_residual > $o ).
% 0.33/0.48
% 0.33/0.48 thf(sy_c_Nominal_Oabs__fun,type,
% 0.33/0.48 abs_fun:
% 0.33/0.48 !>[X: $tType,A: $tType] : ( X > A > X > ( noption @ A ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(sy_c_Nominal_Ofresh,type,
% 0.33/0.48 fresh:
% 0.33/0.48 !>[X: $tType,A: $tType] : ( X > A > $o ) ).
% 0.33/0.48
% 0.33/0.48 thf(sy_c_Product__Type_OPair,type,
% 0.33/0.48 product_Pair:
% 0.33/0.48 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(sy_c_Product__Type_Ointernal__case__prod,type,
% 0.33/0.48 produc2004651681e_prod:
% 0.33/0.48 !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > ( product_prod @ A @ B ) > C ) ).
% 0.33/0.48
% 0.33/0.48 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod,type,
% 0.33/0.48 product_rec_prod:
% 0.33/0.48 !>[A: $tType,B: $tType,T: $tType] : ( ( A > B > T ) > ( product_prod @ A @ B ) > T ) ).
% 0.33/0.48
% 0.33/0.48 thf(sy_c_Rel_Oeqvt,type,
% 0.33/0.48 eqvt:
% 0.33/0.48 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > $o ) ).
% 0.33/0.48
% 0.33/0.48 thf(sy_c_Set_OCollect,type,
% 0.33/0.48 collect:
% 0.33/0.48 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(sy_c_Strong__Late__Sim_Oderivative,type,
% 0.33/0.48 strong2129052853vative: pi > pi > late_subject > name > ( set @ ( product_prod @ pi @ pi ) ) > $o ).
% 0.33/0.48
% 0.33/0.48 thf(sy_c_Strong__Late__Sim_Osimulation,type,
% 0.33/0.48 strong743114133lation: pi > ( set @ ( product_prod @ pi @ pi ) ) > pi > $o ).
% 0.33/0.48
% 0.33/0.48 thf(sy_c_member,type,
% 0.33/0.48 member:
% 0.33/0.48 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.33/0.48
% 0.33/0.48 thf(sy_v_P,type,
% 0.33/0.48 p: pi ).
% 0.33/0.48
% 0.33/0.48 thf(sy_v_PQR____,type,
% 0.33/0.48 pqr: pi ).
% 0.33/0.48
% 0.33/0.48 thf(sy_v_P_H____,type,
% 0.33/0.48 p2: pi ).
% 0.33/0.48
% 0.33/0.48 thf(sy_v_Q,type,
% 0.33/0.48 q: pi ).
% 0.33/0.48
% 0.33/0.48 thf(sy_v_QR____,type,
% 0.33/0.48 qr: pi ).
% 0.33/0.48
% 0.33/0.48 thf(sy_v_Q_H____,type,
% 0.33/0.48 q2: pi ).
% 0.33/0.48
% 0.33/0.48 thf(sy_v_R,type,
% 0.33/0.48 r: pi ).
% 0.33/0.48
% 0.33/0.48 thf(sy_v_Rel,type,
% 0.33/0.48 rel: set @ ( product_prod @ pi @ pi ) ).
% 0.33/0.48
% 0.33/0.48 thf(sy_v__092_060alpha_062____,type,
% 0.33/0.48 alpha: late_freeRes ).
% 0.33/0.48
% 0.33/0.48 thf(sy_v_a____,type,
% 0.33/0.48 a: name ).
% 0.33/0.48
% 0.33/0.48 thf(sy_v_x____,type,
% 0.33/0.48 x: name ).
% 0.33/0.48
% 0.33/0.48 thf(sy_v_y____,type,
% 0.33/0.48 y: name ).
% 0.33/0.48
% 0.33/0.48 % Relevant facts (256)
% 0.33/0.48 thf(fact_0_cClose2_Ohyps_I14_J,axiom,
% 0.33/0.48 alpha = late_TauR ).
% 0.33/0.48
% 0.33/0.48 % cClose2.hyps(14)
% 0.33/0.48 thf(fact_1_cClose2_Ohyps_I6_J,axiom,
% 0.33/0.48 x != y ).
% 0.33/0.48
% 0.33/0.48 % cClose2.hyps(6)
% 0.33/0.48 thf(fact_2_cClose2_Ohyps_I10_J,axiom,
% 0.33/0.48 y != a ).
% 0.33/0.48
% 0.33/0.48 % cClose2.hyps(10)
% 0.33/0.48 thf(fact_3_cClose2_Ohyps_I5_J,axiom,
% 0.33/0.48 x != a ).
% 0.33/0.48
% 0.33/0.48 % cClose2.hyps(5)
% 0.33/0.48 thf(fact_4_Ass,axiom,
% 0.33/0.48 ! [S: pi,T2: pi,U: pi] : ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( par @ ( par @ S @ T2 ) @ U ) @ ( par @ S @ ( par @ T2 @ U ) ) ) @ rel ) ).
% 0.33/0.48
% 0.33/0.48 % Ass
% 0.33/0.48 thf(fact_5_Res,axiom,
% 0.33/0.48 ! [S: pi,T2: pi,X2: name] :
% 0.33/0.48 ( ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ S @ T2 ) @ rel )
% 0.33/0.48 => ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( res @ X2 @ S ) @ ( res @ X2 @ T2 ) ) @ rel ) ) ).
% 0.33/0.48
% 0.33/0.48 % Res
% 0.33/0.48 thf(fact_6__092_060open_062_I_060_092_060nu_062y_062_IP_H_A_092_060parallel_062_AQ_H_091x_058_058_061y_093_J_A_092_060parallel_062_AR_M_A_060_092_060nu_062y_062_IP_H_A_092_060parallel_062_A_IQ_H_A_092_060parallel_062_AR_J_091x_058_058_061y_093_J_J_A_092_060in_062_ARel_092_060close_062,axiom,
% 0.33/0.48 member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( par @ ( res @ y @ ( par @ p2 @ ( subs @ q2 @ x @ y ) ) ) @ r ) @ ( res @ y @ ( par @ p2 @ ( subs @ ( par @ q2 @ r ) @ x @ y ) ) ) ) @ rel ).
% 0.33/0.48
% 0.33/0.48 % \<open>(<\<nu>y>(P' \<parallel> Q'[x::=y]) \<parallel> R, <\<nu>y>(P' \<parallel> (Q' \<parallel> R)[x::=y])) \<in> Rel\<close>
% 0.33/0.48 thf(fact_7__092_060open_062_IP_A_092_060parallel_062_AQ_J_A_092_060parallel_062_AR_A_092_060longmapsto_062_A_092_060tau_062_A_092_060prec_062_A_060_092_060nu_062y_062_IP_H_A_092_060parallel_062_AQ_H_091x_058_058_061y_093_J_A_092_060parallel_062_AR_092_060close_062,axiom,
% 0.33/0.48 late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_FreeR @ late_TauR @ ( par @ ( res @ y @ ( par @ p2 @ ( subs @ q2 @ x @ y ) ) ) @ r ) ) ).
% 0.33/0.48
% 0.33/0.48 % \<open>(P \<parallel> Q) \<parallel> R \<longmapsto> \<tau> \<prec> <\<nu>y>(P' \<parallel> Q'[x::=y]) \<parallel> R\<close>
% 0.33/0.48 thf(fact_8_Free_Ohyps,axiom,
% 0.33/0.48 late_transitions @ ( par @ p @ ( par @ q @ r ) ) @ ( late_FreeR @ alpha @ pqr ) ).
% 0.33/0.48
% 0.33/0.48 % Free.hyps
% 0.33/0.48 thf(fact_9__092_060open_062_I_060_092_060nu_062y_062_IP_H_A_092_060parallel_062_AQ_H_091x_058_058_061y_093_J_A_092_060parallel_062_AR_M_A_060_092_060nu_062y_062_IP_H_A_092_060parallel_062_AQ_H_091x_058_058_061y_093_A_092_060parallel_062_AR_J_J_A_092_060in_062_ARel_092_060close_062,axiom,
% 0.33/0.48 member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( par @ ( res @ y @ ( par @ p2 @ ( subs @ q2 @ x @ y ) ) ) @ r ) @ ( res @ y @ ( par @ p2 @ ( par @ ( subs @ q2 @ x @ y ) @ r ) ) ) ) @ rel ).
% 0.33/0.48
% 0.33/0.48 % \<open>(<\<nu>y>(P' \<parallel> Q'[x::=y]) \<parallel> R, <\<nu>y>(P' \<parallel> Q'[x::=y] \<parallel> R)) \<in> Rel\<close>
% 0.33/0.48 thf(fact_10__092_060open_062P_A_092_060parallel_062_AQ_A_092_060longmapsto_062_A_092_060tau_062_A_092_060prec_062_A_060_092_060nu_062y_062_IP_H_A_092_060parallel_062_AQ_H_091x_058_058_061y_093_J_092_060close_062,axiom,
% 0.33/0.48 late_transitions @ ( par @ p @ q ) @ ( late_FreeR @ late_TauR @ ( res @ y @ ( par @ p2 @ ( subs @ q2 @ x @ y ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % \<open>P \<parallel> Q \<longmapsto> \<tau> \<prec> <\<nu>y>(P' \<parallel> Q'[x::=y])\<close>
% 0.33/0.48 thf(fact_11_cClose2_Ohyps_I13_J,axiom,
% 0.33/0.48 fresh @ name @ pi @ y @ q ).
% 0.33/0.48
% 0.33/0.48 % cClose2.hyps(13)
% 0.33/0.48 thf(fact_12_cClose2_Ohyps_I12_J,axiom,
% 0.33/0.48 fresh @ name @ pi @ x @ q ).
% 0.33/0.48
% 0.33/0.48 % cClose2.hyps(12)
% 0.33/0.48 thf(fact_13_cClose2_Ohyps_I7_J,axiom,
% 0.33/0.48 fresh @ name @ pi @ x @ p2 ).
% 0.33/0.48
% 0.33/0.48 % cClose2.hyps(7)
% 0.33/0.48 thf(fact_14_cClose2_Ohyps_I8_J,axiom,
% 0.33/0.48 fresh @ name @ pi @ y @ p ).
% 0.33/0.48
% 0.33/0.48 % cClose2.hyps(8)
% 0.33/0.48 thf(fact_15_cClose2_Ohyps_I3_J,axiom,
% 0.33/0.48 fresh @ name @ pi @ x @ p ).
% 0.33/0.48
% 0.33/0.48 % cClose2.hyps(3)
% 0.33/0.48 thf(fact_16_cClose2_Ohyps_I9_J,axiom,
% 0.33/0.48 fresh @ name @ pi @ y @ ( par @ q @ r ) ).
% 0.33/0.48
% 0.33/0.48 % cClose2.hyps(9)
% 0.33/0.48 thf(fact_17_cClose2_Ohyps_I4_J,axiom,
% 0.33/0.48 fresh @ name @ pi @ x @ ( par @ q @ r ) ).
% 0.33/0.48
% 0.33/0.48 % cClose2.hyps(4)
% 0.33/0.48 thf(fact_18_simps_I9_J,axiom,
% 0.33/0.48 ! [X2: name,C2: name,D: name,P: pi] :
% 0.33/0.48 ( ( X2 != C2 )
% 0.33/0.48 => ( ( X2 != D )
% 0.33/0.48 => ( ( subs @ ( res @ X2 @ P ) @ C2 @ D )
% 0.33/0.48 = ( res @ X2 @ ( subs @ P @ C2 @ D ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % simps(9)
% 0.33/0.48 thf(fact_19_simps_I8_J,axiom,
% 0.33/0.48 ! [P: pi,Q: pi,C2: name,D: name] :
% 0.33/0.48 ( ( subs @ ( par @ P @ Q ) @ C2 @ D )
% 0.33/0.48 = ( par @ ( subs @ P @ C2 @ D ) @ ( subs @ Q @ C2 @ D ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % simps(8)
% 0.33/0.48 thf(fact_20_FreshExt,axiom,
% 0.33/0.48 ! [X2: name,S: pi,T2: pi,U: pi] :
% 0.33/0.48 ( ( fresh @ name @ pi @ X2 @ S )
% 0.33/0.48 => ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( res @ X2 @ ( par @ ( par @ S @ T2 ) @ U ) ) @ ( par @ S @ ( res @ X2 @ ( par @ T2 @ U ) ) ) ) @ rel ) ) ).
% 0.33/0.48
% 0.33/0.48 % FreshExt
% 0.33/0.48 thf(fact_21_FreshExt_H,axiom,
% 0.33/0.48 ! [X2: name,U: pi,S: pi,T2: pi] :
% 0.33/0.48 ( ( fresh @ name @ pi @ X2 @ U )
% 0.33/0.48 => ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( par @ ( res @ X2 @ ( par @ S @ T2 ) ) @ U ) @ ( res @ X2 @ ( par @ S @ ( par @ T2 @ U ) ) ) ) @ rel ) ) ).
% 0.33/0.48
% 0.33/0.48 % FreshExt'
% 0.33/0.48 thf(fact_22_Par1F,axiom,
% 0.33/0.48 ! [P: pi,Alpha: late_freeRes,P2: pi,Q: pi] :
% 0.33/0.48 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 0.33/0.48 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha @ ( par @ P2 @ Q ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % Par1F
% 0.33/0.48 thf(fact_23_Par2F,axiom,
% 0.33/0.48 ! [Q: pi,Alpha: late_freeRes,Q2: pi,P: pi] :
% 0.33/0.48 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 0.33/0.48 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha @ ( par @ P @ Q2 ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % Par2F
% 0.33/0.48 thf(fact_24_subst__identity,axiom,
% 0.33/0.48 ! [P: pi,A2: name] :
% 0.33/0.48 ( ( subs @ P @ A2 @ A2 )
% 0.33/0.48 = P ) ).
% 0.33/0.48
% 0.33/0.48 % subst_identity
% 0.33/0.48 thf(fact_25__092_060open_062x_A_092_060sharp_062_AR_092_060close_062,axiom,
% 0.33/0.48 fresh @ name @ pi @ x @ r ).
% 0.33/0.48
% 0.33/0.48 % \<open>x \<sharp> R\<close>
% 0.33/0.48 thf(fact_26__092_060open_062y_A_092_060sharp_062_AR_092_060close_062,axiom,
% 0.33/0.48 fresh @ name @ pi @ y @ r ).
% 0.33/0.48
% 0.33/0.48 % \<open>y \<sharp> R\<close>
% 0.33/0.48 thf(fact_27_prod_Oinject,axiom,
% 0.33/0.48 ! [A: $tType,B: $tType,X1: A,X22: B,Y1: A,Y2: B] :
% 0.33/0.48 ( ( ( product_Pair @ A @ B @ X1 @ X22 )
% 0.33/0.48 = ( product_Pair @ A @ B @ Y1 @ Y2 ) )
% 0.33/0.48 = ( ( X1 = Y1 )
% 0.33/0.48 & ( X22 = Y2 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % prod.inject
% 0.33/0.48 thf(fact_28_old_Oprod_Oinject,axiom,
% 0.33/0.48 ! [A: $tType,B: $tType,A2: A,B2: B,A3: A,B3: B] :
% 0.33/0.48 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 0.33/0.48 = ( product_Pair @ A @ B @ A3 @ B3 ) )
% 0.33/0.48 = ( ( A2 = A3 )
% 0.33/0.48 & ( B2 = B3 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % old.prod.inject
% 0.33/0.48 thf(fact_29_cClose2_Ohyps_I11_J,axiom,
% 0.33/0.48 fresh @ name @ pi @ y @ qr ).
% 0.33/0.48
% 0.33/0.48 % cClose2.hyps(11)
% 0.33/0.48 thf(fact_30_pi_Ofresh_I8_J,axiom,
% 0.33/0.48 ! [A2: name,X22: pi,X1: pi] :
% 0.33/0.48 ( ( fresh @ name @ pi @ A2 @ ( par @ X22 @ X1 ) )
% 0.33/0.48 = ( ( fresh @ name @ pi @ A2 @ X22 )
% 0.33/0.48 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % pi.fresh(8)
% 0.33/0.48 thf(fact_31_substTrans,axiom,
% 0.33/0.48 ! [B2: name,P: pi,A2: name,C2: name] :
% 0.33/0.48 ( ( fresh @ name @ pi @ B2 @ P )
% 0.33/0.48 => ( ( subs @ ( subs @ P @ A2 @ B2 ) @ B2 @ C2 )
% 0.33/0.48 = ( subs @ P @ A2 @ C2 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % substTrans
% 0.33/0.48 thf(fact_32_name__exists__fresh,axiom,
% 0.33/0.48 ! [A: $tType] :
% 0.33/0.48 ( ( fs_name @ A )
% 0.33/0.48 => ! [X2: A] :
% 0.33/0.48 ~ ! [C3: name] :
% 0.33/0.48 ~ ( fresh @ name @ A @ C3 @ X2 ) ) ).
% 0.33/0.48
% 0.33/0.48 % name_exists_fresh
% 0.33/0.48 thf(fact_33_freshRes,axiom,
% 0.33/0.48 ! [A2: name,P: pi] : ( fresh @ name @ pi @ A2 @ ( res @ A2 @ P ) ) ).
% 0.33/0.48
% 0.33/0.48 % freshRes
% 0.33/0.48 thf(fact_34_fresh__fact2,axiom,
% 0.33/0.48 ! [A2: name,B2: name,P: pi] :
% 0.33/0.48 ( ( A2 != B2 )
% 0.33/0.48 => ( fresh @ name @ pi @ A2 @ ( subs @ P @ A2 @ B2 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % fresh_fact2
% 0.33/0.48 thf(fact_35_fresh__fact1,axiom,
% 0.33/0.48 ! [A2: name,P: pi,C2: name,B2: name] :
% 0.33/0.48 ( ( fresh @ name @ pi @ A2 @ P )
% 0.33/0.48 => ( ( A2 != C2 )
% 0.33/0.48 => ( fresh @ name @ pi @ A2 @ ( subs @ P @ B2 @ C2 ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % fresh_fact1
% 0.33/0.48 thf(fact_36_forget,axiom,
% 0.33/0.48 ! [A2: name,P: pi,B2: name] :
% 0.33/0.48 ( ( fresh @ name @ pi @ A2 @ P )
% 0.33/0.48 => ( ( subs @ P @ A2 @ B2 )
% 0.33/0.48 = P ) ) ).
% 0.33/0.48
% 0.33/0.48 % forget
% 0.33/0.48 thf(fact_37_freshFreeDerivative_I2_J,axiom,
% 0.33/0.48 ! [P: pi,Alpha: late_freeRes,P2: pi,Y: name] :
% 0.33/0.48 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 0.33/0.48 => ( ( fresh @ name @ pi @ Y @ P )
% 0.33/0.48 => ( fresh @ name @ pi @ Y @ P2 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % freshFreeDerivative(2)
% 0.33/0.48 thf(fact_38_substRes3,axiom,
% 0.33/0.48 ! [B2: name,P: pi,A2: name] :
% 0.33/0.48 ( ( fresh @ name @ pi @ B2 @ P )
% 0.33/0.48 => ( ( subs @ ( res @ A2 @ P ) @ A2 @ B2 )
% 0.33/0.48 = ( res @ B2 @ ( subs @ P @ A2 @ B2 ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % substRes3
% 0.33/0.48 thf(fact_39_substRes2,axiom,
% 0.33/0.48 ! [B2: name,P: pi,A2: name] :
% 0.33/0.48 ( ( fresh @ name @ pi @ B2 @ P )
% 0.33/0.48 => ( ( res @ A2 @ P )
% 0.33/0.48 = ( res @ B2 @ ( subs @ P @ A2 @ B2 ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % substRes2
% 0.33/0.48 thf(fact_40_old_Oprod_Oinducts,axiom,
% 0.33/0.48 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,Prod: product_prod @ A @ B] :
% 0.33/0.48 ( ! [A4: A,B4: B] : ( P @ ( product_Pair @ A @ B @ A4 @ B4 ) )
% 0.33/0.48 => ( P @ Prod ) ) ).
% 0.33/0.48
% 0.33/0.48 % old.prod.inducts
% 0.33/0.48 thf(fact_41_old_Oprod_Oexhaust,axiom,
% 0.33/0.48 ! [A: $tType,B: $tType,Y: product_prod @ A @ B] :
% 0.33/0.48 ~ ! [A4: A,B4: B] :
% 0.33/0.48 ( Y
% 0.33/0.48 != ( product_Pair @ A @ B @ A4 @ B4 ) ) ).
% 0.33/0.48
% 0.33/0.48 % old.prod.exhaust
% 0.33/0.48 thf(fact_42_prod__induct7,axiom,
% 0.33/0.48 ! [G: $tType,F: $tType,E: $tType,D2: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) ) ) ) > $o,X2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) ) )] :
% 0.33/0.48 ( ! [A4: A,B4: B,C3: C,D3: D2,E2: E,F2: F,G2: G] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) @ C3 @ ( product_Pair @ D2 @ ( product_prod @ E @ ( product_prod @ F @ G ) ) @ D3 @ ( product_Pair @ E @ ( product_prod @ F @ G ) @ E2 @ ( product_Pair @ F @ G @ F2 @ G2 ) ) ) ) ) ) )
% 0.33/0.48 => ( P @ X2 ) ) ).
% 0.33/0.48
% 0.33/0.48 % prod_induct7
% 0.33/0.48 thf(fact_43_prod__induct6,axiom,
% 0.33/0.48 ! [F: $tType,E: $tType,D2: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E @ F ) ) ) ) ) > $o,X2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E @ F ) ) ) )] :
% 0.33/0.48 ( ! [A4: A,B4: B,C3: C,D3: D2,E2: E,F2: F] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E @ F ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E @ F ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D2 @ ( product_prod @ E @ F ) ) @ C3 @ ( product_Pair @ D2 @ ( product_prod @ E @ F ) @ D3 @ ( product_Pair @ E @ F @ E2 @ F2 ) ) ) ) ) )
% 0.33/0.48 => ( P @ X2 ) ) ).
% 0.33/0.48
% 0.33/0.48 % prod_induct6
% 0.33/0.48 thf(fact_44_prod__induct5,axiom,
% 0.33/0.48 ! [E: $tType,D2: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ E ) ) ) ) > $o,X2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ E ) ) )] :
% 0.33/0.48 ( ! [A4: A,B4: B,C3: C,D3: D2,E2: E] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ E ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D2 @ E ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D2 @ E ) @ C3 @ ( product_Pair @ D2 @ E @ D3 @ E2 ) ) ) ) )
% 0.33/0.48 => ( P @ X2 ) ) ).
% 0.33/0.48
% 0.33/0.48 % prod_induct5
% 0.33/0.48 thf(fact_45_mem__Collect__eq,axiom,
% 0.33/0.48 ! [A: $tType,A2: A,P: A > $o] :
% 0.33/0.48 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 0.33/0.48 = ( P @ A2 ) ) ).
% 0.33/0.48
% 0.33/0.48 % mem_Collect_eq
% 0.33/0.48 thf(fact_46_Collect__mem__eq,axiom,
% 0.33/0.48 ! [A: $tType,A5: set @ A] :
% 0.33/0.48 ( ( collect @ A
% 0.33/0.48 @ ^ [X3: A] : ( member @ A @ X3 @ A5 ) )
% 0.33/0.48 = A5 ) ).
% 0.33/0.48
% 0.33/0.48 % Collect_mem_eq
% 0.33/0.48 thf(fact_47_Collect__cong,axiom,
% 0.33/0.48 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.33/0.48 ( ! [X4: A] :
% 0.33/0.48 ( ( P @ X4 )
% 0.33/0.48 = ( Q @ X4 ) )
% 0.33/0.48 => ( ( collect @ A @ P )
% 0.33/0.48 = ( collect @ A @ Q ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % Collect_cong
% 0.33/0.48 thf(fact_48_prod__induct4,axiom,
% 0.33/0.48 ! [D2: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D2 ) ) ) > $o,X2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D2 ) )] :
% 0.33/0.48 ( ! [A4: A,B4: B,C3: C,D3: D2] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D2 ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ D2 ) @ B4 @ ( product_Pair @ C @ D2 @ C3 @ D3 ) ) ) )
% 0.33/0.48 => ( P @ X2 ) ) ).
% 0.33/0.48
% 0.33/0.48 % prod_induct4
% 0.33/0.48 thf(fact_49_prod__induct3,axiom,
% 0.33/0.48 ! [C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ C ) ) > $o,X2: product_prod @ A @ ( product_prod @ B @ C )] :
% 0.33/0.48 ( ! [A4: A,B4: B,C3: C] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ C ) @ A4 @ ( product_Pair @ B @ C @ B4 @ C3 ) ) )
% 0.33/0.48 => ( P @ X2 ) ) ).
% 0.33/0.48
% 0.33/0.48 % prod_induct3
% 0.33/0.48 thf(fact_50_prod__cases7,axiom,
% 0.33/0.48 ! [A: $tType,B: $tType,C: $tType,D2: $tType,E: $tType,F: $tType,G: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) ) )] :
% 0.33/0.48 ~ ! [A4: A,B4: B,C3: C,D3: D2,E2: E,F2: F,G2: G] :
% 0.33/0.48 ( Y
% 0.33/0.48 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) @ C3 @ ( product_Pair @ D2 @ ( product_prod @ E @ ( product_prod @ F @ G ) ) @ D3 @ ( product_Pair @ E @ ( product_prod @ F @ G ) @ E2 @ ( product_Pair @ F @ G @ F2 @ G2 ) ) ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % prod_cases7
% 0.33/0.48 thf(fact_51_prod__cases6,axiom,
% 0.33/0.48 ! [A: $tType,B: $tType,C: $tType,D2: $tType,E: $tType,F: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E @ F ) ) ) )] :
% 0.33/0.48 ~ ! [A4: A,B4: B,C3: C,D3: D2,E2: E,F2: F] :
% 0.33/0.48 ( Y
% 0.33/0.48 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E @ F ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E @ F ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D2 @ ( product_prod @ E @ F ) ) @ C3 @ ( product_Pair @ D2 @ ( product_prod @ E @ F ) @ D3 @ ( product_Pair @ E @ F @ E2 @ F2 ) ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % prod_cases6
% 0.33/0.48 thf(fact_52_prod__cases5,axiom,
% 0.33/0.48 ! [A: $tType,B: $tType,C: $tType,D2: $tType,E: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ E ) ) )] :
% 0.33/0.48 ~ ! [A4: A,B4: B,C3: C,D3: D2,E2: E] :
% 0.33/0.48 ( Y
% 0.33/0.48 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ E ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D2 @ E ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D2 @ E ) @ C3 @ ( product_Pair @ D2 @ E @ D3 @ E2 ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % prod_cases5
% 0.33/0.48 thf(fact_53_prod__cases4,axiom,
% 0.33/0.48 ! [A: $tType,B: $tType,C: $tType,D2: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D2 ) )] :
% 0.33/0.48 ~ ! [A4: A,B4: B,C3: C,D3: D2] :
% 0.33/0.48 ( Y
% 0.33/0.48 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D2 ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ D2 ) @ B4 @ ( product_Pair @ C @ D2 @ C3 @ D3 ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % prod_cases4
% 0.33/0.48 thf(fact_54_prod__cases3,axiom,
% 0.33/0.48 ! [A: $tType,B: $tType,C: $tType,Y: product_prod @ A @ ( product_prod @ B @ C )] :
% 0.33/0.48 ~ ! [A4: A,B4: B,C3: C] :
% 0.33/0.48 ( Y
% 0.33/0.48 != ( product_Pair @ A @ ( product_prod @ B @ C ) @ A4 @ ( product_Pair @ B @ C @ B4 @ C3 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % prod_cases3
% 0.33/0.48 thf(fact_55_Pair__inject,axiom,
% 0.33/0.48 ! [A: $tType,B: $tType,A2: A,B2: B,A3: A,B3: B] :
% 0.33/0.48 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 0.33/0.48 = ( product_Pair @ A @ B @ A3 @ B3 ) )
% 0.33/0.48 => ~ ( ( A2 = A3 )
% 0.33/0.48 => ( B2 != B3 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % Pair_inject
% 0.33/0.48 thf(fact_56_prod__cases,axiom,
% 0.33/0.48 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,P3: product_prod @ A @ B] :
% 0.33/0.48 ( ! [A4: A,B4: B] : ( P @ ( product_Pair @ A @ B @ A4 @ B4 ) )
% 0.33/0.48 => ( P @ P3 ) ) ).
% 0.33/0.48
% 0.33/0.48 % prod_cases
% 0.33/0.48 thf(fact_57_surj__pair,axiom,
% 0.33/0.48 ! [A: $tType,B: $tType,P3: product_prod @ A @ B] :
% 0.33/0.48 ? [X4: A,Y3: B] :
% 0.33/0.48 ( P3
% 0.33/0.48 = ( product_Pair @ A @ B @ X4 @ Y3 ) ) ).
% 0.33/0.48
% 0.33/0.48 % surj_pair
% 0.33/0.48 thf(fact_58_pi_Oinject_I7_J,axiom,
% 0.33/0.48 ! [X22: pi,X1: pi,Y2: pi,Y1: pi] :
% 0.33/0.48 ( ( ( par @ X22 @ X1 )
% 0.33/0.48 = ( par @ Y2 @ Y1 ) )
% 0.33/0.48 = ( ( X22 = Y2 )
% 0.33/0.48 & ( X1 = Y1 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % pi.inject(7)
% 0.33/0.48 thf(fact_59_residual_Oinject_I2_J,axiom,
% 0.33/0.48 ! [X22: late_freeRes,X1: pi,Y2: late_freeRes,Y1: pi] :
% 0.33/0.48 ( ( ( late_FreeR @ X22 @ X1 )
% 0.33/0.48 = ( late_FreeR @ Y2 @ Y1 ) )
% 0.33/0.48 = ( ( X22 = Y2 )
% 0.33/0.48 & ( X1 = Y1 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % residual.inject(2)
% 0.33/0.48 thf(fact_60_pi_Odistinct_I85_J,axiom,
% 0.33/0.48 ! [Pi1: pi,Pi2: pi,Name: name,Pi: pi] :
% 0.33/0.48 ( ( par @ Pi1 @ Pi2 )
% 0.33/0.48 != ( res @ Name @ Pi ) ) ).
% 0.33/0.48
% 0.33/0.48 % pi.distinct(85)
% 0.33/0.48 thf(fact_61_cClose2_Ohyps_I2_J,axiom,
% 0.33/0.48 late_transitions @ ( par @ q @ r ) @ ( late_BoundR @ ( late_InputS @ a ) @ x @ qr ) ).
% 0.33/0.48
% 0.33/0.48 % cClose2.hyps(2)
% 0.33/0.48 thf(fact_62_fresh__prod,axiom,
% 0.33/0.48 ! [A: $tType,X: $tType,B: $tType,A2: X,X2: A,Y: B] :
% 0.33/0.48 ( ( fresh @ X @ ( product_prod @ A @ B ) @ A2 @ ( product_Pair @ A @ B @ X2 @ Y ) )
% 0.33/0.48 = ( ( fresh @ X @ A @ A2 @ X2 )
% 0.33/0.48 & ( fresh @ X @ B @ A2 @ Y ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % fresh_prod
% 0.33/0.48 thf(fact_63_cClose2_Ohyps_I1_J,axiom,
% 0.33/0.48 late_transitions @ p @ ( late_BoundR @ ( late_BoundOutputS @ a ) @ y @ p2 ) ).
% 0.33/0.48
% 0.33/0.48 % cClose2.hyps(1)
% 0.33/0.48 thf(fact_64_cPar1_Ohyps,axiom,
% 0.33/0.48 late_transitions @ q @ ( late_BoundR @ ( late_InputS @ a ) @ x @ q2 ) ).
% 0.33/0.48
% 0.33/0.48 % cPar1.hyps
% 0.33/0.48 thf(fact_65_old_Oprod_Orec,axiom,
% 0.33/0.48 ! [A: $tType,T: $tType,B: $tType,F1: A > B > T,A2: A,B2: B] :
% 0.33/0.48 ( ( product_rec_prod @ A @ B @ T @ F1 @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 0.33/0.48 = ( F1 @ A2 @ B2 ) ) ).
% 0.33/0.48
% 0.33/0.48 % old.prod.rec
% 0.33/0.48 thf(fact_66_fresh__prodD_I2_J,axiom,
% 0.33/0.48 ! [B: $tType,A: $tType,C: $tType,A2: A,X2: B,Y: C] :
% 0.33/0.48 ( ( fresh @ A @ ( product_prod @ B @ C ) @ A2 @ ( product_Pair @ B @ C @ X2 @ Y ) )
% 0.33/0.48 => ( fresh @ A @ C @ A2 @ Y ) ) ).
% 0.33/0.48
% 0.33/0.48 % fresh_prodD(2)
% 0.33/0.48 thf(fact_67_fresh__prodD_I1_J,axiom,
% 0.33/0.48 ! [C: $tType,A: $tType,B: $tType,A2: A,X2: B,Y: C] :
% 0.33/0.48 ( ( fresh @ A @ ( product_prod @ B @ C ) @ A2 @ ( product_Pair @ B @ C @ X2 @ Y ) )
% 0.33/0.48 => ( fresh @ A @ B @ A2 @ X2 ) ) ).
% 0.33/0.48
% 0.33/0.48 % fresh_prodD(1)
% 0.33/0.48 thf(fact_68_freeRes_Orecs_I2_J,axiom,
% 0.33/0.48 ! [T: $tType,P: T > $o,F1: name > name > T,F22: T] :
% 0.33/0.48 ( ! [X12: name,X23: name] : ( P @ ( F1 @ X12 @ X23 ) )
% 0.33/0.48 => ( ( P @ F22 )
% 0.33/0.48 => ( ( late_freeRes_rec @ T @ F1 @ F22 @ late_TauR )
% 0.33/0.48 = F22 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % freeRes.recs(2)
% 0.33/0.48 thf(fact_69_resOutputTauTrans,axiom,
% 0.33/0.48 ! [X2: name,A2: name,B2: name,P: pi,P2: pi] :
% 0.33/0.48 ~ ( late_transitions @ ( res @ X2 @ ( output @ A2 @ B2 @ P ) ) @ ( late_FreeR @ late_TauR @ P2 ) ) ).
% 0.33/0.48
% 0.33/0.48 % resOutputTauTrans
% 0.33/0.48 thf(fact_70_subject_Ofresh_I1_J,axiom,
% 0.33/0.48 ! [A2: name,X1: name] :
% 0.33/0.48 ( ( fresh @ name @ late_subject @ A2 @ ( late_InputS @ X1 ) )
% 0.33/0.48 = ( fresh @ name @ name @ A2 @ X1 ) ) ).
% 0.33/0.48
% 0.33/0.48 % subject.fresh(1)
% 0.33/0.48 thf(fact_71_subject_Ofresh_I2_J,axiom,
% 0.33/0.48 ! [A2: name,X1: name] :
% 0.33/0.48 ( ( fresh @ name @ late_subject @ A2 @ ( late_BoundOutputS @ X1 ) )
% 0.33/0.48 = ( fresh @ name @ name @ A2 @ X1 ) ) ).
% 0.33/0.48
% 0.33/0.48 % subject.fresh(2)
% 0.33/0.48 thf(fact_72_Late__Semantics_Osubject_Oinject_I2_J,axiom,
% 0.33/0.48 ! [X1: name,Y1: name] :
% 0.33/0.48 ( ( ( late_BoundOutputS @ X1 )
% 0.33/0.48 = ( late_BoundOutputS @ Y1 ) )
% 0.33/0.48 = ( X1 = Y1 ) ) ).
% 0.33/0.48
% 0.33/0.48 % Late_Semantics.subject.inject(2)
% 0.33/0.48 thf(fact_73_freeRes_Ofresh_I2_J,axiom,
% 0.33/0.48 ! [A2: name] : ( fresh @ name @ late_freeRes @ A2 @ late_TauR ) ).
% 0.33/0.48
% 0.33/0.48 % freeRes.fresh(2)
% 0.33/0.48 thf(fact_74_residual_Ofresh_I2_J,axiom,
% 0.33/0.48 ! [A2: name,X22: late_freeRes,X1: pi] :
% 0.33/0.48 ( ( fresh @ name @ late_residual @ A2 @ ( late_FreeR @ X22 @ X1 ) )
% 0.33/0.48 = ( ( fresh @ name @ late_freeRes @ A2 @ X22 )
% 0.33/0.48 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % residual.fresh(2)
% 0.33/0.48 thf(fact_75_pi_Ofresh_I2_J,axiom,
% 0.33/0.48 ! [A2: name,X32: name,X22: name,X1: pi] :
% 0.33/0.48 ( ( fresh @ name @ pi @ A2 @ ( output @ X32 @ X22 @ X1 ) )
% 0.33/0.48 = ( ( fresh @ name @ name @ A2 @ X32 )
% 0.33/0.48 & ( fresh @ name @ name @ A2 @ X22 )
% 0.33/0.48 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % pi.fresh(2)
% 0.33/0.48 thf(fact_76_pi_Oinject_I1_J,axiom,
% 0.33/0.48 ! [X32: name,X22: name,X1: pi,Y32: name,Y2: name,Y1: pi] :
% 0.33/0.48 ( ( ( output @ X32 @ X22 @ X1 )
% 0.33/0.48 = ( output @ Y32 @ Y2 @ Y1 ) )
% 0.33/0.48 = ( ( X32 = Y32 )
% 0.33/0.48 & ( X22 = Y2 )
% 0.33/0.48 & ( X1 = Y1 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % pi.inject(1)
% 0.33/0.48 thf(fact_77_Late__Semantics_Osubject_Odistinct_I1_J,axiom,
% 0.33/0.48 ! [Name2: name,Name: name] :
% 0.33/0.48 ( ( late_InputS @ Name2 )
% 0.33/0.48 != ( late_BoundOutputS @ Name ) ) ).
% 0.33/0.48
% 0.33/0.48 % Late_Semantics.subject.distinct(1)
% 0.33/0.48 thf(fact_78_subject_Oinducts,axiom,
% 0.33/0.48 ! [P: late_subject > $o,Subject: late_subject] :
% 0.33/0.48 ( ! [Name3: name] : ( P @ ( late_InputS @ Name3 ) )
% 0.33/0.48 => ( ! [Name3: name] : ( P @ ( late_BoundOutputS @ Name3 ) )
% 0.33/0.48 => ( P @ Subject ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % subject.inducts
% 0.33/0.48 thf(fact_79_outputBoundTrans,axiom,
% 0.33/0.48 ! [A2: name,B2: name,P: pi,C2: late_subject,X2: name,P2: pi] :
% 0.33/0.48 ~ ( late_transitions @ ( output @ A2 @ B2 @ P ) @ ( late_BoundR @ C2 @ X2 @ P2 ) ) ).
% 0.33/0.48
% 0.33/0.48 % outputBoundTrans
% 0.33/0.48 thf(fact_80_subject_Ostrong__induct_H,axiom,
% 0.33/0.48 ! [N: $tType,P: N > late_subject > $o,Z: N,Subject: late_subject] :
% 0.33/0.48 ( ! [Name3: name,Z2: N] : ( P @ Z2 @ ( late_InputS @ Name3 ) )
% 0.33/0.48 => ( ! [Name3: name,Z2: N] : ( P @ Z2 @ ( late_BoundOutputS @ Name3 ) )
% 0.33/0.48 => ( P @ Z @ Subject ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % subject.strong_induct'
% 0.33/0.48 thf(fact_81_subject_Ostrong__inducts,axiom,
% 0.33/0.48 ! [A: $tType,P: A > late_subject > $o,Z: A,Subject: late_subject] :
% 0.33/0.48 ( ! [Name3: name,Z2: A] : ( P @ Z2 @ ( late_InputS @ Name3 ) )
% 0.33/0.48 => ( ! [Name3: name,Z2: A] : ( P @ Z2 @ ( late_BoundOutputS @ Name3 ) )
% 0.33/0.48 => ( P @ Z @ Subject ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % subject.strong_inducts
% 0.33/0.48 thf(fact_82_resOutputInputTrans,axiom,
% 0.33/0.48 ! [X2: name,A2: name,B2: name,P: pi,C2: name,Y: name,P2: pi] :
% 0.33/0.48 ~ ( late_transitions @ ( res @ X2 @ ( output @ A2 @ B2 @ P ) ) @ ( late_BoundR @ ( late_InputS @ C2 ) @ Y @ P2 ) ) ).
% 0.33/0.48
% 0.33/0.48 % resOutputInputTrans
% 0.33/0.48 thf(fact_83_Late__Semantics_OResB,axiom,
% 0.33/0.48 ! [P: pi,A2: late_subject,X2: name,P2: pi,Y: name] :
% 0.33/0.48 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P2 ) )
% 0.33/0.48 => ( ( fresh @ name @ late_subject @ Y @ A2 )
% 0.33/0.48 => ( ( Y != X2 )
% 0.33/0.48 => ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A2 @ X2 @ ( res @ Y @ P2 ) ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % Late_Semantics.ResB
% 0.33/0.48 thf(fact_84_freshBoundDerivative_I1_J,axiom,
% 0.33/0.48 ! [P: pi,A2: late_subject,X2: name,P2: pi,Y: name] :
% 0.33/0.48 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P2 ) )
% 0.33/0.48 => ( ( fresh @ name @ pi @ Y @ P )
% 0.33/0.48 => ( fresh @ name @ late_subject @ Y @ A2 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % freshBoundDerivative(1)
% 0.33/0.48 thf(fact_85_outputFreshTrans,axiom,
% 0.33/0.48 ! [A2: name,B2: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 0.33/0.48 ( ( late_transitions @ ( output @ A2 @ B2 @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 0.33/0.48 => ~ ( ( fresh @ name @ late_freeRes @ A2 @ Alpha )
% 0.33/0.48 | ( fresh @ name @ late_freeRes @ B2 @ Alpha ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % outputFreshTrans
% 0.33/0.48 thf(fact_86_residual_Odistinct_I1_J,axiom,
% 0.33/0.48 ! [Subject: late_subject,Name2: name,Pi3: pi,FreeRes: late_freeRes,Pi: pi] :
% 0.33/0.48 ( ( late_BoundR @ Subject @ Name2 @ Pi3 )
% 0.33/0.48 != ( late_FreeR @ FreeRes @ Pi ) ) ).
% 0.33/0.48
% 0.33/0.48 % residual.distinct(1)
% 0.33/0.48 thf(fact_87_residual_Oinducts,axiom,
% 0.33/0.48 ! [P: late_residual > $o,Residual: late_residual] :
% 0.33/0.48 ( ! [Subject2: late_subject,Name3: name,Pi4: pi] : ( P @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) )
% 0.33/0.48 => ( ! [FreeRes2: late_freeRes,Pi4: pi] : ( P @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 0.33/0.48 => ( P @ Residual ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % residual.inducts
% 0.33/0.48 thf(fact_88_pi_Odistinct_I29_J,axiom,
% 0.33/0.48 ! [Name1: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 0.33/0.48 ( ( output @ Name1 @ Name22 @ Pi3 )
% 0.33/0.48 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.33/0.48
% 0.33/0.48 % pi.distinct(29)
% 0.33/0.48 thf(fact_89_pi_Odistinct_I31_J,axiom,
% 0.33/0.48 ! [Name1: name,Name22: name,Pi3: pi,Name: name,Pi: pi] :
% 0.33/0.48 ( ( output @ Name1 @ Name22 @ Pi3 )
% 0.33/0.48 != ( res @ Name @ Pi ) ) ).
% 0.33/0.48
% 0.33/0.48 % pi.distinct(31)
% 0.33/0.48 thf(fact_90_parCasesB_H,axiom,
% 0.33/0.48 ! [P: pi,Q: pi,B2: late_subject,Y: name,P2: pi] :
% 0.33/0.48 ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ B2 @ Y @ P2 ) )
% 0.33/0.48 => ( ! [P4: pi,A4: late_subject,X4: name,P5: pi,Q3: pi] :
% 0.33/0.48 ( ( ( par @ P @ Q )
% 0.33/0.48 = ( par @ P4 @ Q3 ) )
% 0.33/0.48 => ( ( ( late_BoundR @ B2 @ Y @ P2 )
% 0.33/0.48 = ( late_BoundR @ A4 @ X4 @ ( par @ P5 @ Q3 ) ) )
% 0.33/0.48 => ( ( late_transitions @ P4 @ ( late_BoundR @ A4 @ X4 @ P5 ) )
% 0.33/0.48 => ( ( fresh @ name @ pi @ X4 @ P4 )
% 0.33/0.48 => ( ( fresh @ name @ pi @ X4 @ Q3 )
% 0.33/0.48 => ~ ( fresh @ name @ late_subject @ X4 @ A4 ) ) ) ) ) )
% 0.33/0.48 => ~ ! [Q3: pi,A4: late_subject,X4: name,Q4: pi,P4: pi] :
% 0.33/0.48 ( ( ( par @ P @ Q )
% 0.33/0.48 = ( par @ P4 @ Q3 ) )
% 0.33/0.48 => ( ( ( late_BoundR @ B2 @ Y @ P2 )
% 0.33/0.48 = ( late_BoundR @ A4 @ X4 @ ( par @ P4 @ Q4 ) ) )
% 0.33/0.48 => ( ( late_transitions @ Q3 @ ( late_BoundR @ A4 @ X4 @ Q4 ) )
% 0.33/0.48 => ( ( fresh @ name @ pi @ X4 @ P4 )
% 0.33/0.48 => ( ( fresh @ name @ pi @ X4 @ Q3 )
% 0.33/0.48 => ~ ( fresh @ name @ late_subject @ X4 @ A4 ) ) ) ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % parCasesB'
% 0.33/0.48 thf(fact_91_transitions_OPar1B,axiom,
% 0.33/0.48 ! [P: pi,A2: late_subject,X2: name,P2: pi,Q: pi] :
% 0.33/0.48 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P2 ) )
% 0.33/0.48 => ( ( fresh @ name @ pi @ X2 @ P )
% 0.33/0.48 => ( ( fresh @ name @ pi @ X2 @ Q )
% 0.33/0.48 => ( ( fresh @ name @ late_subject @ X2 @ A2 )
% 0.33/0.48 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X2 @ ( par @ P2 @ Q ) ) ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % transitions.Par1B
% 0.33/0.48 thf(fact_92_transitions_OPar2B,axiom,
% 0.33/0.48 ! [Q: pi,A2: late_subject,X2: name,Q2: pi,P: pi] :
% 0.33/0.48 ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X2 @ Q2 ) )
% 0.33/0.48 => ( ( fresh @ name @ pi @ X2 @ P )
% 0.33/0.48 => ( ( fresh @ name @ pi @ X2 @ Q )
% 0.33/0.48 => ( ( fresh @ name @ late_subject @ X2 @ A2 )
% 0.33/0.48 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X2 @ ( par @ P @ Q2 ) ) ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % transitions.Par2B
% 0.33/0.48 thf(fact_93_transitions_OResB,axiom,
% 0.33/0.48 ! [P: pi,A2: late_subject,X2: name,P2: pi,Y: name] :
% 0.33/0.48 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P2 ) )
% 0.33/0.48 => ( ( fresh @ name @ late_subject @ Y @ A2 )
% 0.33/0.48 => ( ( Y != X2 )
% 0.33/0.48 => ( ( fresh @ name @ pi @ X2 @ P )
% 0.33/0.48 => ( ( fresh @ name @ late_subject @ X2 @ A2 )
% 0.33/0.48 => ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A2 @ X2 @ ( res @ Y @ P2 ) ) ) ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % transitions.ResB
% 0.33/0.48 thf(fact_94_freshResidual,axiom,
% 0.33/0.48 ! [P: pi,Rs: late_residual,X2: name] :
% 0.33/0.48 ( ( late_transitions @ P @ Rs )
% 0.33/0.48 => ( ( fresh @ name @ pi @ X2 @ P )
% 0.33/0.48 => ( fresh @ name @ late_residual @ X2 @ Rs ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % freshResidual
% 0.33/0.48 thf(fact_95_freshBoundDerivative_I2_J,axiom,
% 0.33/0.48 ! [P: pi,A2: late_subject,X2: name,P2: pi,Y: name] :
% 0.33/0.48 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P2 ) )
% 0.33/0.48 => ( ( fresh @ name @ pi @ Y @ P )
% 0.33/0.48 => ( ( Y != X2 )
% 0.33/0.48 => ( fresh @ name @ pi @ Y @ P2 ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % freshBoundDerivative(2)
% 0.33/0.48 thf(fact_96_residual_Ostrong__inducts,axiom,
% 0.33/0.48 ! [A: $tType] :
% 0.33/0.48 ( ( fs_name @ A )
% 0.33/0.48 => ! [P: A > late_residual > $o,Z: A,Residual: late_residual] :
% 0.33/0.48 ( ! [Subject2: late_subject,Name3: name,Pi4: pi,Z2: A] :
% 0.33/0.48 ( ( fresh @ name @ A @ Name3 @ Z2 )
% 0.33/0.48 => ( ( fresh @ name @ late_subject @ Name3 @ Subject2 )
% 0.33/0.48 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) ) ) )
% 0.33/0.48 => ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: A] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 0.33/0.48 => ( P @ Z @ Residual ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % residual.strong_inducts
% 0.33/0.48 thf(fact_97_residual_Ostrong__induct,axiom,
% 0.33/0.48 ! [N: $tType] :
% 0.33/0.48 ( ( fs_name @ N )
% 0.33/0.48 => ! [P: N > late_residual > $o,Z: N,Residual: late_residual] :
% 0.33/0.48 ( ! [Subject2: late_subject,Name3: name,Pi4: pi,Z2: N] :
% 0.33/0.48 ( ( fresh @ name @ N @ Name3 @ Z2 )
% 0.33/0.48 => ( ( fresh @ name @ late_subject @ Name3 @ Subject2 )
% 0.33/0.48 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) ) ) )
% 0.33/0.48 => ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: N] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 0.33/0.48 => ( P @ Z @ Residual ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % residual.strong_induct
% 0.33/0.48 thf(fact_98_resTrans_I1_J,axiom,
% 0.33/0.48 ! [X2: name,B2: name,P: pi,Rs: late_residual] :
% 0.33/0.48 ~ ( late_transitions @ ( res @ X2 @ ( output @ X2 @ B2 @ P ) ) @ Rs ) ).
% 0.33/0.48
% 0.33/0.48 % resTrans(1)
% 0.33/0.48 thf(fact_99_Late__Semantics_OClose1,axiom,
% 0.33/0.48 ! [P: pi,A2: name,X2: name,P2: pi,Q: pi,Y: name,Q2: pi] :
% 0.33/0.48 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P2 ) )
% 0.33/0.48 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y @ Q2 ) )
% 0.33/0.48 => ( ( fresh @ name @ pi @ Y @ P )
% 0.33/0.48 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ ( subs @ P2 @ X2 @ Y ) @ Q2 ) ) ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % Late_Semantics.Close1
% 0.33/0.48 thf(fact_100_Late__Semantics_OClose2,axiom,
% 0.33/0.48 ! [P: pi,A2: name,Y: name,P2: pi,Q: pi,X2: name,Q2: pi] :
% 0.33/0.48 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y @ P2 ) )
% 0.33/0.48 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ Q2 ) )
% 0.33/0.48 => ( ( fresh @ name @ pi @ Y @ Q )
% 0.33/0.48 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ P2 @ ( subs @ Q2 @ X2 @ Y ) ) ) ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % Late_Semantics.Close2
% 0.33/0.48 thf(fact_101_transitions_OClose1,axiom,
% 0.33/0.48 ! [P: pi,A2: name,X2: name,P2: pi,Q: pi,Y: name,Q2: pi] :
% 0.33/0.48 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P2 ) )
% 0.33/0.48 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y @ Q2 ) )
% 0.33/0.48 => ( ( fresh @ name @ pi @ X2 @ P )
% 0.33/0.48 => ( ( fresh @ name @ pi @ X2 @ Q )
% 0.33/0.48 => ( ( fresh @ name @ pi @ Y @ P )
% 0.33/0.48 => ( ( fresh @ name @ pi @ Y @ Q )
% 0.33/0.48 => ( ( X2 != A2 )
% 0.33/0.48 => ( ( fresh @ name @ pi @ X2 @ Q2 )
% 0.33/0.48 => ( ( Y != A2 )
% 0.33/0.48 => ( ( fresh @ name @ pi @ Y @ P2 )
% 0.33/0.48 => ( ( X2 != Y )
% 0.33/0.48 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ ( subs @ P2 @ X2 @ Y ) @ Q2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % transitions.Close1
% 0.33/0.48 thf(fact_102_transitions_OClose2,axiom,
% 0.33/0.48 ! [P: pi,A2: name,Y: name,P2: pi,Q: pi,X2: name,Q2: pi] :
% 0.33/0.48 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y @ P2 ) )
% 0.33/0.48 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ Q2 ) )
% 0.33/0.48 => ( ( fresh @ name @ pi @ X2 @ P )
% 0.33/0.48 => ( ( fresh @ name @ pi @ X2 @ Q )
% 0.33/0.48 => ( ( fresh @ name @ pi @ Y @ P )
% 0.33/0.48 => ( ( fresh @ name @ pi @ Y @ Q )
% 0.33/0.48 => ( ( X2 != A2 )
% 0.33/0.48 => ( ( fresh @ name @ pi @ X2 @ P2 )
% 0.33/0.48 => ( ( Y != A2 )
% 0.33/0.48 => ( ( fresh @ name @ pi @ Y @ Q2 )
% 0.33/0.48 => ( ( X2 != Y )
% 0.33/0.48 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ P2 @ ( subs @ Q2 @ X2 @ Y ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % transitions.Close2
% 0.33/0.48 thf(fact_103_resCasesF,axiom,
% 0.33/0.48 ! [X2: name,P: pi,Alpha: late_freeRes,XP: pi,F3: pi > $o] :
% 0.33/0.48 ( ( late_transitions @ ( res @ X2 @ P ) @ ( late_FreeR @ Alpha @ XP ) )
% 0.33/0.48 => ( ! [P5: pi] :
% 0.33/0.48 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P5 ) )
% 0.33/0.48 => ( ( fresh @ name @ late_freeRes @ X2 @ Alpha )
% 0.33/0.48 => ( F3 @ ( res @ X2 @ P5 ) ) ) )
% 0.33/0.48 => ( F3 @ XP ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % resCasesF
% 0.33/0.48 thf(fact_104_resCasesF_H,axiom,
% 0.33/0.48 ! [X2: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 0.33/0.48 ( ( late_transitions @ ( res @ X2 @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 0.33/0.48 => ~ ! [P4: pi,Alpha2: late_freeRes,P5: pi,Y3: name] :
% 0.33/0.48 ( ( ( res @ X2 @ P )
% 0.33/0.48 = ( res @ Y3 @ P4 ) )
% 0.33/0.48 => ( ( ( late_FreeR @ Alpha @ P2 )
% 0.33/0.48 = ( late_FreeR @ Alpha2 @ ( res @ Y3 @ P5 ) ) )
% 0.33/0.48 => ( ( late_transitions @ P4 @ ( late_FreeR @ Alpha2 @ P5 ) )
% 0.33/0.48 => ~ ( fresh @ name @ late_freeRes @ Y3 @ Alpha2 ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % resCasesF'
% 0.33/0.48 thf(fact_105_ResF,axiom,
% 0.33/0.48 ! [P: pi,Alpha: late_freeRes,P2: pi,Y: name] :
% 0.33/0.48 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 0.33/0.48 => ( ( fresh @ name @ late_freeRes @ Y @ Alpha )
% 0.33/0.48 => ( late_transitions @ ( res @ Y @ P ) @ ( late_FreeR @ Alpha @ ( res @ Y @ P2 ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % ResF
% 0.33/0.48 thf(fact_106_Late__Semantics_OPar1B,axiom,
% 0.33/0.48 ! [P: pi,A2: late_subject,X2: name,P2: pi,Q: pi] :
% 0.33/0.48 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P2 ) )
% 0.33/0.48 => ( ( fresh @ name @ pi @ X2 @ Q )
% 0.33/0.48 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X2 @ ( par @ P2 @ Q ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % Late_Semantics.Par1B
% 0.33/0.48 thf(fact_107_Late__Semantics_OPar2B,axiom,
% 0.33/0.48 ! [Q: pi,A2: late_subject,X2: name,Q2: pi,P: pi] :
% 0.33/0.48 ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X2 @ Q2 ) )
% 0.33/0.48 => ( ( fresh @ name @ pi @ X2 @ P )
% 0.33/0.48 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X2 @ ( par @ P @ Q2 ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % Late_Semantics.Par2B
% 0.33/0.48 thf(fact_108_parCasesB,axiom,
% 0.33/0.48 ! [P: pi,Q: pi,A2: late_subject,X2: name,PQ: pi,Prop: pi > $o] :
% 0.33/0.48 ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X2 @ PQ ) )
% 0.33/0.48 => ( ( fresh @ name @ pi @ X2 @ P )
% 0.33/0.48 => ( ( fresh @ name @ pi @ X2 @ Q )
% 0.33/0.48 => ( ! [P5: pi] :
% 0.33/0.48 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P5 ) )
% 0.33/0.48 => ( Prop @ ( par @ P5 @ Q ) ) )
% 0.33/0.48 => ( ! [Q4: pi] :
% 0.33/0.48 ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X2 @ Q4 ) )
% 0.33/0.48 => ( Prop @ ( par @ P @ Q4 ) ) )
% 0.33/0.48 => ( Prop @ PQ ) ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % parCasesB
% 0.33/0.48 thf(fact_109_freshFreeDerivative_I1_J,axiom,
% 0.33/0.48 ! [P: pi,Alpha: late_freeRes,P2: pi,Y: name] :
% 0.33/0.48 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 0.33/0.48 => ( ( fresh @ name @ pi @ Y @ P )
% 0.33/0.48 => ( fresh @ name @ late_freeRes @ Y @ Alpha ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % freshFreeDerivative(1)
% 0.33/0.48 thf(fact_110_outputTauTrans,axiom,
% 0.33/0.48 ! [A2: name,B2: name,P: pi,P2: pi] :
% 0.33/0.48 ~ ( late_transitions @ ( output @ A2 @ B2 @ P ) @ ( late_FreeR @ late_TauR @ P2 ) ) ).
% 0.33/0.48
% 0.33/0.48 % outputTauTrans
% 0.33/0.48 thf(fact_111_transitions_OComm1,axiom,
% 0.33/0.48 ! [P: pi,A2: name,X2: name,P2: pi,Q: pi,B2: name,Q2: pi] :
% 0.33/0.48 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P2 ) )
% 0.33/0.48 => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ Q2 ) )
% 0.33/0.48 => ( ( fresh @ name @ pi @ X2 @ P )
% 0.33/0.48 => ( ( fresh @ name @ pi @ X2 @ Q )
% 0.33/0.48 => ( ( X2 != A2 )
% 0.33/0.48 => ( ( X2 != B2 )
% 0.33/0.48 => ( ( fresh @ name @ pi @ X2 @ Q2 )
% 0.33/0.48 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P2 @ X2 @ B2 ) @ Q2 ) ) ) ) ) ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % transitions.Comm1
% 0.33/0.48 thf(fact_112_transitions_OComm2,axiom,
% 0.33/0.48 ! [P: pi,A2: name,B2: name,P2: pi,Q: pi,X2: name,Q2: pi] :
% 0.33/0.48 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P2 ) )
% 0.33/0.48 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ Q2 ) )
% 0.33/0.48 => ( ( fresh @ name @ pi @ X2 @ P )
% 0.33/0.48 => ( ( fresh @ name @ pi @ X2 @ Q )
% 0.33/0.48 => ( ( X2 != A2 )
% 0.33/0.48 => ( ( X2 != B2 )
% 0.33/0.48 => ( ( fresh @ name @ pi @ X2 @ P2 )
% 0.33/0.48 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P2 @ ( subs @ Q2 @ X2 @ B2 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % transitions.Comm2
% 0.33/0.48 thf(fact_113_Late__Semantics1_Osubject_Oinject_I2_J,axiom,
% 0.33/0.48 ! [X22: name,Y2: name] :
% 0.33/0.48 ( ( ( late_BoundOutputS @ X22 )
% 0.33/0.48 = ( late_BoundOutputS @ Y2 ) )
% 0.33/0.48 = ( X22 = Y2 ) ) ).
% 0.33/0.48
% 0.33/0.48 % Late_Semantics1.subject.inject(2)
% 0.33/0.48 thf(fact_114_Late__Semantics1_Osubject_Oinject_I1_J,axiom,
% 0.33/0.48 ! [X1: name,Y1: name] :
% 0.33/0.48 ( ( ( late_InputS @ X1 )
% 0.33/0.48 = ( late_InputS @ Y1 ) )
% 0.33/0.48 = ( X1 = Y1 ) ) ).
% 0.33/0.48
% 0.33/0.48 % Late_Semantics1.subject.inject(1)
% 0.33/0.48 thf(fact_115_Late__Semantics_OComm1,axiom,
% 0.33/0.48 ! [P: pi,A2: name,X2: name,P2: pi,Q: pi,B2: name,Q2: pi] :
% 0.33/0.48 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P2 ) )
% 0.33/0.48 => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ Q2 ) )
% 0.33/0.48 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P2 @ X2 @ B2 ) @ Q2 ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % Late_Semantics.Comm1
% 0.33/0.48 thf(fact_116_Late__Semantics_OComm2,axiom,
% 0.33/0.48 ! [P: pi,A2: name,B2: name,P2: pi,Q: pi,X2: name,Q2: pi] :
% 0.33/0.48 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P2 ) )
% 0.33/0.48 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ Q2 ) )
% 0.33/0.48 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P2 @ ( subs @ Q2 @ X2 @ B2 ) ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % Late_Semantics.Comm2
% 0.33/0.48 thf(fact_117_subject_Oexhaust,axiom,
% 0.33/0.48 ! [Y: late_subject] :
% 0.33/0.48 ( ! [X12: name] :
% 0.33/0.48 ( Y
% 0.33/0.48 != ( late_InputS @ X12 ) )
% 0.33/0.48 => ~ ! [X23: name] :
% 0.33/0.48 ( Y
% 0.33/0.48 != ( late_BoundOutputS @ X23 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % subject.exhaust
% 0.33/0.48 thf(fact_118_Late__Semantics1_OfreeRes_Oinject,axiom,
% 0.33/0.48 ! [X11: name,X122: name,Y11: name,Y12: name] :
% 0.33/0.48 ( ( ( late_OutputR @ X11 @ X122 )
% 0.33/0.48 = ( late_OutputR @ Y11 @ Y12 ) )
% 0.33/0.48 = ( ( X11 = Y11 )
% 0.33/0.48 & ( X122 = Y12 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % Late_Semantics1.freeRes.inject
% 0.33/0.48 thf(fact_119_Late__Semantics_OfreeRes_Oinject,axiom,
% 0.33/0.48 ! [X22: name,X1: name,Y2: name,Y1: name] :
% 0.33/0.48 ( ( ( late_OutputR @ X22 @ X1 )
% 0.33/0.48 = ( late_OutputR @ Y2 @ Y1 ) )
% 0.33/0.48 = ( ( X22 = Y2 )
% 0.33/0.48 & ( X1 = Y1 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % Late_Semantics.freeRes.inject
% 0.33/0.48 thf(fact_120_name__fresh,axiom,
% 0.33/0.48 ( ( fresh @ name @ name )
% 0.33/0.48 = ( ^ [A6: name,B5: name] : ( A6 != B5 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % name_fresh
% 0.33/0.48 thf(fact_121_freeRes_Ofresh_I1_J,axiom,
% 0.33/0.48 ! [A2: name,X22: name,X1: name] :
% 0.33/0.48 ( ( fresh @ name @ late_freeRes @ A2 @ ( late_OutputR @ X22 @ X1 ) )
% 0.33/0.48 = ( ( fresh @ name @ name @ A2 @ X22 )
% 0.33/0.48 & ( fresh @ name @ name @ A2 @ X1 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % freeRes.fresh(1)
% 0.33/0.48 thf(fact_122_Late__Semantics1_OfreeRes_Odistinct_I1_J,axiom,
% 0.33/0.48 ! [X11: name,X122: name] :
% 0.33/0.48 ( ( late_OutputR @ X11 @ X122 )
% 0.33/0.48 != late_TauR ) ).
% 0.33/0.48
% 0.33/0.48 % Late_Semantics1.freeRes.distinct(1)
% 0.33/0.48 thf(fact_123_freeRes_Oexhaust,axiom,
% 0.33/0.48 ! [Y: late_freeRes] :
% 0.33/0.48 ( ! [X112: name,X123: name] :
% 0.33/0.48 ( Y
% 0.33/0.48 != ( late_OutputR @ X112 @ X123 ) )
% 0.33/0.48 => ( Y = late_TauR ) ) ).
% 0.33/0.48
% 0.33/0.48 % freeRes.exhaust
% 0.33/0.48 thf(fact_124_freeRes_Ostrong__inducts,axiom,
% 0.33/0.48 ! [A: $tType,P: A > late_freeRes > $o,Z: A,FreeRes3: late_freeRes] :
% 0.33/0.48 ( ! [Name12: name,Name23: name,Z2: A] : ( P @ Z2 @ ( late_OutputR @ Name12 @ Name23 ) )
% 0.33/0.48 => ( ! [Z2: A] : ( P @ Z2 @ late_TauR )
% 0.33/0.48 => ( P @ Z @ FreeRes3 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % freeRes.strong_inducts
% 0.33/0.48 thf(fact_125_freeRes_Ostrong__induct_H,axiom,
% 0.33/0.48 ! [N: $tType,P: N > late_freeRes > $o,Z: N,FreeRes3: late_freeRes] :
% 0.33/0.48 ( ! [Name12: name,Name23: name,Z2: N] : ( P @ Z2 @ ( late_OutputR @ Name12 @ Name23 ) )
% 0.33/0.48 => ( ! [Z2: N] : ( P @ Z2 @ late_TauR )
% 0.33/0.48 => ( P @ Z @ FreeRes3 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % freeRes.strong_induct'
% 0.33/0.48 thf(fact_126_freeRes_Oinducts,axiom,
% 0.33/0.48 ! [P: late_freeRes > $o,FreeRes3: late_freeRes] :
% 0.33/0.48 ( ! [Name12: name,Name23: name] : ( P @ ( late_OutputR @ Name12 @ Name23 ) )
% 0.33/0.48 => ( ( P @ late_TauR )
% 0.33/0.48 => ( P @ FreeRes3 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % freeRes.inducts
% 0.33/0.48 thf(fact_127_Late__Semantics_OfreeRes_Odistinct_I1_J,axiom,
% 0.33/0.48 ! [Name1: name,Name22: name] :
% 0.33/0.48 ( ( late_OutputR @ Name1 @ Name22 )
% 0.33/0.48 != late_TauR ) ).
% 0.33/0.48
% 0.33/0.48 % Late_Semantics.freeRes.distinct(1)
% 0.33/0.48 thf(fact_128_freeRes_Orecs_I1_J,axiom,
% 0.33/0.48 ! [T: $tType,P: T > $o,F1: name > name > T,F22: T,Name1: name,Name22: name] :
% 0.33/0.48 ( ! [X12: name,X23: name] : ( P @ ( F1 @ X12 @ X23 ) )
% 0.33/0.48 => ( ( P @ F22 )
% 0.33/0.48 => ( ( late_freeRes_rec @ T @ F1 @ F22 @ ( late_OutputR @ Name1 @ Name22 ) )
% 0.33/0.48 = ( F1 @ Name1 @ Name22 ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % freeRes.recs(1)
% 0.33/0.48 thf(fact_129_Output,axiom,
% 0.33/0.48 ! [A2: name,B2: name,P: pi] : ( late_transitions @ ( output @ A2 @ B2 @ P ) @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P ) ) ).
% 0.33/0.48
% 0.33/0.48 % Output
% 0.33/0.48 thf(fact_130_outputIneqTrans,axiom,
% 0.33/0.48 ! [A2: name,B2: name,P: pi,C2: name,D: name,P2: pi] :
% 0.33/0.48 ( ( late_transitions @ ( output @ A2 @ B2 @ P ) @ ( late_FreeR @ ( late_OutputR @ C2 @ D ) @ P2 ) )
% 0.33/0.48 => ~ ( ( A2 != C2 )
% 0.33/0.48 | ( B2 != D ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % outputIneqTrans
% 0.33/0.48 thf(fact_131_outputCases_H,axiom,
% 0.33/0.48 ! [A2: name,B2: name,P: pi,Rs: late_residual] :
% 0.33/0.48 ( ( late_transitions @ ( output @ A2 @ B2 @ P ) @ Rs )
% 0.33/0.48 => ~ ! [A4: name,B4: name,P4: pi] :
% 0.33/0.48 ( ( ( A2 = A4 )
% 0.33/0.48 & ( B2 = B4 )
% 0.33/0.48 & ( P = P4 ) )
% 0.33/0.48 => ( Rs
% 0.33/0.48 != ( late_FreeR @ ( late_OutputR @ A4 @ B4 ) @ P4 ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % outputCases'
% 0.33/0.48 thf(fact_132_outputCases,axiom,
% 0.33/0.48 ! [A2: name,B2: name,P: pi,Alpha: late_freeRes,P2: pi,Prop: late_freeRes > pi > $o] :
% 0.33/0.48 ( ( late_transitions @ ( output @ A2 @ B2 @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 0.33/0.48 => ( ( ( Alpha
% 0.33/0.48 = ( late_OutputR @ A2 @ B2 ) )
% 0.33/0.48 => ( ( P = P2 )
% 0.33/0.48 => ( Prop @ ( late_OutputR @ A2 @ B2 ) @ P ) ) )
% 0.33/0.48 => ( Prop @ Alpha @ P2 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % outputCases
% 0.33/0.48 thf(fact_133_resOutputOutputTrans,axiom,
% 0.33/0.48 ! [X2: name,A2: name,P: pi,B2: name,Y: name,P2: pi] :
% 0.33/0.48 ~ ( late_transitions @ ( res @ X2 @ ( output @ A2 @ X2 @ P ) ) @ ( late_FreeR @ ( late_OutputR @ B2 @ Y ) @ P2 ) ) ).
% 0.33/0.48
% 0.33/0.48 % resOutputOutputTrans
% 0.33/0.48 thf(fact_134_Open,axiom,
% 0.33/0.48 ! [P: pi,A2: name,B2: name,P2: pi] :
% 0.33/0.48 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P2 ) )
% 0.33/0.48 => ( ( A2 != B2 )
% 0.33/0.48 => ( late_transitions @ ( res @ B2 @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ B2 @ P2 ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % Open
% 0.33/0.48 thf(fact_135_resCasesB_H,axiom,
% 0.33/0.48 ! [X5: name,P: pi,A2: late_subject,Y4: name,P2: pi] :
% 0.33/0.48 ( ( late_transitions @ ( res @ X5 @ P ) @ ( late_BoundR @ A2 @ Y4 @ P2 ) )
% 0.33/0.48 => ( ! [P4: pi,A4: name,B4: name] :
% 0.33/0.48 ( ( ( res @ X5 @ P )
% 0.33/0.48 = ( res @ B4 @ P4 ) )
% 0.33/0.48 => ! [P5: pi] :
% 0.33/0.48 ( ( ( late_BoundR @ A2 @ Y4 @ P2 )
% 0.33/0.48 = ( late_BoundR @ ( late_BoundOutputS @ A4 ) @ B4 @ P5 ) )
% 0.33/0.48 => ( ( late_transitions @ P4 @ ( late_FreeR @ ( late_OutputR @ A4 @ B4 ) @ P5 ) )
% 0.33/0.48 => ( A4 = B4 ) ) ) )
% 0.33/0.48 => ~ ! [P4: pi,A4: late_subject,X4: name,P5: pi,Y3: name] :
% 0.33/0.48 ( ( ( res @ X5 @ P )
% 0.33/0.48 = ( res @ Y3 @ P4 ) )
% 0.33/0.48 => ( ( ( late_BoundR @ A2 @ Y4 @ P2 )
% 0.33/0.48 = ( late_BoundR @ A4 @ X4 @ ( res @ Y3 @ P5 ) ) )
% 0.33/0.48 => ( ( late_transitions @ P4 @ ( late_BoundR @ A4 @ X4 @ P5 ) )
% 0.33/0.48 => ( ( fresh @ name @ late_subject @ Y3 @ A4 )
% 0.33/0.48 => ( ( Y3 != X4 )
% 0.33/0.48 => ( ( fresh @ name @ pi @ X4 @ P4 )
% 0.33/0.48 => ~ ( fresh @ name @ late_subject @ X4 @ A4 ) ) ) ) ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % resCasesB'
% 0.33/0.48 thf(fact_136_resCases_H,axiom,
% 0.33/0.48 ! [X2: name,P: pi,Rs: late_residual] :
% 0.33/0.48 ( ( late_transitions @ ( res @ X2 @ P ) @ Rs )
% 0.33/0.48 => ( ! [P4: pi,A4: name,B4: name] :
% 0.33/0.48 ( ( ( res @ X2 @ P )
% 0.33/0.48 = ( res @ B4 @ P4 ) )
% 0.33/0.48 => ! [P5: pi] :
% 0.33/0.48 ( ( Rs
% 0.33/0.48 = ( late_BoundR @ ( late_BoundOutputS @ A4 ) @ B4 @ P5 ) )
% 0.33/0.48 => ( ( late_transitions @ P4 @ ( late_FreeR @ ( late_OutputR @ A4 @ B4 ) @ P5 ) )
% 0.33/0.48 => ( A4 = B4 ) ) ) )
% 0.33/0.48 => ( ! [P4: pi,A4: late_subject,X4: name,P5: pi,Y3: name] :
% 0.33/0.48 ( ( ( res @ X2 @ P )
% 0.33/0.48 = ( res @ Y3 @ P4 ) )
% 0.33/0.48 => ( ( Rs
% 0.33/0.48 = ( late_BoundR @ A4 @ X4 @ ( res @ Y3 @ P5 ) ) )
% 0.33/0.48 => ( ( late_transitions @ P4 @ ( late_BoundR @ A4 @ X4 @ P5 ) )
% 0.33/0.48 => ( ( fresh @ name @ late_subject @ Y3 @ A4 )
% 0.33/0.48 => ( ( Y3 != X4 )
% 0.33/0.48 => ( ( fresh @ name @ pi @ X4 @ P4 )
% 0.33/0.48 => ~ ( fresh @ name @ late_subject @ X4 @ A4 ) ) ) ) ) ) )
% 0.33/0.48 => ~ ! [P4: pi,Alpha2: late_freeRes,P5: pi,Y3: name] :
% 0.33/0.48 ( ( ( res @ X2 @ P )
% 0.33/0.48 = ( res @ Y3 @ P4 ) )
% 0.33/0.48 => ( ( Rs
% 0.33/0.48 = ( late_FreeR @ Alpha2 @ ( res @ Y3 @ P5 ) ) )
% 0.33/0.48 => ( ( late_transitions @ P4 @ ( late_FreeR @ Alpha2 @ P5 ) )
% 0.33/0.48 => ~ ( fresh @ name @ late_freeRes @ Y3 @ Alpha2 ) ) ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % resCases'
% 0.33/0.48 thf(fact_137_Late__Semantics1_Osubject_Odistinct_I1_J,axiom,
% 0.33/0.48 ! [X1: name,X22: name] :
% 0.33/0.48 ( ( late_InputS @ X1 )
% 0.33/0.48 != ( late_BoundOutputS @ X22 ) ) ).
% 0.33/0.48
% 0.33/0.48 % Late_Semantics1.subject.distinct(1)
% 0.33/0.48 thf(fact_138_subject_Orecs_I2_J,axiom,
% 0.33/0.48 ! [T: $tType,P: T > $o,F1: name > T,F22: name > T,Name2: name] :
% 0.33/0.48 ( ! [X12: name] : ( P @ ( F1 @ X12 ) )
% 0.33/0.48 => ( ! [X12: name] : ( P @ ( F22 @ X12 ) )
% 0.33/0.48 => ( ( late_subject_rec @ T @ F1 @ F22 @ ( late_BoundOutputS @ Name2 ) )
% 0.33/0.48 = ( F22 @ Name2 ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % subject.recs(2)
% 0.33/0.48 thf(fact_139_subject_Orecs_I1_J,axiom,
% 0.33/0.48 ! [T: $tType,P: T > $o,F1: name > T,F22: name > T,Name2: name] :
% 0.33/0.48 ( ! [X12: name] : ( P @ ( F1 @ X12 ) )
% 0.33/0.48 => ( ! [X12: name] : ( P @ ( F22 @ X12 ) )
% 0.33/0.48 => ( ( late_subject_rec @ T @ F1 @ F22 @ ( late_InputS @ Name2 ) )
% 0.33/0.48 = ( F1 @ Name2 ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % subject.recs(1)
% 0.33/0.48 thf(fact_140_resTauOutputTrans,axiom,
% 0.33/0.48 ! [X2: name,P: pi,A2: name,B2: name,P2: pi] :
% 0.33/0.48 ~ ( late_transitions @ ( res @ X2 @ ( tau @ P ) ) @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P2 ) ) ).
% 0.33/0.48
% 0.33/0.48 % resTauOutputTrans
% 0.33/0.48 thf(fact_141_resInputBoundOutputTrans,axiom,
% 0.33/0.48 ! [X2: name,A2: name,Y: name,P: pi,B2: name,Z: name,P2: pi] :
% 0.33/0.48 ~ ( late_transitions @ ( res @ X2 @ ( input @ A2 @ Y @ P ) ) @ ( late_BoundR @ ( late_BoundOutputS @ B2 ) @ Z @ P2 ) ) ).
% 0.33/0.48
% 0.33/0.48 % resInputBoundOutputTrans
% 0.33/0.48 thf(fact_142_pi_Ofresh_I3_J,axiom,
% 0.33/0.48 ! [A2: name,X1: pi] :
% 0.33/0.48 ( ( fresh @ name @ pi @ A2 @ ( tau @ X1 ) )
% 0.33/0.48 = ( fresh @ name @ pi @ A2 @ X1 ) ) ).
% 0.33/0.48
% 0.33/0.48 % pi.fresh(3)
% 0.33/0.48 thf(fact_143_simps_I2_J,axiom,
% 0.33/0.48 ! [P: pi,C2: name,D: name] :
% 0.33/0.48 ( ( subs @ ( tau @ P ) @ C2 @ D )
% 0.33/0.48 = ( tau @ ( subs @ P @ C2 @ D ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % simps(2)
% 0.33/0.48 thf(fact_144_pi_Oinject_I2_J,axiom,
% 0.33/0.48 ! [X1: pi,Y1: pi] :
% 0.33/0.48 ( ( ( tau @ X1 )
% 0.33/0.48 = ( tau @ Y1 ) )
% 0.33/0.48 = ( X1 = Y1 ) ) ).
% 0.33/0.48
% 0.33/0.48 % pi.inject(2)
% 0.33/0.48 thf(fact_145_pi_Odistinct_I35_J,axiom,
% 0.33/0.48 ! [Pi3: pi,Name13: name,Name24: name,Pi: pi] :
% 0.33/0.48 ( ( tau @ Pi3 )
% 0.33/0.48 != ( input @ Name13 @ Name24 @ Pi ) ) ).
% 0.33/0.48
% 0.33/0.48 % pi.distinct(35)
% 0.33/0.48 thf(fact_146_pi_Odistinct_I55_J,axiom,
% 0.33/0.48 ! [Name1: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 0.33/0.48 ( ( input @ Name1 @ Name22 @ Pi3 )
% 0.33/0.48 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.33/0.48
% 0.33/0.48 % pi.distinct(55)
% 0.33/0.48 thf(fact_147_pi_Odistinct_I57_J,axiom,
% 0.33/0.48 ! [Name1: name,Name22: name,Pi3: pi,Name: name,Pi: pi] :
% 0.33/0.48 ( ( input @ Name1 @ Name22 @ Pi3 )
% 0.33/0.48 != ( res @ Name @ Pi ) ) ).
% 0.33/0.48
% 0.33/0.48 % pi.distinct(57)
% 0.33/0.48 thf(fact_148_pi_Odistinct_I43_J,axiom,
% 0.33/0.48 ! [Pi3: pi,Pi12: pi,Pi22: pi] :
% 0.33/0.48 ( ( tau @ Pi3 )
% 0.33/0.48 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.33/0.48
% 0.33/0.48 % pi.distinct(43)
% 0.33/0.48 thf(fact_149_pi_Odistinct_I45_J,axiom,
% 0.33/0.48 ! [Pi3: pi,Name: name,Pi: pi] :
% 0.33/0.48 ( ( tau @ Pi3 )
% 0.33/0.48 != ( res @ Name @ Pi ) ) ).
% 0.33/0.48
% 0.33/0.48 % pi.distinct(45)
% 0.33/0.48 thf(fact_150_pi_Odistinct_I21_J,axiom,
% 0.33/0.48 ! [Name1: name,Name22: name,Pi3: pi,Name13: name,Name24: name,Pi: pi] :
% 0.33/0.48 ( ( output @ Name1 @ Name22 @ Pi3 )
% 0.33/0.48 != ( input @ Name13 @ Name24 @ Pi ) ) ).
% 0.33/0.48
% 0.33/0.48 % pi.distinct(21)
% 0.33/0.48 thf(fact_151_pi_Odistinct_I19_J,axiom,
% 0.33/0.48 ! [Name1: name,Name22: name,Pi3: pi,Pi: pi] :
% 0.33/0.48 ( ( output @ Name1 @ Name22 @ Pi3 )
% 0.33/0.48 != ( tau @ Pi ) ) ).
% 0.33/0.48
% 0.33/0.48 % pi.distinct(19)
% 0.33/0.48 thf(fact_152_resTrans_I2_J,axiom,
% 0.33/0.48 ! [X2: name,Y: name,P: pi,Rs: late_residual] :
% 0.33/0.48 ~ ( late_transitions @ ( res @ X2 @ ( input @ X2 @ Y @ P ) ) @ Rs ) ).
% 0.33/0.48
% 0.33/0.48 % resTrans(2)
% 0.33/0.48 thf(fact_153_inputFreeTrans,axiom,
% 0.33/0.48 ! [A2: name,X2: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 0.33/0.48 ~ ( late_transitions @ ( input @ A2 @ X2 @ P ) @ ( late_FreeR @ Alpha @ P2 ) ) ).
% 0.33/0.48
% 0.33/0.48 % inputFreeTrans
% 0.33/0.48 thf(fact_154_tauBoundTrans,axiom,
% 0.33/0.48 ! [P: pi,A2: late_subject,X2: name,P2: pi] :
% 0.33/0.48 ~ ( late_transitions @ ( tau @ P ) @ ( late_BoundR @ A2 @ X2 @ P2 ) ) ).
% 0.33/0.48
% 0.33/0.48 % tauBoundTrans
% 0.33/0.48 thf(fact_155_resInputFreeTrans,axiom,
% 0.33/0.48 ! [X2: name,A2: name,Y: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 0.33/0.48 ~ ( late_transitions @ ( res @ X2 @ ( input @ A2 @ Y @ P ) ) @ ( late_FreeR @ Alpha @ P2 ) ) ).
% 0.33/0.48
% 0.33/0.48 % resInputFreeTrans
% 0.33/0.48 thf(fact_156_Late__Semantics_OInput,axiom,
% 0.33/0.48 ! [A2: name,X2: name,P: pi] : ( late_transitions @ ( input @ A2 @ X2 @ P ) @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P ) ) ).
% 0.33/0.48
% 0.33/0.48 % Late_Semantics.Input
% 0.33/0.48 thf(fact_157_transitions_OInput,axiom,
% 0.33/0.48 ! [X2: name,A2: name,P: pi] :
% 0.33/0.48 ( ( X2 != A2 )
% 0.33/0.48 => ( late_transitions @ ( input @ A2 @ X2 @ P ) @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % transitions.Input
% 0.33/0.48 thf(fact_158_inputBoundOutputTrans,axiom,
% 0.33/0.48 ! [A2: name,X2: name,P: pi,B2: name,Y: name,P2: pi] :
% 0.33/0.48 ~ ( late_transitions @ ( input @ A2 @ X2 @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ B2 ) @ Y @ P2 ) ) ).
% 0.33/0.48
% 0.33/0.48 % inputBoundOutputTrans
% 0.33/0.48 thf(fact_159_resTauBoundTrans,axiom,
% 0.33/0.48 ! [X2: name,P: pi,A2: late_subject,Y: name,P2: pi] :
% 0.33/0.48 ~ ( late_transitions @ ( res @ X2 @ ( tau @ P ) ) @ ( late_BoundR @ A2 @ Y @ P2 ) ) ).
% 0.33/0.48
% 0.33/0.48 % resTauBoundTrans
% 0.33/0.48 thf(fact_160_inputIneqTrans,axiom,
% 0.33/0.48 ! [A2: name,X2: name,P: pi,B2: late_subject,Y: name,P2: pi] :
% 0.33/0.48 ( ( late_transitions @ ( input @ A2 @ X2 @ P ) @ ( late_BoundR @ B2 @ Y @ P2 ) )
% 0.33/0.48 => ~ ( fresh @ name @ late_subject @ A2 @ B2 ) ) ).
% 0.33/0.48
% 0.33/0.48 % inputIneqTrans
% 0.33/0.48 thf(fact_161_tauOutputTrans,axiom,
% 0.33/0.48 ! [P: pi,A2: name,B2: name,P2: pi] :
% 0.33/0.48 ~ ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P2 ) ) ).
% 0.33/0.48
% 0.33/0.48 % tauOutputTrans
% 0.33/0.48 thf(fact_162_tauCases,axiom,
% 0.33/0.48 ! [P: pi,Alpha: late_freeRes,P2: pi,Prop: late_freeRes > pi > $o] :
% 0.33/0.48 ( ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 0.33/0.48 => ( ( ( Alpha = late_TauR )
% 0.33/0.48 => ( ( P = P2 )
% 0.33/0.48 => ( Prop @ late_TauR @ P ) ) )
% 0.33/0.48 => ( Prop @ Alpha @ P2 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % tauCases
% 0.33/0.48 thf(fact_163_tauCases_H,axiom,
% 0.33/0.48 ! [P: pi,Rs: late_residual] :
% 0.33/0.48 ( ( late_transitions @ ( tau @ P ) @ Rs )
% 0.33/0.48 => ~ ! [P4: pi] :
% 0.33/0.48 ( ( ( tau @ P )
% 0.33/0.48 = ( tau @ P4 ) )
% 0.33/0.48 => ( Rs
% 0.33/0.48 != ( late_FreeR @ late_TauR @ P4 ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % tauCases'
% 0.33/0.48 thf(fact_164_Tau,axiom,
% 0.33/0.48 ! [P: pi] : ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ late_TauR @ P ) ) ).
% 0.33/0.48
% 0.33/0.48 % Tau
% 0.33/0.48 thf(fact_165_residual_Ofresh_I1_J,axiom,
% 0.33/0.48 ! [A2: name,X32: late_subject,X1: name,X22: pi] :
% 0.33/0.48 ( ( fresh @ name @ late_residual @ A2 @ ( late_BoundR @ X32 @ X1 @ X22 ) )
% 0.33/0.48 = ( ( fresh @ name @ late_subject @ A2 @ X32 )
% 0.33/0.48 & ( fresh @ name @ ( name > ( noption @ pi ) ) @ A2 @ ( abs_fun @ name @ pi @ X1 @ X22 ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % residual.fresh(1)
% 0.33/0.48 thf(fact_166_simps_I3_J,axiom,
% 0.33/0.48 ! [A2: name,B2: name,P: pi,C2: name,D: name] :
% 0.33/0.48 ( ( subs @ ( output @ A2 @ B2 @ P ) @ C2 @ D )
% 0.33/0.48 = ( output @ ( subst_name @ A2 @ C2 @ D ) @ ( subst_name @ B2 @ C2 @ D ) @ ( subs @ P @ C2 @ D ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % simps(3)
% 0.33/0.48 thf(fact_167_substInput,axiom,
% 0.33/0.48 ! [X2: name,B2: name,C2: name,A2: name,P: pi] :
% 0.33/0.48 ( ( X2 != B2 )
% 0.33/0.48 => ( ( X2 != C2 )
% 0.33/0.48 => ( ( subs @ ( input @ A2 @ X2 @ P ) @ B2 @ C2 )
% 0.33/0.48 = ( input @ ( subst_name @ A2 @ B2 @ C2 ) @ X2 @ ( subs @ P @ B2 @ C2 ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % substInput
% 0.33/0.48 thf(fact_168_simps_I4_J,axiom,
% 0.33/0.48 ! [X2: name,A2: name,C2: name,D: name,P: pi] :
% 0.33/0.48 ( ( X2 != A2 )
% 0.33/0.48 => ( ( X2 != C2 )
% 0.33/0.48 => ( ( X2 != D )
% 0.33/0.48 => ( ( subs @ ( input @ A2 @ X2 @ P ) @ C2 @ D )
% 0.33/0.48 = ( input @ ( subst_name @ A2 @ C2 @ D ) @ X2 @ ( subs @ P @ C2 @ D ) ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % simps(4)
% 0.33/0.48 thf(fact_169_pi_Ofresh_I9_J,axiom,
% 0.33/0.48 ! [A2: name,X1: name,X22: pi] :
% 0.33/0.48 ( ( fresh @ name @ pi @ A2 @ ( res @ X1 @ X22 ) )
% 0.33/0.48 = ( fresh @ name @ ( name > ( noption @ pi ) ) @ A2 @ ( abs_fun @ name @ pi @ X1 @ X22 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % pi.fresh(9)
% 0.33/0.48 thf(fact_170_pi_Ofresh_I4_J,axiom,
% 0.33/0.48 ! [A2: name,X32: name,X1: name,X22: pi] :
% 0.33/0.48 ( ( fresh @ name @ pi @ A2 @ ( input @ X32 @ X1 @ X22 ) )
% 0.33/0.48 = ( ( fresh @ name @ name @ A2 @ X32 )
% 0.33/0.48 & ( fresh @ name @ ( name > ( noption @ pi ) ) @ A2 @ ( abs_fun @ name @ pi @ X1 @ X22 ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % pi.fresh(4)
% 0.33/0.48 thf(fact_171_pi_Oinject_I3_J,axiom,
% 0.33/0.48 ! [X32: name,X1: name,X22: pi,Y32: name,Y1: name,Y2: pi] :
% 0.33/0.48 ( ( ( input @ X32 @ X1 @ X22 )
% 0.33/0.48 = ( input @ Y32 @ Y1 @ Y2 ) )
% 0.33/0.48 = ( ( X32 = Y32 )
% 0.33/0.48 & ( ( abs_fun @ name @ pi @ X1 @ X22 )
% 0.33/0.48 = ( abs_fun @ name @ pi @ Y1 @ Y2 ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % pi.inject(3)
% 0.33/0.48 thf(fact_172_abs__fun__eq1,axiom,
% 0.33/0.48 ! [X: $tType,A: $tType,A2: X,X2: A,Y: A] :
% 0.33/0.48 ( ( ( abs_fun @ X @ A @ A2 @ X2 )
% 0.33/0.48 = ( abs_fun @ X @ A @ A2 @ Y ) )
% 0.33/0.48 = ( X2 = Y ) ) ).
% 0.33/0.48
% 0.33/0.48 % abs_fun_eq1
% 0.33/0.48 thf(fact_173_subst__name__def,axiom,
% 0.33/0.48 ( subst_name
% 0.33/0.48 = ( ^ [A6: name,B5: name,C4: name] : ( if @ name @ ( A6 = B5 ) @ C4 @ A6 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % subst_name_def
% 0.33/0.48 thf(fact_174_name__fresh__abs,axiom,
% 0.33/0.48 ! [A: $tType] :
% 0.33/0.48 ( ( fs_name @ A )
% 0.33/0.48 => ! [B2: name,A2: name,X2: A] :
% 0.33/0.48 ( ( fresh @ name @ ( name > ( noption @ A ) ) @ B2 @ ( abs_fun @ name @ A @ A2 @ X2 ) )
% 0.33/0.48 = ( ( B2 = A2 )
% 0.33/0.48 | ( fresh @ name @ A @ B2 @ X2 ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % name_fresh_abs
% 0.33/0.48 thf(fact_175_abs__fresh_I1_J,axiom,
% 0.33/0.48 ! [X6: $tType] :
% 0.33/0.48 ( ( fs_name @ X6 )
% 0.33/0.48 => ! [B2: name,A2: name,X2: X6] :
% 0.33/0.48 ( ( fresh @ name @ ( name > ( noption @ X6 ) ) @ B2 @ ( abs_fun @ name @ X6 @ A2 @ X2 ) )
% 0.33/0.48 = ( ( B2 = A2 )
% 0.33/0.48 | ( fresh @ name @ X6 @ B2 @ X2 ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % abs_fresh(1)
% 0.33/0.48 thf(fact_176_residual_Oinject_I1_J,axiom,
% 0.33/0.48 ! [X32: late_subject,X1: name,X22: pi,Y32: late_subject,Y1: name,Y2: pi] :
% 0.33/0.48 ( ( ( late_BoundR @ X32 @ X1 @ X22 )
% 0.33/0.48 = ( late_BoundR @ Y32 @ Y1 @ Y2 ) )
% 0.33/0.48 = ( ( X32 = Y32 )
% 0.33/0.48 & ( ( abs_fun @ name @ pi @ X1 @ X22 )
% 0.33/0.48 = ( abs_fun @ name @ pi @ Y1 @ Y2 ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % residual.inject(1)
% 0.33/0.48 thf(fact_177_pi_Oinject_I8_J,axiom,
% 0.33/0.48 ! [X1: name,X22: pi,Y1: name,Y2: pi] :
% 0.33/0.48 ( ( ( res @ X1 @ X22 )
% 0.33/0.48 = ( res @ Y1 @ Y2 ) )
% 0.33/0.48 = ( ( abs_fun @ name @ pi @ X1 @ X22 )
% 0.33/0.48 = ( abs_fun @ name @ pi @ Y1 @ Y2 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % pi.inject(8)
% 0.33/0.48 thf(fact_178_inputCases_H,axiom,
% 0.33/0.48 ! [A2: name,B2: name,P: pi,Rs: late_residual] :
% 0.33/0.48 ( ( late_transitions @ ( input @ A2 @ B2 @ P ) @ Rs )
% 0.33/0.48 => ~ ! [X4: name,A4: name,P4: pi] :
% 0.33/0.48 ( ( ( A2 = A4 )
% 0.33/0.48 & ( ( abs_fun @ name @ pi @ B2 @ P )
% 0.33/0.48 = ( abs_fun @ name @ pi @ X4 @ P4 ) ) )
% 0.33/0.48 => ( ( Rs
% 0.33/0.48 = ( late_BoundR @ ( late_InputS @ A4 ) @ X4 @ P4 ) )
% 0.33/0.48 => ( X4 = A4 ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % inputCases'
% 0.33/0.48 thf(fact_179_internal__case__prod__conv,axiom,
% 0.33/0.48 ! [B: $tType,A: $tType,C: $tType,C2: B > C > A,A2: B,B2: C] :
% 0.33/0.48 ( ( produc2004651681e_prod @ B @ C @ A @ C2 @ ( product_Pair @ B @ C @ A2 @ B2 ) )
% 0.33/0.48 = ( C2 @ A2 @ B2 ) ) ).
% 0.33/0.48
% 0.33/0.48 % internal_case_prod_conv
% 0.33/0.48 thf(fact_180_resSimCases,axiom,
% 0.33/0.48 ! [A: $tType] :
% 0.33/0.48 ( ( fs_name @ A )
% 0.33/0.48 => ! [Rel: set @ ( product_prod @ pi @ pi ),Q: pi,X2: name,P: pi,C5: A] :
% 0.33/0.48 ( ( eqvt @ pi @ Rel )
% 0.33/0.48 => ( ! [Q4: pi,A4: name] :
% 0.33/0.48 ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A4 @ X2 ) @ Q4 ) )
% 0.33/0.48 => ( ( A4 != X2 )
% 0.33/0.48 => ? [P6: pi] :
% 0.33/0.48 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A4 ) @ X2 @ P6 ) )
% 0.33/0.48 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P6 @ Q4 ) @ Rel ) ) ) )
% 0.33/0.48 => ( ! [Q4: pi,A4: late_subject,Y3: name] :
% 0.33/0.48 ( ( late_transitions @ Q @ ( late_BoundR @ A4 @ Y3 @ Q4 ) )
% 0.33/0.48 => ( ( fresh @ name @ late_subject @ X2 @ A4 )
% 0.33/0.48 => ( ( X2 != Y3 )
% 0.33/0.48 => ( ( fresh @ name @ A @ Y3 @ C5 )
% 0.33/0.48 => ? [P6: pi] :
% 0.33/0.48 ( ( late_transitions @ P @ ( late_BoundR @ A4 @ Y3 @ P6 ) )
% 0.33/0.48 & ( strong2129052853vative @ P6 @ ( res @ X2 @ Q4 ) @ A4 @ Y3 @ Rel ) ) ) ) ) )
% 0.33/0.48 => ( ! [Q4: pi,Alpha2: late_freeRes] :
% 0.33/0.48 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 0.33/0.48 => ( ( fresh @ name @ late_freeRes @ X2 @ Alpha2 )
% 0.33/0.48 => ? [P6: pi] :
% 0.33/0.48 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 0.33/0.48 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P6 @ ( res @ X2 @ Q4 ) ) @ Rel ) ) ) )
% 0.33/0.48 => ( strong743114133lation @ P @ Rel @ ( res @ X2 @ Q ) ) ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % resSimCases
% 0.33/0.48 thf(fact_181_parSym,axiom,
% 0.33/0.48 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi,Q: pi] :
% 0.33/0.48 ( ! [R: pi,S2: pi] : ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( par @ R @ S2 ) @ ( par @ S2 @ R ) ) @ Rel )
% 0.33/0.48 => ( ! [R: pi,S2: pi,X4: name] :
% 0.33/0.48 ( ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ R @ S2 ) @ Rel )
% 0.33/0.48 => ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( res @ X4 @ R ) @ ( res @ X4 @ S2 ) ) @ Rel ) )
% 0.33/0.48 => ( strong743114133lation @ ( par @ P @ Q ) @ Rel @ ( par @ Q @ P ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % parSym
% 0.33/0.48 thf(fact_182_simE_I1_J,axiom,
% 0.33/0.48 ! [P: pi,Rel: set @ ( product_prod @ pi @ pi ),Q: pi,A2: late_subject,X2: name,Q2: pi] :
% 0.33/0.48 ( ( strong743114133lation @ P @ Rel @ Q )
% 0.33/0.48 => ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X2 @ Q2 ) )
% 0.33/0.48 => ( ( fresh @ name @ pi @ X2 @ P )
% 0.33/0.48 => ? [P5: pi] :
% 0.33/0.48 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P5 ) )
% 0.33/0.48 & ( strong2129052853vative @ P5 @ Q2 @ A2 @ X2 @ Rel ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % simE(1)
% 0.33/0.48 thf(fact_183_simE_I2_J,axiom,
% 0.33/0.48 ! [P: pi,Rel: set @ ( product_prod @ pi @ pi ),Q: pi,Alpha: late_freeRes,Q2: pi] :
% 0.33/0.48 ( ( strong743114133lation @ P @ Rel @ Q )
% 0.33/0.48 => ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 0.33/0.48 => ? [P5: pi] :
% 0.33/0.48 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P5 ) )
% 0.33/0.48 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P5 @ Q2 ) @ Rel ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % simE(2)
% 0.33/0.48 thf(fact_184_simCasesCont,axiom,
% 0.33/0.48 ! [A: $tType] :
% 0.33/0.48 ( ( fs_name @ A )
% 0.33/0.48 => ! [Rel: set @ ( product_prod @ pi @ pi ),Q: pi,P: pi,C5: A] :
% 0.33/0.48 ( ( eqvt @ pi @ Rel )
% 0.33/0.48 => ( ! [A4: late_subject,X4: name,Q4: pi] :
% 0.33/0.48 ( ( late_transitions @ Q @ ( late_BoundR @ A4 @ X4 @ Q4 ) )
% 0.33/0.48 => ( ( fresh @ name @ pi @ X4 @ P )
% 0.33/0.48 => ( ( fresh @ name @ pi @ X4 @ Q )
% 0.33/0.48 => ( ( fresh @ name @ late_subject @ X4 @ A4 )
% 0.33/0.48 => ( ( fresh @ name @ A @ X4 @ C5 )
% 0.33/0.48 => ? [P6: pi] :
% 0.33/0.48 ( ( late_transitions @ P @ ( late_BoundR @ A4 @ X4 @ P6 ) )
% 0.33/0.48 & ( strong2129052853vative @ P6 @ Q4 @ A4 @ X4 @ Rel ) ) ) ) ) ) )
% 0.33/0.48 => ( ! [Alpha2: late_freeRes,Q4: pi] :
% 0.33/0.48 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 0.33/0.48 => ? [P6: pi] :
% 0.33/0.48 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 0.33/0.48 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P6 @ Q4 ) @ Rel ) ) )
% 0.33/0.48 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % simCasesCont
% 0.33/0.48 thf(fact_185_simCases,axiom,
% 0.33/0.48 ! [Q: pi,P: pi,Rel: set @ ( product_prod @ pi @ pi )] :
% 0.33/0.48 ( ! [A4: late_subject,Y3: name,Q4: pi] :
% 0.33/0.48 ( ( late_transitions @ Q @ ( late_BoundR @ A4 @ Y3 @ Q4 ) )
% 0.33/0.48 => ( ( fresh @ name @ pi @ Y3 @ P )
% 0.33/0.48 => ? [P6: pi] :
% 0.33/0.48 ( ( late_transitions @ P @ ( late_BoundR @ A4 @ Y3 @ P6 ) )
% 0.33/0.48 & ( strong2129052853vative @ P6 @ Q4 @ A4 @ Y3 @ Rel ) ) ) )
% 0.33/0.48 => ( ! [Alpha2: late_freeRes,Q4: pi] :
% 0.33/0.48 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 0.33/0.48 => ? [P6: pi] :
% 0.33/0.48 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 0.33/0.48 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P6 @ Q4 ) @ Rel ) ) )
% 0.33/0.48 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % simCases
% 0.33/0.48 thf(fact_186_simulation__def,axiom,
% 0.33/0.48 ( strong743114133lation
% 0.33/0.48 = ( ^ [P7: pi,Rel2: set @ ( product_prod @ pi @ pi ),Q5: pi] :
% 0.33/0.48 ( ! [A6: late_subject,X3: name,Q6: pi] :
% 0.33/0.48 ( ( ( late_transitions @ Q5 @ ( late_BoundR @ A6 @ X3 @ Q6 ) )
% 0.33/0.48 & ( fresh @ name @ pi @ X3 @ P7 ) )
% 0.33/0.48 => ? [P8: pi] :
% 0.33/0.48 ( ( late_transitions @ P7 @ ( late_BoundR @ A6 @ X3 @ P8 ) )
% 0.33/0.48 & ( strong2129052853vative @ P8 @ Q6 @ A6 @ X3 @ Rel2 ) ) )
% 0.33/0.48 & ! [Alpha3: late_freeRes,Q6: pi] :
% 0.33/0.48 ( ( late_transitions @ Q5 @ ( late_FreeR @ Alpha3 @ Q6 ) )
% 0.33/0.48 => ? [P8: pi] :
% 0.33/0.48 ( ( late_transitions @ P7 @ ( late_FreeR @ Alpha3 @ P8 ) )
% 0.33/0.48 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P8 @ Q6 ) @ Rel2 ) ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % simulation_def
% 0.33/0.48 thf(fact_187_parZeroRight,axiom,
% 0.33/0.48 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi] :
% 0.33/0.48 ( ! [Q3: pi] : ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ Q3 @ ( par @ Q3 @ piNil ) ) @ Rel )
% 0.33/0.48 => ( strong743114133lation @ P @ Rel @ ( par @ P @ piNil ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % parZeroRight
% 0.33/0.48 thf(fact_188_parZeroLeft,axiom,
% 0.33/0.48 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi] :
% 0.33/0.48 ( ! [Q3: pi] : ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( par @ Q3 @ piNil ) @ Q3 ) @ Rel )
% 0.33/0.48 => ( strong743114133lation @ ( par @ P @ piNil ) @ Rel @ P ) ) ).
% 0.33/0.48
% 0.33/0.48 % parZeroLeft
% 0.33/0.48 thf(fact_189_simps_I5_J,axiom,
% 0.33/0.48 ! [A2: name,B2: name,P: pi,C2: name,D: name] :
% 0.33/0.48 ( ( subs @ ( match @ A2 @ B2 @ P ) @ C2 @ D )
% 0.33/0.48 = ( match @ ( subst_name @ A2 @ C2 @ D ) @ ( subst_name @ B2 @ C2 @ D ) @ ( subs @ P @ C2 @ D ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % simps(5)
% 0.33/0.48 thf(fact_190_pi_Ofresh_I1_J,axiom,
% 0.33/0.48 ! [A2: name] : ( fresh @ name @ pi @ A2 @ piNil ) ).
% 0.33/0.48
% 0.33/0.48 % pi.fresh(1)
% 0.33/0.48 thf(fact_191_simps_I1_J,axiom,
% 0.33/0.48 ! [C2: name,D: name] :
% 0.33/0.48 ( ( subs @ piNil @ C2 @ D )
% 0.33/0.48 = piNil ) ).
% 0.33/0.48
% 0.33/0.48 % simps(1)
% 0.33/0.48 thf(fact_192_pi_Ofresh_I5_J,axiom,
% 0.33/0.48 ! [A2: name,X32: name,X22: name,X1: pi] :
% 0.33/0.48 ( ( fresh @ name @ pi @ A2 @ ( match @ X32 @ X22 @ X1 ) )
% 0.33/0.48 = ( ( fresh @ name @ name @ A2 @ X32 )
% 0.33/0.48 & ( fresh @ name @ name @ A2 @ X22 )
% 0.33/0.48 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % pi.fresh(5)
% 0.33/0.48 thf(fact_193_matchNilLeft,axiom,
% 0.33/0.48 ! [A2: name,B2: name,Rel: set @ ( product_prod @ pi @ pi ),P: pi] :
% 0.33/0.48 ( ( A2 != B2 )
% 0.33/0.48 => ( strong743114133lation @ piNil @ Rel @ ( match @ A2 @ B2 @ P ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % matchNilLeft
% 0.33/0.48 thf(fact_194_nilSimRight,axiom,
% 0.33/0.48 ! [P: pi,Rel: set @ ( product_prod @ pi @ pi )] : ( strong743114133lation @ P @ Rel @ piNil ) ).
% 0.33/0.48
% 0.33/0.48 % nilSimRight
% 0.33/0.48 thf(fact_195_pi_Odistinct_I49_J,axiom,
% 0.33/0.48 ! [Name1: name,Name22: name,Pi3: pi,Name13: name,Name24: name,Pi: pi] :
% 0.33/0.48 ( ( input @ Name1 @ Name22 @ Pi3 )
% 0.33/0.48 != ( match @ Name13 @ Name24 @ Pi ) ) ).
% 0.33/0.48
% 0.33/0.48 % pi.distinct(49)
% 0.33/0.48 thf(fact_196_pi_Odistinct_I5_J,axiom,
% 0.33/0.48 ! [Name13: name,Name24: name,Pi: pi] :
% 0.33/0.48 ( piNil
% 0.33/0.48 != ( input @ Name13 @ Name24 @ Pi ) ) ).
% 0.33/0.48
% 0.33/0.48 % pi.distinct(5)
% 0.33/0.48 thf(fact_197_matchCases,axiom,
% 0.33/0.48 ! [A2: name,B2: name,P: pi,Rs: late_residual,F3: name > name > $o] :
% 0.33/0.48 ( ( late_transitions @ ( match @ A2 @ B2 @ P ) @ Rs )
% 0.33/0.48 => ( ( ( late_transitions @ P @ Rs )
% 0.33/0.48 => ( ( A2 = B2 )
% 0.33/0.48 => ( F3 @ A2 @ A2 ) ) )
% 0.33/0.48 => ( F3 @ A2 @ B2 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % matchCases
% 0.33/0.48 thf(fact_198_matchTrans,axiom,
% 0.33/0.48 ! [A2: name,B2: name,P: pi,Rs: late_residual] :
% 0.33/0.48 ( ( late_transitions @ ( match @ A2 @ B2 @ P ) @ Rs )
% 0.33/0.48 => ( A2 = B2 ) ) ).
% 0.33/0.48
% 0.33/0.48 % matchTrans
% 0.33/0.48 thf(fact_199_matchCases_H,axiom,
% 0.33/0.48 ! [A2: name,B2: name,P: pi,Rs: late_residual] :
% 0.33/0.48 ( ( late_transitions @ ( match @ A2 @ B2 @ P ) @ Rs )
% 0.33/0.48 => ~ ! [P4: pi] :
% 0.33/0.48 ( ( ( B2 = A2 )
% 0.33/0.48 & ( P = P4 ) )
% 0.33/0.48 => ~ ( late_transitions @ P4 @ Rs ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % matchCases'
% 0.33/0.48 thf(fact_200_Match,axiom,
% 0.33/0.48 ! [P: pi,Rs: late_residual,B2: name] :
% 0.33/0.48 ( ( late_transitions @ P @ Rs )
% 0.33/0.48 => ( late_transitions @ ( match @ B2 @ B2 @ P ) @ Rs ) ) ).
% 0.33/0.48
% 0.33/0.48 % Match
% 0.33/0.48 thf(fact_201_nilCases_H,axiom,
% 0.33/0.48 ! [Rs: late_residual] :
% 0.33/0.48 ~ ( late_transitions @ piNil @ Rs ) ).
% 0.33/0.48
% 0.33/0.48 % nilCases'
% 0.33/0.48 thf(fact_202_zeroTrans,axiom,
% 0.33/0.48 ! [Rs: late_residual] :
% 0.33/0.48 ~ ( late_transitions @ piNil @ Rs ) ).
% 0.33/0.48
% 0.33/0.48 % zeroTrans
% 0.33/0.48 thf(fact_203_pi_Odistinct_I65_J,axiom,
% 0.33/0.48 ! [Name1: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 0.33/0.48 ( ( match @ Name1 @ Name22 @ Pi3 )
% 0.33/0.48 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.33/0.48
% 0.33/0.48 % pi.distinct(65)
% 0.33/0.48 thf(fact_204_pi_Odistinct_I67_J,axiom,
% 0.33/0.48 ! [Name1: name,Name22: name,Pi3: pi,Name: name,Pi: pi] :
% 0.33/0.48 ( ( match @ Name1 @ Name22 @ Pi3 )
% 0.33/0.48 != ( res @ Name @ Pi ) ) ).
% 0.33/0.48
% 0.33/0.48 % pi.distinct(67)
% 0.33/0.48 thf(fact_205_pi_Odistinct_I13_J,axiom,
% 0.33/0.48 ! [Pi12: pi,Pi22: pi] :
% 0.33/0.48 ( piNil
% 0.33/0.48 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.33/0.48
% 0.33/0.48 % pi.distinct(13)
% 0.33/0.48 thf(fact_206_pi_Odistinct_I15_J,axiom,
% 0.33/0.48 ! [Name: name,Pi: pi] :
% 0.33/0.48 ( piNil
% 0.33/0.48 != ( res @ Name @ Pi ) ) ).
% 0.33/0.48
% 0.33/0.48 % pi.distinct(15)
% 0.33/0.48 thf(fact_207_pi_Odistinct_I7_J,axiom,
% 0.33/0.48 ! [Name13: name,Name24: name,Pi: pi] :
% 0.33/0.48 ( piNil
% 0.33/0.48 != ( match @ Name13 @ Name24 @ Pi ) ) ).
% 0.33/0.48
% 0.33/0.48 % pi.distinct(7)
% 0.33/0.48 thf(fact_208_pi_Oinject_I4_J,axiom,
% 0.33/0.48 ! [X32: name,X22: name,X1: pi,Y32: name,Y2: name,Y1: pi] :
% 0.33/0.48 ( ( ( match @ X32 @ X22 @ X1 )
% 0.33/0.48 = ( match @ Y32 @ Y2 @ Y1 ) )
% 0.33/0.48 = ( ( X32 = Y32 )
% 0.33/0.48 & ( X22 = Y2 )
% 0.33/0.48 & ( X1 = Y1 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % pi.inject(4)
% 0.33/0.48 thf(fact_209_pi_Odistinct_I3_J,axiom,
% 0.33/0.48 ! [Pi: pi] :
% 0.33/0.48 ( piNil
% 0.33/0.48 != ( tau @ Pi ) ) ).
% 0.33/0.48
% 0.33/0.48 % pi.distinct(3)
% 0.33/0.48 thf(fact_210_pi_Odistinct_I37_J,axiom,
% 0.33/0.48 ! [Pi3: pi,Name13: name,Name24: name,Pi: pi] :
% 0.33/0.48 ( ( tau @ Pi3 )
% 0.33/0.48 != ( match @ Name13 @ Name24 @ Pi ) ) ).
% 0.33/0.48
% 0.33/0.48 % pi.distinct(37)
% 0.33/0.48 thf(fact_211_pi_Odistinct_I1_J,axiom,
% 0.33/0.48 ! [Name13: name,Name24: name,Pi: pi] :
% 0.33/0.48 ( piNil
% 0.33/0.48 != ( output @ Name13 @ Name24 @ Pi ) ) ).
% 0.33/0.48
% 0.33/0.48 % pi.distinct(1)
% 0.33/0.48 thf(fact_212_pi_Odistinct_I23_J,axiom,
% 0.33/0.48 ! [Name1: name,Name22: name,Pi3: pi,Name13: name,Name24: name,Pi: pi] :
% 0.33/0.48 ( ( output @ Name1 @ Name22 @ Pi3 )
% 0.33/0.48 != ( match @ Name13 @ Name24 @ Pi ) ) ).
% 0.33/0.48
% 0.33/0.48 % pi.distinct(23)
% 0.33/0.48 thf(fact_213_resZeroTrans,axiom,
% 0.33/0.48 ! [X2: name,Rs: late_residual] :
% 0.33/0.48 ~ ( late_transitions @ ( res @ X2 @ piNil ) @ Rs ) ).
% 0.33/0.48
% 0.33/0.48 % resZeroTrans
% 0.33/0.48 thf(fact_214_nilSim_I2_J,axiom,
% 0.33/0.48 ! [Rel: set @ ( product_prod @ pi @ pi ),A2: name,X2: name,P: pi] :
% 0.33/0.48 ~ ( strong743114133lation @ piNil @ Rel @ ( input @ A2 @ X2 @ P ) ) ).
% 0.33/0.48
% 0.33/0.48 % nilSim(2)
% 0.33/0.48 thf(fact_215_nilSim_I3_J,axiom,
% 0.33/0.48 ! [Rel: set @ ( product_prod @ pi @ pi ),A2: name,B2: name,P: pi] :
% 0.33/0.48 ~ ( strong743114133lation @ piNil @ Rel @ ( output @ A2 @ B2 @ P ) ) ).
% 0.33/0.48
% 0.33/0.48 % nilSim(3)
% 0.33/0.48 thf(fact_216_nilSim_I1_J,axiom,
% 0.33/0.48 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi] :
% 0.33/0.48 ~ ( strong743114133lation @ piNil @ Rel @ ( tau @ P ) ) ).
% 0.33/0.48
% 0.33/0.48 % nilSim(1)
% 0.33/0.48 thf(fact_217_simps_I6_J,axiom,
% 0.33/0.48 ! [A2: name,B2: name,P: pi,C2: name,D: name] :
% 0.33/0.48 ( ( subs @ ( mismatch @ A2 @ B2 @ P ) @ C2 @ D )
% 0.33/0.48 = ( mismatch @ ( subst_name @ A2 @ C2 @ D ) @ ( subst_name @ B2 @ C2 @ D ) @ ( subs @ P @ C2 @ D ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % simps(6)
% 0.33/0.48 thf(fact_218_pi_Ofresh_I6_J,axiom,
% 0.33/0.48 ! [A2: name,X32: name,X22: name,X1: pi] :
% 0.33/0.48 ( ( fresh @ name @ pi @ A2 @ ( mismatch @ X32 @ X22 @ X1 ) )
% 0.33/0.48 = ( ( fresh @ name @ name @ A2 @ X32 )
% 0.33/0.48 & ( fresh @ name @ name @ A2 @ X22 )
% 0.33/0.48 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % pi.fresh(6)
% 0.33/0.48 thf(fact_219_pi_Odistinct_I9_J,axiom,
% 0.33/0.48 ! [Name13: name,Name24: name,Pi: pi] :
% 0.33/0.48 ( piNil
% 0.33/0.48 != ( mismatch @ Name13 @ Name24 @ Pi ) ) ).
% 0.33/0.48
% 0.33/0.48 % pi.distinct(9)
% 0.33/0.48 thf(fact_220_pi_Odistinct_I61_J,axiom,
% 0.33/0.48 ! [Name1: name,Name22: name,Pi3: pi,Name13: name,Name24: name,Pi: pi] :
% 0.33/0.48 ( ( match @ Name1 @ Name22 @ Pi3 )
% 0.33/0.48 != ( mismatch @ Name13 @ Name24 @ Pi ) ) ).
% 0.33/0.48
% 0.33/0.48 % pi.distinct(61)
% 0.33/0.48 thf(fact_221_pi_Odistinct_I25_J,axiom,
% 0.33/0.48 ! [Name1: name,Name22: name,Pi3: pi,Name13: name,Name24: name,Pi: pi] :
% 0.33/0.48 ( ( output @ Name1 @ Name22 @ Pi3 )
% 0.33/0.48 != ( mismatch @ Name13 @ Name24 @ Pi ) ) ).
% 0.33/0.48
% 0.33/0.48 % pi.distinct(25)
% 0.33/0.48 thf(fact_222_pi_Odistinct_I39_J,axiom,
% 0.33/0.48 ! [Pi3: pi,Name13: name,Name24: name,Pi: pi] :
% 0.33/0.48 ( ( tau @ Pi3 )
% 0.33/0.48 != ( mismatch @ Name13 @ Name24 @ Pi ) ) ).
% 0.33/0.48
% 0.33/0.48 % pi.distinct(39)
% 0.33/0.48 thf(fact_223_pi_Oinject_I5_J,axiom,
% 0.33/0.48 ! [X32: name,X22: name,X1: pi,Y32: name,Y2: name,Y1: pi] :
% 0.33/0.48 ( ( ( mismatch @ X32 @ X22 @ X1 )
% 0.33/0.48 = ( mismatch @ Y32 @ Y2 @ Y1 ) )
% 0.33/0.48 = ( ( X32 = Y32 )
% 0.33/0.48 & ( X22 = Y2 )
% 0.33/0.48 & ( X1 = Y1 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % pi.inject(5)
% 0.33/0.48 thf(fact_224_pi_Odistinct_I75_J,axiom,
% 0.33/0.48 ! [Name1: name,Name22: name,Pi3: pi,Name: name,Pi: pi] :
% 0.33/0.48 ( ( mismatch @ Name1 @ Name22 @ Pi3 )
% 0.33/0.48 != ( res @ Name @ Pi ) ) ).
% 0.33/0.48
% 0.33/0.48 % pi.distinct(75)
% 0.33/0.48 thf(fact_225_pi_Odistinct_I73_J,axiom,
% 0.33/0.48 ! [Name1: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 0.33/0.48 ( ( mismatch @ Name1 @ Name22 @ Pi3 )
% 0.33/0.48 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.33/0.48
% 0.33/0.48 % pi.distinct(73)
% 0.33/0.48 thf(fact_226_Mismatch,axiom,
% 0.33/0.48 ! [P: pi,Rs: late_residual,A2: name,B2: name] :
% 0.33/0.48 ( ( late_transitions @ P @ Rs )
% 0.33/0.48 => ( ( A2 != B2 )
% 0.33/0.48 => ( late_transitions @ ( mismatch @ A2 @ B2 @ P ) @ Rs ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % Mismatch
% 0.33/0.48 thf(fact_227_mismatchCases_H,axiom,
% 0.33/0.48 ! [A2: name,B2: name,P: pi,Rs: late_residual] :
% 0.33/0.48 ( ( late_transitions @ ( mismatch @ A2 @ B2 @ P ) @ Rs )
% 0.33/0.48 => ~ ! [P4: pi,A4: name,B4: name] :
% 0.33/0.48 ( ( ( A2 = A4 )
% 0.33/0.48 & ( B2 = B4 )
% 0.33/0.48 & ( P = P4 ) )
% 0.33/0.48 => ( ( late_transitions @ P4 @ Rs )
% 0.33/0.48 => ( A4 = B4 ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % mismatchCases'
% 0.33/0.48 thf(fact_228_mismatchTrans,axiom,
% 0.33/0.48 ! [A2: name,P: pi,Rs: late_residual] :
% 0.33/0.48 ~ ( late_transitions @ ( mismatch @ A2 @ A2 @ P ) @ Rs ) ).
% 0.33/0.48
% 0.33/0.48 % mismatchTrans
% 0.33/0.48 thf(fact_229_mismatchCases,axiom,
% 0.33/0.48 ! [A2: name,B2: name,P: pi,Rs: late_residual,F3: name > name > $o] :
% 0.33/0.48 ( ( late_transitions @ ( mismatch @ A2 @ B2 @ P ) @ Rs )
% 0.33/0.48 => ( ( ( late_transitions @ P @ Rs )
% 0.33/0.48 => ( ( A2 != B2 )
% 0.33/0.48 => ( F3 @ A2 @ B2 ) ) )
% 0.33/0.48 => ( F3 @ A2 @ B2 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % mismatchCases
% 0.33/0.48 thf(fact_230_pi_Odistinct_I51_J,axiom,
% 0.33/0.48 ! [Name1: name,Name22: name,Pi3: pi,Name13: name,Name24: name,Pi: pi] :
% 0.33/0.48 ( ( input @ Name1 @ Name22 @ Pi3 )
% 0.33/0.48 != ( mismatch @ Name13 @ Name24 @ Pi ) ) ).
% 0.33/0.48
% 0.33/0.48 % pi.distinct(51)
% 0.33/0.48 thf(fact_231_mismatchNilLeft,axiom,
% 0.33/0.48 ! [Rel: set @ ( product_prod @ pi @ pi ),A2: name,P: pi] : ( strong743114133lation @ piNil @ Rel @ ( mismatch @ A2 @ A2 @ P ) ) ).
% 0.33/0.48
% 0.33/0.48 % mismatchNilLeft
% 0.33/0.48 thf(fact_232_pi_Ostrong__induct,axiom,
% 0.33/0.48 ! [N: $tType] :
% 0.33/0.48 ( ( fs_name @ N )
% 0.33/0.48 => ! [P: N > pi > $o,Z: N,Pi3: pi] :
% 0.33/0.48 ( ! [Z2: N] : ( P @ Z2 @ piNil )
% 0.33/0.48 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: N] :
% 0.33/0.48 ( ! [Za: N] : ( P @ Za @ Pi4 )
% 0.33/0.48 => ( P @ Z2 @ ( output @ Name12 @ Name23 @ Pi4 ) ) )
% 0.33/0.48 => ( ! [Pi4: pi,Z2: N] :
% 0.33/0.48 ( ! [Za: N] : ( P @ Za @ Pi4 )
% 0.33/0.48 => ( P @ Z2 @ ( tau @ Pi4 ) ) )
% 0.33/0.48 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: N] :
% 0.33/0.48 ( ( fresh @ name @ N @ Name23 @ Z2 )
% 0.33/0.48 => ( ( fresh @ name @ name @ Name23 @ Name12 )
% 0.33/0.48 => ( ! [Za: N] : ( P @ Za @ Pi4 )
% 0.33/0.48 => ( P @ Z2 @ ( input @ Name12 @ Name23 @ Pi4 ) ) ) ) )
% 0.33/0.48 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: N] :
% 0.33/0.48 ( ! [Za: N] : ( P @ Za @ Pi4 )
% 0.33/0.48 => ( P @ Z2 @ ( match @ Name12 @ Name23 @ Pi4 ) ) )
% 0.33/0.48 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: N] :
% 0.33/0.48 ( ! [Za: N] : ( P @ Za @ Pi4 )
% 0.33/0.48 => ( P @ Z2 @ ( mismatch @ Name12 @ Name23 @ Pi4 ) ) )
% 0.33/0.48 => ( ! [Pi13: pi,Pi23: pi,Z2: N] :
% 0.33/0.48 ( ! [Za: N] : ( P @ Za @ Pi13 )
% 0.33/0.48 => ( ! [Za: N] : ( P @ Za @ Pi23 )
% 0.33/0.48 => ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 0.33/0.48 => ( ! [Pi13: pi,Pi23: pi,Z2: N] :
% 0.33/0.48 ( ! [Za: N] : ( P @ Za @ Pi13 )
% 0.33/0.48 => ( ! [Za: N] : ( P @ Za @ Pi23 )
% 0.33/0.48 => ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
% 0.33/0.48 => ( ! [Name3: name,Pi4: pi,Z2: N] :
% 0.33/0.48 ( ( fresh @ name @ N @ Name3 @ Z2 )
% 0.33/0.48 => ( ! [Za: N] : ( P @ Za @ Pi4 )
% 0.33/0.48 => ( P @ Z2 @ ( res @ Name3 @ Pi4 ) ) ) )
% 0.33/0.48 => ( ! [Pi4: pi,Z2: N] :
% 0.33/0.48 ( ! [Za: N] : ( P @ Za @ Pi4 )
% 0.33/0.48 => ( P @ Z2 @ ( bang @ Pi4 ) ) )
% 0.33/0.48 => ( P @ Z @ Pi3 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % pi.strong_induct
% 0.33/0.48 thf(fact_233_pi_Ostrong__inducts,axiom,
% 0.33/0.48 ! [A: $tType] :
% 0.33/0.48 ( ( fs_name @ A )
% 0.33/0.48 => ! [P: A > pi > $o,Z: A,Pi3: pi] :
% 0.33/0.48 ( ! [Z2: A] : ( P @ Z2 @ piNil )
% 0.33/0.48 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: A] :
% 0.33/0.48 ( ! [Za: A] : ( P @ Za @ Pi4 )
% 0.33/0.48 => ( P @ Z2 @ ( output @ Name12 @ Name23 @ Pi4 ) ) )
% 0.33/0.48 => ( ! [Pi4: pi,Z2: A] :
% 0.33/0.48 ( ! [Za: A] : ( P @ Za @ Pi4 )
% 0.33/0.48 => ( P @ Z2 @ ( tau @ Pi4 ) ) )
% 0.33/0.48 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: A] :
% 0.33/0.48 ( ( fresh @ name @ A @ Name23 @ Z2 )
% 0.33/0.48 => ( ( fresh @ name @ name @ Name23 @ Name12 )
% 0.33/0.48 => ( ! [Za: A] : ( P @ Za @ Pi4 )
% 0.33/0.48 => ( P @ Z2 @ ( input @ Name12 @ Name23 @ Pi4 ) ) ) ) )
% 0.33/0.48 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: A] :
% 0.33/0.48 ( ! [Za: A] : ( P @ Za @ Pi4 )
% 0.33/0.48 => ( P @ Z2 @ ( match @ Name12 @ Name23 @ Pi4 ) ) )
% 0.33/0.48 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: A] :
% 0.33/0.48 ( ! [Za: A] : ( P @ Za @ Pi4 )
% 0.33/0.48 => ( P @ Z2 @ ( mismatch @ Name12 @ Name23 @ Pi4 ) ) )
% 0.33/0.48 => ( ! [Pi13: pi,Pi23: pi,Z2: A] :
% 0.33/0.48 ( ! [Za: A] : ( P @ Za @ Pi13 )
% 0.33/0.48 => ( ! [Za: A] : ( P @ Za @ Pi23 )
% 0.33/0.48 => ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 0.33/0.48 => ( ! [Pi13: pi,Pi23: pi,Z2: A] :
% 0.33/0.48 ( ! [Za: A] : ( P @ Za @ Pi13 )
% 0.33/0.48 => ( ! [Za: A] : ( P @ Za @ Pi23 )
% 0.33/0.48 => ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
% 0.33/0.48 => ( ! [Name3: name,Pi4: pi,Z2: A] :
% 0.33/0.48 ( ( fresh @ name @ A @ Name3 @ Z2 )
% 0.33/0.48 => ( ! [Za: A] : ( P @ Za @ Pi4 )
% 0.33/0.48 => ( P @ Z2 @ ( res @ Name3 @ Pi4 ) ) ) )
% 0.33/0.48 => ( ! [Pi4: pi,Z2: A] :
% 0.33/0.48 ( ! [Za: A] : ( P @ Za @ Pi4 )
% 0.33/0.48 => ( P @ Z2 @ ( bang @ Pi4 ) ) )
% 0.33/0.48 => ( P @ Z @ Pi3 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % pi.strong_inducts
% 0.33/0.48 thf(fact_234_pi_Ofresh_I10_J,axiom,
% 0.33/0.48 ! [A2: name,X1: pi] :
% 0.33/0.48 ( ( fresh @ name @ pi @ A2 @ ( bang @ X1 ) )
% 0.33/0.48 = ( fresh @ name @ pi @ A2 @ X1 ) ) ).
% 0.33/0.48
% 0.33/0.48 % pi.fresh(10)
% 0.33/0.48 thf(fact_235_pi_Ofresh_I7_J,axiom,
% 0.33/0.48 ! [A2: name,X22: pi,X1: pi] :
% 0.33/0.48 ( ( fresh @ name @ pi @ A2 @ ( sum @ X22 @ X1 ) )
% 0.33/0.48 = ( ( fresh @ name @ pi @ A2 @ X22 )
% 0.33/0.48 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % pi.fresh(7)
% 0.33/0.48 thf(fact_236_simps_I10_J,axiom,
% 0.33/0.48 ! [P: pi,C2: name,D: name] :
% 0.33/0.48 ( ( subs @ ( bang @ P ) @ C2 @ D )
% 0.33/0.48 = ( bang @ ( subs @ P @ C2 @ D ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % simps(10)
% 0.33/0.48 thf(fact_237_simps_I7_J,axiom,
% 0.33/0.48 ! [P: pi,Q: pi,C2: name,D: name] :
% 0.33/0.48 ( ( subs @ ( sum @ P @ Q ) @ C2 @ D )
% 0.33/0.48 = ( sum @ ( subs @ P @ C2 @ D ) @ ( subs @ Q @ C2 @ D ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % simps(7)
% 0.33/0.48 thf(fact_238_pi_Odistinct_I77_J,axiom,
% 0.33/0.48 ! [Name1: name,Name22: name,Pi3: pi,Pi: pi] :
% 0.33/0.48 ( ( mismatch @ Name1 @ Name22 @ Pi3 )
% 0.33/0.48 != ( bang @ Pi ) ) ).
% 0.33/0.48
% 0.33/0.48 % pi.distinct(77)
% 0.33/0.48 thf(fact_239_pi_Odistinct_I71_J,axiom,
% 0.33/0.48 ! [Name1: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 0.33/0.48 ( ( mismatch @ Name1 @ Name22 @ Pi3 )
% 0.33/0.48 != ( sum @ Pi12 @ Pi22 ) ) ).
% 0.33/0.48
% 0.33/0.48 % pi.distinct(71)
% 0.33/0.48 thf(fact_240_pi_Odistinct_I59_J,axiom,
% 0.33/0.48 ! [Name1: name,Name22: name,Pi3: pi,Pi: pi] :
% 0.33/0.48 ( ( input @ Name1 @ Name22 @ Pi3 )
% 0.33/0.48 != ( bang @ Pi ) ) ).
% 0.33/0.48
% 0.33/0.48 % pi.distinct(59)
% 0.33/0.48 thf(fact_241_pi_Odistinct_I53_J,axiom,
% 0.33/0.48 ! [Name1: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 0.33/0.48 ( ( input @ Name1 @ Name22 @ Pi3 )
% 0.33/0.48 != ( sum @ Pi12 @ Pi22 ) ) ).
% 0.33/0.48
% 0.33/0.48 % pi.distinct(53)
% 0.33/0.48 thf(fact_242_pi_Odistinct_I47_J,axiom,
% 0.33/0.48 ! [Pi3: pi,Pi: pi] :
% 0.33/0.48 ( ( tau @ Pi3 )
% 0.33/0.48 != ( bang @ Pi ) ) ).
% 0.33/0.48
% 0.33/0.48 % pi.distinct(47)
% 0.33/0.48 thf(fact_243_pi_Odistinct_I41_J,axiom,
% 0.33/0.48 ! [Pi3: pi,Pi12: pi,Pi22: pi] :
% 0.33/0.48 ( ( tau @ Pi3 )
% 0.33/0.48 != ( sum @ Pi12 @ Pi22 ) ) ).
% 0.33/0.48
% 0.33/0.48 % pi.distinct(41)
% 0.33/0.48 thf(fact_244_pi_Odistinct_I79_J,axiom,
% 0.33/0.48 ! [Pi1: pi,Pi2: pi,Pi12: pi,Pi22: pi] :
% 0.33/0.48 ( ( sum @ Pi1 @ Pi2 )
% 0.33/0.48 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.33/0.48
% 0.33/0.48 % pi.distinct(79)
% 0.33/0.48 thf(fact_245_pi_Odistinct_I81_J,axiom,
% 0.33/0.48 ! [Pi1: pi,Pi2: pi,Name: name,Pi: pi] :
% 0.33/0.48 ( ( sum @ Pi1 @ Pi2 )
% 0.33/0.48 != ( res @ Name @ Pi ) ) ).
% 0.33/0.48
% 0.33/0.48 % pi.distinct(81)
% 0.33/0.48 thf(fact_246_pi_Odistinct_I27_J,axiom,
% 0.33/0.48 ! [Name1: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 0.33/0.48 ( ( output @ Name1 @ Name22 @ Pi3 )
% 0.33/0.48 != ( sum @ Pi12 @ Pi22 ) ) ).
% 0.33/0.48
% 0.33/0.48 % pi.distinct(27)
% 0.33/0.48 thf(fact_247_pi_Odistinct_I83_J,axiom,
% 0.33/0.48 ! [Pi1: pi,Pi2: pi,Pi: pi] :
% 0.33/0.48 ( ( sum @ Pi1 @ Pi2 )
% 0.33/0.48 != ( bang @ Pi ) ) ).
% 0.33/0.48
% 0.33/0.48 % pi.distinct(83)
% 0.33/0.48 thf(fact_248_pi_Oinject_I6_J,axiom,
% 0.33/0.48 ! [X22: pi,X1: pi,Y2: pi,Y1: pi] :
% 0.33/0.48 ( ( ( sum @ X22 @ X1 )
% 0.33/0.48 = ( sum @ Y2 @ Y1 ) )
% 0.33/0.48 = ( ( X22 = Y2 )
% 0.33/0.48 & ( X1 = Y1 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % pi.inject(6)
% 0.33/0.48 thf(fact_249_pi_Oinject_I9_J,axiom,
% 0.33/0.48 ! [X1: pi,Y1: pi] :
% 0.33/0.48 ( ( ( bang @ X1 )
% 0.33/0.48 = ( bang @ Y1 ) )
% 0.33/0.48 = ( X1 = Y1 ) ) ).
% 0.33/0.48
% 0.33/0.48 % pi.inject(9)
% 0.33/0.48 thf(fact_250_sumCases,axiom,
% 0.33/0.48 ! [P: pi,Q: pi,Rs: late_residual] :
% 0.33/0.48 ( ( late_transitions @ ( sum @ P @ Q ) @ Rs )
% 0.33/0.49 => ( ~ ( late_transitions @ P @ Rs )
% 0.33/0.49 => ( late_transitions @ Q @ Rs ) ) ) ).
% 0.33/0.49
% 0.33/0.49 % sumCases
% 0.33/0.49 thf(fact_251_sumCases_H,axiom,
% 0.33/0.49 ! [P: pi,Q: pi,Rs: late_residual] :
% 0.33/0.49 ( ( late_transitions @ ( sum @ P @ Q ) @ Rs )
% 0.33/0.49 => ( ~ ( late_transitions @ P @ Rs )
% 0.33/0.49 => ( late_transitions @ Q @ Rs ) ) ) ).
% 0.33/0.49
% 0.33/0.49 % sumCases'
% 0.33/0.49 thf(fact_252_Sum1,axiom,
% 0.33/0.49 ! [P: pi,Rs: late_residual,Q: pi] :
% 0.33/0.49 ( ( late_transitions @ P @ Rs )
% 0.33/0.49 => ( late_transitions @ ( sum @ P @ Q ) @ Rs ) ) ).
% 0.33/0.49
% 0.33/0.49 % Sum1
% 0.33/0.49 thf(fact_253_Sum2,axiom,
% 0.33/0.49 ! [Q: pi,Rs: late_residual,P: pi] :
% 0.33/0.49 ( ( late_transitions @ Q @ Rs )
% 0.33/0.49 => ( late_transitions @ ( sum @ P @ Q ) @ Rs ) ) ).
% 0.33/0.49
% 0.33/0.49 % Sum2
% 0.33/0.49 thf(fact_254_pi_Odistinct_I33_J,axiom,
% 0.33/0.49 ! [Name1: name,Name22: name,Pi3: pi,Pi: pi] :
% 0.33/0.49 ( ( output @ Name1 @ Name22 @ Pi3 )
% 0.33/0.49 != ( bang @ Pi ) ) ).
% 0.33/0.49
% 0.33/0.49 % pi.distinct(33)
% 0.33/0.49 thf(fact_255_pi_Odistinct_I89_J,axiom,
% 0.33/0.49 ! [Name2: name,Pi3: pi,Pi: pi] :
% 0.33/0.49 ( ( res @ Name2 @ Pi3 )
% 0.33/0.49 != ( bang @ Pi ) ) ).
% 0.33/0.49
% 0.33/0.49 % pi.distinct(89)
% 0.33/0.49
% 0.33/0.49 % Type constructors (7)
% 0.33/0.49 thf(tcon_Agent_Opi___Agent_Ofs__name,axiom,
% 0.33/0.49 fs_name @ pi ).
% 0.33/0.49
% 0.33/0.49 thf(tcon_HOL_Obool___Agent_Ofs__name_1,axiom,
% 0.33/0.49 fs_name @ $o ).
% 0.33/0.49
% 0.33/0.49 thf(tcon_Agent_Oname___Agent_Ofs__name_2,axiom,
% 0.33/0.49 fs_name @ name ).
% 0.33/0.49
% 0.33/0.49 thf(tcon_Product__Type_Oprod___Agent_Ofs__name_3,axiom,
% 0.33/0.49 ! [A7: $tType,A8: $tType] :
% 0.33/0.49 ( ( ( fs_name @ A7 )
% 0.33/0.49 & ( fs_name @ A8 ) )
% 0.33/0.49 => ( fs_name @ ( product_prod @ A7 @ A8 ) ) ) ).
% 0.33/0.49
% 0.33/0.49 thf(tcon_Late__Semantics_OfreeRes___Agent_Ofs__name_4,axiom,
% 0.33/0.49 fs_name @ late_freeRes ).
% 0.33/0.49
% 0.33/0.49 thf(tcon_Late__Semantics_Osubject___Agent_Ofs__name_5,axiom,
% 0.33/0.49 fs_name @ late_subject ).
% 0.33/0.49
% 0.33/0.49 thf(tcon_Late__Semantics_Oresidual___Agent_Ofs__name_6,axiom,
% 0.33/0.49 fs_name @ late_residual ).
% 0.33/0.49
% 0.33/0.49 % Helper facts (3)
% 0.33/0.49 thf(help_If_3_1_T,axiom,
% 0.33/0.49 ! [P: $o] :
% 0.33/0.49 ( ( P = $true )
% 0.33/0.49 | ( P = $false ) ) ).
% 0.33/0.49
% 0.33/0.49 thf(help_If_2_1_T,axiom,
% 0.33/0.49 ! [A: $tType,X2: A,Y: A] :
% 0.33/0.49 ( ( if @ A @ $false @ X2 @ Y )
% 0.33/0.49 = Y ) ).
% 0.33/0.49
% 0.33/0.49 thf(help_If_1_1_T,axiom,
% 0.33/0.49 ! [A: $tType,X2: A,Y: A] :
% 0.33/0.49 ( ( if @ A @ $true @ X2 @ Y )
% 0.33/0.49 = X2 ) ).
% 0.33/0.49
% 0.33/0.49 % Conjectures (1)
% 0.33/0.49 thf(conj_0,conjecture,
% 0.33/0.49 ? [P6: pi] :
% 0.33/0.49 ( ( late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_FreeR @ late_TauR @ P6 ) )
% 0.33/0.49 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P6 @ ( res @ y @ ( par @ p2 @ ( subs @ ( par @ q2 @ r ) @ x @ y ) ) ) ) @ rel ) ) ).
% 0.33/0.49
% 0.33/0.49 %------------------------------------------------------------------------------
% 0.33/0.49 ------------------------
% 2.70/1.53 ---- Embedded in THF ---
% 2.70/1.53 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.70/1.53 %%% Generated on Tue Feb 24 08:30:06 EST 2026
% 2.70/1.53 %%% using '$$dhol' embedding, version 1.3.0.
% 2.70/1.53 %%% Logic specification used:
% 2.70/1.53 %%% thf(spec, logic, $$dhol).
% 2.70/1.53
% 2.70/1.53 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.eALBO61dU7/DTF2DTF25766.p
% 2.70/1.53 thf(ty_t_Late__Semantics_Oresidual, type, late_residual: $tType).
% 2.70/1.53 thf(ty_t_Late__Semantics_Osubject, type, late_subject: $tType).
% 2.70/1.53 thf(ty_t_Late__Semantics_OfreeRes, type, late_freeRes: $tType).
% 2.70/1.53 thf(ty_t_Product__Type_Oprod, type, product_prod: ($tType > ($tType > $tType))).
% 2.70/1.53 thf(ty_t_Nominal_Onoption, type, noption: ($tType > $tType)).
% 2.70/1.53 thf(ty_t_Agent_Oname, type, name: $tType).
% 2.70/1.53 thf(ty_t_Agent_Opi, type, pi: $tType).
% 2.70/1.53 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 2.70/1.53 thf(sy_cl_Agent_Ofs__name, type, fs_name: (!> [A:$tType]: ($o))).
% 2.70/1.53 thf(sy_c_Agent_Opi_OBang, type, bang: (pi > pi)).
% 2.70/1.53 thf(sy_c_Agent_Opi_OInput, type, input: (name > (name > (pi > pi)))).
% 2.70/1.53 thf(sy_c_Agent_Opi_OMatch, type, match: (name > (name > (pi > pi)))).
% 2.70/1.53 thf(sy_c_Agent_Opi_OMismatch, type, mismatch: (name > (name > (pi > pi)))).
% 2.70/1.53 thf(sy_c_Agent_Opi_OOutput, type, output: (name > (name > (pi > pi)))).
% 2.70/1.53 thf(sy_c_Agent_Opi_OPar, type, par: (pi > (pi > pi))).
% 2.70/1.53 thf(sy_c_Agent_Opi_OPiNil, type, piNil: pi).
% 2.70/1.53 thf(sy_c_Agent_Opi_ORes, type, res: (name > (pi > pi))).
% 2.70/1.53 thf(sy_c_Agent_Opi_OSum, type, sum: (pi > (pi > pi))).
% 2.70/1.53 thf(sy_c_Agent_Opi_OTau, type, tau: (pi > pi)).
% 2.70/1.53 thf(sy_c_Agent_Osubs, type, subs: (pi > (name > (name > pi)))).
% 2.70/1.53 thf(sy_c_Agent_Osubst__name, type, subst_name: (name > (name > (name > name)))).
% 2.70/1.53 thf(sy_c_If, type, if: (!> [A:$tType]: (($o > (A > (A > A)))))).
% 2.70/1.53 thf(sy_c_Late__Semantics_OfreeRes_OOutputR, type, late_OutputR: (name > (name > late_freeRes))).
% 2.70/1.53 thf(sy_c_Late__Semantics_OfreeRes_OTauR, type, late_TauR: late_freeRes).
% 2.70/1.53 thf(sy_c_Late__Semantics_OfreeRes_OfreeRes__rec, type, late_freeRes_rec: (!> [T:$tType]: (((name > (name > T)) > (T > (late_freeRes > T)))))).
% 2.70/1.53 thf(sy_c_Late__Semantics_Oresidual_OBoundR, type, late_BoundR: (late_subject > (name > (pi > late_residual)))).
% 2.70/1.53 thf(sy_c_Late__Semantics_Oresidual_OFreeR, type, late_FreeR: (late_freeRes > (pi > late_residual))).
% 2.70/1.53 thf(sy_c_Late__Semantics_Osubject_OBoundOutputS, type, late_BoundOutputS: (name > late_subject)).
% 2.70/1.53 thf(sy_c_Late__Semantics_Osubject_OInputS, type, late_InputS: (name > late_subject)).
% 2.70/1.53 thf(sy_c_Late__Semantics_Osubject_Osubject__rec, type, late_subject_rec: (!> [T:$tType]: (((name > T) > ((name > T) > (late_subject > T)))))).
% 2.70/1.53 thf(sy_c_Late__Semantics_Otransitions, type, late_transitions: (pi > (late_residual > $o))).
% 2.70/1.53 thf(sy_c_Nominal_Oabs__fun, type, abs_fun: (!> [X:$tType,A:$tType]: ((X > (A > (X > (noption @ A))))))).
% 2.70/1.53 thf(sy_c_Nominal_Ofresh, type, fresh: (!> [X:$tType,A:$tType]: ((X > (A > $o))))).
% 2.70/1.53 thf(sy_c_Product__Type_OPair, type, product_Pair: (!> [A:$tType,B:$tType]: ((A > (B > ((product_prod @ A) @ B)))))).
% 2.70/1.53 thf(sy_c_Product__Type_Ointernal__case__prod, type, produc2004651681e_prod: (!> [A:$tType,B:$tType,C:$tType]: (((A > (B > C)) > (((product_prod @ A) @ B) > C))))).
% 2.70/1.53 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod, type, product_rec_prod: (!> [A:$tType,B:$tType,T:$tType]: (((A > (B > T)) > (((product_prod @ A) @ B) > T))))).
% 2.70/1.53 thf(sy_c_Rel_Oeqvt, type, eqvt: (!> [A:$tType]: (((set @ ((product_prod @ A) @ A)) > $o)))).
% 2.70/1.53 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 2.70/1.53 thf(sy_c_Strong__Late__Sim_Oderivative, type, strong2129052853vative: (pi > (pi > (late_subject > (name > ((set @ ((product_prod @ pi) @ pi)) > $o)))))).
% 2.70/1.53 thf(sy_c_Strong__Late__Sim_Osimulation, type, strong743114133lation: (pi > ((set @ ((product_prod @ pi) @ pi)) > (pi > $o)))).
% 2.70/1.53 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 2.70/1.53 thf(sy_v_P, type, p: pi).
% 2.70/1.53 thf(sy_v_PQR____, type, pqr: pi).
% 2.70/1.53 thf(sy_v_P_H____, type, p2: pi).
% 2.70/1.53 thf(sy_v_Q, type, q: pi).
% 2.70/1.53 thf(sy_v_QR____, type, qr: pi).
% 2.70/1.53 thf(sy_v_Q_H____, type, q2: pi).
% 2.70/1.53 thf(sy_v_R, type, r: pi).
% 2.70/1.53 thf(sy_v_Rel, type, rel: (set @ ((product_prod @ pi) @ pi))).
% 2.70/1.53 thf(sy_v__092_060alpha_062____, type, alpha: late_freeRes).
% 2.70/1.53 thf(sy_v_a____, type, a: name).
% 2.70/1.53 thf(sy_v_x____, type, x: name).
% 2.70/1.53 thf(sy_v_y____, type, y: name).
% 2.70/1.53 thf(fact_0_cClose2_Ohyps_I14_J, axiom, (alpha = late_TauR)).
% 2.70/1.53 thf(fact_1_cClose2_Ohyps_I6_J, axiom, (x != y)).
% 2.70/1.53 thf(fact_2_cClose2_Ohyps_I10_J, axiom, (y != a)).
% 2.70/1.53 thf(fact_3_cClose2_Ohyps_I5_J, axiom, (x != a)).
% 2.70/1.53 thf(fact_4_Ass, axiom, (! [S:pi,T2:pi,U:pi]: ((((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ ((par @ ((par @ S) @ T2)) @ U)) @ ((par @ S) @ ((par @ T2) @ U)))) @ rel)))).
% 2.70/1.53 thf(fact_5_Res, axiom, (! [S:pi,T2:pi,X2:name]: (((((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ S) @ T2)) @ rel) => (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ ((res @ X2) @ S)) @ ((res @ X2) @ T2))) @ rel))))).
% 2.70/1.53 thf(fact_6__092_060open_062_I_060_092_060nu_062y_062_IP_H_A_092_060parallel_062_AQ_H_091x_058_058_061y_093_J_A_092_060parallel_062_AR_M_A_060_092_060nu_062y_062_IP_H_A_092_060parallel_062_A_IQ_H_A_092_060parallel_062_AR_J_091x_058_058_061y_093_J_J_A_092_060in_062_ARel_092_060close_062, axiom, (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ ((par @ ((res @ y) @ ((par @ p2) @ (((subs @ q2) @ x) @ y)))) @ r)) @ ((res @ y) @ ((par @ p2) @ (((subs @ ((par @ q2) @ r)) @ x) @ y))))) @ rel)).
% 2.70/1.53 thf(fact_7__092_060open_062_IP_A_092_060parallel_062_AQ_J_A_092_060parallel_062_AR_A_092_060longmapsto_062_A_092_060tau_062_A_092_060prec_062_A_060_092_060nu_062y_062_IP_H_A_092_060parallel_062_AQ_H_091x_058_058_061y_093_J_A_092_060parallel_062_AR_092_060close_062, axiom, ((late_transitions @ ((par @ ((par @ p) @ q)) @ r)) @ ((late_FreeR @ late_TauR) @ ((par @ ((res @ y) @ ((par @ p2) @ (((subs @ q2) @ x) @ y)))) @ r)))).
% 2.70/1.53 thf(fact_8_Free_Ohyps, axiom, ((late_transitions @ ((par @ p) @ ((par @ q) @ r))) @ ((late_FreeR @ alpha) @ pqr))).
% 2.70/1.53 thf(fact_9__092_060open_062_I_060_092_060nu_062y_062_IP_H_A_092_060parallel_062_AQ_H_091x_058_058_061y_093_J_A_092_060parallel_062_AR_M_A_060_092_060nu_062y_062_IP_H_A_092_060parallel_062_AQ_H_091x_058_058_061y_093_A_092_060parallel_062_AR_J_J_A_092_060in_062_ARel_092_060close_062, axiom, (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ ((par @ ((res @ y) @ ((par @ p2) @ (((subs @ q2) @ x) @ y)))) @ r)) @ ((res @ y) @ ((par @ p2) @ ((par @ (((subs @ q2) @ x) @ y)) @ r))))) @ rel)).
% 2.70/1.53 thf(fact_10__092_060open_062P_A_092_060parallel_062_AQ_A_092_060longmapsto_062_A_092_060tau_062_A_092_060prec_062_A_060_092_060nu_062y_062_IP_H_A_092_060parallel_062_AQ_H_091x_058_058_061y_093_J_092_060close_062, axiom, ((late_transitions @ ((par @ p) @ q)) @ ((late_FreeR @ late_TauR) @ ((res @ y) @ ((par @ p2) @ (((subs @ q2) @ x) @ y)))))).
% 2.70/1.53 thf(fact_11_cClose2_Ohyps_I13_J, axiom, ((((fresh @ name) @ pi) @ y) @ q)).
% 2.70/1.53 thf(fact_12_cClose2_Ohyps_I12_J, axiom, ((((fresh @ name) @ pi) @ x) @ q)).
% 2.70/1.53 thf(fact_13_cClose2_Ohyps_I7_J, axiom, ((((fresh @ name) @ pi) @ x) @ p2)).
% 2.70/1.53 thf(fact_14_cClose2_Ohyps_I8_J, axiom, ((((fresh @ name) @ pi) @ y) @ p)).
% 2.70/1.53 thf(fact_15_cClose2_Ohyps_I3_J, axiom, ((((fresh @ name) @ pi) @ x) @ p)).
% 2.70/1.53 thf(fact_16_cClose2_Ohyps_I9_J, axiom, ((((fresh @ name) @ pi) @ y) @ ((par @ q) @ r))).
% 2.70/1.53 thf(fact_17_cClose2_Ohyps_I4_J, axiom, ((((fresh @ name) @ pi) @ x) @ ((par @ q) @ r))).
% 2.70/1.53 thf(fact_18_simps_I9_J, axiom, (! [X2:name,C2:name,D:name,P:pi]: (((X2 != C2) => ((X2 != D) => ((((subs @ ((res @ X2) @ P)) @ C2) @ D) = ((res @ X2) @ (((subs @ P) @ C2) @ D)))))))).
% 2.70/1.53 thf(fact_19_simps_I8_J, axiom, (! [P:pi,Q:pi,C2:name,D:name]: (((((subs @ ((par @ P) @ Q)) @ C2) @ D) = ((par @ (((subs @ P) @ C2) @ D)) @ (((subs @ Q) @ C2) @ D)))))).
% 2.70/1.53 thf(fact_20_FreshExt, axiom, (! [X2:name,S:pi,T2:pi,U:pi]: ((((((fresh @ name) @ pi) @ X2) @ S) => (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ ((res @ X2) @ ((par @ ((par @ S) @ T2)) @ U))) @ ((par @ S) @ ((res @ X2) @ ((par @ T2) @ U))))) @ rel))))).
% 2.70/1.53 thf(fact_21_FreshExt_H, axiom, (! [X2:name,U:pi,S:pi,T2:pi]: ((((((fresh @ name) @ pi) @ X2) @ U) => (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ ((par @ ((res @ X2) @ ((par @ S) @ T2))) @ U)) @ ((res @ X2) @ ((par @ S) @ ((par @ T2) @ U))))) @ rel))))).
% 2.70/1.53 thf(fact_22_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))))))).
% 2.70/1.53 thf(fact_23_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))))))).
% 2.70/1.53 thf(fact_24_subst__identity, axiom, (! [P:pi,A2:name]: (((((subs @ P) @ A2) @ A2) = P)))).
% 2.70/1.53 thf(fact_25__092_060open_062x_A_092_060sharp_062_AR_092_060close_062, axiom, ((((fresh @ name) @ pi) @ x) @ r)).
% 2.70/1.53 thf(fact_26__092_060open_062y_A_092_060sharp_062_AR_092_060close_062, axiom, ((((fresh @ name) @ pi) @ y) @ r)).
% 2.70/1.53 thf(fact_27_prod_Oinject, axiom, (! [A:$tType,B:$tType,X1:A,X22:B,Y1:A,Y2:B]: (((((((product_Pair @ A) @ B) @ X1) @ X22) = ((((product_Pair @ A) @ B) @ Y1) @ Y2)) = ((X1 = Y1) & (X22 = Y2)))))).
% 2.70/1.53 thf(fact_28_old_Oprod_Oinject, axiom, (! [A:$tType,B:$tType,A2:A,B2:B,A3:A,B3:B]: (((((((product_Pair @ A) @ B) @ A2) @ B2) = ((((product_Pair @ A) @ B) @ A3) @ B3)) = ((A2 = A3) & (B2 = B3)))))).
% 2.70/1.53 thf(fact_29_cClose2_Ohyps_I11_J, axiom, ((((fresh @ name) @ pi) @ y) @ qr)).
% 2.70/1.53 thf(fact_30_pi_Ofresh_I8_J, axiom, (! [A2:name,X22:pi,X1:pi]: ((((((fresh @ name) @ pi) @ A2) @ ((par @ X22) @ X1)) = (((((fresh @ name) @ pi) @ A2) @ X22) & ((((fresh @ name) @ pi) @ A2) @ X1)))))).
% 2.70/1.53 thf(fact_31_substTrans, axiom, (! [B2:name,P:pi,A2:name,C2:name]: ((((((fresh @ name) @ pi) @ B2) @ P) => ((((subs @ (((subs @ P) @ A2) @ B2)) @ B2) @ C2) = (((subs @ P) @ A2) @ C2)))))).
% 2.70/1.53 thf(fact_32_name__exists__fresh, axiom, (! [A:$tType]: (((fs_name @ A) => (! [X2:A]: ((~ ((! [C3:name]: ((~ (((((fresh @ name) @ A) @ C3) @ X2))))))))))))).
% 2.70/1.53 thf(fact_33_freshRes, axiom, (! [A2:name,P:pi]: (((((fresh @ name) @ pi) @ A2) @ ((res @ A2) @ P))))).
% 2.70/1.53 thf(fact_34_fresh__fact2, axiom, (! [A2:name,B2:name,P:pi]: (((A2 != B2) => ((((fresh @ name) @ pi) @ A2) @ (((subs @ P) @ A2) @ B2)))))).
% 2.70/1.53 thf(fact_35_fresh__fact1, axiom, (! [A2:name,P:pi,C2:name,B2:name]: ((((((fresh @ name) @ pi) @ A2) @ P) => ((A2 != C2) => ((((fresh @ name) @ pi) @ A2) @ (((subs @ P) @ B2) @ C2))))))).
% 2.70/1.53 thf(fact_36_forget, axiom, (! [A2:name,P:pi,B2:name]: ((((((fresh @ name) @ pi) @ A2) @ P) => ((((subs @ P) @ A2) @ B2) = P))))).
% 2.70/1.53 thf(fact_37_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)))))).
% 2.70/1.53 thf(fact_38_substRes3, axiom, (! [B2:name,P:pi,A2:name]: ((((((fresh @ name) @ pi) @ B2) @ P) => ((((subs @ ((res @ A2) @ P)) @ A2) @ B2) = ((res @ B2) @ (((subs @ P) @ A2) @ B2))))))).
% 2.70/1.53 thf(fact_39_substRes2, axiom, (! [B2:name,P:pi,A2:name]: ((((((fresh @ name) @ pi) @ B2) @ P) => (((res @ A2) @ P) = ((res @ B2) @ (((subs @ P) @ A2) @ B2))))))).
% 2.70/1.53 thf(fact_40_old_Oprod_Oinducts, axiom, (! [B:$tType,A:$tType,P:(((product_prod @ A) @ B) > $o),Prod:((product_prod @ A) @ B)]: (((! [A4:A,B4:B]: ((P @ ((((product_Pair @ A) @ B) @ A4) @ B4)))) => (P @ Prod))))).
% 2.70/1.53 thf(fact_41_old_Oprod_Oexhaust, axiom, (! [A:$tType,B:$tType,Y:((product_prod @ A) @ B)]: ((~ ((! [A4:A,B4:B]: ((Y != ((((product_Pair @ A) @ B) @ A4) @ B4))))))))).
% 2.70/1.53 thf(fact_42_prod__induct7, axiom, (! [G:$tType,F:$tType,E:$tType,D2:$tType,C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D2) @ ((product_prod @ E) @ ((product_prod @ F) @ G)))))) > $o),X2:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D2) @ ((product_prod @ E) @ ((product_prod @ F) @ G))))))]: (((! [A4:A,B4:B,C3:C,D3:D2,E2:E,F2:F,G2:G]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D2) @ ((product_prod @ E) @ ((product_prod @ F) @ G)))))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D2) @ ((product_prod @ E) @ ((product_prod @ F) @ G))))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D2) @ ((product_prod @ E) @ ((product_prod @ F) @ G)))) @ C3) @ ((((product_Pair @ D2) @ ((product_prod @ E) @ ((product_prod @ F) @ G))) @ D3) @ ((((product_Pair @ E) @ ((product_prod @ F) @ G)) @ E2) @ ((((product_Pair @ F) @ G) @ F2) @ G2))))))))) => (P @ X2))))).
% 2.70/1.53 thf(fact_43_prod__induct6, axiom, (! [F:$tType,E:$tType,D2:$tType,C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D2) @ ((product_prod @ E) @ F))))) > $o),X2:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D2) @ ((product_prod @ E) @ F)))))]: (((! [A4:A,B4:B,C3:C,D3:D2,E2:E,F2:F]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D2) @ ((product_prod @ E) @ F))))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D2) @ ((product_prod @ E) @ F)))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D2) @ ((product_prod @ E) @ F))) @ C3) @ ((((product_Pair @ D2) @ ((product_prod @ E) @ F)) @ D3) @ ((((product_Pair @ E) @ F) @ E2) @ F2)))))))) => (P @ X2))))).
% 2.70/1.53 thf(fact_44_prod__induct5, axiom, (! [E:$tType,D2:$tType,C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D2) @ E)))) > $o),X2:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D2) @ E))))]: (((! [A4:A,B4:B,C3:C,D3:D2,E2:E]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D2) @ E)))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D2) @ E))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D2) @ E)) @ C3) @ ((((product_Pair @ D2) @ E) @ D3) @ E2))))))) => (P @ X2))))).
% 2.70/1.53 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P)) = (P @ A2))))).
% 2.70/1.53 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A5:(set @ A)]: ((((collect @ A) @ (^ [X3:A]: ((((member @ A) @ X3) @ A5)))) = A5)))).
% 2.70/1.53 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X4:A]: (((P @ X4) = (Q @ X4)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 2.70/1.53 thf(fact_48_prod__induct4, axiom, (! [D2:$tType,C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D2))) > $o),X2:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D2)))]: (((! [A4:A,B4:B,C3:C,D3:D2]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D2))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C) @ D2)) @ B4) @ ((((product_Pair @ C) @ D2) @ C3) @ D3)))))) => (P @ X2))))).
% 2.70/1.53 thf(fact_49_prod__induct3, axiom, (! [C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ C)) > $o),X2:((product_prod @ A) @ ((product_prod @ B) @ C))]: (((! [A4:A,B4:B,C3:C]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ C)) @ A4) @ ((((product_Pair @ B) @ C) @ B4) @ C3))))) => (P @ X2))))).
% 2.70/1.53 thf(fact_50_prod__cases7, axiom, (! [A:$tType,B:$tType,C:$tType,D2:$tType,E:$tType,F:$tType,G:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D2) @ ((product_prod @ E) @ ((product_prod @ F) @ G))))))]: ((~ ((! [A4:A,B4:B,C3:C,D3:D2,E2:E,F2:F,G2:G]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D2) @ ((product_prod @ E) @ ((product_prod @ F) @ G)))))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D2) @ ((product_prod @ E) @ ((product_prod @ F) @ G))))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D2) @ ((product_prod @ E) @ ((product_prod @ F) @ G)))) @ C3) @ ((((product_Pair @ D2) @ ((product_prod @ E) @ ((product_prod @ F) @ G))) @ D3) @ ((((product_Pair @ E) @ ((product_prod @ F) @ G)) @ E2) @ ((((product_Pair @ F) @ G) @ F2) @ G2)))))))))))))).
% 2.70/1.53 thf(fact_51_prod__cases6, axiom, (! [A:$tType,B:$tType,C:$tType,D2:$tType,E:$tType,F:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D2) @ ((product_prod @ E) @ F)))))]: ((~ ((! [A4:A,B4:B,C3:C,D3:D2,E2:E,F2:F]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D2) @ ((product_prod @ E) @ F))))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D2) @ ((product_prod @ E) @ F)))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D2) @ ((product_prod @ E) @ F))) @ C3) @ ((((product_Pair @ D2) @ ((product_prod @ E) @ F)) @ D3) @ ((((product_Pair @ E) @ F) @ E2) @ F2))))))))))))).
% 2.70/1.53 thf(fact_52_prod__cases5, axiom, (! [A:$tType,B:$tType,C:$tType,D2:$tType,E:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D2) @ E))))]: ((~ ((! [A4:A,B4:B,C3:C,D3:D2,E2:E]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D2) @ E)))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D2) @ E))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D2) @ E)) @ C3) @ ((((product_Pair @ D2) @ E) @ D3) @ E2)))))))))))).
% 2.70/1.53 thf(fact_53_prod__cases4, axiom, (! [A:$tType,B:$tType,C:$tType,D2:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D2)))]: ((~ ((! [A4:A,B4:B,C3:C,D3:D2]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D2))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C) @ D2)) @ B4) @ ((((product_Pair @ C) @ D2) @ C3) @ D3))))))))))).
% 2.70/1.53 thf(fact_54_prod__cases3, axiom, (! [A:$tType,B:$tType,C:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ C))]: ((~ ((! [A4:A,B4:B,C3:C]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ C)) @ A4) @ ((((product_Pair @ B) @ C) @ B4) @ C3)))))))))).
% 2.70/1.53 thf(fact_55_Pair__inject, axiom, (! [A:$tType,B:$tType,A2:A,B2:B,A3:A,B3:B]: (((((((product_Pair @ A) @ B) @ A2) @ B2) = ((((product_Pair @ A) @ B) @ A3) @ B3)) => (~ (((A2 = A3) => (B2 != B3)))))))).
% 2.70/1.53 thf(fact_56_prod__cases, axiom, (! [B:$tType,A:$tType,P:(((product_prod @ A) @ B) > $o),P3:((product_prod @ A) @ B)]: (((! [A4:A,B4:B]: ((P @ ((((product_Pair @ A) @ B) @ A4) @ B4)))) => (P @ P3))))).
% 2.70/1.53 thf(fact_57_surj__pair, axiom, (! [A:$tType,B:$tType,P3:((product_prod @ A) @ B)]: ((? [X4:A,Y3:B]: ((P3 = ((((product_Pair @ A) @ B) @ X4) @ Y3))))))).
% 2.70/1.53 thf(fact_58_pi_Oinject_I7_J, axiom, (! [X22:pi,X1:pi,Y2:pi,Y1:pi]: (((((par @ X22) @ X1) = ((par @ Y2) @ Y1)) = ((X22 = Y2) & (X1 = Y1)))))).
% 2.70/1.53 thf(fact_59_residual_Oinject_I2_J, axiom, (! [X22:late_freeRes,X1:pi,Y2:late_freeRes,Y1:pi]: (((((late_FreeR @ X22) @ X1) = ((late_FreeR @ Y2) @ Y1)) = ((X22 = Y2) & (X1 = Y1)))))).
% 2.70/1.53 thf(fact_60_pi_Odistinct_I85_J, axiom, (! [Pi1:pi,Pi2:pi,Name:name,Pi:pi]: ((((par @ Pi1) @ Pi2) != ((res @ Name) @ Pi))))).
% 2.70/1.53 thf(fact_61_cClose2_Ohyps_I2_J, axiom, ((late_transitions @ ((par @ q) @ r)) @ (((late_BoundR @ (late_InputS @ a)) @ x) @ qr))).
% 2.70/1.53 thf(fact_62_fresh__prod, axiom, (! [A:$tType,X:$tType,B:$tType,A2:X,X2:A,Y:B]: ((((((fresh @ X) @ ((product_prod @ A) @ B)) @ A2) @ ((((product_Pair @ A) @ B) @ X2) @ Y)) = (((((fresh @ X) @ A) @ A2) @ X2) & ((((fresh @ X) @ B) @ A2) @ Y)))))).
% 2.70/1.53 thf(fact_63_cClose2_Ohyps_I1_J, axiom, ((late_transitions @ p) @ (((late_BoundR @ (late_BoundOutputS @ a)) @ y) @ p2))).
% 2.70/1.53 thf(fact_64_cPar1_Ohyps, axiom, ((late_transitions @ q) @ (((late_BoundR @ (late_InputS @ a)) @ x) @ q2))).
% 2.70/1.53 thf(fact_65_old_Oprod_Orec, axiom, (! [A:$tType,T:$tType,B:$tType,F1:(A > (B > T)),A2:A,B2:B]: (((((((product_rec_prod @ A) @ B) @ T) @ F1) @ ((((product_Pair @ A) @ B) @ A2) @ B2)) = ((F1 @ A2) @ B2))))).
% 2.70/1.53 thf(fact_66_fresh__prodD_I2_J, axiom, (! [B:$tType,A:$tType,C:$tType,A2:A,X2:B,Y:C]: ((((((fresh @ A) @ ((product_prod @ B) @ C)) @ A2) @ ((((product_Pair @ B) @ C) @ X2) @ Y)) => ((((fresh @ A) @ C) @ A2) @ Y))))).
% 2.70/1.53 thf(fact_67_fresh__prodD_I1_J, axiom, (! [C:$tType,A:$tType,B:$tType,A2:A,X2:B,Y:C]: ((((((fresh @ A) @ ((product_prod @ B) @ C)) @ A2) @ ((((product_Pair @ B) @ C) @ X2) @ Y)) => ((((fresh @ A) @ B) @ A2) @ X2))))).
% 2.70/1.53 thf(fact_68_freeRes_Orecs_I2_J, axiom, (! [T:$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)))))).
% 2.70/1.53 thf(fact_69_resOutputTauTrans, axiom, (! [X2:name,A2:name,B2:name,P:pi,P2:pi]: ((~ (((late_transitions @ ((res @ X2) @ (((output @ A2) @ B2) @ P))) @ ((late_FreeR @ late_TauR) @ P2))))))).
% 2.70/1.53 thf(fact_70_subject_Ofresh_I1_J, axiom, (! [A2:name,X1:name]: ((((((fresh @ name) @ late_subject) @ A2) @ (late_InputS @ X1)) = ((((fresh @ name) @ name) @ A2) @ X1))))).
% 2.70/1.53 thf(fact_71_subject_Ofresh_I2_J, axiom, (! [A2:name,X1:name]: ((((((fresh @ name) @ late_subject) @ A2) @ (late_BoundOutputS @ X1)) = ((((fresh @ name) @ name) @ A2) @ X1))))).
% 2.70/1.53 thf(fact_72_Late__Semantics_Osubject_Oinject_I2_J, axiom, (! [X1:name,Y1:name]: ((((late_BoundOutputS @ X1) = (late_BoundOutputS @ Y1)) = (X1 = Y1))))).
% 2.70/1.53 thf(fact_73_freeRes_Ofresh_I2_J, axiom, (! [A2:name]: (((((fresh @ name) @ late_freeRes) @ A2) @ late_TauR)))).
% 2.70/1.53 thf(fact_74_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)))))).
% 2.70/1.53 thf(fact_75_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))))))).
% 2.70/1.53 thf(fact_76_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))))))).
% 2.70/1.53 thf(fact_77_Late__Semantics_Osubject_Odistinct_I1_J, axiom, (! [Name2:name,Name:name]: (((late_InputS @ Name2) != (late_BoundOutputS @ Name))))).
% 2.70/1.53 thf(fact_78_subject_Oinducts, axiom, (! [P:(late_subject > $o),Subject:late_subject]: (((! [Name3:name]: ((P @ (late_InputS @ Name3)))) => ((! [Name3:name]: ((P @ (late_BoundOutputS @ Name3)))) => (P @ Subject)))))).
% 2.70/1.53 thf(fact_79_outputBoundTrans, axiom, (! [A2:name,B2:name,P:pi,C2:late_subject,X2:name,P2:pi]: ((~ (((late_transitions @ (((output @ A2) @ B2) @ P)) @ (((late_BoundR @ C2) @ X2) @ P2))))))).
% 2.70/1.53 thf(fact_80_subject_Ostrong__induct_H, axiom, (! [N:$tType,P:(N > (late_subject > $o)),Z:N,Subject:late_subject]: (((! [Name3:name,Z2:N]: (((P @ Z2) @ (late_InputS @ Name3)))) => ((! [Name3:name,Z2:N]: (((P @ Z2) @ (late_BoundOutputS @ Name3)))) => ((P @ Z) @ Subject)))))).
% 2.70/1.53 thf(fact_81_subject_Ostrong__inducts, axiom, (! [A:$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)))))).
% 2.70/1.53 thf(fact_82_resOutputInputTrans, axiom, (! [X2:name,A2:name,B2:name,P:pi,C2:name,Y:name,P2:pi]: ((~ (((late_transitions @ ((res @ X2) @ (((output @ A2) @ B2) @ P))) @ (((late_BoundR @ (late_InputS @ C2)) @ Y) @ P2))))))).
% 2.70/1.53 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))))))))).
% 2.70/1.53 thf(fact_84_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)))))).
% 2.70/1.53 thf(fact_85_outputFreshTrans, axiom, (! [A2:name,B2:name,P:pi,Alpha:late_freeRes,P2:pi]: ((((late_transitions @ (((output @ A2) @ B2) @ P)) @ ((late_FreeR @ Alpha) @ P2)) => (~ ((((((fresh @ name) @ late_freeRes) @ A2) @ Alpha) | ((((fresh @ name) @ late_freeRes) @ B2) @ Alpha)))))))).
% 2.70/1.53 thf(fact_86_residual_Odistinct_I1_J, axiom, (! [Subject:late_subject,Name2:name,Pi3:pi,FreeRes:late_freeRes,Pi:pi]: (((((late_BoundR @ Subject) @ Name2) @ Pi3) != ((late_FreeR @ FreeRes) @ Pi))))).
% 2.70/1.53 thf(fact_87_residual_Oinducts, axiom, (! [P:(late_residual > $o),Residual:late_residual]: (((! [Subject2:late_subject,Name3:name,Pi4:pi]: ((P @ (((late_BoundR @ Subject2) @ Name3) @ Pi4)))) => ((! [FreeRes2:late_freeRes,Pi4:pi]: ((P @ ((late_FreeR @ FreeRes2) @ Pi4)))) => (P @ Residual)))))).
% 2.70/1.53 thf(fact_88_pi_Odistinct_I29_J, axiom, (! [Name1:name,Name22:name,Pi3:pi,Pi12:pi,Pi22:pi]: (((((output @ Name1) @ Name22) @ Pi3) != ((par @ Pi12) @ Pi22))))).
% 2.70/1.53 thf(fact_89_pi_Odistinct_I31_J, axiom, (! [Name1:name,Name22:name,Pi3:pi,Name:name,Pi:pi]: (((((output @ Name1) @ Name22) @ Pi3) != ((res @ Name) @ Pi))))).
% 2.70/1.53 thf(fact_90_parCasesB_H, axiom, (! [P:pi,Q:pi,B2:late_subject,Y:name,P2:pi]: ((((late_transitions @ ((par @ P) @ Q)) @ (((late_BoundR @ B2) @ Y) @ P2)) => ((! [P4:pi,A4:late_subject,X4:name,P5:pi,Q3:pi]: (((((par @ P) @ Q) = ((par @ P4) @ Q3)) => (((((late_BoundR @ B2) @ Y) @ P2) = (((late_BoundR @ A4) @ X4) @ ((par @ P5) @ Q3))) => (((late_transitions @ P4) @ (((late_BoundR @ A4) @ X4) @ P5)) => (((((fresh @ name) @ pi) @ X4) @ P4) => (((((fresh @ name) @ pi) @ X4) @ Q3) => (~ (((((fresh @ name) @ late_subject) @ X4) @ A4)))))))))) => (~ ((! [Q3:pi,A4:late_subject,X4:name,Q4:pi,P4:pi]: (((((par @ P) @ Q) = ((par @ P4) @ Q3)) => (((((late_BoundR @ B2) @ Y) @ P2) = (((late_BoundR @ A4) @ X4) @ ((par @ P4) @ Q4))) => (((late_transitions @ Q3) @ (((late_BoundR @ A4) @ X4) @ Q4)) => (((((fresh @ name) @ pi) @ X4) @ P4) => (((((fresh @ name) @ pi) @ X4) @ Q3) => (~ (((((fresh @ name) @ late_subject) @ X4) @ A4))))))))))))))))).
% 2.70/1.53 thf(fact_91_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)))))))))).
% 2.70/1.53 thf(fact_92_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)))))))))).
% 2.70/1.53 thf(fact_93_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))))))))))).
% 2.70/1.53 thf(fact_94_freshResidual, axiom, (! [P:pi,Rs:late_residual,X2:name]: ((((late_transitions @ P) @ Rs) => (((((fresh @ name) @ pi) @ X2) @ P) => ((((fresh @ name) @ late_residual) @ X2) @ Rs)))))).
% 2.70/1.53 thf(fact_95_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))))))).
% 2.70/1.53 thf(fact_96_residual_Ostrong__inducts, axiom, (! [A:$tType]: (((fs_name @ A) => (! [P:(A > (late_residual > $o)),Z:A,Residual:late_residual]: (((! [Subject2:late_subject,Name3:name,Pi4:pi,Z2:A]: ((((((fresh @ name) @ A) @ Name3) @ Z2) => (((((fresh @ name) @ late_subject) @ Name3) @ Subject2) => ((P @ Z2) @ (((late_BoundR @ Subject2) @ Name3) @ Pi4)))))) => ((! [FreeRes2:late_freeRes,Pi4:pi,Z2:A]: (((P @ Z2) @ ((late_FreeR @ FreeRes2) @ Pi4)))) => ((P @ Z) @ Residual))))))))).
% 2.70/1.53 thf(fact_97_residual_Ostrong__induct, axiom, (! [N:$tType]: (((fs_name @ N) => (! [P:(N > (late_residual > $o)),Z:N,Residual:late_residual]: (((! [Subject2:late_subject,Name3:name,Pi4:pi,Z2:N]: ((((((fresh @ name) @ N) @ Name3) @ Z2) => (((((fresh @ name) @ late_subject) @ Name3) @ Subject2) => ((P @ Z2) @ (((late_BoundR @ Subject2) @ Name3) @ Pi4)))))) => ((! [FreeRes2:late_freeRes,Pi4:pi,Z2:N]: (((P @ Z2) @ ((late_FreeR @ FreeRes2) @ Pi4)))) => ((P @ Z) @ Residual))))))))).
% 2.70/1.53 thf(fact_98_resTrans_I1_J, axiom, (! [X2:name,B2:name,P:pi,Rs:late_residual]: ((~ (((late_transitions @ ((res @ X2) @ (((output @ X2) @ B2) @ P))) @ Rs)))))).
% 2.70/1.53 thf(fact_99_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)))))))))).
% 2.70/1.53 thf(fact_100_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))))))))))).
% 2.70/1.53 thf(fact_101_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)))))))))))))))))).
% 2.70/1.53 thf(fact_102_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))))))))))))))))))).
% 2.70/1.53 thf(fact_103_resCasesF, axiom, (! [X2:name,P:pi,Alpha:late_freeRes,XP:pi,F3:(pi > $o)]: ((((late_transitions @ ((res @ X2) @ P)) @ ((late_FreeR @ Alpha) @ XP)) => ((! [P5:pi]: ((((late_transitions @ P) @ ((late_FreeR @ Alpha) @ P5)) => (((((fresh @ name) @ late_freeRes) @ X2) @ Alpha) => (F3 @ ((res @ X2) @ P5)))))) => (F3 @ XP)))))).
% 2.70/1.53 thf(fact_104_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,P5:pi,Y3:name]: (((((res @ X2) @ P) = ((res @ Y3) @ P4)) => ((((late_FreeR @ Alpha) @ P2) = ((late_FreeR @ Alpha2) @ ((res @ Y3) @ P5))) => (((late_transitions @ P4) @ ((late_FreeR @ Alpha2) @ P5)) => (~ (((((fresh @ name) @ late_freeRes) @ Y3) @ Alpha2)))))))))))))).
% 2.70/1.53 thf(fact_105_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)))))))).
% 2.70/1.53 thf(fact_106_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)))))))).
% 2.70/1.53 thf(fact_107_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)))))))).
% 2.70/1.53 thf(fact_108_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) => ((! [P5:pi]: ((((late_transitions @ P) @ (((late_BoundR @ A2) @ X2) @ P5)) => (Prop @ ((par @ P5) @ Q))))) => ((! [Q4:pi]: ((((late_transitions @ Q) @ (((late_BoundR @ A2) @ X2) @ Q4)) => (Prop @ ((par @ P) @ Q4))))) => (Prop @ PQ))))))))).
% 2.70/1.53 thf(fact_109_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)))))).
% 2.70/1.53 thf(fact_110_outputTauTrans, axiom, (! [A2:name,B2:name,P:pi,P2:pi]: ((~ (((late_transitions @ (((output @ A2) @ B2) @ P)) @ ((late_FreeR @ late_TauR) @ P2))))))).
% 2.70/1.53 thf(fact_111_transitions_OComm1, axiom, (! [P:pi,A2:name,X2:name,P2:pi,Q:pi,B2:name,Q2:pi]: ((((late_transitions @ P) @ (((late_BoundR @ (late_InputS @ A2)) @ X2) @ P2)) => (((late_transitions @ Q) @ ((late_FreeR @ ((late_OutputR @ A2) @ B2)) @ Q2)) => (((((fresh @ name) @ pi) @ X2) @ P) => (((((fresh @ name) @ pi) @ X2) @ Q) => ((X2 != A2) => ((X2 != B2) => (((((fresh @ name) @ pi) @ X2) @ Q2) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ late_TauR) @ ((par @ (((subs @ P2) @ X2) @ B2)) @ Q2))))))))))))).
% 2.70/1.53 thf(fact_112_transitions_OComm2, axiom, (! [P:pi,A2:name,B2:name,P2:pi,Q:pi,X2:name,Q2:pi]: ((((late_transitions @ P) @ ((late_FreeR @ ((late_OutputR @ A2) @ B2)) @ P2)) => (((late_transitions @ Q) @ (((late_BoundR @ (late_InputS @ A2)) @ X2) @ Q2)) => (((((fresh @ name) @ pi) @ X2) @ P) => (((((fresh @ name) @ pi) @ X2) @ Q) => ((X2 != A2) => ((X2 != B2) => (((((fresh @ name) @ pi) @ X2) @ P2) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ late_TauR) @ ((par @ P2) @ (((subs @ Q2) @ X2) @ B2)))))))))))))).
% 2.70/1.53 thf(fact_113_Late__Semantics1_Osubject_Oinject_I2_J, axiom, (! [X22:name,Y2:name]: ((((late_BoundOutputS @ X22) = (late_BoundOutputS @ Y2)) = (X22 = Y2))))).
% 2.70/1.53 thf(fact_114_Late__Semantics1_Osubject_Oinject_I1_J, axiom, (! [X1:name,Y1:name]: ((((late_InputS @ X1) = (late_InputS @ Y1)) = (X1 = Y1))))).
% 2.70/1.53 thf(fact_115_Late__Semantics_OComm1, axiom, (! [P:pi,A2:name,X2:name,P2:pi,Q:pi,B2:name,Q2:pi]: ((((late_transitions @ P) @ (((late_BoundR @ (late_InputS @ A2)) @ X2) @ P2)) => (((late_transitions @ Q) @ ((late_FreeR @ ((late_OutputR @ A2) @ B2)) @ Q2)) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ late_TauR) @ ((par @ (((subs @ P2) @ X2) @ B2)) @ Q2)))))))).
% 2.70/1.53 thf(fact_116_Late__Semantics_OComm2, axiom, (! [P:pi,A2:name,B2:name,P2:pi,Q:pi,X2:name,Q2:pi]: ((((late_transitions @ P) @ ((late_FreeR @ ((late_OutputR @ A2) @ B2)) @ P2)) => (((late_transitions @ Q) @ (((late_BoundR @ (late_InputS @ A2)) @ X2) @ Q2)) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ late_TauR) @ ((par @ P2) @ (((subs @ Q2) @ X2) @ B2))))))))).
% 2.70/1.53 thf(fact_117_subject_Oexhaust, axiom, (! [Y:late_subject]: (((! [X12:name]: ((Y != (late_InputS @ X12)))) => (~ ((! [X23:name]: ((Y != (late_BoundOutputS @ X23)))))))))).
% 2.70/1.53 thf(fact_118_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)))))).
% 2.70/1.53 thf(fact_119_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)))))).
% 2.70/1.53 thf(fact_120_name__fresh, axiom, (((fresh @ name) @ name) = (^ [A6:name,B5:name]: ((A6 != B5))))).
% 2.70/1.53 thf(fact_121_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)))))).
% 2.70/1.53 thf(fact_122_Late__Semantics1_OfreeRes_Odistinct_I1_J, axiom, (! [X11:name,X122:name]: ((((late_OutputR @ X11) @ X122) != late_TauR)))).
% 2.70/1.53 thf(fact_123_freeRes_Oexhaust, axiom, (! [Y:late_freeRes]: (((! [X112:name,X123:name]: ((Y != ((late_OutputR @ X112) @ X123)))) => (Y = late_TauR))))).
% 2.70/1.53 thf(fact_124_freeRes_Ostrong__inducts, axiom, (! [A:$tType,P:(A > (late_freeRes > $o)),Z:A,FreeRes3:late_freeRes]: (((! [Name12:name,Name23:name,Z2:A]: (((P @ Z2) @ ((late_OutputR @ Name12) @ Name23)))) => ((! [Z2:A]: (((P @ Z2) @ late_TauR))) => ((P @ Z) @ FreeRes3)))))).
% 2.70/1.53 thf(fact_125_freeRes_Ostrong__induct_H, axiom, (! [N:$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)))))).
% 2.70/1.53 thf(fact_126_freeRes_Oinducts, axiom, (! [P:(late_freeRes > $o),FreeRes3:late_freeRes]: (((! [Name12:name,Name23:name]: ((P @ ((late_OutputR @ Name12) @ Name23)))) => ((P @ late_TauR) => (P @ FreeRes3)))))).
% 2.70/1.53 thf(fact_127_Late__Semantics_OfreeRes_Odistinct_I1_J, axiom, (! [Name1:name,Name22:name]: ((((late_OutputR @ Name1) @ Name22) != late_TauR)))).
% 2.70/1.53 thf(fact_128_freeRes_Orecs_I1_J, axiom, (! [T:$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))))))).
% 2.70/1.53 thf(fact_129_Output, axiom, (! [A2:name,B2:name,P:pi]: (((late_transitions @ (((output @ A2) @ B2) @ P)) @ ((late_FreeR @ ((late_OutputR @ A2) @ B2)) @ P))))).
% 2.70/1.53 thf(fact_130_outputIneqTrans, axiom, (! [A2:name,B2:name,P:pi,C2:name,D:name,P2:pi]: ((((late_transitions @ (((output @ A2) @ B2) @ P)) @ ((late_FreeR @ ((late_OutputR @ C2) @ D)) @ P2)) => (~ (((A2 != C2) | (B2 != D)))))))).
% 2.70/1.53 thf(fact_131_outputCases_H, axiom, (! [A2:name,B2:name,P:pi,Rs:late_residual]: ((((late_transitions @ (((output @ A2) @ B2) @ P)) @ Rs) => (~ ((! [A4:name,B4:name,P4:pi]: ((((A2 = A4) & ((B2 = B4) & (P = P4))) => (Rs != ((late_FreeR @ ((late_OutputR @ A4) @ B4)) @ P4))))))))))).
% 2.70/1.53 thf(fact_132_outputCases, axiom, (! [A2:name,B2:name,P:pi,Alpha:late_freeRes,P2:pi,Prop:(late_freeRes > (pi > $o))]: ((((late_transitions @ (((output @ A2) @ B2) @ P)) @ ((late_FreeR @ Alpha) @ P2)) => (((Alpha = ((late_OutputR @ A2) @ B2)) => ((P = P2) => ((Prop @ ((late_OutputR @ A2) @ B2)) @ P))) => ((Prop @ Alpha) @ P2)))))).
% 2.70/1.53 thf(fact_133_resOutputOutputTrans, axiom, (! [X2:name,A2:name,P:pi,B2:name,Y:name,P2:pi]: ((~ (((late_transitions @ ((res @ X2) @ (((output @ A2) @ X2) @ P))) @ ((late_FreeR @ ((late_OutputR @ B2) @ Y)) @ P2))))))).
% 2.70/1.53 thf(fact_134_Open, axiom, (! [P:pi,A2:name,B2:name,P2:pi]: ((((late_transitions @ P) @ ((late_FreeR @ ((late_OutputR @ A2) @ B2)) @ P2)) => ((A2 != B2) => ((late_transitions @ ((res @ B2) @ P)) @ (((late_BoundR @ (late_BoundOutputS @ A2)) @ B2) @ P2))))))).
% 2.70/1.53 thf(fact_135_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,B4:name]: (((((res @ X5) @ P) = ((res @ B4) @ P4)) => (! [P5:pi]: ((((((late_BoundR @ A2) @ Y4) @ P2) = (((late_BoundR @ (late_BoundOutputS @ A4)) @ B4) @ P5)) => (((late_transitions @ P4) @ ((late_FreeR @ ((late_OutputR @ A4) @ B4)) @ P5)) => (A4 = B4)))))))) => (~ ((! [P4:pi,A4:late_subject,X4:name,P5:pi,Y3:name]: (((((res @ X5) @ P) = ((res @ Y3) @ P4)) => (((((late_BoundR @ A2) @ Y4) @ P2) = (((late_BoundR @ A4) @ X4) @ ((res @ Y3) @ P5))) => (((late_transitions @ P4) @ (((late_BoundR @ A4) @ X4) @ P5)) => (((((fresh @ name) @ late_subject) @ Y3) @ A4) => ((Y3 != X4) => (((((fresh @ name) @ pi) @ X4) @ P4) => (~ (((((fresh @ name) @ late_subject) @ X4) @ A4)))))))))))))))))).
% 2.70/1.53 thf(fact_136_resCases_H, axiom, (! [X2:name,P:pi,Rs:late_residual]: ((((late_transitions @ ((res @ X2) @ P)) @ Rs) => ((! [P4:pi,A4:name,B4:name]: (((((res @ X2) @ P) = ((res @ B4) @ P4)) => (! [P5:pi]: (((Rs = (((late_BoundR @ (late_BoundOutputS @ A4)) @ B4) @ P5)) => (((late_transitions @ P4) @ ((late_FreeR @ ((late_OutputR @ A4) @ B4)) @ P5)) => (A4 = B4)))))))) => ((! [P4:pi,A4:late_subject,X4:name,P5:pi,Y3:name]: (((((res @ X2) @ P) = ((res @ Y3) @ P4)) => ((Rs = (((late_BoundR @ A4) @ X4) @ ((res @ Y3) @ P5))) => (((late_transitions @ P4) @ (((late_BoundR @ A4) @ X4) @ P5)) => (((((fresh @ name) @ late_subject) @ Y3) @ A4) => ((Y3 != X4) => (((((fresh @ name) @ pi) @ X4) @ P4) => (~ (((((fresh @ name) @ late_subject) @ X4) @ A4))))))))))) => (~ ((! [P4:pi,Alpha2:late_freeRes,P5:pi,Y3:name]: (((((res @ X2) @ P) = ((res @ Y3) @ P4)) => ((Rs = ((late_FreeR @ Alpha2) @ ((res @ Y3) @ P5))) => (((late_transitions @ P4) @ ((late_FreeR @ Alpha2) @ P5)) => (~ (((((fresh @ name) @ late_freeRes) @ Y3) @ Alpha2)))))))))))))))).
% 2.70/1.53 thf(fact_137_Late__Semantics1_Osubject_Odistinct_I1_J, axiom, (! [X1:name,X22:name]: (((late_InputS @ X1) != (late_BoundOutputS @ X22))))).
% 2.70/1.53 thf(fact_138_subject_Orecs_I2_J, axiom, (! [T:$tType,P:(T > $o),F1:(name > T),F22:(name > T),Name2:name]: (((! [X12:name]: ((P @ (F1 @ X12)))) => ((! [X12:name]: ((P @ (F22 @ X12)))) => (((((late_subject_rec @ T) @ F1) @ F22) @ (late_BoundOutputS @ Name2)) = (F22 @ Name2))))))).
% 2.70/1.53 thf(fact_139_subject_Orecs_I1_J, axiom, (! [T:$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))))))).
% 2.70/1.53 thf(fact_140_resTauOutputTrans, axiom, (! [X2:name,P:pi,A2:name,B2:name,P2:pi]: ((~ (((late_transitions @ ((res @ X2) @ (tau @ P))) @ ((late_FreeR @ ((late_OutputR @ A2) @ B2)) @ P2))))))).
% 2.70/1.53 thf(fact_141_resInputBoundOutputTrans, axiom, (! [X2:name,A2:name,Y:name,P:pi,B2:name,Z:name,P2:pi]: ((~ (((late_transitions @ ((res @ X2) @ (((input @ A2) @ Y) @ P))) @ (((late_BoundR @ (late_BoundOutputS @ B2)) @ Z) @ P2))))))).
% 2.70/1.53 thf(fact_142_pi_Ofresh_I3_J, axiom, (! [A2:name,X1:pi]: ((((((fresh @ name) @ pi) @ A2) @ (tau @ X1)) = ((((fresh @ name) @ pi) @ A2) @ X1))))).
% 2.70/1.53 thf(fact_143_simps_I2_J, axiom, (! [P:pi,C2:name,D:name]: (((((subs @ (tau @ P)) @ C2) @ D) = (tau @ (((subs @ P) @ C2) @ D)))))).
% 2.70/1.53 thf(fact_144_pi_Oinject_I2_J, axiom, (! [X1:pi,Y1:pi]: ((((tau @ X1) = (tau @ Y1)) = (X1 = Y1))))).
% 2.70/1.53 thf(fact_145_pi_Odistinct_I35_J, axiom, (! [Pi3:pi,Name13:name,Name24:name,Pi:pi]: (((tau @ Pi3) != (((input @ Name13) @ Name24) @ Pi))))).
% 2.70/1.53 thf(fact_146_pi_Odistinct_I55_J, axiom, (! [Name1:name,Name22:name,Pi3:pi,Pi12:pi,Pi22:pi]: (((((input @ Name1) @ Name22) @ Pi3) != ((par @ Pi12) @ Pi22))))).
% 2.70/1.53 thf(fact_147_pi_Odistinct_I57_J, axiom, (! [Name1:name,Name22:name,Pi3:pi,Name:name,Pi:pi]: (((((input @ Name1) @ Name22) @ Pi3) != ((res @ Name) @ Pi))))).
% 2.70/1.53 thf(fact_148_pi_Odistinct_I43_J, axiom, (! [Pi3:pi,Pi12:pi,Pi22:pi]: (((tau @ Pi3) != ((par @ Pi12) @ Pi22))))).
% 2.70/1.53 thf(fact_149_pi_Odistinct_I45_J, axiom, (! [Pi3:pi,Name:name,Pi:pi]: (((tau @ Pi3) != ((res @ Name) @ Pi))))).
% 2.70/1.53 thf(fact_150_pi_Odistinct_I21_J, axiom, (! [Name1:name,Name22:name,Pi3:pi,Name13:name,Name24:name,Pi:pi]: (((((output @ Name1) @ Name22) @ Pi3) != (((input @ Name13) @ Name24) @ Pi))))).
% 2.70/1.53 thf(fact_151_pi_Odistinct_I19_J, axiom, (! [Name1:name,Name22:name,Pi3:pi,Pi:pi]: (((((output @ Name1) @ Name22) @ Pi3) != (tau @ Pi))))).
% 2.70/1.53 thf(fact_152_resTrans_I2_J, axiom, (! [X2:name,Y:name,P:pi,Rs:late_residual]: ((~ (((late_transitions @ ((res @ X2) @ (((input @ X2) @ Y) @ P))) @ Rs)))))).
% 2.70/1.53 thf(fact_153_inputFreeTrans, axiom, (! [A2:name,X2:name,P:pi,Alpha:late_freeRes,P2:pi]: ((~ (((late_transitions @ (((input @ A2) @ X2) @ P)) @ ((late_FreeR @ Alpha) @ P2))))))).
% 2.70/1.53 thf(fact_154_tauBoundTrans, axiom, (! [P:pi,A2:late_subject,X2:name,P2:pi]: ((~ (((late_transitions @ (tau @ P)) @ (((late_BoundR @ A2) @ X2) @ P2))))))).
% 2.70/1.53 thf(fact_155_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))))))).
% 2.70/1.53 thf(fact_156_Late__Semantics_OInput, axiom, (! [A2:name,X2:name,P:pi]: (((late_transitions @ (((input @ A2) @ X2) @ P)) @ (((late_BoundR @ (late_InputS @ A2)) @ X2) @ P))))).
% 2.70/1.53 thf(fact_157_transitions_OInput, axiom, (! [X2:name,A2:name,P:pi]: (((X2 != A2) => ((late_transitions @ (((input @ A2) @ X2) @ P)) @ (((late_BoundR @ (late_InputS @ A2)) @ X2) @ P)))))).
% 2.70/1.53 thf(fact_158_inputBoundOutputTrans, axiom, (! [A2:name,X2:name,P:pi,B2:name,Y:name,P2:pi]: ((~ (((late_transitions @ (((input @ A2) @ X2) @ P)) @ (((late_BoundR @ (late_BoundOutputS @ B2)) @ Y) @ P2))))))).
% 2.70/1.53 thf(fact_159_resTauBoundTrans, axiom, (! [X2:name,P:pi,A2:late_subject,Y:name,P2:pi]: ((~ (((late_transitions @ ((res @ X2) @ (tau @ P))) @ (((late_BoundR @ A2) @ Y) @ P2))))))).
% 2.70/1.53 thf(fact_160_inputIneqTrans, axiom, (! [A2:name,X2:name,P:pi,B2:late_subject,Y:name,P2:pi]: ((((late_transitions @ (((input @ A2) @ X2) @ P)) @ (((late_BoundR @ B2) @ Y) @ P2)) => (~ (((((fresh @ name) @ late_subject) @ A2) @ B2))))))).
% 2.70/1.53 thf(fact_161_tauOutputTrans, axiom, (! [P:pi,A2:name,B2:name,P2:pi]: ((~ (((late_transitions @ (tau @ P)) @ ((late_FreeR @ ((late_OutputR @ A2) @ B2)) @ P2))))))).
% 2.70/1.53 thf(fact_162_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)))))).
% 2.70/1.53 thf(fact_163_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))))))))))).
% 2.70/1.53 thf(fact_164_Tau, axiom, (! [P:pi]: (((late_transitions @ (tau @ P)) @ ((late_FreeR @ late_TauR) @ P))))).
% 2.70/1.53 thf(fact_165_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))))))).
% 2.70/1.53 thf(fact_166_simps_I3_J, axiom, (! [A2:name,B2:name,P:pi,C2:name,D:name]: (((((subs @ (((output @ A2) @ B2) @ P)) @ C2) @ D) = (((output @ (((subst_name @ A2) @ C2) @ D)) @ (((subst_name @ B2) @ C2) @ D)) @ (((subs @ P) @ C2) @ D)))))).
% 2.70/1.53 thf(fact_167_substInput, axiom, (! [X2:name,B2:name,C2:name,A2:name,P:pi]: (((X2 != B2) => ((X2 != C2) => ((((subs @ (((input @ A2) @ X2) @ P)) @ B2) @ C2) = (((input @ (((subst_name @ A2) @ B2) @ C2)) @ X2) @ (((subs @ P) @ B2) @ C2)))))))).
% 2.70/1.53 thf(fact_168_simps_I4_J, axiom, (! [X2:name,A2:name,C2:name,D:name,P:pi]: (((X2 != A2) => ((X2 != C2) => ((X2 != D) => ((((subs @ (((input @ A2) @ X2) @ P)) @ C2) @ D) = (((input @ (((subst_name @ A2) @ C2) @ D)) @ X2) @ (((subs @ P) @ C2) @ D))))))))).
% 2.70/1.53 thf(fact_169_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)))))).
% 2.70/1.53 thf(fact_170_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))))))).
% 2.70/1.53 thf(fact_171_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))))))).
% 2.70/1.53 thf(fact_172_abs__fun__eq1, axiom, (! [X:$tType,A:$tType,A2:X,X2:A,Y:A]: (((((((abs_fun @ X) @ A) @ A2) @ X2) = ((((abs_fun @ X) @ A) @ A2) @ Y)) = (X2 = Y))))).
% 2.70/1.53 thf(fact_173_subst__name__def, axiom, (subst_name = (^ [A6:name,B5:name,C4:name]: (((((if @ name) @ (A6 = B5)) @ C4) @ A6))))).
% 2.70/1.53 thf(fact_174_name__fresh__abs, axiom, (! [A:$tType]: (((fs_name @ A) => (! [B2:name,A2:name,X2:A]: ((((((fresh @ name) @ (name > (noption @ A))) @ B2) @ ((((abs_fun @ name) @ A) @ A2) @ X2)) = ((B2 = A2) | ((((fresh @ name) @ A) @ B2) @ X2))))))))).
% 2.70/1.53 thf(fact_175_abs__fresh_I1_J, axiom, (! [X6:$tType]: (((fs_name @ X6) => (! [B2:name,A2:name,X2:X6]: ((((((fresh @ name) @ (name > (noption @ X6))) @ B2) @ ((((abs_fun @ name) @ X6) @ A2) @ X2)) = ((B2 = A2) | ((((fresh @ name) @ X6) @ B2) @ X2))))))))).
% 2.70/1.53 thf(fact_176_residual_Oinject_I1_J, axiom, (! [X32:late_subject,X1:name,X22:pi,Y32:late_subject,Y1:name,Y2:pi]: ((((((late_BoundR @ X32) @ X1) @ X22) = (((late_BoundR @ Y32) @ Y1) @ Y2)) = ((X32 = Y32) & (((((abs_fun @ name) @ pi) @ X1) @ X22) = ((((abs_fun @ name) @ pi) @ Y1) @ Y2))))))).
% 2.70/1.53 thf(fact_177_pi_Oinject_I8_J, axiom, (! [X1:name,X22:pi,Y1:name,Y2:pi]: (((((res @ X1) @ X22) = ((res @ Y1) @ Y2)) = (((((abs_fun @ name) @ pi) @ X1) @ X22) = ((((abs_fun @ name) @ pi) @ Y1) @ Y2)))))).
% 2.70/1.53 thf(fact_178_inputCases_H, axiom, (! [A2:name,B2:name,P:pi,Rs:late_residual]: ((((late_transitions @ (((input @ A2) @ B2) @ P)) @ Rs) => (~ ((! [X4:name,A4:name,P4:pi]: ((((A2 = A4) & (((((abs_fun @ name) @ pi) @ B2) @ P) = ((((abs_fun @ name) @ pi) @ X4) @ P4))) => ((Rs = (((late_BoundR @ (late_InputS @ A4)) @ X4) @ P4)) => (X4 = A4))))))))))).
% 2.70/1.53 thf(fact_179_internal__case__prod__conv, axiom, (! [B:$tType,A:$tType,C:$tType,C2:(B > (C > A)),A2:B,B2:C]: (((((((produc2004651681e_prod @ B) @ C) @ A) @ C2) @ ((((product_Pair @ B) @ C) @ A2) @ B2)) = ((C2 @ A2) @ B2))))).
% 2.70/1.53 thf(fact_180_resSimCases, axiom, (! [A:$tType]: (((fs_name @ A) => (! [Rel:(set @ ((product_prod @ pi) @ pi)),Q:pi,X2:name,P:pi,C5:A]: ((((eqvt @ pi) @ Rel) => ((! [Q4:pi,A4:name]: ((((late_transitions @ Q) @ ((late_FreeR @ ((late_OutputR @ A4) @ X2)) @ Q4)) => ((A4 != X2) => (? [P6:pi]: ((((late_transitions @ P) @ (((late_BoundR @ (late_BoundOutputS @ A4)) @ X2) @ P6)) & (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ P6) @ Q4)) @ Rel)))))))) => ((! [Q4:pi,A4:late_subject,Y3:name]: ((((late_transitions @ Q) @ (((late_BoundR @ A4) @ Y3) @ Q4)) => (((((fresh @ name) @ late_subject) @ X2) @ A4) => ((X2 != Y3) => (((((fresh @ name) @ A) @ Y3) @ C5) => (? [P6:pi]: ((((late_transitions @ P) @ (((late_BoundR @ A4) @ Y3) @ P6)) & (((((strong2129052853vative @ P6) @ ((res @ X2) @ Q4)) @ A4) @ Y3) @ Rel)))))))))) => ((! [Q4:pi,Alpha2:late_freeRes]: ((((late_transitions @ Q) @ ((late_FreeR @ Alpha2) @ Q4)) => (((((fresh @ name) @ late_freeRes) @ X2) @ Alpha2) => (? [P6:pi]: ((((late_transitions @ P) @ ((late_FreeR @ Alpha2) @ P6)) & (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ P6) @ ((res @ X2) @ Q4))) @ Rel)))))))) => (((strong743114133lation @ P) @ Rel) @ ((res @ X2) @ Q)))))))))))).
% 2.70/1.53 thf(fact_181_parSym, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),P:pi,Q:pi]: (((! [R:pi,S2:pi]: ((((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ ((par @ R) @ S2)) @ ((par @ S2) @ R))) @ Rel))) => ((! [R:pi,S2:pi,X4:name]: (((((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ R) @ S2)) @ Rel) => (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ ((res @ X4) @ R)) @ ((res @ X4) @ S2))) @ Rel)))) => (((strong743114133lation @ ((par @ P) @ Q)) @ Rel) @ ((par @ Q) @ P))))))).
% 2.70/1.53 thf(fact_182_simE_I1_J, axiom, (! [P:pi,Rel:(set @ ((product_prod @ pi) @ pi)),Q:pi,A2:late_subject,X2:name,Q2:pi]: (((((strong743114133lation @ P) @ Rel) @ Q) => (((late_transitions @ Q) @ (((late_BoundR @ A2) @ X2) @ Q2)) => (((((fresh @ name) @ pi) @ X2) @ P) => (? [P5:pi]: ((((late_transitions @ P) @ (((late_BoundR @ A2) @ X2) @ P5)) & (((((strong2129052853vative @ P5) @ Q2) @ A2) @ X2) @ Rel)))))))))).
% 2.70/1.53 thf(fact_183_simE_I2_J, axiom, (! [P:pi,Rel:(set @ ((product_prod @ pi) @ pi)),Q:pi,Alpha:late_freeRes,Q2:pi]: (((((strong743114133lation @ P) @ Rel) @ Q) => (((late_transitions @ Q) @ ((late_FreeR @ Alpha) @ Q2)) => (? [P5:pi]: ((((late_transitions @ P) @ ((late_FreeR @ Alpha) @ P5)) & (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ P5) @ Q2)) @ Rel))))))))).
% 2.70/1.53 thf(fact_184_simCasesCont, axiom, (! [A:$tType]: (((fs_name @ A) => (! [Rel:(set @ ((product_prod @ pi) @ pi)),Q:pi,P:pi,C5:A]: ((((eqvt @ pi) @ Rel) => ((! [A4:late_subject,X4:name,Q4:pi]: ((((late_transitions @ Q) @ (((late_BoundR @ A4) @ X4) @ Q4)) => (((((fresh @ name) @ pi) @ X4) @ P) => (((((fresh @ name) @ pi) @ X4) @ Q) => (((((fresh @ name) @ late_subject) @ X4) @ A4) => (((((fresh @ name) @ A) @ X4) @ C5) => (? [P6:pi]: ((((late_transitions @ P) @ (((late_BoundR @ A4) @ X4) @ P6)) & (((((strong2129052853vative @ P6) @ Q4) @ A4) @ X4) @ Rel))))))))))) => ((! [Alpha2:late_freeRes,Q4:pi]: ((((late_transitions @ Q) @ ((late_FreeR @ Alpha2) @ Q4)) => (? [P6:pi]: ((((late_transitions @ P) @ ((late_FreeR @ Alpha2) @ P6)) & (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ P6) @ Q4)) @ Rel))))))) => (((strong743114133lation @ P) @ Rel) @ Q)))))))))).
% 2.70/1.53 thf(fact_185_simCases, axiom, (! [Q:pi,P:pi,Rel:(set @ ((product_prod @ pi) @ pi))]: (((! [A4:late_subject,Y3:name,Q4:pi]: ((((late_transitions @ Q) @ (((late_BoundR @ A4) @ Y3) @ Q4)) => (((((fresh @ name) @ pi) @ Y3) @ P) => (? [P6:pi]: ((((late_transitions @ P) @ (((late_BoundR @ A4) @ Y3) @ P6)) & (((((strong2129052853vative @ P6) @ Q4) @ A4) @ Y3) @ Rel)))))))) => ((! [Alpha2:late_freeRes,Q4:pi]: ((((late_transitions @ Q) @ ((late_FreeR @ Alpha2) @ Q4)) => (? [P6:pi]: ((((late_transitions @ P) @ ((late_FreeR @ Alpha2) @ P6)) & (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ P6) @ Q4)) @ Rel))))))) => (((strong743114133lation @ P) @ Rel) @ Q)))))).
% 2.70/1.53 thf(fact_186_simulation__def, axiom, (strong743114133lation = (^ [P7:pi,Rel2:(set @ ((product_prod @ pi) @ pi)),Q5:pi]: (((! [A6:late_subject,X3:name,Q6:pi]: (((((late_transitions @ Q5) @ (((late_BoundR @ A6) @ X3) @ Q6)) & ((((fresh @ name) @ pi) @ X3) @ P7)) => (? [P8:pi]: ((((late_transitions @ P7) @ (((late_BoundR @ A6) @ X3) @ P8)) & (((((strong2129052853vative @ P8) @ Q6) @ A6) @ X3) @ Rel2))))))) & (! [Alpha3:late_freeRes,Q6:pi]: ((((late_transitions @ Q5) @ ((late_FreeR @ Alpha3) @ Q6)) => (? [P8:pi]: ((((late_transitions @ P7) @ ((late_FreeR @ Alpha3) @ P8)) & (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ P8) @ Q6)) @ Rel2)))))))))))).
% 2.70/1.53 thf(fact_187_parZeroRight, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),P:pi]: (((! [Q3:pi]: ((((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ Q3) @ ((par @ Q3) @ piNil))) @ Rel))) => (((strong743114133lation @ P) @ Rel) @ ((par @ P) @ piNil)))))).
% 2.70/1.53 thf(fact_188_parZeroLeft, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),P:pi]: (((! [Q3:pi]: ((((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ ((par @ Q3) @ piNil)) @ Q3)) @ Rel))) => (((strong743114133lation @ ((par @ P) @ piNil)) @ Rel) @ P))))).
% 2.70/1.53 thf(fact_189_simps_I5_J, axiom, (! [A2:name,B2:name,P:pi,C2:name,D:name]: (((((subs @ (((match @ A2) @ B2) @ P)) @ C2) @ D) = (((match @ (((subst_name @ A2) @ C2) @ D)) @ (((subst_name @ B2) @ C2) @ D)) @ (((subs @ P) @ C2) @ D)))))).
% 2.70/1.53 thf(fact_190_pi_Ofresh_I1_J, axiom, (! [A2:name]: (((((fresh @ name) @ pi) @ A2) @ piNil)))).
% 2.70/1.53 thf(fact_191_simps_I1_J, axiom, (! [C2:name,D:name]: (((((subs @ piNil) @ C2) @ D) = piNil)))).
% 2.70/1.53 thf(fact_192_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))))))).
% 2.70/1.53 thf(fact_193_matchNilLeft, axiom, (! [A2:name,B2:name,Rel:(set @ ((product_prod @ pi) @ pi)),P:pi]: (((A2 != B2) => (((strong743114133lation @ piNil) @ Rel) @ (((match @ A2) @ B2) @ P)))))).
% 2.70/1.53 thf(fact_194_nilSimRight, axiom, (! [P:pi,Rel:(set @ ((product_prod @ pi) @ pi))]: ((((strong743114133lation @ P) @ Rel) @ piNil)))).
% 2.70/1.53 thf(fact_195_pi_Odistinct_I49_J, axiom, (! [Name1:name,Name22:name,Pi3:pi,Name13:name,Name24:name,Pi:pi]: (((((input @ Name1) @ Name22) @ Pi3) != (((match @ Name13) @ Name24) @ Pi))))).
% 2.70/1.53 thf(fact_196_pi_Odistinct_I5_J, axiom, (! [Name13:name,Name24:name,Pi:pi]: ((piNil != (((input @ Name13) @ Name24) @ Pi))))).
% 2.70/1.53 thf(fact_197_matchCases, axiom, (! [A2:name,B2:name,P:pi,Rs:late_residual,F3:(name > (name > $o))]: ((((late_transitions @ (((match @ A2) @ B2) @ P)) @ Rs) => ((((late_transitions @ P) @ Rs) => ((A2 = B2) => ((F3 @ A2) @ A2))) => ((F3 @ A2) @ B2)))))).
% 2.70/1.53 thf(fact_198_matchTrans, axiom, (! [A2:name,B2:name,P:pi,Rs:late_residual]: ((((late_transitions @ (((match @ A2) @ B2) @ P)) @ Rs) => (A2 = B2))))).
% 2.70/1.53 thf(fact_199_matchCases_H, axiom, (! [A2:name,B2:name,P:pi,Rs:late_residual]: ((((late_transitions @ (((match @ A2) @ B2) @ P)) @ Rs) => (~ ((! [P4:pi]: ((((B2 = A2) & (P = P4)) => (~ (((late_transitions @ P4) @ Rs)))))))))))).
% 2.70/1.53 thf(fact_200_Match, axiom, (! [P:pi,Rs:late_residual,B2:name]: ((((late_transitions @ P) @ Rs) => ((late_transitions @ (((match @ B2) @ B2) @ P)) @ Rs))))).
% 2.70/1.53 thf(fact_201_nilCases_H, axiom, (! [Rs:late_residual]: ((~ (((late_transitions @ piNil) @ Rs)))))).
% 2.70/1.53 thf(fact_202_zeroTrans, axiom, (! [Rs:late_residual]: ((~ (((late_transitions @ piNil) @ Rs)))))).
% 2.70/1.53 thf(fact_203_pi_Odistinct_I65_J, axiom, (! [Name1:name,Name22:name,Pi3:pi,Pi12:pi,Pi22:pi]: (((((match @ Name1) @ Name22) @ Pi3) != ((par @ Pi12) @ Pi22))))).
% 2.70/1.53 thf(fact_204_pi_Odistinct_I67_J, axiom, (! [Name1:name,Name22:name,Pi3:pi,Name:name,Pi:pi]: (((((match @ Name1) @ Name22) @ Pi3) != ((res @ Name) @ Pi))))).
% 2.70/1.53 thf(fact_205_pi_Odistinct_I13_J, axiom, (! [Pi12:pi,Pi22:pi]: ((piNil != ((par @ Pi12) @ Pi22))))).
% 2.70/1.53 thf(fact_206_pi_Odistinct_I15_J, axiom, (! [Name:name,Pi:pi]: ((piNil != ((res @ Name) @ Pi))))).
% 2.70/1.53 thf(fact_207_pi_Odistinct_I7_J, axiom, (! [Name13:name,Name24:name,Pi:pi]: ((piNil != (((match @ Name13) @ Name24) @ Pi))))).
% 2.70/1.53 thf(fact_208_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))))))).
% 2.70/1.53 thf(fact_209_pi_Odistinct_I3_J, axiom, (! [Pi:pi]: ((piNil != (tau @ Pi))))).
% 2.70/1.53 thf(fact_210_pi_Odistinct_I37_J, axiom, (! [Pi3:pi,Name13:name,Name24:name,Pi:pi]: (((tau @ Pi3) != (((match @ Name13) @ Name24) @ Pi))))).
% 2.70/1.53 thf(fact_211_pi_Odistinct_I1_J, axiom, (! [Name13:name,Name24:name,Pi:pi]: ((piNil != (((output @ Name13) @ Name24) @ Pi))))).
% 2.70/1.53 thf(fact_212_pi_Odistinct_I23_J, axiom, (! [Name1:name,Name22:name,Pi3:pi,Name13:name,Name24:name,Pi:pi]: (((((output @ Name1) @ Name22) @ Pi3) != (((match @ Name13) @ Name24) @ Pi))))).
% 2.70/1.53 thf(fact_213_resZeroTrans, axiom, (! [X2:name,Rs:late_residual]: ((~ (((late_transitions @ ((res @ X2) @ piNil)) @ Rs)))))).
% 2.70/1.53 thf(fact_214_nilSim_I2_J, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),A2:name,X2:name,P:pi]: ((~ ((((strong743114133lation @ piNil) @ Rel) @ (((input @ A2) @ X2) @ P))))))).
% 2.70/1.53 thf(fact_215_nilSim_I3_J, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),A2:name,B2:name,P:pi]: ((~ ((((strong743114133lation @ piNil) @ Rel) @ (((output @ A2) @ B2) @ P))))))).
% 2.70/1.53 thf(fact_216_nilSim_I1_J, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),P:pi]: ((~ ((((strong743114133lation @ piNil) @ Rel) @ (tau @ P))))))).
% 2.70/1.53 thf(fact_217_simps_I6_J, axiom, (! [A2:name,B2:name,P:pi,C2:name,D:name]: (((((subs @ (((mismatch @ A2) @ B2) @ P)) @ C2) @ D) = (((mismatch @ (((subst_name @ A2) @ C2) @ D)) @ (((subst_name @ B2) @ C2) @ D)) @ (((subs @ P) @ C2) @ D)))))).
% 2.70/1.53 thf(fact_218_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))))))).
% 2.70/1.53 thf(fact_219_pi_Odistinct_I9_J, axiom, (! [Name13:name,Name24:name,Pi:pi]: ((piNil != (((mismatch @ Name13) @ Name24) @ Pi))))).
% 2.70/1.53 thf(fact_220_pi_Odistinct_I61_J, axiom, (! [Name1:name,Name22:name,Pi3:pi,Name13:name,Name24:name,Pi:pi]: (((((match @ Name1) @ Name22) @ Pi3) != (((mismatch @ Name13) @ Name24) @ Pi))))).
% 2.70/1.53 thf(fact_221_pi_Odistinct_I25_J, axiom, (! [Name1:name,Name22:name,Pi3:pi,Name13:name,Name24:name,Pi:pi]: (((((output @ Name1) @ Name22) @ Pi3) != (((mismatch @ Name13) @ Name24) @ Pi))))).
% 2.70/1.53 thf(fact_222_pi_Odistinct_I39_J, axiom, (! [Pi3:pi,Name13:name,Name24:name,Pi:pi]: (((tau @ Pi3) != (((mismatch @ Name13) @ Name24) @ Pi))))).
% 2.70/1.53 thf(fact_223_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))))))).
% 2.70/1.53 thf(fact_224_pi_Odistinct_I75_J, axiom, (! [Name1:name,Name22:name,Pi3:pi,Name:name,Pi:pi]: (((((mismatch @ Name1) @ Name22) @ Pi3) != ((res @ Name) @ Pi))))).
% 2.70/1.53 thf(fact_225_pi_Odistinct_I73_J, axiom, (! [Name1:name,Name22:name,Pi3:pi,Pi12:pi,Pi22:pi]: (((((mismatch @ Name1) @ Name22) @ Pi3) != ((par @ Pi12) @ Pi22))))).
% 2.70/1.53 thf(fact_226_Mismatch, axiom, (! [P:pi,Rs:late_residual,A2:name,B2:name]: ((((late_transitions @ P) @ Rs) => ((A2 != B2) => ((late_transitions @ (((mismatch @ A2) @ B2) @ P)) @ Rs)))))).
% 2.70/1.53 thf(fact_227_mismatchCases_H, axiom, (! [A2:name,B2:name,P:pi,Rs:late_residual]: ((((late_transitions @ (((mismatch @ A2) @ B2) @ P)) @ Rs) => (~ ((! [P4:pi,A4:name,B4:name]: ((((A2 = A4) & ((B2 = B4) & (P = P4))) => (((late_transitions @ P4) @ Rs) => (A4 = B4))))))))))).
% 2.70/1.53 thf(fact_228_mismatchTrans, axiom, (! [A2:name,P:pi,Rs:late_residual]: ((~ (((late_transitions @ (((mismatch @ A2) @ A2) @ P)) @ Rs)))))).
% 2.70/1.53 thf(fact_229_mismatchCases, axiom, (! [A2:name,B2:name,P:pi,Rs:late_residual,F3:(name > (name > $o))]: ((((late_transitions @ (((mismatch @ A2) @ B2) @ P)) @ Rs) => ((((late_transitions @ P) @ Rs) => ((A2 != B2) => ((F3 @ A2) @ B2))) => ((F3 @ A2) @ B2)))))).
% 2.70/1.53 thf(fact_230_pi_Odistinct_I51_J, axiom, (! [Name1:name,Name22:name,Pi3:pi,Name13:name,Name24:name,Pi:pi]: (((((input @ Name1) @ Name22) @ Pi3) != (((mismatch @ Name13) @ Name24) @ Pi))))).
% 2.70/1.53 thf(fact_231_mismatchNilLeft, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),A2:name,P:pi]: ((((strong743114133lation @ piNil) @ Rel) @ (((mismatch @ A2) @ A2) @ P))))).
% 2.70/1.53 thf(fact_232_pi_Ostrong__induct, axiom, (! [N:$tType]: (((fs_name @ N) => (! [P:(N > (pi > $o)),Z:N,Pi3:pi]: (((! [Z2:N]: (((P @ Z2) @ piNil))) => ((! [Name12:name,Name23:name,Pi4:pi,Z2:N]: (((! [Za:N]: (((P @ Za) @ Pi4))) => ((P @ Z2) @ (((output @ Name12) @ Name23) @ Pi4))))) => ((! [Pi4:pi,Z2:N]: (((! [Za:N]: (((P @ Za) @ Pi4))) => ((P @ Z2) @ (tau @ Pi4))))) => ((! [Name12:name,Name23:name,Pi4:pi,Z2:N]: ((((((fresh @ name) @ N) @ Name23) @ Z2) => (((((fresh @ name) @ name) @ Name23) @ Name12) => ((! [Za:N]: (((P @ Za) @ Pi4))) => ((P @ Z2) @ (((input @ Name12) @ Name23) @ Pi4))))))) => ((! [Name12:name,Name23:name,Pi4:pi,Z2:N]: (((! [Za:N]: (((P @ Za) @ Pi4))) => ((P @ Z2) @ (((match @ Name12) @ Name23) @ Pi4))))) => ((! [Name12:name,Name23:name,Pi4:pi,Z2:N]: (((! [Za:N]: (((P @ Za) @ Pi4))) => ((P @ Z2) @ (((mismatch @ Name12) @ Name23) @ Pi4))))) => ((! [Pi13:pi,Pi23:pi,Z2:N]: (((! [Za:N]: (((P @ Za) @ Pi13))) => ((! [Za:N]: (((P @ Za) @ Pi23))) => ((P @ Z2) @ ((sum @ Pi13) @ Pi23)))))) => ((! [Pi13:pi,Pi23:pi,Z2:N]: (((! [Za:N]: (((P @ Za) @ Pi13))) => ((! [Za:N]: (((P @ Za) @ Pi23))) => ((P @ Z2) @ ((par @ Pi13) @ Pi23)))))) => ((! [Name3:name,Pi4:pi,Z2:N]: ((((((fresh @ name) @ N) @ Name3) @ Z2) => ((! [Za:N]: (((P @ Za) @ Pi4))) => ((P @ Z2) @ ((res @ Name3) @ Pi4)))))) => ((! [Pi4:pi,Z2:N]: (((! [Za:N]: (((P @ Za) @ Pi4))) => ((P @ Z2) @ (bang @ Pi4))))) => ((P @ Z) @ Pi3))))))))))))))))).
% 2.70/1.53 thf(fact_233_pi_Ostrong__inducts, axiom, (! [A:$tType]: (((fs_name @ A) => (! [P:(A > (pi > $o)),Z:A,Pi3:pi]: (((! [Z2:A]: (((P @ Z2) @ piNil))) => ((! [Name12:name,Name23:name,Pi4:pi,Z2:A]: (((! [Za:A]: (((P @ Za) @ Pi4))) => ((P @ Z2) @ (((output @ Name12) @ Name23) @ Pi4))))) => ((! [Pi4:pi,Z2:A]: (((! [Za:A]: (((P @ Za) @ Pi4))) => ((P @ Z2) @ (tau @ Pi4))))) => ((! [Name12:name,Name23:name,Pi4:pi,Z2:A]: ((((((fresh @ name) @ A) @ Name23) @ Z2) => (((((fresh @ name) @ name) @ Name23) @ Name12) => ((! [Za:A]: (((P @ Za) @ Pi4))) => ((P @ Z2) @ (((input @ Name12) @ Name23) @ Pi4))))))) => ((! [Name12:name,Name23:name,Pi4:pi,Z2:A]: (((! [Za:A]: (((P @ Za) @ Pi4))) => ((P @ Z2) @ (((match @ Name12) @ Name23) @ Pi4))))) => ((! [Name12:name,Name23:name,Pi4:pi,Z2:A]: (((! [Za:A]: (((P @ Za) @ Pi4))) => ((P @ Z2) @ (((mismatch @ Name12) @ Name23) @ Pi4))))) => ((! [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,Pi4:pi,Z2:A]: ((((((fresh @ name) @ A) @ Name3) @ Z2) => ((! [Za:A]: (((P @ Za) @ Pi4))) => ((P @ Z2) @ ((res @ Name3) @ Pi4)))))) => ((! [Pi4:pi,Z2:A]: (((! [Za:A]: (((P @ Za) @ Pi4))) => ((P @ Z2) @ (bang @ Pi4))))) => ((P @ Z) @ Pi3))))))))))))))))).
% 2.70/1.53 thf(fact_234_pi_Ofresh_I10_J, axiom, (! [A2:name,X1:pi]: ((((((fresh @ name) @ pi) @ A2) @ (bang @ X1)) = ((((fresh @ name) @ pi) @ A2) @ X1))))).
% 2.70/1.53 thf(fact_235_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)))))).
% 2.70/1.53 thf(fact_236_simps_I10_J, axiom, (! [P:pi,C2:name,D:name]: (((((subs @ (bang @ P)) @ C2) @ D) = (bang @ (((subs @ P) @ C2) @ D)))))).
% 2.70/1.53 thf(fact_237_simps_I7_J, axiom, (! [P:pi,Q:pi,C2:name,D:name]: (((((subs @ ((sum @ P) @ Q)) @ C2) @ D) = ((sum @ (((subs @ P) @ C2) @ D)) @ (((subs @ Q) @ C2) @ D)))))).
% 2.70/1.53 thf(fact_238_pi_Odistinct_I77_J, axiom, (! [Name1:name,Name22:name,Pi3:pi,Pi:pi]: (((((mismatch @ Name1) @ Name22) @ Pi3) != (bang @ Pi))))).
% 2.70/1.53 thf(fact_239_pi_Odistinct_I71_J, axiom, (! [Name1:name,Name22:name,Pi3:pi,Pi12:pi,Pi22:pi]: (((((mismatch @ Name1) @ Name22) @ Pi3) != ((sum @ Pi12) @ Pi22))))).
% 2.70/1.53 thf(fact_240_pi_Odistinct_I59_J, axiom, (! [Name1:name,Name22:name,Pi3:pi,Pi:pi]: (((((input @ Name1) @ Name22) @ Pi3) != (bang @ Pi))))).
% 2.70/1.53 thf(fact_241_pi_Odistinct_I53_J, axiom, (! [Name1:name,Name22:name,Pi3:pi,Pi12:pi,Pi22:pi]: (((((input @ Name1) @ Name22) @ Pi3) != ((sum @ Pi12) @ Pi22))))).
% 2.70/1.53 thf(fact_242_pi_Odistinct_I47_J, axiom, (! [Pi3:pi,Pi:pi]: (((tau @ Pi3) != (bang @ Pi))))).
% 2.70/1.53 thf(fact_243_pi_Odistinct_I41_J, axiom, (! [Pi3:pi,Pi12:pi,Pi22:pi]: (((tau @ Pi3) != ((sum @ Pi12) @ Pi22))))).
% 2.70/1.53 thf(fact_244_pi_Odistinct_I79_J, axiom, (! [Pi1:pi,Pi2:pi,Pi12:pi,Pi22:pi]: ((((sum @ Pi1) @ Pi2) != ((par @ Pi12) @ Pi22))))).
% 2.70/1.53 thf(fact_245_pi_Odistinct_I81_J, axiom, (! [Pi1:pi,Pi2:pi,Name:name,Pi:pi]: ((((sum @ Pi1) @ Pi2) != ((res @ Name) @ Pi))))).
% 2.70/1.53 thf(fact_246_pi_Odistinct_I27_J, axiom, (! [Name1:name,Name22:name,Pi3:pi,Pi12:pi,Pi22:pi]: (((((output @ Name1) @ Name22) @ Pi3) != ((sum @ Pi12) @ Pi22))))).
% 2.70/1.53 thf(fact_247_pi_Odistinct_I83_J, axiom, (! [Pi1:pi,Pi2:pi,Pi:pi]: ((((sum @ Pi1) @ Pi2) != (bang @ Pi))))).
% 2.70/1.53 thf(fact_248_pi_Oinject_I6_J, axiom, (! [X22:pi,X1:pi,Y2:pi,Y1:pi]: (((((sum @ X22) @ X1) = ((sum @ Y2) @ Y1)) = ((X22 = Y2) & (X1 = Y1)))))).
% 2.70/1.53 thf(fact_249_pi_Oinject_I9_J, axiom, (! [X1:pi,Y1:pi]: ((((bang @ X1) = (bang @ Y1)) = (X1 = Y1))))).
% 2.70/1.53 thf(fact_250_sumCases, axiom, (! [P:pi,Q:pi,Rs:late_residual]: ((((late_transitions @ ((sum @ P) @ Q)) @ Rs) => ((~ (((late_transitions @ P) @ Rs))) => ((late_transitions @ Q) @ Rs)))))).
% 2.70/1.53 thf(fact_251_sumCases_H, axiom, (! [P:pi,Q:pi,Rs:late_residual]: ((((late_transitions @ ((sum @ P) @ Q)) @ Rs) => ((~ (((late_transitions @ P) @ Rs))) => ((late_transitions @ Q) @ Rs)))))).
% 2.70/1.53 thf(fact_252_Sum1, axiom, (! [P:pi,Rs:late_residual,Q:pi]: ((((late_transitions @ P) @ Rs) => ((late_transitions @ ((sum @ P) @ Q)) @ Rs))))).
% 2.70/1.53 thf(fact_253_Sum2, axiom, (! [Q:pi,Rs:late_residual,P:pi]: ((((late_transitions @ Q) @ Rs) => ((late_transitions @ ((sum @ P) @ Q)) @ Rs))))).
% 2.70/1.53 thf(fact_254_pi_Odistinct_I33_J, axiom, (! [Name1:name,Name22:name,Pi3:pi,Pi:pi]: (((((output @ Name1) @ Name22) @ Pi3) != (bang @ Pi))))).
% 2.70/1.53 thf(fact_255_pi_Odistinct_I89_J, axiom, (! [Name2:name,Pi3:pi,Pi:pi]: ((((res @ Name2) @ Pi3) != (bang @ Pi))))).
% 2.70/1.53 thf(tcon_Agent_Opi___Agent_Ofs__name, axiom, (fs_name @ pi)).
% 2.70/1.53 thf(tcon_HOL_Obool___Agent_Ofs__name_1, axiom, (fs_name @ $o)).
% 2.70/1.53 thf(tcon_Agent_Oname___Agent_Ofs__name_2, axiom, (fs_name @ name)).
% 2.70/1.53 thf(tcon_Product__Type_Oprod___Agent_Ofs__name_3, axiom, (! [A7:$tType,A8:$tType]: ((((fs_name @ A7) & (fs_name @ A8)) => (fs_name @ ((product_prod @ A7) @ A8)))))).
% 2.70/1.53 thf(tcon_Late__Semantics_OfreeRes___Agent_Ofs__name_4, axiom, (fs_name @ late_freeRes)).
% 2.70/1.53 thf(tcon_Late__Semantics_Osubject___Agent_Ofs__name_5, axiom, (fs_name @ late_subject)).
% 2.70/1.53 thf(tcon_Late__Semantics_Oresidual___Agent_Ofs__name_6, axiom, (fs_name @ late_residual)).
% 2.70/1.53 thf(help_If_3_1_T, axiom, (! [P:$o]: (((P = $true) | (P = $false))))).
% 2.70/1.53 thf(help_If_2_1_T, axiom, (! [A:$tType,X2:A,Y:A]: ((((((if @ A) @ $false) @ X2) @ Y) = Y)))).
% 2.70/1.53 thf(help_If_1_1_T, axiom, (! [A:$tType,X2:A,Y:A]: ((((((if @ A) @ $true) @ X2) @ Y) = X2)))).
% 2.70/1.53 thf(conj_0, conjecture, (? [P6:pi]: ((((late_transitions @ ((par @ ((par @ p) @ q)) @ r)) @ ((late_FreeR @ late_TauR) @ P6)) & (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ P6) @ ((res @ y) @ ((par @ p2) @ (((subs @ ((par @ q2) @ r)) @ x) @ y))))) @ rel))))).
% 2.70/1.53 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.eALBO61dU7/DTF2DTF25766.p
% 2.70/1.53 ------------------------
% 2.70/1.58 ---- Cleaned THF ---
% 2.70/1.58 thf(ty_t_Late__Semantics_Oresidual,type,
% 2.70/1.58 late_residual: $tType ).
% 2.70/1.58
% 2.70/1.58 thf(ty_t_Late__Semantics_Osubject,type,
% 2.70/1.58 late_subject: $tType ).
% 2.70/1.58
% 2.70/1.58 thf(ty_t_Late__Semantics_OfreeRes,type,
% 2.70/1.58 late_freeRes: $tType ).
% 2.70/1.58
% 2.70/1.58 thf(ty_t_Product__Type_Oprod,type,
% 2.70/1.58 product_prod: $tType > $tType > $tType ).
% 2.70/1.58
% 2.70/1.58 thf(ty_t_Nominal_Onoption,type,
% 2.70/1.58 noption: $tType > $tType ).
% 2.70/1.58
% 2.70/1.58 thf(ty_t_Agent_Oname,type,
% 2.70/1.58 name: $tType ).
% 2.70/1.58
% 2.70/1.58 thf(ty_t_Agent_Opi,type,
% 2.70/1.58 pi: $tType ).
% 2.70/1.58
% 2.70/1.58 thf(ty_t_Set_Oset,type,
% 2.70/1.58 set: $tType > $tType ).
% 2.70/1.58
% 2.70/1.58 thf(sy_cl_Agent_Ofs__name,type,
% 2.70/1.58 fs_name:
% 2.70/1.58 !>[A: $tType] : $o ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Agent_Opi_OBang,type,
% 2.70/1.58 bang: pi > pi ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Agent_Opi_OInput,type,
% 2.70/1.58 input: name > name > pi > pi ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Agent_Opi_OMatch,type,
% 2.70/1.58 match: name > name > pi > pi ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Agent_Opi_OMismatch,type,
% 2.70/1.58 mismatch: name > name > pi > pi ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Agent_Opi_OOutput,type,
% 2.70/1.58 output: name > name > pi > pi ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Agent_Opi_OPar,type,
% 2.70/1.58 par: pi > pi > pi ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Agent_Opi_OPiNil,type,
% 2.70/1.58 piNil: pi ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Agent_Opi_ORes,type,
% 2.70/1.58 res: name > pi > pi ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Agent_Opi_OSum,type,
% 2.70/1.58 sum: pi > pi > pi ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Agent_Opi_OTau,type,
% 2.70/1.58 tau: pi > pi ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Agent_Osubs,type,
% 2.70/1.58 subs: pi > name > name > pi ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Agent_Osubst__name,type,
% 2.70/1.58 subst_name: name > name > name > name ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_If,type,
% 2.70/1.58 if:
% 2.70/1.58 !>[A: $tType] : ( $o > A > A > A ) ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Late__Semantics_OfreeRes_OOutputR,type,
% 2.70/1.58 late_OutputR: name > name > late_freeRes ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Late__Semantics_OfreeRes_OTauR,type,
% 2.70/1.58 late_TauR: late_freeRes ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Late__Semantics_OfreeRes_OfreeRes__rec,type,
% 2.70/1.58 late_freeRes_rec:
% 2.70/1.58 !>[T: $tType] : ( ( name > name > T ) > T > late_freeRes > T ) ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Late__Semantics_Oresidual_OBoundR,type,
% 2.70/1.58 late_BoundR: late_subject > name > pi > late_residual ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Late__Semantics_Oresidual_OFreeR,type,
% 2.70/1.58 late_FreeR: late_freeRes > pi > late_residual ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Late__Semantics_Osubject_OBoundOutputS,type,
% 2.70/1.58 late_BoundOutputS: name > late_subject ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Late__Semantics_Osubject_OInputS,type,
% 2.70/1.58 late_InputS: name > late_subject ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Late__Semantics_Osubject_Osubject__rec,type,
% 2.70/1.58 late_subject_rec:
% 2.70/1.58 !>[T: $tType] : ( ( name > T ) > ( name > T ) > late_subject > T ) ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Late__Semantics_Otransitions,type,
% 2.70/1.58 late_transitions: pi > late_residual > $o ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Nominal_Oabs__fun,type,
% 2.70/1.58 abs_fun:
% 2.70/1.58 !>[X: $tType,A: $tType] : ( X > A > X > ( noption @ A ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Nominal_Ofresh,type,
% 2.70/1.58 fresh:
% 2.70/1.58 !>[X: $tType,A: $tType] : ( X > A > $o ) ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Product__Type_OPair,type,
% 2.70/1.58 product_Pair:
% 2.70/1.58 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Product__Type_Ointernal__case__prod,type,
% 2.70/1.58 produc2004651681e_prod:
% 2.70/1.58 !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > ( product_prod @ A @ B ) > C ) ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod,type,
% 2.70/1.58 product_rec_prod:
% 2.70/1.58 !>[A: $tType,B: $tType,T: $tType] : ( ( A > B > T ) > ( product_prod @ A @ B ) > T ) ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Rel_Oeqvt,type,
% 2.70/1.58 eqvt:
% 2.70/1.58 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > $o ) ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Set_OCollect,type,
% 2.70/1.58 collect:
% 2.70/1.58 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Strong__Late__Sim_Oderivative,type,
% 2.70/1.58 strong2129052853vative: pi > pi > late_subject > name > ( set @ ( product_prod @ pi @ pi ) ) > $o ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Strong__Late__Sim_Osimulation,type,
% 2.70/1.58 strong743114133lation: pi > ( set @ ( product_prod @ pi @ pi ) ) > pi > $o ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_member,type,
% 2.70/1.58 member:
% 2.70/1.58 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 2.70/1.58
% 2.70/1.58 thf(sy_v_P,type,
% 2.70/1.58 p: pi ).
% 2.70/1.58
% 2.70/1.58 thf(sy_v_PQR____,type,
% 2.70/1.58 pqr: pi ).
% 2.70/1.58
% 2.70/1.58 thf(sy_v_P_H____,type,
% 2.70/1.58 p2: pi ).
% 2.70/1.58
% 2.70/1.58 thf(sy_v_Q,type,
% 2.70/1.58 q: pi ).
% 2.70/1.58
% 2.70/1.58 thf(sy_v_QR____,type,
% 2.70/1.58 qr: pi ).
% 2.70/1.58
% 2.70/1.58 thf(sy_v_Q_H____,type,
% 2.70/1.58 q2: pi ).
% 2.70/1.58
% 2.70/1.58 thf(sy_v_R,type,
% 2.70/1.58 r: pi ).
% 2.70/1.58
% 2.70/1.58 thf(sy_v_Rel,type,
% 2.70/1.58 rel: set @ ( product_prod @ pi @ pi ) ).
% 2.70/1.58
% 2.70/1.58 thf(sy_v__092_060alpha_062____,type,
% 2.70/1.58 alpha: late_freeRes ).
% 2.70/1.58
% 2.70/1.58 thf(sy_v_a____,type,
% 2.70/1.58 a: name ).
% 2.70/1.58
% 2.70/1.58 thf(sy_v_x____,type,
% 2.70/1.58 x: name ).
% 2.70/1.58
% 2.70/1.58 thf(sy_v_y____,type,
% 2.70/1.58 y: name ).
% 2.70/1.58
% 2.70/1.58 thf(fact_0_cClose2_Ohyps_I14_J,axiom,
% 2.70/1.58 alpha = late_TauR ).
% 2.70/1.58
% 2.70/1.58 thf(fact_1_cClose2_Ohyps_I6_J,axiom,
% 2.70/1.58 x != y ).
% 2.70/1.58
% 2.70/1.58 thf(fact_2_cClose2_Ohyps_I10_J,axiom,
% 2.70/1.58 y != a ).
% 2.70/1.58
% 2.70/1.58 thf(fact_3_cClose2_Ohyps_I5_J,axiom,
% 2.70/1.58 x != a ).
% 2.70/1.58
% 2.70/1.58 thf(fact_4_Ass,axiom,
% 2.70/1.58 ! [S: pi,T2: pi,U: pi] : ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( par @ ( par @ S @ T2 ) @ U ) @ ( par @ S @ ( par @ T2 @ U ) ) ) @ rel ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_5_Res,axiom,
% 2.70/1.58 ! [S: pi,T2: pi,X2: name] :
% 2.70/1.58 ( ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ S @ T2 ) @ rel )
% 2.70/1.58 => ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( res @ X2 @ S ) @ ( res @ X2 @ T2 ) ) @ rel ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_6__092_060open_062_I_060_092_060nu_062y_062_IP_H_A_092_060parallel_062_AQ_H_091x_058_058_061y_093_J_A_092_060parallel_062_AR_M_A_060_092_060nu_062y_062_IP_H_A_092_060parallel_062_A_IQ_H_A_092_060parallel_062_AR_J_091x_058_058_061y_093_J_J_A_092_060in_062_ARel_092_060close_062,axiom,
% 2.70/1.58 member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( par @ ( res @ y @ ( par @ p2 @ ( subs @ q2 @ x @ y ) ) ) @ r ) @ ( res @ y @ ( par @ p2 @ ( subs @ ( par @ q2 @ r ) @ x @ y ) ) ) ) @ rel ).
% 2.70/1.58
% 2.70/1.58 thf(fact_7__092_060open_062_IP_A_092_060parallel_062_AQ_J_A_092_060parallel_062_AR_A_092_060longmapsto_062_A_092_060tau_062_A_092_060prec_062_A_060_092_060nu_062y_062_IP_H_A_092_060parallel_062_AQ_H_091x_058_058_061y_093_J_A_092_060parallel_062_AR_092_060close_062,axiom,
% 2.70/1.58 late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_FreeR @ late_TauR @ ( par @ ( res @ y @ ( par @ p2 @ ( subs @ q2 @ x @ y ) ) ) @ r ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_8_Free_Ohyps,axiom,
% 2.70/1.58 late_transitions @ ( par @ p @ ( par @ q @ r ) ) @ ( late_FreeR @ alpha @ pqr ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_9__092_060open_062_I_060_092_060nu_062y_062_IP_H_A_092_060parallel_062_AQ_H_091x_058_058_061y_093_J_A_092_060parallel_062_AR_M_A_060_092_060nu_062y_062_IP_H_A_092_060parallel_062_AQ_H_091x_058_058_061y_093_A_092_060parallel_062_AR_J_J_A_092_060in_062_ARel_092_060close_062,axiom,
% 2.70/1.58 member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( par @ ( res @ y @ ( par @ p2 @ ( subs @ q2 @ x @ y ) ) ) @ r ) @ ( res @ y @ ( par @ p2 @ ( par @ ( subs @ q2 @ x @ y ) @ r ) ) ) ) @ rel ).
% 2.70/1.58
% 2.70/1.58 thf(fact_10__092_060open_062P_A_092_060parallel_062_AQ_A_092_060longmapsto_062_A_092_060tau_062_A_092_060prec_062_A_060_092_060nu_062y_062_IP_H_A_092_060parallel_062_AQ_H_091x_058_058_061y_093_J_092_060close_062,axiom,
% 2.70/1.58 late_transitions @ ( par @ p @ q ) @ ( late_FreeR @ late_TauR @ ( res @ y @ ( par @ p2 @ ( subs @ q2 @ x @ y ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_11_cClose2_Ohyps_I13_J,axiom,
% 2.70/1.58 fresh @ name @ pi @ y @ q ).
% 2.70/1.58
% 2.70/1.58 thf(fact_12_cClose2_Ohyps_I12_J,axiom,
% 2.70/1.58 fresh @ name @ pi @ x @ q ).
% 2.70/1.58
% 2.70/1.58 thf(fact_13_cClose2_Ohyps_I7_J,axiom,
% 2.70/1.58 fresh @ name @ pi @ x @ p2 ).
% 2.70/1.58
% 2.70/1.58 thf(fact_14_cClose2_Ohyps_I8_J,axiom,
% 2.70/1.58 fresh @ name @ pi @ y @ p ).
% 2.70/1.58
% 2.70/1.58 thf(fact_15_cClose2_Ohyps_I3_J,axiom,
% 2.70/1.58 fresh @ name @ pi @ x @ p ).
% 2.70/1.58
% 2.70/1.58 thf(fact_16_cClose2_Ohyps_I9_J,axiom,
% 2.70/1.58 fresh @ name @ pi @ y @ ( par @ q @ r ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_17_cClose2_Ohyps_I4_J,axiom,
% 2.70/1.58 fresh @ name @ pi @ x @ ( par @ q @ r ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_18_simps_I9_J,axiom,
% 2.70/1.58 ! [X2: name,C2: name,D: name,P: pi] :
% 2.70/1.58 ( ( X2 != C2 )
% 2.70/1.58 => ( ( X2 != D )
% 2.70/1.58 => ( ( subs @ ( res @ X2 @ P ) @ C2 @ D )
% 2.70/1.58 = ( res @ X2 @ ( subs @ P @ C2 @ D ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_19_simps_I8_J,axiom,
% 2.70/1.58 ! [P: pi,Q: pi,C2: name,D: name] :
% 2.70/1.58 ( ( subs @ ( par @ P @ Q ) @ C2 @ D )
% 2.70/1.58 = ( par @ ( subs @ P @ C2 @ D ) @ ( subs @ Q @ C2 @ D ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_20_FreshExt,axiom,
% 2.70/1.58 ! [X2: name,S: pi,T2: pi,U: pi] :
% 2.70/1.58 ( ( fresh @ name @ pi @ X2 @ S )
% 2.70/1.58 => ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( res @ X2 @ ( par @ ( par @ S @ T2 ) @ U ) ) @ ( par @ S @ ( res @ X2 @ ( par @ T2 @ U ) ) ) ) @ rel ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_21_FreshExt_H,axiom,
% 2.70/1.58 ! [X2: name,U: pi,S: pi,T2: pi] :
% 2.70/1.58 ( ( fresh @ name @ pi @ X2 @ U )
% 2.70/1.58 => ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( par @ ( res @ X2 @ ( par @ S @ T2 ) ) @ U ) @ ( res @ X2 @ ( par @ S @ ( par @ T2 @ U ) ) ) ) @ rel ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_22_Par1F,axiom,
% 2.70/1.58 ! [P: pi,Alpha: late_freeRes,P2: pi,Q: pi] :
% 2.70/1.58 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 2.70/1.58 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha @ ( par @ P2 @ Q ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_23_Par2F,axiom,
% 2.70/1.58 ! [Q: pi,Alpha: late_freeRes,Q2: pi,P: pi] :
% 2.70/1.58 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 2.70/1.58 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha @ ( par @ P @ Q2 ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_24_subst__identity,axiom,
% 2.70/1.58 ! [P: pi,A2: name] :
% 2.70/1.58 ( ( subs @ P @ A2 @ A2 )
% 2.70/1.58 = P ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_25__092_060open_062x_A_092_060sharp_062_AR_092_060close_062,axiom,
% 2.70/1.58 fresh @ name @ pi @ x @ r ).
% 2.70/1.58
% 2.70/1.58 thf(fact_26__092_060open_062y_A_092_060sharp_062_AR_092_060close_062,axiom,
% 2.70/1.58 fresh @ name @ pi @ y @ r ).
% 2.70/1.58
% 2.70/1.58 thf(fact_27_prod_Oinject,axiom,
% 2.70/1.58 ! [A: $tType,B: $tType,X1: A,X22: B,Y1: A,Y2: B] :
% 2.70/1.58 ( ( ( product_Pair @ A @ B @ X1 @ X22 )
% 2.70/1.58 = ( product_Pair @ A @ B @ Y1 @ Y2 ) )
% 2.70/1.58 = ( ( X1 = Y1 )
% 2.70/1.58 & ( X22 = Y2 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_28_old_Oprod_Oinject,axiom,
% 2.70/1.58 ! [A: $tType,B: $tType,A2: A,B2: B,A3: A,B3: B] :
% 2.70/1.58 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 2.70/1.58 = ( product_Pair @ A @ B @ A3 @ B3 ) )
% 2.70/1.58 = ( ( A2 = A3 )
% 2.70/1.58 & ( B2 = B3 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_29_cClose2_Ohyps_I11_J,axiom,
% 2.70/1.58 fresh @ name @ pi @ y @ qr ).
% 2.70/1.58
% 2.70/1.58 thf(fact_30_pi_Ofresh_I8_J,axiom,
% 2.70/1.58 ! [A2: name,X22: pi,X1: pi] :
% 2.70/1.58 ( ( fresh @ name @ pi @ A2 @ ( par @ X22 @ X1 ) )
% 2.70/1.58 = ( ( fresh @ name @ pi @ A2 @ X22 )
% 2.70/1.58 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_31_substTrans,axiom,
% 2.70/1.58 ! [B2: name,P: pi,A2: name,C2: name] :
% 2.70/1.58 ( ( fresh @ name @ pi @ B2 @ P )
% 2.70/1.58 => ( ( subs @ ( subs @ P @ A2 @ B2 ) @ B2 @ C2 )
% 2.70/1.58 = ( subs @ P @ A2 @ C2 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_32_name__exists__fresh,axiom,
% 2.70/1.58 ! [A: $tType] :
% 2.70/1.58 ( ( fs_name @ A )
% 2.70/1.58 => ! [X2: A] :
% 2.70/1.58 ~ ! [C3: name] :
% 2.70/1.58 ~ ( fresh @ name @ A @ C3 @ X2 ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_33_freshRes,axiom,
% 2.70/1.58 ! [A2: name,P: pi] : ( fresh @ name @ pi @ A2 @ ( res @ A2 @ P ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_34_fresh__fact2,axiom,
% 2.70/1.58 ! [A2: name,B2: name,P: pi] :
% 2.70/1.58 ( ( A2 != B2 )
% 2.70/1.58 => ( fresh @ name @ pi @ A2 @ ( subs @ P @ A2 @ B2 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_35_fresh__fact1,axiom,
% 2.70/1.58 ! [A2: name,P: pi,C2: name,B2: name] :
% 2.70/1.58 ( ( fresh @ name @ pi @ A2 @ P )
% 2.70/1.58 => ( ( A2 != C2 )
% 2.70/1.58 => ( fresh @ name @ pi @ A2 @ ( subs @ P @ B2 @ C2 ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_36_forget,axiom,
% 2.70/1.58 ! [A2: name,P: pi,B2: name] :
% 2.70/1.58 ( ( fresh @ name @ pi @ A2 @ P )
% 2.70/1.58 => ( ( subs @ P @ A2 @ B2 )
% 2.70/1.58 = P ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_37_freshFreeDerivative_I2_J,axiom,
% 2.70/1.58 ! [P: pi,Alpha: late_freeRes,P2: pi,Y: name] :
% 2.70/1.58 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 2.70/1.58 => ( ( fresh @ name @ pi @ Y @ P )
% 2.70/1.58 => ( fresh @ name @ pi @ Y @ P2 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_38_substRes3,axiom,
% 2.70/1.58 ! [B2: name,P: pi,A2: name] :
% 2.70/1.58 ( ( fresh @ name @ pi @ B2 @ P )
% 2.70/1.58 => ( ( subs @ ( res @ A2 @ P ) @ A2 @ B2 )
% 2.70/1.58 = ( res @ B2 @ ( subs @ P @ A2 @ B2 ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_39_substRes2,axiom,
% 2.70/1.58 ! [B2: name,P: pi,A2: name] :
% 2.70/1.58 ( ( fresh @ name @ pi @ B2 @ P )
% 2.70/1.58 => ( ( res @ A2 @ P )
% 2.70/1.58 = ( res @ B2 @ ( subs @ P @ A2 @ B2 ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_40_old_Oprod_Oinducts,axiom,
% 2.70/1.58 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,Prod: product_prod @ A @ B] :
% 2.70/1.58 ( ! [A4: A,B4: B] : ( P @ ( product_Pair @ A @ B @ A4 @ B4 ) )
% 2.70/1.58 => ( P @ Prod ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_41_old_Oprod_Oexhaust,axiom,
% 2.70/1.58 ! [A: $tType,B: $tType,Y: product_prod @ A @ B] :
% 2.70/1.58 ~ ! [A4: A,B4: B] :
% 2.70/1.58 ( Y
% 2.70/1.58 != ( product_Pair @ A @ B @ A4 @ B4 ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_42_prod__induct7,axiom,
% 2.70/1.58 ! [G: $tType,F: $tType,E: $tType,D2: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) ) ) ) > $o,X2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) ) )] :
% 2.70/1.58 ( ! [A4: A,B4: B,C3: C,D3: D2,E2: E,F2: F,G2: G] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) @ C3 @ ( product_Pair @ D2 @ ( product_prod @ E @ ( product_prod @ F @ G ) ) @ D3 @ ( product_Pair @ E @ ( product_prod @ F @ G ) @ E2 @ ( product_Pair @ F @ G @ F2 @ G2 ) ) ) ) ) ) )
% 2.70/1.58 => ( P @ X2 ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_43_prod__induct6,axiom,
% 2.70/1.58 ! [F: $tType,E: $tType,D2: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E @ F ) ) ) ) ) > $o,X2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E @ F ) ) ) )] :
% 2.70/1.58 ( ! [A4: A,B4: B,C3: C,D3: D2,E2: E,F2: F] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E @ F ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E @ F ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D2 @ ( product_prod @ E @ F ) ) @ C3 @ ( product_Pair @ D2 @ ( product_prod @ E @ F ) @ D3 @ ( product_Pair @ E @ F @ E2 @ F2 ) ) ) ) ) )
% 2.70/1.58 => ( P @ X2 ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_44_prod__induct5,axiom,
% 2.70/1.58 ! [E: $tType,D2: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ E ) ) ) ) > $o,X2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ E ) ) )] :
% 2.70/1.58 ( ! [A4: A,B4: B,C3: C,D3: D2,E2: E] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ E ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D2 @ E ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D2 @ E ) @ C3 @ ( product_Pair @ D2 @ E @ D3 @ E2 ) ) ) ) )
% 2.70/1.58 => ( P @ X2 ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_45_mem__Collect__eq,axiom,
% 2.70/1.58 ! [A: $tType,A2: A,P: A > $o] :
% 2.70/1.58 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 2.70/1.58 = ( P @ A2 ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_46_Collect__mem__eq,axiom,
% 2.70/1.58 ! [A: $tType,A5: set @ A] :
% 2.70/1.58 ( ( collect @ A
% 2.70/1.58 @ ^ [X3: A] : ( member @ A @ X3 @ A5 ) )
% 2.70/1.58 = A5 ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_47_Collect__cong,axiom,
% 2.70/1.58 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.70/1.58 ( ! [X4: A] :
% 2.70/1.58 ( ( P @ X4 )
% 2.70/1.58 = ( Q @ X4 ) )
% 2.70/1.58 => ( ( collect @ A @ P )
% 2.70/1.58 = ( collect @ A @ Q ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_48_prod__induct4,axiom,
% 2.70/1.58 ! [D2: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D2 ) ) ) > $o,X2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D2 ) )] :
% 2.70/1.58 ( ! [A4: A,B4: B,C3: C,D3: D2] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D2 ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ D2 ) @ B4 @ ( product_Pair @ C @ D2 @ C3 @ D3 ) ) ) )
% 2.70/1.58 => ( P @ X2 ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_49_prod__induct3,axiom,
% 2.70/1.58 ! [C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ C ) ) > $o,X2: product_prod @ A @ ( product_prod @ B @ C )] :
% 2.70/1.58 ( ! [A4: A,B4: B,C3: C] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ C ) @ A4 @ ( product_Pair @ B @ C @ B4 @ C3 ) ) )
% 2.70/1.58 => ( P @ X2 ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_50_prod__cases7,axiom,
% 2.70/1.58 ! [A: $tType,B: $tType,C: $tType,D2: $tType,E: $tType,F: $tType,G: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) ) )] :
% 2.70/1.58 ~ ! [A4: A,B4: B,C3: C,D3: D2,E2: E,F2: F,G2: G] :
% 2.70/1.58 ( Y
% 2.70/1.58 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) @ C3 @ ( product_Pair @ D2 @ ( product_prod @ E @ ( product_prod @ F @ G ) ) @ D3 @ ( product_Pair @ E @ ( product_prod @ F @ G ) @ E2 @ ( product_Pair @ F @ G @ F2 @ G2 ) ) ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_51_prod__cases6,axiom,
% 2.70/1.58 ! [A: $tType,B: $tType,C: $tType,D2: $tType,E: $tType,F: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E @ F ) ) ) )] :
% 2.70/1.58 ~ ! [A4: A,B4: B,C3: C,D3: D2,E2: E,F2: F] :
% 2.70/1.58 ( Y
% 2.70/1.58 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E @ F ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D2 @ ( product_prod @ E @ F ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D2 @ ( product_prod @ E @ F ) ) @ C3 @ ( product_Pair @ D2 @ ( product_prod @ E @ F ) @ D3 @ ( product_Pair @ E @ F @ E2 @ F2 ) ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_52_prod__cases5,axiom,
% 2.70/1.58 ! [A: $tType,B: $tType,C: $tType,D2: $tType,E: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ E ) ) )] :
% 2.70/1.58 ~ ! [A4: A,B4: B,C3: C,D3: D2,E2: E] :
% 2.70/1.58 ( Y
% 2.70/1.58 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D2 @ E ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D2 @ E ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D2 @ E ) @ C3 @ ( product_Pair @ D2 @ E @ D3 @ E2 ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_53_prod__cases4,axiom,
% 2.70/1.58 ! [A: $tType,B: $tType,C: $tType,D2: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D2 ) )] :
% 2.70/1.58 ~ ! [A4: A,B4: B,C3: C,D3: D2] :
% 2.70/1.58 ( Y
% 2.70/1.58 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D2 ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ D2 ) @ B4 @ ( product_Pair @ C @ D2 @ C3 @ D3 ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_54_prod__cases3,axiom,
% 2.70/1.58 ! [A: $tType,B: $tType,C: $tType,Y: product_prod @ A @ ( product_prod @ B @ C )] :
% 2.70/1.58 ~ ! [A4: A,B4: B,C3: C] :
% 2.70/1.58 ( Y
% 2.70/1.58 != ( product_Pair @ A @ ( product_prod @ B @ C ) @ A4 @ ( product_Pair @ B @ C @ B4 @ C3 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_55_Pair__inject,axiom,
% 2.70/1.58 ! [A: $tType,B: $tType,A2: A,B2: B,A3: A,B3: B] :
% 2.70/1.58 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 2.70/1.58 = ( product_Pair @ A @ B @ A3 @ B3 ) )
% 2.70/1.58 => ~ ( ( A2 = A3 )
% 2.70/1.58 => ( B2 != B3 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_56_prod__cases,axiom,
% 2.70/1.58 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,P3: product_prod @ A @ B] :
% 2.70/1.58 ( ! [A4: A,B4: B] : ( P @ ( product_Pair @ A @ B @ A4 @ B4 ) )
% 2.70/1.58 => ( P @ P3 ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_57_surj__pair,axiom,
% 2.70/1.58 ! [A: $tType,B: $tType,P3: product_prod @ A @ B] :
% 2.70/1.58 ? [X4: A,Y3: B] :
% 2.70/1.58 ( P3
% 2.70/1.58 = ( product_Pair @ A @ B @ X4 @ Y3 ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_58_pi_Oinject_I7_J,axiom,
% 2.70/1.58 ! [X22: pi,X1: pi,Y2: pi,Y1: pi] :
% 2.70/1.58 ( ( ( par @ X22 @ X1 )
% 2.70/1.58 = ( par @ Y2 @ Y1 ) )
% 2.70/1.58 = ( ( X22 = Y2 )
% 2.70/1.58 & ( X1 = Y1 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_59_residual_Oinject_I2_J,axiom,
% 2.70/1.58 ! [X22: late_freeRes,X1: pi,Y2: late_freeRes,Y1: pi] :
% 2.70/1.58 ( ( ( late_FreeR @ X22 @ X1 )
% 2.70/1.58 = ( late_FreeR @ Y2 @ Y1 ) )
% 2.70/1.58 = ( ( X22 = Y2 )
% 2.70/1.58 & ( X1 = Y1 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_60_pi_Odistinct_I85_J,axiom,
% 2.70/1.58 ! [Pi1: pi,Pi2: pi,Name: name,Pi: pi] :
% 2.70/1.58 ( ( par @ Pi1 @ Pi2 )
% 2.70/1.58 != ( res @ Name @ Pi ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_61_cClose2_Ohyps_I2_J,axiom,
% 2.70/1.58 late_transitions @ ( par @ q @ r ) @ ( late_BoundR @ ( late_InputS @ a ) @ x @ qr ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_62_fresh__prod,axiom,
% 2.70/1.58 ! [A: $tType,X: $tType,B: $tType,A2: X,X2: A,Y: B] :
% 2.70/1.58 ( ( fresh @ X @ ( product_prod @ A @ B ) @ A2 @ ( product_Pair @ A @ B @ X2 @ Y ) )
% 2.70/1.58 = ( ( fresh @ X @ A @ A2 @ X2 )
% 2.70/1.58 & ( fresh @ X @ B @ A2 @ Y ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_63_cClose2_Ohyps_I1_J,axiom,
% 2.70/1.58 late_transitions @ p @ ( late_BoundR @ ( late_BoundOutputS @ a ) @ y @ p2 ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_64_cPar1_Ohyps,axiom,
% 2.70/1.58 late_transitions @ q @ ( late_BoundR @ ( late_InputS @ a ) @ x @ q2 ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_65_old_Oprod_Orec,axiom,
% 2.70/1.58 ! [A: $tType,T: $tType,B: $tType,F1: A > B > T,A2: A,B2: B] :
% 2.70/1.58 ( ( product_rec_prod @ A @ B @ T @ F1 @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 2.70/1.58 = ( F1 @ A2 @ B2 ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_66_fresh__prodD_I2_J,axiom,
% 2.70/1.58 ! [B: $tType,A: $tType,C: $tType,A2: A,X2: B,Y: C] :
% 2.70/1.58 ( ( fresh @ A @ ( product_prod @ B @ C ) @ A2 @ ( product_Pair @ B @ C @ X2 @ Y ) )
% 2.70/1.58 => ( fresh @ A @ C @ A2 @ Y ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_67_fresh__prodD_I1_J,axiom,
% 2.70/1.58 ! [C: $tType,A: $tType,B: $tType,A2: A,X2: B,Y: C] :
% 2.70/1.58 ( ( fresh @ A @ ( product_prod @ B @ C ) @ A2 @ ( product_Pair @ B @ C @ X2 @ Y ) )
% 2.70/1.58 => ( fresh @ A @ B @ A2 @ X2 ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_68_freeRes_Orecs_I2_J,axiom,
% 2.70/1.58 ! [T: $tType,P: T > $o,F1: name > name > T,F22: T] :
% 2.70/1.58 ( ! [X12: name,X23: name] : ( P @ ( F1 @ X12 @ X23 ) )
% 2.70/1.58 => ( ( P @ F22 )
% 2.70/1.58 => ( ( late_freeRes_rec @ T @ F1 @ F22 @ late_TauR )
% 2.70/1.58 = F22 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_69_resOutputTauTrans,axiom,
% 2.70/1.58 ! [X2: name,A2: name,B2: name,P: pi,P2: pi] :
% 2.70/1.58 ~ ( late_transitions @ ( res @ X2 @ ( output @ A2 @ B2 @ P ) ) @ ( late_FreeR @ late_TauR @ P2 ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_70_subject_Ofresh_I1_J,axiom,
% 2.70/1.58 ! [A2: name,X1: name] :
% 2.70/1.58 ( ( fresh @ name @ late_subject @ A2 @ ( late_InputS @ X1 ) )
% 2.70/1.58 = ( fresh @ name @ name @ A2 @ X1 ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_71_subject_Ofresh_I2_J,axiom,
% 2.70/1.58 ! [A2: name,X1: name] :
% 2.70/1.58 ( ( fresh @ name @ late_subject @ A2 @ ( late_BoundOutputS @ X1 ) )
% 2.70/1.58 = ( fresh @ name @ name @ A2 @ X1 ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_72_Late__Semantics_Osubject_Oinject_I2_J,axiom,
% 2.70/1.58 ! [X1: name,Y1: name] :
% 2.70/1.58 ( ( ( late_BoundOutputS @ X1 )
% 2.70/1.58 = ( late_BoundOutputS @ Y1 ) )
% 2.70/1.58 = ( X1 = Y1 ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_73_freeRes_Ofresh_I2_J,axiom,
% 2.70/1.58 ! [A2: name] : ( fresh @ name @ late_freeRes @ A2 @ late_TauR ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_74_residual_Ofresh_I2_J,axiom,
% 2.70/1.58 ! [A2: name,X22: late_freeRes,X1: pi] :
% 2.70/1.58 ( ( fresh @ name @ late_residual @ A2 @ ( late_FreeR @ X22 @ X1 ) )
% 2.70/1.58 = ( ( fresh @ name @ late_freeRes @ A2 @ X22 )
% 2.70/1.58 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_75_pi_Ofresh_I2_J,axiom,
% 2.70/1.58 ! [A2: name,X32: name,X22: name,X1: pi] :
% 2.70/1.58 ( ( fresh @ name @ pi @ A2 @ ( output @ X32 @ X22 @ X1 ) )
% 2.70/1.58 = ( ( fresh @ name @ name @ A2 @ X32 )
% 2.70/1.58 & ( fresh @ name @ name @ A2 @ X22 )
% 2.70/1.58 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_76_pi_Oinject_I1_J,axiom,
% 2.70/1.58 ! [X32: name,X22: name,X1: pi,Y32: name,Y2: name,Y1: pi] :
% 2.70/1.58 ( ( ( output @ X32 @ X22 @ X1 )
% 2.70/1.58 = ( output @ Y32 @ Y2 @ Y1 ) )
% 2.70/1.58 = ( ( X32 = Y32 )
% 2.70/1.58 & ( X22 = Y2 )
% 2.70/1.58 & ( X1 = Y1 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_77_Late__Semantics_Osubject_Odistinct_I1_J,axiom,
% 2.70/1.58 ! [Name2: name,Name: name] :
% 2.70/1.58 ( ( late_InputS @ Name2 )
% 2.70/1.58 != ( late_BoundOutputS @ Name ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_78_subject_Oinducts,axiom,
% 2.70/1.58 ! [P: late_subject > $o,Subject: late_subject] :
% 2.70/1.58 ( ! [Name3: name] : ( P @ ( late_InputS @ Name3 ) )
% 2.70/1.58 => ( ! [Name3: name] : ( P @ ( late_BoundOutputS @ Name3 ) )
% 2.70/1.58 => ( P @ Subject ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_79_outputBoundTrans,axiom,
% 2.70/1.58 ! [A2: name,B2: name,P: pi,C2: late_subject,X2: name,P2: pi] :
% 2.70/1.58 ~ ( late_transitions @ ( output @ A2 @ B2 @ P ) @ ( late_BoundR @ C2 @ X2 @ P2 ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_80_subject_Ostrong__induct_H,axiom,
% 2.70/1.58 ! [N: $tType,P: N > late_subject > $o,Z: N,Subject: late_subject] :
% 2.70/1.58 ( ! [Name3: name,Z2: N] : ( P @ Z2 @ ( late_InputS @ Name3 ) )
% 2.70/1.58 => ( ! [Name3: name,Z2: N] : ( P @ Z2 @ ( late_BoundOutputS @ Name3 ) )
% 2.70/1.58 => ( P @ Z @ Subject ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_81_subject_Ostrong__inducts,axiom,
% 2.70/1.58 ! [A: $tType,P: A > late_subject > $o,Z: A,Subject: late_subject] :
% 2.70/1.58 ( ! [Name3: name,Z2: A] : ( P @ Z2 @ ( late_InputS @ Name3 ) )
% 2.70/1.58 => ( ! [Name3: name,Z2: A] : ( P @ Z2 @ ( late_BoundOutputS @ Name3 ) )
% 2.70/1.58 => ( P @ Z @ Subject ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_82_resOutputInputTrans,axiom,
% 2.70/1.58 ! [X2: name,A2: name,B2: name,P: pi,C2: name,Y: name,P2: pi] :
% 2.70/1.58 ~ ( late_transitions @ ( res @ X2 @ ( output @ A2 @ B2 @ P ) ) @ ( late_BoundR @ ( late_InputS @ C2 ) @ Y @ P2 ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_83_Late__Semantics_OResB,axiom,
% 2.70/1.58 ! [P: pi,A2: late_subject,X2: name,P2: pi,Y: name] :
% 2.70/1.58 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P2 ) )
% 2.70/1.58 => ( ( fresh @ name @ late_subject @ Y @ A2 )
% 2.70/1.58 => ( ( Y != X2 )
% 2.70/1.58 => ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A2 @ X2 @ ( res @ Y @ P2 ) ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_84_freshBoundDerivative_I1_J,axiom,
% 2.70/1.58 ! [P: pi,A2: late_subject,X2: name,P2: pi,Y: name] :
% 2.70/1.58 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P2 ) )
% 2.70/1.58 => ( ( fresh @ name @ pi @ Y @ P )
% 2.70/1.58 => ( fresh @ name @ late_subject @ Y @ A2 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_85_outputFreshTrans,axiom,
% 2.70/1.58 ! [A2: name,B2: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 2.70/1.58 ( ( late_transitions @ ( output @ A2 @ B2 @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 2.70/1.58 => ~ ( ( fresh @ name @ late_freeRes @ A2 @ Alpha )
% 2.70/1.58 | ( fresh @ name @ late_freeRes @ B2 @ Alpha ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_86_residual_Odistinct_I1_J,axiom,
% 2.70/1.58 ! [Subject: late_subject,Name2: name,Pi3: pi,FreeRes: late_freeRes,Pi: pi] :
% 2.70/1.58 ( ( late_BoundR @ Subject @ Name2 @ Pi3 )
% 2.70/1.58 != ( late_FreeR @ FreeRes @ Pi ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_87_residual_Oinducts,axiom,
% 2.70/1.58 ! [P: late_residual > $o,Residual: late_residual] :
% 2.70/1.58 ( ! [Subject2: late_subject,Name3: name,Pi4: pi] : ( P @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) )
% 2.70/1.58 => ( ! [FreeRes2: late_freeRes,Pi4: pi] : ( P @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 2.70/1.58 => ( P @ Residual ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_88_pi_Odistinct_I29_J,axiom,
% 2.70/1.58 ! [Name1: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 2.70/1.58 ( ( output @ Name1 @ Name22 @ Pi3 )
% 2.70/1.58 != ( par @ Pi12 @ Pi22 ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_89_pi_Odistinct_I31_J,axiom,
% 2.70/1.58 ! [Name1: name,Name22: name,Pi3: pi,Name: name,Pi: pi] :
% 2.70/1.58 ( ( output @ Name1 @ Name22 @ Pi3 )
% 2.70/1.58 != ( res @ Name @ Pi ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_90_parCasesB_H,axiom,
% 2.70/1.58 ! [P: pi,Q: pi,B2: late_subject,Y: name,P2: pi] :
% 2.70/1.58 ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ B2 @ Y @ P2 ) )
% 2.70/1.58 => ( ! [P4: pi,A4: late_subject,X4: name,P5: pi,Q3: pi] :
% 2.70/1.58 ( ( ( par @ P @ Q )
% 2.70/1.58 = ( par @ P4 @ Q3 ) )
% 2.70/1.58 => ( ( ( late_BoundR @ B2 @ Y @ P2 )
% 2.70/1.58 = ( late_BoundR @ A4 @ X4 @ ( par @ P5 @ Q3 ) ) )
% 2.70/1.58 => ( ( late_transitions @ P4 @ ( late_BoundR @ A4 @ X4 @ P5 ) )
% 2.70/1.58 => ( ( fresh @ name @ pi @ X4 @ P4 )
% 2.70/1.58 => ( ( fresh @ name @ pi @ X4 @ Q3 )
% 2.70/1.58 => ~ ( fresh @ name @ late_subject @ X4 @ A4 ) ) ) ) ) )
% 2.70/1.58 => ~ ! [Q3: pi,A4: late_subject,X4: name,Q4: pi,P4: pi] :
% 2.70/1.58 ( ( ( par @ P @ Q )
% 2.70/1.58 = ( par @ P4 @ Q3 ) )
% 2.70/1.58 => ( ( ( late_BoundR @ B2 @ Y @ P2 )
% 2.70/1.58 = ( late_BoundR @ A4 @ X4 @ ( par @ P4 @ Q4 ) ) )
% 2.70/1.58 => ( ( late_transitions @ Q3 @ ( late_BoundR @ A4 @ X4 @ Q4 ) )
% 2.70/1.58 => ( ( fresh @ name @ pi @ X4 @ P4 )
% 2.70/1.58 => ( ( fresh @ name @ pi @ X4 @ Q3 )
% 2.70/1.58 => ~ ( fresh @ name @ late_subject @ X4 @ A4 ) ) ) ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_91_transitions_OPar1B,axiom,
% 2.70/1.58 ! [P: pi,A2: late_subject,X2: name,P2: pi,Q: pi] :
% 2.70/1.58 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P2 ) )
% 2.70/1.58 => ( ( fresh @ name @ pi @ X2 @ P )
% 2.70/1.58 => ( ( fresh @ name @ pi @ X2 @ Q )
% 2.70/1.58 => ( ( fresh @ name @ late_subject @ X2 @ A2 )
% 2.70/1.58 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X2 @ ( par @ P2 @ Q ) ) ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_92_transitions_OPar2B,axiom,
% 2.70/1.58 ! [Q: pi,A2: late_subject,X2: name,Q2: pi,P: pi] :
% 2.70/1.58 ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X2 @ Q2 ) )
% 2.70/1.58 => ( ( fresh @ name @ pi @ X2 @ P )
% 2.70/1.58 => ( ( fresh @ name @ pi @ X2 @ Q )
% 2.70/1.58 => ( ( fresh @ name @ late_subject @ X2 @ A2 )
% 2.70/1.58 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X2 @ ( par @ P @ Q2 ) ) ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_93_transitions_OResB,axiom,
% 2.70/1.58 ! [P: pi,A2: late_subject,X2: name,P2: pi,Y: name] :
% 2.70/1.58 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P2 ) )
% 2.70/1.58 => ( ( fresh @ name @ late_subject @ Y @ A2 )
% 2.70/1.58 => ( ( Y != X2 )
% 2.70/1.58 => ( ( fresh @ name @ pi @ X2 @ P )
% 2.70/1.58 => ( ( fresh @ name @ late_subject @ X2 @ A2 )
% 2.70/1.58 => ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A2 @ X2 @ ( res @ Y @ P2 ) ) ) ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_94_freshResidual,axiom,
% 2.70/1.58 ! [P: pi,Rs: late_residual,X2: name] :
% 2.70/1.58 ( ( late_transitions @ P @ Rs )
% 2.70/1.58 => ( ( fresh @ name @ pi @ X2 @ P )
% 2.70/1.58 => ( fresh @ name @ late_residual @ X2 @ Rs ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_95_freshBoundDerivative_I2_J,axiom,
% 2.70/1.58 ! [P: pi,A2: late_subject,X2: name,P2: pi,Y: name] :
% 2.70/1.58 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P2 ) )
% 2.70/1.58 => ( ( fresh @ name @ pi @ Y @ P )
% 2.70/1.58 => ( ( Y != X2 )
% 2.70/1.58 => ( fresh @ name @ pi @ Y @ P2 ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_96_residual_Ostrong__inducts,axiom,
% 2.70/1.58 ! [A: $tType] :
% 2.70/1.58 ( ( fs_name @ A )
% 2.70/1.58 => ! [P: A > late_residual > $o,Z: A,Residual: late_residual] :
% 2.70/1.58 ( ! [Subject2: late_subject,Name3: name,Pi4: pi,Z2: A] :
% 2.70/1.58 ( ( fresh @ name @ A @ Name3 @ Z2 )
% 2.70/1.58 => ( ( fresh @ name @ late_subject @ Name3 @ Subject2 )
% 2.70/1.58 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) ) ) )
% 2.70/1.58 => ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: A] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 2.70/1.58 => ( P @ Z @ Residual ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_97_residual_Ostrong__induct,axiom,
% 2.70/1.58 ! [N: $tType] :
% 2.70/1.58 ( ( fs_name @ N )
% 2.70/1.58 => ! [P: N > late_residual > $o,Z: N,Residual: late_residual] :
% 2.70/1.58 ( ! [Subject2: late_subject,Name3: name,Pi4: pi,Z2: N] :
% 2.70/1.58 ( ( fresh @ name @ N @ Name3 @ Z2 )
% 2.70/1.58 => ( ( fresh @ name @ late_subject @ Name3 @ Subject2 )
% 2.70/1.58 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) ) ) )
% 2.70/1.58 => ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: N] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 2.70/1.58 => ( P @ Z @ Residual ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_98_resTrans_I1_J,axiom,
% 2.70/1.58 ! [X2: name,B2: name,P: pi,Rs: late_residual] :
% 2.70/1.58 ~ ( late_transitions @ ( res @ X2 @ ( output @ X2 @ B2 @ P ) ) @ Rs ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_99_Late__Semantics_OClose1,axiom,
% 2.70/1.58 ! [P: pi,A2: name,X2: name,P2: pi,Q: pi,Y: name,Q2: pi] :
% 2.70/1.58 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P2 ) )
% 2.70/1.58 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y @ Q2 ) )
% 2.70/1.58 => ( ( fresh @ name @ pi @ Y @ P )
% 2.70/1.58 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ ( subs @ P2 @ X2 @ Y ) @ Q2 ) ) ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_100_Late__Semantics_OClose2,axiom,
% 2.70/1.58 ! [P: pi,A2: name,Y: name,P2: pi,Q: pi,X2: name,Q2: pi] :
% 2.70/1.58 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y @ P2 ) )
% 2.70/1.58 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ Q2 ) )
% 2.70/1.58 => ( ( fresh @ name @ pi @ Y @ Q )
% 2.70/1.58 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ P2 @ ( subs @ Q2 @ X2 @ Y ) ) ) ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_101_transitions_OClose1,axiom,
% 2.70/1.58 ! [P: pi,A2: name,X2: name,P2: pi,Q: pi,Y: name,Q2: pi] :
% 2.70/1.58 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P2 ) )
% 2.70/1.58 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y @ Q2 ) )
% 2.70/1.58 => ( ( fresh @ name @ pi @ X2 @ P )
% 2.70/1.58 => ( ( fresh @ name @ pi @ X2 @ Q )
% 2.70/1.58 => ( ( fresh @ name @ pi @ Y @ P )
% 2.70/1.58 => ( ( fresh @ name @ pi @ Y @ Q )
% 2.70/1.58 => ( ( X2 != A2 )
% 2.70/1.58 => ( ( fresh @ name @ pi @ X2 @ Q2 )
% 2.70/1.58 => ( ( Y != A2 )
% 2.70/1.58 => ( ( fresh @ name @ pi @ Y @ P2 )
% 2.70/1.58 => ( ( X2 != Y )
% 2.70/1.58 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ ( subs @ P2 @ X2 @ Y ) @ Q2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_102_transitions_OClose2,axiom,
% 2.70/1.58 ! [P: pi,A2: name,Y: name,P2: pi,Q: pi,X2: name,Q2: pi] :
% 2.70/1.58 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y @ P2 ) )
% 2.70/1.58 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ Q2 ) )
% 2.70/1.58 => ( ( fresh @ name @ pi @ X2 @ P )
% 2.70/1.58 => ( ( fresh @ name @ pi @ X2 @ Q )
% 2.70/1.58 => ( ( fresh @ name @ pi @ Y @ P )
% 2.70/1.58 => ( ( fresh @ name @ pi @ Y @ Q )
% 2.70/1.58 => ( ( X2 != A2 )
% 2.70/1.58 => ( ( fresh @ name @ pi @ X2 @ P2 )
% 2.70/1.58 => ( ( Y != A2 )
% 2.70/1.58 => ( ( fresh @ name @ pi @ Y @ Q2 )
% 2.70/1.58 => ( ( X2 != Y )
% 2.70/1.58 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ P2 @ ( subs @ Q2 @ X2 @ Y ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_103_resCasesF,axiom,
% 2.70/1.58 ! [X2: name,P: pi,Alpha: late_freeRes,XP: pi,F3: pi > $o] :
% 2.70/1.58 ( ( late_transitions @ ( res @ X2 @ P ) @ ( late_FreeR @ Alpha @ XP ) )
% 2.70/1.58 => ( ! [P5: pi] :
% 2.70/1.58 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P5 ) )
% 2.70/1.58 => ( ( fresh @ name @ late_freeRes @ X2 @ Alpha )
% 2.70/1.58 => ( F3 @ ( res @ X2 @ P5 ) ) ) )
% 2.70/1.58 => ( F3 @ XP ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_104_resCasesF_H,axiom,
% 2.70/1.58 ! [X2: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 2.70/1.58 ( ( late_transitions @ ( res @ X2 @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 2.70/1.58 => ~ ! [P4: pi,Alpha2: late_freeRes,P5: pi,Y3: name] :
% 2.70/1.58 ( ( ( res @ X2 @ P )
% 2.70/1.58 = ( res @ Y3 @ P4 ) )
% 2.70/1.58 => ( ( ( late_FreeR @ Alpha @ P2 )
% 2.70/1.58 = ( late_FreeR @ Alpha2 @ ( res @ Y3 @ P5 ) ) )
% 2.70/1.58 => ( ( late_transitions @ P4 @ ( late_FreeR @ Alpha2 @ P5 ) )
% 2.70/1.58 => ~ ( fresh @ name @ late_freeRes @ Y3 @ Alpha2 ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_105_ResF,axiom,
% 2.70/1.58 ! [P: pi,Alpha: late_freeRes,P2: pi,Y: name] :
% 2.70/1.58 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 2.70/1.58 => ( ( fresh @ name @ late_freeRes @ Y @ Alpha )
% 2.70/1.58 => ( late_transitions @ ( res @ Y @ P ) @ ( late_FreeR @ Alpha @ ( res @ Y @ P2 ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_106_Late__Semantics_OPar1B,axiom,
% 2.70/1.58 ! [P: pi,A2: late_subject,X2: name,P2: pi,Q: pi] :
% 2.70/1.58 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P2 ) )
% 2.70/1.58 => ( ( fresh @ name @ pi @ X2 @ Q )
% 2.70/1.58 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X2 @ ( par @ P2 @ Q ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_107_Late__Semantics_OPar2B,axiom,
% 2.70/1.58 ! [Q: pi,A2: late_subject,X2: name,Q2: pi,P: pi] :
% 2.70/1.58 ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X2 @ Q2 ) )
% 2.70/1.58 => ( ( fresh @ name @ pi @ X2 @ P )
% 2.70/1.58 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X2 @ ( par @ P @ Q2 ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_108_parCasesB,axiom,
% 2.70/1.58 ! [P: pi,Q: pi,A2: late_subject,X2: name,PQ: pi,Prop: pi > $o] :
% 2.70/1.58 ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X2 @ PQ ) )
% 2.70/1.58 => ( ( fresh @ name @ pi @ X2 @ P )
% 2.70/1.58 => ( ( fresh @ name @ pi @ X2 @ Q )
% 2.70/1.58 => ( ! [P5: pi] :
% 2.70/1.58 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P5 ) )
% 2.70/1.58 => ( Prop @ ( par @ P5 @ Q ) ) )
% 2.70/1.58 => ( ! [Q4: pi] :
% 2.70/1.58 ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X2 @ Q4 ) )
% 2.70/1.58 => ( Prop @ ( par @ P @ Q4 ) ) )
% 2.70/1.58 => ( Prop @ PQ ) ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_109_freshFreeDerivative_I1_J,axiom,
% 2.70/1.58 ! [P: pi,Alpha: late_freeRes,P2: pi,Y: name] :
% 2.70/1.58 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 2.70/1.58 => ( ( fresh @ name @ pi @ Y @ P )
% 2.70/1.58 => ( fresh @ name @ late_freeRes @ Y @ Alpha ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_110_outputTauTrans,axiom,
% 2.70/1.58 ! [A2: name,B2: name,P: pi,P2: pi] :
% 2.70/1.58 ~ ( late_transitions @ ( output @ A2 @ B2 @ P ) @ ( late_FreeR @ late_TauR @ P2 ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_111_transitions_OComm1,axiom,
% 2.70/1.58 ! [P: pi,A2: name,X2: name,P2: pi,Q: pi,B2: name,Q2: pi] :
% 2.70/1.58 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P2 ) )
% 2.70/1.58 => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ Q2 ) )
% 2.70/1.58 => ( ( fresh @ name @ pi @ X2 @ P )
% 2.70/1.58 => ( ( fresh @ name @ pi @ X2 @ Q )
% 2.70/1.58 => ( ( X2 != A2 )
% 2.70/1.58 => ( ( X2 != B2 )
% 2.70/1.58 => ( ( fresh @ name @ pi @ X2 @ Q2 )
% 2.70/1.58 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P2 @ X2 @ B2 ) @ Q2 ) ) ) ) ) ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_112_transitions_OComm2,axiom,
% 2.70/1.58 ! [P: pi,A2: name,B2: name,P2: pi,Q: pi,X2: name,Q2: pi] :
% 2.70/1.58 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P2 ) )
% 2.70/1.58 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ Q2 ) )
% 2.70/1.58 => ( ( fresh @ name @ pi @ X2 @ P )
% 2.70/1.58 => ( ( fresh @ name @ pi @ X2 @ Q )
% 2.70/1.58 => ( ( X2 != A2 )
% 2.70/1.58 => ( ( X2 != B2 )
% 2.70/1.58 => ( ( fresh @ name @ pi @ X2 @ P2 )
% 2.70/1.58 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P2 @ ( subs @ Q2 @ X2 @ B2 ) ) ) ) ) ) ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_113_Late__Semantics1_Osubject_Oinject_I2_J,axiom,
% 2.70/1.58 ! [X22: name,Y2: name] :
% 2.70/1.58 ( ( ( late_BoundOutputS @ X22 )
% 2.70/1.58 = ( late_BoundOutputS @ Y2 ) )
% 2.70/1.58 = ( X22 = Y2 ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_114_Late__Semantics1_Osubject_Oinject_I1_J,axiom,
% 2.70/1.58 ! [X1: name,Y1: name] :
% 2.70/1.58 ( ( ( late_InputS @ X1 )
% 2.70/1.58 = ( late_InputS @ Y1 ) )
% 2.70/1.58 = ( X1 = Y1 ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_115_Late__Semantics_OComm1,axiom,
% 2.70/1.58 ! [P: pi,A2: name,X2: name,P2: pi,Q: pi,B2: name,Q2: pi] :
% 2.70/1.58 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P2 ) )
% 2.70/1.58 => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ Q2 ) )
% 2.70/1.58 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P2 @ X2 @ B2 ) @ Q2 ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_116_Late__Semantics_OComm2,axiom,
% 2.70/1.58 ! [P: pi,A2: name,B2: name,P2: pi,Q: pi,X2: name,Q2: pi] :
% 2.70/1.58 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P2 ) )
% 2.70/1.58 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ Q2 ) )
% 2.70/1.58 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P2 @ ( subs @ Q2 @ X2 @ B2 ) ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_117_subject_Oexhaust,axiom,
% 2.70/1.58 ! [Y: late_subject] :
% 2.70/1.58 ( ! [X12: name] :
% 2.70/1.58 ( Y
% 2.70/1.58 != ( late_InputS @ X12 ) )
% 2.70/1.58 => ~ ! [X23: name] :
% 2.70/1.58 ( Y
% 2.70/1.58 != ( late_BoundOutputS @ X23 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_118_Late__Semantics1_OfreeRes_Oinject,axiom,
% 2.70/1.58 ! [X11: name,X122: name,Y11: name,Y12: name] :
% 2.70/1.58 ( ( ( late_OutputR @ X11 @ X122 )
% 2.70/1.58 = ( late_OutputR @ Y11 @ Y12 ) )
% 2.70/1.58 = ( ( X11 = Y11 )
% 2.70/1.58 & ( X122 = Y12 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_119_Late__Semantics_OfreeRes_Oinject,axiom,
% 2.70/1.58 ! [X22: name,X1: name,Y2: name,Y1: name] :
% 2.70/1.58 ( ( ( late_OutputR @ X22 @ X1 )
% 2.70/1.58 = ( late_OutputR @ Y2 @ Y1 ) )
% 2.70/1.58 = ( ( X22 = Y2 )
% 2.70/1.58 & ( X1 = Y1 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_120_name__fresh,axiom,
% 2.70/1.58 ( ( fresh @ name @ name )
% 2.70/1.58 = ( ^ [A6: name,B5: name] : ( A6 != B5 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_121_freeRes_Ofresh_I1_J,axiom,
% 2.70/1.58 ! [A2: name,X22: name,X1: name] :
% 2.70/1.58 ( ( fresh @ name @ late_freeRes @ A2 @ ( late_OutputR @ X22 @ X1 ) )
% 2.70/1.58 = ( ( fresh @ name @ name @ A2 @ X22 )
% 2.70/1.58 & ( fresh @ name @ name @ A2 @ X1 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_122_Late__Semantics1_OfreeRes_Odistinct_I1_J,axiom,
% 2.70/1.58 ! [X11: name,X122: name] :
% 2.70/1.58 ( ( late_OutputR @ X11 @ X122 )
% 2.70/1.58 != late_TauR ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_123_freeRes_Oexhaust,axiom,
% 2.70/1.58 ! [Y: late_freeRes] :
% 2.70/1.58 ( ! [X112: name,X123: name] :
% 2.70/1.58 ( Y
% 2.70/1.58 != ( late_OutputR @ X112 @ X123 ) )
% 2.70/1.58 => ( Y = late_TauR ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_124_freeRes_Ostrong__inducts,axiom,
% 2.70/1.58 ! [A: $tType,P: A > late_freeRes > $o,Z: A,FreeRes3: late_freeRes] :
% 2.70/1.58 ( ! [Name12: name,Name23: name,Z2: A] : ( P @ Z2 @ ( late_OutputR @ Name12 @ Name23 ) )
% 2.70/1.58 => ( ! [Z2: A] : ( P @ Z2 @ late_TauR )
% 2.70/1.58 => ( P @ Z @ FreeRes3 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_125_freeRes_Ostrong__induct_H,axiom,
% 2.70/1.58 ! [N: $tType,P: N > late_freeRes > $o,Z: N,FreeRes3: late_freeRes] :
% 2.70/1.58 ( ! [Name12: name,Name23: name,Z2: N] : ( P @ Z2 @ ( late_OutputR @ Name12 @ Name23 ) )
% 2.70/1.58 => ( ! [Z2: N] : ( P @ Z2 @ late_TauR )
% 2.70/1.58 => ( P @ Z @ FreeRes3 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_126_freeRes_Oinducts,axiom,
% 2.70/1.58 ! [P: late_freeRes > $o,FreeRes3: late_freeRes] :
% 2.70/1.58 ( ! [Name12: name,Name23: name] : ( P @ ( late_OutputR @ Name12 @ Name23 ) )
% 2.70/1.58 => ( ( P @ late_TauR )
% 2.70/1.58 => ( P @ FreeRes3 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_127_Late__Semantics_OfreeRes_Odistinct_I1_J,axiom,
% 2.70/1.58 ! [Name1: name,Name22: name] :
% 2.70/1.58 ( ( late_OutputR @ Name1 @ Name22 )
% 2.70/1.58 != late_TauR ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_128_freeRes_Orecs_I1_J,axiom,
% 2.70/1.58 ! [T: $tType,P: T > $o,F1: name > name > T,F22: T,Name1: name,Name22: name] :
% 2.70/1.58 ( ! [X12: name,X23: name] : ( P @ ( F1 @ X12 @ X23 ) )
% 2.70/1.58 => ( ( P @ F22 )
% 2.70/1.58 => ( ( late_freeRes_rec @ T @ F1 @ F22 @ ( late_OutputR @ Name1 @ Name22 ) )
% 2.70/1.58 = ( F1 @ Name1 @ Name22 ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_129_Output,axiom,
% 2.70/1.58 ! [A2: name,B2: name,P: pi] : ( late_transitions @ ( output @ A2 @ B2 @ P ) @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_130_outputIneqTrans,axiom,
% 2.70/1.58 ! [A2: name,B2: name,P: pi,C2: name,D: name,P2: pi] :
% 2.70/1.58 ( ( late_transitions @ ( output @ A2 @ B2 @ P ) @ ( late_FreeR @ ( late_OutputR @ C2 @ D ) @ P2 ) )
% 2.70/1.58 => ~ ( ( A2 != C2 )
% 2.70/1.58 | ( B2 != D ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_131_outputCases_H,axiom,
% 2.70/1.58 ! [A2: name,B2: name,P: pi,Rs: late_residual] :
% 2.70/1.58 ( ( late_transitions @ ( output @ A2 @ B2 @ P ) @ Rs )
% 2.70/1.58 => ~ ! [A4: name,B4: name,P4: pi] :
% 2.70/1.58 ( ( ( A2 = A4 )
% 2.70/1.58 & ( B2 = B4 )
% 2.70/1.58 & ( P = P4 ) )
% 2.70/1.58 => ( Rs
% 2.70/1.58 != ( late_FreeR @ ( late_OutputR @ A4 @ B4 ) @ P4 ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_132_outputCases,axiom,
% 2.70/1.58 ! [A2: name,B2: name,P: pi,Alpha: late_freeRes,P2: pi,Prop: late_freeRes > pi > $o] :
% 2.70/1.58 ( ( late_transitions @ ( output @ A2 @ B2 @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 2.70/1.58 => ( ( ( Alpha
% 2.70/1.58 = ( late_OutputR @ A2 @ B2 ) )
% 2.70/1.58 => ( ( P = P2 )
% 2.70/1.58 => ( Prop @ ( late_OutputR @ A2 @ B2 ) @ P ) ) )
% 2.70/1.58 => ( Prop @ Alpha @ P2 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_133_resOutputOutputTrans,axiom,
% 2.70/1.58 ! [X2: name,A2: name,P: pi,B2: name,Y: name,P2: pi] :
% 2.70/1.58 ~ ( late_transitions @ ( res @ X2 @ ( output @ A2 @ X2 @ P ) ) @ ( late_FreeR @ ( late_OutputR @ B2 @ Y ) @ P2 ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_134_Open,axiom,
% 2.70/1.58 ! [P: pi,A2: name,B2: name,P2: pi] :
% 2.70/1.58 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P2 ) )
% 2.70/1.58 => ( ( A2 != B2 )
% 2.70/1.58 => ( late_transitions @ ( res @ B2 @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ B2 @ P2 ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_135_resCasesB_H,axiom,
% 2.70/1.58 ! [X5: name,P: pi,A2: late_subject,Y4: name,P2: pi] :
% 2.70/1.58 ( ( late_transitions @ ( res @ X5 @ P ) @ ( late_BoundR @ A2 @ Y4 @ P2 ) )
% 2.70/1.58 => ( ! [P4: pi,A4: name,B4: name] :
% 2.70/1.58 ( ( ( res @ X5 @ P )
% 2.70/1.58 = ( res @ B4 @ P4 ) )
% 2.70/1.58 => ! [P5: pi] :
% 2.70/1.58 ( ( ( late_BoundR @ A2 @ Y4 @ P2 )
% 2.70/1.58 = ( late_BoundR @ ( late_BoundOutputS @ A4 ) @ B4 @ P5 ) )
% 2.70/1.58 => ( ( late_transitions @ P4 @ ( late_FreeR @ ( late_OutputR @ A4 @ B4 ) @ P5 ) )
% 2.70/1.58 => ( A4 = B4 ) ) ) )
% 2.70/1.58 => ~ ! [P4: pi,A4: late_subject,X4: name,P5: pi,Y3: name] :
% 2.70/1.58 ( ( ( res @ X5 @ P )
% 2.70/1.58 = ( res @ Y3 @ P4 ) )
% 2.70/1.58 => ( ( ( late_BoundR @ A2 @ Y4 @ P2 )
% 2.70/1.58 = ( late_BoundR @ A4 @ X4 @ ( res @ Y3 @ P5 ) ) )
% 2.70/1.58 => ( ( late_transitions @ P4 @ ( late_BoundR @ A4 @ X4 @ P5 ) )
% 2.70/1.58 => ( ( fresh @ name @ late_subject @ Y3 @ A4 )
% 2.70/1.58 => ( ( Y3 != X4 )
% 2.70/1.58 => ( ( fresh @ name @ pi @ X4 @ P4 )
% 2.70/1.58 => ~ ( fresh @ name @ late_subject @ X4 @ A4 ) ) ) ) ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_136_resCases_H,axiom,
% 2.70/1.58 ! [X2: name,P: pi,Rs: late_residual] :
% 2.70/1.58 ( ( late_transitions @ ( res @ X2 @ P ) @ Rs )
% 2.70/1.58 => ( ! [P4: pi,A4: name,B4: name] :
% 2.70/1.58 ( ( ( res @ X2 @ P )
% 2.70/1.58 = ( res @ B4 @ P4 ) )
% 2.70/1.58 => ! [P5: pi] :
% 2.70/1.58 ( ( Rs
% 2.70/1.58 = ( late_BoundR @ ( late_BoundOutputS @ A4 ) @ B4 @ P5 ) )
% 2.70/1.58 => ( ( late_transitions @ P4 @ ( late_FreeR @ ( late_OutputR @ A4 @ B4 ) @ P5 ) )
% 2.70/1.58 => ( A4 = B4 ) ) ) )
% 2.70/1.58 => ( ! [P4: pi,A4: late_subject,X4: name,P5: pi,Y3: name] :
% 2.70/1.58 ( ( ( res @ X2 @ P )
% 2.70/1.58 = ( res @ Y3 @ P4 ) )
% 2.70/1.58 => ( ( Rs
% 2.70/1.58 = ( late_BoundR @ A4 @ X4 @ ( res @ Y3 @ P5 ) ) )
% 2.70/1.58 => ( ( late_transitions @ P4 @ ( late_BoundR @ A4 @ X4 @ P5 ) )
% 2.70/1.58 => ( ( fresh @ name @ late_subject @ Y3 @ A4 )
% 2.70/1.58 => ( ( Y3 != X4 )
% 2.70/1.58 => ( ( fresh @ name @ pi @ X4 @ P4 )
% 2.70/1.58 => ~ ( fresh @ name @ late_subject @ X4 @ A4 ) ) ) ) ) ) )
% 2.70/1.58 => ~ ! [P4: pi,Alpha2: late_freeRes,P5: pi,Y3: name] :
% 2.70/1.58 ( ( ( res @ X2 @ P )
% 2.70/1.58 = ( res @ Y3 @ P4 ) )
% 2.70/1.58 => ( ( Rs
% 2.70/1.58 = ( late_FreeR @ Alpha2 @ ( res @ Y3 @ P5 ) ) )
% 2.70/1.58 => ( ( late_transitions @ P4 @ ( late_FreeR @ Alpha2 @ P5 ) )
% 2.70/1.58 => ~ ( fresh @ name @ late_freeRes @ Y3 @ Alpha2 ) ) ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_137_Late__Semantics1_Osubject_Odistinct_I1_J,axiom,
% 2.70/1.58 ! [X1: name,X22: name] :
% 2.70/1.58 ( ( late_InputS @ X1 )
% 2.70/1.58 != ( late_BoundOutputS @ X22 ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_138_subject_Orecs_I2_J,axiom,
% 2.70/1.58 ! [T: $tType,P: T > $o,F1: name > T,F22: name > T,Name2: name] :
% 2.70/1.58 ( ! [X12: name] : ( P @ ( F1 @ X12 ) )
% 2.70/1.58 => ( ! [X12: name] : ( P @ ( F22 @ X12 ) )
% 2.70/1.58 => ( ( late_subject_rec @ T @ F1 @ F22 @ ( late_BoundOutputS @ Name2 ) )
% 2.70/1.58 = ( F22 @ Name2 ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_139_subject_Orecs_I1_J,axiom,
% 2.70/1.58 ! [T: $tType,P: T > $o,F1: name > T,F22: name > T,Name2: name] :
% 2.70/1.58 ( ! [X12: name] : ( P @ ( F1 @ X12 ) )
% 2.70/1.58 => ( ! [X12: name] : ( P @ ( F22 @ X12 ) )
% 2.70/1.58 => ( ( late_subject_rec @ T @ F1 @ F22 @ ( late_InputS @ Name2 ) )
% 2.70/1.58 = ( F1 @ Name2 ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_140_resTauOutputTrans,axiom,
% 2.70/1.58 ! [X2: name,P: pi,A2: name,B2: name,P2: pi] :
% 2.70/1.58 ~ ( late_transitions @ ( res @ X2 @ ( tau @ P ) ) @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P2 ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_141_resInputBoundOutputTrans,axiom,
% 2.70/1.58 ! [X2: name,A2: name,Y: name,P: pi,B2: name,Z: name,P2: pi] :
% 2.70/1.58 ~ ( late_transitions @ ( res @ X2 @ ( input @ A2 @ Y @ P ) ) @ ( late_BoundR @ ( late_BoundOutputS @ B2 ) @ Z @ P2 ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_142_pi_Ofresh_I3_J,axiom,
% 2.70/1.58 ! [A2: name,X1: pi] :
% 2.70/1.58 ( ( fresh @ name @ pi @ A2 @ ( tau @ X1 ) )
% 2.70/1.58 = ( fresh @ name @ pi @ A2 @ X1 ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_143_simps_I2_J,axiom,
% 2.70/1.58 ! [P: pi,C2: name,D: name] :
% 2.70/1.58 ( ( subs @ ( tau @ P ) @ C2 @ D )
% 2.70/1.58 = ( tau @ ( subs @ P @ C2 @ D ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_144_pi_Oinject_I2_J,axiom,
% 2.70/1.58 ! [X1: pi,Y1: pi] :
% 2.70/1.58 ( ( ( tau @ X1 )
% 2.70/1.58 = ( tau @ Y1 ) )
% 2.70/1.58 = ( X1 = Y1 ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_145_pi_Odistinct_I35_J,axiom,
% 2.70/1.58 ! [Pi3: pi,Name13: name,Name24: name,Pi: pi] :
% 2.70/1.58 ( ( tau @ Pi3 )
% 2.70/1.58 != ( input @ Name13 @ Name24 @ Pi ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_146_pi_Odistinct_I55_J,axiom,
% 2.70/1.58 ! [Name1: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 2.70/1.58 ( ( input @ Name1 @ Name22 @ Pi3 )
% 2.70/1.58 != ( par @ Pi12 @ Pi22 ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_147_pi_Odistinct_I57_J,axiom,
% 2.70/1.58 ! [Name1: name,Name22: name,Pi3: pi,Name: name,Pi: pi] :
% 2.70/1.58 ( ( input @ Name1 @ Name22 @ Pi3 )
% 2.70/1.58 != ( res @ Name @ Pi ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_148_pi_Odistinct_I43_J,axiom,
% 2.70/1.58 ! [Pi3: pi,Pi12: pi,Pi22: pi] :
% 2.70/1.58 ( ( tau @ Pi3 )
% 2.70/1.58 != ( par @ Pi12 @ Pi22 ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_149_pi_Odistinct_I45_J,axiom,
% 2.70/1.58 ! [Pi3: pi,Name: name,Pi: pi] :
% 2.70/1.58 ( ( tau @ Pi3 )
% 2.70/1.58 != ( res @ Name @ Pi ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_150_pi_Odistinct_I21_J,axiom,
% 2.70/1.58 ! [Name1: name,Name22: name,Pi3: pi,Name13: name,Name24: name,Pi: pi] :
% 2.70/1.58 ( ( output @ Name1 @ Name22 @ Pi3 )
% 2.70/1.58 != ( input @ Name13 @ Name24 @ Pi ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_151_pi_Odistinct_I19_J,axiom,
% 2.70/1.58 ! [Name1: name,Name22: name,Pi3: pi,Pi: pi] :
% 2.70/1.58 ( ( output @ Name1 @ Name22 @ Pi3 )
% 2.70/1.58 != ( tau @ Pi ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_152_resTrans_I2_J,axiom,
% 2.70/1.58 ! [X2: name,Y: name,P: pi,Rs: late_residual] :
% 2.70/1.58 ~ ( late_transitions @ ( res @ X2 @ ( input @ X2 @ Y @ P ) ) @ Rs ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_153_inputFreeTrans,axiom,
% 2.70/1.58 ! [A2: name,X2: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 2.70/1.58 ~ ( late_transitions @ ( input @ A2 @ X2 @ P ) @ ( late_FreeR @ Alpha @ P2 ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_154_tauBoundTrans,axiom,
% 2.70/1.58 ! [P: pi,A2: late_subject,X2: name,P2: pi] :
% 2.70/1.58 ~ ( late_transitions @ ( tau @ P ) @ ( late_BoundR @ A2 @ X2 @ P2 ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_155_resInputFreeTrans,axiom,
% 2.70/1.58 ! [X2: name,A2: name,Y: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 2.70/1.58 ~ ( late_transitions @ ( res @ X2 @ ( input @ A2 @ Y @ P ) ) @ ( late_FreeR @ Alpha @ P2 ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_156_Late__Semantics_OInput,axiom,
% 2.70/1.58 ! [A2: name,X2: name,P: pi] : ( late_transitions @ ( input @ A2 @ X2 @ P ) @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_157_transitions_OInput,axiom,
% 2.70/1.58 ! [X2: name,A2: name,P: pi] :
% 2.70/1.58 ( ( X2 != A2 )
% 2.70/1.58 => ( late_transitions @ ( input @ A2 @ X2 @ P ) @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_158_inputBoundOutputTrans,axiom,
% 2.70/1.58 ! [A2: name,X2: name,P: pi,B2: name,Y: name,P2: pi] :
% 2.70/1.58 ~ ( late_transitions @ ( input @ A2 @ X2 @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ B2 ) @ Y @ P2 ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_159_resTauBoundTrans,axiom,
% 2.70/1.58 ! [X2: name,P: pi,A2: late_subject,Y: name,P2: pi] :
% 2.70/1.58 ~ ( late_transitions @ ( res @ X2 @ ( tau @ P ) ) @ ( late_BoundR @ A2 @ Y @ P2 ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_160_inputIneqTrans,axiom,
% 2.70/1.58 ! [A2: name,X2: name,P: pi,B2: late_subject,Y: name,P2: pi] :
% 2.70/1.58 ( ( late_transitions @ ( input @ A2 @ X2 @ P ) @ ( late_BoundR @ B2 @ Y @ P2 ) )
% 2.70/1.58 => ~ ( fresh @ name @ late_subject @ A2 @ B2 ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_161_tauOutputTrans,axiom,
% 2.70/1.58 ! [P: pi,A2: name,B2: name,P2: pi] :
% 2.70/1.58 ~ ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P2 ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_162_tauCases,axiom,
% 2.70/1.58 ! [P: pi,Alpha: late_freeRes,P2: pi,Prop: late_freeRes > pi > $o] :
% 2.70/1.58 ( ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 2.70/1.58 => ( ( ( Alpha = late_TauR )
% 2.70/1.58 => ( ( P = P2 )
% 2.70/1.58 => ( Prop @ late_TauR @ P ) ) )
% 2.70/1.58 => ( Prop @ Alpha @ P2 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_163_tauCases_H,axiom,
% 2.70/1.58 ! [P: pi,Rs: late_residual] :
% 2.70/1.58 ( ( late_transitions @ ( tau @ P ) @ Rs )
% 2.70/1.58 => ~ ! [P4: pi] :
% 2.70/1.58 ( ( ( tau @ P )
% 2.70/1.58 = ( tau @ P4 ) )
% 2.70/1.58 => ( Rs
% 2.70/1.58 != ( late_FreeR @ late_TauR @ P4 ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_164_Tau,axiom,
% 2.70/1.58 ! [P: pi] : ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ late_TauR @ P ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_165_residual_Ofresh_I1_J,axiom,
% 2.70/1.58 ! [A2: name,X32: late_subject,X1: name,X22: pi] :
% 2.70/1.58 ( ( fresh @ name @ late_residual @ A2 @ ( late_BoundR @ X32 @ X1 @ X22 ) )
% 2.70/1.58 = ( ( fresh @ name @ late_subject @ A2 @ X32 )
% 2.70/1.58 & ( fresh @ name @ ( name > ( noption @ pi ) ) @ A2 @ ( abs_fun @ name @ pi @ X1 @ X22 ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_166_simps_I3_J,axiom,
% 2.70/1.58 ! [A2: name,B2: name,P: pi,C2: name,D: name] :
% 2.70/1.58 ( ( subs @ ( output @ A2 @ B2 @ P ) @ C2 @ D )
% 2.70/1.58 = ( output @ ( subst_name @ A2 @ C2 @ D ) @ ( subst_name @ B2 @ C2 @ D ) @ ( subs @ P @ C2 @ D ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_167_substInput,axiom,
% 2.70/1.58 ! [X2: name,B2: name,C2: name,A2: name,P: pi] :
% 2.70/1.58 ( ( X2 != B2 )
% 2.70/1.58 => ( ( X2 != C2 )
% 2.70/1.58 => ( ( subs @ ( input @ A2 @ X2 @ P ) @ B2 @ C2 )
% 2.70/1.58 = ( input @ ( subst_name @ A2 @ B2 @ C2 ) @ X2 @ ( subs @ P @ B2 @ C2 ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_168_simps_I4_J,axiom,
% 2.70/1.58 ! [X2: name,A2: name,C2: name,D: name,P: pi] :
% 2.70/1.58 ( ( X2 != A2 )
% 2.70/1.58 => ( ( X2 != C2 )
% 2.70/1.58 => ( ( X2 != D )
% 2.70/1.58 => ( ( subs @ ( input @ A2 @ X2 @ P ) @ C2 @ D )
% 2.70/1.58 = ( input @ ( subst_name @ A2 @ C2 @ D ) @ X2 @ ( subs @ P @ C2 @ D ) ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_169_pi_Ofresh_I9_J,axiom,
% 2.70/1.58 ! [A2: name,X1: name,X22: pi] :
% 2.70/1.58 ( ( fresh @ name @ pi @ A2 @ ( res @ X1 @ X22 ) )
% 2.70/1.58 = ( fresh @ name @ ( name > ( noption @ pi ) ) @ A2 @ ( abs_fun @ name @ pi @ X1 @ X22 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_170_pi_Ofresh_I4_J,axiom,
% 2.70/1.58 ! [A2: name,X32: name,X1: name,X22: pi] :
% 2.70/1.58 ( ( fresh @ name @ pi @ A2 @ ( input @ X32 @ X1 @ X22 ) )
% 2.70/1.58 = ( ( fresh @ name @ name @ A2 @ X32 )
% 2.70/1.58 & ( fresh @ name @ ( name > ( noption @ pi ) ) @ A2 @ ( abs_fun @ name @ pi @ X1 @ X22 ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_171_pi_Oinject_I3_J,axiom,
% 2.70/1.58 ! [X32: name,X1: name,X22: pi,Y32: name,Y1: name,Y2: pi] :
% 2.70/1.58 ( ( ( input @ X32 @ X1 @ X22 )
% 2.70/1.58 = ( input @ Y32 @ Y1 @ Y2 ) )
% 2.70/1.58 = ( ( X32 = Y32 )
% 2.70/1.58 & ( ( abs_fun @ name @ pi @ X1 @ X22 )
% 2.70/1.58 = ( abs_fun @ name @ pi @ Y1 @ Y2 ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_172_abs__fun__eq1,axiom,
% 2.70/1.58 ! [X: $tType,A: $tType,A2: X,X2: A,Y: A] :
% 2.70/1.58 ( ( ( abs_fun @ X @ A @ A2 @ X2 )
% 2.70/1.58 = ( abs_fun @ X @ A @ A2 @ Y ) )
% 2.70/1.58 = ( X2 = Y ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_173_subst__name__def,axiom,
% 2.70/1.58 ( subst_name
% 2.70/1.58 = ( ^ [A6: name,B5: name,C4: name] : ( if @ name @ ( A6 = B5 ) @ C4 @ A6 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_174_name__fresh__abs,axiom,
% 2.70/1.58 ! [A: $tType] :
% 2.70/1.58 ( ( fs_name @ A )
% 2.70/1.58 => ! [B2: name,A2: name,X2: A] :
% 2.70/1.58 ( ( fresh @ name @ ( name > ( noption @ A ) ) @ B2 @ ( abs_fun @ name @ A @ A2 @ X2 ) )
% 2.70/1.58 = ( ( B2 = A2 )
% 2.70/1.58 | ( fresh @ name @ A @ B2 @ X2 ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_175_abs__fresh_I1_J,axiom,
% 2.70/1.58 ! [X6: $tType] :
% 2.70/1.58 ( ( fs_name @ X6 )
% 2.70/1.58 => ! [B2: name,A2: name,X2: X6] :
% 2.70/1.58 ( ( fresh @ name @ ( name > ( noption @ X6 ) ) @ B2 @ ( abs_fun @ name @ X6 @ A2 @ X2 ) )
% 2.70/1.58 = ( ( B2 = A2 )
% 2.70/1.58 | ( fresh @ name @ X6 @ B2 @ X2 ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_176_residual_Oinject_I1_J,axiom,
% 2.70/1.58 ! [X32: late_subject,X1: name,X22: pi,Y32: late_subject,Y1: name,Y2: pi] :
% 2.70/1.58 ( ( ( late_BoundR @ X32 @ X1 @ X22 )
% 2.70/1.58 = ( late_BoundR @ Y32 @ Y1 @ Y2 ) )
% 2.70/1.58 = ( ( X32 = Y32 )
% 2.70/1.58 & ( ( abs_fun @ name @ pi @ X1 @ X22 )
% 2.70/1.58 = ( abs_fun @ name @ pi @ Y1 @ Y2 ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_177_pi_Oinject_I8_J,axiom,
% 2.70/1.58 ! [X1: name,X22: pi,Y1: name,Y2: pi] :
% 2.70/1.58 ( ( ( res @ X1 @ X22 )
% 2.70/1.58 = ( res @ Y1 @ Y2 ) )
% 2.70/1.58 = ( ( abs_fun @ name @ pi @ X1 @ X22 )
% 2.70/1.58 = ( abs_fun @ name @ pi @ Y1 @ Y2 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_178_inputCases_H,axiom,
% 2.70/1.58 ! [A2: name,B2: name,P: pi,Rs: late_residual] :
% 2.70/1.58 ( ( late_transitions @ ( input @ A2 @ B2 @ P ) @ Rs )
% 2.70/1.58 => ~ ! [X4: name,A4: name,P4: pi] :
% 2.70/1.58 ( ( ( A2 = A4 )
% 2.70/1.58 & ( ( abs_fun @ name @ pi @ B2 @ P )
% 2.70/1.58 = ( abs_fun @ name @ pi @ X4 @ P4 ) ) )
% 2.70/1.58 => ( ( Rs
% 2.70/1.58 = ( late_BoundR @ ( late_InputS @ A4 ) @ X4 @ P4 ) )
% 2.70/1.58 => ( X4 = A4 ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_179_internal__case__prod__conv,axiom,
% 2.70/1.58 ! [B: $tType,A: $tType,C: $tType,C2: B > C > A,A2: B,B2: C] :
% 2.70/1.58 ( ( produc2004651681e_prod @ B @ C @ A @ C2 @ ( product_Pair @ B @ C @ A2 @ B2 ) )
% 2.70/1.58 = ( C2 @ A2 @ B2 ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_180_resSimCases,axiom,
% 2.70/1.58 ! [A: $tType] :
% 2.70/1.58 ( ( fs_name @ A )
% 2.70/1.58 => ! [Rel: set @ ( product_prod @ pi @ pi ),Q: pi,X2: name,P: pi,C5: A] :
% 2.70/1.58 ( ( eqvt @ pi @ Rel )
% 2.70/1.58 => ( ! [Q4: pi,A4: name] :
% 2.70/1.58 ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A4 @ X2 ) @ Q4 ) )
% 2.70/1.58 => ( ( A4 != X2 )
% 2.70/1.58 => ? [P6: pi] :
% 2.70/1.58 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A4 ) @ X2 @ P6 ) )
% 2.70/1.58 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P6 @ Q4 ) @ Rel ) ) ) )
% 2.70/1.58 => ( ! [Q4: pi,A4: late_subject,Y3: name] :
% 2.70/1.58 ( ( late_transitions @ Q @ ( late_BoundR @ A4 @ Y3 @ Q4 ) )
% 2.70/1.58 => ( ( fresh @ name @ late_subject @ X2 @ A4 )
% 2.70/1.58 => ( ( X2 != Y3 )
% 2.70/1.58 => ( ( fresh @ name @ A @ Y3 @ C5 )
% 2.70/1.58 => ? [P6: pi] :
% 2.70/1.58 ( ( late_transitions @ P @ ( late_BoundR @ A4 @ Y3 @ P6 ) )
% 2.70/1.58 & ( strong2129052853vative @ P6 @ ( res @ X2 @ Q4 ) @ A4 @ Y3 @ Rel ) ) ) ) ) )
% 2.70/1.58 => ( ! [Q4: pi,Alpha2: late_freeRes] :
% 2.70/1.58 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 2.70/1.58 => ( ( fresh @ name @ late_freeRes @ X2 @ Alpha2 )
% 2.70/1.58 => ? [P6: pi] :
% 2.70/1.58 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 2.70/1.58 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P6 @ ( res @ X2 @ Q4 ) ) @ Rel ) ) ) )
% 2.70/1.58 => ( strong743114133lation @ P @ Rel @ ( res @ X2 @ Q ) ) ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_181_parSym,axiom,
% 2.70/1.58 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi,Q: pi] :
% 2.70/1.58 ( ! [R: pi,S2: pi] : ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( par @ R @ S2 ) @ ( par @ S2 @ R ) ) @ Rel )
% 2.70/1.58 => ( ! [R: pi,S2: pi,X4: name] :
% 2.70/1.58 ( ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ R @ S2 ) @ Rel )
% 2.70/1.58 => ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( res @ X4 @ R ) @ ( res @ X4 @ S2 ) ) @ Rel ) )
% 2.70/1.58 => ( strong743114133lation @ ( par @ P @ Q ) @ Rel @ ( par @ Q @ P ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_182_simE_I1_J,axiom,
% 2.70/1.58 ! [P: pi,Rel: set @ ( product_prod @ pi @ pi ),Q: pi,A2: late_subject,X2: name,Q2: pi] :
% 2.70/1.58 ( ( strong743114133lation @ P @ Rel @ Q )
% 2.70/1.58 => ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X2 @ Q2 ) )
% 2.70/1.58 => ( ( fresh @ name @ pi @ X2 @ P )
% 2.70/1.58 => ? [P5: pi] :
% 2.70/1.58 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P5 ) )
% 2.70/1.58 & ( strong2129052853vative @ P5 @ Q2 @ A2 @ X2 @ Rel ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_183_simE_I2_J,axiom,
% 2.70/1.58 ! [P: pi,Rel: set @ ( product_prod @ pi @ pi ),Q: pi,Alpha: late_freeRes,Q2: pi] :
% 2.70/1.58 ( ( strong743114133lation @ P @ Rel @ Q )
% 2.70/1.58 => ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 2.70/1.58 => ? [P5: pi] :
% 2.70/1.58 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P5 ) )
% 2.70/1.58 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P5 @ Q2 ) @ Rel ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_184_simCasesCont,axiom,
% 2.70/1.58 ! [A: $tType] :
% 2.70/1.58 ( ( fs_name @ A )
% 2.70/1.58 => ! [Rel: set @ ( product_prod @ pi @ pi ),Q: pi,P: pi,C5: A] :
% 2.70/1.58 ( ( eqvt @ pi @ Rel )
% 2.70/1.58 => ( ! [A4: late_subject,X4: name,Q4: pi] :
% 2.70/1.58 ( ( late_transitions @ Q @ ( late_BoundR @ A4 @ X4 @ Q4 ) )
% 2.70/1.58 => ( ( fresh @ name @ pi @ X4 @ P )
% 2.70/1.58 => ( ( fresh @ name @ pi @ X4 @ Q )
% 2.70/1.58 => ( ( fresh @ name @ late_subject @ X4 @ A4 )
% 2.70/1.58 => ( ( fresh @ name @ A @ X4 @ C5 )
% 2.70/1.58 => ? [P6: pi] :
% 2.70/1.58 ( ( late_transitions @ P @ ( late_BoundR @ A4 @ X4 @ P6 ) )
% 2.70/1.58 & ( strong2129052853vative @ P6 @ Q4 @ A4 @ X4 @ Rel ) ) ) ) ) ) )
% 2.70/1.58 => ( ! [Alpha2: late_freeRes,Q4: pi] :
% 2.70/1.58 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 2.70/1.58 => ? [P6: pi] :
% 2.70/1.58 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 2.70/1.58 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P6 @ Q4 ) @ Rel ) ) )
% 2.70/1.58 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_185_simCases,axiom,
% 2.70/1.58 ! [Q: pi,P: pi,Rel: set @ ( product_prod @ pi @ pi )] :
% 2.70/1.58 ( ! [A4: late_subject,Y3: name,Q4: pi] :
% 2.70/1.58 ( ( late_transitions @ Q @ ( late_BoundR @ A4 @ Y3 @ Q4 ) )
% 2.70/1.58 => ( ( fresh @ name @ pi @ Y3 @ P )
% 2.70/1.58 => ? [P6: pi] :
% 2.70/1.58 ( ( late_transitions @ P @ ( late_BoundR @ A4 @ Y3 @ P6 ) )
% 2.70/1.58 & ( strong2129052853vative @ P6 @ Q4 @ A4 @ Y3 @ Rel ) ) ) )
% 2.70/1.58 => ( ! [Alpha2: late_freeRes,Q4: pi] :
% 2.70/1.58 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 2.70/1.58 => ? [P6: pi] :
% 2.70/1.58 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 2.70/1.58 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P6 @ Q4 ) @ Rel ) ) )
% 2.70/1.58 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_186_simulation__def,axiom,
% 2.70/1.58 ( strong743114133lation
% 2.70/1.58 = ( ^ [P7: pi,Rel2: set @ ( product_prod @ pi @ pi ),Q5: pi] :
% 2.70/1.58 ( ! [A6: late_subject,X3: name,Q6: pi] :
% 2.70/1.58 ( ( ( late_transitions @ Q5 @ ( late_BoundR @ A6 @ X3 @ Q6 ) )
% 2.70/1.58 & ( fresh @ name @ pi @ X3 @ P7 ) )
% 2.70/1.58 => ? [P8: pi] :
% 2.70/1.58 ( ( late_transitions @ P7 @ ( late_BoundR @ A6 @ X3 @ P8 ) )
% 2.70/1.58 & ( strong2129052853vative @ P8 @ Q6 @ A6 @ X3 @ Rel2 ) ) )
% 2.70/1.58 & ! [Alpha3: late_freeRes,Q6: pi] :
% 2.70/1.58 ( ( late_transitions @ Q5 @ ( late_FreeR @ Alpha3 @ Q6 ) )
% 2.70/1.58 => ? [P8: pi] :
% 2.70/1.58 ( ( late_transitions @ P7 @ ( late_FreeR @ Alpha3 @ P8 ) )
% 2.70/1.58 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P8 @ Q6 ) @ Rel2 ) ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_187_parZeroRight,axiom,
% 2.70/1.58 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi] :
% 2.70/1.58 ( ! [Q3: pi] : ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ Q3 @ ( par @ Q3 @ piNil ) ) @ Rel )
% 2.70/1.58 => ( strong743114133lation @ P @ Rel @ ( par @ P @ piNil ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_188_parZeroLeft,axiom,
% 2.70/1.58 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi] :
% 2.70/1.58 ( ! [Q3: pi] : ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( par @ Q3 @ piNil ) @ Q3 ) @ Rel )
% 2.70/1.58 => ( strong743114133lation @ ( par @ P @ piNil ) @ Rel @ P ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_189_simps_I5_J,axiom,
% 2.70/1.58 ! [A2: name,B2: name,P: pi,C2: name,D: name] :
% 2.70/1.58 ( ( subs @ ( match @ A2 @ B2 @ P ) @ C2 @ D )
% 2.70/1.58 = ( match @ ( subst_name @ A2 @ C2 @ D ) @ ( subst_name @ B2 @ C2 @ D ) @ ( subs @ P @ C2 @ D ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_190_pi_Ofresh_I1_J,axiom,
% 2.70/1.58 ! [A2: name] : ( fresh @ name @ pi @ A2 @ piNil ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_191_simps_I1_J,axiom,
% 2.70/1.58 ! [C2: name,D: name] :
% 2.70/1.58 ( ( subs @ piNil @ C2 @ D )
% 2.70/1.58 = piNil ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_192_pi_Ofresh_I5_J,axiom,
% 2.70/1.58 ! [A2: name,X32: name,X22: name,X1: pi] :
% 2.70/1.58 ( ( fresh @ name @ pi @ A2 @ ( match @ X32 @ X22 @ X1 ) )
% 2.70/1.58 = ( ( fresh @ name @ name @ A2 @ X32 )
% 2.70/1.58 & ( fresh @ name @ name @ A2 @ X22 )
% 2.70/1.58 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_193_matchNilLeft,axiom,
% 2.70/1.58 ! [A2: name,B2: name,Rel: set @ ( product_prod @ pi @ pi ),P: pi] :
% 2.70/1.58 ( ( A2 != B2 )
% 2.70/1.58 => ( strong743114133lation @ piNil @ Rel @ ( match @ A2 @ B2 @ P ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_194_nilSimRight,axiom,
% 2.70/1.58 ! [P: pi,Rel: set @ ( product_prod @ pi @ pi )] : ( strong743114133lation @ P @ Rel @ piNil ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_195_pi_Odistinct_I49_J,axiom,
% 2.70/1.58 ! [Name1: name,Name22: name,Pi3: pi,Name13: name,Name24: name,Pi: pi] :
% 2.70/1.58 ( ( input @ Name1 @ Name22 @ Pi3 )
% 2.70/1.58 != ( match @ Name13 @ Name24 @ Pi ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_196_pi_Odistinct_I5_J,axiom,
% 2.70/1.58 ! [Name13: name,Name24: name,Pi: pi] :
% 2.70/1.58 ( piNil
% 2.70/1.58 != ( input @ Name13 @ Name24 @ Pi ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_197_matchCases,axiom,
% 2.70/1.58 ! [A2: name,B2: name,P: pi,Rs: late_residual,F3: name > name > $o] :
% 2.70/1.58 ( ( late_transitions @ ( match @ A2 @ B2 @ P ) @ Rs )
% 2.70/1.58 => ( ( ( late_transitions @ P @ Rs )
% 2.70/1.58 => ( ( A2 = B2 )
% 2.70/1.58 => ( F3 @ A2 @ A2 ) ) )
% 2.70/1.58 => ( F3 @ A2 @ B2 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_198_matchTrans,axiom,
% 2.70/1.58 ! [A2: name,B2: name,P: pi,Rs: late_residual] :
% 2.70/1.58 ( ( late_transitions @ ( match @ A2 @ B2 @ P ) @ Rs )
% 2.70/1.58 => ( A2 = B2 ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_199_matchCases_H,axiom,
% 2.70/1.58 ! [A2: name,B2: name,P: pi,Rs: late_residual] :
% 2.70/1.58 ( ( late_transitions @ ( match @ A2 @ B2 @ P ) @ Rs )
% 2.70/1.58 => ~ ! [P4: pi] :
% 2.70/1.58 ( ( ( B2 = A2 )
% 2.70/1.58 & ( P = P4 ) )
% 2.70/1.58 => ~ ( late_transitions @ P4 @ Rs ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_200_Match,axiom,
% 2.70/1.58 ! [P: pi,Rs: late_residual,B2: name] :
% 2.70/1.58 ( ( late_transitions @ P @ Rs )
% 2.70/1.58 => ( late_transitions @ ( match @ B2 @ B2 @ P ) @ Rs ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_201_nilCases_H,axiom,
% 2.70/1.58 ! [Rs: late_residual] :
% 2.70/1.58 ~ ( late_transitions @ piNil @ Rs ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_202_zeroTrans,axiom,
% 2.70/1.58 ! [Rs: late_residual] :
% 2.70/1.58 ~ ( late_transitions @ piNil @ Rs ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_203_pi_Odistinct_I65_J,axiom,
% 2.70/1.58 ! [Name1: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 2.70/1.58 ( ( match @ Name1 @ Name22 @ Pi3 )
% 2.70/1.58 != ( par @ Pi12 @ Pi22 ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_204_pi_Odistinct_I67_J,axiom,
% 2.70/1.58 ! [Name1: name,Name22: name,Pi3: pi,Name: name,Pi: pi] :
% 2.70/1.58 ( ( match @ Name1 @ Name22 @ Pi3 )
% 2.70/1.58 != ( res @ Name @ Pi ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_205_pi_Odistinct_I13_J,axiom,
% 2.70/1.58 ! [Pi12: pi,Pi22: pi] :
% 2.70/1.58 ( piNil
% 2.70/1.58 != ( par @ Pi12 @ Pi22 ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_206_pi_Odistinct_I15_J,axiom,
% 2.70/1.58 ! [Name: name,Pi: pi] :
% 2.70/1.58 ( piNil
% 2.70/1.58 != ( res @ Name @ Pi ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_207_pi_Odistinct_I7_J,axiom,
% 2.70/1.58 ! [Name13: name,Name24: name,Pi: pi] :
% 2.70/1.58 ( piNil
% 2.70/1.58 != ( match @ Name13 @ Name24 @ Pi ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_208_pi_Oinject_I4_J,axiom,
% 2.70/1.58 ! [X32: name,X22: name,X1: pi,Y32: name,Y2: name,Y1: pi] :
% 2.70/1.58 ( ( ( match @ X32 @ X22 @ X1 )
% 2.70/1.58 = ( match @ Y32 @ Y2 @ Y1 ) )
% 2.70/1.58 = ( ( X32 = Y32 )
% 2.70/1.58 & ( X22 = Y2 )
% 2.70/1.58 & ( X1 = Y1 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_209_pi_Odistinct_I3_J,axiom,
% 2.70/1.58 ! [Pi: pi] :
% 2.70/1.58 ( piNil
% 2.70/1.58 != ( tau @ Pi ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_210_pi_Odistinct_I37_J,axiom,
% 2.70/1.58 ! [Pi3: pi,Name13: name,Name24: name,Pi: pi] :
% 2.70/1.58 ( ( tau @ Pi3 )
% 2.70/1.58 != ( match @ Name13 @ Name24 @ Pi ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_211_pi_Odistinct_I1_J,axiom,
% 2.70/1.58 ! [Name13: name,Name24: name,Pi: pi] :
% 2.70/1.58 ( piNil
% 2.70/1.58 != ( output @ Name13 @ Name24 @ Pi ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_212_pi_Odistinct_I23_J,axiom,
% 2.70/1.58 ! [Name1: name,Name22: name,Pi3: pi,Name13: name,Name24: name,Pi: pi] :
% 2.70/1.58 ( ( output @ Name1 @ Name22 @ Pi3 )
% 2.70/1.58 != ( match @ Name13 @ Name24 @ Pi ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_213_resZeroTrans,axiom,
% 2.70/1.58 ! [X2: name,Rs: late_residual] :
% 2.70/1.58 ~ ( late_transitions @ ( res @ X2 @ piNil ) @ Rs ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_214_nilSim_I2_J,axiom,
% 2.70/1.58 ! [Rel: set @ ( product_prod @ pi @ pi ),A2: name,X2: name,P: pi] :
% 2.70/1.58 ~ ( strong743114133lation @ piNil @ Rel @ ( input @ A2 @ X2 @ P ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_215_nilSim_I3_J,axiom,
% 2.70/1.58 ! [Rel: set @ ( product_prod @ pi @ pi ),A2: name,B2: name,P: pi] :
% 2.70/1.58 ~ ( strong743114133lation @ piNil @ Rel @ ( output @ A2 @ B2 @ P ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_216_nilSim_I1_J,axiom,
% 2.70/1.58 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi] :
% 2.70/1.58 ~ ( strong743114133lation @ piNil @ Rel @ ( tau @ P ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_217_simps_I6_J,axiom,
% 2.70/1.58 ! [A2: name,B2: name,P: pi,C2: name,D: name] :
% 2.70/1.58 ( ( subs @ ( mismatch @ A2 @ B2 @ P ) @ C2 @ D )
% 2.70/1.58 = ( mismatch @ ( subst_name @ A2 @ C2 @ D ) @ ( subst_name @ B2 @ C2 @ D ) @ ( subs @ P @ C2 @ D ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_218_pi_Ofresh_I6_J,axiom,
% 2.70/1.58 ! [A2: name,X32: name,X22: name,X1: pi] :
% 2.70/1.58 ( ( fresh @ name @ pi @ A2 @ ( mismatch @ X32 @ X22 @ X1 ) )
% 2.70/1.58 = ( ( fresh @ name @ name @ A2 @ X32 )
% 2.70/1.58 & ( fresh @ name @ name @ A2 @ X22 )
% 2.70/1.58 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_219_pi_Odistinct_I9_J,axiom,
% 2.70/1.58 ! [Name13: name,Name24: name,Pi: pi] :
% 2.70/1.58 ( piNil
% 2.70/1.58 != ( mismatch @ Name13 @ Name24 @ Pi ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_220_pi_Odistinct_I61_J,axiom,
% 2.70/1.58 ! [Name1: name,Name22: name,Pi3: pi,Name13: name,Name24: name,Pi: pi] :
% 2.70/1.58 ( ( match @ Name1 @ Name22 @ Pi3 )
% 2.70/1.58 != ( mismatch @ Name13 @ Name24 @ Pi ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_221_pi_Odistinct_I25_J,axiom,
% 2.70/1.58 ! [Name1: name,Name22: name,Pi3: pi,Name13: name,Name24: name,Pi: pi] :
% 2.70/1.58 ( ( output @ Name1 @ Name22 @ Pi3 )
% 2.70/1.58 != ( mismatch @ Name13 @ Name24 @ Pi ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_222_pi_Odistinct_I39_J,axiom,
% 2.70/1.58 ! [Pi3: pi,Name13: name,Name24: name,Pi: pi] :
% 2.70/1.58 ( ( tau @ Pi3 )
% 2.70/1.58 != ( mismatch @ Name13 @ Name24 @ Pi ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_223_pi_Oinject_I5_J,axiom,
% 2.70/1.58 ! [X32: name,X22: name,X1: pi,Y32: name,Y2: name,Y1: pi] :
% 2.70/1.58 ( ( ( mismatch @ X32 @ X22 @ X1 )
% 2.70/1.58 = ( mismatch @ Y32 @ Y2 @ Y1 ) )
% 2.70/1.58 = ( ( X32 = Y32 )
% 2.70/1.58 & ( X22 = Y2 )
% 2.70/1.58 & ( X1 = Y1 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_224_pi_Odistinct_I75_J,axiom,
% 2.70/1.58 ! [Name1: name,Name22: name,Pi3: pi,Name: name,Pi: pi] :
% 2.70/1.58 ( ( mismatch @ Name1 @ Name22 @ Pi3 )
% 2.70/1.58 != ( res @ Name @ Pi ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_225_pi_Odistinct_I73_J,axiom,
% 2.70/1.58 ! [Name1: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 2.70/1.58 ( ( mismatch @ Name1 @ Name22 @ Pi3 )
% 2.70/1.58 != ( par @ Pi12 @ Pi22 ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_226_Mismatch,axiom,
% 2.70/1.58 ! [P: pi,Rs: late_residual,A2: name,B2: name] :
% 2.70/1.58 ( ( late_transitions @ P @ Rs )
% 2.70/1.58 => ( ( A2 != B2 )
% 2.70/1.58 => ( late_transitions @ ( mismatch @ A2 @ B2 @ P ) @ Rs ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_227_mismatchCases_H,axiom,
% 2.70/1.58 ! [A2: name,B2: name,P: pi,Rs: late_residual] :
% 2.70/1.58 ( ( late_transitions @ ( mismatch @ A2 @ B2 @ P ) @ Rs )
% 2.70/1.58 => ~ ! [P4: pi,A4: name,B4: name] :
% 2.70/1.58 ( ( ( A2 = A4 )
% 2.70/1.58 & ( B2 = B4 )
% 2.70/1.58 & ( P = P4 ) )
% 2.70/1.58 => ( ( late_transitions @ P4 @ Rs )
% 2.70/1.58 => ( A4 = B4 ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_228_mismatchTrans,axiom,
% 2.70/1.58 ! [A2: name,P: pi,Rs: late_residual] :
% 2.70/1.58 ~ ( late_transitions @ ( mismatch @ A2 @ A2 @ P ) @ Rs ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_229_mismatchCases,axiom,
% 2.70/1.58 ! [A2: name,B2: name,P: pi,Rs: late_residual,F3: name > name > $o] :
% 2.70/1.58 ( ( late_transitions @ ( mismatch @ A2 @ B2 @ P ) @ Rs )
% 2.70/1.58 => ( ( ( late_transitions @ P @ Rs )
% 2.70/1.58 => ( ( A2 != B2 )
% 2.70/1.58 => ( F3 @ A2 @ B2 ) ) )
% 2.70/1.58 => ( F3 @ A2 @ B2 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_230_pi_Odistinct_I51_J,axiom,
% 2.70/1.58 ! [Name1: name,Name22: name,Pi3: pi,Name13: name,Name24: name,Pi: pi] :
% 2.70/1.58 ( ( input @ Name1 @ Name22 @ Pi3 )
% 2.70/1.58 != ( mismatch @ Name13 @ Name24 @ Pi ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_231_mismatchNilLeft,axiom,
% 2.70/1.58 ! [Rel: set @ ( product_prod @ pi @ pi ),A2: name,P: pi] : ( strong743114133lation @ piNil @ Rel @ ( mismatch @ A2 @ A2 @ P ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_232_pi_Ostrong__induct,axiom,
% 2.70/1.58 ! [N: $tType] :
% 2.70/1.58 ( ( fs_name @ N )
% 2.70/1.58 => ! [P: N > pi > $o,Z: N,Pi3: pi] :
% 2.70/1.58 ( ! [Z2: N] : ( P @ Z2 @ piNil )
% 2.70/1.58 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: N] :
% 2.70/1.58 ( ! [Za: N] : ( P @ Za @ Pi4 )
% 2.70/1.58 => ( P @ Z2 @ ( output @ Name12 @ Name23 @ Pi4 ) ) )
% 2.70/1.58 => ( ! [Pi4: pi,Z2: N] :
% 2.70/1.58 ( ! [Za: N] : ( P @ Za @ Pi4 )
% 2.70/1.58 => ( P @ Z2 @ ( tau @ Pi4 ) ) )
% 2.70/1.58 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: N] :
% 2.70/1.58 ( ( fresh @ name @ N @ Name23 @ Z2 )
% 2.70/1.58 => ( ( fresh @ name @ name @ Name23 @ Name12 )
% 2.70/1.58 => ( ! [Za: N] : ( P @ Za @ Pi4 )
% 2.70/1.58 => ( P @ Z2 @ ( input @ Name12 @ Name23 @ Pi4 ) ) ) ) )
% 2.70/1.58 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: N] :
% 2.70/1.58 ( ! [Za: N] : ( P @ Za @ Pi4 )
% 2.70/1.58 => ( P @ Z2 @ ( match @ Name12 @ Name23 @ Pi4 ) ) )
% 2.70/1.58 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: N] :
% 2.70/1.58 ( ! [Za: N] : ( P @ Za @ Pi4 )
% 2.70/1.58 => ( P @ Z2 @ ( mismatch @ Name12 @ Name23 @ Pi4 ) ) )
% 2.70/1.58 => ( ! [Pi13: pi,Pi23: pi,Z2: N] :
% 2.70/1.58 ( ! [Za: N] : ( P @ Za @ Pi13 )
% 2.70/1.58 => ( ! [Za: N] : ( P @ Za @ Pi23 )
% 2.70/1.58 => ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 2.70/1.58 => ( ! [Pi13: pi,Pi23: pi,Z2: N] :
% 2.70/1.58 ( ! [Za: N] : ( P @ Za @ Pi13 )
% 2.70/1.58 => ( ! [Za: N] : ( P @ Za @ Pi23 )
% 2.70/1.58 => ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
% 2.70/1.58 => ( ! [Name3: name,Pi4: pi,Z2: N] :
% 2.70/1.58 ( ( fresh @ name @ N @ Name3 @ Z2 )
% 2.70/1.58 => ( ! [Za: N] : ( P @ Za @ Pi4 )
% 2.70/1.58 => ( P @ Z2 @ ( res @ Name3 @ Pi4 ) ) ) )
% 2.70/1.58 => ( ! [Pi4: pi,Z2: N] :
% 2.70/1.58 ( ! [Za: N] : ( P @ Za @ Pi4 )
% 2.70/1.58 => ( P @ Z2 @ ( bang @ Pi4 ) ) )
% 2.70/1.58 => ( P @ Z @ Pi3 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_233_pi_Ostrong__inducts,axiom,
% 2.70/1.58 ! [A: $tType] :
% 2.70/1.58 ( ( fs_name @ A )
% 2.70/1.58 => ! [P: A > pi > $o,Z: A,Pi3: pi] :
% 2.70/1.58 ( ! [Z2: A] : ( P @ Z2 @ piNil )
% 2.70/1.58 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: A] :
% 2.70/1.58 ( ! [Za: A] : ( P @ Za @ Pi4 )
% 2.70/1.58 => ( P @ Z2 @ ( output @ Name12 @ Name23 @ Pi4 ) ) )
% 2.70/1.58 => ( ! [Pi4: pi,Z2: A] :
% 2.70/1.58 ( ! [Za: A] : ( P @ Za @ Pi4 )
% 2.70/1.58 => ( P @ Z2 @ ( tau @ Pi4 ) ) )
% 2.70/1.58 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: A] :
% 2.70/1.58 ( ( fresh @ name @ A @ Name23 @ Z2 )
% 2.70/1.58 => ( ( fresh @ name @ name @ Name23 @ Name12 )
% 2.70/1.58 => ( ! [Za: A] : ( P @ Za @ Pi4 )
% 2.70/1.58 => ( P @ Z2 @ ( input @ Name12 @ Name23 @ Pi4 ) ) ) ) )
% 2.70/1.58 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: A] :
% 2.70/1.58 ( ! [Za: A] : ( P @ Za @ Pi4 )
% 2.70/1.58 => ( P @ Z2 @ ( match @ Name12 @ Name23 @ Pi4 ) ) )
% 2.70/1.58 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: A] :
% 2.70/1.58 ( ! [Za: A] : ( P @ Za @ Pi4 )
% 2.70/1.58 => ( P @ Z2 @ ( mismatch @ Name12 @ Name23 @ Pi4 ) ) )
% 2.70/1.58 => ( ! [Pi13: pi,Pi23: pi,Z2: A] :
% 2.70/1.58 ( ! [Za: A] : ( P @ Za @ Pi13 )
% 2.70/1.58 => ( ! [Za: A] : ( P @ Za @ Pi23 )
% 2.70/1.58 => ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 2.70/1.58 => ( ! [Pi13: pi,Pi23: pi,Z2: A] :
% 2.70/1.58 ( ! [Za: A] : ( P @ Za @ Pi13 )
% 2.70/1.58 => ( ! [Za: A] : ( P @ Za @ Pi23 )
% 2.70/1.58 => ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
% 2.70/1.58 => ( ! [Name3: name,Pi4: pi,Z2: A] :
% 2.70/1.58 ( ( fresh @ name @ A @ Name3 @ Z2 )
% 2.70/1.58 => ( ! [Za: A] : ( P @ Za @ Pi4 )
% 2.70/1.58 => ( P @ Z2 @ ( res @ Name3 @ Pi4 ) ) ) )
% 2.70/1.58 => ( ! [Pi4: pi,Z2: A] :
% 2.70/1.58 ( ! [Za: A] : ( P @ Za @ Pi4 )
% 2.70/1.58 => ( P @ Z2 @ ( bang @ Pi4 ) ) )
% 2.70/1.58 => ( P @ Z @ Pi3 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_234_pi_Ofresh_I10_J,axiom,
% 2.70/1.58 ! [A2: name,X1: pi] :
% 2.70/1.58 ( ( fresh @ name @ pi @ A2 @ ( bang @ X1 ) )
% 2.70/1.58 = ( fresh @ name @ pi @ A2 @ X1 ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_235_pi_Ofresh_I7_J,axiom,
% 2.70/1.58 ! [A2: name,X22: pi,X1: pi] :
% 2.70/1.58 ( ( fresh @ name @ pi @ A2 @ ( sum @ X22 @ X1 ) )
% 2.70/1.58 = ( ( fresh @ name @ pi @ A2 @ X22 )
% 2.70/1.58 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_236_simps_I10_J,axiom,
% 2.70/1.58 ! [P: pi,C2: name,D: name] :
% 2.70/1.58 ( ( subs @ ( bang @ P ) @ C2 @ D )
% 2.70/1.58 = ( bang @ ( subs @ P @ C2 @ D ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_237_simps_I7_J,axiom,
% 2.70/1.58 ! [P: pi,Q: pi,C2: name,D: name] :
% 2.70/1.58 ( ( subs @ ( sum @ P @ Q ) @ C2 @ D )
% 2.70/1.58 = ( sum @ ( subs @ P @ C2 @ D ) @ ( subs @ Q @ C2 @ D ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_238_pi_Odistinct_I77_J,axiom,
% 2.70/1.58 ! [Name1: name,Name22: name,Pi3: pi,Pi: pi] :
% 2.70/1.58 ( ( mismatch @ Name1 @ Name22 @ Pi3 )
% 2.70/1.58 != ( bang @ Pi ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_239_pi_Odistinct_I71_J,axiom,
% 2.70/1.58 ! [Name1: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 2.70/1.58 ( ( mismatch @ Name1 @ Name22 @ Pi3 )
% 2.70/1.58 != ( sum @ Pi12 @ Pi22 ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_240_pi_Odistinct_I59_J,axiom,
% 2.70/1.58 ! [Name1: name,Name22: name,Pi3: pi,Pi: pi] :
% 2.70/1.58 ( ( input @ Name1 @ Name22 @ Pi3 )
% 2.70/1.58 != ( bang @ Pi ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_241_pi_Odistinct_I53_J,axiom,
% 2.70/1.58 ! [Name1: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 2.70/1.58 ( ( input @ Name1 @ Name22 @ Pi3 )
% 2.70/1.58 != ( sum @ Pi12 @ Pi22 ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_242_pi_Odistinct_I47_J,axiom,
% 2.70/1.58 ! [Pi3: pi,Pi: pi] :
% 2.70/1.58 ( ( tau @ Pi3 )
% 2.70/1.58 != ( bang @ Pi ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_243_pi_Odistinct_I41_J,axiom,
% 2.70/1.58 ! [Pi3: pi,Pi12: pi,Pi22: pi] :
% 2.70/1.58 ( ( tau @ Pi3 )
% 2.70/1.58 != ( sum @ Pi12 @ Pi22 ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_244_pi_Odistinct_I79_J,axiom,
% 2.70/1.58 ! [Pi1: pi,Pi2: pi,Pi12: pi,Pi22: pi] :
% 2.70/1.58 ( ( sum @ Pi1 @ Pi2 )
% 2.70/1.58 != ( par @ Pi12 @ Pi22 ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_245_pi_Odistinct_I81_J,axiom,
% 2.70/1.58 ! [Pi1: pi,Pi2: pi,Name: name,Pi: pi] :
% 2.70/1.58 ( ( sum @ Pi1 @ Pi2 )
% 2.70/1.58 != ( res @ Name @ Pi ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_246_pi_Odistinct_I27_J,axiom,
% 2.70/1.58 ! [Name1: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 2.70/1.58 ( ( output @ Name1 @ Name22 @ Pi3 )
% 2.70/1.58 != ( sum @ Pi12 @ Pi22 ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_247_pi_Odistinct_I83_J,axiom,
% 2.70/1.58 ! [Pi1: pi,Pi2: pi,Pi: pi] :
% 2.70/1.58 ( ( sum @ Pi1 @ Pi2 )
% 2.70/1.58 != ( bang @ Pi ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_248_pi_Oinject_I6_J,axiom,
% 2.70/1.58 ! [X22: pi,X1: pi,Y2: pi,Y1: pi] :
% 2.70/1.58 ( ( ( sum @ X22 @ X1 )
% 2.70/1.58 = ( sum @ Y2 @ Y1 ) )
% 2.70/1.58 = ( ( X22 = Y2 )
% 2.70/1.58 & ( X1 = Y1 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_249_pi_Oinject_I9_J,axiom,
% 2.70/1.58 ! [X1: pi,Y1: pi] :
% 2.70/1.58 ( ( ( bang @ X1 )
% 2.70/1.58 = ( bang @ Y1 ) )
% 2.70/1.58 = ( X1 = Y1 ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_250_sumCases,axiom,
% 2.70/1.58 ! [P: pi,Q: pi,Rs: late_residual] :
% 2.70/1.58 ( ( late_transitions @ ( sum @ P @ Q ) @ Rs )
% 2.70/1.58 => ( ~ ( late_transitions @ P @ Rs )
% 2.70/1.58 => ( late_transitions @ Q @ Rs ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_251_sumCases_H,axiom,
% 2.70/1.58 ! [P: pi,Q: pi,Rs: late_residual] :
% 2.70/1.58 ( ( late_transitions @ ( sum @ P @ Q ) @ Rs )
% 2.70/1.58 => ( ~ ( late_transitions @ P @ Rs )
% 2.70/1.58 => ( late_transitions @ Q @ Rs ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_252_Sum1,axiom,
% 2.70/1.58 ! [P: pi,Rs: late_residual,Q: pi] :
% 2.70/1.58 ( ( late_transitions @ P @ Rs )
% 2.70/1.58 => ( late_transitions @ ( sum @ P @ Q ) @ Rs ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_253_Sum2,axiom,
% 2.70/1.58 ! [Q: pi,Rs: late_residual,P: pi] :
% 2.70/1.58 ( ( late_transitions @ Q @ Rs )
% 2.70/1.58 => ( late_transitions @ ( sum @ P @ Q ) @ Rs ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_254_pi_Odistinct_I33_J,axiom,
% 2.70/1.58 ! [Name1: name,Name22: name,Pi3: pi,Pi: pi] :
% 2.70/1.58 ( ( output @ Name1 @ Name22 @ Pi3 )
% 2.70/1.58 != ( bang @ Pi ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_255_pi_Odistinct_I89_J,axiom,
% 2.70/1.58 ! [Name2: name,Pi3: pi,Pi: pi] :
% 2.70/1.58 ( ( res @ Name2 @ Pi3 )
% 2.70/1.58 != ( bang @ Pi ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(tcon_Agent_Opi___Agent_Ofs__name,axiom,
% 2.70/1.58 fs_name @ pi ).
% 2.70/1.58
% 2.70/1.58 thf(tcon_HOL_Obool___Agent_Ofs__name_1,axiom,
% 2.70/1.58 fs_name @ $o ).
% 2.70/1.58
% 2.70/1.58 thf(tcon_Agent_Oname___Agent_Ofs__name_2,axiom,
% 2.70/1.58 fs_name @ name ).
% 2.70/1.58
% 2.70/1.58 thf(tcon_Product__Type_Oprod___Agent_Ofs__name_3,axiom,
% 2.70/1.58 ! [A7: $tType,A8: $tType] :
% 2.70/1.58 ( ( ( fs_name @ A7 )
% 2.70/1.58 & ( fs_name @ A8 ) )
% 2.70/1.58 => ( fs_name @ ( product_prod @ A7 @ A8 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(tcon_Late__Semantics_OfreeRes___Agent_Ofs__name_4,axiom,
% 2.70/1.58 fs_name @ late_freeRes ).
% 2.70/1.58
% 2.70/1.58 thf(tcon_Late__Semantics_Osubject___Agent_Ofs__name_5,axiom,
% 2.70/1.58 fs_name @ late_subject ).
% 2.70/1.58
% 2.70/1.58 thf(tcon_Late__Semantics_Oresidual___Agent_Ofs__name_6,axiom,
% 2.70/1.58 fs_name @ late_residual ).
% 2.70/1.58
% 2.70/1.58 thf(help_If_3_1_T,axiom,
% 2.70/1.58 ! [P: $o] :
% 2.70/1.58 ( ( P = $true )
% 2.70/1.58 | ( P = $false ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(help_If_2_1_T,axiom,
% 2.70/1.58 ! [A: $tType,X2: A,Y: A] :
% 2.70/1.58 ( ( if @ A @ $false @ X2 @ Y )
% 2.70/1.58 = Y ) ).
% 2.70/1.58
% 2.70/1.58 thf(help_If_1_1_T,axiom,
% 2.70/1.58 ! [A: $tType,X2: A,Y: A] :
% 2.70/1.58 ( ( if @ A @ $true @ X2 @ Y )
% 2.70/1.58 = X2 ) ).
% 2.70/1.58
% 2.70/1.58 thf(conj_0,conjecture,
% 2.70/1.58 ? [P6: pi] :
% 2.70/1.58 ( ( late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_FreeR @ late_TauR @ P6 ) )
% 2.70/1.58 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P6 @ ( res @ y @ ( par @ p2 @ ( subs @ ( par @ q2 @ r ) @ x @ y ) ) ) ) @ rel ) ) ).
% 2.70/1.58 ------------------------
% 2.80/1.62 % (26100)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_25766 for (2999ds/2Mi)
% 2.80/1.62 % (26096)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_25766 for (2999ds/183Mi)
% 2.80/1.62 % (26098)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_25766 for (2999ds/27Mi)
% 2.80/1.62 % (26100)Instruction limit reached!
% 2.80/1.62 % (26100)------------------------------
% 2.80/1.62 % (26100)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.62 % (26100)Termination reason: Unknown
% 2.80/1.62 % (26100)Termination phase: shuffling
% 2.80/1.62
% 2.80/1.62 % (26100)Memory used [KB]: 1535
% 2.80/1.62 % (26100)Time elapsed: 0.003 s
% 2.80/1.62 % (26100)Instructions burned: 4 (million)
% 2.80/1.62 % (26100)------------------------------
% 2.80/1.62 % (26100)------------------------------
% 2.80/1.62 % (26097)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_25766 for (2999ds/4Mi)
% 2.80/1.62 % (26099)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_25766 for (2999ds/2Mi)
% 2.80/1.62 % (26101)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_25766 for (2999ds/275Mi)
% 2.80/1.62 % (26102)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_25766 for (2999ds/18Mi)
% 2.80/1.63 % (26099)Instruction limit reached!
% 2.80/1.63 % (26099)------------------------------
% 2.80/1.63 % (26099)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.63 % (26099)Termination reason: Unknown
% 2.80/1.63 % (26099)Termination phase: shuffling
% 2.80/1.63
% 2.80/1.63 % (26099)Memory used [KB]: 1407
% 2.80/1.63 % (26099)Time elapsed: 0.004 s
% 2.80/1.63 % (26099)Instructions burned: 3 (million)
% 2.80/1.63 % (26099)------------------------------
% 2.80/1.63 % (26099)------------------------------
% 2.80/1.63 % (26097)Instruction limit reached!
% 2.80/1.63 % (26097)------------------------------
% 2.80/1.63 % (26097)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.63 % (26097)Termination reason: Unknown
% 2.80/1.63 % (26097)Termination phase: shuffling
% 2.80/1.63
% 2.80/1.63 % (26097)Memory used [KB]: 1535
% 2.80/1.63 % (26097)Time elapsed: 0.005 s
% 2.80/1.63 % (26097)Instructions burned: 5 (million)
% 2.80/1.63 % (26097)------------------------------
% 2.80/1.63 % (26097)------------------------------
% 2.80/1.63 % (26098)Instruction limit reached!
% 2.80/1.63 % (26098)------------------------------
% 2.80/1.63 % (26098)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.63 % (26098)Termination reason: Unknown
% 2.80/1.63 % (26098)Termination phase: shuffling
% 2.80/1.63
% 2.80/1.63 % (26098)Memory used [KB]: 1791
% 2.80/1.63 % (26098)Time elapsed: 0.011 s
% 2.80/1.63 % (26098)Instructions burned: 27 (million)
% 2.80/1.63 % (26098)------------------------------
% 2.80/1.63 % (26098)------------------------------
% 2.80/1.63 % (26103)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_25766 for (2999ds/3Mi)
% 2.80/1.63 % (26103)Instruction limit reached!
% 2.80/1.63 % (26103)------------------------------
% 2.80/1.63 % (26103)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.63 % (26103)Termination reason: Unknown
% 2.80/1.63 % (26103)Termination phase: shuffling
% 2.80/1.63
% 2.80/1.63 % (26103)Memory used [KB]: 1407
% 2.80/1.63 % (26103)Time elapsed: 0.003 s
% 2.80/1.63 % (26103)Instructions burned: 5 (million)
% 2.80/1.63 % (26103)------------------------------
% 2.80/1.63 % (26103)------------------------------
% 2.80/1.64 % (26102)Instruction limit reached!
% 2.80/1.64 % (26102)------------------------------
% 2.80/1.64 % (26102)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.64 % (26102)Termination reason: Unknown
% 2.80/1.64 % (26102)Termination phase: shuffling
% 2.80/1.64
% 2.80/1.64 % (26102)Memory used [KB]: 1663
% 2.80/1.64 % (26102)Time elapsed: 0.014 s
% 2.80/1.64 % (26102)Instructions burned: 19 (million)
% 2.80/1.64 % (26102)------------------------------
% 2.80/1.64 % (26102)------------------------------
% 2.80/1.64 % (26106)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_25766 for (2999ds/3Mi)
% 2.80/1.64 % (26106)Instruction limit reached!
% 2.80/1.64 % (26106)------------------------------
% 2.80/1.64 % (26106)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.64 % (26106)Termination reason: Unknown
% 2.80/1.64 % (26106)Termination phase: shuffling
% 2.80/1.64
% 2.80/1.64 % (26106)Memory used [KB]: 1407
% 2.80/1.64 % (26106)Time elapsed: 0.003 s
% 2.80/1.64 % (26106)Instructions burned: 5 (million)
% 2.80/1.64 % (26106)------------------------------
% 2.80/1.64 % (26106)------------------------------
% 2.80/1.64 % (26107)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_25766 for (2999ds/1041Mi)
% 2.80/1.64 % (26104)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_25766 for (2999ds/37Mi)
% 2.80/1.64 % (26105)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_25766 for (2999ds/15Mi)
% 2.80/1.65 % (26109)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_25766 for (2999ds/16Mi)
% 2.80/1.65 % (26108)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_25766 for (2999ds/7Mi)
% 2.80/1.65 % (26109)Instruction limit reached!
% 2.80/1.65 % (26109)------------------------------
% 2.80/1.65 % (26109)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.65 % (26109)Termination reason: Unknown
% 2.80/1.65 % (26109)Termination phase: shuffling
% 2.80/1.65
% 2.80/1.65 % (26109)Memory used [KB]: 1663
% 2.80/1.65 % (26109)Time elapsed: 0.007 s
% 2.80/1.65 % (26109)Instructions burned: 18 (million)
% 2.80/1.65 % (26109)------------------------------
% 2.80/1.65 % (26109)------------------------------
% 2.80/1.65 % (26105)Instruction limit reached!
% 2.80/1.65 % (26105)------------------------------
% 2.80/1.65 % (26105)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.65 % (26105)Termination reason: Unknown
% 2.80/1.65 % (26105)Termination phase: shuffling
% 2.80/1.65
% 2.80/1.65 % (26105)Memory used [KB]: 1663
% 2.80/1.65 % (26105)Time elapsed: 0.012 s
% 2.80/1.65 % (26105)Instructions burned: 16 (million)
% 2.80/1.65 % (26105)------------------------------
% 2.80/1.65 % (26105)------------------------------
% 2.80/1.66 % (26108)Instruction limit reached!
% 2.80/1.66 % (26108)------------------------------
% 2.80/1.66 % (26108)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.66 % (26108)Termination reason: Unknown
% 2.80/1.66 % (26108)Termination phase: shuffling
% 2.80/1.66
% 2.80/1.66 % (26108)Memory used [KB]: 1535
% 2.80/1.66 % (26108)Time elapsed: 0.005 s
% 2.80/1.66 % (26108)Instructions burned: 8 (million)
% 2.80/1.66 % (26108)------------------------------
% 2.80/1.66 % (26108)------------------------------
% 2.80/1.66 % (26104)Instruction limit reached!
% 2.80/1.66 % (26104)------------------------------
% 2.80/1.66 % (26104)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.66 % (26104)Termination reason: Unknown
% 2.80/1.66 % (26104)Termination phase: shuffling
% 2.80/1.66
% 2.80/1.66 % (26104)Memory used [KB]: 2174
% 2.80/1.66 % (26104)Time elapsed: 0.021 s
% 2.80/1.66 % (26104)Instructions burned: 37 (million)
% 2.80/1.66 % (26104)------------------------------
% 2.80/1.66 % (26104)------------------------------
% 2.80/1.66 % (26110)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_25766 for (2999ds/3Mi)
% 2.80/1.66 % (26110)Instruction limit reached!
% 2.80/1.66 % (26110)------------------------------
% 2.80/1.66 % (26110)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.66 % (26110)Termination reason: Unknown
% 2.80/1.66 % (26110)Termination phase: shuffling
% 2.80/1.66
% 2.80/1.66 % (26110)Memory used [KB]: 1407
% 2.80/1.66 % (26110)Time elapsed: 0.002 s
% 2.80/1.66 % (26110)Instructions burned: 3 (million)
% 2.80/1.66 % (26110)------------------------------
% 2.80/1.66 % (26110)------------------------------
% 2.80/1.67 % (26112)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_25766 for (2999ds/7Mi)
% 2.80/1.67 % (26112)Instruction limit reached!
% 2.80/1.67 % (26112)------------------------------
% 2.80/1.67 % (26112)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.67 % (26112)Termination reason: Unknown
% 2.80/1.67 % (26112)Termination phase: shuffling
% 2.80/1.67
% 2.80/1.67 % (26112)Memory used [KB]: 1535
% 2.80/1.67 % (26112)Time elapsed: 0.004 s
% 2.80/1.67 % (26112)Instructions burned: 8 (million)
% 2.80/1.67 % (26112)------------------------------
% 2.80/1.67 % (26112)------------------------------
% 2.80/1.67 % (26096)Instruction limit reached!
% 2.80/1.67 % (26096)------------------------------
% 2.80/1.67 % (26096)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.67 % (26096)Termination reason: Unknown
% 2.80/1.67 % (26096)Termination phase: Saturation
% 2.80/1.67
% 2.80/1.67 % (26096)Memory used [KB]: 7291
% 2.80/1.67 % (26096)Time elapsed: 0.056 s
% 2.80/1.67 % (26096)Instructions burned: 183 (million)
% 2.80/1.67 % (26096)------------------------------
% 2.80/1.67 % (26096)------------------------------
% 2.80/1.67 % (26111)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_25766 for (2999ds/3Mi)
% 2.80/1.67 % (26114)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_25766 for (2999ds/4Mi)
% 2.80/1.67 % (26111)Instruction limit reached!
% 2.80/1.67 % (26111)------------------------------
% 2.80/1.67 % (26111)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.67 % (26111)Termination reason: Unknown
% 2.80/1.67 % (26111)Termination phase: shuffling
% 2.80/1.67
% 2.80/1.67 % (26111)Memory used [KB]: 1407
% 2.80/1.67 % (26111)Time elapsed: 0.004 s
% 2.80/1.67 % (26111)Instructions burned: 3 (million)
% 2.80/1.67 % (26111)------------------------------
% 2.80/1.67 % (26111)------------------------------
% 2.80/1.68 % (26114)Instruction limit reached!
% 2.80/1.68 % (26114)------------------------------
% 2.80/1.68 % (26114)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.68 % (26114)Termination reason: Unknown
% 2.80/1.68 % (26114)Termination phase: shuffling
% 2.80/1.68
% 2.80/1.68 % (26114)Memory used [KB]: 1407
% 2.80/1.68 % (26114)Time elapsed: 0.003 s
% 2.80/1.68 % (26114)Instructions burned: 6 (million)
% 2.80/1.68 % (26114)------------------------------
% 2.80/1.68 % (26114)------------------------------
% 2.80/1.68 % (26113)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_25766 for (2999ds/3Mi)
% 2.80/1.68 % (26115)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_25766 for (2999ds/18Mi)
% 2.80/1.68 % (26101)First to succeed.
% 2.80/1.68 % (26113)Instruction limit reached!
% 2.80/1.68 % (26113)------------------------------
% 2.80/1.68 % (26113)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.68 % (26113)Termination reason: Unknown
% 2.80/1.68 % (26113)Termination phase: shuffling
% 2.80/1.68
% 2.80/1.68 % (26113)Memory used [KB]: 1407
% 2.80/1.68 % (26113)Time elapsed: 0.004 s
% 2.80/1.68 % (26113)Instructions burned: 4 (million)
% 2.80/1.68 % (26113)------------------------------
% 2.80/1.68 % (26113)------------------------------
% 2.80/1.68 % (26101)Refutation found. Thanks to Tanya!
% 2.80/1.68 % SZS status Theorem for DTF2THF_25766
% 2.80/1.68 % SZS output start Proof for DTF2THF_25766
% 2.80/1.68 thf(type_def_5, type, pi: $tType).
% 2.80/1.68 thf(type_def_7, type, name: $tType).
% 2.80/1.68 thf(type_def_8, type, late_freeRes: $tType).
% 2.80/1.68 thf(type_def_9, type, late_subject: $tType).
% 2.80/1.68 thf(type_def_10, type, late_residual: $tType).
% 2.80/1.68 thf(type_def_11, type, noption: ($tType) > $tType).
% 2.80/1.68 thf(type_def_12, type, product_prod: ($tType * $tType) > $tType).
% 2.80/1.68 thf(type_def_13, type, set: ($tType) > $tType).
% 2.80/1.68 thf(func_def_0, type, late_residual: $tType).
% 2.80/1.68 thf(func_def_1, type, late_subject: $tType).
% 2.80/1.68 thf(func_def_2, type, late_freeRes: $tType).
% 2.80/1.68 thf(func_def_3, type, product_prod: ($tType * $tType) > $tType).
% 2.80/1.68 thf(func_def_4, type, noption: ($tType) > $tType).
% 2.80/1.68 thf(func_def_5, type, name: $tType).
% 2.80/1.68 thf(func_def_6, type, pi: $tType).
% 2.80/1.68 thf(func_def_7, type, set: ($tType) > $tType).
% 2.80/1.68 thf(func_def_8, type, fs_name: !>[X0: $tType]:($o)).
% 2.80/1.68 thf(func_def_9, type, bang: pi > pi).
% 2.80/1.68 thf(func_def_10, type, input: name > name > pi > pi).
% 2.80/1.68 thf(func_def_11, type, match: name > name > pi > pi).
% 2.80/1.68 thf(func_def_12, type, mismatch: name > name > pi > pi).
% 2.80/1.68 thf(func_def_13, type, output: name > name > pi > pi).
% 2.80/1.68 thf(func_def_14, type, par: pi > pi > pi).
% 2.80/1.68 thf(func_def_15, type, piNil: pi).
% 2.80/1.68 thf(func_def_16, type, res: name > pi > pi).
% 2.80/1.68 thf(func_def_17, type, sum: pi > pi > pi).
% 2.80/1.68 thf(func_def_18, type, tau: pi > pi).
% 2.80/1.68 thf(func_def_19, type, subs: pi > name > name > pi).
% 2.80/1.68 thf(func_def_20, type, subst_name: name > name > name > name).
% 2.80/1.68 thf(func_def_21, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 2.80/1.68 thf(func_def_22, type, late_OutputR: name > name > late_freeRes).
% 2.80/1.68 thf(func_def_23, type, late_TauR: late_freeRes).
% 2.80/1.68 thf(func_def_24, type, late_freeRes_rec: !>[X0: $tType]:((name > name > X0) > X0 > late_freeRes > X0)).
% 2.80/1.68 thf(func_def_25, type, late_BoundR: late_subject > name > pi > late_residual).
% 2.80/1.68 thf(func_def_26, type, late_FreeR: late_freeRes > pi > late_residual).
% 2.80/1.68 thf(func_def_27, type, late_BoundOutputS: name > late_subject).
% 2.80/1.68 thf(func_def_28, type, late_InputS: name > late_subject).
% 2.80/1.68 thf(func_def_29, type, late_subject_rec: !>[X0: $tType]:((name > X0) > (name > X0) > late_subject > X0)).
% 2.80/1.68 thf(func_def_30, type, late_transitions: pi > late_residual > $o).
% 2.80/1.68 thf(func_def_31, type, abs_fun: !>[X0: $tType, X1: $tType]:(X0 > X1 > X0 > noption @ X1)).
% 2.80/1.68 thf(func_def_32, type, fresh: !>[X0: $tType, X1: $tType]:(X0 > X1 > $o)).
% 2.80/1.68 thf(func_def_33, type, product_Pair: !>[X0: $tType, X1: $tType]:(X0 > X1 > product_prod @ X0 @ X1)).
% 2.80/1.68 thf(func_def_34, type, produc2004651681e_prod: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2)).
% 2.80/1.68 thf(func_def_35, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2)).
% 2.80/1.68 thf(func_def_36, type, eqvt: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > $o)).
% 2.80/1.68 thf(func_def_37, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 2.80/1.68 thf(func_def_38, type, strong2129052853vative: pi > pi > late_subject > name > set @ product_prod @ pi @ pi > $o).
% 2.80/1.68 thf(func_def_39, type, strong743114133lation: pi > set @ product_prod @ pi @ pi > pi > $o).
% 2.80/1.68 thf(func_def_40, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 2.80/1.68 thf(func_def_41, type, p: pi).
% 2.80/1.68 thf(func_def_42, type, pqr: pi).
% 2.80/1.68 thf(func_def_43, type, p2: pi).
% 2.80/1.68 thf(func_def_44, type, q: pi).
% 2.80/1.68 thf(func_def_45, type, qr: pi).
% 2.80/1.68 thf(func_def_46, type, q2: pi).
% 2.80/1.68 thf(func_def_47, type, r: pi).
% 2.80/1.68 thf(func_def_48, type, rel: set @ product_prod @ pi @ pi).
% 2.80/1.68 thf(func_def_49, type, alpha: late_freeRes).
% 2.80/1.68 thf(func_def_50, type, a: name).
% 2.80/1.68 thf(func_def_51, type, x: name).
% 2.80/1.68 thf(func_def_52, type, y: name).
% 2.80/1.68 thf(func_def_70, type, sP0: late_subject > name > pi > pi > pi > $o).
% 2.80/1.68 thf(func_def_71, type, sK1: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4)).
% 2.80/1.68 thf(func_def_72, type, sK2: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3)).
% 2.80/1.68 thf(func_def_73, type, sK3: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 2.80/1.68 thf(func_def_74, type, sK4: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 2.80/1.68 thf(func_def_75, type, sK5: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 2.80/1.68 thf(func_def_76, type, sK6: (late_residual > $o) > late_subject).
% 2.80/1.68 thf(func_def_77, type, sK7: (late_residual > $o) > name).
% 2.80/1.68 thf(func_def_78, type, sK8: (late_residual > $o) > pi).
% 2.80/1.68 thf(func_def_79, type, sK9: (late_residual > $o) > late_freeRes).
% 2.80/1.68 thf(func_def_80, type, sK10: (late_residual > $o) > pi).
% 2.80/1.68 thf(func_def_81, type, sK11: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X0)).
% 2.80/1.68 thf(func_def_82, type, sK12: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X1)).
% 2.80/1.68 thf(func_def_83, type, sK13: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X2)).
% 2.80/1.68 thf(func_def_84, type, sK14: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X3)).
% 2.80/1.68 thf(func_def_85, type, sK15: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X4)).
% 2.80/1.68 thf(func_def_86, type, sK16: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X5)).
% 2.80/1.68 thf(func_def_87, type, sK17: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X0)).
% 2.80/1.68 thf(func_def_88, type, sK18: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X1)).
% 2.80/1.68 thf(func_def_89, type, sK19: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X2)).
% 2.80/1.68 thf(func_def_90, type, sK20: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X3)).
% 2.80/1.68 thf(func_def_91, type, sK21: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X4)).
% 2.80/1.68 thf(func_def_92, type, sK22: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X5)).
% 2.80/1.68 thf(func_def_93, type, sK23: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X6)).
% 2.80/1.68 thf(func_def_94, type, sK24: (pi > $o) > late_freeRes > pi > name > pi).
% 2.80/1.68 thf(func_def_95, type, sK25: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X0)).
% 2.80/1.68 thf(func_def_96, type, sK26: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X1)).
% 2.80/1.68 thf(func_def_97, type, sK27: late_freeRes > name).
% 2.80/1.68 thf(func_def_98, type, sK28: late_freeRes > name).
% 2.80/1.68 thf(func_def_99, type, sK29: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X1)).
% 2.80/1.68 thf(func_def_100, type, sK30: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X0)).
% 2.80/1.68 thf(func_def_101, type, sK31: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X0)).
% 2.80/1.68 thf(func_def_102, type, sK32: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X1)).
% 2.80/1.68 thf(func_def_103, type, sK33: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ product_prod @ X1 @ X2 > X0)).
% 2.80/1.68 thf(func_def_104, type, sK34: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ product_prod @ X1 @ X2 > X1)).
% 2.80/1.68 thf(func_def_105, type, sK35: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ product_prod @ X1 @ X2 > X2)).
% 2.80/1.68 thf(func_def_106, type, sK36: late_residual > pi > name > name > name).
% 2.80/1.68 thf(func_def_107, type, sK37: late_residual > pi > name > name > name).
% 2.80/1.68 thf(func_def_108, type, sK38: late_residual > pi > name > name > pi).
% 2.80/1.68 thf(func_def_109, type, sK39: !>[X0: $tType]:((X0 > late_freeRes > $o) > name)).
% 2.80/1.68 thf(func_def_110, type, sK40: !>[X0: $tType]:((X0 > late_freeRes > $o) > name)).
% 2.80/1.68 thf(func_def_111, type, sK41: !>[X0: $tType]:((X0 > late_freeRes > $o) > X0)).
% 2.80/1.68 thf(func_def_112, type, sK42: !>[X0: $tType]:((X0 > late_freeRes > $o) > X0)).
% 2.80/1.68 thf(func_def_113, type, sK43: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X0)).
% 2.80/1.68 thf(func_def_114, type, sK44: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X1)).
% 2.80/1.68 thf(func_def_115, type, sK45: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X2)).
% 2.80/1.68 thf(func_def_116, type, sK46: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X3)).
% 2.80/1.68 thf(func_def_117, type, sK47: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3)).
% 2.80/1.68 thf(func_def_118, type, sK48: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 2.80/1.68 thf(func_def_119, type, sK49: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 2.80/1.68 thf(func_def_120, type, sK50: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 2.80/1.68 thf(func_def_121, type, sK51: (pi > $o) > name > late_subject > pi > pi > pi).
% 2.80/1.68 thf(func_def_122, type, sK52: (pi > $o) > name > late_subject > pi > pi > pi).
% 2.80/1.68 thf(func_def_123, type, sK53: !>[X0: $tType]:((X0 > late_freeRes > $o) > name)).
% 2.80/1.68 thf(func_def_124, type, sK54: !>[X0: $tType]:((X0 > late_freeRes > $o) > name)).
% 2.80/1.68 thf(func_def_125, type, sK55: !>[X0: $tType]:((X0 > late_freeRes > $o) > X0)).
% 2.80/1.68 thf(func_def_126, type, sK56: !>[X0: $tType]:((X0 > late_freeRes > $o) > X0)).
% 2.80/1.68 thf(func_def_127, type, sK57: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 2.80/1.68 thf(func_def_128, type, sK58: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 2.80/1.68 thf(func_def_129, type, sK59: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 2.80/1.68 thf(func_def_130, type, sK60: (late_freeRes > $o) > name).
% 2.80/1.68 thf(func_def_131, type, sK61: (late_freeRes > $o) > name).
% 2.80/1.68 thf(func_def_132, type, sK62: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X1)).
% 2.80/1.68 thf(func_def_133, type, sK63: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X0)).
% 2.80/1.68 thf(func_def_134, type, sK64: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X6)).
% 2.80/1.68 thf(func_def_135, type, sK65: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X5)).
% 2.80/1.68 thf(func_def_136, type, sK66: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4)).
% 2.80/1.68 thf(func_def_137, type, sK67: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3)).
% 2.80/1.68 thf(func_def_138, type, sK68: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 2.80/1.68 thf(func_def_139, type, sK69: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 2.80/1.68 thf(func_def_140, type, sK70: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 2.80/1.68 thf(func_def_141, type, sK71: pi > late_freeRes > pi > name > pi).
% 2.80/1.68 thf(func_def_142, type, sK72: pi > late_freeRes > pi > name > late_freeRes).
% 2.80/1.68 thf(func_def_143, type, sK73: pi > late_freeRes > pi > name > pi).
% 2.80/1.68 thf(func_def_144, type, sK74: pi > late_freeRes > pi > name > name).
% 2.80/1.68 thf(func_def_145, type, sK75: late_subject > name > pi > pi > pi > pi).
% 2.80/1.68 thf(func_def_146, type, sK76: late_subject > name > pi > pi > pi > late_subject).
% 2.80/1.68 thf(func_def_147, type, sK77: late_subject > name > pi > pi > pi > name).
% 2.80/1.68 thf(func_def_148, type, sK78: late_subject > name > pi > pi > pi > pi).
% 2.80/1.68 thf(func_def_149, type, sK79: late_subject > name > pi > pi > pi > pi).
% 2.80/1.68 thf(func_def_150, type, sK80: pi > name > late_subject > pi > pi > pi).
% 2.80/1.68 thf(func_def_151, type, sK81: pi > name > late_subject > pi > pi > late_subject).
% 2.80/1.68 thf(func_def_152, type, sK82: pi > name > late_subject > pi > pi > name).
% 2.80/1.68 thf(func_def_153, type, sK83: pi > name > late_subject > pi > pi > pi).
% 2.80/1.68 thf(func_def_154, type, sK84: pi > name > late_subject > pi > pi > pi).
% 2.80/1.68 thf(func_def_155, type, sK85: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X0)).
% 2.80/1.68 thf(func_def_156, type, sK86: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X1)).
% 2.80/1.68 thf(func_def_157, type, sK87: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X2)).
% 2.80/1.68 thf(func_def_158, type, sK88: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X3)).
% 2.80/1.68 thf(func_def_159, type, sK89: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X4)).
% 2.80/1.68 thf(func_def_160, type, sK90: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X5)).
% 2.80/1.68 thf(func_def_161, type, sK91: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4)).
% 2.80/1.68 thf(func_def_162, type, sK92: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3)).
% 2.80/1.68 thf(func_def_163, type, sK93: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 2.80/1.68 thf(func_def_164, type, sK94: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 2.80/1.68 thf(func_def_165, type, sK95: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 2.80/1.68 thf(func_def_167, type, ph97: !>[X0: $tType]:(X0)).
% 2.80/1.68 thf(f1006,plain,(
% 2.80/1.68 $false),
% 2.80/1.68 inference(subsumption_resolution,[status(thm)],[f1005,f833])).
% 2.80/1.68 thf(f833,plain,(
% 2.80/1.68 ((late_transitions @ (par @ (par @ p @ q) @ r) @ (late_FreeR @ late_TauR @ (par @ (res @ y @ (par @ p2 @ (subs @ q2 @ x @ y))) @ r))) = $true)),
% 2.80/1.68 inference(cnf_transformation,[status(thm)],[f393])).
% 2.80/1.68 thf(f393,plain,(
% 2.80/1.68 ((late_transitions @ (par @ (par @ p @ q) @ r) @ (late_FreeR @ late_TauR @ (par @ (res @ y @ (par @ p2 @ (subs @ q2 @ x @ y))) @ r))) = $true)),
% 2.80/1.68 inference(fool_elimination,[status(thm)],[f392])).
% 2.80/1.68 thf(f392,plain,(
% 2.80/1.68 (late_transitions @ (par @ (par @ p @ q) @ r) @ (late_FreeR @ late_TauR @ (par @ (res @ y @ (par @ p2 @ (subs @ q2 @ x @ y))) @ r)))),
% 2.80/1.68 inference(rectify,[status(thm)],[f8])).
% 2.80/1.68 thf(f8,axiom,(
% 2.80/1.68 (late_transitions @ (par @ (par @ p @ q) @ r) @ (late_FreeR @ late_TauR @ (par @ (res @ y @ (par @ p2 @ (subs @ q2 @ x @ y))) @ r)))),
% 2.80/1.68 file('/export/starexec/sandbox/tmp/tmp.eALBO61dU7/DTF2THF_25766.p',fact_7__092_060open_062_IP_A_092_060parallel_062_AQ_J_A_092_060parallel_062_AR_A_092_060longmapsto_062_A_092_060tau_062_A_092_060prec_062_A_060_092_060nu_062y_062_IP_H_A_092_060parallel_062_AQ_H_091x_058_058_061y_093_J_A_092_060parallel_062_AR_092_060close_062)).
% 2.80/1.68 thf(f1005,plain,(
% 2.80/1.68 ((late_transitions @ (par @ (par @ p @ q) @ r) @ (late_FreeR @ late_TauR @ (par @ (res @ y @ (par @ p2 @ (subs @ q2 @ x @ y))) @ r))) != $true)),
% 2.80/1.68 inference(trivial_inequality_removal,[status(thm)],[f1002])).
% 2.80/1.68 thf(f1002,plain,(
% 2.80/1.68 ((late_transitions @ (par @ (par @ p @ q) @ r) @ (late_FreeR @ late_TauR @ (par @ (res @ y @ (par @ p2 @ (subs @ q2 @ x @ y))) @ r))) != $true) | ($true != $true)),
% 2.80/1.68 inference(superposition,[status(thm)],[f940,f949])).
% 2.80/1.68 thf(f949,plain,(
% 2.80/1.68 ((member @ product_prod @ pi @ pi @ (product_Pair @ pi @ pi @ (par @ (res @ y @ (par @ p2 @ (subs @ q2 @ x @ y))) @ r) @ (res @ y @ (par @ p2 @ (subs @ (par @ q2 @ r) @ x @ y)))) @ rel) = $true)),
% 2.80/1.68 inference(cnf_transformation,[status(thm)],[f351])).
% 2.80/1.68 thf(f351,plain,(
% 2.80/1.68 ((member @ product_prod @ pi @ pi @ (product_Pair @ pi @ pi @ (par @ (res @ y @ (par @ p2 @ (subs @ q2 @ x @ y))) @ r) @ (res @ y @ (par @ p2 @ (subs @ (par @ q2 @ r) @ x @ y)))) @ rel) = $true)),
% 2.80/1.68 inference(fool_elimination,[status(thm)],[f350])).
% 2.80/1.68 thf(f350,plain,(
% 2.80/1.68 (member @ product_prod @ pi @ pi @ (product_Pair @ pi @ pi @ (par @ (res @ y @ (par @ p2 @ (subs @ q2 @ x @ y))) @ r) @ (res @ y @ (par @ p2 @ (subs @ (par @ q2 @ r) @ x @ y)))) @ rel)),
% 2.80/1.68 inference(rectify,[status(thm)],[f7])).
% 2.80/1.68 thf(f7,axiom,(
% 2.80/1.68 (member @ product_prod @ pi @ pi @ (product_Pair @ pi @ pi @ (par @ (res @ y @ (par @ p2 @ (subs @ q2 @ x @ y))) @ r) @ (res @ y @ (par @ p2 @ (subs @ (par @ q2 @ r) @ x @ y)))) @ rel)),
% 2.80/1.68 file('/export/starexec/sandbox/tmp/tmp.eALBO61dU7/DTF2THF_25766.p',fact_6__092_060open_062_I_060_092_060nu_062y_062_IP_H_A_092_060parallel_062_AQ_H_091x_058_058_061y_093_J_A_092_060parallel_062_AR_M_A_060_092_060nu_062y_062_IP_H_A_092_060parallel_062_A_IQ_H_A_092_060parallel_062_AR_J_091x_058_058_061y_093_J_J_A_092_060in_062_ARel_092_060close_062)).
% 2.80/1.68 thf(f940,plain,(
% 2.80/1.68 ( ! [X0 : pi] : (($true != (member @ product_prod @ pi @ pi @ (product_Pair @ pi @ pi @ X0 @ (res @ y @ (par @ p2 @ (subs @ (par @ q2 @ r) @ x @ y)))) @ rel)) | ($true != (late_transitions @ (par @ (par @ p @ q) @ r) @ (late_FreeR @ late_TauR @ X0)))) )),
% 2.80/1.68 inference(cnf_transformation,[status(thm)],[f683])).
% 2.80/1.68 thf(f683,plain,(
% 2.80/1.68 ! [X0 : pi] : (($true != (late_transitions @ (par @ (par @ p @ q) @ r) @ (late_FreeR @ late_TauR @ X0))) | ($true != (member @ product_prod @ pi @ pi @ (product_Pair @ pi @ pi @ X0 @ (res @ y @ (par @ p2 @ (subs @ (par @ q2 @ r) @ x @ y)))) @ rel)))),
% 2.80/1.68 inference(ennf_transformation,[status(thm)],[f511])).
% 2.80/1.68 thf(f511,plain,(
% 2.80/1.68 ~? [X0 : pi] : (($true = (late_transitions @ (par @ (par @ p @ q) @ r) @ (late_FreeR @ late_TauR @ X0))) & ($true = (member @ product_prod @ pi @ pi @ (product_Pair @ pi @ pi @ X0 @ (res @ y @ (par @ p2 @ (subs @ (par @ q2 @ r) @ x @ y)))) @ rel)))),
% 2.80/1.68 inference(fool_elimination,[status(thm)],[f510])).
% 2.80/1.68 thf(f510,plain,(
% 2.80/1.68 ~? [X0 : pi] : ((late_transitions @ (par @ (par @ p @ q) @ r) @ (late_FreeR @ late_TauR @ X0)) & (member @ product_prod @ pi @ pi @ (product_Pair @ pi @ pi @ X0 @ (res @ y @ (par @ p2 @ (subs @ (par @ q2 @ r) @ x @ y)))) @ rel))),
% 2.80/1.68 inference(rectify,[status(thm)],[f268])).
% 2.80/1.68 thf(f268,negated_conjecture,(
% 2.80/1.68 ~? [X97 : pi] : ((late_transitions @ (par @ (par @ p @ q) @ r) @ (late_FreeR @ late_TauR @ X97)) & (member @ product_prod @ pi @ pi @ (product_Pair @ pi @ pi @ X97 @ (res @ y @ (par @ p2 @ (subs @ (par @ q2 @ r) @ x @ y)))) @ rel))),
% 2.80/1.68 inference(negated_conjecture,[status(cth)],[f267])).
% 2.80/1.68 thf(f267,conjecture,(
% 2.80/1.68 ? [X97 : pi] : ((late_transitions @ (par @ (par @ p @ q) @ r) @ (late_FreeR @ late_TauR @ X97)) & (member @ product_prod @ pi @ pi @ (product_Pair @ pi @ pi @ X97 @ (res @ y @ (par @ p2 @ (subs @ (par @ q2 @ r) @ x @ y)))) @ rel))),
% 2.80/1.68 file('/export/starexec/sandbox/tmp/tmp.eALBO61dU7/DTF2THF_25766.p',conj_0)).
% 2.80/1.68 % SZS output end Proof for DTF2THF_25766
% 2.80/1.68 % (26101)------------------------------
% 2.80/1.68 % (26101)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.68 % (26101)Termination reason: Refutation
% 2.80/1.68
% 2.80/1.68 % (26101)Memory used [KB]: 7164
% 2.80/1.68 % (26101)Time elapsed: 0.058 s
% 2.80/1.68 % (26101)Instructions burned: 96 (million)
% 2.80/1.68 % (26101)------------------------------
% 2.80/1.68 % (26101)------------------------------
% 2.80/1.68 % (26095)Success in time 0.088 s
%------------------------------------------------------------------------------