%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP190^2 : 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 : n031.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 08:56:17 AM UTC 2026
% Result : Theorem 4.05s 2.16s
% Output : Refutation 4.05s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ITP190^2 : TPTP v9.2.1. Released v7.5.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.32 % Computer : n031.cluster.edu
% 0.16/0.32 % Model : x86_64 x86_64
% 0.16/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.32 % Memory : 8042.1875MB
% 0.16/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.32 % CPULimit : 300
% 0.16/0.32 % WCLimit : 300
% 0.16/0.32 % DateTime : Tue Feb 24 08:30:18 EST 2026
% 0.16/0.32 % CPUTime :
% 0.16/0.32 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.43 ---- Original DTF file ---
% 0.17/0.43 thf(spec,logic,$$dhol).
% 0.17/0.43 %------------------------------------------------------------------------------
% 0.17/0.43 % File : ITP190^2 : TPTP v9.2.1. Released v7.5.0.
% 0.17/0.43 % Domain : Interactive Theorem Proving
% 0.17/0.43 % Problem : Sledgehammer Strong_Late_Sim_SC problem prob_808__3416684_1
% 0.17/0.43 % Version : Especial.
% 0.17/0.43 % English :
% 0.17/0.43
% 0.17/0.43 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.17/0.43 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.17/0.43 % Source : [Des21]
% 0.17/0.43 % Names : Strong_Late_Sim_SC/prob_808__3416684_1 [Des21]
% 0.17/0.43
% 0.17/0.43 % Status : Theorem
% 0.17/0.43 % Rating : 0.00 v7.5.0
% 0.17/0.43 % Syntax : Number of formulae : 363 ( 151 unt; 62 typ; 0 def)
% 0.17/0.43 % Number of atoms : 708 ( 289 equ; 0 cnn)
% 0.17/0.43 % Maximal formula atoms : 17 ( 2 avg)
% 0.17/0.43 % Number of connectives : 5253 ( 139 ~; 4 |; 44 &;4652 @)
% 0.17/0.43 % ( 0 <=>; 414 =>; 0 <=; 0 <~>)
% 0.17/0.43 % Maximal formula depth : 28 ( 8 avg)
% 0.17/0.43 % Number of types : 10 ( 9 usr)
% 0.17/0.43 % Number of type conns : 196 ( 196 >; 0 *; 0 +; 0 <<)
% 0.17/0.43 % Number of symbols : 56 ( 53 usr; 16 con; 0-5 aty)
% 0.17/0.43 % Number of variables : 1255 ( 11 ^;1202 !; 15 ?;1255 :)
% 0.17/0.43 % ( 27 !>; 0 ?*; 0 @-; 0 @+)
% 0.17/0.43 % SPC : TH1_THM_EQU_NAR
% 0.17/0.43
% 0.17/0.43 % Comments : This file was generated by Sledgehammer 2021-02-23 16:17:39.352
% 0.17/0.43 %------------------------------------------------------------------------------
% 0.17/0.43 % Could-be-implicit typings (13)
% 0.17/0.43 thf(ty_t_Late__Semantics_Oresidual__Rep,type,
% 0.17/0.43 late_residual_Rep: $tType ).
% 0.17/0.43
% 0.17/0.43 thf(ty_t_Late__Semantics_Osubject__Rep,type,
% 0.17/0.43 late_subject_Rep: $tType ).
% 0.17/0.43
% 0.17/0.43 thf(ty_t_Late__Semantics_OfreeRes__Rep,type,
% 0.17/0.43 late_freeRes_Rep: $tType ).
% 0.17/0.43
% 0.17/0.43 thf(ty_t_Late__Semantics_Oresidual,type,
% 0.17/0.43 late_residual: $tType ).
% 0.17/0.43
% 0.17/0.43 thf(ty_t_Late__Semantics_Osubject,type,
% 0.17/0.43 late_subject: $tType ).
% 0.17/0.43
% 0.17/0.43 thf(ty_t_Late__Semantics_OfreeRes,type,
% 0.17/0.43 late_freeRes: $tType ).
% 0.17/0.43
% 0.17/0.43 thf(ty_t_Product__Type_Oprod,type,
% 0.17/0.43 product_prod: $tType > $tType > $tType ).
% 0.17/0.43
% 0.17/0.43 thf(ty_t_Nominal_Onoption,type,
% 0.17/0.43 noption: $tType > $tType ).
% 0.17/0.43
% 0.17/0.43 thf(ty_t_Agent_Opi__Rep,type,
% 0.17/0.43 pi_Rep: $tType ).
% 0.17/0.43
% 0.17/0.43 thf(ty_t_Agent_Oname,type,
% 0.17/0.43 name: $tType ).
% 0.17/0.43
% 0.17/0.43 thf(ty_t_List_Olist,type,
% 0.17/0.43 list: $tType > $tType ).
% 0.17/0.43
% 0.17/0.43 thf(ty_t_Agent_Opi,type,
% 0.17/0.43 pi: $tType ).
% 0.17/0.43
% 0.17/0.43 thf(ty_t_Set_Oset,type,
% 0.17/0.43 set: $tType > $tType ).
% 0.17/0.43
% 0.17/0.43 % Explicit typings (49)
% 0.17/0.43 thf(sy_cl_HOL_Otype,type,
% 0.17/0.43 type:
% 0.17/0.43 !>[A: $tType] : $o ).
% 0.17/0.43
% 0.17/0.43 thf(sy_cl_Agent_Ofs__name,type,
% 0.17/0.43 fs_name:
% 0.17/0.43 !>[A: $tType] : $o ).
% 0.17/0.43
% 0.17/0.43 thf(sy_cl_Agent_Opt__name,type,
% 0.17/0.43 pt_name:
% 0.17/0.43 !>[A: $tType] : $o ).
% 0.17/0.43
% 0.17/0.43 thf(sy_cl_Orderings_Oord,type,
% 0.17/0.43 ord:
% 0.17/0.43 !>[A: $tType] : $o ).
% 0.17/0.43
% 0.17/0.43 thf(sy_cl_Agent_Ocp__name__name,type,
% 0.17/0.43 cp_name_name:
% 0.17/0.43 !>[A: $tType] : $o ).
% 0.17/0.43
% 0.17/0.43 thf(sy_cl_Orderings_Olinorder,type,
% 0.17/0.43 linorder:
% 0.17/0.43 !>[A: $tType] : $o ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Agent_Opi_OInput,type,
% 0.17/0.43 input: name > name > pi > pi ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Agent_Opi_OPar,type,
% 0.17/0.43 par: pi > pi > pi ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Agent_Opi_ORes,type,
% 0.17/0.43 res: name > pi > pi ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Agent_Orec_Oname__prm__name,type,
% 0.17/0.43 name_prm_name: ( list @ ( product_prod @ name @ name ) ) > name > name ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Agent_Orec_Oswap__name,type,
% 0.17/0.43 swap_name: ( product_prod @ name @ name ) > name > name ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Agent_Osubs,type,
% 0.17/0.43 subs: pi > name > name > pi ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_If,type,
% 0.17/0.43 if:
% 0.17/0.43 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Late__Semantics_OfreeRes_OOutputR,type,
% 0.17/0.43 late_OutputR: name > name > late_freeRes ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Late__Semantics_OfreeRes_OTauR,type,
% 0.17/0.43 late_TauR: late_freeRes ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Late__Semantics_Oresidual_OBoundR,type,
% 0.17/0.43 late_BoundR: late_subject > name > pi > late_residual ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Late__Semantics_Oresidual_OFreeR,type,
% 0.17/0.43 late_FreeR: late_freeRes > pi > late_residual ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Late__Semantics_Oresidual__Rep_OFreeR__Rep,type,
% 0.17/0.43 late_r347633188eR_Rep: late_freeRes > pi > late_residual_Rep ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Late__Semantics_Osubject_OBoundOutputS,type,
% 0.17/0.43 late_BoundOutputS: name > late_subject ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Late__Semantics_Osubject_OInputS,type,
% 0.17/0.43 late_InputS: name > late_subject ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Late__Semantics_Otransitions,type,
% 0.17/0.43 late_transitions: pi > late_residual > $o ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_List_Olist_OCons,type,
% 0.17/0.43 cons:
% 0.17/0.43 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_List_Olist_ONil,type,
% 0.17/0.43 nil:
% 0.17/0.43 !>[A: $tType] : ( list @ A ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_List_Oproduct__lists,type,
% 0.17/0.43 product_lists:
% 0.17/0.43 !>[A: $tType] : ( ( list @ ( list @ A ) ) > ( list @ ( list @ A ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Nominal_Oabs__fun,type,
% 0.17/0.43 abs_fun:
% 0.17/0.43 !>[X: $tType,A: $tType] : ( X > A > X > ( noption @ A ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Nominal_Ofresh,type,
% 0.17/0.43 fresh:
% 0.17/0.43 !>[X: $tType,A: $tType] : ( X > A > $o ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Nominal_Operm,type,
% 0.17/0.43 perm:
% 0.17/0.43 !>[X: $tType,A: $tType] : ( ( list @ ( product_prod @ X @ X ) ) > A > A ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Nominal_Osupports,type,
% 0.17/0.43 supports:
% 0.17/0.43 !>[X: $tType,A: $tType] : ( ( set @ X ) > A > $o ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Nominal_Oswap,type,
% 0.17/0.43 swap:
% 0.17/0.43 !>[X: $tType] : ( ( product_prod @ X @ X ) > X > X ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Product__Type_OPair,type,
% 0.17/0.43 product_Pair:
% 0.17/0.43 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod,type,
% 0.17/0.43 product_rec_prod:
% 0.17/0.43 !>[A: $tType,B: $tType,T: $tType] : ( ( A > B > T ) > ( product_prod @ A @ B ) > T ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Rel_Oeqvt,type,
% 0.17/0.43 eqvt:
% 0.17/0.43 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > $o ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Set_OCollect,type,
% 0.17/0.43 collect:
% 0.17/0.43 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Strong__Late__Sim_Oderivative,type,
% 0.17/0.43 strong2129052853vative: pi > pi > late_subject > name > ( set @ ( product_prod @ pi @ pi ) ) > $o ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Strong__Late__Sim_Osimulation,type,
% 0.17/0.43 strong743114133lation: pi > ( set @ ( product_prod @ pi @ pi ) ) > pi > $o ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_member,type,
% 0.17/0.43 member:
% 0.17/0.43 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_v_P,type,
% 0.17/0.43 p: pi ).
% 0.17/0.43
% 0.17/0.43 thf(sy_v_P_H____,type,
% 0.17/0.43 p2: pi ).
% 0.17/0.43
% 0.17/0.43 thf(sy_v_PxQ____,type,
% 0.17/0.43 pxQ: pi ).
% 0.17/0.43
% 0.17/0.43 thf(sy_v_Q,type,
% 0.17/0.43 q: pi ).
% 0.17/0.43
% 0.17/0.43 thf(sy_v_Q_H____,type,
% 0.17/0.43 q2: pi ).
% 0.17/0.43
% 0.17/0.43 thf(sy_v_Q_Ha____,type,
% 0.17/0.43 q_a: pi ).
% 0.17/0.43
% 0.17/0.43 thf(sy_v_Rel,type,
% 0.17/0.43 rel: set @ ( product_prod @ pi @ pi ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_v__092_060alpha_062____,type,
% 0.17/0.43 alpha: late_freeRes ).
% 0.17/0.43
% 0.17/0.43 thf(sy_v_aa____,type,
% 0.17/0.43 aa: name ).
% 0.17/0.43
% 0.17/0.43 thf(sy_v_b____,type,
% 0.17/0.43 b: name ).
% 0.17/0.43
% 0.17/0.43 thf(sy_v_x,type,
% 0.17/0.43 x: name ).
% 0.17/0.43
% 0.17/0.43 thf(sy_v_y____,type,
% 0.17/0.43 y: name ).
% 0.17/0.43
% 0.17/0.43 thf(sy_v_z____,type,
% 0.17/0.43 z: name ).
% 0.17/0.43
% 0.17/0.43 % Relevant facts (255)
% 0.17/0.43 thf(fact_0__092_060open_062a_A_061_Ab_092_060close_062,axiom,
% 0.17/0.43 aa = b ).
% 0.17/0.43
% 0.17/0.43 % \<open>a = b\<close>
% 0.17/0.43 thf(fact_1_cOpen_Ohyps_I2_J,axiom,
% 0.17/0.43 b != x ).
% 0.17/0.43
% 0.17/0.43 % cOpen.hyps(2)
% 0.17/0.43 thf(fact_2_cClose1_Ohyps_I10_J,axiom,
% 0.17/0.43 z != aa ).
% 0.17/0.43
% 0.17/0.43 % cClose1.hyps(10)
% 0.17/0.43 thf(fact_3_cClose1_Ohyps_I6_J,axiom,
% 0.17/0.43 y != z ).
% 0.17/0.43
% 0.17/0.43 % cClose1.hyps(6)
% 0.17/0.43 thf(fact_4_cClose1_Ohyps_I5_J,axiom,
% 0.17/0.43 y != aa ).
% 0.17/0.43
% 0.17/0.43 % cClose1.hyps(5)
% 0.17/0.43 thf(fact_5__092_060open_062z_A_092_060noteq_062_Ax_092_060close_062,axiom,
% 0.17/0.43 z != x ).
% 0.17/0.43
% 0.17/0.43 % \<open>z \<noteq> x\<close>
% 0.17/0.43 thf(fact_6_cOpen_Ohyps_I1_J,axiom,
% 0.17/0.43 late_transitions @ q @ ( late_FreeR @ ( late_OutputR @ b @ x ) @ q_a ) ).
% 0.17/0.43
% 0.17/0.43 % cOpen.hyps(1)
% 0.17/0.43 thf(fact_7_cOpen_Ohyps_I3_J,axiom,
% 0.17/0.43 ( ( late_BoundOutputS @ aa )
% 0.17/0.43 = ( late_BoundOutputS @ b ) ) ).
% 0.17/0.43
% 0.17/0.43 % cOpen.hyps(3)
% 0.17/0.43 thf(fact_8_cClose1_Ohyps_I14_J,axiom,
% 0.17/0.43 alpha = late_TauR ).
% 0.17/0.43
% 0.17/0.43 % cClose1.hyps(14)
% 0.17/0.43 thf(fact_9_cClose1_Ohyps_I13_J,axiom,
% 0.17/0.43 fresh @ name @ name @ z @ x ).
% 0.17/0.43
% 0.17/0.43 % cClose1.hyps(13)
% 0.17/0.43 thf(fact_10_perm__swap_I1_J,axiom,
% 0.17/0.43 ! [X2: $tType] :
% 0.17/0.43 ( ( pt_name @ X2 )
% 0.17/0.43 => ! [A2: name,B2: name,X3: X2] :
% 0.17/0.43 ( ( perm @ name @ X2 @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ ( perm @ name @ X2 @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ X3 ) )
% 0.17/0.43 = X3 ) ) ).
% 0.17/0.43
% 0.17/0.43 % perm_swap(1)
% 0.17/0.43 thf(fact_11_name__id,axiom,
% 0.17/0.43 ! [X: $tType] :
% 0.17/0.43 ( ( pt_name @ X )
% 0.17/0.43 => ! [A2: name,X3: X] :
% 0.17/0.43 ( ( perm @ name @ X @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ A2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ X3 )
% 0.17/0.43 = X3 ) ) ).
% 0.17/0.43
% 0.17/0.43 % name_id
% 0.17/0.43 thf(fact_12_name__swap,axiom,
% 0.17/0.43 ! [X: $tType] :
% 0.17/0.43 ( ( pt_name @ X )
% 0.17/0.43 => ! [A2: name,B2: name,X3: X] :
% 0.17/0.43 ( ( perm @ name @ X @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ X3 )
% 0.17/0.43 = ( perm @ name @ X @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ B2 @ A2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ X3 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % name_swap
% 0.17/0.43 thf(fact_13_name__swap__bij,axiom,
% 0.17/0.43 ! [X: $tType] :
% 0.17/0.43 ( ( pt_name @ X )
% 0.17/0.43 => ! [A2: name,B2: name,X3: X] :
% 0.17/0.43 ( ( perm @ name @ X @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ ( perm @ name @ X @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ X3 ) )
% 0.17/0.43 = X3 ) ) ).
% 0.17/0.43
% 0.17/0.43 % name_swap_bij
% 0.17/0.43 thf(fact_14_pt__name1,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( pt_name @ A )
% 0.17/0.43 => ! [X3: A] :
% 0.17/0.43 ( ( perm @ name @ A @ ( nil @ ( product_prod @ name @ name ) ) @ X3 )
% 0.17/0.43 = X3 ) ) ).
% 0.17/0.43
% 0.17/0.43 % pt_name1
% 0.17/0.43 thf(fact_15__092_060open_062y_A_092_060noteq_062_Ax_092_060close_062,axiom,
% 0.17/0.43 y != x ).
% 0.17/0.43
% 0.17/0.43 % \<open>y \<noteq> x\<close>
% 0.17/0.43 thf(fact_16_perm__swap_I2_J,axiom,
% 0.17/0.43 ! [X2: $tType] :
% 0.17/0.43 ( ( pt_name @ X2 )
% 0.17/0.43 => ! [A2: name,B2: name,X3: X2] :
% 0.17/0.43 ( ( perm @ name @ X2 @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ ( perm @ name @ X2 @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ B2 @ A2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ X3 ) )
% 0.17/0.43 = X3 ) ) ).
% 0.17/0.43
% 0.17/0.43 % perm_swap(2)
% 0.17/0.43 thf(fact_17_eqvt,axiom,
% 0.17/0.43 ! [X1: pi,X22: late_residual,Pi: list @ ( product_prod @ name @ name )] :
% 0.17/0.43 ( ( late_transitions @ X1 @ X22 )
% 0.17/0.43 => ( late_transitions @ ( perm @ name @ pi @ Pi @ X1 ) @ ( perm @ name @ late_residual @ Pi @ X22 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % eqvt
% 0.17/0.43 thf(fact_18__092_060open_062z_A_092_060sharp_062_AQ_092_060close_062,axiom,
% 0.17/0.43 fresh @ name @ pi @ z @ q ).
% 0.17/0.43
% 0.17/0.43 % \<open>z \<sharp> Q\<close>
% 0.17/0.43 thf(fact_19_Late__Semantics_OfreeRes_Oinject,axiom,
% 0.17/0.43 ! [X22: name,X1: name,Y2: name,Y1: name] :
% 0.17/0.43 ( ( ( late_OutputR @ X22 @ X1 )
% 0.17/0.43 = ( late_OutputR @ Y2 @ Y1 ) )
% 0.17/0.43 = ( ( X22 = Y2 )
% 0.17/0.43 & ( X1 = Y1 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % Late_Semantics.freeRes.inject
% 0.17/0.43 thf(fact_20_Late__Semantics1_OfreeRes_Oinject,axiom,
% 0.17/0.43 ! [X11: name,X12: name,Y11: name,Y12: name] :
% 0.17/0.43 ( ( ( late_OutputR @ X11 @ X12 )
% 0.17/0.43 = ( late_OutputR @ Y11 @ Y12 ) )
% 0.17/0.43 = ( ( X11 = Y11 )
% 0.17/0.43 & ( X12 = Y12 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % Late_Semantics1.freeRes.inject
% 0.17/0.43 thf(fact_21_cClose1_Ohyps_I11_J,axiom,
% 0.17/0.43 fresh @ name @ pi @ z @ p2 ).
% 0.17/0.43
% 0.17/0.43 % cClose1.hyps(11)
% 0.17/0.43 thf(fact_22_cClose1_Ohyps_I7_J,axiom,
% 0.17/0.43 fresh @ name @ pi @ y @ q2 ).
% 0.17/0.43
% 0.17/0.43 % cClose1.hyps(7)
% 0.17/0.43 thf(fact_23_cClose1_Ohyps_I12_J,axiom,
% 0.17/0.43 fresh @ name @ name @ y @ x ).
% 0.17/0.43
% 0.17/0.43 % cClose1.hyps(12)
% 0.17/0.43 thf(fact_24_assms_I1_J,axiom,
% 0.17/0.43 fresh @ name @ pi @ x @ p ).
% 0.17/0.43
% 0.17/0.43 % assms(1)
% 0.17/0.43 thf(fact_25_cClose1_Ohyps_I8_J,axiom,
% 0.17/0.43 fresh @ name @ pi @ z @ p ).
% 0.17/0.43
% 0.17/0.43 % cClose1.hyps(8)
% 0.17/0.43 thf(fact_26_cClose1_Ohyps_I3_J,axiom,
% 0.17/0.43 fresh @ name @ pi @ y @ p ).
% 0.17/0.43
% 0.17/0.43 % cClose1.hyps(3)
% 0.17/0.43 thf(fact_27_residual__perm__empty,axiom,
% 0.17/0.43 ! [Residual_Rep: late_residual_Rep] :
% 0.17/0.43 ( ( perm @ name @ late_residual_Rep @ ( nil @ ( product_prod @ name @ name ) ) @ Residual_Rep )
% 0.17/0.43 = Residual_Rep ) ).
% 0.17/0.43
% 0.17/0.43 % residual_perm_empty
% 0.17/0.43 thf(fact_28_subject__perm__empty,axiom,
% 0.17/0.43 ! [Subject_Rep: late_subject_Rep] :
% 0.17/0.43 ( ( perm @ name @ late_subject_Rep @ ( nil @ ( product_prod @ name @ name ) ) @ Subject_Rep )
% 0.17/0.43 = Subject_Rep ) ).
% 0.17/0.43
% 0.17/0.43 % subject_perm_empty
% 0.17/0.43 thf(fact_29_freeRes__perm__empty,axiom,
% 0.17/0.43 ! [FreeRes_Rep: late_freeRes_Rep] :
% 0.17/0.43 ( ( perm @ name @ late_freeRes_Rep @ ( nil @ ( product_prod @ name @ name ) ) @ FreeRes_Rep )
% 0.17/0.43 = FreeRes_Rep ) ).
% 0.17/0.43
% 0.17/0.43 % freeRes_perm_empty
% 0.17/0.43 thf(fact_30_pi__perm__empty,axiom,
% 0.17/0.43 ! [Pi_Rep: pi_Rep] :
% 0.17/0.43 ( ( perm @ name @ pi_Rep @ ( nil @ ( product_prod @ name @ name ) ) @ Pi_Rep )
% 0.17/0.43 = Pi_Rep ) ).
% 0.17/0.43
% 0.17/0.43 % pi_perm_empty
% 0.17/0.43 thf(fact_31_freeRes_Operm_I1_J,axiom,
% 0.17/0.43 ! [Pi: list @ ( product_prod @ name @ name ),X22: name,X1: name] :
% 0.17/0.43 ( ( perm @ name @ late_freeRes @ Pi @ ( late_OutputR @ X22 @ X1 ) )
% 0.17/0.43 = ( late_OutputR @ ( perm @ name @ name @ Pi @ X22 ) @ ( perm @ name @ name @ Pi @ X1 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % freeRes.perm(1)
% 0.17/0.43 thf(fact_32_subject_Operm_I2_J,axiom,
% 0.17/0.43 ! [Pi: list @ ( product_prod @ name @ name ),X1: name] :
% 0.17/0.43 ( ( perm @ name @ late_subject @ Pi @ ( late_BoundOutputS @ X1 ) )
% 0.17/0.43 = ( late_BoundOutputS @ ( perm @ name @ name @ Pi @ X1 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % subject.perm(2)
% 0.17/0.43 thf(fact_33_Late__Semantics_Osubject_Oinject_I2_J,axiom,
% 0.17/0.43 ! [X1: name,Y1: name] :
% 0.17/0.43 ( ( ( late_BoundOutputS @ X1 )
% 0.17/0.43 = ( late_BoundOutputS @ Y1 ) )
% 0.17/0.43 = ( X1 = Y1 ) ) ).
% 0.17/0.43
% 0.17/0.43 % Late_Semantics.subject.inject(2)
% 0.17/0.43 thf(fact_34_Late__Semantics1_Osubject_Oinject_I2_J,axiom,
% 0.17/0.43 ! [X22: name,Y2: name] :
% 0.17/0.43 ( ( ( late_BoundOutputS @ X22 )
% 0.17/0.43 = ( late_BoundOutputS @ Y2 ) )
% 0.17/0.43 = ( X22 = Y2 ) ) ).
% 0.17/0.43
% 0.17/0.43 % Late_Semantics1.subject.inject(2)
% 0.17/0.43 thf(fact_35_freeRes_Operm_I2_J,axiom,
% 0.17/0.43 ! [Pi: list @ ( product_prod @ name @ name )] :
% 0.17/0.43 ( ( perm @ name @ late_freeRes @ Pi @ late_TauR )
% 0.17/0.43 = late_TauR ) ).
% 0.17/0.43
% 0.17/0.43 % freeRes.perm(2)
% 0.17/0.43 thf(fact_36_name__fresh,axiom,
% 0.17/0.43 ( ( fresh @ name @ name )
% 0.17/0.43 = ( ^ [A3: name,B3: name] : ( A3 != B3 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % name_fresh
% 0.17/0.43 thf(fact_37_residual_Operm_I2_J,axiom,
% 0.17/0.43 ! [Pi: list @ ( product_prod @ name @ name ),X22: late_freeRes,X1: pi] :
% 0.17/0.43 ( ( perm @ name @ late_residual @ Pi @ ( late_FreeR @ X22 @ X1 ) )
% 0.17/0.43 = ( late_FreeR @ ( perm @ name @ late_freeRes @ Pi @ X22 ) @ ( perm @ name @ pi @ Pi @ X1 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % residual.perm(2)
% 0.17/0.43 thf(fact_38_perm__fresh__fresh,axiom,
% 0.17/0.43 ! [X2: $tType] :
% 0.17/0.43 ( ( pt_name @ X2 )
% 0.17/0.43 => ! [A2: name,X3: X2,B2: name] :
% 0.17/0.43 ( ( fresh @ name @ X2 @ A2 @ X3 )
% 0.17/0.43 => ( ( fresh @ name @ X2 @ B2 @ X3 )
% 0.17/0.43 => ( ( perm @ name @ X2 @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ X3 )
% 0.17/0.43 = X3 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % perm_fresh_fresh
% 0.17/0.43 thf(fact_39_name__fresh__fresh,axiom,
% 0.17/0.43 ! [X: $tType] :
% 0.17/0.43 ( ( pt_name @ X )
% 0.17/0.43 => ! [A2: name,X3: X,B2: name] :
% 0.17/0.43 ( ( fresh @ name @ X @ A2 @ X3 )
% 0.17/0.43 => ( ( fresh @ name @ X @ B2 @ X3 )
% 0.17/0.43 => ( ( perm @ name @ X @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ X3 )
% 0.17/0.43 = X3 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % name_fresh_fresh
% 0.17/0.43 thf(fact_40_cClose1_Ohyps_I9_J,axiom,
% 0.17/0.43 fresh @ name @ pi @ z @ ( res @ x @ q ) ).
% 0.17/0.43
% 0.17/0.43 % cClose1.hyps(9)
% 0.17/0.43 thf(fact_41_cClose1_Ohyps_I4_J,axiom,
% 0.17/0.43 fresh @ name @ pi @ y @ ( res @ x @ q ) ).
% 0.17/0.43
% 0.17/0.43 % cClose1.hyps(4)
% 0.17/0.43 thf(fact_42_fresh__perm__app,axiom,
% 0.17/0.43 ! [X2: $tType] :
% 0.17/0.43 ( ( pt_name @ X2 )
% 0.17/0.43 => ! [A2: name,Pi: list @ ( product_prod @ name @ name ),X3: X2] :
% 0.17/0.43 ( ( fresh @ name @ ( list @ ( product_prod @ name @ name ) ) @ A2 @ Pi )
% 0.17/0.43 => ( ( fresh @ name @ X2 @ A2 @ X3 )
% 0.17/0.43 => ( fresh @ name @ X2 @ A2 @ ( perm @ name @ X2 @ Pi @ X3 ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % fresh_perm_app
% 0.17/0.43 thf(fact_43_name__exists__fresh,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( fs_name @ A )
% 0.17/0.43 => ! [X3: A] :
% 0.17/0.43 ~ ! [C: name] :
% 0.17/0.43 ~ ( fresh @ name @ A @ C @ X3 ) ) ).
% 0.17/0.43
% 0.17/0.43 % name_exists_fresh
% 0.17/0.43 thf(fact_44_fresh__eqvt,axiom,
% 0.17/0.43 ! [X2: $tType] :
% 0.17/0.43 ( ( pt_name @ X2 )
% 0.17/0.43 => ! [Pi: list @ ( product_prod @ name @ name ),A2: name,X3: X2] :
% 0.17/0.43 ( ( perm @ name @ $o @ Pi @ ( fresh @ name @ X2 @ A2 @ X3 ) )
% 0.17/0.43 = ( fresh @ name @ X2 @ ( perm @ name @ name @ Pi @ A2 ) @ ( perm @ name @ X2 @ Pi @ X3 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % fresh_eqvt
% 0.17/0.43 thf(fact_45_mem__Collect__eq,axiom,
% 0.17/0.43 ! [A: $tType,A2: A,P: A > $o] :
% 0.17/0.43 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 0.17/0.43 = ( P @ A2 ) ) ).
% 0.17/0.43
% 0.17/0.43 % mem_Collect_eq
% 0.17/0.43 thf(fact_46_Collect__mem__eq,axiom,
% 0.17/0.43 ! [A: $tType,A4: set @ A] :
% 0.17/0.43 ( ( collect @ A
% 0.17/0.43 @ ^ [X4: A] : ( member @ A @ X4 @ A4 ) )
% 0.17/0.43 = A4 ) ).
% 0.17/0.43
% 0.17/0.43 % Collect_mem_eq
% 0.17/0.43 thf(fact_47_Collect__cong,axiom,
% 0.17/0.43 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.17/0.43 ( ! [X5: A] :
% 0.17/0.43 ( ( P @ X5 )
% 0.17/0.43 = ( Q @ X5 ) )
% 0.17/0.43 => ( ( collect @ A @ P )
% 0.17/0.43 = ( collect @ A @ Q ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % Collect_cong
% 0.17/0.43 thf(fact_48_ext,axiom,
% 0.17/0.43 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.17/0.43 ( ! [X5: A] :
% 0.17/0.43 ( ( F @ X5 )
% 0.17/0.43 = ( G @ X5 ) )
% 0.17/0.43 => ( F = G ) ) ).
% 0.17/0.43
% 0.17/0.43 % ext
% 0.17/0.43 thf(fact_49_fresh__bij,axiom,
% 0.17/0.43 ! [X2: $tType] :
% 0.17/0.43 ( ( pt_name @ X2 )
% 0.17/0.43 => ! [Pi: list @ ( product_prod @ name @ name ),A2: name,X3: X2] :
% 0.17/0.43 ( ( fresh @ name @ X2 @ ( perm @ name @ name @ Pi @ A2 ) @ ( perm @ name @ X2 @ Pi @ X3 ) )
% 0.17/0.43 = ( fresh @ name @ X2 @ A2 @ X3 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % fresh_bij
% 0.17/0.43 thf(fact_50_name__calc_I2_J,axiom,
% 0.17/0.43 ! [X3: name] :
% 0.17/0.43 ( ( perm @ name @ name @ ( nil @ ( product_prod @ name @ name ) ) @ X3 )
% 0.17/0.43 = X3 ) ).
% 0.17/0.43
% 0.17/0.43 % name_calc(2)
% 0.17/0.43 thf(fact_51_freeRes_Ostrong__inducts,axiom,
% 0.17/0.43 ! [A: $tType,P: A > late_freeRes > $o,Z: A,FreeRes: late_freeRes] :
% 0.17/0.43 ( ! [Name1: name,Name2: name,Z2: A] : ( P @ Z2 @ ( late_OutputR @ Name1 @ Name2 ) )
% 0.17/0.43 => ( ! [Z2: A] : ( P @ Z2 @ late_TauR )
% 0.17/0.43 => ( P @ Z @ FreeRes ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % freeRes.strong_inducts
% 0.17/0.43 thf(fact_52_freeRes_Ostrong__induct_H,axiom,
% 0.17/0.43 ! [N: $tType,P: N > late_freeRes > $o,Z: N,FreeRes: late_freeRes] :
% 0.17/0.43 ( ! [Name1: name,Name2: name,Z2: N] : ( P @ Z2 @ ( late_OutputR @ Name1 @ Name2 ) )
% 0.17/0.43 => ( ! [Z2: N] : ( P @ Z2 @ late_TauR )
% 0.17/0.43 => ( P @ Z @ FreeRes ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % freeRes.strong_induct'
% 0.17/0.43 thf(fact_53_freeRes_Oexhaust,axiom,
% 0.17/0.43 ! [Y: late_freeRes] :
% 0.17/0.43 ( ! [X112: name,X122: name] :
% 0.17/0.43 ( Y
% 0.17/0.43 != ( late_OutputR @ X112 @ X122 ) )
% 0.17/0.43 => ( Y = late_TauR ) ) ).
% 0.17/0.43
% 0.17/0.43 % freeRes.exhaust
% 0.17/0.43 thf(fact_54_freeRes_Oinducts,axiom,
% 0.17/0.43 ! [P: late_freeRes > $o,FreeRes: late_freeRes] :
% 0.17/0.43 ( ! [Name1: name,Name2: name] : ( P @ ( late_OutputR @ Name1 @ Name2 ) )
% 0.17/0.43 => ( ( P @ late_TauR )
% 0.17/0.43 => ( P @ FreeRes ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % freeRes.inducts
% 0.17/0.43 thf(fact_55_Late__Semantics1_OfreeRes_Odistinct_I1_J,axiom,
% 0.17/0.43 ! [X11: name,X12: name] :
% 0.17/0.43 ( ( late_OutputR @ X11 @ X12 )
% 0.17/0.43 != late_TauR ) ).
% 0.17/0.43
% 0.17/0.43 % Late_Semantics1.freeRes.distinct(1)
% 0.17/0.43 thf(fact_56_Late__Semantics_OfreeRes_Odistinct_I1_J,axiom,
% 0.17/0.43 ! [Name12: name,Name22: name] :
% 0.17/0.43 ( ( late_OutputR @ Name12 @ Name22 )
% 0.17/0.43 != late_TauR ) ).
% 0.17/0.43
% 0.17/0.43 % Late_Semantics.freeRes.distinct(1)
% 0.17/0.43 thf(fact_57_freshFreeDerivative_I2_J,axiom,
% 0.17/0.43 ! [P: pi,Alpha: late_freeRes,P2: pi,Y: name] :
% 0.17/0.43 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 0.17/0.43 => ( ( fresh @ name @ pi @ Y @ P )
% 0.17/0.43 => ( fresh @ name @ pi @ Y @ P2 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % freshFreeDerivative(2)
% 0.17/0.43 thf(fact_58_swap__simps_I1_J,axiom,
% 0.17/0.43 ! [A2: name,B2: name] :
% 0.17/0.43 ( ( perm @ name @ name @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ A2 )
% 0.17/0.43 = B2 ) ).
% 0.17/0.43
% 0.17/0.43 % swap_simps(1)
% 0.17/0.43 thf(fact_59_swap__simps_I2_J,axiom,
% 0.17/0.43 ! [A2: name,B2: name] :
% 0.17/0.43 ( ( perm @ name @ name @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ B2 )
% 0.17/0.43 = A2 ) ).
% 0.17/0.43
% 0.17/0.43 % swap_simps(2)
% 0.17/0.43 thf(fact_60_swap__simps_I3_J,axiom,
% 0.17/0.43 ! [A2: name,C2: name,B2: name] :
% 0.17/0.43 ( ( A2 != C2 )
% 0.17/0.43 => ( ( B2 != C2 )
% 0.17/0.43 => ( ( perm @ name @ name @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ C2 )
% 0.17/0.43 = C2 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % swap_simps(3)
% 0.17/0.43 thf(fact_61_fresh__aux,axiom,
% 0.17/0.43 ! [X2: $tType] :
% 0.17/0.43 ( ( pt_name @ X2 )
% 0.17/0.43 => ! [C2: name,A2: name,X3: X2,B2: name] :
% 0.17/0.43 ( ( C2 != A2 )
% 0.17/0.43 => ( ( fresh @ name @ X2 @ A2 @ X3 )
% 0.17/0.43 => ( ( fresh @ name @ X2 @ C2 @ X3 )
% 0.17/0.43 => ( fresh @ name @ X2 @ C2 @ ( perm @ name @ X2 @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ X3 ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % fresh_aux
% 0.17/0.43 thf(fact_62_cp__name__name1,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( cp_name_name @ A )
% 0.17/0.43 => ! [Pi1: list @ ( product_prod @ name @ name ),Pi2: list @ ( product_prod @ name @ name ),X3: A] :
% 0.17/0.43 ( ( perm @ name @ A @ Pi1 @ ( perm @ name @ A @ Pi2 @ X3 ) )
% 0.17/0.43 = ( perm @ name @ A @ ( perm @ name @ ( list @ ( product_prod @ name @ name ) ) @ Pi1 @ Pi2 ) @ ( perm @ name @ A @ Pi1 @ X3 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % cp_name_name1
% 0.17/0.43 thf(fact_63_name__perm__compose,axiom,
% 0.17/0.43 ! [X: $tType] :
% 0.17/0.43 ( ( pt_name @ X )
% 0.17/0.43 => ! [Pi2: list @ ( product_prod @ name @ name ),Pi1: list @ ( product_prod @ name @ name ),X3: X] :
% 0.17/0.43 ( ( perm @ name @ X @ Pi2 @ ( perm @ name @ X @ Pi1 @ X3 ) )
% 0.17/0.43 = ( perm @ name @ X @ ( perm @ name @ ( list @ ( product_prod @ name @ name ) ) @ Pi2 @ Pi1 ) @ ( perm @ name @ X @ Pi2 @ X3 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % name_perm_compose
% 0.17/0.43 thf(fact_64_perm__compose,axiom,
% 0.17/0.43 ! [X2: $tType] :
% 0.17/0.43 ( ( pt_name @ X2 )
% 0.17/0.43 => ! [Pi2: list @ ( product_prod @ name @ name ),Pi1: list @ ( product_prod @ name @ name ),X3: X2] :
% 0.17/0.43 ( ( perm @ name @ X2 @ Pi2 @ ( perm @ name @ X2 @ Pi1 @ X3 ) )
% 0.17/0.43 = ( perm @ name @ X2 @ ( perm @ name @ ( list @ ( product_prod @ name @ name ) ) @ Pi2 @ Pi1 ) @ ( perm @ name @ X2 @ Pi2 @ X3 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % perm_compose
% 0.17/0.43 thf(fact_65_perm__bij,axiom,
% 0.17/0.43 ! [X2: $tType] :
% 0.17/0.43 ( ( pt_name @ X2 )
% 0.17/0.43 => ! [Pi: list @ ( product_prod @ name @ name ),X3: X2,Y: X2] :
% 0.17/0.43 ( ( ( perm @ name @ X2 @ Pi @ X3 )
% 0.17/0.43 = ( perm @ name @ X2 @ Pi @ Y ) )
% 0.17/0.43 = ( X3 = Y ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % perm_bij
% 0.17/0.43 thf(fact_66_perm__app,axiom,
% 0.17/0.43 ! [B: $tType,X2: $tType] :
% 0.17/0.43 ( ( pt_name @ X2 )
% 0.17/0.43 => ! [Pi: list @ ( product_prod @ name @ name ),F: X2 > B,X3: X2] :
% 0.17/0.43 ( ( perm @ name @ B @ Pi @ ( F @ X3 ) )
% 0.17/0.43 = ( perm @ name @ ( X2 > B ) @ Pi @ F @ ( perm @ name @ X2 @ Pi @ X3 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % perm_app
% 0.17/0.43 thf(fact_67_in__eqvt,axiom,
% 0.17/0.43 ! [X2: $tType] :
% 0.17/0.43 ( ( pt_name @ X2 )
% 0.17/0.43 => ! [Pi: list @ ( product_prod @ name @ name ),X3: X2,X6: set @ X2] :
% 0.17/0.43 ( ( perm @ name @ $o @ Pi @ ( member @ X2 @ X3 @ X6 ) )
% 0.17/0.43 = ( member @ X2 @ ( perm @ name @ X2 @ Pi @ X3 ) @ ( perm @ name @ ( set @ X2 ) @ Pi @ X6 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % in_eqvt
% 0.17/0.43 thf(fact_68_eq__eqvt,axiom,
% 0.17/0.43 ! [X2: $tType] :
% 0.17/0.43 ( ( pt_name @ X2 )
% 0.17/0.43 => ! [Pi: list @ ( product_prod @ name @ name ),X3: X2,Y: X2] :
% 0.17/0.43 ( ( perm @ name @ $o @ Pi @ ( X3 = Y ) )
% 0.17/0.43 = ( ( perm @ name @ X2 @ Pi @ X3 )
% 0.17/0.43 = ( perm @ name @ X2 @ Pi @ Y ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % eq_eqvt
% 0.17/0.43 thf(fact_69_residual_Oinject_I2_J,axiom,
% 0.17/0.43 ! [X22: late_freeRes,X1: pi,Y2: late_freeRes,Y1: pi] :
% 0.17/0.43 ( ( ( late_FreeR @ X22 @ X1 )
% 0.17/0.43 = ( late_FreeR @ Y2 @ Y1 ) )
% 0.17/0.43 = ( ( X22 = Y2 )
% 0.17/0.43 & ( X1 = Y1 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % residual.inject(2)
% 0.17/0.43 thf(fact_70_fresh__prod,axiom,
% 0.17/0.43 ! [A: $tType,X: $tType,B: $tType,A2: X,X3: A,Y: B] :
% 0.17/0.43 ( ( fresh @ X @ ( product_prod @ A @ B ) @ A2 @ ( product_Pair @ A @ B @ X3 @ Y ) )
% 0.17/0.43 = ( ( fresh @ X @ A @ A2 @ X3 )
% 0.17/0.43 & ( fresh @ X @ B @ A2 @ Y ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % fresh_prod
% 0.17/0.43 thf(fact_71_list_Oinject,axiom,
% 0.17/0.43 ! [A: $tType,X21: A,X222: list @ A,Y21: A,Y22: list @ A] :
% 0.17/0.43 ( ( ( cons @ A @ X21 @ X222 )
% 0.17/0.43 = ( cons @ A @ Y21 @ Y22 ) )
% 0.17/0.43 = ( ( X21 = Y21 )
% 0.17/0.43 & ( X222 = Y22 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % list.inject
% 0.17/0.43 thf(fact_72_old_Oprod_Oinject,axiom,
% 0.17/0.43 ! [A: $tType,B: $tType,A2: A,B2: B,A5: A,B4: B] :
% 0.17/0.43 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 0.17/0.43 = ( product_Pair @ A @ B @ A5 @ B4 ) )
% 0.17/0.43 = ( ( A2 = A5 )
% 0.17/0.43 & ( B2 = B4 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % old.prod.inject
% 0.17/0.43 thf(fact_73_prod_Oinject,axiom,
% 0.17/0.43 ! [A: $tType,B: $tType,X1: A,X22: B,Y1: A,Y2: B] :
% 0.17/0.43 ( ( ( product_Pair @ A @ B @ X1 @ X22 )
% 0.17/0.43 = ( product_Pair @ A @ B @ Y1 @ Y2 ) )
% 0.17/0.43 = ( ( X1 = Y1 )
% 0.17/0.43 & ( X22 = Y2 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % prod.inject
% 0.17/0.43 thf(fact_74_cClose1_Ohyps_I2_J,axiom,
% 0.17/0.43 late_transitions @ ( res @ x @ q ) @ ( late_BoundR @ ( late_BoundOutputS @ aa ) @ z @ q2 ) ).
% 0.17/0.43
% 0.17/0.43 % cClose1.hyps(2)
% 0.17/0.43 thf(fact_75_fresh__list__cons,axiom,
% 0.17/0.43 ! [X: $tType,A: $tType,A2: X,X3: A,Xs: list @ A] :
% 0.17/0.43 ( ( fresh @ X @ ( list @ A ) @ A2 @ ( cons @ A @ X3 @ Xs ) )
% 0.17/0.43 = ( ( fresh @ X @ A @ A2 @ X3 )
% 0.17/0.43 & ( fresh @ X @ ( list @ A ) @ A2 @ Xs ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % fresh_list_cons
% 0.17/0.43 thf(fact_76_fresh__prodD_I2_J,axiom,
% 0.17/0.43 ! [B: $tType,A: $tType,C3: $tType,A2: A,X3: B,Y: C3] :
% 0.17/0.43 ( ( fresh @ A @ ( product_prod @ B @ C3 ) @ A2 @ ( product_Pair @ B @ C3 @ X3 @ Y ) )
% 0.17/0.43 => ( fresh @ A @ C3 @ A2 @ Y ) ) ).
% 0.17/0.43
% 0.17/0.43 % fresh_prodD(2)
% 0.17/0.43 thf(fact_77_fresh__prodD_I1_J,axiom,
% 0.17/0.43 ! [C3: $tType,A: $tType,B: $tType,A2: A,X3: B,Y: C3] :
% 0.17/0.43 ( ( fresh @ A @ ( product_prod @ B @ C3 ) @ A2 @ ( product_Pair @ B @ C3 @ X3 @ Y ) )
% 0.17/0.43 => ( fresh @ A @ B @ A2 @ X3 ) ) ).
% 0.17/0.43
% 0.17/0.43 % fresh_prodD(1)
% 0.17/0.43 thf(fact_78_cons__eqvt,axiom,
% 0.17/0.43 ! [X: $tType,A: $tType,Pi: list @ ( product_prod @ X @ X ),X3: A,Xs: list @ A] :
% 0.17/0.43 ( ( perm @ X @ ( list @ A ) @ Pi @ ( cons @ A @ X3 @ Xs ) )
% 0.17/0.43 = ( cons @ A @ ( perm @ X @ A @ Pi @ X3 ) @ ( perm @ X @ ( list @ A ) @ Pi @ Xs ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % cons_eqvt
% 0.17/0.43 thf(fact_79_strict__sorted_Oinduct,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( linorder @ A )
% 0.17/0.43 => ! [P: ( list @ A ) > $o,A0: list @ A] :
% 0.17/0.43 ( ( P @ ( nil @ A ) )
% 0.17/0.43 => ( ! [X5: A,Ys: list @ A] :
% 0.17/0.43 ( ( P @ Ys )
% 0.17/0.43 => ( P @ ( cons @ A @ X5 @ Ys ) ) )
% 0.17/0.43 => ( P @ A0 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % strict_sorted.induct
% 0.17/0.43 thf(fact_80_true__eqvt,axiom,
% 0.17/0.43 ! [A: $tType,Pi: list @ ( product_prod @ A @ A )] : ( perm @ A @ $o @ Pi @ $true ) ).
% 0.17/0.43
% 0.17/0.43 % true_eqvt
% 0.17/0.43 thf(fact_81_false__eqvt,axiom,
% 0.17/0.43 ! [A: $tType,Pi: list @ ( product_prod @ A @ A )] :
% 0.17/0.43 ~ ( perm @ A @ $o @ Pi @ $false ) ).
% 0.17/0.43
% 0.17/0.43 % false_eqvt
% 0.17/0.43 thf(fact_82_freeRes_Ofresh_I2_J,axiom,
% 0.17/0.43 ! [A2: name] : ( fresh @ name @ late_freeRes @ A2 @ late_TauR ) ).
% 0.17/0.43
% 0.17/0.43 % freeRes.fresh(2)
% 0.17/0.43 thf(fact_83_residual_Ofresh_I2_J,axiom,
% 0.17/0.43 ! [A2: name,X22: late_freeRes,X1: pi] :
% 0.17/0.43 ( ( fresh @ name @ late_residual @ A2 @ ( late_FreeR @ X22 @ X1 ) )
% 0.17/0.43 = ( ( fresh @ name @ late_freeRes @ A2 @ X22 )
% 0.17/0.43 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % residual.fresh(2)
% 0.17/0.43 thf(fact_84_freeRes_Ofresh_I1_J,axiom,
% 0.17/0.43 ! [A2: name,X22: name,X1: name] :
% 0.17/0.43 ( ( fresh @ name @ late_freeRes @ A2 @ ( late_OutputR @ X22 @ X1 ) )
% 0.17/0.43 = ( ( fresh @ name @ name @ A2 @ X22 )
% 0.17/0.43 & ( fresh @ name @ name @ A2 @ X1 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % freeRes.fresh(1)
% 0.17/0.43 thf(fact_85_subject_Ofresh_I2_J,axiom,
% 0.17/0.43 ! [A2: name,X1: name] :
% 0.17/0.43 ( ( fresh @ name @ late_subject @ A2 @ ( late_BoundOutputS @ X1 ) )
% 0.17/0.43 = ( fresh @ name @ name @ A2 @ X1 ) ) ).
% 0.17/0.43
% 0.17/0.43 % subject.fresh(2)
% 0.17/0.43 thf(fact_86_pi_Operm_I9_J,axiom,
% 0.17/0.43 ! [Pi: list @ ( product_prod @ name @ name ),X1: name,X22: pi] :
% 0.17/0.43 ( ( perm @ name @ pi @ Pi @ ( res @ X1 @ X22 ) )
% 0.17/0.43 = ( res @ ( perm @ name @ name @ Pi @ X1 ) @ ( perm @ name @ pi @ Pi @ X22 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % pi.perm(9)
% 0.17/0.43 thf(fact_87_cClose1_Ohyps_I1_J,axiom,
% 0.17/0.43 late_transitions @ p @ ( late_BoundR @ ( late_InputS @ aa ) @ y @ p2 ) ).
% 0.17/0.43
% 0.17/0.43 % cClose1.hyps(1)
% 0.17/0.43 thf(fact_88_residual_Operm_I1_J,axiom,
% 0.17/0.43 ! [Pi: list @ ( product_prod @ name @ name ),X32: late_subject,X1: name,X22: pi] :
% 0.17/0.43 ( ( perm @ name @ late_residual @ Pi @ ( late_BoundR @ X32 @ X1 @ X22 ) )
% 0.17/0.43 = ( late_BoundR @ ( perm @ name @ late_subject @ Pi @ X32 ) @ ( perm @ name @ name @ Pi @ X1 ) @ ( perm @ name @ pi @ Pi @ X22 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % residual.perm(1)
% 0.17/0.43 thf(fact_89_name__bij,axiom,
% 0.17/0.43 ! [Pi: list @ ( product_prod @ name @ name ),X3: name,Y: name] :
% 0.17/0.43 ( ( ( perm @ name @ name @ Pi @ X3 )
% 0.17/0.43 = ( perm @ name @ name @ Pi @ Y ) )
% 0.17/0.43 = ( X3 = Y ) ) ).
% 0.17/0.43
% 0.17/0.43 % name_bij
% 0.17/0.43 thf(fact_90_imp__eqvt,axiom,
% 0.17/0.43 ! [A: $tType,Pi: list @ ( product_prod @ A @ A ),A4: $o,B5: $o] :
% 0.17/0.43 ( ( perm @ A @ $o @ Pi
% 0.17/0.43 @ ( A4
% 0.17/0.43 => B5 ) )
% 0.17/0.43 = ( ( perm @ A @ $o @ Pi @ A4 )
% 0.17/0.43 => ( perm @ A @ $o @ Pi @ B5 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % imp_eqvt
% 0.17/0.43 thf(fact_91_neg__eqvt,axiom,
% 0.17/0.43 ! [A: $tType,Pi: list @ ( product_prod @ A @ A ),A4: $o] :
% 0.17/0.43 ( ( perm @ A @ $o @ Pi @ ~ A4 )
% 0.17/0.43 = ( ~ ( perm @ A @ $o @ Pi @ A4 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % neg_eqvt
% 0.17/0.43 thf(fact_92_conj__eqvt,axiom,
% 0.17/0.43 ! [A: $tType,Pi: list @ ( product_prod @ A @ A ),A4: $o,B5: $o] :
% 0.17/0.43 ( ( perm @ A @ $o @ Pi
% 0.17/0.43 @ ( A4
% 0.17/0.43 & B5 ) )
% 0.17/0.43 = ( ( perm @ A @ $o @ Pi @ A4 )
% 0.17/0.43 & ( perm @ A @ $o @ Pi @ B5 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % conj_eqvt
% 0.17/0.43 thf(fact_93_disj__eqvt,axiom,
% 0.17/0.43 ! [A: $tType,Pi: list @ ( product_prod @ A @ A ),A4: $o,B5: $o] :
% 0.17/0.43 ( ( perm @ A @ $o @ Pi
% 0.17/0.43 @ ( A4
% 0.17/0.43 | B5 ) )
% 0.17/0.43 = ( ( perm @ A @ $o @ Pi @ A4 )
% 0.17/0.43 | ( perm @ A @ $o @ Pi @ B5 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % disj_eqvt
% 0.17/0.43 thf(fact_94_perm__boolE,axiom,
% 0.17/0.43 ! [A: $tType,Pi: list @ ( product_prod @ A @ A )] :
% 0.17/0.43 ~ ( perm @ A @ $o @ Pi @ $false ) ).
% 0.17/0.43
% 0.17/0.43 % perm_boolE
% 0.17/0.43 thf(fact_95_perm__boolI,axiom,
% 0.17/0.43 ! [A: $tType,P: $o,Pi: list @ ( product_prod @ A @ A )] :
% 0.17/0.43 ( P
% 0.17/0.43 => ( perm @ A @ $o @ Pi @ P ) ) ).
% 0.17/0.43
% 0.17/0.43 % perm_boolI
% 0.17/0.43 thf(fact_96_Late__Semantics_OResB,axiom,
% 0.17/0.43 ! [P: pi,A2: late_subject,X3: name,P2: pi,Y: name] :
% 0.17/0.43 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X3 @ P2 ) )
% 0.17/0.43 => ( ( fresh @ name @ late_subject @ Y @ A2 )
% 0.17/0.43 => ( ( Y != X3 )
% 0.17/0.43 => ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A2 @ X3 @ ( res @ Y @ P2 ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % Late_Semantics.ResB
% 0.17/0.43 thf(fact_97_pt__set__bij3,axiom,
% 0.17/0.43 ! [X: $tType,A: $tType,Pi: list @ ( product_prod @ X @ X ),X3: A,X6: set @ A] :
% 0.17/0.43 ( ( perm @ X @ $o @ Pi @ ( member @ A @ X3 @ X6 ) )
% 0.17/0.43 = ( member @ A @ X3 @ X6 ) ) ).
% 0.17/0.43
% 0.17/0.43 % pt_set_bij3
% 0.17/0.43 thf(fact_98_perm__bool__def,axiom,
% 0.17/0.43 ! [X: $tType] :
% 0.17/0.43 ( ( perm @ X @ $o )
% 0.17/0.43 = ( ^ [Pi3: list @ ( product_prod @ X @ X ),B3: $o] : B3 ) ) ).
% 0.17/0.43
% 0.17/0.43 % perm_bool_def
% 0.17/0.43 thf(fact_99_nil__eqvt,axiom,
% 0.17/0.43 ! [X: $tType,A: $tType,Pi: list @ ( product_prod @ X @ X )] :
% 0.17/0.43 ( ( perm @ X @ ( list @ A ) @ Pi @ ( nil @ A ) )
% 0.17/0.43 = ( nil @ A ) ) ).
% 0.17/0.43
% 0.17/0.43 % nil_eqvt
% 0.17/0.43 thf(fact_100_fresh__list__nil,axiom,
% 0.17/0.43 ! [X: $tType,A: $tType,A2: X] : ( fresh @ X @ ( list @ A ) @ A2 @ ( nil @ A ) ) ).
% 0.17/0.43
% 0.17/0.43 % fresh_list_nil
% 0.17/0.43 thf(fact_101_transitions_OResB,axiom,
% 0.17/0.43 ! [P: pi,A2: late_subject,X3: name,P2: pi,Y: name] :
% 0.17/0.43 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X3 @ P2 ) )
% 0.17/0.43 => ( ( fresh @ name @ late_subject @ Y @ A2 )
% 0.17/0.43 => ( ( Y != X3 )
% 0.17/0.43 => ( ( fresh @ name @ pi @ X3 @ P )
% 0.17/0.43 => ( ( fresh @ name @ late_subject @ X3 @ A2 )
% 0.17/0.43 => ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A2 @ X3 @ ( res @ Y @ P2 ) ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % transitions.ResB
% 0.17/0.43 thf(fact_102_map__tailrec__rev_Ocases,axiom,
% 0.17/0.43 ! [A: $tType,B: $tType,X3: product_prod @ ( A > B ) @ ( product_prod @ ( list @ A ) @ ( list @ B ) )] :
% 0.17/0.43 ( ! [F2: A > B,Bs: list @ B] :
% 0.17/0.43 ( X3
% 0.17/0.43 != ( product_Pair @ ( A > B ) @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ F2 @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ ( nil @ A ) @ Bs ) ) )
% 0.17/0.43 => ~ ! [F2: A > B,A6: A,As: list @ A,Bs: list @ B] :
% 0.17/0.43 ( X3
% 0.17/0.43 != ( product_Pair @ ( A > B ) @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ F2 @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ ( cons @ A @ A6 @ As ) @ Bs ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % map_tailrec_rev.cases
% 0.17/0.43 thf(fact_103_resCasesF,axiom,
% 0.17/0.43 ! [X3: name,P: pi,Alpha: late_freeRes,XP: pi,F3: pi > $o] :
% 0.17/0.43 ( ( late_transitions @ ( res @ X3 @ P ) @ ( late_FreeR @ Alpha @ XP ) )
% 0.17/0.43 => ( ! [P3: pi] :
% 0.17/0.43 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P3 ) )
% 0.17/0.43 => ( ( fresh @ name @ late_freeRes @ X3 @ Alpha )
% 0.17/0.43 => ( F3 @ ( res @ X3 @ P3 ) ) ) )
% 0.17/0.43 => ( F3 @ XP ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % resCasesF
% 0.17/0.43 thf(fact_104_resCasesF_H,axiom,
% 0.17/0.43 ! [X3: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 0.17/0.43 ( ( late_transitions @ ( res @ X3 @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 0.17/0.43 => ~ ! [P4: pi,Alpha2: late_freeRes,P3: pi,Y3: name] :
% 0.17/0.43 ( ( ( res @ X3 @ P )
% 0.17/0.43 = ( res @ Y3 @ P4 ) )
% 0.17/0.43 => ( ( ( late_FreeR @ Alpha @ P2 )
% 0.17/0.43 = ( late_FreeR @ Alpha2 @ ( res @ Y3 @ P3 ) ) )
% 0.17/0.43 => ( ( late_transitions @ P4 @ ( late_FreeR @ Alpha2 @ P3 ) )
% 0.17/0.43 => ~ ( fresh @ name @ late_freeRes @ Y3 @ Alpha2 ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % resCasesF'
% 0.17/0.43 thf(fact_105_ResF,axiom,
% 0.17/0.43 ! [P: pi,Alpha: late_freeRes,P2: pi,Y: name] :
% 0.17/0.43 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 0.17/0.43 => ( ( fresh @ name @ late_freeRes @ Y @ Alpha )
% 0.17/0.43 => ( late_transitions @ ( res @ Y @ P ) @ ( late_FreeR @ Alpha @ ( res @ Y @ P2 ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % ResF
% 0.17/0.43 thf(fact_106_freshBoundDerivative_I1_J,axiom,
% 0.17/0.43 ! [P: pi,A2: late_subject,X3: name,P2: pi,Y: name] :
% 0.17/0.43 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X3 @ P2 ) )
% 0.17/0.43 => ( ( fresh @ name @ pi @ Y @ P )
% 0.17/0.43 => ( fresh @ name @ late_subject @ Y @ A2 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % freshBoundDerivative(1)
% 0.17/0.43 thf(fact_107_freshRes,axiom,
% 0.17/0.43 ! [A2: name,P: pi] : ( fresh @ name @ pi @ A2 @ ( res @ A2 @ P ) ) ).
% 0.17/0.43
% 0.17/0.43 % freshRes
% 0.17/0.43 thf(fact_108_residual_Odistinct_I1_J,axiom,
% 0.17/0.43 ! [Subject: late_subject,Name: name,Pi: pi,FreeRes2: late_freeRes,Pi4: pi] :
% 0.17/0.43 ( ( late_BoundR @ Subject @ Name @ Pi )
% 0.17/0.43 != ( late_FreeR @ FreeRes2 @ Pi4 ) ) ).
% 0.17/0.43
% 0.17/0.43 % residual.distinct(1)
% 0.17/0.43 thf(fact_109_residual_Oinducts,axiom,
% 0.17/0.43 ! [P: late_residual > $o,Residual: late_residual] :
% 0.17/0.43 ( ! [Subject2: late_subject,Name3: name,Pi5: pi] : ( P @ ( late_BoundR @ Subject2 @ Name3 @ Pi5 ) )
% 0.17/0.43 => ( ! [FreeRes3: late_freeRes,Pi5: pi] : ( P @ ( late_FreeR @ FreeRes3 @ Pi5 ) )
% 0.17/0.43 => ( P @ Residual ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % residual.inducts
% 0.17/0.43 thf(fact_110_resCases_H,axiom,
% 0.17/0.43 ! [X3: name,P: pi,Rs: late_residual] :
% 0.17/0.43 ( ( late_transitions @ ( res @ X3 @ P ) @ Rs )
% 0.17/0.43 => ( ! [P4: pi,A6: name,B6: name] :
% 0.17/0.43 ( ( ( res @ X3 @ P )
% 0.17/0.43 = ( res @ B6 @ P4 ) )
% 0.17/0.43 => ! [P3: pi] :
% 0.17/0.43 ( ( Rs
% 0.17/0.43 = ( late_BoundR @ ( late_BoundOutputS @ A6 ) @ B6 @ P3 ) )
% 0.17/0.43 => ( ( late_transitions @ P4 @ ( late_FreeR @ ( late_OutputR @ A6 @ B6 ) @ P3 ) )
% 0.17/0.43 => ( A6 = B6 ) ) ) )
% 0.17/0.43 => ( ! [P4: pi,A6: late_subject,X5: name,P3: pi,Y3: name] :
% 0.17/0.43 ( ( ( res @ X3 @ P )
% 0.17/0.43 = ( res @ Y3 @ P4 ) )
% 0.17/0.43 => ( ( Rs
% 0.17/0.43 = ( late_BoundR @ A6 @ X5 @ ( res @ Y3 @ P3 ) ) )
% 0.17/0.43 => ( ( late_transitions @ P4 @ ( late_BoundR @ A6 @ X5 @ P3 ) )
% 0.17/0.43 => ( ( fresh @ name @ late_subject @ Y3 @ A6 )
% 0.17/0.43 => ( ( Y3 != X5 )
% 0.17/0.43 => ( ( fresh @ name @ pi @ X5 @ P4 )
% 0.17/0.43 => ~ ( fresh @ name @ late_subject @ X5 @ A6 ) ) ) ) ) ) )
% 0.17/0.43 => ~ ! [P4: pi,Alpha2: late_freeRes,P3: pi,Y3: name] :
% 0.17/0.43 ( ( ( res @ X3 @ P )
% 0.17/0.43 = ( res @ Y3 @ P4 ) )
% 0.17/0.43 => ( ( Rs
% 0.17/0.43 = ( late_FreeR @ Alpha2 @ ( res @ Y3 @ P3 ) ) )
% 0.17/0.43 => ( ( late_transitions @ P4 @ ( late_FreeR @ Alpha2 @ P3 ) )
% 0.17/0.43 => ~ ( fresh @ name @ late_freeRes @ Y3 @ Alpha2 ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % resCases'
% 0.17/0.43 thf(fact_111_arg__min__list_Ocases,axiom,
% 0.17/0.43 ! [B: $tType,A: $tType] :
% 0.17/0.43 ( ( linorder @ B )
% 0.17/0.43 => ! [X3: product_prod @ ( A > B ) @ ( list @ A )] :
% 0.17/0.43 ( ! [F2: A > B,X5: A] :
% 0.17/0.43 ( X3
% 0.17/0.43 != ( product_Pair @ ( A > B ) @ ( list @ A ) @ F2 @ ( cons @ A @ X5 @ ( nil @ A ) ) ) )
% 0.17/0.43 => ( ! [F2: A > B,X5: A,Y3: A,Zs: list @ A] :
% 0.17/0.43 ( X3
% 0.17/0.43 != ( product_Pair @ ( A > B ) @ ( list @ A ) @ F2 @ ( cons @ A @ X5 @ ( cons @ A @ Y3 @ Zs ) ) ) )
% 0.17/0.43 => ~ ! [A6: A > B] :
% 0.17/0.43 ( X3
% 0.17/0.43 != ( product_Pair @ ( A > B ) @ ( list @ A ) @ A6 @ ( nil @ A ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % arg_min_list.cases
% 0.17/0.43 thf(fact_112_sorted__wrt_Ocases,axiom,
% 0.17/0.43 ! [A: $tType,X3: product_prod @ ( A > A > $o ) @ ( list @ A )] :
% 0.17/0.43 ( ! [P4: A > A > $o] :
% 0.17/0.43 ( X3
% 0.17/0.43 != ( product_Pair @ ( A > A > $o ) @ ( list @ A ) @ P4 @ ( nil @ A ) ) )
% 0.17/0.43 => ~ ! [P4: A > A > $o,X5: A,Ys: list @ A] :
% 0.17/0.43 ( X3
% 0.17/0.43 != ( product_Pair @ ( A > A > $o ) @ ( list @ A ) @ P4 @ ( cons @ A @ X5 @ Ys ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % sorted_wrt.cases
% 0.17/0.43 thf(fact_113_successively_Ocases,axiom,
% 0.17/0.43 ! [A: $tType,X3: product_prod @ ( A > A > $o ) @ ( list @ A )] :
% 0.17/0.43 ( ! [P4: A > A > $o] :
% 0.17/0.43 ( X3
% 0.17/0.43 != ( product_Pair @ ( A > A > $o ) @ ( list @ A ) @ P4 @ ( nil @ A ) ) )
% 0.17/0.43 => ( ! [P4: A > A > $o,X5: A] :
% 0.17/0.43 ( X3
% 0.17/0.43 != ( product_Pair @ ( A > A > $o ) @ ( list @ A ) @ P4 @ ( cons @ A @ X5 @ ( nil @ A ) ) ) )
% 0.17/0.43 => ~ ! [P4: A > A > $o,X5: A,Y3: A,Xs2: list @ A] :
% 0.17/0.43 ( X3
% 0.17/0.43 != ( product_Pair @ ( A > A > $o ) @ ( list @ A ) @ P4 @ ( cons @ A @ X5 @ ( cons @ A @ Y3 @ Xs2 ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % successively.cases
% 0.17/0.43 thf(fact_114_splice_Ocases,axiom,
% 0.17/0.43 ! [A: $tType,X3: product_prod @ ( list @ A ) @ ( list @ A )] :
% 0.17/0.43 ( ! [Ys: list @ A] :
% 0.17/0.43 ( X3
% 0.17/0.43 != ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( nil @ A ) @ Ys ) )
% 0.17/0.43 => ~ ! [X5: A,Xs2: list @ A,Ys: list @ A] :
% 0.17/0.43 ( X3
% 0.17/0.43 != ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X5 @ Xs2 ) @ Ys ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % splice.cases
% 0.17/0.43 thf(fact_115_shuffles_Ocases,axiom,
% 0.17/0.43 ! [A: $tType,X3: product_prod @ ( list @ A ) @ ( list @ A )] :
% 0.17/0.43 ( ! [Ys: list @ A] :
% 0.17/0.43 ( X3
% 0.17/0.43 != ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( nil @ A ) @ Ys ) )
% 0.17/0.43 => ( ! [Xs2: list @ A] :
% 0.17/0.43 ( X3
% 0.17/0.43 != ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs2 @ ( nil @ A ) ) )
% 0.17/0.43 => ~ ! [X5: A,Xs2: list @ A,Y3: A,Ys: list @ A] :
% 0.17/0.43 ( X3
% 0.17/0.43 != ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X5 @ Xs2 ) @ ( cons @ A @ Y3 @ Ys ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % shuffles.cases
% 0.17/0.43 thf(fact_116_resCasesB_H,axiom,
% 0.17/0.43 ! [X7: name,P: pi,A2: late_subject,Y4: name,P2: pi] :
% 0.17/0.43 ( ( late_transitions @ ( res @ X7 @ P ) @ ( late_BoundR @ A2 @ Y4 @ P2 ) )
% 0.17/0.43 => ( ! [P4: pi,A6: name,B6: name] :
% 0.17/0.43 ( ( ( res @ X7 @ P )
% 0.17/0.43 = ( res @ B6 @ P4 ) )
% 0.17/0.43 => ! [P3: pi] :
% 0.17/0.43 ( ( ( late_BoundR @ A2 @ Y4 @ P2 )
% 0.17/0.43 = ( late_BoundR @ ( late_BoundOutputS @ A6 ) @ B6 @ P3 ) )
% 0.17/0.43 => ( ( late_transitions @ P4 @ ( late_FreeR @ ( late_OutputR @ A6 @ B6 ) @ P3 ) )
% 0.17/0.43 => ( A6 = B6 ) ) ) )
% 0.17/0.43 => ~ ! [P4: pi,A6: late_subject,X5: name,P3: pi,Y3: name] :
% 0.17/0.43 ( ( ( res @ X7 @ P )
% 0.17/0.43 = ( res @ Y3 @ P4 ) )
% 0.17/0.43 => ( ( ( late_BoundR @ A2 @ Y4 @ P2 )
% 0.17/0.43 = ( late_BoundR @ A6 @ X5 @ ( res @ Y3 @ P3 ) ) )
% 0.17/0.43 => ( ( late_transitions @ P4 @ ( late_BoundR @ A6 @ X5 @ P3 ) )
% 0.17/0.43 => ( ( fresh @ name @ late_subject @ Y3 @ A6 )
% 0.17/0.43 => ( ( Y3 != X5 )
% 0.17/0.43 => ( ( fresh @ name @ pi @ X5 @ P4 )
% 0.17/0.43 => ~ ( fresh @ name @ late_subject @ X5 @ A6 ) ) ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % resCasesB'
% 0.17/0.43 thf(fact_117_Open,axiom,
% 0.17/0.43 ! [P: pi,A2: name,B2: name,P2: pi] :
% 0.17/0.43 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P2 ) )
% 0.17/0.43 => ( ( A2 != B2 )
% 0.17/0.43 => ( late_transitions @ ( res @ B2 @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ B2 @ P2 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % Open
% 0.17/0.43 thf(fact_118_freshResidual,axiom,
% 0.17/0.43 ! [P: pi,Rs: late_residual,X3: name] :
% 0.17/0.43 ( ( late_transitions @ P @ Rs )
% 0.17/0.43 => ( ( fresh @ name @ pi @ X3 @ P )
% 0.17/0.43 => ( fresh @ name @ late_residual @ X3 @ Rs ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % freshResidual
% 0.17/0.43 thf(fact_119_freshBoundDerivative_I2_J,axiom,
% 0.17/0.43 ! [P: pi,A2: late_subject,X3: name,P2: pi,Y: name] :
% 0.17/0.43 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X3 @ P2 ) )
% 0.17/0.43 => ( ( fresh @ name @ pi @ Y @ P )
% 0.17/0.43 => ( ( Y != X3 )
% 0.17/0.43 => ( fresh @ name @ pi @ Y @ P2 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % freshBoundDerivative(2)
% 0.17/0.43 thf(fact_120_residual_Ostrong__inducts,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( fs_name @ A )
% 0.17/0.43 => ! [P: A > late_residual > $o,Z: A,Residual: late_residual] :
% 0.17/0.43 ( ! [Subject2: late_subject,Name3: name,Pi5: pi,Z2: A] :
% 0.17/0.43 ( ( fresh @ name @ A @ Name3 @ Z2 )
% 0.17/0.43 => ( ( fresh @ name @ late_subject @ Name3 @ Subject2 )
% 0.17/0.43 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi5 ) ) ) )
% 0.17/0.43 => ( ! [FreeRes3: late_freeRes,Pi5: pi,Z2: A] : ( P @ Z2 @ ( late_FreeR @ FreeRes3 @ Pi5 ) )
% 0.17/0.43 => ( P @ Z @ Residual ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % residual.strong_inducts
% 0.17/0.43 thf(fact_121_residual_Ostrong__induct,axiom,
% 0.17/0.43 ! [N: $tType] :
% 0.17/0.43 ( ( fs_name @ N )
% 0.17/0.43 => ! [P: N > late_residual > $o,Z: N,Residual: late_residual] :
% 0.17/0.43 ( ! [Subject2: late_subject,Name3: name,Pi5: pi,Z2: N] :
% 0.17/0.43 ( ( fresh @ name @ N @ Name3 @ Z2 )
% 0.17/0.43 => ( ( fresh @ name @ late_subject @ Name3 @ Subject2 )
% 0.17/0.43 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi5 ) ) ) )
% 0.17/0.43 => ( ! [FreeRes3: late_freeRes,Pi5: pi,Z2: N] : ( P @ Z2 @ ( late_FreeR @ FreeRes3 @ Pi5 ) )
% 0.17/0.43 => ( P @ Z @ Residual ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % residual.strong_induct
% 0.17/0.43 thf(fact_122_resCasesB,axiom,
% 0.17/0.43 ! [Y: name,P: pi,A2: late_subject,X3: name,YP: pi,F3: late_subject > pi > $o] :
% 0.17/0.43 ( ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A2 @ X3 @ YP ) )
% 0.17/0.43 => ( ( X3 != Y )
% 0.17/0.43 => ( ( fresh @ name @ pi @ X3 @ P )
% 0.17/0.43 => ( ! [B6: name,P3: pi] :
% 0.17/0.43 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ B6 @ Y ) @ P3 ) )
% 0.17/0.43 => ( ( B6 != Y )
% 0.17/0.43 => ( ( A2
% 0.17/0.43 = ( late_BoundOutputS @ B6 ) )
% 0.17/0.43 => ( F3 @ ( late_BoundOutputS @ B6 ) @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ X3 @ Y ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ P3 ) ) ) ) )
% 0.17/0.43 => ( ! [P3: pi] :
% 0.17/0.43 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X3 @ P3 ) )
% 0.17/0.43 => ( ( fresh @ name @ late_subject @ Y @ A2 )
% 0.17/0.43 => ( F3 @ A2 @ ( res @ Y @ P3 ) ) ) )
% 0.17/0.43 => ( F3 @ A2 @ YP ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % resCasesB
% 0.17/0.43 thf(fact_123_freshFreeDerivative_I1_J,axiom,
% 0.17/0.43 ! [P: pi,Alpha: late_freeRes,P2: pi,Y: name] :
% 0.17/0.43 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 0.17/0.43 => ( ( fresh @ name @ pi @ Y @ P )
% 0.17/0.43 => ( fresh @ name @ late_freeRes @ Y @ Alpha ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % freshFreeDerivative(1)
% 0.17/0.43 thf(fact_124_surj__pair,axiom,
% 0.17/0.43 ! [A: $tType,B: $tType,P5: product_prod @ A @ B] :
% 0.17/0.43 ? [X5: A,Y3: B] :
% 0.17/0.43 ( P5
% 0.17/0.43 = ( product_Pair @ A @ B @ X5 @ Y3 ) ) ).
% 0.17/0.43
% 0.17/0.43 % surj_pair
% 0.17/0.43 thf(fact_125_prod__cases,axiom,
% 0.17/0.43 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,P5: product_prod @ A @ B] :
% 0.17/0.43 ( ! [A6: A,B6: B] : ( P @ ( product_Pair @ A @ B @ A6 @ B6 ) )
% 0.17/0.43 => ( P @ P5 ) ) ).
% 0.17/0.43
% 0.17/0.43 % prod_cases
% 0.17/0.43 thf(fact_126_Pair__inject,axiom,
% 0.17/0.43 ! [A: $tType,B: $tType,A2: A,B2: B,A5: A,B4: B] :
% 0.17/0.43 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 0.17/0.43 = ( product_Pair @ A @ B @ A5 @ B4 ) )
% 0.17/0.43 => ~ ( ( A2 = A5 )
% 0.17/0.43 => ( B2 != B4 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % Pair_inject
% 0.17/0.43 thf(fact_127_prod__cases3,axiom,
% 0.17/0.43 ! [A: $tType,B: $tType,C3: $tType,Y: product_prod @ A @ ( product_prod @ B @ C3 )] :
% 0.17/0.43 ~ ! [A6: A,B6: B,C: C3] :
% 0.17/0.43 ( Y
% 0.17/0.43 != ( product_Pair @ A @ ( product_prod @ B @ C3 ) @ A6 @ ( product_Pair @ B @ C3 @ B6 @ C ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % prod_cases3
% 0.17/0.43 thf(fact_128_prod__cases4,axiom,
% 0.17/0.43 ! [A: $tType,B: $tType,C3: $tType,D: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ D ) )] :
% 0.17/0.43 ~ ! [A6: A,B6: B,C: C3,D2: D] :
% 0.17/0.43 ( Y
% 0.17/0.43 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C3 @ D ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C3 @ D ) @ B6 @ ( product_Pair @ C3 @ D @ C @ D2 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % prod_cases4
% 0.17/0.43 thf(fact_129_prod__cases5,axiom,
% 0.17/0.43 ! [A: $tType,B: $tType,C3: $tType,D: $tType,E: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D @ E ) ) )] :
% 0.17/0.43 ~ ! [A6: A,B6: B,C: C3,D2: D,E2: E] :
% 0.17/0.43 ( Y
% 0.17/0.43 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D @ E ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C3 @ ( product_prod @ D @ E ) ) @ B6 @ ( product_Pair @ C3 @ ( product_prod @ D @ E ) @ C @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % prod_cases5
% 0.17/0.43 thf(fact_130_prod__cases6,axiom,
% 0.17/0.43 ! [A: $tType,B: $tType,C3: $tType,D: $tType,E: $tType,F4: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) ) )] :
% 0.17/0.43 ~ ! [A6: A,B6: B,C: C3,D2: D,E2: E,F2: F4] :
% 0.17/0.43 ( Y
% 0.17/0.43 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C3 @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) ) @ B6 @ ( product_Pair @ C3 @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) @ C @ ( product_Pair @ D @ ( product_prod @ E @ F4 ) @ D2 @ ( product_Pair @ E @ F4 @ E2 @ F2 ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % prod_cases6
% 0.17/0.43 thf(fact_131_prod__cases7,axiom,
% 0.17/0.43 ! [A: $tType,B: $tType,C3: $tType,D: $tType,E: $tType,F4: $tType,G2: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G2 ) ) ) ) )] :
% 0.17/0.43 ~ ! [A6: A,B6: B,C: C3,D2: D,E2: E,F2: F4,G3: G2] :
% 0.17/0.43 ( Y
% 0.17/0.43 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G2 ) ) ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C3 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G2 ) ) ) ) @ B6 @ ( product_Pair @ C3 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G2 ) ) ) @ C @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G2 ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F4 @ G2 ) @ E2 @ ( product_Pair @ F4 @ G2 @ F2 @ G3 ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % prod_cases7
% 0.17/0.43 thf(fact_132_prod__induct3,axiom,
% 0.17/0.43 ! [C3: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ C3 ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ C3 )] :
% 0.17/0.43 ( ! [A6: A,B6: B,C: C3] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ C3 ) @ A6 @ ( product_Pair @ B @ C3 @ B6 @ C ) ) )
% 0.17/0.43 => ( P @ X3 ) ) ).
% 0.17/0.43
% 0.17/0.43 % prod_induct3
% 0.17/0.43 thf(fact_133_prod__induct4,axiom,
% 0.17/0.43 ! [D: $tType,C3: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ D ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ D ) )] :
% 0.17/0.43 ( ! [A6: A,B6: B,C: C3,D2: D] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C3 @ D ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C3 @ D ) @ B6 @ ( product_Pair @ C3 @ D @ C @ D2 ) ) ) )
% 0.17/0.43 => ( P @ X3 ) ) ).
% 0.17/0.43
% 0.17/0.43 % prod_induct4
% 0.17/0.43 thf(fact_134_prod__induct5,axiom,
% 0.17/0.43 ! [E: $tType,D: $tType,C3: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D @ E ) ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D @ E ) ) )] :
% 0.17/0.43 ( ! [A6: A,B6: B,C: C3,D2: D,E2: E] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D @ E ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C3 @ ( product_prod @ D @ E ) ) @ B6 @ ( product_Pair @ C3 @ ( product_prod @ D @ E ) @ C @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) )
% 0.17/0.43 => ( P @ X3 ) ) ).
% 0.17/0.43
% 0.17/0.43 % prod_induct5
% 0.17/0.43 thf(fact_135_prod__induct6,axiom,
% 0.17/0.43 ! [F4: $tType,E: $tType,D: $tType,C3: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) ) )] :
% 0.17/0.43 ( ! [A6: A,B6: B,C: C3,D2: D,E2: E,F2: F4] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C3 @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) ) @ B6 @ ( product_Pair @ C3 @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) @ C @ ( product_Pair @ D @ ( product_prod @ E @ F4 ) @ D2 @ ( product_Pair @ E @ F4 @ E2 @ F2 ) ) ) ) ) )
% 0.17/0.43 => ( P @ X3 ) ) ).
% 0.17/0.43
% 0.17/0.43 % prod_induct6
% 0.17/0.43 thf(fact_136_prod__induct7,axiom,
% 0.17/0.43 ! [G2: $tType,F4: $tType,E: $tType,D: $tType,C3: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G2 ) ) ) ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G2 ) ) ) ) )] :
% 0.17/0.43 ( ! [A6: A,B6: B,C: C3,D2: D,E2: E,F2: F4,G3: G2] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G2 ) ) ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C3 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G2 ) ) ) ) @ B6 @ ( product_Pair @ C3 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G2 ) ) ) @ C @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G2 ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F4 @ G2 ) @ E2 @ ( product_Pair @ F4 @ G2 @ F2 @ G3 ) ) ) ) ) ) )
% 0.17/0.43 => ( P @ X3 ) ) ).
% 0.17/0.43
% 0.17/0.43 % prod_induct7
% 0.17/0.43 thf(fact_137_old_Oprod_Oexhaust,axiom,
% 0.17/0.43 ! [A: $tType,B: $tType,Y: product_prod @ A @ B] :
% 0.17/0.43 ~ ! [A6: A,B6: B] :
% 0.17/0.43 ( Y
% 0.17/0.43 != ( product_Pair @ A @ B @ A6 @ B6 ) ) ).
% 0.17/0.43
% 0.17/0.43 % old.prod.exhaust
% 0.17/0.43 thf(fact_138_old_Oprod_Oinducts,axiom,
% 0.17/0.43 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,Prod: product_prod @ A @ B] :
% 0.17/0.43 ( ! [A6: A,B6: B] : ( P @ ( product_Pair @ A @ B @ A6 @ B6 ) )
% 0.17/0.43 => ( P @ Prod ) ) ).
% 0.17/0.43
% 0.17/0.43 % old.prod.inducts
% 0.17/0.43 thf(fact_139_not__Cons__self2,axiom,
% 0.17/0.43 ! [A: $tType,X3: A,Xs: list @ A] :
% 0.17/0.43 ( ( cons @ A @ X3 @ Xs )
% 0.17/0.43 != Xs ) ).
% 0.17/0.43
% 0.17/0.43 % not_Cons_self2
% 0.17/0.43 thf(fact_140_allE__Nil,axiom,
% 0.17/0.43 ! [A: $tType,P: ( list @ A ) > $o] :
% 0.17/0.43 ( ! [X_1: list @ A] : ( P @ X_1 )
% 0.17/0.43 => ( P @ ( nil @ A ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % allE_Nil
% 0.17/0.43 thf(fact_141_if__eqvt,axiom,
% 0.17/0.43 ! [A: $tType,B: $tType,Pi: list @ ( product_prod @ A @ A ),B2: $o,C1: B,C22: B] :
% 0.17/0.43 ( ( ( perm @ A @ $o @ Pi @ B2 )
% 0.17/0.43 => ( ( perm @ A @ B @ Pi @ ( if @ B @ B2 @ C1 @ C22 ) )
% 0.17/0.43 = ( perm @ A @ B @ Pi @ C1 ) ) )
% 0.17/0.43 & ( ~ ( perm @ A @ $o @ Pi @ B2 )
% 0.17/0.43 => ( ( perm @ A @ B @ Pi @ ( if @ B @ B2 @ C1 @ C22 ) )
% 0.17/0.43 = ( perm @ A @ B @ Pi @ C22 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % if_eqvt
% 0.17/0.43 thf(fact_142_pt__bij3,axiom,
% 0.17/0.43 ! [X: $tType,A: $tType,X3: A,Y: A,Pi: list @ ( product_prod @ X @ X )] :
% 0.17/0.43 ( ( X3 = Y )
% 0.17/0.43 => ( ( perm @ X @ A @ Pi @ X3 )
% 0.17/0.43 = ( perm @ X @ A @ Pi @ Y ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % pt_bij3
% 0.17/0.43 thf(fact_143_abs__fun__if,axiom,
% 0.17/0.43 ! [X: $tType,A: $tType,C2: $o,Pi: list @ ( product_prod @ X @ X ),X3: A,Y: A] :
% 0.17/0.43 ( ( C2
% 0.17/0.43 => ( ( perm @ X @ A @ Pi @ ( if @ A @ C2 @ X3 @ Y ) )
% 0.17/0.43 = ( perm @ X @ A @ Pi @ X3 ) ) )
% 0.17/0.43 & ( ~ C2
% 0.17/0.43 => ( ( perm @ X @ A @ Pi @ ( if @ A @ C2 @ X3 @ Y ) )
% 0.17/0.43 = ( perm @ X @ A @ Pi @ Y ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % abs_fun_if
% 0.17/0.43 thf(fact_144_alphaRes,axiom,
% 0.17/0.43 ! [C2: name,P: pi,A2: name] :
% 0.17/0.43 ( ( fresh @ name @ pi @ C2 @ P )
% 0.17/0.43 => ( ( res @ A2 @ P )
% 0.17/0.43 = ( res @ C2 @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ C2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ P ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % alphaRes
% 0.17/0.43 thf(fact_145_alphaBoundResidual,axiom,
% 0.17/0.43 ! [X7: name,P: pi,A2: late_subject,X3: name] :
% 0.17/0.43 ( ( fresh @ name @ pi @ X7 @ P )
% 0.17/0.43 => ( ( late_BoundR @ A2 @ X3 @ P )
% 0.17/0.43 = ( late_BoundR @ A2 @ X7 @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ X3 @ X7 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ P ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % alphaBoundResidual
% 0.17/0.43 thf(fact_146_perm__prod_Osimps,axiom,
% 0.17/0.43 ! [A: $tType,X: $tType,B: $tType,Pi: list @ ( product_prod @ X @ X ),X3: A,Y: B] :
% 0.17/0.43 ( ( perm @ X @ ( product_prod @ A @ B ) @ Pi @ ( product_Pair @ A @ B @ X3 @ Y ) )
% 0.17/0.43 = ( product_Pair @ A @ B @ ( perm @ X @ A @ Pi @ X3 ) @ ( perm @ X @ B @ Pi @ Y ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % perm_prod.simps
% 0.17/0.43 thf(fact_147_list_Odistinct_I1_J,axiom,
% 0.17/0.43 ! [A: $tType,X21: A,X222: list @ A] :
% 0.17/0.43 ( ( nil @ A )
% 0.17/0.43 != ( cons @ A @ X21 @ X222 ) ) ).
% 0.17/0.43
% 0.17/0.43 % list.distinct(1)
% 0.17/0.43 thf(fact_148_list_OdiscI,axiom,
% 0.17/0.43 ! [A: $tType,List: list @ A,X21: A,X222: list @ A] :
% 0.17/0.43 ( ( List
% 0.17/0.43 = ( cons @ A @ X21 @ X222 ) )
% 0.17/0.43 => ( List
% 0.17/0.43 != ( nil @ A ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % list.discI
% 0.17/0.43 thf(fact_149_list_Oexhaust,axiom,
% 0.17/0.43 ! [A: $tType,Y: list @ A] :
% 0.17/0.43 ( ( Y
% 0.17/0.43 != ( nil @ A ) )
% 0.17/0.43 => ~ ! [X212: A,X223: list @ A] :
% 0.17/0.43 ( Y
% 0.17/0.43 != ( cons @ A @ X212 @ X223 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % list.exhaust
% 0.17/0.43 thf(fact_150_list_Oinducts,axiom,
% 0.17/0.43 ! [A: $tType,P: ( list @ A ) > $o,List: list @ A] :
% 0.17/0.43 ( ( P @ ( nil @ A ) )
% 0.17/0.43 => ( ! [X13: A,X23: list @ A] :
% 0.17/0.43 ( ( P @ X23 )
% 0.17/0.43 => ( P @ ( cons @ A @ X13 @ X23 ) ) )
% 0.17/0.43 => ( P @ List ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % list.inducts
% 0.17/0.43 thf(fact_151_neq__Nil__conv,axiom,
% 0.17/0.43 ! [A: $tType,Xs: list @ A] :
% 0.17/0.43 ( ( Xs
% 0.17/0.43 != ( nil @ A ) )
% 0.17/0.43 = ( ? [Y5: A,Ys2: list @ A] :
% 0.17/0.43 ( Xs
% 0.17/0.43 = ( cons @ A @ Y5 @ Ys2 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % neq_Nil_conv
% 0.17/0.43 thf(fact_152_list__induct2_H,axiom,
% 0.17/0.43 ! [A: $tType,B: $tType,P: ( list @ A ) > ( list @ B ) > $o,Xs: list @ A,Ys3: list @ B] :
% 0.17/0.43 ( ( P @ ( nil @ A ) @ ( nil @ B ) )
% 0.17/0.43 => ( ! [X5: A,Xs2: list @ A] : ( P @ ( cons @ A @ X5 @ Xs2 ) @ ( nil @ B ) )
% 0.17/0.43 => ( ! [Y3: B,Ys: list @ B] : ( P @ ( nil @ A ) @ ( cons @ B @ Y3 @ Ys ) )
% 0.17/0.43 => ( ! [X5: A,Xs2: list @ A,Y3: B,Ys: list @ B] :
% 0.17/0.43 ( ( P @ Xs2 @ Ys )
% 0.17/0.43 => ( P @ ( cons @ A @ X5 @ Xs2 ) @ ( cons @ B @ Y3 @ Ys ) ) )
% 0.17/0.43 => ( P @ Xs @ Ys3 ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % list_induct2'
% 0.17/0.43 thf(fact_153_splice_Oinduct,axiom,
% 0.17/0.43 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 0.17/0.43 ( ! [X_1: list @ A] : ( P @ ( nil @ A ) @ X_1 )
% 0.17/0.43 => ( ! [X5: A,Xs2: list @ A,Ys: list @ A] :
% 0.17/0.43 ( ( P @ Ys @ Xs2 )
% 0.17/0.43 => ( P @ ( cons @ A @ X5 @ Xs2 ) @ Ys ) )
% 0.17/0.43 => ( P @ A0 @ A1 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % splice.induct
% 0.17/0.43 thf(fact_154_induct__list012,axiom,
% 0.17/0.43 ! [A: $tType,P: ( list @ A ) > $o,Xs: list @ A] :
% 0.17/0.43 ( ( P @ ( nil @ A ) )
% 0.17/0.43 => ( ! [X5: A] : ( P @ ( cons @ A @ X5 @ ( nil @ A ) ) )
% 0.17/0.43 => ( ! [X5: A,Y3: A,Zs: list @ A] :
% 0.17/0.43 ( ( P @ Zs )
% 0.17/0.43 => ( ( P @ ( cons @ A @ Y3 @ Zs ) )
% 0.17/0.43 => ( P @ ( cons @ A @ X5 @ ( cons @ A @ Y3 @ Zs ) ) ) ) )
% 0.17/0.43 => ( P @ Xs ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % induct_list012
% 0.17/0.43 thf(fact_155_min__list_Ocases,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( ord @ A )
% 0.17/0.43 => ! [X3: list @ A] :
% 0.17/0.43 ( ! [X5: A,Xs2: list @ A] :
% 0.17/0.43 ( X3
% 0.17/0.43 != ( cons @ A @ X5 @ Xs2 ) )
% 0.17/0.43 => ( X3
% 0.17/0.43 = ( nil @ A ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % min_list.cases
% 0.17/0.43 thf(fact_156_min__list_Oinduct,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( ord @ A )
% 0.17/0.43 => ! [P: ( list @ A ) > $o,A0: list @ A] :
% 0.17/0.43 ( ! [X5: A,Xs2: list @ A] :
% 0.17/0.43 ( ! [X213: A,X224: list @ A] :
% 0.17/0.43 ( ( Xs2
% 0.17/0.43 = ( cons @ A @ X213 @ X224 ) )
% 0.17/0.43 => ( P @ Xs2 ) )
% 0.17/0.43 => ( P @ ( cons @ A @ X5 @ Xs2 ) ) )
% 0.17/0.43 => ( ( P @ ( nil @ A ) )
% 0.17/0.43 => ( P @ A0 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % min_list.induct
% 0.17/0.43 thf(fact_157_shuffles_Oinduct,axiom,
% 0.17/0.43 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 0.17/0.43 ( ! [X_1: list @ A] : ( P @ ( nil @ A ) @ X_1 )
% 0.17/0.43 => ( ! [Xs2: list @ A] : ( P @ Xs2 @ ( nil @ A ) )
% 0.17/0.43 => ( ! [X5: A,Xs2: list @ A,Y3: A,Ys: list @ A] :
% 0.17/0.43 ( ( P @ Xs2 @ ( cons @ A @ Y3 @ Ys ) )
% 0.17/0.43 => ( ( P @ ( cons @ A @ X5 @ Xs2 ) @ Ys )
% 0.17/0.43 => ( P @ ( cons @ A @ X5 @ Xs2 ) @ ( cons @ A @ Y3 @ Ys ) ) ) )
% 0.17/0.43 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % shuffles.induct
% 0.17/0.43 thf(fact_158_transpose_Ocases,axiom,
% 0.17/0.43 ! [A: $tType,X3: list @ ( list @ A )] :
% 0.17/0.43 ( ( X3
% 0.17/0.43 != ( nil @ ( list @ A ) ) )
% 0.17/0.43 => ( ! [Xss: list @ ( list @ A )] :
% 0.17/0.43 ( X3
% 0.17/0.43 != ( cons @ ( list @ A ) @ ( nil @ A ) @ Xss ) )
% 0.17/0.43 => ~ ! [X5: A,Xs2: list @ A,Xss: list @ ( list @ A )] :
% 0.17/0.43 ( X3
% 0.17/0.43 != ( cons @ ( list @ A ) @ ( cons @ A @ X5 @ Xs2 ) @ Xss ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % transpose.cases
% 0.17/0.43 thf(fact_159_remdups__adj_Ocases,axiom,
% 0.17/0.43 ! [A: $tType,X3: list @ A] :
% 0.17/0.43 ( ( X3
% 0.17/0.43 != ( nil @ A ) )
% 0.17/0.43 => ( ! [X5: A] :
% 0.17/0.43 ( X3
% 0.17/0.43 != ( cons @ A @ X5 @ ( nil @ A ) ) )
% 0.17/0.43 => ~ ! [X5: A,Y3: A,Xs2: list @ A] :
% 0.17/0.43 ( X3
% 0.17/0.43 != ( cons @ A @ X5 @ ( cons @ A @ Y3 @ Xs2 ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % remdups_adj.cases
% 0.17/0.43 thf(fact_160_sorted__wrt_Oinduct,axiom,
% 0.17/0.43 ! [A: $tType,P: ( A > A > $o ) > ( list @ A ) > $o,A0: A > A > $o,A1: list @ A] :
% 0.17/0.43 ( ! [P4: A > A > $o] : ( P @ P4 @ ( nil @ A ) )
% 0.17/0.43 => ( ! [P4: A > A > $o,X5: A,Ys: list @ A] :
% 0.17/0.43 ( ( P @ P4 @ Ys )
% 0.17/0.43 => ( P @ P4 @ ( cons @ A @ X5 @ Ys ) ) )
% 0.17/0.43 => ( P @ A0 @ A1 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % sorted_wrt.induct
% 0.17/0.43 thf(fact_161_remdups__adj_Oinduct,axiom,
% 0.17/0.43 ! [A: $tType,P: ( list @ A ) > $o,A0: list @ A] :
% 0.17/0.43 ( ( P @ ( nil @ A ) )
% 0.17/0.43 => ( ! [X5: A] : ( P @ ( cons @ A @ X5 @ ( nil @ A ) ) )
% 0.17/0.43 => ( ! [X5: A,Y3: A,Xs2: list @ A] :
% 0.17/0.43 ( ( ( X5 = Y3 )
% 0.17/0.43 => ( P @ ( cons @ A @ X5 @ Xs2 ) ) )
% 0.17/0.43 => ( ( ( X5 != Y3 )
% 0.17/0.43 => ( P @ ( cons @ A @ Y3 @ Xs2 ) ) )
% 0.17/0.43 => ( P @ ( cons @ A @ X5 @ ( cons @ A @ Y3 @ Xs2 ) ) ) ) )
% 0.17/0.43 => ( P @ A0 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % remdups_adj.induct
% 0.17/0.43 thf(fact_162_arg__min__list_Oinduct,axiom,
% 0.17/0.43 ! [B: $tType,A: $tType] :
% 0.17/0.43 ( ( linorder @ B )
% 0.17/0.43 => ! [P: ( A > B ) > ( list @ A ) > $o,A0: A > B,A1: list @ A] :
% 0.17/0.43 ( ! [F2: A > B,X5: A] : ( P @ F2 @ ( cons @ A @ X5 @ ( nil @ A ) ) )
% 0.17/0.43 => ( ! [F2: A > B,X5: A,Y3: A,Zs: list @ A] :
% 0.17/0.43 ( ( P @ F2 @ ( cons @ A @ Y3 @ Zs ) )
% 0.17/0.43 => ( P @ F2 @ ( cons @ A @ X5 @ ( cons @ A @ Y3 @ Zs ) ) ) )
% 0.17/0.43 => ( ! [A6: A > B] : ( P @ A6 @ ( nil @ A ) )
% 0.17/0.43 => ( P @ A0 @ A1 ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % arg_min_list.induct
% 0.17/0.43 thf(fact_163_successively_Oinduct,axiom,
% 0.17/0.43 ! [A: $tType,P: ( A > A > $o ) > ( list @ A ) > $o,A0: A > A > $o,A1: list @ A] :
% 0.17/0.43 ( ! [P4: A > A > $o] : ( P @ P4 @ ( nil @ A ) )
% 0.17/0.43 => ( ! [P4: A > A > $o,X5: A] : ( P @ P4 @ ( cons @ A @ X5 @ ( nil @ A ) ) )
% 0.17/0.43 => ( ! [P4: A > A > $o,X5: A,Y3: A,Xs2: list @ A] :
% 0.17/0.43 ( ( P @ P4 @ ( cons @ A @ Y3 @ Xs2 ) )
% 0.17/0.43 => ( P @ P4 @ ( cons @ A @ X5 @ ( cons @ A @ Y3 @ Xs2 ) ) ) )
% 0.17/0.43 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % successively.induct
% 0.17/0.43 thf(fact_164_list__nonempty__induct,axiom,
% 0.17/0.43 ! [A: $tType,Xs: list @ A,P: ( list @ A ) > $o] :
% 0.17/0.43 ( ( Xs
% 0.17/0.43 != ( nil @ A ) )
% 0.17/0.43 => ( ! [X5: A] : ( P @ ( cons @ A @ X5 @ ( nil @ A ) ) )
% 0.17/0.43 => ( ! [X5: A,Xs2: list @ A] :
% 0.17/0.43 ( ( Xs2
% 0.17/0.43 != ( nil @ A ) )
% 0.17/0.43 => ( ( P @ Xs2 )
% 0.17/0.43 => ( P @ ( cons @ A @ X5 @ Xs2 ) ) ) )
% 0.17/0.43 => ( P @ Xs ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % list_nonempty_induct
% 0.17/0.43 thf(fact_165_map__tailrec__rev_Oinduct,axiom,
% 0.17/0.43 ! [A: $tType,B: $tType,P: ( A > B ) > ( list @ A ) > ( list @ B ) > $o,A0: A > B,A1: list @ A,A22: list @ B] :
% 0.17/0.43 ( ! [F2: A > B,X_1: list @ B] : ( P @ F2 @ ( nil @ A ) @ X_1 )
% 0.17/0.43 => ( ! [F2: A > B,A6: A,As: list @ A,Bs: list @ B] :
% 0.17/0.43 ( ( P @ F2 @ As @ ( cons @ B @ ( F2 @ A6 ) @ Bs ) )
% 0.17/0.43 => ( P @ F2 @ ( cons @ A @ A6 @ As ) @ Bs ) )
% 0.17/0.43 => ( P @ A0 @ A1 @ A22 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % map_tailrec_rev.induct
% 0.17/0.43 thf(fact_166_strict__sorted_Ocases,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( linorder @ A )
% 0.17/0.43 => ! [X3: list @ A] :
% 0.17/0.43 ( ( X3
% 0.17/0.43 != ( nil @ A ) )
% 0.17/0.43 => ~ ! [X5: A,Ys: list @ A] :
% 0.17/0.43 ( X3
% 0.17/0.43 != ( cons @ A @ X5 @ Ys ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % strict_sorted.cases
% 0.17/0.43 thf(fact_167_Free_Ohyps,axiom,
% 0.17/0.43 late_transitions @ ( par @ p @ ( res @ x @ q ) ) @ ( late_FreeR @ alpha @ pxQ ) ).
% 0.17/0.43
% 0.17/0.43 % Free.hyps
% 0.17/0.43 thf(fact_168_old_Oprod_Orec,axiom,
% 0.17/0.43 ! [A: $tType,T: $tType,B: $tType,F1: A > B > T,A2: A,B2: B] :
% 0.17/0.43 ( ( product_rec_prod @ A @ B @ T @ F1 @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 0.17/0.43 = ( F1 @ A2 @ B2 ) ) ).
% 0.17/0.43
% 0.17/0.43 % old.prod.rec
% 0.17/0.43 thf(fact_169_supports__def,axiom,
% 0.17/0.43 ! [A: $tType,X: $tType] :
% 0.17/0.43 ( ( supports @ X @ A )
% 0.17/0.43 = ( ^ [S: set @ X,X4: A] :
% 0.17/0.43 ! [A3: X,B3: X] :
% 0.17/0.43 ( ( ~ ( member @ X @ A3 @ S )
% 0.17/0.43 & ~ ( member @ X @ B3 @ S ) )
% 0.17/0.43 => ( ( perm @ X @ A @ ( cons @ ( product_prod @ X @ X ) @ ( product_Pair @ X @ X @ A3 @ B3 ) @ ( nil @ ( product_prod @ X @ X ) ) ) @ X4 )
% 0.17/0.43 = X4 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % supports_def
% 0.17/0.43 thf(fact_170_perm__residual__Rep_Osimps_I2_J,axiom,
% 0.17/0.43 ! [X: $tType,Pi: list @ ( product_prod @ X @ X ),FreeRes: late_freeRes,Pia: pi] :
% 0.17/0.43 ( ( perm @ X @ late_residual_Rep @ Pi @ ( late_r347633188eR_Rep @ FreeRes @ Pia ) )
% 0.17/0.43 = ( late_r347633188eR_Rep @ ( perm @ X @ late_freeRes @ Pi @ FreeRes ) @ ( perm @ X @ pi @ Pi @ Pia ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % perm_residual_Rep.simps(2)
% 0.17/0.43 thf(fact_171_alphaInput,axiom,
% 0.17/0.43 ! [C2: name,P: pi,A2: name,X3: name] :
% 0.17/0.43 ( ( fresh @ name @ pi @ C2 @ P )
% 0.17/0.43 => ( ( input @ A2 @ X3 @ P )
% 0.17/0.43 = ( input @ A2 @ C2 @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ X3 @ C2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ P ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % alphaInput
% 0.17/0.43 thf(fact_172_name__calc_I1_J,axiom,
% 0.17/0.43 ! [A2: name,B2: name,Pi: list @ ( product_prod @ name @ name ),X3: name] :
% 0.17/0.43 ( ( perm @ name @ name @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ Pi ) @ X3 )
% 0.17/0.43 = ( swap @ name @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( perm @ name @ name @ Pi @ X3 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % name_calc(1)
% 0.17/0.43 thf(fact_173_Late__Semantics1_Osubject_Oinject_I1_J,axiom,
% 0.17/0.43 ! [X1: name,Y1: name] :
% 0.17/0.43 ( ( ( late_InputS @ X1 )
% 0.17/0.43 = ( late_InputS @ Y1 ) )
% 0.17/0.43 = ( X1 = Y1 ) ) ).
% 0.17/0.43
% 0.17/0.43 % Late_Semantics1.subject.inject(1)
% 0.17/0.43 thf(fact_174_residual__Rep_Oinject_I2_J,axiom,
% 0.17/0.43 ! [X21: late_freeRes,X222: pi,Y21: late_freeRes,Y22: pi] :
% 0.17/0.43 ( ( ( late_r347633188eR_Rep @ X21 @ X222 )
% 0.17/0.43 = ( late_r347633188eR_Rep @ Y21 @ Y22 ) )
% 0.17/0.43 = ( ( X21 = Y21 )
% 0.17/0.43 & ( X222 = Y22 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % residual_Rep.inject(2)
% 0.17/0.43 thf(fact_175_pi_Ofresh_I8_J,axiom,
% 0.17/0.43 ! [A2: name,X22: pi,X1: pi] :
% 0.17/0.43 ( ( fresh @ name @ pi @ A2 @ ( par @ X22 @ X1 ) )
% 0.17/0.43 = ( ( fresh @ name @ pi @ A2 @ X22 )
% 0.17/0.43 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % pi.fresh(8)
% 0.17/0.43 thf(fact_176_pi_Operm_I8_J,axiom,
% 0.17/0.43 ! [Pi: list @ ( product_prod @ name @ name ),X22: pi,X1: pi] :
% 0.17/0.43 ( ( perm @ name @ pi @ Pi @ ( par @ X22 @ X1 ) )
% 0.17/0.43 = ( par @ ( perm @ name @ pi @ Pi @ X22 ) @ ( perm @ name @ pi @ Pi @ X1 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % pi.perm(8)
% 0.17/0.43 thf(fact_177_pi_Operm_I4_J,axiom,
% 0.17/0.43 ! [Pi: list @ ( product_prod @ name @ name ),X32: name,X1: name,X22: pi] :
% 0.17/0.43 ( ( perm @ name @ pi @ Pi @ ( input @ X32 @ X1 @ X22 ) )
% 0.17/0.43 = ( input @ ( perm @ name @ name @ Pi @ X32 ) @ ( perm @ name @ name @ Pi @ X1 ) @ ( perm @ name @ pi @ Pi @ X22 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % pi.perm(4)
% 0.17/0.43 thf(fact_178_subject_Ofresh_I1_J,axiom,
% 0.17/0.43 ! [A2: name,X1: name] :
% 0.17/0.43 ( ( fresh @ name @ late_subject @ A2 @ ( late_InputS @ X1 ) )
% 0.17/0.43 = ( fresh @ name @ name @ A2 @ X1 ) ) ).
% 0.17/0.43
% 0.17/0.43 % subject.fresh(1)
% 0.17/0.43 thf(fact_179_subject_Operm_I1_J,axiom,
% 0.17/0.43 ! [Pi: list @ ( product_prod @ name @ name ),X1: name] :
% 0.17/0.43 ( ( perm @ name @ late_subject @ Pi @ ( late_InputS @ X1 ) )
% 0.17/0.43 = ( late_InputS @ ( perm @ name @ name @ Pi @ X1 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % subject.perm(1)
% 0.17/0.43 thf(fact_180_ScopeExt,axiom,
% 0.17/0.43 ! [Y: name,R: pi,Z: name,S2: pi] :
% 0.17/0.43 ( ( fresh @ name @ pi @ Y @ R )
% 0.17/0.43 => ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( res @ Y @ ( res @ Z @ ( par @ R @ S2 ) ) ) @ ( res @ Z @ ( par @ R @ ( res @ Y @ S2 ) ) ) ) @ rel ) ) ).
% 0.17/0.43
% 0.17/0.43 % ScopeExt
% 0.17/0.43 thf(fact_181_Res,axiom,
% 0.17/0.43 ! [Y: name,R: pi,S2: pi] :
% 0.17/0.43 ( ( fresh @ name @ pi @ Y @ R )
% 0.17/0.43 => ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( res @ Y @ ( par @ R @ S2 ) ) @ ( par @ R @ ( res @ Y @ S2 ) ) ) @ rel ) ) ).
% 0.17/0.43
% 0.17/0.43 % Res
% 0.17/0.43 thf(fact_182_pi_Odistinct_I55_J,axiom,
% 0.17/0.43 ! [Name12: name,Name22: name,Pi: pi,Pi12: pi,Pi22: pi] :
% 0.17/0.43 ( ( input @ Name12 @ Name22 @ Pi )
% 0.17/0.43 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.17/0.43
% 0.17/0.43 % pi.distinct(55)
% 0.17/0.43 thf(fact_183_pi_Oinject_I7_J,axiom,
% 0.17/0.43 ! [X22: pi,X1: pi,Y2: pi,Y1: pi] :
% 0.17/0.43 ( ( ( par @ X22 @ X1 )
% 0.17/0.43 = ( par @ Y2 @ Y1 ) )
% 0.17/0.43 = ( ( X22 = Y2 )
% 0.17/0.43 & ( X1 = Y1 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % pi.inject(7)
% 0.17/0.43 thf(fact_184_pi_Odistinct_I85_J,axiom,
% 0.17/0.43 ! [Pi1: pi,Pi2: pi,Name4: name,Pi4: pi] :
% 0.17/0.43 ( ( par @ Pi1 @ Pi2 )
% 0.17/0.43 != ( res @ Name4 @ Pi4 ) ) ).
% 0.17/0.43
% 0.17/0.43 % pi.distinct(85)
% 0.17/0.43 thf(fact_185_transitions_OInput,axiom,
% 0.17/0.43 ! [X3: name,A2: name,P: pi] :
% 0.17/0.43 ( ( X3 != A2 )
% 0.17/0.43 => ( late_transitions @ ( input @ A2 @ X3 @ P ) @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ P ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % transitions.Input
% 0.17/0.43 thf(fact_186_Late__Semantics_OInput,axiom,
% 0.17/0.43 ! [A2: name,X3: name,P: pi] : ( late_transitions @ ( input @ A2 @ X3 @ P ) @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ P ) ) ).
% 0.17/0.43
% 0.17/0.43 % Late_Semantics.Input
% 0.17/0.43 thf(fact_187_pi_Odistinct_I57_J,axiom,
% 0.17/0.43 ! [Name12: name,Name22: name,Pi: pi,Name4: name,Pi4: pi] :
% 0.17/0.43 ( ( input @ Name12 @ Name22 @ Pi )
% 0.17/0.43 != ( res @ Name4 @ Pi4 ) ) ).
% 0.17/0.43
% 0.17/0.43 % pi.distinct(57)
% 0.17/0.43 thf(fact_188_Late__Semantics_Osubject_Odistinct_I1_J,axiom,
% 0.17/0.43 ! [Name: name,Name4: name] :
% 0.17/0.43 ( ( late_InputS @ Name )
% 0.17/0.43 != ( late_BoundOutputS @ Name4 ) ) ).
% 0.17/0.43
% 0.17/0.43 % Late_Semantics.subject.distinct(1)
% 0.17/0.43 thf(fact_189_Late__Semantics1_Osubject_Odistinct_I1_J,axiom,
% 0.17/0.43 ! [X1: name,X22: name] :
% 0.17/0.43 ( ( late_InputS @ X1 )
% 0.17/0.43 != ( late_BoundOutputS @ X22 ) ) ).
% 0.17/0.43
% 0.17/0.43 % Late_Semantics1.subject.distinct(1)
% 0.17/0.43 thf(fact_190_subject_Oinducts,axiom,
% 0.17/0.43 ! [P: late_subject > $o,Subject: late_subject] :
% 0.17/0.43 ( ! [Name3: name] : ( P @ ( late_InputS @ Name3 ) )
% 0.17/0.43 => ( ! [Name3: name] : ( P @ ( late_BoundOutputS @ Name3 ) )
% 0.17/0.43 => ( P @ Subject ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % subject.inducts
% 0.17/0.43 thf(fact_191_subject_Oexhaust,axiom,
% 0.17/0.43 ! [Y: late_subject] :
% 0.17/0.43 ( ! [X13: name] :
% 0.17/0.43 ( Y
% 0.17/0.43 != ( late_InputS @ X13 ) )
% 0.17/0.43 => ~ ! [X23: name] :
% 0.17/0.43 ( Y
% 0.17/0.43 != ( late_BoundOutputS @ X23 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % subject.exhaust
% 0.17/0.43 thf(fact_192_subject_Ostrong__induct_H,axiom,
% 0.17/0.43 ! [N: $tType,P: N > late_subject > $o,Z: N,Subject: late_subject] :
% 0.17/0.43 ( ! [Name3: name,Z2: N] : ( P @ Z2 @ ( late_InputS @ Name3 ) )
% 0.17/0.43 => ( ! [Name3: name,Z2: N] : ( P @ Z2 @ ( late_BoundOutputS @ Name3 ) )
% 0.17/0.43 => ( P @ Z @ Subject ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % subject.strong_induct'
% 0.17/0.43 thf(fact_193_subject_Ostrong__inducts,axiom,
% 0.17/0.43 ! [A: $tType,P: A > late_subject > $o,Z: A,Subject: late_subject] :
% 0.17/0.43 ( ! [Name3: name,Z2: A] : ( P @ Z2 @ ( late_InputS @ Name3 ) )
% 0.17/0.43 => ( ! [Name3: name,Z2: A] : ( P @ Z2 @ ( late_BoundOutputS @ Name3 ) )
% 0.17/0.43 => ( P @ Z @ Subject ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % subject.strong_inducts
% 0.17/0.43 thf(fact_194_Par2F,axiom,
% 0.17/0.43 ! [Q: pi,Alpha: late_freeRes,Q2: pi,P: pi] :
% 0.17/0.43 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 0.17/0.43 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha @ ( par @ P @ Q2 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % Par2F
% 0.17/0.43 thf(fact_195_Par1F,axiom,
% 0.17/0.43 ! [P: pi,Alpha: late_freeRes,P2: pi,Q: pi] :
% 0.17/0.43 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 0.17/0.43 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha @ ( par @ P2 @ Q ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % Par1F
% 0.17/0.43 thf(fact_196_name__calc_I3_J,axiom,
% 0.17/0.43 ! [A2: name,C2: name,B2: name] :
% 0.17/0.43 ( ( ( A2 = C2 )
% 0.17/0.43 => ( ( swap @ name @ ( product_Pair @ name @ name @ A2 @ B2 ) @ C2 )
% 0.17/0.43 = B2 ) )
% 0.17/0.43 & ( ( A2 != C2 )
% 0.17/0.43 => ( ( ( B2 = C2 )
% 0.17/0.43 => ( ( swap @ name @ ( product_Pair @ name @ name @ A2 @ B2 ) @ C2 )
% 0.17/0.43 = A2 ) )
% 0.17/0.43 & ( ( B2 != C2 )
% 0.17/0.43 => ( ( swap @ name @ ( product_Pair @ name @ name @ A2 @ B2 ) @ C2 )
% 0.17/0.43 = C2 ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % name_calc(3)
% 0.17/0.43 thf(fact_197_resTrans_I2_J,axiom,
% 0.17/0.43 ! [X3: name,Y: name,P: pi,Rs: late_residual] :
% 0.17/0.43 ~ ( late_transitions @ ( res @ X3 @ ( input @ X3 @ Y @ P ) ) @ Rs ) ).
% 0.17/0.43
% 0.17/0.43 % resTrans(2)
% 0.17/0.43 thf(fact_198_inputIneqTrans,axiom,
% 0.17/0.43 ! [A2: name,X3: name,P: pi,B2: late_subject,Y: name,P2: pi] :
% 0.17/0.43 ( ( late_transitions @ ( input @ A2 @ X3 @ P ) @ ( late_BoundR @ B2 @ Y @ P2 ) )
% 0.17/0.43 => ~ ( fresh @ name @ late_subject @ A2 @ B2 ) ) ).
% 0.17/0.43
% 0.17/0.43 % inputIneqTrans
% 0.17/0.43 thf(fact_199_inputFreeTrans,axiom,
% 0.17/0.43 ! [A2: name,X3: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 0.17/0.43 ~ ( late_transitions @ ( input @ A2 @ X3 @ P ) @ ( late_FreeR @ Alpha @ P2 ) ) ).
% 0.17/0.43
% 0.17/0.43 % inputFreeTrans
% 0.17/0.43 thf(fact_200_Late__Semantics_OPar1B,axiom,
% 0.17/0.43 ! [P: pi,A2: late_subject,X3: name,P2: pi,Q: pi] :
% 0.17/0.43 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X3 @ P2 ) )
% 0.17/0.43 => ( ( fresh @ name @ pi @ X3 @ Q )
% 0.17/0.43 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X3 @ ( par @ P2 @ Q ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % Late_Semantics.Par1B
% 0.17/0.43 thf(fact_201_Late__Semantics_OPar2B,axiom,
% 0.17/0.43 ! [Q: pi,A2: late_subject,X3: name,Q2: pi,P: pi] :
% 0.17/0.43 ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X3 @ Q2 ) )
% 0.17/0.43 => ( ( fresh @ name @ pi @ X3 @ P )
% 0.17/0.43 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X3 @ ( par @ P @ Q2 ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % Late_Semantics.Par2B
% 0.17/0.43 thf(fact_202_parCasesB,axiom,
% 0.17/0.43 ! [P: pi,Q: pi,A2: late_subject,X3: name,PQ: pi,Prop: pi > $o] :
% 0.17/0.43 ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X3 @ PQ ) )
% 0.17/0.43 => ( ( fresh @ name @ pi @ X3 @ P )
% 0.17/0.43 => ( ( fresh @ name @ pi @ X3 @ Q )
% 0.17/0.43 => ( ! [P3: pi] :
% 0.17/0.43 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X3 @ P3 ) )
% 0.17/0.43 => ( Prop @ ( par @ P3 @ Q ) ) )
% 0.17/0.43 => ( ! [Q3: pi] :
% 0.17/0.43 ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X3 @ Q3 ) )
% 0.17/0.43 => ( Prop @ ( par @ P @ Q3 ) ) )
% 0.17/0.43 => ( Prop @ PQ ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % parCasesB
% 0.17/0.43 thf(fact_203_parCasesB_H,axiom,
% 0.17/0.43 ! [P: pi,Q: pi,B2: late_subject,Y: name,P2: pi] :
% 0.17/0.43 ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ B2 @ Y @ P2 ) )
% 0.17/0.43 => ( ! [P4: pi,A6: late_subject,X5: name,P3: pi,Q4: pi] :
% 0.17/0.43 ( ( ( par @ P @ Q )
% 0.17/0.43 = ( par @ P4 @ Q4 ) )
% 0.17/0.43 => ( ( ( late_BoundR @ B2 @ Y @ P2 )
% 0.17/0.43 = ( late_BoundR @ A6 @ X5 @ ( par @ P3 @ Q4 ) ) )
% 0.17/0.43 => ( ( late_transitions @ P4 @ ( late_BoundR @ A6 @ X5 @ P3 ) )
% 0.17/0.43 => ( ( fresh @ name @ pi @ X5 @ P4 )
% 0.17/0.43 => ( ( fresh @ name @ pi @ X5 @ Q4 )
% 0.17/0.43 => ~ ( fresh @ name @ late_subject @ X5 @ A6 ) ) ) ) ) )
% 0.17/0.43 => ~ ! [Q4: pi,A6: late_subject,X5: name,Q3: pi,P4: pi] :
% 0.17/0.43 ( ( ( par @ P @ Q )
% 0.17/0.43 = ( par @ P4 @ Q4 ) )
% 0.17/0.43 => ( ( ( late_BoundR @ B2 @ Y @ P2 )
% 0.17/0.43 = ( late_BoundR @ A6 @ X5 @ ( par @ P4 @ Q3 ) ) )
% 0.17/0.43 => ( ( late_transitions @ Q4 @ ( late_BoundR @ A6 @ X5 @ Q3 ) )
% 0.17/0.43 => ( ( fresh @ name @ pi @ X5 @ P4 )
% 0.17/0.43 => ( ( fresh @ name @ pi @ X5 @ Q4 )
% 0.17/0.43 => ~ ( fresh @ name @ late_subject @ X5 @ A6 ) ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % parCasesB'
% 0.17/0.43 thf(fact_204_transitions_OPar1B,axiom,
% 0.17/0.43 ! [P: pi,A2: late_subject,X3: name,P2: pi,Q: pi] :
% 0.17/0.43 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X3 @ P2 ) )
% 0.17/0.43 => ( ( fresh @ name @ pi @ X3 @ P )
% 0.17/0.43 => ( ( fresh @ name @ pi @ X3 @ Q )
% 0.17/0.43 => ( ( fresh @ name @ late_subject @ X3 @ A2 )
% 0.17/0.43 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X3 @ ( par @ P2 @ Q ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % transitions.Par1B
% 0.17/0.43 thf(fact_205_transitions_OPar2B,axiom,
% 0.17/0.43 ! [Q: pi,A2: late_subject,X3: name,Q2: pi,P: pi] :
% 0.17/0.43 ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X3 @ Q2 ) )
% 0.17/0.43 => ( ( fresh @ name @ pi @ X3 @ P )
% 0.17/0.43 => ( ( fresh @ name @ pi @ X3 @ Q )
% 0.17/0.43 => ( ( fresh @ name @ late_subject @ X3 @ A2 )
% 0.17/0.43 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X3 @ ( par @ P @ Q2 ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % transitions.Par2B
% 0.17/0.43 thf(fact_206_resInputFreeTrans,axiom,
% 0.17/0.43 ! [X3: name,A2: name,Y: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 0.17/0.43 ~ ( late_transitions @ ( res @ X3 @ ( input @ A2 @ Y @ P ) ) @ ( late_FreeR @ Alpha @ P2 ) ) ).
% 0.17/0.43
% 0.17/0.43 % resInputFreeTrans
% 0.17/0.43 thf(fact_207_inputBoundOutputTrans,axiom,
% 0.17/0.43 ! [A2: name,X3: name,P: pi,B2: name,Y: name,P2: pi] :
% 0.17/0.43 ~ ( late_transitions @ ( input @ A2 @ X3 @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ B2 ) @ Y @ P2 ) ) ).
% 0.17/0.43
% 0.17/0.43 % inputBoundOutputTrans
% 0.17/0.43 thf(fact_208_inputCases,axiom,
% 0.17/0.43 ! [A2: name,X3: name,P: pi,B2: late_subject,Y: name,YP: pi,Prop: late_subject > name > pi > $o] :
% 0.17/0.43 ( ( late_transitions @ ( input @ A2 @ X3 @ P ) @ ( late_BoundR @ B2 @ Y @ YP ) )
% 0.17/0.43 => ( ( Y != A2 )
% 0.17/0.43 => ( ( Y != X3 )
% 0.17/0.43 => ( ( fresh @ name @ pi @ Y @ P )
% 0.17/0.43 => ( ( ( B2
% 0.17/0.43 = ( late_InputS @ A2 ) )
% 0.17/0.43 => ( ( YP
% 0.17/0.43 = ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ X3 @ Y ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ P ) )
% 0.17/0.43 => ( Prop @ ( late_InputS @ A2 ) @ Y @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ X3 @ Y ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ P ) ) ) )
% 0.17/0.43 => ( Prop @ B2 @ Y @ YP ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % inputCases
% 0.17/0.43 thf(fact_209_resInputBoundOutputTrans,axiom,
% 0.17/0.43 ! [X3: name,A2: name,Y: name,P: pi,B2: name,Z: name,P2: pi] :
% 0.17/0.43 ~ ( late_transitions @ ( res @ X3 @ ( input @ A2 @ Y @ P ) ) @ ( late_BoundR @ ( late_BoundOutputS @ B2 ) @ Z @ P2 ) ) ).
% 0.17/0.43
% 0.17/0.43 % resInputBoundOutputTrans
% 0.17/0.43 thf(fact_210_Late__Semantics_OClose1,axiom,
% 0.17/0.43 ! [P: pi,A2: name,X3: name,P2: pi,Q: pi,Y: name,Q2: pi] :
% 0.17/0.43 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ P2 ) )
% 0.17/0.43 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y @ Q2 ) )
% 0.17/0.43 => ( ( fresh @ name @ pi @ Y @ P )
% 0.17/0.43 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ ( subs @ P2 @ X3 @ Y ) @ Q2 ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % Late_Semantics.Close1
% 0.17/0.43 thf(fact_211_Late__Semantics_OClose2,axiom,
% 0.17/0.43 ! [P: pi,A2: name,Y: name,P2: pi,Q: pi,X3: name,Q2: pi] :
% 0.17/0.43 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y @ P2 ) )
% 0.17/0.43 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ Q2 ) )
% 0.17/0.44 => ( ( fresh @ name @ pi @ Y @ Q )
% 0.17/0.44 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ P2 @ ( subs @ Q2 @ X3 @ Y ) ) ) ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % Late_Semantics.Close2
% 0.17/0.44 thf(fact_212_transitions_OClose1,axiom,
% 0.17/0.44 ! [P: pi,A2: name,X3: name,P2: pi,Q: pi,Y: name,Q2: pi] :
% 0.17/0.44 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ P2 ) )
% 0.17/0.44 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y @ Q2 ) )
% 0.17/0.44 => ( ( fresh @ name @ pi @ X3 @ P )
% 0.17/0.44 => ( ( fresh @ name @ pi @ X3 @ Q )
% 0.17/0.44 => ( ( fresh @ name @ pi @ Y @ P )
% 0.17/0.44 => ( ( fresh @ name @ pi @ Y @ Q )
% 0.17/0.44 => ( ( X3 != A2 )
% 0.17/0.44 => ( ( fresh @ name @ pi @ X3 @ Q2 )
% 0.17/0.44 => ( ( Y != A2 )
% 0.17/0.44 => ( ( fresh @ name @ pi @ Y @ P2 )
% 0.17/0.44 => ( ( X3 != Y )
% 0.17/0.44 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ ( subs @ P2 @ X3 @ Y ) @ Q2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % transitions.Close1
% 0.17/0.44 thf(fact_213_EqvtRel,axiom,
% 0.17/0.44 eqvt @ pi @ rel ).
% 0.17/0.44
% 0.17/0.44 % EqvtRel
% 0.17/0.44 thf(fact_214_subst__identity,axiom,
% 0.17/0.44 ! [P: pi,A2: name] :
% 0.17/0.44 ( ( subs @ P @ A2 @ A2 )
% 0.17/0.44 = P ) ).
% 0.17/0.44
% 0.17/0.44 % subst_identity
% 0.17/0.44 thf(fact_215_simps_I9_J,axiom,
% 0.17/0.44 ! [X3: name,C2: name,D3: name,P: pi] :
% 0.17/0.44 ( ( X3 != C2 )
% 0.17/0.44 => ( ( X3 != D3 )
% 0.17/0.44 => ( ( subs @ ( res @ X3 @ P ) @ C2 @ D3 )
% 0.17/0.44 = ( res @ X3 @ ( subs @ P @ C2 @ D3 ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % simps(9)
% 0.17/0.44 thf(fact_216_simps_I8_J,axiom,
% 0.17/0.44 ! [P: pi,Q: pi,C2: name,D3: name] :
% 0.17/0.44 ( ( subs @ ( par @ P @ Q ) @ C2 @ D3 )
% 0.17/0.44 = ( par @ ( subs @ P @ C2 @ D3 ) @ ( subs @ Q @ C2 @ D3 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % simps(8)
% 0.17/0.44 thf(fact_217_substTrans,axiom,
% 0.17/0.44 ! [B2: name,P: pi,A2: name,C2: name] :
% 0.17/0.44 ( ( fresh @ name @ pi @ B2 @ P )
% 0.17/0.44 => ( ( subs @ ( subs @ P @ A2 @ B2 ) @ B2 @ C2 )
% 0.17/0.44 = ( subs @ P @ A2 @ C2 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % substTrans
% 0.17/0.44 thf(fact_218_forget,axiom,
% 0.17/0.44 ! [A2: name,P: pi,B2: name] :
% 0.17/0.44 ( ( fresh @ name @ pi @ A2 @ P )
% 0.17/0.44 => ( ( subs @ P @ A2 @ B2 )
% 0.17/0.44 = P ) ) ).
% 0.17/0.44
% 0.17/0.44 % forget
% 0.17/0.44 thf(fact_219_fresh__fact1,axiom,
% 0.17/0.44 ! [A2: name,P: pi,C2: name,B2: name] :
% 0.17/0.44 ( ( fresh @ name @ pi @ A2 @ P )
% 0.17/0.44 => ( ( A2 != C2 )
% 0.17/0.44 => ( fresh @ name @ pi @ A2 @ ( subs @ P @ B2 @ C2 ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % fresh_fact1
% 0.17/0.44 thf(fact_220_fresh__fact2,axiom,
% 0.17/0.44 ! [A2: name,B2: name,P: pi] :
% 0.17/0.44 ( ( A2 != B2 )
% 0.17/0.44 => ( fresh @ name @ pi @ A2 @ ( subs @ P @ A2 @ B2 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % fresh_fact2
% 0.17/0.44 thf(fact_221_Agent_OsubstRes3,axiom,
% 0.17/0.44 ! [B2: name,P: pi,A2: name] :
% 0.17/0.44 ( ( fresh @ name @ pi @ B2 @ P )
% 0.17/0.44 => ( ( subs @ ( res @ A2 @ P ) @ A2 @ B2 )
% 0.17/0.44 = ( res @ B2 @ ( subs @ P @ A2 @ B2 ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % Agent.substRes3
% 0.17/0.44 thf(fact_222_substRes2,axiom,
% 0.17/0.44 ! [B2: name,P: pi,A2: name] :
% 0.17/0.44 ( ( fresh @ name @ pi @ B2 @ P )
% 0.17/0.44 => ( ( res @ A2 @ P )
% 0.17/0.44 = ( res @ B2 @ ( subs @ P @ A2 @ B2 ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % substRes2
% 0.17/0.44 thf(fact_223_eqvt__subs,axiom,
% 0.17/0.44 ! [P5: list @ ( product_prod @ name @ name ),P: pi,A2: name,B2: name] :
% 0.17/0.44 ( ( perm @ name @ pi @ P5 @ ( subs @ P @ A2 @ B2 ) )
% 0.17/0.44 = ( subs @ ( perm @ name @ pi @ P5 @ P ) @ ( perm @ name @ name @ P5 @ A2 ) @ ( perm @ name @ name @ P5 @ B2 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % eqvt_subs
% 0.17/0.44 thf(fact_224_Strong__Late__Sim__SC__Mirabelle__dtpyqonsky_OsubstRes3,axiom,
% 0.17/0.44 ! [A2: name,P: pi,X3: name] :
% 0.17/0.44 ( ( subs @ ( res @ A2 @ P ) @ X3 @ A2 )
% 0.17/0.44 = ( res @ X3 @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ X3 @ A2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ P ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % Strong_Late_Sim_SC_Mirabelle_dtpyqonsky.substRes3
% 0.17/0.44 thf(fact_225_renaming,axiom,
% 0.17/0.44 ! [C2: name,P: pi,A2: name,B2: name] :
% 0.17/0.44 ( ( fresh @ name @ pi @ C2 @ P )
% 0.17/0.44 => ( ( subs @ P @ A2 @ B2 )
% 0.17/0.44 = ( subs @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ C2 @ A2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ P ) @ C2 @ B2 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % renaming
% 0.17/0.44 thf(fact_226_injPermSubst,axiom,
% 0.17/0.44 ! [B2: name,P: pi,A2: name] :
% 0.17/0.44 ( ( fresh @ name @ pi @ B2 @ P )
% 0.17/0.44 => ( ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ P )
% 0.17/0.44 = ( subs @ P @ A2 @ B2 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % injPermSubst
% 0.17/0.44 thf(fact_227_Late__Semantics_OComm1,axiom,
% 0.17/0.44 ! [P: pi,A2: name,X3: name,P2: pi,Q: pi,B2: name,Q2: pi] :
% 0.17/0.44 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ P2 ) )
% 0.17/0.44 => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ Q2 ) )
% 0.17/0.44 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P2 @ X3 @ B2 ) @ Q2 ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % Late_Semantics.Comm1
% 0.17/0.44 thf(fact_228_Late__Semantics_OComm2,axiom,
% 0.17/0.44 ! [P: pi,A2: name,B2: name,P2: pi,Q: pi,X3: name,Q2: pi] :
% 0.17/0.44 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P2 ) )
% 0.17/0.44 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ Q2 ) )
% 0.17/0.44 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P2 @ ( subs @ Q2 @ X3 @ B2 ) ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % Late_Semantics.Comm2
% 0.17/0.44 thf(fact_229_transitions_OComm2,axiom,
% 0.17/0.44 ! [P: pi,A2: name,B2: name,P2: pi,Q: pi,X3: name,Q2: pi] :
% 0.17/0.44 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P2 ) )
% 0.17/0.44 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ Q2 ) )
% 0.17/0.44 => ( ( fresh @ name @ pi @ X3 @ P )
% 0.17/0.44 => ( ( fresh @ name @ pi @ X3 @ Q )
% 0.17/0.44 => ( ( X3 != A2 )
% 0.17/0.44 => ( ( X3 != B2 )
% 0.17/0.44 => ( ( fresh @ name @ pi @ X3 @ P2 )
% 0.17/0.44 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P2 @ ( subs @ Q2 @ X3 @ B2 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % transitions.Comm2
% 0.17/0.44 thf(fact_230_transitions_OComm1,axiom,
% 0.17/0.44 ! [P: pi,A2: name,X3: name,P2: pi,Q: pi,B2: name,Q2: pi] :
% 0.17/0.44 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ P2 ) )
% 0.17/0.44 => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ Q2 ) )
% 0.17/0.44 => ( ( fresh @ name @ pi @ X3 @ P )
% 0.17/0.44 => ( ( fresh @ name @ pi @ X3 @ Q )
% 0.17/0.44 => ( ( X3 != A2 )
% 0.17/0.44 => ( ( X3 != B2 )
% 0.17/0.44 => ( ( fresh @ name @ pi @ X3 @ Q2 )
% 0.17/0.44 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P2 @ X3 @ B2 ) @ Q2 ) ) ) ) ) ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % transitions.Comm1
% 0.17/0.44 thf(fact_231_transitions_OClose2,axiom,
% 0.17/0.44 ! [P: pi,A2: name,Y: name,P2: pi,Q: pi,X3: name,Q2: pi] :
% 0.17/0.44 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y @ P2 ) )
% 0.17/0.44 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ Q2 ) )
% 0.17/0.44 => ( ( fresh @ name @ pi @ X3 @ P )
% 0.17/0.44 => ( ( fresh @ name @ pi @ X3 @ Q )
% 0.17/0.44 => ( ( fresh @ name @ pi @ Y @ P )
% 0.17/0.44 => ( ( fresh @ name @ pi @ Y @ Q )
% 0.17/0.44 => ( ( X3 != A2 )
% 0.17/0.44 => ( ( fresh @ name @ pi @ X3 @ P2 )
% 0.17/0.44 => ( ( Y != A2 )
% 0.17/0.44 => ( ( fresh @ name @ pi @ Y @ Q2 )
% 0.17/0.44 => ( ( X3 != Y )
% 0.17/0.44 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ P2 @ ( subs @ Q2 @ X3 @ Y ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % transitions.Close2
% 0.17/0.44 thf(fact_232_product__lists_Osimps_I1_J,axiom,
% 0.17/0.44 ! [A: $tType] :
% 0.17/0.44 ( ( product_lists @ A @ ( nil @ ( list @ A ) ) )
% 0.17/0.44 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % product_lists.simps(1)
% 0.17/0.44 thf(fact_233_Agent_Oswap__name__def,axiom,
% 0.17/0.44 ( ( swap @ name )
% 0.17/0.44 = swap_name ) ).
% 0.17/0.44
% 0.17/0.44 % Agent.swap_name_def
% 0.17/0.44 thf(fact_234_swap__name_Osimps,axiom,
% 0.17/0.44 ! [A2: name,C2: name,B2: name] :
% 0.17/0.44 ( ( ( A2 = C2 )
% 0.17/0.44 => ( ( swap_name @ ( product_Pair @ name @ name @ A2 @ B2 ) @ C2 )
% 0.17/0.44 = B2 ) )
% 0.17/0.44 & ( ( A2 != C2 )
% 0.17/0.44 => ( ( ( B2 = C2 )
% 0.17/0.44 => ( ( swap_name @ ( product_Pair @ name @ name @ A2 @ B2 ) @ C2 )
% 0.17/0.44 = A2 ) )
% 0.17/0.44 & ( ( B2 != C2 )
% 0.17/0.44 => ( ( swap_name @ ( product_Pair @ name @ name @ A2 @ B2 ) @ C2 )
% 0.17/0.44 = C2 ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % swap_name.simps
% 0.17/0.44 thf(fact_235_eqvtRelE,axiom,
% 0.17/0.44 ! [A: $tType] :
% 0.17/0.44 ( ( pt_name @ A )
% 0.17/0.44 => ! [Rel: set @ ( product_prod @ A @ A ),Perm: list @ ( product_prod @ name @ name ),P: A,Q: A] :
% 0.17/0.44 ( ( eqvt @ A @ Rel )
% 0.17/0.44 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ ( perm @ name @ A @ Perm @ P ) @ ( perm @ name @ A @ Perm @ Q ) ) @ Rel )
% 0.17/0.44 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ P @ Q ) @ Rel ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % eqvtRelE
% 0.17/0.44 thf(fact_236_eqvtRelI,axiom,
% 0.17/0.44 ! [A: $tType] :
% 0.17/0.44 ( ( pt_name @ A )
% 0.17/0.44 => ! [Rel: set @ ( product_prod @ A @ A ),P: A,Q: A,Perm: list @ ( product_prod @ name @ name )] :
% 0.17/0.44 ( ( eqvt @ A @ Rel )
% 0.17/0.44 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ P @ Q ) @ Rel )
% 0.17/0.44 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ ( perm @ name @ A @ Perm @ P ) @ ( perm @ name @ A @ Perm @ Q ) ) @ Rel ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % eqvtRelI
% 0.17/0.44 thf(fact_237_eqvt__def,axiom,
% 0.17/0.44 ! [A: $tType] :
% 0.17/0.44 ( ( pt_name @ A )
% 0.17/0.44 => ( ( eqvt @ A )
% 0.17/0.44 = ( ^ [Rel2: set @ ( product_prod @ A @ A )] :
% 0.17/0.44 ! [X4: product_prod @ A @ A,Perm2: list @ ( product_prod @ name @ name )] :
% 0.17/0.44 ( ( member @ ( product_prod @ A @ A ) @ X4 @ Rel2 )
% 0.17/0.44 => ( member @ ( product_prod @ A @ A ) @ ( perm @ name @ ( product_prod @ A @ A ) @ Perm2 @ X4 ) @ Rel2 ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % eqvt_def
% 0.17/0.44 thf(fact_238_name__prm__name_Osimps_I2_J,axiom,
% 0.17/0.44 ! [X3: product_prod @ name @ name,Xs: list @ ( product_prod @ name @ name ),A2: name] :
% 0.17/0.44 ( ( name_prm_name @ ( cons @ ( product_prod @ name @ name ) @ X3 @ Xs ) @ A2 )
% 0.17/0.44 = ( swap_name @ X3 @ ( name_prm_name @ Xs @ A2 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % name_prm_name.simps(2)
% 0.17/0.44 thf(fact_239_resSimCases,axiom,
% 0.17/0.44 ! [A: $tType] :
% 0.17/0.44 ( ( fs_name @ A )
% 0.17/0.44 => ! [Rel: set @ ( product_prod @ pi @ pi ),Q: pi,X3: name,P: pi,C4: A] :
% 0.17/0.44 ( ( eqvt @ pi @ Rel )
% 0.17/0.44 => ( ! [Q3: pi,A6: name] :
% 0.17/0.44 ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A6 @ X3 ) @ Q3 ) )
% 0.17/0.44 => ( ( A6 != X3 )
% 0.17/0.44 => ? [P6: pi] :
% 0.17/0.44 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A6 ) @ X3 @ P6 ) )
% 0.17/0.44 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P6 @ Q3 ) @ Rel ) ) ) )
% 0.17/0.44 => ( ! [Q3: pi,A6: late_subject,Y3: name] :
% 0.17/0.44 ( ( late_transitions @ Q @ ( late_BoundR @ A6 @ Y3 @ Q3 ) )
% 0.17/0.44 => ( ( fresh @ name @ late_subject @ X3 @ A6 )
% 0.17/0.44 => ( ( X3 != Y3 )
% 0.17/0.44 => ( ( fresh @ name @ A @ Y3 @ C4 )
% 0.17/0.44 => ? [P6: pi] :
% 0.17/0.44 ( ( late_transitions @ P @ ( late_BoundR @ A6 @ Y3 @ P6 ) )
% 0.17/0.44 & ( strong2129052853vative @ P6 @ ( res @ X3 @ Q3 ) @ A6 @ Y3 @ Rel ) ) ) ) ) )
% 0.17/0.44 => ( ! [Q3: pi,Alpha2: late_freeRes] :
% 0.17/0.44 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 0.17/0.44 => ( ( fresh @ name @ late_freeRes @ X3 @ Alpha2 )
% 0.17/0.44 => ? [P6: pi] :
% 0.17/0.44 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 0.17/0.44 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P6 @ ( res @ X3 @ Q3 ) ) @ Rel ) ) ) )
% 0.17/0.44 => ( strong743114133lation @ P @ Rel @ ( res @ X3 @ Q ) ) ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % resSimCases
% 0.17/0.44 thf(fact_240_simE_I2_J,axiom,
% 0.17/0.44 ! [P: pi,Rel: set @ ( product_prod @ pi @ pi ),Q: pi,Alpha: late_freeRes,Q2: pi] :
% 0.17/0.44 ( ( strong743114133lation @ P @ Rel @ Q )
% 0.17/0.44 => ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 0.17/0.44 => ? [P3: pi] :
% 0.17/0.44 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P3 ) )
% 0.17/0.44 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P3 @ Q2 ) @ Rel ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % simE(2)
% 0.17/0.44 thf(fact_241_simE_I1_J,axiom,
% 0.17/0.44 ! [P: pi,Rel: set @ ( product_prod @ pi @ pi ),Q: pi,A2: late_subject,X3: name,Q2: pi] :
% 0.17/0.44 ( ( strong743114133lation @ P @ Rel @ Q )
% 0.17/0.44 => ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X3 @ Q2 ) )
% 0.17/0.44 => ( ( fresh @ name @ pi @ X3 @ P )
% 0.17/0.44 => ? [P3: pi] :
% 0.17/0.44 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X3 @ P3 ) )
% 0.17/0.44 & ( strong2129052853vative @ P3 @ Q2 @ A2 @ X3 @ Rel ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % simE(1)
% 0.17/0.44 thf(fact_242_simulation__def,axiom,
% 0.17/0.44 ( strong743114133lation
% 0.17/0.44 = ( ^ [P7: pi,Rel2: set @ ( product_prod @ pi @ pi ),Q5: pi] :
% 0.17/0.44 ( ! [A3: late_subject,X4: name,Q6: pi] :
% 0.17/0.44 ( ( ( late_transitions @ Q5 @ ( late_BoundR @ A3 @ X4 @ Q6 ) )
% 0.17/0.44 & ( fresh @ name @ pi @ X4 @ P7 ) )
% 0.17/0.44 => ? [P8: pi] :
% 0.17/0.44 ( ( late_transitions @ P7 @ ( late_BoundR @ A3 @ X4 @ P8 ) )
% 0.17/0.44 & ( strong2129052853vative @ P8 @ Q6 @ A3 @ X4 @ Rel2 ) ) )
% 0.17/0.44 & ! [Alpha3: late_freeRes,Q6: pi] :
% 0.17/0.44 ( ( late_transitions @ Q5 @ ( late_FreeR @ Alpha3 @ Q6 ) )
% 0.17/0.44 => ? [P8: pi] :
% 0.17/0.44 ( ( late_transitions @ P7 @ ( late_FreeR @ Alpha3 @ P8 ) )
% 0.17/0.44 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P8 @ Q6 ) @ Rel2 ) ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % simulation_def
% 0.17/0.44 thf(fact_243_simCases,axiom,
% 0.17/0.44 ! [Q: pi,P: pi,Rel: set @ ( product_prod @ pi @ pi )] :
% 0.17/0.44 ( ! [A6: late_subject,Y3: name,Q3: pi] :
% 0.17/0.44 ( ( late_transitions @ Q @ ( late_BoundR @ A6 @ Y3 @ Q3 ) )
% 0.17/0.44 => ( ( fresh @ name @ pi @ Y3 @ P )
% 0.17/0.44 => ? [P6: pi] :
% 0.17/0.44 ( ( late_transitions @ P @ ( late_BoundR @ A6 @ Y3 @ P6 ) )
% 0.17/0.44 & ( strong2129052853vative @ P6 @ Q3 @ A6 @ Y3 @ Rel ) ) ) )
% 0.17/0.44 => ( ! [Alpha2: late_freeRes,Q3: pi] :
% 0.17/0.44 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 0.17/0.44 => ? [P6: pi] :
% 0.17/0.44 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 0.17/0.44 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P6 @ Q3 ) @ Rel ) ) )
% 0.17/0.44 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % simCases
% 0.17/0.44 thf(fact_244_name__prm__name_Osimps_I1_J,axiom,
% 0.17/0.44 ! [A2: name] :
% 0.17/0.44 ( ( name_prm_name @ ( nil @ ( product_prod @ name @ name ) ) @ A2 )
% 0.17/0.44 = A2 ) ).
% 0.17/0.44
% 0.17/0.44 % name_prm_name.simps(1)
% 0.17/0.44 thf(fact_245_derivativeEqvtI2,axiom,
% 0.17/0.44 ! [P: pi,Q: pi,A2: late_subject,X3: name,Rel: set @ ( product_prod @ pi @ pi ),Perm: list @ ( product_prod @ name @ name )] :
% 0.17/0.44 ( ( strong2129052853vative @ P @ Q @ A2 @ X3 @ Rel )
% 0.17/0.44 => ( ( eqvt @ pi @ Rel )
% 0.17/0.44 => ( strong2129052853vative @ ( perm @ name @ pi @ Perm @ P ) @ ( perm @ name @ pi @ Perm @ Q ) @ A2 @ ( perm @ name @ name @ Perm @ X3 ) @ Rel ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % derivativeEqvtI2
% 0.17/0.44 thf(fact_246_Agent_Oname__prm__name__def,axiom,
% 0.17/0.44 ( ( perm @ name @ name )
% 0.17/0.44 = name_prm_name ) ).
% 0.17/0.44
% 0.17/0.44 % Agent.name_prm_name_def
% 0.17/0.44 thf(fact_247_parSym,axiom,
% 0.17/0.44 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi,Q: pi] :
% 0.17/0.44 ( ! [R2: pi,S3: pi] : ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( par @ R2 @ S3 ) @ ( par @ S3 @ R2 ) ) @ Rel )
% 0.17/0.44 => ( ! [R2: pi,S3: pi,X5: name] :
% 0.17/0.44 ( ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ R2 @ S3 ) @ Rel )
% 0.17/0.44 => ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( res @ X5 @ R2 ) @ ( res @ X5 @ S3 ) ) @ Rel ) )
% 0.17/0.44 => ( strong743114133lation @ ( par @ P @ Q ) @ Rel @ ( par @ Q @ P ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % parSym
% 0.17/0.44 thf(fact_248_simCasesCont,axiom,
% 0.17/0.44 ! [A: $tType] :
% 0.17/0.44 ( ( fs_name @ A )
% 0.17/0.44 => ! [Rel: set @ ( product_prod @ pi @ pi ),Q: pi,P: pi,C4: A] :
% 0.17/0.44 ( ( eqvt @ pi @ Rel )
% 0.17/0.44 => ( ! [A6: late_subject,X5: name,Q3: pi] :
% 0.17/0.44 ( ( late_transitions @ Q @ ( late_BoundR @ A6 @ X5 @ Q3 ) )
% 0.17/0.44 => ( ( fresh @ name @ pi @ X5 @ P )
% 0.17/0.44 => ( ( fresh @ name @ pi @ X5 @ Q )
% 0.17/0.44 => ( ( fresh @ name @ late_subject @ X5 @ A6 )
% 0.17/0.44 => ( ( fresh @ name @ A @ X5 @ C4 )
% 0.17/0.44 => ? [P6: pi] :
% 0.17/0.44 ( ( late_transitions @ P @ ( late_BoundR @ A6 @ X5 @ P6 ) )
% 0.17/0.44 & ( strong2129052853vative @ P6 @ Q3 @ A6 @ X5 @ Rel ) ) ) ) ) ) )
% 0.17/0.44 => ( ! [Alpha2: late_freeRes,Q3: pi] :
% 0.17/0.44 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 0.17/0.44 => ? [P6: pi] :
% 0.17/0.44 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 0.17/0.44 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P6 @ Q3 ) @ Rel ) ) )
% 0.17/0.44 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % simCasesCont
% 0.17/0.44 thf(fact_249_parAssocLeft,axiom,
% 0.17/0.44 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi,Q: pi,R: pi] :
% 0.17/0.44 ( ! [S3: pi,T2: pi,U: pi] : ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( par @ ( par @ S3 @ T2 ) @ U ) @ ( par @ S3 @ ( par @ T2 @ U ) ) ) @ Rel )
% 0.17/0.44 => ( ! [S3: pi,T2: pi,X5: name] :
% 0.17/0.44 ( ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ S3 @ T2 ) @ Rel )
% 0.17/0.44 => ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( res @ X5 @ S3 ) @ ( res @ X5 @ T2 ) ) @ Rel ) )
% 0.17/0.44 => ( ! [S3: pi,T2: pi,U: pi,X5: name] :
% 0.17/0.44 ( ( fresh @ name @ pi @ X5 @ S3 )
% 0.17/0.44 => ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( res @ X5 @ ( par @ ( par @ S3 @ T2 ) @ U ) ) @ ( par @ S3 @ ( res @ X5 @ ( par @ T2 @ U ) ) ) ) @ Rel ) )
% 0.17/0.44 => ( ! [S3: pi,T2: pi,U: pi,X5: name] :
% 0.17/0.44 ( ( fresh @ name @ pi @ X5 @ U )
% 0.17/0.44 => ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( par @ ( res @ X5 @ ( par @ S3 @ T2 ) ) @ U ) @ ( res @ X5 @ ( par @ S3 @ ( par @ T2 @ U ) ) ) ) @ Rel ) )
% 0.17/0.44 => ( strong743114133lation @ ( par @ ( par @ P @ Q ) @ R ) @ Rel @ ( par @ P @ ( par @ Q @ R ) ) ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % parAssocLeft
% 0.17/0.44 thf(fact_250_derivativeEqvtI,axiom,
% 0.17/0.44 ! [P: pi,Q: pi,A2: late_subject,X3: name,Rel: set @ ( product_prod @ pi @ pi ),Perm: list @ ( product_prod @ name @ name )] :
% 0.17/0.44 ( ( strong2129052853vative @ P @ Q @ A2 @ X3 @ Rel )
% 0.17/0.44 => ( ( eqvt @ pi @ Rel )
% 0.17/0.44 => ( strong2129052853vative @ ( perm @ name @ pi @ Perm @ P ) @ ( perm @ name @ pi @ Perm @ Q ) @ ( perm @ name @ late_subject @ Perm @ A2 ) @ ( perm @ name @ name @ Perm @ X3 ) @ Rel ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % derivativeEqvtI
% 0.17/0.44 thf(fact_251_alpha__fresh_H,axiom,
% 0.17/0.44 ! [X2: $tType] :
% 0.17/0.44 ( ( pt_name @ X2 )
% 0.17/0.44 => ! [A2: name,X3: X2,B2: name,Y: X2,C2: name] :
% 0.17/0.44 ( ( ( abs_fun @ name @ X2 @ A2 @ X3 )
% 0.17/0.44 = ( abs_fun @ name @ X2 @ B2 @ Y ) )
% 0.17/0.44 => ( ( C2 != A2 )
% 0.17/0.44 => ( ( C2 != B2 )
% 0.17/0.44 => ( ( fresh @ name @ X2 @ C2 @ X3 )
% 0.17/0.44 => ( ( fresh @ name @ X2 @ C2 @ Y )
% 0.17/0.44 => ( X3
% 0.17/0.44 = ( perm @ name @ X2 @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ C2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ ( perm @ name @ X2 @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ B2 @ C2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ Y ) ) ) ) ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % alpha_fresh'
% 0.17/0.44 thf(fact_252_name__abs__eq,axiom,
% 0.17/0.44 ! [X: $tType] :
% 0.17/0.44 ( ( pt_name @ X )
% 0.17/0.44 => ! [A2: name,X3: X,B2: name,Y: X] :
% 0.17/0.44 ( ( ( abs_fun @ name @ X @ A2 @ X3 )
% 0.17/0.44 = ( abs_fun @ name @ X @ B2 @ Y ) )
% 0.17/0.44 = ( ( ( A2 = B2 )
% 0.17/0.44 & ( X3 = Y ) )
% 0.17/0.44 | ( ( A2 != B2 )
% 0.17/0.44 & ( X3
% 0.17/0.44 = ( perm @ name @ X @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ Y ) )
% 0.17/0.44 & ( fresh @ name @ X @ A2 @ Y ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % name_abs_eq
% 0.17/0.44 thf(fact_253_pi_Ofresh_I9_J,axiom,
% 0.17/0.44 ! [A2: name,X1: name,X22: pi] :
% 0.17/0.44 ( ( fresh @ name @ pi @ A2 @ ( res @ X1 @ X22 ) )
% 0.17/0.44 = ( fresh @ name @ ( name > ( noption @ pi ) ) @ A2 @ ( abs_fun @ name @ pi @ X1 @ X22 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % pi.fresh(9)
% 0.17/0.44 thf(fact_254_pi_Ofresh_I4_J,axiom,
% 0.17/0.44 ! [A2: name,X32: name,X1: name,X22: pi] :
% 0.17/0.44 ( ( fresh @ name @ pi @ A2 @ ( input @ X32 @ X1 @ X22 ) )
% 0.17/0.44 = ( ( fresh @ name @ name @ A2 @ X32 )
% 0.17/0.44 & ( fresh @ name @ ( name > ( noption @ pi ) ) @ A2 @ ( abs_fun @ name @ pi @ X1 @ X22 ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % pi.fresh(4)
% 0.17/0.44
% 0.17/0.44 % Type constructors (42)
% 0.17/0.44 thf(tcon_fun___Agent_Ocp__name__name,axiom,
% 0.17/0.44 ! [A7: $tType,A8: $tType] :
% 0.17/0.44 ( ( ( cp_name_name @ A7 )
% 0.17/0.44 & ( cp_name_name @ A8 ) )
% 0.17/0.44 => ( cp_name_name @ ( A7 > A8 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(tcon_fun___Orderings_Oord,axiom,
% 0.17/0.44 ! [A7: $tType,A8: $tType] :
% 0.17/0.44 ( ( ord @ A8 )
% 0.17/0.44 => ( ord @ ( A7 > A8 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(tcon_fun___Agent_Opt__name,axiom,
% 0.17/0.44 ! [A7: $tType,A8: $tType] :
% 0.17/0.44 ( ( ( pt_name @ A7 )
% 0.17/0.44 & ( pt_name @ A8 ) )
% 0.17/0.44 => ( pt_name @ ( A7 > A8 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(tcon_Set_Oset___Agent_Ocp__name__name_1,axiom,
% 0.17/0.44 ! [A7: $tType] :
% 0.17/0.44 ( ( cp_name_name @ A7 )
% 0.17/0.44 => ( cp_name_name @ ( set @ A7 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(tcon_Set_Oset___Orderings_Oord_2,axiom,
% 0.17/0.44 ! [A7: $tType] : ( ord @ ( set @ A7 ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(tcon_Set_Oset___Agent_Opt__name_3,axiom,
% 0.17/0.44 ! [A7: $tType] :
% 0.17/0.44 ( ( pt_name @ A7 )
% 0.17/0.44 => ( pt_name @ ( set @ A7 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(tcon_Agent_Opi___Agent_Ocp__name__name_4,axiom,
% 0.17/0.44 cp_name_name @ pi ).
% 0.17/0.44
% 0.17/0.44 thf(tcon_Agent_Opi___Agent_Opt__name_5,axiom,
% 0.17/0.44 pt_name @ pi ).
% 0.17/0.44
% 0.17/0.44 thf(tcon_Agent_Opi___Agent_Ofs__name,axiom,
% 0.17/0.44 fs_name @ pi ).
% 0.17/0.44
% 0.17/0.44 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 0.17/0.44 linorder @ $o ).
% 0.17/0.44
% 0.17/0.44 thf(tcon_HOL_Obool___Agent_Ocp__name__name_6,axiom,
% 0.17/0.44 cp_name_name @ $o ).
% 0.17/0.44
% 0.17/0.44 thf(tcon_HOL_Obool___Orderings_Oord_7,axiom,
% 0.17/0.44 ord @ $o ).
% 0.17/0.44
% 0.17/0.44 thf(tcon_HOL_Obool___Agent_Opt__name_8,axiom,
% 0.17/0.44 pt_name @ $o ).
% 0.17/0.44
% 0.17/0.44 thf(tcon_HOL_Obool___Agent_Ofs__name_9,axiom,
% 0.17/0.44 fs_name @ $o ).
% 0.17/0.44
% 0.17/0.44 thf(tcon_List_Olist___Agent_Ocp__name__name_10,axiom,
% 0.17/0.44 ! [A7: $tType] :
% 0.17/0.44 ( ( cp_name_name @ A7 )
% 0.17/0.44 => ( cp_name_name @ ( list @ A7 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(tcon_List_Olist___Agent_Opt__name_11,axiom,
% 0.17/0.44 ! [A7: $tType] :
% 0.17/0.44 ( ( pt_name @ A7 )
% 0.17/0.44 => ( pt_name @ ( list @ A7 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(tcon_List_Olist___Agent_Ofs__name_12,axiom,
% 0.17/0.44 ! [A7: $tType] :
% 0.17/0.44 ( ( fs_name @ A7 )
% 0.17/0.44 => ( fs_name @ ( list @ A7 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(tcon_Agent_Oname___Agent_Ocp__name__name_13,axiom,
% 0.17/0.44 cp_name_name @ name ).
% 0.17/0.44
% 0.17/0.44 thf(tcon_Agent_Oname___Agent_Opt__name_14,axiom,
% 0.17/0.44 pt_name @ name ).
% 0.17/0.44
% 0.17/0.44 thf(tcon_Agent_Oname___Agent_Ofs__name_15,axiom,
% 0.17/0.44 fs_name @ name ).
% 0.17/0.44
% 0.17/0.44 thf(tcon_Agent_Opi__Rep___Agent_Ocp__name__name_16,axiom,
% 0.17/0.44 cp_name_name @ pi_Rep ).
% 0.17/0.44
% 0.17/0.44 thf(tcon_Agent_Opi__Rep___Agent_Opt__name_17,axiom,
% 0.17/0.44 pt_name @ pi_Rep ).
% 0.17/0.44
% 0.17/0.44 thf(tcon_Nominal_Onoption___Agent_Ocp__name__name_18,axiom,
% 0.17/0.44 ! [A7: $tType] :
% 0.17/0.44 ( ( cp_name_name @ A7 )
% 0.17/0.44 => ( cp_name_name @ ( noption @ A7 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(tcon_Nominal_Onoption___Agent_Opt__name_19,axiom,
% 0.17/0.44 ! [A7: $tType] :
% 0.17/0.44 ( ( pt_name @ A7 )
% 0.17/0.44 => ( pt_name @ ( noption @ A7 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(tcon_Product__Type_Oprod___Agent_Ocp__name__name_20,axiom,
% 0.17/0.44 ! [A7: $tType,A8: $tType] :
% 0.17/0.44 ( ( ( cp_name_name @ A7 )
% 0.17/0.44 & ( cp_name_name @ A8 ) )
% 0.17/0.44 => ( cp_name_name @ ( product_prod @ A7 @ A8 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(tcon_Product__Type_Oprod___Agent_Opt__name_21,axiom,
% 0.17/0.44 ! [A7: $tType,A8: $tType] :
% 0.17/0.44 ( ( ( pt_name @ A7 )
% 0.17/0.44 & ( pt_name @ A8 ) )
% 0.17/0.44 => ( pt_name @ ( product_prod @ A7 @ A8 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(tcon_Product__Type_Oprod___Agent_Ofs__name_22,axiom,
% 0.17/0.44 ! [A7: $tType,A8: $tType] :
% 0.17/0.44 ( ( ( fs_name @ A7 )
% 0.17/0.44 & ( fs_name @ A8 ) )
% 0.17/0.44 => ( fs_name @ ( product_prod @ A7 @ A8 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(tcon_Late__Semantics_OfreeRes___Agent_Ocp__name__name_23,axiom,
% 0.17/0.44 cp_name_name @ late_freeRes ).
% 0.17/0.44
% 0.17/0.44 thf(tcon_Late__Semantics_OfreeRes___Agent_Opt__name_24,axiom,
% 0.17/0.44 pt_name @ late_freeRes ).
% 0.17/0.44
% 0.17/0.44 thf(tcon_Late__Semantics_OfreeRes___Agent_Ofs__name_25,axiom,
% 0.17/0.44 fs_name @ late_freeRes ).
% 0.17/0.44
% 0.17/0.44 thf(tcon_Late__Semantics_Osubject___Agent_Ocp__name__name_26,axiom,
% 0.17/0.44 cp_name_name @ late_subject ).
% 0.17/0.44
% 0.17/0.44 thf(tcon_Late__Semantics_Osubject___Agent_Opt__name_27,axiom,
% 0.17/0.44 pt_name @ late_subject ).
% 0.17/0.44
% 0.17/0.44 thf(tcon_Late__Semantics_Osubject___Agent_Ofs__name_28,axiom,
% 0.17/0.44 fs_name @ late_subject ).
% 0.17/0.44
% 0.17/0.44 thf(tcon_Late__Semantics_Oresidual___Agent_Ocp__name__name_29,axiom,
% 0.17/0.44 cp_name_name @ late_residual ).
% 0.17/0.44
% 0.17/0.44 thf(tcon_Late__Semantics_Oresidual___Agent_Opt__name_30,axiom,
% 0.17/0.44 pt_name @ late_residual ).
% 0.17/0.44
% 0.17/0.44 thf(tcon_Late__Semantics_Oresidual___Agent_Ofs__name_31,axiom,
% 0.17/0.44 fs_name @ late_residual ).
% 0.17/0.44
% 0.17/0.44 thf(tcon_Late__Semantics_OfreeRes__Rep___Agent_Ocp__name__name_32,axiom,
% 0.17/0.44 cp_name_name @ late_freeRes_Rep ).
% 0.17/0.44
% 0.17/0.44 thf(tcon_Late__Semantics_OfreeRes__Rep___Agent_Opt__name_33,axiom,
% 0.17/0.44 pt_name @ late_freeRes_Rep ).
% 0.17/0.44
% 0.17/0.44 thf(tcon_Late__Semantics_Osubject__Rep___Agent_Ocp__name__name_34,axiom,
% 0.17/0.44 cp_name_name @ late_subject_Rep ).
% 0.17/0.44
% 0.17/0.44 thf(tcon_Late__Semantics_Osubject__Rep___Agent_Opt__name_35,axiom,
% 0.17/0.44 pt_name @ late_subject_Rep ).
% 0.17/0.44
% 0.17/0.44 thf(tcon_Late__Semantics_Oresidual__Rep___Agent_Ocp__name__name_36,axiom,
% 0.17/0.44 cp_name_name @ late_residual_Rep ).
% 0.17/0.44
% 0.17/0.44 thf(tcon_Late__Semantics_Oresidual__Rep___Agent_Opt__name_37,axiom,
% 0.17/0.44 pt_name @ late_residual_Rep ).
% 0.17/0.44
% 0.17/0.44 % Helper facts (3)
% 0.17/0.44 thf(help_If_3_1_T,axiom,
% 0.17/0.44 ! [P: $o] :
% 0.17/0.44 ( ( P = $true )
% 0.17/0.44 | ( P = $false ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(help_If_2_1_T,axiom,
% 0.17/0.44 ! [A: $tType,X3: A,Y: A] :
% 0.17/0.44 ( ( if @ A @ $false @ X3 @ Y )
% 0.17/0.44 = Y ) ).
% 0.17/0.44
% 0.17/0.44 thf(help_If_1_1_T,axiom,
% 0.17/0.44 ! [A: $tType,X3: A,Y: A] :
% 0.17/0.44 ( ( if @ A @ $true @ X3 @ Y )
% 0.17/0.44 = X3 ) ).
% 0.17/0.44
% 0.17/0.44 % Conjectures (1)
% 0.17/0.44 thf(conj_0,conjecture,
% 0.17/0.44 late_transitions @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ z @ x ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ q ) @ ( perm @ name @ late_residual @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ z @ x ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ ( late_FreeR @ ( late_OutputR @ aa @ x ) @ q_a ) ) ).
% 0.17/0.44
% 0.17/0.44 %------------------------------------------------------------------------------
% 0.17/0.44 ------------------------
% 3.84/1.96 ---- Embedded in THF ---
% 3.84/1.96 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 3.84/1.96 %%% Generated on Tue Feb 24 08:30:19 EST 2026
% 3.84/1.96 %%% using '$$dhol' embedding, version 1.3.0.
% 3.84/1.96 %%% Logic specification used:
% 3.84/1.96 %%% thf(spec, logic, $$dhol).
% 3.84/1.96
% 3.84/1.96 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.rus05bb90W/DTF2DTF3151.p
% 3.84/1.96 thf(ty_t_Late__Semantics_Oresidual__Rep, type, late_residual_Rep: $tType).
% 3.84/1.96 thf(ty_t_Late__Semantics_Osubject__Rep, type, late_subject_Rep: $tType).
% 3.84/1.96 thf(ty_t_Late__Semantics_OfreeRes__Rep, type, late_freeRes_Rep: $tType).
% 3.84/1.96 thf(ty_t_Late__Semantics_Oresidual, type, late_residual: $tType).
% 3.84/1.96 thf(ty_t_Late__Semantics_Osubject, type, late_subject: $tType).
% 3.84/1.96 thf(ty_t_Late__Semantics_OfreeRes, type, late_freeRes: $tType).
% 3.84/1.96 thf(ty_t_Product__Type_Oprod, type, product_prod: ($tType > ($tType > $tType))).
% 3.84/1.96 thf(ty_t_Nominal_Onoption, type, noption: ($tType > $tType)).
% 3.84/1.96 thf(ty_t_Agent_Opi__Rep, type, pi_Rep: $tType).
% 3.84/1.96 thf(ty_t_Agent_Oname, type, name: $tType).
% 3.84/1.96 thf(ty_t_List_Olist, type, list: ($tType > $tType)).
% 3.84/1.96 thf(ty_t_Agent_Opi, type, pi: $tType).
% 3.84/1.96 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 3.84/1.96 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: ($o))).
% 3.84/1.96 thf(sy_cl_Agent_Ofs__name, type, fs_name: (!> [A:$tType]: ($o))).
% 3.84/1.96 thf(sy_cl_Agent_Opt__name, type, pt_name: (!> [A:$tType]: ($o))).
% 3.84/1.96 thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: ($o))).
% 3.84/1.96 thf(sy_cl_Agent_Ocp__name__name, type, cp_name_name: (!> [A:$tType]: ($o))).
% 3.84/1.96 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: ($o))).
% 3.84/1.96 thf(sy_c_Agent_Opi_OInput, type, input: (name > (name > (pi > pi)))).
% 3.84/1.96 thf(sy_c_Agent_Opi_OPar, type, par: (pi > (pi > pi))).
% 3.84/1.96 thf(sy_c_Agent_Opi_ORes, type, res: (name > (pi > pi))).
% 3.84/1.96 thf(sy_c_Agent_Orec_Oname__prm__name, type, name_prm_name: ((list @ ((product_prod @ name) @ name)) > (name > name))).
% 3.84/1.96 thf(sy_c_Agent_Orec_Oswap__name, type, swap_name: (((product_prod @ name) @ name) > (name > name))).
% 3.84/1.96 thf(sy_c_Agent_Osubs, type, subs: (pi > (name > (name > pi)))).
% 3.84/1.96 thf(sy_c_If, type, if: (!> [A:$tType]: (($o > (A > (A > A)))))).
% 3.84/1.96 thf(sy_c_Late__Semantics_OfreeRes_OOutputR, type, late_OutputR: (name > (name > late_freeRes))).
% 3.84/1.96 thf(sy_c_Late__Semantics_OfreeRes_OTauR, type, late_TauR: late_freeRes).
% 3.84/1.96 thf(sy_c_Late__Semantics_Oresidual_OBoundR, type, late_BoundR: (late_subject > (name > (pi > late_residual)))).
% 3.84/1.96 thf(sy_c_Late__Semantics_Oresidual_OFreeR, type, late_FreeR: (late_freeRes > (pi > late_residual))).
% 3.84/1.96 thf(sy_c_Late__Semantics_Oresidual__Rep_OFreeR__Rep, type, late_r347633188eR_Rep: (late_freeRes > (pi > late_residual_Rep))).
% 3.84/1.96 thf(sy_c_Late__Semantics_Osubject_OBoundOutputS, type, late_BoundOutputS: (name > late_subject)).
% 3.84/1.96 thf(sy_c_Late__Semantics_Osubject_OInputS, type, late_InputS: (name > late_subject)).
% 3.84/1.96 thf(sy_c_Late__Semantics_Otransitions, type, late_transitions: (pi > (late_residual > $o))).
% 3.84/1.96 thf(sy_c_List_Olist_OCons, type, cons: (!> [A:$tType]: ((A > ((list @ A) > (list @ A)))))).
% 3.84/1.96 thf(sy_c_List_Olist_ONil, type, nil: (!> [A:$tType]: ((list @ A)))).
% 3.84/1.96 thf(sy_c_List_Oproduct__lists, type, product_lists: (!> [A:$tType]: (((list @ (list @ A)) > (list @ (list @ A)))))).
% 3.84/1.96 thf(sy_c_Nominal_Oabs__fun, type, abs_fun: (!> [X:$tType,A:$tType]: ((X > (A > (X > (noption @ A))))))).
% 3.84/1.96 thf(sy_c_Nominal_Ofresh, type, fresh: (!> [X:$tType,A:$tType]: ((X > (A > $o))))).
% 3.84/1.96 thf(sy_c_Nominal_Operm, type, perm: (!> [X:$tType,A:$tType]: (((list @ ((product_prod @ X) @ X)) > (A > A))))).
% 3.84/1.96 thf(sy_c_Nominal_Osupports, type, supports: (!> [X:$tType,A:$tType]: (((set @ X) > (A > $o))))).
% 3.84/1.96 thf(sy_c_Nominal_Oswap, type, swap: (!> [X:$tType]: ((((product_prod @ X) @ X) > (X > X))))).
% 3.84/1.96 thf(sy_c_Product__Type_OPair, type, product_Pair: (!> [A:$tType,B:$tType]: ((A > (B > ((product_prod @ A) @ B)))))).
% 3.84/1.96 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod, type, product_rec_prod: (!> [A:$tType,B:$tType,T:$tType]: (((A > (B > T)) > (((product_prod @ A) @ B) > T))))).
% 3.84/1.96 thf(sy_c_Rel_Oeqvt, type, eqvt: (!> [A:$tType]: (((set @ ((product_prod @ A) @ A)) > $o)))).
% 3.84/1.96 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 3.84/1.96 thf(sy_c_Strong__Late__Sim_Oderivative, type, strong2129052853vative: (pi > (pi > (late_subject > (name > ((set @ ((product_prod @ pi) @ pi)) > $o)))))).
% 3.84/1.96 thf(sy_c_Strong__Late__Sim_Osimulation, type, strong743114133lation: (pi > ((set @ ((product_prod @ pi) @ pi)) > (pi > $o)))).
% 3.84/1.96 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 3.84/1.96 thf(sy_v_P, type, p: pi).
% 3.84/1.96 thf(sy_v_P_H____, type, p2: pi).
% 3.84/1.96 thf(sy_v_PxQ____, type, pxQ: pi).
% 3.84/1.96 thf(sy_v_Q, type, q: pi).
% 3.84/1.96 thf(sy_v_Q_H____, type, q2: pi).
% 3.84/1.96 thf(sy_v_Q_Ha____, type, q_a: pi).
% 3.84/1.96 thf(sy_v_Rel, type, rel: (set @ ((product_prod @ pi) @ pi))).
% 3.84/1.96 thf(sy_v__092_060alpha_062____, type, alpha: late_freeRes).
% 3.84/1.96 thf(sy_v_aa____, type, aa: name).
% 3.84/1.96 thf(sy_v_b____, type, b: name).
% 3.84/1.96 thf(sy_v_x, type, x: name).
% 3.84/1.96 thf(sy_v_y____, type, y: name).
% 3.84/1.96 thf(sy_v_z____, type, z: name).
% 3.84/1.96 thf(fact_0__092_060open_062a_A_061_Ab_092_060close_062, axiom, (aa = b)).
% 3.84/1.96 thf(fact_1_cOpen_Ohyps_I2_J, axiom, (b != x)).
% 3.84/1.96 thf(fact_2_cClose1_Ohyps_I10_J, axiom, (z != aa)).
% 3.84/1.96 thf(fact_3_cClose1_Ohyps_I6_J, axiom, (y != z)).
% 3.84/1.96 thf(fact_4_cClose1_Ohyps_I5_J, axiom, (y != aa)).
% 3.84/1.96 thf(fact_5__092_060open_062z_A_092_060noteq_062_Ax_092_060close_062, axiom, (z != x)).
% 3.84/1.96 thf(fact_6_cOpen_Ohyps_I1_J, axiom, ((late_transitions @ q) @ ((late_FreeR @ ((late_OutputR @ b) @ x)) @ q_a))).
% 3.84/1.96 thf(fact_7_cOpen_Ohyps_I3_J, axiom, ((late_BoundOutputS @ aa) = (late_BoundOutputS @ b))).
% 3.84/1.96 thf(fact_8_cClose1_Ohyps_I14_J, axiom, (alpha = late_TauR)).
% 3.84/1.96 thf(fact_9_cClose1_Ohyps_I13_J, axiom, ((((fresh @ name) @ name) @ z) @ x)).
% 3.84/1.96 thf(fact_10_perm__swap_I1_J, axiom, (! [X2:$tType]: (((pt_name @ X2) => (! [A2:name,B2:name,X3:X2]: ((((((perm @ name) @ X2) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ A2) @ B2)) @ (nil @ ((product_prod @ name) @ name)))) @ ((((perm @ name) @ X2) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ A2) @ B2)) @ (nil @ ((product_prod @ name) @ name)))) @ X3)) = X3))))))).
% 3.84/1.96 thf(fact_11_name__id, axiom, (! [X:$tType]: (((pt_name @ X) => (! [A2:name,X3:X]: ((((((perm @ name) @ X) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ A2) @ A2)) @ (nil @ ((product_prod @ name) @ name)))) @ X3) = X3))))))).
% 3.84/1.96 thf(fact_12_name__swap, axiom, (! [X:$tType]: (((pt_name @ X) => (! [A2:name,B2:name,X3:X]: ((((((perm @ name) @ X) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ A2) @ B2)) @ (nil @ ((product_prod @ name) @ name)))) @ X3) = ((((perm @ name) @ X) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ B2) @ A2)) @ (nil @ ((product_prod @ name) @ name)))) @ X3)))))))).
% 3.84/1.96 thf(fact_13_name__swap__bij, axiom, (! [X:$tType]: (((pt_name @ X) => (! [A2:name,B2:name,X3:X]: ((((((perm @ name) @ X) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ A2) @ B2)) @ (nil @ ((product_prod @ name) @ name)))) @ ((((perm @ name) @ X) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ A2) @ B2)) @ (nil @ ((product_prod @ name) @ name)))) @ X3)) = X3))))))).
% 3.84/1.96 thf(fact_14_pt__name1, axiom, (! [A:$tType]: (((pt_name @ A) => (! [X3:A]: ((((((perm @ name) @ A) @ (nil @ ((product_prod @ name) @ name))) @ X3) = X3))))))).
% 3.84/1.96 thf(fact_15__092_060open_062y_A_092_060noteq_062_Ax_092_060close_062, axiom, (y != x)).
% 3.84/1.96 thf(fact_16_perm__swap_I2_J, axiom, (! [X2:$tType]: (((pt_name @ X2) => (! [A2:name,B2:name,X3:X2]: ((((((perm @ name) @ X2) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ A2) @ B2)) @ (nil @ ((product_prod @ name) @ name)))) @ ((((perm @ name) @ X2) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ B2) @ A2)) @ (nil @ ((product_prod @ name) @ name)))) @ X3)) = X3))))))).
% 3.84/1.96 thf(fact_17_eqvt, axiom, (! [X1:pi,X22:late_residual,Pi:(list @ ((product_prod @ name) @ name))]: ((((late_transitions @ X1) @ X22) => ((late_transitions @ ((((perm @ name) @ pi) @ Pi) @ X1)) @ ((((perm @ name) @ late_residual) @ Pi) @ X22)))))).
% 3.84/1.96 thf(fact_18__092_060open_062z_A_092_060sharp_062_AQ_092_060close_062, axiom, ((((fresh @ name) @ pi) @ z) @ q)).
% 3.84/1.96 thf(fact_19_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)))))).
% 3.84/1.96 thf(fact_20_Late__Semantics1_OfreeRes_Oinject, axiom, (! [X11:name,X12:name,Y11:name,Y12:name]: (((((late_OutputR @ X11) @ X12) = ((late_OutputR @ Y11) @ Y12)) = ((X11 = Y11) & (X12 = Y12)))))).
% 3.84/1.96 thf(fact_21_cClose1_Ohyps_I11_J, axiom, ((((fresh @ name) @ pi) @ z) @ p2)).
% 3.84/1.96 thf(fact_22_cClose1_Ohyps_I7_J, axiom, ((((fresh @ name) @ pi) @ y) @ q2)).
% 3.84/1.96 thf(fact_23_cClose1_Ohyps_I12_J, axiom, ((((fresh @ name) @ name) @ y) @ x)).
% 3.84/1.96 thf(fact_24_assms_I1_J, axiom, ((((fresh @ name) @ pi) @ x) @ p)).
% 3.84/1.96 thf(fact_25_cClose1_Ohyps_I8_J, axiom, ((((fresh @ name) @ pi) @ z) @ p)).
% 3.84/1.96 thf(fact_26_cClose1_Ohyps_I3_J, axiom, ((((fresh @ name) @ pi) @ y) @ p)).
% 3.84/1.96 thf(fact_27_residual__perm__empty, axiom, (! [Residual_Rep:late_residual_Rep]: ((((((perm @ name) @ late_residual_Rep) @ (nil @ ((product_prod @ name) @ name))) @ Residual_Rep) = Residual_Rep)))).
% 3.84/1.96 thf(fact_28_subject__perm__empty, axiom, (! [Subject_Rep:late_subject_Rep]: ((((((perm @ name) @ late_subject_Rep) @ (nil @ ((product_prod @ name) @ name))) @ Subject_Rep) = Subject_Rep)))).
% 3.84/1.96 thf(fact_29_freeRes__perm__empty, axiom, (! [FreeRes_Rep:late_freeRes_Rep]: ((((((perm @ name) @ late_freeRes_Rep) @ (nil @ ((product_prod @ name) @ name))) @ FreeRes_Rep) = FreeRes_Rep)))).
% 3.84/1.96 thf(fact_30_pi__perm__empty, axiom, (! [Pi_Rep:pi_Rep]: ((((((perm @ name) @ pi_Rep) @ (nil @ ((product_prod @ name) @ name))) @ Pi_Rep) = Pi_Rep)))).
% 3.84/1.96 thf(fact_31_freeRes_Operm_I1_J, axiom, (! [Pi:(list @ ((product_prod @ name) @ name)),X22:name,X1:name]: ((((((perm @ name) @ late_freeRes) @ Pi) @ ((late_OutputR @ X22) @ X1)) = ((late_OutputR @ ((((perm @ name) @ name) @ Pi) @ X22)) @ ((((perm @ name) @ name) @ Pi) @ X1)))))).
% 3.84/1.96 thf(fact_32_subject_Operm_I2_J, axiom, (! [Pi:(list @ ((product_prod @ name) @ name)),X1:name]: ((((((perm @ name) @ late_subject) @ Pi) @ (late_BoundOutputS @ X1)) = (late_BoundOutputS @ ((((perm @ name) @ name) @ Pi) @ X1)))))).
% 3.84/1.96 thf(fact_33_Late__Semantics_Osubject_Oinject_I2_J, axiom, (! [X1:name,Y1:name]: ((((late_BoundOutputS @ X1) = (late_BoundOutputS @ Y1)) = (X1 = Y1))))).
% 3.84/1.96 thf(fact_34_Late__Semantics1_Osubject_Oinject_I2_J, axiom, (! [X22:name,Y2:name]: ((((late_BoundOutputS @ X22) = (late_BoundOutputS @ Y2)) = (X22 = Y2))))).
% 3.84/1.96 thf(fact_35_freeRes_Operm_I2_J, axiom, (! [Pi:(list @ ((product_prod @ name) @ name))]: ((((((perm @ name) @ late_freeRes) @ Pi) @ late_TauR) = late_TauR)))).
% 3.84/1.96 thf(fact_36_name__fresh, axiom, (((fresh @ name) @ name) = (^ [A3:name,B3:name]: ((A3 != B3))))).
% 3.84/1.96 thf(fact_37_residual_Operm_I2_J, axiom, (! [Pi:(list @ ((product_prod @ name) @ name)),X22:late_freeRes,X1:pi]: ((((((perm @ name) @ late_residual) @ Pi) @ ((late_FreeR @ X22) @ X1)) = ((late_FreeR @ ((((perm @ name) @ late_freeRes) @ Pi) @ X22)) @ ((((perm @ name) @ pi) @ Pi) @ X1)))))).
% 3.84/1.96 thf(fact_38_perm__fresh__fresh, axiom, (! [X2:$tType]: (((pt_name @ X2) => (! [A2:name,X3:X2,B2:name]: ((((((fresh @ name) @ X2) @ A2) @ X3) => (((((fresh @ name) @ X2) @ B2) @ X3) => (((((perm @ name) @ X2) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ A2) @ B2)) @ (nil @ ((product_prod @ name) @ name)))) @ X3) = X3))))))))).
% 3.84/1.96 thf(fact_39_name__fresh__fresh, axiom, (! [X:$tType]: (((pt_name @ X) => (! [A2:name,X3:X,B2:name]: ((((((fresh @ name) @ X) @ A2) @ X3) => (((((fresh @ name) @ X) @ B2) @ X3) => (((((perm @ name) @ X) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ A2) @ B2)) @ (nil @ ((product_prod @ name) @ name)))) @ X3) = X3))))))))).
% 3.84/1.96 thf(fact_40_cClose1_Ohyps_I9_J, axiom, ((((fresh @ name) @ pi) @ z) @ ((res @ x) @ q))).
% 3.84/1.96 thf(fact_41_cClose1_Ohyps_I4_J, axiom, ((((fresh @ name) @ pi) @ y) @ ((res @ x) @ q))).
% 3.84/1.96 thf(fact_42_fresh__perm__app, axiom, (! [X2:$tType]: (((pt_name @ X2) => (! [A2:name,Pi:(list @ ((product_prod @ name) @ name)),X3:X2]: ((((((fresh @ name) @ (list @ ((product_prod @ name) @ name))) @ A2) @ Pi) => (((((fresh @ name) @ X2) @ A2) @ X3) => ((((fresh @ name) @ X2) @ A2) @ ((((perm @ name) @ X2) @ Pi) @ X3)))))))))).
% 3.84/1.96 thf(fact_43_name__exists__fresh, axiom, (! [A:$tType]: (((fs_name @ A) => (! [X3:A]: ((~ ((! [C:name]: ((~ (((((fresh @ name) @ A) @ C) @ X3))))))))))))).
% 3.84/1.96 thf(fact_44_fresh__eqvt, axiom, (! [X2:$tType]: (((pt_name @ X2) => (! [Pi:(list @ ((product_prod @ name) @ name)),A2:name,X3:X2]: ((((((perm @ name) @ $o) @ Pi) @ ((((fresh @ name) @ X2) @ A2) @ X3)) = ((((fresh @ name) @ X2) @ ((((perm @ name) @ name) @ Pi) @ A2)) @ ((((perm @ name) @ X2) @ Pi) @ X3))))))))).
% 3.84/1.96 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P)) = (P @ A2))))).
% 3.84/1.96 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A4:(set @ A)]: ((((collect @ A) @ (^ [X4:A]: ((((member @ A) @ X4) @ A4)))) = A4)))).
% 3.84/1.96 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X5:A]: (((P @ X5) = (Q @ X5)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 3.84/1.96 thf(fact_48_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G:(A > B)]: (((! [X5:A]: (((F @ X5) = (G @ X5)))) => (F = G))))).
% 3.84/1.96 thf(fact_49_fresh__bij, axiom, (! [X2:$tType]: (((pt_name @ X2) => (! [Pi:(list @ ((product_prod @ name) @ name)),A2:name,X3:X2]: ((((((fresh @ name) @ X2) @ ((((perm @ name) @ name) @ Pi) @ A2)) @ ((((perm @ name) @ X2) @ Pi) @ X3)) = ((((fresh @ name) @ X2) @ A2) @ X3)))))))).
% 3.84/1.96 thf(fact_50_name__calc_I2_J, axiom, (! [X3:name]: ((((((perm @ name) @ name) @ (nil @ ((product_prod @ name) @ name))) @ X3) = X3)))).
% 3.84/1.96 thf(fact_51_freeRes_Ostrong__inducts, axiom, (! [A:$tType,P:(A > (late_freeRes > $o)),Z:A,FreeRes:late_freeRes]: (((! [Name1:name,Name2:name,Z2:A]: (((P @ Z2) @ ((late_OutputR @ Name1) @ Name2)))) => ((! [Z2:A]: (((P @ Z2) @ late_TauR))) => ((P @ Z) @ FreeRes)))))).
% 3.84/1.96 thf(fact_52_freeRes_Ostrong__induct_H, axiom, (! [N:$tType,P:(N > (late_freeRes > $o)),Z:N,FreeRes:late_freeRes]: (((! [Name1:name,Name2:name,Z2:N]: (((P @ Z2) @ ((late_OutputR @ Name1) @ Name2)))) => ((! [Z2:N]: (((P @ Z2) @ late_TauR))) => ((P @ Z) @ FreeRes)))))).
% 3.84/1.96 thf(fact_53_freeRes_Oexhaust, axiom, (! [Y:late_freeRes]: (((! [X112:name,X122:name]: ((Y != ((late_OutputR @ X112) @ X122)))) => (Y = late_TauR))))).
% 3.84/1.96 thf(fact_54_freeRes_Oinducts, axiom, (! [P:(late_freeRes > $o),FreeRes:late_freeRes]: (((! [Name1:name,Name2:name]: ((P @ ((late_OutputR @ Name1) @ Name2)))) => ((P @ late_TauR) => (P @ FreeRes)))))).
% 3.84/1.96 thf(fact_55_Late__Semantics1_OfreeRes_Odistinct_I1_J, axiom, (! [X11:name,X12:name]: ((((late_OutputR @ X11) @ X12) != late_TauR)))).
% 3.84/1.96 thf(fact_56_Late__Semantics_OfreeRes_Odistinct_I1_J, axiom, (! [Name12:name,Name22:name]: ((((late_OutputR @ Name12) @ Name22) != late_TauR)))).
% 3.84/1.96 thf(fact_57_freshFreeDerivative_I2_J, axiom, (! [P:pi,Alpha:late_freeRes,P2:pi,Y:name]: ((((late_transitions @ P) @ ((late_FreeR @ Alpha) @ P2)) => (((((fresh @ name) @ pi) @ Y) @ P) => ((((fresh @ name) @ pi) @ Y) @ P2)))))).
% 3.84/1.96 thf(fact_58_swap__simps_I1_J, axiom, (! [A2:name,B2:name]: ((((((perm @ name) @ name) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ A2) @ B2)) @ (nil @ ((product_prod @ name) @ name)))) @ A2) = B2)))).
% 3.84/1.96 thf(fact_59_swap__simps_I2_J, axiom, (! [A2:name,B2:name]: ((((((perm @ name) @ name) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ A2) @ B2)) @ (nil @ ((product_prod @ name) @ name)))) @ B2) = A2)))).
% 3.84/1.96 thf(fact_60_swap__simps_I3_J, axiom, (! [A2:name,C2:name,B2:name]: (((A2 != C2) => ((B2 != C2) => (((((perm @ name) @ name) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ A2) @ B2)) @ (nil @ ((product_prod @ name) @ name)))) @ C2) = C2)))))).
% 3.84/1.96 thf(fact_61_fresh__aux, axiom, (! [X2:$tType]: (((pt_name @ X2) => (! [C2:name,A2:name,X3:X2,B2:name]: (((C2 != A2) => (((((fresh @ name) @ X2) @ A2) @ X3) => (((((fresh @ name) @ X2) @ C2) @ X3) => ((((fresh @ name) @ X2) @ C2) @ ((((perm @ name) @ X2) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ A2) @ B2)) @ (nil @ ((product_prod @ name) @ name)))) @ X3))))))))))).
% 3.84/1.96 thf(fact_62_cp__name__name1, axiom, (! [A:$tType]: (((cp_name_name @ A) => (! [Pi1:(list @ ((product_prod @ name) @ name)),Pi2:(list @ ((product_prod @ name) @ name)),X3:A]: ((((((perm @ name) @ A) @ Pi1) @ ((((perm @ name) @ A) @ Pi2) @ X3)) = ((((perm @ name) @ A) @ ((((perm @ name) @ (list @ ((product_prod @ name) @ name))) @ Pi1) @ Pi2)) @ ((((perm @ name) @ A) @ Pi1) @ X3))))))))).
% 3.84/1.96 thf(fact_63_name__perm__compose, axiom, (! [X:$tType]: (((pt_name @ X) => (! [Pi2:(list @ ((product_prod @ name) @ name)),Pi1:(list @ ((product_prod @ name) @ name)),X3:X]: ((((((perm @ name) @ X) @ Pi2) @ ((((perm @ name) @ X) @ Pi1) @ X3)) = ((((perm @ name) @ X) @ ((((perm @ name) @ (list @ ((product_prod @ name) @ name))) @ Pi2) @ Pi1)) @ ((((perm @ name) @ X) @ Pi2) @ X3))))))))).
% 3.84/1.96 thf(fact_64_perm__compose, axiom, (! [X2:$tType]: (((pt_name @ X2) => (! [Pi2:(list @ ((product_prod @ name) @ name)),Pi1:(list @ ((product_prod @ name) @ name)),X3:X2]: ((((((perm @ name) @ X2) @ Pi2) @ ((((perm @ name) @ X2) @ Pi1) @ X3)) = ((((perm @ name) @ X2) @ ((((perm @ name) @ (list @ ((product_prod @ name) @ name))) @ Pi2) @ Pi1)) @ ((((perm @ name) @ X2) @ Pi2) @ X3))))))))).
% 3.84/1.96 thf(fact_65_perm__bij, axiom, (! [X2:$tType]: (((pt_name @ X2) => (! [Pi:(list @ ((product_prod @ name) @ name)),X3:X2,Y:X2]: (((((((perm @ name) @ X2) @ Pi) @ X3) = ((((perm @ name) @ X2) @ Pi) @ Y)) = (X3 = Y)))))))).
% 3.84/1.96 thf(fact_66_perm__app, axiom, (! [B:$tType,X2:$tType]: (((pt_name @ X2) => (! [Pi:(list @ ((product_prod @ name) @ name)),F:(X2 > B),X3:X2]: ((((((perm @ name) @ B) @ Pi) @ (F @ X3)) = (((((perm @ name) @ (X2 > B)) @ Pi) @ F) @ ((((perm @ name) @ X2) @ Pi) @ X3))))))))).
% 3.84/1.96 thf(fact_67_in__eqvt, axiom, (! [X2:$tType]: (((pt_name @ X2) => (! [Pi:(list @ ((product_prod @ name) @ name)),X3:X2,X6:(set @ X2)]: ((((((perm @ name) @ $o) @ Pi) @ (((member @ X2) @ X3) @ X6)) = (((member @ X2) @ ((((perm @ name) @ X2) @ Pi) @ X3)) @ ((((perm @ name) @ (set @ X2)) @ Pi) @ X6))))))))).
% 3.84/1.96 thf(fact_68_eq__eqvt, axiom, (! [X2:$tType]: (((pt_name @ X2) => (! [Pi:(list @ ((product_prod @ name) @ name)),X3:X2,Y:X2]: ((((((perm @ name) @ $o) @ Pi) @ (X3 = Y)) = (((((perm @ name) @ X2) @ Pi) @ X3) = ((((perm @ name) @ X2) @ Pi) @ Y))))))))).
% 3.84/1.96 thf(fact_69_residual_Oinject_I2_J, axiom, (! [X22:late_freeRes,X1:pi,Y2:late_freeRes,Y1:pi]: (((((late_FreeR @ X22) @ X1) = ((late_FreeR @ Y2) @ Y1)) = ((X22 = Y2) & (X1 = Y1)))))).
% 3.84/1.96 thf(fact_70_fresh__prod, axiom, (! [A:$tType,X:$tType,B:$tType,A2:X,X3:A,Y:B]: ((((((fresh @ X) @ ((product_prod @ A) @ B)) @ A2) @ ((((product_Pair @ A) @ B) @ X3) @ Y)) = (((((fresh @ X) @ A) @ A2) @ X3) & ((((fresh @ X) @ B) @ A2) @ Y)))))).
% 3.84/1.96 thf(fact_71_list_Oinject, axiom, (! [A:$tType,X21:A,X222:(list @ A),Y21:A,Y22:(list @ A)]: ((((((cons @ A) @ X21) @ X222) = (((cons @ A) @ Y21) @ Y22)) = ((X21 = Y21) & (X222 = Y22)))))).
% 3.84/1.96 thf(fact_72_old_Oprod_Oinject, axiom, (! [A:$tType,B:$tType,A2:A,B2:B,A5:A,B4:B]: (((((((product_Pair @ A) @ B) @ A2) @ B2) = ((((product_Pair @ A) @ B) @ A5) @ B4)) = ((A2 = A5) & (B2 = B4)))))).
% 3.84/1.96 thf(fact_73_prod_Oinject, axiom, (! [A:$tType,B:$tType,X1:A,X22:B,Y1:A,Y2:B]: (((((((product_Pair @ A) @ B) @ X1) @ X22) = ((((product_Pair @ A) @ B) @ Y1) @ Y2)) = ((X1 = Y1) & (X22 = Y2)))))).
% 3.84/1.96 thf(fact_74_cClose1_Ohyps_I2_J, axiom, ((late_transitions @ ((res @ x) @ q)) @ (((late_BoundR @ (late_BoundOutputS @ aa)) @ z) @ q2))).
% 3.84/1.96 thf(fact_75_fresh__list__cons, axiom, (! [X:$tType,A:$tType,A2:X,X3:A,Xs:(list @ A)]: ((((((fresh @ X) @ (list @ A)) @ A2) @ (((cons @ A) @ X3) @ Xs)) = (((((fresh @ X) @ A) @ A2) @ X3) & ((((fresh @ X) @ (list @ A)) @ A2) @ Xs)))))).
% 3.84/1.96 thf(fact_76_fresh__prodD_I2_J, axiom, (! [B:$tType,A:$tType,C3:$tType,A2:A,X3:B,Y:C3]: ((((((fresh @ A) @ ((product_prod @ B) @ C3)) @ A2) @ ((((product_Pair @ B) @ C3) @ X3) @ Y)) => ((((fresh @ A) @ C3) @ A2) @ Y))))).
% 3.84/1.96 thf(fact_77_fresh__prodD_I1_J, axiom, (! [C3:$tType,A:$tType,B:$tType,A2:A,X3:B,Y:C3]: ((((((fresh @ A) @ ((product_prod @ B) @ C3)) @ A2) @ ((((product_Pair @ B) @ C3) @ X3) @ Y)) => ((((fresh @ A) @ B) @ A2) @ X3))))).
% 3.84/1.96 thf(fact_78_cons__eqvt, axiom, (! [X:$tType,A:$tType,Pi:(list @ ((product_prod @ X) @ X)),X3:A,Xs:(list @ A)]: ((((((perm @ X) @ (list @ A)) @ Pi) @ (((cons @ A) @ X3) @ Xs)) = (((cons @ A) @ ((((perm @ X) @ A) @ Pi) @ X3)) @ ((((perm @ X) @ (list @ A)) @ Pi) @ Xs)))))).
% 3.84/1.96 thf(fact_79_strict__sorted_Oinduct, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:((list @ A) > $o),A0:(list @ A)]: (((P @ (nil @ A)) => ((! [X5:A,Ys:(list @ A)]: (((P @ Ys) => (P @ (((cons @ A) @ X5) @ Ys))))) => (P @ A0))))))))).
% 3.84/1.96 thf(fact_80_true__eqvt, axiom, (! [A:$tType,Pi:(list @ ((product_prod @ A) @ A))]: (((((perm @ A) @ $o) @ Pi) @ $true)))).
% 3.84/1.96 thf(fact_81_false__eqvt, axiom, (! [A:$tType,Pi:(list @ ((product_prod @ A) @ A))]: ((~ (((((perm @ A) @ $o) @ Pi) @ $false)))))).
% 3.84/1.96 thf(fact_82_freeRes_Ofresh_I2_J, axiom, (! [A2:name]: (((((fresh @ name) @ late_freeRes) @ A2) @ late_TauR)))).
% 3.84/1.96 thf(fact_83_residual_Ofresh_I2_J, axiom, (! [A2:name,X22:late_freeRes,X1:pi]: ((((((fresh @ name) @ late_residual) @ A2) @ ((late_FreeR @ X22) @ X1)) = (((((fresh @ name) @ late_freeRes) @ A2) @ X22) & ((((fresh @ name) @ pi) @ A2) @ X1)))))).
% 3.84/1.96 thf(fact_84_freeRes_Ofresh_I1_J, axiom, (! [A2:name,X22:name,X1:name]: ((((((fresh @ name) @ late_freeRes) @ A2) @ ((late_OutputR @ X22) @ X1)) = (((((fresh @ name) @ name) @ A2) @ X22) & ((((fresh @ name) @ name) @ A2) @ X1)))))).
% 3.84/1.96 thf(fact_85_subject_Ofresh_I2_J, axiom, (! [A2:name,X1:name]: ((((((fresh @ name) @ late_subject) @ A2) @ (late_BoundOutputS @ X1)) = ((((fresh @ name) @ name) @ A2) @ X1))))).
% 3.84/1.96 thf(fact_86_pi_Operm_I9_J, axiom, (! [Pi:(list @ ((product_prod @ name) @ name)),X1:name,X22:pi]: ((((((perm @ name) @ pi) @ Pi) @ ((res @ X1) @ X22)) = ((res @ ((((perm @ name) @ name) @ Pi) @ X1)) @ ((((perm @ name) @ pi) @ Pi) @ X22)))))).
% 3.84/1.96 thf(fact_87_cClose1_Ohyps_I1_J, axiom, ((late_transitions @ p) @ (((late_BoundR @ (late_InputS @ aa)) @ y) @ p2))).
% 3.84/1.96 thf(fact_88_residual_Operm_I1_J, axiom, (! [Pi:(list @ ((product_prod @ name) @ name)),X32:late_subject,X1:name,X22:pi]: ((((((perm @ name) @ late_residual) @ Pi) @ (((late_BoundR @ X32) @ X1) @ X22)) = (((late_BoundR @ ((((perm @ name) @ late_subject) @ Pi) @ X32)) @ ((((perm @ name) @ name) @ Pi) @ X1)) @ ((((perm @ name) @ pi) @ Pi) @ X22)))))).
% 3.84/1.96 thf(fact_89_name__bij, axiom, (! [Pi:(list @ ((product_prod @ name) @ name)),X3:name,Y:name]: (((((((perm @ name) @ name) @ Pi) @ X3) = ((((perm @ name) @ name) @ Pi) @ Y)) = (X3 = Y))))).
% 3.84/1.96 thf(fact_90_imp__eqvt, axiom, (! [A:$tType,Pi:(list @ ((product_prod @ A) @ A)),A4:$o,B5:$o]: ((((((perm @ A) @ $o) @ Pi) @ (A4 => B5)) = (((((perm @ A) @ $o) @ Pi) @ A4) => ((((perm @ A) @ $o) @ Pi) @ B5)))))).
% 3.84/1.96 thf(fact_91_neg__eqvt, axiom, (! [A:$tType,Pi:(list @ ((product_prod @ A) @ A)),A4:$o]: ((((((perm @ A) @ $o) @ Pi) @ (~ (A4))) = (~ (((((perm @ A) @ $o) @ Pi) @ A4))))))).
% 3.84/1.96 thf(fact_92_conj__eqvt, axiom, (! [A:$tType,Pi:(list @ ((product_prod @ A) @ A)),A4:$o,B5:$o]: ((((((perm @ A) @ $o) @ Pi) @ (A4 & B5)) = (((((perm @ A) @ $o) @ Pi) @ A4) & ((((perm @ A) @ $o) @ Pi) @ B5)))))).
% 3.84/1.96 thf(fact_93_disj__eqvt, axiom, (! [A:$tType,Pi:(list @ ((product_prod @ A) @ A)),A4:$o,B5:$o]: ((((((perm @ A) @ $o) @ Pi) @ (A4 | B5)) = (((((perm @ A) @ $o) @ Pi) @ A4) | ((((perm @ A) @ $o) @ Pi) @ B5)))))).
% 3.84/1.96 thf(fact_94_perm__boolE, axiom, (! [A:$tType,Pi:(list @ ((product_prod @ A) @ A))]: ((~ (((((perm @ A) @ $o) @ Pi) @ $false)))))).
% 3.84/1.96 thf(fact_95_perm__boolI, axiom, (! [A:$tType,P:$o,Pi:(list @ ((product_prod @ A) @ A))]: ((P => ((((perm @ A) @ $o) @ Pi) @ P))))).
% 3.84/1.96 thf(fact_96_Late__Semantics_OResB, axiom, (! [P:pi,A2:late_subject,X3:name,P2:pi,Y:name]: ((((late_transitions @ P) @ (((late_BoundR @ A2) @ X3) @ P2)) => (((((fresh @ name) @ late_subject) @ Y) @ A2) => ((Y != X3) => ((late_transitions @ ((res @ Y) @ P)) @ (((late_BoundR @ A2) @ X3) @ ((res @ Y) @ P2))))))))).
% 3.84/1.96 thf(fact_97_pt__set__bij3, axiom, (! [X:$tType,A:$tType,Pi:(list @ ((product_prod @ X) @ X)),X3:A,X6:(set @ A)]: ((((((perm @ X) @ $o) @ Pi) @ (((member @ A) @ X3) @ X6)) = (((member @ A) @ X3) @ X6))))).
% 3.84/1.96 thf(fact_98_perm__bool__def, axiom, (! [X:$tType]: ((((perm @ X) @ $o) = (^ [Pi3:(list @ ((product_prod @ X) @ X)),B3:$o]: (B3)))))).
% 3.84/1.96 thf(fact_99_nil__eqvt, axiom, (! [X:$tType,A:$tType,Pi:(list @ ((product_prod @ X) @ X))]: ((((((perm @ X) @ (list @ A)) @ Pi) @ (nil @ A)) = (nil @ A))))).
% 3.84/1.96 thf(fact_100_fresh__list__nil, axiom, (! [X:$tType,A:$tType,A2:X]: (((((fresh @ X) @ (list @ A)) @ A2) @ (nil @ A))))).
% 3.84/1.96 thf(fact_101_transitions_OResB, axiom, (! [P:pi,A2:late_subject,X3:name,P2:pi,Y:name]: ((((late_transitions @ P) @ (((late_BoundR @ A2) @ X3) @ P2)) => (((((fresh @ name) @ late_subject) @ Y) @ A2) => ((Y != X3) => (((((fresh @ name) @ pi) @ X3) @ P) => (((((fresh @ name) @ late_subject) @ X3) @ A2) => ((late_transitions @ ((res @ Y) @ P)) @ (((late_BoundR @ A2) @ X3) @ ((res @ Y) @ P2))))))))))).
% 3.84/1.96 thf(fact_102_map__tailrec__rev_Ocases, axiom, (! [A:$tType,B:$tType,X3:((product_prod @ (A > B)) @ ((product_prod @ (list @ A)) @ (list @ B)))]: (((! [F2:(A > B),Bs:(list @ B)]: ((X3 != ((((product_Pair @ (A > B)) @ ((product_prod @ (list @ A)) @ (list @ B))) @ F2) @ ((((product_Pair @ (list @ A)) @ (list @ B)) @ (nil @ A)) @ Bs))))) => (~ ((! [F2:(A > B),A6:A,As:(list @ A),Bs:(list @ B)]: ((X3 != ((((product_Pair @ (A > B)) @ ((product_prod @ (list @ A)) @ (list @ B))) @ F2) @ ((((product_Pair @ (list @ A)) @ (list @ B)) @ (((cons @ A) @ A6) @ As)) @ Bs))))))))))).
% 3.84/1.96 thf(fact_103_resCasesF, axiom, (! [X3:name,P:pi,Alpha:late_freeRes,XP:pi,F3:(pi > $o)]: ((((late_transitions @ ((res @ X3) @ P)) @ ((late_FreeR @ Alpha) @ XP)) => ((! [P3:pi]: ((((late_transitions @ P) @ ((late_FreeR @ Alpha) @ P3)) => (((((fresh @ name) @ late_freeRes) @ X3) @ Alpha) => (F3 @ ((res @ X3) @ P3)))))) => (F3 @ XP)))))).
% 3.84/1.96 thf(fact_104_resCasesF_H, axiom, (! [X3:name,P:pi,Alpha:late_freeRes,P2:pi]: ((((late_transitions @ ((res @ X3) @ P)) @ ((late_FreeR @ Alpha) @ P2)) => (~ ((! [P4:pi,Alpha2:late_freeRes,P3:pi,Y3:name]: (((((res @ X3) @ P) = ((res @ Y3) @ P4)) => ((((late_FreeR @ Alpha) @ P2) = ((late_FreeR @ Alpha2) @ ((res @ Y3) @ P3))) => (((late_transitions @ P4) @ ((late_FreeR @ Alpha2) @ P3)) => (~ (((((fresh @ name) @ late_freeRes) @ Y3) @ Alpha2)))))))))))))).
% 3.84/1.96 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)))))))).
% 3.84/1.96 thf(fact_106_freshBoundDerivative_I1_J, axiom, (! [P:pi,A2:late_subject,X3:name,P2:pi,Y:name]: ((((late_transitions @ P) @ (((late_BoundR @ A2) @ X3) @ P2)) => (((((fresh @ name) @ pi) @ Y) @ P) => ((((fresh @ name) @ late_subject) @ Y) @ A2)))))).
% 3.84/1.96 thf(fact_107_freshRes, axiom, (! [A2:name,P:pi]: (((((fresh @ name) @ pi) @ A2) @ ((res @ A2) @ P))))).
% 3.84/1.96 thf(fact_108_residual_Odistinct_I1_J, axiom, (! [Subject:late_subject,Name:name,Pi:pi,FreeRes2:late_freeRes,Pi4:pi]: (((((late_BoundR @ Subject) @ Name) @ Pi) != ((late_FreeR @ FreeRes2) @ Pi4))))).
% 3.84/1.96 thf(fact_109_residual_Oinducts, axiom, (! [P:(late_residual > $o),Residual:late_residual]: (((! [Subject2:late_subject,Name3:name,Pi5:pi]: ((P @ (((late_BoundR @ Subject2) @ Name3) @ Pi5)))) => ((! [FreeRes3:late_freeRes,Pi5:pi]: ((P @ ((late_FreeR @ FreeRes3) @ Pi5)))) => (P @ Residual)))))).
% 3.84/1.96 thf(fact_110_resCases_H, axiom, (! [X3:name,P:pi,Rs:late_residual]: ((((late_transitions @ ((res @ X3) @ P)) @ Rs) => ((! [P4:pi,A6:name,B6:name]: (((((res @ X3) @ P) = ((res @ B6) @ P4)) => (! [P3:pi]: (((Rs = (((late_BoundR @ (late_BoundOutputS @ A6)) @ B6) @ P3)) => (((late_transitions @ P4) @ ((late_FreeR @ ((late_OutputR @ A6) @ B6)) @ P3)) => (A6 = B6)))))))) => ((! [P4:pi,A6:late_subject,X5:name,P3:pi,Y3:name]: (((((res @ X3) @ P) = ((res @ Y3) @ P4)) => ((Rs = (((late_BoundR @ A6) @ X5) @ ((res @ Y3) @ P3))) => (((late_transitions @ P4) @ (((late_BoundR @ A6) @ X5) @ P3)) => (((((fresh @ name) @ late_subject) @ Y3) @ A6) => ((Y3 != X5) => (((((fresh @ name) @ pi) @ X5) @ P4) => (~ (((((fresh @ name) @ late_subject) @ X5) @ A6))))))))))) => (~ ((! [P4:pi,Alpha2:late_freeRes,P3:pi,Y3:name]: (((((res @ X3) @ P) = ((res @ Y3) @ P4)) => ((Rs = ((late_FreeR @ Alpha2) @ ((res @ Y3) @ P3))) => (((late_transitions @ P4) @ ((late_FreeR @ Alpha2) @ P3)) => (~ (((((fresh @ name) @ late_freeRes) @ Y3) @ Alpha2)))))))))))))))).
% 3.84/1.96 thf(fact_111_arg__min__list_Ocases, axiom, (! [B:$tType,A:$tType]: (((linorder @ B) => (! [X3:((product_prod @ (A > B)) @ (list @ A))]: (((! [F2:(A > B),X5:A]: ((X3 != ((((product_Pair @ (A > B)) @ (list @ A)) @ F2) @ (((cons @ A) @ X5) @ (nil @ A)))))) => ((! [F2:(A > B),X5:A,Y3:A,Zs:(list @ A)]: ((X3 != ((((product_Pair @ (A > B)) @ (list @ A)) @ F2) @ (((cons @ A) @ X5) @ (((cons @ A) @ Y3) @ Zs)))))) => (~ ((! [A6:(A > B)]: ((X3 != ((((product_Pair @ (A > B)) @ (list @ A)) @ A6) @ (nil @ A))))))))))))))).
% 3.84/1.96 thf(fact_112_sorted__wrt_Ocases, axiom, (! [A:$tType,X3:((product_prod @ (A > (A > $o))) @ (list @ A))]: (((! [P4:(A > (A > $o))]: ((X3 != ((((product_Pair @ (A > (A > $o))) @ (list @ A)) @ P4) @ (nil @ A))))) => (~ ((! [P4:(A > (A > $o)),X5:A,Ys:(list @ A)]: ((X3 != ((((product_Pair @ (A > (A > $o))) @ (list @ A)) @ P4) @ (((cons @ A) @ X5) @ Ys))))))))))).
% 3.84/1.96 thf(fact_113_successively_Ocases, axiom, (! [A:$tType,X3:((product_prod @ (A > (A > $o))) @ (list @ A))]: (((! [P4:(A > (A > $o))]: ((X3 != ((((product_Pair @ (A > (A > $o))) @ (list @ A)) @ P4) @ (nil @ A))))) => ((! [P4:(A > (A > $o)),X5:A]: ((X3 != ((((product_Pair @ (A > (A > $o))) @ (list @ A)) @ P4) @ (((cons @ A) @ X5) @ (nil @ A)))))) => (~ ((! [P4:(A > (A > $o)),X5:A,Y3:A,Xs2:(list @ A)]: ((X3 != ((((product_Pair @ (A > (A > $o))) @ (list @ A)) @ P4) @ (((cons @ A) @ X5) @ (((cons @ A) @ Y3) @ Xs2))))))))))))).
% 3.84/1.96 thf(fact_114_splice_Ocases, axiom, (! [A:$tType,X3:((product_prod @ (list @ A)) @ (list @ A))]: (((! [Ys:(list @ A)]: ((X3 != ((((product_Pair @ (list @ A)) @ (list @ A)) @ (nil @ A)) @ Ys)))) => (~ ((! [X5:A,Xs2:(list @ A),Ys:(list @ A)]: ((X3 != ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((cons @ A) @ X5) @ Xs2)) @ Ys)))))))))).
% 3.84/1.96 thf(fact_115_shuffles_Ocases, axiom, (! [A:$tType,X3:((product_prod @ (list @ A)) @ (list @ A))]: (((! [Ys:(list @ A)]: ((X3 != ((((product_Pair @ (list @ A)) @ (list @ A)) @ (nil @ A)) @ Ys)))) => ((! [Xs2:(list @ A)]: ((X3 != ((((product_Pair @ (list @ A)) @ (list @ A)) @ Xs2) @ (nil @ A))))) => (~ ((! [X5:A,Xs2:(list @ A),Y3:A,Ys:(list @ A)]: ((X3 != ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((cons @ A) @ X5) @ Xs2)) @ (((cons @ A) @ Y3) @ Ys)))))))))))).
% 3.84/1.96 thf(fact_116_resCasesB_H, axiom, (! [X7:name,P:pi,A2:late_subject,Y4:name,P2:pi]: ((((late_transitions @ ((res @ X7) @ P)) @ (((late_BoundR @ A2) @ Y4) @ P2)) => ((! [P4:pi,A6:name,B6:name]: (((((res @ X7) @ P) = ((res @ B6) @ P4)) => (! [P3:pi]: ((((((late_BoundR @ A2) @ Y4) @ P2) = (((late_BoundR @ (late_BoundOutputS @ A6)) @ B6) @ P3)) => (((late_transitions @ P4) @ ((late_FreeR @ ((late_OutputR @ A6) @ B6)) @ P3)) => (A6 = B6)))))))) => (~ ((! [P4:pi,A6:late_subject,X5:name,P3:pi,Y3:name]: (((((res @ X7) @ P) = ((res @ Y3) @ P4)) => (((((late_BoundR @ A2) @ Y4) @ P2) = (((late_BoundR @ A6) @ X5) @ ((res @ Y3) @ P3))) => (((late_transitions @ P4) @ (((late_BoundR @ A6) @ X5) @ P3)) => (((((fresh @ name) @ late_subject) @ Y3) @ A6) => ((Y3 != X5) => (((((fresh @ name) @ pi) @ X5) @ P4) => (~ (((((fresh @ name) @ late_subject) @ X5) @ A6)))))))))))))))))).
% 3.84/1.96 thf(fact_117_Open, axiom, (! [P:pi,A2:name,B2:name,P2:pi]: ((((late_transitions @ P) @ ((late_FreeR @ ((late_OutputR @ A2) @ B2)) @ P2)) => ((A2 != B2) => ((late_transitions @ ((res @ B2) @ P)) @ (((late_BoundR @ (late_BoundOutputS @ A2)) @ B2) @ P2))))))).
% 3.84/1.96 thf(fact_118_freshResidual, axiom, (! [P:pi,Rs:late_residual,X3:name]: ((((late_transitions @ P) @ Rs) => (((((fresh @ name) @ pi) @ X3) @ P) => ((((fresh @ name) @ late_residual) @ X3) @ Rs)))))).
% 3.84/1.96 thf(fact_119_freshBoundDerivative_I2_J, axiom, (! [P:pi,A2:late_subject,X3:name,P2:pi,Y:name]: ((((late_transitions @ P) @ (((late_BoundR @ A2) @ X3) @ P2)) => (((((fresh @ name) @ pi) @ Y) @ P) => ((Y != X3) => ((((fresh @ name) @ pi) @ Y) @ P2))))))).
% 3.84/1.96 thf(fact_120_residual_Ostrong__inducts, axiom, (! [A:$tType]: (((fs_name @ A) => (! [P:(A > (late_residual > $o)),Z:A,Residual:late_residual]: (((! [Subject2:late_subject,Name3:name,Pi5:pi,Z2:A]: ((((((fresh @ name) @ A) @ Name3) @ Z2) => (((((fresh @ name) @ late_subject) @ Name3) @ Subject2) => ((P @ Z2) @ (((late_BoundR @ Subject2) @ Name3) @ Pi5)))))) => ((! [FreeRes3:late_freeRes,Pi5:pi,Z2:A]: (((P @ Z2) @ ((late_FreeR @ FreeRes3) @ Pi5)))) => ((P @ Z) @ Residual))))))))).
% 3.84/1.96 thf(fact_121_residual_Ostrong__induct, axiom, (! [N:$tType]: (((fs_name @ N) => (! [P:(N > (late_residual > $o)),Z:N,Residual:late_residual]: (((! [Subject2:late_subject,Name3:name,Pi5:pi,Z2:N]: ((((((fresh @ name) @ N) @ Name3) @ Z2) => (((((fresh @ name) @ late_subject) @ Name3) @ Subject2) => ((P @ Z2) @ (((late_BoundR @ Subject2) @ Name3) @ Pi5)))))) => ((! [FreeRes3:late_freeRes,Pi5:pi,Z2:N]: (((P @ Z2) @ ((late_FreeR @ FreeRes3) @ Pi5)))) => ((P @ Z) @ Residual))))))))).
% 3.84/1.96 thf(fact_122_resCasesB, axiom, (! [Y:name,P:pi,A2:late_subject,X3:name,YP:pi,F3:(late_subject > (pi > $o))]: ((((late_transitions @ ((res @ Y) @ P)) @ (((late_BoundR @ A2) @ X3) @ YP)) => ((X3 != Y) => (((((fresh @ name) @ pi) @ X3) @ P) => ((! [B6:name,P3:pi]: ((((late_transitions @ P) @ ((late_FreeR @ ((late_OutputR @ B6) @ Y)) @ P3)) => ((B6 != Y) => ((A2 = (late_BoundOutputS @ B6)) => ((F3 @ (late_BoundOutputS @ B6)) @ ((((perm @ name) @ pi) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ X3) @ Y)) @ (nil @ ((product_prod @ name) @ name)))) @ P3))))))) => ((! [P3:pi]: ((((late_transitions @ P) @ (((late_BoundR @ A2) @ X3) @ P3)) => (((((fresh @ name) @ late_subject) @ Y) @ A2) => ((F3 @ A2) @ ((res @ Y) @ P3)))))) => ((F3 @ A2) @ YP))))))))).
% 3.84/1.96 thf(fact_123_freshFreeDerivative_I1_J, axiom, (! [P:pi,Alpha:late_freeRes,P2:pi,Y:name]: ((((late_transitions @ P) @ ((late_FreeR @ Alpha) @ P2)) => (((((fresh @ name) @ pi) @ Y) @ P) => ((((fresh @ name) @ late_freeRes) @ Y) @ Alpha)))))).
% 3.84/1.96 thf(fact_124_surj__pair, axiom, (! [A:$tType,B:$tType,P5:((product_prod @ A) @ B)]: ((? [X5:A,Y3:B]: ((P5 = ((((product_Pair @ A) @ B) @ X5) @ Y3))))))).
% 3.84/1.96 thf(fact_125_prod__cases, axiom, (! [B:$tType,A:$tType,P:(((product_prod @ A) @ B) > $o),P5:((product_prod @ A) @ B)]: (((! [A6:A,B6:B]: ((P @ ((((product_Pair @ A) @ B) @ A6) @ B6)))) => (P @ P5))))).
% 3.84/1.96 thf(fact_126_Pair__inject, axiom, (! [A:$tType,B:$tType,A2:A,B2:B,A5:A,B4:B]: (((((((product_Pair @ A) @ B) @ A2) @ B2) = ((((product_Pair @ A) @ B) @ A5) @ B4)) => (~ (((A2 = A5) => (B2 != B4)))))))).
% 3.84/1.96 thf(fact_127_prod__cases3, axiom, (! [A:$tType,B:$tType,C3:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ C3))]: ((~ ((! [A6:A,B6:B,C:C3]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ C3)) @ A6) @ ((((product_Pair @ B) @ C3) @ B6) @ C)))))))))).
% 3.84/1.96 thf(fact_128_prod__cases4, axiom, (! [A:$tType,B:$tType,C3:$tType,D:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ D)))]: ((~ ((! [A6:A,B6:B,C:C3,D2:D]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ D))) @ A6) @ ((((product_Pair @ B) @ ((product_prod @ C3) @ D)) @ B6) @ ((((product_Pair @ C3) @ D) @ C) @ D2))))))))))).
% 3.84/1.96 thf(fact_129_prod__cases5, axiom, (! [A:$tType,B:$tType,C3:$tType,D:$tType,E:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ ((product_prod @ D) @ E))))]: ((~ ((! [A6:A,B6:B,C:C3,D2:D,E2:E]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ ((product_prod @ D) @ E)))) @ A6) @ ((((product_Pair @ B) @ ((product_prod @ C3) @ ((product_prod @ D) @ E))) @ B6) @ ((((product_Pair @ C3) @ ((product_prod @ D) @ E)) @ C) @ ((((product_Pair @ D) @ E) @ D2) @ E2)))))))))))).
% 3.84/1.96 thf(fact_130_prod__cases6, axiom, (! [A:$tType,B:$tType,C3:$tType,D:$tType,E:$tType,F4:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ ((product_prod @ D) @ ((product_prod @ E) @ F4)))))]: ((~ ((! [A6:A,B6:B,C:C3,D2:D,E2:E,F2:F4]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ ((product_prod @ D) @ ((product_prod @ E) @ F4))))) @ A6) @ ((((product_Pair @ B) @ ((product_prod @ C3) @ ((product_prod @ D) @ ((product_prod @ E) @ F4)))) @ B6) @ ((((product_Pair @ C3) @ ((product_prod @ D) @ ((product_prod @ E) @ F4))) @ C) @ ((((product_Pair @ D) @ ((product_prod @ E) @ F4)) @ D2) @ ((((product_Pair @ E) @ F4) @ E2) @ F2))))))))))))).
% 3.84/1.96 thf(fact_131_prod__cases7, axiom, (! [A:$tType,B:$tType,C3:$tType,D:$tType,E:$tType,F4:$tType,G2:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F4) @ G2))))))]: ((~ ((! [A6:A,B6:B,C:C3,D2:D,E2:E,F2:F4,G3:G2]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F4) @ G2)))))) @ A6) @ ((((product_Pair @ B) @ ((product_prod @ C3) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F4) @ G2))))) @ B6) @ ((((product_Pair @ C3) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F4) @ G2)))) @ C) @ ((((product_Pair @ D) @ ((product_prod @ E) @ ((product_prod @ F4) @ G2))) @ D2) @ ((((product_Pair @ E) @ ((product_prod @ F4) @ G2)) @ E2) @ ((((product_Pair @ F4) @ G2) @ F2) @ G3)))))))))))))).
% 3.84/1.96 thf(fact_132_prod__induct3, axiom, (! [C3:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ C3)) > $o),X3:((product_prod @ A) @ ((product_prod @ B) @ C3))]: (((! [A6:A,B6:B,C:C3]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ C3)) @ A6) @ ((((product_Pair @ B) @ C3) @ B6) @ C))))) => (P @ X3))))).
% 3.84/1.96 thf(fact_133_prod__induct4, axiom, (! [D:$tType,C3:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ D))) > $o),X3:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ D)))]: (((! [A6:A,B6:B,C:C3,D2:D]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ D))) @ A6) @ ((((product_Pair @ B) @ ((product_prod @ C3) @ D)) @ B6) @ ((((product_Pair @ C3) @ D) @ C) @ D2)))))) => (P @ X3))))).
% 3.84/1.96 thf(fact_134_prod__induct5, axiom, (! [E:$tType,D:$tType,C3:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ ((product_prod @ D) @ E)))) > $o),X3:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ ((product_prod @ D) @ E))))]: (((! [A6:A,B6:B,C:C3,D2:D,E2:E]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ ((product_prod @ D) @ E)))) @ A6) @ ((((product_Pair @ B) @ ((product_prod @ C3) @ ((product_prod @ D) @ E))) @ B6) @ ((((product_Pair @ C3) @ ((product_prod @ D) @ E)) @ C) @ ((((product_Pair @ D) @ E) @ D2) @ E2))))))) => (P @ X3))))).
% 3.84/1.96 thf(fact_135_prod__induct6, axiom, (! [F4:$tType,E:$tType,D:$tType,C3:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ ((product_prod @ D) @ ((product_prod @ E) @ F4))))) > $o),X3:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ ((product_prod @ D) @ ((product_prod @ E) @ F4)))))]: (((! [A6:A,B6:B,C:C3,D2:D,E2:E,F2:F4]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ ((product_prod @ D) @ ((product_prod @ E) @ F4))))) @ A6) @ ((((product_Pair @ B) @ ((product_prod @ C3) @ ((product_prod @ D) @ ((product_prod @ E) @ F4)))) @ B6) @ ((((product_Pair @ C3) @ ((product_prod @ D) @ ((product_prod @ E) @ F4))) @ C) @ ((((product_Pair @ D) @ ((product_prod @ E) @ F4)) @ D2) @ ((((product_Pair @ E) @ F4) @ E2) @ F2)))))))) => (P @ X3))))).
% 3.84/1.96 thf(fact_136_prod__induct7, axiom, (! [G2:$tType,F4:$tType,E:$tType,D:$tType,C3:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F4) @ G2)))))) > $o),X3:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F4) @ G2))))))]: (((! [A6:A,B6:B,C:C3,D2:D,E2:E,F2:F4,G3:G2]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F4) @ G2)))))) @ A6) @ ((((product_Pair @ B) @ ((product_prod @ C3) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F4) @ G2))))) @ B6) @ ((((product_Pair @ C3) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F4) @ G2)))) @ C) @ ((((product_Pair @ D) @ ((product_prod @ E) @ ((product_prod @ F4) @ G2))) @ D2) @ ((((product_Pair @ E) @ ((product_prod @ F4) @ G2)) @ E2) @ ((((product_Pair @ F4) @ G2) @ F2) @ G3))))))))) => (P @ X3))))).
% 3.84/1.96 thf(fact_137_old_Oprod_Oexhaust, axiom, (! [A:$tType,B:$tType,Y:((product_prod @ A) @ B)]: ((~ ((! [A6:A,B6:B]: ((Y != ((((product_Pair @ A) @ B) @ A6) @ B6))))))))).
% 3.84/1.96 thf(fact_138_old_Oprod_Oinducts, axiom, (! [B:$tType,A:$tType,P:(((product_prod @ A) @ B) > $o),Prod:((product_prod @ A) @ B)]: (((! [A6:A,B6:B]: ((P @ ((((product_Pair @ A) @ B) @ A6) @ B6)))) => (P @ Prod))))).
% 3.84/1.96 thf(fact_139_not__Cons__self2, axiom, (! [A:$tType,X3:A,Xs:(list @ A)]: (((((cons @ A) @ X3) @ Xs) != Xs)))).
% 3.84/1.96 thf(fact_140_allE__Nil, axiom, (! [A:$tType,P:((list @ A) > $o)]: (((! [X_1:(list @ A)]: ((P @ X_1))) => (P @ (nil @ A)))))).
% 3.84/1.96 thf(fact_141_if__eqvt, axiom, (! [A:$tType,B:$tType,Pi:(list @ ((product_prod @ A) @ A)),B2:$o,C1:B,C22:B]: (((((((perm @ A) @ $o) @ Pi) @ B2) => (((((perm @ A) @ B) @ Pi) @ ((((if @ B) @ B2) @ C1) @ C22)) = ((((perm @ A) @ B) @ Pi) @ C1))) & ((~ (((((perm @ A) @ $o) @ Pi) @ B2))) => (((((perm @ A) @ B) @ Pi) @ ((((if @ B) @ B2) @ C1) @ C22)) = ((((perm @ A) @ B) @ Pi) @ C22))))))).
% 3.84/1.96 thf(fact_142_pt__bij3, axiom, (! [X:$tType,A:$tType,X3:A,Y:A,Pi:(list @ ((product_prod @ X) @ X))]: (((X3 = Y) => (((((perm @ X) @ A) @ Pi) @ X3) = ((((perm @ X) @ A) @ Pi) @ Y)))))).
% 3.84/1.96 thf(fact_143_abs__fun__if, axiom, (! [X:$tType,A:$tType,C2:$o,Pi:(list @ ((product_prod @ X) @ X)),X3:A,Y:A]: (((C2 => (((((perm @ X) @ A) @ Pi) @ ((((if @ A) @ C2) @ X3) @ Y)) = ((((perm @ X) @ A) @ Pi) @ X3))) & ((~ (C2)) => (((((perm @ X) @ A) @ Pi) @ ((((if @ A) @ C2) @ X3) @ Y)) = ((((perm @ X) @ A) @ Pi) @ Y))))))).
% 3.84/1.96 thf(fact_144_alphaRes, axiom, (! [C2:name,P:pi,A2:name]: ((((((fresh @ name) @ pi) @ C2) @ P) => (((res @ A2) @ P) = ((res @ C2) @ ((((perm @ name) @ pi) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ A2) @ C2)) @ (nil @ ((product_prod @ name) @ name)))) @ P))))))).
% 3.84/1.96 thf(fact_145_alphaBoundResidual, axiom, (! [X7:name,P:pi,A2:late_subject,X3:name]: ((((((fresh @ name) @ pi) @ X7) @ P) => ((((late_BoundR @ A2) @ X3) @ P) = (((late_BoundR @ A2) @ X7) @ ((((perm @ name) @ pi) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ X3) @ X7)) @ (nil @ ((product_prod @ name) @ name)))) @ P))))))).
% 3.84/1.96 thf(fact_146_perm__prod_Osimps, axiom, (! [A:$tType,X:$tType,B:$tType,Pi:(list @ ((product_prod @ X) @ X)),X3:A,Y:B]: ((((((perm @ X) @ ((product_prod @ A) @ B)) @ Pi) @ ((((product_Pair @ A) @ B) @ X3) @ Y)) = ((((product_Pair @ A) @ B) @ ((((perm @ X) @ A) @ Pi) @ X3)) @ ((((perm @ X) @ B) @ Pi) @ Y)))))).
% 3.84/1.96 thf(fact_147_list_Odistinct_I1_J, axiom, (! [A:$tType,X21:A,X222:(list @ A)]: (((nil @ A) != (((cons @ A) @ X21) @ X222))))).
% 3.84/1.96 thf(fact_148_list_OdiscI, axiom, (! [A:$tType,List:(list @ A),X21:A,X222:(list @ A)]: (((List = (((cons @ A) @ X21) @ X222)) => (List != (nil @ A)))))).
% 3.84/1.96 thf(fact_149_list_Oexhaust, axiom, (! [A:$tType,Y:(list @ A)]: (((Y != (nil @ A)) => (~ ((! [X212:A,X223:(list @ A)]: ((Y != (((cons @ A) @ X212) @ X223)))))))))).
% 3.84/1.96 thf(fact_150_list_Oinducts, axiom, (! [A:$tType,P:((list @ A) > $o),List:(list @ A)]: (((P @ (nil @ A)) => ((! [X13:A,X23:(list @ A)]: (((P @ X23) => (P @ (((cons @ A) @ X13) @ X23))))) => (P @ List)))))).
% 3.84/1.96 thf(fact_151_neq__Nil__conv, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) = (? [Y5:A,Ys2:(list @ A)]: ((Xs = (((cons @ A) @ Y5) @ Ys2)))))))).
% 3.84/1.96 thf(fact_152_list__induct2_H, axiom, (! [A:$tType,B:$tType,P:((list @ A) > ((list @ B) > $o)),Xs:(list @ A),Ys3:(list @ B)]: ((((P @ (nil @ A)) @ (nil @ B)) => ((! [X5:A,Xs2:(list @ A)]: (((P @ (((cons @ A) @ X5) @ Xs2)) @ (nil @ B)))) => ((! [Y3:B,Ys:(list @ B)]: (((P @ (nil @ A)) @ (((cons @ B) @ Y3) @ Ys)))) => ((! [X5:A,Xs2:(list @ A),Y3:B,Ys:(list @ B)]: ((((P @ Xs2) @ Ys) => ((P @ (((cons @ A) @ X5) @ Xs2)) @ (((cons @ B) @ Y3) @ Ys))))) => ((P @ Xs) @ Ys3)))))))).
% 3.84/1.96 thf(fact_153_splice_Oinduct, axiom, (! [A:$tType,P:((list @ A) > ((list @ A) > $o)),A0:(list @ A),A1:(list @ A)]: (((! [X_1:(list @ A)]: (((P @ (nil @ A)) @ X_1))) => ((! [X5:A,Xs2:(list @ A),Ys:(list @ A)]: ((((P @ Ys) @ Xs2) => ((P @ (((cons @ A) @ X5) @ Xs2)) @ Ys)))) => ((P @ A0) @ A1)))))).
% 3.84/1.96 thf(fact_154_induct__list012, axiom, (! [A:$tType,P:((list @ A) > $o),Xs:(list @ A)]: (((P @ (nil @ A)) => ((! [X5:A]: ((P @ (((cons @ A) @ X5) @ (nil @ A))))) => ((! [X5:A,Y3:A,Zs:(list @ A)]: (((P @ Zs) => ((P @ (((cons @ A) @ Y3) @ Zs)) => (P @ (((cons @ A) @ X5) @ (((cons @ A) @ Y3) @ Zs))))))) => (P @ Xs))))))).
% 3.84/1.96 thf(fact_155_min__list_Ocases, axiom, (! [A:$tType]: (((ord @ A) => (! [X3:(list @ A)]: (((! [X5:A,Xs2:(list @ A)]: ((X3 != (((cons @ A) @ X5) @ Xs2)))) => (X3 = (nil @ A))))))))).
% 3.84/1.96 thf(fact_156_min__list_Oinduct, axiom, (! [A:$tType]: (((ord @ A) => (! [P:((list @ A) > $o),A0:(list @ A)]: (((! [X5:A,Xs2:(list @ A)]: (((! [X213:A,X224:(list @ A)]: (((Xs2 = (((cons @ A) @ X213) @ X224)) => (P @ Xs2)))) => (P @ (((cons @ A) @ X5) @ Xs2))))) => ((P @ (nil @ A)) => (P @ A0))))))))).
% 3.84/1.96 thf(fact_157_shuffles_Oinduct, axiom, (! [A:$tType,P:((list @ A) > ((list @ A) > $o)),A0:(list @ A),A1:(list @ A)]: (((! [X_1:(list @ A)]: (((P @ (nil @ A)) @ X_1))) => ((! [Xs2:(list @ A)]: (((P @ Xs2) @ (nil @ A)))) => ((! [X5:A,Xs2:(list @ A),Y3:A,Ys:(list @ A)]: ((((P @ Xs2) @ (((cons @ A) @ Y3) @ Ys)) => (((P @ (((cons @ A) @ X5) @ Xs2)) @ Ys) => ((P @ (((cons @ A) @ X5) @ Xs2)) @ (((cons @ A) @ Y3) @ Ys)))))) => ((P @ A0) @ A1))))))).
% 3.84/1.96 thf(fact_158_transpose_Ocases, axiom, (! [A:$tType,X3:(list @ (list @ A))]: (((X3 != (nil @ (list @ A))) => ((! [Xss:(list @ (list @ A))]: ((X3 != (((cons @ (list @ A)) @ (nil @ A)) @ Xss)))) => (~ ((! [X5:A,Xs2:(list @ A),Xss:(list @ (list @ A))]: ((X3 != (((cons @ (list @ A)) @ (((cons @ A) @ X5) @ Xs2)) @ Xss))))))))))).
% 3.84/1.96 thf(fact_159_remdups__adj_Ocases, axiom, (! [A:$tType,X3:(list @ A)]: (((X3 != (nil @ A)) => ((! [X5:A]: ((X3 != (((cons @ A) @ X5) @ (nil @ A))))) => (~ ((! [X5:A,Y3:A,Xs2:(list @ A)]: ((X3 != (((cons @ A) @ X5) @ (((cons @ A) @ Y3) @ Xs2)))))))))))).
% 3.84/1.96 thf(fact_160_sorted__wrt_Oinduct, axiom, (! [A:$tType,P:((A > (A > $o)) > ((list @ A) > $o)),A0:(A > (A > $o)),A1:(list @ A)]: (((! [P4:(A > (A > $o))]: (((P @ P4) @ (nil @ A)))) => ((! [P4:(A > (A > $o)),X5:A,Ys:(list @ A)]: ((((P @ P4) @ Ys) => ((P @ P4) @ (((cons @ A) @ X5) @ Ys))))) => ((P @ A0) @ A1)))))).
% 3.84/1.96 thf(fact_161_remdups__adj_Oinduct, axiom, (! [A:$tType,P:((list @ A) > $o),A0:(list @ A)]: (((P @ (nil @ A)) => ((! [X5:A]: ((P @ (((cons @ A) @ X5) @ (nil @ A))))) => ((! [X5:A,Y3:A,Xs2:(list @ A)]: ((((X5 = Y3) => (P @ (((cons @ A) @ X5) @ Xs2))) => (((X5 != Y3) => (P @ (((cons @ A) @ Y3) @ Xs2))) => (P @ (((cons @ A) @ X5) @ (((cons @ A) @ Y3) @ Xs2))))))) => (P @ A0))))))).
% 3.84/1.96 thf(fact_162_arg__min__list_Oinduct, axiom, (! [B:$tType,A:$tType]: (((linorder @ B) => (! [P:((A > B) > ((list @ A) > $o)),A0:(A > B),A1:(list @ A)]: (((! [F2:(A > B),X5:A]: (((P @ F2) @ (((cons @ A) @ X5) @ (nil @ A))))) => ((! [F2:(A > B),X5:A,Y3:A,Zs:(list @ A)]: ((((P @ F2) @ (((cons @ A) @ Y3) @ Zs)) => ((P @ F2) @ (((cons @ A) @ X5) @ (((cons @ A) @ Y3) @ Zs)))))) => ((! [A6:(A > B)]: (((P @ A6) @ (nil @ A)))) => ((P @ A0) @ A1)))))))))).
% 3.84/1.96 thf(fact_163_successively_Oinduct, axiom, (! [A:$tType,P:((A > (A > $o)) > ((list @ A) > $o)),A0:(A > (A > $o)),A1:(list @ A)]: (((! [P4:(A > (A > $o))]: (((P @ P4) @ (nil @ A)))) => ((! [P4:(A > (A > $o)),X5:A]: (((P @ P4) @ (((cons @ A) @ X5) @ (nil @ A))))) => ((! [P4:(A > (A > $o)),X5:A,Y3:A,Xs2:(list @ A)]: ((((P @ P4) @ (((cons @ A) @ Y3) @ Xs2)) => ((P @ P4) @ (((cons @ A) @ X5) @ (((cons @ A) @ Y3) @ Xs2)))))) => ((P @ A0) @ A1))))))).
% 3.84/1.96 thf(fact_164_list__nonempty__induct, axiom, (! [A:$tType,Xs:(list @ A),P:((list @ A) > $o)]: (((Xs != (nil @ A)) => ((! [X5:A]: ((P @ (((cons @ A) @ X5) @ (nil @ A))))) => ((! [X5:A,Xs2:(list @ A)]: (((Xs2 != (nil @ A)) => ((P @ Xs2) => (P @ (((cons @ A) @ X5) @ Xs2)))))) => (P @ Xs))))))).
% 3.84/1.96 thf(fact_165_map__tailrec__rev_Oinduct, axiom, (! [A:$tType,B:$tType,P:((A > B) > ((list @ A) > ((list @ B) > $o))),A0:(A > B),A1:(list @ A),A22:(list @ B)]: (((! [F2:(A > B),X_1:(list @ B)]: ((((P @ F2) @ (nil @ A)) @ X_1))) => ((! [F2:(A > B),A6:A,As:(list @ A),Bs:(list @ B)]: (((((P @ F2) @ As) @ (((cons @ B) @ (F2 @ A6)) @ Bs)) => (((P @ F2) @ (((cons @ A) @ A6) @ As)) @ Bs)))) => (((P @ A0) @ A1) @ A22)))))).
% 3.84/1.96 thf(fact_166_strict__sorted_Ocases, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:(list @ A)]: (((X3 != (nil @ A)) => (~ ((! [X5:A,Ys:(list @ A)]: ((X3 != (((cons @ A) @ X5) @ Ys))))))))))))).
% 3.84/1.96 thf(fact_167_Free_Ohyps, axiom, ((late_transitions @ ((par @ p) @ ((res @ x) @ q))) @ ((late_FreeR @ alpha) @ pxQ))).
% 3.84/1.96 thf(fact_168_old_Oprod_Orec, axiom, (! [A:$tType,T:$tType,B:$tType,F1:(A > (B > T)),A2:A,B2:B]: (((((((product_rec_prod @ A) @ B) @ T) @ F1) @ ((((product_Pair @ A) @ B) @ A2) @ B2)) = ((F1 @ A2) @ B2))))).
% 3.84/1.96 thf(fact_169_supports__def, axiom, (! [A:$tType,X:$tType]: ((((supports @ X) @ A) = (^ [S:(set @ X),X4:A]: ((! [A3:X,B3:X]: ((((~ ((((member @ X) @ A3) @ S))) & (~ ((((member @ X) @ B3) @ S)))) => (((((perm @ X) @ A) @ (((cons @ ((product_prod @ X) @ X)) @ ((((product_Pair @ X) @ X) @ A3) @ B3)) @ (nil @ ((product_prod @ X) @ X)))) @ X4) = X4)))))))))).
% 3.84/1.96 thf(fact_170_perm__residual__Rep_Osimps_I2_J, axiom, (! [X:$tType,Pi:(list @ ((product_prod @ X) @ X)),FreeRes:late_freeRes,Pia:pi]: ((((((perm @ X) @ late_residual_Rep) @ Pi) @ ((late_r347633188eR_Rep @ FreeRes) @ Pia)) = ((late_r347633188eR_Rep @ ((((perm @ X) @ late_freeRes) @ Pi) @ FreeRes)) @ ((((perm @ X) @ pi) @ Pi) @ Pia)))))).
% 3.84/1.96 thf(fact_171_alphaInput, axiom, (! [C2:name,P:pi,A2:name,X3:name]: ((((((fresh @ name) @ pi) @ C2) @ P) => ((((input @ A2) @ X3) @ P) = (((input @ A2) @ C2) @ ((((perm @ name) @ pi) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ X3) @ C2)) @ (nil @ ((product_prod @ name) @ name)))) @ P))))))).
% 3.84/1.96 thf(fact_172_name__calc_I1_J, axiom, (! [A2:name,B2:name,Pi:(list @ ((product_prod @ name) @ name)),X3:name]: ((((((perm @ name) @ name) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ A2) @ B2)) @ Pi)) @ X3) = (((swap @ name) @ ((((product_Pair @ name) @ name) @ A2) @ B2)) @ ((((perm @ name) @ name) @ Pi) @ X3)))))).
% 3.84/1.96 thf(fact_173_Late__Semantics1_Osubject_Oinject_I1_J, axiom, (! [X1:name,Y1:name]: ((((late_InputS @ X1) = (late_InputS @ Y1)) = (X1 = Y1))))).
% 3.84/1.96 thf(fact_174_residual__Rep_Oinject_I2_J, axiom, (! [X21:late_freeRes,X222:pi,Y21:late_freeRes,Y22:pi]: (((((late_r347633188eR_Rep @ X21) @ X222) = ((late_r347633188eR_Rep @ Y21) @ Y22)) = ((X21 = Y21) & (X222 = Y22)))))).
% 3.84/1.96 thf(fact_175_pi_Ofresh_I8_J, axiom, (! [A2:name,X22:pi,X1:pi]: ((((((fresh @ name) @ pi) @ A2) @ ((par @ X22) @ X1)) = (((((fresh @ name) @ pi) @ A2) @ X22) & ((((fresh @ name) @ pi) @ A2) @ X1)))))).
% 3.84/1.96 thf(fact_176_pi_Operm_I8_J, axiom, (! [Pi:(list @ ((product_prod @ name) @ name)),X22:pi,X1:pi]: ((((((perm @ name) @ pi) @ Pi) @ ((par @ X22) @ X1)) = ((par @ ((((perm @ name) @ pi) @ Pi) @ X22)) @ ((((perm @ name) @ pi) @ Pi) @ X1)))))).
% 3.84/1.96 thf(fact_177_pi_Operm_I4_J, axiom, (! [Pi:(list @ ((product_prod @ name) @ name)),X32:name,X1:name,X22:pi]: ((((((perm @ name) @ pi) @ Pi) @ (((input @ X32) @ X1) @ X22)) = (((input @ ((((perm @ name) @ name) @ Pi) @ X32)) @ ((((perm @ name) @ name) @ Pi) @ X1)) @ ((((perm @ name) @ pi) @ Pi) @ X22)))))).
% 3.84/1.96 thf(fact_178_subject_Ofresh_I1_J, axiom, (! [A2:name,X1:name]: ((((((fresh @ name) @ late_subject) @ A2) @ (late_InputS @ X1)) = ((((fresh @ name) @ name) @ A2) @ X1))))).
% 3.84/1.96 thf(fact_179_subject_Operm_I1_J, axiom, (! [Pi:(list @ ((product_prod @ name) @ name)),X1:name]: ((((((perm @ name) @ late_subject) @ Pi) @ (late_InputS @ X1)) = (late_InputS @ ((((perm @ name) @ name) @ Pi) @ X1)))))).
% 3.84/1.96 thf(fact_180_ScopeExt, axiom, (! [Y:name,R:pi,Z:name,S2:pi]: ((((((fresh @ name) @ pi) @ Y) @ R) => (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ ((res @ Y) @ ((res @ Z) @ ((par @ R) @ S2)))) @ ((res @ Z) @ ((par @ R) @ ((res @ Y) @ S2))))) @ rel))))).
% 3.84/1.96 thf(fact_181_Res, axiom, (! [Y:name,R:pi,S2:pi]: ((((((fresh @ name) @ pi) @ Y) @ R) => (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ ((res @ Y) @ ((par @ R) @ S2))) @ ((par @ R) @ ((res @ Y) @ S2)))) @ rel))))).
% 3.84/1.96 thf(fact_182_pi_Odistinct_I55_J, axiom, (! [Name12:name,Name22:name,Pi:pi,Pi12:pi,Pi22:pi]: (((((input @ Name12) @ Name22) @ Pi) != ((par @ Pi12) @ Pi22))))).
% 3.84/1.96 thf(fact_183_pi_Oinject_I7_J, axiom, (! [X22:pi,X1:pi,Y2:pi,Y1:pi]: (((((par @ X22) @ X1) = ((par @ Y2) @ Y1)) = ((X22 = Y2) & (X1 = Y1)))))).
% 3.84/1.96 thf(fact_184_pi_Odistinct_I85_J, axiom, (! [Pi1:pi,Pi2:pi,Name4:name,Pi4:pi]: ((((par @ Pi1) @ Pi2) != ((res @ Name4) @ Pi4))))).
% 3.84/1.96 thf(fact_185_transitions_OInput, axiom, (! [X3:name,A2:name,P:pi]: (((X3 != A2) => ((late_transitions @ (((input @ A2) @ X3) @ P)) @ (((late_BoundR @ (late_InputS @ A2)) @ X3) @ P)))))).
% 3.84/1.96 thf(fact_186_Late__Semantics_OInput, axiom, (! [A2:name,X3:name,P:pi]: (((late_transitions @ (((input @ A2) @ X3) @ P)) @ (((late_BoundR @ (late_InputS @ A2)) @ X3) @ P))))).
% 3.84/1.96 thf(fact_187_pi_Odistinct_I57_J, axiom, (! [Name12:name,Name22:name,Pi:pi,Name4:name,Pi4:pi]: (((((input @ Name12) @ Name22) @ Pi) != ((res @ Name4) @ Pi4))))).
% 3.84/1.96 thf(fact_188_Late__Semantics_Osubject_Odistinct_I1_J, axiom, (! [Name:name,Name4:name]: (((late_InputS @ Name) != (late_BoundOutputS @ Name4))))).
% 3.84/1.96 thf(fact_189_Late__Semantics1_Osubject_Odistinct_I1_J, axiom, (! [X1:name,X22:name]: (((late_InputS @ X1) != (late_BoundOutputS @ X22))))).
% 3.84/1.96 thf(fact_190_subject_Oinducts, axiom, (! [P:(late_subject > $o),Subject:late_subject]: (((! [Name3:name]: ((P @ (late_InputS @ Name3)))) => ((! [Name3:name]: ((P @ (late_BoundOutputS @ Name3)))) => (P @ Subject)))))).
% 3.84/1.96 thf(fact_191_subject_Oexhaust, axiom, (! [Y:late_subject]: (((! [X13:name]: ((Y != (late_InputS @ X13)))) => (~ ((! [X23:name]: ((Y != (late_BoundOutputS @ X23)))))))))).
% 3.84/1.96 thf(fact_192_subject_Ostrong__induct_H, axiom, (! [N:$tType,P:(N > (late_subject > $o)),Z:N,Subject:late_subject]: (((! [Name3:name,Z2:N]: (((P @ Z2) @ (late_InputS @ Name3)))) => ((! [Name3:name,Z2:N]: (((P @ Z2) @ (late_BoundOutputS @ Name3)))) => ((P @ Z) @ Subject)))))).
% 3.84/1.96 thf(fact_193_subject_Ostrong__inducts, axiom, (! [A:$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)))))).
% 3.84/1.96 thf(fact_194_Par2F, axiom, (! [Q:pi,Alpha:late_freeRes,Q2:pi,P:pi]: ((((late_transitions @ Q) @ ((late_FreeR @ Alpha) @ Q2)) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ Alpha) @ ((par @ P) @ Q2))))))).
% 3.84/1.96 thf(fact_195_Par1F, axiom, (! [P:pi,Alpha:late_freeRes,P2:pi,Q:pi]: ((((late_transitions @ P) @ ((late_FreeR @ Alpha) @ P2)) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ Alpha) @ ((par @ P2) @ Q))))))).
% 3.84/1.96 thf(fact_196_name__calc_I3_J, axiom, (! [A2:name,C2:name,B2:name]: ((((A2 = C2) => ((((swap @ name) @ ((((product_Pair @ name) @ name) @ A2) @ B2)) @ C2) = B2)) & ((A2 != C2) => (((B2 = C2) => ((((swap @ name) @ ((((product_Pair @ name) @ name) @ A2) @ B2)) @ C2) = A2)) & ((B2 != C2) => ((((swap @ name) @ ((((product_Pair @ name) @ name) @ A2) @ B2)) @ C2) = C2)))))))).
% 3.84/1.96 thf(fact_197_resTrans_I2_J, axiom, (! [X3:name,Y:name,P:pi,Rs:late_residual]: ((~ (((late_transitions @ ((res @ X3) @ (((input @ X3) @ Y) @ P))) @ Rs)))))).
% 3.84/1.96 thf(fact_198_inputIneqTrans, axiom, (! [A2:name,X3:name,P:pi,B2:late_subject,Y:name,P2:pi]: ((((late_transitions @ (((input @ A2) @ X3) @ P)) @ (((late_BoundR @ B2) @ Y) @ P2)) => (~ (((((fresh @ name) @ late_subject) @ A2) @ B2))))))).
% 3.84/1.96 thf(fact_199_inputFreeTrans, axiom, (! [A2:name,X3:name,P:pi,Alpha:late_freeRes,P2:pi]: ((~ (((late_transitions @ (((input @ A2) @ X3) @ P)) @ ((late_FreeR @ Alpha) @ P2))))))).
% 3.84/1.96 thf(fact_200_Late__Semantics_OPar1B, axiom, (! [P:pi,A2:late_subject,X3:name,P2:pi,Q:pi]: ((((late_transitions @ P) @ (((late_BoundR @ A2) @ X3) @ P2)) => (((((fresh @ name) @ pi) @ X3) @ Q) => ((late_transitions @ ((par @ P) @ Q)) @ (((late_BoundR @ A2) @ X3) @ ((par @ P2) @ Q)))))))).
% 3.84/1.96 thf(fact_201_Late__Semantics_OPar2B, axiom, (! [Q:pi,A2:late_subject,X3:name,Q2:pi,P:pi]: ((((late_transitions @ Q) @ (((late_BoundR @ A2) @ X3) @ Q2)) => (((((fresh @ name) @ pi) @ X3) @ P) => ((late_transitions @ ((par @ P) @ Q)) @ (((late_BoundR @ A2) @ X3) @ ((par @ P) @ Q2)))))))).
% 3.84/1.96 thf(fact_202_parCasesB, axiom, (! [P:pi,Q:pi,A2:late_subject,X3:name,PQ:pi,Prop:(pi > $o)]: ((((late_transitions @ ((par @ P) @ Q)) @ (((late_BoundR @ A2) @ X3) @ PQ)) => (((((fresh @ name) @ pi) @ X3) @ P) => (((((fresh @ name) @ pi) @ X3) @ Q) => ((! [P3:pi]: ((((late_transitions @ P) @ (((late_BoundR @ A2) @ X3) @ P3)) => (Prop @ ((par @ P3) @ Q))))) => ((! [Q3:pi]: ((((late_transitions @ Q) @ (((late_BoundR @ A2) @ X3) @ Q3)) => (Prop @ ((par @ P) @ Q3))))) => (Prop @ PQ))))))))).
% 3.84/1.96 thf(fact_203_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,A6:late_subject,X5:name,P3:pi,Q4:pi]: (((((par @ P) @ Q) = ((par @ P4) @ Q4)) => (((((late_BoundR @ B2) @ Y) @ P2) = (((late_BoundR @ A6) @ X5) @ ((par @ P3) @ Q4))) => (((late_transitions @ P4) @ (((late_BoundR @ A6) @ X5) @ P3)) => (((((fresh @ name) @ pi) @ X5) @ P4) => (((((fresh @ name) @ pi) @ X5) @ Q4) => (~ (((((fresh @ name) @ late_subject) @ X5) @ A6)))))))))) => (~ ((! [Q4:pi,A6:late_subject,X5:name,Q3:pi,P4:pi]: (((((par @ P) @ Q) = ((par @ P4) @ Q4)) => (((((late_BoundR @ B2) @ Y) @ P2) = (((late_BoundR @ A6) @ X5) @ ((par @ P4) @ Q3))) => (((late_transitions @ Q4) @ (((late_BoundR @ A6) @ X5) @ Q3)) => (((((fresh @ name) @ pi) @ X5) @ P4) => (((((fresh @ name) @ pi) @ X5) @ Q4) => (~ (((((fresh @ name) @ late_subject) @ X5) @ A6))))))))))))))))).
% 3.84/1.96 thf(fact_204_transitions_OPar1B, axiom, (! [P:pi,A2:late_subject,X3:name,P2:pi,Q:pi]: ((((late_transitions @ P) @ (((late_BoundR @ A2) @ X3) @ P2)) => (((((fresh @ name) @ pi) @ X3) @ P) => (((((fresh @ name) @ pi) @ X3) @ Q) => (((((fresh @ name) @ late_subject) @ X3) @ A2) => ((late_transitions @ ((par @ P) @ Q)) @ (((late_BoundR @ A2) @ X3) @ ((par @ P2) @ Q)))))))))).
% 3.84/1.96 thf(fact_205_transitions_OPar2B, axiom, (! [Q:pi,A2:late_subject,X3:name,Q2:pi,P:pi]: ((((late_transitions @ Q) @ (((late_BoundR @ A2) @ X3) @ Q2)) => (((((fresh @ name) @ pi) @ X3) @ P) => (((((fresh @ name) @ pi) @ X3) @ Q) => (((((fresh @ name) @ late_subject) @ X3) @ A2) => ((late_transitions @ ((par @ P) @ Q)) @ (((late_BoundR @ A2) @ X3) @ ((par @ P) @ Q2)))))))))).
% 3.84/1.96 thf(fact_206_resInputFreeTrans, axiom, (! [X3:name,A2:name,Y:name,P:pi,Alpha:late_freeRes,P2:pi]: ((~ (((late_transitions @ ((res @ X3) @ (((input @ A2) @ Y) @ P))) @ ((late_FreeR @ Alpha) @ P2))))))).
% 3.84/1.96 thf(fact_207_inputBoundOutputTrans, axiom, (! [A2:name,X3:name,P:pi,B2:name,Y:name,P2:pi]: ((~ (((late_transitions @ (((input @ A2) @ X3) @ P)) @ (((late_BoundR @ (late_BoundOutputS @ B2)) @ Y) @ P2))))))).
% 3.84/1.96 thf(fact_208_inputCases, axiom, (! [A2:name,X3:name,P:pi,B2:late_subject,Y:name,YP:pi,Prop:(late_subject > (name > (pi > $o)))]: ((((late_transitions @ (((input @ A2) @ X3) @ P)) @ (((late_BoundR @ B2) @ Y) @ YP)) => ((Y != A2) => ((Y != X3) => (((((fresh @ name) @ pi) @ Y) @ P) => (((B2 = (late_InputS @ A2)) => ((YP = ((((perm @ name) @ pi) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ X3) @ Y)) @ (nil @ ((product_prod @ name) @ name)))) @ P)) => (((Prop @ (late_InputS @ A2)) @ Y) @ ((((perm @ name) @ pi) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ X3) @ Y)) @ (nil @ ((product_prod @ name) @ name)))) @ P)))) => (((Prop @ B2) @ Y) @ YP))))))))).
% 3.84/1.96 thf(fact_209_resInputBoundOutputTrans, axiom, (! [X3:name,A2:name,Y:name,P:pi,B2:name,Z:name,P2:pi]: ((~ (((late_transitions @ ((res @ X3) @ (((input @ A2) @ Y) @ P))) @ (((late_BoundR @ (late_BoundOutputS @ B2)) @ Z) @ P2))))))).
% 3.84/1.96 thf(fact_210_Late__Semantics_OClose1, axiom, (! [P:pi,A2:name,X3:name,P2:pi,Q:pi,Y:name,Q2:pi]: ((((late_transitions @ P) @ (((late_BoundR @ (late_InputS @ A2)) @ X3) @ P2)) => (((late_transitions @ Q) @ (((late_BoundR @ (late_BoundOutputS @ A2)) @ Y) @ Q2)) => (((((fresh @ name) @ pi) @ Y) @ P) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ late_TauR) @ ((res @ Y) @ ((par @ (((subs @ P2) @ X3) @ Y)) @ Q2)))))))))).
% 3.84/1.96 thf(fact_211_Late__Semantics_OClose2, axiom, (! [P:pi,A2:name,Y:name,P2:pi,Q:pi,X3:name,Q2:pi]: ((((late_transitions @ P) @ (((late_BoundR @ (late_BoundOutputS @ A2)) @ Y) @ P2)) => (((late_transitions @ Q) @ (((late_BoundR @ (late_InputS @ A2)) @ X3) @ Q2)) => (((((fresh @ name) @ pi) @ Y) @ Q) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ late_TauR) @ ((res @ Y) @ ((par @ P2) @ (((subs @ Q2) @ X3) @ Y))))))))))).
% 3.84/1.96 thf(fact_212_transitions_OClose1, axiom, (! [P:pi,A2:name,X3:name,P2:pi,Q:pi,Y:name,Q2:pi]: ((((late_transitions @ P) @ (((late_BoundR @ (late_InputS @ A2)) @ X3) @ P2)) => (((late_transitions @ Q) @ (((late_BoundR @ (late_BoundOutputS @ A2)) @ Y) @ Q2)) => (((((fresh @ name) @ pi) @ X3) @ P) => (((((fresh @ name) @ pi) @ X3) @ Q) => (((((fresh @ name) @ pi) @ Y) @ P) => (((((fresh @ name) @ pi) @ Y) @ Q) => ((X3 != A2) => (((((fresh @ name) @ pi) @ X3) @ Q2) => ((Y != A2) => (((((fresh @ name) @ pi) @ Y) @ P2) => ((X3 != Y) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ late_TauR) @ ((res @ Y) @ ((par @ (((subs @ P2) @ X3) @ Y)) @ Q2)))))))))))))))))).
% 3.84/1.96 thf(fact_213_EqvtRel, axiom, ((eqvt @ pi) @ rel)).
% 3.84/1.96 thf(fact_214_subst__identity, axiom, (! [P:pi,A2:name]: (((((subs @ P) @ A2) @ A2) = P)))).
% 3.84/1.96 thf(fact_215_simps_I9_J, axiom, (! [X3:name,C2:name,D3:name,P:pi]: (((X3 != C2) => ((X3 != D3) => ((((subs @ ((res @ X3) @ P)) @ C2) @ D3) = ((res @ X3) @ (((subs @ P) @ C2) @ D3)))))))).
% 3.84/1.96 thf(fact_216_simps_I8_J, axiom, (! [P:pi,Q:pi,C2:name,D3:name]: (((((subs @ ((par @ P) @ Q)) @ C2) @ D3) = ((par @ (((subs @ P) @ C2) @ D3)) @ (((subs @ Q) @ C2) @ D3)))))).
% 3.84/1.96 thf(fact_217_substTrans, axiom, (! [B2:name,P:pi,A2:name,C2:name]: ((((((fresh @ name) @ pi) @ B2) @ P) => ((((subs @ (((subs @ P) @ A2) @ B2)) @ B2) @ C2) = (((subs @ P) @ A2) @ C2)))))).
% 3.84/1.96 thf(fact_218_forget, axiom, (! [A2:name,P:pi,B2:name]: ((((((fresh @ name) @ pi) @ A2) @ P) => ((((subs @ P) @ A2) @ B2) = P))))).
% 3.84/1.96 thf(fact_219_fresh__fact1, axiom, (! [A2:name,P:pi,C2:name,B2:name]: ((((((fresh @ name) @ pi) @ A2) @ P) => ((A2 != C2) => ((((fresh @ name) @ pi) @ A2) @ (((subs @ P) @ B2) @ C2))))))).
% 3.84/1.96 thf(fact_220_fresh__fact2, axiom, (! [A2:name,B2:name,P:pi]: (((A2 != B2) => ((((fresh @ name) @ pi) @ A2) @ (((subs @ P) @ A2) @ B2)))))).
% 3.84/1.96 thf(fact_221_Agent_OsubstRes3, axiom, (! [B2:name,P:pi,A2:name]: ((((((fresh @ name) @ pi) @ B2) @ P) => ((((subs @ ((res @ A2) @ P)) @ A2) @ B2) = ((res @ B2) @ (((subs @ P) @ A2) @ B2))))))).
% 3.84/1.96 thf(fact_222_substRes2, axiom, (! [B2:name,P:pi,A2:name]: ((((((fresh @ name) @ pi) @ B2) @ P) => (((res @ A2) @ P) = ((res @ B2) @ (((subs @ P) @ A2) @ B2))))))).
% 3.84/1.96 thf(fact_223_eqvt__subs, axiom, (! [P5:(list @ ((product_prod @ name) @ name)),P:pi,A2:name,B2:name]: ((((((perm @ name) @ pi) @ P5) @ (((subs @ P) @ A2) @ B2)) = (((subs @ ((((perm @ name) @ pi) @ P5) @ P)) @ ((((perm @ name) @ name) @ P5) @ A2)) @ ((((perm @ name) @ name) @ P5) @ B2)))))).
% 3.84/1.96 thf(fact_224_Strong__Late__Sim__SC__Mirabelle__dtpyqonsky_OsubstRes3, axiom, (! [A2:name,P:pi,X3:name]: (((((subs @ ((res @ A2) @ P)) @ X3) @ A2) = ((res @ X3) @ ((((perm @ name) @ pi) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ X3) @ A2)) @ (nil @ ((product_prod @ name) @ name)))) @ P)))))).
% 3.84/1.96 thf(fact_225_renaming, axiom, (! [C2:name,P:pi,A2:name,B2:name]: ((((((fresh @ name) @ pi) @ C2) @ P) => ((((subs @ P) @ A2) @ B2) = (((subs @ ((((perm @ name) @ pi) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ C2) @ A2)) @ (nil @ ((product_prod @ name) @ name)))) @ P)) @ C2) @ B2)))))).
% 3.84/1.96 thf(fact_226_injPermSubst, axiom, (! [B2:name,P:pi,A2:name]: ((((((fresh @ name) @ pi) @ B2) @ P) => (((((perm @ name) @ pi) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ A2) @ B2)) @ (nil @ ((product_prod @ name) @ name)))) @ P) = (((subs @ P) @ A2) @ B2)))))).
% 3.84/1.96 thf(fact_227_Late__Semantics_OComm1, axiom, (! [P:pi,A2:name,X3:name,P2:pi,Q:pi,B2:name,Q2:pi]: ((((late_transitions @ P) @ (((late_BoundR @ (late_InputS @ A2)) @ X3) @ P2)) => (((late_transitions @ Q) @ ((late_FreeR @ ((late_OutputR @ A2) @ B2)) @ Q2)) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ late_TauR) @ ((par @ (((subs @ P2) @ X3) @ B2)) @ Q2)))))))).
% 3.84/1.96 thf(fact_228_Late__Semantics_OComm2, axiom, (! [P:pi,A2:name,B2:name,P2:pi,Q:pi,X3:name,Q2:pi]: ((((late_transitions @ P) @ ((late_FreeR @ ((late_OutputR @ A2) @ B2)) @ P2)) => (((late_transitions @ Q) @ (((late_BoundR @ (late_InputS @ A2)) @ X3) @ Q2)) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ late_TauR) @ ((par @ P2) @ (((subs @ Q2) @ X3) @ B2))))))))).
% 3.84/1.96 thf(fact_229_transitions_OComm2, axiom, (! [P:pi,A2:name,B2:name,P2:pi,Q:pi,X3:name,Q2:pi]: ((((late_transitions @ P) @ ((late_FreeR @ ((late_OutputR @ A2) @ B2)) @ P2)) => (((late_transitions @ Q) @ (((late_BoundR @ (late_InputS @ A2)) @ X3) @ Q2)) => (((((fresh @ name) @ pi) @ X3) @ P) => (((((fresh @ name) @ pi) @ X3) @ Q) => ((X3 != A2) => ((X3 != B2) => (((((fresh @ name) @ pi) @ X3) @ P2) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ late_TauR) @ ((par @ P2) @ (((subs @ Q2) @ X3) @ B2)))))))))))))).
% 3.84/1.96 thf(fact_230_transitions_OComm1, axiom, (! [P:pi,A2:name,X3:name,P2:pi,Q:pi,B2:name,Q2:pi]: ((((late_transitions @ P) @ (((late_BoundR @ (late_InputS @ A2)) @ X3) @ P2)) => (((late_transitions @ Q) @ ((late_FreeR @ ((late_OutputR @ A2) @ B2)) @ Q2)) => (((((fresh @ name) @ pi) @ X3) @ P) => (((((fresh @ name) @ pi) @ X3) @ Q) => ((X3 != A2) => ((X3 != B2) => (((((fresh @ name) @ pi) @ X3) @ Q2) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ late_TauR) @ ((par @ (((subs @ P2) @ X3) @ B2)) @ Q2))))))))))))).
% 3.84/1.96 thf(fact_231_transitions_OClose2, axiom, (! [P:pi,A2:name,Y:name,P2:pi,Q:pi,X3:name,Q2:pi]: ((((late_transitions @ P) @ (((late_BoundR @ (late_BoundOutputS @ A2)) @ Y) @ P2)) => (((late_transitions @ Q) @ (((late_BoundR @ (late_InputS @ A2)) @ X3) @ Q2)) => (((((fresh @ name) @ pi) @ X3) @ P) => (((((fresh @ name) @ pi) @ X3) @ Q) => (((((fresh @ name) @ pi) @ Y) @ P) => (((((fresh @ name) @ pi) @ Y) @ Q) => ((X3 != A2) => (((((fresh @ name) @ pi) @ X3) @ P2) => ((Y != A2) => (((((fresh @ name) @ pi) @ Y) @ Q2) => ((X3 != Y) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ late_TauR) @ ((res @ Y) @ ((par @ P2) @ (((subs @ Q2) @ X3) @ Y))))))))))))))))))).
% 3.84/1.96 thf(fact_232_product__lists_Osimps_I1_J, axiom, (! [A:$tType]: ((((product_lists @ A) @ (nil @ (list @ A))) = (((cons @ (list @ A)) @ (nil @ A)) @ (nil @ (list @ A))))))).
% 3.84/1.96 thf(fact_233_Agent_Oswap__name__def, axiom, ((swap @ name) = swap_name)).
% 3.84/1.96 thf(fact_234_swap__name_Osimps, axiom, (! [A2:name,C2:name,B2:name]: ((((A2 = C2) => (((swap_name @ ((((product_Pair @ name) @ name) @ A2) @ B2)) @ C2) = B2)) & ((A2 != C2) => (((B2 = C2) => (((swap_name @ ((((product_Pair @ name) @ name) @ A2) @ B2)) @ C2) = A2)) & ((B2 != C2) => (((swap_name @ ((((product_Pair @ name) @ name) @ A2) @ B2)) @ C2) = C2)))))))).
% 3.84/1.96 thf(fact_235_eqvtRelE, axiom, (! [A:$tType]: (((pt_name @ A) => (! [Rel:(set @ ((product_prod @ A) @ A)),Perm:(list @ ((product_prod @ name) @ name)),P:A,Q:A]: ((((eqvt @ A) @ Rel) => ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ ((((perm @ name) @ A) @ Perm) @ P)) @ ((((perm @ name) @ A) @ Perm) @ Q))) @ Rel) => (((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ P) @ Q)) @ Rel))))))))).
% 3.84/1.96 thf(fact_236_eqvtRelI, axiom, (! [A:$tType]: (((pt_name @ A) => (! [Rel:(set @ ((product_prod @ A) @ A)),P:A,Q:A,Perm:(list @ ((product_prod @ name) @ name))]: ((((eqvt @ A) @ Rel) => ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ P) @ Q)) @ Rel) => (((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ ((((perm @ name) @ A) @ Perm) @ P)) @ ((((perm @ name) @ A) @ Perm) @ Q))) @ Rel))))))))).
% 3.84/1.96 thf(fact_237_eqvt__def, axiom, (! [A:$tType]: (((pt_name @ A) => ((eqvt @ A) = (^ [Rel2:(set @ ((product_prod @ A) @ A))]: ((! [X4:((product_prod @ A) @ A),Perm2:(list @ ((product_prod @ name) @ name))]: (((((member @ ((product_prod @ A) @ A)) @ X4) @ Rel2) => (((member @ ((product_prod @ A) @ A)) @ ((((perm @ name) @ ((product_prod @ A) @ A)) @ Perm2) @ X4)) @ Rel2))))))))))).
% 3.84/1.96 thf(fact_238_name__prm__name_Osimps_I2_J, axiom, (! [X3:((product_prod @ name) @ name),Xs:(list @ ((product_prod @ name) @ name)),A2:name]: ((((name_prm_name @ (((cons @ ((product_prod @ name) @ name)) @ X3) @ Xs)) @ A2) = ((swap_name @ X3) @ ((name_prm_name @ Xs) @ A2)))))).
% 3.84/1.96 thf(fact_239_resSimCases, axiom, (! [A:$tType]: (((fs_name @ A) => (! [Rel:(set @ ((product_prod @ pi) @ pi)),Q:pi,X3:name,P:pi,C4:A]: ((((eqvt @ pi) @ Rel) => ((! [Q3:pi,A6:name]: ((((late_transitions @ Q) @ ((late_FreeR @ ((late_OutputR @ A6) @ X3)) @ Q3)) => ((A6 != X3) => (? [P6:pi]: ((((late_transitions @ P) @ (((late_BoundR @ (late_BoundOutputS @ A6)) @ X3) @ P6)) & (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ P6) @ Q3)) @ Rel)))))))) => ((! [Q3:pi,A6:late_subject,Y3:name]: ((((late_transitions @ Q) @ (((late_BoundR @ A6) @ Y3) @ Q3)) => (((((fresh @ name) @ late_subject) @ X3) @ A6) => ((X3 != Y3) => (((((fresh @ name) @ A) @ Y3) @ C4) => (? [P6:pi]: ((((late_transitions @ P) @ (((late_BoundR @ A6) @ Y3) @ P6)) & (((((strong2129052853vative @ P6) @ ((res @ X3) @ Q3)) @ A6) @ Y3) @ Rel)))))))))) => ((! [Q3:pi,Alpha2:late_freeRes]: ((((late_transitions @ Q) @ ((late_FreeR @ Alpha2) @ Q3)) => (((((fresh @ name) @ late_freeRes) @ X3) @ Alpha2) => (? [P6:pi]: ((((late_transitions @ P) @ ((late_FreeR @ Alpha2) @ P6)) & (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ P6) @ ((res @ X3) @ Q3))) @ Rel)))))))) => (((strong743114133lation @ P) @ Rel) @ ((res @ X3) @ Q)))))))))))).
% 3.84/1.96 thf(fact_240_simE_I2_J, axiom, (! [P:pi,Rel:(set @ ((product_prod @ pi) @ pi)),Q:pi,Alpha:late_freeRes,Q2:pi]: (((((strong743114133lation @ P) @ Rel) @ Q) => (((late_transitions @ Q) @ ((late_FreeR @ Alpha) @ Q2)) => (? [P3:pi]: ((((late_transitions @ P) @ ((late_FreeR @ Alpha) @ P3)) & (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ P3) @ Q2)) @ Rel))))))))).
% 3.84/1.96 thf(fact_241_simE_I1_J, axiom, (! [P:pi,Rel:(set @ ((product_prod @ pi) @ pi)),Q:pi,A2:late_subject,X3:name,Q2:pi]: (((((strong743114133lation @ P) @ Rel) @ Q) => (((late_transitions @ Q) @ (((late_BoundR @ A2) @ X3) @ Q2)) => (((((fresh @ name) @ pi) @ X3) @ P) => (? [P3:pi]: ((((late_transitions @ P) @ (((late_BoundR @ A2) @ X3) @ P3)) & (((((strong2129052853vative @ P3) @ Q2) @ A2) @ X3) @ Rel)))))))))).
% 3.84/1.96 thf(fact_242_simulation__def, axiom, (strong743114133lation = (^ [P7:pi,Rel2:(set @ ((product_prod @ pi) @ pi)),Q5:pi]: (((! [A3:late_subject,X4:name,Q6:pi]: (((((late_transitions @ Q5) @ (((late_BoundR @ A3) @ X4) @ Q6)) & ((((fresh @ name) @ pi) @ X4) @ P7)) => (? [P8:pi]: ((((late_transitions @ P7) @ (((late_BoundR @ A3) @ X4) @ P8)) & (((((strong2129052853vative @ P8) @ Q6) @ A3) @ X4) @ 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)))))))))))).
% 3.84/1.96 thf(fact_243_simCases, axiom, (! [Q:pi,P:pi,Rel:(set @ ((product_prod @ pi) @ pi))]: (((! [A6:late_subject,Y3:name,Q3:pi]: ((((late_transitions @ Q) @ (((late_BoundR @ A6) @ Y3) @ Q3)) => (((((fresh @ name) @ pi) @ Y3) @ P) => (? [P6:pi]: ((((late_transitions @ P) @ (((late_BoundR @ A6) @ Y3) @ P6)) & (((((strong2129052853vative @ P6) @ Q3) @ A6) @ Y3) @ Rel)))))))) => ((! [Alpha2:late_freeRes,Q3:pi]: ((((late_transitions @ Q) @ ((late_FreeR @ Alpha2) @ Q3)) => (? [P6:pi]: ((((late_transitions @ P) @ ((late_FreeR @ Alpha2) @ P6)) & (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ P6) @ Q3)) @ Rel))))))) => (((strong743114133lation @ P) @ Rel) @ Q)))))).
% 3.84/1.96 thf(fact_244_name__prm__name_Osimps_I1_J, axiom, (! [A2:name]: ((((name_prm_name @ (nil @ ((product_prod @ name) @ name))) @ A2) = A2)))).
% 3.84/1.96 thf(fact_245_derivativeEqvtI2, axiom, (! [P:pi,Q:pi,A2:late_subject,X3:name,Rel:(set @ ((product_prod @ pi) @ pi)),Perm:(list @ ((product_prod @ name) @ name))]: (((((((strong2129052853vative @ P) @ Q) @ A2) @ X3) @ Rel) => (((eqvt @ pi) @ Rel) => (((((strong2129052853vative @ ((((perm @ name) @ pi) @ Perm) @ P)) @ ((((perm @ name) @ pi) @ Perm) @ Q)) @ A2) @ ((((perm @ name) @ name) @ Perm) @ X3)) @ Rel)))))).
% 3.84/1.96 thf(fact_246_Agent_Oname__prm__name__def, axiom, (((perm @ name) @ name) = name_prm_name)).
% 3.84/1.96 thf(fact_247_parSym, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),P:pi,Q:pi]: (((! [R2:pi,S3:pi]: ((((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ ((par @ R2) @ S3)) @ ((par @ S3) @ R2))) @ Rel))) => ((! [R2:pi,S3:pi,X5:name]: (((((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ R2) @ S3)) @ Rel) => (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ ((res @ X5) @ R2)) @ ((res @ X5) @ S3))) @ Rel)))) => (((strong743114133lation @ ((par @ P) @ Q)) @ Rel) @ ((par @ Q) @ P))))))).
% 3.84/1.96 thf(fact_248_simCasesCont, axiom, (! [A:$tType]: (((fs_name @ A) => (! [Rel:(set @ ((product_prod @ pi) @ pi)),Q:pi,P:pi,C4:A]: ((((eqvt @ pi) @ Rel) => ((! [A6:late_subject,X5:name,Q3:pi]: ((((late_transitions @ Q) @ (((late_BoundR @ A6) @ X5) @ Q3)) => (((((fresh @ name) @ pi) @ X5) @ P) => (((((fresh @ name) @ pi) @ X5) @ Q) => (((((fresh @ name) @ late_subject) @ X5) @ A6) => (((((fresh @ name) @ A) @ X5) @ C4) => (? [P6:pi]: ((((late_transitions @ P) @ (((late_BoundR @ A6) @ X5) @ P6)) & (((((strong2129052853vative @ P6) @ Q3) @ A6) @ X5) @ Rel))))))))))) => ((! [Alpha2:late_freeRes,Q3:pi]: ((((late_transitions @ Q) @ ((late_FreeR @ Alpha2) @ Q3)) => (? [P6:pi]: ((((late_transitions @ P) @ ((late_FreeR @ Alpha2) @ P6)) & (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ P6) @ Q3)) @ Rel))))))) => (((strong743114133lation @ P) @ Rel) @ Q)))))))))).
% 3.84/1.96 thf(fact_249_parAssocLeft, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),P:pi,Q:pi,R:pi]: (((! [S3:pi,T2:pi,U:pi]: ((((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ ((par @ ((par @ S3) @ T2)) @ U)) @ ((par @ S3) @ ((par @ T2) @ U)))) @ Rel))) => ((! [S3:pi,T2:pi,X5:name]: (((((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ S3) @ T2)) @ Rel) => (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ ((res @ X5) @ S3)) @ ((res @ X5) @ T2))) @ Rel)))) => ((! [S3:pi,T2:pi,U:pi,X5:name]: ((((((fresh @ name) @ pi) @ X5) @ S3) => (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ ((res @ X5) @ ((par @ ((par @ S3) @ T2)) @ U))) @ ((par @ S3) @ ((res @ X5) @ ((par @ T2) @ U))))) @ Rel)))) => ((! [S3:pi,T2:pi,U:pi,X5:name]: ((((((fresh @ name) @ pi) @ X5) @ U) => (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ ((par @ ((res @ X5) @ ((par @ S3) @ T2))) @ U)) @ ((res @ X5) @ ((par @ S3) @ ((par @ T2) @ U))))) @ Rel)))) => (((strong743114133lation @ ((par @ ((par @ P) @ Q)) @ R)) @ Rel) @ ((par @ P) @ ((par @ Q) @ R)))))))))).
% 3.84/1.96 thf(fact_250_derivativeEqvtI, axiom, (! [P:pi,Q:pi,A2:late_subject,X3:name,Rel:(set @ ((product_prod @ pi) @ pi)),Perm:(list @ ((product_prod @ name) @ name))]: (((((((strong2129052853vative @ P) @ Q) @ A2) @ X3) @ Rel) => (((eqvt @ pi) @ Rel) => (((((strong2129052853vative @ ((((perm @ name) @ pi) @ Perm) @ P)) @ ((((perm @ name) @ pi) @ Perm) @ Q)) @ ((((perm @ name) @ late_subject) @ Perm) @ A2)) @ ((((perm @ name) @ name) @ Perm) @ X3)) @ Rel)))))).
% 3.84/1.96 thf(fact_251_alpha__fresh_H, axiom, (! [X2:$tType]: (((pt_name @ X2) => (! [A2:name,X3:X2,B2:name,Y:X2,C2:name]: (((((((abs_fun @ name) @ X2) @ A2) @ X3) = ((((abs_fun @ name) @ X2) @ B2) @ Y)) => ((C2 != A2) => ((C2 != B2) => (((((fresh @ name) @ X2) @ C2) @ X3) => (((((fresh @ name) @ X2) @ C2) @ Y) => (X3 = ((((perm @ name) @ X2) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ A2) @ C2)) @ (nil @ ((product_prod @ name) @ name)))) @ ((((perm @ name) @ X2) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ B2) @ C2)) @ (nil @ ((product_prod @ name) @ name)))) @ Y)))))))))))))).
% 3.84/1.96 thf(fact_252_name__abs__eq, axiom, (! [X:$tType]: (((pt_name @ X) => (! [A2:name,X3:X,B2:name,Y:X]: (((((((abs_fun @ name) @ X) @ A2) @ X3) = ((((abs_fun @ name) @ X) @ B2) @ Y)) = (((A2 = B2) & (X3 = Y)) | ((A2 != B2) & ((X3 = ((((perm @ name) @ X) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ A2) @ B2)) @ (nil @ ((product_prod @ name) @ name)))) @ Y)) & ((((fresh @ name) @ X) @ A2) @ Y))))))))))).
% 3.84/1.96 thf(fact_253_pi_Ofresh_I9_J, axiom, (! [A2:name,X1:name,X22:pi]: ((((((fresh @ name) @ pi) @ A2) @ ((res @ X1) @ X22)) = ((((fresh @ name) @ (name > (noption @ pi))) @ A2) @ ((((abs_fun @ name) @ pi) @ X1) @ X22)))))).
% 3.84/1.96 thf(fact_254_pi_Ofresh_I4_J, axiom, (! [A2:name,X32:name,X1:name,X22:pi]: ((((((fresh @ name) @ pi) @ A2) @ (((input @ X32) @ X1) @ X22)) = (((((fresh @ name) @ name) @ A2) @ X32) & ((((fresh @ name) @ (name > (noption @ pi))) @ A2) @ ((((abs_fun @ name) @ pi) @ X1) @ X22))))))).
% 3.84/1.96 thf(tcon_fun___Agent_Ocp__name__name, axiom, (! [A7:$tType,A8:$tType]: ((((cp_name_name @ A7) & (cp_name_name @ A8)) => (cp_name_name @ (A7 > A8)))))).
% 3.84/1.96 thf(tcon_fun___Orderings_Oord, axiom, (! [A7:$tType,A8:$tType]: (((ord @ A8) => (ord @ (A7 > A8)))))).
% 3.84/1.96 thf(tcon_fun___Agent_Opt__name, axiom, (! [A7:$tType,A8:$tType]: ((((pt_name @ A7) & (pt_name @ A8)) => (pt_name @ (A7 > A8)))))).
% 3.84/1.96 thf(tcon_Set_Oset___Agent_Ocp__name__name_1, axiom, (! [A7:$tType]: (((cp_name_name @ A7) => (cp_name_name @ (set @ A7)))))).
% 3.84/1.96 thf(tcon_Set_Oset___Orderings_Oord_2, axiom, (! [A7:$tType]: ((ord @ (set @ A7))))).
% 3.84/1.96 thf(tcon_Set_Oset___Agent_Opt__name_3, axiom, (! [A7:$tType]: (((pt_name @ A7) => (pt_name @ (set @ A7)))))).
% 3.84/1.96 thf(tcon_Agent_Opi___Agent_Ocp__name__name_4, axiom, (cp_name_name @ pi)).
% 3.84/1.96 thf(tcon_Agent_Opi___Agent_Opt__name_5, axiom, (pt_name @ pi)).
% 3.84/1.96 thf(tcon_Agent_Opi___Agent_Ofs__name, axiom, (fs_name @ pi)).
% 3.84/1.96 thf(tcon_HOL_Obool___Orderings_Olinorder, axiom, (linorder @ $o)).
% 3.84/1.96 thf(tcon_HOL_Obool___Agent_Ocp__name__name_6, axiom, (cp_name_name @ $o)).
% 3.84/1.96 thf(tcon_HOL_Obool___Orderings_Oord_7, axiom, (ord @ $o)).
% 3.84/1.96 thf(tcon_HOL_Obool___Agent_Opt__name_8, axiom, (pt_name @ $o)).
% 3.84/1.96 thf(tcon_HOL_Obool___Agent_Ofs__name_9, axiom, (fs_name @ $o)).
% 3.84/1.96 thf(tcon_List_Olist___Agent_Ocp__name__name_10, axiom, (! [A7:$tType]: (((cp_name_name @ A7) => (cp_name_name @ (list @ A7)))))).
% 3.84/1.96 thf(tcon_List_Olist___Agent_Opt__name_11, axiom, (! [A7:$tType]: (((pt_name @ A7) => (pt_name @ (list @ A7)))))).
% 3.84/1.96 thf(tcon_List_Olist___Agent_Ofs__name_12, axiom, (! [A7:$tType]: (((fs_name @ A7) => (fs_name @ (list @ A7)))))).
% 3.84/1.96 thf(tcon_Agent_Oname___Agent_Ocp__name__name_13, axiom, (cp_name_name @ name)).
% 3.84/1.96 thf(tcon_Agent_Oname___Agent_Opt__name_14, axiom, (pt_name @ name)).
% 3.84/1.96 thf(tcon_Agent_Oname___Agent_Ofs__name_15, axiom, (fs_name @ name)).
% 3.84/1.96 thf(tcon_Agent_Opi__Rep___Agent_Ocp__name__name_16, axiom, (cp_name_name @ pi_Rep)).
% 3.84/1.96 thf(tcon_Agent_Opi__Rep___Agent_Opt__name_17, axiom, (pt_name @ pi_Rep)).
% 3.84/1.96 thf(tcon_Nominal_Onoption___Agent_Ocp__name__name_18, axiom, (! [A7:$tType]: (((cp_name_name @ A7) => (cp_name_name @ (noption @ A7)))))).
% 3.84/1.96 thf(tcon_Nominal_Onoption___Agent_Opt__name_19, axiom, (! [A7:$tType]: (((pt_name @ A7) => (pt_name @ (noption @ A7)))))).
% 3.84/1.96 thf(tcon_Product__Type_Oprod___Agent_Ocp__name__name_20, axiom, (! [A7:$tType,A8:$tType]: ((((cp_name_name @ A7) & (cp_name_name @ A8)) => (cp_name_name @ ((product_prod @ A7) @ A8)))))).
% 3.84/1.96 thf(tcon_Product__Type_Oprod___Agent_Opt__name_21, axiom, (! [A7:$tType,A8:$tType]: ((((pt_name @ A7) & (pt_name @ A8)) => (pt_name @ ((product_prod @ A7) @ A8)))))).
% 3.84/1.96 thf(tcon_Product__Type_Oprod___Agent_Ofs__name_22, axiom, (! [A7:$tType,A8:$tType]: ((((fs_name @ A7) & (fs_name @ A8)) => (fs_name @ ((product_prod @ A7) @ A8)))))).
% 3.84/1.96 thf(tcon_Late__Semantics_OfreeRes___Agent_Ocp__name__name_23, axiom, (cp_name_name @ late_freeRes)).
% 3.84/1.96 thf(tcon_Late__Semantics_OfreeRes___Agent_Opt__name_24, axiom, (pt_name @ late_freeRes)).
% 3.84/1.96 thf(tcon_Late__Semantics_OfreeRes___Agent_Ofs__name_25, axiom, (fs_name @ late_freeRes)).
% 3.84/1.96 thf(tcon_Late__Semantics_Osubject___Agent_Ocp__name__name_26, axiom, (cp_name_name @ late_subject)).
% 3.84/1.96 thf(tcon_Late__Semantics_Osubject___Agent_Opt__name_27, axiom, (pt_name @ late_subject)).
% 3.84/1.96 thf(tcon_Late__Semantics_Osubject___Agent_Ofs__name_28, axiom, (fs_name @ late_subject)).
% 3.84/1.96 thf(tcon_Late__Semantics_Oresidual___Agent_Ocp__name__name_29, axiom, (cp_name_name @ late_residual)).
% 3.84/1.96 thf(tcon_Late__Semantics_Oresidual___Agent_Opt__name_30, axiom, (pt_name @ late_residual)).
% 3.84/1.96 thf(tcon_Late__Semantics_Oresidual___Agent_Ofs__name_31, axiom, (fs_name @ late_residual)).
% 3.84/1.96 thf(tcon_Late__Semantics_OfreeRes__Rep___Agent_Ocp__name__name_32, axiom, (cp_name_name @ late_freeRes_Rep)).
% 3.84/1.96 thf(tcon_Late__Semantics_OfreeRes__Rep___Agent_Opt__name_33, axiom, (pt_name @ late_freeRes_Rep)).
% 3.84/1.96 thf(tcon_Late__Semantics_Osubject__Rep___Agent_Ocp__name__name_34, axiom, (cp_name_name @ late_subject_Rep)).
% 3.84/1.96 thf(tcon_Late__Semantics_Osubject__Rep___Agent_Opt__name_35, axiom, (pt_name @ late_subject_Rep)).
% 3.84/1.96 thf(tcon_Late__Semantics_Oresidual__Rep___Agent_Ocp__name__name_36, axiom, (cp_name_name @ late_residual_Rep)).
% 3.84/1.96 thf(tcon_Late__Semantics_Oresidual__Rep___Agent_Opt__name_37, axiom, (pt_name @ late_residual_Rep)).
% 3.84/1.96 thf(help_If_3_1_T, axiom, (! [P:$o]: (((P = $true) | (P = $false))))).
% 3.84/1.96 thf(help_If_2_1_T, axiom, (! [A:$tType,X3:A,Y:A]: ((((((if @ A) @ $false) @ X3) @ Y) = Y)))).
% 3.84/1.96 thf(help_If_1_1_T, axiom, (! [A:$tType,X3:A,Y:A]: ((((((if @ A) @ $true) @ X3) @ Y) = X3)))).
% 3.84/1.96 thf(conj_0, conjecture, ((late_transitions @ ((((perm @ name) @ pi) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ z) @ x)) @ (nil @ ((product_prod @ name) @ name)))) @ q)) @ ((((perm @ name) @ late_residual) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ z) @ x)) @ (nil @ ((product_prod @ name) @ name)))) @ ((late_FreeR @ ((late_OutputR @ aa) @ x)) @ q_a)))).
% 3.84/1.96 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.rus05bb90W/DTF2DTF3151.p
% 3.84/1.96 ------------------------
% 3.84/2.03 ---- Cleaned THF ---
% 4.03/2.03 thf(ty_t_Late__Semantics_Oresidual__Rep,type,
% 4.03/2.03 late_residual_Rep: $tType ).
% 4.03/2.03
% 4.03/2.03 thf(ty_t_Late__Semantics_Osubject__Rep,type,
% 4.03/2.03 late_subject_Rep: $tType ).
% 4.03/2.03
% 4.03/2.03 thf(ty_t_Late__Semantics_OfreeRes__Rep,type,
% 4.03/2.03 late_freeRes_Rep: $tType ).
% 4.03/2.03
% 4.03/2.03 thf(ty_t_Late__Semantics_Oresidual,type,
% 4.03/2.03 late_residual: $tType ).
% 4.03/2.03
% 4.03/2.03 thf(ty_t_Late__Semantics_Osubject,type,
% 4.03/2.03 late_subject: $tType ).
% 4.03/2.03
% 4.03/2.03 thf(ty_t_Late__Semantics_OfreeRes,type,
% 4.03/2.03 late_freeRes: $tType ).
% 4.03/2.03
% 4.03/2.03 thf(ty_t_Product__Type_Oprod,type,
% 4.03/2.03 product_prod: $tType > $tType > $tType ).
% 4.03/2.03
% 4.03/2.03 thf(ty_t_Nominal_Onoption,type,
% 4.03/2.03 noption: $tType > $tType ).
% 4.03/2.03
% 4.03/2.03 thf(ty_t_Agent_Opi__Rep,type,
% 4.03/2.03 pi_Rep: $tType ).
% 4.03/2.03
% 4.03/2.03 thf(ty_t_Agent_Oname,type,
% 4.03/2.03 name: $tType ).
% 4.03/2.03
% 4.03/2.03 thf(ty_t_List_Olist,type,
% 4.03/2.03 list: $tType > $tType ).
% 4.03/2.03
% 4.03/2.03 thf(ty_t_Agent_Opi,type,
% 4.03/2.03 pi: $tType ).
% 4.03/2.03
% 4.03/2.03 thf(ty_t_Set_Oset,type,
% 4.03/2.03 set: $tType > $tType ).
% 4.03/2.03
% 4.03/2.03 thf(sy_cl_HOL_Otype,type,
% 4.03/2.03 type:
% 4.03/2.03 !>[A: $tType] : $o ).
% 4.03/2.03
% 4.03/2.03 thf(sy_cl_Agent_Ofs__name,type,
% 4.03/2.03 fs_name:
% 4.03/2.03 !>[A: $tType] : $o ).
% 4.03/2.03
% 4.03/2.03 thf(sy_cl_Agent_Opt__name,type,
% 4.03/2.03 pt_name:
% 4.03/2.03 !>[A: $tType] : $o ).
% 4.03/2.03
% 4.03/2.03 thf(sy_cl_Orderings_Oord,type,
% 4.03/2.03 ord:
% 4.03/2.03 !>[A: $tType] : $o ).
% 4.03/2.03
% 4.03/2.03 thf(sy_cl_Agent_Ocp__name__name,type,
% 4.03/2.03 cp_name_name:
% 4.03/2.03 !>[A: $tType] : $o ).
% 4.03/2.03
% 4.03/2.03 thf(sy_cl_Orderings_Olinorder,type,
% 4.03/2.03 linorder:
% 4.03/2.03 !>[A: $tType] : $o ).
% 4.03/2.03
% 4.03/2.03 thf(sy_c_Agent_Opi_OInput,type,
% 4.03/2.03 input: name > name > pi > pi ).
% 4.03/2.03
% 4.03/2.03 thf(sy_c_Agent_Opi_OPar,type,
% 4.03/2.03 par: pi > pi > pi ).
% 4.03/2.03
% 4.03/2.03 thf(sy_c_Agent_Opi_ORes,type,
% 4.03/2.03 res: name > pi > pi ).
% 4.03/2.03
% 4.03/2.03 thf(sy_c_Agent_Orec_Oname__prm__name,type,
% 4.03/2.03 name_prm_name: ( list @ ( product_prod @ name @ name ) ) > name > name ).
% 4.03/2.03
% 4.03/2.03 thf(sy_c_Agent_Orec_Oswap__name,type,
% 4.03/2.03 swap_name: ( product_prod @ name @ name ) > name > name ).
% 4.03/2.03
% 4.03/2.03 thf(sy_c_Agent_Osubs,type,
% 4.03/2.03 subs: pi > name > name > pi ).
% 4.03/2.03
% 4.03/2.03 thf(sy_c_If,type,
% 4.03/2.03 if:
% 4.03/2.03 !>[A: $tType] : ( $o > A > A > A ) ).
% 4.03/2.03
% 4.03/2.03 thf(sy_c_Late__Semantics_OfreeRes_OOutputR,type,
% 4.03/2.03 late_OutputR: name > name > late_freeRes ).
% 4.03/2.03
% 4.03/2.03 thf(sy_c_Late__Semantics_OfreeRes_OTauR,type,
% 4.03/2.03 late_TauR: late_freeRes ).
% 4.03/2.03
% 4.03/2.03 thf(sy_c_Late__Semantics_Oresidual_OBoundR,type,
% 4.03/2.03 late_BoundR: late_subject > name > pi > late_residual ).
% 4.03/2.03
% 4.03/2.03 thf(sy_c_Late__Semantics_Oresidual_OFreeR,type,
% 4.03/2.03 late_FreeR: late_freeRes > pi > late_residual ).
% 4.03/2.03
% 4.03/2.03 thf(sy_c_Late__Semantics_Oresidual__Rep_OFreeR__Rep,type,
% 4.03/2.03 late_r347633188eR_Rep: late_freeRes > pi > late_residual_Rep ).
% 4.03/2.03
% 4.03/2.03 thf(sy_c_Late__Semantics_Osubject_OBoundOutputS,type,
% 4.03/2.03 late_BoundOutputS: name > late_subject ).
% 4.03/2.03
% 4.03/2.03 thf(sy_c_Late__Semantics_Osubject_OInputS,type,
% 4.03/2.03 late_InputS: name > late_subject ).
% 4.03/2.03
% 4.03/2.03 thf(sy_c_Late__Semantics_Otransitions,type,
% 4.03/2.03 late_transitions: pi > late_residual > $o ).
% 4.03/2.03
% 4.03/2.03 thf(sy_c_List_Olist_OCons,type,
% 4.03/2.03 cons:
% 4.03/2.03 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(sy_c_List_Olist_ONil,type,
% 4.03/2.03 nil:
% 4.03/2.03 !>[A: $tType] : ( list @ A ) ).
% 4.03/2.03
% 4.03/2.03 thf(sy_c_List_Oproduct__lists,type,
% 4.03/2.03 product_lists:
% 4.03/2.03 !>[A: $tType] : ( ( list @ ( list @ A ) ) > ( list @ ( list @ A ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(sy_c_Nominal_Oabs__fun,type,
% 4.03/2.03 abs_fun:
% 4.03/2.03 !>[X: $tType,A: $tType] : ( X > A > X > ( noption @ A ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(sy_c_Nominal_Ofresh,type,
% 4.03/2.03 fresh:
% 4.03/2.03 !>[X: $tType,A: $tType] : ( X > A > $o ) ).
% 4.03/2.03
% 4.03/2.03 thf(sy_c_Nominal_Operm,type,
% 4.03/2.03 perm:
% 4.03/2.03 !>[X: $tType,A: $tType] : ( ( list @ ( product_prod @ X @ X ) ) > A > A ) ).
% 4.03/2.03
% 4.03/2.03 thf(sy_c_Nominal_Osupports,type,
% 4.03/2.03 supports:
% 4.03/2.03 !>[X: $tType,A: $tType] : ( ( set @ X ) > A > $o ) ).
% 4.03/2.03
% 4.03/2.03 thf(sy_c_Nominal_Oswap,type,
% 4.03/2.03 swap:
% 4.03/2.03 !>[X: $tType] : ( ( product_prod @ X @ X ) > X > X ) ).
% 4.03/2.03
% 4.03/2.03 thf(sy_c_Product__Type_OPair,type,
% 4.03/2.03 product_Pair:
% 4.03/2.03 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod,type,
% 4.03/2.03 product_rec_prod:
% 4.03/2.03 !>[A: $tType,B: $tType,T: $tType] : ( ( A > B > T ) > ( product_prod @ A @ B ) > T ) ).
% 4.03/2.03
% 4.03/2.03 thf(sy_c_Rel_Oeqvt,type,
% 4.03/2.03 eqvt:
% 4.03/2.03 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > $o ) ).
% 4.03/2.03
% 4.03/2.03 thf(sy_c_Set_OCollect,type,
% 4.03/2.03 collect:
% 4.03/2.03 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(sy_c_Strong__Late__Sim_Oderivative,type,
% 4.03/2.03 strong2129052853vative: pi > pi > late_subject > name > ( set @ ( product_prod @ pi @ pi ) ) > $o ).
% 4.03/2.03
% 4.03/2.03 thf(sy_c_Strong__Late__Sim_Osimulation,type,
% 4.03/2.03 strong743114133lation: pi > ( set @ ( product_prod @ pi @ pi ) ) > pi > $o ).
% 4.03/2.03
% 4.03/2.03 thf(sy_c_member,type,
% 4.03/2.03 member:
% 4.03/2.03 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 4.03/2.03
% 4.03/2.03 thf(sy_v_P,type,
% 4.03/2.03 p: pi ).
% 4.03/2.03
% 4.03/2.03 thf(sy_v_P_H____,type,
% 4.03/2.03 p2: pi ).
% 4.03/2.03
% 4.03/2.03 thf(sy_v_PxQ____,type,
% 4.03/2.03 pxQ: pi ).
% 4.03/2.03
% 4.03/2.03 thf(sy_v_Q,type,
% 4.03/2.03 q: pi ).
% 4.03/2.03
% 4.03/2.03 thf(sy_v_Q_H____,type,
% 4.03/2.03 q2: pi ).
% 4.03/2.03
% 4.03/2.03 thf(sy_v_Q_Ha____,type,
% 4.03/2.03 q_a: pi ).
% 4.03/2.03
% 4.03/2.03 thf(sy_v_Rel,type,
% 4.03/2.03 rel: set @ ( product_prod @ pi @ pi ) ).
% 4.03/2.03
% 4.03/2.03 thf(sy_v__092_060alpha_062____,type,
% 4.03/2.03 alpha: late_freeRes ).
% 4.03/2.03
% 4.03/2.03 thf(sy_v_aa____,type,
% 4.03/2.03 aa: name ).
% 4.03/2.03
% 4.03/2.03 thf(sy_v_b____,type,
% 4.03/2.03 b: name ).
% 4.03/2.03
% 4.03/2.03 thf(sy_v_x,type,
% 4.03/2.03 x: name ).
% 4.03/2.03
% 4.03/2.03 thf(sy_v_y____,type,
% 4.03/2.03 y: name ).
% 4.03/2.03
% 4.03/2.03 thf(sy_v_z____,type,
% 4.03/2.03 z: name ).
% 4.03/2.03
% 4.03/2.03 thf(fact_0__092_060open_062a_A_061_Ab_092_060close_062,axiom,
% 4.03/2.03 aa = b ).
% 4.03/2.03
% 4.03/2.03 thf(fact_1_cOpen_Ohyps_I2_J,axiom,
% 4.03/2.03 b != x ).
% 4.03/2.03
% 4.03/2.03 thf(fact_2_cClose1_Ohyps_I10_J,axiom,
% 4.03/2.03 z != aa ).
% 4.03/2.03
% 4.03/2.03 thf(fact_3_cClose1_Ohyps_I6_J,axiom,
% 4.03/2.03 y != z ).
% 4.03/2.03
% 4.03/2.03 thf(fact_4_cClose1_Ohyps_I5_J,axiom,
% 4.03/2.03 y != aa ).
% 4.03/2.03
% 4.03/2.03 thf(fact_5__092_060open_062z_A_092_060noteq_062_Ax_092_060close_062,axiom,
% 4.03/2.03 z != x ).
% 4.03/2.03
% 4.03/2.03 thf(fact_6_cOpen_Ohyps_I1_J,axiom,
% 4.03/2.03 late_transitions @ q @ ( late_FreeR @ ( late_OutputR @ b @ x ) @ q_a ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_7_cOpen_Ohyps_I3_J,axiom,
% 4.03/2.03 ( ( late_BoundOutputS @ aa )
% 4.03/2.03 = ( late_BoundOutputS @ b ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_8_cClose1_Ohyps_I14_J,axiom,
% 4.03/2.03 alpha = late_TauR ).
% 4.03/2.03
% 4.03/2.03 thf(fact_9_cClose1_Ohyps_I13_J,axiom,
% 4.03/2.03 fresh @ name @ name @ z @ x ).
% 4.03/2.03
% 4.03/2.03 thf(fact_10_perm__swap_I1_J,axiom,
% 4.03/2.03 ! [X2: $tType] :
% 4.03/2.03 ( ( pt_name @ X2 )
% 4.03/2.03 => ! [A2: name,B2: name,X3: X2] :
% 4.03/2.03 ( ( perm @ name @ X2 @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ ( perm @ name @ X2 @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ X3 ) )
% 4.03/2.03 = X3 ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_11_name__id,axiom,
% 4.03/2.03 ! [X: $tType] :
% 4.03/2.03 ( ( pt_name @ X )
% 4.03/2.03 => ! [A2: name,X3: X] :
% 4.03/2.03 ( ( perm @ name @ X @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ A2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ X3 )
% 4.03/2.03 = X3 ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_12_name__swap,axiom,
% 4.03/2.03 ! [X: $tType] :
% 4.03/2.03 ( ( pt_name @ X )
% 4.03/2.03 => ! [A2: name,B2: name,X3: X] :
% 4.03/2.03 ( ( perm @ name @ X @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ X3 )
% 4.03/2.03 = ( perm @ name @ X @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ B2 @ A2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ X3 ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_13_name__swap__bij,axiom,
% 4.03/2.03 ! [X: $tType] :
% 4.03/2.03 ( ( pt_name @ X )
% 4.03/2.03 => ! [A2: name,B2: name,X3: X] :
% 4.03/2.03 ( ( perm @ name @ X @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ ( perm @ name @ X @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ X3 ) )
% 4.03/2.03 = X3 ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_14_pt__name1,axiom,
% 4.03/2.03 ! [A: $tType] :
% 4.03/2.03 ( ( pt_name @ A )
% 4.03/2.03 => ! [X3: A] :
% 4.03/2.03 ( ( perm @ name @ A @ ( nil @ ( product_prod @ name @ name ) ) @ X3 )
% 4.03/2.03 = X3 ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_15__092_060open_062y_A_092_060noteq_062_Ax_092_060close_062,axiom,
% 4.03/2.03 y != x ).
% 4.03/2.03
% 4.03/2.03 thf(fact_16_perm__swap_I2_J,axiom,
% 4.03/2.03 ! [X2: $tType] :
% 4.03/2.03 ( ( pt_name @ X2 )
% 4.03/2.03 => ! [A2: name,B2: name,X3: X2] :
% 4.03/2.03 ( ( perm @ name @ X2 @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ ( perm @ name @ X2 @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ B2 @ A2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ X3 ) )
% 4.03/2.03 = X3 ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_17_eqvt,axiom,
% 4.03/2.03 ! [X1: pi,X22: late_residual,Pi: list @ ( product_prod @ name @ name )] :
% 4.03/2.03 ( ( late_transitions @ X1 @ X22 )
% 4.03/2.03 => ( late_transitions @ ( perm @ name @ pi @ Pi @ X1 ) @ ( perm @ name @ late_residual @ Pi @ X22 ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_18__092_060open_062z_A_092_060sharp_062_AQ_092_060close_062,axiom,
% 4.03/2.03 fresh @ name @ pi @ z @ q ).
% 4.03/2.03
% 4.03/2.03 thf(fact_19_Late__Semantics_OfreeRes_Oinject,axiom,
% 4.03/2.03 ! [X22: name,X1: name,Y2: name,Y1: name] :
% 4.03/2.03 ( ( ( late_OutputR @ X22 @ X1 )
% 4.03/2.03 = ( late_OutputR @ Y2 @ Y1 ) )
% 4.03/2.03 = ( ( X22 = Y2 )
% 4.03/2.03 & ( X1 = Y1 ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_20_Late__Semantics1_OfreeRes_Oinject,axiom,
% 4.03/2.03 ! [X11: name,X12: name,Y11: name,Y12: name] :
% 4.03/2.03 ( ( ( late_OutputR @ X11 @ X12 )
% 4.03/2.03 = ( late_OutputR @ Y11 @ Y12 ) )
% 4.03/2.03 = ( ( X11 = Y11 )
% 4.03/2.03 & ( X12 = Y12 ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_21_cClose1_Ohyps_I11_J,axiom,
% 4.03/2.03 fresh @ name @ pi @ z @ p2 ).
% 4.03/2.03
% 4.03/2.03 thf(fact_22_cClose1_Ohyps_I7_J,axiom,
% 4.03/2.03 fresh @ name @ pi @ y @ q2 ).
% 4.03/2.03
% 4.03/2.03 thf(fact_23_cClose1_Ohyps_I12_J,axiom,
% 4.03/2.03 fresh @ name @ name @ y @ x ).
% 4.03/2.03
% 4.03/2.03 thf(fact_24_assms_I1_J,axiom,
% 4.03/2.03 fresh @ name @ pi @ x @ p ).
% 4.03/2.03
% 4.03/2.03 thf(fact_25_cClose1_Ohyps_I8_J,axiom,
% 4.03/2.03 fresh @ name @ pi @ z @ p ).
% 4.03/2.03
% 4.03/2.03 thf(fact_26_cClose1_Ohyps_I3_J,axiom,
% 4.03/2.03 fresh @ name @ pi @ y @ p ).
% 4.03/2.03
% 4.03/2.03 thf(fact_27_residual__perm__empty,axiom,
% 4.03/2.03 ! [Residual_Rep: late_residual_Rep] :
% 4.03/2.03 ( ( perm @ name @ late_residual_Rep @ ( nil @ ( product_prod @ name @ name ) ) @ Residual_Rep )
% 4.03/2.03 = Residual_Rep ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_28_subject__perm__empty,axiom,
% 4.03/2.03 ! [Subject_Rep: late_subject_Rep] :
% 4.03/2.03 ( ( perm @ name @ late_subject_Rep @ ( nil @ ( product_prod @ name @ name ) ) @ Subject_Rep )
% 4.03/2.03 = Subject_Rep ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_29_freeRes__perm__empty,axiom,
% 4.03/2.03 ! [FreeRes_Rep: late_freeRes_Rep] :
% 4.03/2.03 ( ( perm @ name @ late_freeRes_Rep @ ( nil @ ( product_prod @ name @ name ) ) @ FreeRes_Rep )
% 4.03/2.03 = FreeRes_Rep ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_30_pi__perm__empty,axiom,
% 4.03/2.03 ! [Pi_Rep: pi_Rep] :
% 4.03/2.03 ( ( perm @ name @ pi_Rep @ ( nil @ ( product_prod @ name @ name ) ) @ Pi_Rep )
% 4.03/2.03 = Pi_Rep ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_31_freeRes_Operm_I1_J,axiom,
% 4.03/2.03 ! [Pi: list @ ( product_prod @ name @ name ),X22: name,X1: name] :
% 4.03/2.03 ( ( perm @ name @ late_freeRes @ Pi @ ( late_OutputR @ X22 @ X1 ) )
% 4.03/2.03 = ( late_OutputR @ ( perm @ name @ name @ Pi @ X22 ) @ ( perm @ name @ name @ Pi @ X1 ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_32_subject_Operm_I2_J,axiom,
% 4.03/2.03 ! [Pi: list @ ( product_prod @ name @ name ),X1: name] :
% 4.03/2.03 ( ( perm @ name @ late_subject @ Pi @ ( late_BoundOutputS @ X1 ) )
% 4.03/2.03 = ( late_BoundOutputS @ ( perm @ name @ name @ Pi @ X1 ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_33_Late__Semantics_Osubject_Oinject_I2_J,axiom,
% 4.03/2.03 ! [X1: name,Y1: name] :
% 4.03/2.03 ( ( ( late_BoundOutputS @ X1 )
% 4.03/2.03 = ( late_BoundOutputS @ Y1 ) )
% 4.03/2.03 = ( X1 = Y1 ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_34_Late__Semantics1_Osubject_Oinject_I2_J,axiom,
% 4.03/2.03 ! [X22: name,Y2: name] :
% 4.03/2.03 ( ( ( late_BoundOutputS @ X22 )
% 4.03/2.03 = ( late_BoundOutputS @ Y2 ) )
% 4.03/2.03 = ( X22 = Y2 ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_35_freeRes_Operm_I2_J,axiom,
% 4.03/2.03 ! [Pi: list @ ( product_prod @ name @ name )] :
% 4.03/2.03 ( ( perm @ name @ late_freeRes @ Pi @ late_TauR )
% 4.03/2.03 = late_TauR ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_36_name__fresh,axiom,
% 4.03/2.03 ( ( fresh @ name @ name )
% 4.03/2.03 = ( ^ [A3: name,B3: name] : ( A3 != B3 ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_37_residual_Operm_I2_J,axiom,
% 4.03/2.03 ! [Pi: list @ ( product_prod @ name @ name ),X22: late_freeRes,X1: pi] :
% 4.03/2.03 ( ( perm @ name @ late_residual @ Pi @ ( late_FreeR @ X22 @ X1 ) )
% 4.03/2.03 = ( late_FreeR @ ( perm @ name @ late_freeRes @ Pi @ X22 ) @ ( perm @ name @ pi @ Pi @ X1 ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_38_perm__fresh__fresh,axiom,
% 4.03/2.03 ! [X2: $tType] :
% 4.03/2.03 ( ( pt_name @ X2 )
% 4.03/2.03 => ! [A2: name,X3: X2,B2: name] :
% 4.03/2.03 ( ( fresh @ name @ X2 @ A2 @ X3 )
% 4.03/2.03 => ( ( fresh @ name @ X2 @ B2 @ X3 )
% 4.03/2.03 => ( ( perm @ name @ X2 @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ X3 )
% 4.03/2.03 = X3 ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_39_name__fresh__fresh,axiom,
% 4.03/2.03 ! [X: $tType] :
% 4.03/2.03 ( ( pt_name @ X )
% 4.03/2.03 => ! [A2: name,X3: X,B2: name] :
% 4.03/2.03 ( ( fresh @ name @ X @ A2 @ X3 )
% 4.03/2.03 => ( ( fresh @ name @ X @ B2 @ X3 )
% 4.03/2.03 => ( ( perm @ name @ X @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ X3 )
% 4.03/2.03 = X3 ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_40_cClose1_Ohyps_I9_J,axiom,
% 4.03/2.03 fresh @ name @ pi @ z @ ( res @ x @ q ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_41_cClose1_Ohyps_I4_J,axiom,
% 4.03/2.03 fresh @ name @ pi @ y @ ( res @ x @ q ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_42_fresh__perm__app,axiom,
% 4.03/2.03 ! [X2: $tType] :
% 4.03/2.03 ( ( pt_name @ X2 )
% 4.03/2.03 => ! [A2: name,Pi: list @ ( product_prod @ name @ name ),X3: X2] :
% 4.03/2.03 ( ( fresh @ name @ ( list @ ( product_prod @ name @ name ) ) @ A2 @ Pi )
% 4.03/2.03 => ( ( fresh @ name @ X2 @ A2 @ X3 )
% 4.03/2.03 => ( fresh @ name @ X2 @ A2 @ ( perm @ name @ X2 @ Pi @ X3 ) ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_43_name__exists__fresh,axiom,
% 4.03/2.03 ! [A: $tType] :
% 4.03/2.03 ( ( fs_name @ A )
% 4.03/2.03 => ! [X3: A] :
% 4.03/2.03 ~ ! [C: name] :
% 4.03/2.03 ~ ( fresh @ name @ A @ C @ X3 ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_44_fresh__eqvt,axiom,
% 4.03/2.03 ! [X2: $tType] :
% 4.03/2.03 ( ( pt_name @ X2 )
% 4.03/2.03 => ! [Pi: list @ ( product_prod @ name @ name ),A2: name,X3: X2] :
% 4.03/2.03 ( ( perm @ name @ $o @ Pi @ ( fresh @ name @ X2 @ A2 @ X3 ) )
% 4.03/2.03 = ( fresh @ name @ X2 @ ( perm @ name @ name @ Pi @ A2 ) @ ( perm @ name @ X2 @ Pi @ X3 ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_45_mem__Collect__eq,axiom,
% 4.03/2.03 ! [A: $tType,A2: A,P: A > $o] :
% 4.03/2.03 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 4.03/2.03 = ( P @ A2 ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_46_Collect__mem__eq,axiom,
% 4.03/2.03 ! [A: $tType,A4: set @ A] :
% 4.03/2.03 ( ( collect @ A
% 4.03/2.03 @ ^ [X4: A] : ( member @ A @ X4 @ A4 ) )
% 4.03/2.03 = A4 ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_47_Collect__cong,axiom,
% 4.03/2.03 ! [A: $tType,P: A > $o,Q: A > $o] :
% 4.03/2.03 ( ! [X5: A] :
% 4.03/2.03 ( ( P @ X5 )
% 4.03/2.03 = ( Q @ X5 ) )
% 4.03/2.03 => ( ( collect @ A @ P )
% 4.03/2.03 = ( collect @ A @ Q ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_48_ext,axiom,
% 4.03/2.03 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 4.03/2.03 ( ! [X5: A] :
% 4.03/2.03 ( ( F @ X5 )
% 4.03/2.03 = ( G @ X5 ) )
% 4.03/2.03 => ( F = G ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_49_fresh__bij,axiom,
% 4.03/2.03 ! [X2: $tType] :
% 4.03/2.03 ( ( pt_name @ X2 )
% 4.03/2.03 => ! [Pi: list @ ( product_prod @ name @ name ),A2: name,X3: X2] :
% 4.03/2.03 ( ( fresh @ name @ X2 @ ( perm @ name @ name @ Pi @ A2 ) @ ( perm @ name @ X2 @ Pi @ X3 ) )
% 4.03/2.03 = ( fresh @ name @ X2 @ A2 @ X3 ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_50_name__calc_I2_J,axiom,
% 4.03/2.03 ! [X3: name] :
% 4.03/2.03 ( ( perm @ name @ name @ ( nil @ ( product_prod @ name @ name ) ) @ X3 )
% 4.03/2.03 = X3 ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_51_freeRes_Ostrong__inducts,axiom,
% 4.03/2.03 ! [A: $tType,P: A > late_freeRes > $o,Z: A,FreeRes: late_freeRes] :
% 4.03/2.03 ( ! [Name1: name,Name2: name,Z2: A] : ( P @ Z2 @ ( late_OutputR @ Name1 @ Name2 ) )
% 4.03/2.03 => ( ! [Z2: A] : ( P @ Z2 @ late_TauR )
% 4.03/2.03 => ( P @ Z @ FreeRes ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_52_freeRes_Ostrong__induct_H,axiom,
% 4.03/2.03 ! [N: $tType,P: N > late_freeRes > $o,Z: N,FreeRes: late_freeRes] :
% 4.03/2.03 ( ! [Name1: name,Name2: name,Z2: N] : ( P @ Z2 @ ( late_OutputR @ Name1 @ Name2 ) )
% 4.03/2.03 => ( ! [Z2: N] : ( P @ Z2 @ late_TauR )
% 4.03/2.03 => ( P @ Z @ FreeRes ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_53_freeRes_Oexhaust,axiom,
% 4.03/2.03 ! [Y: late_freeRes] :
% 4.03/2.03 ( ! [X112: name,X122: name] :
% 4.03/2.03 ( Y
% 4.03/2.03 != ( late_OutputR @ X112 @ X122 ) )
% 4.03/2.03 => ( Y = late_TauR ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_54_freeRes_Oinducts,axiom,
% 4.03/2.03 ! [P: late_freeRes > $o,FreeRes: late_freeRes] :
% 4.03/2.03 ( ! [Name1: name,Name2: name] : ( P @ ( late_OutputR @ Name1 @ Name2 ) )
% 4.03/2.03 => ( ( P @ late_TauR )
% 4.03/2.03 => ( P @ FreeRes ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_55_Late__Semantics1_OfreeRes_Odistinct_I1_J,axiom,
% 4.03/2.03 ! [X11: name,X12: name] :
% 4.03/2.03 ( ( late_OutputR @ X11 @ X12 )
% 4.03/2.03 != late_TauR ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_56_Late__Semantics_OfreeRes_Odistinct_I1_J,axiom,
% 4.03/2.03 ! [Name12: name,Name22: name] :
% 4.03/2.03 ( ( late_OutputR @ Name12 @ Name22 )
% 4.03/2.03 != late_TauR ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_57_freshFreeDerivative_I2_J,axiom,
% 4.03/2.03 ! [P: pi,Alpha: late_freeRes,P2: pi,Y: name] :
% 4.03/2.03 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 4.03/2.03 => ( ( fresh @ name @ pi @ Y @ P )
% 4.03/2.03 => ( fresh @ name @ pi @ Y @ P2 ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_58_swap__simps_I1_J,axiom,
% 4.03/2.03 ! [A2: name,B2: name] :
% 4.03/2.03 ( ( perm @ name @ name @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ A2 )
% 4.03/2.03 = B2 ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_59_swap__simps_I2_J,axiom,
% 4.03/2.03 ! [A2: name,B2: name] :
% 4.03/2.03 ( ( perm @ name @ name @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ B2 )
% 4.03/2.03 = A2 ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_60_swap__simps_I3_J,axiom,
% 4.03/2.03 ! [A2: name,C2: name,B2: name] :
% 4.03/2.03 ( ( A2 != C2 )
% 4.03/2.03 => ( ( B2 != C2 )
% 4.03/2.03 => ( ( perm @ name @ name @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ C2 )
% 4.03/2.03 = C2 ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_61_fresh__aux,axiom,
% 4.03/2.03 ! [X2: $tType] :
% 4.03/2.03 ( ( pt_name @ X2 )
% 4.03/2.03 => ! [C2: name,A2: name,X3: X2,B2: name] :
% 4.03/2.03 ( ( C2 != A2 )
% 4.03/2.03 => ( ( fresh @ name @ X2 @ A2 @ X3 )
% 4.03/2.03 => ( ( fresh @ name @ X2 @ C2 @ X3 )
% 4.03/2.03 => ( fresh @ name @ X2 @ C2 @ ( perm @ name @ X2 @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ X3 ) ) ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_62_cp__name__name1,axiom,
% 4.03/2.03 ! [A: $tType] :
% 4.03/2.03 ( ( cp_name_name @ A )
% 4.03/2.03 => ! [Pi1: list @ ( product_prod @ name @ name ),Pi2: list @ ( product_prod @ name @ name ),X3: A] :
% 4.03/2.03 ( ( perm @ name @ A @ Pi1 @ ( perm @ name @ A @ Pi2 @ X3 ) )
% 4.03/2.03 = ( perm @ name @ A @ ( perm @ name @ ( list @ ( product_prod @ name @ name ) ) @ Pi1 @ Pi2 ) @ ( perm @ name @ A @ Pi1 @ X3 ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_63_name__perm__compose,axiom,
% 4.03/2.03 ! [X: $tType] :
% 4.03/2.03 ( ( pt_name @ X )
% 4.03/2.03 => ! [Pi2: list @ ( product_prod @ name @ name ),Pi1: list @ ( product_prod @ name @ name ),X3: X] :
% 4.03/2.03 ( ( perm @ name @ X @ Pi2 @ ( perm @ name @ X @ Pi1 @ X3 ) )
% 4.03/2.03 = ( perm @ name @ X @ ( perm @ name @ ( list @ ( product_prod @ name @ name ) ) @ Pi2 @ Pi1 ) @ ( perm @ name @ X @ Pi2 @ X3 ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_64_perm__compose,axiom,
% 4.03/2.03 ! [X2: $tType] :
% 4.03/2.03 ( ( pt_name @ X2 )
% 4.03/2.03 => ! [Pi2: list @ ( product_prod @ name @ name ),Pi1: list @ ( product_prod @ name @ name ),X3: X2] :
% 4.03/2.03 ( ( perm @ name @ X2 @ Pi2 @ ( perm @ name @ X2 @ Pi1 @ X3 ) )
% 4.03/2.03 = ( perm @ name @ X2 @ ( perm @ name @ ( list @ ( product_prod @ name @ name ) ) @ Pi2 @ Pi1 ) @ ( perm @ name @ X2 @ Pi2 @ X3 ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_65_perm__bij,axiom,
% 4.03/2.03 ! [X2: $tType] :
% 4.03/2.03 ( ( pt_name @ X2 )
% 4.03/2.03 => ! [Pi: list @ ( product_prod @ name @ name ),X3: X2,Y: X2] :
% 4.03/2.03 ( ( ( perm @ name @ X2 @ Pi @ X3 )
% 4.03/2.03 = ( perm @ name @ X2 @ Pi @ Y ) )
% 4.03/2.03 = ( X3 = Y ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_66_perm__app,axiom,
% 4.03/2.03 ! [B: $tType,X2: $tType] :
% 4.03/2.03 ( ( pt_name @ X2 )
% 4.03/2.03 => ! [Pi: list @ ( product_prod @ name @ name ),F: X2 > B,X3: X2] :
% 4.03/2.03 ( ( perm @ name @ B @ Pi @ ( F @ X3 ) )
% 4.03/2.03 = ( perm @ name @ ( X2 > B ) @ Pi @ F @ ( perm @ name @ X2 @ Pi @ X3 ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_67_in__eqvt,axiom,
% 4.03/2.03 ! [X2: $tType] :
% 4.03/2.03 ( ( pt_name @ X2 )
% 4.03/2.03 => ! [Pi: list @ ( product_prod @ name @ name ),X3: X2,X6: set @ X2] :
% 4.03/2.03 ( ( perm @ name @ $o @ Pi @ ( member @ X2 @ X3 @ X6 ) )
% 4.03/2.03 = ( member @ X2 @ ( perm @ name @ X2 @ Pi @ X3 ) @ ( perm @ name @ ( set @ X2 ) @ Pi @ X6 ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_68_eq__eqvt,axiom,
% 4.03/2.03 ! [X2: $tType] :
% 4.03/2.03 ( ( pt_name @ X2 )
% 4.03/2.03 => ! [Pi: list @ ( product_prod @ name @ name ),X3: X2,Y: X2] :
% 4.03/2.03 ( ( perm @ name @ $o @ Pi @ ( X3 = Y ) )
% 4.03/2.03 = ( ( perm @ name @ X2 @ Pi @ X3 )
% 4.03/2.03 = ( perm @ name @ X2 @ Pi @ Y ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_69_residual_Oinject_I2_J,axiom,
% 4.03/2.03 ! [X22: late_freeRes,X1: pi,Y2: late_freeRes,Y1: pi] :
% 4.03/2.03 ( ( ( late_FreeR @ X22 @ X1 )
% 4.03/2.03 = ( late_FreeR @ Y2 @ Y1 ) )
% 4.03/2.03 = ( ( X22 = Y2 )
% 4.03/2.03 & ( X1 = Y1 ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_70_fresh__prod,axiom,
% 4.03/2.03 ! [A: $tType,X: $tType,B: $tType,A2: X,X3: A,Y: B] :
% 4.03/2.03 ( ( fresh @ X @ ( product_prod @ A @ B ) @ A2 @ ( product_Pair @ A @ B @ X3 @ Y ) )
% 4.03/2.03 = ( ( fresh @ X @ A @ A2 @ X3 )
% 4.03/2.03 & ( fresh @ X @ B @ A2 @ Y ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_71_list_Oinject,axiom,
% 4.03/2.03 ! [A: $tType,X21: A,X222: list @ A,Y21: A,Y22: list @ A] :
% 4.03/2.03 ( ( ( cons @ A @ X21 @ X222 )
% 4.03/2.03 = ( cons @ A @ Y21 @ Y22 ) )
% 4.03/2.03 = ( ( X21 = Y21 )
% 4.03/2.03 & ( X222 = Y22 ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_72_old_Oprod_Oinject,axiom,
% 4.03/2.03 ! [A: $tType,B: $tType,A2: A,B2: B,A5: A,B4: B] :
% 4.03/2.03 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 4.03/2.03 = ( product_Pair @ A @ B @ A5 @ B4 ) )
% 4.03/2.03 = ( ( A2 = A5 )
% 4.03/2.03 & ( B2 = B4 ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_73_prod_Oinject,axiom,
% 4.03/2.03 ! [A: $tType,B: $tType,X1: A,X22: B,Y1: A,Y2: B] :
% 4.03/2.03 ( ( ( product_Pair @ A @ B @ X1 @ X22 )
% 4.03/2.03 = ( product_Pair @ A @ B @ Y1 @ Y2 ) )
% 4.03/2.03 = ( ( X1 = Y1 )
% 4.03/2.03 & ( X22 = Y2 ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_74_cClose1_Ohyps_I2_J,axiom,
% 4.03/2.03 late_transitions @ ( res @ x @ q ) @ ( late_BoundR @ ( late_BoundOutputS @ aa ) @ z @ q2 ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_75_fresh__list__cons,axiom,
% 4.03/2.03 ! [X: $tType,A: $tType,A2: X,X3: A,Xs: list @ A] :
% 4.03/2.03 ( ( fresh @ X @ ( list @ A ) @ A2 @ ( cons @ A @ X3 @ Xs ) )
% 4.03/2.03 = ( ( fresh @ X @ A @ A2 @ X3 )
% 4.03/2.03 & ( fresh @ X @ ( list @ A ) @ A2 @ Xs ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_76_fresh__prodD_I2_J,axiom,
% 4.03/2.03 ! [B: $tType,A: $tType,C3: $tType,A2: A,X3: B,Y: C3] :
% 4.03/2.03 ( ( fresh @ A @ ( product_prod @ B @ C3 ) @ A2 @ ( product_Pair @ B @ C3 @ X3 @ Y ) )
% 4.03/2.03 => ( fresh @ A @ C3 @ A2 @ Y ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_77_fresh__prodD_I1_J,axiom,
% 4.03/2.03 ! [C3: $tType,A: $tType,B: $tType,A2: A,X3: B,Y: C3] :
% 4.03/2.03 ( ( fresh @ A @ ( product_prod @ B @ C3 ) @ A2 @ ( product_Pair @ B @ C3 @ X3 @ Y ) )
% 4.03/2.03 => ( fresh @ A @ B @ A2 @ X3 ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_78_cons__eqvt,axiom,
% 4.03/2.03 ! [X: $tType,A: $tType,Pi: list @ ( product_prod @ X @ X ),X3: A,Xs: list @ A] :
% 4.03/2.03 ( ( perm @ X @ ( list @ A ) @ Pi @ ( cons @ A @ X3 @ Xs ) )
% 4.03/2.03 = ( cons @ A @ ( perm @ X @ A @ Pi @ X3 ) @ ( perm @ X @ ( list @ A ) @ Pi @ Xs ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_79_strict__sorted_Oinduct,axiom,
% 4.03/2.03 ! [A: $tType] :
% 4.03/2.03 ( ( linorder @ A )
% 4.03/2.03 => ! [P: ( list @ A ) > $o,A0: list @ A] :
% 4.03/2.03 ( ( P @ ( nil @ A ) )
% 4.03/2.03 => ( ! [X5: A,Ys: list @ A] :
% 4.03/2.03 ( ( P @ Ys )
% 4.03/2.03 => ( P @ ( cons @ A @ X5 @ Ys ) ) )
% 4.03/2.03 => ( P @ A0 ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_80_true__eqvt,axiom,
% 4.03/2.03 ! [A: $tType,Pi: list @ ( product_prod @ A @ A )] : ( perm @ A @ $o @ Pi @ $true ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_81_false__eqvt,axiom,
% 4.03/2.03 ! [A: $tType,Pi: list @ ( product_prod @ A @ A )] :
% 4.03/2.03 ~ ( perm @ A @ $o @ Pi @ $false ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_82_freeRes_Ofresh_I2_J,axiom,
% 4.03/2.03 ! [A2: name] : ( fresh @ name @ late_freeRes @ A2 @ late_TauR ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_83_residual_Ofresh_I2_J,axiom,
% 4.03/2.03 ! [A2: name,X22: late_freeRes,X1: pi] :
% 4.03/2.03 ( ( fresh @ name @ late_residual @ A2 @ ( late_FreeR @ X22 @ X1 ) )
% 4.03/2.03 = ( ( fresh @ name @ late_freeRes @ A2 @ X22 )
% 4.03/2.03 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_84_freeRes_Ofresh_I1_J,axiom,
% 4.03/2.03 ! [A2: name,X22: name,X1: name] :
% 4.03/2.03 ( ( fresh @ name @ late_freeRes @ A2 @ ( late_OutputR @ X22 @ X1 ) )
% 4.03/2.03 = ( ( fresh @ name @ name @ A2 @ X22 )
% 4.03/2.03 & ( fresh @ name @ name @ A2 @ X1 ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_85_subject_Ofresh_I2_J,axiom,
% 4.03/2.03 ! [A2: name,X1: name] :
% 4.03/2.03 ( ( fresh @ name @ late_subject @ A2 @ ( late_BoundOutputS @ X1 ) )
% 4.03/2.03 = ( fresh @ name @ name @ A2 @ X1 ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_86_pi_Operm_I9_J,axiom,
% 4.03/2.03 ! [Pi: list @ ( product_prod @ name @ name ),X1: name,X22: pi] :
% 4.03/2.03 ( ( perm @ name @ pi @ Pi @ ( res @ X1 @ X22 ) )
% 4.03/2.03 = ( res @ ( perm @ name @ name @ Pi @ X1 ) @ ( perm @ name @ pi @ Pi @ X22 ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_87_cClose1_Ohyps_I1_J,axiom,
% 4.03/2.03 late_transitions @ p @ ( late_BoundR @ ( late_InputS @ aa ) @ y @ p2 ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_88_residual_Operm_I1_J,axiom,
% 4.03/2.03 ! [Pi: list @ ( product_prod @ name @ name ),X32: late_subject,X1: name,X22: pi] :
% 4.03/2.03 ( ( perm @ name @ late_residual @ Pi @ ( late_BoundR @ X32 @ X1 @ X22 ) )
% 4.03/2.03 = ( late_BoundR @ ( perm @ name @ late_subject @ Pi @ X32 ) @ ( perm @ name @ name @ Pi @ X1 ) @ ( perm @ name @ pi @ Pi @ X22 ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_89_name__bij,axiom,
% 4.03/2.03 ! [Pi: list @ ( product_prod @ name @ name ),X3: name,Y: name] :
% 4.03/2.03 ( ( ( perm @ name @ name @ Pi @ X3 )
% 4.03/2.03 = ( perm @ name @ name @ Pi @ Y ) )
% 4.03/2.03 = ( X3 = Y ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_90_imp__eqvt,axiom,
% 4.03/2.03 ! [A: $tType,Pi: list @ ( product_prod @ A @ A ),A4: $o,B5: $o] :
% 4.03/2.03 ( ( perm @ A @ $o @ Pi
% 4.03/2.03 @ ( A4
% 4.03/2.03 => B5 ) )
% 4.03/2.03 = ( ( perm @ A @ $o @ Pi @ A4 )
% 4.03/2.03 => ( perm @ A @ $o @ Pi @ B5 ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_91_neg__eqvt,axiom,
% 4.03/2.03 ! [A: $tType,Pi: list @ ( product_prod @ A @ A ),A4: $o] :
% 4.03/2.03 ( ( perm @ A @ $o @ Pi @ ~ A4 )
% 4.03/2.03 = ( ~ ( perm @ A @ $o @ Pi @ A4 ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_92_conj__eqvt,axiom,
% 4.03/2.03 ! [A: $tType,Pi: list @ ( product_prod @ A @ A ),A4: $o,B5: $o] :
% 4.03/2.03 ( ( perm @ A @ $o @ Pi
% 4.03/2.03 @ ( A4
% 4.03/2.03 & B5 ) )
% 4.03/2.03 = ( ( perm @ A @ $o @ Pi @ A4 )
% 4.03/2.03 & ( perm @ A @ $o @ Pi @ B5 ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_93_disj__eqvt,axiom,
% 4.03/2.03 ! [A: $tType,Pi: list @ ( product_prod @ A @ A ),A4: $o,B5: $o] :
% 4.03/2.03 ( ( perm @ A @ $o @ Pi
% 4.03/2.03 @ ( A4
% 4.03/2.03 | B5 ) )
% 4.03/2.03 = ( ( perm @ A @ $o @ Pi @ A4 )
% 4.03/2.03 | ( perm @ A @ $o @ Pi @ B5 ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_94_perm__boolE,axiom,
% 4.03/2.03 ! [A: $tType,Pi: list @ ( product_prod @ A @ A )] :
% 4.03/2.03 ~ ( perm @ A @ $o @ Pi @ $false ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_95_perm__boolI,axiom,
% 4.03/2.03 ! [A: $tType,P: $o,Pi: list @ ( product_prod @ A @ A )] :
% 4.03/2.03 ( P
% 4.03/2.03 => ( perm @ A @ $o @ Pi @ P ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_96_Late__Semantics_OResB,axiom,
% 4.03/2.03 ! [P: pi,A2: late_subject,X3: name,P2: pi,Y: name] :
% 4.03/2.03 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X3 @ P2 ) )
% 4.03/2.03 => ( ( fresh @ name @ late_subject @ Y @ A2 )
% 4.03/2.03 => ( ( Y != X3 )
% 4.03/2.03 => ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A2 @ X3 @ ( res @ Y @ P2 ) ) ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_97_pt__set__bij3,axiom,
% 4.03/2.03 ! [X: $tType,A: $tType,Pi: list @ ( product_prod @ X @ X ),X3: A,X6: set @ A] :
% 4.03/2.03 ( ( perm @ X @ $o @ Pi @ ( member @ A @ X3 @ X6 ) )
% 4.03/2.03 = ( member @ A @ X3 @ X6 ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_98_perm__bool__def,axiom,
% 4.03/2.03 ! [X: $tType] :
% 4.03/2.03 ( ( perm @ X @ $o )
% 4.03/2.03 = ( ^ [Pi3: list @ ( product_prod @ X @ X ),B3: $o] : B3 ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_99_nil__eqvt,axiom,
% 4.03/2.03 ! [X: $tType,A: $tType,Pi: list @ ( product_prod @ X @ X )] :
% 4.03/2.03 ( ( perm @ X @ ( list @ A ) @ Pi @ ( nil @ A ) )
% 4.03/2.03 = ( nil @ A ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_100_fresh__list__nil,axiom,
% 4.03/2.03 ! [X: $tType,A: $tType,A2: X] : ( fresh @ X @ ( list @ A ) @ A2 @ ( nil @ A ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_101_transitions_OResB,axiom,
% 4.03/2.03 ! [P: pi,A2: late_subject,X3: name,P2: pi,Y: name] :
% 4.03/2.03 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X3 @ P2 ) )
% 4.03/2.03 => ( ( fresh @ name @ late_subject @ Y @ A2 )
% 4.03/2.03 => ( ( Y != X3 )
% 4.03/2.03 => ( ( fresh @ name @ pi @ X3 @ P )
% 4.03/2.03 => ( ( fresh @ name @ late_subject @ X3 @ A2 )
% 4.03/2.03 => ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A2 @ X3 @ ( res @ Y @ P2 ) ) ) ) ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_102_map__tailrec__rev_Ocases,axiom,
% 4.03/2.03 ! [A: $tType,B: $tType,X3: product_prod @ ( A > B ) @ ( product_prod @ ( list @ A ) @ ( list @ B ) )] :
% 4.03/2.03 ( ! [F2: A > B,Bs: list @ B] :
% 4.03/2.03 ( X3
% 4.03/2.03 != ( product_Pair @ ( A > B ) @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ F2 @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ ( nil @ A ) @ Bs ) ) )
% 4.03/2.03 => ~ ! [F2: A > B,A6: A,As: list @ A,Bs: list @ B] :
% 4.03/2.03 ( X3
% 4.03/2.03 != ( product_Pair @ ( A > B ) @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ F2 @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ ( cons @ A @ A6 @ As ) @ Bs ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_103_resCasesF,axiom,
% 4.03/2.03 ! [X3: name,P: pi,Alpha: late_freeRes,XP: pi,F3: pi > $o] :
% 4.03/2.03 ( ( late_transitions @ ( res @ X3 @ P ) @ ( late_FreeR @ Alpha @ XP ) )
% 4.03/2.03 => ( ! [P3: pi] :
% 4.03/2.03 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P3 ) )
% 4.03/2.03 => ( ( fresh @ name @ late_freeRes @ X3 @ Alpha )
% 4.03/2.03 => ( F3 @ ( res @ X3 @ P3 ) ) ) )
% 4.03/2.03 => ( F3 @ XP ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_104_resCasesF_H,axiom,
% 4.03/2.03 ! [X3: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 4.03/2.03 ( ( late_transitions @ ( res @ X3 @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 4.03/2.03 => ~ ! [P4: pi,Alpha2: late_freeRes,P3: pi,Y3: name] :
% 4.03/2.03 ( ( ( res @ X3 @ P )
% 4.03/2.03 = ( res @ Y3 @ P4 ) )
% 4.03/2.03 => ( ( ( late_FreeR @ Alpha @ P2 )
% 4.03/2.03 = ( late_FreeR @ Alpha2 @ ( res @ Y3 @ P3 ) ) )
% 4.03/2.03 => ( ( late_transitions @ P4 @ ( late_FreeR @ Alpha2 @ P3 ) )
% 4.03/2.03 => ~ ( fresh @ name @ late_freeRes @ Y3 @ Alpha2 ) ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_105_ResF,axiom,
% 4.03/2.03 ! [P: pi,Alpha: late_freeRes,P2: pi,Y: name] :
% 4.03/2.03 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 4.03/2.03 => ( ( fresh @ name @ late_freeRes @ Y @ Alpha )
% 4.03/2.03 => ( late_transitions @ ( res @ Y @ P ) @ ( late_FreeR @ Alpha @ ( res @ Y @ P2 ) ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_106_freshBoundDerivative_I1_J,axiom,
% 4.03/2.03 ! [P: pi,A2: late_subject,X3: name,P2: pi,Y: name] :
% 4.03/2.03 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X3 @ P2 ) )
% 4.03/2.03 => ( ( fresh @ name @ pi @ Y @ P )
% 4.03/2.03 => ( fresh @ name @ late_subject @ Y @ A2 ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_107_freshRes,axiom,
% 4.03/2.03 ! [A2: name,P: pi] : ( fresh @ name @ pi @ A2 @ ( res @ A2 @ P ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_108_residual_Odistinct_I1_J,axiom,
% 4.03/2.03 ! [Subject: late_subject,Name: name,Pi: pi,FreeRes2: late_freeRes,Pi4: pi] :
% 4.03/2.03 ( ( late_BoundR @ Subject @ Name @ Pi )
% 4.03/2.03 != ( late_FreeR @ FreeRes2 @ Pi4 ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_109_residual_Oinducts,axiom,
% 4.03/2.03 ! [P: late_residual > $o,Residual: late_residual] :
% 4.03/2.03 ( ! [Subject2: late_subject,Name3: name,Pi5: pi] : ( P @ ( late_BoundR @ Subject2 @ Name3 @ Pi5 ) )
% 4.03/2.03 => ( ! [FreeRes3: late_freeRes,Pi5: pi] : ( P @ ( late_FreeR @ FreeRes3 @ Pi5 ) )
% 4.03/2.03 => ( P @ Residual ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_110_resCases_H,axiom,
% 4.03/2.03 ! [X3: name,P: pi,Rs: late_residual] :
% 4.03/2.03 ( ( late_transitions @ ( res @ X3 @ P ) @ Rs )
% 4.03/2.03 => ( ! [P4: pi,A6: name,B6: name] :
% 4.03/2.03 ( ( ( res @ X3 @ P )
% 4.03/2.03 = ( res @ B6 @ P4 ) )
% 4.03/2.03 => ! [P3: pi] :
% 4.03/2.03 ( ( Rs
% 4.03/2.03 = ( late_BoundR @ ( late_BoundOutputS @ A6 ) @ B6 @ P3 ) )
% 4.03/2.03 => ( ( late_transitions @ P4 @ ( late_FreeR @ ( late_OutputR @ A6 @ B6 ) @ P3 ) )
% 4.03/2.03 => ( A6 = B6 ) ) ) )
% 4.03/2.03 => ( ! [P4: pi,A6: late_subject,X5: name,P3: pi,Y3: name] :
% 4.03/2.03 ( ( ( res @ X3 @ P )
% 4.03/2.03 = ( res @ Y3 @ P4 ) )
% 4.03/2.03 => ( ( Rs
% 4.03/2.03 = ( late_BoundR @ A6 @ X5 @ ( res @ Y3 @ P3 ) ) )
% 4.03/2.03 => ( ( late_transitions @ P4 @ ( late_BoundR @ A6 @ X5 @ P3 ) )
% 4.03/2.03 => ( ( fresh @ name @ late_subject @ Y3 @ A6 )
% 4.03/2.03 => ( ( Y3 != X5 )
% 4.03/2.03 => ( ( fresh @ name @ pi @ X5 @ P4 )
% 4.03/2.03 => ~ ( fresh @ name @ late_subject @ X5 @ A6 ) ) ) ) ) ) )
% 4.03/2.03 => ~ ! [P4: pi,Alpha2: late_freeRes,P3: pi,Y3: name] :
% 4.03/2.03 ( ( ( res @ X3 @ P )
% 4.03/2.03 = ( res @ Y3 @ P4 ) )
% 4.03/2.03 => ( ( Rs
% 4.03/2.03 = ( late_FreeR @ Alpha2 @ ( res @ Y3 @ P3 ) ) )
% 4.03/2.03 => ( ( late_transitions @ P4 @ ( late_FreeR @ Alpha2 @ P3 ) )
% 4.03/2.03 => ~ ( fresh @ name @ late_freeRes @ Y3 @ Alpha2 ) ) ) ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_111_arg__min__list_Ocases,axiom,
% 4.03/2.03 ! [B: $tType,A: $tType] :
% 4.03/2.03 ( ( linorder @ B )
% 4.03/2.03 => ! [X3: product_prod @ ( A > B ) @ ( list @ A )] :
% 4.03/2.03 ( ! [F2: A > B,X5: A] :
% 4.03/2.03 ( X3
% 4.03/2.03 != ( product_Pair @ ( A > B ) @ ( list @ A ) @ F2 @ ( cons @ A @ X5 @ ( nil @ A ) ) ) )
% 4.03/2.03 => ( ! [F2: A > B,X5: A,Y3: A,Zs: list @ A] :
% 4.03/2.03 ( X3
% 4.03/2.03 != ( product_Pair @ ( A > B ) @ ( list @ A ) @ F2 @ ( cons @ A @ X5 @ ( cons @ A @ Y3 @ Zs ) ) ) )
% 4.03/2.03 => ~ ! [A6: A > B] :
% 4.03/2.03 ( X3
% 4.03/2.03 != ( product_Pair @ ( A > B ) @ ( list @ A ) @ A6 @ ( nil @ A ) ) ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_112_sorted__wrt_Ocases,axiom,
% 4.03/2.03 ! [A: $tType,X3: product_prod @ ( A > A > $o ) @ ( list @ A )] :
% 4.03/2.03 ( ! [P4: A > A > $o] :
% 4.03/2.03 ( X3
% 4.03/2.03 != ( product_Pair @ ( A > A > $o ) @ ( list @ A ) @ P4 @ ( nil @ A ) ) )
% 4.03/2.03 => ~ ! [P4: A > A > $o,X5: A,Ys: list @ A] :
% 4.03/2.03 ( X3
% 4.03/2.03 != ( product_Pair @ ( A > A > $o ) @ ( list @ A ) @ P4 @ ( cons @ A @ X5 @ Ys ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_113_successively_Ocases,axiom,
% 4.03/2.03 ! [A: $tType,X3: product_prod @ ( A > A > $o ) @ ( list @ A )] :
% 4.03/2.03 ( ! [P4: A > A > $o] :
% 4.03/2.03 ( X3
% 4.03/2.03 != ( product_Pair @ ( A > A > $o ) @ ( list @ A ) @ P4 @ ( nil @ A ) ) )
% 4.03/2.03 => ( ! [P4: A > A > $o,X5: A] :
% 4.03/2.03 ( X3
% 4.03/2.03 != ( product_Pair @ ( A > A > $o ) @ ( list @ A ) @ P4 @ ( cons @ A @ X5 @ ( nil @ A ) ) ) )
% 4.03/2.03 => ~ ! [P4: A > A > $o,X5: A,Y3: A,Xs2: list @ A] :
% 4.03/2.03 ( X3
% 4.03/2.03 != ( product_Pair @ ( A > A > $o ) @ ( list @ A ) @ P4 @ ( cons @ A @ X5 @ ( cons @ A @ Y3 @ Xs2 ) ) ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_114_splice_Ocases,axiom,
% 4.03/2.03 ! [A: $tType,X3: product_prod @ ( list @ A ) @ ( list @ A )] :
% 4.03/2.03 ( ! [Ys: list @ A] :
% 4.03/2.03 ( X3
% 4.03/2.03 != ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( nil @ A ) @ Ys ) )
% 4.03/2.03 => ~ ! [X5: A,Xs2: list @ A,Ys: list @ A] :
% 4.03/2.03 ( X3
% 4.03/2.03 != ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X5 @ Xs2 ) @ Ys ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_115_shuffles_Ocases,axiom,
% 4.03/2.03 ! [A: $tType,X3: product_prod @ ( list @ A ) @ ( list @ A )] :
% 4.03/2.03 ( ! [Ys: list @ A] :
% 4.03/2.03 ( X3
% 4.03/2.03 != ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( nil @ A ) @ Ys ) )
% 4.03/2.03 => ( ! [Xs2: list @ A] :
% 4.03/2.03 ( X3
% 4.03/2.03 != ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs2 @ ( nil @ A ) ) )
% 4.03/2.03 => ~ ! [X5: A,Xs2: list @ A,Y3: A,Ys: list @ A] :
% 4.03/2.03 ( X3
% 4.03/2.03 != ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X5 @ Xs2 ) @ ( cons @ A @ Y3 @ Ys ) ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_116_resCasesB_H,axiom,
% 4.03/2.03 ! [X7: name,P: pi,A2: late_subject,Y4: name,P2: pi] :
% 4.03/2.03 ( ( late_transitions @ ( res @ X7 @ P ) @ ( late_BoundR @ A2 @ Y4 @ P2 ) )
% 4.03/2.03 => ( ! [P4: pi,A6: name,B6: name] :
% 4.03/2.03 ( ( ( res @ X7 @ P )
% 4.03/2.03 = ( res @ B6 @ P4 ) )
% 4.03/2.03 => ! [P3: pi] :
% 4.03/2.03 ( ( ( late_BoundR @ A2 @ Y4 @ P2 )
% 4.03/2.03 = ( late_BoundR @ ( late_BoundOutputS @ A6 ) @ B6 @ P3 ) )
% 4.03/2.03 => ( ( late_transitions @ P4 @ ( late_FreeR @ ( late_OutputR @ A6 @ B6 ) @ P3 ) )
% 4.03/2.03 => ( A6 = B6 ) ) ) )
% 4.03/2.03 => ~ ! [P4: pi,A6: late_subject,X5: name,P3: pi,Y3: name] :
% 4.03/2.03 ( ( ( res @ X7 @ P )
% 4.03/2.03 = ( res @ Y3 @ P4 ) )
% 4.03/2.03 => ( ( ( late_BoundR @ A2 @ Y4 @ P2 )
% 4.03/2.03 = ( late_BoundR @ A6 @ X5 @ ( res @ Y3 @ P3 ) ) )
% 4.03/2.03 => ( ( late_transitions @ P4 @ ( late_BoundR @ A6 @ X5 @ P3 ) )
% 4.03/2.03 => ( ( fresh @ name @ late_subject @ Y3 @ A6 )
% 4.03/2.03 => ( ( Y3 != X5 )
% 4.03/2.03 => ( ( fresh @ name @ pi @ X5 @ P4 )
% 4.03/2.03 => ~ ( fresh @ name @ late_subject @ X5 @ A6 ) ) ) ) ) ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_117_Open,axiom,
% 4.03/2.03 ! [P: pi,A2: name,B2: name,P2: pi] :
% 4.03/2.03 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P2 ) )
% 4.03/2.03 => ( ( A2 != B2 )
% 4.03/2.03 => ( late_transitions @ ( res @ B2 @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ B2 @ P2 ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_118_freshResidual,axiom,
% 4.03/2.03 ! [P: pi,Rs: late_residual,X3: name] :
% 4.03/2.03 ( ( late_transitions @ P @ Rs )
% 4.03/2.03 => ( ( fresh @ name @ pi @ X3 @ P )
% 4.03/2.03 => ( fresh @ name @ late_residual @ X3 @ Rs ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_119_freshBoundDerivative_I2_J,axiom,
% 4.03/2.03 ! [P: pi,A2: late_subject,X3: name,P2: pi,Y: name] :
% 4.03/2.03 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X3 @ P2 ) )
% 4.03/2.03 => ( ( fresh @ name @ pi @ Y @ P )
% 4.03/2.03 => ( ( Y != X3 )
% 4.03/2.03 => ( fresh @ name @ pi @ Y @ P2 ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_120_residual_Ostrong__inducts,axiom,
% 4.03/2.03 ! [A: $tType] :
% 4.03/2.03 ( ( fs_name @ A )
% 4.03/2.03 => ! [P: A > late_residual > $o,Z: A,Residual: late_residual] :
% 4.03/2.03 ( ! [Subject2: late_subject,Name3: name,Pi5: pi,Z2: A] :
% 4.03/2.03 ( ( fresh @ name @ A @ Name3 @ Z2 )
% 4.03/2.03 => ( ( fresh @ name @ late_subject @ Name3 @ Subject2 )
% 4.03/2.03 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi5 ) ) ) )
% 4.03/2.03 => ( ! [FreeRes3: late_freeRes,Pi5: pi,Z2: A] : ( P @ Z2 @ ( late_FreeR @ FreeRes3 @ Pi5 ) )
% 4.03/2.03 => ( P @ Z @ Residual ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_121_residual_Ostrong__induct,axiom,
% 4.03/2.03 ! [N: $tType] :
% 4.03/2.03 ( ( fs_name @ N )
% 4.03/2.03 => ! [P: N > late_residual > $o,Z: N,Residual: late_residual] :
% 4.03/2.03 ( ! [Subject2: late_subject,Name3: name,Pi5: pi,Z2: N] :
% 4.03/2.03 ( ( fresh @ name @ N @ Name3 @ Z2 )
% 4.03/2.03 => ( ( fresh @ name @ late_subject @ Name3 @ Subject2 )
% 4.03/2.03 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi5 ) ) ) )
% 4.03/2.03 => ( ! [FreeRes3: late_freeRes,Pi5: pi,Z2: N] : ( P @ Z2 @ ( late_FreeR @ FreeRes3 @ Pi5 ) )
% 4.03/2.03 => ( P @ Z @ Residual ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_122_resCasesB,axiom,
% 4.03/2.03 ! [Y: name,P: pi,A2: late_subject,X3: name,YP: pi,F3: late_subject > pi > $o] :
% 4.03/2.03 ( ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A2 @ X3 @ YP ) )
% 4.03/2.03 => ( ( X3 != Y )
% 4.03/2.03 => ( ( fresh @ name @ pi @ X3 @ P )
% 4.03/2.03 => ( ! [B6: name,P3: pi] :
% 4.03/2.03 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ B6 @ Y ) @ P3 ) )
% 4.03/2.03 => ( ( B6 != Y )
% 4.03/2.03 => ( ( A2
% 4.03/2.03 = ( late_BoundOutputS @ B6 ) )
% 4.03/2.03 => ( F3 @ ( late_BoundOutputS @ B6 ) @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ X3 @ Y ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ P3 ) ) ) ) )
% 4.03/2.03 => ( ! [P3: pi] :
% 4.03/2.03 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X3 @ P3 ) )
% 4.03/2.03 => ( ( fresh @ name @ late_subject @ Y @ A2 )
% 4.03/2.03 => ( F3 @ A2 @ ( res @ Y @ P3 ) ) ) )
% 4.03/2.03 => ( F3 @ A2 @ YP ) ) ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_123_freshFreeDerivative_I1_J,axiom,
% 4.03/2.03 ! [P: pi,Alpha: late_freeRes,P2: pi,Y: name] :
% 4.03/2.03 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 4.03/2.03 => ( ( fresh @ name @ pi @ Y @ P )
% 4.03/2.03 => ( fresh @ name @ late_freeRes @ Y @ Alpha ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_124_surj__pair,axiom,
% 4.03/2.03 ! [A: $tType,B: $tType,P5: product_prod @ A @ B] :
% 4.03/2.03 ? [X5: A,Y3: B] :
% 4.03/2.03 ( P5
% 4.03/2.03 = ( product_Pair @ A @ B @ X5 @ Y3 ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_125_prod__cases,axiom,
% 4.03/2.03 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,P5: product_prod @ A @ B] :
% 4.03/2.03 ( ! [A6: A,B6: B] : ( P @ ( product_Pair @ A @ B @ A6 @ B6 ) )
% 4.03/2.03 => ( P @ P5 ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_126_Pair__inject,axiom,
% 4.03/2.03 ! [A: $tType,B: $tType,A2: A,B2: B,A5: A,B4: B] :
% 4.03/2.03 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 4.03/2.03 = ( product_Pair @ A @ B @ A5 @ B4 ) )
% 4.03/2.03 => ~ ( ( A2 = A5 )
% 4.03/2.03 => ( B2 != B4 ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_127_prod__cases3,axiom,
% 4.03/2.03 ! [A: $tType,B: $tType,C3: $tType,Y: product_prod @ A @ ( product_prod @ B @ C3 )] :
% 4.03/2.03 ~ ! [A6: A,B6: B,C: C3] :
% 4.03/2.03 ( Y
% 4.03/2.03 != ( product_Pair @ A @ ( product_prod @ B @ C3 ) @ A6 @ ( product_Pair @ B @ C3 @ B6 @ C ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_128_prod__cases4,axiom,
% 4.03/2.03 ! [A: $tType,B: $tType,C3: $tType,D: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ D ) )] :
% 4.03/2.03 ~ ! [A6: A,B6: B,C: C3,D2: D] :
% 4.03/2.03 ( Y
% 4.03/2.03 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C3 @ D ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C3 @ D ) @ B6 @ ( product_Pair @ C3 @ D @ C @ D2 ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_129_prod__cases5,axiom,
% 4.03/2.03 ! [A: $tType,B: $tType,C3: $tType,D: $tType,E: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D @ E ) ) )] :
% 4.03/2.03 ~ ! [A6: A,B6: B,C: C3,D2: D,E2: E] :
% 4.03/2.03 ( Y
% 4.03/2.03 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D @ E ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C3 @ ( product_prod @ D @ E ) ) @ B6 @ ( product_Pair @ C3 @ ( product_prod @ D @ E ) @ C @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_130_prod__cases6,axiom,
% 4.03/2.03 ! [A: $tType,B: $tType,C3: $tType,D: $tType,E: $tType,F4: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) ) )] :
% 4.03/2.03 ~ ! [A6: A,B6: B,C: C3,D2: D,E2: E,F2: F4] :
% 4.03/2.03 ( Y
% 4.03/2.03 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C3 @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) ) @ B6 @ ( product_Pair @ C3 @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) @ C @ ( product_Pair @ D @ ( product_prod @ E @ F4 ) @ D2 @ ( product_Pair @ E @ F4 @ E2 @ F2 ) ) ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_131_prod__cases7,axiom,
% 4.03/2.03 ! [A: $tType,B: $tType,C3: $tType,D: $tType,E: $tType,F4: $tType,G2: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G2 ) ) ) ) )] :
% 4.03/2.03 ~ ! [A6: A,B6: B,C: C3,D2: D,E2: E,F2: F4,G3: G2] :
% 4.03/2.03 ( Y
% 4.03/2.03 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G2 ) ) ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C3 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G2 ) ) ) ) @ B6 @ ( product_Pair @ C3 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G2 ) ) ) @ C @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G2 ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F4 @ G2 ) @ E2 @ ( product_Pair @ F4 @ G2 @ F2 @ G3 ) ) ) ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_132_prod__induct3,axiom,
% 4.03/2.03 ! [C3: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ C3 ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ C3 )] :
% 4.03/2.03 ( ! [A6: A,B6: B,C: C3] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ C3 ) @ A6 @ ( product_Pair @ B @ C3 @ B6 @ C ) ) )
% 4.03/2.03 => ( P @ X3 ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_133_prod__induct4,axiom,
% 4.03/2.03 ! [D: $tType,C3: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ D ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ D ) )] :
% 4.03/2.03 ( ! [A6: A,B6: B,C: C3,D2: D] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C3 @ D ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C3 @ D ) @ B6 @ ( product_Pair @ C3 @ D @ C @ D2 ) ) ) )
% 4.03/2.03 => ( P @ X3 ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_134_prod__induct5,axiom,
% 4.03/2.03 ! [E: $tType,D: $tType,C3: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D @ E ) ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D @ E ) ) )] :
% 4.03/2.03 ( ! [A6: A,B6: B,C: C3,D2: D,E2: E] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D @ E ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C3 @ ( product_prod @ D @ E ) ) @ B6 @ ( product_Pair @ C3 @ ( product_prod @ D @ E ) @ C @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) )
% 4.03/2.03 => ( P @ X3 ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_135_prod__induct6,axiom,
% 4.03/2.03 ! [F4: $tType,E: $tType,D: $tType,C3: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) ) )] :
% 4.03/2.03 ( ! [A6: A,B6: B,C: C3,D2: D,E2: E,F2: F4] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C3 @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) ) @ B6 @ ( product_Pair @ C3 @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) @ C @ ( product_Pair @ D @ ( product_prod @ E @ F4 ) @ D2 @ ( product_Pair @ E @ F4 @ E2 @ F2 ) ) ) ) ) )
% 4.03/2.03 => ( P @ X3 ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_136_prod__induct7,axiom,
% 4.03/2.03 ! [G2: $tType,F4: $tType,E: $tType,D: $tType,C3: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G2 ) ) ) ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G2 ) ) ) ) )] :
% 4.03/2.03 ( ! [A6: A,B6: B,C: C3,D2: D,E2: E,F2: F4,G3: G2] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G2 ) ) ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C3 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G2 ) ) ) ) @ B6 @ ( product_Pair @ C3 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G2 ) ) ) @ C @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G2 ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F4 @ G2 ) @ E2 @ ( product_Pair @ F4 @ G2 @ F2 @ G3 ) ) ) ) ) ) )
% 4.03/2.03 => ( P @ X3 ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_137_old_Oprod_Oexhaust,axiom,
% 4.03/2.03 ! [A: $tType,B: $tType,Y: product_prod @ A @ B] :
% 4.03/2.03 ~ ! [A6: A,B6: B] :
% 4.03/2.03 ( Y
% 4.03/2.03 != ( product_Pair @ A @ B @ A6 @ B6 ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_138_old_Oprod_Oinducts,axiom,
% 4.03/2.03 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,Prod: product_prod @ A @ B] :
% 4.03/2.03 ( ! [A6: A,B6: B] : ( P @ ( product_Pair @ A @ B @ A6 @ B6 ) )
% 4.03/2.03 => ( P @ Prod ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_139_not__Cons__self2,axiom,
% 4.03/2.03 ! [A: $tType,X3: A,Xs: list @ A] :
% 4.03/2.03 ( ( cons @ A @ X3 @ Xs )
% 4.03/2.03 != Xs ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_140_allE__Nil,axiom,
% 4.03/2.03 ! [A: $tType,P: ( list @ A ) > $o] :
% 4.03/2.03 ( ! [X_1: list @ A] : ( P @ X_1 )
% 4.03/2.03 => ( P @ ( nil @ A ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_141_if__eqvt,axiom,
% 4.03/2.03 ! [A: $tType,B: $tType,Pi: list @ ( product_prod @ A @ A ),B2: $o,C1: B,C22: B] :
% 4.03/2.03 ( ( ( perm @ A @ $o @ Pi @ B2 )
% 4.03/2.03 => ( ( perm @ A @ B @ Pi @ ( if @ B @ B2 @ C1 @ C22 ) )
% 4.03/2.03 = ( perm @ A @ B @ Pi @ C1 ) ) )
% 4.03/2.03 & ( ~ ( perm @ A @ $o @ Pi @ B2 )
% 4.03/2.03 => ( ( perm @ A @ B @ Pi @ ( if @ B @ B2 @ C1 @ C22 ) )
% 4.03/2.03 = ( perm @ A @ B @ Pi @ C22 ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_142_pt__bij3,axiom,
% 4.03/2.03 ! [X: $tType,A: $tType,X3: A,Y: A,Pi: list @ ( product_prod @ X @ X )] :
% 4.03/2.03 ( ( X3 = Y )
% 4.03/2.03 => ( ( perm @ X @ A @ Pi @ X3 )
% 4.03/2.03 = ( perm @ X @ A @ Pi @ Y ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_143_abs__fun__if,axiom,
% 4.03/2.03 ! [X: $tType,A: $tType,C2: $o,Pi: list @ ( product_prod @ X @ X ),X3: A,Y: A] :
% 4.03/2.03 ( ( C2
% 4.03/2.03 => ( ( perm @ X @ A @ Pi @ ( if @ A @ C2 @ X3 @ Y ) )
% 4.03/2.03 = ( perm @ X @ A @ Pi @ X3 ) ) )
% 4.03/2.03 & ( ~ C2
% 4.03/2.03 => ( ( perm @ X @ A @ Pi @ ( if @ A @ C2 @ X3 @ Y ) )
% 4.03/2.03 = ( perm @ X @ A @ Pi @ Y ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_144_alphaRes,axiom,
% 4.03/2.03 ! [C2: name,P: pi,A2: name] :
% 4.03/2.03 ( ( fresh @ name @ pi @ C2 @ P )
% 4.03/2.03 => ( ( res @ A2 @ P )
% 4.03/2.03 = ( res @ C2 @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ C2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ P ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_145_alphaBoundResidual,axiom,
% 4.03/2.03 ! [X7: name,P: pi,A2: late_subject,X3: name] :
% 4.03/2.03 ( ( fresh @ name @ pi @ X7 @ P )
% 4.03/2.03 => ( ( late_BoundR @ A2 @ X3 @ P )
% 4.03/2.03 = ( late_BoundR @ A2 @ X7 @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ X3 @ X7 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ P ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_146_perm__prod_Osimps,axiom,
% 4.03/2.03 ! [A: $tType,X: $tType,B: $tType,Pi: list @ ( product_prod @ X @ X ),X3: A,Y: B] :
% 4.03/2.03 ( ( perm @ X @ ( product_prod @ A @ B ) @ Pi @ ( product_Pair @ A @ B @ X3 @ Y ) )
% 4.03/2.03 = ( product_Pair @ A @ B @ ( perm @ X @ A @ Pi @ X3 ) @ ( perm @ X @ B @ Pi @ Y ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_147_list_Odistinct_I1_J,axiom,
% 4.03/2.03 ! [A: $tType,X21: A,X222: list @ A] :
% 4.03/2.03 ( ( nil @ A )
% 4.03/2.03 != ( cons @ A @ X21 @ X222 ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_148_list_OdiscI,axiom,
% 4.03/2.03 ! [A: $tType,List: list @ A,X21: A,X222: list @ A] :
% 4.03/2.03 ( ( List
% 4.03/2.03 = ( cons @ A @ X21 @ X222 ) )
% 4.03/2.03 => ( List
% 4.03/2.03 != ( nil @ A ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_149_list_Oexhaust,axiom,
% 4.03/2.03 ! [A: $tType,Y: list @ A] :
% 4.03/2.03 ( ( Y
% 4.03/2.03 != ( nil @ A ) )
% 4.03/2.03 => ~ ! [X212: A,X223: list @ A] :
% 4.03/2.03 ( Y
% 4.03/2.03 != ( cons @ A @ X212 @ X223 ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_150_list_Oinducts,axiom,
% 4.03/2.03 ! [A: $tType,P: ( list @ A ) > $o,List: list @ A] :
% 4.03/2.03 ( ( P @ ( nil @ A ) )
% 4.03/2.03 => ( ! [X13: A,X23: list @ A] :
% 4.03/2.03 ( ( P @ X23 )
% 4.03/2.03 => ( P @ ( cons @ A @ X13 @ X23 ) ) )
% 4.03/2.03 => ( P @ List ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_151_neq__Nil__conv,axiom,
% 4.03/2.03 ! [A: $tType,Xs: list @ A] :
% 4.03/2.03 ( ( Xs
% 4.03/2.03 != ( nil @ A ) )
% 4.03/2.03 = ( ? [Y5: A,Ys2: list @ A] :
% 4.03/2.03 ( Xs
% 4.03/2.03 = ( cons @ A @ Y5 @ Ys2 ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_152_list__induct2_H,axiom,
% 4.03/2.03 ! [A: $tType,B: $tType,P: ( list @ A ) > ( list @ B ) > $o,Xs: list @ A,Ys3: list @ B] :
% 4.03/2.03 ( ( P @ ( nil @ A ) @ ( nil @ B ) )
% 4.03/2.03 => ( ! [X5: A,Xs2: list @ A] : ( P @ ( cons @ A @ X5 @ Xs2 ) @ ( nil @ B ) )
% 4.03/2.03 => ( ! [Y3: B,Ys: list @ B] : ( P @ ( nil @ A ) @ ( cons @ B @ Y3 @ Ys ) )
% 4.03/2.03 => ( ! [X5: A,Xs2: list @ A,Y3: B,Ys: list @ B] :
% 4.03/2.03 ( ( P @ Xs2 @ Ys )
% 4.03/2.03 => ( P @ ( cons @ A @ X5 @ Xs2 ) @ ( cons @ B @ Y3 @ Ys ) ) )
% 4.03/2.03 => ( P @ Xs @ Ys3 ) ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_153_splice_Oinduct,axiom,
% 4.03/2.03 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 4.03/2.03 ( ! [X_1: list @ A] : ( P @ ( nil @ A ) @ X_1 )
% 4.03/2.03 => ( ! [X5: A,Xs2: list @ A,Ys: list @ A] :
% 4.03/2.03 ( ( P @ Ys @ Xs2 )
% 4.03/2.03 => ( P @ ( cons @ A @ X5 @ Xs2 ) @ Ys ) )
% 4.03/2.03 => ( P @ A0 @ A1 ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_154_induct__list012,axiom,
% 4.03/2.03 ! [A: $tType,P: ( list @ A ) > $o,Xs: list @ A] :
% 4.03/2.03 ( ( P @ ( nil @ A ) )
% 4.03/2.03 => ( ! [X5: A] : ( P @ ( cons @ A @ X5 @ ( nil @ A ) ) )
% 4.03/2.03 => ( ! [X5: A,Y3: A,Zs: list @ A] :
% 4.03/2.03 ( ( P @ Zs )
% 4.03/2.03 => ( ( P @ ( cons @ A @ Y3 @ Zs ) )
% 4.03/2.03 => ( P @ ( cons @ A @ X5 @ ( cons @ A @ Y3 @ Zs ) ) ) ) )
% 4.03/2.03 => ( P @ Xs ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_155_min__list_Ocases,axiom,
% 4.03/2.03 ! [A: $tType] :
% 4.03/2.03 ( ( ord @ A )
% 4.03/2.03 => ! [X3: list @ A] :
% 4.03/2.03 ( ! [X5: A,Xs2: list @ A] :
% 4.03/2.03 ( X3
% 4.03/2.03 != ( cons @ A @ X5 @ Xs2 ) )
% 4.03/2.03 => ( X3
% 4.03/2.03 = ( nil @ A ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_156_min__list_Oinduct,axiom,
% 4.03/2.03 ! [A: $tType] :
% 4.03/2.03 ( ( ord @ A )
% 4.03/2.03 => ! [P: ( list @ A ) > $o,A0: list @ A] :
% 4.03/2.03 ( ! [X5: A,Xs2: list @ A] :
% 4.03/2.03 ( ! [X213: A,X224: list @ A] :
% 4.03/2.03 ( ( Xs2
% 4.03/2.03 = ( cons @ A @ X213 @ X224 ) )
% 4.03/2.03 => ( P @ Xs2 ) )
% 4.03/2.03 => ( P @ ( cons @ A @ X5 @ Xs2 ) ) )
% 4.03/2.03 => ( ( P @ ( nil @ A ) )
% 4.03/2.03 => ( P @ A0 ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_157_shuffles_Oinduct,axiom,
% 4.03/2.03 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 4.03/2.03 ( ! [X_1: list @ A] : ( P @ ( nil @ A ) @ X_1 )
% 4.03/2.03 => ( ! [Xs2: list @ A] : ( P @ Xs2 @ ( nil @ A ) )
% 4.03/2.03 => ( ! [X5: A,Xs2: list @ A,Y3: A,Ys: list @ A] :
% 4.03/2.03 ( ( P @ Xs2 @ ( cons @ A @ Y3 @ Ys ) )
% 4.03/2.03 => ( ( P @ ( cons @ A @ X5 @ Xs2 ) @ Ys )
% 4.03/2.03 => ( P @ ( cons @ A @ X5 @ Xs2 ) @ ( cons @ A @ Y3 @ Ys ) ) ) )
% 4.03/2.03 => ( P @ A0 @ A1 ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_158_transpose_Ocases,axiom,
% 4.03/2.03 ! [A: $tType,X3: list @ ( list @ A )] :
% 4.03/2.03 ( ( X3
% 4.03/2.03 != ( nil @ ( list @ A ) ) )
% 4.03/2.03 => ( ! [Xss: list @ ( list @ A )] :
% 4.03/2.03 ( X3
% 4.03/2.03 != ( cons @ ( list @ A ) @ ( nil @ A ) @ Xss ) )
% 4.03/2.03 => ~ ! [X5: A,Xs2: list @ A,Xss: list @ ( list @ A )] :
% 4.03/2.03 ( X3
% 4.03/2.03 != ( cons @ ( list @ A ) @ ( cons @ A @ X5 @ Xs2 ) @ Xss ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_159_remdups__adj_Ocases,axiom,
% 4.03/2.03 ! [A: $tType,X3: list @ A] :
% 4.03/2.03 ( ( X3
% 4.03/2.03 != ( nil @ A ) )
% 4.03/2.03 => ( ! [X5: A] :
% 4.03/2.03 ( X3
% 4.03/2.03 != ( cons @ A @ X5 @ ( nil @ A ) ) )
% 4.03/2.03 => ~ ! [X5: A,Y3: A,Xs2: list @ A] :
% 4.03/2.03 ( X3
% 4.03/2.03 != ( cons @ A @ X5 @ ( cons @ A @ Y3 @ Xs2 ) ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_160_sorted__wrt_Oinduct,axiom,
% 4.03/2.03 ! [A: $tType,P: ( A > A > $o ) > ( list @ A ) > $o,A0: A > A > $o,A1: list @ A] :
% 4.03/2.03 ( ! [P4: A > A > $o] : ( P @ P4 @ ( nil @ A ) )
% 4.03/2.03 => ( ! [P4: A > A > $o,X5: A,Ys: list @ A] :
% 4.03/2.03 ( ( P @ P4 @ Ys )
% 4.03/2.03 => ( P @ P4 @ ( cons @ A @ X5 @ Ys ) ) )
% 4.03/2.03 => ( P @ A0 @ A1 ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_161_remdups__adj_Oinduct,axiom,
% 4.03/2.03 ! [A: $tType,P: ( list @ A ) > $o,A0: list @ A] :
% 4.03/2.03 ( ( P @ ( nil @ A ) )
% 4.03/2.03 => ( ! [X5: A] : ( P @ ( cons @ A @ X5 @ ( nil @ A ) ) )
% 4.03/2.03 => ( ! [X5: A,Y3: A,Xs2: list @ A] :
% 4.03/2.03 ( ( ( X5 = Y3 )
% 4.03/2.03 => ( P @ ( cons @ A @ X5 @ Xs2 ) ) )
% 4.03/2.03 => ( ( ( X5 != Y3 )
% 4.03/2.03 => ( P @ ( cons @ A @ Y3 @ Xs2 ) ) )
% 4.03/2.03 => ( P @ ( cons @ A @ X5 @ ( cons @ A @ Y3 @ Xs2 ) ) ) ) )
% 4.03/2.03 => ( P @ A0 ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_162_arg__min__list_Oinduct,axiom,
% 4.03/2.03 ! [B: $tType,A: $tType] :
% 4.03/2.03 ( ( linorder @ B )
% 4.03/2.03 => ! [P: ( A > B ) > ( list @ A ) > $o,A0: A > B,A1: list @ A] :
% 4.03/2.03 ( ! [F2: A > B,X5: A] : ( P @ F2 @ ( cons @ A @ X5 @ ( nil @ A ) ) )
% 4.03/2.03 => ( ! [F2: A > B,X5: A,Y3: A,Zs: list @ A] :
% 4.03/2.03 ( ( P @ F2 @ ( cons @ A @ Y3 @ Zs ) )
% 4.03/2.03 => ( P @ F2 @ ( cons @ A @ X5 @ ( cons @ A @ Y3 @ Zs ) ) ) )
% 4.03/2.03 => ( ! [A6: A > B] : ( P @ A6 @ ( nil @ A ) )
% 4.03/2.03 => ( P @ A0 @ A1 ) ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_163_successively_Oinduct,axiom,
% 4.03/2.03 ! [A: $tType,P: ( A > A > $o ) > ( list @ A ) > $o,A0: A > A > $o,A1: list @ A] :
% 4.03/2.03 ( ! [P4: A > A > $o] : ( P @ P4 @ ( nil @ A ) )
% 4.03/2.03 => ( ! [P4: A > A > $o,X5: A] : ( P @ P4 @ ( cons @ A @ X5 @ ( nil @ A ) ) )
% 4.03/2.03 => ( ! [P4: A > A > $o,X5: A,Y3: A,Xs2: list @ A] :
% 4.03/2.03 ( ( P @ P4 @ ( cons @ A @ Y3 @ Xs2 ) )
% 4.03/2.03 => ( P @ P4 @ ( cons @ A @ X5 @ ( cons @ A @ Y3 @ Xs2 ) ) ) )
% 4.03/2.03 => ( P @ A0 @ A1 ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_164_list__nonempty__induct,axiom,
% 4.03/2.03 ! [A: $tType,Xs: list @ A,P: ( list @ A ) > $o] :
% 4.03/2.03 ( ( Xs
% 4.03/2.03 != ( nil @ A ) )
% 4.03/2.03 => ( ! [X5: A] : ( P @ ( cons @ A @ X5 @ ( nil @ A ) ) )
% 4.03/2.03 => ( ! [X5: A,Xs2: list @ A] :
% 4.03/2.03 ( ( Xs2
% 4.03/2.03 != ( nil @ A ) )
% 4.03/2.03 => ( ( P @ Xs2 )
% 4.03/2.03 => ( P @ ( cons @ A @ X5 @ Xs2 ) ) ) )
% 4.03/2.03 => ( P @ Xs ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_165_map__tailrec__rev_Oinduct,axiom,
% 4.03/2.03 ! [A: $tType,B: $tType,P: ( A > B ) > ( list @ A ) > ( list @ B ) > $o,A0: A > B,A1: list @ A,A22: list @ B] :
% 4.03/2.03 ( ! [F2: A > B,X_1: list @ B] : ( P @ F2 @ ( nil @ A ) @ X_1 )
% 4.03/2.03 => ( ! [F2: A > B,A6: A,As: list @ A,Bs: list @ B] :
% 4.03/2.03 ( ( P @ F2 @ As @ ( cons @ B @ ( F2 @ A6 ) @ Bs ) )
% 4.03/2.03 => ( P @ F2 @ ( cons @ A @ A6 @ As ) @ Bs ) )
% 4.03/2.03 => ( P @ A0 @ A1 @ A22 ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_166_strict__sorted_Ocases,axiom,
% 4.03/2.03 ! [A: $tType] :
% 4.03/2.03 ( ( linorder @ A )
% 4.03/2.03 => ! [X3: list @ A] :
% 4.03/2.03 ( ( X3
% 4.03/2.03 != ( nil @ A ) )
% 4.03/2.03 => ~ ! [X5: A,Ys: list @ A] :
% 4.03/2.03 ( X3
% 4.03/2.03 != ( cons @ A @ X5 @ Ys ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_167_Free_Ohyps,axiom,
% 4.03/2.03 late_transitions @ ( par @ p @ ( res @ x @ q ) ) @ ( late_FreeR @ alpha @ pxQ ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_168_old_Oprod_Orec,axiom,
% 4.03/2.03 ! [A: $tType,T: $tType,B: $tType,F1: A > B > T,A2: A,B2: B] :
% 4.03/2.03 ( ( product_rec_prod @ A @ B @ T @ F1 @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 4.03/2.03 = ( F1 @ A2 @ B2 ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_169_supports__def,axiom,
% 4.03/2.03 ! [A: $tType,X: $tType] :
% 4.03/2.03 ( ( supports @ X @ A )
% 4.03/2.03 = ( ^ [S: set @ X,X4: A] :
% 4.03/2.03 ! [A3: X,B3: X] :
% 4.03/2.03 ( ( ~ ( member @ X @ A3 @ S )
% 4.03/2.03 & ~ ( member @ X @ B3 @ S ) )
% 4.03/2.03 => ( ( perm @ X @ A @ ( cons @ ( product_prod @ X @ X ) @ ( product_Pair @ X @ X @ A3 @ B3 ) @ ( nil @ ( product_prod @ X @ X ) ) ) @ X4 )
% 4.03/2.03 = X4 ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_170_perm__residual__Rep_Osimps_I2_J,axiom,
% 4.03/2.03 ! [X: $tType,Pi: list @ ( product_prod @ X @ X ),FreeRes: late_freeRes,Pia: pi] :
% 4.03/2.03 ( ( perm @ X @ late_residual_Rep @ Pi @ ( late_r347633188eR_Rep @ FreeRes @ Pia ) )
% 4.03/2.03 = ( late_r347633188eR_Rep @ ( perm @ X @ late_freeRes @ Pi @ FreeRes ) @ ( perm @ X @ pi @ Pi @ Pia ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_171_alphaInput,axiom,
% 4.03/2.03 ! [C2: name,P: pi,A2: name,X3: name] :
% 4.03/2.03 ( ( fresh @ name @ pi @ C2 @ P )
% 4.03/2.03 => ( ( input @ A2 @ X3 @ P )
% 4.03/2.03 = ( input @ A2 @ C2 @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ X3 @ C2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ P ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_172_name__calc_I1_J,axiom,
% 4.03/2.03 ! [A2: name,B2: name,Pi: list @ ( product_prod @ name @ name ),X3: name] :
% 4.03/2.03 ( ( perm @ name @ name @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ Pi ) @ X3 )
% 4.03/2.03 = ( swap @ name @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( perm @ name @ name @ Pi @ X3 ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_173_Late__Semantics1_Osubject_Oinject_I1_J,axiom,
% 4.03/2.03 ! [X1: name,Y1: name] :
% 4.03/2.03 ( ( ( late_InputS @ X1 )
% 4.03/2.03 = ( late_InputS @ Y1 ) )
% 4.03/2.03 = ( X1 = Y1 ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_174_residual__Rep_Oinject_I2_J,axiom,
% 4.03/2.03 ! [X21: late_freeRes,X222: pi,Y21: late_freeRes,Y22: pi] :
% 4.03/2.03 ( ( ( late_r347633188eR_Rep @ X21 @ X222 )
% 4.03/2.03 = ( late_r347633188eR_Rep @ Y21 @ Y22 ) )
% 4.03/2.03 = ( ( X21 = Y21 )
% 4.03/2.03 & ( X222 = Y22 ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_175_pi_Ofresh_I8_J,axiom,
% 4.03/2.03 ! [A2: name,X22: pi,X1: pi] :
% 4.03/2.03 ( ( fresh @ name @ pi @ A2 @ ( par @ X22 @ X1 ) )
% 4.03/2.03 = ( ( fresh @ name @ pi @ A2 @ X22 )
% 4.03/2.03 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_176_pi_Operm_I8_J,axiom,
% 4.03/2.03 ! [Pi: list @ ( product_prod @ name @ name ),X22: pi,X1: pi] :
% 4.03/2.03 ( ( perm @ name @ pi @ Pi @ ( par @ X22 @ X1 ) )
% 4.03/2.03 = ( par @ ( perm @ name @ pi @ Pi @ X22 ) @ ( perm @ name @ pi @ Pi @ X1 ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_177_pi_Operm_I4_J,axiom,
% 4.03/2.03 ! [Pi: list @ ( product_prod @ name @ name ),X32: name,X1: name,X22: pi] :
% 4.03/2.03 ( ( perm @ name @ pi @ Pi @ ( input @ X32 @ X1 @ X22 ) )
% 4.03/2.03 = ( input @ ( perm @ name @ name @ Pi @ X32 ) @ ( perm @ name @ name @ Pi @ X1 ) @ ( perm @ name @ pi @ Pi @ X22 ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_178_subject_Ofresh_I1_J,axiom,
% 4.03/2.03 ! [A2: name,X1: name] :
% 4.03/2.03 ( ( fresh @ name @ late_subject @ A2 @ ( late_InputS @ X1 ) )
% 4.03/2.03 = ( fresh @ name @ name @ A2 @ X1 ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_179_subject_Operm_I1_J,axiom,
% 4.03/2.03 ! [Pi: list @ ( product_prod @ name @ name ),X1: name] :
% 4.03/2.03 ( ( perm @ name @ late_subject @ Pi @ ( late_InputS @ X1 ) )
% 4.03/2.03 = ( late_InputS @ ( perm @ name @ name @ Pi @ X1 ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_180_ScopeExt,axiom,
% 4.03/2.03 ! [Y: name,R: pi,Z: name,S2: pi] :
% 4.03/2.03 ( ( fresh @ name @ pi @ Y @ R )
% 4.03/2.03 => ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( res @ Y @ ( res @ Z @ ( par @ R @ S2 ) ) ) @ ( res @ Z @ ( par @ R @ ( res @ Y @ S2 ) ) ) ) @ rel ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_181_Res,axiom,
% 4.03/2.03 ! [Y: name,R: pi,S2: pi] :
% 4.03/2.03 ( ( fresh @ name @ pi @ Y @ R )
% 4.03/2.03 => ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( res @ Y @ ( par @ R @ S2 ) ) @ ( par @ R @ ( res @ Y @ S2 ) ) ) @ rel ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_182_pi_Odistinct_I55_J,axiom,
% 4.03/2.03 ! [Name12: name,Name22: name,Pi: pi,Pi12: pi,Pi22: pi] :
% 4.03/2.03 ( ( input @ Name12 @ Name22 @ Pi )
% 4.03/2.03 != ( par @ Pi12 @ Pi22 ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_183_pi_Oinject_I7_J,axiom,
% 4.03/2.03 ! [X22: pi,X1: pi,Y2: pi,Y1: pi] :
% 4.03/2.03 ( ( ( par @ X22 @ X1 )
% 4.03/2.03 = ( par @ Y2 @ Y1 ) )
% 4.03/2.03 = ( ( X22 = Y2 )
% 4.03/2.03 & ( X1 = Y1 ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_184_pi_Odistinct_I85_J,axiom,
% 4.03/2.03 ! [Pi1: pi,Pi2: pi,Name4: name,Pi4: pi] :
% 4.03/2.03 ( ( par @ Pi1 @ Pi2 )
% 4.03/2.03 != ( res @ Name4 @ Pi4 ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_185_transitions_OInput,axiom,
% 4.03/2.03 ! [X3: name,A2: name,P: pi] :
% 4.03/2.03 ( ( X3 != A2 )
% 4.03/2.03 => ( late_transitions @ ( input @ A2 @ X3 @ P ) @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ P ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_186_Late__Semantics_OInput,axiom,
% 4.03/2.03 ! [A2: name,X3: name,P: pi] : ( late_transitions @ ( input @ A2 @ X3 @ P ) @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ P ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_187_pi_Odistinct_I57_J,axiom,
% 4.03/2.03 ! [Name12: name,Name22: name,Pi: pi,Name4: name,Pi4: pi] :
% 4.03/2.03 ( ( input @ Name12 @ Name22 @ Pi )
% 4.03/2.03 != ( res @ Name4 @ Pi4 ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_188_Late__Semantics_Osubject_Odistinct_I1_J,axiom,
% 4.03/2.03 ! [Name: name,Name4: name] :
% 4.03/2.03 ( ( late_InputS @ Name )
% 4.03/2.03 != ( late_BoundOutputS @ Name4 ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_189_Late__Semantics1_Osubject_Odistinct_I1_J,axiom,
% 4.03/2.03 ! [X1: name,X22: name] :
% 4.03/2.03 ( ( late_InputS @ X1 )
% 4.03/2.03 != ( late_BoundOutputS @ X22 ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_190_subject_Oinducts,axiom,
% 4.03/2.03 ! [P: late_subject > $o,Subject: late_subject] :
% 4.03/2.03 ( ! [Name3: name] : ( P @ ( late_InputS @ Name3 ) )
% 4.03/2.03 => ( ! [Name3: name] : ( P @ ( late_BoundOutputS @ Name3 ) )
% 4.03/2.03 => ( P @ Subject ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_191_subject_Oexhaust,axiom,
% 4.03/2.03 ! [Y: late_subject] :
% 4.03/2.03 ( ! [X13: name] :
% 4.03/2.03 ( Y
% 4.03/2.03 != ( late_InputS @ X13 ) )
% 4.03/2.03 => ~ ! [X23: name] :
% 4.03/2.03 ( Y
% 4.03/2.03 != ( late_BoundOutputS @ X23 ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_192_subject_Ostrong__induct_H,axiom,
% 4.03/2.03 ! [N: $tType,P: N > late_subject > $o,Z: N,Subject: late_subject] :
% 4.03/2.03 ( ! [Name3: name,Z2: N] : ( P @ Z2 @ ( late_InputS @ Name3 ) )
% 4.03/2.03 => ( ! [Name3: name,Z2: N] : ( P @ Z2 @ ( late_BoundOutputS @ Name3 ) )
% 4.03/2.03 => ( P @ Z @ Subject ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_193_subject_Ostrong__inducts,axiom,
% 4.03/2.03 ! [A: $tType,P: A > late_subject > $o,Z: A,Subject: late_subject] :
% 4.03/2.03 ( ! [Name3: name,Z2: A] : ( P @ Z2 @ ( late_InputS @ Name3 ) )
% 4.03/2.03 => ( ! [Name3: name,Z2: A] : ( P @ Z2 @ ( late_BoundOutputS @ Name3 ) )
% 4.03/2.03 => ( P @ Z @ Subject ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_194_Par2F,axiom,
% 4.03/2.03 ! [Q: pi,Alpha: late_freeRes,Q2: pi,P: pi] :
% 4.03/2.03 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 4.03/2.03 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha @ ( par @ P @ Q2 ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_195_Par1F,axiom,
% 4.03/2.03 ! [P: pi,Alpha: late_freeRes,P2: pi,Q: pi] :
% 4.03/2.03 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 4.03/2.03 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha @ ( par @ P2 @ Q ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_196_name__calc_I3_J,axiom,
% 4.03/2.03 ! [A2: name,C2: name,B2: name] :
% 4.03/2.03 ( ( ( A2 = C2 )
% 4.03/2.03 => ( ( swap @ name @ ( product_Pair @ name @ name @ A2 @ B2 ) @ C2 )
% 4.03/2.03 = B2 ) )
% 4.03/2.03 & ( ( A2 != C2 )
% 4.03/2.03 => ( ( ( B2 = C2 )
% 4.03/2.03 => ( ( swap @ name @ ( product_Pair @ name @ name @ A2 @ B2 ) @ C2 )
% 4.03/2.03 = A2 ) )
% 4.03/2.03 & ( ( B2 != C2 )
% 4.03/2.03 => ( ( swap @ name @ ( product_Pair @ name @ name @ A2 @ B2 ) @ C2 )
% 4.03/2.03 = C2 ) ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_197_resTrans_I2_J,axiom,
% 4.03/2.03 ! [X3: name,Y: name,P: pi,Rs: late_residual] :
% 4.03/2.03 ~ ( late_transitions @ ( res @ X3 @ ( input @ X3 @ Y @ P ) ) @ Rs ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_198_inputIneqTrans,axiom,
% 4.03/2.03 ! [A2: name,X3: name,P: pi,B2: late_subject,Y: name,P2: pi] :
% 4.03/2.03 ( ( late_transitions @ ( input @ A2 @ X3 @ P ) @ ( late_BoundR @ B2 @ Y @ P2 ) )
% 4.03/2.03 => ~ ( fresh @ name @ late_subject @ A2 @ B2 ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_199_inputFreeTrans,axiom,
% 4.03/2.03 ! [A2: name,X3: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 4.03/2.03 ~ ( late_transitions @ ( input @ A2 @ X3 @ P ) @ ( late_FreeR @ Alpha @ P2 ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_200_Late__Semantics_OPar1B,axiom,
% 4.03/2.03 ! [P: pi,A2: late_subject,X3: name,P2: pi,Q: pi] :
% 4.03/2.03 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X3 @ P2 ) )
% 4.03/2.03 => ( ( fresh @ name @ pi @ X3 @ Q )
% 4.03/2.03 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X3 @ ( par @ P2 @ Q ) ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_201_Late__Semantics_OPar2B,axiom,
% 4.03/2.03 ! [Q: pi,A2: late_subject,X3: name,Q2: pi,P: pi] :
% 4.03/2.03 ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X3 @ Q2 ) )
% 4.03/2.03 => ( ( fresh @ name @ pi @ X3 @ P )
% 4.03/2.03 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X3 @ ( par @ P @ Q2 ) ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_202_parCasesB,axiom,
% 4.03/2.03 ! [P: pi,Q: pi,A2: late_subject,X3: name,PQ: pi,Prop: pi > $o] :
% 4.03/2.03 ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X3 @ PQ ) )
% 4.03/2.03 => ( ( fresh @ name @ pi @ X3 @ P )
% 4.03/2.03 => ( ( fresh @ name @ pi @ X3 @ Q )
% 4.03/2.03 => ( ! [P3: pi] :
% 4.03/2.03 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X3 @ P3 ) )
% 4.03/2.03 => ( Prop @ ( par @ P3 @ Q ) ) )
% 4.03/2.03 => ( ! [Q3: pi] :
% 4.03/2.03 ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X3 @ Q3 ) )
% 4.03/2.03 => ( Prop @ ( par @ P @ Q3 ) ) )
% 4.03/2.03 => ( Prop @ PQ ) ) ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_203_parCasesB_H,axiom,
% 4.03/2.03 ! [P: pi,Q: pi,B2: late_subject,Y: name,P2: pi] :
% 4.03/2.03 ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ B2 @ Y @ P2 ) )
% 4.03/2.03 => ( ! [P4: pi,A6: late_subject,X5: name,P3: pi,Q4: pi] :
% 4.03/2.03 ( ( ( par @ P @ Q )
% 4.03/2.03 = ( par @ P4 @ Q4 ) )
% 4.03/2.03 => ( ( ( late_BoundR @ B2 @ Y @ P2 )
% 4.03/2.03 = ( late_BoundR @ A6 @ X5 @ ( par @ P3 @ Q4 ) ) )
% 4.03/2.03 => ( ( late_transitions @ P4 @ ( late_BoundR @ A6 @ X5 @ P3 ) )
% 4.03/2.03 => ( ( fresh @ name @ pi @ X5 @ P4 )
% 4.03/2.03 => ( ( fresh @ name @ pi @ X5 @ Q4 )
% 4.03/2.03 => ~ ( fresh @ name @ late_subject @ X5 @ A6 ) ) ) ) ) )
% 4.03/2.03 => ~ ! [Q4: pi,A6: late_subject,X5: name,Q3: pi,P4: pi] :
% 4.03/2.03 ( ( ( par @ P @ Q )
% 4.03/2.03 = ( par @ P4 @ Q4 ) )
% 4.03/2.03 => ( ( ( late_BoundR @ B2 @ Y @ P2 )
% 4.03/2.03 = ( late_BoundR @ A6 @ X5 @ ( par @ P4 @ Q3 ) ) )
% 4.03/2.03 => ( ( late_transitions @ Q4 @ ( late_BoundR @ A6 @ X5 @ Q3 ) )
% 4.03/2.03 => ( ( fresh @ name @ pi @ X5 @ P4 )
% 4.03/2.03 => ( ( fresh @ name @ pi @ X5 @ Q4 )
% 4.03/2.03 => ~ ( fresh @ name @ late_subject @ X5 @ A6 ) ) ) ) ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_204_transitions_OPar1B,axiom,
% 4.03/2.03 ! [P: pi,A2: late_subject,X3: name,P2: pi,Q: pi] :
% 4.03/2.03 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X3 @ P2 ) )
% 4.03/2.03 => ( ( fresh @ name @ pi @ X3 @ P )
% 4.03/2.03 => ( ( fresh @ name @ pi @ X3 @ Q )
% 4.03/2.03 => ( ( fresh @ name @ late_subject @ X3 @ A2 )
% 4.03/2.03 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X3 @ ( par @ P2 @ Q ) ) ) ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_205_transitions_OPar2B,axiom,
% 4.03/2.03 ! [Q: pi,A2: late_subject,X3: name,Q2: pi,P: pi] :
% 4.03/2.03 ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X3 @ Q2 ) )
% 4.03/2.03 => ( ( fresh @ name @ pi @ X3 @ P )
% 4.03/2.03 => ( ( fresh @ name @ pi @ X3 @ Q )
% 4.03/2.03 => ( ( fresh @ name @ late_subject @ X3 @ A2 )
% 4.03/2.03 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X3 @ ( par @ P @ Q2 ) ) ) ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_206_resInputFreeTrans,axiom,
% 4.03/2.03 ! [X3: name,A2: name,Y: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 4.03/2.03 ~ ( late_transitions @ ( res @ X3 @ ( input @ A2 @ Y @ P ) ) @ ( late_FreeR @ Alpha @ P2 ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_207_inputBoundOutputTrans,axiom,
% 4.03/2.03 ! [A2: name,X3: name,P: pi,B2: name,Y: name,P2: pi] :
% 4.03/2.03 ~ ( late_transitions @ ( input @ A2 @ X3 @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ B2 ) @ Y @ P2 ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_208_inputCases,axiom,
% 4.03/2.03 ! [A2: name,X3: name,P: pi,B2: late_subject,Y: name,YP: pi,Prop: late_subject > name > pi > $o] :
% 4.03/2.03 ( ( late_transitions @ ( input @ A2 @ X3 @ P ) @ ( late_BoundR @ B2 @ Y @ YP ) )
% 4.03/2.03 => ( ( Y != A2 )
% 4.03/2.03 => ( ( Y != X3 )
% 4.03/2.03 => ( ( fresh @ name @ pi @ Y @ P )
% 4.03/2.03 => ( ( ( B2
% 4.03/2.03 = ( late_InputS @ A2 ) )
% 4.03/2.03 => ( ( YP
% 4.03/2.03 = ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ X3 @ Y ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ P ) )
% 4.03/2.03 => ( Prop @ ( late_InputS @ A2 ) @ Y @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ X3 @ Y ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ P ) ) ) )
% 4.03/2.03 => ( Prop @ B2 @ Y @ YP ) ) ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_209_resInputBoundOutputTrans,axiom,
% 4.03/2.03 ! [X3: name,A2: name,Y: name,P: pi,B2: name,Z: name,P2: pi] :
% 4.03/2.03 ~ ( late_transitions @ ( res @ X3 @ ( input @ A2 @ Y @ P ) ) @ ( late_BoundR @ ( late_BoundOutputS @ B2 ) @ Z @ P2 ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_210_Late__Semantics_OClose1,axiom,
% 4.03/2.03 ! [P: pi,A2: name,X3: name,P2: pi,Q: pi,Y: name,Q2: pi] :
% 4.03/2.03 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ P2 ) )
% 4.03/2.03 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y @ Q2 ) )
% 4.03/2.03 => ( ( fresh @ name @ pi @ Y @ P )
% 4.03/2.03 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ ( subs @ P2 @ X3 @ Y ) @ Q2 ) ) ) ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_211_Late__Semantics_OClose2,axiom,
% 4.03/2.03 ! [P: pi,A2: name,Y: name,P2: pi,Q: pi,X3: name,Q2: pi] :
% 4.03/2.03 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y @ P2 ) )
% 4.03/2.03 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ Q2 ) )
% 4.03/2.03 => ( ( fresh @ name @ pi @ Y @ Q )
% 4.03/2.03 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ P2 @ ( subs @ Q2 @ X3 @ Y ) ) ) ) ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_212_transitions_OClose1,axiom,
% 4.03/2.03 ! [P: pi,A2: name,X3: name,P2: pi,Q: pi,Y: name,Q2: pi] :
% 4.03/2.03 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ P2 ) )
% 4.03/2.03 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y @ Q2 ) )
% 4.03/2.03 => ( ( fresh @ name @ pi @ X3 @ P )
% 4.03/2.03 => ( ( fresh @ name @ pi @ X3 @ Q )
% 4.03/2.03 => ( ( fresh @ name @ pi @ Y @ P )
% 4.03/2.03 => ( ( fresh @ name @ pi @ Y @ Q )
% 4.03/2.03 => ( ( X3 != A2 )
% 4.03/2.03 => ( ( fresh @ name @ pi @ X3 @ Q2 )
% 4.03/2.03 => ( ( Y != A2 )
% 4.03/2.03 => ( ( fresh @ name @ pi @ Y @ P2 )
% 4.03/2.03 => ( ( X3 != Y )
% 4.03/2.03 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ ( subs @ P2 @ X3 @ Y ) @ Q2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_213_EqvtRel,axiom,
% 4.03/2.03 eqvt @ pi @ rel ).
% 4.03/2.03
% 4.03/2.03 thf(fact_214_subst__identity,axiom,
% 4.03/2.03 ! [P: pi,A2: name] :
% 4.03/2.03 ( ( subs @ P @ A2 @ A2 )
% 4.03/2.03 = P ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_215_simps_I9_J,axiom,
% 4.03/2.03 ! [X3: name,C2: name,D3: name,P: pi] :
% 4.03/2.03 ( ( X3 != C2 )
% 4.03/2.03 => ( ( X3 != D3 )
% 4.03/2.03 => ( ( subs @ ( res @ X3 @ P ) @ C2 @ D3 )
% 4.03/2.03 = ( res @ X3 @ ( subs @ P @ C2 @ D3 ) ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_216_simps_I8_J,axiom,
% 4.03/2.03 ! [P: pi,Q: pi,C2: name,D3: name] :
% 4.03/2.03 ( ( subs @ ( par @ P @ Q ) @ C2 @ D3 )
% 4.03/2.03 = ( par @ ( subs @ P @ C2 @ D3 ) @ ( subs @ Q @ C2 @ D3 ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_217_substTrans,axiom,
% 4.03/2.03 ! [B2: name,P: pi,A2: name,C2: name] :
% 4.03/2.03 ( ( fresh @ name @ pi @ B2 @ P )
% 4.03/2.03 => ( ( subs @ ( subs @ P @ A2 @ B2 ) @ B2 @ C2 )
% 4.03/2.03 = ( subs @ P @ A2 @ C2 ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_218_forget,axiom,
% 4.03/2.03 ! [A2: name,P: pi,B2: name] :
% 4.03/2.03 ( ( fresh @ name @ pi @ A2 @ P )
% 4.03/2.03 => ( ( subs @ P @ A2 @ B2 )
% 4.03/2.03 = P ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_219_fresh__fact1,axiom,
% 4.03/2.03 ! [A2: name,P: pi,C2: name,B2: name] :
% 4.03/2.03 ( ( fresh @ name @ pi @ A2 @ P )
% 4.03/2.03 => ( ( A2 != C2 )
% 4.03/2.03 => ( fresh @ name @ pi @ A2 @ ( subs @ P @ B2 @ C2 ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_220_fresh__fact2,axiom,
% 4.03/2.03 ! [A2: name,B2: name,P: pi] :
% 4.03/2.03 ( ( A2 != B2 )
% 4.03/2.03 => ( fresh @ name @ pi @ A2 @ ( subs @ P @ A2 @ B2 ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_221_Agent_OsubstRes3,axiom,
% 4.03/2.03 ! [B2: name,P: pi,A2: name] :
% 4.03/2.03 ( ( fresh @ name @ pi @ B2 @ P )
% 4.03/2.03 => ( ( subs @ ( res @ A2 @ P ) @ A2 @ B2 )
% 4.03/2.03 = ( res @ B2 @ ( subs @ P @ A2 @ B2 ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_222_substRes2,axiom,
% 4.03/2.03 ! [B2: name,P: pi,A2: name] :
% 4.03/2.03 ( ( fresh @ name @ pi @ B2 @ P )
% 4.03/2.03 => ( ( res @ A2 @ P )
% 4.03/2.03 = ( res @ B2 @ ( subs @ P @ A2 @ B2 ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_223_eqvt__subs,axiom,
% 4.03/2.03 ! [P5: list @ ( product_prod @ name @ name ),P: pi,A2: name,B2: name] :
% 4.03/2.03 ( ( perm @ name @ pi @ P5 @ ( subs @ P @ A2 @ B2 ) )
% 4.03/2.03 = ( subs @ ( perm @ name @ pi @ P5 @ P ) @ ( perm @ name @ name @ P5 @ A2 ) @ ( perm @ name @ name @ P5 @ B2 ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_224_Strong__Late__Sim__SC__Mirabelle__dtpyqonsky_OsubstRes3,axiom,
% 4.03/2.03 ! [A2: name,P: pi,X3: name] :
% 4.03/2.03 ( ( subs @ ( res @ A2 @ P ) @ X3 @ A2 )
% 4.03/2.03 = ( res @ X3 @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ X3 @ A2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ P ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_225_renaming,axiom,
% 4.03/2.03 ! [C2: name,P: pi,A2: name,B2: name] :
% 4.03/2.03 ( ( fresh @ name @ pi @ C2 @ P )
% 4.03/2.03 => ( ( subs @ P @ A2 @ B2 )
% 4.03/2.03 = ( subs @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ C2 @ A2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ P ) @ C2 @ B2 ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_226_injPermSubst,axiom,
% 4.03/2.03 ! [B2: name,P: pi,A2: name] :
% 4.03/2.03 ( ( fresh @ name @ pi @ B2 @ P )
% 4.03/2.03 => ( ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ P )
% 4.03/2.03 = ( subs @ P @ A2 @ B2 ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_227_Late__Semantics_OComm1,axiom,
% 4.03/2.03 ! [P: pi,A2: name,X3: name,P2: pi,Q: pi,B2: name,Q2: pi] :
% 4.03/2.03 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ P2 ) )
% 4.03/2.03 => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ Q2 ) )
% 4.03/2.03 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P2 @ X3 @ B2 ) @ Q2 ) ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_228_Late__Semantics_OComm2,axiom,
% 4.03/2.03 ! [P: pi,A2: name,B2: name,P2: pi,Q: pi,X3: name,Q2: pi] :
% 4.03/2.03 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P2 ) )
% 4.03/2.03 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ Q2 ) )
% 4.03/2.03 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P2 @ ( subs @ Q2 @ X3 @ B2 ) ) ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_229_transitions_OComm2,axiom,
% 4.03/2.03 ! [P: pi,A2: name,B2: name,P2: pi,Q: pi,X3: name,Q2: pi] :
% 4.03/2.03 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P2 ) )
% 4.03/2.03 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ Q2 ) )
% 4.03/2.03 => ( ( fresh @ name @ pi @ X3 @ P )
% 4.03/2.03 => ( ( fresh @ name @ pi @ X3 @ Q )
% 4.03/2.03 => ( ( X3 != A2 )
% 4.03/2.03 => ( ( X3 != B2 )
% 4.03/2.03 => ( ( fresh @ name @ pi @ X3 @ P2 )
% 4.03/2.03 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P2 @ ( subs @ Q2 @ X3 @ B2 ) ) ) ) ) ) ) ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_230_transitions_OComm1,axiom,
% 4.03/2.03 ! [P: pi,A2: name,X3: name,P2: pi,Q: pi,B2: name,Q2: pi] :
% 4.03/2.03 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ P2 ) )
% 4.03/2.03 => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ Q2 ) )
% 4.03/2.03 => ( ( fresh @ name @ pi @ X3 @ P )
% 4.03/2.03 => ( ( fresh @ name @ pi @ X3 @ Q )
% 4.03/2.03 => ( ( X3 != A2 )
% 4.03/2.03 => ( ( X3 != B2 )
% 4.03/2.03 => ( ( fresh @ name @ pi @ X3 @ Q2 )
% 4.03/2.03 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P2 @ X3 @ B2 ) @ Q2 ) ) ) ) ) ) ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_231_transitions_OClose2,axiom,
% 4.03/2.03 ! [P: pi,A2: name,Y: name,P2: pi,Q: pi,X3: name,Q2: pi] :
% 4.03/2.03 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y @ P2 ) )
% 4.03/2.03 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X3 @ Q2 ) )
% 4.03/2.03 => ( ( fresh @ name @ pi @ X3 @ P )
% 4.03/2.03 => ( ( fresh @ name @ pi @ X3 @ Q )
% 4.03/2.03 => ( ( fresh @ name @ pi @ Y @ P )
% 4.03/2.03 => ( ( fresh @ name @ pi @ Y @ Q )
% 4.03/2.03 => ( ( X3 != A2 )
% 4.03/2.03 => ( ( fresh @ name @ pi @ X3 @ P2 )
% 4.03/2.03 => ( ( Y != A2 )
% 4.03/2.03 => ( ( fresh @ name @ pi @ Y @ Q2 )
% 4.03/2.03 => ( ( X3 != Y )
% 4.03/2.03 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ P2 @ ( subs @ Q2 @ X3 @ Y ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_232_product__lists_Osimps_I1_J,axiom,
% 4.03/2.03 ! [A: $tType] :
% 4.03/2.03 ( ( product_lists @ A @ ( nil @ ( list @ A ) ) )
% 4.03/2.03 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_233_Agent_Oswap__name__def,axiom,
% 4.03/2.03 ( ( swap @ name )
% 4.03/2.03 = swap_name ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_234_swap__name_Osimps,axiom,
% 4.03/2.03 ! [A2: name,C2: name,B2: name] :
% 4.03/2.03 ( ( ( A2 = C2 )
% 4.03/2.03 => ( ( swap_name @ ( product_Pair @ name @ name @ A2 @ B2 ) @ C2 )
% 4.03/2.03 = B2 ) )
% 4.03/2.03 & ( ( A2 != C2 )
% 4.03/2.03 => ( ( ( B2 = C2 )
% 4.03/2.03 => ( ( swap_name @ ( product_Pair @ name @ name @ A2 @ B2 ) @ C2 )
% 4.03/2.03 = A2 ) )
% 4.03/2.03 & ( ( B2 != C2 )
% 4.03/2.03 => ( ( swap_name @ ( product_Pair @ name @ name @ A2 @ B2 ) @ C2 )
% 4.03/2.03 = C2 ) ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_235_eqvtRelE,axiom,
% 4.03/2.03 ! [A: $tType] :
% 4.03/2.03 ( ( pt_name @ A )
% 4.03/2.03 => ! [Rel: set @ ( product_prod @ A @ A ),Perm: list @ ( product_prod @ name @ name ),P: A,Q: A] :
% 4.03/2.03 ( ( eqvt @ A @ Rel )
% 4.03/2.03 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ ( perm @ name @ A @ Perm @ P ) @ ( perm @ name @ A @ Perm @ Q ) ) @ Rel )
% 4.03/2.03 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ P @ Q ) @ Rel ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_236_eqvtRelI,axiom,
% 4.03/2.03 ! [A: $tType] :
% 4.03/2.03 ( ( pt_name @ A )
% 4.03/2.03 => ! [Rel: set @ ( product_prod @ A @ A ),P: A,Q: A,Perm: list @ ( product_prod @ name @ name )] :
% 4.03/2.03 ( ( eqvt @ A @ Rel )
% 4.03/2.03 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ P @ Q ) @ Rel )
% 4.03/2.03 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ ( perm @ name @ A @ Perm @ P ) @ ( perm @ name @ A @ Perm @ Q ) ) @ Rel ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_237_eqvt__def,axiom,
% 4.03/2.03 ! [A: $tType] :
% 4.03/2.03 ( ( pt_name @ A )
% 4.03/2.03 => ( ( eqvt @ A )
% 4.03/2.03 = ( ^ [Rel2: set @ ( product_prod @ A @ A )] :
% 4.03/2.03 ! [X4: product_prod @ A @ A,Perm2: list @ ( product_prod @ name @ name )] :
% 4.03/2.03 ( ( member @ ( product_prod @ A @ A ) @ X4 @ Rel2 )
% 4.03/2.03 => ( member @ ( product_prod @ A @ A ) @ ( perm @ name @ ( product_prod @ A @ A ) @ Perm2 @ X4 ) @ Rel2 ) ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_238_name__prm__name_Osimps_I2_J,axiom,
% 4.03/2.03 ! [X3: product_prod @ name @ name,Xs: list @ ( product_prod @ name @ name ),A2: name] :
% 4.03/2.03 ( ( name_prm_name @ ( cons @ ( product_prod @ name @ name ) @ X3 @ Xs ) @ A2 )
% 4.03/2.03 = ( swap_name @ X3 @ ( name_prm_name @ Xs @ A2 ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_239_resSimCases,axiom,
% 4.03/2.03 ! [A: $tType] :
% 4.03/2.03 ( ( fs_name @ A )
% 4.03/2.03 => ! [Rel: set @ ( product_prod @ pi @ pi ),Q: pi,X3: name,P: pi,C4: A] :
% 4.03/2.03 ( ( eqvt @ pi @ Rel )
% 4.03/2.03 => ( ! [Q3: pi,A6: name] :
% 4.03/2.03 ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A6 @ X3 ) @ Q3 ) )
% 4.03/2.03 => ( ( A6 != X3 )
% 4.03/2.03 => ? [P6: pi] :
% 4.03/2.03 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A6 ) @ X3 @ P6 ) )
% 4.03/2.03 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P6 @ Q3 ) @ Rel ) ) ) )
% 4.03/2.03 => ( ! [Q3: pi,A6: late_subject,Y3: name] :
% 4.03/2.03 ( ( late_transitions @ Q @ ( late_BoundR @ A6 @ Y3 @ Q3 ) )
% 4.03/2.03 => ( ( fresh @ name @ late_subject @ X3 @ A6 )
% 4.03/2.03 => ( ( X3 != Y3 )
% 4.03/2.03 => ( ( fresh @ name @ A @ Y3 @ C4 )
% 4.03/2.03 => ? [P6: pi] :
% 4.03/2.03 ( ( late_transitions @ P @ ( late_BoundR @ A6 @ Y3 @ P6 ) )
% 4.03/2.03 & ( strong2129052853vative @ P6 @ ( res @ X3 @ Q3 ) @ A6 @ Y3 @ Rel ) ) ) ) ) )
% 4.03/2.03 => ( ! [Q3: pi,Alpha2: late_freeRes] :
% 4.03/2.03 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 4.03/2.03 => ( ( fresh @ name @ late_freeRes @ X3 @ Alpha2 )
% 4.03/2.03 => ? [P6: pi] :
% 4.03/2.03 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 4.03/2.03 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P6 @ ( res @ X3 @ Q3 ) ) @ Rel ) ) ) )
% 4.03/2.03 => ( strong743114133lation @ P @ Rel @ ( res @ X3 @ Q ) ) ) ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_240_simE_I2_J,axiom,
% 4.03/2.03 ! [P: pi,Rel: set @ ( product_prod @ pi @ pi ),Q: pi,Alpha: late_freeRes,Q2: pi] :
% 4.03/2.03 ( ( strong743114133lation @ P @ Rel @ Q )
% 4.03/2.03 => ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 4.03/2.03 => ? [P3: pi] :
% 4.03/2.03 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P3 ) )
% 4.03/2.03 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P3 @ Q2 ) @ Rel ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_241_simE_I1_J,axiom,
% 4.03/2.03 ! [P: pi,Rel: set @ ( product_prod @ pi @ pi ),Q: pi,A2: late_subject,X3: name,Q2: pi] :
% 4.03/2.03 ( ( strong743114133lation @ P @ Rel @ Q )
% 4.03/2.03 => ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X3 @ Q2 ) )
% 4.03/2.03 => ( ( fresh @ name @ pi @ X3 @ P )
% 4.03/2.03 => ? [P3: pi] :
% 4.03/2.03 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X3 @ P3 ) )
% 4.03/2.03 & ( strong2129052853vative @ P3 @ Q2 @ A2 @ X3 @ Rel ) ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_242_simulation__def,axiom,
% 4.03/2.03 ( strong743114133lation
% 4.03/2.03 = ( ^ [P7: pi,Rel2: set @ ( product_prod @ pi @ pi ),Q5: pi] :
% 4.03/2.03 ( ! [A3: late_subject,X4: name,Q6: pi] :
% 4.03/2.03 ( ( ( late_transitions @ Q5 @ ( late_BoundR @ A3 @ X4 @ Q6 ) )
% 4.03/2.03 & ( fresh @ name @ pi @ X4 @ P7 ) )
% 4.03/2.03 => ? [P8: pi] :
% 4.03/2.03 ( ( late_transitions @ P7 @ ( late_BoundR @ A3 @ X4 @ P8 ) )
% 4.03/2.03 & ( strong2129052853vative @ P8 @ Q6 @ A3 @ X4 @ Rel2 ) ) )
% 4.03/2.03 & ! [Alpha3: late_freeRes,Q6: pi] :
% 4.03/2.03 ( ( late_transitions @ Q5 @ ( late_FreeR @ Alpha3 @ Q6 ) )
% 4.03/2.03 => ? [P8: pi] :
% 4.03/2.03 ( ( late_transitions @ P7 @ ( late_FreeR @ Alpha3 @ P8 ) )
% 4.03/2.03 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P8 @ Q6 ) @ Rel2 ) ) ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_243_simCases,axiom,
% 4.03/2.03 ! [Q: pi,P: pi,Rel: set @ ( product_prod @ pi @ pi )] :
% 4.03/2.03 ( ! [A6: late_subject,Y3: name,Q3: pi] :
% 4.03/2.03 ( ( late_transitions @ Q @ ( late_BoundR @ A6 @ Y3 @ Q3 ) )
% 4.03/2.03 => ( ( fresh @ name @ pi @ Y3 @ P )
% 4.03/2.03 => ? [P6: pi] :
% 4.03/2.03 ( ( late_transitions @ P @ ( late_BoundR @ A6 @ Y3 @ P6 ) )
% 4.03/2.03 & ( strong2129052853vative @ P6 @ Q3 @ A6 @ Y3 @ Rel ) ) ) )
% 4.03/2.03 => ( ! [Alpha2: late_freeRes,Q3: pi] :
% 4.03/2.03 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 4.03/2.03 => ? [P6: pi] :
% 4.03/2.03 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 4.03/2.03 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P6 @ Q3 ) @ Rel ) ) )
% 4.03/2.03 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_244_name__prm__name_Osimps_I1_J,axiom,
% 4.03/2.03 ! [A2: name] :
% 4.03/2.03 ( ( name_prm_name @ ( nil @ ( product_prod @ name @ name ) ) @ A2 )
% 4.03/2.03 = A2 ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_245_derivativeEqvtI2,axiom,
% 4.03/2.03 ! [P: pi,Q: pi,A2: late_subject,X3: name,Rel: set @ ( product_prod @ pi @ pi ),Perm: list @ ( product_prod @ name @ name )] :
% 4.03/2.03 ( ( strong2129052853vative @ P @ Q @ A2 @ X3 @ Rel )
% 4.03/2.03 => ( ( eqvt @ pi @ Rel )
% 4.03/2.03 => ( strong2129052853vative @ ( perm @ name @ pi @ Perm @ P ) @ ( perm @ name @ pi @ Perm @ Q ) @ A2 @ ( perm @ name @ name @ Perm @ X3 ) @ Rel ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_246_Agent_Oname__prm__name__def,axiom,
% 4.03/2.03 ( ( perm @ name @ name )
% 4.03/2.03 = name_prm_name ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_247_parSym,axiom,
% 4.03/2.03 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi,Q: pi] :
% 4.03/2.03 ( ! [R2: pi,S3: pi] : ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( par @ R2 @ S3 ) @ ( par @ S3 @ R2 ) ) @ Rel )
% 4.03/2.03 => ( ! [R2: pi,S3: pi,X5: name] :
% 4.03/2.03 ( ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ R2 @ S3 ) @ Rel )
% 4.03/2.03 => ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( res @ X5 @ R2 ) @ ( res @ X5 @ S3 ) ) @ Rel ) )
% 4.03/2.03 => ( strong743114133lation @ ( par @ P @ Q ) @ Rel @ ( par @ Q @ P ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_248_simCasesCont,axiom,
% 4.03/2.03 ! [A: $tType] :
% 4.03/2.03 ( ( fs_name @ A )
% 4.03/2.03 => ! [Rel: set @ ( product_prod @ pi @ pi ),Q: pi,P: pi,C4: A] :
% 4.03/2.03 ( ( eqvt @ pi @ Rel )
% 4.03/2.03 => ( ! [A6: late_subject,X5: name,Q3: pi] :
% 4.03/2.03 ( ( late_transitions @ Q @ ( late_BoundR @ A6 @ X5 @ Q3 ) )
% 4.03/2.03 => ( ( fresh @ name @ pi @ X5 @ P )
% 4.03/2.03 => ( ( fresh @ name @ pi @ X5 @ Q )
% 4.03/2.03 => ( ( fresh @ name @ late_subject @ X5 @ A6 )
% 4.03/2.03 => ( ( fresh @ name @ A @ X5 @ C4 )
% 4.03/2.03 => ? [P6: pi] :
% 4.03/2.03 ( ( late_transitions @ P @ ( late_BoundR @ A6 @ X5 @ P6 ) )
% 4.03/2.03 & ( strong2129052853vative @ P6 @ Q3 @ A6 @ X5 @ Rel ) ) ) ) ) ) )
% 4.03/2.03 => ( ! [Alpha2: late_freeRes,Q3: pi] :
% 4.03/2.03 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 4.03/2.03 => ? [P6: pi] :
% 4.03/2.03 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 4.03/2.03 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P6 @ Q3 ) @ Rel ) ) )
% 4.03/2.03 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_249_parAssocLeft,axiom,
% 4.03/2.03 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi,Q: pi,R: pi] :
% 4.03/2.03 ( ! [S3: pi,T2: pi,U: pi] : ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( par @ ( par @ S3 @ T2 ) @ U ) @ ( par @ S3 @ ( par @ T2 @ U ) ) ) @ Rel )
% 4.03/2.03 => ( ! [S3: pi,T2: pi,X5: name] :
% 4.03/2.03 ( ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ S3 @ T2 ) @ Rel )
% 4.03/2.03 => ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( res @ X5 @ S3 ) @ ( res @ X5 @ T2 ) ) @ Rel ) )
% 4.03/2.03 => ( ! [S3: pi,T2: pi,U: pi,X5: name] :
% 4.03/2.03 ( ( fresh @ name @ pi @ X5 @ S3 )
% 4.03/2.03 => ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( res @ X5 @ ( par @ ( par @ S3 @ T2 ) @ U ) ) @ ( par @ S3 @ ( res @ X5 @ ( par @ T2 @ U ) ) ) ) @ Rel ) )
% 4.03/2.03 => ( ! [S3: pi,T2: pi,U: pi,X5: name] :
% 4.03/2.03 ( ( fresh @ name @ pi @ X5 @ U )
% 4.03/2.03 => ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( par @ ( res @ X5 @ ( par @ S3 @ T2 ) ) @ U ) @ ( res @ X5 @ ( par @ S3 @ ( par @ T2 @ U ) ) ) ) @ Rel ) )
% 4.03/2.03 => ( strong743114133lation @ ( par @ ( par @ P @ Q ) @ R ) @ Rel @ ( par @ P @ ( par @ Q @ R ) ) ) ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_250_derivativeEqvtI,axiom,
% 4.03/2.03 ! [P: pi,Q: pi,A2: late_subject,X3: name,Rel: set @ ( product_prod @ pi @ pi ),Perm: list @ ( product_prod @ name @ name )] :
% 4.03/2.03 ( ( strong2129052853vative @ P @ Q @ A2 @ X3 @ Rel )
% 4.03/2.03 => ( ( eqvt @ pi @ Rel )
% 4.03/2.03 => ( strong2129052853vative @ ( perm @ name @ pi @ Perm @ P ) @ ( perm @ name @ pi @ Perm @ Q ) @ ( perm @ name @ late_subject @ Perm @ A2 ) @ ( perm @ name @ name @ Perm @ X3 ) @ Rel ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_251_alpha__fresh_H,axiom,
% 4.03/2.03 ! [X2: $tType] :
% 4.03/2.03 ( ( pt_name @ X2 )
% 4.03/2.03 => ! [A2: name,X3: X2,B2: name,Y: X2,C2: name] :
% 4.03/2.03 ( ( ( abs_fun @ name @ X2 @ A2 @ X3 )
% 4.03/2.03 = ( abs_fun @ name @ X2 @ B2 @ Y ) )
% 4.03/2.03 => ( ( C2 != A2 )
% 4.03/2.03 => ( ( C2 != B2 )
% 4.03/2.03 => ( ( fresh @ name @ X2 @ C2 @ X3 )
% 4.03/2.03 => ( ( fresh @ name @ X2 @ C2 @ Y )
% 4.03/2.03 => ( X3
% 4.03/2.03 = ( perm @ name @ X2 @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ C2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ ( perm @ name @ X2 @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ B2 @ C2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ Y ) ) ) ) ) ) ) ) ) ).
% 4.03/2.03
% 4.03/2.03 thf(fact_252_name__abs__eq,axiom,
% 4.03/2.03 ! [X: $tType] :
% 4.03/2.03 ( ( pt_name @ X )
% 4.03/2.03 => ! [A2: name,X3: X,B2: name,Y: X] :
% 4.03/2.03 ( ( ( abs_fun @ name @ X @ A2 @ X3 )
% 4.03/2.04 = ( abs_fun @ name @ X @ B2 @ Y ) )
% 4.03/2.04 = ( ( ( A2 = B2 )
% 4.03/2.04 & ( X3 = Y ) )
% 4.03/2.04 | ( ( A2 != B2 )
% 4.03/2.04 & ( X3
% 4.03/2.04 = ( perm @ name @ X @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ Y ) )
% 4.03/2.04 & ( fresh @ name @ X @ A2 @ Y ) ) ) ) ) ).
% 4.03/2.04
% 4.03/2.04 thf(fact_253_pi_Ofresh_I9_J,axiom,
% 4.03/2.04 ! [A2: name,X1: name,X22: pi] :
% 4.03/2.04 ( ( fresh @ name @ pi @ A2 @ ( res @ X1 @ X22 ) )
% 4.03/2.04 = ( fresh @ name @ ( name > ( noption @ pi ) ) @ A2 @ ( abs_fun @ name @ pi @ X1 @ X22 ) ) ) ).
% 4.03/2.04
% 4.03/2.04 thf(fact_254_pi_Ofresh_I4_J,axiom,
% 4.03/2.04 ! [A2: name,X32: name,X1: name,X22: pi] :
% 4.03/2.04 ( ( fresh @ name @ pi @ A2 @ ( input @ X32 @ X1 @ X22 ) )
% 4.03/2.04 = ( ( fresh @ name @ name @ A2 @ X32 )
% 4.03/2.04 & ( fresh @ name @ ( name > ( noption @ pi ) ) @ A2 @ ( abs_fun @ name @ pi @ X1 @ X22 ) ) ) ) ).
% 4.03/2.04
% 4.03/2.04 thf(tcon_fun___Agent_Ocp__name__name,axiom,
% 4.03/2.04 ! [A7: $tType,A8: $tType] :
% 4.03/2.04 ( ( ( cp_name_name @ A7 )
% 4.03/2.04 & ( cp_name_name @ A8 ) )
% 4.03/2.04 => ( cp_name_name @ ( A7 > A8 ) ) ) ).
% 4.03/2.04
% 4.03/2.04 thf(tcon_fun___Orderings_Oord,axiom,
% 4.03/2.04 ! [A7: $tType,A8: $tType] :
% 4.03/2.04 ( ( ord @ A8 )
% 4.03/2.04 => ( ord @ ( A7 > A8 ) ) ) ).
% 4.03/2.04
% 4.03/2.04 thf(tcon_fun___Agent_Opt__name,axiom,
% 4.03/2.04 ! [A7: $tType,A8: $tType] :
% 4.03/2.04 ( ( ( pt_name @ A7 )
% 4.03/2.04 & ( pt_name @ A8 ) )
% 4.03/2.04 => ( pt_name @ ( A7 > A8 ) ) ) ).
% 4.03/2.04
% 4.03/2.04 thf(tcon_Set_Oset___Agent_Ocp__name__name_1,axiom,
% 4.03/2.04 ! [A7: $tType] :
% 4.03/2.04 ( ( cp_name_name @ A7 )
% 4.03/2.04 => ( cp_name_name @ ( set @ A7 ) ) ) ).
% 4.03/2.04
% 4.03/2.04 thf(tcon_Set_Oset___Orderings_Oord_2,axiom,
% 4.03/2.04 ! [A7: $tType] : ( ord @ ( set @ A7 ) ) ).
% 4.03/2.04
% 4.03/2.04 thf(tcon_Set_Oset___Agent_Opt__name_3,axiom,
% 4.03/2.04 ! [A7: $tType] :
% 4.03/2.04 ( ( pt_name @ A7 )
% 4.03/2.04 => ( pt_name @ ( set @ A7 ) ) ) ).
% 4.03/2.04
% 4.03/2.04 thf(tcon_Agent_Opi___Agent_Ocp__name__name_4,axiom,
% 4.03/2.04 cp_name_name @ pi ).
% 4.03/2.04
% 4.03/2.04 thf(tcon_Agent_Opi___Agent_Opt__name_5,axiom,
% 4.03/2.04 pt_name @ pi ).
% 4.03/2.04
% 4.03/2.04 thf(tcon_Agent_Opi___Agent_Ofs__name,axiom,
% 4.03/2.04 fs_name @ pi ).
% 4.03/2.04
% 4.03/2.04 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 4.03/2.04 linorder @ $o ).
% 4.03/2.04
% 4.03/2.04 thf(tcon_HOL_Obool___Agent_Ocp__name__name_6,axiom,
% 4.03/2.04 cp_name_name @ $o ).
% 4.03/2.04
% 4.03/2.04 thf(tcon_HOL_Obool___Orderings_Oord_7,axiom,
% 4.03/2.04 ord @ $o ).
% 4.03/2.04
% 4.03/2.04 thf(tcon_HOL_Obool___Agent_Opt__name_8,axiom,
% 4.03/2.04 pt_name @ $o ).
% 4.03/2.04
% 4.03/2.04 thf(tcon_HOL_Obool___Agent_Ofs__name_9,axiom,
% 4.03/2.04 fs_name @ $o ).
% 4.03/2.04
% 4.03/2.04 thf(tcon_List_Olist___Agent_Ocp__name__name_10,axiom,
% 4.03/2.04 ! [A7: $tType] :
% 4.03/2.04 ( ( cp_name_name @ A7 )
% 4.03/2.04 => ( cp_name_name @ ( list @ A7 ) ) ) ).
% 4.03/2.04
% 4.03/2.04 thf(tcon_List_Olist___Agent_Opt__name_11,axiom,
% 4.03/2.04 ! [A7: $tType] :
% 4.03/2.04 ( ( pt_name @ A7 )
% 4.03/2.04 => ( pt_name @ ( list @ A7 ) ) ) ).
% 4.03/2.04
% 4.03/2.04 thf(tcon_List_Olist___Agent_Ofs__name_12,axiom,
% 4.03/2.04 ! [A7: $tType] :
% 4.03/2.04 ( ( fs_name @ A7 )
% 4.03/2.04 => ( fs_name @ ( list @ A7 ) ) ) ).
% 4.03/2.04
% 4.03/2.04 thf(tcon_Agent_Oname___Agent_Ocp__name__name_13,axiom,
% 4.03/2.04 cp_name_name @ name ).
% 4.03/2.04
% 4.03/2.04 thf(tcon_Agent_Oname___Agent_Opt__name_14,axiom,
% 4.03/2.04 pt_name @ name ).
% 4.03/2.04
% 4.03/2.04 thf(tcon_Agent_Oname___Agent_Ofs__name_15,axiom,
% 4.03/2.04 fs_name @ name ).
% 4.03/2.04
% 4.03/2.04 thf(tcon_Agent_Opi__Rep___Agent_Ocp__name__name_16,axiom,
% 4.03/2.04 cp_name_name @ pi_Rep ).
% 4.03/2.04
% 4.03/2.04 thf(tcon_Agent_Opi__Rep___Agent_Opt__name_17,axiom,
% 4.03/2.04 pt_name @ pi_Rep ).
% 4.03/2.04
% 4.03/2.04 thf(tcon_Nominal_Onoption___Agent_Ocp__name__name_18,axiom,
% 4.03/2.04 ! [A7: $tType] :
% 4.03/2.04 ( ( cp_name_name @ A7 )
% 4.03/2.04 => ( cp_name_name @ ( noption @ A7 ) ) ) ).
% 4.03/2.04
% 4.03/2.04 thf(tcon_Nominal_Onoption___Agent_Opt__name_19,axiom,
% 4.03/2.04 ! [A7: $tType] :
% 4.03/2.04 ( ( pt_name @ A7 )
% 4.03/2.04 => ( pt_name @ ( noption @ A7 ) ) ) ).
% 4.03/2.04
% 4.03/2.04 thf(tcon_Product__Type_Oprod___Agent_Ocp__name__name_20,axiom,
% 4.03/2.04 ! [A7: $tType,A8: $tType] :
% 4.03/2.04 ( ( ( cp_name_name @ A7 )
% 4.03/2.04 & ( cp_name_name @ A8 ) )
% 4.03/2.04 => ( cp_name_name @ ( product_prod @ A7 @ A8 ) ) ) ).
% 4.03/2.04
% 4.03/2.04 thf(tcon_Product__Type_Oprod___Agent_Opt__name_21,axiom,
% 4.03/2.04 ! [A7: $tType,A8: $tType] :
% 4.03/2.04 ( ( ( pt_name @ A7 )
% 4.03/2.04 & ( pt_name @ A8 ) )
% 4.03/2.04 => ( pt_name @ ( product_prod @ A7 @ A8 ) ) ) ).
% 4.03/2.04
% 4.03/2.04 thf(tcon_Product__Type_Oprod___Agent_Ofs__name_22,axiom,
% 4.03/2.04 ! [A7: $tType,A8: $tType] :
% 4.03/2.04 ( ( ( fs_name @ A7 )
% 4.03/2.04 & ( fs_name @ A8 ) )
% 4.03/2.04 => ( fs_name @ ( product_prod @ A7 @ A8 ) ) ) ).
% 4.03/2.04
% 4.03/2.04 thf(tcon_Late__Semantics_OfreeRes___Agent_Ocp__name__name_23,axiom,
% 4.03/2.04 cp_name_name @ late_freeRes ).
% 4.03/2.04
% 4.03/2.04 thf(tcon_Late__Semantics_OfreeRes___Agent_Opt__name_24,axiom,
% 4.03/2.04 pt_name @ late_freeRes ).
% 4.03/2.04
% 4.03/2.04 thf(tcon_Late__Semantics_OfreeRes___Agent_Ofs__name_25,axiom,
% 4.03/2.04 fs_name @ late_freeRes ).
% 4.03/2.04
% 4.03/2.04 thf(tcon_Late__Semantics_Osubject___Agent_Ocp__name__name_26,axiom,
% 4.03/2.04 cp_name_name @ late_subject ).
% 4.03/2.04
% 4.03/2.04 thf(tcon_Late__Semantics_Osubject___Agent_Opt__name_27,axiom,
% 4.03/2.04 pt_name @ late_subject ).
% 4.03/2.04
% 4.03/2.04 thf(tcon_Late__Semantics_Osubject___Agent_Ofs__name_28,axiom,
% 4.03/2.04 fs_name @ late_subject ).
% 4.03/2.04
% 4.03/2.04 thf(tcon_Late__Semantics_Oresidual___Agent_Ocp__name__name_29,axiom,
% 4.03/2.04 cp_name_name @ late_residual ).
% 4.03/2.04
% 4.03/2.04 thf(tcon_Late__Semantics_Oresidual___Agent_Opt__name_30,axiom,
% 4.03/2.04 pt_name @ late_residual ).
% 4.03/2.04
% 4.03/2.04 thf(tcon_Late__Semantics_Oresidual___Agent_Ofs__name_31,axiom,
% 4.03/2.04 fs_name @ late_residual ).
% 4.03/2.04
% 4.03/2.04 thf(tcon_Late__Semantics_OfreeRes__Rep___Agent_Ocp__name__name_32,axiom,
% 4.03/2.04 cp_name_name @ late_freeRes_Rep ).
% 4.03/2.04
% 4.03/2.04 thf(tcon_Late__Semantics_OfreeRes__Rep___Agent_Opt__name_33,axiom,
% 4.03/2.04 pt_name @ late_freeRes_Rep ).
% 4.03/2.04
% 4.03/2.04 thf(tcon_Late__Semantics_Osubject__Rep___Agent_Ocp__name__name_34,axiom,
% 4.03/2.04 cp_name_name @ late_subject_Rep ).
% 4.03/2.04
% 4.03/2.04 thf(tcon_Late__Semantics_Osubject__Rep___Agent_Opt__name_35,axiom,
% 4.03/2.04 pt_name @ late_subject_Rep ).
% 4.03/2.04
% 4.03/2.04 thf(tcon_Late__Semantics_Oresidual__Rep___Agent_Ocp__name__name_36,axiom,
% 4.03/2.04 cp_name_name @ late_residual_Rep ).
% 4.03/2.04
% 4.03/2.04 thf(tcon_Late__Semantics_Oresidual__Rep___Agent_Opt__name_37,axiom,
% 4.03/2.04 pt_name @ late_residual_Rep ).
% 4.03/2.04
% 4.03/2.04 thf(help_If_3_1_T,axiom,
% 4.03/2.04 ! [P: $o] :
% 4.03/2.04 ( ( P = $true )
% 4.03/2.04 | ( P = $false ) ) ).
% 4.03/2.04
% 4.03/2.04 thf(help_If_2_1_T,axiom,
% 4.03/2.04 ! [A: $tType,X3: A,Y: A] :
% 4.03/2.04 ( ( if @ A @ $false @ X3 @ Y )
% 4.03/2.04 = Y ) ).
% 4.03/2.04
% 4.03/2.04 thf(help_If_1_1_T,axiom,
% 4.03/2.04 ! [A: $tType,X3: A,Y: A] :
% 4.03/2.04 ( ( if @ A @ $true @ X3 @ Y )
% 4.03/2.04 = X3 ) ).
% 4.03/2.04
% 4.03/2.04 thf(conj_0,conjecture,
% 4.03/2.04 late_transitions @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ z @ x ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ q ) @ ( perm @ name @ late_residual @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ z @ x ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ ( late_FreeR @ ( late_OutputR @ aa @ x ) @ q_a ) ) ).
% 4.03/2.04 ------------------------
% 4.03/2.08 % (3255)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_3151 for (2999ds/2Mi)
% 4.03/2.08 % (3254)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_3151 for (2999ds/2Mi)
% 4.03/2.08 % (3253)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_3151 for (2999ds/27Mi)
% 4.03/2.08 % (3256)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_3151 for (2999ds/275Mi)
% 4.03/2.08 % (3257)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_3151 for (2999ds/18Mi)
% 4.03/2.08 % (3251)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_3151 for (2999ds/183Mi)
% 4.03/2.08 % (3252)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_3151 for (2999ds/4Mi)
% 4.03/2.08 % (3254)Instruction limit reached!
% 4.03/2.08 % (3254)------------------------------
% 4.03/2.08 % (3254)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.03/2.08 % (3254)Termination reason: Unknown
% 4.03/2.08 % (3255)Instruction limit reached!
% 4.03/2.08 % (3255)------------------------------
% 4.03/2.08 % (3255)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.03/2.08 % (3254)Termination phase: shuffling
% 4.03/2.08
% 4.03/2.08 % (3254)Memory used [KB]: 1407
% 4.03/2.08 % (3254)Time elapsed: 0.003 s
% 4.03/2.08 % (3254)Instructions burned: 2 (million)
% 4.03/2.08 % (3254)------------------------------
% 4.03/2.08 % (3254)------------------------------
% 4.03/2.08 % (3255)Termination reason: Unknown
% 4.03/2.08 % (3255)Termination phase: shuffling
% 4.03/2.08
% 4.03/2.08 % (3255)Memory used [KB]: 1407
% 4.03/2.08 % (3255)Time elapsed: 0.004 s
% 4.03/2.08 % (3255)Instructions burned: 2 (million)
% 4.03/2.08 % (3255)------------------------------
% 4.03/2.08 % (3255)------------------------------
% 4.03/2.09 % (3252)Instruction limit reached!
% 4.03/2.09 % (3252)------------------------------
% 4.03/2.09 % (3252)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.03/2.09 % (3252)Termination reason: Unknown
% 4.03/2.09 % (3252)Termination phase: shuffling
% 4.03/2.09
% 4.03/2.09 % (3252)Memory used [KB]: 1535
% 4.03/2.09 % (3252)Time elapsed: 0.004 s
% 4.03/2.09 % (3252)Instructions burned: 4 (million)
% 4.03/2.09 % (3252)------------------------------
% 4.03/2.09 % (3252)------------------------------
% 4.03/2.10 % (3257)Instruction limit reached!
% 4.03/2.10 % (3257)------------------------------
% 4.03/2.10 % (3257)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.03/2.10 % (3257)Termination reason: Unknown
% 4.03/2.10 % (3257)Termination phase: shuffling
% 4.03/2.10
% 4.03/2.10 % (3257)Memory used [KB]: 1791
% 4.03/2.10 % (3257)Time elapsed: 0.014 s
% 4.03/2.10 % (3257)Instructions burned: 18 (million)
% 4.03/2.10 % (3257)------------------------------
% 4.03/2.10 % (3257)------------------------------
% 4.03/2.10 % (3253)Instruction limit reached!
% 4.03/2.10 % (3253)------------------------------
% 4.03/2.10 % (3253)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.03/2.10 % (3253)Termination reason: Unknown
% 4.03/2.10 % (3253)Termination phase: shuffling
% 4.03/2.10
% 4.03/2.10 % (3253)Memory used [KB]: 1918
% 4.03/2.10 % (3253)Time elapsed: 0.017 s
% 4.03/2.10 % (3253)Instructions burned: 28 (million)
% 4.03/2.10 % (3253)------------------------------
% 4.03/2.10 % (3253)------------------------------
% 4.03/2.10 % (3258)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_3151 for (2999ds/3Mi)
% 4.03/2.10 % (3259)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_3151 for (2999ds/37Mi)
% 4.03/2.10 % (3260)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_3151 for (2999ds/15Mi)
% 4.03/2.11 % (3258)Instruction limit reached!
% 4.03/2.11 % (3258)------------------------------
% 4.03/2.11 % (3258)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.03/2.11 % (3258)Termination reason: Unknown
% 4.03/2.11 % (3258)Termination phase: shuffling
% 4.03/2.11
% 4.03/2.11 % (3258)Memory used [KB]: 1407
% 4.03/2.11 % (3258)Time elapsed: 0.004 s
% 4.03/2.11 % (3258)Instructions burned: 3 (million)
% 4.03/2.11 % (3258)------------------------------
% 4.03/2.11 % (3258)------------------------------
% 4.03/2.11 % (3260)Instruction limit reached!
% 4.03/2.11 % (3260)------------------------------
% 4.03/2.11 % (3260)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.03/2.11 % (3260)Termination reason: Unknown
% 4.03/2.11 % (3260)Termination phase: shuffling
% 4.03/2.11
% 4.03/2.11 % (3260)Memory used [KB]: 1663
% 4.03/2.11 % (3260)Time elapsed: 0.010 s
% 4.03/2.11 % (3260)Instructions burned: 15 (million)
% 4.03/2.11 % (3260)------------------------------
% 4.03/2.11 % (3260)------------------------------
% 4.03/2.12 % (3261)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_3151 for (2999ds/3Mi)
% 4.03/2.12 % (3261)Instruction limit reached!
% 4.03/2.12 % (3261)------------------------------
% 4.03/2.12 % (3261)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.03/2.12 % (3261)Termination reason: Unknown
% 4.03/2.12 % (3261)Termination phase: shuffling
% 4.03/2.12
% 4.03/2.12 % (3261)Memory used [KB]: 1407
% 4.03/2.12 % (3261)Time elapsed: 0.004 s
% 4.03/2.12 % (3261)Instructions burned: 4 (million)
% 4.03/2.12 % (3261)------------------------------
% 4.03/2.12 % (3261)------------------------------
% 4.03/2.12 % (3262)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_3151 for (2999ds/1041Mi)
% 4.03/2.12 % (3259)Instruction limit reached!
% 4.03/2.12 % (3259)------------------------------
% 4.03/2.12 % (3259)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.03/2.12 % (3259)Termination reason: Unknown
% 4.03/2.12 % (3259)Termination phase: shuffling
% 4.03/2.12
% 4.03/2.12 % (3259)Memory used [KB]: 2174
% 4.03/2.12 % (3259)Time elapsed: 0.022 s
% 4.03/2.12 % (3259)Instructions burned: 38 (million)
% 4.03/2.12 % (3259)------------------------------
% 4.03/2.12 % (3259)------------------------------
% 4.03/2.13 % (3263)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_3151 for (2999ds/7Mi)
% 4.05/2.13 % (3263)Instruction limit reached!
% 4.05/2.13 % (3263)------------------------------
% 4.05/2.13 % (3263)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.05/2.13 % (3263)Termination reason: Unknown
% 4.05/2.13 % (3263)Termination phase: shuffling
% 4.05/2.13
% 4.05/2.13 % (3263)Memory used [KB]: 1535
% 4.05/2.13 % (3263)Time elapsed: 0.006 s
% 4.05/2.13 % (3263)Instructions burned: 7 (million)
% 4.05/2.13 % (3263)------------------------------
% 4.05/2.13 % (3263)------------------------------
% 4.05/2.13 % (3264)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_3151 for (2999ds/16Mi)
% 4.05/2.14 % (3265)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_3151 for (2999ds/3Mi)
% 4.05/2.14 % (3265)Instruction limit reached!
% 4.05/2.14 % (3265)------------------------------
% 4.05/2.14 % (3265)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.05/2.14 % (3265)Termination reason: Unknown
% 4.05/2.14 % (3265)Termination phase: shuffling
% 4.05/2.14
% 4.05/2.14 % (3265)Memory used [KB]: 1407
% 4.05/2.14 % (3265)Time elapsed: 0.004 s
% 4.05/2.14 % (3265)Instructions burned: 3 (million)
% 4.05/2.14 % (3265)------------------------------
% 4.05/2.14 % (3265)------------------------------
% 4.05/2.14 % (3264)Instruction limit reached!
% 4.05/2.14 % (3264)------------------------------
% 4.05/2.14 % (3264)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.05/2.14 % (3264)Termination reason: Unknown
% 4.05/2.14 % (3264)Termination phase: shuffling
% 4.05/2.14
% 4.05/2.14 % (3264)Memory used [KB]: 1791
% 4.05/2.14 % (3264)Time elapsed: 0.011 s
% 4.05/2.14 % (3264)Instructions burned: 16 (million)
% 4.05/2.14 % (3264)------------------------------
% 4.05/2.14 % (3264)------------------------------
% 4.05/2.14 % (3266)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_3151 for (2999ds/3Mi)
% 4.05/2.14 % (3266)Instruction limit reached!
% 4.05/2.14 % (3266)------------------------------
% 4.05/2.14 % (3266)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.05/2.14 % (3266)Termination reason: Unknown
% 4.05/2.14 % (3266)Termination phase: shuffling
% 4.05/2.14
% 4.05/2.14 % (3266)Memory used [KB]: 1407
% 4.05/2.14 % (3266)Time elapsed: 0.003 s
% 4.05/2.14 % (3266)Instructions burned: 3 (million)
% 4.05/2.14 % (3266)------------------------------
% 4.05/2.14 % (3266)------------------------------
% 4.05/2.15 % (3267)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_3151 for (2999ds/7Mi)
% 4.05/2.15 % (3256)First to succeed.
% 4.05/2.15 % (3267)Instruction limit reached!
% 4.05/2.15 % (3267)------------------------------
% 4.05/2.15 % (3267)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.05/2.15 % (3267)Termination reason: Unknown
% 4.05/2.15 % (3267)Termination phase: shuffling
% 4.05/2.15
% 4.05/2.15 % (3267)Memory used [KB]: 1535
% 4.05/2.15 % (3267)Time elapsed: 0.005 s
% 4.05/2.15 % (3267)Instructions burned: 7 (million)
% 4.05/2.15 % (3267)------------------------------
% 4.05/2.15 % (3267)------------------------------
% 4.05/2.16 % (3256)Refutation found. Thanks to Tanya!
% 4.05/2.16 % SZS status Theorem for DTF2THF_3151
% 4.05/2.16 % SZS output start Proof for DTF2THF_3151
% 4.05/2.16 thf(type_def_5, type, name: $tType).
% 4.05/2.16 thf(type_def_6, type, pi: $tType).
% 4.05/2.16 thf(type_def_8, type, product_prod: ($tType * $tType) > $tType).
% 4.05/2.16 thf(type_def_9, type, list: ($tType) > $tType).
% 4.05/2.16 thf(type_def_10, type, late_freeRes: $tType).
% 4.05/2.16 thf(type_def_11, type, late_subject: $tType).
% 4.05/2.16 thf(type_def_12, type, late_residual: $tType).
% 4.05/2.16 thf(type_def_13, type, late_residual_Rep: $tType).
% 4.05/2.16 thf(type_def_14, type, noption: ($tType) > $tType).
% 4.05/2.16 thf(type_def_15, type, set: ($tType) > $tType).
% 4.05/2.16 thf(type_def_16, type, late_subject_Rep: $tType).
% 4.05/2.16 thf(type_def_17, type, late_freeRes_Rep: $tType).
% 4.05/2.16 thf(type_def_18, type, pi_Rep: $tType).
% 4.05/2.16 thf(func_def_0, type, late_residual_Rep: $tType).
% 4.05/2.16 thf(func_def_1, type, late_subject_Rep: $tType).
% 4.05/2.16 thf(func_def_2, type, late_freeRes_Rep: $tType).
% 4.05/2.16 thf(func_def_3, type, late_residual: $tType).
% 4.05/2.16 thf(func_def_4, type, late_subject: $tType).
% 4.05/2.16 thf(func_def_5, type, late_freeRes: $tType).
% 4.05/2.16 thf(func_def_6, type, product_prod: ($tType * $tType) > $tType).
% 4.05/2.16 thf(func_def_7, type, noption: ($tType) > $tType).
% 4.05/2.16 thf(func_def_8, type, pi_Rep: $tType).
% 4.05/2.16 thf(func_def_9, type, name: $tType).
% 4.05/2.16 thf(func_def_10, type, list: ($tType) > $tType).
% 4.05/2.16 thf(func_def_11, type, pi: $tType).
% 4.05/2.16 thf(func_def_12, type, set: ($tType) > $tType).
% 4.05/2.16 thf(func_def_13, type, type: !>[X0: $tType]:($o)).
% 4.05/2.16 thf(func_def_14, type, fs_name: !>[X0: $tType]:($o)).
% 4.05/2.16 thf(func_def_15, type, pt_name: !>[X0: $tType]:($o)).
% 4.05/2.16 thf(func_def_16, type, ord: !>[X0: $tType]:($o)).
% 4.05/2.16 thf(func_def_17, type, cp_name_name: !>[X0: $tType]:($o)).
% 4.05/2.16 thf(func_def_18, type, linorder: !>[X0: $tType]:($o)).
% 4.05/2.16 thf(func_def_19, type, input: name > name > pi > pi).
% 4.05/2.16 thf(func_def_20, type, par: pi > pi > pi).
% 4.05/2.16 thf(func_def_21, type, res: name > pi > pi).
% 4.05/2.16 thf(func_def_22, type, name_prm_name: list @ product_prod @ name @ name > name > name).
% 4.05/2.16 thf(func_def_23, type, swap_name: product_prod @ name @ name > name > name).
% 4.05/2.16 thf(func_def_24, type, subs: pi > name > name > pi).
% 4.05/2.16 thf(func_def_25, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 4.05/2.16 thf(func_def_26, type, late_OutputR: name > name > late_freeRes).
% 4.05/2.16 thf(func_def_27, type, late_TauR: late_freeRes).
% 4.05/2.16 thf(func_def_28, type, late_BoundR: late_subject > name > pi > late_residual).
% 4.05/2.16 thf(func_def_29, type, late_FreeR: late_freeRes > pi > late_residual).
% 4.05/2.16 thf(func_def_30, type, late_r347633188eR_Rep: late_freeRes > pi > late_residual_Rep).
% 4.05/2.16 thf(func_def_31, type, late_BoundOutputS: name > late_subject).
% 4.05/2.16 thf(func_def_32, type, late_InputS: name > late_subject).
% 4.05/2.16 thf(func_def_33, type, late_transitions: pi > late_residual > $o).
% 4.05/2.16 thf(func_def_34, type, cons: !>[X0: $tType]:(X0 > list @ X0 > list @ X0)).
% 4.05/2.16 thf(func_def_35, type, nil: !>[X0: $tType]:(list @ X0)).
% 4.05/2.16 thf(func_def_36, type, product_lists: !>[X0: $tType]:(list @ list @ X0 > list @ list @ X0)).
% 4.05/2.16 thf(func_def_37, type, abs_fun: !>[X0: $tType, X1: $tType]:(X0 > X1 > X0 > noption @ X1)).
% 4.05/2.16 thf(func_def_38, type, fresh: !>[X0: $tType, X1: $tType]:(X0 > X1 > $o)).
% 4.05/2.16 thf(func_def_39, type, perm: !>[X0: $tType, X1: $tType]:(list @ product_prod @ X0 @ X0 > X1 > X1)).
% 4.05/2.16 thf(func_def_40, type, supports: !>[X0: $tType, X1: $tType]:(set @ X0 > X1 > $o)).
% 4.05/2.16 thf(func_def_41, type, swap: !>[X0: $tType]:(product_prod @ X0 @ X0 > X0 > X0)).
% 4.05/2.16 thf(func_def_42, type, product_Pair: !>[X0: $tType, X1: $tType]:(X0 > X1 > product_prod @ X0 @ X1)).
% 4.05/2.16 thf(func_def_43, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2)).
% 4.05/2.16 thf(func_def_44, type, eqvt: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > $o)).
% 4.05/2.16 thf(func_def_45, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 4.05/2.16 thf(func_def_46, type, strong2129052853vative: pi > pi > late_subject > name > set @ product_prod @ pi @ pi > $o).
% 4.05/2.16 thf(func_def_47, type, strong743114133lation: pi > set @ product_prod @ pi @ pi > pi > $o).
% 4.05/2.16 thf(func_def_48, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 4.05/2.16 thf(func_def_49, type, p: pi).
% 4.05/2.16 thf(func_def_50, type, p2: pi).
% 4.05/2.16 thf(func_def_51, type, pxQ: pi).
% 4.05/2.16 thf(func_def_52, type, q: pi).
% 4.05/2.16 thf(func_def_53, type, q2: pi).
% 4.05/2.16 thf(func_def_54, type, q_a: pi).
% 4.05/2.16 thf(func_def_55, type, rel: set @ product_prod @ pi @ pi).
% 4.05/2.16 thf(func_def_56, type, alpha: late_freeRes).
% 4.05/2.16 thf(func_def_57, type, aa: name).
% 4.05/2.16 thf(func_def_58, type, b: name).
% 4.05/2.16 thf(func_def_59, type, x: name).
% 4.05/2.16 thf(func_def_60, type, y: name).
% 4.05/2.16 thf(func_def_61, type, z: name).
% 4.05/2.16 thf(func_def_80, type, sP0: late_subject > name > pi > name > pi > $o).
% 4.05/2.16 thf(func_def_81, type, sP1: name > pi > late_residual > $o).
% 4.05/2.16 thf(func_def_82, type, sP2: late_residual > name > pi > $o).
% 4.05/2.16 thf(func_def_83, type, sP3: late_subject > pi > (late_subject > pi > $o) > name > name > $o).
% 4.05/2.16 thf(func_def_84, type, sK4: !>[X0: $tType]:(product_prod @ (X0 > X0 > $o) @ list @ X0 > X0 > X0 > $o)).
% 4.05/2.16 thf(func_def_85, type, sK5: !>[X0: $tType]:(product_prod @ (X0 > X0 > $o) @ list @ X0 > X0 > X0 > $o)).
% 4.05/2.16 thf(func_def_86, type, sK6: !>[X0: $tType]:(product_prod @ (X0 > X0 > $o) @ list @ X0 > X0)).
% 4.05/2.16 thf(func_def_87, type, sK7: !>[X0: $tType]:(product_prod @ (X0 > X0 > $o) @ list @ X0 > list @ X0)).
% 4.05/2.16 thf(func_def_88, type, sK8: !>[X0: $tType]:(list @ X0 > X0)).
% 4.05/2.16 thf(func_def_89, type, sK9: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 4.05/2.16 thf(func_def_90, type, sK10: pi > late_freeRes > pi > name > pi).
% 4.05/2.16 thf(func_def_91, type, sK11: pi > late_freeRes > pi > name > late_freeRes).
% 4.05/2.16 thf(func_def_92, type, sK12: pi > late_freeRes > pi > name > pi).
% 4.05/2.16 thf(func_def_93, type, sK13: pi > late_freeRes > pi > name > name).
% 4.05/2.16 thf(func_def_94, type, sK14: !>[X0: $tType, X1: $tType]:(product_prod @ (X0 > X1) @ product_prod @ list @ X0 @ list @ X1 > X0 > X1)).
% 4.05/2.16 thf(func_def_95, type, sK15: !>[X0: $tType, X1: $tType]:(product_prod @ (X0 > X1) @ product_prod @ list @ X0 @ list @ X1 > X0)).
% 4.05/2.16 thf(func_def_96, type, sK16: !>[X0: $tType, X1: $tType]:(product_prod @ (X0 > X1) @ product_prod @ list @ X0 @ list @ X1 > list @ X0)).
% 4.05/2.16 thf(func_def_97, type, sK17: !>[X0: $tType, X1: $tType]:(product_prod @ (X0 > X1) @ product_prod @ list @ X0 @ list @ X1 > list @ X1)).
% 4.05/2.16 thf(func_def_98, type, sK18: !>[X0: $tType, X1: $tType]:(product_prod @ (X0 > X1) @ product_prod @ list @ X0 @ list @ X1 > X0 > X1)).
% 4.05/2.16 thf(func_def_99, type, sK19: !>[X0: $tType, X1: $tType]:(product_prod @ (X0 > X1) @ product_prod @ list @ X0 @ list @ X1 > list @ X1)).
% 4.05/2.16 thf(func_def_100, type, sK20: !>[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)).
% 4.05/2.16 thf(func_def_101, type, sK21: !>[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)).
% 4.05/2.16 thf(func_def_102, type, sK22: !>[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)).
% 4.05/2.16 thf(func_def_103, type, sK23: !>[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)).
% 4.05/2.16 thf(func_def_104, type, sK24: !>[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)).
% 4.05/2.16 thf(func_def_105, type, sK25: !>[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)).
% 4.05/2.16 thf(func_def_106, type, sK26: !>[X0: $tType]:(product_prod @ (X0 > X0 > $o) @ list @ X0 > X0 > X0 > $o)).
% 4.05/2.16 thf(func_def_107, type, sK27: !>[X0: $tType]:(product_prod @ (X0 > X0 > $o) @ list @ X0 > X0 > X0 > $o)).
% 4.05/2.16 thf(func_def_108, type, sK28: !>[X0: $tType]:(product_prod @ (X0 > X0 > $o) @ list @ X0 > X0)).
% 4.05/2.16 thf(func_def_109, type, sK29: !>[X0: $tType]:(product_prod @ (X0 > X0 > $o) @ list @ X0 > X0)).
% 4.05/2.16 thf(func_def_110, type, sK30: !>[X0: $tType]:(product_prod @ (X0 > X0 > $o) @ list @ X0 > list @ X0)).
% 4.05/2.16 thf(func_def_111, type, sK31: !>[X0: $tType]:(product_prod @ (X0 > X0 > $o) @ list @ X0 > X0 > X0 > $o)).
% 4.05/2.16 thf(func_def_112, type, sK32: !>[X0: $tType]:(product_prod @ (X0 > X0 > $o) @ list @ X0 > X0)).
% 4.05/2.16 thf(func_def_113, type, sK33: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3)).
% 4.05/2.16 thf(func_def_114, type, sK34: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 4.05/2.16 thf(func_def_115, type, sK35: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 4.05/2.16 thf(func_def_116, type, sK36: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 4.05/2.16 thf(func_def_117, type, sK37: !>[X0: $tType]:(product_prod @ list @ X0 @ list @ X0 > X0)).
% 4.05/2.16 thf(func_def_118, type, sK38: !>[X0: $tType]:(product_prod @ list @ X0 @ list @ X0 > list @ X0)).
% 4.05/2.16 thf(func_def_119, type, sK39: !>[X0: $tType]:(product_prod @ list @ X0 @ list @ X0 > list @ X0)).
% 4.05/2.16 thf(func_def_120, type, sK40: !>[X0: $tType]:(product_prod @ list @ X0 @ list @ X0 > list @ X0)).
% 4.05/2.16 thf(func_def_121, type, sK41: (pi > $o) > late_freeRes > pi > name > pi).
% 4.05/2.16 thf(func_def_122, type, sK42: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 4.05/2.16 thf(func_def_123, type, sK43: !>[X0: $tType]:(list @ list @ X0 > list @ list @ X0)).
% 4.05/2.16 thf(func_def_124, type, sK44: !>[X0: $tType]:(list @ list @ X0 > X0)).
% 4.05/2.16 thf(func_def_125, type, sK45: !>[X0: $tType]:(list @ list @ X0 > list @ X0)).
% 4.05/2.16 thf(func_def_126, type, sK46: !>[X0: $tType]:(list @ list @ X0 > list @ list @ X0)).
% 4.05/2.16 thf(func_def_127, type, sK47: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o)).
% 4.05/2.16 thf(func_def_128, type, sK48: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0)).
% 4.05/2.16 thf(func_def_129, type, sK49: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0)).
% 4.05/2.16 thf(func_def_130, type, sK50: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > list @ X0)).
% 4.05/2.16 thf(func_def_131, type, sK51: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o)).
% 4.05/2.16 thf(func_def_132, type, sK52: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0)).
% 4.05/2.16 thf(func_def_133, type, sK53: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o)).
% 4.05/2.16 thf(func_def_134, type, sK54: late_subject > name > pi > name > pi > pi).
% 4.05/2.16 thf(func_def_135, type, sK55: late_subject > name > pi > name > pi > late_subject).
% 4.05/2.16 thf(func_def_136, type, sK56: late_subject > name > pi > name > pi > name).
% 4.05/2.16 thf(func_def_137, type, sK57: late_subject > name > pi > name > pi > pi).
% 4.05/2.16 thf(func_def_138, type, sK58: late_subject > name > pi > name > pi > name).
% 4.05/2.16 thf(func_def_139, type, sK59: pi > name > late_subject > pi > name > pi).
% 4.05/2.16 thf(func_def_140, type, sK60: pi > name > late_subject > pi > name > name).
% 4.05/2.16 thf(func_def_141, type, sK61: pi > name > late_subject > pi > name > name).
% 4.05/2.16 thf(func_def_142, type, sK62: pi > name > late_subject > pi > name > pi).
% 4.05/2.16 thf(func_def_143, type, sK63: late_residual > name > pi > pi).
% 4.05/2.16 thf(func_def_144, type, sK64: late_residual > name > pi > late_freeRes).
% 4.05/2.16 thf(func_def_145, type, sK65: late_residual > name > pi > pi).
% 4.05/2.16 thf(func_def_146, type, sK66: late_residual > name > pi > name).
% 4.05/2.16 thf(func_def_147, type, sK67: name > pi > late_residual > pi).
% 4.05/2.16 thf(func_def_148, type, sK68: name > pi > late_residual > late_subject).
% 4.05/2.16 thf(func_def_149, type, sK69: name > pi > late_residual > name).
% 4.05/2.16 thf(func_def_150, type, sK70: name > pi > late_residual > pi).
% 4.05/2.16 thf(func_def_151, type, sK71: name > pi > late_residual > name).
% 4.05/2.16 thf(func_def_152, type, sK72: late_residual > pi > name > pi).
% 4.05/2.16 thf(func_def_153, type, sK73: late_residual > pi > name > name).
% 4.05/2.16 thf(func_def_154, type, sK74: late_residual > pi > name > name).
% 4.05/2.16 thf(func_def_155, type, sK75: late_residual > pi > name > pi).
% 4.05/2.16 thf(func_def_156, type, sK76: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 4.05/2.16 thf(func_def_157, type, sK77: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 4.05/2.16 thf(func_def_158, type, sK78: !>[X0: $tType]:(list @ X0 > X0)).
% 4.05/2.16 thf(func_def_159, type, sK79: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 4.05/2.16 thf(func_def_160, type, sK80: !>[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)).
% 4.05/2.16 thf(func_def_161, type, sK81: !>[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)).
% 4.05/2.16 thf(func_def_162, type, sK82: !>[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)).
% 4.05/2.16 thf(func_def_163, type, sK83: !>[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)).
% 4.05/2.16 thf(func_def_164, type, sK84: !>[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)).
% 4.05/2.16 thf(func_def_165, type, sK85: !>[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)).
% 4.05/2.16 thf(func_def_166, type, sK86: !>[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)).
% 4.05/2.16 thf(func_def_167, type, sK87: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 4.05/2.16 thf(func_def_168, type, sK88: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o)).
% 4.05/2.16 thf(func_def_169, type, sK89: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o)).
% 4.05/2.16 thf(func_def_170, type, sK90: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0)).
% 4.05/2.16 thf(func_def_171, type, sK91: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > list @ X0)).
% 4.05/2.16 thf(func_def_172, type, sK92: late_subject > pi > (late_subject > pi > $o) > name > name > name).
% 4.05/2.16 thf(func_def_173, type, sK93: late_subject > pi > (late_subject > pi > $o) > name > name > pi).
% 4.05/2.16 thf(func_def_174, type, sK94: (late_subject > pi > $o) > name > late_subject > pi > name > pi).
% 4.05/2.16 thf(func_def_175, type, sK95: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X0)).
% 4.05/2.16 thf(func_def_176, type, sK96: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X1)).
% 4.05/2.16 thf(func_def_177, type, sK97: (late_residual > $o) > late_freeRes).
% 4.05/2.16 thf(func_def_178, type, sK98: (late_residual > $o) > pi).
% 4.05/2.16 thf(func_def_179, type, sK99: (late_residual > $o) > late_subject).
% 4.05/2.16 thf(func_def_180, type, sK100: (late_residual > $o) > name).
% 4.05/2.16 thf(func_def_181, type, sK101: (late_residual > $o) > pi).
% 4.05/2.16 thf(func_def_182, type, sK102: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 4.05/2.16 thf(func_def_183, type, sK103: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 4.05/2.16 thf(func_def_184, type, sK104: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 4.05/2.16 thf(func_def_185, type, sK105: !>[X0: $tType]:(product_prod @ list @ X0 @ list @ X0 > X0)).
% 4.05/2.16 thf(func_def_186, type, sK106: !>[X0: $tType]:(product_prod @ list @ X0 @ list @ X0 > list @ X0)).
% 4.05/2.16 thf(func_def_187, type, sK107: !>[X0: $tType]:(product_prod @ list @ X0 @ list @ X0 > X0)).
% 4.05/2.16 thf(func_def_188, type, sK108: !>[X0: $tType]:(product_prod @ list @ X0 @ list @ X0 > list @ X0)).
% 4.05/2.16 thf(func_def_189, type, sK109: !>[X0: $tType]:(product_prod @ list @ X0 @ list @ X0 > list @ X0)).
% 4.05/2.16 thf(func_def_190, type, sK110: !>[X0: $tType]:(product_prod @ list @ X0 @ list @ X0 > list @ X0)).
% 4.05/2.16 thf(func_def_191, type, sK111: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 4.05/2.16 thf(func_def_192, type, sK112: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 4.05/2.16 thf(func_def_193, type, sK113: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 4.05/2.16 thf(func_def_194, type, sK114: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 4.05/2.16 thf(func_def_195, type, sK115: !>[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)).
% 4.05/2.16 thf(func_def_196, type, sK116: !>[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)).
% 4.05/2.16 thf(func_def_197, type, sK117: !>[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)).
% 4.05/2.16 thf(func_def_198, type, sK118: !>[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)).
% 4.05/2.16 thf(func_def_199, type, sK119: !>[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)).
% 4.05/2.16 thf(func_def_200, type, sK120: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X0)).
% 4.05/2.16 thf(func_def_201, type, sK121: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X1)).
% 4.05/2.16 thf(func_def_202, type, sK122: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 4.05/2.16 thf(func_def_203, type, sK123: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 4.05/2.16 thf(func_def_204, type, sK124: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 4.05/2.16 thf(func_def_205, type, sK125: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 4.05/2.16 thf(func_def_206, type, sK126: !>[X0: $tType]:(list @ X0 > X0)).
% 4.05/2.16 thf(func_def_207, type, sK127: !>[X0: $tType]:(list @ X0 > X0)).
% 4.05/2.16 thf(func_def_208, type, sK128: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 4.05/2.16 thf(func_def_209, type, sK129: !>[X0: $tType]:(list @ X0 > X0)).
% 4.05/2.16 thf(func_def_210, type, sK130: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X1)).
% 4.05/2.16 thf(func_def_211, type, sK131: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X0)).
% 4.05/2.16 thf(func_def_212, type, sK132: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X0)).
% 4.05/2.16 thf(func_def_213, type, sK133: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X1)).
% 4.05/2.16 thf(func_def_214, type, sK134: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X2)).
% 4.05/2.16 thf(func_def_215, type, sK135: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X3)).
% 4.05/2.16 thf(func_def_216, type, sK136: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X0)).
% 4.05/2.16 thf(func_def_217, type, sK137: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X0)).
% 4.05/2.16 thf(func_def_218, type, sK138: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X0)).
% 4.05/2.16 thf(func_def_219, type, sK139: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X0)).
% 4.05/2.16 thf(func_def_220, type, sK140: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X1)).
% 4.05/2.16 thf(func_def_221, type, sK141: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X1)).
% 4.05/2.16 thf(func_def_222, type, sK142: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X1)).
% 4.05/2.16 thf(func_def_223, type, sK143: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X1)).
% 4.05/2.16 thf(func_def_224, type, sK144: !>[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)).
% 4.05/2.16 thf(func_def_225, type, sK145: !>[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)).
% 4.05/2.16 thf(func_def_226, type, sK146: !>[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)).
% 4.05/2.16 thf(func_def_227, type, sK147: !>[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)).
% 4.05/2.16 thf(func_def_228, type, sK148: !>[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)).
% 4.05/2.16 thf(func_def_229, type, sK149: !>[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)).
% 4.05/2.16 thf(func_def_230, type, sK150: !>[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)).
% 4.05/2.16 thf(func_def_231, type, sK151: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 4.05/2.16 thf(func_def_232, type, sK152: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 4.05/2.16 thf(func_def_233, type, sK153: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 4.05/2.16 thf(func_def_234, type, sK154: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X0)).
% 4.05/2.16 thf(func_def_235, type, sK155: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X1)).
% 4.05/2.16 thf(func_def_236, type, sK156: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X2)).
% 4.05/2.16 thf(func_def_237, type, sK157: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X3)).
% 4.05/2.16 thf(func_def_238, type, sK158: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X4)).
% 4.05/2.16 thf(func_def_239, type, sK159: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 4.05/2.16 thf(func_def_240, type, sK160: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 4.05/2.16 thf(func_def_241, type, sK161: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 4.05/2.16 thf(func_def_242, type, sK162: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 4.05/2.16 thf(func_def_243, type, sK163: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 4.05/2.16 thf(func_def_244, type, sK164: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 4.05/2.16 thf(func_def_245, type, sK165: !>[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)).
% 4.05/2.16 thf(func_def_246, type, sK166: !>[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)).
% 4.05/2.16 thf(func_def_247, type, sK167: !>[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)).
% 4.05/2.16 thf(func_def_248, type, sK168: !>[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)).
% 4.05/2.16 thf(func_def_249, type, sK169: !>[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)).
% 4.05/2.16 thf(func_def_250, type, sK170: !>[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)).
% 4.05/2.16 thf(func_def_251, type, sK171: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X1)).
% 4.05/2.16 thf(func_def_252, type, sK172: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X0)).
% 4.05/2.16 thf(func_def_253, type, sK173: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ product_prod @ X1 @ X2 > X0)).
% 4.05/2.16 thf(func_def_254, type, sK174: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ product_prod @ X1 @ X2 > X1)).
% 4.05/2.16 thf(func_def_255, type, sK175: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ product_prod @ X1 @ X2 > X2)).
% 4.05/2.16 thf(func_def_256, type, sK176: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 4.05/2.16 thf(func_def_257, type, sK177: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 4.05/2.16 thf(func_def_258, type, sK178: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 4.05/2.16 thf(func_def_259, type, sK179: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 4.05/2.16 thf(func_def_260, type, sK180: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > X0 > X1)).
% 4.05/2.16 thf(func_def_261, type, sK181: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > list @ X1)).
% 4.05/2.16 thf(func_def_262, type, sK182: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > X0 > X1)).
% 4.05/2.16 thf(func_def_263, type, sK183: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > X0)).
% 4.05/2.16 thf(func_def_264, type, sK184: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > list @ X0)).
% 4.05/2.16 thf(func_def_265, type, sK185: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > list @ X1)).
% 4.05/2.16 thf(func_def_267, type, ph187: !>[X0: $tType]:(X0)).
% 4.05/2.16 thf(f1245,plain,(
% 4.05/2.16 $false),
% 4.05/2.16 inference(subsumption_resolution,[status(thm)],[f1244,f1055])).
% 4.05/2.16 thf(f1055,plain,(
% 4.05/2.16 ((late_transitions @ q @ (late_FreeR @ (late_OutputR @ b @ x) @ q_a)) = $true)),
% 4.05/2.16 inference(cnf_transformation,[status(thm)],[f629])).
% 4.05/2.16 thf(f629,plain,(
% 4.05/2.16 ((late_transitions @ q @ (late_FreeR @ (late_OutputR @ b @ x) @ q_a)) = $true)),
% 4.05/2.16 inference(fool_elimination,[status(thm)],[f628])).
% 4.05/2.16 thf(f628,plain,(
% 4.05/2.16 (late_transitions @ q @ (late_FreeR @ (late_OutputR @ b @ x) @ q_a))),
% 4.05/2.16 inference(rectify,[status(thm)],[f7])).
% 4.05/2.16 thf(f7,axiom,(
% 4.05/2.16 (late_transitions @ q @ (late_FreeR @ (late_OutputR @ b @ x) @ q_a))),
% 4.05/2.16 file('/export/starexec/sandbox/tmp/tmp.rus05bb90W/DTF2THF_3151.p',fact_6_cOpen_Ohyps_I1_J)).
% 4.05/2.16 thf(f1244,plain,(
% 4.05/2.16 ((late_transitions @ q @ (late_FreeR @ (late_OutputR @ b @ x) @ q_a)) != $true)),
% 4.05/2.16 inference(trivial_inequality_removal,[status(thm)],[f1243])).
% 4.05/2.16 thf(f1243,plain,(
% 4.05/2.16 ($true != $true) | ((late_transitions @ q @ (late_FreeR @ (late_OutputR @ b @ x) @ q_a)) != $true)),
% 4.05/2.16 inference(superposition,[status(thm)],[f1219,f1067])).
% 4.05/2.16 thf(f1067,plain,(
% 4.05/2.16 ( ! [X2 : list @ product_prod @ name @ name,X0 : pi,X1 : late_residual] : (((late_transitions @ (perm @ name @ pi @ X2 @ X0) @ (perm @ name @ late_residual @ X2 @ X1)) = $true) | ((late_transitions @ X0 @ X1) != $true)) )),
% 4.05/2.16 inference(cnf_transformation,[status(thm)],[f785])).
% 4.05/2.16 thf(f785,plain,(
% 4.05/2.16 ! [X0 : pi,X1 : late_residual,X2 : list @ product_prod @ name @ name] : (((late_transitions @ X0 @ X1) != $true) | ((late_transitions @ (perm @ name @ pi @ X2 @ X0) @ (perm @ name @ late_residual @ X2 @ X1)) = $true))),
% 4.05/2.16 inference(ennf_transformation,[status(thm)],[f415])).
% 4.05/2.16 thf(f415,plain,(
% 4.05/2.16 ! [X0 : pi,X1 : late_residual,X2 : list @ product_prod @ name @ name] : (((late_transitions @ X0 @ X1) = $true) => ((late_transitions @ (perm @ name @ pi @ X2 @ X0) @ (perm @ name @ late_residual @ X2 @ X1)) = $true))),
% 4.05/2.16 inference(fool_elimination,[status(thm)],[f414])).
% 4.05/2.16 thf(f414,plain,(
% 4.05/2.16 ! [X0 : pi,X1 : late_residual,X2 : list @ product_prod @ name @ name] : ((late_transitions @ X0 @ X1) => (late_transitions @ (perm @ name @ pi @ X2 @ X0) @ (perm @ name @ late_residual @ X2 @ X1)))),
% 4.05/2.16 inference(rectify,[status(thm)],[f18])).
% 4.05/2.16 thf(f18,axiom,(
% 4.05/2.16 ! [X8 : pi,X9 : late_residual,X10 : list @ product_prod @ name @ name] : ((late_transitions @ X8 @ X9) => (late_transitions @ (perm @ name @ pi @ X10 @ X8) @ (perm @ name @ late_residual @ X10 @ X9)))),
% 4.05/2.16 file('/export/starexec/sandbox/tmp/tmp.rus05bb90W/DTF2THF_3151.p',fact_17_eqvt)).
% 4.05/2.16 thf(f1219,plain,(
% 4.05/2.16 ((late_transitions @ (perm @ name @ pi @ (cons @ product_prod @ name @ name @ (product_Pair @ name @ name @ z @ x) @ nil @ product_prod @ name @ name) @ q) @ (perm @ name @ late_residual @ (cons @ product_prod @ name @ name @ (product_Pair @ name @ name @ z @ x) @ nil @ product_prod @ name @ name) @ (late_FreeR @ (late_OutputR @ b @ x) @ q_a))) != $true)),
% 4.05/2.16 inference(definition_unfolding,[status(thm)],[f1070,f1054])).
% 4.05/2.16 thf(f1054,plain,(
% 4.05/2.16 (aa = b)),
% 4.05/2.16 inference(cnf_transformation,[status(thm)],[f1])).
% 4.05/2.16 thf(f1,axiom,(
% 4.05/2.16 (aa = b)),
% 4.05/2.16 file('/export/starexec/sandbox/tmp/tmp.rus05bb90W/DTF2THF_3151.p',fact_0__092_060open_062a_A_061_Ab_092_060close_062)).
% 4.05/2.16 thf(f1070,plain,(
% 4.05/2.16 ((late_transitions @ (perm @ name @ pi @ (cons @ product_prod @ name @ name @ (product_Pair @ name @ name @ z @ x) @ nil @ product_prod @ name @ name) @ q) @ (perm @ name @ late_residual @ (cons @ product_prod @ name @ name @ (product_Pair @ name @ name @ z @ x) @ nil @ product_prod @ name @ name) @ (late_FreeR @ (late_OutputR @ aa @ x) @ q_a))) != $true)),
% 4.05/2.16 inference(cnf_transformation,[status(thm)],[f744])).
% 4.05/2.16 thf(f744,plain,(
% 4.05/2.16 ((late_transitions @ (perm @ name @ pi @ (cons @ product_prod @ name @ name @ (product_Pair @ name @ name @ z @ x) @ nil @ product_prod @ name @ name) @ q) @ (perm @ name @ late_residual @ (cons @ product_prod @ name @ name @ (product_Pair @ name @ name @ z @ x) @ nil @ product_prod @ name @ name) @ (late_FreeR @ (late_OutputR @ aa @ x) @ q_a))) != $true)),
% 4.05/2.16 inference(flattening,[status(thm)],[f521])).
% 4.05/2.16 thf(f521,plain,(
% 4.05/2.16 ~((late_transitions @ (perm @ name @ pi @ (cons @ product_prod @ name @ name @ (product_Pair @ name @ name @ z @ x) @ nil @ product_prod @ name @ name) @ q) @ (perm @ name @ late_residual @ (cons @ product_prod @ name @ name @ (product_Pair @ name @ name @ z @ x) @ nil @ product_prod @ name @ name) @ (late_FreeR @ (late_OutputR @ aa @ x) @ q_a))) = $true)),
% 4.05/2.16 inference(fool_elimination,[status(thm)],[f520])).
% 4.05/2.16 thf(f520,plain,(
% 4.05/2.16 ~(late_transitions @ (perm @ name @ pi @ (cons @ product_prod @ name @ name @ (product_Pair @ name @ name @ z @ x) @ nil @ product_prod @ name @ name) @ q) @ (perm @ name @ late_residual @ (cons @ product_prod @ name @ name @ (product_Pair @ name @ name @ z @ x) @ nil @ product_prod @ name @ name) @ (late_FreeR @ (late_OutputR @ aa @ x) @ q_a)))),
% 4.05/2.16 inference(rectify,[status(thm)],[f302])).
% 4.05/2.16 thf(f302,negated_conjecture,(
% 4.05/2.16 ~(late_transitions @ (perm @ name @ pi @ (cons @ product_prod @ name @ name @ (product_Pair @ name @ name @ z @ x) @ nil @ product_prod @ name @ name) @ q) @ (perm @ name @ late_residual @ (cons @ product_prod @ name @ name @ (product_Pair @ name @ name @ z @ x) @ nil @ product_prod @ name @ name) @ (late_FreeR @ (late_OutputR @ aa @ x) @ q_a)))),
% 4.05/2.16 inference(negated_conjecture,[status(cth)],[f301])).
% 4.05/2.16 thf(f301,conjecture,(
% 4.05/2.16 (late_transitions @ (perm @ name @ pi @ (cons @ product_prod @ name @ name @ (product_Pair @ name @ name @ z @ x) @ nil @ product_prod @ name @ name) @ q) @ (perm @ name @ late_residual @ (cons @ product_prod @ name @ name @ (product_Pair @ name @ name @ z @ x) @ nil @ product_prod @ name @ name) @ (late_FreeR @ (late_OutputR @ aa @ x) @ q_a)))),
% 4.05/2.16 file('/export/starexec/sandbox/tmp/tmp.rus05bb90W/DTF2THF_3151.p',conj_0)).
% 4.05/2.16 % SZS output end Proof for DTF2THF_3151
% 4.05/2.16 % (3256)------------------------------
% 4.05/2.16 % (3256)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.05/2.16 % (3256)Termination reason: Refutation
% 4.05/2.16
% 4.05/2.16 % (3256)Memory used [KB]: 7547
% 4.05/2.16 % (3256)Time elapsed: 0.073 s
% 4.05/2.16 % (3256)Instructions burned: 120 (million)
% 4.05/2.16 % (3256)------------------------------
% 4.05/2.16 % (3256)------------------------------
% 4.05/2.16 % (3250)Success in time 0.106 s
%------------------------------------------------------------------------------