%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP191^2 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n013.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 : ContradictoryAxioms 2.94s 1.77s
% Output : Refutation 2.94s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ITP191^2 : TPTP v9.2.1. Released v7.5.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n013.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 08:29:08 EST 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.19/0.44 ---- Original DTF file ---
% 0.19/0.44 thf(spec,logic,$$dhol).
% 0.19/0.44 %------------------------------------------------------------------------------
% 0.19/0.44 % File : ITP191^2 : TPTP v9.2.1. Released v7.5.0.
% 0.19/0.44 % Domain : Interactive Theorem Proving
% 0.19/0.44 % Problem : Sledgehammer Strong_Late_Sim_SC problem prob_894__3417700_1
% 0.19/0.44 % Version : Especial.
% 0.19/0.44 % English :
% 0.19/0.44
% 0.19/0.44 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.19/0.44 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.19/0.44 % Source : [Des21]
% 0.19/0.44 % Names : Strong_Late_Sim_SC/prob_894__3417700_1 [Des21]
% 0.19/0.44
% 0.19/0.44 % Status : ContradictoryAxioms
% 0.19/0.44 % Rating : 0.00 v8.1.0, 0.25 v7.5.0
% 0.19/0.44 % Syntax : Number of formulae : 372 ( 156 unt; 66 typ; 0 def)
% 0.19/0.44 % Number of atoms : 697 ( 273 equ; 0 cnn)
% 0.19/0.44 % Maximal formula atoms : 17 ( 2 avg)
% 0.19/0.44 % Number of connectives : 5200 ( 134 ~; 3 |; 39 &;4614 @)
% 0.19/0.44 % ( 0 <=>; 410 =>; 0 <=; 0 <~>)
% 0.19/0.44 % Maximal formula depth : 28 ( 8 avg)
% 0.19/0.44 % Number of types : 11 ( 10 usr)
% 0.19/0.44 % Number of type conns : 196 ( 196 >; 0 *; 0 +; 0 <<)
% 0.19/0.44 % Number of symbols : 59 ( 56 usr; 18 con; 0-5 aty)
% 0.19/0.44 % Number of variables : 1252 ( 11 ^;1196 !; 16 ?;1252 :)
% 0.19/0.44 % ( 29 !>; 0 ?*; 0 @-; 0 @+)
% 0.19/0.44 % SPC : TH1_THM_EQU_NAR
% 0.19/0.44
% 0.19/0.44 % Comments : This file was generated by Sledgehammer 2021-02-23 16:17:53.702
% 0.19/0.44 %------------------------------------------------------------------------------
% 0.19/0.44 % Could-be-implicit typings (14)
% 0.19/0.44 thf(ty_t_Late__Semantics_Oresidual__Rep,type,
% 0.19/0.44 late_residual_Rep: $tType ).
% 0.19/0.44
% 0.19/0.44 thf(ty_t_Late__Semantics_Osubject__Rep,type,
% 0.19/0.44 late_subject_Rep: $tType ).
% 0.19/0.44
% 0.19/0.44 thf(ty_t_Late__Semantics_OfreeRes__Rep,type,
% 0.19/0.44 late_freeRes_Rep: $tType ).
% 0.19/0.44
% 0.19/0.44 thf(ty_t_Late__Semantics_Oresidual,type,
% 0.19/0.44 late_residual: $tType ).
% 0.19/0.44
% 0.19/0.44 thf(ty_t_Late__Semantics_Osubject,type,
% 0.19/0.44 late_subject: $tType ).
% 0.19/0.44
% 0.19/0.44 thf(ty_t_Late__Semantics_OfreeRes,type,
% 0.19/0.44 late_freeRes: $tType ).
% 0.19/0.44
% 0.19/0.44 thf(ty_t_Product__Type_Ounit,type,
% 0.19/0.44 product_unit: $tType ).
% 0.19/0.44
% 0.19/0.44 thf(ty_t_Product__Type_Oprod,type,
% 0.19/0.44 product_prod: $tType > $tType > $tType ).
% 0.19/0.44
% 0.19/0.44 thf(ty_t_Nominal_Onoption,type,
% 0.19/0.44 noption: $tType > $tType ).
% 0.19/0.44
% 0.19/0.44 thf(ty_t_Agent_Opi__Rep,type,
% 0.19/0.44 pi_Rep: $tType ).
% 0.19/0.44
% 0.19/0.44 thf(ty_t_Agent_Oname,type,
% 0.19/0.44 name: $tType ).
% 0.19/0.44
% 0.19/0.44 thf(ty_t_List_Olist,type,
% 0.19/0.44 list: $tType > $tType ).
% 0.19/0.44
% 0.19/0.44 thf(ty_t_Agent_Opi,type,
% 0.19/0.44 pi: $tType ).
% 0.19/0.44
% 0.19/0.44 thf(ty_t_Set_Oset,type,
% 0.19/0.44 set: $tType > $tType ).
% 0.19/0.44
% 0.19/0.44 % Explicit typings (52)
% 0.19/0.44 thf(sy_cl_HOL_Otype,type,
% 0.19/0.44 type:
% 0.19/0.44 !>[A: $tType] : $o ).
% 0.19/0.44
% 0.19/0.44 thf(sy_cl_Agent_Ofs__name,type,
% 0.19/0.44 fs_name:
% 0.19/0.44 !>[A: $tType] : $o ).
% 0.19/0.44
% 0.19/0.44 thf(sy_cl_Agent_Opt__name,type,
% 0.19/0.44 pt_name:
% 0.19/0.44 !>[A: $tType] : $o ).
% 0.19/0.44
% 0.19/0.44 thf(sy_cl_Orderings_Oord,type,
% 0.19/0.44 ord:
% 0.19/0.44 !>[A: $tType] : $o ).
% 0.19/0.44
% 0.19/0.44 thf(sy_cl_Agent_Ocp__name__name,type,
% 0.19/0.44 cp_name_name:
% 0.19/0.44 !>[A: $tType] : $o ).
% 0.19/0.44
% 0.19/0.44 thf(sy_cl_Orderings_Olinorder,type,
% 0.19/0.44 linorder:
% 0.19/0.44 !>[A: $tType] : $o ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Agent_Opi_OInput,type,
% 0.19/0.44 input: name > name > pi > pi ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Agent_Opi_OPar,type,
% 0.19/0.44 par: pi > pi > pi ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Agent_Opi_ORes,type,
% 0.19/0.44 res: name > pi > pi ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Agent_Orec_Oswap__name,type,
% 0.19/0.44 swap_name: ( product_prod @ name @ name ) > name > name ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Agent_Osubs,type,
% 0.19/0.44 subs: pi > name > name > pi ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_HOL_Odefault__class_Odefault,type,
% 0.19/0.44 default_default:
% 0.19/0.44 !>[A: $tType] : A ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_If,type,
% 0.19/0.44 if:
% 0.19/0.44 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Late__Semantics_OfreeRes_OOutputR,type,
% 0.19/0.44 late_OutputR: name > name > late_freeRes ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Late__Semantics_OfreeRes_OTauR,type,
% 0.19/0.44 late_TauR: late_freeRes ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Late__Semantics_Oresidual_OBoundR,type,
% 0.19/0.44 late_BoundR: late_subject > name > pi > late_residual ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Late__Semantics_Oresidual_OFreeR,type,
% 0.19/0.44 late_FreeR: late_freeRes > pi > late_residual ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Late__Semantics_Oresidual__Rep_OFreeR__Rep,type,
% 0.19/0.44 late_r347633188eR_Rep: late_freeRes > pi > late_residual_Rep ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Late__Semantics_Osubject_OBoundOutputS,type,
% 0.19/0.44 late_BoundOutputS: name > late_subject ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Late__Semantics_Osubject_OInputS,type,
% 0.19/0.44 late_InputS: name > late_subject ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Late__Semantics_Otransitions,type,
% 0.19/0.44 late_transitions: pi > late_residual > $o ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_List_Olist_OCons,type,
% 0.19/0.44 cons:
% 0.19/0.44 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_List_Olist_ONil,type,
% 0.19/0.44 nil:
% 0.19/0.44 !>[A: $tType] : ( list @ A ) ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_List_Oproduct__lists,type,
% 0.19/0.44 product_lists:
% 0.19/0.44 !>[A: $tType] : ( ( list @ ( list @ A ) ) > ( list @ ( list @ A ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Nominal_Oabs__fun,type,
% 0.19/0.44 abs_fun:
% 0.19/0.44 !>[X: $tType,A: $tType] : ( X > A > X > ( noption @ A ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Nominal_Ofresh,type,
% 0.19/0.44 fresh:
% 0.19/0.44 !>[X: $tType,A: $tType] : ( X > A > $o ) ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Nominal_Operm,type,
% 0.19/0.44 perm:
% 0.19/0.44 !>[X: $tType,A: $tType] : ( ( list @ ( product_prod @ X @ X ) ) > A > A ) ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Nominal_Osupports,type,
% 0.19/0.44 supports:
% 0.19/0.44 !>[X: $tType,A: $tType] : ( ( set @ X ) > A > $o ) ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Nominal_Oswap,type,
% 0.19/0.44 swap:
% 0.19/0.44 !>[X: $tType] : ( ( product_prod @ X @ X ) > X > X ) ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Product__Type_OPair,type,
% 0.19/0.44 product_Pair:
% 0.19/0.44 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Product__Type_OUnity,type,
% 0.19/0.44 product_Unity: product_unit ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod,type,
% 0.19/0.44 product_rec_prod:
% 0.19/0.44 !>[A: $tType,B: $tType,T: $tType] : ( ( A > B > T ) > ( product_prod @ A @ B ) > T ) ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Product__Type_Oold_Ounit_Orec__unit,type,
% 0.19/0.44 product_rec_unit:
% 0.19/0.44 !>[T: $tType] : ( T > product_unit > T ) ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Rel_Oeqvt,type,
% 0.19/0.44 eqvt:
% 0.19/0.44 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > $o ) ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Set_OCollect,type,
% 0.19/0.44 collect:
% 0.19/0.44 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Strong__Late__Sim_Oderivative,type,
% 0.19/0.44 strong2129052853vative: pi > pi > late_subject > name > ( set @ ( product_prod @ pi @ pi ) ) > $o ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Strong__Late__Sim_Osimulation,type,
% 0.19/0.44 strong743114133lation: pi > ( set @ ( product_prod @ pi @ pi ) ) > pi > $o ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_member,type,
% 0.19/0.44 member:
% 0.19/0.44 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.19/0.44
% 0.19/0.44 thf(sy_v_P,type,
% 0.19/0.44 p: pi ).
% 0.19/0.44
% 0.19/0.44 thf(sy_v_PQ____,type,
% 0.19/0.44 pq: pi ).
% 0.19/0.44
% 0.19/0.44 thf(sy_v_P_H____,type,
% 0.19/0.44 p2: pi ).
% 0.19/0.44
% 0.19/0.44 thf(sy_v_Q,type,
% 0.19/0.44 q: pi ).
% 0.19/0.44
% 0.19/0.44 thf(sy_v_Q_H____,type,
% 0.19/0.44 q2: pi ).
% 0.19/0.44
% 0.19/0.44 thf(sy_v_Rel,type,
% 0.19/0.44 rel: set @ ( product_prod @ pi @ pi ) ).
% 0.19/0.44
% 0.19/0.44 thf(sy_v_aa____,type,
% 0.19/0.44 aa: late_subject ).
% 0.19/0.44
% 0.19/0.44 thf(sy_v_ab____,type,
% 0.19/0.44 ab: name ).
% 0.19/0.44
% 0.19/0.44 thf(sy_v_b____,type,
% 0.19/0.44 b: name ).
% 0.19/0.44
% 0.19/0.44 thf(sy_v_c____,type,
% 0.19/0.44 c: name ).
% 0.19/0.44
% 0.19/0.44 thf(sy_v_x,type,
% 0.19/0.44 x: name ).
% 0.19/0.44
% 0.19/0.44 thf(sy_v_xPQ____,type,
% 0.19/0.44 xPQ: pi ).
% 0.19/0.44
% 0.19/0.44 thf(sy_v_y____,type,
% 0.19/0.44 y: name ).
% 0.19/0.44
% 0.19/0.44 thf(sy_v_ya____,type,
% 0.19/0.44 ya: name ).
% 0.19/0.44
% 0.19/0.44 % Relevant facts (255)
% 0.19/0.44 thf(fact_0_cComm1_Ohyps_I5_J,axiom,
% 0.19/0.44 ya != b ).
% 0.19/0.44
% 0.19/0.44 % cComm1.hyps(5)
% 0.19/0.44 thf(fact_1_cComm1_Ohyps_I9_J,axiom,
% 0.19/0.44 ( ( late_OutputR @ ab @ x )
% 0.19/0.44 = late_TauR ) ).
% 0.19/0.44
% 0.19/0.44 % cComm1.hyps(9)
% 0.19/0.44 thf(fact_2_cOpen_Ohyps_I2_J,axiom,
% 0.19/0.44 ab != x ).
% 0.19/0.44
% 0.19/0.44 % cOpen.hyps(2)
% 0.19/0.44 thf(fact_3_cComm1_Ohyps_I6_J,axiom,
% 0.19/0.44 ya != c ).
% 0.19/0.44
% 0.19/0.44 % cComm1.hyps(6)
% 0.19/0.44 thf(fact_4_cOpen_Ohyps_I3_J,axiom,
% 0.19/0.44 ( aa
% 0.19/0.44 = ( late_BoundOutputS @ ab ) ) ).
% 0.19/0.44
% 0.19/0.44 % cOpen.hyps(3)
% 0.19/0.44 thf(fact_5_assms_I3_J,axiom,
% 0.19/0.44 eqvt @ pi @ rel ).
% 0.19/0.44
% 0.19/0.44 % assms(3)
% 0.19/0.44 thf(fact_6__092_060open_062y_____A_092_060noteq_062_Ax_092_060close_062,axiom,
% 0.19/0.44 y != x ).
% 0.19/0.44
% 0.19/0.44 % \<open>y__ \<noteq> x\<close>
% 0.19/0.44 thf(fact_7_Bound_Ohyps_I1_J,axiom,
% 0.19/0.44 late_transitions @ ( res @ x @ ( par @ p @ q ) ) @ ( late_BoundR @ aa @ y @ xPQ ) ).
% 0.19/0.44
% 0.19/0.44 % Bound.hyps(1)
% 0.19/0.44 thf(fact_8_assms_I1_J,axiom,
% 0.19/0.44 fresh @ name @ pi @ x @ p ).
% 0.19/0.44
% 0.19/0.44 % assms(1)
% 0.19/0.44 thf(fact_9_cComm1_Ohyps_I3_J,axiom,
% 0.19/0.44 fresh @ name @ pi @ ya @ p ).
% 0.19/0.44
% 0.19/0.44 % cComm1.hyps(3)
% 0.19/0.44 thf(fact_10_cComm1_Ohyps_I4_J,axiom,
% 0.19/0.44 fresh @ name @ pi @ ya @ q ).
% 0.19/0.44
% 0.19/0.44 % cComm1.hyps(4)
% 0.19/0.44 thf(fact_11_cComm1_Ohyps_I7_J,axiom,
% 0.19/0.44 fresh @ name @ pi @ ya @ q2 ).
% 0.19/0.44
% 0.19/0.44 % cComm1.hyps(7)
% 0.19/0.44 thf(fact_12_Bound_Ohyps_I3_J,axiom,
% 0.19/0.44 fresh @ name @ pi @ y @ ( res @ x @ ( par @ p @ q ) ) ).
% 0.19/0.44
% 0.19/0.44 % Bound.hyps(3)
% 0.19/0.44 thf(fact_13_Bound_Ohyps_I2_J,axiom,
% 0.19/0.44 fresh @ name @ pi @ y @ ( par @ p @ ( res @ x @ q ) ) ).
% 0.19/0.44
% 0.19/0.44 % Bound.hyps(2)
% 0.19/0.44 thf(fact_14_Strong__Late__Sim__SC__Mirabelle__dtpyqonsky_OsubstRes3,axiom,
% 0.19/0.44 ! [A2: name,P: pi,X2: name] :
% 0.19/0.44 ( ( subs @ ( res @ A2 @ P ) @ X2 @ A2 )
% 0.19/0.44 = ( res @ X2 @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ X2 @ A2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ P ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % Strong_Late_Sim_SC_Mirabelle_dtpyqonsky.substRes3
% 0.19/0.44 thf(fact_15_cComm1_Ohyps_I1_J,axiom,
% 0.19/0.44 late_transitions @ p @ ( late_BoundR @ ( late_InputS @ b ) @ ya @ p2 ) ).
% 0.19/0.44
% 0.19/0.44 % cComm1.hyps(1)
% 0.19/0.44 thf(fact_16_perm__swap_I1_J,axiom,
% 0.19/0.44 ! [X3: $tType] :
% 0.19/0.44 ( ( pt_name @ X3 )
% 0.19/0.44 => ! [A2: name,B2: name,X2: X3] :
% 0.19/0.44 ( ( perm @ name @ X3 @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ ( perm @ name @ X3 @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ X2 ) )
% 0.19/0.44 = X2 ) ) ).
% 0.19/0.44
% 0.19/0.44 % perm_swap(1)
% 0.19/0.44 thf(fact_17_name__id,axiom,
% 0.19/0.44 ! [X: $tType] :
% 0.19/0.44 ( ( pt_name @ X )
% 0.19/0.44 => ! [A2: name,X2: X] :
% 0.19/0.44 ( ( perm @ name @ X @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ A2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ X2 )
% 0.19/0.44 = X2 ) ) ).
% 0.19/0.44
% 0.19/0.44 % name_id
% 0.19/0.44 thf(fact_18_name__swap,axiom,
% 0.19/0.44 ! [X: $tType] :
% 0.19/0.44 ( ( pt_name @ X )
% 0.19/0.44 => ! [A2: name,B2: name,X2: X] :
% 0.19/0.44 ( ( perm @ name @ X @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ X2 )
% 0.19/0.44 = ( perm @ name @ X @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ B2 @ A2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ X2 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % name_swap
% 0.19/0.44 thf(fact_19_name__swap__bij,axiom,
% 0.19/0.44 ! [X: $tType] :
% 0.19/0.44 ( ( pt_name @ X )
% 0.19/0.44 => ! [A2: name,B2: name,X2: X] :
% 0.19/0.44 ( ( 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 ) ) ) @ X2 ) )
% 0.19/0.44 = X2 ) ) ).
% 0.19/0.44
% 0.19/0.44 % name_swap_bij
% 0.19/0.44 thf(fact_20_cOpen_Ohyps_I1_J,axiom,
% 0.19/0.44 late_transitions @ ( par @ p @ q ) @ ( late_FreeR @ ( late_OutputR @ ab @ x ) @ pq ) ).
% 0.19/0.44
% 0.19/0.44 % cOpen.hyps(1)
% 0.19/0.44 thf(fact_21_pi_Operm_I8_J,axiom,
% 0.19/0.44 ! [Pi: list @ ( product_prod @ name @ name ),X22: pi,X1: pi] :
% 0.19/0.44 ( ( perm @ name @ pi @ Pi @ ( par @ X22 @ X1 ) )
% 0.19/0.44 = ( par @ ( perm @ name @ pi @ Pi @ X22 ) @ ( perm @ name @ pi @ Pi @ X1 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % pi.perm(8)
% 0.19/0.44 thf(fact_22_simps_I8_J,axiom,
% 0.19/0.44 ! [P: pi,Q: pi,C: name,D: name] :
% 0.19/0.44 ( ( subs @ ( par @ P @ Q ) @ C @ D )
% 0.19/0.44 = ( par @ ( subs @ P @ C @ D ) @ ( subs @ Q @ C @ D ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % simps(8)
% 0.19/0.44 thf(fact_23_simps_I9_J,axiom,
% 0.19/0.44 ! [X2: name,C: name,D: name,P: pi] :
% 0.19/0.44 ( ( X2 != C )
% 0.19/0.44 => ( ( X2 != D )
% 0.19/0.44 => ( ( subs @ ( res @ X2 @ P ) @ C @ D )
% 0.19/0.44 = ( res @ X2 @ ( subs @ P @ C @ D ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % simps(9)
% 0.19/0.44 thf(fact_24_pt__name1,axiom,
% 0.19/0.44 ! [A: $tType] :
% 0.19/0.44 ( ( pt_name @ A )
% 0.19/0.44 => ! [X2: A] :
% 0.19/0.44 ( ( perm @ name @ A @ ( nil @ ( product_prod @ name @ name ) ) @ X2 )
% 0.19/0.44 = X2 ) ) ).
% 0.19/0.44
% 0.19/0.44 % pt_name1
% 0.19/0.44 thf(fact_25_cComm1_Ohyps_I2_J,axiom,
% 0.19/0.44 late_transitions @ q @ ( late_FreeR @ ( late_OutputR @ b @ c ) @ q2 ) ).
% 0.19/0.44
% 0.19/0.44 % cComm1.hyps(2)
% 0.19/0.44 thf(fact_26__092_060open_062y_____A_092_060sharp_062_AP_A_092_060parallel_062_AQ_092_060close_062,axiom,
% 0.19/0.44 fresh @ name @ pi @ y @ ( par @ p @ q ) ).
% 0.19/0.44
% 0.19/0.44 % \<open>y__ \<sharp> P \<parallel> Q\<close>
% 0.19/0.44 thf(fact_27_subst__identity,axiom,
% 0.19/0.44 ! [P: pi,A2: name] :
% 0.19/0.44 ( ( subs @ P @ A2 @ A2 )
% 0.19/0.44 = P ) ).
% 0.19/0.44
% 0.19/0.44 % subst_identity
% 0.19/0.44 thf(fact_28_pi__perm__empty,axiom,
% 0.19/0.44 ! [Pi_Rep: pi_Rep] :
% 0.19/0.44 ( ( perm @ name @ pi_Rep @ ( nil @ ( product_prod @ name @ name ) ) @ Pi_Rep )
% 0.19/0.44 = Pi_Rep ) ).
% 0.19/0.44
% 0.19/0.44 % pi_perm_empty
% 0.19/0.44 thf(fact_29__092_060open_062y_____A_092_060sharp_062_AP_092_060close_062,axiom,
% 0.19/0.44 fresh @ name @ pi @ y @ p ).
% 0.19/0.44
% 0.19/0.44 % \<open>y__ \<sharp> P\<close>
% 0.19/0.44 thf(fact_30__092_060open_062y_____A_092_060sharp_062_AQ_092_060close_062,axiom,
% 0.19/0.44 fresh @ name @ pi @ y @ q ).
% 0.19/0.44
% 0.19/0.44 % \<open>y__ \<sharp> Q\<close>
% 0.19/0.45 thf(fact_31_pi_Ofresh_I8_J,axiom,
% 0.19/0.45 ! [A2: name,X22: pi,X1: pi] :
% 0.19/0.45 ( ( fresh @ name @ pi @ A2 @ ( par @ X22 @ X1 ) )
% 0.19/0.45 = ( ( fresh @ name @ pi @ A2 @ X22 )
% 0.19/0.45 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % pi.fresh(8)
% 0.19/0.45 thf(fact_32_pi_Operm_I9_J,axiom,
% 0.19/0.45 ! [Pi: list @ ( product_prod @ name @ name ),X1: name,X22: pi] :
% 0.19/0.45 ( ( perm @ name @ pi @ Pi @ ( res @ X1 @ X22 ) )
% 0.19/0.45 = ( res @ ( perm @ name @ name @ Pi @ X1 ) @ ( perm @ name @ pi @ Pi @ X22 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % pi.perm(9)
% 0.19/0.45 thf(fact_33_perm__fresh__fresh,axiom,
% 0.19/0.45 ! [X3: $tType] :
% 0.19/0.45 ( ( pt_name @ X3 )
% 0.19/0.45 => ! [A2: name,X2: X3,B2: name] :
% 0.19/0.45 ( ( fresh @ name @ X3 @ A2 @ X2 )
% 0.19/0.45 => ( ( fresh @ name @ X3 @ B2 @ X2 )
% 0.19/0.45 => ( ( perm @ name @ X3 @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ X2 )
% 0.19/0.45 = X2 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % perm_fresh_fresh
% 0.19/0.45 thf(fact_34_name__fresh__fresh,axiom,
% 0.19/0.45 ! [X: $tType] :
% 0.19/0.45 ( ( pt_name @ X )
% 0.19/0.45 => ! [A2: name,X2: X,B2: name] :
% 0.19/0.45 ( ( fresh @ name @ X @ A2 @ X2 )
% 0.19/0.45 => ( ( fresh @ name @ X @ B2 @ X2 )
% 0.19/0.45 => ( ( perm @ name @ X @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ X2 )
% 0.19/0.45 = X2 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % name_fresh_fresh
% 0.19/0.45 thf(fact_35_Bound_Ohyps_I4_J,axiom,
% 0.19/0.45 fresh @ name @ late_subject @ y @ aa ).
% 0.19/0.45
% 0.19/0.45 % Bound.hyps(4)
% 0.19/0.45 thf(fact_36_fresh__perm__app,axiom,
% 0.19/0.45 ! [X3: $tType] :
% 0.19/0.45 ( ( pt_name @ X3 )
% 0.19/0.45 => ! [A2: name,Pi: list @ ( product_prod @ name @ name ),X2: X3] :
% 0.19/0.45 ( ( fresh @ name @ ( list @ ( product_prod @ name @ name ) ) @ A2 @ Pi )
% 0.19/0.45 => ( ( fresh @ name @ X3 @ A2 @ X2 )
% 0.19/0.45 => ( fresh @ name @ X3 @ A2 @ ( perm @ name @ X3 @ Pi @ X2 ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % fresh_perm_app
% 0.19/0.45 thf(fact_37_name__exists__fresh,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( fs_name @ A )
% 0.19/0.45 => ! [X2: A] :
% 0.19/0.45 ~ ! [C2: name] :
% 0.19/0.45 ~ ( fresh @ name @ A @ C2 @ X2 ) ) ).
% 0.19/0.45
% 0.19/0.45 % name_exists_fresh
% 0.19/0.45 thf(fact_38_fresh__eqvt,axiom,
% 0.19/0.45 ! [X3: $tType] :
% 0.19/0.45 ( ( pt_name @ X3 )
% 0.19/0.45 => ! [Pi: list @ ( product_prod @ name @ name ),A2: name,X2: X3] :
% 0.19/0.45 ( ( perm @ name @ $o @ Pi @ ( fresh @ name @ X3 @ A2 @ X2 ) )
% 0.19/0.45 = ( fresh @ name @ X3 @ ( perm @ name @ name @ Pi @ A2 ) @ ( perm @ name @ X3 @ Pi @ X2 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % fresh_eqvt
% 0.19/0.45 thf(fact_39_fresh__bij,axiom,
% 0.19/0.45 ! [X3: $tType] :
% 0.19/0.45 ( ( pt_name @ X3 )
% 0.19/0.45 => ! [Pi: list @ ( product_prod @ name @ name ),A2: name,X2: X3] :
% 0.19/0.45 ( ( fresh @ name @ X3 @ ( perm @ name @ name @ Pi @ A2 ) @ ( perm @ name @ X3 @ Pi @ X2 ) )
% 0.19/0.45 = ( fresh @ name @ X3 @ A2 @ X2 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % fresh_bij
% 0.19/0.45 thf(fact_40_freshRes,axiom,
% 0.19/0.45 ! [A2: name,P: pi] : ( fresh @ name @ pi @ A2 @ ( res @ A2 @ P ) ) ).
% 0.19/0.45
% 0.19/0.45 % freshRes
% 0.19/0.45 thf(fact_41_fresh__fact2,axiom,
% 0.19/0.45 ! [A2: name,B2: name,P: pi] :
% 0.19/0.45 ( ( A2 != B2 )
% 0.19/0.45 => ( fresh @ name @ pi @ A2 @ ( subs @ P @ A2 @ B2 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % fresh_fact2
% 0.19/0.45 thf(fact_42_fresh__fact1,axiom,
% 0.19/0.45 ! [A2: name,P: pi,C: name,B2: name] :
% 0.19/0.45 ( ( fresh @ name @ pi @ A2 @ P )
% 0.19/0.45 => ( ( A2 != C )
% 0.19/0.45 => ( fresh @ name @ pi @ A2 @ ( subs @ P @ B2 @ C ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % fresh_fact1
% 0.19/0.45 thf(fact_43_forget,axiom,
% 0.19/0.45 ! [A2: name,P: pi,B2: name] :
% 0.19/0.45 ( ( fresh @ name @ pi @ A2 @ P )
% 0.19/0.45 => ( ( subs @ P @ A2 @ B2 )
% 0.19/0.45 = P ) ) ).
% 0.19/0.45
% 0.19/0.45 % forget
% 0.19/0.45 thf(fact_44_name__calc_I2_J,axiom,
% 0.19/0.45 ! [X2: name] :
% 0.19/0.45 ( ( perm @ name @ name @ ( nil @ ( product_prod @ name @ name ) ) @ X2 )
% 0.19/0.45 = X2 ) ).
% 0.19/0.45
% 0.19/0.45 % name_calc(2)
% 0.19/0.45 thf(fact_45_mem__Collect__eq,axiom,
% 0.19/0.45 ! [A: $tType,A2: A,P: A > $o] :
% 0.19/0.45 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 0.19/0.45 = ( P @ A2 ) ) ).
% 0.19/0.45
% 0.19/0.45 % mem_Collect_eq
% 0.19/0.45 thf(fact_46_Collect__mem__eq,axiom,
% 0.19/0.45 ! [A: $tType,A3: set @ A] :
% 0.19/0.45 ( ( collect @ A
% 0.19/0.45 @ ^ [X4: A] : ( member @ A @ X4 @ A3 ) )
% 0.19/0.45 = A3 ) ).
% 0.19/0.45
% 0.19/0.45 % Collect_mem_eq
% 0.19/0.45 thf(fact_47_Collect__cong,axiom,
% 0.19/0.45 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.19/0.45 ( ! [X5: A] :
% 0.19/0.45 ( ( P @ X5 )
% 0.19/0.45 = ( Q @ X5 ) )
% 0.19/0.45 => ( ( collect @ A @ P )
% 0.19/0.45 = ( collect @ A @ Q ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % Collect_cong
% 0.19/0.45 thf(fact_48_ext,axiom,
% 0.19/0.45 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.19/0.45 ( ! [X5: A] :
% 0.19/0.45 ( ( F @ X5 )
% 0.19/0.45 = ( G @ X5 ) )
% 0.19/0.45 => ( F = G ) ) ).
% 0.19/0.45
% 0.19/0.45 % ext
% 0.19/0.45 thf(fact_49_Agent_OsubstRes3,axiom,
% 0.19/0.45 ! [B2: name,P: pi,A2: name] :
% 0.19/0.45 ( ( fresh @ name @ pi @ B2 @ P )
% 0.19/0.45 => ( ( subs @ ( res @ A2 @ P ) @ A2 @ B2 )
% 0.19/0.45 = ( res @ B2 @ ( subs @ P @ A2 @ B2 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % Agent.substRes3
% 0.19/0.45 thf(fact_50_substRes2,axiom,
% 0.19/0.45 ! [B2: name,P: pi,A2: name] :
% 0.19/0.45 ( ( fresh @ name @ pi @ B2 @ P )
% 0.19/0.45 => ( ( res @ A2 @ P )
% 0.19/0.45 = ( res @ B2 @ ( subs @ P @ A2 @ B2 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % substRes2
% 0.19/0.45 thf(fact_51_eqvt__subs,axiom,
% 0.19/0.45 ! [P2: list @ ( product_prod @ name @ name ),P: pi,A2: name,B2: name] :
% 0.19/0.45 ( ( perm @ name @ pi @ P2 @ ( subs @ P @ A2 @ B2 ) )
% 0.19/0.45 = ( subs @ ( perm @ name @ pi @ P2 @ P ) @ ( perm @ name @ name @ P2 @ A2 ) @ ( perm @ name @ name @ P2 @ B2 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % eqvt_subs
% 0.19/0.45 thf(fact_52_swap__simps_I1_J,axiom,
% 0.19/0.45 ! [A2: name,B2: name] :
% 0.19/0.45 ( ( perm @ name @ name @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ A2 )
% 0.19/0.45 = B2 ) ).
% 0.19/0.45
% 0.19/0.45 % swap_simps(1)
% 0.19/0.45 thf(fact_53_swap__simps_I2_J,axiom,
% 0.19/0.45 ! [A2: name,B2: name] :
% 0.19/0.45 ( ( perm @ name @ name @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ B2 )
% 0.19/0.45 = A2 ) ).
% 0.19/0.45
% 0.19/0.45 % swap_simps(2)
% 0.19/0.45 thf(fact_54_swap__simps_I3_J,axiom,
% 0.19/0.45 ! [A2: name,C: name,B2: name] :
% 0.19/0.45 ( ( A2 != C )
% 0.19/0.45 => ( ( B2 != C )
% 0.19/0.45 => ( ( perm @ name @ name @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ C )
% 0.19/0.45 = C ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % swap_simps(3)
% 0.19/0.45 thf(fact_55_fresh__aux,axiom,
% 0.19/0.45 ! [X3: $tType] :
% 0.19/0.45 ( ( pt_name @ X3 )
% 0.19/0.45 => ! [C: name,A2: name,X2: X3,B2: name] :
% 0.19/0.45 ( ( C != A2 )
% 0.19/0.45 => ( ( fresh @ name @ X3 @ A2 @ X2 )
% 0.19/0.45 => ( ( fresh @ name @ X3 @ C @ X2 )
% 0.19/0.45 => ( fresh @ name @ X3 @ C @ ( perm @ name @ X3 @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ X2 ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % fresh_aux
% 0.19/0.45 thf(fact_56_cp__name__name1,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( cp_name_name @ A )
% 0.19/0.45 => ! [Pi1: list @ ( product_prod @ name @ name ),Pi2: list @ ( product_prod @ name @ name ),X2: A] :
% 0.19/0.45 ( ( perm @ name @ A @ Pi1 @ ( perm @ name @ A @ Pi2 @ X2 ) )
% 0.19/0.45 = ( perm @ name @ A @ ( perm @ name @ ( list @ ( product_prod @ name @ name ) ) @ Pi1 @ Pi2 ) @ ( perm @ name @ A @ Pi1 @ X2 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % cp_name_name1
% 0.19/0.45 thf(fact_57_name__perm__compose,axiom,
% 0.19/0.45 ! [X: $tType] :
% 0.19/0.45 ( ( pt_name @ X )
% 0.19/0.45 => ! [Pi2: list @ ( product_prod @ name @ name ),Pi1: list @ ( product_prod @ name @ name ),X2: X] :
% 0.19/0.45 ( ( perm @ name @ X @ Pi2 @ ( perm @ name @ X @ Pi1 @ X2 ) )
% 0.19/0.45 = ( perm @ name @ X @ ( perm @ name @ ( list @ ( product_prod @ name @ name ) ) @ Pi2 @ Pi1 ) @ ( perm @ name @ X @ Pi2 @ X2 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % name_perm_compose
% 0.19/0.45 thf(fact_58_perm__compose,axiom,
% 0.19/0.45 ! [X3: $tType] :
% 0.19/0.45 ( ( pt_name @ X3 )
% 0.19/0.45 => ! [Pi2: list @ ( product_prod @ name @ name ),Pi1: list @ ( product_prod @ name @ name ),X2: X3] :
% 0.19/0.45 ( ( perm @ name @ X3 @ Pi2 @ ( perm @ name @ X3 @ Pi1 @ X2 ) )
% 0.19/0.45 = ( perm @ name @ X3 @ ( perm @ name @ ( list @ ( product_prod @ name @ name ) ) @ Pi2 @ Pi1 ) @ ( perm @ name @ X3 @ Pi2 @ X2 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % perm_compose
% 0.19/0.45 thf(fact_59_perm__bij,axiom,
% 0.19/0.45 ! [X3: $tType] :
% 0.19/0.45 ( ( pt_name @ X3 )
% 0.19/0.45 => ! [Pi: list @ ( product_prod @ name @ name ),X2: X3,Y: X3] :
% 0.19/0.45 ( ( ( perm @ name @ X3 @ Pi @ X2 )
% 0.19/0.45 = ( perm @ name @ X3 @ Pi @ Y ) )
% 0.19/0.45 = ( X2 = Y ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % perm_bij
% 0.19/0.45 thf(fact_60_perm__app,axiom,
% 0.19/0.45 ! [B: $tType,X3: $tType] :
% 0.19/0.45 ( ( pt_name @ X3 )
% 0.19/0.45 => ! [Pi: list @ ( product_prod @ name @ name ),F: X3 > B,X2: X3] :
% 0.19/0.45 ( ( perm @ name @ B @ Pi @ ( F @ X2 ) )
% 0.19/0.45 = ( perm @ name @ ( X3 > B ) @ Pi @ F @ ( perm @ name @ X3 @ Pi @ X2 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % perm_app
% 0.19/0.45 thf(fact_61_in__eqvt,axiom,
% 0.19/0.45 ! [X3: $tType] :
% 0.19/0.45 ( ( pt_name @ X3 )
% 0.19/0.45 => ! [Pi: list @ ( product_prod @ name @ name ),X2: X3,X6: set @ X3] :
% 0.19/0.45 ( ( perm @ name @ $o @ Pi @ ( member @ X3 @ X2 @ X6 ) )
% 0.19/0.45 = ( member @ X3 @ ( perm @ name @ X3 @ Pi @ X2 ) @ ( perm @ name @ ( set @ X3 ) @ Pi @ X6 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % in_eqvt
% 0.19/0.45 thf(fact_62_eq__eqvt,axiom,
% 0.19/0.45 ! [X3: $tType] :
% 0.19/0.45 ( ( pt_name @ X3 )
% 0.19/0.45 => ! [Pi: list @ ( product_prod @ name @ name ),X2: X3,Y: X3] :
% 0.19/0.45 ( ( perm @ name @ $o @ Pi @ ( X2 = Y ) )
% 0.19/0.45 = ( ( perm @ name @ X3 @ Pi @ X2 )
% 0.19/0.45 = ( perm @ name @ X3 @ Pi @ Y ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % eq_eqvt
% 0.19/0.45 thf(fact_63_pi_Oinject_I7_J,axiom,
% 0.19/0.45 ! [X22: pi,X1: pi,Y2: pi,Y1: pi] :
% 0.19/0.45 ( ( ( par @ X22 @ X1 )
% 0.19/0.45 = ( par @ Y2 @ Y1 ) )
% 0.19/0.45 = ( ( X22 = Y2 )
% 0.19/0.45 & ( X1 = Y1 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % pi.inject(7)
% 0.19/0.45 thf(fact_64_alphaRes,axiom,
% 0.19/0.45 ! [C: name,P: pi,A2: name] :
% 0.19/0.45 ( ( fresh @ name @ pi @ C @ P )
% 0.19/0.45 => ( ( res @ A2 @ P )
% 0.19/0.45 = ( res @ C @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ C ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ P ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % alphaRes
% 0.19/0.45 thf(fact_65_injPermSubst,axiom,
% 0.19/0.45 ! [B2: name,P: pi,A2: name] :
% 0.19/0.45 ( ( fresh @ name @ pi @ B2 @ P )
% 0.19/0.45 => ( ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ P )
% 0.19/0.45 = ( subs @ P @ A2 @ B2 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % injPermSubst
% 0.19/0.45 thf(fact_66_renaming,axiom,
% 0.19/0.45 ! [C: name,P: pi,A2: name,B2: name] :
% 0.19/0.45 ( ( fresh @ name @ pi @ C @ P )
% 0.19/0.45 => ( ( subs @ P @ A2 @ B2 )
% 0.19/0.45 = ( subs @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ C @ A2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ P ) @ C @ B2 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % renaming
% 0.19/0.45 thf(fact_67_pi_Odistinct_I85_J,axiom,
% 0.19/0.45 ! [Pi1: pi,Pi2: pi,Name: name,Pi3: pi] :
% 0.19/0.45 ( ( par @ Pi1 @ Pi2 )
% 0.19/0.45 != ( res @ Name @ Pi3 ) ) ).
% 0.19/0.45
% 0.19/0.45 % pi.distinct(85)
% 0.19/0.45 thf(fact_68_perm__swap_I2_J,axiom,
% 0.19/0.45 ! [X3: $tType] :
% 0.19/0.45 ( ( pt_name @ X3 )
% 0.19/0.45 => ! [A2: name,B2: name,X2: X3] :
% 0.19/0.45 ( ( perm @ name @ X3 @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ ( perm @ name @ X3 @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ B2 @ A2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ X2 ) )
% 0.19/0.45 = X2 ) ) ).
% 0.19/0.45
% 0.19/0.45 % perm_swap(2)
% 0.19/0.45 thf(fact_69_transitions_OClose2,axiom,
% 0.19/0.45 ! [P: pi,A2: name,Y: name,P3: pi,Q: pi,X2: name,Q2: pi] :
% 0.19/0.45 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y @ P3 ) )
% 0.19/0.45 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ Q2 ) )
% 0.19/0.45 => ( ( fresh @ name @ pi @ X2 @ P )
% 0.19/0.45 => ( ( fresh @ name @ pi @ X2 @ Q )
% 0.19/0.45 => ( ( fresh @ name @ pi @ Y @ P )
% 0.19/0.45 => ( ( fresh @ name @ pi @ Y @ Q )
% 0.19/0.45 => ( ( X2 != A2 )
% 0.19/0.45 => ( ( fresh @ name @ pi @ X2 @ P3 )
% 0.19/0.45 => ( ( Y != A2 )
% 0.19/0.45 => ( ( fresh @ name @ pi @ Y @ Q2 )
% 0.19/0.45 => ( ( X2 != Y )
% 0.19/0.45 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ P3 @ ( subs @ Q2 @ X2 @ Y ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % transitions.Close2
% 0.19/0.45 thf(fact_70_transitions_OClose1,axiom,
% 0.19/0.45 ! [P: pi,A2: name,X2: name,P3: pi,Q: pi,Y: name,Q2: pi] :
% 0.19/0.45 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P3 ) )
% 0.19/0.45 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y @ Q2 ) )
% 0.19/0.45 => ( ( fresh @ name @ pi @ X2 @ P )
% 0.19/0.45 => ( ( fresh @ name @ pi @ X2 @ Q )
% 0.19/0.45 => ( ( fresh @ name @ pi @ Y @ P )
% 0.19/0.45 => ( ( fresh @ name @ pi @ Y @ Q )
% 0.19/0.45 => ( ( X2 != A2 )
% 0.19/0.45 => ( ( fresh @ name @ pi @ X2 @ Q2 )
% 0.19/0.45 => ( ( Y != A2 )
% 0.19/0.45 => ( ( fresh @ name @ pi @ Y @ P3 )
% 0.19/0.45 => ( ( X2 != Y )
% 0.19/0.45 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ ( subs @ P3 @ X2 @ Y ) @ Q2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % transitions.Close1
% 0.19/0.45 thf(fact_71_Late__Semantics_OClose2,axiom,
% 0.19/0.45 ! [P: pi,A2: name,Y: name,P3: pi,Q: pi,X2: name,Q2: pi] :
% 0.19/0.45 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y @ P3 ) )
% 0.19/0.45 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ Q2 ) )
% 0.19/0.45 => ( ( fresh @ name @ pi @ Y @ Q )
% 0.19/0.45 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ P3 @ ( subs @ Q2 @ X2 @ Y ) ) ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % Late_Semantics.Close2
% 0.19/0.45 thf(fact_72_Late__Semantics_OClose1,axiom,
% 0.19/0.45 ! [P: pi,A2: name,X2: name,P3: pi,Q: pi,Y: name,Q2: pi] :
% 0.19/0.45 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P3 ) )
% 0.19/0.45 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y @ Q2 ) )
% 0.19/0.45 => ( ( fresh @ name @ pi @ Y @ P )
% 0.19/0.45 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ ( subs @ P3 @ X2 @ Y ) @ Q2 ) ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % Late_Semantics.Close1
% 0.19/0.45 thf(fact_73_transitions_OComm2,axiom,
% 0.19/0.45 ! [P: pi,A2: name,B2: name,P3: pi,Q: pi,X2: name,Q2: pi] :
% 0.19/0.45 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P3 ) )
% 0.19/0.45 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ Q2 ) )
% 0.19/0.45 => ( ( fresh @ name @ pi @ X2 @ P )
% 0.19/0.45 => ( ( fresh @ name @ pi @ X2 @ Q )
% 0.19/0.45 => ( ( X2 != A2 )
% 0.19/0.45 => ( ( X2 != B2 )
% 0.19/0.45 => ( ( fresh @ name @ pi @ X2 @ P3 )
% 0.19/0.45 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P3 @ ( subs @ Q2 @ X2 @ B2 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % transitions.Comm2
% 0.19/0.45 thf(fact_74_transitions_OComm1,axiom,
% 0.19/0.45 ! [P: pi,A2: name,X2: name,P3: pi,Q: pi,B2: name,Q2: pi] :
% 0.19/0.45 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P3 ) )
% 0.19/0.45 => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ Q2 ) )
% 0.19/0.45 => ( ( fresh @ name @ pi @ X2 @ P )
% 0.19/0.45 => ( ( fresh @ name @ pi @ X2 @ Q )
% 0.19/0.45 => ( ( X2 != A2 )
% 0.19/0.45 => ( ( X2 != B2 )
% 0.19/0.45 => ( ( fresh @ name @ pi @ X2 @ Q2 )
% 0.19/0.45 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P3 @ X2 @ B2 ) @ Q2 ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % transitions.Comm1
% 0.19/0.45 thf(fact_75_Late__Semantics_OComm2,axiom,
% 0.19/0.45 ! [P: pi,A2: name,B2: name,P3: pi,Q: pi,X2: name,Q2: pi] :
% 0.19/0.45 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P3 ) )
% 0.19/0.45 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ Q2 ) )
% 0.19/0.45 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P3 @ ( subs @ Q2 @ X2 @ B2 ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % Late_Semantics.Comm2
% 0.19/0.45 thf(fact_76_Late__Semantics_OComm1,axiom,
% 0.19/0.45 ! [P: pi,A2: name,X2: name,P3: pi,Q: pi,B2: name,Q2: pi] :
% 0.19/0.45 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P3 ) )
% 0.19/0.45 => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ Q2 ) )
% 0.19/0.45 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P3 @ X2 @ B2 ) @ Q2 ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % Late_Semantics.Comm1
% 0.19/0.45 thf(fact_77_alphaBoundResidual,axiom,
% 0.19/0.45 ! [X7: name,P: pi,A2: late_subject,X2: name] :
% 0.19/0.45 ( ( fresh @ name @ pi @ X7 @ P )
% 0.19/0.45 => ( ( late_BoundR @ A2 @ X2 @ P )
% 0.19/0.45 = ( late_BoundR @ A2 @ X7 @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ X2 @ X7 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ P ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % alphaBoundResidual
% 0.19/0.45 thf(fact_78_freeRes__perm__empty,axiom,
% 0.19/0.45 ! [FreeRes_Rep: late_freeRes_Rep] :
% 0.19/0.45 ( ( perm @ name @ late_freeRes_Rep @ ( nil @ ( product_prod @ name @ name ) ) @ FreeRes_Rep )
% 0.19/0.45 = FreeRes_Rep ) ).
% 0.19/0.45
% 0.19/0.45 % freeRes_perm_empty
% 0.19/0.45 thf(fact_79_subject__perm__empty,axiom,
% 0.19/0.45 ! [Subject_Rep: late_subject_Rep] :
% 0.19/0.45 ( ( perm @ name @ late_subject_Rep @ ( nil @ ( product_prod @ name @ name ) ) @ Subject_Rep )
% 0.19/0.45 = Subject_Rep ) ).
% 0.19/0.45
% 0.19/0.45 % subject_perm_empty
% 0.19/0.45 thf(fact_80_residual__perm__empty,axiom,
% 0.19/0.45 ! [Residual_Rep: late_residual_Rep] :
% 0.19/0.45 ( ( perm @ name @ late_residual_Rep @ ( nil @ ( product_prod @ name @ name ) ) @ Residual_Rep )
% 0.19/0.45 = Residual_Rep ) ).
% 0.19/0.45
% 0.19/0.45 % residual_perm_empty
% 0.19/0.45 thf(fact_81_freeRes_Ofresh_I1_J,axiom,
% 0.19/0.45 ! [A2: name,X22: name,X1: name] :
% 0.19/0.45 ( ( fresh @ name @ late_freeRes @ A2 @ ( late_OutputR @ X22 @ X1 ) )
% 0.19/0.45 = ( ( fresh @ name @ name @ A2 @ X22 )
% 0.19/0.45 & ( fresh @ name @ name @ A2 @ X1 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % freeRes.fresh(1)
% 0.19/0.45 thf(fact_82_Late__Semantics_OfreeRes_Oinject,axiom,
% 0.19/0.45 ! [X22: name,X1: name,Y2: name,Y1: name] :
% 0.19/0.45 ( ( ( late_OutputR @ X22 @ X1 )
% 0.19/0.45 = ( late_OutputR @ Y2 @ Y1 ) )
% 0.19/0.45 = ( ( X22 = Y2 )
% 0.19/0.45 & ( X1 = Y1 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % Late_Semantics.freeRes.inject
% 0.19/0.45 thf(fact_83_Late__Semantics_Osubject_Oinject_I2_J,axiom,
% 0.19/0.45 ! [X1: name,Y1: name] :
% 0.19/0.45 ( ( ( late_BoundOutputS @ X1 )
% 0.19/0.45 = ( late_BoundOutputS @ Y1 ) )
% 0.19/0.45 = ( X1 = Y1 ) ) ).
% 0.19/0.45
% 0.19/0.45 % Late_Semantics.subject.inject(2)
% 0.19/0.45 thf(fact_84_freeRes_Ofresh_I2_J,axiom,
% 0.19/0.45 ! [A2: name] : ( fresh @ name @ late_freeRes @ A2 @ late_TauR ) ).
% 0.19/0.45
% 0.19/0.45 % freeRes.fresh(2)
% 0.19/0.45 thf(fact_85_freeRes_Operm_I2_J,axiom,
% 0.19/0.45 ! [Pi: list @ ( product_prod @ name @ name )] :
% 0.19/0.45 ( ( perm @ name @ late_freeRes @ Pi @ late_TauR )
% 0.19/0.45 = late_TauR ) ).
% 0.19/0.45
% 0.19/0.45 % freeRes.perm(2)
% 0.19/0.45 thf(fact_86_cComm1_Ohyps_I8_J,axiom,
% 0.19/0.45 fresh @ name @ product_unit @ ya @ product_Unity ).
% 0.19/0.45
% 0.19/0.45 % cComm1.hyps(8)
% 0.19/0.45 thf(fact_87_residual_Ofresh_I2_J,axiom,
% 0.19/0.45 ! [A2: name,X22: late_freeRes,X1: pi] :
% 0.19/0.45 ( ( fresh @ name @ late_residual @ A2 @ ( late_FreeR @ X22 @ X1 ) )
% 0.19/0.45 = ( ( fresh @ name @ late_freeRes @ A2 @ X22 )
% 0.19/0.45 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % residual.fresh(2)
% 0.19/0.45 thf(fact_88_substTrans,axiom,
% 0.19/0.45 ! [B2: name,P: pi,A2: name,C: name] :
% 0.19/0.45 ( ( fresh @ name @ pi @ B2 @ P )
% 0.19/0.45 => ( ( subs @ ( subs @ P @ A2 @ B2 ) @ B2 @ C )
% 0.19/0.45 = ( subs @ P @ A2 @ C ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % substTrans
% 0.19/0.45 thf(fact_89_residual_Operm_I2_J,axiom,
% 0.19/0.45 ! [Pi: list @ ( product_prod @ name @ name ),X22: late_freeRes,X1: pi] :
% 0.19/0.45 ( ( perm @ name @ late_residual @ Pi @ ( late_FreeR @ X22 @ X1 ) )
% 0.19/0.45 = ( late_FreeR @ ( perm @ name @ late_freeRes @ Pi @ X22 ) @ ( perm @ name @ pi @ Pi @ X1 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % residual.perm(2)
% 0.19/0.45 thf(fact_90_freeRes_Operm_I1_J,axiom,
% 0.19/0.45 ! [Pi: list @ ( product_prod @ name @ name ),X22: name,X1: name] :
% 0.19/0.45 ( ( perm @ name @ late_freeRes @ Pi @ ( late_OutputR @ X22 @ X1 ) )
% 0.19/0.45 = ( late_OutputR @ ( perm @ name @ name @ Pi @ X22 ) @ ( perm @ name @ name @ Pi @ X1 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % freeRes.perm(1)
% 0.19/0.45 thf(fact_91_subject_Operm_I1_J,axiom,
% 0.19/0.45 ! [Pi: list @ ( product_prod @ name @ name ),X1: name] :
% 0.19/0.45 ( ( perm @ name @ late_subject @ Pi @ ( late_InputS @ X1 ) )
% 0.19/0.45 = ( late_InputS @ ( perm @ name @ name @ Pi @ X1 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % subject.perm(1)
% 0.19/0.45 thf(fact_92_subject_Operm_I2_J,axiom,
% 0.19/0.45 ! [Pi: list @ ( product_prod @ name @ name ),X1: name] :
% 0.19/0.45 ( ( perm @ name @ late_subject @ Pi @ ( late_BoundOutputS @ X1 ) )
% 0.19/0.45 = ( late_BoundOutputS @ ( perm @ name @ name @ Pi @ X1 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % subject.perm(2)
% 0.19/0.45 thf(fact_93_subject_Ofresh_I2_J,axiom,
% 0.19/0.45 ! [A2: name,X1: name] :
% 0.19/0.45 ( ( fresh @ name @ late_subject @ A2 @ ( late_BoundOutputS @ X1 ) )
% 0.19/0.45 = ( fresh @ name @ name @ A2 @ X1 ) ) ).
% 0.19/0.45
% 0.19/0.45 % subject.fresh(2)
% 0.19/0.45 thf(fact_94_subject_Ofresh_I1_J,axiom,
% 0.19/0.45 ! [A2: name,X1: name] :
% 0.19/0.45 ( ( fresh @ name @ late_subject @ A2 @ ( late_InputS @ X1 ) )
% 0.19/0.45 = ( fresh @ name @ name @ A2 @ X1 ) ) ).
% 0.19/0.45
% 0.19/0.45 % subject.fresh(1)
% 0.19/0.45 thf(fact_95_residual_Operm_I1_J,axiom,
% 0.19/0.45 ! [Pi: list @ ( product_prod @ name @ name ),X32: late_subject,X1: name,X22: pi] :
% 0.19/0.45 ( ( perm @ name @ late_residual @ Pi @ ( late_BoundR @ X32 @ X1 @ X22 ) )
% 0.19/0.45 = ( late_BoundR @ ( perm @ name @ late_subject @ Pi @ X32 ) @ ( perm @ name @ name @ Pi @ X1 ) @ ( perm @ name @ pi @ Pi @ X22 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % residual.perm(1)
% 0.19/0.45 thf(fact_96_name__bij,axiom,
% 0.19/0.45 ! [Pi: list @ ( product_prod @ name @ name ),X2: name,Y: name] :
% 0.19/0.45 ( ( ( perm @ name @ name @ Pi @ X2 )
% 0.19/0.45 = ( perm @ name @ name @ Pi @ Y ) )
% 0.19/0.45 = ( X2 = Y ) ) ).
% 0.19/0.45
% 0.19/0.45 % name_bij
% 0.19/0.45 thf(fact_97_freshResidual,axiom,
% 0.19/0.45 ! [P: pi,Rs: late_residual,X2: name] :
% 0.19/0.45 ( ( late_transitions @ P @ Rs )
% 0.19/0.45 => ( ( fresh @ name @ pi @ X2 @ P )
% 0.19/0.45 => ( fresh @ name @ late_residual @ X2 @ Rs ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % freshResidual
% 0.19/0.45 thf(fact_98_resCasesF,axiom,
% 0.19/0.45 ! [X2: name,P: pi,Alpha: late_freeRes,XP: pi,F2: pi > $o] :
% 0.19/0.45 ( ( late_transitions @ ( res @ X2 @ P ) @ ( late_FreeR @ Alpha @ XP ) )
% 0.19/0.45 => ( ! [P4: pi] :
% 0.19/0.45 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P4 ) )
% 0.19/0.45 => ( ( fresh @ name @ late_freeRes @ X2 @ Alpha )
% 0.19/0.45 => ( F2 @ ( res @ X2 @ P4 ) ) ) )
% 0.19/0.45 => ( F2 @ XP ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % resCasesF
% 0.19/0.45 thf(fact_99_resCasesF_H,axiom,
% 0.19/0.45 ! [X2: name,P: pi,Alpha: late_freeRes,P3: pi] :
% 0.19/0.45 ( ( late_transitions @ ( res @ X2 @ P ) @ ( late_FreeR @ Alpha @ P3 ) )
% 0.19/0.45 => ~ ! [P5: pi,Alpha2: late_freeRes,P4: pi,Y3: name] :
% 0.19/0.45 ( ( ( res @ X2 @ P )
% 0.19/0.45 = ( res @ Y3 @ P5 ) )
% 0.19/0.45 => ( ( ( late_FreeR @ Alpha @ P3 )
% 0.19/0.45 = ( late_FreeR @ Alpha2 @ ( res @ Y3 @ P4 ) ) )
% 0.19/0.45 => ( ( late_transitions @ P5 @ ( late_FreeR @ Alpha2 @ P4 ) )
% 0.19/0.45 => ~ ( fresh @ name @ late_freeRes @ Y3 @ Alpha2 ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % resCasesF'
% 0.19/0.45 thf(fact_100_ResF,axiom,
% 0.19/0.45 ! [P: pi,Alpha: late_freeRes,P3: pi,Y: name] :
% 0.19/0.45 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P3 ) )
% 0.19/0.45 => ( ( fresh @ name @ late_freeRes @ Y @ Alpha )
% 0.19/0.45 => ( late_transitions @ ( res @ Y @ P ) @ ( late_FreeR @ Alpha @ ( res @ Y @ P3 ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % ResF
% 0.19/0.45 thf(fact_101_Late__Semantics_OResB,axiom,
% 0.19/0.45 ! [P: pi,A2: late_subject,X2: name,P3: pi,Y: name] :
% 0.19/0.45 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P3 ) )
% 0.19/0.45 => ( ( fresh @ name @ late_subject @ Y @ A2 )
% 0.19/0.45 => ( ( Y != X2 )
% 0.19/0.45 => ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A2 @ X2 @ ( res @ Y @ P3 ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % Late_Semantics.ResB
% 0.19/0.45 thf(fact_102_freshFreeDerivative_I1_J,axiom,
% 0.19/0.45 ! [P: pi,Alpha: late_freeRes,P3: pi,Y: name] :
% 0.19/0.45 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P3 ) )
% 0.19/0.45 => ( ( fresh @ name @ pi @ Y @ P )
% 0.19/0.45 => ( fresh @ name @ late_freeRes @ Y @ Alpha ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % freshFreeDerivative(1)
% 0.19/0.45 thf(fact_103_freshBoundDerivative_I1_J,axiom,
% 0.19/0.45 ! [P: pi,A2: late_subject,X2: name,P3: pi,Y: name] :
% 0.19/0.45 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P3 ) )
% 0.19/0.45 => ( ( fresh @ name @ pi @ Y @ P )
% 0.19/0.45 => ( fresh @ name @ late_subject @ Y @ A2 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % freshBoundDerivative(1)
% 0.19/0.45 thf(fact_104_transitions_OResB,axiom,
% 0.19/0.45 ! [P: pi,A2: late_subject,X2: name,P3: pi,Y: name] :
% 0.19/0.45 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P3 ) )
% 0.19/0.45 => ( ( fresh @ name @ late_subject @ Y @ A2 )
% 0.19/0.45 => ( ( Y != X2 )
% 0.19/0.45 => ( ( fresh @ name @ pi @ X2 @ P )
% 0.19/0.45 => ( ( fresh @ name @ late_subject @ X2 @ A2 )
% 0.19/0.45 => ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A2 @ X2 @ ( res @ Y @ P3 ) ) ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % transitions.ResB
% 0.19/0.45 thf(fact_105_parCasesB_H,axiom,
% 0.19/0.45 ! [P: pi,Q: pi,B2: late_subject,Y: name,P3: pi] :
% 0.19/0.45 ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ B2 @ Y @ P3 ) )
% 0.19/0.45 => ( ! [P5: pi,A4: late_subject,X5: name,P4: pi,Q3: pi] :
% 0.19/0.45 ( ( ( par @ P @ Q )
% 0.19/0.45 = ( par @ P5 @ Q3 ) )
% 0.19/0.45 => ( ( ( late_BoundR @ B2 @ Y @ P3 )
% 0.19/0.45 = ( late_BoundR @ A4 @ X5 @ ( par @ P4 @ Q3 ) ) )
% 0.19/0.45 => ( ( late_transitions @ P5 @ ( late_BoundR @ A4 @ X5 @ P4 ) )
% 0.19/0.45 => ( ( fresh @ name @ pi @ X5 @ P5 )
% 0.19/0.45 => ( ( fresh @ name @ pi @ X5 @ Q3 )
% 0.19/0.45 => ~ ( fresh @ name @ late_subject @ X5 @ A4 ) ) ) ) ) )
% 0.19/0.45 => ~ ! [Q3: pi,A4: late_subject,X5: name,Q4: pi,P5: pi] :
% 0.19/0.45 ( ( ( par @ P @ Q )
% 0.19/0.45 = ( par @ P5 @ Q3 ) )
% 0.19/0.45 => ( ( ( late_BoundR @ B2 @ Y @ P3 )
% 0.19/0.45 = ( late_BoundR @ A4 @ X5 @ ( par @ P5 @ Q4 ) ) )
% 0.19/0.45 => ( ( late_transitions @ Q3 @ ( late_BoundR @ A4 @ X5 @ Q4 ) )
% 0.19/0.45 => ( ( fresh @ name @ pi @ X5 @ P5 )
% 0.19/0.45 => ( ( fresh @ name @ pi @ X5 @ Q3 )
% 0.19/0.45 => ~ ( fresh @ name @ late_subject @ X5 @ A4 ) ) ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % parCasesB'
% 0.19/0.45 thf(fact_106_transitions_OPar1B,axiom,
% 0.19/0.45 ! [P: pi,A2: late_subject,X2: name,P3: pi,Q: pi] :
% 0.19/0.45 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P3 ) )
% 0.19/0.45 => ( ( fresh @ name @ pi @ X2 @ P )
% 0.19/0.45 => ( ( fresh @ name @ pi @ X2 @ Q )
% 0.19/0.45 => ( ( fresh @ name @ late_subject @ X2 @ A2 )
% 0.19/0.45 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X2 @ ( par @ P3 @ Q ) ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % transitions.Par1B
% 0.19/0.45 thf(fact_107_transitions_OPar2B,axiom,
% 0.19/0.45 ! [Q: pi,A2: late_subject,X2: name,Q2: pi,P: pi] :
% 0.19/0.45 ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X2 @ Q2 ) )
% 0.19/0.45 => ( ( fresh @ name @ pi @ X2 @ P )
% 0.19/0.45 => ( ( fresh @ name @ pi @ X2 @ Q )
% 0.19/0.45 => ( ( fresh @ name @ late_subject @ X2 @ A2 )
% 0.19/0.45 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X2 @ ( par @ P @ Q2 ) ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % transitions.Par2B
% 0.19/0.45 thf(fact_108_resCases_H,axiom,
% 0.19/0.45 ! [X2: name,P: pi,Rs: late_residual] :
% 0.19/0.45 ( ( late_transitions @ ( res @ X2 @ P ) @ Rs )
% 0.19/0.45 => ( ! [P5: pi,A4: name,B3: name] :
% 0.19/0.45 ( ( ( res @ X2 @ P )
% 0.19/0.45 = ( res @ B3 @ P5 ) )
% 0.19/0.45 => ! [P4: pi] :
% 0.19/0.45 ( ( Rs
% 0.19/0.45 = ( late_BoundR @ ( late_BoundOutputS @ A4 ) @ B3 @ P4 ) )
% 0.19/0.45 => ( ( late_transitions @ P5 @ ( late_FreeR @ ( late_OutputR @ A4 @ B3 ) @ P4 ) )
% 0.19/0.45 => ( A4 = B3 ) ) ) )
% 0.19/0.45 => ( ! [P5: pi,A4: late_subject,X5: name,P4: pi,Y3: name] :
% 0.19/0.45 ( ( ( res @ X2 @ P )
% 0.19/0.45 = ( res @ Y3 @ P5 ) )
% 0.19/0.45 => ( ( Rs
% 0.19/0.45 = ( late_BoundR @ A4 @ X5 @ ( res @ Y3 @ P4 ) ) )
% 0.19/0.45 => ( ( late_transitions @ P5 @ ( late_BoundR @ A4 @ X5 @ P4 ) )
% 0.19/0.45 => ( ( fresh @ name @ late_subject @ Y3 @ A4 )
% 0.19/0.45 => ( ( Y3 != X5 )
% 0.19/0.45 => ( ( fresh @ name @ pi @ X5 @ P5 )
% 0.19/0.45 => ~ ( fresh @ name @ late_subject @ X5 @ A4 ) ) ) ) ) ) )
% 0.19/0.45 => ~ ! [P5: pi,Alpha2: late_freeRes,P4: pi,Y3: name] :
% 0.19/0.45 ( ( ( res @ X2 @ P )
% 0.19/0.45 = ( res @ Y3 @ P5 ) )
% 0.19/0.45 => ( ( Rs
% 0.19/0.45 = ( late_FreeR @ Alpha2 @ ( res @ Y3 @ P4 ) ) )
% 0.19/0.45 => ( ( late_transitions @ P5 @ ( late_FreeR @ Alpha2 @ P4 ) )
% 0.19/0.45 => ~ ( fresh @ name @ late_freeRes @ Y3 @ Alpha2 ) ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % resCases'
% 0.19/0.45 thf(fact_109_residual_Oinject_I2_J,axiom,
% 0.19/0.45 ! [X22: late_freeRes,X1: pi,Y2: late_freeRes,Y1: pi] :
% 0.19/0.45 ( ( ( late_FreeR @ X22 @ X1 )
% 0.19/0.45 = ( late_FreeR @ Y2 @ Y1 ) )
% 0.19/0.45 = ( ( X22 = Y2 )
% 0.19/0.45 & ( X1 = Y1 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % residual.inject(2)
% 0.19/0.45 thf(fact_110_resCasesB_H,axiom,
% 0.19/0.45 ! [X7: name,P: pi,A2: late_subject,Y4: name,P3: pi] :
% 0.19/0.45 ( ( late_transitions @ ( res @ X7 @ P ) @ ( late_BoundR @ A2 @ Y4 @ P3 ) )
% 0.19/0.45 => ( ! [P5: pi,A4: name,B3: name] :
% 0.19/0.45 ( ( ( res @ X7 @ P )
% 0.19/0.45 = ( res @ B3 @ P5 ) )
% 0.19/0.45 => ! [P4: pi] :
% 0.19/0.45 ( ( ( late_BoundR @ A2 @ Y4 @ P3 )
% 0.19/0.45 = ( late_BoundR @ ( late_BoundOutputS @ A4 ) @ B3 @ P4 ) )
% 0.19/0.45 => ( ( late_transitions @ P5 @ ( late_FreeR @ ( late_OutputR @ A4 @ B3 ) @ P4 ) )
% 0.19/0.45 => ( A4 = B3 ) ) ) )
% 0.19/0.45 => ~ ! [P5: pi,A4: late_subject,X5: name,P4: pi,Y3: name] :
% 0.19/0.45 ( ( ( res @ X7 @ P )
% 0.19/0.45 = ( res @ Y3 @ P5 ) )
% 0.19/0.45 => ( ( ( late_BoundR @ A2 @ Y4 @ P3 )
% 0.19/0.45 = ( late_BoundR @ A4 @ X5 @ ( res @ Y3 @ P4 ) ) )
% 0.19/0.45 => ( ( late_transitions @ P5 @ ( late_BoundR @ A4 @ X5 @ P4 ) )
% 0.19/0.45 => ( ( fresh @ name @ late_subject @ Y3 @ A4 )
% 0.19/0.45 => ( ( Y3 != X5 )
% 0.19/0.45 => ( ( fresh @ name @ pi @ X5 @ P5 )
% 0.19/0.45 => ~ ( fresh @ name @ late_subject @ X5 @ A4 ) ) ) ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % resCasesB'
% 0.19/0.45 thf(fact_111_residual_Odistinct_I1_J,axiom,
% 0.19/0.45 ! [Subject: late_subject,Name2: name,Pi: pi,FreeRes: late_freeRes,Pi3: pi] :
% 0.19/0.45 ( ( late_BoundR @ Subject @ Name2 @ Pi )
% 0.19/0.45 != ( late_FreeR @ FreeRes @ Pi3 ) ) ).
% 0.19/0.45
% 0.19/0.45 % residual.distinct(1)
% 0.19/0.45 thf(fact_112_residual_Oinducts,axiom,
% 0.19/0.45 ! [P: late_residual > $o,Residual: late_residual] :
% 0.19/0.45 ( ! [Subject2: late_subject,Name3: name,Pi4: pi] : ( P @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) )
% 0.19/0.45 => ( ! [FreeRes2: late_freeRes,Pi4: pi] : ( P @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 0.19/0.45 => ( P @ Residual ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % residual.inducts
% 0.19/0.45 thf(fact_113_eqvt,axiom,
% 0.19/0.45 ! [X1: pi,X22: late_residual,Pi: list @ ( product_prod @ name @ name )] :
% 0.19/0.45 ( ( late_transitions @ X1 @ X22 )
% 0.19/0.45 => ( late_transitions @ ( perm @ name @ pi @ Pi @ X1 ) @ ( perm @ name @ late_residual @ Pi @ X22 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % eqvt
% 0.19/0.45 thf(fact_114_freeRes_Ostrong__inducts,axiom,
% 0.19/0.45 ! [A: $tType,P: A > late_freeRes > $o,Z: A,FreeRes3: late_freeRes] :
% 0.19/0.45 ( ! [Name1: name,Name22: name,Z2: A] : ( P @ Z2 @ ( late_OutputR @ Name1 @ Name22 ) )
% 0.19/0.45 => ( ! [Z2: A] : ( P @ Z2 @ late_TauR )
% 0.19/0.45 => ( P @ Z @ FreeRes3 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % freeRes.strong_inducts
% 0.19/0.45 thf(fact_115_freeRes_Ostrong__induct_H,axiom,
% 0.19/0.45 ! [N: $tType,P: N > late_freeRes > $o,Z: N,FreeRes3: late_freeRes] :
% 0.19/0.45 ( ! [Name1: name,Name22: name,Z2: N] : ( P @ Z2 @ ( late_OutputR @ Name1 @ Name22 ) )
% 0.19/0.45 => ( ! [Z2: N] : ( P @ Z2 @ late_TauR )
% 0.19/0.45 => ( P @ Z @ FreeRes3 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % freeRes.strong_induct'
% 0.19/0.45 thf(fact_116_freeRes_Oinducts,axiom,
% 0.19/0.45 ! [P: late_freeRes > $o,FreeRes3: late_freeRes] :
% 0.19/0.45 ( ! [Name1: name,Name22: name] : ( P @ ( late_OutputR @ Name1 @ Name22 ) )
% 0.19/0.45 => ( ( P @ late_TauR )
% 0.19/0.45 => ( P @ FreeRes3 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % freeRes.inducts
% 0.19/0.45 thf(fact_117_Late__Semantics_OfreeRes_Odistinct_I1_J,axiom,
% 0.19/0.45 ! [Name12: name,Name23: name] :
% 0.19/0.45 ( ( late_OutputR @ Name12 @ Name23 )
% 0.19/0.45 != late_TauR ) ).
% 0.19/0.45
% 0.19/0.45 % Late_Semantics.freeRes.distinct(1)
% 0.19/0.45 thf(fact_118_Late__Semantics_Osubject_Odistinct_I1_J,axiom,
% 0.19/0.45 ! [Name2: name,Name: name] :
% 0.19/0.45 ( ( late_InputS @ Name2 )
% 0.19/0.45 != ( late_BoundOutputS @ Name ) ) ).
% 0.19/0.45
% 0.19/0.45 % Late_Semantics.subject.distinct(1)
% 0.19/0.45 thf(fact_119_subject_Oinducts,axiom,
% 0.19/0.45 ! [P: late_subject > $o,Subject: late_subject] :
% 0.19/0.45 ( ! [Name3: name] : ( P @ ( late_InputS @ Name3 ) )
% 0.19/0.45 => ( ! [Name3: name] : ( P @ ( late_BoundOutputS @ Name3 ) )
% 0.19/0.45 => ( P @ Subject ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % subject.inducts
% 0.19/0.45 thf(fact_120_subject_Ostrong__induct_H,axiom,
% 0.19/0.45 ! [N: $tType,P: N > late_subject > $o,Z: N,Subject: late_subject] :
% 0.19/0.45 ( ! [Name3: name,Z2: N] : ( P @ Z2 @ ( late_InputS @ Name3 ) )
% 0.19/0.45 => ( ! [Name3: name,Z2: N] : ( P @ Z2 @ ( late_BoundOutputS @ Name3 ) )
% 0.19/0.45 => ( P @ Z @ Subject ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % subject.strong_induct'
% 0.19/0.45 thf(fact_121_subject_Ostrong__inducts,axiom,
% 0.19/0.45 ! [A: $tType,P: A > late_subject > $o,Z: A,Subject: late_subject] :
% 0.19/0.45 ( ! [Name3: name,Z2: A] : ( P @ Z2 @ ( late_InputS @ Name3 ) )
% 0.19/0.45 => ( ! [Name3: name,Z2: A] : ( P @ Z2 @ ( late_BoundOutputS @ Name3 ) )
% 0.19/0.45 => ( P @ Z @ Subject ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % subject.strong_inducts
% 0.19/0.45 thf(fact_122_resCasesB,axiom,
% 0.19/0.45 ! [Y: name,P: pi,A2: late_subject,X2: name,YP: pi,F2: late_subject > pi > $o] :
% 0.19/0.45 ( ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A2 @ X2 @ YP ) )
% 0.19/0.45 => ( ( X2 != Y )
% 0.19/0.45 => ( ( fresh @ name @ pi @ X2 @ P )
% 0.19/0.45 => ( ! [B3: name,P4: pi] :
% 0.19/0.45 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ B3 @ Y ) @ P4 ) )
% 0.19/0.45 => ( ( B3 != Y )
% 0.19/0.45 => ( ( A2
% 0.19/0.45 = ( late_BoundOutputS @ B3 ) )
% 0.19/0.45 => ( F2 @ ( late_BoundOutputS @ B3 ) @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ X2 @ Y ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ P4 ) ) ) ) )
% 0.19/0.45 => ( ! [P4: pi] :
% 0.19/0.45 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P4 ) )
% 0.19/0.45 => ( ( fresh @ name @ late_subject @ Y @ A2 )
% 0.19/0.45 => ( F2 @ A2 @ ( res @ Y @ P4 ) ) ) )
% 0.19/0.45 => ( F2 @ A2 @ YP ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % resCasesB
% 0.19/0.45 thf(fact_123_Par1F,axiom,
% 0.19/0.45 ! [P: pi,Alpha: late_freeRes,P3: pi,Q: pi] :
% 0.19/0.45 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P3 ) )
% 0.19/0.45 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha @ ( par @ P3 @ Q ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % Par1F
% 0.19/0.45 thf(fact_124_Par2F,axiom,
% 0.19/0.45 ! [Q: pi,Alpha: late_freeRes,Q2: pi,P: pi] :
% 0.19/0.45 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 0.19/0.45 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha @ ( par @ P @ Q2 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % Par2F
% 0.19/0.45 thf(fact_125_freshBoundDerivative_I2_J,axiom,
% 0.19/0.45 ! [P: pi,A2: late_subject,X2: name,P3: pi,Y: name] :
% 0.19/0.45 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P3 ) )
% 0.19/0.45 => ( ( fresh @ name @ pi @ Y @ P )
% 0.19/0.45 => ( ( Y != X2 )
% 0.19/0.45 => ( fresh @ name @ pi @ Y @ P3 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % freshBoundDerivative(2)
% 0.19/0.45 thf(fact_126_residual_Ostrong__inducts,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( fs_name @ A )
% 0.19/0.45 => ! [P: A > late_residual > $o,Z: A,Residual: late_residual] :
% 0.19/0.45 ( ! [Subject2: late_subject,Name3: name,Pi4: pi,Z2: A] :
% 0.19/0.45 ( ( fresh @ name @ A @ Name3 @ Z2 )
% 0.19/0.45 => ( ( fresh @ name @ late_subject @ Name3 @ Subject2 )
% 0.19/0.45 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) ) ) )
% 0.19/0.45 => ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: A] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 0.19/0.45 => ( P @ Z @ Residual ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % residual.strong_inducts
% 0.19/0.45 thf(fact_127_residual_Ostrong__induct,axiom,
% 0.19/0.45 ! [N: $tType] :
% 0.19/0.45 ( ( fs_name @ N )
% 0.19/0.45 => ! [P: N > late_residual > $o,Z: N,Residual: late_residual] :
% 0.19/0.45 ( ! [Subject2: late_subject,Name3: name,Pi4: pi,Z2: N] :
% 0.19/0.45 ( ( fresh @ name @ N @ Name3 @ Z2 )
% 0.19/0.45 => ( ( fresh @ name @ late_subject @ Name3 @ Subject2 )
% 0.19/0.45 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) ) ) )
% 0.19/0.45 => ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: N] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 0.19/0.45 => ( P @ Z @ Residual ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % residual.strong_induct
% 0.19/0.45 thf(fact_128_freshFreeDerivative_I2_J,axiom,
% 0.19/0.45 ! [P: pi,Alpha: late_freeRes,P3: pi,Y: name] :
% 0.19/0.45 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P3 ) )
% 0.19/0.45 => ( ( fresh @ name @ pi @ Y @ P )
% 0.19/0.45 => ( fresh @ name @ pi @ Y @ P3 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % freshFreeDerivative(2)
% 0.19/0.45 thf(fact_129_Late__Semantics_OPar1B,axiom,
% 0.19/0.45 ! [P: pi,A2: late_subject,X2: name,P3: pi,Q: pi] :
% 0.19/0.45 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P3 ) )
% 0.19/0.45 => ( ( fresh @ name @ pi @ X2 @ Q )
% 0.19/0.45 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X2 @ ( par @ P3 @ Q ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % Late_Semantics.Par1B
% 0.19/0.45 thf(fact_130_Late__Semantics_OPar2B,axiom,
% 0.19/0.45 ! [Q: pi,A2: late_subject,X2: name,Q2: pi,P: pi] :
% 0.19/0.45 ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X2 @ Q2 ) )
% 0.19/0.45 => ( ( fresh @ name @ pi @ X2 @ P )
% 0.19/0.45 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X2 @ ( par @ P @ Q2 ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % Late_Semantics.Par2B
% 0.19/0.45 thf(fact_131_parCasesB,axiom,
% 0.19/0.45 ! [P: pi,Q: pi,A2: late_subject,X2: name,PQ: pi,Prop: pi > $o] :
% 0.19/0.45 ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X2 @ PQ ) )
% 0.19/0.45 => ( ( fresh @ name @ pi @ X2 @ P )
% 0.19/0.45 => ( ( fresh @ name @ pi @ X2 @ Q )
% 0.19/0.45 => ( ! [P4: pi] :
% 0.19/0.45 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P4 ) )
% 0.19/0.45 => ( Prop @ ( par @ P4 @ Q ) ) )
% 0.19/0.45 => ( ! [Q4: pi] :
% 0.19/0.45 ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X2 @ Q4 ) )
% 0.19/0.45 => ( Prop @ ( par @ P @ Q4 ) ) )
% 0.19/0.45 => ( Prop @ PQ ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % parCasesB
% 0.19/0.45 thf(fact_132_Open,axiom,
% 0.19/0.45 ! [P: pi,A2: name,B2: name,P3: pi] :
% 0.19/0.45 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P3 ) )
% 0.19/0.45 => ( ( A2 != B2 )
% 0.19/0.45 => ( late_transitions @ ( res @ B2 @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ B2 @ P3 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % Open
% 0.19/0.45 thf(fact_133_derivativeEqvtI2,axiom,
% 0.19/0.45 ! [P: pi,Q: pi,A2: late_subject,X2: name,Rel: set @ ( product_prod @ pi @ pi ),Perm: list @ ( product_prod @ name @ name )] :
% 0.19/0.45 ( ( strong2129052853vative @ P @ Q @ A2 @ X2 @ Rel )
% 0.19/0.45 => ( ( eqvt @ pi @ Rel )
% 0.19/0.45 => ( strong2129052853vative @ ( perm @ name @ pi @ Perm @ P ) @ ( perm @ name @ pi @ Perm @ Q ) @ A2 @ ( perm @ name @ name @ Perm @ X2 ) @ Rel ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % derivativeEqvtI2
% 0.19/0.45 thf(fact_134_derivativeEqvtI,axiom,
% 0.19/0.45 ! [P: pi,Q: pi,A2: late_subject,X2: name,Rel: set @ ( product_prod @ pi @ pi ),Perm: list @ ( product_prod @ name @ name )] :
% 0.19/0.45 ( ( strong2129052853vative @ P @ Q @ A2 @ X2 @ Rel )
% 0.19/0.45 => ( ( eqvt @ pi @ Rel )
% 0.19/0.45 => ( strong2129052853vative @ ( perm @ name @ pi @ Perm @ P ) @ ( perm @ name @ pi @ Perm @ Q ) @ ( perm @ name @ late_subject @ Perm @ A2 ) @ ( perm @ name @ name @ Perm @ X2 ) @ Rel ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % derivativeEqvtI
% 0.19/0.45 thf(fact_135_fresh__prod,axiom,
% 0.19/0.45 ! [A: $tType,X: $tType,B: $tType,A2: X,X2: A,Y: B] :
% 0.19/0.45 ( ( fresh @ X @ ( product_prod @ A @ B ) @ A2 @ ( product_Pair @ A @ B @ X2 @ Y ) )
% 0.19/0.45 = ( ( fresh @ X @ A @ A2 @ X2 )
% 0.19/0.45 & ( fresh @ X @ B @ A2 @ Y ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % fresh_prod
% 0.19/0.45 thf(fact_136_Res,axiom,
% 0.19/0.45 ! [Y: name,R: pi,S: pi] :
% 0.19/0.45 ( ( fresh @ name @ pi @ Y @ R )
% 0.19/0.45 => ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( par @ R @ ( res @ Y @ S ) ) @ ( res @ Y @ ( par @ R @ S ) ) ) @ rel ) ) ).
% 0.19/0.45
% 0.19/0.45 % Res
% 0.19/0.45 thf(fact_137_ScopeExt,axiom,
% 0.19/0.45 ! [Y: name,R: pi,Z: name,S: pi] :
% 0.19/0.45 ( ( fresh @ name @ pi @ Y @ R )
% 0.19/0.45 => ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( res @ Z @ ( par @ R @ ( res @ Y @ S ) ) ) @ ( res @ Y @ ( res @ Z @ ( par @ R @ S ) ) ) ) @ rel ) ) ).
% 0.19/0.45
% 0.19/0.45 % ScopeExt
% 0.19/0.45 thf(fact_138_fresh__list__cons,axiom,
% 0.19/0.45 ! [X: $tType,A: $tType,A2: X,X2: A,Xs: list @ A] :
% 0.19/0.45 ( ( fresh @ X @ ( list @ A ) @ A2 @ ( cons @ A @ X2 @ Xs ) )
% 0.19/0.45 = ( ( fresh @ X @ A @ A2 @ X2 )
% 0.19/0.45 & ( fresh @ X @ ( list @ A ) @ A2 @ Xs ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % fresh_list_cons
% 0.19/0.45 thf(fact_139_Bound_Ohyps_I5_J,axiom,
% 0.19/0.45 fresh @ name @ ( product_prod @ name @ ( product_prod @ pi @ pi ) ) @ y @ ( product_Pair @ name @ ( product_prod @ pi @ pi ) @ x @ ( product_Pair @ pi @ pi @ p @ q ) ) ).
% 0.19/0.45
% 0.19/0.45 % Bound.hyps(5)
% 0.19/0.45 thf(fact_140_false__eqvt,axiom,
% 0.19/0.45 ! [A: $tType,Pi: list @ ( product_prod @ A @ A )] :
% 0.19/0.45 ~ ( perm @ A @ $o @ Pi @ $false ) ).
% 0.19/0.45
% 0.19/0.45 % false_eqvt
% 0.19/0.45 thf(fact_141_true__eqvt,axiom,
% 0.19/0.45 ! [A: $tType,Pi: list @ ( product_prod @ A @ A )] : ( perm @ A @ $o @ Pi @ $true ) ).
% 0.19/0.45
% 0.19/0.45 % true_eqvt
% 0.19/0.45 thf(fact_142_name__fresh,axiom,
% 0.19/0.45 ( ( fresh @ name @ name )
% 0.19/0.45 = ( ^ [A5: name,B4: name] : ( A5 != B4 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % name_fresh
% 0.19/0.45 thf(fact_143_fresh__unit,axiom,
% 0.19/0.45 ! [A: $tType,A2: A] : ( fresh @ A @ product_unit @ A2 @ product_Unity ) ).
% 0.19/0.45
% 0.19/0.45 % fresh_unit
% 0.19/0.45 thf(fact_144_freshUnit,axiom,
% 0.19/0.45 ! [Y: name] : ( fresh @ name @ product_unit @ Y @ product_Unity ) ).
% 0.19/0.45
% 0.19/0.45 % freshUnit
% 0.19/0.45 thf(fact_145_allE__Nil,axiom,
% 0.19/0.45 ! [A: $tType,P: ( list @ A ) > $o] :
% 0.19/0.45 ( ! [X_1: list @ A] : ( P @ X_1 )
% 0.19/0.45 => ( P @ ( nil @ A ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % allE_Nil
% 0.19/0.45 thf(fact_146_abs__fun__if,axiom,
% 0.19/0.45 ! [X: $tType,A: $tType,C: $o,Pi: list @ ( product_prod @ X @ X ),X2: A,Y: A] :
% 0.19/0.45 ( ( C
% 0.19/0.45 => ( ( perm @ X @ A @ Pi @ ( if @ A @ C @ X2 @ Y ) )
% 0.19/0.45 = ( perm @ X @ A @ Pi @ X2 ) ) )
% 0.19/0.45 & ( ~ C
% 0.19/0.45 => ( ( perm @ X @ A @ Pi @ ( if @ A @ C @ X2 @ Y ) )
% 0.19/0.45 = ( perm @ X @ A @ Pi @ Y ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % abs_fun_if
% 0.19/0.45 thf(fact_147_pt__bij3,axiom,
% 0.19/0.45 ! [X: $tType,A: $tType,X2: A,Y: A,Pi: list @ ( product_prod @ X @ X )] :
% 0.19/0.45 ( ( X2 = Y )
% 0.19/0.45 => ( ( perm @ X @ A @ Pi @ X2 )
% 0.19/0.45 = ( perm @ X @ A @ Pi @ Y ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % pt_bij3
% 0.19/0.45 thf(fact_148_perm__bool__def,axiom,
% 0.19/0.45 ! [X: $tType] :
% 0.19/0.45 ( ( perm @ X @ $o )
% 0.19/0.45 = ( ^ [Pi5: list @ ( product_prod @ X @ X ),B4: $o] : B4 ) ) ).
% 0.19/0.45
% 0.19/0.45 % perm_bool_def
% 0.19/0.45 thf(fact_149_pt__set__bij3,axiom,
% 0.19/0.45 ! [X: $tType,A: $tType,Pi: list @ ( product_prod @ X @ X ),X2: A,X6: set @ A] :
% 0.19/0.45 ( ( perm @ X @ $o @ Pi @ ( member @ A @ X2 @ X6 ) )
% 0.19/0.45 = ( member @ A @ X2 @ X6 ) ) ).
% 0.19/0.45
% 0.19/0.45 % pt_set_bij3
% 0.19/0.45 thf(fact_150_perm__boolI,axiom,
% 0.19/0.45 ! [A: $tType,P: $o,Pi: list @ ( product_prod @ A @ A )] :
% 0.19/0.45 ( P
% 0.19/0.45 => ( perm @ A @ $o @ Pi @ P ) ) ).
% 0.19/0.45
% 0.19/0.45 % perm_boolI
% 0.19/0.45 thf(fact_151_perm__boolE,axiom,
% 0.19/0.45 ! [A: $tType,Pi: list @ ( product_prod @ A @ A )] :
% 0.19/0.45 ~ ( perm @ A @ $o @ Pi @ $false ) ).
% 0.19/0.45
% 0.19/0.45 % perm_boolE
% 0.19/0.45 thf(fact_152_disj__eqvt,axiom,
% 0.19/0.45 ! [A: $tType,Pi: list @ ( product_prod @ A @ A ),A3: $o,B5: $o] :
% 0.19/0.45 ( ( perm @ A @ $o @ Pi
% 0.19/0.45 @ ( A3
% 0.19/0.45 | B5 ) )
% 0.19/0.45 = ( ( perm @ A @ $o @ Pi @ A3 )
% 0.19/0.45 | ( perm @ A @ $o @ Pi @ B5 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % disj_eqvt
% 0.19/0.45 thf(fact_153_conj__eqvt,axiom,
% 0.19/0.45 ! [A: $tType,Pi: list @ ( product_prod @ A @ A ),A3: $o,B5: $o] :
% 0.19/0.45 ( ( perm @ A @ $o @ Pi
% 0.19/0.45 @ ( A3
% 0.19/0.45 & B5 ) )
% 0.19/0.45 = ( ( perm @ A @ $o @ Pi @ A3 )
% 0.19/0.45 & ( perm @ A @ $o @ Pi @ B5 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % conj_eqvt
% 0.19/0.45 thf(fact_154_neg__eqvt,axiom,
% 0.19/0.45 ! [A: $tType,Pi: list @ ( product_prod @ A @ A ),A3: $o] :
% 0.19/0.45 ( ( perm @ A @ $o @ Pi @ ~ A3 )
% 0.19/0.45 = ( ~ ( perm @ A @ $o @ Pi @ A3 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % neg_eqvt
% 0.19/0.45 thf(fact_155_imp__eqvt,axiom,
% 0.19/0.45 ! [A: $tType,Pi: list @ ( product_prod @ A @ A ),A3: $o,B5: $o] :
% 0.19/0.45 ( ( perm @ A @ $o @ Pi
% 0.19/0.45 @ ( A3
% 0.19/0.45 => B5 ) )
% 0.19/0.45 = ( ( perm @ A @ $o @ Pi @ A3 )
% 0.19/0.45 => ( perm @ A @ $o @ Pi @ B5 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % imp_eqvt
% 0.19/0.45 thf(fact_156_perm__prod_Osimps,axiom,
% 0.19/0.45 ! [A: $tType,X: $tType,B: $tType,Pi: list @ ( product_prod @ X @ X ),X2: A,Y: B] :
% 0.19/0.45 ( ( perm @ X @ ( product_prod @ A @ B ) @ Pi @ ( product_Pair @ A @ B @ X2 @ Y ) )
% 0.19/0.45 = ( product_Pair @ A @ B @ ( perm @ X @ A @ Pi @ X2 ) @ ( perm @ X @ B @ Pi @ Y ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % perm_prod.simps
% 0.19/0.45 thf(fact_157_fresh__prodD_I2_J,axiom,
% 0.19/0.45 ! [B: $tType,A: $tType,C3: $tType,A2: A,X2: B,Y: C3] :
% 0.19/0.45 ( ( fresh @ A @ ( product_prod @ B @ C3 ) @ A2 @ ( product_Pair @ B @ C3 @ X2 @ Y ) )
% 0.19/0.45 => ( fresh @ A @ C3 @ A2 @ Y ) ) ).
% 0.19/0.45
% 0.19/0.45 % fresh_prodD(2)
% 0.19/0.45 thf(fact_158_fresh__prodD_I1_J,axiom,
% 0.19/0.45 ! [C3: $tType,A: $tType,B: $tType,A2: A,X2: B,Y: C3] :
% 0.19/0.45 ( ( fresh @ A @ ( product_prod @ B @ C3 ) @ A2 @ ( product_Pair @ B @ C3 @ X2 @ Y ) )
% 0.19/0.45 => ( fresh @ A @ B @ A2 @ X2 ) ) ).
% 0.19/0.45
% 0.19/0.45 % fresh_prodD(1)
% 0.19/0.45 thf(fact_159_if__eqvt,axiom,
% 0.19/0.45 ! [A: $tType,B: $tType,Pi: list @ ( product_prod @ A @ A ),B2: $o,C1: B,C22: B] :
% 0.19/0.45 ( ( ( perm @ A @ $o @ Pi @ B2 )
% 0.19/0.45 => ( ( perm @ A @ B @ Pi @ ( if @ B @ B2 @ C1 @ C22 ) )
% 0.19/0.45 = ( perm @ A @ B @ Pi @ C1 ) ) )
% 0.19/0.45 & ( ~ ( perm @ A @ $o @ Pi @ B2 )
% 0.19/0.45 => ( ( perm @ A @ B @ Pi @ ( if @ B @ B2 @ C1 @ C22 ) )
% 0.19/0.45 = ( perm @ A @ B @ Pi @ C22 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % if_eqvt
% 0.19/0.45 thf(fact_160_nil__eqvt,axiom,
% 0.19/0.45 ! [X: $tType,A: $tType,Pi: list @ ( product_prod @ X @ X )] :
% 0.19/0.45 ( ( perm @ X @ ( list @ A ) @ Pi @ ( nil @ A ) )
% 0.19/0.45 = ( nil @ A ) ) ).
% 0.19/0.45
% 0.19/0.45 % nil_eqvt
% 0.19/0.45 thf(fact_161_fresh__list__nil,axiom,
% 0.19/0.45 ! [X: $tType,A: $tType,A2: X] : ( fresh @ X @ ( list @ A ) @ A2 @ ( nil @ A ) ) ).
% 0.19/0.45
% 0.19/0.45 % fresh_list_nil
% 0.19/0.45 thf(fact_162_cons__eqvt,axiom,
% 0.19/0.45 ! [X: $tType,A: $tType,Pi: list @ ( product_prod @ X @ X ),X2: A,Xs: list @ A] :
% 0.19/0.45 ( ( perm @ X @ ( list @ A ) @ Pi @ ( cons @ A @ X2 @ Xs ) )
% 0.19/0.45 = ( cons @ A @ ( perm @ X @ A @ Pi @ X2 ) @ ( perm @ X @ ( list @ A ) @ Pi @ Xs ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % cons_eqvt
% 0.19/0.45 thf(fact_163_resSimCases,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( fs_name @ A )
% 0.19/0.45 => ! [Rel: set @ ( product_prod @ pi @ pi ),Q: pi,X2: name,P: pi,C4: A] :
% 0.19/0.45 ( ( eqvt @ pi @ Rel )
% 0.19/0.45 => ( ! [Q4: pi,A4: name] :
% 0.19/0.45 ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A4 @ X2 ) @ Q4 ) )
% 0.19/0.45 => ( ( A4 != X2 )
% 0.19/0.45 => ? [P6: pi] :
% 0.19/0.45 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A4 ) @ X2 @ P6 ) )
% 0.19/0.45 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P6 @ Q4 ) @ Rel ) ) ) )
% 0.19/0.45 => ( ! [Q4: pi,A4: late_subject,Y3: name] :
% 0.19/0.45 ( ( late_transitions @ Q @ ( late_BoundR @ A4 @ Y3 @ Q4 ) )
% 0.19/0.45 => ( ( fresh @ name @ late_subject @ X2 @ A4 )
% 0.19/0.45 => ( ( X2 != Y3 )
% 0.19/0.45 => ( ( fresh @ name @ A @ Y3 @ C4 )
% 0.19/0.45 => ? [P6: pi] :
% 0.19/0.45 ( ( late_transitions @ P @ ( late_BoundR @ A4 @ Y3 @ P6 ) )
% 0.19/0.45 & ( strong2129052853vative @ P6 @ ( res @ X2 @ Q4 ) @ A4 @ Y3 @ Rel ) ) ) ) ) )
% 0.19/0.45 => ( ! [Q4: pi,Alpha2: late_freeRes] :
% 0.19/0.45 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 0.19/0.45 => ( ( fresh @ name @ late_freeRes @ X2 @ Alpha2 )
% 0.19/0.45 => ? [P6: pi] :
% 0.19/0.45 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 0.19/0.45 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P6 @ ( res @ X2 @ Q4 ) ) @ Rel ) ) ) )
% 0.19/0.45 => ( strong743114133lation @ P @ Rel @ ( res @ X2 @ Q ) ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % resSimCases
% 0.19/0.45 thf(fact_164_simCasesCont,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( fs_name @ A )
% 0.19/0.45 => ! [Rel: set @ ( product_prod @ pi @ pi ),Q: pi,P: pi,C4: A] :
% 0.19/0.45 ( ( eqvt @ pi @ Rel )
% 0.19/0.45 => ( ! [A4: late_subject,X5: name,Q4: pi] :
% 0.19/0.45 ( ( late_transitions @ Q @ ( late_BoundR @ A4 @ X5 @ Q4 ) )
% 0.19/0.45 => ( ( fresh @ name @ pi @ X5 @ P )
% 0.19/0.45 => ( ( fresh @ name @ pi @ X5 @ Q )
% 0.19/0.45 => ( ( fresh @ name @ late_subject @ X5 @ A4 )
% 0.19/0.45 => ( ( fresh @ name @ A @ X5 @ C4 )
% 0.19/0.45 => ? [P6: pi] :
% 0.19/0.45 ( ( late_transitions @ P @ ( late_BoundR @ A4 @ X5 @ P6 ) )
% 0.19/0.45 & ( strong2129052853vative @ P6 @ Q4 @ A4 @ X5 @ Rel ) ) ) ) ) ) )
% 0.19/0.45 => ( ! [Alpha2: late_freeRes,Q4: pi] :
% 0.19/0.45 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 0.19/0.45 => ? [P6: pi] :
% 0.19/0.45 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 0.19/0.45 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P6 @ Q4 ) @ Rel ) ) )
% 0.19/0.45 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % simCasesCont
% 0.19/0.45 thf(fact_165_eqvtRelI,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( pt_name @ A )
% 0.19/0.45 => ! [Rel: set @ ( product_prod @ A @ A ),P: A,Q: A,Perm: list @ ( product_prod @ name @ name )] :
% 0.19/0.45 ( ( eqvt @ A @ Rel )
% 0.19/0.45 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ P @ Q ) @ Rel )
% 0.19/0.45 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ ( perm @ name @ A @ Perm @ P ) @ ( perm @ name @ A @ Perm @ Q ) ) @ Rel ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % eqvtRelI
% 0.19/0.45 thf(fact_166_eqvtRelE,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( pt_name @ A )
% 0.19/0.45 => ! [Rel: set @ ( product_prod @ A @ A ),Perm: list @ ( product_prod @ name @ name ),P: A,Q: A] :
% 0.19/0.45 ( ( eqvt @ A @ Rel )
% 0.19/0.45 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ ( perm @ name @ A @ Perm @ P ) @ ( perm @ name @ A @ Perm @ Q ) ) @ Rel )
% 0.19/0.45 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ P @ Q ) @ Rel ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % eqvtRelE
% 0.19/0.45 thf(fact_167_perm__unit_Osimps,axiom,
% 0.19/0.45 ! [X: $tType,Pi: list @ ( product_prod @ X @ X )] :
% 0.19/0.45 ( ( perm @ X @ product_unit @ Pi @ product_Unity )
% 0.19/0.45 = product_Unity ) ).
% 0.19/0.45
% 0.19/0.45 % perm_unit.simps
% 0.19/0.45 thf(fact_168_parSym,axiom,
% 0.19/0.45 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi,Q: pi] :
% 0.19/0.45 ( ! [R2: pi,S2: pi] : ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( par @ R2 @ S2 ) @ ( par @ S2 @ R2 ) ) @ Rel )
% 0.19/0.45 => ( ! [R2: pi,S2: pi,X5: name] :
% 0.19/0.45 ( ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ R2 @ S2 ) @ Rel )
% 0.19/0.45 => ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( res @ X5 @ R2 ) @ ( res @ X5 @ S2 ) ) @ Rel ) )
% 0.19/0.45 => ( strong743114133lation @ ( par @ P @ Q ) @ Rel @ ( par @ Q @ P ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % parSym
% 0.19/0.45 thf(fact_169_simE_I2_J,axiom,
% 0.19/0.45 ! [P: pi,Rel: set @ ( product_prod @ pi @ pi ),Q: pi,Alpha: late_freeRes,Q2: pi] :
% 0.19/0.45 ( ( strong743114133lation @ P @ Rel @ Q )
% 0.19/0.45 => ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 0.19/0.45 => ? [P4: pi] :
% 0.19/0.45 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P4 ) )
% 0.19/0.45 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P4 @ Q2 ) @ Rel ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % simE(2)
% 0.19/0.45 thf(fact_170_eqvt__def,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( pt_name @ A )
% 0.19/0.45 => ( ( eqvt @ A )
% 0.19/0.45 = ( ^ [Rel2: set @ ( product_prod @ A @ A )] :
% 0.19/0.45 ! [X4: product_prod @ A @ A,Perm2: list @ ( product_prod @ name @ name )] :
% 0.19/0.45 ( ( member @ ( product_prod @ A @ A ) @ X4 @ Rel2 )
% 0.19/0.45 => ( member @ ( product_prod @ A @ A ) @ ( perm @ name @ ( product_prod @ A @ A ) @ Perm2 @ X4 ) @ Rel2 ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % eqvt_def
% 0.19/0.45 thf(fact_171_parAssocLeft,axiom,
% 0.19/0.45 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi,Q: pi,R: pi] :
% 0.19/0.45 ( ! [S2: pi,T2: pi,U: pi] : ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( par @ ( par @ S2 @ T2 ) @ U ) @ ( par @ S2 @ ( par @ T2 @ U ) ) ) @ Rel )
% 0.19/0.45 => ( ! [S2: pi,T2: pi,X5: name] :
% 0.19/0.45 ( ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ S2 @ T2 ) @ Rel )
% 0.19/0.45 => ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( res @ X5 @ S2 ) @ ( res @ X5 @ T2 ) ) @ Rel ) )
% 0.19/0.45 => ( ! [S2: pi,T2: pi,U: pi,X5: name] :
% 0.19/0.45 ( ( fresh @ name @ pi @ X5 @ S2 )
% 0.19/0.45 => ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( res @ X5 @ ( par @ ( par @ S2 @ T2 ) @ U ) ) @ ( par @ S2 @ ( res @ X5 @ ( par @ T2 @ U ) ) ) ) @ Rel ) )
% 0.19/0.45 => ( ! [S2: pi,T2: pi,U: pi,X5: name] :
% 0.19/0.45 ( ( fresh @ name @ pi @ X5 @ U )
% 0.19/0.45 => ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( par @ ( res @ X5 @ ( par @ S2 @ T2 ) ) @ U ) @ ( res @ X5 @ ( par @ S2 @ ( par @ T2 @ U ) ) ) ) @ Rel ) )
% 0.19/0.45 => ( strong743114133lation @ ( par @ ( par @ P @ Q ) @ R ) @ Rel @ ( par @ P @ ( par @ Q @ R ) ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % parAssocLeft
% 0.19/0.45 thf(fact_172_simE_I1_J,axiom,
% 0.19/0.45 ! [P: pi,Rel: set @ ( product_prod @ pi @ pi ),Q: pi,A2: late_subject,X2: name,Q2: pi] :
% 0.19/0.45 ( ( strong743114133lation @ P @ Rel @ Q )
% 0.19/0.45 => ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X2 @ Q2 ) )
% 0.19/0.45 => ( ( fresh @ name @ pi @ X2 @ P )
% 0.19/0.45 => ? [P4: pi] :
% 0.19/0.45 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P4 ) )
% 0.19/0.45 & ( strong2129052853vative @ P4 @ Q2 @ A2 @ X2 @ Rel ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % simE(1)
% 0.19/0.45 thf(fact_173_simCases,axiom,
% 0.19/0.45 ! [Q: pi,P: pi,Rel: set @ ( product_prod @ pi @ pi )] :
% 0.19/0.45 ( ! [A4: late_subject,Y3: name,Q4: pi] :
% 0.19/0.45 ( ( late_transitions @ Q @ ( late_BoundR @ A4 @ Y3 @ Q4 ) )
% 0.19/0.45 => ( ( fresh @ name @ pi @ Y3 @ P )
% 0.19/0.45 => ? [P6: pi] :
% 0.19/0.45 ( ( late_transitions @ P @ ( late_BoundR @ A4 @ Y3 @ P6 ) )
% 0.19/0.45 & ( strong2129052853vative @ P6 @ Q4 @ A4 @ Y3 @ Rel ) ) ) )
% 0.19/0.45 => ( ! [Alpha2: late_freeRes,Q4: pi] :
% 0.19/0.45 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 0.19/0.45 => ? [P6: pi] :
% 0.19/0.45 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 0.19/0.45 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P6 @ Q4 ) @ Rel ) ) )
% 0.19/0.45 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % simCases
% 0.19/0.45 thf(fact_174_simulation__def,axiom,
% 0.19/0.45 ( strong743114133lation
% 0.19/0.45 = ( ^ [P7: pi,Rel2: set @ ( product_prod @ pi @ pi ),Q5: pi] :
% 0.19/0.45 ( ! [A5: late_subject,X4: name,Q6: pi] :
% 0.19/0.45 ( ( ( late_transitions @ Q5 @ ( late_BoundR @ A5 @ X4 @ Q6 ) )
% 0.19/0.45 & ( fresh @ name @ pi @ X4 @ P7 ) )
% 0.19/0.45 => ? [P8: pi] :
% 0.19/0.45 ( ( late_transitions @ P7 @ ( late_BoundR @ A5 @ X4 @ P8 ) )
% 0.19/0.45 & ( strong2129052853vative @ P8 @ Q6 @ A5 @ X4 @ Rel2 ) ) )
% 0.19/0.45 & ! [Alpha3: late_freeRes,Q6: pi] :
% 0.19/0.45 ( ( late_transitions @ Q5 @ ( late_FreeR @ Alpha3 @ Q6 ) )
% 0.19/0.45 => ? [P8: pi] :
% 0.19/0.45 ( ( late_transitions @ P7 @ ( late_FreeR @ Alpha3 @ P8 ) )
% 0.19/0.45 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P8 @ Q6 ) @ Rel2 ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % simulation_def
% 0.19/0.45 thf(fact_175_Late__Semantics1_Osubject_Oinject_I2_J,axiom,
% 0.19/0.45 ! [X22: name,Y2: name] :
% 0.19/0.45 ( ( ( late_BoundOutputS @ X22 )
% 0.19/0.45 = ( late_BoundOutputS @ Y2 ) )
% 0.19/0.45 = ( X22 = Y2 ) ) ).
% 0.19/0.45
% 0.19/0.45 % Late_Semantics1.subject.inject(2)
% 0.19/0.45 thf(fact_176_Late__Semantics1_Osubject_Oinject_I1_J,axiom,
% 0.19/0.45 ! [X1: name,Y1: name] :
% 0.19/0.45 ( ( ( late_InputS @ X1 )
% 0.19/0.45 = ( late_InputS @ Y1 ) )
% 0.19/0.45 = ( X1 = Y1 ) ) ).
% 0.19/0.45
% 0.19/0.45 % Late_Semantics1.subject.inject(1)
% 0.19/0.45 thf(fact_177_Late__Semantics1_OfreeRes_Oinject,axiom,
% 0.19/0.45 ! [X11: name,X12: name,Y11: name,Y12: name] :
% 0.19/0.45 ( ( ( late_OutputR @ X11 @ X12 )
% 0.19/0.45 = ( late_OutputR @ Y11 @ Y12 ) )
% 0.19/0.45 = ( ( X11 = Y11 )
% 0.19/0.45 & ( X12 = Y12 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % Late_Semantics1.freeRes.inject
% 0.19/0.45 thf(fact_178_Late__Semantics1_OfreeRes_Odistinct_I1_J,axiom,
% 0.19/0.45 ! [X11: name,X12: name] :
% 0.19/0.45 ( ( late_OutputR @ X11 @ X12 )
% 0.19/0.45 != late_TauR ) ).
% 0.19/0.45
% 0.19/0.45 % Late_Semantics1.freeRes.distinct(1)
% 0.19/0.45 thf(fact_179_freeRes_Oexhaust,axiom,
% 0.19/0.45 ! [Y: late_freeRes] :
% 0.19/0.45 ( ! [X112: name,X122: name] :
% 0.19/0.45 ( Y
% 0.19/0.45 != ( late_OutputR @ X112 @ X122 ) )
% 0.19/0.45 => ( Y = late_TauR ) ) ).
% 0.19/0.45
% 0.19/0.45 % freeRes.exhaust
% 0.19/0.45 thf(fact_180_subject_Oexhaust,axiom,
% 0.19/0.45 ! [Y: late_subject] :
% 0.19/0.45 ( ! [X13: name] :
% 0.19/0.45 ( Y
% 0.19/0.45 != ( late_InputS @ X13 ) )
% 0.19/0.45 => ~ ! [X23: name] :
% 0.19/0.45 ( Y
% 0.19/0.45 != ( late_BoundOutputS @ X23 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % subject.exhaust
% 0.19/0.45 thf(fact_181_Late__Semantics1_Osubject_Odistinct_I1_J,axiom,
% 0.19/0.45 ! [X1: name,X22: name] :
% 0.19/0.45 ( ( late_InputS @ X1 )
% 0.19/0.45 != ( late_BoundOutputS @ X22 ) ) ).
% 0.19/0.45
% 0.19/0.45 % Late_Semantics1.subject.distinct(1)
% 0.19/0.45 thf(fact_182_inputCases,axiom,
% 0.19/0.45 ! [A2: name,X2: name,P: pi,B2: late_subject,Y: name,YP: pi,Prop: late_subject > name > pi > $o] :
% 0.19/0.45 ( ( late_transitions @ ( input @ A2 @ X2 @ P ) @ ( late_BoundR @ B2 @ Y @ YP ) )
% 0.19/0.45 => ( ( Y != A2 )
% 0.19/0.45 => ( ( Y != X2 )
% 0.19/0.45 => ( ( fresh @ name @ pi @ Y @ P )
% 0.19/0.45 => ( ( ( B2
% 0.19/0.45 = ( late_InputS @ A2 ) )
% 0.19/0.45 => ( ( YP
% 0.19/0.45 = ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ X2 @ Y ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ P ) )
% 0.19/0.45 => ( Prop @ ( late_InputS @ A2 ) @ Y @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ X2 @ Y ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ P ) ) ) )
% 0.19/0.45 => ( Prop @ B2 @ Y @ YP ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % inputCases
% 0.19/0.45 thf(fact_183_list_Oinject,axiom,
% 0.19/0.45 ! [A: $tType,X21: A,X222: list @ A,Y21: A,Y22: list @ A] :
% 0.19/0.45 ( ( ( cons @ A @ X21 @ X222 )
% 0.19/0.45 = ( cons @ A @ Y21 @ Y22 ) )
% 0.19/0.45 = ( ( X21 = Y21 )
% 0.19/0.45 & ( X222 = Y22 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % list.inject
% 0.19/0.45 thf(fact_184_old_Oprod_Oinject,axiom,
% 0.19/0.45 ! [A: $tType,B: $tType,A2: A,B2: B,A6: A,B6: B] :
% 0.19/0.45 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 0.19/0.45 = ( product_Pair @ A @ B @ A6 @ B6 ) )
% 0.19/0.45 = ( ( A2 = A6 )
% 0.19/0.45 & ( B2 = B6 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % old.prod.inject
% 0.19/0.45 thf(fact_185_prod_Oinject,axiom,
% 0.19/0.45 ! [A: $tType,B: $tType,X1: A,X22: B,Y1: A,Y2: B] :
% 0.19/0.45 ( ( ( product_Pair @ A @ B @ X1 @ X22 )
% 0.19/0.45 = ( product_Pair @ A @ B @ Y1 @ Y2 ) )
% 0.19/0.45 = ( ( X1 = Y1 )
% 0.19/0.45 & ( X22 = Y2 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % prod.inject
% 0.19/0.45 thf(fact_186_pi_Operm_I4_J,axiom,
% 0.19/0.45 ! [Pi: list @ ( product_prod @ name @ name ),X32: name,X1: name,X22: pi] :
% 0.19/0.45 ( ( perm @ name @ pi @ Pi @ ( input @ X32 @ X1 @ X22 ) )
% 0.19/0.45 = ( input @ ( perm @ name @ name @ Pi @ X32 ) @ ( perm @ name @ name @ Pi @ X1 ) @ ( perm @ name @ pi @ Pi @ X22 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % pi.perm(4)
% 0.19/0.45 thf(fact_187_pi_Odistinct_I57_J,axiom,
% 0.19/0.45 ! [Name12: name,Name23: name,Pi: pi,Name: name,Pi3: pi] :
% 0.19/0.45 ( ( input @ Name12 @ Name23 @ Pi )
% 0.19/0.45 != ( res @ Name @ Pi3 ) ) ).
% 0.19/0.45
% 0.19/0.45 % pi.distinct(57)
% 0.19/0.45 thf(fact_188_pi_Odistinct_I55_J,axiom,
% 0.19/0.45 ! [Name12: name,Name23: name,Pi: pi,Pi12: pi,Pi22: pi] :
% 0.19/0.45 ( ( input @ Name12 @ Name23 @ Pi )
% 0.19/0.45 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.19/0.45
% 0.19/0.45 % pi.distinct(55)
% 0.19/0.45 thf(fact_189_resTrans_I2_J,axiom,
% 0.19/0.45 ! [X2: name,Y: name,P: pi,Rs: late_residual] :
% 0.19/0.45 ~ ( late_transitions @ ( res @ X2 @ ( input @ X2 @ Y @ P ) ) @ Rs ) ).
% 0.19/0.45
% 0.19/0.45 % resTrans(2)
% 0.19/0.45 thf(fact_190_inputFreeTrans,axiom,
% 0.19/0.45 ! [A2: name,X2: name,P: pi,Alpha: late_freeRes,P3: pi] :
% 0.19/0.45 ~ ( late_transitions @ ( input @ A2 @ X2 @ P ) @ ( late_FreeR @ Alpha @ P3 ) ) ).
% 0.19/0.45
% 0.19/0.45 % inputFreeTrans
% 0.19/0.45 thf(fact_191_surj__pair,axiom,
% 0.19/0.45 ! [A: $tType,B: $tType,P2: product_prod @ A @ B] :
% 0.19/0.45 ? [X5: A,Y3: B] :
% 0.19/0.45 ( P2
% 0.19/0.45 = ( product_Pair @ A @ B @ X5 @ Y3 ) ) ).
% 0.19/0.45
% 0.19/0.45 % surj_pair
% 0.19/0.45 thf(fact_192_prod__cases,axiom,
% 0.19/0.45 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,P2: product_prod @ A @ B] :
% 0.19/0.45 ( ! [A4: A,B3: B] : ( P @ ( product_Pair @ A @ B @ A4 @ B3 ) )
% 0.19/0.45 => ( P @ P2 ) ) ).
% 0.19/0.45
% 0.19/0.45 % prod_cases
% 0.19/0.45 thf(fact_193_Pair__inject,axiom,
% 0.19/0.45 ! [A: $tType,B: $tType,A2: A,B2: B,A6: A,B6: B] :
% 0.19/0.45 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 0.19/0.45 = ( product_Pair @ A @ B @ A6 @ B6 ) )
% 0.19/0.45 => ~ ( ( A2 = A6 )
% 0.19/0.45 => ( B2 != B6 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % Pair_inject
% 0.19/0.45 thf(fact_194_old_Oprod_Oexhaust,axiom,
% 0.19/0.45 ! [A: $tType,B: $tType,Y: product_prod @ A @ B] :
% 0.19/0.45 ~ ! [A4: A,B3: B] :
% 0.19/0.45 ( Y
% 0.19/0.45 != ( product_Pair @ A @ B @ A4 @ B3 ) ) ).
% 0.19/0.45
% 0.19/0.45 % old.prod.exhaust
% 0.19/0.45 thf(fact_195_old_Oprod_Oinducts,axiom,
% 0.19/0.45 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,Prod: product_prod @ A @ B] :
% 0.19/0.45 ( ! [A4: A,B3: B] : ( P @ ( product_Pair @ A @ B @ A4 @ B3 ) )
% 0.19/0.45 => ( P @ Prod ) ) ).
% 0.19/0.45
% 0.19/0.45 % old.prod.inducts
% 0.19/0.45 thf(fact_196_not__Cons__self2,axiom,
% 0.19/0.45 ! [A: $tType,X2: A,Xs: list @ A] :
% 0.19/0.45 ( ( cons @ A @ X2 @ Xs )
% 0.19/0.45 != Xs ) ).
% 0.19/0.45
% 0.19/0.45 % not_Cons_self2
% 0.19/0.45 thf(fact_197_resInputFreeTrans,axiom,
% 0.19/0.45 ! [X2: name,A2: name,Y: name,P: pi,Alpha: late_freeRes,P3: pi] :
% 0.19/0.45 ~ ( late_transitions @ ( res @ X2 @ ( input @ A2 @ Y @ P ) ) @ ( late_FreeR @ Alpha @ P3 ) ) ).
% 0.19/0.45
% 0.19/0.45 % resInputFreeTrans
% 0.19/0.45 thf(fact_198_old_Ounit_Oinducts,axiom,
% 0.19/0.45 ! [P: product_unit > $o,Unit: product_unit] :
% 0.19/0.45 ( ( P @ product_Unity )
% 0.19/0.45 => ( P @ Unit ) ) ).
% 0.19/0.45
% 0.19/0.45 % old.unit.inducts
% 0.19/0.45 thf(fact_199_old_Ounit_Oexhaust,axiom,
% 0.19/0.45 ! [Y: product_unit] : ( Y = product_Unity ) ).
% 0.19/0.45
% 0.19/0.45 % old.unit.exhaust
% 0.19/0.45 thf(fact_200_inputBoundOutputTrans,axiom,
% 0.19/0.45 ! [A2: name,X2: name,P: pi,B2: name,Y: name,P3: pi] :
% 0.19/0.45 ~ ( late_transitions @ ( input @ A2 @ X2 @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ B2 ) @ Y @ P3 ) ) ).
% 0.19/0.45
% 0.19/0.45 % inputBoundOutputTrans
% 0.19/0.45 thf(fact_201_Late__Semantics_OInput,axiom,
% 0.19/0.45 ! [A2: name,X2: name,P: pi] : ( late_transitions @ ( input @ A2 @ X2 @ P ) @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P ) ) ).
% 0.19/0.45
% 0.19/0.45 % Late_Semantics.Input
% 0.19/0.45 thf(fact_202_transitions_OInput,axiom,
% 0.19/0.45 ! [X2: name,A2: name,P: pi] :
% 0.19/0.45 ( ( X2 != A2 )
% 0.19/0.45 => ( late_transitions @ ( input @ A2 @ X2 @ P ) @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % transitions.Input
% 0.19/0.45 thf(fact_203_inputIneqTrans,axiom,
% 0.19/0.45 ! [A2: name,X2: name,P: pi,B2: late_subject,Y: name,P3: pi] :
% 0.19/0.45 ( ( late_transitions @ ( input @ A2 @ X2 @ P ) @ ( late_BoundR @ B2 @ Y @ P3 ) )
% 0.19/0.45 => ~ ( fresh @ name @ late_subject @ A2 @ B2 ) ) ).
% 0.19/0.45
% 0.19/0.45 % inputIneqTrans
% 0.19/0.45 thf(fact_204_resInputBoundOutputTrans,axiom,
% 0.19/0.45 ! [X2: name,A2: name,Y: name,P: pi,B2: name,Z: name,P3: pi] :
% 0.19/0.45 ~ ( late_transitions @ ( res @ X2 @ ( input @ A2 @ Y @ P ) ) @ ( late_BoundR @ ( late_BoundOutputS @ B2 ) @ Z @ P3 ) ) ).
% 0.19/0.45
% 0.19/0.45 % resInputBoundOutputTrans
% 0.19/0.45 thf(fact_205_alphaInput,axiom,
% 0.19/0.45 ! [C: name,P: pi,A2: name,X2: name] :
% 0.19/0.45 ( ( fresh @ name @ pi @ C @ P )
% 0.19/0.45 => ( ( input @ A2 @ X2 @ P )
% 0.19/0.45 = ( input @ A2 @ C @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ X2 @ C ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ P ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % alphaInput
% 0.19/0.45 thf(fact_206_list_Odistinct_I1_J,axiom,
% 0.19/0.45 ! [A: $tType,X21: A,X222: list @ A] :
% 0.19/0.45 ( ( nil @ A )
% 0.19/0.45 != ( cons @ A @ X21 @ X222 ) ) ).
% 0.19/0.45
% 0.19/0.45 % list.distinct(1)
% 0.19/0.45 thf(fact_207_list_OdiscI,axiom,
% 0.19/0.45 ! [A: $tType,List: list @ A,X21: A,X222: list @ A] :
% 0.19/0.45 ( ( List
% 0.19/0.45 = ( cons @ A @ X21 @ X222 ) )
% 0.19/0.45 => ( List
% 0.19/0.45 != ( nil @ A ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % list.discI
% 0.19/0.45 thf(fact_208_list_Oexhaust,axiom,
% 0.19/0.45 ! [A: $tType,Y: list @ A] :
% 0.19/0.45 ( ( Y
% 0.19/0.45 != ( nil @ A ) )
% 0.19/0.45 => ~ ! [X212: A,X223: list @ A] :
% 0.19/0.45 ( Y
% 0.19/0.45 != ( cons @ A @ X212 @ X223 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % list.exhaust
% 0.19/0.45 thf(fact_209_list_Oinducts,axiom,
% 0.19/0.45 ! [A: $tType,P: ( list @ A ) > $o,List: list @ A] :
% 0.19/0.45 ( ( P @ ( nil @ A ) )
% 0.19/0.45 => ( ! [X13: A,X23: list @ A] :
% 0.19/0.45 ( ( P @ X23 )
% 0.19/0.45 => ( P @ ( cons @ A @ X13 @ X23 ) ) )
% 0.19/0.45 => ( P @ List ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % list.inducts
% 0.19/0.45 thf(fact_210_neq__Nil__conv,axiom,
% 0.19/0.45 ! [A: $tType,Xs: list @ A] :
% 0.19/0.45 ( ( Xs
% 0.19/0.45 != ( nil @ A ) )
% 0.19/0.45 = ( ? [Y5: A,Ys: list @ A] :
% 0.19/0.45 ( Xs
% 0.19/0.45 = ( cons @ A @ Y5 @ Ys ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % neq_Nil_conv
% 0.19/0.45 thf(fact_211_list__induct2_H,axiom,
% 0.19/0.45 ! [A: $tType,B: $tType,P: ( list @ A ) > ( list @ B ) > $o,Xs: list @ A,Ys2: list @ B] :
% 0.19/0.45 ( ( P @ ( nil @ A ) @ ( nil @ B ) )
% 0.19/0.45 => ( ! [X5: A,Xs2: list @ A] : ( P @ ( cons @ A @ X5 @ Xs2 ) @ ( nil @ B ) )
% 0.19/0.45 => ( ! [Y3: B,Ys3: list @ B] : ( P @ ( nil @ A ) @ ( cons @ B @ Y3 @ Ys3 ) )
% 0.19/0.45 => ( ! [X5: A,Xs2: list @ A,Y3: B,Ys3: list @ B] :
% 0.19/0.45 ( ( P @ Xs2 @ Ys3 )
% 0.19/0.45 => ( P @ ( cons @ A @ X5 @ Xs2 ) @ ( cons @ B @ Y3 @ Ys3 ) ) )
% 0.19/0.45 => ( P @ Xs @ Ys2 ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % list_induct2'
% 0.30/0.45 thf(fact_212_splice_Oinduct,axiom,
% 0.30/0.45 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 0.30/0.45 ( ! [X_1: list @ A] : ( P @ ( nil @ A ) @ X_1 )
% 0.30/0.45 => ( ! [X5: A,Xs2: list @ A,Ys3: list @ A] :
% 0.30/0.45 ( ( P @ Ys3 @ Xs2 )
% 0.30/0.45 => ( P @ ( cons @ A @ X5 @ Xs2 ) @ Ys3 ) )
% 0.30/0.45 => ( P @ A0 @ A1 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % splice.induct
% 0.30/0.45 thf(fact_213_induct__list012,axiom,
% 0.30/0.45 ! [A: $tType,P: ( list @ A ) > $o,Xs: list @ A] :
% 0.30/0.45 ( ( P @ ( nil @ A ) )
% 0.30/0.45 => ( ! [X5: A] : ( P @ ( cons @ A @ X5 @ ( nil @ A ) ) )
% 0.30/0.45 => ( ! [X5: A,Y3: A,Zs: list @ A] :
% 0.30/0.45 ( ( P @ Zs )
% 0.30/0.45 => ( ( P @ ( cons @ A @ Y3 @ Zs ) )
% 0.30/0.45 => ( P @ ( cons @ A @ X5 @ ( cons @ A @ Y3 @ Zs ) ) ) ) )
% 0.30/0.45 => ( P @ Xs ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % induct_list012
% 0.30/0.45 thf(fact_214_min__list_Ocases,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( ord @ A )
% 0.30/0.45 => ! [X2: list @ A] :
% 0.30/0.45 ( ! [X5: A,Xs2: list @ A] :
% 0.30/0.45 ( X2
% 0.30/0.45 != ( cons @ A @ X5 @ Xs2 ) )
% 0.30/0.45 => ( X2
% 0.30/0.45 = ( nil @ A ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % min_list.cases
% 0.30/0.45 thf(fact_215_min__list_Oinduct,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( ord @ A )
% 0.30/0.45 => ! [P: ( list @ A ) > $o,A0: list @ A] :
% 0.30/0.45 ( ! [X5: A,Xs2: list @ A] :
% 0.30/0.45 ( ! [X213: A,X224: list @ A] :
% 0.30/0.45 ( ( Xs2
% 0.30/0.45 = ( cons @ A @ X213 @ X224 ) )
% 0.30/0.45 => ( P @ Xs2 ) )
% 0.30/0.45 => ( P @ ( cons @ A @ X5 @ Xs2 ) ) )
% 0.30/0.45 => ( ( P @ ( nil @ A ) )
% 0.30/0.45 => ( P @ A0 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % min_list.induct
% 0.30/0.45 thf(fact_216_shuffles_Oinduct,axiom,
% 0.30/0.45 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 0.30/0.45 ( ! [X_1: list @ A] : ( P @ ( nil @ A ) @ X_1 )
% 0.30/0.45 => ( ! [Xs2: list @ A] : ( P @ Xs2 @ ( nil @ A ) )
% 0.30/0.45 => ( ! [X5: A,Xs2: list @ A,Y3: A,Ys3: list @ A] :
% 0.30/0.45 ( ( P @ Xs2 @ ( cons @ A @ Y3 @ Ys3 ) )
% 0.30/0.45 => ( ( P @ ( cons @ A @ X5 @ Xs2 ) @ Ys3 )
% 0.30/0.45 => ( P @ ( cons @ A @ X5 @ Xs2 ) @ ( cons @ A @ Y3 @ Ys3 ) ) ) )
% 0.30/0.45 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % shuffles.induct
% 0.30/0.45 thf(fact_217_transpose_Ocases,axiom,
% 0.30/0.45 ! [A: $tType,X2: list @ ( list @ A )] :
% 0.30/0.45 ( ( X2
% 0.30/0.45 != ( nil @ ( list @ A ) ) )
% 0.30/0.45 => ( ! [Xss: list @ ( list @ A )] :
% 0.30/0.45 ( X2
% 0.30/0.45 != ( cons @ ( list @ A ) @ ( nil @ A ) @ Xss ) )
% 0.30/0.45 => ~ ! [X5: A,Xs2: list @ A,Xss: list @ ( list @ A )] :
% 0.30/0.45 ( X2
% 0.30/0.45 != ( cons @ ( list @ A ) @ ( cons @ A @ X5 @ Xs2 ) @ Xss ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % transpose.cases
% 0.30/0.45 thf(fact_218_remdups__adj_Ocases,axiom,
% 0.30/0.45 ! [A: $tType,X2: list @ A] :
% 0.30/0.45 ( ( X2
% 0.30/0.45 != ( nil @ A ) )
% 0.30/0.45 => ( ! [X5: A] :
% 0.30/0.45 ( X2
% 0.30/0.45 != ( cons @ A @ X5 @ ( nil @ A ) ) )
% 0.30/0.45 => ~ ! [X5: A,Y3: A,Xs2: list @ A] :
% 0.30/0.45 ( X2
% 0.30/0.45 != ( cons @ A @ X5 @ ( cons @ A @ Y3 @ Xs2 ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % remdups_adj.cases
% 0.30/0.45 thf(fact_219_sorted__wrt_Oinduct,axiom,
% 0.30/0.45 ! [A: $tType,P: ( A > A > $o ) > ( list @ A ) > $o,A0: A > A > $o,A1: list @ A] :
% 0.30/0.45 ( ! [P5: A > A > $o] : ( P @ P5 @ ( nil @ A ) )
% 0.30/0.45 => ( ! [P5: A > A > $o,X5: A,Ys3: list @ A] :
% 0.30/0.45 ( ( P @ P5 @ Ys3 )
% 0.30/0.45 => ( P @ P5 @ ( cons @ A @ X5 @ Ys3 ) ) )
% 0.30/0.45 => ( P @ A0 @ A1 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % sorted_wrt.induct
% 0.30/0.45 thf(fact_220_remdups__adj_Oinduct,axiom,
% 0.30/0.45 ! [A: $tType,P: ( list @ A ) > $o,A0: list @ A] :
% 0.30/0.45 ( ( P @ ( nil @ A ) )
% 0.30/0.45 => ( ! [X5: A] : ( P @ ( cons @ A @ X5 @ ( nil @ A ) ) )
% 0.30/0.45 => ( ! [X5: A,Y3: A,Xs2: list @ A] :
% 0.30/0.45 ( ( ( X5 = Y3 )
% 0.30/0.45 => ( P @ ( cons @ A @ X5 @ Xs2 ) ) )
% 0.30/0.45 => ( ( ( X5 != Y3 )
% 0.30/0.45 => ( P @ ( cons @ A @ Y3 @ Xs2 ) ) )
% 0.30/0.45 => ( P @ ( cons @ A @ X5 @ ( cons @ A @ Y3 @ Xs2 ) ) ) ) )
% 0.30/0.45 => ( P @ A0 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % remdups_adj.induct
% 0.30/0.45 thf(fact_221_arg__min__list_Oinduct,axiom,
% 0.30/0.45 ! [B: $tType,A: $tType] :
% 0.30/0.45 ( ( linorder @ B )
% 0.30/0.45 => ! [P: ( A > B ) > ( list @ A ) > $o,A0: A > B,A1: list @ A] :
% 0.30/0.45 ( ! [F3: A > B,X5: A] : ( P @ F3 @ ( cons @ A @ X5 @ ( nil @ A ) ) )
% 0.30/0.45 => ( ! [F3: A > B,X5: A,Y3: A,Zs: list @ A] :
% 0.30/0.45 ( ( P @ F3 @ ( cons @ A @ Y3 @ Zs ) )
% 0.30/0.45 => ( P @ F3 @ ( cons @ A @ X5 @ ( cons @ A @ Y3 @ Zs ) ) ) )
% 0.30/0.45 => ( ! [A4: A > B] : ( P @ A4 @ ( nil @ A ) )
% 0.30/0.45 => ( P @ A0 @ A1 ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % arg_min_list.induct
% 0.30/0.45 thf(fact_222_successively_Oinduct,axiom,
% 0.30/0.45 ! [A: $tType,P: ( A > A > $o ) > ( list @ A ) > $o,A0: A > A > $o,A1: list @ A] :
% 0.30/0.45 ( ! [P5: A > A > $o] : ( P @ P5 @ ( nil @ A ) )
% 0.30/0.45 => ( ! [P5: A > A > $o,X5: A] : ( P @ P5 @ ( cons @ A @ X5 @ ( nil @ A ) ) )
% 0.30/0.45 => ( ! [P5: A > A > $o,X5: A,Y3: A,Xs2: list @ A] :
% 0.30/0.45 ( ( P @ P5 @ ( cons @ A @ Y3 @ Xs2 ) )
% 0.30/0.45 => ( P @ P5 @ ( cons @ A @ X5 @ ( cons @ A @ Y3 @ Xs2 ) ) ) )
% 0.30/0.45 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % successively.induct
% 0.30/0.45 thf(fact_223_list__nonempty__induct,axiom,
% 0.30/0.45 ! [A: $tType,Xs: list @ A,P: ( list @ A ) > $o] :
% 0.30/0.45 ( ( Xs
% 0.30/0.45 != ( nil @ A ) )
% 0.30/0.45 => ( ! [X5: A] : ( P @ ( cons @ A @ X5 @ ( nil @ A ) ) )
% 0.30/0.45 => ( ! [X5: A,Xs2: list @ A] :
% 0.30/0.45 ( ( Xs2
% 0.30/0.45 != ( nil @ A ) )
% 0.30/0.45 => ( ( P @ Xs2 )
% 0.30/0.45 => ( P @ ( cons @ A @ X5 @ Xs2 ) ) ) )
% 0.30/0.45 => ( P @ Xs ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % list_nonempty_induct
% 0.30/0.45 thf(fact_224_map__tailrec__rev_Oinduct,axiom,
% 0.30/0.45 ! [A: $tType,B: $tType,P: ( A > B ) > ( list @ A ) > ( list @ B ) > $o,A0: A > B,A1: list @ A,A22: list @ B] :
% 0.30/0.45 ( ! [F3: A > B,X_1: list @ B] : ( P @ F3 @ ( nil @ A ) @ X_1 )
% 0.30/0.45 => ( ! [F3: A > B,A4: A,As: list @ A,Bs: list @ B] :
% 0.30/0.45 ( ( P @ F3 @ As @ ( cons @ B @ ( F3 @ A4 ) @ Bs ) )
% 0.30/0.45 => ( P @ F3 @ ( cons @ A @ A4 @ As ) @ Bs ) )
% 0.30/0.45 => ( P @ A0 @ A1 @ A22 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % map_tailrec_rev.induct
% 0.30/0.45 thf(fact_225_strict__sorted_Ocases,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( linorder @ A )
% 0.30/0.45 => ! [X2: list @ A] :
% 0.30/0.45 ( ( X2
% 0.30/0.45 != ( nil @ A ) )
% 0.30/0.45 => ~ ! [X5: A,Ys3: list @ A] :
% 0.30/0.45 ( X2
% 0.30/0.45 != ( cons @ A @ X5 @ Ys3 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % strict_sorted.cases
% 0.30/0.45 thf(fact_226_strict__sorted_Oinduct,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( linorder @ A )
% 0.30/0.45 => ! [P: ( list @ A ) > $o,A0: list @ A] :
% 0.30/0.45 ( ( P @ ( nil @ A ) )
% 0.30/0.45 => ( ! [X5: A,Ys3: list @ A] :
% 0.30/0.45 ( ( P @ Ys3 )
% 0.30/0.45 => ( P @ ( cons @ A @ X5 @ Ys3 ) ) )
% 0.30/0.45 => ( P @ A0 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % strict_sorted.induct
% 0.30/0.45 thf(fact_227_splice_Ocases,axiom,
% 0.30/0.45 ! [A: $tType,X2: product_prod @ ( list @ A ) @ ( list @ A )] :
% 0.30/0.45 ( ! [Ys3: list @ A] :
% 0.30/0.45 ( X2
% 0.30/0.45 != ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( nil @ A ) @ Ys3 ) )
% 0.30/0.45 => ~ ! [X5: A,Xs2: list @ A,Ys3: list @ A] :
% 0.30/0.45 ( X2
% 0.30/0.45 != ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X5 @ Xs2 ) @ Ys3 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % splice.cases
% 0.30/0.45 thf(fact_228_shuffles_Ocases,axiom,
% 0.30/0.45 ! [A: $tType,X2: product_prod @ ( list @ A ) @ ( list @ A )] :
% 0.30/0.45 ( ! [Ys3: list @ A] :
% 0.30/0.45 ( X2
% 0.30/0.45 != ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( nil @ A ) @ Ys3 ) )
% 0.30/0.45 => ( ! [Xs2: list @ A] :
% 0.30/0.45 ( X2
% 0.30/0.45 != ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs2 @ ( nil @ A ) ) )
% 0.30/0.45 => ~ ! [X5: A,Xs2: list @ A,Y3: A,Ys3: list @ A] :
% 0.30/0.45 ( X2
% 0.30/0.45 != ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X5 @ Xs2 ) @ ( cons @ A @ Y3 @ Ys3 ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % shuffles.cases
% 0.30/0.45 thf(fact_229_sorted__wrt_Ocases,axiom,
% 0.30/0.45 ! [A: $tType,X2: product_prod @ ( A > A > $o ) @ ( list @ A )] :
% 0.30/0.45 ( ! [P5: A > A > $o] :
% 0.30/0.45 ( X2
% 0.30/0.45 != ( product_Pair @ ( A > A > $o ) @ ( list @ A ) @ P5 @ ( nil @ A ) ) )
% 0.30/0.45 => ~ ! [P5: A > A > $o,X5: A,Ys3: list @ A] :
% 0.30/0.45 ( X2
% 0.30/0.45 != ( product_Pair @ ( A > A > $o ) @ ( list @ A ) @ P5 @ ( cons @ A @ X5 @ Ys3 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % sorted_wrt.cases
% 0.30/0.45 thf(fact_230_successively_Ocases,axiom,
% 0.30/0.45 ! [A: $tType,X2: product_prod @ ( A > A > $o ) @ ( list @ A )] :
% 0.30/0.45 ( ! [P5: A > A > $o] :
% 0.30/0.45 ( X2
% 0.30/0.45 != ( product_Pair @ ( A > A > $o ) @ ( list @ A ) @ P5 @ ( nil @ A ) ) )
% 0.30/0.45 => ( ! [P5: A > A > $o,X5: A] :
% 0.30/0.45 ( X2
% 0.30/0.45 != ( product_Pair @ ( A > A > $o ) @ ( list @ A ) @ P5 @ ( cons @ A @ X5 @ ( nil @ A ) ) ) )
% 0.30/0.45 => ~ ! [P5: A > A > $o,X5: A,Y3: A,Xs2: list @ A] :
% 0.30/0.45 ( X2
% 0.30/0.45 != ( product_Pair @ ( A > A > $o ) @ ( list @ A ) @ P5 @ ( cons @ A @ X5 @ ( cons @ A @ Y3 @ Xs2 ) ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % successively.cases
% 0.30/0.45 thf(fact_231_arg__min__list_Ocases,axiom,
% 0.30/0.45 ! [B: $tType,A: $tType] :
% 0.30/0.45 ( ( linorder @ B )
% 0.30/0.45 => ! [X2: product_prod @ ( A > B ) @ ( list @ A )] :
% 0.30/0.45 ( ! [F3: A > B,X5: A] :
% 0.30/0.45 ( X2
% 0.30/0.45 != ( product_Pair @ ( A > B ) @ ( list @ A ) @ F3 @ ( cons @ A @ X5 @ ( nil @ A ) ) ) )
% 0.30/0.45 => ( ! [F3: A > B,X5: A,Y3: A,Zs: list @ A] :
% 0.30/0.45 ( X2
% 0.30/0.45 != ( product_Pair @ ( A > B ) @ ( list @ A ) @ F3 @ ( cons @ A @ X5 @ ( cons @ A @ Y3 @ Zs ) ) ) )
% 0.30/0.45 => ~ ! [A4: A > B] :
% 0.30/0.45 ( X2
% 0.30/0.45 != ( product_Pair @ ( A > B ) @ ( list @ A ) @ A4 @ ( nil @ A ) ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % arg_min_list.cases
% 0.30/0.45 thf(fact_232_map__tailrec__rev_Ocases,axiom,
% 0.30/0.45 ! [A: $tType,B: $tType,X2: product_prod @ ( A > B ) @ ( product_prod @ ( list @ A ) @ ( list @ B ) )] :
% 0.30/0.45 ( ! [F3: A > B,Bs: list @ B] :
% 0.30/0.45 ( X2
% 0.30/0.45 != ( product_Pair @ ( A > B ) @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ F3 @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ ( nil @ A ) @ Bs ) ) )
% 0.30/0.45 => ~ ! [F3: A > B,A4: A,As: list @ A,Bs: list @ B] :
% 0.30/0.45 ( X2
% 0.30/0.45 != ( product_Pair @ ( A > B ) @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ F3 @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ ( cons @ A @ A4 @ As ) @ Bs ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % map_tailrec_rev.cases
% 0.30/0.45 thf(fact_233_prod__cases3,axiom,
% 0.30/0.45 ! [A: $tType,B: $tType,C3: $tType,Y: product_prod @ A @ ( product_prod @ B @ C3 )] :
% 0.30/0.45 ~ ! [A4: A,B3: B,C2: C3] :
% 0.30/0.45 ( Y
% 0.30/0.45 != ( product_Pair @ A @ ( product_prod @ B @ C3 ) @ A4 @ ( product_Pair @ B @ C3 @ B3 @ C2 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % prod_cases3
% 0.30/0.45 thf(fact_234_prod__cases4,axiom,
% 0.30/0.45 ! [A: $tType,B: $tType,C3: $tType,D2: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ D2 ) )] :
% 0.30/0.45 ~ ! [A4: A,B3: B,C2: C3,D3: D2] :
% 0.30/0.45 ( Y
% 0.30/0.45 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C3 @ D2 ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C3 @ D2 ) @ B3 @ ( product_Pair @ C3 @ D2 @ C2 @ D3 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % prod_cases4
% 0.30/0.45 thf(fact_235_prod__cases5,axiom,
% 0.30/0.45 ! [A: $tType,B: $tType,C3: $tType,D2: $tType,E: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ E ) ) )] :
% 0.30/0.45 ~ ! [A4: A,B3: B,C2: C3,D3: D2,E2: E] :
% 0.30/0.45 ( Y
% 0.30/0.45 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ E ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ E ) ) @ B3 @ ( product_Pair @ C3 @ ( product_prod @ D2 @ E ) @ C2 @ ( product_Pair @ D2 @ E @ D3 @ E2 ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % prod_cases5
% 0.30/0.45 thf(fact_236_prod__cases6,axiom,
% 0.30/0.45 ! [A: $tType,B: $tType,C3: $tType,D2: $tType,E: $tType,F4: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ F4 ) ) ) )] :
% 0.30/0.45 ~ ! [A4: A,B3: B,C2: C3,D3: D2,E2: E,F3: F4] :
% 0.30/0.45 ( Y
% 0.30/0.45 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ F4 ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ F4 ) ) ) @ B3 @ ( product_Pair @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ F4 ) ) @ C2 @ ( product_Pair @ D2 @ ( product_prod @ E @ F4 ) @ D3 @ ( product_Pair @ E @ F4 @ E2 @ F3 ) ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % prod_cases6
% 0.30/0.45 thf(fact_237_prod__cases7,axiom,
% 0.30/0.45 ! [A: $tType,B: $tType,C3: $tType,D2: $tType,E: $tType,F4: $tType,G2: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F4 @ G2 ) ) ) ) )] :
% 0.30/0.45 ~ ! [A4: A,B3: B,C2: C3,D3: D2,E2: E,F3: F4,G3: G2] :
% 0.30/0.45 ( Y
% 0.30/0.45 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F4 @ G2 ) ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F4 @ G2 ) ) ) ) @ B3 @ ( product_Pair @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F4 @ G2 ) ) ) @ C2 @ ( product_Pair @ D2 @ ( product_prod @ E @ ( product_prod @ F4 @ G2 ) ) @ D3 @ ( product_Pair @ E @ ( product_prod @ F4 @ G2 ) @ E2 @ ( product_Pair @ F4 @ G2 @ F3 @ G3 ) ) ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % prod_cases7
% 0.30/0.45 thf(fact_238_prod__induct3,axiom,
% 0.30/0.45 ! [C3: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ C3 ) ) > $o,X2: product_prod @ A @ ( product_prod @ B @ C3 )] :
% 0.30/0.45 ( ! [A4: A,B3: B,C2: C3] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ C3 ) @ A4 @ ( product_Pair @ B @ C3 @ B3 @ C2 ) ) )
% 0.30/0.45 => ( P @ X2 ) ) ).
% 0.30/0.45
% 0.30/0.45 % prod_induct3
% 0.30/0.45 thf(fact_239_prod__induct4,axiom,
% 0.30/0.45 ! [D2: $tType,C3: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ D2 ) ) ) > $o,X2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ D2 ) )] :
% 0.30/0.45 ( ! [A4: A,B3: B,C2: C3,D3: D2] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C3 @ D2 ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C3 @ D2 ) @ B3 @ ( product_Pair @ C3 @ D2 @ C2 @ D3 ) ) ) )
% 0.30/0.45 => ( P @ X2 ) ) ).
% 0.30/0.45
% 0.30/0.45 % prod_induct4
% 0.30/0.45 thf(fact_240_prod__induct5,axiom,
% 0.30/0.45 ! [E: $tType,D2: $tType,C3: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ E ) ) ) ) > $o,X2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ E ) ) )] :
% 0.30/0.45 ( ! [A4: A,B3: B,C2: C3,D3: D2,E2: E] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ E ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ E ) ) @ B3 @ ( product_Pair @ C3 @ ( product_prod @ D2 @ E ) @ C2 @ ( product_Pair @ D2 @ E @ D3 @ E2 ) ) ) ) )
% 0.30/0.45 => ( P @ X2 ) ) ).
% 0.30/0.45
% 0.30/0.45 % prod_induct5
% 0.30/0.45 thf(fact_241_prod__induct6,axiom,
% 0.30/0.45 ! [F4: $tType,E: $tType,D2: $tType,C3: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ F4 ) ) ) ) ) > $o,X2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ F4 ) ) ) )] :
% 0.30/0.45 ( ! [A4: A,B3: B,C2: C3,D3: D2,E2: E,F3: F4] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ F4 ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ F4 ) ) ) @ B3 @ ( product_Pair @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ F4 ) ) @ C2 @ ( product_Pair @ D2 @ ( product_prod @ E @ F4 ) @ D3 @ ( product_Pair @ E @ F4 @ E2 @ F3 ) ) ) ) ) )
% 0.30/0.45 => ( P @ X2 ) ) ).
% 0.30/0.45
% 0.30/0.45 % prod_induct6
% 0.30/0.45 thf(fact_242_prod__induct7,axiom,
% 0.30/0.45 ! [G2: $tType,F4: $tType,E: $tType,D2: $tType,C3: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F4 @ G2 ) ) ) ) ) ) > $o,X2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F4 @ G2 ) ) ) ) )] :
% 0.30/0.45 ( ! [A4: A,B3: B,C2: C3,D3: D2,E2: E,F3: F4,G3: G2] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F4 @ G2 ) ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F4 @ G2 ) ) ) ) @ B3 @ ( product_Pair @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F4 @ G2 ) ) ) @ C2 @ ( product_Pair @ D2 @ ( product_prod @ E @ ( product_prod @ F4 @ G2 ) ) @ D3 @ ( product_Pair @ E @ ( product_prod @ F4 @ G2 ) @ E2 @ ( product_Pair @ F4 @ G2 @ F3 @ G3 ) ) ) ) ) ) )
% 0.30/0.45 => ( P @ X2 ) ) ).
% 0.30/0.45
% 0.30/0.45 % prod_induct7
% 0.30/0.45 thf(fact_243_old_Ounit_Orec,axiom,
% 0.30/0.45 ! [T: $tType,F1: T] :
% 0.30/0.45 ( ( product_rec_unit @ T @ F1 @ product_Unity )
% 0.30/0.45 = F1 ) ).
% 0.30/0.45
% 0.30/0.45 % old.unit.rec
% 0.30/0.45 thf(fact_244_old_Oprod_Orec,axiom,
% 0.30/0.45 ! [A: $tType,T: $tType,B: $tType,F1: A > B > T,A2: A,B2: B] :
% 0.30/0.45 ( ( product_rec_prod @ A @ B @ T @ F1 @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 0.30/0.45 = ( F1 @ A2 @ B2 ) ) ).
% 0.30/0.45
% 0.30/0.45 % old.prod.rec
% 0.30/0.45 thf(fact_245_default__unit__def,axiom,
% 0.30/0.45 ( ( default_default @ product_unit )
% 0.30/0.45 = product_Unity ) ).
% 0.30/0.45
% 0.30/0.45 % default_unit_def
% 0.30/0.45 thf(fact_246_supports__def,axiom,
% 0.30/0.45 ! [A: $tType,X: $tType] :
% 0.30/0.45 ( ( supports @ X @ A )
% 0.30/0.45 = ( ^ [S3: set @ X,X4: A] :
% 0.30/0.45 ! [A5: X,B4: X] :
% 0.30/0.45 ( ( ~ ( member @ X @ A5 @ S3 )
% 0.30/0.45 & ~ ( member @ X @ B4 @ S3 ) )
% 0.30/0.45 => ( ( perm @ X @ A @ ( cons @ ( product_prod @ X @ X ) @ ( product_Pair @ X @ X @ A5 @ B4 ) @ ( nil @ ( product_prod @ X @ X ) ) ) @ X4 )
% 0.30/0.45 = X4 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % supports_def
% 0.30/0.45 thf(fact_247_perm__residual__Rep_Osimps_I2_J,axiom,
% 0.30/0.45 ! [X: $tType,Pi: list @ ( product_prod @ X @ X ),FreeRes3: late_freeRes,Pia: pi] :
% 0.30/0.45 ( ( perm @ X @ late_residual_Rep @ Pi @ ( late_r347633188eR_Rep @ FreeRes3 @ Pia ) )
% 0.30/0.45 = ( late_r347633188eR_Rep @ ( perm @ X @ late_freeRes @ Pi @ FreeRes3 ) @ ( perm @ X @ pi @ Pi @ Pia ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % perm_residual_Rep.simps(2)
% 0.30/0.45 thf(fact_248_residual__Rep_Oinject_I2_J,axiom,
% 0.30/0.45 ! [X21: late_freeRes,X222: pi,Y21: late_freeRes,Y22: pi] :
% 0.30/0.45 ( ( ( late_r347633188eR_Rep @ X21 @ X222 )
% 0.30/0.45 = ( late_r347633188eR_Rep @ Y21 @ Y22 ) )
% 0.30/0.45 = ( ( X21 = Y21 )
% 0.30/0.45 & ( X222 = Y22 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % residual_Rep.inject(2)
% 0.30/0.45 thf(fact_249_product__lists_Osimps_I1_J,axiom,
% 0.30/0.45 ! [A: $tType] :
% 0.30/0.45 ( ( product_lists @ A @ ( nil @ ( list @ A ) ) )
% 0.30/0.45 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % product_lists.simps(1)
% 0.30/0.45 thf(fact_250_name__calc_I1_J,axiom,
% 0.30/0.45 ! [A2: name,B2: name,Pi: list @ ( product_prod @ name @ name ),X2: name] :
% 0.30/0.45 ( ( perm @ name @ name @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ Pi ) @ X2 )
% 0.30/0.45 = ( swap @ name @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( perm @ name @ name @ Pi @ X2 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % name_calc(1)
% 0.30/0.45 thf(fact_251_name__calc_I3_J,axiom,
% 0.30/0.45 ! [A2: name,C: name,B2: name] :
% 0.30/0.45 ( ( ( A2 = C )
% 0.30/0.45 => ( ( swap @ name @ ( product_Pair @ name @ name @ A2 @ B2 ) @ C )
% 0.30/0.45 = B2 ) )
% 0.30/0.45 & ( ( A2 != C )
% 0.30/0.45 => ( ( ( B2 = C )
% 0.30/0.45 => ( ( swap @ name @ ( product_Pair @ name @ name @ A2 @ B2 ) @ C )
% 0.30/0.45 = A2 ) )
% 0.30/0.45 & ( ( B2 != C )
% 0.30/0.45 => ( ( swap @ name @ ( product_Pair @ name @ name @ A2 @ B2 ) @ C )
% 0.30/0.45 = C ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % name_calc(3)
% 0.30/0.45 thf(fact_252_Agent_Oswap__name__def,axiom,
% 0.30/0.45 ( ( swap @ name )
% 0.30/0.45 = swap_name ) ).
% 0.30/0.45
% 0.30/0.45 % Agent.swap_name_def
% 0.30/0.45 thf(fact_253_alpha__fresh_H,axiom,
% 0.30/0.45 ! [X3: $tType] :
% 0.30/0.45 ( ( pt_name @ X3 )
% 0.30/0.45 => ! [A2: name,X2: X3,B2: name,Y: X3,C: name] :
% 0.30/0.45 ( ( ( abs_fun @ name @ X3 @ A2 @ X2 )
% 0.30/0.45 = ( abs_fun @ name @ X3 @ B2 @ Y ) )
% 0.30/0.45 => ( ( C != A2 )
% 0.30/0.45 => ( ( C != B2 )
% 0.30/0.45 => ( ( fresh @ name @ X3 @ C @ X2 )
% 0.30/0.45 => ( ( fresh @ name @ X3 @ C @ Y )
% 0.30/0.45 => ( X2
% 0.30/0.45 = ( perm @ name @ X3 @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ C ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ ( perm @ name @ X3 @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ B2 @ C ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ Y ) ) ) ) ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % alpha_fresh'
% 0.30/0.45 thf(fact_254_pi_Ofresh_I9_J,axiom,
% 0.30/0.45 ! [A2: name,X1: name,X22: pi] :
% 0.30/0.45 ( ( fresh @ name @ pi @ A2 @ ( res @ X1 @ X22 ) )
% 0.30/0.45 = ( fresh @ name @ ( name > ( noption @ pi ) ) @ A2 @ ( abs_fun @ name @ pi @ X1 @ X22 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % pi.fresh(9)
% 0.30/0.45
% 0.30/0.45 % Type constructors (47)
% 0.30/0.45 thf(tcon_fun___Agent_Ocp__name__name,axiom,
% 0.30/0.45 ! [A7: $tType,A8: $tType] :
% 0.30/0.45 ( ( ( cp_name_name @ A7 )
% 0.30/0.45 & ( cp_name_name @ A8 ) )
% 0.30/0.45 => ( cp_name_name @ ( A7 > A8 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(tcon_fun___Orderings_Oord,axiom,
% 0.30/0.45 ! [A7: $tType,A8: $tType] :
% 0.30/0.45 ( ( ord @ A8 )
% 0.30/0.45 => ( ord @ ( A7 > A8 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(tcon_fun___Agent_Opt__name,axiom,
% 0.30/0.45 ! [A7: $tType,A8: $tType] :
% 0.30/0.45 ( ( ( pt_name @ A7 )
% 0.30/0.45 & ( pt_name @ A8 ) )
% 0.30/0.45 => ( pt_name @ ( A7 > A8 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(tcon_Set_Oset___Agent_Ocp__name__name_1,axiom,
% 0.30/0.45 ! [A7: $tType] :
% 0.30/0.45 ( ( cp_name_name @ A7 )
% 0.30/0.45 => ( cp_name_name @ ( set @ A7 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(tcon_Set_Oset___Orderings_Oord_2,axiom,
% 0.30/0.45 ! [A7: $tType] : ( ord @ ( set @ A7 ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(tcon_Set_Oset___Agent_Opt__name_3,axiom,
% 0.30/0.45 ! [A7: $tType] :
% 0.30/0.45 ( ( pt_name @ A7 )
% 0.30/0.45 => ( pt_name @ ( set @ A7 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(tcon_Agent_Opi___Agent_Ocp__name__name_4,axiom,
% 0.30/0.45 cp_name_name @ pi ).
% 0.30/0.45
% 0.30/0.45 thf(tcon_Agent_Opi___Agent_Opt__name_5,axiom,
% 0.30/0.45 pt_name @ pi ).
% 0.30/0.45
% 0.30/0.45 thf(tcon_Agent_Opi___Agent_Ofs__name,axiom,
% 0.30/0.45 fs_name @ pi ).
% 0.30/0.45
% 0.30/0.45 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 0.30/0.45 linorder @ $o ).
% 0.30/0.45
% 0.30/0.45 thf(tcon_HOL_Obool___Agent_Ocp__name__name_6,axiom,
% 0.30/0.45 cp_name_name @ $o ).
% 0.30/0.45
% 0.30/0.45 thf(tcon_HOL_Obool___Orderings_Oord_7,axiom,
% 0.30/0.45 ord @ $o ).
% 0.30/0.45
% 0.30/0.45 thf(tcon_HOL_Obool___Agent_Opt__name_8,axiom,
% 0.30/0.45 pt_name @ $o ).
% 0.30/0.45
% 0.30/0.45 thf(tcon_HOL_Obool___Agent_Ofs__name_9,axiom,
% 0.30/0.45 fs_name @ $o ).
% 0.30/0.45
% 0.30/0.45 thf(tcon_List_Olist___Agent_Ocp__name__name_10,axiom,
% 0.30/0.45 ! [A7: $tType] :
% 0.30/0.45 ( ( cp_name_name @ A7 )
% 0.30/0.45 => ( cp_name_name @ ( list @ A7 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(tcon_List_Olist___Agent_Opt__name_11,axiom,
% 0.30/0.45 ! [A7: $tType] :
% 0.30/0.45 ( ( pt_name @ A7 )
% 0.30/0.45 => ( pt_name @ ( list @ A7 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(tcon_List_Olist___Agent_Ofs__name_12,axiom,
% 0.30/0.45 ! [A7: $tType] :
% 0.30/0.45 ( ( fs_name @ A7 )
% 0.30/0.45 => ( fs_name @ ( list @ A7 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(tcon_Agent_Oname___Agent_Ocp__name__name_13,axiom,
% 0.30/0.45 cp_name_name @ name ).
% 0.30/0.45
% 0.30/0.45 thf(tcon_Agent_Oname___Agent_Opt__name_14,axiom,
% 0.30/0.45 pt_name @ name ).
% 0.30/0.45
% 0.30/0.45 thf(tcon_Agent_Oname___Agent_Ofs__name_15,axiom,
% 0.30/0.45 fs_name @ name ).
% 0.30/0.45
% 0.30/0.45 thf(tcon_Agent_Opi__Rep___Agent_Ocp__name__name_16,axiom,
% 0.30/0.45 cp_name_name @ pi_Rep ).
% 0.30/0.45
% 0.30/0.45 thf(tcon_Agent_Opi__Rep___Agent_Opt__name_17,axiom,
% 0.30/0.45 pt_name @ pi_Rep ).
% 0.30/0.45
% 0.30/0.45 thf(tcon_Nominal_Onoption___Agent_Ocp__name__name_18,axiom,
% 0.30/0.45 ! [A7: $tType] :
% 0.30/0.45 ( ( cp_name_name @ A7 )
% 0.30/0.45 => ( cp_name_name @ ( noption @ A7 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(tcon_Nominal_Onoption___Agent_Opt__name_19,axiom,
% 0.30/0.45 ! [A7: $tType] :
% 0.30/0.45 ( ( pt_name @ A7 )
% 0.30/0.45 => ( pt_name @ ( noption @ A7 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(tcon_Product__Type_Oprod___Agent_Ocp__name__name_20,axiom,
% 0.30/0.45 ! [A7: $tType,A8: $tType] :
% 0.30/0.45 ( ( ( cp_name_name @ A7 )
% 0.30/0.45 & ( cp_name_name @ A8 ) )
% 0.30/0.45 => ( cp_name_name @ ( product_prod @ A7 @ A8 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(tcon_Product__Type_Oprod___Agent_Opt__name_21,axiom,
% 0.30/0.45 ! [A7: $tType,A8: $tType] :
% 0.30/0.45 ( ( ( pt_name @ A7 )
% 0.30/0.45 & ( pt_name @ A8 ) )
% 0.30/0.45 => ( pt_name @ ( product_prod @ A7 @ A8 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(tcon_Product__Type_Oprod___Agent_Ofs__name_22,axiom,
% 0.30/0.45 ! [A7: $tType,A8: $tType] :
% 0.30/0.45 ( ( ( fs_name @ A7 )
% 0.30/0.45 & ( fs_name @ A8 ) )
% 0.30/0.45 => ( fs_name @ ( product_prod @ A7 @ A8 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(tcon_Product__Type_Ounit___Orderings_Olinorder_23,axiom,
% 0.30/0.45 linorder @ product_unit ).
% 0.30/0.45
% 0.30/0.45 thf(tcon_Product__Type_Ounit___Agent_Ocp__name__name_24,axiom,
% 0.30/0.45 cp_name_name @ product_unit ).
% 0.30/0.45
% 0.30/0.45 thf(tcon_Product__Type_Ounit___Orderings_Oord_25,axiom,
% 0.30/0.45 ord @ product_unit ).
% 0.30/0.45
% 0.30/0.45 thf(tcon_Product__Type_Ounit___Agent_Opt__name_26,axiom,
% 0.30/0.45 pt_name @ product_unit ).
% 0.30/0.45
% 0.30/0.45 thf(tcon_Product__Type_Ounit___Agent_Ofs__name_27,axiom,
% 0.30/0.45 fs_name @ product_unit ).
% 0.30/0.45
% 0.30/0.45 thf(tcon_Late__Semantics_OfreeRes___Agent_Ocp__name__name_28,axiom,
% 0.30/0.45 cp_name_name @ late_freeRes ).
% 0.30/0.45
% 0.30/0.45 thf(tcon_Late__Semantics_OfreeRes___Agent_Opt__name_29,axiom,
% 0.30/0.45 pt_name @ late_freeRes ).
% 0.30/0.45
% 0.30/0.45 thf(tcon_Late__Semantics_OfreeRes___Agent_Ofs__name_30,axiom,
% 0.30/0.45 fs_name @ late_freeRes ).
% 0.30/0.45
% 0.30/0.45 thf(tcon_Late__Semantics_Osubject___Agent_Ocp__name__name_31,axiom,
% 0.30/0.45 cp_name_name @ late_subject ).
% 0.30/0.45
% 0.30/0.45 thf(tcon_Late__Semantics_Osubject___Agent_Opt__name_32,axiom,
% 0.30/0.45 pt_name @ late_subject ).
% 0.30/0.45
% 0.30/0.45 thf(tcon_Late__Semantics_Osubject___Agent_Ofs__name_33,axiom,
% 0.30/0.45 fs_name @ late_subject ).
% 0.30/0.45
% 0.30/0.45 thf(tcon_Late__Semantics_Oresidual___Agent_Ocp__name__name_34,axiom,
% 0.30/0.45 cp_name_name @ late_residual ).
% 0.30/0.45
% 0.30/0.45 thf(tcon_Late__Semantics_Oresidual___Agent_Opt__name_35,axiom,
% 0.30/0.45 pt_name @ late_residual ).
% 0.30/0.45
% 0.30/0.45 thf(tcon_Late__Semantics_Oresidual___Agent_Ofs__name_36,axiom,
% 0.30/0.45 fs_name @ late_residual ).
% 0.30/0.45
% 0.30/0.45 thf(tcon_Late__Semantics_OfreeRes__Rep___Agent_Ocp__name__name_37,axiom,
% 0.30/0.45 cp_name_name @ late_freeRes_Rep ).
% 0.30/0.45
% 0.30/0.45 thf(tcon_Late__Semantics_OfreeRes__Rep___Agent_Opt__name_38,axiom,
% 0.30/0.45 pt_name @ late_freeRes_Rep ).
% 0.30/0.45
% 0.30/0.45 thf(tcon_Late__Semantics_Osubject__Rep___Agent_Ocp__name__name_39,axiom,
% 0.30/0.45 cp_name_name @ late_subject_Rep ).
% 0.30/0.45
% 0.30/0.45 thf(tcon_Late__Semantics_Osubject__Rep___Agent_Opt__name_40,axiom,
% 0.30/0.45 pt_name @ late_subject_Rep ).
% 0.30/0.45
% 0.30/0.45 thf(tcon_Late__Semantics_Oresidual__Rep___Agent_Ocp__name__name_41,axiom,
% 0.30/0.45 cp_name_name @ late_residual_Rep ).
% 0.30/0.45
% 0.30/0.45 thf(tcon_Late__Semantics_Oresidual__Rep___Agent_Opt__name_42,axiom,
% 0.30/0.45 pt_name @ late_residual_Rep ).
% 0.30/0.45
% 0.30/0.45 % Helper facts (3)
% 0.30/0.45 thf(help_If_3_1_T,axiom,
% 0.30/0.45 ! [P: $o] :
% 0.30/0.45 ( ( P = $true )
% 0.30/0.45 | ( P = $false ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(help_If_2_1_T,axiom,
% 0.30/0.45 ! [A: $tType,X2: A,Y: A] :
% 0.30/0.45 ( ( if @ A @ $false @ X2 @ Y )
% 0.30/0.45 = Y ) ).
% 0.30/0.45
% 0.30/0.45 thf(help_If_1_1_T,axiom,
% 0.30/0.45 ! [A: $tType,X2: A,Y: A] :
% 0.30/0.45 ( ( if @ A @ $true @ X2 @ Y )
% 0.30/0.45 = X2 ) ).
% 0.30/0.45
% 0.30/0.45 % Conjectures (1)
% 0.30/0.45 thf(conj_0,conjecture,
% 0.30/0.45 ? [P6: pi] :
% 0.30/0.45 ( ( late_transitions @ ( par @ p @ ( res @ x @ q ) ) @ ( late_BoundR @ ( late_BoundOutputS @ ab ) @ y @ P6 ) )
% 0.30/0.45 & ( strong2129052853vative @ P6 @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ y @ x ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ ( par @ ( subs @ p2 @ ya @ c ) @ q2 ) ) @ ( late_BoundOutputS @ ab ) @ y @ rel ) ) ).
% 0.30/0.45
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 ------------------------
% 2.87/1.51 ---- Embedded in THF ---
% 2.87/1.51 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.87/1.51 %%% Generated on Tue Feb 24 08:29:09 EST 2026
% 2.87/1.51 %%% using '$$dhol' embedding, version 1.3.0.
% 2.87/1.51 %%% Logic specification used:
% 2.87/1.51 %%% thf(spec, logic, $$dhol).
% 2.87/1.51
% 2.87/1.51 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.l6Rd1czx4d/DTF2DTF25458.p
% 2.87/1.51 thf(ty_t_Late__Semantics_Oresidual__Rep, type, late_residual_Rep: $tType).
% 2.87/1.51 thf(ty_t_Late__Semantics_Osubject__Rep, type, late_subject_Rep: $tType).
% 2.87/1.51 thf(ty_t_Late__Semantics_OfreeRes__Rep, type, late_freeRes_Rep: $tType).
% 2.87/1.51 thf(ty_t_Late__Semantics_Oresidual, type, late_residual: $tType).
% 2.87/1.51 thf(ty_t_Late__Semantics_Osubject, type, late_subject: $tType).
% 2.87/1.51 thf(ty_t_Late__Semantics_OfreeRes, type, late_freeRes: $tType).
% 2.87/1.51 thf(ty_t_Product__Type_Ounit, type, product_unit: $tType).
% 2.87/1.51 thf(ty_t_Product__Type_Oprod, type, product_prod: ($tType > ($tType > $tType))).
% 2.87/1.51 thf(ty_t_Nominal_Onoption, type, noption: ($tType > $tType)).
% 2.87/1.51 thf(ty_t_Agent_Opi__Rep, type, pi_Rep: $tType).
% 2.87/1.51 thf(ty_t_Agent_Oname, type, name: $tType).
% 2.87/1.51 thf(ty_t_List_Olist, type, list: ($tType > $tType)).
% 2.87/1.51 thf(ty_t_Agent_Opi, type, pi: $tType).
% 2.87/1.51 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 2.87/1.51 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: ($o))).
% 2.87/1.51 thf(sy_cl_Agent_Ofs__name, type, fs_name: (!> [A:$tType]: ($o))).
% 2.87/1.51 thf(sy_cl_Agent_Opt__name, type, pt_name: (!> [A:$tType]: ($o))).
% 2.87/1.51 thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: ($o))).
% 2.87/1.51 thf(sy_cl_Agent_Ocp__name__name, type, cp_name_name: (!> [A:$tType]: ($o))).
% 2.87/1.51 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: ($o))).
% 2.87/1.51 thf(sy_c_Agent_Opi_OInput, type, input: (name > (name > (pi > pi)))).
% 2.87/1.51 thf(sy_c_Agent_Opi_OPar, type, par: (pi > (pi > pi))).
% 2.87/1.51 thf(sy_c_Agent_Opi_ORes, type, res: (name > (pi > pi))).
% 2.87/1.51 thf(sy_c_Agent_Orec_Oswap__name, type, swap_name: (((product_prod @ name) @ name) > (name > name))).
% 2.87/1.51 thf(sy_c_Agent_Osubs, type, subs: (pi > (name > (name > pi)))).
% 2.87/1.51 thf(sy_c_HOL_Odefault__class_Odefault, type, default_default: (!> [A:$tType]: (A))).
% 2.87/1.51 thf(sy_c_If, type, if: (!> [A:$tType]: (($o > (A > (A > A)))))).
% 2.87/1.51 thf(sy_c_Late__Semantics_OfreeRes_OOutputR, type, late_OutputR: (name > (name > late_freeRes))).
% 2.87/1.51 thf(sy_c_Late__Semantics_OfreeRes_OTauR, type, late_TauR: late_freeRes).
% 2.87/1.51 thf(sy_c_Late__Semantics_Oresidual_OBoundR, type, late_BoundR: (late_subject > (name > (pi > late_residual)))).
% 2.87/1.51 thf(sy_c_Late__Semantics_Oresidual_OFreeR, type, late_FreeR: (late_freeRes > (pi > late_residual))).
% 2.87/1.51 thf(sy_c_Late__Semantics_Oresidual__Rep_OFreeR__Rep, type, late_r347633188eR_Rep: (late_freeRes > (pi > late_residual_Rep))).
% 2.87/1.51 thf(sy_c_Late__Semantics_Osubject_OBoundOutputS, type, late_BoundOutputS: (name > late_subject)).
% 2.87/1.51 thf(sy_c_Late__Semantics_Osubject_OInputS, type, late_InputS: (name > late_subject)).
% 2.87/1.51 thf(sy_c_Late__Semantics_Otransitions, type, late_transitions: (pi > (late_residual > $o))).
% 2.87/1.51 thf(sy_c_List_Olist_OCons, type, cons: (!> [A:$tType]: ((A > ((list @ A) > (list @ A)))))).
% 2.87/1.51 thf(sy_c_List_Olist_ONil, type, nil: (!> [A:$tType]: ((list @ A)))).
% 2.87/1.51 thf(sy_c_List_Oproduct__lists, type, product_lists: (!> [A:$tType]: (((list @ (list @ A)) > (list @ (list @ A)))))).
% 2.87/1.51 thf(sy_c_Nominal_Oabs__fun, type, abs_fun: (!> [X:$tType,A:$tType]: ((X > (A > (X > (noption @ A))))))).
% 2.87/1.51 thf(sy_c_Nominal_Ofresh, type, fresh: (!> [X:$tType,A:$tType]: ((X > (A > $o))))).
% 2.87/1.51 thf(sy_c_Nominal_Operm, type, perm: (!> [X:$tType,A:$tType]: (((list @ ((product_prod @ X) @ X)) > (A > A))))).
% 2.87/1.51 thf(sy_c_Nominal_Osupports, type, supports: (!> [X:$tType,A:$tType]: (((set @ X) > (A > $o))))).
% 2.87/1.51 thf(sy_c_Nominal_Oswap, type, swap: (!> [X:$tType]: ((((product_prod @ X) @ X) > (X > X))))).
% 2.87/1.51 thf(sy_c_Product__Type_OPair, type, product_Pair: (!> [A:$tType,B:$tType]: ((A > (B > ((product_prod @ A) @ B)))))).
% 2.87/1.51 thf(sy_c_Product__Type_OUnity, type, product_Unity: product_unit).
% 2.87/1.51 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod, type, product_rec_prod: (!> [A:$tType,B:$tType,T:$tType]: (((A > (B > T)) > (((product_prod @ A) @ B) > T))))).
% 2.87/1.51 thf(sy_c_Product__Type_Oold_Ounit_Orec__unit, type, product_rec_unit: (!> [T:$tType]: ((T > (product_unit > T))))).
% 2.87/1.51 thf(sy_c_Rel_Oeqvt, type, eqvt: (!> [A:$tType]: (((set @ ((product_prod @ A) @ A)) > $o)))).
% 2.87/1.51 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 2.87/1.51 thf(sy_c_Strong__Late__Sim_Oderivative, type, strong2129052853vative: (pi > (pi > (late_subject > (name > ((set @ ((product_prod @ pi) @ pi)) > $o)))))).
% 2.87/1.51 thf(sy_c_Strong__Late__Sim_Osimulation, type, strong743114133lation: (pi > ((set @ ((product_prod @ pi) @ pi)) > (pi > $o)))).
% 2.87/1.51 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 2.87/1.51 thf(sy_v_P, type, p: pi).
% 2.87/1.51 thf(sy_v_PQ____, type, pq: pi).
% 2.87/1.51 thf(sy_v_P_H____, type, p2: pi).
% 2.87/1.51 thf(sy_v_Q, type, q: pi).
% 2.87/1.51 thf(sy_v_Q_H____, type, q2: pi).
% 2.87/1.51 thf(sy_v_Rel, type, rel: (set @ ((product_prod @ pi) @ pi))).
% 2.87/1.51 thf(sy_v_aa____, type, aa: late_subject).
% 2.87/1.51 thf(sy_v_ab____, type, ab: name).
% 2.87/1.51 thf(sy_v_b____, type, b: name).
% 2.87/1.51 thf(sy_v_c____, type, c: name).
% 2.87/1.51 thf(sy_v_x, type, x: name).
% 2.87/1.51 thf(sy_v_xPQ____, type, xPQ: pi).
% 2.87/1.51 thf(sy_v_y____, type, y: name).
% 2.87/1.51 thf(sy_v_ya____, type, ya: name).
% 2.87/1.51 thf(fact_0_cComm1_Ohyps_I5_J, axiom, (ya != b)).
% 2.87/1.51 thf(fact_1_cComm1_Ohyps_I9_J, axiom, (((late_OutputR @ ab) @ x) = late_TauR)).
% 2.87/1.51 thf(fact_2_cOpen_Ohyps_I2_J, axiom, (ab != x)).
% 2.87/1.51 thf(fact_3_cComm1_Ohyps_I6_J, axiom, (ya != c)).
% 2.87/1.51 thf(fact_4_cOpen_Ohyps_I3_J, axiom, (aa = (late_BoundOutputS @ ab))).
% 2.87/1.51 thf(fact_5_assms_I3_J, axiom, ((eqvt @ pi) @ rel)).
% 2.87/1.51 thf(fact_6__092_060open_062y_____A_092_060noteq_062_Ax_092_060close_062, axiom, (y != x)).
% 2.87/1.51 thf(fact_7_Bound_Ohyps_I1_J, axiom, ((late_transitions @ ((res @ x) @ ((par @ p) @ q))) @ (((late_BoundR @ aa) @ y) @ xPQ))).
% 2.87/1.51 thf(fact_8_assms_I1_J, axiom, ((((fresh @ name) @ pi) @ x) @ p)).
% 2.87/1.51 thf(fact_9_cComm1_Ohyps_I3_J, axiom, ((((fresh @ name) @ pi) @ ya) @ p)).
% 2.87/1.51 thf(fact_10_cComm1_Ohyps_I4_J, axiom, ((((fresh @ name) @ pi) @ ya) @ q)).
% 2.87/1.51 thf(fact_11_cComm1_Ohyps_I7_J, axiom, ((((fresh @ name) @ pi) @ ya) @ q2)).
% 2.87/1.51 thf(fact_12_Bound_Ohyps_I3_J, axiom, ((((fresh @ name) @ pi) @ y) @ ((res @ x) @ ((par @ p) @ q)))).
% 2.87/1.51 thf(fact_13_Bound_Ohyps_I2_J, axiom, ((((fresh @ name) @ pi) @ y) @ ((par @ p) @ ((res @ x) @ q)))).
% 2.87/1.51 thf(fact_14_Strong__Late__Sim__SC__Mirabelle__dtpyqonsky_OsubstRes3, axiom, (! [A2:name,P:pi,X2:name]: (((((subs @ ((res @ A2) @ P)) @ X2) @ A2) = ((res @ X2) @ ((((perm @ name) @ pi) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ X2) @ A2)) @ (nil @ ((product_prod @ name) @ name)))) @ P)))))).
% 2.87/1.51 thf(fact_15_cComm1_Ohyps_I1_J, axiom, ((late_transitions @ p) @ (((late_BoundR @ (late_InputS @ b)) @ ya) @ p2))).
% 2.87/1.51 thf(fact_16_perm__swap_I1_J, axiom, (! [X3:$tType]: (((pt_name @ X3) => (! [A2:name,B2:name,X2:X3]: ((((((perm @ name) @ X3) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ A2) @ B2)) @ (nil @ ((product_prod @ name) @ name)))) @ ((((perm @ name) @ X3) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ A2) @ B2)) @ (nil @ ((product_prod @ name) @ name)))) @ X2)) = X2))))))).
% 2.87/1.51 thf(fact_17_name__id, axiom, (! [X:$tType]: (((pt_name @ X) => (! [A2:name,X2:X]: ((((((perm @ name) @ X) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ A2) @ A2)) @ (nil @ ((product_prod @ name) @ name)))) @ X2) = X2))))))).
% 2.87/1.51 thf(fact_18_name__swap, axiom, (! [X:$tType]: (((pt_name @ X) => (! [A2:name,B2:name,X2:X]: ((((((perm @ name) @ X) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ A2) @ B2)) @ (nil @ ((product_prod @ name) @ name)))) @ X2) = ((((perm @ name) @ X) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ B2) @ A2)) @ (nil @ ((product_prod @ name) @ name)))) @ X2)))))))).
% 2.87/1.51 thf(fact_19_name__swap__bij, axiom, (! [X:$tType]: (((pt_name @ X) => (! [A2:name,B2:name,X2:X]: ((((((perm @ name) @ X) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ A2) @ B2)) @ (nil @ ((product_prod @ name) @ name)))) @ ((((perm @ name) @ X) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ A2) @ B2)) @ (nil @ ((product_prod @ name) @ name)))) @ X2)) = X2))))))).
% 2.87/1.51 thf(fact_20_cOpen_Ohyps_I1_J, axiom, ((late_transitions @ ((par @ p) @ q)) @ ((late_FreeR @ ((late_OutputR @ ab) @ x)) @ pq))).
% 2.87/1.51 thf(fact_21_pi_Operm_I8_J, axiom, (! [Pi:(list @ ((product_prod @ name) @ name)),X22:pi,X1:pi]: ((((((perm @ name) @ pi) @ Pi) @ ((par @ X22) @ X1)) = ((par @ ((((perm @ name) @ pi) @ Pi) @ X22)) @ ((((perm @ name) @ pi) @ Pi) @ X1)))))).
% 2.87/1.51 thf(fact_22_simps_I8_J, axiom, (! [P:pi,Q:pi,C:name,D:name]: (((((subs @ ((par @ P) @ Q)) @ C) @ D) = ((par @ (((subs @ P) @ C) @ D)) @ (((subs @ Q) @ C) @ D)))))).
% 2.87/1.51 thf(fact_23_simps_I9_J, axiom, (! [X2:name,C:name,D:name,P:pi]: (((X2 != C) => ((X2 != D) => ((((subs @ ((res @ X2) @ P)) @ C) @ D) = ((res @ X2) @ (((subs @ P) @ C) @ D)))))))).
% 2.87/1.51 thf(fact_24_pt__name1, axiom, (! [A:$tType]: (((pt_name @ A) => (! [X2:A]: ((((((perm @ name) @ A) @ (nil @ ((product_prod @ name) @ name))) @ X2) = X2))))))).
% 2.87/1.51 thf(fact_25_cComm1_Ohyps_I2_J, axiom, ((late_transitions @ q) @ ((late_FreeR @ ((late_OutputR @ b) @ c)) @ q2))).
% 2.87/1.51 thf(fact_26__092_060open_062y_____A_092_060sharp_062_AP_A_092_060parallel_062_AQ_092_060close_062, axiom, ((((fresh @ name) @ pi) @ y) @ ((par @ p) @ q))).
% 2.87/1.51 thf(fact_27_subst__identity, axiom, (! [P:pi,A2:name]: (((((subs @ P) @ A2) @ A2) = P)))).
% 2.87/1.51 thf(fact_28_pi__perm__empty, axiom, (! [Pi_Rep:pi_Rep]: ((((((perm @ name) @ pi_Rep) @ (nil @ ((product_prod @ name) @ name))) @ Pi_Rep) = Pi_Rep)))).
% 2.87/1.51 thf(fact_29__092_060open_062y_____A_092_060sharp_062_AP_092_060close_062, axiom, ((((fresh @ name) @ pi) @ y) @ p)).
% 2.87/1.51 thf(fact_30__092_060open_062y_____A_092_060sharp_062_AQ_092_060close_062, axiom, ((((fresh @ name) @ pi) @ y) @ q)).
% 2.87/1.51 thf(fact_31_pi_Ofresh_I8_J, axiom, (! [A2:name,X22:pi,X1:pi]: ((((((fresh @ name) @ pi) @ A2) @ ((par @ X22) @ X1)) = (((((fresh @ name) @ pi) @ A2) @ X22) & ((((fresh @ name) @ pi) @ A2) @ X1)))))).
% 2.87/1.51 thf(fact_32_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)))))).
% 2.87/1.51 thf(fact_33_perm__fresh__fresh, axiom, (! [X3:$tType]: (((pt_name @ X3) => (! [A2:name,X2:X3,B2:name]: ((((((fresh @ name) @ X3) @ A2) @ X2) => (((((fresh @ name) @ X3) @ B2) @ X2) => (((((perm @ name) @ X3) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ A2) @ B2)) @ (nil @ ((product_prod @ name) @ name)))) @ X2) = X2))))))))).
% 2.87/1.51 thf(fact_34_name__fresh__fresh, axiom, (! [X:$tType]: (((pt_name @ X) => (! [A2:name,X2:X,B2:name]: ((((((fresh @ name) @ X) @ A2) @ X2) => (((((fresh @ name) @ X) @ B2) @ X2) => (((((perm @ name) @ X) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ A2) @ B2)) @ (nil @ ((product_prod @ name) @ name)))) @ X2) = X2))))))))).
% 2.87/1.51 thf(fact_35_Bound_Ohyps_I4_J, axiom, ((((fresh @ name) @ late_subject) @ y) @ aa)).
% 2.87/1.51 thf(fact_36_fresh__perm__app, axiom, (! [X3:$tType]: (((pt_name @ X3) => (! [A2:name,Pi:(list @ ((product_prod @ name) @ name)),X2:X3]: ((((((fresh @ name) @ (list @ ((product_prod @ name) @ name))) @ A2) @ Pi) => (((((fresh @ name) @ X3) @ A2) @ X2) => ((((fresh @ name) @ X3) @ A2) @ ((((perm @ name) @ X3) @ Pi) @ X2)))))))))).
% 2.87/1.51 thf(fact_37_name__exists__fresh, axiom, (! [A:$tType]: (((fs_name @ A) => (! [X2:A]: ((~ ((! [C2:name]: ((~ (((((fresh @ name) @ A) @ C2) @ X2))))))))))))).
% 2.87/1.51 thf(fact_38_fresh__eqvt, axiom, (! [X3:$tType]: (((pt_name @ X3) => (! [Pi:(list @ ((product_prod @ name) @ name)),A2:name,X2:X3]: ((((((perm @ name) @ $o) @ Pi) @ ((((fresh @ name) @ X3) @ A2) @ X2)) = ((((fresh @ name) @ X3) @ ((((perm @ name) @ name) @ Pi) @ A2)) @ ((((perm @ name) @ X3) @ Pi) @ X2))))))))).
% 2.87/1.51 thf(fact_39_fresh__bij, axiom, (! [X3:$tType]: (((pt_name @ X3) => (! [Pi:(list @ ((product_prod @ name) @ name)),A2:name,X2:X3]: ((((((fresh @ name) @ X3) @ ((((perm @ name) @ name) @ Pi) @ A2)) @ ((((perm @ name) @ X3) @ Pi) @ X2)) = ((((fresh @ name) @ X3) @ A2) @ X2)))))))).
% 2.87/1.51 thf(fact_40_freshRes, axiom, (! [A2:name,P:pi]: (((((fresh @ name) @ pi) @ A2) @ ((res @ A2) @ P))))).
% 2.87/1.51 thf(fact_41_fresh__fact2, axiom, (! [A2:name,B2:name,P:pi]: (((A2 != B2) => ((((fresh @ name) @ pi) @ A2) @ (((subs @ P) @ A2) @ B2)))))).
% 2.87/1.51 thf(fact_42_fresh__fact1, axiom, (! [A2:name,P:pi,C:name,B2:name]: ((((((fresh @ name) @ pi) @ A2) @ P) => ((A2 != C) => ((((fresh @ name) @ pi) @ A2) @ (((subs @ P) @ B2) @ C))))))).
% 2.87/1.51 thf(fact_43_forget, axiom, (! [A2:name,P:pi,B2:name]: ((((((fresh @ name) @ pi) @ A2) @ P) => ((((subs @ P) @ A2) @ B2) = P))))).
% 2.87/1.51 thf(fact_44_name__calc_I2_J, axiom, (! [X2:name]: ((((((perm @ name) @ name) @ (nil @ ((product_prod @ name) @ name))) @ X2) = X2)))).
% 2.87/1.51 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P)) = (P @ A2))))).
% 2.87/1.51 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A3:(set @ A)]: ((((collect @ A) @ (^ [X4:A]: ((((member @ A) @ X4) @ A3)))) = A3)))).
% 2.87/1.51 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X5:A]: (((P @ X5) = (Q @ X5)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 2.87/1.51 thf(fact_48_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G:(A > B)]: (((! [X5:A]: (((F @ X5) = (G @ X5)))) => (F = G))))).
% 2.87/1.51 thf(fact_49_Agent_OsubstRes3, axiom, (! [B2:name,P:pi,A2:name]: ((((((fresh @ name) @ pi) @ B2) @ P) => ((((subs @ ((res @ A2) @ P)) @ A2) @ B2) = ((res @ B2) @ (((subs @ P) @ A2) @ B2))))))).
% 2.87/1.51 thf(fact_50_substRes2, axiom, (! [B2:name,P:pi,A2:name]: ((((((fresh @ name) @ pi) @ B2) @ P) => (((res @ A2) @ P) = ((res @ B2) @ (((subs @ P) @ A2) @ B2))))))).
% 2.87/1.51 thf(fact_51_eqvt__subs, axiom, (! [P2:(list @ ((product_prod @ name) @ name)),P:pi,A2:name,B2:name]: ((((((perm @ name) @ pi) @ P2) @ (((subs @ P) @ A2) @ B2)) = (((subs @ ((((perm @ name) @ pi) @ P2) @ P)) @ ((((perm @ name) @ name) @ P2) @ A2)) @ ((((perm @ name) @ name) @ P2) @ B2)))))).
% 2.87/1.51 thf(fact_52_swap__simps_I1_J, axiom, (! [A2:name,B2:name]: ((((((perm @ name) @ name) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ A2) @ B2)) @ (nil @ ((product_prod @ name) @ name)))) @ A2) = B2)))).
% 2.87/1.51 thf(fact_53_swap__simps_I2_J, axiom, (! [A2:name,B2:name]: ((((((perm @ name) @ name) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ A2) @ B2)) @ (nil @ ((product_prod @ name) @ name)))) @ B2) = A2)))).
% 2.87/1.51 thf(fact_54_swap__simps_I3_J, axiom, (! [A2:name,C:name,B2:name]: (((A2 != C) => ((B2 != C) => (((((perm @ name) @ name) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ A2) @ B2)) @ (nil @ ((product_prod @ name) @ name)))) @ C) = C)))))).
% 2.87/1.51 thf(fact_55_fresh__aux, axiom, (! [X3:$tType]: (((pt_name @ X3) => (! [C:name,A2:name,X2:X3,B2:name]: (((C != A2) => (((((fresh @ name) @ X3) @ A2) @ X2) => (((((fresh @ name) @ X3) @ C) @ X2) => ((((fresh @ name) @ X3) @ C) @ ((((perm @ name) @ X3) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ A2) @ B2)) @ (nil @ ((product_prod @ name) @ name)))) @ X2))))))))))).
% 2.87/1.51 thf(fact_56_cp__name__name1, axiom, (! [A:$tType]: (((cp_name_name @ A) => (! [Pi1:(list @ ((product_prod @ name) @ name)),Pi2:(list @ ((product_prod @ name) @ name)),X2:A]: ((((((perm @ name) @ A) @ Pi1) @ ((((perm @ name) @ A) @ Pi2) @ X2)) = ((((perm @ name) @ A) @ ((((perm @ name) @ (list @ ((product_prod @ name) @ name))) @ Pi1) @ Pi2)) @ ((((perm @ name) @ A) @ Pi1) @ X2))))))))).
% 2.87/1.51 thf(fact_57_name__perm__compose, axiom, (! [X:$tType]: (((pt_name @ X) => (! [Pi2:(list @ ((product_prod @ name) @ name)),Pi1:(list @ ((product_prod @ name) @ name)),X2:X]: ((((((perm @ name) @ X) @ Pi2) @ ((((perm @ name) @ X) @ Pi1) @ X2)) = ((((perm @ name) @ X) @ ((((perm @ name) @ (list @ ((product_prod @ name) @ name))) @ Pi2) @ Pi1)) @ ((((perm @ name) @ X) @ Pi2) @ X2))))))))).
% 2.87/1.51 thf(fact_58_perm__compose, axiom, (! [X3:$tType]: (((pt_name @ X3) => (! [Pi2:(list @ ((product_prod @ name) @ name)),Pi1:(list @ ((product_prod @ name) @ name)),X2:X3]: ((((((perm @ name) @ X3) @ Pi2) @ ((((perm @ name) @ X3) @ Pi1) @ X2)) = ((((perm @ name) @ X3) @ ((((perm @ name) @ (list @ ((product_prod @ name) @ name))) @ Pi2) @ Pi1)) @ ((((perm @ name) @ X3) @ Pi2) @ X2))))))))).
% 2.87/1.51 thf(fact_59_perm__bij, axiom, (! [X3:$tType]: (((pt_name @ X3) => (! [Pi:(list @ ((product_prod @ name) @ name)),X2:X3,Y:X3]: (((((((perm @ name) @ X3) @ Pi) @ X2) = ((((perm @ name) @ X3) @ Pi) @ Y)) = (X2 = Y)))))))).
% 2.87/1.51 thf(fact_60_perm__app, axiom, (! [B:$tType,X3:$tType]: (((pt_name @ X3) => (! [Pi:(list @ ((product_prod @ name) @ name)),F:(X3 > B),X2:X3]: ((((((perm @ name) @ B) @ Pi) @ (F @ X2)) = (((((perm @ name) @ (X3 > B)) @ Pi) @ F) @ ((((perm @ name) @ X3) @ Pi) @ X2))))))))).
% 2.87/1.51 thf(fact_61_in__eqvt, axiom, (! [X3:$tType]: (((pt_name @ X3) => (! [Pi:(list @ ((product_prod @ name) @ name)),X2:X3,X6:(set @ X3)]: ((((((perm @ name) @ $o) @ Pi) @ (((member @ X3) @ X2) @ X6)) = (((member @ X3) @ ((((perm @ name) @ X3) @ Pi) @ X2)) @ ((((perm @ name) @ (set @ X3)) @ Pi) @ X6))))))))).
% 2.87/1.51 thf(fact_62_eq__eqvt, axiom, (! [X3:$tType]: (((pt_name @ X3) => (! [Pi:(list @ ((product_prod @ name) @ name)),X2:X3,Y:X3]: ((((((perm @ name) @ $o) @ Pi) @ (X2 = Y)) = (((((perm @ name) @ X3) @ Pi) @ X2) = ((((perm @ name) @ X3) @ Pi) @ Y))))))))).
% 2.87/1.51 thf(fact_63_pi_Oinject_I7_J, axiom, (! [X22:pi,X1:pi,Y2:pi,Y1:pi]: (((((par @ X22) @ X1) = ((par @ Y2) @ Y1)) = ((X22 = Y2) & (X1 = Y1)))))).
% 2.87/1.51 thf(fact_64_alphaRes, axiom, (! [C:name,P:pi,A2:name]: ((((((fresh @ name) @ pi) @ C) @ P) => (((res @ A2) @ P) = ((res @ C) @ ((((perm @ name) @ pi) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ A2) @ C)) @ (nil @ ((product_prod @ name) @ name)))) @ P))))))).
% 2.87/1.51 thf(fact_65_injPermSubst, axiom, (! [B2:name,P:pi,A2:name]: ((((((fresh @ name) @ pi) @ B2) @ P) => (((((perm @ name) @ pi) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ A2) @ B2)) @ (nil @ ((product_prod @ name) @ name)))) @ P) = (((subs @ P) @ A2) @ B2)))))).
% 2.87/1.51 thf(fact_66_renaming, axiom, (! [C:name,P:pi,A2:name,B2:name]: ((((((fresh @ name) @ pi) @ C) @ P) => ((((subs @ P) @ A2) @ B2) = (((subs @ ((((perm @ name) @ pi) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ C) @ A2)) @ (nil @ ((product_prod @ name) @ name)))) @ P)) @ C) @ B2)))))).
% 2.87/1.51 thf(fact_67_pi_Odistinct_I85_J, axiom, (! [Pi1:pi,Pi2:pi,Name:name,Pi3:pi]: ((((par @ Pi1) @ Pi2) != ((res @ Name) @ Pi3))))).
% 2.87/1.51 thf(fact_68_perm__swap_I2_J, axiom, (! [X3:$tType]: (((pt_name @ X3) => (! [A2:name,B2:name,X2:X3]: ((((((perm @ name) @ X3) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ A2) @ B2)) @ (nil @ ((product_prod @ name) @ name)))) @ ((((perm @ name) @ X3) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ B2) @ A2)) @ (nil @ ((product_prod @ name) @ name)))) @ X2)) = X2))))))).
% 2.87/1.51 thf(fact_69_transitions_OClose2, axiom, (! [P:pi,A2:name,Y:name,P3:pi,Q:pi,X2:name,Q2:pi]: ((((late_transitions @ P) @ (((late_BoundR @ (late_BoundOutputS @ A2)) @ Y) @ P3)) => (((late_transitions @ Q) @ (((late_BoundR @ (late_InputS @ A2)) @ X2) @ Q2)) => (((((fresh @ name) @ pi) @ X2) @ P) => (((((fresh @ name) @ pi) @ X2) @ Q) => (((((fresh @ name) @ pi) @ Y) @ P) => (((((fresh @ name) @ pi) @ Y) @ Q) => ((X2 != A2) => (((((fresh @ name) @ pi) @ X2) @ P3) => ((Y != A2) => (((((fresh @ name) @ pi) @ Y) @ Q2) => ((X2 != Y) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ late_TauR) @ ((res @ Y) @ ((par @ P3) @ (((subs @ Q2) @ X2) @ Y))))))))))))))))))).
% 2.87/1.51 thf(fact_70_transitions_OClose1, axiom, (! [P:pi,A2:name,X2:name,P3:pi,Q:pi,Y:name,Q2:pi]: ((((late_transitions @ P) @ (((late_BoundR @ (late_InputS @ A2)) @ X2) @ P3)) => (((late_transitions @ Q) @ (((late_BoundR @ (late_BoundOutputS @ A2)) @ Y) @ Q2)) => (((((fresh @ name) @ pi) @ X2) @ P) => (((((fresh @ name) @ pi) @ X2) @ Q) => (((((fresh @ name) @ pi) @ Y) @ P) => (((((fresh @ name) @ pi) @ Y) @ Q) => ((X2 != A2) => (((((fresh @ name) @ pi) @ X2) @ Q2) => ((Y != A2) => (((((fresh @ name) @ pi) @ Y) @ P3) => ((X2 != Y) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ late_TauR) @ ((res @ Y) @ ((par @ (((subs @ P3) @ X2) @ Y)) @ Q2)))))))))))))))))).
% 2.87/1.51 thf(fact_71_Late__Semantics_OClose2, axiom, (! [P:pi,A2:name,Y:name,P3:pi,Q:pi,X2:name,Q2:pi]: ((((late_transitions @ P) @ (((late_BoundR @ (late_BoundOutputS @ A2)) @ Y) @ P3)) => (((late_transitions @ Q) @ (((late_BoundR @ (late_InputS @ A2)) @ X2) @ Q2)) => (((((fresh @ name) @ pi) @ Y) @ Q) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ late_TauR) @ ((res @ Y) @ ((par @ P3) @ (((subs @ Q2) @ X2) @ Y))))))))))).
% 2.87/1.51 thf(fact_72_Late__Semantics_OClose1, axiom, (! [P:pi,A2:name,X2:name,P3:pi,Q:pi,Y:name,Q2:pi]: ((((late_transitions @ P) @ (((late_BoundR @ (late_InputS @ A2)) @ X2) @ P3)) => (((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 @ P3) @ X2) @ Y)) @ Q2)))))))))).
% 2.87/1.51 thf(fact_73_transitions_OComm2, axiom, (! [P:pi,A2:name,B2:name,P3:pi,Q:pi,X2:name,Q2:pi]: ((((late_transitions @ P) @ ((late_FreeR @ ((late_OutputR @ A2) @ B2)) @ P3)) => (((late_transitions @ Q) @ (((late_BoundR @ (late_InputS @ A2)) @ X2) @ Q2)) => (((((fresh @ name) @ pi) @ X2) @ P) => (((((fresh @ name) @ pi) @ X2) @ Q) => ((X2 != A2) => ((X2 != B2) => (((((fresh @ name) @ pi) @ X2) @ P3) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ late_TauR) @ ((par @ P3) @ (((subs @ Q2) @ X2) @ B2)))))))))))))).
% 2.87/1.51 thf(fact_74_transitions_OComm1, axiom, (! [P:pi,A2:name,X2:name,P3:pi,Q:pi,B2:name,Q2:pi]: ((((late_transitions @ P) @ (((late_BoundR @ (late_InputS @ A2)) @ X2) @ P3)) => (((late_transitions @ Q) @ ((late_FreeR @ ((late_OutputR @ A2) @ B2)) @ Q2)) => (((((fresh @ name) @ pi) @ X2) @ P) => (((((fresh @ name) @ pi) @ X2) @ Q) => ((X2 != A2) => ((X2 != B2) => (((((fresh @ name) @ pi) @ X2) @ Q2) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ late_TauR) @ ((par @ (((subs @ P3) @ X2) @ B2)) @ Q2))))))))))))).
% 2.87/1.51 thf(fact_75_Late__Semantics_OComm2, axiom, (! [P:pi,A2:name,B2:name,P3:pi,Q:pi,X2:name,Q2:pi]: ((((late_transitions @ P) @ ((late_FreeR @ ((late_OutputR @ A2) @ B2)) @ P3)) => (((late_transitions @ Q) @ (((late_BoundR @ (late_InputS @ A2)) @ X2) @ Q2)) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ late_TauR) @ ((par @ P3) @ (((subs @ Q2) @ X2) @ B2))))))))).
% 2.87/1.51 thf(fact_76_Late__Semantics_OComm1, axiom, (! [P:pi,A2:name,X2:name,P3:pi,Q:pi,B2:name,Q2:pi]: ((((late_transitions @ P) @ (((late_BoundR @ (late_InputS @ A2)) @ X2) @ P3)) => (((late_transitions @ Q) @ ((late_FreeR @ ((late_OutputR @ A2) @ B2)) @ Q2)) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ late_TauR) @ ((par @ (((subs @ P3) @ X2) @ B2)) @ Q2)))))))).
% 2.87/1.51 thf(fact_77_alphaBoundResidual, axiom, (! [X7:name,P:pi,A2:late_subject,X2:name]: ((((((fresh @ name) @ pi) @ X7) @ P) => ((((late_BoundR @ A2) @ X2) @ P) = (((late_BoundR @ A2) @ X7) @ ((((perm @ name) @ pi) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ X2) @ X7)) @ (nil @ ((product_prod @ name) @ name)))) @ P))))))).
% 2.87/1.51 thf(fact_78_freeRes__perm__empty, axiom, (! [FreeRes_Rep:late_freeRes_Rep]: ((((((perm @ name) @ late_freeRes_Rep) @ (nil @ ((product_prod @ name) @ name))) @ FreeRes_Rep) = FreeRes_Rep)))).
% 2.87/1.51 thf(fact_79_subject__perm__empty, axiom, (! [Subject_Rep:late_subject_Rep]: ((((((perm @ name) @ late_subject_Rep) @ (nil @ ((product_prod @ name) @ name))) @ Subject_Rep) = Subject_Rep)))).
% 2.87/1.51 thf(fact_80_residual__perm__empty, axiom, (! [Residual_Rep:late_residual_Rep]: ((((((perm @ name) @ late_residual_Rep) @ (nil @ ((product_prod @ name) @ name))) @ Residual_Rep) = Residual_Rep)))).
% 2.87/1.51 thf(fact_81_freeRes_Ofresh_I1_J, axiom, (! [A2:name,X22:name,X1:name]: ((((((fresh @ name) @ late_freeRes) @ A2) @ ((late_OutputR @ X22) @ X1)) = (((((fresh @ name) @ name) @ A2) @ X22) & ((((fresh @ name) @ name) @ A2) @ X1)))))).
% 2.87/1.51 thf(fact_82_Late__Semantics_OfreeRes_Oinject, axiom, (! [X22:name,X1:name,Y2:name,Y1:name]: (((((late_OutputR @ X22) @ X1) = ((late_OutputR @ Y2) @ Y1)) = ((X22 = Y2) & (X1 = Y1)))))).
% 2.87/1.51 thf(fact_83_Late__Semantics_Osubject_Oinject_I2_J, axiom, (! [X1:name,Y1:name]: ((((late_BoundOutputS @ X1) = (late_BoundOutputS @ Y1)) = (X1 = Y1))))).
% 2.87/1.51 thf(fact_84_freeRes_Ofresh_I2_J, axiom, (! [A2:name]: (((((fresh @ name) @ late_freeRes) @ A2) @ late_TauR)))).
% 2.87/1.51 thf(fact_85_freeRes_Operm_I2_J, axiom, (! [Pi:(list @ ((product_prod @ name) @ name))]: ((((((perm @ name) @ late_freeRes) @ Pi) @ late_TauR) = late_TauR)))).
% 2.87/1.51 thf(fact_86_cComm1_Ohyps_I8_J, axiom, ((((fresh @ name) @ product_unit) @ ya) @ product_Unity)).
% 2.87/1.51 thf(fact_87_residual_Ofresh_I2_J, axiom, (! [A2:name,X22:late_freeRes,X1:pi]: ((((((fresh @ name) @ late_residual) @ A2) @ ((late_FreeR @ X22) @ X1)) = (((((fresh @ name) @ late_freeRes) @ A2) @ X22) & ((((fresh @ name) @ pi) @ A2) @ X1)))))).
% 2.87/1.51 thf(fact_88_substTrans, axiom, (! [B2:name,P:pi,A2:name,C:name]: ((((((fresh @ name) @ pi) @ B2) @ P) => ((((subs @ (((subs @ P) @ A2) @ B2)) @ B2) @ C) = (((subs @ P) @ A2) @ C)))))).
% 2.87/1.51 thf(fact_89_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)))))).
% 2.87/1.51 thf(fact_90_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)))))).
% 2.87/1.51 thf(fact_91_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)))))).
% 2.87/1.51 thf(fact_92_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)))))).
% 2.87/1.51 thf(fact_93_subject_Ofresh_I2_J, axiom, (! [A2:name,X1:name]: ((((((fresh @ name) @ late_subject) @ A2) @ (late_BoundOutputS @ X1)) = ((((fresh @ name) @ name) @ A2) @ X1))))).
% 2.87/1.51 thf(fact_94_subject_Ofresh_I1_J, axiom, (! [A2:name,X1:name]: ((((((fresh @ name) @ late_subject) @ A2) @ (late_InputS @ X1)) = ((((fresh @ name) @ name) @ A2) @ X1))))).
% 2.87/1.51 thf(fact_95_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)))))).
% 2.87/1.51 thf(fact_96_name__bij, axiom, (! [Pi:(list @ ((product_prod @ name) @ name)),X2:name,Y:name]: (((((((perm @ name) @ name) @ Pi) @ X2) = ((((perm @ name) @ name) @ Pi) @ Y)) = (X2 = Y))))).
% 2.87/1.51 thf(fact_97_freshResidual, axiom, (! [P:pi,Rs:late_residual,X2:name]: ((((late_transitions @ P) @ Rs) => (((((fresh @ name) @ pi) @ X2) @ P) => ((((fresh @ name) @ late_residual) @ X2) @ Rs)))))).
% 2.87/1.51 thf(fact_98_resCasesF, axiom, (! [X2:name,P:pi,Alpha:late_freeRes,XP:pi,F2:(pi > $o)]: ((((late_transitions @ ((res @ X2) @ P)) @ ((late_FreeR @ Alpha) @ XP)) => ((! [P4:pi]: ((((late_transitions @ P) @ ((late_FreeR @ Alpha) @ P4)) => (((((fresh @ name) @ late_freeRes) @ X2) @ Alpha) => (F2 @ ((res @ X2) @ P4)))))) => (F2 @ XP)))))).
% 2.87/1.51 thf(fact_99_resCasesF_H, axiom, (! [X2:name,P:pi,Alpha:late_freeRes,P3:pi]: ((((late_transitions @ ((res @ X2) @ P)) @ ((late_FreeR @ Alpha) @ P3)) => (~ ((! [P5:pi,Alpha2:late_freeRes,P4:pi,Y3:name]: (((((res @ X2) @ P) = ((res @ Y3) @ P5)) => ((((late_FreeR @ Alpha) @ P3) = ((late_FreeR @ Alpha2) @ ((res @ Y3) @ P4))) => (((late_transitions @ P5) @ ((late_FreeR @ Alpha2) @ P4)) => (~ (((((fresh @ name) @ late_freeRes) @ Y3) @ Alpha2)))))))))))))).
% 2.87/1.51 thf(fact_100_ResF, axiom, (! [P:pi,Alpha:late_freeRes,P3:pi,Y:name]: ((((late_transitions @ P) @ ((late_FreeR @ Alpha) @ P3)) => (((((fresh @ name) @ late_freeRes) @ Y) @ Alpha) => ((late_transitions @ ((res @ Y) @ P)) @ ((late_FreeR @ Alpha) @ ((res @ Y) @ P3)))))))).
% 2.87/1.51 thf(fact_101_Late__Semantics_OResB, axiom, (! [P:pi,A2:late_subject,X2:name,P3:pi,Y:name]: ((((late_transitions @ P) @ (((late_BoundR @ A2) @ X2) @ P3)) => (((((fresh @ name) @ late_subject) @ Y) @ A2) => ((Y != X2) => ((late_transitions @ ((res @ Y) @ P)) @ (((late_BoundR @ A2) @ X2) @ ((res @ Y) @ P3))))))))).
% 2.87/1.51 thf(fact_102_freshFreeDerivative_I1_J, axiom, (! [P:pi,Alpha:late_freeRes,P3:pi,Y:name]: ((((late_transitions @ P) @ ((late_FreeR @ Alpha) @ P3)) => (((((fresh @ name) @ pi) @ Y) @ P) => ((((fresh @ name) @ late_freeRes) @ Y) @ Alpha)))))).
% 2.87/1.51 thf(fact_103_freshBoundDerivative_I1_J, axiom, (! [P:pi,A2:late_subject,X2:name,P3:pi,Y:name]: ((((late_transitions @ P) @ (((late_BoundR @ A2) @ X2) @ P3)) => (((((fresh @ name) @ pi) @ Y) @ P) => ((((fresh @ name) @ late_subject) @ Y) @ A2)))))).
% 2.87/1.51 thf(fact_104_transitions_OResB, axiom, (! [P:pi,A2:late_subject,X2:name,P3:pi,Y:name]: ((((late_transitions @ P) @ (((late_BoundR @ A2) @ X2) @ P3)) => (((((fresh @ name) @ late_subject) @ Y) @ A2) => ((Y != X2) => (((((fresh @ name) @ pi) @ X2) @ P) => (((((fresh @ name) @ late_subject) @ X2) @ A2) => ((late_transitions @ ((res @ Y) @ P)) @ (((late_BoundR @ A2) @ X2) @ ((res @ Y) @ P3))))))))))).
% 2.87/1.51 thf(fact_105_parCasesB_H, axiom, (! [P:pi,Q:pi,B2:late_subject,Y:name,P3:pi]: ((((late_transitions @ ((par @ P) @ Q)) @ (((late_BoundR @ B2) @ Y) @ P3)) => ((! [P5:pi,A4:late_subject,X5:name,P4:pi,Q3:pi]: (((((par @ P) @ Q) = ((par @ P5) @ Q3)) => (((((late_BoundR @ B2) @ Y) @ P3) = (((late_BoundR @ A4) @ X5) @ ((par @ P4) @ Q3))) => (((late_transitions @ P5) @ (((late_BoundR @ A4) @ X5) @ P4)) => (((((fresh @ name) @ pi) @ X5) @ P5) => (((((fresh @ name) @ pi) @ X5) @ Q3) => (~ (((((fresh @ name) @ late_subject) @ X5) @ A4)))))))))) => (~ ((! [Q3:pi,A4:late_subject,X5:name,Q4:pi,P5:pi]: (((((par @ P) @ Q) = ((par @ P5) @ Q3)) => (((((late_BoundR @ B2) @ Y) @ P3) = (((late_BoundR @ A4) @ X5) @ ((par @ P5) @ Q4))) => (((late_transitions @ Q3) @ (((late_BoundR @ A4) @ X5) @ Q4)) => (((((fresh @ name) @ pi) @ X5) @ P5) => (((((fresh @ name) @ pi) @ X5) @ Q3) => (~ (((((fresh @ name) @ late_subject) @ X5) @ A4))))))))))))))))).
% 2.87/1.51 thf(fact_106_transitions_OPar1B, axiom, (! [P:pi,A2:late_subject,X2:name,P3:pi,Q:pi]: ((((late_transitions @ P) @ (((late_BoundR @ A2) @ X2) @ P3)) => (((((fresh @ name) @ pi) @ X2) @ P) => (((((fresh @ name) @ pi) @ X2) @ Q) => (((((fresh @ name) @ late_subject) @ X2) @ A2) => ((late_transitions @ ((par @ P) @ Q)) @ (((late_BoundR @ A2) @ X2) @ ((par @ P3) @ Q)))))))))).
% 2.87/1.51 thf(fact_107_transitions_OPar2B, axiom, (! [Q:pi,A2:late_subject,X2:name,Q2:pi,P:pi]: ((((late_transitions @ Q) @ (((late_BoundR @ A2) @ X2) @ Q2)) => (((((fresh @ name) @ pi) @ X2) @ P) => (((((fresh @ name) @ pi) @ X2) @ Q) => (((((fresh @ name) @ late_subject) @ X2) @ A2) => ((late_transitions @ ((par @ P) @ Q)) @ (((late_BoundR @ A2) @ X2) @ ((par @ P) @ Q2)))))))))).
% 2.87/1.51 thf(fact_108_resCases_H, axiom, (! [X2:name,P:pi,Rs:late_residual]: ((((late_transitions @ ((res @ X2) @ P)) @ Rs) => ((! [P5:pi,A4:name,B3:name]: (((((res @ X2) @ P) = ((res @ B3) @ P5)) => (! [P4:pi]: (((Rs = (((late_BoundR @ (late_BoundOutputS @ A4)) @ B3) @ P4)) => (((late_transitions @ P5) @ ((late_FreeR @ ((late_OutputR @ A4) @ B3)) @ P4)) => (A4 = B3)))))))) => ((! [P5:pi,A4:late_subject,X5:name,P4:pi,Y3:name]: (((((res @ X2) @ P) = ((res @ Y3) @ P5)) => ((Rs = (((late_BoundR @ A4) @ X5) @ ((res @ Y3) @ P4))) => (((late_transitions @ P5) @ (((late_BoundR @ A4) @ X5) @ P4)) => (((((fresh @ name) @ late_subject) @ Y3) @ A4) => ((Y3 != X5) => (((((fresh @ name) @ pi) @ X5) @ P5) => (~ (((((fresh @ name) @ late_subject) @ X5) @ A4))))))))))) => (~ ((! [P5:pi,Alpha2:late_freeRes,P4:pi,Y3:name]: (((((res @ X2) @ P) = ((res @ Y3) @ P5)) => ((Rs = ((late_FreeR @ Alpha2) @ ((res @ Y3) @ P4))) => (((late_transitions @ P5) @ ((late_FreeR @ Alpha2) @ P4)) => (~ (((((fresh @ name) @ late_freeRes) @ Y3) @ Alpha2)))))))))))))))).
% 2.87/1.51 thf(fact_109_residual_Oinject_I2_J, axiom, (! [X22:late_freeRes,X1:pi,Y2:late_freeRes,Y1:pi]: (((((late_FreeR @ X22) @ X1) = ((late_FreeR @ Y2) @ Y1)) = ((X22 = Y2) & (X1 = Y1)))))).
% 2.87/1.51 thf(fact_110_resCasesB_H, axiom, (! [X7:name,P:pi,A2:late_subject,Y4:name,P3:pi]: ((((late_transitions @ ((res @ X7) @ P)) @ (((late_BoundR @ A2) @ Y4) @ P3)) => ((! [P5:pi,A4:name,B3:name]: (((((res @ X7) @ P) = ((res @ B3) @ P5)) => (! [P4:pi]: ((((((late_BoundR @ A2) @ Y4) @ P3) = (((late_BoundR @ (late_BoundOutputS @ A4)) @ B3) @ P4)) => (((late_transitions @ P5) @ ((late_FreeR @ ((late_OutputR @ A4) @ B3)) @ P4)) => (A4 = B3)))))))) => (~ ((! [P5:pi,A4:late_subject,X5:name,P4:pi,Y3:name]: (((((res @ X7) @ P) = ((res @ Y3) @ P5)) => (((((late_BoundR @ A2) @ Y4) @ P3) = (((late_BoundR @ A4) @ X5) @ ((res @ Y3) @ P4))) => (((late_transitions @ P5) @ (((late_BoundR @ A4) @ X5) @ P4)) => (((((fresh @ name) @ late_subject) @ Y3) @ A4) => ((Y3 != X5) => (((((fresh @ name) @ pi) @ X5) @ P5) => (~ (((((fresh @ name) @ late_subject) @ X5) @ A4)))))))))))))))))).
% 2.87/1.51 thf(fact_111_residual_Odistinct_I1_J, axiom, (! [Subject:late_subject,Name2:name,Pi:pi,FreeRes:late_freeRes,Pi3:pi]: (((((late_BoundR @ Subject) @ Name2) @ Pi) != ((late_FreeR @ FreeRes) @ Pi3))))).
% 2.87/1.51 thf(fact_112_residual_Oinducts, axiom, (! [P:(late_residual > $o),Residual:late_residual]: (((! [Subject2:late_subject,Name3:name,Pi4:pi]: ((P @ (((late_BoundR @ Subject2) @ Name3) @ Pi4)))) => ((! [FreeRes2:late_freeRes,Pi4:pi]: ((P @ ((late_FreeR @ FreeRes2) @ Pi4)))) => (P @ Residual)))))).
% 2.87/1.51 thf(fact_113_eqvt, axiom, (! [X1:pi,X22:late_residual,Pi:(list @ ((product_prod @ name) @ name))]: ((((late_transitions @ X1) @ X22) => ((late_transitions @ ((((perm @ name) @ pi) @ Pi) @ X1)) @ ((((perm @ name) @ late_residual) @ Pi) @ X22)))))).
% 2.87/1.51 thf(fact_114_freeRes_Ostrong__inducts, axiom, (! [A:$tType,P:(A > (late_freeRes > $o)),Z:A,FreeRes3:late_freeRes]: (((! [Name1:name,Name22:name,Z2:A]: (((P @ Z2) @ ((late_OutputR @ Name1) @ Name22)))) => ((! [Z2:A]: (((P @ Z2) @ late_TauR))) => ((P @ Z) @ FreeRes3)))))).
% 2.87/1.51 thf(fact_115_freeRes_Ostrong__induct_H, axiom, (! [N:$tType,P:(N > (late_freeRes > $o)),Z:N,FreeRes3:late_freeRes]: (((! [Name1:name,Name22:name,Z2:N]: (((P @ Z2) @ ((late_OutputR @ Name1) @ Name22)))) => ((! [Z2:N]: (((P @ Z2) @ late_TauR))) => ((P @ Z) @ FreeRes3)))))).
% 2.87/1.51 thf(fact_116_freeRes_Oinducts, axiom, (! [P:(late_freeRes > $o),FreeRes3:late_freeRes]: (((! [Name1:name,Name22:name]: ((P @ ((late_OutputR @ Name1) @ Name22)))) => ((P @ late_TauR) => (P @ FreeRes3)))))).
% 2.87/1.51 thf(fact_117_Late__Semantics_OfreeRes_Odistinct_I1_J, axiom, (! [Name12:name,Name23:name]: ((((late_OutputR @ Name12) @ Name23) != late_TauR)))).
% 2.87/1.51 thf(fact_118_Late__Semantics_Osubject_Odistinct_I1_J, axiom, (! [Name2:name,Name:name]: (((late_InputS @ Name2) != (late_BoundOutputS @ Name))))).
% 2.87/1.51 thf(fact_119_subject_Oinducts, axiom, (! [P:(late_subject > $o),Subject:late_subject]: (((! [Name3:name]: ((P @ (late_InputS @ Name3)))) => ((! [Name3:name]: ((P @ (late_BoundOutputS @ Name3)))) => (P @ Subject)))))).
% 2.87/1.51 thf(fact_120_subject_Ostrong__induct_H, axiom, (! [N:$tType,P:(N > (late_subject > $o)),Z:N,Subject:late_subject]: (((! [Name3:name,Z2:N]: (((P @ Z2) @ (late_InputS @ Name3)))) => ((! [Name3:name,Z2:N]: (((P @ Z2) @ (late_BoundOutputS @ Name3)))) => ((P @ Z) @ Subject)))))).
% 2.87/1.51 thf(fact_121_subject_Ostrong__inducts, axiom, (! [A:$tType,P:(A > (late_subject > $o)),Z:A,Subject:late_subject]: (((! [Name3:name,Z2:A]: (((P @ Z2) @ (late_InputS @ Name3)))) => ((! [Name3:name,Z2:A]: (((P @ Z2) @ (late_BoundOutputS @ Name3)))) => ((P @ Z) @ Subject)))))).
% 2.87/1.51 thf(fact_122_resCasesB, axiom, (! [Y:name,P:pi,A2:late_subject,X2:name,YP:pi,F2:(late_subject > (pi > $o))]: ((((late_transitions @ ((res @ Y) @ P)) @ (((late_BoundR @ A2) @ X2) @ YP)) => ((X2 != Y) => (((((fresh @ name) @ pi) @ X2) @ P) => ((! [B3:name,P4:pi]: ((((late_transitions @ P) @ ((late_FreeR @ ((late_OutputR @ B3) @ Y)) @ P4)) => ((B3 != Y) => ((A2 = (late_BoundOutputS @ B3)) => ((F2 @ (late_BoundOutputS @ B3)) @ ((((perm @ name) @ pi) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ X2) @ Y)) @ (nil @ ((product_prod @ name) @ name)))) @ P4))))))) => ((! [P4:pi]: ((((late_transitions @ P) @ (((late_BoundR @ A2) @ X2) @ P4)) => (((((fresh @ name) @ late_subject) @ Y) @ A2) => ((F2 @ A2) @ ((res @ Y) @ P4)))))) => ((F2 @ A2) @ YP))))))))).
% 2.87/1.51 thf(fact_123_Par1F, axiom, (! [P:pi,Alpha:late_freeRes,P3:pi,Q:pi]: ((((late_transitions @ P) @ ((late_FreeR @ Alpha) @ P3)) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ Alpha) @ ((par @ P3) @ Q))))))).
% 2.87/1.51 thf(fact_124_Par2F, axiom, (! [Q:pi,Alpha:late_freeRes,Q2:pi,P:pi]: ((((late_transitions @ Q) @ ((late_FreeR @ Alpha) @ Q2)) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ Alpha) @ ((par @ P) @ Q2))))))).
% 2.87/1.51 thf(fact_125_freshBoundDerivative_I2_J, axiom, (! [P:pi,A2:late_subject,X2:name,P3:pi,Y:name]: ((((late_transitions @ P) @ (((late_BoundR @ A2) @ X2) @ P3)) => (((((fresh @ name) @ pi) @ Y) @ P) => ((Y != X2) => ((((fresh @ name) @ pi) @ Y) @ P3))))))).
% 2.87/1.51 thf(fact_126_residual_Ostrong__inducts, axiom, (! [A:$tType]: (((fs_name @ A) => (! [P:(A > (late_residual > $o)),Z:A,Residual:late_residual]: (((! [Subject2:late_subject,Name3:name,Pi4:pi,Z2:A]: ((((((fresh @ name) @ A) @ Name3) @ Z2) => (((((fresh @ name) @ late_subject) @ Name3) @ Subject2) => ((P @ Z2) @ (((late_BoundR @ Subject2) @ Name3) @ Pi4)))))) => ((! [FreeRes2:late_freeRes,Pi4:pi,Z2:A]: (((P @ Z2) @ ((late_FreeR @ FreeRes2) @ Pi4)))) => ((P @ Z) @ Residual))))))))).
% 2.87/1.51 thf(fact_127_residual_Ostrong__induct, axiom, (! [N:$tType]: (((fs_name @ N) => (! [P:(N > (late_residual > $o)),Z:N,Residual:late_residual]: (((! [Subject2:late_subject,Name3:name,Pi4:pi,Z2:N]: ((((((fresh @ name) @ N) @ Name3) @ Z2) => (((((fresh @ name) @ late_subject) @ Name3) @ Subject2) => ((P @ Z2) @ (((late_BoundR @ Subject2) @ Name3) @ Pi4)))))) => ((! [FreeRes2:late_freeRes,Pi4:pi,Z2:N]: (((P @ Z2) @ ((late_FreeR @ FreeRes2) @ Pi4)))) => ((P @ Z) @ Residual))))))))).
% 2.87/1.51 thf(fact_128_freshFreeDerivative_I2_J, axiom, (! [P:pi,Alpha:late_freeRes,P3:pi,Y:name]: ((((late_transitions @ P) @ ((late_FreeR @ Alpha) @ P3)) => (((((fresh @ name) @ pi) @ Y) @ P) => ((((fresh @ name) @ pi) @ Y) @ P3)))))).
% 2.87/1.51 thf(fact_129_Late__Semantics_OPar1B, axiom, (! [P:pi,A2:late_subject,X2:name,P3:pi,Q:pi]: ((((late_transitions @ P) @ (((late_BoundR @ A2) @ X2) @ P3)) => (((((fresh @ name) @ pi) @ X2) @ Q) => ((late_transitions @ ((par @ P) @ Q)) @ (((late_BoundR @ A2) @ X2) @ ((par @ P3) @ Q)))))))).
% 2.87/1.51 thf(fact_130_Late__Semantics_OPar2B, axiom, (! [Q:pi,A2:late_subject,X2:name,Q2:pi,P:pi]: ((((late_transitions @ Q) @ (((late_BoundR @ A2) @ X2) @ Q2)) => (((((fresh @ name) @ pi) @ X2) @ P) => ((late_transitions @ ((par @ P) @ Q)) @ (((late_BoundR @ A2) @ X2) @ ((par @ P) @ Q2)))))))).
% 2.87/1.51 thf(fact_131_parCasesB, axiom, (! [P:pi,Q:pi,A2:late_subject,X2:name,PQ:pi,Prop:(pi > $o)]: ((((late_transitions @ ((par @ P) @ Q)) @ (((late_BoundR @ A2) @ X2) @ PQ)) => (((((fresh @ name) @ pi) @ X2) @ P) => (((((fresh @ name) @ pi) @ X2) @ Q) => ((! [P4:pi]: ((((late_transitions @ P) @ (((late_BoundR @ A2) @ X2) @ P4)) => (Prop @ ((par @ P4) @ Q))))) => ((! [Q4:pi]: ((((late_transitions @ Q) @ (((late_BoundR @ A2) @ X2) @ Q4)) => (Prop @ ((par @ P) @ Q4))))) => (Prop @ PQ))))))))).
% 2.87/1.51 thf(fact_132_Open, axiom, (! [P:pi,A2:name,B2:name,P3:pi]: ((((late_transitions @ P) @ ((late_FreeR @ ((late_OutputR @ A2) @ B2)) @ P3)) => ((A2 != B2) => ((late_transitions @ ((res @ B2) @ P)) @ (((late_BoundR @ (late_BoundOutputS @ A2)) @ B2) @ P3))))))).
% 2.87/1.51 thf(fact_133_derivativeEqvtI2, axiom, (! [P:pi,Q:pi,A2:late_subject,X2:name,Rel:(set @ ((product_prod @ pi) @ pi)),Perm:(list @ ((product_prod @ name) @ name))]: (((((((strong2129052853vative @ P) @ Q) @ A2) @ X2) @ Rel) => (((eqvt @ pi) @ Rel) => (((((strong2129052853vative @ ((((perm @ name) @ pi) @ Perm) @ P)) @ ((((perm @ name) @ pi) @ Perm) @ Q)) @ A2) @ ((((perm @ name) @ name) @ Perm) @ X2)) @ Rel)))))).
% 2.87/1.51 thf(fact_134_derivativeEqvtI, axiom, (! [P:pi,Q:pi,A2:late_subject,X2:name,Rel:(set @ ((product_prod @ pi) @ pi)),Perm:(list @ ((product_prod @ name) @ name))]: (((((((strong2129052853vative @ P) @ Q) @ A2) @ X2) @ Rel) => (((eqvt @ pi) @ Rel) => (((((strong2129052853vative @ ((((perm @ name) @ pi) @ Perm) @ P)) @ ((((perm @ name) @ pi) @ Perm) @ Q)) @ ((((perm @ name) @ late_subject) @ Perm) @ A2)) @ ((((perm @ name) @ name) @ Perm) @ X2)) @ Rel)))))).
% 2.87/1.51 thf(fact_135_fresh__prod, axiom, (! [A:$tType,X:$tType,B:$tType,A2:X,X2:A,Y:B]: ((((((fresh @ X) @ ((product_prod @ A) @ B)) @ A2) @ ((((product_Pair @ A) @ B) @ X2) @ Y)) = (((((fresh @ X) @ A) @ A2) @ X2) & ((((fresh @ X) @ B) @ A2) @ Y)))))).
% 2.87/1.51 thf(fact_136_Res, axiom, (! [Y:name,R:pi,S:pi]: ((((((fresh @ name) @ pi) @ Y) @ R) => (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ ((par @ R) @ ((res @ Y) @ S))) @ ((res @ Y) @ ((par @ R) @ S)))) @ rel))))).
% 2.87/1.51 thf(fact_137_ScopeExt, axiom, (! [Y:name,R:pi,Z:name,S:pi]: ((((((fresh @ name) @ pi) @ Y) @ R) => (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ ((res @ Z) @ ((par @ R) @ ((res @ Y) @ S)))) @ ((res @ Y) @ ((res @ Z) @ ((par @ R) @ S))))) @ rel))))).
% 2.87/1.51 thf(fact_138_fresh__list__cons, axiom, (! [X:$tType,A:$tType,A2:X,X2:A,Xs:(list @ A)]: ((((((fresh @ X) @ (list @ A)) @ A2) @ (((cons @ A) @ X2) @ Xs)) = (((((fresh @ X) @ A) @ A2) @ X2) & ((((fresh @ X) @ (list @ A)) @ A2) @ Xs)))))).
% 2.87/1.51 thf(fact_139_Bound_Ohyps_I5_J, axiom, ((((fresh @ name) @ ((product_prod @ name) @ ((product_prod @ pi) @ pi))) @ y) @ ((((product_Pair @ name) @ ((product_prod @ pi) @ pi)) @ x) @ ((((product_Pair @ pi) @ pi) @ p) @ q)))).
% 2.87/1.51 thf(fact_140_false__eqvt, axiom, (! [A:$tType,Pi:(list @ ((product_prod @ A) @ A))]: ((~ (((((perm @ A) @ $o) @ Pi) @ $false)))))).
% 2.87/1.51 thf(fact_141_true__eqvt, axiom, (! [A:$tType,Pi:(list @ ((product_prod @ A) @ A))]: (((((perm @ A) @ $o) @ Pi) @ $true)))).
% 2.87/1.51 thf(fact_142_name__fresh, axiom, (((fresh @ name) @ name) = (^ [A5:name,B4:name]: ((A5 != B4))))).
% 2.87/1.51 thf(fact_143_fresh__unit, axiom, (! [A:$tType,A2:A]: (((((fresh @ A) @ product_unit) @ A2) @ product_Unity)))).
% 2.87/1.51 thf(fact_144_freshUnit, axiom, (! [Y:name]: (((((fresh @ name) @ product_unit) @ Y) @ product_Unity)))).
% 2.87/1.51 thf(fact_145_allE__Nil, axiom, (! [A:$tType,P:((list @ A) > $o)]: (((! [X_1:(list @ A)]: ((P @ X_1))) => (P @ (nil @ A)))))).
% 2.87/1.51 thf(fact_146_abs__fun__if, axiom, (! [X:$tType,A:$tType,C:$o,Pi:(list @ ((product_prod @ X) @ X)),X2:A,Y:A]: (((C => (((((perm @ X) @ A) @ Pi) @ ((((if @ A) @ C) @ X2) @ Y)) = ((((perm @ X) @ A) @ Pi) @ X2))) & ((~ (C)) => (((((perm @ X) @ A) @ Pi) @ ((((if @ A) @ C) @ X2) @ Y)) = ((((perm @ X) @ A) @ Pi) @ Y))))))).
% 2.87/1.51 thf(fact_147_pt__bij3, axiom, (! [X:$tType,A:$tType,X2:A,Y:A,Pi:(list @ ((product_prod @ X) @ X))]: (((X2 = Y) => (((((perm @ X) @ A) @ Pi) @ X2) = ((((perm @ X) @ A) @ Pi) @ Y)))))).
% 2.87/1.51 thf(fact_148_perm__bool__def, axiom, (! [X:$tType]: ((((perm @ X) @ $o) = (^ [Pi5:(list @ ((product_prod @ X) @ X)),B4:$o]: (B4)))))).
% 2.87/1.51 thf(fact_149_pt__set__bij3, axiom, (! [X:$tType,A:$tType,Pi:(list @ ((product_prod @ X) @ X)),X2:A,X6:(set @ A)]: ((((((perm @ X) @ $o) @ Pi) @ (((member @ A) @ X2) @ X6)) = (((member @ A) @ X2) @ X6))))).
% 2.87/1.51 thf(fact_150_perm__boolI, axiom, (! [A:$tType,P:$o,Pi:(list @ ((product_prod @ A) @ A))]: ((P => ((((perm @ A) @ $o) @ Pi) @ P))))).
% 2.87/1.51 thf(fact_151_perm__boolE, axiom, (! [A:$tType,Pi:(list @ ((product_prod @ A) @ A))]: ((~ (((((perm @ A) @ $o) @ Pi) @ $false)))))).
% 2.87/1.51 thf(fact_152_disj__eqvt, axiom, (! [A:$tType,Pi:(list @ ((product_prod @ A) @ A)),A3:$o,B5:$o]: ((((((perm @ A) @ $o) @ Pi) @ (A3 | B5)) = (((((perm @ A) @ $o) @ Pi) @ A3) | ((((perm @ A) @ $o) @ Pi) @ B5)))))).
% 2.87/1.51 thf(fact_153_conj__eqvt, axiom, (! [A:$tType,Pi:(list @ ((product_prod @ A) @ A)),A3:$o,B5:$o]: ((((((perm @ A) @ $o) @ Pi) @ (A3 & B5)) = (((((perm @ A) @ $o) @ Pi) @ A3) & ((((perm @ A) @ $o) @ Pi) @ B5)))))).
% 2.87/1.51 thf(fact_154_neg__eqvt, axiom, (! [A:$tType,Pi:(list @ ((product_prod @ A) @ A)),A3:$o]: ((((((perm @ A) @ $o) @ Pi) @ (~ (A3))) = (~ (((((perm @ A) @ $o) @ Pi) @ A3))))))).
% 2.87/1.51 thf(fact_155_imp__eqvt, axiom, (! [A:$tType,Pi:(list @ ((product_prod @ A) @ A)),A3:$o,B5:$o]: ((((((perm @ A) @ $o) @ Pi) @ (A3 => B5)) = (((((perm @ A) @ $o) @ Pi) @ A3) => ((((perm @ A) @ $o) @ Pi) @ B5)))))).
% 2.87/1.51 thf(fact_156_perm__prod_Osimps, axiom, (! [A:$tType,X:$tType,B:$tType,Pi:(list @ ((product_prod @ X) @ X)),X2:A,Y:B]: ((((((perm @ X) @ ((product_prod @ A) @ B)) @ Pi) @ ((((product_Pair @ A) @ B) @ X2) @ Y)) = ((((product_Pair @ A) @ B) @ ((((perm @ X) @ A) @ Pi) @ X2)) @ ((((perm @ X) @ B) @ Pi) @ Y)))))).
% 2.87/1.51 thf(fact_157_fresh__prodD_I2_J, axiom, (! [B:$tType,A:$tType,C3:$tType,A2:A,X2:B,Y:C3]: ((((((fresh @ A) @ ((product_prod @ B) @ C3)) @ A2) @ ((((product_Pair @ B) @ C3) @ X2) @ Y)) => ((((fresh @ A) @ C3) @ A2) @ Y))))).
% 2.87/1.51 thf(fact_158_fresh__prodD_I1_J, axiom, (! [C3:$tType,A:$tType,B:$tType,A2:A,X2:B,Y:C3]: ((((((fresh @ A) @ ((product_prod @ B) @ C3)) @ A2) @ ((((product_Pair @ B) @ C3) @ X2) @ Y)) => ((((fresh @ A) @ B) @ A2) @ X2))))).
% 2.87/1.51 thf(fact_159_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) @ $o) @ Pi) @ B2))) => (((((perm @ A) @ B) @ Pi) @ ((((if @ B) @ B2) @ C1) @ C22)) = ((((perm @ A) @ B) @ Pi) @ C22))))))).
% 2.87/1.51 thf(fact_160_nil__eqvt, axiom, (! [X:$tType,A:$tType,Pi:(list @ ((product_prod @ X) @ X))]: ((((((perm @ X) @ (list @ A)) @ Pi) @ (nil @ A)) = (nil @ A))))).
% 2.87/1.51 thf(fact_161_fresh__list__nil, axiom, (! [X:$tType,A:$tType,A2:X]: (((((fresh @ X) @ (list @ A)) @ A2) @ (nil @ A))))).
% 2.87/1.51 thf(fact_162_cons__eqvt, axiom, (! [X:$tType,A:$tType,Pi:(list @ ((product_prod @ X) @ X)),X2:A,Xs:(list @ A)]: ((((((perm @ X) @ (list @ A)) @ Pi) @ (((cons @ A) @ X2) @ Xs)) = (((cons @ A) @ ((((perm @ X) @ A) @ Pi) @ X2)) @ ((((perm @ X) @ (list @ A)) @ Pi) @ Xs)))))).
% 2.87/1.51 thf(fact_163_resSimCases, axiom, (! [A:$tType]: (((fs_name @ A) => (! [Rel:(set @ ((product_prod @ pi) @ pi)),Q:pi,X2:name,P:pi,C4:A]: ((((eqvt @ pi) @ Rel) => ((! [Q4:pi,A4:name]: ((((late_transitions @ Q) @ ((late_FreeR @ ((late_OutputR @ A4) @ X2)) @ Q4)) => ((A4 != X2) => (? [P6:pi]: ((((late_transitions @ P) @ (((late_BoundR @ (late_BoundOutputS @ A4)) @ X2) @ P6)) & (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ P6) @ Q4)) @ Rel)))))))) => ((! [Q4:pi,A4:late_subject,Y3:name]: ((((late_transitions @ Q) @ (((late_BoundR @ A4) @ Y3) @ Q4)) => (((((fresh @ name) @ late_subject) @ X2) @ A4) => ((X2 != Y3) => (((((fresh @ name) @ A) @ Y3) @ C4) => (? [P6:pi]: ((((late_transitions @ P) @ (((late_BoundR @ A4) @ Y3) @ P6)) & (((((strong2129052853vative @ P6) @ ((res @ X2) @ Q4)) @ A4) @ Y3) @ Rel)))))))))) => ((! [Q4:pi,Alpha2:late_freeRes]: ((((late_transitions @ Q) @ ((late_FreeR @ Alpha2) @ Q4)) => (((((fresh @ name) @ late_freeRes) @ X2) @ Alpha2) => (? [P6:pi]: ((((late_transitions @ P) @ ((late_FreeR @ Alpha2) @ P6)) & (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ P6) @ ((res @ X2) @ Q4))) @ Rel)))))))) => (((strong743114133lation @ P) @ Rel) @ ((res @ X2) @ Q)))))))))))).
% 2.87/1.51 thf(fact_164_simCasesCont, axiom, (! [A:$tType]: (((fs_name @ A) => (! [Rel:(set @ ((product_prod @ pi) @ pi)),Q:pi,P:pi,C4:A]: ((((eqvt @ pi) @ Rel) => ((! [A4:late_subject,X5:name,Q4:pi]: ((((late_transitions @ Q) @ (((late_BoundR @ A4) @ X5) @ Q4)) => (((((fresh @ name) @ pi) @ X5) @ P) => (((((fresh @ name) @ pi) @ X5) @ Q) => (((((fresh @ name) @ late_subject) @ X5) @ A4) => (((((fresh @ name) @ A) @ X5) @ C4) => (? [P6:pi]: ((((late_transitions @ P) @ (((late_BoundR @ A4) @ X5) @ P6)) & (((((strong2129052853vative @ P6) @ Q4) @ A4) @ X5) @ Rel))))))))))) => ((! [Alpha2:late_freeRes,Q4:pi]: ((((late_transitions @ Q) @ ((late_FreeR @ Alpha2) @ Q4)) => (? [P6:pi]: ((((late_transitions @ P) @ ((late_FreeR @ Alpha2) @ P6)) & (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ P6) @ Q4)) @ Rel))))))) => (((strong743114133lation @ P) @ Rel) @ Q)))))))))).
% 2.87/1.51 thf(fact_165_eqvtRelI, axiom, (! [A:$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))))))))).
% 2.87/1.51 thf(fact_166_eqvtRelE, axiom, (! [A:$tType]: (((pt_name @ A) => (! [Rel:(set @ ((product_prod @ A) @ A)),Perm:(list @ ((product_prod @ name) @ name)),P:A,Q:A]: ((((eqvt @ A) @ Rel) => ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ ((((perm @ name) @ A) @ Perm) @ P)) @ ((((perm @ name) @ A) @ Perm) @ Q))) @ Rel) => (((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ P) @ Q)) @ Rel))))))))).
% 2.87/1.51 thf(fact_167_perm__unit_Osimps, axiom, (! [X:$tType,Pi:(list @ ((product_prod @ X) @ X))]: ((((((perm @ X) @ product_unit) @ Pi) @ product_Unity) = product_Unity)))).
% 2.87/1.51 thf(fact_168_parSym, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),P:pi,Q:pi]: (((! [R2:pi,S2:pi]: ((((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ ((par @ R2) @ S2)) @ ((par @ S2) @ R2))) @ Rel))) => ((! [R2:pi,S2:pi,X5:name]: (((((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ R2) @ S2)) @ Rel) => (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ ((res @ X5) @ R2)) @ ((res @ X5) @ S2))) @ Rel)))) => (((strong743114133lation @ ((par @ P) @ Q)) @ Rel) @ ((par @ Q) @ P))))))).
% 2.87/1.51 thf(fact_169_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)) => (? [P4:pi]: ((((late_transitions @ P) @ ((late_FreeR @ Alpha) @ P4)) & (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ P4) @ Q2)) @ Rel))))))))).
% 2.87/1.51 thf(fact_170_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))))))))))).
% 2.87/1.51 thf(fact_171_parAssocLeft, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),P:pi,Q:pi,R:pi]: (((! [S2:pi,T2:pi,U:pi]: ((((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ ((par @ ((par @ S2) @ T2)) @ U)) @ ((par @ S2) @ ((par @ T2) @ U)))) @ Rel))) => ((! [S2:pi,T2:pi,X5:name]: (((((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ S2) @ T2)) @ Rel) => (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ ((res @ X5) @ S2)) @ ((res @ X5) @ T2))) @ Rel)))) => ((! [S2:pi,T2:pi,U:pi,X5:name]: ((((((fresh @ name) @ pi) @ X5) @ S2) => (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ ((res @ X5) @ ((par @ ((par @ S2) @ T2)) @ U))) @ ((par @ S2) @ ((res @ X5) @ ((par @ T2) @ U))))) @ Rel)))) => ((! [S2:pi,T2:pi,U:pi,X5:name]: ((((((fresh @ name) @ pi) @ X5) @ U) => (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ ((par @ ((res @ X5) @ ((par @ S2) @ T2))) @ U)) @ ((res @ X5) @ ((par @ S2) @ ((par @ T2) @ U))))) @ Rel)))) => (((strong743114133lation @ ((par @ ((par @ P) @ Q)) @ R)) @ Rel) @ ((par @ P) @ ((par @ Q) @ R)))))))))).
% 2.87/1.51 thf(fact_172_simE_I1_J, axiom, (! [P:pi,Rel:(set @ ((product_prod @ pi) @ pi)),Q:pi,A2:late_subject,X2:name,Q2:pi]: (((((strong743114133lation @ P) @ Rel) @ Q) => (((late_transitions @ Q) @ (((late_BoundR @ A2) @ X2) @ Q2)) => (((((fresh @ name) @ pi) @ X2) @ P) => (? [P4:pi]: ((((late_transitions @ P) @ (((late_BoundR @ A2) @ X2) @ P4)) & (((((strong2129052853vative @ P4) @ Q2) @ A2) @ X2) @ Rel)))))))))).
% 2.87/1.51 thf(fact_173_simCases, axiom, (! [Q:pi,P:pi,Rel:(set @ ((product_prod @ pi) @ pi))]: (((! [A4:late_subject,Y3:name,Q4:pi]: ((((late_transitions @ Q) @ (((late_BoundR @ A4) @ Y3) @ Q4)) => (((((fresh @ name) @ pi) @ Y3) @ P) => (? [P6:pi]: ((((late_transitions @ P) @ (((late_BoundR @ A4) @ Y3) @ P6)) & (((((strong2129052853vative @ P6) @ Q4) @ A4) @ Y3) @ Rel)))))))) => ((! [Alpha2:late_freeRes,Q4:pi]: ((((late_transitions @ Q) @ ((late_FreeR @ Alpha2) @ Q4)) => (? [P6:pi]: ((((late_transitions @ P) @ ((late_FreeR @ Alpha2) @ P6)) & (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ P6) @ Q4)) @ Rel))))))) => (((strong743114133lation @ P) @ Rel) @ Q)))))).
% 2.87/1.51 thf(fact_174_simulation__def, axiom, (strong743114133lation = (^ [P7:pi,Rel2:(set @ ((product_prod @ pi) @ pi)),Q5:pi]: (((! [A5:late_subject,X4:name,Q6:pi]: (((((late_transitions @ Q5) @ (((late_BoundR @ A5) @ X4) @ Q6)) & ((((fresh @ name) @ pi) @ X4) @ P7)) => (? [P8:pi]: ((((late_transitions @ P7) @ (((late_BoundR @ A5) @ X4) @ P8)) & (((((strong2129052853vative @ P8) @ Q6) @ A5) @ 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)))))))))))).
% 2.87/1.51 thf(fact_175_Late__Semantics1_Osubject_Oinject_I2_J, axiom, (! [X22:name,Y2:name]: ((((late_BoundOutputS @ X22) = (late_BoundOutputS @ Y2)) = (X22 = Y2))))).
% 2.87/1.51 thf(fact_176_Late__Semantics1_Osubject_Oinject_I1_J, axiom, (! [X1:name,Y1:name]: ((((late_InputS @ X1) = (late_InputS @ Y1)) = (X1 = Y1))))).
% 2.87/1.51 thf(fact_177_Late__Semantics1_OfreeRes_Oinject, axiom, (! [X11:name,X12:name,Y11:name,Y12:name]: (((((late_OutputR @ X11) @ X12) = ((late_OutputR @ Y11) @ Y12)) = ((X11 = Y11) & (X12 = Y12)))))).
% 2.87/1.51 thf(fact_178_Late__Semantics1_OfreeRes_Odistinct_I1_J, axiom, (! [X11:name,X12:name]: ((((late_OutputR @ X11) @ X12) != late_TauR)))).
% 2.87/1.51 thf(fact_179_freeRes_Oexhaust, axiom, (! [Y:late_freeRes]: (((! [X112:name,X122:name]: ((Y != ((late_OutputR @ X112) @ X122)))) => (Y = late_TauR))))).
% 2.87/1.51 thf(fact_180_subject_Oexhaust, axiom, (! [Y:late_subject]: (((! [X13:name]: ((Y != (late_InputS @ X13)))) => (~ ((! [X23:name]: ((Y != (late_BoundOutputS @ X23)))))))))).
% 2.87/1.51 thf(fact_181_Late__Semantics1_Osubject_Odistinct_I1_J, axiom, (! [X1:name,X22:name]: (((late_InputS @ X1) != (late_BoundOutputS @ X22))))).
% 2.87/1.51 thf(fact_182_inputCases, axiom, (! [A2:name,X2:name,P:pi,B2:late_subject,Y:name,YP:pi,Prop:(late_subject > (name > (pi > $o)))]: ((((late_transitions @ (((input @ A2) @ X2) @ P)) @ (((late_BoundR @ B2) @ Y) @ YP)) => ((Y != A2) => ((Y != X2) => (((((fresh @ name) @ pi) @ Y) @ P) => (((B2 = (late_InputS @ A2)) => ((YP = ((((perm @ name) @ pi) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ X2) @ Y)) @ (nil @ ((product_prod @ name) @ name)))) @ P)) => (((Prop @ (late_InputS @ A2)) @ Y) @ ((((perm @ name) @ pi) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ X2) @ Y)) @ (nil @ ((product_prod @ name) @ name)))) @ P)))) => (((Prop @ B2) @ Y) @ YP))))))))).
% 2.87/1.51 thf(fact_183_list_Oinject, axiom, (! [A:$tType,X21:A,X222:(list @ A),Y21:A,Y22:(list @ A)]: ((((((cons @ A) @ X21) @ X222) = (((cons @ A) @ Y21) @ Y22)) = ((X21 = Y21) & (X222 = Y22)))))).
% 2.87/1.51 thf(fact_184_old_Oprod_Oinject, axiom, (! [A:$tType,B:$tType,A2:A,B2:B,A6:A,B6:B]: (((((((product_Pair @ A) @ B) @ A2) @ B2) = ((((product_Pair @ A) @ B) @ A6) @ B6)) = ((A2 = A6) & (B2 = B6)))))).
% 2.87/1.51 thf(fact_185_prod_Oinject, axiom, (! [A:$tType,B:$tType,X1:A,X22:B,Y1:A,Y2:B]: (((((((product_Pair @ A) @ B) @ X1) @ X22) = ((((product_Pair @ A) @ B) @ Y1) @ Y2)) = ((X1 = Y1) & (X22 = Y2)))))).
% 2.87/1.51 thf(fact_186_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)))))).
% 2.87/1.51 thf(fact_187_pi_Odistinct_I57_J, axiom, (! [Name12:name,Name23:name,Pi:pi,Name:name,Pi3:pi]: (((((input @ Name12) @ Name23) @ Pi) != ((res @ Name) @ Pi3))))).
% 2.87/1.51 thf(fact_188_pi_Odistinct_I55_J, axiom, (! [Name12:name,Name23:name,Pi:pi,Pi12:pi,Pi22:pi]: (((((input @ Name12) @ Name23) @ Pi) != ((par @ Pi12) @ Pi22))))).
% 2.87/1.51 thf(fact_189_resTrans_I2_J, axiom, (! [X2:name,Y:name,P:pi,Rs:late_residual]: ((~ (((late_transitions @ ((res @ X2) @ (((input @ X2) @ Y) @ P))) @ Rs)))))).
% 2.87/1.51 thf(fact_190_inputFreeTrans, axiom, (! [A2:name,X2:name,P:pi,Alpha:late_freeRes,P3:pi]: ((~ (((late_transitions @ (((input @ A2) @ X2) @ P)) @ ((late_FreeR @ Alpha) @ P3))))))).
% 2.87/1.51 thf(fact_191_surj__pair, axiom, (! [A:$tType,B:$tType,P2:((product_prod @ A) @ B)]: ((? [X5:A,Y3:B]: ((P2 = ((((product_Pair @ A) @ B) @ X5) @ Y3))))))).
% 2.87/1.51 thf(fact_192_prod__cases, axiom, (! [B:$tType,A:$tType,P:(((product_prod @ A) @ B) > $o),P2:((product_prod @ A) @ B)]: (((! [A4:A,B3:B]: ((P @ ((((product_Pair @ A) @ B) @ A4) @ B3)))) => (P @ P2))))).
% 2.87/1.51 thf(fact_193_Pair__inject, axiom, (! [A:$tType,B:$tType,A2:A,B2:B,A6:A,B6:B]: (((((((product_Pair @ A) @ B) @ A2) @ B2) = ((((product_Pair @ A) @ B) @ A6) @ B6)) => (~ (((A2 = A6) => (B2 != B6)))))))).
% 2.87/1.51 thf(fact_194_old_Oprod_Oexhaust, axiom, (! [A:$tType,B:$tType,Y:((product_prod @ A) @ B)]: ((~ ((! [A4:A,B3:B]: ((Y != ((((product_Pair @ A) @ B) @ A4) @ B3))))))))).
% 2.87/1.51 thf(fact_195_old_Oprod_Oinducts, axiom, (! [B:$tType,A:$tType,P:(((product_prod @ A) @ B) > $o),Prod:((product_prod @ A) @ B)]: (((! [A4:A,B3:B]: ((P @ ((((product_Pair @ A) @ B) @ A4) @ B3)))) => (P @ Prod))))).
% 2.87/1.51 thf(fact_196_not__Cons__self2, axiom, (! [A:$tType,X2:A,Xs:(list @ A)]: (((((cons @ A) @ X2) @ Xs) != Xs)))).
% 2.87/1.51 thf(fact_197_resInputFreeTrans, axiom, (! [X2:name,A2:name,Y:name,P:pi,Alpha:late_freeRes,P3:pi]: ((~ (((late_transitions @ ((res @ X2) @ (((input @ A2) @ Y) @ P))) @ ((late_FreeR @ Alpha) @ P3))))))).
% 2.87/1.51 thf(fact_198_old_Ounit_Oinducts, axiom, (! [P:(product_unit > $o),Unit:product_unit]: (((P @ product_Unity) => (P @ Unit))))).
% 2.87/1.51 thf(fact_199_old_Ounit_Oexhaust, axiom, (! [Y:product_unit]: ((Y = product_Unity)))).
% 2.87/1.51 thf(fact_200_inputBoundOutputTrans, axiom, (! [A2:name,X2:name,P:pi,B2:name,Y:name,P3:pi]: ((~ (((late_transitions @ (((input @ A2) @ X2) @ P)) @ (((late_BoundR @ (late_BoundOutputS @ B2)) @ Y) @ P3))))))).
% 2.87/1.51 thf(fact_201_Late__Semantics_OInput, axiom, (! [A2:name,X2:name,P:pi]: (((late_transitions @ (((input @ A2) @ X2) @ P)) @ (((late_BoundR @ (late_InputS @ A2)) @ X2) @ P))))).
% 2.87/1.51 thf(fact_202_transitions_OInput, axiom, (! [X2:name,A2:name,P:pi]: (((X2 != A2) => ((late_transitions @ (((input @ A2) @ X2) @ P)) @ (((late_BoundR @ (late_InputS @ A2)) @ X2) @ P)))))).
% 2.87/1.51 thf(fact_203_inputIneqTrans, axiom, (! [A2:name,X2:name,P:pi,B2:late_subject,Y:name,P3:pi]: ((((late_transitions @ (((input @ A2) @ X2) @ P)) @ (((late_BoundR @ B2) @ Y) @ P3)) => (~ (((((fresh @ name) @ late_subject) @ A2) @ B2))))))).
% 2.87/1.51 thf(fact_204_resInputBoundOutputTrans, axiom, (! [X2:name,A2:name,Y:name,P:pi,B2:name,Z:name,P3:pi]: ((~ (((late_transitions @ ((res @ X2) @ (((input @ A2) @ Y) @ P))) @ (((late_BoundR @ (late_BoundOutputS @ B2)) @ Z) @ P3))))))).
% 2.87/1.51 thf(fact_205_alphaInput, axiom, (! [C:name,P:pi,A2:name,X2:name]: ((((((fresh @ name) @ pi) @ C) @ P) => ((((input @ A2) @ X2) @ P) = (((input @ A2) @ C) @ ((((perm @ name) @ pi) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ X2) @ C)) @ (nil @ ((product_prod @ name) @ name)))) @ P))))))).
% 2.87/1.51 thf(fact_206_list_Odistinct_I1_J, axiom, (! [A:$tType,X21:A,X222:(list @ A)]: (((nil @ A) != (((cons @ A) @ X21) @ X222))))).
% 2.87/1.51 thf(fact_207_list_OdiscI, axiom, (! [A:$tType,List:(list @ A),X21:A,X222:(list @ A)]: (((List = (((cons @ A) @ X21) @ X222)) => (List != (nil @ A)))))).
% 2.87/1.51 thf(fact_208_list_Oexhaust, axiom, (! [A:$tType,Y:(list @ A)]: (((Y != (nil @ A)) => (~ ((! [X212:A,X223:(list @ A)]: ((Y != (((cons @ A) @ X212) @ X223)))))))))).
% 2.87/1.51 thf(fact_209_list_Oinducts, axiom, (! [A:$tType,P:((list @ A) > $o),List:(list @ A)]: (((P @ (nil @ A)) => ((! [X13:A,X23:(list @ A)]: (((P @ X23) => (P @ (((cons @ A) @ X13) @ X23))))) => (P @ List)))))).
% 2.87/1.51 thf(fact_210_neq__Nil__conv, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) = (? [Y5:A,Ys:(list @ A)]: ((Xs = (((cons @ A) @ Y5) @ Ys)))))))).
% 2.87/1.51 thf(fact_211_list__induct2_H, axiom, (! [A:$tType,B:$tType,P:((list @ A) > ((list @ B) > $o)),Xs:(list @ A),Ys2:(list @ B)]: ((((P @ (nil @ A)) @ (nil @ B)) => ((! [X5:A,Xs2:(list @ A)]: (((P @ (((cons @ A) @ X5) @ Xs2)) @ (nil @ B)))) => ((! [Y3:B,Ys3:(list @ B)]: (((P @ (nil @ A)) @ (((cons @ B) @ Y3) @ Ys3)))) => ((! [X5:A,Xs2:(list @ A),Y3:B,Ys3:(list @ B)]: ((((P @ Xs2) @ Ys3) => ((P @ (((cons @ A) @ X5) @ Xs2)) @ (((cons @ B) @ Y3) @ Ys3))))) => ((P @ Xs) @ Ys2)))))))).
% 2.87/1.51 thf(fact_212_splice_Oinduct, axiom, (! [A:$tType,P:((list @ A) > ((list @ A) > $o)),A0:(list @ A),A1:(list @ A)]: (((! [X_1:(list @ A)]: (((P @ (nil @ A)) @ X_1))) => ((! [X5:A,Xs2:(list @ A),Ys3:(list @ A)]: ((((P @ Ys3) @ Xs2) => ((P @ (((cons @ A) @ X5) @ Xs2)) @ Ys3)))) => ((P @ A0) @ A1)))))).
% 2.87/1.51 thf(fact_213_induct__list012, axiom, (! [A:$tType,P:((list @ A) > $o),Xs:(list @ A)]: (((P @ (nil @ A)) => ((! [X5:A]: ((P @ (((cons @ A) @ X5) @ (nil @ A))))) => ((! [X5:A,Y3:A,Zs:(list @ A)]: (((P @ Zs) => ((P @ (((cons @ A) @ Y3) @ Zs)) => (P @ (((cons @ A) @ X5) @ (((cons @ A) @ Y3) @ Zs))))))) => (P @ Xs))))))).
% 2.87/1.51 thf(fact_214_min__list_Ocases, axiom, (! [A:$tType]: (((ord @ A) => (! [X2:(list @ A)]: (((! [X5:A,Xs2:(list @ A)]: ((X2 != (((cons @ A) @ X5) @ Xs2)))) => (X2 = (nil @ A))))))))).
% 2.87/1.51 thf(fact_215_min__list_Oinduct, axiom, (! [A:$tType]: (((ord @ A) => (! [P:((list @ A) > $o),A0:(list @ A)]: (((! [X5:A,Xs2:(list @ A)]: (((! [X213:A,X224:(list @ A)]: (((Xs2 = (((cons @ A) @ X213) @ X224)) => (P @ Xs2)))) => (P @ (((cons @ A) @ X5) @ Xs2))))) => ((P @ (nil @ A)) => (P @ A0))))))))).
% 2.87/1.51 thf(fact_216_shuffles_Oinduct, axiom, (! [A:$tType,P:((list @ A) > ((list @ A) > $o)),A0:(list @ A),A1:(list @ A)]: (((! [X_1:(list @ A)]: (((P @ (nil @ A)) @ X_1))) => ((! [Xs2:(list @ A)]: (((P @ Xs2) @ (nil @ A)))) => ((! [X5:A,Xs2:(list @ A),Y3:A,Ys3:(list @ A)]: ((((P @ Xs2) @ (((cons @ A) @ Y3) @ Ys3)) => (((P @ (((cons @ A) @ X5) @ Xs2)) @ Ys3) => ((P @ (((cons @ A) @ X5) @ Xs2)) @ (((cons @ A) @ Y3) @ Ys3)))))) => ((P @ A0) @ A1))))))).
% 2.87/1.51 thf(fact_217_transpose_Ocases, axiom, (! [A:$tType,X2:(list @ (list @ A))]: (((X2 != (nil @ (list @ A))) => ((! [Xss:(list @ (list @ A))]: ((X2 != (((cons @ (list @ A)) @ (nil @ A)) @ Xss)))) => (~ ((! [X5:A,Xs2:(list @ A),Xss:(list @ (list @ A))]: ((X2 != (((cons @ (list @ A)) @ (((cons @ A) @ X5) @ Xs2)) @ Xss))))))))))).
% 2.87/1.51 thf(fact_218_remdups__adj_Ocases, axiom, (! [A:$tType,X2:(list @ A)]: (((X2 != (nil @ A)) => ((! [X5:A]: ((X2 != (((cons @ A) @ X5) @ (nil @ A))))) => (~ ((! [X5:A,Y3:A,Xs2:(list @ A)]: ((X2 != (((cons @ A) @ X5) @ (((cons @ A) @ Y3) @ Xs2)))))))))))).
% 2.87/1.51 thf(fact_219_sorted__wrt_Oinduct, axiom, (! [A:$tType,P:((A > (A > $o)) > ((list @ A) > $o)),A0:(A > (A > $o)),A1:(list @ A)]: (((! [P5:(A > (A > $o))]: (((P @ P5) @ (nil @ A)))) => ((! [P5:(A > (A > $o)),X5:A,Ys3:(list @ A)]: ((((P @ P5) @ Ys3) => ((P @ P5) @ (((cons @ A) @ X5) @ Ys3))))) => ((P @ A0) @ A1)))))).
% 2.87/1.51 thf(fact_220_remdups__adj_Oinduct, axiom, (! [A:$tType,P:((list @ A) > $o),A0:(list @ A)]: (((P @ (nil @ A)) => ((! [X5:A]: ((P @ (((cons @ A) @ X5) @ (nil @ A))))) => ((! [X5:A,Y3:A,Xs2:(list @ A)]: ((((X5 = Y3) => (P @ (((cons @ A) @ X5) @ Xs2))) => (((X5 != Y3) => (P @ (((cons @ A) @ Y3) @ Xs2))) => (P @ (((cons @ A) @ X5) @ (((cons @ A) @ Y3) @ Xs2))))))) => (P @ A0))))))).
% 2.87/1.51 thf(fact_221_arg__min__list_Oinduct, axiom, (! [B:$tType,A:$tType]: (((linorder @ B) => (! [P:((A > B) > ((list @ A) > $o)),A0:(A > B),A1:(list @ A)]: (((! [F3:(A > B),X5:A]: (((P @ F3) @ (((cons @ A) @ X5) @ (nil @ A))))) => ((! [F3:(A > B),X5:A,Y3:A,Zs:(list @ A)]: ((((P @ F3) @ (((cons @ A) @ Y3) @ Zs)) => ((P @ F3) @ (((cons @ A) @ X5) @ (((cons @ A) @ Y3) @ Zs)))))) => ((! [A4:(A > B)]: (((P @ A4) @ (nil @ A)))) => ((P @ A0) @ A1)))))))))).
% 2.87/1.51 thf(fact_222_successively_Oinduct, axiom, (! [A:$tType,P:((A > (A > $o)) > ((list @ A) > $o)),A0:(A > (A > $o)),A1:(list @ A)]: (((! [P5:(A > (A > $o))]: (((P @ P5) @ (nil @ A)))) => ((! [P5:(A > (A > $o)),X5:A]: (((P @ P5) @ (((cons @ A) @ X5) @ (nil @ A))))) => ((! [P5:(A > (A > $o)),X5:A,Y3:A,Xs2:(list @ A)]: ((((P @ P5) @ (((cons @ A) @ Y3) @ Xs2)) => ((P @ P5) @ (((cons @ A) @ X5) @ (((cons @ A) @ Y3) @ Xs2)))))) => ((P @ A0) @ A1))))))).
% 2.87/1.51 thf(fact_223_list__nonempty__induct, axiom, (! [A:$tType,Xs:(list @ A),P:((list @ A) > $o)]: (((Xs != (nil @ A)) => ((! [X5:A]: ((P @ (((cons @ A) @ X5) @ (nil @ A))))) => ((! [X5:A,Xs2:(list @ A)]: (((Xs2 != (nil @ A)) => ((P @ Xs2) => (P @ (((cons @ A) @ X5) @ Xs2)))))) => (P @ Xs))))))).
% 2.87/1.51 thf(fact_224_map__tailrec__rev_Oinduct, axiom, (! [A:$tType,B:$tType,P:((A > B) > ((list @ A) > ((list @ B) > $o))),A0:(A > B),A1:(list @ A),A22:(list @ B)]: (((! [F3:(A > B),X_1:(list @ B)]: ((((P @ F3) @ (nil @ A)) @ X_1))) => ((! [F3:(A > B),A4:A,As:(list @ A),Bs:(list @ B)]: (((((P @ F3) @ As) @ (((cons @ B) @ (F3 @ A4)) @ Bs)) => (((P @ F3) @ (((cons @ A) @ A4) @ As)) @ Bs)))) => (((P @ A0) @ A1) @ A22)))))).
% 2.87/1.51 thf(fact_225_strict__sorted_Ocases, axiom, (! [A:$tType]: (((linorder @ A) => (! [X2:(list @ A)]: (((X2 != (nil @ A)) => (~ ((! [X5:A,Ys3:(list @ A)]: ((X2 != (((cons @ A) @ X5) @ Ys3))))))))))))).
% 2.87/1.51 thf(fact_226_strict__sorted_Oinduct, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:((list @ A) > $o),A0:(list @ A)]: (((P @ (nil @ A)) => ((! [X5:A,Ys3:(list @ A)]: (((P @ Ys3) => (P @ (((cons @ A) @ X5) @ Ys3))))) => (P @ A0))))))))).
% 2.87/1.51 thf(fact_227_splice_Ocases, axiom, (! [A:$tType,X2:((product_prod @ (list @ A)) @ (list @ A))]: (((! [Ys3:(list @ A)]: ((X2 != ((((product_Pair @ (list @ A)) @ (list @ A)) @ (nil @ A)) @ Ys3)))) => (~ ((! [X5:A,Xs2:(list @ A),Ys3:(list @ A)]: ((X2 != ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((cons @ A) @ X5) @ Xs2)) @ Ys3)))))))))).
% 2.87/1.51 thf(fact_228_shuffles_Ocases, axiom, (! [A:$tType,X2:((product_prod @ (list @ A)) @ (list @ A))]: (((! [Ys3:(list @ A)]: ((X2 != ((((product_Pair @ (list @ A)) @ (list @ A)) @ (nil @ A)) @ Ys3)))) => ((! [Xs2:(list @ A)]: ((X2 != ((((product_Pair @ (list @ A)) @ (list @ A)) @ Xs2) @ (nil @ A))))) => (~ ((! [X5:A,Xs2:(list @ A),Y3:A,Ys3:(list @ A)]: ((X2 != ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((cons @ A) @ X5) @ Xs2)) @ (((cons @ A) @ Y3) @ Ys3)))))))))))).
% 2.87/1.51 thf(fact_229_sorted__wrt_Ocases, axiom, (! [A:$tType,X2:((product_prod @ (A > (A > $o))) @ (list @ A))]: (((! [P5:(A > (A > $o))]: ((X2 != ((((product_Pair @ (A > (A > $o))) @ (list @ A)) @ P5) @ (nil @ A))))) => (~ ((! [P5:(A > (A > $o)),X5:A,Ys3:(list @ A)]: ((X2 != ((((product_Pair @ (A > (A > $o))) @ (list @ A)) @ P5) @ (((cons @ A) @ X5) @ Ys3))))))))))).
% 2.87/1.51 thf(fact_230_successively_Ocases, axiom, (! [A:$tType,X2:((product_prod @ (A > (A > $o))) @ (list @ A))]: (((! [P5:(A > (A > $o))]: ((X2 != ((((product_Pair @ (A > (A > $o))) @ (list @ A)) @ P5) @ (nil @ A))))) => ((! [P5:(A > (A > $o)),X5:A]: ((X2 != ((((product_Pair @ (A > (A > $o))) @ (list @ A)) @ P5) @ (((cons @ A) @ X5) @ (nil @ A)))))) => (~ ((! [P5:(A > (A > $o)),X5:A,Y3:A,Xs2:(list @ A)]: ((X2 != ((((product_Pair @ (A > (A > $o))) @ (list @ A)) @ P5) @ (((cons @ A) @ X5) @ (((cons @ A) @ Y3) @ Xs2))))))))))))).
% 2.87/1.51 thf(fact_231_arg__min__list_Ocases, axiom, (! [B:$tType,A:$tType]: (((linorder @ B) => (! [X2:((product_prod @ (A > B)) @ (list @ A))]: (((! [F3:(A > B),X5:A]: ((X2 != ((((product_Pair @ (A > B)) @ (list @ A)) @ F3) @ (((cons @ A) @ X5) @ (nil @ A)))))) => ((! [F3:(A > B),X5:A,Y3:A,Zs:(list @ A)]: ((X2 != ((((product_Pair @ (A > B)) @ (list @ A)) @ F3) @ (((cons @ A) @ X5) @ (((cons @ A) @ Y3) @ Zs)))))) => (~ ((! [A4:(A > B)]: ((X2 != ((((product_Pair @ (A > B)) @ (list @ A)) @ A4) @ (nil @ A))))))))))))))).
% 2.87/1.51 thf(fact_232_map__tailrec__rev_Ocases, axiom, (! [A:$tType,B:$tType,X2:((product_prod @ (A > B)) @ ((product_prod @ (list @ A)) @ (list @ B)))]: (((! [F3:(A > B),Bs:(list @ B)]: ((X2 != ((((product_Pair @ (A > B)) @ ((product_prod @ (list @ A)) @ (list @ B))) @ F3) @ ((((product_Pair @ (list @ A)) @ (list @ B)) @ (nil @ A)) @ Bs))))) => (~ ((! [F3:(A > B),A4:A,As:(list @ A),Bs:(list @ B)]: ((X2 != ((((product_Pair @ (A > B)) @ ((product_prod @ (list @ A)) @ (list @ B))) @ F3) @ ((((product_Pair @ (list @ A)) @ (list @ B)) @ (((cons @ A) @ A4) @ As)) @ Bs))))))))))).
% 2.87/1.51 thf(fact_233_prod__cases3, axiom, (! [A:$tType,B:$tType,C3:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ C3))]: ((~ ((! [A4:A,B3:B,C2:C3]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ C3)) @ A4) @ ((((product_Pair @ B) @ C3) @ B3) @ C2)))))))))).
% 2.87/1.51 thf(fact_234_prod__cases4, axiom, (! [A:$tType,B:$tType,C3:$tType,D2:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ D2)))]: ((~ ((! [A4:A,B3:B,C2:C3,D3:D2]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ D2))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C3) @ D2)) @ B3) @ ((((product_Pair @ C3) @ D2) @ C2) @ D3))))))))))).
% 2.87/1.51 thf(fact_235_prod__cases5, axiom, (! [A:$tType,B:$tType,C3:$tType,D2:$tType,E:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ ((product_prod @ D2) @ E))))]: ((~ ((! [A4:A,B3:B,C2:C3,D3:D2,E2:E]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ ((product_prod @ D2) @ E)))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C3) @ ((product_prod @ D2) @ E))) @ B3) @ ((((product_Pair @ C3) @ ((product_prod @ D2) @ E)) @ C2) @ ((((product_Pair @ D2) @ E) @ D3) @ E2)))))))))))).
% 2.87/1.51 thf(fact_236_prod__cases6, axiom, (! [A:$tType,B:$tType,C3:$tType,D2:$tType,E:$tType,F4:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ ((product_prod @ D2) @ ((product_prod @ E) @ F4)))))]: ((~ ((! [A4:A,B3:B,C2:C3,D3:D2,E2:E,F3:F4]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ ((product_prod @ D2) @ ((product_prod @ E) @ F4))))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C3) @ ((product_prod @ D2) @ ((product_prod @ E) @ F4)))) @ B3) @ ((((product_Pair @ C3) @ ((product_prod @ D2) @ ((product_prod @ E) @ F4))) @ C2) @ ((((product_Pair @ D2) @ ((product_prod @ E) @ F4)) @ D3) @ ((((product_Pair @ E) @ F4) @ E2) @ F3))))))))))))).
% 2.87/1.51 thf(fact_237_prod__cases7, axiom, (! [A:$tType,B:$tType,C3:$tType,D2:$tType,E:$tType,F4:$tType,G2:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ ((product_prod @ D2) @ ((product_prod @ E) @ ((product_prod @ F4) @ G2))))))]: ((~ ((! [A4:A,B3:B,C2:C3,D3:D2,E2:E,F3:F4,G3:G2]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ ((product_prod @ D2) @ ((product_prod @ E) @ ((product_prod @ F4) @ G2)))))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C3) @ ((product_prod @ D2) @ ((product_prod @ E) @ ((product_prod @ F4) @ G2))))) @ B3) @ ((((product_Pair @ C3) @ ((product_prod @ D2) @ ((product_prod @ E) @ ((product_prod @ F4) @ G2)))) @ C2) @ ((((product_Pair @ D2) @ ((product_prod @ E) @ ((product_prod @ F4) @ G2))) @ D3) @ ((((product_Pair @ E) @ ((product_prod @ F4) @ G2)) @ E2) @ ((((product_Pair @ F4) @ G2) @ F3) @ G3)))))))))))))).
% 2.87/1.51 thf(fact_238_prod__induct3, axiom, (! [C3:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ C3)) > $o),X2:((product_prod @ A) @ ((product_prod @ B) @ C3))]: (((! [A4:A,B3:B,C2:C3]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ C3)) @ A4) @ ((((product_Pair @ B) @ C3) @ B3) @ C2))))) => (P @ X2))))).
% 2.87/1.51 thf(fact_239_prod__induct4, axiom, (! [D2:$tType,C3:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ D2))) > $o),X2:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ D2)))]: (((! [A4:A,B3:B,C2:C3,D3:D2]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ D2))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C3) @ D2)) @ B3) @ ((((product_Pair @ C3) @ D2) @ C2) @ D3)))))) => (P @ X2))))).
% 2.87/1.51 thf(fact_240_prod__induct5, axiom, (! [E:$tType,D2:$tType,C3:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ ((product_prod @ D2) @ E)))) > $o),X2:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ ((product_prod @ D2) @ E))))]: (((! [A4:A,B3:B,C2:C3,D3:D2,E2:E]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ ((product_prod @ D2) @ E)))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C3) @ ((product_prod @ D2) @ E))) @ B3) @ ((((product_Pair @ C3) @ ((product_prod @ D2) @ E)) @ C2) @ ((((product_Pair @ D2) @ E) @ D3) @ E2))))))) => (P @ X2))))).
% 2.87/1.51 thf(fact_241_prod__induct6, axiom, (! [F4:$tType,E:$tType,D2:$tType,C3:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ ((product_prod @ D2) @ ((product_prod @ E) @ F4))))) > $o),X2:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ ((product_prod @ D2) @ ((product_prod @ E) @ F4)))))]: (((! [A4:A,B3:B,C2:C3,D3:D2,E2:E,F3:F4]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ ((product_prod @ D2) @ ((product_prod @ E) @ F4))))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C3) @ ((product_prod @ D2) @ ((product_prod @ E) @ F4)))) @ B3) @ ((((product_Pair @ C3) @ ((product_prod @ D2) @ ((product_prod @ E) @ F4))) @ C2) @ ((((product_Pair @ D2) @ ((product_prod @ E) @ F4)) @ D3) @ ((((product_Pair @ E) @ F4) @ E2) @ F3)))))))) => (P @ X2))))).
% 2.87/1.51 thf(fact_242_prod__induct7, axiom, (! [G2:$tType,F4:$tType,E:$tType,D2:$tType,C3:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ ((product_prod @ D2) @ ((product_prod @ E) @ ((product_prod @ F4) @ G2)))))) > $o),X2:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ ((product_prod @ D2) @ ((product_prod @ E) @ ((product_prod @ F4) @ G2))))))]: (((! [A4:A,B3:B,C2:C3,D3:D2,E2:E,F3:F4,G3:G2]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ ((product_prod @ D2) @ ((product_prod @ E) @ ((product_prod @ F4) @ G2)))))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C3) @ ((product_prod @ D2) @ ((product_prod @ E) @ ((product_prod @ F4) @ G2))))) @ B3) @ ((((product_Pair @ C3) @ ((product_prod @ D2) @ ((product_prod @ E) @ ((product_prod @ F4) @ G2)))) @ C2) @ ((((product_Pair @ D2) @ ((product_prod @ E) @ ((product_prod @ F4) @ G2))) @ D3) @ ((((product_Pair @ E) @ ((product_prod @ F4) @ G2)) @ E2) @ ((((product_Pair @ F4) @ G2) @ F3) @ G3))))))))) => (P @ X2))))).
% 2.87/1.51 thf(fact_243_old_Ounit_Orec, axiom, (! [T:$tType,F1:T]: (((((product_rec_unit @ T) @ F1) @ product_Unity) = F1)))).
% 2.87/1.51 thf(fact_244_old_Oprod_Orec, axiom, (! [A:$tType,T:$tType,B:$tType,F1:(A > (B > T)),A2:A,B2:B]: (((((((product_rec_prod @ A) @ B) @ T) @ F1) @ ((((product_Pair @ A) @ B) @ A2) @ B2)) = ((F1 @ A2) @ B2))))).
% 2.87/1.51 thf(fact_245_default__unit__def, axiom, ((default_default @ product_unit) = product_Unity)).
% 2.87/1.51 thf(fact_246_supports__def, axiom, (! [A:$tType,X:$tType]: ((((supports @ X) @ A) = (^ [S3:(set @ X),X4:A]: ((! [A5:X,B4:X]: ((((~ ((((member @ X) @ A5) @ S3))) & (~ ((((member @ X) @ B4) @ S3)))) => (((((perm @ X) @ A) @ (((cons @ ((product_prod @ X) @ X)) @ ((((product_Pair @ X) @ X) @ A5) @ B4)) @ (nil @ ((product_prod @ X) @ X)))) @ X4) = X4)))))))))).
% 2.87/1.51 thf(fact_247_perm__residual__Rep_Osimps_I2_J, axiom, (! [X:$tType,Pi:(list @ ((product_prod @ X) @ X)),FreeRes3:late_freeRes,Pia:pi]: ((((((perm @ X) @ late_residual_Rep) @ Pi) @ ((late_r347633188eR_Rep @ FreeRes3) @ Pia)) = ((late_r347633188eR_Rep @ ((((perm @ X) @ late_freeRes) @ Pi) @ FreeRes3)) @ ((((perm @ X) @ pi) @ Pi) @ Pia)))))).
% 2.87/1.51 thf(fact_248_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)))))).
% 2.87/1.51 thf(fact_249_product__lists_Osimps_I1_J, axiom, (! [A:$tType]: ((((product_lists @ A) @ (nil @ (list @ A))) = (((cons @ (list @ A)) @ (nil @ A)) @ (nil @ (list @ A))))))).
% 2.87/1.51 thf(fact_250_name__calc_I1_J, axiom, (! [A2:name,B2:name,Pi:(list @ ((product_prod @ name) @ name)),X2:name]: ((((((perm @ name) @ name) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ A2) @ B2)) @ Pi)) @ X2) = (((swap @ name) @ ((((product_Pair @ name) @ name) @ A2) @ B2)) @ ((((perm @ name) @ name) @ Pi) @ X2)))))).
% 2.87/1.51 thf(fact_251_name__calc_I3_J, axiom, (! [A2:name,C:name,B2:name]: ((((A2 = C) => ((((swap @ name) @ ((((product_Pair @ name) @ name) @ A2) @ B2)) @ C) = B2)) & ((A2 != C) => (((B2 = C) => ((((swap @ name) @ ((((product_Pair @ name) @ name) @ A2) @ B2)) @ C) = A2)) & ((B2 != C) => ((((swap @ name) @ ((((product_Pair @ name) @ name) @ A2) @ B2)) @ C) = C)))))))).
% 2.87/1.51 thf(fact_252_Agent_Oswap__name__def, axiom, ((swap @ name) = swap_name)).
% 2.87/1.51 thf(fact_253_alpha__fresh_H, axiom, (! [X3:$tType]: (((pt_name @ X3) => (! [A2:name,X2:X3,B2:name,Y:X3,C:name]: (((((((abs_fun @ name) @ X3) @ A2) @ X2) = ((((abs_fun @ name) @ X3) @ B2) @ Y)) => ((C != A2) => ((C != B2) => (((((fresh @ name) @ X3) @ C) @ X2) => (((((fresh @ name) @ X3) @ C) @ Y) => (X2 = ((((perm @ name) @ X3) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ A2) @ C)) @ (nil @ ((product_prod @ name) @ name)))) @ ((((perm @ name) @ X3) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ B2) @ C)) @ (nil @ ((product_prod @ name) @ name)))) @ Y)))))))))))))).
% 2.87/1.51 thf(fact_254_pi_Ofresh_I9_J, axiom, (! [A2:name,X1:name,X22:pi]: ((((((fresh @ name) @ pi) @ A2) @ ((res @ X1) @ X22)) = ((((fresh @ name) @ (name > (noption @ pi))) @ A2) @ ((((abs_fun @ name) @ pi) @ X1) @ X22)))))).
% 2.87/1.51 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)))))).
% 2.87/1.51 thf(tcon_fun___Orderings_Oord, axiom, (! [A7:$tType,A8:$tType]: (((ord @ A8) => (ord @ (A7 > A8)))))).
% 2.87/1.51 thf(tcon_fun___Agent_Opt__name, axiom, (! [A7:$tType,A8:$tType]: ((((pt_name @ A7) & (pt_name @ A8)) => (pt_name @ (A7 > A8)))))).
% 2.87/1.51 thf(tcon_Set_Oset___Agent_Ocp__name__name_1, axiom, (! [A7:$tType]: (((cp_name_name @ A7) => (cp_name_name @ (set @ A7)))))).
% 2.87/1.51 thf(tcon_Set_Oset___Orderings_Oord_2, axiom, (! [A7:$tType]: ((ord @ (set @ A7))))).
% 2.87/1.51 thf(tcon_Set_Oset___Agent_Opt__name_3, axiom, (! [A7:$tType]: (((pt_name @ A7) => (pt_name @ (set @ A7)))))).
% 2.87/1.51 thf(tcon_Agent_Opi___Agent_Ocp__name__name_4, axiom, (cp_name_name @ pi)).
% 2.87/1.51 thf(tcon_Agent_Opi___Agent_Opt__name_5, axiom, (pt_name @ pi)).
% 2.87/1.51 thf(tcon_Agent_Opi___Agent_Ofs__name, axiom, (fs_name @ pi)).
% 2.87/1.51 thf(tcon_HOL_Obool___Orderings_Olinorder, axiom, (linorder @ $o)).
% 2.87/1.51 thf(tcon_HOL_Obool___Agent_Ocp__name__name_6, axiom, (cp_name_name @ $o)).
% 2.87/1.51 thf(tcon_HOL_Obool___Orderings_Oord_7, axiom, (ord @ $o)).
% 2.87/1.51 thf(tcon_HOL_Obool___Agent_Opt__name_8, axiom, (pt_name @ $o)).
% 2.87/1.51 thf(tcon_HOL_Obool___Agent_Ofs__name_9, axiom, (fs_name @ $o)).
% 2.87/1.51 thf(tcon_List_Olist___Agent_Ocp__name__name_10, axiom, (! [A7:$tType]: (((cp_name_name @ A7) => (cp_name_name @ (list @ A7)))))).
% 2.87/1.51 thf(tcon_List_Olist___Agent_Opt__name_11, axiom, (! [A7:$tType]: (((pt_name @ A7) => (pt_name @ (list @ A7)))))).
% 2.87/1.51 thf(tcon_List_Olist___Agent_Ofs__name_12, axiom, (! [A7:$tType]: (((fs_name @ A7) => (fs_name @ (list @ A7)))))).
% 2.87/1.51 thf(tcon_Agent_Oname___Agent_Ocp__name__name_13, axiom, (cp_name_name @ name)).
% 2.87/1.51 thf(tcon_Agent_Oname___Agent_Opt__name_14, axiom, (pt_name @ name)).
% 2.87/1.51 thf(tcon_Agent_Oname___Agent_Ofs__name_15, axiom, (fs_name @ name)).
% 2.87/1.51 thf(tcon_Agent_Opi__Rep___Agent_Ocp__name__name_16, axiom, (cp_name_name @ pi_Rep)).
% 2.87/1.51 thf(tcon_Agent_Opi__Rep___Agent_Opt__name_17, axiom, (pt_name @ pi_Rep)).
% 2.87/1.51 thf(tcon_Nominal_Onoption___Agent_Ocp__name__name_18, axiom, (! [A7:$tType]: (((cp_name_name @ A7) => (cp_name_name @ (noption @ A7)))))).
% 2.87/1.51 thf(tcon_Nominal_Onoption___Agent_Opt__name_19, axiom, (! [A7:$tType]: (((pt_name @ A7) => (pt_name @ (noption @ A7)))))).
% 2.87/1.51 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)))))).
% 2.87/1.51 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)))))).
% 2.87/1.51 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)))))).
% 2.87/1.51 thf(tcon_Product__Type_Ounit___Orderings_Olinorder_23, axiom, (linorder @ product_unit)).
% 2.87/1.51 thf(tcon_Product__Type_Ounit___Agent_Ocp__name__name_24, axiom, (cp_name_name @ product_unit)).
% 2.87/1.51 thf(tcon_Product__Type_Ounit___Orderings_Oord_25, axiom, (ord @ product_unit)).
% 2.87/1.51 thf(tcon_Product__Type_Ounit___Agent_Opt__name_26, axiom, (pt_name @ product_unit)).
% 2.87/1.51 thf(tcon_Product__Type_Ounit___Agent_Ofs__name_27, axiom, (fs_name @ product_unit)).
% 2.87/1.51 thf(tcon_Late__Semantics_OfreeRes___Agent_Ocp__name__name_28, axiom, (cp_name_name @ late_freeRes)).
% 2.87/1.51 thf(tcon_Late__Semantics_OfreeRes___Agent_Opt__name_29, axiom, (pt_name @ late_freeRes)).
% 2.87/1.51 thf(tcon_Late__Semantics_OfreeRes___Agent_Ofs__name_30, axiom, (fs_name @ late_freeRes)).
% 2.87/1.51 thf(tcon_Late__Semantics_Osubject___Agent_Ocp__name__name_31, axiom, (cp_name_name @ late_subject)).
% 2.87/1.51 thf(tcon_Late__Semantics_Osubject___Agent_Opt__name_32, axiom, (pt_name @ late_subject)).
% 2.87/1.51 thf(tcon_Late__Semantics_Osubject___Agent_Ofs__name_33, axiom, (fs_name @ late_subject)).
% 2.87/1.51 thf(tcon_Late__Semantics_Oresidual___Agent_Ocp__name__name_34, axiom, (cp_name_name @ late_residual)).
% 2.87/1.51 thf(tcon_Late__Semantics_Oresidual___Agent_Opt__name_35, axiom, (pt_name @ late_residual)).
% 2.87/1.51 thf(tcon_Late__Semantics_Oresidual___Agent_Ofs__name_36, axiom, (fs_name @ late_residual)).
% 2.87/1.51 thf(tcon_Late__Semantics_OfreeRes__Rep___Agent_Ocp__name__name_37, axiom, (cp_name_name @ late_freeRes_Rep)).
% 2.87/1.51 thf(tcon_Late__Semantics_OfreeRes__Rep___Agent_Opt__name_38, axiom, (pt_name @ late_freeRes_Rep)).
% 2.87/1.51 thf(tcon_Late__Semantics_Osubject__Rep___Agent_Ocp__name__name_39, axiom, (cp_name_name @ late_subject_Rep)).
% 2.87/1.51 thf(tcon_Late__Semantics_Osubject__Rep___Agent_Opt__name_40, axiom, (pt_name @ late_subject_Rep)).
% 2.87/1.51 thf(tcon_Late__Semantics_Oresidual__Rep___Agent_Ocp__name__name_41, axiom, (cp_name_name @ late_residual_Rep)).
% 2.87/1.51 thf(tcon_Late__Semantics_Oresidual__Rep___Agent_Opt__name_42, axiom, (pt_name @ late_residual_Rep)).
% 2.87/1.51 thf(help_If_3_1_T, axiom, (! [P:$o]: (((P = $true) | (P = $false))))).
% 2.87/1.51 thf(help_If_2_1_T, axiom, (! [A:$tType,X2:A,Y:A]: ((((((if @ A) @ $false) @ X2) @ Y) = Y)))).
% 2.87/1.51 thf(help_If_1_1_T, axiom, (! [A:$tType,X2:A,Y:A]: ((((((if @ A) @ $true) @ X2) @ Y) = X2)))).
% 2.87/1.51 thf(conj_0, conjecture, (? [P6:pi]: ((((late_transitions @ ((par @ p) @ ((res @ x) @ q))) @ (((late_BoundR @ (late_BoundOutputS @ ab)) @ y) @ P6)) & (((((strong2129052853vative @ P6) @ ((((perm @ name) @ pi) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ y) @ x)) @ (nil @ ((product_prod @ name) @ name)))) @ ((par @ (((subs @ p2) @ ya) @ c)) @ q2))) @ (late_BoundOutputS @ ab)) @ y) @ rel))))).
% 2.87/1.51 % SZS output end ListOfTHF for /export/starexec/sandbox2/tmp/tmp.l6Rd1czx4d/DTF2DTF25458.p
% 2.87/1.51 ------------------------
% 2.87/1.55 ---- Cleaned THF ---
% 2.87/1.55 thf(ty_t_Late__Semantics_Oresidual__Rep,type,
% 2.87/1.55 late_residual_Rep: $tType ).
% 2.87/1.55
% 2.87/1.55 thf(ty_t_Late__Semantics_Osubject__Rep,type,
% 2.87/1.55 late_subject_Rep: $tType ).
% 2.87/1.55
% 2.87/1.55 thf(ty_t_Late__Semantics_OfreeRes__Rep,type,
% 2.87/1.55 late_freeRes_Rep: $tType ).
% 2.87/1.55
% 2.87/1.55 thf(ty_t_Late__Semantics_Oresidual,type,
% 2.87/1.55 late_residual: $tType ).
% 2.87/1.55
% 2.87/1.55 thf(ty_t_Late__Semantics_Osubject,type,
% 2.87/1.55 late_subject: $tType ).
% 2.87/1.55
% 2.87/1.55 thf(ty_t_Late__Semantics_OfreeRes,type,
% 2.87/1.55 late_freeRes: $tType ).
% 2.87/1.55
% 2.87/1.55 thf(ty_t_Product__Type_Ounit,type,
% 2.87/1.55 product_unit: $tType ).
% 2.87/1.55
% 2.87/1.55 thf(ty_t_Product__Type_Oprod,type,
% 2.87/1.55 product_prod: $tType > $tType > $tType ).
% 2.87/1.55
% 2.87/1.55 thf(ty_t_Nominal_Onoption,type,
% 2.87/1.55 noption: $tType > $tType ).
% 2.87/1.55
% 2.87/1.55 thf(ty_t_Agent_Opi__Rep,type,
% 2.87/1.55 pi_Rep: $tType ).
% 2.87/1.55
% 2.87/1.55 thf(ty_t_Agent_Oname,type,
% 2.87/1.55 name: $tType ).
% 2.87/1.55
% 2.87/1.55 thf(ty_t_List_Olist,type,
% 2.87/1.55 list: $tType > $tType ).
% 2.87/1.55
% 2.87/1.55 thf(ty_t_Agent_Opi,type,
% 2.87/1.55 pi: $tType ).
% 2.87/1.55
% 2.87/1.55 thf(ty_t_Set_Oset,type,
% 2.87/1.55 set: $tType > $tType ).
% 2.87/1.55
% 2.87/1.55 thf(sy_cl_HOL_Otype,type,
% 2.87/1.55 type:
% 2.87/1.55 !>[A: $tType] : $o ).
% 2.87/1.55
% 2.87/1.55 thf(sy_cl_Agent_Ofs__name,type,
% 2.87/1.55 fs_name:
% 2.87/1.55 !>[A: $tType] : $o ).
% 2.87/1.55
% 2.87/1.55 thf(sy_cl_Agent_Opt__name,type,
% 2.87/1.55 pt_name:
% 2.87/1.55 !>[A: $tType] : $o ).
% 2.87/1.55
% 2.87/1.55 thf(sy_cl_Orderings_Oord,type,
% 2.87/1.55 ord:
% 2.87/1.55 !>[A: $tType] : $o ).
% 2.87/1.55
% 2.87/1.55 thf(sy_cl_Agent_Ocp__name__name,type,
% 2.87/1.55 cp_name_name:
% 2.87/1.55 !>[A: $tType] : $o ).
% 2.87/1.55
% 2.87/1.55 thf(sy_cl_Orderings_Olinorder,type,
% 2.87/1.55 linorder:
% 2.87/1.55 !>[A: $tType] : $o ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Agent_Opi_OInput,type,
% 2.87/1.55 input: name > name > pi > pi ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Agent_Opi_OPar,type,
% 2.87/1.55 par: pi > pi > pi ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Agent_Opi_ORes,type,
% 2.87/1.55 res: name > pi > pi ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Agent_Orec_Oswap__name,type,
% 2.87/1.55 swap_name: ( product_prod @ name @ name ) > name > name ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Agent_Osubs,type,
% 2.87/1.55 subs: pi > name > name > pi ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_HOL_Odefault__class_Odefault,type,
% 2.87/1.55 default_default:
% 2.87/1.55 !>[A: $tType] : A ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_If,type,
% 2.87/1.55 if:
% 2.87/1.55 !>[A: $tType] : ( $o > A > A > A ) ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Late__Semantics_OfreeRes_OOutputR,type,
% 2.87/1.55 late_OutputR: name > name > late_freeRes ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Late__Semantics_OfreeRes_OTauR,type,
% 2.87/1.55 late_TauR: late_freeRes ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Late__Semantics_Oresidual_OBoundR,type,
% 2.87/1.55 late_BoundR: late_subject > name > pi > late_residual ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Late__Semantics_Oresidual_OFreeR,type,
% 2.87/1.55 late_FreeR: late_freeRes > pi > late_residual ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Late__Semantics_Oresidual__Rep_OFreeR__Rep,type,
% 2.87/1.55 late_r347633188eR_Rep: late_freeRes > pi > late_residual_Rep ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Late__Semantics_Osubject_OBoundOutputS,type,
% 2.87/1.55 late_BoundOutputS: name > late_subject ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Late__Semantics_Osubject_OInputS,type,
% 2.87/1.55 late_InputS: name > late_subject ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Late__Semantics_Otransitions,type,
% 2.87/1.55 late_transitions: pi > late_residual > $o ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_List_Olist_OCons,type,
% 2.87/1.55 cons:
% 2.87/1.55 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_List_Olist_ONil,type,
% 2.87/1.55 nil:
% 2.87/1.55 !>[A: $tType] : ( list @ A ) ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_List_Oproduct__lists,type,
% 2.87/1.55 product_lists:
% 2.87/1.55 !>[A: $tType] : ( ( list @ ( list @ A ) ) > ( list @ ( list @ A ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Nominal_Oabs__fun,type,
% 2.87/1.55 abs_fun:
% 2.87/1.55 !>[X: $tType,A: $tType] : ( X > A > X > ( noption @ A ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Nominal_Ofresh,type,
% 2.87/1.55 fresh:
% 2.87/1.55 !>[X: $tType,A: $tType] : ( X > A > $o ) ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Nominal_Operm,type,
% 2.87/1.55 perm:
% 2.87/1.55 !>[X: $tType,A: $tType] : ( ( list @ ( product_prod @ X @ X ) ) > A > A ) ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Nominal_Osupports,type,
% 2.87/1.55 supports:
% 2.87/1.55 !>[X: $tType,A: $tType] : ( ( set @ X ) > A > $o ) ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Nominal_Oswap,type,
% 2.87/1.55 swap:
% 2.87/1.55 !>[X: $tType] : ( ( product_prod @ X @ X ) > X > X ) ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Product__Type_OPair,type,
% 2.87/1.55 product_Pair:
% 2.87/1.55 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Product__Type_OUnity,type,
% 2.87/1.55 product_Unity: product_unit ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod,type,
% 2.87/1.55 product_rec_prod:
% 2.87/1.55 !>[A: $tType,B: $tType,T: $tType] : ( ( A > B > T ) > ( product_prod @ A @ B ) > T ) ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Product__Type_Oold_Ounit_Orec__unit,type,
% 2.87/1.55 product_rec_unit:
% 2.87/1.55 !>[T: $tType] : ( T > product_unit > T ) ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Rel_Oeqvt,type,
% 2.87/1.55 eqvt:
% 2.87/1.55 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > $o ) ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Set_OCollect,type,
% 2.87/1.55 collect:
% 2.87/1.55 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Strong__Late__Sim_Oderivative,type,
% 2.87/1.55 strong2129052853vative: pi > pi > late_subject > name > ( set @ ( product_prod @ pi @ pi ) ) > $o ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Strong__Late__Sim_Osimulation,type,
% 2.87/1.55 strong743114133lation: pi > ( set @ ( product_prod @ pi @ pi ) ) > pi > $o ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_member,type,
% 2.87/1.55 member:
% 2.87/1.55 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 2.87/1.55
% 2.87/1.55 thf(sy_v_P,type,
% 2.87/1.55 p: pi ).
% 2.87/1.55
% 2.87/1.55 thf(sy_v_PQ____,type,
% 2.87/1.55 pq: pi ).
% 2.87/1.55
% 2.87/1.55 thf(sy_v_P_H____,type,
% 2.87/1.55 p2: pi ).
% 2.87/1.55
% 2.87/1.55 thf(sy_v_Q,type,
% 2.87/1.55 q: pi ).
% 2.87/1.55
% 2.87/1.55 thf(sy_v_Q_H____,type,
% 2.87/1.55 q2: pi ).
% 2.87/1.55
% 2.87/1.55 thf(sy_v_Rel,type,
% 2.87/1.55 rel: set @ ( product_prod @ pi @ pi ) ).
% 2.87/1.55
% 2.87/1.55 thf(sy_v_aa____,type,
% 2.87/1.55 aa: late_subject ).
% 2.87/1.55
% 2.87/1.55 thf(sy_v_ab____,type,
% 2.87/1.55 ab: name ).
% 2.87/1.55
% 2.87/1.55 thf(sy_v_b____,type,
% 2.87/1.55 b: name ).
% 2.87/1.55
% 2.87/1.55 thf(sy_v_c____,type,
% 2.87/1.55 c: name ).
% 2.87/1.55
% 2.87/1.55 thf(sy_v_x,type,
% 2.87/1.55 x: name ).
% 2.87/1.55
% 2.87/1.55 thf(sy_v_xPQ____,type,
% 2.87/1.55 xPQ: pi ).
% 2.87/1.55
% 2.87/1.55 thf(sy_v_y____,type,
% 2.87/1.55 y: name ).
% 2.87/1.55
% 2.87/1.55 thf(sy_v_ya____,type,
% 2.87/1.55 ya: name ).
% 2.87/1.55
% 2.87/1.55 thf(fact_0_cComm1_Ohyps_I5_J,axiom,
% 2.87/1.55 ya != b ).
% 2.87/1.55
% 2.87/1.55 thf(fact_1_cComm1_Ohyps_I9_J,axiom,
% 2.87/1.55 ( ( late_OutputR @ ab @ x )
% 2.87/1.55 = late_TauR ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_2_cOpen_Ohyps_I2_J,axiom,
% 2.87/1.55 ab != x ).
% 2.87/1.55
% 2.87/1.55 thf(fact_3_cComm1_Ohyps_I6_J,axiom,
% 2.87/1.55 ya != c ).
% 2.87/1.55
% 2.87/1.55 thf(fact_4_cOpen_Ohyps_I3_J,axiom,
% 2.87/1.55 ( aa
% 2.87/1.55 = ( late_BoundOutputS @ ab ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_5_assms_I3_J,axiom,
% 2.87/1.55 eqvt @ pi @ rel ).
% 2.87/1.55
% 2.87/1.55 thf(fact_6__092_060open_062y_____A_092_060noteq_062_Ax_092_060close_062,axiom,
% 2.87/1.55 y != x ).
% 2.87/1.55
% 2.87/1.55 thf(fact_7_Bound_Ohyps_I1_J,axiom,
% 2.87/1.55 late_transitions @ ( res @ x @ ( par @ p @ q ) ) @ ( late_BoundR @ aa @ y @ xPQ ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_8_assms_I1_J,axiom,
% 2.87/1.55 fresh @ name @ pi @ x @ p ).
% 2.87/1.55
% 2.87/1.55 thf(fact_9_cComm1_Ohyps_I3_J,axiom,
% 2.87/1.55 fresh @ name @ pi @ ya @ p ).
% 2.87/1.55
% 2.87/1.55 thf(fact_10_cComm1_Ohyps_I4_J,axiom,
% 2.87/1.55 fresh @ name @ pi @ ya @ q ).
% 2.87/1.55
% 2.87/1.55 thf(fact_11_cComm1_Ohyps_I7_J,axiom,
% 2.87/1.55 fresh @ name @ pi @ ya @ q2 ).
% 2.87/1.55
% 2.87/1.55 thf(fact_12_Bound_Ohyps_I3_J,axiom,
% 2.87/1.55 fresh @ name @ pi @ y @ ( res @ x @ ( par @ p @ q ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_13_Bound_Ohyps_I2_J,axiom,
% 2.87/1.55 fresh @ name @ pi @ y @ ( par @ p @ ( res @ x @ q ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_14_Strong__Late__Sim__SC__Mirabelle__dtpyqonsky_OsubstRes3,axiom,
% 2.87/1.55 ! [A2: name,P: pi,X2: name] :
% 2.87/1.55 ( ( subs @ ( res @ A2 @ P ) @ X2 @ A2 )
% 2.87/1.55 = ( res @ X2 @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ X2 @ A2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ P ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_15_cComm1_Ohyps_I1_J,axiom,
% 2.87/1.55 late_transitions @ p @ ( late_BoundR @ ( late_InputS @ b ) @ ya @ p2 ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_16_perm__swap_I1_J,axiom,
% 2.87/1.55 ! [X3: $tType] :
% 2.87/1.55 ( ( pt_name @ X3 )
% 2.87/1.55 => ! [A2: name,B2: name,X2: X3] :
% 2.87/1.55 ( ( perm @ name @ X3 @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ ( perm @ name @ X3 @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ X2 ) )
% 2.87/1.55 = X2 ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_17_name__id,axiom,
% 2.87/1.55 ! [X: $tType] :
% 2.87/1.55 ( ( pt_name @ X )
% 2.87/1.55 => ! [A2: name,X2: X] :
% 2.87/1.55 ( ( perm @ name @ X @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ A2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ X2 )
% 2.87/1.55 = X2 ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_18_name__swap,axiom,
% 2.87/1.55 ! [X: $tType] :
% 2.87/1.55 ( ( pt_name @ X )
% 2.87/1.55 => ! [A2: name,B2: name,X2: X] :
% 2.87/1.55 ( ( perm @ name @ X @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ X2 )
% 2.87/1.55 = ( perm @ name @ X @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ B2 @ A2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ X2 ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_19_name__swap__bij,axiom,
% 2.87/1.55 ! [X: $tType] :
% 2.87/1.55 ( ( pt_name @ X )
% 2.87/1.55 => ! [A2: name,B2: name,X2: X] :
% 2.87/1.55 ( ( 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 ) ) ) @ X2 ) )
% 2.87/1.55 = X2 ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_20_cOpen_Ohyps_I1_J,axiom,
% 2.87/1.55 late_transitions @ ( par @ p @ q ) @ ( late_FreeR @ ( late_OutputR @ ab @ x ) @ pq ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_21_pi_Operm_I8_J,axiom,
% 2.87/1.55 ! [Pi: list @ ( product_prod @ name @ name ),X22: pi,X1: pi] :
% 2.87/1.55 ( ( perm @ name @ pi @ Pi @ ( par @ X22 @ X1 ) )
% 2.87/1.55 = ( par @ ( perm @ name @ pi @ Pi @ X22 ) @ ( perm @ name @ pi @ Pi @ X1 ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_22_simps_I8_J,axiom,
% 2.87/1.55 ! [P: pi,Q: pi,C: name,D: name] :
% 2.87/1.55 ( ( subs @ ( par @ P @ Q ) @ C @ D )
% 2.87/1.55 = ( par @ ( subs @ P @ C @ D ) @ ( subs @ Q @ C @ D ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_23_simps_I9_J,axiom,
% 2.87/1.55 ! [X2: name,C: name,D: name,P: pi] :
% 2.87/1.55 ( ( X2 != C )
% 2.87/1.55 => ( ( X2 != D )
% 2.87/1.55 => ( ( subs @ ( res @ X2 @ P ) @ C @ D )
% 2.87/1.55 = ( res @ X2 @ ( subs @ P @ C @ D ) ) ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_24_pt__name1,axiom,
% 2.87/1.55 ! [A: $tType] :
% 2.87/1.55 ( ( pt_name @ A )
% 2.87/1.55 => ! [X2: A] :
% 2.87/1.55 ( ( perm @ name @ A @ ( nil @ ( product_prod @ name @ name ) ) @ X2 )
% 2.87/1.55 = X2 ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_25_cComm1_Ohyps_I2_J,axiom,
% 2.87/1.55 late_transitions @ q @ ( late_FreeR @ ( late_OutputR @ b @ c ) @ q2 ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_26__092_060open_062y_____A_092_060sharp_062_AP_A_092_060parallel_062_AQ_092_060close_062,axiom,
% 2.87/1.55 fresh @ name @ pi @ y @ ( par @ p @ q ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_27_subst__identity,axiom,
% 2.87/1.55 ! [P: pi,A2: name] :
% 2.87/1.55 ( ( subs @ P @ A2 @ A2 )
% 2.87/1.55 = P ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_28_pi__perm__empty,axiom,
% 2.87/1.55 ! [Pi_Rep: pi_Rep] :
% 2.87/1.55 ( ( perm @ name @ pi_Rep @ ( nil @ ( product_prod @ name @ name ) ) @ Pi_Rep )
% 2.87/1.55 = Pi_Rep ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_29__092_060open_062y_____A_092_060sharp_062_AP_092_060close_062,axiom,
% 2.87/1.55 fresh @ name @ pi @ y @ p ).
% 2.87/1.55
% 2.87/1.55 thf(fact_30__092_060open_062y_____A_092_060sharp_062_AQ_092_060close_062,axiom,
% 2.87/1.55 fresh @ name @ pi @ y @ q ).
% 2.87/1.55
% 2.87/1.55 thf(fact_31_pi_Ofresh_I8_J,axiom,
% 2.87/1.55 ! [A2: name,X22: pi,X1: pi] :
% 2.87/1.55 ( ( fresh @ name @ pi @ A2 @ ( par @ X22 @ X1 ) )
% 2.87/1.55 = ( ( fresh @ name @ pi @ A2 @ X22 )
% 2.87/1.55 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_32_pi_Operm_I9_J,axiom,
% 2.87/1.55 ! [Pi: list @ ( product_prod @ name @ name ),X1: name,X22: pi] :
% 2.87/1.55 ( ( perm @ name @ pi @ Pi @ ( res @ X1 @ X22 ) )
% 2.87/1.55 = ( res @ ( perm @ name @ name @ Pi @ X1 ) @ ( perm @ name @ pi @ Pi @ X22 ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_33_perm__fresh__fresh,axiom,
% 2.87/1.55 ! [X3: $tType] :
% 2.87/1.55 ( ( pt_name @ X3 )
% 2.87/1.55 => ! [A2: name,X2: X3,B2: name] :
% 2.87/1.55 ( ( fresh @ name @ X3 @ A2 @ X2 )
% 2.87/1.55 => ( ( fresh @ name @ X3 @ B2 @ X2 )
% 2.87/1.55 => ( ( perm @ name @ X3 @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ X2 )
% 2.87/1.55 = X2 ) ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_34_name__fresh__fresh,axiom,
% 2.87/1.55 ! [X: $tType] :
% 2.87/1.55 ( ( pt_name @ X )
% 2.87/1.55 => ! [A2: name,X2: X,B2: name] :
% 2.87/1.55 ( ( fresh @ name @ X @ A2 @ X2 )
% 2.87/1.55 => ( ( fresh @ name @ X @ B2 @ X2 )
% 2.87/1.55 => ( ( perm @ name @ X @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ X2 )
% 2.87/1.55 = X2 ) ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_35_Bound_Ohyps_I4_J,axiom,
% 2.87/1.55 fresh @ name @ late_subject @ y @ aa ).
% 2.87/1.55
% 2.87/1.55 thf(fact_36_fresh__perm__app,axiom,
% 2.87/1.55 ! [X3: $tType] :
% 2.87/1.55 ( ( pt_name @ X3 )
% 2.87/1.55 => ! [A2: name,Pi: list @ ( product_prod @ name @ name ),X2: X3] :
% 2.87/1.55 ( ( fresh @ name @ ( list @ ( product_prod @ name @ name ) ) @ A2 @ Pi )
% 2.87/1.55 => ( ( fresh @ name @ X3 @ A2 @ X2 )
% 2.87/1.55 => ( fresh @ name @ X3 @ A2 @ ( perm @ name @ X3 @ Pi @ X2 ) ) ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_37_name__exists__fresh,axiom,
% 2.87/1.55 ! [A: $tType] :
% 2.87/1.55 ( ( fs_name @ A )
% 2.87/1.55 => ! [X2: A] :
% 2.87/1.55 ~ ! [C2: name] :
% 2.87/1.55 ~ ( fresh @ name @ A @ C2 @ X2 ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_38_fresh__eqvt,axiom,
% 2.87/1.55 ! [X3: $tType] :
% 2.87/1.55 ( ( pt_name @ X3 )
% 2.87/1.55 => ! [Pi: list @ ( product_prod @ name @ name ),A2: name,X2: X3] :
% 2.87/1.55 ( ( perm @ name @ $o @ Pi @ ( fresh @ name @ X3 @ A2 @ X2 ) )
% 2.87/1.55 = ( fresh @ name @ X3 @ ( perm @ name @ name @ Pi @ A2 ) @ ( perm @ name @ X3 @ Pi @ X2 ) ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_39_fresh__bij,axiom,
% 2.87/1.55 ! [X3: $tType] :
% 2.87/1.55 ( ( pt_name @ X3 )
% 2.87/1.55 => ! [Pi: list @ ( product_prod @ name @ name ),A2: name,X2: X3] :
% 2.87/1.55 ( ( fresh @ name @ X3 @ ( perm @ name @ name @ Pi @ A2 ) @ ( perm @ name @ X3 @ Pi @ X2 ) )
% 2.87/1.55 = ( fresh @ name @ X3 @ A2 @ X2 ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_40_freshRes,axiom,
% 2.87/1.55 ! [A2: name,P: pi] : ( fresh @ name @ pi @ A2 @ ( res @ A2 @ P ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_41_fresh__fact2,axiom,
% 2.87/1.55 ! [A2: name,B2: name,P: pi] :
% 2.87/1.55 ( ( A2 != B2 )
% 2.87/1.55 => ( fresh @ name @ pi @ A2 @ ( subs @ P @ A2 @ B2 ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_42_fresh__fact1,axiom,
% 2.87/1.55 ! [A2: name,P: pi,C: name,B2: name] :
% 2.87/1.55 ( ( fresh @ name @ pi @ A2 @ P )
% 2.87/1.55 => ( ( A2 != C )
% 2.87/1.55 => ( fresh @ name @ pi @ A2 @ ( subs @ P @ B2 @ C ) ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_43_forget,axiom,
% 2.87/1.55 ! [A2: name,P: pi,B2: name] :
% 2.87/1.55 ( ( fresh @ name @ pi @ A2 @ P )
% 2.87/1.55 => ( ( subs @ P @ A2 @ B2 )
% 2.87/1.55 = P ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_44_name__calc_I2_J,axiom,
% 2.87/1.55 ! [X2: name] :
% 2.87/1.55 ( ( perm @ name @ name @ ( nil @ ( product_prod @ name @ name ) ) @ X2 )
% 2.87/1.55 = X2 ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_45_mem__Collect__eq,axiom,
% 2.87/1.55 ! [A: $tType,A2: A,P: A > $o] :
% 2.87/1.55 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 2.87/1.55 = ( P @ A2 ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_46_Collect__mem__eq,axiom,
% 2.87/1.55 ! [A: $tType,A3: set @ A] :
% 2.87/1.55 ( ( collect @ A
% 2.87/1.55 @ ^ [X4: A] : ( member @ A @ X4 @ A3 ) )
% 2.87/1.55 = A3 ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_47_Collect__cong,axiom,
% 2.87/1.55 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.87/1.55 ( ! [X5: A] :
% 2.87/1.55 ( ( P @ X5 )
% 2.87/1.55 = ( Q @ X5 ) )
% 2.87/1.55 => ( ( collect @ A @ P )
% 2.87/1.55 = ( collect @ A @ Q ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_48_ext,axiom,
% 2.87/1.55 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 2.87/1.55 ( ! [X5: A] :
% 2.87/1.55 ( ( F @ X5 )
% 2.87/1.55 = ( G @ X5 ) )
% 2.87/1.55 => ( F = G ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_49_Agent_OsubstRes3,axiom,
% 2.87/1.55 ! [B2: name,P: pi,A2: name] :
% 2.87/1.55 ( ( fresh @ name @ pi @ B2 @ P )
% 2.87/1.55 => ( ( subs @ ( res @ A2 @ P ) @ A2 @ B2 )
% 2.87/1.55 = ( res @ B2 @ ( subs @ P @ A2 @ B2 ) ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_50_substRes2,axiom,
% 2.87/1.55 ! [B2: name,P: pi,A2: name] :
% 2.87/1.55 ( ( fresh @ name @ pi @ B2 @ P )
% 2.87/1.55 => ( ( res @ A2 @ P )
% 2.87/1.55 = ( res @ B2 @ ( subs @ P @ A2 @ B2 ) ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_51_eqvt__subs,axiom,
% 2.87/1.55 ! [P2: list @ ( product_prod @ name @ name ),P: pi,A2: name,B2: name] :
% 2.87/1.55 ( ( perm @ name @ pi @ P2 @ ( subs @ P @ A2 @ B2 ) )
% 2.87/1.55 = ( subs @ ( perm @ name @ pi @ P2 @ P ) @ ( perm @ name @ name @ P2 @ A2 ) @ ( perm @ name @ name @ P2 @ B2 ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_52_swap__simps_I1_J,axiom,
% 2.87/1.55 ! [A2: name,B2: name] :
% 2.87/1.55 ( ( perm @ name @ name @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ A2 )
% 2.87/1.55 = B2 ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_53_swap__simps_I2_J,axiom,
% 2.87/1.55 ! [A2: name,B2: name] :
% 2.87/1.55 ( ( perm @ name @ name @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ B2 )
% 2.87/1.55 = A2 ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_54_swap__simps_I3_J,axiom,
% 2.87/1.55 ! [A2: name,C: name,B2: name] :
% 2.87/1.55 ( ( A2 != C )
% 2.87/1.55 => ( ( B2 != C )
% 2.87/1.55 => ( ( perm @ name @ name @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ C )
% 2.87/1.55 = C ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_55_fresh__aux,axiom,
% 2.87/1.55 ! [X3: $tType] :
% 2.87/1.55 ( ( pt_name @ X3 )
% 2.87/1.55 => ! [C: name,A2: name,X2: X3,B2: name] :
% 2.87/1.55 ( ( C != A2 )
% 2.87/1.55 => ( ( fresh @ name @ X3 @ A2 @ X2 )
% 2.87/1.55 => ( ( fresh @ name @ X3 @ C @ X2 )
% 2.87/1.55 => ( fresh @ name @ X3 @ C @ ( perm @ name @ X3 @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ X2 ) ) ) ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_56_cp__name__name1,axiom,
% 2.87/1.55 ! [A: $tType] :
% 2.87/1.55 ( ( cp_name_name @ A )
% 2.87/1.55 => ! [Pi1: list @ ( product_prod @ name @ name ),Pi2: list @ ( product_prod @ name @ name ),X2: A] :
% 2.87/1.55 ( ( perm @ name @ A @ Pi1 @ ( perm @ name @ A @ Pi2 @ X2 ) )
% 2.87/1.55 = ( perm @ name @ A @ ( perm @ name @ ( list @ ( product_prod @ name @ name ) ) @ Pi1 @ Pi2 ) @ ( perm @ name @ A @ Pi1 @ X2 ) ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_57_name__perm__compose,axiom,
% 2.87/1.55 ! [X: $tType] :
% 2.87/1.55 ( ( pt_name @ X )
% 2.87/1.55 => ! [Pi2: list @ ( product_prod @ name @ name ),Pi1: list @ ( product_prod @ name @ name ),X2: X] :
% 2.87/1.55 ( ( perm @ name @ X @ Pi2 @ ( perm @ name @ X @ Pi1 @ X2 ) )
% 2.87/1.55 = ( perm @ name @ X @ ( perm @ name @ ( list @ ( product_prod @ name @ name ) ) @ Pi2 @ Pi1 ) @ ( perm @ name @ X @ Pi2 @ X2 ) ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_58_perm__compose,axiom,
% 2.87/1.55 ! [X3: $tType] :
% 2.87/1.55 ( ( pt_name @ X3 )
% 2.87/1.55 => ! [Pi2: list @ ( product_prod @ name @ name ),Pi1: list @ ( product_prod @ name @ name ),X2: X3] :
% 2.87/1.55 ( ( perm @ name @ X3 @ Pi2 @ ( perm @ name @ X3 @ Pi1 @ X2 ) )
% 2.87/1.55 = ( perm @ name @ X3 @ ( perm @ name @ ( list @ ( product_prod @ name @ name ) ) @ Pi2 @ Pi1 ) @ ( perm @ name @ X3 @ Pi2 @ X2 ) ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_59_perm__bij,axiom,
% 2.87/1.55 ! [X3: $tType] :
% 2.87/1.55 ( ( pt_name @ X3 )
% 2.87/1.55 => ! [Pi: list @ ( product_prod @ name @ name ),X2: X3,Y: X3] :
% 2.87/1.55 ( ( ( perm @ name @ X3 @ Pi @ X2 )
% 2.87/1.55 = ( perm @ name @ X3 @ Pi @ Y ) )
% 2.87/1.55 = ( X2 = Y ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_60_perm__app,axiom,
% 2.87/1.55 ! [B: $tType,X3: $tType] :
% 2.87/1.55 ( ( pt_name @ X3 )
% 2.87/1.55 => ! [Pi: list @ ( product_prod @ name @ name ),F: X3 > B,X2: X3] :
% 2.87/1.55 ( ( perm @ name @ B @ Pi @ ( F @ X2 ) )
% 2.87/1.55 = ( perm @ name @ ( X3 > B ) @ Pi @ F @ ( perm @ name @ X3 @ Pi @ X2 ) ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_61_in__eqvt,axiom,
% 2.87/1.55 ! [X3: $tType] :
% 2.87/1.55 ( ( pt_name @ X3 )
% 2.87/1.55 => ! [Pi: list @ ( product_prod @ name @ name ),X2: X3,X6: set @ X3] :
% 2.87/1.55 ( ( perm @ name @ $o @ Pi @ ( member @ X3 @ X2 @ X6 ) )
% 2.87/1.55 = ( member @ X3 @ ( perm @ name @ X3 @ Pi @ X2 ) @ ( perm @ name @ ( set @ X3 ) @ Pi @ X6 ) ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_62_eq__eqvt,axiom,
% 2.87/1.55 ! [X3: $tType] :
% 2.87/1.55 ( ( pt_name @ X3 )
% 2.87/1.55 => ! [Pi: list @ ( product_prod @ name @ name ),X2: X3,Y: X3] :
% 2.87/1.55 ( ( perm @ name @ $o @ Pi @ ( X2 = Y ) )
% 2.87/1.55 = ( ( perm @ name @ X3 @ Pi @ X2 )
% 2.87/1.55 = ( perm @ name @ X3 @ Pi @ Y ) ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_63_pi_Oinject_I7_J,axiom,
% 2.87/1.55 ! [X22: pi,X1: pi,Y2: pi,Y1: pi] :
% 2.87/1.55 ( ( ( par @ X22 @ X1 )
% 2.87/1.55 = ( par @ Y2 @ Y1 ) )
% 2.87/1.55 = ( ( X22 = Y2 )
% 2.87/1.55 & ( X1 = Y1 ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_64_alphaRes,axiom,
% 2.87/1.55 ! [C: name,P: pi,A2: name] :
% 2.87/1.55 ( ( fresh @ name @ pi @ C @ P )
% 2.87/1.55 => ( ( res @ A2 @ P )
% 2.87/1.55 = ( res @ C @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ C ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ P ) ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_65_injPermSubst,axiom,
% 2.87/1.55 ! [B2: name,P: pi,A2: name] :
% 2.87/1.55 ( ( fresh @ name @ pi @ B2 @ P )
% 2.87/1.55 => ( ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ P )
% 2.87/1.55 = ( subs @ P @ A2 @ B2 ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_66_renaming,axiom,
% 2.87/1.55 ! [C: name,P: pi,A2: name,B2: name] :
% 2.87/1.55 ( ( fresh @ name @ pi @ C @ P )
% 2.87/1.55 => ( ( subs @ P @ A2 @ B2 )
% 2.87/1.55 = ( subs @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ C @ A2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ P ) @ C @ B2 ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_67_pi_Odistinct_I85_J,axiom,
% 2.87/1.55 ! [Pi1: pi,Pi2: pi,Name: name,Pi3: pi] :
% 2.87/1.55 ( ( par @ Pi1 @ Pi2 )
% 2.87/1.55 != ( res @ Name @ Pi3 ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_68_perm__swap_I2_J,axiom,
% 2.87/1.55 ! [X3: $tType] :
% 2.87/1.55 ( ( pt_name @ X3 )
% 2.87/1.55 => ! [A2: name,B2: name,X2: X3] :
% 2.87/1.55 ( ( perm @ name @ X3 @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ ( perm @ name @ X3 @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ B2 @ A2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ X2 ) )
% 2.87/1.55 = X2 ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_69_transitions_OClose2,axiom,
% 2.87/1.55 ! [P: pi,A2: name,Y: name,P3: pi,Q: pi,X2: name,Q2: pi] :
% 2.87/1.55 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y @ P3 ) )
% 2.87/1.55 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ Q2 ) )
% 2.87/1.55 => ( ( fresh @ name @ pi @ X2 @ P )
% 2.87/1.55 => ( ( fresh @ name @ pi @ X2 @ Q )
% 2.87/1.55 => ( ( fresh @ name @ pi @ Y @ P )
% 2.87/1.55 => ( ( fresh @ name @ pi @ Y @ Q )
% 2.87/1.55 => ( ( X2 != A2 )
% 2.87/1.55 => ( ( fresh @ name @ pi @ X2 @ P3 )
% 2.87/1.55 => ( ( Y != A2 )
% 2.87/1.55 => ( ( fresh @ name @ pi @ Y @ Q2 )
% 2.87/1.55 => ( ( X2 != Y )
% 2.87/1.55 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ P3 @ ( subs @ Q2 @ X2 @ Y ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_70_transitions_OClose1,axiom,
% 2.87/1.55 ! [P: pi,A2: name,X2: name,P3: pi,Q: pi,Y: name,Q2: pi] :
% 2.87/1.55 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P3 ) )
% 2.87/1.55 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y @ Q2 ) )
% 2.87/1.55 => ( ( fresh @ name @ pi @ X2 @ P )
% 2.87/1.55 => ( ( fresh @ name @ pi @ X2 @ Q )
% 2.87/1.55 => ( ( fresh @ name @ pi @ Y @ P )
% 2.87/1.55 => ( ( fresh @ name @ pi @ Y @ Q )
% 2.87/1.55 => ( ( X2 != A2 )
% 2.87/1.55 => ( ( fresh @ name @ pi @ X2 @ Q2 )
% 2.87/1.55 => ( ( Y != A2 )
% 2.87/1.55 => ( ( fresh @ name @ pi @ Y @ P3 )
% 2.87/1.55 => ( ( X2 != Y )
% 2.87/1.55 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ ( subs @ P3 @ X2 @ Y ) @ Q2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_71_Late__Semantics_OClose2,axiom,
% 2.87/1.55 ! [P: pi,A2: name,Y: name,P3: pi,Q: pi,X2: name,Q2: pi] :
% 2.87/1.55 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y @ P3 ) )
% 2.87/1.55 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ Q2 ) )
% 2.87/1.55 => ( ( fresh @ name @ pi @ Y @ Q )
% 2.87/1.55 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ P3 @ ( subs @ Q2 @ X2 @ Y ) ) ) ) ) ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_72_Late__Semantics_OClose1,axiom,
% 2.87/1.55 ! [P: pi,A2: name,X2: name,P3: pi,Q: pi,Y: name,Q2: pi] :
% 2.87/1.55 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P3 ) )
% 2.87/1.55 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y @ Q2 ) )
% 2.87/1.55 => ( ( fresh @ name @ pi @ Y @ P )
% 2.87/1.55 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ ( subs @ P3 @ X2 @ Y ) @ Q2 ) ) ) ) ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_73_transitions_OComm2,axiom,
% 2.87/1.55 ! [P: pi,A2: name,B2: name,P3: pi,Q: pi,X2: name,Q2: pi] :
% 2.87/1.55 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P3 ) )
% 2.87/1.55 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ Q2 ) )
% 2.87/1.55 => ( ( fresh @ name @ pi @ X2 @ P )
% 2.87/1.55 => ( ( fresh @ name @ pi @ X2 @ Q )
% 2.87/1.55 => ( ( X2 != A2 )
% 2.87/1.55 => ( ( X2 != B2 )
% 2.87/1.55 => ( ( fresh @ name @ pi @ X2 @ P3 )
% 2.87/1.55 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P3 @ ( subs @ Q2 @ X2 @ B2 ) ) ) ) ) ) ) ) ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_74_transitions_OComm1,axiom,
% 2.87/1.55 ! [P: pi,A2: name,X2: name,P3: pi,Q: pi,B2: name,Q2: pi] :
% 2.87/1.55 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P3 ) )
% 2.87/1.55 => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ Q2 ) )
% 2.87/1.55 => ( ( fresh @ name @ pi @ X2 @ P )
% 2.87/1.55 => ( ( fresh @ name @ pi @ X2 @ Q )
% 2.87/1.55 => ( ( X2 != A2 )
% 2.87/1.55 => ( ( X2 != B2 )
% 2.87/1.55 => ( ( fresh @ name @ pi @ X2 @ Q2 )
% 2.87/1.55 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P3 @ X2 @ B2 ) @ Q2 ) ) ) ) ) ) ) ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_75_Late__Semantics_OComm2,axiom,
% 2.87/1.55 ! [P: pi,A2: name,B2: name,P3: pi,Q: pi,X2: name,Q2: pi] :
% 2.87/1.55 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P3 ) )
% 2.87/1.55 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ Q2 ) )
% 2.87/1.55 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P3 @ ( subs @ Q2 @ X2 @ B2 ) ) ) ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_76_Late__Semantics_OComm1,axiom,
% 2.87/1.55 ! [P: pi,A2: name,X2: name,P3: pi,Q: pi,B2: name,Q2: pi] :
% 2.87/1.55 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P3 ) )
% 2.87/1.55 => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ Q2 ) )
% 2.87/1.55 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P3 @ X2 @ B2 ) @ Q2 ) ) ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_77_alphaBoundResidual,axiom,
% 2.87/1.55 ! [X7: name,P: pi,A2: late_subject,X2: name] :
% 2.87/1.55 ( ( fresh @ name @ pi @ X7 @ P )
% 2.87/1.55 => ( ( late_BoundR @ A2 @ X2 @ P )
% 2.87/1.55 = ( late_BoundR @ A2 @ X7 @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ X2 @ X7 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ P ) ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_78_freeRes__perm__empty,axiom,
% 2.87/1.55 ! [FreeRes_Rep: late_freeRes_Rep] :
% 2.87/1.55 ( ( perm @ name @ late_freeRes_Rep @ ( nil @ ( product_prod @ name @ name ) ) @ FreeRes_Rep )
% 2.87/1.55 = FreeRes_Rep ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_79_subject__perm__empty,axiom,
% 2.87/1.55 ! [Subject_Rep: late_subject_Rep] :
% 2.87/1.55 ( ( perm @ name @ late_subject_Rep @ ( nil @ ( product_prod @ name @ name ) ) @ Subject_Rep )
% 2.87/1.55 = Subject_Rep ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_80_residual__perm__empty,axiom,
% 2.87/1.55 ! [Residual_Rep: late_residual_Rep] :
% 2.87/1.55 ( ( perm @ name @ late_residual_Rep @ ( nil @ ( product_prod @ name @ name ) ) @ Residual_Rep )
% 2.87/1.55 = Residual_Rep ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_81_freeRes_Ofresh_I1_J,axiom,
% 2.87/1.55 ! [A2: name,X22: name,X1: name] :
% 2.87/1.55 ( ( fresh @ name @ late_freeRes @ A2 @ ( late_OutputR @ X22 @ X1 ) )
% 2.87/1.55 = ( ( fresh @ name @ name @ A2 @ X22 )
% 2.87/1.55 & ( fresh @ name @ name @ A2 @ X1 ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_82_Late__Semantics_OfreeRes_Oinject,axiom,
% 2.87/1.55 ! [X22: name,X1: name,Y2: name,Y1: name] :
% 2.87/1.55 ( ( ( late_OutputR @ X22 @ X1 )
% 2.87/1.55 = ( late_OutputR @ Y2 @ Y1 ) )
% 2.87/1.55 = ( ( X22 = Y2 )
% 2.87/1.55 & ( X1 = Y1 ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_83_Late__Semantics_Osubject_Oinject_I2_J,axiom,
% 2.87/1.55 ! [X1: name,Y1: name] :
% 2.87/1.55 ( ( ( late_BoundOutputS @ X1 )
% 2.87/1.55 = ( late_BoundOutputS @ Y1 ) )
% 2.87/1.55 = ( X1 = Y1 ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_84_freeRes_Ofresh_I2_J,axiom,
% 2.87/1.55 ! [A2: name] : ( fresh @ name @ late_freeRes @ A2 @ late_TauR ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_85_freeRes_Operm_I2_J,axiom,
% 2.87/1.55 ! [Pi: list @ ( product_prod @ name @ name )] :
% 2.87/1.55 ( ( perm @ name @ late_freeRes @ Pi @ late_TauR )
% 2.87/1.55 = late_TauR ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_86_cComm1_Ohyps_I8_J,axiom,
% 2.87/1.55 fresh @ name @ product_unit @ ya @ product_Unity ).
% 2.87/1.55
% 2.87/1.55 thf(fact_87_residual_Ofresh_I2_J,axiom,
% 2.87/1.55 ! [A2: name,X22: late_freeRes,X1: pi] :
% 2.87/1.55 ( ( fresh @ name @ late_residual @ A2 @ ( late_FreeR @ X22 @ X1 ) )
% 2.87/1.55 = ( ( fresh @ name @ late_freeRes @ A2 @ X22 )
% 2.87/1.55 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_88_substTrans,axiom,
% 2.87/1.55 ! [B2: name,P: pi,A2: name,C: name] :
% 2.87/1.55 ( ( fresh @ name @ pi @ B2 @ P )
% 2.87/1.55 => ( ( subs @ ( subs @ P @ A2 @ B2 ) @ B2 @ C )
% 2.87/1.55 = ( subs @ P @ A2 @ C ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_89_residual_Operm_I2_J,axiom,
% 2.87/1.55 ! [Pi: list @ ( product_prod @ name @ name ),X22: late_freeRes,X1: pi] :
% 2.87/1.55 ( ( perm @ name @ late_residual @ Pi @ ( late_FreeR @ X22 @ X1 ) )
% 2.87/1.55 = ( late_FreeR @ ( perm @ name @ late_freeRes @ Pi @ X22 ) @ ( perm @ name @ pi @ Pi @ X1 ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_90_freeRes_Operm_I1_J,axiom,
% 2.87/1.55 ! [Pi: list @ ( product_prod @ name @ name ),X22: name,X1: name] :
% 2.87/1.55 ( ( perm @ name @ late_freeRes @ Pi @ ( late_OutputR @ X22 @ X1 ) )
% 2.87/1.55 = ( late_OutputR @ ( perm @ name @ name @ Pi @ X22 ) @ ( perm @ name @ name @ Pi @ X1 ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_91_subject_Operm_I1_J,axiom,
% 2.87/1.55 ! [Pi: list @ ( product_prod @ name @ name ),X1: name] :
% 2.87/1.55 ( ( perm @ name @ late_subject @ Pi @ ( late_InputS @ X1 ) )
% 2.87/1.55 = ( late_InputS @ ( perm @ name @ name @ Pi @ X1 ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_92_subject_Operm_I2_J,axiom,
% 2.87/1.55 ! [Pi: list @ ( product_prod @ name @ name ),X1: name] :
% 2.87/1.55 ( ( perm @ name @ late_subject @ Pi @ ( late_BoundOutputS @ X1 ) )
% 2.87/1.55 = ( late_BoundOutputS @ ( perm @ name @ name @ Pi @ X1 ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_93_subject_Ofresh_I2_J,axiom,
% 2.87/1.55 ! [A2: name,X1: name] :
% 2.87/1.55 ( ( fresh @ name @ late_subject @ A2 @ ( late_BoundOutputS @ X1 ) )
% 2.87/1.55 = ( fresh @ name @ name @ A2 @ X1 ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_94_subject_Ofresh_I1_J,axiom,
% 2.87/1.55 ! [A2: name,X1: name] :
% 2.87/1.55 ( ( fresh @ name @ late_subject @ A2 @ ( late_InputS @ X1 ) )
% 2.87/1.55 = ( fresh @ name @ name @ A2 @ X1 ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_95_residual_Operm_I1_J,axiom,
% 2.87/1.55 ! [Pi: list @ ( product_prod @ name @ name ),X32: late_subject,X1: name,X22: pi] :
% 2.87/1.55 ( ( perm @ name @ late_residual @ Pi @ ( late_BoundR @ X32 @ X1 @ X22 ) )
% 2.87/1.55 = ( late_BoundR @ ( perm @ name @ late_subject @ Pi @ X32 ) @ ( perm @ name @ name @ Pi @ X1 ) @ ( perm @ name @ pi @ Pi @ X22 ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_96_name__bij,axiom,
% 2.87/1.55 ! [Pi: list @ ( product_prod @ name @ name ),X2: name,Y: name] :
% 2.87/1.55 ( ( ( perm @ name @ name @ Pi @ X2 )
% 2.87/1.55 = ( perm @ name @ name @ Pi @ Y ) )
% 2.87/1.55 = ( X2 = Y ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_97_freshResidual,axiom,
% 2.87/1.55 ! [P: pi,Rs: late_residual,X2: name] :
% 2.87/1.55 ( ( late_transitions @ P @ Rs )
% 2.87/1.55 => ( ( fresh @ name @ pi @ X2 @ P )
% 2.87/1.55 => ( fresh @ name @ late_residual @ X2 @ Rs ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_98_resCasesF,axiom,
% 2.87/1.55 ! [X2: name,P: pi,Alpha: late_freeRes,XP: pi,F2: pi > $o] :
% 2.87/1.55 ( ( late_transitions @ ( res @ X2 @ P ) @ ( late_FreeR @ Alpha @ XP ) )
% 2.87/1.55 => ( ! [P4: pi] :
% 2.87/1.55 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P4 ) )
% 2.87/1.55 => ( ( fresh @ name @ late_freeRes @ X2 @ Alpha )
% 2.87/1.55 => ( F2 @ ( res @ X2 @ P4 ) ) ) )
% 2.87/1.55 => ( F2 @ XP ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_99_resCasesF_H,axiom,
% 2.87/1.55 ! [X2: name,P: pi,Alpha: late_freeRes,P3: pi] :
% 2.87/1.55 ( ( late_transitions @ ( res @ X2 @ P ) @ ( late_FreeR @ Alpha @ P3 ) )
% 2.87/1.55 => ~ ! [P5: pi,Alpha2: late_freeRes,P4: pi,Y3: name] :
% 2.87/1.55 ( ( ( res @ X2 @ P )
% 2.87/1.55 = ( res @ Y3 @ P5 ) )
% 2.87/1.55 => ( ( ( late_FreeR @ Alpha @ P3 )
% 2.87/1.55 = ( late_FreeR @ Alpha2 @ ( res @ Y3 @ P4 ) ) )
% 2.87/1.55 => ( ( late_transitions @ P5 @ ( late_FreeR @ Alpha2 @ P4 ) )
% 2.87/1.55 => ~ ( fresh @ name @ late_freeRes @ Y3 @ Alpha2 ) ) ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_100_ResF,axiom,
% 2.87/1.55 ! [P: pi,Alpha: late_freeRes,P3: pi,Y: name] :
% 2.87/1.55 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P3 ) )
% 2.87/1.55 => ( ( fresh @ name @ late_freeRes @ Y @ Alpha )
% 2.87/1.55 => ( late_transitions @ ( res @ Y @ P ) @ ( late_FreeR @ Alpha @ ( res @ Y @ P3 ) ) ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_101_Late__Semantics_OResB,axiom,
% 2.87/1.55 ! [P: pi,A2: late_subject,X2: name,P3: pi,Y: name] :
% 2.87/1.55 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P3 ) )
% 2.87/1.55 => ( ( fresh @ name @ late_subject @ Y @ A2 )
% 2.87/1.55 => ( ( Y != X2 )
% 2.87/1.55 => ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A2 @ X2 @ ( res @ Y @ P3 ) ) ) ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_102_freshFreeDerivative_I1_J,axiom,
% 2.87/1.55 ! [P: pi,Alpha: late_freeRes,P3: pi,Y: name] :
% 2.87/1.55 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P3 ) )
% 2.87/1.55 => ( ( fresh @ name @ pi @ Y @ P )
% 2.87/1.55 => ( fresh @ name @ late_freeRes @ Y @ Alpha ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_103_freshBoundDerivative_I1_J,axiom,
% 2.87/1.55 ! [P: pi,A2: late_subject,X2: name,P3: pi,Y: name] :
% 2.87/1.55 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P3 ) )
% 2.87/1.55 => ( ( fresh @ name @ pi @ Y @ P )
% 2.87/1.55 => ( fresh @ name @ late_subject @ Y @ A2 ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_104_transitions_OResB,axiom,
% 2.87/1.55 ! [P: pi,A2: late_subject,X2: name,P3: pi,Y: name] :
% 2.87/1.55 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P3 ) )
% 2.87/1.55 => ( ( fresh @ name @ late_subject @ Y @ A2 )
% 2.87/1.55 => ( ( Y != X2 )
% 2.87/1.55 => ( ( fresh @ name @ pi @ X2 @ P )
% 2.87/1.55 => ( ( fresh @ name @ late_subject @ X2 @ A2 )
% 2.87/1.55 => ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A2 @ X2 @ ( res @ Y @ P3 ) ) ) ) ) ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_105_parCasesB_H,axiom,
% 2.87/1.55 ! [P: pi,Q: pi,B2: late_subject,Y: name,P3: pi] :
% 2.87/1.55 ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ B2 @ Y @ P3 ) )
% 2.87/1.55 => ( ! [P5: pi,A4: late_subject,X5: name,P4: pi,Q3: pi] :
% 2.87/1.55 ( ( ( par @ P @ Q )
% 2.87/1.55 = ( par @ P5 @ Q3 ) )
% 2.87/1.55 => ( ( ( late_BoundR @ B2 @ Y @ P3 )
% 2.87/1.55 = ( late_BoundR @ A4 @ X5 @ ( par @ P4 @ Q3 ) ) )
% 2.87/1.55 => ( ( late_transitions @ P5 @ ( late_BoundR @ A4 @ X5 @ P4 ) )
% 2.87/1.55 => ( ( fresh @ name @ pi @ X5 @ P5 )
% 2.87/1.55 => ( ( fresh @ name @ pi @ X5 @ Q3 )
% 2.87/1.55 => ~ ( fresh @ name @ late_subject @ X5 @ A4 ) ) ) ) ) )
% 2.87/1.55 => ~ ! [Q3: pi,A4: late_subject,X5: name,Q4: pi,P5: pi] :
% 2.87/1.55 ( ( ( par @ P @ Q )
% 2.87/1.55 = ( par @ P5 @ Q3 ) )
% 2.87/1.55 => ( ( ( late_BoundR @ B2 @ Y @ P3 )
% 2.87/1.55 = ( late_BoundR @ A4 @ X5 @ ( par @ P5 @ Q4 ) ) )
% 2.87/1.55 => ( ( late_transitions @ Q3 @ ( late_BoundR @ A4 @ X5 @ Q4 ) )
% 2.87/1.55 => ( ( fresh @ name @ pi @ X5 @ P5 )
% 2.87/1.55 => ( ( fresh @ name @ pi @ X5 @ Q3 )
% 2.87/1.55 => ~ ( fresh @ name @ late_subject @ X5 @ A4 ) ) ) ) ) ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_106_transitions_OPar1B,axiom,
% 2.87/1.55 ! [P: pi,A2: late_subject,X2: name,P3: pi,Q: pi] :
% 2.87/1.55 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P3 ) )
% 2.87/1.55 => ( ( fresh @ name @ pi @ X2 @ P )
% 2.87/1.55 => ( ( fresh @ name @ pi @ X2 @ Q )
% 2.87/1.55 => ( ( fresh @ name @ late_subject @ X2 @ A2 )
% 2.87/1.55 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X2 @ ( par @ P3 @ Q ) ) ) ) ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_107_transitions_OPar2B,axiom,
% 2.87/1.55 ! [Q: pi,A2: late_subject,X2: name,Q2: pi,P: pi] :
% 2.87/1.55 ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X2 @ Q2 ) )
% 2.87/1.55 => ( ( fresh @ name @ pi @ X2 @ P )
% 2.87/1.55 => ( ( fresh @ name @ pi @ X2 @ Q )
% 2.87/1.55 => ( ( fresh @ name @ late_subject @ X2 @ A2 )
% 2.87/1.55 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X2 @ ( par @ P @ Q2 ) ) ) ) ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_108_resCases_H,axiom,
% 2.87/1.55 ! [X2: name,P: pi,Rs: late_residual] :
% 2.87/1.55 ( ( late_transitions @ ( res @ X2 @ P ) @ Rs )
% 2.87/1.55 => ( ! [P5: pi,A4: name,B3: name] :
% 2.87/1.55 ( ( ( res @ X2 @ P )
% 2.87/1.55 = ( res @ B3 @ P5 ) )
% 2.87/1.55 => ! [P4: pi] :
% 2.87/1.55 ( ( Rs
% 2.87/1.55 = ( late_BoundR @ ( late_BoundOutputS @ A4 ) @ B3 @ P4 ) )
% 2.87/1.55 => ( ( late_transitions @ P5 @ ( late_FreeR @ ( late_OutputR @ A4 @ B3 ) @ P4 ) )
% 2.87/1.55 => ( A4 = B3 ) ) ) )
% 2.87/1.55 => ( ! [P5: pi,A4: late_subject,X5: name,P4: pi,Y3: name] :
% 2.87/1.55 ( ( ( res @ X2 @ P )
% 2.87/1.55 = ( res @ Y3 @ P5 ) )
% 2.87/1.55 => ( ( Rs
% 2.87/1.55 = ( late_BoundR @ A4 @ X5 @ ( res @ Y3 @ P4 ) ) )
% 2.87/1.55 => ( ( late_transitions @ P5 @ ( late_BoundR @ A4 @ X5 @ P4 ) )
% 2.87/1.55 => ( ( fresh @ name @ late_subject @ Y3 @ A4 )
% 2.87/1.55 => ( ( Y3 != X5 )
% 2.87/1.55 => ( ( fresh @ name @ pi @ X5 @ P5 )
% 2.87/1.55 => ~ ( fresh @ name @ late_subject @ X5 @ A4 ) ) ) ) ) ) )
% 2.87/1.55 => ~ ! [P5: pi,Alpha2: late_freeRes,P4: pi,Y3: name] :
% 2.87/1.55 ( ( ( res @ X2 @ P )
% 2.87/1.55 = ( res @ Y3 @ P5 ) )
% 2.87/1.55 => ( ( Rs
% 2.87/1.55 = ( late_FreeR @ Alpha2 @ ( res @ Y3 @ P4 ) ) )
% 2.87/1.55 => ( ( late_transitions @ P5 @ ( late_FreeR @ Alpha2 @ P4 ) )
% 2.87/1.55 => ~ ( fresh @ name @ late_freeRes @ Y3 @ Alpha2 ) ) ) ) ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_109_residual_Oinject_I2_J,axiom,
% 2.87/1.55 ! [X22: late_freeRes,X1: pi,Y2: late_freeRes,Y1: pi] :
% 2.87/1.55 ( ( ( late_FreeR @ X22 @ X1 )
% 2.87/1.55 = ( late_FreeR @ Y2 @ Y1 ) )
% 2.87/1.55 = ( ( X22 = Y2 )
% 2.87/1.55 & ( X1 = Y1 ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_110_resCasesB_H,axiom,
% 2.87/1.55 ! [X7: name,P: pi,A2: late_subject,Y4: name,P3: pi] :
% 2.87/1.55 ( ( late_transitions @ ( res @ X7 @ P ) @ ( late_BoundR @ A2 @ Y4 @ P3 ) )
% 2.87/1.55 => ( ! [P5: pi,A4: name,B3: name] :
% 2.87/1.55 ( ( ( res @ X7 @ P )
% 2.87/1.55 = ( res @ B3 @ P5 ) )
% 2.87/1.55 => ! [P4: pi] :
% 2.87/1.55 ( ( ( late_BoundR @ A2 @ Y4 @ P3 )
% 2.87/1.55 = ( late_BoundR @ ( late_BoundOutputS @ A4 ) @ B3 @ P4 ) )
% 2.87/1.55 => ( ( late_transitions @ P5 @ ( late_FreeR @ ( late_OutputR @ A4 @ B3 ) @ P4 ) )
% 2.87/1.55 => ( A4 = B3 ) ) ) )
% 2.87/1.55 => ~ ! [P5: pi,A4: late_subject,X5: name,P4: pi,Y3: name] :
% 2.87/1.55 ( ( ( res @ X7 @ P )
% 2.87/1.55 = ( res @ Y3 @ P5 ) )
% 2.87/1.55 => ( ( ( late_BoundR @ A2 @ Y4 @ P3 )
% 2.87/1.55 = ( late_BoundR @ A4 @ X5 @ ( res @ Y3 @ P4 ) ) )
% 2.87/1.55 => ( ( late_transitions @ P5 @ ( late_BoundR @ A4 @ X5 @ P4 ) )
% 2.87/1.55 => ( ( fresh @ name @ late_subject @ Y3 @ A4 )
% 2.87/1.55 => ( ( Y3 != X5 )
% 2.87/1.55 => ( ( fresh @ name @ pi @ X5 @ P5 )
% 2.87/1.55 => ~ ( fresh @ name @ late_subject @ X5 @ A4 ) ) ) ) ) ) ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_111_residual_Odistinct_I1_J,axiom,
% 2.87/1.55 ! [Subject: late_subject,Name2: name,Pi: pi,FreeRes: late_freeRes,Pi3: pi] :
% 2.87/1.55 ( ( late_BoundR @ Subject @ Name2 @ Pi )
% 2.87/1.55 != ( late_FreeR @ FreeRes @ Pi3 ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_112_residual_Oinducts,axiom,
% 2.87/1.55 ! [P: late_residual > $o,Residual: late_residual] :
% 2.87/1.55 ( ! [Subject2: late_subject,Name3: name,Pi4: pi] : ( P @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) )
% 2.87/1.55 => ( ! [FreeRes2: late_freeRes,Pi4: pi] : ( P @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 2.87/1.55 => ( P @ Residual ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_113_eqvt,axiom,
% 2.87/1.55 ! [X1: pi,X22: late_residual,Pi: list @ ( product_prod @ name @ name )] :
% 2.87/1.55 ( ( late_transitions @ X1 @ X22 )
% 2.87/1.55 => ( late_transitions @ ( perm @ name @ pi @ Pi @ X1 ) @ ( perm @ name @ late_residual @ Pi @ X22 ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_114_freeRes_Ostrong__inducts,axiom,
% 2.87/1.55 ! [A: $tType,P: A > late_freeRes > $o,Z: A,FreeRes3: late_freeRes] :
% 2.87/1.55 ( ! [Name1: name,Name22: name,Z2: A] : ( P @ Z2 @ ( late_OutputR @ Name1 @ Name22 ) )
% 2.87/1.55 => ( ! [Z2: A] : ( P @ Z2 @ late_TauR )
% 2.87/1.55 => ( P @ Z @ FreeRes3 ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_115_freeRes_Ostrong__induct_H,axiom,
% 2.87/1.55 ! [N: $tType,P: N > late_freeRes > $o,Z: N,FreeRes3: late_freeRes] :
% 2.87/1.55 ( ! [Name1: name,Name22: name,Z2: N] : ( P @ Z2 @ ( late_OutputR @ Name1 @ Name22 ) )
% 2.87/1.55 => ( ! [Z2: N] : ( P @ Z2 @ late_TauR )
% 2.87/1.55 => ( P @ Z @ FreeRes3 ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_116_freeRes_Oinducts,axiom,
% 2.87/1.55 ! [P: late_freeRes > $o,FreeRes3: late_freeRes] :
% 2.87/1.55 ( ! [Name1: name,Name22: name] : ( P @ ( late_OutputR @ Name1 @ Name22 ) )
% 2.87/1.55 => ( ( P @ late_TauR )
% 2.87/1.55 => ( P @ FreeRes3 ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_117_Late__Semantics_OfreeRes_Odistinct_I1_J,axiom,
% 2.87/1.55 ! [Name12: name,Name23: name] :
% 2.87/1.55 ( ( late_OutputR @ Name12 @ Name23 )
% 2.87/1.55 != late_TauR ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_118_Late__Semantics_Osubject_Odistinct_I1_J,axiom,
% 2.87/1.55 ! [Name2: name,Name: name] :
% 2.87/1.55 ( ( late_InputS @ Name2 )
% 2.87/1.55 != ( late_BoundOutputS @ Name ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_119_subject_Oinducts,axiom,
% 2.87/1.55 ! [P: late_subject > $o,Subject: late_subject] :
% 2.87/1.55 ( ! [Name3: name] : ( P @ ( late_InputS @ Name3 ) )
% 2.87/1.55 => ( ! [Name3: name] : ( P @ ( late_BoundOutputS @ Name3 ) )
% 2.87/1.55 => ( P @ Subject ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_120_subject_Ostrong__induct_H,axiom,
% 2.87/1.55 ! [N: $tType,P: N > late_subject > $o,Z: N,Subject: late_subject] :
% 2.87/1.55 ( ! [Name3: name,Z2: N] : ( P @ Z2 @ ( late_InputS @ Name3 ) )
% 2.87/1.55 => ( ! [Name3: name,Z2: N] : ( P @ Z2 @ ( late_BoundOutputS @ Name3 ) )
% 2.87/1.55 => ( P @ Z @ Subject ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_121_subject_Ostrong__inducts,axiom,
% 2.87/1.55 ! [A: $tType,P: A > late_subject > $o,Z: A,Subject: late_subject] :
% 2.87/1.55 ( ! [Name3: name,Z2: A] : ( P @ Z2 @ ( late_InputS @ Name3 ) )
% 2.87/1.55 => ( ! [Name3: name,Z2: A] : ( P @ Z2 @ ( late_BoundOutputS @ Name3 ) )
% 2.87/1.55 => ( P @ Z @ Subject ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_122_resCasesB,axiom,
% 2.87/1.55 ! [Y: name,P: pi,A2: late_subject,X2: name,YP: pi,F2: late_subject > pi > $o] :
% 2.87/1.55 ( ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A2 @ X2 @ YP ) )
% 2.87/1.55 => ( ( X2 != Y )
% 2.87/1.55 => ( ( fresh @ name @ pi @ X2 @ P )
% 2.87/1.55 => ( ! [B3: name,P4: pi] :
% 2.87/1.55 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ B3 @ Y ) @ P4 ) )
% 2.87/1.55 => ( ( B3 != Y )
% 2.87/1.55 => ( ( A2
% 2.87/1.55 = ( late_BoundOutputS @ B3 ) )
% 2.87/1.55 => ( F2 @ ( late_BoundOutputS @ B3 ) @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ X2 @ Y ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ P4 ) ) ) ) )
% 2.87/1.55 => ( ! [P4: pi] :
% 2.87/1.55 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P4 ) )
% 2.87/1.55 => ( ( fresh @ name @ late_subject @ Y @ A2 )
% 2.87/1.55 => ( F2 @ A2 @ ( res @ Y @ P4 ) ) ) )
% 2.87/1.55 => ( F2 @ A2 @ YP ) ) ) ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_123_Par1F,axiom,
% 2.87/1.55 ! [P: pi,Alpha: late_freeRes,P3: pi,Q: pi] :
% 2.87/1.55 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P3 ) )
% 2.87/1.55 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha @ ( par @ P3 @ Q ) ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_124_Par2F,axiom,
% 2.87/1.55 ! [Q: pi,Alpha: late_freeRes,Q2: pi,P: pi] :
% 2.87/1.55 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 2.87/1.55 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha @ ( par @ P @ Q2 ) ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_125_freshBoundDerivative_I2_J,axiom,
% 2.87/1.55 ! [P: pi,A2: late_subject,X2: name,P3: pi,Y: name] :
% 2.87/1.55 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P3 ) )
% 2.87/1.55 => ( ( fresh @ name @ pi @ Y @ P )
% 2.87/1.55 => ( ( Y != X2 )
% 2.87/1.55 => ( fresh @ name @ pi @ Y @ P3 ) ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_126_residual_Ostrong__inducts,axiom,
% 2.87/1.55 ! [A: $tType] :
% 2.87/1.55 ( ( fs_name @ A )
% 2.87/1.55 => ! [P: A > late_residual > $o,Z: A,Residual: late_residual] :
% 2.87/1.55 ( ! [Subject2: late_subject,Name3: name,Pi4: pi,Z2: A] :
% 2.87/1.55 ( ( fresh @ name @ A @ Name3 @ Z2 )
% 2.87/1.55 => ( ( fresh @ name @ late_subject @ Name3 @ Subject2 )
% 2.87/1.55 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) ) ) )
% 2.87/1.55 => ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: A] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 2.87/1.55 => ( P @ Z @ Residual ) ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_127_residual_Ostrong__induct,axiom,
% 2.87/1.55 ! [N: $tType] :
% 2.87/1.55 ( ( fs_name @ N )
% 2.87/1.55 => ! [P: N > late_residual > $o,Z: N,Residual: late_residual] :
% 2.87/1.55 ( ! [Subject2: late_subject,Name3: name,Pi4: pi,Z2: N] :
% 2.87/1.55 ( ( fresh @ name @ N @ Name3 @ Z2 )
% 2.87/1.55 => ( ( fresh @ name @ late_subject @ Name3 @ Subject2 )
% 2.87/1.55 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) ) ) )
% 2.87/1.55 => ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: N] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 2.87/1.55 => ( P @ Z @ Residual ) ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_128_freshFreeDerivative_I2_J,axiom,
% 2.87/1.55 ! [P: pi,Alpha: late_freeRes,P3: pi,Y: name] :
% 2.87/1.55 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P3 ) )
% 2.87/1.55 => ( ( fresh @ name @ pi @ Y @ P )
% 2.87/1.55 => ( fresh @ name @ pi @ Y @ P3 ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_129_Late__Semantics_OPar1B,axiom,
% 2.87/1.55 ! [P: pi,A2: late_subject,X2: name,P3: pi,Q: pi] :
% 2.87/1.55 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P3 ) )
% 2.87/1.55 => ( ( fresh @ name @ pi @ X2 @ Q )
% 2.87/1.55 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X2 @ ( par @ P3 @ Q ) ) ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_130_Late__Semantics_OPar2B,axiom,
% 2.87/1.55 ! [Q: pi,A2: late_subject,X2: name,Q2: pi,P: pi] :
% 2.87/1.55 ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X2 @ Q2 ) )
% 2.87/1.55 => ( ( fresh @ name @ pi @ X2 @ P )
% 2.87/1.55 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X2 @ ( par @ P @ Q2 ) ) ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_131_parCasesB,axiom,
% 2.87/1.55 ! [P: pi,Q: pi,A2: late_subject,X2: name,PQ: pi,Prop: pi > $o] :
% 2.87/1.55 ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X2 @ PQ ) )
% 2.87/1.55 => ( ( fresh @ name @ pi @ X2 @ P )
% 2.87/1.55 => ( ( fresh @ name @ pi @ X2 @ Q )
% 2.87/1.55 => ( ! [P4: pi] :
% 2.87/1.55 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P4 ) )
% 2.87/1.55 => ( Prop @ ( par @ P4 @ Q ) ) )
% 2.87/1.55 => ( ! [Q4: pi] :
% 2.87/1.55 ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X2 @ Q4 ) )
% 2.87/1.55 => ( Prop @ ( par @ P @ Q4 ) ) )
% 2.87/1.55 => ( Prop @ PQ ) ) ) ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_132_Open,axiom,
% 2.87/1.55 ! [P: pi,A2: name,B2: name,P3: pi] :
% 2.87/1.55 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P3 ) )
% 2.87/1.55 => ( ( A2 != B2 )
% 2.87/1.55 => ( late_transitions @ ( res @ B2 @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ B2 @ P3 ) ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_133_derivativeEqvtI2,axiom,
% 2.87/1.55 ! [P: pi,Q: pi,A2: late_subject,X2: name,Rel: set @ ( product_prod @ pi @ pi ),Perm: list @ ( product_prod @ name @ name )] :
% 2.87/1.55 ( ( strong2129052853vative @ P @ Q @ A2 @ X2 @ Rel )
% 2.87/1.55 => ( ( eqvt @ pi @ Rel )
% 2.87/1.55 => ( strong2129052853vative @ ( perm @ name @ pi @ Perm @ P ) @ ( perm @ name @ pi @ Perm @ Q ) @ A2 @ ( perm @ name @ name @ Perm @ X2 ) @ Rel ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_134_derivativeEqvtI,axiom,
% 2.87/1.55 ! [P: pi,Q: pi,A2: late_subject,X2: name,Rel: set @ ( product_prod @ pi @ pi ),Perm: list @ ( product_prod @ name @ name )] :
% 2.87/1.55 ( ( strong2129052853vative @ P @ Q @ A2 @ X2 @ Rel )
% 2.87/1.55 => ( ( eqvt @ pi @ Rel )
% 2.87/1.55 => ( strong2129052853vative @ ( perm @ name @ pi @ Perm @ P ) @ ( perm @ name @ pi @ Perm @ Q ) @ ( perm @ name @ late_subject @ Perm @ A2 ) @ ( perm @ name @ name @ Perm @ X2 ) @ Rel ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_135_fresh__prod,axiom,
% 2.87/1.55 ! [A: $tType,X: $tType,B: $tType,A2: X,X2: A,Y: B] :
% 2.87/1.55 ( ( fresh @ X @ ( product_prod @ A @ B ) @ A2 @ ( product_Pair @ A @ B @ X2 @ Y ) )
% 2.87/1.55 = ( ( fresh @ X @ A @ A2 @ X2 )
% 2.87/1.55 & ( fresh @ X @ B @ A2 @ Y ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_136_Res,axiom,
% 2.87/1.55 ! [Y: name,R: pi,S: pi] :
% 2.87/1.55 ( ( fresh @ name @ pi @ Y @ R )
% 2.87/1.55 => ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( par @ R @ ( res @ Y @ S ) ) @ ( res @ Y @ ( par @ R @ S ) ) ) @ rel ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_137_ScopeExt,axiom,
% 2.87/1.55 ! [Y: name,R: pi,Z: name,S: pi] :
% 2.87/1.55 ( ( fresh @ name @ pi @ Y @ R )
% 2.87/1.55 => ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( res @ Z @ ( par @ R @ ( res @ Y @ S ) ) ) @ ( res @ Y @ ( res @ Z @ ( par @ R @ S ) ) ) ) @ rel ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_138_fresh__list__cons,axiom,
% 2.87/1.55 ! [X: $tType,A: $tType,A2: X,X2: A,Xs: list @ A] :
% 2.87/1.55 ( ( fresh @ X @ ( list @ A ) @ A2 @ ( cons @ A @ X2 @ Xs ) )
% 2.87/1.55 = ( ( fresh @ X @ A @ A2 @ X2 )
% 2.87/1.55 & ( fresh @ X @ ( list @ A ) @ A2 @ Xs ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_139_Bound_Ohyps_I5_J,axiom,
% 2.87/1.55 fresh @ name @ ( product_prod @ name @ ( product_prod @ pi @ pi ) ) @ y @ ( product_Pair @ name @ ( product_prod @ pi @ pi ) @ x @ ( product_Pair @ pi @ pi @ p @ q ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_140_false__eqvt,axiom,
% 2.87/1.55 ! [A: $tType,Pi: list @ ( product_prod @ A @ A )] :
% 2.87/1.55 ~ ( perm @ A @ $o @ Pi @ $false ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_141_true__eqvt,axiom,
% 2.87/1.55 ! [A: $tType,Pi: list @ ( product_prod @ A @ A )] : ( perm @ A @ $o @ Pi @ $true ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_142_name__fresh,axiom,
% 2.87/1.55 ( ( fresh @ name @ name )
% 2.87/1.55 = ( ^ [A5: name,B4: name] : ( A5 != B4 ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_143_fresh__unit,axiom,
% 2.87/1.55 ! [A: $tType,A2: A] : ( fresh @ A @ product_unit @ A2 @ product_Unity ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_144_freshUnit,axiom,
% 2.87/1.55 ! [Y: name] : ( fresh @ name @ product_unit @ Y @ product_Unity ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_145_allE__Nil,axiom,
% 2.87/1.55 ! [A: $tType,P: ( list @ A ) > $o] :
% 2.87/1.55 ( ! [X_1: list @ A] : ( P @ X_1 )
% 2.87/1.55 => ( P @ ( nil @ A ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_146_abs__fun__if,axiom,
% 2.87/1.55 ! [X: $tType,A: $tType,C: $o,Pi: list @ ( product_prod @ X @ X ),X2: A,Y: A] :
% 2.87/1.55 ( ( C
% 2.87/1.55 => ( ( perm @ X @ A @ Pi @ ( if @ A @ C @ X2 @ Y ) )
% 2.87/1.55 = ( perm @ X @ A @ Pi @ X2 ) ) )
% 2.87/1.55 & ( ~ C
% 2.87/1.55 => ( ( perm @ X @ A @ Pi @ ( if @ A @ C @ X2 @ Y ) )
% 2.87/1.55 = ( perm @ X @ A @ Pi @ Y ) ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_147_pt__bij3,axiom,
% 2.87/1.55 ! [X: $tType,A: $tType,X2: A,Y: A,Pi: list @ ( product_prod @ X @ X )] :
% 2.87/1.55 ( ( X2 = Y )
% 2.87/1.55 => ( ( perm @ X @ A @ Pi @ X2 )
% 2.87/1.55 = ( perm @ X @ A @ Pi @ Y ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_148_perm__bool__def,axiom,
% 2.87/1.55 ! [X: $tType] :
% 2.87/1.55 ( ( perm @ X @ $o )
% 2.87/1.55 = ( ^ [Pi5: list @ ( product_prod @ X @ X ),B4: $o] : B4 ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_149_pt__set__bij3,axiom,
% 2.87/1.55 ! [X: $tType,A: $tType,Pi: list @ ( product_prod @ X @ X ),X2: A,X6: set @ A] :
% 2.87/1.55 ( ( perm @ X @ $o @ Pi @ ( member @ A @ X2 @ X6 ) )
% 2.87/1.55 = ( member @ A @ X2 @ X6 ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_150_perm__boolI,axiom,
% 2.87/1.55 ! [A: $tType,P: $o,Pi: list @ ( product_prod @ A @ A )] :
% 2.87/1.55 ( P
% 2.87/1.55 => ( perm @ A @ $o @ Pi @ P ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_151_perm__boolE,axiom,
% 2.87/1.55 ! [A: $tType,Pi: list @ ( product_prod @ A @ A )] :
% 2.87/1.55 ~ ( perm @ A @ $o @ Pi @ $false ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_152_disj__eqvt,axiom,
% 2.87/1.55 ! [A: $tType,Pi: list @ ( product_prod @ A @ A ),A3: $o,B5: $o] :
% 2.87/1.55 ( ( perm @ A @ $o @ Pi
% 2.87/1.55 @ ( A3
% 2.87/1.55 | B5 ) )
% 2.87/1.55 = ( ( perm @ A @ $o @ Pi @ A3 )
% 2.87/1.55 | ( perm @ A @ $o @ Pi @ B5 ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_153_conj__eqvt,axiom,
% 2.87/1.55 ! [A: $tType,Pi: list @ ( product_prod @ A @ A ),A3: $o,B5: $o] :
% 2.87/1.55 ( ( perm @ A @ $o @ Pi
% 2.87/1.55 @ ( A3
% 2.87/1.55 & B5 ) )
% 2.87/1.55 = ( ( perm @ A @ $o @ Pi @ A3 )
% 2.87/1.55 & ( perm @ A @ $o @ Pi @ B5 ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_154_neg__eqvt,axiom,
% 2.87/1.55 ! [A: $tType,Pi: list @ ( product_prod @ A @ A ),A3: $o] :
% 2.87/1.55 ( ( perm @ A @ $o @ Pi @ ~ A3 )
% 2.87/1.55 = ( ~ ( perm @ A @ $o @ Pi @ A3 ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_155_imp__eqvt,axiom,
% 2.87/1.55 ! [A: $tType,Pi: list @ ( product_prod @ A @ A ),A3: $o,B5: $o] :
% 2.87/1.55 ( ( perm @ A @ $o @ Pi
% 2.87/1.55 @ ( A3
% 2.87/1.55 => B5 ) )
% 2.87/1.55 = ( ( perm @ A @ $o @ Pi @ A3 )
% 2.87/1.55 => ( perm @ A @ $o @ Pi @ B5 ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_156_perm__prod_Osimps,axiom,
% 2.87/1.55 ! [A: $tType,X: $tType,B: $tType,Pi: list @ ( product_prod @ X @ X ),X2: A,Y: B] :
% 2.87/1.55 ( ( perm @ X @ ( product_prod @ A @ B ) @ Pi @ ( product_Pair @ A @ B @ X2 @ Y ) )
% 2.87/1.55 = ( product_Pair @ A @ B @ ( perm @ X @ A @ Pi @ X2 ) @ ( perm @ X @ B @ Pi @ Y ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_157_fresh__prodD_I2_J,axiom,
% 2.87/1.55 ! [B: $tType,A: $tType,C3: $tType,A2: A,X2: B,Y: C3] :
% 2.87/1.55 ( ( fresh @ A @ ( product_prod @ B @ C3 ) @ A2 @ ( product_Pair @ B @ C3 @ X2 @ Y ) )
% 2.87/1.55 => ( fresh @ A @ C3 @ A2 @ Y ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_158_fresh__prodD_I1_J,axiom,
% 2.87/1.55 ! [C3: $tType,A: $tType,B: $tType,A2: A,X2: B,Y: C3] :
% 2.87/1.55 ( ( fresh @ A @ ( product_prod @ B @ C3 ) @ A2 @ ( product_Pair @ B @ C3 @ X2 @ Y ) )
% 2.87/1.55 => ( fresh @ A @ B @ A2 @ X2 ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_159_if__eqvt,axiom,
% 2.87/1.55 ! [A: $tType,B: $tType,Pi: list @ ( product_prod @ A @ A ),B2: $o,C1: B,C22: B] :
% 2.87/1.55 ( ( ( perm @ A @ $o @ Pi @ B2 )
% 2.87/1.55 => ( ( perm @ A @ B @ Pi @ ( if @ B @ B2 @ C1 @ C22 ) )
% 2.87/1.55 = ( perm @ A @ B @ Pi @ C1 ) ) )
% 2.87/1.55 & ( ~ ( perm @ A @ $o @ Pi @ B2 )
% 2.87/1.55 => ( ( perm @ A @ B @ Pi @ ( if @ B @ B2 @ C1 @ C22 ) )
% 2.87/1.55 = ( perm @ A @ B @ Pi @ C22 ) ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_160_nil__eqvt,axiom,
% 2.87/1.55 ! [X: $tType,A: $tType,Pi: list @ ( product_prod @ X @ X )] :
% 2.87/1.55 ( ( perm @ X @ ( list @ A ) @ Pi @ ( nil @ A ) )
% 2.87/1.55 = ( nil @ A ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_161_fresh__list__nil,axiom,
% 2.87/1.55 ! [X: $tType,A: $tType,A2: X] : ( fresh @ X @ ( list @ A ) @ A2 @ ( nil @ A ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_162_cons__eqvt,axiom,
% 2.87/1.55 ! [X: $tType,A: $tType,Pi: list @ ( product_prod @ X @ X ),X2: A,Xs: list @ A] :
% 2.87/1.55 ( ( perm @ X @ ( list @ A ) @ Pi @ ( cons @ A @ X2 @ Xs ) )
% 2.87/1.55 = ( cons @ A @ ( perm @ X @ A @ Pi @ X2 ) @ ( perm @ X @ ( list @ A ) @ Pi @ Xs ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_163_resSimCases,axiom,
% 2.87/1.55 ! [A: $tType] :
% 2.87/1.55 ( ( fs_name @ A )
% 2.87/1.55 => ! [Rel: set @ ( product_prod @ pi @ pi ),Q: pi,X2: name,P: pi,C4: A] :
% 2.87/1.55 ( ( eqvt @ pi @ Rel )
% 2.87/1.55 => ( ! [Q4: pi,A4: name] :
% 2.87/1.55 ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A4 @ X2 ) @ Q4 ) )
% 2.87/1.55 => ( ( A4 != X2 )
% 2.87/1.55 => ? [P6: pi] :
% 2.87/1.55 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A4 ) @ X2 @ P6 ) )
% 2.87/1.55 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P6 @ Q4 ) @ Rel ) ) ) )
% 2.87/1.55 => ( ! [Q4: pi,A4: late_subject,Y3: name] :
% 2.87/1.55 ( ( late_transitions @ Q @ ( late_BoundR @ A4 @ Y3 @ Q4 ) )
% 2.87/1.55 => ( ( fresh @ name @ late_subject @ X2 @ A4 )
% 2.87/1.55 => ( ( X2 != Y3 )
% 2.87/1.55 => ( ( fresh @ name @ A @ Y3 @ C4 )
% 2.87/1.55 => ? [P6: pi] :
% 2.87/1.55 ( ( late_transitions @ P @ ( late_BoundR @ A4 @ Y3 @ P6 ) )
% 2.87/1.55 & ( strong2129052853vative @ P6 @ ( res @ X2 @ Q4 ) @ A4 @ Y3 @ Rel ) ) ) ) ) )
% 2.87/1.55 => ( ! [Q4: pi,Alpha2: late_freeRes] :
% 2.87/1.55 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 2.87/1.55 => ( ( fresh @ name @ late_freeRes @ X2 @ Alpha2 )
% 2.87/1.55 => ? [P6: pi] :
% 2.87/1.55 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 2.87/1.55 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P6 @ ( res @ X2 @ Q4 ) ) @ Rel ) ) ) )
% 2.87/1.55 => ( strong743114133lation @ P @ Rel @ ( res @ X2 @ Q ) ) ) ) ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_164_simCasesCont,axiom,
% 2.87/1.55 ! [A: $tType] :
% 2.87/1.55 ( ( fs_name @ A )
% 2.87/1.55 => ! [Rel: set @ ( product_prod @ pi @ pi ),Q: pi,P: pi,C4: A] :
% 2.87/1.55 ( ( eqvt @ pi @ Rel )
% 2.87/1.55 => ( ! [A4: late_subject,X5: name,Q4: pi] :
% 2.87/1.55 ( ( late_transitions @ Q @ ( late_BoundR @ A4 @ X5 @ Q4 ) )
% 2.87/1.55 => ( ( fresh @ name @ pi @ X5 @ P )
% 2.87/1.55 => ( ( fresh @ name @ pi @ X5 @ Q )
% 2.87/1.55 => ( ( fresh @ name @ late_subject @ X5 @ A4 )
% 2.87/1.55 => ( ( fresh @ name @ A @ X5 @ C4 )
% 2.87/1.55 => ? [P6: pi] :
% 2.87/1.55 ( ( late_transitions @ P @ ( late_BoundR @ A4 @ X5 @ P6 ) )
% 2.87/1.55 & ( strong2129052853vative @ P6 @ Q4 @ A4 @ X5 @ Rel ) ) ) ) ) ) )
% 2.87/1.55 => ( ! [Alpha2: late_freeRes,Q4: pi] :
% 2.87/1.55 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 2.87/1.55 => ? [P6: pi] :
% 2.87/1.55 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 2.87/1.55 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P6 @ Q4 ) @ Rel ) ) )
% 2.87/1.55 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_165_eqvtRelI,axiom,
% 2.87/1.55 ! [A: $tType] :
% 2.87/1.55 ( ( pt_name @ A )
% 2.87/1.55 => ! [Rel: set @ ( product_prod @ A @ A ),P: A,Q: A,Perm: list @ ( product_prod @ name @ name )] :
% 2.87/1.55 ( ( eqvt @ A @ Rel )
% 2.87/1.55 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ P @ Q ) @ Rel )
% 2.87/1.55 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ ( perm @ name @ A @ Perm @ P ) @ ( perm @ name @ A @ Perm @ Q ) ) @ Rel ) ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_166_eqvtRelE,axiom,
% 2.87/1.55 ! [A: $tType] :
% 2.87/1.55 ( ( pt_name @ A )
% 2.87/1.55 => ! [Rel: set @ ( product_prod @ A @ A ),Perm: list @ ( product_prod @ name @ name ),P: A,Q: A] :
% 2.87/1.55 ( ( eqvt @ A @ Rel )
% 2.87/1.55 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ ( perm @ name @ A @ Perm @ P ) @ ( perm @ name @ A @ Perm @ Q ) ) @ Rel )
% 2.87/1.55 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ P @ Q ) @ Rel ) ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_167_perm__unit_Osimps,axiom,
% 2.87/1.55 ! [X: $tType,Pi: list @ ( product_prod @ X @ X )] :
% 2.87/1.55 ( ( perm @ X @ product_unit @ Pi @ product_Unity )
% 2.87/1.55 = product_Unity ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_168_parSym,axiom,
% 2.87/1.55 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi,Q: pi] :
% 2.87/1.55 ( ! [R2: pi,S2: pi] : ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( par @ R2 @ S2 ) @ ( par @ S2 @ R2 ) ) @ Rel )
% 2.87/1.55 => ( ! [R2: pi,S2: pi,X5: name] :
% 2.87/1.55 ( ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ R2 @ S2 ) @ Rel )
% 2.87/1.55 => ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( res @ X5 @ R2 ) @ ( res @ X5 @ S2 ) ) @ Rel ) )
% 2.87/1.55 => ( strong743114133lation @ ( par @ P @ Q ) @ Rel @ ( par @ Q @ P ) ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_169_simE_I2_J,axiom,
% 2.87/1.55 ! [P: pi,Rel: set @ ( product_prod @ pi @ pi ),Q: pi,Alpha: late_freeRes,Q2: pi] :
% 2.87/1.55 ( ( strong743114133lation @ P @ Rel @ Q )
% 2.87/1.55 => ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 2.87/1.55 => ? [P4: pi] :
% 2.87/1.55 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P4 ) )
% 2.87/1.55 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P4 @ Q2 ) @ Rel ) ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_170_eqvt__def,axiom,
% 2.87/1.55 ! [A: $tType] :
% 2.87/1.55 ( ( pt_name @ A )
% 2.87/1.55 => ( ( eqvt @ A )
% 2.87/1.55 = ( ^ [Rel2: set @ ( product_prod @ A @ A )] :
% 2.87/1.55 ! [X4: product_prod @ A @ A,Perm2: list @ ( product_prod @ name @ name )] :
% 2.87/1.55 ( ( member @ ( product_prod @ A @ A ) @ X4 @ Rel2 )
% 2.87/1.55 => ( member @ ( product_prod @ A @ A ) @ ( perm @ name @ ( product_prod @ A @ A ) @ Perm2 @ X4 ) @ Rel2 ) ) ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_171_parAssocLeft,axiom,
% 2.87/1.55 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi,Q: pi,R: pi] :
% 2.87/1.55 ( ! [S2: pi,T2: pi,U: pi] : ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( par @ ( par @ S2 @ T2 ) @ U ) @ ( par @ S2 @ ( par @ T2 @ U ) ) ) @ Rel )
% 2.87/1.55 => ( ! [S2: pi,T2: pi,X5: name] :
% 2.87/1.55 ( ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ S2 @ T2 ) @ Rel )
% 2.87/1.55 => ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( res @ X5 @ S2 ) @ ( res @ X5 @ T2 ) ) @ Rel ) )
% 2.87/1.55 => ( ! [S2: pi,T2: pi,U: pi,X5: name] :
% 2.87/1.55 ( ( fresh @ name @ pi @ X5 @ S2 )
% 2.87/1.55 => ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( res @ X5 @ ( par @ ( par @ S2 @ T2 ) @ U ) ) @ ( par @ S2 @ ( res @ X5 @ ( par @ T2 @ U ) ) ) ) @ Rel ) )
% 2.87/1.55 => ( ! [S2: pi,T2: pi,U: pi,X5: name] :
% 2.87/1.55 ( ( fresh @ name @ pi @ X5 @ U )
% 2.87/1.55 => ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( par @ ( res @ X5 @ ( par @ S2 @ T2 ) ) @ U ) @ ( res @ X5 @ ( par @ S2 @ ( par @ T2 @ U ) ) ) ) @ Rel ) )
% 2.87/1.55 => ( strong743114133lation @ ( par @ ( par @ P @ Q ) @ R ) @ Rel @ ( par @ P @ ( par @ Q @ R ) ) ) ) ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_172_simE_I1_J,axiom,
% 2.87/1.55 ! [P: pi,Rel: set @ ( product_prod @ pi @ pi ),Q: pi,A2: late_subject,X2: name,Q2: pi] :
% 2.87/1.55 ( ( strong743114133lation @ P @ Rel @ Q )
% 2.87/1.55 => ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X2 @ Q2 ) )
% 2.87/1.55 => ( ( fresh @ name @ pi @ X2 @ P )
% 2.87/1.55 => ? [P4: pi] :
% 2.87/1.55 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P4 ) )
% 2.87/1.55 & ( strong2129052853vative @ P4 @ Q2 @ A2 @ X2 @ Rel ) ) ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_173_simCases,axiom,
% 2.87/1.55 ! [Q: pi,P: pi,Rel: set @ ( product_prod @ pi @ pi )] :
% 2.87/1.55 ( ! [A4: late_subject,Y3: name,Q4: pi] :
% 2.87/1.55 ( ( late_transitions @ Q @ ( late_BoundR @ A4 @ Y3 @ Q4 ) )
% 2.87/1.55 => ( ( fresh @ name @ pi @ Y3 @ P )
% 2.87/1.55 => ? [P6: pi] :
% 2.87/1.55 ( ( late_transitions @ P @ ( late_BoundR @ A4 @ Y3 @ P6 ) )
% 2.87/1.55 & ( strong2129052853vative @ P6 @ Q4 @ A4 @ Y3 @ Rel ) ) ) )
% 2.87/1.55 => ( ! [Alpha2: late_freeRes,Q4: pi] :
% 2.87/1.55 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 2.87/1.55 => ? [P6: pi] :
% 2.87/1.55 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 2.87/1.55 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P6 @ Q4 ) @ Rel ) ) )
% 2.87/1.55 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_174_simulation__def,axiom,
% 2.87/1.55 ( strong743114133lation
% 2.87/1.55 = ( ^ [P7: pi,Rel2: set @ ( product_prod @ pi @ pi ),Q5: pi] :
% 2.87/1.55 ( ! [A5: late_subject,X4: name,Q6: pi] :
% 2.87/1.55 ( ( ( late_transitions @ Q5 @ ( late_BoundR @ A5 @ X4 @ Q6 ) )
% 2.87/1.55 & ( fresh @ name @ pi @ X4 @ P7 ) )
% 2.87/1.55 => ? [P8: pi] :
% 2.87/1.55 ( ( late_transitions @ P7 @ ( late_BoundR @ A5 @ X4 @ P8 ) )
% 2.87/1.55 & ( strong2129052853vative @ P8 @ Q6 @ A5 @ X4 @ Rel2 ) ) )
% 2.87/1.55 & ! [Alpha3: late_freeRes,Q6: pi] :
% 2.87/1.55 ( ( late_transitions @ Q5 @ ( late_FreeR @ Alpha3 @ Q6 ) )
% 2.87/1.55 => ? [P8: pi] :
% 2.87/1.55 ( ( late_transitions @ P7 @ ( late_FreeR @ Alpha3 @ P8 ) )
% 2.87/1.55 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P8 @ Q6 ) @ Rel2 ) ) ) ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_175_Late__Semantics1_Osubject_Oinject_I2_J,axiom,
% 2.87/1.55 ! [X22: name,Y2: name] :
% 2.87/1.55 ( ( ( late_BoundOutputS @ X22 )
% 2.87/1.55 = ( late_BoundOutputS @ Y2 ) )
% 2.87/1.55 = ( X22 = Y2 ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_176_Late__Semantics1_Osubject_Oinject_I1_J,axiom,
% 2.87/1.55 ! [X1: name,Y1: name] :
% 2.87/1.55 ( ( ( late_InputS @ X1 )
% 2.87/1.55 = ( late_InputS @ Y1 ) )
% 2.87/1.55 = ( X1 = Y1 ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_177_Late__Semantics1_OfreeRes_Oinject,axiom,
% 2.87/1.55 ! [X11: name,X12: name,Y11: name,Y12: name] :
% 2.87/1.55 ( ( ( late_OutputR @ X11 @ X12 )
% 2.87/1.55 = ( late_OutputR @ Y11 @ Y12 ) )
% 2.87/1.55 = ( ( X11 = Y11 )
% 2.87/1.55 & ( X12 = Y12 ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_178_Late__Semantics1_OfreeRes_Odistinct_I1_J,axiom,
% 2.87/1.55 ! [X11: name,X12: name] :
% 2.87/1.55 ( ( late_OutputR @ X11 @ X12 )
% 2.87/1.55 != late_TauR ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_179_freeRes_Oexhaust,axiom,
% 2.87/1.55 ! [Y: late_freeRes] :
% 2.87/1.55 ( ! [X112: name,X122: name] :
% 2.87/1.55 ( Y
% 2.87/1.55 != ( late_OutputR @ X112 @ X122 ) )
% 2.87/1.55 => ( Y = late_TauR ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_180_subject_Oexhaust,axiom,
% 2.87/1.55 ! [Y: late_subject] :
% 2.87/1.55 ( ! [X13: name] :
% 2.87/1.55 ( Y
% 2.87/1.55 != ( late_InputS @ X13 ) )
% 2.87/1.55 => ~ ! [X23: name] :
% 2.87/1.55 ( Y
% 2.87/1.55 != ( late_BoundOutputS @ X23 ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_181_Late__Semantics1_Osubject_Odistinct_I1_J,axiom,
% 2.87/1.55 ! [X1: name,X22: name] :
% 2.87/1.55 ( ( late_InputS @ X1 )
% 2.87/1.55 != ( late_BoundOutputS @ X22 ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_182_inputCases,axiom,
% 2.87/1.55 ! [A2: name,X2: name,P: pi,B2: late_subject,Y: name,YP: pi,Prop: late_subject > name > pi > $o] :
% 2.87/1.55 ( ( late_transitions @ ( input @ A2 @ X2 @ P ) @ ( late_BoundR @ B2 @ Y @ YP ) )
% 2.87/1.55 => ( ( Y != A2 )
% 2.87/1.55 => ( ( Y != X2 )
% 2.87/1.55 => ( ( fresh @ name @ pi @ Y @ P )
% 2.87/1.55 => ( ( ( B2
% 2.87/1.55 = ( late_InputS @ A2 ) )
% 2.87/1.55 => ( ( YP
% 2.87/1.55 = ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ X2 @ Y ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ P ) )
% 2.87/1.55 => ( Prop @ ( late_InputS @ A2 ) @ Y @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ X2 @ Y ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ P ) ) ) )
% 2.87/1.55 => ( Prop @ B2 @ Y @ YP ) ) ) ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_183_list_Oinject,axiom,
% 2.87/1.55 ! [A: $tType,X21: A,X222: list @ A,Y21: A,Y22: list @ A] :
% 2.87/1.55 ( ( ( cons @ A @ X21 @ X222 )
% 2.87/1.55 = ( cons @ A @ Y21 @ Y22 ) )
% 2.87/1.55 = ( ( X21 = Y21 )
% 2.87/1.55 & ( X222 = Y22 ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_184_old_Oprod_Oinject,axiom,
% 2.87/1.55 ! [A: $tType,B: $tType,A2: A,B2: B,A6: A,B6: B] :
% 2.87/1.55 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 2.87/1.55 = ( product_Pair @ A @ B @ A6 @ B6 ) )
% 2.87/1.55 = ( ( A2 = A6 )
% 2.87/1.55 & ( B2 = B6 ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_185_prod_Oinject,axiom,
% 2.87/1.55 ! [A: $tType,B: $tType,X1: A,X22: B,Y1: A,Y2: B] :
% 2.87/1.55 ( ( ( product_Pair @ A @ B @ X1 @ X22 )
% 2.87/1.55 = ( product_Pair @ A @ B @ Y1 @ Y2 ) )
% 2.87/1.55 = ( ( X1 = Y1 )
% 2.87/1.55 & ( X22 = Y2 ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_186_pi_Operm_I4_J,axiom,
% 2.87/1.55 ! [Pi: list @ ( product_prod @ name @ name ),X32: name,X1: name,X22: pi] :
% 2.87/1.55 ( ( perm @ name @ pi @ Pi @ ( input @ X32 @ X1 @ X22 ) )
% 2.87/1.55 = ( input @ ( perm @ name @ name @ Pi @ X32 ) @ ( perm @ name @ name @ Pi @ X1 ) @ ( perm @ name @ pi @ Pi @ X22 ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_187_pi_Odistinct_I57_J,axiom,
% 2.87/1.55 ! [Name12: name,Name23: name,Pi: pi,Name: name,Pi3: pi] :
% 2.87/1.55 ( ( input @ Name12 @ Name23 @ Pi )
% 2.87/1.55 != ( res @ Name @ Pi3 ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_188_pi_Odistinct_I55_J,axiom,
% 2.87/1.55 ! [Name12: name,Name23: name,Pi: pi,Pi12: pi,Pi22: pi] :
% 2.87/1.55 ( ( input @ Name12 @ Name23 @ Pi )
% 2.87/1.55 != ( par @ Pi12 @ Pi22 ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_189_resTrans_I2_J,axiom,
% 2.87/1.56 ! [X2: name,Y: name,P: pi,Rs: late_residual] :
% 2.87/1.56 ~ ( late_transitions @ ( res @ X2 @ ( input @ X2 @ Y @ P ) ) @ Rs ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_190_inputFreeTrans,axiom,
% 2.87/1.56 ! [A2: name,X2: name,P: pi,Alpha: late_freeRes,P3: pi] :
% 2.87/1.56 ~ ( late_transitions @ ( input @ A2 @ X2 @ P ) @ ( late_FreeR @ Alpha @ P3 ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_191_surj__pair,axiom,
% 2.87/1.56 ! [A: $tType,B: $tType,P2: product_prod @ A @ B] :
% 2.87/1.56 ? [X5: A,Y3: B] :
% 2.87/1.56 ( P2
% 2.87/1.56 = ( product_Pair @ A @ B @ X5 @ Y3 ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_192_prod__cases,axiom,
% 2.87/1.56 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,P2: product_prod @ A @ B] :
% 2.87/1.56 ( ! [A4: A,B3: B] : ( P @ ( product_Pair @ A @ B @ A4 @ B3 ) )
% 2.87/1.56 => ( P @ P2 ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_193_Pair__inject,axiom,
% 2.87/1.56 ! [A: $tType,B: $tType,A2: A,B2: B,A6: A,B6: B] :
% 2.87/1.56 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 2.87/1.56 = ( product_Pair @ A @ B @ A6 @ B6 ) )
% 2.87/1.56 => ~ ( ( A2 = A6 )
% 2.87/1.56 => ( B2 != B6 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_194_old_Oprod_Oexhaust,axiom,
% 2.87/1.56 ! [A: $tType,B: $tType,Y: product_prod @ A @ B] :
% 2.87/1.56 ~ ! [A4: A,B3: B] :
% 2.87/1.56 ( Y
% 2.87/1.56 != ( product_Pair @ A @ B @ A4 @ B3 ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_195_old_Oprod_Oinducts,axiom,
% 2.87/1.56 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,Prod: product_prod @ A @ B] :
% 2.87/1.56 ( ! [A4: A,B3: B] : ( P @ ( product_Pair @ A @ B @ A4 @ B3 ) )
% 2.87/1.56 => ( P @ Prod ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_196_not__Cons__self2,axiom,
% 2.87/1.56 ! [A: $tType,X2: A,Xs: list @ A] :
% 2.87/1.56 ( ( cons @ A @ X2 @ Xs )
% 2.87/1.56 != Xs ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_197_resInputFreeTrans,axiom,
% 2.87/1.56 ! [X2: name,A2: name,Y: name,P: pi,Alpha: late_freeRes,P3: pi] :
% 2.87/1.56 ~ ( late_transitions @ ( res @ X2 @ ( input @ A2 @ Y @ P ) ) @ ( late_FreeR @ Alpha @ P3 ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_198_old_Ounit_Oinducts,axiom,
% 2.87/1.56 ! [P: product_unit > $o,Unit: product_unit] :
% 2.87/1.56 ( ( P @ product_Unity )
% 2.87/1.56 => ( P @ Unit ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_199_old_Ounit_Oexhaust,axiom,
% 2.87/1.56 ! [Y: product_unit] : ( Y = product_Unity ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_200_inputBoundOutputTrans,axiom,
% 2.87/1.56 ! [A2: name,X2: name,P: pi,B2: name,Y: name,P3: pi] :
% 2.87/1.56 ~ ( late_transitions @ ( input @ A2 @ X2 @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ B2 ) @ Y @ P3 ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_201_Late__Semantics_OInput,axiom,
% 2.87/1.56 ! [A2: name,X2: name,P: pi] : ( late_transitions @ ( input @ A2 @ X2 @ P ) @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_202_transitions_OInput,axiom,
% 2.87/1.56 ! [X2: name,A2: name,P: pi] :
% 2.87/1.56 ( ( X2 != A2 )
% 2.87/1.56 => ( late_transitions @ ( input @ A2 @ X2 @ P ) @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_203_inputIneqTrans,axiom,
% 2.87/1.56 ! [A2: name,X2: name,P: pi,B2: late_subject,Y: name,P3: pi] :
% 2.87/1.56 ( ( late_transitions @ ( input @ A2 @ X2 @ P ) @ ( late_BoundR @ B2 @ Y @ P3 ) )
% 2.87/1.56 => ~ ( fresh @ name @ late_subject @ A2 @ B2 ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_204_resInputBoundOutputTrans,axiom,
% 2.87/1.56 ! [X2: name,A2: name,Y: name,P: pi,B2: name,Z: name,P3: pi] :
% 2.87/1.56 ~ ( late_transitions @ ( res @ X2 @ ( input @ A2 @ Y @ P ) ) @ ( late_BoundR @ ( late_BoundOutputS @ B2 ) @ Z @ P3 ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_205_alphaInput,axiom,
% 2.87/1.56 ! [C: name,P: pi,A2: name,X2: name] :
% 2.87/1.56 ( ( fresh @ name @ pi @ C @ P )
% 2.87/1.56 => ( ( input @ A2 @ X2 @ P )
% 2.87/1.56 = ( input @ A2 @ C @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ X2 @ C ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ P ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_206_list_Odistinct_I1_J,axiom,
% 2.87/1.56 ! [A: $tType,X21: A,X222: list @ A] :
% 2.87/1.56 ( ( nil @ A )
% 2.87/1.56 != ( cons @ A @ X21 @ X222 ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_207_list_OdiscI,axiom,
% 2.87/1.56 ! [A: $tType,List: list @ A,X21: A,X222: list @ A] :
% 2.87/1.56 ( ( List
% 2.87/1.56 = ( cons @ A @ X21 @ X222 ) )
% 2.87/1.56 => ( List
% 2.87/1.56 != ( nil @ A ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_208_list_Oexhaust,axiom,
% 2.87/1.56 ! [A: $tType,Y: list @ A] :
% 2.87/1.56 ( ( Y
% 2.87/1.56 != ( nil @ A ) )
% 2.87/1.56 => ~ ! [X212: A,X223: list @ A] :
% 2.87/1.56 ( Y
% 2.87/1.56 != ( cons @ A @ X212 @ X223 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_209_list_Oinducts,axiom,
% 2.87/1.56 ! [A: $tType,P: ( list @ A ) > $o,List: list @ A] :
% 2.87/1.56 ( ( P @ ( nil @ A ) )
% 2.87/1.56 => ( ! [X13: A,X23: list @ A] :
% 2.87/1.56 ( ( P @ X23 )
% 2.87/1.56 => ( P @ ( cons @ A @ X13 @ X23 ) ) )
% 2.87/1.56 => ( P @ List ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_210_neq__Nil__conv,axiom,
% 2.87/1.56 ! [A: $tType,Xs: list @ A] :
% 2.87/1.56 ( ( Xs
% 2.87/1.56 != ( nil @ A ) )
% 2.87/1.56 = ( ? [Y5: A,Ys: list @ A] :
% 2.87/1.56 ( Xs
% 2.87/1.56 = ( cons @ A @ Y5 @ Ys ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_211_list__induct2_H,axiom,
% 2.87/1.56 ! [A: $tType,B: $tType,P: ( list @ A ) > ( list @ B ) > $o,Xs: list @ A,Ys2: list @ B] :
% 2.87/1.56 ( ( P @ ( nil @ A ) @ ( nil @ B ) )
% 2.87/1.56 => ( ! [X5: A,Xs2: list @ A] : ( P @ ( cons @ A @ X5 @ Xs2 ) @ ( nil @ B ) )
% 2.87/1.56 => ( ! [Y3: B,Ys3: list @ B] : ( P @ ( nil @ A ) @ ( cons @ B @ Y3 @ Ys3 ) )
% 2.87/1.56 => ( ! [X5: A,Xs2: list @ A,Y3: B,Ys3: list @ B] :
% 2.87/1.56 ( ( P @ Xs2 @ Ys3 )
% 2.87/1.56 => ( P @ ( cons @ A @ X5 @ Xs2 ) @ ( cons @ B @ Y3 @ Ys3 ) ) )
% 2.87/1.56 => ( P @ Xs @ Ys2 ) ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_212_splice_Oinduct,axiom,
% 2.87/1.56 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 2.87/1.56 ( ! [X_1: list @ A] : ( P @ ( nil @ A ) @ X_1 )
% 2.87/1.56 => ( ! [X5: A,Xs2: list @ A,Ys3: list @ A] :
% 2.87/1.56 ( ( P @ Ys3 @ Xs2 )
% 2.87/1.56 => ( P @ ( cons @ A @ X5 @ Xs2 ) @ Ys3 ) )
% 2.87/1.56 => ( P @ A0 @ A1 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_213_induct__list012,axiom,
% 2.87/1.56 ! [A: $tType,P: ( list @ A ) > $o,Xs: list @ A] :
% 2.87/1.56 ( ( P @ ( nil @ A ) )
% 2.87/1.56 => ( ! [X5: A] : ( P @ ( cons @ A @ X5 @ ( nil @ A ) ) )
% 2.87/1.56 => ( ! [X5: A,Y3: A,Zs: list @ A] :
% 2.87/1.56 ( ( P @ Zs )
% 2.87/1.56 => ( ( P @ ( cons @ A @ Y3 @ Zs ) )
% 2.87/1.56 => ( P @ ( cons @ A @ X5 @ ( cons @ A @ Y3 @ Zs ) ) ) ) )
% 2.87/1.56 => ( P @ Xs ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_214_min__list_Ocases,axiom,
% 2.87/1.56 ! [A: $tType] :
% 2.87/1.56 ( ( ord @ A )
% 2.87/1.56 => ! [X2: list @ A] :
% 2.87/1.56 ( ! [X5: A,Xs2: list @ A] :
% 2.87/1.56 ( X2
% 2.87/1.56 != ( cons @ A @ X5 @ Xs2 ) )
% 2.87/1.56 => ( X2
% 2.87/1.56 = ( nil @ A ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_215_min__list_Oinduct,axiom,
% 2.87/1.56 ! [A: $tType] :
% 2.87/1.56 ( ( ord @ A )
% 2.87/1.56 => ! [P: ( list @ A ) > $o,A0: list @ A] :
% 2.87/1.56 ( ! [X5: A,Xs2: list @ A] :
% 2.87/1.56 ( ! [X213: A,X224: list @ A] :
% 2.87/1.56 ( ( Xs2
% 2.87/1.56 = ( cons @ A @ X213 @ X224 ) )
% 2.87/1.56 => ( P @ Xs2 ) )
% 2.87/1.56 => ( P @ ( cons @ A @ X5 @ Xs2 ) ) )
% 2.87/1.56 => ( ( P @ ( nil @ A ) )
% 2.87/1.56 => ( P @ A0 ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_216_shuffles_Oinduct,axiom,
% 2.87/1.56 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 2.87/1.56 ( ! [X_1: list @ A] : ( P @ ( nil @ A ) @ X_1 )
% 2.87/1.56 => ( ! [Xs2: list @ A] : ( P @ Xs2 @ ( nil @ A ) )
% 2.87/1.56 => ( ! [X5: A,Xs2: list @ A,Y3: A,Ys3: list @ A] :
% 2.87/1.56 ( ( P @ Xs2 @ ( cons @ A @ Y3 @ Ys3 ) )
% 2.87/1.56 => ( ( P @ ( cons @ A @ X5 @ Xs2 ) @ Ys3 )
% 2.87/1.56 => ( P @ ( cons @ A @ X5 @ Xs2 ) @ ( cons @ A @ Y3 @ Ys3 ) ) ) )
% 2.87/1.56 => ( P @ A0 @ A1 ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_217_transpose_Ocases,axiom,
% 2.87/1.56 ! [A: $tType,X2: list @ ( list @ A )] :
% 2.87/1.56 ( ( X2
% 2.87/1.56 != ( nil @ ( list @ A ) ) )
% 2.87/1.56 => ( ! [Xss: list @ ( list @ A )] :
% 2.87/1.56 ( X2
% 2.87/1.56 != ( cons @ ( list @ A ) @ ( nil @ A ) @ Xss ) )
% 2.87/1.56 => ~ ! [X5: A,Xs2: list @ A,Xss: list @ ( list @ A )] :
% 2.87/1.56 ( X2
% 2.87/1.56 != ( cons @ ( list @ A ) @ ( cons @ A @ X5 @ Xs2 ) @ Xss ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_218_remdups__adj_Ocases,axiom,
% 2.87/1.56 ! [A: $tType,X2: list @ A] :
% 2.87/1.56 ( ( X2
% 2.87/1.56 != ( nil @ A ) )
% 2.87/1.56 => ( ! [X5: A] :
% 2.87/1.56 ( X2
% 2.87/1.56 != ( cons @ A @ X5 @ ( nil @ A ) ) )
% 2.87/1.56 => ~ ! [X5: A,Y3: A,Xs2: list @ A] :
% 2.87/1.56 ( X2
% 2.87/1.56 != ( cons @ A @ X5 @ ( cons @ A @ Y3 @ Xs2 ) ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_219_sorted__wrt_Oinduct,axiom,
% 2.87/1.56 ! [A: $tType,P: ( A > A > $o ) > ( list @ A ) > $o,A0: A > A > $o,A1: list @ A] :
% 2.87/1.56 ( ! [P5: A > A > $o] : ( P @ P5 @ ( nil @ A ) )
% 2.87/1.56 => ( ! [P5: A > A > $o,X5: A,Ys3: list @ A] :
% 2.87/1.56 ( ( P @ P5 @ Ys3 )
% 2.87/1.56 => ( P @ P5 @ ( cons @ A @ X5 @ Ys3 ) ) )
% 2.87/1.56 => ( P @ A0 @ A1 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_220_remdups__adj_Oinduct,axiom,
% 2.87/1.56 ! [A: $tType,P: ( list @ A ) > $o,A0: list @ A] :
% 2.87/1.56 ( ( P @ ( nil @ A ) )
% 2.87/1.56 => ( ! [X5: A] : ( P @ ( cons @ A @ X5 @ ( nil @ A ) ) )
% 2.87/1.56 => ( ! [X5: A,Y3: A,Xs2: list @ A] :
% 2.87/1.56 ( ( ( X5 = Y3 )
% 2.87/1.56 => ( P @ ( cons @ A @ X5 @ Xs2 ) ) )
% 2.87/1.56 => ( ( ( X5 != Y3 )
% 2.87/1.56 => ( P @ ( cons @ A @ Y3 @ Xs2 ) ) )
% 2.87/1.56 => ( P @ ( cons @ A @ X5 @ ( cons @ A @ Y3 @ Xs2 ) ) ) ) )
% 2.87/1.56 => ( P @ A0 ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_221_arg__min__list_Oinduct,axiom,
% 2.87/1.56 ! [B: $tType,A: $tType] :
% 2.87/1.56 ( ( linorder @ B )
% 2.87/1.56 => ! [P: ( A > B ) > ( list @ A ) > $o,A0: A > B,A1: list @ A] :
% 2.87/1.56 ( ! [F3: A > B,X5: A] : ( P @ F3 @ ( cons @ A @ X5 @ ( nil @ A ) ) )
% 2.87/1.56 => ( ! [F3: A > B,X5: A,Y3: A,Zs: list @ A] :
% 2.87/1.56 ( ( P @ F3 @ ( cons @ A @ Y3 @ Zs ) )
% 2.87/1.56 => ( P @ F3 @ ( cons @ A @ X5 @ ( cons @ A @ Y3 @ Zs ) ) ) )
% 2.87/1.56 => ( ! [A4: A > B] : ( P @ A4 @ ( nil @ A ) )
% 2.87/1.56 => ( P @ A0 @ A1 ) ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_222_successively_Oinduct,axiom,
% 2.87/1.56 ! [A: $tType,P: ( A > A > $o ) > ( list @ A ) > $o,A0: A > A > $o,A1: list @ A] :
% 2.87/1.56 ( ! [P5: A > A > $o] : ( P @ P5 @ ( nil @ A ) )
% 2.87/1.56 => ( ! [P5: A > A > $o,X5: A] : ( P @ P5 @ ( cons @ A @ X5 @ ( nil @ A ) ) )
% 2.87/1.56 => ( ! [P5: A > A > $o,X5: A,Y3: A,Xs2: list @ A] :
% 2.87/1.56 ( ( P @ P5 @ ( cons @ A @ Y3 @ Xs2 ) )
% 2.87/1.56 => ( P @ P5 @ ( cons @ A @ X5 @ ( cons @ A @ Y3 @ Xs2 ) ) ) )
% 2.87/1.56 => ( P @ A0 @ A1 ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_223_list__nonempty__induct,axiom,
% 2.87/1.56 ! [A: $tType,Xs: list @ A,P: ( list @ A ) > $o] :
% 2.87/1.56 ( ( Xs
% 2.87/1.56 != ( nil @ A ) )
% 2.87/1.56 => ( ! [X5: A] : ( P @ ( cons @ A @ X5 @ ( nil @ A ) ) )
% 2.87/1.56 => ( ! [X5: A,Xs2: list @ A] :
% 2.87/1.56 ( ( Xs2
% 2.87/1.56 != ( nil @ A ) )
% 2.87/1.56 => ( ( P @ Xs2 )
% 2.87/1.56 => ( P @ ( cons @ A @ X5 @ Xs2 ) ) ) )
% 2.87/1.56 => ( P @ Xs ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_224_map__tailrec__rev_Oinduct,axiom,
% 2.87/1.56 ! [A: $tType,B: $tType,P: ( A > B ) > ( list @ A ) > ( list @ B ) > $o,A0: A > B,A1: list @ A,A22: list @ B] :
% 2.87/1.56 ( ! [F3: A > B,X_1: list @ B] : ( P @ F3 @ ( nil @ A ) @ X_1 )
% 2.87/1.56 => ( ! [F3: A > B,A4: A,As: list @ A,Bs: list @ B] :
% 2.87/1.56 ( ( P @ F3 @ As @ ( cons @ B @ ( F3 @ A4 ) @ Bs ) )
% 2.87/1.56 => ( P @ F3 @ ( cons @ A @ A4 @ As ) @ Bs ) )
% 2.87/1.56 => ( P @ A0 @ A1 @ A22 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_225_strict__sorted_Ocases,axiom,
% 2.87/1.56 ! [A: $tType] :
% 2.87/1.56 ( ( linorder @ A )
% 2.87/1.56 => ! [X2: list @ A] :
% 2.87/1.56 ( ( X2
% 2.87/1.56 != ( nil @ A ) )
% 2.87/1.56 => ~ ! [X5: A,Ys3: list @ A] :
% 2.87/1.56 ( X2
% 2.87/1.56 != ( cons @ A @ X5 @ Ys3 ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_226_strict__sorted_Oinduct,axiom,
% 2.87/1.56 ! [A: $tType] :
% 2.87/1.56 ( ( linorder @ A )
% 2.87/1.56 => ! [P: ( list @ A ) > $o,A0: list @ A] :
% 2.87/1.56 ( ( P @ ( nil @ A ) )
% 2.87/1.56 => ( ! [X5: A,Ys3: list @ A] :
% 2.87/1.56 ( ( P @ Ys3 )
% 2.87/1.56 => ( P @ ( cons @ A @ X5 @ Ys3 ) ) )
% 2.87/1.56 => ( P @ A0 ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_227_splice_Ocases,axiom,
% 2.87/1.56 ! [A: $tType,X2: product_prod @ ( list @ A ) @ ( list @ A )] :
% 2.87/1.56 ( ! [Ys3: list @ A] :
% 2.87/1.56 ( X2
% 2.87/1.56 != ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( nil @ A ) @ Ys3 ) )
% 2.87/1.56 => ~ ! [X5: A,Xs2: list @ A,Ys3: list @ A] :
% 2.87/1.56 ( X2
% 2.87/1.56 != ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X5 @ Xs2 ) @ Ys3 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_228_shuffles_Ocases,axiom,
% 2.87/1.56 ! [A: $tType,X2: product_prod @ ( list @ A ) @ ( list @ A )] :
% 2.87/1.56 ( ! [Ys3: list @ A] :
% 2.87/1.56 ( X2
% 2.87/1.56 != ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( nil @ A ) @ Ys3 ) )
% 2.87/1.56 => ( ! [Xs2: list @ A] :
% 2.87/1.56 ( X2
% 2.87/1.56 != ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs2 @ ( nil @ A ) ) )
% 2.87/1.56 => ~ ! [X5: A,Xs2: list @ A,Y3: A,Ys3: list @ A] :
% 2.87/1.56 ( X2
% 2.87/1.56 != ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X5 @ Xs2 ) @ ( cons @ A @ Y3 @ Ys3 ) ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_229_sorted__wrt_Ocases,axiom,
% 2.87/1.56 ! [A: $tType,X2: product_prod @ ( A > A > $o ) @ ( list @ A )] :
% 2.87/1.56 ( ! [P5: A > A > $o] :
% 2.87/1.56 ( X2
% 2.87/1.56 != ( product_Pair @ ( A > A > $o ) @ ( list @ A ) @ P5 @ ( nil @ A ) ) )
% 2.87/1.56 => ~ ! [P5: A > A > $o,X5: A,Ys3: list @ A] :
% 2.87/1.56 ( X2
% 2.87/1.56 != ( product_Pair @ ( A > A > $o ) @ ( list @ A ) @ P5 @ ( cons @ A @ X5 @ Ys3 ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_230_successively_Ocases,axiom,
% 2.87/1.56 ! [A: $tType,X2: product_prod @ ( A > A > $o ) @ ( list @ A )] :
% 2.87/1.56 ( ! [P5: A > A > $o] :
% 2.87/1.56 ( X2
% 2.87/1.56 != ( product_Pair @ ( A > A > $o ) @ ( list @ A ) @ P5 @ ( nil @ A ) ) )
% 2.87/1.56 => ( ! [P5: A > A > $o,X5: A] :
% 2.87/1.56 ( X2
% 2.87/1.56 != ( product_Pair @ ( A > A > $o ) @ ( list @ A ) @ P5 @ ( cons @ A @ X5 @ ( nil @ A ) ) ) )
% 2.87/1.56 => ~ ! [P5: A > A > $o,X5: A,Y3: A,Xs2: list @ A] :
% 2.87/1.56 ( X2
% 2.87/1.56 != ( product_Pair @ ( A > A > $o ) @ ( list @ A ) @ P5 @ ( cons @ A @ X5 @ ( cons @ A @ Y3 @ Xs2 ) ) ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_231_arg__min__list_Ocases,axiom,
% 2.87/1.56 ! [B: $tType,A: $tType] :
% 2.87/1.56 ( ( linorder @ B )
% 2.87/1.56 => ! [X2: product_prod @ ( A > B ) @ ( list @ A )] :
% 2.87/1.56 ( ! [F3: A > B,X5: A] :
% 2.87/1.56 ( X2
% 2.87/1.56 != ( product_Pair @ ( A > B ) @ ( list @ A ) @ F3 @ ( cons @ A @ X5 @ ( nil @ A ) ) ) )
% 2.87/1.56 => ( ! [F3: A > B,X5: A,Y3: A,Zs: list @ A] :
% 2.87/1.56 ( X2
% 2.87/1.56 != ( product_Pair @ ( A > B ) @ ( list @ A ) @ F3 @ ( cons @ A @ X5 @ ( cons @ A @ Y3 @ Zs ) ) ) )
% 2.87/1.56 => ~ ! [A4: A > B] :
% 2.87/1.56 ( X2
% 2.87/1.56 != ( product_Pair @ ( A > B ) @ ( list @ A ) @ A4 @ ( nil @ A ) ) ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_232_map__tailrec__rev_Ocases,axiom,
% 2.87/1.56 ! [A: $tType,B: $tType,X2: product_prod @ ( A > B ) @ ( product_prod @ ( list @ A ) @ ( list @ B ) )] :
% 2.87/1.56 ( ! [F3: A > B,Bs: list @ B] :
% 2.87/1.56 ( X2
% 2.87/1.56 != ( product_Pair @ ( A > B ) @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ F3 @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ ( nil @ A ) @ Bs ) ) )
% 2.87/1.56 => ~ ! [F3: A > B,A4: A,As: list @ A,Bs: list @ B] :
% 2.87/1.56 ( X2
% 2.87/1.56 != ( product_Pair @ ( A > B ) @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ F3 @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ ( cons @ A @ A4 @ As ) @ Bs ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_233_prod__cases3,axiom,
% 2.87/1.56 ! [A: $tType,B: $tType,C3: $tType,Y: product_prod @ A @ ( product_prod @ B @ C3 )] :
% 2.87/1.56 ~ ! [A4: A,B3: B,C2: C3] :
% 2.87/1.56 ( Y
% 2.87/1.56 != ( product_Pair @ A @ ( product_prod @ B @ C3 ) @ A4 @ ( product_Pair @ B @ C3 @ B3 @ C2 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_234_prod__cases4,axiom,
% 2.87/1.56 ! [A: $tType,B: $tType,C3: $tType,D2: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ D2 ) )] :
% 2.87/1.56 ~ ! [A4: A,B3: B,C2: C3,D3: D2] :
% 2.87/1.56 ( Y
% 2.87/1.56 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C3 @ D2 ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C3 @ D2 ) @ B3 @ ( product_Pair @ C3 @ D2 @ C2 @ D3 ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_235_prod__cases5,axiom,
% 2.87/1.56 ! [A: $tType,B: $tType,C3: $tType,D2: $tType,E: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ E ) ) )] :
% 2.87/1.56 ~ ! [A4: A,B3: B,C2: C3,D3: D2,E2: E] :
% 2.87/1.56 ( Y
% 2.87/1.56 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ E ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ E ) ) @ B3 @ ( product_Pair @ C3 @ ( product_prod @ D2 @ E ) @ C2 @ ( product_Pair @ D2 @ E @ D3 @ E2 ) ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_236_prod__cases6,axiom,
% 2.87/1.56 ! [A: $tType,B: $tType,C3: $tType,D2: $tType,E: $tType,F4: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ F4 ) ) ) )] :
% 2.87/1.56 ~ ! [A4: A,B3: B,C2: C3,D3: D2,E2: E,F3: F4] :
% 2.87/1.56 ( Y
% 2.87/1.56 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ F4 ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ F4 ) ) ) @ B3 @ ( product_Pair @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ F4 ) ) @ C2 @ ( product_Pair @ D2 @ ( product_prod @ E @ F4 ) @ D3 @ ( product_Pair @ E @ F4 @ E2 @ F3 ) ) ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_237_prod__cases7,axiom,
% 2.87/1.56 ! [A: $tType,B: $tType,C3: $tType,D2: $tType,E: $tType,F4: $tType,G2: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F4 @ G2 ) ) ) ) )] :
% 2.87/1.56 ~ ! [A4: A,B3: B,C2: C3,D3: D2,E2: E,F3: F4,G3: G2] :
% 2.87/1.56 ( Y
% 2.87/1.56 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F4 @ G2 ) ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F4 @ G2 ) ) ) ) @ B3 @ ( product_Pair @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F4 @ G2 ) ) ) @ C2 @ ( product_Pair @ D2 @ ( product_prod @ E @ ( product_prod @ F4 @ G2 ) ) @ D3 @ ( product_Pair @ E @ ( product_prod @ F4 @ G2 ) @ E2 @ ( product_Pair @ F4 @ G2 @ F3 @ G3 ) ) ) ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_238_prod__induct3,axiom,
% 2.87/1.56 ! [C3: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ C3 ) ) > $o,X2: product_prod @ A @ ( product_prod @ B @ C3 )] :
% 2.87/1.56 ( ! [A4: A,B3: B,C2: C3] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ C3 ) @ A4 @ ( product_Pair @ B @ C3 @ B3 @ C2 ) ) )
% 2.87/1.56 => ( P @ X2 ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_239_prod__induct4,axiom,
% 2.87/1.56 ! [D2: $tType,C3: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ D2 ) ) ) > $o,X2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ D2 ) )] :
% 2.87/1.56 ( ! [A4: A,B3: B,C2: C3,D3: D2] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C3 @ D2 ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C3 @ D2 ) @ B3 @ ( product_Pair @ C3 @ D2 @ C2 @ D3 ) ) ) )
% 2.87/1.56 => ( P @ X2 ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_240_prod__induct5,axiom,
% 2.87/1.56 ! [E: $tType,D2: $tType,C3: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ E ) ) ) ) > $o,X2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ E ) ) )] :
% 2.87/1.56 ( ! [A4: A,B3: B,C2: C3,D3: D2,E2: E] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ E ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ E ) ) @ B3 @ ( product_Pair @ C3 @ ( product_prod @ D2 @ E ) @ C2 @ ( product_Pair @ D2 @ E @ D3 @ E2 ) ) ) ) )
% 2.87/1.56 => ( P @ X2 ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_241_prod__induct6,axiom,
% 2.87/1.56 ! [F4: $tType,E: $tType,D2: $tType,C3: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ F4 ) ) ) ) ) > $o,X2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ F4 ) ) ) )] :
% 2.87/1.56 ( ! [A4: A,B3: B,C2: C3,D3: D2,E2: E,F3: F4] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ F4 ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ F4 ) ) ) @ B3 @ ( product_Pair @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ F4 ) ) @ C2 @ ( product_Pair @ D2 @ ( product_prod @ E @ F4 ) @ D3 @ ( product_Pair @ E @ F4 @ E2 @ F3 ) ) ) ) ) )
% 2.87/1.56 => ( P @ X2 ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_242_prod__induct7,axiom,
% 2.87/1.56 ! [G2: $tType,F4: $tType,E: $tType,D2: $tType,C3: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F4 @ G2 ) ) ) ) ) ) > $o,X2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F4 @ G2 ) ) ) ) )] :
% 2.87/1.56 ( ! [A4: A,B3: B,C2: C3,D3: D2,E2: E,F3: F4,G3: G2] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F4 @ G2 ) ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F4 @ G2 ) ) ) ) @ B3 @ ( product_Pair @ C3 @ ( product_prod @ D2 @ ( product_prod @ E @ ( product_prod @ F4 @ G2 ) ) ) @ C2 @ ( product_Pair @ D2 @ ( product_prod @ E @ ( product_prod @ F4 @ G2 ) ) @ D3 @ ( product_Pair @ E @ ( product_prod @ F4 @ G2 ) @ E2 @ ( product_Pair @ F4 @ G2 @ F3 @ G3 ) ) ) ) ) ) )
% 2.87/1.56 => ( P @ X2 ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_243_old_Ounit_Orec,axiom,
% 2.87/1.56 ! [T: $tType,F1: T] :
% 2.87/1.56 ( ( product_rec_unit @ T @ F1 @ product_Unity )
% 2.87/1.56 = F1 ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_244_old_Oprod_Orec,axiom,
% 2.87/1.56 ! [A: $tType,T: $tType,B: $tType,F1: A > B > T,A2: A,B2: B] :
% 2.87/1.56 ( ( product_rec_prod @ A @ B @ T @ F1 @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 2.87/1.56 = ( F1 @ A2 @ B2 ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_245_default__unit__def,axiom,
% 2.87/1.56 ( ( default_default @ product_unit )
% 2.87/1.56 = product_Unity ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_246_supports__def,axiom,
% 2.87/1.56 ! [A: $tType,X: $tType] :
% 2.87/1.56 ( ( supports @ X @ A )
% 2.87/1.56 = ( ^ [S3: set @ X,X4: A] :
% 2.87/1.56 ! [A5: X,B4: X] :
% 2.87/1.56 ( ( ~ ( member @ X @ A5 @ S3 )
% 2.87/1.56 & ~ ( member @ X @ B4 @ S3 ) )
% 2.87/1.56 => ( ( perm @ X @ A @ ( cons @ ( product_prod @ X @ X ) @ ( product_Pair @ X @ X @ A5 @ B4 ) @ ( nil @ ( product_prod @ X @ X ) ) ) @ X4 )
% 2.87/1.56 = X4 ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_247_perm__residual__Rep_Osimps_I2_J,axiom,
% 2.87/1.56 ! [X: $tType,Pi: list @ ( product_prod @ X @ X ),FreeRes3: late_freeRes,Pia: pi] :
% 2.87/1.56 ( ( perm @ X @ late_residual_Rep @ Pi @ ( late_r347633188eR_Rep @ FreeRes3 @ Pia ) )
% 2.87/1.56 = ( late_r347633188eR_Rep @ ( perm @ X @ late_freeRes @ Pi @ FreeRes3 ) @ ( perm @ X @ pi @ Pi @ Pia ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_248_residual__Rep_Oinject_I2_J,axiom,
% 2.87/1.56 ! [X21: late_freeRes,X222: pi,Y21: late_freeRes,Y22: pi] :
% 2.87/1.56 ( ( ( late_r347633188eR_Rep @ X21 @ X222 )
% 2.87/1.56 = ( late_r347633188eR_Rep @ Y21 @ Y22 ) )
% 2.87/1.56 = ( ( X21 = Y21 )
% 2.87/1.56 & ( X222 = Y22 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_249_product__lists_Osimps_I1_J,axiom,
% 2.87/1.56 ! [A: $tType] :
% 2.87/1.56 ( ( product_lists @ A @ ( nil @ ( list @ A ) ) )
% 2.87/1.56 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_250_name__calc_I1_J,axiom,
% 2.87/1.56 ! [A2: name,B2: name,Pi: list @ ( product_prod @ name @ name ),X2: name] :
% 2.87/1.56 ( ( perm @ name @ name @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ Pi ) @ X2 )
% 2.87/1.56 = ( swap @ name @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( perm @ name @ name @ Pi @ X2 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_251_name__calc_I3_J,axiom,
% 2.87/1.56 ! [A2: name,C: name,B2: name] :
% 2.87/1.56 ( ( ( A2 = C )
% 2.87/1.56 => ( ( swap @ name @ ( product_Pair @ name @ name @ A2 @ B2 ) @ C )
% 2.87/1.56 = B2 ) )
% 2.87/1.56 & ( ( A2 != C )
% 2.87/1.56 => ( ( ( B2 = C )
% 2.87/1.56 => ( ( swap @ name @ ( product_Pair @ name @ name @ A2 @ B2 ) @ C )
% 2.87/1.56 = A2 ) )
% 2.87/1.56 & ( ( B2 != C )
% 2.87/1.56 => ( ( swap @ name @ ( product_Pair @ name @ name @ A2 @ B2 ) @ C )
% 2.87/1.56 = C ) ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_252_Agent_Oswap__name__def,axiom,
% 2.87/1.56 ( ( swap @ name )
% 2.87/1.56 = swap_name ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_253_alpha__fresh_H,axiom,
% 2.87/1.56 ! [X3: $tType] :
% 2.87/1.56 ( ( pt_name @ X3 )
% 2.87/1.56 => ! [A2: name,X2: X3,B2: name,Y: X3,C: name] :
% 2.87/1.56 ( ( ( abs_fun @ name @ X3 @ A2 @ X2 )
% 2.87/1.56 = ( abs_fun @ name @ X3 @ B2 @ Y ) )
% 2.87/1.56 => ( ( C != A2 )
% 2.87/1.56 => ( ( C != B2 )
% 2.87/1.56 => ( ( fresh @ name @ X3 @ C @ X2 )
% 2.87/1.56 => ( ( fresh @ name @ X3 @ C @ Y )
% 2.87/1.56 => ( X2
% 2.87/1.56 = ( perm @ name @ X3 @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ C ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ ( perm @ name @ X3 @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ B2 @ C ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ Y ) ) ) ) ) ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_254_pi_Ofresh_I9_J,axiom,
% 2.87/1.56 ! [A2: name,X1: name,X22: pi] :
% 2.87/1.56 ( ( fresh @ name @ pi @ A2 @ ( res @ X1 @ X22 ) )
% 2.87/1.56 = ( fresh @ name @ ( name > ( noption @ pi ) ) @ A2 @ ( abs_fun @ name @ pi @ X1 @ X22 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(tcon_fun___Agent_Ocp__name__name,axiom,
% 2.87/1.56 ! [A7: $tType,A8: $tType] :
% 2.87/1.56 ( ( ( cp_name_name @ A7 )
% 2.87/1.56 & ( cp_name_name @ A8 ) )
% 2.87/1.56 => ( cp_name_name @ ( A7 > A8 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(tcon_fun___Orderings_Oord,axiom,
% 2.87/1.56 ! [A7: $tType,A8: $tType] :
% 2.87/1.56 ( ( ord @ A8 )
% 2.87/1.56 => ( ord @ ( A7 > A8 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(tcon_fun___Agent_Opt__name,axiom,
% 2.87/1.56 ! [A7: $tType,A8: $tType] :
% 2.87/1.56 ( ( ( pt_name @ A7 )
% 2.87/1.56 & ( pt_name @ A8 ) )
% 2.87/1.56 => ( pt_name @ ( A7 > A8 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(tcon_Set_Oset___Agent_Ocp__name__name_1,axiom,
% 2.87/1.56 ! [A7: $tType] :
% 2.87/1.56 ( ( cp_name_name @ A7 )
% 2.87/1.56 => ( cp_name_name @ ( set @ A7 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(tcon_Set_Oset___Orderings_Oord_2,axiom,
% 2.87/1.56 ! [A7: $tType] : ( ord @ ( set @ A7 ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(tcon_Set_Oset___Agent_Opt__name_3,axiom,
% 2.87/1.56 ! [A7: $tType] :
% 2.87/1.56 ( ( pt_name @ A7 )
% 2.87/1.56 => ( pt_name @ ( set @ A7 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(tcon_Agent_Opi___Agent_Ocp__name__name_4,axiom,
% 2.87/1.56 cp_name_name @ pi ).
% 2.87/1.56
% 2.87/1.56 thf(tcon_Agent_Opi___Agent_Opt__name_5,axiom,
% 2.87/1.56 pt_name @ pi ).
% 2.87/1.56
% 2.87/1.56 thf(tcon_Agent_Opi___Agent_Ofs__name,axiom,
% 2.87/1.56 fs_name @ pi ).
% 2.87/1.56
% 2.87/1.56 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 2.87/1.56 linorder @ $o ).
% 2.87/1.56
% 2.87/1.56 thf(tcon_HOL_Obool___Agent_Ocp__name__name_6,axiom,
% 2.87/1.56 cp_name_name @ $o ).
% 2.87/1.56
% 2.87/1.56 thf(tcon_HOL_Obool___Orderings_Oord_7,axiom,
% 2.87/1.56 ord @ $o ).
% 2.87/1.56
% 2.87/1.56 thf(tcon_HOL_Obool___Agent_Opt__name_8,axiom,
% 2.87/1.56 pt_name @ $o ).
% 2.87/1.56
% 2.87/1.56 thf(tcon_HOL_Obool___Agent_Ofs__name_9,axiom,
% 2.87/1.56 fs_name @ $o ).
% 2.87/1.56
% 2.87/1.56 thf(tcon_List_Olist___Agent_Ocp__name__name_10,axiom,
% 2.87/1.56 ! [A7: $tType] :
% 2.87/1.56 ( ( cp_name_name @ A7 )
% 2.87/1.56 => ( cp_name_name @ ( list @ A7 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(tcon_List_Olist___Agent_Opt__name_11,axiom,
% 2.87/1.56 ! [A7: $tType] :
% 2.87/1.56 ( ( pt_name @ A7 )
% 2.87/1.56 => ( pt_name @ ( list @ A7 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(tcon_List_Olist___Agent_Ofs__name_12,axiom,
% 2.87/1.56 ! [A7: $tType] :
% 2.87/1.56 ( ( fs_name @ A7 )
% 2.87/1.56 => ( fs_name @ ( list @ A7 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(tcon_Agent_Oname___Agent_Ocp__name__name_13,axiom,
% 2.87/1.56 cp_name_name @ name ).
% 2.87/1.56
% 2.87/1.56 thf(tcon_Agent_Oname___Agent_Opt__name_14,axiom,
% 2.87/1.56 pt_name @ name ).
% 2.87/1.56
% 2.87/1.56 thf(tcon_Agent_Oname___Agent_Ofs__name_15,axiom,
% 2.87/1.56 fs_name @ name ).
% 2.87/1.56
% 2.87/1.56 thf(tcon_Agent_Opi__Rep___Agent_Ocp__name__name_16,axiom,
% 2.87/1.56 cp_name_name @ pi_Rep ).
% 2.87/1.56
% 2.87/1.56 thf(tcon_Agent_Opi__Rep___Agent_Opt__name_17,axiom,
% 2.87/1.56 pt_name @ pi_Rep ).
% 2.87/1.56
% 2.87/1.56 thf(tcon_Nominal_Onoption___Agent_Ocp__name__name_18,axiom,
% 2.87/1.56 ! [A7: $tType] :
% 2.87/1.56 ( ( cp_name_name @ A7 )
% 2.87/1.56 => ( cp_name_name @ ( noption @ A7 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(tcon_Nominal_Onoption___Agent_Opt__name_19,axiom,
% 2.87/1.56 ! [A7: $tType] :
% 2.87/1.56 ( ( pt_name @ A7 )
% 2.87/1.56 => ( pt_name @ ( noption @ A7 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(tcon_Product__Type_Oprod___Agent_Ocp__name__name_20,axiom,
% 2.87/1.56 ! [A7: $tType,A8: $tType] :
% 2.87/1.56 ( ( ( cp_name_name @ A7 )
% 2.87/1.56 & ( cp_name_name @ A8 ) )
% 2.87/1.56 => ( cp_name_name @ ( product_prod @ A7 @ A8 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(tcon_Product__Type_Oprod___Agent_Opt__name_21,axiom,
% 2.87/1.56 ! [A7: $tType,A8: $tType] :
% 2.87/1.56 ( ( ( pt_name @ A7 )
% 2.87/1.56 & ( pt_name @ A8 ) )
% 2.87/1.56 => ( pt_name @ ( product_prod @ A7 @ A8 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(tcon_Product__Type_Oprod___Agent_Ofs__name_22,axiom,
% 2.87/1.56 ! [A7: $tType,A8: $tType] :
% 2.87/1.56 ( ( ( fs_name @ A7 )
% 2.87/1.56 & ( fs_name @ A8 ) )
% 2.87/1.56 => ( fs_name @ ( product_prod @ A7 @ A8 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(tcon_Product__Type_Ounit___Orderings_Olinorder_23,axiom,
% 2.87/1.56 linorder @ product_unit ).
% 2.87/1.56
% 2.87/1.56 thf(tcon_Product__Type_Ounit___Agent_Ocp__name__name_24,axiom,
% 2.87/1.56 cp_name_name @ product_unit ).
% 2.87/1.56
% 2.87/1.56 thf(tcon_Product__Type_Ounit___Orderings_Oord_25,axiom,
% 2.87/1.56 ord @ product_unit ).
% 2.87/1.56
% 2.87/1.56 thf(tcon_Product__Type_Ounit___Agent_Opt__name_26,axiom,
% 2.87/1.56 pt_name @ product_unit ).
% 2.87/1.56
% 2.87/1.56 thf(tcon_Product__Type_Ounit___Agent_Ofs__name_27,axiom,
% 2.87/1.56 fs_name @ product_unit ).
% 2.87/1.56
% 2.87/1.56 thf(tcon_Late__Semantics_OfreeRes___Agent_Ocp__name__name_28,axiom,
% 2.87/1.56 cp_name_name @ late_freeRes ).
% 2.87/1.56
% 2.87/1.56 thf(tcon_Late__Semantics_OfreeRes___Agent_Opt__name_29,axiom,
% 2.87/1.56 pt_name @ late_freeRes ).
% 2.87/1.56
% 2.87/1.56 thf(tcon_Late__Semantics_OfreeRes___Agent_Ofs__name_30,axiom,
% 2.87/1.56 fs_name @ late_freeRes ).
% 2.87/1.56
% 2.87/1.56 thf(tcon_Late__Semantics_Osubject___Agent_Ocp__name__name_31,axiom,
% 2.87/1.56 cp_name_name @ late_subject ).
% 2.87/1.56
% 2.87/1.56 thf(tcon_Late__Semantics_Osubject___Agent_Opt__name_32,axiom,
% 2.87/1.56 pt_name @ late_subject ).
% 2.87/1.56
% 2.87/1.56 thf(tcon_Late__Semantics_Osubject___Agent_Ofs__name_33,axiom,
% 2.87/1.56 fs_name @ late_subject ).
% 2.87/1.56
% 2.87/1.56 thf(tcon_Late__Semantics_Oresidual___Agent_Ocp__name__name_34,axiom,
% 2.87/1.56 cp_name_name @ late_residual ).
% 2.87/1.56
% 2.87/1.56 thf(tcon_Late__Semantics_Oresidual___Agent_Opt__name_35,axiom,
% 2.87/1.56 pt_name @ late_residual ).
% 2.87/1.56
% 2.87/1.56 thf(tcon_Late__Semantics_Oresidual___Agent_Ofs__name_36,axiom,
% 2.87/1.56 fs_name @ late_residual ).
% 2.87/1.56
% 2.87/1.56 thf(tcon_Late__Semantics_OfreeRes__Rep___Agent_Ocp__name__name_37,axiom,
% 2.87/1.56 cp_name_name @ late_freeRes_Rep ).
% 2.87/1.56
% 2.87/1.56 thf(tcon_Late__Semantics_OfreeRes__Rep___Agent_Opt__name_38,axiom,
% 2.87/1.56 pt_name @ late_freeRes_Rep ).
% 2.87/1.56
% 2.87/1.56 thf(tcon_Late__Semantics_Osubject__Rep___Agent_Ocp__name__name_39,axiom,
% 2.87/1.56 cp_name_name @ late_subject_Rep ).
% 2.87/1.56
% 2.87/1.56 thf(tcon_Late__Semantics_Osubject__Rep___Agent_Opt__name_40,axiom,
% 2.87/1.56 pt_name @ late_subject_Rep ).
% 2.87/1.56
% 2.87/1.56 thf(tcon_Late__Semantics_Oresidual__Rep___Agent_Ocp__name__name_41,axiom,
% 2.87/1.56 cp_name_name @ late_residual_Rep ).
% 2.87/1.56
% 2.87/1.56 thf(tcon_Late__Semantics_Oresidual__Rep___Agent_Opt__name_42,axiom,
% 2.87/1.56 pt_name @ late_residual_Rep ).
% 2.87/1.56
% 2.87/1.56 thf(help_If_3_1_T,axiom,
% 2.87/1.56 ! [P: $o] :
% 2.87/1.56 ( ( P = $true )
% 2.87/1.56 | ( P = $false ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(help_If_2_1_T,axiom,
% 2.87/1.56 ! [A: $tType,X2: A,Y: A] :
% 2.87/1.56 ( ( if @ A @ $false @ X2 @ Y )
% 2.87/1.56 = Y ) ).
% 2.87/1.56
% 2.87/1.56 thf(help_If_1_1_T,axiom,
% 2.87/1.56 ! [A: $tType,X2: A,Y: A] :
% 2.87/1.56 ( ( if @ A @ $true @ X2 @ Y )
% 2.87/1.56 = X2 ) ).
% 2.87/1.56
% 2.87/1.56 thf(conj_0,conjecture,
% 2.87/1.56 ? [P6: pi] :
% 2.87/1.56 ( ( late_transitions @ ( par @ p @ ( res @ x @ q ) ) @ ( late_BoundR @ ( late_BoundOutputS @ ab ) @ y @ P6 ) )
% 2.87/1.56 & ( strong2129052853vative @ P6 @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ y @ x ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ ( par @ ( subs @ p2 @ ya @ c ) @ q2 ) ) @ ( late_BoundOutputS @ ab ) @ y @ rel ) ) ).
% 2.87/1.56 ------------------------
% 2.87/1.58 % (25672)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_25458 for (2999ds/27Mi)
% 2.87/1.58 % (25674)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_25458 for (2999ds/2Mi)
% 2.87/1.58 % (25674)Instruction limit reached!
% 2.87/1.58 % (25674)------------------------------
% 2.87/1.58 % (25674)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.58 % (25674)Termination reason: Unknown
% 2.87/1.58 % (25674)Termination phase: shuffling
% 2.87/1.58
% 2.87/1.58 % (25671)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_25458 for (2999ds/4Mi)
% 2.87/1.58 % (25674)Memory used [KB]: 1407
% 2.87/1.58 % (25674)Time elapsed: 0.002 s
% 2.87/1.58 % (25674)Instructions burned: 2 (million)
% 2.87/1.58 % (25674)------------------------------
% 2.87/1.58 % (25674)------------------------------
% 2.87/1.58 % (25671)Instruction limit reached!
% 2.87/1.58 % (25671)------------------------------
% 2.87/1.58 % (25671)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.58 % (25671)Termination reason: Unknown
% 2.87/1.58 % (25671)Termination phase: shuffling
% 2.87/1.58
% 2.87/1.58 % (25671)Memory used [KB]: 1535
% 2.87/1.58 % (25671)Time elapsed: 0.003 s
% 2.87/1.58 % (25671)Instructions burned: 6 (million)
% 2.87/1.58 % (25671)------------------------------
% 2.87/1.58 % (25671)------------------------------
% 2.87/1.59 % (25670)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_25458 for (2999ds/183Mi)
% 2.87/1.59 % (25675)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_25458 for (2999ds/275Mi)
% 2.87/1.59 % (25673)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_25458 for (2999ds/2Mi)
% 2.87/1.59 % (25676)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_25458 for (2999ds/18Mi)
% 2.87/1.59 % (25672)Instruction limit reached!
% 2.87/1.59 % (25672)------------------------------
% 2.87/1.59 % (25672)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.59 % (25672)Termination reason: Unknown
% 2.87/1.59 % (25672)Termination phase: shuffling
% 2.87/1.59
% 2.87/1.59 % (25672)Memory used [KB]: 1918
% 2.87/1.59 % (25672)Time elapsed: 0.011 s
% 2.87/1.59 % (25672)Instructions burned: 29 (million)
% 2.87/1.59 % (25672)------------------------------
% 2.87/1.59 % (25672)------------------------------
% 2.87/1.59 % (25673)Instruction limit reached!
% 2.87/1.59 % (25673)------------------------------
% 2.87/1.59 % (25673)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.59 % (25673)Termination reason: Unknown
% 2.87/1.59 % (25673)Termination phase: shuffling
% 2.87/1.59
% 2.87/1.59 % (25673)Memory used [KB]: 1407
% 2.87/1.59 % (25673)Time elapsed: 0.004 s
% 2.87/1.59 % (25673)Instructions burned: 3 (million)
% 2.87/1.59 % (25673)------------------------------
% 2.87/1.59 % (25673)------------------------------
% 2.87/1.59 % (25677)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_25458 for (2999ds/3Mi)
% 2.87/1.59 % (25677)Instruction limit reached!
% 2.87/1.59 % (25677)------------------------------
% 2.87/1.59 % (25677)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.59 % (25677)Termination reason: Unknown
% 2.87/1.59 % (25677)Termination phase: shuffling
% 2.87/1.59
% 2.87/1.59 % (25677)Memory used [KB]: 1407
% 2.87/1.59 % (25677)Time elapsed: 0.002 s
% 2.87/1.59 % (25677)Instructions burned: 3 (million)
% 2.87/1.59 % (25677)------------------------------
% 2.87/1.59 % (25677)------------------------------
% 2.87/1.59 % (25678)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_25458 for (2999ds/37Mi)
% 2.94/1.60 % (25679)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_25458 for (2999ds/15Mi)
% 2.94/1.60 % (25676)Instruction limit reached!
% 2.94/1.60 % (25676)------------------------------
% 2.94/1.60 % (25676)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/1.60 % (25676)Termination reason: Unknown
% 2.94/1.60 % (25676)Termination phase: shuffling
% 2.94/1.60
% 2.94/1.60 % (25676)Memory used [KB]: 1791
% 2.94/1.60 % (25676)Time elapsed: 0.014 s
% 2.94/1.60 % (25676)Instructions burned: 19 (million)
% 2.94/1.60 % (25676)------------------------------
% 2.94/1.60 % (25676)------------------------------
% 2.94/1.60 % (25681)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_25458 for (2999ds/1041Mi)
% 2.94/1.60 % (25678)Instruction limit reached!
% 2.94/1.60 % (25678)------------------------------
% 2.94/1.60 % (25678)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/1.60 % (25678)Termination reason: Unknown
% 2.94/1.60 % (25678)Termination phase: shuffling
% 2.94/1.60
% 2.94/1.60 % (25678)Memory used [KB]: 2174
% 2.94/1.60 % (25678)Time elapsed: 0.013 s
% 2.94/1.60 % (25678)Instructions burned: 40 (million)
% 2.94/1.60 % (25678)------------------------------
% 2.94/1.60 % (25678)------------------------------
% 2.94/1.61 % (25679)Instruction limit reached!
% 2.94/1.61 % (25679)------------------------------
% 2.94/1.61 % (25679)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/1.61 % (25679)Termination reason: Unknown
% 2.94/1.61 % (25679)Termination phase: shuffling
% 2.94/1.61
% 2.94/1.61 % (25679)Memory used [KB]: 1791
% 2.94/1.61 % (25679)Time elapsed: 0.007 s
% 2.94/1.61 % (25679)Instructions burned: 17 (million)
% 2.94/1.61 % (25679)------------------------------
% 2.94/1.61 % (25679)------------------------------
% 2.94/1.61 % (25680)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_25458 for (2999ds/3Mi)
% 2.94/1.61 % (25680)Instruction limit reached!
% 2.94/1.61 % (25680)------------------------------
% 2.94/1.61 % (25680)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/1.61 % (25680)Termination reason: Unknown
% 2.94/1.61 % (25680)Termination phase: shuffling
% 2.94/1.61
% 2.94/1.61 % (25680)Memory used [KB]: 1407
% 2.94/1.61 % (25680)Time elapsed: 0.004 s
% 2.94/1.61 % (25680)Instructions burned: 3 (million)
% 2.94/1.61 % (25680)------------------------------
% 2.94/1.61 % (25680)------------------------------
% 2.94/1.61 % (25683)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_25458 for (2999ds/16Mi)
% 2.94/1.61 % (25684)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_25458 for (2999ds/3Mi)
% 2.94/1.62 % (25684)Instruction limit reached!
% 2.94/1.62 % (25684)------------------------------
% 2.94/1.62 % (25684)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/1.62 % (25684)Termination reason: Unknown
% 2.94/1.62 % (25684)Termination phase: shuffling
% 2.94/1.62
% 2.94/1.62 % (25684)Memory used [KB]: 1535
% 2.94/1.62 % (25684)Time elapsed: 0.003 s
% 2.94/1.62 % (25684)Instructions burned: 5 (million)
% 2.94/1.62 % (25684)------------------------------
% 2.94/1.62 % (25684)------------------------------
% 2.94/1.62 % (25682)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_25458 for (2999ds/7Mi)
% 2.94/1.62 % (25683)Instruction limit reached!
% 2.94/1.62 % (25683)------------------------------
% 2.94/1.62 % (25683)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/1.62 % (25683)Termination reason: Unknown
% 2.94/1.62 % (25683)Termination phase: shuffling
% 2.94/1.62
% 2.94/1.62 % (25683)Memory used [KB]: 1791
% 2.94/1.62 % (25683)Time elapsed: 0.007 s
% 2.94/1.62 % (25683)Instructions burned: 18 (million)
% 2.94/1.62 % (25683)------------------------------
% 2.94/1.62 % (25683)------------------------------
% 2.94/1.62 % (25682)Instruction limit reached!
% 2.94/1.62 % (25682)------------------------------
% 2.94/1.62 % (25682)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/1.62 % (25682)Termination reason: Unknown
% 2.94/1.62 % (25682)Termination phase: shuffling
% 2.94/1.62
% 2.94/1.62 % (25682)Memory used [KB]: 1663
% 2.94/1.62 % (25682)Time elapsed: 0.007 s
% 2.94/1.62 % (25682)Instructions burned: 8 (million)
% 2.94/1.62 % (25682)------------------------------
% 2.94/1.62 % (25682)------------------------------
% 2.94/1.63 % (25686)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_25458 for (2999ds/7Mi)
% 2.94/1.63 % (25685)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_25458 for (2999ds/3Mi)
% 2.94/1.63 % (25686)Instruction limit reached!
% 2.94/1.63 % (25686)------------------------------
% 2.94/1.63 % (25686)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/1.63 % (25686)Termination reason: Unknown
% 2.94/1.63 % (25686)Termination phase: shuffling
% 2.94/1.63
% 2.94/1.63 % (25686)Memory used [KB]: 1663
% 2.94/1.63 % (25686)Time elapsed: 0.004 s
% 2.94/1.63 % (25686)Instructions burned: 9 (million)
% 2.94/1.63 % (25686)------------------------------
% 2.94/1.63 % (25686)------------------------------
% 2.94/1.63 % (25685)Instruction limit reached!
% 2.94/1.63 % (25685)------------------------------
% 2.94/1.63 % (25685)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/1.63 % (25685)Termination reason: Unknown
% 2.94/1.63 % (25685)Termination phase: shuffling
% 2.94/1.63
% 2.94/1.63 % (25685)Memory used [KB]: 1407
% 2.94/1.63 % (25685)Time elapsed: 0.004 s
% 2.94/1.63 % (25685)Instructions burned: 3 (million)
% 2.94/1.63 % (25685)------------------------------
% 2.94/1.63 % (25685)------------------------------
% 2.94/1.63 % (25687)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_25458 for (2999ds/3Mi)
% 2.94/1.63 % (25687)Instruction limit reached!
% 2.94/1.63 % (25687)------------------------------
% 2.94/1.63 % (25687)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/1.63 % (25687)Termination reason: Unknown
% 2.94/1.63 % (25687)Termination phase: shuffling
% 2.94/1.63
% 2.94/1.63 % (25687)Memory used [KB]: 1535
% 2.94/1.63 % (25687)Time elapsed: 0.002 s
% 2.94/1.63 % (25687)Instructions burned: 3 (million)
% 2.94/1.63 % (25687)------------------------------
% 2.94/1.63 % (25687)------------------------------
% 2.94/1.64 % (25689)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_25458 for (2999ds/18Mi)
% 2.94/1.64 % (25691)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_25458 for (2999ds/6Mi)
% 2.94/1.64 % (25688)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_25458 for (2999ds/4Mi)
% 2.94/1.64 % (25691)Instruction limit reached!
% 2.94/1.64 % (25691)------------------------------
% 2.94/1.64 % (25691)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/1.64 % (25691)Termination reason: Unknown
% 2.94/1.64 % (25691)Termination phase: shuffling
% 2.94/1.64
% 2.94/1.64 % (25691)Memory used [KB]: 1535
% 2.94/1.64 % (25691)Time elapsed: 0.003 s
% 2.94/1.64 % (25691)Instructions burned: 6 (million)
% 2.94/1.64 % (25691)------------------------------
% 2.94/1.64 % (25691)------------------------------
% 2.94/1.64 % (25688)Instruction limit reached!
% 2.94/1.64 % (25688)------------------------------
% 2.94/1.64 % (25688)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/1.64 % (25688)Termination reason: Unknown
% 2.94/1.64 % (25688)Termination phase: shuffling
% 2.94/1.64
% 2.94/1.64 % (25688)Memory used [KB]: 1535
% 2.94/1.64 % (25688)Time elapsed: 0.005 s
% 2.94/1.64 % (25688)Instructions burned: 5 (million)
% 2.94/1.64 % (25688)------------------------------
% 2.94/1.64 % (25688)------------------------------
% 2.94/1.64 % (25689)Instruction limit reached!
% 2.94/1.64 % (25689)------------------------------
% 2.94/1.64 % (25689)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/1.64 % (25689)Termination reason: Unknown
% 2.94/1.64 % (25689)Termination phase: shuffling
% 2.94/1.64
% 2.94/1.64 % (25689)Memory used [KB]: 1791
% 2.94/1.64 % (25689)Time elapsed: 0.007 s
% 2.94/1.64 % (25689)Instructions burned: 19 (million)
% 2.94/1.64 % (25689)------------------------------
% 2.94/1.64 % (25689)------------------------------
% 2.94/1.65 % (25690)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_25458 for (2999ds/710Mi)
% 2.94/1.65 % (25692)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_25458 for (2999ds/902Mi)
% 2.94/1.65 % (25694)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_25458 for (2999ds/5Mi)
% 2.94/1.66 % (25694)Instruction limit reached!
% 2.94/1.66 % (25694)------------------------------
% 2.94/1.66 % (25694)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/1.66 % (25694)Termination reason: Unknown
% 2.94/1.66 % (25694)Termination phase: shuffling
% 2.94/1.66
% 2.94/1.66 % (25694)Memory used [KB]: 1663
% 2.94/1.66 % (25694)Time elapsed: 0.003 s
% 2.94/1.66 % (25694)Instructions burned: 7 (million)
% 2.94/1.66 % (25694)------------------------------
% 2.94/1.66 % (25694)------------------------------
% 2.94/1.66 % (25693)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_25458 for (2999ds/21Mi)
% 2.94/1.67 % (25695)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_25458 for (2999ds/6Mi)
% 2.94/1.67 % (25695)Instruction limit reached!
% 2.94/1.67 % (25695)------------------------------
% 2.94/1.67 % (25695)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/1.67 % (25695)Termination reason: Unknown
% 2.94/1.67 % (25695)Termination phase: shuffling
% 2.94/1.67
% 2.94/1.67 % (25695)Memory used [KB]: 1663
% 2.94/1.67 % (25695)Time elapsed: 0.004 s
% 2.94/1.67 % (25695)Instructions burned: 9 (million)
% 2.94/1.67 % (25695)------------------------------
% 2.94/1.67 % (25695)------------------------------
% 2.94/1.67 % (25693)Instruction limit reached!
% 2.94/1.67 % (25693)------------------------------
% 2.94/1.67 % (25693)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/1.67 % (25693)Termination reason: Unknown
% 2.94/1.67 % (25693)Termination phase: shuffling
% 2.94/1.67
% 2.94/1.67 % (25693)Memory used [KB]: 1791
% 2.94/1.67 % (25693)Time elapsed: 0.015 s
% 2.94/1.67 % (25693)Instructions burned: 21 (million)
% 2.94/1.67 % (25693)------------------------------
% 2.94/1.67 % (25693)------------------------------
% 2.94/1.68 % (25696)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_25458 for (2998ds/377Mi)
% 2.94/1.68 % (25670)Instruction limit reached!
% 2.94/1.68 % (25670)------------------------------
% 2.94/1.68 % (25670)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/1.68 % (25670)Termination reason: Unknown
% 2.94/1.68 % (25670)Termination phase: Saturation
% 2.94/1.68
% 2.94/1.68 % (25670)Memory used [KB]: 7419
% 2.94/1.68 % (25670)Time elapsed: 0.099 s
% 2.94/1.68 % (25670)Instructions burned: 184 (million)
% 2.94/1.68 % (25670)------------------------------
% 2.94/1.68 % (25670)------------------------------
% 2.94/1.69 % (25697)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_25458 for (2998ds/779Mi)
% 2.94/1.70 % (25698)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_25458 for (2998ds/19Mi)
% 2.94/1.70 % (25675)Instruction limit reached!
% 2.94/1.70 % (25675)------------------------------
% 2.94/1.70 % (25675)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/1.70 % (25675)Termination reason: Unknown
% 2.94/1.70 % (25675)Termination phase: Saturation
% 2.94/1.70
% 2.94/1.70 % (25675)Memory used [KB]: 8571
% 2.94/1.70 % (25675)Time elapsed: 0.114 s
% 2.94/1.70 % (25675)Instructions burned: 275 (million)
% 2.94/1.70 % (25675)------------------------------
% 2.94/1.70 % (25675)------------------------------
% 2.94/1.71 % (25698)Instruction limit reached!
% 2.94/1.71 % (25698)------------------------------
% 2.94/1.71 % (25698)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/1.71 % (25698)Termination reason: Unknown
% 2.94/1.71 % (25698)Termination phase: shuffling
% 2.94/1.71
% 2.94/1.71 % (25698)Memory used [KB]: 1918
% 2.94/1.71 % (25698)Time elapsed: 0.008 s
% 2.94/1.71 % (25698)Instructions burned: 19 (million)
% 2.94/1.71 % (25698)------------------------------
% 2.94/1.71 % (25698)------------------------------
% 2.94/1.71 % (25699)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_25458 for (2998ds/879Mi)
% 2.94/1.72 % (25700)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_25458 for (2998ds/17Mi)
% 2.94/1.72 % (25700)Instruction limit reached!
% 2.94/1.72 % (25700)------------------------------
% 2.94/1.72 % (25700)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/1.72 % (25700)Termination reason: Unknown
% 2.94/1.72 % (25700)Termination phase: shuffling
% 2.94/1.72
% 2.94/1.72 % (25700)Memory used [KB]: 1791
% 2.94/1.72 % (25700)Time elapsed: 0.008 s
% 2.94/1.72 % (25700)Instructions burned: 18 (million)
% 2.94/1.72 % (25700)------------------------------
% 2.94/1.72 % (25700)------------------------------
% 2.94/1.73 % (25701)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_25458 for (2998ds/3Mi)
% 2.94/1.73 % (25701)Instruction limit reached!
% 2.94/1.73 % (25701)------------------------------
% 2.94/1.73 % (25701)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/1.73 % (25701)Termination reason: Unknown
% 2.94/1.73 % (25701)Termination phase: shuffling
% 2.94/1.73
% 2.94/1.73 % (25701)Memory used [KB]: 1407
% 2.94/1.73 % (25701)Time elapsed: 0.003 s
% 2.94/1.73 % (25701)Instructions burned: 4 (million)
% 2.94/1.73 % (25701)------------------------------
% 2.94/1.73 % (25701)------------------------------
% 2.94/1.74 % (25702)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_25458 for (2998ds/30Mi)
% 2.94/1.76 % (25702)Instruction limit reached!
% 2.94/1.76 % (25702)------------------------------
% 2.94/1.76 % (25702)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/1.76 % (25702)Termination reason: Unknown
% 2.94/1.76 % (25702)Termination phase: shuffling
% 2.94/1.76
% 2.94/1.76 % (25702)Memory used [KB]: 2046
% 2.94/1.76 % (25702)Time elapsed: 0.013 s
% 2.94/1.76 % (25702)Instructions burned: 32 (million)
% 2.94/1.76 % (25702)------------------------------
% 2.94/1.76 % (25702)------------------------------
% 2.94/1.76 % (25681)First to succeed.
% 2.94/1.77 % (25681)Refutation found. Thanks to Tanya!
% 2.94/1.77 % SZS status ContradictoryAxioms for DTF2THF_25458
% 2.94/1.77 % SZS output start Proof for DTF2THF_25458
% 2.94/1.77 thf(type_def_5, type, name: $tType).
% 2.94/1.77 thf(type_def_6, type, pi: $tType).
% 2.94/1.77 thf(type_def_8, type, product_prod: ($tType * $tType) > $tType).
% 2.94/1.77 thf(type_def_9, type, late_freeRes: $tType).
% 2.94/1.77 thf(type_def_10, type, late_subject: $tType).
% 2.94/1.77 thf(type_def_11, type, late_residual: $tType).
% 2.94/1.77 thf(type_def_12, type, late_residual_Rep: $tType).
% 2.94/1.77 thf(type_def_13, type, list: ($tType) > $tType).
% 2.94/1.77 thf(type_def_14, type, noption: ($tType) > $tType).
% 2.94/1.77 thf(type_def_15, type, set: ($tType) > $tType).
% 2.94/1.77 thf(type_def_16, type, product_unit: $tType).
% 2.94/1.77 thf(type_def_17, type, pi_Rep: $tType).
% 2.94/1.77 thf(type_def_18, type, late_freeRes_Rep: $tType).
% 2.94/1.77 thf(type_def_19, type, late_subject_Rep: $tType).
% 2.94/1.77 thf(func_def_0, type, late_residual_Rep: $tType).
% 2.94/1.77 thf(func_def_1, type, late_subject_Rep: $tType).
% 2.94/1.77 thf(func_def_2, type, late_freeRes_Rep: $tType).
% 2.94/1.77 thf(func_def_3, type, late_residual: $tType).
% 2.94/1.77 thf(func_def_4, type, late_subject: $tType).
% 2.94/1.77 thf(func_def_5, type, late_freeRes: $tType).
% 2.94/1.77 thf(func_def_6, type, product_unit: $tType).
% 2.94/1.77 thf(func_def_7, type, product_prod: ($tType * $tType) > $tType).
% 2.94/1.77 thf(func_def_8, type, noption: ($tType) > $tType).
% 2.94/1.77 thf(func_def_9, type, pi_Rep: $tType).
% 2.94/1.77 thf(func_def_10, type, name: $tType).
% 2.94/1.77 thf(func_def_11, type, list: ($tType) > $tType).
% 2.94/1.77 thf(func_def_12, type, pi: $tType).
% 2.94/1.77 thf(func_def_13, type, set: ($tType) > $tType).
% 2.94/1.77 thf(func_def_14, type, type: !>[X0: $tType]:($o)).
% 2.94/1.77 thf(func_def_15, type, fs_name: !>[X0: $tType]:($o)).
% 2.94/1.77 thf(func_def_16, type, pt_name: !>[X0: $tType]:($o)).
% 2.94/1.77 thf(func_def_17, type, ord: !>[X0: $tType]:($o)).
% 2.94/1.77 thf(func_def_18, type, cp_name_name: !>[X0: $tType]:($o)).
% 2.94/1.77 thf(func_def_19, type, linorder: !>[X0: $tType]:($o)).
% 2.94/1.77 thf(func_def_20, type, input: name > name > pi > pi).
% 2.94/1.77 thf(func_def_21, type, par: pi > pi > pi).
% 2.94/1.77 thf(func_def_22, type, res: name > pi > pi).
% 2.94/1.77 thf(func_def_23, type, swap_name: product_prod @ name @ name > name > name).
% 2.94/1.77 thf(func_def_24, type, subs: pi > name > name > pi).
% 2.94/1.77 thf(func_def_25, type, default_default: !>[X0: $tType]:(X0)).
% 2.94/1.77 thf(func_def_26, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 2.94/1.77 thf(func_def_27, type, late_OutputR: name > name > late_freeRes).
% 2.94/1.77 thf(func_def_28, type, late_TauR: late_freeRes).
% 2.94/1.77 thf(func_def_29, type, late_BoundR: late_subject > name > pi > late_residual).
% 2.94/1.77 thf(func_def_30, type, late_FreeR: late_freeRes > pi > late_residual).
% 2.94/1.77 thf(func_def_31, type, late_r347633188eR_Rep: late_freeRes > pi > late_residual_Rep).
% 2.94/1.77 thf(func_def_32, type, late_BoundOutputS: name > late_subject).
% 2.94/1.77 thf(func_def_33, type, late_InputS: name > late_subject).
% 2.94/1.77 thf(func_def_34, type, late_transitions: pi > late_residual > $o).
% 2.94/1.77 thf(func_def_35, type, cons: !>[X0: $tType]:(X0 > list @ X0 > list @ X0)).
% 2.94/1.77 thf(func_def_36, type, nil: !>[X0: $tType]:(list @ X0)).
% 2.94/1.77 thf(func_def_37, type, product_lists: !>[X0: $tType]:(list @ list @ X0 > list @ list @ X0)).
% 2.94/1.77 thf(func_def_38, type, abs_fun: !>[X0: $tType, X1: $tType]:(X0 > X1 > X0 > noption @ X1)).
% 2.94/1.77 thf(func_def_39, type, fresh: !>[X0: $tType, X1: $tType]:(X0 > X1 > $o)).
% 2.94/1.77 thf(func_def_40, type, perm: !>[X0: $tType, X1: $tType]:(list @ product_prod @ X0 @ X0 > X1 > X1)).
% 2.94/1.77 thf(func_def_41, type, supports: !>[X0: $tType, X1: $tType]:(set @ X0 > X1 > $o)).
% 2.94/1.77 thf(func_def_42, type, swap: !>[X0: $tType]:(product_prod @ X0 @ X0 > X0 > X0)).
% 2.94/1.77 thf(func_def_43, type, product_Pair: !>[X0: $tType, X1: $tType]:(X0 > X1 > product_prod @ X0 @ X1)).
% 2.94/1.77 thf(func_def_44, type, product_Unity: product_unit).
% 2.94/1.77 thf(func_def_45, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2)).
% 2.94/1.77 thf(func_def_46, type, product_rec_unit: !>[X0: $tType]:(X0 > product_unit > X0)).
% 2.94/1.77 thf(func_def_47, type, eqvt: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > $o)).
% 2.94/1.77 thf(func_def_48, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 2.94/1.77 thf(func_def_49, type, strong2129052853vative: pi > pi > late_subject > name > set @ product_prod @ pi @ pi > $o).
% 2.94/1.77 thf(func_def_50, type, strong743114133lation: pi > set @ product_prod @ pi @ pi > pi > $o).
% 2.94/1.77 thf(func_def_51, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 2.94/1.77 thf(func_def_52, type, p: pi).
% 2.94/1.77 thf(func_def_53, type, pq: pi).
% 2.94/1.77 thf(func_def_54, type, p2: pi).
% 2.94/1.77 thf(func_def_55, type, q: pi).
% 2.94/1.77 thf(func_def_56, type, q2: pi).
% 2.94/1.77 thf(func_def_57, type, rel: set @ product_prod @ pi @ pi).
% 2.94/1.77 thf(func_def_58, type, aa: late_subject).
% 2.94/1.77 thf(func_def_59, type, ab: name).
% 2.94/1.77 thf(func_def_60, type, b: name).
% 2.94/1.77 thf(func_def_61, type, c: name).
% 2.94/1.77 thf(func_def_62, type, x: name).
% 2.94/1.77 thf(func_def_63, type, xPQ: pi).
% 2.94/1.77 thf(func_def_64, type, y: name).
% 2.94/1.77 thf(func_def_65, type, ya: name).
% 2.94/1.77 thf(func_def_88, type, ph1: !>[X0: $tType]:(X0)).
% 2.94/1.77 thf(f2317,plain,(
% 2.94/1.77 $false),
% 2.94/1.77 inference(equality_resolution,[status(thm)],[f2308])).
% 2.94/1.77 thf(f2308,plain,(
% 2.94/1.77 ( ! [X2 : name,X1 : name] : (((late_OutputR @ ab @ x) != (late_OutputR @ X2 @ X1))) )),
% 2.94/1.77 inference(equality_proxy_clausification,[status(thm)],[f2297])).
% 2.94/1.77 thf(f2297,plain,(
% 2.94/1.77 ( ! [X2 : name,X1 : name] : (($false = ((late_OutputR @ ab @ x) = (late_OutputR @ X2 @ X1)))) )),
% 2.94/1.77 inference(not_proxy_clausification,[status(thm)],[f2280])).
% 2.94/1.77 thf(f2280,plain,(
% 2.94/1.77 ( ! [X2 : name,X1 : name] : (($true = (~ ((late_OutputR @ ab @ x) = (late_OutputR @ X2 @ X1))))) )),
% 2.94/1.77 inference(beta_eta_normalization,[status(thm)],[f2279])).
% 2.94/1.77 thf(f2279,plain,(
% 2.94/1.77 ( ! [X2 : name,X1 : name] : (($true = ((^[Y0 : name]: (~ ((late_OutputR @ ab @ x) = (late_OutputR @ Y0 @ X1)))) @ X2))) )),
% 2.94/1.77 inference(pi_clausification,[status(thm)],[f2262])).
% 2.94/1.77 thf(f2262,plain,(
% 2.94/1.77 ( ! [X1 : name] : (($true = (!! @ name @ (^[Y0 : name]: (~ ((late_OutputR @ ab @ x) = (late_OutputR @ Y0 @ X1))))))) )),
% 2.94/1.77 inference(beta_eta_normalization,[status(thm)],[f2261])).
% 2.94/1.77 thf(f2261,plain,(
% 2.94/1.77 ( ! [X1 : name] : (($true = ((^[Y0 : name]: (!! @ name @ (^[Y1 : name]: (~ ((late_OutputR @ ab @ x) = (late_OutputR @ Y1 @ Y0)))))) @ X1))) )),
% 2.94/1.77 inference(pi_clausification,[status(thm)],[f1433])).
% 2.94/1.77 thf(f1433,plain,(
% 2.94/1.77 ($true = (!! @ name @ (^[Y0 : name]: (!! @ name @ (^[Y1 : name]: (~ ((late_OutputR @ ab @ x) = (late_OutputR @ Y1 @ Y0))))))))),
% 2.94/1.77 inference(definition_unfolding,[status(thm)],[f1273,f1131])).
% 2.94/1.77 thf(f1131,plain,(
% 2.94/1.77 ((late_OutputR @ ab @ x) = late_TauR)),
% 2.94/1.77 inference(cnf_transformation,[status(thm)],[f777])).
% 2.94/1.77 thf(f777,plain,(
% 2.94/1.77 ((late_OutputR @ ab @ x) = late_TauR)),
% 2.94/1.77 inference(fool_elimination,[status(thm)],[f2])).
% 2.94/1.77 thf(f2,axiom,(
% 2.94/1.77 ((late_OutputR @ ab @ x) = late_TauR)),
% 2.94/1.77 file('/export/starexec/sandbox2/tmp/tmp.l6Rd1czx4d/DTF2THF_25458.p',fact_1_cComm1_Ohyps_I9_J)).
% 2.94/1.77 thf(f1273,plain,(
% 2.94/1.77 ((!! @ name @ (^[Y0 : name]: (!! @ name @ (^[Y1 : name]: (~ (late_TauR = (late_OutputR @ Y1 @ Y0))))))) = $true)),
% 2.94/1.77 inference(cnf_transformation,[status(thm)],[f581])).
% 2.94/1.77 thf(f581,plain,(
% 2.94/1.77 ((!! @ name @ (^[Y0 : name]: (!! @ name @ (^[Y1 : name]: (~ (late_TauR = (late_OutputR @ Y1 @ Y0))))))) = $true)),
% 2.94/1.77 inference(fool_elimination,[status(thm)],[f580])).
% 2.94/1.77 thf(f580,plain,(
% 2.94/1.77 ! [X0 : name,X1 : name] : (late_TauR != (late_OutputR @ X0 @ X1))),
% 2.94/1.77 inference(rectify,[status(thm)],[f179])).
% 2.94/1.77 thf(f179,axiom,(
% 2.94/1.77 ! [X96 : name,X97 : name] : (late_TauR != (late_OutputR @ X96 @ X97))),
% 2.94/1.77 file('/export/starexec/sandbox2/tmp/tmp.l6Rd1czx4d/DTF2THF_25458.p',fact_178_Late__Semantics1_OfreeRes_Odistinct_I1_J)).
% 2.94/1.77 % SZS output end Proof for DTF2THF_25458
% 2.94/1.77 % (25681)------------------------------
% 2.94/1.77 % (25681)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/1.77 % (25681)Termination reason: Refutation
% 2.94/1.77
% 2.94/1.77 % (25681)Memory used [KB]: 9466
% 2.94/1.77 % (25681)Time elapsed: 0.165 s
% 2.94/1.77 % (25681)Instructions burned: 553 (million)
% 2.94/1.77 % (25681)------------------------------
% 2.94/1.77 % (25681)------------------------------
% 2.94/1.77 % (25669)Success in time 0.198 s
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