%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP182^2 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n019.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 08:56:13 AM UTC 2026
% Result : Theorem 4.64s 2.05s
% Output : Refutation 4.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP182^2 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n019.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 08:29:09 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : ITP182^2 : TPTP v9.2.1. Released v7.5.0.
% 0.30/0.46 % Domain : Interactive Theorem Proving
% 0.30/0.46 % Problem : Sledgehammer Strong_Late_Sim_SC problem prob_279__3411076_1
% 0.30/0.46 % Version : Especial.
% 0.30/0.46 % English :
% 0.30/0.46
% 0.30/0.46 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.30/0.46 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.30/0.46 % Source : [Des21]
% 0.30/0.46 % Names : Strong_Late_Sim_SC/prob_279__3411076_1 [Des21]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % Rating : 0.00 v7.5.0
% 0.30/0.46 % Syntax : Number of formulae : 362 ( 142 unt; 57 typ; 0 def)
% 0.30/0.46 % Number of atoms : 737 ( 247 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 17 ( 2 avg)
% 0.30/0.46 % Number of connectives : 4949 ( 117 ~; 4 |; 44 &;4374 @)
% 0.30/0.46 % ( 0 <=>; 410 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 28 ( 8 avg)
% 0.30/0.46 % Number of types : 10 ( 9 usr)
% 0.30/0.46 % Number of type conns : 203 ( 203 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 51 ( 48 usr; 11 con; 0-5 aty)
% 0.30/0.46 % Number of variables : 1249 ( 36 ^;1167 !; 15 ?;1249 :)
% 0.30/0.46 % ( 31 !>; 0 ?*; 0 @-; 0 @+)
% 0.30/0.46 % SPC : TH1_THM_EQU_NAR
% 0.30/0.46
% 0.30/0.46 % Comments : This file was generated by Sledgehammer 2021-02-23 16:16:02.313
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % Could-be-implicit typings (12)
% 0.30/0.46 thf(ty_t_Late__Semantics_Oresidual__Rep,type,
% 0.30/0.46 late_residual_Rep: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_t_Late__Semantics_Osubject__Rep,type,
% 0.30/0.46 late_subject_Rep: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_t_Late__Semantics_OfreeRes__Rep,type,
% 0.30/0.46 late_freeRes_Rep: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_t_Late__Semantics_Oresidual,type,
% 0.30/0.46 late_residual: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_t_Late__Semantics_Osubject,type,
% 0.30/0.46 late_subject: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_t_Late__Semantics_OfreeRes,type,
% 0.30/0.46 late_freeRes: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_t_Product__Type_Oprod,type,
% 0.30/0.46 product_prod: $tType > $tType > $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_t_Agent_Opi__Rep,type,
% 0.30/0.46 pi_Rep: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_t_Agent_Oname,type,
% 0.30/0.46 name: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_t_List_Olist,type,
% 0.30/0.46 list: $tType > $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_t_Agent_Opi,type,
% 0.30/0.46 pi: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_t_Set_Oset,type,
% 0.30/0.46 set: $tType > $tType ).
% 0.30/0.46
% 0.30/0.46 % Explicit typings (45)
% 0.30/0.46 thf(sy_cl_HOL_Otype,type,
% 0.30/0.46 type:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Agent_Ofs__name,type,
% 0.30/0.46 fs_name:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Agent_Opt__name,type,
% 0.30/0.46 pt_name:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Orderings_Oord,type,
% 0.30/0.46 ord:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Orderings_Oorder,type,
% 0.30/0.46 order:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Agent_Ocp__name__name,type,
% 0.30/0.46 cp_name_name:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Orderings_Olinorder,type,
% 0.30/0.46 linorder:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Orderings_Opreorder,type,
% 0.30/0.46 preorder:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Agent_Opi_OInput,type,
% 0.30/0.46 input: name > name > pi > pi ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Agent_Opi_ORes,type,
% 0.30/0.46 res: name > pi > pi ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Agent_Opi_OSum,type,
% 0.30/0.46 sum: pi > pi > pi ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_BNF__Greatest__Fixpoint_Oshift,type,
% 0.30/0.46 bNF_Greatest_shift:
% 0.30/0.46 !>[A: $tType,B: $tType] : ( ( ( list @ A ) > B ) > A > ( list @ A ) > B ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_If,type,
% 0.30/0.46 if:
% 0.30/0.46 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Late__Semantics_OfreeRes_OOutputR,type,
% 0.30/0.46 late_OutputR: name > name > late_freeRes ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Late__Semantics_Oresidual_OBoundR,type,
% 0.30/0.46 late_BoundR: late_subject > name > pi > late_residual ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Late__Semantics_Oresidual_OFreeR,type,
% 0.30/0.46 late_FreeR: late_freeRes > pi > late_residual ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Late__Semantics_Oresidual__Rep_OFreeR__Rep,type,
% 0.30/0.46 late_r347633188eR_Rep: late_freeRes > pi > late_residual_Rep ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Late__Semantics_Osubject_OBoundOutputS,type,
% 0.30/0.46 late_BoundOutputS: name > late_subject ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Late__Semantics_Osubject_OInputS,type,
% 0.30/0.46 late_InputS: name > late_subject ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Late__Semantics_Otransitions,type,
% 0.30/0.46 late_transitions: pi > late_residual > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List_Olist_OCons,type,
% 0.30/0.46 cons:
% 0.30/0.46 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List_Olist_ONil,type,
% 0.30/0.46 nil:
% 0.30/0.46 !>[A: $tType] : ( list @ A ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List_Oproduct__lists,type,
% 0.30/0.46 product_lists:
% 0.30/0.46 !>[A: $tType] : ( ( list @ ( list @ A ) ) > ( list @ ( list @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Nominal_Ofresh,type,
% 0.30/0.46 fresh:
% 0.30/0.46 !>[X: $tType,A: $tType] : ( X > A > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Nominal_Operm,type,
% 0.30/0.46 perm:
% 0.30/0.46 !>[X: $tType,A: $tType] : ( ( list @ ( product_prod @ X @ X ) ) > A > A ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Nominal_Osupports,type,
% 0.30/0.46 supports:
% 0.30/0.46 !>[X: $tType,A: $tType] : ( ( set @ X ) > A > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Nominal_Oswap,type,
% 0.30/0.46 swap:
% 0.30/0.46 !>[X: $tType] : ( ( product_prod @ X @ X ) > X > X ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.30/0.46 ord_less_eq:
% 0.30/0.46 !>[A: $tType] : ( A > A > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Product__Type_OPair,type,
% 0.30/0.46 product_Pair:
% 0.30/0.46 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod,type,
% 0.30/0.46 product_rec_prod:
% 0.30/0.46 !>[A: $tType,B: $tType,T: $tType] : ( ( A > B > T ) > ( product_prod @ A @ B ) > T ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Rel_Oeqvt,type,
% 0.30/0.46 eqvt:
% 0.30/0.46 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Relation_OId,type,
% 0.30/0.46 id:
% 0.30/0.46 !>[A: $tType] : ( set @ ( product_prod @ A @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Set_OCollect,type,
% 0.30/0.46 collect:
% 0.30/0.46 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Strong__Late__Sim_Oderivative,type,
% 0.30/0.46 strong2129052853vative: pi > pi > late_subject > name > ( set @ ( product_prod @ pi @ pi ) ) > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Strong__Late__Sim_Osimulation,type,
% 0.30/0.46 strong743114133lation: pi > ( set @ ( product_prod @ pi @ pi ) ) > pi > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_member,type,
% 0.30/0.46 member:
% 0.30/0.46 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_P,type,
% 0.30/0.46 p: pi ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_PQ____,type,
% 0.30/0.46 pq: pi ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_P_H____,type,
% 0.30/0.46 p2: pi ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_Q,type,
% 0.30/0.46 q: pi ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_Rel,type,
% 0.30/0.46 rel: set @ ( product_prod @ pi @ pi ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_a____,type,
% 0.30/0.46 a: late_subject ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_aa____,type,
% 0.30/0.46 aa: name ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_x,type,
% 0.30/0.46 x: name ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_y____,type,
% 0.30/0.46 y: name ).
% 0.30/0.46
% 0.30/0.46 % Relevant facts (255)
% 0.30/0.46 thf(fact_0_Id,axiom,
% 0.30/0.46 ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ rel ).
% 0.30/0.46
% 0.30/0.46 % Id
% 0.30/0.46 thf(fact_1_cOpen_Ohyps_I2_J,axiom,
% 0.30/0.46 aa != x ).
% 0.30/0.46
% 0.30/0.46 % cOpen.hyps(2)
% 0.30/0.46 thf(fact_2_cOpen_Ohyps_I3_J,axiom,
% 0.30/0.46 ( a
% 0.30/0.46 = ( late_BoundOutputS @ aa ) ) ).
% 0.30/0.46
% 0.30/0.46 % cOpen.hyps(3)
% 0.30/0.46 thf(fact_3__092_060open_062y_A_092_060noteq_062_Ax_092_060close_062,axiom,
% 0.30/0.46 y != x ).
% 0.30/0.46
% 0.30/0.46 % \<open>y \<noteq> x\<close>
% 0.30/0.46 thf(fact_4_Eqvt,axiom,
% 0.30/0.46 eqvt @ pi @ rel ).
% 0.30/0.46
% 0.30/0.46 % Eqvt
% 0.30/0.46 thf(fact_5_perm__swap_I1_J,axiom,
% 0.30/0.46 ! [X2: $tType] :
% 0.30/0.46 ( ( pt_name @ X2 )
% 0.30/0.46 => ! [A2: name,B2: name,X3: X2] :
% 0.30/0.46 ( ( perm @ name @ X2 @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ ( perm @ name @ X2 @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ X3 ) )
% 0.30/0.46 = X3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % perm_swap(1)
% 0.30/0.46 thf(fact_6_name__id,axiom,
% 0.30/0.46 ! [X: $tType] :
% 0.30/0.46 ( ( pt_name @ X )
% 0.30/0.46 => ! [A2: name,X3: X] :
% 0.30/0.46 ( ( perm @ name @ X @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ A2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ X3 )
% 0.30/0.46 = X3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % name_id
% 0.30/0.46 thf(fact_7_name__swap,axiom,
% 0.30/0.46 ! [X: $tType] :
% 0.30/0.46 ( ( pt_name @ X )
% 0.30/0.46 => ! [A2: name,B2: name,X3: X] :
% 0.30/0.46 ( ( perm @ name @ X @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ X3 )
% 0.30/0.46 = ( perm @ name @ X @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ B2 @ A2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ X3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % name_swap
% 0.30/0.46 thf(fact_8_name__swap__bij,axiom,
% 0.30/0.46 ! [X: $tType] :
% 0.30/0.46 ( ( pt_name @ X )
% 0.30/0.46 => ! [A2: name,B2: name,X3: X] :
% 0.30/0.46 ( ( perm @ name @ X @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ ( perm @ name @ X @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ X3 ) )
% 0.30/0.46 = X3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % name_swap_bij
% 0.30/0.46 thf(fact_9_pt__name1,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( pt_name @ A )
% 0.30/0.46 => ! [X3: A] :
% 0.30/0.46 ( ( perm @ name @ A @ ( nil @ ( product_prod @ name @ name ) ) @ X3 )
% 0.30/0.46 = X3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % pt_name1
% 0.30/0.46 thf(fact_10_perm__swap_I2_J,axiom,
% 0.30/0.46 ! [X2: $tType] :
% 0.30/0.46 ( ( pt_name @ X2 )
% 0.30/0.46 => ! [A2: name,B2: name,X3: X2] :
% 0.30/0.46 ( ( perm @ name @ X2 @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ ( perm @ name @ X2 @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ B2 @ A2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ X3 ) )
% 0.30/0.46 = X3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % perm_swap(2)
% 0.30/0.46 thf(fact_11_Late__Semantics_Osubject_Oinject_I2_J,axiom,
% 0.30/0.46 ! [X1: name,Y1: name] :
% 0.30/0.46 ( ( ( late_BoundOutputS @ X1 )
% 0.30/0.46 = ( late_BoundOutputS @ Y1 ) )
% 0.30/0.46 = ( X1 = Y1 ) ) ).
% 0.30/0.46
% 0.30/0.46 % Late_Semantics.subject.inject(2)
% 0.30/0.46 thf(fact_12_Late__Semantics1_Osubject_Oinject_I2_J,axiom,
% 0.30/0.46 ! [X22: name,Y2: name] :
% 0.30/0.46 ( ( ( late_BoundOutputS @ X22 )
% 0.30/0.46 = ( late_BoundOutputS @ Y2 ) )
% 0.30/0.46 = ( X22 = Y2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % Late_Semantics1.subject.inject(2)
% 0.30/0.46 thf(fact_13__092_060open_062y_A_092_060sharp_062_AP_H_092_060close_062,axiom,
% 0.30/0.46 fresh @ name @ pi @ y @ p2 ).
% 0.30/0.46
% 0.30/0.46 % \<open>y \<sharp> P'\<close>
% 0.30/0.46 thf(fact_14_list_Oinject,axiom,
% 0.30/0.46 ! [A: $tType,X21: A,X222: list @ A,Y21: A,Y22: list @ A] :
% 0.30/0.46 ( ( ( cons @ A @ X21 @ X222 )
% 0.30/0.46 = ( cons @ A @ Y21 @ Y22 ) )
% 0.30/0.46 = ( ( X21 = Y21 )
% 0.30/0.46 & ( X222 = Y22 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % list.inject
% 0.30/0.46 thf(fact_15_prod_Oinject,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,X1: A,X22: B,Y1: A,Y2: B] :
% 0.30/0.46 ( ( ( product_Pair @ A @ B @ X1 @ X22 )
% 0.30/0.46 = ( product_Pair @ A @ B @ Y1 @ Y2 ) )
% 0.30/0.46 = ( ( X1 = Y1 )
% 0.30/0.46 & ( X22 = Y2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod.inject
% 0.30/0.46 thf(fact_16_old_Oprod_Oinject,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,A2: A,B2: B,A3: A,B3: B] :
% 0.30/0.46 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 0.30/0.46 = ( product_Pair @ A @ B @ A3 @ B3 ) )
% 0.30/0.46 = ( ( A2 = A3 )
% 0.30/0.46 & ( B2 = B3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % old.prod.inject
% 0.30/0.46 thf(fact_17_residual__perm__empty,axiom,
% 0.30/0.46 ! [Residual_Rep: late_residual_Rep] :
% 0.30/0.46 ( ( perm @ name @ late_residual_Rep @ ( nil @ ( product_prod @ name @ name ) ) @ Residual_Rep )
% 0.30/0.46 = Residual_Rep ) ).
% 0.30/0.46
% 0.30/0.46 % residual_perm_empty
% 0.30/0.46 thf(fact_18_subject__perm__empty,axiom,
% 0.30/0.46 ! [Subject_Rep: late_subject_Rep] :
% 0.30/0.46 ( ( perm @ name @ late_subject_Rep @ ( nil @ ( product_prod @ name @ name ) ) @ Subject_Rep )
% 0.30/0.46 = Subject_Rep ) ).
% 0.30/0.46
% 0.30/0.46 % subject_perm_empty
% 0.30/0.46 thf(fact_19_freeRes__perm__empty,axiom,
% 0.30/0.46 ! [FreeRes_Rep: late_freeRes_Rep] :
% 0.30/0.46 ( ( perm @ name @ late_freeRes_Rep @ ( nil @ ( product_prod @ name @ name ) ) @ FreeRes_Rep )
% 0.30/0.46 = FreeRes_Rep ) ).
% 0.30/0.46
% 0.30/0.46 % freeRes_perm_empty
% 0.30/0.46 thf(fact_20_pi__perm__empty,axiom,
% 0.30/0.46 ! [Pi_Rep: pi_Rep] :
% 0.30/0.46 ( ( perm @ name @ pi_Rep @ ( nil @ ( product_prod @ name @ name ) ) @ Pi_Rep )
% 0.30/0.46 = Pi_Rep ) ).
% 0.30/0.46
% 0.30/0.46 % pi_perm_empty
% 0.30/0.46 thf(fact_21_subject_Operm_I2_J,axiom,
% 0.30/0.46 ! [Pi: list @ ( product_prod @ name @ name ),X1: name] :
% 0.30/0.46 ( ( perm @ name @ late_subject @ Pi @ ( late_BoundOutputS @ X1 ) )
% 0.30/0.46 = ( late_BoundOutputS @ ( perm @ name @ name @ Pi @ X1 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subject.perm(2)
% 0.30/0.46 thf(fact_22_perm__fresh__fresh,axiom,
% 0.30/0.46 ! [X2: $tType] :
% 0.30/0.46 ( ( pt_name @ X2 )
% 0.30/0.46 => ! [A2: name,X3: X2,B2: name] :
% 0.30/0.46 ( ( fresh @ name @ X2 @ A2 @ X3 )
% 0.30/0.46 => ( ( fresh @ name @ X2 @ B2 @ X3 )
% 0.30/0.46 => ( ( perm @ name @ X2 @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ X3 )
% 0.30/0.46 = X3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % perm_fresh_fresh
% 0.30/0.46 thf(fact_23_name__fresh__fresh,axiom,
% 0.30/0.46 ! [X: $tType] :
% 0.30/0.46 ( ( pt_name @ X )
% 0.30/0.46 => ! [A2: name,X3: X,B2: name] :
% 0.30/0.46 ( ( fresh @ name @ X @ A2 @ X3 )
% 0.30/0.46 => ( ( fresh @ name @ X @ B2 @ X3 )
% 0.30/0.46 => ( ( perm @ name @ X @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ X3 )
% 0.30/0.46 = X3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % name_fresh_fresh
% 0.30/0.46 thf(fact_24_Bound_Ohyps_I4_J,axiom,
% 0.30/0.46 fresh @ name @ late_subject @ y @ a ).
% 0.30/0.46
% 0.30/0.46 % Bound.hyps(4)
% 0.30/0.46 thf(fact_25_subseteq__eqvt,axiom,
% 0.30/0.46 ! [X2: $tType] :
% 0.30/0.46 ( ( pt_name @ X2 )
% 0.30/0.46 => ! [Pi: list @ ( product_prod @ name @ name ),X4: set @ X2,Y: set @ X2] :
% 0.30/0.46 ( ( perm @ name @ $o @ Pi @ ( ord_less_eq @ ( set @ X2 ) @ X4 @ Y ) )
% 0.30/0.46 = ( ord_less_eq @ ( set @ X2 ) @ ( perm @ name @ ( set @ X2 ) @ Pi @ X4 ) @ ( perm @ name @ ( set @ X2 ) @ Pi @ Y ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subseteq_eqvt
% 0.30/0.46 thf(fact_26_fresh__perm__app,axiom,
% 0.30/0.46 ! [X2: $tType] :
% 0.30/0.46 ( ( pt_name @ X2 )
% 0.30/0.46 => ! [A2: name,Pi: list @ ( product_prod @ name @ name ),X3: X2] :
% 0.30/0.46 ( ( fresh @ name @ ( list @ ( product_prod @ name @ name ) ) @ A2 @ Pi )
% 0.30/0.46 => ( ( fresh @ name @ X2 @ A2 @ X3 )
% 0.30/0.46 => ( fresh @ name @ X2 @ A2 @ ( perm @ name @ X2 @ Pi @ X3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % fresh_perm_app
% 0.30/0.46 thf(fact_27_name__exists__fresh,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( fs_name @ A )
% 0.30/0.46 => ! [X3: A] :
% 0.30/0.46 ~ ! [C: name] :
% 0.30/0.46 ~ ( fresh @ name @ A @ C @ X3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % name_exists_fresh
% 0.30/0.46 thf(fact_28_fresh__eqvt,axiom,
% 0.30/0.46 ! [X2: $tType] :
% 0.30/0.46 ( ( pt_name @ X2 )
% 0.30/0.46 => ! [Pi: list @ ( product_prod @ name @ name ),A2: name,X3: X2] :
% 0.30/0.46 ( ( perm @ name @ $o @ Pi @ ( fresh @ name @ X2 @ A2 @ X3 ) )
% 0.30/0.46 = ( fresh @ name @ X2 @ ( perm @ name @ name @ Pi @ A2 ) @ ( perm @ name @ X2 @ Pi @ X3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % fresh_eqvt
% 0.30/0.46 thf(fact_29_fresh__bij,axiom,
% 0.30/0.46 ! [X2: $tType] :
% 0.30/0.46 ( ( pt_name @ X2 )
% 0.30/0.46 => ! [Pi: list @ ( product_prod @ name @ name ),A2: name,X3: X2] :
% 0.30/0.46 ( ( fresh @ name @ X2 @ ( perm @ name @ name @ Pi @ A2 ) @ ( perm @ name @ X2 @ Pi @ X3 ) )
% 0.30/0.46 = ( fresh @ name @ X2 @ A2 @ X3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % fresh_bij
% 0.30/0.46 thf(fact_30_map__tailrec__rev_Ocases,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,X3: product_prod @ ( A > B ) @ ( product_prod @ ( list @ A ) @ ( list @ B ) )] :
% 0.30/0.46 ( ! [F: A > B,Bs: list @ B] :
% 0.30/0.46 ( X3
% 0.30/0.46 != ( product_Pair @ ( A > B ) @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ F @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ ( nil @ A ) @ Bs ) ) )
% 0.30/0.46 => ~ ! [F: A > B,A4: A,As: list @ A,Bs: list @ B] :
% 0.30/0.46 ( X3
% 0.30/0.46 != ( product_Pair @ ( A > B ) @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ F @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ ( cons @ A @ A4 @ As ) @ Bs ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % map_tailrec_rev.cases
% 0.30/0.46 thf(fact_31_name__calc_I2_J,axiom,
% 0.30/0.46 ! [X3: name] :
% 0.30/0.46 ( ( perm @ name @ name @ ( nil @ ( product_prod @ name @ name ) ) @ X3 )
% 0.30/0.46 = X3 ) ).
% 0.30/0.46
% 0.30/0.46 % name_calc(2)
% 0.30/0.46 thf(fact_32_arg__min__list_Ocases,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( linorder @ B )
% 0.30/0.46 => ! [X3: product_prod @ ( A > B ) @ ( list @ A )] :
% 0.30/0.46 ( ! [F: A > B,X5: A] :
% 0.30/0.46 ( X3
% 0.30/0.46 != ( product_Pair @ ( A > B ) @ ( list @ A ) @ F @ ( cons @ A @ X5 @ ( nil @ A ) ) ) )
% 0.30/0.46 => ( ! [F: A > B,X5: A,Y3: A,Zs: list @ A] :
% 0.30/0.46 ( X3
% 0.30/0.46 != ( product_Pair @ ( A > B ) @ ( list @ A ) @ F @ ( cons @ A @ X5 @ ( cons @ A @ Y3 @ Zs ) ) ) )
% 0.30/0.46 => ~ ! [A4: A > B] :
% 0.30/0.46 ( X3
% 0.30/0.46 != ( product_Pair @ ( A > B ) @ ( list @ A ) @ A4 @ ( nil @ A ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % arg_min_list.cases
% 0.30/0.46 thf(fact_33_successively_Ocases,axiom,
% 0.30/0.46 ! [A: $tType,X3: product_prod @ ( A > A > $o ) @ ( list @ A )] :
% 0.30/0.46 ( ! [P: A > A > $o] :
% 0.30/0.46 ( X3
% 0.30/0.46 != ( product_Pair @ ( A > A > $o ) @ ( list @ A ) @ P @ ( nil @ A ) ) )
% 0.30/0.46 => ( ! [P: A > A > $o,X5: A] :
% 0.30/0.46 ( X3
% 0.30/0.46 != ( product_Pair @ ( A > A > $o ) @ ( list @ A ) @ P @ ( cons @ A @ X5 @ ( nil @ A ) ) ) )
% 0.30/0.46 => ~ ! [P: A > A > $o,X5: A,Y3: A,Xs: list @ A] :
% 0.30/0.46 ( X3
% 0.30/0.46 != ( product_Pair @ ( A > A > $o ) @ ( list @ A ) @ P @ ( cons @ A @ X5 @ ( cons @ A @ Y3 @ Xs ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % successively.cases
% 0.30/0.46 thf(fact_34_sorted__wrt_Ocases,axiom,
% 0.30/0.46 ! [A: $tType,X3: product_prod @ ( A > A > $o ) @ ( list @ A )] :
% 0.30/0.46 ( ! [P: A > A > $o] :
% 0.30/0.46 ( X3
% 0.30/0.46 != ( product_Pair @ ( A > A > $o ) @ ( list @ A ) @ P @ ( nil @ A ) ) )
% 0.30/0.46 => ~ ! [P: A > A > $o,X5: A,Ys: list @ A] :
% 0.30/0.46 ( X3
% 0.30/0.46 != ( product_Pair @ ( A > A > $o ) @ ( list @ A ) @ P @ ( cons @ A @ X5 @ Ys ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sorted_wrt.cases
% 0.30/0.46 thf(fact_35_shuffles_Ocases,axiom,
% 0.30/0.46 ! [A: $tType,X3: product_prod @ ( list @ A ) @ ( list @ A )] :
% 0.30/0.46 ( ! [Ys: list @ A] :
% 0.30/0.46 ( X3
% 0.30/0.46 != ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( nil @ A ) @ Ys ) )
% 0.30/0.46 => ( ! [Xs: list @ A] :
% 0.30/0.46 ( X3
% 0.30/0.46 != ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ ( nil @ A ) ) )
% 0.30/0.46 => ~ ! [X5: A,Xs: list @ A,Y3: A,Ys: list @ A] :
% 0.30/0.46 ( X3
% 0.30/0.46 != ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X5 @ Xs ) @ ( cons @ A @ Y3 @ Ys ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % shuffles.cases
% 0.30/0.46 thf(fact_36_splice_Ocases,axiom,
% 0.30/0.46 ! [A: $tType,X3: product_prod @ ( list @ A ) @ ( list @ A )] :
% 0.30/0.46 ( ! [Ys: list @ A] :
% 0.30/0.46 ( X3
% 0.30/0.46 != ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( nil @ A ) @ Ys ) )
% 0.30/0.46 => ~ ! [X5: A,Xs: list @ A,Ys: list @ A] :
% 0.30/0.46 ( X3
% 0.30/0.46 != ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X5 @ Xs ) @ Ys ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % splice.cases
% 0.30/0.46 thf(fact_37_swap__simps_I1_J,axiom,
% 0.30/0.46 ! [A2: name,B2: name] :
% 0.30/0.46 ( ( perm @ name @ name @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ A2 )
% 0.30/0.46 = B2 ) ).
% 0.30/0.46
% 0.30/0.46 % swap_simps(1)
% 0.30/0.46 thf(fact_38_swap__simps_I2_J,axiom,
% 0.30/0.46 ! [A2: name,B2: name] :
% 0.30/0.46 ( ( perm @ name @ name @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ B2 )
% 0.30/0.46 = A2 ) ).
% 0.30/0.46
% 0.30/0.46 % swap_simps(2)
% 0.30/0.46 thf(fact_39_swap__simps_I3_J,axiom,
% 0.30/0.46 ! [A2: name,C2: name,B2: name] :
% 0.30/0.46 ( ( A2 != C2 )
% 0.30/0.46 => ( ( B2 != C2 )
% 0.30/0.46 => ( ( perm @ name @ name @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ C2 )
% 0.30/0.46 = C2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % swap_simps(3)
% 0.30/0.46 thf(fact_40_fresh__aux,axiom,
% 0.30/0.46 ! [X2: $tType] :
% 0.30/0.46 ( ( pt_name @ X2 )
% 0.30/0.46 => ! [C2: name,A2: name,X3: X2,B2: name] :
% 0.30/0.46 ( ( C2 != A2 )
% 0.30/0.46 => ( ( fresh @ name @ X2 @ A2 @ X3 )
% 0.30/0.46 => ( ( fresh @ name @ X2 @ C2 @ X3 )
% 0.30/0.46 => ( fresh @ name @ X2 @ C2 @ ( perm @ name @ X2 @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ X3 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % fresh_aux
% 0.30/0.46 thf(fact_41_old_Oprod_Oinducts,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,P2: ( product_prod @ A @ B ) > $o,Prod: product_prod @ A @ B] :
% 0.30/0.46 ( ! [A4: A,B4: B] : ( P2 @ ( product_Pair @ A @ B @ A4 @ B4 ) )
% 0.30/0.46 => ( P2 @ Prod ) ) ).
% 0.30/0.46
% 0.30/0.46 % old.prod.inducts
% 0.30/0.46 thf(fact_42_old_Oprod_Oexhaust,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,Y4: product_prod @ A @ B] :
% 0.30/0.46 ~ ! [A4: A,B4: B] :
% 0.30/0.46 ( Y4
% 0.30/0.46 != ( product_Pair @ A @ B @ A4 @ B4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % old.prod.exhaust
% 0.30/0.46 thf(fact_43_prod__induct7,axiom,
% 0.30/0.46 ! [G: $tType,F2: $tType,E: $tType,D: $tType,C3: $tType,B: $tType,A: $tType,P2: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G ) ) ) ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G ) ) ) ) )] :
% 0.30/0.46 ( ! [A4: A,B4: B,C: C3,D2: D,E2: E,F: F2,G2: G] : ( P2 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G ) ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C3 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G ) ) ) ) @ B4 @ ( product_Pair @ C3 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G ) ) ) @ C @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F2 @ G ) @ E2 @ ( product_Pair @ F2 @ G @ F @ G2 ) ) ) ) ) ) )
% 0.30/0.46 => ( P2 @ X3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_induct7
% 0.30/0.46 thf(fact_44_prod__induct6,axiom,
% 0.30/0.46 ! [F2: $tType,E: $tType,D: $tType,C3: $tType,B: $tType,A: $tType,P2: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) ) )] :
% 0.30/0.46 ( ! [A4: A,B4: B,C: C3,D2: D,E2: E,F: F2] : ( P2 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C3 @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) ) @ B4 @ ( product_Pair @ C3 @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) @ C @ ( product_Pair @ D @ ( product_prod @ E @ F2 ) @ D2 @ ( product_Pair @ E @ F2 @ E2 @ F ) ) ) ) ) )
% 0.30/0.46 => ( P2 @ X3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_induct6
% 0.30/0.46 thf(fact_45_mem__Collect__eq,axiom,
% 0.30/0.46 ! [A: $tType,A2: A,P2: A > $o] :
% 0.30/0.46 ( ( member @ A @ A2 @ ( collect @ A @ P2 ) )
% 0.30/0.46 = ( P2 @ A2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % mem_Collect_eq
% 0.30/0.46 thf(fact_46_Collect__mem__eq,axiom,
% 0.30/0.46 ! [A: $tType,A5: set @ A] :
% 0.30/0.46 ( ( collect @ A
% 0.30/0.46 @ ^ [X6: A] : ( member @ A @ X6 @ A5 ) )
% 0.30/0.46 = A5 ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_mem_eq
% 0.30/0.46 thf(fact_47_Collect__cong,axiom,
% 0.30/0.46 ! [A: $tType,P2: A > $o,Q: A > $o] :
% 0.30/0.46 ( ! [X5: A] :
% 0.30/0.46 ( ( P2 @ X5 )
% 0.30/0.46 = ( Q @ X5 ) )
% 0.30/0.46 => ( ( collect @ A @ P2 )
% 0.30/0.46 = ( collect @ A @ Q ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_cong
% 0.30/0.46 thf(fact_48_ext,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,F3: A > B,G3: A > B] :
% 0.30/0.46 ( ! [X5: A] :
% 0.30/0.46 ( ( F3 @ X5 )
% 0.30/0.46 = ( G3 @ X5 ) )
% 0.30/0.46 => ( F3 = G3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % ext
% 0.30/0.46 thf(fact_49_prod__induct5,axiom,
% 0.30/0.46 ! [E: $tType,D: $tType,C3: $tType,B: $tType,A: $tType,P2: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D @ E ) ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D @ E ) ) )] :
% 0.30/0.46 ( ! [A4: A,B4: B,C: C3,D2: D,E2: E] : ( P2 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D @ E ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C3 @ ( product_prod @ D @ E ) ) @ B4 @ ( product_Pair @ C3 @ ( product_prod @ D @ E ) @ C @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) )
% 0.30/0.46 => ( P2 @ X3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_induct5
% 0.30/0.46 thf(fact_50_prod__induct4,axiom,
% 0.30/0.46 ! [D: $tType,C3: $tType,B: $tType,A: $tType,P2: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ D ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ D ) )] :
% 0.30/0.46 ( ! [A4: A,B4: B,C: C3,D2: D] : ( P2 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C3 @ D ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C3 @ D ) @ B4 @ ( product_Pair @ C3 @ D @ C @ D2 ) ) ) )
% 0.30/0.46 => ( P2 @ X3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_induct4
% 0.30/0.46 thf(fact_51_prod__induct3,axiom,
% 0.30/0.46 ! [C3: $tType,B: $tType,A: $tType,P2: ( product_prod @ A @ ( product_prod @ B @ C3 ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ C3 )] :
% 0.30/0.46 ( ! [A4: A,B4: B,C: C3] : ( P2 @ ( product_Pair @ A @ ( product_prod @ B @ C3 ) @ A4 @ ( product_Pair @ B @ C3 @ B4 @ C ) ) )
% 0.30/0.46 => ( P2 @ X3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_induct3
% 0.30/0.46 thf(fact_52_prod__cases7,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,C3: $tType,D: $tType,E: $tType,F2: $tType,G: $tType,Y4: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G ) ) ) ) )] :
% 0.30/0.46 ~ ! [A4: A,B4: B,C: C3,D2: D,E2: E,F: F2,G2: G] :
% 0.30/0.46 ( Y4
% 0.30/0.46 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G ) ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C3 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G ) ) ) ) @ B4 @ ( product_Pair @ C3 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G ) ) ) @ C @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F2 @ G ) @ E2 @ ( product_Pair @ F2 @ G @ F @ G2 ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_cases7
% 0.30/0.46 thf(fact_53_prod__cases6,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,C3: $tType,D: $tType,E: $tType,F2: $tType,Y4: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) ) )] :
% 0.30/0.46 ~ ! [A4: A,B4: B,C: C3,D2: D,E2: E,F: F2] :
% 0.30/0.46 ( Y4
% 0.30/0.46 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C3 @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) ) @ B4 @ ( product_Pair @ C3 @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) @ C @ ( product_Pair @ D @ ( product_prod @ E @ F2 ) @ D2 @ ( product_Pair @ E @ F2 @ E2 @ F ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_cases6
% 0.30/0.46 thf(fact_54_prod__cases5,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,C3: $tType,D: $tType,E: $tType,Y4: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D @ E ) ) )] :
% 0.30/0.46 ~ ! [A4: A,B4: B,C: C3,D2: D,E2: E] :
% 0.30/0.46 ( Y4
% 0.30/0.46 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D @ E ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C3 @ ( product_prod @ D @ E ) ) @ B4 @ ( product_Pair @ C3 @ ( product_prod @ D @ E ) @ C @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_cases5
% 0.30/0.46 thf(fact_55_prod__cases4,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,C3: $tType,D: $tType,Y4: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ D ) )] :
% 0.30/0.46 ~ ! [A4: A,B4: B,C: C3,D2: D] :
% 0.30/0.46 ( Y4
% 0.30/0.46 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C3 @ D ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C3 @ D ) @ B4 @ ( product_Pair @ C3 @ D @ C @ D2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_cases4
% 0.30/0.46 thf(fact_56_prod__cases3,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,C3: $tType,Y4: product_prod @ A @ ( product_prod @ B @ C3 )] :
% 0.30/0.46 ~ ! [A4: A,B4: B,C: C3] :
% 0.30/0.46 ( Y4
% 0.30/0.46 != ( product_Pair @ A @ ( product_prod @ B @ C3 ) @ A4 @ ( product_Pair @ B @ C3 @ B4 @ C ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_cases3
% 0.30/0.46 thf(fact_57_Pair__inject,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,A2: A,B2: B,A3: A,B3: B] :
% 0.30/0.46 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 0.30/0.46 = ( product_Pair @ A @ B @ A3 @ B3 ) )
% 0.30/0.46 => ~ ( ( A2 = A3 )
% 0.30/0.46 => ( B2 != B3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Pair_inject
% 0.30/0.46 thf(fact_58_prod__cases,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,P2: ( product_prod @ A @ B ) > $o,P3: product_prod @ A @ B] :
% 0.30/0.46 ( ! [A4: A,B4: B] : ( P2 @ ( product_Pair @ A @ B @ A4 @ B4 ) )
% 0.30/0.46 => ( P2 @ P3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_cases
% 0.30/0.46 thf(fact_59_surj__pair,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,P3: product_prod @ A @ B] :
% 0.30/0.46 ? [X5: A,Y3: B] :
% 0.30/0.46 ( P3
% 0.30/0.46 = ( product_Pair @ A @ B @ X5 @ Y3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % surj_pair
% 0.30/0.46 thf(fact_60_not__Cons__self2,axiom,
% 0.30/0.46 ! [A: $tType,X3: A,Xs2: list @ A] :
% 0.30/0.46 ( ( cons @ A @ X3 @ Xs2 )
% 0.30/0.46 != Xs2 ) ).
% 0.30/0.46
% 0.30/0.46 % not_Cons_self2
% 0.30/0.46 thf(fact_61_cp__name__name1,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( cp_name_name @ A )
% 0.30/0.46 => ! [Pi1: list @ ( product_prod @ name @ name ),Pi2: list @ ( product_prod @ name @ name ),X3: A] :
% 0.30/0.46 ( ( perm @ name @ A @ Pi1 @ ( perm @ name @ A @ Pi2 @ X3 ) )
% 0.30/0.46 = ( perm @ name @ A @ ( perm @ name @ ( list @ ( product_prod @ name @ name ) ) @ Pi1 @ Pi2 ) @ ( perm @ name @ A @ Pi1 @ X3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % cp_name_name1
% 0.30/0.46 thf(fact_62_name__perm__compose,axiom,
% 0.30/0.46 ! [X: $tType] :
% 0.30/0.46 ( ( pt_name @ X )
% 0.30/0.46 => ! [Pi2: list @ ( product_prod @ name @ name ),Pi1: list @ ( product_prod @ name @ name ),X3: X] :
% 0.30/0.46 ( ( perm @ name @ X @ Pi2 @ ( perm @ name @ X @ Pi1 @ X3 ) )
% 0.30/0.46 = ( perm @ name @ X @ ( perm @ name @ ( list @ ( product_prod @ name @ name ) ) @ Pi2 @ Pi1 ) @ ( perm @ name @ X @ Pi2 @ X3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % name_perm_compose
% 0.30/0.46 thf(fact_63_perm__compose,axiom,
% 0.30/0.46 ! [X2: $tType] :
% 0.30/0.46 ( ( pt_name @ X2 )
% 0.30/0.46 => ! [Pi2: list @ ( product_prod @ name @ name ),Pi1: list @ ( product_prod @ name @ name ),X3: X2] :
% 0.30/0.46 ( ( perm @ name @ X2 @ Pi2 @ ( perm @ name @ X2 @ Pi1 @ X3 ) )
% 0.30/0.46 = ( perm @ name @ X2 @ ( perm @ name @ ( list @ ( product_prod @ name @ name ) ) @ Pi2 @ Pi1 ) @ ( perm @ name @ X2 @ Pi2 @ X3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % perm_compose
% 0.30/0.46 thf(fact_64_perm__bij,axiom,
% 0.30/0.46 ! [X2: $tType] :
% 0.30/0.46 ( ( pt_name @ X2 )
% 0.30/0.46 => ! [Pi: list @ ( product_prod @ name @ name ),X3: X2,Y4: X2] :
% 0.30/0.46 ( ( ( perm @ name @ X2 @ Pi @ X3 )
% 0.30/0.46 = ( perm @ name @ X2 @ Pi @ Y4 ) )
% 0.30/0.46 = ( X3 = Y4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % perm_bij
% 0.30/0.46 thf(fact_65_perm__app,axiom,
% 0.30/0.46 ! [B: $tType,X2: $tType] :
% 0.30/0.46 ( ( pt_name @ X2 )
% 0.30/0.46 => ! [Pi: list @ ( product_prod @ name @ name ),F3: X2 > B,X3: X2] :
% 0.30/0.46 ( ( perm @ name @ B @ Pi @ ( F3 @ X3 ) )
% 0.30/0.46 = ( perm @ name @ ( X2 > B ) @ Pi @ F3 @ ( perm @ name @ X2 @ Pi @ X3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % perm_app
% 0.30/0.46 thf(fact_66_in__eqvt,axiom,
% 0.30/0.46 ! [X2: $tType] :
% 0.30/0.46 ( ( pt_name @ X2 )
% 0.30/0.46 => ! [Pi: list @ ( product_prod @ name @ name ),X3: X2,X4: set @ X2] :
% 0.30/0.46 ( ( perm @ name @ $o @ Pi @ ( member @ X2 @ X3 @ X4 ) )
% 0.30/0.46 = ( member @ X2 @ ( perm @ name @ X2 @ Pi @ X3 ) @ ( perm @ name @ ( set @ X2 ) @ Pi @ X4 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % in_eqvt
% 0.30/0.46 thf(fact_67_eq__eqvt,axiom,
% 0.30/0.46 ! [X2: $tType] :
% 0.30/0.46 ( ( pt_name @ X2 )
% 0.30/0.46 => ! [Pi: list @ ( product_prod @ name @ name ),X3: X2,Y4: X2] :
% 0.30/0.46 ( ( perm @ name @ $o @ Pi @ ( X3 = Y4 ) )
% 0.30/0.46 = ( ( perm @ name @ X2 @ Pi @ X3 )
% 0.30/0.46 = ( perm @ name @ X2 @ Pi @ Y4 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % eq_eqvt
% 0.30/0.46 thf(fact_68_strict__sorted_Oinduct,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [P2: ( list @ A ) > $o,A0: list @ A] :
% 0.30/0.46 ( ( P2 @ ( nil @ A ) )
% 0.30/0.46 => ( ! [X5: A,Ys: list @ A] :
% 0.30/0.46 ( ( P2 @ Ys )
% 0.30/0.46 => ( P2 @ ( cons @ A @ X5 @ Ys ) ) )
% 0.30/0.46 => ( P2 @ A0 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % strict_sorted.induct
% 0.30/0.46 thf(fact_69_strict__sorted_Ocases,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [X3: list @ A] :
% 0.30/0.46 ( ( X3
% 0.30/0.46 != ( nil @ A ) )
% 0.30/0.46 => ~ ! [X5: A,Ys: list @ A] :
% 0.30/0.46 ( X3
% 0.30/0.46 != ( cons @ A @ X5 @ Ys ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % strict_sorted.cases
% 0.30/0.46 thf(fact_70_map__tailrec__rev_Oinduct,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,P2: ( A > B ) > ( list @ A ) > ( list @ B ) > $o,A0: A > B,A1: list @ A,A22: list @ B] :
% 0.30/0.46 ( ! [F: A > B,X_1: list @ B] : ( P2 @ F @ ( nil @ A ) @ X_1 )
% 0.30/0.46 => ( ! [F: A > B,A4: A,As: list @ A,Bs: list @ B] :
% 0.30/0.46 ( ( P2 @ F @ As @ ( cons @ B @ ( F @ A4 ) @ Bs ) )
% 0.30/0.46 => ( P2 @ F @ ( cons @ A @ A4 @ As ) @ Bs ) )
% 0.30/0.46 => ( P2 @ A0 @ A1 @ A22 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % map_tailrec_rev.induct
% 0.30/0.46 thf(fact_71_list__nonempty__induct,axiom,
% 0.30/0.46 ! [A: $tType,Xs2: list @ A,P2: ( list @ A ) > $o] :
% 0.30/0.46 ( ( Xs2
% 0.30/0.46 != ( nil @ A ) )
% 0.30/0.46 => ( ! [X5: A] : ( P2 @ ( cons @ A @ X5 @ ( nil @ A ) ) )
% 0.30/0.46 => ( ! [X5: A,Xs: list @ A] :
% 0.30/0.46 ( ( Xs
% 0.30/0.46 != ( nil @ A ) )
% 0.30/0.46 => ( ( P2 @ Xs )
% 0.30/0.46 => ( P2 @ ( cons @ A @ X5 @ Xs ) ) ) )
% 0.30/0.46 => ( P2 @ Xs2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % list_nonempty_induct
% 0.30/0.46 thf(fact_72_successively_Oinduct,axiom,
% 0.30/0.46 ! [A: $tType,P2: ( A > A > $o ) > ( list @ A ) > $o,A0: A > A > $o,A1: list @ A] :
% 0.30/0.46 ( ! [P: A > A > $o] : ( P2 @ P @ ( nil @ A ) )
% 0.30/0.46 => ( ! [P: A > A > $o,X5: A] : ( P2 @ P @ ( cons @ A @ X5 @ ( nil @ A ) ) )
% 0.30/0.46 => ( ! [P: A > A > $o,X5: A,Y3: A,Xs: list @ A] :
% 0.30/0.46 ( ( P2 @ P @ ( cons @ A @ Y3 @ Xs ) )
% 0.30/0.46 => ( P2 @ P @ ( cons @ A @ X5 @ ( cons @ A @ Y3 @ Xs ) ) ) )
% 0.30/0.46 => ( P2 @ A0 @ A1 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % successively.induct
% 0.30/0.46 thf(fact_73_arg__min__list_Oinduct,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( linorder @ B )
% 0.30/0.46 => ! [P2: ( A > B ) > ( list @ A ) > $o,A0: A > B,A1: list @ A] :
% 0.30/0.46 ( ! [F: A > B,X5: A] : ( P2 @ F @ ( cons @ A @ X5 @ ( nil @ A ) ) )
% 0.30/0.46 => ( ! [F: A > B,X5: A,Y3: A,Zs: list @ A] :
% 0.30/0.46 ( ( P2 @ F @ ( cons @ A @ Y3 @ Zs ) )
% 0.30/0.46 => ( P2 @ F @ ( cons @ A @ X5 @ ( cons @ A @ Y3 @ Zs ) ) ) )
% 0.30/0.46 => ( ! [A4: A > B] : ( P2 @ A4 @ ( nil @ A ) )
% 0.30/0.46 => ( P2 @ A0 @ A1 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % arg_min_list.induct
% 0.30/0.46 thf(fact_74_remdups__adj_Oinduct,axiom,
% 0.30/0.46 ! [A: $tType,P2: ( list @ A ) > $o,A0: list @ A] :
% 0.30/0.46 ( ( P2 @ ( nil @ A ) )
% 0.30/0.46 => ( ! [X5: A] : ( P2 @ ( cons @ A @ X5 @ ( nil @ A ) ) )
% 0.30/0.46 => ( ! [X5: A,Y3: A,Xs: list @ A] :
% 0.30/0.46 ( ( ( X5 = Y3 )
% 0.30/0.46 => ( P2 @ ( cons @ A @ X5 @ Xs ) ) )
% 0.30/0.46 => ( ( ( X5 != Y3 )
% 0.30/0.46 => ( P2 @ ( cons @ A @ Y3 @ Xs ) ) )
% 0.30/0.46 => ( P2 @ ( cons @ A @ X5 @ ( cons @ A @ Y3 @ Xs ) ) ) ) )
% 0.30/0.46 => ( P2 @ A0 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % remdups_adj.induct
% 0.30/0.46 thf(fact_75_sorted__wrt_Oinduct,axiom,
% 0.30/0.46 ! [A: $tType,P2: ( A > A > $o ) > ( list @ A ) > $o,A0: A > A > $o,A1: list @ A] :
% 0.30/0.46 ( ! [P: A > A > $o] : ( P2 @ P @ ( nil @ A ) )
% 0.30/0.46 => ( ! [P: A > A > $o,X5: A,Ys: list @ A] :
% 0.30/0.46 ( ( P2 @ P @ Ys )
% 0.30/0.46 => ( P2 @ P @ ( cons @ A @ X5 @ Ys ) ) )
% 0.30/0.46 => ( P2 @ A0 @ A1 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sorted_wrt.induct
% 0.30/0.46 thf(fact_76_remdups__adj_Ocases,axiom,
% 0.30/0.46 ! [A: $tType,X3: list @ A] :
% 0.30/0.46 ( ( X3
% 0.30/0.46 != ( nil @ A ) )
% 0.30/0.46 => ( ! [X5: A] :
% 0.30/0.46 ( X3
% 0.30/0.46 != ( cons @ A @ X5 @ ( nil @ A ) ) )
% 0.30/0.46 => ~ ! [X5: A,Y3: A,Xs: list @ A] :
% 0.30/0.46 ( X3
% 0.30/0.46 != ( cons @ A @ X5 @ ( cons @ A @ Y3 @ Xs ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % remdups_adj.cases
% 0.30/0.46 thf(fact_77_transpose_Ocases,axiom,
% 0.30/0.46 ! [A: $tType,X3: list @ ( list @ A )] :
% 0.30/0.46 ( ( X3
% 0.30/0.46 != ( nil @ ( list @ A ) ) )
% 0.30/0.46 => ( ! [Xss: list @ ( list @ A )] :
% 0.30/0.46 ( X3
% 0.30/0.46 != ( cons @ ( list @ A ) @ ( nil @ A ) @ Xss ) )
% 0.30/0.46 => ~ ! [X5: A,Xs: list @ A,Xss: list @ ( list @ A )] :
% 0.30/0.46 ( X3
% 0.30/0.46 != ( cons @ ( list @ A ) @ ( cons @ A @ X5 @ Xs ) @ Xss ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % transpose.cases
% 0.30/0.46 thf(fact_78_shuffles_Oinduct,axiom,
% 0.30/0.46 ! [A: $tType,P2: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 0.30/0.46 ( ! [X_1: list @ A] : ( P2 @ ( nil @ A ) @ X_1 )
% 0.30/0.46 => ( ! [Xs: list @ A] : ( P2 @ Xs @ ( nil @ A ) )
% 0.30/0.46 => ( ! [X5: A,Xs: list @ A,Y3: A,Ys: list @ A] :
% 0.30/0.46 ( ( P2 @ Xs @ ( cons @ A @ Y3 @ Ys ) )
% 0.30/0.46 => ( ( P2 @ ( cons @ A @ X5 @ Xs ) @ Ys )
% 0.30/0.46 => ( P2 @ ( cons @ A @ X5 @ Xs ) @ ( cons @ A @ Y3 @ Ys ) ) ) )
% 0.30/0.46 => ( P2 @ A0 @ A1 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % shuffles.induct
% 0.30/0.46 thf(fact_79_min__list_Oinduct,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ord @ A )
% 0.30/0.46 => ! [P2: ( list @ A ) > $o,A0: list @ A] :
% 0.30/0.46 ( ! [X5: A,Xs: list @ A] :
% 0.30/0.46 ( ! [X212: A,X223: list @ A] :
% 0.30/0.46 ( ( Xs
% 0.30/0.46 = ( cons @ A @ X212 @ X223 ) )
% 0.30/0.46 => ( P2 @ Xs ) )
% 0.30/0.46 => ( P2 @ ( cons @ A @ X5 @ Xs ) ) )
% 0.30/0.46 => ( ( P2 @ ( nil @ A ) )
% 0.30/0.46 => ( P2 @ A0 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % min_list.induct
% 0.30/0.46 thf(fact_80_min__list_Ocases,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ord @ A )
% 0.30/0.46 => ! [X3: list @ A] :
% 0.30/0.46 ( ! [X5: A,Xs: list @ A] :
% 0.30/0.46 ( X3
% 0.30/0.46 != ( cons @ A @ X5 @ Xs ) )
% 0.30/0.46 => ( X3
% 0.30/0.46 = ( nil @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % min_list.cases
% 0.30/0.46 thf(fact_81_induct__list012,axiom,
% 0.30/0.46 ! [A: $tType,P2: ( list @ A ) > $o,Xs2: list @ A] :
% 0.30/0.46 ( ( P2 @ ( nil @ A ) )
% 0.30/0.46 => ( ! [X5: A] : ( P2 @ ( cons @ A @ X5 @ ( nil @ A ) ) )
% 0.30/0.46 => ( ! [X5: A,Y3: A,Zs: list @ A] :
% 0.30/0.46 ( ( P2 @ Zs )
% 0.30/0.46 => ( ( P2 @ ( cons @ A @ Y3 @ Zs ) )
% 0.30/0.46 => ( P2 @ ( cons @ A @ X5 @ ( cons @ A @ Y3 @ Zs ) ) ) ) )
% 0.30/0.46 => ( P2 @ Xs2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % induct_list012
% 0.30/0.46 thf(fact_82_splice_Oinduct,axiom,
% 0.30/0.46 ! [A: $tType,P2: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 0.30/0.46 ( ! [X_1: list @ A] : ( P2 @ ( nil @ A ) @ X_1 )
% 0.30/0.46 => ( ! [X5: A,Xs: list @ A,Ys: list @ A] :
% 0.30/0.46 ( ( P2 @ Ys @ Xs )
% 0.30/0.46 => ( P2 @ ( cons @ A @ X5 @ Xs ) @ Ys ) )
% 0.30/0.46 => ( P2 @ A0 @ A1 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % splice.induct
% 0.30/0.46 thf(fact_83_list__induct2_H,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,P2: ( list @ A ) > ( list @ B ) > $o,Xs2: list @ A,Ys2: list @ B] :
% 0.30/0.46 ( ( P2 @ ( nil @ A ) @ ( nil @ B ) )
% 0.30/0.46 => ( ! [X5: A,Xs: list @ A] : ( P2 @ ( cons @ A @ X5 @ Xs ) @ ( nil @ B ) )
% 0.30/0.46 => ( ! [Y3: B,Ys: list @ B] : ( P2 @ ( nil @ A ) @ ( cons @ B @ Y3 @ Ys ) )
% 0.30/0.46 => ( ! [X5: A,Xs: list @ A,Y3: B,Ys: list @ B] :
% 0.30/0.46 ( ( P2 @ Xs @ Ys )
% 0.30/0.46 => ( P2 @ ( cons @ A @ X5 @ Xs ) @ ( cons @ B @ Y3 @ Ys ) ) )
% 0.30/0.46 => ( P2 @ Xs2 @ Ys2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % list_induct2'
% 0.30/0.46 thf(fact_84_neq__Nil__conv,axiom,
% 0.30/0.46 ! [A: $tType,Xs2: list @ A] :
% 0.30/0.46 ( ( Xs2
% 0.30/0.46 != ( nil @ A ) )
% 0.30/0.46 = ( ? [Y5: A,Ys3: list @ A] :
% 0.30/0.46 ( Xs2
% 0.30/0.46 = ( cons @ A @ Y5 @ Ys3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % neq_Nil_conv
% 0.30/0.46 thf(fact_85_list_Oinducts,axiom,
% 0.30/0.46 ! [A: $tType,P2: ( list @ A ) > $o,List: list @ A] :
% 0.30/0.46 ( ( P2 @ ( nil @ A ) )
% 0.30/0.46 => ( ! [X12: A,X23: list @ A] :
% 0.30/0.46 ( ( P2 @ X23 )
% 0.30/0.46 => ( P2 @ ( cons @ A @ X12 @ X23 ) ) )
% 0.30/0.46 => ( P2 @ List ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % list.inducts
% 0.30/0.46 thf(fact_86_list_Oexhaust,axiom,
% 0.30/0.46 ! [A: $tType,Y4: list @ A] :
% 0.30/0.46 ( ( Y4
% 0.30/0.46 != ( nil @ A ) )
% 0.30/0.46 => ~ ! [X213: A,X224: list @ A] :
% 0.30/0.46 ( Y4
% 0.30/0.46 != ( cons @ A @ X213 @ X224 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % list.exhaust
% 0.30/0.46 thf(fact_87_list_OdiscI,axiom,
% 0.30/0.46 ! [A: $tType,List: list @ A,X21: A,X222: list @ A] :
% 0.30/0.46 ( ( List
% 0.30/0.46 = ( cons @ A @ X21 @ X222 ) )
% 0.30/0.46 => ( List
% 0.30/0.46 != ( nil @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % list.discI
% 0.30/0.46 thf(fact_88_list_Odistinct_I1_J,axiom,
% 0.30/0.46 ! [A: $tType,X21: A,X222: list @ A] :
% 0.30/0.46 ( ( nil @ A )
% 0.30/0.46 != ( cons @ A @ X21 @ X222 ) ) ).
% 0.30/0.46
% 0.30/0.46 % list.distinct(1)
% 0.30/0.46 thf(fact_89__092_060open_062y_A_092_060sharp_062_AQ_092_060close_062,axiom,
% 0.30/0.46 fresh @ name @ pi @ y @ q ).
% 0.30/0.46
% 0.30/0.46 % \<open>y \<sharp> Q\<close>
% 0.30/0.46 thf(fact_90_pair__in__Id__conv,axiom,
% 0.30/0.46 ! [A: $tType,A2: A,B2: A] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ ( id @ A ) )
% 0.30/0.46 = ( A2 = B2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % pair_in_Id_conv
% 0.30/0.46 thf(fact_91_IdI,axiom,
% 0.30/0.46 ! [A: $tType,A2: A] : ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ A2 ) @ ( id @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 % IdI
% 0.30/0.46 thf(fact_92_fresh__prod,axiom,
% 0.30/0.46 ! [A: $tType,X: $tType,B: $tType,A2: X,X3: A,Y4: B] :
% 0.30/0.46 ( ( fresh @ X @ ( product_prod @ A @ B ) @ A2 @ ( product_Pair @ A @ B @ X3 @ Y4 ) )
% 0.30/0.46 = ( ( fresh @ X @ A @ A2 @ X3 )
% 0.30/0.46 & ( fresh @ X @ B @ A2 @ Y4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % fresh_prod
% 0.30/0.46 thf(fact_93__092_060open_062y_A_092_060sharp_062_AP_092_060close_062,axiom,
% 0.30/0.46 fresh @ name @ pi @ y @ p ).
% 0.30/0.46
% 0.30/0.46 % \<open>y \<sharp> P\<close>
% 0.30/0.46 thf(fact_94_derivativeReflexive,axiom,
% 0.30/0.46 ! [Rel: set @ ( product_prod @ pi @ pi ),P2: pi,A2: late_subject,X3: name] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 0.30/0.46 => ( strong2129052853vative @ P2 @ P2 @ A2 @ X3 @ Rel ) ) ).
% 0.30/0.46
% 0.30/0.46 % derivativeReflexive
% 0.30/0.46 thf(fact_95_derivativeEqvtI,axiom,
% 0.30/0.46 ! [P2: pi,Q: pi,A2: late_subject,X3: name,Rel: set @ ( product_prod @ pi @ pi ),Perm: list @ ( product_prod @ name @ name )] :
% 0.30/0.46 ( ( strong2129052853vative @ P2 @ Q @ A2 @ X3 @ Rel )
% 0.30/0.46 => ( ( eqvt @ pi @ Rel )
% 0.30/0.46 => ( strong2129052853vative @ ( perm @ name @ pi @ Perm @ P2 ) @ ( perm @ name @ pi @ Perm @ Q ) @ ( perm @ name @ late_subject @ Perm @ A2 ) @ ( perm @ name @ name @ Perm @ X3 ) @ Rel ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % derivativeEqvtI
% 0.30/0.46 thf(fact_96_derivativeEqvtI2,axiom,
% 0.30/0.46 ! [P2: pi,Q: pi,A2: late_subject,X3: name,Rel: set @ ( product_prod @ pi @ pi ),Perm: list @ ( product_prod @ name @ name )] :
% 0.30/0.46 ( ( strong2129052853vative @ P2 @ Q @ A2 @ X3 @ Rel )
% 0.30/0.46 => ( ( eqvt @ pi @ Rel )
% 0.30/0.46 => ( strong2129052853vative @ ( perm @ name @ pi @ Perm @ P2 ) @ ( perm @ name @ pi @ Perm @ Q ) @ A2 @ ( perm @ name @ name @ Perm @ X3 ) @ Rel ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % derivativeEqvtI2
% 0.30/0.46 thf(fact_97_old_Oprod_Orec,axiom,
% 0.30/0.46 ! [A: $tType,T: $tType,B: $tType,F1: A > B > T,A2: A,B2: B] :
% 0.30/0.46 ( ( product_rec_prod @ A @ B @ T @ F1 @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 0.30/0.46 = ( F1 @ A2 @ B2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % old.prod.rec
% 0.30/0.46 thf(fact_98_eqvtRelI,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( pt_name @ A )
% 0.30/0.46 => ! [Rel: set @ ( product_prod @ A @ A ),P2: A,Q: A,Perm: list @ ( product_prod @ name @ name )] :
% 0.30/0.46 ( ( eqvt @ A @ Rel )
% 0.30/0.46 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ P2 @ Q ) @ Rel )
% 0.30/0.46 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ ( perm @ name @ A @ Perm @ P2 ) @ ( perm @ name @ A @ Perm @ Q ) ) @ Rel ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % eqvtRelI
% 0.30/0.46 thf(fact_99_Bound_Ohyps_I5_J,axiom,
% 0.30/0.46 fresh @ name @ ( product_prod @ name @ ( product_prod @ pi @ pi ) ) @ y @ ( product_Pair @ name @ ( product_prod @ pi @ pi ) @ x @ ( product_Pair @ pi @ pi @ p @ q ) ) ).
% 0.30/0.46
% 0.30/0.46 % Bound.hyps(5)
% 0.30/0.46 thf(fact_100_true__eqvt,axiom,
% 0.30/0.46 ! [A: $tType,Pi: list @ ( product_prod @ A @ A )] : ( perm @ A @ $o @ Pi @ $true ) ).
% 0.30/0.46
% 0.30/0.46 % true_eqvt
% 0.30/0.46 thf(fact_101_false__eqvt,axiom,
% 0.30/0.46 ! [A: $tType,Pi: list @ ( product_prod @ A @ A )] :
% 0.30/0.46 ~ ( perm @ A @ $o @ Pi @ $false ) ).
% 0.30/0.46
% 0.30/0.46 % false_eqvt
% 0.30/0.46 thf(fact_102_subject_Ofresh_I2_J,axiom,
% 0.30/0.46 ! [A2: name,X1: name] :
% 0.30/0.46 ( ( fresh @ name @ late_subject @ A2 @ ( late_BoundOutputS @ X1 ) )
% 0.30/0.46 = ( fresh @ name @ name @ A2 @ X1 ) ) ).
% 0.30/0.46
% 0.30/0.46 % subject.fresh(2)
% 0.30/0.46 thf(fact_103_name__bij,axiom,
% 0.30/0.46 ! [Pi: list @ ( product_prod @ name @ name ),X3: name,Y4: name] :
% 0.30/0.46 ( ( ( perm @ name @ name @ Pi @ X3 )
% 0.30/0.46 = ( perm @ name @ name @ Pi @ Y4 ) )
% 0.30/0.46 = ( X3 = Y4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % name_bij
% 0.30/0.46 thf(fact_104_imp__eqvt,axiom,
% 0.30/0.46 ! [A: $tType,Pi: list @ ( product_prod @ A @ A ),A5: $o,B5: $o] :
% 0.30/0.46 ( ( perm @ A @ $o @ Pi
% 0.30/0.46 @ ( A5
% 0.30/0.46 => B5 ) )
% 0.30/0.46 = ( ( perm @ A @ $o @ Pi @ A5 )
% 0.30/0.46 => ( perm @ A @ $o @ Pi @ B5 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % imp_eqvt
% 0.30/0.46 thf(fact_105_neg__eqvt,axiom,
% 0.30/0.46 ! [A: $tType,Pi: list @ ( product_prod @ A @ A ),A5: $o] :
% 0.30/0.46 ( ( perm @ A @ $o @ Pi @ ~ A5 )
% 0.30/0.46 = ( ~ ( perm @ A @ $o @ Pi @ A5 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % neg_eqvt
% 0.30/0.46 thf(fact_106_conj__eqvt,axiom,
% 0.30/0.46 ! [A: $tType,Pi: list @ ( product_prod @ A @ A ),A5: $o,B5: $o] :
% 0.30/0.46 ( ( perm @ A @ $o @ Pi
% 0.30/0.46 @ ( A5
% 0.30/0.46 & B5 ) )
% 0.30/0.46 = ( ( perm @ A @ $o @ Pi @ A5 )
% 0.30/0.46 & ( perm @ A @ $o @ Pi @ B5 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % conj_eqvt
% 0.30/0.46 thf(fact_107_disj__eqvt,axiom,
% 0.30/0.46 ! [A: $tType,Pi: list @ ( product_prod @ A @ A ),A5: $o,B5: $o] :
% 0.30/0.46 ( ( perm @ A @ $o @ Pi
% 0.30/0.46 @ ( A5
% 0.30/0.46 | B5 ) )
% 0.30/0.46 = ( ( perm @ A @ $o @ Pi @ A5 )
% 0.30/0.46 | ( perm @ A @ $o @ Pi @ B5 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % disj_eqvt
% 0.30/0.46 thf(fact_108_perm__boolE,axiom,
% 0.30/0.46 ! [A: $tType,Pi: list @ ( product_prod @ A @ A )] :
% 0.30/0.46 ~ ( perm @ A @ $o @ Pi @ $false ) ).
% 0.30/0.46
% 0.30/0.46 % perm_boolE
% 0.30/0.46 thf(fact_109_perm__boolI,axiom,
% 0.30/0.46 ! [A: $tType,P2: $o,Pi: list @ ( product_prod @ A @ A )] :
% 0.30/0.46 ( P2
% 0.30/0.46 => ( perm @ A @ $o @ Pi @ P2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % perm_boolI
% 0.30/0.46 thf(fact_110_pt__set__bij3,axiom,
% 0.30/0.46 ! [X: $tType,A: $tType,Pi: list @ ( product_prod @ X @ X ),X3: A,X4: set @ A] :
% 0.30/0.46 ( ( perm @ X @ $o @ Pi @ ( member @ A @ X3 @ X4 ) )
% 0.30/0.46 = ( member @ A @ X3 @ X4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % pt_set_bij3
% 0.30/0.46 thf(fact_111_perm__bool__def,axiom,
% 0.30/0.46 ! [X: $tType] :
% 0.30/0.46 ( ( perm @ X @ $o )
% 0.30/0.46 = ( ^ [Pi3: list @ ( product_prod @ X @ X ),B6: $o] : B6 ) ) ).
% 0.30/0.46
% 0.30/0.46 % perm_bool_def
% 0.30/0.46 thf(fact_112_nil__eqvt,axiom,
% 0.30/0.46 ! [X: $tType,A: $tType,Pi: list @ ( product_prod @ X @ X )] :
% 0.30/0.46 ( ( perm @ X @ ( list @ A ) @ Pi @ ( nil @ A ) )
% 0.30/0.46 = ( nil @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 % nil_eqvt
% 0.30/0.46 thf(fact_113_fresh__list__nil,axiom,
% 0.30/0.46 ! [X: $tType,A: $tType,A2: X] : ( fresh @ X @ ( list @ A ) @ A2 @ ( nil @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 % fresh_list_nil
% 0.30/0.46 thf(fact_114_allE__Nil,axiom,
% 0.30/0.46 ! [A: $tType,P2: ( list @ A ) > $o] :
% 0.30/0.46 ( ! [X_1: list @ A] : ( P2 @ X_1 )
% 0.30/0.46 => ( P2 @ ( nil @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % allE_Nil
% 0.30/0.46 thf(fact_115_if__eqvt,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,Pi: list @ ( product_prod @ A @ A ),B2: $o,C1: B,C22: B] :
% 0.30/0.46 ( ( ( perm @ A @ $o @ Pi @ B2 )
% 0.30/0.46 => ( ( perm @ A @ B @ Pi @ ( if @ B @ B2 @ C1 @ C22 ) )
% 0.30/0.46 = ( perm @ A @ B @ Pi @ C1 ) ) )
% 0.30/0.46 & ( ~ ( perm @ A @ $o @ Pi @ B2 )
% 0.30/0.46 => ( ( perm @ A @ B @ Pi @ ( if @ B @ B2 @ C1 @ C22 ) )
% 0.30/0.46 = ( perm @ A @ B @ Pi @ C22 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % if_eqvt
% 0.30/0.46 thf(fact_116_pt__bij3,axiom,
% 0.30/0.46 ! [X: $tType,A: $tType,X3: A,Y4: A,Pi: list @ ( product_prod @ X @ X )] :
% 0.30/0.46 ( ( X3 = Y4 )
% 0.30/0.46 => ( ( perm @ X @ A @ Pi @ X3 )
% 0.30/0.46 = ( perm @ X @ A @ Pi @ Y4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % pt_bij3
% 0.30/0.46 thf(fact_117_abs__fun__if,axiom,
% 0.30/0.46 ! [X: $tType,A: $tType,C2: $o,Pi: list @ ( product_prod @ X @ X ),X3: A,Y4: A] :
% 0.30/0.46 ( ( C2
% 0.30/0.46 => ( ( perm @ X @ A @ Pi @ ( if @ A @ C2 @ X3 @ Y4 ) )
% 0.30/0.46 = ( perm @ X @ A @ Pi @ X3 ) ) )
% 0.30/0.46 & ( ~ C2
% 0.30/0.46 => ( ( perm @ X @ A @ Pi @ ( if @ A @ C2 @ X3 @ Y4 ) )
% 0.30/0.46 = ( perm @ X @ A @ Pi @ Y4 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % abs_fun_if
% 0.30/0.46 thf(fact_118_eqvt__def,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( pt_name @ A )
% 0.30/0.46 => ( ( eqvt @ A )
% 0.30/0.46 = ( ^ [Rel2: set @ ( product_prod @ A @ A )] :
% 0.30/0.46 ! [X6: product_prod @ A @ A,Perm2: list @ ( product_prod @ name @ name )] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ A ) @ X6 @ Rel2 )
% 0.30/0.46 => ( member @ ( product_prod @ A @ A ) @ ( perm @ name @ ( product_prod @ A @ A ) @ Perm2 @ X6 ) @ Rel2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % eqvt_def
% 0.30/0.46 thf(fact_119_perm__prod_Osimps,axiom,
% 0.30/0.46 ! [A: $tType,X: $tType,B: $tType,Pi: list @ ( product_prod @ X @ X ),X3: A,Y4: B] :
% 0.30/0.46 ( ( perm @ X @ ( product_prod @ A @ B ) @ Pi @ ( product_Pair @ A @ B @ X3 @ Y4 ) )
% 0.30/0.46 = ( product_Pair @ A @ B @ ( perm @ X @ A @ Pi @ X3 ) @ ( perm @ X @ B @ Pi @ Y4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % perm_prod.simps
% 0.30/0.46 thf(fact_120_cons__eqvt,axiom,
% 0.30/0.46 ! [X: $tType,A: $tType,Pi: list @ ( product_prod @ X @ X ),X3: A,Xs2: list @ A] :
% 0.30/0.46 ( ( perm @ X @ ( list @ A ) @ Pi @ ( cons @ A @ X3 @ Xs2 ) )
% 0.30/0.46 = ( cons @ A @ ( perm @ X @ A @ Pi @ X3 ) @ ( perm @ X @ ( list @ A ) @ Pi @ Xs2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % cons_eqvt
% 0.30/0.46 thf(fact_121_fresh__prodD_I1_J,axiom,
% 0.30/0.46 ! [C3: $tType,A: $tType,B: $tType,A2: A,X3: B,Y4: C3] :
% 0.30/0.46 ( ( fresh @ A @ ( product_prod @ B @ C3 ) @ A2 @ ( product_Pair @ B @ C3 @ X3 @ Y4 ) )
% 0.30/0.46 => ( fresh @ A @ B @ A2 @ X3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % fresh_prodD(1)
% 0.30/0.46 thf(fact_122_fresh__prodD_I2_J,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,C3: $tType,A2: A,X3: B,Y4: C3] :
% 0.30/0.46 ( ( fresh @ A @ ( product_prod @ B @ C3 ) @ A2 @ ( product_Pair @ B @ C3 @ X3 @ Y4 ) )
% 0.30/0.46 => ( fresh @ A @ C3 @ A2 @ Y4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % fresh_prodD(2)
% 0.30/0.46 thf(fact_123_fresh__list__cons,axiom,
% 0.30/0.46 ! [X: $tType,A: $tType,A2: X,X3: A,Xs2: list @ A] :
% 0.30/0.46 ( ( fresh @ X @ ( list @ A ) @ A2 @ ( cons @ A @ X3 @ Xs2 ) )
% 0.30/0.46 = ( ( fresh @ X @ A @ A2 @ X3 )
% 0.30/0.46 & ( fresh @ X @ ( list @ A ) @ A2 @ Xs2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % fresh_list_cons
% 0.30/0.46 thf(fact_124_subrelI,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,R: set @ ( product_prod @ A @ B ),S: set @ ( product_prod @ A @ B )] :
% 0.30/0.46 ( ! [X5: A,Y3: B] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X5 @ Y3 ) @ R )
% 0.30/0.46 => ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X5 @ Y3 ) @ S ) )
% 0.30/0.46 => ( ord_less_eq @ ( set @ ( product_prod @ A @ B ) ) @ R @ S ) ) ).
% 0.30/0.46
% 0.30/0.46 % subrelI
% 0.30/0.46 thf(fact_125_IdE,axiom,
% 0.30/0.46 ! [A: $tType,P3: product_prod @ A @ A] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ A ) @ P3 @ ( id @ A ) )
% 0.30/0.46 => ~ ! [X5: A] :
% 0.30/0.46 ( P3
% 0.30/0.46 != ( product_Pair @ A @ A @ X5 @ X5 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % IdE
% 0.30/0.46 thf(fact_126_derivativeMonotonic,axiom,
% 0.30/0.46 ! [P2: pi,Q: pi,A2: late_subject,X3: name,A5: set @ ( product_prod @ pi @ pi ),B5: set @ ( product_prod @ pi @ pi )] :
% 0.30/0.46 ( ( strong2129052853vative @ P2 @ Q @ A2 @ X3 @ A5 )
% 0.30/0.46 => ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ A5 @ B5 )
% 0.30/0.46 => ( strong2129052853vative @ P2 @ Q @ A2 @ X3 @ B5 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % derivativeMonotonic
% 0.30/0.46 thf(fact_127_eqvtRelE,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( pt_name @ A )
% 0.30/0.46 => ! [Rel: set @ ( product_prod @ A @ A ),Perm: list @ ( product_prod @ name @ name ),P2: A,Q: A] :
% 0.30/0.46 ( ( eqvt @ A @ Rel )
% 0.30/0.46 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ ( perm @ name @ A @ Perm @ P2 ) @ ( perm @ name @ A @ Perm @ Q ) ) @ Rel )
% 0.30/0.46 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ P2 @ Q ) @ Rel ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % eqvtRelE
% 0.30/0.46 thf(fact_128_Bound_Ohyps_I3_J,axiom,
% 0.30/0.46 fresh @ name @ pi @ y @ ( sum @ ( res @ x @ p ) @ ( res @ x @ q ) ) ).
% 0.30/0.46
% 0.30/0.46 % Bound.hyps(3)
% 0.30/0.46 thf(fact_129_Bound_Ohyps_I2_J,axiom,
% 0.30/0.46 fresh @ name @ pi @ y @ ( res @ x @ ( sum @ p @ q ) ) ).
% 0.30/0.46
% 0.30/0.46 % Bound.hyps(2)
% 0.30/0.46 thf(fact_130_subset__antisym,axiom,
% 0.30/0.46 ! [A: $tType,A5: set @ A,B5: set @ A] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ A5 @ B5 )
% 0.30/0.46 => ( ( ord_less_eq @ ( set @ A ) @ B5 @ A5 )
% 0.30/0.46 => ( A5 = B5 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_antisym
% 0.30/0.46 thf(fact_131_subsetI,axiom,
% 0.30/0.46 ! [A: $tType,A5: set @ A,B5: set @ A] :
% 0.30/0.46 ( ! [X5: A] :
% 0.30/0.46 ( ( member @ A @ X5 @ A5 )
% 0.30/0.46 => ( member @ A @ X5 @ B5 ) )
% 0.30/0.46 => ( ord_less_eq @ ( set @ A ) @ A5 @ B5 ) ) ).
% 0.30/0.46
% 0.30/0.46 % subsetI
% 0.30/0.46 thf(fact_132_order__refl,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( preorder @ A )
% 0.30/0.46 => ! [X3: A] : ( ord_less_eq @ A @ X3 @ X3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_refl
% 0.30/0.46 thf(fact_133_name__fresh,axiom,
% 0.30/0.46 ( ( fresh @ name @ name )
% 0.30/0.46 = ( ^ [A6: name,B6: name] : ( A6 != B6 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % name_fresh
% 0.30/0.46 thf(fact_134_pi_Ofresh_I7_J,axiom,
% 0.30/0.46 ! [A2: name,X22: pi,X1: pi] :
% 0.30/0.46 ( ( fresh @ name @ pi @ A2 @ ( sum @ X22 @ X1 ) )
% 0.30/0.46 = ( ( fresh @ name @ pi @ A2 @ X22 )
% 0.30/0.46 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % pi.fresh(7)
% 0.30/0.46 thf(fact_135_pi_Operm_I7_J,axiom,
% 0.30/0.46 ! [Pi: list @ ( product_prod @ name @ name ),X22: pi,X1: pi] :
% 0.30/0.46 ( ( perm @ name @ pi @ Pi @ ( sum @ X22 @ X1 ) )
% 0.30/0.46 = ( sum @ ( perm @ name @ pi @ Pi @ X22 ) @ ( perm @ name @ pi @ Pi @ X1 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % pi.perm(7)
% 0.30/0.46 thf(fact_136_pi_Operm_I9_J,axiom,
% 0.30/0.46 ! [Pi: list @ ( product_prod @ name @ name ),X1: name,X22: pi] :
% 0.30/0.46 ( ( perm @ name @ pi @ Pi @ ( res @ X1 @ X22 ) )
% 0.30/0.46 = ( res @ ( perm @ name @ name @ Pi @ X1 ) @ ( perm @ name @ pi @ Pi @ X22 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % pi.perm(9)
% 0.30/0.46 thf(fact_137_pi_Odistinct_I81_J,axiom,
% 0.30/0.46 ! [Pi1: pi,Pi2: pi,Name: name,Pi4: pi] :
% 0.30/0.46 ( ( sum @ Pi1 @ Pi2 )
% 0.30/0.46 != ( res @ Name @ Pi4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % pi.distinct(81)
% 0.30/0.46 thf(fact_138_pi_Oinject_I6_J,axiom,
% 0.30/0.46 ! [X22: pi,X1: pi,Y2: pi,Y1: pi] :
% 0.30/0.46 ( ( ( sum @ X22 @ X1 )
% 0.30/0.46 = ( sum @ Y2 @ Y1 ) )
% 0.30/0.46 = ( ( X22 = Y2 )
% 0.30/0.46 & ( X1 = Y1 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % pi.inject(6)
% 0.30/0.46 thf(fact_139_freshRes,axiom,
% 0.30/0.46 ! [A2: name,P2: pi] : ( fresh @ name @ pi @ A2 @ ( res @ A2 @ P2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % freshRes
% 0.30/0.46 thf(fact_140_le__funD,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( ord @ B )
% 0.30/0.46 => ! [F3: A > B,G3: A > B,X3: A] :
% 0.30/0.46 ( ( ord_less_eq @ ( A > B ) @ F3 @ G3 )
% 0.30/0.46 => ( ord_less_eq @ B @ ( F3 @ X3 ) @ ( G3 @ X3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_funD
% 0.30/0.46 thf(fact_141_le__funE,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( ord @ B )
% 0.30/0.46 => ! [F3: A > B,G3: A > B,X3: A] :
% 0.30/0.46 ( ( ord_less_eq @ ( A > B ) @ F3 @ G3 )
% 0.30/0.46 => ( ord_less_eq @ B @ ( F3 @ X3 ) @ ( G3 @ X3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_funE
% 0.30/0.46 thf(fact_142_le__funI,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( ord @ B )
% 0.30/0.46 => ! [F3: A > B,G3: A > B] :
% 0.30/0.46 ( ! [X5: A] : ( ord_less_eq @ B @ ( F3 @ X5 ) @ ( G3 @ X5 ) )
% 0.30/0.46 => ( ord_less_eq @ ( A > B ) @ F3 @ G3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_funI
% 0.30/0.46 thf(fact_143_le__fun__def,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( ord @ B )
% 0.30/0.46 => ( ( ord_less_eq @ ( A > B ) )
% 0.30/0.46 = ( ^ [F4: A > B,G4: A > B] :
% 0.30/0.46 ! [X6: A] : ( ord_less_eq @ B @ ( F4 @ X6 ) @ ( G4 @ X6 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_fun_def
% 0.30/0.46 thf(fact_144_order__subst1,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType] :
% 0.30/0.46 ( ( ( order @ B )
% 0.30/0.46 & ( order @ A ) )
% 0.30/0.46 => ! [A2: A,F3: B > A,B2: B,C2: B] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A2 @ ( F3 @ B2 ) )
% 0.30/0.46 => ( ( ord_less_eq @ B @ B2 @ C2 )
% 0.30/0.46 => ( ! [X5: B,Y3: B] :
% 0.30/0.46 ( ( ord_less_eq @ B @ X5 @ Y3 )
% 0.30/0.46 => ( ord_less_eq @ A @ ( F3 @ X5 ) @ ( F3 @ Y3 ) ) )
% 0.30/0.46 => ( ord_less_eq @ A @ A2 @ ( F3 @ C2 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_subst1
% 0.30/0.46 thf(fact_145_order__subst2,axiom,
% 0.30/0.46 ! [A: $tType,C3: $tType] :
% 0.30/0.46 ( ( ( order @ C3 )
% 0.30/0.46 & ( order @ A ) )
% 0.30/0.46 => ! [A2: A,B2: A,F3: A > C3,C2: C3] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.30/0.46 => ( ( ord_less_eq @ C3 @ ( F3 @ B2 ) @ C2 )
% 0.30/0.46 => ( ! [X5: A,Y3: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ X5 @ Y3 )
% 0.30/0.46 => ( ord_less_eq @ C3 @ ( F3 @ X5 ) @ ( F3 @ Y3 ) ) )
% 0.30/0.46 => ( ord_less_eq @ C3 @ ( F3 @ A2 ) @ C2 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % order_subst2
% 0.30/0.47 thf(fact_146_ord__eq__le__subst,axiom,
% 0.30/0.47 ! [A: $tType,B: $tType] :
% 0.30/0.47 ( ( ( ord @ B )
% 0.30/0.47 & ( ord @ A ) )
% 0.30/0.47 => ! [A2: A,F3: B > A,B2: B,C2: B] :
% 0.30/0.47 ( ( A2
% 0.30/0.47 = ( F3 @ B2 ) )
% 0.30/0.47 => ( ( ord_less_eq @ B @ B2 @ C2 )
% 0.30/0.47 => ( ! [X5: B,Y3: B] :
% 0.30/0.47 ( ( ord_less_eq @ B @ X5 @ Y3 )
% 0.30/0.47 => ( ord_less_eq @ A @ ( F3 @ X5 ) @ ( F3 @ Y3 ) ) )
% 0.30/0.47 => ( ord_less_eq @ A @ A2 @ ( F3 @ C2 ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % ord_eq_le_subst
% 0.30/0.47 thf(fact_147_ord__le__eq__subst,axiom,
% 0.30/0.47 ! [A: $tType,B: $tType] :
% 0.30/0.47 ( ( ( ord @ B )
% 0.30/0.47 & ( ord @ A ) )
% 0.30/0.47 => ! [A2: A,B2: A,F3: A > B,C2: B] :
% 0.30/0.47 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.30/0.47 => ( ( ( F3 @ B2 )
% 0.30/0.47 = C2 )
% 0.30/0.47 => ( ! [X5: A,Y3: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ X5 @ Y3 )
% 0.30/0.47 => ( ord_less_eq @ B @ ( F3 @ X5 ) @ ( F3 @ Y3 ) ) )
% 0.30/0.47 => ( ord_less_eq @ B @ ( F3 @ A2 ) @ C2 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % ord_le_eq_subst
% 0.30/0.47 thf(fact_148_eq__iff,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( order @ A )
% 0.30/0.47 => ( ( ^ [Y6: A,Z: A] : ( Y6 = Z ) )
% 0.30/0.47 = ( ^ [X6: A,Y5: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ X6 @ Y5 )
% 0.30/0.47 & ( ord_less_eq @ A @ Y5 @ X6 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % eq_iff
% 0.30/0.47 thf(fact_149_antisym,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( order @ A )
% 0.30/0.47 => ! [X3: A,Y4: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ X3 @ Y4 )
% 0.30/0.47 => ( ( ord_less_eq @ A @ Y4 @ X3 )
% 0.30/0.47 => ( X3 = Y4 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % antisym
% 0.30/0.47 thf(fact_150_linear,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ! [X3: A,Y4: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ X3 @ Y4 )
% 0.30/0.47 | ( ord_less_eq @ A @ Y4 @ X3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % linear
% 0.30/0.47 thf(fact_151_eq__refl,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( preorder @ A )
% 0.30/0.47 => ! [X3: A,Y4: A] :
% 0.30/0.47 ( ( X3 = Y4 )
% 0.30/0.47 => ( ord_less_eq @ A @ X3 @ Y4 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % eq_refl
% 0.30/0.47 thf(fact_152_le__cases,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ! [X3: A,Y4: A] :
% 0.30/0.47 ( ~ ( ord_less_eq @ A @ X3 @ Y4 )
% 0.30/0.47 => ( ord_less_eq @ A @ Y4 @ X3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % le_cases
% 0.30/0.47 thf(fact_153_order_Otrans,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( order @ A )
% 0.30/0.47 => ! [A2: A,B2: A,C2: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.30/0.47 => ( ( ord_less_eq @ A @ B2 @ C2 )
% 0.30/0.47 => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % order.trans
% 0.30/0.47 thf(fact_154_le__cases3,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ! [X3: A,Y4: A,Z2: A] :
% 0.30/0.47 ( ( ( ord_less_eq @ A @ X3 @ Y4 )
% 0.30/0.47 => ~ ( ord_less_eq @ A @ Y4 @ Z2 ) )
% 0.30/0.47 => ( ( ( ord_less_eq @ A @ Y4 @ X3 )
% 0.30/0.47 => ~ ( ord_less_eq @ A @ X3 @ Z2 ) )
% 0.30/0.47 => ( ( ( ord_less_eq @ A @ X3 @ Z2 )
% 0.30/0.47 => ~ ( ord_less_eq @ A @ Z2 @ Y4 ) )
% 0.30/0.47 => ( ( ( ord_less_eq @ A @ Z2 @ Y4 )
% 0.30/0.47 => ~ ( ord_less_eq @ A @ Y4 @ X3 ) )
% 0.30/0.47 => ( ( ( ord_less_eq @ A @ Y4 @ Z2 )
% 0.30/0.47 => ~ ( ord_less_eq @ A @ Z2 @ X3 ) )
% 0.30/0.47 => ~ ( ( ord_less_eq @ A @ Z2 @ X3 )
% 0.30/0.47 => ~ ( ord_less_eq @ A @ X3 @ Y4 ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % le_cases3
% 0.30/0.47 thf(fact_155_antisym__conv,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( order @ A )
% 0.30/0.47 => ! [Y4: A,X3: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ Y4 @ X3 )
% 0.30/0.47 => ( ( ord_less_eq @ A @ X3 @ Y4 )
% 0.30/0.47 = ( X3 = Y4 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % antisym_conv
% 0.30/0.47 thf(fact_156_order__class_Oorder_Oeq__iff,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( order @ A )
% 0.30/0.47 => ( ( ^ [Y6: A,Z: A] : ( Y6 = Z ) )
% 0.30/0.47 = ( ^ [A6: A,B6: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ A6 @ B6 )
% 0.30/0.47 & ( ord_less_eq @ A @ B6 @ A6 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % order_class.order.eq_iff
% 0.30/0.47 thf(fact_157_ord__eq__le__trans,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( ord @ A )
% 0.30/0.47 => ! [A2: A,B2: A,C2: A] :
% 0.30/0.47 ( ( A2 = B2 )
% 0.30/0.47 => ( ( ord_less_eq @ A @ B2 @ C2 )
% 0.30/0.47 => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % ord_eq_le_trans
% 0.30/0.47 thf(fact_158_ord__le__eq__trans,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( ord @ A )
% 0.30/0.47 => ! [A2: A,B2: A,C2: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.30/0.47 => ( ( B2 = C2 )
% 0.30/0.47 => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % ord_le_eq_trans
% 0.30/0.47 thf(fact_159_order__class_Oorder_Oantisym,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( order @ A )
% 0.30/0.47 => ! [A2: A,B2: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.30/0.47 => ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.30/0.47 => ( A2 = B2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % order_class.order.antisym
% 0.30/0.47 thf(fact_160_order__trans,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( preorder @ A )
% 0.30/0.47 => ! [X3: A,Y4: A,Z2: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ X3 @ Y4 )
% 0.30/0.47 => ( ( ord_less_eq @ A @ Y4 @ Z2 )
% 0.30/0.47 => ( ord_less_eq @ A @ X3 @ Z2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % order_trans
% 0.30/0.47 thf(fact_161_dual__order_Orefl,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( order @ A )
% 0.30/0.47 => ! [A2: A] : ( ord_less_eq @ A @ A2 @ A2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % dual_order.refl
% 0.30/0.47 thf(fact_162_linorder__wlog,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ! [P2: A > A > $o,A2: A,B2: A] :
% 0.30/0.47 ( ! [A4: A,B4: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ A4 @ B4 )
% 0.30/0.47 => ( P2 @ A4 @ B4 ) )
% 0.30/0.47 => ( ! [A4: A,B4: A] :
% 0.30/0.47 ( ( P2 @ B4 @ A4 )
% 0.30/0.47 => ( P2 @ A4 @ B4 ) )
% 0.30/0.47 => ( P2 @ A2 @ B2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % linorder_wlog
% 0.30/0.47 thf(fact_163_dual__order_Otrans,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( order @ A )
% 0.30/0.47 => ! [B2: A,A2: A,C2: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.30/0.47 => ( ( ord_less_eq @ A @ C2 @ B2 )
% 0.30/0.47 => ( ord_less_eq @ A @ C2 @ A2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % dual_order.trans
% 0.30/0.47 thf(fact_164_dual__order_Oeq__iff,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( order @ A )
% 0.30/0.47 => ( ( ^ [Y6: A,Z: A] : ( Y6 = Z ) )
% 0.30/0.47 = ( ^ [A6: A,B6: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ B6 @ A6 )
% 0.30/0.47 & ( ord_less_eq @ A @ A6 @ B6 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % dual_order.eq_iff
% 0.30/0.47 thf(fact_165_dual__order_Oantisym,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( order @ A )
% 0.30/0.47 => ! [B2: A,A2: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.30/0.47 => ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.30/0.47 => ( A2 = B2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % dual_order.antisym
% 0.30/0.47 thf(fact_166_in__mono,axiom,
% 0.30/0.47 ! [A: $tType,A5: set @ A,B5: set @ A,X3: A] :
% 0.30/0.47 ( ( ord_less_eq @ ( set @ A ) @ A5 @ B5 )
% 0.30/0.47 => ( ( member @ A @ X3 @ A5 )
% 0.30/0.47 => ( member @ A @ X3 @ B5 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % in_mono
% 0.30/0.47 thf(fact_167_subsetD,axiom,
% 0.30/0.47 ! [A: $tType,A5: set @ A,B5: set @ A,C2: A] :
% 0.30/0.47 ( ( ord_less_eq @ ( set @ A ) @ A5 @ B5 )
% 0.30/0.47 => ( ( member @ A @ C2 @ A5 )
% 0.30/0.47 => ( member @ A @ C2 @ B5 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % subsetD
% 0.30/0.47 thf(fact_168_equalityE,axiom,
% 0.30/0.47 ! [A: $tType,A5: set @ A,B5: set @ A] :
% 0.30/0.47 ( ( A5 = B5 )
% 0.30/0.47 => ~ ( ( ord_less_eq @ ( set @ A ) @ A5 @ B5 )
% 0.30/0.47 => ~ ( ord_less_eq @ ( set @ A ) @ B5 @ A5 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % equalityE
% 0.30/0.47 thf(fact_169_subset__eq,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( ord_less_eq @ ( set @ A ) )
% 0.30/0.47 = ( ^ [A7: set @ A,B7: set @ A] :
% 0.30/0.47 ! [X6: A] :
% 0.30/0.47 ( ( member @ A @ X6 @ A7 )
% 0.30/0.47 => ( member @ A @ X6 @ B7 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % subset_eq
% 0.30/0.47 thf(fact_170_equalityD1,axiom,
% 0.30/0.47 ! [A: $tType,A5: set @ A,B5: set @ A] :
% 0.30/0.47 ( ( A5 = B5 )
% 0.30/0.47 => ( ord_less_eq @ ( set @ A ) @ A5 @ B5 ) ) ).
% 0.30/0.47
% 0.30/0.47 % equalityD1
% 0.30/0.47 thf(fact_171_equalityD2,axiom,
% 0.30/0.47 ! [A: $tType,A5: set @ A,B5: set @ A] :
% 0.30/0.47 ( ( A5 = B5 )
% 0.30/0.47 => ( ord_less_eq @ ( set @ A ) @ B5 @ A5 ) ) ).
% 0.30/0.47
% 0.30/0.47 % equalityD2
% 0.30/0.47 thf(fact_172_subset__iff,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( ord_less_eq @ ( set @ A ) )
% 0.30/0.47 = ( ^ [A7: set @ A,B7: set @ A] :
% 0.30/0.47 ! [T2: A] :
% 0.30/0.47 ( ( member @ A @ T2 @ A7 )
% 0.30/0.47 => ( member @ A @ T2 @ B7 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % subset_iff
% 0.30/0.47 thf(fact_173_subset__refl,axiom,
% 0.30/0.47 ! [A: $tType,A5: set @ A] : ( ord_less_eq @ ( set @ A ) @ A5 @ A5 ) ).
% 0.30/0.47
% 0.30/0.47 % subset_refl
% 0.30/0.47 thf(fact_174_Collect__mono,axiom,
% 0.30/0.47 ! [A: $tType,P2: A > $o,Q: A > $o] :
% 0.30/0.47 ( ! [X5: A] :
% 0.30/0.47 ( ( P2 @ X5 )
% 0.30/0.47 => ( Q @ X5 ) )
% 0.30/0.47 => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P2 ) @ ( collect @ A @ Q ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Collect_mono
% 0.30/0.47 thf(fact_175_subset__trans,axiom,
% 0.30/0.47 ! [A: $tType,A5: set @ A,B5: set @ A,C4: set @ A] :
% 0.30/0.47 ( ( ord_less_eq @ ( set @ A ) @ A5 @ B5 )
% 0.30/0.47 => ( ( ord_less_eq @ ( set @ A ) @ B5 @ C4 )
% 0.30/0.47 => ( ord_less_eq @ ( set @ A ) @ A5 @ C4 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % subset_trans
% 0.30/0.47 thf(fact_176_set__eq__subset,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( ^ [Y6: set @ A,Z: set @ A] : ( Y6 = Z ) )
% 0.30/0.47 = ( ^ [A7: set @ A,B7: set @ A] :
% 0.30/0.47 ( ( ord_less_eq @ ( set @ A ) @ A7 @ B7 )
% 0.30/0.47 & ( ord_less_eq @ ( set @ A ) @ B7 @ A7 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % set_eq_subset
% 0.30/0.47 thf(fact_177_Collect__mono__iff,axiom,
% 0.30/0.47 ! [A: $tType,P2: A > $o,Q: A > $o] :
% 0.30/0.47 ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P2 ) @ ( collect @ A @ Q ) )
% 0.30/0.47 = ( ! [X6: A] :
% 0.30/0.47 ( ( P2 @ X6 )
% 0.30/0.47 => ( Q @ X6 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Collect_mono_iff
% 0.30/0.47 thf(fact_178_alphaRes,axiom,
% 0.30/0.47 ! [C2: name,P2: pi,A2: name] :
% 0.30/0.47 ( ( fresh @ name @ pi @ C2 @ P2 )
% 0.30/0.47 => ( ( res @ A2 @ P2 )
% 0.30/0.47 = ( res @ C2 @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ C2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ P2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % alphaRes
% 0.30/0.47 thf(fact_179_calculation,axiom,
% 0.30/0.47 late_transitions @ ( res @ x @ ( sum @ p @ q ) ) @ ( late_BoundR @ ( late_BoundOutputS @ aa ) @ y @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ y @ x ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ p2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % calculation
% 0.30/0.47 thf(fact_180_Bound_Ohyps_I1_J,axiom,
% 0.30/0.47 late_transitions @ ( sum @ ( res @ x @ p ) @ ( res @ x @ q ) ) @ ( late_BoundR @ a @ y @ pq ) ).
% 0.30/0.47
% 0.30/0.47 % Bound.hyps(1)
% 0.30/0.47 thf(fact_181__092_060open_062_060_092_060nu_062x_062_IP_A_092_060oplus_062_AQ_J_A_092_060longmapsto_062_Aa_060_092_060nu_062x_062_A_092_060prec_062_AP_H_092_060close_062,axiom,
% 0.30/0.47 late_transitions @ ( res @ x @ ( sum @ p @ q ) ) @ ( late_BoundR @ ( late_BoundOutputS @ aa ) @ x @ p2 ) ).
% 0.30/0.47
% 0.30/0.47 % \<open><\<nu>x>(P \<oplus> Q) \<longmapsto> a<\<nu>x> \<prec> P'\<close>
% 0.30/0.47 thf(fact_182_sumResLeft,axiom,
% 0.30/0.47 ! [Rel: set @ ( product_prod @ pi @ pi ),X3: name,P2: pi,Q: pi] :
% 0.30/0.47 ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 0.30/0.47 => ( ( eqvt @ pi @ Rel )
% 0.30/0.47 => ( strong743114133lation @ ( sum @ ( res @ X3 @ P2 ) @ ( res @ X3 @ Q ) ) @ Rel @ ( res @ X3 @ ( sum @ P2 @ Q ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % sumResLeft
% 0.30/0.47 thf(fact_183_cSum1_Ohyps,axiom,
% 0.30/0.47 late_transitions @ ( res @ x @ p ) @ ( late_BoundR @ a @ y @ pq ) ).
% 0.30/0.47
% 0.30/0.47 % cSum1.hyps
% 0.30/0.47 thf(fact_184_residual_Operm_I1_J,axiom,
% 0.30/0.47 ! [Pi: list @ ( product_prod @ name @ name ),X32: late_subject,X1: name,X22: pi] :
% 0.30/0.47 ( ( perm @ name @ late_residual @ Pi @ ( late_BoundR @ X32 @ X1 @ X22 ) )
% 0.30/0.47 = ( late_BoundR @ ( perm @ name @ late_subject @ Pi @ X32 ) @ ( perm @ name @ name @ Pi @ X1 ) @ ( perm @ name @ pi @ Pi @ X22 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % residual.perm(1)
% 0.30/0.47 thf(fact_185_freshBoundDerivative_I1_J,axiom,
% 0.30/0.47 ! [P2: pi,A2: late_subject,X3: name,P4: pi,Y4: name] :
% 0.30/0.47 ( ( late_transitions @ P2 @ ( late_BoundR @ A2 @ X3 @ P4 ) )
% 0.30/0.47 => ( ( fresh @ name @ pi @ Y4 @ P2 )
% 0.30/0.47 => ( fresh @ name @ late_subject @ Y4 @ A2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % freshBoundDerivative(1)
% 0.30/0.47 thf(fact_186_Late__Semantics_OResB,axiom,
% 0.30/0.47 ! [P2: pi,A2: late_subject,X3: name,P4: pi,Y4: name] :
% 0.30/0.47 ( ( late_transitions @ P2 @ ( late_BoundR @ A2 @ X3 @ P4 ) )
% 0.30/0.47 => ( ( fresh @ name @ late_subject @ Y4 @ A2 )
% 0.30/0.47 => ( ( Y4 != X3 )
% 0.30/0.47 => ( late_transitions @ ( res @ Y4 @ P2 ) @ ( late_BoundR @ A2 @ X3 @ ( res @ Y4 @ P4 ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Late_Semantics.ResB
% 0.30/0.47 thf(fact_187_freshBoundDerivative_I2_J,axiom,
% 0.30/0.47 ! [P2: pi,A2: late_subject,X3: name,P4: pi,Y4: name] :
% 0.30/0.47 ( ( late_transitions @ P2 @ ( late_BoundR @ A2 @ X3 @ P4 ) )
% 0.30/0.47 => ( ( fresh @ name @ pi @ Y4 @ P2 )
% 0.30/0.47 => ( ( Y4 != X3 )
% 0.30/0.47 => ( fresh @ name @ pi @ Y4 @ P4 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % freshBoundDerivative(2)
% 0.30/0.47 thf(fact_188_simE_I1_J,axiom,
% 0.30/0.47 ! [P2: pi,Rel: set @ ( product_prod @ pi @ pi ),Q: pi,A2: late_subject,X3: name,Q2: pi] :
% 0.30/0.47 ( ( strong743114133lation @ P2 @ Rel @ Q )
% 0.30/0.47 => ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X3 @ Q2 ) )
% 0.30/0.47 => ( ( fresh @ name @ pi @ X3 @ P2 )
% 0.30/0.47 => ? [P5: pi] :
% 0.30/0.47 ( ( late_transitions @ P2 @ ( late_BoundR @ A2 @ X3 @ P5 ) )
% 0.30/0.47 & ( strong2129052853vative @ P5 @ Q2 @ A2 @ X3 @ Rel ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % simE(1)
% 0.30/0.47 thf(fact_189_Sum2,axiom,
% 0.30/0.47 ! [Q: pi,Rs: late_residual,P2: pi] :
% 0.30/0.47 ( ( late_transitions @ Q @ Rs )
% 0.30/0.47 => ( late_transitions @ ( sum @ P2 @ Q ) @ Rs ) ) ).
% 0.30/0.47
% 0.30/0.47 % Sum2
% 0.30/0.47 thf(fact_190_Sum1,axiom,
% 0.30/0.47 ! [P2: pi,Rs: late_residual,Q: pi] :
% 0.30/0.47 ( ( late_transitions @ P2 @ Rs )
% 0.30/0.47 => ( late_transitions @ ( sum @ P2 @ Q ) @ Rs ) ) ).
% 0.30/0.47
% 0.30/0.47 % Sum1
% 0.30/0.47 thf(fact_191_sumCases_H,axiom,
% 0.30/0.47 ! [P2: pi,Q: pi,Rs: late_residual] :
% 0.30/0.47 ( ( late_transitions @ ( sum @ P2 @ Q ) @ Rs )
% 0.30/0.47 => ( ~ ( late_transitions @ P2 @ Rs )
% 0.30/0.47 => ( late_transitions @ Q @ Rs ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % sumCases'
% 0.30/0.47 thf(fact_192_sumCases,axiom,
% 0.30/0.47 ! [P2: pi,Q: pi,Rs: late_residual] :
% 0.30/0.47 ( ( late_transitions @ ( sum @ P2 @ Q ) @ Rs )
% 0.30/0.47 => ( ~ ( late_transitions @ P2 @ Rs )
% 0.30/0.47 => ( late_transitions @ Q @ Rs ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % sumCases
% 0.30/0.47 thf(fact_193_freshResidual,axiom,
% 0.30/0.47 ! [P2: pi,Rs: late_residual,X3: name] :
% 0.30/0.47 ( ( late_transitions @ P2 @ Rs )
% 0.30/0.47 => ( ( fresh @ name @ pi @ X3 @ P2 )
% 0.30/0.47 => ( fresh @ name @ late_residual @ X3 @ Rs ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % freshResidual
% 0.30/0.47 thf(fact_194_eqvt,axiom,
% 0.30/0.47 ! [X1: pi,X22: late_residual,Pi: list @ ( product_prod @ name @ name )] :
% 0.30/0.47 ( ( late_transitions @ X1 @ X22 )
% 0.30/0.47 => ( late_transitions @ ( perm @ name @ pi @ Pi @ X1 ) @ ( perm @ name @ late_residual @ Pi @ X22 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % eqvt
% 0.30/0.47 thf(fact_195_transitions_OResB,axiom,
% 0.30/0.47 ! [P2: pi,A2: late_subject,X3: name,P4: pi,Y4: name] :
% 0.30/0.47 ( ( late_transitions @ P2 @ ( late_BoundR @ A2 @ X3 @ P4 ) )
% 0.30/0.47 => ( ( fresh @ name @ late_subject @ Y4 @ A2 )
% 0.30/0.47 => ( ( Y4 != X3 )
% 0.30/0.47 => ( ( fresh @ name @ pi @ X3 @ P2 )
% 0.30/0.47 => ( ( fresh @ name @ late_subject @ X3 @ A2 )
% 0.30/0.47 => ( late_transitions @ ( res @ Y4 @ P2 ) @ ( late_BoundR @ A2 @ X3 @ ( res @ Y4 @ P4 ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % transitions.ResB
% 0.30/0.47 thf(fact_196_monotonic,axiom,
% 0.30/0.47 ! [P2: pi,A5: set @ ( product_prod @ pi @ pi ),P4: pi,B5: set @ ( product_prod @ pi @ pi )] :
% 0.30/0.47 ( ( strong743114133lation @ P2 @ A5 @ P4 )
% 0.30/0.47 => ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ A5 @ B5 )
% 0.30/0.47 => ( strong743114133lation @ P2 @ B5 @ P4 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % monotonic
% 0.30/0.47 thf(fact_197_Strong__Late__Sim_Oreflexive,axiom,
% 0.30/0.47 ! [Rel: set @ ( product_prod @ pi @ pi ),P2: pi] :
% 0.30/0.47 ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 0.30/0.47 => ( strong743114133lation @ P2 @ Rel @ P2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % Strong_Late_Sim.reflexive
% 0.30/0.47 thf(fact_198_sumIdempRight,axiom,
% 0.30/0.47 ! [Rel: set @ ( product_prod @ pi @ pi ),P2: pi] :
% 0.30/0.47 ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 0.30/0.47 => ( strong743114133lation @ ( sum @ P2 @ P2 ) @ Rel @ P2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % sumIdempRight
% 0.30/0.47 thf(fact_199_sumAssocRight,axiom,
% 0.30/0.47 ! [Rel: set @ ( product_prod @ pi @ pi ),P2: pi,Q: pi,R2: pi] :
% 0.30/0.47 ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 0.30/0.47 => ( strong743114133lation @ ( sum @ P2 @ ( sum @ Q @ R2 ) ) @ Rel @ ( sum @ ( sum @ P2 @ Q ) @ R2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % sumAssocRight
% 0.30/0.47 thf(fact_200_sumIdempLeft,axiom,
% 0.30/0.47 ! [Rel: set @ ( product_prod @ pi @ pi ),P2: pi] :
% 0.30/0.47 ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 0.30/0.47 => ( strong743114133lation @ P2 @ Rel @ ( sum @ P2 @ P2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % sumIdempLeft
% 0.30/0.47 thf(fact_201_sumAssocLeft,axiom,
% 0.30/0.47 ! [Rel: set @ ( product_prod @ pi @ pi ),P2: pi,Q: pi,R2: pi] :
% 0.30/0.47 ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 0.30/0.47 => ( strong743114133lation @ ( sum @ ( sum @ P2 @ Q ) @ R2 ) @ Rel @ ( sum @ P2 @ ( sum @ Q @ R2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % sumAssocLeft
% 0.30/0.47 thf(fact_202_sumSym,axiom,
% 0.30/0.47 ! [Rel: set @ ( product_prod @ pi @ pi ),P2: pi,Q: pi] :
% 0.30/0.47 ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 0.30/0.47 => ( strong743114133lation @ ( sum @ P2 @ Q ) @ Rel @ ( sum @ Q @ P2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % sumSym
% 0.30/0.47 thf(fact_203_eqvtI,axiom,
% 0.30/0.47 ! [P2: pi,Rel: set @ ( product_prod @ pi @ pi ),Q: pi,Rel3: set @ ( product_prod @ pi @ pi ),Perm: list @ ( product_prod @ name @ name )] :
% 0.30/0.47 ( ( strong743114133lation @ P2 @ Rel @ Q )
% 0.30/0.47 => ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ Rel @ Rel3 )
% 0.30/0.47 => ( ( eqvt @ pi @ Rel3 )
% 0.30/0.47 => ( strong743114133lation @ ( perm @ name @ pi @ Perm @ P2 ) @ Rel3 @ ( perm @ name @ pi @ Perm @ Q ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % eqvtI
% 0.30/0.47 thf(fact_204_alphaBoundResidual,axiom,
% 0.30/0.47 ! [X7: name,P2: pi,A2: late_subject,X3: name] :
% 0.30/0.47 ( ( fresh @ name @ pi @ X7 @ P2 )
% 0.30/0.47 => ( ( late_BoundR @ A2 @ X3 @ P2 )
% 0.30/0.47 = ( late_BoundR @ A2 @ X7 @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ X3 @ X7 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ P2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % alphaBoundResidual
% 0.30/0.47 thf(fact_205_cOpen_Ohyps_I1_J,axiom,
% 0.30/0.47 late_transitions @ p @ ( late_FreeR @ ( late_OutputR @ aa @ x ) @ p2 ) ).
% 0.30/0.47
% 0.30/0.47 % cOpen.hyps(1)
% 0.30/0.47 thf(fact_206_simCasesCont,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( fs_name @ A )
% 0.30/0.47 => ! [Rel: set @ ( product_prod @ pi @ pi ),Q: pi,P2: pi,C4: A] :
% 0.30/0.47 ( ( eqvt @ pi @ Rel )
% 0.30/0.47 => ( ! [A4: late_subject,X5: name,Q3: pi] :
% 0.30/0.47 ( ( late_transitions @ Q @ ( late_BoundR @ A4 @ X5 @ Q3 ) )
% 0.30/0.47 => ( ( fresh @ name @ pi @ X5 @ P2 )
% 0.30/0.47 => ( ( fresh @ name @ pi @ X5 @ Q )
% 0.30/0.47 => ( ( fresh @ name @ late_subject @ X5 @ A4 )
% 0.30/0.47 => ( ( fresh @ name @ A @ X5 @ C4 )
% 0.30/0.47 => ? [P6: pi] :
% 0.30/0.47 ( ( late_transitions @ P2 @ ( late_BoundR @ A4 @ X5 @ P6 ) )
% 0.30/0.47 & ( strong2129052853vative @ P6 @ Q3 @ A4 @ X5 @ Rel ) ) ) ) ) ) )
% 0.30/0.47 => ( ! [Alpha: late_freeRes,Q3: pi] :
% 0.30/0.47 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q3 ) )
% 0.30/0.47 => ? [P6: pi] :
% 0.30/0.47 ( ( late_transitions @ P2 @ ( late_FreeR @ Alpha @ P6 ) )
% 0.30/0.47 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P6 @ Q3 ) @ Rel ) ) )
% 0.30/0.47 => ( strong743114133lation @ P2 @ Rel @ Q ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % simCasesCont
% 0.30/0.47 thf(fact_207__092_060open_062P_A_092_060oplus_062_AQ_A_092_060longmapsto_062_Aa_091x_093_A_092_060prec_062_AP_H_092_060close_062,axiom,
% 0.30/0.47 late_transitions @ ( sum @ p @ q ) @ ( late_FreeR @ ( late_OutputR @ aa @ x ) @ p2 ) ).
% 0.30/0.47
% 0.30/0.47 % \<open>P \<oplus> Q \<longmapsto> a[x] \<prec> P'\<close>
% 0.30/0.47 thf(fact_208_Late__Semantics1_OfreeRes_Oinject,axiom,
% 0.30/0.47 ! [X11: name,X122: name,Y11: name,Y12: name] :
% 0.30/0.47 ( ( ( late_OutputR @ X11 @ X122 )
% 0.30/0.47 = ( late_OutputR @ Y11 @ Y12 ) )
% 0.30/0.47 = ( ( X11 = Y11 )
% 0.30/0.47 & ( X122 = Y12 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Late_Semantics1.freeRes.inject
% 0.30/0.47 thf(fact_209_Late__Semantics_OfreeRes_Oinject,axiom,
% 0.30/0.47 ! [X22: name,X1: name,Y2: name,Y1: name] :
% 0.30/0.47 ( ( ( late_OutputR @ X22 @ X1 )
% 0.30/0.47 = ( late_OutputR @ Y2 @ Y1 ) )
% 0.30/0.47 = ( ( X22 = Y2 )
% 0.30/0.47 & ( X1 = Y1 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Late_Semantics.freeRes.inject
% 0.30/0.47 thf(fact_210_freeRes_Operm_I1_J,axiom,
% 0.30/0.47 ! [Pi: list @ ( product_prod @ name @ name ),X22: name,X1: name] :
% 0.30/0.47 ( ( perm @ name @ late_freeRes @ Pi @ ( late_OutputR @ X22 @ X1 ) )
% 0.30/0.47 = ( late_OutputR @ ( perm @ name @ name @ Pi @ X22 ) @ ( perm @ name @ name @ Pi @ X1 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % freeRes.perm(1)
% 0.30/0.47 thf(fact_211_freeRes_Ofresh_I1_J,axiom,
% 0.30/0.47 ! [A2: name,X22: name,X1: name] :
% 0.30/0.47 ( ( fresh @ name @ late_freeRes @ A2 @ ( late_OutputR @ X22 @ X1 ) )
% 0.30/0.47 = ( ( fresh @ name @ name @ A2 @ X22 )
% 0.30/0.47 & ( fresh @ name @ name @ A2 @ X1 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % freeRes.fresh(1)
% 0.30/0.47 thf(fact_212_residual_Operm_I2_J,axiom,
% 0.30/0.47 ! [Pi: list @ ( product_prod @ name @ name ),X22: late_freeRes,X1: pi] :
% 0.30/0.47 ( ( perm @ name @ late_residual @ Pi @ ( late_FreeR @ X22 @ X1 ) )
% 0.30/0.47 = ( late_FreeR @ ( perm @ name @ late_freeRes @ Pi @ X22 ) @ ( perm @ name @ pi @ Pi @ X1 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % residual.perm(2)
% 0.30/0.47 thf(fact_213_residual_Ofresh_I2_J,axiom,
% 0.30/0.47 ! [A2: name,X22: late_freeRes,X1: pi] :
% 0.30/0.47 ( ( fresh @ name @ late_residual @ A2 @ ( late_FreeR @ X22 @ X1 ) )
% 0.30/0.47 = ( ( fresh @ name @ late_freeRes @ A2 @ X22 )
% 0.30/0.47 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % residual.fresh(2)
% 0.30/0.47 thf(fact_214_residual_Odistinct_I1_J,axiom,
% 0.30/0.47 ! [Subject: late_subject,Name2: name,Pi: pi,FreeRes: late_freeRes,Pi4: pi] :
% 0.30/0.47 ( ( late_BoundR @ Subject @ Name2 @ Pi )
% 0.30/0.47 != ( late_FreeR @ FreeRes @ Pi4 ) ) ).
% 0.30/0.47
% 0.30/0.47 % residual.distinct(1)
% 0.30/0.47 thf(fact_215_residual_Oinducts,axiom,
% 0.30/0.47 ! [P2: late_residual > $o,Residual: late_residual] :
% 0.30/0.47 ( ! [Subject2: late_subject,Name3: name,Pi5: pi] : ( P2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi5 ) )
% 0.30/0.47 => ( ! [FreeRes2: late_freeRes,Pi5: pi] : ( P2 @ ( late_FreeR @ FreeRes2 @ Pi5 ) )
% 0.30/0.47 => ( P2 @ Residual ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % residual.inducts
% 0.30/0.47 thf(fact_216_residual_Oinject_I2_J,axiom,
% 0.30/0.47 ! [X22: late_freeRes,X1: pi,Y2: late_freeRes,Y1: pi] :
% 0.30/0.47 ( ( ( late_FreeR @ X22 @ X1 )
% 0.30/0.47 = ( late_FreeR @ Y2 @ Y1 ) )
% 0.30/0.47 = ( ( X22 = Y2 )
% 0.30/0.47 & ( X1 = Y1 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % residual.inject(2)
% 0.30/0.47 thf(fact_217_ResF,axiom,
% 0.30/0.47 ! [P2: pi,Alpha2: late_freeRes,P4: pi,Y4: name] :
% 0.30/0.47 ( ( late_transitions @ P2 @ ( late_FreeR @ Alpha2 @ P4 ) )
% 0.30/0.47 => ( ( fresh @ name @ late_freeRes @ Y4 @ Alpha2 )
% 0.30/0.47 => ( late_transitions @ ( res @ Y4 @ P2 ) @ ( late_FreeR @ Alpha2 @ ( res @ Y4 @ P4 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % ResF
% 0.30/0.47 thf(fact_218_resCasesF_H,axiom,
% 0.30/0.47 ! [X3: name,P2: pi,Alpha2: late_freeRes,P4: pi] :
% 0.30/0.47 ( ( late_transitions @ ( res @ X3 @ P2 ) @ ( late_FreeR @ Alpha2 @ P4 ) )
% 0.30/0.47 => ~ ! [P: pi,Alpha: late_freeRes,P5: pi,Y3: name] :
% 0.30/0.47 ( ( ( res @ X3 @ P2 )
% 0.30/0.47 = ( res @ Y3 @ P ) )
% 0.30/0.47 => ( ( ( late_FreeR @ Alpha2 @ P4 )
% 0.30/0.47 = ( late_FreeR @ Alpha @ ( res @ Y3 @ P5 ) ) )
% 0.30/0.47 => ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P5 ) )
% 0.30/0.47 => ~ ( fresh @ name @ late_freeRes @ Y3 @ Alpha ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % resCasesF'
% 0.30/0.47 thf(fact_219_resCasesF,axiom,
% 0.30/0.47 ! [X3: name,P2: pi,Alpha2: late_freeRes,XP: pi,F5: pi > $o] :
% 0.30/0.47 ( ( late_transitions @ ( res @ X3 @ P2 ) @ ( late_FreeR @ Alpha2 @ XP ) )
% 0.30/0.47 => ( ! [P5: pi] :
% 0.30/0.47 ( ( late_transitions @ P2 @ ( late_FreeR @ Alpha2 @ P5 ) )
% 0.30/0.47 => ( ( fresh @ name @ late_freeRes @ X3 @ Alpha2 )
% 0.30/0.47 => ( F5 @ ( res @ X3 @ P5 ) ) ) )
% 0.30/0.47 => ( F5 @ XP ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % resCasesF
% 0.30/0.47 thf(fact_220_freshFreeDerivative_I2_J,axiom,
% 0.30/0.47 ! [P2: pi,Alpha2: late_freeRes,P4: pi,Y4: name] :
% 0.30/0.47 ( ( late_transitions @ P2 @ ( late_FreeR @ Alpha2 @ P4 ) )
% 0.30/0.47 => ( ( fresh @ name @ pi @ Y4 @ P2 )
% 0.30/0.47 => ( fresh @ name @ pi @ Y4 @ P4 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % freshFreeDerivative(2)
% 0.30/0.47 thf(fact_221_freshFreeDerivative_I1_J,axiom,
% 0.30/0.47 ! [P2: pi,Alpha2: late_freeRes,P4: pi,Y4: name] :
% 0.30/0.47 ( ( late_transitions @ P2 @ ( late_FreeR @ Alpha2 @ P4 ) )
% 0.30/0.47 => ( ( fresh @ name @ pi @ Y4 @ P2 )
% 0.30/0.47 => ( fresh @ name @ late_freeRes @ Y4 @ Alpha2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % freshFreeDerivative(1)
% 0.30/0.47 thf(fact_222_Open,axiom,
% 0.30/0.47 ! [P2: pi,A2: name,B2: name,P4: pi] :
% 0.30/0.47 ( ( late_transitions @ P2 @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P4 ) )
% 0.30/0.47 => ( ( A2 != B2 )
% 0.30/0.47 => ( late_transitions @ ( res @ B2 @ P2 ) @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ B2 @ P4 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Open
% 0.30/0.47 thf(fact_223_residual_Ostrong__inducts,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( fs_name @ A )
% 0.30/0.47 => ! [P2: A > late_residual > $o,Z2: A,Residual: late_residual] :
% 0.30/0.47 ( ! [Subject2: late_subject,Name3: name,Pi5: pi,Z3: A] :
% 0.30/0.47 ( ( fresh @ name @ A @ Name3 @ Z3 )
% 0.30/0.47 => ( ( fresh @ name @ late_subject @ Name3 @ Subject2 )
% 0.30/0.47 => ( P2 @ Z3 @ ( late_BoundR @ Subject2 @ Name3 @ Pi5 ) ) ) )
% 0.30/0.47 => ( ! [FreeRes2: late_freeRes,Pi5: pi,Z3: A] : ( P2 @ Z3 @ ( late_FreeR @ FreeRes2 @ Pi5 ) )
% 0.30/0.47 => ( P2 @ Z2 @ Residual ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % residual.strong_inducts
% 0.30/0.47 thf(fact_224_residual_Ostrong__induct,axiom,
% 0.30/0.47 ! [N: $tType] :
% 0.30/0.47 ( ( fs_name @ N )
% 0.30/0.47 => ! [P2: N > late_residual > $o,Z2: N,Residual: late_residual] :
% 0.30/0.47 ( ! [Subject2: late_subject,Name3: name,Pi5: pi,Z3: N] :
% 0.30/0.47 ( ( fresh @ name @ N @ Name3 @ Z3 )
% 0.30/0.47 => ( ( fresh @ name @ late_subject @ Name3 @ Subject2 )
% 0.30/0.47 => ( P2 @ Z3 @ ( late_BoundR @ Subject2 @ Name3 @ Pi5 ) ) ) )
% 0.30/0.47 => ( ! [FreeRes2: late_freeRes,Pi5: pi,Z3: N] : ( P2 @ Z3 @ ( late_FreeR @ FreeRes2 @ Pi5 ) )
% 0.30/0.47 => ( P2 @ Z2 @ Residual ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % residual.strong_induct
% 0.30/0.47 thf(fact_225_simE_I2_J,axiom,
% 0.30/0.47 ! [P2: pi,Rel: set @ ( product_prod @ pi @ pi ),Q: pi,Alpha2: late_freeRes,Q2: pi] :
% 0.30/0.47 ( ( strong743114133lation @ P2 @ Rel @ Q )
% 0.30/0.47 => ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q2 ) )
% 0.30/0.47 => ? [P5: pi] :
% 0.30/0.47 ( ( late_transitions @ P2 @ ( late_FreeR @ Alpha2 @ P5 ) )
% 0.30/0.47 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P5 @ Q2 ) @ Rel ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % simE(2)
% 0.30/0.47 thf(fact_226_resCasesB_H,axiom,
% 0.30/0.47 ! [X7: name,P2: pi,A2: late_subject,Y7: name,P4: pi] :
% 0.30/0.47 ( ( late_transitions @ ( res @ X7 @ P2 ) @ ( late_BoundR @ A2 @ Y7 @ P4 ) )
% 0.30/0.47 => ( ! [P: pi,A4: name,B4: name] :
% 0.30/0.47 ( ( ( res @ X7 @ P2 )
% 0.30/0.47 = ( res @ B4 @ P ) )
% 0.30/0.47 => ! [P5: pi] :
% 0.30/0.47 ( ( ( late_BoundR @ A2 @ Y7 @ P4 )
% 0.30/0.47 = ( late_BoundR @ ( late_BoundOutputS @ A4 ) @ B4 @ P5 ) )
% 0.30/0.47 => ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A4 @ B4 ) @ P5 ) )
% 0.30/0.47 => ( A4 = B4 ) ) ) )
% 0.30/0.47 => ~ ! [P: pi,A4: late_subject,X5: name,P5: pi,Y3: name] :
% 0.30/0.47 ( ( ( res @ X7 @ P2 )
% 0.30/0.47 = ( res @ Y3 @ P ) )
% 0.30/0.47 => ( ( ( late_BoundR @ A2 @ Y7 @ P4 )
% 0.30/0.47 = ( late_BoundR @ A4 @ X5 @ ( res @ Y3 @ P5 ) ) )
% 0.30/0.47 => ( ( late_transitions @ P @ ( late_BoundR @ A4 @ X5 @ P5 ) )
% 0.30/0.47 => ( ( fresh @ name @ late_subject @ Y3 @ A4 )
% 0.30/0.47 => ( ( Y3 != X5 )
% 0.30/0.47 => ( ( fresh @ name @ pi @ X5 @ P )
% 0.30/0.47 => ~ ( fresh @ name @ late_subject @ X5 @ A4 ) ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % resCasesB'
% 0.30/0.47 thf(fact_227_resCases_H,axiom,
% 0.30/0.47 ! [X3: name,P2: pi,Rs: late_residual] :
% 0.30/0.47 ( ( late_transitions @ ( res @ X3 @ P2 ) @ Rs )
% 0.30/0.47 => ( ! [P: pi,A4: name,B4: name] :
% 0.30/0.47 ( ( ( res @ X3 @ P2 )
% 0.30/0.47 = ( res @ B4 @ P ) )
% 0.30/0.47 => ! [P5: pi] :
% 0.30/0.47 ( ( Rs
% 0.30/0.47 = ( late_BoundR @ ( late_BoundOutputS @ A4 ) @ B4 @ P5 ) )
% 0.30/0.47 => ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A4 @ B4 ) @ P5 ) )
% 0.30/0.47 => ( A4 = B4 ) ) ) )
% 0.30/0.47 => ( ! [P: pi,A4: late_subject,X5: name,P5: pi,Y3: name] :
% 0.30/0.47 ( ( ( res @ X3 @ P2 )
% 0.30/0.47 = ( res @ Y3 @ P ) )
% 0.30/0.47 => ( ( Rs
% 0.30/0.47 = ( late_BoundR @ A4 @ X5 @ ( res @ Y3 @ P5 ) ) )
% 0.30/0.47 => ( ( late_transitions @ P @ ( late_BoundR @ A4 @ X5 @ P5 ) )
% 0.30/0.47 => ( ( fresh @ name @ late_subject @ Y3 @ A4 )
% 0.30/0.47 => ( ( Y3 != X5 )
% 0.30/0.47 => ( ( fresh @ name @ pi @ X5 @ P )
% 0.30/0.47 => ~ ( fresh @ name @ late_subject @ X5 @ A4 ) ) ) ) ) ) )
% 0.30/0.47 => ~ ! [P: pi,Alpha: late_freeRes,P5: pi,Y3: name] :
% 0.30/0.47 ( ( ( res @ X3 @ P2 )
% 0.30/0.47 = ( res @ Y3 @ P ) )
% 0.30/0.47 => ( ( Rs
% 0.30/0.47 = ( late_FreeR @ Alpha @ ( res @ Y3 @ P5 ) ) )
% 0.30/0.47 => ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P5 ) )
% 0.30/0.47 => ~ ( fresh @ name @ late_freeRes @ Y3 @ Alpha ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % resCases'
% 0.30/0.47 thf(fact_228_resCasesB,axiom,
% 0.30/0.47 ! [Y4: name,P2: pi,A2: late_subject,X3: name,YP: pi,F5: late_subject > pi > $o] :
% 0.30/0.47 ( ( late_transitions @ ( res @ Y4 @ P2 ) @ ( late_BoundR @ A2 @ X3 @ YP ) )
% 0.30/0.47 => ( ( X3 != Y4 )
% 0.30/0.47 => ( ( fresh @ name @ pi @ X3 @ P2 )
% 0.30/0.47 => ( ! [B4: name,P5: pi] :
% 0.30/0.47 ( ( late_transitions @ P2 @ ( late_FreeR @ ( late_OutputR @ B4 @ Y4 ) @ P5 ) )
% 0.30/0.47 => ( ( B4 != Y4 )
% 0.30/0.47 => ( ( A2
% 0.30/0.47 = ( late_BoundOutputS @ B4 ) )
% 0.30/0.47 => ( F5 @ ( late_BoundOutputS @ B4 ) @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ X3 @ Y4 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ P5 ) ) ) ) )
% 0.30/0.47 => ( ! [P5: pi] :
% 0.30/0.47 ( ( late_transitions @ P2 @ ( late_BoundR @ A2 @ X3 @ P5 ) )
% 0.30/0.47 => ( ( fresh @ name @ late_subject @ Y4 @ A2 )
% 0.30/0.47 => ( F5 @ A2 @ ( res @ Y4 @ P5 ) ) ) )
% 0.30/0.47 => ( F5 @ A2 @ YP ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % resCasesB
% 0.30/0.47 thf(fact_229_resSimCases,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( fs_name @ A )
% 0.30/0.47 => ! [Rel: set @ ( product_prod @ pi @ pi ),Q: pi,X3: name,P2: pi,C4: A] :
% 0.30/0.47 ( ( eqvt @ pi @ Rel )
% 0.30/0.47 => ( ! [Q3: pi,A4: name] :
% 0.30/0.47 ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A4 @ X3 ) @ Q3 ) )
% 0.30/0.47 => ( ( A4 != X3 )
% 0.30/0.47 => ? [P6: pi] :
% 0.30/0.47 ( ( late_transitions @ P2 @ ( late_BoundR @ ( late_BoundOutputS @ A4 ) @ X3 @ P6 ) )
% 0.30/0.47 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P6 @ Q3 ) @ Rel ) ) ) )
% 0.30/0.47 => ( ! [Q3: pi,A4: late_subject,Y3: name] :
% 0.30/0.47 ( ( late_transitions @ Q @ ( late_BoundR @ A4 @ Y3 @ Q3 ) )
% 0.30/0.47 => ( ( fresh @ name @ late_subject @ X3 @ A4 )
% 0.30/0.47 => ( ( X3 != Y3 )
% 0.30/0.47 => ( ( fresh @ name @ A @ Y3 @ C4 )
% 0.30/0.47 => ? [P6: pi] :
% 0.30/0.47 ( ( late_transitions @ P2 @ ( late_BoundR @ A4 @ Y3 @ P6 ) )
% 0.30/0.47 & ( strong2129052853vative @ P6 @ ( res @ X3 @ Q3 ) @ A4 @ Y3 @ Rel ) ) ) ) ) )
% 0.30/0.47 => ( ! [Q3: pi,Alpha: late_freeRes] :
% 0.30/0.47 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q3 ) )
% 0.30/0.47 => ( ( fresh @ name @ late_freeRes @ X3 @ Alpha )
% 0.30/0.47 => ? [P6: pi] :
% 0.30/0.47 ( ( late_transitions @ P2 @ ( late_FreeR @ Alpha @ P6 ) )
% 0.30/0.47 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P6 @ ( res @ X3 @ Q3 ) ) @ Rel ) ) ) )
% 0.30/0.47 => ( strong743114133lation @ P2 @ Rel @ ( res @ X3 @ Q ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % resSimCases
% 0.30/0.47 thf(fact_230_simulation__def,axiom,
% 0.30/0.47 ( strong743114133lation
% 0.30/0.47 = ( ^ [P7: pi,Rel2: set @ ( product_prod @ pi @ pi ),Q4: pi] :
% 0.30/0.47 ( ! [A6: late_subject,X6: name,Q5: pi] :
% 0.30/0.47 ( ( ( late_transitions @ Q4 @ ( late_BoundR @ A6 @ X6 @ Q5 ) )
% 0.30/0.47 & ( fresh @ name @ pi @ X6 @ P7 ) )
% 0.30/0.47 => ? [P8: pi] :
% 0.30/0.47 ( ( late_transitions @ P7 @ ( late_BoundR @ A6 @ X6 @ P8 ) )
% 0.30/0.47 & ( strong2129052853vative @ P8 @ Q5 @ A6 @ X6 @ Rel2 ) ) )
% 0.30/0.47 & ! [Alpha3: late_freeRes,Q5: pi] :
% 0.30/0.47 ( ( late_transitions @ Q4 @ ( late_FreeR @ Alpha3 @ Q5 ) )
% 0.30/0.47 => ? [P8: pi] :
% 0.30/0.47 ( ( late_transitions @ P7 @ ( late_FreeR @ Alpha3 @ P8 ) )
% 0.30/0.47 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P8 @ Q5 ) @ Rel2 ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % simulation_def
% 0.30/0.47 thf(fact_231_simCases,axiom,
% 0.30/0.47 ! [Q: pi,P2: pi,Rel: set @ ( product_prod @ pi @ pi )] :
% 0.30/0.47 ( ! [A4: late_subject,Y3: name,Q3: pi] :
% 0.30/0.47 ( ( late_transitions @ Q @ ( late_BoundR @ A4 @ Y3 @ Q3 ) )
% 0.30/0.47 => ( ( fresh @ name @ pi @ Y3 @ P2 )
% 0.30/0.47 => ? [P6: pi] :
% 0.30/0.47 ( ( late_transitions @ P2 @ ( late_BoundR @ A4 @ Y3 @ P6 ) )
% 0.30/0.47 & ( strong2129052853vative @ P6 @ Q3 @ A4 @ Y3 @ Rel ) ) ) )
% 0.30/0.47 => ( ! [Alpha: late_freeRes,Q3: pi] :
% 0.30/0.47 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q3 ) )
% 0.30/0.47 => ? [P6: pi] :
% 0.30/0.47 ( ( late_transitions @ P2 @ ( late_FreeR @ Alpha @ P6 ) )
% 0.30/0.47 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P6 @ Q3 ) @ Rel ) ) )
% 0.30/0.47 => ( strong743114133lation @ P2 @ Rel @ Q ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % simCases
% 0.30/0.47 thf(fact_232_supports__def,axiom,
% 0.30/0.47 ! [A: $tType,X: $tType] :
% 0.30/0.47 ( ( supports @ X @ A )
% 0.30/0.47 = ( ^ [S2: set @ X,X6: A] :
% 0.30/0.47 ! [A6: X,B6: X] :
% 0.30/0.47 ( ( ~ ( member @ X @ A6 @ S2 )
% 0.30/0.47 & ~ ( member @ X @ B6 @ S2 ) )
% 0.30/0.47 => ( ( perm @ X @ A @ ( cons @ ( product_prod @ X @ X ) @ ( product_Pair @ X @ X @ A6 @ B6 ) @ ( nil @ ( product_prod @ X @ X ) ) ) @ X6 )
% 0.30/0.47 = X6 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % supports_def
% 0.30/0.47 thf(fact_233_IdD,axiom,
% 0.30/0.47 ! [A: $tType,A2: A,B2: A] :
% 0.30/0.47 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ ( id @ A ) )
% 0.30/0.47 => ( A2 = B2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % IdD
% 0.30/0.47 thf(fact_234_supports__subset,axiom,
% 0.30/0.47 ! [X: $tType,A: $tType,S1: set @ X,X3: A,S22: set @ X] :
% 0.30/0.47 ( ( supports @ X @ A @ S1 @ X3 )
% 0.30/0.47 => ( ( ord_less_eq @ ( set @ X ) @ S1 @ S22 )
% 0.30/0.47 => ( supports @ X @ A @ S22 @ X3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % supports_subset
% 0.30/0.47 thf(fact_235_shift__def,axiom,
% 0.30/0.47 ! [B: $tType,A: $tType] :
% 0.30/0.47 ( ( bNF_Greatest_shift @ A @ B )
% 0.30/0.47 = ( ^ [Lab: ( list @ A ) > B,K: A,Kl: list @ A] : ( Lab @ ( cons @ A @ K @ Kl ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % shift_def
% 0.30/0.47 thf(fact_236_perm__residual__Rep_Osimps_I2_J,axiom,
% 0.30/0.47 ! [X: $tType,Pi: list @ ( product_prod @ X @ X ),FreeRes3: late_freeRes,Pia: pi] :
% 0.30/0.47 ( ( perm @ X @ late_residual_Rep @ Pi @ ( late_r347633188eR_Rep @ FreeRes3 @ Pia ) )
% 0.30/0.47 = ( late_r347633188eR_Rep @ ( perm @ X @ late_freeRes @ Pi @ FreeRes3 ) @ ( perm @ X @ pi @ Pi @ Pia ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % perm_residual_Rep.simps(2)
% 0.30/0.47 thf(fact_237_residual__Rep_Oinject_I2_J,axiom,
% 0.30/0.47 ! [X21: late_freeRes,X222: pi,Y21: late_freeRes,Y22: pi] :
% 0.30/0.47 ( ( ( late_r347633188eR_Rep @ X21 @ X222 )
% 0.30/0.47 = ( late_r347633188eR_Rep @ Y21 @ Y22 ) )
% 0.30/0.47 = ( ( X21 = Y21 )
% 0.30/0.47 & ( X222 = Y22 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % residual_Rep.inject(2)
% 0.30/0.47 thf(fact_238_alphaInput,axiom,
% 0.30/0.47 ! [C2: name,P2: pi,A2: name,X3: name] :
% 0.30/0.47 ( ( fresh @ name @ pi @ C2 @ P2 )
% 0.30/0.47 => ( ( input @ A2 @ X3 @ P2 )
% 0.30/0.47 = ( input @ A2 @ C2 @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ X3 @ C2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ P2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % alphaInput
% 0.30/0.47 thf(fact_239_product__lists_Osimps_I1_J,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( product_lists @ A @ ( nil @ ( list @ A ) ) )
% 0.30/0.47 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % product_lists.simps(1)
% 0.30/0.47 thf(fact_240_pi_Operm_I4_J,axiom,
% 0.30/0.47 ! [Pi: list @ ( product_prod @ name @ name ),X32: name,X1: name,X22: pi] :
% 0.30/0.47 ( ( perm @ name @ pi @ Pi @ ( input @ X32 @ X1 @ X22 ) )
% 0.30/0.47 = ( input @ ( perm @ name @ name @ Pi @ X32 ) @ ( perm @ name @ name @ Pi @ X1 ) @ ( perm @ name @ pi @ Pi @ X22 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % pi.perm(4)
% 0.30/0.47 thf(fact_241_resTrans_I2_J,axiom,
% 0.30/0.47 ! [X3: name,Y4: name,P2: pi,Rs: late_residual] :
% 0.30/0.47 ~ ( late_transitions @ ( res @ X3 @ ( input @ X3 @ Y4 @ P2 ) ) @ Rs ) ).
% 0.30/0.47
% 0.30/0.47 % resTrans(2)
% 0.30/0.47 thf(fact_242_pi_Odistinct_I53_J,axiom,
% 0.30/0.47 ! [Name1: name,Name22: name,Pi: pi,Pi12: pi,Pi22: pi] :
% 0.30/0.47 ( ( input @ Name1 @ Name22 @ Pi )
% 0.30/0.47 != ( sum @ Pi12 @ Pi22 ) ) ).
% 0.30/0.47
% 0.30/0.47 % pi.distinct(53)
% 0.30/0.47 thf(fact_243_pi_Odistinct_I57_J,axiom,
% 0.30/0.47 ! [Name1: name,Name22: name,Pi: pi,Name: name,Pi4: pi] :
% 0.30/0.47 ( ( input @ Name1 @ Name22 @ Pi )
% 0.30/0.47 != ( res @ Name @ Pi4 ) ) ).
% 0.30/0.47
% 0.30/0.47 % pi.distinct(57)
% 0.30/0.47 thf(fact_244_inputFreeTrans,axiom,
% 0.30/0.47 ! [A2: name,X3: name,P2: pi,Alpha2: late_freeRes,P4: pi] :
% 0.30/0.47 ~ ( late_transitions @ ( input @ A2 @ X3 @ P2 ) @ ( late_FreeR @ Alpha2 @ P4 ) ) ).
% 0.30/0.47
% 0.30/0.47 % inputFreeTrans
% 0.30/0.47 thf(fact_245_resInputFreeTrans,axiom,
% 0.30/0.47 ! [X3: name,A2: name,Y4: name,P2: pi,Alpha2: late_freeRes,P4: pi] :
% 0.30/0.47 ~ ( late_transitions @ ( res @ X3 @ ( input @ A2 @ Y4 @ P2 ) ) @ ( late_FreeR @ Alpha2 @ P4 ) ) ).
% 0.30/0.47
% 0.30/0.47 % resInputFreeTrans
% 0.30/0.47 thf(fact_246_inputBoundOutputTrans,axiom,
% 0.30/0.47 ! [A2: name,X3: name,P2: pi,B2: name,Y4: name,P4: pi] :
% 0.30/0.47 ~ ( late_transitions @ ( input @ A2 @ X3 @ P2 ) @ ( late_BoundR @ ( late_BoundOutputS @ B2 ) @ Y4 @ P4 ) ) ).
% 0.30/0.47
% 0.30/0.47 % inputBoundOutputTrans
% 0.30/0.47 thf(fact_247_inputIneqTrans,axiom,
% 0.30/0.47 ! [A2: name,X3: name,P2: pi,B2: late_subject,Y4: name,P4: pi] :
% 0.30/0.47 ( ( late_transitions @ ( input @ A2 @ X3 @ P2 ) @ ( late_BoundR @ B2 @ Y4 @ P4 ) )
% 0.30/0.47 => ~ ( fresh @ name @ late_subject @ A2 @ B2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % inputIneqTrans
% 0.30/0.47 thf(fact_248_resInputBoundOutputTrans,axiom,
% 0.30/0.47 ! [X3: name,A2: name,Y4: name,P2: pi,B2: name,Z2: name,P4: pi] :
% 0.30/0.47 ~ ( late_transitions @ ( res @ X3 @ ( input @ A2 @ Y4 @ P2 ) ) @ ( late_BoundR @ ( late_BoundOutputS @ B2 ) @ Z2 @ P4 ) ) ).
% 0.30/0.47
% 0.30/0.47 % resInputBoundOutputTrans
% 0.30/0.47 thf(fact_249_inputCases,axiom,
% 0.30/0.47 ! [A2: name,X3: name,P2: pi,B2: late_subject,Y4: name,YP: pi,Prop: late_subject > name > pi > $o] :
% 0.30/0.47 ( ( late_transitions @ ( input @ A2 @ X3 @ P2 ) @ ( late_BoundR @ B2 @ Y4 @ YP ) )
% 0.30/0.47 => ( ( Y4 != A2 )
% 0.30/0.47 => ( ( Y4 != X3 )
% 0.30/0.47 => ( ( fresh @ name @ pi @ Y4 @ P2 )
% 0.30/0.47 => ( ( ( B2
% 0.30/0.47 = ( late_InputS @ A2 ) )
% 0.30/0.47 => ( ( YP
% 0.30/0.47 = ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ X3 @ Y4 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ P2 ) )
% 0.30/0.47 => ( Prop @ ( late_InputS @ A2 ) @ Y4 @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ X3 @ Y4 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ P2 ) ) ) )
% 0.30/0.47 => ( Prop @ B2 @ Y4 @ YP ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % inputCases
% 0.30/0.47 thf(fact_250_name__calc_I1_J,axiom,
% 0.30/0.47 ! [A2: name,B2: name,Pi: list @ ( product_prod @ name @ name ),X3: name] :
% 0.30/0.47 ( ( perm @ name @ name @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ Pi ) @ X3 )
% 0.30/0.47 = ( swap @ name @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( perm @ name @ name @ Pi @ X3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % name_calc(1)
% 0.30/0.47 thf(fact_251_Late__Semantics1_Osubject_Oinject_I1_J,axiom,
% 0.30/0.47 ! [X1: name,Y1: name] :
% 0.30/0.47 ( ( ( late_InputS @ X1 )
% 0.30/0.47 = ( late_InputS @ Y1 ) )
% 0.30/0.47 = ( X1 = Y1 ) ) ).
% 0.30/0.47
% 0.30/0.47 % Late_Semantics1.subject.inject(1)
% 0.30/0.47 thf(fact_252_subject_Ofresh_I1_J,axiom,
% 0.30/0.47 ! [A2: name,X1: name] :
% 0.30/0.47 ( ( fresh @ name @ late_subject @ A2 @ ( late_InputS @ X1 ) )
% 0.30/0.47 = ( fresh @ name @ name @ A2 @ X1 ) ) ).
% 0.30/0.47
% 0.30/0.47 % subject.fresh(1)
% 0.30/0.47 thf(fact_253_subject_Operm_I1_J,axiom,
% 0.30/0.47 ! [Pi: list @ ( product_prod @ name @ name ),X1: name] :
% 0.30/0.47 ( ( perm @ name @ late_subject @ Pi @ ( late_InputS @ X1 ) )
% 0.30/0.47 = ( late_InputS @ ( perm @ name @ name @ Pi @ X1 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % subject.perm(1)
% 0.30/0.47 thf(fact_254_Late__Semantics_Osubject_Odistinct_I1_J,axiom,
% 0.30/0.47 ! [Name2: name,Name: name] :
% 0.30/0.47 ( ( late_InputS @ Name2 )
% 0.30/0.47 != ( late_BoundOutputS @ Name ) ) ).
% 0.30/0.47
% 0.30/0.47 % Late_Semantics.subject.distinct(1)
% 0.30/0.47
% 0.30/0.47 % Type constructors (46)
% 0.30/0.47 thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.30/0.47 ! [A8: $tType,A9: $tType] :
% 0.30/0.47 ( ( preorder @ A9 )
% 0.30/0.47 => ( preorder @ ( A8 > A9 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_fun___Agent_Ocp__name__name,axiom,
% 0.30/0.47 ! [A8: $tType,A9: $tType] :
% 0.30/0.47 ( ( ( cp_name_name @ A8 )
% 0.30/0.47 & ( cp_name_name @ A9 ) )
% 0.30/0.47 => ( cp_name_name @ ( A8 > A9 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.30/0.47 ! [A8: $tType,A9: $tType] :
% 0.30/0.47 ( ( order @ A9 )
% 0.30/0.47 => ( order @ ( A8 > A9 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_fun___Orderings_Oord,axiom,
% 0.30/0.47 ! [A8: $tType,A9: $tType] :
% 0.30/0.47 ( ( ord @ A9 )
% 0.30/0.47 => ( ord @ ( A8 > A9 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_fun___Agent_Opt__name,axiom,
% 0.30/0.47 ! [A8: $tType,A9: $tType] :
% 0.30/0.47 ( ( ( pt_name @ A8 )
% 0.30/0.47 & ( pt_name @ A9 ) )
% 0.30/0.47 => ( pt_name @ ( A8 > A9 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Set_Oset___Orderings_Opreorder_1,axiom,
% 0.30/0.47 ! [A8: $tType] : ( preorder @ ( set @ A8 ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Set_Oset___Agent_Ocp__name__name_2,axiom,
% 0.30/0.47 ! [A8: $tType] :
% 0.30/0.47 ( ( cp_name_name @ A8 )
% 0.30/0.47 => ( cp_name_name @ ( set @ A8 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Set_Oset___Orderings_Oorder_3,axiom,
% 0.30/0.47 ! [A8: $tType] : ( order @ ( set @ A8 ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Set_Oset___Orderings_Oord_4,axiom,
% 0.30/0.47 ! [A8: $tType] : ( ord @ ( set @ A8 ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Set_Oset___Agent_Opt__name_5,axiom,
% 0.30/0.47 ! [A8: $tType] :
% 0.30/0.47 ( ( pt_name @ A8 )
% 0.30/0.47 => ( pt_name @ ( set @ A8 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Agent_Opi___Agent_Ocp__name__name_6,axiom,
% 0.30/0.47 cp_name_name @ pi ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Agent_Opi___Agent_Opt__name_7,axiom,
% 0.30/0.47 pt_name @ pi ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Agent_Opi___Agent_Ofs__name,axiom,
% 0.30/0.47 fs_name @ pi ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_HOL_Obool___Orderings_Opreorder_8,axiom,
% 0.30/0.47 preorder @ $o ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 0.30/0.47 linorder @ $o ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_HOL_Obool___Agent_Ocp__name__name_9,axiom,
% 0.30/0.47 cp_name_name @ $o ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_HOL_Obool___Orderings_Oorder_10,axiom,
% 0.30/0.47 order @ $o ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_HOL_Obool___Orderings_Oord_11,axiom,
% 0.30/0.47 ord @ $o ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_HOL_Obool___Agent_Opt__name_12,axiom,
% 0.30/0.47 pt_name @ $o ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_HOL_Obool___Agent_Ofs__name_13,axiom,
% 0.30/0.47 fs_name @ $o ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_List_Olist___Agent_Ocp__name__name_14,axiom,
% 0.30/0.47 ! [A8: $tType] :
% 0.30/0.47 ( ( cp_name_name @ A8 )
% 0.30/0.47 => ( cp_name_name @ ( list @ A8 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_List_Olist___Agent_Opt__name_15,axiom,
% 0.30/0.47 ! [A8: $tType] :
% 0.30/0.47 ( ( pt_name @ A8 )
% 0.30/0.47 => ( pt_name @ ( list @ A8 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_List_Olist___Agent_Ofs__name_16,axiom,
% 0.30/0.47 ! [A8: $tType] :
% 0.30/0.47 ( ( fs_name @ A8 )
% 0.30/0.47 => ( fs_name @ ( list @ A8 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Agent_Oname___Agent_Ocp__name__name_17,axiom,
% 0.30/0.47 cp_name_name @ name ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Agent_Oname___Agent_Opt__name_18,axiom,
% 0.30/0.47 pt_name @ name ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Agent_Oname___Agent_Ofs__name_19,axiom,
% 0.30/0.47 fs_name @ name ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Agent_Opi__Rep___Agent_Ocp__name__name_20,axiom,
% 0.30/0.47 cp_name_name @ pi_Rep ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Agent_Opi__Rep___Agent_Opt__name_21,axiom,
% 0.30/0.47 pt_name @ pi_Rep ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Product__Type_Oprod___Agent_Ocp__name__name_22,axiom,
% 0.30/0.47 ! [A8: $tType,A9: $tType] :
% 0.30/0.47 ( ( ( cp_name_name @ A8 )
% 0.30/0.47 & ( cp_name_name @ A9 ) )
% 0.30/0.47 => ( cp_name_name @ ( product_prod @ A8 @ A9 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Product__Type_Oprod___Agent_Opt__name_23,axiom,
% 0.30/0.47 ! [A8: $tType,A9: $tType] :
% 0.30/0.47 ( ( ( pt_name @ A8 )
% 0.30/0.47 & ( pt_name @ A9 ) )
% 0.30/0.47 => ( pt_name @ ( product_prod @ A8 @ A9 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Product__Type_Oprod___Agent_Ofs__name_24,axiom,
% 0.30/0.47 ! [A8: $tType,A9: $tType] :
% 0.30/0.47 ( ( ( fs_name @ A8 )
% 0.30/0.47 & ( fs_name @ A9 ) )
% 0.30/0.47 => ( fs_name @ ( product_prod @ A8 @ A9 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Late__Semantics_OfreeRes___Agent_Ocp__name__name_25,axiom,
% 0.30/0.47 cp_name_name @ late_freeRes ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Late__Semantics_OfreeRes___Agent_Opt__name_26,axiom,
% 0.30/0.47 pt_name @ late_freeRes ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Late__Semantics_OfreeRes___Agent_Ofs__name_27,axiom,
% 0.30/0.47 fs_name @ late_freeRes ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Late__Semantics_Osubject___Agent_Ocp__name__name_28,axiom,
% 0.30/0.47 cp_name_name @ late_subject ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Late__Semantics_Osubject___Agent_Opt__name_29,axiom,
% 0.30/0.47 pt_name @ late_subject ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Late__Semantics_Osubject___Agent_Ofs__name_30,axiom,
% 0.30/0.47 fs_name @ late_subject ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Late__Semantics_Oresidual___Agent_Ocp__name__name_31,axiom,
% 0.30/0.47 cp_name_name @ late_residual ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Late__Semantics_Oresidual___Agent_Opt__name_32,axiom,
% 0.30/0.47 pt_name @ late_residual ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Late__Semantics_Oresidual___Agent_Ofs__name_33,axiom,
% 0.30/0.47 fs_name @ late_residual ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Late__Semantics_OfreeRes__Rep___Agent_Ocp__name__name_34,axiom,
% 0.30/0.47 cp_name_name @ late_freeRes_Rep ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Late__Semantics_OfreeRes__Rep___Agent_Opt__name_35,axiom,
% 0.30/0.47 pt_name @ late_freeRes_Rep ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Late__Semantics_Osubject__Rep___Agent_Ocp__name__name_36,axiom,
% 0.30/0.47 cp_name_name @ late_subject_Rep ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Late__Semantics_Osubject__Rep___Agent_Opt__name_37,axiom,
% 0.30/0.47 pt_name @ late_subject_Rep ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Late__Semantics_Oresidual__Rep___Agent_Ocp__name__name_38,axiom,
% 0.30/0.47 cp_name_name @ late_residual_Rep ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Late__Semantics_Oresidual__Rep___Agent_Opt__name_39,axiom,
% 0.30/0.47 pt_name @ late_residual_Rep ).
% 0.30/0.47
% 0.30/0.47 % Helper facts (3)
% 0.30/0.47 thf(help_If_3_1_T,axiom,
% 0.30/0.47 ! [P2: $o] :
% 0.30/0.47 ( ( P2 = $true )
% 0.30/0.47 | ( P2 = $false ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(help_If_2_1_T,axiom,
% 0.30/0.47 ! [A: $tType,X3: A,Y4: A] :
% 0.30/0.47 ( ( if @ A @ $false @ X3 @ Y4 )
% 0.30/0.47 = Y4 ) ).
% 0.30/0.47
% 0.30/0.47 thf(help_If_1_1_T,axiom,
% 0.30/0.47 ! [A: $tType,X3: A,Y4: A] :
% 0.30/0.47 ( ( if @ A @ $true @ X3 @ Y4 )
% 0.30/0.47 = X3 ) ).
% 0.30/0.47
% 0.30/0.47 % Conjectures (1)
% 0.30/0.47 thf(conj_0,conjecture,
% 0.30/0.47 strong2129052853vative @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ y @ x ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ p2 ) @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ y @ x ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ p2 ) @ ( late_BoundOutputS @ aa ) @ y @ rel ).
% 0.30/0.47
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 ------------------------
% 3.96/1.85 ---- Embedded in THF ---
% 3.96/1.85 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 3.96/1.85 %%% Generated on Tue Feb 24 08:29:10 EST 2026
% 3.96/1.85 %%% using '$$dhol' embedding, version 1.3.0.
% 3.96/1.85 %%% Logic specification used:
% 3.96/1.85 %%% thf(spec, logic, $$dhol).
% 3.96/1.85
% 3.96/1.85 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.g7e8TF9fEe/DTF2DTF17774.p
% 3.96/1.85 thf(ty_t_Late__Semantics_Oresidual__Rep, type, late_residual_Rep: $tType).
% 3.96/1.85 thf(ty_t_Late__Semantics_Osubject__Rep, type, late_subject_Rep: $tType).
% 3.96/1.85 thf(ty_t_Late__Semantics_OfreeRes__Rep, type, late_freeRes_Rep: $tType).
% 3.96/1.85 thf(ty_t_Late__Semantics_Oresidual, type, late_residual: $tType).
% 3.96/1.85 thf(ty_t_Late__Semantics_Osubject, type, late_subject: $tType).
% 3.96/1.85 thf(ty_t_Late__Semantics_OfreeRes, type, late_freeRes: $tType).
% 3.96/1.85 thf(ty_t_Product__Type_Oprod, type, product_prod: ($tType > ($tType > $tType))).
% 3.96/1.85 thf(ty_t_Agent_Opi__Rep, type, pi_Rep: $tType).
% 3.96/1.85 thf(ty_t_Agent_Oname, type, name: $tType).
% 3.96/1.85 thf(ty_t_List_Olist, type, list: ($tType > $tType)).
% 3.96/1.85 thf(ty_t_Agent_Opi, type, pi: $tType).
% 3.96/1.85 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 3.96/1.85 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: ($o))).
% 3.96/1.85 thf(sy_cl_Agent_Ofs__name, type, fs_name: (!> [A:$tType]: ($o))).
% 3.96/1.85 thf(sy_cl_Agent_Opt__name, type, pt_name: (!> [A:$tType]: ($o))).
% 3.96/1.85 thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: ($o))).
% 3.96/1.85 thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: ($o))).
% 3.96/1.85 thf(sy_cl_Agent_Ocp__name__name, type, cp_name_name: (!> [A:$tType]: ($o))).
% 3.96/1.85 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: ($o))).
% 3.96/1.85 thf(sy_cl_Orderings_Opreorder, type, preorder: (!> [A:$tType]: ($o))).
% 3.96/1.85 thf(sy_c_Agent_Opi_OInput, type, input: (name > (name > (pi > pi)))).
% 3.96/1.85 thf(sy_c_Agent_Opi_ORes, type, res: (name > (pi > pi))).
% 3.96/1.85 thf(sy_c_Agent_Opi_OSum, type, sum: (pi > (pi > pi))).
% 3.96/1.85 thf(sy_c_BNF__Greatest__Fixpoint_Oshift, type, bNF_Greatest_shift: (!> [A:$tType,B:$tType]: ((((list @ A) > B) > (A > ((list @ A) > B)))))).
% 3.96/1.85 thf(sy_c_If, type, if: (!> [A:$tType]: (($o > (A > (A > A)))))).
% 3.96/1.85 thf(sy_c_Late__Semantics_OfreeRes_OOutputR, type, late_OutputR: (name > (name > late_freeRes))).
% 3.96/1.85 thf(sy_c_Late__Semantics_Oresidual_OBoundR, type, late_BoundR: (late_subject > (name > (pi > late_residual)))).
% 3.96/1.85 thf(sy_c_Late__Semantics_Oresidual_OFreeR, type, late_FreeR: (late_freeRes > (pi > late_residual))).
% 3.96/1.85 thf(sy_c_Late__Semantics_Oresidual__Rep_OFreeR__Rep, type, late_r347633188eR_Rep: (late_freeRes > (pi > late_residual_Rep))).
% 3.96/1.85 thf(sy_c_Late__Semantics_Osubject_OBoundOutputS, type, late_BoundOutputS: (name > late_subject)).
% 3.96/1.85 thf(sy_c_Late__Semantics_Osubject_OInputS, type, late_InputS: (name > late_subject)).
% 3.96/1.85 thf(sy_c_Late__Semantics_Otransitions, type, late_transitions: (pi > (late_residual > $o))).
% 3.96/1.85 thf(sy_c_List_Olist_OCons, type, cons: (!> [A:$tType]: ((A > ((list @ A) > (list @ A)))))).
% 3.96/1.85 thf(sy_c_List_Olist_ONil, type, nil: (!> [A:$tType]: ((list @ A)))).
% 3.96/1.85 thf(sy_c_List_Oproduct__lists, type, product_lists: (!> [A:$tType]: (((list @ (list @ A)) > (list @ (list @ A)))))).
% 3.96/1.85 thf(sy_c_Nominal_Ofresh, type, fresh: (!> [X:$tType,A:$tType]: ((X > (A > $o))))).
% 3.96/1.85 thf(sy_c_Nominal_Operm, type, perm: (!> [X:$tType,A:$tType]: (((list @ ((product_prod @ X) @ X)) > (A > A))))).
% 3.96/1.85 thf(sy_c_Nominal_Osupports, type, supports: (!> [X:$tType,A:$tType]: (((set @ X) > (A > $o))))).
% 3.96/1.85 thf(sy_c_Nominal_Oswap, type, swap: (!> [X:$tType]: ((((product_prod @ X) @ X) > (X > X))))).
% 3.96/1.85 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 3.96/1.85 thf(sy_c_Product__Type_OPair, type, product_Pair: (!> [A:$tType,B:$tType]: ((A > (B > ((product_prod @ A) @ B)))))).
% 3.96/1.85 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod, type, product_rec_prod: (!> [A:$tType,B:$tType,T:$tType]: (((A > (B > T)) > (((product_prod @ A) @ B) > T))))).
% 3.96/1.85 thf(sy_c_Rel_Oeqvt, type, eqvt: (!> [A:$tType]: (((set @ ((product_prod @ A) @ A)) > $o)))).
% 3.96/1.85 thf(sy_c_Relation_OId, type, id: (!> [A:$tType]: ((set @ ((product_prod @ A) @ A))))).
% 3.96/1.85 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 3.96/1.85 thf(sy_c_Strong__Late__Sim_Oderivative, type, strong2129052853vative: (pi > (pi > (late_subject > (name > ((set @ ((product_prod @ pi) @ pi)) > $o)))))).
% 3.96/1.85 thf(sy_c_Strong__Late__Sim_Osimulation, type, strong743114133lation: (pi > ((set @ ((product_prod @ pi) @ pi)) > (pi > $o)))).
% 3.96/1.85 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 3.96/1.85 thf(sy_v_P, type, p: pi).
% 3.96/1.85 thf(sy_v_PQ____, type, pq: pi).
% 3.96/1.85 thf(sy_v_P_H____, type, p2: pi).
% 3.96/1.85 thf(sy_v_Q, type, q: pi).
% 3.96/1.85 thf(sy_v_Rel, type, rel: (set @ ((product_prod @ pi) @ pi))).
% 3.96/1.85 thf(sy_v_a____, type, a: late_subject).
% 3.96/1.85 thf(sy_v_aa____, type, aa: name).
% 3.96/1.85 thf(sy_v_x, type, x: name).
% 3.96/1.85 thf(sy_v_y____, type, y: name).
% 3.96/1.85 thf(fact_0_Id, axiom, (((ord_less_eq @ (set @ ((product_prod @ pi) @ pi))) @ (id @ pi)) @ rel)).
% 3.96/1.85 thf(fact_1_cOpen_Ohyps_I2_J, axiom, (aa != x)).
% 3.96/1.85 thf(fact_2_cOpen_Ohyps_I3_J, axiom, (a = (late_BoundOutputS @ aa))).
% 3.96/1.85 thf(fact_3__092_060open_062y_A_092_060noteq_062_Ax_092_060close_062, axiom, (y != x)).
% 3.96/1.85 thf(fact_4_Eqvt, axiom, ((eqvt @ pi) @ rel)).
% 3.96/1.85 thf(fact_5_perm__swap_I1_J, axiom, (! [X2:$tType]: (((pt_name @ X2) => (! [A2:name,B2:name,X3:X2]: ((((((perm @ name) @ X2) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ A2) @ B2)) @ (nil @ ((product_prod @ name) @ name)))) @ ((((perm @ name) @ X2) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ A2) @ B2)) @ (nil @ ((product_prod @ name) @ name)))) @ X3)) = X3))))))).
% 3.96/1.85 thf(fact_6_name__id, axiom, (! [X:$tType]: (((pt_name @ X) => (! [A2:name,X3:X]: ((((((perm @ name) @ X) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ A2) @ A2)) @ (nil @ ((product_prod @ name) @ name)))) @ X3) = X3))))))).
% 3.96/1.85 thf(fact_7_name__swap, axiom, (! [X:$tType]: (((pt_name @ X) => (! [A2:name,B2:name,X3:X]: ((((((perm @ name) @ X) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ A2) @ B2)) @ (nil @ ((product_prod @ name) @ name)))) @ X3) = ((((perm @ name) @ X) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ B2) @ A2)) @ (nil @ ((product_prod @ name) @ name)))) @ X3)))))))).
% 3.96/1.85 thf(fact_8_name__swap__bij, axiom, (! [X:$tType]: (((pt_name @ X) => (! [A2:name,B2:name,X3:X]: ((((((perm @ name) @ X) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ A2) @ B2)) @ (nil @ ((product_prod @ name) @ name)))) @ ((((perm @ name) @ X) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ A2) @ B2)) @ (nil @ ((product_prod @ name) @ name)))) @ X3)) = X3))))))).
% 3.96/1.85 thf(fact_9_pt__name1, axiom, (! [A:$tType]: (((pt_name @ A) => (! [X3:A]: ((((((perm @ name) @ A) @ (nil @ ((product_prod @ name) @ name))) @ X3) = X3))))))).
% 3.96/1.85 thf(fact_10_perm__swap_I2_J, axiom, (! [X2:$tType]: (((pt_name @ X2) => (! [A2:name,B2:name,X3:X2]: ((((((perm @ name) @ X2) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ A2) @ B2)) @ (nil @ ((product_prod @ name) @ name)))) @ ((((perm @ name) @ X2) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ B2) @ A2)) @ (nil @ ((product_prod @ name) @ name)))) @ X3)) = X3))))))).
% 3.96/1.85 thf(fact_11_Late__Semantics_Osubject_Oinject_I2_J, axiom, (! [X1:name,Y1:name]: ((((late_BoundOutputS @ X1) = (late_BoundOutputS @ Y1)) = (X1 = Y1))))).
% 3.96/1.85 thf(fact_12_Late__Semantics1_Osubject_Oinject_I2_J, axiom, (! [X22:name,Y2:name]: ((((late_BoundOutputS @ X22) = (late_BoundOutputS @ Y2)) = (X22 = Y2))))).
% 3.96/1.85 thf(fact_13__092_060open_062y_A_092_060sharp_062_AP_H_092_060close_062, axiom, ((((fresh @ name) @ pi) @ y) @ p2)).
% 3.96/1.85 thf(fact_14_list_Oinject, axiom, (! [A:$tType,X21:A,X222:(list @ A),Y21:A,Y22:(list @ A)]: ((((((cons @ A) @ X21) @ X222) = (((cons @ A) @ Y21) @ Y22)) = ((X21 = Y21) & (X222 = Y22)))))).
% 3.96/1.85 thf(fact_15_prod_Oinject, axiom, (! [A:$tType,B:$tType,X1:A,X22:B,Y1:A,Y2:B]: (((((((product_Pair @ A) @ B) @ X1) @ X22) = ((((product_Pair @ A) @ B) @ Y1) @ Y2)) = ((X1 = Y1) & (X22 = Y2)))))).
% 3.96/1.85 thf(fact_16_old_Oprod_Oinject, axiom, (! [A:$tType,B:$tType,A2:A,B2:B,A3:A,B3:B]: (((((((product_Pair @ A) @ B) @ A2) @ B2) = ((((product_Pair @ A) @ B) @ A3) @ B3)) = ((A2 = A3) & (B2 = B3)))))).
% 3.96/1.85 thf(fact_17_residual__perm__empty, axiom, (! [Residual_Rep:late_residual_Rep]: ((((((perm @ name) @ late_residual_Rep) @ (nil @ ((product_prod @ name) @ name))) @ Residual_Rep) = Residual_Rep)))).
% 3.96/1.85 thf(fact_18_subject__perm__empty, axiom, (! [Subject_Rep:late_subject_Rep]: ((((((perm @ name) @ late_subject_Rep) @ (nil @ ((product_prod @ name) @ name))) @ Subject_Rep) = Subject_Rep)))).
% 3.96/1.85 thf(fact_19_freeRes__perm__empty, axiom, (! [FreeRes_Rep:late_freeRes_Rep]: ((((((perm @ name) @ late_freeRes_Rep) @ (nil @ ((product_prod @ name) @ name))) @ FreeRes_Rep) = FreeRes_Rep)))).
% 3.96/1.85 thf(fact_20_pi__perm__empty, axiom, (! [Pi_Rep:pi_Rep]: ((((((perm @ name) @ pi_Rep) @ (nil @ ((product_prod @ name) @ name))) @ Pi_Rep) = Pi_Rep)))).
% 3.96/1.85 thf(fact_21_subject_Operm_I2_J, axiom, (! [Pi:(list @ ((product_prod @ name) @ name)),X1:name]: ((((((perm @ name) @ late_subject) @ Pi) @ (late_BoundOutputS @ X1)) = (late_BoundOutputS @ ((((perm @ name) @ name) @ Pi) @ X1)))))).
% 3.96/1.85 thf(fact_22_perm__fresh__fresh, axiom, (! [X2:$tType]: (((pt_name @ X2) => (! [A2:name,X3:X2,B2:name]: ((((((fresh @ name) @ X2) @ A2) @ X3) => (((((fresh @ name) @ X2) @ B2) @ X3) => (((((perm @ name) @ X2) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ A2) @ B2)) @ (nil @ ((product_prod @ name) @ name)))) @ X3) = X3))))))))).
% 3.96/1.85 thf(fact_23_name__fresh__fresh, axiom, (! [X:$tType]: (((pt_name @ X) => (! [A2:name,X3:X,B2:name]: ((((((fresh @ name) @ X) @ A2) @ X3) => (((((fresh @ name) @ X) @ B2) @ X3) => (((((perm @ name) @ X) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ A2) @ B2)) @ (nil @ ((product_prod @ name) @ name)))) @ X3) = X3))))))))).
% 3.96/1.85 thf(fact_24_Bound_Ohyps_I4_J, axiom, ((((fresh @ name) @ late_subject) @ y) @ a)).
% 3.96/1.85 thf(fact_25_subseteq__eqvt, axiom, (! [X2:$tType]: (((pt_name @ X2) => (! [Pi:(list @ ((product_prod @ name) @ name)),X4:(set @ X2),Y:(set @ X2)]: ((((((perm @ name) @ $o) @ Pi) @ (((ord_less_eq @ (set @ X2)) @ X4) @ Y)) = (((ord_less_eq @ (set @ X2)) @ ((((perm @ name) @ (set @ X2)) @ Pi) @ X4)) @ ((((perm @ name) @ (set @ X2)) @ Pi) @ Y))))))))).
% 3.96/1.85 thf(fact_26_fresh__perm__app, axiom, (! [X2:$tType]: (((pt_name @ X2) => (! [A2:name,Pi:(list @ ((product_prod @ name) @ name)),X3:X2]: ((((((fresh @ name) @ (list @ ((product_prod @ name) @ name))) @ A2) @ Pi) => (((((fresh @ name) @ X2) @ A2) @ X3) => ((((fresh @ name) @ X2) @ A2) @ ((((perm @ name) @ X2) @ Pi) @ X3)))))))))).
% 3.96/1.85 thf(fact_27_name__exists__fresh, axiom, (! [A:$tType]: (((fs_name @ A) => (! [X3:A]: ((~ ((! [C:name]: ((~ (((((fresh @ name) @ A) @ C) @ X3))))))))))))).
% 3.96/1.85 thf(fact_28_fresh__eqvt, axiom, (! [X2:$tType]: (((pt_name @ X2) => (! [Pi:(list @ ((product_prod @ name) @ name)),A2:name,X3:X2]: ((((((perm @ name) @ $o) @ Pi) @ ((((fresh @ name) @ X2) @ A2) @ X3)) = ((((fresh @ name) @ X2) @ ((((perm @ name) @ name) @ Pi) @ A2)) @ ((((perm @ name) @ X2) @ Pi) @ X3))))))))).
% 3.96/1.85 thf(fact_29_fresh__bij, axiom, (! [X2:$tType]: (((pt_name @ X2) => (! [Pi:(list @ ((product_prod @ name) @ name)),A2:name,X3:X2]: ((((((fresh @ name) @ X2) @ ((((perm @ name) @ name) @ Pi) @ A2)) @ ((((perm @ name) @ X2) @ Pi) @ X3)) = ((((fresh @ name) @ X2) @ A2) @ X3)))))))).
% 3.96/1.85 thf(fact_30_map__tailrec__rev_Ocases, axiom, (! [A:$tType,B:$tType,X3:((product_prod @ (A > B)) @ ((product_prod @ (list @ A)) @ (list @ B)))]: (((! [F:(A > B),Bs:(list @ B)]: ((X3 != ((((product_Pair @ (A > B)) @ ((product_prod @ (list @ A)) @ (list @ B))) @ F) @ ((((product_Pair @ (list @ A)) @ (list @ B)) @ (nil @ A)) @ Bs))))) => (~ ((! [F:(A > B),A4:A,As:(list @ A),Bs:(list @ B)]: ((X3 != ((((product_Pair @ (A > B)) @ ((product_prod @ (list @ A)) @ (list @ B))) @ F) @ ((((product_Pair @ (list @ A)) @ (list @ B)) @ (((cons @ A) @ A4) @ As)) @ Bs))))))))))).
% 3.96/1.85 thf(fact_31_name__calc_I2_J, axiom, (! [X3:name]: ((((((perm @ name) @ name) @ (nil @ ((product_prod @ name) @ name))) @ X3) = X3)))).
% 3.96/1.85 thf(fact_32_arg__min__list_Ocases, axiom, (! [B:$tType,A:$tType]: (((linorder @ B) => (! [X3:((product_prod @ (A > B)) @ (list @ A))]: (((! [F:(A > B),X5:A]: ((X3 != ((((product_Pair @ (A > B)) @ (list @ A)) @ F) @ (((cons @ A) @ X5) @ (nil @ A)))))) => ((! [F:(A > B),X5:A,Y3:A,Zs:(list @ A)]: ((X3 != ((((product_Pair @ (A > B)) @ (list @ A)) @ F) @ (((cons @ A) @ X5) @ (((cons @ A) @ Y3) @ Zs)))))) => (~ ((! [A4:(A > B)]: ((X3 != ((((product_Pair @ (A > B)) @ (list @ A)) @ A4) @ (nil @ A))))))))))))))).
% 3.96/1.85 thf(fact_33_successively_Ocases, axiom, (! [A:$tType,X3:((product_prod @ (A > (A > $o))) @ (list @ A))]: (((! [P:(A > (A > $o))]: ((X3 != ((((product_Pair @ (A > (A > $o))) @ (list @ A)) @ P) @ (nil @ A))))) => ((! [P:(A > (A > $o)),X5:A]: ((X3 != ((((product_Pair @ (A > (A > $o))) @ (list @ A)) @ P) @ (((cons @ A) @ X5) @ (nil @ A)))))) => (~ ((! [P:(A > (A > $o)),X5:A,Y3:A,Xs:(list @ A)]: ((X3 != ((((product_Pair @ (A > (A > $o))) @ (list @ A)) @ P) @ (((cons @ A) @ X5) @ (((cons @ A) @ Y3) @ Xs))))))))))))).
% 3.96/1.85 thf(fact_34_sorted__wrt_Ocases, axiom, (! [A:$tType,X3:((product_prod @ (A > (A > $o))) @ (list @ A))]: (((! [P:(A > (A > $o))]: ((X3 != ((((product_Pair @ (A > (A > $o))) @ (list @ A)) @ P) @ (nil @ A))))) => (~ ((! [P:(A > (A > $o)),X5:A,Ys:(list @ A)]: ((X3 != ((((product_Pair @ (A > (A > $o))) @ (list @ A)) @ P) @ (((cons @ A) @ X5) @ Ys))))))))))).
% 3.96/1.85 thf(fact_35_shuffles_Ocases, axiom, (! [A:$tType,X3:((product_prod @ (list @ A)) @ (list @ A))]: (((! [Ys:(list @ A)]: ((X3 != ((((product_Pair @ (list @ A)) @ (list @ A)) @ (nil @ A)) @ Ys)))) => ((! [Xs:(list @ A)]: ((X3 != ((((product_Pair @ (list @ A)) @ (list @ A)) @ Xs) @ (nil @ A))))) => (~ ((! [X5:A,Xs:(list @ A),Y3:A,Ys:(list @ A)]: ((X3 != ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((cons @ A) @ X5) @ Xs)) @ (((cons @ A) @ Y3) @ Ys)))))))))))).
% 3.96/1.85 thf(fact_36_splice_Ocases, axiom, (! [A:$tType,X3:((product_prod @ (list @ A)) @ (list @ A))]: (((! [Ys:(list @ A)]: ((X3 != ((((product_Pair @ (list @ A)) @ (list @ A)) @ (nil @ A)) @ Ys)))) => (~ ((! [X5:A,Xs:(list @ A),Ys:(list @ A)]: ((X3 != ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((cons @ A) @ X5) @ Xs)) @ Ys)))))))))).
% 3.96/1.85 thf(fact_37_swap__simps_I1_J, axiom, (! [A2:name,B2:name]: ((((((perm @ name) @ name) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ A2) @ B2)) @ (nil @ ((product_prod @ name) @ name)))) @ A2) = B2)))).
% 3.96/1.85 thf(fact_38_swap__simps_I2_J, axiom, (! [A2:name,B2:name]: ((((((perm @ name) @ name) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ A2) @ B2)) @ (nil @ ((product_prod @ name) @ name)))) @ B2) = A2)))).
% 3.96/1.85 thf(fact_39_swap__simps_I3_J, axiom, (! [A2:name,C2:name,B2:name]: (((A2 != C2) => ((B2 != C2) => (((((perm @ name) @ name) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ A2) @ B2)) @ (nil @ ((product_prod @ name) @ name)))) @ C2) = C2)))))).
% 3.96/1.85 thf(fact_40_fresh__aux, axiom, (! [X2:$tType]: (((pt_name @ X2) => (! [C2:name,A2:name,X3:X2,B2:name]: (((C2 != A2) => (((((fresh @ name) @ X2) @ A2) @ X3) => (((((fresh @ name) @ X2) @ C2) @ X3) => ((((fresh @ name) @ X2) @ C2) @ ((((perm @ name) @ X2) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ A2) @ B2)) @ (nil @ ((product_prod @ name) @ name)))) @ X3))))))))))).
% 3.96/1.85 thf(fact_41_old_Oprod_Oinducts, axiom, (! [B:$tType,A:$tType,P2:(((product_prod @ A) @ B) > $o),Prod:((product_prod @ A) @ B)]: (((! [A4:A,B4:B]: ((P2 @ ((((product_Pair @ A) @ B) @ A4) @ B4)))) => (P2 @ Prod))))).
% 3.96/1.85 thf(fact_42_old_Oprod_Oexhaust, axiom, (! [A:$tType,B:$tType,Y4:((product_prod @ A) @ B)]: ((~ ((! [A4:A,B4:B]: ((Y4 != ((((product_Pair @ A) @ B) @ A4) @ B4))))))))).
% 3.96/1.85 thf(fact_43_prod__induct7, axiom, (! [G:$tType,F2:$tType,E:$tType,D:$tType,C3:$tType,B:$tType,A:$tType,P2:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F2) @ G)))))) > $o),X3:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F2) @ G))))))]: (((! [A4:A,B4:B,C:C3,D2:D,E2:E,F:F2,G2:G]: ((P2 @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F2) @ G)))))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C3) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F2) @ G))))) @ B4) @ ((((product_Pair @ C3) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F2) @ G)))) @ C) @ ((((product_Pair @ D) @ ((product_prod @ E) @ ((product_prod @ F2) @ G))) @ D2) @ ((((product_Pair @ E) @ ((product_prod @ F2) @ G)) @ E2) @ ((((product_Pair @ F2) @ G) @ F) @ G2))))))))) => (P2 @ X3))))).
% 3.96/1.85 thf(fact_44_prod__induct6, axiom, (! [F2:$tType,E:$tType,D:$tType,C3:$tType,B:$tType,A:$tType,P2:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ ((product_prod @ D) @ ((product_prod @ E) @ F2))))) > $o),X3:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ ((product_prod @ D) @ ((product_prod @ E) @ F2)))))]: (((! [A4:A,B4:B,C:C3,D2:D,E2:E,F:F2]: ((P2 @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ ((product_prod @ D) @ ((product_prod @ E) @ F2))))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C3) @ ((product_prod @ D) @ ((product_prod @ E) @ F2)))) @ B4) @ ((((product_Pair @ C3) @ ((product_prod @ D) @ ((product_prod @ E) @ F2))) @ C) @ ((((product_Pair @ D) @ ((product_prod @ E) @ F2)) @ D2) @ ((((product_Pair @ E) @ F2) @ E2) @ F)))))))) => (P2 @ X3))))).
% 3.96/1.85 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P2:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P2)) = (P2 @ A2))))).
% 3.96/1.85 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A5:(set @ A)]: ((((collect @ A) @ (^ [X6:A]: ((((member @ A) @ X6) @ A5)))) = A5)))).
% 3.96/1.85 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P2:(A > $o),Q:(A > $o)]: (((! [X5:A]: (((P2 @ X5) = (Q @ X5)))) => (((collect @ A) @ P2) = ((collect @ A) @ Q)))))).
% 3.96/1.85 thf(fact_48_ext, axiom, (! [B:$tType,A:$tType,F3:(A > B),G3:(A > B)]: (((! [X5:A]: (((F3 @ X5) = (G3 @ X5)))) => (F3 = G3))))).
% 3.96/1.85 thf(fact_49_prod__induct5, axiom, (! [E:$tType,D:$tType,C3:$tType,B:$tType,A:$tType,P2:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ ((product_prod @ D) @ E)))) > $o),X3:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ ((product_prod @ D) @ E))))]: (((! [A4:A,B4:B,C:C3,D2:D,E2:E]: ((P2 @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ ((product_prod @ D) @ E)))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C3) @ ((product_prod @ D) @ E))) @ B4) @ ((((product_Pair @ C3) @ ((product_prod @ D) @ E)) @ C) @ ((((product_Pair @ D) @ E) @ D2) @ E2))))))) => (P2 @ X3))))).
% 3.96/1.85 thf(fact_50_prod__induct4, axiom, (! [D:$tType,C3:$tType,B:$tType,A:$tType,P2:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ D))) > $o),X3:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ D)))]: (((! [A4:A,B4:B,C:C3,D2:D]: ((P2 @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ D))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C3) @ D)) @ B4) @ ((((product_Pair @ C3) @ D) @ C) @ D2)))))) => (P2 @ X3))))).
% 3.96/1.85 thf(fact_51_prod__induct3, axiom, (! [C3:$tType,B:$tType,A:$tType,P2:(((product_prod @ A) @ ((product_prod @ B) @ C3)) > $o),X3:((product_prod @ A) @ ((product_prod @ B) @ C3))]: (((! [A4:A,B4:B,C:C3]: ((P2 @ ((((product_Pair @ A) @ ((product_prod @ B) @ C3)) @ A4) @ ((((product_Pair @ B) @ C3) @ B4) @ C))))) => (P2 @ X3))))).
% 3.96/1.85 thf(fact_52_prod__cases7, axiom, (! [A:$tType,B:$tType,C3:$tType,D:$tType,E:$tType,F2:$tType,G:$tType,Y4:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F2) @ G))))))]: ((~ ((! [A4:A,B4:B,C:C3,D2:D,E2:E,F:F2,G2:G]: ((Y4 != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F2) @ G)))))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C3) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F2) @ G))))) @ B4) @ ((((product_Pair @ C3) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F2) @ G)))) @ C) @ ((((product_Pair @ D) @ ((product_prod @ E) @ ((product_prod @ F2) @ G))) @ D2) @ ((((product_Pair @ E) @ ((product_prod @ F2) @ G)) @ E2) @ ((((product_Pair @ F2) @ G) @ F) @ G2)))))))))))))).
% 3.96/1.85 thf(fact_53_prod__cases6, axiom, (! [A:$tType,B:$tType,C3:$tType,D:$tType,E:$tType,F2:$tType,Y4:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ ((product_prod @ D) @ ((product_prod @ E) @ F2)))))]: ((~ ((! [A4:A,B4:B,C:C3,D2:D,E2:E,F:F2]: ((Y4 != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ ((product_prod @ D) @ ((product_prod @ E) @ F2))))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C3) @ ((product_prod @ D) @ ((product_prod @ E) @ F2)))) @ B4) @ ((((product_Pair @ C3) @ ((product_prod @ D) @ ((product_prod @ E) @ F2))) @ C) @ ((((product_Pair @ D) @ ((product_prod @ E) @ F2)) @ D2) @ ((((product_Pair @ E) @ F2) @ E2) @ F))))))))))))).
% 3.96/1.85 thf(fact_54_prod__cases5, axiom, (! [A:$tType,B:$tType,C3:$tType,D:$tType,E:$tType,Y4:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ ((product_prod @ D) @ E))))]: ((~ ((! [A4:A,B4:B,C:C3,D2:D,E2:E]: ((Y4 != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ ((product_prod @ D) @ E)))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C3) @ ((product_prod @ D) @ E))) @ B4) @ ((((product_Pair @ C3) @ ((product_prod @ D) @ E)) @ C) @ ((((product_Pair @ D) @ E) @ D2) @ E2)))))))))))).
% 3.96/1.85 thf(fact_55_prod__cases4, axiom, (! [A:$tType,B:$tType,C3:$tType,D:$tType,Y4:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ D)))]: ((~ ((! [A4:A,B4:B,C:C3,D2:D]: ((Y4 != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C3) @ D))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C3) @ D)) @ B4) @ ((((product_Pair @ C3) @ D) @ C) @ D2))))))))))).
% 3.96/1.85 thf(fact_56_prod__cases3, axiom, (! [A:$tType,B:$tType,C3:$tType,Y4:((product_prod @ A) @ ((product_prod @ B) @ C3))]: ((~ ((! [A4:A,B4:B,C:C3]: ((Y4 != ((((product_Pair @ A) @ ((product_prod @ B) @ C3)) @ A4) @ ((((product_Pair @ B) @ C3) @ B4) @ C)))))))))).
% 3.96/1.85 thf(fact_57_Pair__inject, axiom, (! [A:$tType,B:$tType,A2:A,B2:B,A3:A,B3:B]: (((((((product_Pair @ A) @ B) @ A2) @ B2) = ((((product_Pair @ A) @ B) @ A3) @ B3)) => (~ (((A2 = A3) => (B2 != B3)))))))).
% 3.96/1.85 thf(fact_58_prod__cases, axiom, (! [B:$tType,A:$tType,P2:(((product_prod @ A) @ B) > $o),P3:((product_prod @ A) @ B)]: (((! [A4:A,B4:B]: ((P2 @ ((((product_Pair @ A) @ B) @ A4) @ B4)))) => (P2 @ P3))))).
% 3.96/1.85 thf(fact_59_surj__pair, axiom, (! [A:$tType,B:$tType,P3:((product_prod @ A) @ B)]: ((? [X5:A,Y3:B]: ((P3 = ((((product_Pair @ A) @ B) @ X5) @ Y3))))))).
% 3.96/1.85 thf(fact_60_not__Cons__self2, axiom, (! [A:$tType,X3:A,Xs2:(list @ A)]: (((((cons @ A) @ X3) @ Xs2) != Xs2)))).
% 3.96/1.85 thf(fact_61_cp__name__name1, axiom, (! [A:$tType]: (((cp_name_name @ A) => (! [Pi1:(list @ ((product_prod @ name) @ name)),Pi2:(list @ ((product_prod @ name) @ name)),X3:A]: ((((((perm @ name) @ A) @ Pi1) @ ((((perm @ name) @ A) @ Pi2) @ X3)) = ((((perm @ name) @ A) @ ((((perm @ name) @ (list @ ((product_prod @ name) @ name))) @ Pi1) @ Pi2)) @ ((((perm @ name) @ A) @ Pi1) @ X3))))))))).
% 3.96/1.85 thf(fact_62_name__perm__compose, axiom, (! [X:$tType]: (((pt_name @ X) => (! [Pi2:(list @ ((product_prod @ name) @ name)),Pi1:(list @ ((product_prod @ name) @ name)),X3:X]: ((((((perm @ name) @ X) @ Pi2) @ ((((perm @ name) @ X) @ Pi1) @ X3)) = ((((perm @ name) @ X) @ ((((perm @ name) @ (list @ ((product_prod @ name) @ name))) @ Pi2) @ Pi1)) @ ((((perm @ name) @ X) @ Pi2) @ X3))))))))).
% 3.96/1.85 thf(fact_63_perm__compose, axiom, (! [X2:$tType]: (((pt_name @ X2) => (! [Pi2:(list @ ((product_prod @ name) @ name)),Pi1:(list @ ((product_prod @ name) @ name)),X3:X2]: ((((((perm @ name) @ X2) @ Pi2) @ ((((perm @ name) @ X2) @ Pi1) @ X3)) = ((((perm @ name) @ X2) @ ((((perm @ name) @ (list @ ((product_prod @ name) @ name))) @ Pi2) @ Pi1)) @ ((((perm @ name) @ X2) @ Pi2) @ X3))))))))).
% 3.96/1.85 thf(fact_64_perm__bij, axiom, (! [X2:$tType]: (((pt_name @ X2) => (! [Pi:(list @ ((product_prod @ name) @ name)),X3:X2,Y4:X2]: (((((((perm @ name) @ X2) @ Pi) @ X3) = ((((perm @ name) @ X2) @ Pi) @ Y4)) = (X3 = Y4)))))))).
% 3.96/1.85 thf(fact_65_perm__app, axiom, (! [B:$tType,X2:$tType]: (((pt_name @ X2) => (! [Pi:(list @ ((product_prod @ name) @ name)),F3:(X2 > B),X3:X2]: ((((((perm @ name) @ B) @ Pi) @ (F3 @ X3)) = (((((perm @ name) @ (X2 > B)) @ Pi) @ F3) @ ((((perm @ name) @ X2) @ Pi) @ X3))))))))).
% 3.96/1.85 thf(fact_66_in__eqvt, axiom, (! [X2:$tType]: (((pt_name @ X2) => (! [Pi:(list @ ((product_prod @ name) @ name)),X3:X2,X4:(set @ X2)]: ((((((perm @ name) @ $o) @ Pi) @ (((member @ X2) @ X3) @ X4)) = (((member @ X2) @ ((((perm @ name) @ X2) @ Pi) @ X3)) @ ((((perm @ name) @ (set @ X2)) @ Pi) @ X4))))))))).
% 3.96/1.85 thf(fact_67_eq__eqvt, axiom, (! [X2:$tType]: (((pt_name @ X2) => (! [Pi:(list @ ((product_prod @ name) @ name)),X3:X2,Y4:X2]: ((((((perm @ name) @ $o) @ Pi) @ (X3 = Y4)) = (((((perm @ name) @ X2) @ Pi) @ X3) = ((((perm @ name) @ X2) @ Pi) @ Y4))))))))).
% 3.96/1.85 thf(fact_68_strict__sorted_Oinduct, axiom, (! [A:$tType]: (((linorder @ A) => (! [P2:((list @ A) > $o),A0:(list @ A)]: (((P2 @ (nil @ A)) => ((! [X5:A,Ys:(list @ A)]: (((P2 @ Ys) => (P2 @ (((cons @ A) @ X5) @ Ys))))) => (P2 @ A0))))))))).
% 3.96/1.85 thf(fact_69_strict__sorted_Ocases, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:(list @ A)]: (((X3 != (nil @ A)) => (~ ((! [X5:A,Ys:(list @ A)]: ((X3 != (((cons @ A) @ X5) @ Ys))))))))))))).
% 3.96/1.85 thf(fact_70_map__tailrec__rev_Oinduct, axiom, (! [A:$tType,B:$tType,P2:((A > B) > ((list @ A) > ((list @ B) > $o))),A0:(A > B),A1:(list @ A),A22:(list @ B)]: (((! [F:(A > B),X_1:(list @ B)]: ((((P2 @ F) @ (nil @ A)) @ X_1))) => ((! [F:(A > B),A4:A,As:(list @ A),Bs:(list @ B)]: (((((P2 @ F) @ As) @ (((cons @ B) @ (F @ A4)) @ Bs)) => (((P2 @ F) @ (((cons @ A) @ A4) @ As)) @ Bs)))) => (((P2 @ A0) @ A1) @ A22)))))).
% 3.96/1.85 thf(fact_71_list__nonempty__induct, axiom, (! [A:$tType,Xs2:(list @ A),P2:((list @ A) > $o)]: (((Xs2 != (nil @ A)) => ((! [X5:A]: ((P2 @ (((cons @ A) @ X5) @ (nil @ A))))) => ((! [X5:A,Xs:(list @ A)]: (((Xs != (nil @ A)) => ((P2 @ Xs) => (P2 @ (((cons @ A) @ X5) @ Xs)))))) => (P2 @ Xs2))))))).
% 3.96/1.85 thf(fact_72_successively_Oinduct, axiom, (! [A:$tType,P2:((A > (A > $o)) > ((list @ A) > $o)),A0:(A > (A > $o)),A1:(list @ A)]: (((! [P:(A > (A > $o))]: (((P2 @ P) @ (nil @ A)))) => ((! [P:(A > (A > $o)),X5:A]: (((P2 @ P) @ (((cons @ A) @ X5) @ (nil @ A))))) => ((! [P:(A > (A > $o)),X5:A,Y3:A,Xs:(list @ A)]: ((((P2 @ P) @ (((cons @ A) @ Y3) @ Xs)) => ((P2 @ P) @ (((cons @ A) @ X5) @ (((cons @ A) @ Y3) @ Xs)))))) => ((P2 @ A0) @ A1))))))).
% 3.96/1.85 thf(fact_73_arg__min__list_Oinduct, axiom, (! [B:$tType,A:$tType]: (((linorder @ B) => (! [P2:((A > B) > ((list @ A) > $o)),A0:(A > B),A1:(list @ A)]: (((! [F:(A > B),X5:A]: (((P2 @ F) @ (((cons @ A) @ X5) @ (nil @ A))))) => ((! [F:(A > B),X5:A,Y3:A,Zs:(list @ A)]: ((((P2 @ F) @ (((cons @ A) @ Y3) @ Zs)) => ((P2 @ F) @ (((cons @ A) @ X5) @ (((cons @ A) @ Y3) @ Zs)))))) => ((! [A4:(A > B)]: (((P2 @ A4) @ (nil @ A)))) => ((P2 @ A0) @ A1)))))))))).
% 3.96/1.85 thf(fact_74_remdups__adj_Oinduct, axiom, (! [A:$tType,P2:((list @ A) > $o),A0:(list @ A)]: (((P2 @ (nil @ A)) => ((! [X5:A]: ((P2 @ (((cons @ A) @ X5) @ (nil @ A))))) => ((! [X5:A,Y3:A,Xs:(list @ A)]: ((((X5 = Y3) => (P2 @ (((cons @ A) @ X5) @ Xs))) => (((X5 != Y3) => (P2 @ (((cons @ A) @ Y3) @ Xs))) => (P2 @ (((cons @ A) @ X5) @ (((cons @ A) @ Y3) @ Xs))))))) => (P2 @ A0))))))).
% 3.96/1.85 thf(fact_75_sorted__wrt_Oinduct, axiom, (! [A:$tType,P2:((A > (A > $o)) > ((list @ A) > $o)),A0:(A > (A > $o)),A1:(list @ A)]: (((! [P:(A > (A > $o))]: (((P2 @ P) @ (nil @ A)))) => ((! [P:(A > (A > $o)),X5:A,Ys:(list @ A)]: ((((P2 @ P) @ Ys) => ((P2 @ P) @ (((cons @ A) @ X5) @ Ys))))) => ((P2 @ A0) @ A1)))))).
% 3.96/1.85 thf(fact_76_remdups__adj_Ocases, axiom, (! [A:$tType,X3:(list @ A)]: (((X3 != (nil @ A)) => ((! [X5:A]: ((X3 != (((cons @ A) @ X5) @ (nil @ A))))) => (~ ((! [X5:A,Y3:A,Xs:(list @ A)]: ((X3 != (((cons @ A) @ X5) @ (((cons @ A) @ Y3) @ Xs)))))))))))).
% 3.96/1.85 thf(fact_77_transpose_Ocases, axiom, (! [A:$tType,X3:(list @ (list @ A))]: (((X3 != (nil @ (list @ A))) => ((! [Xss:(list @ (list @ A))]: ((X3 != (((cons @ (list @ A)) @ (nil @ A)) @ Xss)))) => (~ ((! [X5:A,Xs:(list @ A),Xss:(list @ (list @ A))]: ((X3 != (((cons @ (list @ A)) @ (((cons @ A) @ X5) @ Xs)) @ Xss))))))))))).
% 3.96/1.85 thf(fact_78_shuffles_Oinduct, axiom, (! [A:$tType,P2:((list @ A) > ((list @ A) > $o)),A0:(list @ A),A1:(list @ A)]: (((! [X_1:(list @ A)]: (((P2 @ (nil @ A)) @ X_1))) => ((! [Xs:(list @ A)]: (((P2 @ Xs) @ (nil @ A)))) => ((! [X5:A,Xs:(list @ A),Y3:A,Ys:(list @ A)]: ((((P2 @ Xs) @ (((cons @ A) @ Y3) @ Ys)) => (((P2 @ (((cons @ A) @ X5) @ Xs)) @ Ys) => ((P2 @ (((cons @ A) @ X5) @ Xs)) @ (((cons @ A) @ Y3) @ Ys)))))) => ((P2 @ A0) @ A1))))))).
% 3.96/1.85 thf(fact_79_min__list_Oinduct, axiom, (! [A:$tType]: (((ord @ A) => (! [P2:((list @ A) > $o),A0:(list @ A)]: (((! [X5:A,Xs:(list @ A)]: (((! [X212:A,X223:(list @ A)]: (((Xs = (((cons @ A) @ X212) @ X223)) => (P2 @ Xs)))) => (P2 @ (((cons @ A) @ X5) @ Xs))))) => ((P2 @ (nil @ A)) => (P2 @ A0))))))))).
% 3.96/1.85 thf(fact_80_min__list_Ocases, axiom, (! [A:$tType]: (((ord @ A) => (! [X3:(list @ A)]: (((! [X5:A,Xs:(list @ A)]: ((X3 != (((cons @ A) @ X5) @ Xs)))) => (X3 = (nil @ A))))))))).
% 3.96/1.85 thf(fact_81_induct__list012, axiom, (! [A:$tType,P2:((list @ A) > $o),Xs2:(list @ A)]: (((P2 @ (nil @ A)) => ((! [X5:A]: ((P2 @ (((cons @ A) @ X5) @ (nil @ A))))) => ((! [X5:A,Y3:A,Zs:(list @ A)]: (((P2 @ Zs) => ((P2 @ (((cons @ A) @ Y3) @ Zs)) => (P2 @ (((cons @ A) @ X5) @ (((cons @ A) @ Y3) @ Zs))))))) => (P2 @ Xs2))))))).
% 3.96/1.85 thf(fact_82_splice_Oinduct, axiom, (! [A:$tType,P2:((list @ A) > ((list @ A) > $o)),A0:(list @ A),A1:(list @ A)]: (((! [X_1:(list @ A)]: (((P2 @ (nil @ A)) @ X_1))) => ((! [X5:A,Xs:(list @ A),Ys:(list @ A)]: ((((P2 @ Ys) @ Xs) => ((P2 @ (((cons @ A) @ X5) @ Xs)) @ Ys)))) => ((P2 @ A0) @ A1)))))).
% 3.96/1.85 thf(fact_83_list__induct2_H, axiom, (! [A:$tType,B:$tType,P2:((list @ A) > ((list @ B) > $o)),Xs2:(list @ A),Ys2:(list @ B)]: ((((P2 @ (nil @ A)) @ (nil @ B)) => ((! [X5:A,Xs:(list @ A)]: (((P2 @ (((cons @ A) @ X5) @ Xs)) @ (nil @ B)))) => ((! [Y3:B,Ys:(list @ B)]: (((P2 @ (nil @ A)) @ (((cons @ B) @ Y3) @ Ys)))) => ((! [X5:A,Xs:(list @ A),Y3:B,Ys:(list @ B)]: ((((P2 @ Xs) @ Ys) => ((P2 @ (((cons @ A) @ X5) @ Xs)) @ (((cons @ B) @ Y3) @ Ys))))) => ((P2 @ Xs2) @ Ys2)))))))).
% 3.96/1.85 thf(fact_84_neq__Nil__conv, axiom, (! [A:$tType,Xs2:(list @ A)]: (((Xs2 != (nil @ A)) = (? [Y5:A,Ys3:(list @ A)]: ((Xs2 = (((cons @ A) @ Y5) @ Ys3)))))))).
% 3.96/1.85 thf(fact_85_list_Oinducts, axiom, (! [A:$tType,P2:((list @ A) > $o),List:(list @ A)]: (((P2 @ (nil @ A)) => ((! [X12:A,X23:(list @ A)]: (((P2 @ X23) => (P2 @ (((cons @ A) @ X12) @ X23))))) => (P2 @ List)))))).
% 3.96/1.85 thf(fact_86_list_Oexhaust, axiom, (! [A:$tType,Y4:(list @ A)]: (((Y4 != (nil @ A)) => (~ ((! [X213:A,X224:(list @ A)]: ((Y4 != (((cons @ A) @ X213) @ X224)))))))))).
% 3.96/1.85 thf(fact_87_list_OdiscI, axiom, (! [A:$tType,List:(list @ A),X21:A,X222:(list @ A)]: (((List = (((cons @ A) @ X21) @ X222)) => (List != (nil @ A)))))).
% 3.96/1.85 thf(fact_88_list_Odistinct_I1_J, axiom, (! [A:$tType,X21:A,X222:(list @ A)]: (((nil @ A) != (((cons @ A) @ X21) @ X222))))).
% 3.96/1.85 thf(fact_89__092_060open_062y_A_092_060sharp_062_AQ_092_060close_062, axiom, ((((fresh @ name) @ pi) @ y) @ q)).
% 3.96/1.85 thf(fact_90_pair__in__Id__conv, axiom, (! [A:$tType,A2:A,B2:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A2) @ B2)) @ (id @ A)) = (A2 = B2))))).
% 3.96/1.85 thf(fact_91_IdI, axiom, (! [A:$tType,A2:A]: ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A2) @ A2)) @ (id @ A))))).
% 3.96/1.85 thf(fact_92_fresh__prod, axiom, (! [A:$tType,X:$tType,B:$tType,A2:X,X3:A,Y4:B]: ((((((fresh @ X) @ ((product_prod @ A) @ B)) @ A2) @ ((((product_Pair @ A) @ B) @ X3) @ Y4)) = (((((fresh @ X) @ A) @ A2) @ X3) & ((((fresh @ X) @ B) @ A2) @ Y4)))))).
% 3.96/1.85 thf(fact_93__092_060open_062y_A_092_060sharp_062_AP_092_060close_062, axiom, ((((fresh @ name) @ pi) @ y) @ p)).
% 3.96/1.85 thf(fact_94_derivativeReflexive, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),P2:pi,A2:late_subject,X3:name]: (((((ord_less_eq @ (set @ ((product_prod @ pi) @ pi))) @ (id @ pi)) @ Rel) => (((((strong2129052853vative @ P2) @ P2) @ A2) @ X3) @ Rel))))).
% 3.96/1.85 thf(fact_95_derivativeEqvtI, axiom, (! [P2:pi,Q:pi,A2:late_subject,X3:name,Rel:(set @ ((product_prod @ pi) @ pi)),Perm:(list @ ((product_prod @ name) @ name))]: (((((((strong2129052853vative @ P2) @ Q) @ A2) @ X3) @ Rel) => (((eqvt @ pi) @ Rel) => (((((strong2129052853vative @ ((((perm @ name) @ pi) @ Perm) @ P2)) @ ((((perm @ name) @ pi) @ Perm) @ Q)) @ ((((perm @ name) @ late_subject) @ Perm) @ A2)) @ ((((perm @ name) @ name) @ Perm) @ X3)) @ Rel)))))).
% 3.96/1.85 thf(fact_96_derivativeEqvtI2, axiom, (! [P2:pi,Q:pi,A2:late_subject,X3:name,Rel:(set @ ((product_prod @ pi) @ pi)),Perm:(list @ ((product_prod @ name) @ name))]: (((((((strong2129052853vative @ P2) @ Q) @ A2) @ X3) @ Rel) => (((eqvt @ pi) @ Rel) => (((((strong2129052853vative @ ((((perm @ name) @ pi) @ Perm) @ P2)) @ ((((perm @ name) @ pi) @ Perm) @ Q)) @ A2) @ ((((perm @ name) @ name) @ Perm) @ X3)) @ Rel)))))).
% 3.96/1.85 thf(fact_97_old_Oprod_Orec, axiom, (! [A:$tType,T:$tType,B:$tType,F1:(A > (B > T)),A2:A,B2:B]: (((((((product_rec_prod @ A) @ B) @ T) @ F1) @ ((((product_Pair @ A) @ B) @ A2) @ B2)) = ((F1 @ A2) @ B2))))).
% 3.96/1.85 thf(fact_98_eqvtRelI, axiom, (! [A:$tType]: (((pt_name @ A) => (! [Rel:(set @ ((product_prod @ A) @ A)),P2:A,Q:A,Perm:(list @ ((product_prod @ name) @ name))]: ((((eqvt @ A) @ Rel) => ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ P2) @ Q)) @ Rel) => (((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ ((((perm @ name) @ A) @ Perm) @ P2)) @ ((((perm @ name) @ A) @ Perm) @ Q))) @ Rel))))))))).
% 3.96/1.85 thf(fact_99_Bound_Ohyps_I5_J, axiom, ((((fresh @ name) @ ((product_prod @ name) @ ((product_prod @ pi) @ pi))) @ y) @ ((((product_Pair @ name) @ ((product_prod @ pi) @ pi)) @ x) @ ((((product_Pair @ pi) @ pi) @ p) @ q)))).
% 3.96/1.85 thf(fact_100_true__eqvt, axiom, (! [A:$tType,Pi:(list @ ((product_prod @ A) @ A))]: (((((perm @ A) @ $o) @ Pi) @ $true)))).
% 3.96/1.85 thf(fact_101_false__eqvt, axiom, (! [A:$tType,Pi:(list @ ((product_prod @ A) @ A))]: ((~ (((((perm @ A) @ $o) @ Pi) @ $false)))))).
% 3.96/1.85 thf(fact_102_subject_Ofresh_I2_J, axiom, (! [A2:name,X1:name]: ((((((fresh @ name) @ late_subject) @ A2) @ (late_BoundOutputS @ X1)) = ((((fresh @ name) @ name) @ A2) @ X1))))).
% 3.96/1.85 thf(fact_103_name__bij, axiom, (! [Pi:(list @ ((product_prod @ name) @ name)),X3:name,Y4:name]: (((((((perm @ name) @ name) @ Pi) @ X3) = ((((perm @ name) @ name) @ Pi) @ Y4)) = (X3 = Y4))))).
% 3.96/1.85 thf(fact_104_imp__eqvt, axiom, (! [A:$tType,Pi:(list @ ((product_prod @ A) @ A)),A5:$o,B5:$o]: ((((((perm @ A) @ $o) @ Pi) @ (A5 => B5)) = (((((perm @ A) @ $o) @ Pi) @ A5) => ((((perm @ A) @ $o) @ Pi) @ B5)))))).
% 3.96/1.85 thf(fact_105_neg__eqvt, axiom, (! [A:$tType,Pi:(list @ ((product_prod @ A) @ A)),A5:$o]: ((((((perm @ A) @ $o) @ Pi) @ (~ (A5))) = (~ (((((perm @ A) @ $o) @ Pi) @ A5))))))).
% 3.96/1.85 thf(fact_106_conj__eqvt, axiom, (! [A:$tType,Pi:(list @ ((product_prod @ A) @ A)),A5:$o,B5:$o]: ((((((perm @ A) @ $o) @ Pi) @ (A5 & B5)) = (((((perm @ A) @ $o) @ Pi) @ A5) & ((((perm @ A) @ $o) @ Pi) @ B5)))))).
% 3.96/1.85 thf(fact_107_disj__eqvt, axiom, (! [A:$tType,Pi:(list @ ((product_prod @ A) @ A)),A5:$o,B5:$o]: ((((((perm @ A) @ $o) @ Pi) @ (A5 | B5)) = (((((perm @ A) @ $o) @ Pi) @ A5) | ((((perm @ A) @ $o) @ Pi) @ B5)))))).
% 3.96/1.85 thf(fact_108_perm__boolE, axiom, (! [A:$tType,Pi:(list @ ((product_prod @ A) @ A))]: ((~ (((((perm @ A) @ $o) @ Pi) @ $false)))))).
% 3.96/1.85 thf(fact_109_perm__boolI, axiom, (! [A:$tType,P2:$o,Pi:(list @ ((product_prod @ A) @ A))]: ((P2 => ((((perm @ A) @ $o) @ Pi) @ P2))))).
% 3.96/1.85 thf(fact_110_pt__set__bij3, axiom, (! [X:$tType,A:$tType,Pi:(list @ ((product_prod @ X) @ X)),X3:A,X4:(set @ A)]: ((((((perm @ X) @ $o) @ Pi) @ (((member @ A) @ X3) @ X4)) = (((member @ A) @ X3) @ X4))))).
% 3.96/1.85 thf(fact_111_perm__bool__def, axiom, (! [X:$tType]: ((((perm @ X) @ $o) = (^ [Pi3:(list @ ((product_prod @ X) @ X)),B6:$o]: (B6)))))).
% 3.96/1.85 thf(fact_112_nil__eqvt, axiom, (! [X:$tType,A:$tType,Pi:(list @ ((product_prod @ X) @ X))]: ((((((perm @ X) @ (list @ A)) @ Pi) @ (nil @ A)) = (nil @ A))))).
% 3.96/1.85 thf(fact_113_fresh__list__nil, axiom, (! [X:$tType,A:$tType,A2:X]: (((((fresh @ X) @ (list @ A)) @ A2) @ (nil @ A))))).
% 3.96/1.85 thf(fact_114_allE__Nil, axiom, (! [A:$tType,P2:((list @ A) > $o)]: (((! [X_1:(list @ A)]: ((P2 @ X_1))) => (P2 @ (nil @ A)))))).
% 3.96/1.85 thf(fact_115_if__eqvt, axiom, (! [A:$tType,B:$tType,Pi:(list @ ((product_prod @ A) @ A)),B2:$o,C1:B,C22:B]: (((((((perm @ A) @ $o) @ Pi) @ B2) => (((((perm @ A) @ B) @ Pi) @ ((((if @ B) @ B2) @ C1) @ C22)) = ((((perm @ A) @ B) @ Pi) @ C1))) & ((~ (((((perm @ A) @ $o) @ Pi) @ B2))) => (((((perm @ A) @ B) @ Pi) @ ((((if @ B) @ B2) @ C1) @ C22)) = ((((perm @ A) @ B) @ Pi) @ C22))))))).
% 3.96/1.85 thf(fact_116_pt__bij3, axiom, (! [X:$tType,A:$tType,X3:A,Y4:A,Pi:(list @ ((product_prod @ X) @ X))]: (((X3 = Y4) => (((((perm @ X) @ A) @ Pi) @ X3) = ((((perm @ X) @ A) @ Pi) @ Y4)))))).
% 3.96/1.85 thf(fact_117_abs__fun__if, axiom, (! [X:$tType,A:$tType,C2:$o,Pi:(list @ ((product_prod @ X) @ X)),X3:A,Y4:A]: (((C2 => (((((perm @ X) @ A) @ Pi) @ ((((if @ A) @ C2) @ X3) @ Y4)) = ((((perm @ X) @ A) @ Pi) @ X3))) & ((~ (C2)) => (((((perm @ X) @ A) @ Pi) @ ((((if @ A) @ C2) @ X3) @ Y4)) = ((((perm @ X) @ A) @ Pi) @ Y4))))))).
% 3.96/1.85 thf(fact_118_eqvt__def, axiom, (! [A:$tType]: (((pt_name @ A) => ((eqvt @ A) = (^ [Rel2:(set @ ((product_prod @ A) @ A))]: ((! [X6:((product_prod @ A) @ A),Perm2:(list @ ((product_prod @ name) @ name))]: (((((member @ ((product_prod @ A) @ A)) @ X6) @ Rel2) => (((member @ ((product_prod @ A) @ A)) @ ((((perm @ name) @ ((product_prod @ A) @ A)) @ Perm2) @ X6)) @ Rel2))))))))))).
% 3.96/1.85 thf(fact_119_perm__prod_Osimps, axiom, (! [A:$tType,X:$tType,B:$tType,Pi:(list @ ((product_prod @ X) @ X)),X3:A,Y4:B]: ((((((perm @ X) @ ((product_prod @ A) @ B)) @ Pi) @ ((((product_Pair @ A) @ B) @ X3) @ Y4)) = ((((product_Pair @ A) @ B) @ ((((perm @ X) @ A) @ Pi) @ X3)) @ ((((perm @ X) @ B) @ Pi) @ Y4)))))).
% 3.96/1.85 thf(fact_120_cons__eqvt, axiom, (! [X:$tType,A:$tType,Pi:(list @ ((product_prod @ X) @ X)),X3:A,Xs2:(list @ A)]: ((((((perm @ X) @ (list @ A)) @ Pi) @ (((cons @ A) @ X3) @ Xs2)) = (((cons @ A) @ ((((perm @ X) @ A) @ Pi) @ X3)) @ ((((perm @ X) @ (list @ A)) @ Pi) @ Xs2)))))).
% 3.96/1.85 thf(fact_121_fresh__prodD_I1_J, axiom, (! [C3:$tType,A:$tType,B:$tType,A2:A,X3:B,Y4:C3]: ((((((fresh @ A) @ ((product_prod @ B) @ C3)) @ A2) @ ((((product_Pair @ B) @ C3) @ X3) @ Y4)) => ((((fresh @ A) @ B) @ A2) @ X3))))).
% 3.96/1.85 thf(fact_122_fresh__prodD_I2_J, axiom, (! [B:$tType,A:$tType,C3:$tType,A2:A,X3:B,Y4:C3]: ((((((fresh @ A) @ ((product_prod @ B) @ C3)) @ A2) @ ((((product_Pair @ B) @ C3) @ X3) @ Y4)) => ((((fresh @ A) @ C3) @ A2) @ Y4))))).
% 3.96/1.85 thf(fact_123_fresh__list__cons, axiom, (! [X:$tType,A:$tType,A2:X,X3:A,Xs2:(list @ A)]: ((((((fresh @ X) @ (list @ A)) @ A2) @ (((cons @ A) @ X3) @ Xs2)) = (((((fresh @ X) @ A) @ A2) @ X3) & ((((fresh @ X) @ (list @ A)) @ A2) @ Xs2)))))).
% 3.96/1.85 thf(fact_124_subrelI, axiom, (! [B:$tType,A:$tType,R:(set @ ((product_prod @ A) @ B)),S:(set @ ((product_prod @ A) @ B))]: (((! [X5:A,Y3:B]: (((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X5) @ Y3)) @ R) => (((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X5) @ Y3)) @ S)))) => (((ord_less_eq @ (set @ ((product_prod @ A) @ B))) @ R) @ S))))).
% 3.96/1.85 thf(fact_125_IdE, axiom, (! [A:$tType,P3:((product_prod @ A) @ A)]: (((((member @ ((product_prod @ A) @ A)) @ P3) @ (id @ A)) => (~ ((! [X5:A]: ((P3 != ((((product_Pair @ A) @ A) @ X5) @ X5)))))))))).
% 3.96/1.85 thf(fact_126_derivativeMonotonic, axiom, (! [P2:pi,Q:pi,A2:late_subject,X3:name,A5:(set @ ((product_prod @ pi) @ pi)),B5:(set @ ((product_prod @ pi) @ pi))]: (((((((strong2129052853vative @ P2) @ Q) @ A2) @ X3) @ A5) => ((((ord_less_eq @ (set @ ((product_prod @ pi) @ pi))) @ A5) @ B5) => (((((strong2129052853vative @ P2) @ Q) @ A2) @ X3) @ B5)))))).
% 3.96/1.85 thf(fact_127_eqvtRelE, axiom, (! [A:$tType]: (((pt_name @ A) => (! [Rel:(set @ ((product_prod @ A) @ A)),Perm:(list @ ((product_prod @ name) @ name)),P2:A,Q:A]: ((((eqvt @ A) @ Rel) => ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ ((((perm @ name) @ A) @ Perm) @ P2)) @ ((((perm @ name) @ A) @ Perm) @ Q))) @ Rel) => (((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ P2) @ Q)) @ Rel))))))))).
% 3.96/1.85 thf(fact_128_Bound_Ohyps_I3_J, axiom, ((((fresh @ name) @ pi) @ y) @ ((sum @ ((res @ x) @ p)) @ ((res @ x) @ q)))).
% 3.96/1.85 thf(fact_129_Bound_Ohyps_I2_J, axiom, ((((fresh @ name) @ pi) @ y) @ ((res @ x) @ ((sum @ p) @ q)))).
% 3.96/1.85 thf(fact_130_subset__antisym, axiom, (! [A:$tType,A5:(set @ A),B5:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A5) @ B5) => ((((ord_less_eq @ (set @ A)) @ B5) @ A5) => (A5 = B5)))))).
% 3.96/1.85 thf(fact_131_subsetI, axiom, (! [A:$tType,A5:(set @ A),B5:(set @ A)]: (((! [X5:A]: (((((member @ A) @ X5) @ A5) => (((member @ A) @ X5) @ B5)))) => (((ord_less_eq @ (set @ A)) @ A5) @ B5))))).
% 3.96/1.85 thf(fact_132_order__refl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A]: ((((ord_less_eq @ A) @ X3) @ X3))))))).
% 3.96/1.85 thf(fact_133_name__fresh, axiom, (((fresh @ name) @ name) = (^ [A6:name,B6:name]: ((A6 != B6))))).
% 3.96/1.85 thf(fact_134_pi_Ofresh_I7_J, axiom, (! [A2:name,X22:pi,X1:pi]: ((((((fresh @ name) @ pi) @ A2) @ ((sum @ X22) @ X1)) = (((((fresh @ name) @ pi) @ A2) @ X22) & ((((fresh @ name) @ pi) @ A2) @ X1)))))).
% 3.96/1.85 thf(fact_135_pi_Operm_I7_J, axiom, (! [Pi:(list @ ((product_prod @ name) @ name)),X22:pi,X1:pi]: ((((((perm @ name) @ pi) @ Pi) @ ((sum @ X22) @ X1)) = ((sum @ ((((perm @ name) @ pi) @ Pi) @ X22)) @ ((((perm @ name) @ pi) @ Pi) @ X1)))))).
% 3.96/1.85 thf(fact_136_pi_Operm_I9_J, axiom, (! [Pi:(list @ ((product_prod @ name) @ name)),X1:name,X22:pi]: ((((((perm @ name) @ pi) @ Pi) @ ((res @ X1) @ X22)) = ((res @ ((((perm @ name) @ name) @ Pi) @ X1)) @ ((((perm @ name) @ pi) @ Pi) @ X22)))))).
% 3.96/1.85 thf(fact_137_pi_Odistinct_I81_J, axiom, (! [Pi1:pi,Pi2:pi,Name:name,Pi4:pi]: ((((sum @ Pi1) @ Pi2) != ((res @ Name) @ Pi4))))).
% 3.96/1.85 thf(fact_138_pi_Oinject_I6_J, axiom, (! [X22:pi,X1:pi,Y2:pi,Y1:pi]: (((((sum @ X22) @ X1) = ((sum @ Y2) @ Y1)) = ((X22 = Y2) & (X1 = Y1)))))).
% 3.96/1.85 thf(fact_139_freshRes, axiom, (! [A2:name,P2:pi]: (((((fresh @ name) @ pi) @ A2) @ ((res @ A2) @ P2))))).
% 3.96/1.85 thf(fact_140_le__funD, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F3:(A > B),G3:(A > B),X3:A]: (((((ord_less_eq @ (A > B)) @ F3) @ G3) => (((ord_less_eq @ B) @ (F3 @ X3)) @ (G3 @ X3))))))))).
% 3.96/1.85 thf(fact_141_le__funE, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F3:(A > B),G3:(A > B),X3:A]: (((((ord_less_eq @ (A > B)) @ F3) @ G3) => (((ord_less_eq @ B) @ (F3 @ X3)) @ (G3 @ X3))))))))).
% 3.96/1.85 thf(fact_142_le__funI, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F3:(A > B),G3:(A > B)]: (((! [X5:A]: ((((ord_less_eq @ B) @ (F3 @ X5)) @ (G3 @ X5)))) => (((ord_less_eq @ (A > B)) @ F3) @ G3)))))))).
% 3.96/1.85 thf(fact_143_le__fun__def, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => ((ord_less_eq @ (A > B)) = (^ [F4:(A > B),G4:(A > B)]: ((! [X6:A]: ((((ord_less_eq @ B) @ (F4 @ X6)) @ (G4 @ X6))))))))))).
% 3.96/1.85 thf(fact_144_order__subst1, axiom, (! [A:$tType,B:$tType]: ((((order @ B) & (order @ A)) => (! [A2:A,F3:(B > A),B2:B,C2:B]: (((((ord_less_eq @ A) @ A2) @ (F3 @ B2)) => ((((ord_less_eq @ B) @ B2) @ C2) => ((! [X5:B,Y3:B]: (((((ord_less_eq @ B) @ X5) @ Y3) => (((ord_less_eq @ A) @ (F3 @ X5)) @ (F3 @ Y3))))) => (((ord_less_eq @ A) @ A2) @ (F3 @ C2))))))))))).
% 3.96/1.85 thf(fact_145_order__subst2, axiom, (! [A:$tType,C3:$tType]: ((((order @ C3) & (order @ A)) => (! [A2:A,B2:A,F3:(A > C3),C2:C3]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ C3) @ (F3 @ B2)) @ C2) => ((! [X5:A,Y3:A]: (((((ord_less_eq @ A) @ X5) @ Y3) => (((ord_less_eq @ C3) @ (F3 @ X5)) @ (F3 @ Y3))))) => (((ord_less_eq @ C3) @ (F3 @ A2)) @ C2)))))))))).
% 3.96/1.85 thf(fact_146_ord__eq__le__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A2:A,F3:(B > A),B2:B,C2:B]: (((A2 = (F3 @ B2)) => ((((ord_less_eq @ B) @ B2) @ C2) => ((! [X5:B,Y3:B]: (((((ord_less_eq @ B) @ X5) @ Y3) => (((ord_less_eq @ A) @ (F3 @ X5)) @ (F3 @ Y3))))) => (((ord_less_eq @ A) @ A2) @ (F3 @ C2))))))))))).
% 3.96/1.85 thf(fact_147_ord__le__eq__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A2:A,B2:A,F3:(A > B),C2:B]: (((((ord_less_eq @ A) @ A2) @ B2) => (((F3 @ B2) = C2) => ((! [X5:A,Y3:A]: (((((ord_less_eq @ A) @ X5) @ Y3) => (((ord_less_eq @ B) @ (F3 @ X5)) @ (F3 @ Y3))))) => (((ord_less_eq @ B) @ (F3 @ A2)) @ C2)))))))))).
% 3.96/1.85 thf(fact_148_eq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y6:A,Z:A]: ((Y6 = Z))) = (^ [X6:A,Y5:A]: (((((ord_less_eq @ A) @ X6) @ Y5) & (((ord_less_eq @ A) @ Y5) @ X6))))))))).
% 3.96/1.85 thf(fact_149_antisym, axiom, (! [A:$tType]: (((order @ A) => (! [X3:A,Y4:A]: (((((ord_less_eq @ A) @ X3) @ Y4) => ((((ord_less_eq @ A) @ Y4) @ X3) => (X3 = Y4))))))))).
% 3.96/1.85 thf(fact_150_linear, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y4:A]: (((((ord_less_eq @ A) @ X3) @ Y4) | (((ord_less_eq @ A) @ Y4) @ X3)))))))).
% 3.96/1.85 thf(fact_151_eq__refl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A,Y4:A]: (((X3 = Y4) => (((ord_less_eq @ A) @ X3) @ Y4)))))))).
% 3.96/1.85 thf(fact_152_le__cases, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y4:A]: (((~ ((((ord_less_eq @ A) @ X3) @ Y4))) => (((ord_less_eq @ A) @ Y4) @ X3)))))))).
% 3.96/1.85 thf(fact_153_order_Otrans, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B2:A,C2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ B2) @ C2) => (((ord_less_eq @ A) @ A2) @ C2))))))))).
% 3.96/1.85 thf(fact_154_le__cases3, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y4:A,Z2:A]: ((((((ord_less_eq @ A) @ X3) @ Y4) => (~ ((((ord_less_eq @ A) @ Y4) @ Z2)))) => (((((ord_less_eq @ A) @ Y4) @ X3) => (~ ((((ord_less_eq @ A) @ X3) @ Z2)))) => (((((ord_less_eq @ A) @ X3) @ Z2) => (~ ((((ord_less_eq @ A) @ Z2) @ Y4)))) => (((((ord_less_eq @ A) @ Z2) @ Y4) => (~ ((((ord_less_eq @ A) @ Y4) @ X3)))) => (((((ord_less_eq @ A) @ Y4) @ Z2) => (~ ((((ord_less_eq @ A) @ Z2) @ X3)))) => (~ (((((ord_less_eq @ A) @ Z2) @ X3) => (~ ((((ord_less_eq @ A) @ X3) @ Y4))))))))))))))))).
% 3.96/1.85 thf(fact_155_antisym__conv, axiom, (! [A:$tType]: (((order @ A) => (! [Y4:A,X3:A]: (((((ord_less_eq @ A) @ Y4) @ X3) => ((((ord_less_eq @ A) @ X3) @ Y4) = (X3 = Y4))))))))).
% 3.96/1.85 thf(fact_156_order__class_Oorder_Oeq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y6:A,Z:A]: ((Y6 = Z))) = (^ [A6:A,B6:A]: (((((ord_less_eq @ A) @ A6) @ B6) & (((ord_less_eq @ A) @ B6) @ A6))))))))).
% 3.96/1.85 thf(fact_157_ord__eq__le__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A2:A,B2:A,C2:A]: (((A2 = B2) => ((((ord_less_eq @ A) @ B2) @ C2) => (((ord_less_eq @ A) @ A2) @ C2))))))))).
% 3.96/1.85 thf(fact_158_ord__le__eq__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A2:A,B2:A,C2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((B2 = C2) => (((ord_less_eq @ A) @ A2) @ C2))))))))).
% 3.96/1.85 thf(fact_159_order__class_Oorder_Oantisym, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ B2) @ A2) => (A2 = B2))))))))).
% 3.96/1.85 thf(fact_160_order__trans, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A,Y4:A,Z2:A]: (((((ord_less_eq @ A) @ X3) @ Y4) => ((((ord_less_eq @ A) @ Y4) @ Z2) => (((ord_less_eq @ A) @ X3) @ Z2))))))))).
% 3.96/1.85 thf(fact_161_dual__order_Orefl, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A]: ((((ord_less_eq @ A) @ A2) @ A2))))))).
% 3.96/1.85 thf(fact_162_linorder__wlog, axiom, (! [A:$tType]: (((linorder @ A) => (! [P2:(A > (A > $o)),A2:A,B2:A]: (((! [A4:A,B4:A]: (((((ord_less_eq @ A) @ A4) @ B4) => ((P2 @ A4) @ B4)))) => ((! [A4:A,B4:A]: ((((P2 @ B4) @ A4) => ((P2 @ A4) @ B4)))) => ((P2 @ A2) @ B2))))))))).
% 3.96/1.85 thf(fact_163_dual__order_Otrans, axiom, (! [A:$tType]: (((order @ A) => (! [B2:A,A2:A,C2:A]: (((((ord_less_eq @ A) @ B2) @ A2) => ((((ord_less_eq @ A) @ C2) @ B2) => (((ord_less_eq @ A) @ C2) @ A2))))))))).
% 3.96/1.85 thf(fact_164_dual__order_Oeq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y6:A,Z:A]: ((Y6 = Z))) = (^ [A6:A,B6:A]: (((((ord_less_eq @ A) @ B6) @ A6) & (((ord_less_eq @ A) @ A6) @ B6))))))))).
% 3.96/1.85 thf(fact_165_dual__order_Oantisym, axiom, (! [A:$tType]: (((order @ A) => (! [B2:A,A2:A]: (((((ord_less_eq @ A) @ B2) @ A2) => ((((ord_less_eq @ A) @ A2) @ B2) => (A2 = B2))))))))).
% 3.96/1.85 thf(fact_166_in__mono, axiom, (! [A:$tType,A5:(set @ A),B5:(set @ A),X3:A]: (((((ord_less_eq @ (set @ A)) @ A5) @ B5) => ((((member @ A) @ X3) @ A5) => (((member @ A) @ X3) @ B5)))))).
% 3.96/1.85 thf(fact_167_subsetD, axiom, (! [A:$tType,A5:(set @ A),B5:(set @ A),C2:A]: (((((ord_less_eq @ (set @ A)) @ A5) @ B5) => ((((member @ A) @ C2) @ A5) => (((member @ A) @ C2) @ B5)))))).
% 3.96/1.85 thf(fact_168_equalityE, axiom, (! [A:$tType,A5:(set @ A),B5:(set @ A)]: (((A5 = B5) => (~ (((((ord_less_eq @ (set @ A)) @ A5) @ B5) => (~ ((((ord_less_eq @ (set @ A)) @ B5) @ A5)))))))))).
% 3.96/1.85 thf(fact_169_subset__eq, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A7:(set @ A),B7:(set @ A)]: ((! [X6:A]: (((((member @ A) @ X6) @ A7) => (((member @ A) @ X6) @ B7)))))))))).
% 3.96/1.85 thf(fact_170_equalityD1, axiom, (! [A:$tType,A5:(set @ A),B5:(set @ A)]: (((A5 = B5) => (((ord_less_eq @ (set @ A)) @ A5) @ B5))))).
% 3.96/1.85 thf(fact_171_equalityD2, axiom, (! [A:$tType,A5:(set @ A),B5:(set @ A)]: (((A5 = B5) => (((ord_less_eq @ (set @ A)) @ B5) @ A5))))).
% 3.96/1.85 thf(fact_172_subset__iff, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A7:(set @ A),B7:(set @ A)]: ((! [T2:A]: (((((member @ A) @ T2) @ A7) => (((member @ A) @ T2) @ B7)))))))))).
% 3.96/1.85 thf(fact_173_subset__refl, axiom, (! [A:$tType,A5:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ A5) @ A5)))).
% 3.96/1.85 thf(fact_174_Collect__mono, axiom, (! [A:$tType,P2:(A > $o),Q:(A > $o)]: (((! [X5:A]: (((P2 @ X5) => (Q @ X5)))) => (((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P2)) @ ((collect @ A) @ Q)))))).
% 3.96/1.85 thf(fact_175_subset__trans, axiom, (! [A:$tType,A5:(set @ A),B5:(set @ A),C4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A5) @ B5) => ((((ord_less_eq @ (set @ A)) @ B5) @ C4) => (((ord_less_eq @ (set @ A)) @ A5) @ C4)))))).
% 3.96/1.85 thf(fact_176_set__eq__subset, axiom, (! [A:$tType]: (((^ [Y6:(set @ A),Z:(set @ A)]: ((Y6 = Z))) = (^ [A7:(set @ A),B7:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A7) @ B7) & (((ord_less_eq @ (set @ A)) @ B7) @ A7)))))))).
% 3.96/1.85 thf(fact_177_Collect__mono__iff, axiom, (! [A:$tType,P2:(A > $o),Q:(A > $o)]: (((((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P2)) @ ((collect @ A) @ Q)) = (! [X6:A]: (((P2 @ X6) => (Q @ X6)))))))).
% 3.96/1.85 thf(fact_178_alphaRes, axiom, (! [C2:name,P2:pi,A2:name]: ((((((fresh @ name) @ pi) @ C2) @ P2) => (((res @ A2) @ P2) = ((res @ C2) @ ((((perm @ name) @ pi) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ A2) @ C2)) @ (nil @ ((product_prod @ name) @ name)))) @ P2))))))).
% 3.96/1.85 thf(fact_179_calculation, axiom, ((late_transitions @ ((res @ x) @ ((sum @ p) @ q))) @ (((late_BoundR @ (late_BoundOutputS @ aa)) @ y) @ ((((perm @ name) @ pi) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ y) @ x)) @ (nil @ ((product_prod @ name) @ name)))) @ p2)))).
% 3.96/1.85 thf(fact_180_Bound_Ohyps_I1_J, axiom, ((late_transitions @ ((sum @ ((res @ x) @ p)) @ ((res @ x) @ q))) @ (((late_BoundR @ a) @ y) @ pq))).
% 3.96/1.85 thf(fact_181__092_060open_062_060_092_060nu_062x_062_IP_A_092_060oplus_062_AQ_J_A_092_060longmapsto_062_Aa_060_092_060nu_062x_062_A_092_060prec_062_AP_H_092_060close_062, axiom, ((late_transitions @ ((res @ x) @ ((sum @ p) @ q))) @ (((late_BoundR @ (late_BoundOutputS @ aa)) @ x) @ p2))).
% 3.96/1.85 thf(fact_182_sumResLeft, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),X3:name,P2:pi,Q:pi]: (((((ord_less_eq @ (set @ ((product_prod @ pi) @ pi))) @ (id @ pi)) @ Rel) => (((eqvt @ pi) @ Rel) => (((strong743114133lation @ ((sum @ ((res @ X3) @ P2)) @ ((res @ X3) @ Q))) @ Rel) @ ((res @ X3) @ ((sum @ P2) @ Q)))))))).
% 3.96/1.85 thf(fact_183_cSum1_Ohyps, axiom, ((late_transitions @ ((res @ x) @ p)) @ (((late_BoundR @ a) @ y) @ pq))).
% 3.96/1.85 thf(fact_184_residual_Operm_I1_J, axiom, (! [Pi:(list @ ((product_prod @ name) @ name)),X32:late_subject,X1:name,X22:pi]: ((((((perm @ name) @ late_residual) @ Pi) @ (((late_BoundR @ X32) @ X1) @ X22)) = (((late_BoundR @ ((((perm @ name) @ late_subject) @ Pi) @ X32)) @ ((((perm @ name) @ name) @ Pi) @ X1)) @ ((((perm @ name) @ pi) @ Pi) @ X22)))))).
% 3.96/1.85 thf(fact_185_freshBoundDerivative_I1_J, axiom, (! [P2:pi,A2:late_subject,X3:name,P4:pi,Y4:name]: ((((late_transitions @ P2) @ (((late_BoundR @ A2) @ X3) @ P4)) => (((((fresh @ name) @ pi) @ Y4) @ P2) => ((((fresh @ name) @ late_subject) @ Y4) @ A2)))))).
% 3.96/1.85 thf(fact_186_Late__Semantics_OResB, axiom, (! [P2:pi,A2:late_subject,X3:name,P4:pi,Y4:name]: ((((late_transitions @ P2) @ (((late_BoundR @ A2) @ X3) @ P4)) => (((((fresh @ name) @ late_subject) @ Y4) @ A2) => ((Y4 != X3) => ((late_transitions @ ((res @ Y4) @ P2)) @ (((late_BoundR @ A2) @ X3) @ ((res @ Y4) @ P4))))))))).
% 3.96/1.85 thf(fact_187_freshBoundDerivative_I2_J, axiom, (! [P2:pi,A2:late_subject,X3:name,P4:pi,Y4:name]: ((((late_transitions @ P2) @ (((late_BoundR @ A2) @ X3) @ P4)) => (((((fresh @ name) @ pi) @ Y4) @ P2) => ((Y4 != X3) => ((((fresh @ name) @ pi) @ Y4) @ P4))))))).
% 3.96/1.85 thf(fact_188_simE_I1_J, axiom, (! [P2:pi,Rel:(set @ ((product_prod @ pi) @ pi)),Q:pi,A2:late_subject,X3:name,Q2:pi]: (((((strong743114133lation @ P2) @ Rel) @ Q) => (((late_transitions @ Q) @ (((late_BoundR @ A2) @ X3) @ Q2)) => (((((fresh @ name) @ pi) @ X3) @ P2) => (? [P5:pi]: ((((late_transitions @ P2) @ (((late_BoundR @ A2) @ X3) @ P5)) & (((((strong2129052853vative @ P5) @ Q2) @ A2) @ X3) @ Rel)))))))))).
% 3.96/1.85 thf(fact_189_Sum2, axiom, (! [Q:pi,Rs:late_residual,P2:pi]: ((((late_transitions @ Q) @ Rs) => ((late_transitions @ ((sum @ P2) @ Q)) @ Rs))))).
% 3.96/1.85 thf(fact_190_Sum1, axiom, (! [P2:pi,Rs:late_residual,Q:pi]: ((((late_transitions @ P2) @ Rs) => ((late_transitions @ ((sum @ P2) @ Q)) @ Rs))))).
% 3.96/1.85 thf(fact_191_sumCases_H, axiom, (! [P2:pi,Q:pi,Rs:late_residual]: ((((late_transitions @ ((sum @ P2) @ Q)) @ Rs) => ((~ (((late_transitions @ P2) @ Rs))) => ((late_transitions @ Q) @ Rs)))))).
% 3.96/1.85 thf(fact_192_sumCases, axiom, (! [P2:pi,Q:pi,Rs:late_residual]: ((((late_transitions @ ((sum @ P2) @ Q)) @ Rs) => ((~ (((late_transitions @ P2) @ Rs))) => ((late_transitions @ Q) @ Rs)))))).
% 3.96/1.85 thf(fact_193_freshResidual, axiom, (! [P2:pi,Rs:late_residual,X3:name]: ((((late_transitions @ P2) @ Rs) => (((((fresh @ name) @ pi) @ X3) @ P2) => ((((fresh @ name) @ late_residual) @ X3) @ Rs)))))).
% 3.96/1.85 thf(fact_194_eqvt, axiom, (! [X1:pi,X22:late_residual,Pi:(list @ ((product_prod @ name) @ name))]: ((((late_transitions @ X1) @ X22) => ((late_transitions @ ((((perm @ name) @ pi) @ Pi) @ X1)) @ ((((perm @ name) @ late_residual) @ Pi) @ X22)))))).
% 3.96/1.85 thf(fact_195_transitions_OResB, axiom, (! [P2:pi,A2:late_subject,X3:name,P4:pi,Y4:name]: ((((late_transitions @ P2) @ (((late_BoundR @ A2) @ X3) @ P4)) => (((((fresh @ name) @ late_subject) @ Y4) @ A2) => ((Y4 != X3) => (((((fresh @ name) @ pi) @ X3) @ P2) => (((((fresh @ name) @ late_subject) @ X3) @ A2) => ((late_transitions @ ((res @ Y4) @ P2)) @ (((late_BoundR @ A2) @ X3) @ ((res @ Y4) @ P4))))))))))).
% 3.96/1.85 thf(fact_196_monotonic, axiom, (! [P2:pi,A5:(set @ ((product_prod @ pi) @ pi)),P4:pi,B5:(set @ ((product_prod @ pi) @ pi))]: (((((strong743114133lation @ P2) @ A5) @ P4) => ((((ord_less_eq @ (set @ ((product_prod @ pi) @ pi))) @ A5) @ B5) => (((strong743114133lation @ P2) @ B5) @ P4)))))).
% 3.96/1.85 thf(fact_197_Strong__Late__Sim_Oreflexive, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),P2:pi]: (((((ord_less_eq @ (set @ ((product_prod @ pi) @ pi))) @ (id @ pi)) @ Rel) => (((strong743114133lation @ P2) @ Rel) @ P2))))).
% 3.96/1.85 thf(fact_198_sumIdempRight, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),P2:pi]: (((((ord_less_eq @ (set @ ((product_prod @ pi) @ pi))) @ (id @ pi)) @ Rel) => (((strong743114133lation @ ((sum @ P2) @ P2)) @ Rel) @ P2))))).
% 3.96/1.85 thf(fact_199_sumAssocRight, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),P2:pi,Q:pi,R2:pi]: (((((ord_less_eq @ (set @ ((product_prod @ pi) @ pi))) @ (id @ pi)) @ Rel) => (((strong743114133lation @ ((sum @ P2) @ ((sum @ Q) @ R2))) @ Rel) @ ((sum @ ((sum @ P2) @ Q)) @ R2)))))).
% 3.96/1.85 thf(fact_200_sumIdempLeft, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),P2:pi]: (((((ord_less_eq @ (set @ ((product_prod @ pi) @ pi))) @ (id @ pi)) @ Rel) => (((strong743114133lation @ P2) @ Rel) @ ((sum @ P2) @ P2)))))).
% 3.96/1.85 thf(fact_201_sumAssocLeft, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),P2:pi,Q:pi,R2:pi]: (((((ord_less_eq @ (set @ ((product_prod @ pi) @ pi))) @ (id @ pi)) @ Rel) => (((strong743114133lation @ ((sum @ ((sum @ P2) @ Q)) @ R2)) @ Rel) @ ((sum @ P2) @ ((sum @ Q) @ R2))))))).
% 3.96/1.85 thf(fact_202_sumSym, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),P2:pi,Q:pi]: (((((ord_less_eq @ (set @ ((product_prod @ pi) @ pi))) @ (id @ pi)) @ Rel) => (((strong743114133lation @ ((sum @ P2) @ Q)) @ Rel) @ ((sum @ Q) @ P2)))))).
% 3.96/1.85 thf(fact_203_eqvtI, axiom, (! [P2:pi,Rel:(set @ ((product_prod @ pi) @ pi)),Q:pi,Rel3:(set @ ((product_prod @ pi) @ pi)),Perm:(list @ ((product_prod @ name) @ name))]: (((((strong743114133lation @ P2) @ Rel) @ Q) => ((((ord_less_eq @ (set @ ((product_prod @ pi) @ pi))) @ Rel) @ Rel3) => (((eqvt @ pi) @ Rel3) => (((strong743114133lation @ ((((perm @ name) @ pi) @ Perm) @ P2)) @ Rel3) @ ((((perm @ name) @ pi) @ Perm) @ Q)))))))).
% 3.96/1.85 thf(fact_204_alphaBoundResidual, axiom, (! [X7:name,P2:pi,A2:late_subject,X3:name]: ((((((fresh @ name) @ pi) @ X7) @ P2) => ((((late_BoundR @ A2) @ X3) @ P2) = (((late_BoundR @ A2) @ X7) @ ((((perm @ name) @ pi) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ X3) @ X7)) @ (nil @ ((product_prod @ name) @ name)))) @ P2))))))).
% 3.96/1.85 thf(fact_205_cOpen_Ohyps_I1_J, axiom, ((late_transitions @ p) @ ((late_FreeR @ ((late_OutputR @ aa) @ x)) @ p2))).
% 3.96/1.85 thf(fact_206_simCasesCont, axiom, (! [A:$tType]: (((fs_name @ A) => (! [Rel:(set @ ((product_prod @ pi) @ pi)),Q:pi,P2:pi,C4:A]: ((((eqvt @ pi) @ Rel) => ((! [A4:late_subject,X5:name,Q3:pi]: ((((late_transitions @ Q) @ (((late_BoundR @ A4) @ X5) @ Q3)) => (((((fresh @ name) @ pi) @ X5) @ P2) => (((((fresh @ name) @ pi) @ X5) @ Q) => (((((fresh @ name) @ late_subject) @ X5) @ A4) => (((((fresh @ name) @ A) @ X5) @ C4) => (? [P6:pi]: ((((late_transitions @ P2) @ (((late_BoundR @ A4) @ X5) @ P6)) & (((((strong2129052853vative @ P6) @ Q3) @ A4) @ X5) @ Rel))))))))))) => ((! [Alpha:late_freeRes,Q3:pi]: ((((late_transitions @ Q) @ ((late_FreeR @ Alpha) @ Q3)) => (? [P6:pi]: ((((late_transitions @ P2) @ ((late_FreeR @ Alpha) @ P6)) & (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ P6) @ Q3)) @ Rel))))))) => (((strong743114133lation @ P2) @ Rel) @ Q)))))))))).
% 3.96/1.85 thf(fact_207__092_060open_062P_A_092_060oplus_062_AQ_A_092_060longmapsto_062_Aa_091x_093_A_092_060prec_062_AP_H_092_060close_062, axiom, ((late_transitions @ ((sum @ p) @ q)) @ ((late_FreeR @ ((late_OutputR @ aa) @ x)) @ p2))).
% 3.96/1.85 thf(fact_208_Late__Semantics1_OfreeRes_Oinject, axiom, (! [X11:name,X122:name,Y11:name,Y12:name]: (((((late_OutputR @ X11) @ X122) = ((late_OutputR @ Y11) @ Y12)) = ((X11 = Y11) & (X122 = Y12)))))).
% 3.96/1.85 thf(fact_209_Late__Semantics_OfreeRes_Oinject, axiom, (! [X22:name,X1:name,Y2:name,Y1:name]: (((((late_OutputR @ X22) @ X1) = ((late_OutputR @ Y2) @ Y1)) = ((X22 = Y2) & (X1 = Y1)))))).
% 3.96/1.85 thf(fact_210_freeRes_Operm_I1_J, axiom, (! [Pi:(list @ ((product_prod @ name) @ name)),X22:name,X1:name]: ((((((perm @ name) @ late_freeRes) @ Pi) @ ((late_OutputR @ X22) @ X1)) = ((late_OutputR @ ((((perm @ name) @ name) @ Pi) @ X22)) @ ((((perm @ name) @ name) @ Pi) @ X1)))))).
% 3.96/1.85 thf(fact_211_freeRes_Ofresh_I1_J, axiom, (! [A2:name,X22:name,X1:name]: ((((((fresh @ name) @ late_freeRes) @ A2) @ ((late_OutputR @ X22) @ X1)) = (((((fresh @ name) @ name) @ A2) @ X22) & ((((fresh @ name) @ name) @ A2) @ X1)))))).
% 3.96/1.85 thf(fact_212_residual_Operm_I2_J, axiom, (! [Pi:(list @ ((product_prod @ name) @ name)),X22:late_freeRes,X1:pi]: ((((((perm @ name) @ late_residual) @ Pi) @ ((late_FreeR @ X22) @ X1)) = ((late_FreeR @ ((((perm @ name) @ late_freeRes) @ Pi) @ X22)) @ ((((perm @ name) @ pi) @ Pi) @ X1)))))).
% 3.96/1.85 thf(fact_213_residual_Ofresh_I2_J, axiom, (! [A2:name,X22:late_freeRes,X1:pi]: ((((((fresh @ name) @ late_residual) @ A2) @ ((late_FreeR @ X22) @ X1)) = (((((fresh @ name) @ late_freeRes) @ A2) @ X22) & ((((fresh @ name) @ pi) @ A2) @ X1)))))).
% 3.96/1.85 thf(fact_214_residual_Odistinct_I1_J, axiom, (! [Subject:late_subject,Name2:name,Pi:pi,FreeRes:late_freeRes,Pi4:pi]: (((((late_BoundR @ Subject) @ Name2) @ Pi) != ((late_FreeR @ FreeRes) @ Pi4))))).
% 3.96/1.85 thf(fact_215_residual_Oinducts, axiom, (! [P2:(late_residual > $o),Residual:late_residual]: (((! [Subject2:late_subject,Name3:name,Pi5:pi]: ((P2 @ (((late_BoundR @ Subject2) @ Name3) @ Pi5)))) => ((! [FreeRes2:late_freeRes,Pi5:pi]: ((P2 @ ((late_FreeR @ FreeRes2) @ Pi5)))) => (P2 @ Residual)))))).
% 3.96/1.85 thf(fact_216_residual_Oinject_I2_J, axiom, (! [X22:late_freeRes,X1:pi,Y2:late_freeRes,Y1:pi]: (((((late_FreeR @ X22) @ X1) = ((late_FreeR @ Y2) @ Y1)) = ((X22 = Y2) & (X1 = Y1)))))).
% 3.96/1.85 thf(fact_217_ResF, axiom, (! [P2:pi,Alpha2:late_freeRes,P4:pi,Y4:name]: ((((late_transitions @ P2) @ ((late_FreeR @ Alpha2) @ P4)) => (((((fresh @ name) @ late_freeRes) @ Y4) @ Alpha2) => ((late_transitions @ ((res @ Y4) @ P2)) @ ((late_FreeR @ Alpha2) @ ((res @ Y4) @ P4)))))))).
% 3.96/1.85 thf(fact_218_resCasesF_H, axiom, (! [X3:name,P2:pi,Alpha2:late_freeRes,P4:pi]: ((((late_transitions @ ((res @ X3) @ P2)) @ ((late_FreeR @ Alpha2) @ P4)) => (~ ((! [P:pi,Alpha:late_freeRes,P5:pi,Y3:name]: (((((res @ X3) @ P2) = ((res @ Y3) @ P)) => ((((late_FreeR @ Alpha2) @ P4) = ((late_FreeR @ Alpha) @ ((res @ Y3) @ P5))) => (((late_transitions @ P) @ ((late_FreeR @ Alpha) @ P5)) => (~ (((((fresh @ name) @ late_freeRes) @ Y3) @ Alpha)))))))))))))).
% 3.96/1.85 thf(fact_219_resCasesF, axiom, (! [X3:name,P2:pi,Alpha2:late_freeRes,XP:pi,F5:(pi > $o)]: ((((late_transitions @ ((res @ X3) @ P2)) @ ((late_FreeR @ Alpha2) @ XP)) => ((! [P5:pi]: ((((late_transitions @ P2) @ ((late_FreeR @ Alpha2) @ P5)) => (((((fresh @ name) @ late_freeRes) @ X3) @ Alpha2) => (F5 @ ((res @ X3) @ P5)))))) => (F5 @ XP)))))).
% 3.96/1.85 thf(fact_220_freshFreeDerivative_I2_J, axiom, (! [P2:pi,Alpha2:late_freeRes,P4:pi,Y4:name]: ((((late_transitions @ P2) @ ((late_FreeR @ Alpha2) @ P4)) => (((((fresh @ name) @ pi) @ Y4) @ P2) => ((((fresh @ name) @ pi) @ Y4) @ P4)))))).
% 3.96/1.85 thf(fact_221_freshFreeDerivative_I1_J, axiom, (! [P2:pi,Alpha2:late_freeRes,P4:pi,Y4:name]: ((((late_transitions @ P2) @ ((late_FreeR @ Alpha2) @ P4)) => (((((fresh @ name) @ pi) @ Y4) @ P2) => ((((fresh @ name) @ late_freeRes) @ Y4) @ Alpha2)))))).
% 3.96/1.85 thf(fact_222_Open, axiom, (! [P2:pi,A2:name,B2:name,P4:pi]: ((((late_transitions @ P2) @ ((late_FreeR @ ((late_OutputR @ A2) @ B2)) @ P4)) => ((A2 != B2) => ((late_transitions @ ((res @ B2) @ P2)) @ (((late_BoundR @ (late_BoundOutputS @ A2)) @ B2) @ P4))))))).
% 3.96/1.85 thf(fact_223_residual_Ostrong__inducts, axiom, (! [A:$tType]: (((fs_name @ A) => (! [P2:(A > (late_residual > $o)),Z2:A,Residual:late_residual]: (((! [Subject2:late_subject,Name3:name,Pi5:pi,Z3:A]: ((((((fresh @ name) @ A) @ Name3) @ Z3) => (((((fresh @ name) @ late_subject) @ Name3) @ Subject2) => ((P2 @ Z3) @ (((late_BoundR @ Subject2) @ Name3) @ Pi5)))))) => ((! [FreeRes2:late_freeRes,Pi5:pi,Z3:A]: (((P2 @ Z3) @ ((late_FreeR @ FreeRes2) @ Pi5)))) => ((P2 @ Z2) @ Residual))))))))).
% 3.96/1.85 thf(fact_224_residual_Ostrong__induct, axiom, (! [N:$tType]: (((fs_name @ N) => (! [P2:(N > (late_residual > $o)),Z2:N,Residual:late_residual]: (((! [Subject2:late_subject,Name3:name,Pi5:pi,Z3:N]: ((((((fresh @ name) @ N) @ Name3) @ Z3) => (((((fresh @ name) @ late_subject) @ Name3) @ Subject2) => ((P2 @ Z3) @ (((late_BoundR @ Subject2) @ Name3) @ Pi5)))))) => ((! [FreeRes2:late_freeRes,Pi5:pi,Z3:N]: (((P2 @ Z3) @ ((late_FreeR @ FreeRes2) @ Pi5)))) => ((P2 @ Z2) @ Residual))))))))).
% 3.96/1.85 thf(fact_225_simE_I2_J, axiom, (! [P2:pi,Rel:(set @ ((product_prod @ pi) @ pi)),Q:pi,Alpha2:late_freeRes,Q2:pi]: (((((strong743114133lation @ P2) @ Rel) @ Q) => (((late_transitions @ Q) @ ((late_FreeR @ Alpha2) @ Q2)) => (? [P5:pi]: ((((late_transitions @ P2) @ ((late_FreeR @ Alpha2) @ P5)) & (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ P5) @ Q2)) @ Rel))))))))).
% 3.96/1.85 thf(fact_226_resCasesB_H, axiom, (! [X7:name,P2:pi,A2:late_subject,Y7:name,P4:pi]: ((((late_transitions @ ((res @ X7) @ P2)) @ (((late_BoundR @ A2) @ Y7) @ P4)) => ((! [P:pi,A4:name,B4:name]: (((((res @ X7) @ P2) = ((res @ B4) @ P)) => (! [P5:pi]: ((((((late_BoundR @ A2) @ Y7) @ P4) = (((late_BoundR @ (late_BoundOutputS @ A4)) @ B4) @ P5)) => (((late_transitions @ P) @ ((late_FreeR @ ((late_OutputR @ A4) @ B4)) @ P5)) => (A4 = B4)))))))) => (~ ((! [P:pi,A4:late_subject,X5:name,P5:pi,Y3:name]: (((((res @ X7) @ P2) = ((res @ Y3) @ P)) => (((((late_BoundR @ A2) @ Y7) @ P4) = (((late_BoundR @ A4) @ X5) @ ((res @ Y3) @ P5))) => (((late_transitions @ P) @ (((late_BoundR @ A4) @ X5) @ P5)) => (((((fresh @ name) @ late_subject) @ Y3) @ A4) => ((Y3 != X5) => (((((fresh @ name) @ pi) @ X5) @ P) => (~ (((((fresh @ name) @ late_subject) @ X5) @ A4)))))))))))))))))).
% 3.96/1.85 thf(fact_227_resCases_H, axiom, (! [X3:name,P2:pi,Rs:late_residual]: ((((late_transitions @ ((res @ X3) @ P2)) @ Rs) => ((! [P:pi,A4:name,B4:name]: (((((res @ X3) @ P2) = ((res @ B4) @ P)) => (! [P5:pi]: (((Rs = (((late_BoundR @ (late_BoundOutputS @ A4)) @ B4) @ P5)) => (((late_transitions @ P) @ ((late_FreeR @ ((late_OutputR @ A4) @ B4)) @ P5)) => (A4 = B4)))))))) => ((! [P:pi,A4:late_subject,X5:name,P5:pi,Y3:name]: (((((res @ X3) @ P2) = ((res @ Y3) @ P)) => ((Rs = (((late_BoundR @ A4) @ X5) @ ((res @ Y3) @ P5))) => (((late_transitions @ P) @ (((late_BoundR @ A4) @ X5) @ P5)) => (((((fresh @ name) @ late_subject) @ Y3) @ A4) => ((Y3 != X5) => (((((fresh @ name) @ pi) @ X5) @ P) => (~ (((((fresh @ name) @ late_subject) @ X5) @ A4))))))))))) => (~ ((! [P:pi,Alpha:late_freeRes,P5:pi,Y3:name]: (((((res @ X3) @ P2) = ((res @ Y3) @ P)) => ((Rs = ((late_FreeR @ Alpha) @ ((res @ Y3) @ P5))) => (((late_transitions @ P) @ ((late_FreeR @ Alpha) @ P5)) => (~ (((((fresh @ name) @ late_freeRes) @ Y3) @ Alpha)))))))))))))))).
% 3.96/1.85 thf(fact_228_resCasesB, axiom, (! [Y4:name,P2:pi,A2:late_subject,X3:name,YP:pi,F5:(late_subject > (pi > $o))]: ((((late_transitions @ ((res @ Y4) @ P2)) @ (((late_BoundR @ A2) @ X3) @ YP)) => ((X3 != Y4) => (((((fresh @ name) @ pi) @ X3) @ P2) => ((! [B4:name,P5:pi]: ((((late_transitions @ P2) @ ((late_FreeR @ ((late_OutputR @ B4) @ Y4)) @ P5)) => ((B4 != Y4) => ((A2 = (late_BoundOutputS @ B4)) => ((F5 @ (late_BoundOutputS @ B4)) @ ((((perm @ name) @ pi) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ X3) @ Y4)) @ (nil @ ((product_prod @ name) @ name)))) @ P5))))))) => ((! [P5:pi]: ((((late_transitions @ P2) @ (((late_BoundR @ A2) @ X3) @ P5)) => (((((fresh @ name) @ late_subject) @ Y4) @ A2) => ((F5 @ A2) @ ((res @ Y4) @ P5)))))) => ((F5 @ A2) @ YP))))))))).
% 3.96/1.85 thf(fact_229_resSimCases, axiom, (! [A:$tType]: (((fs_name @ A) => (! [Rel:(set @ ((product_prod @ pi) @ pi)),Q:pi,X3:name,P2:pi,C4:A]: ((((eqvt @ pi) @ Rel) => ((! [Q3:pi,A4:name]: ((((late_transitions @ Q) @ ((late_FreeR @ ((late_OutputR @ A4) @ X3)) @ Q3)) => ((A4 != X3) => (? [P6:pi]: ((((late_transitions @ P2) @ (((late_BoundR @ (late_BoundOutputS @ A4)) @ X3) @ P6)) & (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ P6) @ Q3)) @ Rel)))))))) => ((! [Q3:pi,A4:late_subject,Y3:name]: ((((late_transitions @ Q) @ (((late_BoundR @ A4) @ Y3) @ Q3)) => (((((fresh @ name) @ late_subject) @ X3) @ A4) => ((X3 != Y3) => (((((fresh @ name) @ A) @ Y3) @ C4) => (? [P6:pi]: ((((late_transitions @ P2) @ (((late_BoundR @ A4) @ Y3) @ P6)) & (((((strong2129052853vative @ P6) @ ((res @ X3) @ Q3)) @ A4) @ Y3) @ Rel)))))))))) => ((! [Q3:pi,Alpha:late_freeRes]: ((((late_transitions @ Q) @ ((late_FreeR @ Alpha) @ Q3)) => (((((fresh @ name) @ late_freeRes) @ X3) @ Alpha) => (? [P6:pi]: ((((late_transitions @ P2) @ ((late_FreeR @ Alpha) @ P6)) & (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ P6) @ ((res @ X3) @ Q3))) @ Rel)))))))) => (((strong743114133lation @ P2) @ Rel) @ ((res @ X3) @ Q)))))))))))).
% 3.96/1.85 thf(fact_230_simulation__def, axiom, (strong743114133lation = (^ [P7:pi,Rel2:(set @ ((product_prod @ pi) @ pi)),Q4:pi]: (((! [A6:late_subject,X6:name,Q5:pi]: (((((late_transitions @ Q4) @ (((late_BoundR @ A6) @ X6) @ Q5)) & ((((fresh @ name) @ pi) @ X6) @ P7)) => (? [P8:pi]: ((((late_transitions @ P7) @ (((late_BoundR @ A6) @ X6) @ P8)) & (((((strong2129052853vative @ P8) @ Q5) @ A6) @ X6) @ Rel2))))))) & (! [Alpha3:late_freeRes,Q5:pi]: ((((late_transitions @ Q4) @ ((late_FreeR @ Alpha3) @ Q5)) => (? [P8:pi]: ((((late_transitions @ P7) @ ((late_FreeR @ Alpha3) @ P8)) & (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ P8) @ Q5)) @ Rel2)))))))))))).
% 3.96/1.85 thf(fact_231_simCases, axiom, (! [Q:pi,P2:pi,Rel:(set @ ((product_prod @ pi) @ pi))]: (((! [A4:late_subject,Y3:name,Q3:pi]: ((((late_transitions @ Q) @ (((late_BoundR @ A4) @ Y3) @ Q3)) => (((((fresh @ name) @ pi) @ Y3) @ P2) => (? [P6:pi]: ((((late_transitions @ P2) @ (((late_BoundR @ A4) @ Y3) @ P6)) & (((((strong2129052853vative @ P6) @ Q3) @ A4) @ Y3) @ Rel)))))))) => ((! [Alpha:late_freeRes,Q3:pi]: ((((late_transitions @ Q) @ ((late_FreeR @ Alpha) @ Q3)) => (? [P6:pi]: ((((late_transitions @ P2) @ ((late_FreeR @ Alpha) @ P6)) & (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ P6) @ Q3)) @ Rel))))))) => (((strong743114133lation @ P2) @ Rel) @ Q)))))).
% 3.96/1.85 thf(fact_232_supports__def, axiom, (! [A:$tType,X:$tType]: ((((supports @ X) @ A) = (^ [S2:(set @ X),X6:A]: ((! [A6:X,B6:X]: ((((~ ((((member @ X) @ A6) @ S2))) & (~ ((((member @ X) @ B6) @ S2)))) => (((((perm @ X) @ A) @ (((cons @ ((product_prod @ X) @ X)) @ ((((product_Pair @ X) @ X) @ A6) @ B6)) @ (nil @ ((product_prod @ X) @ X)))) @ X6) = X6)))))))))).
% 3.96/1.85 thf(fact_233_IdD, axiom, (! [A:$tType,A2:A,B2:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A2) @ B2)) @ (id @ A)) => (A2 = B2))))).
% 3.96/1.85 thf(fact_234_supports__subset, axiom, (! [X:$tType,A:$tType,S1:(set @ X),X3:A,S22:(set @ X)]: ((((((supports @ X) @ A) @ S1) @ X3) => ((((ord_less_eq @ (set @ X)) @ S1) @ S22) => ((((supports @ X) @ A) @ S22) @ X3)))))).
% 3.96/1.85 thf(fact_235_shift__def, axiom, (! [B:$tType,A:$tType]: ((((bNF_Greatest_shift @ A) @ B) = (^ [Lab:((list @ A) > B),K:A,Kl:(list @ A)]: ((Lab @ (((cons @ A) @ K) @ Kl)))))))).
% 3.96/1.85 thf(fact_236_perm__residual__Rep_Osimps_I2_J, axiom, (! [X:$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)))))).
% 3.96/1.85 thf(fact_237_residual__Rep_Oinject_I2_J, axiom, (! [X21:late_freeRes,X222:pi,Y21:late_freeRes,Y22:pi]: (((((late_r347633188eR_Rep @ X21) @ X222) = ((late_r347633188eR_Rep @ Y21) @ Y22)) = ((X21 = Y21) & (X222 = Y22)))))).
% 3.96/1.85 thf(fact_238_alphaInput, axiom, (! [C2:name,P2:pi,A2:name,X3:name]: ((((((fresh @ name) @ pi) @ C2) @ P2) => ((((input @ A2) @ X3) @ P2) = (((input @ A2) @ C2) @ ((((perm @ name) @ pi) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ X3) @ C2)) @ (nil @ ((product_prod @ name) @ name)))) @ P2))))))).
% 3.96/1.85 thf(fact_239_product__lists_Osimps_I1_J, axiom, (! [A:$tType]: ((((product_lists @ A) @ (nil @ (list @ A))) = (((cons @ (list @ A)) @ (nil @ A)) @ (nil @ (list @ A))))))).
% 3.96/1.85 thf(fact_240_pi_Operm_I4_J, axiom, (! [Pi:(list @ ((product_prod @ name) @ name)),X32:name,X1:name,X22:pi]: ((((((perm @ name) @ pi) @ Pi) @ (((input @ X32) @ X1) @ X22)) = (((input @ ((((perm @ name) @ name) @ Pi) @ X32)) @ ((((perm @ name) @ name) @ Pi) @ X1)) @ ((((perm @ name) @ pi) @ Pi) @ X22)))))).
% 3.96/1.85 thf(fact_241_resTrans_I2_J, axiom, (! [X3:name,Y4:name,P2:pi,Rs:late_residual]: ((~ (((late_transitions @ ((res @ X3) @ (((input @ X3) @ Y4) @ P2))) @ Rs)))))).
% 3.96/1.85 thf(fact_242_pi_Odistinct_I53_J, axiom, (! [Name1:name,Name22:name,Pi:pi,Pi12:pi,Pi22:pi]: (((((input @ Name1) @ Name22) @ Pi) != ((sum @ Pi12) @ Pi22))))).
% 3.96/1.85 thf(fact_243_pi_Odistinct_I57_J, axiom, (! [Name1:name,Name22:name,Pi:pi,Name:name,Pi4:pi]: (((((input @ Name1) @ Name22) @ Pi) != ((res @ Name) @ Pi4))))).
% 3.96/1.85 thf(fact_244_inputFreeTrans, axiom, (! [A2:name,X3:name,P2:pi,Alpha2:late_freeRes,P4:pi]: ((~ (((late_transitions @ (((input @ A2) @ X3) @ P2)) @ ((late_FreeR @ Alpha2) @ P4))))))).
% 3.96/1.85 thf(fact_245_resInputFreeTrans, axiom, (! [X3:name,A2:name,Y4:name,P2:pi,Alpha2:late_freeRes,P4:pi]: ((~ (((late_transitions @ ((res @ X3) @ (((input @ A2) @ Y4) @ P2))) @ ((late_FreeR @ Alpha2) @ P4))))))).
% 3.96/1.85 thf(fact_246_inputBoundOutputTrans, axiom, (! [A2:name,X3:name,P2:pi,B2:name,Y4:name,P4:pi]: ((~ (((late_transitions @ (((input @ A2) @ X3) @ P2)) @ (((late_BoundR @ (late_BoundOutputS @ B2)) @ Y4) @ P4))))))).
% 3.96/1.85 thf(fact_247_inputIneqTrans, axiom, (! [A2:name,X3:name,P2:pi,B2:late_subject,Y4:name,P4:pi]: ((((late_transitions @ (((input @ A2) @ X3) @ P2)) @ (((late_BoundR @ B2) @ Y4) @ P4)) => (~ (((((fresh @ name) @ late_subject) @ A2) @ B2))))))).
% 3.96/1.85 thf(fact_248_resInputBoundOutputTrans, axiom, (! [X3:name,A2:name,Y4:name,P2:pi,B2:name,Z2:name,P4:pi]: ((~ (((late_transitions @ ((res @ X3) @ (((input @ A2) @ Y4) @ P2))) @ (((late_BoundR @ (late_BoundOutputS @ B2)) @ Z2) @ P4))))))).
% 3.96/1.85 thf(fact_249_inputCases, axiom, (! [A2:name,X3:name,P2:pi,B2:late_subject,Y4:name,YP:pi,Prop:(late_subject > (name > (pi > $o)))]: ((((late_transitions @ (((input @ A2) @ X3) @ P2)) @ (((late_BoundR @ B2) @ Y4) @ YP)) => ((Y4 != A2) => ((Y4 != X3) => (((((fresh @ name) @ pi) @ Y4) @ P2) => (((B2 = (late_InputS @ A2)) => ((YP = ((((perm @ name) @ pi) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ X3) @ Y4)) @ (nil @ ((product_prod @ name) @ name)))) @ P2)) => (((Prop @ (late_InputS @ A2)) @ Y4) @ ((((perm @ name) @ pi) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ X3) @ Y4)) @ (nil @ ((product_prod @ name) @ name)))) @ P2)))) => (((Prop @ B2) @ Y4) @ YP))))))))).
% 3.96/1.85 thf(fact_250_name__calc_I1_J, axiom, (! [A2:name,B2:name,Pi:(list @ ((product_prod @ name) @ name)),X3:name]: ((((((perm @ name) @ name) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ A2) @ B2)) @ Pi)) @ X3) = (((swap @ name) @ ((((product_Pair @ name) @ name) @ A2) @ B2)) @ ((((perm @ name) @ name) @ Pi) @ X3)))))).
% 3.96/1.85 thf(fact_251_Late__Semantics1_Osubject_Oinject_I1_J, axiom, (! [X1:name,Y1:name]: ((((late_InputS @ X1) = (late_InputS @ Y1)) = (X1 = Y1))))).
% 3.96/1.85 thf(fact_252_subject_Ofresh_I1_J, axiom, (! [A2:name,X1:name]: ((((((fresh @ name) @ late_subject) @ A2) @ (late_InputS @ X1)) = ((((fresh @ name) @ name) @ A2) @ X1))))).
% 3.96/1.85 thf(fact_253_subject_Operm_I1_J, axiom, (! [Pi:(list @ ((product_prod @ name) @ name)),X1:name]: ((((((perm @ name) @ late_subject) @ Pi) @ (late_InputS @ X1)) = (late_InputS @ ((((perm @ name) @ name) @ Pi) @ X1)))))).
% 3.96/1.85 thf(fact_254_Late__Semantics_Osubject_Odistinct_I1_J, axiom, (! [Name2:name,Name:name]: (((late_InputS @ Name2) != (late_BoundOutputS @ Name))))).
% 3.96/1.85 thf(tcon_fun___Orderings_Opreorder, axiom, (! [A8:$tType,A9:$tType]: (((preorder @ A9) => (preorder @ (A8 > A9)))))).
% 3.96/1.85 thf(tcon_fun___Agent_Ocp__name__name, axiom, (! [A8:$tType,A9:$tType]: ((((cp_name_name @ A8) & (cp_name_name @ A9)) => (cp_name_name @ (A8 > A9)))))).
% 3.96/1.85 thf(tcon_fun___Orderings_Oorder, axiom, (! [A8:$tType,A9:$tType]: (((order @ A9) => (order @ (A8 > A9)))))).
% 3.96/1.85 thf(tcon_fun___Orderings_Oord, axiom, (! [A8:$tType,A9:$tType]: (((ord @ A9) => (ord @ (A8 > A9)))))).
% 3.96/1.85 thf(tcon_fun___Agent_Opt__name, axiom, (! [A8:$tType,A9:$tType]: ((((pt_name @ A8) & (pt_name @ A9)) => (pt_name @ (A8 > A9)))))).
% 3.96/1.85 thf(tcon_Set_Oset___Orderings_Opreorder_1, axiom, (! [A8:$tType]: ((preorder @ (set @ A8))))).
% 3.96/1.85 thf(tcon_Set_Oset___Agent_Ocp__name__name_2, axiom, (! [A8:$tType]: (((cp_name_name @ A8) => (cp_name_name @ (set @ A8)))))).
% 3.96/1.85 thf(tcon_Set_Oset___Orderings_Oorder_3, axiom, (! [A8:$tType]: ((order @ (set @ A8))))).
% 3.96/1.85 thf(tcon_Set_Oset___Orderings_Oord_4, axiom, (! [A8:$tType]: ((ord @ (set @ A8))))).
% 3.96/1.85 thf(tcon_Set_Oset___Agent_Opt__name_5, axiom, (! [A8:$tType]: (((pt_name @ A8) => (pt_name @ (set @ A8)))))).
% 3.96/1.85 thf(tcon_Agent_Opi___Agent_Ocp__name__name_6, axiom, (cp_name_name @ pi)).
% 3.96/1.85 thf(tcon_Agent_Opi___Agent_Opt__name_7, axiom, (pt_name @ pi)).
% 3.96/1.85 thf(tcon_Agent_Opi___Agent_Ofs__name, axiom, (fs_name @ pi)).
% 3.96/1.85 thf(tcon_HOL_Obool___Orderings_Opreorder_8, axiom, (preorder @ $o)).
% 3.96/1.85 thf(tcon_HOL_Obool___Orderings_Olinorder, axiom, (linorder @ $o)).
% 3.96/1.85 thf(tcon_HOL_Obool___Agent_Ocp__name__name_9, axiom, (cp_name_name @ $o)).
% 3.96/1.85 thf(tcon_HOL_Obool___Orderings_Oorder_10, axiom, (order @ $o)).
% 3.96/1.85 thf(tcon_HOL_Obool___Orderings_Oord_11, axiom, (ord @ $o)).
% 3.96/1.85 thf(tcon_HOL_Obool___Agent_Opt__name_12, axiom, (pt_name @ $o)).
% 3.96/1.85 thf(tcon_HOL_Obool___Agent_Ofs__name_13, axiom, (fs_name @ $o)).
% 3.96/1.85 thf(tcon_List_Olist___Agent_Ocp__name__name_14, axiom, (! [A8:$tType]: (((cp_name_name @ A8) => (cp_name_name @ (list @ A8)))))).
% 3.96/1.85 thf(tcon_List_Olist___Agent_Opt__name_15, axiom, (! [A8:$tType]: (((pt_name @ A8) => (pt_name @ (list @ A8)))))).
% 3.96/1.85 thf(tcon_List_Olist___Agent_Ofs__name_16, axiom, (! [A8:$tType]: (((fs_name @ A8) => (fs_name @ (list @ A8)))))).
% 3.96/1.85 thf(tcon_Agent_Oname___Agent_Ocp__name__name_17, axiom, (cp_name_name @ name)).
% 3.96/1.85 thf(tcon_Agent_Oname___Agent_Opt__name_18, axiom, (pt_name @ name)).
% 3.96/1.85 thf(tcon_Agent_Oname___Agent_Ofs__name_19, axiom, (fs_name @ name)).
% 3.96/1.85 thf(tcon_Agent_Opi__Rep___Agent_Ocp__name__name_20, axiom, (cp_name_name @ pi_Rep)).
% 3.96/1.85 thf(tcon_Agent_Opi__Rep___Agent_Opt__name_21, axiom, (pt_name @ pi_Rep)).
% 3.96/1.85 thf(tcon_Product__Type_Oprod___Agent_Ocp__name__name_22, axiom, (! [A8:$tType,A9:$tType]: ((((cp_name_name @ A8) & (cp_name_name @ A9)) => (cp_name_name @ ((product_prod @ A8) @ A9)))))).
% 3.96/1.85 thf(tcon_Product__Type_Oprod___Agent_Opt__name_23, axiom, (! [A8:$tType,A9:$tType]: ((((pt_name @ A8) & (pt_name @ A9)) => (pt_name @ ((product_prod @ A8) @ A9)))))).
% 3.96/1.85 thf(tcon_Product__Type_Oprod___Agent_Ofs__name_24, axiom, (! [A8:$tType,A9:$tType]: ((((fs_name @ A8) & (fs_name @ A9)) => (fs_name @ ((product_prod @ A8) @ A9)))))).
% 3.96/1.85 thf(tcon_Late__Semantics_OfreeRes___Agent_Ocp__name__name_25, axiom, (cp_name_name @ late_freeRes)).
% 3.96/1.85 thf(tcon_Late__Semantics_OfreeRes___Agent_Opt__name_26, axiom, (pt_name @ late_freeRes)).
% 3.96/1.85 thf(tcon_Late__Semantics_OfreeRes___Agent_Ofs__name_27, axiom, (fs_name @ late_freeRes)).
% 3.96/1.85 thf(tcon_Late__Semantics_Osubject___Agent_Ocp__name__name_28, axiom, (cp_name_name @ late_subject)).
% 3.96/1.85 thf(tcon_Late__Semantics_Osubject___Agent_Opt__name_29, axiom, (pt_name @ late_subject)).
% 3.96/1.85 thf(tcon_Late__Semantics_Osubject___Agent_Ofs__name_30, axiom, (fs_name @ late_subject)).
% 3.96/1.85 thf(tcon_Late__Semantics_Oresidual___Agent_Ocp__name__name_31, axiom, (cp_name_name @ late_residual)).
% 3.96/1.85 thf(tcon_Late__Semantics_Oresidual___Agent_Opt__name_32, axiom, (pt_name @ late_residual)).
% 3.96/1.85 thf(tcon_Late__Semantics_Oresidual___Agent_Ofs__name_33, axiom, (fs_name @ late_residual)).
% 3.96/1.85 thf(tcon_Late__Semantics_OfreeRes__Rep___Agent_Ocp__name__name_34, axiom, (cp_name_name @ late_freeRes_Rep)).
% 3.96/1.85 thf(tcon_Late__Semantics_OfreeRes__Rep___Agent_Opt__name_35, axiom, (pt_name @ late_freeRes_Rep)).
% 3.96/1.85 thf(tcon_Late__Semantics_Osubject__Rep___Agent_Ocp__name__name_36, axiom, (cp_name_name @ late_subject_Rep)).
% 3.96/1.85 thf(tcon_Late__Semantics_Osubject__Rep___Agent_Opt__name_37, axiom, (pt_name @ late_subject_Rep)).
% 3.96/1.85 thf(tcon_Late__Semantics_Oresidual__Rep___Agent_Ocp__name__name_38, axiom, (cp_name_name @ late_residual_Rep)).
% 3.96/1.85 thf(tcon_Late__Semantics_Oresidual__Rep___Agent_Opt__name_39, axiom, (pt_name @ late_residual_Rep)).
% 3.96/1.85 thf(help_If_3_1_T, axiom, (! [P2:$o]: (((P2 = $true) | (P2 = $false))))).
% 3.96/1.85 thf(help_If_2_1_T, axiom, (! [A:$tType,X3:A,Y4:A]: ((((((if @ A) @ $false) @ X3) @ Y4) = Y4)))).
% 3.96/1.85 thf(help_If_1_1_T, axiom, (! [A:$tType,X3:A,Y4:A]: ((((((if @ A) @ $true) @ X3) @ Y4) = X3)))).
% 3.96/1.85 thf(conj_0, conjecture, (((((strong2129052853vative @ ((((perm @ name) @ pi) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ y) @ x)) @ (nil @ ((product_prod @ name) @ name)))) @ p2)) @ ((((perm @ name) @ pi) @ (((cons @ ((product_prod @ name) @ name)) @ ((((product_Pair @ name) @ name) @ y) @ x)) @ (nil @ ((product_prod @ name) @ name)))) @ p2)) @ (late_BoundOutputS @ aa)) @ y) @ rel)).
% 3.96/1.85 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.g7e8TF9fEe/DTF2DTF17774.p
% 3.96/1.85 ------------------------
% 4.04/1.91 ---- Cleaned THF ---
% 4.04/1.91 thf(ty_t_Late__Semantics_Oresidual__Rep,type,
% 4.04/1.91 late_residual_Rep: $tType ).
% 4.04/1.91
% 4.04/1.91 thf(ty_t_Late__Semantics_Osubject__Rep,type,
% 4.04/1.91 late_subject_Rep: $tType ).
% 4.04/1.91
% 4.04/1.91 thf(ty_t_Late__Semantics_OfreeRes__Rep,type,
% 4.04/1.91 late_freeRes_Rep: $tType ).
% 4.04/1.91
% 4.04/1.91 thf(ty_t_Late__Semantics_Oresidual,type,
% 4.04/1.91 late_residual: $tType ).
% 4.04/1.91
% 4.04/1.91 thf(ty_t_Late__Semantics_Osubject,type,
% 4.04/1.91 late_subject: $tType ).
% 4.04/1.91
% 4.04/1.91 thf(ty_t_Late__Semantics_OfreeRes,type,
% 4.04/1.91 late_freeRes: $tType ).
% 4.04/1.91
% 4.04/1.91 thf(ty_t_Product__Type_Oprod,type,
% 4.04/1.91 product_prod: $tType > $tType > $tType ).
% 4.04/1.91
% 4.04/1.91 thf(ty_t_Agent_Opi__Rep,type,
% 4.04/1.91 pi_Rep: $tType ).
% 4.04/1.91
% 4.04/1.91 thf(ty_t_Agent_Oname,type,
% 4.04/1.91 name: $tType ).
% 4.04/1.91
% 4.04/1.91 thf(ty_t_List_Olist,type,
% 4.04/1.91 list: $tType > $tType ).
% 4.04/1.91
% 4.04/1.91 thf(ty_t_Agent_Opi,type,
% 4.04/1.91 pi: $tType ).
% 4.04/1.91
% 4.04/1.91 thf(ty_t_Set_Oset,type,
% 4.04/1.91 set: $tType > $tType ).
% 4.04/1.91
% 4.04/1.91 thf(sy_cl_HOL_Otype,type,
% 4.04/1.91 type:
% 4.04/1.91 !>[A: $tType] : $o ).
% 4.04/1.91
% 4.04/1.91 thf(sy_cl_Agent_Ofs__name,type,
% 4.04/1.91 fs_name:
% 4.04/1.91 !>[A: $tType] : $o ).
% 4.04/1.91
% 4.04/1.91 thf(sy_cl_Agent_Opt__name,type,
% 4.04/1.91 pt_name:
% 4.04/1.91 !>[A: $tType] : $o ).
% 4.04/1.91
% 4.04/1.91 thf(sy_cl_Orderings_Oord,type,
% 4.04/1.91 ord:
% 4.04/1.91 !>[A: $tType] : $o ).
% 4.04/1.91
% 4.04/1.91 thf(sy_cl_Orderings_Oorder,type,
% 4.04/1.91 order:
% 4.04/1.91 !>[A: $tType] : $o ).
% 4.04/1.91
% 4.04/1.91 thf(sy_cl_Agent_Ocp__name__name,type,
% 4.04/1.91 cp_name_name:
% 4.04/1.91 !>[A: $tType] : $o ).
% 4.04/1.91
% 4.04/1.91 thf(sy_cl_Orderings_Olinorder,type,
% 4.04/1.91 linorder:
% 4.04/1.91 !>[A: $tType] : $o ).
% 4.04/1.91
% 4.04/1.91 thf(sy_cl_Orderings_Opreorder,type,
% 4.04/1.91 preorder:
% 4.04/1.91 !>[A: $tType] : $o ).
% 4.04/1.91
% 4.04/1.91 thf(sy_c_Agent_Opi_OInput,type,
% 4.04/1.91 input: name > name > pi > pi ).
% 4.04/1.91
% 4.04/1.91 thf(sy_c_Agent_Opi_ORes,type,
% 4.04/1.91 res: name > pi > pi ).
% 4.04/1.91
% 4.04/1.91 thf(sy_c_Agent_Opi_OSum,type,
% 4.04/1.91 sum: pi > pi > pi ).
% 4.04/1.91
% 4.04/1.91 thf(sy_c_BNF__Greatest__Fixpoint_Oshift,type,
% 4.04/1.91 bNF_Greatest_shift:
% 4.04/1.91 !>[A: $tType,B: $tType] : ( ( ( list @ A ) > B ) > A > ( list @ A ) > B ) ).
% 4.04/1.91
% 4.04/1.91 thf(sy_c_If,type,
% 4.04/1.91 if:
% 4.04/1.91 !>[A: $tType] : ( $o > A > A > A ) ).
% 4.04/1.91
% 4.04/1.91 thf(sy_c_Late__Semantics_OfreeRes_OOutputR,type,
% 4.04/1.91 late_OutputR: name > name > late_freeRes ).
% 4.04/1.91
% 4.04/1.91 thf(sy_c_Late__Semantics_Oresidual_OBoundR,type,
% 4.04/1.91 late_BoundR: late_subject > name > pi > late_residual ).
% 4.04/1.91
% 4.04/1.91 thf(sy_c_Late__Semantics_Oresidual_OFreeR,type,
% 4.04/1.91 late_FreeR: late_freeRes > pi > late_residual ).
% 4.04/1.91
% 4.04/1.91 thf(sy_c_Late__Semantics_Oresidual__Rep_OFreeR__Rep,type,
% 4.04/1.91 late_r347633188eR_Rep: late_freeRes > pi > late_residual_Rep ).
% 4.04/1.91
% 4.04/1.91 thf(sy_c_Late__Semantics_Osubject_OBoundOutputS,type,
% 4.04/1.91 late_BoundOutputS: name > late_subject ).
% 4.04/1.91
% 4.04/1.91 thf(sy_c_Late__Semantics_Osubject_OInputS,type,
% 4.04/1.91 late_InputS: name > late_subject ).
% 4.04/1.91
% 4.04/1.91 thf(sy_c_Late__Semantics_Otransitions,type,
% 4.04/1.91 late_transitions: pi > late_residual > $o ).
% 4.04/1.91
% 4.04/1.91 thf(sy_c_List_Olist_OCons,type,
% 4.04/1.91 cons:
% 4.04/1.91 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 4.04/1.91
% 4.04/1.91 thf(sy_c_List_Olist_ONil,type,
% 4.04/1.91 nil:
% 4.04/1.91 !>[A: $tType] : ( list @ A ) ).
% 4.04/1.91
% 4.04/1.91 thf(sy_c_List_Oproduct__lists,type,
% 4.04/1.91 product_lists:
% 4.04/1.91 !>[A: $tType] : ( ( list @ ( list @ A ) ) > ( list @ ( list @ A ) ) ) ).
% 4.04/1.91
% 4.04/1.91 thf(sy_c_Nominal_Ofresh,type,
% 4.04/1.91 fresh:
% 4.04/1.91 !>[X: $tType,A: $tType] : ( X > A > $o ) ).
% 4.04/1.91
% 4.04/1.91 thf(sy_c_Nominal_Operm,type,
% 4.04/1.91 perm:
% 4.04/1.91 !>[X: $tType,A: $tType] : ( ( list @ ( product_prod @ X @ X ) ) > A > A ) ).
% 4.04/1.91
% 4.04/1.91 thf(sy_c_Nominal_Osupports,type,
% 4.04/1.91 supports:
% 4.04/1.91 !>[X: $tType,A: $tType] : ( ( set @ X ) > A > $o ) ).
% 4.04/1.91
% 4.04/1.91 thf(sy_c_Nominal_Oswap,type,
% 4.04/1.91 swap:
% 4.04/1.91 !>[X: $tType] : ( ( product_prod @ X @ X ) > X > X ) ).
% 4.04/1.91
% 4.04/1.91 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 4.04/1.91 ord_less_eq:
% 4.04/1.91 !>[A: $tType] : ( A > A > $o ) ).
% 4.04/1.91
% 4.04/1.91 thf(sy_c_Product__Type_OPair,type,
% 4.04/1.91 product_Pair:
% 4.04/1.91 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 4.04/1.91
% 4.04/1.91 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod,type,
% 4.04/1.91 product_rec_prod:
% 4.04/1.91 !>[A: $tType,B: $tType,T: $tType] : ( ( A > B > T ) > ( product_prod @ A @ B ) > T ) ).
% 4.04/1.91
% 4.04/1.91 thf(sy_c_Rel_Oeqvt,type,
% 4.04/1.91 eqvt:
% 4.04/1.91 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > $o ) ).
% 4.04/1.91
% 4.04/1.91 thf(sy_c_Relation_OId,type,
% 4.04/1.91 id:
% 4.04/1.91 !>[A: $tType] : ( set @ ( product_prod @ A @ A ) ) ).
% 4.04/1.91
% 4.04/1.91 thf(sy_c_Set_OCollect,type,
% 4.04/1.91 collect:
% 4.04/1.91 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 4.04/1.91
% 4.04/1.91 thf(sy_c_Strong__Late__Sim_Oderivative,type,
% 4.04/1.91 strong2129052853vative: pi > pi > late_subject > name > ( set @ ( product_prod @ pi @ pi ) ) > $o ).
% 4.04/1.91
% 4.04/1.91 thf(sy_c_Strong__Late__Sim_Osimulation,type,
% 4.04/1.91 strong743114133lation: pi > ( set @ ( product_prod @ pi @ pi ) ) > pi > $o ).
% 4.04/1.91
% 4.04/1.91 thf(sy_c_member,type,
% 4.04/1.91 member:
% 4.04/1.91 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 4.04/1.91
% 4.04/1.91 thf(sy_v_P,type,
% 4.04/1.91 p: pi ).
% 4.04/1.91
% 4.04/1.91 thf(sy_v_PQ____,type,
% 4.04/1.91 pq: pi ).
% 4.04/1.91
% 4.04/1.91 thf(sy_v_P_H____,type,
% 4.04/1.91 p2: pi ).
% 4.04/1.91
% 4.04/1.91 thf(sy_v_Q,type,
% 4.04/1.91 q: pi ).
% 4.04/1.91
% 4.04/1.91 thf(sy_v_Rel,type,
% 4.04/1.91 rel: set @ ( product_prod @ pi @ pi ) ).
% 4.04/1.91
% 4.04/1.91 thf(sy_v_a____,type,
% 4.04/1.91 a: late_subject ).
% 4.04/1.91
% 4.04/1.91 thf(sy_v_aa____,type,
% 4.04/1.91 aa: name ).
% 4.04/1.91
% 4.04/1.91 thf(sy_v_x,type,
% 4.04/1.91 x: name ).
% 4.04/1.91
% 4.04/1.91 thf(sy_v_y____,type,
% 4.04/1.91 y: name ).
% 4.04/1.91
% 4.04/1.91 thf(fact_0_Id,axiom,
% 4.04/1.91 ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ rel ).
% 4.04/1.91
% 4.04/1.91 thf(fact_1_cOpen_Ohyps_I2_J,axiom,
% 4.04/1.91 aa != x ).
% 4.04/1.91
% 4.04/1.91 thf(fact_2_cOpen_Ohyps_I3_J,axiom,
% 4.04/1.91 ( a
% 4.04/1.91 = ( late_BoundOutputS @ aa ) ) ).
% 4.04/1.91
% 4.04/1.91 thf(fact_3__092_060open_062y_A_092_060noteq_062_Ax_092_060close_062,axiom,
% 4.04/1.91 y != x ).
% 4.04/1.91
% 4.04/1.91 thf(fact_4_Eqvt,axiom,
% 4.04/1.91 eqvt @ pi @ rel ).
% 4.04/1.91
% 4.04/1.91 thf(fact_5_perm__swap_I1_J,axiom,
% 4.04/1.91 ! [X2: $tType] :
% 4.04/1.91 ( ( pt_name @ X2 )
% 4.04/1.91 => ! [A2: name,B2: name,X3: X2] :
% 4.04/1.91 ( ( perm @ name @ X2 @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ ( perm @ name @ X2 @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ X3 ) )
% 4.04/1.91 = X3 ) ) ).
% 4.04/1.91
% 4.04/1.91 thf(fact_6_name__id,axiom,
% 4.04/1.91 ! [X: $tType] :
% 4.04/1.91 ( ( pt_name @ X )
% 4.04/1.91 => ! [A2: name,X3: X] :
% 4.04/1.91 ( ( perm @ name @ X @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ A2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ X3 )
% 4.04/1.91 = X3 ) ) ).
% 4.04/1.91
% 4.04/1.91 thf(fact_7_name__swap,axiom,
% 4.04/1.91 ! [X: $tType] :
% 4.04/1.91 ( ( pt_name @ X )
% 4.04/1.91 => ! [A2: name,B2: name,X3: X] :
% 4.04/1.91 ( ( perm @ name @ X @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ X3 )
% 4.04/1.91 = ( perm @ name @ X @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ B2 @ A2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ X3 ) ) ) ).
% 4.04/1.91
% 4.04/1.91 thf(fact_8_name__swap__bij,axiom,
% 4.04/1.91 ! [X: $tType] :
% 4.04/1.91 ( ( pt_name @ X )
% 4.04/1.91 => ! [A2: name,B2: name,X3: X] :
% 4.04/1.91 ( ( perm @ name @ X @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ ( perm @ name @ X @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ X3 ) )
% 4.04/1.91 = X3 ) ) ).
% 4.04/1.91
% 4.04/1.91 thf(fact_9_pt__name1,axiom,
% 4.04/1.91 ! [A: $tType] :
% 4.04/1.91 ( ( pt_name @ A )
% 4.04/1.91 => ! [X3: A] :
% 4.04/1.91 ( ( perm @ name @ A @ ( nil @ ( product_prod @ name @ name ) ) @ X3 )
% 4.04/1.91 = X3 ) ) ).
% 4.04/1.91
% 4.04/1.91 thf(fact_10_perm__swap_I2_J,axiom,
% 4.04/1.91 ! [X2: $tType] :
% 4.04/1.91 ( ( pt_name @ X2 )
% 4.04/1.91 => ! [A2: name,B2: name,X3: X2] :
% 4.04/1.91 ( ( perm @ name @ X2 @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ ( perm @ name @ X2 @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ B2 @ A2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ X3 ) )
% 4.04/1.91 = X3 ) ) ).
% 4.04/1.91
% 4.04/1.91 thf(fact_11_Late__Semantics_Osubject_Oinject_I2_J,axiom,
% 4.04/1.91 ! [X1: name,Y1: name] :
% 4.04/1.91 ( ( ( late_BoundOutputS @ X1 )
% 4.04/1.91 = ( late_BoundOutputS @ Y1 ) )
% 4.04/1.91 = ( X1 = Y1 ) ) ).
% 4.04/1.91
% 4.04/1.91 thf(fact_12_Late__Semantics1_Osubject_Oinject_I2_J,axiom,
% 4.04/1.91 ! [X22: name,Y2: name] :
% 4.04/1.91 ( ( ( late_BoundOutputS @ X22 )
% 4.04/1.91 = ( late_BoundOutputS @ Y2 ) )
% 4.04/1.91 = ( X22 = Y2 ) ) ).
% 4.04/1.91
% 4.04/1.91 thf(fact_13__092_060open_062y_A_092_060sharp_062_AP_H_092_060close_062,axiom,
% 4.04/1.91 fresh @ name @ pi @ y @ p2 ).
% 4.04/1.91
% 4.04/1.91 thf(fact_14_list_Oinject,axiom,
% 4.04/1.91 ! [A: $tType,X21: A,X222: list @ A,Y21: A,Y22: list @ A] :
% 4.04/1.91 ( ( ( cons @ A @ X21 @ X222 )
% 4.04/1.91 = ( cons @ A @ Y21 @ Y22 ) )
% 4.04/1.91 = ( ( X21 = Y21 )
% 4.04/1.91 & ( X222 = Y22 ) ) ) ).
% 4.04/1.91
% 4.04/1.91 thf(fact_15_prod_Oinject,axiom,
% 4.04/1.91 ! [A: $tType,B: $tType,X1: A,X22: B,Y1: A,Y2: B] :
% 4.04/1.91 ( ( ( product_Pair @ A @ B @ X1 @ X22 )
% 4.04/1.91 = ( product_Pair @ A @ B @ Y1 @ Y2 ) )
% 4.04/1.91 = ( ( X1 = Y1 )
% 4.04/1.91 & ( X22 = Y2 ) ) ) ).
% 4.04/1.91
% 4.04/1.91 thf(fact_16_old_Oprod_Oinject,axiom,
% 4.04/1.91 ! [A: $tType,B: $tType,A2: A,B2: B,A3: A,B3: B] :
% 4.04/1.91 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 4.04/1.91 = ( product_Pair @ A @ B @ A3 @ B3 ) )
% 4.04/1.91 = ( ( A2 = A3 )
% 4.04/1.91 & ( B2 = B3 ) ) ) ).
% 4.04/1.91
% 4.04/1.91 thf(fact_17_residual__perm__empty,axiom,
% 4.04/1.91 ! [Residual_Rep: late_residual_Rep] :
% 4.04/1.91 ( ( perm @ name @ late_residual_Rep @ ( nil @ ( product_prod @ name @ name ) ) @ Residual_Rep )
% 4.04/1.91 = Residual_Rep ) ).
% 4.04/1.91
% 4.04/1.91 thf(fact_18_subject__perm__empty,axiom,
% 4.04/1.91 ! [Subject_Rep: late_subject_Rep] :
% 4.04/1.91 ( ( perm @ name @ late_subject_Rep @ ( nil @ ( product_prod @ name @ name ) ) @ Subject_Rep )
% 4.04/1.91 = Subject_Rep ) ).
% 4.04/1.91
% 4.04/1.91 thf(fact_19_freeRes__perm__empty,axiom,
% 4.04/1.91 ! [FreeRes_Rep: late_freeRes_Rep] :
% 4.04/1.91 ( ( perm @ name @ late_freeRes_Rep @ ( nil @ ( product_prod @ name @ name ) ) @ FreeRes_Rep )
% 4.04/1.91 = FreeRes_Rep ) ).
% 4.04/1.91
% 4.04/1.91 thf(fact_20_pi__perm__empty,axiom,
% 4.04/1.91 ! [Pi_Rep: pi_Rep] :
% 4.04/1.91 ( ( perm @ name @ pi_Rep @ ( nil @ ( product_prod @ name @ name ) ) @ Pi_Rep )
% 4.04/1.91 = Pi_Rep ) ).
% 4.04/1.91
% 4.04/1.91 thf(fact_21_subject_Operm_I2_J,axiom,
% 4.04/1.91 ! [Pi: list @ ( product_prod @ name @ name ),X1: name] :
% 4.04/1.91 ( ( perm @ name @ late_subject @ Pi @ ( late_BoundOutputS @ X1 ) )
% 4.04/1.91 = ( late_BoundOutputS @ ( perm @ name @ name @ Pi @ X1 ) ) ) ).
% 4.04/1.91
% 4.04/1.91 thf(fact_22_perm__fresh__fresh,axiom,
% 4.04/1.91 ! [X2: $tType] :
% 4.04/1.91 ( ( pt_name @ X2 )
% 4.04/1.91 => ! [A2: name,X3: X2,B2: name] :
% 4.04/1.91 ( ( fresh @ name @ X2 @ A2 @ X3 )
% 4.04/1.91 => ( ( fresh @ name @ X2 @ B2 @ X3 )
% 4.04/1.91 => ( ( perm @ name @ X2 @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ X3 )
% 4.04/1.91 = X3 ) ) ) ) ).
% 4.04/1.91
% 4.04/1.91 thf(fact_23_name__fresh__fresh,axiom,
% 4.04/1.91 ! [X: $tType] :
% 4.04/1.91 ( ( pt_name @ X )
% 4.04/1.91 => ! [A2: name,X3: X,B2: name] :
% 4.04/1.91 ( ( fresh @ name @ X @ A2 @ X3 )
% 4.04/1.91 => ( ( fresh @ name @ X @ B2 @ X3 )
% 4.04/1.91 => ( ( perm @ name @ X @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ X3 )
% 4.04/1.91 = X3 ) ) ) ) ).
% 4.04/1.91
% 4.04/1.91 thf(fact_24_Bound_Ohyps_I4_J,axiom,
% 4.04/1.91 fresh @ name @ late_subject @ y @ a ).
% 4.04/1.91
% 4.04/1.91 thf(fact_25_subseteq__eqvt,axiom,
% 4.04/1.91 ! [X2: $tType] :
% 4.04/1.91 ( ( pt_name @ X2 )
% 4.04/1.91 => ! [Pi: list @ ( product_prod @ name @ name ),X4: set @ X2,Y: set @ X2] :
% 4.04/1.91 ( ( perm @ name @ $o @ Pi @ ( ord_less_eq @ ( set @ X2 ) @ X4 @ Y ) )
% 4.04/1.91 = ( ord_less_eq @ ( set @ X2 ) @ ( perm @ name @ ( set @ X2 ) @ Pi @ X4 ) @ ( perm @ name @ ( set @ X2 ) @ Pi @ Y ) ) ) ) ).
% 4.04/1.91
% 4.04/1.91 thf(fact_26_fresh__perm__app,axiom,
% 4.04/1.91 ! [X2: $tType] :
% 4.04/1.91 ( ( pt_name @ X2 )
% 4.04/1.91 => ! [A2: name,Pi: list @ ( product_prod @ name @ name ),X3: X2] :
% 4.04/1.91 ( ( fresh @ name @ ( list @ ( product_prod @ name @ name ) ) @ A2 @ Pi )
% 4.04/1.91 => ( ( fresh @ name @ X2 @ A2 @ X3 )
% 4.04/1.91 => ( fresh @ name @ X2 @ A2 @ ( perm @ name @ X2 @ Pi @ X3 ) ) ) ) ) ).
% 4.04/1.91
% 4.04/1.91 thf(fact_27_name__exists__fresh,axiom,
% 4.04/1.91 ! [A: $tType] :
% 4.04/1.91 ( ( fs_name @ A )
% 4.04/1.91 => ! [X3: A] :
% 4.04/1.91 ~ ! [C: name] :
% 4.04/1.91 ~ ( fresh @ name @ A @ C @ X3 ) ) ).
% 4.04/1.91
% 4.04/1.91 thf(fact_28_fresh__eqvt,axiom,
% 4.04/1.91 ! [X2: $tType] :
% 4.04/1.91 ( ( pt_name @ X2 )
% 4.04/1.91 => ! [Pi: list @ ( product_prod @ name @ name ),A2: name,X3: X2] :
% 4.04/1.91 ( ( perm @ name @ $o @ Pi @ ( fresh @ name @ X2 @ A2 @ X3 ) )
% 4.04/1.91 = ( fresh @ name @ X2 @ ( perm @ name @ name @ Pi @ A2 ) @ ( perm @ name @ X2 @ Pi @ X3 ) ) ) ) ).
% 4.04/1.91
% 4.04/1.91 thf(fact_29_fresh__bij,axiom,
% 4.04/1.91 ! [X2: $tType] :
% 4.04/1.91 ( ( pt_name @ X2 )
% 4.04/1.91 => ! [Pi: list @ ( product_prod @ name @ name ),A2: name,X3: X2] :
% 4.04/1.91 ( ( fresh @ name @ X2 @ ( perm @ name @ name @ Pi @ A2 ) @ ( perm @ name @ X2 @ Pi @ X3 ) )
% 4.04/1.91 = ( fresh @ name @ X2 @ A2 @ X3 ) ) ) ).
% 4.04/1.91
% 4.04/1.91 thf(fact_30_map__tailrec__rev_Ocases,axiom,
% 4.04/1.91 ! [A: $tType,B: $tType,X3: product_prod @ ( A > B ) @ ( product_prod @ ( list @ A ) @ ( list @ B ) )] :
% 4.04/1.91 ( ! [F: A > B,Bs: list @ B] :
% 4.04/1.91 ( X3
% 4.04/1.91 != ( product_Pair @ ( A > B ) @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ F @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ ( nil @ A ) @ Bs ) ) )
% 4.04/1.91 => ~ ! [F: A > B,A4: A,As: list @ A,Bs: list @ B] :
% 4.04/1.91 ( X3
% 4.04/1.91 != ( product_Pair @ ( A > B ) @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ F @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ ( cons @ A @ A4 @ As ) @ Bs ) ) ) ) ).
% 4.04/1.91
% 4.04/1.91 thf(fact_31_name__calc_I2_J,axiom,
% 4.04/1.91 ! [X3: name] :
% 4.04/1.91 ( ( perm @ name @ name @ ( nil @ ( product_prod @ name @ name ) ) @ X3 )
% 4.04/1.91 = X3 ) ).
% 4.04/1.91
% 4.04/1.91 thf(fact_32_arg__min__list_Ocases,axiom,
% 4.04/1.91 ! [B: $tType,A: $tType] :
% 4.04/1.91 ( ( linorder @ B )
% 4.04/1.91 => ! [X3: product_prod @ ( A > B ) @ ( list @ A )] :
% 4.04/1.91 ( ! [F: A > B,X5: A] :
% 4.04/1.91 ( X3
% 4.04/1.91 != ( product_Pair @ ( A > B ) @ ( list @ A ) @ F @ ( cons @ A @ X5 @ ( nil @ A ) ) ) )
% 4.04/1.91 => ( ! [F: A > B,X5: A,Y3: A,Zs: list @ A] :
% 4.04/1.91 ( X3
% 4.04/1.91 != ( product_Pair @ ( A > B ) @ ( list @ A ) @ F @ ( cons @ A @ X5 @ ( cons @ A @ Y3 @ Zs ) ) ) )
% 4.04/1.91 => ~ ! [A4: A > B] :
% 4.04/1.91 ( X3
% 4.04/1.91 != ( product_Pair @ ( A > B ) @ ( list @ A ) @ A4 @ ( nil @ A ) ) ) ) ) ) ).
% 4.04/1.91
% 4.04/1.91 thf(fact_33_successively_Ocases,axiom,
% 4.04/1.91 ! [A: $tType,X3: product_prod @ ( A > A > $o ) @ ( list @ A )] :
% 4.04/1.91 ( ! [P: A > A > $o] :
% 4.04/1.91 ( X3
% 4.04/1.91 != ( product_Pair @ ( A > A > $o ) @ ( list @ A ) @ P @ ( nil @ A ) ) )
% 4.04/1.91 => ( ! [P: A > A > $o,X5: A] :
% 4.04/1.91 ( X3
% 4.04/1.91 != ( product_Pair @ ( A > A > $o ) @ ( list @ A ) @ P @ ( cons @ A @ X5 @ ( nil @ A ) ) ) )
% 4.04/1.91 => ~ ! [P: A > A > $o,X5: A,Y3: A,Xs: list @ A] :
% 4.04/1.91 ( X3
% 4.04/1.91 != ( product_Pair @ ( A > A > $o ) @ ( list @ A ) @ P @ ( cons @ A @ X5 @ ( cons @ A @ Y3 @ Xs ) ) ) ) ) ) ).
% 4.04/1.91
% 4.04/1.91 thf(fact_34_sorted__wrt_Ocases,axiom,
% 4.04/1.91 ! [A: $tType,X3: product_prod @ ( A > A > $o ) @ ( list @ A )] :
% 4.04/1.91 ( ! [P: A > A > $o] :
% 4.04/1.91 ( X3
% 4.04/1.91 != ( product_Pair @ ( A > A > $o ) @ ( list @ A ) @ P @ ( nil @ A ) ) )
% 4.04/1.91 => ~ ! [P: A > A > $o,X5: A,Ys: list @ A] :
% 4.04/1.91 ( X3
% 4.04/1.91 != ( product_Pair @ ( A > A > $o ) @ ( list @ A ) @ P @ ( cons @ A @ X5 @ Ys ) ) ) ) ).
% 4.04/1.91
% 4.04/1.91 thf(fact_35_shuffles_Ocases,axiom,
% 4.04/1.91 ! [A: $tType,X3: product_prod @ ( list @ A ) @ ( list @ A )] :
% 4.04/1.91 ( ! [Ys: list @ A] :
% 4.04/1.91 ( X3
% 4.04/1.91 != ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( nil @ A ) @ Ys ) )
% 4.04/1.91 => ( ! [Xs: list @ A] :
% 4.04/1.91 ( X3
% 4.04/1.91 != ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ ( nil @ A ) ) )
% 4.04/1.91 => ~ ! [X5: A,Xs: list @ A,Y3: A,Ys: list @ A] :
% 4.04/1.91 ( X3
% 4.04/1.91 != ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X5 @ Xs ) @ ( cons @ A @ Y3 @ Ys ) ) ) ) ) ).
% 4.04/1.91
% 4.04/1.91 thf(fact_36_splice_Ocases,axiom,
% 4.04/1.91 ! [A: $tType,X3: product_prod @ ( list @ A ) @ ( list @ A )] :
% 4.04/1.91 ( ! [Ys: list @ A] :
% 4.04/1.91 ( X3
% 4.04/1.91 != ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( nil @ A ) @ Ys ) )
% 4.04/1.91 => ~ ! [X5: A,Xs: list @ A,Ys: list @ A] :
% 4.04/1.91 ( X3
% 4.04/1.91 != ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X5 @ Xs ) @ Ys ) ) ) ).
% 4.04/1.91
% 4.04/1.91 thf(fact_37_swap__simps_I1_J,axiom,
% 4.04/1.91 ! [A2: name,B2: name] :
% 4.04/1.91 ( ( perm @ name @ name @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ A2 )
% 4.04/1.91 = B2 ) ).
% 4.04/1.91
% 4.04/1.91 thf(fact_38_swap__simps_I2_J,axiom,
% 4.04/1.91 ! [A2: name,B2: name] :
% 4.04/1.91 ( ( perm @ name @ name @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ B2 )
% 4.04/1.91 = A2 ) ).
% 4.04/1.91
% 4.04/1.91 thf(fact_39_swap__simps_I3_J,axiom,
% 4.04/1.91 ! [A2: name,C2: name,B2: name] :
% 4.04/1.91 ( ( A2 != C2 )
% 4.04/1.91 => ( ( B2 != C2 )
% 4.04/1.91 => ( ( perm @ name @ name @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ C2 )
% 4.04/1.91 = C2 ) ) ) ).
% 4.04/1.91
% 4.04/1.91 thf(fact_40_fresh__aux,axiom,
% 4.04/1.91 ! [X2: $tType] :
% 4.04/1.91 ( ( pt_name @ X2 )
% 4.04/1.91 => ! [C2: name,A2: name,X3: X2,B2: name] :
% 4.04/1.91 ( ( C2 != A2 )
% 4.04/1.91 => ( ( fresh @ name @ X2 @ A2 @ X3 )
% 4.04/1.91 => ( ( fresh @ name @ X2 @ C2 @ X3 )
% 4.04/1.91 => ( fresh @ name @ X2 @ C2 @ ( perm @ name @ X2 @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ X3 ) ) ) ) ) ) ).
% 4.04/1.91
% 4.04/1.91 thf(fact_41_old_Oprod_Oinducts,axiom,
% 4.04/1.91 ! [B: $tType,A: $tType,P2: ( product_prod @ A @ B ) > $o,Prod: product_prod @ A @ B] :
% 4.04/1.91 ( ! [A4: A,B4: B] : ( P2 @ ( product_Pair @ A @ B @ A4 @ B4 ) )
% 4.04/1.91 => ( P2 @ Prod ) ) ).
% 4.04/1.91
% 4.04/1.91 thf(fact_42_old_Oprod_Oexhaust,axiom,
% 4.04/1.91 ! [A: $tType,B: $tType,Y4: product_prod @ A @ B] :
% 4.04/1.91 ~ ! [A4: A,B4: B] :
% 4.04/1.91 ( Y4
% 4.04/1.91 != ( product_Pair @ A @ B @ A4 @ B4 ) ) ).
% 4.04/1.91
% 4.04/1.91 thf(fact_43_prod__induct7,axiom,
% 4.04/1.91 ! [G: $tType,F2: $tType,E: $tType,D: $tType,C3: $tType,B: $tType,A: $tType,P2: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G ) ) ) ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G ) ) ) ) )] :
% 4.04/1.91 ( ! [A4: A,B4: B,C: C3,D2: D,E2: E,F: F2,G2: G] : ( P2 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G ) ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C3 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G ) ) ) ) @ B4 @ ( product_Pair @ C3 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G ) ) ) @ C @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F2 @ G ) @ E2 @ ( product_Pair @ F2 @ G @ F @ G2 ) ) ) ) ) ) )
% 4.04/1.91 => ( P2 @ X3 ) ) ).
% 4.04/1.91
% 4.04/1.91 thf(fact_44_prod__induct6,axiom,
% 4.04/1.91 ! [F2: $tType,E: $tType,D: $tType,C3: $tType,B: $tType,A: $tType,P2: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) ) )] :
% 4.04/1.91 ( ! [A4: A,B4: B,C: C3,D2: D,E2: E,F: F2] : ( P2 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C3 @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) ) @ B4 @ ( product_Pair @ C3 @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) @ C @ ( product_Pair @ D @ ( product_prod @ E @ F2 ) @ D2 @ ( product_Pair @ E @ F2 @ E2 @ F ) ) ) ) ) )
% 4.04/1.91 => ( P2 @ X3 ) ) ).
% 4.04/1.91
% 4.04/1.91 thf(fact_45_mem__Collect__eq,axiom,
% 4.04/1.91 ! [A: $tType,A2: A,P2: A > $o] :
% 4.04/1.91 ( ( member @ A @ A2 @ ( collect @ A @ P2 ) )
% 4.04/1.91 = ( P2 @ A2 ) ) ).
% 4.04/1.91
% 4.04/1.91 thf(fact_46_Collect__mem__eq,axiom,
% 4.04/1.91 ! [A: $tType,A5: set @ A] :
% 4.04/1.91 ( ( collect @ A
% 4.04/1.91 @ ^ [X6: A] : ( member @ A @ X6 @ A5 ) )
% 4.04/1.91 = A5 ) ).
% 4.04/1.91
% 4.04/1.91 thf(fact_47_Collect__cong,axiom,
% 4.04/1.91 ! [A: $tType,P2: A > $o,Q: A > $o] :
% 4.04/1.91 ( ! [X5: A] :
% 4.04/1.91 ( ( P2 @ X5 )
% 4.04/1.91 = ( Q @ X5 ) )
% 4.04/1.91 => ( ( collect @ A @ P2 )
% 4.04/1.91 = ( collect @ A @ Q ) ) ) ).
% 4.04/1.91
% 4.04/1.91 thf(fact_48_ext,axiom,
% 4.04/1.91 ! [B: $tType,A: $tType,F3: A > B,G3: A > B] :
% 4.04/1.91 ( ! [X5: A] :
% 4.04/1.91 ( ( F3 @ X5 )
% 4.04/1.91 = ( G3 @ X5 ) )
% 4.04/1.91 => ( F3 = G3 ) ) ).
% 4.04/1.91
% 4.04/1.91 thf(fact_49_prod__induct5,axiom,
% 4.04/1.91 ! [E: $tType,D: $tType,C3: $tType,B: $tType,A: $tType,P2: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D @ E ) ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D @ E ) ) )] :
% 4.04/1.91 ( ! [A4: A,B4: B,C: C3,D2: D,E2: E] : ( P2 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D @ E ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C3 @ ( product_prod @ D @ E ) ) @ B4 @ ( product_Pair @ C3 @ ( product_prod @ D @ E ) @ C @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) )
% 4.04/1.91 => ( P2 @ X3 ) ) ).
% 4.04/1.91
% 4.04/1.91 thf(fact_50_prod__induct4,axiom,
% 4.04/1.91 ! [D: $tType,C3: $tType,B: $tType,A: $tType,P2: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ D ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ D ) )] :
% 4.04/1.91 ( ! [A4: A,B4: B,C: C3,D2: D] : ( P2 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C3 @ D ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C3 @ D ) @ B4 @ ( product_Pair @ C3 @ D @ C @ D2 ) ) ) )
% 4.04/1.91 => ( P2 @ X3 ) ) ).
% 4.04/1.91
% 4.04/1.91 thf(fact_51_prod__induct3,axiom,
% 4.04/1.91 ! [C3: $tType,B: $tType,A: $tType,P2: ( product_prod @ A @ ( product_prod @ B @ C3 ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ C3 )] :
% 4.04/1.91 ( ! [A4: A,B4: B,C: C3] : ( P2 @ ( product_Pair @ A @ ( product_prod @ B @ C3 ) @ A4 @ ( product_Pair @ B @ C3 @ B4 @ C ) ) )
% 4.04/1.91 => ( P2 @ X3 ) ) ).
% 4.04/1.91
% 4.04/1.91 thf(fact_52_prod__cases7,axiom,
% 4.04/1.91 ! [A: $tType,B: $tType,C3: $tType,D: $tType,E: $tType,F2: $tType,G: $tType,Y4: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G ) ) ) ) )] :
% 4.04/1.91 ~ ! [A4: A,B4: B,C: C3,D2: D,E2: E,F: F2,G2: G] :
% 4.04/1.91 ( Y4
% 4.04/1.91 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G ) ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C3 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G ) ) ) ) @ B4 @ ( product_Pair @ C3 @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G ) ) ) @ C @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F2 @ G ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F2 @ G ) @ E2 @ ( product_Pair @ F2 @ G @ F @ G2 ) ) ) ) ) ) ) ).
% 4.04/1.91
% 4.04/1.91 thf(fact_53_prod__cases6,axiom,
% 4.04/1.91 ! [A: $tType,B: $tType,C3: $tType,D: $tType,E: $tType,F2: $tType,Y4: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) ) )] :
% 4.04/1.91 ~ ! [A4: A,B4: B,C: C3,D2: D,E2: E,F: F2] :
% 4.04/1.91 ( Y4
% 4.04/1.91 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C3 @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) ) @ B4 @ ( product_Pair @ C3 @ ( product_prod @ D @ ( product_prod @ E @ F2 ) ) @ C @ ( product_Pair @ D @ ( product_prod @ E @ F2 ) @ D2 @ ( product_Pair @ E @ F2 @ E2 @ F ) ) ) ) ) ) ).
% 4.04/1.91
% 4.04/1.91 thf(fact_54_prod__cases5,axiom,
% 4.04/1.91 ! [A: $tType,B: $tType,C3: $tType,D: $tType,E: $tType,Y4: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D @ E ) ) )] :
% 4.04/1.91 ~ ! [A4: A,B4: B,C: C3,D2: D,E2: E] :
% 4.04/1.91 ( Y4
% 4.04/1.91 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C3 @ ( product_prod @ D @ E ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C3 @ ( product_prod @ D @ E ) ) @ B4 @ ( product_Pair @ C3 @ ( product_prod @ D @ E ) @ C @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) ) ).
% 4.04/1.91
% 4.04/1.91 thf(fact_55_prod__cases4,axiom,
% 4.04/1.91 ! [A: $tType,B: $tType,C3: $tType,D: $tType,Y4: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C3 @ D ) )] :
% 4.04/1.91 ~ ! [A4: A,B4: B,C: C3,D2: D] :
% 4.04/1.91 ( Y4
% 4.04/1.91 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C3 @ D ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C3 @ D ) @ B4 @ ( product_Pair @ C3 @ D @ C @ D2 ) ) ) ) ).
% 4.04/1.91
% 4.04/1.91 thf(fact_56_prod__cases3,axiom,
% 4.04/1.91 ! [A: $tType,B: $tType,C3: $tType,Y4: product_prod @ A @ ( product_prod @ B @ C3 )] :
% 4.04/1.91 ~ ! [A4: A,B4: B,C: C3] :
% 4.04/1.91 ( Y4
% 4.04/1.91 != ( product_Pair @ A @ ( product_prod @ B @ C3 ) @ A4 @ ( product_Pair @ B @ C3 @ B4 @ C ) ) ) ).
% 4.04/1.91
% 4.04/1.91 thf(fact_57_Pair__inject,axiom,
% 4.04/1.91 ! [A: $tType,B: $tType,A2: A,B2: B,A3: A,B3: B] :
% 4.04/1.91 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 4.04/1.91 = ( product_Pair @ A @ B @ A3 @ B3 ) )
% 4.04/1.91 => ~ ( ( A2 = A3 )
% 4.04/1.91 => ( B2 != B3 ) ) ) ).
% 4.04/1.91
% 4.04/1.91 thf(fact_58_prod__cases,axiom,
% 4.04/1.91 ! [B: $tType,A: $tType,P2: ( product_prod @ A @ B ) > $o,P3: product_prod @ A @ B] :
% 4.04/1.91 ( ! [A4: A,B4: B] : ( P2 @ ( product_Pair @ A @ B @ A4 @ B4 ) )
% 4.04/1.91 => ( P2 @ P3 ) ) ).
% 4.04/1.91
% 4.04/1.91 thf(fact_59_surj__pair,axiom,
% 4.04/1.91 ! [A: $tType,B: $tType,P3: product_prod @ A @ B] :
% 4.04/1.91 ? [X5: A,Y3: B] :
% 4.04/1.91 ( P3
% 4.04/1.91 = ( product_Pair @ A @ B @ X5 @ Y3 ) ) ).
% 4.04/1.91
% 4.04/1.91 thf(fact_60_not__Cons__self2,axiom,
% 4.04/1.91 ! [A: $tType,X3: A,Xs2: list @ A] :
% 4.04/1.92 ( ( cons @ A @ X3 @ Xs2 )
% 4.04/1.92 != Xs2 ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_61_cp__name__name1,axiom,
% 4.04/1.92 ! [A: $tType] :
% 4.04/1.92 ( ( cp_name_name @ A )
% 4.04/1.92 => ! [Pi1: list @ ( product_prod @ name @ name ),Pi2: list @ ( product_prod @ name @ name ),X3: A] :
% 4.04/1.92 ( ( perm @ name @ A @ Pi1 @ ( perm @ name @ A @ Pi2 @ X3 ) )
% 4.04/1.92 = ( perm @ name @ A @ ( perm @ name @ ( list @ ( product_prod @ name @ name ) ) @ Pi1 @ Pi2 ) @ ( perm @ name @ A @ Pi1 @ X3 ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_62_name__perm__compose,axiom,
% 4.04/1.92 ! [X: $tType] :
% 4.04/1.92 ( ( pt_name @ X )
% 4.04/1.92 => ! [Pi2: list @ ( product_prod @ name @ name ),Pi1: list @ ( product_prod @ name @ name ),X3: X] :
% 4.04/1.92 ( ( perm @ name @ X @ Pi2 @ ( perm @ name @ X @ Pi1 @ X3 ) )
% 4.04/1.92 = ( perm @ name @ X @ ( perm @ name @ ( list @ ( product_prod @ name @ name ) ) @ Pi2 @ Pi1 ) @ ( perm @ name @ X @ Pi2 @ X3 ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_63_perm__compose,axiom,
% 4.04/1.92 ! [X2: $tType] :
% 4.04/1.92 ( ( pt_name @ X2 )
% 4.04/1.92 => ! [Pi2: list @ ( product_prod @ name @ name ),Pi1: list @ ( product_prod @ name @ name ),X3: X2] :
% 4.04/1.92 ( ( perm @ name @ X2 @ Pi2 @ ( perm @ name @ X2 @ Pi1 @ X3 ) )
% 4.04/1.92 = ( perm @ name @ X2 @ ( perm @ name @ ( list @ ( product_prod @ name @ name ) ) @ Pi2 @ Pi1 ) @ ( perm @ name @ X2 @ Pi2 @ X3 ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_64_perm__bij,axiom,
% 4.04/1.92 ! [X2: $tType] :
% 4.04/1.92 ( ( pt_name @ X2 )
% 4.04/1.92 => ! [Pi: list @ ( product_prod @ name @ name ),X3: X2,Y4: X2] :
% 4.04/1.92 ( ( ( perm @ name @ X2 @ Pi @ X3 )
% 4.04/1.92 = ( perm @ name @ X2 @ Pi @ Y4 ) )
% 4.04/1.92 = ( X3 = Y4 ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_65_perm__app,axiom,
% 4.04/1.92 ! [B: $tType,X2: $tType] :
% 4.04/1.92 ( ( pt_name @ X2 )
% 4.04/1.92 => ! [Pi: list @ ( product_prod @ name @ name ),F3: X2 > B,X3: X2] :
% 4.04/1.92 ( ( perm @ name @ B @ Pi @ ( F3 @ X3 ) )
% 4.04/1.92 = ( perm @ name @ ( X2 > B ) @ Pi @ F3 @ ( perm @ name @ X2 @ Pi @ X3 ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_66_in__eqvt,axiom,
% 4.04/1.92 ! [X2: $tType] :
% 4.04/1.92 ( ( pt_name @ X2 )
% 4.04/1.92 => ! [Pi: list @ ( product_prod @ name @ name ),X3: X2,X4: set @ X2] :
% 4.04/1.92 ( ( perm @ name @ $o @ Pi @ ( member @ X2 @ X3 @ X4 ) )
% 4.04/1.92 = ( member @ X2 @ ( perm @ name @ X2 @ Pi @ X3 ) @ ( perm @ name @ ( set @ X2 ) @ Pi @ X4 ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_67_eq__eqvt,axiom,
% 4.04/1.92 ! [X2: $tType] :
% 4.04/1.92 ( ( pt_name @ X2 )
% 4.04/1.92 => ! [Pi: list @ ( product_prod @ name @ name ),X3: X2,Y4: X2] :
% 4.04/1.92 ( ( perm @ name @ $o @ Pi @ ( X3 = Y4 ) )
% 4.04/1.92 = ( ( perm @ name @ X2 @ Pi @ X3 )
% 4.04/1.92 = ( perm @ name @ X2 @ Pi @ Y4 ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_68_strict__sorted_Oinduct,axiom,
% 4.04/1.92 ! [A: $tType] :
% 4.04/1.92 ( ( linorder @ A )
% 4.04/1.92 => ! [P2: ( list @ A ) > $o,A0: list @ A] :
% 4.04/1.92 ( ( P2 @ ( nil @ A ) )
% 4.04/1.92 => ( ! [X5: A,Ys: list @ A] :
% 4.04/1.92 ( ( P2 @ Ys )
% 4.04/1.92 => ( P2 @ ( cons @ A @ X5 @ Ys ) ) )
% 4.04/1.92 => ( P2 @ A0 ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_69_strict__sorted_Ocases,axiom,
% 4.04/1.92 ! [A: $tType] :
% 4.04/1.92 ( ( linorder @ A )
% 4.04/1.92 => ! [X3: list @ A] :
% 4.04/1.92 ( ( X3
% 4.04/1.92 != ( nil @ A ) )
% 4.04/1.92 => ~ ! [X5: A,Ys: list @ A] :
% 4.04/1.92 ( X3
% 4.04/1.92 != ( cons @ A @ X5 @ Ys ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_70_map__tailrec__rev_Oinduct,axiom,
% 4.04/1.92 ! [A: $tType,B: $tType,P2: ( A > B ) > ( list @ A ) > ( list @ B ) > $o,A0: A > B,A1: list @ A,A22: list @ B] :
% 4.04/1.92 ( ! [F: A > B,X_1: list @ B] : ( P2 @ F @ ( nil @ A ) @ X_1 )
% 4.04/1.92 => ( ! [F: A > B,A4: A,As: list @ A,Bs: list @ B] :
% 4.04/1.92 ( ( P2 @ F @ As @ ( cons @ B @ ( F @ A4 ) @ Bs ) )
% 4.04/1.92 => ( P2 @ F @ ( cons @ A @ A4 @ As ) @ Bs ) )
% 4.04/1.92 => ( P2 @ A0 @ A1 @ A22 ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_71_list__nonempty__induct,axiom,
% 4.04/1.92 ! [A: $tType,Xs2: list @ A,P2: ( list @ A ) > $o] :
% 4.04/1.92 ( ( Xs2
% 4.04/1.92 != ( nil @ A ) )
% 4.04/1.92 => ( ! [X5: A] : ( P2 @ ( cons @ A @ X5 @ ( nil @ A ) ) )
% 4.04/1.92 => ( ! [X5: A,Xs: list @ A] :
% 4.04/1.92 ( ( Xs
% 4.04/1.92 != ( nil @ A ) )
% 4.04/1.92 => ( ( P2 @ Xs )
% 4.04/1.92 => ( P2 @ ( cons @ A @ X5 @ Xs ) ) ) )
% 4.04/1.92 => ( P2 @ Xs2 ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_72_successively_Oinduct,axiom,
% 4.04/1.92 ! [A: $tType,P2: ( A > A > $o ) > ( list @ A ) > $o,A0: A > A > $o,A1: list @ A] :
% 4.04/1.92 ( ! [P: A > A > $o] : ( P2 @ P @ ( nil @ A ) )
% 4.04/1.92 => ( ! [P: A > A > $o,X5: A] : ( P2 @ P @ ( cons @ A @ X5 @ ( nil @ A ) ) )
% 4.04/1.92 => ( ! [P: A > A > $o,X5: A,Y3: A,Xs: list @ A] :
% 4.04/1.92 ( ( P2 @ P @ ( cons @ A @ Y3 @ Xs ) )
% 4.04/1.92 => ( P2 @ P @ ( cons @ A @ X5 @ ( cons @ A @ Y3 @ Xs ) ) ) )
% 4.04/1.92 => ( P2 @ A0 @ A1 ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_73_arg__min__list_Oinduct,axiom,
% 4.04/1.92 ! [B: $tType,A: $tType] :
% 4.04/1.92 ( ( linorder @ B )
% 4.04/1.92 => ! [P2: ( A > B ) > ( list @ A ) > $o,A0: A > B,A1: list @ A] :
% 4.04/1.92 ( ! [F: A > B,X5: A] : ( P2 @ F @ ( cons @ A @ X5 @ ( nil @ A ) ) )
% 4.04/1.92 => ( ! [F: A > B,X5: A,Y3: A,Zs: list @ A] :
% 4.04/1.92 ( ( P2 @ F @ ( cons @ A @ Y3 @ Zs ) )
% 4.04/1.92 => ( P2 @ F @ ( cons @ A @ X5 @ ( cons @ A @ Y3 @ Zs ) ) ) )
% 4.04/1.92 => ( ! [A4: A > B] : ( P2 @ A4 @ ( nil @ A ) )
% 4.04/1.92 => ( P2 @ A0 @ A1 ) ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_74_remdups__adj_Oinduct,axiom,
% 4.04/1.92 ! [A: $tType,P2: ( list @ A ) > $o,A0: list @ A] :
% 4.04/1.92 ( ( P2 @ ( nil @ A ) )
% 4.04/1.92 => ( ! [X5: A] : ( P2 @ ( cons @ A @ X5 @ ( nil @ A ) ) )
% 4.04/1.92 => ( ! [X5: A,Y3: A,Xs: list @ A] :
% 4.04/1.92 ( ( ( X5 = Y3 )
% 4.04/1.92 => ( P2 @ ( cons @ A @ X5 @ Xs ) ) )
% 4.04/1.92 => ( ( ( X5 != Y3 )
% 4.04/1.92 => ( P2 @ ( cons @ A @ Y3 @ Xs ) ) )
% 4.04/1.92 => ( P2 @ ( cons @ A @ X5 @ ( cons @ A @ Y3 @ Xs ) ) ) ) )
% 4.04/1.92 => ( P2 @ A0 ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_75_sorted__wrt_Oinduct,axiom,
% 4.04/1.92 ! [A: $tType,P2: ( A > A > $o ) > ( list @ A ) > $o,A0: A > A > $o,A1: list @ A] :
% 4.04/1.92 ( ! [P: A > A > $o] : ( P2 @ P @ ( nil @ A ) )
% 4.04/1.92 => ( ! [P: A > A > $o,X5: A,Ys: list @ A] :
% 4.04/1.92 ( ( P2 @ P @ Ys )
% 4.04/1.92 => ( P2 @ P @ ( cons @ A @ X5 @ Ys ) ) )
% 4.04/1.92 => ( P2 @ A0 @ A1 ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_76_remdups__adj_Ocases,axiom,
% 4.04/1.92 ! [A: $tType,X3: list @ A] :
% 4.04/1.92 ( ( X3
% 4.04/1.92 != ( nil @ A ) )
% 4.04/1.92 => ( ! [X5: A] :
% 4.04/1.92 ( X3
% 4.04/1.92 != ( cons @ A @ X5 @ ( nil @ A ) ) )
% 4.04/1.92 => ~ ! [X5: A,Y3: A,Xs: list @ A] :
% 4.04/1.92 ( X3
% 4.04/1.92 != ( cons @ A @ X5 @ ( cons @ A @ Y3 @ Xs ) ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_77_transpose_Ocases,axiom,
% 4.04/1.92 ! [A: $tType,X3: list @ ( list @ A )] :
% 4.04/1.92 ( ( X3
% 4.04/1.92 != ( nil @ ( list @ A ) ) )
% 4.04/1.92 => ( ! [Xss: list @ ( list @ A )] :
% 4.04/1.92 ( X3
% 4.04/1.92 != ( cons @ ( list @ A ) @ ( nil @ A ) @ Xss ) )
% 4.04/1.92 => ~ ! [X5: A,Xs: list @ A,Xss: list @ ( list @ A )] :
% 4.04/1.92 ( X3
% 4.04/1.92 != ( cons @ ( list @ A ) @ ( cons @ A @ X5 @ Xs ) @ Xss ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_78_shuffles_Oinduct,axiom,
% 4.04/1.92 ! [A: $tType,P2: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 4.04/1.92 ( ! [X_1: list @ A] : ( P2 @ ( nil @ A ) @ X_1 )
% 4.04/1.92 => ( ! [Xs: list @ A] : ( P2 @ Xs @ ( nil @ A ) )
% 4.04/1.92 => ( ! [X5: A,Xs: list @ A,Y3: A,Ys: list @ A] :
% 4.04/1.92 ( ( P2 @ Xs @ ( cons @ A @ Y3 @ Ys ) )
% 4.04/1.92 => ( ( P2 @ ( cons @ A @ X5 @ Xs ) @ Ys )
% 4.04/1.92 => ( P2 @ ( cons @ A @ X5 @ Xs ) @ ( cons @ A @ Y3 @ Ys ) ) ) )
% 4.04/1.92 => ( P2 @ A0 @ A1 ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_79_min__list_Oinduct,axiom,
% 4.04/1.92 ! [A: $tType] :
% 4.04/1.92 ( ( ord @ A )
% 4.04/1.92 => ! [P2: ( list @ A ) > $o,A0: list @ A] :
% 4.04/1.92 ( ! [X5: A,Xs: list @ A] :
% 4.04/1.92 ( ! [X212: A,X223: list @ A] :
% 4.04/1.92 ( ( Xs
% 4.04/1.92 = ( cons @ A @ X212 @ X223 ) )
% 4.04/1.92 => ( P2 @ Xs ) )
% 4.04/1.92 => ( P2 @ ( cons @ A @ X5 @ Xs ) ) )
% 4.04/1.92 => ( ( P2 @ ( nil @ A ) )
% 4.04/1.92 => ( P2 @ A0 ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_80_min__list_Ocases,axiom,
% 4.04/1.92 ! [A: $tType] :
% 4.04/1.92 ( ( ord @ A )
% 4.04/1.92 => ! [X3: list @ A] :
% 4.04/1.92 ( ! [X5: A,Xs: list @ A] :
% 4.04/1.92 ( X3
% 4.04/1.92 != ( cons @ A @ X5 @ Xs ) )
% 4.04/1.92 => ( X3
% 4.04/1.92 = ( nil @ A ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_81_induct__list012,axiom,
% 4.04/1.92 ! [A: $tType,P2: ( list @ A ) > $o,Xs2: list @ A] :
% 4.04/1.92 ( ( P2 @ ( nil @ A ) )
% 4.04/1.92 => ( ! [X5: A] : ( P2 @ ( cons @ A @ X5 @ ( nil @ A ) ) )
% 4.04/1.92 => ( ! [X5: A,Y3: A,Zs: list @ A] :
% 4.04/1.92 ( ( P2 @ Zs )
% 4.04/1.92 => ( ( P2 @ ( cons @ A @ Y3 @ Zs ) )
% 4.04/1.92 => ( P2 @ ( cons @ A @ X5 @ ( cons @ A @ Y3 @ Zs ) ) ) ) )
% 4.04/1.92 => ( P2 @ Xs2 ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_82_splice_Oinduct,axiom,
% 4.04/1.92 ! [A: $tType,P2: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 4.04/1.92 ( ! [X_1: list @ A] : ( P2 @ ( nil @ A ) @ X_1 )
% 4.04/1.92 => ( ! [X5: A,Xs: list @ A,Ys: list @ A] :
% 4.04/1.92 ( ( P2 @ Ys @ Xs )
% 4.04/1.92 => ( P2 @ ( cons @ A @ X5 @ Xs ) @ Ys ) )
% 4.04/1.92 => ( P2 @ A0 @ A1 ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_83_list__induct2_H,axiom,
% 4.04/1.92 ! [A: $tType,B: $tType,P2: ( list @ A ) > ( list @ B ) > $o,Xs2: list @ A,Ys2: list @ B] :
% 4.04/1.92 ( ( P2 @ ( nil @ A ) @ ( nil @ B ) )
% 4.04/1.92 => ( ! [X5: A,Xs: list @ A] : ( P2 @ ( cons @ A @ X5 @ Xs ) @ ( nil @ B ) )
% 4.04/1.92 => ( ! [Y3: B,Ys: list @ B] : ( P2 @ ( nil @ A ) @ ( cons @ B @ Y3 @ Ys ) )
% 4.04/1.92 => ( ! [X5: A,Xs: list @ A,Y3: B,Ys: list @ B] :
% 4.04/1.92 ( ( P2 @ Xs @ Ys )
% 4.04/1.92 => ( P2 @ ( cons @ A @ X5 @ Xs ) @ ( cons @ B @ Y3 @ Ys ) ) )
% 4.04/1.92 => ( P2 @ Xs2 @ Ys2 ) ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_84_neq__Nil__conv,axiom,
% 4.04/1.92 ! [A: $tType,Xs2: list @ A] :
% 4.04/1.92 ( ( Xs2
% 4.04/1.92 != ( nil @ A ) )
% 4.04/1.92 = ( ? [Y5: A,Ys3: list @ A] :
% 4.04/1.92 ( Xs2
% 4.04/1.92 = ( cons @ A @ Y5 @ Ys3 ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_85_list_Oinducts,axiom,
% 4.04/1.92 ! [A: $tType,P2: ( list @ A ) > $o,List: list @ A] :
% 4.04/1.92 ( ( P2 @ ( nil @ A ) )
% 4.04/1.92 => ( ! [X12: A,X23: list @ A] :
% 4.04/1.92 ( ( P2 @ X23 )
% 4.04/1.92 => ( P2 @ ( cons @ A @ X12 @ X23 ) ) )
% 4.04/1.92 => ( P2 @ List ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_86_list_Oexhaust,axiom,
% 4.04/1.92 ! [A: $tType,Y4: list @ A] :
% 4.04/1.92 ( ( Y4
% 4.04/1.92 != ( nil @ A ) )
% 4.04/1.92 => ~ ! [X213: A,X224: list @ A] :
% 4.04/1.92 ( Y4
% 4.04/1.92 != ( cons @ A @ X213 @ X224 ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_87_list_OdiscI,axiom,
% 4.04/1.92 ! [A: $tType,List: list @ A,X21: A,X222: list @ A] :
% 4.04/1.92 ( ( List
% 4.04/1.92 = ( cons @ A @ X21 @ X222 ) )
% 4.04/1.92 => ( List
% 4.04/1.92 != ( nil @ A ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_88_list_Odistinct_I1_J,axiom,
% 4.04/1.92 ! [A: $tType,X21: A,X222: list @ A] :
% 4.04/1.92 ( ( nil @ A )
% 4.04/1.92 != ( cons @ A @ X21 @ X222 ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_89__092_060open_062y_A_092_060sharp_062_AQ_092_060close_062,axiom,
% 4.04/1.92 fresh @ name @ pi @ y @ q ).
% 4.04/1.92
% 4.04/1.92 thf(fact_90_pair__in__Id__conv,axiom,
% 4.04/1.92 ! [A: $tType,A2: A,B2: A] :
% 4.04/1.92 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ ( id @ A ) )
% 4.04/1.92 = ( A2 = B2 ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_91_IdI,axiom,
% 4.04/1.92 ! [A: $tType,A2: A] : ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ A2 ) @ ( id @ A ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_92_fresh__prod,axiom,
% 4.04/1.92 ! [A: $tType,X: $tType,B: $tType,A2: X,X3: A,Y4: B] :
% 4.04/1.92 ( ( fresh @ X @ ( product_prod @ A @ B ) @ A2 @ ( product_Pair @ A @ B @ X3 @ Y4 ) )
% 4.04/1.92 = ( ( fresh @ X @ A @ A2 @ X3 )
% 4.04/1.92 & ( fresh @ X @ B @ A2 @ Y4 ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_93__092_060open_062y_A_092_060sharp_062_AP_092_060close_062,axiom,
% 4.04/1.92 fresh @ name @ pi @ y @ p ).
% 4.04/1.92
% 4.04/1.92 thf(fact_94_derivativeReflexive,axiom,
% 4.04/1.92 ! [Rel: set @ ( product_prod @ pi @ pi ),P2: pi,A2: late_subject,X3: name] :
% 4.04/1.92 ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 4.04/1.92 => ( strong2129052853vative @ P2 @ P2 @ A2 @ X3 @ Rel ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_95_derivativeEqvtI,axiom,
% 4.04/1.92 ! [P2: pi,Q: pi,A2: late_subject,X3: name,Rel: set @ ( product_prod @ pi @ pi ),Perm: list @ ( product_prod @ name @ name )] :
% 4.04/1.92 ( ( strong2129052853vative @ P2 @ Q @ A2 @ X3 @ Rel )
% 4.04/1.92 => ( ( eqvt @ pi @ Rel )
% 4.04/1.92 => ( strong2129052853vative @ ( perm @ name @ pi @ Perm @ P2 ) @ ( perm @ name @ pi @ Perm @ Q ) @ ( perm @ name @ late_subject @ Perm @ A2 ) @ ( perm @ name @ name @ Perm @ X3 ) @ Rel ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_96_derivativeEqvtI2,axiom,
% 4.04/1.92 ! [P2: pi,Q: pi,A2: late_subject,X3: name,Rel: set @ ( product_prod @ pi @ pi ),Perm: list @ ( product_prod @ name @ name )] :
% 4.04/1.92 ( ( strong2129052853vative @ P2 @ Q @ A2 @ X3 @ Rel )
% 4.04/1.92 => ( ( eqvt @ pi @ Rel )
% 4.04/1.92 => ( strong2129052853vative @ ( perm @ name @ pi @ Perm @ P2 ) @ ( perm @ name @ pi @ Perm @ Q ) @ A2 @ ( perm @ name @ name @ Perm @ X3 ) @ Rel ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_97_old_Oprod_Orec,axiom,
% 4.04/1.92 ! [A: $tType,T: $tType,B: $tType,F1: A > B > T,A2: A,B2: B] :
% 4.04/1.92 ( ( product_rec_prod @ A @ B @ T @ F1 @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 4.04/1.92 = ( F1 @ A2 @ B2 ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_98_eqvtRelI,axiom,
% 4.04/1.92 ! [A: $tType] :
% 4.04/1.92 ( ( pt_name @ A )
% 4.04/1.92 => ! [Rel: set @ ( product_prod @ A @ A ),P2: A,Q: A,Perm: list @ ( product_prod @ name @ name )] :
% 4.04/1.92 ( ( eqvt @ A @ Rel )
% 4.04/1.92 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ P2 @ Q ) @ Rel )
% 4.04/1.92 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ ( perm @ name @ A @ Perm @ P2 ) @ ( perm @ name @ A @ Perm @ Q ) ) @ Rel ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_99_Bound_Ohyps_I5_J,axiom,
% 4.04/1.92 fresh @ name @ ( product_prod @ name @ ( product_prod @ pi @ pi ) ) @ y @ ( product_Pair @ name @ ( product_prod @ pi @ pi ) @ x @ ( product_Pair @ pi @ pi @ p @ q ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_100_true__eqvt,axiom,
% 4.04/1.92 ! [A: $tType,Pi: list @ ( product_prod @ A @ A )] : ( perm @ A @ $o @ Pi @ $true ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_101_false__eqvt,axiom,
% 4.04/1.92 ! [A: $tType,Pi: list @ ( product_prod @ A @ A )] :
% 4.04/1.92 ~ ( perm @ A @ $o @ Pi @ $false ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_102_subject_Ofresh_I2_J,axiom,
% 4.04/1.92 ! [A2: name,X1: name] :
% 4.04/1.92 ( ( fresh @ name @ late_subject @ A2 @ ( late_BoundOutputS @ X1 ) )
% 4.04/1.92 = ( fresh @ name @ name @ A2 @ X1 ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_103_name__bij,axiom,
% 4.04/1.92 ! [Pi: list @ ( product_prod @ name @ name ),X3: name,Y4: name] :
% 4.04/1.92 ( ( ( perm @ name @ name @ Pi @ X3 )
% 4.04/1.92 = ( perm @ name @ name @ Pi @ Y4 ) )
% 4.04/1.92 = ( X3 = Y4 ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_104_imp__eqvt,axiom,
% 4.04/1.92 ! [A: $tType,Pi: list @ ( product_prod @ A @ A ),A5: $o,B5: $o] :
% 4.04/1.92 ( ( perm @ A @ $o @ Pi
% 4.04/1.92 @ ( A5
% 4.04/1.92 => B5 ) )
% 4.04/1.92 = ( ( perm @ A @ $o @ Pi @ A5 )
% 4.04/1.92 => ( perm @ A @ $o @ Pi @ B5 ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_105_neg__eqvt,axiom,
% 4.04/1.92 ! [A: $tType,Pi: list @ ( product_prod @ A @ A ),A5: $o] :
% 4.04/1.92 ( ( perm @ A @ $o @ Pi @ ~ A5 )
% 4.04/1.92 = ( ~ ( perm @ A @ $o @ Pi @ A5 ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_106_conj__eqvt,axiom,
% 4.04/1.92 ! [A: $tType,Pi: list @ ( product_prod @ A @ A ),A5: $o,B5: $o] :
% 4.04/1.92 ( ( perm @ A @ $o @ Pi
% 4.04/1.92 @ ( A5
% 4.04/1.92 & B5 ) )
% 4.04/1.92 = ( ( perm @ A @ $o @ Pi @ A5 )
% 4.04/1.92 & ( perm @ A @ $o @ Pi @ B5 ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_107_disj__eqvt,axiom,
% 4.04/1.92 ! [A: $tType,Pi: list @ ( product_prod @ A @ A ),A5: $o,B5: $o] :
% 4.04/1.92 ( ( perm @ A @ $o @ Pi
% 4.04/1.92 @ ( A5
% 4.04/1.92 | B5 ) )
% 4.04/1.92 = ( ( perm @ A @ $o @ Pi @ A5 )
% 4.04/1.92 | ( perm @ A @ $o @ Pi @ B5 ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_108_perm__boolE,axiom,
% 4.04/1.92 ! [A: $tType,Pi: list @ ( product_prod @ A @ A )] :
% 4.04/1.92 ~ ( perm @ A @ $o @ Pi @ $false ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_109_perm__boolI,axiom,
% 4.04/1.92 ! [A: $tType,P2: $o,Pi: list @ ( product_prod @ A @ A )] :
% 4.04/1.92 ( P2
% 4.04/1.92 => ( perm @ A @ $o @ Pi @ P2 ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_110_pt__set__bij3,axiom,
% 4.04/1.92 ! [X: $tType,A: $tType,Pi: list @ ( product_prod @ X @ X ),X3: A,X4: set @ A] :
% 4.04/1.92 ( ( perm @ X @ $o @ Pi @ ( member @ A @ X3 @ X4 ) )
% 4.04/1.92 = ( member @ A @ X3 @ X4 ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_111_perm__bool__def,axiom,
% 4.04/1.92 ! [X: $tType] :
% 4.04/1.92 ( ( perm @ X @ $o )
% 4.04/1.92 = ( ^ [Pi3: list @ ( product_prod @ X @ X ),B6: $o] : B6 ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_112_nil__eqvt,axiom,
% 4.04/1.92 ! [X: $tType,A: $tType,Pi: list @ ( product_prod @ X @ X )] :
% 4.04/1.92 ( ( perm @ X @ ( list @ A ) @ Pi @ ( nil @ A ) )
% 4.04/1.92 = ( nil @ A ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_113_fresh__list__nil,axiom,
% 4.04/1.92 ! [X: $tType,A: $tType,A2: X] : ( fresh @ X @ ( list @ A ) @ A2 @ ( nil @ A ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_114_allE__Nil,axiom,
% 4.04/1.92 ! [A: $tType,P2: ( list @ A ) > $o] :
% 4.04/1.92 ( ! [X_1: list @ A] : ( P2 @ X_1 )
% 4.04/1.92 => ( P2 @ ( nil @ A ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_115_if__eqvt,axiom,
% 4.04/1.92 ! [A: $tType,B: $tType,Pi: list @ ( product_prod @ A @ A ),B2: $o,C1: B,C22: B] :
% 4.04/1.92 ( ( ( perm @ A @ $o @ Pi @ B2 )
% 4.04/1.92 => ( ( perm @ A @ B @ Pi @ ( if @ B @ B2 @ C1 @ C22 ) )
% 4.04/1.92 = ( perm @ A @ B @ Pi @ C1 ) ) )
% 4.04/1.92 & ( ~ ( perm @ A @ $o @ Pi @ B2 )
% 4.04/1.92 => ( ( perm @ A @ B @ Pi @ ( if @ B @ B2 @ C1 @ C22 ) )
% 4.04/1.92 = ( perm @ A @ B @ Pi @ C22 ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_116_pt__bij3,axiom,
% 4.04/1.92 ! [X: $tType,A: $tType,X3: A,Y4: A,Pi: list @ ( product_prod @ X @ X )] :
% 4.04/1.92 ( ( X3 = Y4 )
% 4.04/1.92 => ( ( perm @ X @ A @ Pi @ X3 )
% 4.04/1.92 = ( perm @ X @ A @ Pi @ Y4 ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_117_abs__fun__if,axiom,
% 4.04/1.92 ! [X: $tType,A: $tType,C2: $o,Pi: list @ ( product_prod @ X @ X ),X3: A,Y4: A] :
% 4.04/1.92 ( ( C2
% 4.04/1.92 => ( ( perm @ X @ A @ Pi @ ( if @ A @ C2 @ X3 @ Y4 ) )
% 4.04/1.92 = ( perm @ X @ A @ Pi @ X3 ) ) )
% 4.04/1.92 & ( ~ C2
% 4.04/1.92 => ( ( perm @ X @ A @ Pi @ ( if @ A @ C2 @ X3 @ Y4 ) )
% 4.04/1.92 = ( perm @ X @ A @ Pi @ Y4 ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_118_eqvt__def,axiom,
% 4.04/1.92 ! [A: $tType] :
% 4.04/1.92 ( ( pt_name @ A )
% 4.04/1.92 => ( ( eqvt @ A )
% 4.04/1.92 = ( ^ [Rel2: set @ ( product_prod @ A @ A )] :
% 4.04/1.92 ! [X6: product_prod @ A @ A,Perm2: list @ ( product_prod @ name @ name )] :
% 4.04/1.92 ( ( member @ ( product_prod @ A @ A ) @ X6 @ Rel2 )
% 4.04/1.92 => ( member @ ( product_prod @ A @ A ) @ ( perm @ name @ ( product_prod @ A @ A ) @ Perm2 @ X6 ) @ Rel2 ) ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_119_perm__prod_Osimps,axiom,
% 4.04/1.92 ! [A: $tType,X: $tType,B: $tType,Pi: list @ ( product_prod @ X @ X ),X3: A,Y4: B] :
% 4.04/1.92 ( ( perm @ X @ ( product_prod @ A @ B ) @ Pi @ ( product_Pair @ A @ B @ X3 @ Y4 ) )
% 4.04/1.92 = ( product_Pair @ A @ B @ ( perm @ X @ A @ Pi @ X3 ) @ ( perm @ X @ B @ Pi @ Y4 ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_120_cons__eqvt,axiom,
% 4.04/1.92 ! [X: $tType,A: $tType,Pi: list @ ( product_prod @ X @ X ),X3: A,Xs2: list @ A] :
% 4.04/1.92 ( ( perm @ X @ ( list @ A ) @ Pi @ ( cons @ A @ X3 @ Xs2 ) )
% 4.04/1.92 = ( cons @ A @ ( perm @ X @ A @ Pi @ X3 ) @ ( perm @ X @ ( list @ A ) @ Pi @ Xs2 ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_121_fresh__prodD_I1_J,axiom,
% 4.04/1.92 ! [C3: $tType,A: $tType,B: $tType,A2: A,X3: B,Y4: C3] :
% 4.04/1.92 ( ( fresh @ A @ ( product_prod @ B @ C3 ) @ A2 @ ( product_Pair @ B @ C3 @ X3 @ Y4 ) )
% 4.04/1.92 => ( fresh @ A @ B @ A2 @ X3 ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_122_fresh__prodD_I2_J,axiom,
% 4.04/1.92 ! [B: $tType,A: $tType,C3: $tType,A2: A,X3: B,Y4: C3] :
% 4.04/1.92 ( ( fresh @ A @ ( product_prod @ B @ C3 ) @ A2 @ ( product_Pair @ B @ C3 @ X3 @ Y4 ) )
% 4.04/1.92 => ( fresh @ A @ C3 @ A2 @ Y4 ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_123_fresh__list__cons,axiom,
% 4.04/1.92 ! [X: $tType,A: $tType,A2: X,X3: A,Xs2: list @ A] :
% 4.04/1.92 ( ( fresh @ X @ ( list @ A ) @ A2 @ ( cons @ A @ X3 @ Xs2 ) )
% 4.04/1.92 = ( ( fresh @ X @ A @ A2 @ X3 )
% 4.04/1.92 & ( fresh @ X @ ( list @ A ) @ A2 @ Xs2 ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_124_subrelI,axiom,
% 4.04/1.92 ! [B: $tType,A: $tType,R: set @ ( product_prod @ A @ B ),S: set @ ( product_prod @ A @ B )] :
% 4.04/1.92 ( ! [X5: A,Y3: B] :
% 4.04/1.92 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X5 @ Y3 ) @ R )
% 4.04/1.92 => ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X5 @ Y3 ) @ S ) )
% 4.04/1.92 => ( ord_less_eq @ ( set @ ( product_prod @ A @ B ) ) @ R @ S ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_125_IdE,axiom,
% 4.04/1.92 ! [A: $tType,P3: product_prod @ A @ A] :
% 4.04/1.92 ( ( member @ ( product_prod @ A @ A ) @ P3 @ ( id @ A ) )
% 4.04/1.92 => ~ ! [X5: A] :
% 4.04/1.92 ( P3
% 4.04/1.92 != ( product_Pair @ A @ A @ X5 @ X5 ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_126_derivativeMonotonic,axiom,
% 4.04/1.92 ! [P2: pi,Q: pi,A2: late_subject,X3: name,A5: set @ ( product_prod @ pi @ pi ),B5: set @ ( product_prod @ pi @ pi )] :
% 4.04/1.92 ( ( strong2129052853vative @ P2 @ Q @ A2 @ X3 @ A5 )
% 4.04/1.92 => ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ A5 @ B5 )
% 4.04/1.92 => ( strong2129052853vative @ P2 @ Q @ A2 @ X3 @ B5 ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_127_eqvtRelE,axiom,
% 4.04/1.92 ! [A: $tType] :
% 4.04/1.92 ( ( pt_name @ A )
% 4.04/1.92 => ! [Rel: set @ ( product_prod @ A @ A ),Perm: list @ ( product_prod @ name @ name ),P2: A,Q: A] :
% 4.04/1.92 ( ( eqvt @ A @ Rel )
% 4.04/1.92 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ ( perm @ name @ A @ Perm @ P2 ) @ ( perm @ name @ A @ Perm @ Q ) ) @ Rel )
% 4.04/1.92 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ P2 @ Q ) @ Rel ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_128_Bound_Ohyps_I3_J,axiom,
% 4.04/1.92 fresh @ name @ pi @ y @ ( sum @ ( res @ x @ p ) @ ( res @ x @ q ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_129_Bound_Ohyps_I2_J,axiom,
% 4.04/1.92 fresh @ name @ pi @ y @ ( res @ x @ ( sum @ p @ q ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_130_subset__antisym,axiom,
% 4.04/1.92 ! [A: $tType,A5: set @ A,B5: set @ A] :
% 4.04/1.92 ( ( ord_less_eq @ ( set @ A ) @ A5 @ B5 )
% 4.04/1.92 => ( ( ord_less_eq @ ( set @ A ) @ B5 @ A5 )
% 4.04/1.92 => ( A5 = B5 ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_131_subsetI,axiom,
% 4.04/1.92 ! [A: $tType,A5: set @ A,B5: set @ A] :
% 4.04/1.92 ( ! [X5: A] :
% 4.04/1.92 ( ( member @ A @ X5 @ A5 )
% 4.04/1.92 => ( member @ A @ X5 @ B5 ) )
% 4.04/1.92 => ( ord_less_eq @ ( set @ A ) @ A5 @ B5 ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_132_order__refl,axiom,
% 4.04/1.92 ! [A: $tType] :
% 4.04/1.92 ( ( preorder @ A )
% 4.04/1.92 => ! [X3: A] : ( ord_less_eq @ A @ X3 @ X3 ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_133_name__fresh,axiom,
% 4.04/1.92 ( ( fresh @ name @ name )
% 4.04/1.92 = ( ^ [A6: name,B6: name] : ( A6 != B6 ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_134_pi_Ofresh_I7_J,axiom,
% 4.04/1.92 ! [A2: name,X22: pi,X1: pi] :
% 4.04/1.92 ( ( fresh @ name @ pi @ A2 @ ( sum @ X22 @ X1 ) )
% 4.04/1.92 = ( ( fresh @ name @ pi @ A2 @ X22 )
% 4.04/1.92 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_135_pi_Operm_I7_J,axiom,
% 4.04/1.92 ! [Pi: list @ ( product_prod @ name @ name ),X22: pi,X1: pi] :
% 4.04/1.92 ( ( perm @ name @ pi @ Pi @ ( sum @ X22 @ X1 ) )
% 4.04/1.92 = ( sum @ ( perm @ name @ pi @ Pi @ X22 ) @ ( perm @ name @ pi @ Pi @ X1 ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_136_pi_Operm_I9_J,axiom,
% 4.04/1.92 ! [Pi: list @ ( product_prod @ name @ name ),X1: name,X22: pi] :
% 4.04/1.92 ( ( perm @ name @ pi @ Pi @ ( res @ X1 @ X22 ) )
% 4.04/1.92 = ( res @ ( perm @ name @ name @ Pi @ X1 ) @ ( perm @ name @ pi @ Pi @ X22 ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_137_pi_Odistinct_I81_J,axiom,
% 4.04/1.92 ! [Pi1: pi,Pi2: pi,Name: name,Pi4: pi] :
% 4.04/1.92 ( ( sum @ Pi1 @ Pi2 )
% 4.04/1.92 != ( res @ Name @ Pi4 ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_138_pi_Oinject_I6_J,axiom,
% 4.04/1.92 ! [X22: pi,X1: pi,Y2: pi,Y1: pi] :
% 4.04/1.92 ( ( ( sum @ X22 @ X1 )
% 4.04/1.92 = ( sum @ Y2 @ Y1 ) )
% 4.04/1.92 = ( ( X22 = Y2 )
% 4.04/1.92 & ( X1 = Y1 ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_139_freshRes,axiom,
% 4.04/1.92 ! [A2: name,P2: pi] : ( fresh @ name @ pi @ A2 @ ( res @ A2 @ P2 ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_140_le__funD,axiom,
% 4.04/1.92 ! [B: $tType,A: $tType] :
% 4.04/1.92 ( ( ord @ B )
% 4.04/1.92 => ! [F3: A > B,G3: A > B,X3: A] :
% 4.04/1.92 ( ( ord_less_eq @ ( A > B ) @ F3 @ G3 )
% 4.04/1.92 => ( ord_less_eq @ B @ ( F3 @ X3 ) @ ( G3 @ X3 ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_141_le__funE,axiom,
% 4.04/1.92 ! [B: $tType,A: $tType] :
% 4.04/1.92 ( ( ord @ B )
% 4.04/1.92 => ! [F3: A > B,G3: A > B,X3: A] :
% 4.04/1.92 ( ( ord_less_eq @ ( A > B ) @ F3 @ G3 )
% 4.04/1.92 => ( ord_less_eq @ B @ ( F3 @ X3 ) @ ( G3 @ X3 ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_142_le__funI,axiom,
% 4.04/1.92 ! [B: $tType,A: $tType] :
% 4.04/1.92 ( ( ord @ B )
% 4.04/1.92 => ! [F3: A > B,G3: A > B] :
% 4.04/1.92 ( ! [X5: A] : ( ord_less_eq @ B @ ( F3 @ X5 ) @ ( G3 @ X5 ) )
% 4.04/1.92 => ( ord_less_eq @ ( A > B ) @ F3 @ G3 ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_143_le__fun__def,axiom,
% 4.04/1.92 ! [B: $tType,A: $tType] :
% 4.04/1.92 ( ( ord @ B )
% 4.04/1.92 => ( ( ord_less_eq @ ( A > B ) )
% 4.04/1.92 = ( ^ [F4: A > B,G4: A > B] :
% 4.04/1.92 ! [X6: A] : ( ord_less_eq @ B @ ( F4 @ X6 ) @ ( G4 @ X6 ) ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_144_order__subst1,axiom,
% 4.04/1.92 ! [A: $tType,B: $tType] :
% 4.04/1.92 ( ( ( order @ B )
% 4.04/1.92 & ( order @ A ) )
% 4.04/1.92 => ! [A2: A,F3: B > A,B2: B,C2: B] :
% 4.04/1.92 ( ( ord_less_eq @ A @ A2 @ ( F3 @ B2 ) )
% 4.04/1.92 => ( ( ord_less_eq @ B @ B2 @ C2 )
% 4.04/1.92 => ( ! [X5: B,Y3: B] :
% 4.04/1.92 ( ( ord_less_eq @ B @ X5 @ Y3 )
% 4.04/1.92 => ( ord_less_eq @ A @ ( F3 @ X5 ) @ ( F3 @ Y3 ) ) )
% 4.04/1.92 => ( ord_less_eq @ A @ A2 @ ( F3 @ C2 ) ) ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_145_order__subst2,axiom,
% 4.04/1.92 ! [A: $tType,C3: $tType] :
% 4.04/1.92 ( ( ( order @ C3 )
% 4.04/1.92 & ( order @ A ) )
% 4.04/1.92 => ! [A2: A,B2: A,F3: A > C3,C2: C3] :
% 4.04/1.92 ( ( ord_less_eq @ A @ A2 @ B2 )
% 4.04/1.92 => ( ( ord_less_eq @ C3 @ ( F3 @ B2 ) @ C2 )
% 4.04/1.92 => ( ! [X5: A,Y3: A] :
% 4.04/1.92 ( ( ord_less_eq @ A @ X5 @ Y3 )
% 4.04/1.92 => ( ord_less_eq @ C3 @ ( F3 @ X5 ) @ ( F3 @ Y3 ) ) )
% 4.04/1.92 => ( ord_less_eq @ C3 @ ( F3 @ A2 ) @ C2 ) ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_146_ord__eq__le__subst,axiom,
% 4.04/1.92 ! [A: $tType,B: $tType] :
% 4.04/1.92 ( ( ( ord @ B )
% 4.04/1.92 & ( ord @ A ) )
% 4.04/1.92 => ! [A2: A,F3: B > A,B2: B,C2: B] :
% 4.04/1.92 ( ( A2
% 4.04/1.92 = ( F3 @ B2 ) )
% 4.04/1.92 => ( ( ord_less_eq @ B @ B2 @ C2 )
% 4.04/1.92 => ( ! [X5: B,Y3: B] :
% 4.04/1.92 ( ( ord_less_eq @ B @ X5 @ Y3 )
% 4.04/1.92 => ( ord_less_eq @ A @ ( F3 @ X5 ) @ ( F3 @ Y3 ) ) )
% 4.04/1.92 => ( ord_less_eq @ A @ A2 @ ( F3 @ C2 ) ) ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_147_ord__le__eq__subst,axiom,
% 4.04/1.92 ! [A: $tType,B: $tType] :
% 4.04/1.92 ( ( ( ord @ B )
% 4.04/1.92 & ( ord @ A ) )
% 4.04/1.92 => ! [A2: A,B2: A,F3: A > B,C2: B] :
% 4.04/1.92 ( ( ord_less_eq @ A @ A2 @ B2 )
% 4.04/1.92 => ( ( ( F3 @ B2 )
% 4.04/1.92 = C2 )
% 4.04/1.92 => ( ! [X5: A,Y3: A] :
% 4.04/1.92 ( ( ord_less_eq @ A @ X5 @ Y3 )
% 4.04/1.92 => ( ord_less_eq @ B @ ( F3 @ X5 ) @ ( F3 @ Y3 ) ) )
% 4.04/1.92 => ( ord_less_eq @ B @ ( F3 @ A2 ) @ C2 ) ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_148_eq__iff,axiom,
% 4.04/1.92 ! [A: $tType] :
% 4.04/1.92 ( ( order @ A )
% 4.04/1.92 => ( ( ^ [Y6: A,Z: A] : ( Y6 = Z ) )
% 4.04/1.92 = ( ^ [X6: A,Y5: A] :
% 4.04/1.92 ( ( ord_less_eq @ A @ X6 @ Y5 )
% 4.04/1.92 & ( ord_less_eq @ A @ Y5 @ X6 ) ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_149_antisym,axiom,
% 4.04/1.92 ! [A: $tType] :
% 4.04/1.92 ( ( order @ A )
% 4.04/1.92 => ! [X3: A,Y4: A] :
% 4.04/1.92 ( ( ord_less_eq @ A @ X3 @ Y4 )
% 4.04/1.92 => ( ( ord_less_eq @ A @ Y4 @ X3 )
% 4.04/1.92 => ( X3 = Y4 ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_150_linear,axiom,
% 4.04/1.92 ! [A: $tType] :
% 4.04/1.92 ( ( linorder @ A )
% 4.04/1.92 => ! [X3: A,Y4: A] :
% 4.04/1.92 ( ( ord_less_eq @ A @ X3 @ Y4 )
% 4.04/1.92 | ( ord_less_eq @ A @ Y4 @ X3 ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_151_eq__refl,axiom,
% 4.04/1.92 ! [A: $tType] :
% 4.04/1.92 ( ( preorder @ A )
% 4.04/1.92 => ! [X3: A,Y4: A] :
% 4.04/1.92 ( ( X3 = Y4 )
% 4.04/1.92 => ( ord_less_eq @ A @ X3 @ Y4 ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_152_le__cases,axiom,
% 4.04/1.92 ! [A: $tType] :
% 4.04/1.92 ( ( linorder @ A )
% 4.04/1.92 => ! [X3: A,Y4: A] :
% 4.04/1.92 ( ~ ( ord_less_eq @ A @ X3 @ Y4 )
% 4.04/1.92 => ( ord_less_eq @ A @ Y4 @ X3 ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_153_order_Otrans,axiom,
% 4.04/1.92 ! [A: $tType] :
% 4.04/1.92 ( ( order @ A )
% 4.04/1.92 => ! [A2: A,B2: A,C2: A] :
% 4.04/1.92 ( ( ord_less_eq @ A @ A2 @ B2 )
% 4.04/1.92 => ( ( ord_less_eq @ A @ B2 @ C2 )
% 4.04/1.92 => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_154_le__cases3,axiom,
% 4.04/1.92 ! [A: $tType] :
% 4.04/1.92 ( ( linorder @ A )
% 4.04/1.92 => ! [X3: A,Y4: A,Z2: A] :
% 4.04/1.92 ( ( ( ord_less_eq @ A @ X3 @ Y4 )
% 4.04/1.92 => ~ ( ord_less_eq @ A @ Y4 @ Z2 ) )
% 4.04/1.92 => ( ( ( ord_less_eq @ A @ Y4 @ X3 )
% 4.04/1.92 => ~ ( ord_less_eq @ A @ X3 @ Z2 ) )
% 4.04/1.92 => ( ( ( ord_less_eq @ A @ X3 @ Z2 )
% 4.04/1.92 => ~ ( ord_less_eq @ A @ Z2 @ Y4 ) )
% 4.04/1.92 => ( ( ( ord_less_eq @ A @ Z2 @ Y4 )
% 4.04/1.92 => ~ ( ord_less_eq @ A @ Y4 @ X3 ) )
% 4.04/1.92 => ( ( ( ord_less_eq @ A @ Y4 @ Z2 )
% 4.04/1.92 => ~ ( ord_less_eq @ A @ Z2 @ X3 ) )
% 4.04/1.92 => ~ ( ( ord_less_eq @ A @ Z2 @ X3 )
% 4.04/1.92 => ~ ( ord_less_eq @ A @ X3 @ Y4 ) ) ) ) ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_155_antisym__conv,axiom,
% 4.04/1.92 ! [A: $tType] :
% 4.04/1.92 ( ( order @ A )
% 4.04/1.92 => ! [Y4: A,X3: A] :
% 4.04/1.92 ( ( ord_less_eq @ A @ Y4 @ X3 )
% 4.04/1.92 => ( ( ord_less_eq @ A @ X3 @ Y4 )
% 4.04/1.92 = ( X3 = Y4 ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_156_order__class_Oorder_Oeq__iff,axiom,
% 4.04/1.92 ! [A: $tType] :
% 4.04/1.92 ( ( order @ A )
% 4.04/1.92 => ( ( ^ [Y6: A,Z: A] : ( Y6 = Z ) )
% 4.04/1.92 = ( ^ [A6: A,B6: A] :
% 4.04/1.92 ( ( ord_less_eq @ A @ A6 @ B6 )
% 4.04/1.92 & ( ord_less_eq @ A @ B6 @ A6 ) ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_157_ord__eq__le__trans,axiom,
% 4.04/1.92 ! [A: $tType] :
% 4.04/1.92 ( ( ord @ A )
% 4.04/1.92 => ! [A2: A,B2: A,C2: A] :
% 4.04/1.92 ( ( A2 = B2 )
% 4.04/1.92 => ( ( ord_less_eq @ A @ B2 @ C2 )
% 4.04/1.92 => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_158_ord__le__eq__trans,axiom,
% 4.04/1.92 ! [A: $tType] :
% 4.04/1.92 ( ( ord @ A )
% 4.04/1.92 => ! [A2: A,B2: A,C2: A] :
% 4.04/1.92 ( ( ord_less_eq @ A @ A2 @ B2 )
% 4.04/1.92 => ( ( B2 = C2 )
% 4.04/1.92 => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_159_order__class_Oorder_Oantisym,axiom,
% 4.04/1.92 ! [A: $tType] :
% 4.04/1.92 ( ( order @ A )
% 4.04/1.92 => ! [A2: A,B2: A] :
% 4.04/1.92 ( ( ord_less_eq @ A @ A2 @ B2 )
% 4.04/1.92 => ( ( ord_less_eq @ A @ B2 @ A2 )
% 4.04/1.92 => ( A2 = B2 ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_160_order__trans,axiom,
% 4.04/1.92 ! [A: $tType] :
% 4.04/1.92 ( ( preorder @ A )
% 4.04/1.92 => ! [X3: A,Y4: A,Z2: A] :
% 4.04/1.92 ( ( ord_less_eq @ A @ X3 @ Y4 )
% 4.04/1.92 => ( ( ord_less_eq @ A @ Y4 @ Z2 )
% 4.04/1.92 => ( ord_less_eq @ A @ X3 @ Z2 ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_161_dual__order_Orefl,axiom,
% 4.04/1.92 ! [A: $tType] :
% 4.04/1.92 ( ( order @ A )
% 4.04/1.92 => ! [A2: A] : ( ord_less_eq @ A @ A2 @ A2 ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_162_linorder__wlog,axiom,
% 4.04/1.92 ! [A: $tType] :
% 4.04/1.92 ( ( linorder @ A )
% 4.04/1.92 => ! [P2: A > A > $o,A2: A,B2: A] :
% 4.04/1.92 ( ! [A4: A,B4: A] :
% 4.04/1.92 ( ( ord_less_eq @ A @ A4 @ B4 )
% 4.04/1.92 => ( P2 @ A4 @ B4 ) )
% 4.04/1.92 => ( ! [A4: A,B4: A] :
% 4.04/1.92 ( ( P2 @ B4 @ A4 )
% 4.04/1.92 => ( P2 @ A4 @ B4 ) )
% 4.04/1.92 => ( P2 @ A2 @ B2 ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_163_dual__order_Otrans,axiom,
% 4.04/1.92 ! [A: $tType] :
% 4.04/1.92 ( ( order @ A )
% 4.04/1.92 => ! [B2: A,A2: A,C2: A] :
% 4.04/1.92 ( ( ord_less_eq @ A @ B2 @ A2 )
% 4.04/1.92 => ( ( ord_less_eq @ A @ C2 @ B2 )
% 4.04/1.92 => ( ord_less_eq @ A @ C2 @ A2 ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_164_dual__order_Oeq__iff,axiom,
% 4.04/1.92 ! [A: $tType] :
% 4.04/1.92 ( ( order @ A )
% 4.04/1.92 => ( ( ^ [Y6: A,Z: A] : ( Y6 = Z ) )
% 4.04/1.92 = ( ^ [A6: A,B6: A] :
% 4.04/1.92 ( ( ord_less_eq @ A @ B6 @ A6 )
% 4.04/1.92 & ( ord_less_eq @ A @ A6 @ B6 ) ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_165_dual__order_Oantisym,axiom,
% 4.04/1.92 ! [A: $tType] :
% 4.04/1.92 ( ( order @ A )
% 4.04/1.92 => ! [B2: A,A2: A] :
% 4.04/1.92 ( ( ord_less_eq @ A @ B2 @ A2 )
% 4.04/1.92 => ( ( ord_less_eq @ A @ A2 @ B2 )
% 4.04/1.92 => ( A2 = B2 ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_166_in__mono,axiom,
% 4.04/1.92 ! [A: $tType,A5: set @ A,B5: set @ A,X3: A] :
% 4.04/1.92 ( ( ord_less_eq @ ( set @ A ) @ A5 @ B5 )
% 4.04/1.92 => ( ( member @ A @ X3 @ A5 )
% 4.04/1.92 => ( member @ A @ X3 @ B5 ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_167_subsetD,axiom,
% 4.04/1.92 ! [A: $tType,A5: set @ A,B5: set @ A,C2: A] :
% 4.04/1.92 ( ( ord_less_eq @ ( set @ A ) @ A5 @ B5 )
% 4.04/1.92 => ( ( member @ A @ C2 @ A5 )
% 4.04/1.92 => ( member @ A @ C2 @ B5 ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_168_equalityE,axiom,
% 4.04/1.92 ! [A: $tType,A5: set @ A,B5: set @ A] :
% 4.04/1.92 ( ( A5 = B5 )
% 4.04/1.92 => ~ ( ( ord_less_eq @ ( set @ A ) @ A5 @ B5 )
% 4.04/1.92 => ~ ( ord_less_eq @ ( set @ A ) @ B5 @ A5 ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_169_subset__eq,axiom,
% 4.04/1.92 ! [A: $tType] :
% 4.04/1.92 ( ( ord_less_eq @ ( set @ A ) )
% 4.04/1.92 = ( ^ [A7: set @ A,B7: set @ A] :
% 4.04/1.92 ! [X6: A] :
% 4.04/1.92 ( ( member @ A @ X6 @ A7 )
% 4.04/1.92 => ( member @ A @ X6 @ B7 ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_170_equalityD1,axiom,
% 4.04/1.92 ! [A: $tType,A5: set @ A,B5: set @ A] :
% 4.04/1.92 ( ( A5 = B5 )
% 4.04/1.92 => ( ord_less_eq @ ( set @ A ) @ A5 @ B5 ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_171_equalityD2,axiom,
% 4.04/1.92 ! [A: $tType,A5: set @ A,B5: set @ A] :
% 4.04/1.92 ( ( A5 = B5 )
% 4.04/1.92 => ( ord_less_eq @ ( set @ A ) @ B5 @ A5 ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_172_subset__iff,axiom,
% 4.04/1.92 ! [A: $tType] :
% 4.04/1.92 ( ( ord_less_eq @ ( set @ A ) )
% 4.04/1.92 = ( ^ [A7: set @ A,B7: set @ A] :
% 4.04/1.92 ! [T2: A] :
% 4.04/1.92 ( ( member @ A @ T2 @ A7 )
% 4.04/1.92 => ( member @ A @ T2 @ B7 ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_173_subset__refl,axiom,
% 4.04/1.92 ! [A: $tType,A5: set @ A] : ( ord_less_eq @ ( set @ A ) @ A5 @ A5 ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_174_Collect__mono,axiom,
% 4.04/1.92 ! [A: $tType,P2: A > $o,Q: A > $o] :
% 4.04/1.92 ( ! [X5: A] :
% 4.04/1.92 ( ( P2 @ X5 )
% 4.04/1.92 => ( Q @ X5 ) )
% 4.04/1.92 => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P2 ) @ ( collect @ A @ Q ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_175_subset__trans,axiom,
% 4.04/1.92 ! [A: $tType,A5: set @ A,B5: set @ A,C4: set @ A] :
% 4.04/1.92 ( ( ord_less_eq @ ( set @ A ) @ A5 @ B5 )
% 4.04/1.92 => ( ( ord_less_eq @ ( set @ A ) @ B5 @ C4 )
% 4.04/1.92 => ( ord_less_eq @ ( set @ A ) @ A5 @ C4 ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_176_set__eq__subset,axiom,
% 4.04/1.92 ! [A: $tType] :
% 4.04/1.92 ( ( ^ [Y6: set @ A,Z: set @ A] : ( Y6 = Z ) )
% 4.04/1.92 = ( ^ [A7: set @ A,B7: set @ A] :
% 4.04/1.92 ( ( ord_less_eq @ ( set @ A ) @ A7 @ B7 )
% 4.04/1.92 & ( ord_less_eq @ ( set @ A ) @ B7 @ A7 ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_177_Collect__mono__iff,axiom,
% 4.04/1.92 ! [A: $tType,P2: A > $o,Q: A > $o] :
% 4.04/1.92 ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P2 ) @ ( collect @ A @ Q ) )
% 4.04/1.92 = ( ! [X6: A] :
% 4.04/1.92 ( ( P2 @ X6 )
% 4.04/1.92 => ( Q @ X6 ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_178_alphaRes,axiom,
% 4.04/1.92 ! [C2: name,P2: pi,A2: name] :
% 4.04/1.92 ( ( fresh @ name @ pi @ C2 @ P2 )
% 4.04/1.92 => ( ( res @ A2 @ P2 )
% 4.04/1.92 = ( res @ C2 @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ C2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ P2 ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_179_calculation,axiom,
% 4.04/1.92 late_transitions @ ( res @ x @ ( sum @ p @ q ) ) @ ( late_BoundR @ ( late_BoundOutputS @ aa ) @ y @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ y @ x ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ p2 ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_180_Bound_Ohyps_I1_J,axiom,
% 4.04/1.92 late_transitions @ ( sum @ ( res @ x @ p ) @ ( res @ x @ q ) ) @ ( late_BoundR @ a @ y @ pq ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_181__092_060open_062_060_092_060nu_062x_062_IP_A_092_060oplus_062_AQ_J_A_092_060longmapsto_062_Aa_060_092_060nu_062x_062_A_092_060prec_062_AP_H_092_060close_062,axiom,
% 4.04/1.92 late_transitions @ ( res @ x @ ( sum @ p @ q ) ) @ ( late_BoundR @ ( late_BoundOutputS @ aa ) @ x @ p2 ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_182_sumResLeft,axiom,
% 4.04/1.92 ! [Rel: set @ ( product_prod @ pi @ pi ),X3: name,P2: pi,Q: pi] :
% 4.04/1.92 ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 4.04/1.92 => ( ( eqvt @ pi @ Rel )
% 4.04/1.92 => ( strong743114133lation @ ( sum @ ( res @ X3 @ P2 ) @ ( res @ X3 @ Q ) ) @ Rel @ ( res @ X3 @ ( sum @ P2 @ Q ) ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_183_cSum1_Ohyps,axiom,
% 4.04/1.92 late_transitions @ ( res @ x @ p ) @ ( late_BoundR @ a @ y @ pq ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_184_residual_Operm_I1_J,axiom,
% 4.04/1.92 ! [Pi: list @ ( product_prod @ name @ name ),X32: late_subject,X1: name,X22: pi] :
% 4.04/1.92 ( ( perm @ name @ late_residual @ Pi @ ( late_BoundR @ X32 @ X1 @ X22 ) )
% 4.04/1.92 = ( late_BoundR @ ( perm @ name @ late_subject @ Pi @ X32 ) @ ( perm @ name @ name @ Pi @ X1 ) @ ( perm @ name @ pi @ Pi @ X22 ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_185_freshBoundDerivative_I1_J,axiom,
% 4.04/1.92 ! [P2: pi,A2: late_subject,X3: name,P4: pi,Y4: name] :
% 4.04/1.92 ( ( late_transitions @ P2 @ ( late_BoundR @ A2 @ X3 @ P4 ) )
% 4.04/1.92 => ( ( fresh @ name @ pi @ Y4 @ P2 )
% 4.04/1.92 => ( fresh @ name @ late_subject @ Y4 @ A2 ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_186_Late__Semantics_OResB,axiom,
% 4.04/1.92 ! [P2: pi,A2: late_subject,X3: name,P4: pi,Y4: name] :
% 4.04/1.92 ( ( late_transitions @ P2 @ ( late_BoundR @ A2 @ X3 @ P4 ) )
% 4.04/1.92 => ( ( fresh @ name @ late_subject @ Y4 @ A2 )
% 4.04/1.92 => ( ( Y4 != X3 )
% 4.04/1.92 => ( late_transitions @ ( res @ Y4 @ P2 ) @ ( late_BoundR @ A2 @ X3 @ ( res @ Y4 @ P4 ) ) ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_187_freshBoundDerivative_I2_J,axiom,
% 4.04/1.92 ! [P2: pi,A2: late_subject,X3: name,P4: pi,Y4: name] :
% 4.04/1.92 ( ( late_transitions @ P2 @ ( late_BoundR @ A2 @ X3 @ P4 ) )
% 4.04/1.92 => ( ( fresh @ name @ pi @ Y4 @ P2 )
% 4.04/1.92 => ( ( Y4 != X3 )
% 4.04/1.92 => ( fresh @ name @ pi @ Y4 @ P4 ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_188_simE_I1_J,axiom,
% 4.04/1.92 ! [P2: pi,Rel: set @ ( product_prod @ pi @ pi ),Q: pi,A2: late_subject,X3: name,Q2: pi] :
% 4.04/1.92 ( ( strong743114133lation @ P2 @ Rel @ Q )
% 4.04/1.92 => ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X3 @ Q2 ) )
% 4.04/1.92 => ( ( fresh @ name @ pi @ X3 @ P2 )
% 4.04/1.92 => ? [P5: pi] :
% 4.04/1.92 ( ( late_transitions @ P2 @ ( late_BoundR @ A2 @ X3 @ P5 ) )
% 4.04/1.92 & ( strong2129052853vative @ P5 @ Q2 @ A2 @ X3 @ Rel ) ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_189_Sum2,axiom,
% 4.04/1.92 ! [Q: pi,Rs: late_residual,P2: pi] :
% 4.04/1.92 ( ( late_transitions @ Q @ Rs )
% 4.04/1.92 => ( late_transitions @ ( sum @ P2 @ Q ) @ Rs ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_190_Sum1,axiom,
% 4.04/1.92 ! [P2: pi,Rs: late_residual,Q: pi] :
% 4.04/1.92 ( ( late_transitions @ P2 @ Rs )
% 4.04/1.92 => ( late_transitions @ ( sum @ P2 @ Q ) @ Rs ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_191_sumCases_H,axiom,
% 4.04/1.92 ! [P2: pi,Q: pi,Rs: late_residual] :
% 4.04/1.92 ( ( late_transitions @ ( sum @ P2 @ Q ) @ Rs )
% 4.04/1.92 => ( ~ ( late_transitions @ P2 @ Rs )
% 4.04/1.92 => ( late_transitions @ Q @ Rs ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_192_sumCases,axiom,
% 4.04/1.92 ! [P2: pi,Q: pi,Rs: late_residual] :
% 4.04/1.92 ( ( late_transitions @ ( sum @ P2 @ Q ) @ Rs )
% 4.04/1.92 => ( ~ ( late_transitions @ P2 @ Rs )
% 4.04/1.92 => ( late_transitions @ Q @ Rs ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_193_freshResidual,axiom,
% 4.04/1.92 ! [P2: pi,Rs: late_residual,X3: name] :
% 4.04/1.92 ( ( late_transitions @ P2 @ Rs )
% 4.04/1.92 => ( ( fresh @ name @ pi @ X3 @ P2 )
% 4.04/1.92 => ( fresh @ name @ late_residual @ X3 @ Rs ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_194_eqvt,axiom,
% 4.04/1.92 ! [X1: pi,X22: late_residual,Pi: list @ ( product_prod @ name @ name )] :
% 4.04/1.92 ( ( late_transitions @ X1 @ X22 )
% 4.04/1.92 => ( late_transitions @ ( perm @ name @ pi @ Pi @ X1 ) @ ( perm @ name @ late_residual @ Pi @ X22 ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_195_transitions_OResB,axiom,
% 4.04/1.92 ! [P2: pi,A2: late_subject,X3: name,P4: pi,Y4: name] :
% 4.04/1.92 ( ( late_transitions @ P2 @ ( late_BoundR @ A2 @ X3 @ P4 ) )
% 4.04/1.92 => ( ( fresh @ name @ late_subject @ Y4 @ A2 )
% 4.04/1.92 => ( ( Y4 != X3 )
% 4.04/1.92 => ( ( fresh @ name @ pi @ X3 @ P2 )
% 4.04/1.92 => ( ( fresh @ name @ late_subject @ X3 @ A2 )
% 4.04/1.92 => ( late_transitions @ ( res @ Y4 @ P2 ) @ ( late_BoundR @ A2 @ X3 @ ( res @ Y4 @ P4 ) ) ) ) ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_196_monotonic,axiom,
% 4.04/1.92 ! [P2: pi,A5: set @ ( product_prod @ pi @ pi ),P4: pi,B5: set @ ( product_prod @ pi @ pi )] :
% 4.04/1.92 ( ( strong743114133lation @ P2 @ A5 @ P4 )
% 4.04/1.92 => ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ A5 @ B5 )
% 4.04/1.92 => ( strong743114133lation @ P2 @ B5 @ P4 ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_197_Strong__Late__Sim_Oreflexive,axiom,
% 4.04/1.92 ! [Rel: set @ ( product_prod @ pi @ pi ),P2: pi] :
% 4.04/1.92 ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 4.04/1.92 => ( strong743114133lation @ P2 @ Rel @ P2 ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_198_sumIdempRight,axiom,
% 4.04/1.92 ! [Rel: set @ ( product_prod @ pi @ pi ),P2: pi] :
% 4.04/1.92 ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 4.04/1.92 => ( strong743114133lation @ ( sum @ P2 @ P2 ) @ Rel @ P2 ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_199_sumAssocRight,axiom,
% 4.04/1.92 ! [Rel: set @ ( product_prod @ pi @ pi ),P2: pi,Q: pi,R2: pi] :
% 4.04/1.92 ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 4.04/1.92 => ( strong743114133lation @ ( sum @ P2 @ ( sum @ Q @ R2 ) ) @ Rel @ ( sum @ ( sum @ P2 @ Q ) @ R2 ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_200_sumIdempLeft,axiom,
% 4.04/1.92 ! [Rel: set @ ( product_prod @ pi @ pi ),P2: pi] :
% 4.04/1.92 ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 4.04/1.92 => ( strong743114133lation @ P2 @ Rel @ ( sum @ P2 @ P2 ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_201_sumAssocLeft,axiom,
% 4.04/1.92 ! [Rel: set @ ( product_prod @ pi @ pi ),P2: pi,Q: pi,R2: pi] :
% 4.04/1.92 ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 4.04/1.92 => ( strong743114133lation @ ( sum @ ( sum @ P2 @ Q ) @ R2 ) @ Rel @ ( sum @ P2 @ ( sum @ Q @ R2 ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_202_sumSym,axiom,
% 4.04/1.92 ! [Rel: set @ ( product_prod @ pi @ pi ),P2: pi,Q: pi] :
% 4.04/1.92 ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 4.04/1.92 => ( strong743114133lation @ ( sum @ P2 @ Q ) @ Rel @ ( sum @ Q @ P2 ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_203_eqvtI,axiom,
% 4.04/1.92 ! [P2: pi,Rel: set @ ( product_prod @ pi @ pi ),Q: pi,Rel3: set @ ( product_prod @ pi @ pi ),Perm: list @ ( product_prod @ name @ name )] :
% 4.04/1.92 ( ( strong743114133lation @ P2 @ Rel @ Q )
% 4.04/1.92 => ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ Rel @ Rel3 )
% 4.04/1.92 => ( ( eqvt @ pi @ Rel3 )
% 4.04/1.92 => ( strong743114133lation @ ( perm @ name @ pi @ Perm @ P2 ) @ Rel3 @ ( perm @ name @ pi @ Perm @ Q ) ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_204_alphaBoundResidual,axiom,
% 4.04/1.92 ! [X7: name,P2: pi,A2: late_subject,X3: name] :
% 4.04/1.92 ( ( fresh @ name @ pi @ X7 @ P2 )
% 4.04/1.92 => ( ( late_BoundR @ A2 @ X3 @ P2 )
% 4.04/1.92 = ( late_BoundR @ A2 @ X7 @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ X3 @ X7 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ P2 ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_205_cOpen_Ohyps_I1_J,axiom,
% 4.04/1.92 late_transitions @ p @ ( late_FreeR @ ( late_OutputR @ aa @ x ) @ p2 ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_206_simCasesCont,axiom,
% 4.04/1.92 ! [A: $tType] :
% 4.04/1.92 ( ( fs_name @ A )
% 4.04/1.92 => ! [Rel: set @ ( product_prod @ pi @ pi ),Q: pi,P2: pi,C4: A] :
% 4.04/1.92 ( ( eqvt @ pi @ Rel )
% 4.04/1.92 => ( ! [A4: late_subject,X5: name,Q3: pi] :
% 4.04/1.92 ( ( late_transitions @ Q @ ( late_BoundR @ A4 @ X5 @ Q3 ) )
% 4.04/1.92 => ( ( fresh @ name @ pi @ X5 @ P2 )
% 4.04/1.92 => ( ( fresh @ name @ pi @ X5 @ Q )
% 4.04/1.92 => ( ( fresh @ name @ late_subject @ X5 @ A4 )
% 4.04/1.92 => ( ( fresh @ name @ A @ X5 @ C4 )
% 4.04/1.92 => ? [P6: pi] :
% 4.04/1.92 ( ( late_transitions @ P2 @ ( late_BoundR @ A4 @ X5 @ P6 ) )
% 4.04/1.92 & ( strong2129052853vative @ P6 @ Q3 @ A4 @ X5 @ Rel ) ) ) ) ) ) )
% 4.04/1.92 => ( ! [Alpha: late_freeRes,Q3: pi] :
% 4.04/1.92 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q3 ) )
% 4.04/1.92 => ? [P6: pi] :
% 4.04/1.92 ( ( late_transitions @ P2 @ ( late_FreeR @ Alpha @ P6 ) )
% 4.04/1.92 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P6 @ Q3 ) @ Rel ) ) )
% 4.04/1.92 => ( strong743114133lation @ P2 @ Rel @ Q ) ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_207__092_060open_062P_A_092_060oplus_062_AQ_A_092_060longmapsto_062_Aa_091x_093_A_092_060prec_062_AP_H_092_060close_062,axiom,
% 4.04/1.92 late_transitions @ ( sum @ p @ q ) @ ( late_FreeR @ ( late_OutputR @ aa @ x ) @ p2 ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_208_Late__Semantics1_OfreeRes_Oinject,axiom,
% 4.04/1.92 ! [X11: name,X122: name,Y11: name,Y12: name] :
% 4.04/1.92 ( ( ( late_OutputR @ X11 @ X122 )
% 4.04/1.92 = ( late_OutputR @ Y11 @ Y12 ) )
% 4.04/1.92 = ( ( X11 = Y11 )
% 4.04/1.92 & ( X122 = Y12 ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_209_Late__Semantics_OfreeRes_Oinject,axiom,
% 4.04/1.92 ! [X22: name,X1: name,Y2: name,Y1: name] :
% 4.04/1.92 ( ( ( late_OutputR @ X22 @ X1 )
% 4.04/1.92 = ( late_OutputR @ Y2 @ Y1 ) )
% 4.04/1.92 = ( ( X22 = Y2 )
% 4.04/1.92 & ( X1 = Y1 ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_210_freeRes_Operm_I1_J,axiom,
% 4.04/1.92 ! [Pi: list @ ( product_prod @ name @ name ),X22: name,X1: name] :
% 4.04/1.92 ( ( perm @ name @ late_freeRes @ Pi @ ( late_OutputR @ X22 @ X1 ) )
% 4.04/1.92 = ( late_OutputR @ ( perm @ name @ name @ Pi @ X22 ) @ ( perm @ name @ name @ Pi @ X1 ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_211_freeRes_Ofresh_I1_J,axiom,
% 4.04/1.92 ! [A2: name,X22: name,X1: name] :
% 4.04/1.92 ( ( fresh @ name @ late_freeRes @ A2 @ ( late_OutputR @ X22 @ X1 ) )
% 4.04/1.92 = ( ( fresh @ name @ name @ A2 @ X22 )
% 4.04/1.92 & ( fresh @ name @ name @ A2 @ X1 ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_212_residual_Operm_I2_J,axiom,
% 4.04/1.92 ! [Pi: list @ ( product_prod @ name @ name ),X22: late_freeRes,X1: pi] :
% 4.04/1.92 ( ( perm @ name @ late_residual @ Pi @ ( late_FreeR @ X22 @ X1 ) )
% 4.04/1.92 = ( late_FreeR @ ( perm @ name @ late_freeRes @ Pi @ X22 ) @ ( perm @ name @ pi @ Pi @ X1 ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_213_residual_Ofresh_I2_J,axiom,
% 4.04/1.92 ! [A2: name,X22: late_freeRes,X1: pi] :
% 4.04/1.92 ( ( fresh @ name @ late_residual @ A2 @ ( late_FreeR @ X22 @ X1 ) )
% 4.04/1.92 = ( ( fresh @ name @ late_freeRes @ A2 @ X22 )
% 4.04/1.92 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_214_residual_Odistinct_I1_J,axiom,
% 4.04/1.92 ! [Subject: late_subject,Name2: name,Pi: pi,FreeRes: late_freeRes,Pi4: pi] :
% 4.04/1.92 ( ( late_BoundR @ Subject @ Name2 @ Pi )
% 4.04/1.92 != ( late_FreeR @ FreeRes @ Pi4 ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_215_residual_Oinducts,axiom,
% 4.04/1.92 ! [P2: late_residual > $o,Residual: late_residual] :
% 4.04/1.92 ( ! [Subject2: late_subject,Name3: name,Pi5: pi] : ( P2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi5 ) )
% 4.04/1.92 => ( ! [FreeRes2: late_freeRes,Pi5: pi] : ( P2 @ ( late_FreeR @ FreeRes2 @ Pi5 ) )
% 4.04/1.92 => ( P2 @ Residual ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_216_residual_Oinject_I2_J,axiom,
% 4.04/1.92 ! [X22: late_freeRes,X1: pi,Y2: late_freeRes,Y1: pi] :
% 4.04/1.92 ( ( ( late_FreeR @ X22 @ X1 )
% 4.04/1.92 = ( late_FreeR @ Y2 @ Y1 ) )
% 4.04/1.92 = ( ( X22 = Y2 )
% 4.04/1.92 & ( X1 = Y1 ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_217_ResF,axiom,
% 4.04/1.92 ! [P2: pi,Alpha2: late_freeRes,P4: pi,Y4: name] :
% 4.04/1.92 ( ( late_transitions @ P2 @ ( late_FreeR @ Alpha2 @ P4 ) )
% 4.04/1.92 => ( ( fresh @ name @ late_freeRes @ Y4 @ Alpha2 )
% 4.04/1.92 => ( late_transitions @ ( res @ Y4 @ P2 ) @ ( late_FreeR @ Alpha2 @ ( res @ Y4 @ P4 ) ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_218_resCasesF_H,axiom,
% 4.04/1.92 ! [X3: name,P2: pi,Alpha2: late_freeRes,P4: pi] :
% 4.04/1.92 ( ( late_transitions @ ( res @ X3 @ P2 ) @ ( late_FreeR @ Alpha2 @ P4 ) )
% 4.04/1.92 => ~ ! [P: pi,Alpha: late_freeRes,P5: pi,Y3: name] :
% 4.04/1.92 ( ( ( res @ X3 @ P2 )
% 4.04/1.92 = ( res @ Y3 @ P ) )
% 4.04/1.92 => ( ( ( late_FreeR @ Alpha2 @ P4 )
% 4.04/1.92 = ( late_FreeR @ Alpha @ ( res @ Y3 @ P5 ) ) )
% 4.04/1.92 => ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P5 ) )
% 4.04/1.92 => ~ ( fresh @ name @ late_freeRes @ Y3 @ Alpha ) ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_219_resCasesF,axiom,
% 4.04/1.92 ! [X3: name,P2: pi,Alpha2: late_freeRes,XP: pi,F5: pi > $o] :
% 4.04/1.92 ( ( late_transitions @ ( res @ X3 @ P2 ) @ ( late_FreeR @ Alpha2 @ XP ) )
% 4.04/1.92 => ( ! [P5: pi] :
% 4.04/1.92 ( ( late_transitions @ P2 @ ( late_FreeR @ Alpha2 @ P5 ) )
% 4.04/1.92 => ( ( fresh @ name @ late_freeRes @ X3 @ Alpha2 )
% 4.04/1.92 => ( F5 @ ( res @ X3 @ P5 ) ) ) )
% 4.04/1.92 => ( F5 @ XP ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_220_freshFreeDerivative_I2_J,axiom,
% 4.04/1.92 ! [P2: pi,Alpha2: late_freeRes,P4: pi,Y4: name] :
% 4.04/1.92 ( ( late_transitions @ P2 @ ( late_FreeR @ Alpha2 @ P4 ) )
% 4.04/1.92 => ( ( fresh @ name @ pi @ Y4 @ P2 )
% 4.04/1.92 => ( fresh @ name @ pi @ Y4 @ P4 ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_221_freshFreeDerivative_I1_J,axiom,
% 4.04/1.92 ! [P2: pi,Alpha2: late_freeRes,P4: pi,Y4: name] :
% 4.04/1.92 ( ( late_transitions @ P2 @ ( late_FreeR @ Alpha2 @ P4 ) )
% 4.04/1.92 => ( ( fresh @ name @ pi @ Y4 @ P2 )
% 4.04/1.92 => ( fresh @ name @ late_freeRes @ Y4 @ Alpha2 ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_222_Open,axiom,
% 4.04/1.92 ! [P2: pi,A2: name,B2: name,P4: pi] :
% 4.04/1.92 ( ( late_transitions @ P2 @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P4 ) )
% 4.04/1.92 => ( ( A2 != B2 )
% 4.04/1.92 => ( late_transitions @ ( res @ B2 @ P2 ) @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ B2 @ P4 ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_223_residual_Ostrong__inducts,axiom,
% 4.04/1.92 ! [A: $tType] :
% 4.04/1.92 ( ( fs_name @ A )
% 4.04/1.92 => ! [P2: A > late_residual > $o,Z2: A,Residual: late_residual] :
% 4.04/1.92 ( ! [Subject2: late_subject,Name3: name,Pi5: pi,Z3: A] :
% 4.04/1.92 ( ( fresh @ name @ A @ Name3 @ Z3 )
% 4.04/1.92 => ( ( fresh @ name @ late_subject @ Name3 @ Subject2 )
% 4.04/1.92 => ( P2 @ Z3 @ ( late_BoundR @ Subject2 @ Name3 @ Pi5 ) ) ) )
% 4.04/1.92 => ( ! [FreeRes2: late_freeRes,Pi5: pi,Z3: A] : ( P2 @ Z3 @ ( late_FreeR @ FreeRes2 @ Pi5 ) )
% 4.04/1.92 => ( P2 @ Z2 @ Residual ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_224_residual_Ostrong__induct,axiom,
% 4.04/1.92 ! [N: $tType] :
% 4.04/1.92 ( ( fs_name @ N )
% 4.04/1.92 => ! [P2: N > late_residual > $o,Z2: N,Residual: late_residual] :
% 4.04/1.92 ( ! [Subject2: late_subject,Name3: name,Pi5: pi,Z3: N] :
% 4.04/1.92 ( ( fresh @ name @ N @ Name3 @ Z3 )
% 4.04/1.92 => ( ( fresh @ name @ late_subject @ Name3 @ Subject2 )
% 4.04/1.92 => ( P2 @ Z3 @ ( late_BoundR @ Subject2 @ Name3 @ Pi5 ) ) ) )
% 4.04/1.92 => ( ! [FreeRes2: late_freeRes,Pi5: pi,Z3: N] : ( P2 @ Z3 @ ( late_FreeR @ FreeRes2 @ Pi5 ) )
% 4.04/1.92 => ( P2 @ Z2 @ Residual ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_225_simE_I2_J,axiom,
% 4.04/1.92 ! [P2: pi,Rel: set @ ( product_prod @ pi @ pi ),Q: pi,Alpha2: late_freeRes,Q2: pi] :
% 4.04/1.92 ( ( strong743114133lation @ P2 @ Rel @ Q )
% 4.04/1.92 => ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q2 ) )
% 4.04/1.92 => ? [P5: pi] :
% 4.04/1.92 ( ( late_transitions @ P2 @ ( late_FreeR @ Alpha2 @ P5 ) )
% 4.04/1.92 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P5 @ Q2 ) @ Rel ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_226_resCasesB_H,axiom,
% 4.04/1.92 ! [X7: name,P2: pi,A2: late_subject,Y7: name,P4: pi] :
% 4.04/1.92 ( ( late_transitions @ ( res @ X7 @ P2 ) @ ( late_BoundR @ A2 @ Y7 @ P4 ) )
% 4.04/1.92 => ( ! [P: pi,A4: name,B4: name] :
% 4.04/1.92 ( ( ( res @ X7 @ P2 )
% 4.04/1.92 = ( res @ B4 @ P ) )
% 4.04/1.92 => ! [P5: pi] :
% 4.04/1.92 ( ( ( late_BoundR @ A2 @ Y7 @ P4 )
% 4.04/1.92 = ( late_BoundR @ ( late_BoundOutputS @ A4 ) @ B4 @ P5 ) )
% 4.04/1.92 => ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A4 @ B4 ) @ P5 ) )
% 4.04/1.92 => ( A4 = B4 ) ) ) )
% 4.04/1.92 => ~ ! [P: pi,A4: late_subject,X5: name,P5: pi,Y3: name] :
% 4.04/1.92 ( ( ( res @ X7 @ P2 )
% 4.04/1.92 = ( res @ Y3 @ P ) )
% 4.04/1.92 => ( ( ( late_BoundR @ A2 @ Y7 @ P4 )
% 4.04/1.92 = ( late_BoundR @ A4 @ X5 @ ( res @ Y3 @ P5 ) ) )
% 4.04/1.92 => ( ( late_transitions @ P @ ( late_BoundR @ A4 @ X5 @ P5 ) )
% 4.04/1.92 => ( ( fresh @ name @ late_subject @ Y3 @ A4 )
% 4.04/1.92 => ( ( Y3 != X5 )
% 4.04/1.92 => ( ( fresh @ name @ pi @ X5 @ P )
% 4.04/1.92 => ~ ( fresh @ name @ late_subject @ X5 @ A4 ) ) ) ) ) ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_227_resCases_H,axiom,
% 4.04/1.92 ! [X3: name,P2: pi,Rs: late_residual] :
% 4.04/1.92 ( ( late_transitions @ ( res @ X3 @ P2 ) @ Rs )
% 4.04/1.92 => ( ! [P: pi,A4: name,B4: name] :
% 4.04/1.92 ( ( ( res @ X3 @ P2 )
% 4.04/1.92 = ( res @ B4 @ P ) )
% 4.04/1.92 => ! [P5: pi] :
% 4.04/1.92 ( ( Rs
% 4.04/1.92 = ( late_BoundR @ ( late_BoundOutputS @ A4 ) @ B4 @ P5 ) )
% 4.04/1.92 => ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A4 @ B4 ) @ P5 ) )
% 4.04/1.92 => ( A4 = B4 ) ) ) )
% 4.04/1.92 => ( ! [P: pi,A4: late_subject,X5: name,P5: pi,Y3: name] :
% 4.04/1.92 ( ( ( res @ X3 @ P2 )
% 4.04/1.92 = ( res @ Y3 @ P ) )
% 4.04/1.92 => ( ( Rs
% 4.04/1.92 = ( late_BoundR @ A4 @ X5 @ ( res @ Y3 @ P5 ) ) )
% 4.04/1.92 => ( ( late_transitions @ P @ ( late_BoundR @ A4 @ X5 @ P5 ) )
% 4.04/1.92 => ( ( fresh @ name @ late_subject @ Y3 @ A4 )
% 4.04/1.92 => ( ( Y3 != X5 )
% 4.04/1.92 => ( ( fresh @ name @ pi @ X5 @ P )
% 4.04/1.92 => ~ ( fresh @ name @ late_subject @ X5 @ A4 ) ) ) ) ) ) )
% 4.04/1.92 => ~ ! [P: pi,Alpha: late_freeRes,P5: pi,Y3: name] :
% 4.04/1.92 ( ( ( res @ X3 @ P2 )
% 4.04/1.92 = ( res @ Y3 @ P ) )
% 4.04/1.92 => ( ( Rs
% 4.04/1.92 = ( late_FreeR @ Alpha @ ( res @ Y3 @ P5 ) ) )
% 4.04/1.92 => ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P5 ) )
% 4.04/1.92 => ~ ( fresh @ name @ late_freeRes @ Y3 @ Alpha ) ) ) ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_228_resCasesB,axiom,
% 4.04/1.92 ! [Y4: name,P2: pi,A2: late_subject,X3: name,YP: pi,F5: late_subject > pi > $o] :
% 4.04/1.92 ( ( late_transitions @ ( res @ Y4 @ P2 ) @ ( late_BoundR @ A2 @ X3 @ YP ) )
% 4.04/1.92 => ( ( X3 != Y4 )
% 4.04/1.92 => ( ( fresh @ name @ pi @ X3 @ P2 )
% 4.04/1.92 => ( ! [B4: name,P5: pi] :
% 4.04/1.92 ( ( late_transitions @ P2 @ ( late_FreeR @ ( late_OutputR @ B4 @ Y4 ) @ P5 ) )
% 4.04/1.92 => ( ( B4 != Y4 )
% 4.04/1.92 => ( ( A2
% 4.04/1.92 = ( late_BoundOutputS @ B4 ) )
% 4.04/1.92 => ( F5 @ ( late_BoundOutputS @ B4 ) @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ X3 @ Y4 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ P5 ) ) ) ) )
% 4.04/1.92 => ( ! [P5: pi] :
% 4.04/1.92 ( ( late_transitions @ P2 @ ( late_BoundR @ A2 @ X3 @ P5 ) )
% 4.04/1.92 => ( ( fresh @ name @ late_subject @ Y4 @ A2 )
% 4.04/1.92 => ( F5 @ A2 @ ( res @ Y4 @ P5 ) ) ) )
% 4.04/1.92 => ( F5 @ A2 @ YP ) ) ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_229_resSimCases,axiom,
% 4.04/1.92 ! [A: $tType] :
% 4.04/1.92 ( ( fs_name @ A )
% 4.04/1.92 => ! [Rel: set @ ( product_prod @ pi @ pi ),Q: pi,X3: name,P2: pi,C4: A] :
% 4.04/1.92 ( ( eqvt @ pi @ Rel )
% 4.04/1.92 => ( ! [Q3: pi,A4: name] :
% 4.04/1.92 ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A4 @ X3 ) @ Q3 ) )
% 4.04/1.92 => ( ( A4 != X3 )
% 4.04/1.92 => ? [P6: pi] :
% 4.04/1.92 ( ( late_transitions @ P2 @ ( late_BoundR @ ( late_BoundOutputS @ A4 ) @ X3 @ P6 ) )
% 4.04/1.92 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P6 @ Q3 ) @ Rel ) ) ) )
% 4.04/1.92 => ( ! [Q3: pi,A4: late_subject,Y3: name] :
% 4.04/1.92 ( ( late_transitions @ Q @ ( late_BoundR @ A4 @ Y3 @ Q3 ) )
% 4.04/1.92 => ( ( fresh @ name @ late_subject @ X3 @ A4 )
% 4.04/1.92 => ( ( X3 != Y3 )
% 4.04/1.92 => ( ( fresh @ name @ A @ Y3 @ C4 )
% 4.04/1.92 => ? [P6: pi] :
% 4.04/1.92 ( ( late_transitions @ P2 @ ( late_BoundR @ A4 @ Y3 @ P6 ) )
% 4.04/1.92 & ( strong2129052853vative @ P6 @ ( res @ X3 @ Q3 ) @ A4 @ Y3 @ Rel ) ) ) ) ) )
% 4.04/1.92 => ( ! [Q3: pi,Alpha: late_freeRes] :
% 4.04/1.92 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q3 ) )
% 4.04/1.92 => ( ( fresh @ name @ late_freeRes @ X3 @ Alpha )
% 4.04/1.92 => ? [P6: pi] :
% 4.04/1.92 ( ( late_transitions @ P2 @ ( late_FreeR @ Alpha @ P6 ) )
% 4.04/1.92 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P6 @ ( res @ X3 @ Q3 ) ) @ Rel ) ) ) )
% 4.04/1.92 => ( strong743114133lation @ P2 @ Rel @ ( res @ X3 @ Q ) ) ) ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_230_simulation__def,axiom,
% 4.04/1.92 ( strong743114133lation
% 4.04/1.92 = ( ^ [P7: pi,Rel2: set @ ( product_prod @ pi @ pi ),Q4: pi] :
% 4.04/1.92 ( ! [A6: late_subject,X6: name,Q5: pi] :
% 4.04/1.92 ( ( ( late_transitions @ Q4 @ ( late_BoundR @ A6 @ X6 @ Q5 ) )
% 4.04/1.92 & ( fresh @ name @ pi @ X6 @ P7 ) )
% 4.04/1.92 => ? [P8: pi] :
% 4.04/1.92 ( ( late_transitions @ P7 @ ( late_BoundR @ A6 @ X6 @ P8 ) )
% 4.04/1.92 & ( strong2129052853vative @ P8 @ Q5 @ A6 @ X6 @ Rel2 ) ) )
% 4.04/1.92 & ! [Alpha3: late_freeRes,Q5: pi] :
% 4.04/1.92 ( ( late_transitions @ Q4 @ ( late_FreeR @ Alpha3 @ Q5 ) )
% 4.04/1.92 => ? [P8: pi] :
% 4.04/1.92 ( ( late_transitions @ P7 @ ( late_FreeR @ Alpha3 @ P8 ) )
% 4.04/1.92 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P8 @ Q5 ) @ Rel2 ) ) ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_231_simCases,axiom,
% 4.04/1.92 ! [Q: pi,P2: pi,Rel: set @ ( product_prod @ pi @ pi )] :
% 4.04/1.92 ( ! [A4: late_subject,Y3: name,Q3: pi] :
% 4.04/1.92 ( ( late_transitions @ Q @ ( late_BoundR @ A4 @ Y3 @ Q3 ) )
% 4.04/1.92 => ( ( fresh @ name @ pi @ Y3 @ P2 )
% 4.04/1.92 => ? [P6: pi] :
% 4.04/1.92 ( ( late_transitions @ P2 @ ( late_BoundR @ A4 @ Y3 @ P6 ) )
% 4.04/1.92 & ( strong2129052853vative @ P6 @ Q3 @ A4 @ Y3 @ Rel ) ) ) )
% 4.04/1.92 => ( ! [Alpha: late_freeRes,Q3: pi] :
% 4.04/1.92 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q3 ) )
% 4.04/1.92 => ? [P6: pi] :
% 4.04/1.92 ( ( late_transitions @ P2 @ ( late_FreeR @ Alpha @ P6 ) )
% 4.04/1.92 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P6 @ Q3 ) @ Rel ) ) )
% 4.04/1.92 => ( strong743114133lation @ P2 @ Rel @ Q ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_232_supports__def,axiom,
% 4.04/1.92 ! [A: $tType,X: $tType] :
% 4.04/1.92 ( ( supports @ X @ A )
% 4.04/1.92 = ( ^ [S2: set @ X,X6: A] :
% 4.04/1.92 ! [A6: X,B6: X] :
% 4.04/1.92 ( ( ~ ( member @ X @ A6 @ S2 )
% 4.04/1.92 & ~ ( member @ X @ B6 @ S2 ) )
% 4.04/1.92 => ( ( perm @ X @ A @ ( cons @ ( product_prod @ X @ X ) @ ( product_Pair @ X @ X @ A6 @ B6 ) @ ( nil @ ( product_prod @ X @ X ) ) ) @ X6 )
% 4.04/1.92 = X6 ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_233_IdD,axiom,
% 4.04/1.92 ! [A: $tType,A2: A,B2: A] :
% 4.04/1.92 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ ( id @ A ) )
% 4.04/1.92 => ( A2 = B2 ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_234_supports__subset,axiom,
% 4.04/1.92 ! [X: $tType,A: $tType,S1: set @ X,X3: A,S22: set @ X] :
% 4.04/1.92 ( ( supports @ X @ A @ S1 @ X3 )
% 4.04/1.92 => ( ( ord_less_eq @ ( set @ X ) @ S1 @ S22 )
% 4.04/1.92 => ( supports @ X @ A @ S22 @ X3 ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_235_shift__def,axiom,
% 4.04/1.92 ! [B: $tType,A: $tType] :
% 4.04/1.92 ( ( bNF_Greatest_shift @ A @ B )
% 4.04/1.92 = ( ^ [Lab: ( list @ A ) > B,K: A,Kl: list @ A] : ( Lab @ ( cons @ A @ K @ Kl ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_236_perm__residual__Rep_Osimps_I2_J,axiom,
% 4.04/1.92 ! [X: $tType,Pi: list @ ( product_prod @ X @ X ),FreeRes3: late_freeRes,Pia: pi] :
% 4.04/1.92 ( ( perm @ X @ late_residual_Rep @ Pi @ ( late_r347633188eR_Rep @ FreeRes3 @ Pia ) )
% 4.04/1.92 = ( late_r347633188eR_Rep @ ( perm @ X @ late_freeRes @ Pi @ FreeRes3 ) @ ( perm @ X @ pi @ Pi @ Pia ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_237_residual__Rep_Oinject_I2_J,axiom,
% 4.04/1.92 ! [X21: late_freeRes,X222: pi,Y21: late_freeRes,Y22: pi] :
% 4.04/1.92 ( ( ( late_r347633188eR_Rep @ X21 @ X222 )
% 4.04/1.92 = ( late_r347633188eR_Rep @ Y21 @ Y22 ) )
% 4.04/1.92 = ( ( X21 = Y21 )
% 4.04/1.92 & ( X222 = Y22 ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_238_alphaInput,axiom,
% 4.04/1.92 ! [C2: name,P2: pi,A2: name,X3: name] :
% 4.04/1.92 ( ( fresh @ name @ pi @ C2 @ P2 )
% 4.04/1.92 => ( ( input @ A2 @ X3 @ P2 )
% 4.04/1.92 = ( input @ A2 @ C2 @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ X3 @ C2 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ P2 ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_239_product__lists_Osimps_I1_J,axiom,
% 4.04/1.92 ! [A: $tType] :
% 4.04/1.92 ( ( product_lists @ A @ ( nil @ ( list @ A ) ) )
% 4.04/1.92 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_240_pi_Operm_I4_J,axiom,
% 4.04/1.92 ! [Pi: list @ ( product_prod @ name @ name ),X32: name,X1: name,X22: pi] :
% 4.04/1.92 ( ( perm @ name @ pi @ Pi @ ( input @ X32 @ X1 @ X22 ) )
% 4.04/1.92 = ( input @ ( perm @ name @ name @ Pi @ X32 ) @ ( perm @ name @ name @ Pi @ X1 ) @ ( perm @ name @ pi @ Pi @ X22 ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_241_resTrans_I2_J,axiom,
% 4.04/1.92 ! [X3: name,Y4: name,P2: pi,Rs: late_residual] :
% 4.04/1.92 ~ ( late_transitions @ ( res @ X3 @ ( input @ X3 @ Y4 @ P2 ) ) @ Rs ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_242_pi_Odistinct_I53_J,axiom,
% 4.04/1.92 ! [Name1: name,Name22: name,Pi: pi,Pi12: pi,Pi22: pi] :
% 4.04/1.92 ( ( input @ Name1 @ Name22 @ Pi )
% 4.04/1.92 != ( sum @ Pi12 @ Pi22 ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_243_pi_Odistinct_I57_J,axiom,
% 4.04/1.92 ! [Name1: name,Name22: name,Pi: pi,Name: name,Pi4: pi] :
% 4.04/1.92 ( ( input @ Name1 @ Name22 @ Pi )
% 4.04/1.92 != ( res @ Name @ Pi4 ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_244_inputFreeTrans,axiom,
% 4.04/1.92 ! [A2: name,X3: name,P2: pi,Alpha2: late_freeRes,P4: pi] :
% 4.04/1.92 ~ ( late_transitions @ ( input @ A2 @ X3 @ P2 ) @ ( late_FreeR @ Alpha2 @ P4 ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_245_resInputFreeTrans,axiom,
% 4.04/1.92 ! [X3: name,A2: name,Y4: name,P2: pi,Alpha2: late_freeRes,P4: pi] :
% 4.04/1.92 ~ ( late_transitions @ ( res @ X3 @ ( input @ A2 @ Y4 @ P2 ) ) @ ( late_FreeR @ Alpha2 @ P4 ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_246_inputBoundOutputTrans,axiom,
% 4.04/1.92 ! [A2: name,X3: name,P2: pi,B2: name,Y4: name,P4: pi] :
% 4.04/1.92 ~ ( late_transitions @ ( input @ A2 @ X3 @ P2 ) @ ( late_BoundR @ ( late_BoundOutputS @ B2 ) @ Y4 @ P4 ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_247_inputIneqTrans,axiom,
% 4.04/1.92 ! [A2: name,X3: name,P2: pi,B2: late_subject,Y4: name,P4: pi] :
% 4.04/1.92 ( ( late_transitions @ ( input @ A2 @ X3 @ P2 ) @ ( late_BoundR @ B2 @ Y4 @ P4 ) )
% 4.04/1.92 => ~ ( fresh @ name @ late_subject @ A2 @ B2 ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_248_resInputBoundOutputTrans,axiom,
% 4.04/1.92 ! [X3: name,A2: name,Y4: name,P2: pi,B2: name,Z2: name,P4: pi] :
% 4.04/1.92 ~ ( late_transitions @ ( res @ X3 @ ( input @ A2 @ Y4 @ P2 ) ) @ ( late_BoundR @ ( late_BoundOutputS @ B2 ) @ Z2 @ P4 ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_249_inputCases,axiom,
% 4.04/1.92 ! [A2: name,X3: name,P2: pi,B2: late_subject,Y4: name,YP: pi,Prop: late_subject > name > pi > $o] :
% 4.04/1.92 ( ( late_transitions @ ( input @ A2 @ X3 @ P2 ) @ ( late_BoundR @ B2 @ Y4 @ YP ) )
% 4.04/1.92 => ( ( Y4 != A2 )
% 4.04/1.92 => ( ( Y4 != X3 )
% 4.04/1.92 => ( ( fresh @ name @ pi @ Y4 @ P2 )
% 4.04/1.92 => ( ( ( B2
% 4.04/1.92 = ( late_InputS @ A2 ) )
% 4.04/1.92 => ( ( YP
% 4.04/1.92 = ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ X3 @ Y4 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ P2 ) )
% 4.04/1.92 => ( Prop @ ( late_InputS @ A2 ) @ Y4 @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ X3 @ Y4 ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ P2 ) ) ) )
% 4.04/1.92 => ( Prop @ B2 @ Y4 @ YP ) ) ) ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_250_name__calc_I1_J,axiom,
% 4.04/1.92 ! [A2: name,B2: name,Pi: list @ ( product_prod @ name @ name ),X3: name] :
% 4.04/1.92 ( ( perm @ name @ name @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A2 @ B2 ) @ Pi ) @ X3 )
% 4.04/1.92 = ( swap @ name @ ( product_Pair @ name @ name @ A2 @ B2 ) @ ( perm @ name @ name @ Pi @ X3 ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_251_Late__Semantics1_Osubject_Oinject_I1_J,axiom,
% 4.04/1.92 ! [X1: name,Y1: name] :
% 4.04/1.92 ( ( ( late_InputS @ X1 )
% 4.04/1.92 = ( late_InputS @ Y1 ) )
% 4.04/1.92 = ( X1 = Y1 ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_252_subject_Ofresh_I1_J,axiom,
% 4.04/1.92 ! [A2: name,X1: name] :
% 4.04/1.92 ( ( fresh @ name @ late_subject @ A2 @ ( late_InputS @ X1 ) )
% 4.04/1.92 = ( fresh @ name @ name @ A2 @ X1 ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_253_subject_Operm_I1_J,axiom,
% 4.04/1.92 ! [Pi: list @ ( product_prod @ name @ name ),X1: name] :
% 4.04/1.92 ( ( perm @ name @ late_subject @ Pi @ ( late_InputS @ X1 ) )
% 4.04/1.92 = ( late_InputS @ ( perm @ name @ name @ Pi @ X1 ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(fact_254_Late__Semantics_Osubject_Odistinct_I1_J,axiom,
% 4.04/1.92 ! [Name2: name,Name: name] :
% 4.04/1.92 ( ( late_InputS @ Name2 )
% 4.04/1.92 != ( late_BoundOutputS @ Name ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(tcon_fun___Orderings_Opreorder,axiom,
% 4.04/1.92 ! [A8: $tType,A9: $tType] :
% 4.04/1.92 ( ( preorder @ A9 )
% 4.04/1.92 => ( preorder @ ( A8 > A9 ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(tcon_fun___Agent_Ocp__name__name,axiom,
% 4.04/1.92 ! [A8: $tType,A9: $tType] :
% 4.04/1.92 ( ( ( cp_name_name @ A8 )
% 4.04/1.92 & ( cp_name_name @ A9 ) )
% 4.04/1.92 => ( cp_name_name @ ( A8 > A9 ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(tcon_fun___Orderings_Oorder,axiom,
% 4.04/1.92 ! [A8: $tType,A9: $tType] :
% 4.04/1.92 ( ( order @ A9 )
% 4.04/1.92 => ( order @ ( A8 > A9 ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(tcon_fun___Orderings_Oord,axiom,
% 4.04/1.92 ! [A8: $tType,A9: $tType] :
% 4.04/1.92 ( ( ord @ A9 )
% 4.04/1.92 => ( ord @ ( A8 > A9 ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(tcon_fun___Agent_Opt__name,axiom,
% 4.04/1.92 ! [A8: $tType,A9: $tType] :
% 4.04/1.92 ( ( ( pt_name @ A8 )
% 4.04/1.92 & ( pt_name @ A9 ) )
% 4.04/1.92 => ( pt_name @ ( A8 > A9 ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(tcon_Set_Oset___Orderings_Opreorder_1,axiom,
% 4.04/1.92 ! [A8: $tType] : ( preorder @ ( set @ A8 ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(tcon_Set_Oset___Agent_Ocp__name__name_2,axiom,
% 4.04/1.92 ! [A8: $tType] :
% 4.04/1.92 ( ( cp_name_name @ A8 )
% 4.04/1.92 => ( cp_name_name @ ( set @ A8 ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(tcon_Set_Oset___Orderings_Oorder_3,axiom,
% 4.04/1.92 ! [A8: $tType] : ( order @ ( set @ A8 ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(tcon_Set_Oset___Orderings_Oord_4,axiom,
% 4.04/1.92 ! [A8: $tType] : ( ord @ ( set @ A8 ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(tcon_Set_Oset___Agent_Opt__name_5,axiom,
% 4.04/1.92 ! [A8: $tType] :
% 4.04/1.92 ( ( pt_name @ A8 )
% 4.04/1.92 => ( pt_name @ ( set @ A8 ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(tcon_Agent_Opi___Agent_Ocp__name__name_6,axiom,
% 4.04/1.92 cp_name_name @ pi ).
% 4.04/1.92
% 4.04/1.92 thf(tcon_Agent_Opi___Agent_Opt__name_7,axiom,
% 4.04/1.92 pt_name @ pi ).
% 4.04/1.92
% 4.04/1.92 thf(tcon_Agent_Opi___Agent_Ofs__name,axiom,
% 4.04/1.92 fs_name @ pi ).
% 4.04/1.92
% 4.04/1.92 thf(tcon_HOL_Obool___Orderings_Opreorder_8,axiom,
% 4.04/1.92 preorder @ $o ).
% 4.04/1.92
% 4.04/1.92 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 4.04/1.92 linorder @ $o ).
% 4.04/1.92
% 4.04/1.92 thf(tcon_HOL_Obool___Agent_Ocp__name__name_9,axiom,
% 4.04/1.92 cp_name_name @ $o ).
% 4.04/1.92
% 4.04/1.92 thf(tcon_HOL_Obool___Orderings_Oorder_10,axiom,
% 4.04/1.92 order @ $o ).
% 4.04/1.92
% 4.04/1.92 thf(tcon_HOL_Obool___Orderings_Oord_11,axiom,
% 4.04/1.92 ord @ $o ).
% 4.04/1.92
% 4.04/1.92 thf(tcon_HOL_Obool___Agent_Opt__name_12,axiom,
% 4.04/1.92 pt_name @ $o ).
% 4.04/1.92
% 4.04/1.92 thf(tcon_HOL_Obool___Agent_Ofs__name_13,axiom,
% 4.04/1.92 fs_name @ $o ).
% 4.04/1.92
% 4.04/1.92 thf(tcon_List_Olist___Agent_Ocp__name__name_14,axiom,
% 4.04/1.92 ! [A8: $tType] :
% 4.04/1.92 ( ( cp_name_name @ A8 )
% 4.04/1.92 => ( cp_name_name @ ( list @ A8 ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(tcon_List_Olist___Agent_Opt__name_15,axiom,
% 4.04/1.92 ! [A8: $tType] :
% 4.04/1.92 ( ( pt_name @ A8 )
% 4.04/1.92 => ( pt_name @ ( list @ A8 ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(tcon_List_Olist___Agent_Ofs__name_16,axiom,
% 4.04/1.92 ! [A8: $tType] :
% 4.04/1.92 ( ( fs_name @ A8 )
% 4.04/1.92 => ( fs_name @ ( list @ A8 ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(tcon_Agent_Oname___Agent_Ocp__name__name_17,axiom,
% 4.04/1.92 cp_name_name @ name ).
% 4.04/1.92
% 4.04/1.92 thf(tcon_Agent_Oname___Agent_Opt__name_18,axiom,
% 4.04/1.92 pt_name @ name ).
% 4.04/1.92
% 4.04/1.92 thf(tcon_Agent_Oname___Agent_Ofs__name_19,axiom,
% 4.04/1.92 fs_name @ name ).
% 4.04/1.92
% 4.04/1.92 thf(tcon_Agent_Opi__Rep___Agent_Ocp__name__name_20,axiom,
% 4.04/1.92 cp_name_name @ pi_Rep ).
% 4.04/1.92
% 4.04/1.92 thf(tcon_Agent_Opi__Rep___Agent_Opt__name_21,axiom,
% 4.04/1.92 pt_name @ pi_Rep ).
% 4.04/1.92
% 4.04/1.92 thf(tcon_Product__Type_Oprod___Agent_Ocp__name__name_22,axiom,
% 4.04/1.92 ! [A8: $tType,A9: $tType] :
% 4.04/1.92 ( ( ( cp_name_name @ A8 )
% 4.04/1.92 & ( cp_name_name @ A9 ) )
% 4.04/1.92 => ( cp_name_name @ ( product_prod @ A8 @ A9 ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(tcon_Product__Type_Oprod___Agent_Opt__name_23,axiom,
% 4.04/1.92 ! [A8: $tType,A9: $tType] :
% 4.04/1.92 ( ( ( pt_name @ A8 )
% 4.04/1.92 & ( pt_name @ A9 ) )
% 4.04/1.92 => ( pt_name @ ( product_prod @ A8 @ A9 ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(tcon_Product__Type_Oprod___Agent_Ofs__name_24,axiom,
% 4.04/1.92 ! [A8: $tType,A9: $tType] :
% 4.04/1.92 ( ( ( fs_name @ A8 )
% 4.04/1.92 & ( fs_name @ A9 ) )
% 4.04/1.92 => ( fs_name @ ( product_prod @ A8 @ A9 ) ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(tcon_Late__Semantics_OfreeRes___Agent_Ocp__name__name_25,axiom,
% 4.04/1.92 cp_name_name @ late_freeRes ).
% 4.04/1.92
% 4.04/1.92 thf(tcon_Late__Semantics_OfreeRes___Agent_Opt__name_26,axiom,
% 4.04/1.92 pt_name @ late_freeRes ).
% 4.04/1.92
% 4.04/1.92 thf(tcon_Late__Semantics_OfreeRes___Agent_Ofs__name_27,axiom,
% 4.04/1.92 fs_name @ late_freeRes ).
% 4.04/1.92
% 4.04/1.92 thf(tcon_Late__Semantics_Osubject___Agent_Ocp__name__name_28,axiom,
% 4.04/1.92 cp_name_name @ late_subject ).
% 4.04/1.92
% 4.04/1.92 thf(tcon_Late__Semantics_Osubject___Agent_Opt__name_29,axiom,
% 4.04/1.92 pt_name @ late_subject ).
% 4.04/1.92
% 4.04/1.92 thf(tcon_Late__Semantics_Osubject___Agent_Ofs__name_30,axiom,
% 4.04/1.92 fs_name @ late_subject ).
% 4.04/1.92
% 4.04/1.92 thf(tcon_Late__Semantics_Oresidual___Agent_Ocp__name__name_31,axiom,
% 4.04/1.92 cp_name_name @ late_residual ).
% 4.04/1.92
% 4.04/1.92 thf(tcon_Late__Semantics_Oresidual___Agent_Opt__name_32,axiom,
% 4.04/1.92 pt_name @ late_residual ).
% 4.04/1.92
% 4.04/1.92 thf(tcon_Late__Semantics_Oresidual___Agent_Ofs__name_33,axiom,
% 4.04/1.92 fs_name @ late_residual ).
% 4.04/1.92
% 4.04/1.92 thf(tcon_Late__Semantics_OfreeRes__Rep___Agent_Ocp__name__name_34,axiom,
% 4.04/1.92 cp_name_name @ late_freeRes_Rep ).
% 4.04/1.92
% 4.04/1.92 thf(tcon_Late__Semantics_OfreeRes__Rep___Agent_Opt__name_35,axiom,
% 4.04/1.92 pt_name @ late_freeRes_Rep ).
% 4.04/1.92
% 4.04/1.92 thf(tcon_Late__Semantics_Osubject__Rep___Agent_Ocp__name__name_36,axiom,
% 4.04/1.92 cp_name_name @ late_subject_Rep ).
% 4.04/1.92
% 4.04/1.92 thf(tcon_Late__Semantics_Osubject__Rep___Agent_Opt__name_37,axiom,
% 4.04/1.92 pt_name @ late_subject_Rep ).
% 4.04/1.92
% 4.04/1.92 thf(tcon_Late__Semantics_Oresidual__Rep___Agent_Ocp__name__name_38,axiom,
% 4.04/1.92 cp_name_name @ late_residual_Rep ).
% 4.04/1.92
% 4.04/1.92 thf(tcon_Late__Semantics_Oresidual__Rep___Agent_Opt__name_39,axiom,
% 4.04/1.92 pt_name @ late_residual_Rep ).
% 4.04/1.92
% 4.04/1.92 thf(help_If_3_1_T,axiom,
% 4.04/1.92 ! [P2: $o] :
% 4.04/1.92 ( ( P2 = $true )
% 4.04/1.92 | ( P2 = $false ) ) ).
% 4.04/1.92
% 4.04/1.92 thf(help_If_2_1_T,axiom,
% 4.04/1.92 ! [A: $tType,X3: A,Y4: A] :
% 4.04/1.92 ( ( if @ A @ $false @ X3 @ Y4 )
% 4.04/1.92 = Y4 ) ).
% 4.04/1.92
% 4.04/1.92 thf(help_If_1_1_T,axiom,
% 4.04/1.92 ! [A: $tType,X3: A,Y4: A] :
% 4.04/1.92 ( ( if @ A @ $true @ X3 @ Y4 )
% 4.04/1.92 = X3 ) ).
% 4.04/1.92
% 4.04/1.92 thf(conj_0,conjecture,
% 4.04/1.92 strong2129052853vative @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ y @ x ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ p2 ) @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ y @ x ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ p2 ) @ ( late_BoundOutputS @ aa ) @ y @ rel ).
% 4.04/1.92 ------------------------
% 4.04/1.96 % (17882)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_17774 for (2999ds/27Mi)
% 4.04/1.96 % (17885)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_17774 for (2999ds/275Mi)
% 4.04/1.96 % (17886)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_17774 for (2999ds/18Mi)
% 4.04/1.96 % (17880)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_17774 for (2999ds/183Mi)
% 4.04/1.96 % (17883)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_17774 for (2999ds/2Mi)
% 4.04/1.96 % (17881)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_17774 for (2999ds/4Mi)
% 4.04/1.96 % (17884)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_17774 for (2999ds/2Mi)
% 4.04/1.96 % (17883)Instruction limit reached!
% 4.04/1.96 % (17883)------------------------------
% 4.04/1.96 % (17883)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.04/1.96 % (17883)Termination reason: Unknown
% 4.04/1.96 % (17884)Instruction limit reached!
% 4.04/1.96 % (17884)------------------------------
% 4.04/1.96 % (17884)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.04/1.96 % (17883)Termination phase: shuffling
% 4.04/1.96
% 4.04/1.96 % (17883)Memory used [KB]: 1407
% 4.04/1.96 % (17883)Time elapsed: 0.003 s
% 4.04/1.96 % (17883)Instructions burned: 2 (million)
% 4.04/1.96 % (17883)------------------------------
% 4.04/1.96 % (17883)------------------------------
% 4.04/1.96 % (17884)Termination reason: Unknown
% 4.04/1.96 % (17884)Termination phase: shuffling
% 4.04/1.96
% 4.04/1.96 % (17884)Memory used [KB]: 1407
% 4.04/1.96 % (17884)Time elapsed: 0.003 s
% 4.04/1.96 % (17884)Instructions burned: 2 (million)
% 4.04/1.96 % (17884)------------------------------
% 4.04/1.96 % (17884)------------------------------
% 4.04/1.97 % (17881)Instruction limit reached!
% 4.04/1.97 % (17881)------------------------------
% 4.04/1.97 % (17881)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.04/1.97 % (17881)Termination reason: Unknown
% 4.04/1.97 % (17881)Termination phase: shuffling
% 4.04/1.97
% 4.04/1.97 % (17881)Memory used [KB]: 1535
% 4.04/1.97 % (17881)Time elapsed: 0.005 s
% 4.04/1.97 % (17881)Instructions burned: 5 (million)
% 4.04/1.97 % (17881)------------------------------
% 4.04/1.97 % (17881)------------------------------
% 4.04/1.97 % (17886)Instruction limit reached!
% 4.04/1.97 % (17886)------------------------------
% 4.04/1.97 % (17886)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.04/1.97 % (17886)Termination reason: Unknown
% 4.04/1.97 % (17886)Termination phase: shuffling
% 4.04/1.97
% 4.04/1.97 % (17886)Memory used [KB]: 1791
% 4.04/1.97 % (17886)Time elapsed: 0.013 s
% 4.04/1.97 % (17886)Instructions burned: 18 (million)
% 4.04/1.97 % (17886)------------------------------
% 4.04/1.97 % (17886)------------------------------
% 4.04/1.98 % (17882)Instruction limit reached!
% 4.04/1.98 % (17882)------------------------------
% 4.04/1.98 % (17882)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.04/1.98 % (17882)Termination reason: Unknown
% 4.04/1.98 % (17882)Termination phase: shuffling
% 4.04/1.98
% 4.04/1.98 % (17882)Memory used [KB]: 1918
% 4.04/1.98 % (17882)Time elapsed: 0.017 s
% 4.04/1.98 % (17882)Instructions burned: 27 (million)
% 4.04/1.98 % (17882)------------------------------
% 4.04/1.98 % (17882)------------------------------
% 4.04/1.98 % (17889)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_17774 for (2999ds/15Mi)
% 4.04/1.98 % (17888)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_17774 for (2999ds/37Mi)
% 4.04/1.98 % (17887)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_17774 for (2999ds/3Mi)
% 4.04/1.99 % (17887)Instruction limit reached!
% 4.04/1.99 % (17887)------------------------------
% 4.04/1.99 % (17887)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.04/1.99 % (17887)Termination reason: Unknown
% 4.04/1.99 % (17887)Termination phase: shuffling
% 4.04/1.99
% 4.04/1.99 % (17887)Memory used [KB]: 1407
% 4.04/1.99 % (17887)Time elapsed: 0.004 s
% 4.04/1.99 % (17887)Instructions burned: 4 (million)
% 4.04/1.99 % (17887)------------------------------
% 4.04/1.99 % (17887)------------------------------
% 4.04/1.99 % (17889)Instruction limit reached!
% 4.04/1.99 % (17889)------------------------------
% 4.04/1.99 % (17889)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.04/1.99 % (17889)Termination reason: Unknown
% 4.04/1.99 % (17889)Termination phase: shuffling
% 4.04/1.99
% 4.04/1.99 % (17889)Memory used [KB]: 1791
% 4.04/1.99 % (17889)Time elapsed: 0.011 s
% 4.04/1.99 % (17889)Instructions burned: 16 (million)
% 4.04/1.99 % (17889)------------------------------
% 4.04/1.99 % (17889)------------------------------
% 4.04/1.99 % (17890)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_17774 for (2999ds/3Mi)
% 4.04/2.00 % (17890)Instruction limit reached!
% 4.04/2.00 % (17890)------------------------------
% 4.04/2.00 % (17890)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.04/2.00 % (17890)Termination reason: Unknown
% 4.04/2.00 % (17890)Termination phase: shuffling
% 4.04/2.00
% 4.04/2.00 % (17890)Memory used [KB]: 1407
% 4.04/2.00 % (17890)Time elapsed: 0.004 s
% 4.04/2.00 % (17890)Instructions burned: 3 (million)
% 4.04/2.00 % (17890)------------------------------
% 4.04/2.00 % (17890)------------------------------
% 4.04/2.00 % (17891)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_17774 for (2999ds/1041Mi)
% 4.04/2.00 % (17888)Instruction limit reached!
% 4.04/2.00 % (17888)------------------------------
% 4.04/2.00 % (17888)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.04/2.00 % (17888)Termination reason: Unknown
% 4.04/2.00 % (17888)Termination phase: shuffling
% 4.04/2.00
% 4.04/2.00 % (17888)Memory used [KB]: 2174
% 4.04/2.00 % (17888)Time elapsed: 0.021 s
% 4.04/2.00 % (17888)Instructions burned: 37 (million)
% 4.04/2.00 % (17888)------------------------------
% 4.04/2.00 % (17888)------------------------------
% 4.04/2.01 % (17892)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_17774 for (2999ds/7Mi)
% 4.04/2.01 % (17892)Instruction limit reached!
% 4.04/2.01 % (17892)------------------------------
% 4.04/2.01 % (17892)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.04/2.01 % (17892)Termination reason: Unknown
% 4.04/2.01 % (17892)Termination phase: shuffling
% 4.04/2.01
% 4.04/2.01 % (17892)Memory used [KB]: 1535
% 4.04/2.01 % (17892)Time elapsed: 0.007 s
% 4.04/2.01 % (17892)Instructions burned: 8 (million)
% 4.04/2.01 % (17892)------------------------------
% 4.04/2.01 % (17892)------------------------------
% 4.04/2.01 % (17893)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_17774 for (2999ds/16Mi)
% 4.04/2.02 % (17894)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_17774 for (2999ds/3Mi)
% 4.04/2.02 % (17894)Instruction limit reached!
% 4.04/2.02 % (17894)------------------------------
% 4.04/2.02 % (17894)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.04/2.02 % (17894)Termination reason: Unknown
% 4.04/2.02 % (17894)Termination phase: shuffling
% 4.04/2.02
% 4.04/2.02 % (17894)Memory used [KB]: 1407
% 4.04/2.02 % (17894)Time elapsed: 0.004 s
% 4.04/2.02 % (17894)Instructions burned: 3 (million)
% 4.04/2.02 % (17894)------------------------------
% 4.04/2.02 % (17894)------------------------------
% 4.04/2.02 % (17893)Instruction limit reached!
% 4.04/2.02 % (17893)------------------------------
% 4.04/2.02 % (17893)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.04/2.02 % (17893)Termination reason: Unknown
% 4.04/2.02 % (17893)Termination phase: shuffling
% 4.04/2.02
% 4.04/2.02 % (17893)Memory used [KB]: 1791
% 4.04/2.02 % (17893)Time elapsed: 0.011 s
% 4.04/2.02 % (17893)Instructions burned: 16 (million)
% 4.04/2.02 % (17893)------------------------------
% 4.04/2.02 % (17893)------------------------------
% 4.04/2.02 % (17895)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_17774 for (2999ds/3Mi)
% 4.04/2.03 % (17895)Instruction limit reached!
% 4.04/2.03 % (17895)------------------------------
% 4.04/2.03 % (17895)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.04/2.03 % (17895)Termination reason: Unknown
% 4.04/2.03 % (17895)Termination phase: shuffling
% 4.04/2.03
% 4.04/2.03 % (17895)Memory used [KB]: 1407
% 4.04/2.03 % (17895)Time elapsed: 0.005 s
% 4.04/2.03 % (17895)Instructions burned: 4 (million)
% 4.04/2.03 % (17895)------------------------------
% 4.04/2.03 % (17895)------------------------------
% 4.64/2.03 % (17896)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_17774 for (2999ds/7Mi)
% 4.64/2.04 % (17896)Instruction limit reached!
% 4.64/2.04 % (17896)------------------------------
% 4.64/2.04 % (17896)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.64/2.04 % (17896)Termination reason: Unknown
% 4.64/2.04 % (17896)Termination phase: shuffling
% 4.64/2.04
% 4.64/2.04 % (17896)Memory used [KB]: 1663
% 4.64/2.04 % (17896)Time elapsed: 0.007 s
% 4.64/2.04 % (17896)Instructions burned: 8 (million)
% 4.64/2.04 % (17896)------------------------------
% 4.64/2.04 % (17896)------------------------------
% 4.64/2.04 % (17897)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_17774 for (2999ds/3Mi)
% 4.64/2.04 % (17897)Instruction limit reached!
% 4.64/2.04 % (17897)------------------------------
% 4.64/2.04 % (17897)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.64/2.04 % (17897)Termination reason: Unknown
% 4.64/2.04 % (17897)Termination phase: shuffling
% 4.64/2.04
% 4.64/2.04 % (17897)Memory used [KB]: 1407
% 4.64/2.04 % (17897)Time elapsed: 0.004 s
% 4.64/2.04 % (17897)Instructions burned: 3 (million)
% 4.64/2.04 % (17897)------------------------------
% 4.64/2.04 % (17897)------------------------------
% 4.64/2.04 % (17898)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_17774 for (2999ds/4Mi)
% 4.64/2.04 % (17898)Instruction limit reached!
% 4.64/2.04 % (17898)------------------------------
% 4.64/2.04 % (17898)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.64/2.04 % (17898)Termination reason: Unknown
% 4.64/2.04 % (17898)Termination phase: shuffling
% 4.64/2.04
% 4.64/2.04 % (17898)Memory used [KB]: 1535
% 4.64/2.04 % (17898)Time elapsed: 0.005 s
% 4.64/2.04 % (17898)Instructions burned: 5 (million)
% 4.64/2.04 % (17898)------------------------------
% 4.64/2.04 % (17898)------------------------------
% 4.64/2.05 % (17885)First to succeed.
% 4.64/2.05 % (17899)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_17774 for (2999ds/18Mi)
% 4.64/2.05 % (17885)Refutation found. Thanks to Tanya!
% 4.64/2.05 % SZS status Theorem for DTF2THF_17774
% 4.64/2.05 % SZS output start Proof for DTF2THF_17774
% 4.64/2.05 thf(type_def_5, type, name: $tType).
% 4.64/2.05 thf(type_def_6, type, pi: $tType).
% 4.64/2.05 thf(type_def_8, type, list: ($tType) > $tType).
% 4.64/2.05 thf(type_def_9, type, late_freeRes: $tType).
% 4.64/2.05 thf(type_def_10, type, late_subject: $tType).
% 4.64/2.05 thf(type_def_11, type, late_residual: $tType).
% 4.64/2.05 thf(type_def_12, type, late_residual_Rep: $tType).
% 4.64/2.05 thf(type_def_13, type, product_prod: ($tType * $tType) > $tType).
% 4.64/2.05 thf(type_def_14, type, set: ($tType) > $tType).
% 4.64/2.05 thf(type_def_15, type, late_subject_Rep: $tType).
% 4.64/2.05 thf(type_def_16, type, late_freeRes_Rep: $tType).
% 4.64/2.05 thf(type_def_17, type, pi_Rep: $tType).
% 4.64/2.05 thf(func_def_0, type, late_residual_Rep: $tType).
% 4.64/2.05 thf(func_def_1, type, late_subject_Rep: $tType).
% 4.64/2.05 thf(func_def_2, type, late_freeRes_Rep: $tType).
% 4.64/2.05 thf(func_def_3, type, late_residual: $tType).
% 4.64/2.05 thf(func_def_4, type, late_subject: $tType).
% 4.64/2.05 thf(func_def_5, type, late_freeRes: $tType).
% 4.64/2.05 thf(func_def_6, type, product_prod: ($tType * $tType) > $tType).
% 4.64/2.05 thf(func_def_7, type, pi_Rep: $tType).
% 4.64/2.05 thf(func_def_8, type, name: $tType).
% 4.64/2.05 thf(func_def_9, type, list: ($tType) > $tType).
% 4.64/2.05 thf(func_def_10, type, pi: $tType).
% 4.64/2.05 thf(func_def_11, type, set: ($tType) > $tType).
% 4.64/2.05 thf(func_def_12, type, type: !>[X0: $tType]:($o)).
% 4.64/2.05 thf(func_def_13, type, fs_name: !>[X0: $tType]:($o)).
% 4.64/2.05 thf(func_def_14, type, pt_name: !>[X0: $tType]:($o)).
% 4.64/2.05 thf(func_def_15, type, ord: !>[X0: $tType]:($o)).
% 4.64/2.05 thf(func_def_16, type, order: !>[X0: $tType]:($o)).
% 4.64/2.05 thf(func_def_17, type, cp_name_name: !>[X0: $tType]:($o)).
% 4.64/2.05 thf(func_def_18, type, linorder: !>[X0: $tType]:($o)).
% 4.64/2.05 thf(func_def_19, type, preorder: !>[X0: $tType]:($o)).
% 4.64/2.05 thf(func_def_20, type, input: name > name > pi > pi).
% 4.64/2.05 thf(func_def_21, type, res: name > pi > pi).
% 4.64/2.05 thf(func_def_22, type, sum: pi > pi > pi).
% 4.64/2.05 thf(func_def_23, type, bNF_Greatest_shift: !>[X0: $tType, X1: $tType]:((list @ X0 > X1) > X0 > list @ X0 > X1)).
% 4.64/2.05 thf(func_def_24, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 4.64/2.05 thf(func_def_25, type, late_OutputR: name > name > late_freeRes).
% 4.64/2.05 thf(func_def_26, type, late_BoundR: late_subject > name > pi > late_residual).
% 4.64/2.05 thf(func_def_27, type, late_FreeR: late_freeRes > pi > late_residual).
% 4.64/2.05 thf(func_def_28, type, late_r347633188eR_Rep: late_freeRes > pi > late_residual_Rep).
% 4.64/2.05 thf(func_def_29, type, late_BoundOutputS: name > late_subject).
% 4.64/2.05 thf(func_def_30, type, late_InputS: name > late_subject).
% 4.64/2.05 thf(func_def_31, type, late_transitions: pi > late_residual > $o).
% 4.64/2.05 thf(func_def_32, type, cons: !>[X0: $tType]:(X0 > list @ X0 > list @ X0)).
% 4.64/2.05 thf(func_def_33, type, nil: !>[X0: $tType]:(list @ X0)).
% 4.64/2.05 thf(func_def_34, type, product_lists: !>[X0: $tType]:(list @ list @ X0 > list @ list @ X0)).
% 4.64/2.05 thf(func_def_35, type, fresh: !>[X0: $tType, X1: $tType]:(X0 > X1 > $o)).
% 4.64/2.05 thf(func_def_36, type, perm: !>[X0: $tType, X1: $tType]:(list @ product_prod @ X0 @ X0 > X1 > X1)).
% 4.64/2.05 thf(func_def_37, type, supports: !>[X0: $tType, X1: $tType]:(set @ X0 > X1 > $o)).
% 4.64/2.05 thf(func_def_38, type, swap: !>[X0: $tType]:(product_prod @ X0 @ X0 > X0 > X0)).
% 4.64/2.05 thf(func_def_39, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 4.64/2.05 thf(func_def_40, type, product_Pair: !>[X0: $tType, X1: $tType]:(X0 > X1 > product_prod @ X0 @ X1)).
% 4.64/2.05 thf(func_def_41, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2)).
% 4.64/2.05 thf(func_def_42, type, eqvt: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > $o)).
% 4.64/2.05 thf(func_def_43, type, id: !>[X0: $tType]:(set @ product_prod @ X0 @ X0)).
% 4.64/2.05 thf(func_def_44, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 4.64/2.05 thf(func_def_45, type, strong2129052853vative: pi > pi > late_subject > name > set @ product_prod @ pi @ pi > $o).
% 4.64/2.05 thf(func_def_46, type, strong743114133lation: pi > set @ product_prod @ pi @ pi > pi > $o).
% 4.64/2.05 thf(func_def_47, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 4.64/2.05 thf(func_def_48, type, p: pi).
% 4.64/2.05 thf(func_def_49, type, pq: pi).
% 4.64/2.05 thf(func_def_50, type, p2: pi).
% 4.64/2.05 thf(func_def_51, type, q: pi).
% 4.64/2.05 thf(func_def_52, type, rel: set @ product_prod @ pi @ pi).
% 4.64/2.05 thf(func_def_53, type, a: late_subject).
% 4.64/2.05 thf(func_def_54, type, aa: name).
% 4.64/2.05 thf(func_def_55, type, x: name).
% 4.64/2.05 thf(func_def_56, type, y: name).
% 4.64/2.05 thf(func_def_75, type, sP0: name > pi > late_subject > name > pi > $o).
% 4.64/2.05 thf(func_def_76, type, sP1: name > pi > late_residual > $o).
% 4.64/2.05 thf(func_def_77, type, sP2: name > pi > late_residual > $o).
% 4.64/2.05 thf(func_def_78, type, sP3: late_subject > pi > (late_subject > pi > $o) > name > name > $o).
% 4.64/2.05 thf(func_def_79, type, sP4: !>[X0: $tType]:(set @ product_prod @ pi @ pi > pi > X0 > name > pi > $o)).
% 4.64/2.05 thf(func_def_80, type, sP5: pi > pi > name > set @ product_prod @ pi @ pi > $o).
% 4.64/2.05 thf(func_def_81, type, sP6: !>[X0: $tType]:(X0 > set @ product_prod @ pi @ pi > pi > pi > $o)).
% 4.64/2.05 thf(func_def_82, type, sK7: !>[X0: $tType]:(list @ list @ X0 > X0)).
% 4.64/2.05 thf(func_def_83, type, sK8: !>[X0: $tType]:(list @ list @ X0 > list @ X0)).
% 4.64/2.05 thf(func_def_84, type, sK9: !>[X0: $tType]:(list @ list @ X0 > list @ list @ X0)).
% 4.64/2.05 thf(func_def_85, type, sK10: !>[X0: $tType]:(list @ list @ X0 > list @ list @ X0)).
% 4.64/2.05 thf(func_def_86, type, sK11: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3)).
% 4.64/2.05 thf(func_def_87, type, sK12: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 4.64/2.05 thf(func_def_88, type, sK13: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 4.64/2.05 thf(func_def_89, type, sK14: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 4.64/2.05 thf(func_def_90, type, sK15: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 4.64/2.05 thf(func_def_91, type, sK16: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 4.64/2.05 thf(func_def_92, type, sK17: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 4.64/2.05 thf(func_def_93, type, sK18: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 4.64/2.05 thf(func_def_94, type, sK19: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 4.64/2.05 thf(func_def_95, type, sK20: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 4.64/2.05 thf(func_def_96, type, sK21: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > X0 > X1)).
% 4.64/2.05 thf(func_def_97, type, sK22: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > list @ X1)).
% 4.64/2.05 thf(func_def_98, type, sK23: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > X0 > X1)).
% 4.64/2.05 thf(func_def_99, type, sK24: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > X0)).
% 4.64/2.05 thf(func_def_100, type, sK25: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > list @ X0)).
% 4.64/2.05 thf(func_def_101, type, sK26: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > list @ X1)).
% 4.64/2.05 thf(func_def_102, type, sK27: pi > name > late_subject > set @ product_prod @ pi @ pi > pi > pi).
% 4.64/2.05 thf(func_def_103, type, sK28: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X0)).
% 4.64/2.05 thf(func_def_104, type, sK29: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X1)).
% 4.64/2.05 thf(func_def_105, type, sK30: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X2)).
% 4.64/2.05 thf(func_def_106, type, sK31: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X3)).
% 4.64/2.05 thf(func_def_107, type, sK32: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X4)).
% 4.64/2.05 thf(func_def_108, type, sK33: !>[X0: $tType, X1: $tType]:(product_prod @ (X0 > X1) @ product_prod @ list @ X0 @ list @ X1 > X0 > X1)).
% 4.64/2.05 thf(func_def_109, type, sK34: !>[X0: $tType, X1: $tType]:(product_prod @ (X0 > X1) @ product_prod @ list @ X0 @ list @ X1 > X0)).
% 4.64/2.05 thf(func_def_110, type, sK35: !>[X0: $tType, X1: $tType]:(product_prod @ (X0 > X1) @ product_prod @ list @ X0 @ list @ X1 > list @ X0)).
% 4.64/2.05 thf(func_def_111, type, sK36: !>[X0: $tType, X1: $tType]:(product_prod @ (X0 > X1) @ product_prod @ list @ X0 @ list @ X1 > list @ X1)).
% 4.64/2.05 thf(func_def_112, type, sK37: !>[X0: $tType, X1: $tType]:(product_prod @ (X0 > X1) @ product_prod @ list @ X0 @ list @ X1 > X0 > X1)).
% 4.64/2.05 thf(func_def_113, type, sK38: !>[X0: $tType, X1: $tType]:(product_prod @ (X0 > X1) @ product_prod @ list @ X0 @ list @ X1 > list @ X1)).
% 4.64/2.05 thf(func_def_114, type, sK39: set @ product_prod @ pi @ pi > pi > pi > late_freeRes).
% 4.64/2.05 thf(func_def_115, type, sK40: set @ product_prod @ pi @ pi > pi > pi > pi).
% 4.64/2.05 thf(func_def_116, type, sK41: set @ product_prod @ pi @ pi > pi > pi > late_subject).
% 4.64/2.05 thf(func_def_117, type, sK42: set @ product_prod @ pi @ pi > pi > pi > name).
% 4.64/2.05 thf(func_def_118, type, sK43: set @ product_prod @ pi @ pi > pi > pi > pi).
% 4.64/2.05 thf(func_def_119, type, sK44: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X1)).
% 4.64/2.05 thf(func_def_120, type, sK45: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X0)).
% 4.64/2.05 thf(func_def_121, type, sK46: name > pi > late_subject > name > pi > pi).
% 4.64/2.05 thf(func_def_122, type, sK47: name > pi > late_subject > name > pi > late_subject).
% 4.64/2.05 thf(func_def_123, type, sK48: name > pi > late_subject > name > pi > name).
% 4.64/2.05 thf(func_def_124, type, sK49: name > pi > late_subject > name > pi > pi).
% 4.64/2.05 thf(func_def_125, type, sK50: name > pi > late_subject > name > pi > name).
% 4.64/2.05 thf(func_def_126, type, sK51: pi > name > late_subject > pi > name > pi).
% 4.64/2.05 thf(func_def_127, type, sK52: pi > name > late_subject > pi > name > name).
% 4.64/2.05 thf(func_def_128, type, sK53: pi > name > late_subject > pi > name > name).
% 4.64/2.05 thf(func_def_129, type, sK54: pi > name > late_subject > pi > name > pi).
% 4.64/2.05 thf(func_def_130, type, sK55: !>[X0: $tType]:(set @ X0 > set @ X0 > X0)).
% 4.64/2.05 thf(func_def_131, type, sK56: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X6)).
% 4.64/2.05 thf(func_def_132, type, sK57: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X5)).
% 4.64/2.05 thf(func_def_133, type, sK58: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4)).
% 4.64/2.05 thf(func_def_134, type, sK59: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3)).
% 4.64/2.05 thf(func_def_135, type, sK60: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 4.64/2.05 thf(func_def_136, type, sK61: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 4.64/2.05 thf(func_def_137, type, sK62: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 4.64/2.05 thf(func_def_138, type, sK63: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X0)).
% 4.64/2.05 thf(func_def_139, type, sK64: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X1)).
% 4.64/2.05 thf(func_def_140, type, sK65: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X2)).
% 4.64/2.05 thf(func_def_141, type, sK66: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X3)).
% 4.64/2.05 thf(func_def_142, type, sK67: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X4)).
% 4.64/2.05 thf(func_def_143, type, sK68: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X5)).
% 4.64/2.05 thf(func_def_144, type, sK69: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o)).
% 4.64/2.05 thf(func_def_145, type, sK70: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o)).
% 4.64/2.05 thf(func_def_146, type, sK71: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0)).
% 4.64/2.05 thf(func_def_147, type, sK72: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > list @ X0)).
% 4.64/2.05 thf(func_def_148, type, sK73: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4)).
% 4.64/2.05 thf(func_def_149, type, sK74: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3)).
% 4.64/2.05 thf(func_def_150, type, sK75: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 4.64/2.05 thf(func_def_151, type, sK76: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 4.64/2.05 thf(func_def_152, type, sK77: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 4.64/2.05 thf(func_def_153, type, sK78: !>[X0: $tType, X1: $tType]:(set @ product_prod @ X1 @ X0 > set @ product_prod @ X1 @ X0 > X1)).
% 4.64/2.05 thf(func_def_154, type, sK79: !>[X0: $tType, X1: $tType]:(set @ product_prod @ X1 @ X0 > set @ product_prod @ X1 @ X0 > X0)).
% 4.64/2.05 thf(func_def_155, type, sK80: pi > late_freeRes > pi > name > pi).
% 4.64/2.05 thf(func_def_156, type, sK81: pi > late_freeRes > pi > name > late_freeRes).
% 4.64/2.05 thf(func_def_157, type, sK82: pi > late_freeRes > pi > name > pi).
% 4.64/2.05 thf(func_def_158, type, sK83: pi > late_freeRes > pi > name > name).
% 4.64/2.05 thf(func_def_159, type, sK84: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X0)).
% 4.64/2.05 thf(func_def_160, type, sK85: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X1)).
% 4.64/2.05 thf(func_def_161, type, sK86: !>[X0: $tType]:(list @ X0 > X0)).
% 4.64/2.05 thf(func_def_162, type, sK87: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 4.64/2.05 thf(func_def_163, type, sK88: !>[X0: $tType]:(product_prod @ (X0 > X0 > $o) @ list @ X0 > X0 > X0 > $o)).
% 4.64/2.05 thf(func_def_164, type, sK89: !>[X0: $tType]:(product_prod @ (X0 > X0 > $o) @ list @ X0 > X0)).
% 4.64/2.05 thf(func_def_165, type, sK90: !>[X0: $tType]:(product_prod @ (X0 > X0 > $o) @ list @ X0 > X0)).
% 4.64/2.05 thf(func_def_166, type, sK91: !>[X0: $tType]:(product_prod @ (X0 > X0 > $o) @ list @ X0 > list @ X0)).
% 4.64/2.05 thf(func_def_167, type, sK92: !>[X0: $tType]:(product_prod @ (X0 > X0 > $o) @ list @ X0 > X0 > X0 > $o)).
% 4.64/2.05 thf(func_def_168, type, sK93: !>[X0: $tType]:(product_prod @ (X0 > X0 > $o) @ list @ X0 > X0 > X0 > $o)).
% 4.64/2.05 thf(func_def_169, type, sK94: !>[X0: $tType]:(product_prod @ (X0 > X0 > $o) @ list @ X0 > X0)).
% 4.64/2.05 thf(func_def_170, type, sK95: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X0)).
% 4.64/2.05 thf(func_def_171, type, sK96: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X1)).
% 4.64/2.05 thf(func_def_172, type, sK97: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X2)).
% 4.64/2.05 thf(func_def_173, type, sK98: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X3)).
% 4.64/2.05 thf(func_def_174, type, sK99: !>[X0: $tType]:(list @ X0 > X0)).
% 4.64/2.05 thf(func_def_175, type, sK100: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 4.64/2.05 thf(func_def_176, type, sK101: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 4.64/2.05 thf(func_def_177, type, sK102: name > pi > late_residual > pi).
% 4.64/2.05 thf(func_def_178, type, sK103: name > pi > late_residual > name).
% 4.64/2.05 thf(func_def_179, type, sK104: name > pi > late_residual > name).
% 4.64/2.05 thf(func_def_180, type, sK105: name > pi > late_residual > pi).
% 4.64/2.05 thf(func_def_181, type, sK106: name > pi > late_residual > pi).
% 4.64/2.05 thf(func_def_182, type, sK107: name > pi > late_residual > late_subject).
% 4.64/2.05 thf(func_def_183, type, sK108: name > pi > late_residual > name).
% 4.64/2.05 thf(func_def_184, type, sK109: name > pi > late_residual > pi).
% 4.64/2.05 thf(func_def_185, type, sK110: name > pi > late_residual > name).
% 4.64/2.05 thf(func_def_186, type, sK111: late_residual > pi > name > pi).
% 4.64/2.05 thf(func_def_187, type, sK112: late_residual > pi > name > late_freeRes).
% 4.64/2.05 thf(func_def_188, type, sK113: late_residual > pi > name > pi).
% 4.64/2.05 thf(func_def_189, type, sK114: late_residual > pi > name > name).
% 4.64/2.05 thf(func_def_190, type, sK115: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ product_prod @ X1 @ X2 > X0)).
% 4.64/2.05 thf(func_def_191, type, sK116: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ product_prod @ X1 @ X2 > X1)).
% 4.64/2.05 thf(func_def_192, type, sK117: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ product_prod @ X1 @ X2 > X2)).
% 4.64/2.05 thf(func_def_193, type, sK118: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X5)).
% 4.64/2.05 thf(func_def_194, type, sK119: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4)).
% 4.64/2.05 thf(func_def_195, type, sK120: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3)).
% 4.64/2.05 thf(func_def_196, type, sK121: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 4.64/2.05 thf(func_def_197, type, sK122: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 4.64/2.05 thf(func_def_198, type, sK123: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 4.64/2.05 thf(func_def_199, type, sK124: !>[X0: $tType]:(product_prod @ list @ X0 @ list @ X0 > X0)).
% 4.64/2.05 thf(func_def_200, type, sK125: !>[X0: $tType]:(product_prod @ list @ X0 @ list @ X0 > list @ X0)).
% 4.64/2.05 thf(func_def_201, type, sK126: !>[X0: $tType]:(product_prod @ list @ X0 @ list @ X0 > list @ X0)).
% 4.64/2.05 thf(func_def_202, type, sK127: !>[X0: $tType]:(product_prod @ list @ X0 @ list @ X0 > list @ X0)).
% 4.64/2.05 thf(func_def_203, type, sK128: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 4.64/2.05 thf(func_def_204, type, sK129: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 4.64/2.05 thf(func_def_205, type, sK130: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 4.64/2.05 thf(func_def_206, type, sK131: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 4.64/2.05 thf(func_def_207, type, sK132: !>[X0: $tType]:(product_prod @ (X0 > X0 > $o) @ list @ X0 > X0 > X0 > $o)).
% 4.64/2.05 thf(func_def_208, type, sK133: !>[X0: $tType]:(product_prod @ (X0 > X0 > $o) @ list @ X0 > X0)).
% 4.64/2.05 thf(func_def_209, type, sK134: !>[X0: $tType]:(product_prod @ (X0 > X0 > $o) @ list @ X0 > list @ X0)).
% 4.64/2.05 thf(func_def_210, type, sK135: !>[X0: $tType]:(product_prod @ (X0 > X0 > $o) @ list @ X0 > X0 > X0 > $o)).
% 4.64/2.05 thf(func_def_211, type, sK136: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 4.64/2.05 thf(func_def_212, type, sK137: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 4.64/2.05 thf(func_def_213, type, sK138: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 4.64/2.05 thf(func_def_214, type, sK139: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 4.64/2.05 thf(func_def_215, type, sK140: (late_residual > $o) > late_freeRes).
% 4.64/2.05 thf(func_def_216, type, sK141: (late_residual > $o) > pi).
% 4.64/2.05 thf(func_def_217, type, sK142: (late_residual > $o) > late_subject).
% 4.64/2.05 thf(func_def_218, type, sK143: (late_residual > $o) > name).
% 4.64/2.05 thf(func_def_219, type, sK144: (late_residual > $o) > pi).
% 4.64/2.05 thf(func_def_220, type, sK145: !>[X0: $tType]:(X0 > name)).
% 4.64/2.05 thf(func_def_221, type, sK146: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X0)).
% 4.64/2.05 thf(func_def_222, type, sK147: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X0)).
% 4.64/2.05 thf(func_def_223, type, sK148: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X1)).
% 4.64/2.05 thf(func_def_224, type, sK149: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X1)).
% 4.64/2.05 thf(func_def_225, type, sK150: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X1)).
% 4.64/2.05 thf(func_def_226, type, sK151: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X1)).
% 4.64/2.05 thf(func_def_227, type, sK152: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X0)).
% 4.64/2.05 thf(func_def_228, type, sK153: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X0)).
% 4.64/2.05 thf(func_def_229, type, sK154: late_subject > pi > (late_subject > pi > $o) > name > name > name).
% 4.64/2.05 thf(func_def_230, type, sK155: late_subject > pi > (late_subject > pi > $o) > name > name > pi).
% 4.64/2.05 thf(func_def_231, type, sK156: (late_subject > pi > $o) > name > late_subject > pi > name > pi).
% 4.64/2.05 thf(func_def_232, type, sK157: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 4.64/2.05 thf(func_def_233, type, sK158: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 4.64/2.05 thf(func_def_234, type, sK159: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 4.64/2.05 thf(func_def_235, type, sK160: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 4.64/2.05 thf(func_def_236, type, sK161: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X0)).
% 4.64/2.05 thf(func_def_237, type, sK162: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X1)).
% 4.64/2.05 thf(func_def_238, type, sK163: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X2)).
% 4.64/2.05 thf(func_def_239, type, sK164: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X3)).
% 4.64/2.05 thf(func_def_240, type, sK165: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X4)).
% 4.64/2.05 thf(func_def_241, type, sK166: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X5)).
% 4.64/2.05 thf(func_def_242, type, sK167: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X6)).
% 4.64/2.05 thf(func_def_243, type, sK168: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X0)).
% 4.64/2.05 thf(func_def_244, type, sK169: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X1)).
% 4.64/2.05 thf(func_def_245, type, sK170: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X1)).
% 4.64/2.05 thf(func_def_246, type, sK171: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X0)).
% 4.64/2.05 thf(func_def_247, type, sK172: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 4.64/2.05 thf(func_def_248, type, sK173: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 4.64/2.05 thf(func_def_249, type, sK174: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 4.64/2.05 thf(func_def_250, type, sK175: pi > late_freeRes > set @ product_prod @ pi @ pi > pi > pi).
% 4.64/2.05 thf(func_def_251, type, sK176: !>[X0: $tType]:(product_prod @ X0 @ X0 > X0)).
% 4.64/2.05 thf(func_def_252, type, sK177: !>[X0: $tType]:((X0 > late_residual > $o) > late_subject)).
% 4.64/2.05 thf(func_def_253, type, sK178: !>[X0: $tType]:((X0 > late_residual > $o) > name)).
% 4.64/2.05 thf(func_def_254, type, sK179: !>[X0: $tType]:((X0 > late_residual > $o) > pi)).
% 4.64/2.05 thf(func_def_255, type, sK180: !>[X0: $tType]:((X0 > late_residual > $o) > X0)).
% 4.64/2.05 thf(func_def_256, type, sK181: !>[X0: $tType]:((X0 > late_residual > $o) > late_freeRes)).
% 4.64/2.05 thf(func_def_257, type, sK182: !>[X0: $tType]:((X0 > late_residual > $o) > pi)).
% 4.64/2.05 thf(func_def_258, type, sK183: !>[X0: $tType]:((X0 > late_residual > $o) > X0)).
% 4.64/2.05 thf(func_def_259, type, sK184: pi > pi > name > set @ product_prod @ pi @ pi > pi).
% 4.64/2.05 thf(func_def_260, type, sK185: pi > pi > name > set @ product_prod @ pi @ pi > name).
% 4.64/2.05 thf(func_def_261, type, sK186: !>[X0: $tType]:(set @ product_prod @ pi @ pi > pi > X0 > name > pi > pi)).
% 4.64/2.05 thf(func_def_262, type, sK187: !>[X0: $tType]:(set @ product_prod @ pi @ pi > pi > X0 > name > pi > late_subject)).
% 4.64/2.05 thf(func_def_263, type, sK188: !>[X0: $tType]:(set @ product_prod @ pi @ pi > pi > X0 > name > pi > name)).
% 4.64/2.05 thf(func_def_264, type, sK189: pi > name > pi > set @ product_prod @ pi @ pi > pi).
% 4.64/2.05 thf(func_def_265, type, sK190: pi > name > pi > set @ product_prod @ pi @ pi > late_freeRes).
% 4.64/2.05 thf(func_def_266, type, sK191: !>[X0: $tType]:(product_prod @ list @ X0 @ list @ X0 > list @ X0)).
% 4.64/2.05 thf(func_def_267, type, sK192: !>[X0: $tType]:(product_prod @ list @ X0 @ list @ X0 > X0)).
% 4.64/2.05 thf(func_def_268, type, sK193: !>[X0: $tType]:(product_prod @ list @ X0 @ list @ X0 > list @ X0)).
% 4.64/2.05 thf(func_def_269, type, sK194: !>[X0: $tType]:(product_prod @ list @ X0 @ list @ X0 > X0)).
% 4.64/2.05 thf(func_def_270, type, sK195: !>[X0: $tType]:(product_prod @ list @ X0 @ list @ X0 > list @ X0)).
% 4.64/2.05 thf(func_def_271, type, sK196: !>[X0: $tType]:(product_prod @ list @ X0 @ list @ X0 > list @ X0)).
% 4.64/2.05 thf(func_def_272, type, sK197: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 4.64/2.05 thf(func_def_273, type, sK198: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 4.64/2.05 thf(func_def_274, type, sK199: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 4.64/2.05 thf(func_def_275, type, sK200: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 4.64/2.05 thf(func_def_276, type, sK201: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 4.64/2.05 thf(func_def_277, type, sK202: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 4.64/2.05 thf(func_def_278, type, sK203: !>[X0: $tType]:(list @ X0 > X0)).
% 4.64/2.05 thf(func_def_279, type, sK204: !>[X0: $tType]:(list @ X0 > X0)).
% 4.64/2.05 thf(func_def_280, type, sK205: !>[X0: $tType]:(list @ X0 > X0)).
% 4.64/2.05 thf(func_def_281, type, sK206: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 4.64/2.05 thf(func_def_282, type, sK207: !>[X0: $tType]:((X0 > late_residual > $o) > late_freeRes)).
% 4.64/2.05 thf(func_def_283, type, sK208: !>[X0: $tType]:((X0 > late_residual > $o) > pi)).
% 4.64/2.05 thf(func_def_284, type, sK209: !>[X0: $tType]:((X0 > late_residual > $o) > X0)).
% 4.64/2.05 thf(func_def_285, type, sK210: !>[X0: $tType]:((X0 > late_residual > $o) > late_subject)).
% 4.64/2.05 thf(func_def_286, type, sK211: !>[X0: $tType]:((X0 > late_residual > $o) > name)).
% 4.64/2.05 thf(func_def_287, type, sK212: !>[X0: $tType]:((X0 > late_residual > $o) > pi)).
% 4.64/2.05 thf(func_def_288, type, sK213: !>[X0: $tType]:((X0 > late_residual > $o) > X0)).
% 4.64/2.05 thf(func_def_289, type, sK214: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o)).
% 4.64/2.05 thf(func_def_290, type, sK215: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0)).
% 4.64/2.05 thf(func_def_291, type, sK216: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o)).
% 4.64/2.05 thf(func_def_292, type, sK217: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o)).
% 4.64/2.05 thf(func_def_293, type, sK218: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0)).
% 4.64/2.05 thf(func_def_294, type, sK219: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0)).
% 4.64/2.05 thf(func_def_295, type, sK220: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > list @ X0)).
% 4.64/2.05 thf(func_def_296, type, sK221: (pi > $o) > late_freeRes > pi > name > pi).
% 4.64/2.05 thf(func_def_297, type, sK222: !>[X0: $tType]:(X0 > set @ product_prod @ pi @ pi > pi > pi > late_subject)).
% 4.64/2.05 thf(func_def_298, type, sK223: !>[X0: $tType]:(X0 > set @ product_prod @ pi @ pi > pi > pi > name)).
% 4.64/2.05 thf(func_def_299, type, sK224: !>[X0: $tType]:(X0 > set @ product_prod @ pi @ pi > pi > pi > pi)).
% 4.64/2.05 thf(func_def_300, type, sK225: pi > pi > set @ product_prod @ pi @ pi > late_freeRes).
% 4.64/2.05 thf(func_def_301, type, sK226: pi > pi > set @ product_prod @ pi @ pi > pi).
% 4.64/2.05 thf(func_def_303, type, ph228: !>[X0: $tType]:(X0)).
% 4.64/2.05 thf(f1526,plain,(
% 4.64/2.05 $false),
% 4.64/2.05 inference(subsumption_resolution,[status(thm)],[f1525,f1438])).
% 4.64/2.05 thf(f1438,plain,(
% 4.64/2.05 ((ord_less_eq @ set @ product_prod @ pi @ pi @ id @ pi @ rel) = $true)),
% 4.64/2.05 inference(cnf_transformation,[status(thm)],[f537])).
% 4.64/2.05 thf(f537,plain,(
% 4.64/2.05 ((ord_less_eq @ set @ product_prod @ pi @ pi @ id @ pi @ rel) = $true)),
% 4.64/2.05 inference(fool_elimination,[status(thm)],[f536])).
% 4.64/2.05 thf(f536,plain,(
% 4.64/2.05 (ord_less_eq @ set @ product_prod @ pi @ pi @ id @ pi @ rel)),
% 4.64/2.05 inference(rectify,[status(thm)],[f1])).
% 4.64/2.05 thf(f1,axiom,(
% 4.64/2.05 (ord_less_eq @ set @ product_prod @ pi @ pi @ id @ pi @ rel)),
% 4.64/2.05 file('/export/starexec/sandbox/tmp/tmp.g7e8TF9fEe/DTF2THF_17774.p',fact_0_Id)).
% 4.64/2.05 thf(f1525,plain,(
% 4.64/2.05 ((ord_less_eq @ set @ product_prod @ pi @ pi @ id @ pi @ rel) != $true)),
% 4.64/2.05 inference(trivial_inequality_removal,[status(thm)],[f1522])).
% 4.64/2.05 thf(f1522,plain,(
% 4.64/2.05 ((ord_less_eq @ set @ product_prod @ pi @ pi @ id @ pi @ rel) != $true) | ($true != $true)),
% 4.64/2.05 inference(superposition,[status(thm)],[f1280,f1415])).
% 4.64/2.05 thf(f1415,plain,(
% 4.64/2.05 ( ! [X2 : late_subject,X3 : name,X0 : set @ product_prod @ pi @ pi,X1 : pi] : (((strong2129052853vative @ X1 @ X1 @ X2 @ X3 @ X0) = $true) | ((ord_less_eq @ set @ product_prod @ pi @ pi @ id @ pi @ X0) != $true)) )),
% 4.64/2.05 inference(cnf_transformation,[status(thm)],[f979])).
% 4.64/2.05 thf(f979,plain,(
% 4.64/2.05 ! [X0 : set @ product_prod @ pi @ pi,X1 : pi,X2 : late_subject,X3 : name] : (((ord_less_eq @ set @ product_prod @ pi @ pi @ id @ pi @ X0) != $true) | ((strong2129052853vative @ X1 @ X1 @ X2 @ X3 @ X0) = $true))),
% 4.64/2.05 inference(ennf_transformation,[status(thm)],[f315])).
% 4.64/2.05 thf(f315,plain,(
% 4.64/2.05 ! [X0 : set @ product_prod @ pi @ pi,X1 : pi,X2 : late_subject,X3 : name] : (((ord_less_eq @ set @ product_prod @ pi @ pi @ id @ pi @ X0) = $true) => ((strong2129052853vative @ X1 @ X1 @ X2 @ X3 @ X0) = $true))),
% 4.64/2.05 inference(fool_elimination,[status(thm)],[f314])).
% 4.64/2.05 thf(f314,plain,(
% 4.64/2.05 ! [X0 : set @ product_prod @ pi @ pi,X1 : pi,X2 : late_subject,X3 : name] : ((ord_less_eq @ set @ product_prod @ pi @ pi @ id @ pi @ X0) => (strong2129052853vative @ X1 @ X1 @ X2 @ X3 @ X0))),
% 4.64/2.05 inference(rectify,[status(thm)],[f95])).
% 4.64/2.05 thf(f95,axiom,(
% 4.64/2.05 ! [X73 : set @ product_prod @ pi @ pi,X37 : pi,X5 : late_subject,X7 : name] : ((ord_less_eq @ set @ product_prod @ pi @ pi @ id @ pi @ X73) => (strong2129052853vative @ X37 @ X37 @ X5 @ X7 @ X73))),
% 4.64/2.05 file('/export/starexec/sandbox/tmp/tmp.g7e8TF9fEe/DTF2THF_17774.p',fact_94_derivativeReflexive)).
% 4.64/2.05 thf(f1280,plain,(
% 4.64/2.05 ((strong2129052853vative @ (perm @ name @ pi @ (cons @ product_prod @ name @ name @ (product_Pair @ name @ name @ y @ x) @ nil @ product_prod @ name @ name) @ p2) @ (perm @ name @ pi @ (cons @ product_prod @ name @ name @ (product_Pair @ name @ name @ y @ x) @ nil @ product_prod @ name @ name) @ p2) @ (late_BoundOutputS @ aa) @ y @ rel) != $true)),
% 4.64/2.05 inference(cnf_transformation,[status(thm)],[f804])).
% 4.64/2.05 thf(f804,plain,(
% 4.64/2.05 ((strong2129052853vative @ (perm @ name @ pi @ (cons @ product_prod @ name @ name @ (product_Pair @ name @ name @ y @ x) @ nil @ product_prod @ name @ name) @ p2) @ (perm @ name @ pi @ (cons @ product_prod @ name @ name @ (product_Pair @ name @ name @ y @ x) @ nil @ product_prod @ name @ name) @ p2) @ (late_BoundOutputS @ aa) @ y @ rel) != $true)),
% 4.64/2.05 inference(flattening,[status(thm)],[f717])).
% 4.64/2.05 thf(f717,plain,(
% 4.64/2.05 ~((strong2129052853vative @ (perm @ name @ pi @ (cons @ product_prod @ name @ name @ (product_Pair @ name @ name @ y @ x) @ nil @ product_prod @ name @ name) @ p2) @ (perm @ name @ pi @ (cons @ product_prod @ name @ name @ (product_Pair @ name @ name @ y @ x) @ nil @ product_prod @ name @ name) @ p2) @ (late_BoundOutputS @ aa) @ y @ rel) = $true)),
% 4.64/2.05 inference(fool_elimination,[status(thm)],[f716])).
% 4.64/2.05 thf(f716,plain,(
% 4.64/2.05 ~(strong2129052853vative @ (perm @ name @ pi @ (cons @ product_prod @ name @ name @ (product_Pair @ name @ name @ y @ x) @ nil @ product_prod @ name @ name) @ p2) @ (perm @ name @ pi @ (cons @ product_prod @ name @ name @ (product_Pair @ name @ name @ y @ x) @ nil @ product_prod @ name @ name) @ p2) @ (late_BoundOutputS @ aa) @ y @ rel)),
% 4.64/2.05 inference(rectify,[status(thm)],[f306])).
% 4.64/2.05 thf(f306,negated_conjecture,(
% 4.64/2.05 ~(strong2129052853vative @ (perm @ name @ pi @ (cons @ product_prod @ name @ name @ (product_Pair @ name @ name @ y @ x) @ nil @ product_prod @ name @ name) @ p2) @ (perm @ name @ pi @ (cons @ product_prod @ name @ name @ (product_Pair @ name @ name @ y @ x) @ nil @ product_prod @ name @ name) @ p2) @ (late_BoundOutputS @ aa) @ y @ rel)),
% 4.64/2.05 inference(negated_conjecture,[status(cth)],[f305])).
% 4.64/2.05 thf(f305,conjecture,(
% 4.64/2.05 (strong2129052853vative @ (perm @ name @ pi @ (cons @ product_prod @ name @ name @ (product_Pair @ name @ name @ y @ x) @ nil @ product_prod @ name @ name) @ p2) @ (perm @ name @ pi @ (cons @ product_prod @ name @ name @ (product_Pair @ name @ name @ y @ x) @ nil @ product_prod @ name @ name) @ p2) @ (late_BoundOutputS @ aa) @ y @ rel)),
% 4.64/2.05 file('/export/starexec/sandbox/tmp/tmp.g7e8TF9fEe/DTF2THF_17774.p',conj_0)).
% 4.64/2.05 % SZS output end Proof for DTF2THF_17774
% 4.64/2.05 % (17885)------------------------------
% 4.64/2.05 % (17885)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.64/2.05 % (17885)Termination reason: Refutation
% 4.64/2.05
% 4.64/2.05 % (17885)Memory used [KB]: 7931
% 4.64/2.05 % (17885)Time elapsed: 0.087 s
% 4.64/2.05 % (17885)Instructions burned: 146 (million)
% 4.64/2.05 % (17885)------------------------------
% 4.64/2.05 % (17885)------------------------------
% 4.64/2.05 % (17879)Success in time 0.117 s
%------------------------------------------------------------------------------