TSTP Solution File: ITP182^1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP182^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n004.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 : Thu Aug 31 03:18:57 EDT 2023
% Result : Theorem 0.86s 1.09s
% Output : Proof 0.86s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.19 % Problem : ITP182^1 : TPTP v8.1.2. Released v7.5.0.
% 0.20/0.20 % Command : do_cvc5 %s %d
% 0.20/0.42 % Computer : n004.cluster.edu
% 0.20/0.42 % Model : x86_64 x86_64
% 0.20/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.42 % Memory : 8042.1875MB
% 0.20/0.42 % OS : Linux 3.10.0-693.el7.x86_64
% 0.20/0.42 % CPULimit : 300
% 0.20/0.42 % WCLimit : 300
% 0.20/0.42 % DateTime : Sun Aug 27 10:18:22 EDT 2023
% 0.20/0.42 % CPUTime :
% 0.27/0.61 %----Proving TH0
% 0.27/0.62 %------------------------------------------------------------------------------
% 0.27/0.62 % File : ITP182^1 : TPTP v8.1.2. Released v7.5.0.
% 0.27/0.62 % Domain : Interactive Theorem Proving
% 0.27/0.62 % Problem : Sledgehammer Strong_Late_Sim_SC problem prob_279__3411076_1
% 0.27/0.62 % Version : Especial.
% 0.27/0.62 % English :
% 0.27/0.62
% 0.27/0.62 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.27/0.62 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.27/0.62 % Source : [Des21]
% 0.27/0.62 % Names : Strong_Late_Sim_SC/prob_279__3411076_1 [Des21]
% 0.27/0.62
% 0.27/0.62 % Status : Theorem
% 0.27/0.62 % Rating : 0.15 v8.1.0, 0.18 v7.5.0
% 0.27/0.62 % Syntax : Number of formulae : 557 ( 219 unt; 192 typ; 0 def)
% 0.27/0.62 % Number of atoms : 849 ( 387 equ; 0 cnn)
% 0.27/0.62 % Maximal formula atoms : 16 ( 2 avg)
% 0.27/0.62 % Number of connectives : 3597 ( 111 ~; 1 |; 50 &;3097 @)
% 0.27/0.62 % ( 0 <=>; 338 =>; 0 <=; 0 <~>)
% 0.27/0.62 % Maximal formula depth : 23 ( 7 avg)
% 0.27/0.62 % Number of types : 47 ( 46 usr)
% 0.27/0.62 % Number of type conns : 371 ( 371 >; 0 *; 0 +; 0 <<)
% 0.27/0.62 % Number of symbols : 149 ( 146 usr; 15 con; 0-5 aty)
% 0.27/0.62 % Number of variables : 1211 ( 15 ^;1182 !; 14 ?;1211 :)
% 0.27/0.62 % SPC : TH0_THM_EQU_NAR
% 0.27/0.62
% 0.27/0.62 % Comments : This file was generated by Sledgehammer 2021-02-23 15:30:40.333
% 0.27/0.62 %------------------------------------------------------------------------------
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% 0.27/0.62 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__Osubject_001t__Agent__Opi____Rep,type,
% 0.27/0.62 produc843063281pi_Rep: late_subject > pi_Rep > produc257012921pi_Rep ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__Osubject_001t__Late____Semantics__OfreeRes,type,
% 0.27/0.62 produc242091907reeRes: late_subject > late_freeRes > produc355105483reeRes ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__Osubject_001t__Late____Semantics__Osubject,type,
% 0.27/0.62 produc1465345179ubject: late_subject > late_subject > produc1359399907ubject ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J_J_001t__List__Olist_It__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J_J,type,
% 0.27/0.62 produc208131031e_name: list_P227219501e_name > list_P227219501e_name > produc890461031e_name ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Rel_Oeqvt_001t__Agent__Oname,type,
% 0.27/0.62 eqvt_name: set_Pr443758855e_name > $o ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Rel_Oeqvt_001t__Agent__Opi,type,
% 0.27/0.62 eqvt_pi: set_Pr1834926343_pi_pi > $o ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Rel_Oeqvt_001t__Agent__Opi____Rep,type,
% 0.27/0.62 eqvt_pi_Rep: set_Pr1131282415pi_Rep > $o ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Rel_Oeqvt_001t__Late____Semantics__OfreeRes,type,
% 0.27/0.62 eqvt_Late_freeRes: set_Pr1780909331reeRes > $o ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Rel_Oeqvt_001t__Late____Semantics__Osubject,type,
% 0.27/0.62 eqvt_Late_subject: set_Pr806375235ubject > $o ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Relation_OId_001t__Agent__Oname,type,
% 0.27/0.62 id_name: set_Pr443758855e_name ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Relation_OId_001t__Agent__Opi,type,
% 0.27/0.62 id_pi: set_Pr1834926343_pi_pi ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J,type,
% 0.27/0.62 collec1051790738_pi_pi: ( product_prod_pi_pi > $o ) > set_Pr1834926343_pi_pi ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Strong__Late__Sim_Oderivative,type,
% 0.27/0.62 strong2129052853vative: pi > pi > late_subject > name > set_Pr1834926343_pi_pi > $o ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_Strong__Late__Sim_Osimulation,type,
% 0.27/0.62 strong743114133lation: pi > set_Pr1834926343_pi_pi > pi > $o ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_member_001t__Agent__Oname,type,
% 0.27/0.62 member_name: name > set_name > $o ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_member_001t__Agent__Opi,type,
% 0.27/0.62 member_pi: pi > set_pi > $o ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_member_001t__Agent__Opi____Rep,type,
% 0.27/0.62 member_pi_Rep: pi_Rep > set_pi_Rep > $o ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_member_001t__Late____Semantics__OfreeRes,type,
% 0.27/0.62 member_Late_freeRes: late_freeRes > set_Late_freeRes > $o ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_member_001t__Late____Semantics__Osubject,type,
% 0.27/0.62 member_Late_subject: late_subject > set_Late_subject > $o ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_member_001t__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J,type,
% 0.27/0.62 member695284560e_name: produc367475239e_name > set_Pr443758855e_name > $o ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_member_001t__Product____Type__Oprod_It__Agent__Oname_Mt__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J,type,
% 0.27/0.62 member540268543_pi_pi: produc1141751126_pi_pi > set_Pr1654044726_pi_pi > $o ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_member_001t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J,type,
% 0.27/0.62 member558706512_pi_pi: product_prod_pi_pi > set_Pr1834926343_pi_pi > $o ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_member_001t__Product____Type__Oprod_It__Agent__Opi____Rep_Mt__Agent__Opi____Rep_J,type,
% 0.27/0.62 member1671908408pi_Rep: produc1212344719pi_Rep > set_Pr1131282415pi_Rep > $o ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_member_001t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Late____Semantics__OfreeRes_J,type,
% 0.27/0.62 member1584979804reeRes: produc1357834675reeRes > set_Pr1780909331reeRes > $o ).
% 0.27/0.62
% 0.27/0.62 thf(sy_c_member_001t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Late____Semantics__Osubject_J,type,
% 0.27/0.62 member1586545036ubject: produc1359399907ubject > set_Pr806375235ubject > $o ).
% 0.27/0.62
% 0.27/0.62 thf(sy_v_P,type,
% 0.27/0.62 p: pi ).
% 0.27/0.62
% 0.27/0.62 thf(sy_v_PQ____,type,
% 0.27/0.62 pq: pi ).
% 0.27/0.62
% 0.27/0.62 thf(sy_v_P_H____,type,
% 0.27/0.62 p2: pi ).
% 0.27/0.62
% 0.27/0.62 thf(sy_v_Q,type,
% 0.27/0.62 q: pi ).
% 0.27/0.62
% 0.27/0.62 thf(sy_v_Rel,type,
% 0.27/0.62 rel: set_Pr1834926343_pi_pi ).
% 0.27/0.62
% 0.27/0.62 thf(sy_v_a____,type,
% 0.27/0.62 a: late_subject ).
% 0.27/0.62
% 0.27/0.62 thf(sy_v_aa____,type,
% 0.27/0.62 aa: name ).
% 0.27/0.62
% 0.27/0.62 thf(sy_v_x,type,
% 0.27/0.62 x: name ).
% 0.27/0.62
% 0.27/0.62 thf(sy_v_y____,type,
% 0.27/0.62 y: name ).
% 0.27/0.62
% 0.27/0.62 % Relevant facts (353)
% 0.27/0.62 thf(fact_0_Id,axiom,
% 0.27/0.62 ord_le630093991_pi_pi @ id_pi @ rel ).
% 0.27/0.62
% 0.27/0.62 % Id
% 0.27/0.62 thf(fact_1_cOpen_Ohyps_I2_J,axiom,
% 0.27/0.62 aa != x ).
% 0.27/0.62
% 0.27/0.62 % cOpen.hyps(2)
% 0.27/0.62 thf(fact_2_cOpen_Ohyps_I3_J,axiom,
% 0.27/0.62 ( a
% 0.27/0.62 = ( late_BoundOutputS @ aa ) ) ).
% 0.27/0.62
% 0.27/0.62 % cOpen.hyps(3)
% 0.27/0.62 thf(fact_3__092_060open_062y_A_092_060noteq_062_Ax_092_060close_062,axiom,
% 0.27/0.62 y != x ).
% 0.27/0.62
% 0.27/0.62 % \<open>y \<noteq> x\<close>
% 0.27/0.62 thf(fact_4_Eqvt,axiom,
% 0.27/0.62 eqvt_pi @ rel ).
% 0.27/0.62
% 0.27/0.62 % Eqvt
% 0.27/0.62 thf(fact_5_perm__swap_I1_J,axiom,
% 0.27/0.62 ! [A: name,B: name,X: late_subject] :
% 0.27/0.62 ( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) )
% 0.27/0.62 = X ) ).
% 0.27/0.62
% 0.27/0.62 % perm_swap(1)
% 0.27/0.62 thf(fact_6_perm__swap_I1_J,axiom,
% 0.27/0.62 ! [A: name,B: name,X: late_freeRes] :
% 0.27/0.62 ( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) )
% 0.27/0.62 = X ) ).
% 0.27/0.62
% 0.27/0.62 % perm_swap(1)
% 0.27/0.62 thf(fact_7_perm__swap_I1_J,axiom,
% 0.27/0.62 ! [A: name,B: name,X: pi_Rep] :
% 0.27/0.62 ( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) )
% 0.27/0.62 = X ) ).
% 0.27/0.62
% 0.27/0.62 % perm_swap(1)
% 0.27/0.62 thf(fact_8_perm__swap_I1_J,axiom,
% 0.27/0.62 ! [A: name,B: name,X: name] :
% 0.27/0.62 ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) )
% 0.27/0.62 = X ) ).
% 0.27/0.62
% 0.27/0.62 % perm_swap(1)
% 0.27/0.62 thf(fact_9_perm__swap_I1_J,axiom,
% 0.27/0.62 ! [A: name,B: name,X: pi] :
% 0.27/0.62 ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) )
% 0.27/0.62 = X ) ).
% 0.27/0.62
% 0.27/0.62 % perm_swap(1)
% 0.27/0.62 thf(fact_10_name__id,axiom,
% 0.27/0.62 ! [A: name,X: late_subject] :
% 0.27/0.62 ( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ A ) @ nil_Pr743626285e_name ) @ X )
% 0.27/0.62 = X ) ).
% 0.27/0.62
% 0.27/0.62 % name_id
% 0.27/0.62 thf(fact_11_name__id,axiom,
% 0.27/0.62 ! [A: name,X: late_freeRes] :
% 0.27/0.62 ( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ A ) @ nil_Pr743626285e_name ) @ X )
% 0.27/0.62 = X ) ).
% 0.27/0.62
% 0.27/0.62 % name_id
% 0.27/0.62 thf(fact_12_name__id,axiom,
% 0.27/0.62 ! [A: name,X: pi_Rep] :
% 0.27/0.62 ( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ A ) @ nil_Pr743626285e_name ) @ X )
% 0.27/0.62 = X ) ).
% 0.27/0.62
% 0.27/0.62 % name_id
% 0.27/0.62 thf(fact_13_name__id,axiom,
% 0.27/0.62 ! [A: name,X: name] :
% 0.27/0.62 ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ A ) @ nil_Pr743626285e_name ) @ X )
% 0.27/0.62 = X ) ).
% 0.27/0.62
% 0.27/0.62 % name_id
% 0.27/0.62 thf(fact_14_name__id,axiom,
% 0.27/0.62 ! [A: name,X: pi] :
% 0.27/0.62 ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ A ) @ nil_Pr743626285e_name ) @ X )
% 0.27/0.62 = X ) ).
% 0.27/0.62
% 0.27/0.62 % name_id
% 0.27/0.62 thf(fact_15_name__swap,axiom,
% 0.27/0.62 ! [A: name,B: name,X: late_subject] :
% 0.27/0.62 ( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.27/0.62 = ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) ) ).
% 0.27/0.62
% 0.27/0.62 % name_swap
% 0.27/0.62 thf(fact_16_name__swap,axiom,
% 0.27/0.62 ! [A: name,B: name,X: late_freeRes] :
% 0.27/0.62 ( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.27/0.62 = ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) ) ).
% 0.27/0.62
% 0.27/0.62 % name_swap
% 0.27/0.62 thf(fact_17_name__swap,axiom,
% 0.27/0.62 ! [A: name,B: name,X: pi_Rep] :
% 0.27/0.62 ( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.27/0.62 = ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) ) ).
% 0.27/0.62
% 0.27/0.62 % name_swap
% 0.27/0.62 thf(fact_18_name__swap,axiom,
% 0.27/0.62 ! [A: name,B: name,X: name] :
% 0.27/0.62 ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.27/0.62 = ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) ) ).
% 0.27/0.62
% 0.27/0.62 % name_swap
% 0.27/0.62 thf(fact_19_name__swap,axiom,
% 0.27/0.62 ! [A: name,B: name,X: pi] :
% 0.27/0.62 ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.27/0.62 = ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) ) ).
% 0.27/0.62
% 0.27/0.62 % name_swap
% 0.27/0.62 thf(fact_20_name__swap__bij,axiom,
% 0.27/0.62 ! [A: name,B: name,X: late_subject] :
% 0.27/0.62 ( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) )
% 0.27/0.62 = X ) ).
% 0.27/0.62
% 0.27/0.62 % name_swap_bij
% 0.27/0.62 thf(fact_21_name__swap__bij,axiom,
% 0.27/0.62 ! [A: name,B: name,X: late_freeRes] :
% 0.27/0.62 ( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) )
% 0.27/0.62 = X ) ).
% 0.27/0.62
% 0.27/0.62 % name_swap_bij
% 0.27/0.62 thf(fact_22_name__swap__bij,axiom,
% 0.27/0.62 ! [A: name,B: name,X: pi_Rep] :
% 0.27/0.62 ( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) )
% 0.27/0.62 = X ) ).
% 0.27/0.62
% 0.27/0.62 % name_swap_bij
% 0.27/0.62 thf(fact_23_name__swap__bij,axiom,
% 0.27/0.62 ! [A: name,B: name,X: name] :
% 0.27/0.62 ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) )
% 0.27/0.62 = X ) ).
% 0.27/0.62
% 0.27/0.62 % name_swap_bij
% 0.27/0.62 thf(fact_24_name__swap__bij,axiom,
% 0.27/0.62 ! [A: name,B: name,X: pi] :
% 0.27/0.62 ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) )
% 0.27/0.62 = X ) ).
% 0.27/0.62
% 0.27/0.62 % name_swap_bij
% 0.27/0.62 thf(fact_25_pt__name1,axiom,
% 0.27/0.62 ! [X: late_subject] :
% 0.27/0.62 ( ( perm_n1559866809ubject @ nil_Pr743626285e_name @ X )
% 0.27/0.62 = X ) ).
% 0.27/0.62
% 0.27/0.62 % pt_name1
% 0.27/0.62 thf(fact_26_pt__name1,axiom,
% 0.27/0.62 ! [X: late_freeRes] :
% 0.27/0.62 ( ( perm_n336613537reeRes @ nil_Pr743626285e_name @ X )
% 0.27/0.62 = X ) ).
% 0.27/0.62
% 0.27/0.62 % pt_name1
% 0.27/0.62 thf(fact_27_pt__name1,axiom,
% 0.27/0.62 ! [X: pi_Rep] :
% 0.27/0.62 ( ( perm_name_pi_Rep @ nil_Pr743626285e_name @ X )
% 0.27/0.62 = X ) ).
% 0.27/0.62
% 0.27/0.62 % pt_name1
% 0.27/0.62 thf(fact_28_pt__name1,axiom,
% 0.27/0.62 ! [X: name] :
% 0.27/0.62 ( ( perm_name_name @ nil_Pr743626285e_name @ X )
% 0.27/0.62 = X ) ).
% 0.27/0.62
% 0.27/0.62 % pt_name1
% 0.27/0.62 thf(fact_29_pt__name1,axiom,
% 0.27/0.62 ! [X: pi] :
% 0.27/0.62 ( ( perm_name_pi @ nil_Pr743626285e_name @ X )
% 0.27/0.62 = X ) ).
% 0.27/0.62
% 0.27/0.62 % pt_name1
% 0.27/0.62 thf(fact_30_perm__swap_I2_J,axiom,
% 0.27/0.62 ! [A: name,B: name,X: late_subject] :
% 0.27/0.62 ( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) )
% 0.27/0.62 = X ) ).
% 0.27/0.62
% 0.27/0.62 % perm_swap(2)
% 0.27/0.62 thf(fact_31_perm__swap_I2_J,axiom,
% 0.27/0.62 ! [A: name,B: name,X: late_freeRes] :
% 0.27/0.62 ( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) )
% 0.27/0.62 = X ) ).
% 0.27/0.62
% 0.27/0.62 % perm_swap(2)
% 0.27/0.62 thf(fact_32_perm__swap_I2_J,axiom,
% 0.27/0.62 ! [A: name,B: name,X: pi_Rep] :
% 0.27/0.62 ( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) )
% 0.27/0.62 = X ) ).
% 0.27/0.62
% 0.27/0.62 % perm_swap(2)
% 0.27/0.62 thf(fact_33_perm__swap_I2_J,axiom,
% 0.27/0.62 ! [A: name,B: name,X: name] :
% 0.27/0.62 ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) )
% 0.27/0.62 = X ) ).
% 0.27/0.62
% 0.27/0.62 % perm_swap(2)
% 0.27/0.62 thf(fact_34_perm__swap_I2_J,axiom,
% 0.27/0.62 ! [A: name,B: name,X: pi] :
% 0.27/0.62 ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) )
% 0.27/0.62 = X ) ).
% 0.27/0.62
% 0.27/0.62 % perm_swap(2)
% 0.27/0.62 thf(fact_35_Late__Semantics_Osubject_Oinject_I2_J,axiom,
% 0.27/0.62 ! [X1: name,Y1: name] :
% 0.27/0.62 ( ( ( late_BoundOutputS @ X1 )
% 0.27/0.62 = ( late_BoundOutputS @ Y1 ) )
% 0.27/0.62 = ( X1 = Y1 ) ) ).
% 0.27/0.62
% 0.27/0.62 % Late_Semantics.subject.inject(2)
% 0.27/0.62 thf(fact_36_Late__Semantics1_Osubject_Oinject_I2_J,axiom,
% 0.27/0.62 ! [X2: name,Y2: name] :
% 0.27/0.62 ( ( ( late_BoundOutputS @ X2 )
% 0.27/0.62 = ( late_BoundOutputS @ Y2 ) )
% 0.27/0.62 = ( X2 = Y2 ) ) ).
% 0.27/0.62
% 0.27/0.62 % Late_Semantics1.subject.inject(2)
% 0.27/0.62 thf(fact_37__092_060open_062y_A_092_060sharp_062_AP_H_092_060close_062,axiom,
% 0.27/0.62 fresh_name_pi @ y @ p2 ).
% 0.27/0.62
% 0.27/0.62 % \<open>y \<sharp> P'\<close>
% 0.27/0.62 thf(fact_38_list_Oinject,axiom,
% 0.27/0.62 ! [X21: produc367475239e_name,X22: list_P227219501e_name,Y21: produc367475239e_name,Y22: list_P227219501e_name] :
% 0.27/0.62 ( ( ( cons_P1213805021e_name @ X21 @ X22 )
% 0.27/0.62 = ( cons_P1213805021e_name @ Y21 @ Y22 ) )
% 0.27/0.62 = ( ( X21 = Y21 )
% 0.27/0.62 & ( X22 = Y22 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % list.inject
% 0.27/0.62 thf(fact_39_prod_Oinject,axiom,
% 0.27/0.62 ! [X1: name,X2: name,Y1: name,Y2: name] :
% 0.27/0.62 ( ( ( produc1570949143e_name @ X1 @ X2 )
% 0.27/0.62 = ( produc1570949143e_name @ Y1 @ Y2 ) )
% 0.27/0.62 = ( ( X1 = Y1 )
% 0.27/0.62 & ( X2 = Y2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % prod.inject
% 0.27/0.62 thf(fact_40_prod_Oinject,axiom,
% 0.27/0.62 ! [X1: name,X2: product_prod_pi_pi,Y1: name,Y2: product_prod_pi_pi] :
% 0.27/0.62 ( ( ( produc235456326_pi_pi @ X1 @ X2 )
% 0.27/0.62 = ( produc235456326_pi_pi @ Y1 @ Y2 ) )
% 0.27/0.62 = ( ( X1 = Y1 )
% 0.27/0.62 & ( X2 = Y2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % prod.inject
% 0.27/0.62 thf(fact_41_prod_Oinject,axiom,
% 0.27/0.62 ! [X1: pi,X2: pi,Y1: pi,Y2: pi] :
% 0.27/0.62 ( ( ( product_Pair_pi_pi @ X1 @ X2 )
% 0.27/0.62 = ( product_Pair_pi_pi @ Y1 @ Y2 ) )
% 0.27/0.62 = ( ( X1 = Y1 )
% 0.27/0.62 & ( X2 = Y2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % prod.inject
% 0.27/0.62 thf(fact_42_old_Oprod_Oinject,axiom,
% 0.27/0.62 ! [A: name,B: name,A2: name,B2: name] :
% 0.27/0.62 ( ( ( produc1570949143e_name @ A @ B )
% 0.27/0.62 = ( produc1570949143e_name @ A2 @ B2 ) )
% 0.27/0.62 = ( ( A = A2 )
% 0.27/0.62 & ( B = B2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % old.prod.inject
% 0.27/0.62 thf(fact_43_old_Oprod_Oinject,axiom,
% 0.27/0.62 ! [A: name,B: product_prod_pi_pi,A2: name,B2: product_prod_pi_pi] :
% 0.27/0.62 ( ( ( produc235456326_pi_pi @ A @ B )
% 0.27/0.62 = ( produc235456326_pi_pi @ A2 @ B2 ) )
% 0.27/0.62 = ( ( A = A2 )
% 0.27/0.62 & ( B = B2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % old.prod.inject
% 0.27/0.62 thf(fact_44_old_Oprod_Oinject,axiom,
% 0.27/0.62 ! [A: pi,B: pi,A2: pi,B2: pi] :
% 0.27/0.62 ( ( ( product_Pair_pi_pi @ A @ B )
% 0.27/0.62 = ( product_Pair_pi_pi @ A2 @ B2 ) )
% 0.27/0.62 = ( ( A = A2 )
% 0.27/0.62 & ( B = B2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % old.prod.inject
% 0.27/0.62 thf(fact_45_residual__perm__empty,axiom,
% 0.27/0.62 ! [Residual_Rep: late_residual_Rep] :
% 0.27/0.62 ( ( perm_n890803237al_Rep @ nil_Pr743626285e_name @ Residual_Rep )
% 0.27/0.62 = Residual_Rep ) ).
% 0.27/0.62
% 0.27/0.62 % residual_perm_empty
% 0.27/0.62 thf(fact_46_subject__perm__empty,axiom,
% 0.27/0.62 ! [Subject_Rep: late_subject_Rep] :
% 0.27/0.62 ( ( perm_n697952036ct_Rep @ nil_Pr743626285e_name @ Subject_Rep )
% 0.27/0.62 = Subject_Rep ) ).
% 0.27/0.62
% 0.27/0.62 % subject_perm_empty
% 0.27/0.62 thf(fact_47_freeRes__perm__empty,axiom,
% 0.27/0.62 ! [FreeRes_Rep: late_freeRes_Rep] :
% 0.27/0.62 ( ( perm_n1938283068es_Rep @ nil_Pr743626285e_name @ FreeRes_Rep )
% 0.27/0.62 = FreeRes_Rep ) ).
% 0.27/0.62
% 0.27/0.62 % freeRes_perm_empty
% 0.27/0.62 thf(fact_48_pi__perm__empty,axiom,
% 0.27/0.62 ! [Pi_Rep: pi_Rep] :
% 0.27/0.62 ( ( perm_name_pi_Rep @ nil_Pr743626285e_name @ Pi_Rep )
% 0.27/0.62 = Pi_Rep ) ).
% 0.27/0.62
% 0.27/0.62 % pi_perm_empty
% 0.27/0.62 thf(fact_49_subject_Operm_I2_J,axiom,
% 0.27/0.62 ! [Pi: list_P227219501e_name,X1: name] :
% 0.27/0.62 ( ( perm_n1559866809ubject @ Pi @ ( late_BoundOutputS @ X1 ) )
% 0.27/0.62 = ( late_BoundOutputS @ ( perm_name_name @ Pi @ X1 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % subject.perm(2)
% 0.27/0.62 thf(fact_50_perm__fresh__fresh,axiom,
% 0.27/0.62 ! [A: name,X: pi_Rep,B: name] :
% 0.27/0.62 ( ( fresh_name_pi_Rep @ A @ X )
% 0.27/0.62 => ( ( fresh_name_pi_Rep @ B @ X )
% 0.27/0.62 => ( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.27/0.62 = X ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % perm_fresh_fresh
% 0.27/0.62 thf(fact_51_perm__fresh__fresh,axiom,
% 0.27/0.62 ! [A: name,X: late_subject,B: name] :
% 0.27/0.62 ( ( fresh_717452603ubject @ A @ X )
% 0.27/0.62 => ( ( fresh_717452603ubject @ B @ X )
% 0.27/0.62 => ( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.27/0.62 = X ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % perm_fresh_fresh
% 0.27/0.62 thf(fact_52_perm__fresh__fresh,axiom,
% 0.27/0.62 ! [A: name,X: late_freeRes,B: name] :
% 0.27/0.62 ( ( fresh_1641682979reeRes @ A @ X )
% 0.27/0.62 => ( ( fresh_1641682979reeRes @ B @ X )
% 0.27/0.62 => ( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.27/0.62 = X ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % perm_fresh_fresh
% 0.27/0.62 thf(fact_53_perm__fresh__fresh,axiom,
% 0.27/0.62 ! [A: name,X: produc1141751126_pi_pi,B: name] :
% 0.27/0.62 ( ( fresh_1376661020_pi_pi @ A @ X )
% 0.27/0.62 => ( ( fresh_1376661020_pi_pi @ B @ X )
% 0.27/0.62 => ( ( perm_n1255502110_pi_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.27/0.62 = X ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % perm_fresh_fresh
% 0.27/0.62 thf(fact_54_perm__fresh__fresh,axiom,
% 0.27/0.62 ! [A: name,X: name,B: name] :
% 0.27/0.62 ( ( fresh_name_name @ A @ X )
% 0.27/0.62 => ( ( fresh_name_name @ B @ X )
% 0.27/0.62 => ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.27/0.62 = X ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % perm_fresh_fresh
% 0.27/0.62 thf(fact_55_perm__fresh__fresh,axiom,
% 0.27/0.62 ! [A: name,X: pi,B: name] :
% 0.27/0.62 ( ( fresh_name_pi @ A @ X )
% 0.27/0.62 => ( ( fresh_name_pi @ B @ X )
% 0.27/0.62 => ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.27/0.62 = X ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % perm_fresh_fresh
% 0.27/0.62 thf(fact_56_name__fresh__fresh,axiom,
% 0.27/0.62 ! [A: name,X: pi_Rep,B: name] :
% 0.27/0.62 ( ( fresh_name_pi_Rep @ A @ X )
% 0.27/0.62 => ( ( fresh_name_pi_Rep @ B @ X )
% 0.27/0.62 => ( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.27/0.62 = X ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % name_fresh_fresh
% 0.27/0.62 thf(fact_57_name__fresh__fresh,axiom,
% 0.27/0.62 ! [A: name,X: late_subject,B: name] :
% 0.27/0.62 ( ( fresh_717452603ubject @ A @ X )
% 0.27/0.62 => ( ( fresh_717452603ubject @ B @ X )
% 0.27/0.62 => ( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.27/0.62 = X ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % name_fresh_fresh
% 0.27/0.62 thf(fact_58_name__fresh__fresh,axiom,
% 0.27/0.62 ! [A: name,X: late_freeRes,B: name] :
% 0.27/0.62 ( ( fresh_1641682979reeRes @ A @ X )
% 0.27/0.62 => ( ( fresh_1641682979reeRes @ B @ X )
% 0.27/0.62 => ( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.27/0.62 = X ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % name_fresh_fresh
% 0.27/0.62 thf(fact_59_name__fresh__fresh,axiom,
% 0.27/0.62 ! [A: name,X: produc1141751126_pi_pi,B: name] :
% 0.27/0.62 ( ( fresh_1376661020_pi_pi @ A @ X )
% 0.27/0.62 => ( ( fresh_1376661020_pi_pi @ B @ X )
% 0.27/0.62 => ( ( perm_n1255502110_pi_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.27/0.62 = X ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % name_fresh_fresh
% 0.27/0.62 thf(fact_60_name__fresh__fresh,axiom,
% 0.27/0.62 ! [A: name,X: name,B: name] :
% 0.27/0.62 ( ( fresh_name_name @ A @ X )
% 0.27/0.62 => ( ( fresh_name_name @ B @ X )
% 0.27/0.62 => ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.27/0.62 = X ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % name_fresh_fresh
% 0.27/0.62 thf(fact_61_name__fresh__fresh,axiom,
% 0.27/0.62 ! [A: name,X: pi,B: name] :
% 0.27/0.62 ( ( fresh_name_pi @ A @ X )
% 0.27/0.62 => ( ( fresh_name_pi @ B @ X )
% 0.27/0.62 => ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.27/0.62 = X ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % name_fresh_fresh
% 0.27/0.62 thf(fact_62_Bound_Ohyps_I4_J,axiom,
% 0.27/0.62 fresh_717452603ubject @ y @ a ).
% 0.27/0.62
% 0.27/0.62 % Bound.hyps(4)
% 0.27/0.62 thf(fact_63_subseteq__eqvt,axiom,
% 0.27/0.62 ! [Pi: list_P227219501e_name,X3: set_Pr1834926343_pi_pi,Y: set_Pr1834926343_pi_pi] :
% 0.27/0.62 ( ( perm_name_o @ Pi @ ( ord_le630093991_pi_pi @ X3 @ Y ) )
% 0.27/0.62 = ( ord_le630093991_pi_pi @ ( perm_n675238095_pi_pi @ Pi @ X3 ) @ ( perm_n675238095_pi_pi @ Pi @ Y ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % subseteq_eqvt
% 0.27/0.62 thf(fact_64_fresh__perm__app,axiom,
% 0.27/0.62 ! [A: name,Pi: list_P227219501e_name,X: pi_Rep] :
% 0.27/0.62 ( ( fresh_922791155e_name @ A @ Pi )
% 0.27/0.62 => ( ( fresh_name_pi_Rep @ A @ X )
% 0.27/0.62 => ( fresh_name_pi_Rep @ A @ ( perm_name_pi_Rep @ Pi @ X ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % fresh_perm_app
% 0.27/0.62 thf(fact_65_fresh__perm__app,axiom,
% 0.27/0.62 ! [A: name,Pi: list_P227219501e_name,X: late_subject] :
% 0.27/0.62 ( ( fresh_922791155e_name @ A @ Pi )
% 0.27/0.62 => ( ( fresh_717452603ubject @ A @ X )
% 0.27/0.62 => ( fresh_717452603ubject @ A @ ( perm_n1559866809ubject @ Pi @ X ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % fresh_perm_app
% 0.27/0.62 thf(fact_66_fresh__perm__app,axiom,
% 0.27/0.62 ! [A: name,Pi: list_P227219501e_name,X: late_freeRes] :
% 0.27/0.62 ( ( fresh_922791155e_name @ A @ Pi )
% 0.27/0.62 => ( ( fresh_1641682979reeRes @ A @ X )
% 0.27/0.62 => ( fresh_1641682979reeRes @ A @ ( perm_n336613537reeRes @ Pi @ X ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % fresh_perm_app
% 0.27/0.62 thf(fact_67_fresh__perm__app,axiom,
% 0.27/0.62 ! [A: name,Pi: list_P227219501e_name,X: produc1141751126_pi_pi] :
% 0.27/0.62 ( ( fresh_922791155e_name @ A @ Pi )
% 0.27/0.62 => ( ( fresh_1376661020_pi_pi @ A @ X )
% 0.27/0.62 => ( fresh_1376661020_pi_pi @ A @ ( perm_n1255502110_pi_pi @ Pi @ X ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % fresh_perm_app
% 0.27/0.62 thf(fact_68_fresh__perm__app,axiom,
% 0.27/0.62 ! [A: name,Pi: list_P227219501e_name,X: name] :
% 0.27/0.62 ( ( fresh_922791155e_name @ A @ Pi )
% 0.27/0.62 => ( ( fresh_name_name @ A @ X )
% 0.27/0.62 => ( fresh_name_name @ A @ ( perm_name_name @ Pi @ X ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % fresh_perm_app
% 0.27/0.62 thf(fact_69_fresh__perm__app,axiom,
% 0.27/0.62 ! [A: name,Pi: list_P227219501e_name,X: pi] :
% 0.27/0.62 ( ( fresh_922791155e_name @ A @ Pi )
% 0.27/0.62 => ( ( fresh_name_pi @ A @ X )
% 0.27/0.62 => ( fresh_name_pi @ A @ ( perm_name_pi @ Pi @ X ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % fresh_perm_app
% 0.27/0.62 thf(fact_70_name__exists__fresh,axiom,
% 0.27/0.62 ! [X: late_subject] :
% 0.27/0.62 ~ ! [C: name] :
% 0.27/0.62 ~ ( fresh_717452603ubject @ C @ X ) ).
% 0.27/0.62
% 0.27/0.62 % name_exists_fresh
% 0.27/0.62 thf(fact_71_name__exists__fresh,axiom,
% 0.27/0.62 ! [X: late_freeRes] :
% 0.27/0.62 ~ ! [C: name] :
% 0.27/0.62 ~ ( fresh_1641682979reeRes @ C @ X ) ).
% 0.27/0.62
% 0.27/0.62 % name_exists_fresh
% 0.27/0.62 thf(fact_72_name__exists__fresh,axiom,
% 0.27/0.62 ! [X: produc1141751126_pi_pi] :
% 0.27/0.62 ~ ! [C: name] :
% 0.27/0.62 ~ ( fresh_1376661020_pi_pi @ C @ X ) ).
% 0.27/0.62
% 0.27/0.62 % name_exists_fresh
% 0.27/0.62 thf(fact_73_name__exists__fresh,axiom,
% 0.27/0.62 ! [X: name] :
% 0.27/0.62 ~ ! [C: name] :
% 0.27/0.62 ~ ( fresh_name_name @ C @ X ) ).
% 0.27/0.62
% 0.27/0.62 % name_exists_fresh
% 0.27/0.62 thf(fact_74_name__exists__fresh,axiom,
% 0.27/0.62 ! [X: pi] :
% 0.27/0.62 ~ ! [C: name] :
% 0.27/0.62 ~ ( fresh_name_pi @ C @ X ) ).
% 0.27/0.62
% 0.27/0.62 % name_exists_fresh
% 0.27/0.62 thf(fact_75_fresh__eqvt,axiom,
% 0.27/0.62 ! [Pi: list_P227219501e_name,A: name,X: pi_Rep] :
% 0.27/0.62 ( ( perm_name_o @ Pi @ ( fresh_name_pi_Rep @ A @ X ) )
% 0.27/0.62 = ( fresh_name_pi_Rep @ ( perm_name_name @ Pi @ A ) @ ( perm_name_pi_Rep @ Pi @ X ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % fresh_eqvt
% 0.27/0.62 thf(fact_76_fresh__eqvt,axiom,
% 0.27/0.62 ! [Pi: list_P227219501e_name,A: name,X: late_subject] :
% 0.27/0.62 ( ( perm_name_o @ Pi @ ( fresh_717452603ubject @ A @ X ) )
% 0.27/0.62 = ( fresh_717452603ubject @ ( perm_name_name @ Pi @ A ) @ ( perm_n1559866809ubject @ Pi @ X ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % fresh_eqvt
% 0.27/0.62 thf(fact_77_fresh__eqvt,axiom,
% 0.27/0.62 ! [Pi: list_P227219501e_name,A: name,X: late_freeRes] :
% 0.27/0.62 ( ( perm_name_o @ Pi @ ( fresh_1641682979reeRes @ A @ X ) )
% 0.27/0.62 = ( fresh_1641682979reeRes @ ( perm_name_name @ Pi @ A ) @ ( perm_n336613537reeRes @ Pi @ X ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % fresh_eqvt
% 0.27/0.62 thf(fact_78_fresh__eqvt,axiom,
% 0.27/0.62 ! [Pi: list_P227219501e_name,A: name,X: produc1141751126_pi_pi] :
% 0.27/0.62 ( ( perm_name_o @ Pi @ ( fresh_1376661020_pi_pi @ A @ X ) )
% 0.27/0.62 = ( fresh_1376661020_pi_pi @ ( perm_name_name @ Pi @ A ) @ ( perm_n1255502110_pi_pi @ Pi @ X ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % fresh_eqvt
% 0.27/0.62 thf(fact_79_fresh__eqvt,axiom,
% 0.27/0.62 ! [Pi: list_P227219501e_name,A: name,X: name] :
% 0.27/0.62 ( ( perm_name_o @ Pi @ ( fresh_name_name @ A @ X ) )
% 0.27/0.62 = ( fresh_name_name @ ( perm_name_name @ Pi @ A ) @ ( perm_name_name @ Pi @ X ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % fresh_eqvt
% 0.27/0.62 thf(fact_80_fresh__eqvt,axiom,
% 0.27/0.62 ! [Pi: list_P227219501e_name,A: name,X: pi] :
% 0.27/0.62 ( ( perm_name_o @ Pi @ ( fresh_name_pi @ A @ X ) )
% 0.27/0.62 = ( fresh_name_pi @ ( perm_name_name @ Pi @ A ) @ ( perm_name_pi @ Pi @ X ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % fresh_eqvt
% 0.27/0.62 thf(fact_81_fresh__bij,axiom,
% 0.27/0.62 ! [Pi: list_P227219501e_name,A: name,X: pi_Rep] :
% 0.27/0.62 ( ( fresh_name_pi_Rep @ ( perm_name_name @ Pi @ A ) @ ( perm_name_pi_Rep @ Pi @ X ) )
% 0.27/0.62 = ( fresh_name_pi_Rep @ A @ X ) ) ).
% 0.27/0.62
% 0.27/0.62 % fresh_bij
% 0.27/0.62 thf(fact_82_fresh__bij,axiom,
% 0.27/0.62 ! [Pi: list_P227219501e_name,A: name,X: late_subject] :
% 0.27/0.62 ( ( fresh_717452603ubject @ ( perm_name_name @ Pi @ A ) @ ( perm_n1559866809ubject @ Pi @ X ) )
% 0.27/0.62 = ( fresh_717452603ubject @ A @ X ) ) ).
% 0.27/0.62
% 0.27/0.62 % fresh_bij
% 0.27/0.62 thf(fact_83_fresh__bij,axiom,
% 0.27/0.62 ! [Pi: list_P227219501e_name,A: name,X: late_freeRes] :
% 0.27/0.62 ( ( fresh_1641682979reeRes @ ( perm_name_name @ Pi @ A ) @ ( perm_n336613537reeRes @ Pi @ X ) )
% 0.27/0.62 = ( fresh_1641682979reeRes @ A @ X ) ) ).
% 0.27/0.62
% 0.27/0.62 % fresh_bij
% 0.27/0.62 thf(fact_84_fresh__bij,axiom,
% 0.27/0.62 ! [Pi: list_P227219501e_name,A: name,X: produc1141751126_pi_pi] :
% 0.27/0.62 ( ( fresh_1376661020_pi_pi @ ( perm_name_name @ Pi @ A ) @ ( perm_n1255502110_pi_pi @ Pi @ X ) )
% 0.27/0.62 = ( fresh_1376661020_pi_pi @ A @ X ) ) ).
% 0.27/0.62
% 0.27/0.62 % fresh_bij
% 0.27/0.62 thf(fact_85_fresh__bij,axiom,
% 0.27/0.62 ! [Pi: list_P227219501e_name,A: name,X: name] :
% 0.27/0.62 ( ( fresh_name_name @ ( perm_name_name @ Pi @ A ) @ ( perm_name_name @ Pi @ X ) )
% 0.27/0.62 = ( fresh_name_name @ A @ X ) ) ).
% 0.27/0.62
% 0.27/0.62 % fresh_bij
% 0.27/0.62 thf(fact_86_fresh__bij,axiom,
% 0.27/0.62 ! [Pi: list_P227219501e_name,A: name,X: pi] :
% 0.27/0.62 ( ( fresh_name_pi @ ( perm_name_name @ Pi @ A ) @ ( perm_name_pi @ Pi @ X ) )
% 0.27/0.62 = ( fresh_name_pi @ A @ X ) ) ).
% 0.27/0.62
% 0.27/0.62 % fresh_bij
% 0.27/0.62 thf(fact_87_name__calc_I2_J,axiom,
% 0.27/0.62 ! [X: name] :
% 0.27/0.62 ( ( perm_name_name @ nil_Pr743626285e_name @ X )
% 0.27/0.62 = X ) ).
% 0.27/0.62
% 0.27/0.62 % name_calc(2)
% 0.27/0.62 thf(fact_88_successively_Ocases,axiom,
% 0.27/0.62 ! [X: produc1872410278e_name] :
% 0.27/0.62 ( ! [P: produc367475239e_name > produc367475239e_name > $o] :
% 0.27/0.62 ( X
% 0.27/0.62 != ( produc1069608854e_name @ P @ nil_Pr743626285e_name ) )
% 0.27/0.62 => ( ! [P: produc367475239e_name > produc367475239e_name > $o,X4: produc367475239e_name] :
% 0.27/0.62 ( X
% 0.27/0.62 != ( produc1069608854e_name @ P @ ( cons_P1213805021e_name @ X4 @ nil_Pr743626285e_name ) ) )
% 0.27/0.62 => ~ ! [P: produc367475239e_name > produc367475239e_name > $o,X4: produc367475239e_name,Y3: produc367475239e_name,Xs: list_P227219501e_name] :
% 0.27/0.62 ( X
% 0.27/0.62 != ( produc1069608854e_name @ P @ ( cons_P1213805021e_name @ X4 @ ( cons_P1213805021e_name @ Y3 @ Xs ) ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % successively.cases
% 0.27/0.62 thf(fact_89_sorted__wrt_Ocases,axiom,
% 0.27/0.62 ! [X: produc1872410278e_name] :
% 0.27/0.62 ( ! [P: produc367475239e_name > produc367475239e_name > $o] :
% 0.27/0.62 ( X
% 0.27/0.62 != ( produc1069608854e_name @ P @ nil_Pr743626285e_name ) )
% 0.27/0.62 => ~ ! [P: produc367475239e_name > produc367475239e_name > $o,X4: produc367475239e_name,Ys: list_P227219501e_name] :
% 0.27/0.62 ( X
% 0.27/0.62 != ( produc1069608854e_name @ P @ ( cons_P1213805021e_name @ X4 @ Ys ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % sorted_wrt.cases
% 0.27/0.62 thf(fact_90_shuffles_Ocases,axiom,
% 0.27/0.62 ! [X: produc890461031e_name] :
% 0.27/0.62 ( ! [Ys: list_P227219501e_name] :
% 0.27/0.62 ( X
% 0.27/0.62 != ( produc208131031e_name @ nil_Pr743626285e_name @ Ys ) )
% 0.27/0.62 => ( ! [Xs: list_P227219501e_name] :
% 0.27/0.62 ( X
% 0.27/0.62 != ( produc208131031e_name @ Xs @ nil_Pr743626285e_name ) )
% 0.27/0.62 => ~ ! [X4: produc367475239e_name,Xs: list_P227219501e_name,Y3: produc367475239e_name,Ys: list_P227219501e_name] :
% 0.27/0.63 ( X
% 0.27/0.63 != ( produc208131031e_name @ ( cons_P1213805021e_name @ X4 @ Xs ) @ ( cons_P1213805021e_name @ Y3 @ Ys ) ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % shuffles.cases
% 0.27/0.63 thf(fact_91_splice_Ocases,axiom,
% 0.27/0.63 ! [X: produc890461031e_name] :
% 0.27/0.63 ( ! [Ys: list_P227219501e_name] :
% 0.27/0.63 ( X
% 0.27/0.63 != ( produc208131031e_name @ nil_Pr743626285e_name @ Ys ) )
% 0.27/0.63 => ~ ! [X4: produc367475239e_name,Xs: list_P227219501e_name,Ys: list_P227219501e_name] :
% 0.27/0.63 ( X
% 0.27/0.63 != ( produc208131031e_name @ ( cons_P1213805021e_name @ X4 @ Xs ) @ Ys ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % splice.cases
% 0.27/0.63 thf(fact_92_swap__simps_I1_J,axiom,
% 0.27/0.63 ! [A: name,B: name] :
% 0.27/0.63 ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ A )
% 0.27/0.63 = B ) ).
% 0.27/0.63
% 0.27/0.63 % swap_simps(1)
% 0.27/0.63 thf(fact_93_swap__simps_I2_J,axiom,
% 0.27/0.63 ! [A: name,B: name] :
% 0.27/0.63 ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ B )
% 0.27/0.63 = A ) ).
% 0.27/0.63
% 0.27/0.63 % swap_simps(2)
% 0.27/0.63 thf(fact_94_swap__simps_I3_J,axiom,
% 0.27/0.63 ! [A: name,C2: name,B: name] :
% 0.27/0.63 ( ( A != C2 )
% 0.27/0.63 => ( ( B != C2 )
% 0.27/0.63 => ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ C2 )
% 0.27/0.63 = C2 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % swap_simps(3)
% 0.27/0.63 thf(fact_95_fresh__aux,axiom,
% 0.27/0.63 ! [C2: name,A: name,X: pi_Rep,B: name] :
% 0.27/0.63 ( ( C2 != A )
% 0.27/0.63 => ( ( fresh_name_pi_Rep @ A @ X )
% 0.27/0.63 => ( ( fresh_name_pi_Rep @ C2 @ X )
% 0.27/0.63 => ( fresh_name_pi_Rep @ C2 @ ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % fresh_aux
% 0.27/0.63 thf(fact_96_fresh__aux,axiom,
% 0.27/0.63 ! [C2: name,A: name,X: late_subject,B: name] :
% 0.27/0.63 ( ( C2 != A )
% 0.27/0.63 => ( ( fresh_717452603ubject @ A @ X )
% 0.27/0.63 => ( ( fresh_717452603ubject @ C2 @ X )
% 0.27/0.63 => ( fresh_717452603ubject @ C2 @ ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % fresh_aux
% 0.27/0.63 thf(fact_97_fresh__aux,axiom,
% 0.27/0.63 ! [C2: name,A: name,X: late_freeRes,B: name] :
% 0.27/0.63 ( ( C2 != A )
% 0.27/0.63 => ( ( fresh_1641682979reeRes @ A @ X )
% 0.27/0.63 => ( ( fresh_1641682979reeRes @ C2 @ X )
% 0.27/0.63 => ( fresh_1641682979reeRes @ C2 @ ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % fresh_aux
% 0.27/0.63 thf(fact_98_fresh__aux,axiom,
% 0.27/0.63 ! [C2: name,A: name,X: produc1141751126_pi_pi,B: name] :
% 0.27/0.63 ( ( C2 != A )
% 0.27/0.63 => ( ( fresh_1376661020_pi_pi @ A @ X )
% 0.27/0.63 => ( ( fresh_1376661020_pi_pi @ C2 @ X )
% 0.27/0.63 => ( fresh_1376661020_pi_pi @ C2 @ ( perm_n1255502110_pi_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % fresh_aux
% 0.27/0.63 thf(fact_99_fresh__aux,axiom,
% 0.27/0.63 ! [C2: name,A: name,X: name,B: name] :
% 0.27/0.63 ( ( C2 != A )
% 0.27/0.63 => ( ( fresh_name_name @ A @ X )
% 0.27/0.63 => ( ( fresh_name_name @ C2 @ X )
% 0.27/0.63 => ( fresh_name_name @ C2 @ ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % fresh_aux
% 0.27/0.63 thf(fact_100_fresh__aux,axiom,
% 0.27/0.63 ! [C2: name,A: name,X: pi,B: name] :
% 0.27/0.63 ( ( C2 != A )
% 0.27/0.63 => ( ( fresh_name_pi @ A @ X )
% 0.27/0.63 => ( ( fresh_name_pi @ C2 @ X )
% 0.27/0.63 => ( fresh_name_pi @ C2 @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % fresh_aux
% 0.27/0.63 thf(fact_101_old_Oprod_Oinducts,axiom,
% 0.27/0.63 ! [P2: produc367475239e_name > $o,Prod: produc367475239e_name] :
% 0.27/0.63 ( ! [A3: name,B3: name] : ( P2 @ ( produc1570949143e_name @ A3 @ B3 ) )
% 0.27/0.63 => ( P2 @ Prod ) ) ).
% 0.27/0.63
% 0.27/0.63 % old.prod.inducts
% 0.27/0.63 thf(fact_102_old_Oprod_Oinducts,axiom,
% 0.27/0.63 ! [P2: produc1141751126_pi_pi > $o,Prod: produc1141751126_pi_pi] :
% 0.27/0.63 ( ! [A3: name,B3: product_prod_pi_pi] : ( P2 @ ( produc235456326_pi_pi @ A3 @ B3 ) )
% 0.27/0.63 => ( P2 @ Prod ) ) ).
% 0.27/0.63
% 0.27/0.63 % old.prod.inducts
% 0.27/0.63 thf(fact_103_old_Oprod_Oinducts,axiom,
% 0.27/0.63 ! [P2: product_prod_pi_pi > $o,Prod: product_prod_pi_pi] :
% 0.27/0.63 ( ! [A3: pi,B3: pi] : ( P2 @ ( product_Pair_pi_pi @ A3 @ B3 ) )
% 0.27/0.63 => ( P2 @ Prod ) ) ).
% 0.27/0.63
% 0.27/0.63 % old.prod.inducts
% 0.27/0.63 thf(fact_104_old_Oprod_Oexhaust,axiom,
% 0.27/0.63 ! [Y4: produc367475239e_name] :
% 0.27/0.63 ~ ! [A3: name,B3: name] :
% 0.27/0.63 ( Y4
% 0.27/0.63 != ( produc1570949143e_name @ A3 @ B3 ) ) ).
% 0.27/0.63
% 0.27/0.63 % old.prod.exhaust
% 0.27/0.63 thf(fact_105_old_Oprod_Oexhaust,axiom,
% 0.27/0.63 ! [Y4: produc1141751126_pi_pi] :
% 0.27/0.63 ~ ! [A3: name,B3: product_prod_pi_pi] :
% 0.27/0.63 ( Y4
% 0.27/0.63 != ( produc235456326_pi_pi @ A3 @ B3 ) ) ).
% 0.27/0.63
% 0.27/0.63 % old.prod.exhaust
% 0.27/0.63 thf(fact_106_old_Oprod_Oexhaust,axiom,
% 0.27/0.63 ! [Y4: product_prod_pi_pi] :
% 0.27/0.63 ~ ! [A3: pi,B3: pi] :
% 0.27/0.63 ( Y4
% 0.27/0.63 != ( product_Pair_pi_pi @ A3 @ B3 ) ) ).
% 0.27/0.63
% 0.27/0.63 % old.prod.exhaust
% 0.27/0.63 thf(fact_107_mem__Collect__eq,axiom,
% 0.27/0.63 ! [A: product_prod_pi_pi,P2: product_prod_pi_pi > $o] :
% 0.27/0.63 ( ( member558706512_pi_pi @ A @ ( collec1051790738_pi_pi @ P2 ) )
% 0.27/0.63 = ( P2 @ A ) ) ).
% 0.27/0.63
% 0.27/0.63 % mem_Collect_eq
% 0.27/0.63 thf(fact_108_Collect__mem__eq,axiom,
% 0.27/0.63 ! [A4: set_Pr1834926343_pi_pi] :
% 0.27/0.63 ( ( collec1051790738_pi_pi
% 0.27/0.63 @ ^ [X5: product_prod_pi_pi] : ( member558706512_pi_pi @ X5 @ A4 ) )
% 0.27/0.63 = A4 ) ).
% 0.27/0.63
% 0.27/0.63 % Collect_mem_eq
% 0.27/0.63 thf(fact_109_prod__induct3,axiom,
% 0.27/0.63 ! [P2: produc1141751126_pi_pi > $o,X: produc1141751126_pi_pi] :
% 0.27/0.63 ( ! [A3: name,B3: pi,C: pi] : ( P2 @ ( produc235456326_pi_pi @ A3 @ ( product_Pair_pi_pi @ B3 @ C ) ) )
% 0.27/0.63 => ( P2 @ X ) ) ).
% 0.27/0.63
% 0.27/0.63 % prod_induct3
% 0.27/0.63 thf(fact_110_prod__cases3,axiom,
% 0.27/0.63 ! [Y4: produc1141751126_pi_pi] :
% 0.27/0.63 ~ ! [A3: name,B3: pi,C: pi] :
% 0.27/0.63 ( Y4
% 0.27/0.63 != ( produc235456326_pi_pi @ A3 @ ( product_Pair_pi_pi @ B3 @ C ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % prod_cases3
% 0.27/0.63 thf(fact_111_Pair__inject,axiom,
% 0.27/0.63 ! [A: name,B: name,A2: name,B2: name] :
% 0.27/0.63 ( ( ( produc1570949143e_name @ A @ B )
% 0.27/0.63 = ( produc1570949143e_name @ A2 @ B2 ) )
% 0.27/0.63 => ~ ( ( A = A2 )
% 0.27/0.63 => ( B != B2 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % Pair_inject
% 0.27/0.63 thf(fact_112_Pair__inject,axiom,
% 0.27/0.63 ! [A: name,B: product_prod_pi_pi,A2: name,B2: product_prod_pi_pi] :
% 0.27/0.63 ( ( ( produc235456326_pi_pi @ A @ B )
% 0.27/0.63 = ( produc235456326_pi_pi @ A2 @ B2 ) )
% 0.27/0.63 => ~ ( ( A = A2 )
% 0.27/0.63 => ( B != B2 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % Pair_inject
% 0.27/0.63 thf(fact_113_Pair__inject,axiom,
% 0.27/0.63 ! [A: pi,B: pi,A2: pi,B2: pi] :
% 0.27/0.63 ( ( ( product_Pair_pi_pi @ A @ B )
% 0.27/0.63 = ( product_Pair_pi_pi @ A2 @ B2 ) )
% 0.27/0.63 => ~ ( ( A = A2 )
% 0.27/0.63 => ( B != B2 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % Pair_inject
% 0.27/0.63 thf(fact_114_prod__cases,axiom,
% 0.27/0.63 ! [P2: produc367475239e_name > $o,P3: produc367475239e_name] :
% 0.27/0.63 ( ! [A3: name,B3: name] : ( P2 @ ( produc1570949143e_name @ A3 @ B3 ) )
% 0.27/0.63 => ( P2 @ P3 ) ) ).
% 0.27/0.63
% 0.27/0.63 % prod_cases
% 0.27/0.63 thf(fact_115_prod__cases,axiom,
% 0.27/0.63 ! [P2: produc1141751126_pi_pi > $o,P3: produc1141751126_pi_pi] :
% 0.27/0.63 ( ! [A3: name,B3: product_prod_pi_pi] : ( P2 @ ( produc235456326_pi_pi @ A3 @ B3 ) )
% 0.27/0.63 => ( P2 @ P3 ) ) ).
% 0.27/0.63
% 0.27/0.63 % prod_cases
% 0.27/0.63 thf(fact_116_prod__cases,axiom,
% 0.27/0.63 ! [P2: product_prod_pi_pi > $o,P3: product_prod_pi_pi] :
% 0.27/0.63 ( ! [A3: pi,B3: pi] : ( P2 @ ( product_Pair_pi_pi @ A3 @ B3 ) )
% 0.27/0.63 => ( P2 @ P3 ) ) ).
% 0.27/0.63
% 0.27/0.63 % prod_cases
% 0.27/0.63 thf(fact_117_surj__pair,axiom,
% 0.27/0.63 ! [P3: produc367475239e_name] :
% 0.27/0.63 ? [X4: name,Y3: name] :
% 0.27/0.63 ( P3
% 0.27/0.63 = ( produc1570949143e_name @ X4 @ Y3 ) ) ).
% 0.27/0.63
% 0.27/0.63 % surj_pair
% 0.27/0.63 thf(fact_118_surj__pair,axiom,
% 0.27/0.63 ! [P3: produc1141751126_pi_pi] :
% 0.27/0.63 ? [X4: name,Y3: product_prod_pi_pi] :
% 0.27/0.63 ( P3
% 0.27/0.63 = ( produc235456326_pi_pi @ X4 @ Y3 ) ) ).
% 0.27/0.63
% 0.27/0.63 % surj_pair
% 0.27/0.63 thf(fact_119_surj__pair,axiom,
% 0.27/0.63 ! [P3: product_prod_pi_pi] :
% 0.27/0.63 ? [X4: pi,Y3: pi] :
% 0.27/0.63 ( P3
% 0.27/0.63 = ( product_Pair_pi_pi @ X4 @ Y3 ) ) ).
% 0.27/0.63
% 0.27/0.63 % surj_pair
% 0.27/0.63 thf(fact_120_not__Cons__self2,axiom,
% 0.27/0.63 ! [X: produc367475239e_name,Xs2: list_P227219501e_name] :
% 0.27/0.63 ( ( cons_P1213805021e_name @ X @ Xs2 )
% 0.27/0.63 != Xs2 ) ).
% 0.27/0.63
% 0.27/0.63 % not_Cons_self2
% 0.27/0.63 thf(fact_121_cp__name__name1,axiom,
% 0.27/0.63 ! [Pi1: list_P227219501e_name,Pi2: list_P227219501e_name,X: late_subject] :
% 0.27/0.63 ( ( perm_n1559866809ubject @ Pi1 @ ( perm_n1559866809ubject @ Pi2 @ X ) )
% 0.27/0.63 = ( perm_n1559866809ubject @ ( perm_n1160739829e_name @ Pi1 @ Pi2 ) @ ( perm_n1559866809ubject @ Pi1 @ X ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % cp_name_name1
% 0.27/0.63 thf(fact_122_cp__name__name1,axiom,
% 0.27/0.63 ! [Pi1: list_P227219501e_name,Pi2: list_P227219501e_name,X: late_freeRes] :
% 0.27/0.63 ( ( perm_n336613537reeRes @ Pi1 @ ( perm_n336613537reeRes @ Pi2 @ X ) )
% 0.27/0.63 = ( perm_n336613537reeRes @ ( perm_n1160739829e_name @ Pi1 @ Pi2 ) @ ( perm_n336613537reeRes @ Pi1 @ X ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % cp_name_name1
% 0.27/0.63 thf(fact_123_cp__name__name1,axiom,
% 0.27/0.63 ! [Pi1: list_P227219501e_name,Pi2: list_P227219501e_name,X: pi_Rep] :
% 0.27/0.63 ( ( perm_name_pi_Rep @ Pi1 @ ( perm_name_pi_Rep @ Pi2 @ X ) )
% 0.27/0.63 = ( perm_name_pi_Rep @ ( perm_n1160739829e_name @ Pi1 @ Pi2 ) @ ( perm_name_pi_Rep @ Pi1 @ X ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % cp_name_name1
% 0.27/0.63 thf(fact_124_cp__name__name1,axiom,
% 0.27/0.63 ! [Pi1: list_P227219501e_name,Pi2: list_P227219501e_name,X: name] :
% 0.27/0.63 ( ( perm_name_name @ Pi1 @ ( perm_name_name @ Pi2 @ X ) )
% 0.27/0.63 = ( perm_name_name @ ( perm_n1160739829e_name @ Pi1 @ Pi2 ) @ ( perm_name_name @ Pi1 @ X ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % cp_name_name1
% 0.27/0.63 thf(fact_125_cp__name__name1,axiom,
% 0.27/0.63 ! [Pi1: list_P227219501e_name,Pi2: list_P227219501e_name,X: pi] :
% 0.27/0.63 ( ( perm_name_pi @ Pi1 @ ( perm_name_pi @ Pi2 @ X ) )
% 0.27/0.63 = ( perm_name_pi @ ( perm_n1160739829e_name @ Pi1 @ Pi2 ) @ ( perm_name_pi @ Pi1 @ X ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % cp_name_name1
% 0.27/0.63 thf(fact_126_name__perm__compose,axiom,
% 0.27/0.63 ! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: late_subject] :
% 0.27/0.63 ( ( perm_n1559866809ubject @ Pi2 @ ( perm_n1559866809ubject @ Pi1 @ X ) )
% 0.27/0.63 = ( perm_n1559866809ubject @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_n1559866809ubject @ Pi2 @ X ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % name_perm_compose
% 0.27/0.63 thf(fact_127_name__perm__compose,axiom,
% 0.27/0.63 ! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: late_freeRes] :
% 0.27/0.63 ( ( perm_n336613537reeRes @ Pi2 @ ( perm_n336613537reeRes @ Pi1 @ X ) )
% 0.27/0.63 = ( perm_n336613537reeRes @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_n336613537reeRes @ Pi2 @ X ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % name_perm_compose
% 0.27/0.63 thf(fact_128_name__perm__compose,axiom,
% 0.27/0.63 ! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: pi_Rep] :
% 0.27/0.63 ( ( perm_name_pi_Rep @ Pi2 @ ( perm_name_pi_Rep @ Pi1 @ X ) )
% 0.27/0.63 = ( perm_name_pi_Rep @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_name_pi_Rep @ Pi2 @ X ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % name_perm_compose
% 0.27/0.63 thf(fact_129_name__perm__compose,axiom,
% 0.27/0.63 ! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: name] :
% 0.27/0.63 ( ( perm_name_name @ Pi2 @ ( perm_name_name @ Pi1 @ X ) )
% 0.27/0.63 = ( perm_name_name @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_name_name @ Pi2 @ X ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % name_perm_compose
% 0.27/0.63 thf(fact_130_name__perm__compose,axiom,
% 0.27/0.63 ! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: pi] :
% 0.27/0.63 ( ( perm_name_pi @ Pi2 @ ( perm_name_pi @ Pi1 @ X ) )
% 0.27/0.63 = ( perm_name_pi @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_name_pi @ Pi2 @ X ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % name_perm_compose
% 0.27/0.63 thf(fact_131_perm__compose,axiom,
% 0.27/0.63 ! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: late_subject] :
% 0.27/0.63 ( ( perm_n1559866809ubject @ Pi2 @ ( perm_n1559866809ubject @ Pi1 @ X ) )
% 0.27/0.63 = ( perm_n1559866809ubject @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_n1559866809ubject @ Pi2 @ X ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % perm_compose
% 0.27/0.63 thf(fact_132_perm__compose,axiom,
% 0.27/0.63 ! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: late_freeRes] :
% 0.27/0.63 ( ( perm_n336613537reeRes @ Pi2 @ ( perm_n336613537reeRes @ Pi1 @ X ) )
% 0.27/0.63 = ( perm_n336613537reeRes @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_n336613537reeRes @ Pi2 @ X ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % perm_compose
% 0.27/0.63 thf(fact_133_perm__compose,axiom,
% 0.27/0.63 ! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: pi_Rep] :
% 0.27/0.63 ( ( perm_name_pi_Rep @ Pi2 @ ( perm_name_pi_Rep @ Pi1 @ X ) )
% 0.27/0.63 = ( perm_name_pi_Rep @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_name_pi_Rep @ Pi2 @ X ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % perm_compose
% 0.27/0.63 thf(fact_134_perm__compose,axiom,
% 0.27/0.63 ! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: name] :
% 0.27/0.63 ( ( perm_name_name @ Pi2 @ ( perm_name_name @ Pi1 @ X ) )
% 0.27/0.63 = ( perm_name_name @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_name_name @ Pi2 @ X ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % perm_compose
% 0.27/0.63 thf(fact_135_perm__compose,axiom,
% 0.27/0.63 ! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: pi] :
% 0.27/0.63 ( ( perm_name_pi @ Pi2 @ ( perm_name_pi @ Pi1 @ X ) )
% 0.27/0.63 = ( perm_name_pi @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_name_pi @ Pi2 @ X ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % perm_compose
% 0.27/0.63 thf(fact_136_perm__bij,axiom,
% 0.27/0.63 ! [Pi: list_P227219501e_name,X: late_subject,Y4: late_subject] :
% 0.27/0.63 ( ( ( perm_n1559866809ubject @ Pi @ X )
% 0.27/0.63 = ( perm_n1559866809ubject @ Pi @ Y4 ) )
% 0.27/0.63 = ( X = Y4 ) ) ).
% 0.27/0.63
% 0.27/0.63 % perm_bij
% 0.27/0.63 thf(fact_137_perm__bij,axiom,
% 0.27/0.63 ! [Pi: list_P227219501e_name,X: late_freeRes,Y4: late_freeRes] :
% 0.27/0.63 ( ( ( perm_n336613537reeRes @ Pi @ X )
% 0.27/0.63 = ( perm_n336613537reeRes @ Pi @ Y4 ) )
% 0.27/0.63 = ( X = Y4 ) ) ).
% 0.27/0.63
% 0.27/0.63 % perm_bij
% 0.27/0.63 thf(fact_138_perm__bij,axiom,
% 0.27/0.63 ! [Pi: list_P227219501e_name,X: pi_Rep,Y4: pi_Rep] :
% 0.27/0.63 ( ( ( perm_name_pi_Rep @ Pi @ X )
% 0.27/0.63 = ( perm_name_pi_Rep @ Pi @ Y4 ) )
% 0.27/0.63 = ( X = Y4 ) ) ).
% 0.27/0.63
% 0.27/0.63 % perm_bij
% 0.27/0.63 thf(fact_139_perm__bij,axiom,
% 0.27/0.63 ! [Pi: list_P227219501e_name,X: name,Y4: name] :
% 0.27/0.63 ( ( ( perm_name_name @ Pi @ X )
% 0.27/0.63 = ( perm_name_name @ Pi @ Y4 ) )
% 0.27/0.63 = ( X = Y4 ) ) ).
% 0.27/0.63
% 0.27/0.63 % perm_bij
% 0.27/0.63 thf(fact_140_perm__bij,axiom,
% 0.27/0.63 ! [Pi: list_P227219501e_name,X: pi,Y4: pi] :
% 0.27/0.63 ( ( ( perm_name_pi @ Pi @ X )
% 0.27/0.63 = ( perm_name_pi @ Pi @ Y4 ) )
% 0.27/0.63 = ( X = Y4 ) ) ).
% 0.27/0.63
% 0.27/0.63 % perm_bij
% 0.27/0.63 thf(fact_141_perm__app,axiom,
% 0.27/0.63 ! [Pi: list_P227219501e_name,F: late_subject > late_subject,X: late_subject] :
% 0.27/0.63 ( ( perm_n1559866809ubject @ Pi @ ( F @ X ) )
% 0.27/0.63 = ( perm_n1447856217ubject @ Pi @ F @ ( perm_n1559866809ubject @ Pi @ X ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % perm_app
% 0.27/0.63 thf(fact_142_perm__app,axiom,
% 0.27/0.63 ! [Pi: list_P227219501e_name,F: late_freeRes > late_subject,X: late_freeRes] :
% 0.27/0.63 ( ( perm_n1559866809ubject @ Pi @ ( F @ X ) )
% 0.27/0.63 = ( perm_n303101761ubject @ Pi @ F @ ( perm_n336613537reeRes @ Pi @ X ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % perm_app
% 0.27/0.63 thf(fact_143_perm__app,axiom,
% 0.27/0.63 ! [Pi: list_P227219501e_name,F: pi_Rep > late_subject,X: pi_Rep] :
% 0.27/0.63 ( ( perm_n1559866809ubject @ Pi @ ( F @ X ) )
% 0.27/0.63 = ( perm_n698371375ubject @ Pi @ F @ ( perm_name_pi_Rep @ Pi @ X ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % perm_app
% 0.27/0.63 thf(fact_144_perm__app,axiom,
% 0.27/0.63 ! [Pi: list_P227219501e_name,F: name > late_subject,X: name] :
% 0.27/0.63 ( ( perm_n1559866809ubject @ Pi @ ( F @ X ) )
% 0.27/0.63 = ( perm_n1387060402ubject @ Pi @ F @ ( perm_name_name @ Pi @ X ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % perm_app
% 0.27/0.63 thf(fact_145_perm__app,axiom,
% 0.27/0.63 ! [Pi: list_P227219501e_name,F: pi > late_subject,X: pi] :
% 0.27/0.63 ( ( perm_n1559866809ubject @ Pi @ ( F @ X ) )
% 0.27/0.63 = ( perm_n190055296ubject @ Pi @ F @ ( perm_name_pi @ Pi @ X ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % perm_app
% 0.27/0.63 thf(fact_146_perm__app,axiom,
% 0.27/0.63 ! [Pi: list_P227219501e_name,F: late_subject > late_freeRes,X: late_subject] :
% 0.27/0.63 ( ( perm_n336613537reeRes @ Pi @ ( F @ X ) )
% 0.27/0.63 = ( perm_n443561793reeRes @ Pi @ F @ ( perm_n1559866809ubject @ Pi @ X ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % perm_app
% 0.27/0.63 thf(fact_147_perm__app,axiom,
% 0.27/0.63 ! [Pi: list_P227219501e_name,F: late_freeRes > late_freeRes,X: late_freeRes] :
% 0.27/0.63 ( ( perm_n336613537reeRes @ Pi @ ( F @ X ) )
% 0.27/0.63 = ( perm_n1446290985reeRes @ Pi @ F @ ( perm_n336613537reeRes @ Pi @ X ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % perm_app
% 0.27/0.63 thf(fact_148_perm__app,axiom,
% 0.27/0.63 ! [Pi: list_P227219501e_name,F: pi_Rep > late_freeRes,X: pi_Rep] :
% 0.27/0.63 ( ( perm_n336613537reeRes @ Pi @ ( F @ X ) )
% 0.27/0.63 = ( perm_n1841560599reeRes @ Pi @ F @ ( perm_name_pi_Rep @ Pi @ X ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % perm_app
% 0.27/0.63 thf(fact_149_perm__app,axiom,
% 0.27/0.63 ! [Pi: list_P227219501e_name,F: name > late_freeRes,X: name] :
% 0.27/0.63 ( ( perm_n336613537reeRes @ Pi @ ( F @ X ) )
% 0.27/0.63 = ( perm_n382765978reeRes @ Pi @ F @ ( perm_name_name @ Pi @ X ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % perm_app
% 0.27/0.63 thf(fact_150_perm__app,axiom,
% 0.27/0.63 ! [Pi: list_P227219501e_name,F: pi > late_freeRes,X: pi] :
% 0.27/0.63 ( ( perm_n336613537reeRes @ Pi @ ( F @ X ) )
% 0.27/0.63 = ( perm_n1333244520reeRes @ Pi @ F @ ( perm_name_pi @ Pi @ X ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % perm_app
% 0.27/0.63 thf(fact_151_in__eqvt,axiom,
% 0.27/0.63 ! [Pi: list_P227219501e_name,X: product_prod_pi_pi,X3: set_Pr1834926343_pi_pi] :
% 0.27/0.63 ( ( perm_name_o @ Pi @ ( member558706512_pi_pi @ X @ X3 ) )
% 0.27/0.63 = ( member558706512_pi_pi @ ( perm_n1415585007_pi_pi @ Pi @ X ) @ ( perm_n675238095_pi_pi @ Pi @ X3 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % in_eqvt
% 0.27/0.63 thf(fact_152_in__eqvt,axiom,
% 0.27/0.63 ! [Pi: list_P227219501e_name,X: late_subject,X3: set_Late_subject] :
% 0.27/0.63 ( ( perm_name_o @ Pi @ ( member_Late_subject @ X @ X3 ) )
% 0.27/0.63 = ( member_Late_subject @ ( perm_n1559866809ubject @ Pi @ X ) @ ( perm_n412725103ubject @ Pi @ X3 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % in_eqvt
% 0.27/0.63 thf(fact_153_in__eqvt,axiom,
% 0.27/0.63 ! [Pi: list_P227219501e_name,X: late_freeRes,X3: set_Late_freeRes] :
% 0.27/0.63 ( ( perm_name_o @ Pi @ ( member_Late_freeRes @ X @ X3 ) )
% 0.27/0.63 = ( member_Late_freeRes @ ( perm_n336613537reeRes @ Pi @ X ) @ ( perm_n1555914327reeRes @ Pi @ X3 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % in_eqvt
% 0.27/0.63 thf(fact_154_in__eqvt,axiom,
% 0.27/0.63 ! [Pi: list_P227219501e_name,X: pi_Rep,X3: set_pi_Rep] :
% 0.27/0.63 ( ( perm_name_o @ Pi @ ( member_pi_Rep @ X @ X3 ) )
% 0.27/0.63 = ( member_pi_Rep @ ( perm_name_pi_Rep @ Pi @ X ) @ ( perm_name_set_pi_Rep @ Pi @ X3 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % in_eqvt
% 0.27/0.63 thf(fact_155_in__eqvt,axiom,
% 0.27/0.63 ! [Pi: list_P227219501e_name,X: name,X3: set_name] :
% 0.27/0.63 ( ( perm_name_o @ Pi @ ( member_name @ X @ X3 ) )
% 0.27/0.63 = ( member_name @ ( perm_name_name @ Pi @ X ) @ ( perm_name_set_name @ Pi @ X3 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % in_eqvt
% 0.27/0.63 thf(fact_156_in__eqvt,axiom,
% 0.27/0.63 ! [Pi: list_P227219501e_name,X: pi,X3: set_pi] :
% 0.27/0.63 ( ( perm_name_o @ Pi @ ( member_pi @ X @ X3 ) )
% 0.27/0.63 = ( member_pi @ ( perm_name_pi @ Pi @ X ) @ ( perm_name_set_pi @ Pi @ X3 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % in_eqvt
% 0.27/0.63 thf(fact_157_eq__eqvt,axiom,
% 0.27/0.63 ! [Pi: list_P227219501e_name,X: late_subject,Y4: late_subject] :
% 0.27/0.63 ( ( perm_name_o @ Pi @ ( X = Y4 ) )
% 0.27/0.63 = ( ( perm_n1559866809ubject @ Pi @ X )
% 0.27/0.63 = ( perm_n1559866809ubject @ Pi @ Y4 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % eq_eqvt
% 0.27/0.63 thf(fact_158_eq__eqvt,axiom,
% 0.27/0.63 ! [Pi: list_P227219501e_name,X: late_freeRes,Y4: late_freeRes] :
% 0.27/0.63 ( ( perm_name_o @ Pi @ ( X = Y4 ) )
% 0.27/0.63 = ( ( perm_n336613537reeRes @ Pi @ X )
% 0.27/0.63 = ( perm_n336613537reeRes @ Pi @ Y4 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % eq_eqvt
% 0.27/0.63 thf(fact_159_eq__eqvt,axiom,
% 0.27/0.63 ! [Pi: list_P227219501e_name,X: pi_Rep,Y4: pi_Rep] :
% 0.27/0.63 ( ( perm_name_o @ Pi @ ( X = Y4 ) )
% 0.27/0.63 = ( ( perm_name_pi_Rep @ Pi @ X )
% 0.27/0.63 = ( perm_name_pi_Rep @ Pi @ Y4 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % eq_eqvt
% 0.27/0.63 thf(fact_160_eq__eqvt,axiom,
% 0.27/0.63 ! [Pi: list_P227219501e_name,X: name,Y4: name] :
% 0.27/0.63 ( ( perm_name_o @ Pi @ ( X = Y4 ) )
% 0.27/0.63 = ( ( perm_name_name @ Pi @ X )
% 0.27/0.63 = ( perm_name_name @ Pi @ Y4 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % eq_eqvt
% 0.27/0.63 thf(fact_161_eq__eqvt,axiom,
% 0.27/0.63 ! [Pi: list_P227219501e_name,X: pi,Y4: pi] :
% 0.27/0.63 ( ( perm_name_o @ Pi @ ( X = Y4 ) )
% 0.27/0.63 = ( ( perm_name_pi @ Pi @ X )
% 0.27/0.63 = ( perm_name_pi @ Pi @ Y4 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % eq_eqvt
% 0.27/0.63 thf(fact_162_map__tailrec__rev_Oinduct,axiom,
% 0.27/0.63 ! [P2: ( produc367475239e_name > produc367475239e_name ) > list_P227219501e_name > list_P227219501e_name > $o,A0: produc367475239e_name > produc367475239e_name,A1: list_P227219501e_name,A22: list_P227219501e_name] :
% 0.27/0.63 ( ! [F2: produc367475239e_name > produc367475239e_name,X_1: list_P227219501e_name] : ( P2 @ F2 @ nil_Pr743626285e_name @ X_1 )
% 0.27/0.63 => ( ! [F2: produc367475239e_name > produc367475239e_name,A3: produc367475239e_name,As: list_P227219501e_name,Bs: list_P227219501e_name] :
% 0.27/0.63 ( ( P2 @ F2 @ As @ ( cons_P1213805021e_name @ ( F2 @ A3 ) @ Bs ) )
% 0.27/0.63 => ( P2 @ F2 @ ( cons_P1213805021e_name @ A3 @ As ) @ Bs ) )
% 0.27/0.63 => ( P2 @ A0 @ A1 @ A22 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % map_tailrec_rev.induct
% 0.27/0.63 thf(fact_163_list__nonempty__induct,axiom,
% 0.27/0.63 ! [Xs2: list_P227219501e_name,P2: list_P227219501e_name > $o] :
% 0.27/0.63 ( ( Xs2 != nil_Pr743626285e_name )
% 0.27/0.63 => ( ! [X4: produc367475239e_name] : ( P2 @ ( cons_P1213805021e_name @ X4 @ nil_Pr743626285e_name ) )
% 0.27/0.63 => ( ! [X4: produc367475239e_name,Xs: list_P227219501e_name] :
% 0.27/0.63 ( ( Xs != nil_Pr743626285e_name )
% 0.27/0.63 => ( ( P2 @ Xs )
% 0.27/0.63 => ( P2 @ ( cons_P1213805021e_name @ X4 @ Xs ) ) ) )
% 0.27/0.63 => ( P2 @ Xs2 ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % list_nonempty_induct
% 0.27/0.63 thf(fact_164_successively_Oinduct,axiom,
% 0.27/0.63 ! [P2: ( produc367475239e_name > produc367475239e_name > $o ) > list_P227219501e_name > $o,A0: produc367475239e_name > produc367475239e_name > $o,A1: list_P227219501e_name] :
% 0.27/0.63 ( ! [P: produc367475239e_name > produc367475239e_name > $o] : ( P2 @ P @ nil_Pr743626285e_name )
% 0.27/0.63 => ( ! [P: produc367475239e_name > produc367475239e_name > $o,X4: produc367475239e_name] : ( P2 @ P @ ( cons_P1213805021e_name @ X4 @ nil_Pr743626285e_name ) )
% 0.27/0.63 => ( ! [P: produc367475239e_name > produc367475239e_name > $o,X4: produc367475239e_name,Y3: produc367475239e_name,Xs: list_P227219501e_name] :
% 0.27/0.63 ( ( P2 @ P @ ( cons_P1213805021e_name @ Y3 @ Xs ) )
% 0.27/0.63 => ( P2 @ P @ ( cons_P1213805021e_name @ X4 @ ( cons_P1213805021e_name @ Y3 @ Xs ) ) ) )
% 0.27/0.63 => ( P2 @ A0 @ A1 ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % successively.induct
% 0.27/0.63 thf(fact_165_remdups__adj_Oinduct,axiom,
% 0.27/0.63 ! [P2: list_P227219501e_name > $o,A0: list_P227219501e_name] :
% 0.27/0.63 ( ( P2 @ nil_Pr743626285e_name )
% 0.27/0.63 => ( ! [X4: produc367475239e_name] : ( P2 @ ( cons_P1213805021e_name @ X4 @ nil_Pr743626285e_name ) )
% 0.27/0.63 => ( ! [X4: produc367475239e_name,Y3: produc367475239e_name,Xs: list_P227219501e_name] :
% 0.27/0.63 ( ( ( X4 = Y3 )
% 0.27/0.63 => ( P2 @ ( cons_P1213805021e_name @ X4 @ Xs ) ) )
% 0.27/0.63 => ( ( ( X4 != Y3 )
% 0.27/0.63 => ( P2 @ ( cons_P1213805021e_name @ Y3 @ Xs ) ) )
% 0.27/0.63 => ( P2 @ ( cons_P1213805021e_name @ X4 @ ( cons_P1213805021e_name @ Y3 @ Xs ) ) ) ) )
% 0.27/0.63 => ( P2 @ A0 ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % remdups_adj.induct
% 0.27/0.63 thf(fact_166_sorted__wrt_Oinduct,axiom,
% 0.27/0.63 ! [P2: ( produc367475239e_name > produc367475239e_name > $o ) > list_P227219501e_name > $o,A0: produc367475239e_name > produc367475239e_name > $o,A1: list_P227219501e_name] :
% 0.27/0.63 ( ! [P: produc367475239e_name > produc367475239e_name > $o] : ( P2 @ P @ nil_Pr743626285e_name )
% 0.27/0.63 => ( ! [P: produc367475239e_name > produc367475239e_name > $o,X4: produc367475239e_name,Ys: list_P227219501e_name] :
% 0.27/0.63 ( ( P2 @ P @ Ys )
% 0.27/0.63 => ( P2 @ P @ ( cons_P1213805021e_name @ X4 @ Ys ) ) )
% 0.27/0.63 => ( P2 @ A0 @ A1 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % sorted_wrt.induct
% 0.27/0.63 thf(fact_167_remdups__adj_Ocases,axiom,
% 0.27/0.63 ! [X: list_P227219501e_name] :
% 0.27/0.63 ( ( X != nil_Pr743626285e_name )
% 0.27/0.63 => ( ! [X4: produc367475239e_name] :
% 0.27/0.63 ( X
% 0.27/0.63 != ( cons_P1213805021e_name @ X4 @ nil_Pr743626285e_name ) )
% 0.27/0.63 => ~ ! [X4: produc367475239e_name,Y3: produc367475239e_name,Xs: list_P227219501e_name] :
% 0.27/0.63 ( X
% 0.27/0.63 != ( cons_P1213805021e_name @ X4 @ ( cons_P1213805021e_name @ Y3 @ Xs ) ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % remdups_adj.cases
% 0.27/0.63 thf(fact_168_transpose_Ocases,axiom,
% 0.27/0.63 ! [X: list_l1406151091e_name] :
% 0.27/0.63 ( ( X != nil_li29751603e_name )
% 0.27/0.63 => ( ! [Xss: list_l1406151091e_name] :
% 0.27/0.63 ( X
% 0.27/0.63 != ( cons_l798145763e_name @ nil_Pr743626285e_name @ Xss ) )
% 0.27/0.63 => ~ ! [X4: produc367475239e_name,Xs: list_P227219501e_name,Xss: list_l1406151091e_name] :
% 0.27/0.63 ( X
% 0.27/0.63 != ( cons_l798145763e_name @ ( cons_P1213805021e_name @ X4 @ Xs ) @ Xss ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % transpose.cases
% 0.27/0.63 thf(fact_169_shuffles_Oinduct,axiom,
% 0.27/0.63 ! [P2: list_P227219501e_name > list_P227219501e_name > $o,A0: list_P227219501e_name,A1: list_P227219501e_name] :
% 0.27/0.63 ( ! [X_1: list_P227219501e_name] : ( P2 @ nil_Pr743626285e_name @ X_1 )
% 0.27/0.63 => ( ! [Xs: list_P227219501e_name] : ( P2 @ Xs @ nil_Pr743626285e_name )
% 0.27/0.63 => ( ! [X4: produc367475239e_name,Xs: list_P227219501e_name,Y3: produc367475239e_name,Ys: list_P227219501e_name] :
% 0.27/0.63 ( ( P2 @ Xs @ ( cons_P1213805021e_name @ Y3 @ Ys ) )
% 0.27/0.63 => ( ( P2 @ ( cons_P1213805021e_name @ X4 @ Xs ) @ Ys )
% 0.27/0.63 => ( P2 @ ( cons_P1213805021e_name @ X4 @ Xs ) @ ( cons_P1213805021e_name @ Y3 @ Ys ) ) ) )
% 0.27/0.63 => ( P2 @ A0 @ A1 ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % shuffles.induct
% 0.27/0.63 thf(fact_170_induct__list012,axiom,
% 0.27/0.63 ! [P2: list_P227219501e_name > $o,Xs2: list_P227219501e_name] :
% 0.27/0.63 ( ( P2 @ nil_Pr743626285e_name )
% 0.27/0.63 => ( ! [X4: produc367475239e_name] : ( P2 @ ( cons_P1213805021e_name @ X4 @ nil_Pr743626285e_name ) )
% 0.27/0.63 => ( ! [X4: produc367475239e_name,Y3: produc367475239e_name,Zs: list_P227219501e_name] :
% 0.27/0.63 ( ( P2 @ Zs )
% 0.27/0.63 => ( ( P2 @ ( cons_P1213805021e_name @ Y3 @ Zs ) )
% 0.27/0.63 => ( P2 @ ( cons_P1213805021e_name @ X4 @ ( cons_P1213805021e_name @ Y3 @ Zs ) ) ) ) )
% 0.27/0.63 => ( P2 @ Xs2 ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % induct_list012
% 0.27/0.63 thf(fact_171_splice_Oinduct,axiom,
% 0.27/0.63 ! [P2: list_P227219501e_name > list_P227219501e_name > $o,A0: list_P227219501e_name,A1: list_P227219501e_name] :
% 0.27/0.63 ( ! [X_1: list_P227219501e_name] : ( P2 @ nil_Pr743626285e_name @ X_1 )
% 0.27/0.63 => ( ! [X4: produc367475239e_name,Xs: list_P227219501e_name,Ys: list_P227219501e_name] :
% 0.27/0.63 ( ( P2 @ Ys @ Xs )
% 0.27/0.63 => ( P2 @ ( cons_P1213805021e_name @ X4 @ Xs ) @ Ys ) )
% 0.27/0.63 => ( P2 @ A0 @ A1 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % splice.induct
% 0.27/0.63 thf(fact_172_list__induct2_H,axiom,
% 0.27/0.63 ! [P2: list_P227219501e_name > list_P227219501e_name > $o,Xs2: list_P227219501e_name,Ys2: list_P227219501e_name] :
% 0.27/0.63 ( ( P2 @ nil_Pr743626285e_name @ nil_Pr743626285e_name )
% 0.27/0.63 => ( ! [X4: produc367475239e_name,Xs: list_P227219501e_name] : ( P2 @ ( cons_P1213805021e_name @ X4 @ Xs ) @ nil_Pr743626285e_name )
% 0.27/0.63 => ( ! [Y3: produc367475239e_name,Ys: list_P227219501e_name] : ( P2 @ nil_Pr743626285e_name @ ( cons_P1213805021e_name @ Y3 @ Ys ) )
% 0.27/0.63 => ( ! [X4: produc367475239e_name,Xs: list_P227219501e_name,Y3: produc367475239e_name,Ys: list_P227219501e_name] :
% 0.27/0.63 ( ( P2 @ Xs @ Ys )
% 0.27/0.63 => ( P2 @ ( cons_P1213805021e_name @ X4 @ Xs ) @ ( cons_P1213805021e_name @ Y3 @ Ys ) ) )
% 0.27/0.63 => ( P2 @ Xs2 @ Ys2 ) ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % list_induct2'
% 0.27/0.63 thf(fact_173_neq__Nil__conv,axiom,
% 0.27/0.63 ! [Xs2: list_P227219501e_name] :
% 0.27/0.63 ( ( Xs2 != nil_Pr743626285e_name )
% 0.27/0.63 = ( ? [Y5: produc367475239e_name,Ys3: list_P227219501e_name] :
% 0.27/0.63 ( Xs2
% 0.27/0.63 = ( cons_P1213805021e_name @ Y5 @ Ys3 ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % neq_Nil_conv
% 0.27/0.63 thf(fact_174_list_Oinducts,axiom,
% 0.27/0.63 ! [P2: list_P227219501e_name > $o,List: list_P227219501e_name] :
% 0.27/0.63 ( ( P2 @ nil_Pr743626285e_name )
% 0.27/0.63 => ( ! [X12: produc367475239e_name,X23: list_P227219501e_name] :
% 0.27/0.63 ( ( P2 @ X23 )
% 0.27/0.63 => ( P2 @ ( cons_P1213805021e_name @ X12 @ X23 ) ) )
% 0.27/0.63 => ( P2 @ List ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % list.inducts
% 0.27/0.63 thf(fact_175_list_Oexhaust,axiom,
% 0.27/0.63 ! [Y4: list_P227219501e_name] :
% 0.27/0.63 ( ( Y4 != nil_Pr743626285e_name )
% 0.27/0.63 => ~ ! [X212: produc367475239e_name,X222: list_P227219501e_name] :
% 0.27/0.63 ( Y4
% 0.27/0.63 != ( cons_P1213805021e_name @ X212 @ X222 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % list.exhaust
% 0.27/0.63 thf(fact_176_list_OdiscI,axiom,
% 0.27/0.63 ! [List: list_P227219501e_name,X21: produc367475239e_name,X22: list_P227219501e_name] :
% 0.27/0.63 ( ( List
% 0.27/0.63 = ( cons_P1213805021e_name @ X21 @ X22 ) )
% 0.27/0.63 => ( List != nil_Pr743626285e_name ) ) ).
% 0.27/0.63
% 0.27/0.63 % list.discI
% 0.27/0.63 thf(fact_177_list_Odistinct_I1_J,axiom,
% 0.27/0.63 ! [X21: produc367475239e_name,X22: list_P227219501e_name] :
% 0.27/0.63 ( nil_Pr743626285e_name
% 0.27/0.63 != ( cons_P1213805021e_name @ X21 @ X22 ) ) ).
% 0.27/0.63
% 0.27/0.63 % list.distinct(1)
% 0.27/0.63 thf(fact_178__092_060open_062y_A_092_060sharp_062_AQ_092_060close_062,axiom,
% 0.27/0.63 fresh_name_pi @ y @ q ).
% 0.27/0.63
% 0.27/0.63 % \<open>y \<sharp> Q\<close>
% 0.27/0.63 thf(fact_179_pair__in__Id__conv,axiom,
% 0.27/0.63 ! [A: name,B: name] :
% 0.27/0.63 ( ( member695284560e_name @ ( produc1570949143e_name @ A @ B ) @ id_name )
% 0.27/0.63 = ( A = B ) ) ).
% 0.27/0.63
% 0.27/0.63 % pair_in_Id_conv
% 0.27/0.63 thf(fact_180_pair__in__Id__conv,axiom,
% 0.27/0.63 ! [A: pi,B: pi] :
% 0.27/0.63 ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ A @ B ) @ id_pi )
% 0.27/0.63 = ( A = B ) ) ).
% 0.27/0.63
% 0.27/0.63 % pair_in_Id_conv
% 0.27/0.63 thf(fact_181_IdI,axiom,
% 0.27/0.63 ! [A: name] : ( member695284560e_name @ ( produc1570949143e_name @ A @ A ) @ id_name ) ).
% 0.27/0.63
% 0.27/0.63 % IdI
% 0.27/0.63 thf(fact_182_IdI,axiom,
% 0.27/0.63 ! [A: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ A @ A ) @ id_pi ) ).
% 0.27/0.63
% 0.27/0.63 % IdI
% 0.27/0.63 thf(fact_183_fresh__prod,axiom,
% 0.27/0.63 ! [A: name,X: late_subject,Y4: late_subject] :
% 0.27/0.63 ( ( fresh_495373993ubject @ A @ ( produc1465345179ubject @ X @ Y4 ) )
% 0.27/0.63 = ( ( fresh_717452603ubject @ A @ X )
% 0.27/0.63 & ( fresh_717452603ubject @ A @ Y4 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % fresh_prod
% 0.27/0.63 thf(fact_184_fresh__prod,axiom,
% 0.27/0.63 ! [A: name,X: late_subject,Y4: late_freeRes] :
% 0.27/0.63 ( ( fresh_1638563217reeRes @ A @ ( produc242091907reeRes @ X @ Y4 ) )
% 0.27/0.63 = ( ( fresh_717452603ubject @ A @ X )
% 0.27/0.63 & ( fresh_1641682979reeRes @ A @ Y4 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % fresh_prod
% 0.27/0.63 thf(fact_185_fresh__prod,axiom,
% 0.27/0.63 ! [A: name,X: late_subject,Y4: name] :
% 0.27/0.63 ( ( fresh_1953561446t_name @ A @ ( produc1647375838t_name @ X @ Y4 ) )
% 0.27/0.63 = ( ( fresh_717452603ubject @ A @ X )
% 0.27/0.63 & ( fresh_name_name @ A @ Y4 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % fresh_prod
% 0.27/0.63 thf(fact_186_fresh__prod,axiom,
% 0.27/0.63 ! [A: name,X: late_subject,Y4: pi] :
% 0.27/0.63 ( ( fresh_994896692ect_pi @ A @ ( produc324947500ect_pi @ X @ Y4 ) )
% 0.27/0.63 = ( ( fresh_717452603ubject @ A @ X )
% 0.27/0.63 & ( fresh_name_pi @ A @ Y4 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % fresh_prod
% 0.27/0.63 thf(fact_187_fresh__prod,axiom,
% 0.27/0.63 ! [A: name,X: late_freeRes,Y4: late_subject] :
% 0.27/0.63 ( ( fresh_1498103185ubject @ A @ ( produc320590723ubject @ X @ Y4 ) )
% 0.27/0.63 = ( ( fresh_1641682979reeRes @ A @ X )
% 0.27/0.63 & ( fresh_717452603ubject @ A @ Y4 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % fresh_prod
% 0.27/0.63 thf(fact_188_fresh__prod,axiom,
% 0.27/0.63 ! [A: name,X: late_freeRes,Y4: late_freeRes] :
% 0.27/0.63 ( ( fresh_493808761reeRes @ A @ ( produc1244821099reeRes @ X @ Y4 ) )
% 0.27/0.63 = ( ( fresh_1641682979reeRes @ A @ X )
% 0.27/0.63 & ( fresh_1641682979reeRes @ A @ Y4 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % fresh_prod
% 0.27/0.63 thf(fact_189_fresh__prod,axiom,
% 0.27/0.63 ! [A: name,X: late_freeRes,Y4: name] :
% 0.27/0.63 ( ( fresh_2007541374s_name @ A @ ( produc1701355766s_name @ X @ Y4 ) )
% 0.27/0.63 = ( ( fresh_1641682979reeRes @ A @ X )
% 0.27/0.63 & ( fresh_name_name @ A @ Y4 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % fresh_prod
% 0.27/0.63 thf(fact_190_fresh__prod,axiom,
% 0.27/0.63 ! [A: name,X: late_freeRes,Y4: pi] :
% 0.27/0.63 ( ( fresh_1847501388Res_pi @ A @ ( produc1177552196Res_pi @ X @ Y4 ) )
% 0.27/0.63 = ( ( fresh_1641682979reeRes @ A @ X )
% 0.27/0.63 & ( fresh_name_pi @ A @ Y4 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % fresh_prod
% 0.27/0.63 thf(fact_191_fresh__prod,axiom,
% 0.27/0.63 ! [A: name,X: name,Y4: late_subject] :
% 0.27/0.63 ( ( fresh_820177506ubject @ A @ ( produc607574050ubject @ X @ Y4 ) )
% 0.27/0.63 = ( ( fresh_name_name @ A @ X )
% 0.27/0.63 & ( fresh_717452603ubject @ A @ Y4 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % fresh_prod
% 0.27/0.63 thf(fact_192_fresh__prod,axiom,
% 0.27/0.63 ! [A: name,X: name,Y4: late_freeRes] :
% 0.27/0.63 ( ( fresh_1963366730reeRes @ A @ ( produc1531804426reeRes @ X @ Y4 ) )
% 0.27/0.63 = ( ( fresh_name_name @ A @ X )
% 0.27/0.63 & ( fresh_1641682979reeRes @ A @ Y4 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % fresh_prod
% 0.27/0.63 thf(fact_193__092_060open_062y_A_092_060sharp_062_AP_092_060close_062,axiom,
% 0.27/0.63 fresh_name_pi @ y @ p ).
% 0.27/0.63
% 0.27/0.63 % \<open>y \<sharp> P\<close>
% 0.27/0.63 thf(fact_194_derivativeReflexive,axiom,
% 0.27/0.63 ! [Rel: set_Pr1834926343_pi_pi,P2: pi,A: late_subject,X: name] :
% 0.27/0.63 ( ( ord_le630093991_pi_pi @ id_pi @ Rel )
% 0.27/0.63 => ( strong2129052853vative @ P2 @ P2 @ A @ X @ Rel ) ) ).
% 0.27/0.63
% 0.27/0.63 % derivativeReflexive
% 0.27/0.63 thf(fact_195_derivativeEqvtI,axiom,
% 0.27/0.63 ! [P2: pi,Q: pi,A: late_subject,X: name,Rel: set_Pr1834926343_pi_pi,Perm: list_P227219501e_name] :
% 0.27/0.63 ( ( strong2129052853vative @ P2 @ Q @ A @ X @ Rel )
% 0.27/0.63 => ( ( eqvt_pi @ Rel )
% 0.27/0.63 => ( strong2129052853vative @ ( perm_name_pi @ Perm @ P2 ) @ ( perm_name_pi @ Perm @ Q ) @ ( perm_n1559866809ubject @ Perm @ A ) @ ( perm_name_name @ Perm @ X ) @ Rel ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % derivativeEqvtI
% 0.27/0.63 thf(fact_196_derivativeEqvtI2,axiom,
% 0.27/0.63 ! [P2: pi,Q: pi,A: late_subject,X: name,Rel: set_Pr1834926343_pi_pi,Perm: list_P227219501e_name] :
% 0.27/0.63 ( ( strong2129052853vative @ P2 @ Q @ A @ X @ Rel )
% 0.27/0.63 => ( ( eqvt_pi @ Rel )
% 0.27/0.63 => ( strong2129052853vative @ ( perm_name_pi @ Perm @ P2 ) @ ( perm_name_pi @ Perm @ Q ) @ A @ ( perm_name_name @ Perm @ X ) @ Rel ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % derivativeEqvtI2
% 0.27/0.63 thf(fact_197_eqvtRelI,axiom,
% 0.27/0.63 ! [Rel: set_Pr806375235ubject,P2: late_subject,Q: late_subject,Perm: list_P227219501e_name] :
% 0.27/0.63 ( ( eqvt_Late_subject @ Rel )
% 0.27/0.63 => ( ( member1586545036ubject @ ( produc1465345179ubject @ P2 @ Q ) @ Rel )
% 0.27/0.63 => ( member1586545036ubject @ ( produc1465345179ubject @ ( perm_n1559866809ubject @ Perm @ P2 ) @ ( perm_n1559866809ubject @ Perm @ Q ) ) @ Rel ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % eqvtRelI
% 0.27/0.63 thf(fact_198_eqvtRelI,axiom,
% 0.27/0.63 ! [Rel: set_Pr1780909331reeRes,P2: late_freeRes,Q: late_freeRes,Perm: list_P227219501e_name] :
% 0.27/0.63 ( ( eqvt_Late_freeRes @ Rel )
% 0.27/0.63 => ( ( member1584979804reeRes @ ( produc1244821099reeRes @ P2 @ Q ) @ Rel )
% 0.27/0.63 => ( member1584979804reeRes @ ( produc1244821099reeRes @ ( perm_n336613537reeRes @ Perm @ P2 ) @ ( perm_n336613537reeRes @ Perm @ Q ) ) @ Rel ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % eqvtRelI
% 0.27/0.63 thf(fact_199_eqvtRelI,axiom,
% 0.27/0.63 ! [Rel: set_Pr1131282415pi_Rep,P2: pi_Rep,Q: pi_Rep,Perm: list_P227219501e_name] :
% 0.27/0.63 ( ( eqvt_pi_Rep @ Rel )
% 0.27/0.63 => ( ( member1671908408pi_Rep @ ( produc784048711pi_Rep @ P2 @ Q ) @ Rel )
% 0.27/0.63 => ( member1671908408pi_Rep @ ( produc784048711pi_Rep @ ( perm_name_pi_Rep @ Perm @ P2 ) @ ( perm_name_pi_Rep @ Perm @ Q ) ) @ Rel ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % eqvtRelI
% 0.27/0.63 thf(fact_200_eqvtRelI,axiom,
% 0.27/0.63 ! [Rel: set_Pr443758855e_name,P2: name,Q: name,Perm: list_P227219501e_name] :
% 0.27/0.63 ( ( eqvt_name @ Rel )
% 0.27/0.63 => ( ( member695284560e_name @ ( produc1570949143e_name @ P2 @ Q ) @ Rel )
% 0.27/0.63 => ( member695284560e_name @ ( produc1570949143e_name @ ( perm_name_name @ Perm @ P2 ) @ ( perm_name_name @ Perm @ Q ) ) @ Rel ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % eqvtRelI
% 0.27/0.63 thf(fact_201_eqvtRelI,axiom,
% 0.27/0.63 ! [Rel: set_Pr1834926343_pi_pi,P2: pi,Q: pi,Perm: list_P227219501e_name] :
% 0.27/0.63 ( ( eqvt_pi @ Rel )
% 0.27/0.63 => ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P2 @ Q ) @ Rel )
% 0.27/0.63 => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( perm_name_pi @ Perm @ P2 ) @ ( perm_name_pi @ Perm @ Q ) ) @ Rel ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % eqvtRelI
% 0.27/0.63 thf(fact_202_Bound_Ohyps_I5_J,axiom,
% 0.27/0.63 fresh_1376661020_pi_pi @ y @ ( produc235456326_pi_pi @ x @ ( product_Pair_pi_pi @ p @ q ) ) ).
% 0.27/0.63
% 0.27/0.63 % Bound.hyps(5)
% 0.27/0.63 thf(fact_203_subject_Ofresh_I2_J,axiom,
% 0.27/0.63 ! [A: name,X1: name] :
% 0.27/0.63 ( ( fresh_717452603ubject @ A @ ( late_BoundOutputS @ X1 ) )
% 0.27/0.63 = ( fresh_name_name @ A @ X1 ) ) ).
% 0.27/0.63
% 0.27/0.63 % subject.fresh(2)
% 0.27/0.63 thf(fact_204_name__bij,axiom,
% 0.27/0.63 ! [Pi: list_P227219501e_name,X: name,Y4: name] :
% 0.27/0.63 ( ( ( perm_name_name @ Pi @ X )
% 0.27/0.63 = ( perm_name_name @ Pi @ Y4 ) )
% 0.27/0.63 = ( X = Y4 ) ) ).
% 0.27/0.63
% 0.27/0.63 % name_bij
% 0.27/0.63 thf(fact_205_allE__Nil,axiom,
% 0.27/0.63 ! [P2: list_P227219501e_name > $o] :
% 0.27/0.63 ( ! [X_1: list_P227219501e_name] : ( P2 @ X_1 )
% 0.27/0.63 => ( P2 @ nil_Pr743626285e_name ) ) ).
% 0.27/0.63
% 0.27/0.63 % allE_Nil
% 0.27/0.63 thf(fact_206_if__eqvt,axiom,
% 0.27/0.63 ! [Pi: list_P227219501e_name,B: $o,C1: late_subject,C22: late_subject] :
% 0.27/0.63 ( ( ( perm_name_o @ Pi @ B )
% 0.27/0.63 => ( ( perm_n1559866809ubject @ Pi @ ( if_Late_subject @ B @ C1 @ C22 ) )
% 0.27/0.63 = ( perm_n1559866809ubject @ Pi @ C1 ) ) )
% 0.27/0.63 & ( ~ ( perm_name_o @ Pi @ B )
% 0.27/0.63 => ( ( perm_n1559866809ubject @ Pi @ ( if_Late_subject @ B @ C1 @ C22 ) )
% 0.27/0.63 = ( perm_n1559866809ubject @ Pi @ C22 ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % if_eqvt
% 0.27/0.63 thf(fact_207_if__eqvt,axiom,
% 0.27/0.63 ! [Pi: list_P227219501e_name,B: $o,C1: late_freeRes,C22: late_freeRes] :
% 0.27/0.63 ( ( ( perm_name_o @ Pi @ B )
% 0.27/0.63 => ( ( perm_n336613537reeRes @ Pi @ ( if_Late_freeRes @ B @ C1 @ C22 ) )
% 0.27/0.63 = ( perm_n336613537reeRes @ Pi @ C1 ) ) )
% 0.27/0.63 & ( ~ ( perm_name_o @ Pi @ B )
% 0.27/0.63 => ( ( perm_n336613537reeRes @ Pi @ ( if_Late_freeRes @ B @ C1 @ C22 ) )
% 0.27/0.63 = ( perm_n336613537reeRes @ Pi @ C22 ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % if_eqvt
% 0.27/0.63 thf(fact_208_if__eqvt,axiom,
% 0.27/0.63 ! [Pi: list_P227219501e_name,B: $o,C1: pi_Rep,C22: pi_Rep] :
% 0.27/0.63 ( ( ( perm_name_o @ Pi @ B )
% 0.27/0.63 => ( ( perm_name_pi_Rep @ Pi @ ( if_pi_Rep @ B @ C1 @ C22 ) )
% 0.27/0.63 = ( perm_name_pi_Rep @ Pi @ C1 ) ) )
% 0.27/0.63 & ( ~ ( perm_name_o @ Pi @ B )
% 0.27/0.63 => ( ( perm_name_pi_Rep @ Pi @ ( if_pi_Rep @ B @ C1 @ C22 ) )
% 0.27/0.63 = ( perm_name_pi_Rep @ Pi @ C22 ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % if_eqvt
% 0.27/0.63 thf(fact_209_if__eqvt,axiom,
% 0.27/0.63 ! [Pi: list_P227219501e_name,B: $o,C1: name,C22: name] :
% 0.27/0.63 ( ( ( perm_name_o @ Pi @ B )
% 0.27/0.63 => ( ( perm_name_name @ Pi @ ( if_name @ B @ C1 @ C22 ) )
% 0.27/0.63 = ( perm_name_name @ Pi @ C1 ) ) )
% 0.27/0.63 & ( ~ ( perm_name_o @ Pi @ B )
% 0.27/0.63 => ( ( perm_name_name @ Pi @ ( if_name @ B @ C1 @ C22 ) )
% 0.27/0.63 = ( perm_name_name @ Pi @ C22 ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % if_eqvt
% 0.27/0.63 thf(fact_210_if__eqvt,axiom,
% 0.27/0.63 ! [Pi: list_P227219501e_name,B: $o,C1: pi,C22: pi] :
% 0.27/0.63 ( ( ( perm_name_o @ Pi @ B )
% 0.27/0.63 => ( ( perm_name_pi @ Pi @ ( if_pi @ B @ C1 @ C22 ) )
% 0.27/0.63 = ( perm_name_pi @ Pi @ C1 ) ) )
% 0.27/0.63 & ( ~ ( perm_name_o @ Pi @ B )
% 0.27/0.63 => ( ( perm_name_pi @ Pi @ ( if_pi @ B @ C1 @ C22 ) )
% 0.27/0.63 = ( perm_name_pi @ Pi @ C22 ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % if_eqvt
% 0.27/0.63 thf(fact_211_pt__bij3,axiom,
% 0.27/0.63 ! [X: late_subject,Y4: late_subject,Pi: list_P227219501e_name] :
% 0.27/0.63 ( ( X = Y4 )
% 0.27/0.63 => ( ( perm_n1559866809ubject @ Pi @ X )
% 0.27/0.63 = ( perm_n1559866809ubject @ Pi @ Y4 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % pt_bij3
% 0.27/0.63 thf(fact_212_pt__bij3,axiom,
% 0.27/0.63 ! [X: late_freeRes,Y4: late_freeRes,Pi: list_P227219501e_name] :
% 0.27/0.63 ( ( X = Y4 )
% 0.27/0.63 => ( ( perm_n336613537reeRes @ Pi @ X )
% 0.27/0.63 = ( perm_n336613537reeRes @ Pi @ Y4 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % pt_bij3
% 0.27/0.63 thf(fact_213_pt__bij3,axiom,
% 0.27/0.63 ! [X: pi_Rep,Y4: pi_Rep,Pi: list_P227219501e_name] :
% 0.27/0.63 ( ( X = Y4 )
% 0.27/0.63 => ( ( perm_name_pi_Rep @ Pi @ X )
% 0.27/0.63 = ( perm_name_pi_Rep @ Pi @ Y4 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % pt_bij3
% 0.27/0.63 thf(fact_214_pt__bij3,axiom,
% 0.27/0.63 ! [X: name,Y4: name,Pi: list_P227219501e_name] :
% 0.27/0.63 ( ( X = Y4 )
% 0.27/0.63 => ( ( perm_name_name @ Pi @ X )
% 0.27/0.63 = ( perm_name_name @ Pi @ Y4 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % pt_bij3
% 0.27/0.63 thf(fact_215_pt__bij3,axiom,
% 0.27/0.63 ! [X: pi,Y4: pi,Pi: list_P227219501e_name] :
% 0.27/0.63 ( ( X = Y4 )
% 0.27/0.63 => ( ( perm_name_pi @ Pi @ X )
% 0.27/0.63 = ( perm_name_pi @ Pi @ Y4 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % pt_bij3
% 0.27/0.63 thf(fact_216_abs__fun__if,axiom,
% 0.27/0.63 ! [C2: $o,Pi: list_P227219501e_name,X: late_subject,Y4: late_subject] :
% 0.27/0.63 ( ( C2
% 0.27/0.63 => ( ( perm_n1559866809ubject @ Pi @ ( if_Late_subject @ C2 @ X @ Y4 ) )
% 0.27/0.63 = ( perm_n1559866809ubject @ Pi @ X ) ) )
% 0.27/0.63 & ( ~ C2
% 0.27/0.63 => ( ( perm_n1559866809ubject @ Pi @ ( if_Late_subject @ C2 @ X @ Y4 ) )
% 0.27/0.63 = ( perm_n1559866809ubject @ Pi @ Y4 ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % abs_fun_if
% 0.27/0.63 thf(fact_217_abs__fun__if,axiom,
% 0.27/0.63 ! [C2: $o,Pi: list_P227219501e_name,X: late_freeRes,Y4: late_freeRes] :
% 0.27/0.63 ( ( C2
% 0.27/0.63 => ( ( perm_n336613537reeRes @ Pi @ ( if_Late_freeRes @ C2 @ X @ Y4 ) )
% 0.27/0.63 = ( perm_n336613537reeRes @ Pi @ X ) ) )
% 0.27/0.63 & ( ~ C2
% 0.27/0.63 => ( ( perm_n336613537reeRes @ Pi @ ( if_Late_freeRes @ C2 @ X @ Y4 ) )
% 0.27/0.63 = ( perm_n336613537reeRes @ Pi @ Y4 ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % abs_fun_if
% 0.27/0.63 thf(fact_218_abs__fun__if,axiom,
% 0.27/0.63 ! [C2: $o,Pi: list_P227219501e_name,X: pi_Rep,Y4: pi_Rep] :
% 0.27/0.63 ( ( C2
% 0.27/0.63 => ( ( perm_name_pi_Rep @ Pi @ ( if_pi_Rep @ C2 @ X @ Y4 ) )
% 0.27/0.63 = ( perm_name_pi_Rep @ Pi @ X ) ) )
% 0.27/0.63 & ( ~ C2
% 0.27/0.63 => ( ( perm_name_pi_Rep @ Pi @ ( if_pi_Rep @ C2 @ X @ Y4 ) )
% 0.27/0.63 = ( perm_name_pi_Rep @ Pi @ Y4 ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % abs_fun_if
% 0.27/0.63 thf(fact_219_abs__fun__if,axiom,
% 0.27/0.63 ! [C2: $o,Pi: list_P227219501e_name,X: name,Y4: name] :
% 0.27/0.63 ( ( C2
% 0.27/0.63 => ( ( perm_name_name @ Pi @ ( if_name @ C2 @ X @ Y4 ) )
% 0.27/0.63 = ( perm_name_name @ Pi @ X ) ) )
% 0.27/0.63 & ( ~ C2
% 0.27/0.63 => ( ( perm_name_name @ Pi @ ( if_name @ C2 @ X @ Y4 ) )
% 0.27/0.63 = ( perm_name_name @ Pi @ Y4 ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % abs_fun_if
% 0.27/0.63 thf(fact_220_abs__fun__if,axiom,
% 0.27/0.63 ! [C2: $o,Pi: list_P227219501e_name,X: pi,Y4: pi] :
% 0.27/0.63 ( ( C2
% 0.27/0.63 => ( ( perm_name_pi @ Pi @ ( if_pi @ C2 @ X @ Y4 ) )
% 0.27/0.63 = ( perm_name_pi @ Pi @ X ) ) )
% 0.27/0.63 & ( ~ C2
% 0.27/0.63 => ( ( perm_name_pi @ Pi @ ( if_pi @ C2 @ X @ Y4 ) )
% 0.27/0.63 = ( perm_name_pi @ Pi @ Y4 ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % abs_fun_if
% 0.27/0.63 thf(fact_221_eqvt__def,axiom,
% 0.27/0.63 ( eqvt_pi
% 0.27/0.63 = ( ^ [Rel2: set_Pr1834926343_pi_pi] :
% 0.27/0.63 ! [X5: product_prod_pi_pi,Perm2: list_P227219501e_name] :
% 0.27/0.63 ( ( member558706512_pi_pi @ X5 @ Rel2 )
% 0.27/0.63 => ( member558706512_pi_pi @ ( perm_n1415585007_pi_pi @ Perm2 @ X5 ) @ Rel2 ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % eqvt_def
% 0.27/0.63 thf(fact_222_perm__prod_Osimps,axiom,
% 0.27/0.63 ! [Pi: list_P227219501e_name,X: late_subject,Y4: late_subject] :
% 0.27/0.63 ( ( perm_n171497387ubject @ Pi @ ( produc1465345179ubject @ X @ Y4 ) )
% 0.27/0.63 = ( produc1465345179ubject @ ( perm_n1559866809ubject @ Pi @ X ) @ ( perm_n1559866809ubject @ Pi @ Y4 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % perm_prod.simps
% 0.27/0.63 thf(fact_223_perm__prod_Osimps,axiom,
% 0.27/0.63 ! [Pi: list_P227219501e_name,X: late_subject,Y4: late_freeRes] :
% 0.27/0.63 ( ( perm_n1314686611reeRes @ Pi @ ( produc242091907reeRes @ X @ Y4 ) )
% 0.27/0.63 = ( produc242091907reeRes @ ( perm_n1559866809ubject @ Pi @ X ) @ ( perm_n336613537reeRes @ Pi @ Y4 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % perm_prod.simps
% 0.27/0.63 thf(fact_224_perm__prod_Osimps,axiom,
% 0.27/0.63 ! [Pi: list_P227219501e_name,X: late_subject,Y4: pi_Rep] :
% 0.27/0.63 ( ( perm_n1467004033pi_Rep @ Pi @ ( produc843063281pi_Rep @ X @ Y4 ) )
% 0.27/0.63 = ( produc843063281pi_Rep @ ( perm_n1559866809ubject @ Pi @ X ) @ ( perm_name_pi_Rep @ Pi @ Y4 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % perm_prod.simps
% 0.27/0.63 thf(fact_225_perm__prod_Osimps,axiom,
% 0.27/0.63 ! [Pi: list_P227219501e_name,X: late_subject,Y4: name] :
% 0.27/0.63 ( ( perm_n204483300t_name @ Pi @ ( produc1647375838t_name @ X @ Y4 ) )
% 0.27/0.63 = ( produc1647375838t_name @ ( perm_n1559866809ubject @ Pi @ X ) @ ( perm_name_name @ Pi @ Y4 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % perm_prod.simps
% 0.27/0.63 thf(fact_226_perm__prod_Osimps,axiom,
% 0.27/0.63 ! [Pi: list_P227219501e_name,X: late_subject,Y4: pi] :
% 0.27/0.63 ( ( perm_n359102898ect_pi @ Pi @ ( produc324947500ect_pi @ X @ Y4 ) )
% 0.27/0.63 = ( produc324947500ect_pi @ ( perm_n1559866809ubject @ Pi @ X ) @ ( perm_name_pi @ Pi @ Y4 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % perm_prod.simps
% 0.27/0.63 thf(fact_227_perm__prod_Osimps,axiom,
% 0.27/0.63 ! [Pi: list_P227219501e_name,X: late_freeRes,Y4: late_subject] :
% 0.27/0.63 ( ( perm_n1174226579ubject @ Pi @ ( produc320590723ubject @ X @ Y4 ) )
% 0.27/0.63 = ( produc320590723ubject @ ( perm_n336613537reeRes @ Pi @ X ) @ ( perm_n1559866809ubject @ Pi @ Y4 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % perm_prod.simps
% 0.27/0.63 thf(fact_228_perm__prod_Osimps,axiom,
% 0.27/0.63 ! [Pi: list_P227219501e_name,X: late_freeRes,Y4: late_freeRes] :
% 0.27/0.63 ( ( perm_n169932155reeRes @ Pi @ ( produc1244821099reeRes @ X @ Y4 ) )
% 0.27/0.63 = ( produc1244821099reeRes @ ( perm_n336613537reeRes @ Pi @ X ) @ ( perm_n336613537reeRes @ Pi @ Y4 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % perm_prod.simps
% 0.27/0.63 thf(fact_229_perm__prod_Osimps,axiom,
% 0.27/0.63 ! [Pi: list_P227219501e_name,X: late_freeRes,Y4: pi_Rep] :
% 0.27/0.63 ( ( perm_n840427369pi_Rep @ Pi @ ( produc216486617pi_Rep @ X @ Y4 ) )
% 0.27/0.63 = ( produc216486617pi_Rep @ ( perm_n336613537reeRes @ Pi @ X ) @ ( perm_name_pi_Rep @ Pi @ Y4 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % perm_prod.simps
% 0.27/0.63 thf(fact_230_perm__prod_Osimps,axiom,
% 0.27/0.63 ! [Pi: list_P227219501e_name,X: late_freeRes,Y4: name] :
% 0.27/0.63 ( ( perm_n258463228s_name @ Pi @ ( produc1701355766s_name @ X @ Y4 ) )
% 0.27/0.63 = ( produc1701355766s_name @ ( perm_n336613537reeRes @ Pi @ X ) @ ( perm_name_name @ Pi @ Y4 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % perm_prod.simps
% 0.27/0.63 thf(fact_231_perm__prod_Osimps,axiom,
% 0.27/0.63 ! [Pi: list_P227219501e_name,X: late_freeRes,Y4: pi] :
% 0.27/0.63 ( ( perm_n1211707594Res_pi @ Pi @ ( produc1177552196Res_pi @ X @ Y4 ) )
% 0.27/0.63 = ( produc1177552196Res_pi @ ( perm_n336613537reeRes @ Pi @ X ) @ ( perm_name_pi @ Pi @ Y4 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % perm_prod.simps
% 0.27/0.63 thf(fact_232_cons__eqvt,axiom,
% 0.27/0.63 ! [Pi: list_P227219501e_name,X: late_subject,Xs2: list_Late_subject] :
% 0.27/0.63 ( ( perm_n1812647369ubject @ Pi @ ( cons_Late_subject @ X @ Xs2 ) )
% 0.27/0.63 = ( cons_Late_subject @ ( perm_n1559866809ubject @ Pi @ X ) @ ( perm_n1812647369ubject @ Pi @ Xs2 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % cons_eqvt
% 0.27/0.63 thf(fact_233_cons__eqvt,axiom,
% 0.27/0.63 ! [Pi: list_P227219501e_name,X: late_freeRes,Xs2: list_Late_freeRes] :
% 0.27/0.63 ( ( perm_n808352945reeRes @ Pi @ ( cons_Late_freeRes @ X @ Xs2 ) )
% 0.27/0.63 = ( cons_Late_freeRes @ ( perm_n336613537reeRes @ Pi @ X ) @ ( perm_n808352945reeRes @ Pi @ Xs2 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % cons_eqvt
% 0.27/0.63 thf(fact_234_cons__eqvt,axiom,
% 0.27/0.63 ! [Pi: list_P227219501e_name,X: pi_Rep,Xs2: list_pi_Rep] :
% 0.27/0.63 ( ( perm_n729617823pi_Rep @ Pi @ ( cons_pi_Rep @ X @ Xs2 ) )
% 0.27/0.63 = ( cons_pi_Rep @ ( perm_name_pi_Rep @ Pi @ X ) @ ( perm_n729617823pi_Rep @ Pi @ Xs2 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % cons_eqvt
% 0.27/0.63 thf(fact_235_cons__eqvt,axiom,
% 0.27/0.63 ! [Pi: list_P227219501e_name,X: name,Xs2: list_name] :
% 0.27/0.63 ( ( perm_name_list_name @ Pi @ ( cons_name @ X @ Xs2 ) )
% 0.27/0.63 = ( cons_name @ ( perm_name_name @ Pi @ X ) @ ( perm_name_list_name @ Pi @ Xs2 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % cons_eqvt
% 0.27/0.63 thf(fact_236_cons__eqvt,axiom,
% 0.27/0.63 ! [Pi: list_P227219501e_name,X: pi,Xs2: list_pi] :
% 0.27/0.63 ( ( perm_name_list_pi @ Pi @ ( cons_pi @ X @ Xs2 ) )
% 0.27/0.63 = ( cons_pi @ ( perm_name_pi @ Pi @ X ) @ ( perm_name_list_pi @ Pi @ Xs2 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % cons_eqvt
% 0.27/0.63 thf(fact_237_fresh__prodD_I1_J,axiom,
% 0.27/0.63 ! [A: name,X: name,Y4: name] :
% 0.27/0.63 ( ( fresh_441084397e_name @ A @ ( produc1570949143e_name @ X @ Y4 ) )
% 0.27/0.63 => ( fresh_name_name @ A @ X ) ) ).
% 0.27/0.63
% 0.27/0.63 % fresh_prodD(1)
% 0.27/0.63 thf(fact_238_fresh__prodD_I1_J,axiom,
% 0.27/0.63 ! [A: name,X: name,Y4: product_prod_pi_pi] :
% 0.27/0.63 ( ( fresh_1376661020_pi_pi @ A @ ( produc235456326_pi_pi @ X @ Y4 ) )
% 0.27/0.63 => ( fresh_name_name @ A @ X ) ) ).
% 0.27/0.63
% 0.27/0.63 % fresh_prodD(1)
% 0.27/0.63 thf(fact_239_fresh__prodD_I1_J,axiom,
% 0.27/0.63 ! [A: name,X: pi,Y4: pi] :
% 0.27/0.63 ( ( fresh_1627595501_pi_pi @ A @ ( product_Pair_pi_pi @ X @ Y4 ) )
% 0.27/0.63 => ( fresh_name_pi @ A @ X ) ) ).
% 0.27/0.63
% 0.27/0.63 % fresh_prodD(1)
% 0.27/0.63 thf(fact_240_fresh__prodD_I2_J,axiom,
% 0.27/0.63 ! [A: name,X: name,Y4: name] :
% 0.27/0.63 ( ( fresh_441084397e_name @ A @ ( produc1570949143e_name @ X @ Y4 ) )
% 0.27/0.63 => ( fresh_name_name @ A @ Y4 ) ) ).
% 0.27/0.63
% 0.27/0.63 % fresh_prodD(2)
% 0.27/0.63 thf(fact_241_fresh__prodD_I2_J,axiom,
% 0.27/0.63 ! [A: name,X: name,Y4: product_prod_pi_pi] :
% 0.27/0.63 ( ( fresh_1376661020_pi_pi @ A @ ( produc235456326_pi_pi @ X @ Y4 ) )
% 0.27/0.63 => ( fresh_1627595501_pi_pi @ A @ Y4 ) ) ).
% 0.27/0.63
% 0.27/0.63 % fresh_prodD(2)
% 0.27/0.63 thf(fact_242_fresh__prodD_I2_J,axiom,
% 0.27/0.63 ! [A: name,X: pi,Y4: pi] :
% 0.27/0.63 ( ( fresh_1627595501_pi_pi @ A @ ( product_Pair_pi_pi @ X @ Y4 ) )
% 0.27/0.63 => ( fresh_name_pi @ A @ Y4 ) ) ).
% 0.27/0.63
% 0.27/0.63 % fresh_prodD(2)
% 0.27/0.63 thf(fact_243_fresh__list__cons,axiom,
% 0.27/0.63 ! [A: name,X: late_subject,Xs2: list_Late_subject] :
% 0.27/0.63 ( ( fresh_838462539ubject @ A @ ( cons_Late_subject @ X @ Xs2 ) )
% 0.27/0.63 = ( ( fresh_717452603ubject @ A @ X )
% 0.27/0.63 & ( fresh_838462539ubject @ A @ Xs2 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % fresh_list_cons
% 0.27/0.63 thf(fact_244_fresh__list__cons,axiom,
% 0.27/0.63 ! [A: name,X: late_freeRes,Xs2: list_Late_freeRes] :
% 0.27/0.63 ( ( fresh_1981651763reeRes @ A @ ( cons_Late_freeRes @ X @ Xs2 ) )
% 0.27/0.63 = ( ( fresh_1641682979reeRes @ A @ X )
% 0.27/0.63 & ( fresh_1981651763reeRes @ A @ Xs2 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % fresh_list_cons
% 0.27/0.63 thf(fact_245_fresh__list__cons,axiom,
% 0.27/0.63 ! [A: name,X: produc1141751126_pi_pi,Xs2: list_P431515740_pi_pi] :
% 0.27/0.63 ( ( fresh_1958133282_pi_pi @ A @ ( cons_P749510156_pi_pi @ X @ Xs2 ) )
% 0.27/0.63 = ( ( fresh_1376661020_pi_pi @ A @ X )
% 0.27/0.63 & ( fresh_1958133282_pi_pi @ A @ Xs2 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % fresh_list_cons
% 0.27/0.63 thf(fact_246_fresh__list__cons,axiom,
% 0.27/0.63 ! [A: name,X: name,Xs2: list_name] :
% 0.27/0.63 ( ( fresh_name_list_name @ A @ ( cons_name @ X @ Xs2 ) )
% 0.27/0.63 = ( ( fresh_name_name @ A @ X )
% 0.27/0.63 & ( fresh_name_list_name @ A @ Xs2 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % fresh_list_cons
% 0.27/0.63 thf(fact_247_fresh__list__cons,axiom,
% 0.27/0.63 ! [A: name,X: pi,Xs2: list_pi] :
% 0.27/0.63 ( ( fresh_name_list_pi @ A @ ( cons_pi @ X @ Xs2 ) )
% 0.27/0.63 = ( ( fresh_name_pi @ A @ X )
% 0.27/0.63 & ( fresh_name_list_pi @ A @ Xs2 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % fresh_list_cons
% 0.27/0.63 thf(fact_248_subrelI,axiom,
% 0.27/0.63 ! [R: set_Pr443758855e_name,S: set_Pr443758855e_name] :
% 0.27/0.63 ( ! [X4: name,Y3: name] :
% 0.27/0.63 ( ( member695284560e_name @ ( produc1570949143e_name @ X4 @ Y3 ) @ R )
% 0.27/0.63 => ( member695284560e_name @ ( produc1570949143e_name @ X4 @ Y3 ) @ S ) )
% 0.27/0.63 => ( ord_le793202855e_name @ R @ S ) ) ).
% 0.27/0.63
% 0.27/0.63 % subrelI
% 0.27/0.63 thf(fact_249_subrelI,axiom,
% 0.27/0.63 ! [R: set_Pr1654044726_pi_pi,S: set_Pr1654044726_pi_pi] :
% 0.27/0.63 ( ! [X4: name,Y3: product_prod_pi_pi] :
% 0.27/0.63 ( ( member540268543_pi_pi @ ( produc235456326_pi_pi @ X4 @ Y3 ) @ R )
% 0.27/0.63 => ( member540268543_pi_pi @ ( produc235456326_pi_pi @ X4 @ Y3 ) @ S ) )
% 0.27/0.63 => ( ord_le797229014_pi_pi @ R @ S ) ) ).
% 0.27/0.63
% 0.27/0.63 % subrelI
% 0.27/0.63 thf(fact_250_subrelI,axiom,
% 0.27/0.63 ! [R: set_Pr1834926343_pi_pi,S: set_Pr1834926343_pi_pi] :
% 0.27/0.63 ( ! [X4: pi,Y3: pi] :
% 0.27/0.63 ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ X4 @ Y3 ) @ R )
% 0.27/0.63 => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ X4 @ Y3 ) @ S ) )
% 0.27/0.63 => ( ord_le630093991_pi_pi @ R @ S ) ) ).
% 0.27/0.63
% 0.27/0.63 % subrelI
% 0.27/0.63 thf(fact_251_IdE,axiom,
% 0.27/0.63 ! [P3: produc367475239e_name] :
% 0.27/0.63 ( ( member695284560e_name @ P3 @ id_name )
% 0.27/0.63 => ~ ! [X4: name] :
% 0.27/0.63 ( P3
% 0.27/0.63 != ( produc1570949143e_name @ X4 @ X4 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % IdE
% 0.27/0.63 thf(fact_252_IdE,axiom,
% 0.27/0.63 ! [P3: product_prod_pi_pi] :
% 0.27/0.63 ( ( member558706512_pi_pi @ P3 @ id_pi )
% 0.27/0.63 => ~ ! [X4: pi] :
% 0.27/0.63 ( P3
% 0.27/0.63 != ( product_Pair_pi_pi @ X4 @ X4 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % IdE
% 0.27/0.63 thf(fact_253_derivativeMonotonic,axiom,
% 0.27/0.63 ! [P2: pi,Q: pi,A: late_subject,X: name,A4: set_Pr1834926343_pi_pi,B4: set_Pr1834926343_pi_pi] :
% 0.27/0.63 ( ( strong2129052853vative @ P2 @ Q @ A @ X @ A4 )
% 0.27/0.63 => ( ( ord_le630093991_pi_pi @ A4 @ B4 )
% 0.27/0.63 => ( strong2129052853vative @ P2 @ Q @ A @ X @ B4 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % derivativeMonotonic
% 0.27/0.63 thf(fact_254_eqvtRelE,axiom,
% 0.27/0.63 ! [Rel: set_Pr806375235ubject,Perm: list_P227219501e_name,P2: late_subject,Q: late_subject] :
% 0.27/0.63 ( ( eqvt_Late_subject @ Rel )
% 0.27/0.63 => ( ( member1586545036ubject @ ( produc1465345179ubject @ ( perm_n1559866809ubject @ Perm @ P2 ) @ ( perm_n1559866809ubject @ Perm @ Q ) ) @ Rel )
% 0.27/0.63 => ( member1586545036ubject @ ( produc1465345179ubject @ P2 @ Q ) @ Rel ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % eqvtRelE
% 0.27/0.63 thf(fact_255_eqvtRelE,axiom,
% 0.27/0.63 ! [Rel: set_Pr1780909331reeRes,Perm: list_P227219501e_name,P2: late_freeRes,Q: late_freeRes] :
% 0.27/0.63 ( ( eqvt_Late_freeRes @ Rel )
% 0.27/0.63 => ( ( member1584979804reeRes @ ( produc1244821099reeRes @ ( perm_n336613537reeRes @ Perm @ P2 ) @ ( perm_n336613537reeRes @ Perm @ Q ) ) @ Rel )
% 0.27/0.63 => ( member1584979804reeRes @ ( produc1244821099reeRes @ P2 @ Q ) @ Rel ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % eqvtRelE
% 0.27/0.63 thf(fact_256_eqvtRelE,axiom,
% 0.27/0.63 ! [Rel: set_Pr1131282415pi_Rep,Perm: list_P227219501e_name,P2: pi_Rep,Q: pi_Rep] :
% 0.27/0.63 ( ( eqvt_pi_Rep @ Rel )
% 0.27/0.63 => ( ( member1671908408pi_Rep @ ( produc784048711pi_Rep @ ( perm_name_pi_Rep @ Perm @ P2 ) @ ( perm_name_pi_Rep @ Perm @ Q ) ) @ Rel )
% 0.27/0.63 => ( member1671908408pi_Rep @ ( produc784048711pi_Rep @ P2 @ Q ) @ Rel ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % eqvtRelE
% 0.27/0.63 thf(fact_257_eqvtRelE,axiom,
% 0.27/0.63 ! [Rel: set_Pr443758855e_name,Perm: list_P227219501e_name,P2: name,Q: name] :
% 0.27/0.63 ( ( eqvt_name @ Rel )
% 0.27/0.63 => ( ( member695284560e_name @ ( produc1570949143e_name @ ( perm_name_name @ Perm @ P2 ) @ ( perm_name_name @ Perm @ Q ) ) @ Rel )
% 0.27/0.63 => ( member695284560e_name @ ( produc1570949143e_name @ P2 @ Q ) @ Rel ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % eqvtRelE
% 0.27/0.63 thf(fact_258_eqvtRelE,axiom,
% 0.27/0.63 ! [Rel: set_Pr1834926343_pi_pi,Perm: list_P227219501e_name,P2: pi,Q: pi] :
% 0.27/0.63 ( ( eqvt_pi @ Rel )
% 0.27/0.63 => ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( perm_name_pi @ Perm @ P2 ) @ ( perm_name_pi @ Perm @ Q ) ) @ Rel )
% 0.27/0.63 => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P2 @ Q ) @ Rel ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % eqvtRelE
% 0.27/0.63 thf(fact_259_Bound_Ohyps_I3_J,axiom,
% 0.27/0.63 fresh_name_pi @ y @ ( sum @ ( res @ x @ p ) @ ( res @ x @ q ) ) ).
% 0.27/0.63
% 0.27/0.63 % Bound.hyps(3)
% 0.27/0.63 thf(fact_260_Bound_Ohyps_I2_J,axiom,
% 0.27/0.63 fresh_name_pi @ y @ ( res @ x @ ( sum @ p @ q ) ) ).
% 0.27/0.63
% 0.27/0.63 % Bound.hyps(2)
% 0.27/0.63 thf(fact_261_subset__antisym,axiom,
% 0.27/0.63 ! [A4: set_Pr1834926343_pi_pi,B4: set_Pr1834926343_pi_pi] :
% 0.27/0.63 ( ( ord_le630093991_pi_pi @ A4 @ B4 )
% 0.27/0.63 => ( ( ord_le630093991_pi_pi @ B4 @ A4 )
% 0.27/0.63 => ( A4 = B4 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % subset_antisym
% 0.27/0.63 thf(fact_262_subsetI,axiom,
% 0.27/0.63 ! [A4: set_Pr1834926343_pi_pi,B4: set_Pr1834926343_pi_pi] :
% 0.27/0.63 ( ! [X4: product_prod_pi_pi] :
% 0.27/0.63 ( ( member558706512_pi_pi @ X4 @ A4 )
% 0.27/0.63 => ( member558706512_pi_pi @ X4 @ B4 ) )
% 0.27/0.63 => ( ord_le630093991_pi_pi @ A4 @ B4 ) ) ).
% 0.27/0.63
% 0.27/0.63 % subsetI
% 0.27/0.63 thf(fact_263_order__refl,axiom,
% 0.27/0.63 ! [X: set_Pr1834926343_pi_pi] : ( ord_le630093991_pi_pi @ X @ X ) ).
% 0.27/0.63
% 0.27/0.63 % order_refl
% 0.27/0.63 thf(fact_264_name__fresh,axiom,
% 0.27/0.63 ( fresh_name_name
% 0.27/0.63 = ( ^ [A5: name,B5: name] : ( A5 != B5 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % name_fresh
% 0.27/0.63 thf(fact_265_pi_Ofresh_I7_J,axiom,
% 0.27/0.63 ! [A: name,X2: pi,X1: pi] :
% 0.27/0.63 ( ( fresh_name_pi @ A @ ( sum @ X2 @ X1 ) )
% 0.27/0.63 = ( ( fresh_name_pi @ A @ X2 )
% 0.27/0.63 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % pi.fresh(7)
% 0.27/0.63 thf(fact_266_pi_Operm_I7_J,axiom,
% 0.27/0.63 ! [Pi: list_P227219501e_name,X2: pi,X1: pi] :
% 0.27/0.63 ( ( perm_name_pi @ Pi @ ( sum @ X2 @ X1 ) )
% 0.27/0.63 = ( sum @ ( perm_name_pi @ Pi @ X2 ) @ ( perm_name_pi @ Pi @ X1 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % pi.perm(7)
% 0.27/0.63 thf(fact_267_pi_Operm_I9_J,axiom,
% 0.27/0.63 ! [Pi: list_P227219501e_name,X1: name,X2: pi] :
% 0.27/0.63 ( ( perm_name_pi @ Pi @ ( res @ X1 @ X2 ) )
% 0.27/0.63 = ( res @ ( perm_name_name @ Pi @ X1 ) @ ( perm_name_pi @ Pi @ X2 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % pi.perm(9)
% 0.27/0.63 thf(fact_268_pi_Odistinct_I81_J,axiom,
% 0.27/0.63 ! [Pi1: pi,Pi2: pi,Name: name,Pi3: pi] :
% 0.27/0.63 ( ( sum @ Pi1 @ Pi2 )
% 0.27/0.63 != ( res @ Name @ Pi3 ) ) ).
% 0.27/0.63
% 0.27/0.63 % pi.distinct(81)
% 0.27/0.63 thf(fact_269_pi_Oinject_I6_J,axiom,
% 0.27/0.63 ! [X2: pi,X1: pi,Y2: pi,Y1: pi] :
% 0.27/0.63 ( ( ( sum @ X2 @ X1 )
% 0.27/0.63 = ( sum @ Y2 @ Y1 ) )
% 0.27/0.63 = ( ( X2 = Y2 )
% 0.27/0.63 & ( X1 = Y1 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % pi.inject(6)
% 0.27/0.63 thf(fact_270_freshRes,axiom,
% 0.27/0.63 ! [A: name,P2: pi] : ( fresh_name_pi @ A @ ( res @ A @ P2 ) ) ).
% 0.27/0.63
% 0.27/0.63 % freshRes
% 0.27/0.63 thf(fact_271_order__subst1,axiom,
% 0.27/0.63 ! [A: set_Pr1834926343_pi_pi,F: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C2: set_Pr1834926343_pi_pi] :
% 0.27/0.63 ( ( ord_le630093991_pi_pi @ A @ ( F @ B ) )
% 0.27/0.63 => ( ( ord_le630093991_pi_pi @ B @ C2 )
% 0.27/0.63 => ( ! [X4: set_Pr1834926343_pi_pi,Y3: set_Pr1834926343_pi_pi] :
% 0.27/0.63 ( ( ord_le630093991_pi_pi @ X4 @ Y3 )
% 0.27/0.63 => ( ord_le630093991_pi_pi @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 0.27/0.63 => ( ord_le630093991_pi_pi @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % order_subst1
% 0.27/0.63 thf(fact_272_order__subst2,axiom,
% 0.27/0.63 ! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,F: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi,C2: set_Pr1834926343_pi_pi] :
% 0.27/0.63 ( ( ord_le630093991_pi_pi @ A @ B )
% 0.27/0.63 => ( ( ord_le630093991_pi_pi @ ( F @ B ) @ C2 )
% 0.27/0.63 => ( ! [X4: set_Pr1834926343_pi_pi,Y3: set_Pr1834926343_pi_pi] :
% 0.27/0.63 ( ( ord_le630093991_pi_pi @ X4 @ Y3 )
% 0.27/0.63 => ( ord_le630093991_pi_pi @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 0.27/0.63 => ( ord_le630093991_pi_pi @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % order_subst2
% 0.27/0.63 thf(fact_273_ord__eq__le__subst,axiom,
% 0.27/0.63 ! [A: set_Pr1834926343_pi_pi,F: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C2: set_Pr1834926343_pi_pi] :
% 0.27/0.63 ( ( A
% 0.27/0.63 = ( F @ B ) )
% 0.27/0.63 => ( ( ord_le630093991_pi_pi @ B @ C2 )
% 0.27/0.63 => ( ! [X4: set_Pr1834926343_pi_pi,Y3: set_Pr1834926343_pi_pi] :
% 0.27/0.63 ( ( ord_le630093991_pi_pi @ X4 @ Y3 )
% 0.27/0.63 => ( ord_le630093991_pi_pi @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 0.27/0.63 => ( ord_le630093991_pi_pi @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % ord_eq_le_subst
% 0.27/0.63 thf(fact_274_ord__le__eq__subst,axiom,
% 0.27/0.63 ! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,F: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi,C2: set_Pr1834926343_pi_pi] :
% 0.27/0.63 ( ( ord_le630093991_pi_pi @ A @ B )
% 0.27/0.63 => ( ( ( F @ B )
% 0.27/0.63 = C2 )
% 0.27/0.63 => ( ! [X4: set_Pr1834926343_pi_pi,Y3: set_Pr1834926343_pi_pi] :
% 0.27/0.63 ( ( ord_le630093991_pi_pi @ X4 @ Y3 )
% 0.27/0.63 => ( ord_le630093991_pi_pi @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 0.27/0.63 => ( ord_le630093991_pi_pi @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % ord_le_eq_subst
% 0.27/0.63 thf(fact_275_eq__iff,axiom,
% 0.27/0.63 ( ( ^ [Y6: set_Pr1834926343_pi_pi,Z: set_Pr1834926343_pi_pi] : ( Y6 = Z ) )
% 0.27/0.63 = ( ^ [X5: set_Pr1834926343_pi_pi,Y5: set_Pr1834926343_pi_pi] :
% 0.27/0.63 ( ( ord_le630093991_pi_pi @ X5 @ Y5 )
% 0.27/0.63 & ( ord_le630093991_pi_pi @ Y5 @ X5 ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % eq_iff
% 0.27/0.63 thf(fact_276_antisym,axiom,
% 0.27/0.63 ! [X: set_Pr1834926343_pi_pi,Y4: set_Pr1834926343_pi_pi] :
% 0.27/0.63 ( ( ord_le630093991_pi_pi @ X @ Y4 )
% 0.27/0.63 => ( ( ord_le630093991_pi_pi @ Y4 @ X )
% 0.27/0.63 => ( X = Y4 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % antisym
% 0.27/0.63 thf(fact_277_eq__refl,axiom,
% 0.27/0.63 ! [X: set_Pr1834926343_pi_pi,Y4: set_Pr1834926343_pi_pi] :
% 0.27/0.63 ( ( X = Y4 )
% 0.27/0.63 => ( ord_le630093991_pi_pi @ X @ Y4 ) ) ).
% 0.27/0.63
% 0.27/0.63 % eq_refl
% 0.27/0.63 thf(fact_278_order_Otrans,axiom,
% 0.27/0.63 ! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C2: set_Pr1834926343_pi_pi] :
% 0.27/0.63 ( ( ord_le630093991_pi_pi @ A @ B )
% 0.27/0.63 => ( ( ord_le630093991_pi_pi @ B @ C2 )
% 0.27/0.63 => ( ord_le630093991_pi_pi @ A @ C2 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % order.trans
% 0.27/0.63 thf(fact_279_antisym__conv,axiom,
% 0.27/0.63 ! [Y4: set_Pr1834926343_pi_pi,X: set_Pr1834926343_pi_pi] :
% 0.27/0.63 ( ( ord_le630093991_pi_pi @ Y4 @ X )
% 0.27/0.63 => ( ( ord_le630093991_pi_pi @ X @ Y4 )
% 0.27/0.63 = ( X = Y4 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % antisym_conv
% 0.27/0.63 thf(fact_280_order__class_Oorder_Oeq__iff,axiom,
% 0.27/0.63 ( ( ^ [Y6: set_Pr1834926343_pi_pi,Z: set_Pr1834926343_pi_pi] : ( Y6 = Z ) )
% 0.27/0.63 = ( ^ [A5: set_Pr1834926343_pi_pi,B5: set_Pr1834926343_pi_pi] :
% 0.27/0.63 ( ( ord_le630093991_pi_pi @ A5 @ B5 )
% 0.27/0.63 & ( ord_le630093991_pi_pi @ B5 @ A5 ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % order_class.order.eq_iff
% 0.27/0.63 thf(fact_281_ord__eq__le__trans,axiom,
% 0.27/0.63 ! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C2: set_Pr1834926343_pi_pi] :
% 0.27/0.63 ( ( A = B )
% 0.27/0.63 => ( ( ord_le630093991_pi_pi @ B @ C2 )
% 0.27/0.63 => ( ord_le630093991_pi_pi @ A @ C2 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % ord_eq_le_trans
% 0.27/0.63 thf(fact_282_ord__le__eq__trans,axiom,
% 0.27/0.63 ! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C2: set_Pr1834926343_pi_pi] :
% 0.27/0.63 ( ( ord_le630093991_pi_pi @ A @ B )
% 0.27/0.63 => ( ( B = C2 )
% 0.27/0.63 => ( ord_le630093991_pi_pi @ A @ C2 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % ord_le_eq_trans
% 0.27/0.63 thf(fact_283_order__class_Oorder_Oantisym,axiom,
% 0.27/0.63 ! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi] :
% 0.27/0.63 ( ( ord_le630093991_pi_pi @ A @ B )
% 0.27/0.63 => ( ( ord_le630093991_pi_pi @ B @ A )
% 0.27/0.63 => ( A = B ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % order_class.order.antisym
% 0.27/0.63 thf(fact_284_order__trans,axiom,
% 0.27/0.63 ! [X: set_Pr1834926343_pi_pi,Y4: set_Pr1834926343_pi_pi,Z2: set_Pr1834926343_pi_pi] :
% 0.27/0.63 ( ( ord_le630093991_pi_pi @ X @ Y4 )
% 0.27/0.63 => ( ( ord_le630093991_pi_pi @ Y4 @ Z2 )
% 0.27/0.63 => ( ord_le630093991_pi_pi @ X @ Z2 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % order_trans
% 0.27/0.63 thf(fact_285_dual__order_Orefl,axiom,
% 0.27/0.63 ! [A: set_Pr1834926343_pi_pi] : ( ord_le630093991_pi_pi @ A @ A ) ).
% 0.27/0.63
% 0.27/0.63 % dual_order.refl
% 0.27/0.63 thf(fact_286_alphaRes,axiom,
% 0.27/0.63 ! [C2: name,P2: pi,A: name] :
% 0.27/0.63 ( ( fresh_name_pi @ C2 @ P2 )
% 0.27/0.63 => ( ( res @ A @ P2 )
% 0.27/0.63 = ( res @ C2 @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ C2 ) @ nil_Pr743626285e_name ) @ P2 ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % alphaRes
% 0.27/0.63 thf(fact_287_calculation,axiom,
% 0.27/0.63 late_transitions @ ( res @ x @ ( sum @ p @ q ) ) @ ( late_BoundR @ ( late_BoundOutputS @ aa ) @ y @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ y @ x ) @ nil_Pr743626285e_name ) @ p2 ) ) ).
% 0.27/0.63
% 0.27/0.63 % calculation
% 0.27/0.63 thf(fact_288_Bound_Ohyps_I1_J,axiom,
% 0.27/0.63 late_transitions @ ( sum @ ( res @ x @ p ) @ ( res @ x @ q ) ) @ ( late_BoundR @ a @ y @ pq ) ).
% 0.27/0.63
% 0.27/0.63 % Bound.hyps(1)
% 0.27/0.63 thf(fact_289__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,
% 0.27/0.63 late_transitions @ ( res @ x @ ( sum @ p @ q ) ) @ ( late_BoundR @ ( late_BoundOutputS @ aa ) @ x @ p2 ) ).
% 0.27/0.63
% 0.27/0.63 % \<open><\<nu>x>(P \<oplus> Q) \<longmapsto> a<\<nu>x> \<prec> P'\<close>
% 0.27/0.63 thf(fact_290_sumResLeft,axiom,
% 0.27/0.63 ! [Rel: set_Pr1834926343_pi_pi,X: name,P2: pi,Q: pi] :
% 0.27/0.63 ( ( ord_le630093991_pi_pi @ id_pi @ Rel )
% 0.27/0.63 => ( ( eqvt_pi @ Rel )
% 0.27/0.63 => ( strong743114133lation @ ( sum @ ( res @ X @ P2 ) @ ( res @ X @ Q ) ) @ Rel @ ( res @ X @ ( sum @ P2 @ Q ) ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % sumResLeft
% 0.27/0.63 thf(fact_291_cSum1_Ohyps,axiom,
% 0.27/0.63 late_transitions @ ( res @ x @ p ) @ ( late_BoundR @ a @ y @ pq ) ).
% 0.27/0.63
% 0.27/0.63 % cSum1.hyps
% 0.27/0.63 thf(fact_292_residual_Operm_I1_J,axiom,
% 0.27/0.63 ! [Pi: list_P227219501e_name,X32: late_subject,X1: name,X2: pi] :
% 0.27/0.63 ( ( perm_n414416632sidual @ Pi @ ( late_BoundR @ X32 @ X1 @ X2 ) )
% 0.27/0.63 = ( late_BoundR @ ( perm_n1559866809ubject @ Pi @ X32 ) @ ( perm_name_name @ Pi @ X1 ) @ ( perm_name_pi @ Pi @ X2 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % residual.perm(1)
% 0.27/0.63 thf(fact_293_freshBoundDerivative_I1_J,axiom,
% 0.27/0.63 ! [P2: pi,A: late_subject,X: name,P4: pi,Y4: name] :
% 0.27/0.63 ( ( late_transitions @ P2 @ ( late_BoundR @ A @ X @ P4 ) )
% 0.27/0.63 => ( ( fresh_name_pi @ Y4 @ P2 )
% 0.27/0.63 => ( fresh_717452603ubject @ Y4 @ A ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % freshBoundDerivative(1)
% 0.27/0.63 thf(fact_294_Late__Semantics_OResB,axiom,
% 0.27/0.63 ! [P2: pi,A: late_subject,X: name,P4: pi,Y4: name] :
% 0.27/0.63 ( ( late_transitions @ P2 @ ( late_BoundR @ A @ X @ P4 ) )
% 0.27/0.63 => ( ( fresh_717452603ubject @ Y4 @ A )
% 0.27/0.63 => ( ( Y4 != X )
% 0.27/0.63 => ( late_transitions @ ( res @ Y4 @ P2 ) @ ( late_BoundR @ A @ X @ ( res @ Y4 @ P4 ) ) ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % Late_Semantics.ResB
% 0.27/0.63 thf(fact_295_freshBoundDerivative_I2_J,axiom,
% 0.27/0.63 ! [P2: pi,A: late_subject,X: name,P4: pi,Y4: name] :
% 0.27/0.63 ( ( late_transitions @ P2 @ ( late_BoundR @ A @ X @ P4 ) )
% 0.27/0.63 => ( ( fresh_name_pi @ Y4 @ P2 )
% 0.27/0.63 => ( ( Y4 != X )
% 0.27/0.63 => ( fresh_name_pi @ Y4 @ P4 ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % freshBoundDerivative(2)
% 0.27/0.63 thf(fact_296_simE_I1_J,axiom,
% 0.27/0.63 ! [P2: pi,Rel: set_Pr1834926343_pi_pi,Q: pi,A: late_subject,X: name,Q2: pi] :
% 0.27/0.63 ( ( strong743114133lation @ P2 @ Rel @ Q )
% 0.27/0.63 => ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q2 ) )
% 0.27/0.63 => ( ( fresh_name_pi @ X @ P2 )
% 0.27/0.63 => ? [P5: pi] :
% 0.27/0.63 ( ( late_transitions @ P2 @ ( late_BoundR @ A @ X @ P5 ) )
% 0.27/0.63 & ( strong2129052853vative @ P5 @ Q2 @ A @ X @ Rel ) ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % simE(1)
% 0.27/0.63 thf(fact_297_Sum2,axiom,
% 0.27/0.63 ! [Q: pi,Rs: late_residual,P2: pi] :
% 0.27/0.63 ( ( late_transitions @ Q @ Rs )
% 0.27/0.63 => ( late_transitions @ ( sum @ P2 @ Q ) @ Rs ) ) ).
% 0.27/0.63
% 0.27/0.63 % Sum2
% 0.27/0.63 thf(fact_298_Sum1,axiom,
% 0.27/0.63 ! [P2: pi,Rs: late_residual,Q: pi] :
% 0.27/0.63 ( ( late_transitions @ P2 @ Rs )
% 0.27/0.63 => ( late_transitions @ ( sum @ P2 @ Q ) @ Rs ) ) ).
% 0.27/0.63
% 0.27/0.63 % Sum1
% 0.27/0.63 thf(fact_299_sumCases_H,axiom,
% 0.27/0.63 ! [P2: pi,Q: pi,Rs: late_residual] :
% 0.27/0.63 ( ( late_transitions @ ( sum @ P2 @ Q ) @ Rs )
% 0.27/0.63 => ( ~ ( late_transitions @ P2 @ Rs )
% 0.27/0.63 => ( late_transitions @ Q @ Rs ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % sumCases'
% 0.27/0.63 thf(fact_300_sumCases,axiom,
% 0.27/0.63 ! [P2: pi,Q: pi,Rs: late_residual] :
% 0.27/0.63 ( ( late_transitions @ ( sum @ P2 @ Q ) @ Rs )
% 0.27/0.63 => ( ~ ( late_transitions @ P2 @ Rs )
% 0.27/0.63 => ( late_transitions @ Q @ Rs ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % sumCases
% 0.27/0.63 thf(fact_301_freshResidual,axiom,
% 0.27/0.63 ! [P2: pi,Rs: late_residual,X: name] :
% 0.27/0.63 ( ( late_transitions @ P2 @ Rs )
% 0.27/0.63 => ( ( fresh_name_pi @ X @ P2 )
% 0.27/0.63 => ( fresh_81631222sidual @ X @ Rs ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % freshResidual
% 0.27/0.63 thf(fact_302_eqvt,axiom,
% 0.27/0.63 ! [X1: pi,X2: late_residual,Pi: list_P227219501e_name] :
% 0.27/0.63 ( ( late_transitions @ X1 @ X2 )
% 0.27/0.63 => ( late_transitions @ ( perm_name_pi @ Pi @ X1 ) @ ( perm_n414416632sidual @ Pi @ X2 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % eqvt
% 0.27/0.63 thf(fact_303_transitions_OResB,axiom,
% 0.27/0.63 ! [P2: pi,A: late_subject,X: name,P4: pi,Y4: name] :
% 0.27/0.63 ( ( late_transitions @ P2 @ ( late_BoundR @ A @ X @ P4 ) )
% 0.27/0.63 => ( ( fresh_717452603ubject @ Y4 @ A )
% 0.27/0.63 => ( ( Y4 != X )
% 0.27/0.63 => ( ( fresh_name_pi @ X @ P2 )
% 0.27/0.63 => ( ( fresh_717452603ubject @ X @ A )
% 0.27/0.63 => ( late_transitions @ ( res @ Y4 @ P2 ) @ ( late_BoundR @ A @ X @ ( res @ Y4 @ P4 ) ) ) ) ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % transitions.ResB
% 0.27/0.63 thf(fact_304_monotonic,axiom,
% 0.27/0.63 ! [P2: pi,A4: set_Pr1834926343_pi_pi,P4: pi,B4: set_Pr1834926343_pi_pi] :
% 0.27/0.63 ( ( strong743114133lation @ P2 @ A4 @ P4 )
% 0.27/0.63 => ( ( ord_le630093991_pi_pi @ A4 @ B4 )
% 0.27/0.63 => ( strong743114133lation @ P2 @ B4 @ P4 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % monotonic
% 0.27/0.63 thf(fact_305_Strong__Late__Sim_Oreflexive,axiom,
% 0.27/0.63 ! [Rel: set_Pr1834926343_pi_pi,P2: pi] :
% 0.27/0.63 ( ( ord_le630093991_pi_pi @ id_pi @ Rel )
% 0.27/0.63 => ( strong743114133lation @ P2 @ Rel @ P2 ) ) ).
% 0.27/0.63
% 0.27/0.63 % Strong_Late_Sim.reflexive
% 0.27/0.63 thf(fact_306_sumIdempRight,axiom,
% 0.27/0.63 ! [Rel: set_Pr1834926343_pi_pi,P2: pi] :
% 0.27/0.63 ( ( ord_le630093991_pi_pi @ id_pi @ Rel )
% 0.27/0.63 => ( strong743114133lation @ ( sum @ P2 @ P2 ) @ Rel @ P2 ) ) ).
% 0.27/0.63
% 0.27/0.63 % sumIdempRight
% 0.27/0.63 thf(fact_307_sumAssocRight,axiom,
% 0.27/0.63 ! [Rel: set_Pr1834926343_pi_pi,P2: pi,Q: pi,R2: pi] :
% 0.27/0.63 ( ( ord_le630093991_pi_pi @ id_pi @ Rel )
% 0.27/0.63 => ( strong743114133lation @ ( sum @ P2 @ ( sum @ Q @ R2 ) ) @ Rel @ ( sum @ ( sum @ P2 @ Q ) @ R2 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % sumAssocRight
% 0.27/0.63 thf(fact_308_sumIdempLeft,axiom,
% 0.27/0.63 ! [Rel: set_Pr1834926343_pi_pi,P2: pi] :
% 0.27/0.63 ( ( ord_le630093991_pi_pi @ id_pi @ Rel )
% 0.27/0.63 => ( strong743114133lation @ P2 @ Rel @ ( sum @ P2 @ P2 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % sumIdempLeft
% 0.27/0.63 thf(fact_309_sumAssocLeft,axiom,
% 0.27/0.63 ! [Rel: set_Pr1834926343_pi_pi,P2: pi,Q: pi,R2: pi] :
% 0.27/0.63 ( ( ord_le630093991_pi_pi @ id_pi @ Rel )
% 0.27/0.63 => ( strong743114133lation @ ( sum @ ( sum @ P2 @ Q ) @ R2 ) @ Rel @ ( sum @ P2 @ ( sum @ Q @ R2 ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % sumAssocLeft
% 0.27/0.63 thf(fact_310_sumSym,axiom,
% 0.27/0.63 ! [Rel: set_Pr1834926343_pi_pi,P2: pi,Q: pi] :
% 0.27/0.63 ( ( ord_le630093991_pi_pi @ id_pi @ Rel )
% 0.27/0.63 => ( strong743114133lation @ ( sum @ P2 @ Q ) @ Rel @ ( sum @ Q @ P2 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % sumSym
% 0.27/0.63 thf(fact_311_eqvtI,axiom,
% 0.27/0.63 ! [P2: pi,Rel: set_Pr1834926343_pi_pi,Q: pi,Rel3: set_Pr1834926343_pi_pi,Perm: list_P227219501e_name] :
% 0.27/0.63 ( ( strong743114133lation @ P2 @ Rel @ Q )
% 0.27/0.63 => ( ( ord_le630093991_pi_pi @ Rel @ Rel3 )
% 0.27/0.63 => ( ( eqvt_pi @ Rel3 )
% 0.27/0.63 => ( strong743114133lation @ ( perm_name_pi @ Perm @ P2 ) @ Rel3 @ ( perm_name_pi @ Perm @ Q ) ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % eqvtI
% 0.27/0.63 thf(fact_312_alphaBoundResidual,axiom,
% 0.27/0.63 ! [X6: name,P2: pi,A: late_subject,X: name] :
% 0.27/0.63 ( ( fresh_name_pi @ X6 @ P2 )
% 0.27/0.63 => ( ( late_BoundR @ A @ X @ P2 )
% 0.27/0.63 = ( late_BoundR @ A @ X6 @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ X @ X6 ) @ nil_Pr743626285e_name ) @ P2 ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % alphaBoundResidual
% 0.27/0.63 thf(fact_313_cOpen_Ohyps_I1_J,axiom,
% 0.27/0.63 late_transitions @ p @ ( late_FreeR @ ( late_OutputR @ aa @ x ) @ p2 ) ).
% 0.27/0.63
% 0.27/0.63 % cOpen.hyps(1)
% 0.27/0.63 thf(fact_314__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,
% 0.27/0.63 late_transitions @ ( sum @ p @ q ) @ ( late_FreeR @ ( late_OutputR @ aa @ x ) @ p2 ) ).
% 0.27/0.63
% 0.27/0.63 % \<open>P \<oplus> Q \<longmapsto> a[x] \<prec> P'\<close>
% 0.27/0.63 thf(fact_315_Late__Semantics1_OfreeRes_Oinject,axiom,
% 0.27/0.63 ! [X11: name,X122: name,Y11: name,Y12: name] :
% 0.27/0.63 ( ( ( late_OutputR @ X11 @ X122 )
% 0.27/0.63 = ( late_OutputR @ Y11 @ Y12 ) )
% 0.27/0.63 = ( ( X11 = Y11 )
% 0.27/0.63 & ( X122 = Y12 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % Late_Semantics1.freeRes.inject
% 0.27/0.63 thf(fact_316_Late__Semantics_OfreeRes_Oinject,axiom,
% 0.27/0.63 ! [X2: name,X1: name,Y2: name,Y1: name] :
% 0.27/0.63 ( ( ( late_OutputR @ X2 @ X1 )
% 0.27/0.63 = ( late_OutputR @ Y2 @ Y1 ) )
% 0.27/0.63 = ( ( X2 = Y2 )
% 0.27/0.63 & ( X1 = Y1 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % Late_Semantics.freeRes.inject
% 0.27/0.63 thf(fact_317_freeRes_Operm_I1_J,axiom,
% 0.27/0.63 ! [Pi: list_P227219501e_name,X2: name,X1: name] :
% 0.27/0.63 ( ( perm_n336613537reeRes @ Pi @ ( late_OutputR @ X2 @ X1 ) )
% 0.27/0.63 = ( late_OutputR @ ( perm_name_name @ Pi @ X2 ) @ ( perm_name_name @ Pi @ X1 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % freeRes.perm(1)
% 0.27/0.63 thf(fact_318_freeRes_Ofresh_I1_J,axiom,
% 0.27/0.63 ! [A: name,X2: name,X1: name] :
% 0.27/0.63 ( ( fresh_1641682979reeRes @ A @ ( late_OutputR @ X2 @ X1 ) )
% 0.27/0.63 = ( ( fresh_name_name @ A @ X2 )
% 0.27/0.63 & ( fresh_name_name @ A @ X1 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % freeRes.fresh(1)
% 0.27/0.63 thf(fact_319_residual_Operm_I2_J,axiom,
% 0.27/0.63 ! [Pi: list_P227219501e_name,X2: late_freeRes,X1: pi] :
% 0.27/0.63 ( ( perm_n414416632sidual @ Pi @ ( late_FreeR @ X2 @ X1 ) )
% 0.27/0.63 = ( late_FreeR @ ( perm_n336613537reeRes @ Pi @ X2 ) @ ( perm_name_pi @ Pi @ X1 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % residual.perm(2)
% 0.27/0.63 thf(fact_320_residual_Ofresh_I2_J,axiom,
% 0.27/0.63 ! [A: name,X2: late_freeRes,X1: pi] :
% 0.27/0.63 ( ( fresh_81631222sidual @ A @ ( late_FreeR @ X2 @ X1 ) )
% 0.27/0.63 = ( ( fresh_1641682979reeRes @ A @ X2 )
% 0.27/0.63 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % residual.fresh(2)
% 0.27/0.63 thf(fact_321_residual_Odistinct_I1_J,axiom,
% 0.27/0.63 ! [Subject: late_subject,Name2: name,Pi: pi,FreeRes: late_freeRes,Pi3: pi] :
% 0.27/0.63 ( ( late_BoundR @ Subject @ Name2 @ Pi )
% 0.27/0.63 != ( late_FreeR @ FreeRes @ Pi3 ) ) ).
% 0.27/0.63
% 0.27/0.63 % residual.distinct(1)
% 0.27/0.63 thf(fact_322_residual_Oinducts,axiom,
% 0.27/0.63 ! [P2: late_residual > $o,Residual: late_residual] :
% 0.27/0.63 ( ! [Subject2: late_subject,Name3: name,Pi4: pi] : ( P2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) )
% 0.27/0.63 => ( ! [FreeRes2: late_freeRes,Pi4: pi] : ( P2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 0.27/0.63 => ( P2 @ Residual ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % residual.inducts
% 0.27/0.63 thf(fact_323_residual_Oinject_I2_J,axiom,
% 0.27/0.63 ! [X2: late_freeRes,X1: pi,Y2: late_freeRes,Y1: pi] :
% 0.27/0.63 ( ( ( late_FreeR @ X2 @ X1 )
% 0.27/0.63 = ( late_FreeR @ Y2 @ Y1 ) )
% 0.27/0.63 = ( ( X2 = Y2 )
% 0.27/0.63 & ( X1 = Y1 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % residual.inject(2)
% 0.27/0.63 thf(fact_324_ResF,axiom,
% 0.27/0.63 ! [P2: pi,Alpha: late_freeRes,P4: pi,Y4: name] :
% 0.27/0.63 ( ( late_transitions @ P2 @ ( late_FreeR @ Alpha @ P4 ) )
% 0.27/0.63 => ( ( fresh_1641682979reeRes @ Y4 @ Alpha )
% 0.27/0.63 => ( late_transitions @ ( res @ Y4 @ P2 ) @ ( late_FreeR @ Alpha @ ( res @ Y4 @ P4 ) ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % ResF
% 0.27/0.63 thf(fact_325_resCasesF_H,axiom,
% 0.27/0.63 ! [X: name,P2: pi,Alpha: late_freeRes,P4: pi] :
% 0.27/0.63 ( ( late_transitions @ ( res @ X @ P2 ) @ ( late_FreeR @ Alpha @ P4 ) )
% 0.27/0.63 => ~ ! [P: pi,Alpha2: late_freeRes,P5: pi,Y3: name] :
% 0.27/0.63 ( ( ( res @ X @ P2 )
% 0.27/0.63 = ( res @ Y3 @ P ) )
% 0.27/0.63 => ( ( ( late_FreeR @ Alpha @ P4 )
% 0.27/0.63 = ( late_FreeR @ Alpha2 @ ( res @ Y3 @ P5 ) ) )
% 0.27/0.63 => ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P5 ) )
% 0.27/0.63 => ~ ( fresh_1641682979reeRes @ Y3 @ Alpha2 ) ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % resCasesF'
% 0.27/0.63 thf(fact_326_resCasesF,axiom,
% 0.27/0.63 ! [X: name,P2: pi,Alpha: late_freeRes,XP: pi,F3: pi > $o] :
% 0.27/0.63 ( ( late_transitions @ ( res @ X @ P2 ) @ ( late_FreeR @ Alpha @ XP ) )
% 0.27/0.63 => ( ! [P5: pi] :
% 0.27/0.63 ( ( late_transitions @ P2 @ ( late_FreeR @ Alpha @ P5 ) )
% 0.27/0.63 => ( ( fresh_1641682979reeRes @ X @ Alpha )
% 0.27/0.63 => ( F3 @ ( res @ X @ P5 ) ) ) )
% 0.27/0.63 => ( F3 @ XP ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % resCasesF
% 0.27/0.63 thf(fact_327_freshFreeDerivative_I2_J,axiom,
% 0.27/0.63 ! [P2: pi,Alpha: late_freeRes,P4: pi,Y4: name] :
% 0.27/0.63 ( ( late_transitions @ P2 @ ( late_FreeR @ Alpha @ P4 ) )
% 0.27/0.63 => ( ( fresh_name_pi @ Y4 @ P2 )
% 0.27/0.63 => ( fresh_name_pi @ Y4 @ P4 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % freshFreeDerivative(2)
% 0.27/0.63 thf(fact_328_freshFreeDerivative_I1_J,axiom,
% 0.27/0.63 ! [P2: pi,Alpha: late_freeRes,P4: pi,Y4: name] :
% 0.27/0.63 ( ( late_transitions @ P2 @ ( late_FreeR @ Alpha @ P4 ) )
% 0.27/0.63 => ( ( fresh_name_pi @ Y4 @ P2 )
% 0.27/0.63 => ( fresh_1641682979reeRes @ Y4 @ Alpha ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % freshFreeDerivative(1)
% 0.27/0.63 thf(fact_329_Open,axiom,
% 0.27/0.63 ! [P2: pi,A: name,B: name,P4: pi] :
% 0.27/0.63 ( ( late_transitions @ P2 @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P4 ) )
% 0.27/0.63 => ( ( A != B )
% 0.27/0.63 => ( late_transitions @ ( res @ B @ P2 ) @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ B @ P4 ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % Open
% 0.27/0.63 thf(fact_330_simE_I2_J,axiom,
% 0.27/0.63 ! [P2: pi,Rel: set_Pr1834926343_pi_pi,Q: pi,Alpha: late_freeRes,Q2: pi] :
% 0.27/0.63 ( ( strong743114133lation @ P2 @ Rel @ Q )
% 0.27/0.63 => ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 0.27/0.63 => ? [P5: pi] :
% 0.27/0.63 ( ( late_transitions @ P2 @ ( late_FreeR @ Alpha @ P5 ) )
% 0.27/0.63 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P5 @ Q2 ) @ Rel ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % simE(2)
% 0.27/0.63 thf(fact_331_resCasesB_H,axiom,
% 0.27/0.63 ! [X6: name,P2: pi,A: late_subject,Y7: name,P4: pi] :
% 0.27/0.63 ( ( late_transitions @ ( res @ X6 @ P2 ) @ ( late_BoundR @ A @ Y7 @ P4 ) )
% 0.27/0.63 => ( ! [P: pi,A3: name,B3: name] :
% 0.27/0.63 ( ( ( res @ X6 @ P2 )
% 0.27/0.63 = ( res @ B3 @ P ) )
% 0.27/0.63 => ! [P5: pi] :
% 0.27/0.63 ( ( ( late_BoundR @ A @ Y7 @ P4 )
% 0.27/0.63 = ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ B3 @ P5 ) )
% 0.27/0.63 => ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A3 @ B3 ) @ P5 ) )
% 0.27/0.63 => ( A3 = B3 ) ) ) )
% 0.27/0.63 => ~ ! [P: pi,A3: late_subject,X4: name,P5: pi,Y3: name] :
% 0.27/0.63 ( ( ( res @ X6 @ P2 )
% 0.27/0.63 = ( res @ Y3 @ P ) )
% 0.27/0.63 => ( ( ( late_BoundR @ A @ Y7 @ P4 )
% 0.27/0.63 = ( late_BoundR @ A3 @ X4 @ ( res @ Y3 @ P5 ) ) )
% 0.27/0.63 => ( ( late_transitions @ P @ ( late_BoundR @ A3 @ X4 @ P5 ) )
% 0.27/0.63 => ( ( fresh_717452603ubject @ Y3 @ A3 )
% 0.27/0.63 => ( ( Y3 != X4 )
% 0.27/0.63 => ( ( fresh_name_pi @ X4 @ P )
% 0.27/0.63 => ~ ( fresh_717452603ubject @ X4 @ A3 ) ) ) ) ) ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % resCasesB'
% 0.27/0.63 thf(fact_332_resCases_H,axiom,
% 0.27/0.63 ! [X: name,P2: pi,Rs: late_residual] :
% 0.27/0.63 ( ( late_transitions @ ( res @ X @ P2 ) @ Rs )
% 0.27/0.63 => ( ! [P: pi,A3: name,B3: name] :
% 0.27/0.63 ( ( ( res @ X @ P2 )
% 0.27/0.63 = ( res @ B3 @ P ) )
% 0.27/0.63 => ! [P5: pi] :
% 0.27/0.63 ( ( Rs
% 0.27/0.63 = ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ B3 @ P5 ) )
% 0.27/0.63 => ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A3 @ B3 ) @ P5 ) )
% 0.27/0.63 => ( A3 = B3 ) ) ) )
% 0.27/0.63 => ( ! [P: pi,A3: late_subject,X4: name,P5: pi,Y3: name] :
% 0.27/0.63 ( ( ( res @ X @ P2 )
% 0.27/0.63 = ( res @ Y3 @ P ) )
% 0.27/0.63 => ( ( Rs
% 0.27/0.63 = ( late_BoundR @ A3 @ X4 @ ( res @ Y3 @ P5 ) ) )
% 0.27/0.63 => ( ( late_transitions @ P @ ( late_BoundR @ A3 @ X4 @ P5 ) )
% 0.27/0.63 => ( ( fresh_717452603ubject @ Y3 @ A3 )
% 0.27/0.63 => ( ( Y3 != X4 )
% 0.27/0.63 => ( ( fresh_name_pi @ X4 @ P )
% 0.27/0.63 => ~ ( fresh_717452603ubject @ X4 @ A3 ) ) ) ) ) ) )
% 0.27/0.63 => ~ ! [P: pi,Alpha2: late_freeRes,P5: pi,Y3: name] :
% 0.27/0.63 ( ( ( res @ X @ P2 )
% 0.27/0.63 = ( res @ Y3 @ P ) )
% 0.27/0.63 => ( ( Rs
% 0.27/0.63 = ( late_FreeR @ Alpha2 @ ( res @ Y3 @ P5 ) ) )
% 0.27/0.63 => ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P5 ) )
% 0.27/0.63 => ~ ( fresh_1641682979reeRes @ Y3 @ Alpha2 ) ) ) ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % resCases'
% 0.27/0.63 thf(fact_333_resCasesB,axiom,
% 0.27/0.63 ! [Y4: name,P2: pi,A: late_subject,X: name,YP: pi,F3: late_subject > pi > $o] :
% 0.27/0.63 ( ( late_transitions @ ( res @ Y4 @ P2 ) @ ( late_BoundR @ A @ X @ YP ) )
% 0.27/0.63 => ( ( X != Y4 )
% 0.27/0.63 => ( ( fresh_name_pi @ X @ P2 )
% 0.27/0.63 => ( ! [B3: name,P5: pi] :
% 0.27/0.63 ( ( late_transitions @ P2 @ ( late_FreeR @ ( late_OutputR @ B3 @ Y4 ) @ P5 ) )
% 0.27/0.63 => ( ( B3 != Y4 )
% 0.27/0.63 => ( ( A
% 0.27/0.63 = ( late_BoundOutputS @ B3 ) )
% 0.27/0.63 => ( F3 @ ( late_BoundOutputS @ B3 ) @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ X @ Y4 ) @ nil_Pr743626285e_name ) @ P5 ) ) ) ) )
% 0.27/0.63 => ( ! [P5: pi] :
% 0.27/0.63 ( ( late_transitions @ P2 @ ( late_BoundR @ A @ X @ P5 ) )
% 0.27/0.63 => ( ( fresh_717452603ubject @ Y4 @ A )
% 0.27/0.63 => ( F3 @ A @ ( res @ Y4 @ P5 ) ) ) )
% 0.27/0.63 => ( F3 @ A @ YP ) ) ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % resCasesB
% 0.27/0.63 thf(fact_334_simulation__def,axiom,
% 0.27/0.63 ( strong743114133lation
% 0.27/0.63 = ( ^ [P6: pi,Rel2: set_Pr1834926343_pi_pi,Q3: pi] :
% 0.27/0.63 ( ! [A5: late_subject,X5: name,Q4: pi] :
% 0.27/0.63 ( ( ( late_transitions @ Q3 @ ( late_BoundR @ A5 @ X5 @ Q4 ) )
% 0.27/0.63 & ( fresh_name_pi @ X5 @ P6 ) )
% 0.27/0.63 => ? [P7: pi] :
% 0.27/0.63 ( ( late_transitions @ P6 @ ( late_BoundR @ A5 @ X5 @ P7 ) )
% 0.27/0.63 & ( strong2129052853vative @ P7 @ Q4 @ A5 @ X5 @ Rel2 ) ) )
% 0.27/0.63 & ! [Alpha3: late_freeRes,Q4: pi] :
% 0.27/0.63 ( ( late_transitions @ Q3 @ ( late_FreeR @ Alpha3 @ Q4 ) )
% 0.27/0.63 => ? [P7: pi] :
% 0.27/0.63 ( ( late_transitions @ P6 @ ( late_FreeR @ Alpha3 @ P7 ) )
% 0.27/0.63 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P7 @ Q4 ) @ Rel2 ) ) ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % simulation_def
% 0.27/0.63 thf(fact_335_simCases,axiom,
% 0.27/0.63 ! [Q: pi,P2: pi,Rel: set_Pr1834926343_pi_pi] :
% 0.27/0.63 ( ! [A3: late_subject,Y3: name,Q5: pi] :
% 0.27/0.63 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ Y3 @ Q5 ) )
% 0.27/0.63 => ( ( fresh_name_pi @ Y3 @ P2 )
% 0.27/0.63 => ? [P8: pi] :
% 0.27/0.63 ( ( late_transitions @ P2 @ ( late_BoundR @ A3 @ Y3 @ P8 ) )
% 0.27/0.63 & ( strong2129052853vative @ P8 @ Q5 @ A3 @ Y3 @ Rel ) ) ) )
% 0.27/0.63 => ( ! [Alpha2: late_freeRes,Q5: pi] :
% 0.27/0.63 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q5 ) )
% 0.27/0.63 => ? [P8: pi] :
% 0.27/0.63 ( ( late_transitions @ P2 @ ( late_FreeR @ Alpha2 @ P8 ) )
% 0.27/0.63 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P8 @ Q5 ) @ Rel ) ) )
% 0.27/0.63 => ( strong743114133lation @ P2 @ Rel @ Q ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % simCases
% 0.27/0.63 thf(fact_336_residual__Rep_Oinject_I2_J,axiom,
% 0.27/0.63 ! [X21: late_freeRes,X22: pi,Y21: late_freeRes,Y22: pi] :
% 0.27/0.63 ( ( ( late_r347633188eR_Rep @ X21 @ X22 )
% 0.27/0.63 = ( late_r347633188eR_Rep @ Y21 @ Y22 ) )
% 0.27/0.63 = ( ( X21 = Y21 )
% 0.27/0.63 & ( X22 = Y22 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % residual_Rep.inject(2)
% 0.27/0.63 thf(fact_337_alphaInput,axiom,
% 0.27/0.63 ! [C2: name,P2: pi,A: name,X: name] :
% 0.27/0.63 ( ( fresh_name_pi @ C2 @ P2 )
% 0.27/0.63 => ( ( input @ A @ X @ P2 )
% 0.27/0.63 = ( input @ A @ C2 @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ X @ C2 ) @ nil_Pr743626285e_name ) @ P2 ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % alphaInput
% 0.27/0.63 thf(fact_338_pi_Operm_I4_J,axiom,
% 0.27/0.63 ! [Pi: list_P227219501e_name,X32: name,X1: name,X2: pi] :
% 0.27/0.63 ( ( perm_name_pi @ Pi @ ( input @ X32 @ X1 @ X2 ) )
% 0.27/0.63 = ( input @ ( perm_name_name @ Pi @ X32 ) @ ( perm_name_name @ Pi @ X1 ) @ ( perm_name_pi @ Pi @ X2 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % pi.perm(4)
% 0.27/0.63 thf(fact_339_resTrans_I2_J,axiom,
% 0.27/0.63 ! [X: name,Y4: name,P2: pi,Rs: late_residual] :
% 0.27/0.63 ~ ( late_transitions @ ( res @ X @ ( input @ X @ Y4 @ P2 ) ) @ Rs ) ).
% 0.27/0.63
% 0.27/0.63 % resTrans(2)
% 0.27/0.63 thf(fact_340_pi_Odistinct_I53_J,axiom,
% 0.27/0.63 ! [Name1: name,Name22: name,Pi: pi,Pi12: pi,Pi22: pi] :
% 0.27/0.63 ( ( input @ Name1 @ Name22 @ Pi )
% 0.27/0.63 != ( sum @ Pi12 @ Pi22 ) ) ).
% 0.27/0.63
% 0.27/0.63 % pi.distinct(53)
% 0.27/0.63 thf(fact_341_pi_Odistinct_I57_J,axiom,
% 0.27/0.63 ! [Name1: name,Name22: name,Pi: pi,Name: name,Pi3: pi] :
% 0.27/0.63 ( ( input @ Name1 @ Name22 @ Pi )
% 0.27/0.63 != ( res @ Name @ Pi3 ) ) ).
% 0.27/0.63
% 0.27/0.63 % pi.distinct(57)
% 0.27/0.63 thf(fact_342_inputFreeTrans,axiom,
% 0.27/0.63 ! [A: name,X: name,P2: pi,Alpha: late_freeRes,P4: pi] :
% 0.27/0.63 ~ ( late_transitions @ ( input @ A @ X @ P2 ) @ ( late_FreeR @ Alpha @ P4 ) ) ).
% 0.27/0.63
% 0.27/0.63 % inputFreeTrans
% 0.27/0.63 thf(fact_343_resInputFreeTrans,axiom,
% 0.27/0.63 ! [X: name,A: name,Y4: name,P2: pi,Alpha: late_freeRes,P4: pi] :
% 0.27/0.63 ~ ( late_transitions @ ( res @ X @ ( input @ A @ Y4 @ P2 ) ) @ ( late_FreeR @ Alpha @ P4 ) ) ).
% 0.27/0.63
% 0.27/0.63 % resInputFreeTrans
% 0.27/0.63 thf(fact_344_inputBoundOutputTrans,axiom,
% 0.27/0.63 ! [A: name,X: name,P2: pi,B: name,Y4: name,P4: pi] :
% 0.27/0.63 ~ ( late_transitions @ ( input @ A @ X @ P2 ) @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ Y4 @ P4 ) ) ).
% 0.27/0.63
% 0.27/0.63 % inputBoundOutputTrans
% 0.27/0.63 thf(fact_345_inputIneqTrans,axiom,
% 0.27/0.63 ! [A: name,X: name,P2: pi,B: late_subject,Y4: name,P4: pi] :
% 0.27/0.63 ( ( late_transitions @ ( input @ A @ X @ P2 ) @ ( late_BoundR @ B @ Y4 @ P4 ) )
% 0.27/0.63 => ~ ( fresh_717452603ubject @ A @ B ) ) ).
% 0.27/0.63
% 0.27/0.63 % inputIneqTrans
% 0.27/0.63 thf(fact_346_resInputBoundOutputTrans,axiom,
% 0.27/0.63 ! [X: name,A: name,Y4: name,P2: pi,B: name,Z2: name,P4: pi] :
% 0.27/0.63 ~ ( late_transitions @ ( res @ X @ ( input @ A @ Y4 @ P2 ) ) @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ Z2 @ P4 ) ) ).
% 0.27/0.63
% 0.27/0.63 % resInputBoundOutputTrans
% 0.27/0.63 thf(fact_347_inputCases,axiom,
% 0.27/0.63 ! [A: name,X: name,P2: pi,B: late_subject,Y4: name,YP: pi,Prop: late_subject > name > pi > $o] :
% 0.27/0.63 ( ( late_transitions @ ( input @ A @ X @ P2 ) @ ( late_BoundR @ B @ Y4 @ YP ) )
% 0.27/0.63 => ( ( Y4 != A )
% 0.27/0.63 => ( ( Y4 != X )
% 0.27/0.63 => ( ( fresh_name_pi @ Y4 @ P2 )
% 0.27/0.63 => ( ( ( B
% 0.27/0.63 = ( late_InputS @ A ) )
% 0.27/0.63 => ( ( YP
% 0.27/0.63 = ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ X @ Y4 ) @ nil_Pr743626285e_name ) @ P2 ) )
% 0.27/0.63 => ( Prop @ ( late_InputS @ A ) @ Y4 @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ X @ Y4 ) @ nil_Pr743626285e_name ) @ P2 ) ) ) )
% 0.27/0.63 => ( Prop @ B @ Y4 @ YP ) ) ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % inputCases
% 0.27/0.63 thf(fact_348_name__calc_I1_J,axiom,
% 0.27/0.63 ! [A: name,B: name,Pi: list_P227219501e_name,X: name] :
% 0.27/0.63 ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ Pi ) @ X )
% 0.27/0.63 = ( swap_name @ ( produc1570949143e_name @ A @ B ) @ ( perm_name_name @ Pi @ X ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % name_calc(1)
% 0.27/0.63 thf(fact_349_Late__Semantics1_Osubject_Oinject_I1_J,axiom,
% 0.27/0.63 ! [X1: name,Y1: name] :
% 0.27/0.63 ( ( ( late_InputS @ X1 )
% 0.27/0.63 = ( late_InputS @ Y1 ) )
% 0.27/0.63 = ( X1 = Y1 ) ) ).
% 0.27/0.63
% 0.27/0.63 % Late_Semantics1.subject.inject(1)
% 0.27/0.63 thf(fact_350_subject_Ofresh_I1_J,axiom,
% 0.27/0.63 ! [A: name,X1: name] :
% 0.27/0.63 ( ( fresh_717452603ubject @ A @ ( late_InputS @ X1 ) )
% 0.27/0.63 = ( fresh_name_name @ A @ X1 ) ) ).
% 0.27/0.63
% 0.27/0.63 % subject.fresh(1)
% 0.27/0.63 thf(fact_351_subject_Operm_I1_J,axiom,
% 0.27/0.63 ! [Pi: list_P227219501e_name,X1: name] :
% 0.27/0.63 ( ( perm_n1559866809ubject @ Pi @ ( late_InputS @ X1 ) )
% 0.27/0.63 = ( late_InputS @ ( perm_name_name @ Pi @ X1 ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % subject.perm(1)
% 0.27/0.63 thf(fact_352_Late__Semantics_Osubject_Odistinct_I1_J,axiom,
% 0.27/0.63 ! [Name2: name,Name: name] :
% 0.27/0.63 ( ( late_InputS @ Name2 )
% 0.27/0.63 != ( late_BoundOutputS @ Name ) ) ).
% 0.27/0.63
% 0.27/0.63 % Late_Semantics.subject.distinct(1)
% 0.27/0.63
% 0.27/0.63 % Helper facts (11)
% 0.27/0.63 thf(help_If_2_1_If_001t__Agent__Opi_T,axiom,
% 0.27/0.63 ! [X: pi,Y4: pi] :
% 0.27/0.63 ( ( if_pi @ $false @ X @ Y4 )
% 0.27/0.63 = Y4 ) ).
% 0.27/0.63
% 0.27/0.63 thf(help_If_1_1_If_001t__Agent__Opi_T,axiom,
% 0.27/0.63 ! [X: pi,Y4: pi] :
% 0.27/0.63 ( ( if_pi @ $true @ X @ Y4 )
% 0.27/0.63 = X ) ).
% 0.27/0.63
% 0.27/0.63 thf(help_If_2_1_If_001t__Agent__Oname_T,axiom,
% 0.27/0.63 ! [X: name,Y4: name] :
% 0.27/0.63 ( ( if_name @ $false @ X @ Y4 )
% 0.27/0.63 = Y4 ) ).
% 0.27/0.63
% 0.27/0.63 thf(help_If_1_1_If_001t__Agent__Oname_T,axiom,
% 0.27/0.63 ! [X: name,Y4: name] :
% 0.27/0.63 ( ( if_name @ $true @ X @ Y4 )
% 0.27/0.63 = X ) ).
% 0.27/0.63
% 0.27/0.63 thf(help_If_2_1_If_001t__Agent__Opi____Rep_T,axiom,
% 0.27/0.63 ! [X: pi_Rep,Y4: pi_Rep] :
% 0.27/0.63 ( ( if_pi_Rep @ $false @ X @ Y4 )
% 0.27/0.63 = Y4 ) ).
% 0.27/0.63
% 0.27/0.63 thf(help_If_1_1_If_001t__Agent__Opi____Rep_T,axiom,
% 0.27/0.63 ! [X: pi_Rep,Y4: pi_Rep] :
% 0.27/0.63 ( ( if_pi_Rep @ $true @ X @ Y4 )
% 0.27/0.63 = X ) ).
% 0.27/0.63
% 0.27/0.63 thf(help_If_2_1_If_001t__Late____Semantics__OfreeRes_T,axiom,
% 0.27/0.63 ! [X: late_freeRes,Y4: late_freeRes] :
% 0.27/0.63 ( ( if_Late_freeRes @ $false @ X @ Y4 )
% 0.27/0.72 = Y4 ) ).
% 0.27/0.72
% 0.27/0.72 thf(help_If_1_1_If_001t__Late____Semantics__OfreeRes_T,axiom,
% 0.27/0.72 ! [X: late_freeRes,Y4: late_freeRes] :
% 0.27/0.72 ( ( if_Late_freeRes @ $true @ X @ Y4 )
% 0.27/0.72 = X ) ).
% 0.27/0.72
% 0.27/0.72 thf(help_If_3_1_If_001t__Late____Semantics__Osubject_T,axiom,
% 0.27/0.72 ! [P2: $o] :
% 0.27/0.72 ( ( P2 = $true )
% 0.27/0.72 | ( P2 = $false ) ) ).
% 0.27/0.72
% 0.27/0.72 thf(help_If_2_1_If_001t__Late____Semantics__Osubject_T,axiom,
% 0.27/0.72 ! [X: late_subject,Y4: late_subject] :
% 0.27/0.72 ( ( if_Late_subject @ $false @ X @ Y4 )
% 0.27/0.72 = Y4 ) ).
% 0.27/0.72
% 0.27/0.72 thf(help_If_1_1_If_001t__Late____Semantics__Osubject_T,axiom,
% 0.27/0.72 ! [X: late_subject,Y4: late_subject] :
% 0.27/0.72 ( ( if_Late_subject @ $true @ X @ Y4 )
% 0.27/0.72 = X ) ).
% 0.27/0.72
% 0.27/0.72 % Conjectures (1)
% 0.27/0.72 thf(conj_0,conjecture,
% 0.27/0.72 strong2129052853vative @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ y @ x ) @ nil_Pr743626285e_name ) @ p2 ) @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ y @ x ) @ nil_Pr743626285e_name ) @ p2 ) @ ( late_BoundOutputS @ aa ) @ y @ rel ).
% 0.27/0.72
% 0.27/0.72 %------------------------------------------------------------------------------
% 0.27/0.72 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.JqjIyQ9UTf/cvc5---1.0.5_23592.p...
% 0.27/0.72 (declare-sort $$unsorted 0)
% 0.27/0.72 (declare-sort tptp.produc1872410278e_name 0)
% 0.27/0.72 (declare-sort tptp.produc890461031e_name 0)
% 0.27/0.72 (declare-sort tptp.list_P431515740_pi_pi 0)
% 0.27/0.72 (declare-sort tptp.set_Pr1654044726_pi_pi 0)
% 0.27/0.72 (declare-sort tptp.set_Pr806375235ubject 0)
% 0.27/0.72 (declare-sort tptp.set_Pr1780909331reeRes 0)
% 0.27/0.72 (declare-sort tptp.produc1141751126_pi_pi 0)
% 0.27/0.72 (declare-sort tptp.list_l1406151091e_name 0)
% 0.27/0.72 (declare-sort tptp.produc1359399907ubject 0)
% 0.27/0.72 (declare-sort tptp.produc355105483reeRes 0)
% 0.27/0.72 (declare-sort tptp.produc214645451ubject 0)
% 0.27/0.72 (declare-sort tptp.produc1357834675reeRes 0)
% 0.27/0.72 (declare-sort tptp.set_Pr1131282415pi_Rep 0)
% 0.27/0.72 (declare-sort tptp.produc257012921pi_Rep 0)
% 0.27/0.72 (declare-sort tptp.produc1777919905pi_Rep 0)
% 0.27/0.72 (declare-sort tptp.list_P227219501e_name 0)
% 0.27/0.72 (declare-sort tptp.set_Pr443758855e_name 0)
% 0.27/0.72 (declare-sort tptp.produc1998742700t_name 0)
% 0.27/0.72 (declare-sort tptp.produc2052722628s_name 0)
% 0.27/0.72 (declare-sort tptp.produc865358760ubject 0)
% 0.27/0.72 (declare-sort tptp.produc2008547984reeRes 0)
% 0.27/0.72 (declare-sort tptp.produc140253050ect_pi 0)
% 0.27/0.72 (declare-sort tptp.produc992857746Res_pi 0)
% 0.27/0.72 (declare-sort tptp.set_Pr1834926343_pi_pi 0)
% 0.27/0.72 (declare-sort tptp.produc1212344719pi_Rep 0)
% 0.27/0.72 (declare-sort tptp.produc367475239e_name 0)
% 0.27/0.72 (declare-sort tptp.product_prod_pi_pi 0)
% 0.27/0.72 (declare-sort tptp.list_Late_subject 0)
% 0.27/0.72 (declare-sort tptp.list_Late_freeRes 0)
% 0.27/0.72 (declare-sort tptp.set_Late_subject 0)
% 0.27/0.72 (declare-sort tptp.set_Late_freeRes 0)
% 0.27/0.72 (declare-sort tptp.list_pi_Rep 0)
% 0.27/0.72 (declare-sort tptp.late_residual_Rep 0)
% 0.27/0.72 (declare-sort tptp.late_subject_Rep 0)
% 0.27/0.72 (declare-sort tptp.late_freeRes_Rep 0)
% 0.27/0.72 (declare-sort tptp.set_pi_Rep 0)
% 0.27/0.72 (declare-sort tptp.list_name 0)
% 0.27/0.72 (declare-sort tptp.set_name 0)
% 0.27/0.72 (declare-sort tptp.list_pi 0)
% 0.27/0.72 (declare-sort tptp.late_residual 0)
% 0.27/0.72 (declare-sort tptp.late_subject 0)
% 0.27/0.72 (declare-sort tptp.late_freeRes 0)
% 0.27/0.72 (declare-sort tptp.set_pi 0)
% 0.27/0.72 (declare-sort tptp.pi_Rep 0)
% 0.27/0.72 (declare-sort tptp.name 0)
% 0.27/0.72 (declare-sort tptp.pi 0)
% 0.27/0.72 (declare-fun tptp.input (tptp.name tptp.name tptp.pi) tptp.pi)
% 0.27/0.72 (declare-fun tptp.res (tptp.name tptp.pi) tptp.pi)
% 0.27/0.72 (declare-fun tptp.sum (tptp.pi tptp.pi) tptp.pi)
% 0.27/0.72 (declare-fun tptp.if_name (Bool tptp.name tptp.name) tptp.name)
% 0.27/0.72 (declare-fun tptp.if_pi (Bool tptp.pi tptp.pi) tptp.pi)
% 0.27/0.72 (declare-fun tptp.if_pi_Rep (Bool tptp.pi_Rep tptp.pi_Rep) tptp.pi_Rep)
% 0.27/0.72 (declare-fun tptp.if_Late_freeRes (Bool tptp.late_freeRes tptp.late_freeRes) tptp.late_freeRes)
% 0.27/0.72 (declare-fun tptp.if_Late_subject (Bool tptp.late_subject tptp.late_subject) tptp.late_subject)
% 0.27/0.72 (declare-fun tptp.late_OutputR (tptp.name tptp.name) tptp.late_freeRes)
% 0.27/0.72 (declare-fun tptp.late_BoundR (tptp.late_subject tptp.name tptp.pi) tptp.late_residual)
% 0.27/0.72 (declare-fun tptp.late_FreeR (tptp.late_freeRes tptp.pi) tptp.late_residual)
% 0.27/0.72 (declare-fun tptp.late_r347633188eR_Rep (tptp.late_freeRes tptp.pi) tptp.late_residual_Rep)
% 0.27/0.72 (declare-fun tptp.late_BoundOutputS (tptp.name) tptp.late_subject)
% 0.27/0.72 (declare-fun tptp.late_InputS (tptp.name) tptp.late_subject)
% 0.27/0.72 (declare-fun tptp.late_transitions (tptp.pi tptp.late_residual) Bool)
% 0.27/0.72 (declare-fun tptp.cons_name (tptp.name tptp.list_name) tptp.list_name)
% 0.27/0.72 (declare-fun tptp.cons_pi (tptp.pi tptp.list_pi) tptp.list_pi)
% 0.27/0.72 (declare-fun tptp.cons_pi_Rep (tptp.pi_Rep tptp.list_pi_Rep) tptp.list_pi_Rep)
% 0.27/0.72 (declare-fun tptp.cons_Late_freeRes (tptp.late_freeRes tptp.list_Late_freeRes) tptp.list_Late_freeRes)
% 0.27/0.72 (declare-fun tptp.cons_Late_subject (tptp.late_subject tptp.list_Late_subject) tptp.list_Late_subject)
% 0.27/0.72 (declare-fun tptp.cons_l798145763e_name (tptp.list_P227219501e_name tptp.list_l1406151091e_name) tptp.list_l1406151091e_name)
% 0.27/0.72 (declare-fun tptp.cons_P1213805021e_name (tptp.produc367475239e_name tptp.list_P227219501e_name) tptp.list_P227219501e_name)
% 0.27/0.72 (declare-fun tptp.cons_P749510156_pi_pi (tptp.produc1141751126_pi_pi tptp.list_P431515740_pi_pi) tptp.list_P431515740_pi_pi)
% 0.27/0.72 (declare-fun tptp.nil_li29751603e_name () tptp.list_l1406151091e_name)
% 0.27/0.72 (declare-fun tptp.nil_Pr743626285e_name () tptp.list_P227219501e_name)
% 0.27/0.72 (declare-fun tptp.fresh_name_name (tptp.name tptp.name) Bool)
% 0.27/0.72 (declare-fun tptp.fresh_name_pi (tptp.name tptp.pi) Bool)
% 0.27/0.72 (declare-fun tptp.fresh_name_pi_Rep (tptp.name tptp.pi_Rep) Bool)
% 0.27/0.72 (declare-fun tptp.fresh_1641682979reeRes (tptp.name tptp.late_freeRes) Bool)
% 0.27/0.72 (declare-fun tptp.fresh_81631222sidual (tptp.name tptp.late_residual) Bool)
% 0.27/0.72 (declare-fun tptp.fresh_717452603ubject (tptp.name tptp.late_subject) Bool)
% 0.27/0.72 (declare-fun tptp.fresh_name_list_name (tptp.name tptp.list_name) Bool)
% 0.27/0.72 (declare-fun tptp.fresh_name_list_pi (tptp.name tptp.list_pi) Bool)
% 0.27/0.72 (declare-fun tptp.fresh_1981651763reeRes (tptp.name tptp.list_Late_freeRes) Bool)
% 0.27/0.72 (declare-fun tptp.fresh_838462539ubject (tptp.name tptp.list_Late_subject) Bool)
% 0.27/0.72 (declare-fun tptp.fresh_922791155e_name (tptp.name tptp.list_P227219501e_name) Bool)
% 0.27/0.72 (declare-fun tptp.fresh_1958133282_pi_pi (tptp.name tptp.list_P431515740_pi_pi) Bool)
% 0.27/0.72 (declare-fun tptp.fresh_441084397e_name (tptp.name tptp.produc367475239e_name) Bool)
% 0.27/0.72 (declare-fun tptp.fresh_1963366730reeRes (tptp.name tptp.produc2008547984reeRes) Bool)
% 0.27/0.72 (declare-fun tptp.fresh_820177506ubject (tptp.name tptp.produc865358760ubject) Bool)
% 0.27/0.72 (declare-fun tptp.fresh_1376661020_pi_pi (tptp.name tptp.produc1141751126_pi_pi) Bool)
% 0.27/0.72 (declare-fun tptp.fresh_1627595501_pi_pi (tptp.name tptp.product_prod_pi_pi) Bool)
% 0.27/0.72 (declare-fun tptp.fresh_2007541374s_name (tptp.name tptp.produc2052722628s_name) Bool)
% 0.27/0.72 (declare-fun tptp.fresh_1847501388Res_pi (tptp.name tptp.produc992857746Res_pi) Bool)
% 0.27/0.72 (declare-fun tptp.fresh_493808761reeRes (tptp.name tptp.produc1357834675reeRes) Bool)
% 0.27/0.72 (declare-fun tptp.fresh_1498103185ubject (tptp.name tptp.produc214645451ubject) Bool)
% 0.27/0.72 (declare-fun tptp.fresh_1953561446t_name (tptp.name tptp.produc1998742700t_name) Bool)
% 0.27/0.72 (declare-fun tptp.fresh_994896692ect_pi (tptp.name tptp.produc140253050ect_pi) Bool)
% 0.27/0.72 (declare-fun tptp.fresh_1638563217reeRes (tptp.name tptp.produc355105483reeRes) Bool)
% 0.27/0.72 (declare-fun tptp.fresh_495373993ubject (tptp.name tptp.produc1359399907ubject) Bool)
% 0.27/0.72 (declare-fun tptp.perm_n382765978reeRes (tptp.list_P227219501e_name (-> tptp.name tptp.late_freeRes) tptp.name) tptp.late_freeRes)
% 0.27/0.72 (declare-fun tptp.perm_n1387060402ubject (tptp.list_P227219501e_name (-> tptp.name tptp.late_subject) tptp.name) tptp.late_subject)
% 0.27/0.72 (declare-fun tptp.perm_n1333244520reeRes (tptp.list_P227219501e_name (-> tptp.pi tptp.late_freeRes) tptp.pi) tptp.late_freeRes)
% 0.27/0.72 (declare-fun tptp.perm_n190055296ubject (tptp.list_P227219501e_name (-> tptp.pi tptp.late_subject) tptp.pi) tptp.late_subject)
% 0.27/0.72 (declare-fun tptp.perm_n1841560599reeRes (tptp.list_P227219501e_name (-> tptp.pi_Rep tptp.late_freeRes) tptp.pi_Rep) tptp.late_freeRes)
% 0.27/0.72 (declare-fun tptp.perm_n698371375ubject (tptp.list_P227219501e_name (-> tptp.pi_Rep tptp.late_subject) tptp.pi_Rep) tptp.late_subject)
% 0.27/0.72 (declare-fun tptp.perm_n1446290985reeRes (tptp.list_P227219501e_name (-> tptp.late_freeRes tptp.late_freeRes) tptp.late_freeRes) tptp.late_freeRes)
% 0.27/0.72 (declare-fun tptp.perm_n303101761ubject (tptp.list_P227219501e_name (-> tptp.late_freeRes tptp.late_subject) tptp.late_freeRes) tptp.late_subject)
% 0.27/0.72 (declare-fun tptp.perm_n443561793reeRes (tptp.list_P227219501e_name (-> tptp.late_subject tptp.late_freeRes) tptp.late_subject) tptp.late_freeRes)
% 0.27/0.72 (declare-fun tptp.perm_n1447856217ubject (tptp.list_P227219501e_name (-> tptp.late_subject tptp.late_subject) tptp.late_subject) tptp.late_subject)
% 0.27/0.72 (declare-fun tptp.perm_name_o (tptp.list_P227219501e_name Bool) Bool)
% 0.27/0.72 (declare-fun tptp.perm_name_name (tptp.list_P227219501e_name tptp.name) tptp.name)
% 0.27/0.72 (declare-fun tptp.perm_name_pi (tptp.list_P227219501e_name tptp.pi) tptp.pi)
% 0.27/0.72 (declare-fun tptp.perm_name_pi_Rep (tptp.list_P227219501e_name tptp.pi_Rep) tptp.pi_Rep)
% 0.27/0.72 (declare-fun tptp.perm_n336613537reeRes (tptp.list_P227219501e_name tptp.late_freeRes) tptp.late_freeRes)
% 0.27/0.72 (declare-fun tptp.perm_n1938283068es_Rep (tptp.list_P227219501e_name tptp.late_freeRes_Rep) tptp.late_freeRes_Rep)
% 0.27/0.72 (declare-fun tptp.perm_n414416632sidual (tptp.list_P227219501e_name tptp.late_residual) tptp.late_residual)
% 0.27/0.72 (declare-fun tptp.perm_n890803237al_Rep (tptp.list_P227219501e_name tptp.late_residual_Rep) tptp.late_residual_Rep)
% 0.27/0.72 (declare-fun tptp.perm_n1559866809ubject (tptp.list_P227219501e_name tptp.late_subject) tptp.late_subject)
% 0.27/0.72 (declare-fun tptp.perm_n697952036ct_Rep (tptp.list_P227219501e_name tptp.late_subject_Rep) tptp.late_subject_Rep)
% 0.27/0.72 (declare-fun tptp.perm_name_list_name (tptp.list_P227219501e_name tptp.list_name) tptp.list_name)
% 0.27/0.72 (declare-fun tptp.perm_name_list_pi (tptp.list_P227219501e_name tptp.list_pi) tptp.list_pi)
% 0.27/0.72 (declare-fun tptp.perm_n729617823pi_Rep (tptp.list_P227219501e_name tptp.list_pi_Rep) tptp.list_pi_Rep)
% 0.27/0.72 (declare-fun tptp.perm_n808352945reeRes (tptp.list_P227219501e_name tptp.list_Late_freeRes) tptp.list_Late_freeRes)
% 0.27/0.72 (declare-fun tptp.perm_n1812647369ubject (tptp.list_P227219501e_name tptp.list_Late_subject) tptp.list_Late_subject)
% 0.27/0.72 (declare-fun tptp.perm_n1160739829e_name (tptp.list_P227219501e_name tptp.list_P227219501e_name) tptp.list_P227219501e_name)
% 0.27/0.72 (declare-fun tptp.perm_n1255502110_pi_pi (tptp.list_P227219501e_name tptp.produc1141751126_pi_pi) tptp.produc1141751126_pi_pi)
% 0.27/0.72 (declare-fun tptp.perm_n1415585007_pi_pi (tptp.list_P227219501e_name tptp.product_prod_pi_pi) tptp.product_prod_pi_pi)
% 0.27/0.72 (declare-fun tptp.perm_n258463228s_name (tptp.list_P227219501e_name tptp.produc2052722628s_name) tptp.produc2052722628s_name)
% 0.27/0.72 (declare-fun tptp.perm_n1211707594Res_pi (tptp.list_P227219501e_name tptp.produc992857746Res_pi) tptp.produc992857746Res_pi)
% 0.27/0.72 (declare-fun tptp.perm_n840427369pi_Rep (tptp.list_P227219501e_name tptp.produc1777919905pi_Rep) tptp.produc1777919905pi_Rep)
% 0.27/0.72 (declare-fun tptp.perm_n169932155reeRes (tptp.list_P227219501e_name tptp.produc1357834675reeRes) tptp.produc1357834675reeRes)
% 0.27/0.72 (declare-fun tptp.perm_n1174226579ubject (tptp.list_P227219501e_name tptp.produc214645451ubject) tptp.produc214645451ubject)
% 0.27/0.72 (declare-fun tptp.perm_n204483300t_name (tptp.list_P227219501e_name tptp.produc1998742700t_name) tptp.produc1998742700t_name)
% 0.27/0.72 (declare-fun tptp.perm_n359102898ect_pi (tptp.list_P227219501e_name tptp.produc140253050ect_pi) tptp.produc140253050ect_pi)
% 0.27/0.72 (declare-fun tptp.perm_n1467004033pi_Rep (tptp.list_P227219501e_name tptp.produc257012921pi_Rep) tptp.produc257012921pi_Rep)
% 0.27/0.72 (declare-fun tptp.perm_n1314686611reeRes (tptp.list_P227219501e_name tptp.produc355105483reeRes) tptp.produc355105483reeRes)
% 0.27/0.72 (declare-fun tptp.perm_n171497387ubject (tptp.list_P227219501e_name tptp.produc1359399907ubject) tptp.produc1359399907ubject)
% 0.27/0.72 (declare-fun tptp.perm_name_set_name (tptp.list_P227219501e_name tptp.set_name) tptp.set_name)
% 0.27/0.72 (declare-fun tptp.perm_name_set_pi (tptp.list_P227219501e_name tptp.set_pi) tptp.set_pi)
% 0.27/0.72 (declare-fun tptp.perm_name_set_pi_Rep (tptp.list_P227219501e_name tptp.set_pi_Rep) tptp.set_pi_Rep)
% 0.27/0.72 (declare-fun tptp.perm_n1555914327reeRes (tptp.list_P227219501e_name tptp.set_Late_freeRes) tptp.set_Late_freeRes)
% 0.27/0.72 (declare-fun tptp.perm_n412725103ubject (tptp.list_P227219501e_name tptp.set_Late_subject) tptp.set_Late_subject)
% 0.27/0.72 (declare-fun tptp.perm_n675238095_pi_pi (tptp.list_P227219501e_name tptp.set_Pr1834926343_pi_pi) tptp.set_Pr1834926343_pi_pi)
% 0.27/0.72 (declare-fun tptp.swap_name (tptp.produc367475239e_name tptp.name) tptp.name)
% 0.27/0.72 (declare-fun tptp.ord_le793202855e_name (tptp.set_Pr443758855e_name tptp.set_Pr443758855e_name) Bool)
% 0.27/0.72 (declare-fun tptp.ord_le797229014_pi_pi (tptp.set_Pr1654044726_pi_pi tptp.set_Pr1654044726_pi_pi) Bool)
% 0.27/0.72 (declare-fun tptp.ord_le630093991_pi_pi (tptp.set_Pr1834926343_pi_pi tptp.set_Pr1834926343_pi_pi) Bool)
% 0.27/0.72 (declare-fun tptp.produc1069608854e_name ((-> tptp.produc367475239e_name tptp.produc367475239e_name Bool) tptp.list_P227219501e_name) tptp.produc1872410278e_name)
% 0.27/0.72 (declare-fun tptp.produc1570949143e_name (tptp.name tptp.name) tptp.produc367475239e_name)
% 0.27/0.72 (declare-fun tptp.produc1531804426reeRes (tptp.name tptp.late_freeRes) tptp.produc2008547984reeRes)
% 0.27/0.72 (declare-fun tptp.produc607574050ubject (tptp.name tptp.late_subject) tptp.produc865358760ubject)
% 0.27/0.72 (declare-fun tptp.produc235456326_pi_pi (tptp.name tptp.product_prod_pi_pi) tptp.produc1141751126_pi_pi)
% 0.27/0.72 (declare-fun tptp.product_Pair_pi_pi (tptp.pi tptp.pi) tptp.product_prod_pi_pi)
% 0.27/0.72 (declare-fun tptp.produc784048711pi_Rep (tptp.pi_Rep tptp.pi_Rep) tptp.produc1212344719pi_Rep)
% 0.27/0.72 (declare-fun tptp.produc1701355766s_name (tptp.late_freeRes tptp.name) tptp.produc2052722628s_name)
% 0.27/0.72 (declare-fun tptp.produc1177552196Res_pi (tptp.late_freeRes tptp.pi) tptp.produc992857746Res_pi)
% 0.27/0.72 (declare-fun tptp.produc216486617pi_Rep (tptp.late_freeRes tptp.pi_Rep) tptp.produc1777919905pi_Rep)
% 0.27/0.72 (declare-fun tptp.produc1244821099reeRes (tptp.late_freeRes tptp.late_freeRes) tptp.produc1357834675reeRes)
% 0.27/0.72 (declare-fun tptp.produc320590723ubject (tptp.late_freeRes tptp.late_subject) tptp.produc214645451ubject)
% 0.27/0.72 (declare-fun tptp.produc1647375838t_name (tptp.late_subject tptp.name) tptp.produc1998742700t_name)
% 0.27/0.72 (declare-fun tptp.produc324947500ect_pi (tptp.late_subject tptp.pi) tptp.produc140253050ect_pi)
% 0.27/0.72 (declare-fun tptp.produc843063281pi_Rep (tptp.late_subject tptp.pi_Rep) tptp.produc257012921pi_Rep)
% 0.27/0.72 (declare-fun tptp.produc242091907reeRes (tptp.late_subject tptp.late_freeRes) tptp.produc355105483reeRes)
% 0.27/0.72 (declare-fun tptp.produc1465345179ubject (tptp.late_subject tptp.late_subject) tptp.produc1359399907ubject)
% 0.27/0.72 (declare-fun tptp.produc208131031e_name (tptp.list_P227219501e_name tptp.list_P227219501e_name) tptp.produc890461031e_name)
% 0.27/0.72 (declare-fun tptp.eqvt_name (tptp.set_Pr443758855e_name) Bool)
% 0.27/0.72 (declare-fun tptp.eqvt_pi (tptp.set_Pr1834926343_pi_pi) Bool)
% 0.27/0.72 (declare-fun tptp.eqvt_pi_Rep (tptp.set_Pr1131282415pi_Rep) Bool)
% 0.27/0.72 (declare-fun tptp.eqvt_Late_freeRes (tptp.set_Pr1780909331reeRes) Bool)
% 0.27/0.72 (declare-fun tptp.eqvt_Late_subject (tptp.set_Pr806375235ubject) Bool)
% 0.27/0.72 (declare-fun tptp.id_name () tptp.set_Pr443758855e_name)
% 0.27/0.72 (declare-fun tptp.id_pi () tptp.set_Pr1834926343_pi_pi)
% 0.27/0.72 (declare-fun tptp.collec1051790738_pi_pi ((-> tptp.product_prod_pi_pi Bool)) tptp.set_Pr1834926343_pi_pi)
% 0.27/0.72 (declare-fun tptp.strong2129052853vative (tptp.pi tptp.pi tptp.late_subject tptp.name tptp.set_Pr1834926343_pi_pi) Bool)
% 0.27/0.72 (declare-fun tptp.strong743114133lation (tptp.pi tptp.set_Pr1834926343_pi_pi tptp.pi) Bool)
% 0.27/0.72 (declare-fun tptp.member_name (tptp.name tptp.set_name) Bool)
% 0.27/0.72 (declare-fun tptp.member_pi (tptp.pi tptp.set_pi) Bool)
% 0.27/0.72 (declare-fun tptp.member_pi_Rep (tptp.pi_Rep tptp.set_pi_Rep) Bool)
% 0.27/0.72 (declare-fun tptp.member_Late_freeRes (tptp.late_freeRes tptp.set_Late_freeRes) Bool)
% 0.27/0.72 (declare-fun tptp.member_Late_subject (tptp.late_subject tptp.set_Late_subject) Bool)
% 0.27/0.72 (declare-fun tptp.member695284560e_name (tptp.produc367475239e_name tptp.set_Pr443758855e_name) Bool)
% 0.27/0.72 (declare-fun tptp.member540268543_pi_pi (tptp.produc1141751126_pi_pi tptp.set_Pr1654044726_pi_pi) Bool)
% 0.27/0.72 (declare-fun tptp.member558706512_pi_pi (tptp.product_prod_pi_pi tptp.set_Pr1834926343_pi_pi) Bool)
% 0.27/0.72 (declare-fun tptp.member1671908408pi_Rep (tptp.produc1212344719pi_Rep tptp.set_Pr1131282415pi_Rep) Bool)
% 0.27/0.72 (declare-fun tptp.member1584979804reeRes (tptp.produc1357834675reeRes tptp.set_Pr1780909331reeRes) Bool)
% 0.27/0.72 (declare-fun tptp.member1586545036ubject (tptp.produc1359399907ubject tptp.set_Pr806375235ubject) Bool)
% 0.27/0.72 (declare-fun tptp.p () tptp.pi)
% 0.27/0.72 (declare-fun tptp.pq () tptp.pi)
% 0.27/0.72 (declare-fun tptp.p2 () tptp.pi)
% 0.27/0.72 (declare-fun tptp.q () tptp.pi)
% 0.27/0.72 (declare-fun tptp.rel () tptp.set_Pr1834926343_pi_pi)
% 0.27/0.72 (declare-fun tptp.a () tptp.late_subject)
% 0.27/0.72 (declare-fun tptp.aa () tptp.name)
% 0.27/0.72 (declare-fun tptp.x () tptp.name)
% 0.27/0.72 (declare-fun tptp.y () tptp.name)
% 0.27/0.72 (assert (@ (@ tptp.ord_le630093991_pi_pi tptp.id_pi) tptp.rel))
% 0.27/0.72 (assert (not (= tptp.aa tptp.x)))
% 0.27/0.72 (assert (= tptp.a (@ tptp.late_BoundOutputS tptp.aa)))
% 0.27/0.72 (assert (not (= tptp.y tptp.x)))
% 0.27/0.72 (assert (@ tptp.eqvt_pi tptp.rel))
% 0.27/0.72 (assert (forall ((A tptp.name) (B tptp.name) (X tptp.late_subject)) (let ((_let_1 (@ tptp.perm_n1559866809ubject (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name A) B)) tptp.nil_Pr743626285e_name)))) (= (@ _let_1 (@ _let_1 X)) X))))
% 0.27/0.72 (assert (forall ((A tptp.name) (B tptp.name) (X tptp.late_freeRes)) (let ((_let_1 (@ tptp.perm_n336613537reeRes (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name A) B)) tptp.nil_Pr743626285e_name)))) (= (@ _let_1 (@ _let_1 X)) X))))
% 0.27/0.72 (assert (forall ((A tptp.name) (B tptp.name) (X tptp.pi_Rep)) (let ((_let_1 (@ tptp.perm_name_pi_Rep (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name A) B)) tptp.nil_Pr743626285e_name)))) (= (@ _let_1 (@ _let_1 X)) X))))
% 0.27/0.72 (assert (forall ((A tptp.name) (B tptp.name) (X tptp.name)) (let ((_let_1 (@ tptp.perm_name_name (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name A) B)) tptp.nil_Pr743626285e_name)))) (= (@ _let_1 (@ _let_1 X)) X))))
% 0.27/0.72 (assert (forall ((A tptp.name) (B tptp.name) (X tptp.pi)) (let ((_let_1 (@ tptp.perm_name_pi (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name A) B)) tptp.nil_Pr743626285e_name)))) (= (@ _let_1 (@ _let_1 X)) X))))
% 0.27/0.72 (assert (forall ((A tptp.name) (X tptp.late_subject)) (= (@ (@ tptp.perm_n1559866809ubject (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name A) A)) tptp.nil_Pr743626285e_name)) X) X)))
% 0.27/0.72 (assert (forall ((A tptp.name) (X tptp.late_freeRes)) (= (@ (@ tptp.perm_n336613537reeRes (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name A) A)) tptp.nil_Pr743626285e_name)) X) X)))
% 0.27/0.72 (assert (forall ((A tptp.name) (X tptp.pi_Rep)) (= (@ (@ tptp.perm_name_pi_Rep (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name A) A)) tptp.nil_Pr743626285e_name)) X) X)))
% 0.27/0.72 (assert (forall ((A tptp.name) (X tptp.name)) (= (@ (@ tptp.perm_name_name (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name A) A)) tptp.nil_Pr743626285e_name)) X) X)))
% 0.27/0.72 (assert (forall ((A tptp.name) (X tptp.pi)) (= (@ (@ tptp.perm_name_pi (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name A) A)) tptp.nil_Pr743626285e_name)) X) X)))
% 0.27/0.72 (assert (forall ((A tptp.name) (B tptp.name) (X tptp.late_subject)) (= (@ (@ tptp.perm_n1559866809ubject (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name A) B)) tptp.nil_Pr743626285e_name)) X) (@ (@ tptp.perm_n1559866809ubject (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name B) A)) tptp.nil_Pr743626285e_name)) X))))
% 0.27/0.72 (assert (forall ((A tptp.name) (B tptp.name) (X tptp.late_freeRes)) (= (@ (@ tptp.perm_n336613537reeRes (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name A) B)) tptp.nil_Pr743626285e_name)) X) (@ (@ tptp.perm_n336613537reeRes (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name B) A)) tptp.nil_Pr743626285e_name)) X))))
% 0.27/0.72 (assert (forall ((A tptp.name) (B tptp.name) (X tptp.pi_Rep)) (= (@ (@ tptp.perm_name_pi_Rep (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name A) B)) tptp.nil_Pr743626285e_name)) X) (@ (@ tptp.perm_name_pi_Rep (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name B) A)) tptp.nil_Pr743626285e_name)) X))))
% 0.27/0.72 (assert (forall ((A tptp.name) (B tptp.name) (X tptp.name)) (= (@ (@ tptp.perm_name_name (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name A) B)) tptp.nil_Pr743626285e_name)) X) (@ (@ tptp.perm_name_name (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name B) A)) tptp.nil_Pr743626285e_name)) X))))
% 0.27/0.72 (assert (forall ((A tptp.name) (B tptp.name) (X tptp.pi)) (= (@ (@ tptp.perm_name_pi (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name A) B)) tptp.nil_Pr743626285e_name)) X) (@ (@ tptp.perm_name_pi (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name B) A)) tptp.nil_Pr743626285e_name)) X))))
% 0.27/0.72 (assert (forall ((A tptp.name) (B tptp.name) (X tptp.late_subject)) (let ((_let_1 (@ tptp.perm_n1559866809ubject (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name A) B)) tptp.nil_Pr743626285e_name)))) (= (@ _let_1 (@ _let_1 X)) X))))
% 0.27/0.72 (assert (forall ((A tptp.name) (B tptp.name) (X tptp.late_freeRes)) (let ((_let_1 (@ tptp.perm_n336613537reeRes (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name A) B)) tptp.nil_Pr743626285e_name)))) (= (@ _let_1 (@ _let_1 X)) X))))
% 0.27/0.72 (assert (forall ((A tptp.name) (B tptp.name) (X tptp.pi_Rep)) (let ((_let_1 (@ tptp.perm_name_pi_Rep (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name A) B)) tptp.nil_Pr743626285e_name)))) (= (@ _let_1 (@ _let_1 X)) X))))
% 0.27/0.72 (assert (forall ((A tptp.name) (B tptp.name) (X tptp.name)) (let ((_let_1 (@ tptp.perm_name_name (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name A) B)) tptp.nil_Pr743626285e_name)))) (= (@ _let_1 (@ _let_1 X)) X))))
% 0.27/0.72 (assert (forall ((A tptp.name) (B tptp.name) (X tptp.pi)) (let ((_let_1 (@ tptp.perm_name_pi (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name A) B)) tptp.nil_Pr743626285e_name)))) (= (@ _let_1 (@ _let_1 X)) X))))
% 0.27/0.72 (assert (forall ((X tptp.late_subject)) (= (@ (@ tptp.perm_n1559866809ubject tptp.nil_Pr743626285e_name) X) X)))
% 0.27/0.72 (assert (forall ((X tptp.late_freeRes)) (= (@ (@ tptp.perm_n336613537reeRes tptp.nil_Pr743626285e_name) X) X)))
% 0.27/0.72 (assert (forall ((X tptp.pi_Rep)) (= (@ (@ tptp.perm_name_pi_Rep tptp.nil_Pr743626285e_name) X) X)))
% 0.27/0.72 (assert (forall ((X tptp.name)) (= (@ (@ tptp.perm_name_name tptp.nil_Pr743626285e_name) X) X)))
% 0.27/0.72 (assert (forall ((X tptp.pi)) (= (@ (@ tptp.perm_name_pi tptp.nil_Pr743626285e_name) X) X)))
% 0.27/0.72 (assert (forall ((A tptp.name) (B tptp.name) (X tptp.late_subject)) (= (@ (@ tptp.perm_n1559866809ubject (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name A) B)) tptp.nil_Pr743626285e_name)) (@ (@ tptp.perm_n1559866809ubject (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name B) A)) tptp.nil_Pr743626285e_name)) X)) X)))
% 0.27/0.72 (assert (forall ((A tptp.name) (B tptp.name) (X tptp.late_freeRes)) (= (@ (@ tptp.perm_n336613537reeRes (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name A) B)) tptp.nil_Pr743626285e_name)) (@ (@ tptp.perm_n336613537reeRes (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name B) A)) tptp.nil_Pr743626285e_name)) X)) X)))
% 0.27/0.72 (assert (forall ((A tptp.name) (B tptp.name) (X tptp.pi_Rep)) (= (@ (@ tptp.perm_name_pi_Rep (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name A) B)) tptp.nil_Pr743626285e_name)) (@ (@ tptp.perm_name_pi_Rep (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name B) A)) tptp.nil_Pr743626285e_name)) X)) X)))
% 0.27/0.72 (assert (forall ((A tptp.name) (B tptp.name) (X tptp.name)) (= (@ (@ tptp.perm_name_name (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name A) B)) tptp.nil_Pr743626285e_name)) (@ (@ tptp.perm_name_name (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name B) A)) tptp.nil_Pr743626285e_name)) X)) X)))
% 0.27/0.72 (assert (forall ((A tptp.name) (B tptp.name) (X tptp.pi)) (= (@ (@ tptp.perm_name_pi (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name A) B)) tptp.nil_Pr743626285e_name)) (@ (@ tptp.perm_name_pi (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name B) A)) tptp.nil_Pr743626285e_name)) X)) X)))
% 0.27/0.72 (assert (forall ((X1 tptp.name) (Y1 tptp.name)) (= (= (@ tptp.late_BoundOutputS X1) (@ tptp.late_BoundOutputS Y1)) (= X1 Y1))))
% 0.27/0.72 (assert (forall ((X2 tptp.name) (Y2 tptp.name)) (= (= (@ tptp.late_BoundOutputS X2) (@ tptp.late_BoundOutputS Y2)) (= X2 Y2))))
% 0.27/0.72 (assert (@ (@ tptp.fresh_name_pi tptp.y) tptp.p2))
% 0.27/0.72 (assert (forall ((X21 tptp.produc367475239e_name) (X22 tptp.list_P227219501e_name) (Y21 tptp.produc367475239e_name) (Y22 tptp.list_P227219501e_name)) (= (= (@ (@ tptp.cons_P1213805021e_name X21) X22) (@ (@ tptp.cons_P1213805021e_name Y21) Y22)) (and (= X21 Y21) (= X22 Y22)))))
% 0.27/0.72 (assert (forall ((X1 tptp.name) (X2 tptp.name) (Y1 tptp.name) (Y2 tptp.name)) (= (= (@ (@ tptp.produc1570949143e_name X1) X2) (@ (@ tptp.produc1570949143e_name Y1) Y2)) (and (= X1 Y1) (= X2 Y2)))))
% 0.27/0.72 (assert (forall ((X1 tptp.name) (X2 tptp.product_prod_pi_pi) (Y1 tptp.name) (Y2 tptp.product_prod_pi_pi)) (= (= (@ (@ tptp.produc235456326_pi_pi X1) X2) (@ (@ tptp.produc235456326_pi_pi Y1) Y2)) (and (= X1 Y1) (= X2 Y2)))))
% 0.27/0.72 (assert (forall ((X1 tptp.pi) (X2 tptp.pi) (Y1 tptp.pi) (Y2 tptp.pi)) (= (= (@ (@ tptp.product_Pair_pi_pi X1) X2) (@ (@ tptp.product_Pair_pi_pi Y1) Y2)) (and (= X1 Y1) (= X2 Y2)))))
% 0.27/0.72 (assert (forall ((A tptp.name) (B tptp.name) (A2 tptp.name) (B2 tptp.name)) (= (= (@ (@ tptp.produc1570949143e_name A) B) (@ (@ tptp.produc1570949143e_name A2) B2)) (and (= A A2) (= B B2)))))
% 0.27/0.72 (assert (forall ((A tptp.name) (B tptp.product_prod_pi_pi) (A2 tptp.name) (B2 tptp.product_prod_pi_pi)) (= (= (@ (@ tptp.produc235456326_pi_pi A) B) (@ (@ tptp.produc235456326_pi_pi A2) B2)) (and (= A A2) (= B B2)))))
% 0.27/0.72 (assert (forall ((A tptp.pi) (B tptp.pi) (A2 tptp.pi) (B2 tptp.pi)) (= (= (@ (@ tptp.product_Pair_pi_pi A) B) (@ (@ tptp.product_Pair_pi_pi A2) B2)) (and (= A A2) (= B B2)))))
% 0.27/0.72 (assert (forall ((Residual_Rep tptp.late_residual_Rep)) (= (@ (@ tptp.perm_n890803237al_Rep tptp.nil_Pr743626285e_name) Residual_Rep) Residual_Rep)))
% 0.27/0.72 (assert (forall ((Subject_Rep tptp.late_subject_Rep)) (= (@ (@ tptp.perm_n697952036ct_Rep tptp.nil_Pr743626285e_name) Subject_Rep) Subject_Rep)))
% 0.27/0.72 (assert (forall ((FreeRes_Rep tptp.late_freeRes_Rep)) (= (@ (@ tptp.perm_n1938283068es_Rep tptp.nil_Pr743626285e_name) FreeRes_Rep) FreeRes_Rep)))
% 0.27/0.72 (assert (forall ((Pi_Rep tptp.pi_Rep)) (= (@ (@ tptp.perm_name_pi_Rep tptp.nil_Pr743626285e_name) Pi_Rep) Pi_Rep)))
% 0.27/0.72 (assert (forall ((Pi tptp.list_P227219501e_name) (X1 tptp.name)) (= (@ (@ tptp.perm_n1559866809ubject Pi) (@ tptp.late_BoundOutputS X1)) (@ tptp.late_BoundOutputS (@ (@ tptp.perm_name_name Pi) X1)))))
% 0.27/0.72 (assert (forall ((A tptp.name) (X tptp.pi_Rep) (B tptp.name)) (=> (@ (@ tptp.fresh_name_pi_Rep A) X) (=> (@ (@ tptp.fresh_name_pi_Rep B) X) (= (@ (@ tptp.perm_name_pi_Rep (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name A) B)) tptp.nil_Pr743626285e_name)) X) X)))))
% 0.27/0.72 (assert (forall ((A tptp.name) (X tptp.late_subject) (B tptp.name)) (=> (@ (@ tptp.fresh_717452603ubject A) X) (=> (@ (@ tptp.fresh_717452603ubject B) X) (= (@ (@ tptp.perm_n1559866809ubject (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name A) B)) tptp.nil_Pr743626285e_name)) X) X)))))
% 0.27/0.72 (assert (forall ((A tptp.name) (X tptp.late_freeRes) (B tptp.name)) (=> (@ (@ tptp.fresh_1641682979reeRes A) X) (=> (@ (@ tptp.fresh_1641682979reeRes B) X) (= (@ (@ tptp.perm_n336613537reeRes (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name A) B)) tptp.nil_Pr743626285e_name)) X) X)))))
% 0.27/0.72 (assert (forall ((A tptp.name) (X tptp.produc1141751126_pi_pi) (B tptp.name)) (=> (@ (@ tptp.fresh_1376661020_pi_pi A) X) (=> (@ (@ tptp.fresh_1376661020_pi_pi B) X) (= (@ (@ tptp.perm_n1255502110_pi_pi (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name A) B)) tptp.nil_Pr743626285e_name)) X) X)))))
% 0.27/0.72 (assert (forall ((A tptp.name) (X tptp.name) (B tptp.name)) (=> (@ (@ tptp.fresh_name_name A) X) (=> (@ (@ tptp.fresh_name_name B) X) (= (@ (@ tptp.perm_name_name (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name A) B)) tptp.nil_Pr743626285e_name)) X) X)))))
% 0.27/0.72 (assert (forall ((A tptp.name) (X tptp.pi) (B tptp.name)) (=> (@ (@ tptp.fresh_name_pi A) X) (=> (@ (@ tptp.fresh_name_pi B) X) (= (@ (@ tptp.perm_name_pi (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name A) B)) tptp.nil_Pr743626285e_name)) X) X)))))
% 0.27/0.72 (assert (forall ((A tptp.name) (X tptp.pi_Rep) (B tptp.name)) (=> (@ (@ tptp.fresh_name_pi_Rep A) X) (=> (@ (@ tptp.fresh_name_pi_Rep B) X) (= (@ (@ tptp.perm_name_pi_Rep (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name A) B)) tptp.nil_Pr743626285e_name)) X) X)))))
% 0.27/0.72 (assert (forall ((A tptp.name) (X tptp.late_subject) (B tptp.name)) (=> (@ (@ tptp.fresh_717452603ubject A) X) (=> (@ (@ tptp.fresh_717452603ubject B) X) (= (@ (@ tptp.perm_n1559866809ubject (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name A) B)) tptp.nil_Pr743626285e_name)) X) X)))))
% 0.27/0.72 (assert (forall ((A tptp.name) (X tptp.late_freeRes) (B tptp.name)) (=> (@ (@ tptp.fresh_1641682979reeRes A) X) (=> (@ (@ tptp.fresh_1641682979reeRes B) X) (= (@ (@ tptp.perm_n336613537reeRes (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name A) B)) tptp.nil_Pr743626285e_name)) X) X)))))
% 0.27/0.72 (assert (forall ((A tptp.name) (X tptp.produc1141751126_pi_pi) (B tptp.name)) (=> (@ (@ tptp.fresh_1376661020_pi_pi A) X) (=> (@ (@ tptp.fresh_1376661020_pi_pi B) X) (= (@ (@ tptp.perm_n1255502110_pi_pi (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name A) B)) tptp.nil_Pr743626285e_name)) X) X)))))
% 0.27/0.72 (assert (forall ((A tptp.name) (X tptp.name) (B tptp.name)) (=> (@ (@ tptp.fresh_name_name A) X) (=> (@ (@ tptp.fresh_name_name B) X) (= (@ (@ tptp.perm_name_name (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name A) B)) tptp.nil_Pr743626285e_name)) X) X)))))
% 0.27/0.72 (assert (forall ((A tptp.name) (X tptp.pi) (B tptp.name)) (=> (@ (@ tptp.fresh_name_pi A) X) (=> (@ (@ tptp.fresh_name_pi B) X) (= (@ (@ tptp.perm_name_pi (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name A) B)) tptp.nil_Pr743626285e_name)) X) X)))))
% 0.27/0.72 (assert (@ (@ tptp.fresh_717452603ubject tptp.y) tptp.a))
% 0.27/0.72 (assert (forall ((Pi tptp.list_P227219501e_name) (X3 tptp.set_Pr1834926343_pi_pi) (Y tptp.set_Pr1834926343_pi_pi)) (let ((_let_1 (@ tptp.perm_n675238095_pi_pi Pi))) (= (@ (@ tptp.perm_name_o Pi) (@ (@ tptp.ord_le630093991_pi_pi X3) Y)) (@ (@ tptp.ord_le630093991_pi_pi (@ _let_1 X3)) (@ _let_1 Y))))))
% 0.27/0.72 (assert (forall ((A tptp.name) (Pi tptp.list_P227219501e_name) (X tptp.pi_Rep)) (let ((_let_1 (@ tptp.fresh_name_pi_Rep A))) (=> (@ (@ tptp.fresh_922791155e_name A) Pi) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.perm_name_pi_Rep Pi) X)))))))
% 0.27/0.72 (assert (forall ((A tptp.name) (Pi tptp.list_P227219501e_name) (X tptp.late_subject)) (let ((_let_1 (@ tptp.fresh_717452603ubject A))) (=> (@ (@ tptp.fresh_922791155e_name A) Pi) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.perm_n1559866809ubject Pi) X)))))))
% 0.27/0.72 (assert (forall ((A tptp.name) (Pi tptp.list_P227219501e_name) (X tptp.late_freeRes)) (let ((_let_1 (@ tptp.fresh_1641682979reeRes A))) (=> (@ (@ tptp.fresh_922791155e_name A) Pi) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.perm_n336613537reeRes Pi) X)))))))
% 0.27/0.72 (assert (forall ((A tptp.name) (Pi tptp.list_P227219501e_name) (X tptp.produc1141751126_pi_pi)) (let ((_let_1 (@ tptp.fresh_1376661020_pi_pi A))) (=> (@ (@ tptp.fresh_922791155e_name A) Pi) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.perm_n1255502110_pi_pi Pi) X)))))))
% 0.27/0.72 (assert (forall ((A tptp.name) (Pi tptp.list_P227219501e_name) (X tptp.name)) (let ((_let_1 (@ tptp.fresh_name_name A))) (=> (@ (@ tptp.fresh_922791155e_name A) Pi) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.perm_name_name Pi) X)))))))
% 0.27/0.72 (assert (forall ((A tptp.name) (Pi tptp.list_P227219501e_name) (X tptp.pi)) (let ((_let_1 (@ tptp.fresh_name_pi A))) (=> (@ (@ tptp.fresh_922791155e_name A) Pi) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.perm_name_pi Pi) X)))))))
% 0.27/0.72 (assert (forall ((X tptp.late_subject)) (not (forall ((C tptp.name)) (not (@ (@ tptp.fresh_717452603ubject C) X))))))
% 0.27/0.72 (assert (forall ((X tptp.late_freeRes)) (not (forall ((C tptp.name)) (not (@ (@ tptp.fresh_1641682979reeRes C) X))))))
% 0.27/0.72 (assert (forall ((X tptp.produc1141751126_pi_pi)) (not (forall ((C tptp.name)) (not (@ (@ tptp.fresh_1376661020_pi_pi C) X))))))
% 0.27/0.72 (assert (forall ((X tptp.name)) (not (forall ((C tptp.name)) (not (@ (@ tptp.fresh_name_name C) X))))))
% 0.27/0.72 (assert (forall ((X tptp.pi)) (not (forall ((C tptp.name)) (not (@ (@ tptp.fresh_name_pi C) X))))))
% 0.27/0.72 (assert (forall ((Pi tptp.list_P227219501e_name) (A tptp.name) (X tptp.pi_Rep)) (= (@ (@ tptp.perm_name_o Pi) (@ (@ tptp.fresh_name_pi_Rep A) X)) (@ (@ tptp.fresh_name_pi_Rep (@ (@ tptp.perm_name_name Pi) A)) (@ (@ tptp.perm_name_pi_Rep Pi) X)))))
% 0.27/0.72 (assert (forall ((Pi tptp.list_P227219501e_name) (A tptp.name) (X tptp.late_subject)) (= (@ (@ tptp.perm_name_o Pi) (@ (@ tptp.fresh_717452603ubject A) X)) (@ (@ tptp.fresh_717452603ubject (@ (@ tptp.perm_name_name Pi) A)) (@ (@ tptp.perm_n1559866809ubject Pi) X)))))
% 0.27/0.72 (assert (forall ((Pi tptp.list_P227219501e_name) (A tptp.name) (X tptp.late_freeRes)) (= (@ (@ tptp.perm_name_o Pi) (@ (@ tptp.fresh_1641682979reeRes A) X)) (@ (@ tptp.fresh_1641682979reeRes (@ (@ tptp.perm_name_name Pi) A)) (@ (@ tptp.perm_n336613537reeRes Pi) X)))))
% 0.27/0.72 (assert (forall ((Pi tptp.list_P227219501e_name) (A tptp.name) (X tptp.produc1141751126_pi_pi)) (= (@ (@ tptp.perm_name_o Pi) (@ (@ tptp.fresh_1376661020_pi_pi A) X)) (@ (@ tptp.fresh_1376661020_pi_pi (@ (@ tptp.perm_name_name Pi) A)) (@ (@ tptp.perm_n1255502110_pi_pi Pi) X)))))
% 0.27/0.72 (assert (forall ((Pi tptp.list_P227219501e_name) (A tptp.name) (X tptp.name)) (let ((_let_1 (@ tptp.perm_name_name Pi))) (= (@ (@ tptp.perm_name_o Pi) (@ (@ tptp.fresh_name_name A) X)) (@ (@ tptp.fresh_name_name (@ _let_1 A)) (@ _let_1 X))))))
% 0.27/0.72 (assert (forall ((Pi tptp.list_P227219501e_name) (A tptp.name) (X tptp.pi)) (= (@ (@ tptp.perm_name_o Pi) (@ (@ tptp.fresh_name_pi A) X)) (@ (@ tptp.fresh_name_pi (@ (@ tptp.perm_name_name Pi) A)) (@ (@ tptp.perm_name_pi Pi) X)))))
% 0.27/0.72 (assert (forall ((Pi tptp.list_P227219501e_name) (A tptp.name) (X tptp.pi_Rep)) (= (@ (@ tptp.fresh_name_pi_Rep (@ (@ tptp.perm_name_name Pi) A)) (@ (@ tptp.perm_name_pi_Rep Pi) X)) (@ (@ tptp.fresh_name_pi_Rep A) X))))
% 0.27/0.72 (assert (forall ((Pi tptp.list_P227219501e_name) (A tptp.name) (X tptp.late_subject)) (= (@ (@ tptp.fresh_717452603ubject (@ (@ tptp.perm_name_name Pi) A)) (@ (@ tptp.perm_n1559866809ubject Pi) X)) (@ (@ tptp.fresh_717452603ubject A) X))))
% 0.27/0.72 (assert (forall ((Pi tptp.list_P227219501e_name) (A tptp.name) (X tptp.late_freeRes)) (= (@ (@ tptp.fresh_1641682979reeRes (@ (@ tptp.perm_name_name Pi) A)) (@ (@ tptp.perm_n336613537reeRes Pi) X)) (@ (@ tptp.fresh_1641682979reeRes A) X))))
% 0.27/0.72 (assert (forall ((Pi tptp.list_P227219501e_name) (A tptp.name) (X tptp.produc1141751126_pi_pi)) (= (@ (@ tptp.fresh_1376661020_pi_pi (@ (@ tptp.perm_name_name Pi) A)) (@ (@ tptp.perm_n1255502110_pi_pi Pi) X)) (@ (@ tptp.fresh_1376661020_pi_pi A) X))))
% 0.27/0.72 (assert (forall ((Pi tptp.list_P227219501e_name) (A tptp.name) (X tptp.name)) (let ((_let_1 (@ tptp.perm_name_name Pi))) (= (@ (@ tptp.fresh_name_name (@ _let_1 A)) (@ _let_1 X)) (@ (@ tptp.fresh_name_name A) X)))))
% 0.27/0.72 (assert (forall ((Pi tptp.list_P227219501e_name) (A tptp.name) (X tptp.pi)) (= (@ (@ tptp.fresh_name_pi (@ (@ tptp.perm_name_name Pi) A)) (@ (@ tptp.perm_name_pi Pi) X)) (@ (@ tptp.fresh_name_pi A) X))))
% 0.27/0.72 (assert (forall ((X tptp.name)) (= (@ (@ tptp.perm_name_name tptp.nil_Pr743626285e_name) X) X)))
% 0.27/0.72 (assert (forall ((X tptp.produc1872410278e_name)) (=> (forall ((P (-> tptp.produc367475239e_name tptp.produc367475239e_name Bool))) (not (= X (@ (@ tptp.produc1069608854e_name P) tptp.nil_Pr743626285e_name)))) (=> (forall ((P (-> tptp.produc367475239e_name tptp.produc367475239e_name Bool)) (X4 tptp.produc367475239e_name)) (not (= X (@ (@ tptp.produc1069608854e_name P) (@ (@ tptp.cons_P1213805021e_name X4) tptp.nil_Pr743626285e_name))))) (not (forall ((P (-> tptp.produc367475239e_name tptp.produc367475239e_name Bool)) (X4 tptp.produc367475239e_name) (Y3 tptp.produc367475239e_name) (Xs tptp.list_P227219501e_name)) (not (= X (@ (@ tptp.produc1069608854e_name P) (@ (@ tptp.cons_P1213805021e_name X4) (@ (@ tptp.cons_P1213805021e_name Y3) Xs)))))))))))
% 0.27/0.72 (assert (forall ((X tptp.produc1872410278e_name)) (=> (forall ((P (-> tptp.produc367475239e_name tptp.produc367475239e_name Bool))) (not (= X (@ (@ tptp.produc1069608854e_name P) tptp.nil_Pr743626285e_name)))) (not (forall ((P (-> tptp.produc367475239e_name tptp.produc367475239e_name Bool)) (X4 tptp.produc367475239e_name) (Ys tptp.list_P227219501e_name)) (not (= X (@ (@ tptp.produc1069608854e_name P) (@ (@ tptp.cons_P1213805021e_name X4) Ys)))))))))
% 0.27/0.72 (assert (forall ((X tptp.produc890461031e_name)) (=> (forall ((Ys tptp.list_P227219501e_name)) (not (= X (@ (@ tptp.produc208131031e_name tptp.nil_Pr743626285e_name) Ys)))) (=> (forall ((Xs tptp.list_P227219501e_name)) (not (= X (@ (@ tptp.produc208131031e_name Xs) tptp.nil_Pr743626285e_name)))) (not (forall ((X4 tptp.produc367475239e_name) (Xs tptp.list_P227219501e_name) (Y3 tptp.produc367475239e_name) (Ys tptp.list_P227219501e_name)) (not (= X (@ (@ tptp.produc208131031e_name (@ (@ tptp.cons_P1213805021e_name X4) Xs)) (@ (@ tptp.cons_P1213805021e_name Y3) Ys))))))))))
% 0.27/0.72 (assert (forall ((X tptp.produc890461031e_name)) (=> (forall ((Ys tptp.list_P227219501e_name)) (not (= X (@ (@ tptp.produc208131031e_name tptp.nil_Pr743626285e_name) Ys)))) (not (forall ((X4 tptp.produc367475239e_name) (Xs tptp.list_P227219501e_name) (Ys tptp.list_P227219501e_name)) (not (= X (@ (@ tptp.produc208131031e_name (@ (@ tptp.cons_P1213805021e_name X4) Xs)) Ys))))))))
% 0.27/0.72 (assert (forall ((A tptp.name) (B tptp.name)) (= (@ (@ tptp.perm_name_name (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name A) B)) tptp.nil_Pr743626285e_name)) A) B)))
% 0.27/0.72 (assert (forall ((A tptp.name) (B tptp.name)) (= (@ (@ tptp.perm_name_name (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name A) B)) tptp.nil_Pr743626285e_name)) B) A)))
% 0.27/0.72 (assert (forall ((A tptp.name) (C2 tptp.name) (B tptp.name)) (=> (not (= A C2)) (=> (not (= B C2)) (= (@ (@ tptp.perm_name_name (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name A) B)) tptp.nil_Pr743626285e_name)) C2) C2)))))
% 0.27/0.72 (assert (forall ((C2 tptp.name) (A tptp.name) (X tptp.pi_Rep) (B tptp.name)) (let ((_let_1 (@ tptp.fresh_name_pi_Rep C2))) (=> (not (= C2 A)) (=> (@ (@ tptp.fresh_name_pi_Rep A) X) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.perm_name_pi_Rep (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name A) B)) tptp.nil_Pr743626285e_name)) X))))))))
% 0.27/0.72 (assert (forall ((C2 tptp.name) (A tptp.name) (X tptp.late_subject) (B tptp.name)) (let ((_let_1 (@ tptp.fresh_717452603ubject C2))) (=> (not (= C2 A)) (=> (@ (@ tptp.fresh_717452603ubject A) X) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.perm_n1559866809ubject (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name A) B)) tptp.nil_Pr743626285e_name)) X))))))))
% 0.27/0.72 (assert (forall ((C2 tptp.name) (A tptp.name) (X tptp.late_freeRes) (B tptp.name)) (let ((_let_1 (@ tptp.fresh_1641682979reeRes C2))) (=> (not (= C2 A)) (=> (@ (@ tptp.fresh_1641682979reeRes A) X) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.perm_n336613537reeRes (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name A) B)) tptp.nil_Pr743626285e_name)) X))))))))
% 0.27/0.72 (assert (forall ((C2 tptp.name) (A tptp.name) (X tptp.produc1141751126_pi_pi) (B tptp.name)) (let ((_let_1 (@ tptp.fresh_1376661020_pi_pi C2))) (=> (not (= C2 A)) (=> (@ (@ tptp.fresh_1376661020_pi_pi A) X) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.perm_n1255502110_pi_pi (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name A) B)) tptp.nil_Pr743626285e_name)) X))))))))
% 0.27/0.72 (assert (forall ((C2 tptp.name) (A tptp.name) (X tptp.name) (B tptp.name)) (let ((_let_1 (@ tptp.fresh_name_name C2))) (=> (not (= C2 A)) (=> (@ (@ tptp.fresh_name_name A) X) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.perm_name_name (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name A) B)) tptp.nil_Pr743626285e_name)) X))))))))
% 0.27/0.72 (assert (forall ((C2 tptp.name) (A tptp.name) (X tptp.pi) (B tptp.name)) (let ((_let_1 (@ tptp.fresh_name_pi C2))) (=> (not (= C2 A)) (=> (@ (@ tptp.fresh_name_pi A) X) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.perm_name_pi (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name A) B)) tptp.nil_Pr743626285e_name)) X))))))))
% 0.27/0.72 (assert (forall ((P2 (-> tptp.produc367475239e_name Bool)) (Prod tptp.produc367475239e_name)) (=> (forall ((A3 tptp.name) (B3 tptp.name)) (@ P2 (@ (@ tptp.produc1570949143e_name A3) B3))) (@ P2 Prod))))
% 0.27/0.72 (assert (forall ((P2 (-> tptp.produc1141751126_pi_pi Bool)) (Prod tptp.produc1141751126_pi_pi)) (=> (forall ((A3 tptp.name) (B3 tptp.product_prod_pi_pi)) (@ P2 (@ (@ tptp.produc235456326_pi_pi A3) B3))) (@ P2 Prod))))
% 0.27/0.72 (assert (forall ((P2 (-> tptp.product_prod_pi_pi Bool)) (Prod tptp.product_prod_pi_pi)) (=> (forall ((A3 tptp.pi) (B3 tptp.pi)) (@ P2 (@ (@ tptp.product_Pair_pi_pi A3) B3))) (@ P2 Prod))))
% 0.27/0.72 (assert (forall ((Y4 tptp.produc367475239e_name)) (not (forall ((A3 tptp.name) (B3 tptp.name)) (not (= Y4 (@ (@ tptp.produc1570949143e_name A3) B3)))))))
% 0.27/0.72 (assert (forall ((Y4 tptp.produc1141751126_pi_pi)) (not (forall ((A3 tptp.name) (B3 tptp.product_prod_pi_pi)) (not (= Y4 (@ (@ tptp.produc235456326_pi_pi A3) B3)))))))
% 0.27/0.72 (assert (forall ((Y4 tptp.product_prod_pi_pi)) (not (forall ((A3 tptp.pi) (B3 tptp.pi)) (not (= Y4 (@ (@ tptp.product_Pair_pi_pi A3) B3)))))))
% 0.27/0.72 (assert (forall ((A tptp.product_prod_pi_pi) (P2 (-> tptp.product_prod_pi_pi Bool))) (= (@ (@ tptp.member558706512_pi_pi A) (@ tptp.collec1051790738_pi_pi P2)) (@ P2 A))))
% 0.27/0.72 (assert (forall ((A4 tptp.set_Pr1834926343_pi_pi)) (= (@ tptp.collec1051790738_pi_pi (lambda ((X5 tptp.product_prod_pi_pi)) (@ (@ tptp.member558706512_pi_pi X5) A4))) A4)))
% 0.27/0.72 (assert (forall ((P2 (-> tptp.produc1141751126_pi_pi Bool)) (X tptp.produc1141751126_pi_pi)) (=> (forall ((A3 tptp.name) (B3 tptp.pi) (C tptp.pi)) (@ P2 (@ (@ tptp.produc235456326_pi_pi A3) (@ (@ tptp.product_Pair_pi_pi B3) C)))) (@ P2 X))))
% 0.27/0.72 (assert (forall ((Y4 tptp.produc1141751126_pi_pi)) (not (forall ((A3 tptp.name) (B3 tptp.pi) (C tptp.pi)) (not (= Y4 (@ (@ tptp.produc235456326_pi_pi A3) (@ (@ tptp.product_Pair_pi_pi B3) C))))))))
% 0.27/0.72 (assert (forall ((A tptp.name) (B tptp.name) (A2 tptp.name) (B2 tptp.name)) (=> (= (@ (@ tptp.produc1570949143e_name A) B) (@ (@ tptp.produc1570949143e_name A2) B2)) (not (=> (= A A2) (not (= B B2)))))))
% 0.27/0.72 (assert (forall ((A tptp.name) (B tptp.product_prod_pi_pi) (A2 tptp.name) (B2 tptp.product_prod_pi_pi)) (=> (= (@ (@ tptp.produc235456326_pi_pi A) B) (@ (@ tptp.produc235456326_pi_pi A2) B2)) (not (=> (= A A2) (not (= B B2)))))))
% 0.27/0.72 (assert (forall ((A tptp.pi) (B tptp.pi) (A2 tptp.pi) (B2 tptp.pi)) (=> (= (@ (@ tptp.product_Pair_pi_pi A) B) (@ (@ tptp.product_Pair_pi_pi A2) B2)) (not (=> (= A A2) (not (= B B2)))))))
% 0.27/0.72 (assert (forall ((P2 (-> tptp.produc367475239e_name Bool)) (P3 tptp.produc367475239e_name)) (=> (forall ((A3 tptp.name) (B3 tptp.name)) (@ P2 (@ (@ tptp.produc1570949143e_name A3) B3))) (@ P2 P3))))
% 0.27/0.72 (assert (forall ((P2 (-> tptp.produc1141751126_pi_pi Bool)) (P3 tptp.produc1141751126_pi_pi)) (=> (forall ((A3 tptp.name) (B3 tptp.product_prod_pi_pi)) (@ P2 (@ (@ tptp.produc235456326_pi_pi A3) B3))) (@ P2 P3))))
% 0.27/0.72 (assert (forall ((P2 (-> tptp.product_prod_pi_pi Bool)) (P3 tptp.product_prod_pi_pi)) (=> (forall ((A3 tptp.pi) (B3 tptp.pi)) (@ P2 (@ (@ tptp.product_Pair_pi_pi A3) B3))) (@ P2 P3))))
% 0.27/0.72 (assert (forall ((P3 tptp.produc367475239e_name)) (exists ((X4 tptp.name) (Y3 tptp.name)) (= P3 (@ (@ tptp.produc1570949143e_name X4) Y3)))))
% 0.27/0.72 (assert (forall ((P3 tptp.produc1141751126_pi_pi)) (exists ((X4 tptp.name) (Y3 tptp.product_prod_pi_pi)) (= P3 (@ (@ tptp.produc235456326_pi_pi X4) Y3)))))
% 0.27/0.72 (assert (forall ((P3 tptp.product_prod_pi_pi)) (exists ((X4 tptp.pi) (Y3 tptp.pi)) (= P3 (@ (@ tptp.product_Pair_pi_pi X4) Y3)))))
% 0.27/0.72 (assert (forall ((X tptp.produc367475239e_name) (Xs2 tptp.list_P227219501e_name)) (not (= (@ (@ tptp.cons_P1213805021e_name X) Xs2) Xs2))))
% 0.27/0.72 (assert (forall ((Pi1 tptp.list_P227219501e_name) (Pi2 tptp.list_P227219501e_name) (X tptp.late_subject)) (let ((_let_1 (@ tptp.perm_n1559866809ubject Pi1))) (= (@ _let_1 (@ (@ tptp.perm_n1559866809ubject Pi2) X)) (@ (@ tptp.perm_n1559866809ubject (@ (@ tptp.perm_n1160739829e_name Pi1) Pi2)) (@ _let_1 X))))))
% 0.27/0.72 (assert (forall ((Pi1 tptp.list_P227219501e_name) (Pi2 tptp.list_P227219501e_name) (X tptp.late_freeRes)) (let ((_let_1 (@ tptp.perm_n336613537reeRes Pi1))) (= (@ _let_1 (@ (@ tptp.perm_n336613537reeRes Pi2) X)) (@ (@ tptp.perm_n336613537reeRes (@ (@ tptp.perm_n1160739829e_name Pi1) Pi2)) (@ _let_1 X))))))
% 0.27/0.72 (assert (forall ((Pi1 tptp.list_P227219501e_name) (Pi2 tptp.list_P227219501e_name) (X tptp.pi_Rep)) (let ((_let_1 (@ tptp.perm_name_pi_Rep Pi1))) (= (@ _let_1 (@ (@ tptp.perm_name_pi_Rep Pi2) X)) (@ (@ tptp.perm_name_pi_Rep (@ (@ tptp.perm_n1160739829e_name Pi1) Pi2)) (@ _let_1 X))))))
% 0.27/0.72 (assert (forall ((Pi1 tptp.list_P227219501e_name) (Pi2 tptp.list_P227219501e_name) (X tptp.name)) (let ((_let_1 (@ tptp.perm_name_name Pi1))) (= (@ _let_1 (@ (@ tptp.perm_name_name Pi2) X)) (@ (@ tptp.perm_name_name (@ (@ tptp.perm_n1160739829e_name Pi1) Pi2)) (@ _let_1 X))))))
% 0.27/0.72 (assert (forall ((Pi1 tptp.list_P227219501e_name) (Pi2 tptp.list_P227219501e_name) (X tptp.pi)) (let ((_let_1 (@ tptp.perm_name_pi Pi1))) (= (@ _let_1 (@ (@ tptp.perm_name_pi Pi2) X)) (@ (@ tptp.perm_name_pi (@ (@ tptp.perm_n1160739829e_name Pi1) Pi2)) (@ _let_1 X))))))
% 0.27/0.72 (assert (forall ((Pi2 tptp.list_P227219501e_name) (Pi1 tptp.list_P227219501e_name) (X tptp.late_subject)) (let ((_let_1 (@ tptp.perm_n1559866809ubject Pi2))) (= (@ _let_1 (@ (@ tptp.perm_n1559866809ubject Pi1) X)) (@ (@ tptp.perm_n1559866809ubject (@ (@ tptp.perm_n1160739829e_name Pi2) Pi1)) (@ _let_1 X))))))
% 0.27/0.72 (assert (forall ((Pi2 tptp.list_P227219501e_name) (Pi1 tptp.list_P227219501e_name) (X tptp.late_freeRes)) (let ((_let_1 (@ tptp.perm_n336613537reeRes Pi2))) (= (@ _let_1 (@ (@ tptp.perm_n336613537reeRes Pi1) X)) (@ (@ tptp.perm_n336613537reeRes (@ (@ tptp.perm_n1160739829e_name Pi2) Pi1)) (@ _let_1 X))))))
% 0.27/0.72 (assert (forall ((Pi2 tptp.list_P227219501e_name) (Pi1 tptp.list_P227219501e_name) (X tptp.pi_Rep)) (let ((_let_1 (@ tptp.perm_name_pi_Rep Pi2))) (= (@ _let_1 (@ (@ tptp.perm_name_pi_Rep Pi1) X)) (@ (@ tptp.perm_name_pi_Rep (@ (@ tptp.perm_n1160739829e_name Pi2) Pi1)) (@ _let_1 X))))))
% 0.27/0.72 (assert (forall ((Pi2 tptp.list_P227219501e_name) (Pi1 tptp.list_P227219501e_name) (X tptp.name)) (let ((_let_1 (@ tptp.perm_name_name Pi2))) (= (@ _let_1 (@ (@ tptp.perm_name_name Pi1) X)) (@ (@ tptp.perm_name_name (@ (@ tptp.perm_n1160739829e_name Pi2) Pi1)) (@ _let_1 X))))))
% 0.27/0.72 (assert (forall ((Pi2 tptp.list_P227219501e_name) (Pi1 tptp.list_P227219501e_name) (X tptp.pi)) (let ((_let_1 (@ tptp.perm_name_pi Pi2))) (= (@ _let_1 (@ (@ tptp.perm_name_pi Pi1) X)) (@ (@ tptp.perm_name_pi (@ (@ tptp.perm_n1160739829e_name Pi2) Pi1)) (@ _let_1 X))))))
% 0.27/0.72 (assert (forall ((Pi2 tptp.list_P227219501e_name) (Pi1 tptp.list_P227219501e_name) (X tptp.late_subject)) (let ((_let_1 (@ tptp.perm_n1559866809ubject Pi2))) (= (@ _let_1 (@ (@ tptp.perm_n1559866809ubject Pi1) X)) (@ (@ tptp.perm_n1559866809ubject (@ (@ tptp.perm_n1160739829e_name Pi2) Pi1)) (@ _let_1 X))))))
% 0.27/0.72 (assert (forall ((Pi2 tptp.list_P227219501e_name) (Pi1 tptp.list_P227219501e_name) (X tptp.late_freeRes)) (let ((_let_1 (@ tptp.perm_n336613537reeRes Pi2))) (= (@ _let_1 (@ (@ tptp.perm_n336613537reeRes Pi1) X)) (@ (@ tptp.perm_n336613537reeRes (@ (@ tptp.perm_n1160739829e_name Pi2) Pi1)) (@ _let_1 X))))))
% 0.27/0.72 (assert (forall ((Pi2 tptp.list_P227219501e_name) (Pi1 tptp.list_P227219501e_name) (X tptp.pi_Rep)) (let ((_let_1 (@ tptp.perm_name_pi_Rep Pi2))) (= (@ _let_1 (@ (@ tptp.perm_name_pi_Rep Pi1) X)) (@ (@ tptp.perm_name_pi_Rep (@ (@ tptp.perm_n1160739829e_name Pi2) Pi1)) (@ _let_1 X))))))
% 0.27/0.72 (assert (forall ((Pi2 tptp.list_P227219501e_name) (Pi1 tptp.list_P227219501e_name) (X tptp.name)) (let ((_let_1 (@ tptp.perm_name_name Pi2))) (= (@ _let_1 (@ (@ tptp.perm_name_name Pi1) X)) (@ (@ tptp.perm_name_name (@ (@ tptp.perm_n1160739829e_name Pi2) Pi1)) (@ _let_1 X))))))
% 0.27/0.72 (assert (forall ((Pi2 tptp.list_P227219501e_name) (Pi1 tptp.list_P227219501e_name) (X tptp.pi)) (let ((_let_1 (@ tptp.perm_name_pi Pi2))) (= (@ _let_1 (@ (@ tptp.perm_name_pi Pi1) X)) (@ (@ tptp.perm_name_pi (@ (@ tptp.perm_n1160739829e_name Pi2) Pi1)) (@ _let_1 X))))))
% 0.27/0.72 (assert (forall ((Pi tptp.list_P227219501e_name) (X tptp.late_subject) (Y4 tptp.late_subject)) (let ((_let_1 (@ tptp.perm_n1559866809ubject Pi))) (= (= (@ _let_1 X) (@ _let_1 Y4)) (= X Y4)))))
% 0.27/0.72 (assert (forall ((Pi tptp.list_P227219501e_name) (X tptp.late_freeRes) (Y4 tptp.late_freeRes)) (let ((_let_1 (@ tptp.perm_n336613537reeRes Pi))) (= (= (@ _let_1 X) (@ _let_1 Y4)) (= X Y4)))))
% 0.27/0.72 (assert (forall ((Pi tptp.list_P227219501e_name) (X tptp.pi_Rep) (Y4 tptp.pi_Rep)) (let ((_let_1 (@ tptp.perm_name_pi_Rep Pi))) (= (= (@ _let_1 X) (@ _let_1 Y4)) (= X Y4)))))
% 0.27/0.72 (assert (forall ((Pi tptp.list_P227219501e_name) (X tptp.name) (Y4 tptp.name)) (let ((_let_1 (@ tptp.perm_name_name Pi))) (= (= (@ _let_1 X) (@ _let_1 Y4)) (= X Y4)))))
% 0.27/0.72 (assert (forall ((Pi tptp.list_P227219501e_name) (X tptp.pi) (Y4 tptp.pi)) (let ((_let_1 (@ tptp.perm_name_pi Pi))) (= (= (@ _let_1 X) (@ _let_1 Y4)) (= X Y4)))))
% 0.27/0.72 (assert (forall ((Pi tptp.list_P227219501e_name) (F (-> tptp.late_subject tptp.late_subject)) (X tptp.late_subject)) (let ((_let_1 (@ tptp.perm_n1559866809ubject Pi))) (= (@ _let_1 (@ F X)) (@ (@ (@ tptp.perm_n1447856217ubject Pi) F) (@ _let_1 X))))))
% 0.27/0.72 (assert (forall ((Pi tptp.list_P227219501e_name) (F (-> tptp.late_freeRes tptp.late_subject)) (X tptp.late_freeRes)) (= (@ (@ tptp.perm_n1559866809ubject Pi) (@ F X)) (@ (@ (@ tptp.perm_n303101761ubject Pi) F) (@ (@ tptp.perm_n336613537reeRes Pi) X)))))
% 0.27/0.72 (assert (forall ((Pi tptp.list_P227219501e_name) (F (-> tptp.pi_Rep tptp.late_subject)) (X tptp.pi_Rep)) (= (@ (@ tptp.perm_n1559866809ubject Pi) (@ F X)) (@ (@ (@ tptp.perm_n698371375ubject Pi) F) (@ (@ tptp.perm_name_pi_Rep Pi) X)))))
% 0.27/0.72 (assert (forall ((Pi tptp.list_P227219501e_name) (F (-> tptp.name tptp.late_subject)) (X tptp.name)) (= (@ (@ tptp.perm_n1559866809ubject Pi) (@ F X)) (@ (@ (@ tptp.perm_n1387060402ubject Pi) F) (@ (@ tptp.perm_name_name Pi) X)))))
% 0.27/0.73 (assert (forall ((Pi tptp.list_P227219501e_name) (F (-> tptp.pi tptp.late_subject)) (X tptp.pi)) (= (@ (@ tptp.perm_n1559866809ubject Pi) (@ F X)) (@ (@ (@ tptp.perm_n190055296ubject Pi) F) (@ (@ tptp.perm_name_pi Pi) X)))))
% 0.27/0.73 (assert (forall ((Pi tptp.list_P227219501e_name) (F (-> tptp.late_subject tptp.late_freeRes)) (X tptp.late_subject)) (= (@ (@ tptp.perm_n336613537reeRes Pi) (@ F X)) (@ (@ (@ tptp.perm_n443561793reeRes Pi) F) (@ (@ tptp.perm_n1559866809ubject Pi) X)))))
% 0.27/0.73 (assert (forall ((Pi tptp.list_P227219501e_name) (F (-> tptp.late_freeRes tptp.late_freeRes)) (X tptp.late_freeRes)) (let ((_let_1 (@ tptp.perm_n336613537reeRes Pi))) (= (@ _let_1 (@ F X)) (@ (@ (@ tptp.perm_n1446290985reeRes Pi) F) (@ _let_1 X))))))
% 0.27/0.73 (assert (forall ((Pi tptp.list_P227219501e_name) (F (-> tptp.pi_Rep tptp.late_freeRes)) (X tptp.pi_Rep)) (= (@ (@ tptp.perm_n336613537reeRes Pi) (@ F X)) (@ (@ (@ tptp.perm_n1841560599reeRes Pi) F) (@ (@ tptp.perm_name_pi_Rep Pi) X)))))
% 0.27/0.73 (assert (forall ((Pi tptp.list_P227219501e_name) (F (-> tptp.name tptp.late_freeRes)) (X tptp.name)) (= (@ (@ tptp.perm_n336613537reeRes Pi) (@ F X)) (@ (@ (@ tptp.perm_n382765978reeRes Pi) F) (@ (@ tptp.perm_name_name Pi) X)))))
% 0.27/0.73 (assert (forall ((Pi tptp.list_P227219501e_name) (F (-> tptp.pi tptp.late_freeRes)) (X tptp.pi)) (= (@ (@ tptp.perm_n336613537reeRes Pi) (@ F X)) (@ (@ (@ tptp.perm_n1333244520reeRes Pi) F) (@ (@ tptp.perm_name_pi Pi) X)))))
% 0.27/0.73 (assert (forall ((Pi tptp.list_P227219501e_name) (X tptp.product_prod_pi_pi) (X3 tptp.set_Pr1834926343_pi_pi)) (= (@ (@ tptp.perm_name_o Pi) (@ (@ tptp.member558706512_pi_pi X) X3)) (@ (@ tptp.member558706512_pi_pi (@ (@ tptp.perm_n1415585007_pi_pi Pi) X)) (@ (@ tptp.perm_n675238095_pi_pi Pi) X3)))))
% 0.27/0.73 (assert (forall ((Pi tptp.list_P227219501e_name) (X tptp.late_subject) (X3 tptp.set_Late_subject)) (= (@ (@ tptp.perm_name_o Pi) (@ (@ tptp.member_Late_subject X) X3)) (@ (@ tptp.member_Late_subject (@ (@ tptp.perm_n1559866809ubject Pi) X)) (@ (@ tptp.perm_n412725103ubject Pi) X3)))))
% 0.27/0.73 (assert (forall ((Pi tptp.list_P227219501e_name) (X tptp.late_freeRes) (X3 tptp.set_Late_freeRes)) (= (@ (@ tptp.perm_name_o Pi) (@ (@ tptp.member_Late_freeRes X) X3)) (@ (@ tptp.member_Late_freeRes (@ (@ tptp.perm_n336613537reeRes Pi) X)) (@ (@ tptp.perm_n1555914327reeRes Pi) X3)))))
% 0.27/0.73 (assert (forall ((Pi tptp.list_P227219501e_name) (X tptp.pi_Rep) (X3 tptp.set_pi_Rep)) (= (@ (@ tptp.perm_name_o Pi) (@ (@ tptp.member_pi_Rep X) X3)) (@ (@ tptp.member_pi_Rep (@ (@ tptp.perm_name_pi_Rep Pi) X)) (@ (@ tptp.perm_name_set_pi_Rep Pi) X3)))))
% 0.27/0.73 (assert (forall ((Pi tptp.list_P227219501e_name) (X tptp.name) (X3 tptp.set_name)) (= (@ (@ tptp.perm_name_o Pi) (@ (@ tptp.member_name X) X3)) (@ (@ tptp.member_name (@ (@ tptp.perm_name_name Pi) X)) (@ (@ tptp.perm_name_set_name Pi) X3)))))
% 0.27/0.73 (assert (forall ((Pi tptp.list_P227219501e_name) (X tptp.pi) (X3 tptp.set_pi)) (= (@ (@ tptp.perm_name_o Pi) (@ (@ tptp.member_pi X) X3)) (@ (@ tptp.member_pi (@ (@ tptp.perm_name_pi Pi) X)) (@ (@ tptp.perm_name_set_pi Pi) X3)))))
% 0.27/0.73 (assert (forall ((Pi tptp.list_P227219501e_name) (X tptp.late_subject) (Y4 tptp.late_subject)) (let ((_let_1 (@ tptp.perm_n1559866809ubject Pi))) (= (@ (@ tptp.perm_name_o Pi) (= X Y4)) (= (@ _let_1 X) (@ _let_1 Y4))))))
% 0.27/0.73 (assert (forall ((Pi tptp.list_P227219501e_name) (X tptp.late_freeRes) (Y4 tptp.late_freeRes)) (let ((_let_1 (@ tptp.perm_n336613537reeRes Pi))) (= (@ (@ tptp.perm_name_o Pi) (= X Y4)) (= (@ _let_1 X) (@ _let_1 Y4))))))
% 0.27/0.73 (assert (forall ((Pi tptp.list_P227219501e_name) (X tptp.pi_Rep) (Y4 tptp.pi_Rep)) (let ((_let_1 (@ tptp.perm_name_pi_Rep Pi))) (= (@ (@ tptp.perm_name_o Pi) (= X Y4)) (= (@ _let_1 X) (@ _let_1 Y4))))))
% 0.27/0.73 (assert (forall ((Pi tptp.list_P227219501e_name) (X tptp.name) (Y4 tptp.name)) (let ((_let_1 (@ tptp.perm_name_name Pi))) (= (@ (@ tptp.perm_name_o Pi) (= X Y4)) (= (@ _let_1 X) (@ _let_1 Y4))))))
% 0.27/0.73 (assert (forall ((Pi tptp.list_P227219501e_name) (X tptp.pi) (Y4 tptp.pi)) (let ((_let_1 (@ tptp.perm_name_pi Pi))) (= (@ (@ tptp.perm_name_o Pi) (= X Y4)) (= (@ _let_1 X) (@ _let_1 Y4))))))
% 0.27/0.73 (assert (forall ((P2 (-> (-> tptp.produc367475239e_name tptp.produc367475239e_name) tptp.list_P227219501e_name tptp.list_P227219501e_name Bool)) (A0 (-> tptp.produc367475239e_name tptp.produc367475239e_name)) (A1 tptp.list_P227219501e_name) (A22 tptp.list_P227219501e_name)) (=> (forall ((F2 (-> tptp.produc367475239e_name tptp.produc367475239e_name)) (X_1 tptp.list_P227219501e_name)) (@ (@ (@ P2 F2) tptp.nil_Pr743626285e_name) X_1)) (=> (forall ((F2 (-> tptp.produc367475239e_name tptp.produc367475239e_name)) (A3 tptp.produc367475239e_name) (As tptp.list_P227219501e_name) (Bs tptp.list_P227219501e_name)) (let ((_let_1 (@ P2 F2))) (=> (@ (@ _let_1 As) (@ (@ tptp.cons_P1213805021e_name (@ F2 A3)) Bs)) (@ (@ _let_1 (@ (@ tptp.cons_P1213805021e_name A3) As)) Bs)))) (@ (@ (@ P2 A0) A1) A22)))))
% 0.27/0.73 (assert (forall ((Xs2 tptp.list_P227219501e_name) (P2 (-> tptp.list_P227219501e_name Bool))) (=> (not (= Xs2 tptp.nil_Pr743626285e_name)) (=> (forall ((X4 tptp.produc367475239e_name)) (@ P2 (@ (@ tptp.cons_P1213805021e_name X4) tptp.nil_Pr743626285e_name))) (=> (forall ((X4 tptp.produc367475239e_name) (Xs tptp.list_P227219501e_name)) (=> (not (= Xs tptp.nil_Pr743626285e_name)) (=> (@ P2 Xs) (@ P2 (@ (@ tptp.cons_P1213805021e_name X4) Xs))))) (@ P2 Xs2))))))
% 0.27/0.73 (assert (forall ((P2 (-> (-> tptp.produc367475239e_name tptp.produc367475239e_name Bool) tptp.list_P227219501e_name Bool)) (A0 (-> tptp.produc367475239e_name tptp.produc367475239e_name Bool)) (A1 tptp.list_P227219501e_name)) (=> (forall ((P (-> tptp.produc367475239e_name tptp.produc367475239e_name Bool))) (@ (@ P2 P) tptp.nil_Pr743626285e_name)) (=> (forall ((P (-> tptp.produc367475239e_name tptp.produc367475239e_name Bool)) (X4 tptp.produc367475239e_name)) (@ (@ P2 P) (@ (@ tptp.cons_P1213805021e_name X4) tptp.nil_Pr743626285e_name))) (=> (forall ((P (-> tptp.produc367475239e_name tptp.produc367475239e_name Bool)) (X4 tptp.produc367475239e_name) (Y3 tptp.produc367475239e_name) (Xs tptp.list_P227219501e_name)) (let ((_let_1 (@ (@ tptp.cons_P1213805021e_name Y3) Xs))) (let ((_let_2 (@ P2 P))) (=> (@ _let_2 _let_1) (@ _let_2 (@ (@ tptp.cons_P1213805021e_name X4) _let_1)))))) (@ (@ P2 A0) A1))))))
% 0.27/0.73 (assert (forall ((P2 (-> tptp.list_P227219501e_name Bool)) (A0 tptp.list_P227219501e_name)) (=> (@ P2 tptp.nil_Pr743626285e_name) (=> (forall ((X4 tptp.produc367475239e_name)) (@ P2 (@ (@ tptp.cons_P1213805021e_name X4) tptp.nil_Pr743626285e_name))) (=> (forall ((X4 tptp.produc367475239e_name) (Y3 tptp.produc367475239e_name) (Xs tptp.list_P227219501e_name)) (let ((_let_1 (@ (@ tptp.cons_P1213805021e_name Y3) Xs))) (let ((_let_2 (@ tptp.cons_P1213805021e_name X4))) (let ((_let_3 (= X4 Y3))) (=> (=> _let_3 (@ P2 (@ _let_2 Xs))) (=> (=> (not _let_3) (@ P2 _let_1)) (@ P2 (@ _let_2 _let_1)))))))) (@ P2 A0))))))
% 0.27/0.73 (assert (forall ((P2 (-> (-> tptp.produc367475239e_name tptp.produc367475239e_name Bool) tptp.list_P227219501e_name Bool)) (A0 (-> tptp.produc367475239e_name tptp.produc367475239e_name Bool)) (A1 tptp.list_P227219501e_name)) (=> (forall ((P (-> tptp.produc367475239e_name tptp.produc367475239e_name Bool))) (@ (@ P2 P) tptp.nil_Pr743626285e_name)) (=> (forall ((P (-> tptp.produc367475239e_name tptp.produc367475239e_name Bool)) (X4 tptp.produc367475239e_name) (Ys tptp.list_P227219501e_name)) (let ((_let_1 (@ P2 P))) (=> (@ _let_1 Ys) (@ _let_1 (@ (@ tptp.cons_P1213805021e_name X4) Ys))))) (@ (@ P2 A0) A1)))))
% 0.27/0.73 (assert (forall ((X tptp.list_P227219501e_name)) (=> (not (= X tptp.nil_Pr743626285e_name)) (=> (forall ((X4 tptp.produc367475239e_name)) (not (= X (@ (@ tptp.cons_P1213805021e_name X4) tptp.nil_Pr743626285e_name)))) (not (forall ((X4 tptp.produc367475239e_name) (Y3 tptp.produc367475239e_name) (Xs tptp.list_P227219501e_name)) (not (= X (@ (@ tptp.cons_P1213805021e_name X4) (@ (@ tptp.cons_P1213805021e_name Y3) Xs))))))))))
% 0.27/0.73 (assert (forall ((X tptp.list_l1406151091e_name)) (=> (not (= X tptp.nil_li29751603e_name)) (=> (forall ((Xss tptp.list_l1406151091e_name)) (not (= X (@ (@ tptp.cons_l798145763e_name tptp.nil_Pr743626285e_name) Xss)))) (not (forall ((X4 tptp.produc367475239e_name) (Xs tptp.list_P227219501e_name) (Xss tptp.list_l1406151091e_name)) (not (= X (@ (@ tptp.cons_l798145763e_name (@ (@ tptp.cons_P1213805021e_name X4) Xs)) Xss)))))))))
% 0.27/0.73 (assert (forall ((P2 (-> tptp.list_P227219501e_name tptp.list_P227219501e_name Bool)) (A0 tptp.list_P227219501e_name) (A1 tptp.list_P227219501e_name)) (=> (forall ((X_1 tptp.list_P227219501e_name)) (@ (@ P2 tptp.nil_Pr743626285e_name) X_1)) (=> (forall ((Xs tptp.list_P227219501e_name)) (@ (@ P2 Xs) tptp.nil_Pr743626285e_name)) (=> (forall ((X4 tptp.produc367475239e_name) (Xs tptp.list_P227219501e_name) (Y3 tptp.produc367475239e_name) (Ys tptp.list_P227219501e_name)) (let ((_let_1 (@ (@ tptp.cons_P1213805021e_name Y3) Ys))) (let ((_let_2 (@ P2 (@ (@ tptp.cons_P1213805021e_name X4) Xs)))) (=> (@ (@ P2 Xs) _let_1) (=> (@ _let_2 Ys) (@ _let_2 _let_1)))))) (@ (@ P2 A0) A1))))))
% 0.27/0.73 (assert (forall ((P2 (-> tptp.list_P227219501e_name Bool)) (Xs2 tptp.list_P227219501e_name)) (=> (@ P2 tptp.nil_Pr743626285e_name) (=> (forall ((X4 tptp.produc367475239e_name)) (@ P2 (@ (@ tptp.cons_P1213805021e_name X4) tptp.nil_Pr743626285e_name))) (=> (forall ((X4 tptp.produc367475239e_name) (Y3 tptp.produc367475239e_name) (Zs tptp.list_P227219501e_name)) (let ((_let_1 (@ (@ tptp.cons_P1213805021e_name Y3) Zs))) (=> (@ P2 Zs) (=> (@ P2 _let_1) (@ P2 (@ (@ tptp.cons_P1213805021e_name X4) _let_1)))))) (@ P2 Xs2))))))
% 0.27/0.73 (assert (forall ((P2 (-> tptp.list_P227219501e_name tptp.list_P227219501e_name Bool)) (A0 tptp.list_P227219501e_name) (A1 tptp.list_P227219501e_name)) (=> (forall ((X_1 tptp.list_P227219501e_name)) (@ (@ P2 tptp.nil_Pr743626285e_name) X_1)) (=> (forall ((X4 tptp.produc367475239e_name) (Xs tptp.list_P227219501e_name) (Ys tptp.list_P227219501e_name)) (=> (@ (@ P2 Ys) Xs) (@ (@ P2 (@ (@ tptp.cons_P1213805021e_name X4) Xs)) Ys))) (@ (@ P2 A0) A1)))))
% 0.27/0.73 (assert (forall ((P2 (-> tptp.list_P227219501e_name tptp.list_P227219501e_name Bool)) (Xs2 tptp.list_P227219501e_name) (Ys2 tptp.list_P227219501e_name)) (=> (@ (@ P2 tptp.nil_Pr743626285e_name) tptp.nil_Pr743626285e_name) (=> (forall ((X4 tptp.produc367475239e_name) (Xs tptp.list_P227219501e_name)) (@ (@ P2 (@ (@ tptp.cons_P1213805021e_name X4) Xs)) tptp.nil_Pr743626285e_name)) (=> (forall ((Y3 tptp.produc367475239e_name) (Ys tptp.list_P227219501e_name)) (@ (@ P2 tptp.nil_Pr743626285e_name) (@ (@ tptp.cons_P1213805021e_name Y3) Ys))) (=> (forall ((X4 tptp.produc367475239e_name) (Xs tptp.list_P227219501e_name) (Y3 tptp.produc367475239e_name) (Ys tptp.list_P227219501e_name)) (=> (@ (@ P2 Xs) Ys) (@ (@ P2 (@ (@ tptp.cons_P1213805021e_name X4) Xs)) (@ (@ tptp.cons_P1213805021e_name Y3) Ys)))) (@ (@ P2 Xs2) Ys2)))))))
% 0.27/0.73 (assert (forall ((Xs2 tptp.list_P227219501e_name)) (= (not (= Xs2 tptp.nil_Pr743626285e_name)) (exists ((Y5 tptp.produc367475239e_name) (Ys3 tptp.list_P227219501e_name)) (= Xs2 (@ (@ tptp.cons_P1213805021e_name Y5) Ys3))))))
% 0.27/0.73 (assert (forall ((P2 (-> tptp.list_P227219501e_name Bool)) (List tptp.list_P227219501e_name)) (=> (@ P2 tptp.nil_Pr743626285e_name) (=> (forall ((X12 tptp.produc367475239e_name) (X23 tptp.list_P227219501e_name)) (=> (@ P2 X23) (@ P2 (@ (@ tptp.cons_P1213805021e_name X12) X23)))) (@ P2 List)))))
% 0.27/0.73 (assert (forall ((Y4 tptp.list_P227219501e_name)) (=> (not (= Y4 tptp.nil_Pr743626285e_name)) (not (forall ((X212 tptp.produc367475239e_name) (X222 tptp.list_P227219501e_name)) (not (= Y4 (@ (@ tptp.cons_P1213805021e_name X212) X222))))))))
% 0.27/0.73 (assert (forall ((List tptp.list_P227219501e_name) (X21 tptp.produc367475239e_name) (X22 tptp.list_P227219501e_name)) (=> (= List (@ (@ tptp.cons_P1213805021e_name X21) X22)) (not (= List tptp.nil_Pr743626285e_name)))))
% 0.27/0.73 (assert (forall ((X21 tptp.produc367475239e_name) (X22 tptp.list_P227219501e_name)) (not (= tptp.nil_Pr743626285e_name (@ (@ tptp.cons_P1213805021e_name X21) X22)))))
% 0.27/0.73 (assert (@ (@ tptp.fresh_name_pi tptp.y) tptp.q))
% 0.27/0.73 (assert (forall ((A tptp.name) (B tptp.name)) (= (@ (@ tptp.member695284560e_name (@ (@ tptp.produc1570949143e_name A) B)) tptp.id_name) (= A B))))
% 0.27/0.73 (assert (forall ((A tptp.pi) (B tptp.pi)) (= (@ (@ tptp.member558706512_pi_pi (@ (@ tptp.product_Pair_pi_pi A) B)) tptp.id_pi) (= A B))))
% 0.27/0.73 (assert (forall ((A tptp.name)) (@ (@ tptp.member695284560e_name (@ (@ tptp.produc1570949143e_name A) A)) tptp.id_name)))
% 0.27/0.73 (assert (forall ((A tptp.pi)) (@ (@ tptp.member558706512_pi_pi (@ (@ tptp.product_Pair_pi_pi A) A)) tptp.id_pi)))
% 0.27/0.73 (assert (forall ((A tptp.name) (X tptp.late_subject) (Y4 tptp.late_subject)) (let ((_let_1 (@ tptp.fresh_717452603ubject A))) (= (@ (@ tptp.fresh_495373993ubject A) (@ (@ tptp.produc1465345179ubject X) Y4)) (and (@ _let_1 X) (@ _let_1 Y4))))))
% 0.27/0.73 (assert (forall ((A tptp.name) (X tptp.late_subject) (Y4 tptp.late_freeRes)) (= (@ (@ tptp.fresh_1638563217reeRes A) (@ (@ tptp.produc242091907reeRes X) Y4)) (and (@ (@ tptp.fresh_717452603ubject A) X) (@ (@ tptp.fresh_1641682979reeRes A) Y4)))))
% 0.27/0.73 (assert (forall ((A tptp.name) (X tptp.late_subject) (Y4 tptp.name)) (= (@ (@ tptp.fresh_1953561446t_name A) (@ (@ tptp.produc1647375838t_name X) Y4)) (and (@ (@ tptp.fresh_717452603ubject A) X) (@ (@ tptp.fresh_name_name A) Y4)))))
% 0.27/0.73 (assert (forall ((A tptp.name) (X tptp.late_subject) (Y4 tptp.pi)) (= (@ (@ tptp.fresh_994896692ect_pi A) (@ (@ tptp.produc324947500ect_pi X) Y4)) (and (@ (@ tptp.fresh_717452603ubject A) X) (@ (@ tptp.fresh_name_pi A) Y4)))))
% 0.27/0.73 (assert (forall ((A tptp.name) (X tptp.late_freeRes) (Y4 tptp.late_subject)) (= (@ (@ tptp.fresh_1498103185ubject A) (@ (@ tptp.produc320590723ubject X) Y4)) (and (@ (@ tptp.fresh_1641682979reeRes A) X) (@ (@ tptp.fresh_717452603ubject A) Y4)))))
% 0.27/0.73 (assert (forall ((A tptp.name) (X tptp.late_freeRes) (Y4 tptp.late_freeRes)) (let ((_let_1 (@ tptp.fresh_1641682979reeRes A))) (= (@ (@ tptp.fresh_493808761reeRes A) (@ (@ tptp.produc1244821099reeRes X) Y4)) (and (@ _let_1 X) (@ _let_1 Y4))))))
% 0.27/0.73 (assert (forall ((A tptp.name) (X tptp.late_freeRes) (Y4 tptp.name)) (= (@ (@ tptp.fresh_2007541374s_name A) (@ (@ tptp.produc1701355766s_name X) Y4)) (and (@ (@ tptp.fresh_1641682979reeRes A) X) (@ (@ tptp.fresh_name_name A) Y4)))))
% 0.27/0.73 (assert (forall ((A tptp.name) (X tptp.late_freeRes) (Y4 tptp.pi)) (= (@ (@ tptp.fresh_1847501388Res_pi A) (@ (@ tptp.produc1177552196Res_pi X) Y4)) (and (@ (@ tptp.fresh_1641682979reeRes A) X) (@ (@ tptp.fresh_name_pi A) Y4)))))
% 0.27/0.73 (assert (forall ((A tptp.name) (X tptp.name) (Y4 tptp.late_subject)) (= (@ (@ tptp.fresh_820177506ubject A) (@ (@ tptp.produc607574050ubject X) Y4)) (and (@ (@ tptp.fresh_name_name A) X) (@ (@ tptp.fresh_717452603ubject A) Y4)))))
% 0.27/0.73 (assert (forall ((A tptp.name) (X tptp.name) (Y4 tptp.late_freeRes)) (= (@ (@ tptp.fresh_1963366730reeRes A) (@ (@ tptp.produc1531804426reeRes X) Y4)) (and (@ (@ tptp.fresh_name_name A) X) (@ (@ tptp.fresh_1641682979reeRes A) Y4)))))
% 0.27/0.73 (assert (@ (@ tptp.fresh_name_pi tptp.y) tptp.p))
% 0.27/0.73 (assert (forall ((Rel tptp.set_Pr1834926343_pi_pi) (P2 tptp.pi) (A tptp.late_subject) (X tptp.name)) (=> (@ (@ tptp.ord_le630093991_pi_pi tptp.id_pi) Rel) (@ (@ (@ (@ (@ tptp.strong2129052853vative P2) P2) A) X) Rel))))
% 0.27/0.73 (assert (forall ((P2 tptp.pi) (Q tptp.pi) (A tptp.late_subject) (X tptp.name) (Rel tptp.set_Pr1834926343_pi_pi) (Perm tptp.list_P227219501e_name)) (let ((_let_1 (@ tptp.perm_name_pi Perm))) (=> (@ (@ (@ (@ (@ tptp.strong2129052853vative P2) Q) A) X) Rel) (=> (@ tptp.eqvt_pi Rel) (@ (@ (@ (@ (@ tptp.strong2129052853vative (@ _let_1 P2)) (@ _let_1 Q)) (@ (@ tptp.perm_n1559866809ubject Perm) A)) (@ (@ tptp.perm_name_name Perm) X)) Rel))))))
% 0.27/0.73 (assert (forall ((P2 tptp.pi) (Q tptp.pi) (A tptp.late_subject) (X tptp.name) (Rel tptp.set_Pr1834926343_pi_pi) (Perm tptp.list_P227219501e_name)) (let ((_let_1 (@ tptp.perm_name_pi Perm))) (=> (@ (@ (@ (@ (@ tptp.strong2129052853vative P2) Q) A) X) Rel) (=> (@ tptp.eqvt_pi Rel) (@ (@ (@ (@ (@ tptp.strong2129052853vative (@ _let_1 P2)) (@ _let_1 Q)) A) (@ (@ tptp.perm_name_name Perm) X)) Rel))))))
% 0.27/0.73 (assert (forall ((Rel tptp.set_Pr806375235ubject) (P2 tptp.late_subject) (Q tptp.late_subject) (Perm tptp.list_P227219501e_name)) (let ((_let_1 (@ tptp.perm_n1559866809ubject Perm))) (=> (@ tptp.eqvt_Late_subject Rel) (=> (@ (@ tptp.member1586545036ubject (@ (@ tptp.produc1465345179ubject P2) Q)) Rel) (@ (@ tptp.member1586545036ubject (@ (@ tptp.produc1465345179ubject (@ _let_1 P2)) (@ _let_1 Q))) Rel))))))
% 0.27/0.73 (assert (forall ((Rel tptp.set_Pr1780909331reeRes) (P2 tptp.late_freeRes) (Q tptp.late_freeRes) (Perm tptp.list_P227219501e_name)) (let ((_let_1 (@ tptp.perm_n336613537reeRes Perm))) (=> (@ tptp.eqvt_Late_freeRes Rel) (=> (@ (@ tptp.member1584979804reeRes (@ (@ tptp.produc1244821099reeRes P2) Q)) Rel) (@ (@ tptp.member1584979804reeRes (@ (@ tptp.produc1244821099reeRes (@ _let_1 P2)) (@ _let_1 Q))) Rel))))))
% 0.27/0.73 (assert (forall ((Rel tptp.set_Pr1131282415pi_Rep) (P2 tptp.pi_Rep) (Q tptp.pi_Rep) (Perm tptp.list_P227219501e_name)) (let ((_let_1 (@ tptp.perm_name_pi_Rep Perm))) (=> (@ tptp.eqvt_pi_Rep Rel) (=> (@ (@ tptp.member1671908408pi_Rep (@ (@ tptp.produc784048711pi_Rep P2) Q)) Rel) (@ (@ tptp.member1671908408pi_Rep (@ (@ tptp.produc784048711pi_Rep (@ _let_1 P2)) (@ _let_1 Q))) Rel))))))
% 0.27/0.73 (assert (forall ((Rel tptp.set_Pr443758855e_name) (P2 tptp.name) (Q tptp.name) (Perm tptp.list_P227219501e_name)) (let ((_let_1 (@ tptp.perm_name_name Perm))) (=> (@ tptp.eqvt_name Rel) (=> (@ (@ tptp.member695284560e_name (@ (@ tptp.produc1570949143e_name P2) Q)) Rel) (@ (@ tptp.member695284560e_name (@ (@ tptp.produc1570949143e_name (@ _let_1 P2)) (@ _let_1 Q))) Rel))))))
% 0.27/0.73 (assert (forall ((Rel tptp.set_Pr1834926343_pi_pi) (P2 tptp.pi) (Q tptp.pi) (Perm tptp.list_P227219501e_name)) (let ((_let_1 (@ tptp.perm_name_pi Perm))) (=> (@ tptp.eqvt_pi Rel) (=> (@ (@ tptp.member558706512_pi_pi (@ (@ tptp.product_Pair_pi_pi P2) Q)) Rel) (@ (@ tptp.member558706512_pi_pi (@ (@ tptp.product_Pair_pi_pi (@ _let_1 P2)) (@ _let_1 Q))) Rel))))))
% 0.27/0.73 (assert (@ (@ tptp.fresh_1376661020_pi_pi tptp.y) (@ (@ tptp.produc235456326_pi_pi tptp.x) (@ (@ tptp.product_Pair_pi_pi tptp.p) tptp.q))))
% 0.27/0.73 (assert (forall ((A tptp.name) (X1 tptp.name)) (= (@ (@ tptp.fresh_717452603ubject A) (@ tptp.late_BoundOutputS X1)) (@ (@ tptp.fresh_name_name A) X1))))
% 0.27/0.73 (assert (forall ((Pi tptp.list_P227219501e_name) (X tptp.name) (Y4 tptp.name)) (let ((_let_1 (@ tptp.perm_name_name Pi))) (= (= (@ _let_1 X) (@ _let_1 Y4)) (= X Y4)))))
% 0.27/0.73 (assert (forall ((P2 (-> tptp.list_P227219501e_name Bool))) (=> (forall ((X_1 tptp.list_P227219501e_name)) (@ P2 X_1)) (@ P2 tptp.nil_Pr743626285e_name))))
% 0.27/0.73 (assert (forall ((Pi tptp.list_P227219501e_name) (B Bool) (C1 tptp.late_subject) (C22 tptp.late_subject)) (let ((_let_1 (@ tptp.perm_n1559866809ubject Pi))) (let ((_let_2 (@ _let_1 (@ (@ (@ tptp.if_Late_subject B) C1) C22)))) (let ((_let_3 (@ (@ tptp.perm_name_o Pi) B))) (and (=> _let_3 (= _let_2 (@ _let_1 C1))) (=> (not _let_3) (= _let_2 (@ _let_1 C22)))))))))
% 0.27/0.73 (assert (forall ((Pi tptp.list_P227219501e_name) (B Bool) (C1 tptp.late_freeRes) (C22 tptp.late_freeRes)) (let ((_let_1 (@ tptp.perm_n336613537reeRes Pi))) (let ((_let_2 (@ _let_1 (@ (@ (@ tptp.if_Late_freeRes B) C1) C22)))) (let ((_let_3 (@ (@ tptp.perm_name_o Pi) B))) (and (=> _let_3 (= _let_2 (@ _let_1 C1))) (=> (not _let_3) (= _let_2 (@ _let_1 C22)))))))))
% 0.27/0.73 (assert (forall ((Pi tptp.list_P227219501e_name) (B Bool) (C1 tptp.pi_Rep) (C22 tptp.pi_Rep)) (let ((_let_1 (@ tptp.perm_name_pi_Rep Pi))) (let ((_let_2 (@ _let_1 (@ (@ (@ tptp.if_pi_Rep B) C1) C22)))) (let ((_let_3 (@ (@ tptp.perm_name_o Pi) B))) (and (=> _let_3 (= _let_2 (@ _let_1 C1))) (=> (not _let_3) (= _let_2 (@ _let_1 C22)))))))))
% 0.27/0.73 (assert (forall ((Pi tptp.list_P227219501e_name) (B Bool) (C1 tptp.name) (C22 tptp.name)) (let ((_let_1 (@ tptp.perm_name_name Pi))) (let ((_let_2 (@ _let_1 (@ (@ (@ tptp.if_name B) C1) C22)))) (let ((_let_3 (@ (@ tptp.perm_name_o Pi) B))) (and (=> _let_3 (= _let_2 (@ _let_1 C1))) (=> (not _let_3) (= _let_2 (@ _let_1 C22)))))))))
% 0.27/0.73 (assert (forall ((Pi tptp.list_P227219501e_name) (B Bool) (C1 tptp.pi) (C22 tptp.pi)) (let ((_let_1 (@ tptp.perm_name_pi Pi))) (let ((_let_2 (@ _let_1 (@ (@ (@ tptp.if_pi B) C1) C22)))) (let ((_let_3 (@ (@ tptp.perm_name_o Pi) B))) (and (=> _let_3 (= _let_2 (@ _let_1 C1))) (=> (not _let_3) (= _let_2 (@ _let_1 C22)))))))))
% 0.27/0.73 (assert (forall ((X tptp.late_subject) (Y4 tptp.late_subject) (Pi tptp.list_P227219501e_name)) (let ((_let_1 (@ tptp.perm_n1559866809ubject Pi))) (=> (= X Y4) (= (@ _let_1 X) (@ _let_1 Y4))))))
% 0.27/0.73 (assert (forall ((X tptp.late_freeRes) (Y4 tptp.late_freeRes) (Pi tptp.list_P227219501e_name)) (let ((_let_1 (@ tptp.perm_n336613537reeRes Pi))) (=> (= X Y4) (= (@ _let_1 X) (@ _let_1 Y4))))))
% 0.27/0.73 (assert (forall ((X tptp.pi_Rep) (Y4 tptp.pi_Rep) (Pi tptp.list_P227219501e_name)) (let ((_let_1 (@ tptp.perm_name_pi_Rep Pi))) (=> (= X Y4) (= (@ _let_1 X) (@ _let_1 Y4))))))
% 0.27/0.73 (assert (forall ((X tptp.name) (Y4 tptp.name) (Pi tptp.list_P227219501e_name)) (let ((_let_1 (@ tptp.perm_name_name Pi))) (=> (= X Y4) (= (@ _let_1 X) (@ _let_1 Y4))))))
% 0.27/0.73 (assert (forall ((X tptp.pi) (Y4 tptp.pi) (Pi tptp.list_P227219501e_name)) (let ((_let_1 (@ tptp.perm_name_pi Pi))) (=> (= X Y4) (= (@ _let_1 X) (@ _let_1 Y4))))))
% 0.27/0.73 (assert (forall ((C2 Bool) (Pi tptp.list_P227219501e_name) (X tptp.late_subject) (Y4 tptp.late_subject)) (let ((_let_1 (@ tptp.perm_n1559866809ubject Pi))) (let ((_let_2 (@ _let_1 (@ (@ (@ tptp.if_Late_subject C2) X) Y4)))) (and (=> C2 (= _let_2 (@ _let_1 X))) (=> (not C2) (= _let_2 (@ _let_1 Y4))))))))
% 0.27/0.73 (assert (forall ((C2 Bool) (Pi tptp.list_P227219501e_name) (X tptp.late_freeRes) (Y4 tptp.late_freeRes)) (let ((_let_1 (@ tptp.perm_n336613537reeRes Pi))) (let ((_let_2 (@ _let_1 (@ (@ (@ tptp.if_Late_freeRes C2) X) Y4)))) (and (=> C2 (= _let_2 (@ _let_1 X))) (=> (not C2) (= _let_2 (@ _let_1 Y4))))))))
% 0.27/0.73 (assert (forall ((C2 Bool) (Pi tptp.list_P227219501e_name) (X tptp.pi_Rep) (Y4 tptp.pi_Rep)) (let ((_let_1 (@ tptp.perm_name_pi_Rep Pi))) (let ((_let_2 (@ _let_1 (@ (@ (@ tptp.if_pi_Rep C2) X) Y4)))) (and (=> C2 (= _let_2 (@ _let_1 X))) (=> (not C2) (= _let_2 (@ _let_1 Y4))))))))
% 0.27/0.73 (assert (forall ((C2 Bool) (Pi tptp.list_P227219501e_name) (X tptp.name) (Y4 tptp.name)) (let ((_let_1 (@ tptp.perm_name_name Pi))) (let ((_let_2 (@ _let_1 (@ (@ (@ tptp.if_name C2) X) Y4)))) (and (=> C2 (= _let_2 (@ _let_1 X))) (=> (not C2) (= _let_2 (@ _let_1 Y4))))))))
% 0.27/0.73 (assert (forall ((C2 Bool) (Pi tptp.list_P227219501e_name) (X tptp.pi) (Y4 tptp.pi)) (let ((_let_1 (@ tptp.perm_name_pi Pi))) (let ((_let_2 (@ _let_1 (@ (@ (@ tptp.if_pi C2) X) Y4)))) (and (=> C2 (= _let_2 (@ _let_1 X))) (=> (not C2) (= _let_2 (@ _let_1 Y4))))))))
% 0.27/0.73 (assert (= tptp.eqvt_pi (lambda ((Rel2 tptp.set_Pr1834926343_pi_pi)) (forall ((X5 tptp.product_prod_pi_pi) (Perm2 tptp.list_P227219501e_name)) (=> (@ (@ tptp.member558706512_pi_pi X5) Rel2) (@ (@ tptp.member558706512_pi_pi (@ (@ tptp.perm_n1415585007_pi_pi Perm2) X5)) Rel2))))))
% 0.27/0.73 (assert (forall ((Pi tptp.list_P227219501e_name) (X tptp.late_subject) (Y4 tptp.late_subject)) (let ((_let_1 (@ tptp.perm_n1559866809ubject Pi))) (= (@ (@ tptp.perm_n171497387ubject Pi) (@ (@ tptp.produc1465345179ubject X) Y4)) (@ (@ tptp.produc1465345179ubject (@ _let_1 X)) (@ _let_1 Y4))))))
% 0.27/0.73 (assert (forall ((Pi tptp.list_P227219501e_name) (X tptp.late_subject) (Y4 tptp.late_freeRes)) (= (@ (@ tptp.perm_n1314686611reeRes Pi) (@ (@ tptp.produc242091907reeRes X) Y4)) (@ (@ tptp.produc242091907reeRes (@ (@ tptp.perm_n1559866809ubject Pi) X)) (@ (@ tptp.perm_n336613537reeRes Pi) Y4)))))
% 0.27/0.73 (assert (forall ((Pi tptp.list_P227219501e_name) (X tptp.late_subject) (Y4 tptp.pi_Rep)) (= (@ (@ tptp.perm_n1467004033pi_Rep Pi) (@ (@ tptp.produc843063281pi_Rep X) Y4)) (@ (@ tptp.produc843063281pi_Rep (@ (@ tptp.perm_n1559866809ubject Pi) X)) (@ (@ tptp.perm_name_pi_Rep Pi) Y4)))))
% 0.27/0.73 (assert (forall ((Pi tptp.list_P227219501e_name) (X tptp.late_subject) (Y4 tptp.name)) (= (@ (@ tptp.perm_n204483300t_name Pi) (@ (@ tptp.produc1647375838t_name X) Y4)) (@ (@ tptp.produc1647375838t_name (@ (@ tptp.perm_n1559866809ubject Pi) X)) (@ (@ tptp.perm_name_name Pi) Y4)))))
% 0.27/0.73 (assert (forall ((Pi tptp.list_P227219501e_name) (X tptp.late_subject) (Y4 tptp.pi)) (= (@ (@ tptp.perm_n359102898ect_pi Pi) (@ (@ tptp.produc324947500ect_pi X) Y4)) (@ (@ tptp.produc324947500ect_pi (@ (@ tptp.perm_n1559866809ubject Pi) X)) (@ (@ tptp.perm_name_pi Pi) Y4)))))
% 0.27/0.73 (assert (forall ((Pi tptp.list_P227219501e_name) (X tptp.late_freeRes) (Y4 tptp.late_subject)) (= (@ (@ tptp.perm_n1174226579ubject Pi) (@ (@ tptp.produc320590723ubject X) Y4)) (@ (@ tptp.produc320590723ubject (@ (@ tptp.perm_n336613537reeRes Pi) X)) (@ (@ tptp.perm_n1559866809ubject Pi) Y4)))))
% 0.27/0.73 (assert (forall ((Pi tptp.list_P227219501e_name) (X tptp.late_freeRes) (Y4 tptp.late_freeRes)) (let ((_let_1 (@ tptp.perm_n336613537reeRes Pi))) (= (@ (@ tptp.perm_n169932155reeRes Pi) (@ (@ tptp.produc1244821099reeRes X) Y4)) (@ (@ tptp.produc1244821099reeRes (@ _let_1 X)) (@ _let_1 Y4))))))
% 0.27/0.73 (assert (forall ((Pi tptp.list_P227219501e_name) (X tptp.late_freeRes) (Y4 tptp.pi_Rep)) (= (@ (@ tptp.perm_n840427369pi_Rep Pi) (@ (@ tptp.produc216486617pi_Rep X) Y4)) (@ (@ tptp.produc216486617pi_Rep (@ (@ tptp.perm_n336613537reeRes Pi) X)) (@ (@ tptp.perm_name_pi_Rep Pi) Y4)))))
% 0.27/0.73 (assert (forall ((Pi tptp.list_P227219501e_name) (X tptp.late_freeRes) (Y4 tptp.name)) (= (@ (@ tptp.perm_n258463228s_name Pi) (@ (@ tptp.produc1701355766s_name X) Y4)) (@ (@ tptp.produc1701355766s_name (@ (@ tptp.perm_n336613537reeRes Pi) X)) (@ (@ tptp.perm_name_name Pi) Y4)))))
% 0.27/0.73 (assert (forall ((Pi tptp.list_P227219501e_name) (X tptp.late_freeRes) (Y4 tptp.pi)) (= (@ (@ tptp.perm_n1211707594Res_pi Pi) (@ (@ tptp.produc1177552196Res_pi X) Y4)) (@ (@ tptp.produc1177552196Res_pi (@ (@ tptp.perm_n336613537reeRes Pi) X)) (@ (@ tptp.perm_name_pi Pi) Y4)))))
% 0.27/0.73 (assert (forall ((Pi tptp.list_P227219501e_name) (X tptp.late_subject) (Xs2 tptp.list_Late_subject)) (let ((_let_1 (@ tptp.perm_n1812647369ubject Pi))) (= (@ _let_1 (@ (@ tptp.cons_Late_subject X) Xs2)) (@ (@ tptp.cons_Late_subject (@ (@ tptp.perm_n1559866809ubject Pi) X)) (@ _let_1 Xs2))))))
% 0.27/0.73 (assert (forall ((Pi tptp.list_P227219501e_name) (X tptp.late_freeRes) (Xs2 tptp.list_Late_freeRes)) (let ((_let_1 (@ tptp.perm_n808352945reeRes Pi))) (= (@ _let_1 (@ (@ tptp.cons_Late_freeRes X) Xs2)) (@ (@ tptp.cons_Late_freeRes (@ (@ tptp.perm_n336613537reeRes Pi) X)) (@ _let_1 Xs2))))))
% 0.27/0.73 (assert (forall ((Pi tptp.list_P227219501e_name) (X tptp.pi_Rep) (Xs2 tptp.list_pi_Rep)) (let ((_let_1 (@ tptp.perm_n729617823pi_Rep Pi))) (= (@ _let_1 (@ (@ tptp.cons_pi_Rep X) Xs2)) (@ (@ tptp.cons_pi_Rep (@ (@ tptp.perm_name_pi_Rep Pi) X)) (@ _let_1 Xs2))))))
% 0.27/0.73 (assert (forall ((Pi tptp.list_P227219501e_name) (X tptp.name) (Xs2 tptp.list_name)) (let ((_let_1 (@ tptp.perm_name_list_name Pi))) (= (@ _let_1 (@ (@ tptp.cons_name X) Xs2)) (@ (@ tptp.cons_name (@ (@ tptp.perm_name_name Pi) X)) (@ _let_1 Xs2))))))
% 0.27/0.73 (assert (forall ((Pi tptp.list_P227219501e_name) (X tptp.pi) (Xs2 tptp.list_pi)) (let ((_let_1 (@ tptp.perm_name_list_pi Pi))) (= (@ _let_1 (@ (@ tptp.cons_pi X) Xs2)) (@ (@ tptp.cons_pi (@ (@ tptp.perm_name_pi Pi) X)) (@ _let_1 Xs2))))))
% 0.27/0.73 (assert (forall ((A tptp.name) (X tptp.name) (Y4 tptp.name)) (=> (@ (@ tptp.fresh_441084397e_name A) (@ (@ tptp.produc1570949143e_name X) Y4)) (@ (@ tptp.fresh_name_name A) X))))
% 0.27/0.73 (assert (forall ((A tptp.name) (X tptp.name) (Y4 tptp.product_prod_pi_pi)) (=> (@ (@ tptp.fresh_1376661020_pi_pi A) (@ (@ tptp.produc235456326_pi_pi X) Y4)) (@ (@ tptp.fresh_name_name A) X))))
% 0.27/0.73 (assert (forall ((A tptp.name) (X tptp.pi) (Y4 tptp.pi)) (=> (@ (@ tptp.fresh_1627595501_pi_pi A) (@ (@ tptp.product_Pair_pi_pi X) Y4)) (@ (@ tptp.fresh_name_pi A) X))))
% 0.27/0.73 (assert (forall ((A tptp.name) (X tptp.name) (Y4 tptp.name)) (=> (@ (@ tptp.fresh_441084397e_name A) (@ (@ tptp.produc1570949143e_name X) Y4)) (@ (@ tptp.fresh_name_name A) Y4))))
% 0.27/0.73 (assert (forall ((A tptp.name) (X tptp.name) (Y4 tptp.product_prod_pi_pi)) (=> (@ (@ tptp.fresh_1376661020_pi_pi A) (@ (@ tptp.produc235456326_pi_pi X) Y4)) (@ (@ tptp.fresh_1627595501_pi_pi A) Y4))))
% 0.27/0.73 (assert (forall ((A tptp.name) (X tptp.pi) (Y4 tptp.pi)) (=> (@ (@ tptp.fresh_1627595501_pi_pi A) (@ (@ tptp.product_Pair_pi_pi X) Y4)) (@ (@ tptp.fresh_name_pi A) Y4))))
% 0.27/0.73 (assert (forall ((A tptp.name) (X tptp.late_subject) (Xs2 tptp.list_Late_subject)) (let ((_let_1 (@ tptp.fresh_838462539ubject A))) (= (@ _let_1 (@ (@ tptp.cons_Late_subject X) Xs2)) (and (@ (@ tptp.fresh_717452603ubject A) X) (@ _let_1 Xs2))))))
% 0.27/0.73 (assert (forall ((A tptp.name) (X tptp.late_freeRes) (Xs2 tptp.list_Late_freeRes)) (let ((_let_1 (@ tptp.fresh_1981651763reeRes A))) (= (@ _let_1 (@ (@ tptp.cons_Late_freeRes X) Xs2)) (and (@ (@ tptp.fresh_1641682979reeRes A) X) (@ _let_1 Xs2))))))
% 0.27/0.73 (assert (forall ((A tptp.name) (X tptp.produc1141751126_pi_pi) (Xs2 tptp.list_P431515740_pi_pi)) (let ((_let_1 (@ tptp.fresh_1958133282_pi_pi A))) (= (@ _let_1 (@ (@ tptp.cons_P749510156_pi_pi X) Xs2)) (and (@ (@ tptp.fresh_1376661020_pi_pi A) X) (@ _let_1 Xs2))))))
% 0.27/0.73 (assert (forall ((A tptp.name) (X tptp.name) (Xs2 tptp.list_name)) (let ((_let_1 (@ tptp.fresh_name_list_name A))) (= (@ _let_1 (@ (@ tptp.cons_name X) Xs2)) (and (@ (@ tptp.fresh_name_name A) X) (@ _let_1 Xs2))))))
% 0.27/0.73 (assert (forall ((A tptp.name) (X tptp.pi) (Xs2 tptp.list_pi)) (let ((_let_1 (@ tptp.fresh_name_list_pi A))) (= (@ _let_1 (@ (@ tptp.cons_pi X) Xs2)) (and (@ (@ tptp.fresh_name_pi A) X) (@ _let_1 Xs2))))))
% 0.27/0.73 (assert (forall ((R tptp.set_Pr443758855e_name) (S tptp.set_Pr443758855e_name)) (=> (forall ((X4 tptp.name) (Y3 tptp.name)) (let ((_let_1 (@ tptp.member695284560e_name (@ (@ tptp.produc1570949143e_name X4) Y3)))) (=> (@ _let_1 R) (@ _let_1 S)))) (@ (@ tptp.ord_le793202855e_name R) S))))
% 0.27/0.73 (assert (forall ((R tptp.set_Pr1654044726_pi_pi) (S tptp.set_Pr1654044726_pi_pi)) (=> (forall ((X4 tptp.name) (Y3 tptp.product_prod_pi_pi)) (let ((_let_1 (@ tptp.member540268543_pi_pi (@ (@ tptp.produc235456326_pi_pi X4) Y3)))) (=> (@ _let_1 R) (@ _let_1 S)))) (@ (@ tptp.ord_le797229014_pi_pi R) S))))
% 0.27/0.73 (assert (forall ((R tptp.set_Pr1834926343_pi_pi) (S tptp.set_Pr1834926343_pi_pi)) (=> (forall ((X4 tptp.pi) (Y3 tptp.pi)) (let ((_let_1 (@ tptp.member558706512_pi_pi (@ (@ tptp.product_Pair_pi_pi X4) Y3)))) (=> (@ _let_1 R) (@ _let_1 S)))) (@ (@ tptp.ord_le630093991_pi_pi R) S))))
% 0.27/0.73 (assert (forall ((P3 tptp.produc367475239e_name)) (=> (@ (@ tptp.member695284560e_name P3) tptp.id_name) (not (forall ((X4 tptp.name)) (not (= P3 (@ (@ tptp.produc1570949143e_name X4) X4))))))))
% 0.27/0.73 (assert (forall ((P3 tptp.product_prod_pi_pi)) (=> (@ (@ tptp.member558706512_pi_pi P3) tptp.id_pi) (not (forall ((X4 tptp.pi)) (not (= P3 (@ (@ tptp.product_Pair_pi_pi X4) X4))))))))
% 0.27/0.73 (assert (forall ((P2 tptp.pi) (Q tptp.pi) (A tptp.late_subject) (X tptp.name) (A4 tptp.set_Pr1834926343_pi_pi) (B4 tptp.set_Pr1834926343_pi_pi)) (let ((_let_1 (@ (@ (@ (@ tptp.strong2129052853vative P2) Q) A) X))) (=> (@ _let_1 A4) (=> (@ (@ tptp.ord_le630093991_pi_pi A4) B4) (@ _let_1 B4))))))
% 0.27/0.73 (assert (forall ((Rel tptp.set_Pr806375235ubject) (Perm tptp.list_P227219501e_name) (P2 tptp.late_subject) (Q tptp.late_subject)) (let ((_let_1 (@ tptp.perm_n1559866809ubject Perm))) (=> (@ tptp.eqvt_Late_subject Rel) (=> (@ (@ tptp.member1586545036ubject (@ (@ tptp.produc1465345179ubject (@ _let_1 P2)) (@ _let_1 Q))) Rel) (@ (@ tptp.member1586545036ubject (@ (@ tptp.produc1465345179ubject P2) Q)) Rel))))))
% 0.27/0.73 (assert (forall ((Rel tptp.set_Pr1780909331reeRes) (Perm tptp.list_P227219501e_name) (P2 tptp.late_freeRes) (Q tptp.late_freeRes)) (let ((_let_1 (@ tptp.perm_n336613537reeRes Perm))) (=> (@ tptp.eqvt_Late_freeRes Rel) (=> (@ (@ tptp.member1584979804reeRes (@ (@ tptp.produc1244821099reeRes (@ _let_1 P2)) (@ _let_1 Q))) Rel) (@ (@ tptp.member1584979804reeRes (@ (@ tptp.produc1244821099reeRes P2) Q)) Rel))))))
% 0.27/0.73 (assert (forall ((Rel tptp.set_Pr1131282415pi_Rep) (Perm tptp.list_P227219501e_name) (P2 tptp.pi_Rep) (Q tptp.pi_Rep)) (let ((_let_1 (@ tptp.perm_name_pi_Rep Perm))) (=> (@ tptp.eqvt_pi_Rep Rel) (=> (@ (@ tptp.member1671908408pi_Rep (@ (@ tptp.produc784048711pi_Rep (@ _let_1 P2)) (@ _let_1 Q))) Rel) (@ (@ tptp.member1671908408pi_Rep (@ (@ tptp.produc784048711pi_Rep P2) Q)) Rel))))))
% 0.27/0.73 (assert (forall ((Rel tptp.set_Pr443758855e_name) (Perm tptp.list_P227219501e_name) (P2 tptp.name) (Q tptp.name)) (let ((_let_1 (@ tptp.perm_name_name Perm))) (=> (@ tptp.eqvt_name Rel) (=> (@ (@ tptp.member695284560e_name (@ (@ tptp.produc1570949143e_name (@ _let_1 P2)) (@ _let_1 Q))) Rel) (@ (@ tptp.member695284560e_name (@ (@ tptp.produc1570949143e_name P2) Q)) Rel))))))
% 0.27/0.73 (assert (forall ((Rel tptp.set_Pr1834926343_pi_pi) (Perm tptp.list_P227219501e_name) (P2 tptp.pi) (Q tptp.pi)) (let ((_let_1 (@ tptp.perm_name_pi Perm))) (=> (@ tptp.eqvt_pi Rel) (=> (@ (@ tptp.member558706512_pi_pi (@ (@ tptp.product_Pair_pi_pi (@ _let_1 P2)) (@ _let_1 Q))) Rel) (@ (@ tptp.member558706512_pi_pi (@ (@ tptp.product_Pair_pi_pi P2) Q)) Rel))))))
% 0.27/0.73 (assert (let ((_let_1 (@ tptp.res tptp.x))) (@ (@ tptp.fresh_name_pi tptp.y) (@ (@ tptp.sum (@ _let_1 tptp.p)) (@ _let_1 tptp.q)))))
% 0.27/0.73 (assert (@ (@ tptp.fresh_name_pi tptp.y) (@ (@ tptp.res tptp.x) (@ (@ tptp.sum tptp.p) tptp.q))))
% 0.27/0.73 (assert (forall ((A4 tptp.set_Pr1834926343_pi_pi) (B4 tptp.set_Pr1834926343_pi_pi)) (=> (@ (@ tptp.ord_le630093991_pi_pi A4) B4) (=> (@ (@ tptp.ord_le630093991_pi_pi B4) A4) (= A4 B4)))))
% 0.27/0.73 (assert (forall ((A4 tptp.set_Pr1834926343_pi_pi) (B4 tptp.set_Pr1834926343_pi_pi)) (=> (forall ((X4 tptp.product_prod_pi_pi)) (let ((_let_1 (@ tptp.member558706512_pi_pi X4))) (=> (@ _let_1 A4) (@ _let_1 B4)))) (@ (@ tptp.ord_le630093991_pi_pi A4) B4))))
% 0.27/0.73 (assert (forall ((X tptp.set_Pr1834926343_pi_pi)) (@ (@ tptp.ord_le630093991_pi_pi X) X)))
% 0.27/0.73 (assert (= tptp.fresh_name_name (lambda ((A5 tptp.name) (B5 tptp.name)) (not (= A5 B5)))))
% 0.27/0.73 (assert (forall ((A tptp.name) (X2 tptp.pi) (X1 tptp.pi)) (let ((_let_1 (@ tptp.fresh_name_pi A))) (= (@ _let_1 (@ (@ tptp.sum X2) X1)) (and (@ _let_1 X2) (@ _let_1 X1))))))
% 0.27/0.73 (assert (forall ((Pi tptp.list_P227219501e_name) (X2 tptp.pi) (X1 tptp.pi)) (let ((_let_1 (@ tptp.perm_name_pi Pi))) (= (@ _let_1 (@ (@ tptp.sum X2) X1)) (@ (@ tptp.sum (@ _let_1 X2)) (@ _let_1 X1))))))
% 0.27/0.73 (assert (forall ((Pi tptp.list_P227219501e_name) (X1 tptp.name) (X2 tptp.pi)) (let ((_let_1 (@ tptp.perm_name_pi Pi))) (= (@ _let_1 (@ (@ tptp.res X1) X2)) (@ (@ tptp.res (@ (@ tptp.perm_name_name Pi) X1)) (@ _let_1 X2))))))
% 0.27/0.73 (assert (forall ((Pi1 tptp.pi) (Pi2 tptp.pi) (Name tptp.name) (Pi3 tptp.pi)) (not (= (@ (@ tptp.sum Pi1) Pi2) (@ (@ tptp.res Name) Pi3)))))
% 0.27/0.73 (assert (forall ((X2 tptp.pi) (X1 tptp.pi) (Y2 tptp.pi) (Y1 tptp.pi)) (= (= (@ (@ tptp.sum X2) X1) (@ (@ tptp.sum Y2) Y1)) (and (= X2 Y2) (= X1 Y1)))))
% 0.27/0.73 (assert (forall ((A tptp.name) (P2 tptp.pi)) (@ (@ tptp.fresh_name_pi A) (@ (@ tptp.res A) P2))))
% 0.27/0.73 (assert (forall ((A tptp.set_Pr1834926343_pi_pi) (F (-> tptp.set_Pr1834926343_pi_pi tptp.set_Pr1834926343_pi_pi)) (B tptp.set_Pr1834926343_pi_pi) (C2 tptp.set_Pr1834926343_pi_pi)) (let ((_let_1 (@ tptp.ord_le630093991_pi_pi A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_le630093991_pi_pi B) C2) (=> (forall ((X4 tptp.set_Pr1834926343_pi_pi) (Y3 tptp.set_Pr1834926343_pi_pi)) (=> (@ (@ tptp.ord_le630093991_pi_pi X4) Y3) (@ (@ tptp.ord_le630093991_pi_pi (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C2))))))))
% 0.27/0.73 (assert (forall ((A tptp.set_Pr1834926343_pi_pi) (B tptp.set_Pr1834926343_pi_pi) (F (-> tptp.set_Pr1834926343_pi_pi tptp.set_Pr1834926343_pi_pi)) (C2 tptp.set_Pr1834926343_pi_pi)) (=> (@ (@ tptp.ord_le630093991_pi_pi A) B) (=> (@ (@ tptp.ord_le630093991_pi_pi (@ F B)) C2) (=> (forall ((X4 tptp.set_Pr1834926343_pi_pi) (Y3 tptp.set_Pr1834926343_pi_pi)) (=> (@ (@ tptp.ord_le630093991_pi_pi X4) Y3) (@ (@ tptp.ord_le630093991_pi_pi (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_le630093991_pi_pi (@ F A)) C2))))))
% 0.27/0.73 (assert (forall ((A tptp.set_Pr1834926343_pi_pi) (F (-> tptp.set_Pr1834926343_pi_pi tptp.set_Pr1834926343_pi_pi)) (B tptp.set_Pr1834926343_pi_pi) (C2 tptp.set_Pr1834926343_pi_pi)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_le630093991_pi_pi B) C2) (=> (forall ((X4 tptp.set_Pr1834926343_pi_pi) (Y3 tptp.set_Pr1834926343_pi_pi)) (=> (@ (@ tptp.ord_le630093991_pi_pi X4) Y3) (@ (@ tptp.ord_le630093991_pi_pi (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_le630093991_pi_pi A) (@ F C2)))))))
% 0.27/0.73 (assert (forall ((A tptp.set_Pr1834926343_pi_pi) (B tptp.set_Pr1834926343_pi_pi) (F (-> tptp.set_Pr1834926343_pi_pi tptp.set_Pr1834926343_pi_pi)) (C2 tptp.set_Pr1834926343_pi_pi)) (=> (@ (@ tptp.ord_le630093991_pi_pi A) B) (=> (= (@ F B) C2) (=> (forall ((X4 tptp.set_Pr1834926343_pi_pi) (Y3 tptp.set_Pr1834926343_pi_pi)) (=> (@ (@ tptp.ord_le630093991_pi_pi X4) Y3) (@ (@ tptp.ord_le630093991_pi_pi (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_le630093991_pi_pi (@ F A)) C2))))))
% 0.27/0.73 (assert (= (lambda ((Y6 tptp.set_Pr1834926343_pi_pi) (Z tptp.set_Pr1834926343_pi_pi)) (= Y6 Z)) (lambda ((X5 tptp.set_Pr1834926343_pi_pi) (Y5 tptp.set_Pr1834926343_pi_pi)) (and (@ (@ tptp.ord_le630093991_pi_pi X5) Y5) (@ (@ tptp.ord_le630093991_pi_pi Y5) X5)))))
% 0.27/0.73 (assert (forall ((X tptp.set_Pr1834926343_pi_pi) (Y4 tptp.set_Pr1834926343_pi_pi)) (=> (@ (@ tptp.ord_le630093991_pi_pi X) Y4) (=> (@ (@ tptp.ord_le630093991_pi_pi Y4) X) (= X Y4)))))
% 0.27/0.73 (assert (forall ((X tptp.set_Pr1834926343_pi_pi) (Y4 tptp.set_Pr1834926343_pi_pi)) (=> (= X Y4) (@ (@ tptp.ord_le630093991_pi_pi X) Y4))))
% 0.27/0.73 (assert (forall ((A tptp.set_Pr1834926343_pi_pi) (B tptp.set_Pr1834926343_pi_pi) (C2 tptp.set_Pr1834926343_pi_pi)) (let ((_let_1 (@ tptp.ord_le630093991_pi_pi A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_le630093991_pi_pi B) C2) (@ _let_1 C2))))))
% 0.27/0.73 (assert (forall ((Y4 tptp.set_Pr1834926343_pi_pi) (X tptp.set_Pr1834926343_pi_pi)) (=> (@ (@ tptp.ord_le630093991_pi_pi Y4) X) (= (@ (@ tptp.ord_le630093991_pi_pi X) Y4) (= X Y4)))))
% 0.27/0.73 (assert (= (lambda ((Y6 tptp.set_Pr1834926343_pi_pi) (Z tptp.set_Pr1834926343_pi_pi)) (= Y6 Z)) (lambda ((A5 tptp.set_Pr1834926343_pi_pi) (B5 tptp.set_Pr1834926343_pi_pi)) (and (@ (@ tptp.ord_le630093991_pi_pi A5) B5) (@ (@ tptp.ord_le630093991_pi_pi B5) A5)))))
% 0.27/0.73 (assert (forall ((A tptp.set_Pr1834926343_pi_pi) (B tptp.set_Pr1834926343_pi_pi) (C2 tptp.set_Pr1834926343_pi_pi)) (=> (= A B) (=> (@ (@ tptp.ord_le630093991_pi_pi B) C2) (@ (@ tptp.ord_le630093991_pi_pi A) C2)))))
% 0.27/0.73 (assert (forall ((A tptp.set_Pr1834926343_pi_pi) (B tptp.set_Pr1834926343_pi_pi) (C2 tptp.set_Pr1834926343_pi_pi)) (let ((_let_1 (@ tptp.ord_le630093991_pi_pi A))) (=> (@ _let_1 B) (=> (= B C2) (@ _let_1 C2))))))
% 0.27/0.73 (assert (forall ((A tptp.set_Pr1834926343_pi_pi) (B tptp.set_Pr1834926343_pi_pi)) (=> (@ (@ tptp.ord_le630093991_pi_pi A) B) (=> (@ (@ tptp.ord_le630093991_pi_pi B) A) (= A B)))))
% 0.27/0.73 (assert (forall ((X tptp.set_Pr1834926343_pi_pi) (Y4 tptp.set_Pr1834926343_pi_pi) (Z2 tptp.set_Pr1834926343_pi_pi)) (let ((_let_1 (@ tptp.ord_le630093991_pi_pi X))) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_le630093991_pi_pi Y4) Z2) (@ _let_1 Z2))))))
% 0.27/0.73 (assert (forall ((A tptp.set_Pr1834926343_pi_pi)) (@ (@ tptp.ord_le630093991_pi_pi A) A)))
% 0.27/0.73 (assert (forall ((C2 tptp.name) (P2 tptp.pi) (A tptp.name)) (=> (@ (@ tptp.fresh_name_pi C2) P2) (= (@ (@ tptp.res A) P2) (@ (@ tptp.res C2) (@ (@ tptp.perm_name_pi (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name A) C2)) tptp.nil_Pr743626285e_name)) P2))))))
% 0.27/0.73 (assert (@ (@ tptp.late_transitions (@ (@ tptp.res tptp.x) (@ (@ tptp.sum tptp.p) tptp.q))) (@ (@ (@ tptp.late_BoundR (@ tptp.late_BoundOutputS tptp.aa)) tptp.y) (@ (@ tptp.perm_name_pi (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name tptp.y) tptp.x)) tptp.nil_Pr743626285e_name)) tptp.p2))))
% 0.27/0.73 (assert (let ((_let_1 (@ tptp.res tptp.x))) (@ (@ tptp.late_transitions (@ (@ tptp.sum (@ _let_1 tptp.p)) (@ _let_1 tptp.q))) (@ (@ (@ tptp.late_BoundR tptp.a) tptp.y) tptp.pq))))
% 0.27/0.73 (assert (@ (@ tptp.late_transitions (@ (@ tptp.res tptp.x) (@ (@ tptp.sum tptp.p) tptp.q))) (@ (@ (@ tptp.late_BoundR (@ tptp.late_BoundOutputS tptp.aa)) tptp.x) tptp.p2)))
% 0.27/0.73 (assert (forall ((Rel tptp.set_Pr1834926343_pi_pi) (X tptp.name) (P2 tptp.pi) (Q tptp.pi)) (let ((_let_1 (@ tptp.res X))) (=> (@ (@ tptp.ord_le630093991_pi_pi tptp.id_pi) Rel) (=> (@ tptp.eqvt_pi Rel) (@ (@ (@ tptp.strong743114133lation (@ (@ tptp.sum (@ _let_1 P2)) (@ _let_1 Q))) Rel) (@ _let_1 (@ (@ tptp.sum P2) Q))))))))
% 0.27/0.73 (assert (@ (@ tptp.late_transitions (@ (@ tptp.res tptp.x) tptp.p)) (@ (@ (@ tptp.late_BoundR tptp.a) tptp.y) tptp.pq)))
% 0.27/0.73 (assert (forall ((Pi tptp.list_P227219501e_name) (X32 tptp.late_subject) (X1 tptp.name) (X2 tptp.pi)) (= (@ (@ tptp.perm_n414416632sidual Pi) (@ (@ (@ tptp.late_BoundR X32) X1) X2)) (@ (@ (@ tptp.late_BoundR (@ (@ tptp.perm_n1559866809ubject Pi) X32)) (@ (@ tptp.perm_name_name Pi) X1)) (@ (@ tptp.perm_name_pi Pi) X2)))))
% 0.27/0.73 (assert (forall ((P2 tptp.pi) (A tptp.late_subject) (X tptp.name) (P4 tptp.pi) (Y4 tptp.name)) (=> (@ (@ tptp.late_transitions P2) (@ (@ (@ tptp.late_BoundR A) X) P4)) (=> (@ (@ tptp.fresh_name_pi Y4) P2) (@ (@ tptp.fresh_717452603ubject Y4) A)))))
% 0.27/0.73 (assert (forall ((P2 tptp.pi) (A tptp.late_subject) (X tptp.name) (P4 tptp.pi) (Y4 tptp.name)) (let ((_let_1 (@ tptp.res Y4))) (let ((_let_2 (@ (@ tptp.late_BoundR A) X))) (=> (@ (@ tptp.late_transitions P2) (@ _let_2 P4)) (=> (@ (@ tptp.fresh_717452603ubject Y4) A) (=> (not (= Y4 X)) (@ (@ tptp.late_transitions (@ _let_1 P2)) (@ _let_2 (@ _let_1 P4))))))))))
% 0.27/0.73 (assert (forall ((P2 tptp.pi) (A tptp.late_subject) (X tptp.name) (P4 tptp.pi) (Y4 tptp.name)) (let ((_let_1 (@ tptp.fresh_name_pi Y4))) (=> (@ (@ tptp.late_transitions P2) (@ (@ (@ tptp.late_BoundR A) X) P4)) (=> (@ _let_1 P2) (=> (not (= Y4 X)) (@ _let_1 P4)))))))
% 0.27/0.73 (assert (forall ((P2 tptp.pi) (Rel tptp.set_Pr1834926343_pi_pi) (Q tptp.pi) (A tptp.late_subject) (X tptp.name) (Q2 tptp.pi)) (=> (@ (@ (@ tptp.strong743114133lation P2) Rel) Q) (=> (@ (@ tptp.late_transitions Q) (@ (@ (@ tptp.late_BoundR A) X) Q2)) (=> (@ (@ tptp.fresh_name_pi X) P2) (exists ((P5 tptp.pi)) (and (@ (@ tptp.late_transitions P2) (@ (@ (@ tptp.late_BoundR A) X) P5)) (@ (@ (@ (@ (@ tptp.strong2129052853vative P5) Q2) A) X) Rel))))))))
% 0.27/0.73 (assert (forall ((Q tptp.pi) (Rs tptp.late_residual) (P2 tptp.pi)) (=> (@ (@ tptp.late_transitions Q) Rs) (@ (@ tptp.late_transitions (@ (@ tptp.sum P2) Q)) Rs))))
% 0.27/0.73 (assert (forall ((P2 tptp.pi) (Rs tptp.late_residual) (Q tptp.pi)) (=> (@ (@ tptp.late_transitions P2) Rs) (@ (@ tptp.late_transitions (@ (@ tptp.sum P2) Q)) Rs))))
% 0.27/0.73 (assert (forall ((P2 tptp.pi) (Q tptp.pi) (Rs tptp.late_residual)) (=> (@ (@ tptp.late_transitions (@ (@ tptp.sum P2) Q)) Rs) (=> (not (@ (@ tptp.late_transitions P2) Rs)) (@ (@ tptp.late_transitions Q) Rs)))))
% 0.27/0.73 (assert (forall ((P2 tptp.pi) (Q tptp.pi) (Rs tptp.late_residual)) (=> (@ (@ tptp.late_transitions (@ (@ tptp.sum P2) Q)) Rs) (=> (not (@ (@ tptp.late_transitions P2) Rs)) (@ (@ tptp.late_transitions Q) Rs)))))
% 0.27/0.73 (assert (forall ((P2 tptp.pi) (Rs tptp.late_residual) (X tptp.name)) (=> (@ (@ tptp.late_transitions P2) Rs) (=> (@ (@ tptp.fresh_name_pi X) P2) (@ (@ tptp.fresh_81631222sidual X) Rs)))))
% 0.27/0.73 (assert (forall ((X1 tptp.pi) (X2 tptp.late_residual) (Pi tptp.list_P227219501e_name)) (=> (@ (@ tptp.late_transitions X1) X2) (@ (@ tptp.late_transitions (@ (@ tptp.perm_name_pi Pi) X1)) (@ (@ tptp.perm_n414416632sidual Pi) X2)))))
% 0.27/0.73 (assert (forall ((P2 tptp.pi) (A tptp.late_subject) (X tptp.name) (P4 tptp.pi) (Y4 tptp.name)) (let ((_let_1 (@ tptp.res Y4))) (let ((_let_2 (@ (@ tptp.late_BoundR A) X))) (=> (@ (@ tptp.late_transitions P2) (@ _let_2 P4)) (=> (@ (@ tptp.fresh_717452603ubject Y4) A) (=> (not (= Y4 X)) (=> (@ (@ tptp.fresh_name_pi X) P2) (=> (@ (@ tptp.fresh_717452603ubject X) A) (@ (@ tptp.late_transitions (@ _let_1 P2)) (@ _let_2 (@ _let_1 P4))))))))))))
% 0.27/0.73 (assert (forall ((P2 tptp.pi) (A4 tptp.set_Pr1834926343_pi_pi) (P4 tptp.pi) (B4 tptp.set_Pr1834926343_pi_pi)) (let ((_let_1 (@ tptp.strong743114133lation P2))) (=> (@ (@ _let_1 A4) P4) (=> (@ (@ tptp.ord_le630093991_pi_pi A4) B4) (@ (@ _let_1 B4) P4))))))
% 0.27/0.73 (assert (forall ((Rel tptp.set_Pr1834926343_pi_pi) (P2 tptp.pi)) (=> (@ (@ tptp.ord_le630093991_pi_pi tptp.id_pi) Rel) (@ (@ (@ tptp.strong743114133lation P2) Rel) P2))))
% 0.27/0.73 (assert (forall ((Rel tptp.set_Pr1834926343_pi_pi) (P2 tptp.pi)) (=> (@ (@ tptp.ord_le630093991_pi_pi tptp.id_pi) Rel) (@ (@ (@ tptp.strong743114133lation (@ (@ tptp.sum P2) P2)) Rel) P2))))
% 0.27/0.73 (assert (forall ((Rel tptp.set_Pr1834926343_pi_pi) (P2 tptp.pi) (Q tptp.pi) (R2 tptp.pi)) (let ((_let_1 (@ tptp.sum P2))) (=> (@ (@ tptp.ord_le630093991_pi_pi tptp.id_pi) Rel) (@ (@ (@ tptp.strong743114133lation (@ _let_1 (@ (@ tptp.sum Q) R2))) Rel) (@ (@ tptp.sum (@ _let_1 Q)) R2))))))
% 0.27/0.73 (assert (forall ((Rel tptp.set_Pr1834926343_pi_pi) (P2 tptp.pi)) (=> (@ (@ tptp.ord_le630093991_pi_pi tptp.id_pi) Rel) (@ (@ (@ tptp.strong743114133lation P2) Rel) (@ (@ tptp.sum P2) P2)))))
% 0.27/0.73 (assert (forall ((Rel tptp.set_Pr1834926343_pi_pi) (P2 tptp.pi) (Q tptp.pi) (R2 tptp.pi)) (let ((_let_1 (@ tptp.sum P2))) (=> (@ (@ tptp.ord_le630093991_pi_pi tptp.id_pi) Rel) (@ (@ (@ tptp.strong743114133lation (@ (@ tptp.sum (@ _let_1 Q)) R2)) Rel) (@ _let_1 (@ (@ tptp.sum Q) R2)))))))
% 0.27/0.73 (assert (forall ((Rel tptp.set_Pr1834926343_pi_pi) (P2 tptp.pi) (Q tptp.pi)) (=> (@ (@ tptp.ord_le630093991_pi_pi tptp.id_pi) Rel) (@ (@ (@ tptp.strong743114133lation (@ (@ tptp.sum P2) Q)) Rel) (@ (@ tptp.sum Q) P2)))))
% 0.27/0.73 (assert (forall ((P2 tptp.pi) (Rel tptp.set_Pr1834926343_pi_pi) (Q tptp.pi) (Rel3 tptp.set_Pr1834926343_pi_pi) (Perm tptp.list_P227219501e_name)) (let ((_let_1 (@ tptp.perm_name_pi Perm))) (=> (@ (@ (@ tptp.strong743114133lation P2) Rel) Q) (=> (@ (@ tptp.ord_le630093991_pi_pi Rel) Rel3) (=> (@ tptp.eqvt_pi Rel3) (@ (@ (@ tptp.strong743114133lation (@ _let_1 P2)) Rel3) (@ _let_1 Q))))))))
% 0.27/0.73 (assert (forall ((X6 tptp.name) (P2 tptp.pi) (A tptp.late_subject) (X tptp.name)) (let ((_let_1 (@ tptp.late_BoundR A))) (=> (@ (@ tptp.fresh_name_pi X6) P2) (= (@ (@ _let_1 X) P2) (@ (@ _let_1 X6) (@ (@ tptp.perm_name_pi (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name X) X6)) tptp.nil_Pr743626285e_name)) P2)))))))
% 0.27/0.73 (assert (@ (@ tptp.late_transitions tptp.p) (@ (@ tptp.late_FreeR (@ (@ tptp.late_OutputR tptp.aa) tptp.x)) tptp.p2)))
% 0.27/0.73 (assert (@ (@ tptp.late_transitions (@ (@ tptp.sum tptp.p) tptp.q)) (@ (@ tptp.late_FreeR (@ (@ tptp.late_OutputR tptp.aa) tptp.x)) tptp.p2)))
% 0.27/0.73 (assert (forall ((X11 tptp.name) (X122 tptp.name) (Y11 tptp.name) (Y12 tptp.name)) (= (= (@ (@ tptp.late_OutputR X11) X122) (@ (@ tptp.late_OutputR Y11) Y12)) (and (= X11 Y11) (= X122 Y12)))))
% 0.27/0.73 (assert (forall ((X2 tptp.name) (X1 tptp.name) (Y2 tptp.name) (Y1 tptp.name)) (= (= (@ (@ tptp.late_OutputR X2) X1) (@ (@ tptp.late_OutputR Y2) Y1)) (and (= X2 Y2) (= X1 Y1)))))
% 0.27/0.73 (assert (forall ((Pi tptp.list_P227219501e_name) (X2 tptp.name) (X1 tptp.name)) (let ((_let_1 (@ tptp.perm_name_name Pi))) (= (@ (@ tptp.perm_n336613537reeRes Pi) (@ (@ tptp.late_OutputR X2) X1)) (@ (@ tptp.late_OutputR (@ _let_1 X2)) (@ _let_1 X1))))))
% 0.27/0.73 (assert (forall ((A tptp.name) (X2 tptp.name) (X1 tptp.name)) (let ((_let_1 (@ tptp.fresh_name_name A))) (= (@ (@ tptp.fresh_1641682979reeRes A) (@ (@ tptp.late_OutputR X2) X1)) (and (@ _let_1 X2) (@ _let_1 X1))))))
% 0.27/0.73 (assert (forall ((Pi tptp.list_P227219501e_name) (X2 tptp.late_freeRes) (X1 tptp.pi)) (= (@ (@ tptp.perm_n414416632sidual Pi) (@ (@ tptp.late_FreeR X2) X1)) (@ (@ tptp.late_FreeR (@ (@ tptp.perm_n336613537reeRes Pi) X2)) (@ (@ tptp.perm_name_pi Pi) X1)))))
% 0.27/0.73 (assert (forall ((A tptp.name) (X2 tptp.late_freeRes) (X1 tptp.pi)) (= (@ (@ tptp.fresh_81631222sidual A) (@ (@ tptp.late_FreeR X2) X1)) (and (@ (@ tptp.fresh_1641682979reeRes A) X2) (@ (@ tptp.fresh_name_pi A) X1)))))
% 0.27/0.73 (assert (forall ((Subject tptp.late_subject) (Name2 tptp.name) (Pi tptp.pi) (FreeRes tptp.late_freeRes) (Pi3 tptp.pi)) (not (= (@ (@ (@ tptp.late_BoundR Subject) Name2) Pi) (@ (@ tptp.late_FreeR FreeRes) Pi3)))))
% 0.27/0.73 (assert (forall ((P2 (-> tptp.late_residual Bool)) (Residual tptp.late_residual)) (=> (forall ((Subject2 tptp.late_subject) (Name3 tptp.name) (Pi4 tptp.pi)) (@ P2 (@ (@ (@ tptp.late_BoundR Subject2) Name3) Pi4))) (=> (forall ((FreeRes2 tptp.late_freeRes) (Pi4 tptp.pi)) (@ P2 (@ (@ tptp.late_FreeR FreeRes2) Pi4))) (@ P2 Residual)))))
% 0.27/0.73 (assert (forall ((X2 tptp.late_freeRes) (X1 tptp.pi) (Y2 tptp.late_freeRes) (Y1 tptp.pi)) (= (= (@ (@ tptp.late_FreeR X2) X1) (@ (@ tptp.late_FreeR Y2) Y1)) (and (= X2 Y2) (= X1 Y1)))))
% 0.27/0.73 (assert (forall ((P2 tptp.pi) (Alpha tptp.late_freeRes) (P4 tptp.pi) (Y4 tptp.name)) (let ((_let_1 (@ tptp.res Y4))) (let ((_let_2 (@ tptp.late_FreeR Alpha))) (=> (@ (@ tptp.late_transitions P2) (@ _let_2 P4)) (=> (@ (@ tptp.fresh_1641682979reeRes Y4) Alpha) (@ (@ tptp.late_transitions (@ _let_1 P2)) (@ _let_2 (@ _let_1 P4)))))))))
% 0.27/0.73 (assert (forall ((X tptp.name) (P2 tptp.pi) (Alpha tptp.late_freeRes) (P4 tptp.pi)) (=> (@ (@ tptp.late_transitions (@ (@ tptp.res X) P2)) (@ (@ tptp.late_FreeR Alpha) P4)) (not (forall ((P tptp.pi) (Alpha2 tptp.late_freeRes) (P5 tptp.pi) (Y3 tptp.name)) (let ((_let_1 (@ tptp.late_FreeR Alpha2))) (let ((_let_2 (@ tptp.res Y3))) (=> (= (@ (@ tptp.res X) P2) (@ _let_2 P)) (=> (= (@ (@ tptp.late_FreeR Alpha) P4) (@ _let_1 (@ _let_2 P5))) (=> (@ (@ tptp.late_transitions P) (@ _let_1 P5)) (not (@ (@ tptp.fresh_1641682979reeRes Y3) Alpha2))))))))))))
% 0.27/0.73 (assert (forall ((X tptp.name) (P2 tptp.pi) (Alpha tptp.late_freeRes) (XP tptp.pi) (F3 (-> tptp.pi Bool))) (=> (@ (@ tptp.late_transitions (@ (@ tptp.res X) P2)) (@ (@ tptp.late_FreeR Alpha) XP)) (=> (forall ((P5 tptp.pi)) (=> (@ (@ tptp.late_transitions P2) (@ (@ tptp.late_FreeR Alpha) P5)) (=> (@ (@ tptp.fresh_1641682979reeRes X) Alpha) (@ F3 (@ (@ tptp.res X) P5))))) (@ F3 XP)))))
% 0.27/0.73 (assert (forall ((P2 tptp.pi) (Alpha tptp.late_freeRes) (P4 tptp.pi) (Y4 tptp.name)) (let ((_let_1 (@ tptp.fresh_name_pi Y4))) (=> (@ (@ tptp.late_transitions P2) (@ (@ tptp.late_FreeR Alpha) P4)) (=> (@ _let_1 P2) (@ _let_1 P4))))))
% 0.27/0.73 (assert (forall ((P2 tptp.pi) (Alpha tptp.late_freeRes) (P4 tptp.pi) (Y4 tptp.name)) (=> (@ (@ tptp.late_transitions P2) (@ (@ tptp.late_FreeR Alpha) P4)) (=> (@ (@ tptp.fresh_name_pi Y4) P2) (@ (@ tptp.fresh_1641682979reeRes Y4) Alpha)))))
% 0.27/0.73 (assert (forall ((P2 tptp.pi) (A tptp.name) (B tptp.name) (P4 tptp.pi)) (=> (@ (@ tptp.late_transitions P2) (@ (@ tptp.late_FreeR (@ (@ tptp.late_OutputR A) B)) P4)) (=> (not (= A B)) (@ (@ tptp.late_transitions (@ (@ tptp.res B) P2)) (@ (@ (@ tptp.late_BoundR (@ tptp.late_BoundOutputS A)) B) P4))))))
% 0.27/0.73 (assert (forall ((P2 tptp.pi) (Rel tptp.set_Pr1834926343_pi_pi) (Q tptp.pi) (Alpha tptp.late_freeRes) (Q2 tptp.pi)) (=> (@ (@ (@ tptp.strong743114133lation P2) Rel) Q) (=> (@ (@ tptp.late_transitions Q) (@ (@ tptp.late_FreeR Alpha) Q2)) (exists ((P5 tptp.pi)) (and (@ (@ tptp.late_transitions P2) (@ (@ tptp.late_FreeR Alpha) P5)) (@ (@ tptp.member558706512_pi_pi (@ (@ tptp.product_Pair_pi_pi P5) Q2)) Rel)))))))
% 0.27/0.73 (assert (forall ((X6 tptp.name) (P2 tptp.pi) (A tptp.late_subject) (Y7 tptp.name) (P4 tptp.pi)) (=> (@ (@ tptp.late_transitions (@ (@ tptp.res X6) P2)) (@ (@ (@ tptp.late_BoundR A) Y7) P4)) (=> (forall ((P tptp.pi) (A3 tptp.name) (B3 tptp.name)) (=> (= (@ (@ tptp.res X6) P2) (@ (@ tptp.res B3) P)) (forall ((P5 tptp.pi)) (=> (= (@ (@ (@ tptp.late_BoundR A) Y7) P4) (@ (@ (@ tptp.late_BoundR (@ tptp.late_BoundOutputS A3)) B3) P5)) (=> (@ (@ tptp.late_transitions P) (@ (@ tptp.late_FreeR (@ (@ tptp.late_OutputR A3) B3)) P5)) (= A3 B3)))))) (not (forall ((P tptp.pi) (A3 tptp.late_subject) (X4 tptp.name) (P5 tptp.pi) (Y3 tptp.name)) (let ((_let_1 (@ (@ tptp.late_BoundR A3) X4))) (let ((_let_2 (@ tptp.res Y3))) (=> (= (@ (@ tptp.res X6) P2) (@ _let_2 P)) (=> (= (@ (@ (@ tptp.late_BoundR A) Y7) P4) (@ _let_1 (@ _let_2 P5))) (=> (@ (@ tptp.late_transitions P) (@ _let_1 P5)) (=> (@ (@ tptp.fresh_717452603ubject Y3) A3) (=> (not (= Y3 X4)) (=> (@ (@ tptp.fresh_name_pi X4) P) (not (@ (@ tptp.fresh_717452603ubject X4) A3))))))))))))))))
% 0.27/0.73 (assert (forall ((X tptp.name) (P2 tptp.pi) (Rs tptp.late_residual)) (=> (@ (@ tptp.late_transitions (@ (@ tptp.res X) P2)) Rs) (=> (forall ((P tptp.pi) (A3 tptp.name) (B3 tptp.name)) (=> (= (@ (@ tptp.res X) P2) (@ (@ tptp.res B3) P)) (forall ((P5 tptp.pi)) (=> (= Rs (@ (@ (@ tptp.late_BoundR (@ tptp.late_BoundOutputS A3)) B3) P5)) (=> (@ (@ tptp.late_transitions P) (@ (@ tptp.late_FreeR (@ (@ tptp.late_OutputR A3) B3)) P5)) (= A3 B3)))))) (=> (forall ((P tptp.pi) (A3 tptp.late_subject) (X4 tptp.name) (P5 tptp.pi) (Y3 tptp.name)) (let ((_let_1 (@ (@ tptp.late_BoundR A3) X4))) (let ((_let_2 (@ tptp.res Y3))) (=> (= (@ (@ tptp.res X) P2) (@ _let_2 P)) (=> (= Rs (@ _let_1 (@ _let_2 P5))) (=> (@ (@ tptp.late_transitions P) (@ _let_1 P5)) (=> (@ (@ tptp.fresh_717452603ubject Y3) A3) (=> (not (= Y3 X4)) (=> (@ (@ tptp.fresh_name_pi X4) P) (not (@ (@ tptp.fresh_717452603ubject X4) A3))))))))))) (not (forall ((P tptp.pi) (Alpha2 tptp.late_freeRes) (P5 tptp.pi) (Y3 tptp.name)) (let ((_let_1 (@ tptp.late_FreeR Alpha2))) (let ((_let_2 (@ tptp.res Y3))) (=> (= (@ (@ tptp.res X) P2) (@ _let_2 P)) (=> (= Rs (@ _let_1 (@ _let_2 P5))) (=> (@ (@ tptp.late_transitions P) (@ _let_1 P5)) (not (@ (@ tptp.fresh_1641682979reeRes Y3) Alpha2))))))))))))))
% 0.27/0.73 (assert (forall ((Y4 tptp.name) (P2 tptp.pi) (A tptp.late_subject) (X tptp.name) (YP tptp.pi) (F3 (-> tptp.late_subject tptp.pi Bool))) (=> (@ (@ tptp.late_transitions (@ (@ tptp.res Y4) P2)) (@ (@ (@ tptp.late_BoundR A) X) YP)) (=> (not (= X Y4)) (=> (@ (@ tptp.fresh_name_pi X) P2) (=> (forall ((B3 tptp.name) (P5 tptp.pi)) (let ((_let_1 (@ tptp.late_BoundOutputS B3))) (=> (@ (@ tptp.late_transitions P2) (@ (@ tptp.late_FreeR (@ (@ tptp.late_OutputR B3) Y4)) P5)) (=> (not (= B3 Y4)) (=> (= A _let_1) (@ (@ F3 _let_1) (@ (@ tptp.perm_name_pi (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name X) Y4)) tptp.nil_Pr743626285e_name)) P5))))))) (=> (forall ((P5 tptp.pi)) (=> (@ (@ tptp.late_transitions P2) (@ (@ (@ tptp.late_BoundR A) X) P5)) (=> (@ (@ tptp.fresh_717452603ubject Y4) A) (@ (@ F3 A) (@ (@ tptp.res Y4) P5))))) (@ (@ F3 A) YP))))))))
% 0.27/0.73 (assert (= tptp.strong743114133lation (lambda ((P6 tptp.pi) (Rel2 tptp.set_Pr1834926343_pi_pi) (Q3 tptp.pi)) (and (forall ((A5 tptp.late_subject) (X5 tptp.name) (Q4 tptp.pi)) (=> (and (@ (@ tptp.late_transitions Q3) (@ (@ (@ tptp.late_BoundR A5) X5) Q4)) (@ (@ tptp.fresh_name_pi X5) P6)) (exists ((P7 tptp.pi)) (and (@ (@ tptp.late_transitions P6) (@ (@ (@ tptp.late_BoundR A5) X5) P7)) (@ (@ (@ (@ (@ tptp.strong2129052853vative P7) Q4) A5) X5) Rel2))))) (forall ((Alpha3 tptp.late_freeRes) (Q4 tptp.pi)) (=> (@ (@ tptp.late_transitions Q3) (@ (@ tptp.late_FreeR Alpha3) Q4)) (exists ((P7 tptp.pi)) (and (@ (@ tptp.late_transitions P6) (@ (@ tptp.late_FreeR Alpha3) P7)) (@ (@ tptp.member558706512_pi_pi (@ (@ tptp.product_Pair_pi_pi P7) Q4)) Rel2)))))))))
% 0.27/0.73 (assert (forall ((Q tptp.pi) (P2 tptp.pi) (Rel tptp.set_Pr1834926343_pi_pi)) (=> (forall ((A3 tptp.late_subject) (Y3 tptp.name) (Q5 tptp.pi)) (=> (@ (@ tptp.late_transitions Q) (@ (@ (@ tptp.late_BoundR A3) Y3) Q5)) (=> (@ (@ tptp.fresh_name_pi Y3) P2) (exists ((P8 tptp.pi)) (and (@ (@ tptp.late_transitions P2) (@ (@ (@ tptp.late_BoundR A3) Y3) P8)) (@ (@ (@ (@ (@ tptp.strong2129052853vative P8) Q5) A3) Y3) Rel)))))) (=> (forall ((Alpha2 tptp.late_freeRes) (Q5 tptp.pi)) (=> (@ (@ tptp.late_transitions Q) (@ (@ tptp.late_FreeR Alpha2) Q5)) (exists ((P8 tptp.pi)) (and (@ (@ tptp.late_transitions P2) (@ (@ tptp.late_FreeR Alpha2) P8)) (@ (@ tptp.member558706512_pi_pi (@ (@ tptp.product_Pair_pi_pi P8) Q5)) Rel))))) (@ (@ (@ tptp.strong743114133lation P2) Rel) Q)))))
% 0.27/0.73 (assert (forall ((X21 tptp.late_freeRes) (X22 tptp.pi) (Y21 tptp.late_freeRes) (Y22 tptp.pi)) (= (= (@ (@ tptp.late_r347633188eR_Rep X21) X22) (@ (@ tptp.late_r347633188eR_Rep Y21) Y22)) (and (= X21 Y21) (= X22 Y22)))))
% 0.27/0.73 (assert (forall ((C2 tptp.name) (P2 tptp.pi) (A tptp.name) (X tptp.name)) (let ((_let_1 (@ tptp.input A))) (=> (@ (@ tptp.fresh_name_pi C2) P2) (= (@ (@ _let_1 X) P2) (@ (@ _let_1 C2) (@ (@ tptp.perm_name_pi (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name X) C2)) tptp.nil_Pr743626285e_name)) P2)))))))
% 0.27/0.73 (assert (forall ((Pi tptp.list_P227219501e_name) (X32 tptp.name) (X1 tptp.name) (X2 tptp.pi)) (let ((_let_1 (@ tptp.perm_name_pi Pi))) (let ((_let_2 (@ tptp.perm_name_name Pi))) (= (@ _let_1 (@ (@ (@ tptp.input X32) X1) X2)) (@ (@ (@ tptp.input (@ _let_2 X32)) (@ _let_2 X1)) (@ _let_1 X2)))))))
% 0.27/0.73 (assert (forall ((X tptp.name) (Y4 tptp.name) (P2 tptp.pi) (Rs tptp.late_residual)) (not (@ (@ tptp.late_transitions (@ (@ tptp.res X) (@ (@ (@ tptp.input X) Y4) P2))) Rs))))
% 0.27/0.73 (assert (forall ((Name1 tptp.name) (Name22 tptp.name) (Pi tptp.pi) (Pi12 tptp.pi) (Pi22 tptp.pi)) (not (= (@ (@ (@ tptp.input Name1) Name22) Pi) (@ (@ tptp.sum Pi12) Pi22)))))
% 0.27/0.73 (assert (forall ((Name1 tptp.name) (Name22 tptp.name) (Pi tptp.pi) (Name tptp.name) (Pi3 tptp.pi)) (not (= (@ (@ (@ tptp.input Name1) Name22) Pi) (@ (@ tptp.res Name) Pi3)))))
% 0.27/0.73 (assert (forall ((A tptp.name) (X tptp.name) (P2 tptp.pi) (Alpha tptp.late_freeRes) (P4 tptp.pi)) (not (@ (@ tptp.late_transitions (@ (@ (@ tptp.input A) X) P2)) (@ (@ tptp.late_FreeR Alpha) P4)))))
% 0.27/0.73 (assert (forall ((X tptp.name) (A tptp.name) (Y4 tptp.name) (P2 tptp.pi) (Alpha tptp.late_freeRes) (P4 tptp.pi)) (not (@ (@ tptp.late_transitions (@ (@ tptp.res X) (@ (@ (@ tptp.input A) Y4) P2))) (@ (@ tptp.late_FreeR Alpha) P4)))))
% 0.27/0.73 (assert (forall ((A tptp.name) (X tptp.name) (P2 tptp.pi) (B tptp.name) (Y4 tptp.name) (P4 tptp.pi)) (not (@ (@ tptp.late_transitions (@ (@ (@ tptp.input A) X) P2)) (@ (@ (@ tptp.late_BoundR (@ tptp.late_BoundOutputS B)) Y4) P4)))))
% 0.27/0.73 (assert (forall ((A tptp.name) (X tptp.name) (P2 tptp.pi) (B tptp.late_subject) (Y4 tptp.name) (P4 tptp.pi)) (=> (@ (@ tptp.late_transitions (@ (@ (@ tptp.input A) X) P2)) (@ (@ (@ tptp.late_BoundR B) Y4) P4)) (not (@ (@ tptp.fresh_717452603ubject A) B)))))
% 0.27/0.73 (assert (forall ((X tptp.name) (A tptp.name) (Y4 tptp.name) (P2 tptp.pi) (B tptp.name) (Z2 tptp.name) (P4 tptp.pi)) (not (@ (@ tptp.late_transitions (@ (@ tptp.res X) (@ (@ (@ tptp.input A) Y4) P2))) (@ (@ (@ tptp.late_BoundR (@ tptp.late_BoundOutputS B)) Z2) P4)))))
% 0.27/0.73 (assert (forall ((A tptp.name) (X tptp.name) (P2 tptp.pi) (B tptp.late_subject) (Y4 tptp.name) (YP tptp.pi) (Prop (-> tptp.late_subject tptp.name tptp.pi Bool))) (let ((_let_1 (@ (@ tptp.perm_name_pi (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name X) Y4)) tptp.nil_Pr743626285e_name)) P2))) (let ((_let_2 (@ tptp.late_InputS A))) (=> (@ (@ tptp.late_transitions (@ (@ (@ tptp.input A) X) P2)) (@ (@ (@ tptp.late_BoundR B) Y4) YP)) (=> (not (= Y4 A)) (=> (not (= Y4 X)) (=> (@ (@ tptp.fresh_name_pi Y4) P2) (=> (=> (= B _let_2) (=> (= YP _let_1) (@ (@ (@ Prop _let_2) Y4) _let_1))) (@ (@ (@ Prop B) Y4) YP))))))))))
% 0.27/0.73 (assert (forall ((A tptp.name) (B tptp.name) (Pi tptp.list_P227219501e_name) (X tptp.name)) (let ((_let_1 (@ (@ tptp.produc1570949143e_name A) B))) (= (@ (@ tptp.perm_name_name (@ (@ tptp.cons_P1213805021e_name _let_1) Pi)) X) (@ (@ tptp.swap_name _let_1) (@ (@ tptp.perm_name_name Pi) X))))))
% 0.27/0.73 (assert (forall ((X1 tptp.name) (Y1 tptp.name)) (= (= (@ tptp.late_InputS X1) (@ tptp.late_InputS Y1)) (= X1 Y1))))
% 0.27/0.73 (assert (forall ((A tptp.name) (X1 tptp.name)) (= (@ (@ tptp.fresh_717452603ubject A) (@ tptp.late_InputS X1)) (@ (@ tptp.fresh_name_name A) X1))))
% 0.27/0.73 (assert (forall ((Pi tptp.list_P227219501e_name) (X1 tptp.name)) (= (@ (@ tptp.perm_n1559866809ubject Pi) (@ tptp.late_InputS X1)) (@ tptp.late_InputS (@ (@ tptp.perm_name_name Pi) X1)))))
% 0.27/0.73 (assert (forall ((Name2 tptp.name) (Name tptp.name)) (not (= (@ tptp.late_InputS Name2) (@ tptp.late_BoundOutputS Name)))))
% 0.27/0.73 (assert (forall ((X tptp.pi) (Y4 tptp.pi)) (= (@ (@ (@ tptp.if_pi false) X) Y4) Y4)))
% 0.27/0.73 (assert (forall ((X tptp.pi) (Y4 tptp.pi)) (= (@ (@ (@ tptp.if_pi true) X) Y4) X)))
% 0.27/0.73 (assert (forall ((X tptp.name) (Y4 tptp.name)) (= (@ (@ (@ tptp.if_name false) X) Y4) Y4)))
% 0.27/0.73 (assert (forall ((X tptp.name) (Y4 tptp.name)) (= (@ (@ (@ tptp.if_name true) X) Y4) X)))
% 0.27/0.73 (assert (forall ((X tptp.pi_Rep) (Y4 tptp.pi_Rep)) (= (@ (@ (@ tptp.if_pi_Rep false) X) Y4) Y4)))
% 0.27/0.73 (assert (forall ((X tptp.pi_Rep) (Y4 tptp.pi_Rep)) (= (@ (@ (@ tptp.if_pi_Rep true) X) Y4) X)))
% 0.27/0.73 (assert (forall ((X tptp.late_freeRes) (Y4 tptp.late_freeRes)) (= (@ (@ (@ tptp.if_Late_freeRes false) X) Y4) Y4)))
% 0.27/0.73 (assert (forall ((X tptp.late_freeRes) (Y4 tptp.late_freeRes)) (= (@ (@ (@ tptp.if_Late_freeRes true) X) Y4) X)))
% 0.86/1.09 (assert (forall ((P2 Bool)) (or (= P2 true) (= P2 false))))
% 0.86/1.09 (assert (forall ((X tptp.late_subject) (Y4 tptp.late_subject)) (= (@ (@ (@ tptp.if_Late_subject false) X) Y4) Y4)))
% 0.86/1.09 (assert (forall ((X tptp.late_subject) (Y4 tptp.late_subject)) (= (@ (@ (@ tptp.if_Late_subject true) X) Y4) X)))
% 0.86/1.09 (assert (let ((_let_1 (@ (@ tptp.perm_name_pi (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name tptp.y) tptp.x)) tptp.nil_Pr743626285e_name)) tptp.p2))) (not (@ (@ (@ (@ (@ tptp.strong2129052853vative _let_1) _let_1) (@ tptp.late_BoundOutputS tptp.aa)) tptp.y) tptp.rel))))
% 0.86/1.09 (set-info :filename cvc5---1.0.5_23592)
% 0.86/1.09 (check-sat-assuming ( true ))
% 0.86/1.09 ------- get file name : TPTP file name is ITP182^1
% 0.86/1.09 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_23592.smt2...
% 0.86/1.09 --- Run --ho-elim --full-saturate-quant at 10...
% 0.86/1.09 % SZS status Theorem for ITP182^1
% 0.86/1.09 % SZS output start Proof for ITP182^1
% 0.86/1.09 (
% 0.86/1.09 (let ((_let_1 (@ tptp.late_BoundOutputS tptp.aa))) (let ((_let_2 (@ (@ tptp.perm_name_pi (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name tptp.y) tptp.x)) tptp.nil_Pr743626285e_name)) tptp.p2))) (let ((_let_3 (not (@ (@ (@ (@ (@ tptp.strong2129052853vative _let_2) _let_2) _let_1) tptp.y) tptp.rel)))) (let ((_let_4 (@ (@ tptp.late_FreeR (@ (@ tptp.late_OutputR tptp.aa) tptp.x)) tptp.p2))) (let ((_let_5 (@ (@ tptp.sum tptp.p) tptp.q))) (let ((_let_6 (@ (@ (@ tptp.late_BoundR tptp.a) tptp.y) tptp.pq))) (let ((_let_7 (@ tptp.res tptp.x))) (let ((_let_8 (@ _let_7 tptp.p))) (let ((_let_9 (@ tptp.late_BoundR _let_1))) (let ((_let_10 (@ _let_7 _let_5))) (let ((_let_11 (@ tptp.late_transitions _let_10))) (let ((_let_12 (@ (@ tptp.sum _let_8) (@ _let_7 tptp.q)))) (let ((_let_13 (@ tptp.fresh_name_pi tptp.y))) (let ((_let_14 (forall ((Rel tptp.set_Pr1834926343_pi_pi) (P2 tptp.pi) (A tptp.late_subject) (X tptp.name)) (=> (@ (@ tptp.ord_le630093991_pi_pi tptp.id_pi) Rel) (@ (@ (@ (@ (@ tptp.strong2129052853vative P2) P2) A) X) Rel))))) (let ((_let_15 (@ (@ tptp.ord_le630093991_pi_pi tptp.id_pi) tptp.rel))) (let ((_let_16 (forall ((Rel tptp.set_Pr1834926343_pi_pi) (P2 tptp.pi) (A tptp.late_subject) (X tptp.name)) (or (not (ho_9 (ho_8 k_11 tptp.id_pi) Rel)) (ho_9 (ho_240 (ho_239 (ho_238 (ho_237 k_236 P2) P2) A) X) Rel))))) (let ((_let_17 (ho_44 k_43 tptp.aa))) (let ((_let_18 (ho_42 (ho_41 k_40 (ho_27 (ho_26 k_25 (ho_24 (ho_23 k_22 tptp.y) tptp.x)) tptp.nil_Pr743626285e_name)) tptp.p2))) (let ((_let_19 (ho_9 (ho_240 (ho_239 (ho_238 (ho_237 k_236 _let_18) _let_18) _let_17) tptp.y) tptp.rel))) (let ((_let_20 (ho_9 (ho_8 k_11 tptp.id_pi) tptp.rel))) (let ((_let_21 (not _let_20))) (let ((_let_22 (or _let_21 _let_19))) (let ((_let_23 (EQ_RESOLVE (ASSUME :args (_let_14)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((Rel tptp.set_Pr1834926343_pi_pi) (P2 tptp.pi) (A tptp.late_subject) (X tptp.name)) (or (not (@ (@ tptp.ord_le630093991_pi_pi tptp.id_pi) Rel)) (@ (@ (@ (@ (@ tptp.strong2129052853vative P2) P2) A) X) Rel))) _let_16))))))) (let ((_let_24 (not _let_22))) (let ((_let_25 (forall ((u |u_(-> tptp.name tptp.produc1998742700t_name Bool)|) (e |u_(-> tptp.produc1998742700t_name Bool)|) (i tptp.name)) (not (forall ((v |u_(-> tptp.name tptp.produc1998742700t_name Bool)|)) (not (forall ((ii tptp.name)) (= (ho_192 v ii) (ite (= i ii) e (ho_192 u ii)))))))))) (let ((_let_26 (forall ((x |u_(-> tptp.name tptp.produc1998742700t_name Bool)|) (y |u_(-> tptp.name tptp.produc1998742700t_name Bool)|)) (or (not (forall ((z tptp.name)) (= (ho_192 x z) (ho_192 y z)))) (= x y))))) (let ((_let_27 (forall ((u |u_(-> tptp.pi tptp.late_subject tptp.name tptp.set_Pr1834926343_pi_pi Bool)|) (e |u_(-> tptp.late_subject tptp.name tptp.set_Pr1834926343_pi_pi Bool)|) (i tptp.pi)) (not (forall ((v |u_(-> tptp.pi tptp.late_subject tptp.name tptp.set_Pr1834926343_pi_pi Bool)|)) (not (forall ((ii tptp.pi)) (= (ho_238 v ii) (ite (= i ii) e (ho_238 u ii)))))))))) (let ((_let_28 (forall ((x |u_(-> tptp.pi tptp.late_subject tptp.name tptp.set_Pr1834926343_pi_pi Bool)|) (y |u_(-> tptp.pi tptp.late_subject tptp.name tptp.set_Pr1834926343_pi_pi Bool)|)) (or (not (forall ((z tptp.pi)) (= (ho_238 x z) (ho_238 y z)))) (= x y))))) (let ((_let_29 (forall ((u |u_(-> tptp.pi_Rep tptp.produc257012921pi_Rep)|) (e tptp.produc257012921pi_Rep) (i tptp.pi_Rep)) (not (forall ((v |u_(-> tptp.pi_Rep tptp.produc257012921pi_Rep)|)) (not (forall ((ii tptp.pi_Rep)) (= (ho_280 v ii) (ite (= i ii) e (ho_280 u ii)))))))))) (let ((_let_30 (forall ((x |u_(-> tptp.pi_Rep tptp.produc257012921pi_Rep)|) (y |u_(-> tptp.pi_Rep tptp.produc257012921pi_Rep)|)) (or (not (forall ((z tptp.pi_Rep)) (= (ho_280 x z) (ho_280 y z)))) (= x y))))) (let ((_let_31 (forall ((u |u_(-> tptp.name tptp.produc1998742700t_name)|) (e tptp.produc1998742700t_name) (i tptp.name)) (not (forall ((v |u_(-> tptp.name tptp.produc1998742700t_name)|)) (not (forall ((ii tptp.name)) (= (ho_190 v ii) (ite (= i ii) e (ho_190 u ii)))))))))) (let ((_let_32 (forall ((x |u_(-> tptp.name tptp.produc1998742700t_name)|) (y |u_(-> tptp.name tptp.produc1998742700t_name)|)) (or (not (forall ((z tptp.name)) (= (ho_190 x z) (ho_190 y z)))) (= x y))))) (let ((_let_33 (forall ((u |u_(-> tptp.name tptp.produc1359399907ubject Bool)|) (e |u_(-> tptp.produc1359399907ubject Bool)|) (i tptp.name)) (not (forall ((v |u_(-> tptp.name tptp.produc1359399907ubject Bool)|)) (not (forall ((ii tptp.name)) (= (ho_180 v ii) (ite (= i ii) e (ho_180 u ii)))))))))) (let ((_let_34 (forall ((x |u_(-> tptp.name tptp.produc1359399907ubject Bool)|) (y |u_(-> tptp.name tptp.produc1359399907ubject Bool)|)) (or (not (forall ((z tptp.name)) (= (ho_180 x z) (ho_180 y z)))) (= x y))))) (let ((_let_35 (forall ((u |u_(-> tptp.late_subject tptp.produc1359399907ubject)|) (e tptp.produc1359399907ubject) (i tptp.late_subject)) (not (forall ((v |u_(-> tptp.late_subject tptp.produc1359399907ubject)|)) (not (forall ((ii tptp.late_subject)) (= (ho_178 v ii) (ite (= i ii) e (ho_178 u ii)))))))))) (let ((_let_36 (forall ((x |u_(-> tptp.late_subject tptp.produc1359399907ubject)|) (y |u_(-> tptp.late_subject tptp.produc1359399907ubject)|)) (or (not (forall ((z tptp.late_subject)) (= (ho_178 x z) (ho_178 y z)))) (= x y))))) (let ((_let_37 (forall ((u |u_(-> tptp.list_P227219501e_name tptp.produc355105483reeRes tptp.produc355105483reeRes)|) (e |u_(-> tptp.produc355105483reeRes tptp.produc355105483reeRes)|) (i tptp.list_P227219501e_name)) (not (forall ((v |u_(-> tptp.list_P227219501e_name tptp.produc355105483reeRes tptp.produc355105483reeRes)|)) (not (forall ((ii tptp.list_P227219501e_name)) (= (ho_276 v ii) (ite (= i ii) e (ho_276 u ii)))))))))) (let ((_let_38 (forall ((x |u_(-> tptp.list_P227219501e_name tptp.produc355105483reeRes tptp.produc355105483reeRes)|) (y |u_(-> tptp.list_P227219501e_name tptp.produc355105483reeRes tptp.produc355105483reeRes)|)) (or (not (forall ((z tptp.list_P227219501e_name)) (= (ho_276 x z) (ho_276 y z)))) (= x y))))) (let ((_let_39 (forall ((u |u_(-> tptp.list_P227219501e_name tptp.list_l1406151091e_name tptp.list_l1406151091e_name)|) (e |u_(-> tptp.list_l1406151091e_name tptp.list_l1406151091e_name)|) (i tptp.list_P227219501e_name)) (not (forall ((v |u_(-> tptp.list_P227219501e_name tptp.list_l1406151091e_name tptp.list_l1406151091e_name)|)) (not (forall ((ii tptp.list_P227219501e_name)) (= (ho_171 v ii) (ite (= i ii) e (ho_171 u ii)))))))))) (let ((_let_40 (forall ((x |u_(-> tptp.list_P227219501e_name tptp.list_l1406151091e_name tptp.list_l1406151091e_name)|) (y |u_(-> tptp.list_P227219501e_name tptp.list_l1406151091e_name tptp.list_l1406151091e_name)|)) (or (not (forall ((z tptp.list_P227219501e_name)) (= (ho_171 x z) (ho_171 y z)))) (= x y))))) (let ((_let_41 (forall ((u |u_(-> tptp.late_residual_Rep tptp.late_residual_Rep)|) (e tptp.late_residual_Rep) (i tptp.late_residual_Rep)) (not (forall ((v |u_(-> tptp.late_residual_Rep tptp.late_residual_Rep)|)) (not (forall ((ii tptp.late_residual_Rep)) (= (ho_56 v ii) (ite (= i ii) e (ho_56 u ii)))))))))) (let ((_let_42 (forall ((x |u_(-> tptp.late_residual_Rep tptp.late_residual_Rep)|) (y |u_(-> tptp.late_residual_Rep tptp.late_residual_Rep)|)) (or (not (forall ((z tptp.late_residual_Rep)) (= (ho_56 x z) (ho_56 y z)))) (= x y))))) (let ((_let_43 (forall ((u |u_(-> tptp.late_subject tptp.late_subject tptp.late_subject)|) (e |u_(-> tptp.late_subject tptp.late_subject)|) (i tptp.late_subject)) (not (forall ((v |u_(-> tptp.late_subject tptp.late_subject tptp.late_subject)|)) (not (forall ((ii tptp.late_subject)) (= (ho_259 v ii) (ite (= i ii) e (ho_259 u ii)))))))))) (let ((_let_44 (forall ((x |u_(-> tptp.late_subject tptp.late_subject tptp.late_subject)|) (y |u_(-> tptp.late_subject tptp.late_subject tptp.late_subject)|)) (or (not (forall ((z tptp.late_subject)) (= (ho_259 x z) (ho_259 y z)))) (= x y))))) (let ((_let_45 (forall ((u |u_(-> tptp.list_P227219501e_name tptp.list_P227219501e_name Bool)|) (e |u_(-> tptp.list_P227219501e_name Bool)|) (i tptp.list_P227219501e_name)) (not (forall ((v |u_(-> tptp.list_P227219501e_name tptp.list_P227219501e_name Bool)|)) (not (forall ((ii tptp.list_P227219501e_name)) (= (ho_168 v ii) (ite (= i ii) e (ho_168 u ii)))))))))) (let ((_let_46 (forall ((x |u_(-> tptp.list_P227219501e_name tptp.list_P227219501e_name Bool)|) (y |u_(-> tptp.list_P227219501e_name tptp.list_P227219501e_name Bool)|)) (or (not (forall ((z tptp.list_P227219501e_name)) (= (ho_168 x z) (ho_168 y z)))) (= x y))))) (let ((_let_47 (forall ((u |u_(-> tptp.set_Pr1780909331reeRes Bool)|) (e Bool) (i tptp.set_Pr1780909331reeRes)) (not (forall ((v |u_(-> tptp.set_Pr1780909331reeRes Bool)|)) (not (forall ((ii tptp.set_Pr1780909331reeRes)) (= (ho_247 v ii) (ite (= i ii) e (ho_247 u ii)))))))))) (let ((_let_48 (forall ((x |u_(-> tptp.set_Pr1780909331reeRes Bool)|) (y |u_(-> tptp.set_Pr1780909331reeRes Bool)|)) (or (not (forall ((z tptp.set_Pr1780909331reeRes)) (= (ho_247 x z) (ho_247 y z)))) (= x y))))) (let ((_let_49 (forall ((u |u_(-> tptp.name tptp.set_name Bool)|) (e |u_(-> tptp.set_name Bool)|) (i tptp.name)) (not (forall ((v |u_(-> tptp.name tptp.set_name Bool)|)) (not (forall ((ii tptp.name)) (= (ho_158 v ii) (ite (= i ii) e (ho_158 u ii)))))))))) (let ((_let_50 (forall ((x |u_(-> tptp.name tptp.set_name Bool)|) (y |u_(-> tptp.name tptp.set_name Bool)|)) (or (not (forall ((z tptp.name)) (= (ho_158 x z) (ho_158 y z)))) (= x y))))) (let ((_let_51 (forall ((u |u_(-> tptp.set_name Bool)|) (e Bool) (i tptp.set_name)) (not (forall ((v |u_(-> tptp.set_name Bool)|)) (not (forall ((ii tptp.set_name)) (= (ho_159 v ii) (ite (= i ii) e (ho_159 u ii)))))))))) (let ((_let_52 (forall ((x |u_(-> tptp.set_name Bool)|) (y |u_(-> tptp.set_name Bool)|)) (or (not (forall ((z tptp.set_name)) (= (ho_159 x z) (ho_159 y z)))) (= x y))))) (let ((_let_53 (forall ((u |u_(-> tptp.produc214645451ubject tptp.produc214645451ubject)|) (e tptp.produc214645451ubject) (i tptp.produc214645451ubject)) (not (forall ((v |u_(-> tptp.produc214645451ubject tptp.produc214645451ubject)|)) (not (forall ((ii tptp.produc214645451ubject)) (= (ho_292 v ii) (ite (= i ii) e (ho_292 u ii)))))))))) (let ((_let_54 (forall ((x |u_(-> tptp.produc214645451ubject tptp.produc214645451ubject)|) (y |u_(-> tptp.produc214645451ubject tptp.produc214645451ubject)|)) (or (not (forall ((z tptp.produc214645451ubject)) (= (ho_292 x z) (ho_292 y z)))) (= x y))))) (let ((_let_55 (forall ((u |u_(-> tptp.pi_Rep tptp.set_pi_Rep Bool)|) (e |u_(-> tptp.set_pi_Rep Bool)|) (i tptp.pi_Rep)) (not (forall ((v |u_(-> tptp.pi_Rep tptp.set_pi_Rep Bool)|)) (not (forall ((ii tptp.pi_Rep)) (= (ho_152 v ii) (ite (= i ii) e (ho_152 u ii)))))))))) (let ((_let_56 (forall ((x |u_(-> tptp.pi_Rep tptp.set_pi_Rep Bool)|) (y |u_(-> tptp.pi_Rep tptp.set_pi_Rep Bool)|)) (or (not (forall ((z tptp.pi_Rep)) (= (ho_152 x z) (ho_152 y z)))) (= x y))))) (let ((_let_57 (forall ((u |u_(-> tptp.late_freeRes tptp.produc1357834675reeRes)|) (e tptp.produc1357834675reeRes) (i tptp.late_freeRes)) (not (forall ((v |u_(-> tptp.late_freeRes tptp.produc1357834675reeRes)|)) (not (forall ((ii tptp.late_freeRes)) (= (ho_208 v ii) (ite (= i ii) e (ho_208 u ii)))))))))) (let ((_let_58 (forall ((x |u_(-> tptp.late_freeRes tptp.produc1357834675reeRes)|) (y |u_(-> tptp.late_freeRes tptp.produc1357834675reeRes)|)) (or (not (forall ((z tptp.late_freeRes)) (= (ho_208 x z) (ho_208 y z)))) (= x y))))) (let ((_let_59 (forall ((u |u_(-> tptp.list_P227219501e_name tptp.set_pi_Rep tptp.set_pi_Rep)|) (e |u_(-> tptp.set_pi_Rep tptp.set_pi_Rep)|) (i tptp.list_P227219501e_name)) (not (forall ((v |u_(-> tptp.list_P227219501e_name tptp.set_pi_Rep tptp.set_pi_Rep)|)) (not (forall ((ii tptp.list_P227219501e_name)) (= (ho_149 v ii) (ite (= i ii) e (ho_149 u ii)))))))))) (let ((_let_60 (forall ((x |u_(-> tptp.list_P227219501e_name tptp.set_pi_Rep tptp.set_pi_Rep)|) (y |u_(-> tptp.list_P227219501e_name tptp.set_pi_Rep tptp.set_pi_Rep)|)) (or (not (forall ((z tptp.list_P227219501e_name)) (= (ho_149 x z) (ho_149 y z)))) (= x y))))) (let ((_let_61 (forall ((u |u_(-> tptp.produc367475239e_name tptp.produc367475239e_name)|) (e tptp.produc367475239e_name) (i tptp.produc367475239e_name)) (not (forall ((v |u_(-> tptp.produc367475239e_name tptp.produc367475239e_name)|)) (not (forall ((ii tptp.produc367475239e_name)) (= (ho_166 v ii) (ite (= i ii) e (ho_166 u ii)))))))))) (let ((_let_62 (forall ((x |u_(-> tptp.produc367475239e_name tptp.produc367475239e_name)|) (y |u_(-> tptp.produc367475239e_name tptp.produc367475239e_name)|)) (or (not (forall ((z tptp.produc367475239e_name)) (= (ho_166 x z) (ho_166 y z)))) (= x y))))) (let ((_let_63 (forall ((u |u_(-> tptp.late_freeRes tptp.set_Late_freeRes Bool)|) (e |u_(-> tptp.set_Late_freeRes Bool)|) (i tptp.late_freeRes)) (not (forall ((v |u_(-> tptp.late_freeRes tptp.set_Late_freeRes Bool)|)) (not (forall ((ii tptp.late_freeRes)) (= (ho_146 v ii) (ite (= i ii) e (ho_146 u ii)))))))))) (let ((_let_64 (forall ((x |u_(-> tptp.late_freeRes tptp.set_Late_freeRes Bool)|) (y |u_(-> tptp.late_freeRes tptp.set_Late_freeRes Bool)|)) (or (not (forall ((z tptp.late_freeRes)) (= (ho_146 x z) (ho_146 y z)))) (= x y))))) (let ((_let_65 (forall ((u |u_(-> tptp.pi tptp.set_pi Bool)|) (e |u_(-> tptp.set_pi Bool)|) (i tptp.pi)) (not (forall ((v |u_(-> tptp.pi tptp.set_pi Bool)|)) (not (forall ((ii tptp.pi)) (= (ho_164 v ii) (ite (= i ii) e (ho_164 u ii)))))))))) (let ((_let_66 (forall ((x |u_(-> tptp.pi tptp.set_pi Bool)|) (y |u_(-> tptp.pi tptp.set_pi Bool)|)) (or (not (forall ((z tptp.pi)) (= (ho_164 x z) (ho_164 y z)))) (= x y))))) (let ((_let_67 (forall ((u |u_(-> tptp.produc1357834675reeRes Bool)|) (e Bool) (i tptp.produc1357834675reeRes)) (not (forall ((v |u_(-> tptp.produc1357834675reeRes Bool)|)) (not (forall ((ii tptp.produc1357834675reeRes)) (= (ho_211 v ii) (ite (= i ii) e (ho_211 u ii)))))))))) (let ((_let_68 (forall ((x |u_(-> tptp.produc1357834675reeRes Bool)|) (y |u_(-> tptp.produc1357834675reeRes Bool)|)) (or (not (forall ((z tptp.produc1357834675reeRes)) (= (ho_211 x z) (ho_211 y z)))) (= x y))))) (let ((_let_69 (forall ((u |u_(-> tptp.set_Late_freeRes Bool)|) (e Bool) (i tptp.set_Late_freeRes)) (not (forall ((v |u_(-> tptp.set_Late_freeRes Bool)|)) (not (forall ((ii tptp.set_Late_freeRes)) (= (ho_147 v ii) (ite (= i ii) e (ho_147 u ii)))))))))) (let ((_let_70 (forall ((x |u_(-> tptp.set_Late_freeRes Bool)|) (y |u_(-> tptp.set_Late_freeRes Bool)|)) (or (not (forall ((z tptp.set_Late_freeRes)) (= (ho_147 x z) (ho_147 y z)))) (= x y))))) (let ((_let_71 (forall ((u |u_(-> tptp.list_P227219501e_name _u_(-> tptp.pi tptp.late_freeRes)_ tptp.pi tptp.late_freeRes)|) (e |u_(-> _u_(-> tptp.pi tptp.late_freeRes)_ tptp.pi tptp.late_freeRes)|) (i tptp.list_P227219501e_name)) (not (forall ((v |u_(-> tptp.list_P227219501e_name _u_(-> tptp.pi tptp.late_freeRes)_ tptp.pi tptp.late_freeRes)|)) (not (forall ((ii tptp.list_P227219501e_name)) (= (ho_134 v ii) (ite (= i ii) e (ho_134 u ii)))))))))) (let ((_let_72 (forall ((x |u_(-> tptp.list_P227219501e_name _u_(-> tptp.pi tptp.late_freeRes)_ tptp.pi tptp.late_freeRes)|) (y |u_(-> tptp.list_P227219501e_name _u_(-> tptp.pi tptp.late_freeRes)_ tptp.pi tptp.late_freeRes)|)) (or (not (forall ((z tptp.list_P227219501e_name)) (= (ho_134 x z) (ho_134 y z)))) (= x y))))) (let ((_let_73 (forall ((u |u_(-> tptp.list_P227219501e_name tptp.set_Late_freeRes tptp.set_Late_freeRes)|) (e |u_(-> tptp.set_Late_freeRes tptp.set_Late_freeRes)|) (i tptp.list_P227219501e_name)) (not (forall ((v |u_(-> tptp.list_P227219501e_name tptp.set_Late_freeRes tptp.set_Late_freeRes)|)) (not (forall ((ii tptp.list_P227219501e_name)) (= (ho_143 v ii) (ite (= i ii) e (ho_143 u ii)))))))))) (let ((_let_74 (forall ((x |u_(-> tptp.list_P227219501e_name tptp.set_Late_freeRes tptp.set_Late_freeRes)|) (y |u_(-> tptp.list_P227219501e_name tptp.set_Late_freeRes tptp.set_Late_freeRes)|)) (or (not (forall ((z tptp.list_P227219501e_name)) (= (ho_143 x z) (ho_143 y z)))) (= x y))))) (let ((_let_75 (forall ((u |u_(-> tptp.late_subject tptp.set_Late_subject Bool)|) (e |u_(-> tptp.set_Late_subject Bool)|) (i tptp.late_subject)) (not (forall ((v |u_(-> tptp.late_subject tptp.set_Late_subject Bool)|)) (not (forall ((ii tptp.late_subject)) (= (ho_140 v ii) (ite (= i ii) e (ho_140 u ii)))))))))) (let ((_let_76 (forall ((x |u_(-> tptp.late_subject tptp.set_Late_subject Bool)|) (y |u_(-> tptp.late_subject tptp.set_Late_subject Bool)|)) (or (not (forall ((z tptp.late_subject)) (= (ho_140 x z) (ho_140 y z)))) (= x y))))) (let ((_let_77 (forall ((u |u_(-> tptp.list_P227219501e_name tptp.set_Late_subject tptp.set_Late_subject)|) (e |u_(-> tptp.set_Late_subject tptp.set_Late_subject)|) (i tptp.list_P227219501e_name)) (not (forall ((v |u_(-> tptp.list_P227219501e_name tptp.set_Late_subject tptp.set_Late_subject)|)) (not (forall ((ii tptp.list_P227219501e_name)) (= (ho_137 v ii) (ite (= i ii) e (ho_137 u ii)))))))))) (let ((_let_78 (forall ((x |u_(-> tptp.list_P227219501e_name tptp.set_Late_subject tptp.set_Late_subject)|) (y |u_(-> tptp.list_P227219501e_name tptp.set_Late_subject tptp.set_Late_subject)|)) (or (not (forall ((z tptp.list_P227219501e_name)) (= (ho_137 x z) (ho_137 y z)))) (= x y))))) (let ((_let_79 (forall ((u |u_(-> tptp.produc2052722628s_name tptp.produc2052722628s_name)|) (e tptp.produc2052722628s_name) (i tptp.produc2052722628s_name)) (not (forall ((v |u_(-> tptp.produc2052722628s_name tptp.produc2052722628s_name)|)) (not (forall ((ii tptp.produc2052722628s_name)) (= (ho_304 v ii) (ite (= i ii) e (ho_304 u ii)))))))))) (let ((_let_80 (forall ((x |u_(-> tptp.produc2052722628s_name tptp.produc2052722628s_name)|) (y |u_(-> tptp.produc2052722628s_name tptp.produc2052722628s_name)|)) (or (not (forall ((z tptp.produc2052722628s_name)) (= (ho_304 x z) (ho_304 y z)))) (= x y))))) (let ((_let_81 (forall ((u |u_(-> tptp.set_Late_subject tptp.set_Late_subject)|) (e tptp.set_Late_subject) (i tptp.set_Late_subject)) (not (forall ((v |u_(-> tptp.set_Late_subject tptp.set_Late_subject)|)) (not (forall ((ii tptp.set_Late_subject)) (= (ho_138 v ii) (ite (= i ii) e (ho_138 u ii)))))))))) (let ((_let_82 (forall ((x |u_(-> tptp.set_Late_subject tptp.set_Late_subject)|) (y |u_(-> tptp.set_Late_subject tptp.set_Late_subject)|)) (or (not (forall ((z tptp.set_Late_subject)) (= (ho_138 x z) (ho_138 y z)))) (= x y))))) (let ((_let_83 (forall ((u |u_(-> tptp.produc1359399907ubject Bool)|) (e Bool) (i tptp.produc1359399907ubject)) (not (forall ((v |u_(-> tptp.produc1359399907ubject Bool)|)) (not (forall ((ii tptp.produc1359399907ubject)) (= (ho_181 v ii) (ite (= i ii) e (ho_181 u ii)))))))))) (let ((_let_84 (forall ((x |u_(-> tptp.produc1359399907ubject Bool)|) (y |u_(-> tptp.produc1359399907ubject Bool)|)) (or (not (forall ((z tptp.produc1359399907ubject)) (= (ho_181 x z) (ho_181 y z)))) (= x y))))) (let ((_let_85 (forall ((u |u_(-> tptp.list_P227219501e_name tptp.produc257012921pi_Rep tptp.produc257012921pi_Rep)|) (e |u_(-> tptp.produc257012921pi_Rep tptp.produc257012921pi_Rep)|) (i tptp.list_P227219501e_name)) (not (forall ((v |u_(-> tptp.list_P227219501e_name tptp.produc257012921pi_Rep tptp.produc257012921pi_Rep)|)) (not (forall ((ii tptp.list_P227219501e_name)) (= (ho_282 v ii) (ite (= i ii) e (ho_282 u ii)))))))))) (let ((_let_86 (forall ((x |u_(-> tptp.list_P227219501e_name tptp.produc257012921pi_Rep tptp.produc257012921pi_Rep)|) (y |u_(-> tptp.list_P227219501e_name tptp.produc257012921pi_Rep tptp.produc257012921pi_Rep)|)) (or (not (forall ((z tptp.list_P227219501e_name)) (= (ho_282 x z) (ho_282 y z)))) (= x y))))) (let ((_let_87 (forall ((u |u_(-> _u_(-> tptp.pi tptp.late_freeRes)_ tptp.pi tptp.late_freeRes)|) (e |u_(-> tptp.pi tptp.late_freeRes)|) (i |u_(-> tptp.pi tptp.late_freeRes)|)) (not (forall ((v |u_(-> _u_(-> tptp.pi tptp.late_freeRes)_ tptp.pi tptp.late_freeRes)|)) (not (forall ((ii |u_(-> tptp.pi tptp.late_freeRes)|)) (= (ho_135 v ii) (ite (= i ii) e (ho_135 u ii)))))))))) (let ((_let_88 (forall ((x |u_(-> _u_(-> tptp.pi tptp.late_freeRes)_ tptp.pi tptp.late_freeRes)|) (y |u_(-> _u_(-> tptp.pi tptp.late_freeRes)_ tptp.pi tptp.late_freeRes)|)) (or (not (forall ((z |u_(-> tptp.pi tptp.late_freeRes)|)) (= (ho_135 x z) (ho_135 y z)))) (= x y))))) (let ((_let_89 (forall ((u |u_(-> tptp.produc1359399907ubject tptp.produc1359399907ubject)|) (e tptp.produc1359399907ubject) (i tptp.produc1359399907ubject)) (not (forall ((v |u_(-> tptp.produc1359399907ubject tptp.produc1359399907ubject)|)) (not (forall ((ii tptp.produc1359399907ubject)) (= (ho_274 v ii) (ite (= i ii) e (ho_274 u ii)))))))))) (let ((_let_90 (forall ((x |u_(-> tptp.produc1359399907ubject tptp.produc1359399907ubject)|) (y |u_(-> tptp.produc1359399907ubject tptp.produc1359399907ubject)|)) (or (not (forall ((z tptp.produc1359399907ubject)) (= (ho_274 x z) (ho_274 y z)))) (= x y))))) (let ((_let_91 (forall ((u |u_(-> tptp.name tptp.late_residual Bool)|) (e |u_(-> tptp.late_residual Bool)|) (i tptp.name)) (not (forall ((v |u_(-> tptp.name tptp.late_residual Bool)|)) (not (forall ((ii tptp.name)) (= (ho_378 v ii) (ite (= i ii) e (ho_378 u ii)))))))))) (let ((_let_92 (forall ((x |u_(-> tptp.name tptp.late_residual Bool)|) (y |u_(-> tptp.name tptp.late_residual Bool)|)) (or (not (forall ((z tptp.name)) (= (ho_378 x z) (ho_378 y z)))) (= x y))))) (let ((_let_93 (forall ((u |u_(-> tptp.late_subject tptp.pi tptp.produc140253050ect_pi)|) (e |u_(-> tptp.pi tptp.produc140253050ect_pi)|) (i tptp.late_subject)) (not (forall ((v |u_(-> tptp.late_subject tptp.pi tptp.produc140253050ect_pi)|)) (not (forall ((ii tptp.late_subject)) (= (ho_195 v ii) (ite (= i ii) e (ho_195 u ii)))))))))) (let ((_let_94 (forall ((x |u_(-> tptp.late_subject tptp.pi tptp.produc140253050ect_pi)|) (y |u_(-> tptp.late_subject tptp.pi tptp.produc140253050ect_pi)|)) (or (not (forall ((z tptp.late_subject)) (= (ho_195 x z) (ho_195 y z)))) (= x y))))) (let ((_let_95 (forall ((u |u_(-> tptp.late_freeRes tptp.produc355105483reeRes)|) (e tptp.produc355105483reeRes) (i tptp.late_freeRes)) (not (forall ((v |u_(-> tptp.late_freeRes tptp.produc355105483reeRes)|)) (not (forall ((ii tptp.late_freeRes)) (= (ho_184 v ii) (ite (= i ii) e (ho_184 u ii)))))))))) (let ((_let_96 (forall ((x |u_(-> tptp.late_freeRes tptp.produc355105483reeRes)|) (y |u_(-> tptp.late_freeRes tptp.produc355105483reeRes)|)) (or (not (forall ((z tptp.late_freeRes)) (= (ho_184 x z) (ho_184 y z)))) (= x y))))) (let ((_let_97 (forall ((u |u_(-> _u_(-> tptp.late_freeRes tptp.late_subject)_ tptp.late_freeRes tptp.late_subject)|) (e |u_(-> tptp.late_freeRes tptp.late_subject)|) (i |u_(-> tptp.late_freeRes tptp.late_subject)|)) (not (forall ((v |u_(-> _u_(-> tptp.late_freeRes tptp.late_subject)_ tptp.late_freeRes tptp.late_subject)|)) (not (forall ((ii |u_(-> tptp.late_freeRes tptp.late_subject)|)) (= (ho_105 v ii) (ite (= i ii) e (ho_105 u ii)))))))))) (let ((_let_98 (forall ((x |u_(-> _u_(-> tptp.late_freeRes tptp.late_subject)_ tptp.late_freeRes tptp.late_subject)|) (y |u_(-> _u_(-> tptp.late_freeRes tptp.late_subject)_ tptp.late_freeRes tptp.late_subject)|)) (or (not (forall ((z |u_(-> tptp.late_freeRes tptp.late_subject)|)) (= (ho_105 x z) (ho_105 y z)))) (= x y))))) (let ((_let_99 (forall ((u |u_(-> tptp.pi tptp.late_freeRes)|) (e tptp.late_freeRes) (i tptp.pi)) (not (forall ((v |u_(-> tptp.pi tptp.late_freeRes)|)) (not (forall ((ii tptp.pi)) (= (ho_132 v ii) (ite (= i ii) e (ho_132 u ii)))))))))) (let ((_let_100 (forall ((x |u_(-> tptp.pi tptp.late_freeRes)|) (y |u_(-> tptp.pi tptp.late_freeRes)|)) (or (not (forall ((z tptp.pi)) (= (ho_132 x z) (ho_132 y z)))) (= x y))))) (let ((_let_101 (forall ((u |u_(-> tptp.list_P227219501e_name _u_(-> tptp.name tptp.late_freeRes)_ tptp.name tptp.late_freeRes)|) (e |u_(-> _u_(-> tptp.name tptp.late_freeRes)_ tptp.name tptp.late_freeRes)|) (i tptp.list_P227219501e_name)) (not (forall ((v |u_(-> tptp.list_P227219501e_name _u_(-> tptp.name tptp.late_freeRes)_ tptp.name tptp.late_freeRes)|)) (not (forall ((ii tptp.list_P227219501e_name)) (= (ho_130 v ii) (ite (= i ii) e (ho_130 u ii)))))))))) (let ((_let_102 (forall ((x |u_(-> tptp.list_P227219501e_name _u_(-> tptp.name tptp.late_freeRes)_ tptp.name tptp.late_freeRes)|) (y |u_(-> tptp.list_P227219501e_name _u_(-> tptp.name tptp.late_freeRes)_ tptp.name tptp.late_freeRes)|)) (or (not (forall ((z tptp.list_P227219501e_name)) (= (ho_130 x z) (ho_130 y z)))) (= x y))))) (let ((_let_103 (forall ((u |u_(-> _u_(-> tptp.name tptp.late_freeRes)_ tptp.name tptp.late_freeRes)|) (e |u_(-> tptp.name tptp.late_freeRes)|) (i |u_(-> tptp.name tptp.late_freeRes)|)) (not (forall ((v |u_(-> _u_(-> tptp.name tptp.late_freeRes)_ tptp.name tptp.late_freeRes)|)) (not (forall ((ii |u_(-> tptp.name tptp.late_freeRes)|)) (= (ho_131 v ii) (ite (= i ii) e (ho_131 u ii)))))))))) (let ((_let_104 (forall ((x |u_(-> _u_(-> tptp.name tptp.late_freeRes)_ tptp.name tptp.late_freeRes)|) (y |u_(-> _u_(-> tptp.name tptp.late_freeRes)_ tptp.name tptp.late_freeRes)|)) (or (not (forall ((z |u_(-> tptp.name tptp.late_freeRes)|)) (= (ho_131 x z) (ho_131 y z)))) (= x y))))) (let ((_let_105 (forall ((u |u_(-> tptp.name tptp.late_freeRes)|) (e tptp.late_freeRes) (i tptp.name)) (not (forall ((v |u_(-> tptp.name tptp.late_freeRes)|)) (not (forall ((ii tptp.name)) (= (ho_128 v ii) (ite (= i ii) e (ho_128 u ii)))))))))) (let ((_let_106 (forall ((x |u_(-> tptp.name tptp.late_freeRes)|) (y |u_(-> tptp.name tptp.late_freeRes)|)) (or (not (forall ((z tptp.name)) (= (ho_128 x z) (ho_128 y z)))) (= x y))))) (let ((_let_107 (forall ((u |u_(-> tptp.late_subject Bool)|) (e Bool) (i tptp.late_subject)) (not (forall ((v |u_(-> tptp.late_subject Bool)|)) (not (forall ((ii tptp.late_subject)) (= (ho_68 v ii) (ite (= i ii) e (ho_68 u ii)))))))))) (let ((_let_108 (forall ((x |u_(-> tptp.late_subject Bool)|) (y |u_(-> tptp.late_subject Bool)|)) (or (not (forall ((z tptp.late_subject)) (= (ho_68 x z) (ho_68 y z)))) (= x y))))) (let ((_let_109 (forall ((u |u_(-> tptp.list_P227219501e_name tptp.set_name tptp.set_name)|) (e |u_(-> tptp.set_name tptp.set_name)|) (i tptp.list_P227219501e_name)) (not (forall ((v |u_(-> tptp.list_P227219501e_name tptp.set_name tptp.set_name)|)) (not (forall ((ii tptp.list_P227219501e_name)) (= (ho_155 v ii) (ite (= i ii) e (ho_155 u ii)))))))))) (let ((_let_110 (forall ((x |u_(-> tptp.list_P227219501e_name tptp.set_name tptp.set_name)|) (y |u_(-> tptp.list_P227219501e_name tptp.set_name tptp.set_name)|)) (or (not (forall ((z tptp.list_P227219501e_name)) (= (ho_155 x z) (ho_155 y z)))) (= x y))))) (let ((_let_111 (forall ((u |u_(-> _u_(-> tptp.pi_Rep tptp.late_freeRes)_ tptp.pi_Rep tptp.late_freeRes)|) (e |u_(-> tptp.pi_Rep tptp.late_freeRes)|) (i |u_(-> tptp.pi_Rep tptp.late_freeRes)|)) (not (forall ((v |u_(-> _u_(-> tptp.pi_Rep tptp.late_freeRes)_ tptp.pi_Rep tptp.late_freeRes)|)) (not (forall ((ii |u_(-> tptp.pi_Rep tptp.late_freeRes)|)) (= (ho_127 v ii) (ite (= i ii) e (ho_127 u ii)))))))))) (let ((_let_112 (forall ((x |u_(-> _u_(-> tptp.pi_Rep tptp.late_freeRes)_ tptp.pi_Rep tptp.late_freeRes)|) (y |u_(-> _u_(-> tptp.pi_Rep tptp.late_freeRes)_ tptp.pi_Rep tptp.late_freeRes)|)) (or (not (forall ((z |u_(-> tptp.pi_Rep tptp.late_freeRes)|)) (= (ho_127 x z) (ho_127 y z)))) (= x y))))) (let ((_let_113 (forall ((u |u_(-> tptp.set_Late_subject Bool)|) (e Bool) (i tptp.set_Late_subject)) (not (forall ((v |u_(-> tptp.set_Late_subject Bool)|)) (not (forall ((ii tptp.set_Late_subject)) (= (ho_141 v ii) (ite (= i ii) e (ho_141 u ii)))))))))) (let ((_let_114 (forall ((x |u_(-> tptp.set_Late_subject Bool)|) (y |u_(-> tptp.set_Late_subject Bool)|)) (or (not (forall ((z tptp.set_Late_subject)) (= (ho_141 x z) (ho_141 y z)))) (= x y))))) (let ((_let_115 (forall ((u |u_(-> tptp.name tptp.produc1357834675reeRes Bool)|) (e |u_(-> tptp.produc1357834675reeRes Bool)|) (i tptp.name)) (not (forall ((v |u_(-> tptp.name tptp.produc1357834675reeRes Bool)|)) (not (forall ((ii tptp.name)) (= (ho_210 v ii) (ite (= i ii) e (ho_210 u ii)))))))))) (let ((_let_116 (forall ((x |u_(-> tptp.name tptp.produc1357834675reeRes Bool)|) (y |u_(-> tptp.name tptp.produc1357834675reeRes Bool)|)) (or (not (forall ((z tptp.name)) (= (ho_210 x z) (ho_210 y z)))) (= x y))))) (let ((_let_117 (forall ((u |u_(-> tptp.list_P227219501e_name _u_(-> tptp.late_freeRes tptp.late_freeRes)_ tptp.late_freeRes tptp.late_freeRes)|) (e |u_(-> _u_(-> tptp.late_freeRes tptp.late_freeRes)_ tptp.late_freeRes tptp.late_freeRes)|) (i tptp.list_P227219501e_name)) (not (forall ((v |u_(-> tptp.list_P227219501e_name _u_(-> tptp.late_freeRes tptp.late_freeRes)_ tptp.late_freeRes tptp.late_freeRes)|)) (not (forall ((ii tptp.list_P227219501e_name)) (= (ho_122 v ii) (ite (= i ii) e (ho_122 u ii)))))))))) (let ((_let_118 (forall ((x |u_(-> tptp.list_P227219501e_name _u_(-> tptp.late_freeRes tptp.late_freeRes)_ tptp.late_freeRes tptp.late_freeRes)|) (y |u_(-> tptp.list_P227219501e_name _u_(-> tptp.late_freeRes tptp.late_freeRes)_ tptp.late_freeRes tptp.late_freeRes)|)) (or (not (forall ((z tptp.list_P227219501e_name)) (= (ho_122 x z) (ho_122 y z)))) (= x y))))) (let ((_let_119 (forall ((u |u_(-> tptp.list_P227219501e_name _u_(-> tptp.late_subject tptp.late_freeRes)_ tptp.late_subject tptp.late_freeRes)|) (e |u_(-> _u_(-> tptp.late_subject tptp.late_freeRes)_ tptp.late_subject tptp.late_freeRes)|) (i tptp.list_P227219501e_name)) (not (forall ((v |u_(-> tptp.list_P227219501e_name _u_(-> tptp.late_subject tptp.late_freeRes)_ tptp.late_subject tptp.late_freeRes)|)) (not (forall ((ii tptp.list_P227219501e_name)) (= (ho_119 v ii) (ite (= i ii) e (ho_119 u ii)))))))))) (let ((_let_120 (forall ((x |u_(-> tptp.list_P227219501e_name _u_(-> tptp.late_subject tptp.late_freeRes)_ tptp.late_subject tptp.late_freeRes)|) (y |u_(-> tptp.list_P227219501e_name _u_(-> tptp.late_subject tptp.late_freeRes)_ tptp.late_subject tptp.late_freeRes)|)) (or (not (forall ((z tptp.list_P227219501e_name)) (= (ho_119 x z) (ho_119 y z)))) (= x y))))) (let ((_let_121 (forall ((u |u_(-> tptp.set_pi_Rep Bool)|) (e Bool) (i tptp.set_pi_Rep)) (not (forall ((v |u_(-> tptp.set_pi_Rep Bool)|)) (not (forall ((ii tptp.set_pi_Rep)) (= (ho_153 v ii) (ite (= i ii) e (ho_153 u ii)))))))))) (let ((_let_122 (forall ((x |u_(-> tptp.set_pi_Rep Bool)|) (y |u_(-> tptp.set_pi_Rep Bool)|)) (or (not (forall ((z tptp.set_pi_Rep)) (= (ho_153 x z) (ho_153 y z)))) (= x y))))) (let ((_let_123 (forall ((u |u_(-> _u_(-> tptp.late_subject tptp.late_freeRes)_ tptp.late_subject tptp.late_freeRes)|) (e |u_(-> tptp.late_subject tptp.late_freeRes)|) (i |u_(-> tptp.late_subject tptp.late_freeRes)|)) (not (forall ((v |u_(-> _u_(-> tptp.late_subject tptp.late_freeRes)_ tptp.late_subject tptp.late_freeRes)|)) (not (forall ((ii |u_(-> tptp.late_subject tptp.late_freeRes)|)) (= (ho_120 v ii) (ite (= i ii) e (ho_120 u ii)))))))))) (let ((_let_124 (forall ((x |u_(-> _u_(-> tptp.late_subject tptp.late_freeRes)_ tptp.late_subject tptp.late_freeRes)|) (y |u_(-> _u_(-> tptp.late_subject tptp.late_freeRes)_ tptp.late_subject tptp.late_freeRes)|)) (or (not (forall ((z |u_(-> tptp.late_subject tptp.late_freeRes)|)) (= (ho_120 x z) (ho_120 y z)))) (= x y))))) (let ((_let_125 (forall ((u |u_(-> tptp.late_subject tptp.late_freeRes tptp.produc355105483reeRes)|) (e |u_(-> tptp.late_freeRes tptp.produc355105483reeRes)|) (i tptp.late_subject)) (not (forall ((v |u_(-> tptp.late_subject tptp.late_freeRes tptp.produc355105483reeRes)|)) (not (forall ((ii tptp.late_subject)) (= (ho_183 v ii) (ite (= i ii) e (ho_183 u ii)))))))))) (let ((_let_126 (forall ((x |u_(-> tptp.late_subject tptp.late_freeRes tptp.produc355105483reeRes)|) (y |u_(-> tptp.late_subject tptp.late_freeRes tptp.produc355105483reeRes)|)) (or (not (forall ((z tptp.late_subject)) (= (ho_183 x z) (ho_183 y z)))) (= x y))))) (let ((_let_127 (forall ((u |u_(-> tptp.list_P227219501e_name _u_(-> tptp.pi tptp.late_subject)_ tptp.pi tptp.late_subject)|) (e |u_(-> _u_(-> tptp.pi tptp.late_subject)_ tptp.pi tptp.late_subject)|) (i tptp.list_P227219501e_name)) (not (forall ((v |u_(-> tptp.list_P227219501e_name _u_(-> tptp.pi tptp.late_subject)_ tptp.pi tptp.late_subject)|)) (not (forall ((ii tptp.list_P227219501e_name)) (= (ho_115 v ii) (ite (= i ii) e (ho_115 u ii)))))))))) (let ((_let_128 (forall ((x |u_(-> tptp.list_P227219501e_name _u_(-> tptp.pi tptp.late_subject)_ tptp.pi tptp.late_subject)|) (y |u_(-> tptp.list_P227219501e_name _u_(-> tptp.pi tptp.late_subject)_ tptp.pi tptp.late_subject)|)) (or (not (forall ((z tptp.list_P227219501e_name)) (= (ho_115 x z) (ho_115 y z)))) (= x y))))) (let ((_let_129 (forall ((u |u_(-> _u_(-> tptp.produc367475239e_name tptp.produc367475239e_name)_ tptp.list_P227219501e_name tptp.list_P227219501e_name Bool)|) (e |u_(-> tptp.list_P227219501e_name tptp.list_P227219501e_name Bool)|) (i |u_(-> tptp.produc367475239e_name tptp.produc367475239e_name)|)) (not (forall ((v |u_(-> _u_(-> tptp.produc367475239e_name tptp.produc367475239e_name)_ tptp.list_P227219501e_name tptp.list_P227219501e_name Bool)|)) (not (forall ((ii |u_(-> tptp.produc367475239e_name tptp.produc367475239e_name)|)) (= (ho_167 v ii) (ite (= i ii) e (ho_167 u ii)))))))))) (let ((_let_130 (forall ((x |u_(-> _u_(-> tptp.produc367475239e_name tptp.produc367475239e_name)_ tptp.list_P227219501e_name tptp.list_P227219501e_name Bool)|) (y |u_(-> _u_(-> tptp.produc367475239e_name tptp.produc367475239e_name)_ tptp.list_P227219501e_name tptp.list_P227219501e_name Bool)|)) (or (not (forall ((z |u_(-> tptp.produc367475239e_name tptp.produc367475239e_name)|)) (= (ho_167 x z) (ho_167 y z)))) (= x y))))) (let ((_let_131 (forall ((u |u_(-> tptp.late_subject tptp.late_subject tptp.produc1359399907ubject)|) (e |u_(-> tptp.late_subject tptp.produc1359399907ubject)|) (i tptp.late_subject)) (not (forall ((v |u_(-> tptp.late_subject tptp.late_subject tptp.produc1359399907ubject)|)) (not (forall ((ii tptp.late_subject)) (= (ho_177 v ii) (ite (= i ii) e (ho_177 u ii)))))))))) (let ((_let_132 (forall ((x |u_(-> tptp.late_subject tptp.late_subject tptp.produc1359399907ubject)|) (y |u_(-> tptp.late_subject tptp.late_subject tptp.produc1359399907ubject)|)) (or (not (forall ((z tptp.late_subject)) (= (ho_177 x z) (ho_177 y z)))) (= x y))))) (let ((_let_133 (forall ((u |u_(-> _u_(-> tptp.pi tptp.late_subject)_ tptp.pi tptp.late_subject)|) (e |u_(-> tptp.pi tptp.late_subject)|) (i |u_(-> tptp.pi tptp.late_subject)|)) (not (forall ((v |u_(-> _u_(-> tptp.pi tptp.late_subject)_ tptp.pi tptp.late_subject)|)) (not (forall ((ii |u_(-> tptp.pi tptp.late_subject)|)) (= (ho_116 v ii) (ite (= i ii) e (ho_116 u ii)))))))))) (let ((_let_134 (forall ((x |u_(-> _u_(-> tptp.pi tptp.late_subject)_ tptp.pi tptp.late_subject)|) (y |u_(-> _u_(-> tptp.pi tptp.late_subject)_ tptp.pi tptp.late_subject)|)) (or (not (forall ((z |u_(-> tptp.pi tptp.late_subject)|)) (= (ho_116 x z) (ho_116 y z)))) (= x y))))) (let ((_let_135 (forall ((u |u_(-> tptp.pi tptp.product_prod_pi_pi)|) (e tptp.product_prod_pi_pi) (i tptp.pi)) (not (forall ((v |u_(-> tptp.pi tptp.product_prod_pi_pi)|)) (not (forall ((ii tptp.pi)) (= (ho_53 v ii) (ite (= i ii) e (ho_53 u ii)))))))))) (let ((_let_136 (forall ((x |u_(-> tptp.pi tptp.product_prod_pi_pi)|) (y |u_(-> tptp.pi tptp.product_prod_pi_pi)|)) (or (not (forall ((z tptp.pi)) (= (ho_53 x z) (ho_53 y z)))) (= x y))))) (let ((_let_137 (forall ((u |u_(-> tptp.pi tptp.late_subject)|) (e tptp.late_subject) (i tptp.pi)) (not (forall ((v |u_(-> tptp.pi tptp.late_subject)|)) (not (forall ((ii tptp.pi)) (= (ho_113 v ii) (ite (= i ii) e (ho_113 u ii)))))))))) (let ((_let_138 (forall ((x |u_(-> tptp.pi tptp.late_subject)|) (y |u_(-> tptp.pi tptp.late_subject)|)) (or (not (forall ((z tptp.pi)) (= (ho_113 x z) (ho_113 y z)))) (= x y))))) (let ((_let_139 (forall ((u |u_(-> tptp.name tptp.name tptp.name)|) (e |u_(-> tptp.name tptp.name)|) (i tptp.name)) (not (forall ((v |u_(-> tptp.name tptp.name tptp.name)|)) (not (forall ((ii tptp.name)) (= (ho_268 v ii) (ite (= i ii) e (ho_268 u ii)))))))))) (let ((_let_140 (forall ((x |u_(-> tptp.name tptp.name tptp.name)|) (y |u_(-> tptp.name tptp.name tptp.name)|)) (or (not (forall ((z tptp.name)) (= (ho_268 x z) (ho_268 y z)))) (= x y))))) (let ((_let_141 (forall ((u |u_(-> tptp.produc1998742700t_name tptp.produc1998742700t_name)|) (e tptp.produc1998742700t_name) (i tptp.produc1998742700t_name)) (not (forall ((v |u_(-> tptp.produc1998742700t_name tptp.produc1998742700t_name)|)) (not (forall ((ii tptp.produc1998742700t_name)) (= (ho_286 v ii) (ite (= i ii) e (ho_286 u ii)))))))))) (let ((_let_142 (forall ((x |u_(-> tptp.produc1998742700t_name tptp.produc1998742700t_name)|) (y |u_(-> tptp.produc1998742700t_name tptp.produc1998742700t_name)|)) (or (not (forall ((z tptp.produc1998742700t_name)) (= (ho_286 x z) (ho_286 y z)))) (= x y))))) (let ((_let_143 (forall ((u |u_(-> tptp.late_subject tptp.name tptp.produc1998742700t_name)|) (e |u_(-> tptp.name tptp.produc1998742700t_name)|) (i tptp.late_subject)) (not (forall ((v |u_(-> tptp.late_subject tptp.name tptp.produc1998742700t_name)|)) (not (forall ((ii tptp.late_subject)) (= (ho_189 v ii) (ite (= i ii) e (ho_189 u ii)))))))))) (let ((_let_144 (forall ((x |u_(-> tptp.late_subject tptp.name tptp.produc1998742700t_name)|) (y |u_(-> tptp.late_subject tptp.name tptp.produc1998742700t_name)|)) (or (not (forall ((z tptp.late_subject)) (= (ho_189 x z) (ho_189 y z)))) (= x y))))) (let ((_let_145 (forall ((u |u_(-> tptp.pi tptp.produc140253050ect_pi)|) (e tptp.produc140253050ect_pi) (i tptp.pi)) (not (forall ((v |u_(-> tptp.pi tptp.produc140253050ect_pi)|)) (not (forall ((ii tptp.pi)) (= (ho_196 v ii) (ite (= i ii) e (ho_196 u ii)))))))))) (let ((_let_146 (forall ((x |u_(-> tptp.pi tptp.produc140253050ect_pi)|) (y |u_(-> tptp.pi tptp.produc140253050ect_pi)|)) (or (not (forall ((z tptp.pi)) (= (ho_196 x z) (ho_196 y z)))) (= x y))))) (let ((_let_147 (forall ((u |u_(-> tptp.produc355105483reeRes Bool)|) (e Bool) (i tptp.produc355105483reeRes)) (not (forall ((v |u_(-> tptp.produc355105483reeRes Bool)|)) (not (forall ((ii tptp.produc355105483reeRes)) (= (ho_187 v ii) (ite (= i ii) e (ho_187 u ii)))))))))) (let ((_let_148 (forall ((x |u_(-> tptp.produc355105483reeRes Bool)|) (y |u_(-> tptp.produc355105483reeRes Bool)|)) (or (not (forall ((z tptp.produc355105483reeRes)) (= (ho_187 x z) (ho_187 y z)))) (= x y))))) (let ((_let_149 (forall ((u |u_(-> tptp.list_P227219501e_name _u_(-> tptp.name tptp.late_subject)_ tptp.name tptp.late_subject)|) (e |u_(-> _u_(-> tptp.name tptp.late_subject)_ tptp.name tptp.late_subject)|) (i tptp.list_P227219501e_name)) (not (forall ((v |u_(-> tptp.list_P227219501e_name _u_(-> tptp.name tptp.late_subject)_ tptp.name tptp.late_subject)|)) (not (forall ((ii tptp.list_P227219501e_name)) (= (ho_111 v ii) (ite (= i ii) e (ho_111 u ii)))))))))) (let ((_let_150 (forall ((x |u_(-> tptp.list_P227219501e_name _u_(-> tptp.name tptp.late_subject)_ tptp.name tptp.late_subject)|) (y |u_(-> tptp.list_P227219501e_name _u_(-> tptp.name tptp.late_subject)_ tptp.name tptp.late_subject)|)) (or (not (forall ((z tptp.list_P227219501e_name)) (= (ho_111 x z) (ho_111 y z)))) (= x y))))) (let ((_let_151 (forall ((u |u_(-> tptp.set_Pr443758855e_name Bool)|) (e Bool) (i tptp.set_Pr443758855e_name)) (not (forall ((v |u_(-> tptp.set_Pr443758855e_name Bool)|)) (not (forall ((ii tptp.set_Pr443758855e_name)) (= (ho_175 v ii) (ite (= i ii) e (ho_175 u ii)))))))))) (let ((_let_152 (forall ((x |u_(-> tptp.set_Pr443758855e_name Bool)|) (y |u_(-> tptp.set_Pr443758855e_name Bool)|)) (or (not (forall ((z tptp.set_Pr443758855e_name)) (= (ho_175 x z) (ho_175 y z)))) (= x y))))) (let ((_let_153 (forall ((u |u_(-> tptp.list_P227219501e_name _u_(-> tptp.pi_Rep tptp.late_subject)_ tptp.pi_Rep tptp.late_subject)|) (e |u_(-> _u_(-> tptp.pi_Rep tptp.late_subject)_ tptp.pi_Rep tptp.late_subject)|) (i tptp.list_P227219501e_name)) (not (forall ((v |u_(-> tptp.list_P227219501e_name _u_(-> tptp.pi_Rep tptp.late_subject)_ tptp.pi_Rep tptp.late_subject)|)) (not (forall ((ii tptp.list_P227219501e_name)) (= (ho_108 v ii) (ite (= i ii) e (ho_108 u ii)))))))))) (let ((_let_154 (forall ((x |u_(-> tptp.list_P227219501e_name _u_(-> tptp.pi_Rep tptp.late_subject)_ tptp.pi_Rep tptp.late_subject)|) (y |u_(-> tptp.list_P227219501e_name _u_(-> tptp.pi_Rep tptp.late_subject)_ tptp.pi_Rep tptp.late_subject)|)) (or (not (forall ((z tptp.list_P227219501e_name)) (= (ho_108 x z) (ho_108 y z)))) (= x y))))) (let ((_let_155 (forall ((u |u_(-> tptp.pi_Rep tptp.late_freeRes)|) (e tptp.late_freeRes) (i tptp.pi_Rep)) (not (forall ((v |u_(-> tptp.pi_Rep tptp.late_freeRes)|)) (not (forall ((ii tptp.pi_Rep)) (= (ho_124 v ii) (ite (= i ii) e (ho_124 u ii)))))))))) (let ((_let_156 (forall ((x |u_(-> tptp.pi_Rep tptp.late_freeRes)|) (y |u_(-> tptp.pi_Rep tptp.late_freeRes)|)) (or (not (forall ((z tptp.pi_Rep)) (= (ho_124 x z) (ho_124 y z)))) (= x y))))) (let ((_let_157 (forall ((u |u_(-> _u_(-> tptp.pi_Rep tptp.late_subject)_ tptp.pi_Rep tptp.late_subject)|) (e |u_(-> tptp.pi_Rep tptp.late_subject)|) (i |u_(-> tptp.pi_Rep tptp.late_subject)|)) (not (forall ((v |u_(-> _u_(-> tptp.pi_Rep tptp.late_subject)_ tptp.pi_Rep tptp.late_subject)|)) (not (forall ((ii |u_(-> tptp.pi_Rep tptp.late_subject)|)) (= (ho_109 v ii) (ite (= i ii) e (ho_109 u ii)))))))))) (let ((_let_158 (forall ((x |u_(-> _u_(-> tptp.pi_Rep tptp.late_subject)_ tptp.pi_Rep tptp.late_subject)|) (y |u_(-> _u_(-> tptp.pi_Rep tptp.late_subject)_ tptp.pi_Rep tptp.late_subject)|)) (or (not (forall ((z |u_(-> tptp.pi_Rep tptp.late_subject)|)) (= (ho_109 x z) (ho_109 y z)))) (= x y))))) (let ((_let_159 (forall ((u |u_(-> tptp.produc1998742700t_name Bool)|) (e Bool) (i tptp.produc1998742700t_name)) (not (forall ((v |u_(-> tptp.produc1998742700t_name Bool)|)) (not (forall ((ii tptp.produc1998742700t_name)) (= (ho_193 v ii) (ite (= i ii) e (ho_193 u ii)))))))))) (let ((_let_160 (forall ((x |u_(-> tptp.produc1998742700t_name Bool)|) (y |u_(-> tptp.produc1998742700t_name Bool)|)) (or (not (forall ((z tptp.produc1998742700t_name)) (= (ho_193 x z) (ho_193 y z)))) (= x y))))) (let ((_let_161 (forall ((u |u_(-> tptp.pi_Rep tptp.late_subject)|) (e tptp.late_subject) (i tptp.pi_Rep)) (not (forall ((v |u_(-> tptp.pi_Rep tptp.late_subject)|)) (not (forall ((ii tptp.pi_Rep)) (= (ho_106 v ii) (ite (= i ii) e (ho_106 u ii)))))))))) (let ((_let_162 (forall ((x |u_(-> tptp.pi_Rep tptp.late_subject)|) (y |u_(-> tptp.pi_Rep tptp.late_subject)|)) (or (not (forall ((z tptp.pi_Rep)) (= (ho_106 x z) (ho_106 y z)))) (= x y))))) (let ((_let_163 (forall ((u |u_(-> tptp.list_P227219501e_name _u_(-> tptp.late_freeRes tptp.late_subject)_ tptp.late_freeRes tptp.late_subject)|) (e |u_(-> _u_(-> tptp.late_freeRes tptp.late_subject)_ tptp.late_freeRes tptp.late_subject)|) (i tptp.list_P227219501e_name)) (not (forall ((v |u_(-> tptp.list_P227219501e_name _u_(-> tptp.late_freeRes tptp.late_subject)_ tptp.late_freeRes tptp.late_subject)|)) (not (forall ((ii tptp.list_P227219501e_name)) (= (ho_104 v ii) (ite (= i ii) e (ho_104 u ii)))))))))) (let ((_let_164 (forall ((x |u_(-> tptp.list_P227219501e_name _u_(-> tptp.late_freeRes tptp.late_subject)_ tptp.late_freeRes tptp.late_subject)|) (y |u_(-> tptp.list_P227219501e_name _u_(-> tptp.late_freeRes tptp.late_subject)_ tptp.late_freeRes tptp.late_subject)|)) (or (not (forall ((z tptp.list_P227219501e_name)) (= (ho_104 x z) (ho_104 y z)))) (= x y))))) (let ((_let_165 (forall ((u |u_(-> tptp.late_freeRes tptp.late_subject)|) (e tptp.late_subject) (i tptp.late_freeRes)) (not (forall ((v |u_(-> tptp.late_freeRes tptp.late_subject)|)) (not (forall ((ii tptp.late_freeRes)) (= (ho_102 v ii) (ite (= i ii) e (ho_102 u ii)))))))))) (let ((_let_166 (forall ((x |u_(-> tptp.late_freeRes tptp.late_subject)|) (y |u_(-> tptp.late_freeRes tptp.late_subject)|)) (or (not (forall ((z tptp.late_freeRes)) (= (ho_102 x z) (ho_102 y z)))) (= x y))))) (let ((_let_167 (forall ((u |u_(-> tptp.pi tptp.pi tptp.product_prod_pi_pi)|) (e |u_(-> tptp.pi tptp.product_prod_pi_pi)|) (i tptp.pi)) (not (forall ((v |u_(-> tptp.pi tptp.pi tptp.product_prod_pi_pi)|)) (not (forall ((ii tptp.pi)) (= (ho_52 v ii) (ite (= i ii) e (ho_52 u ii)))))))))) (let ((_let_168 (forall ((x |u_(-> tptp.pi tptp.pi tptp.product_prod_pi_pi)|) (y |u_(-> tptp.pi tptp.pi tptp.product_prod_pi_pi)|)) (or (not (forall ((z tptp.pi)) (= (ho_52 x z) (ho_52 y z)))) (= x y))))) (let ((_let_169 (forall ((u |u_(-> tptp.product_prod_pi_pi tptp.set_Pr1834926343_pi_pi Bool)|) (e |u_(-> tptp.set_Pr1834926343_pi_pi Bool)|) (i tptp.product_prod_pi_pi)) (not (forall ((v |u_(-> tptp.product_prod_pi_pi tptp.set_Pr1834926343_pi_pi Bool)|)) (not (forall ((ii tptp.product_prod_pi_pi)) (= (ho_18 v ii) (ite (= i ii) e (ho_18 u ii)))))))))) (let ((_let_170 (forall ((x |u_(-> tptp.product_prod_pi_pi tptp.set_Pr1834926343_pi_pi Bool)|) (y |u_(-> tptp.product_prod_pi_pi tptp.set_Pr1834926343_pi_pi Bool)|)) (or (not (forall ((z tptp.product_prod_pi_pi)) (= (ho_18 x z) (ho_18 y z)))) (= x y))))) (let ((_let_171 (forall ((u |u_(-> tptp.list_name tptp.list_name)|) (e tptp.list_name) (i tptp.list_name)) (not (forall ((v |u_(-> tptp.list_name tptp.list_name)|)) (not (forall ((ii tptp.list_name)) (= (ho_325 v ii) (ite (= i ii) e (ho_325 u ii)))))))))) (let ((_let_172 (forall ((x |u_(-> tptp.list_name tptp.list_name)|) (y |u_(-> tptp.list_name tptp.list_name)|)) (or (not (forall ((z tptp.list_name)) (= (ho_325 x z) (ho_325 y z)))) (= x y))))) (let ((_let_173 (forall ((u |u_(-> _u_(-> tptp.name tptp.late_subject)_ tptp.name tptp.late_subject)|) (e |u_(-> tptp.name tptp.late_subject)|) (i |u_(-> tptp.name tptp.late_subject)|)) (not (forall ((v |u_(-> _u_(-> tptp.name tptp.late_subject)_ tptp.name tptp.late_subject)|)) (not (forall ((ii |u_(-> tptp.name tptp.late_subject)|)) (= (ho_112 v ii) (ite (= i ii) e (ho_112 u ii)))))))))) (let ((_let_174 (forall ((x |u_(-> _u_(-> tptp.name tptp.late_subject)_ tptp.name tptp.late_subject)|) (y |u_(-> _u_(-> tptp.name tptp.late_subject)_ tptp.name tptp.late_subject)|)) (or (not (forall ((z |u_(-> tptp.name tptp.late_subject)|)) (= (ho_112 x z) (ho_112 y z)))) (= x y))))) (let ((_let_175 (forall ((u |u_(-> tptp.late_freeRes tptp.late_freeRes tptp.produc1357834675reeRes)|) (e |u_(-> tptp.late_freeRes tptp.produc1357834675reeRes)|) (i tptp.late_freeRes)) (not (forall ((v |u_(-> tptp.late_freeRes tptp.late_freeRes tptp.produc1357834675reeRes)|)) (not (forall ((ii tptp.late_freeRes)) (= (ho_207 v ii) (ite (= i ii) e (ho_207 u ii)))))))))) (let ((_let_176 (forall ((x |u_(-> tptp.late_freeRes tptp.late_freeRes tptp.produc1357834675reeRes)|) (y |u_(-> tptp.late_freeRes tptp.late_freeRes tptp.produc1357834675reeRes)|)) (or (not (forall ((z tptp.late_freeRes)) (= (ho_207 x z) (ho_207 y z)))) (= x y))))) (let ((_let_177 (forall ((u |u_(-> tptp.late_subject tptp.late_subject)|) (e tptp.late_subject) (i tptp.late_subject)) (not (forall ((v |u_(-> tptp.late_subject tptp.late_subject)|)) (not (forall ((ii tptp.late_subject)) (= (ho_30 v ii) (ite (= i ii) e (ho_30 u ii)))))))))) (let ((_let_178 (forall ((x |u_(-> tptp.late_subject tptp.late_subject)|) (y |u_(-> tptp.late_subject tptp.late_subject)|)) (or (not (forall ((z tptp.late_subject)) (= (ho_30 x z) (ho_30 y z)))) (= x y))))) (let ((_let_179 (forall ((u |u_(-> tptp.list_P227219501e_name tptp.produc1872410278e_name)|) (e tptp.produc1872410278e_name) (i tptp.list_P227219501e_name)) (not (forall ((v |u_(-> tptp.list_P227219501e_name tptp.produc1872410278e_name)|)) (not (forall ((ii tptp.list_P227219501e_name)) (= (ho_90 v ii) (ite (= i ii) e (ho_90 u ii)))))))))) (let ((_let_180 (forall ((x |u_(-> tptp.list_P227219501e_name tptp.produc1872410278e_name)|) (y |u_(-> tptp.list_P227219501e_name tptp.produc1872410278e_name)|)) (or (not (forall ((z tptp.list_P227219501e_name)) (= (ho_90 x z) (ho_90 y z)))) (= x y))))) (let ((_let_181 (forall ((u |u_(-> tptp.late_subject tptp.late_freeRes)|) (e tptp.late_freeRes) (i tptp.late_subject)) (not (forall ((v |u_(-> tptp.late_subject tptp.late_freeRes)|)) (not (forall ((ii tptp.late_subject)) (= (ho_117 v ii) (ite (= i ii) e (ho_117 u ii)))))))))) (let ((_let_182 (forall ((x |u_(-> tptp.late_subject tptp.late_freeRes)|) (y |u_(-> tptp.late_subject tptp.late_freeRes)|)) (or (not (forall ((z tptp.late_subject)) (= (ho_117 x z) (ho_117 y z)))) (= x y))))) (let ((_let_183 (forall ((u |u_(-> tptp.name tptp.product_prod_pi_pi tptp.produc1141751126_pi_pi)|) (e |u_(-> tptp.product_prod_pi_pi tptp.produc1141751126_pi_pi)|) (i tptp.name)) (not (forall ((v |u_(-> tptp.name tptp.product_prod_pi_pi tptp.produc1141751126_pi_pi)|)) (not (forall ((ii tptp.name)) (= (ho_49 v ii) (ite (= i ii) e (ho_49 u ii)))))))))) (let ((_let_184 (forall ((x |u_(-> tptp.name tptp.product_prod_pi_pi tptp.produc1141751126_pi_pi)|) (y |u_(-> tptp.name tptp.product_prod_pi_pi tptp.produc1141751126_pi_pi)|)) (or (not (forall ((z tptp.name)) (= (ho_49 x z) (ho_49 y z)))) (= x y))))) (let ((_let_185 (forall ((u |u_(-> Bool Bool)|) (e Bool) (i Bool)) (not (forall ((v |u_(-> Bool Bool)|)) (not (forall ((ii Bool)) (= (ho_83 v ii) (ite (= i ii) e (ho_83 u ii)))))))))) (let ((_let_186 (forall ((x |u_(-> Bool Bool)|) (y |u_(-> Bool Bool)|)) (or (not (forall ((z Bool)) (= (ho_83 x z) (ho_83 y z)))) (= x y))))) (let ((_let_187 (forall ((u |u_(-> tptp.set_name tptp.set_name)|) (e tptp.set_name) (i tptp.set_name)) (not (forall ((v |u_(-> tptp.set_name tptp.set_name)|)) (not (forall ((ii tptp.set_name)) (= (ho_156 v ii) (ite (= i ii) e (ho_156 u ii)))))))))) (let ((_let_188 (forall ((x |u_(-> tptp.set_name tptp.set_name)|) (y |u_(-> tptp.set_name tptp.set_name)|)) (or (not (forall ((z tptp.set_name)) (= (ho_156 x z) (ho_156 y z)))) (= x y))))) (let ((_let_189 (forall ((u |u_(-> tptp.list_P227219501e_name tptp.list_name tptp.list_name)|) (e |u_(-> tptp.list_name tptp.list_name)|) (i tptp.list_P227219501e_name)) (not (forall ((v |u_(-> tptp.list_P227219501e_name tptp.list_name tptp.list_name)|)) (not (forall ((ii tptp.list_P227219501e_name)) (= (ho_324 v ii) (ite (= i ii) e (ho_324 u ii)))))))))) (let ((_let_190 (forall ((x |u_(-> tptp.list_P227219501e_name tptp.list_name tptp.list_name)|) (y |u_(-> tptp.list_P227219501e_name tptp.list_name tptp.list_name)|)) (or (not (forall ((z tptp.list_P227219501e_name)) (= (ho_324 x z) (ho_324 y z)))) (= x y))))) (let ((_let_191 (forall ((u |u_(-> tptp.name tptp.pi Bool)|) (e |u_(-> tptp.pi Bool)|) (i tptp.name)) (not (forall ((v |u_(-> tptp.name tptp.pi Bool)|)) (not (forall ((ii tptp.name)) (= (ho_46 v ii) (ite (= i ii) e (ho_46 u ii)))))))))) (let ((_let_192 (forall ((x |u_(-> tptp.name tptp.pi Bool)|) (y |u_(-> tptp.name tptp.pi Bool)|)) (or (not (forall ((z tptp.name)) (= (ho_46 x z) (ho_46 y z)))) (= x y))))) (let ((_let_193 (forall ((u |u_(-> tptp.product_prod_pi_pi tptp.produc1141751126_pi_pi)|) (e tptp.produc1141751126_pi_pi) (i tptp.product_prod_pi_pi)) (not (forall ((v |u_(-> tptp.product_prod_pi_pi tptp.produc1141751126_pi_pi)|)) (not (forall ((ii tptp.product_prod_pi_pi)) (= (ho_50 v ii) (ite (= i ii) e (ho_50 u ii)))))))))) (let ((_let_194 (forall ((x |u_(-> tptp.product_prod_pi_pi tptp.produc1141751126_pi_pi)|) (y |u_(-> tptp.product_prod_pi_pi tptp.produc1141751126_pi_pi)|)) (or (not (forall ((z tptp.product_prod_pi_pi)) (= (ho_50 x z) (ho_50 y z)))) (= x y))))) (let ((_let_195 (forall ((u |u_(-> tptp.name tptp.late_subject)|) (e tptp.late_subject) (i tptp.name)) (not (forall ((v |u_(-> tptp.name tptp.late_subject)|)) (not (forall ((ii tptp.name)) (= (ho_44 v ii) (ite (= i ii) e (ho_44 u ii)))))))))) (let ((_let_196 (forall ((x |u_(-> tptp.name tptp.late_subject)|) (y |u_(-> tptp.name tptp.late_subject)|)) (or (not (forall ((z tptp.name)) (= (ho_44 x z) (ho_44 y z)))) (= x y))))) (let ((_let_197 (forall ((u |u_(-> tptp.list_P227219501e_name tptp.late_subject tptp.late_subject)|) (e |u_(-> tptp.late_subject tptp.late_subject)|) (i tptp.list_P227219501e_name)) (not (forall ((v |u_(-> tptp.list_P227219501e_name tptp.late_subject tptp.late_subject)|)) (not (forall ((ii tptp.list_P227219501e_name)) (= (ho_29 v ii) (ite (= i ii) e (ho_29 u ii)))))))))) (let ((_let_198 (forall ((x |u_(-> tptp.list_P227219501e_name tptp.late_subject tptp.late_subject)|) (y |u_(-> tptp.list_P227219501e_name tptp.late_subject tptp.late_subject)|)) (or (not (forall ((z tptp.list_P227219501e_name)) (= (ho_29 x z) (ho_29 y z)))) (= x y))))) (let ((_let_199 (forall ((u |u_(-> tptp.list_P227219501e_name tptp.pi tptp.pi)|) (e |u_(-> tptp.pi tptp.pi)|) (i tptp.list_P227219501e_name)) (not (forall ((v |u_(-> tptp.list_P227219501e_name tptp.pi tptp.pi)|)) (not (forall ((ii tptp.list_P227219501e_name)) (= (ho_41 v ii) (ite (= i ii) e (ho_41 u ii)))))))))) (let ((_let_200 (forall ((x |u_(-> tptp.list_P227219501e_name tptp.pi tptp.pi)|) (y |u_(-> tptp.list_P227219501e_name tptp.pi tptp.pi)|)) (or (not (forall ((z tptp.list_P227219501e_name)) (= (ho_41 x z) (ho_41 y z)))) (= x y))))) (let ((_let_201 (forall ((u |u_(-> tptp.late_subject_Rep tptp.late_subject_Rep)|) (e tptp.late_subject_Rep) (i tptp.late_subject_Rep)) (not (forall ((v |u_(-> tptp.late_subject_Rep tptp.late_subject_Rep)|)) (not (forall ((ii tptp.late_subject_Rep)) (= (ho_59 v ii) (ite (= i ii) e (ho_59 u ii)))))))))) (let ((_let_202 (forall ((x |u_(-> tptp.late_subject_Rep tptp.late_subject_Rep)|) (y |u_(-> tptp.late_subject_Rep tptp.late_subject_Rep)|)) (or (not (forall ((z tptp.late_subject_Rep)) (= (ho_59 x z) (ho_59 y z)))) (= x y))))) (let ((_let_203 (forall ((u |u_(-> tptp.name tptp.produc355105483reeRes Bool)|) (e |u_(-> tptp.produc355105483reeRes Bool)|) (i tptp.name)) (not (forall ((v |u_(-> tptp.name tptp.produc355105483reeRes Bool)|)) (not (forall ((ii tptp.name)) (= (ho_186 v ii) (ite (= i ii) e (ho_186 u ii)))))))))) (let ((_let_204 (forall ((x |u_(-> tptp.name tptp.produc355105483reeRes Bool)|) (y |u_(-> tptp.name tptp.produc355105483reeRes Bool)|)) (or (not (forall ((z tptp.name)) (= (ho_186 x z) (ho_186 y z)))) (= x y))))) (let ((_let_205 (forall ((u |u_(-> tptp.name tptp.set_Pr1834926343_pi_pi Bool)|) (e |u_(-> tptp.set_Pr1834926343_pi_pi Bool)|) (i tptp.name)) (not (forall ((v |u_(-> tptp.name tptp.set_Pr1834926343_pi_pi Bool)|)) (not (forall ((ii tptp.name)) (= (ho_240 v ii) (ite (= i ii) e (ho_240 u ii)))))))))) (let ((_let_206 (forall ((x |u_(-> tptp.name tptp.set_Pr1834926343_pi_pi Bool)|) (y |u_(-> tptp.name tptp.set_Pr1834926343_pi_pi Bool)|)) (or (not (forall ((z tptp.name)) (= (ho_240 x z) (ho_240 y z)))) (= x y))))) (let ((_let_207 (forall ((u |u_(-> tptp.pi tptp.pi)|) (e tptp.pi) (i tptp.pi)) (not (forall ((v |u_(-> tptp.pi tptp.pi)|)) (not (forall ((ii tptp.pi)) (= (ho_42 v ii) (ite (= i ii) e (ho_42 u ii)))))))))) (let ((_let_208 (forall ((x |u_(-> tptp.pi tptp.pi)|) (y |u_(-> tptp.pi tptp.pi)|)) (or (not (forall ((z tptp.pi)) (= (ho_42 x z) (ho_42 y z)))) (= x y))))) (let ((_let_209 (forall ((u |u_(-> tptp.name tptp.produc214645451ubject Bool)|) (e |u_(-> tptp.produc214645451ubject Bool)|) (i tptp.name)) (not (forall ((v |u_(-> tptp.name tptp.produc214645451ubject Bool)|)) (not (forall ((ii tptp.name)) (= (ho_204 v ii) (ite (= i ii) e (ho_204 u ii)))))))))) (let ((_let_210 (forall ((x |u_(-> tptp.name tptp.produc214645451ubject Bool)|) (y |u_(-> tptp.name tptp.produc214645451ubject Bool)|)) (or (not (forall ((z tptp.name)) (= (ho_204 x z) (ho_204 y z)))) (= x y))))) (let ((_let_211 (forall ((u |u_(-> tptp.produc257012921pi_Rep tptp.produc257012921pi_Rep)|) (e tptp.produc257012921pi_Rep) (i tptp.produc257012921pi_Rep)) (not (forall ((v |u_(-> tptp.produc257012921pi_Rep tptp.produc257012921pi_Rep)|)) (not (forall ((ii tptp.produc257012921pi_Rep)) (= (ho_283 v ii) (ite (= i ii) e (ho_283 u ii)))))))))) (let ((_let_212 (forall ((x |u_(-> tptp.produc257012921pi_Rep tptp.produc257012921pi_Rep)|) (y |u_(-> tptp.produc257012921pi_Rep tptp.produc257012921pi_Rep)|)) (or (not (forall ((z tptp.produc257012921pi_Rep)) (= (ho_283 x z) (ho_283 y z)))) (= x y))))) (let ((_let_213 (forall ((u |u_(-> tptp.pi Bool)|) (e Bool) (i tptp.pi)) (not (forall ((v |u_(-> tptp.pi Bool)|)) (not (forall ((ii tptp.pi)) (= (ho_47 v ii) (ite (= i ii) e (ho_47 u ii)))))))))) (let ((_let_214 (forall ((x |u_(-> tptp.pi Bool)|) (y |u_(-> tptp.pi Bool)|)) (or (not (forall ((z tptp.pi)) (= (ho_47 x z) (ho_47 y z)))) (= x y))))) (let ((_let_215 (forall ((u |u_(-> tptp.list_P227219501e_name tptp.set_pi tptp.set_pi)|) (e |u_(-> tptp.set_pi tptp.set_pi)|) (i tptp.list_P227219501e_name)) (not (forall ((v |u_(-> tptp.list_P227219501e_name tptp.set_pi tptp.set_pi)|)) (not (forall ((ii tptp.list_P227219501e_name)) (= (ho_161 v ii) (ite (= i ii) e (ho_161 u ii)))))))))) (let ((_let_216 (forall ((x |u_(-> tptp.list_P227219501e_name tptp.set_pi tptp.set_pi)|) (y |u_(-> tptp.list_P227219501e_name tptp.set_pi tptp.set_pi)|)) (or (not (forall ((z tptp.list_P227219501e_name)) (= (ho_161 x z) (ho_161 y z)))) (= x y))))) (let ((_let_217 (forall ((u |u_(-> tptp.list_P227219501e_name tptp.produc890461031e_name)|) (e tptp.produc890461031e_name) (i tptp.list_P227219501e_name)) (not (forall ((v |u_(-> tptp.list_P227219501e_name tptp.produc890461031e_name)|)) (not (forall ((ii tptp.list_P227219501e_name)) (= (ho_93 v ii) (ite (= i ii) e (ho_93 u ii)))))))))) (let ((_let_218 (forall ((x |u_(-> tptp.list_P227219501e_name tptp.produc890461031e_name)|) (y |u_(-> tptp.list_P227219501e_name tptp.produc890461031e_name)|)) (or (not (forall ((z tptp.list_P227219501e_name)) (= (ho_93 x z) (ho_93 y z)))) (= x y))))) (let ((_let_219 (forall ((u |u_(-> tptp.list_P227219501e_name tptp.pi_Rep tptp.pi_Rep)|) (e |u_(-> tptp.pi_Rep tptp.pi_Rep)|) (i tptp.list_P227219501e_name)) (not (forall ((v |u_(-> tptp.list_P227219501e_name tptp.pi_Rep tptp.pi_Rep)|)) (not (forall ((ii tptp.list_P227219501e_name)) (= (ho_35 v ii) (ite (= i ii) e (ho_35 u ii)))))))))) (let ((_let_220 (forall ((x |u_(-> tptp.list_P227219501e_name tptp.pi_Rep tptp.pi_Rep)|) (y |u_(-> tptp.list_P227219501e_name tptp.pi_Rep tptp.pi_Rep)|)) (or (not (forall ((z tptp.list_P227219501e_name)) (= (ho_35 x z) (ho_35 y z)))) (= x y))))) (let ((_let_221 (forall ((u |u_(-> tptp.list_P227219501e_name tptp.late_freeRes tptp.late_freeRes)|) (e |u_(-> tptp.late_freeRes tptp.late_freeRes)|) (i tptp.list_P227219501e_name)) (not (forall ((v |u_(-> tptp.list_P227219501e_name tptp.late_freeRes tptp.late_freeRes)|)) (not (forall ((ii tptp.list_P227219501e_name)) (= (ho_32 v ii) (ite (= i ii) e (ho_32 u ii)))))))))) (let ((_let_222 (forall ((x |u_(-> tptp.list_P227219501e_name tptp.late_freeRes tptp.late_freeRes)|) (y |u_(-> tptp.list_P227219501e_name tptp.late_freeRes tptp.late_freeRes)|)) (or (not (forall ((z tptp.list_P227219501e_name)) (= (ho_32 x z) (ho_32 y z)))) (= x y))))) (let ((_let_223 (forall ((u |u_(-> tptp.list_Late_freeRes Bool)|) (e Bool) (i tptp.list_Late_freeRes)) (not (forall ((v |u_(-> tptp.list_Late_freeRes Bool)|)) (not (forall ((ii tptp.list_Late_freeRes)) (= (ho_342 v ii) (ite (= i ii) e (ho_342 u ii)))))))))) (let ((_let_224 (forall ((x |u_(-> tptp.list_Late_freeRes Bool)|) (y |u_(-> tptp.list_Late_freeRes Bool)|)) (or (not (forall ((z tptp.list_Late_freeRes)) (= (ho_342 x z) (ho_342 y z)))) (= x y))))) (let ((_let_225 (forall ((u |u_(-> _u_(-> tptp.product_prod_pi_pi Bool)_ tptp.set_Pr1834926343_pi_pi)|) (e tptp.set_Pr1834926343_pi_pi) (i |u_(-> tptp.product_prod_pi_pi Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.product_prod_pi_pi Bool)_ tptp.set_Pr1834926343_pi_pi)|)) (not (forall ((ii |u_(-> tptp.product_prod_pi_pi Bool)|)) (= (ho_96 v ii) (ite (= i ii) e (ho_96 u ii)))))))))) (let ((_let_226 (forall ((x |u_(-> _u_(-> tptp.product_prod_pi_pi Bool)_ tptp.set_Pr1834926343_pi_pi)|) (y |u_(-> _u_(-> tptp.product_prod_pi_pi Bool)_ tptp.set_Pr1834926343_pi_pi)|)) (or (not (forall ((z |u_(-> tptp.product_prod_pi_pi Bool)|)) (= (ho_96 x z) (ho_96 y z)))) (= x y))))) (let ((_let_227 (forall ((u |u_(-> tptp.name tptp.pi tptp.late_residual)|) (e |u_(-> tptp.pi tptp.late_residual)|) (i tptp.name)) (not (forall ((v |u_(-> tptp.name tptp.pi tptp.late_residual)|)) (not (forall ((ii tptp.name)) (= (ho_367 v ii) (ite (= i ii) e (ho_367 u ii)))))))))) (let ((_let_228 (forall ((x |u_(-> tptp.name tptp.pi tptp.late_residual)|) (y |u_(-> tptp.name tptp.pi tptp.late_residual)|)) (or (not (forall ((z tptp.name)) (= (ho_367 x z) (ho_367 y z)))) (= x y))))) (let ((_let_229 (forall ((u |u_(-> tptp.set_Pr1834926343_pi_pi Bool)|) (e Bool) (i tptp.set_Pr1834926343_pi_pi)) (not (forall ((v |u_(-> tptp.set_Pr1834926343_pi_pi Bool)|)) (not (forall ((ii tptp.set_Pr1834926343_pi_pi)) (= (ho_9 v ii) (ite (= i ii) e (ho_9 u ii)))))))))) (let ((_let_230 (forall ((x |u_(-> tptp.set_Pr1834926343_pi_pi Bool)|) (y |u_(-> tptp.set_Pr1834926343_pi_pi Bool)|)) (or (not (forall ((z tptp.set_Pr1834926343_pi_pi)) (= (ho_9 x z) (ho_9 y z)))) (= x y))))) (let ((_let_231 (forall ((u |u_(-> tptp.late_freeRes tptp.late_freeRes)|) (e tptp.late_freeRes) (i tptp.late_freeRes)) (not (forall ((v |u_(-> tptp.late_freeRes tptp.late_freeRes)|)) (not (forall ((ii tptp.late_freeRes)) (= (ho_33 v ii) (ite (= i ii) e (ho_33 u ii)))))))))) (let ((_let_232 (forall ((x |u_(-> tptp.late_freeRes tptp.late_freeRes)|) (y |u_(-> tptp.late_freeRes tptp.late_freeRes)|)) (or (not (forall ((z tptp.late_freeRes)) (= (ho_33 x z) (ho_33 y z)))) (= x y))))) (let ((_let_233 (forall ((u |u_(-> tptp.produc1141751126_pi_pi Bool)|) (e Bool) (i tptp.produc1141751126_pi_pi)) (not (forall ((v |u_(-> tptp.produc1141751126_pi_pi Bool)|)) (not (forall ((ii tptp.produc1141751126_pi_pi)) (= (ho_77 v ii) (ite (= i ii) e (ho_77 u ii)))))))))) (let ((_let_234 (forall ((x |u_(-> tptp.produc1141751126_pi_pi Bool)|) (y |u_(-> tptp.produc1141751126_pi_pi Bool)|)) (or (not (forall ((z tptp.produc1141751126_pi_pi)) (= (ho_77 x z) (ho_77 y z)))) (= x y))))) (let ((_let_235 (forall ((u |u_(-> tptp.list_l1406151091e_name tptp.list_l1406151091e_name)|) (e tptp.list_l1406151091e_name) (i tptp.list_l1406151091e_name)) (not (forall ((v |u_(-> tptp.list_l1406151091e_name tptp.list_l1406151091e_name)|)) (not (forall ((ii tptp.list_l1406151091e_name)) (= (ho_172 v ii) (ite (= i ii) e (ho_172 u ii)))))))))) (let ((_let_236 (forall ((x |u_(-> tptp.list_l1406151091e_name tptp.list_l1406151091e_name)|) (y |u_(-> tptp.list_l1406151091e_name tptp.list_l1406151091e_name)|)) (or (not (forall ((z tptp.list_l1406151091e_name)) (= (ho_172 x z) (ho_172 y z)))) (= x y))))) (let ((_let_237 (forall ((u |u_(-> _u_(-> tptp.late_subject tptp.late_subject)_ tptp.late_subject tptp.late_subject)|) (e |u_(-> tptp.late_subject tptp.late_subject)|) (i |u_(-> tptp.late_subject tptp.late_subject)|)) (not (forall ((v |u_(-> _u_(-> tptp.late_subject tptp.late_subject)_ tptp.late_subject tptp.late_subject)|)) (not (forall ((ii |u_(-> tptp.late_subject tptp.late_subject)|)) (= (ho_101 v ii) (ite (= i ii) e (ho_101 u ii)))))))))) (let ((_let_238 (forall ((x |u_(-> _u_(-> tptp.late_subject tptp.late_subject)_ tptp.late_subject tptp.late_subject)|) (y |u_(-> _u_(-> tptp.late_subject tptp.late_subject)_ tptp.late_subject tptp.late_subject)|)) (or (not (forall ((z |u_(-> tptp.late_subject tptp.late_subject)|)) (= (ho_101 x z) (ho_101 y z)))) (= x y))))) (let ((_let_239 (forall ((u |u_(-> tptp.name tptp.name)|) (e tptp.name) (i tptp.name)) (not (forall ((v |u_(-> tptp.name tptp.name)|)) (not (forall ((ii tptp.name)) (= (ho_39 v ii) (ite (= i ii) e (ho_39 u ii)))))))))) (let ((_let_240 (forall ((x |u_(-> tptp.name tptp.name)|) (y |u_(-> tptp.name tptp.name)|)) (or (not (forall ((z tptp.name)) (= (ho_39 x z) (ho_39 y z)))) (= x y))))) (let ((_let_241 (forall ((u |u_(-> tptp.name tptp.produc2008547984reeRes Bool)|) (e |u_(-> tptp.produc2008547984reeRes Bool)|) (i tptp.name)) (not (forall ((v |u_(-> tptp.name tptp.produc2008547984reeRes Bool)|)) (not (forall ((ii tptp.name)) (= (ho_234 v ii) (ite (= i ii) e (ho_234 u ii)))))))))) (let ((_let_242 (forall ((x |u_(-> tptp.name tptp.produc2008547984reeRes Bool)|) (y |u_(-> tptp.name tptp.produc2008547984reeRes Bool)|)) (or (not (forall ((z tptp.name)) (= (ho_234 x z) (ho_234 y z)))) (= x y))))) (let ((_let_243 (forall ((u |u_(-> tptp.set_Pr1834926343_pi_pi tptp.set_Pr1834926343_pi_pi Bool)|) (e |u_(-> tptp.set_Pr1834926343_pi_pi Bool)|) (i tptp.set_Pr1834926343_pi_pi)) (not (forall ((v |u_(-> tptp.set_Pr1834926343_pi_pi tptp.set_Pr1834926343_pi_pi Bool)|)) (not (forall ((ii tptp.set_Pr1834926343_pi_pi)) (= (ho_8 v ii) (ite (= i ii) e (ho_8 u ii)))))))))) (let ((_let_244 (forall ((x |u_(-> tptp.set_Pr1834926343_pi_pi tptp.set_Pr1834926343_pi_pi Bool)|) (y |u_(-> tptp.set_Pr1834926343_pi_pi tptp.set_Pr1834926343_pi_pi Bool)|)) (or (not (forall ((z tptp.set_Pr1834926343_pi_pi)) (= (ho_8 x z) (ho_8 y z)))) (= x y))))) (let ((_let_245 (forall ((u |u_(-> tptp.pi_Rep tptp.produc1212344719pi_Rep)|) (e tptp.produc1212344719pi_Rep) (i tptp.pi_Rep)) (not (forall ((v |u_(-> tptp.pi_Rep tptp.produc1212344719pi_Rep)|)) (not (forall ((ii tptp.pi_Rep)) (= (ho_251 v ii) (ite (= i ii) e (ho_251 u ii)))))))))) (let ((_let_246 (forall ((x |u_(-> tptp.pi_Rep tptp.produc1212344719pi_Rep)|) (y |u_(-> tptp.pi_Rep tptp.produc1212344719pi_Rep)|)) (or (not (forall ((z tptp.pi_Rep)) (= (ho_251 x z) (ho_251 y z)))) (= x y))))) (let ((_let_247 (forall ((u |u_(-> tptp.late_freeRes Bool)|) (e Bool) (i tptp.late_freeRes)) (not (forall ((v |u_(-> tptp.late_freeRes Bool)|)) (not (forall ((ii tptp.late_freeRes)) (= (ho_71 v ii) (ite (= i ii) e (ho_71 u ii)))))))))) (let ((_let_248 (forall ((x |u_(-> tptp.late_freeRes Bool)|) (y |u_(-> tptp.late_freeRes Bool)|)) (or (not (forall ((z tptp.late_freeRes)) (= (ho_71 x z) (ho_71 y z)))) (= x y))))) (let ((_let_249 (forall ((u |u_(-> tptp.list_P227219501e_name tptp.name tptp.name)|) (e |u_(-> tptp.name tptp.name)|) (i tptp.list_P227219501e_name)) (not (forall ((v |u_(-> tptp.list_P227219501e_name tptp.name tptp.name)|)) (not (forall ((ii tptp.list_P227219501e_name)) (= (ho_38 v ii) (ite (= i ii) e (ho_38 u ii)))))))))) (let ((_let_250 (forall ((x |u_(-> tptp.list_P227219501e_name tptp.name tptp.name)|) (y |u_(-> tptp.list_P227219501e_name tptp.name tptp.name)|)) (or (not (forall ((z tptp.list_P227219501e_name)) (= (ho_38 x z) (ho_38 y z)))) (= x y))))) (let ((_let_251 (forall ((u |u_(-> tptp.set_pi_Rep tptp.set_pi_Rep)|) (e tptp.set_pi_Rep) (i tptp.set_pi_Rep)) (not (forall ((v |u_(-> tptp.set_pi_Rep tptp.set_pi_Rep)|)) (not (forall ((ii tptp.set_pi_Rep)) (= (ho_150 v ii) (ite (= i ii) e (ho_150 u ii)))))))))) (let ((_let_252 (forall ((x |u_(-> tptp.set_pi_Rep tptp.set_pi_Rep)|) (y |u_(-> tptp.set_pi_Rep tptp.set_pi_Rep)|)) (or (not (forall ((z tptp.set_pi_Rep)) (= (ho_150 x z) (ho_150 y z)))) (= x y))))) (let ((_let_253 (forall ((u |u_(-> tptp.list_P227219501e_name tptp.product_prod_pi_pi tptp.product_prod_pi_pi)|) (e |u_(-> tptp.product_prod_pi_pi tptp.product_prod_pi_pi)|) (i tptp.list_P227219501e_name)) (not (forall ((v |u_(-> tptp.list_P227219501e_name tptp.product_prod_pi_pi tptp.product_prod_pi_pi)|)) (not (forall ((ii tptp.list_P227219501e_name)) (= (ho_20 v ii) (ite (= i ii) e (ho_20 u ii)))))))))) (let ((_let_254 (forall ((x |u_(-> tptp.list_P227219501e_name tptp.product_prod_pi_pi tptp.product_prod_pi_pi)|) (y |u_(-> tptp.list_P227219501e_name tptp.product_prod_pi_pi tptp.product_prod_pi_pi)|)) (or (not (forall ((z tptp.list_P227219501e_name)) (= (ho_20 x z) (ho_20 y z)))) (= x y))))) (let ((_let_255 (forall ((u |u_(-> tptp.name tptp.produc367475239e_name)|) (e tptp.produc367475239e_name) (i tptp.name)) (not (forall ((v |u_(-> tptp.name tptp.produc367475239e_name)|)) (not (forall ((ii tptp.name)) (= (ho_24 v ii) (ite (= i ii) e (ho_24 u ii)))))))))) (let ((_let_256 (forall ((x |u_(-> tptp.name tptp.produc367475239e_name)|) (y |u_(-> tptp.name tptp.produc367475239e_name)|)) (or (not (forall ((z tptp.name)) (= (ho_24 x z) (ho_24 y z)))) (= x y))))) (let ((_let_257 (forall ((u |u_(-> tptp.pi tptp.late_residual Bool)|) (e |u_(-> tptp.late_residual Bool)|) (i tptp.pi)) (not (forall ((v |u_(-> tptp.pi tptp.late_residual Bool)|)) (not (forall ((ii tptp.pi)) (= (ho_370 v ii) (ite (= i ii) e (ho_370 u ii)))))))))) (let ((_let_258 (forall ((x |u_(-> tptp.pi tptp.late_residual Bool)|) (y |u_(-> tptp.pi tptp.late_residual Bool)|)) (or (not (forall ((z tptp.pi)) (= (ho_370 x z) (ho_370 y z)))) (= x y))))) (let ((_let_259 (forall ((u |u_(-> _u_(-> tptp.late_freeRes tptp.late_freeRes)_ tptp.late_freeRes tptp.late_freeRes)|) (e |u_(-> tptp.late_freeRes tptp.late_freeRes)|) (i |u_(-> tptp.late_freeRes tptp.late_freeRes)|)) (not (forall ((v |u_(-> _u_(-> tptp.late_freeRes tptp.late_freeRes)_ tptp.late_freeRes tptp.late_freeRes)|)) (not (forall ((ii |u_(-> tptp.late_freeRes tptp.late_freeRes)|)) (= (ho_123 v ii) (ite (= i ii) e (ho_123 u ii)))))))))) (let ((_let_260 (forall ((x |u_(-> _u_(-> tptp.late_freeRes tptp.late_freeRes)_ tptp.late_freeRes tptp.late_freeRes)|) (y |u_(-> _u_(-> tptp.late_freeRes tptp.late_freeRes)_ tptp.late_freeRes tptp.late_freeRes)|)) (or (not (forall ((z |u_(-> tptp.late_freeRes tptp.late_freeRes)|)) (= (ho_123 x z) (ho_123 y z)))) (= x y))))) (let ((_let_261 (forall ((u |u_(-> tptp.produc367475239e_name tptp.set_Pr443758855e_name Bool)|) (e |u_(-> tptp.set_Pr443758855e_name Bool)|) (i tptp.produc367475239e_name)) (not (forall ((v |u_(-> tptp.produc367475239e_name tptp.set_Pr443758855e_name Bool)|)) (not (forall ((ii tptp.produc367475239e_name)) (= (ho_174 v ii) (ite (= i ii) e (ho_174 u ii)))))))))) (let ((_let_262 (forall ((x |u_(-> tptp.produc367475239e_name tptp.set_Pr443758855e_name Bool)|) (y |u_(-> tptp.produc367475239e_name tptp.set_Pr443758855e_name Bool)|)) (or (not (forall ((z tptp.produc367475239e_name)) (= (ho_174 x z) (ho_174 y z)))) (= x y))))) (let ((_let_263 (forall ((u |u_(-> tptp.produc367475239e_name tptp.list_P227219501e_name tptp.list_P227219501e_name)|) (e |u_(-> tptp.list_P227219501e_name tptp.list_P227219501e_name)|) (i tptp.produc367475239e_name)) (not (forall ((v |u_(-> tptp.produc367475239e_name tptp.list_P227219501e_name tptp.list_P227219501e_name)|)) (not (forall ((ii tptp.produc367475239e_name)) (= (ho_26 v ii) (ite (= i ii) e (ho_26 u ii)))))))))) (let ((_let_264 (forall ((x |u_(-> tptp.produc367475239e_name tptp.list_P227219501e_name tptp.list_P227219501e_name)|) (y |u_(-> tptp.produc367475239e_name tptp.list_P227219501e_name tptp.list_P227219501e_name)|)) (or (not (forall ((z tptp.produc367475239e_name)) (= (ho_26 x z) (ho_26 y z)))) (= x y))))) (let ((_let_265 (forall ((u |u_(-> tptp.pi tptp.late_residual_Rep)|) (e tptp.late_residual_Rep) (i tptp.pi)) (not (forall ((v |u_(-> tptp.pi tptp.late_residual_Rep)|)) (not (forall ((ii tptp.pi)) (= (ho_384 v ii) (ite (= i ii) e (ho_384 u ii)))))))))) (let ((_let_266 (forall ((x |u_(-> tptp.pi tptp.late_residual_Rep)|) (y |u_(-> tptp.pi tptp.late_residual_Rep)|)) (or (not (forall ((z tptp.pi)) (= (ho_384 x z) (ho_384 y z)))) (= x y))))) (let ((_let_267 (forall ((u |u_(-> tptp.list_P227219501e_name tptp.list_P227219501e_name)|) (e tptp.list_P227219501e_name) (i tptp.list_P227219501e_name)) (not (forall ((v |u_(-> tptp.list_P227219501e_name tptp.list_P227219501e_name)|)) (not (forall ((ii tptp.list_P227219501e_name)) (= (ho_27 v ii) (ite (= i ii) e (ho_27 u ii)))))))))) (let ((_let_268 (forall ((x |u_(-> tptp.list_P227219501e_name tptp.list_P227219501e_name)|) (y |u_(-> tptp.list_P227219501e_name tptp.list_P227219501e_name)|)) (or (not (forall ((z tptp.list_P227219501e_name)) (= (ho_27 x z) (ho_27 y z)))) (= x y))))) (let ((_let_269 (forall ((u |u_(-> tptp.list_P227219501e_name _u_(-> tptp.late_subject tptp.late_subject)_ tptp.late_subject tptp.late_subject)|) (e |u_(-> _u_(-> tptp.late_subject tptp.late_subject)_ tptp.late_subject tptp.late_subject)|) (i tptp.list_P227219501e_name)) (not (forall ((v |u_(-> tptp.list_P227219501e_name _u_(-> tptp.late_subject tptp.late_subject)_ tptp.late_subject tptp.late_subject)|)) (not (forall ((ii tptp.list_P227219501e_name)) (= (ho_100 v ii) (ite (= i ii) e (ho_100 u ii)))))))))) (let ((_let_270 (forall ((x |u_(-> tptp.list_P227219501e_name _u_(-> tptp.late_subject tptp.late_subject)_ tptp.late_subject tptp.late_subject)|) (y |u_(-> tptp.list_P227219501e_name _u_(-> tptp.late_subject tptp.late_subject)_ tptp.late_subject tptp.late_subject)|)) (or (not (forall ((z tptp.list_P227219501e_name)) (= (ho_100 x z) (ho_100 y z)))) (= x y))))) (let ((_let_271 (forall ((u |u_(-> tptp.late_subject tptp.pi Bool)|) (e |u_(-> tptp.pi Bool)|) (i tptp.late_subject)) (not (forall ((v |u_(-> tptp.late_subject tptp.pi Bool)|)) (not (forall ((ii tptp.late_subject)) (= (ho_381 v ii) (ite (= i ii) e (ho_381 u ii)))))))))) (let ((_let_272 (forall ((x |u_(-> tptp.late_subject tptp.pi Bool)|) (y |u_(-> tptp.late_subject tptp.pi Bool)|)) (or (not (forall ((z tptp.late_subject)) (= (ho_381 x z) (ho_381 y z)))) (= x y))))) (let ((_let_273 (forall ((u |u_(-> tptp.product_prod_pi_pi Bool)|) (e Bool) (i tptp.product_prod_pi_pi)) (not (forall ((v |u_(-> tptp.product_prod_pi_pi Bool)|)) (not (forall ((ii tptp.product_prod_pi_pi)) (= (ho_16 v ii) (ite (= i ii) e (ho_16 u ii)))))))))) (let ((_let_274 (forall ((x |u_(-> tptp.product_prod_pi_pi Bool)|) (y |u_(-> tptp.product_prod_pi_pi Bool)|)) (or (not (forall ((z tptp.product_prod_pi_pi)) (= (ho_16 x z) (ho_16 y z)))) (= x y))))) (let ((_let_275 (forall ((u |u_(-> tptp.product_prod_pi_pi tptp.product_prod_pi_pi)|) (e tptp.product_prod_pi_pi) (i tptp.product_prod_pi_pi)) (not (forall ((v |u_(-> tptp.product_prod_pi_pi tptp.product_prod_pi_pi)|)) (not (forall ((ii tptp.product_prod_pi_pi)) (= (ho_21 v ii) (ite (= i ii) e (ho_21 u ii)))))))))) (let ((_let_276 (forall ((x |u_(-> tptp.product_prod_pi_pi tptp.product_prod_pi_pi)|) (y |u_(-> tptp.product_prod_pi_pi tptp.product_prod_pi_pi)|)) (or (not (forall ((z tptp.product_prod_pi_pi)) (= (ho_21 x z) (ho_21 y z)))) (= x y))))) (let ((_let_277 (forall ((u |u_(-> tptp.late_freeRes tptp.produc2008547984reeRes)|) (e tptp.produc2008547984reeRes) (i tptp.late_freeRes)) (not (forall ((v |u_(-> tptp.late_freeRes tptp.produc2008547984reeRes)|)) (not (forall ((ii tptp.late_freeRes)) (= (ho_232 v ii) (ite (= i ii) e (ho_232 u ii)))))))))) (let ((_let_278 (forall ((x |u_(-> tptp.late_freeRes tptp.produc2008547984reeRes)|) (y |u_(-> tptp.late_freeRes tptp.produc2008547984reeRes)|)) (or (not (forall ((z tptp.late_freeRes)) (= (ho_232 x z) (ho_232 y z)))) (= x y))))) (let ((_let_279 (forall ((u |u_(-> tptp.name tptp.produc367475239e_name Bool)|) (e |u_(-> tptp.produc367475239e_name Bool)|) (i tptp.name)) (not (forall ((v |u_(-> tptp.name tptp.produc367475239e_name Bool)|)) (not (forall ((ii tptp.name)) (= (ho_334 v ii) (ite (= i ii) e (ho_334 u ii)))))))))) (let ((_let_280 (forall ((x |u_(-> tptp.name tptp.produc367475239e_name Bool)|) (y |u_(-> tptp.name tptp.produc367475239e_name Bool)|)) (or (not (forall ((z tptp.name)) (= (ho_334 x z) (ho_334 y z)))) (= x y))))) (let ((_let_281 (forall ((u |u_(-> tptp.set_Late_freeRes tptp.set_Late_freeRes)|) (e tptp.set_Late_freeRes) (i tptp.set_Late_freeRes)) (not (forall ((v |u_(-> tptp.set_Late_freeRes tptp.set_Late_freeRes)|)) (not (forall ((ii tptp.set_Late_freeRes)) (= (ho_144 v ii) (ite (= i ii) e (ho_144 u ii)))))))))) (let ((_let_282 (forall ((x |u_(-> tptp.set_Late_freeRes tptp.set_Late_freeRes)|) (y |u_(-> tptp.set_Late_freeRes tptp.set_Late_freeRes)|)) (or (not (forall ((z tptp.set_Late_freeRes)) (= (ho_144 x z) (ho_144 y z)))) (= x y))))) (let ((_let_283 (forall ((u |u_(-> tptp.list_P227219501e_name tptp.late_residual_Rep tptp.late_residual_Rep)|) (e |u_(-> tptp.late_residual_Rep tptp.late_residual_Rep)|) (i tptp.list_P227219501e_name)) (not (forall ((v |u_(-> tptp.list_P227219501e_name tptp.late_residual_Rep tptp.late_residual_Rep)|)) (not (forall ((ii tptp.list_P227219501e_name)) (= (ho_55 v ii) (ite (= i ii) e (ho_55 u ii)))))))))) (let ((_let_284 (forall ((x |u_(-> tptp.list_P227219501e_name tptp.late_residual_Rep tptp.late_residual_Rep)|) (y |u_(-> tptp.list_P227219501e_name tptp.late_residual_Rep tptp.late_residual_Rep)|)) (or (not (forall ((z tptp.list_P227219501e_name)) (= (ho_55 x z) (ho_55 y z)))) (= x y))))) (let ((_let_285 (forall ((u |u_(-> tptp.list_P227219501e_name tptp.late_subject_Rep tptp.late_subject_Rep)|) (e |u_(-> tptp.late_subject_Rep tptp.late_subject_Rep)|) (i tptp.list_P227219501e_name)) (not (forall ((v |u_(-> tptp.list_P227219501e_name tptp.late_subject_Rep tptp.late_subject_Rep)|)) (not (forall ((ii tptp.list_P227219501e_name)) (= (ho_58 v ii) (ite (= i ii) e (ho_58 u ii)))))))))) (let ((_let_286 (forall ((x |u_(-> tptp.list_P227219501e_name tptp.late_subject_Rep tptp.late_subject_Rep)|) (y |u_(-> tptp.list_P227219501e_name tptp.late_subject_Rep tptp.late_subject_Rep)|)) (or (not (forall ((z tptp.list_P227219501e_name)) (= (ho_58 x z) (ho_58 y z)))) (= x y))))) (let ((_let_287 (forall ((u |u_(-> tptp.produc1141751126_pi_pi tptp.produc1141751126_pi_pi)|) (e tptp.produc1141751126_pi_pi) (i tptp.produc1141751126_pi_pi)) (not (forall ((v |u_(-> tptp.produc1141751126_pi_pi tptp.produc1141751126_pi_pi)|)) (not (forall ((ii tptp.produc1141751126_pi_pi)) (= (ho_74 v ii) (ite (= i ii) e (ho_74 u ii)))))))))) (let ((_let_288 (forall ((x |u_(-> tptp.produc1141751126_pi_pi tptp.produc1141751126_pi_pi)|) (y |u_(-> tptp.produc1141751126_pi_pi tptp.produc1141751126_pi_pi)|)) (or (not (forall ((z tptp.produc1141751126_pi_pi)) (= (ho_74 x z) (ho_74 y z)))) (= x y))))) (let ((_let_289 (forall ((u |u_(-> _u_(-> tptp.produc367475239e_name tptp.produc367475239e_name Bool)_ tptp.list_P227219501e_name Bool)|) (e |u_(-> tptp.list_P227219501e_name Bool)|) (i |u_(-> tptp.produc367475239e_name tptp.produc367475239e_name Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.produc367475239e_name tptp.produc367475239e_name Bool)_ tptp.list_P227219501e_name Bool)|)) (not (forall ((ii |u_(-> tptp.produc367475239e_name tptp.produc367475239e_name Bool)|)) (= (ho_169 v ii) (ite (= i ii) e (ho_169 u ii)))))))))) (let ((_let_290 (forall ((x |u_(-> _u_(-> tptp.produc367475239e_name tptp.produc367475239e_name Bool)_ tptp.list_P227219501e_name Bool)|) (y |u_(-> _u_(-> tptp.produc367475239e_name tptp.produc367475239e_name Bool)_ tptp.list_P227219501e_name Bool)|)) (or (not (forall ((z |u_(-> tptp.produc367475239e_name tptp.produc367475239e_name Bool)|)) (= (ho_169 x z) (ho_169 y z)))) (= x y))))) (let ((_let_291 (forall ((u |u_(-> tptp.produc1141751126_pi_pi tptp.list_P431515740_pi_pi tptp.list_P431515740_pi_pi)|) (e |u_(-> tptp.list_P431515740_pi_pi tptp.list_P431515740_pi_pi)|) (i tptp.produc1141751126_pi_pi)) (not (forall ((v |u_(-> tptp.produc1141751126_pi_pi tptp.list_P431515740_pi_pi tptp.list_P431515740_pi_pi)|)) (not (forall ((ii tptp.produc1141751126_pi_pi)) (= (ho_347 v ii) (ite (= i ii) e (ho_347 u ii)))))))))) (let ((_let_292 (forall ((x |u_(-> tptp.produc1141751126_pi_pi tptp.list_P431515740_pi_pi tptp.list_P431515740_pi_pi)|) (y |u_(-> tptp.produc1141751126_pi_pi tptp.list_P431515740_pi_pi tptp.list_P431515740_pi_pi)|)) (or (not (forall ((z tptp.produc1141751126_pi_pi)) (= (ho_347 x z) (ho_347 y z)))) (= x y))))) (let ((_let_293 (forall ((u |u_(-> _u_(-> tptp.produc367475239e_name tptp.produc367475239e_name Bool)_ tptp.list_P227219501e_name tptp.produc1872410278e_name)|) (e |u_(-> tptp.list_P227219501e_name tptp.produc1872410278e_name)|) (i |u_(-> tptp.produc367475239e_name tptp.produc367475239e_name Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.produc367475239e_name tptp.produc367475239e_name Bool)_ tptp.list_P227219501e_name tptp.produc1872410278e_name)|)) (not (forall ((ii |u_(-> tptp.produc367475239e_name tptp.produc367475239e_name Bool)|)) (= (ho_89 v ii) (ite (= i ii) e (ho_89 u ii)))))))))) (let ((_let_294 (forall ((x |u_(-> _u_(-> tptp.produc367475239e_name tptp.produc367475239e_name Bool)_ tptp.list_P227219501e_name tptp.produc1872410278e_name)|) (y |u_(-> _u_(-> tptp.produc367475239e_name tptp.produc367475239e_name Bool)_ tptp.list_P227219501e_name tptp.produc1872410278e_name)|)) (or (not (forall ((z |u_(-> tptp.produc367475239e_name tptp.produc367475239e_name Bool)|)) (= (ho_89 x z) (ho_89 y z)))) (= x y))))) (let ((_let_295 (forall ((u |u_(-> tptp.pi_Rep tptp.pi_Rep)|) (e tptp.pi_Rep) (i tptp.pi_Rep)) (not (forall ((v |u_(-> tptp.pi_Rep tptp.pi_Rep)|)) (not (forall ((ii tptp.pi_Rep)) (= (ho_36 v ii) (ite (= i ii) e (ho_36 u ii)))))))))) (let ((_let_296 (forall ((x |u_(-> tptp.pi_Rep tptp.pi_Rep)|) (y |u_(-> tptp.pi_Rep tptp.pi_Rep)|)) (or (not (forall ((z tptp.pi_Rep)) (= (ho_36 x z) (ho_36 y z)))) (= x y))))) (let ((_let_297 (forall ((u |u_(-> tptp.name tptp.list_name Bool)|) (e |u_(-> tptp.list_name Bool)|) (i tptp.name)) (not (forall ((v |u_(-> tptp.name tptp.list_name Bool)|)) (not (forall ((ii tptp.name)) (= (ho_350 v ii) (ite (= i ii) e (ho_350 u ii)))))))))) (let ((_let_298 (forall ((x |u_(-> tptp.name tptp.list_name Bool)|) (y |u_(-> tptp.name tptp.list_name Bool)|)) (or (not (forall ((z tptp.name)) (= (ho_350 x z) (ho_350 y z)))) (= x y))))) (let ((_let_299 (forall ((u |u_(-> tptp.list_P227219501e_name tptp.set_Pr1834926343_pi_pi tptp.set_Pr1834926343_pi_pi)|) (e |u_(-> tptp.set_Pr1834926343_pi_pi tptp.set_Pr1834926343_pi_pi)|) (i tptp.list_P227219501e_name)) (not (forall ((v |u_(-> tptp.list_P227219501e_name tptp.set_Pr1834926343_pi_pi tptp.set_Pr1834926343_pi_pi)|)) (not (forall ((ii tptp.list_P227219501e_name)) (= (ho_79 v ii) (ite (= i ii) e (ho_79 u ii)))))))))) (let ((_let_300 (forall ((x |u_(-> tptp.list_P227219501e_name tptp.set_Pr1834926343_pi_pi tptp.set_Pr1834926343_pi_pi)|) (y |u_(-> tptp.list_P227219501e_name tptp.set_Pr1834926343_pi_pi tptp.set_Pr1834926343_pi_pi)|)) (or (not (forall ((z tptp.list_P227219501e_name)) (= (ho_79 x z) (ho_79 y z)))) (= x y))))) (let ((_let_301 (forall ((u |u_(-> tptp.late_freeRes_Rep tptp.late_freeRes_Rep)|) (e tptp.late_freeRes_Rep) (i tptp.late_freeRes_Rep)) (not (forall ((v |u_(-> tptp.late_freeRes_Rep tptp.late_freeRes_Rep)|)) (not (forall ((ii tptp.late_freeRes_Rep)) (= (ho_62 v ii) (ite (= i ii) e (ho_62 u ii)))))))))) (let ((_let_302 (forall ((x |u_(-> tptp.late_freeRes_Rep tptp.late_freeRes_Rep)|) (y |u_(-> tptp.late_freeRes_Rep tptp.late_freeRes_Rep)|)) (or (not (forall ((z tptp.late_freeRes_Rep)) (= (ho_62 x z) (ho_62 y z)))) (= x y))))) (let ((_let_303 (forall ((u |u_(-> tptp.name tptp.late_freeRes Bool)|) (e |u_(-> tptp.late_freeRes Bool)|) (i tptp.name)) (not (forall ((v |u_(-> tptp.name tptp.late_freeRes Bool)|)) (not (forall ((ii tptp.name)) (= (ho_70 v ii) (ite (= i ii) e (ho_70 u ii)))))))))) (let ((_let_304 (forall ((x |u_(-> tptp.name tptp.late_freeRes Bool)|) (y |u_(-> tptp.name tptp.late_freeRes Bool)|)) (or (not (forall ((z tptp.name)) (= (ho_70 x z) (ho_70 y z)))) (= x y))))) (let ((_let_305 (forall ((u |u_(-> tptp.list_P227219501e_name tptp.late_freeRes_Rep tptp.late_freeRes_Rep)|) (e |u_(-> tptp.late_freeRes_Rep tptp.late_freeRes_Rep)|) (i tptp.list_P227219501e_name)) (not (forall ((v |u_(-> tptp.list_P227219501e_name tptp.late_freeRes_Rep tptp.late_freeRes_Rep)|)) (not (forall ((ii tptp.list_P227219501e_name)) (= (ho_61 v ii) (ite (= i ii) e (ho_61 u ii)))))))))) (let ((_let_306 (forall ((x |u_(-> tptp.list_P227219501e_name tptp.late_freeRes_Rep tptp.late_freeRes_Rep)|) (y |u_(-> tptp.list_P227219501e_name tptp.late_freeRes_Rep tptp.late_freeRes_Rep)|)) (or (not (forall ((z tptp.list_P227219501e_name)) (= (ho_61 x z) (ho_61 y z)))) (= x y))))) (let ((_let_307 (forall ((u |u_(-> tptp.set_Pr1834926343_pi_pi tptp.product_prod_pi_pi Bool)|) (e |u_(-> tptp.product_prod_pi_pi Bool)|) (i tptp.set_Pr1834926343_pi_pi)) (not (forall ((v |u_(-> tptp.set_Pr1834926343_pi_pi tptp.product_prod_pi_pi Bool)|)) (not (forall ((ii tptp.set_Pr1834926343_pi_pi)) (= (ho_15 v ii) (ite (= i ii) e (ho_15 u ii)))))))))) (let ((_let_308 (forall ((x |u_(-> tptp.set_Pr1834926343_pi_pi tptp.product_prod_pi_pi Bool)|) (y |u_(-> tptp.set_Pr1834926343_pi_pi tptp.product_prod_pi_pi Bool)|)) (or (not (forall ((z tptp.set_Pr1834926343_pi_pi)) (= (ho_15 x z) (ho_15 y z)))) (= x y))))) (let ((_let_309 (forall ((u |u_(-> tptp.name tptp.produc1141751126_pi_pi Bool)|) (e |u_(-> tptp.produc1141751126_pi_pi Bool)|) (i tptp.name)) (not (forall ((v |u_(-> tptp.name tptp.produc1141751126_pi_pi Bool)|)) (not (forall ((ii tptp.name)) (= (ho_76 v ii) (ite (= i ii) e (ho_76 u ii)))))))))) (let ((_let_310 (forall ((x |u_(-> tptp.name tptp.produc1141751126_pi_pi Bool)|) (y |u_(-> tptp.name tptp.produc1141751126_pi_pi Bool)|)) (or (not (forall ((z tptp.name)) (= (ho_76 x z) (ho_76 y z)))) (= x y))))) (let ((_let_311 (forall ((u |u_(-> tptp.pi_Rep Bool)|) (e Bool) (i tptp.pi_Rep)) (not (forall ((v |u_(-> tptp.pi_Rep Bool)|)) (not (forall ((ii tptp.pi_Rep)) (= (ho_65 v ii) (ite (= i ii) e (ho_65 u ii)))))))))) (let ((_let_312 (forall ((x |u_(-> tptp.pi_Rep Bool)|) (y |u_(-> tptp.pi_Rep Bool)|)) (or (not (forall ((z tptp.pi_Rep)) (= (ho_65 x z) (ho_65 y z)))) (= x y))))) (let ((_let_313 (forall ((u |u_(-> tptp.name tptp.pi_Rep Bool)|) (e |u_(-> tptp.pi_Rep Bool)|) (i tptp.name)) (not (forall ((v |u_(-> tptp.name tptp.pi_Rep Bool)|)) (not (forall ((ii tptp.name)) (= (ho_64 v ii) (ite (= i ii) e (ho_64 u ii)))))))))) (let ((_let_314 (forall ((x |u_(-> tptp.name tptp.pi_Rep Bool)|) (y |u_(-> tptp.name tptp.pi_Rep Bool)|)) (or (not (forall ((z tptp.name)) (= (ho_64 x z) (ho_64 y z)))) (= x y))))) (let ((_let_315 (forall ((u |u_(-> tptp.list_P227219501e_name _u_(-> tptp.pi_Rep tptp.late_freeRes)_ tptp.pi_Rep tptp.late_freeRes)|) (e |u_(-> _u_(-> tptp.pi_Rep tptp.late_freeRes)_ tptp.pi_Rep tptp.late_freeRes)|) (i tptp.list_P227219501e_name)) (not (forall ((v |u_(-> tptp.list_P227219501e_name _u_(-> tptp.pi_Rep tptp.late_freeRes)_ tptp.pi_Rep tptp.late_freeRes)|)) (not (forall ((ii tptp.list_P227219501e_name)) (= (ho_126 v ii) (ite (= i ii) e (ho_126 u ii)))))))))) (let ((_let_316 (forall ((x |u_(-> tptp.list_P227219501e_name _u_(-> tptp.pi_Rep tptp.late_freeRes)_ tptp.pi_Rep tptp.late_freeRes)|) (y |u_(-> tptp.list_P227219501e_name _u_(-> tptp.pi_Rep tptp.late_freeRes)_ tptp.pi_Rep tptp.late_freeRes)|)) (or (not (forall ((z tptp.list_P227219501e_name)) (= (ho_126 x z) (ho_126 y z)))) (= x y))))) (let ((_let_317 (forall ((u |u_(-> tptp.name tptp.late_subject Bool)|) (e |u_(-> tptp.late_subject Bool)|) (i tptp.name)) (not (forall ((v |u_(-> tptp.name tptp.late_subject Bool)|)) (not (forall ((ii tptp.name)) (= (ho_67 v ii) (ite (= i ii) e (ho_67 u ii)))))))))) (let ((_let_318 (forall ((x |u_(-> tptp.name tptp.late_subject Bool)|) (y |u_(-> tptp.name tptp.late_subject Bool)|)) (or (not (forall ((z tptp.name)) (= (ho_67 x z) (ho_67 y z)))) (= x y))))) (let ((_let_319 (forall ((u |u_(-> tptp.list_P227219501e_name tptp.produc1141751126_pi_pi tptp.produc1141751126_pi_pi)|) (e |u_(-> tptp.produc1141751126_pi_pi tptp.produc1141751126_pi_pi)|) (i tptp.list_P227219501e_name)) (not (forall ((v |u_(-> tptp.list_P227219501e_name tptp.produc1141751126_pi_pi tptp.produc1141751126_pi_pi)|)) (not (forall ((ii tptp.list_P227219501e_name)) (= (ho_73 v ii) (ite (= i ii) e (ho_73 u ii)))))))))) (let ((_let_320 (forall ((x |u_(-> tptp.list_P227219501e_name tptp.produc1141751126_pi_pi tptp.produc1141751126_pi_pi)|) (y |u_(-> tptp.list_P227219501e_name tptp.produc1141751126_pi_pi tptp.produc1141751126_pi_pi)|)) (or (not (forall ((z tptp.list_P227219501e_name)) (= (ho_73 x z) (ho_73 y z)))) (= x y))))) (let ((_let_321 (forall ((u |u_(-> tptp.set_pi Bool)|) (e Bool) (i tptp.set_pi)) (not (forall ((v |u_(-> tptp.set_pi Bool)|)) (not (forall ((ii tptp.set_pi)) (= (ho_165 v ii) (ite (= i ii) e (ho_165 u ii)))))))))) (let ((_let_322 (forall ((x |u_(-> tptp.set_pi Bool)|) (y |u_(-> tptp.set_pi Bool)|)) (or (not (forall ((z tptp.set_pi)) (= (ho_165 x z) (ho_165 y z)))) (= x y))))) (let ((_let_323 (forall ((u |u_(-> tptp.produc1357834675reeRes tptp.produc1357834675reeRes)|) (e tptp.produc1357834675reeRes) (i tptp.produc1357834675reeRes)) (not (forall ((v |u_(-> tptp.produc1357834675reeRes tptp.produc1357834675reeRes)|)) (not (forall ((ii tptp.produc1357834675reeRes)) (= (ho_295 v ii) (ite (= i ii) e (ho_295 u ii)))))))))) (let ((_let_324 (forall ((x |u_(-> tptp.produc1357834675reeRes tptp.produc1357834675reeRes)|) (y |u_(-> tptp.produc1357834675reeRes tptp.produc1357834675reeRes)|)) (or (not (forall ((z tptp.produc1357834675reeRes)) (= (ho_295 x z) (ho_295 y z)))) (= x y))))) (let ((_let_325 (forall ((u |u_(-> tptp.set_Pr1834926343_pi_pi tptp.set_Pr1834926343_pi_pi)|) (e tptp.set_Pr1834926343_pi_pi) (i tptp.set_Pr1834926343_pi_pi)) (not (forall ((v |u_(-> tptp.set_Pr1834926343_pi_pi tptp.set_Pr1834926343_pi_pi)|)) (not (forall ((ii tptp.set_Pr1834926343_pi_pi)) (= (ho_80 v ii) (ite (= i ii) e (ho_80 u ii)))))))))) (let ((_let_326 (forall ((x |u_(-> tptp.set_Pr1834926343_pi_pi tptp.set_Pr1834926343_pi_pi)|) (y |u_(-> tptp.set_Pr1834926343_pi_pi tptp.set_Pr1834926343_pi_pi)|)) (or (not (forall ((z tptp.set_Pr1834926343_pi_pi)) (= (ho_80 x z) (ho_80 y z)))) (= x y))))) (let ((_let_327 (forall ((u |u_(-> tptp.list_P227219501e_name Bool Bool)|) (e |u_(-> Bool Bool)|) (i tptp.list_P227219501e_name)) (not (forall ((v |u_(-> tptp.list_P227219501e_name Bool Bool)|)) (not (forall ((ii tptp.list_P227219501e_name)) (= (ho_82 v ii) (ite (= i ii) e (ho_82 u ii)))))))))) (let ((_let_328 (forall ((x |u_(-> tptp.list_P227219501e_name Bool Bool)|) (y |u_(-> tptp.list_P227219501e_name Bool Bool)|)) (or (not (forall ((z tptp.list_P227219501e_name)) (= (ho_82 x z) (ho_82 y z)))) (= x y))))) (let ((_let_329 (forall ((u |u_(-> tptp.set_pi tptp.set_pi)|) (e tptp.set_pi) (i tptp.set_pi)) (not (forall ((v |u_(-> tptp.set_pi tptp.set_pi)|)) (not (forall ((ii tptp.set_pi)) (= (ho_162 v ii) (ite (= i ii) e (ho_162 u ii)))))))))) (let ((_let_330 (forall ((x |u_(-> tptp.set_pi tptp.set_pi)|) (y |u_(-> tptp.set_pi tptp.set_pi)|)) (or (not (forall ((z tptp.set_pi)) (= (ho_162 x z) (ho_162 y z)))) (= x y))))) (let ((_let_331 (forall ((u |u_(-> tptp.list_P227219501e_name tptp.produc992857746Res_pi tptp.produc992857746Res_pi)|) (e |u_(-> tptp.produc992857746Res_pi tptp.produc992857746Res_pi)|) (i tptp.list_P227219501e_name)) (not (forall ((v |u_(-> tptp.list_P227219501e_name tptp.produc992857746Res_pi tptp.produc992857746Res_pi)|)) (not (forall ((ii tptp.list_P227219501e_name)) (= (ho_306 v ii) (ite (= i ii) e (ho_306 u ii)))))))))) (let ((_let_332 (forall ((x |u_(-> tptp.list_P227219501e_name tptp.produc992857746Res_pi tptp.produc992857746Res_pi)|) (y |u_(-> tptp.list_P227219501e_name tptp.produc992857746Res_pi tptp.produc992857746Res_pi)|)) (or (not (forall ((z tptp.list_P227219501e_name)) (= (ho_306 x z) (ho_306 y z)))) (= x y))))) (let ((_let_333 (forall ((u |u_(-> tptp.name tptp.list_P227219501e_name Bool)|) (e |u_(-> tptp.list_P227219501e_name Bool)|) (i tptp.name)) (not (forall ((v |u_(-> tptp.name tptp.list_P227219501e_name Bool)|)) (not (forall ((ii tptp.name)) (= (ho_85 v ii) (ite (= i ii) e (ho_85 u ii)))))))))) (let ((_let_334 (forall ((x |u_(-> tptp.name tptp.list_P227219501e_name Bool)|) (y |u_(-> tptp.name tptp.list_P227219501e_name Bool)|)) (or (not (forall ((z tptp.name)) (= (ho_85 x z) (ho_85 y z)))) (= x y))))) (let ((_let_335 (forall ((u |u_(-> tptp.name tptp.name tptp.produc367475239e_name)|) (e |u_(-> tptp.name tptp.produc367475239e_name)|) (i tptp.name)) (not (forall ((v |u_(-> tptp.name tptp.name tptp.produc367475239e_name)|)) (not (forall ((ii tptp.name)) (= (ho_23 v ii) (ite (= i ii) e (ho_23 u ii)))))))))) (let ((_let_336 (forall ((x |u_(-> tptp.name tptp.name tptp.produc367475239e_name)|) (y |u_(-> tptp.name tptp.name tptp.produc367475239e_name)|)) (or (not (forall ((z tptp.name)) (= (ho_23 x z) (ho_23 y z)))) (= x y))))) (let ((_let_337 (forall ((u |u_(-> tptp.list_P227219501e_name Bool)|) (e Bool) (i tptp.list_P227219501e_name)) (not (forall ((v |u_(-> tptp.list_P227219501e_name Bool)|)) (not (forall ((ii tptp.list_P227219501e_name)) (= (ho_86 v ii) (ite (= i ii) e (ho_86 u ii)))))))))) (let ((_let_338 (forall ((x |u_(-> tptp.list_P227219501e_name Bool)|) (y |u_(-> tptp.list_P227219501e_name Bool)|)) (or (not (forall ((z tptp.list_P227219501e_name)) (= (ho_86 x z) (ho_86 y z)))) (= x y))))) (let ((_let_339 (forall ((u |u_(-> tptp.name tptp.list_Late_freeRes Bool)|) (e |u_(-> tptp.list_Late_freeRes Bool)|) (i tptp.name)) (not (forall ((v |u_(-> tptp.name tptp.list_Late_freeRes Bool)|)) (not (forall ((ii tptp.name)) (= (ho_341 v ii) (ite (= i ii) e (ho_341 u ii)))))))))) (let ((_let_340 (forall ((x |u_(-> tptp.name tptp.list_Late_freeRes Bool)|) (y |u_(-> tptp.name tptp.list_Late_freeRes Bool)|)) (or (not (forall ((z tptp.name)) (= (ho_341 x z) (ho_341 y z)))) (= x y))))) (let ((_let_341 (forall ((u |u_(-> tptp.produc367475239e_name tptp.produc367475239e_name Bool)|) (e |u_(-> tptp.produc367475239e_name Bool)|) (i tptp.produc367475239e_name)) (not (forall ((v |u_(-> tptp.produc367475239e_name tptp.produc367475239e_name Bool)|)) (not (forall ((ii tptp.produc367475239e_name)) (= (ho_87 v ii) (ite (= i ii) e (ho_87 u ii)))))))))) (let ((_let_342 (forall ((x |u_(-> tptp.produc367475239e_name tptp.produc367475239e_name Bool)|) (y |u_(-> tptp.produc367475239e_name tptp.produc367475239e_name Bool)|)) (or (not (forall ((z tptp.produc367475239e_name)) (= (ho_87 x z) (ho_87 y z)))) (= x y))))) (let ((_let_343 (forall ((u |u_(-> tptp.list_P227219501e_name tptp.list_P227219501e_name tptp.produc890461031e_name)|) (e |u_(-> tptp.list_P227219501e_name tptp.produc890461031e_name)|) (i tptp.list_P227219501e_name)) (not (forall ((v |u_(-> tptp.list_P227219501e_name tptp.list_P227219501e_name tptp.produc890461031e_name)|)) (not (forall ((ii tptp.list_P227219501e_name)) (= (ho_92 v ii) (ite (= i ii) e (ho_92 u ii)))))))))) (let ((_let_344 (forall ((x |u_(-> tptp.list_P227219501e_name tptp.list_P227219501e_name tptp.produc890461031e_name)|) (y |u_(-> tptp.list_P227219501e_name tptp.list_P227219501e_name tptp.produc890461031e_name)|)) (or (not (forall ((z tptp.list_P227219501e_name)) (= (ho_92 x z) (ho_92 y z)))) (= x y))))) (let ((_let_345 (forall ((u |u_(-> tptp.produc367475239e_name Bool)|) (e Bool) (i tptp.produc367475239e_name)) (not (forall ((v |u_(-> tptp.produc367475239e_name Bool)|)) (not (forall ((ii tptp.produc367475239e_name)) (= (ho_94 v ii) (ite (= i ii) e (ho_94 u ii)))))))))) (let ((_let_346 (forall ((x |u_(-> tptp.produc367475239e_name Bool)|) (y |u_(-> tptp.produc367475239e_name Bool)|)) (or (not (forall ((z tptp.produc367475239e_name)) (= (ho_94 x z) (ho_94 y z)))) (= x y))))) (let ((_let_347 (forall ((u |u_(-> tptp.list_P431515740_pi_pi tptp.list_P431515740_pi_pi)|) (e tptp.list_P431515740_pi_pi) (i tptp.list_P431515740_pi_pi)) (not (forall ((v |u_(-> tptp.list_P431515740_pi_pi tptp.list_P431515740_pi_pi)|)) (not (forall ((ii tptp.list_P431515740_pi_pi)) (= (ho_348 v ii) (ite (= i ii) e (ho_348 u ii)))))))))) (let ((_let_348 (forall ((x |u_(-> tptp.list_P431515740_pi_pi tptp.list_P431515740_pi_pi)|) (y |u_(-> tptp.list_P431515740_pi_pi tptp.list_P431515740_pi_pi)|)) (or (not (forall ((z tptp.list_P431515740_pi_pi)) (= (ho_348 x z) (ho_348 y z)))) (= x y))))) (let ((_let_349 (forall ((u |u_(-> tptp.list_P227219501e_name tptp.list_P227219501e_name tptp.list_P227219501e_name)|) (e |u_(-> tptp.list_P227219501e_name tptp.list_P227219501e_name)|) (i tptp.list_P227219501e_name)) (not (forall ((v |u_(-> tptp.list_P227219501e_name tptp.list_P227219501e_name tptp.list_P227219501e_name)|)) (not (forall ((ii tptp.list_P227219501e_name)) (= (ho_98 v ii) (ite (= i ii) e (ho_98 u ii)))))))))) (let ((_let_350 (forall ((x |u_(-> tptp.list_P227219501e_name tptp.list_P227219501e_name tptp.list_P227219501e_name)|) (y |u_(-> tptp.list_P227219501e_name tptp.list_P227219501e_name tptp.list_P227219501e_name)|)) (or (not (forall ((z tptp.list_P227219501e_name)) (= (ho_98 x z) (ho_98 y z)))) (= x y))))) (let ((_let_351 (forall ((u |u_(-> tptp.produc140253050ect_pi Bool)|) (e Bool) (i tptp.produc140253050ect_pi)) (not (forall ((v |u_(-> tptp.produc140253050ect_pi Bool)|)) (not (forall ((ii tptp.produc140253050ect_pi)) (= (ho_199 v ii) (ite (= i ii) e (ho_199 u ii)))))))))) (let ((_let_352 (forall ((x |u_(-> tptp.produc140253050ect_pi Bool)|) (y |u_(-> tptp.produc140253050ect_pi Bool)|)) (or (not (forall ((z tptp.produc140253050ect_pi)) (= (ho_199 x z) (ho_199 y z)))) (= x y))))) (let ((_let_353 (forall ((u |u_(-> tptp.late_freeRes tptp.late_subject tptp.produc214645451ubject)|) (e |u_(-> tptp.late_subject tptp.produc214645451ubject)|) (i tptp.late_freeRes)) (not (forall ((v |u_(-> tptp.late_freeRes tptp.late_subject tptp.produc214645451ubject)|)) (not (forall ((ii tptp.late_freeRes)) (= (ho_201 v ii) (ite (= i ii) e (ho_201 u ii)))))))))) (let ((_let_354 (forall ((x |u_(-> tptp.late_freeRes tptp.late_subject tptp.produc214645451ubject)|) (y |u_(-> tptp.late_freeRes tptp.late_subject tptp.produc214645451ubject)|)) (or (not (forall ((z tptp.late_freeRes)) (= (ho_201 x z) (ho_201 y z)))) (= x y))))) (let ((_let_355 (forall ((u |u_(-> tptp.late_subject tptp.name tptp.pi Bool)|) (e |u_(-> tptp.name tptp.pi Bool)|) (i tptp.late_subject)) (not (forall ((v |u_(-> tptp.late_subject tptp.name tptp.pi Bool)|)) (not (forall ((ii tptp.late_subject)) (= (ho_387 v ii) (ite (= i ii) e (ho_387 u ii)))))))))) (let ((_let_356 (forall ((x |u_(-> tptp.late_subject tptp.name tptp.pi Bool)|) (y |u_(-> tptp.late_subject tptp.name tptp.pi Bool)|)) (or (not (forall ((z tptp.late_subject)) (= (ho_387 x z) (ho_387 y z)))) (= x y))))) (let ((_let_357 (forall ((u |u_(-> tptp.name tptp.produc140253050ect_pi Bool)|) (e |u_(-> tptp.produc140253050ect_pi Bool)|) (i tptp.name)) (not (forall ((v |u_(-> tptp.name tptp.produc140253050ect_pi Bool)|)) (not (forall ((ii tptp.name)) (= (ho_198 v ii) (ite (= i ii) e (ho_198 u ii)))))))))) (let ((_let_358 (forall ((x |u_(-> tptp.name tptp.produc140253050ect_pi Bool)|) (y |u_(-> tptp.name tptp.produc140253050ect_pi Bool)|)) (or (not (forall ((z tptp.name)) (= (ho_198 x z) (ho_198 y z)))) (= x y))))) (let ((_let_359 (forall ((u |u_(-> tptp.late_subject tptp.name tptp.set_Pr1834926343_pi_pi Bool)|) (e |u_(-> tptp.name tptp.set_Pr1834926343_pi_pi Bool)|) (i tptp.late_subject)) (not (forall ((v |u_(-> tptp.late_subject tptp.name tptp.set_Pr1834926343_pi_pi Bool)|)) (not (forall ((ii tptp.late_subject)) (= (ho_239 v ii) (ite (= i ii) e (ho_239 u ii)))))))))) (let ((_let_360 (forall ((x |u_(-> tptp.late_subject tptp.name tptp.set_Pr1834926343_pi_pi Bool)|) (y |u_(-> tptp.late_subject tptp.name tptp.set_Pr1834926343_pi_pi Bool)|)) (or (not (forall ((z tptp.late_subject)) (= (ho_239 x z) (ho_239 y z)))) (= x y))))) (let ((_let_361 (forall ((u |u_(-> tptp.late_subject tptp.produc214645451ubject)|) (e tptp.produc214645451ubject) (i tptp.late_subject)) (not (forall ((v |u_(-> tptp.late_subject tptp.produc214645451ubject)|)) (not (forall ((ii tptp.late_subject)) (= (ho_202 v ii) (ite (= i ii) e (ho_202 u ii)))))))))) (let ((_let_362 (forall ((x |u_(-> tptp.late_subject tptp.produc214645451ubject)|) (y |u_(-> tptp.late_subject tptp.produc214645451ubject)|)) (or (not (forall ((z tptp.late_subject)) (= (ho_202 x z) (ho_202 y z)))) (= x y))))) (let ((_let_363 (forall ((u |u_(-> tptp.produc214645451ubject Bool)|) (e Bool) (i tptp.produc214645451ubject)) (not (forall ((v |u_(-> tptp.produc214645451ubject Bool)|)) (not (forall ((ii tptp.produc214645451ubject)) (= (ho_205 v ii) (ite (= i ii) e (ho_205 u ii)))))))))) (let ((_let_364 (forall ((x |u_(-> tptp.produc214645451ubject Bool)|) (y |u_(-> tptp.produc214645451ubject Bool)|)) (or (not (forall ((z tptp.produc214645451ubject)) (= (ho_205 x z) (ho_205 y z)))) (= x y))))) (let ((_let_365 (forall ((u |u_(-> tptp.name tptp.produc2052722628s_name)|) (e tptp.produc2052722628s_name) (i tptp.name)) (not (forall ((v |u_(-> tptp.name tptp.produc2052722628s_name)|)) (not (forall ((ii tptp.name)) (= (ho_214 v ii) (ite (= i ii) e (ho_214 u ii)))))))))) (let ((_let_366 (forall ((x |u_(-> tptp.name tptp.produc2052722628s_name)|) (y |u_(-> tptp.name tptp.produc2052722628s_name)|)) (or (not (forall ((z tptp.name)) (= (ho_214 x z) (ho_214 y z)))) (= x y))))) (let ((_let_367 (forall ((u |u_(-> tptp.late_freeRes tptp.pi tptp.late_residual)|) (e |u_(-> tptp.pi tptp.late_residual)|) (i tptp.late_freeRes)) (not (forall ((v |u_(-> tptp.late_freeRes tptp.pi tptp.late_residual)|)) (not (forall ((ii tptp.late_freeRes)) (= (ho_373 v ii) (ite (= i ii) e (ho_373 u ii)))))))))) (let ((_let_368 (forall ((x |u_(-> tptp.late_freeRes tptp.pi tptp.late_residual)|) (y |u_(-> tptp.late_freeRes tptp.pi tptp.late_residual)|)) (or (not (forall ((z tptp.late_freeRes)) (= (ho_373 x z) (ho_373 y z)))) (= x y))))) (let ((_let_369 (forall ((u |u_(-> tptp.late_freeRes tptp.name tptp.produc2052722628s_name)|) (e |u_(-> tptp.name tptp.produc2052722628s_name)|) (i tptp.late_freeRes)) (not (forall ((v |u_(-> tptp.late_freeRes tptp.name tptp.produc2052722628s_name)|)) (not (forall ((ii tptp.late_freeRes)) (= (ho_213 v ii) (ite (= i ii) e (ho_213 u ii)))))))))) (let ((_let_370 (forall ((x |u_(-> tptp.late_freeRes tptp.name tptp.produc2052722628s_name)|) (y |u_(-> tptp.late_freeRes tptp.name tptp.produc2052722628s_name)|)) (or (not (forall ((z tptp.late_freeRes)) (= (ho_213 x z) (ho_213 y z)))) (= x y))))) (let ((_let_371 (forall ((u |u_(-> tptp.produc2052722628s_name Bool)|) (e Bool) (i tptp.produc2052722628s_name)) (not (forall ((v |u_(-> tptp.produc2052722628s_name Bool)|)) (not (forall ((ii tptp.produc2052722628s_name)) (= (ho_217 v ii) (ite (= i ii) e (ho_217 u ii)))))))))) (let ((_let_372 (forall ((x |u_(-> tptp.produc2052722628s_name Bool)|) (y |u_(-> tptp.produc2052722628s_name Bool)|)) (or (not (forall ((z tptp.produc2052722628s_name)) (= (ho_217 x z) (ho_217 y z)))) (= x y))))) (let ((_let_373 (forall ((u |u_(-> tptp.late_subject tptp.name tptp.pi tptp.late_residual)|) (e |u_(-> tptp.name tptp.pi tptp.late_residual)|) (i tptp.late_subject)) (not (forall ((v |u_(-> tptp.late_subject tptp.name tptp.pi tptp.late_residual)|)) (not (forall ((ii tptp.late_subject)) (= (ho_366 v ii) (ite (= i ii) e (ho_366 u ii)))))))))) (let ((_let_374 (forall ((x |u_(-> tptp.late_subject tptp.name tptp.pi tptp.late_residual)|) (y |u_(-> tptp.late_subject tptp.name tptp.pi tptp.late_residual)|)) (or (not (forall ((z tptp.late_subject)) (= (ho_366 x z) (ho_366 y z)))) (= x y))))) (let ((_let_375 (forall ((u |u_(-> tptp.name tptp.produc2052722628s_name Bool)|) (e |u_(-> tptp.produc2052722628s_name Bool)|) (i tptp.name)) (not (forall ((v |u_(-> tptp.name tptp.produc2052722628s_name Bool)|)) (not (forall ((ii tptp.name)) (= (ho_216 v ii) (ite (= i ii) e (ho_216 u ii)))))))))) (let ((_let_376 (forall ((x |u_(-> tptp.name tptp.produc2052722628s_name Bool)|) (y |u_(-> tptp.name tptp.produc2052722628s_name Bool)|)) (or (not (forall ((z tptp.name)) (= (ho_216 x z) (ho_216 y z)))) (= x y))))) (let ((_let_377 (forall ((u |u_(-> tptp.pi tptp.produc992857746Res_pi)|) (e tptp.produc992857746Res_pi) (i tptp.pi)) (not (forall ((v |u_(-> tptp.pi tptp.produc992857746Res_pi)|)) (not (forall ((ii tptp.pi)) (= (ho_220 v ii) (ite (= i ii) e (ho_220 u ii)))))))))) (let ((_let_378 (forall ((x |u_(-> tptp.pi tptp.produc992857746Res_pi)|) (y |u_(-> tptp.pi tptp.produc992857746Res_pi)|)) (or (not (forall ((z tptp.pi)) (= (ho_220 x z) (ho_220 y z)))) (= x y))))) (let ((_let_379 (forall ((u |u_(-> tptp.late_subject tptp.list_Late_subject tptp.list_Late_subject)|) (e |u_(-> tptp.list_Late_subject tptp.list_Late_subject)|) (i tptp.late_subject)) (not (forall ((v |u_(-> tptp.late_subject tptp.list_Late_subject tptp.list_Late_subject)|)) (not (forall ((ii tptp.late_subject)) (= (ho_312 v ii) (ite (= i ii) e (ho_312 u ii)))))))))) (let ((_let_380 (forall ((x |u_(-> tptp.late_subject tptp.list_Late_subject tptp.list_Late_subject)|) (y |u_(-> tptp.late_subject tptp.list_Late_subject tptp.list_Late_subject)|)) (or (not (forall ((z tptp.late_subject)) (= (ho_312 x z) (ho_312 y z)))) (= x y))))) (let ((_let_381 (forall ((u |u_(-> tptp.late_freeRes tptp.pi tptp.produc992857746Res_pi)|) (e |u_(-> tptp.pi tptp.produc992857746Res_pi)|) (i tptp.late_freeRes)) (not (forall ((v |u_(-> tptp.late_freeRes tptp.pi tptp.produc992857746Res_pi)|)) (not (forall ((ii tptp.late_freeRes)) (= (ho_219 v ii) (ite (= i ii) e (ho_219 u ii)))))))))) (let ((_let_382 (forall ((x |u_(-> tptp.late_freeRes tptp.pi tptp.produc992857746Res_pi)|) (y |u_(-> tptp.late_freeRes tptp.pi tptp.produc992857746Res_pi)|)) (or (not (forall ((z tptp.late_freeRes)) (= (ho_219 x z) (ho_219 y z)))) (= x y))))) (let ((_let_383 (forall ((u |u_(-> tptp.produc992857746Res_pi Bool)|) (e Bool) (i tptp.produc992857746Res_pi)) (not (forall ((v |u_(-> tptp.produc992857746Res_pi Bool)|)) (not (forall ((ii tptp.produc992857746Res_pi)) (= (ho_223 v ii) (ite (= i ii) e (ho_223 u ii)))))))))) (let ((_let_384 (forall ((x |u_(-> tptp.produc992857746Res_pi Bool)|) (y |u_(-> tptp.produc992857746Res_pi Bool)|)) (or (not (forall ((z tptp.produc992857746Res_pi)) (= (ho_223 x z) (ho_223 y z)))) (= x y))))) (let ((_let_385 (forall ((u |u_(-> tptp.late_freeRes tptp.list_Late_freeRes tptp.list_Late_freeRes)|) (e |u_(-> tptp.list_Late_freeRes tptp.list_Late_freeRes)|) (i tptp.late_freeRes)) (not (forall ((v |u_(-> tptp.late_freeRes tptp.list_Late_freeRes tptp.list_Late_freeRes)|)) (not (forall ((ii tptp.late_freeRes)) (= (ho_317 v ii) (ite (= i ii) e (ho_317 u ii)))))))))) (let ((_let_386 (forall ((x |u_(-> tptp.late_freeRes tptp.list_Late_freeRes tptp.list_Late_freeRes)|) (y |u_(-> tptp.late_freeRes tptp.list_Late_freeRes tptp.list_Late_freeRes)|)) (or (not (forall ((z tptp.late_freeRes)) (= (ho_317 x z) (ho_317 y z)))) (= x y))))) (let ((_let_387 (forall ((u |u_(-> tptp.name tptp.produc992857746Res_pi Bool)|) (e |u_(-> tptp.produc992857746Res_pi Bool)|) (i tptp.name)) (not (forall ((v |u_(-> tptp.name tptp.produc992857746Res_pi Bool)|)) (not (forall ((ii tptp.name)) (= (ho_222 v ii) (ite (= i ii) e (ho_222 u ii)))))))))) (let ((_let_388 (forall ((x |u_(-> tptp.name tptp.produc992857746Res_pi Bool)|) (y |u_(-> tptp.name tptp.produc992857746Res_pi Bool)|)) (or (not (forall ((z tptp.name)) (= (ho_222 x z) (ho_222 y z)))) (= x y))))) (let ((_let_389 (forall ((u |u_(-> tptp.pi_Rep tptp.pi_Rep tptp.pi_Rep)|) (e |u_(-> tptp.pi_Rep tptp.pi_Rep)|) (i tptp.pi_Rep)) (not (forall ((v |u_(-> tptp.pi_Rep tptp.pi_Rep tptp.pi_Rep)|)) (not (forall ((ii tptp.pi_Rep)) (= (ho_265 v ii) (ite (= i ii) e (ho_265 u ii)))))))))) (let ((_let_390 (forall ((x |u_(-> tptp.pi_Rep tptp.pi_Rep tptp.pi_Rep)|) (y |u_(-> tptp.pi_Rep tptp.pi_Rep tptp.pi_Rep)|)) (or (not (forall ((z tptp.pi_Rep)) (= (ho_265 x z) (ho_265 y z)))) (= x y))))) (let ((_let_391 (forall ((u |u_(-> tptp.late_subject tptp.produc865358760ubject)|) (e tptp.produc865358760ubject) (i tptp.late_subject)) (not (forall ((v |u_(-> tptp.late_subject tptp.produc865358760ubject)|)) (not (forall ((ii tptp.late_subject)) (= (ho_226 v ii) (ite (= i ii) e (ho_226 u ii)))))))))) (let ((_let_392 (forall ((x |u_(-> tptp.late_subject tptp.produc865358760ubject)|) (y |u_(-> tptp.late_subject tptp.produc865358760ubject)|)) (or (not (forall ((z tptp.late_subject)) (= (ho_226 x z) (ho_226 y z)))) (= x y))))) (let ((_let_393 (forall ((u |u_(-> tptp.name tptp.late_subject tptp.produc865358760ubject)|) (e |u_(-> tptp.late_subject tptp.produc865358760ubject)|) (i tptp.name)) (not (forall ((v |u_(-> tptp.name tptp.late_subject tptp.produc865358760ubject)|)) (not (forall ((ii tptp.name)) (= (ho_225 v ii) (ite (= i ii) e (ho_225 u ii)))))))))) (let ((_let_394 (forall ((x |u_(-> tptp.name tptp.late_subject tptp.produc865358760ubject)|) (y |u_(-> tptp.name tptp.late_subject tptp.produc865358760ubject)|)) (or (not (forall ((z tptp.name)) (= (ho_225 x z) (ho_225 y z)))) (= x y))))) (let ((_let_395 (forall ((u |u_(-> tptp.produc865358760ubject Bool)|) (e Bool) (i tptp.produc865358760ubject)) (not (forall ((v |u_(-> tptp.produc865358760ubject Bool)|)) (not (forall ((ii tptp.produc865358760ubject)) (= (ho_229 v ii) (ite (= i ii) e (ho_229 u ii)))))))))) (let ((_let_396 (forall ((x |u_(-> tptp.produc865358760ubject Bool)|) (y |u_(-> tptp.produc865358760ubject Bool)|)) (or (not (forall ((z tptp.produc865358760ubject)) (= (ho_229 x z) (ho_229 y z)))) (= x y))))) (let ((_let_397 (forall ((u |u_(-> tptp.name tptp.produc865358760ubject Bool)|) (e |u_(-> tptp.produc865358760ubject Bool)|) (i tptp.name)) (not (forall ((v |u_(-> tptp.name tptp.produc865358760ubject Bool)|)) (not (forall ((ii tptp.name)) (= (ho_228 v ii) (ite (= i ii) e (ho_228 u ii)))))))))) (let ((_let_398 (forall ((x |u_(-> tptp.name tptp.produc865358760ubject Bool)|) (y |u_(-> tptp.name tptp.produc865358760ubject Bool)|)) (or (not (forall ((z tptp.name)) (= (ho_228 x z) (ho_228 y z)))) (= x y))))) (let ((_let_399 (forall ((u |u_(-> tptp.name tptp.late_freeRes tptp.produc2008547984reeRes)|) (e |u_(-> tptp.late_freeRes tptp.produc2008547984reeRes)|) (i tptp.name)) (not (forall ((v |u_(-> tptp.name tptp.late_freeRes tptp.produc2008547984reeRes)|)) (not (forall ((ii tptp.name)) (= (ho_231 v ii) (ite (= i ii) e (ho_231 u ii)))))))))) (let ((_let_400 (forall ((x |u_(-> tptp.name tptp.late_freeRes tptp.produc2008547984reeRes)|) (y |u_(-> tptp.name tptp.late_freeRes tptp.produc2008547984reeRes)|)) (or (not (forall ((z tptp.name)) (= (ho_231 x z) (ho_231 y z)))) (= x y))))) (let ((_let_401 (forall ((u |u_(-> tptp.produc992857746Res_pi tptp.produc992857746Res_pi)|) (e tptp.produc992857746Res_pi) (i tptp.produc992857746Res_pi)) (not (forall ((v |u_(-> tptp.produc992857746Res_pi tptp.produc992857746Res_pi)|)) (not (forall ((ii tptp.produc992857746Res_pi)) (= (ho_307 v ii) (ite (= i ii) e (ho_307 u ii)))))))))) (let ((_let_402 (forall ((x |u_(-> tptp.produc992857746Res_pi tptp.produc992857746Res_pi)|) (y |u_(-> tptp.produc992857746Res_pi tptp.produc992857746Res_pi)|)) (or (not (forall ((z tptp.produc992857746Res_pi)) (= (ho_307 x z) (ho_307 y z)))) (= x y))))) (let ((_let_403 (forall ((u |u_(-> tptp.produc2008547984reeRes Bool)|) (e Bool) (i tptp.produc2008547984reeRes)) (not (forall ((v |u_(-> tptp.produc2008547984reeRes Bool)|)) (not (forall ((ii tptp.produc2008547984reeRes)) (= (ho_235 v ii) (ite (= i ii) e (ho_235 u ii)))))))))) (let ((_let_404 (forall ((x |u_(-> tptp.produc2008547984reeRes Bool)|) (y |u_(-> tptp.produc2008547984reeRes Bool)|)) (or (not (forall ((z tptp.produc2008547984reeRes)) (= (ho_235 x z) (ho_235 y z)))) (= x y))))) (let ((_let_405 (forall ((u |u_(-> tptp.name tptp.list_P431515740_pi_pi Bool)|) (e |u_(-> tptp.list_P431515740_pi_pi Bool)|) (i tptp.name)) (not (forall ((v |u_(-> tptp.name tptp.list_P431515740_pi_pi Bool)|)) (not (forall ((ii tptp.name)) (= (ho_344 v ii) (ite (= i ii) e (ho_344 u ii)))))))))) (let ((_let_406 (forall ((x |u_(-> tptp.name tptp.list_P431515740_pi_pi Bool)|) (y |u_(-> tptp.name tptp.list_P431515740_pi_pi Bool)|)) (or (not (forall ((z tptp.name)) (= (ho_344 x z) (ho_344 y z)))) (= x y))))) (let ((_let_407 (forall ((u |u_(-> tptp.pi tptp.pi tptp.late_subject tptp.name tptp.set_Pr1834926343_pi_pi Bool)|) (e |u_(-> tptp.pi tptp.late_subject tptp.name tptp.set_Pr1834926343_pi_pi Bool)|) (i tptp.pi)) (not (forall ((v |u_(-> tptp.pi tptp.pi tptp.late_subject tptp.name tptp.set_Pr1834926343_pi_pi Bool)|)) (not (forall ((ii tptp.pi)) (= (ho_237 v ii) (ite (= i ii) e (ho_237 u ii)))))))))) (let ((_let_408 (forall ((x |u_(-> tptp.pi tptp.pi tptp.late_subject tptp.name tptp.set_Pr1834926343_pi_pi Bool)|) (y |u_(-> tptp.pi tptp.pi tptp.late_subject tptp.name tptp.set_Pr1834926343_pi_pi Bool)|)) (or (not (forall ((z tptp.pi)) (= (ho_237 x z) (ho_237 y z)))) (= x y))))) (let ((_let_409 (forall ((u |u_(-> tptp.pi tptp.late_residual)|) (e tptp.late_residual) (i tptp.pi)) (not (forall ((v |u_(-> tptp.pi tptp.late_residual)|)) (not (forall ((ii tptp.pi)) (= (ho_368 v ii) (ite (= i ii) e (ho_368 u ii)))))))))) (let ((_let_410 (forall ((x |u_(-> tptp.pi tptp.late_residual)|) (y |u_(-> tptp.pi tptp.late_residual)|)) (or (not (forall ((z tptp.pi)) (= (ho_368 x z) (ho_368 y z)))) (= x y))))) (let ((_let_411 (forall ((u |u_(-> tptp.set_Pr806375235ubject Bool)|) (e Bool) (i tptp.set_Pr806375235ubject)) (not (forall ((v |u_(-> tptp.set_Pr806375235ubject Bool)|)) (not (forall ((ii tptp.set_Pr806375235ubject)) (= (ho_243 v ii) (ite (= i ii) e (ho_243 u ii)))))))))) (let ((_let_412 (forall ((x |u_(-> tptp.set_Pr806375235ubject Bool)|) (y |u_(-> tptp.set_Pr806375235ubject Bool)|)) (or (not (forall ((z tptp.set_Pr806375235ubject)) (= (ho_243 x z) (ho_243 y z)))) (= x y))))) (let ((_let_413 (forall ((u |u_(-> tptp.produc1359399907ubject tptp.set_Pr806375235ubject Bool)|) (e |u_(-> tptp.set_Pr806375235ubject Bool)|) (i tptp.produc1359399907ubject)) (not (forall ((v |u_(-> tptp.produc1359399907ubject tptp.set_Pr806375235ubject Bool)|)) (not (forall ((ii tptp.produc1359399907ubject)) (= (ho_242 v ii) (ite (= i ii) e (ho_242 u ii)))))))))) (let ((_let_414 (forall ((x |u_(-> tptp.produc1359399907ubject tptp.set_Pr806375235ubject Bool)|) (y |u_(-> tptp.produc1359399907ubject tptp.set_Pr806375235ubject Bool)|)) (or (not (forall ((z tptp.produc1359399907ubject)) (= (ho_242 x z) (ho_242 y z)))) (= x y))))) (let ((_let_415 (forall ((u |u_(-> tptp.produc1357834675reeRes tptp.set_Pr1780909331reeRes Bool)|) (e |u_(-> tptp.set_Pr1780909331reeRes Bool)|) (i tptp.produc1357834675reeRes)) (not (forall ((v |u_(-> tptp.produc1357834675reeRes tptp.set_Pr1780909331reeRes Bool)|)) (not (forall ((ii tptp.produc1357834675reeRes)) (= (ho_246 v ii) (ite (= i ii) e (ho_246 u ii)))))))))) (let ((_let_416 (forall ((x |u_(-> tptp.produc1357834675reeRes tptp.set_Pr1780909331reeRes Bool)|) (y |u_(-> tptp.produc1357834675reeRes tptp.set_Pr1780909331reeRes Bool)|)) (or (not (forall ((z tptp.produc1357834675reeRes)) (= (ho_246 x z) (ho_246 y z)))) (= x y))))) (let ((_let_417 (forall ((u |u_(-> tptp.set_Pr1131282415pi_Rep Bool)|) (e Bool) (i tptp.set_Pr1131282415pi_Rep)) (not (forall ((v |u_(-> tptp.set_Pr1131282415pi_Rep Bool)|)) (not (forall ((ii tptp.set_Pr1131282415pi_Rep)) (= (ho_254 v ii) (ite (= i ii) e (ho_254 u ii)))))))))) (let ((_let_418 (forall ((x |u_(-> tptp.set_Pr1131282415pi_Rep Bool)|) (y |u_(-> tptp.set_Pr1131282415pi_Rep Bool)|)) (or (not (forall ((z tptp.set_Pr1131282415pi_Rep)) (= (ho_254 x z) (ho_254 y z)))) (= x y))))) (let ((_let_419 (forall ((u |u_(-> tptp.pi_Rep tptp.pi_Rep tptp.produc1212344719pi_Rep)|) (e |u_(-> tptp.pi_Rep tptp.produc1212344719pi_Rep)|) (i tptp.pi_Rep)) (not (forall ((v |u_(-> tptp.pi_Rep tptp.pi_Rep tptp.produc1212344719pi_Rep)|)) (not (forall ((ii tptp.pi_Rep)) (= (ho_250 v ii) (ite (= i ii) e (ho_250 u ii)))))))))) (let ((_let_420 (forall ((x |u_(-> tptp.pi_Rep tptp.pi_Rep tptp.produc1212344719pi_Rep)|) (y |u_(-> tptp.pi_Rep tptp.pi_Rep tptp.produc1212344719pi_Rep)|)) (or (not (forall ((z tptp.pi_Rep)) (= (ho_250 x z) (ho_250 y z)))) (= x y))))) (let ((_let_421 (forall ((u |u_(-> tptp.produc1212344719pi_Rep tptp.set_Pr1131282415pi_Rep Bool)|) (e |u_(-> tptp.set_Pr1131282415pi_Rep Bool)|) (i tptp.produc1212344719pi_Rep)) (not (forall ((v |u_(-> tptp.produc1212344719pi_Rep tptp.set_Pr1131282415pi_Rep Bool)|)) (not (forall ((ii tptp.produc1212344719pi_Rep)) (= (ho_253 v ii) (ite (= i ii) e (ho_253 u ii)))))))))) (let ((_let_422 (forall ((x |u_(-> tptp.produc1212344719pi_Rep tptp.set_Pr1131282415pi_Rep Bool)|) (y |u_(-> tptp.produc1212344719pi_Rep tptp.set_Pr1131282415pi_Rep Bool)|)) (or (not (forall ((z tptp.produc1212344719pi_Rep)) (= (ho_253 x z) (ho_253 y z)))) (= x y))))) (let ((_let_423 (forall ((u |u_(-> Bool tptp.late_subject tptp.late_subject tptp.late_subject)|) (e |u_(-> tptp.late_subject tptp.late_subject tptp.late_subject)|) (i Bool)) (not (forall ((v |u_(-> Bool tptp.late_subject tptp.late_subject tptp.late_subject)|)) (not (forall ((ii Bool)) (= (ho_258 v ii) (ite (= i ii) e (ho_258 u ii)))))))))) (let ((_let_424 (forall ((x |u_(-> Bool tptp.late_subject tptp.late_subject tptp.late_subject)|) (y |u_(-> Bool tptp.late_subject tptp.late_subject tptp.late_subject)|)) (or (not (forall ((z Bool)) (= (ho_258 x z) (ho_258 y z)))) (= x y))))) (let ((_let_425 (forall ((u |u_(-> tptp.late_freeRes tptp.late_freeRes tptp.late_freeRes)|) (e |u_(-> tptp.late_freeRes tptp.late_freeRes)|) (i tptp.late_freeRes)) (not (forall ((v |u_(-> tptp.late_freeRes tptp.late_freeRes tptp.late_freeRes)|)) (not (forall ((ii tptp.late_freeRes)) (= (ho_262 v ii) (ite (= i ii) e (ho_262 u ii)))))))))) (let ((_let_426 (forall ((x |u_(-> tptp.late_freeRes tptp.late_freeRes tptp.late_freeRes)|) (y |u_(-> tptp.late_freeRes tptp.late_freeRes tptp.late_freeRes)|)) (or (not (forall ((z tptp.late_freeRes)) (= (ho_262 x z) (ho_262 y z)))) (= x y))))) (let ((_let_427 (forall ((u |u_(-> tptp.name tptp.list_pi Bool)|) (e |u_(-> tptp.list_pi Bool)|) (i tptp.name)) (not (forall ((v |u_(-> tptp.name tptp.list_pi Bool)|)) (not (forall ((ii tptp.name)) (= (ho_353 v ii) (ite (= i ii) e (ho_353 u ii)))))))))) (let ((_let_428 (forall ((x |u_(-> tptp.name tptp.list_pi Bool)|) (y |u_(-> tptp.name tptp.list_pi Bool)|)) (or (not (forall ((z tptp.name)) (= (ho_353 x z) (ho_353 y z)))) (= x y))))) (let ((_let_429 (forall ((u |u_(-> Bool tptp.late_freeRes tptp.late_freeRes tptp.late_freeRes)|) (e |u_(-> tptp.late_freeRes tptp.late_freeRes tptp.late_freeRes)|) (i Bool)) (not (forall ((v |u_(-> Bool tptp.late_freeRes tptp.late_freeRes tptp.late_freeRes)|)) (not (forall ((ii Bool)) (= (ho_261 v ii) (ite (= i ii) e (ho_261 u ii)))))))))) (let ((_let_430 (forall ((x |u_(-> Bool tptp.late_freeRes tptp.late_freeRes tptp.late_freeRes)|) (y |u_(-> Bool tptp.late_freeRes tptp.late_freeRes tptp.late_freeRes)|)) (or (not (forall ((z Bool)) (= (ho_261 x z) (ho_261 y z)))) (= x y))))) (let ((_let_431 (forall ((u |u_(-> Bool tptp.pi_Rep tptp.pi_Rep tptp.pi_Rep)|) (e |u_(-> tptp.pi_Rep tptp.pi_Rep tptp.pi_Rep)|) (i Bool)) (not (forall ((v |u_(-> Bool tptp.pi_Rep tptp.pi_Rep tptp.pi_Rep)|)) (not (forall ((ii Bool)) (= (ho_264 v ii) (ite (= i ii) e (ho_264 u ii)))))))))) (let ((_let_432 (forall ((x |u_(-> Bool tptp.pi_Rep tptp.pi_Rep tptp.pi_Rep)|) (y |u_(-> Bool tptp.pi_Rep tptp.pi_Rep tptp.pi_Rep)|)) (or (not (forall ((z Bool)) (= (ho_264 x z) (ho_264 y z)))) (= x y))))) (let ((_let_433 (forall ((u |u_(-> Bool tptp.name tptp.name tptp.name)|) (e |u_(-> tptp.name tptp.name tptp.name)|) (i Bool)) (not (forall ((v |u_(-> Bool tptp.name tptp.name tptp.name)|)) (not (forall ((ii Bool)) (= (ho_267 v ii) (ite (= i ii) e (ho_267 u ii)))))))))) (let ((_let_434 (forall ((x |u_(-> Bool tptp.name tptp.name tptp.name)|) (y |u_(-> Bool tptp.name tptp.name tptp.name)|)) (or (not (forall ((z Bool)) (= (ho_267 x z) (ho_267 y z)))) (= x y))))) (let ((_let_435 (forall ((u |u_(-> tptp.pi tptp.pi tptp.pi)|) (e |u_(-> tptp.pi tptp.pi)|) (i tptp.pi)) (not (forall ((v |u_(-> tptp.pi tptp.pi tptp.pi)|)) (not (forall ((ii tptp.pi)) (= (ho_271 v ii) (ite (= i ii) e (ho_271 u ii)))))))))) (let ((_let_436 (forall ((x |u_(-> tptp.pi tptp.pi tptp.pi)|) (y |u_(-> tptp.pi tptp.pi tptp.pi)|)) (or (not (forall ((z tptp.pi)) (= (ho_271 x z) (ho_271 y z)))) (= x y))))) (let ((_let_437 (forall ((u |u_(-> Bool tptp.pi tptp.pi tptp.pi)|) (e |u_(-> tptp.pi tptp.pi tptp.pi)|) (i Bool)) (not (forall ((v |u_(-> Bool tptp.pi tptp.pi tptp.pi)|)) (not (forall ((ii Bool)) (= (ho_270 v ii) (ite (= i ii) e (ho_270 u ii)))))))))) (let ((_let_438 (forall ((x |u_(-> Bool tptp.pi tptp.pi tptp.pi)|) (y |u_(-> Bool tptp.pi tptp.pi tptp.pi)|)) (or (not (forall ((z Bool)) (= (ho_270 x z) (ho_270 y z)))) (= x y))))) (let ((_let_439 (forall ((u |u_(-> tptp.list_P227219501e_name tptp.produc1359399907ubject tptp.produc1359399907ubject)|) (e |u_(-> tptp.produc1359399907ubject tptp.produc1359399907ubject)|) (i tptp.list_P227219501e_name)) (not (forall ((v |u_(-> tptp.list_P227219501e_name tptp.produc1359399907ubject tptp.produc1359399907ubject)|)) (not (forall ((ii tptp.list_P227219501e_name)) (= (ho_273 v ii) (ite (= i ii) e (ho_273 u ii)))))))))) (let ((_let_440 (forall ((x |u_(-> tptp.list_P227219501e_name tptp.produc1359399907ubject tptp.produc1359399907ubject)|) (y |u_(-> tptp.list_P227219501e_name tptp.produc1359399907ubject tptp.produc1359399907ubject)|)) (or (not (forall ((z tptp.list_P227219501e_name)) (= (ho_273 x z) (ho_273 y z)))) (= x y))))) (let ((_let_441 (forall ((u |u_(-> tptp.list_pi Bool)|) (e Bool) (i tptp.list_pi)) (not (forall ((v |u_(-> tptp.list_pi Bool)|)) (not (forall ((ii tptp.list_pi)) (= (ho_354 v ii) (ite (= i ii) e (ho_354 u ii)))))))))) (let ((_let_442 (forall ((x |u_(-> tptp.list_pi Bool)|) (y |u_(-> tptp.list_pi Bool)|)) (or (not (forall ((z tptp.list_pi)) (= (ho_354 x z) (ho_354 y z)))) (= x y))))) (let ((_let_443 (forall ((u |u_(-> tptp.produc355105483reeRes tptp.produc355105483reeRes)|) (e tptp.produc355105483reeRes) (i tptp.produc355105483reeRes)) (not (forall ((v |u_(-> tptp.produc355105483reeRes tptp.produc355105483reeRes)|)) (not (forall ((ii tptp.produc355105483reeRes)) (= (ho_277 v ii) (ite (= i ii) e (ho_277 u ii)))))))))) (let ((_let_444 (forall ((x |u_(-> tptp.produc355105483reeRes tptp.produc355105483reeRes)|) (y |u_(-> tptp.produc355105483reeRes tptp.produc355105483reeRes)|)) (or (not (forall ((z tptp.produc355105483reeRes)) (= (ho_277 x z) (ho_277 y z)))) (= x y))))) (let ((_let_445 (forall ((u |u_(-> tptp.late_subject tptp.pi_Rep tptp.produc257012921pi_Rep)|) (e |u_(-> tptp.pi_Rep tptp.produc257012921pi_Rep)|) (i tptp.late_subject)) (not (forall ((v |u_(-> tptp.late_subject tptp.pi_Rep tptp.produc257012921pi_Rep)|)) (not (forall ((ii tptp.late_subject)) (= (ho_279 v ii) (ite (= i ii) e (ho_279 u ii)))))))))) (let ((_let_446 (forall ((x |u_(-> tptp.late_subject tptp.pi_Rep tptp.produc257012921pi_Rep)|) (y |u_(-> tptp.late_subject tptp.pi_Rep tptp.produc257012921pi_Rep)|)) (or (not (forall ((z tptp.late_subject)) (= (ho_279 x z) (ho_279 y z)))) (= x y))))) (let ((_let_447 (forall ((u |u_(-> tptp.list_P227219501e_name tptp.produc1998742700t_name tptp.produc1998742700t_name)|) (e |u_(-> tptp.produc1998742700t_name tptp.produc1998742700t_name)|) (i tptp.list_P227219501e_name)) (not (forall ((v |u_(-> tptp.list_P227219501e_name tptp.produc1998742700t_name tptp.produc1998742700t_name)|)) (not (forall ((ii tptp.list_P227219501e_name)) (= (ho_285 v ii) (ite (= i ii) e (ho_285 u ii)))))))))) (let ((_let_448 (forall ((x |u_(-> tptp.list_P227219501e_name tptp.produc1998742700t_name tptp.produc1998742700t_name)|) (y |u_(-> tptp.list_P227219501e_name tptp.produc1998742700t_name tptp.produc1998742700t_name)|)) (or (not (forall ((z tptp.list_P227219501e_name)) (= (ho_285 x z) (ho_285 y z)))) (= x y))))) (let ((_let_449 (forall ((u |u_(-> tptp.produc1777919905pi_Rep tptp.produc1777919905pi_Rep)|) (e tptp.produc1777919905pi_Rep) (i tptp.produc1777919905pi_Rep)) (not (forall ((v |u_(-> tptp.produc1777919905pi_Rep tptp.produc1777919905pi_Rep)|)) (not (forall ((ii tptp.produc1777919905pi_Rep)) (= (ho_301 v ii) (ite (= i ii) e (ho_301 u ii)))))))))) (let ((_let_450 (forall ((x |u_(-> tptp.produc1777919905pi_Rep tptp.produc1777919905pi_Rep)|) (y |u_(-> tptp.produc1777919905pi_Rep tptp.produc1777919905pi_Rep)|)) (or (not (forall ((z tptp.produc1777919905pi_Rep)) (= (ho_301 x z) (ho_301 y z)))) (= x y))))) (let ((_let_451 (forall ((u |u_(-> tptp.produc140253050ect_pi tptp.produc140253050ect_pi)|) (e tptp.produc140253050ect_pi) (i tptp.produc140253050ect_pi)) (not (forall ((v |u_(-> tptp.produc140253050ect_pi tptp.produc140253050ect_pi)|)) (not (forall ((ii tptp.produc140253050ect_pi)) (= (ho_289 v ii) (ite (= i ii) e (ho_289 u ii)))))))))) (let ((_let_452 (forall ((x |u_(-> tptp.produc140253050ect_pi tptp.produc140253050ect_pi)|) (y |u_(-> tptp.produc140253050ect_pi tptp.produc140253050ect_pi)|)) (or (not (forall ((z tptp.produc140253050ect_pi)) (= (ho_289 x z) (ho_289 y z)))) (= x y))))) (let ((_let_453 (forall ((u |u_(-> tptp.list_P227219501e_name tptp.produc140253050ect_pi tptp.produc140253050ect_pi)|) (e |u_(-> tptp.produc140253050ect_pi tptp.produc140253050ect_pi)|) (i tptp.list_P227219501e_name)) (not (forall ((v |u_(-> tptp.list_P227219501e_name tptp.produc140253050ect_pi tptp.produc140253050ect_pi)|)) (not (forall ((ii tptp.list_P227219501e_name)) (= (ho_288 v ii) (ite (= i ii) e (ho_288 u ii)))))))))) (let ((_let_454 (forall ((x |u_(-> tptp.list_P227219501e_name tptp.produc140253050ect_pi tptp.produc140253050ect_pi)|) (y |u_(-> tptp.list_P227219501e_name tptp.produc140253050ect_pi tptp.produc140253050ect_pi)|)) (or (not (forall ((z tptp.list_P227219501e_name)) (= (ho_288 x z) (ho_288 y z)))) (= x y))))) (let ((_let_455 (forall ((u |u_(-> tptp.pi_Rep tptp.produc1777919905pi_Rep)|) (e tptp.produc1777919905pi_Rep) (i tptp.pi_Rep)) (not (forall ((v |u_(-> tptp.pi_Rep tptp.produc1777919905pi_Rep)|)) (not (forall ((ii tptp.pi_Rep)) (= (ho_298 v ii) (ite (= i ii) e (ho_298 u ii)))))))))) (let ((_let_456 (forall ((x |u_(-> tptp.pi_Rep tptp.produc1777919905pi_Rep)|) (y |u_(-> tptp.pi_Rep tptp.produc1777919905pi_Rep)|)) (or (not (forall ((z tptp.pi_Rep)) (= (ho_298 x z) (ho_298 y z)))) (= x y))))) (let ((_let_457 (forall ((u |u_(-> tptp.list_P227219501e_name tptp.produc214645451ubject tptp.produc214645451ubject)|) (e |u_(-> tptp.produc214645451ubject tptp.produc214645451ubject)|) (i tptp.list_P227219501e_name)) (not (forall ((v |u_(-> tptp.list_P227219501e_name tptp.produc214645451ubject tptp.produc214645451ubject)|)) (not (forall ((ii tptp.list_P227219501e_name)) (= (ho_291 v ii) (ite (= i ii) e (ho_291 u ii)))))))))) (let ((_let_458 (forall ((x |u_(-> tptp.list_P227219501e_name tptp.produc214645451ubject tptp.produc214645451ubject)|) (y |u_(-> tptp.list_P227219501e_name tptp.produc214645451ubject tptp.produc214645451ubject)|)) (or (not (forall ((z tptp.list_P227219501e_name)) (= (ho_291 x z) (ho_291 y z)))) (= x y))))) (let ((_let_459 (forall ((u |u_(-> tptp.list_P227219501e_name tptp.produc1357834675reeRes tptp.produc1357834675reeRes)|) (e |u_(-> tptp.produc1357834675reeRes tptp.produc1357834675reeRes)|) (i tptp.list_P227219501e_name)) (not (forall ((v |u_(-> tptp.list_P227219501e_name tptp.produc1357834675reeRes tptp.produc1357834675reeRes)|)) (not (forall ((ii tptp.list_P227219501e_name)) (= (ho_294 v ii) (ite (= i ii) e (ho_294 u ii)))))))))) (let ((_let_460 (forall ((x |u_(-> tptp.list_P227219501e_name tptp.produc1357834675reeRes tptp.produc1357834675reeRes)|) (y |u_(-> tptp.list_P227219501e_name tptp.produc1357834675reeRes tptp.produc1357834675reeRes)|)) (or (not (forall ((z tptp.list_P227219501e_name)) (= (ho_294 x z) (ho_294 y z)))) (= x y))))) (let ((_let_461 (forall ((u |u_(-> tptp.late_freeRes tptp.pi_Rep tptp.produc1777919905pi_Rep)|) (e |u_(-> tptp.pi_Rep tptp.produc1777919905pi_Rep)|) (i tptp.late_freeRes)) (not (forall ((v |u_(-> tptp.late_freeRes tptp.pi_Rep tptp.produc1777919905pi_Rep)|)) (not (forall ((ii tptp.late_freeRes)) (= (ho_297 v ii) (ite (= i ii) e (ho_297 u ii)))))))))) (let ((_let_462 (forall ((x |u_(-> tptp.late_freeRes tptp.pi_Rep tptp.produc1777919905pi_Rep)|) (y |u_(-> tptp.late_freeRes tptp.pi_Rep tptp.produc1777919905pi_Rep)|)) (or (not (forall ((z tptp.late_freeRes)) (= (ho_297 x z) (ho_297 y z)))) (= x y))))) (let ((_let_463 (forall ((u |u_(-> tptp.list_P227219501e_name tptp.produc1777919905pi_Rep tptp.produc1777919905pi_Rep)|) (e |u_(-> tptp.produc1777919905pi_Rep tptp.produc1777919905pi_Rep)|) (i tptp.list_P227219501e_name)) (not (forall ((v |u_(-> tptp.list_P227219501e_name tptp.produc1777919905pi_Rep tptp.produc1777919905pi_Rep)|)) (not (forall ((ii tptp.list_P227219501e_name)) (= (ho_300 v ii) (ite (= i ii) e (ho_300 u ii)))))))))) (let ((_let_464 (forall ((x |u_(-> tptp.list_P227219501e_name tptp.produc1777919905pi_Rep tptp.produc1777919905pi_Rep)|) (y |u_(-> tptp.list_P227219501e_name tptp.produc1777919905pi_Rep tptp.produc1777919905pi_Rep)|)) (or (not (forall ((z tptp.list_P227219501e_name)) (= (ho_300 x z) (ho_300 y z)))) (= x y))))) (let ((_let_465 (forall ((u |u_(-> tptp.list_P227219501e_name tptp.produc2052722628s_name tptp.produc2052722628s_name)|) (e |u_(-> tptp.produc2052722628s_name tptp.produc2052722628s_name)|) (i tptp.list_P227219501e_name)) (not (forall ((v |u_(-> tptp.list_P227219501e_name tptp.produc2052722628s_name tptp.produc2052722628s_name)|)) (not (forall ((ii tptp.list_P227219501e_name)) (= (ho_303 v ii) (ite (= i ii) e (ho_303 u ii)))))))))) (let ((_let_466 (forall ((x |u_(-> tptp.list_P227219501e_name tptp.produc2052722628s_name tptp.produc2052722628s_name)|) (y |u_(-> tptp.list_P227219501e_name tptp.produc2052722628s_name tptp.produc2052722628s_name)|)) (or (not (forall ((z tptp.list_P227219501e_name)) (= (ho_303 x z) (ho_303 y z)))) (= x y))))) (let ((_let_467 (forall ((u |u_(-> tptp.list_Late_subject tptp.list_Late_subject)|) (e tptp.list_Late_subject) (i tptp.list_Late_subject)) (not (forall ((v |u_(-> tptp.list_Late_subject tptp.list_Late_subject)|)) (not (forall ((ii tptp.list_Late_subject)) (= (ho_310 v ii) (ite (= i ii) e (ho_310 u ii)))))))))) (let ((_let_468 (forall ((x |u_(-> tptp.list_Late_subject tptp.list_Late_subject)|) (y |u_(-> tptp.list_Late_subject tptp.list_Late_subject)|)) (or (not (forall ((z tptp.list_Late_subject)) (= (ho_310 x z) (ho_310 y z)))) (= x y))))) (let ((_let_469 (forall ((u |u_(-> tptp.list_P227219501e_name tptp.list_Late_subject tptp.list_Late_subject)|) (e |u_(-> tptp.list_Late_subject tptp.list_Late_subject)|) (i tptp.list_P227219501e_name)) (not (forall ((v |u_(-> tptp.list_P227219501e_name tptp.list_Late_subject tptp.list_Late_subject)|)) (not (forall ((ii tptp.list_P227219501e_name)) (= (ho_309 v ii) (ite (= i ii) e (ho_309 u ii)))))))))) (let ((_let_470 (forall ((x |u_(-> tptp.list_P227219501e_name tptp.list_Late_subject tptp.list_Late_subject)|) (y |u_(-> tptp.list_P227219501e_name tptp.list_Late_subject tptp.list_Late_subject)|)) (or (not (forall ((z tptp.list_P227219501e_name)) (= (ho_309 x z) (ho_309 y z)))) (= x y))))) (let ((_let_471 (forall ((u |u_(-> tptp.list_Late_freeRes tptp.list_Late_freeRes)|) (e tptp.list_Late_freeRes) (i tptp.list_Late_freeRes)) (not (forall ((v |u_(-> tptp.list_Late_freeRes tptp.list_Late_freeRes)|)) (not (forall ((ii tptp.list_Late_freeRes)) (= (ho_315 v ii) (ite (= i ii) e (ho_315 u ii)))))))))) (let ((_let_472 (forall ((x |u_(-> tptp.list_Late_freeRes tptp.list_Late_freeRes)|) (y |u_(-> tptp.list_Late_freeRes tptp.list_Late_freeRes)|)) (or (not (forall ((z tptp.list_Late_freeRes)) (= (ho_315 x z) (ho_315 y z)))) (= x y))))) (let ((_let_473 (forall ((u |u_(-> tptp.list_P227219501e_name tptp.list_Late_freeRes tptp.list_Late_freeRes)|) (e |u_(-> tptp.list_Late_freeRes tptp.list_Late_freeRes)|) (i tptp.list_P227219501e_name)) (not (forall ((v |u_(-> tptp.list_P227219501e_name tptp.list_Late_freeRes tptp.list_Late_freeRes)|)) (not (forall ((ii tptp.list_P227219501e_name)) (= (ho_314 v ii) (ite (= i ii) e (ho_314 u ii)))))))))) (let ((_let_474 (forall ((x |u_(-> tptp.list_P227219501e_name tptp.list_Late_freeRes tptp.list_Late_freeRes)|) (y |u_(-> tptp.list_P227219501e_name tptp.list_Late_freeRes tptp.list_Late_freeRes)|)) (or (not (forall ((z tptp.list_P227219501e_name)) (= (ho_314 x z) (ho_314 y z)))) (= x y))))) (let ((_let_475 (forall ((u |u_(-> tptp.list_pi_Rep tptp.list_pi_Rep)|) (e tptp.list_pi_Rep) (i tptp.list_pi_Rep)) (not (forall ((v |u_(-> tptp.list_pi_Rep tptp.list_pi_Rep)|)) (not (forall ((ii tptp.list_pi_Rep)) (= (ho_320 v ii) (ite (= i ii) e (ho_320 u ii)))))))))) (let ((_let_476 (forall ((x |u_(-> tptp.list_pi_Rep tptp.list_pi_Rep)|) (y |u_(-> tptp.list_pi_Rep tptp.list_pi_Rep)|)) (or (not (forall ((z tptp.list_pi_Rep)) (= (ho_320 x z) (ho_320 y z)))) (= x y))))) (let ((_let_477 (forall ((u |u_(-> tptp.list_P227219501e_name tptp.list_pi_Rep tptp.list_pi_Rep)|) (e |u_(-> tptp.list_pi_Rep tptp.list_pi_Rep)|) (i tptp.list_P227219501e_name)) (not (forall ((v |u_(-> tptp.list_P227219501e_name tptp.list_pi_Rep tptp.list_pi_Rep)|)) (not (forall ((ii tptp.list_P227219501e_name)) (= (ho_319 v ii) (ite (= i ii) e (ho_319 u ii)))))))))) (let ((_let_478 (forall ((x |u_(-> tptp.list_P227219501e_name tptp.list_pi_Rep tptp.list_pi_Rep)|) (y |u_(-> tptp.list_P227219501e_name tptp.list_pi_Rep tptp.list_pi_Rep)|)) (or (not (forall ((z tptp.list_P227219501e_name)) (= (ho_319 x z) (ho_319 y z)))) (= x y))))) (let ((_let_479 (forall ((u |u_(-> tptp.pi_Rep tptp.list_pi_Rep tptp.list_pi_Rep)|) (e |u_(-> tptp.list_pi_Rep tptp.list_pi_Rep)|) (i tptp.pi_Rep)) (not (forall ((v |u_(-> tptp.pi_Rep tptp.list_pi_Rep tptp.list_pi_Rep)|)) (not (forall ((ii tptp.pi_Rep)) (= (ho_322 v ii) (ite (= i ii) e (ho_322 u ii)))))))))) (let ((_let_480 (forall ((x |u_(-> tptp.pi_Rep tptp.list_pi_Rep tptp.list_pi_Rep)|) (y |u_(-> tptp.pi_Rep tptp.list_pi_Rep tptp.list_pi_Rep)|)) (or (not (forall ((z tptp.pi_Rep)) (= (ho_322 x z) (ho_322 y z)))) (= x y))))) (let ((_let_481 (forall ((u |u_(-> tptp.name tptp.list_name tptp.list_name)|) (e |u_(-> tptp.list_name tptp.list_name)|) (i tptp.name)) (not (forall ((v |u_(-> tptp.name tptp.list_name tptp.list_name)|)) (not (forall ((ii tptp.name)) (= (ho_327 v ii) (ite (= i ii) e (ho_327 u ii)))))))))) (let ((_let_482 (forall ((x |u_(-> tptp.name tptp.list_name tptp.list_name)|) (y |u_(-> tptp.name tptp.list_name tptp.list_name)|)) (or (not (forall ((z tptp.name)) (= (ho_327 x z) (ho_327 y z)))) (= x y))))) (let ((_let_483 (forall ((u |u_(-> tptp.list_pi tptp.list_pi)|) (e tptp.list_pi) (i tptp.list_pi)) (not (forall ((v |u_(-> tptp.list_pi tptp.list_pi)|)) (not (forall ((ii tptp.list_pi)) (= (ho_330 v ii) (ite (= i ii) e (ho_330 u ii)))))))))) (let ((_let_484 (forall ((x |u_(-> tptp.list_pi tptp.list_pi)|) (y |u_(-> tptp.list_pi tptp.list_pi)|)) (or (not (forall ((z tptp.list_pi)) (= (ho_330 x z) (ho_330 y z)))) (= x y))))) (let ((_let_485 (forall ((u |u_(-> tptp.pi tptp.list_pi tptp.list_pi)|) (e |u_(-> tptp.list_pi tptp.list_pi)|) (i tptp.pi)) (not (forall ((v |u_(-> tptp.pi tptp.list_pi tptp.list_pi)|)) (not (forall ((ii tptp.pi)) (= (ho_332 v ii) (ite (= i ii) e (ho_332 u ii)))))))))) (let ((_let_486 (forall ((x |u_(-> tptp.pi tptp.list_pi tptp.list_pi)|) (y |u_(-> tptp.pi tptp.list_pi tptp.list_pi)|)) (or (not (forall ((z tptp.pi)) (= (ho_332 x z) (ho_332 y z)))) (= x y))))) (let ((_let_487 (forall ((u |u_(-> tptp.list_P227219501e_name tptp.list_pi tptp.list_pi)|) (e |u_(-> tptp.list_pi tptp.list_pi)|) (i tptp.list_P227219501e_name)) (not (forall ((v |u_(-> tptp.list_P227219501e_name tptp.list_pi tptp.list_pi)|)) (not (forall ((ii tptp.list_P227219501e_name)) (= (ho_329 v ii) (ite (= i ii) e (ho_329 u ii)))))))))) (let ((_let_488 (forall ((x |u_(-> tptp.list_P227219501e_name tptp.list_pi tptp.list_pi)|) (y |u_(-> tptp.list_P227219501e_name tptp.list_pi tptp.list_pi)|)) (or (not (forall ((z tptp.list_P227219501e_name)) (= (ho_329 x z) (ho_329 y z)))) (= x y))))) (let ((_let_489 (forall ((u |u_(-> tptp.name tptp.product_prod_pi_pi Bool)|) (e |u_(-> tptp.product_prod_pi_pi Bool)|) (i tptp.name)) (not (forall ((v |u_(-> tptp.name tptp.product_prod_pi_pi Bool)|)) (not (forall ((ii tptp.name)) (= (ho_336 v ii) (ite (= i ii) e (ho_336 u ii)))))))))) (let ((_let_490 (forall ((x |u_(-> tptp.name tptp.product_prod_pi_pi Bool)|) (y |u_(-> tptp.name tptp.product_prod_pi_pi Bool)|)) (or (not (forall ((z tptp.name)) (= (ho_336 x z) (ho_336 y z)))) (= x y))))) (let ((_let_491 (forall ((u |u_(-> tptp.list_Late_subject Bool)|) (e Bool) (i tptp.list_Late_subject)) (not (forall ((v |u_(-> tptp.list_Late_subject Bool)|)) (not (forall ((ii tptp.list_Late_subject)) (= (ho_339 v ii) (ite (= i ii) e (ho_339 u ii)))))))))) (let ((_let_492 (forall ((x |u_(-> tptp.list_Late_subject Bool)|) (y |u_(-> tptp.list_Late_subject Bool)|)) (or (not (forall ((z tptp.list_Late_subject)) (= (ho_339 x z) (ho_339 y z)))) (= x y))))) (let ((_let_493 (forall ((u |u_(-> tptp.name tptp.list_Late_subject Bool)|) (e |u_(-> tptp.list_Late_subject Bool)|) (i tptp.name)) (not (forall ((v |u_(-> tptp.name tptp.list_Late_subject Bool)|)) (not (forall ((ii tptp.name)) (= (ho_338 v ii) (ite (= i ii) e (ho_338 u ii)))))))))) (let ((_let_494 (forall ((x |u_(-> tptp.name tptp.list_Late_subject Bool)|) (y |u_(-> tptp.name tptp.list_Late_subject Bool)|)) (or (not (forall ((z tptp.name)) (= (ho_338 x z) (ho_338 y z)))) (= x y))))) (let ((_let_495 (forall ((u |u_(-> tptp.list_P431515740_pi_pi Bool)|) (e Bool) (i tptp.list_P431515740_pi_pi)) (not (forall ((v |u_(-> tptp.list_P431515740_pi_pi Bool)|)) (not (forall ((ii tptp.list_P431515740_pi_pi)) (= (ho_345 v ii) (ite (= i ii) e (ho_345 u ii)))))))))) (let ((_let_496 (forall ((x |u_(-> tptp.list_P431515740_pi_pi Bool)|) (y |u_(-> tptp.list_P431515740_pi_pi Bool)|)) (or (not (forall ((z tptp.list_P431515740_pi_pi)) (= (ho_345 x z) (ho_345 y z)))) (= x y))))) (let ((_let_497 (forall ((u |u_(-> tptp.list_name Bool)|) (e Bool) (i tptp.list_name)) (not (forall ((v |u_(-> tptp.list_name Bool)|)) (not (forall ((ii tptp.list_name)) (= (ho_351 v ii) (ite (= i ii) e (ho_351 u ii)))))))))) (let ((_let_498 (forall ((x |u_(-> tptp.list_name Bool)|) (y |u_(-> tptp.list_name Bool)|)) (or (not (forall ((z tptp.list_name)) (= (ho_351 x z) (ho_351 y z)))) (= x y))))) (let ((_let_499 (forall ((u |u_(-> tptp.set_Pr443758855e_name tptp.set_Pr443758855e_name Bool)|) (e |u_(-> tptp.set_Pr443758855e_name Bool)|) (i tptp.set_Pr443758855e_name)) (not (forall ((v |u_(-> tptp.set_Pr443758855e_name tptp.set_Pr443758855e_name Bool)|)) (not (forall ((ii tptp.set_Pr443758855e_name)) (= (ho_356 v ii) (ite (= i ii) e (ho_356 u ii)))))))))) (let ((_let_500 (forall ((x |u_(-> tptp.set_Pr443758855e_name tptp.set_Pr443758855e_name Bool)|) (y |u_(-> tptp.set_Pr443758855e_name tptp.set_Pr443758855e_name Bool)|)) (or (not (forall ((z tptp.set_Pr443758855e_name)) (= (ho_356 x z) (ho_356 y z)))) (= x y))))) (let ((_let_501 (forall ((u |u_(-> tptp.set_Pr1654044726_pi_pi Bool)|) (e Bool) (i tptp.set_Pr1654044726_pi_pi)) (not (forall ((v |u_(-> tptp.set_Pr1654044726_pi_pi Bool)|)) (not (forall ((ii tptp.set_Pr1654044726_pi_pi)) (= (ho_359 v ii) (ite (= i ii) e (ho_359 u ii)))))))))) (let ((_let_502 (forall ((x |u_(-> tptp.set_Pr1654044726_pi_pi Bool)|) (y |u_(-> tptp.set_Pr1654044726_pi_pi Bool)|)) (or (not (forall ((z tptp.set_Pr1654044726_pi_pi)) (= (ho_359 x z) (ho_359 y z)))) (= x y))))) (let ((_let_503 (forall ((u |u_(-> tptp.set_Pr1654044726_pi_pi tptp.set_Pr1654044726_pi_pi Bool)|) (e |u_(-> tptp.set_Pr1654044726_pi_pi Bool)|) (i tptp.set_Pr1654044726_pi_pi)) (not (forall ((v |u_(-> tptp.set_Pr1654044726_pi_pi tptp.set_Pr1654044726_pi_pi Bool)|)) (not (forall ((ii tptp.set_Pr1654044726_pi_pi)) (= (ho_358 v ii) (ite (= i ii) e (ho_358 u ii)))))))))) (let ((_let_504 (forall ((x |u_(-> tptp.set_Pr1654044726_pi_pi tptp.set_Pr1654044726_pi_pi Bool)|) (y |u_(-> tptp.set_Pr1654044726_pi_pi tptp.set_Pr1654044726_pi_pi Bool)|)) (or (not (forall ((z tptp.set_Pr1654044726_pi_pi)) (= (ho_358 x z) (ho_358 y z)))) (= x y))))) (let ((_let_505 (forall ((u |u_(-> tptp.produc1141751126_pi_pi tptp.set_Pr1654044726_pi_pi Bool)|) (e |u_(-> tptp.set_Pr1654044726_pi_pi Bool)|) (i tptp.produc1141751126_pi_pi)) (not (forall ((v |u_(-> tptp.produc1141751126_pi_pi tptp.set_Pr1654044726_pi_pi Bool)|)) (not (forall ((ii tptp.produc1141751126_pi_pi)) (= (ho_361 v ii) (ite (= i ii) e (ho_361 u ii)))))))))) (let ((_let_506 (forall ((x |u_(-> tptp.produc1141751126_pi_pi tptp.set_Pr1654044726_pi_pi Bool)|) (y |u_(-> tptp.produc1141751126_pi_pi tptp.set_Pr1654044726_pi_pi Bool)|)) (or (not (forall ((z tptp.produc1141751126_pi_pi)) (= (ho_361 x z) (ho_361 y z)))) (= x y))))) (let ((_let_507 (forall ((u |u_(-> tptp.name tptp.pi tptp.pi)|) (e |u_(-> tptp.pi tptp.pi)|) (i tptp.name)) (not (forall ((v |u_(-> tptp.name tptp.pi tptp.pi)|)) (not (forall ((ii tptp.name)) (= (ho_363 v ii) (ite (= i ii) e (ho_363 u ii)))))))))) (let ((_let_508 (forall ((x |u_(-> tptp.name tptp.pi tptp.pi)|) (y |u_(-> tptp.name tptp.pi tptp.pi)|)) (or (not (forall ((z tptp.name)) (= (ho_363 x z) (ho_363 y z)))) (= x y))))) (let ((_let_509 (forall ((u |u_(-> tptp.late_residual Bool)|) (e Bool) (i tptp.late_residual)) (not (forall ((v |u_(-> tptp.late_residual Bool)|)) (not (forall ((ii tptp.late_residual)) (= (ho_371 v ii) (ite (= i ii) e (ho_371 u ii)))))))))) (let ((_let_510 (forall ((x |u_(-> tptp.late_residual Bool)|) (y |u_(-> tptp.late_residual Bool)|)) (or (not (forall ((z tptp.late_residual)) (= (ho_371 x z) (ho_371 y z)))) (= x y))))) (let ((_let_511 (forall ((u |u_(-> tptp.late_residual tptp.late_residual)|) (e tptp.late_residual) (i tptp.late_residual)) (not (forall ((v |u_(-> tptp.late_residual tptp.late_residual)|)) (not (forall ((ii tptp.late_residual)) (= (ho_376 v ii) (ite (= i ii) e (ho_376 u ii)))))))))) (let ((_let_512 (forall ((x |u_(-> tptp.late_residual tptp.late_residual)|) (y |u_(-> tptp.late_residual tptp.late_residual)|)) (or (not (forall ((z tptp.late_residual)) (= (ho_376 x z) (ho_376 y z)))) (= x y))))) (let ((_let_513 (forall ((u |u_(-> tptp.list_P227219501e_name tptp.late_residual tptp.late_residual)|) (e |u_(-> tptp.late_residual tptp.late_residual)|) (i tptp.list_P227219501e_name)) (not (forall ((v |u_(-> tptp.list_P227219501e_name tptp.late_residual tptp.late_residual)|)) (not (forall ((ii tptp.list_P227219501e_name)) (= (ho_375 v ii) (ite (= i ii) e (ho_375 u ii)))))))))) (let ((_let_514 (forall ((x |u_(-> tptp.list_P227219501e_name tptp.late_residual tptp.late_residual)|) (y |u_(-> tptp.list_P227219501e_name tptp.late_residual tptp.late_residual)|)) (or (not (forall ((z tptp.list_P227219501e_name)) (= (ho_375 x z) (ho_375 y z)))) (= x y))))) (let ((_let_515 (forall ((u |u_(-> tptp.name tptp.name tptp.late_freeRes)|) (e |u_(-> tptp.name tptp.late_freeRes)|) (i tptp.name)) (not (forall ((v |u_(-> tptp.name tptp.name tptp.late_freeRes)|)) (not (forall ((ii tptp.name)) (= (ho_380 v ii) (ite (= i ii) e (ho_380 u ii)))))))))) (let ((_let_516 (forall ((x |u_(-> tptp.name tptp.name tptp.late_freeRes)|) (y |u_(-> tptp.name tptp.name tptp.late_freeRes)|)) (or (not (forall ((z tptp.name)) (= (ho_380 x z) (ho_380 y z)))) (= x y))))) (let ((_let_517 (forall ((u |u_(-> tptp.late_freeRes tptp.pi tptp.late_residual_Rep)|) (e |u_(-> tptp.pi tptp.late_residual_Rep)|) (i tptp.late_freeRes)) (not (forall ((v |u_(-> tptp.late_freeRes tptp.pi tptp.late_residual_Rep)|)) (not (forall ((ii tptp.late_freeRes)) (= (ho_383 v ii) (ite (= i ii) e (ho_383 u ii)))))))))) (let ((_let_518 (forall ((x |u_(-> tptp.late_freeRes tptp.pi tptp.late_residual_Rep)|) (y |u_(-> tptp.late_freeRes tptp.pi tptp.late_residual_Rep)|)) (or (not (forall ((z tptp.late_freeRes)) (= (ho_383 x z) (ho_383 y z)))) (= x y))))) (let ((_let_519 (forall ((u |u_(-> tptp.name tptp.name tptp.pi tptp.pi)|) (e |u_(-> tptp.name tptp.pi tptp.pi)|) (i tptp.name)) (not (forall ((v |u_(-> tptp.name tptp.name tptp.pi tptp.pi)|)) (not (forall ((ii tptp.name)) (= (ho_386 v ii) (ite (= i ii) e (ho_386 u ii)))))))))) (let ((_let_520 (forall ((x |u_(-> tptp.name tptp.name tptp.pi tptp.pi)|) (y |u_(-> tptp.name tptp.name tptp.pi tptp.pi)|)) (or (not (forall ((z tptp.name)) (= (ho_386 x z) (ho_386 y z)))) (= x y))))) (let ((_let_521 (forall ((u |u_(-> tptp.produc367475239e_name tptp.name tptp.name)|) (e |u_(-> tptp.name tptp.name)|) (i tptp.produc367475239e_name)) (not (forall ((v |u_(-> tptp.produc367475239e_name tptp.name tptp.name)|)) (not (forall ((ii tptp.produc367475239e_name)) (= (ho_390 v ii) (ite (= i ii) e (ho_390 u ii)))))))))) (let ((_let_522 (forall ((x |u_(-> tptp.produc367475239e_name tptp.name tptp.name)|) (y |u_(-> tptp.produc367475239e_name tptp.name tptp.name)|)) (or (not (forall ((z tptp.produc367475239e_name)) (= (ho_390 x z) (ho_390 y z)))) (= x y))))) (let ((_let_523 (forall ((BOUND_VARIABLE_10592 tptp.set_Pr1834926343_pi_pi) (BOUND_VARIABLE_10593 tptp.set_Pr1834926343_pi_pi)) (= (= BOUND_VARIABLE_10592 BOUND_VARIABLE_10593) (ho_9 (ho_8 k_7 BOUND_VARIABLE_10592) BOUND_VARIABLE_10593))))) (let ((_let_524 (forall ((BOUND_VARIABLE_10581 tptp.set_Pr1834926343_pi_pi) (BOUND_VARIABLE_10582 tptp.set_Pr1834926343_pi_pi)) (= (ho_9 (ho_8 k_10 BOUND_VARIABLE_10581) BOUND_VARIABLE_10582) (and (ho_9 (ho_8 k_11 BOUND_VARIABLE_10581) BOUND_VARIABLE_10582) (ho_9 (ho_8 k_11 BOUND_VARIABLE_10582) BOUND_VARIABLE_10581)))))) (let ((_let_525 (forall ((BOUND_VARIABLE_10574 tptp.set_Pr1834926343_pi_pi) (BOUND_VARIABLE_10575 tptp.set_Pr1834926343_pi_pi)) (= (= BOUND_VARIABLE_10574 BOUND_VARIABLE_10575) (ho_9 (ho_8 k_12 BOUND_VARIABLE_10574) BOUND_VARIABLE_10575))))) (let ((_let_526 (forall ((BOUND_VARIABLE_10563 tptp.set_Pr1834926343_pi_pi) (BOUND_VARIABLE_10564 tptp.set_Pr1834926343_pi_pi)) (= (ho_9 (ho_8 k_13 BOUND_VARIABLE_10563) BOUND_VARIABLE_10564) (and (ho_9 (ho_8 k_11 BOUND_VARIABLE_10563) BOUND_VARIABLE_10564) (ho_9 (ho_8 k_11 BOUND_VARIABLE_10564) BOUND_VARIABLE_10563)))))) (let ((_let_527 (forall ((BOUND_VARIABLE_10555 tptp.set_Pr1834926343_pi_pi) (BOUND_VARIABLE_10556 tptp.product_prod_pi_pi)) (= (ho_16 (ho_15 k_14 BOUND_VARIABLE_10555) BOUND_VARIABLE_10556) (ho_9 (ho_18 k_17 BOUND_VARIABLE_10556) BOUND_VARIABLE_10555))))) (let ((_let_528 (forall ((BOUND_VARIABLE_10592 tptp.set_Pr1834926343_pi_pi) (BOUND_VARIABLE_10593 tptp.set_Pr1834926343_pi_pi)) (= (= BOUND_VARIABLE_10592 BOUND_VARIABLE_10593) (ll_6 BOUND_VARIABLE_10592 BOUND_VARIABLE_10593))))) (let ((_let_529 (forall ((BOUND_VARIABLE_10581 tptp.set_Pr1834926343_pi_pi) (BOUND_VARIABLE_10582 tptp.set_Pr1834926343_pi_pi)) (= (and (@ (@ tptp.ord_le630093991_pi_pi BOUND_VARIABLE_10581) BOUND_VARIABLE_10582) (@ (@ tptp.ord_le630093991_pi_pi BOUND_VARIABLE_10582) BOUND_VARIABLE_10581)) (ll_5 BOUND_VARIABLE_10581 BOUND_VARIABLE_10582))))) (let ((_let_530 (forall ((BOUND_VARIABLE_10574 tptp.set_Pr1834926343_pi_pi) (BOUND_VARIABLE_10575 tptp.set_Pr1834926343_pi_pi)) (= (= BOUND_VARIABLE_10574 BOUND_VARIABLE_10575) (ll_4 BOUND_VARIABLE_10574 BOUND_VARIABLE_10575))))) (let ((_let_531 (forall ((BOUND_VARIABLE_10563 tptp.set_Pr1834926343_pi_pi) (BOUND_VARIABLE_10564 tptp.set_Pr1834926343_pi_pi)) (= (and (@ (@ tptp.ord_le630093991_pi_pi BOUND_VARIABLE_10563) BOUND_VARIABLE_10564) (@ (@ tptp.ord_le630093991_pi_pi BOUND_VARIABLE_10564) BOUND_VARIABLE_10563)) (ll_3 BOUND_VARIABLE_10563 BOUND_VARIABLE_10564))))) (let ((_let_532 (forall ((BOUND_VARIABLE_10555 tptp.set_Pr1834926343_pi_pi) (BOUND_VARIABLE_10556 tptp.product_prod_pi_pi)) (= (@ (@ tptp.member558706512_pi_pi BOUND_VARIABLE_10556) BOUND_VARIABLE_10555) (ll_2 BOUND_VARIABLE_10555 BOUND_VARIABLE_10556))))) (let ((_let_533 (and _let_15 _let_532 _let_531 _let_530 _let_529 _let_528))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_23 :args (tptp.rel _let_18 _let_17 tptp.y QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_16))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_22)) :args ((or _let_19 _let_21 _let_24))) (EQ_RESOLVE (ASSUME :args (_let_3)) (PREPROCESS :args ((= _let_3 (not _let_19))))) (AND_ELIM (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (MACRO_SR_PRED_TRANSFORM (AND_INTRO (ASSUME :args (_let_15)) (PREPROCESS :args ((and _let_532 _let_531 _let_530 _let_529 _let_528)))) :args (_let_533)) (PREPROCESS :args ((= _let_533 (and _let_20 _let_527 _let_526 _let_525 _let_524 _let_523))))) (PREPROCESS :args ((and _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 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tptp.name)) (= (@ (@ tptp.perm_name_name (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name A) B)) tptp.nil_Pr743626285e_name)) X) (@ (@ tptp.perm_name_name (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name B) A)) tptp.nil_Pr743626285e_name)) X))) (forall ((A tptp.name) (B tptp.name) (X tptp.pi)) (= (@ (@ tptp.perm_name_pi (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name A) B)) tptp.nil_Pr743626285e_name)) X) (@ (@ tptp.perm_name_pi (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name B) A)) tptp.nil_Pr743626285e_name)) X))) (forall ((A tptp.name) (B tptp.name) (X tptp.late_subject)) (let ((_let_1 (@ tptp.perm_n1559866809ubject (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name A) B)) tptp.nil_Pr743626285e_name)))) (= (@ _let_1 (@ _let_1 X)) X))) (forall ((A tptp.name) (B tptp.name) (X tptp.late_freeRes)) (let ((_let_1 (@ tptp.perm_n336613537reeRes (@ (@ tptp.cons_P1213805021e_name (@ (@ 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(@ (@ tptp.perm_name_pi_Rep (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name A) B)) tptp.nil_Pr743626285e_name)) (@ (@ tptp.perm_name_pi_Rep (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name B) A)) tptp.nil_Pr743626285e_name)) X)) X)) (forall ((A tptp.name) (B tptp.name) (X tptp.name)) (= (@ (@ tptp.perm_name_name (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name A) B)) tptp.nil_Pr743626285e_name)) (@ (@ tptp.perm_name_name (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name B) A)) tptp.nil_Pr743626285e_name)) X)) X)) (forall ((A tptp.name) (B tptp.name) (X tptp.pi)) (= (@ (@ tptp.perm_name_pi (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name A) B)) tptp.nil_Pr743626285e_name)) (@ (@ tptp.perm_name_pi (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name B) A)) tptp.nil_Pr743626285e_name)) X)) X)) (forall ((X1 tptp.name) (Y1 tptp.name)) (= (= (@ tptp.late_BoundOutputS X1) (@ 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(and (= X1 Y1) (= X2 Y2)))) (forall ((A tptp.name) (B tptp.name) (A2 tptp.name) (B2 tptp.name)) (= (= (@ (@ tptp.produc1570949143e_name A) B) (@ (@ tptp.produc1570949143e_name A2) B2)) (and (= A A2) (= B B2)))) (forall ((A tptp.name) (B tptp.product_prod_pi_pi) (A2 tptp.name) (B2 tptp.product_prod_pi_pi)) (= (= (@ (@ tptp.produc235456326_pi_pi A) B) (@ (@ tptp.produc235456326_pi_pi A2) B2)) (and (= A A2) (= B B2)))) (forall ((A tptp.pi) (B tptp.pi) (A2 tptp.pi) (B2 tptp.pi)) (= (= (@ (@ tptp.product_Pair_pi_pi A) B) (@ (@ tptp.product_Pair_pi_pi A2) B2)) (and (= A A2) (= B B2)))) (forall ((Residual_Rep tptp.late_residual_Rep)) (= (@ (@ tptp.perm_n890803237al_Rep tptp.nil_Pr743626285e_name) Residual_Rep) Residual_Rep)) (forall ((Subject_Rep tptp.late_subject_Rep)) (= (@ (@ tptp.perm_n697952036ct_Rep tptp.nil_Pr743626285e_name) Subject_Rep) Subject_Rep)) (forall ((FreeRes_Rep tptp.late_freeRes_Rep)) (= (@ (@ tptp.perm_n1938283068es_Rep tptp.nil_Pr743626285e_name) FreeRes_Rep) FreeRes_Rep)) (forall ((Pi_Rep tptp.pi_Rep)) (= (@ (@ tptp.perm_name_pi_Rep tptp.nil_Pr743626285e_name) Pi_Rep) Pi_Rep)) (forall ((Pi tptp.list_P227219501e_name) (X1 tptp.name)) (= (@ (@ tptp.perm_n1559866809ubject Pi) (@ tptp.late_BoundOutputS X1)) (@ tptp.late_BoundOutputS (@ (@ tptp.perm_name_name Pi) X1)))) (forall ((A tptp.name) (X tptp.pi_Rep) (B tptp.name)) (=> (@ (@ tptp.fresh_name_pi_Rep A) X) (=> (@ (@ tptp.fresh_name_pi_Rep B) X) (= (@ (@ tptp.perm_name_pi_Rep (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name A) B)) tptp.nil_Pr743626285e_name)) X) X)))) (forall ((A tptp.name) (X tptp.late_subject) (B tptp.name)) (=> (@ (@ tptp.fresh_717452603ubject A) X) (=> (@ (@ tptp.fresh_717452603ubject B) X) (= (@ (@ tptp.perm_n1559866809ubject (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name A) B)) tptp.nil_Pr743626285e_name)) X) X)))) (forall ((A tptp.name) (X tptp.late_freeRes) (B tptp.name)) (=> (@ (@ tptp.fresh_1641682979reeRes A) X) (=> (@ (@ 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tptp.nil_Pr743626285e_name)) X) X)))) (forall ((A tptp.name) (X tptp.pi_Rep) (B tptp.name)) (=> (@ (@ tptp.fresh_name_pi_Rep A) X) (=> (@ (@ tptp.fresh_name_pi_Rep B) X) (= (@ (@ tptp.perm_name_pi_Rep (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name A) B)) tptp.nil_Pr743626285e_name)) X) X)))) (forall ((A tptp.name) (X tptp.late_subject) (B tptp.name)) (=> (@ (@ tptp.fresh_717452603ubject A) X) (=> (@ (@ tptp.fresh_717452603ubject B) X) (= (@ (@ tptp.perm_n1559866809ubject (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name A) B)) tptp.nil_Pr743626285e_name)) X) X)))) (forall ((A tptp.name) (X tptp.late_freeRes) (B tptp.name)) (=> (@ (@ tptp.fresh_1641682979reeRes A) X) (=> (@ (@ tptp.fresh_1641682979reeRes B) X) (= (@ (@ tptp.perm_n336613537reeRes (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name A) B)) tptp.nil_Pr743626285e_name)) X) X)))) (forall ((A tptp.name) (X tptp.produc1141751126_pi_pi) (B tptp.name)) (=> (@ (@ tptp.fresh_1376661020_pi_pi A) X) (=> (@ (@ tptp.fresh_1376661020_pi_pi B) X) (= (@ (@ tptp.perm_n1255502110_pi_pi (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name A) B)) tptp.nil_Pr743626285e_name)) X) X)))) (forall ((A tptp.name) (X tptp.name) (B tptp.name)) (=> (@ (@ tptp.fresh_name_name A) X) (=> (@ (@ tptp.fresh_name_name B) X) (= (@ (@ tptp.perm_name_name (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name A) B)) tptp.nil_Pr743626285e_name)) X) X)))) (forall ((A tptp.name) (X tptp.pi) (B tptp.name)) (=> (@ (@ tptp.fresh_name_pi A) X) (=> (@ (@ tptp.fresh_name_pi B) X) (= (@ (@ tptp.perm_name_pi (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name A) B)) tptp.nil_Pr743626285e_name)) X) X)))) (@ (@ tptp.fresh_717452603ubject tptp.y) tptp.a) (forall ((Pi tptp.list_P227219501e_name) (X3 tptp.set_Pr1834926343_pi_pi) (Y tptp.set_Pr1834926343_pi_pi)) (let ((_let_1 (@ tptp.perm_n675238095_pi_pi Pi))) (= (@ (@ tptp.perm_name_o Pi) (@ (@ tptp.ord_le630093991_pi_pi X3) Y)) (@ (@ tptp.ord_le630093991_pi_pi (@ _let_1 X3)) (@ _let_1 Y))))) (forall ((A tptp.name) (Pi tptp.list_P227219501e_name) (X tptp.pi_Rep)) (let ((_let_1 (@ tptp.fresh_name_pi_Rep A))) (=> (@ (@ tptp.fresh_922791155e_name A) Pi) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.perm_name_pi_Rep Pi) X)))))) (forall ((A tptp.name) (Pi tptp.list_P227219501e_name) (X tptp.late_subject)) (let ((_let_1 (@ tptp.fresh_717452603ubject A))) (=> (@ (@ tptp.fresh_922791155e_name A) Pi) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.perm_n1559866809ubject Pi) X)))))) (forall ((A tptp.name) (Pi tptp.list_P227219501e_name) (X tptp.late_freeRes)) (let ((_let_1 (@ tptp.fresh_1641682979reeRes A))) (=> (@ (@ tptp.fresh_922791155e_name A) Pi) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.perm_n336613537reeRes Pi) X)))))) (forall ((A tptp.name) (Pi tptp.list_P227219501e_name) (X tptp.produc1141751126_pi_pi)) (let ((_let_1 (@ tptp.fresh_1376661020_pi_pi A))) (=> (@ (@ tptp.fresh_922791155e_name A) Pi) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.perm_n1255502110_pi_pi Pi) X)))))) (forall ((A tptp.name) (Pi tptp.list_P227219501e_name) (X tptp.name)) (let ((_let_1 (@ tptp.fresh_name_name A))) (=> (@ (@ tptp.fresh_922791155e_name A) Pi) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.perm_name_name Pi) X)))))) (forall ((A tptp.name) (Pi tptp.list_P227219501e_name) (X tptp.pi)) (let ((_let_1 (@ tptp.fresh_name_pi A))) (=> (@ (@ tptp.fresh_922791155e_name A) Pi) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.perm_name_pi Pi) X)))))) (forall ((X tptp.late_subject)) (not (forall ((C tptp.name)) (not (@ (@ tptp.fresh_717452603ubject C) X))))) (forall ((X tptp.late_freeRes)) (not (forall ((C tptp.name)) (not (@ (@ tptp.fresh_1641682979reeRes C) X))))) (forall ((X tptp.produc1141751126_pi_pi)) (not (forall ((C tptp.name)) (not (@ (@ tptp.fresh_1376661020_pi_pi C) X))))) (forall ((X tptp.name)) (not (forall ((C tptp.name)) (not (@ (@ tptp.fresh_name_name C) X))))) (forall ((X tptp.pi)) (not (forall ((C tptp.name)) (not (@ (@ tptp.fresh_name_pi C) X))))) (forall ((Pi tptp.list_P227219501e_name) (A tptp.name) (X tptp.pi_Rep)) (= (@ (@ tptp.perm_name_o Pi) (@ (@ tptp.fresh_name_pi_Rep A) X)) (@ (@ tptp.fresh_name_pi_Rep (@ (@ tptp.perm_name_name Pi) A)) (@ (@ tptp.perm_name_pi_Rep Pi) X)))) (forall ((Pi tptp.list_P227219501e_name) (A tptp.name) (X tptp.late_subject)) (= (@ (@ tptp.perm_name_o Pi) (@ (@ tptp.fresh_717452603ubject A) X)) (@ (@ tptp.fresh_717452603ubject (@ (@ tptp.perm_name_name Pi) A)) (@ (@ tptp.perm_n1559866809ubject Pi) X)))) (forall ((Pi tptp.list_P227219501e_name) (A tptp.name) (X tptp.late_freeRes)) (= (@ (@ tptp.perm_name_o Pi) (@ (@ tptp.fresh_1641682979reeRes A) X)) (@ (@ tptp.fresh_1641682979reeRes (@ (@ tptp.perm_name_name Pi) A)) (@ (@ tptp.perm_n336613537reeRes Pi) X)))) (forall ((Pi tptp.list_P227219501e_name) (A tptp.name) (X tptp.produc1141751126_pi_pi)) (= (@ (@ tptp.perm_name_o Pi) (@ (@ tptp.fresh_1376661020_pi_pi A) X)) (@ (@ tptp.fresh_1376661020_pi_pi (@ (@ tptp.perm_name_name Pi) A)) (@ (@ tptp.perm_n1255502110_pi_pi Pi) X)))) (forall ((Pi tptp.list_P227219501e_name) (A tptp.name) (X tptp.name)) (let ((_let_1 (@ tptp.perm_name_name Pi))) (= (@ (@ tptp.perm_name_o Pi) (@ (@ tptp.fresh_name_name A) X)) (@ (@ tptp.fresh_name_name (@ _let_1 A)) (@ _let_1 X))))) (forall ((Pi tptp.list_P227219501e_name) (A tptp.name) (X tptp.pi)) (= (@ (@ tptp.perm_name_o Pi) (@ (@ tptp.fresh_name_pi A) X)) (@ (@ tptp.fresh_name_pi (@ (@ tptp.perm_name_name Pi) A)) (@ (@ tptp.perm_name_pi Pi) X)))) (forall ((Pi tptp.list_P227219501e_name) (A tptp.name) (X tptp.pi_Rep)) (= (@ (@ tptp.fresh_name_pi_Rep (@ (@ tptp.perm_name_name Pi) A)) (@ (@ tptp.perm_name_pi_Rep Pi) X)) (@ (@ tptp.fresh_name_pi_Rep A) X))) (forall ((Pi tptp.list_P227219501e_name) (A tptp.name) (X tptp.late_subject)) (= (@ (@ tptp.fresh_717452603ubject (@ (@ tptp.perm_name_name Pi) A)) (@ (@ tptp.perm_n1559866809ubject Pi) X)) (@ (@ tptp.fresh_717452603ubject A) X))) (forall ((Pi tptp.list_P227219501e_name) (A tptp.name) (X tptp.late_freeRes)) (= (@ (@ tptp.fresh_1641682979reeRes (@ (@ tptp.perm_name_name Pi) A)) (@ (@ tptp.perm_n336613537reeRes Pi) X)) (@ (@ tptp.fresh_1641682979reeRes A) X))) (forall ((Pi tptp.list_P227219501e_name) (A tptp.name) (X tptp.produc1141751126_pi_pi)) (= (@ (@ tptp.fresh_1376661020_pi_pi (@ (@ tptp.perm_name_name Pi) A)) (@ (@ tptp.perm_n1255502110_pi_pi Pi) X)) (@ (@ tptp.fresh_1376661020_pi_pi A) X))) (forall ((Pi tptp.list_P227219501e_name) (A tptp.name) (X tptp.name)) (let ((_let_1 (@ tptp.perm_name_name Pi))) (= (@ (@ tptp.fresh_name_name (@ _let_1 A)) (@ _let_1 X)) (@ (@ tptp.fresh_name_name A) X)))) (forall ((Pi tptp.list_P227219501e_name) (A tptp.name) (X tptp.pi)) (= (@ (@ tptp.fresh_name_pi (@ (@ tptp.perm_name_name Pi) A)) (@ (@ tptp.perm_name_pi Pi) X)) (@ (@ tptp.fresh_name_pi A) X))) (forall ((X tptp.name)) (= (@ (@ tptp.perm_name_name tptp.nil_Pr743626285e_name) X) X)) (forall ((X tptp.produc1872410278e_name)) (=> (forall ((P (-> tptp.produc367475239e_name tptp.produc367475239e_name Bool))) (not (= X (@ (@ tptp.produc1069608854e_name P) tptp.nil_Pr743626285e_name)))) (=> (forall ((P (-> tptp.produc367475239e_name tptp.produc367475239e_name Bool)) (X4 tptp.produc367475239e_name)) (not (= X (@ (@ tptp.produc1069608854e_name P) (@ (@ tptp.cons_P1213805021e_name X4) tptp.nil_Pr743626285e_name))))) (not (forall ((P (-> tptp.produc367475239e_name tptp.produc367475239e_name Bool)) (X4 tptp.produc367475239e_name) (Y3 tptp.produc367475239e_name) (Xs tptp.list_P227219501e_name)) (not (= X (@ (@ tptp.produc1069608854e_name P) (@ (@ tptp.cons_P1213805021e_name X4) (@ (@ tptp.cons_P1213805021e_name Y3) Xs)))))))))) (forall ((X tptp.produc1872410278e_name)) (=> (forall ((P (-> tptp.produc367475239e_name tptp.produc367475239e_name Bool))) (not (= X (@ (@ tptp.produc1069608854e_name P) tptp.nil_Pr743626285e_name)))) (not (forall ((P (-> tptp.produc367475239e_name tptp.produc367475239e_name Bool)) (X4 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(not (= X (@ (@ tptp.produc208131031e_name (@ (@ tptp.cons_P1213805021e_name X4) Xs)) Ys))))))) (forall ((A tptp.name) (B tptp.name)) (= (@ (@ tptp.perm_name_name (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name A) B)) tptp.nil_Pr743626285e_name)) A) B)) (forall ((A tptp.name) (B tptp.name)) (= (@ (@ tptp.perm_name_name (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name A) B)) tptp.nil_Pr743626285e_name)) B) A)) (forall ((A tptp.name) (C2 tptp.name) (B tptp.name)) (=> (not (= A C2)) (=> (not (= B C2)) (= (@ (@ tptp.perm_name_name (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name A) B)) tptp.nil_Pr743626285e_name)) C2) C2)))) (forall ((C2 tptp.name) (A tptp.name) (X tptp.pi_Rep) (B tptp.name)) (let ((_let_1 (@ tptp.fresh_name_pi_Rep C2))) (=> (not (= C2 A)) (=> (@ (@ tptp.fresh_name_pi_Rep A) X) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.perm_name_pi_Rep (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name A) B)) tptp.nil_Pr743626285e_name)) X))))))) (forall ((C2 tptp.name) (A tptp.name) (X tptp.late_subject) (B tptp.name)) (let ((_let_1 (@ tptp.fresh_717452603ubject C2))) (=> (not (= C2 A)) (=> (@ (@ tptp.fresh_717452603ubject A) X) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.perm_n1559866809ubject (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name A) B)) tptp.nil_Pr743626285e_name)) X))))))) (forall ((C2 tptp.name) (A tptp.name) (X tptp.late_freeRes) (B tptp.name)) (let ((_let_1 (@ tptp.fresh_1641682979reeRes C2))) (=> (not (= C2 A)) (=> (@ (@ tptp.fresh_1641682979reeRes A) X) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.perm_n336613537reeRes (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name A) B)) tptp.nil_Pr743626285e_name)) X))))))) (forall ((C2 tptp.name) (A tptp.name) (X tptp.produc1141751126_pi_pi) (B tptp.name)) (let ((_let_1 (@ tptp.fresh_1376661020_pi_pi C2))) (=> (not (= C2 A)) (=> (@ (@ tptp.fresh_1376661020_pi_pi A) X) (=> (@ _let_1 X) (@ _let_1 (@ (@ 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((P2 (-> tptp.produc1141751126_pi_pi Bool)) (Prod tptp.produc1141751126_pi_pi)) (=> (forall ((A3 tptp.name) (B3 tptp.product_prod_pi_pi)) (@ P2 (@ (@ tptp.produc235456326_pi_pi A3) B3))) (@ P2 Prod))) (forall ((P2 (-> tptp.product_prod_pi_pi Bool)) (Prod tptp.product_prod_pi_pi)) (=> (forall ((A3 tptp.pi) (B3 tptp.pi)) (@ P2 (@ (@ tptp.product_Pair_pi_pi A3) B3))) (@ P2 Prod))) (forall ((Y4 tptp.produc367475239e_name)) (not (forall ((A3 tptp.name) (B3 tptp.name)) (not (= Y4 (@ (@ tptp.produc1570949143e_name A3) B3)))))) (forall ((Y4 tptp.produc1141751126_pi_pi)) (not (forall ((A3 tptp.name) (B3 tptp.product_prod_pi_pi)) (not (= Y4 (@ (@ tptp.produc235456326_pi_pi A3) B3)))))) (forall ((Y4 tptp.product_prod_pi_pi)) (not (forall ((A3 tptp.pi) (B3 tptp.pi)) (not (= Y4 (@ (@ tptp.product_Pair_pi_pi A3) B3)))))) (forall ((A tptp.product_prod_pi_pi) (P2 (-> tptp.product_prod_pi_pi Bool))) (= (@ (@ tptp.member558706512_pi_pi A) (@ tptp.collec1051790738_pi_pi P2)) (@ P2 A))) (forall ((A4 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X))))) (forall ((Pi2 tptp.list_P227219501e_name) (Pi1 tptp.list_P227219501e_name) (X tptp.late_freeRes)) (let ((_let_1 (@ tptp.perm_n336613537reeRes Pi2))) (= (@ _let_1 (@ (@ tptp.perm_n336613537reeRes Pi1) X)) (@ (@ tptp.perm_n336613537reeRes (@ (@ tptp.perm_n1160739829e_name Pi2) Pi1)) (@ _let_1 X))))) (forall ((Pi2 tptp.list_P227219501e_name) (Pi1 tptp.list_P227219501e_name) (X tptp.pi_Rep)) (let ((_let_1 (@ tptp.perm_name_pi_Rep Pi2))) (= (@ _let_1 (@ (@ tptp.perm_name_pi_Rep Pi1) X)) (@ (@ tptp.perm_name_pi_Rep (@ (@ tptp.perm_n1160739829e_name Pi2) Pi1)) (@ _let_1 X))))) (forall ((Pi2 tptp.list_P227219501e_name) (Pi1 tptp.list_P227219501e_name) (X tptp.name)) (let ((_let_1 (@ tptp.perm_name_name Pi2))) (= (@ _let_1 (@ (@ tptp.perm_name_name Pi1) X)) (@ (@ tptp.perm_name_name (@ (@ tptp.perm_n1160739829e_name Pi2) Pi1)) (@ _let_1 X))))) (forall ((Pi2 tptp.list_P227219501e_name) (Pi1 tptp.list_P227219501e_name) (X tptp.pi)) (let ((_let_1 (@ tptp.perm_name_pi Pi2))) (= (@ _let_1 (@ 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(forall ((Pi2 tptp.list_P227219501e_name) (Pi1 tptp.list_P227219501e_name) (X tptp.name)) (let ((_let_1 (@ tptp.perm_name_name Pi2))) (= (@ _let_1 (@ (@ tptp.perm_name_name Pi1) X)) (@ (@ tptp.perm_name_name (@ (@ tptp.perm_n1160739829e_name Pi2) Pi1)) (@ _let_1 X))))) (forall ((Pi2 tptp.list_P227219501e_name) (Pi1 tptp.list_P227219501e_name) (X tptp.pi)) (let ((_let_1 (@ tptp.perm_name_pi Pi2))) (= (@ _let_1 (@ (@ tptp.perm_name_pi Pi1) X)) (@ (@ tptp.perm_name_pi (@ (@ tptp.perm_n1160739829e_name Pi2) Pi1)) (@ _let_1 X))))) (forall ((Pi tptp.list_P227219501e_name) (X tptp.late_subject) (Y4 tptp.late_subject)) (let ((_let_1 (@ tptp.perm_n1559866809ubject Pi))) (= (= (@ _let_1 X) (@ _let_1 Y4)) (= X Y4)))) (forall ((Pi tptp.list_P227219501e_name) (X tptp.late_freeRes) (Y4 tptp.late_freeRes)) (let ((_let_1 (@ tptp.perm_n336613537reeRes Pi))) (= (= (@ _let_1 X) (@ _let_1 Y4)) (= X Y4)))) (forall ((Pi tptp.list_P227219501e_name) (X tptp.pi_Rep) (Y4 tptp.pi_Rep)) (let ((_let_1 (@ 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(forall ((P2 (-> (-> tptp.produc367475239e_name tptp.produc367475239e_name Bool) tptp.list_P227219501e_name Bool)) (A0 (-> tptp.produc367475239e_name tptp.produc367475239e_name Bool)) (A1 tptp.list_P227219501e_name)) (=> (forall ((P (-> tptp.produc367475239e_name tptp.produc367475239e_name Bool))) (@ (@ P2 P) tptp.nil_Pr743626285e_name)) (=> (forall ((P (-> tptp.produc367475239e_name tptp.produc367475239e_name Bool)) (X4 tptp.produc367475239e_name) (Ys tptp.list_P227219501e_name)) (let ((_let_1 (@ P2 P))) (=> (@ _let_1 Ys) (@ _let_1 (@ (@ tptp.cons_P1213805021e_name X4) Ys))))) (@ (@ P2 A0) A1)))) (forall ((X tptp.list_P227219501e_name)) (=> (not (= X tptp.nil_Pr743626285e_name)) (=> (forall ((X4 tptp.produc367475239e_name)) (not (= X (@ (@ tptp.cons_P1213805021e_name X4) tptp.nil_Pr743626285e_name)))) (not (forall ((X4 tptp.produc367475239e_name) (Y3 tptp.produc367475239e_name) (Xs tptp.list_P227219501e_name)) (not (= X (@ (@ tptp.cons_P1213805021e_name X4) (@ (@ tptp.cons_P1213805021e_name Y3) Xs))))))))) (forall ((X tptp.list_l1406151091e_name)) (=> (not (= X tptp.nil_li29751603e_name)) (=> (forall ((Xss tptp.list_l1406151091e_name)) (not (= X (@ (@ tptp.cons_l798145763e_name tptp.nil_Pr743626285e_name) Xss)))) (not (forall ((X4 tptp.produc367475239e_name) (Xs tptp.list_P227219501e_name) (Xss tptp.list_l1406151091e_name)) (not (= X (@ (@ tptp.cons_l798145763e_name (@ (@ tptp.cons_P1213805021e_name X4) Xs)) Xss)))))))) (forall ((P2 (-> tptp.list_P227219501e_name tptp.list_P227219501e_name Bool)) (A0 tptp.list_P227219501e_name) (A1 tptp.list_P227219501e_name)) (=> (forall ((X_1 tptp.list_P227219501e_name)) (@ (@ P2 tptp.nil_Pr743626285e_name) X_1)) (=> (forall ((Xs tptp.list_P227219501e_name)) (@ (@ P2 Xs) tptp.nil_Pr743626285e_name)) (=> (forall ((X4 tptp.produc367475239e_name) (Xs tptp.list_P227219501e_name) (Y3 tptp.produc367475239e_name) (Ys tptp.list_P227219501e_name)) (let ((_let_1 (@ (@ tptp.cons_P1213805021e_name Y3) Ys))) (let ((_let_2 (@ P2 (@ (@ tptp.cons_P1213805021e_name X4) Xs)))) (=> (@ (@ P2 Xs) _let_1) (=> (@ _let_2 Ys) (@ _let_2 _let_1)))))) (@ (@ P2 A0) A1))))) (forall ((P2 (-> tptp.list_P227219501e_name Bool)) (Xs2 tptp.list_P227219501e_name)) (=> (@ P2 tptp.nil_Pr743626285e_name) (=> (forall ((X4 tptp.produc367475239e_name)) (@ P2 (@ (@ tptp.cons_P1213805021e_name X4) tptp.nil_Pr743626285e_name))) (=> (forall ((X4 tptp.produc367475239e_name) (Y3 tptp.produc367475239e_name) (Zs tptp.list_P227219501e_name)) (let ((_let_1 (@ (@ tptp.cons_P1213805021e_name Y3) Zs))) (=> (@ P2 Zs) (=> (@ P2 _let_1) (@ P2 (@ (@ tptp.cons_P1213805021e_name X4) _let_1)))))) (@ P2 Xs2))))) (forall ((P2 (-> tptp.list_P227219501e_name tptp.list_P227219501e_name Bool)) (A0 tptp.list_P227219501e_name) (A1 tptp.list_P227219501e_name)) (=> (forall ((X_1 tptp.list_P227219501e_name)) (@ (@ P2 tptp.nil_Pr743626285e_name) X_1)) (=> (forall ((X4 tptp.produc367475239e_name) (Xs tptp.list_P227219501e_name) (Ys tptp.list_P227219501e_name)) (=> (@ (@ P2 Ys) Xs) (@ (@ P2 (@ (@ tptp.cons_P1213805021e_name X4) Xs)) Ys))) (@ (@ P2 A0) A1)))) (forall ((P2 (-> tptp.list_P227219501e_name tptp.list_P227219501e_name Bool)) (Xs2 tptp.list_P227219501e_name) (Ys2 tptp.list_P227219501e_name)) (=> (@ (@ P2 tptp.nil_Pr743626285e_name) tptp.nil_Pr743626285e_name) (=> (forall ((X4 tptp.produc367475239e_name) (Xs tptp.list_P227219501e_name)) (@ (@ P2 (@ (@ tptp.cons_P1213805021e_name X4) Xs)) tptp.nil_Pr743626285e_name)) (=> (forall ((Y3 tptp.produc367475239e_name) (Ys tptp.list_P227219501e_name)) (@ (@ P2 tptp.nil_Pr743626285e_name) (@ (@ tptp.cons_P1213805021e_name Y3) Ys))) (=> (forall ((X4 tptp.produc367475239e_name) (Xs tptp.list_P227219501e_name) (Y3 tptp.produc367475239e_name) (Ys tptp.list_P227219501e_name)) (=> (@ (@ P2 Xs) Ys) (@ (@ P2 (@ (@ tptp.cons_P1213805021e_name X4) Xs)) (@ (@ tptp.cons_P1213805021e_name Y3) Ys)))) (@ (@ P2 Xs2) Ys2)))))) (forall ((Xs2 tptp.list_P227219501e_name)) (= (not (= Xs2 tptp.nil_Pr743626285e_name)) (exists ((Y5 tptp.produc367475239e_name) (Ys3 tptp.list_P227219501e_name)) (= Xs2 (@ (@ tptp.cons_P1213805021e_name Y5) Ys3))))) (forall ((P2 (-> tptp.list_P227219501e_name Bool)) (List tptp.list_P227219501e_name)) (=> (@ P2 tptp.nil_Pr743626285e_name) (=> (forall ((X12 tptp.produc367475239e_name) (X23 tptp.list_P227219501e_name)) (=> (@ P2 X23) (@ P2 (@ (@ tptp.cons_P1213805021e_name X12) X23)))) (@ P2 List)))) (forall ((Y4 tptp.list_P227219501e_name)) (=> (not (= Y4 tptp.nil_Pr743626285e_name)) (not (forall ((X212 tptp.produc367475239e_name) (X222 tptp.list_P227219501e_name)) (not (= Y4 (@ (@ tptp.cons_P1213805021e_name X212) X222))))))) (forall ((List tptp.list_P227219501e_name) (X21 tptp.produc367475239e_name) (X22 tptp.list_P227219501e_name)) (=> (= List (@ (@ tptp.cons_P1213805021e_name X21) X22)) (not (= List tptp.nil_Pr743626285e_name)))) (forall ((X21 tptp.produc367475239e_name) (X22 tptp.list_P227219501e_name)) (not (= tptp.nil_Pr743626285e_name (@ (@ tptp.cons_P1213805021e_name X21) X22)))) (@ _let_13 tptp.q) (forall ((A tptp.name) (B tptp.name)) (= (@ (@ tptp.member695284560e_name (@ (@ tptp.produc1570949143e_name A) B)) tptp.id_name) (= A B))) (forall ((A tptp.pi) (B tptp.pi)) (= (@ (@ tptp.member558706512_pi_pi (@ (@ tptp.product_Pair_pi_pi A) B)) tptp.id_pi) (= A B))) (forall ((A tptp.name)) (@ (@ tptp.member695284560e_name (@ (@ tptp.produc1570949143e_name A) A)) tptp.id_name)) (forall ((A tptp.pi)) (@ (@ tptp.member558706512_pi_pi (@ (@ tptp.product_Pair_pi_pi A) A)) tptp.id_pi)) (forall ((A tptp.name) (X tptp.late_subject) (Y4 tptp.late_subject)) (let ((_let_1 (@ tptp.fresh_717452603ubject A))) (= (@ (@ tptp.fresh_495373993ubject A) (@ (@ tptp.produc1465345179ubject X) Y4)) (and (@ _let_1 X) (@ _let_1 Y4))))) (forall ((A tptp.name) (X tptp.late_subject) (Y4 tptp.late_freeRes)) (= (@ (@ tptp.fresh_1638563217reeRes A) (@ (@ tptp.produc242091907reeRes X) Y4)) (and (@ (@ tptp.fresh_717452603ubject A) X) (@ (@ tptp.fresh_1641682979reeRes A) Y4)))) (forall ((A tptp.name) (X tptp.late_subject) (Y4 tptp.name)) (= (@ (@ tptp.fresh_1953561446t_name A) (@ (@ tptp.produc1647375838t_name X) Y4)) (and (@ (@ tptp.fresh_717452603ubject A) X) (@ (@ tptp.fresh_name_name A) Y4)))) (forall ((A tptp.name) (X tptp.late_subject) (Y4 tptp.pi)) (= (@ (@ tptp.fresh_994896692ect_pi A) (@ (@ tptp.produc324947500ect_pi X) Y4)) (and (@ (@ tptp.fresh_717452603ubject A) X) (@ (@ tptp.fresh_name_pi A) Y4)))) (forall ((A tptp.name) (X tptp.late_freeRes) (Y4 tptp.late_subject)) (= (@ (@ tptp.fresh_1498103185ubject A) (@ (@ tptp.produc320590723ubject X) Y4)) (and (@ (@ tptp.fresh_1641682979reeRes A) X) (@ (@ tptp.fresh_717452603ubject A) Y4)))) (forall ((A tptp.name) (X tptp.late_freeRes) (Y4 tptp.late_freeRes)) (let ((_let_1 (@ tptp.fresh_1641682979reeRes A))) (= (@ (@ tptp.fresh_493808761reeRes A) (@ (@ tptp.produc1244821099reeRes X) Y4)) (and (@ _let_1 X) (@ _let_1 Y4))))) (forall ((A tptp.name) (X tptp.late_freeRes) (Y4 tptp.name)) (= (@ (@ tptp.fresh_2007541374s_name A) (@ (@ tptp.produc1701355766s_name X) Y4)) (and (@ (@ tptp.fresh_1641682979reeRes A) X) (@ (@ tptp.fresh_name_name A) Y4)))) (forall ((A tptp.name) (X tptp.late_freeRes) (Y4 tptp.pi)) (= (@ (@ tptp.fresh_1847501388Res_pi A) (@ (@ tptp.produc1177552196Res_pi X) Y4)) (and (@ (@ tptp.fresh_1641682979reeRes A) X) (@ (@ tptp.fresh_name_pi A) Y4)))) (forall ((A tptp.name) (X tptp.name) (Y4 tptp.late_subject)) (= (@ (@ tptp.fresh_820177506ubject A) (@ (@ tptp.produc607574050ubject X) Y4)) (and (@ (@ tptp.fresh_name_name A) X) (@ (@ tptp.fresh_717452603ubject A) Y4)))) (forall ((A tptp.name) (X tptp.name) (Y4 tptp.late_freeRes)) (= (@ (@ tptp.fresh_1963366730reeRes A) (@ (@ tptp.produc1531804426reeRes X) Y4)) (and (@ (@ tptp.fresh_name_name A) X) (@ (@ tptp.fresh_1641682979reeRes A) Y4)))) (@ _let_13 tptp.p) _let_14 (forall ((P2 tptp.pi) (Q tptp.pi) (A tptp.late_subject) (X tptp.name) (Rel tptp.set_Pr1834926343_pi_pi) (Perm tptp.list_P227219501e_name)) (let ((_let_1 (@ tptp.perm_name_pi Perm))) (=> (@ (@ (@ (@ (@ tptp.strong2129052853vative P2) Q) A) X) Rel) (=> (@ tptp.eqvt_pi Rel) (@ (@ (@ (@ (@ tptp.strong2129052853vative (@ _let_1 P2)) (@ _let_1 Q)) (@ (@ tptp.perm_n1559866809ubject Perm) A)) (@ (@ tptp.perm_name_name Perm) X)) Rel))))) (forall ((P2 tptp.pi) (Q tptp.pi) (A tptp.late_subject) (X tptp.name) (Rel tptp.set_Pr1834926343_pi_pi) (Perm tptp.list_P227219501e_name)) (let ((_let_1 (@ tptp.perm_name_pi Perm))) (=> (@ (@ (@ (@ (@ tptp.strong2129052853vative P2) Q) A) X) Rel) (=> (@ tptp.eqvt_pi Rel) (@ (@ (@ (@ (@ tptp.strong2129052853vative (@ _let_1 P2)) (@ _let_1 Q)) A) (@ (@ tptp.perm_name_name Perm) X)) Rel))))) (forall ((Rel tptp.set_Pr806375235ubject) (P2 tptp.late_subject) (Q tptp.late_subject) (Perm tptp.list_P227219501e_name)) (let ((_let_1 (@ tptp.perm_n1559866809ubject Perm))) (=> (@ tptp.eqvt_Late_subject Rel) (=> (@ (@ tptp.member1586545036ubject (@ (@ tptp.produc1465345179ubject P2) Q)) Rel) (@ (@ tptp.member1586545036ubject (@ (@ tptp.produc1465345179ubject (@ _let_1 P2)) (@ _let_1 Q))) Rel))))) (forall ((Rel tptp.set_Pr1780909331reeRes) (P2 tptp.late_freeRes) (Q tptp.late_freeRes) (Perm tptp.list_P227219501e_name)) (let ((_let_1 (@ tptp.perm_n336613537reeRes Perm))) (=> (@ tptp.eqvt_Late_freeRes Rel) (=> (@ (@ tptp.member1584979804reeRes (@ (@ tptp.produc1244821099reeRes P2) Q)) Rel) (@ (@ tptp.member1584979804reeRes (@ (@ tptp.produc1244821099reeRes (@ _let_1 P2)) (@ _let_1 Q))) Rel))))) (forall ((Rel tptp.set_Pr1131282415pi_Rep) (P2 tptp.pi_Rep) (Q tptp.pi_Rep) (Perm tptp.list_P227219501e_name)) (let ((_let_1 (@ tptp.perm_name_pi_Rep Perm))) (=> (@ tptp.eqvt_pi_Rep Rel) (=> (@ (@ tptp.member1671908408pi_Rep (@ (@ tptp.produc784048711pi_Rep P2) Q)) Rel) (@ (@ tptp.member1671908408pi_Rep (@ (@ tptp.produc784048711pi_Rep (@ _let_1 P2)) (@ _let_1 Q))) Rel))))) (forall ((Rel tptp.set_Pr443758855e_name) (P2 tptp.name) (Q tptp.name) (Perm tptp.list_P227219501e_name)) (let ((_let_1 (@ tptp.perm_name_name Perm))) (=> (@ tptp.eqvt_name Rel) (=> (@ (@ tptp.member695284560e_name (@ (@ tptp.produc1570949143e_name P2) Q)) Rel) (@ (@ tptp.member695284560e_name (@ (@ tptp.produc1570949143e_name (@ _let_1 P2)) (@ _let_1 Q))) Rel))))) (forall ((Rel tptp.set_Pr1834926343_pi_pi) (P2 tptp.pi) (Q tptp.pi) (Perm tptp.list_P227219501e_name)) (let ((_let_1 (@ tptp.perm_name_pi Perm))) (=> (@ tptp.eqvt_pi Rel) (=> (@ (@ tptp.member558706512_pi_pi (@ (@ tptp.product_Pair_pi_pi P2) Q)) Rel) (@ (@ tptp.member558706512_pi_pi (@ (@ tptp.product_Pair_pi_pi (@ _let_1 P2)) (@ _let_1 Q))) Rel))))) (@ (@ tptp.fresh_1376661020_pi_pi tptp.y) (@ (@ tptp.produc235456326_pi_pi tptp.x) (@ (@ tptp.product_Pair_pi_pi tptp.p) tptp.q))) (forall ((A tptp.name) (X1 tptp.name)) (= (@ (@ tptp.fresh_717452603ubject A) (@ tptp.late_BoundOutputS X1)) (@ (@ tptp.fresh_name_name A) X1))) (forall ((Pi tptp.list_P227219501e_name) (X tptp.name) (Y4 tptp.name)) (let ((_let_1 (@ tptp.perm_name_name Pi))) (= (= (@ _let_1 X) (@ _let_1 Y4)) (= X Y4)))) (forall ((P2 (-> tptp.list_P227219501e_name Bool))) (=> (forall ((X_1 tptp.list_P227219501e_name)) (@ P2 X_1)) (@ P2 tptp.nil_Pr743626285e_name))) (forall ((Pi tptp.list_P227219501e_name) (B Bool) (C1 tptp.late_subject) (C22 tptp.late_subject)) (let ((_let_1 (@ tptp.perm_n1559866809ubject Pi))) (let ((_let_2 (@ _let_1 (@ (@ (@ tptp.if_Late_subject B) C1) C22)))) (let ((_let_3 (@ (@ tptp.perm_name_o Pi) B))) (and (=> _let_3 (= _let_2 (@ _let_1 C1))) (=> (not _let_3) (= _let_2 (@ _let_1 C22)))))))) (forall ((Pi tptp.list_P227219501e_name) (B Bool) (C1 tptp.late_freeRes) (C22 tptp.late_freeRes)) (let ((_let_1 (@ tptp.perm_n336613537reeRes Pi))) (let ((_let_2 (@ _let_1 (@ (@ (@ tptp.if_Late_freeRes B) C1) C22)))) (let ((_let_3 (@ (@ tptp.perm_name_o Pi) B))) (and (=> _let_3 (= _let_2 (@ _let_1 C1))) (=> (not _let_3) (= _let_2 (@ _let_1 C22)))))))) (forall ((Pi tptp.list_P227219501e_name) (B Bool) (C1 tptp.pi_Rep) (C22 tptp.pi_Rep)) (let ((_let_1 (@ tptp.perm_name_pi_Rep Pi))) (let ((_let_2 (@ _let_1 (@ (@ (@ tptp.if_pi_Rep B) C1) C22)))) (let ((_let_3 (@ (@ tptp.perm_name_o Pi) B))) (and (=> _let_3 (= _let_2 (@ _let_1 C1))) (=> (not _let_3) (= _let_2 (@ _let_1 C22)))))))) (forall ((Pi tptp.list_P227219501e_name) (B Bool) (C1 tptp.name) (C22 tptp.name)) (let ((_let_1 (@ tptp.perm_name_name Pi))) (let ((_let_2 (@ _let_1 (@ (@ (@ tptp.if_name B) C1) C22)))) (let ((_let_3 (@ (@ tptp.perm_name_o Pi) B))) (and (=> _let_3 (= _let_2 (@ _let_1 C1))) (=> (not _let_3) (= _let_2 (@ _let_1 C22)))))))) (forall ((Pi tptp.list_P227219501e_name) (B Bool) (C1 tptp.pi) (C22 tptp.pi)) (let ((_let_1 (@ tptp.perm_name_pi Pi))) (let ((_let_2 (@ _let_1 (@ (@ (@ tptp.if_pi B) C1) C22)))) (let ((_let_3 (@ (@ tptp.perm_name_o Pi) B))) (and (=> _let_3 (= _let_2 (@ _let_1 C1))) (=> (not _let_3) (= _let_2 (@ _let_1 C22)))))))) (forall ((X tptp.late_subject) (Y4 tptp.late_subject) (Pi tptp.list_P227219501e_name)) (let ((_let_1 (@ tptp.perm_n1559866809ubject Pi))) (=> (= X Y4) (= (@ _let_1 X) (@ _let_1 Y4))))) (forall ((X tptp.late_freeRes) (Y4 tptp.late_freeRes) (Pi tptp.list_P227219501e_name)) (let ((_let_1 (@ tptp.perm_n336613537reeRes Pi))) (=> (= X Y4) (= (@ _let_1 X) (@ _let_1 Y4))))) (forall ((X tptp.pi_Rep) (Y4 tptp.pi_Rep) (Pi tptp.list_P227219501e_name)) (let ((_let_1 (@ tptp.perm_name_pi_Rep Pi))) (=> (= X Y4) (= (@ _let_1 X) (@ _let_1 Y4))))) (forall ((X tptp.name) (Y4 tptp.name) (Pi tptp.list_P227219501e_name)) (let ((_let_1 (@ tptp.perm_name_name Pi))) (=> (= X Y4) (= (@ _let_1 X) (@ _let_1 Y4))))) (forall ((X tptp.pi) (Y4 tptp.pi) (Pi tptp.list_P227219501e_name)) (let ((_let_1 (@ tptp.perm_name_pi Pi))) (=> (= X Y4) (= (@ _let_1 X) (@ _let_1 Y4))))) (forall ((C2 Bool) (Pi tptp.list_P227219501e_name) (X tptp.late_subject) (Y4 tptp.late_subject)) (let ((_let_1 (@ tptp.perm_n1559866809ubject Pi))) (let ((_let_2 (@ _let_1 (@ (@ (@ tptp.if_Late_subject C2) X) Y4)))) (and (=> C2 (= _let_2 (@ _let_1 X))) (=> (not C2) (= _let_2 (@ _let_1 Y4))))))) (forall ((C2 Bool) (Pi tptp.list_P227219501e_name) (X tptp.late_freeRes) (Y4 tptp.late_freeRes)) (let ((_let_1 (@ tptp.perm_n336613537reeRes Pi))) (let ((_let_2 (@ _let_1 (@ (@ (@ tptp.if_Late_freeRes C2) X) Y4)))) (and (=> C2 (= _let_2 (@ _let_1 X))) (=> (not C2) (= _let_2 (@ _let_1 Y4))))))) (forall ((C2 Bool) (Pi tptp.list_P227219501e_name) (X tptp.pi_Rep) (Y4 tptp.pi_Rep)) (let ((_let_1 (@ tptp.perm_name_pi_Rep Pi))) (let ((_let_2 (@ _let_1 (@ (@ (@ tptp.if_pi_Rep C2) X) Y4)))) (and (=> C2 (= _let_2 (@ _let_1 X))) (=> (not C2) (= _let_2 (@ _let_1 Y4))))))) (forall ((C2 Bool) (Pi tptp.list_P227219501e_name) (X tptp.name) (Y4 tptp.name)) (let ((_let_1 (@ tptp.perm_name_name Pi))) (let ((_let_2 (@ _let_1 (@ (@ (@ tptp.if_name C2) X) Y4)))) (and (=> C2 (= _let_2 (@ _let_1 X))) (=> (not C2) (= _let_2 (@ _let_1 Y4))))))) (forall ((C2 Bool) (Pi tptp.list_P227219501e_name) (X tptp.pi) (Y4 tptp.pi)) (let ((_let_1 (@ tptp.perm_name_pi Pi))) (let ((_let_2 (@ _let_1 (@ (@ (@ tptp.if_pi C2) X) Y4)))) (and (=> C2 (= _let_2 (@ _let_1 X))) (=> (not C2) (= _let_2 (@ _let_1 Y4))))))) (= tptp.eqvt_pi (lambda ((Rel2 tptp.set_Pr1834926343_pi_pi)) (forall ((X5 tptp.product_prod_pi_pi) (Perm2 tptp.list_P227219501e_name)) (=> (@ (@ tptp.member558706512_pi_pi X5) Rel2) (@ (@ tptp.member558706512_pi_pi (@ (@ tptp.perm_n1415585007_pi_pi Perm2) X5)) Rel2))))) (forall ((Pi tptp.list_P227219501e_name) (X tptp.late_subject) (Y4 tptp.late_subject)) (let ((_let_1 (@ tptp.perm_n1559866809ubject Pi))) (= (@ (@ tptp.perm_n171497387ubject Pi) (@ (@ tptp.produc1465345179ubject X) Y4)) (@ (@ tptp.produc1465345179ubject (@ _let_1 X)) (@ _let_1 Y4))))) (forall ((Pi tptp.list_P227219501e_name) (X tptp.late_subject) (Y4 tptp.late_freeRes)) (= (@ (@ tptp.perm_n1314686611reeRes Pi) (@ (@ tptp.produc242091907reeRes X) Y4)) (@ (@ tptp.produc242091907reeRes (@ (@ tptp.perm_n1559866809ubject Pi) X)) (@ (@ tptp.perm_n336613537reeRes Pi) Y4)))) (forall ((Pi tptp.list_P227219501e_name) (X tptp.late_subject) (Y4 tptp.pi_Rep)) (= (@ (@ tptp.perm_n1467004033pi_Rep Pi) (@ (@ tptp.produc843063281pi_Rep X) Y4)) (@ (@ tptp.produc843063281pi_Rep (@ (@ tptp.perm_n1559866809ubject Pi) X)) (@ (@ tptp.perm_name_pi_Rep Pi) Y4)))) (forall ((Pi tptp.list_P227219501e_name) (X tptp.late_subject) (Y4 tptp.name)) (= (@ (@ tptp.perm_n204483300t_name Pi) (@ (@ tptp.produc1647375838t_name X) Y4)) (@ (@ tptp.produc1647375838t_name (@ (@ tptp.perm_n1559866809ubject Pi) X)) (@ (@ tptp.perm_name_name Pi) Y4)))) (forall ((Pi tptp.list_P227219501e_name) (X tptp.late_subject) (Y4 tptp.pi)) (= (@ (@ tptp.perm_n359102898ect_pi Pi) (@ (@ tptp.produc324947500ect_pi X) Y4)) (@ (@ tptp.produc324947500ect_pi (@ (@ tptp.perm_n1559866809ubject Pi) X)) (@ (@ tptp.perm_name_pi Pi) Y4)))) (forall ((Pi tptp.list_P227219501e_name) (X tptp.late_freeRes) (Y4 tptp.late_subject)) (= (@ (@ tptp.perm_n1174226579ubject Pi) (@ (@ tptp.produc320590723ubject X) Y4)) (@ (@ tptp.produc320590723ubject (@ (@ tptp.perm_n336613537reeRes Pi) X)) (@ (@ tptp.perm_n1559866809ubject Pi) Y4)))) (forall ((Pi tptp.list_P227219501e_name) (X tptp.late_freeRes) (Y4 tptp.late_freeRes)) (let ((_let_1 (@ tptp.perm_n336613537reeRes Pi))) (= (@ (@ tptp.perm_n169932155reeRes Pi) (@ (@ tptp.produc1244821099reeRes X) Y4)) (@ (@ tptp.produc1244821099reeRes (@ _let_1 X)) (@ _let_1 Y4))))) (forall ((Pi tptp.list_P227219501e_name) (X tptp.late_freeRes) (Y4 tptp.pi_Rep)) (= (@ (@ tptp.perm_n840427369pi_Rep Pi) (@ (@ tptp.produc216486617pi_Rep X) Y4)) (@ (@ tptp.produc216486617pi_Rep (@ (@ tptp.perm_n336613537reeRes Pi) X)) (@ (@ tptp.perm_name_pi_Rep Pi) Y4)))) (forall ((Pi tptp.list_P227219501e_name) (X tptp.late_freeRes) (Y4 tptp.name)) (= (@ (@ tptp.perm_n258463228s_name Pi) (@ (@ tptp.produc1701355766s_name X) Y4)) (@ (@ tptp.produc1701355766s_name (@ (@ tptp.perm_n336613537reeRes Pi) X)) (@ (@ tptp.perm_name_name Pi) Y4)))) (forall ((Pi tptp.list_P227219501e_name) (X tptp.late_freeRes) (Y4 tptp.pi)) (= (@ (@ tptp.perm_n1211707594Res_pi Pi) (@ (@ tptp.produc1177552196Res_pi X) Y4)) (@ (@ tptp.produc1177552196Res_pi (@ (@ tptp.perm_n336613537reeRes Pi) X)) (@ (@ tptp.perm_name_pi Pi) Y4)))) (forall ((Pi tptp.list_P227219501e_name) (X tptp.late_subject) (Xs2 tptp.list_Late_subject)) (let ((_let_1 (@ tptp.perm_n1812647369ubject Pi))) (= (@ _let_1 (@ (@ tptp.cons_Late_subject X) Xs2)) (@ (@ tptp.cons_Late_subject (@ (@ tptp.perm_n1559866809ubject Pi) X)) (@ _let_1 Xs2))))) (forall ((Pi tptp.list_P227219501e_name) (X tptp.late_freeRes) (Xs2 tptp.list_Late_freeRes)) (let ((_let_1 (@ tptp.perm_n808352945reeRes Pi))) (= (@ _let_1 (@ (@ tptp.cons_Late_freeRes X) Xs2)) (@ (@ tptp.cons_Late_freeRes (@ (@ tptp.perm_n336613537reeRes Pi) X)) (@ _let_1 Xs2))))) (forall ((Pi tptp.list_P227219501e_name) (X tptp.pi_Rep) (Xs2 tptp.list_pi_Rep)) (let ((_let_1 (@ tptp.perm_n729617823pi_Rep Pi))) (= (@ _let_1 (@ (@ tptp.cons_pi_Rep X) Xs2)) (@ (@ tptp.cons_pi_Rep (@ (@ tptp.perm_name_pi_Rep Pi) X)) (@ _let_1 Xs2))))) (forall ((Pi tptp.list_P227219501e_name) (X tptp.name) (Xs2 tptp.list_name)) (let ((_let_1 (@ tptp.perm_name_list_name Pi))) (= (@ _let_1 (@ (@ tptp.cons_name X) Xs2)) (@ (@ tptp.cons_name (@ (@ tptp.perm_name_name Pi) X)) (@ _let_1 Xs2))))) (forall ((Pi tptp.list_P227219501e_name) (X tptp.pi) (Xs2 tptp.list_pi)) (let ((_let_1 (@ tptp.perm_name_list_pi Pi))) (= (@ _let_1 (@ (@ tptp.cons_pi X) Xs2)) (@ (@ tptp.cons_pi (@ (@ tptp.perm_name_pi Pi) X)) (@ _let_1 Xs2))))) (forall ((A tptp.name) (X tptp.name) (Y4 tptp.name)) (=> (@ (@ tptp.fresh_441084397e_name A) (@ (@ tptp.produc1570949143e_name X) Y4)) (@ (@ tptp.fresh_name_name A) X))) (forall ((A tptp.name) (X tptp.name) (Y4 tptp.product_prod_pi_pi)) (=> (@ (@ tptp.fresh_1376661020_pi_pi A) (@ (@ tptp.produc235456326_pi_pi X) Y4)) (@ (@ tptp.fresh_name_name A) X))) (forall ((A tptp.name) (X tptp.pi) (Y4 tptp.pi)) (=> (@ (@ tptp.fresh_1627595501_pi_pi A) (@ (@ tptp.product_Pair_pi_pi X) Y4)) (@ (@ tptp.fresh_name_pi A) X))) (forall ((A tptp.name) (X tptp.name) (Y4 tptp.name)) (=> (@ (@ tptp.fresh_441084397e_name A) (@ (@ tptp.produc1570949143e_name X) Y4)) (@ (@ tptp.fresh_name_name A) Y4))) (forall ((A tptp.name) (X tptp.name) (Y4 tptp.product_prod_pi_pi)) (=> (@ (@ tptp.fresh_1376661020_pi_pi A) (@ (@ tptp.produc235456326_pi_pi X) Y4)) (@ (@ tptp.fresh_1627595501_pi_pi A) Y4))) (forall ((A tptp.name) (X tptp.pi) (Y4 tptp.pi)) (=> (@ (@ tptp.fresh_1627595501_pi_pi A) (@ (@ tptp.product_Pair_pi_pi X) Y4)) (@ (@ tptp.fresh_name_pi A) Y4))) (forall ((A tptp.name) (X tptp.late_subject) (Xs2 tptp.list_Late_subject)) (let ((_let_1 (@ tptp.fresh_838462539ubject A))) (= (@ _let_1 (@ (@ tptp.cons_Late_subject X) Xs2)) (and (@ (@ tptp.fresh_717452603ubject A) X) (@ _let_1 Xs2))))) (forall ((A tptp.name) (X tptp.late_freeRes) (Xs2 tptp.list_Late_freeRes)) (let ((_let_1 (@ tptp.fresh_1981651763reeRes A))) (= (@ _let_1 (@ (@ tptp.cons_Late_freeRes X) Xs2)) (and (@ (@ tptp.fresh_1641682979reeRes A) X) (@ _let_1 Xs2))))) (forall ((A tptp.name) (X tptp.produc1141751126_pi_pi) (Xs2 tptp.list_P431515740_pi_pi)) (let ((_let_1 (@ tptp.fresh_1958133282_pi_pi A))) (= (@ _let_1 (@ (@ tptp.cons_P749510156_pi_pi X) Xs2)) (and (@ (@ tptp.fresh_1376661020_pi_pi A) X) (@ _let_1 Xs2))))) (forall ((A tptp.name) (X tptp.name) (Xs2 tptp.list_name)) (let ((_let_1 (@ tptp.fresh_name_list_name A))) (= (@ _let_1 (@ (@ tptp.cons_name X) Xs2)) (and (@ (@ tptp.fresh_name_name A) X) (@ _let_1 Xs2))))) (forall ((A tptp.name) (X tptp.pi) (Xs2 tptp.list_pi)) (let ((_let_1 (@ tptp.fresh_name_list_pi A))) (= (@ _let_1 (@ (@ tptp.cons_pi X) Xs2)) (and (@ (@ tptp.fresh_name_pi A) X) (@ _let_1 Xs2))))) (forall ((R tptp.set_Pr443758855e_name) (S tptp.set_Pr443758855e_name)) (=> (forall ((X4 tptp.name) (Y3 tptp.name)) (let ((_let_1 (@ tptp.member695284560e_name (@ (@ tptp.produc1570949143e_name X4) Y3)))) (=> (@ _let_1 R) (@ _let_1 S)))) (@ (@ tptp.ord_le793202855e_name R) S))) (forall ((R tptp.set_Pr1654044726_pi_pi) (S tptp.set_Pr1654044726_pi_pi)) (=> (forall ((X4 tptp.name) (Y3 tptp.product_prod_pi_pi)) (let ((_let_1 (@ tptp.member540268543_pi_pi (@ (@ tptp.produc235456326_pi_pi X4) Y3)))) (=> (@ _let_1 R) (@ _let_1 S)))) (@ (@ tptp.ord_le797229014_pi_pi R) S))) (forall ((R tptp.set_Pr1834926343_pi_pi) (S tptp.set_Pr1834926343_pi_pi)) (=> (forall ((X4 tptp.pi) (Y3 tptp.pi)) (let ((_let_1 (@ tptp.member558706512_pi_pi (@ (@ tptp.product_Pair_pi_pi X4) Y3)))) (=> (@ _let_1 R) (@ _let_1 S)))) (@ (@ tptp.ord_le630093991_pi_pi R) S))) (forall ((P3 tptp.produc367475239e_name)) (=> (@ (@ tptp.member695284560e_name P3) tptp.id_name) (not (forall ((X4 tptp.name)) (not (= P3 (@ (@ tptp.produc1570949143e_name X4) X4))))))) (forall ((P3 tptp.product_prod_pi_pi)) (=> (@ (@ tptp.member558706512_pi_pi P3) tptp.id_pi) (not (forall ((X4 tptp.pi)) (not (= P3 (@ (@ tptp.product_Pair_pi_pi X4) X4))))))) (forall ((P2 tptp.pi) (Q tptp.pi) (A tptp.late_subject) (X tptp.name) (A4 tptp.set_Pr1834926343_pi_pi) (B4 tptp.set_Pr1834926343_pi_pi)) (let ((_let_1 (@ (@ (@ (@ tptp.strong2129052853vative P2) Q) A) X))) (=> (@ _let_1 A4) (=> (@ (@ tptp.ord_le630093991_pi_pi A4) B4) (@ _let_1 B4))))) (forall ((Rel tptp.set_Pr806375235ubject) (Perm tptp.list_P227219501e_name) (P2 tptp.late_subject) (Q tptp.late_subject)) (let ((_let_1 (@ tptp.perm_n1559866809ubject Perm))) (=> (@ tptp.eqvt_Late_subject Rel) (=> (@ (@ tptp.member1586545036ubject (@ (@ tptp.produc1465345179ubject (@ _let_1 P2)) (@ _let_1 Q))) Rel) (@ (@ tptp.member1586545036ubject (@ (@ tptp.produc1465345179ubject P2) Q)) Rel))))) (forall ((Rel tptp.set_Pr1780909331reeRes) (Perm tptp.list_P227219501e_name) (P2 tptp.late_freeRes) (Q tptp.late_freeRes)) (let ((_let_1 (@ tptp.perm_n336613537reeRes Perm))) (=> (@ tptp.eqvt_Late_freeRes Rel) (=> (@ (@ tptp.member1584979804reeRes (@ (@ tptp.produc1244821099reeRes (@ _let_1 P2)) (@ _let_1 Q))) Rel) (@ (@ tptp.member1584979804reeRes (@ (@ tptp.produc1244821099reeRes P2) Q)) Rel))))) (forall ((Rel tptp.set_Pr1131282415pi_Rep) (Perm tptp.list_P227219501e_name) (P2 tptp.pi_Rep) (Q tptp.pi_Rep)) (let ((_let_1 (@ tptp.perm_name_pi_Rep Perm))) (=> (@ tptp.eqvt_pi_Rep Rel) (=> (@ (@ tptp.member1671908408pi_Rep (@ (@ tptp.produc784048711pi_Rep (@ _let_1 P2)) (@ _let_1 Q))) Rel) (@ (@ tptp.member1671908408pi_Rep (@ (@ tptp.produc784048711pi_Rep P2) Q)) Rel))))) (forall ((Rel tptp.set_Pr443758855e_name) (Perm tptp.list_P227219501e_name) (P2 tptp.name) (Q tptp.name)) (let ((_let_1 (@ tptp.perm_name_name Perm))) (=> (@ tptp.eqvt_name Rel) (=> (@ (@ tptp.member695284560e_name (@ (@ tptp.produc1570949143e_name (@ _let_1 P2)) (@ _let_1 Q))) Rel) (@ (@ tptp.member695284560e_name (@ (@ tptp.produc1570949143e_name P2) Q)) Rel))))) (forall ((Rel tptp.set_Pr1834926343_pi_pi) (Perm tptp.list_P227219501e_name) (P2 tptp.pi) (Q tptp.pi)) (let ((_let_1 (@ tptp.perm_name_pi Perm))) (=> (@ tptp.eqvt_pi Rel) (=> (@ (@ tptp.member558706512_pi_pi (@ (@ tptp.product_Pair_pi_pi (@ _let_1 P2)) (@ _let_1 Q))) Rel) (@ (@ tptp.member558706512_pi_pi (@ (@ tptp.product_Pair_pi_pi P2) Q)) Rel))))) (@ _let_13 _let_12) (@ _let_13 _let_10) (forall ((A4 tptp.set_Pr1834926343_pi_pi) (B4 tptp.set_Pr1834926343_pi_pi)) (=> (@ (@ tptp.ord_le630093991_pi_pi A4) B4) (=> (@ (@ tptp.ord_le630093991_pi_pi B4) A4) (= A4 B4)))) (forall ((A4 tptp.set_Pr1834926343_pi_pi) (B4 tptp.set_Pr1834926343_pi_pi)) (=> (forall ((X4 tptp.product_prod_pi_pi)) (let ((_let_1 (@ tptp.member558706512_pi_pi X4))) (=> (@ _let_1 A4) (@ _let_1 B4)))) (@ (@ tptp.ord_le630093991_pi_pi A4) B4))) (forall ((X tptp.set_Pr1834926343_pi_pi)) (@ (@ tptp.ord_le630093991_pi_pi X) X)) (= tptp.fresh_name_name (lambda ((A5 tptp.name) (B5 tptp.name)) (not (= A5 B5)))) (forall ((A tptp.name) (X2 tptp.pi) (X1 tptp.pi)) (let ((_let_1 (@ tptp.fresh_name_pi A))) (= (@ _let_1 (@ (@ tptp.sum X2) X1)) (and (@ _let_1 X2) (@ _let_1 X1))))) (forall ((Pi tptp.list_P227219501e_name) (X2 tptp.pi) (X1 tptp.pi)) (let ((_let_1 (@ tptp.perm_name_pi Pi))) (= (@ _let_1 (@ (@ tptp.sum X2) X1)) (@ (@ tptp.sum (@ _let_1 X2)) (@ _let_1 X1))))) (forall ((Pi tptp.list_P227219501e_name) (X1 tptp.name) (X2 tptp.pi)) (let ((_let_1 (@ tptp.perm_name_pi Pi))) (= (@ _let_1 (@ (@ tptp.res X1) X2)) (@ (@ tptp.res (@ (@ tptp.perm_name_name Pi) X1)) (@ _let_1 X2))))) (forall ((Pi1 tptp.pi) (Pi2 tptp.pi) (Name tptp.name) (Pi3 tptp.pi)) (not (= (@ (@ tptp.sum Pi1) Pi2) (@ (@ tptp.res Name) Pi3)))) (forall ((X2 tptp.pi) (X1 tptp.pi) (Y2 tptp.pi) (Y1 tptp.pi)) (= (= (@ (@ tptp.sum X2) X1) (@ (@ tptp.sum Y2) Y1)) (and (= X2 Y2) (= X1 Y1)))) (forall ((A tptp.name) (P2 tptp.pi)) (@ (@ tptp.fresh_name_pi A) (@ (@ tptp.res A) P2))) (forall ((A tptp.set_Pr1834926343_pi_pi) (F (-> tptp.set_Pr1834926343_pi_pi tptp.set_Pr1834926343_pi_pi)) (B tptp.set_Pr1834926343_pi_pi) (C2 tptp.set_Pr1834926343_pi_pi)) (let ((_let_1 (@ tptp.ord_le630093991_pi_pi A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_le630093991_pi_pi B) C2) (=> (forall ((X4 tptp.set_Pr1834926343_pi_pi) (Y3 tptp.set_Pr1834926343_pi_pi)) (=> (@ (@ tptp.ord_le630093991_pi_pi X4) Y3) (@ (@ tptp.ord_le630093991_pi_pi (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C2))))))) (forall ((A tptp.set_Pr1834926343_pi_pi) (B tptp.set_Pr1834926343_pi_pi) (F (-> tptp.set_Pr1834926343_pi_pi tptp.set_Pr1834926343_pi_pi)) (C2 tptp.set_Pr1834926343_pi_pi)) (=> (@ (@ tptp.ord_le630093991_pi_pi A) B) (=> (@ (@ tptp.ord_le630093991_pi_pi (@ F B)) C2) (=> (forall ((X4 tptp.set_Pr1834926343_pi_pi) (Y3 tptp.set_Pr1834926343_pi_pi)) (=> (@ (@ tptp.ord_le630093991_pi_pi X4) Y3) (@ (@ tptp.ord_le630093991_pi_pi (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_le630093991_pi_pi (@ F A)) C2))))) (forall ((A tptp.set_Pr1834926343_pi_pi) (F (-> tptp.set_Pr1834926343_pi_pi tptp.set_Pr1834926343_pi_pi)) (B tptp.set_Pr1834926343_pi_pi) (C2 tptp.set_Pr1834926343_pi_pi)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_le630093991_pi_pi B) C2) (=> (forall ((X4 tptp.set_Pr1834926343_pi_pi) (Y3 tptp.set_Pr1834926343_pi_pi)) (=> (@ (@ tptp.ord_le630093991_pi_pi X4) Y3) (@ (@ tptp.ord_le630093991_pi_pi (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_le630093991_pi_pi A) (@ F C2)))))) (forall ((A tptp.set_Pr1834926343_pi_pi) (B tptp.set_Pr1834926343_pi_pi) (F (-> tptp.set_Pr1834926343_pi_pi tptp.set_Pr1834926343_pi_pi)) (C2 tptp.set_Pr1834926343_pi_pi)) (=> (@ (@ tptp.ord_le630093991_pi_pi A) B) (=> (= (@ F B) C2) (=> (forall ((X4 tptp.set_Pr1834926343_pi_pi) (Y3 tptp.set_Pr1834926343_pi_pi)) (=> (@ (@ tptp.ord_le630093991_pi_pi X4) Y3) (@ (@ tptp.ord_le630093991_pi_pi (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_le630093991_pi_pi (@ F A)) C2))))) (= (lambda ((Y6 tptp.set_Pr1834926343_pi_pi) (Z tptp.set_Pr1834926343_pi_pi)) (= Y6 Z)) (lambda ((X5 tptp.set_Pr1834926343_pi_pi) (Y5 tptp.set_Pr1834926343_pi_pi)) (and (@ (@ tptp.ord_le630093991_pi_pi X5) Y5) (@ (@ tptp.ord_le630093991_pi_pi Y5) X5)))) (forall ((X tptp.set_Pr1834926343_pi_pi) (Y4 tptp.set_Pr1834926343_pi_pi)) (=> (@ (@ tptp.ord_le630093991_pi_pi X) Y4) (=> (@ (@ tptp.ord_le630093991_pi_pi Y4) X) (= X Y4)))) (forall ((X tptp.set_Pr1834926343_pi_pi) (Y4 tptp.set_Pr1834926343_pi_pi)) (=> (= X Y4) (@ (@ tptp.ord_le630093991_pi_pi X) Y4))) (forall ((A tptp.set_Pr1834926343_pi_pi) (B tptp.set_Pr1834926343_pi_pi) (C2 tptp.set_Pr1834926343_pi_pi)) (let ((_let_1 (@ tptp.ord_le630093991_pi_pi A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_le630093991_pi_pi B) C2) (@ _let_1 C2))))) (forall ((Y4 tptp.set_Pr1834926343_pi_pi) (X tptp.set_Pr1834926343_pi_pi)) (=> (@ (@ tptp.ord_le630093991_pi_pi Y4) X) (= (@ (@ tptp.ord_le630093991_pi_pi X) Y4) (= X Y4)))) (= (lambda ((Y6 tptp.set_Pr1834926343_pi_pi) (Z tptp.set_Pr1834926343_pi_pi)) (= Y6 Z)) (lambda ((A5 tptp.set_Pr1834926343_pi_pi) (B5 tptp.set_Pr1834926343_pi_pi)) (and (@ (@ tptp.ord_le630093991_pi_pi A5) B5) (@ (@ tptp.ord_le630093991_pi_pi B5) A5)))) (forall ((A tptp.set_Pr1834926343_pi_pi) (B tptp.set_Pr1834926343_pi_pi) (C2 tptp.set_Pr1834926343_pi_pi)) (=> (= A B) (=> (@ (@ tptp.ord_le630093991_pi_pi B) C2) (@ (@ tptp.ord_le630093991_pi_pi A) C2)))) (forall ((A tptp.set_Pr1834926343_pi_pi) (B tptp.set_Pr1834926343_pi_pi) (C2 tptp.set_Pr1834926343_pi_pi)) (let ((_let_1 (@ tptp.ord_le630093991_pi_pi A))) (=> (@ _let_1 B) (=> (= B C2) (@ _let_1 C2))))) (forall ((A tptp.set_Pr1834926343_pi_pi) (B tptp.set_Pr1834926343_pi_pi)) (=> (@ (@ tptp.ord_le630093991_pi_pi A) B) (=> (@ (@ tptp.ord_le630093991_pi_pi B) A) (= A B)))) (forall ((X tptp.set_Pr1834926343_pi_pi) (Y4 tptp.set_Pr1834926343_pi_pi) (Z2 tptp.set_Pr1834926343_pi_pi)) (let ((_let_1 (@ tptp.ord_le630093991_pi_pi X))) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_le630093991_pi_pi Y4) Z2) (@ _let_1 Z2))))) (forall ((A tptp.set_Pr1834926343_pi_pi)) (@ (@ tptp.ord_le630093991_pi_pi A) A)) (forall ((C2 tptp.name) (P2 tptp.pi) (A tptp.name)) (=> (@ (@ tptp.fresh_name_pi C2) P2) (= (@ (@ tptp.res A) P2) (@ (@ tptp.res C2) (@ (@ tptp.perm_name_pi (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name A) C2)) tptp.nil_Pr743626285e_name)) P2))))) (@ _let_11 (@ (@ _let_9 tptp.y) _let_2)) (@ (@ tptp.late_transitions _let_12) _let_6) (@ _let_11 (@ (@ _let_9 tptp.x) tptp.p2)) (forall ((Rel tptp.set_Pr1834926343_pi_pi) (X tptp.name) (P2 tptp.pi) (Q tptp.pi)) (let ((_let_1 (@ tptp.res X))) (=> (@ (@ tptp.ord_le630093991_pi_pi tptp.id_pi) Rel) (=> (@ tptp.eqvt_pi Rel) (@ (@ (@ tptp.strong743114133lation (@ (@ tptp.sum (@ _let_1 P2)) (@ _let_1 Q))) Rel) (@ _let_1 (@ (@ tptp.sum P2) Q))))))) (@ (@ tptp.late_transitions _let_8) _let_6) (forall ((Pi tptp.list_P227219501e_name) (X32 tptp.late_subject) (X1 tptp.name) (X2 tptp.pi)) (= (@ (@ tptp.perm_n414416632sidual Pi) (@ (@ (@ tptp.late_BoundR X32) X1) X2)) (@ (@ (@ tptp.late_BoundR (@ (@ tptp.perm_n1559866809ubject Pi) X32)) (@ (@ tptp.perm_name_name Pi) X1)) (@ (@ tptp.perm_name_pi Pi) X2)))) (forall ((P2 tptp.pi) (A tptp.late_subject) (X tptp.name) (P4 tptp.pi) (Y4 tptp.name)) (=> (@ (@ tptp.late_transitions P2) (@ (@ (@ tptp.late_BoundR A) X) P4)) (=> (@ (@ tptp.fresh_name_pi Y4) P2) (@ (@ tptp.fresh_717452603ubject Y4) A)))) (forall ((P2 tptp.pi) (A tptp.late_subject) (X tptp.name) (P4 tptp.pi) (Y4 tptp.name)) (let ((_let_1 (@ tptp.res Y4))) (let ((_let_2 (@ (@ tptp.late_BoundR A) X))) (=> (@ (@ tptp.late_transitions P2) (@ _let_2 P4)) (=> (@ (@ tptp.fresh_717452603ubject Y4) A) (=> (not (= Y4 X)) (@ (@ tptp.late_transitions (@ _let_1 P2)) (@ _let_2 (@ _let_1 P4))))))))) (forall ((P2 tptp.pi) (A tptp.late_subject) (X tptp.name) (P4 tptp.pi) (Y4 tptp.name)) (let ((_let_1 (@ tptp.fresh_name_pi Y4))) (=> (@ (@ tptp.late_transitions P2) (@ (@ (@ tptp.late_BoundR A) X) P4)) (=> (@ _let_1 P2) (=> (not (= Y4 X)) (@ _let_1 P4)))))) (forall ((P2 tptp.pi) (Rel tptp.set_Pr1834926343_pi_pi) (Q tptp.pi) (A tptp.late_subject) (X tptp.name) (Q2 tptp.pi)) (=> (@ (@ (@ tptp.strong743114133lation P2) Rel) Q) (=> (@ (@ tptp.late_transitions Q) (@ (@ (@ tptp.late_BoundR A) X) Q2)) (=> (@ (@ tptp.fresh_name_pi X) P2) (exists ((P5 tptp.pi)) (and (@ (@ tptp.late_transitions P2) (@ (@ (@ tptp.late_BoundR A) X) P5)) (@ (@ (@ (@ (@ tptp.strong2129052853vative P5) Q2) A) X) Rel))))))) (forall ((Q tptp.pi) (Rs tptp.late_residual) (P2 tptp.pi)) (=> (@ (@ tptp.late_transitions Q) Rs) (@ (@ tptp.late_transitions (@ (@ tptp.sum P2) Q)) Rs))) (forall ((P2 tptp.pi) (Rs tptp.late_residual) (Q tptp.pi)) (=> (@ (@ tptp.late_transitions P2) Rs) (@ (@ tptp.late_transitions (@ (@ tptp.sum P2) Q)) Rs))) (forall ((P2 tptp.pi) (Q tptp.pi) (Rs tptp.late_residual)) (=> (@ (@ tptp.late_transitions (@ (@ tptp.sum P2) Q)) Rs) (=> (not (@ (@ tptp.late_transitions P2) Rs)) (@ (@ tptp.late_transitions Q) Rs)))) (forall ((P2 tptp.pi) (Q tptp.pi) (Rs tptp.late_residual)) (=> (@ (@ tptp.late_transitions (@ (@ tptp.sum P2) Q)) Rs) (=> (not (@ (@ tptp.late_transitions P2) Rs)) (@ (@ tptp.late_transitions Q) Rs)))) (forall ((P2 tptp.pi) (Rs tptp.late_residual) (X tptp.name)) (=> (@ (@ tptp.late_transitions P2) Rs) (=> (@ (@ 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tptp.set_Pr1834926343_pi_pi) (P2 tptp.pi)) (=> (@ (@ tptp.ord_le630093991_pi_pi tptp.id_pi) Rel) (@ (@ (@ tptp.strong743114133lation P2) Rel) P2))) (forall ((Rel tptp.set_Pr1834926343_pi_pi) (P2 tptp.pi)) (=> (@ (@ tptp.ord_le630093991_pi_pi tptp.id_pi) Rel) (@ (@ (@ tptp.strong743114133lation (@ (@ tptp.sum P2) P2)) Rel) P2))) (forall ((Rel tptp.set_Pr1834926343_pi_pi) (P2 tptp.pi) (Q tptp.pi) (R2 tptp.pi)) (let ((_let_1 (@ tptp.sum P2))) (=> (@ (@ tptp.ord_le630093991_pi_pi tptp.id_pi) Rel) (@ (@ (@ tptp.strong743114133lation (@ _let_1 (@ (@ tptp.sum Q) R2))) Rel) (@ (@ tptp.sum (@ _let_1 Q)) R2))))) (forall ((Rel tptp.set_Pr1834926343_pi_pi) (P2 tptp.pi)) (=> (@ (@ tptp.ord_le630093991_pi_pi tptp.id_pi) Rel) (@ (@ (@ tptp.strong743114133lation P2) Rel) (@ (@ tptp.sum P2) P2)))) (forall ((Rel tptp.set_Pr1834926343_pi_pi) (P2 tptp.pi) (Q tptp.pi) (R2 tptp.pi)) (let ((_let_1 (@ tptp.sum P2))) (=> (@ (@ tptp.ord_le630093991_pi_pi tptp.id_pi) Rel) (@ (@ (@ tptp.strong743114133lation (@ (@ tptp.sum (@ _let_1 Q)) R2)) Rel) (@ _let_1 (@ (@ tptp.sum Q) R2)))))) (forall ((Rel tptp.set_Pr1834926343_pi_pi) (P2 tptp.pi) (Q tptp.pi)) (=> (@ (@ tptp.ord_le630093991_pi_pi tptp.id_pi) Rel) (@ (@ (@ tptp.strong743114133lation (@ (@ tptp.sum P2) Q)) Rel) (@ (@ tptp.sum Q) P2)))) (forall ((P2 tptp.pi) (Rel tptp.set_Pr1834926343_pi_pi) (Q tptp.pi) (Rel3 tptp.set_Pr1834926343_pi_pi) (Perm tptp.list_P227219501e_name)) (let ((_let_1 (@ tptp.perm_name_pi Perm))) (=> (@ (@ (@ tptp.strong743114133lation P2) Rel) Q) (=> (@ (@ tptp.ord_le630093991_pi_pi Rel) Rel3) (=> (@ tptp.eqvt_pi Rel3) (@ (@ (@ tptp.strong743114133lation (@ _let_1 P2)) Rel3) (@ _let_1 Q))))))) (forall ((X6 tptp.name) (P2 tptp.pi) (A tptp.late_subject) (X tptp.name)) (let ((_let_1 (@ tptp.late_BoundR A))) (=> (@ (@ tptp.fresh_name_pi X6) P2) (= (@ (@ _let_1 X) P2) (@ (@ _let_1 X6) (@ (@ tptp.perm_name_pi (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name X) X6)) tptp.nil_Pr743626285e_name)) P2)))))) (@ (@ tptp.late_transitions tptp.p) _let_4) (@ (@ tptp.late_transitions _let_5) _let_4) (forall ((X11 tptp.name) (X122 tptp.name) (Y11 tptp.name) (Y12 tptp.name)) (= (= (@ (@ tptp.late_OutputR X11) X122) (@ (@ tptp.late_OutputR Y11) Y12)) (and (= X11 Y11) (= X122 Y12)))) (forall ((X2 tptp.name) (X1 tptp.name) (Y2 tptp.name) (Y1 tptp.name)) (= (= (@ (@ tptp.late_OutputR X2) X1) (@ (@ tptp.late_OutputR Y2) Y1)) (and (= X2 Y2) (= X1 Y1)))) (forall ((Pi tptp.list_P227219501e_name) (X2 tptp.name) (X1 tptp.name)) (let ((_let_1 (@ tptp.perm_name_name Pi))) (= (@ (@ tptp.perm_n336613537reeRes Pi) (@ (@ tptp.late_OutputR X2) X1)) (@ (@ tptp.late_OutputR (@ _let_1 X2)) (@ _let_1 X1))))) (forall ((A tptp.name) (X2 tptp.name) (X1 tptp.name)) (let ((_let_1 (@ tptp.fresh_name_name A))) (= (@ (@ tptp.fresh_1641682979reeRes A) (@ (@ tptp.late_OutputR X2) X1)) (and (@ _let_1 X2) (@ _let_1 X1))))) (forall ((Pi tptp.list_P227219501e_name) (X2 tptp.late_freeRes) (X1 tptp.pi)) (= (@ (@ 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tptp.late_freeRes) (XP tptp.pi) (F3 (-> tptp.pi Bool))) (=> (@ (@ tptp.late_transitions (@ (@ tptp.res X) P2)) (@ (@ tptp.late_FreeR Alpha) XP)) (=> (forall ((P5 tptp.pi)) (=> (@ (@ tptp.late_transitions P2) (@ (@ tptp.late_FreeR Alpha) P5)) (=> (@ (@ tptp.fresh_1641682979reeRes X) Alpha) (@ F3 (@ (@ tptp.res X) P5))))) (@ F3 XP)))) (forall ((P2 tptp.pi) (Alpha tptp.late_freeRes) (P4 tptp.pi) (Y4 tptp.name)) (let ((_let_1 (@ tptp.fresh_name_pi Y4))) (=> (@ (@ tptp.late_transitions P2) (@ (@ tptp.late_FreeR Alpha) P4)) (=> (@ _let_1 P2) (@ _let_1 P4))))) (forall ((P2 tptp.pi) (Alpha tptp.late_freeRes) (P4 tptp.pi) (Y4 tptp.name)) (=> (@ (@ tptp.late_transitions P2) (@ (@ tptp.late_FreeR Alpha) P4)) (=> (@ (@ tptp.fresh_name_pi Y4) P2) (@ (@ tptp.fresh_1641682979reeRes Y4) Alpha)))) (forall ((P2 tptp.pi) (A tptp.name) (B tptp.name) (P4 tptp.pi)) (=> (@ (@ tptp.late_transitions P2) (@ (@ tptp.late_FreeR (@ (@ tptp.late_OutputR A) B)) P4)) (=> (not (= A B)) (@ (@ tptp.late_transitions (@ 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B3)) P5)) (= A3 B3)))))) (not (forall ((P tptp.pi) (A3 tptp.late_subject) (X4 tptp.name) (P5 tptp.pi) (Y3 tptp.name)) (let ((_let_1 (@ (@ tptp.late_BoundR A3) X4))) (let ((_let_2 (@ tptp.res Y3))) (=> (= (@ (@ tptp.res X6) P2) (@ _let_2 P)) (=> (= (@ (@ (@ tptp.late_BoundR A) Y7) P4) (@ _let_1 (@ _let_2 P5))) (=> (@ (@ tptp.late_transitions P) (@ _let_1 P5)) (=> (@ (@ tptp.fresh_717452603ubject Y3) A3) (=> (not (= Y3 X4)) (=> (@ (@ tptp.fresh_name_pi X4) P) (not (@ (@ tptp.fresh_717452603ubject X4) A3))))))))))))))) (forall ((X tptp.name) (P2 tptp.pi) (Rs tptp.late_residual)) (=> (@ (@ tptp.late_transitions (@ (@ tptp.res X) P2)) Rs) (=> (forall ((P tptp.pi) (A3 tptp.name) (B3 tptp.name)) (=> (= (@ (@ tptp.res X) P2) (@ (@ tptp.res B3) P)) (forall ((P5 tptp.pi)) (=> (= Rs (@ (@ (@ tptp.late_BoundR (@ tptp.late_BoundOutputS A3)) B3) P5)) (=> (@ (@ tptp.late_transitions P) (@ (@ tptp.late_FreeR (@ (@ tptp.late_OutputR A3) B3)) P5)) (= A3 B3)))))) (=> (forall ((P tptp.pi) (A3 tptp.late_subject) (X4 tptp.name) (P5 tptp.pi) (Y3 tptp.name)) (let ((_let_1 (@ (@ tptp.late_BoundR A3) X4))) (let ((_let_2 (@ tptp.res Y3))) (=> (= (@ (@ tptp.res X) P2) (@ _let_2 P)) (=> (= Rs (@ _let_1 (@ _let_2 P5))) (=> (@ (@ tptp.late_transitions P) (@ _let_1 P5)) (=> (@ (@ tptp.fresh_717452603ubject Y3) A3) (=> (not (= Y3 X4)) (=> (@ (@ tptp.fresh_name_pi X4) P) (not (@ (@ tptp.fresh_717452603ubject X4) A3))))))))))) (not (forall ((P tptp.pi) (Alpha2 tptp.late_freeRes) (P5 tptp.pi) (Y3 tptp.name)) (let ((_let_1 (@ tptp.late_FreeR Alpha2))) (let ((_let_2 (@ tptp.res Y3))) (=> (= (@ (@ tptp.res X) P2) (@ _let_2 P)) (=> (= Rs (@ _let_1 (@ _let_2 P5))) (=> (@ (@ tptp.late_transitions P) (@ _let_1 P5)) (not (@ (@ tptp.fresh_1641682979reeRes Y3) Alpha2))))))))))))) (forall ((Y4 tptp.name) (P2 tptp.pi) (A tptp.late_subject) (X tptp.name) (YP tptp.pi) (F3 (-> tptp.late_subject tptp.pi Bool))) (=> (@ (@ tptp.late_transitions (@ (@ tptp.res Y4) P2)) (@ (@ (@ tptp.late_BoundR A) X) YP)) (=> (not (= X Y4)) (=> (@ (@ tptp.fresh_name_pi X) P2) (=> (forall ((B3 tptp.name) (P5 tptp.pi)) (let ((_let_1 (@ tptp.late_BoundOutputS B3))) (=> (@ (@ tptp.late_transitions P2) (@ (@ tptp.late_FreeR (@ (@ tptp.late_OutputR B3) Y4)) P5)) (=> (not (= B3 Y4)) (=> (= A _let_1) (@ (@ F3 _let_1) (@ (@ tptp.perm_name_pi (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name X) Y4)) tptp.nil_Pr743626285e_name)) P5))))))) (=> (forall ((P5 tptp.pi)) (=> (@ (@ tptp.late_transitions P2) (@ (@ (@ tptp.late_BoundR A) X) P5)) (=> (@ (@ tptp.fresh_717452603ubject Y4) A) (@ (@ F3 A) (@ (@ tptp.res Y4) P5))))) (@ (@ F3 A) YP))))))) (= tptp.strong743114133lation (lambda ((P6 tptp.pi) (Rel2 tptp.set_Pr1834926343_pi_pi) (Q3 tptp.pi)) (and (forall ((A5 tptp.late_subject) (X5 tptp.name) (Q4 tptp.pi)) (=> (and (@ (@ tptp.late_transitions Q3) (@ (@ (@ tptp.late_BoundR A5) X5) Q4)) (@ (@ tptp.fresh_name_pi X5) P6)) (exists ((P7 tptp.pi)) (and (@ (@ tptp.late_transitions P6) (@ (@ (@ tptp.late_BoundR A5) X5) P7)) (@ (@ (@ (@ (@ tptp.strong2129052853vative P7) Q4) A5) X5) Rel2))))) (forall ((Alpha3 tptp.late_freeRes) (Q4 tptp.pi)) (=> (@ (@ tptp.late_transitions Q3) (@ (@ tptp.late_FreeR Alpha3) Q4)) (exists ((P7 tptp.pi)) (and (@ (@ tptp.late_transitions P6) (@ (@ tptp.late_FreeR Alpha3) P7)) (@ (@ tptp.member558706512_pi_pi (@ (@ tptp.product_Pair_pi_pi P7) Q4)) Rel2)))))))) (forall ((Q tptp.pi) (P2 tptp.pi) (Rel tptp.set_Pr1834926343_pi_pi)) (=> (forall ((A3 tptp.late_subject) (Y3 tptp.name) (Q5 tptp.pi)) (=> (@ (@ tptp.late_transitions Q) (@ (@ (@ tptp.late_BoundR A3) Y3) Q5)) (=> (@ (@ tptp.fresh_name_pi Y3) P2) (exists ((P8 tptp.pi)) (and (@ (@ tptp.late_transitions P2) (@ (@ (@ tptp.late_BoundR A3) Y3) P8)) (@ (@ (@ (@ (@ tptp.strong2129052853vative P8) Q5) A3) Y3) Rel)))))) (=> (forall ((Alpha2 tptp.late_freeRes) (Q5 tptp.pi)) (=> (@ (@ tptp.late_transitions Q) (@ (@ tptp.late_FreeR Alpha2) Q5)) (exists ((P8 tptp.pi)) (and (@ (@ tptp.late_transitions P2) (@ (@ tptp.late_FreeR Alpha2) P8)) (@ (@ tptp.member558706512_pi_pi (@ (@ tptp.product_Pair_pi_pi P8) Q5)) Rel))))) (@ (@ (@ tptp.strong743114133lation P2) Rel) Q)))) (forall ((X21 tptp.late_freeRes) (X22 tptp.pi) (Y21 tptp.late_freeRes) (Y22 tptp.pi)) (= (= (@ (@ tptp.late_r347633188eR_Rep X21) X22) (@ (@ tptp.late_r347633188eR_Rep Y21) Y22)) (and (= X21 Y21) (= X22 Y22)))) (forall ((C2 tptp.name) (P2 tptp.pi) (A tptp.name) (X tptp.name)) (let ((_let_1 (@ tptp.input A))) (=> (@ (@ tptp.fresh_name_pi C2) P2) (= (@ (@ _let_1 X) P2) (@ (@ _let_1 C2) (@ (@ tptp.perm_name_pi (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name X) C2)) tptp.nil_Pr743626285e_name)) P2)))))) (forall ((Pi tptp.list_P227219501e_name) (X32 tptp.name) (X1 tptp.name) (X2 tptp.pi)) (let ((_let_1 (@ tptp.perm_name_pi Pi))) (let ((_let_2 (@ tptp.perm_name_name Pi))) (= (@ _let_1 (@ (@ (@ tptp.input X32) X1) X2)) (@ (@ (@ tptp.input (@ _let_2 X32)) (@ _let_2 X1)) (@ _let_1 X2)))))) (forall ((X tptp.name) (Y4 tptp.name) (P2 tptp.pi) (Rs tptp.late_residual)) (not (@ (@ tptp.late_transitions (@ (@ tptp.res X) (@ (@ (@ tptp.input X) Y4) P2))) Rs))) (forall ((Name1 tptp.name) (Name22 tptp.name) (Pi tptp.pi) (Pi12 tptp.pi) (Pi22 tptp.pi)) (not (= (@ (@ (@ tptp.input Name1) Name22) Pi) (@ (@ tptp.sum Pi12) Pi22)))) (forall ((Name1 tptp.name) (Name22 tptp.name) (Pi tptp.pi) (Name tptp.name) (Pi3 tptp.pi)) (not (= (@ (@ (@ tptp.input Name1) Name22) Pi) (@ (@ tptp.res Name) Pi3)))) (forall ((A tptp.name) (X tptp.name) (P2 tptp.pi) (Alpha tptp.late_freeRes) (P4 tptp.pi)) (not (@ (@ tptp.late_transitions (@ (@ (@ tptp.input A) X) P2)) (@ (@ tptp.late_FreeR Alpha) P4)))) (forall ((X tptp.name) (A tptp.name) (Y4 tptp.name) (P2 tptp.pi) (Alpha tptp.late_freeRes) (P4 tptp.pi)) (not (@ (@ tptp.late_transitions (@ (@ tptp.res X) (@ (@ (@ tptp.input A) Y4) P2))) (@ (@ tptp.late_FreeR Alpha) P4)))) (forall ((A tptp.name) (X tptp.name) (P2 tptp.pi) (B tptp.name) (Y4 tptp.name) (P4 tptp.pi)) (not (@ (@ tptp.late_transitions (@ (@ (@ tptp.input A) X) P2)) (@ (@ (@ tptp.late_BoundR (@ tptp.late_BoundOutputS B)) Y4) P4)))) (forall ((A tptp.name) (X tptp.name) (P2 tptp.pi) (B tptp.late_subject) (Y4 tptp.name) (P4 tptp.pi)) (=> (@ (@ tptp.late_transitions (@ (@ (@ tptp.input A) X) P2)) (@ (@ (@ tptp.late_BoundR B) Y4) P4)) (not (@ (@ tptp.fresh_717452603ubject A) B)))) (forall ((X tptp.name) (A tptp.name) (Y4 tptp.name) (P2 tptp.pi) (B tptp.name) (Z2 tptp.name) (P4 tptp.pi)) (not (@ (@ tptp.late_transitions (@ (@ tptp.res X) (@ (@ (@ tptp.input A) Y4) P2))) (@ (@ (@ tptp.late_BoundR (@ tptp.late_BoundOutputS B)) Z2) P4)))) (forall ((A tptp.name) (X tptp.name) (P2 tptp.pi) (B tptp.late_subject) (Y4 tptp.name) (YP tptp.pi) (Prop (-> tptp.late_subject tptp.name tptp.pi Bool))) (let ((_let_1 (@ (@ tptp.perm_name_pi (@ (@ tptp.cons_P1213805021e_name (@ (@ tptp.produc1570949143e_name X) Y4)) tptp.nil_Pr743626285e_name)) P2))) (let ((_let_2 (@ tptp.late_InputS A))) (=> (@ (@ tptp.late_transitions (@ (@ (@ tptp.input A) X) P2)) (@ (@ (@ tptp.late_BoundR B) Y4) YP)) (=> (not (= Y4 A)) (=> (not (= Y4 X)) (=> (@ (@ tptp.fresh_name_pi Y4) P2) (=> (=> (= B _let_2) (=> (= YP _let_1) (@ (@ (@ Prop _let_2) Y4) _let_1))) (@ (@ (@ Prop B) Y4) YP))))))))) (forall ((A tptp.name) (B tptp.name) (Pi tptp.list_P227219501e_name) (X tptp.name)) (let ((_let_1 (@ (@ tptp.produc1570949143e_name A) B))) (= (@ (@ tptp.perm_name_name (@ (@ tptp.cons_P1213805021e_name _let_1) Pi)) X) (@ (@ tptp.swap_name _let_1) (@ (@ tptp.perm_name_name Pi) X))))) (forall ((X1 tptp.name) (Y1 tptp.name)) (= (= (@ tptp.late_InputS X1) (@ tptp.late_InputS Y1)) (= X1 Y1))) (forall ((A tptp.name) (X1 tptp.name)) (= (@ (@ tptp.fresh_717452603ubject A) (@ tptp.late_InputS X1)) (@ (@ tptp.fresh_name_name A) X1))) (forall ((Pi tptp.list_P227219501e_name) (X1 tptp.name)) (= (@ (@ tptp.perm_n1559866809ubject Pi) (@ tptp.late_InputS X1)) (@ tptp.late_InputS (@ (@ tptp.perm_name_name Pi) X1)))) (forall ((Name2 tptp.name) (Name tptp.name)) (not (= (@ tptp.late_InputS Name2) (@ tptp.late_BoundOutputS Name)))) (forall ((X tptp.pi) (Y4 tptp.pi)) (= (@ (@ (@ tptp.if_pi false) X) Y4) Y4)) (forall ((X tptp.pi) (Y4 tptp.pi)) (= (@ (@ (@ tptp.if_pi true) X) Y4) X)) (forall ((X tptp.name) (Y4 tptp.name)) (= (@ (@ (@ tptp.if_name false) X) Y4) Y4)) (forall ((X tptp.name) (Y4 tptp.name)) (= (@ (@ (@ tptp.if_name true) X) Y4) X)) (forall ((X tptp.pi_Rep) (Y4 tptp.pi_Rep)) (= (@ (@ (@ tptp.if_pi_Rep false) X) Y4) Y4)) (forall ((X tptp.pi_Rep) (Y4 tptp.pi_Rep)) (= (@ (@ (@ tptp.if_pi_Rep true) X) Y4) X)) (forall ((X tptp.late_freeRes) (Y4 tptp.late_freeRes)) (= (@ (@ (@ tptp.if_Late_freeRes false) X) Y4) Y4)) (forall ((X tptp.late_freeRes) (Y4 tptp.late_freeRes)) (= (@ (@ (@ tptp.if_Late_freeRes true) X) Y4) X)) (forall ((P2 Bool)) (or (= P2 true) (= P2 false))) (forall ((X tptp.late_subject) (Y4 tptp.late_subject)) (= (@ (@ (@ tptp.if_Late_subject false) X) Y4) Y4)) (forall ((X tptp.late_subject) (Y4 tptp.late_subject)) (= (@ (@ (@ tptp.if_Late_subject true) X) Y4) X)) _let_3 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.86/1.09 )
% 0.86/1.09 % SZS output end Proof for ITP182^1
% 0.86/1.09 % cvc5---1.0.5 exiting
% 0.86/1.09 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------