TSTP Solution File: ITP092^1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP092^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n021.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 03:18:10 EDT 2023
% Result : Theorem 1.01s 1.28s
% Output : Proof 1.01s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.21 % Problem : ITP092^1 : TPTP v8.1.2. Released v7.5.0.
% 0.13/0.22 % Command : do_cvc5 %s %d
% 0.20/0.41 % Computer : n021.cluster.edu
% 0.20/0.41 % Model : x86_64 x86_64
% 0.20/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.41 % Memory : 8042.1875MB
% 0.20/0.41 % OS : Linux 3.10.0-693.el7.x86_64
% 0.20/0.41 % CPULimit : 300
% 0.20/0.41 % WCLimit : 300
% 0.20/0.41 % DateTime : Sun Aug 27 15:23:28 EDT 2023
% 0.20/0.41 % CPUTime :
% 0.25/0.56 %----Proving TH0
% 0.25/0.56 %------------------------------------------------------------------------------
% 0.25/0.56 % File : ITP092^1 : TPTP v8.1.2. Released v7.5.0.
% 0.25/0.56 % Domain : Interactive Theorem Proving
% 0.25/0.56 % Problem : Sledgehammer Kuratowski problem prob_158__5524402_1
% 0.25/0.56 % Version : Especial.
% 0.25/0.56 % English :
% 0.25/0.56
% 0.25/0.56 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.25/0.56 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.25/0.56 % Source : [Des21]
% 0.25/0.56 % Names : Kuratowski/prob_158__5524402_1 [Des21]
% 0.25/0.56
% 0.25/0.56 % Status : Theorem
% 0.25/0.56 % Rating : 0.54 v8.1.0, 0.45 v7.5.0
% 0.25/0.56 % Syntax : Number of formulae : 566 ( 174 unt; 207 typ; 0 def)
% 0.25/0.56 % Number of atoms : 1080 ( 694 equ; 0 cnn)
% 0.25/0.56 % Maximal formula atoms : 26 ( 3 avg)
% 0.25/0.56 % Number of connectives : 4874 ( 229 ~; 59 |; 141 &;3982 @)
% 0.25/0.56 % ( 0 <=>; 463 =>; 0 <=; 0 <~>)
% 0.25/0.56 % Maximal formula depth : 29 ( 8 avg)
% 0.25/0.56 % Number of types : 56 ( 55 usr)
% 0.25/0.56 % Number of type conns : 475 ( 475 >; 0 *; 0 +; 0 <<)
% 0.25/0.56 % Number of symbols : 155 ( 152 usr; 9 con; 0-3 aty)
% 0.25/0.56 % Number of variables : 1599 ( 12 ^;1498 !; 89 ?;1599 :)
% 0.25/0.56 % SPC : TH0_THM_EQU_NAR
% 0.25/0.56
% 0.25/0.56 % Comments : This file was generated by Sledgehammer 2021-02-23 15:44:40.460
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% 0.25/0.56 member1899387664od_a_a: produc1990712039od_a_a > set_Pr1295299783od_a_a > $o ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__a_J_Mt__Product____Type__Oprod_Itf__a_Mtf__a_J_J,type,
% 0.25/0.56 member2057358096od_a_a: produc1572603623od_a_a > set_Pr1948701895od_a_a > $o ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_member_001t__Product____Type__Oprod_Itf__a_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J_J,type,
% 0.25/0.56 member1474739327od_a_a: produc1701253078od_a_a > set_Pr248149174od_a_a > $o ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_member_001t__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J_Mtf__a_J_J,type,
% 0.25/0.56 member1904151562_a_a_a: produc1197928545_a_a_a > set_Pr110478017_a_a_a > $o ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_member_001t__Product____Type__Oprod_Itf__a_Mtf__a_J,type,
% 0.25/0.56 member449909584od_a_a: product_prod_a_a > set_Product_prod_a_a > $o ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_member_001tf__a,type,
% 0.25/0.56 member_a2: a > set_a > $o ).
% 0.25/0.56
% 0.25/0.56 thf(sy_v_e,type,
% 0.25/0.56 e: product_prod_a_a ).
% 0.25/0.56
% 0.25/0.56 thf(sy_v_es,type,
% 0.25/0.56 es: list_P1467822637od_a_a ).
% 0.25/0.56
% 0.25/0.56 % Relevant facts (355)
% 0.25/0.56 thf(fact_0_assms,axiom,
% 0.25/0.56 kurato1072996284sing_a @ ( cons_P1921020637od_a_a @ e @ es ) ).
% 0.25/0.56
% 0.25/0.56 % assms
% 0.25/0.56 thf(fact_1_progressing__def,axiom,
% 0.25/0.56 ( kurato1404746725od_a_a
% 0.25/0.56 = ( ^ [P: list_P1891567085od_a_a] :
% 0.25/0.56 ! [Xs: list_P1891567085od_a_a,X: product_prod_a_a,Y: product_prod_a_a,Ys: list_P1891567085od_a_a] :
% 0.25/0.56 ( P
% 0.25/0.56 != ( append864718978od_a_a @ Xs @ ( cons_P1070399645od_a_a @ ( produc1474507607od_a_a @ X @ Y ) @ ( cons_P1070399645od_a_a @ ( produc1474507607od_a_a @ Y @ X ) @ Ys ) ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % progressing_def
% 0.25/0.56 thf(fact_2_progressing__def,axiom,
% 0.25/0.56 ( kurato292963650list_a
% 0.25/0.56 = ( ^ [P: list_P601816365list_a] :
% 0.25/0.56 ! [Xs: list_P601816365list_a,X: list_a,Y: list_a,Ys: list_P601816365list_a] :
% 0.25/0.56 ( P
% 0.25/0.56 != ( append750086082list_a @ Xs @ ( cons_P2080942813list_a @ ( produc1448356631list_a @ X @ Y ) @ ( cons_P2080942813list_a @ ( produc1448356631list_a @ Y @ X ) @ Ys ) ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % progressing_def
% 0.25/0.56 thf(fact_3_progressing__def,axiom,
% 0.25/0.56 ( kurato1072996284sing_a
% 0.25/0.56 = ( ^ [P: list_P1467822637od_a_a] :
% 0.25/0.56 ! [Xs: list_P1467822637od_a_a,X: a,Y: a,Ys: list_P1467822637od_a_a] :
% 0.25/0.56 ( P
% 0.25/0.56 != ( append1574001858od_a_a @ Xs @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ X @ Y ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ Y @ X ) @ Ys ) ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % progressing_def
% 0.25/0.56 thf(fact_4_append_Oassoc,axiom,
% 0.25/0.56 ! [A: list_a,B: list_a,C: list_a] :
% 0.25/0.56 ( ( append_a @ ( append_a @ A @ B ) @ C )
% 0.25/0.56 = ( append_a @ A @ ( append_a @ B @ C ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % append.assoc
% 0.25/0.56 thf(fact_5_append_Oassoc,axiom,
% 0.25/0.56 ! [A: list_P1891567085od_a_a,B: list_P1891567085od_a_a,C: list_P1891567085od_a_a] :
% 0.25/0.56 ( ( append864718978od_a_a @ ( append864718978od_a_a @ A @ B ) @ C )
% 0.25/0.56 = ( append864718978od_a_a @ A @ ( append864718978od_a_a @ B @ C ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % append.assoc
% 0.25/0.56 thf(fact_6_append_Oassoc,axiom,
% 0.25/0.56 ! [A: list_l1108175539od_a_a,B: list_l1108175539od_a_a,C: list_l1108175539od_a_a] :
% 0.25/0.56 ( ( append2141280328od_a_a @ ( append2141280328od_a_a @ A @ B ) @ C )
% 0.25/0.56 = ( append2141280328od_a_a @ A @ ( append2141280328od_a_a @ B @ C ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % append.assoc
% 0.25/0.56 thf(fact_7_append_Oassoc,axiom,
% 0.25/0.56 ! [A: list_P1467822637od_a_a,B: list_P1467822637od_a_a,C: list_P1467822637od_a_a] :
% 0.25/0.56 ( ( append1574001858od_a_a @ ( append1574001858od_a_a @ A @ B ) @ C )
% 0.25/0.56 = ( append1574001858od_a_a @ A @ ( append1574001858od_a_a @ B @ C ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % append.assoc
% 0.25/0.56 thf(fact_8_append__assoc,axiom,
% 0.25/0.56 ! [Xs2: list_a,Ys2: list_a,Zs: list_a] :
% 0.25/0.56 ( ( append_a @ ( append_a @ Xs2 @ Ys2 ) @ Zs )
% 0.25/0.56 = ( append_a @ Xs2 @ ( append_a @ Ys2 @ Zs ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % append_assoc
% 0.25/0.56 thf(fact_9_append__assoc,axiom,
% 0.25/0.56 ! [Xs2: list_P1891567085od_a_a,Ys2: list_P1891567085od_a_a,Zs: list_P1891567085od_a_a] :
% 0.25/0.56 ( ( append864718978od_a_a @ ( append864718978od_a_a @ Xs2 @ Ys2 ) @ Zs )
% 0.25/0.56 = ( append864718978od_a_a @ Xs2 @ ( append864718978od_a_a @ Ys2 @ Zs ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % append_assoc
% 0.25/0.56 thf(fact_10_append__assoc,axiom,
% 0.25/0.56 ! [Xs2: list_l1108175539od_a_a,Ys2: list_l1108175539od_a_a,Zs: list_l1108175539od_a_a] :
% 0.25/0.56 ( ( append2141280328od_a_a @ ( append2141280328od_a_a @ Xs2 @ Ys2 ) @ Zs )
% 0.25/0.56 = ( append2141280328od_a_a @ Xs2 @ ( append2141280328od_a_a @ Ys2 @ Zs ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % append_assoc
% 0.25/0.56 thf(fact_11_append__assoc,axiom,
% 0.25/0.56 ! [Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a,Zs: list_P1467822637od_a_a] :
% 0.25/0.56 ( ( append1574001858od_a_a @ ( append1574001858od_a_a @ Xs2 @ Ys2 ) @ Zs )
% 0.25/0.56 = ( append1574001858od_a_a @ Xs2 @ ( append1574001858od_a_a @ Ys2 @ Zs ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % append_assoc
% 0.25/0.56 thf(fact_12_append__same__eq,axiom,
% 0.25/0.56 ! [Ys2: list_a,Xs2: list_a,Zs: list_a] :
% 0.25/0.56 ( ( ( append_a @ Ys2 @ Xs2 )
% 0.25/0.56 = ( append_a @ Zs @ Xs2 ) )
% 0.25/0.56 = ( Ys2 = Zs ) ) ).
% 0.25/0.56
% 0.25/0.56 % append_same_eq
% 0.25/0.56 thf(fact_13_append__same__eq,axiom,
% 0.25/0.56 ! [Ys2: list_P1891567085od_a_a,Xs2: list_P1891567085od_a_a,Zs: list_P1891567085od_a_a] :
% 0.25/0.56 ( ( ( append864718978od_a_a @ Ys2 @ Xs2 )
% 0.25/0.56 = ( append864718978od_a_a @ Zs @ Xs2 ) )
% 0.25/0.56 = ( Ys2 = Zs ) ) ).
% 0.25/0.56
% 0.25/0.56 % append_same_eq
% 0.25/0.56 thf(fact_14_append__same__eq,axiom,
% 0.25/0.56 ! [Ys2: list_l1108175539od_a_a,Xs2: list_l1108175539od_a_a,Zs: list_l1108175539od_a_a] :
% 0.25/0.56 ( ( ( append2141280328od_a_a @ Ys2 @ Xs2 )
% 0.25/0.56 = ( append2141280328od_a_a @ Zs @ Xs2 ) )
% 0.25/0.56 = ( Ys2 = Zs ) ) ).
% 0.25/0.56
% 0.25/0.56 % append_same_eq
% 0.25/0.56 thf(fact_15_append__same__eq,axiom,
% 0.25/0.56 ! [Ys2: list_P1467822637od_a_a,Xs2: list_P1467822637od_a_a,Zs: list_P1467822637od_a_a] :
% 0.25/0.56 ( ( ( append1574001858od_a_a @ Ys2 @ Xs2 )
% 0.25/0.56 = ( append1574001858od_a_a @ Zs @ Xs2 ) )
% 0.25/0.56 = ( Ys2 = Zs ) ) ).
% 0.25/0.56
% 0.25/0.56 % append_same_eq
% 0.25/0.56 thf(fact_16_same__append__eq,axiom,
% 0.25/0.56 ! [Xs2: list_a,Ys2: list_a,Zs: list_a] :
% 0.25/0.56 ( ( ( append_a @ Xs2 @ Ys2 )
% 0.25/0.56 = ( append_a @ Xs2 @ Zs ) )
% 0.25/0.56 = ( Ys2 = Zs ) ) ).
% 0.25/0.56
% 0.25/0.56 % same_append_eq
% 0.25/0.56 thf(fact_17_same__append__eq,axiom,
% 0.25/0.56 ! [Xs2: list_P1891567085od_a_a,Ys2: list_P1891567085od_a_a,Zs: list_P1891567085od_a_a] :
% 0.25/0.56 ( ( ( append864718978od_a_a @ Xs2 @ Ys2 )
% 0.25/0.56 = ( append864718978od_a_a @ Xs2 @ Zs ) )
% 0.25/0.56 = ( Ys2 = Zs ) ) ).
% 0.25/0.56
% 0.25/0.56 % same_append_eq
% 0.25/0.56 thf(fact_18_same__append__eq,axiom,
% 0.25/0.56 ! [Xs2: list_l1108175539od_a_a,Ys2: list_l1108175539od_a_a,Zs: list_l1108175539od_a_a] :
% 0.25/0.56 ( ( ( append2141280328od_a_a @ Xs2 @ Ys2 )
% 0.25/0.56 = ( append2141280328od_a_a @ Xs2 @ Zs ) )
% 0.25/0.56 = ( Ys2 = Zs ) ) ).
% 0.25/0.56
% 0.25/0.56 % same_append_eq
% 0.25/0.56 thf(fact_19_same__append__eq,axiom,
% 0.25/0.56 ! [Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a,Zs: list_P1467822637od_a_a] :
% 0.25/0.56 ( ( ( append1574001858od_a_a @ Xs2 @ Ys2 )
% 0.25/0.56 = ( append1574001858od_a_a @ Xs2 @ Zs ) )
% 0.25/0.56 = ( Ys2 = Zs ) ) ).
% 0.25/0.56
% 0.25/0.56 % same_append_eq
% 0.25/0.56 thf(fact_20_list_Oinject,axiom,
% 0.25/0.56 ! [X21: a,X22: list_a,Y21: a,Y22: list_a] :
% 0.25/0.56 ( ( ( cons_a @ X21 @ X22 )
% 0.25/0.56 = ( cons_a @ Y21 @ Y22 ) )
% 0.25/0.56 = ( ( X21 = Y21 )
% 0.25/0.56 & ( X22 = Y22 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % list.inject
% 0.25/0.56 thf(fact_21_list_Oinject,axiom,
% 0.25/0.56 ! [X21: produc1572603623od_a_a,X22: list_P1891567085od_a_a,Y21: produc1572603623od_a_a,Y22: list_P1891567085od_a_a] :
% 0.25/0.56 ( ( ( cons_P1070399645od_a_a @ X21 @ X22 )
% 0.25/0.56 = ( cons_P1070399645od_a_a @ Y21 @ Y22 ) )
% 0.25/0.56 = ( ( X21 = Y21 )
% 0.25/0.56 & ( X22 = Y22 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % list.inject
% 0.25/0.56 thf(fact_22_list_Oinject,axiom,
% 0.25/0.56 ! [X21: list_P1467822637od_a_a,X22: list_l1108175539od_a_a,Y21: list_P1467822637od_a_a,Y22: list_l1108175539od_a_a] :
% 0.25/0.56 ( ( ( cons_l724116707od_a_a @ X21 @ X22 )
% 0.25/0.56 = ( cons_l724116707od_a_a @ Y21 @ Y22 ) )
% 0.25/0.56 = ( ( X21 = Y21 )
% 0.25/0.56 & ( X22 = Y22 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % list.inject
% 0.25/0.56 thf(fact_23_list_Oinject,axiom,
% 0.25/0.56 ! [X21: a > nat,X22: list_a_nat,Y21: a > nat,Y22: list_a_nat] :
% 0.25/0.56 ( ( ( cons_a_nat @ X21 @ X22 )
% 0.25/0.56 = ( cons_a_nat @ Y21 @ Y22 ) )
% 0.25/0.56 = ( ( X21 = Y21 )
% 0.25/0.56 & ( X22 = Y22 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % list.inject
% 0.25/0.56 thf(fact_24_list_Oinject,axiom,
% 0.25/0.56 ! [X21: product_prod_a_a,X22: list_P1467822637od_a_a,Y21: product_prod_a_a,Y22: list_P1467822637od_a_a] :
% 0.25/0.56 ( ( ( cons_P1921020637od_a_a @ X21 @ X22 )
% 0.25/0.56 = ( cons_P1921020637od_a_a @ Y21 @ Y22 ) )
% 0.25/0.56 = ( ( X21 = Y21 )
% 0.25/0.56 & ( X22 = Y22 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % list.inject
% 0.25/0.56 thf(fact_25_prod_Oinject,axiom,
% 0.25/0.56 ! [X1: list_P1467822637od_a_a,X2: a,Y1: list_P1467822637od_a_a,Y2: a] :
% 0.25/0.56 ( ( ( produc998622632_a_a_a @ X1 @ X2 )
% 0.25/0.56 = ( produc998622632_a_a_a @ Y1 @ Y2 ) )
% 0.25/0.56 = ( ( X1 = Y1 )
% 0.25/0.56 & ( X2 = Y2 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % prod.inject
% 0.25/0.56 thf(fact_26_prod_Oinject,axiom,
% 0.25/0.56 ! [X1: list_a,X2: list_a,Y1: list_a,Y2: list_a] :
% 0.25/0.56 ( ( ( produc1448356631list_a @ X1 @ X2 )
% 0.25/0.56 = ( produc1448356631list_a @ Y1 @ Y2 ) )
% 0.25/0.56 = ( ( X1 = Y1 )
% 0.25/0.56 & ( X2 = Y2 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % prod.inject
% 0.25/0.56 thf(fact_27_prod_Oinject,axiom,
% 0.25/0.56 ! [X1: product_prod_a_a > product_prod_a_a > $o,X2: list_P1467822637od_a_a,Y1: product_prod_a_a > product_prod_a_a > $o,Y2: list_P1467822637od_a_a] :
% 0.25/0.56 ( ( ( produc214132118od_a_a @ X1 @ X2 )
% 0.25/0.56 = ( produc214132118od_a_a @ Y1 @ Y2 ) )
% 0.25/0.56 = ( ( X1 = Y1 )
% 0.25/0.56 & ( X2 = Y2 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % prod.inject
% 0.25/0.56 thf(fact_28_prod_Oinject,axiom,
% 0.25/0.56 ! [X1: a,X2: produc657167928_a_a_a,Y1: a,Y2: produc657167928_a_a_a] :
% 0.25/0.56 ( ( ( produc1440321489_a_a_a @ X1 @ X2 )
% 0.25/0.56 = ( produc1440321489_a_a_a @ Y1 @ Y2 ) )
% 0.25/0.56 = ( ( X1 = Y1 )
% 0.25/0.56 & ( X2 = Y2 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % prod.inject
% 0.25/0.56 thf(fact_29_prod_Oinject,axiom,
% 0.25/0.56 ! [X1: a,X2: list_P1467822637od_a_a,Y1: a,Y2: list_P1467822637od_a_a] :
% 0.25/0.56 ( ( ( produc575024326od_a_a @ X1 @ X2 )
% 0.25/0.56 = ( produc575024326od_a_a @ Y1 @ Y2 ) )
% 0.25/0.56 = ( ( X1 = Y1 )
% 0.25/0.56 & ( X2 = Y2 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % prod.inject
% 0.25/0.56 thf(fact_30_prod_Oinject,axiom,
% 0.25/0.56 ! [X1: a,X2: a,Y1: a,Y2: a] :
% 0.25/0.56 ( ( ( product_Pair_a_a @ X1 @ X2 )
% 0.25/0.56 = ( product_Pair_a_a @ Y1 @ Y2 ) )
% 0.25/0.56 = ( ( X1 = Y1 )
% 0.25/0.56 & ( X2 = Y2 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % prod.inject
% 0.25/0.56 thf(fact_31_old_Oprod_Oinject,axiom,
% 0.25/0.56 ! [A: list_P1467822637od_a_a,B: a,A2: list_P1467822637od_a_a,B2: a] :
% 0.25/0.56 ( ( ( produc998622632_a_a_a @ A @ B )
% 0.25/0.56 = ( produc998622632_a_a_a @ A2 @ B2 ) )
% 0.25/0.56 = ( ( A = A2 )
% 0.25/0.56 & ( B = B2 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % old.prod.inject
% 0.25/0.56 thf(fact_32_old_Oprod_Oinject,axiom,
% 0.25/0.56 ! [A: list_a,B: list_a,A2: list_a,B2: list_a] :
% 0.25/0.56 ( ( ( produc1448356631list_a @ A @ B )
% 0.25/0.56 = ( produc1448356631list_a @ A2 @ B2 ) )
% 0.25/0.56 = ( ( A = A2 )
% 0.25/0.56 & ( B = B2 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % old.prod.inject
% 0.25/0.56 thf(fact_33_old_Oprod_Oinject,axiom,
% 0.25/0.56 ! [A: product_prod_a_a > product_prod_a_a > $o,B: list_P1467822637od_a_a,A2: product_prod_a_a > product_prod_a_a > $o,B2: list_P1467822637od_a_a] :
% 0.25/0.56 ( ( ( produc214132118od_a_a @ A @ B )
% 0.25/0.56 = ( produc214132118od_a_a @ A2 @ B2 ) )
% 0.25/0.56 = ( ( A = A2 )
% 0.25/0.56 & ( B = B2 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % old.prod.inject
% 0.25/0.56 thf(fact_34_old_Oprod_Oinject,axiom,
% 0.25/0.56 ! [A: a,B: produc657167928_a_a_a,A2: a,B2: produc657167928_a_a_a] :
% 0.25/0.56 ( ( ( produc1440321489_a_a_a @ A @ B )
% 0.25/0.56 = ( produc1440321489_a_a_a @ A2 @ B2 ) )
% 0.25/0.56 = ( ( A = A2 )
% 0.25/0.56 & ( B = B2 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % old.prod.inject
% 0.25/0.56 thf(fact_35_old_Oprod_Oinject,axiom,
% 0.25/0.56 ! [A: a,B: list_P1467822637od_a_a,A2: a,B2: list_P1467822637od_a_a] :
% 0.25/0.56 ( ( ( produc575024326od_a_a @ A @ B )
% 0.25/0.56 = ( produc575024326od_a_a @ A2 @ B2 ) )
% 0.25/0.56 = ( ( A = A2 )
% 0.25/0.56 & ( B = B2 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % old.prod.inject
% 0.25/0.56 thf(fact_36_old_Oprod_Oinject,axiom,
% 0.25/0.56 ! [A: a,B: a,A2: a,B2: a] :
% 0.25/0.56 ( ( ( product_Pair_a_a @ A @ B )
% 0.25/0.56 = ( product_Pair_a_a @ A2 @ B2 ) )
% 0.25/0.56 = ( ( A = A2 )
% 0.25/0.56 & ( B = B2 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % old.prod.inject
% 0.25/0.56 thf(fact_37_Cons__eq__appendI,axiom,
% 0.25/0.57 ! [X3: a,Xs1: list_a,Ys2: list_a,Xs2: list_a,Zs: list_a] :
% 0.25/0.57 ( ( ( cons_a @ X3 @ Xs1 )
% 0.25/0.57 = Ys2 )
% 0.25/0.57 => ( ( Xs2
% 0.25/0.57 = ( append_a @ Xs1 @ Zs ) )
% 0.25/0.57 => ( ( cons_a @ X3 @ Xs2 )
% 0.25/0.57 = ( append_a @ Ys2 @ Zs ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % Cons_eq_appendI
% 0.25/0.57 thf(fact_38_Cons__eq__appendI,axiom,
% 0.25/0.57 ! [X3: produc1572603623od_a_a,Xs1: list_P1891567085od_a_a,Ys2: list_P1891567085od_a_a,Xs2: list_P1891567085od_a_a,Zs: list_P1891567085od_a_a] :
% 0.25/0.57 ( ( ( cons_P1070399645od_a_a @ X3 @ Xs1 )
% 0.25/0.57 = Ys2 )
% 0.25/0.57 => ( ( Xs2
% 0.25/0.57 = ( append864718978od_a_a @ Xs1 @ Zs ) )
% 0.25/0.57 => ( ( cons_P1070399645od_a_a @ X3 @ Xs2 )
% 0.25/0.57 = ( append864718978od_a_a @ Ys2 @ Zs ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % Cons_eq_appendI
% 0.25/0.57 thf(fact_39_Cons__eq__appendI,axiom,
% 0.25/0.57 ! [X3: list_P1467822637od_a_a,Xs1: list_l1108175539od_a_a,Ys2: list_l1108175539od_a_a,Xs2: list_l1108175539od_a_a,Zs: list_l1108175539od_a_a] :
% 0.25/0.57 ( ( ( cons_l724116707od_a_a @ X3 @ Xs1 )
% 0.25/0.57 = Ys2 )
% 0.25/0.57 => ( ( Xs2
% 0.25/0.57 = ( append2141280328od_a_a @ Xs1 @ Zs ) )
% 0.25/0.57 => ( ( cons_l724116707od_a_a @ X3 @ Xs2 )
% 0.25/0.57 = ( append2141280328od_a_a @ Ys2 @ Zs ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % Cons_eq_appendI
% 0.25/0.57 thf(fact_40_Cons__eq__appendI,axiom,
% 0.25/0.57 ! [X3: a > nat,Xs1: list_a_nat,Ys2: list_a_nat,Xs2: list_a_nat,Zs: list_a_nat] :
% 0.25/0.57 ( ( ( cons_a_nat @ X3 @ Xs1 )
% 0.25/0.57 = Ys2 )
% 0.25/0.57 => ( ( Xs2
% 0.25/0.57 = ( append_a_nat @ Xs1 @ Zs ) )
% 0.25/0.57 => ( ( cons_a_nat @ X3 @ Xs2 )
% 0.25/0.57 = ( append_a_nat @ Ys2 @ Zs ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % Cons_eq_appendI
% 0.25/0.57 thf(fact_41_Cons__eq__appendI,axiom,
% 0.25/0.57 ! [X3: product_prod_a_a,Xs1: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a,Xs2: list_P1467822637od_a_a,Zs: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( ( cons_P1921020637od_a_a @ X3 @ Xs1 )
% 0.25/0.57 = Ys2 )
% 0.25/0.57 => ( ( Xs2
% 0.25/0.57 = ( append1574001858od_a_a @ Xs1 @ Zs ) )
% 0.25/0.57 => ( ( cons_P1921020637od_a_a @ X3 @ Xs2 )
% 0.25/0.57 = ( append1574001858od_a_a @ Ys2 @ Zs ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % Cons_eq_appendI
% 0.25/0.57 thf(fact_42_append__Cons,axiom,
% 0.25/0.57 ! [X3: a,Xs2: list_a,Ys2: list_a] :
% 0.25/0.57 ( ( append_a @ ( cons_a @ X3 @ Xs2 ) @ Ys2 )
% 0.25/0.57 = ( cons_a @ X3 @ ( append_a @ Xs2 @ Ys2 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % append_Cons
% 0.25/0.57 thf(fact_43_append__Cons,axiom,
% 0.25/0.57 ! [X3: produc1572603623od_a_a,Xs2: list_P1891567085od_a_a,Ys2: list_P1891567085od_a_a] :
% 0.25/0.57 ( ( append864718978od_a_a @ ( cons_P1070399645od_a_a @ X3 @ Xs2 ) @ Ys2 )
% 0.25/0.57 = ( cons_P1070399645od_a_a @ X3 @ ( append864718978od_a_a @ Xs2 @ Ys2 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % append_Cons
% 0.25/0.57 thf(fact_44_append__Cons,axiom,
% 0.25/0.57 ! [X3: list_P1467822637od_a_a,Xs2: list_l1108175539od_a_a,Ys2: list_l1108175539od_a_a] :
% 0.25/0.57 ( ( append2141280328od_a_a @ ( cons_l724116707od_a_a @ X3 @ Xs2 ) @ Ys2 )
% 0.25/0.57 = ( cons_l724116707od_a_a @ X3 @ ( append2141280328od_a_a @ Xs2 @ Ys2 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % append_Cons
% 0.25/0.57 thf(fact_45_append__Cons,axiom,
% 0.25/0.57 ! [X3: a > nat,Xs2: list_a_nat,Ys2: list_a_nat] :
% 0.25/0.57 ( ( append_a_nat @ ( cons_a_nat @ X3 @ Xs2 ) @ Ys2 )
% 0.25/0.57 = ( cons_a_nat @ X3 @ ( append_a_nat @ Xs2 @ Ys2 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % append_Cons
% 0.25/0.57 thf(fact_46_append__Cons,axiom,
% 0.25/0.57 ! [X3: product_prod_a_a,Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( append1574001858od_a_a @ ( cons_P1921020637od_a_a @ X3 @ Xs2 ) @ Ys2 )
% 0.25/0.57 = ( cons_P1921020637od_a_a @ X3 @ ( append1574001858od_a_a @ Xs2 @ Ys2 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % append_Cons
% 0.25/0.57 thf(fact_47_append__eq__appendI,axiom,
% 0.25/0.57 ! [Xs2: list_a,Xs1: list_a,Zs: list_a,Ys2: list_a,Us: list_a] :
% 0.25/0.57 ( ( ( append_a @ Xs2 @ Xs1 )
% 0.25/0.57 = Zs )
% 0.25/0.57 => ( ( Ys2
% 0.25/0.57 = ( append_a @ Xs1 @ Us ) )
% 0.25/0.57 => ( ( append_a @ Xs2 @ Ys2 )
% 0.25/0.57 = ( append_a @ Zs @ Us ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % append_eq_appendI
% 0.25/0.57 thf(fact_48_append__eq__appendI,axiom,
% 0.25/0.57 ! [Xs2: list_P1891567085od_a_a,Xs1: list_P1891567085od_a_a,Zs: list_P1891567085od_a_a,Ys2: list_P1891567085od_a_a,Us: list_P1891567085od_a_a] :
% 0.25/0.57 ( ( ( append864718978od_a_a @ Xs2 @ Xs1 )
% 0.25/0.57 = Zs )
% 0.25/0.57 => ( ( Ys2
% 0.25/0.57 = ( append864718978od_a_a @ Xs1 @ Us ) )
% 0.25/0.57 => ( ( append864718978od_a_a @ Xs2 @ Ys2 )
% 0.25/0.57 = ( append864718978od_a_a @ Zs @ Us ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % append_eq_appendI
% 0.25/0.57 thf(fact_49_append__eq__appendI,axiom,
% 0.25/0.57 ! [Xs2: list_l1108175539od_a_a,Xs1: list_l1108175539od_a_a,Zs: list_l1108175539od_a_a,Ys2: list_l1108175539od_a_a,Us: list_l1108175539od_a_a] :
% 0.25/0.57 ( ( ( append2141280328od_a_a @ Xs2 @ Xs1 )
% 0.25/0.57 = Zs )
% 0.25/0.57 => ( ( Ys2
% 0.25/0.57 = ( append2141280328od_a_a @ Xs1 @ Us ) )
% 0.25/0.57 => ( ( append2141280328od_a_a @ Xs2 @ Ys2 )
% 0.25/0.57 = ( append2141280328od_a_a @ Zs @ Us ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % append_eq_appendI
% 0.25/0.57 thf(fact_50_append__eq__appendI,axiom,
% 0.25/0.57 ! [Xs2: list_P1467822637od_a_a,Xs1: list_P1467822637od_a_a,Zs: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a,Us: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( ( append1574001858od_a_a @ Xs2 @ Xs1 )
% 0.25/0.57 = Zs )
% 0.25/0.57 => ( ( Ys2
% 0.25/0.57 = ( append1574001858od_a_a @ Xs1 @ Us ) )
% 0.25/0.57 => ( ( append1574001858od_a_a @ Xs2 @ Ys2 )
% 0.25/0.57 = ( append1574001858od_a_a @ Zs @ Us ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % append_eq_appendI
% 0.25/0.57 thf(fact_51_append__eq__append__conv2,axiom,
% 0.25/0.57 ! [Xs2: list_a,Ys2: list_a,Zs: list_a,Ts: list_a] :
% 0.25/0.57 ( ( ( append_a @ Xs2 @ Ys2 )
% 0.25/0.57 = ( append_a @ Zs @ Ts ) )
% 0.25/0.57 = ( ? [Us2: list_a] :
% 0.25/0.57 ( ( ( Xs2
% 0.25/0.57 = ( append_a @ Zs @ Us2 ) )
% 0.25/0.57 & ( ( append_a @ Us2 @ Ys2 )
% 0.25/0.57 = Ts ) )
% 0.25/0.57 | ( ( ( append_a @ Xs2 @ Us2 )
% 0.25/0.57 = Zs )
% 0.25/0.57 & ( Ys2
% 0.25/0.57 = ( append_a @ Us2 @ Ts ) ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % append_eq_append_conv2
% 0.25/0.57 thf(fact_52_append__eq__append__conv2,axiom,
% 0.25/0.57 ! [Xs2: list_P1891567085od_a_a,Ys2: list_P1891567085od_a_a,Zs: list_P1891567085od_a_a,Ts: list_P1891567085od_a_a] :
% 0.25/0.57 ( ( ( append864718978od_a_a @ Xs2 @ Ys2 )
% 0.25/0.57 = ( append864718978od_a_a @ Zs @ Ts ) )
% 0.25/0.57 = ( ? [Us2: list_P1891567085od_a_a] :
% 0.25/0.57 ( ( ( Xs2
% 0.25/0.57 = ( append864718978od_a_a @ Zs @ Us2 ) )
% 0.25/0.57 & ( ( append864718978od_a_a @ Us2 @ Ys2 )
% 0.25/0.57 = Ts ) )
% 0.25/0.57 | ( ( ( append864718978od_a_a @ Xs2 @ Us2 )
% 0.25/0.57 = Zs )
% 0.25/0.57 & ( Ys2
% 0.25/0.57 = ( append864718978od_a_a @ Us2 @ Ts ) ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % append_eq_append_conv2
% 0.25/0.57 thf(fact_53_append__eq__append__conv2,axiom,
% 0.25/0.57 ! [Xs2: list_l1108175539od_a_a,Ys2: list_l1108175539od_a_a,Zs: list_l1108175539od_a_a,Ts: list_l1108175539od_a_a] :
% 0.25/0.57 ( ( ( append2141280328od_a_a @ Xs2 @ Ys2 )
% 0.25/0.57 = ( append2141280328od_a_a @ Zs @ Ts ) )
% 0.25/0.57 = ( ? [Us2: list_l1108175539od_a_a] :
% 0.25/0.57 ( ( ( Xs2
% 0.25/0.57 = ( append2141280328od_a_a @ Zs @ Us2 ) )
% 0.25/0.57 & ( ( append2141280328od_a_a @ Us2 @ Ys2 )
% 0.25/0.57 = Ts ) )
% 0.25/0.57 | ( ( ( append2141280328od_a_a @ Xs2 @ Us2 )
% 0.25/0.57 = Zs )
% 0.25/0.57 & ( Ys2
% 0.25/0.57 = ( append2141280328od_a_a @ Us2 @ Ts ) ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % append_eq_append_conv2
% 0.25/0.57 thf(fact_54_append__eq__append__conv2,axiom,
% 0.25/0.57 ! [Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a,Zs: list_P1467822637od_a_a,Ts: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( ( append1574001858od_a_a @ Xs2 @ Ys2 )
% 0.25/0.57 = ( append1574001858od_a_a @ Zs @ Ts ) )
% 0.25/0.57 = ( ? [Us2: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( ( Xs2
% 0.25/0.57 = ( append1574001858od_a_a @ Zs @ Us2 ) )
% 0.25/0.57 & ( ( append1574001858od_a_a @ Us2 @ Ys2 )
% 0.25/0.57 = Ts ) )
% 0.25/0.57 | ( ( ( append1574001858od_a_a @ Xs2 @ Us2 )
% 0.25/0.57 = Zs )
% 0.25/0.57 & ( Ys2
% 0.25/0.57 = ( append1574001858od_a_a @ Us2 @ Ts ) ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % append_eq_append_conv2
% 0.25/0.57 thf(fact_55_old_Oprod_Oinducts,axiom,
% 0.25/0.57 ! [P2: produc657167928_a_a_a > $o,Prod: produc657167928_a_a_a] :
% 0.25/0.57 ( ! [A3: list_P1467822637od_a_a,B3: a] : ( P2 @ ( produc998622632_a_a_a @ A3 @ B3 ) )
% 0.25/0.57 => ( P2 @ Prod ) ) ).
% 0.25/0.57
% 0.25/0.57 % old.prod.inducts
% 0.25/0.57 thf(fact_56_old_Oprod_Oinducts,axiom,
% 0.25/0.57 ! [P2: produc864062247list_a > $o,Prod: produc864062247list_a] :
% 0.25/0.57 ( ! [A3: list_a,B3: list_a] : ( P2 @ ( produc1448356631list_a @ A3 @ B3 ) )
% 0.25/0.57 => ( P2 @ Prod ) ) ).
% 0.25/0.57
% 0.25/0.57 % old.prod.inducts
% 0.25/0.57 thf(fact_57_old_Oprod_Oinducts,axiom,
% 0.25/0.57 ! [P2: produc501911462od_a_a > $o,Prod: produc501911462od_a_a] :
% 0.25/0.57 ( ! [A3: product_prod_a_a > product_prod_a_a > $o,B3: list_P1467822637od_a_a] : ( P2 @ ( produc214132118od_a_a @ A3 @ B3 ) )
% 0.25/0.57 => ( P2 @ Prod ) ) ).
% 0.25/0.57
% 0.25/0.57 % old.prod.inducts
% 0.25/0.57 thf(fact_58_old_Oprod_Oinducts,axiom,
% 0.25/0.57 ! [P2: produc1197928545_a_a_a > $o,Prod: produc1197928545_a_a_a] :
% 0.25/0.57 ( ! [A3: a,B3: produc657167928_a_a_a] : ( P2 @ ( produc1440321489_a_a_a @ A3 @ B3 ) )
% 0.25/0.57 => ( P2 @ Prod ) ) ).
% 0.25/0.57
% 0.25/0.57 % old.prod.inducts
% 0.25/0.57 thf(fact_59_old_Oprod_Oinducts,axiom,
% 0.25/0.57 ! [P2: produc1701253078od_a_a > $o,Prod: produc1701253078od_a_a] :
% 0.25/0.57 ( ! [A3: a,B3: list_P1467822637od_a_a] : ( P2 @ ( produc575024326od_a_a @ A3 @ B3 ) )
% 0.25/0.57 => ( P2 @ Prod ) ) ).
% 0.25/0.57
% 0.25/0.57 % old.prod.inducts
% 0.25/0.57 thf(fact_60_old_Oprod_Oinducts,axiom,
% 0.25/0.57 ! [P2: product_prod_a_a > $o,Prod: product_prod_a_a] :
% 0.25/0.57 ( ! [A3: a,B3: a] : ( P2 @ ( product_Pair_a_a @ A3 @ B3 ) )
% 0.25/0.57 => ( P2 @ Prod ) ) ).
% 0.25/0.57
% 0.25/0.57 % old.prod.inducts
% 0.25/0.57 thf(fact_61_old_Oprod_Oexhaust,axiom,
% 0.25/0.57 ! [Y3: produc657167928_a_a_a] :
% 0.25/0.57 ~ ! [A3: list_P1467822637od_a_a,B3: a] :
% 0.25/0.57 ( Y3
% 0.25/0.57 != ( produc998622632_a_a_a @ A3 @ B3 ) ) ).
% 0.25/0.57
% 0.25/0.57 % old.prod.exhaust
% 0.25/0.57 thf(fact_62_old_Oprod_Oexhaust,axiom,
% 0.25/0.57 ! [Y3: produc864062247list_a] :
% 0.25/0.57 ~ ! [A3: list_a,B3: list_a] :
% 0.25/0.57 ( Y3
% 0.25/0.57 != ( produc1448356631list_a @ A3 @ B3 ) ) ).
% 0.25/0.57
% 0.25/0.57 % old.prod.exhaust
% 0.25/0.57 thf(fact_63_old_Oprod_Oexhaust,axiom,
% 0.25/0.57 ! [Y3: produc501911462od_a_a] :
% 0.25/0.57 ~ ! [A3: product_prod_a_a > product_prod_a_a > $o,B3: list_P1467822637od_a_a] :
% 0.25/0.57 ( Y3
% 0.25/0.57 != ( produc214132118od_a_a @ A3 @ B3 ) ) ).
% 0.25/0.57
% 0.25/0.57 % old.prod.exhaust
% 0.25/0.57 thf(fact_64_old_Oprod_Oexhaust,axiom,
% 0.25/0.57 ! [Y3: produc1197928545_a_a_a] :
% 0.25/0.57 ~ ! [A3: a,B3: produc657167928_a_a_a] :
% 0.25/0.57 ( Y3
% 0.25/0.57 != ( produc1440321489_a_a_a @ A3 @ B3 ) ) ).
% 0.25/0.57
% 0.25/0.57 % old.prod.exhaust
% 0.25/0.57 thf(fact_65_old_Oprod_Oexhaust,axiom,
% 0.25/0.57 ! [Y3: produc1701253078od_a_a] :
% 0.25/0.57 ~ ! [A3: a,B3: list_P1467822637od_a_a] :
% 0.25/0.57 ( Y3
% 0.25/0.57 != ( produc575024326od_a_a @ A3 @ B3 ) ) ).
% 0.25/0.57
% 0.25/0.57 % old.prod.exhaust
% 0.25/0.57 thf(fact_66_old_Oprod_Oexhaust,axiom,
% 0.25/0.57 ! [Y3: product_prod_a_a] :
% 0.25/0.57 ~ ! [A3: a,B3: a] :
% 0.25/0.57 ( Y3
% 0.25/0.57 != ( product_Pair_a_a @ A3 @ B3 ) ) ).
% 0.25/0.57
% 0.25/0.57 % old.prod.exhaust
% 0.25/0.57 thf(fact_67_prod__induct3,axiom,
% 0.25/0.57 ! [P2: produc1197928545_a_a_a > $o,X3: produc1197928545_a_a_a] :
% 0.25/0.57 ( ! [A3: a,B3: list_P1467822637od_a_a,C2: a] : ( P2 @ ( produc1440321489_a_a_a @ A3 @ ( produc998622632_a_a_a @ B3 @ C2 ) ) )
% 0.25/0.57 => ( P2 @ X3 ) ) ).
% 0.25/0.57
% 0.25/0.57 % prod_induct3
% 0.25/0.57 thf(fact_68_prod__cases3,axiom,
% 0.25/0.57 ! [Y3: produc1197928545_a_a_a] :
% 0.25/0.57 ~ ! [A3: a,B3: list_P1467822637od_a_a,C2: a] :
% 0.25/0.57 ( Y3
% 0.25/0.57 != ( produc1440321489_a_a_a @ A3 @ ( produc998622632_a_a_a @ B3 @ C2 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % prod_cases3
% 0.25/0.57 thf(fact_69_Pair__inject,axiom,
% 0.25/0.57 ! [A: list_P1467822637od_a_a,B: a,A2: list_P1467822637od_a_a,B2: a] :
% 0.25/0.57 ( ( ( produc998622632_a_a_a @ A @ B )
% 0.25/0.57 = ( produc998622632_a_a_a @ A2 @ B2 ) )
% 0.25/0.57 => ~ ( ( A = A2 )
% 0.25/0.57 => ( B != B2 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % Pair_inject
% 0.25/0.57 thf(fact_70_Pair__inject,axiom,
% 0.25/0.57 ! [A: list_a,B: list_a,A2: list_a,B2: list_a] :
% 0.25/0.57 ( ( ( produc1448356631list_a @ A @ B )
% 0.25/0.57 = ( produc1448356631list_a @ A2 @ B2 ) )
% 0.25/0.57 => ~ ( ( A = A2 )
% 0.25/0.57 => ( B != B2 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % Pair_inject
% 0.25/0.57 thf(fact_71_Pair__inject,axiom,
% 0.25/0.57 ! [A: product_prod_a_a > product_prod_a_a > $o,B: list_P1467822637od_a_a,A2: product_prod_a_a > product_prod_a_a > $o,B2: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( ( produc214132118od_a_a @ A @ B )
% 0.25/0.57 = ( produc214132118od_a_a @ A2 @ B2 ) )
% 0.25/0.57 => ~ ( ( A = A2 )
% 0.25/0.57 => ( B != B2 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % Pair_inject
% 0.25/0.57 thf(fact_72_Pair__inject,axiom,
% 0.25/0.57 ! [A: a,B: produc657167928_a_a_a,A2: a,B2: produc657167928_a_a_a] :
% 0.25/0.57 ( ( ( produc1440321489_a_a_a @ A @ B )
% 0.25/0.57 = ( produc1440321489_a_a_a @ A2 @ B2 ) )
% 0.25/0.57 => ~ ( ( A = A2 )
% 0.25/0.57 => ( B != B2 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % Pair_inject
% 0.25/0.57 thf(fact_73_Pair__inject,axiom,
% 0.25/0.57 ! [A: a,B: list_P1467822637od_a_a,A2: a,B2: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( ( produc575024326od_a_a @ A @ B )
% 0.25/0.57 = ( produc575024326od_a_a @ A2 @ B2 ) )
% 0.25/0.57 => ~ ( ( A = A2 )
% 0.25/0.57 => ( B != B2 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % Pair_inject
% 0.25/0.57 thf(fact_74_Pair__inject,axiom,
% 0.25/0.57 ! [A: a,B: a,A2: a,B2: a] :
% 0.25/0.57 ( ( ( product_Pair_a_a @ A @ B )
% 0.25/0.57 = ( product_Pair_a_a @ A2 @ B2 ) )
% 0.25/0.57 => ~ ( ( A = A2 )
% 0.25/0.57 => ( B != B2 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % Pair_inject
% 0.25/0.57 thf(fact_75_prod__cases,axiom,
% 0.25/0.57 ! [P2: produc657167928_a_a_a > $o,P3: produc657167928_a_a_a] :
% 0.25/0.57 ( ! [A3: list_P1467822637od_a_a,B3: a] : ( P2 @ ( produc998622632_a_a_a @ A3 @ B3 ) )
% 0.25/0.57 => ( P2 @ P3 ) ) ).
% 0.25/0.57
% 0.25/0.57 % prod_cases
% 0.25/0.57 thf(fact_76_prod__cases,axiom,
% 0.25/0.57 ! [P2: produc864062247list_a > $o,P3: produc864062247list_a] :
% 0.25/0.57 ( ! [A3: list_a,B3: list_a] : ( P2 @ ( produc1448356631list_a @ A3 @ B3 ) )
% 0.25/0.57 => ( P2 @ P3 ) ) ).
% 0.25/0.57
% 0.25/0.57 % prod_cases
% 0.25/0.57 thf(fact_77_prod__cases,axiom,
% 0.25/0.57 ! [P2: produc501911462od_a_a > $o,P3: produc501911462od_a_a] :
% 0.25/0.57 ( ! [A3: product_prod_a_a > product_prod_a_a > $o,B3: list_P1467822637od_a_a] : ( P2 @ ( produc214132118od_a_a @ A3 @ B3 ) )
% 0.25/0.57 => ( P2 @ P3 ) ) ).
% 0.25/0.57
% 0.25/0.57 % prod_cases
% 0.25/0.57 thf(fact_78_prod__cases,axiom,
% 0.25/0.57 ! [P2: produc1197928545_a_a_a > $o,P3: produc1197928545_a_a_a] :
% 0.25/0.57 ( ! [A3: a,B3: produc657167928_a_a_a] : ( P2 @ ( produc1440321489_a_a_a @ A3 @ B3 ) )
% 0.25/0.57 => ( P2 @ P3 ) ) ).
% 0.25/0.57
% 0.25/0.57 % prod_cases
% 0.25/0.57 thf(fact_79_prod__cases,axiom,
% 0.25/0.57 ! [P2: produc1701253078od_a_a > $o,P3: produc1701253078od_a_a] :
% 0.25/0.57 ( ! [A3: a,B3: list_P1467822637od_a_a] : ( P2 @ ( produc575024326od_a_a @ A3 @ B3 ) )
% 0.25/0.57 => ( P2 @ P3 ) ) ).
% 0.25/0.57
% 0.25/0.57 % prod_cases
% 0.25/0.57 thf(fact_80_prod__cases,axiom,
% 0.25/0.57 ! [P2: product_prod_a_a > $o,P3: product_prod_a_a] :
% 0.25/0.57 ( ! [A3: a,B3: a] : ( P2 @ ( product_Pair_a_a @ A3 @ B3 ) )
% 0.25/0.57 => ( P2 @ P3 ) ) ).
% 0.25/0.57
% 0.25/0.57 % prod_cases
% 0.25/0.57 thf(fact_81_surj__pair,axiom,
% 0.25/0.57 ! [P3: produc657167928_a_a_a] :
% 0.25/0.57 ? [X4: list_P1467822637od_a_a,Y4: a] :
% 0.25/0.57 ( P3
% 0.25/0.57 = ( produc998622632_a_a_a @ X4 @ Y4 ) ) ).
% 0.25/0.57
% 0.25/0.57 % surj_pair
% 0.25/0.57 thf(fact_82_surj__pair,axiom,
% 0.25/0.57 ! [P3: produc864062247list_a] :
% 0.25/0.57 ? [X4: list_a,Y4: list_a] :
% 0.25/0.57 ( P3
% 0.25/0.57 = ( produc1448356631list_a @ X4 @ Y4 ) ) ).
% 0.25/0.57
% 0.25/0.57 % surj_pair
% 0.25/0.57 thf(fact_83_surj__pair,axiom,
% 0.25/0.57 ! [P3: produc501911462od_a_a] :
% 0.25/0.57 ? [X4: product_prod_a_a > product_prod_a_a > $o,Y4: list_P1467822637od_a_a] :
% 0.25/0.57 ( P3
% 0.25/0.57 = ( produc214132118od_a_a @ X4 @ Y4 ) ) ).
% 0.25/0.57
% 0.25/0.57 % surj_pair
% 0.25/0.57 thf(fact_84_surj__pair,axiom,
% 0.25/0.57 ! [P3: produc1197928545_a_a_a] :
% 0.25/0.57 ? [X4: a,Y4: produc657167928_a_a_a] :
% 0.25/0.57 ( P3
% 0.25/0.57 = ( produc1440321489_a_a_a @ X4 @ Y4 ) ) ).
% 0.25/0.57
% 0.25/0.57 % surj_pair
% 0.25/0.57 thf(fact_85_surj__pair,axiom,
% 0.25/0.57 ! [P3: produc1701253078od_a_a] :
% 0.25/0.57 ? [X4: a,Y4: list_P1467822637od_a_a] :
% 0.25/0.57 ( P3
% 0.25/0.57 = ( produc575024326od_a_a @ X4 @ Y4 ) ) ).
% 0.25/0.57
% 0.25/0.57 % surj_pair
% 0.25/0.57 thf(fact_86_surj__pair,axiom,
% 0.25/0.57 ! [P3: product_prod_a_a] :
% 0.25/0.57 ? [X4: a,Y4: a] :
% 0.25/0.57 ( P3
% 0.25/0.57 = ( product_Pair_a_a @ X4 @ Y4 ) ) ).
% 0.25/0.57
% 0.25/0.57 % surj_pair
% 0.25/0.57 thf(fact_87_not__Cons__self2,axiom,
% 0.25/0.57 ! [X3: a,Xs2: list_a] :
% 0.25/0.57 ( ( cons_a @ X3 @ Xs2 )
% 0.25/0.57 != Xs2 ) ).
% 0.25/0.57
% 0.25/0.57 % not_Cons_self2
% 0.25/0.57 thf(fact_88_not__Cons__self2,axiom,
% 0.25/0.57 ! [X3: produc1572603623od_a_a,Xs2: list_P1891567085od_a_a] :
% 0.25/0.57 ( ( cons_P1070399645od_a_a @ X3 @ Xs2 )
% 0.25/0.57 != Xs2 ) ).
% 0.25/0.57
% 0.25/0.57 % not_Cons_self2
% 0.25/0.57 thf(fact_89_not__Cons__self2,axiom,
% 0.25/0.57 ! [X3: list_P1467822637od_a_a,Xs2: list_l1108175539od_a_a] :
% 0.25/0.57 ( ( cons_l724116707od_a_a @ X3 @ Xs2 )
% 0.25/0.57 != Xs2 ) ).
% 0.25/0.57
% 0.25/0.57 % not_Cons_self2
% 0.25/0.57 thf(fact_90_not__Cons__self2,axiom,
% 0.25/0.57 ! [X3: a > nat,Xs2: list_a_nat] :
% 0.25/0.57 ( ( cons_a_nat @ X3 @ Xs2 )
% 0.25/0.57 != Xs2 ) ).
% 0.25/0.57
% 0.25/0.57 % not_Cons_self2
% 0.25/0.57 thf(fact_91_not__Cons__self2,axiom,
% 0.25/0.57 ! [X3: product_prod_a_a,Xs2: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( cons_P1921020637od_a_a @ X3 @ Xs2 )
% 0.25/0.57 != Xs2 ) ).
% 0.25/0.57
% 0.25/0.57 % not_Cons_self2
% 0.25/0.57 thf(fact_92_bind__simps_I2_J,axiom,
% 0.25/0.57 ! [X3: product_prod_a_a,Xs2: list_P1467822637od_a_a,F: product_prod_a_a > list_P1467822637od_a_a] :
% 0.25/0.57 ( ( bind_P1783625031od_a_a @ ( cons_P1921020637od_a_a @ X3 @ Xs2 ) @ F )
% 0.25/0.57 = ( append1574001858od_a_a @ ( F @ X3 ) @ ( bind_P1783625031od_a_a @ Xs2 @ F ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % bind_simps(2)
% 0.25/0.57 thf(fact_93_bind__simps_I2_J,axiom,
% 0.25/0.57 ! [X3: a,Xs2: list_a,F: a > list_a] :
% 0.25/0.57 ( ( bind_a_a @ ( cons_a @ X3 @ Xs2 ) @ F )
% 0.25/0.57 = ( append_a @ ( F @ X3 ) @ ( bind_a_a @ Xs2 @ F ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % bind_simps(2)
% 0.25/0.57 thf(fact_94_bind__simps_I2_J,axiom,
% 0.25/0.57 ! [X3: product_prod_a_a,Xs2: list_P1467822637od_a_a,F: product_prod_a_a > list_a] :
% 0.25/0.57 ( ( bind_P293964574_a_a_a @ ( cons_P1921020637od_a_a @ X3 @ Xs2 ) @ F )
% 0.25/0.57 = ( append_a @ ( F @ X3 ) @ ( bind_P293964574_a_a_a @ Xs2 @ F ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % bind_simps(2)
% 0.25/0.57 thf(fact_95_bind__simps_I2_J,axiom,
% 0.25/0.57 ! [X3: a,Xs2: list_a,F: a > list_P1467822637od_a_a] :
% 0.25/0.57 ( ( bind_a1679112752od_a_a @ ( cons_a @ X3 @ Xs2 ) @ F )
% 0.25/0.57 = ( append1574001858od_a_a @ ( F @ X3 ) @ ( bind_a1679112752od_a_a @ Xs2 @ F ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % bind_simps(2)
% 0.25/0.57 thf(fact_96_bind__simps_I2_J,axiom,
% 0.25/0.57 ! [X3: a > nat,Xs2: list_a_nat,F: ( a > nat ) > list_a] :
% 0.25/0.57 ( ( bind_a_nat_a @ ( cons_a_nat @ X3 @ Xs2 ) @ F )
% 0.25/0.57 = ( append_a @ ( F @ X3 ) @ ( bind_a_nat_a @ Xs2 @ F ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % bind_simps(2)
% 0.25/0.57 thf(fact_97_bind__simps_I2_J,axiom,
% 0.25/0.57 ! [X3: a,Xs2: list_a,F: a > list_l1108175539od_a_a] :
% 0.25/0.57 ( ( bind_a883992246od_a_a @ ( cons_a @ X3 @ Xs2 ) @ F )
% 0.25/0.57 = ( append2141280328od_a_a @ ( F @ X3 ) @ ( bind_a883992246od_a_a @ Xs2 @ F ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % bind_simps(2)
% 0.25/0.57 thf(fact_98_bind__simps_I2_J,axiom,
% 0.25/0.57 ! [X3: list_P1467822637od_a_a,Xs2: list_l1108175539od_a_a,F: list_P1467822637od_a_a > list_a] :
% 0.25/0.57 ( ( bind_l1307590552_a_a_a @ ( cons_l724116707od_a_a @ X3 @ Xs2 ) @ F )
% 0.25/0.57 = ( append_a @ ( F @ X3 ) @ ( bind_l1307590552_a_a_a @ Xs2 @ F ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % bind_simps(2)
% 0.25/0.57 thf(fact_99_bind__simps_I2_J,axiom,
% 0.25/0.57 ! [X3: a > nat,Xs2: list_a_nat,F: ( a > nat ) > list_P1467822637od_a_a] :
% 0.25/0.57 ( ( bind_a1190333103od_a_a @ ( cons_a_nat @ X3 @ Xs2 ) @ F )
% 0.25/0.57 = ( append1574001858od_a_a @ ( F @ X3 ) @ ( bind_a1190333103od_a_a @ Xs2 @ F ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % bind_simps(2)
% 0.25/0.57 thf(fact_100_bind__simps_I2_J,axiom,
% 0.25/0.57 ! [X3: product_prod_a_a,Xs2: list_P1467822637od_a_a,F: product_prod_a_a > list_l1108175539od_a_a] :
% 0.25/0.57 ( ( bind_P240085581od_a_a @ ( cons_P1921020637od_a_a @ X3 @ Xs2 ) @ F )
% 0.25/0.57 = ( append2141280328od_a_a @ ( F @ X3 ) @ ( bind_P240085581od_a_a @ Xs2 @ F ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % bind_simps(2)
% 0.25/0.57 thf(fact_101_bind__simps_I2_J,axiom,
% 0.25/0.57 ! [X3: list_P1467822637od_a_a,Xs2: list_l1108175539od_a_a,F: list_P1467822637od_a_a > list_P1467822637od_a_a] :
% 0.25/0.57 ( ( bind_l618536897od_a_a @ ( cons_l724116707od_a_a @ X3 @ Xs2 ) @ F )
% 0.25/0.57 = ( append1574001858od_a_a @ ( F @ X3 ) @ ( bind_l618536897od_a_a @ Xs2 @ F ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % bind_simps(2)
% 0.25/0.57 thf(fact_102_maps__simps_I1_J,axiom,
% 0.25/0.57 ! [F: product_prod_a_a > list_P1467822637od_a_a,X3: product_prod_a_a,Xs2: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( maps_P1529886977od_a_a @ F @ ( cons_P1921020637od_a_a @ X3 @ Xs2 ) )
% 0.25/0.57 = ( append1574001858od_a_a @ ( F @ X3 ) @ ( maps_P1529886977od_a_a @ F @ Xs2 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % maps_simps(1)
% 0.25/0.57 thf(fact_103_maps__simps_I1_J,axiom,
% 0.25/0.57 ! [F: a > list_a,X3: a,Xs2: list_a] :
% 0.25/0.57 ( ( maps_a_a @ F @ ( cons_a @ X3 @ Xs2 ) )
% 0.25/0.57 = ( append_a @ ( F @ X3 ) @ ( maps_a_a @ F @ Xs2 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % maps_simps(1)
% 0.25/0.57 thf(fact_104_maps__simps_I1_J,axiom,
% 0.25/0.57 ! [F: product_prod_a_a > list_a,X3: product_prod_a_a,Xs2: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( maps_P321755352_a_a_a @ F @ ( cons_P1921020637od_a_a @ X3 @ Xs2 ) )
% 0.25/0.57 = ( append_a @ ( F @ X3 ) @ ( maps_P321755352_a_a_a @ F @ Xs2 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % maps_simps(1)
% 0.25/0.57 thf(fact_105_maps__simps_I1_J,axiom,
% 0.25/0.57 ! [F: a > list_P1467822637od_a_a,X3: a,Xs2: list_a] :
% 0.25/0.57 ( ( maps_a1706903530od_a_a @ F @ ( cons_a @ X3 @ Xs2 ) )
% 0.25/0.57 = ( append1574001858od_a_a @ ( F @ X3 ) @ ( maps_a1706903530od_a_a @ F @ Xs2 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % maps_simps(1)
% 0.25/0.57 thf(fact_106_maps__simps_I1_J,axiom,
% 0.25/0.57 ! [F: ( a > nat ) > list_a,X3: a > nat,Xs2: list_a_nat] :
% 0.25/0.57 ( ( maps_a_nat_a @ F @ ( cons_a_nat @ X3 @ Xs2 ) )
% 0.25/0.57 = ( append_a @ ( F @ X3 ) @ ( maps_a_nat_a @ F @ Xs2 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % maps_simps(1)
% 0.25/0.57 thf(fact_107_maps__simps_I1_J,axiom,
% 0.25/0.57 ! [F: a > list_l1108175539od_a_a,X3: a,Xs2: list_a] :
% 0.25/0.57 ( ( maps_a667520880od_a_a @ F @ ( cons_a @ X3 @ Xs2 ) )
% 0.25/0.57 = ( append2141280328od_a_a @ ( F @ X3 ) @ ( maps_a667520880od_a_a @ F @ Xs2 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % maps_simps(1)
% 0.25/0.57 thf(fact_108_maps__simps_I1_J,axiom,
% 0.25/0.57 ! [F: list_P1467822637od_a_a > list_a,X3: list_P1467822637od_a_a,Xs2: list_l1108175539od_a_a] :
% 0.25/0.57 ( ( maps_l1091119186_a_a_a @ F @ ( cons_l724116707od_a_a @ X3 @ Xs2 ) )
% 0.25/0.57 = ( append_a @ ( F @ X3 ) @ ( maps_l1091119186_a_a_a @ F @ Xs2 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % maps_simps(1)
% 0.25/0.57 thf(fact_109_maps__simps_I1_J,axiom,
% 0.25/0.57 ! [F: ( a > nat ) > list_P1467822637od_a_a,X3: a > nat,Xs2: list_a_nat] :
% 0.25/0.57 ( ( maps_a836827497od_a_a @ F @ ( cons_a_nat @ X3 @ Xs2 ) )
% 0.25/0.57 = ( append1574001858od_a_a @ ( F @ X3 ) @ ( maps_a836827497od_a_a @ F @ Xs2 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % maps_simps(1)
% 0.25/0.57 thf(fact_110_maps__simps_I1_J,axiom,
% 0.25/0.57 ! [F: product_prod_a_a > list_l1108175539od_a_a,X3: product_prod_a_a,Xs2: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( maps_P739084551od_a_a @ F @ ( cons_P1921020637od_a_a @ X3 @ Xs2 ) )
% 0.25/0.57 = ( append2141280328od_a_a @ ( F @ X3 ) @ ( maps_P739084551od_a_a @ F @ Xs2 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % maps_simps(1)
% 0.25/0.57 thf(fact_111_maps__simps_I1_J,axiom,
% 0.25/0.57 ! [F: list_P1467822637od_a_a > list_P1467822637od_a_a,X3: list_P1467822637od_a_a,Xs2: list_l1108175539od_a_a] :
% 0.25/0.57 ( ( maps_l1117535867od_a_a @ F @ ( cons_l724116707od_a_a @ X3 @ Xs2 ) )
% 0.25/0.57 = ( append1574001858od_a_a @ ( F @ X3 ) @ ( maps_l1117535867od_a_a @ F @ Xs2 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % maps_simps(1)
% 0.25/0.57 thf(fact_112_lexord__append__left__rightI,axiom,
% 0.25/0.57 ! [A: produc1572603623od_a_a,B: produc1572603623od_a_a,R: set_Pr1295299783od_a_a,U: list_P1891567085od_a_a,X3: list_P1891567085od_a_a,Y3: list_P1891567085od_a_a] :
% 0.25/0.57 ( ( member1899387664od_a_a @ ( produc1935643479od_a_a @ A @ B ) @ R )
% 0.25/0.57 => ( member1254757008od_a_a @ ( produc461662679od_a_a @ ( append864718978od_a_a @ U @ ( cons_P1070399645od_a_a @ A @ X3 ) ) @ ( append864718978od_a_a @ U @ ( cons_P1070399645od_a_a @ B @ Y3 ) ) ) @ ( lexord931792858od_a_a @ R ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % lexord_append_left_rightI
% 0.25/0.57 thf(fact_113_lexord__append__left__rightI,axiom,
% 0.25/0.57 ! [A: list_P1467822637od_a_a,B: list_P1467822637od_a_a,R: set_Pr800560199od_a_a,U: list_l1108175539od_a_a,X3: list_l1108175539od_a_a,Y3: list_l1108175539od_a_a] :
% 0.25/0.57 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ A @ B ) @ R )
% 0.25/0.57 => ( member8108048od_a_a @ ( produc915218007od_a_a @ ( append2141280328od_a_a @ U @ ( cons_l724116707od_a_a @ A @ X3 ) ) @ ( append2141280328od_a_a @ U @ ( cons_l724116707od_a_a @ B @ Y3 ) ) ) @ ( lexord1284731808od_a_a @ R ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % lexord_append_left_rightI
% 0.25/0.57 thf(fact_114_lexord__append__left__rightI,axiom,
% 0.25/0.57 ! [A: a > nat,B: a > nat,R: set_Pr1940702919_a_nat,U: list_a_nat,X3: list_a_nat,Y3: list_a_nat] :
% 0.25/0.57 ( ( member125757712_a_nat @ ( produc1569872215_a_nat @ A @ B ) @ R )
% 0.25/0.57 => ( member688761744_a_nat @ ( produc1430747863_a_nat @ ( append_a_nat @ U @ ( cons_a_nat @ A @ X3 ) ) @ ( append_a_nat @ U @ ( cons_a_nat @ B @ Y3 ) ) ) @ ( lexord_a_nat @ R ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % lexord_append_left_rightI
% 0.25/0.57 thf(fact_115_lexord__append__left__rightI,axiom,
% 0.25/0.57 ! [A: list_a,B: list_a,R: set_Pr1971762695list_a,U: list_list_a,X3: list_list_a,Y3: list_list_a] :
% 0.25/0.57 ( ( member1250517072list_a @ ( produc1448356631list_a @ A @ B ) @ R )
% 0.25/0.57 => ( member888406864list_a @ ( produc2583831list_a @ ( append_list_a @ U @ ( cons_list_a @ A @ X3 ) ) @ ( append_list_a @ U @ ( cons_list_a @ B @ Y3 ) ) ) @ ( lexord_list_a @ R ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % lexord_append_left_rightI
% 0.25/0.57 thf(fact_116_lexord__append__left__rightI,axiom,
% 0.25/0.57 ! [A: product_prod_a_a,B: product_prod_a_a,R: set_Pr1948701895od_a_a,U: list_P1467822637od_a_a,X3: list_P1467822637od_a_a,Y3: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ B ) @ R )
% 0.25/0.57 => ( member1691432592od_a_a @ ( produc85179863od_a_a @ ( append1574001858od_a_a @ U @ ( cons_P1921020637od_a_a @ A @ X3 ) ) @ ( append1574001858od_a_a @ U @ ( cons_P1921020637od_a_a @ B @ Y3 ) ) ) @ ( lexord673907738od_a_a @ R ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % lexord_append_left_rightI
% 0.25/0.57 thf(fact_117_lexord__append__left__rightI,axiom,
% 0.25/0.57 ! [A: a,B: a,R: set_Product_prod_a_a,U: list_a,X3: list_a,Y3: list_a] :
% 0.25/0.57 ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ R )
% 0.25/0.57 => ( member1250517072list_a @ ( produc1448356631list_a @ ( append_a @ U @ ( cons_a @ A @ X3 ) ) @ ( append_a @ U @ ( cons_a @ B @ Y3 ) ) ) @ ( lexord_a @ R ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % lexord_append_left_rightI
% 0.25/0.57 thf(fact_118_zip__Cons__Cons,axiom,
% 0.25/0.57 ! [X3: a,Xs2: list_a,Y3: a,Ys2: list_a] :
% 0.25/0.57 ( ( zip_a_a @ ( cons_a @ X3 @ Xs2 ) @ ( cons_a @ Y3 @ Ys2 ) )
% 0.25/0.57 = ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ ( zip_a_a @ Xs2 @ Ys2 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % zip_Cons_Cons
% 0.25/0.57 thf(fact_119_zip__Cons__Cons,axiom,
% 0.25/0.57 ! [X3: product_prod_a_a,Xs2: list_P1467822637od_a_a,Y3: product_prod_a_a,Ys2: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( zip_Pr792472183od_a_a @ ( cons_P1921020637od_a_a @ X3 @ Xs2 ) @ ( cons_P1921020637od_a_a @ Y3 @ Ys2 ) )
% 0.25/0.57 = ( cons_P1070399645od_a_a @ ( produc1474507607od_a_a @ X3 @ Y3 ) @ ( zip_Pr792472183od_a_a @ Xs2 @ Ys2 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % zip_Cons_Cons
% 0.25/0.57 thf(fact_120_zip__Cons__Cons,axiom,
% 0.25/0.57 ! [X3: product_prod_a_a,Xs2: list_P1467822637od_a_a,Y3: a,Ys2: list_a] :
% 0.25/0.57 ( ( zip_Pr201224270_a_a_a @ ( cons_P1921020637od_a_a @ X3 @ Xs2 ) @ ( cons_a @ Y3 @ Ys2 ) )
% 0.25/0.57 = ( cons_P86081012_a_a_a @ ( produc2061588782_a_a_a @ X3 @ Y3 ) @ ( zip_Pr201224270_a_a_a @ Xs2 @ Ys2 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % zip_Cons_Cons
% 0.25/0.57 thf(fact_121_zip__Cons__Cons,axiom,
% 0.25/0.57 ! [X3: a,Xs2: list_a,Y3: product_prod_a_a,Ys2: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( zip_a_1586372448od_a_a @ ( cons_a @ X3 @ Xs2 ) @ ( cons_P1921020637od_a_a @ Y3 @ Ys2 ) )
% 0.25/0.57 = ( cons_P991044742od_a_a @ ( produc1299253312od_a_a @ X3 @ Y3 ) @ ( zip_a_1586372448od_a_a @ Xs2 @ Ys2 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % zip_Cons_Cons
% 0.25/0.57 thf(fact_122_zip__Cons__Cons,axiom,
% 0.25/0.57 ! [X3: a,Xs2: list_a,Y3: a > nat,Ys2: list_a_nat] :
% 0.25/0.57 ( ( zip_a_a_nat @ ( cons_a @ X3 @ Xs2 ) @ ( cons_a_nat @ Y3 @ Ys2 ) )
% 0.25/0.57 = ( cons_P1915851550_a_nat @ ( product_Pair_a_a_nat @ X3 @ Y3 ) @ ( zip_a_a_nat @ Xs2 @ Ys2 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % zip_Cons_Cons
% 0.25/0.57 thf(fact_123_zip__Cons__Cons,axiom,
% 0.25/0.57 ! [X3: a > nat,Xs2: list_a_nat,Y3: a,Ys2: list_a] :
% 0.25/0.57 ( ( zip_a_nat_a @ ( cons_a_nat @ X3 @ Xs2 ) @ ( cons_a @ Y3 @ Ys2 ) )
% 0.25/0.57 = ( cons_P896312284_nat_a @ ( product_Pair_a_nat_a @ X3 @ Y3 ) @ ( zip_a_nat_a @ Xs2 @ Ys2 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % zip_Cons_Cons
% 0.25/0.57 thf(fact_124_zip__Cons__Cons,axiom,
% 0.25/0.57 ! [X3: list_a,Xs2: list_list_a,Y3: list_a,Ys2: list_list_a] :
% 0.25/0.57 ( ( zip_list_a_list_a @ ( cons_list_a @ X3 @ Xs2 ) @ ( cons_list_a @ Y3 @ Ys2 ) )
% 0.25/0.57 = ( cons_P2080942813list_a @ ( produc1448356631list_a @ X3 @ Y3 ) @ ( zip_list_a_list_a @ Xs2 @ Ys2 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % zip_Cons_Cons
% 0.25/0.57 thf(fact_125_zip__Cons__Cons,axiom,
% 0.25/0.57 ! [X3: list_P1467822637od_a_a,Xs2: list_l1108175539od_a_a,Y3: a,Ys2: list_a] :
% 0.25/0.57 ( ( zip_li245157064_a_a_a @ ( cons_l724116707od_a_a @ X3 @ Xs2 ) @ ( cons_a @ Y3 @ Ys2 ) )
% 0.25/0.57 = ( cons_P169173742_a_a_a @ ( produc998622632_a_a_a @ X3 @ Y3 ) @ ( zip_li245157064_a_a_a @ Xs2 @ Ys2 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % zip_Cons_Cons
% 0.25/0.57 thf(fact_126_zip__Cons__Cons,axiom,
% 0.25/0.57 ! [X3: a,Xs2: list_a,Y3: list_P1467822637od_a_a,Ys2: list_l1108175539od_a_a] :
% 0.25/0.57 ( ( zip_a_1969042406od_a_a @ ( cons_a @ X3 @ Xs2 ) @ ( cons_l724116707od_a_a @ Y3 @ Ys2 ) )
% 0.25/0.57 = ( cons_P1213258892od_a_a @ ( produc575024326od_a_a @ X3 @ Y3 ) @ ( zip_a_1969042406od_a_a @ Xs2 @ Ys2 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % zip_Cons_Cons
% 0.25/0.57 thf(fact_127_zip__Cons__Cons,axiom,
% 0.25/0.57 ! [X3: product_prod_a_a,Xs2: list_P1467822637od_a_a,Y3: a > nat,Ys2: list_a_nat] :
% 0.25/0.57 ( ( zip_Pr24086287_a_nat @ ( cons_P1921020637od_a_a @ X3 @ Xs2 ) @ ( cons_a_nat @ Y3 @ Ys2 ) )
% 0.25/0.57 = ( cons_P659009461_a_nat @ ( produc825466863_a_nat @ X3 @ Y3 ) @ ( zip_Pr24086287_a_nat @ Xs2 @ Ys2 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % zip_Cons_Cons
% 0.25/0.57 thf(fact_128_listrel1I,axiom,
% 0.25/0.57 ! [X3: produc1572603623od_a_a,Y3: produc1572603623od_a_a,R: set_Pr1295299783od_a_a,Xs2: list_P1891567085od_a_a,Us: list_P1891567085od_a_a,Vs: list_P1891567085od_a_a,Ys2: list_P1891567085od_a_a] :
% 0.25/0.57 ( ( member1899387664od_a_a @ ( produc1935643479od_a_a @ X3 @ Y3 ) @ R )
% 0.25/0.57 => ( ( Xs2
% 0.25/0.57 = ( append864718978od_a_a @ Us @ ( cons_P1070399645od_a_a @ X3 @ Vs ) ) )
% 0.25/0.57 => ( ( Ys2
% 0.25/0.57 = ( append864718978od_a_a @ Us @ ( cons_P1070399645od_a_a @ Y3 @ Vs ) ) )
% 0.25/0.57 => ( member1254757008od_a_a @ ( produc461662679od_a_a @ Xs2 @ Ys2 ) @ ( listre1832537542od_a_a @ R ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % listrel1I
% 0.25/0.57 thf(fact_129_listrel1I,axiom,
% 0.25/0.57 ! [X3: list_P1467822637od_a_a,Y3: list_P1467822637od_a_a,R: set_Pr800560199od_a_a,Xs2: list_l1108175539od_a_a,Us: list_l1108175539od_a_a,Vs: list_l1108175539od_a_a,Ys2: list_l1108175539od_a_a] :
% 0.25/0.57 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ X3 @ Y3 ) @ R )
% 0.25/0.57 => ( ( Xs2
% 0.25/0.57 = ( append2141280328od_a_a @ Us @ ( cons_l724116707od_a_a @ X3 @ Vs ) ) )
% 0.25/0.57 => ( ( Ys2
% 0.25/0.57 = ( append2141280328od_a_a @ Us @ ( cons_l724116707od_a_a @ Y3 @ Vs ) ) )
% 0.25/0.57 => ( member8108048od_a_a @ ( produc915218007od_a_a @ Xs2 @ Ys2 ) @ ( listre651914124od_a_a @ R ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % listrel1I
% 0.25/0.57 thf(fact_130_listrel1I,axiom,
% 0.25/0.57 ! [X3: a > nat,Y3: a > nat,R: set_Pr1940702919_a_nat,Xs2: list_a_nat,Us: list_a_nat,Vs: list_a_nat,Ys2: list_a_nat] :
% 0.25/0.57 ( ( member125757712_a_nat @ ( produc1569872215_a_nat @ X3 @ Y3 ) @ R )
% 0.25/0.57 => ( ( Xs2
% 0.25/0.57 = ( append_a_nat @ Us @ ( cons_a_nat @ X3 @ Vs ) ) )
% 0.25/0.57 => ( ( Ys2
% 0.25/0.57 = ( append_a_nat @ Us @ ( cons_a_nat @ Y3 @ Vs ) ) )
% 0.25/0.57 => ( member688761744_a_nat @ ( produc1430747863_a_nat @ Xs2 @ Ys2 ) @ ( listrel1_a_nat @ R ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % listrel1I
% 0.25/0.57 thf(fact_131_listrel1I,axiom,
% 0.25/0.57 ! [X3: list_a,Y3: list_a,R: set_Pr1971762695list_a,Xs2: list_list_a,Us: list_list_a,Vs: list_list_a,Ys2: list_list_a] :
% 0.25/0.57 ( ( member1250517072list_a @ ( produc1448356631list_a @ X3 @ Y3 ) @ R )
% 0.25/0.57 => ( ( Xs2
% 0.25/0.57 = ( append_list_a @ Us @ ( cons_list_a @ X3 @ Vs ) ) )
% 0.25/0.57 => ( ( Ys2
% 0.25/0.57 = ( append_list_a @ Us @ ( cons_list_a @ Y3 @ Vs ) ) )
% 0.25/0.57 => ( member888406864list_a @ ( produc2583831list_a @ Xs2 @ Ys2 ) @ ( listrel1_list_a @ R ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % listrel1I
% 0.25/0.57 thf(fact_132_listrel1I,axiom,
% 0.25/0.57 ! [X3: product_prod_a_a,Y3: product_prod_a_a,R: set_Pr1948701895od_a_a,Xs2: list_P1467822637od_a_a,Us: list_P1467822637od_a_a,Vs: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X3 @ Y3 ) @ R )
% 0.25/0.57 => ( ( Xs2
% 0.25/0.57 = ( append1574001858od_a_a @ Us @ ( cons_P1921020637od_a_a @ X3 @ Vs ) ) )
% 0.25/0.57 => ( ( Ys2
% 0.25/0.57 = ( append1574001858od_a_a @ Us @ ( cons_P1921020637od_a_a @ Y3 @ Vs ) ) )
% 0.25/0.57 => ( member1691432592od_a_a @ ( produc85179863od_a_a @ Xs2 @ Ys2 ) @ ( listre944824838od_a_a @ R ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % listrel1I
% 0.25/0.57 thf(fact_133_listrel1I,axiom,
% 0.25/0.57 ! [X3: a,Y3: a,R: set_Product_prod_a_a,Xs2: list_a,Us: list_a,Vs: list_a,Ys2: list_a] :
% 0.25/0.57 ( ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ R )
% 0.25/0.57 => ( ( Xs2
% 0.25/0.57 = ( append_a @ Us @ ( cons_a @ X3 @ Vs ) ) )
% 0.25/0.57 => ( ( Ys2
% 0.25/0.57 = ( append_a @ Us @ ( cons_a @ Y3 @ Vs ) ) )
% 0.25/0.57 => ( member1250517072list_a @ ( produc1448356631list_a @ Xs2 @ Ys2 ) @ ( listrel1_a @ R ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % listrel1I
% 0.25/0.57 thf(fact_134_listrel1E,axiom,
% 0.25/0.57 ! [Xs2: list_P1891567085od_a_a,Ys2: list_P1891567085od_a_a,R: set_Pr1295299783od_a_a] :
% 0.25/0.57 ( ( member1254757008od_a_a @ ( produc461662679od_a_a @ Xs2 @ Ys2 ) @ ( listre1832537542od_a_a @ R ) )
% 0.25/0.57 => ~ ! [X4: produc1572603623od_a_a,Y4: produc1572603623od_a_a] :
% 0.25/0.57 ( ( member1899387664od_a_a @ ( produc1935643479od_a_a @ X4 @ Y4 ) @ R )
% 0.25/0.57 => ! [Us3: list_P1891567085od_a_a,Vs2: list_P1891567085od_a_a] :
% 0.25/0.57 ( ( Xs2
% 0.25/0.57 = ( append864718978od_a_a @ Us3 @ ( cons_P1070399645od_a_a @ X4 @ Vs2 ) ) )
% 0.25/0.57 => ( Ys2
% 0.25/0.57 != ( append864718978od_a_a @ Us3 @ ( cons_P1070399645od_a_a @ Y4 @ Vs2 ) ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % listrel1E
% 0.25/0.57 thf(fact_135_listrel1E,axiom,
% 0.25/0.57 ! [Xs2: list_l1108175539od_a_a,Ys2: list_l1108175539od_a_a,R: set_Pr800560199od_a_a] :
% 0.25/0.57 ( ( member8108048od_a_a @ ( produc915218007od_a_a @ Xs2 @ Ys2 ) @ ( listre651914124od_a_a @ R ) )
% 0.25/0.57 => ~ ! [X4: list_P1467822637od_a_a,Y4: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ X4 @ Y4 ) @ R )
% 0.25/0.57 => ! [Us3: list_l1108175539od_a_a,Vs2: list_l1108175539od_a_a] :
% 0.25/0.57 ( ( Xs2
% 0.25/0.57 = ( append2141280328od_a_a @ Us3 @ ( cons_l724116707od_a_a @ X4 @ Vs2 ) ) )
% 0.25/0.57 => ( Ys2
% 0.25/0.57 != ( append2141280328od_a_a @ Us3 @ ( cons_l724116707od_a_a @ Y4 @ Vs2 ) ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % listrel1E
% 0.25/0.57 thf(fact_136_listrel1E,axiom,
% 0.25/0.57 ! [Xs2: list_a_nat,Ys2: list_a_nat,R: set_Pr1940702919_a_nat] :
% 0.25/0.57 ( ( member688761744_a_nat @ ( produc1430747863_a_nat @ Xs2 @ Ys2 ) @ ( listrel1_a_nat @ R ) )
% 0.25/0.57 => ~ ! [X4: a > nat,Y4: a > nat] :
% 0.25/0.57 ( ( member125757712_a_nat @ ( produc1569872215_a_nat @ X4 @ Y4 ) @ R )
% 0.25/0.57 => ! [Us3: list_a_nat,Vs2: list_a_nat] :
% 0.25/0.57 ( ( Xs2
% 0.25/0.57 = ( append_a_nat @ Us3 @ ( cons_a_nat @ X4 @ Vs2 ) ) )
% 0.25/0.57 => ( Ys2
% 0.25/0.57 != ( append_a_nat @ Us3 @ ( cons_a_nat @ Y4 @ Vs2 ) ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % listrel1E
% 0.25/0.57 thf(fact_137_listrel1E,axiom,
% 0.25/0.57 ! [Xs2: list_list_a,Ys2: list_list_a,R: set_Pr1971762695list_a] :
% 0.25/0.57 ( ( member888406864list_a @ ( produc2583831list_a @ Xs2 @ Ys2 ) @ ( listrel1_list_a @ R ) )
% 0.25/0.57 => ~ ! [X4: list_a,Y4: list_a] :
% 0.25/0.57 ( ( member1250517072list_a @ ( produc1448356631list_a @ X4 @ Y4 ) @ R )
% 0.25/0.57 => ! [Us3: list_list_a,Vs2: list_list_a] :
% 0.25/0.57 ( ( Xs2
% 0.25/0.57 = ( append_list_a @ Us3 @ ( cons_list_a @ X4 @ Vs2 ) ) )
% 0.25/0.57 => ( Ys2
% 0.25/0.57 != ( append_list_a @ Us3 @ ( cons_list_a @ Y4 @ Vs2 ) ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % listrel1E
% 0.25/0.57 thf(fact_138_listrel1E,axiom,
% 0.25/0.57 ! [Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a,R: set_Pr1948701895od_a_a] :
% 0.25/0.57 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ Xs2 @ Ys2 ) @ ( listre944824838od_a_a @ R ) )
% 0.25/0.57 => ~ ! [X4: product_prod_a_a,Y4: product_prod_a_a] :
% 0.25/0.57 ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X4 @ Y4 ) @ R )
% 0.25/0.57 => ! [Us3: list_P1467822637od_a_a,Vs2: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( Xs2
% 0.25/0.57 = ( append1574001858od_a_a @ Us3 @ ( cons_P1921020637od_a_a @ X4 @ Vs2 ) ) )
% 0.25/0.57 => ( Ys2
% 0.25/0.57 != ( append1574001858od_a_a @ Us3 @ ( cons_P1921020637od_a_a @ Y4 @ Vs2 ) ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % listrel1E
% 0.25/0.57 thf(fact_139_listrel1E,axiom,
% 0.25/0.57 ! [Xs2: list_a,Ys2: list_a,R: set_Product_prod_a_a] :
% 0.25/0.57 ( ( member1250517072list_a @ ( produc1448356631list_a @ Xs2 @ Ys2 ) @ ( listrel1_a @ R ) )
% 0.25/0.57 => ~ ! [X4: a,Y4: a] :
% 0.25/0.57 ( ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y4 ) @ R )
% 0.25/0.57 => ! [Us3: list_a,Vs2: list_a] :
% 0.25/0.57 ( ( Xs2
% 0.25/0.57 = ( append_a @ Us3 @ ( cons_a @ X4 @ Vs2 ) ) )
% 0.25/0.57 => ( Ys2
% 0.25/0.57 != ( append_a @ Us3 @ ( cons_a @ Y4 @ Vs2 ) ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % listrel1E
% 0.25/0.57 thf(fact_140_member__rec_I1_J,axiom,
% 0.25/0.57 ! [X3: a,Xs2: list_a,Y3: a] :
% 0.25/0.57 ( ( member_a @ ( cons_a @ X3 @ Xs2 ) @ Y3 )
% 0.25/0.57 = ( ( X3 = Y3 )
% 0.25/0.57 | ( member_a @ Xs2 @ Y3 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % member_rec(1)
% 0.25/0.57 thf(fact_141_member__rec_I1_J,axiom,
% 0.25/0.57 ! [X3: produc1572603623od_a_a,Xs2: list_P1891567085od_a_a,Y3: produc1572603623od_a_a] :
% 0.25/0.57 ( ( member2070313346od_a_a @ ( cons_P1070399645od_a_a @ X3 @ Xs2 ) @ Y3 )
% 0.25/0.57 = ( ( X3 = Y3 )
% 0.25/0.57 | ( member2070313346od_a_a @ Xs2 @ Y3 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % member_rec(1)
% 0.25/0.57 thf(fact_142_member__rec_I1_J,axiom,
% 0.25/0.57 ! [X3: list_P1467822637od_a_a,Xs2: list_l1108175539od_a_a,Y3: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( member261538120od_a_a @ ( cons_l724116707od_a_a @ X3 @ Xs2 ) @ Y3 )
% 0.25/0.57 = ( ( X3 = Y3 )
% 0.25/0.57 | ( member261538120od_a_a @ Xs2 @ Y3 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % member_rec(1)
% 0.25/0.57 thf(fact_143_member__rec_I1_J,axiom,
% 0.25/0.57 ! [X3: a > nat,Xs2: list_a_nat,Y3: a > nat] :
% 0.25/0.57 ( ( member_a_nat @ ( cons_a_nat @ X3 @ Xs2 ) @ Y3 )
% 0.25/0.57 = ( ( X3 = Y3 )
% 0.25/0.57 | ( member_a_nat @ Xs2 @ Y3 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % member_rec(1)
% 0.25/0.57 thf(fact_144_member__rec_I1_J,axiom,
% 0.25/0.57 ! [X3: product_prod_a_a,Xs2: list_P1467822637od_a_a,Y3: product_prod_a_a] :
% 0.25/0.57 ( ( member1112491458od_a_a @ ( cons_P1921020637od_a_a @ X3 @ Xs2 ) @ Y3 )
% 0.25/0.57 = ( ( X3 = Y3 )
% 0.25/0.57 | ( member1112491458od_a_a @ Xs2 @ Y3 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % member_rec(1)
% 0.25/0.57 thf(fact_145_ssubst__Pair__rhs,axiom,
% 0.25/0.57 ! [R: list_P1467822637od_a_a,S: list_P1467822637od_a_a,R2: set_Pr800560199od_a_a,S2: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ R @ S ) @ R2 )
% 0.25/0.57 => ( ( S2 = S )
% 0.25/0.57 => ( member1691432592od_a_a @ ( produc85179863od_a_a @ R @ S2 ) @ R2 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % ssubst_Pair_rhs
% 0.25/0.57 thf(fact_146_ssubst__Pair__rhs,axiom,
% 0.25/0.57 ! [R: list_P1467822637od_a_a,S: a,R2: set_Pr1525541400_a_a_a,S2: a] :
% 0.25/0.57 ( ( member430654177_a_a_a @ ( produc998622632_a_a_a @ R @ S ) @ R2 )
% 0.25/0.57 => ( ( S2 = S )
% 0.25/0.57 => ( member430654177_a_a_a @ ( produc998622632_a_a_a @ R @ S2 ) @ R2 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % ssubst_Pair_rhs
% 0.25/0.57 thf(fact_147_ssubst__Pair__rhs,axiom,
% 0.25/0.57 ! [R: list_a,S: list_a,R2: set_Pr1971762695list_a,S2: list_a] :
% 0.25/0.57 ( ( member1250517072list_a @ ( produc1448356631list_a @ R @ S ) @ R2 )
% 0.25/0.57 => ( ( S2 = S )
% 0.25/0.57 => ( member1250517072list_a @ ( produc1448356631list_a @ R @ S2 ) @ R2 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % ssubst_Pair_rhs
% 0.25/0.57 thf(fact_148_ssubst__Pair__rhs,axiom,
% 0.25/0.57 ! [R: product_prod_a_a > product_prod_a_a > $o,S: list_P1467822637od_a_a,R2: set_Pr727105414od_a_a,S2: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( member372644687od_a_a @ ( produc214132118od_a_a @ R @ S ) @ R2 )
% 0.25/0.57 => ( ( S2 = S )
% 0.25/0.57 => ( member372644687od_a_a @ ( produc214132118od_a_a @ R @ S2 ) @ R2 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % ssubst_Pair_rhs
% 0.25/0.57 thf(fact_149_ssubst__Pair__rhs,axiom,
% 0.25/0.57 ! [R: a,S: produc657167928_a_a_a,R2: set_Pr110478017_a_a_a,S2: produc657167928_a_a_a] :
% 0.25/0.57 ( ( member1904151562_a_a_a @ ( produc1440321489_a_a_a @ R @ S ) @ R2 )
% 0.25/0.57 => ( ( S2 = S )
% 0.25/0.57 => ( member1904151562_a_a_a @ ( produc1440321489_a_a_a @ R @ S2 ) @ R2 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % ssubst_Pair_rhs
% 0.25/0.57 thf(fact_150_ssubst__Pair__rhs,axiom,
% 0.25/0.57 ! [R: a,S: list_P1467822637od_a_a,R2: set_Pr248149174od_a_a,S2: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( member1474739327od_a_a @ ( produc575024326od_a_a @ R @ S ) @ R2 )
% 0.25/0.57 => ( ( S2 = S )
% 0.25/0.57 => ( member1474739327od_a_a @ ( produc575024326od_a_a @ R @ S2 ) @ R2 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % ssubst_Pair_rhs
% 0.25/0.57 thf(fact_151_ssubst__Pair__rhs,axiom,
% 0.25/0.57 ! [R: a,S: a,R2: set_Product_prod_a_a,S2: a] :
% 0.25/0.57 ( ( member449909584od_a_a @ ( product_Pair_a_a @ R @ S ) @ R2 )
% 0.25/0.57 => ( ( S2 = S )
% 0.25/0.57 => ( member449909584od_a_a @ ( product_Pair_a_a @ R @ S2 ) @ R2 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % ssubst_Pair_rhs
% 0.25/0.57 thf(fact_152_subdivide_Oinduct,axiom,
% 0.25/0.57 ! [P2: pair_p1891813445t_unit > produc864062247list_a > list_a > $o,A0: pair_p1891813445t_unit,A1: produc864062247list_a,A22: list_a] :
% 0.25/0.57 ( ! [G: pair_p1891813445t_unit,U2: list_a,V: list_a,X_1: list_a] : ( P2 @ G @ ( produc1448356631list_a @ U2 @ V ) @ X_1 )
% 0.25/0.57 => ( P2 @ A0 @ A1 @ A22 ) ) ).
% 0.25/0.57
% 0.25/0.57 % subdivide.induct
% 0.25/0.57 thf(fact_153_subdivide_Oinduct,axiom,
% 0.25/0.57 ! [P2: pair_p125712459t_unit > product_prod_a_a > a > $o,A0: pair_p125712459t_unit,A1: product_prod_a_a,A22: a] :
% 0.25/0.57 ( ! [G: pair_p125712459t_unit,U2: a,V: a,X_1: a] : ( P2 @ G @ ( product_Pair_a_a @ U2 @ V ) @ X_1 )
% 0.25/0.57 => ( P2 @ A0 @ A1 @ A22 ) ) ).
% 0.25/0.57
% 0.25/0.57 % subdivide.induct
% 0.25/0.57 thf(fact_154_Cons__listrel1__Cons,axiom,
% 0.25/0.57 ! [X3: produc1572603623od_a_a,Xs2: list_P1891567085od_a_a,Y3: produc1572603623od_a_a,Ys2: list_P1891567085od_a_a,R: set_Pr1295299783od_a_a] :
% 0.25/0.57 ( ( member1254757008od_a_a @ ( produc461662679od_a_a @ ( cons_P1070399645od_a_a @ X3 @ Xs2 ) @ ( cons_P1070399645od_a_a @ Y3 @ Ys2 ) ) @ ( listre1832537542od_a_a @ R ) )
% 0.25/0.57 = ( ( ( member1899387664od_a_a @ ( produc1935643479od_a_a @ X3 @ Y3 ) @ R )
% 0.25/0.57 & ( Xs2 = Ys2 ) )
% 0.25/0.57 | ( ( X3 = Y3 )
% 0.25/0.57 & ( member1254757008od_a_a @ ( produc461662679od_a_a @ Xs2 @ Ys2 ) @ ( listre1832537542od_a_a @ R ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % Cons_listrel1_Cons
% 0.25/0.57 thf(fact_155_Cons__listrel1__Cons,axiom,
% 0.25/0.57 ! [X3: list_P1467822637od_a_a,Xs2: list_l1108175539od_a_a,Y3: list_P1467822637od_a_a,Ys2: list_l1108175539od_a_a,R: set_Pr800560199od_a_a] :
% 0.25/0.57 ( ( member8108048od_a_a @ ( produc915218007od_a_a @ ( cons_l724116707od_a_a @ X3 @ Xs2 ) @ ( cons_l724116707od_a_a @ Y3 @ Ys2 ) ) @ ( listre651914124od_a_a @ R ) )
% 0.25/0.57 = ( ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ X3 @ Y3 ) @ R )
% 0.25/0.57 & ( Xs2 = Ys2 ) )
% 0.25/0.57 | ( ( X3 = Y3 )
% 0.25/0.57 & ( member8108048od_a_a @ ( produc915218007od_a_a @ Xs2 @ Ys2 ) @ ( listre651914124od_a_a @ R ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % Cons_listrel1_Cons
% 0.25/0.57 thf(fact_156_Cons__listrel1__Cons,axiom,
% 0.25/0.57 ! [X3: a > nat,Xs2: list_a_nat,Y3: a > nat,Ys2: list_a_nat,R: set_Pr1940702919_a_nat] :
% 0.25/0.57 ( ( member688761744_a_nat @ ( produc1430747863_a_nat @ ( cons_a_nat @ X3 @ Xs2 ) @ ( cons_a_nat @ Y3 @ Ys2 ) ) @ ( listrel1_a_nat @ R ) )
% 0.25/0.57 = ( ( ( member125757712_a_nat @ ( produc1569872215_a_nat @ X3 @ Y3 ) @ R )
% 0.25/0.57 & ( Xs2 = Ys2 ) )
% 0.25/0.57 | ( ( X3 = Y3 )
% 0.25/0.57 & ( member688761744_a_nat @ ( produc1430747863_a_nat @ Xs2 @ Ys2 ) @ ( listrel1_a_nat @ R ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % Cons_listrel1_Cons
% 0.25/0.57 thf(fact_157_Cons__listrel1__Cons,axiom,
% 0.25/0.57 ! [X3: list_a,Xs2: list_list_a,Y3: list_a,Ys2: list_list_a,R: set_Pr1971762695list_a] :
% 0.25/0.57 ( ( member888406864list_a @ ( produc2583831list_a @ ( cons_list_a @ X3 @ Xs2 ) @ ( cons_list_a @ Y3 @ Ys2 ) ) @ ( listrel1_list_a @ R ) )
% 0.25/0.57 = ( ( ( member1250517072list_a @ ( produc1448356631list_a @ X3 @ Y3 ) @ R )
% 0.25/0.57 & ( Xs2 = Ys2 ) )
% 0.25/0.57 | ( ( X3 = Y3 )
% 0.25/0.57 & ( member888406864list_a @ ( produc2583831list_a @ Xs2 @ Ys2 ) @ ( listrel1_list_a @ R ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % Cons_listrel1_Cons
% 0.25/0.57 thf(fact_158_Cons__listrel1__Cons,axiom,
% 0.25/0.57 ! [X3: product_prod_a_a,Xs2: list_P1467822637od_a_a,Y3: product_prod_a_a,Ys2: list_P1467822637od_a_a,R: set_Pr1948701895od_a_a] :
% 0.25/0.57 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ ( cons_P1921020637od_a_a @ X3 @ Xs2 ) @ ( cons_P1921020637od_a_a @ Y3 @ Ys2 ) ) @ ( listre944824838od_a_a @ R ) )
% 0.25/0.57 = ( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X3 @ Y3 ) @ R )
% 0.25/0.57 & ( Xs2 = Ys2 ) )
% 0.25/0.57 | ( ( X3 = Y3 )
% 0.25/0.57 & ( member1691432592od_a_a @ ( produc85179863od_a_a @ Xs2 @ Ys2 ) @ ( listre944824838od_a_a @ R ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % Cons_listrel1_Cons
% 0.25/0.57 thf(fact_159_Cons__listrel1__Cons,axiom,
% 0.25/0.57 ! [X3: a,Xs2: list_a,Y3: a,Ys2: list_a,R: set_Product_prod_a_a] :
% 0.25/0.57 ( ( member1250517072list_a @ ( produc1448356631list_a @ ( cons_a @ X3 @ Xs2 ) @ ( cons_a @ Y3 @ Ys2 ) ) @ ( listrel1_a @ R ) )
% 0.25/0.57 = ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ R )
% 0.25/0.57 & ( Xs2 = Ys2 ) )
% 0.25/0.57 | ( ( X3 = Y3 )
% 0.25/0.57 & ( member1250517072list_a @ ( produc1448356631list_a @ Xs2 @ Ys2 ) @ ( listrel1_a @ R ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % Cons_listrel1_Cons
% 0.25/0.57 thf(fact_160_lexord__cons__cons,axiom,
% 0.25/0.57 ! [A: produc1572603623od_a_a,X3: list_P1891567085od_a_a,B: produc1572603623od_a_a,Y3: list_P1891567085od_a_a,R: set_Pr1295299783od_a_a] :
% 0.25/0.57 ( ( member1254757008od_a_a @ ( produc461662679od_a_a @ ( cons_P1070399645od_a_a @ A @ X3 ) @ ( cons_P1070399645od_a_a @ B @ Y3 ) ) @ ( lexord931792858od_a_a @ R ) )
% 0.25/0.57 = ( ( member1899387664od_a_a @ ( produc1935643479od_a_a @ A @ B ) @ R )
% 0.25/0.57 | ( ( A = B )
% 0.25/0.57 & ( member1254757008od_a_a @ ( produc461662679od_a_a @ X3 @ Y3 ) @ ( lexord931792858od_a_a @ R ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % lexord_cons_cons
% 0.25/0.57 thf(fact_161_lexord__cons__cons,axiom,
% 0.25/0.57 ! [A: list_P1467822637od_a_a,X3: list_l1108175539od_a_a,B: list_P1467822637od_a_a,Y3: list_l1108175539od_a_a,R: set_Pr800560199od_a_a] :
% 0.25/0.57 ( ( member8108048od_a_a @ ( produc915218007od_a_a @ ( cons_l724116707od_a_a @ A @ X3 ) @ ( cons_l724116707od_a_a @ B @ Y3 ) ) @ ( lexord1284731808od_a_a @ R ) )
% 0.25/0.57 = ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ A @ B ) @ R )
% 0.25/0.57 | ( ( A = B )
% 0.25/0.57 & ( member8108048od_a_a @ ( produc915218007od_a_a @ X3 @ Y3 ) @ ( lexord1284731808od_a_a @ R ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % lexord_cons_cons
% 0.25/0.57 thf(fact_162_lexord__cons__cons,axiom,
% 0.25/0.57 ! [A: a > nat,X3: list_a_nat,B: a > nat,Y3: list_a_nat,R: set_Pr1940702919_a_nat] :
% 0.25/0.57 ( ( member688761744_a_nat @ ( produc1430747863_a_nat @ ( cons_a_nat @ A @ X3 ) @ ( cons_a_nat @ B @ Y3 ) ) @ ( lexord_a_nat @ R ) )
% 0.25/0.57 = ( ( member125757712_a_nat @ ( produc1569872215_a_nat @ A @ B ) @ R )
% 0.25/0.57 | ( ( A = B )
% 0.25/0.57 & ( member688761744_a_nat @ ( produc1430747863_a_nat @ X3 @ Y3 ) @ ( lexord_a_nat @ R ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % lexord_cons_cons
% 0.25/0.57 thf(fact_163_lexord__cons__cons,axiom,
% 0.25/0.57 ! [A: list_a,X3: list_list_a,B: list_a,Y3: list_list_a,R: set_Pr1971762695list_a] :
% 0.25/0.57 ( ( member888406864list_a @ ( produc2583831list_a @ ( cons_list_a @ A @ X3 ) @ ( cons_list_a @ B @ Y3 ) ) @ ( lexord_list_a @ R ) )
% 0.25/0.57 = ( ( member1250517072list_a @ ( produc1448356631list_a @ A @ B ) @ R )
% 0.25/0.57 | ( ( A = B )
% 0.25/0.57 & ( member888406864list_a @ ( produc2583831list_a @ X3 @ Y3 ) @ ( lexord_list_a @ R ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % lexord_cons_cons
% 0.25/0.57 thf(fact_164_lexord__cons__cons,axiom,
% 0.25/0.57 ! [A: product_prod_a_a,X3: list_P1467822637od_a_a,B: product_prod_a_a,Y3: list_P1467822637od_a_a,R: set_Pr1948701895od_a_a] :
% 0.25/0.57 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ ( cons_P1921020637od_a_a @ A @ X3 ) @ ( cons_P1921020637od_a_a @ B @ Y3 ) ) @ ( lexord673907738od_a_a @ R ) )
% 0.25/0.57 = ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ B ) @ R )
% 0.25/0.57 | ( ( A = B )
% 0.25/0.57 & ( member1691432592od_a_a @ ( produc85179863od_a_a @ X3 @ Y3 ) @ ( lexord673907738od_a_a @ R ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % lexord_cons_cons
% 0.25/0.57 thf(fact_165_lexord__cons__cons,axiom,
% 0.25/0.57 ! [A: a,X3: list_a,B: a,Y3: list_a,R: set_Product_prod_a_a] :
% 0.25/0.57 ( ( member1250517072list_a @ ( produc1448356631list_a @ ( cons_a @ A @ X3 ) @ ( cons_a @ B @ Y3 ) ) @ ( lexord_a @ R ) )
% 0.25/0.57 = ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ R )
% 0.25/0.57 | ( ( A = B )
% 0.25/0.57 & ( member1250517072list_a @ ( produc1448356631list_a @ X3 @ Y3 ) @ ( lexord_a @ R ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % lexord_cons_cons
% 0.25/0.57 thf(fact_166_listrel1I2,axiom,
% 0.25/0.57 ! [Xs2: list_P1891567085od_a_a,Ys2: list_P1891567085od_a_a,R: set_Pr1295299783od_a_a,X3: produc1572603623od_a_a] :
% 0.25/0.57 ( ( member1254757008od_a_a @ ( produc461662679od_a_a @ Xs2 @ Ys2 ) @ ( listre1832537542od_a_a @ R ) )
% 0.25/0.57 => ( member1254757008od_a_a @ ( produc461662679od_a_a @ ( cons_P1070399645od_a_a @ X3 @ Xs2 ) @ ( cons_P1070399645od_a_a @ X3 @ Ys2 ) ) @ ( listre1832537542od_a_a @ R ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % listrel1I2
% 0.25/0.57 thf(fact_167_listrel1I2,axiom,
% 0.25/0.57 ! [Xs2: list_l1108175539od_a_a,Ys2: list_l1108175539od_a_a,R: set_Pr800560199od_a_a,X3: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( member8108048od_a_a @ ( produc915218007od_a_a @ Xs2 @ Ys2 ) @ ( listre651914124od_a_a @ R ) )
% 0.25/0.57 => ( member8108048od_a_a @ ( produc915218007od_a_a @ ( cons_l724116707od_a_a @ X3 @ Xs2 ) @ ( cons_l724116707od_a_a @ X3 @ Ys2 ) ) @ ( listre651914124od_a_a @ R ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % listrel1I2
% 0.25/0.57 thf(fact_168_listrel1I2,axiom,
% 0.25/0.57 ! [Xs2: list_a_nat,Ys2: list_a_nat,R: set_Pr1940702919_a_nat,X3: a > nat] :
% 0.25/0.57 ( ( member688761744_a_nat @ ( produc1430747863_a_nat @ Xs2 @ Ys2 ) @ ( listrel1_a_nat @ R ) )
% 0.25/0.57 => ( member688761744_a_nat @ ( produc1430747863_a_nat @ ( cons_a_nat @ X3 @ Xs2 ) @ ( cons_a_nat @ X3 @ Ys2 ) ) @ ( listrel1_a_nat @ R ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % listrel1I2
% 0.25/0.57 thf(fact_169_listrel1I2,axiom,
% 0.25/0.57 ! [Xs2: list_a,Ys2: list_a,R: set_Product_prod_a_a,X3: a] :
% 0.25/0.57 ( ( member1250517072list_a @ ( produc1448356631list_a @ Xs2 @ Ys2 ) @ ( listrel1_a @ R ) )
% 0.25/0.57 => ( member1250517072list_a @ ( produc1448356631list_a @ ( cons_a @ X3 @ Xs2 ) @ ( cons_a @ X3 @ Ys2 ) ) @ ( listrel1_a @ R ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % listrel1I2
% 0.25/0.57 thf(fact_170_listrel1I2,axiom,
% 0.25/0.57 ! [Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a,R: set_Pr1948701895od_a_a,X3: product_prod_a_a] :
% 0.25/0.57 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ Xs2 @ Ys2 ) @ ( listre944824838od_a_a @ R ) )
% 0.25/0.57 => ( member1691432592od_a_a @ ( produc85179863od_a_a @ ( cons_P1921020637od_a_a @ X3 @ Xs2 ) @ ( cons_P1921020637od_a_a @ X3 @ Ys2 ) ) @ ( listre944824838od_a_a @ R ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % listrel1I2
% 0.25/0.57 thf(fact_171_append__listrel1I,axiom,
% 0.25/0.57 ! [Xs2: list_P1891567085od_a_a,Ys2: list_P1891567085od_a_a,R: set_Pr1295299783od_a_a,Us: list_P1891567085od_a_a,Vs: list_P1891567085od_a_a] :
% 0.25/0.57 ( ( ( ( member1254757008od_a_a @ ( produc461662679od_a_a @ Xs2 @ Ys2 ) @ ( listre1832537542od_a_a @ R ) )
% 0.25/0.57 & ( Us = Vs ) )
% 0.25/0.57 | ( ( Xs2 = Ys2 )
% 0.25/0.57 & ( member1254757008od_a_a @ ( produc461662679od_a_a @ Us @ Vs ) @ ( listre1832537542od_a_a @ R ) ) ) )
% 0.25/0.57 => ( member1254757008od_a_a @ ( produc461662679od_a_a @ ( append864718978od_a_a @ Xs2 @ Us ) @ ( append864718978od_a_a @ Ys2 @ Vs ) ) @ ( listre1832537542od_a_a @ R ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % append_listrel1I
% 0.25/0.57 thf(fact_172_append__listrel1I,axiom,
% 0.25/0.57 ! [Xs2: list_l1108175539od_a_a,Ys2: list_l1108175539od_a_a,R: set_Pr800560199od_a_a,Us: list_l1108175539od_a_a,Vs: list_l1108175539od_a_a] :
% 0.25/0.57 ( ( ( ( member8108048od_a_a @ ( produc915218007od_a_a @ Xs2 @ Ys2 ) @ ( listre651914124od_a_a @ R ) )
% 0.25/0.57 & ( Us = Vs ) )
% 0.25/0.57 | ( ( Xs2 = Ys2 )
% 0.25/0.57 & ( member8108048od_a_a @ ( produc915218007od_a_a @ Us @ Vs ) @ ( listre651914124od_a_a @ R ) ) ) )
% 0.25/0.57 => ( member8108048od_a_a @ ( produc915218007od_a_a @ ( append2141280328od_a_a @ Xs2 @ Us ) @ ( append2141280328od_a_a @ Ys2 @ Vs ) ) @ ( listre651914124od_a_a @ R ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % append_listrel1I
% 0.25/0.57 thf(fact_173_append__listrel1I,axiom,
% 0.25/0.57 ! [Xs2: list_a,Ys2: list_a,R: set_Product_prod_a_a,Us: list_a,Vs: list_a] :
% 0.25/0.57 ( ( ( ( member1250517072list_a @ ( produc1448356631list_a @ Xs2 @ Ys2 ) @ ( listrel1_a @ R ) )
% 0.25/0.57 & ( Us = Vs ) )
% 0.25/0.57 | ( ( Xs2 = Ys2 )
% 0.25/0.57 & ( member1250517072list_a @ ( produc1448356631list_a @ Us @ Vs ) @ ( listrel1_a @ R ) ) ) )
% 0.25/0.57 => ( member1250517072list_a @ ( produc1448356631list_a @ ( append_a @ Xs2 @ Us ) @ ( append_a @ Ys2 @ Vs ) ) @ ( listrel1_a @ R ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % append_listrel1I
% 0.25/0.57 thf(fact_174_append__listrel1I,axiom,
% 0.25/0.57 ! [Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a,R: set_Pr1948701895od_a_a,Us: list_P1467822637od_a_a,Vs: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ Xs2 @ Ys2 ) @ ( listre944824838od_a_a @ R ) )
% 0.25/0.57 & ( Us = Vs ) )
% 0.25/0.57 | ( ( Xs2 = Ys2 )
% 0.25/0.57 & ( member1691432592od_a_a @ ( produc85179863od_a_a @ Us @ Vs ) @ ( listre944824838od_a_a @ R ) ) ) )
% 0.25/0.57 => ( member1691432592od_a_a @ ( produc85179863od_a_a @ ( append1574001858od_a_a @ Xs2 @ Us ) @ ( append1574001858od_a_a @ Ys2 @ Vs ) ) @ ( listre944824838od_a_a @ R ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % append_listrel1I
% 0.25/0.57 thf(fact_175_lexord__linear,axiom,
% 0.25/0.57 ! [R: set_Pr800560199od_a_a,X3: list_l1108175539od_a_a,Y3: list_l1108175539od_a_a] :
% 0.25/0.57 ( ! [A3: list_P1467822637od_a_a,B3: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ A3 @ B3 ) @ R )
% 0.25/0.57 | ( A3 = B3 )
% 0.25/0.57 | ( member1691432592od_a_a @ ( produc85179863od_a_a @ B3 @ A3 ) @ R ) )
% 0.25/0.57 => ( ( member8108048od_a_a @ ( produc915218007od_a_a @ X3 @ Y3 ) @ ( lexord1284731808od_a_a @ R ) )
% 0.25/0.57 | ( X3 = Y3 )
% 0.25/0.57 | ( member8108048od_a_a @ ( produc915218007od_a_a @ Y3 @ X3 ) @ ( lexord1284731808od_a_a @ R ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % lexord_linear
% 0.25/0.57 thf(fact_176_lexord__linear,axiom,
% 0.25/0.57 ! [R: set_Pr1948701895od_a_a,X3: list_P1467822637od_a_a,Y3: list_P1467822637od_a_a] :
% 0.25/0.57 ( ! [A3: product_prod_a_a,B3: product_prod_a_a] :
% 0.25/0.57 ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A3 @ B3 ) @ R )
% 0.25/0.57 | ( A3 = B3 )
% 0.25/0.57 | ( member2057358096od_a_a @ ( produc1474507607od_a_a @ B3 @ A3 ) @ R ) )
% 0.25/0.57 => ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ X3 @ Y3 ) @ ( lexord673907738od_a_a @ R ) )
% 0.25/0.57 | ( X3 = Y3 )
% 0.25/0.57 | ( member1691432592od_a_a @ ( produc85179863od_a_a @ Y3 @ X3 ) @ ( lexord673907738od_a_a @ R ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % lexord_linear
% 0.25/0.57 thf(fact_177_lexord__linear,axiom,
% 0.25/0.57 ! [R: set_Pr1971762695list_a,X3: list_list_a,Y3: list_list_a] :
% 0.25/0.57 ( ! [A3: list_a,B3: list_a] :
% 0.25/0.57 ( ( member1250517072list_a @ ( produc1448356631list_a @ A3 @ B3 ) @ R )
% 0.25/0.57 | ( A3 = B3 )
% 0.25/0.57 | ( member1250517072list_a @ ( produc1448356631list_a @ B3 @ A3 ) @ R ) )
% 0.25/0.57 => ( ( member888406864list_a @ ( produc2583831list_a @ X3 @ Y3 ) @ ( lexord_list_a @ R ) )
% 0.25/0.57 | ( X3 = Y3 )
% 0.25/0.57 | ( member888406864list_a @ ( produc2583831list_a @ Y3 @ X3 ) @ ( lexord_list_a @ R ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % lexord_linear
% 0.25/0.57 thf(fact_178_lexord__linear,axiom,
% 0.25/0.57 ! [R: set_Product_prod_a_a,X3: list_a,Y3: list_a] :
% 0.25/0.57 ( ! [A3: a,B3: a] :
% 0.25/0.57 ( ( member449909584od_a_a @ ( product_Pair_a_a @ A3 @ B3 ) @ R )
% 0.25/0.57 | ( A3 = B3 )
% 0.25/0.57 | ( member449909584od_a_a @ ( product_Pair_a_a @ B3 @ A3 ) @ R ) )
% 0.25/0.57 => ( ( member1250517072list_a @ ( produc1448356631list_a @ X3 @ Y3 ) @ ( lexord_a @ R ) )
% 0.25/0.57 | ( X3 = Y3 )
% 0.25/0.57 | ( member1250517072list_a @ ( produc1448356631list_a @ Y3 @ X3 ) @ ( lexord_a @ R ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % lexord_linear
% 0.25/0.57 thf(fact_179_mem__Collect__eq,axiom,
% 0.25/0.57 ! [A: produc651658087od_a_a,P2: produc651658087od_a_a > $o] :
% 0.25/0.57 ( ( member1691432592od_a_a @ A @ ( collec1566074578od_a_a @ P2 ) )
% 0.25/0.57 = ( P2 @ A ) ) ).
% 0.25/0.57
% 0.25/0.57 % mem_Collect_eq
% 0.25/0.57 thf(fact_180_mem__Collect__eq,axiom,
% 0.25/0.57 ! [A: produc864062247list_a,P2: produc864062247list_a > $o] :
% 0.25/0.57 ( ( member1250517072list_a @ A @ ( collec656258194list_a @ P2 ) )
% 0.25/0.57 = ( P2 @ A ) ) ).
% 0.25/0.57
% 0.25/0.57 % mem_Collect_eq
% 0.25/0.57 thf(fact_181_mem__Collect__eq,axiom,
% 0.25/0.57 ! [A: product_prod_a_a,P2: product_prod_a_a > $o] :
% 0.25/0.57 ( ( member449909584od_a_a @ A @ ( collec645855634od_a_a @ P2 ) )
% 0.25/0.57 = ( P2 @ A ) ) ).
% 0.25/0.57
% 0.25/0.57 % mem_Collect_eq
% 0.25/0.57 thf(fact_182_mem__Collect__eq,axiom,
% 0.25/0.57 ! [A: list_P1467822637od_a_a,P2: list_P1467822637od_a_a > $o] :
% 0.25/0.57 ( ( member1578987478od_a_a @ A @ ( collec1811041560od_a_a @ P2 ) )
% 0.25/0.57 = ( P2 @ A ) ) ).
% 0.25/0.57
% 0.25/0.57 % mem_Collect_eq
% 0.25/0.57 thf(fact_183_mem__Collect__eq,axiom,
% 0.25/0.57 ! [A: a,P2: a > $o] :
% 0.25/0.57 ( ( member_a2 @ A @ ( collect_a @ P2 ) )
% 0.25/0.57 = ( P2 @ A ) ) ).
% 0.25/0.57
% 0.25/0.57 % mem_Collect_eq
% 0.25/0.57 thf(fact_184_Collect__mem__eq,axiom,
% 0.25/0.57 ! [A4: set_Pr1971762695list_a] :
% 0.25/0.57 ( ( collec656258194list_a
% 0.25/0.57 @ ^ [X: produc864062247list_a] : ( member1250517072list_a @ X @ A4 ) )
% 0.25/0.57 = A4 ) ).
% 0.25/0.57
% 0.25/0.57 % Collect_mem_eq
% 0.25/0.57 thf(fact_185_Collect__mem__eq,axiom,
% 0.25/0.57 ! [A4: set_Product_prod_a_a] :
% 0.25/0.57 ( ( collec645855634od_a_a
% 0.25/0.57 @ ^ [X: product_prod_a_a] : ( member449909584od_a_a @ X @ A4 ) )
% 0.25/0.57 = A4 ) ).
% 0.25/0.57
% 0.25/0.57 % Collect_mem_eq
% 0.25/0.57 thf(fact_186_Collect__mem__eq,axiom,
% 0.25/0.57 ! [A4: set_li562223245od_a_a] :
% 0.25/0.57 ( ( collec1811041560od_a_a
% 0.25/0.57 @ ^ [X: list_P1467822637od_a_a] : ( member1578987478od_a_a @ X @ A4 ) )
% 0.25/0.57 = A4 ) ).
% 0.25/0.57
% 0.25/0.57 % Collect_mem_eq
% 0.25/0.57 thf(fact_187_Collect__mem__eq,axiom,
% 0.25/0.57 ! [A4: set_a] :
% 0.25/0.57 ( ( collect_a
% 0.25/0.57 @ ^ [X: a] : ( member_a2 @ X @ A4 ) )
% 0.25/0.57 = A4 ) ).
% 0.25/0.57
% 0.25/0.57 % Collect_mem_eq
% 0.25/0.57 thf(fact_188_lexord__irreflexive,axiom,
% 0.25/0.57 ! [R: set_Product_prod_a_a,Xs2: list_a] :
% 0.25/0.57 ( ! [X4: a] :
% 0.25/0.57 ~ ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ X4 ) @ R )
% 0.25/0.57 => ~ ( member1250517072list_a @ ( produc1448356631list_a @ Xs2 @ Xs2 ) @ ( lexord_a @ R ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % lexord_irreflexive
% 0.25/0.57 thf(fact_189_lexord__append__leftI,axiom,
% 0.25/0.57 ! [U: list_P1467822637od_a_a,V2: list_P1467822637od_a_a,R: set_Pr1948701895od_a_a,X3: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ U @ V2 ) @ ( lexord673907738od_a_a @ R ) )
% 0.25/0.57 => ( member1691432592od_a_a @ ( produc85179863od_a_a @ ( append1574001858od_a_a @ X3 @ U ) @ ( append1574001858od_a_a @ X3 @ V2 ) ) @ ( lexord673907738od_a_a @ R ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % lexord_append_leftI
% 0.25/0.57 thf(fact_190_listrel1I1,axiom,
% 0.25/0.57 ! [X3: product_prod_a_a,Y3: product_prod_a_a,R: set_Pr1948701895od_a_a,Xs2: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X3 @ Y3 ) @ R )
% 0.25/0.57 => ( member1691432592od_a_a @ ( produc85179863od_a_a @ ( cons_P1921020637od_a_a @ X3 @ Xs2 ) @ ( cons_P1921020637od_a_a @ Y3 @ Xs2 ) ) @ ( listre944824838od_a_a @ R ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % listrel1I1
% 0.25/0.57 thf(fact_191_listrel1I1,axiom,
% 0.25/0.57 ! [X3: a,Y3: a,R: set_Product_prod_a_a,Xs2: list_a] :
% 0.25/0.57 ( ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ R )
% 0.25/0.57 => ( member1250517072list_a @ ( produc1448356631list_a @ ( cons_a @ X3 @ Xs2 ) @ ( cons_a @ Y3 @ Xs2 ) ) @ ( listrel1_a @ R ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % listrel1I1
% 0.25/0.57 thf(fact_192_Cons__listrel1E1,axiom,
% 0.25/0.57 ! [X3: product_prod_a_a,Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a,R: set_Pr1948701895od_a_a] :
% 0.25/0.57 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ ( cons_P1921020637od_a_a @ X3 @ Xs2 ) @ Ys2 ) @ ( listre944824838od_a_a @ R ) )
% 0.25/0.57 => ( ! [Y4: product_prod_a_a] :
% 0.25/0.57 ( ( Ys2
% 0.25/0.57 = ( cons_P1921020637od_a_a @ Y4 @ Xs2 ) )
% 0.25/0.57 => ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X3 @ Y4 ) @ R ) )
% 0.25/0.57 => ~ ! [Zs2: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( Ys2
% 0.25/0.57 = ( cons_P1921020637od_a_a @ X3 @ Zs2 ) )
% 0.25/0.57 => ~ ( member1691432592od_a_a @ ( produc85179863od_a_a @ Xs2 @ Zs2 ) @ ( listre944824838od_a_a @ R ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % Cons_listrel1E1
% 0.25/0.57 thf(fact_193_Cons__listrel1E1,axiom,
% 0.25/0.57 ! [X3: a,Xs2: list_a,Ys2: list_a,R: set_Product_prod_a_a] :
% 0.25/0.57 ( ( member1250517072list_a @ ( produc1448356631list_a @ ( cons_a @ X3 @ Xs2 ) @ Ys2 ) @ ( listrel1_a @ R ) )
% 0.25/0.57 => ( ! [Y4: a] :
% 0.25/0.57 ( ( Ys2
% 0.25/0.57 = ( cons_a @ Y4 @ Xs2 ) )
% 0.25/0.57 => ~ ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y4 ) @ R ) )
% 0.25/0.57 => ~ ! [Zs2: list_a] :
% 0.25/0.57 ( ( Ys2
% 0.25/0.57 = ( cons_a @ X3 @ Zs2 ) )
% 0.25/0.57 => ~ ( member1250517072list_a @ ( produc1448356631list_a @ Xs2 @ Zs2 ) @ ( listrel1_a @ R ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % Cons_listrel1E1
% 0.25/0.57 thf(fact_194_Cons__listrel1E2,axiom,
% 0.25/0.57 ! [Xs2: list_P1467822637od_a_a,Y3: product_prod_a_a,Ys2: list_P1467822637od_a_a,R: set_Pr1948701895od_a_a] :
% 0.25/0.57 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ Xs2 @ ( cons_P1921020637od_a_a @ Y3 @ Ys2 ) ) @ ( listre944824838od_a_a @ R ) )
% 0.25/0.57 => ( ! [X4: product_prod_a_a] :
% 0.25/0.57 ( ( Xs2
% 0.25/0.57 = ( cons_P1921020637od_a_a @ X4 @ Ys2 ) )
% 0.25/0.57 => ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X4 @ Y3 ) @ R ) )
% 0.25/0.57 => ~ ! [Zs2: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( Xs2
% 0.25/0.57 = ( cons_P1921020637od_a_a @ Y3 @ Zs2 ) )
% 0.25/0.57 => ~ ( member1691432592od_a_a @ ( produc85179863od_a_a @ Zs2 @ Ys2 ) @ ( listre944824838od_a_a @ R ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % Cons_listrel1E2
% 0.25/0.57 thf(fact_195_Cons__listrel1E2,axiom,
% 0.25/0.57 ! [Xs2: list_a,Y3: a,Ys2: list_a,R: set_Product_prod_a_a] :
% 0.25/0.57 ( ( member1250517072list_a @ ( produc1448356631list_a @ Xs2 @ ( cons_a @ Y3 @ Ys2 ) ) @ ( listrel1_a @ R ) )
% 0.25/0.57 => ( ! [X4: a] :
% 0.25/0.57 ( ( Xs2
% 0.25/0.57 = ( cons_a @ X4 @ Ys2 ) )
% 0.25/0.57 => ~ ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y3 ) @ R ) )
% 0.25/0.57 => ~ ! [Zs2: list_a] :
% 0.25/0.57 ( ( Xs2
% 0.25/0.57 = ( cons_a @ Y3 @ Zs2 ) )
% 0.25/0.57 => ~ ( member1250517072list_a @ ( produc1448356631list_a @ Zs2 @ Ys2 ) @ ( listrel1_a @ R ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % Cons_listrel1E2
% 0.25/0.57 thf(fact_196_lexord__append__leftD,axiom,
% 0.25/0.57 ! [X3: list_P1467822637od_a_a,U: list_P1467822637od_a_a,V2: list_P1467822637od_a_a,R: set_Pr1948701895od_a_a] :
% 0.25/0.57 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ ( append1574001858od_a_a @ X3 @ U ) @ ( append1574001858od_a_a @ X3 @ V2 ) ) @ ( lexord673907738od_a_a @ R ) )
% 0.25/0.57 => ( ! [A3: product_prod_a_a] :
% 0.25/0.57 ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A3 @ A3 ) @ R )
% 0.25/0.57 => ( member1691432592od_a_a @ ( produc85179863od_a_a @ U @ V2 ) @ ( lexord673907738od_a_a @ R ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % lexord_append_leftD
% 0.25/0.57 thf(fact_197_lexord__append__leftD,axiom,
% 0.25/0.57 ! [X3: list_a,U: list_a,V2: list_a,R: set_Product_prod_a_a] :
% 0.25/0.57 ( ( member1250517072list_a @ ( produc1448356631list_a @ ( append_a @ X3 @ U ) @ ( append_a @ X3 @ V2 ) ) @ ( lexord_a @ R ) )
% 0.25/0.57 => ( ! [A3: a] :
% 0.25/0.57 ~ ( member449909584od_a_a @ ( product_Pair_a_a @ A3 @ A3 ) @ R )
% 0.25/0.57 => ( member1250517072list_a @ ( produc1448356631list_a @ U @ V2 ) @ ( lexord_a @ R ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % lexord_append_leftD
% 0.25/0.57 thf(fact_198_lexord__append__rightI,axiom,
% 0.25/0.57 ! [Y3: list_P1467822637od_a_a,X3: list_P1467822637od_a_a,R: set_Pr1948701895od_a_a] :
% 0.25/0.57 ( ? [B4: product_prod_a_a,Z: list_P1467822637od_a_a] :
% 0.25/0.57 ( Y3
% 0.25/0.57 = ( cons_P1921020637od_a_a @ B4 @ Z ) )
% 0.25/0.57 => ( member1691432592od_a_a @ ( produc85179863od_a_a @ X3 @ ( append1574001858od_a_a @ X3 @ Y3 ) ) @ ( lexord673907738od_a_a @ R ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % lexord_append_rightI
% 0.25/0.57 thf(fact_199_zip__eq__ConsE,axiom,
% 0.25/0.57 ! [Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a,Xy: produc1572603623od_a_a,Xys: list_P1891567085od_a_a] :
% 0.25/0.57 ( ( ( zip_Pr792472183od_a_a @ Xs2 @ Ys2 )
% 0.25/0.57 = ( cons_P1070399645od_a_a @ Xy @ Xys ) )
% 0.25/0.57 => ~ ! [X4: product_prod_a_a,Xs3: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( Xs2
% 0.25/0.57 = ( cons_P1921020637od_a_a @ X4 @ Xs3 ) )
% 0.25/0.57 => ! [Y4: product_prod_a_a,Ys3: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( Ys2
% 0.25/0.57 = ( cons_P1921020637od_a_a @ Y4 @ Ys3 ) )
% 0.25/0.57 => ( ( Xy
% 0.25/0.57 = ( produc1474507607od_a_a @ X4 @ Y4 ) )
% 0.25/0.57 => ( Xys
% 0.25/0.57 != ( zip_Pr792472183od_a_a @ Xs3 @ Ys3 ) ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % zip_eq_ConsE
% 0.25/0.57 thf(fact_200_zip__eq__ConsE,axiom,
% 0.25/0.57 ! [Xs2: list_a,Ys2: list_a,Xy: product_prod_a_a,Xys: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( ( zip_a_a @ Xs2 @ Ys2 )
% 0.25/0.57 = ( cons_P1921020637od_a_a @ Xy @ Xys ) )
% 0.25/0.57 => ~ ! [X4: a,Xs3: list_a] :
% 0.25/0.57 ( ( Xs2
% 0.25/0.57 = ( cons_a @ X4 @ Xs3 ) )
% 0.25/0.57 => ! [Y4: a,Ys3: list_a] :
% 0.25/0.57 ( ( Ys2
% 0.25/0.57 = ( cons_a @ Y4 @ Ys3 ) )
% 0.25/0.57 => ( ( Xy
% 0.25/0.57 = ( product_Pair_a_a @ X4 @ Y4 ) )
% 0.25/0.57 => ( Xys
% 0.25/0.57 != ( zip_a_a @ Xs3 @ Ys3 ) ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % zip_eq_ConsE
% 0.25/0.57 thf(fact_201_subdivide_Ocases,axiom,
% 0.25/0.57 ! [X3: produc1912141786_a_a_a] :
% 0.25/0.57 ~ ! [G: pair_p125712459t_unit,U2: a,V: a,W: a] :
% 0.25/0.57 ( X3
% 0.25/0.57 != ( produc74075722_a_a_a @ G @ ( produc2061588782_a_a_a @ ( product_Pair_a_a @ U2 @ V ) @ W ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % subdivide.cases
% 0.25/0.57 thf(fact_202_lexord__same__pref__if__irrefl,axiom,
% 0.25/0.57 ! [R: set_Pr1948701895od_a_a,Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a,Zs: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( irrefl76447196od_a_a @ R )
% 0.25/0.57 => ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ ( append1574001858od_a_a @ Xs2 @ Ys2 ) @ ( append1574001858od_a_a @ Xs2 @ Zs ) ) @ ( lexord673907738od_a_a @ R ) )
% 0.25/0.57 = ( member1691432592od_a_a @ ( produc85179863od_a_a @ Ys2 @ Zs ) @ ( lexord673907738od_a_a @ R ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % lexord_same_pref_if_irrefl
% 0.25/0.57 thf(fact_203_snoc__listrel1__snoc__iff,axiom,
% 0.25/0.57 ! [Xs2: list_P1467822637od_a_a,X3: product_prod_a_a,Ys2: list_P1467822637od_a_a,Y3: product_prod_a_a,R: set_Pr1948701895od_a_a] :
% 0.25/0.57 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ ( append1574001858od_a_a @ Xs2 @ ( cons_P1921020637od_a_a @ X3 @ nil_Product_prod_a_a ) ) @ ( append1574001858od_a_a @ Ys2 @ ( cons_P1921020637od_a_a @ Y3 @ nil_Product_prod_a_a ) ) ) @ ( listre944824838od_a_a @ R ) )
% 0.25/0.57 = ( ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ Xs2 @ Ys2 ) @ ( listre944824838od_a_a @ R ) )
% 0.25/0.57 & ( X3 = Y3 ) )
% 0.25/0.57 | ( ( Xs2 = Ys2 )
% 0.25/0.57 & ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X3 @ Y3 ) @ R ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % snoc_listrel1_snoc_iff
% 0.25/0.57 thf(fact_204_snoc__listrel1__snoc__iff,axiom,
% 0.25/0.57 ! [Xs2: list_a,X3: a,Ys2: list_a,Y3: a,R: set_Product_prod_a_a] :
% 0.25/0.57 ( ( member1250517072list_a @ ( produc1448356631list_a @ ( append_a @ Xs2 @ ( cons_a @ X3 @ nil_a ) ) @ ( append_a @ Ys2 @ ( cons_a @ Y3 @ nil_a ) ) ) @ ( listrel1_a @ R ) )
% 0.25/0.57 = ( ( ( member1250517072list_a @ ( produc1448356631list_a @ Xs2 @ Ys2 ) @ ( listrel1_a @ R ) )
% 0.25/0.57 & ( X3 = Y3 ) )
% 0.25/0.57 | ( ( Xs2 = Ys2 )
% 0.25/0.57 & ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ R ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % snoc_listrel1_snoc_iff
% 0.25/0.57 thf(fact_205_lexord__Nil__left,axiom,
% 0.25/0.57 ! [Y3: list_P1467822637od_a_a,R: set_Pr1948701895od_a_a] :
% 0.25/0.57 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ nil_Product_prod_a_a @ Y3 ) @ ( lexord673907738od_a_a @ R ) )
% 0.25/0.57 = ( ? [A5: product_prod_a_a,X: list_P1467822637od_a_a] :
% 0.25/0.57 ( Y3
% 0.25/0.57 = ( cons_P1921020637od_a_a @ A5 @ X ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % lexord_Nil_left
% 0.25/0.57 thf(fact_206_lexord__same__pref__iff,axiom,
% 0.25/0.57 ! [Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a,Zs: list_P1467822637od_a_a,R: set_Pr1948701895od_a_a] :
% 0.25/0.57 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ ( append1574001858od_a_a @ Xs2 @ Ys2 ) @ ( append1574001858od_a_a @ Xs2 @ Zs ) ) @ ( lexord673907738od_a_a @ R ) )
% 0.25/0.57 = ( ? [X: product_prod_a_a] :
% 0.25/0.57 ( ( member449909584od_a_a @ X @ ( set_Product_prod_a_a2 @ Xs2 ) )
% 0.25/0.57 & ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X @ X ) @ R ) )
% 0.25/0.57 | ( member1691432592od_a_a @ ( produc85179863od_a_a @ Ys2 @ Zs ) @ ( lexord673907738od_a_a @ R ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % lexord_same_pref_iff
% 0.25/0.57 thf(fact_207_lexord__same__pref__iff,axiom,
% 0.25/0.57 ! [Xs2: list_a,Ys2: list_a,Zs: list_a,R: set_Product_prod_a_a] :
% 0.25/0.57 ( ( member1250517072list_a @ ( produc1448356631list_a @ ( append_a @ Xs2 @ Ys2 ) @ ( append_a @ Xs2 @ Zs ) ) @ ( lexord_a @ R ) )
% 0.25/0.57 = ( ? [X: a] :
% 0.25/0.57 ( ( member_a2 @ X @ ( set_a2 @ Xs2 ) )
% 0.25/0.57 & ( member449909584od_a_a @ ( product_Pair_a_a @ X @ X ) @ R ) )
% 0.25/0.57 | ( member1250517072list_a @ ( produc1448356631list_a @ Ys2 @ Zs ) @ ( lexord_a @ R ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % lexord_same_pref_iff
% 0.25/0.57 thf(fact_208_zip__append,axiom,
% 0.25/0.57 ! [Xs2: list_a,Us: list_a,Ys2: list_a,Vs: list_a] :
% 0.25/0.57 ( ( ( size_size_list_a @ Xs2 )
% 0.25/0.57 = ( size_size_list_a @ Us ) )
% 0.25/0.57 => ( ( zip_a_a @ ( append_a @ Xs2 @ Ys2 ) @ ( append_a @ Us @ Vs ) )
% 0.25/0.57 = ( append1574001858od_a_a @ ( zip_a_a @ Xs2 @ Us ) @ ( zip_a_a @ Ys2 @ Vs ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % zip_append
% 0.25/0.57 thf(fact_209_zip__append,axiom,
% 0.25/0.57 ! [Xs2: list_P1467822637od_a_a,Us: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a,Vs: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( ( size_s642698393od_a_a @ Xs2 )
% 0.25/0.57 = ( size_s642698393od_a_a @ Us ) )
% 0.25/0.57 => ( ( zip_Pr792472183od_a_a @ ( append1574001858od_a_a @ Xs2 @ Ys2 ) @ ( append1574001858od_a_a @ Us @ Vs ) )
% 0.25/0.57 = ( append864718978od_a_a @ ( zip_Pr792472183od_a_a @ Xs2 @ Us ) @ ( zip_Pr792472183od_a_a @ Ys2 @ Vs ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % zip_append
% 0.25/0.57 thf(fact_210_lex__append__leftD,axiom,
% 0.25/0.57 ! [R: set_Pr1948701895od_a_a,Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a,Zs: list_P1467822637od_a_a] :
% 0.25/0.57 ( ! [X4: product_prod_a_a] :
% 0.25/0.57 ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X4 @ X4 ) @ R )
% 0.25/0.57 => ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ ( append1574001858od_a_a @ Xs2 @ Ys2 ) @ ( append1574001858od_a_a @ Xs2 @ Zs ) ) @ ( lex_Product_prod_a_a @ R ) )
% 0.25/0.57 => ( member1691432592od_a_a @ ( produc85179863od_a_a @ Ys2 @ Zs ) @ ( lex_Product_prod_a_a @ R ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % lex_append_leftD
% 0.25/0.57 thf(fact_211_lex__append__leftD,axiom,
% 0.25/0.57 ! [R: set_Product_prod_a_a,Xs2: list_a,Ys2: list_a,Zs: list_a] :
% 0.25/0.57 ( ! [X4: a] :
% 0.25/0.57 ~ ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ X4 ) @ R )
% 0.25/0.57 => ( ( member1250517072list_a @ ( produc1448356631list_a @ ( append_a @ Xs2 @ Ys2 ) @ ( append_a @ Xs2 @ Zs ) ) @ ( lex_a @ R ) )
% 0.25/0.57 => ( member1250517072list_a @ ( produc1448356631list_a @ Ys2 @ Zs ) @ ( lex_a @ R ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % lex_append_leftD
% 0.25/0.57 thf(fact_212_lex__append__left__iff,axiom,
% 0.25/0.57 ! [R: set_Pr1948701895od_a_a,Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a,Zs: list_P1467822637od_a_a] :
% 0.25/0.57 ( ! [X4: product_prod_a_a] :
% 0.25/0.57 ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X4 @ X4 ) @ R )
% 0.25/0.57 => ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ ( append1574001858od_a_a @ Xs2 @ Ys2 ) @ ( append1574001858od_a_a @ Xs2 @ Zs ) ) @ ( lex_Product_prod_a_a @ R ) )
% 0.25/0.57 = ( member1691432592od_a_a @ ( produc85179863od_a_a @ Ys2 @ Zs ) @ ( lex_Product_prod_a_a @ R ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % lex_append_left_iff
% 0.25/0.57 thf(fact_213_lex__append__left__iff,axiom,
% 0.25/0.57 ! [R: set_Product_prod_a_a,Xs2: list_a,Ys2: list_a,Zs: list_a] :
% 0.25/0.57 ( ! [X4: a] :
% 0.25/0.57 ~ ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ X4 ) @ R )
% 0.25/0.57 => ( ( member1250517072list_a @ ( produc1448356631list_a @ ( append_a @ Xs2 @ Ys2 ) @ ( append_a @ Xs2 @ Zs ) ) @ ( lex_a @ R ) )
% 0.25/0.57 = ( member1250517072list_a @ ( produc1448356631list_a @ Ys2 @ Zs ) @ ( lex_a @ R ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % lex_append_left_iff
% 0.25/0.57 thf(fact_214_append_Oright__neutral,axiom,
% 0.25/0.57 ! [A: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( append1574001858od_a_a @ A @ nil_Product_prod_a_a )
% 0.25/0.57 = A ) ).
% 0.25/0.57
% 0.25/0.57 % append.right_neutral
% 0.25/0.57 thf(fact_215_append__is__Nil__conv,axiom,
% 0.25/0.57 ! [Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( ( append1574001858od_a_a @ Xs2 @ Ys2 )
% 0.25/0.57 = nil_Product_prod_a_a )
% 0.25/0.57 = ( ( Xs2 = nil_Product_prod_a_a )
% 0.25/0.57 & ( Ys2 = nil_Product_prod_a_a ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % append_is_Nil_conv
% 0.25/0.57 thf(fact_216_Nil__is__append__conv,axiom,
% 0.25/0.57 ! [Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( nil_Product_prod_a_a
% 0.25/0.57 = ( append1574001858od_a_a @ Xs2 @ Ys2 ) )
% 0.25/0.57 = ( ( Xs2 = nil_Product_prod_a_a )
% 0.25/0.57 & ( Ys2 = nil_Product_prod_a_a ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % Nil_is_append_conv
% 0.25/0.57 thf(fact_217_self__append__conv2,axiom,
% 0.25/0.57 ! [Ys2: list_P1467822637od_a_a,Xs2: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( Ys2
% 0.25/0.57 = ( append1574001858od_a_a @ Xs2 @ Ys2 ) )
% 0.25/0.57 = ( Xs2 = nil_Product_prod_a_a ) ) ).
% 0.25/0.57
% 0.25/0.57 % self_append_conv2
% 0.25/0.57 thf(fact_218_append__self__conv2,axiom,
% 0.25/0.57 ! [Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( ( append1574001858od_a_a @ Xs2 @ Ys2 )
% 0.25/0.57 = Ys2 )
% 0.25/0.57 = ( Xs2 = nil_Product_prod_a_a ) ) ).
% 0.25/0.57
% 0.25/0.57 % append_self_conv2
% 0.25/0.57 thf(fact_219_self__append__conv,axiom,
% 0.25/0.57 ! [Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( Xs2
% 0.25/0.57 = ( append1574001858od_a_a @ Xs2 @ Ys2 ) )
% 0.25/0.57 = ( Ys2 = nil_Product_prod_a_a ) ) ).
% 0.25/0.57
% 0.25/0.57 % self_append_conv
% 0.25/0.57 thf(fact_220_append__self__conv,axiom,
% 0.25/0.57 ! [Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( ( append1574001858od_a_a @ Xs2 @ Ys2 )
% 0.25/0.57 = Xs2 )
% 0.25/0.57 = ( Ys2 = nil_Product_prod_a_a ) ) ).
% 0.25/0.57
% 0.25/0.57 % append_self_conv
% 0.25/0.57 thf(fact_221_append__Nil2,axiom,
% 0.25/0.57 ! [Xs2: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( append1574001858od_a_a @ Xs2 @ nil_Product_prod_a_a )
% 0.25/0.57 = Xs2 ) ).
% 0.25/0.57
% 0.25/0.57 % append_Nil2
% 0.25/0.57 thf(fact_222_append__eq__append__conv,axiom,
% 0.25/0.57 ! [Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a,Us: list_P1467822637od_a_a,Vs: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( ( ( size_s642698393od_a_a @ Xs2 )
% 0.25/0.57 = ( size_s642698393od_a_a @ Ys2 ) )
% 0.25/0.57 | ( ( size_s642698393od_a_a @ Us )
% 0.25/0.57 = ( size_s642698393od_a_a @ Vs ) ) )
% 0.25/0.57 => ( ( ( append1574001858od_a_a @ Xs2 @ Us )
% 0.25/0.57 = ( append1574001858od_a_a @ Ys2 @ Vs ) )
% 0.25/0.57 = ( ( Xs2 = Ys2 )
% 0.25/0.57 & ( Us = Vs ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % append_eq_append_conv
% 0.25/0.57 thf(fact_223_append1__eq__conv,axiom,
% 0.25/0.57 ! [Xs2: list_P1467822637od_a_a,X3: product_prod_a_a,Ys2: list_P1467822637od_a_a,Y3: product_prod_a_a] :
% 0.25/0.57 ( ( ( append1574001858od_a_a @ Xs2 @ ( cons_P1921020637od_a_a @ X3 @ nil_Product_prod_a_a ) )
% 0.25/0.57 = ( append1574001858od_a_a @ Ys2 @ ( cons_P1921020637od_a_a @ Y3 @ nil_Product_prod_a_a ) ) )
% 0.25/0.57 = ( ( Xs2 = Ys2 )
% 0.25/0.57 & ( X3 = Y3 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % append1_eq_conv
% 0.25/0.57 thf(fact_224_Cons__in__lex,axiom,
% 0.25/0.57 ! [X3: product_prod_a_a,Xs2: list_P1467822637od_a_a,Y3: product_prod_a_a,Ys2: list_P1467822637od_a_a,R: set_Pr1948701895od_a_a] :
% 0.25/0.57 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ ( cons_P1921020637od_a_a @ X3 @ Xs2 ) @ ( cons_P1921020637od_a_a @ Y3 @ Ys2 ) ) @ ( lex_Product_prod_a_a @ R ) )
% 0.25/0.57 = ( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X3 @ Y3 ) @ R )
% 0.25/0.57 & ( ( size_s642698393od_a_a @ Xs2 )
% 0.25/0.57 = ( size_s642698393od_a_a @ Ys2 ) ) )
% 0.25/0.57 | ( ( X3 = Y3 )
% 0.25/0.57 & ( member1691432592od_a_a @ ( produc85179863od_a_a @ Xs2 @ Ys2 ) @ ( lex_Product_prod_a_a @ R ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % Cons_in_lex
% 0.25/0.57 thf(fact_225_Cons__in__lex,axiom,
% 0.25/0.57 ! [X3: a,Xs2: list_a,Y3: a,Ys2: list_a,R: set_Product_prod_a_a] :
% 0.25/0.57 ( ( member1250517072list_a @ ( produc1448356631list_a @ ( cons_a @ X3 @ Xs2 ) @ ( cons_a @ Y3 @ Ys2 ) ) @ ( lex_a @ R ) )
% 0.25/0.57 = ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ R )
% 0.25/0.57 & ( ( size_size_list_a @ Xs2 )
% 0.25/0.57 = ( size_size_list_a @ Ys2 ) ) )
% 0.25/0.57 | ( ( X3 = Y3 )
% 0.25/0.57 & ( member1250517072list_a @ ( produc1448356631list_a @ Xs2 @ Ys2 ) @ ( lex_a @ R ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % Cons_in_lex
% 0.25/0.57 thf(fact_226_in__set__impl__in__set__zip1,axiom,
% 0.25/0.57 ! [Xs2: list_a,Ys2: list_a,X3: a] :
% 0.25/0.57 ( ( ( size_size_list_a @ Xs2 )
% 0.25/0.57 = ( size_size_list_a @ Ys2 ) )
% 0.25/0.57 => ( ( member_a2 @ X3 @ ( set_a2 @ Xs2 ) )
% 0.25/0.57 => ~ ! [Y4: a] :
% 0.25/0.57 ~ ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y4 ) @ ( set_Product_prod_a_a2 @ ( zip_a_a @ Xs2 @ Ys2 ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % in_set_impl_in_set_zip1
% 0.25/0.57 thf(fact_227_in__set__impl__in__set__zip2,axiom,
% 0.25/0.57 ! [Xs2: list_a,Ys2: list_a,Y3: a] :
% 0.25/0.57 ( ( ( size_size_list_a @ Xs2 )
% 0.25/0.57 = ( size_size_list_a @ Ys2 ) )
% 0.25/0.57 => ( ( member_a2 @ Y3 @ ( set_a2 @ Ys2 ) )
% 0.25/0.57 => ~ ! [X4: a] :
% 0.25/0.57 ~ ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y3 ) @ ( set_Product_prod_a_a2 @ ( zip_a_a @ Xs2 @ Ys2 ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % in_set_impl_in_set_zip2
% 0.25/0.57 thf(fact_228_list__induct4,axiom,
% 0.25/0.57 ! [Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a,Zs: list_P1467822637od_a_a,Ws: list_P1467822637od_a_a,P2: list_P1467822637od_a_a > list_P1467822637od_a_a > list_P1467822637od_a_a > list_P1467822637od_a_a > $o] :
% 0.25/0.57 ( ( ( size_s642698393od_a_a @ Xs2 )
% 0.25/0.57 = ( size_s642698393od_a_a @ Ys2 ) )
% 0.25/0.57 => ( ( ( size_s642698393od_a_a @ Ys2 )
% 0.25/0.57 = ( size_s642698393od_a_a @ Zs ) )
% 0.25/0.57 => ( ( ( size_s642698393od_a_a @ Zs )
% 0.25/0.57 = ( size_s642698393od_a_a @ Ws ) )
% 0.25/0.57 => ( ( P2 @ nil_Product_prod_a_a @ nil_Product_prod_a_a @ nil_Product_prod_a_a @ nil_Product_prod_a_a )
% 0.25/0.57 => ( ! [X4: product_prod_a_a,Xs4: list_P1467822637od_a_a,Y4: product_prod_a_a,Ys4: list_P1467822637od_a_a,Z2: product_prod_a_a,Zs2: list_P1467822637od_a_a,W: product_prod_a_a,Ws2: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( ( size_s642698393od_a_a @ Xs4 )
% 0.25/0.57 = ( size_s642698393od_a_a @ Ys4 ) )
% 0.25/0.57 => ( ( ( size_s642698393od_a_a @ Ys4 )
% 0.25/0.57 = ( size_s642698393od_a_a @ Zs2 ) )
% 0.25/0.57 => ( ( ( size_s642698393od_a_a @ Zs2 )
% 0.25/0.57 = ( size_s642698393od_a_a @ Ws2 ) )
% 0.25/0.57 => ( ( P2 @ Xs4 @ Ys4 @ Zs2 @ Ws2 )
% 0.25/0.57 => ( P2 @ ( cons_P1921020637od_a_a @ X4 @ Xs4 ) @ ( cons_P1921020637od_a_a @ Y4 @ Ys4 ) @ ( cons_P1921020637od_a_a @ Z2 @ Zs2 ) @ ( cons_P1921020637od_a_a @ W @ Ws2 ) ) ) ) ) )
% 0.25/0.57 => ( P2 @ Xs2 @ Ys2 @ Zs @ Ws ) ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % list_induct4
% 0.25/0.57 thf(fact_229_list__induct3,axiom,
% 0.25/0.57 ! [Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a,Zs: list_P1467822637od_a_a,P2: list_P1467822637od_a_a > list_P1467822637od_a_a > list_P1467822637od_a_a > $o] :
% 0.25/0.57 ( ( ( size_s642698393od_a_a @ Xs2 )
% 0.25/0.57 = ( size_s642698393od_a_a @ Ys2 ) )
% 0.25/0.57 => ( ( ( size_s642698393od_a_a @ Ys2 )
% 0.25/0.57 = ( size_s642698393od_a_a @ Zs ) )
% 0.25/0.57 => ( ( P2 @ nil_Product_prod_a_a @ nil_Product_prod_a_a @ nil_Product_prod_a_a )
% 0.25/0.57 => ( ! [X4: product_prod_a_a,Xs4: list_P1467822637od_a_a,Y4: product_prod_a_a,Ys4: list_P1467822637od_a_a,Z2: product_prod_a_a,Zs2: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( ( size_s642698393od_a_a @ Xs4 )
% 0.25/0.57 = ( size_s642698393od_a_a @ Ys4 ) )
% 0.25/0.57 => ( ( ( size_s642698393od_a_a @ Ys4 )
% 0.25/0.57 = ( size_s642698393od_a_a @ Zs2 ) )
% 0.25/0.57 => ( ( P2 @ Xs4 @ Ys4 @ Zs2 )
% 0.25/0.57 => ( P2 @ ( cons_P1921020637od_a_a @ X4 @ Xs4 ) @ ( cons_P1921020637od_a_a @ Y4 @ Ys4 ) @ ( cons_P1921020637od_a_a @ Z2 @ Zs2 ) ) ) ) )
% 0.25/0.57 => ( P2 @ Xs2 @ Ys2 @ Zs ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % list_induct3
% 0.25/0.57 thf(fact_230_list__induct2,axiom,
% 0.25/0.57 ! [Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a,P2: list_P1467822637od_a_a > list_P1467822637od_a_a > $o] :
% 0.25/0.57 ( ( ( size_s642698393od_a_a @ Xs2 )
% 0.25/0.57 = ( size_s642698393od_a_a @ Ys2 ) )
% 0.25/0.57 => ( ( P2 @ nil_Product_prod_a_a @ nil_Product_prod_a_a )
% 0.25/0.57 => ( ! [X4: product_prod_a_a,Xs4: list_P1467822637od_a_a,Y4: product_prod_a_a,Ys4: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( ( size_s642698393od_a_a @ Xs4 )
% 0.25/0.57 = ( size_s642698393od_a_a @ Ys4 ) )
% 0.25/0.57 => ( ( P2 @ Xs4 @ Ys4 )
% 0.25/0.57 => ( P2 @ ( cons_P1921020637od_a_a @ X4 @ Xs4 ) @ ( cons_P1921020637od_a_a @ Y4 @ Ys4 ) ) ) )
% 0.25/0.57 => ( P2 @ Xs2 @ Ys2 ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % list_induct2
% 0.25/0.57 thf(fact_231_transpose_Ocases,axiom,
% 0.25/0.57 ! [X3: list_l1108175539od_a_a] :
% 0.25/0.57 ( ( X3 != nil_li1885598003od_a_a )
% 0.25/0.57 => ( ! [Xss: list_l1108175539od_a_a] :
% 0.25/0.57 ( X3
% 0.25/0.57 != ( cons_l724116707od_a_a @ nil_Product_prod_a_a @ Xss ) )
% 0.25/0.57 => ~ ! [X4: product_prod_a_a,Xs4: list_P1467822637od_a_a,Xss: list_l1108175539od_a_a] :
% 0.25/0.57 ( X3
% 0.25/0.57 != ( cons_l724116707od_a_a @ ( cons_P1921020637od_a_a @ X4 @ Xs4 ) @ Xss ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % transpose.cases
% 0.25/0.57 thf(fact_232_set__zip__rightD,axiom,
% 0.25/0.57 ! [X3: a,Y3: a,Xs2: list_a,Ys2: list_a] :
% 0.25/0.57 ( ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ ( set_Product_prod_a_a2 @ ( zip_a_a @ Xs2 @ Ys2 ) ) )
% 0.25/0.57 => ( member_a2 @ Y3 @ ( set_a2 @ Ys2 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % set_zip_rightD
% 0.25/0.57 thf(fact_233_set__zip__leftD,axiom,
% 0.25/0.57 ! [X3: a,Y3: a,Xs2: list_a,Ys2: list_a] :
% 0.25/0.57 ( ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ ( set_Product_prod_a_a2 @ ( zip_a_a @ Xs2 @ Ys2 ) ) )
% 0.25/0.57 => ( member_a2 @ X3 @ ( set_a2 @ Xs2 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % set_zip_leftD
% 0.25/0.57 thf(fact_234_in__set__zipE,axiom,
% 0.25/0.57 ! [X3: a,Y3: a,Xs2: list_a,Ys2: list_a] :
% 0.25/0.57 ( ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ ( set_Product_prod_a_a2 @ ( zip_a_a @ Xs2 @ Ys2 ) ) )
% 0.25/0.57 => ~ ( ( member_a2 @ X3 @ ( set_a2 @ Xs2 ) )
% 0.25/0.57 => ~ ( member_a2 @ Y3 @ ( set_a2 @ Ys2 ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % in_set_zipE
% 0.25/0.57 thf(fact_235_zip__same,axiom,
% 0.25/0.57 ! [A: a,B: a,Xs2: list_a] :
% 0.25/0.57 ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ ( set_Product_prod_a_a2 @ ( zip_a_a @ Xs2 @ Xs2 ) ) )
% 0.25/0.57 = ( ( member_a2 @ A @ ( set_a2 @ Xs2 ) )
% 0.25/0.57 & ( A = B ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % zip_same
% 0.25/0.57 thf(fact_236_same__length__different,axiom,
% 0.25/0.57 ! [Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( Xs2 != Ys2 )
% 0.25/0.57 => ( ( ( size_s642698393od_a_a @ Xs2 )
% 0.25/0.57 = ( size_s642698393od_a_a @ Ys2 ) )
% 0.25/0.57 => ? [Pre: list_P1467822637od_a_a,X4: product_prod_a_a,Xs3: list_P1467822637od_a_a,Y4: product_prod_a_a,Ys3: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( X4 != Y4 )
% 0.25/0.57 & ( Xs2
% 0.25/0.57 = ( append1574001858od_a_a @ Pre @ ( append1574001858od_a_a @ ( cons_P1921020637od_a_a @ X4 @ nil_Product_prod_a_a ) @ Xs3 ) ) )
% 0.25/0.57 & ( Ys2
% 0.25/0.57 = ( append1574001858od_a_a @ Pre @ ( append1574001858od_a_a @ ( cons_P1921020637od_a_a @ Y4 @ nil_Product_prod_a_a ) @ Ys3 ) ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % same_length_different
% 0.25/0.57 thf(fact_237_list_Oset__cases,axiom,
% 0.25/0.57 ! [E: product_prod_a_a,A: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( member449909584od_a_a @ E @ ( set_Product_prod_a_a2 @ A ) )
% 0.25/0.57 => ( ! [Z22: list_P1467822637od_a_a] :
% 0.25/0.57 ( A
% 0.25/0.57 != ( cons_P1921020637od_a_a @ E @ Z22 ) )
% 0.25/0.57 => ~ ! [Z1: product_prod_a_a,Z22: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( A
% 0.25/0.57 = ( cons_P1921020637od_a_a @ Z1 @ Z22 ) )
% 0.25/0.57 => ~ ( member449909584od_a_a @ E @ ( set_Product_prod_a_a2 @ Z22 ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % list.set_cases
% 0.25/0.57 thf(fact_238_set__ConsD,axiom,
% 0.25/0.57 ! [Y3: product_prod_a_a,X3: product_prod_a_a,Xs2: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( member449909584od_a_a @ Y3 @ ( set_Product_prod_a_a2 @ ( cons_P1921020637od_a_a @ X3 @ Xs2 ) ) )
% 0.25/0.57 => ( ( Y3 = X3 )
% 0.25/0.57 | ( member449909584od_a_a @ Y3 @ ( set_Product_prod_a_a2 @ Xs2 ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % set_ConsD
% 0.25/0.57 thf(fact_239_list_Oset__intros_I1_J,axiom,
% 0.25/0.57 ! [X21: product_prod_a_a,X22: list_P1467822637od_a_a] : ( member449909584od_a_a @ X21 @ ( set_Product_prod_a_a2 @ ( cons_P1921020637od_a_a @ X21 @ X22 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % list.set_intros(1)
% 0.25/0.57 thf(fact_240_list_Oset__intros_I2_J,axiom,
% 0.25/0.57 ! [Y3: product_prod_a_a,X22: list_P1467822637od_a_a,X21: product_prod_a_a] :
% 0.25/0.57 ( ( member449909584od_a_a @ Y3 @ ( set_Product_prod_a_a2 @ X22 ) )
% 0.25/0.57 => ( member449909584od_a_a @ Y3 @ ( set_Product_prod_a_a2 @ ( cons_P1921020637od_a_a @ X21 @ X22 ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % list.set_intros(2)
% 0.25/0.57 thf(fact_241_lex__append__rightI,axiom,
% 0.25/0.57 ! [Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a,R: set_Pr1948701895od_a_a,Vs: list_P1467822637od_a_a,Us: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ Xs2 @ Ys2 ) @ ( lex_Product_prod_a_a @ R ) )
% 0.25/0.57 => ( ( ( size_s642698393od_a_a @ Vs )
% 0.25/0.57 = ( size_s642698393od_a_a @ Us ) )
% 0.25/0.57 => ( member1691432592od_a_a @ ( produc85179863od_a_a @ ( append1574001858od_a_a @ Xs2 @ Us ) @ ( append1574001858od_a_a @ Ys2 @ Vs ) ) @ ( lex_Product_prod_a_a @ R ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % lex_append_rightI
% 0.25/0.57 thf(fact_242_sorted__wrt_Ocases,axiom,
% 0.25/0.57 ! [X3: produc501911462od_a_a] :
% 0.25/0.57 ( ! [P4: product_prod_a_a > product_prod_a_a > $o] :
% 0.25/0.57 ( X3
% 0.25/0.57 != ( produc214132118od_a_a @ P4 @ nil_Product_prod_a_a ) )
% 0.25/0.57 => ~ ! [P4: product_prod_a_a > product_prod_a_a > $o,X4: product_prod_a_a,Ys4: list_P1467822637od_a_a] :
% 0.25/0.57 ( X3
% 0.25/0.57 != ( produc214132118od_a_a @ P4 @ ( cons_P1921020637od_a_a @ X4 @ Ys4 ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % sorted_wrt.cases
% 0.25/0.57 thf(fact_243_successively_Ocases,axiom,
% 0.25/0.57 ! [X3: produc501911462od_a_a] :
% 0.25/0.57 ( ! [P4: product_prod_a_a > product_prod_a_a > $o] :
% 0.25/0.57 ( X3
% 0.25/0.57 != ( produc214132118od_a_a @ P4 @ nil_Product_prod_a_a ) )
% 0.25/0.57 => ( ! [P4: product_prod_a_a > product_prod_a_a > $o,X4: product_prod_a_a] :
% 0.25/0.57 ( X3
% 0.25/0.57 != ( produc214132118od_a_a @ P4 @ ( cons_P1921020637od_a_a @ X4 @ nil_Product_prod_a_a ) ) )
% 0.25/0.57 => ~ ! [P4: product_prod_a_a > product_prod_a_a > $o,X4: product_prod_a_a,Y4: product_prod_a_a,Xs4: list_P1467822637od_a_a] :
% 0.25/0.57 ( X3
% 0.25/0.57 != ( produc214132118od_a_a @ P4 @ ( cons_P1921020637od_a_a @ X4 @ ( cons_P1921020637od_a_a @ Y4 @ Xs4 ) ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % successively.cases
% 0.25/0.57 thf(fact_244_map__tailrec__rev_Oinduct,axiom,
% 0.25/0.57 ! [P2: ( product_prod_a_a > product_prod_a_a ) > list_P1467822637od_a_a > list_P1467822637od_a_a > $o,A0: product_prod_a_a > product_prod_a_a,A1: list_P1467822637od_a_a,A22: list_P1467822637od_a_a] :
% 0.25/0.57 ( ! [F2: product_prod_a_a > product_prod_a_a,X_1: list_P1467822637od_a_a] : ( P2 @ F2 @ nil_Product_prod_a_a @ X_1 )
% 0.25/0.57 => ( ! [F2: product_prod_a_a > product_prod_a_a,A3: product_prod_a_a,As: list_P1467822637od_a_a,Bs: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( P2 @ F2 @ As @ ( cons_P1921020637od_a_a @ ( F2 @ A3 ) @ Bs ) )
% 0.25/0.57 => ( P2 @ F2 @ ( cons_P1921020637od_a_a @ A3 @ As ) @ Bs ) )
% 0.25/0.57 => ( P2 @ A0 @ A1 @ A22 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % map_tailrec_rev.induct
% 0.25/0.57 thf(fact_245_list__nonempty__induct,axiom,
% 0.25/0.57 ! [Xs2: list_P1467822637od_a_a,P2: list_P1467822637od_a_a > $o] :
% 0.25/0.57 ( ( Xs2 != nil_Product_prod_a_a )
% 0.25/0.57 => ( ! [X4: product_prod_a_a] : ( P2 @ ( cons_P1921020637od_a_a @ X4 @ nil_Product_prod_a_a ) )
% 0.25/0.57 => ( ! [X4: product_prod_a_a,Xs4: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( Xs4 != nil_Product_prod_a_a )
% 0.25/0.57 => ( ( P2 @ Xs4 )
% 0.25/0.57 => ( P2 @ ( cons_P1921020637od_a_a @ X4 @ Xs4 ) ) ) )
% 0.25/0.57 => ( P2 @ Xs2 ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % list_nonempty_induct
% 0.25/0.57 thf(fact_246_successively_Oinduct,axiom,
% 0.25/0.57 ! [P2: ( product_prod_a_a > product_prod_a_a > $o ) > list_P1467822637od_a_a > $o,A0: product_prod_a_a > product_prod_a_a > $o,A1: list_P1467822637od_a_a] :
% 0.25/0.57 ( ! [P4: product_prod_a_a > product_prod_a_a > $o] : ( P2 @ P4 @ nil_Product_prod_a_a )
% 0.25/0.57 => ( ! [P4: product_prod_a_a > product_prod_a_a > $o,X4: product_prod_a_a] : ( P2 @ P4 @ ( cons_P1921020637od_a_a @ X4 @ nil_Product_prod_a_a ) )
% 0.25/0.57 => ( ! [P4: product_prod_a_a > product_prod_a_a > $o,X4: product_prod_a_a,Y4: product_prod_a_a,Xs4: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( P2 @ P4 @ ( cons_P1921020637od_a_a @ Y4 @ Xs4 ) )
% 0.25/0.57 => ( P2 @ P4 @ ( cons_P1921020637od_a_a @ X4 @ ( cons_P1921020637od_a_a @ Y4 @ Xs4 ) ) ) )
% 0.25/0.57 => ( P2 @ A0 @ A1 ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % successively.induct
% 0.25/0.57 thf(fact_247_remdups__adj_Oinduct,axiom,
% 0.25/0.57 ! [P2: list_P1467822637od_a_a > $o,A0: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( P2 @ nil_Product_prod_a_a )
% 0.25/0.57 => ( ! [X4: product_prod_a_a] : ( P2 @ ( cons_P1921020637od_a_a @ X4 @ nil_Product_prod_a_a ) )
% 0.25/0.57 => ( ! [X4: product_prod_a_a,Y4: product_prod_a_a,Xs4: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( ( X4 = Y4 )
% 0.25/0.57 => ( P2 @ ( cons_P1921020637od_a_a @ X4 @ Xs4 ) ) )
% 0.25/0.57 => ( ( ( X4 != Y4 )
% 0.25/0.57 => ( P2 @ ( cons_P1921020637od_a_a @ Y4 @ Xs4 ) ) )
% 0.25/0.57 => ( P2 @ ( cons_P1921020637od_a_a @ X4 @ ( cons_P1921020637od_a_a @ Y4 @ Xs4 ) ) ) ) )
% 0.25/0.57 => ( P2 @ A0 ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % remdups_adj.induct
% 0.25/0.57 thf(fact_248_sorted__wrt_Oinduct,axiom,
% 0.25/0.57 ! [P2: ( product_prod_a_a > product_prod_a_a > $o ) > list_P1467822637od_a_a > $o,A0: product_prod_a_a > product_prod_a_a > $o,A1: list_P1467822637od_a_a] :
% 0.25/0.57 ( ! [P4: product_prod_a_a > product_prod_a_a > $o] : ( P2 @ P4 @ nil_Product_prod_a_a )
% 0.25/0.57 => ( ! [P4: product_prod_a_a > product_prod_a_a > $o,X4: product_prod_a_a,Ys4: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( P2 @ P4 @ Ys4 )
% 0.25/0.57 => ( P2 @ P4 @ ( cons_P1921020637od_a_a @ X4 @ Ys4 ) ) )
% 0.25/0.57 => ( P2 @ A0 @ A1 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % sorted_wrt.induct
% 0.25/0.57 thf(fact_249_remdups__adj_Ocases,axiom,
% 0.25/0.57 ! [X3: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( X3 != nil_Product_prod_a_a )
% 0.25/0.57 => ( ! [X4: product_prod_a_a] :
% 0.25/0.57 ( X3
% 0.25/0.57 != ( cons_P1921020637od_a_a @ X4 @ nil_Product_prod_a_a ) )
% 0.25/0.57 => ~ ! [X4: product_prod_a_a,Y4: product_prod_a_a,Xs4: list_P1467822637od_a_a] :
% 0.25/0.57 ( X3
% 0.25/0.57 != ( cons_P1921020637od_a_a @ X4 @ ( cons_P1921020637od_a_a @ Y4 @ Xs4 ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % remdups_adj.cases
% 0.25/0.57 thf(fact_250_shuffles_Oinduct,axiom,
% 0.25/0.57 ! [P2: list_P1467822637od_a_a > list_P1467822637od_a_a > $o,A0: list_P1467822637od_a_a,A1: list_P1467822637od_a_a] :
% 0.25/0.57 ( ! [X_1: list_P1467822637od_a_a] : ( P2 @ nil_Product_prod_a_a @ X_1 )
% 0.25/0.57 => ( ! [Xs4: list_P1467822637od_a_a] : ( P2 @ Xs4 @ nil_Product_prod_a_a )
% 0.25/0.57 => ( ! [X4: product_prod_a_a,Xs4: list_P1467822637od_a_a,Y4: product_prod_a_a,Ys4: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( P2 @ Xs4 @ ( cons_P1921020637od_a_a @ Y4 @ Ys4 ) )
% 0.25/0.57 => ( ( P2 @ ( cons_P1921020637od_a_a @ X4 @ Xs4 ) @ Ys4 )
% 0.25/0.57 => ( P2 @ ( cons_P1921020637od_a_a @ X4 @ Xs4 ) @ ( cons_P1921020637od_a_a @ Y4 @ Ys4 ) ) ) )
% 0.25/0.57 => ( P2 @ A0 @ A1 ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % shuffles.induct
% 0.25/0.57 thf(fact_251_induct__list012,axiom,
% 0.25/0.57 ! [P2: list_P1467822637od_a_a > $o,Xs2: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( P2 @ nil_Product_prod_a_a )
% 0.25/0.57 => ( ! [X4: product_prod_a_a] : ( P2 @ ( cons_P1921020637od_a_a @ X4 @ nil_Product_prod_a_a ) )
% 0.25/0.57 => ( ! [X4: product_prod_a_a,Y4: product_prod_a_a,Zs2: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( P2 @ Zs2 )
% 0.25/0.57 => ( ( P2 @ ( cons_P1921020637od_a_a @ Y4 @ Zs2 ) )
% 0.25/0.57 => ( P2 @ ( cons_P1921020637od_a_a @ X4 @ ( cons_P1921020637od_a_a @ Y4 @ Zs2 ) ) ) ) )
% 0.25/0.57 => ( P2 @ Xs2 ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % induct_list012
% 0.25/0.57 thf(fact_252_splice_Oinduct,axiom,
% 0.25/0.57 ! [P2: list_P1467822637od_a_a > list_P1467822637od_a_a > $o,A0: list_P1467822637od_a_a,A1: list_P1467822637od_a_a] :
% 0.25/0.57 ( ! [X_1: list_P1467822637od_a_a] : ( P2 @ nil_Product_prod_a_a @ X_1 )
% 0.25/0.57 => ( ! [X4: product_prod_a_a,Xs4: list_P1467822637od_a_a,Ys4: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( P2 @ Ys4 @ Xs4 )
% 0.25/0.57 => ( P2 @ ( cons_P1921020637od_a_a @ X4 @ Xs4 ) @ Ys4 ) )
% 0.25/0.57 => ( P2 @ A0 @ A1 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % splice.induct
% 0.25/0.57 thf(fact_253_list__induct2_H,axiom,
% 0.25/0.57 ! [P2: list_P1467822637od_a_a > list_P1467822637od_a_a > $o,Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( P2 @ nil_Product_prod_a_a @ nil_Product_prod_a_a )
% 0.25/0.57 => ( ! [X4: product_prod_a_a,Xs4: list_P1467822637od_a_a] : ( P2 @ ( cons_P1921020637od_a_a @ X4 @ Xs4 ) @ nil_Product_prod_a_a )
% 0.25/0.57 => ( ! [Y4: product_prod_a_a,Ys4: list_P1467822637od_a_a] : ( P2 @ nil_Product_prod_a_a @ ( cons_P1921020637od_a_a @ Y4 @ Ys4 ) )
% 0.25/0.57 => ( ! [X4: product_prod_a_a,Xs4: list_P1467822637od_a_a,Y4: product_prod_a_a,Ys4: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( P2 @ Xs4 @ Ys4 )
% 0.25/0.57 => ( P2 @ ( cons_P1921020637od_a_a @ X4 @ Xs4 ) @ ( cons_P1921020637od_a_a @ Y4 @ Ys4 ) ) )
% 0.25/0.57 => ( P2 @ Xs2 @ Ys2 ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % list_induct2'
% 0.25/0.57 thf(fact_254_neq__Nil__conv,axiom,
% 0.25/0.57 ! [Xs2: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( Xs2 != nil_Product_prod_a_a )
% 0.25/0.57 = ( ? [Y: product_prod_a_a,Ys: list_P1467822637od_a_a] :
% 0.25/0.57 ( Xs2
% 0.25/0.57 = ( cons_P1921020637od_a_a @ Y @ Ys ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % neq_Nil_conv
% 0.25/0.57 thf(fact_255_list_Oinducts,axiom,
% 0.25/0.57 ! [P2: list_P1467822637od_a_a > $o,List: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( P2 @ nil_Product_prod_a_a )
% 0.25/0.57 => ( ! [X12: product_prod_a_a,X23: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( P2 @ X23 )
% 0.25/0.57 => ( P2 @ ( cons_P1921020637od_a_a @ X12 @ X23 ) ) )
% 0.25/0.57 => ( P2 @ List ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % list.inducts
% 0.25/0.57 thf(fact_256_list_Oexhaust,axiom,
% 0.25/0.57 ! [Y3: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( Y3 != nil_Product_prod_a_a )
% 0.25/0.57 => ~ ! [X212: product_prod_a_a,X222: list_P1467822637od_a_a] :
% 0.25/0.57 ( Y3
% 0.25/0.57 != ( cons_P1921020637od_a_a @ X212 @ X222 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % list.exhaust
% 0.25/0.57 thf(fact_257_list_OdiscI,axiom,
% 0.25/0.57 ! [List: list_P1467822637od_a_a,X21: product_prod_a_a,X22: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( List
% 0.25/0.57 = ( cons_P1921020637od_a_a @ X21 @ X22 ) )
% 0.25/0.57 => ( List != nil_Product_prod_a_a ) ) ).
% 0.25/0.57
% 0.25/0.57 % list.discI
% 0.25/0.57 thf(fact_258_list_Odistinct_I1_J,axiom,
% 0.25/0.57 ! [X21: product_prod_a_a,X22: list_P1467822637od_a_a] :
% 0.25/0.57 ( nil_Product_prod_a_a
% 0.25/0.57 != ( cons_P1921020637od_a_a @ X21 @ X22 ) ) ).
% 0.25/0.57
% 0.25/0.57 % list.distinct(1)
% 0.25/0.57 thf(fact_259_append_Oleft__neutral,axiom,
% 0.25/0.57 ! [A: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( append1574001858od_a_a @ nil_Product_prod_a_a @ A )
% 0.25/0.57 = A ) ).
% 0.25/0.57
% 0.25/0.57 % append.left_neutral
% 0.25/0.57 thf(fact_260_append__Nil,axiom,
% 0.25/0.57 ! [Ys2: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( append1574001858od_a_a @ nil_Product_prod_a_a @ Ys2 )
% 0.25/0.57 = Ys2 ) ).
% 0.25/0.57
% 0.25/0.57 % append_Nil
% 0.25/0.57 thf(fact_261_eq__Nil__appendI,axiom,
% 0.25/0.57 ! [Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( Xs2 = Ys2 )
% 0.25/0.57 => ( Xs2
% 0.25/0.57 = ( append1574001858od_a_a @ nil_Product_prod_a_a @ Ys2 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % eq_Nil_appendI
% 0.25/0.57 thf(fact_262_pcas_Ocases,axiom,
% 0.25/0.57 ! [X3: produc1197928545_a_a_a] :
% 0.25/0.57 ( ! [U2: a,V: a] :
% 0.25/0.57 ( X3
% 0.25/0.57 != ( produc1440321489_a_a_a @ U2 @ ( produc998622632_a_a_a @ nil_Product_prod_a_a @ V ) ) )
% 0.25/0.57 => ~ ! [U2: a,E2: product_prod_a_a,Es: list_P1467822637od_a_a,V: a] :
% 0.25/0.57 ( X3
% 0.25/0.57 != ( produc1440321489_a_a_a @ U2 @ ( produc998622632_a_a_a @ ( cons_P1921020637od_a_a @ E2 @ Es ) @ V ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % pcas.cases
% 0.25/0.57 thf(fact_263_progressing__Nil,axiom,
% 0.25/0.57 kurato1072996284sing_a @ nil_Product_prod_a_a ).
% 0.25/0.57
% 0.25/0.57 % progressing_Nil
% 0.25/0.57 thf(fact_264_split__list__first__prop__iff,axiom,
% 0.25/0.57 ! [Xs2: list_P1467822637od_a_a,P2: product_prod_a_a > $o] :
% 0.25/0.57 ( ( ? [X: product_prod_a_a] :
% 0.25/0.57 ( ( member449909584od_a_a @ X @ ( set_Product_prod_a_a2 @ Xs2 ) )
% 0.25/0.57 & ( P2 @ X ) ) )
% 0.25/0.57 = ( ? [Ys: list_P1467822637od_a_a,X: product_prod_a_a] :
% 0.25/0.57 ( ? [Zs3: list_P1467822637od_a_a] :
% 0.25/0.57 ( Xs2
% 0.25/0.57 = ( append1574001858od_a_a @ Ys @ ( cons_P1921020637od_a_a @ X @ Zs3 ) ) )
% 0.25/0.57 & ( P2 @ X )
% 0.25/0.57 & ! [Y: product_prod_a_a] :
% 0.25/0.57 ( ( member449909584od_a_a @ Y @ ( set_Product_prod_a_a2 @ Ys ) )
% 0.25/0.57 => ~ ( P2 @ Y ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % split_list_first_prop_iff
% 0.25/0.57 thf(fact_265_split__list__last__prop__iff,axiom,
% 0.25/0.57 ! [Xs2: list_P1467822637od_a_a,P2: product_prod_a_a > $o] :
% 0.25/0.57 ( ( ? [X: product_prod_a_a] :
% 0.25/0.57 ( ( member449909584od_a_a @ X @ ( set_Product_prod_a_a2 @ Xs2 ) )
% 0.25/0.57 & ( P2 @ X ) ) )
% 0.25/0.57 = ( ? [Ys: list_P1467822637od_a_a,X: product_prod_a_a,Zs3: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( Xs2
% 0.25/0.57 = ( append1574001858od_a_a @ Ys @ ( cons_P1921020637od_a_a @ X @ Zs3 ) ) )
% 0.25/0.57 & ( P2 @ X )
% 0.25/0.57 & ! [Y: product_prod_a_a] :
% 0.25/0.57 ( ( member449909584od_a_a @ Y @ ( set_Product_prod_a_a2 @ Zs3 ) )
% 0.25/0.57 => ~ ( P2 @ Y ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % split_list_last_prop_iff
% 0.25/0.57 thf(fact_266_in__set__conv__decomp__first,axiom,
% 0.25/0.57 ! [X3: product_prod_a_a,Xs2: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( member449909584od_a_a @ X3 @ ( set_Product_prod_a_a2 @ Xs2 ) )
% 0.25/0.57 = ( ? [Ys: list_P1467822637od_a_a,Zs3: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( Xs2
% 0.25/0.57 = ( append1574001858od_a_a @ Ys @ ( cons_P1921020637od_a_a @ X3 @ Zs3 ) ) )
% 0.25/0.57 & ~ ( member449909584od_a_a @ X3 @ ( set_Product_prod_a_a2 @ Ys ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % in_set_conv_decomp_first
% 0.25/0.57 thf(fact_267_in__set__conv__decomp__last,axiom,
% 0.25/0.57 ! [X3: product_prod_a_a,Xs2: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( member449909584od_a_a @ X3 @ ( set_Product_prod_a_a2 @ Xs2 ) )
% 0.25/0.57 = ( ? [Ys: list_P1467822637od_a_a,Zs3: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( Xs2
% 0.25/0.57 = ( append1574001858od_a_a @ Ys @ ( cons_P1921020637od_a_a @ X3 @ Zs3 ) ) )
% 0.25/0.57 & ~ ( member449909584od_a_a @ X3 @ ( set_Product_prod_a_a2 @ Zs3 ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % in_set_conv_decomp_last
% 0.25/0.57 thf(fact_268_split__list__first__propE,axiom,
% 0.25/0.57 ! [Xs2: list_P1467822637od_a_a,P2: product_prod_a_a > $o] :
% 0.25/0.57 ( ? [X5: product_prod_a_a] :
% 0.25/0.57 ( ( member449909584od_a_a @ X5 @ ( set_Product_prod_a_a2 @ Xs2 ) )
% 0.25/0.57 & ( P2 @ X5 ) )
% 0.25/0.57 => ~ ! [Ys4: list_P1467822637od_a_a,X4: product_prod_a_a] :
% 0.25/0.57 ( ? [Zs2: list_P1467822637od_a_a] :
% 0.25/0.57 ( Xs2
% 0.25/0.57 = ( append1574001858od_a_a @ Ys4 @ ( cons_P1921020637od_a_a @ X4 @ Zs2 ) ) )
% 0.25/0.57 => ( ( P2 @ X4 )
% 0.25/0.57 => ~ ! [Xa: product_prod_a_a] :
% 0.25/0.57 ( ( member449909584od_a_a @ Xa @ ( set_Product_prod_a_a2 @ Ys4 ) )
% 0.25/0.57 => ~ ( P2 @ Xa ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % split_list_first_propE
% 0.25/0.57 thf(fact_269_split__list__last__propE,axiom,
% 0.25/0.57 ! [Xs2: list_P1467822637od_a_a,P2: product_prod_a_a > $o] :
% 0.25/0.57 ( ? [X5: product_prod_a_a] :
% 0.25/0.57 ( ( member449909584od_a_a @ X5 @ ( set_Product_prod_a_a2 @ Xs2 ) )
% 0.25/0.57 & ( P2 @ X5 ) )
% 0.25/0.57 => ~ ! [Ys4: list_P1467822637od_a_a,X4: product_prod_a_a,Zs2: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( Xs2
% 0.25/0.57 = ( append1574001858od_a_a @ Ys4 @ ( cons_P1921020637od_a_a @ X4 @ Zs2 ) ) )
% 0.25/0.57 => ( ( P2 @ X4 )
% 0.25/0.57 => ~ ! [Xa: product_prod_a_a] :
% 0.25/0.57 ( ( member449909584od_a_a @ Xa @ ( set_Product_prod_a_a2 @ Zs2 ) )
% 0.25/0.57 => ~ ( P2 @ Xa ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % split_list_last_propE
% 0.25/0.57 thf(fact_270_split__list__first__prop,axiom,
% 0.25/0.57 ! [Xs2: list_P1467822637od_a_a,P2: product_prod_a_a > $o] :
% 0.25/0.57 ( ? [X5: product_prod_a_a] :
% 0.25/0.57 ( ( member449909584od_a_a @ X5 @ ( set_Product_prod_a_a2 @ Xs2 ) )
% 0.25/0.57 & ( P2 @ X5 ) )
% 0.25/0.57 => ? [Ys4: list_P1467822637od_a_a,X4: product_prod_a_a] :
% 0.25/0.57 ( ? [Zs2: list_P1467822637od_a_a] :
% 0.25/0.57 ( Xs2
% 0.25/0.57 = ( append1574001858od_a_a @ Ys4 @ ( cons_P1921020637od_a_a @ X4 @ Zs2 ) ) )
% 0.25/0.57 & ( P2 @ X4 )
% 0.25/0.57 & ! [Xa: product_prod_a_a] :
% 0.25/0.57 ( ( member449909584od_a_a @ Xa @ ( set_Product_prod_a_a2 @ Ys4 ) )
% 0.25/0.57 => ~ ( P2 @ Xa ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % split_list_first_prop
% 0.25/0.57 thf(fact_271_split__list__last__prop,axiom,
% 0.25/0.57 ! [Xs2: list_P1467822637od_a_a,P2: product_prod_a_a > $o] :
% 0.25/0.57 ( ? [X5: product_prod_a_a] :
% 0.25/0.57 ( ( member449909584od_a_a @ X5 @ ( set_Product_prod_a_a2 @ Xs2 ) )
% 0.25/0.57 & ( P2 @ X5 ) )
% 0.25/0.57 => ? [Ys4: list_P1467822637od_a_a,X4: product_prod_a_a,Zs2: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( Xs2
% 0.25/0.57 = ( append1574001858od_a_a @ Ys4 @ ( cons_P1921020637od_a_a @ X4 @ Zs2 ) ) )
% 0.25/0.57 & ( P2 @ X4 )
% 0.25/0.57 & ! [Xa: product_prod_a_a] :
% 0.25/0.57 ( ( member449909584od_a_a @ Xa @ ( set_Product_prod_a_a2 @ Zs2 ) )
% 0.25/0.57 => ~ ( P2 @ Xa ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % split_list_last_prop
% 0.25/0.57 thf(fact_272_in__set__conv__decomp,axiom,
% 0.25/0.57 ! [X3: product_prod_a_a,Xs2: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( member449909584od_a_a @ X3 @ ( set_Product_prod_a_a2 @ Xs2 ) )
% 0.25/0.57 = ( ? [Ys: list_P1467822637od_a_a,Zs3: list_P1467822637od_a_a] :
% 0.25/0.57 ( Xs2
% 0.25/0.57 = ( append1574001858od_a_a @ Ys @ ( cons_P1921020637od_a_a @ X3 @ Zs3 ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % in_set_conv_decomp
% 0.25/0.57 thf(fact_273_append__Cons__eq__iff,axiom,
% 0.25/0.57 ! [X3: product_prod_a_a,Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a,Xs5: list_P1467822637od_a_a,Ys5: list_P1467822637od_a_a] :
% 0.25/0.57 ( ~ ( member449909584od_a_a @ X3 @ ( set_Product_prod_a_a2 @ Xs2 ) )
% 0.25/0.57 => ( ~ ( member449909584od_a_a @ X3 @ ( set_Product_prod_a_a2 @ Ys2 ) )
% 0.25/0.57 => ( ( ( append1574001858od_a_a @ Xs2 @ ( cons_P1921020637od_a_a @ X3 @ Ys2 ) )
% 0.25/0.57 = ( append1574001858od_a_a @ Xs5 @ ( cons_P1921020637od_a_a @ X3 @ Ys5 ) ) )
% 0.25/0.57 = ( ( Xs2 = Xs5 )
% 0.25/0.57 & ( Ys2 = Ys5 ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % append_Cons_eq_iff
% 0.25/0.57 thf(fact_274_split__list__propE,axiom,
% 0.25/0.57 ! [Xs2: list_P1467822637od_a_a,P2: product_prod_a_a > $o] :
% 0.25/0.57 ( ? [X5: product_prod_a_a] :
% 0.25/0.57 ( ( member449909584od_a_a @ X5 @ ( set_Product_prod_a_a2 @ Xs2 ) )
% 0.25/0.57 & ( P2 @ X5 ) )
% 0.25/0.57 => ~ ! [Ys4: list_P1467822637od_a_a,X4: product_prod_a_a] :
% 0.25/0.57 ( ? [Zs2: list_P1467822637od_a_a] :
% 0.25/0.57 ( Xs2
% 0.25/0.57 = ( append1574001858od_a_a @ Ys4 @ ( cons_P1921020637od_a_a @ X4 @ Zs2 ) ) )
% 0.25/0.57 => ~ ( P2 @ X4 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % split_list_propE
% 0.25/0.57 thf(fact_275_split__list__first,axiom,
% 0.25/0.57 ! [X3: product_prod_a_a,Xs2: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( member449909584od_a_a @ X3 @ ( set_Product_prod_a_a2 @ Xs2 ) )
% 0.25/0.57 => ? [Ys4: list_P1467822637od_a_a,Zs2: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( Xs2
% 0.25/0.57 = ( append1574001858od_a_a @ Ys4 @ ( cons_P1921020637od_a_a @ X3 @ Zs2 ) ) )
% 0.25/0.57 & ~ ( member449909584od_a_a @ X3 @ ( set_Product_prod_a_a2 @ Ys4 ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % split_list_first
% 0.25/0.57 thf(fact_276_split__list__prop,axiom,
% 0.25/0.57 ! [Xs2: list_P1467822637od_a_a,P2: product_prod_a_a > $o] :
% 0.25/0.57 ( ? [X5: product_prod_a_a] :
% 0.25/0.57 ( ( member449909584od_a_a @ X5 @ ( set_Product_prod_a_a2 @ Xs2 ) )
% 0.25/0.57 & ( P2 @ X5 ) )
% 0.25/0.57 => ? [Ys4: list_P1467822637od_a_a,X4: product_prod_a_a] :
% 0.25/0.57 ( ? [Zs2: list_P1467822637od_a_a] :
% 0.25/0.57 ( Xs2
% 0.25/0.57 = ( append1574001858od_a_a @ Ys4 @ ( cons_P1921020637od_a_a @ X4 @ Zs2 ) ) )
% 0.25/0.57 & ( P2 @ X4 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % split_list_prop
% 0.25/0.57 thf(fact_277_split__list__last,axiom,
% 0.25/0.57 ! [X3: product_prod_a_a,Xs2: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( member449909584od_a_a @ X3 @ ( set_Product_prod_a_a2 @ Xs2 ) )
% 0.25/0.57 => ? [Ys4: list_P1467822637od_a_a,Zs2: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( Xs2
% 0.25/0.57 = ( append1574001858od_a_a @ Ys4 @ ( cons_P1921020637od_a_a @ X3 @ Zs2 ) ) )
% 0.25/0.57 & ~ ( member449909584od_a_a @ X3 @ ( set_Product_prod_a_a2 @ Zs2 ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % split_list_last
% 0.25/0.57 thf(fact_278_split__list,axiom,
% 0.25/0.57 ! [X3: product_prod_a_a,Xs2: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( member449909584od_a_a @ X3 @ ( set_Product_prod_a_a2 @ Xs2 ) )
% 0.25/0.57 => ? [Ys4: list_P1467822637od_a_a,Zs2: list_P1467822637od_a_a] :
% 0.25/0.57 ( Xs2
% 0.25/0.57 = ( append1574001858od_a_a @ Ys4 @ ( cons_P1921020637od_a_a @ X3 @ Zs2 ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % split_list
% 0.25/0.57 thf(fact_279_rev__nonempty__induct,axiom,
% 0.25/0.57 ! [Xs2: list_P1467822637od_a_a,P2: list_P1467822637od_a_a > $o] :
% 0.25/0.57 ( ( Xs2 != nil_Product_prod_a_a )
% 0.25/0.57 => ( ! [X4: product_prod_a_a] : ( P2 @ ( cons_P1921020637od_a_a @ X4 @ nil_Product_prod_a_a ) )
% 0.25/0.57 => ( ! [X4: product_prod_a_a,Xs4: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( Xs4 != nil_Product_prod_a_a )
% 0.25/0.57 => ( ( P2 @ Xs4 )
% 0.25/0.57 => ( P2 @ ( append1574001858od_a_a @ Xs4 @ ( cons_P1921020637od_a_a @ X4 @ nil_Product_prod_a_a ) ) ) ) )
% 0.25/0.57 => ( P2 @ Xs2 ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % rev_nonempty_induct
% 0.25/0.57 thf(fact_280_append__eq__Cons__conv,axiom,
% 0.25/0.57 ! [Ys2: list_P1467822637od_a_a,Zs: list_P1467822637od_a_a,X3: product_prod_a_a,Xs2: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( ( append1574001858od_a_a @ Ys2 @ Zs )
% 0.25/0.57 = ( cons_P1921020637od_a_a @ X3 @ Xs2 ) )
% 0.25/0.57 = ( ( ( Ys2 = nil_Product_prod_a_a )
% 0.25/0.57 & ( Zs
% 0.25/0.57 = ( cons_P1921020637od_a_a @ X3 @ Xs2 ) ) )
% 0.25/0.57 | ? [Ys6: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( Ys2
% 0.25/0.57 = ( cons_P1921020637od_a_a @ X3 @ Ys6 ) )
% 0.25/0.57 & ( ( append1574001858od_a_a @ Ys6 @ Zs )
% 0.25/0.57 = Xs2 ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % append_eq_Cons_conv
% 0.25/0.57 thf(fact_281_Cons__eq__append__conv,axiom,
% 0.25/0.57 ! [X3: product_prod_a_a,Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a,Zs: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( ( cons_P1921020637od_a_a @ X3 @ Xs2 )
% 0.25/0.57 = ( append1574001858od_a_a @ Ys2 @ Zs ) )
% 0.25/0.57 = ( ( ( Ys2 = nil_Product_prod_a_a )
% 0.25/0.57 & ( ( cons_P1921020637od_a_a @ X3 @ Xs2 )
% 0.25/0.57 = Zs ) )
% 0.25/0.57 | ? [Ys6: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( ( cons_P1921020637od_a_a @ X3 @ Ys6 )
% 0.25/0.57 = Ys2 )
% 0.25/0.57 & ( Xs2
% 0.25/0.57 = ( append1574001858od_a_a @ Ys6 @ Zs ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % Cons_eq_append_conv
% 0.25/0.57 thf(fact_282_rev__exhaust,axiom,
% 0.25/0.57 ! [Xs2: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( Xs2 != nil_Product_prod_a_a )
% 0.25/0.57 => ~ ! [Ys4: list_P1467822637od_a_a,Y4: product_prod_a_a] :
% 0.25/0.57 ( Xs2
% 0.25/0.57 != ( append1574001858od_a_a @ Ys4 @ ( cons_P1921020637od_a_a @ Y4 @ nil_Product_prod_a_a ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % rev_exhaust
% 0.25/0.57 thf(fact_283_rev__induct,axiom,
% 0.25/0.57 ! [P2: list_P1467822637od_a_a > $o,Xs2: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( P2 @ nil_Product_prod_a_a )
% 0.25/0.57 => ( ! [X4: product_prod_a_a,Xs4: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( P2 @ Xs4 )
% 0.25/0.57 => ( P2 @ ( append1574001858od_a_a @ Xs4 @ ( cons_P1921020637od_a_a @ X4 @ nil_Product_prod_a_a ) ) ) )
% 0.25/0.57 => ( P2 @ Xs2 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % rev_induct
% 0.25/0.57 thf(fact_284_shuffles_Ocases,axiom,
% 0.25/0.57 ! [X3: produc651658087od_a_a] :
% 0.25/0.57 ( ! [Ys4: list_P1467822637od_a_a] :
% 0.25/0.57 ( X3
% 0.25/0.57 != ( produc85179863od_a_a @ nil_Product_prod_a_a @ Ys4 ) )
% 0.25/0.57 => ( ! [Xs4: list_P1467822637od_a_a] :
% 0.25/0.57 ( X3
% 0.25/0.57 != ( produc85179863od_a_a @ Xs4 @ nil_Product_prod_a_a ) )
% 0.25/0.57 => ~ ! [X4: product_prod_a_a,Xs4: list_P1467822637od_a_a,Y4: product_prod_a_a,Ys4: list_P1467822637od_a_a] :
% 0.25/0.57 ( X3
% 0.25/0.57 != ( produc85179863od_a_a @ ( cons_P1921020637od_a_a @ X4 @ Xs4 ) @ ( cons_P1921020637od_a_a @ Y4 @ Ys4 ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % shuffles.cases
% 0.25/0.57 thf(fact_285_sd__path_Oinduct,axiom,
% 0.25/0.57 ! [P2: product_prod_a_a > a > list_P1467822637od_a_a > $o,A0: product_prod_a_a,A1: a,A22: list_P1467822637od_a_a] :
% 0.25/0.57 ( ! [Uu: product_prod_a_a,Uv: a] : ( P2 @ Uu @ Uv @ nil_Product_prod_a_a )
% 0.25/0.57 => ( ! [U2: a,V: a,W: a,E2: product_prod_a_a,Es: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( P2 @ ( product_Pair_a_a @ U2 @ V ) @ W @ Es )
% 0.25/0.57 => ( P2 @ ( product_Pair_a_a @ U2 @ V ) @ W @ ( cons_P1921020637od_a_a @ E2 @ Es ) ) )
% 0.25/0.57 => ( P2 @ A0 @ A1 @ A22 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % sd_path.induct
% 0.25/0.57 thf(fact_286_co__path_Oinduct,axiom,
% 0.25/0.57 ! [P2: product_prod_a_a > a > list_P1467822637od_a_a > $o,A0: product_prod_a_a,A1: a,A22: list_P1467822637od_a_a] :
% 0.25/0.57 ( ! [Uu: product_prod_a_a,Uv: a] : ( P2 @ Uu @ Uv @ nil_Product_prod_a_a )
% 0.25/0.57 => ( ! [Uw: product_prod_a_a,Ux: a,E2: product_prod_a_a] : ( P2 @ Uw @ Ux @ ( cons_P1921020637od_a_a @ E2 @ nil_Product_prod_a_a ) )
% 0.25/0.57 => ( ! [U2: a,V: a,W: a,E1: product_prod_a_a,E22: product_prod_a_a,Es: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( ( ( E1
% 0.25/0.57 = ( product_Pair_a_a @ U2 @ W ) )
% 0.25/0.57 & ( E22
% 0.25/0.57 = ( product_Pair_a_a @ W @ V ) ) )
% 0.25/0.57 => ( P2 @ ( product_Pair_a_a @ U2 @ V ) @ W @ Es ) )
% 0.25/0.57 => ( ( ~ ( ( E1
% 0.25/0.57 = ( product_Pair_a_a @ U2 @ W ) )
% 0.25/0.57 & ( E22
% 0.25/0.57 = ( product_Pair_a_a @ W @ V ) ) )
% 0.25/0.57 => ( ( ( E1
% 0.25/0.57 = ( product_Pair_a_a @ V @ W ) )
% 0.25/0.57 & ( E22
% 0.25/0.57 = ( product_Pair_a_a @ W @ U2 ) ) )
% 0.25/0.57 => ( P2 @ ( product_Pair_a_a @ U2 @ V ) @ W @ Es ) ) )
% 0.25/0.57 => ( ( ~ ( ( E1
% 0.25/0.57 = ( product_Pair_a_a @ U2 @ W ) )
% 0.25/0.57 & ( E22
% 0.25/0.57 = ( product_Pair_a_a @ W @ V ) ) )
% 0.25/0.57 => ( ~ ( ( E1
% 0.25/0.57 = ( product_Pair_a_a @ V @ W ) )
% 0.25/0.57 & ( E22
% 0.25/0.57 = ( product_Pair_a_a @ W @ U2 ) ) )
% 0.25/0.57 => ( P2 @ ( product_Pair_a_a @ U2 @ V ) @ W @ ( cons_P1921020637od_a_a @ E22 @ Es ) ) ) )
% 0.25/0.57 => ( P2 @ ( product_Pair_a_a @ U2 @ V ) @ W @ ( cons_P1921020637od_a_a @ E1 @ ( cons_P1921020637od_a_a @ E22 @ Es ) ) ) ) ) )
% 0.25/0.57 => ( P2 @ A0 @ A1 @ A22 ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % co_path.induct
% 0.25/0.57 thf(fact_287_sd__path_Ocases,axiom,
% 0.25/0.57 ! [X3: produc821581462od_a_a] :
% 0.25/0.57 ( ! [Uu: product_prod_a_a,Uv: a] :
% 0.25/0.57 ( X3
% 0.25/0.57 != ( produc600870406od_a_a @ Uu @ ( produc575024326od_a_a @ Uv @ nil_Product_prod_a_a ) ) )
% 0.25/0.57 => ~ ! [U2: a,V: a,W: a,E2: product_prod_a_a,Es: list_P1467822637od_a_a] :
% 0.25/0.57 ( X3
% 0.25/0.57 != ( produc600870406od_a_a @ ( product_Pair_a_a @ U2 @ V ) @ ( produc575024326od_a_a @ W @ ( cons_P1921020637od_a_a @ E2 @ Es ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % sd_path.cases
% 0.25/0.57 thf(fact_288_co__path_Ocases,axiom,
% 0.25/0.57 ! [X3: produc821581462od_a_a] :
% 0.25/0.57 ( ! [Uu: product_prod_a_a,Uv: a] :
% 0.25/0.57 ( X3
% 0.25/0.57 != ( produc600870406od_a_a @ Uu @ ( produc575024326od_a_a @ Uv @ nil_Product_prod_a_a ) ) )
% 0.25/0.57 => ( ! [Uw: product_prod_a_a,Ux: a,E2: product_prod_a_a] :
% 0.25/0.57 ( X3
% 0.25/0.57 != ( produc600870406od_a_a @ Uw @ ( produc575024326od_a_a @ Ux @ ( cons_P1921020637od_a_a @ E2 @ nil_Product_prod_a_a ) ) ) )
% 0.25/0.57 => ~ ! [U2: a,V: a,W: a,E1: product_prod_a_a,E22: product_prod_a_a,Es: list_P1467822637od_a_a] :
% 0.25/0.57 ( X3
% 0.25/0.57 != ( produc600870406od_a_a @ ( product_Pair_a_a @ U2 @ V ) @ ( produc575024326od_a_a @ W @ ( cons_P1921020637od_a_a @ E1 @ ( cons_P1921020637od_a_a @ E22 @ Es ) ) ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % co_path.cases
% 0.25/0.57 thf(fact_289_lex__append__leftI,axiom,
% 0.25/0.57 ! [Ys2: list_P1467822637od_a_a,Zs: list_P1467822637od_a_a,R: set_Pr1948701895od_a_a,Xs2: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ Ys2 @ Zs ) @ ( lex_Product_prod_a_a @ R ) )
% 0.25/0.57 => ( member1691432592od_a_a @ ( produc85179863od_a_a @ ( append1574001858od_a_a @ Xs2 @ Ys2 ) @ ( append1574001858od_a_a @ Xs2 @ Zs ) ) @ ( lex_Product_prod_a_a @ R ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % lex_append_leftI
% 0.25/0.57 thf(fact_290_progressing__single,axiom,
% 0.25/0.57 ! [E: product_prod_a_a] : ( kurato1072996284sing_a @ ( cons_P1921020637od_a_a @ E @ nil_Product_prod_a_a ) ) ).
% 0.25/0.57
% 0.25/0.57 % progressing_single
% 0.25/0.57 thf(fact_291_lexord__partial__trans,axiom,
% 0.25/0.57 ! [Xs2: list_a,R: set_Product_prod_a_a,Ys2: list_a,Zs: list_a] :
% 0.25/0.57 ( ! [X4: a,Y4: a,Z2: a] :
% 0.25/0.57 ( ( member_a2 @ X4 @ ( set_a2 @ Xs2 ) )
% 0.25/0.57 => ( ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y4 ) @ R )
% 0.25/0.57 => ( ( member449909584od_a_a @ ( product_Pair_a_a @ Y4 @ Z2 ) @ R )
% 0.25/0.57 => ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Z2 ) @ R ) ) ) )
% 0.25/0.57 => ( ( member1250517072list_a @ ( produc1448356631list_a @ Xs2 @ Ys2 ) @ ( lexord_a @ R ) )
% 0.25/0.57 => ( ( member1250517072list_a @ ( produc1448356631list_a @ Ys2 @ Zs ) @ ( lexord_a @ R ) )
% 0.25/0.57 => ( member1250517072list_a @ ( produc1448356631list_a @ Xs2 @ Zs ) @ ( lexord_a @ R ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % lexord_partial_trans
% 0.25/0.57 thf(fact_292_lexord__sufE,axiom,
% 0.25/0.57 ! [Xs2: list_P1467822637od_a_a,Zs: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a,Qs: list_P1467822637od_a_a,R: set_Pr1948701895od_a_a] :
% 0.25/0.57 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ ( append1574001858od_a_a @ Xs2 @ Zs ) @ ( append1574001858od_a_a @ Ys2 @ Qs ) ) @ ( lexord673907738od_a_a @ R ) )
% 0.25/0.57 => ( ( Xs2 != Ys2 )
% 0.25/0.57 => ( ( ( size_s642698393od_a_a @ Xs2 )
% 0.25/0.57 = ( size_s642698393od_a_a @ Ys2 ) )
% 0.25/0.57 => ( ( ( size_s642698393od_a_a @ Zs )
% 0.25/0.57 = ( size_s642698393od_a_a @ Qs ) )
% 0.25/0.57 => ( member1691432592od_a_a @ ( produc85179863od_a_a @ Xs2 @ Ys2 ) @ ( lexord673907738od_a_a @ R ) ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % lexord_sufE
% 0.25/0.57 thf(fact_293_subset__eq__mset__impl_Ocases,axiom,
% 0.25/0.57 ! [X3: produc651658087od_a_a] :
% 0.25/0.57 ( ! [Ys4: list_P1467822637od_a_a] :
% 0.25/0.57 ( X3
% 0.25/0.57 != ( produc85179863od_a_a @ nil_Product_prod_a_a @ Ys4 ) )
% 0.25/0.57 => ~ ! [X4: product_prod_a_a,Xs4: list_P1467822637od_a_a,Ys4: list_P1467822637od_a_a] :
% 0.25/0.57 ( X3
% 0.25/0.57 != ( produc85179863od_a_a @ ( cons_P1921020637od_a_a @ X4 @ Xs4 ) @ Ys4 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % subset_eq_mset_impl.cases
% 0.25/0.57 thf(fact_294_asym_Oinducts,axiom,
% 0.25/0.57 ! [X3: set_Product_prod_a_a,P2: set_Product_prod_a_a > $o] :
% 0.25/0.57 ( ( asym_a @ X3 )
% 0.25/0.57 => ( ! [R3: set_Product_prod_a_a] :
% 0.25/0.57 ( ! [A6: a,B4: a] :
% 0.25/0.57 ( ( member449909584od_a_a @ ( product_Pair_a_a @ A6 @ B4 ) @ R3 )
% 0.25/0.57 => ~ ( member449909584od_a_a @ ( product_Pair_a_a @ B4 @ A6 ) @ R3 ) )
% 0.25/0.57 => ( P2 @ R3 ) )
% 0.25/0.57 => ( P2 @ X3 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % asym.inducts
% 0.25/0.57 thf(fact_295_asym_Ointros,axiom,
% 0.25/0.57 ! [R2: set_Product_prod_a_a] :
% 0.25/0.57 ( ! [A3: a,B3: a] :
% 0.25/0.57 ( ( member449909584od_a_a @ ( product_Pair_a_a @ A3 @ B3 ) @ R2 )
% 0.25/0.57 => ~ ( member449909584od_a_a @ ( product_Pair_a_a @ B3 @ A3 ) @ R2 ) )
% 0.25/0.57 => ( asym_a @ R2 ) ) ).
% 0.25/0.57
% 0.25/0.57 % asym.intros
% 0.25/0.57 thf(fact_296_asym_Osimps,axiom,
% 0.25/0.57 ( asym_a
% 0.25/0.57 = ( ^ [A5: set_Product_prod_a_a] :
% 0.25/0.57 ? [R4: set_Product_prod_a_a] :
% 0.25/0.57 ( ( A5 = R4 )
% 0.25/0.57 & ! [X: a,Y: a] :
% 0.25/0.57 ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ R4 )
% 0.25/0.57 => ~ ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ X ) @ R4 ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % asym.simps
% 0.25/0.57 thf(fact_297_asym_Ocases,axiom,
% 0.25/0.57 ! [A: set_Product_prod_a_a] :
% 0.25/0.57 ( ( asym_a @ A )
% 0.25/0.57 => ! [A6: a,B4: a] :
% 0.25/0.57 ( ( member449909584od_a_a @ ( product_Pair_a_a @ A6 @ B4 ) @ A )
% 0.25/0.57 => ~ ( member449909584od_a_a @ ( product_Pair_a_a @ B4 @ A6 ) @ A ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % asym.cases
% 0.25/0.57 thf(fact_298_asym__iff,axiom,
% 0.25/0.57 ( asym_a
% 0.25/0.57 = ( ^ [R4: set_Product_prod_a_a] :
% 0.25/0.57 ! [X: a,Y: a] :
% 0.25/0.57 ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ R4 )
% 0.25/0.57 => ~ ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ X ) @ R4 ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % asym_iff
% 0.25/0.57 thf(fact_299_irreflI,axiom,
% 0.25/0.57 ! [R2: set_Product_prod_a_a] :
% 0.25/0.57 ( ! [A3: a] :
% 0.25/0.57 ~ ( member449909584od_a_a @ ( product_Pair_a_a @ A3 @ A3 ) @ R2 )
% 0.25/0.57 => ( irrefl_a @ R2 ) ) ).
% 0.25/0.57
% 0.25/0.57 % irreflI
% 0.25/0.57 thf(fact_300_irrefl__def,axiom,
% 0.25/0.57 ( irrefl_a
% 0.25/0.57 = ( ^ [R5: set_Product_prod_a_a] :
% 0.25/0.57 ! [A5: a] :
% 0.25/0.57 ~ ( member449909584od_a_a @ ( product_Pair_a_a @ A5 @ A5 ) @ R5 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % irrefl_def
% 0.25/0.57 thf(fact_301_asymD,axiom,
% 0.25/0.57 ! [R2: set_Product_prod_a_a,X3: a,Y3: a] :
% 0.25/0.57 ( ( asym_a @ R2 )
% 0.25/0.57 => ( ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ R2 )
% 0.25/0.57 => ~ ( member449909584od_a_a @ ( product_Pair_a_a @ Y3 @ X3 ) @ R2 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % asymD
% 0.25/0.57 thf(fact_302_inverse__permutation__of__list_Ocases,axiom,
% 0.25/0.57 ! [X3: produc657167928_a_a_a] :
% 0.25/0.57 ( ! [X4: a] :
% 0.25/0.57 ( X3
% 0.25/0.57 != ( produc998622632_a_a_a @ nil_Product_prod_a_a @ X4 ) )
% 0.25/0.57 => ~ ! [Y4: a,X6: a,Xs4: list_P1467822637od_a_a,X4: a] :
% 0.25/0.57 ( X3
% 0.25/0.57 != ( produc998622632_a_a_a @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ Y4 @ X6 ) @ Xs4 ) @ X4 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % inverse_permutation_of_list.cases
% 0.25/0.57 thf(fact_303_inverse__permutation__of__list_Oinduct,axiom,
% 0.25/0.57 ! [P2: list_P1467822637od_a_a > a > $o,A0: list_P1467822637od_a_a,A1: a] :
% 0.25/0.57 ( ! [X_1: a] : ( P2 @ nil_Product_prod_a_a @ X_1 )
% 0.25/0.57 => ( ! [Y4: a,X6: a,Xs4: list_P1467822637od_a_a,X4: a] :
% 0.25/0.57 ( ( ( X4 != X6 )
% 0.25/0.57 => ( P2 @ Xs4 @ X4 ) )
% 0.25/0.57 => ( P2 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ Y4 @ X6 ) @ Xs4 ) @ X4 ) )
% 0.25/0.57 => ( P2 @ A0 @ A1 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % inverse_permutation_of_list.induct
% 0.25/0.57 thf(fact_304_sd__path_Osimps_I2_J,axiom,
% 0.25/0.57 ! [U: a,V2: a,W2: a,E: product_prod_a_a,Es2: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( pair_sd_path_a @ ( product_Pair_a_a @ U @ V2 ) @ W2 @ ( cons_P1921020637od_a_a @ E @ Es2 ) )
% 0.25/0.57 = ( append1574001858od_a_a
% 0.25/0.57 @ ( if_lis321365491od_a_a
% 0.25/0.57 @ ( E
% 0.25/0.57 = ( product_Pair_a_a @ U @ V2 ) )
% 0.25/0.57 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ U @ W2 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ W2 @ V2 ) @ nil_Product_prod_a_a ) )
% 0.25/0.57 @ ( if_lis321365491od_a_a
% 0.25/0.57 @ ( E
% 0.25/0.57 = ( product_Pair_a_a @ V2 @ U ) )
% 0.25/0.57 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ V2 @ W2 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ W2 @ U ) @ nil_Product_prod_a_a ) )
% 0.25/0.57 @ ( cons_P1921020637od_a_a @ E @ nil_Product_prod_a_a ) ) )
% 0.25/0.57 @ ( pair_sd_path_a @ ( product_Pair_a_a @ U @ V2 ) @ W2 @ Es2 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % sd_path.simps(2)
% 0.25/0.57 thf(fact_305_sd__path__id,axiom,
% 0.25/0.57 ! [X3: a,Y3: a,P3: list_P1467822637od_a_a,W2: a] :
% 0.25/0.57 ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ ( set_Product_prod_a_a2 @ P3 ) )
% 0.25/0.57 => ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ Y3 @ X3 ) @ ( set_Product_prod_a_a2 @ P3 ) )
% 0.25/0.57 => ( ( pair_sd_path_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ W2 @ P3 )
% 0.25/0.57 = P3 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % sd_path_id
% 0.25/0.57 thf(fact_306_sd__path_Oelims,axiom,
% 0.25/0.57 ! [X3: product_prod_a_a,Xa2: a,Xb: list_P1467822637od_a_a,Y3: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( ( pair_sd_path_a @ X3 @ Xa2 @ Xb )
% 0.25/0.57 = Y3 )
% 0.25/0.57 => ( ( ( Xb = nil_Product_prod_a_a )
% 0.25/0.57 => ( Y3 != nil_Product_prod_a_a ) )
% 0.25/0.57 => ~ ! [U2: a,V: a] :
% 0.25/0.57 ( ( X3
% 0.25/0.57 = ( product_Pair_a_a @ U2 @ V ) )
% 0.25/0.57 => ! [E2: product_prod_a_a,Es: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( Xb
% 0.25/0.57 = ( cons_P1921020637od_a_a @ E2 @ Es ) )
% 0.25/0.57 => ( Y3
% 0.25/0.57 != ( append1574001858od_a_a
% 0.25/0.57 @ ( if_lis321365491od_a_a
% 0.25/0.57 @ ( E2
% 0.25/0.57 = ( product_Pair_a_a @ U2 @ V ) )
% 0.25/0.57 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ U2 @ Xa2 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ Xa2 @ V ) @ nil_Product_prod_a_a ) )
% 0.25/0.57 @ ( if_lis321365491od_a_a
% 0.25/0.57 @ ( E2
% 0.25/0.57 = ( product_Pair_a_a @ V @ U2 ) )
% 0.25/0.57 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ V @ Xa2 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ Xa2 @ U2 ) @ nil_Product_prod_a_a ) )
% 0.25/0.57 @ ( cons_P1921020637od_a_a @ E2 @ nil_Product_prod_a_a ) ) )
% 0.25/0.57 @ ( pair_sd_path_a @ ( product_Pair_a_a @ U2 @ V ) @ Xa2 @ Es ) ) ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % sd_path.elims
% 0.25/0.57 thf(fact_307_the__elem__set,axiom,
% 0.25/0.57 ! [X3: product_prod_a_a] :
% 0.25/0.57 ( ( the_el1640649244od_a_a @ ( set_Product_prod_a_a2 @ ( cons_P1921020637od_a_a @ X3 @ nil_Product_prod_a_a ) ) )
% 0.25/0.57 = X3 ) ).
% 0.25/0.57
% 0.25/0.57 % the_elem_set
% 0.25/0.57 thf(fact_308_sd__path_Opelims,axiom,
% 0.25/0.57 ! [X3: product_prod_a_a,Xa2: a,Xb: list_P1467822637od_a_a,Y3: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( ( pair_sd_path_a @ X3 @ Xa2 @ Xb )
% 0.25/0.57 = Y3 )
% 0.25/0.57 => ( ( accp_P1029463583od_a_a @ pair_sd_path_rel_a @ ( produc600870406od_a_a @ X3 @ ( produc575024326od_a_a @ Xa2 @ Xb ) ) )
% 0.25/0.57 => ( ( ( Xb = nil_Product_prod_a_a )
% 0.25/0.57 => ( ( Y3 = nil_Product_prod_a_a )
% 0.25/0.57 => ~ ( accp_P1029463583od_a_a @ pair_sd_path_rel_a @ ( produc600870406od_a_a @ X3 @ ( produc575024326od_a_a @ Xa2 @ nil_Product_prod_a_a ) ) ) ) )
% 0.25/0.57 => ~ ! [U2: a,V: a] :
% 0.25/0.57 ( ( X3
% 0.25/0.57 = ( product_Pair_a_a @ U2 @ V ) )
% 0.25/0.57 => ! [E2: product_prod_a_a,Es: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( Xb
% 0.25/0.57 = ( cons_P1921020637od_a_a @ E2 @ Es ) )
% 0.25/0.57 => ( ( Y3
% 0.25/0.57 = ( append1574001858od_a_a
% 0.25/0.57 @ ( if_lis321365491od_a_a
% 0.25/0.57 @ ( E2
% 0.25/0.57 = ( product_Pair_a_a @ U2 @ V ) )
% 0.25/0.57 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ U2 @ Xa2 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ Xa2 @ V ) @ nil_Product_prod_a_a ) )
% 0.25/0.57 @ ( if_lis321365491od_a_a
% 0.25/0.57 @ ( E2
% 0.25/0.57 = ( product_Pair_a_a @ V @ U2 ) )
% 0.25/0.57 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ V @ Xa2 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ Xa2 @ U2 ) @ nil_Product_prod_a_a ) )
% 0.25/0.57 @ ( cons_P1921020637od_a_a @ E2 @ nil_Product_prod_a_a ) ) )
% 0.25/0.57 @ ( pair_sd_path_a @ ( product_Pair_a_a @ U2 @ V ) @ Xa2 @ Es ) ) )
% 0.25/0.57 => ~ ( accp_P1029463583od_a_a @ pair_sd_path_rel_a @ ( produc600870406od_a_a @ ( product_Pair_a_a @ U2 @ V ) @ ( produc575024326od_a_a @ Xa2 @ ( cons_P1921020637od_a_a @ E2 @ Es ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % sd_path.pelims
% 0.25/0.57 thf(fact_309_list__exhaust2,axiom,
% 0.25/0.57 ! [Y3: list_P1467822637od_a_a,Ya: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( ( Y3 = nil_Product_prod_a_a )
% 0.25/0.57 => ( Ya != nil_Product_prod_a_a ) )
% 0.25/0.57 => ( ( ( Y3 = nil_Product_prod_a_a )
% 0.25/0.57 => ! [X212: product_prod_a_a,X222: list_P1467822637od_a_a] :
% 0.25/0.57 ( Ya
% 0.25/0.57 != ( cons_P1921020637od_a_a @ X212 @ X222 ) ) )
% 0.25/0.57 => ( ( ? [X212: product_prod_a_a,X222: list_P1467822637od_a_a] :
% 0.25/0.57 ( Y3
% 0.25/0.57 = ( cons_P1921020637od_a_a @ X212 @ X222 ) )
% 0.25/0.57 => ( Ya != nil_Product_prod_a_a ) )
% 0.25/0.57 => ~ ( ? [X212: product_prod_a_a,X222: list_P1467822637od_a_a] :
% 0.25/0.57 ( Y3
% 0.25/0.57 = ( cons_P1921020637od_a_a @ X212 @ X222 ) )
% 0.25/0.57 => ! [X21a: product_prod_a_a,X22a: list_P1467822637od_a_a] :
% 0.25/0.57 ( Ya
% 0.25/0.57 != ( cons_P1921020637od_a_a @ X21a @ X22a ) ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % list_exhaust2
% 0.25/0.57 thf(fact_310_list__exhaust__NSC,axiom,
% 0.25/0.57 ! [Xs2: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( Xs2 != nil_Product_prod_a_a )
% 0.25/0.57 => ( ! [X4: product_prod_a_a] :
% 0.25/0.57 ( Xs2
% 0.25/0.57 != ( cons_P1921020637od_a_a @ X4 @ nil_Product_prod_a_a ) )
% 0.25/0.57 => ~ ! [X4: product_prod_a_a,Y4: product_prod_a_a,Ys4: list_P1467822637od_a_a] :
% 0.25/0.57 ( Xs2
% 0.25/0.57 != ( cons_P1921020637od_a_a @ X4 @ ( cons_P1921020637od_a_a @ Y4 @ Ys4 ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % list_exhaust_NSC
% 0.25/0.57 thf(fact_311_lenlex__append2,axiom,
% 0.25/0.57 ! [R2: set_Pr1948701895od_a_a,Us: list_P1467822637od_a_a,Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( irrefl76447196od_a_a @ R2 )
% 0.25/0.57 => ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ ( append1574001858od_a_a @ Us @ Xs2 ) @ ( append1574001858od_a_a @ Us @ Ys2 ) ) @ ( lenlex2038501170od_a_a @ R2 ) )
% 0.25/0.57 = ( member1691432592od_a_a @ ( produc85179863od_a_a @ Xs2 @ Ys2 ) @ ( lenlex2038501170od_a_a @ R2 ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % lenlex_append2
% 0.25/0.57 thf(fact_312_lenlex__irreflexive,axiom,
% 0.25/0.57 ! [R: set_Product_prod_a_a,Xs2: list_a] :
% 0.25/0.57 ( ! [X4: a] :
% 0.25/0.57 ~ ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ X4 ) @ R )
% 0.25/0.57 => ~ ( member1250517072list_a @ ( produc1448356631list_a @ Xs2 @ Xs2 ) @ ( lenlex_a @ R ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % lenlex_irreflexive
% 0.25/0.57 thf(fact_313_lenlex__append1,axiom,
% 0.25/0.57 ! [Us: list_P1467822637od_a_a,Xs2: list_P1467822637od_a_a,R2: set_Pr1948701895od_a_a,Vs: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ Us @ Xs2 ) @ ( lenlex2038501170od_a_a @ R2 ) )
% 0.25/0.57 => ( ( ( size_s642698393od_a_a @ Vs )
% 0.25/0.57 = ( size_s642698393od_a_a @ Ys2 ) )
% 0.25/0.57 => ( member1691432592od_a_a @ ( produc85179863od_a_a @ ( append1574001858od_a_a @ Us @ Vs ) @ ( append1574001858od_a_a @ Xs2 @ Ys2 ) ) @ ( lenlex2038501170od_a_a @ R2 ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % lenlex_append1
% 0.25/0.57 thf(fact_314_co__path_Opelims,axiom,
% 0.25/0.57 ! [X3: product_prod_a_a,Xa2: a,Xb: list_P1467822637od_a_a,Y3: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( ( pair_co_path_a @ X3 @ Xa2 @ Xb )
% 0.25/0.57 = Y3 )
% 0.25/0.57 => ( ( accp_P1029463583od_a_a @ pair_co_path_rel_a @ ( produc600870406od_a_a @ X3 @ ( produc575024326od_a_a @ Xa2 @ Xb ) ) )
% 0.25/0.57 => ( ( ( Xb = nil_Product_prod_a_a )
% 0.25/0.57 => ( ( Y3 = nil_Product_prod_a_a )
% 0.25/0.57 => ~ ( accp_P1029463583od_a_a @ pair_co_path_rel_a @ ( produc600870406od_a_a @ X3 @ ( produc575024326od_a_a @ Xa2 @ nil_Product_prod_a_a ) ) ) ) )
% 0.25/0.57 => ( ! [E2: product_prod_a_a] :
% 0.25/0.57 ( ( Xb
% 0.25/0.57 = ( cons_P1921020637od_a_a @ E2 @ nil_Product_prod_a_a ) )
% 0.25/0.57 => ( ( Y3
% 0.25/0.57 = ( cons_P1921020637od_a_a @ E2 @ nil_Product_prod_a_a ) )
% 0.25/0.57 => ~ ( accp_P1029463583od_a_a @ pair_co_path_rel_a @ ( produc600870406od_a_a @ X3 @ ( produc575024326od_a_a @ Xa2 @ ( cons_P1921020637od_a_a @ E2 @ nil_Product_prod_a_a ) ) ) ) ) )
% 0.25/0.57 => ~ ! [U2: a,V: a] :
% 0.25/0.57 ( ( X3
% 0.25/0.57 = ( product_Pair_a_a @ U2 @ V ) )
% 0.25/0.57 => ! [E1: product_prod_a_a,E22: product_prod_a_a,Es: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( Xb
% 0.25/0.57 = ( cons_P1921020637od_a_a @ E1 @ ( cons_P1921020637od_a_a @ E22 @ Es ) ) )
% 0.25/0.57 => ( ( ( ( ( E1
% 0.25/0.57 = ( product_Pair_a_a @ U2 @ Xa2 ) )
% 0.25/0.57 & ( E22
% 0.25/0.57 = ( product_Pair_a_a @ Xa2 @ V ) ) )
% 0.25/0.57 => ( Y3
% 0.25/0.57 = ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ U2 @ V ) @ ( pair_co_path_a @ ( product_Pair_a_a @ U2 @ V ) @ Xa2 @ Es ) ) ) )
% 0.25/0.57 & ( ~ ( ( E1
% 0.25/0.57 = ( product_Pair_a_a @ U2 @ Xa2 ) )
% 0.25/0.57 & ( E22
% 0.25/0.57 = ( product_Pair_a_a @ Xa2 @ V ) ) )
% 0.25/0.57 => ( ( ( ( E1
% 0.25/0.57 = ( product_Pair_a_a @ V @ Xa2 ) )
% 0.25/0.57 & ( E22
% 0.25/0.57 = ( product_Pair_a_a @ Xa2 @ U2 ) ) )
% 0.25/0.57 => ( Y3
% 0.25/0.57 = ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ V @ U2 ) @ ( pair_co_path_a @ ( product_Pair_a_a @ U2 @ V ) @ Xa2 @ Es ) ) ) )
% 0.25/0.57 & ( ~ ( ( E1
% 0.25/0.57 = ( product_Pair_a_a @ V @ Xa2 ) )
% 0.25/0.57 & ( E22
% 0.25/0.57 = ( product_Pair_a_a @ Xa2 @ U2 ) ) )
% 0.25/0.57 => ( Y3
% 0.25/0.57 = ( cons_P1921020637od_a_a @ E1 @ ( pair_co_path_a @ ( product_Pair_a_a @ U2 @ V ) @ Xa2 @ ( cons_P1921020637od_a_a @ E22 @ Es ) ) ) ) ) ) ) )
% 0.25/0.57 => ~ ( accp_P1029463583od_a_a @ pair_co_path_rel_a @ ( produc600870406od_a_a @ ( product_Pair_a_a @ U2 @ V ) @ ( produc575024326od_a_a @ Xa2 @ ( cons_P1921020637od_a_a @ E1 @ ( cons_P1921020637od_a_a @ E22 @ Es ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % co_path.pelims
% 0.25/0.57 thf(fact_315_pawalk__verts_Osimps_I1_J,axiom,
% 0.25/0.57 ! [U: product_prod_a_a] :
% 0.25/0.57 ( ( pair_p2140537249od_a_a @ U @ nil_Pr1049924845od_a_a )
% 0.25/0.57 = ( cons_P1921020637od_a_a @ U @ nil_Product_prod_a_a ) ) ).
% 0.25/0.57
% 0.25/0.57 % pawalk_verts.simps(1)
% 0.25/0.57 thf(fact_316_co__path_Osimps_I3_J,axiom,
% 0.25/0.57 ! [E12: product_prod_a_a,U: a,W2: a,E23: product_prod_a_a,V2: a,Es2: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( ( ( E12
% 0.25/0.57 = ( product_Pair_a_a @ U @ W2 ) )
% 0.25/0.57 & ( E23
% 0.25/0.57 = ( product_Pair_a_a @ W2 @ V2 ) ) )
% 0.25/0.57 => ( ( pair_co_path_a @ ( product_Pair_a_a @ U @ V2 ) @ W2 @ ( cons_P1921020637od_a_a @ E12 @ ( cons_P1921020637od_a_a @ E23 @ Es2 ) ) )
% 0.25/0.57 = ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ U @ V2 ) @ ( pair_co_path_a @ ( product_Pair_a_a @ U @ V2 ) @ W2 @ Es2 ) ) ) )
% 0.25/0.57 & ( ~ ( ( E12
% 0.25/0.57 = ( product_Pair_a_a @ U @ W2 ) )
% 0.25/0.57 & ( E23
% 0.25/0.57 = ( product_Pair_a_a @ W2 @ V2 ) ) )
% 0.25/0.57 => ( ( ( ( E12
% 0.25/0.57 = ( product_Pair_a_a @ V2 @ W2 ) )
% 0.25/0.57 & ( E23
% 0.25/0.57 = ( product_Pair_a_a @ W2 @ U ) ) )
% 0.25/0.57 => ( ( pair_co_path_a @ ( product_Pair_a_a @ U @ V2 ) @ W2 @ ( cons_P1921020637od_a_a @ E12 @ ( cons_P1921020637od_a_a @ E23 @ Es2 ) ) )
% 0.25/0.57 = ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ V2 @ U ) @ ( pair_co_path_a @ ( product_Pair_a_a @ U @ V2 ) @ W2 @ Es2 ) ) ) )
% 0.25/0.57 & ( ~ ( ( E12
% 0.25/0.57 = ( product_Pair_a_a @ V2 @ W2 ) )
% 0.25/0.57 & ( E23
% 0.25/0.57 = ( product_Pair_a_a @ W2 @ U ) ) )
% 0.25/0.57 => ( ( pair_co_path_a @ ( product_Pair_a_a @ U @ V2 ) @ W2 @ ( cons_P1921020637od_a_a @ E12 @ ( cons_P1921020637od_a_a @ E23 @ Es2 ) ) )
% 0.25/0.57 = ( cons_P1921020637od_a_a @ E12 @ ( pair_co_path_a @ ( product_Pair_a_a @ U @ V2 ) @ W2 @ ( cons_P1921020637od_a_a @ E23 @ Es2 ) ) ) ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % co_path.simps(3)
% 0.25/0.57 thf(fact_317_co__path_Osimps_I2_J,axiom,
% 0.25/0.57 ! [Uw2: product_prod_a_a,Ux2: a,E: product_prod_a_a] :
% 0.25/0.57 ( ( pair_co_path_a @ Uw2 @ Ux2 @ ( cons_P1921020637od_a_a @ E @ nil_Product_prod_a_a ) )
% 0.25/0.57 = ( cons_P1921020637od_a_a @ E @ nil_Product_prod_a_a ) ) ).
% 0.25/0.57
% 0.25/0.57 % co_path.simps(2)
% 0.25/0.57 thf(fact_318_co__path_Oelims,axiom,
% 0.25/0.57 ! [X3: product_prod_a_a,Xa2: a,Xb: list_P1467822637od_a_a,Y3: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( ( pair_co_path_a @ X3 @ Xa2 @ Xb )
% 0.25/0.57 = Y3 )
% 0.25/0.57 => ( ( ( Xb = nil_Product_prod_a_a )
% 0.25/0.57 => ( Y3 != nil_Product_prod_a_a ) )
% 0.25/0.57 => ( ! [E2: product_prod_a_a] :
% 0.25/0.57 ( ( Xb
% 0.25/0.57 = ( cons_P1921020637od_a_a @ E2 @ nil_Product_prod_a_a ) )
% 0.25/0.57 => ( Y3
% 0.25/0.57 != ( cons_P1921020637od_a_a @ E2 @ nil_Product_prod_a_a ) ) )
% 0.25/0.57 => ~ ! [U2: a,V: a] :
% 0.25/0.57 ( ( X3
% 0.25/0.57 = ( product_Pair_a_a @ U2 @ V ) )
% 0.25/0.57 => ! [E1: product_prod_a_a,E22: product_prod_a_a,Es: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( Xb
% 0.25/0.57 = ( cons_P1921020637od_a_a @ E1 @ ( cons_P1921020637od_a_a @ E22 @ Es ) ) )
% 0.25/0.57 => ~ ( ( ( ( E1
% 0.25/0.57 = ( product_Pair_a_a @ U2 @ Xa2 ) )
% 0.25/0.57 & ( E22
% 0.25/0.57 = ( product_Pair_a_a @ Xa2 @ V ) ) )
% 0.25/0.57 => ( Y3
% 0.25/0.57 = ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ U2 @ V ) @ ( pair_co_path_a @ ( product_Pair_a_a @ U2 @ V ) @ Xa2 @ Es ) ) ) )
% 0.25/0.57 & ( ~ ( ( E1
% 0.25/0.57 = ( product_Pair_a_a @ U2 @ Xa2 ) )
% 0.25/0.57 & ( E22
% 0.25/0.57 = ( product_Pair_a_a @ Xa2 @ V ) ) )
% 0.25/0.57 => ( ( ( ( E1
% 0.25/0.57 = ( product_Pair_a_a @ V @ Xa2 ) )
% 0.25/0.57 & ( E22
% 0.25/0.57 = ( product_Pair_a_a @ Xa2 @ U2 ) ) )
% 0.25/0.57 => ( Y3
% 0.25/0.57 = ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ V @ U2 ) @ ( pair_co_path_a @ ( product_Pair_a_a @ U2 @ V ) @ Xa2 @ Es ) ) ) )
% 0.25/0.57 & ( ~ ( ( E1
% 0.25/0.57 = ( product_Pair_a_a @ V @ Xa2 ) )
% 0.25/0.57 & ( E22
% 0.25/0.57 = ( product_Pair_a_a @ Xa2 @ U2 ) ) )
% 0.25/0.57 => ( Y3
% 0.25/0.57 = ( cons_P1921020637od_a_a @ E1 @ ( pair_co_path_a @ ( product_Pair_a_a @ U2 @ V ) @ Xa2 @ ( cons_P1921020637od_a_a @ E22 @ Es ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % co_path.elims
% 0.25/0.57 thf(fact_319_co__sd__id,axiom,
% 0.25/0.57 ! [U: a,W2: a,P3: list_P1467822637od_a_a,V2: a] :
% 0.25/0.57 ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ U @ W2 ) @ ( set_Product_prod_a_a2 @ P3 ) )
% 0.25/0.57 => ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ V2 @ W2 ) @ ( set_Product_prod_a_a2 @ P3 ) )
% 0.25/0.57 => ( ( pair_co_path_a @ ( product_Pair_a_a @ U @ V2 ) @ W2 @ ( pair_sd_path_a @ ( product_Pair_a_a @ U @ V2 ) @ W2 @ P3 ) )
% 0.25/0.57 = P3 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % co_sd_id
% 0.25/0.57 thf(fact_320_Cons__lenlex__iff,axiom,
% 0.25/0.57 ! [M: product_prod_a_a,Ms: list_P1467822637od_a_a,N: product_prod_a_a,Ns: list_P1467822637od_a_a,R: set_Pr1948701895od_a_a] :
% 0.25/0.57 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ ( cons_P1921020637od_a_a @ M @ Ms ) @ ( cons_P1921020637od_a_a @ N @ Ns ) ) @ ( lenlex2038501170od_a_a @ R ) )
% 0.25/0.57 = ( ( ord_less_nat @ ( size_s642698393od_a_a @ Ms ) @ ( size_s642698393od_a_a @ Ns ) )
% 0.25/0.57 | ( ( ( size_s642698393od_a_a @ Ms )
% 0.25/0.57 = ( size_s642698393od_a_a @ Ns ) )
% 0.25/0.57 & ( member2057358096od_a_a @ ( produc1474507607od_a_a @ M @ N ) @ R ) )
% 0.25/0.57 | ( ( M = N )
% 0.25/0.57 & ( member1691432592od_a_a @ ( produc85179863od_a_a @ Ms @ Ns ) @ ( lenlex2038501170od_a_a @ R ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % Cons_lenlex_iff
% 0.25/0.57 thf(fact_321_Cons__lenlex__iff,axiom,
% 0.25/0.57 ! [M: a,Ms: list_a,N: a,Ns: list_a,R: set_Product_prod_a_a] :
% 0.25/0.57 ( ( member1250517072list_a @ ( produc1448356631list_a @ ( cons_a @ M @ Ms ) @ ( cons_a @ N @ Ns ) ) @ ( lenlex_a @ R ) )
% 0.25/0.57 = ( ( ord_less_nat @ ( size_size_list_a @ Ms ) @ ( size_size_list_a @ Ns ) )
% 0.25/0.57 | ( ( ( size_size_list_a @ Ms )
% 0.25/0.57 = ( size_size_list_a @ Ns ) )
% 0.25/0.57 & ( member449909584od_a_a @ ( product_Pair_a_a @ M @ N ) @ R ) )
% 0.25/0.57 | ( ( M = N )
% 0.25/0.57 & ( member1250517072list_a @ ( produc1448356631list_a @ Ms @ Ns ) @ ( lenlex_a @ R ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % Cons_lenlex_iff
% 0.25/0.57 thf(fact_322_Cons__in__subseqsD,axiom,
% 0.25/0.57 ! [Y3: product_prod_a_a,Ys2: list_P1467822637od_a_a,Xs2: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( member1578987478od_a_a @ ( cons_P1921020637od_a_a @ Y3 @ Ys2 ) @ ( set_li1284606018od_a_a @ ( subseq2115548028od_a_a @ Xs2 ) ) )
% 0.25/0.57 => ( member1578987478od_a_a @ Ys2 @ ( set_li1284606018od_a_a @ ( subseq2115548028od_a_a @ Xs2 ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % Cons_in_subseqsD
% 0.25/0.57 thf(fact_323_in__measures_I2_J,axiom,
% 0.25/0.57 ! [X3: a,Y3: a,F: a > nat,Fs: list_a_nat] :
% 0.25/0.57 ( ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ ( measures_a @ ( cons_a_nat @ F @ Fs ) ) )
% 0.25/0.57 = ( ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y3 ) )
% 0.25/0.57 | ( ( ( F @ X3 )
% 0.25/0.57 = ( F @ Y3 ) )
% 0.25/0.57 & ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ ( measures_a @ Fs ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % in_measures(2)
% 0.25/0.57 thf(fact_324_inverse__permutation__of__list_Oelims,axiom,
% 0.25/0.57 ! [X3: list_P1467822637od_a_a,Xa2: a,Y3: a] :
% 0.25/0.57 ( ( ( invers1007791577list_a @ X3 @ Xa2 )
% 0.25/0.57 = Y3 )
% 0.25/0.57 => ( ( ( X3 = nil_Product_prod_a_a )
% 0.25/0.57 => ( Y3 != Xa2 ) )
% 0.25/0.57 => ~ ! [Y4: a,X6: a,Xs4: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( X3
% 0.25/0.57 = ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ Y4 @ X6 ) @ Xs4 ) )
% 0.25/0.57 => ~ ( ( ( Xa2 = X6 )
% 0.25/0.57 => ( Y3 = Y4 ) )
% 0.25/0.57 & ( ( Xa2 != X6 )
% 0.25/0.57 => ( Y3
% 0.25/0.57 = ( invers1007791577list_a @ Xs4 @ Xa2 ) ) ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % inverse_permutation_of_list.elims
% 0.25/0.57 thf(fact_325_in__measures_I1_J,axiom,
% 0.25/0.57 ! [X3: a,Y3: a] :
% 0.25/0.57 ~ ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ ( measures_a @ nil_a_nat ) ) ).
% 0.25/0.57
% 0.25/0.57 % in_measures(1)
% 0.25/0.57 thf(fact_326_eval__inverse__permutation__of__list_I3_J,axiom,
% 0.25/0.57 ! [X3: a,X7: a,Y5: a,Xs2: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( X3 != X7 )
% 0.25/0.57 => ( ( invers1007791577list_a @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ Y5 @ X7 ) @ Xs2 ) @ X3 )
% 0.25/0.57 = ( invers1007791577list_a @ Xs2 @ X3 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % eval_inverse_permutation_of_list(3)
% 0.25/0.57 thf(fact_327_eval__inverse__permutation__of__list_I2_J,axiom,
% 0.25/0.57 ! [X3: a,X7: a,Y3: a,Xs2: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( X3 = X7 )
% 0.25/0.57 => ( ( invers1007791577list_a @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ Y3 @ X7 ) @ Xs2 ) @ X3 )
% 0.25/0.57 = Y3 ) ) ).
% 0.25/0.57
% 0.25/0.57 % eval_inverse_permutation_of_list(2)
% 0.25/0.57 thf(fact_328_inverse__permutation__of__list_Osimps_I2_J,axiom,
% 0.25/0.57 ! [X3: a,X7: a,Y3: a,Xs2: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( ( X3 = X7 )
% 0.25/0.57 => ( ( invers1007791577list_a @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ Y3 @ X7 ) @ Xs2 ) @ X3 )
% 0.25/0.57 = Y3 ) )
% 0.25/0.57 & ( ( X3 != X7 )
% 0.25/0.57 => ( ( invers1007791577list_a @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ Y3 @ X7 ) @ Xs2 ) @ X3 )
% 0.25/0.57 = ( invers1007791577list_a @ Xs2 @ X3 ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % inverse_permutation_of_list.simps(2)
% 0.25/0.57 thf(fact_329_measures__less,axiom,
% 0.25/0.57 ! [F: a > nat,X3: a,Y3: a,Fs: list_a_nat] :
% 0.25/0.57 ( ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y3 ) )
% 0.25/0.57 => ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ ( measures_a @ ( cons_a_nat @ F @ Fs ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % measures_less
% 0.25/0.57 thf(fact_330_inverse__permutation__of__list__unique,axiom,
% 0.25/0.57 ! [Xs2: list_P1467822637od_a_a,A4: set_a,X3: a,Y3: a] :
% 0.25/0.57 ( ( list_permutes_a @ Xs2 @ A4 )
% 0.25/0.57 => ( ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ ( set_Product_prod_a_a2 @ Xs2 ) )
% 0.25/0.57 => ( ( invers1007791577list_a @ Xs2 @ Y3 )
% 0.25/0.57 = X3 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % inverse_permutation_of_list_unique
% 0.25/0.57 thf(fact_331_eval__permutation__of__list_I3_J,axiom,
% 0.25/0.57 ! [X3: a,X7: a,Y5: a,Xs2: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( X3 != X7 )
% 0.25/0.57 => ( ( permut1422637723list_a @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ X7 @ Y5 ) @ Xs2 ) @ X3 )
% 0.25/0.57 = ( permut1422637723list_a @ Xs2 @ X3 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % eval_permutation_of_list(3)
% 0.25/0.57 thf(fact_332_eval__permutation__of__list_I2_J,axiom,
% 0.25/0.57 ! [X3: a,X7: a,Y3: a,Xs2: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( X3 = X7 )
% 0.25/0.57 => ( ( permut1422637723list_a @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ X7 @ Y3 ) @ Xs2 ) @ X3 )
% 0.25/0.57 = Y3 ) ) ).
% 0.25/0.57
% 0.25/0.57 % eval_permutation_of_list(2)
% 0.25/0.57 thf(fact_333_permutation__of__list__unique,axiom,
% 0.25/0.57 ! [Xs2: list_P1467822637od_a_a,A4: set_a,X3: a,Y3: a] :
% 0.25/0.57 ( ( list_permutes_a @ Xs2 @ A4 )
% 0.25/0.57 => ( ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ ( set_Product_prod_a_a2 @ Xs2 ) )
% 0.25/0.57 => ( ( permut1422637723list_a @ Xs2 @ X3 )
% 0.25/0.57 = Y3 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % permutation_of_list_unique
% 0.25/0.57 thf(fact_334_permutation__of__list__Cons,axiom,
% 0.25/0.57 ! [X3: a,X7: a,Y3: a,Xs2: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( ( X3 = X7 )
% 0.25/0.57 => ( ( permut1422637723list_a @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ Xs2 ) @ X7 )
% 0.25/0.57 = Y3 ) )
% 0.25/0.57 & ( ( X3 != X7 )
% 0.25/0.57 => ( ( permut1422637723list_a @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ Xs2 ) @ X7 )
% 0.25/0.57 = ( permut1422637723list_a @ Xs2 @ X7 ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % permutation_of_list_Cons
% 0.25/0.57 thf(fact_335_not__in__set__insert,axiom,
% 0.25/0.57 ! [X3: product_prod_a_a,Xs2: list_P1467822637od_a_a] :
% 0.25/0.57 ( ~ ( member449909584od_a_a @ X3 @ ( set_Product_prod_a_a2 @ Xs2 ) )
% 0.25/0.57 => ( ( insert2123825731od_a_a @ X3 @ Xs2 )
% 0.25/0.57 = ( cons_P1921020637od_a_a @ X3 @ Xs2 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % not_in_set_insert
% 0.25/0.57 thf(fact_336_insert__Nil,axiom,
% 0.25/0.57 ! [X3: product_prod_a_a] :
% 0.25/0.57 ( ( insert2123825731od_a_a @ X3 @ nil_Product_prod_a_a )
% 0.25/0.57 = ( cons_P1921020637od_a_a @ X3 @ nil_Product_prod_a_a ) ) ).
% 0.25/0.57
% 0.25/0.57 % insert_Nil
% 0.25/0.57 thf(fact_337_List_Oinsert__def,axiom,
% 0.25/0.57 ( insert2123825731od_a_a
% 0.25/0.57 = ( ^ [X: product_prod_a_a,Xs: list_P1467822637od_a_a] : ( if_lis321365491od_a_a @ ( member449909584od_a_a @ X @ ( set_Product_prod_a_a2 @ Xs ) ) @ Xs @ ( cons_P1921020637od_a_a @ X @ Xs ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % List.insert_def
% 0.25/0.57 thf(fact_338_concat__eq__append__conv,axiom,
% 0.25/0.57 ! [Xss2: list_l1108175539od_a_a,Ys2: list_P1467822637od_a_a,Zs: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( ( concat1878217064od_a_a @ Xss2 )
% 0.25/0.57 = ( append1574001858od_a_a @ Ys2 @ Zs ) )
% 0.25/0.57 = ( ( ( Xss2 = nil_li1885598003od_a_a )
% 0.25/0.57 => ( ( Ys2 = nil_Product_prod_a_a )
% 0.25/0.57 & ( Zs = nil_Product_prod_a_a ) ) )
% 0.25/0.57 & ( ( Xss2 != nil_li1885598003od_a_a )
% 0.25/0.57 => ? [Xss1: list_l1108175539od_a_a,Xs: list_P1467822637od_a_a,Xs6: list_P1467822637od_a_a,Xss22: list_l1108175539od_a_a] :
% 0.25/0.57 ( ( Xss2
% 0.25/0.57 = ( append2141280328od_a_a @ Xss1 @ ( cons_l724116707od_a_a @ ( append1574001858od_a_a @ Xs @ Xs6 ) @ Xss22 ) ) )
% 0.25/0.57 & ( Ys2
% 0.25/0.57 = ( append1574001858od_a_a @ ( concat1878217064od_a_a @ Xss1 ) @ Xs ) )
% 0.25/0.57 & ( Zs
% 0.25/0.57 = ( append1574001858od_a_a @ Xs6 @ ( concat1878217064od_a_a @ Xss22 ) ) ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % concat_eq_append_conv
% 0.25/0.57 thf(fact_339_inverse__permutation__of__list_Opelims,axiom,
% 0.25/0.57 ! [X3: list_P1467822637od_a_a,Xa2: a,Y3: a] :
% 0.25/0.57 ( ( ( invers1007791577list_a @ X3 @ Xa2 )
% 0.25/0.57 = Y3 )
% 0.25/0.57 => ( ( accp_P941981633_a_a_a @ invers214109608_rel_a @ ( produc998622632_a_a_a @ X3 @ Xa2 ) )
% 0.25/0.57 => ( ( ( X3 = nil_Product_prod_a_a )
% 0.25/0.57 => ( ( Y3 = Xa2 )
% 0.25/0.57 => ~ ( accp_P941981633_a_a_a @ invers214109608_rel_a @ ( produc998622632_a_a_a @ nil_Product_prod_a_a @ Xa2 ) ) ) )
% 0.25/0.57 => ~ ! [Y4: a,X6: a,Xs4: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( X3
% 0.25/0.57 = ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ Y4 @ X6 ) @ Xs4 ) )
% 0.25/0.57 => ( ( ( ( Xa2 = X6 )
% 0.25/0.57 => ( Y3 = Y4 ) )
% 0.25/0.57 & ( ( Xa2 != X6 )
% 0.25/0.57 => ( Y3
% 0.25/0.57 = ( invers1007791577list_a @ Xs4 @ Xa2 ) ) ) )
% 0.25/0.57 => ~ ( accp_P941981633_a_a_a @ invers214109608_rel_a @ ( produc998622632_a_a_a @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ Y4 @ X6 ) @ Xs4 ) @ Xa2 ) ) ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % inverse_permutation_of_list.pelims
% 0.25/0.57 thf(fact_340_concat__append,axiom,
% 0.25/0.57 ! [Xs2: list_l1108175539od_a_a,Ys2: list_l1108175539od_a_a] :
% 0.25/0.57 ( ( concat1878217064od_a_a @ ( append2141280328od_a_a @ Xs2 @ Ys2 ) )
% 0.25/0.57 = ( append1574001858od_a_a @ ( concat1878217064od_a_a @ Xs2 ) @ ( concat1878217064od_a_a @ Ys2 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % concat_append
% 0.25/0.57 thf(fact_341_concat_Osimps_I2_J,axiom,
% 0.25/0.57 ! [X3: list_P1467822637od_a_a,Xs2: list_l1108175539od_a_a] :
% 0.25/0.57 ( ( concat1878217064od_a_a @ ( cons_l724116707od_a_a @ X3 @ Xs2 ) )
% 0.25/0.57 = ( append1574001858od_a_a @ X3 @ ( concat1878217064od_a_a @ Xs2 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % concat.simps(2)
% 0.25/0.57 thf(fact_342_concat__eq__appendD,axiom,
% 0.25/0.57 ! [Xss2: list_l1108175539od_a_a,Ys2: list_P1467822637od_a_a,Zs: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( ( concat1878217064od_a_a @ Xss2 )
% 0.25/0.57 = ( append1574001858od_a_a @ Ys2 @ Zs ) )
% 0.25/0.57 => ( ( Xss2 != nil_li1885598003od_a_a )
% 0.25/0.57 => ? [Xss12: list_l1108175539od_a_a,Xs4: list_P1467822637od_a_a,Xs3: list_P1467822637od_a_a,Xss23: list_l1108175539od_a_a] :
% 0.25/0.57 ( ( Xss2
% 0.25/0.57 = ( append2141280328od_a_a @ Xss12 @ ( cons_l724116707od_a_a @ ( append1574001858od_a_a @ Xs4 @ Xs3 ) @ Xss23 ) ) )
% 0.25/0.57 & ( Ys2
% 0.25/0.57 = ( append1574001858od_a_a @ ( concat1878217064od_a_a @ Xss12 ) @ Xs4 ) )
% 0.25/0.57 & ( Zs
% 0.25/0.57 = ( append1574001858od_a_a @ Xs3 @ ( concat1878217064od_a_a @ Xss23 ) ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % concat_eq_appendD
% 0.25/0.57 thf(fact_343_listrel_Oinducts,axiom,
% 0.25/0.57 ! [X1: list_P1467822637od_a_a,X2: list_P1467822637od_a_a,R: set_Pr1948701895od_a_a,P2: list_P1467822637od_a_a > list_P1467822637od_a_a > $o] :
% 0.25/0.57 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ X1 @ X2 ) @ ( listre2074280881od_a_a @ R ) )
% 0.25/0.57 => ( ( P2 @ nil_Product_prod_a_a @ nil_Product_prod_a_a )
% 0.25/0.57 => ( ! [X4: product_prod_a_a,Y4: product_prod_a_a,Xs4: list_P1467822637od_a_a,Ys4: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X4 @ Y4 ) @ R )
% 0.25/0.57 => ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ Xs4 @ Ys4 ) @ ( listre2074280881od_a_a @ R ) )
% 0.25/0.57 => ( ( P2 @ Xs4 @ Ys4 )
% 0.25/0.57 => ( P2 @ ( cons_P1921020637od_a_a @ X4 @ Xs4 ) @ ( cons_P1921020637od_a_a @ Y4 @ Ys4 ) ) ) ) )
% 0.25/0.57 => ( P2 @ X1 @ X2 ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % listrel.inducts
% 0.25/0.57 thf(fact_344_listrel_Oinducts,axiom,
% 0.25/0.57 ! [X1: list_a,X2: list_a,R: set_Product_prod_a_a,P2: list_a > list_a > $o] :
% 0.25/0.57 ( ( member1250517072list_a @ ( produc1448356631list_a @ X1 @ X2 ) @ ( listrel_a_a @ R ) )
% 0.25/0.57 => ( ( P2 @ nil_a @ nil_a )
% 0.25/0.57 => ( ! [X4: a,Y4: a,Xs4: list_a,Ys4: list_a] :
% 0.25/0.57 ( ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y4 ) @ R )
% 0.25/0.57 => ( ( member1250517072list_a @ ( produc1448356631list_a @ Xs4 @ Ys4 ) @ ( listrel_a_a @ R ) )
% 0.25/0.57 => ( ( P2 @ Xs4 @ Ys4 )
% 0.25/0.57 => ( P2 @ ( cons_a @ X4 @ Xs4 ) @ ( cons_a @ Y4 @ Ys4 ) ) ) ) )
% 0.25/0.57 => ( P2 @ X1 @ X2 ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % listrel.inducts
% 0.25/0.57 thf(fact_345_listrel_OCons,axiom,
% 0.25/0.57 ! [X3: product_prod_a_a,Y3: product_prod_a_a,R: set_Pr1948701895od_a_a,Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X3 @ Y3 ) @ R )
% 0.25/0.57 => ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ Xs2 @ Ys2 ) @ ( listre2074280881od_a_a @ R ) )
% 0.25/0.57 => ( member1691432592od_a_a @ ( produc85179863od_a_a @ ( cons_P1921020637od_a_a @ X3 @ Xs2 ) @ ( cons_P1921020637od_a_a @ Y3 @ Ys2 ) ) @ ( listre2074280881od_a_a @ R ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % listrel.Cons
% 0.25/0.57 thf(fact_346_listrel_OCons,axiom,
% 0.25/0.57 ! [X3: a,Y3: a,R: set_Product_prod_a_a,Xs2: list_a,Ys2: list_a] :
% 0.25/0.57 ( ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ R )
% 0.25/0.57 => ( ( member1250517072list_a @ ( produc1448356631list_a @ Xs2 @ Ys2 ) @ ( listrel_a_a @ R ) )
% 0.25/0.57 => ( member1250517072list_a @ ( produc1448356631list_a @ ( cons_a @ X3 @ Xs2 ) @ ( cons_a @ Y3 @ Ys2 ) ) @ ( listrel_a_a @ R ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % listrel.Cons
% 0.25/0.57 thf(fact_347_listrel__Cons1,axiom,
% 0.25/0.57 ! [Y3: product_prod_a_a,Ys2: list_P1467822637od_a_a,Xs2: list_P1467822637od_a_a,R: set_Pr1948701895od_a_a] :
% 0.25/0.57 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ ( cons_P1921020637od_a_a @ Y3 @ Ys2 ) @ Xs2 ) @ ( listre2074280881od_a_a @ R ) )
% 0.25/0.57 => ~ ! [Y4: product_prod_a_a,Ys4: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( Xs2
% 0.25/0.57 = ( cons_P1921020637od_a_a @ Y4 @ Ys4 ) )
% 0.25/0.57 => ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ Y3 @ Y4 ) @ R )
% 0.25/0.57 => ~ ( member1691432592od_a_a @ ( produc85179863od_a_a @ Ys2 @ Ys4 ) @ ( listre2074280881od_a_a @ R ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % listrel_Cons1
% 0.25/0.57 thf(fact_348_listrel__Cons1,axiom,
% 0.25/0.57 ! [Y3: a,Ys2: list_a,Xs2: list_a,R: set_Product_prod_a_a] :
% 0.25/0.57 ( ( member1250517072list_a @ ( produc1448356631list_a @ ( cons_a @ Y3 @ Ys2 ) @ Xs2 ) @ ( listrel_a_a @ R ) )
% 0.25/0.57 => ~ ! [Y4: a,Ys4: list_a] :
% 0.25/0.57 ( ( Xs2
% 0.25/0.57 = ( cons_a @ Y4 @ Ys4 ) )
% 0.25/0.57 => ( ( member449909584od_a_a @ ( product_Pair_a_a @ Y3 @ Y4 ) @ R )
% 0.25/0.57 => ~ ( member1250517072list_a @ ( produc1448356631list_a @ Ys2 @ Ys4 ) @ ( listrel_a_a @ R ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % listrel_Cons1
% 0.25/0.57 thf(fact_349_listrel__Cons2,axiom,
% 0.25/0.57 ! [Xs2: list_P1467822637od_a_a,Y3: product_prod_a_a,Ys2: list_P1467822637od_a_a,R: set_Pr1948701895od_a_a] :
% 0.25/0.57 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ Xs2 @ ( cons_P1921020637od_a_a @ Y3 @ Ys2 ) ) @ ( listre2074280881od_a_a @ R ) )
% 0.25/0.57 => ~ ! [X4: product_prod_a_a,Xs4: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( Xs2
% 0.25/0.57 = ( cons_P1921020637od_a_a @ X4 @ Xs4 ) )
% 0.25/0.57 => ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X4 @ Y3 ) @ R )
% 0.25/0.57 => ~ ( member1691432592od_a_a @ ( produc85179863od_a_a @ Xs4 @ Ys2 ) @ ( listre2074280881od_a_a @ R ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % listrel_Cons2
% 0.25/0.57 thf(fact_350_listrel__Cons2,axiom,
% 0.25/0.57 ! [Xs2: list_a,Y3: a,Ys2: list_a,R: set_Product_prod_a_a] :
% 0.25/0.57 ( ( member1250517072list_a @ ( produc1448356631list_a @ Xs2 @ ( cons_a @ Y3 @ Ys2 ) ) @ ( listrel_a_a @ R ) )
% 0.25/0.57 => ~ ! [X4: a,Xs4: list_a] :
% 0.25/0.57 ( ( Xs2
% 0.25/0.57 = ( cons_a @ X4 @ Xs4 ) )
% 0.25/0.57 => ( ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y3 ) @ R )
% 0.25/0.57 => ~ ( member1250517072list_a @ ( produc1448356631list_a @ Xs4 @ Ys2 ) @ ( listrel_a_a @ R ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % listrel_Cons2
% 0.25/0.57 thf(fact_351_listrel_Ocases,axiom,
% 0.25/0.57 ! [A1: list_P1467822637od_a_a,A22: list_P1467822637od_a_a,R: set_Pr1948701895od_a_a] :
% 0.25/0.57 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ A1 @ A22 ) @ ( listre2074280881od_a_a @ R ) )
% 0.25/0.57 => ( ( ( A1 = nil_Product_prod_a_a )
% 0.25/0.57 => ( A22 != nil_Product_prod_a_a ) )
% 0.25/0.57 => ~ ! [X4: product_prod_a_a,Y4: product_prod_a_a,Xs4: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( A1
% 0.25/0.57 = ( cons_P1921020637od_a_a @ X4 @ Xs4 ) )
% 0.25/0.57 => ! [Ys4: list_P1467822637od_a_a] :
% 0.25/0.57 ( ( A22
% 0.25/0.57 = ( cons_P1921020637od_a_a @ Y4 @ Ys4 ) )
% 0.25/0.57 => ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X4 @ Y4 ) @ R )
% 0.25/0.57 => ~ ( member1691432592od_a_a @ ( produc85179863od_a_a @ Xs4 @ Ys4 ) @ ( listre2074280881od_a_a @ R ) ) ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % listrel.cases
% 0.25/0.57 thf(fact_352_listrel_Ocases,axiom,
% 0.25/0.57 ! [A1: list_a,A22: list_a,R: set_Product_prod_a_a] :
% 0.25/0.57 ( ( member1250517072list_a @ ( produc1448356631list_a @ A1 @ A22 ) @ ( listrel_a_a @ R ) )
% 0.25/0.57 => ( ( ( A1 = nil_a )
% 0.25/0.57 => ( A22 != nil_a ) )
% 0.25/0.57 => ~ ! [X4: a,Y4: a,Xs4: list_a] :
% 0.25/0.57 ( ( A1
% 0.25/0.57 = ( cons_a @ X4 @ Xs4 ) )
% 0.25/0.57 => ! [Ys4: list_a] :
% 0.25/0.57 ( ( A22
% 0.25/0.57 = ( cons_a @ Y4 @ Ys4 ) )
% 0.25/0.57 => ( ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y4 ) @ R )
% 0.25/0.57 => ~ ( member1250517072list_a @ ( produc1448356631list_a @ Xs4 @ Ys4 ) @ ( listrel_a_a @ R ) ) ) ) ) ) ) ).
% 0.25/0.64
% 0.25/0.64 % listrel.cases
% 0.25/0.64 thf(fact_353_listrel_Osimps,axiom,
% 0.25/0.64 ! [A1: list_P1467822637od_a_a,A22: list_P1467822637od_a_a,R: set_Pr1948701895od_a_a] :
% 0.25/0.64 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ A1 @ A22 ) @ ( listre2074280881od_a_a @ R ) )
% 0.25/0.64 = ( ( ( A1 = nil_Product_prod_a_a )
% 0.25/0.64 & ( A22 = nil_Product_prod_a_a ) )
% 0.25/0.64 | ? [X: product_prod_a_a,Y: product_prod_a_a,Xs: list_P1467822637od_a_a,Ys: list_P1467822637od_a_a] :
% 0.25/0.64 ( ( A1
% 0.25/0.64 = ( cons_P1921020637od_a_a @ X @ Xs ) )
% 0.25/0.64 & ( A22
% 0.25/0.64 = ( cons_P1921020637od_a_a @ Y @ Ys ) )
% 0.25/0.64 & ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X @ Y ) @ R )
% 0.25/0.64 & ( member1691432592od_a_a @ ( produc85179863od_a_a @ Xs @ Ys ) @ ( listre2074280881od_a_a @ R ) ) ) ) ) ).
% 0.25/0.64
% 0.25/0.64 % listrel.simps
% 0.25/0.64 thf(fact_354_listrel_Osimps,axiom,
% 0.25/0.64 ! [A1: list_a,A22: list_a,R: set_Product_prod_a_a] :
% 0.25/0.64 ( ( member1250517072list_a @ ( produc1448356631list_a @ A1 @ A22 ) @ ( listrel_a_a @ R ) )
% 0.25/0.64 = ( ( ( A1 = nil_a )
% 0.25/0.64 & ( A22 = nil_a ) )
% 0.25/0.64 | ? [X: a,Y: a,Xs: list_a,Ys: list_a] :
% 0.25/0.64 ( ( A1
% 0.25/0.64 = ( cons_a @ X @ Xs ) )
% 0.25/0.64 & ( A22
% 0.25/0.64 = ( cons_a @ Y @ Ys ) )
% 0.25/0.64 & ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ R )
% 0.25/0.64 & ( member1250517072list_a @ ( produc1448356631list_a @ Xs @ Ys ) @ ( listrel_a_a @ R ) ) ) ) ) ).
% 0.25/0.64
% 0.25/0.64 % listrel.simps
% 0.25/0.64
% 0.25/0.64 % Helper facts (3)
% 0.25/0.64 thf(help_If_3_1_If_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J_T,axiom,
% 0.25/0.64 ! [P2: $o] :
% 0.25/0.64 ( ( P2 = $true )
% 0.25/0.64 | ( P2 = $false ) ) ).
% 0.25/0.64
% 0.25/0.64 thf(help_If_2_1_If_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J_T,axiom,
% 0.25/0.64 ! [X3: list_P1467822637od_a_a,Y3: list_P1467822637od_a_a] :
% 0.25/0.64 ( ( if_lis321365491od_a_a @ $false @ X3 @ Y3 )
% 0.25/0.64 = Y3 ) ).
% 0.25/0.64
% 0.25/0.64 thf(help_If_1_1_If_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J_T,axiom,
% 0.25/0.64 ! [X3: list_P1467822637od_a_a,Y3: list_P1467822637od_a_a] :
% 0.25/0.64 ( ( if_lis321365491od_a_a @ $true @ X3 @ Y3 )
% 0.25/0.64 = X3 ) ).
% 0.25/0.64
% 0.25/0.64 % Conjectures (1)
% 0.25/0.64 thf(conj_0,conjecture,
% 0.25/0.64 ! [Xs4: list_P1467822637od_a_a,X4: a,Y4: a,Ys4: list_P1467822637od_a_a] :
% 0.25/0.64 ( es
% 0.25/0.64 != ( append1574001858od_a_a @ Xs4 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ X4 @ Y4 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ Y4 @ X4 ) @ Ys4 ) ) ) ) ).
% 0.25/0.64
% 0.25/0.64 %------------------------------------------------------------------------------
% 0.25/0.64 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.XY8FgSAv8i/cvc5---1.0.5_7160.p...
% 0.25/0.64 (declare-sort $$unsorted 0)
% 0.25/0.64 (declare-sort tptp.set_Pr779272263od_a_a 0)
% 0.25/0.64 (declare-sort tptp.produc205693799od_a_a 0)
% 0.25/0.64 (declare-sort tptp.set_Pr1295299783od_a_a 0)
% 0.25/0.64 (declare-sort tptp.produc1990712039od_a_a 0)
% 0.25/0.64 (declare-sort tptp.produc1912141786_a_a_a 0)
% 0.25/0.64 (declare-sort tptp.set_Pr727105414od_a_a 0)
% 0.25/0.64 (declare-sort tptp.set_Pr1239640519od_a_a 0)
% 0.25/0.64 (declare-sort tptp.produc501911462od_a_a 0)
% 0.25/0.64 (declare-sort tptp.produc657724903od_a_a 0)
% 0.25/0.64 (declare-sort tptp.produc821581462od_a_a 0)
% 0.25/0.64 (declare-sort tptp.set_Pr800560199od_a_a 0)
% 0.25/0.64 (declare-sort tptp.produc651658087od_a_a 0)
% 0.25/0.64 (declare-sort tptp.set_Pr110478017_a_a_a 0)
% 0.25/0.64 (declare-sort tptp.set_Pr753687879_a_nat 0)
% 0.25/0.64 (declare-sort tptp.produc1197928545_a_a_a 0)
% 0.25/0.64 (declare-sort tptp.list_P1891567085od_a_a 0)
% 0.25/0.64 (declare-sort tptp.set_Pr1948701895od_a_a 0)
% 0.25/0.64 (declare-sort tptp.set_Pr1742859527list_a 0)
% 0.25/0.64 (declare-sort tptp.pair_p1891813445t_unit 0)
% 0.25/0.64 (declare-sort tptp.produc1334933863_a_nat 0)
% 0.25/0.64 (declare-sort tptp.list_P1435957893_a_nat 0)
% 0.25/0.64 (declare-sort tptp.produc1572603623od_a_a 0)
% 0.25/0.64 (declare-sort tptp.produc403652391list_a 0)
% 0.25/0.64 (declare-sort tptp.list_P1175580892od_a_a 0)
% 0.25/0.64 (declare-sort tptp.list_P305489470_a_a_a 0)
% 0.25/0.64 (declare-sort tptp.set_Pr248149174od_a_a 0)
% 0.25/0.64 (declare-sort tptp.set_Pr1525541400_a_a_a 0)
% 0.25/0.64 (declare-sort tptp.pair_p125712459t_unit 0)
% 0.25/0.64 (declare-sort tptp.set_Pr1940702919_a_nat 0)
% 0.25/0.64 (declare-sort tptp.produc664688895_a_nat 0)
% 0.25/0.64 (declare-sort tptp.produc1701253078od_a_a 0)
% 0.25/0.64 (declare-sort tptp.produc657167928_a_a_a 0)
% 0.25/0.64 (declare-sort tptp.list_P1458844246od_a_a 0)
% 0.25/0.64 (declare-sort tptp.list_P319927492_a_a_a 0)
% 0.25/0.64 (declare-sort tptp.list_P601816365list_a 0)
% 0.25/0.64 (declare-sort tptp.set_Pr1971762695list_a 0)
% 0.25/0.64 (declare-sort tptp.produc1178641895_a_nat 0)
% 0.25/0.64 (declare-sort tptp.list_P576104046_a_nat 0)
% 0.25/0.64 (declare-sort tptp.list_P916011052_nat_a 0)
% 0.25/0.64 (declare-sort tptp.produc1921647824od_a_a 0)
% 0.25/0.64 (declare-sort tptp.produc1016684094_a_a_a 0)
% 0.25/0.64 (declare-sort tptp.produc864062247list_a 0)
% 0.25/0.64 (declare-sort tptp.list_l1108175539od_a_a 0)
% 0.25/0.64 (declare-sort tptp.set_li562223245od_a_a 0)
% 0.25/0.64 (declare-sort tptp.product_prod_a_a_nat 0)
% 0.25/0.64 (declare-sort tptp.product_prod_a_nat_a 0)
% 0.25/0.64 (declare-sort tptp.list_P1467822637od_a_a 0)
% 0.25/0.64 (declare-sort tptp.set_Product_prod_a_a 0)
% 0.25/0.64 (declare-sort tptp.list_a_nat 0)
% 0.25/0.64 (declare-sort tptp.product_prod_a_a 0)
% 0.25/0.64 (declare-sort tptp.list_list_a 0)
% 0.25/0.64 (declare-sort tptp.list_a 0)
% 0.25/0.64 (declare-sort tptp.set_a 0)
% 0.25/0.64 (declare-sort tptp.nat 0)
% 0.25/0.64 (declare-sort tptp.a 0)
% 0.25/0.64 (declare-fun tptp.if_lis321365491od_a_a (Bool tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a) tptp.list_P1467822637od_a_a)
% 0.25/0.64 (declare-fun tptp.kurato292963650list_a (tptp.list_P601816365list_a) Bool)
% 0.25/0.64 (declare-fun tptp.kurato1404746725od_a_a (tptp.list_P1891567085od_a_a) Bool)
% 0.25/0.64 (declare-fun tptp.kurato1072996284sing_a (tptp.list_P1467822637od_a_a) Bool)
% 0.25/0.64 (declare-fun tptp.append_a_nat (tptp.list_a_nat tptp.list_a_nat) tptp.list_a_nat)
% 0.25/0.64 (declare-fun tptp.append2141280328od_a_a (tptp.list_l1108175539od_a_a tptp.list_l1108175539od_a_a) tptp.list_l1108175539od_a_a)
% 0.25/0.64 (declare-fun tptp.append_list_a (tptp.list_list_a tptp.list_list_a) tptp.list_list_a)
% 0.25/0.64 (declare-fun tptp.append750086082list_a (tptp.list_P601816365list_a tptp.list_P601816365list_a) tptp.list_P601816365list_a)
% 0.25/0.64 (declare-fun tptp.append864718978od_a_a (tptp.list_P1891567085od_a_a tptp.list_P1891567085od_a_a) tptp.list_P1891567085od_a_a)
% 0.25/0.64 (declare-fun tptp.append1574001858od_a_a (tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a) tptp.list_P1467822637od_a_a)
% 0.25/0.64 (declare-fun tptp.append_a (tptp.list_a tptp.list_a) tptp.list_a)
% 0.25/0.64 (declare-fun tptp.bind_a1190333103od_a_a (tptp.list_a_nat (-> (-> tptp.a tptp.nat) tptp.list_P1467822637od_a_a)) tptp.list_P1467822637od_a_a)
% 0.25/0.64 (declare-fun tptp.bind_a_nat_a (tptp.list_a_nat (-> (-> tptp.a tptp.nat) tptp.list_a)) tptp.list_a)
% 0.25/0.64 (declare-fun tptp.bind_l618536897od_a_a (tptp.list_l1108175539od_a_a (-> tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a)) tptp.list_P1467822637od_a_a)
% 0.25/0.64 (declare-fun tptp.bind_l1307590552_a_a_a (tptp.list_l1108175539od_a_a (-> tptp.list_P1467822637od_a_a tptp.list_a)) tptp.list_a)
% 0.25/0.64 (declare-fun tptp.bind_P240085581od_a_a (tptp.list_P1467822637od_a_a (-> tptp.product_prod_a_a tptp.list_l1108175539od_a_a)) tptp.list_l1108175539od_a_a)
% 0.25/0.64 (declare-fun tptp.bind_P1783625031od_a_a (tptp.list_P1467822637od_a_a (-> tptp.product_prod_a_a tptp.list_P1467822637od_a_a)) tptp.list_P1467822637od_a_a)
% 0.25/0.64 (declare-fun tptp.bind_P293964574_a_a_a (tptp.list_P1467822637od_a_a (-> tptp.product_prod_a_a tptp.list_a)) tptp.list_a)
% 0.25/0.64 (declare-fun tptp.bind_a883992246od_a_a (tptp.list_a (-> tptp.a tptp.list_l1108175539od_a_a)) tptp.list_l1108175539od_a_a)
% 0.25/0.64 (declare-fun tptp.bind_a1679112752od_a_a (tptp.list_a (-> tptp.a tptp.list_P1467822637od_a_a)) tptp.list_P1467822637od_a_a)
% 0.25/0.64 (declare-fun tptp.bind_a_a (tptp.list_a (-> tptp.a tptp.list_a)) tptp.list_a)
% 0.25/0.64 (declare-fun tptp.concat1878217064od_a_a (tptp.list_l1108175539od_a_a) tptp.list_P1467822637od_a_a)
% 0.25/0.64 (declare-fun tptp.insert2123825731od_a_a (tptp.product_prod_a_a tptp.list_P1467822637od_a_a) tptp.list_P1467822637od_a_a)
% 0.25/0.64 (declare-fun tptp.lenlex2038501170od_a_a (tptp.set_Pr1948701895od_a_a) tptp.set_Pr800560199od_a_a)
% 0.25/0.64 (declare-fun tptp.lenlex_a (tptp.set_Product_prod_a_a) tptp.set_Pr1971762695list_a)
% 0.25/0.64 (declare-fun tptp.lex_Product_prod_a_a (tptp.set_Pr1948701895od_a_a) tptp.set_Pr800560199od_a_a)
% 0.25/0.64 (declare-fun tptp.lex_a (tptp.set_Product_prod_a_a) tptp.set_Pr1971762695list_a)
% 0.25/0.64 (declare-fun tptp.lexord_a_nat (tptp.set_Pr1940702919_a_nat) tptp.set_Pr753687879_a_nat)
% 0.25/0.64 (declare-fun tptp.lexord1284731808od_a_a (tptp.set_Pr800560199od_a_a) tptp.set_Pr1239640519od_a_a)
% 0.25/0.64 (declare-fun tptp.lexord_list_a (tptp.set_Pr1971762695list_a) tptp.set_Pr1742859527list_a)
% 0.25/0.64 (declare-fun tptp.lexord931792858od_a_a (tptp.set_Pr1295299783od_a_a) tptp.set_Pr779272263od_a_a)
% 0.25/0.64 (declare-fun tptp.lexord673907738od_a_a (tptp.set_Pr1948701895od_a_a) tptp.set_Pr800560199od_a_a)
% 0.25/0.64 (declare-fun tptp.lexord_a (tptp.set_Product_prod_a_a) tptp.set_Pr1971762695list_a)
% 0.25/0.64 (declare-fun tptp.cons_a_nat ((-> tptp.a tptp.nat) tptp.list_a_nat) tptp.list_a_nat)
% 0.25/0.64 (declare-fun tptp.cons_l724116707od_a_a (tptp.list_P1467822637od_a_a tptp.list_l1108175539od_a_a) tptp.list_l1108175539od_a_a)
% 0.25/0.64 (declare-fun tptp.cons_list_a (tptp.list_a tptp.list_list_a) tptp.list_list_a)
% 0.25/0.64 (declare-fun tptp.cons_P896312284_nat_a (tptp.product_prod_a_nat_a tptp.list_P916011052_nat_a) tptp.list_P916011052_nat_a)
% 0.25/0.64 (declare-fun tptp.cons_P169173742_a_a_a (tptp.produc657167928_a_a_a tptp.list_P305489470_a_a_a) tptp.list_P305489470_a_a_a)
% 0.25/0.64 (declare-fun tptp.cons_P2080942813list_a (tptp.produc864062247list_a tptp.list_P601816365list_a) tptp.list_P601816365list_a)
% 0.25/0.64 (declare-fun tptp.cons_P659009461_a_nat (tptp.produc664688895_a_nat tptp.list_P1435957893_a_nat) tptp.list_P1435957893_a_nat)
% 0.25/0.64 (declare-fun tptp.cons_P1070399645od_a_a (tptp.produc1572603623od_a_a tptp.list_P1891567085od_a_a) tptp.list_P1891567085od_a_a)
% 0.25/0.64 (declare-fun tptp.cons_P86081012_a_a_a (tptp.produc1016684094_a_a_a tptp.list_P319927492_a_a_a) tptp.list_P319927492_a_a_a)
% 0.25/0.64 (declare-fun tptp.cons_P1915851550_a_nat (tptp.product_prod_a_a_nat tptp.list_P576104046_a_nat) tptp.list_P576104046_a_nat)
% 0.25/0.64 (declare-fun tptp.cons_P1213258892od_a_a (tptp.produc1701253078od_a_a tptp.list_P1175580892od_a_a) tptp.list_P1175580892od_a_a)
% 0.25/0.64 (declare-fun tptp.cons_P991044742od_a_a (tptp.produc1921647824od_a_a tptp.list_P1458844246od_a_a) tptp.list_P1458844246od_a_a)
% 0.25/0.64 (declare-fun tptp.cons_P1921020637od_a_a (tptp.product_prod_a_a tptp.list_P1467822637od_a_a) tptp.list_P1467822637od_a_a)
% 0.25/0.64 (declare-fun tptp.cons_a (tptp.a tptp.list_a) tptp.list_a)
% 0.25/0.64 (declare-fun tptp.nil_a_nat () tptp.list_a_nat)
% 0.25/0.64 (declare-fun tptp.nil_li1885598003od_a_a () tptp.list_l1108175539od_a_a)
% 0.25/0.64 (declare-fun tptp.nil_Pr1049924845od_a_a () tptp.list_P1891567085od_a_a)
% 0.25/0.64 (declare-fun tptp.nil_Product_prod_a_a () tptp.list_P1467822637od_a_a)
% 0.25/0.64 (declare-fun tptp.nil_a () tptp.list_a)
% 0.25/0.64 (declare-fun tptp.set_li1284606018od_a_a (tptp.list_l1108175539od_a_a) tptp.set_li562223245od_a_a)
% 0.25/0.64 (declare-fun tptp.set_Product_prod_a_a2 (tptp.list_P1467822637od_a_a) tptp.set_Product_prod_a_a)
% 0.25/0.64 (declare-fun tptp.set_a2 (tptp.list_a) tptp.set_a)
% 0.25/0.64 (declare-fun tptp.listrel1_a_nat (tptp.set_Pr1940702919_a_nat) tptp.set_Pr753687879_a_nat)
% 0.25/0.64 (declare-fun tptp.listre651914124od_a_a (tptp.set_Pr800560199od_a_a) tptp.set_Pr1239640519od_a_a)
% 0.25/0.64 (declare-fun tptp.listrel1_list_a (tptp.set_Pr1971762695list_a) tptp.set_Pr1742859527list_a)
% 0.25/0.64 (declare-fun tptp.listre1832537542od_a_a (tptp.set_Pr1295299783od_a_a) tptp.set_Pr779272263od_a_a)
% 0.25/0.64 (declare-fun tptp.listre944824838od_a_a (tptp.set_Pr1948701895od_a_a) tptp.set_Pr800560199od_a_a)
% 0.25/0.64 (declare-fun tptp.listrel1_a (tptp.set_Product_prod_a_a) tptp.set_Pr1971762695list_a)
% 0.25/0.64 (declare-fun tptp.listre2074280881od_a_a (tptp.set_Pr1948701895od_a_a) tptp.set_Pr800560199od_a_a)
% 0.25/0.64 (declare-fun tptp.listrel_a_a (tptp.set_Product_prod_a_a) tptp.set_Pr1971762695list_a)
% 0.25/0.64 (declare-fun tptp.maps_a836827497od_a_a ((-> (-> tptp.a tptp.nat) tptp.list_P1467822637od_a_a) tptp.list_a_nat) tptp.list_P1467822637od_a_a)
% 0.25/0.64 (declare-fun tptp.maps_a_nat_a ((-> (-> tptp.a tptp.nat) tptp.list_a) tptp.list_a_nat) tptp.list_a)
% 0.25/0.64 (declare-fun tptp.maps_l1117535867od_a_a ((-> tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a) tptp.list_l1108175539od_a_a) tptp.list_P1467822637od_a_a)
% 0.25/0.64 (declare-fun tptp.maps_l1091119186_a_a_a ((-> tptp.list_P1467822637od_a_a tptp.list_a) tptp.list_l1108175539od_a_a) tptp.list_a)
% 0.25/0.64 (declare-fun tptp.maps_P739084551od_a_a ((-> tptp.product_prod_a_a tptp.list_l1108175539od_a_a) tptp.list_P1467822637od_a_a) tptp.list_l1108175539od_a_a)
% 0.25/0.64 (declare-fun tptp.maps_P1529886977od_a_a ((-> tptp.product_prod_a_a tptp.list_P1467822637od_a_a) tptp.list_P1467822637od_a_a) tptp.list_P1467822637od_a_a)
% 0.25/0.64 (declare-fun tptp.maps_P321755352_a_a_a ((-> tptp.product_prod_a_a tptp.list_a) tptp.list_P1467822637od_a_a) tptp.list_a)
% 0.25/0.64 (declare-fun tptp.maps_a667520880od_a_a ((-> tptp.a tptp.list_l1108175539od_a_a) tptp.list_a) tptp.list_l1108175539od_a_a)
% 0.25/0.64 (declare-fun tptp.maps_a1706903530od_a_a ((-> tptp.a tptp.list_P1467822637od_a_a) tptp.list_a) tptp.list_P1467822637od_a_a)
% 0.25/0.64 (declare-fun tptp.maps_a_a ((-> tptp.a tptp.list_a) tptp.list_a) tptp.list_a)
% 0.25/0.64 (declare-fun tptp.measures_a (tptp.list_a_nat) tptp.set_Product_prod_a_a)
% 0.25/0.64 (declare-fun tptp.member_a_nat (tptp.list_a_nat (-> tptp.a tptp.nat)) Bool)
% 0.25/0.64 (declare-fun tptp.member261538120od_a_a (tptp.list_l1108175539od_a_a tptp.list_P1467822637od_a_a) Bool)
% 0.25/0.64 (declare-fun tptp.member2070313346od_a_a (tptp.list_P1891567085od_a_a tptp.produc1572603623od_a_a) Bool)
% 0.25/0.64 (declare-fun tptp.member1112491458od_a_a (tptp.list_P1467822637od_a_a tptp.product_prod_a_a) Bool)
% 0.25/0.64 (declare-fun tptp.member_a (tptp.list_a tptp.a) Bool)
% 0.25/0.64 (declare-fun tptp.subseq2115548028od_a_a (tptp.list_P1467822637od_a_a) tptp.list_l1108175539od_a_a)
% 0.25/0.64 (declare-fun tptp.zip_a_nat_a (tptp.list_a_nat tptp.list_a) tptp.list_P916011052_nat_a)
% 0.25/0.64 (declare-fun tptp.zip_li245157064_a_a_a (tptp.list_l1108175539od_a_a tptp.list_a) tptp.list_P305489470_a_a_a)
% 0.25/0.64 (declare-fun tptp.zip_list_a_list_a (tptp.list_list_a tptp.list_list_a) tptp.list_P601816365list_a)
% 0.25/0.64 (declare-fun tptp.zip_Pr24086287_a_nat (tptp.list_P1467822637od_a_a tptp.list_a_nat) tptp.list_P1435957893_a_nat)
% 0.25/0.64 (declare-fun tptp.zip_Pr792472183od_a_a (tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a) tptp.list_P1891567085od_a_a)
% 0.25/0.64 (declare-fun tptp.zip_Pr201224270_a_a_a (tptp.list_P1467822637od_a_a tptp.list_a) tptp.list_P319927492_a_a_a)
% 0.25/0.64 (declare-fun tptp.zip_a_a_nat (tptp.list_a tptp.list_a_nat) tptp.list_P576104046_a_nat)
% 0.25/0.64 (declare-fun tptp.zip_a_1969042406od_a_a (tptp.list_a tptp.list_l1108175539od_a_a) tptp.list_P1175580892od_a_a)
% 0.25/0.64 (declare-fun tptp.zip_a_1586372448od_a_a (tptp.list_a tptp.list_P1467822637od_a_a) tptp.list_P1458844246od_a_a)
% 0.25/0.64 (declare-fun tptp.zip_a_a (tptp.list_a tptp.list_a) tptp.list_P1467822637od_a_a)
% 0.25/0.64 (declare-fun tptp.size_s642698393od_a_a (tptp.list_P1467822637od_a_a) tptp.nat)
% 0.25/0.64 (declare-fun tptp.size_size_list_a (tptp.list_a) tptp.nat)
% 0.25/0.64 (declare-fun tptp.ord_less_nat (tptp.nat tptp.nat) Bool)
% 0.25/0.64 (declare-fun tptp.pair_co_path_a (tptp.product_prod_a_a tptp.a tptp.list_P1467822637od_a_a) tptp.list_P1467822637od_a_a)
% 0.25/0.64 (declare-fun tptp.pair_co_path_rel_a (tptp.produc821581462od_a_a tptp.produc821581462od_a_a) Bool)
% 0.25/0.64 (declare-fun tptp.pair_p2140537249od_a_a (tptp.product_prod_a_a tptp.list_P1891567085od_a_a) tptp.list_P1467822637od_a_a)
% 0.25/0.64 (declare-fun tptp.pair_sd_path_a (tptp.product_prod_a_a tptp.a tptp.list_P1467822637od_a_a) tptp.list_P1467822637od_a_a)
% 0.25/0.64 (declare-fun tptp.pair_sd_path_rel_a (tptp.produc821581462od_a_a tptp.produc821581462od_a_a) Bool)
% 0.25/0.64 (declare-fun tptp.invers1007791577list_a (tptp.list_P1467822637od_a_a tptp.a) tptp.a)
% 0.25/0.64 (declare-fun tptp.invers214109608_rel_a (tptp.produc657167928_a_a_a tptp.produc657167928_a_a_a) Bool)
% 0.25/0.64 (declare-fun tptp.list_permutes_a (tptp.list_P1467822637od_a_a tptp.set_a) Bool)
% 0.25/0.64 (declare-fun tptp.permut1422637723list_a (tptp.list_P1467822637od_a_a tptp.a) tptp.a)
% 0.25/0.64 (declare-fun tptp.produc214132118od_a_a ((-> tptp.product_prod_a_a tptp.product_prod_a_a Bool) tptp.list_P1467822637od_a_a) tptp.produc501911462od_a_a)
% 0.25/0.64 (declare-fun tptp.produc1569872215_a_nat ((-> tptp.a tptp.nat) (-> tptp.a tptp.nat)) tptp.produc1178641895_a_nat)
% 0.25/0.64 (declare-fun tptp.product_Pair_a_nat_a ((-> tptp.a tptp.nat) tptp.a) tptp.product_prod_a_nat_a)
% 0.25/0.64 (declare-fun tptp.produc1430747863_a_nat (tptp.list_a_nat tptp.list_a_nat) tptp.produc1334933863_a_nat)
% 0.25/0.64 (declare-fun tptp.produc915218007od_a_a (tptp.list_l1108175539od_a_a tptp.list_l1108175539od_a_a) tptp.produc657724903od_a_a)
% 0.25/0.64 (declare-fun tptp.produc2583831list_a (tptp.list_list_a tptp.list_list_a) tptp.produc403652391list_a)
% 0.25/0.64 (declare-fun tptp.produc461662679od_a_a (tptp.list_P1891567085od_a_a tptp.list_P1891567085od_a_a) tptp.produc205693799od_a_a)
% 0.25/0.64 (declare-fun tptp.produc85179863od_a_a (tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a) tptp.produc651658087od_a_a)
% 0.25/0.64 (declare-fun tptp.produc998622632_a_a_a (tptp.list_P1467822637od_a_a tptp.a) tptp.produc657167928_a_a_a)
% 0.25/0.64 (declare-fun tptp.produc1448356631list_a (tptp.list_a tptp.list_a) tptp.produc864062247list_a)
% 0.25/0.64 (declare-fun tptp.produc74075722_a_a_a (tptp.pair_p125712459t_unit tptp.produc1016684094_a_a_a) tptp.produc1912141786_a_a_a)
% 0.25/0.64 (declare-fun tptp.produc1935643479od_a_a (tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a) tptp.produc1990712039od_a_a)
% 0.25/0.64 (declare-fun tptp.produc825466863_a_nat (tptp.product_prod_a_a (-> tptp.a tptp.nat)) tptp.produc664688895_a_nat)
% 0.25/0.64 (declare-fun tptp.produc600870406od_a_a (tptp.product_prod_a_a tptp.produc1701253078od_a_a) tptp.produc821581462od_a_a)
% 0.25/0.64 (declare-fun tptp.produc1474507607od_a_a (tptp.product_prod_a_a tptp.product_prod_a_a) tptp.produc1572603623od_a_a)
% 0.25/0.64 (declare-fun tptp.produc2061588782_a_a_a (tptp.product_prod_a_a tptp.a) tptp.produc1016684094_a_a_a)
% 0.25/0.64 (declare-fun tptp.product_Pair_a_a_nat (tptp.a (-> tptp.a tptp.nat)) tptp.product_prod_a_a_nat)
% 0.25/0.64 (declare-fun tptp.produc575024326od_a_a (tptp.a tptp.list_P1467822637od_a_a) tptp.produc1701253078od_a_a)
% 0.25/0.64 (declare-fun tptp.produc1440321489_a_a_a (tptp.a tptp.produc657167928_a_a_a) tptp.produc1197928545_a_a_a)
% 0.25/0.64 (declare-fun tptp.produc1299253312od_a_a (tptp.a tptp.product_prod_a_a) tptp.produc1921647824od_a_a)
% 0.25/0.64 (declare-fun tptp.product_Pair_a_a (tptp.a tptp.a) tptp.product_prod_a_a)
% 0.25/0.64 (declare-fun tptp.asym_a (tptp.set_Product_prod_a_a) Bool)
% 0.25/0.64 (declare-fun tptp.irrefl76447196od_a_a (tptp.set_Pr1948701895od_a_a) Bool)
% 0.25/0.64 (declare-fun tptp.irrefl_a (tptp.set_Product_prod_a_a) Bool)
% 0.25/0.64 (declare-fun tptp.collec1811041560od_a_a ((-> tptp.list_P1467822637od_a_a Bool)) tptp.set_li562223245od_a_a)
% 0.25/0.64 (declare-fun tptp.collec1566074578od_a_a ((-> tptp.produc651658087od_a_a Bool)) tptp.set_Pr800560199od_a_a)
% 0.25/0.64 (declare-fun tptp.collec656258194list_a ((-> tptp.produc864062247list_a Bool)) tptp.set_Pr1971762695list_a)
% 0.25/0.64 (declare-fun tptp.collec645855634od_a_a ((-> tptp.product_prod_a_a Bool)) tptp.set_Product_prod_a_a)
% 0.25/0.64 (declare-fun tptp.collect_a ((-> tptp.a Bool)) tptp.set_a)
% 0.25/0.64 (declare-fun tptp.the_el1640649244od_a_a (tptp.set_Product_prod_a_a) tptp.product_prod_a_a)
% 0.25/0.64 (declare-fun tptp.accp_P941981633_a_a_a ((-> tptp.produc657167928_a_a_a tptp.produc657167928_a_a_a Bool) tptp.produc657167928_a_a_a) Bool)
% 0.25/0.64 (declare-fun tptp.accp_P1029463583od_a_a ((-> tptp.produc821581462od_a_a tptp.produc821581462od_a_a Bool) tptp.produc821581462od_a_a) Bool)
% 0.25/0.64 (declare-fun tptp.member1578987478od_a_a (tptp.list_P1467822637od_a_a tptp.set_li562223245od_a_a) Bool)
% 0.25/0.64 (declare-fun tptp.member372644687od_a_a (tptp.produc501911462od_a_a tptp.set_Pr727105414od_a_a) Bool)
% 0.25/0.64 (declare-fun tptp.member125757712_a_nat (tptp.produc1178641895_a_nat tptp.set_Pr1940702919_a_nat) Bool)
% 0.25/0.64 (declare-fun tptp.member688761744_a_nat (tptp.produc1334933863_a_nat tptp.set_Pr753687879_a_nat) Bool)
% 0.25/0.64 (declare-fun tptp.member8108048od_a_a (tptp.produc657724903od_a_a tptp.set_Pr1239640519od_a_a) Bool)
% 0.25/0.64 (declare-fun tptp.member888406864list_a (tptp.produc403652391list_a tptp.set_Pr1742859527list_a) Bool)
% 0.25/0.64 (declare-fun tptp.member1254757008od_a_a (tptp.produc205693799od_a_a tptp.set_Pr779272263od_a_a) Bool)
% 0.25/0.64 (declare-fun tptp.member1691432592od_a_a (tptp.produc651658087od_a_a tptp.set_Pr800560199od_a_a) Bool)
% 0.25/0.64 (declare-fun tptp.member430654177_a_a_a (tptp.produc657167928_a_a_a tptp.set_Pr1525541400_a_a_a) Bool)
% 0.25/0.64 (declare-fun tptp.member1250517072list_a (tptp.produc864062247list_a tptp.set_Pr1971762695list_a) Bool)
% 0.25/0.64 (declare-fun tptp.member1899387664od_a_a (tptp.produc1990712039od_a_a tptp.set_Pr1295299783od_a_a) Bool)
% 0.25/0.64 (declare-fun tptp.member2057358096od_a_a (tptp.produc1572603623od_a_a tptp.set_Pr1948701895od_a_a) Bool)
% 0.25/0.64 (declare-fun tptp.member1474739327od_a_a (tptp.produc1701253078od_a_a tptp.set_Pr248149174od_a_a) Bool)
% 0.25/0.64 (declare-fun tptp.member1904151562_a_a_a (tptp.produc1197928545_a_a_a tptp.set_Pr110478017_a_a_a) Bool)
% 0.25/0.64 (declare-fun tptp.member449909584od_a_a (tptp.product_prod_a_a tptp.set_Product_prod_a_a) Bool)
% 0.25/0.64 (declare-fun tptp.member_a2 (tptp.a tptp.set_a) Bool)
% 0.25/0.64 (declare-fun tptp.e () tptp.product_prod_a_a)
% 0.25/0.64 (declare-fun tptp.es () tptp.list_P1467822637od_a_a)
% 0.25/0.64 (assert (@ tptp.kurato1072996284sing_a (@ (@ tptp.cons_P1921020637od_a_a tptp.e) tptp.es)))
% 0.25/0.64 (assert (= tptp.kurato1404746725od_a_a (lambda ((P tptp.list_P1891567085od_a_a)) (forall ((Xs tptp.list_P1891567085od_a_a) (X tptp.product_prod_a_a) (Y tptp.product_prod_a_a) (Ys tptp.list_P1891567085od_a_a)) (not (= P (@ (@ tptp.append864718978od_a_a Xs) (@ (@ tptp.cons_P1070399645od_a_a (@ (@ tptp.produc1474507607od_a_a X) Y)) (@ (@ tptp.cons_P1070399645od_a_a (@ (@ tptp.produc1474507607od_a_a Y) X)) Ys)))))))))
% 0.25/0.64 (assert (= tptp.kurato292963650list_a (lambda ((P tptp.list_P601816365list_a)) (forall ((Xs tptp.list_P601816365list_a) (X tptp.list_a) (Y tptp.list_a) (Ys tptp.list_P601816365list_a)) (not (= P (@ (@ tptp.append750086082list_a Xs) (@ (@ tptp.cons_P2080942813list_a (@ (@ tptp.produc1448356631list_a X) Y)) (@ (@ tptp.cons_P2080942813list_a (@ (@ tptp.produc1448356631list_a Y) X)) Ys)))))))))
% 0.25/0.64 (assert (= tptp.kurato1072996284sing_a (lambda ((P tptp.list_P1467822637od_a_a)) (forall ((Xs tptp.list_P1467822637od_a_a) (X tptp.a) (Y tptp.a) (Ys tptp.list_P1467822637od_a_a)) (not (= P (@ (@ tptp.append1574001858od_a_a Xs) (@ (@ tptp.cons_P1921020637od_a_a (@ (@ tptp.product_Pair_a_a X) Y)) (@ (@ tptp.cons_P1921020637od_a_a (@ (@ tptp.product_Pair_a_a Y) X)) Ys)))))))))
% 0.25/0.64 (assert (forall ((A tptp.list_a) (B tptp.list_a) (C tptp.list_a)) (let ((_let_1 (@ tptp.append_a A))) (= (@ (@ tptp.append_a (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.append_a B) C))))))
% 0.25/0.64 (assert (forall ((A tptp.list_P1891567085od_a_a) (B tptp.list_P1891567085od_a_a) (C tptp.list_P1891567085od_a_a)) (let ((_let_1 (@ tptp.append864718978od_a_a A))) (= (@ (@ tptp.append864718978od_a_a (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.append864718978od_a_a B) C))))))
% 0.25/0.64 (assert (forall ((A tptp.list_l1108175539od_a_a) (B tptp.list_l1108175539od_a_a) (C tptp.list_l1108175539od_a_a)) (let ((_let_1 (@ tptp.append2141280328od_a_a A))) (= (@ (@ tptp.append2141280328od_a_a (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.append2141280328od_a_a B) C))))))
% 0.25/0.64 (assert (forall ((A tptp.list_P1467822637od_a_a) (B tptp.list_P1467822637od_a_a) (C tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ tptp.append1574001858od_a_a A))) (= (@ (@ tptp.append1574001858od_a_a (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.append1574001858od_a_a B) C))))))
% 0.25/0.64 (assert (forall ((Xs2 tptp.list_a) (Ys2 tptp.list_a) (Zs tptp.list_a)) (let ((_let_1 (@ tptp.append_a Xs2))) (= (@ (@ tptp.append_a (@ _let_1 Ys2)) Zs) (@ _let_1 (@ (@ tptp.append_a Ys2) Zs))))))
% 0.25/0.64 (assert (forall ((Xs2 tptp.list_P1891567085od_a_a) (Ys2 tptp.list_P1891567085od_a_a) (Zs tptp.list_P1891567085od_a_a)) (let ((_let_1 (@ tptp.append864718978od_a_a Xs2))) (= (@ (@ tptp.append864718978od_a_a (@ _let_1 Ys2)) Zs) (@ _let_1 (@ (@ tptp.append864718978od_a_a Ys2) Zs))))))
% 0.25/0.64 (assert (forall ((Xs2 tptp.list_l1108175539od_a_a) (Ys2 tptp.list_l1108175539od_a_a) (Zs tptp.list_l1108175539od_a_a)) (let ((_let_1 (@ tptp.append2141280328od_a_a Xs2))) (= (@ (@ tptp.append2141280328od_a_a (@ _let_1 Ys2)) Zs) (@ _let_1 (@ (@ tptp.append2141280328od_a_a Ys2) Zs))))))
% 0.25/0.64 (assert (forall ((Xs2 tptp.list_P1467822637od_a_a) (Ys2 tptp.list_P1467822637od_a_a) (Zs tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ tptp.append1574001858od_a_a Xs2))) (= (@ (@ tptp.append1574001858od_a_a (@ _let_1 Ys2)) Zs) (@ _let_1 (@ (@ tptp.append1574001858od_a_a Ys2) Zs))))))
% 0.25/0.64 (assert (forall ((Ys2 tptp.list_a) (Xs2 tptp.list_a) (Zs tptp.list_a)) (= (= (@ (@ tptp.append_a Ys2) Xs2) (@ (@ tptp.append_a Zs) Xs2)) (= Ys2 Zs))))
% 0.25/0.64 (assert (forall ((Ys2 tptp.list_P1891567085od_a_a) (Xs2 tptp.list_P1891567085od_a_a) (Zs tptp.list_P1891567085od_a_a)) (= (= (@ (@ tptp.append864718978od_a_a Ys2) Xs2) (@ (@ tptp.append864718978od_a_a Zs) Xs2)) (= Ys2 Zs))))
% 0.25/0.64 (assert (forall ((Ys2 tptp.list_l1108175539od_a_a) (Xs2 tptp.list_l1108175539od_a_a) (Zs tptp.list_l1108175539od_a_a)) (= (= (@ (@ tptp.append2141280328od_a_a Ys2) Xs2) (@ (@ tptp.append2141280328od_a_a Zs) Xs2)) (= Ys2 Zs))))
% 0.25/0.64 (assert (forall ((Ys2 tptp.list_P1467822637od_a_a) (Xs2 tptp.list_P1467822637od_a_a) (Zs tptp.list_P1467822637od_a_a)) (= (= (@ (@ tptp.append1574001858od_a_a Ys2) Xs2) (@ (@ tptp.append1574001858od_a_a Zs) Xs2)) (= Ys2 Zs))))
% 0.25/0.64 (assert (forall ((Xs2 tptp.list_a) (Ys2 tptp.list_a) (Zs tptp.list_a)) (let ((_let_1 (@ tptp.append_a Xs2))) (= (= (@ _let_1 Ys2) (@ _let_1 Zs)) (= Ys2 Zs)))))
% 0.25/0.64 (assert (forall ((Xs2 tptp.list_P1891567085od_a_a) (Ys2 tptp.list_P1891567085od_a_a) (Zs tptp.list_P1891567085od_a_a)) (let ((_let_1 (@ tptp.append864718978od_a_a Xs2))) (= (= (@ _let_1 Ys2) (@ _let_1 Zs)) (= Ys2 Zs)))))
% 0.25/0.64 (assert (forall ((Xs2 tptp.list_l1108175539od_a_a) (Ys2 tptp.list_l1108175539od_a_a) (Zs tptp.list_l1108175539od_a_a)) (let ((_let_1 (@ tptp.append2141280328od_a_a Xs2))) (= (= (@ _let_1 Ys2) (@ _let_1 Zs)) (= Ys2 Zs)))))
% 0.25/0.64 (assert (forall ((Xs2 tptp.list_P1467822637od_a_a) (Ys2 tptp.list_P1467822637od_a_a) (Zs tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ tptp.append1574001858od_a_a Xs2))) (= (= (@ _let_1 Ys2) (@ _let_1 Zs)) (= Ys2 Zs)))))
% 0.25/0.64 (assert (forall ((X21 tptp.a) (X22 tptp.list_a) (Y21 tptp.a) (Y22 tptp.list_a)) (= (= (@ (@ tptp.cons_a X21) X22) (@ (@ tptp.cons_a Y21) Y22)) (and (= X21 Y21) (= X22 Y22)))))
% 0.25/0.64 (assert (forall ((X21 tptp.produc1572603623od_a_a) (X22 tptp.list_P1891567085od_a_a) (Y21 tptp.produc1572603623od_a_a) (Y22 tptp.list_P1891567085od_a_a)) (= (= (@ (@ tptp.cons_P1070399645od_a_a X21) X22) (@ (@ tptp.cons_P1070399645od_a_a Y21) Y22)) (and (= X21 Y21) (= X22 Y22)))))
% 0.25/0.64 (assert (forall ((X21 tptp.list_P1467822637od_a_a) (X22 tptp.list_l1108175539od_a_a) (Y21 tptp.list_P1467822637od_a_a) (Y22 tptp.list_l1108175539od_a_a)) (= (= (@ (@ tptp.cons_l724116707od_a_a X21) X22) (@ (@ tptp.cons_l724116707od_a_a Y21) Y22)) (and (= X21 Y21) (= X22 Y22)))))
% 0.25/0.64 (assert (forall ((X21 (-> tptp.a tptp.nat)) (X22 tptp.list_a_nat) (Y21 (-> tptp.a tptp.nat)) (Y22 tptp.list_a_nat)) (= (= (@ (@ tptp.cons_a_nat X21) X22) (@ (@ tptp.cons_a_nat Y21) Y22)) (and (= X21 Y21) (= X22 Y22)))))
% 0.25/0.64 (assert (forall ((X21 tptp.product_prod_a_a) (X22 tptp.list_P1467822637od_a_a) (Y21 tptp.product_prod_a_a) (Y22 tptp.list_P1467822637od_a_a)) (= (= (@ (@ tptp.cons_P1921020637od_a_a X21) X22) (@ (@ tptp.cons_P1921020637od_a_a Y21) Y22)) (and (= X21 Y21) (= X22 Y22)))))
% 0.25/0.64 (assert (forall ((X1 tptp.list_P1467822637od_a_a) (X2 tptp.a) (Y1 tptp.list_P1467822637od_a_a) (Y2 tptp.a)) (= (= (@ (@ tptp.produc998622632_a_a_a X1) X2) (@ (@ tptp.produc998622632_a_a_a Y1) Y2)) (and (= X1 Y1) (= X2 Y2)))))
% 0.25/0.64 (assert (forall ((X1 tptp.list_a) (X2 tptp.list_a) (Y1 tptp.list_a) (Y2 tptp.list_a)) (= (= (@ (@ tptp.produc1448356631list_a X1) X2) (@ (@ tptp.produc1448356631list_a Y1) Y2)) (and (= X1 Y1) (= X2 Y2)))))
% 0.25/0.64 (assert (forall ((X1 (-> tptp.product_prod_a_a tptp.product_prod_a_a Bool)) (X2 tptp.list_P1467822637od_a_a) (Y1 (-> tptp.product_prod_a_a tptp.product_prod_a_a Bool)) (Y2 tptp.list_P1467822637od_a_a)) (= (= (@ (@ tptp.produc214132118od_a_a X1) X2) (@ (@ tptp.produc214132118od_a_a Y1) Y2)) (and (= X1 Y1) (= X2 Y2)))))
% 0.25/0.64 (assert (forall ((X1 tptp.a) (X2 tptp.produc657167928_a_a_a) (Y1 tptp.a) (Y2 tptp.produc657167928_a_a_a)) (= (= (@ (@ tptp.produc1440321489_a_a_a X1) X2) (@ (@ tptp.produc1440321489_a_a_a Y1) Y2)) (and (= X1 Y1) (= X2 Y2)))))
% 0.25/0.64 (assert (forall ((X1 tptp.a) (X2 tptp.list_P1467822637od_a_a) (Y1 tptp.a) (Y2 tptp.list_P1467822637od_a_a)) (= (= (@ (@ tptp.produc575024326od_a_a X1) X2) (@ (@ tptp.produc575024326od_a_a Y1) Y2)) (and (= X1 Y1) (= X2 Y2)))))
% 0.25/0.64 (assert (forall ((X1 tptp.a) (X2 tptp.a) (Y1 tptp.a) (Y2 tptp.a)) (= (= (@ (@ tptp.product_Pair_a_a X1) X2) (@ (@ tptp.product_Pair_a_a Y1) Y2)) (and (= X1 Y1) (= X2 Y2)))))
% 0.25/0.64 (assert (forall ((A tptp.list_P1467822637od_a_a) (B tptp.a) (A2 tptp.list_P1467822637od_a_a) (B2 tptp.a)) (= (= (@ (@ tptp.produc998622632_a_a_a A) B) (@ (@ tptp.produc998622632_a_a_a A2) B2)) (and (= A A2) (= B B2)))))
% 0.25/0.64 (assert (forall ((A tptp.list_a) (B tptp.list_a) (A2 tptp.list_a) (B2 tptp.list_a)) (= (= (@ (@ tptp.produc1448356631list_a A) B) (@ (@ tptp.produc1448356631list_a A2) B2)) (and (= A A2) (= B B2)))))
% 0.25/0.64 (assert (forall ((A (-> tptp.product_prod_a_a tptp.product_prod_a_a Bool)) (B tptp.list_P1467822637od_a_a) (A2 (-> tptp.product_prod_a_a tptp.product_prod_a_a Bool)) (B2 tptp.list_P1467822637od_a_a)) (= (= (@ (@ tptp.produc214132118od_a_a A) B) (@ (@ tptp.produc214132118od_a_a A2) B2)) (and (= A A2) (= B B2)))))
% 0.25/0.64 (assert (forall ((A tptp.a) (B tptp.produc657167928_a_a_a) (A2 tptp.a) (B2 tptp.produc657167928_a_a_a)) (= (= (@ (@ tptp.produc1440321489_a_a_a A) B) (@ (@ tptp.produc1440321489_a_a_a A2) B2)) (and (= A A2) (= B B2)))))
% 0.25/0.64 (assert (forall ((A tptp.a) (B tptp.list_P1467822637od_a_a) (A2 tptp.a) (B2 tptp.list_P1467822637od_a_a)) (= (= (@ (@ tptp.produc575024326od_a_a A) B) (@ (@ tptp.produc575024326od_a_a A2) B2)) (and (= A A2) (= B B2)))))
% 0.25/0.64 (assert (forall ((A tptp.a) (B tptp.a) (A2 tptp.a) (B2 tptp.a)) (= (= (@ (@ tptp.product_Pair_a_a A) B) (@ (@ tptp.product_Pair_a_a A2) B2)) (and (= A A2) (= B B2)))))
% 0.25/0.64 (assert (forall ((X3 tptp.a) (Xs1 tptp.list_a) (Ys2 tptp.list_a) (Xs2 tptp.list_a) (Zs tptp.list_a)) (let ((_let_1 (@ tptp.cons_a X3))) (=> (= (@ _let_1 Xs1) Ys2) (=> (= Xs2 (@ (@ tptp.append_a Xs1) Zs)) (= (@ _let_1 Xs2) (@ (@ tptp.append_a Ys2) Zs)))))))
% 0.25/0.64 (assert (forall ((X3 tptp.produc1572603623od_a_a) (Xs1 tptp.list_P1891567085od_a_a) (Ys2 tptp.list_P1891567085od_a_a) (Xs2 tptp.list_P1891567085od_a_a) (Zs tptp.list_P1891567085od_a_a)) (let ((_let_1 (@ tptp.cons_P1070399645od_a_a X3))) (=> (= (@ _let_1 Xs1) Ys2) (=> (= Xs2 (@ (@ tptp.append864718978od_a_a Xs1) Zs)) (= (@ _let_1 Xs2) (@ (@ tptp.append864718978od_a_a Ys2) Zs)))))))
% 0.25/0.64 (assert (forall ((X3 tptp.list_P1467822637od_a_a) (Xs1 tptp.list_l1108175539od_a_a) (Ys2 tptp.list_l1108175539od_a_a) (Xs2 tptp.list_l1108175539od_a_a) (Zs tptp.list_l1108175539od_a_a)) (let ((_let_1 (@ tptp.cons_l724116707od_a_a X3))) (=> (= (@ _let_1 Xs1) Ys2) (=> (= Xs2 (@ (@ tptp.append2141280328od_a_a Xs1) Zs)) (= (@ _let_1 Xs2) (@ (@ tptp.append2141280328od_a_a Ys2) Zs)))))))
% 0.25/0.64 (assert (forall ((X3 (-> tptp.a tptp.nat)) (Xs1 tptp.list_a_nat) (Ys2 tptp.list_a_nat) (Xs2 tptp.list_a_nat) (Zs tptp.list_a_nat)) (let ((_let_1 (@ tptp.cons_a_nat X3))) (=> (= (@ _let_1 Xs1) Ys2) (=> (= Xs2 (@ (@ tptp.append_a_nat Xs1) Zs)) (= (@ _let_1 Xs2) (@ (@ tptp.append_a_nat Ys2) Zs)))))))
% 0.25/0.64 (assert (forall ((X3 tptp.product_prod_a_a) (Xs1 tptp.list_P1467822637od_a_a) (Ys2 tptp.list_P1467822637od_a_a) (Xs2 tptp.list_P1467822637od_a_a) (Zs tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ tptp.cons_P1921020637od_a_a X3))) (=> (= (@ _let_1 Xs1) Ys2) (=> (= Xs2 (@ (@ tptp.append1574001858od_a_a Xs1) Zs)) (= (@ _let_1 Xs2) (@ (@ tptp.append1574001858od_a_a Ys2) Zs)))))))
% 0.25/0.64 (assert (forall ((X3 tptp.a) (Xs2 tptp.list_a) (Ys2 tptp.list_a)) (let ((_let_1 (@ tptp.cons_a X3))) (= (@ (@ tptp.append_a (@ _let_1 Xs2)) Ys2) (@ _let_1 (@ (@ tptp.append_a Xs2) Ys2))))))
% 0.25/0.64 (assert (forall ((X3 tptp.produc1572603623od_a_a) (Xs2 tptp.list_P1891567085od_a_a) (Ys2 tptp.list_P1891567085od_a_a)) (let ((_let_1 (@ tptp.cons_P1070399645od_a_a X3))) (= (@ (@ tptp.append864718978od_a_a (@ _let_1 Xs2)) Ys2) (@ _let_1 (@ (@ tptp.append864718978od_a_a Xs2) Ys2))))))
% 0.25/0.64 (assert (forall ((X3 tptp.list_P1467822637od_a_a) (Xs2 tptp.list_l1108175539od_a_a) (Ys2 tptp.list_l1108175539od_a_a)) (let ((_let_1 (@ tptp.cons_l724116707od_a_a X3))) (= (@ (@ tptp.append2141280328od_a_a (@ _let_1 Xs2)) Ys2) (@ _let_1 (@ (@ tptp.append2141280328od_a_a Xs2) Ys2))))))
% 0.25/0.64 (assert (forall ((X3 (-> tptp.a tptp.nat)) (Xs2 tptp.list_a_nat) (Ys2 tptp.list_a_nat)) (let ((_let_1 (@ tptp.cons_a_nat X3))) (= (@ (@ tptp.append_a_nat (@ _let_1 Xs2)) Ys2) (@ _let_1 (@ (@ tptp.append_a_nat Xs2) Ys2))))))
% 0.25/0.64 (assert (forall ((X3 tptp.product_prod_a_a) (Xs2 tptp.list_P1467822637od_a_a) (Ys2 tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ tptp.cons_P1921020637od_a_a X3))) (= (@ (@ tptp.append1574001858od_a_a (@ _let_1 Xs2)) Ys2) (@ _let_1 (@ (@ tptp.append1574001858od_a_a Xs2) Ys2))))))
% 0.25/0.64 (assert (forall ((Xs2 tptp.list_a) (Xs1 tptp.list_a) (Zs tptp.list_a) (Ys2 tptp.list_a) (Us tptp.list_a)) (let ((_let_1 (@ tptp.append_a Xs2))) (=> (= (@ _let_1 Xs1) Zs) (=> (= Ys2 (@ (@ tptp.append_a Xs1) Us)) (= (@ _let_1 Ys2) (@ (@ tptp.append_a Zs) Us)))))))
% 0.25/0.64 (assert (forall ((Xs2 tptp.list_P1891567085od_a_a) (Xs1 tptp.list_P1891567085od_a_a) (Zs tptp.list_P1891567085od_a_a) (Ys2 tptp.list_P1891567085od_a_a) (Us tptp.list_P1891567085od_a_a)) (let ((_let_1 (@ tptp.append864718978od_a_a Xs2))) (=> (= (@ _let_1 Xs1) Zs) (=> (= Ys2 (@ (@ tptp.append864718978od_a_a Xs1) Us)) (= (@ _let_1 Ys2) (@ (@ tptp.append864718978od_a_a Zs) Us)))))))
% 0.25/0.64 (assert (forall ((Xs2 tptp.list_l1108175539od_a_a) (Xs1 tptp.list_l1108175539od_a_a) (Zs tptp.list_l1108175539od_a_a) (Ys2 tptp.list_l1108175539od_a_a) (Us tptp.list_l1108175539od_a_a)) (let ((_let_1 (@ tptp.append2141280328od_a_a Xs2))) (=> (= (@ _let_1 Xs1) Zs) (=> (= Ys2 (@ (@ tptp.append2141280328od_a_a Xs1) Us)) (= (@ _let_1 Ys2) (@ (@ tptp.append2141280328od_a_a Zs) Us)))))))
% 0.25/0.64 (assert (forall ((Xs2 tptp.list_P1467822637od_a_a) (Xs1 tptp.list_P1467822637od_a_a) (Zs tptp.list_P1467822637od_a_a) (Ys2 tptp.list_P1467822637od_a_a) (Us tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ tptp.append1574001858od_a_a Xs2))) (=> (= (@ _let_1 Xs1) Zs) (=> (= Ys2 (@ (@ tptp.append1574001858od_a_a Xs1) Us)) (= (@ _let_1 Ys2) (@ (@ tptp.append1574001858od_a_a Zs) Us)))))))
% 0.25/0.64 (assert (forall ((Xs2 tptp.list_a) (Ys2 tptp.list_a) (Zs tptp.list_a) (Ts tptp.list_a)) (= (= (@ (@ tptp.append_a Xs2) Ys2) (@ (@ tptp.append_a Zs) Ts)) (exists ((Us2 tptp.list_a)) (let ((_let_1 (@ tptp.append_a Us2))) (or (and (= Xs2 (@ (@ tptp.append_a Zs) Us2)) (= (@ _let_1 Ys2) Ts)) (and (= (@ (@ tptp.append_a Xs2) Us2) Zs) (= Ys2 (@ _let_1 Ts)))))))))
% 0.25/0.64 (assert (forall ((Xs2 tptp.list_P1891567085od_a_a) (Ys2 tptp.list_P1891567085od_a_a) (Zs tptp.list_P1891567085od_a_a) (Ts tptp.list_P1891567085od_a_a)) (= (= (@ (@ tptp.append864718978od_a_a Xs2) Ys2) (@ (@ tptp.append864718978od_a_a Zs) Ts)) (exists ((Us2 tptp.list_P1891567085od_a_a)) (let ((_let_1 (@ tptp.append864718978od_a_a Us2))) (or (and (= Xs2 (@ (@ tptp.append864718978od_a_a Zs) Us2)) (= (@ _let_1 Ys2) Ts)) (and (= (@ (@ tptp.append864718978od_a_a Xs2) Us2) Zs) (= Ys2 (@ _let_1 Ts)))))))))
% 0.25/0.64 (assert (forall ((Xs2 tptp.list_l1108175539od_a_a) (Ys2 tptp.list_l1108175539od_a_a) (Zs tptp.list_l1108175539od_a_a) (Ts tptp.list_l1108175539od_a_a)) (= (= (@ (@ tptp.append2141280328od_a_a Xs2) Ys2) (@ (@ tptp.append2141280328od_a_a Zs) Ts)) (exists ((Us2 tptp.list_l1108175539od_a_a)) (let ((_let_1 (@ tptp.append2141280328od_a_a Us2))) (or (and (= Xs2 (@ (@ tptp.append2141280328od_a_a Zs) Us2)) (= (@ _let_1 Ys2) Ts)) (and (= (@ (@ tptp.append2141280328od_a_a Xs2) Us2) Zs) (= Ys2 (@ _let_1 Ts)))))))))
% 0.25/0.64 (assert (forall ((Xs2 tptp.list_P1467822637od_a_a) (Ys2 tptp.list_P1467822637od_a_a) (Zs tptp.list_P1467822637od_a_a) (Ts tptp.list_P1467822637od_a_a)) (= (= (@ (@ tptp.append1574001858od_a_a Xs2) Ys2) (@ (@ tptp.append1574001858od_a_a Zs) Ts)) (exists ((Us2 tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ tptp.append1574001858od_a_a Us2))) (or (and (= Xs2 (@ (@ tptp.append1574001858od_a_a Zs) Us2)) (= (@ _let_1 Ys2) Ts)) (and (= (@ (@ tptp.append1574001858od_a_a Xs2) Us2) Zs) (= Ys2 (@ _let_1 Ts)))))))))
% 0.25/0.64 (assert (forall ((P2 (-> tptp.produc657167928_a_a_a Bool)) (Prod tptp.produc657167928_a_a_a)) (=> (forall ((A3 tptp.list_P1467822637od_a_a) (B3 tptp.a)) (@ P2 (@ (@ tptp.produc998622632_a_a_a A3) B3))) (@ P2 Prod))))
% 0.25/0.64 (assert (forall ((P2 (-> tptp.produc864062247list_a Bool)) (Prod tptp.produc864062247list_a)) (=> (forall ((A3 tptp.list_a) (B3 tptp.list_a)) (@ P2 (@ (@ tptp.produc1448356631list_a A3) B3))) (@ P2 Prod))))
% 0.25/0.64 (assert (forall ((P2 (-> tptp.produc501911462od_a_a Bool)) (Prod tptp.produc501911462od_a_a)) (=> (forall ((A3 (-> tptp.product_prod_a_a tptp.product_prod_a_a Bool)) (B3 tptp.list_P1467822637od_a_a)) (@ P2 (@ (@ tptp.produc214132118od_a_a A3) B3))) (@ P2 Prod))))
% 0.25/0.64 (assert (forall ((P2 (-> tptp.produc1197928545_a_a_a Bool)) (Prod tptp.produc1197928545_a_a_a)) (=> (forall ((A3 tptp.a) (B3 tptp.produc657167928_a_a_a)) (@ P2 (@ (@ tptp.produc1440321489_a_a_a A3) B3))) (@ P2 Prod))))
% 0.25/0.64 (assert (forall ((P2 (-> tptp.produc1701253078od_a_a Bool)) (Prod tptp.produc1701253078od_a_a)) (=> (forall ((A3 tptp.a) (B3 tptp.list_P1467822637od_a_a)) (@ P2 (@ (@ tptp.produc575024326od_a_a A3) B3))) (@ P2 Prod))))
% 0.25/0.64 (assert (forall ((P2 (-> tptp.product_prod_a_a Bool)) (Prod tptp.product_prod_a_a)) (=> (forall ((A3 tptp.a) (B3 tptp.a)) (@ P2 (@ (@ tptp.product_Pair_a_a A3) B3))) (@ P2 Prod))))
% 0.25/0.64 (assert (forall ((Y3 tptp.produc657167928_a_a_a)) (not (forall ((A3 tptp.list_P1467822637od_a_a) (B3 tptp.a)) (not (= Y3 (@ (@ tptp.produc998622632_a_a_a A3) B3)))))))
% 0.25/0.64 (assert (forall ((Y3 tptp.produc864062247list_a)) (not (forall ((A3 tptp.list_a) (B3 tptp.list_a)) (not (= Y3 (@ (@ tptp.produc1448356631list_a A3) B3)))))))
% 0.25/0.64 (assert (forall ((Y3 tptp.produc501911462od_a_a)) (not (forall ((A3 (-> tptp.product_prod_a_a tptp.product_prod_a_a Bool)) (B3 tptp.list_P1467822637od_a_a)) (not (= Y3 (@ (@ tptp.produc214132118od_a_a A3) B3)))))))
% 0.25/0.64 (assert (forall ((Y3 tptp.produc1197928545_a_a_a)) (not (forall ((A3 tptp.a) (B3 tptp.produc657167928_a_a_a)) (not (= Y3 (@ (@ tptp.produc1440321489_a_a_a A3) B3)))))))
% 0.25/0.64 (assert (forall ((Y3 tptp.produc1701253078od_a_a)) (not (forall ((A3 tptp.a) (B3 tptp.list_P1467822637od_a_a)) (not (= Y3 (@ (@ tptp.produc575024326od_a_a A3) B3)))))))
% 0.25/0.64 (assert (forall ((Y3 tptp.product_prod_a_a)) (not (forall ((A3 tptp.a) (B3 tptp.a)) (not (= Y3 (@ (@ tptp.product_Pair_a_a A3) B3)))))))
% 0.25/0.64 (assert (forall ((P2 (-> tptp.produc1197928545_a_a_a Bool)) (X3 tptp.produc1197928545_a_a_a)) (=> (forall ((A3 tptp.a) (B3 tptp.list_P1467822637od_a_a) (C2 tptp.a)) (@ P2 (@ (@ tptp.produc1440321489_a_a_a A3) (@ (@ tptp.produc998622632_a_a_a B3) C2)))) (@ P2 X3))))
% 0.25/0.64 (assert (forall ((Y3 tptp.produc1197928545_a_a_a)) (not (forall ((A3 tptp.a) (B3 tptp.list_P1467822637od_a_a) (C2 tptp.a)) (not (= Y3 (@ (@ tptp.produc1440321489_a_a_a A3) (@ (@ tptp.produc998622632_a_a_a B3) C2))))))))
% 0.25/0.64 (assert (forall ((A tptp.list_P1467822637od_a_a) (B tptp.a) (A2 tptp.list_P1467822637od_a_a) (B2 tptp.a)) (=> (= (@ (@ tptp.produc998622632_a_a_a A) B) (@ (@ tptp.produc998622632_a_a_a A2) B2)) (not (=> (= A A2) (not (= B B2)))))))
% 0.25/0.64 (assert (forall ((A tptp.list_a) (B tptp.list_a) (A2 tptp.list_a) (B2 tptp.list_a)) (=> (= (@ (@ tptp.produc1448356631list_a A) B) (@ (@ tptp.produc1448356631list_a A2) B2)) (not (=> (= A A2) (not (= B B2)))))))
% 0.25/0.64 (assert (forall ((A (-> tptp.product_prod_a_a tptp.product_prod_a_a Bool)) (B tptp.list_P1467822637od_a_a) (A2 (-> tptp.product_prod_a_a tptp.product_prod_a_a Bool)) (B2 tptp.list_P1467822637od_a_a)) (=> (= (@ (@ tptp.produc214132118od_a_a A) B) (@ (@ tptp.produc214132118od_a_a A2) B2)) (not (=> (= A A2) (not (= B B2)))))))
% 0.25/0.64 (assert (forall ((A tptp.a) (B tptp.produc657167928_a_a_a) (A2 tptp.a) (B2 tptp.produc657167928_a_a_a)) (=> (= (@ (@ tptp.produc1440321489_a_a_a A) B) (@ (@ tptp.produc1440321489_a_a_a A2) B2)) (not (=> (= A A2) (not (= B B2)))))))
% 0.25/0.64 (assert (forall ((A tptp.a) (B tptp.list_P1467822637od_a_a) (A2 tptp.a) (B2 tptp.list_P1467822637od_a_a)) (=> (= (@ (@ tptp.produc575024326od_a_a A) B) (@ (@ tptp.produc575024326od_a_a A2) B2)) (not (=> (= A A2) (not (= B B2)))))))
% 0.25/0.64 (assert (forall ((A tptp.a) (B tptp.a) (A2 tptp.a) (B2 tptp.a)) (=> (= (@ (@ tptp.product_Pair_a_a A) B) (@ (@ tptp.product_Pair_a_a A2) B2)) (not (=> (= A A2) (not (= B B2)))))))
% 0.25/0.64 (assert (forall ((P2 (-> tptp.produc657167928_a_a_a Bool)) (P3 tptp.produc657167928_a_a_a)) (=> (forall ((A3 tptp.list_P1467822637od_a_a) (B3 tptp.a)) (@ P2 (@ (@ tptp.produc998622632_a_a_a A3) B3))) (@ P2 P3))))
% 0.25/0.64 (assert (forall ((P2 (-> tptp.produc864062247list_a Bool)) (P3 tptp.produc864062247list_a)) (=> (forall ((A3 tptp.list_a) (B3 tptp.list_a)) (@ P2 (@ (@ tptp.produc1448356631list_a A3) B3))) (@ P2 P3))))
% 0.25/0.64 (assert (forall ((P2 (-> tptp.produc501911462od_a_a Bool)) (P3 tptp.produc501911462od_a_a)) (=> (forall ((A3 (-> tptp.product_prod_a_a tptp.product_prod_a_a Bool)) (B3 tptp.list_P1467822637od_a_a)) (@ P2 (@ (@ tptp.produc214132118od_a_a A3) B3))) (@ P2 P3))))
% 0.25/0.64 (assert (forall ((P2 (-> tptp.produc1197928545_a_a_a Bool)) (P3 tptp.produc1197928545_a_a_a)) (=> (forall ((A3 tptp.a) (B3 tptp.produc657167928_a_a_a)) (@ P2 (@ (@ tptp.produc1440321489_a_a_a A3) B3))) (@ P2 P3))))
% 0.25/0.64 (assert (forall ((P2 (-> tptp.produc1701253078od_a_a Bool)) (P3 tptp.produc1701253078od_a_a)) (=> (forall ((A3 tptp.a) (B3 tptp.list_P1467822637od_a_a)) (@ P2 (@ (@ tptp.produc575024326od_a_a A3) B3))) (@ P2 P3))))
% 0.25/0.64 (assert (forall ((P2 (-> tptp.product_prod_a_a Bool)) (P3 tptp.product_prod_a_a)) (=> (forall ((A3 tptp.a) (B3 tptp.a)) (@ P2 (@ (@ tptp.product_Pair_a_a A3) B3))) (@ P2 P3))))
% 0.25/0.64 (assert (forall ((P3 tptp.produc657167928_a_a_a)) (exists ((X4 tptp.list_P1467822637od_a_a) (Y4 tptp.a)) (= P3 (@ (@ tptp.produc998622632_a_a_a X4) Y4)))))
% 0.25/0.64 (assert (forall ((P3 tptp.produc864062247list_a)) (exists ((X4 tptp.list_a) (Y4 tptp.list_a)) (= P3 (@ (@ tptp.produc1448356631list_a X4) Y4)))))
% 0.25/0.64 (assert (forall ((P3 tptp.produc501911462od_a_a)) (exists ((X4 (-> tptp.product_prod_a_a tptp.product_prod_a_a Bool)) (Y4 tptp.list_P1467822637od_a_a)) (= P3 (@ (@ tptp.produc214132118od_a_a X4) Y4)))))
% 0.25/0.64 (assert (forall ((P3 tptp.produc1197928545_a_a_a)) (exists ((X4 tptp.a) (Y4 tptp.produc657167928_a_a_a)) (= P3 (@ (@ tptp.produc1440321489_a_a_a X4) Y4)))))
% 0.25/0.64 (assert (forall ((P3 tptp.produc1701253078od_a_a)) (exists ((X4 tptp.a) (Y4 tptp.list_P1467822637od_a_a)) (= P3 (@ (@ tptp.produc575024326od_a_a X4) Y4)))))
% 0.25/0.64 (assert (forall ((P3 tptp.product_prod_a_a)) (exists ((X4 tptp.a) (Y4 tptp.a)) (= P3 (@ (@ tptp.product_Pair_a_a X4) Y4)))))
% 0.25/0.64 (assert (forall ((X3 tptp.a) (Xs2 tptp.list_a)) (not (= (@ (@ tptp.cons_a X3) Xs2) Xs2))))
% 0.25/0.64 (assert (forall ((X3 tptp.produc1572603623od_a_a) (Xs2 tptp.list_P1891567085od_a_a)) (not (= (@ (@ tptp.cons_P1070399645od_a_a X3) Xs2) Xs2))))
% 0.25/0.64 (assert (forall ((X3 tptp.list_P1467822637od_a_a) (Xs2 tptp.list_l1108175539od_a_a)) (not (= (@ (@ tptp.cons_l724116707od_a_a X3) Xs2) Xs2))))
% 0.25/0.64 (assert (forall ((X3 (-> tptp.a tptp.nat)) (Xs2 tptp.list_a_nat)) (not (= (@ (@ tptp.cons_a_nat X3) Xs2) Xs2))))
% 0.25/0.64 (assert (forall ((X3 tptp.product_prod_a_a) (Xs2 tptp.list_P1467822637od_a_a)) (not (= (@ (@ tptp.cons_P1921020637od_a_a X3) Xs2) Xs2))))
% 0.25/0.64 (assert (forall ((X3 tptp.product_prod_a_a) (Xs2 tptp.list_P1467822637od_a_a) (F (-> tptp.product_prod_a_a tptp.list_P1467822637od_a_a))) (= (@ (@ tptp.bind_P1783625031od_a_a (@ (@ tptp.cons_P1921020637od_a_a X3) Xs2)) F) (@ (@ tptp.append1574001858od_a_a (@ F X3)) (@ (@ tptp.bind_P1783625031od_a_a Xs2) F)))))
% 0.25/0.64 (assert (forall ((X3 tptp.a) (Xs2 tptp.list_a) (F (-> tptp.a tptp.list_a))) (= (@ (@ tptp.bind_a_a (@ (@ tptp.cons_a X3) Xs2)) F) (@ (@ tptp.append_a (@ F X3)) (@ (@ tptp.bind_a_a Xs2) F)))))
% 0.25/0.64 (assert (forall ((X3 tptp.product_prod_a_a) (Xs2 tptp.list_P1467822637od_a_a) (F (-> tptp.product_prod_a_a tptp.list_a))) (= (@ (@ tptp.bind_P293964574_a_a_a (@ (@ tptp.cons_P1921020637od_a_a X3) Xs2)) F) (@ (@ tptp.append_a (@ F X3)) (@ (@ tptp.bind_P293964574_a_a_a Xs2) F)))))
% 0.25/0.64 (assert (forall ((X3 tptp.a) (Xs2 tptp.list_a) (F (-> tptp.a tptp.list_P1467822637od_a_a))) (= (@ (@ tptp.bind_a1679112752od_a_a (@ (@ tptp.cons_a X3) Xs2)) F) (@ (@ tptp.append1574001858od_a_a (@ F X3)) (@ (@ tptp.bind_a1679112752od_a_a Xs2) F)))))
% 0.25/0.64 (assert (forall ((X3 (-> tptp.a tptp.nat)) (Xs2 tptp.list_a_nat) (F (-> (-> tptp.a tptp.nat) tptp.list_a))) (= (@ (@ tptp.bind_a_nat_a (@ (@ tptp.cons_a_nat X3) Xs2)) F) (@ (@ tptp.append_a (@ F X3)) (@ (@ tptp.bind_a_nat_a Xs2) F)))))
% 0.25/0.64 (assert (forall ((X3 tptp.a) (Xs2 tptp.list_a) (F (-> tptp.a tptp.list_l1108175539od_a_a))) (= (@ (@ tptp.bind_a883992246od_a_a (@ (@ tptp.cons_a X3) Xs2)) F) (@ (@ tptp.append2141280328od_a_a (@ F X3)) (@ (@ tptp.bind_a883992246od_a_a Xs2) F)))))
% 0.25/0.64 (assert (forall ((X3 tptp.list_P1467822637od_a_a) (Xs2 tptp.list_l1108175539od_a_a) (F (-> tptp.list_P1467822637od_a_a tptp.list_a))) (= (@ (@ tptp.bind_l1307590552_a_a_a (@ (@ tptp.cons_l724116707od_a_a X3) Xs2)) F) (@ (@ tptp.append_a (@ F X3)) (@ (@ tptp.bind_l1307590552_a_a_a Xs2) F)))))
% 0.25/0.64 (assert (forall ((X3 (-> tptp.a tptp.nat)) (Xs2 tptp.list_a_nat) (F (-> (-> tptp.a tptp.nat) tptp.list_P1467822637od_a_a))) (= (@ (@ tptp.bind_a1190333103od_a_a (@ (@ tptp.cons_a_nat X3) Xs2)) F) (@ (@ tptp.append1574001858od_a_a (@ F X3)) (@ (@ tptp.bind_a1190333103od_a_a Xs2) F)))))
% 0.25/0.64 (assert (forall ((X3 tptp.product_prod_a_a) (Xs2 tptp.list_P1467822637od_a_a) (F (-> tptp.product_prod_a_a tptp.list_l1108175539od_a_a))) (= (@ (@ tptp.bind_P240085581od_a_a (@ (@ tptp.cons_P1921020637od_a_a X3) Xs2)) F) (@ (@ tptp.append2141280328od_a_a (@ F X3)) (@ (@ tptp.bind_P240085581od_a_a Xs2) F)))))
% 0.25/0.64 (assert (forall ((X3 tptp.list_P1467822637od_a_a) (Xs2 tptp.list_l1108175539od_a_a) (F (-> tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a))) (= (@ (@ tptp.bind_l618536897od_a_a (@ (@ tptp.cons_l724116707od_a_a X3) Xs2)) F) (@ (@ tptp.append1574001858od_a_a (@ F X3)) (@ (@ tptp.bind_l618536897od_a_a Xs2) F)))))
% 0.25/0.64 (assert (forall ((F (-> tptp.product_prod_a_a tptp.list_P1467822637od_a_a)) (X3 tptp.product_prod_a_a) (Xs2 tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ tptp.maps_P1529886977od_a_a F))) (= (@ _let_1 (@ (@ tptp.cons_P1921020637od_a_a X3) Xs2)) (@ (@ tptp.append1574001858od_a_a (@ F X3)) (@ _let_1 Xs2))))))
% 0.25/0.64 (assert (forall ((F (-> tptp.a tptp.list_a)) (X3 tptp.a) (Xs2 tptp.list_a)) (let ((_let_1 (@ tptp.maps_a_a F))) (= (@ _let_1 (@ (@ tptp.cons_a X3) Xs2)) (@ (@ tptp.append_a (@ F X3)) (@ _let_1 Xs2))))))
% 0.25/0.64 (assert (forall ((F (-> tptp.product_prod_a_a tptp.list_a)) (X3 tptp.product_prod_a_a) (Xs2 tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ tptp.maps_P321755352_a_a_a F))) (= (@ _let_1 (@ (@ tptp.cons_P1921020637od_a_a X3) Xs2)) (@ (@ tptp.append_a (@ F X3)) (@ _let_1 Xs2))))))
% 0.25/0.64 (assert (forall ((F (-> tptp.a tptp.list_P1467822637od_a_a)) (X3 tptp.a) (Xs2 tptp.list_a)) (let ((_let_1 (@ tptp.maps_a1706903530od_a_a F))) (= (@ _let_1 (@ (@ tptp.cons_a X3) Xs2)) (@ (@ tptp.append1574001858od_a_a (@ F X3)) (@ _let_1 Xs2))))))
% 0.25/0.64 (assert (forall ((F (-> (-> tptp.a tptp.nat) tptp.list_a)) (X3 (-> tptp.a tptp.nat)) (Xs2 tptp.list_a_nat)) (let ((_let_1 (@ tptp.maps_a_nat_a F))) (= (@ _let_1 (@ (@ tptp.cons_a_nat X3) Xs2)) (@ (@ tptp.append_a (@ F X3)) (@ _let_1 Xs2))))))
% 0.25/0.64 (assert (forall ((F (-> tptp.a tptp.list_l1108175539od_a_a)) (X3 tptp.a) (Xs2 tptp.list_a)) (let ((_let_1 (@ tptp.maps_a667520880od_a_a F))) (= (@ _let_1 (@ (@ tptp.cons_a X3) Xs2)) (@ (@ tptp.append2141280328od_a_a (@ F X3)) (@ _let_1 Xs2))))))
% 0.25/0.64 (assert (forall ((F (-> tptp.list_P1467822637od_a_a tptp.list_a)) (X3 tptp.list_P1467822637od_a_a) (Xs2 tptp.list_l1108175539od_a_a)) (let ((_let_1 (@ tptp.maps_l1091119186_a_a_a F))) (= (@ _let_1 (@ (@ tptp.cons_l724116707od_a_a X3) Xs2)) (@ (@ tptp.append_a (@ F X3)) (@ _let_1 Xs2))))))
% 0.25/0.64 (assert (forall ((F (-> (-> tptp.a tptp.nat) tptp.list_P1467822637od_a_a)) (X3 (-> tptp.a tptp.nat)) (Xs2 tptp.list_a_nat)) (let ((_let_1 (@ tptp.maps_a836827497od_a_a F))) (= (@ _let_1 (@ (@ tptp.cons_a_nat X3) Xs2)) (@ (@ tptp.append1574001858od_a_a (@ F X3)) (@ _let_1 Xs2))))))
% 0.25/0.64 (assert (forall ((F (-> tptp.product_prod_a_a tptp.list_l1108175539od_a_a)) (X3 tptp.product_prod_a_a) (Xs2 tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ tptp.maps_P739084551od_a_a F))) (= (@ _let_1 (@ (@ tptp.cons_P1921020637od_a_a X3) Xs2)) (@ (@ tptp.append2141280328od_a_a (@ F X3)) (@ _let_1 Xs2))))))
% 0.25/0.64 (assert (forall ((F (-> tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a)) (X3 tptp.list_P1467822637od_a_a) (Xs2 tptp.list_l1108175539od_a_a)) (let ((_let_1 (@ tptp.maps_l1117535867od_a_a F))) (= (@ _let_1 (@ (@ tptp.cons_l724116707od_a_a X3) Xs2)) (@ (@ tptp.append1574001858od_a_a (@ F X3)) (@ _let_1 Xs2))))))
% 0.25/0.64 (assert (forall ((A tptp.produc1572603623od_a_a) (B tptp.produc1572603623od_a_a) (R tptp.set_Pr1295299783od_a_a) (U tptp.list_P1891567085od_a_a) (X3 tptp.list_P1891567085od_a_a) (Y3 tptp.list_P1891567085od_a_a)) (let ((_let_1 (@ tptp.append864718978od_a_a U))) (=> (@ (@ tptp.member1899387664od_a_a (@ (@ tptp.produc1935643479od_a_a A) B)) R) (@ (@ tptp.member1254757008od_a_a (@ (@ tptp.produc461662679od_a_a (@ _let_1 (@ (@ tptp.cons_P1070399645od_a_a A) X3))) (@ _let_1 (@ (@ tptp.cons_P1070399645od_a_a B) Y3)))) (@ tptp.lexord931792858od_a_a R))))))
% 0.25/0.64 (assert (forall ((A tptp.list_P1467822637od_a_a) (B tptp.list_P1467822637od_a_a) (R tptp.set_Pr800560199od_a_a) (U tptp.list_l1108175539od_a_a) (X3 tptp.list_l1108175539od_a_a) (Y3 tptp.list_l1108175539od_a_a)) (let ((_let_1 (@ tptp.append2141280328od_a_a U))) (=> (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a A) B)) R) (@ (@ tptp.member8108048od_a_a (@ (@ tptp.produc915218007od_a_a (@ _let_1 (@ (@ tptp.cons_l724116707od_a_a A) X3))) (@ _let_1 (@ (@ tptp.cons_l724116707od_a_a B) Y3)))) (@ tptp.lexord1284731808od_a_a R))))))
% 0.25/0.64 (assert (forall ((A (-> tptp.a tptp.nat)) (B (-> tptp.a tptp.nat)) (R tptp.set_Pr1940702919_a_nat) (U tptp.list_a_nat) (X3 tptp.list_a_nat) (Y3 tptp.list_a_nat)) (let ((_let_1 (@ tptp.append_a_nat U))) (=> (@ (@ tptp.member125757712_a_nat (@ (@ tptp.produc1569872215_a_nat A) B)) R) (@ (@ tptp.member688761744_a_nat (@ (@ tptp.produc1430747863_a_nat (@ _let_1 (@ (@ tptp.cons_a_nat A) X3))) (@ _let_1 (@ (@ tptp.cons_a_nat B) Y3)))) (@ tptp.lexord_a_nat R))))))
% 0.25/0.64 (assert (forall ((A tptp.list_a) (B tptp.list_a) (R tptp.set_Pr1971762695list_a) (U tptp.list_list_a) (X3 tptp.list_list_a) (Y3 tptp.list_list_a)) (let ((_let_1 (@ tptp.append_list_a U))) (=> (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a A) B)) R) (@ (@ tptp.member888406864list_a (@ (@ tptp.produc2583831list_a (@ _let_1 (@ (@ tptp.cons_list_a A) X3))) (@ _let_1 (@ (@ tptp.cons_list_a B) Y3)))) (@ tptp.lexord_list_a R))))))
% 0.25/0.64 (assert (forall ((A tptp.product_prod_a_a) (B tptp.product_prod_a_a) (R tptp.set_Pr1948701895od_a_a) (U tptp.list_P1467822637od_a_a) (X3 tptp.list_P1467822637od_a_a) (Y3 tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ tptp.append1574001858od_a_a U))) (=> (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a A) B)) R) (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a (@ _let_1 (@ (@ tptp.cons_P1921020637od_a_a A) X3))) (@ _let_1 (@ (@ tptp.cons_P1921020637od_a_a B) Y3)))) (@ tptp.lexord673907738od_a_a R))))))
% 0.25/0.64 (assert (forall ((A tptp.a) (B tptp.a) (R tptp.set_Product_prod_a_a) (U tptp.list_a) (X3 tptp.list_a) (Y3 tptp.list_a)) (let ((_let_1 (@ tptp.append_a U))) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a A) B)) R) (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a (@ _let_1 (@ (@ tptp.cons_a A) X3))) (@ _let_1 (@ (@ tptp.cons_a B) Y3)))) (@ tptp.lexord_a R))))))
% 0.25/0.64 (assert (forall ((X3 tptp.a) (Xs2 tptp.list_a) (Y3 tptp.a) (Ys2 tptp.list_a)) (= (@ (@ tptp.zip_a_a (@ (@ tptp.cons_a X3) Xs2)) (@ (@ tptp.cons_a Y3) Ys2)) (@ (@ tptp.cons_P1921020637od_a_a (@ (@ tptp.product_Pair_a_a X3) Y3)) (@ (@ tptp.zip_a_a Xs2) Ys2)))))
% 0.25/0.64 (assert (forall ((X3 tptp.product_prod_a_a) (Xs2 tptp.list_P1467822637od_a_a) (Y3 tptp.product_prod_a_a) (Ys2 tptp.list_P1467822637od_a_a)) (= (@ (@ tptp.zip_Pr792472183od_a_a (@ (@ tptp.cons_P1921020637od_a_a X3) Xs2)) (@ (@ tptp.cons_P1921020637od_a_a Y3) Ys2)) (@ (@ tptp.cons_P1070399645od_a_a (@ (@ tptp.produc1474507607od_a_a X3) Y3)) (@ (@ tptp.zip_Pr792472183od_a_a Xs2) Ys2)))))
% 0.25/0.64 (assert (forall ((X3 tptp.product_prod_a_a) (Xs2 tptp.list_P1467822637od_a_a) (Y3 tptp.a) (Ys2 tptp.list_a)) (= (@ (@ tptp.zip_Pr201224270_a_a_a (@ (@ tptp.cons_P1921020637od_a_a X3) Xs2)) (@ (@ tptp.cons_a Y3) Ys2)) (@ (@ tptp.cons_P86081012_a_a_a (@ (@ tptp.produc2061588782_a_a_a X3) Y3)) (@ (@ tptp.zip_Pr201224270_a_a_a Xs2) Ys2)))))
% 0.25/0.64 (assert (forall ((X3 tptp.a) (Xs2 tptp.list_a) (Y3 tptp.product_prod_a_a) (Ys2 tptp.list_P1467822637od_a_a)) (= (@ (@ tptp.zip_a_1586372448od_a_a (@ (@ tptp.cons_a X3) Xs2)) (@ (@ tptp.cons_P1921020637od_a_a Y3) Ys2)) (@ (@ tptp.cons_P991044742od_a_a (@ (@ tptp.produc1299253312od_a_a X3) Y3)) (@ (@ tptp.zip_a_1586372448od_a_a Xs2) Ys2)))))
% 0.25/0.64 (assert (forall ((X3 tptp.a) (Xs2 tptp.list_a) (Y3 (-> tptp.a tptp.nat)) (Ys2 tptp.list_a_nat)) (= (@ (@ tptp.zip_a_a_nat (@ (@ tptp.cons_a X3) Xs2)) (@ (@ tptp.cons_a_nat Y3) Ys2)) (@ (@ tptp.cons_P1915851550_a_nat (@ (@ tptp.product_Pair_a_a_nat X3) Y3)) (@ (@ tptp.zip_a_a_nat Xs2) Ys2)))))
% 0.25/0.64 (assert (forall ((X3 (-> tptp.a tptp.nat)) (Xs2 tptp.list_a_nat) (Y3 tptp.a) (Ys2 tptp.list_a)) (= (@ (@ tptp.zip_a_nat_a (@ (@ tptp.cons_a_nat X3) Xs2)) (@ (@ tptp.cons_a Y3) Ys2)) (@ (@ tptp.cons_P896312284_nat_a (@ (@ tptp.product_Pair_a_nat_a X3) Y3)) (@ (@ tptp.zip_a_nat_a Xs2) Ys2)))))
% 0.25/0.64 (assert (forall ((X3 tptp.list_a) (Xs2 tptp.list_list_a) (Y3 tptp.list_a) (Ys2 tptp.list_list_a)) (= (@ (@ tptp.zip_list_a_list_a (@ (@ tptp.cons_list_a X3) Xs2)) (@ (@ tptp.cons_list_a Y3) Ys2)) (@ (@ tptp.cons_P2080942813list_a (@ (@ tptp.produc1448356631list_a X3) Y3)) (@ (@ tptp.zip_list_a_list_a Xs2) Ys2)))))
% 0.25/0.64 (assert (forall ((X3 tptp.list_P1467822637od_a_a) (Xs2 tptp.list_l1108175539od_a_a) (Y3 tptp.a) (Ys2 tptp.list_a)) (= (@ (@ tptp.zip_li245157064_a_a_a (@ (@ tptp.cons_l724116707od_a_a X3) Xs2)) (@ (@ tptp.cons_a Y3) Ys2)) (@ (@ tptp.cons_P169173742_a_a_a (@ (@ tptp.produc998622632_a_a_a X3) Y3)) (@ (@ tptp.zip_li245157064_a_a_a Xs2) Ys2)))))
% 0.25/0.64 (assert (forall ((X3 tptp.a) (Xs2 tptp.list_a) (Y3 tptp.list_P1467822637od_a_a) (Ys2 tptp.list_l1108175539od_a_a)) (= (@ (@ tptp.zip_a_1969042406od_a_a (@ (@ tptp.cons_a X3) Xs2)) (@ (@ tptp.cons_l724116707od_a_a Y3) Ys2)) (@ (@ tptp.cons_P1213258892od_a_a (@ (@ tptp.produc575024326od_a_a X3) Y3)) (@ (@ tptp.zip_a_1969042406od_a_a Xs2) Ys2)))))
% 0.25/0.64 (assert (forall ((X3 tptp.product_prod_a_a) (Xs2 tptp.list_P1467822637od_a_a) (Y3 (-> tptp.a tptp.nat)) (Ys2 tptp.list_a_nat)) (= (@ (@ tptp.zip_Pr24086287_a_nat (@ (@ tptp.cons_P1921020637od_a_a X3) Xs2)) (@ (@ tptp.cons_a_nat Y3) Ys2)) (@ (@ tptp.cons_P659009461_a_nat (@ (@ tptp.produc825466863_a_nat X3) Y3)) (@ (@ tptp.zip_Pr24086287_a_nat Xs2) Ys2)))))
% 0.25/0.64 (assert (forall ((X3 tptp.produc1572603623od_a_a) (Y3 tptp.produc1572603623od_a_a) (R tptp.set_Pr1295299783od_a_a) (Xs2 tptp.list_P1891567085od_a_a) (Us tptp.list_P1891567085od_a_a) (Vs tptp.list_P1891567085od_a_a) (Ys2 tptp.list_P1891567085od_a_a)) (let ((_let_1 (@ tptp.append864718978od_a_a Us))) (=> (@ (@ tptp.member1899387664od_a_a (@ (@ tptp.produc1935643479od_a_a X3) Y3)) R) (=> (= Xs2 (@ _let_1 (@ (@ tptp.cons_P1070399645od_a_a X3) Vs))) (=> (= Ys2 (@ _let_1 (@ (@ tptp.cons_P1070399645od_a_a Y3) Vs))) (@ (@ tptp.member1254757008od_a_a (@ (@ tptp.produc461662679od_a_a Xs2) Ys2)) (@ tptp.listre1832537542od_a_a R))))))))
% 0.25/0.64 (assert (forall ((X3 tptp.list_P1467822637od_a_a) (Y3 tptp.list_P1467822637od_a_a) (R tptp.set_Pr800560199od_a_a) (Xs2 tptp.list_l1108175539od_a_a) (Us tptp.list_l1108175539od_a_a) (Vs tptp.list_l1108175539od_a_a) (Ys2 tptp.list_l1108175539od_a_a)) (let ((_let_1 (@ tptp.append2141280328od_a_a Us))) (=> (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a X3) Y3)) R) (=> (= Xs2 (@ _let_1 (@ (@ tptp.cons_l724116707od_a_a X3) Vs))) (=> (= Ys2 (@ _let_1 (@ (@ tptp.cons_l724116707od_a_a Y3) Vs))) (@ (@ tptp.member8108048od_a_a (@ (@ tptp.produc915218007od_a_a Xs2) Ys2)) (@ tptp.listre651914124od_a_a R))))))))
% 0.25/0.64 (assert (forall ((X3 (-> tptp.a tptp.nat)) (Y3 (-> tptp.a tptp.nat)) (R tptp.set_Pr1940702919_a_nat) (Xs2 tptp.list_a_nat) (Us tptp.list_a_nat) (Vs tptp.list_a_nat) (Ys2 tptp.list_a_nat)) (let ((_let_1 (@ tptp.append_a_nat Us))) (=> (@ (@ tptp.member125757712_a_nat (@ (@ tptp.produc1569872215_a_nat X3) Y3)) R) (=> (= Xs2 (@ _let_1 (@ (@ tptp.cons_a_nat X3) Vs))) (=> (= Ys2 (@ _let_1 (@ (@ tptp.cons_a_nat Y3) Vs))) (@ (@ tptp.member688761744_a_nat (@ (@ tptp.produc1430747863_a_nat Xs2) Ys2)) (@ tptp.listrel1_a_nat R))))))))
% 0.25/0.64 (assert (forall ((X3 tptp.list_a) (Y3 tptp.list_a) (R tptp.set_Pr1971762695list_a) (Xs2 tptp.list_list_a) (Us tptp.list_list_a) (Vs tptp.list_list_a) (Ys2 tptp.list_list_a)) (let ((_let_1 (@ tptp.append_list_a Us))) (=> (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a X3) Y3)) R) (=> (= Xs2 (@ _let_1 (@ (@ tptp.cons_list_a X3) Vs))) (=> (= Ys2 (@ _let_1 (@ (@ tptp.cons_list_a Y3) Vs))) (@ (@ tptp.member888406864list_a (@ (@ tptp.produc2583831list_a Xs2) Ys2)) (@ tptp.listrel1_list_a R))))))))
% 0.25/0.64 (assert (forall ((X3 tptp.product_prod_a_a) (Y3 tptp.product_prod_a_a) (R tptp.set_Pr1948701895od_a_a) (Xs2 tptp.list_P1467822637od_a_a) (Us tptp.list_P1467822637od_a_a) (Vs tptp.list_P1467822637od_a_a) (Ys2 tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ tptp.append1574001858od_a_a Us))) (=> (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a X3) Y3)) R) (=> (= Xs2 (@ _let_1 (@ (@ tptp.cons_P1921020637od_a_a X3) Vs))) (=> (= Ys2 (@ _let_1 (@ (@ tptp.cons_P1921020637od_a_a Y3) Vs))) (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a Xs2) Ys2)) (@ tptp.listre944824838od_a_a R))))))))
% 0.25/0.64 (assert (forall ((X3 tptp.a) (Y3 tptp.a) (R tptp.set_Product_prod_a_a) (Xs2 tptp.list_a) (Us tptp.list_a) (Vs tptp.list_a) (Ys2 tptp.list_a)) (let ((_let_1 (@ tptp.append_a Us))) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X3) Y3)) R) (=> (= Xs2 (@ _let_1 (@ (@ tptp.cons_a X3) Vs))) (=> (= Ys2 (@ _let_1 (@ (@ tptp.cons_a Y3) Vs))) (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a Xs2) Ys2)) (@ tptp.listrel1_a R))))))))
% 0.25/0.64 (assert (forall ((Xs2 tptp.list_P1891567085od_a_a) (Ys2 tptp.list_P1891567085od_a_a) (R tptp.set_Pr1295299783od_a_a)) (=> (@ (@ tptp.member1254757008od_a_a (@ (@ tptp.produc461662679od_a_a Xs2) Ys2)) (@ tptp.listre1832537542od_a_a R)) (not (forall ((X4 tptp.produc1572603623od_a_a) (Y4 tptp.produc1572603623od_a_a)) (=> (@ (@ tptp.member1899387664od_a_a (@ (@ tptp.produc1935643479od_a_a X4) Y4)) R) (forall ((Us3 tptp.list_P1891567085od_a_a) (Vs2 tptp.list_P1891567085od_a_a)) (let ((_let_1 (@ tptp.append864718978od_a_a Us3))) (=> (= Xs2 (@ _let_1 (@ (@ tptp.cons_P1070399645od_a_a X4) Vs2))) (not (= Ys2 (@ _let_1 (@ (@ tptp.cons_P1070399645od_a_a Y4) Vs2)))))))))))))
% 0.25/0.64 (assert (forall ((Xs2 tptp.list_l1108175539od_a_a) (Ys2 tptp.list_l1108175539od_a_a) (R tptp.set_Pr800560199od_a_a)) (=> (@ (@ tptp.member8108048od_a_a (@ (@ tptp.produc915218007od_a_a Xs2) Ys2)) (@ tptp.listre651914124od_a_a R)) (not (forall ((X4 tptp.list_P1467822637od_a_a) (Y4 tptp.list_P1467822637od_a_a)) (=> (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a X4) Y4)) R) (forall ((Us3 tptp.list_l1108175539od_a_a) (Vs2 tptp.list_l1108175539od_a_a)) (let ((_let_1 (@ tptp.append2141280328od_a_a Us3))) (=> (= Xs2 (@ _let_1 (@ (@ tptp.cons_l724116707od_a_a X4) Vs2))) (not (= Ys2 (@ _let_1 (@ (@ tptp.cons_l724116707od_a_a Y4) Vs2)))))))))))))
% 0.25/0.64 (assert (forall ((Xs2 tptp.list_a_nat) (Ys2 tptp.list_a_nat) (R tptp.set_Pr1940702919_a_nat)) (=> (@ (@ tptp.member688761744_a_nat (@ (@ tptp.produc1430747863_a_nat Xs2) Ys2)) (@ tptp.listrel1_a_nat R)) (not (forall ((X4 (-> tptp.a tptp.nat)) (Y4 (-> tptp.a tptp.nat))) (=> (@ (@ tptp.member125757712_a_nat (@ (@ tptp.produc1569872215_a_nat X4) Y4)) R) (forall ((Us3 tptp.list_a_nat) (Vs2 tptp.list_a_nat)) (let ((_let_1 (@ tptp.append_a_nat Us3))) (=> (= Xs2 (@ _let_1 (@ (@ tptp.cons_a_nat X4) Vs2))) (not (= Ys2 (@ _let_1 (@ (@ tptp.cons_a_nat Y4) Vs2)))))))))))))
% 0.25/0.64 (assert (forall ((Xs2 tptp.list_list_a) (Ys2 tptp.list_list_a) (R tptp.set_Pr1971762695list_a)) (=> (@ (@ tptp.member888406864list_a (@ (@ tptp.produc2583831list_a Xs2) Ys2)) (@ tptp.listrel1_list_a R)) (not (forall ((X4 tptp.list_a) (Y4 tptp.list_a)) (=> (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a X4) Y4)) R) (forall ((Us3 tptp.list_list_a) (Vs2 tptp.list_list_a)) (let ((_let_1 (@ tptp.append_list_a Us3))) (=> (= Xs2 (@ _let_1 (@ (@ tptp.cons_list_a X4) Vs2))) (not (= Ys2 (@ _let_1 (@ (@ tptp.cons_list_a Y4) Vs2)))))))))))))
% 0.25/0.64 (assert (forall ((Xs2 tptp.list_P1467822637od_a_a) (Ys2 tptp.list_P1467822637od_a_a) (R tptp.set_Pr1948701895od_a_a)) (=> (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a Xs2) Ys2)) (@ tptp.listre944824838od_a_a R)) (not (forall ((X4 tptp.product_prod_a_a) (Y4 tptp.product_prod_a_a)) (=> (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a X4) Y4)) R) (forall ((Us3 tptp.list_P1467822637od_a_a) (Vs2 tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ tptp.append1574001858od_a_a Us3))) (=> (= Xs2 (@ _let_1 (@ (@ tptp.cons_P1921020637od_a_a X4) Vs2))) (not (= Ys2 (@ _let_1 (@ (@ tptp.cons_P1921020637od_a_a Y4) Vs2)))))))))))))
% 0.25/0.64 (assert (forall ((Xs2 tptp.list_a) (Ys2 tptp.list_a) (R tptp.set_Product_prod_a_a)) (=> (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a Xs2) Ys2)) (@ tptp.listrel1_a R)) (not (forall ((X4 tptp.a) (Y4 tptp.a)) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X4) Y4)) R) (forall ((Us3 tptp.list_a) (Vs2 tptp.list_a)) (let ((_let_1 (@ tptp.append_a Us3))) (=> (= Xs2 (@ _let_1 (@ (@ tptp.cons_a X4) Vs2))) (not (= Ys2 (@ _let_1 (@ (@ tptp.cons_a Y4) Vs2)))))))))))))
% 0.25/0.64 (assert (forall ((X3 tptp.a) (Xs2 tptp.list_a) (Y3 tptp.a)) (= (@ (@ tptp.member_a (@ (@ tptp.cons_a X3) Xs2)) Y3) (or (= X3 Y3) (@ (@ tptp.member_a Xs2) Y3)))))
% 0.25/0.64 (assert (forall ((X3 tptp.produc1572603623od_a_a) (Xs2 tptp.list_P1891567085od_a_a) (Y3 tptp.produc1572603623od_a_a)) (= (@ (@ tptp.member2070313346od_a_a (@ (@ tptp.cons_P1070399645od_a_a X3) Xs2)) Y3) (or (= X3 Y3) (@ (@ tptp.member2070313346od_a_a Xs2) Y3)))))
% 0.25/0.64 (assert (forall ((X3 tptp.list_P1467822637od_a_a) (Xs2 tptp.list_l1108175539od_a_a) (Y3 tptp.list_P1467822637od_a_a)) (= (@ (@ tptp.member261538120od_a_a (@ (@ tptp.cons_l724116707od_a_a X3) Xs2)) Y3) (or (= X3 Y3) (@ (@ tptp.member261538120od_a_a Xs2) Y3)))))
% 0.25/0.64 (assert (forall ((X3 (-> tptp.a tptp.nat)) (Xs2 tptp.list_a_nat) (Y3 (-> tptp.a tptp.nat))) (= (@ (@ tptp.member_a_nat (@ (@ tptp.cons_a_nat X3) Xs2)) Y3) (or (= X3 Y3) (@ (@ tptp.member_a_nat Xs2) Y3)))))
% 0.25/0.64 (assert (forall ((X3 tptp.product_prod_a_a) (Xs2 tptp.list_P1467822637od_a_a) (Y3 tptp.product_prod_a_a)) (= (@ (@ tptp.member1112491458od_a_a (@ (@ tptp.cons_P1921020637od_a_a X3) Xs2)) Y3) (or (= X3 Y3) (@ (@ tptp.member1112491458od_a_a Xs2) Y3)))))
% 0.25/0.64 (assert (forall ((R tptp.list_P1467822637od_a_a) (S tptp.list_P1467822637od_a_a) (R2 tptp.set_Pr800560199od_a_a) (S2 tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ tptp.produc85179863od_a_a R))) (=> (@ (@ tptp.member1691432592od_a_a (@ _let_1 S)) R2) (=> (= S2 S) (@ (@ tptp.member1691432592od_a_a (@ _let_1 S2)) R2))))))
% 0.25/0.64 (assert (forall ((R tptp.list_P1467822637od_a_a) (S tptp.a) (R2 tptp.set_Pr1525541400_a_a_a) (S2 tptp.a)) (let ((_let_1 (@ tptp.produc998622632_a_a_a R))) (=> (@ (@ tptp.member430654177_a_a_a (@ _let_1 S)) R2) (=> (= S2 S) (@ (@ tptp.member430654177_a_a_a (@ _let_1 S2)) R2))))))
% 0.25/0.64 (assert (forall ((R tptp.list_a) (S tptp.list_a) (R2 tptp.set_Pr1971762695list_a) (S2 tptp.list_a)) (let ((_let_1 (@ tptp.produc1448356631list_a R))) (=> (@ (@ tptp.member1250517072list_a (@ _let_1 S)) R2) (=> (= S2 S) (@ (@ tptp.member1250517072list_a (@ _let_1 S2)) R2))))))
% 0.25/0.64 (assert (forall ((R (-> tptp.product_prod_a_a tptp.product_prod_a_a Bool)) (S tptp.list_P1467822637od_a_a) (R2 tptp.set_Pr727105414od_a_a) (S2 tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ tptp.produc214132118od_a_a R))) (=> (@ (@ tptp.member372644687od_a_a (@ _let_1 S)) R2) (=> (= S2 S) (@ (@ tptp.member372644687od_a_a (@ _let_1 S2)) R2))))))
% 0.25/0.64 (assert (forall ((R tptp.a) (S tptp.produc657167928_a_a_a) (R2 tptp.set_Pr110478017_a_a_a) (S2 tptp.produc657167928_a_a_a)) (let ((_let_1 (@ tptp.produc1440321489_a_a_a R))) (=> (@ (@ tptp.member1904151562_a_a_a (@ _let_1 S)) R2) (=> (= S2 S) (@ (@ tptp.member1904151562_a_a_a (@ _let_1 S2)) R2))))))
% 0.25/0.64 (assert (forall ((R tptp.a) (S tptp.list_P1467822637od_a_a) (R2 tptp.set_Pr248149174od_a_a) (S2 tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ tptp.produc575024326od_a_a R))) (=> (@ (@ tptp.member1474739327od_a_a (@ _let_1 S)) R2) (=> (= S2 S) (@ (@ tptp.member1474739327od_a_a (@ _let_1 S2)) R2))))))
% 0.25/0.64 (assert (forall ((R tptp.a) (S tptp.a) (R2 tptp.set_Product_prod_a_a) (S2 tptp.a)) (let ((_let_1 (@ tptp.product_Pair_a_a R))) (=> (@ (@ tptp.member449909584od_a_a (@ _let_1 S)) R2) (=> (= S2 S) (@ (@ tptp.member449909584od_a_a (@ _let_1 S2)) R2))))))
% 0.25/0.64 (assert (forall ((P2 (-> tptp.pair_p1891813445t_unit tptp.produc864062247list_a tptp.list_a Bool)) (A0 tptp.pair_p1891813445t_unit) (A1 tptp.produc864062247list_a) (A22 tptp.list_a)) (=> (forall ((G tptp.pair_p1891813445t_unit) (U2 tptp.list_a) (V tptp.list_a) (X_1 tptp.list_a)) (@ (@ (@ P2 G) (@ (@ tptp.produc1448356631list_a U2) V)) X_1)) (@ (@ (@ P2 A0) A1) A22))))
% 0.25/0.64 (assert (forall ((P2 (-> tptp.pair_p125712459t_unit tptp.product_prod_a_a tptp.a Bool)) (A0 tptp.pair_p125712459t_unit) (A1 tptp.product_prod_a_a) (A22 tptp.a)) (=> (forall ((G tptp.pair_p125712459t_unit) (U2 tptp.a) (V tptp.a) (X_1 tptp.a)) (@ (@ (@ P2 G) (@ (@ tptp.product_Pair_a_a U2) V)) X_1)) (@ (@ (@ P2 A0) A1) A22))))
% 0.25/0.64 (assert (forall ((X3 tptp.produc1572603623od_a_a) (Xs2 tptp.list_P1891567085od_a_a) (Y3 tptp.produc1572603623od_a_a) (Ys2 tptp.list_P1891567085od_a_a) (R tptp.set_Pr1295299783od_a_a)) (let ((_let_1 (@ tptp.listre1832537542od_a_a R))) (= (@ (@ tptp.member1254757008od_a_a (@ (@ tptp.produc461662679od_a_a (@ (@ tptp.cons_P1070399645od_a_a X3) Xs2)) (@ (@ tptp.cons_P1070399645od_a_a Y3) Ys2))) _let_1) (or (and (@ (@ tptp.member1899387664od_a_a (@ (@ tptp.produc1935643479od_a_a X3) Y3)) R) (= Xs2 Ys2)) (and (= X3 Y3) (@ (@ tptp.member1254757008od_a_a (@ (@ tptp.produc461662679od_a_a Xs2) Ys2)) _let_1)))))))
% 0.25/0.64 (assert (forall ((X3 tptp.list_P1467822637od_a_a) (Xs2 tptp.list_l1108175539od_a_a) (Y3 tptp.list_P1467822637od_a_a) (Ys2 tptp.list_l1108175539od_a_a) (R tptp.set_Pr800560199od_a_a)) (let ((_let_1 (@ tptp.listre651914124od_a_a R))) (= (@ (@ tptp.member8108048od_a_a (@ (@ tptp.produc915218007od_a_a (@ (@ tptp.cons_l724116707od_a_a X3) Xs2)) (@ (@ tptp.cons_l724116707od_a_a Y3) Ys2))) _let_1) (or (and (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a X3) Y3)) R) (= Xs2 Ys2)) (and (= X3 Y3) (@ (@ tptp.member8108048od_a_a (@ (@ tptp.produc915218007od_a_a Xs2) Ys2)) _let_1)))))))
% 0.25/0.64 (assert (forall ((X3 (-> tptp.a tptp.nat)) (Xs2 tptp.list_a_nat) (Y3 (-> tptp.a tptp.nat)) (Ys2 tptp.list_a_nat) (R tptp.set_Pr1940702919_a_nat)) (let ((_let_1 (@ tptp.listrel1_a_nat R))) (= (@ (@ tptp.member688761744_a_nat (@ (@ tptp.produc1430747863_a_nat (@ (@ tptp.cons_a_nat X3) Xs2)) (@ (@ tptp.cons_a_nat Y3) Ys2))) _let_1) (or (and (@ (@ tptp.member125757712_a_nat (@ (@ tptp.produc1569872215_a_nat X3) Y3)) R) (= Xs2 Ys2)) (and (= X3 Y3) (@ (@ tptp.member688761744_a_nat (@ (@ tptp.produc1430747863_a_nat Xs2) Ys2)) _let_1)))))))
% 0.25/0.64 (assert (forall ((X3 tptp.list_a) (Xs2 tptp.list_list_a) (Y3 tptp.list_a) (Ys2 tptp.list_list_a) (R tptp.set_Pr1971762695list_a)) (let ((_let_1 (@ tptp.listrel1_list_a R))) (= (@ (@ tptp.member888406864list_a (@ (@ tptp.produc2583831list_a (@ (@ tptp.cons_list_a X3) Xs2)) (@ (@ tptp.cons_list_a Y3) Ys2))) _let_1) (or (and (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a X3) Y3)) R) (= Xs2 Ys2)) (and (= X3 Y3) (@ (@ tptp.member888406864list_a (@ (@ tptp.produc2583831list_a Xs2) Ys2)) _let_1)))))))
% 0.25/0.64 (assert (forall ((X3 tptp.product_prod_a_a) (Xs2 tptp.list_P1467822637od_a_a) (Y3 tptp.product_prod_a_a) (Ys2 tptp.list_P1467822637od_a_a) (R tptp.set_Pr1948701895od_a_a)) (let ((_let_1 (@ tptp.listre944824838od_a_a R))) (= (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a (@ (@ tptp.cons_P1921020637od_a_a X3) Xs2)) (@ (@ tptp.cons_P1921020637od_a_a Y3) Ys2))) _let_1) (or (and (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a X3) Y3)) R) (= Xs2 Ys2)) (and (= X3 Y3) (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a Xs2) Ys2)) _let_1)))))))
% 0.25/0.64 (assert (forall ((X3 tptp.a) (Xs2 tptp.list_a) (Y3 tptp.a) (Ys2 tptp.list_a) (R tptp.set_Product_prod_a_a)) (let ((_let_1 (@ tptp.listrel1_a R))) (= (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a (@ (@ tptp.cons_a X3) Xs2)) (@ (@ tptp.cons_a Y3) Ys2))) _let_1) (or (and (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X3) Y3)) R) (= Xs2 Ys2)) (and (= X3 Y3) (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a Xs2) Ys2)) _let_1)))))))
% 0.25/0.64 (assert (forall ((A tptp.produc1572603623od_a_a) (X3 tptp.list_P1891567085od_a_a) (B tptp.produc1572603623od_a_a) (Y3 tptp.list_P1891567085od_a_a) (R tptp.set_Pr1295299783od_a_a)) (let ((_let_1 (@ tptp.lexord931792858od_a_a R))) (= (@ (@ tptp.member1254757008od_a_a (@ (@ tptp.produc461662679od_a_a (@ (@ tptp.cons_P1070399645od_a_a A) X3)) (@ (@ tptp.cons_P1070399645od_a_a B) Y3))) _let_1) (or (@ (@ tptp.member1899387664od_a_a (@ (@ tptp.produc1935643479od_a_a A) B)) R) (and (= A B) (@ (@ tptp.member1254757008od_a_a (@ (@ tptp.produc461662679od_a_a X3) Y3)) _let_1)))))))
% 0.25/0.64 (assert (forall ((A tptp.list_P1467822637od_a_a) (X3 tptp.list_l1108175539od_a_a) (B tptp.list_P1467822637od_a_a) (Y3 tptp.list_l1108175539od_a_a) (R tptp.set_Pr800560199od_a_a)) (let ((_let_1 (@ tptp.lexord1284731808od_a_a R))) (= (@ (@ tptp.member8108048od_a_a (@ (@ tptp.produc915218007od_a_a (@ (@ tptp.cons_l724116707od_a_a A) X3)) (@ (@ tptp.cons_l724116707od_a_a B) Y3))) _let_1) (or (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a A) B)) R) (and (= A B) (@ (@ tptp.member8108048od_a_a (@ (@ tptp.produc915218007od_a_a X3) Y3)) _let_1)))))))
% 0.25/0.64 (assert (forall ((A (-> tptp.a tptp.nat)) (X3 tptp.list_a_nat) (B (-> tptp.a tptp.nat)) (Y3 tptp.list_a_nat) (R tptp.set_Pr1940702919_a_nat)) (let ((_let_1 (@ tptp.lexord_a_nat R))) (= (@ (@ tptp.member688761744_a_nat (@ (@ tptp.produc1430747863_a_nat (@ (@ tptp.cons_a_nat A) X3)) (@ (@ tptp.cons_a_nat B) Y3))) _let_1) (or (@ (@ tptp.member125757712_a_nat (@ (@ tptp.produc1569872215_a_nat A) B)) R) (and (= A B) (@ (@ tptp.member688761744_a_nat (@ (@ tptp.produc1430747863_a_nat X3) Y3)) _let_1)))))))
% 0.25/0.64 (assert (forall ((A tptp.list_a) (X3 tptp.list_list_a) (B tptp.list_a) (Y3 tptp.list_list_a) (R tptp.set_Pr1971762695list_a)) (let ((_let_1 (@ tptp.lexord_list_a R))) (= (@ (@ tptp.member888406864list_a (@ (@ tptp.produc2583831list_a (@ (@ tptp.cons_list_a A) X3)) (@ (@ tptp.cons_list_a B) Y3))) _let_1) (or (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a A) B)) R) (and (= A B) (@ (@ tptp.member888406864list_a (@ (@ tptp.produc2583831list_a X3) Y3)) _let_1)))))))
% 0.25/0.64 (assert (forall ((A tptp.product_prod_a_a) (X3 tptp.list_P1467822637od_a_a) (B tptp.product_prod_a_a) (Y3 tptp.list_P1467822637od_a_a) (R tptp.set_Pr1948701895od_a_a)) (let ((_let_1 (@ tptp.lexord673907738od_a_a R))) (= (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a (@ (@ tptp.cons_P1921020637od_a_a A) X3)) (@ (@ tptp.cons_P1921020637od_a_a B) Y3))) _let_1) (or (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a A) B)) R) (and (= A B) (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a X3) Y3)) _let_1)))))))
% 0.25/0.64 (assert (forall ((A tptp.a) (X3 tptp.list_a) (B tptp.a) (Y3 tptp.list_a) (R tptp.set_Product_prod_a_a)) (let ((_let_1 (@ tptp.lexord_a R))) (= (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a (@ (@ tptp.cons_a A) X3)) (@ (@ tptp.cons_a B) Y3))) _let_1) (or (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a A) B)) R) (and (= A B) (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a X3) Y3)) _let_1)))))))
% 0.25/0.64 (assert (forall ((Xs2 tptp.list_P1891567085od_a_a) (Ys2 tptp.list_P1891567085od_a_a) (R tptp.set_Pr1295299783od_a_a) (X3 tptp.produc1572603623od_a_a)) (let ((_let_1 (@ tptp.listre1832537542od_a_a R))) (let ((_let_2 (@ tptp.cons_P1070399645od_a_a X3))) (=> (@ (@ tptp.member1254757008od_a_a (@ (@ tptp.produc461662679od_a_a Xs2) Ys2)) _let_1) (@ (@ tptp.member1254757008od_a_a (@ (@ tptp.produc461662679od_a_a (@ _let_2 Xs2)) (@ _let_2 Ys2))) _let_1))))))
% 0.25/0.64 (assert (forall ((Xs2 tptp.list_l1108175539od_a_a) (Ys2 tptp.list_l1108175539od_a_a) (R tptp.set_Pr800560199od_a_a) (X3 tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ tptp.listre651914124od_a_a R))) (let ((_let_2 (@ tptp.cons_l724116707od_a_a X3))) (=> (@ (@ tptp.member8108048od_a_a (@ (@ tptp.produc915218007od_a_a Xs2) Ys2)) _let_1) (@ (@ tptp.member8108048od_a_a (@ (@ tptp.produc915218007od_a_a (@ _let_2 Xs2)) (@ _let_2 Ys2))) _let_1))))))
% 0.25/0.64 (assert (forall ((Xs2 tptp.list_a_nat) (Ys2 tptp.list_a_nat) (R tptp.set_Pr1940702919_a_nat) (X3 (-> tptp.a tptp.nat))) (let ((_let_1 (@ tptp.listrel1_a_nat R))) (let ((_let_2 (@ tptp.cons_a_nat X3))) (=> (@ (@ tptp.member688761744_a_nat (@ (@ tptp.produc1430747863_a_nat Xs2) Ys2)) _let_1) (@ (@ tptp.member688761744_a_nat (@ (@ tptp.produc1430747863_a_nat (@ _let_2 Xs2)) (@ _let_2 Ys2))) _let_1))))))
% 0.25/0.64 (assert (forall ((Xs2 tptp.list_a) (Ys2 tptp.list_a) (R tptp.set_Product_prod_a_a) (X3 tptp.a)) (let ((_let_1 (@ tptp.listrel1_a R))) (let ((_let_2 (@ tptp.cons_a X3))) (=> (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a Xs2) Ys2)) _let_1) (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a (@ _let_2 Xs2)) (@ _let_2 Ys2))) _let_1))))))
% 0.25/0.64 (assert (forall ((Xs2 tptp.list_P1467822637od_a_a) (Ys2 tptp.list_P1467822637od_a_a) (R tptp.set_Pr1948701895od_a_a) (X3 tptp.product_prod_a_a)) (let ((_let_1 (@ tptp.listre944824838od_a_a R))) (let ((_let_2 (@ tptp.cons_P1921020637od_a_a X3))) (=> (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a Xs2) Ys2)) _let_1) (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a (@ _let_2 Xs2)) (@ _let_2 Ys2))) _let_1))))))
% 0.25/0.64 (assert (forall ((Xs2 tptp.list_P1891567085od_a_a) (Ys2 tptp.list_P1891567085od_a_a) (R tptp.set_Pr1295299783od_a_a) (Us tptp.list_P1891567085od_a_a) (Vs tptp.list_P1891567085od_a_a)) (let ((_let_1 (@ tptp.listre1832537542od_a_a R))) (=> (or (and (@ (@ tptp.member1254757008od_a_a (@ (@ tptp.produc461662679od_a_a Xs2) Ys2)) _let_1) (= Us Vs)) (and (= Xs2 Ys2) (@ (@ tptp.member1254757008od_a_a (@ (@ tptp.produc461662679od_a_a Us) Vs)) _let_1))) (@ (@ tptp.member1254757008od_a_a (@ (@ tptp.produc461662679od_a_a (@ (@ tptp.append864718978od_a_a Xs2) Us)) (@ (@ tptp.append864718978od_a_a Ys2) Vs))) _let_1)))))
% 0.25/0.64 (assert (forall ((Xs2 tptp.list_l1108175539od_a_a) (Ys2 tptp.list_l1108175539od_a_a) (R tptp.set_Pr800560199od_a_a) (Us tptp.list_l1108175539od_a_a) (Vs tptp.list_l1108175539od_a_a)) (let ((_let_1 (@ tptp.listre651914124od_a_a R))) (=> (or (and (@ (@ tptp.member8108048od_a_a (@ (@ tptp.produc915218007od_a_a Xs2) Ys2)) _let_1) (= Us Vs)) (and (= Xs2 Ys2) (@ (@ tptp.member8108048od_a_a (@ (@ tptp.produc915218007od_a_a Us) Vs)) _let_1))) (@ (@ tptp.member8108048od_a_a (@ (@ tptp.produc915218007od_a_a (@ (@ tptp.append2141280328od_a_a Xs2) Us)) (@ (@ tptp.append2141280328od_a_a Ys2) Vs))) _let_1)))))
% 0.25/0.64 (assert (forall ((Xs2 tptp.list_a) (Ys2 tptp.list_a) (R tptp.set_Product_prod_a_a) (Us tptp.list_a) (Vs tptp.list_a)) (let ((_let_1 (@ tptp.listrel1_a R))) (=> (or (and (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a Xs2) Ys2)) _let_1) (= Us Vs)) (and (= Xs2 Ys2) (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a Us) Vs)) _let_1))) (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a (@ (@ tptp.append_a Xs2) Us)) (@ (@ tptp.append_a Ys2) Vs))) _let_1)))))
% 0.25/0.64 (assert (forall ((Xs2 tptp.list_P1467822637od_a_a) (Ys2 tptp.list_P1467822637od_a_a) (R tptp.set_Pr1948701895od_a_a) (Us tptp.list_P1467822637od_a_a) (Vs tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ tptp.listre944824838od_a_a R))) (=> (or (and (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a Xs2) Ys2)) _let_1) (= Us Vs)) (and (= Xs2 Ys2) (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a Us) Vs)) _let_1))) (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a (@ (@ tptp.append1574001858od_a_a Xs2) Us)) (@ (@ tptp.append1574001858od_a_a Ys2) Vs))) _let_1)))))
% 0.25/0.64 (assert (forall ((R tptp.set_Pr800560199od_a_a) (X3 tptp.list_l1108175539od_a_a) (Y3 tptp.list_l1108175539od_a_a)) (let ((_let_1 (@ tptp.lexord1284731808od_a_a R))) (=> (forall ((A3 tptp.list_P1467822637od_a_a) (B3 tptp.list_P1467822637od_a_a)) (or (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a A3) B3)) R) (= A3 B3) (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a B3) A3)) R))) (or (@ (@ tptp.member8108048od_a_a (@ (@ tptp.produc915218007od_a_a X3) Y3)) _let_1) (= X3 Y3) (@ (@ tptp.member8108048od_a_a (@ (@ tptp.produc915218007od_a_a Y3) X3)) _let_1))))))
% 0.25/0.64 (assert (forall ((R tptp.set_Pr1948701895od_a_a) (X3 tptp.list_P1467822637od_a_a) (Y3 tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ tptp.lexord673907738od_a_a R))) (=> (forall ((A3 tptp.product_prod_a_a) (B3 tptp.product_prod_a_a)) (or (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a A3) B3)) R) (= A3 B3) (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a B3) A3)) R))) (or (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a X3) Y3)) _let_1) (= X3 Y3) (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a Y3) X3)) _let_1))))))
% 0.25/0.64 (assert (forall ((R tptp.set_Pr1971762695list_a) (X3 tptp.list_list_a) (Y3 tptp.list_list_a)) (let ((_let_1 (@ tptp.lexord_list_a R))) (=> (forall ((A3 tptp.list_a) (B3 tptp.list_a)) (or (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a A3) B3)) R) (= A3 B3) (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a B3) A3)) R))) (or (@ (@ tptp.member888406864list_a (@ (@ tptp.produc2583831list_a X3) Y3)) _let_1) (= X3 Y3) (@ (@ tptp.member888406864list_a (@ (@ tptp.produc2583831list_a Y3) X3)) _let_1))))))
% 0.25/0.64 (assert (forall ((R tptp.set_Product_prod_a_a) (X3 tptp.list_a) (Y3 tptp.list_a)) (let ((_let_1 (@ tptp.lexord_a R))) (=> (forall ((A3 tptp.a) (B3 tptp.a)) (or (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a A3) B3)) R) (= A3 B3) (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a B3) A3)) R))) (or (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a X3) Y3)) _let_1) (= X3 Y3) (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a Y3) X3)) _let_1))))))
% 0.25/0.64 (assert (forall ((A tptp.produc651658087od_a_a) (P2 (-> tptp.produc651658087od_a_a Bool))) (= (@ (@ tptp.member1691432592od_a_a A) (@ tptp.collec1566074578od_a_a P2)) (@ P2 A))))
% 0.25/0.64 (assert (forall ((A tptp.produc864062247list_a) (P2 (-> tptp.produc864062247list_a Bool))) (= (@ (@ tptp.member1250517072list_a A) (@ tptp.collec656258194list_a P2)) (@ P2 A))))
% 0.25/0.64 (assert (forall ((A tptp.product_prod_a_a) (P2 (-> tptp.product_prod_a_a Bool))) (= (@ (@ tptp.member449909584od_a_a A) (@ tptp.collec645855634od_a_a P2)) (@ P2 A))))
% 0.25/0.64 (assert (forall ((A tptp.list_P1467822637od_a_a) (P2 (-> tptp.list_P1467822637od_a_a Bool))) (= (@ (@ tptp.member1578987478od_a_a A) (@ tptp.collec1811041560od_a_a P2)) (@ P2 A))))
% 0.25/0.64 (assert (forall ((A tptp.a) (P2 (-> tptp.a Bool))) (= (@ (@ tptp.member_a2 A) (@ tptp.collect_a P2)) (@ P2 A))))
% 0.25/0.64 (assert (forall ((A4 tptp.set_Pr1971762695list_a)) (= (@ tptp.collec656258194list_a (lambda ((X tptp.produc864062247list_a)) (@ (@ tptp.member1250517072list_a X) A4))) A4)))
% 0.25/0.64 (assert (forall ((A4 tptp.set_Product_prod_a_a)) (= (@ tptp.collec645855634od_a_a (lambda ((X tptp.product_prod_a_a)) (@ (@ tptp.member449909584od_a_a X) A4))) A4)))
% 0.25/0.64 (assert (forall ((A4 tptp.set_li562223245od_a_a)) (= (@ tptp.collec1811041560od_a_a (lambda ((X tptp.list_P1467822637od_a_a)) (@ (@ tptp.member1578987478od_a_a X) A4))) A4)))
% 0.25/0.64 (assert (forall ((A4 tptp.set_a)) (= (@ tptp.collect_a (lambda ((X tptp.a)) (@ (@ tptp.member_a2 X) A4))) A4)))
% 0.25/0.64 (assert (forall ((R tptp.set_Product_prod_a_a) (Xs2 tptp.list_a)) (=> (forall ((X4 tptp.a)) (not (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X4) X4)) R))) (not (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a Xs2) Xs2)) (@ tptp.lexord_a R))))))
% 0.25/0.64 (assert (forall ((U tptp.list_P1467822637od_a_a) (V2 tptp.list_P1467822637od_a_a) (R tptp.set_Pr1948701895od_a_a) (X3 tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ tptp.lexord673907738od_a_a R))) (let ((_let_2 (@ tptp.append1574001858od_a_a X3))) (=> (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a U) V2)) _let_1) (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a (@ _let_2 U)) (@ _let_2 V2))) _let_1))))))
% 0.25/0.64 (assert (forall ((X3 tptp.product_prod_a_a) (Y3 tptp.product_prod_a_a) (R tptp.set_Pr1948701895od_a_a) (Xs2 tptp.list_P1467822637od_a_a)) (=> (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a X3) Y3)) R) (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a (@ (@ tptp.cons_P1921020637od_a_a X3) Xs2)) (@ (@ tptp.cons_P1921020637od_a_a Y3) Xs2))) (@ tptp.listre944824838od_a_a R)))))
% 0.25/0.64 (assert (forall ((X3 tptp.a) (Y3 tptp.a) (R tptp.set_Product_prod_a_a) (Xs2 tptp.list_a)) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X3) Y3)) R) (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a (@ (@ tptp.cons_a X3) Xs2)) (@ (@ tptp.cons_a Y3) Xs2))) (@ tptp.listrel1_a R)))))
% 0.25/0.64 (assert (forall ((X3 tptp.product_prod_a_a) (Xs2 tptp.list_P1467822637od_a_a) (Ys2 tptp.list_P1467822637od_a_a) (R tptp.set_Pr1948701895od_a_a)) (=> (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a (@ (@ tptp.cons_P1921020637od_a_a X3) Xs2)) Ys2)) (@ tptp.listre944824838od_a_a R)) (=> (forall ((Y4 tptp.product_prod_a_a)) (=> (= Ys2 (@ (@ tptp.cons_P1921020637od_a_a Y4) Xs2)) (not (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a X3) Y4)) R)))) (not (forall ((Zs2 tptp.list_P1467822637od_a_a)) (=> (= Ys2 (@ (@ tptp.cons_P1921020637od_a_a X3) Zs2)) (not (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a Xs2) Zs2)) (@ tptp.listre944824838od_a_a R))))))))))
% 0.25/0.64 (assert (forall ((X3 tptp.a) (Xs2 tptp.list_a) (Ys2 tptp.list_a) (R tptp.set_Product_prod_a_a)) (=> (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a (@ (@ tptp.cons_a X3) Xs2)) Ys2)) (@ tptp.listrel1_a R)) (=> (forall ((Y4 tptp.a)) (=> (= Ys2 (@ (@ tptp.cons_a Y4) Xs2)) (not (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X3) Y4)) R)))) (not (forall ((Zs2 tptp.list_a)) (=> (= Ys2 (@ (@ tptp.cons_a X3) Zs2)) (not (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a Xs2) Zs2)) (@ tptp.listrel1_a R))))))))))
% 0.25/0.64 (assert (forall ((Xs2 tptp.list_P1467822637od_a_a) (Y3 tptp.product_prod_a_a) (Ys2 tptp.list_P1467822637od_a_a) (R tptp.set_Pr1948701895od_a_a)) (=> (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a Xs2) (@ (@ tptp.cons_P1921020637od_a_a Y3) Ys2))) (@ tptp.listre944824838od_a_a R)) (=> (forall ((X4 tptp.product_prod_a_a)) (=> (= Xs2 (@ (@ tptp.cons_P1921020637od_a_a X4) Ys2)) (not (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a X4) Y3)) R)))) (not (forall ((Zs2 tptp.list_P1467822637od_a_a)) (=> (= Xs2 (@ (@ tptp.cons_P1921020637od_a_a Y3) Zs2)) (not (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a Zs2) Ys2)) (@ tptp.listre944824838od_a_a R))))))))))
% 0.25/0.64 (assert (forall ((Xs2 tptp.list_a) (Y3 tptp.a) (Ys2 tptp.list_a) (R tptp.set_Product_prod_a_a)) (=> (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a Xs2) (@ (@ tptp.cons_a Y3) Ys2))) (@ tptp.listrel1_a R)) (=> (forall ((X4 tptp.a)) (=> (= Xs2 (@ (@ tptp.cons_a X4) Ys2)) (not (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X4) Y3)) R)))) (not (forall ((Zs2 tptp.list_a)) (=> (= Xs2 (@ (@ tptp.cons_a Y3) Zs2)) (not (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a Zs2) Ys2)) (@ tptp.listrel1_a R))))))))))
% 0.25/0.64 (assert (forall ((X3 tptp.list_P1467822637od_a_a) (U tptp.list_P1467822637od_a_a) (V2 tptp.list_P1467822637od_a_a) (R tptp.set_Pr1948701895od_a_a)) (let ((_let_1 (@ tptp.lexord673907738od_a_a R))) (let ((_let_2 (@ tptp.append1574001858od_a_a X3))) (=> (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a (@ _let_2 U)) (@ _let_2 V2))) _let_1) (=> (forall ((A3 tptp.product_prod_a_a)) (not (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a A3) A3)) R))) (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a U) V2)) _let_1)))))))
% 0.25/0.64 (assert (forall ((X3 tptp.list_a) (U tptp.list_a) (V2 tptp.list_a) (R tptp.set_Product_prod_a_a)) (let ((_let_1 (@ tptp.lexord_a R))) (let ((_let_2 (@ tptp.append_a X3))) (=> (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a (@ _let_2 U)) (@ _let_2 V2))) _let_1) (=> (forall ((A3 tptp.a)) (not (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a A3) A3)) R))) (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a U) V2)) _let_1)))))))
% 0.25/0.64 (assert (forall ((Y3 tptp.list_P1467822637od_a_a) (X3 tptp.list_P1467822637od_a_a) (R tptp.set_Pr1948701895od_a_a)) (=> (exists ((B4 tptp.product_prod_a_a) (Z tptp.list_P1467822637od_a_a)) (= Y3 (@ (@ tptp.cons_P1921020637od_a_a B4) Z))) (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a X3) (@ (@ tptp.append1574001858od_a_a X3) Y3))) (@ tptp.lexord673907738od_a_a R)))))
% 0.25/0.64 (assert (forall ((Xs2 tptp.list_P1467822637od_a_a) (Ys2 tptp.list_P1467822637od_a_a) (Xy tptp.produc1572603623od_a_a) (Xys tptp.list_P1891567085od_a_a)) (=> (= (@ (@ tptp.zip_Pr792472183od_a_a Xs2) Ys2) (@ (@ tptp.cons_P1070399645od_a_a Xy) Xys)) (not (forall ((X4 tptp.product_prod_a_a) (Xs3 tptp.list_P1467822637od_a_a)) (=> (= Xs2 (@ (@ tptp.cons_P1921020637od_a_a X4) Xs3)) (forall ((Y4 tptp.product_prod_a_a) (Ys3 tptp.list_P1467822637od_a_a)) (=> (= Ys2 (@ (@ tptp.cons_P1921020637od_a_a Y4) Ys3)) (=> (= Xy (@ (@ tptp.produc1474507607od_a_a X4) Y4)) (not (= Xys (@ (@ tptp.zip_Pr792472183od_a_a Xs3) Ys3))))))))))))
% 0.25/0.64 (assert (forall ((Xs2 tptp.list_a) (Ys2 tptp.list_a) (Xy tptp.product_prod_a_a) (Xys tptp.list_P1467822637od_a_a)) (=> (= (@ (@ tptp.zip_a_a Xs2) Ys2) (@ (@ tptp.cons_P1921020637od_a_a Xy) Xys)) (not (forall ((X4 tptp.a) (Xs3 tptp.list_a)) (=> (= Xs2 (@ (@ tptp.cons_a X4) Xs3)) (forall ((Y4 tptp.a) (Ys3 tptp.list_a)) (=> (= Ys2 (@ (@ tptp.cons_a Y4) Ys3)) (=> (= Xy (@ (@ tptp.product_Pair_a_a X4) Y4)) (not (= Xys (@ (@ tptp.zip_a_a Xs3) Ys3))))))))))))
% 0.25/0.64 (assert (forall ((X3 tptp.produc1912141786_a_a_a)) (not (forall ((G tptp.pair_p125712459t_unit) (U2 tptp.a) (V tptp.a) (W tptp.a)) (not (= X3 (@ (@ tptp.produc74075722_a_a_a G) (@ (@ tptp.produc2061588782_a_a_a (@ (@ tptp.product_Pair_a_a U2) V)) W))))))))
% 0.25/0.64 (assert (forall ((R tptp.set_Pr1948701895od_a_a) (Xs2 tptp.list_P1467822637od_a_a) (Ys2 tptp.list_P1467822637od_a_a) (Zs tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ tptp.lexord673907738od_a_a R))) (let ((_let_2 (@ tptp.append1574001858od_a_a Xs2))) (=> (@ tptp.irrefl76447196od_a_a R) (= (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a (@ _let_2 Ys2)) (@ _let_2 Zs))) _let_1) (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a Ys2) Zs)) _let_1)))))))
% 0.25/0.64 (assert (forall ((Xs2 tptp.list_P1467822637od_a_a) (X3 tptp.product_prod_a_a) (Ys2 tptp.list_P1467822637od_a_a) (Y3 tptp.product_prod_a_a) (R tptp.set_Pr1948701895od_a_a)) (let ((_let_1 (@ tptp.listre944824838od_a_a R))) (= (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a (@ (@ tptp.append1574001858od_a_a Xs2) (@ (@ tptp.cons_P1921020637od_a_a X3) tptp.nil_Product_prod_a_a))) (@ (@ tptp.append1574001858od_a_a Ys2) (@ (@ tptp.cons_P1921020637od_a_a Y3) tptp.nil_Product_prod_a_a)))) _let_1) (or (and (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a Xs2) Ys2)) _let_1) (= X3 Y3)) (and (= Xs2 Ys2) (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a X3) Y3)) R)))))))
% 0.25/0.64 (assert (forall ((Xs2 tptp.list_a) (X3 tptp.a) (Ys2 tptp.list_a) (Y3 tptp.a) (R tptp.set_Product_prod_a_a)) (let ((_let_1 (@ tptp.listrel1_a R))) (= (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a (@ (@ tptp.append_a Xs2) (@ (@ tptp.cons_a X3) tptp.nil_a))) (@ (@ tptp.append_a Ys2) (@ (@ tptp.cons_a Y3) tptp.nil_a)))) _let_1) (or (and (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a Xs2) Ys2)) _let_1) (= X3 Y3)) (and (= Xs2 Ys2) (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X3) Y3)) R)))))))
% 0.25/0.64 (assert (forall ((Y3 tptp.list_P1467822637od_a_a) (R tptp.set_Pr1948701895od_a_a)) (= (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a tptp.nil_Product_prod_a_a) Y3)) (@ tptp.lexord673907738od_a_a R)) (exists ((A5 tptp.product_prod_a_a) (X tptp.list_P1467822637od_a_a)) (= Y3 (@ (@ tptp.cons_P1921020637od_a_a A5) X))))))
% 0.25/0.64 (assert (forall ((Xs2 tptp.list_P1467822637od_a_a) (Ys2 tptp.list_P1467822637od_a_a) (Zs tptp.list_P1467822637od_a_a) (R tptp.set_Pr1948701895od_a_a)) (let ((_let_1 (@ tptp.lexord673907738od_a_a R))) (let ((_let_2 (@ tptp.append1574001858od_a_a Xs2))) (= (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a (@ _let_2 Ys2)) (@ _let_2 Zs))) _let_1) (or (exists ((X tptp.product_prod_a_a)) (and (@ (@ tptp.member449909584od_a_a X) (@ tptp.set_Product_prod_a_a2 Xs2)) (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a X) X)) R))) (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a Ys2) Zs)) _let_1)))))))
% 0.25/0.64 (assert (forall ((Xs2 tptp.list_a) (Ys2 tptp.list_a) (Zs tptp.list_a) (R tptp.set_Product_prod_a_a)) (let ((_let_1 (@ tptp.lexord_a R))) (let ((_let_2 (@ tptp.append_a Xs2))) (= (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a (@ _let_2 Ys2)) (@ _let_2 Zs))) _let_1) (or (exists ((X tptp.a)) (and (@ (@ tptp.member_a2 X) (@ tptp.set_a2 Xs2)) (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X) X)) R))) (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a Ys2) Zs)) _let_1)))))))
% 0.25/0.64 (assert (forall ((Xs2 tptp.list_a) (Us tptp.list_a) (Ys2 tptp.list_a) (Vs tptp.list_a)) (=> (= (@ tptp.size_size_list_a Xs2) (@ tptp.size_size_list_a Us)) (= (@ (@ tptp.zip_a_a (@ (@ tptp.append_a Xs2) Ys2)) (@ (@ tptp.append_a Us) Vs)) (@ (@ tptp.append1574001858od_a_a (@ (@ tptp.zip_a_a Xs2) Us)) (@ (@ tptp.zip_a_a Ys2) Vs))))))
% 0.25/0.64 (assert (forall ((Xs2 tptp.list_P1467822637od_a_a) (Us tptp.list_P1467822637od_a_a) (Ys2 tptp.list_P1467822637od_a_a) (Vs tptp.list_P1467822637od_a_a)) (=> (= (@ tptp.size_s642698393od_a_a Xs2) (@ tptp.size_s642698393od_a_a Us)) (= (@ (@ tptp.zip_Pr792472183od_a_a (@ (@ tptp.append1574001858od_a_a Xs2) Ys2)) (@ (@ tptp.append1574001858od_a_a Us) Vs)) (@ (@ tptp.append864718978od_a_a (@ (@ tptp.zip_Pr792472183od_a_a Xs2) Us)) (@ (@ tptp.zip_Pr792472183od_a_a Ys2) Vs))))))
% 0.25/0.64 (assert (forall ((R tptp.set_Pr1948701895od_a_a) (Xs2 tptp.list_P1467822637od_a_a) (Ys2 tptp.list_P1467822637od_a_a) (Zs tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ tptp.lex_Product_prod_a_a R))) (let ((_let_2 (@ tptp.append1574001858od_a_a Xs2))) (=> (forall ((X4 tptp.product_prod_a_a)) (not (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a X4) X4)) R))) (=> (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a (@ _let_2 Ys2)) (@ _let_2 Zs))) _let_1) (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a Ys2) Zs)) _let_1)))))))
% 0.25/0.64 (assert (forall ((R tptp.set_Product_prod_a_a) (Xs2 tptp.list_a) (Ys2 tptp.list_a) (Zs tptp.list_a)) (let ((_let_1 (@ tptp.lex_a R))) (let ((_let_2 (@ tptp.append_a Xs2))) (=> (forall ((X4 tptp.a)) (not (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X4) X4)) R))) (=> (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a (@ _let_2 Ys2)) (@ _let_2 Zs))) _let_1) (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a Ys2) Zs)) _let_1)))))))
% 0.25/0.64 (assert (forall ((R tptp.set_Pr1948701895od_a_a) (Xs2 tptp.list_P1467822637od_a_a) (Ys2 tptp.list_P1467822637od_a_a) (Zs tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ tptp.lex_Product_prod_a_a R))) (let ((_let_2 (@ tptp.append1574001858od_a_a Xs2))) (=> (forall ((X4 tptp.product_prod_a_a)) (not (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a X4) X4)) R))) (= (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a (@ _let_2 Ys2)) (@ _let_2 Zs))) _let_1) (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a Ys2) Zs)) _let_1)))))))
% 0.25/0.64 (assert (forall ((R tptp.set_Product_prod_a_a) (Xs2 tptp.list_a) (Ys2 tptp.list_a) (Zs tptp.list_a)) (let ((_let_1 (@ tptp.lex_a R))) (let ((_let_2 (@ tptp.append_a Xs2))) (=> (forall ((X4 tptp.a)) (not (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X4) X4)) R))) (= (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a (@ _let_2 Ys2)) (@ _let_2 Zs))) _let_1) (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a Ys2) Zs)) _let_1)))))))
% 0.25/0.64 (assert (forall ((A tptp.list_P1467822637od_a_a)) (= (@ (@ tptp.append1574001858od_a_a A) tptp.nil_Product_prod_a_a) A)))
% 0.25/0.64 (assert (forall ((Xs2 tptp.list_P1467822637od_a_a) (Ys2 tptp.list_P1467822637od_a_a)) (= (= (@ (@ tptp.append1574001858od_a_a Xs2) Ys2) tptp.nil_Product_prod_a_a) (and (= Xs2 tptp.nil_Product_prod_a_a) (= Ys2 tptp.nil_Product_prod_a_a)))))
% 0.25/0.64 (assert (forall ((Xs2 tptp.list_P1467822637od_a_a) (Ys2 tptp.list_P1467822637od_a_a)) (= (= tptp.nil_Product_prod_a_a (@ (@ tptp.append1574001858od_a_a Xs2) Ys2)) (and (= Xs2 tptp.nil_Product_prod_a_a) (= Ys2 tptp.nil_Product_prod_a_a)))))
% 0.25/0.64 (assert (forall ((Ys2 tptp.list_P1467822637od_a_a) (Xs2 tptp.list_P1467822637od_a_a)) (= (= Ys2 (@ (@ tptp.append1574001858od_a_a Xs2) Ys2)) (= Xs2 tptp.nil_Product_prod_a_a))))
% 0.25/0.64 (assert (forall ((Xs2 tptp.list_P1467822637od_a_a) (Ys2 tptp.list_P1467822637od_a_a)) (= (= (@ (@ tptp.append1574001858od_a_a Xs2) Ys2) Ys2) (= Xs2 tptp.nil_Product_prod_a_a))))
% 0.25/0.64 (assert (forall ((Xs2 tptp.list_P1467822637od_a_a) (Ys2 tptp.list_P1467822637od_a_a)) (= (= Xs2 (@ (@ tptp.append1574001858od_a_a Xs2) Ys2)) (= Ys2 tptp.nil_Product_prod_a_a))))
% 0.25/0.64 (assert (forall ((Xs2 tptp.list_P1467822637od_a_a) (Ys2 tptp.list_P1467822637od_a_a)) (= (= (@ (@ tptp.append1574001858od_a_a Xs2) Ys2) Xs2) (= Ys2 tptp.nil_Product_prod_a_a))))
% 0.25/0.64 (assert (forall ((Xs2 tptp.list_P1467822637od_a_a)) (= (@ (@ tptp.append1574001858od_a_a Xs2) tptp.nil_Product_prod_a_a) Xs2)))
% 0.25/0.64 (assert (forall ((Xs2 tptp.list_P1467822637od_a_a) (Ys2 tptp.list_P1467822637od_a_a) (Us tptp.list_P1467822637od_a_a) (Vs tptp.list_P1467822637od_a_a)) (=> (or (= (@ tptp.size_s642698393od_a_a Xs2) (@ tptp.size_s642698393od_a_a Ys2)) (= (@ tptp.size_s642698393od_a_a Us) (@ tptp.size_s642698393od_a_a Vs))) (= (= (@ (@ tptp.append1574001858od_a_a Xs2) Us) (@ (@ tptp.append1574001858od_a_a Ys2) Vs)) (and (= Xs2 Ys2) (= Us Vs))))))
% 0.25/0.64 (assert (forall ((Xs2 tptp.list_P1467822637od_a_a) (X3 tptp.product_prod_a_a) (Ys2 tptp.list_P1467822637od_a_a) (Y3 tptp.product_prod_a_a)) (= (= (@ (@ tptp.append1574001858od_a_a Xs2) (@ (@ tptp.cons_P1921020637od_a_a X3) tptp.nil_Product_prod_a_a)) (@ (@ tptp.append1574001858od_a_a Ys2) (@ (@ tptp.cons_P1921020637od_a_a Y3) tptp.nil_Product_prod_a_a))) (and (= Xs2 Ys2) (= X3 Y3)))))
% 0.25/0.64 (assert (forall ((X3 tptp.product_prod_a_a) (Xs2 tptp.list_P1467822637od_a_a) (Y3 tptp.product_prod_a_a) (Ys2 tptp.list_P1467822637od_a_a) (R tptp.set_Pr1948701895od_a_a)) (let ((_let_1 (@ tptp.lex_Product_prod_a_a R))) (= (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a (@ (@ tptp.cons_P1921020637od_a_a X3) Xs2)) (@ (@ tptp.cons_P1921020637od_a_a Y3) Ys2))) _let_1) (or (and (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a X3) Y3)) R) (= (@ tptp.size_s642698393od_a_a Xs2) (@ tptp.size_s642698393od_a_a Ys2))) (and (= X3 Y3) (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a Xs2) Ys2)) _let_1)))))))
% 0.25/0.64 (assert (forall ((X3 tptp.a) (Xs2 tptp.list_a) (Y3 tptp.a) (Ys2 tptp.list_a) (R tptp.set_Product_prod_a_a)) (let ((_let_1 (@ tptp.lex_a R))) (= (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a (@ (@ tptp.cons_a X3) Xs2)) (@ (@ tptp.cons_a Y3) Ys2))) _let_1) (or (and (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X3) Y3)) R) (= (@ tptp.size_size_list_a Xs2) (@ tptp.size_size_list_a Ys2))) (and (= X3 Y3) (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a Xs2) Ys2)) _let_1)))))))
% 0.25/0.64 (assert (forall ((Xs2 tptp.list_a) (Ys2 tptp.list_a) (X3 tptp.a)) (=> (= (@ tptp.size_size_list_a Xs2) (@ tptp.size_size_list_a Ys2)) (=> (@ (@ tptp.member_a2 X3) (@ tptp.set_a2 Xs2)) (not (forall ((Y4 tptp.a)) (not (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X3) Y4)) (@ tptp.set_Product_prod_a_a2 (@ (@ tptp.zip_a_a Xs2) Ys2))))))))))
% 0.25/0.64 (assert (forall ((Xs2 tptp.list_a) (Ys2 tptp.list_a) (Y3 tptp.a)) (=> (= (@ tptp.size_size_list_a Xs2) (@ tptp.size_size_list_a Ys2)) (=> (@ (@ tptp.member_a2 Y3) (@ tptp.set_a2 Ys2)) (not (forall ((X4 tptp.a)) (not (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X4) Y3)) (@ tptp.set_Product_prod_a_a2 (@ (@ tptp.zip_a_a Xs2) Ys2))))))))))
% 0.25/0.64 (assert (forall ((Xs2 tptp.list_P1467822637od_a_a) (Ys2 tptp.list_P1467822637od_a_a) (Zs tptp.list_P1467822637od_a_a) (Ws tptp.list_P1467822637od_a_a) (P2 (-> tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a Bool))) (let ((_let_1 (@ tptp.size_s642698393od_a_a Zs))) (let ((_let_2 (@ tptp.size_s642698393od_a_a Ys2))) (=> (= (@ tptp.size_s642698393od_a_a Xs2) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_s642698393od_a_a Ws)) (=> (@ (@ (@ (@ P2 tptp.nil_Product_prod_a_a) tptp.nil_Product_prod_a_a) tptp.nil_Product_prod_a_a) tptp.nil_Product_prod_a_a) (=> (forall ((X4 tptp.product_prod_a_a) (Xs4 tptp.list_P1467822637od_a_a) (Y4 tptp.product_prod_a_a) (Ys4 tptp.list_P1467822637od_a_a) (Z2 tptp.product_prod_a_a) (Zs2 tptp.list_P1467822637od_a_a) (W tptp.product_prod_a_a) (Ws2 tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ tptp.size_s642698393od_a_a Zs2))) (let ((_let_2 (@ tptp.size_s642698393od_a_a Ys4))) (=> (= (@ tptp.size_s642698393od_a_a Xs4) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_s642698393od_a_a Ws2)) (=> (@ (@ (@ (@ P2 Xs4) Ys4) Zs2) Ws2) (@ (@ (@ (@ P2 (@ (@ tptp.cons_P1921020637od_a_a X4) Xs4)) (@ (@ tptp.cons_P1921020637od_a_a Y4) Ys4)) (@ (@ tptp.cons_P1921020637od_a_a Z2) Zs2)) (@ (@ tptp.cons_P1921020637od_a_a W) Ws2))))))))) (@ (@ (@ (@ P2 Xs2) Ys2) Zs) Ws))))))))))
% 0.25/0.64 (assert (forall ((Xs2 tptp.list_P1467822637od_a_a) (Ys2 tptp.list_P1467822637od_a_a) (Zs tptp.list_P1467822637od_a_a) (P2 (-> tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a Bool))) (let ((_let_1 (@ tptp.size_s642698393od_a_a Ys2))) (=> (= (@ tptp.size_s642698393od_a_a Xs2) _let_1) (=> (= _let_1 (@ tptp.size_s642698393od_a_a Zs)) (=> (@ (@ (@ P2 tptp.nil_Product_prod_a_a) tptp.nil_Product_prod_a_a) tptp.nil_Product_prod_a_a) (=> (forall ((X4 tptp.product_prod_a_a) (Xs4 tptp.list_P1467822637od_a_a) (Y4 tptp.product_prod_a_a) (Ys4 tptp.list_P1467822637od_a_a) (Z2 tptp.product_prod_a_a) (Zs2 tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ tptp.size_s642698393od_a_a Ys4))) (=> (= (@ tptp.size_s642698393od_a_a Xs4) _let_1) (=> (= _let_1 (@ tptp.size_s642698393od_a_a Zs2)) (=> (@ (@ (@ P2 Xs4) Ys4) Zs2) (@ (@ (@ P2 (@ (@ tptp.cons_P1921020637od_a_a X4) Xs4)) (@ (@ tptp.cons_P1921020637od_a_a Y4) Ys4)) (@ (@ tptp.cons_P1921020637od_a_a Z2) Zs2))))))) (@ (@ (@ P2 Xs2) Ys2) Zs))))))))
% 0.25/0.64 (assert (forall ((Xs2 tptp.list_P1467822637od_a_a) (Ys2 tptp.list_P1467822637od_a_a) (P2 (-> tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a Bool))) (=> (= (@ tptp.size_s642698393od_a_a Xs2) (@ tptp.size_s642698393od_a_a Ys2)) (=> (@ (@ P2 tptp.nil_Product_prod_a_a) tptp.nil_Product_prod_a_a) (=> (forall ((X4 tptp.product_prod_a_a) (Xs4 tptp.list_P1467822637od_a_a) (Y4 tptp.product_prod_a_a) (Ys4 tptp.list_P1467822637od_a_a)) (=> (= (@ tptp.size_s642698393od_a_a Xs4) (@ tptp.size_s642698393od_a_a Ys4)) (=> (@ (@ P2 Xs4) Ys4) (@ (@ P2 (@ (@ tptp.cons_P1921020637od_a_a X4) Xs4)) (@ (@ tptp.cons_P1921020637od_a_a Y4) Ys4))))) (@ (@ P2 Xs2) Ys2))))))
% 0.25/0.64 (assert (forall ((X3 tptp.list_l1108175539od_a_a)) (=> (not (= X3 tptp.nil_li1885598003od_a_a)) (=> (forall ((Xss tptp.list_l1108175539od_a_a)) (not (= X3 (@ (@ tptp.cons_l724116707od_a_a tptp.nil_Product_prod_a_a) Xss)))) (not (forall ((X4 tptp.product_prod_a_a) (Xs4 tptp.list_P1467822637od_a_a) (Xss tptp.list_l1108175539od_a_a)) (not (= X3 (@ (@ tptp.cons_l724116707od_a_a (@ (@ tptp.cons_P1921020637od_a_a X4) Xs4)) Xss)))))))))
% 0.25/0.64 (assert (forall ((X3 tptp.a) (Y3 tptp.a) (Xs2 tptp.list_a) (Ys2 tptp.list_a)) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X3) Y3)) (@ tptp.set_Product_prod_a_a2 (@ (@ tptp.zip_a_a Xs2) Ys2))) (@ (@ tptp.member_a2 Y3) (@ tptp.set_a2 Ys2)))))
% 0.25/0.64 (assert (forall ((X3 tptp.a) (Y3 tptp.a) (Xs2 tptp.list_a) (Ys2 tptp.list_a)) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X3) Y3)) (@ tptp.set_Product_prod_a_a2 (@ (@ tptp.zip_a_a Xs2) Ys2))) (@ (@ tptp.member_a2 X3) (@ tptp.set_a2 Xs2)))))
% 0.25/0.64 (assert (forall ((X3 tptp.a) (Y3 tptp.a) (Xs2 tptp.list_a) (Ys2 tptp.list_a)) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X3) Y3)) (@ tptp.set_Product_prod_a_a2 (@ (@ tptp.zip_a_a Xs2) Ys2))) (not (=> (@ (@ tptp.member_a2 X3) (@ tptp.set_a2 Xs2)) (not (@ (@ tptp.member_a2 Y3) (@ tptp.set_a2 Ys2))))))))
% 0.25/0.64 (assert (forall ((A tptp.a) (B tptp.a) (Xs2 tptp.list_a)) (= (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a A) B)) (@ tptp.set_Product_prod_a_a2 (@ (@ tptp.zip_a_a Xs2) Xs2))) (and (@ (@ tptp.member_a2 A) (@ tptp.set_a2 Xs2)) (= A B)))))
% 0.25/0.64 (assert (forall ((Xs2 tptp.list_P1467822637od_a_a) (Ys2 tptp.list_P1467822637od_a_a)) (=> (not (= Xs2 Ys2)) (=> (= (@ tptp.size_s642698393od_a_a Xs2) (@ tptp.size_s642698393od_a_a Ys2)) (exists ((Pre tptp.list_P1467822637od_a_a) (X4 tptp.product_prod_a_a) (Xs3 tptp.list_P1467822637od_a_a) (Y4 tptp.product_prod_a_a) (Ys3 tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ tptp.append1574001858od_a_a Pre))) (and (not (= X4 Y4)) (= Xs2 (@ _let_1 (@ (@ tptp.append1574001858od_a_a (@ (@ tptp.cons_P1921020637od_a_a X4) tptp.nil_Product_prod_a_a)) Xs3))) (= Ys2 (@ _let_1 (@ (@ tptp.append1574001858od_a_a (@ (@ tptp.cons_P1921020637od_a_a Y4) tptp.nil_Product_prod_a_a)) Ys3))))))))))
% 0.25/0.64 (assert (forall ((E tptp.product_prod_a_a) (A tptp.list_P1467822637od_a_a)) (=> (@ (@ tptp.member449909584od_a_a E) (@ tptp.set_Product_prod_a_a2 A)) (=> (forall ((Z22 tptp.list_P1467822637od_a_a)) (not (= A (@ (@ tptp.cons_P1921020637od_a_a E) Z22)))) (not (forall ((Z1 tptp.product_prod_a_a) (Z22 tptp.list_P1467822637od_a_a)) (=> (= A (@ (@ tptp.cons_P1921020637od_a_a Z1) Z22)) (not (@ (@ tptp.member449909584od_a_a E) (@ tptp.set_Product_prod_a_a2 Z22))))))))))
% 0.25/0.64 (assert (forall ((Y3 tptp.product_prod_a_a) (X3 tptp.product_prod_a_a) (Xs2 tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ tptp.member449909584od_a_a Y3))) (=> (@ _let_1 (@ tptp.set_Product_prod_a_a2 (@ (@ tptp.cons_P1921020637od_a_a X3) Xs2))) (or (= Y3 X3) (@ _let_1 (@ tptp.set_Product_prod_a_a2 Xs2)))))))
% 0.25/0.64 (assert (forall ((X21 tptp.product_prod_a_a) (X22 tptp.list_P1467822637od_a_a)) (@ (@ tptp.member449909584od_a_a X21) (@ tptp.set_Product_prod_a_a2 (@ (@ tptp.cons_P1921020637od_a_a X21) X22)))))
% 0.25/0.64 (assert (forall ((Y3 tptp.product_prod_a_a) (X22 tptp.list_P1467822637od_a_a) (X21 tptp.product_prod_a_a)) (let ((_let_1 (@ tptp.member449909584od_a_a Y3))) (=> (@ _let_1 (@ tptp.set_Product_prod_a_a2 X22)) (@ _let_1 (@ tptp.set_Product_prod_a_a2 (@ (@ tptp.cons_P1921020637od_a_a X21) X22)))))))
% 0.25/0.64 (assert (forall ((Xs2 tptp.list_P1467822637od_a_a) (Ys2 tptp.list_P1467822637od_a_a) (R tptp.set_Pr1948701895od_a_a) (Vs tptp.list_P1467822637od_a_a) (Us tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ tptp.lex_Product_prod_a_a R))) (=> (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a Xs2) Ys2)) _let_1) (=> (= (@ tptp.size_s642698393od_a_a Vs) (@ tptp.size_s642698393od_a_a Us)) (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a (@ (@ tptp.append1574001858od_a_a Xs2) Us)) (@ (@ tptp.append1574001858od_a_a Ys2) Vs))) _let_1))))))
% 0.25/0.64 (assert (forall ((X3 tptp.produc501911462od_a_a)) (=> (forall ((P4 (-> tptp.product_prod_a_a tptp.product_prod_a_a Bool))) (not (= X3 (@ (@ tptp.produc214132118od_a_a P4) tptp.nil_Product_prod_a_a)))) (not (forall ((P4 (-> tptp.product_prod_a_a tptp.product_prod_a_a Bool)) (X4 tptp.product_prod_a_a) (Ys4 tptp.list_P1467822637od_a_a)) (not (= X3 (@ (@ tptp.produc214132118od_a_a P4) (@ (@ tptp.cons_P1921020637od_a_a X4) Ys4)))))))))
% 0.25/0.65 (assert (forall ((X3 tptp.produc501911462od_a_a)) (=> (forall ((P4 (-> tptp.product_prod_a_a tptp.product_prod_a_a Bool))) (not (= X3 (@ (@ tptp.produc214132118od_a_a P4) tptp.nil_Product_prod_a_a)))) (=> (forall ((P4 (-> tptp.product_prod_a_a tptp.product_prod_a_a Bool)) (X4 tptp.product_prod_a_a)) (not (= X3 (@ (@ tptp.produc214132118od_a_a P4) (@ (@ tptp.cons_P1921020637od_a_a X4) tptp.nil_Product_prod_a_a))))) (not (forall ((P4 (-> tptp.product_prod_a_a tptp.product_prod_a_a Bool)) (X4 tptp.product_prod_a_a) (Y4 tptp.product_prod_a_a) (Xs4 tptp.list_P1467822637od_a_a)) (not (= X3 (@ (@ tptp.produc214132118od_a_a P4) (@ (@ tptp.cons_P1921020637od_a_a X4) (@ (@ tptp.cons_P1921020637od_a_a Y4) Xs4)))))))))))
% 0.25/0.65 (assert (forall ((P2 (-> (-> tptp.product_prod_a_a tptp.product_prod_a_a) tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a Bool)) (A0 (-> tptp.product_prod_a_a tptp.product_prod_a_a)) (A1 tptp.list_P1467822637od_a_a) (A22 tptp.list_P1467822637od_a_a)) (=> (forall ((F2 (-> tptp.product_prod_a_a tptp.product_prod_a_a)) (X_1 tptp.list_P1467822637od_a_a)) (@ (@ (@ P2 F2) tptp.nil_Product_prod_a_a) X_1)) (=> (forall ((F2 (-> tptp.product_prod_a_a tptp.product_prod_a_a)) (A3 tptp.product_prod_a_a) (As tptp.list_P1467822637od_a_a) (Bs tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ P2 F2))) (=> (@ (@ _let_1 As) (@ (@ tptp.cons_P1921020637od_a_a (@ F2 A3)) Bs)) (@ (@ _let_1 (@ (@ tptp.cons_P1921020637od_a_a A3) As)) Bs)))) (@ (@ (@ P2 A0) A1) A22)))))
% 0.25/0.65 (assert (forall ((Xs2 tptp.list_P1467822637od_a_a) (P2 (-> tptp.list_P1467822637od_a_a Bool))) (=> (not (= Xs2 tptp.nil_Product_prod_a_a)) (=> (forall ((X4 tptp.product_prod_a_a)) (@ P2 (@ (@ tptp.cons_P1921020637od_a_a X4) tptp.nil_Product_prod_a_a))) (=> (forall ((X4 tptp.product_prod_a_a) (Xs4 tptp.list_P1467822637od_a_a)) (=> (not (= Xs4 tptp.nil_Product_prod_a_a)) (=> (@ P2 Xs4) (@ P2 (@ (@ tptp.cons_P1921020637od_a_a X4) Xs4))))) (@ P2 Xs2))))))
% 0.25/0.65 (assert (forall ((P2 (-> (-> tptp.product_prod_a_a tptp.product_prod_a_a Bool) tptp.list_P1467822637od_a_a Bool)) (A0 (-> tptp.product_prod_a_a tptp.product_prod_a_a Bool)) (A1 tptp.list_P1467822637od_a_a)) (=> (forall ((P4 (-> tptp.product_prod_a_a tptp.product_prod_a_a Bool))) (@ (@ P2 P4) tptp.nil_Product_prod_a_a)) (=> (forall ((P4 (-> tptp.product_prod_a_a tptp.product_prod_a_a Bool)) (X4 tptp.product_prod_a_a)) (@ (@ P2 P4) (@ (@ tptp.cons_P1921020637od_a_a X4) tptp.nil_Product_prod_a_a))) (=> (forall ((P4 (-> tptp.product_prod_a_a tptp.product_prod_a_a Bool)) (X4 tptp.product_prod_a_a) (Y4 tptp.product_prod_a_a) (Xs4 tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ (@ tptp.cons_P1921020637od_a_a Y4) Xs4))) (let ((_let_2 (@ P2 P4))) (=> (@ _let_2 _let_1) (@ _let_2 (@ (@ tptp.cons_P1921020637od_a_a X4) _let_1)))))) (@ (@ P2 A0) A1))))))
% 0.25/0.65 (assert (forall ((P2 (-> tptp.list_P1467822637od_a_a Bool)) (A0 tptp.list_P1467822637od_a_a)) (=> (@ P2 tptp.nil_Product_prod_a_a) (=> (forall ((X4 tptp.product_prod_a_a)) (@ P2 (@ (@ tptp.cons_P1921020637od_a_a X4) tptp.nil_Product_prod_a_a))) (=> (forall ((X4 tptp.product_prod_a_a) (Y4 tptp.product_prod_a_a) (Xs4 tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ (@ tptp.cons_P1921020637od_a_a Y4) Xs4))) (let ((_let_2 (@ tptp.cons_P1921020637od_a_a X4))) (let ((_let_3 (= X4 Y4))) (=> (=> _let_3 (@ P2 (@ _let_2 Xs4))) (=> (=> (not _let_3) (@ P2 _let_1)) (@ P2 (@ _let_2 _let_1)))))))) (@ P2 A0))))))
% 0.25/0.65 (assert (forall ((P2 (-> (-> tptp.product_prod_a_a tptp.product_prod_a_a Bool) tptp.list_P1467822637od_a_a Bool)) (A0 (-> tptp.product_prod_a_a tptp.product_prod_a_a Bool)) (A1 tptp.list_P1467822637od_a_a)) (=> (forall ((P4 (-> tptp.product_prod_a_a tptp.product_prod_a_a Bool))) (@ (@ P2 P4) tptp.nil_Product_prod_a_a)) (=> (forall ((P4 (-> tptp.product_prod_a_a tptp.product_prod_a_a Bool)) (X4 tptp.product_prod_a_a) (Ys4 tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ P2 P4))) (=> (@ _let_1 Ys4) (@ _let_1 (@ (@ tptp.cons_P1921020637od_a_a X4) Ys4))))) (@ (@ P2 A0) A1)))))
% 0.25/0.65 (assert (forall ((X3 tptp.list_P1467822637od_a_a)) (=> (not (= X3 tptp.nil_Product_prod_a_a)) (=> (forall ((X4 tptp.product_prod_a_a)) (not (= X3 (@ (@ tptp.cons_P1921020637od_a_a X4) tptp.nil_Product_prod_a_a)))) (not (forall ((X4 tptp.product_prod_a_a) (Y4 tptp.product_prod_a_a) (Xs4 tptp.list_P1467822637od_a_a)) (not (= X3 (@ (@ tptp.cons_P1921020637od_a_a X4) (@ (@ tptp.cons_P1921020637od_a_a Y4) Xs4))))))))))
% 0.25/0.65 (assert (forall ((P2 (-> tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a Bool)) (A0 tptp.list_P1467822637od_a_a) (A1 tptp.list_P1467822637od_a_a)) (=> (forall ((X_1 tptp.list_P1467822637od_a_a)) (@ (@ P2 tptp.nil_Product_prod_a_a) X_1)) (=> (forall ((Xs4 tptp.list_P1467822637od_a_a)) (@ (@ P2 Xs4) tptp.nil_Product_prod_a_a)) (=> (forall ((X4 tptp.product_prod_a_a) (Xs4 tptp.list_P1467822637od_a_a) (Y4 tptp.product_prod_a_a) (Ys4 tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ (@ tptp.cons_P1921020637od_a_a Y4) Ys4))) (let ((_let_2 (@ P2 (@ (@ tptp.cons_P1921020637od_a_a X4) Xs4)))) (=> (@ (@ P2 Xs4) _let_1) (=> (@ _let_2 Ys4) (@ _let_2 _let_1)))))) (@ (@ P2 A0) A1))))))
% 0.25/0.65 (assert (forall ((P2 (-> tptp.list_P1467822637od_a_a Bool)) (Xs2 tptp.list_P1467822637od_a_a)) (=> (@ P2 tptp.nil_Product_prod_a_a) (=> (forall ((X4 tptp.product_prod_a_a)) (@ P2 (@ (@ tptp.cons_P1921020637od_a_a X4) tptp.nil_Product_prod_a_a))) (=> (forall ((X4 tptp.product_prod_a_a) (Y4 tptp.product_prod_a_a) (Zs2 tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ (@ tptp.cons_P1921020637od_a_a Y4) Zs2))) (=> (@ P2 Zs2) (=> (@ P2 _let_1) (@ P2 (@ (@ tptp.cons_P1921020637od_a_a X4) _let_1)))))) (@ P2 Xs2))))))
% 0.25/0.65 (assert (forall ((P2 (-> tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a Bool)) (A0 tptp.list_P1467822637od_a_a) (A1 tptp.list_P1467822637od_a_a)) (=> (forall ((X_1 tptp.list_P1467822637od_a_a)) (@ (@ P2 tptp.nil_Product_prod_a_a) X_1)) (=> (forall ((X4 tptp.product_prod_a_a) (Xs4 tptp.list_P1467822637od_a_a) (Ys4 tptp.list_P1467822637od_a_a)) (=> (@ (@ P2 Ys4) Xs4) (@ (@ P2 (@ (@ tptp.cons_P1921020637od_a_a X4) Xs4)) Ys4))) (@ (@ P2 A0) A1)))))
% 0.25/0.65 (assert (forall ((P2 (-> tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a Bool)) (Xs2 tptp.list_P1467822637od_a_a) (Ys2 tptp.list_P1467822637od_a_a)) (=> (@ (@ P2 tptp.nil_Product_prod_a_a) tptp.nil_Product_prod_a_a) (=> (forall ((X4 tptp.product_prod_a_a) (Xs4 tptp.list_P1467822637od_a_a)) (@ (@ P2 (@ (@ tptp.cons_P1921020637od_a_a X4) Xs4)) tptp.nil_Product_prod_a_a)) (=> (forall ((Y4 tptp.product_prod_a_a) (Ys4 tptp.list_P1467822637od_a_a)) (@ (@ P2 tptp.nil_Product_prod_a_a) (@ (@ tptp.cons_P1921020637od_a_a Y4) Ys4))) (=> (forall ((X4 tptp.product_prod_a_a) (Xs4 tptp.list_P1467822637od_a_a) (Y4 tptp.product_prod_a_a) (Ys4 tptp.list_P1467822637od_a_a)) (=> (@ (@ P2 Xs4) Ys4) (@ (@ P2 (@ (@ tptp.cons_P1921020637od_a_a X4) Xs4)) (@ (@ tptp.cons_P1921020637od_a_a Y4) Ys4)))) (@ (@ P2 Xs2) Ys2)))))))
% 0.25/0.65 (assert (forall ((Xs2 tptp.list_P1467822637od_a_a)) (= (not (= Xs2 tptp.nil_Product_prod_a_a)) (exists ((Y tptp.product_prod_a_a) (Ys tptp.list_P1467822637od_a_a)) (= Xs2 (@ (@ tptp.cons_P1921020637od_a_a Y) Ys))))))
% 0.25/0.65 (assert (forall ((P2 (-> tptp.list_P1467822637od_a_a Bool)) (List tptp.list_P1467822637od_a_a)) (=> (@ P2 tptp.nil_Product_prod_a_a) (=> (forall ((X12 tptp.product_prod_a_a) (X23 tptp.list_P1467822637od_a_a)) (=> (@ P2 X23) (@ P2 (@ (@ tptp.cons_P1921020637od_a_a X12) X23)))) (@ P2 List)))))
% 0.25/0.65 (assert (forall ((Y3 tptp.list_P1467822637od_a_a)) (=> (not (= Y3 tptp.nil_Product_prod_a_a)) (not (forall ((X212 tptp.product_prod_a_a) (X222 tptp.list_P1467822637od_a_a)) (not (= Y3 (@ (@ tptp.cons_P1921020637od_a_a X212) X222))))))))
% 0.25/0.65 (assert (forall ((List tptp.list_P1467822637od_a_a) (X21 tptp.product_prod_a_a) (X22 tptp.list_P1467822637od_a_a)) (=> (= List (@ (@ tptp.cons_P1921020637od_a_a X21) X22)) (not (= List tptp.nil_Product_prod_a_a)))))
% 0.25/0.65 (assert (forall ((X21 tptp.product_prod_a_a) (X22 tptp.list_P1467822637od_a_a)) (not (= tptp.nil_Product_prod_a_a (@ (@ tptp.cons_P1921020637od_a_a X21) X22)))))
% 0.25/0.65 (assert (forall ((A tptp.list_P1467822637od_a_a)) (= (@ (@ tptp.append1574001858od_a_a tptp.nil_Product_prod_a_a) A) A)))
% 0.25/0.65 (assert (forall ((Ys2 tptp.list_P1467822637od_a_a)) (= (@ (@ tptp.append1574001858od_a_a tptp.nil_Product_prod_a_a) Ys2) Ys2)))
% 0.25/0.65 (assert (forall ((Xs2 tptp.list_P1467822637od_a_a) (Ys2 tptp.list_P1467822637od_a_a)) (=> (= Xs2 Ys2) (= Xs2 (@ (@ tptp.append1574001858od_a_a tptp.nil_Product_prod_a_a) Ys2)))))
% 0.25/0.65 (assert (forall ((X3 tptp.produc1197928545_a_a_a)) (=> (forall ((U2 tptp.a) (V tptp.a)) (not (= X3 (@ (@ tptp.produc1440321489_a_a_a U2) (@ (@ tptp.produc998622632_a_a_a tptp.nil_Product_prod_a_a) V))))) (not (forall ((U2 tptp.a) (E2 tptp.product_prod_a_a) (Es tptp.list_P1467822637od_a_a) (V tptp.a)) (not (= X3 (@ (@ tptp.produc1440321489_a_a_a U2) (@ (@ tptp.produc998622632_a_a_a (@ (@ tptp.cons_P1921020637od_a_a E2) Es)) V)))))))))
% 0.25/0.65 (assert (@ tptp.kurato1072996284sing_a tptp.nil_Product_prod_a_a))
% 0.25/0.65 (assert (forall ((Xs2 tptp.list_P1467822637od_a_a) (P2 (-> tptp.product_prod_a_a Bool))) (= (exists ((X tptp.product_prod_a_a)) (and (@ (@ tptp.member449909584od_a_a X) (@ tptp.set_Product_prod_a_a2 Xs2)) (@ P2 X))) (exists ((Ys tptp.list_P1467822637od_a_a) (X tptp.product_prod_a_a)) (and (exists ((Zs3 tptp.list_P1467822637od_a_a)) (= Xs2 (@ (@ tptp.append1574001858od_a_a Ys) (@ (@ tptp.cons_P1921020637od_a_a X) Zs3)))) (@ P2 X) (forall ((Y tptp.product_prod_a_a)) (=> (@ (@ tptp.member449909584od_a_a Y) (@ tptp.set_Product_prod_a_a2 Ys)) (not (@ P2 Y)))))))))
% 0.25/0.65 (assert (forall ((Xs2 tptp.list_P1467822637od_a_a) (P2 (-> tptp.product_prod_a_a Bool))) (= (exists ((X tptp.product_prod_a_a)) (and (@ (@ tptp.member449909584od_a_a X) (@ tptp.set_Product_prod_a_a2 Xs2)) (@ P2 X))) (exists ((Ys tptp.list_P1467822637od_a_a) (X tptp.product_prod_a_a) (Zs3 tptp.list_P1467822637od_a_a)) (and (= Xs2 (@ (@ tptp.append1574001858od_a_a Ys) (@ (@ tptp.cons_P1921020637od_a_a X) Zs3))) (@ P2 X) (forall ((Y tptp.product_prod_a_a)) (=> (@ (@ tptp.member449909584od_a_a Y) (@ tptp.set_Product_prod_a_a2 Zs3)) (not (@ P2 Y)))))))))
% 0.25/0.65 (assert (forall ((X3 tptp.product_prod_a_a) (Xs2 tptp.list_P1467822637od_a_a)) (= (@ (@ tptp.member449909584od_a_a X3) (@ tptp.set_Product_prod_a_a2 Xs2)) (exists ((Ys tptp.list_P1467822637od_a_a) (Zs3 tptp.list_P1467822637od_a_a)) (and (= Xs2 (@ (@ tptp.append1574001858od_a_a Ys) (@ (@ tptp.cons_P1921020637od_a_a X3) Zs3))) (not (@ (@ tptp.member449909584od_a_a X3) (@ tptp.set_Product_prod_a_a2 Ys))))))))
% 0.25/0.65 (assert (forall ((X3 tptp.product_prod_a_a) (Xs2 tptp.list_P1467822637od_a_a)) (= (@ (@ tptp.member449909584od_a_a X3) (@ tptp.set_Product_prod_a_a2 Xs2)) (exists ((Ys tptp.list_P1467822637od_a_a) (Zs3 tptp.list_P1467822637od_a_a)) (and (= Xs2 (@ (@ tptp.append1574001858od_a_a Ys) (@ (@ tptp.cons_P1921020637od_a_a X3) Zs3))) (not (@ (@ tptp.member449909584od_a_a X3) (@ tptp.set_Product_prod_a_a2 Zs3))))))))
% 0.25/0.65 (assert (forall ((Xs2 tptp.list_P1467822637od_a_a) (P2 (-> tptp.product_prod_a_a Bool))) (=> (exists ((X5 tptp.product_prod_a_a)) (and (@ (@ tptp.member449909584od_a_a X5) (@ tptp.set_Product_prod_a_a2 Xs2)) (@ P2 X5))) (not (forall ((Ys4 tptp.list_P1467822637od_a_a) (X4 tptp.product_prod_a_a)) (=> (exists ((Zs2 tptp.list_P1467822637od_a_a)) (= Xs2 (@ (@ tptp.append1574001858od_a_a Ys4) (@ (@ tptp.cons_P1921020637od_a_a X4) Zs2)))) (=> (@ P2 X4) (not (forall ((Xa tptp.product_prod_a_a)) (=> (@ (@ tptp.member449909584od_a_a Xa) (@ tptp.set_Product_prod_a_a2 Ys4)) (not (@ P2 Xa))))))))))))
% 0.25/0.65 (assert (forall ((Xs2 tptp.list_P1467822637od_a_a) (P2 (-> tptp.product_prod_a_a Bool))) (=> (exists ((X5 tptp.product_prod_a_a)) (and (@ (@ tptp.member449909584od_a_a X5) (@ tptp.set_Product_prod_a_a2 Xs2)) (@ P2 X5))) (not (forall ((Ys4 tptp.list_P1467822637od_a_a) (X4 tptp.product_prod_a_a) (Zs2 tptp.list_P1467822637od_a_a)) (=> (= Xs2 (@ (@ tptp.append1574001858od_a_a Ys4) (@ (@ tptp.cons_P1921020637od_a_a X4) Zs2))) (=> (@ P2 X4) (not (forall ((Xa tptp.product_prod_a_a)) (=> (@ (@ tptp.member449909584od_a_a Xa) (@ tptp.set_Product_prod_a_a2 Zs2)) (not (@ P2 Xa))))))))))))
% 0.25/0.65 (assert (forall ((Xs2 tptp.list_P1467822637od_a_a) (P2 (-> tptp.product_prod_a_a Bool))) (=> (exists ((X5 tptp.product_prod_a_a)) (and (@ (@ tptp.member449909584od_a_a X5) (@ tptp.set_Product_prod_a_a2 Xs2)) (@ P2 X5))) (exists ((Ys4 tptp.list_P1467822637od_a_a) (X4 tptp.product_prod_a_a)) (and (exists ((Zs2 tptp.list_P1467822637od_a_a)) (= Xs2 (@ (@ tptp.append1574001858od_a_a Ys4) (@ (@ tptp.cons_P1921020637od_a_a X4) Zs2)))) (@ P2 X4) (forall ((Xa tptp.product_prod_a_a)) (=> (@ (@ tptp.member449909584od_a_a Xa) (@ tptp.set_Product_prod_a_a2 Ys4)) (not (@ P2 Xa)))))))))
% 0.25/0.65 (assert (forall ((Xs2 tptp.list_P1467822637od_a_a) (P2 (-> tptp.product_prod_a_a Bool))) (=> (exists ((X5 tptp.product_prod_a_a)) (and (@ (@ tptp.member449909584od_a_a X5) (@ tptp.set_Product_prod_a_a2 Xs2)) (@ P2 X5))) (exists ((Ys4 tptp.list_P1467822637od_a_a) (X4 tptp.product_prod_a_a) (Zs2 tptp.list_P1467822637od_a_a)) (and (= Xs2 (@ (@ tptp.append1574001858od_a_a Ys4) (@ (@ tptp.cons_P1921020637od_a_a X4) Zs2))) (@ P2 X4) (forall ((Xa tptp.product_prod_a_a)) (=> (@ (@ tptp.member449909584od_a_a Xa) (@ tptp.set_Product_prod_a_a2 Zs2)) (not (@ P2 Xa)))))))))
% 0.25/0.65 (assert (forall ((X3 tptp.product_prod_a_a) (Xs2 tptp.list_P1467822637od_a_a)) (= (@ (@ tptp.member449909584od_a_a X3) (@ tptp.set_Product_prod_a_a2 Xs2)) (exists ((Ys tptp.list_P1467822637od_a_a) (Zs3 tptp.list_P1467822637od_a_a)) (= Xs2 (@ (@ tptp.append1574001858od_a_a Ys) (@ (@ tptp.cons_P1921020637od_a_a X3) Zs3)))))))
% 0.25/0.65 (assert (forall ((X3 tptp.product_prod_a_a) (Xs2 tptp.list_P1467822637od_a_a) (Ys2 tptp.list_P1467822637od_a_a) (Xs5 tptp.list_P1467822637od_a_a) (Ys5 tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ tptp.cons_P1921020637od_a_a X3))) (let ((_let_2 (@ tptp.member449909584od_a_a X3))) (=> (not (@ _let_2 (@ tptp.set_Product_prod_a_a2 Xs2))) (=> (not (@ _let_2 (@ tptp.set_Product_prod_a_a2 Ys2))) (= (= (@ (@ tptp.append1574001858od_a_a Xs2) (@ _let_1 Ys2)) (@ (@ tptp.append1574001858od_a_a Xs5) (@ _let_1 Ys5))) (and (= Xs2 Xs5) (= Ys2 Ys5)))))))))
% 0.25/0.65 (assert (forall ((Xs2 tptp.list_P1467822637od_a_a) (P2 (-> tptp.product_prod_a_a Bool))) (=> (exists ((X5 tptp.product_prod_a_a)) (and (@ (@ tptp.member449909584od_a_a X5) (@ tptp.set_Product_prod_a_a2 Xs2)) (@ P2 X5))) (not (forall ((Ys4 tptp.list_P1467822637od_a_a) (X4 tptp.product_prod_a_a)) (=> (exists ((Zs2 tptp.list_P1467822637od_a_a)) (= Xs2 (@ (@ tptp.append1574001858od_a_a Ys4) (@ (@ tptp.cons_P1921020637od_a_a X4) Zs2)))) (not (@ P2 X4))))))))
% 0.25/0.65 (assert (forall ((X3 tptp.product_prod_a_a) (Xs2 tptp.list_P1467822637od_a_a)) (=> (@ (@ tptp.member449909584od_a_a X3) (@ tptp.set_Product_prod_a_a2 Xs2)) (exists ((Ys4 tptp.list_P1467822637od_a_a) (Zs2 tptp.list_P1467822637od_a_a)) (and (= Xs2 (@ (@ tptp.append1574001858od_a_a Ys4) (@ (@ tptp.cons_P1921020637od_a_a X3) Zs2))) (not (@ (@ tptp.member449909584od_a_a X3) (@ tptp.set_Product_prod_a_a2 Ys4))))))))
% 0.25/0.65 (assert (forall ((Xs2 tptp.list_P1467822637od_a_a) (P2 (-> tptp.product_prod_a_a Bool))) (=> (exists ((X5 tptp.product_prod_a_a)) (and (@ (@ tptp.member449909584od_a_a X5) (@ tptp.set_Product_prod_a_a2 Xs2)) (@ P2 X5))) (exists ((Ys4 tptp.list_P1467822637od_a_a) (X4 tptp.product_prod_a_a)) (and (exists ((Zs2 tptp.list_P1467822637od_a_a)) (= Xs2 (@ (@ tptp.append1574001858od_a_a Ys4) (@ (@ tptp.cons_P1921020637od_a_a X4) Zs2)))) (@ P2 X4))))))
% 0.25/0.65 (assert (forall ((X3 tptp.product_prod_a_a) (Xs2 tptp.list_P1467822637od_a_a)) (=> (@ (@ tptp.member449909584od_a_a X3) (@ tptp.set_Product_prod_a_a2 Xs2)) (exists ((Ys4 tptp.list_P1467822637od_a_a) (Zs2 tptp.list_P1467822637od_a_a)) (and (= Xs2 (@ (@ tptp.append1574001858od_a_a Ys4) (@ (@ tptp.cons_P1921020637od_a_a X3) Zs2))) (not (@ (@ tptp.member449909584od_a_a X3) (@ tptp.set_Product_prod_a_a2 Zs2))))))))
% 0.25/0.65 (assert (forall ((X3 tptp.product_prod_a_a) (Xs2 tptp.list_P1467822637od_a_a)) (=> (@ (@ tptp.member449909584od_a_a X3) (@ tptp.set_Product_prod_a_a2 Xs2)) (exists ((Ys4 tptp.list_P1467822637od_a_a) (Zs2 tptp.list_P1467822637od_a_a)) (= Xs2 (@ (@ tptp.append1574001858od_a_a Ys4) (@ (@ tptp.cons_P1921020637od_a_a X3) Zs2)))))))
% 0.25/0.65 (assert (forall ((Xs2 tptp.list_P1467822637od_a_a) (P2 (-> tptp.list_P1467822637od_a_a Bool))) (=> (not (= Xs2 tptp.nil_Product_prod_a_a)) (=> (forall ((X4 tptp.product_prod_a_a)) (@ P2 (@ (@ tptp.cons_P1921020637od_a_a X4) tptp.nil_Product_prod_a_a))) (=> (forall ((X4 tptp.product_prod_a_a) (Xs4 tptp.list_P1467822637od_a_a)) (=> (not (= Xs4 tptp.nil_Product_prod_a_a)) (=> (@ P2 Xs4) (@ P2 (@ (@ tptp.append1574001858od_a_a Xs4) (@ (@ tptp.cons_P1921020637od_a_a X4) tptp.nil_Product_prod_a_a)))))) (@ P2 Xs2))))))
% 0.25/0.65 (assert (forall ((Ys2 tptp.list_P1467822637od_a_a) (Zs tptp.list_P1467822637od_a_a) (X3 tptp.product_prod_a_a) (Xs2 tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ (@ tptp.cons_P1921020637od_a_a X3) Xs2))) (= (= (@ (@ tptp.append1574001858od_a_a Ys2) Zs) _let_1) (or (and (= Ys2 tptp.nil_Product_prod_a_a) (= Zs _let_1)) (exists ((Ys6 tptp.list_P1467822637od_a_a)) (and (= Ys2 (@ (@ tptp.cons_P1921020637od_a_a X3) Ys6)) (= (@ (@ tptp.append1574001858od_a_a Ys6) Zs) Xs2))))))))
% 0.25/0.65 (assert (forall ((X3 tptp.product_prod_a_a) (Xs2 tptp.list_P1467822637od_a_a) (Ys2 tptp.list_P1467822637od_a_a) (Zs tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ (@ tptp.cons_P1921020637od_a_a X3) Xs2))) (= (= _let_1 (@ (@ tptp.append1574001858od_a_a Ys2) Zs)) (or (and (= Ys2 tptp.nil_Product_prod_a_a) (= _let_1 Zs)) (exists ((Ys6 tptp.list_P1467822637od_a_a)) (and (= (@ (@ tptp.cons_P1921020637od_a_a X3) Ys6) Ys2) (= Xs2 (@ (@ tptp.append1574001858od_a_a Ys6) Zs)))))))))
% 0.25/0.65 (assert (forall ((Xs2 tptp.list_P1467822637od_a_a)) (=> (not (= Xs2 tptp.nil_Product_prod_a_a)) (not (forall ((Ys4 tptp.list_P1467822637od_a_a) (Y4 tptp.product_prod_a_a)) (not (= Xs2 (@ (@ tptp.append1574001858od_a_a Ys4) (@ (@ tptp.cons_P1921020637od_a_a Y4) tptp.nil_Product_prod_a_a)))))))))
% 0.25/0.65 (assert (forall ((P2 (-> tptp.list_P1467822637od_a_a Bool)) (Xs2 tptp.list_P1467822637od_a_a)) (=> (@ P2 tptp.nil_Product_prod_a_a) (=> (forall ((X4 tptp.product_prod_a_a) (Xs4 tptp.list_P1467822637od_a_a)) (=> (@ P2 Xs4) (@ P2 (@ (@ tptp.append1574001858od_a_a Xs4) (@ (@ tptp.cons_P1921020637od_a_a X4) tptp.nil_Product_prod_a_a))))) (@ P2 Xs2)))))
% 0.25/0.65 (assert (forall ((X3 tptp.produc651658087od_a_a)) (=> (forall ((Ys4 tptp.list_P1467822637od_a_a)) (not (= X3 (@ (@ tptp.produc85179863od_a_a tptp.nil_Product_prod_a_a) Ys4)))) (=> (forall ((Xs4 tptp.list_P1467822637od_a_a)) (not (= X3 (@ (@ tptp.produc85179863od_a_a Xs4) tptp.nil_Product_prod_a_a)))) (not (forall ((X4 tptp.product_prod_a_a) (Xs4 tptp.list_P1467822637od_a_a) (Y4 tptp.product_prod_a_a) (Ys4 tptp.list_P1467822637od_a_a)) (not (= X3 (@ (@ tptp.produc85179863od_a_a (@ (@ tptp.cons_P1921020637od_a_a X4) Xs4)) (@ (@ tptp.cons_P1921020637od_a_a Y4) Ys4))))))))))
% 0.25/0.65 (assert (forall ((P2 (-> tptp.product_prod_a_a tptp.a tptp.list_P1467822637od_a_a Bool)) (A0 tptp.product_prod_a_a) (A1 tptp.a) (A22 tptp.list_P1467822637od_a_a)) (=> (forall ((Uu tptp.product_prod_a_a) (Uv tptp.a)) (@ (@ (@ P2 Uu) Uv) tptp.nil_Product_prod_a_a)) (=> (forall ((U2 tptp.a) (V tptp.a) (W tptp.a) (E2 tptp.product_prod_a_a) (Es tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ (@ P2 (@ (@ tptp.product_Pair_a_a U2) V)) W))) (=> (@ _let_1 Es) (@ _let_1 (@ (@ tptp.cons_P1921020637od_a_a E2) Es))))) (@ (@ (@ P2 A0) A1) A22)))))
% 0.25/0.65 (assert (forall ((P2 (-> tptp.product_prod_a_a tptp.a tptp.list_P1467822637od_a_a Bool)) (A0 tptp.product_prod_a_a) (A1 tptp.a) (A22 tptp.list_P1467822637od_a_a)) (=> (forall ((Uu tptp.product_prod_a_a) (Uv tptp.a)) (@ (@ (@ P2 Uu) Uv) tptp.nil_Product_prod_a_a)) (=> (forall ((Uw tptp.product_prod_a_a) (Ux tptp.a) (E2 tptp.product_prod_a_a)) (@ (@ (@ P2 Uw) Ux) (@ (@ tptp.cons_P1921020637od_a_a E2) tptp.nil_Product_prod_a_a))) (=> (forall ((U2 tptp.a) (V tptp.a) (W tptp.a) (E1 tptp.product_prod_a_a) (E22 tptp.product_prod_a_a) (Es tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ (@ tptp.cons_P1921020637od_a_a E22) Es))) (let ((_let_2 (@ tptp.product_Pair_a_a U2))) (let ((_let_3 (@ (@ P2 (@ _let_2 V)) W))) (let ((_let_4 (@ tptp.product_Pair_a_a W))) (let ((_let_5 (and (= E1 (@ (@ tptp.product_Pair_a_a V) W)) (= E22 (@ _let_4 U2))))) (let ((_let_6 (and (= E1 (@ _let_2 W)) (= E22 (@ _let_4 V))))) (let ((_let_7 (not _let_6))) (let ((_let_8 (@ _let_3 Es))) (=> (=> _let_6 _let_8) (=> (=> _let_7 (=> _let_5 _let_8)) (=> (=> _let_7 (=> (not _let_5) (@ _let_3 _let_1))) (@ _let_3 (@ (@ tptp.cons_P1921020637od_a_a E1) _let_1)))))))))))))) (@ (@ (@ P2 A0) A1) A22))))))
% 0.25/0.65 (assert (forall ((X3 tptp.produc821581462od_a_a)) (=> (forall ((Uu tptp.product_prod_a_a) (Uv tptp.a)) (not (= X3 (@ (@ tptp.produc600870406od_a_a Uu) (@ (@ tptp.produc575024326od_a_a Uv) tptp.nil_Product_prod_a_a))))) (not (forall ((U2 tptp.a) (V tptp.a) (W tptp.a) (E2 tptp.product_prod_a_a) (Es tptp.list_P1467822637od_a_a)) (not (= X3 (@ (@ tptp.produc600870406od_a_a (@ (@ tptp.product_Pair_a_a U2) V)) (@ (@ tptp.produc575024326od_a_a W) (@ (@ tptp.cons_P1921020637od_a_a E2) Es))))))))))
% 0.25/0.65 (assert (forall ((X3 tptp.produc821581462od_a_a)) (=> (forall ((Uu tptp.product_prod_a_a) (Uv tptp.a)) (not (= X3 (@ (@ tptp.produc600870406od_a_a Uu) (@ (@ tptp.produc575024326od_a_a Uv) tptp.nil_Product_prod_a_a))))) (=> (forall ((Uw tptp.product_prod_a_a) (Ux tptp.a) (E2 tptp.product_prod_a_a)) (not (= X3 (@ (@ tptp.produc600870406od_a_a Uw) (@ (@ tptp.produc575024326od_a_a Ux) (@ (@ tptp.cons_P1921020637od_a_a E2) tptp.nil_Product_prod_a_a)))))) (not (forall ((U2 tptp.a) (V tptp.a) (W tptp.a) (E1 tptp.product_prod_a_a) (E22 tptp.product_prod_a_a) (Es tptp.list_P1467822637od_a_a)) (not (= X3 (@ (@ tptp.produc600870406od_a_a (@ (@ tptp.product_Pair_a_a U2) V)) (@ (@ tptp.produc575024326od_a_a W) (@ (@ tptp.cons_P1921020637od_a_a E1) (@ (@ tptp.cons_P1921020637od_a_a E22) Es))))))))))))
% 0.25/0.65 (assert (forall ((Ys2 tptp.list_P1467822637od_a_a) (Zs tptp.list_P1467822637od_a_a) (R tptp.set_Pr1948701895od_a_a) (Xs2 tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ tptp.lex_Product_prod_a_a R))) (let ((_let_2 (@ tptp.append1574001858od_a_a Xs2))) (=> (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a Ys2) Zs)) _let_1) (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a (@ _let_2 Ys2)) (@ _let_2 Zs))) _let_1))))))
% 0.25/0.65 (assert (forall ((E tptp.product_prod_a_a)) (@ tptp.kurato1072996284sing_a (@ (@ tptp.cons_P1921020637od_a_a E) tptp.nil_Product_prod_a_a))))
% 0.25/0.65 (assert (forall ((Xs2 tptp.list_a) (R tptp.set_Product_prod_a_a) (Ys2 tptp.list_a) (Zs tptp.list_a)) (let ((_let_1 (@ tptp.lexord_a R))) (let ((_let_2 (@ tptp.produc1448356631list_a Xs2))) (=> (forall ((X4 tptp.a) (Y4 tptp.a) (Z2 tptp.a)) (let ((_let_1 (@ tptp.product_Pair_a_a X4))) (=> (@ (@ tptp.member_a2 X4) (@ tptp.set_a2 Xs2)) (=> (@ (@ tptp.member449909584od_a_a (@ _let_1 Y4)) R) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a Y4) Z2)) R) (@ (@ tptp.member449909584od_a_a (@ _let_1 Z2)) R)))))) (=> (@ (@ tptp.member1250517072list_a (@ _let_2 Ys2)) _let_1) (=> (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a Ys2) Zs)) _let_1) (@ (@ tptp.member1250517072list_a (@ _let_2 Zs)) _let_1))))))))
% 0.25/0.65 (assert (forall ((Xs2 tptp.list_P1467822637od_a_a) (Zs tptp.list_P1467822637od_a_a) (Ys2 tptp.list_P1467822637od_a_a) (Qs tptp.list_P1467822637od_a_a) (R tptp.set_Pr1948701895od_a_a)) (let ((_let_1 (@ tptp.lexord673907738od_a_a R))) (=> (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a (@ (@ tptp.append1574001858od_a_a Xs2) Zs)) (@ (@ tptp.append1574001858od_a_a Ys2) Qs))) _let_1) (=> (not (= Xs2 Ys2)) (=> (= (@ tptp.size_s642698393od_a_a Xs2) (@ tptp.size_s642698393od_a_a Ys2)) (=> (= (@ tptp.size_s642698393od_a_a Zs) (@ tptp.size_s642698393od_a_a Qs)) (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a Xs2) Ys2)) _let_1))))))))
% 0.25/0.65 (assert (forall ((X3 tptp.produc651658087od_a_a)) (=> (forall ((Ys4 tptp.list_P1467822637od_a_a)) (not (= X3 (@ (@ tptp.produc85179863od_a_a tptp.nil_Product_prod_a_a) Ys4)))) (not (forall ((X4 tptp.product_prod_a_a) (Xs4 tptp.list_P1467822637od_a_a) (Ys4 tptp.list_P1467822637od_a_a)) (not (= X3 (@ (@ tptp.produc85179863od_a_a (@ (@ tptp.cons_P1921020637od_a_a X4) Xs4)) Ys4))))))))
% 0.25/0.65 (assert (forall ((X3 tptp.set_Product_prod_a_a) (P2 (-> tptp.set_Product_prod_a_a Bool))) (=> (@ tptp.asym_a X3) (=> (forall ((R3 tptp.set_Product_prod_a_a)) (=> (forall ((A6 tptp.a) (B4 tptp.a)) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a A6) B4)) R3) (not (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a B4) A6)) R3)))) (@ P2 R3))) (@ P2 X3)))))
% 0.25/0.65 (assert (forall ((R2 tptp.set_Product_prod_a_a)) (=> (forall ((A3 tptp.a) (B3 tptp.a)) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a A3) B3)) R2) (not (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a B3) A3)) R2)))) (@ tptp.asym_a R2))))
% 0.25/0.65 (assert (= tptp.asym_a (lambda ((A5 tptp.set_Product_prod_a_a)) (exists ((R4 tptp.set_Product_prod_a_a)) (and (= A5 R4) (forall ((X tptp.a) (Y tptp.a)) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X) Y)) R4) (not (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a Y) X)) R4)))))))))
% 0.25/0.65 (assert (forall ((A tptp.set_Product_prod_a_a)) (=> (@ tptp.asym_a A) (forall ((A6 tptp.a) (B4 tptp.a)) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a A6) B4)) A) (not (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a B4) A6)) A)))))))
% 0.25/0.65 (assert (= tptp.asym_a (lambda ((R4 tptp.set_Product_prod_a_a)) (forall ((X tptp.a) (Y tptp.a)) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X) Y)) R4) (not (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a Y) X)) R4)))))))
% 0.25/0.65 (assert (forall ((R2 tptp.set_Product_prod_a_a)) (=> (forall ((A3 tptp.a)) (not (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a A3) A3)) R2))) (@ tptp.irrefl_a R2))))
% 0.25/0.65 (assert (= tptp.irrefl_a (lambda ((R5 tptp.set_Product_prod_a_a)) (forall ((A5 tptp.a)) (not (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a A5) A5)) R5))))))
% 0.25/0.65 (assert (forall ((R2 tptp.set_Product_prod_a_a) (X3 tptp.a) (Y3 tptp.a)) (=> (@ tptp.asym_a R2) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X3) Y3)) R2) (not (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a Y3) X3)) R2))))))
% 0.25/0.65 (assert (forall ((X3 tptp.produc657167928_a_a_a)) (=> (forall ((X4 tptp.a)) (not (= X3 (@ (@ tptp.produc998622632_a_a_a tptp.nil_Product_prod_a_a) X4)))) (not (forall ((Y4 tptp.a) (X6 tptp.a) (Xs4 tptp.list_P1467822637od_a_a) (X4 tptp.a)) (not (= X3 (@ (@ tptp.produc998622632_a_a_a (@ (@ tptp.cons_P1921020637od_a_a (@ (@ tptp.product_Pair_a_a Y4) X6)) Xs4)) X4))))))))
% 0.25/0.65 (assert (forall ((P2 (-> tptp.list_P1467822637od_a_a tptp.a Bool)) (A0 tptp.list_P1467822637od_a_a) (A1 tptp.a)) (=> (forall ((X_1 tptp.a)) (@ (@ P2 tptp.nil_Product_prod_a_a) X_1)) (=> (forall ((Y4 tptp.a) (X6 tptp.a) (Xs4 tptp.list_P1467822637od_a_a) (X4 tptp.a)) (=> (=> (not (= X4 X6)) (@ (@ P2 Xs4) X4)) (@ (@ P2 (@ (@ tptp.cons_P1921020637od_a_a (@ (@ tptp.product_Pair_a_a Y4) X6)) Xs4)) X4))) (@ (@ P2 A0) A1)))))
% 0.25/0.65 (assert (forall ((U tptp.a) (V2 tptp.a) (W2 tptp.a) (E tptp.product_prod_a_a) (Es2 tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ tptp.product_Pair_a_a U))) (let ((_let_2 (@ _let_1 V2))) (let ((_let_3 (@ (@ tptp.pair_sd_path_a _let_2) W2))) (let ((_let_4 (@ tptp.cons_P1921020637od_a_a E))) (let ((_let_5 (@ tptp.product_Pair_a_a W2))) (let ((_let_6 (@ tptp.product_Pair_a_a V2))) (= (@ _let_3 (@ _let_4 Es2)) (@ (@ tptp.append1574001858od_a_a (@ (@ (@ tptp.if_lis321365491od_a_a (= E _let_2)) (@ (@ tptp.cons_P1921020637od_a_a (@ _let_1 W2)) (@ (@ tptp.cons_P1921020637od_a_a (@ _let_5 V2)) tptp.nil_Product_prod_a_a))) (@ (@ (@ tptp.if_lis321365491od_a_a (= E (@ _let_6 U))) (@ (@ tptp.cons_P1921020637od_a_a (@ _let_6 W2)) (@ (@ tptp.cons_P1921020637od_a_a (@ _let_5 U)) tptp.nil_Product_prod_a_a))) (@ _let_4 tptp.nil_Product_prod_a_a)))) (@ _let_3 Es2)))))))))))
% 0.25/0.65 (assert (forall ((X3 tptp.a) (Y3 tptp.a) (P3 tptp.list_P1467822637od_a_a) (W2 tptp.a)) (let ((_let_1 (@ (@ tptp.product_Pair_a_a X3) Y3))) (let ((_let_2 (@ tptp.set_Product_prod_a_a2 P3))) (=> (not (@ (@ tptp.member449909584od_a_a _let_1) _let_2)) (=> (not (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a Y3) X3)) _let_2)) (= (@ (@ (@ tptp.pair_sd_path_a _let_1) W2) P3) P3)))))))
% 0.25/0.65 (assert (forall ((X3 tptp.product_prod_a_a) (Xa2 tptp.a) (Xb tptp.list_P1467822637od_a_a) (Y3 tptp.list_P1467822637od_a_a)) (=> (= (@ (@ (@ tptp.pair_sd_path_a X3) Xa2) Xb) Y3) (=> (=> (= Xb tptp.nil_Product_prod_a_a) (not (= Y3 tptp.nil_Product_prod_a_a))) (not (forall ((U2 tptp.a) (V tptp.a)) (=> (= X3 (@ (@ tptp.product_Pair_a_a U2) V)) (forall ((E2 tptp.product_prod_a_a) (Es tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ tptp.product_Pair_a_a U2))) (let ((_let_2 (@ _let_1 V))) (let ((_let_3 (@ tptp.cons_P1921020637od_a_a E2))) (let ((_let_4 (@ tptp.product_Pair_a_a Xa2))) (let ((_let_5 (@ tptp.product_Pair_a_a V))) (=> (= Xb (@ _let_3 Es)) (not (= Y3 (@ (@ tptp.append1574001858od_a_a (@ (@ (@ tptp.if_lis321365491od_a_a (= E2 _let_2)) (@ (@ tptp.cons_P1921020637od_a_a (@ _let_1 Xa2)) (@ (@ tptp.cons_P1921020637od_a_a (@ _let_4 V)) tptp.nil_Product_prod_a_a))) (@ (@ (@ tptp.if_lis321365491od_a_a (= E2 (@ _let_5 U2))) (@ (@ tptp.cons_P1921020637od_a_a (@ _let_5 Xa2)) (@ (@ tptp.cons_P1921020637od_a_a (@ _let_4 U2)) tptp.nil_Product_prod_a_a))) (@ _let_3 tptp.nil_Product_prod_a_a)))) (@ (@ (@ tptp.pair_sd_path_a _let_2) Xa2) Es))))))))))))))))))
% 0.25/0.65 (assert (forall ((X3 tptp.product_prod_a_a)) (= (@ tptp.the_el1640649244od_a_a (@ tptp.set_Product_prod_a_a2 (@ (@ tptp.cons_P1921020637od_a_a X3) tptp.nil_Product_prod_a_a))) X3)))
% 0.25/0.65 (assert (forall ((X3 tptp.product_prod_a_a) (Xa2 tptp.a) (Xb tptp.list_P1467822637od_a_a) (Y3 tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ tptp.produc575024326od_a_a Xa2))) (let ((_let_2 (@ tptp.produc600870406od_a_a X3))) (let ((_let_3 (@ tptp.accp_P1029463583od_a_a tptp.pair_sd_path_rel_a))) (=> (= (@ (@ (@ tptp.pair_sd_path_a X3) Xa2) Xb) Y3) (=> (@ _let_3 (@ _let_2 (@ _let_1 Xb))) (=> (=> (= Xb tptp.nil_Product_prod_a_a) (=> (= Y3 tptp.nil_Product_prod_a_a) (not (@ _let_3 (@ _let_2 (@ _let_1 tptp.nil_Product_prod_a_a)))))) (not (forall ((U2 tptp.a) (V tptp.a)) (=> (= X3 (@ (@ tptp.product_Pair_a_a U2) V)) (forall ((E2 tptp.product_prod_a_a) (Es tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ tptp.cons_P1921020637od_a_a E2))) (let ((_let_2 (@ _let_1 Es))) (let ((_let_3 (@ tptp.product_Pair_a_a U2))) (let ((_let_4 (@ _let_3 V))) (let ((_let_5 (@ tptp.product_Pair_a_a Xa2))) (let ((_let_6 (@ tptp.product_Pair_a_a V))) (=> (= Xb _let_2) (=> (= Y3 (@ (@ tptp.append1574001858od_a_a (@ (@ (@ tptp.if_lis321365491od_a_a (= E2 _let_4)) (@ (@ tptp.cons_P1921020637od_a_a (@ _let_3 Xa2)) (@ (@ tptp.cons_P1921020637od_a_a (@ _let_5 V)) tptp.nil_Product_prod_a_a))) (@ (@ (@ tptp.if_lis321365491od_a_a (= E2 (@ _let_6 U2))) (@ (@ tptp.cons_P1921020637od_a_a (@ _let_6 Xa2)) (@ (@ tptp.cons_P1921020637od_a_a (@ _let_5 U2)) tptp.nil_Product_prod_a_a))) (@ _let_1 tptp.nil_Product_prod_a_a)))) (@ (@ (@ tptp.pair_sd_path_a _let_4) Xa2) Es))) (not (@ (@ tptp.accp_P1029463583od_a_a tptp.pair_sd_path_rel_a) (@ (@ tptp.produc600870406od_a_a _let_4) (@ (@ tptp.produc575024326od_a_a Xa2) _let_2))))))))))))))))))))))))
% 0.25/0.65 (assert (forall ((Y3 tptp.list_P1467822637od_a_a) (Ya tptp.list_P1467822637od_a_a)) (let ((_let_1 (not (= Ya tptp.nil_Product_prod_a_a)))) (let ((_let_2 (= Y3 tptp.nil_Product_prod_a_a))) (=> (=> _let_2 _let_1) (=> (=> _let_2 (forall ((X212 tptp.product_prod_a_a) (X222 tptp.list_P1467822637od_a_a)) (not (= Ya (@ (@ tptp.cons_P1921020637od_a_a X212) X222))))) (=> (=> (exists ((X212 tptp.product_prod_a_a) (X222 tptp.list_P1467822637od_a_a)) (= Y3 (@ (@ tptp.cons_P1921020637od_a_a X212) X222))) _let_1) (not (=> (exists ((X212 tptp.product_prod_a_a) (X222 tptp.list_P1467822637od_a_a)) (= Y3 (@ (@ tptp.cons_P1921020637od_a_a X212) X222))) (forall ((X21a tptp.product_prod_a_a) (X22a tptp.list_P1467822637od_a_a)) (not (= Ya (@ (@ tptp.cons_P1921020637od_a_a X21a) X22a)))))))))))))
% 0.25/0.65 (assert (forall ((Xs2 tptp.list_P1467822637od_a_a)) (=> (not (= Xs2 tptp.nil_Product_prod_a_a)) (=> (forall ((X4 tptp.product_prod_a_a)) (not (= Xs2 (@ (@ tptp.cons_P1921020637od_a_a X4) tptp.nil_Product_prod_a_a)))) (not (forall ((X4 tptp.product_prod_a_a) (Y4 tptp.product_prod_a_a) (Ys4 tptp.list_P1467822637od_a_a)) (not (= Xs2 (@ (@ tptp.cons_P1921020637od_a_a X4) (@ (@ tptp.cons_P1921020637od_a_a Y4) Ys4))))))))))
% 0.25/0.65 (assert (forall ((R2 tptp.set_Pr1948701895od_a_a) (Us tptp.list_P1467822637od_a_a) (Xs2 tptp.list_P1467822637od_a_a) (Ys2 tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ tptp.lenlex2038501170od_a_a R2))) (let ((_let_2 (@ tptp.append1574001858od_a_a Us))) (=> (@ tptp.irrefl76447196od_a_a R2) (= (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a (@ _let_2 Xs2)) (@ _let_2 Ys2))) _let_1) (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a Xs2) Ys2)) _let_1)))))))
% 0.25/0.65 (assert (forall ((R tptp.set_Product_prod_a_a) (Xs2 tptp.list_a)) (=> (forall ((X4 tptp.a)) (not (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X4) X4)) R))) (not (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a Xs2) Xs2)) (@ tptp.lenlex_a R))))))
% 0.25/0.65 (assert (forall ((Us tptp.list_P1467822637od_a_a) (Xs2 tptp.list_P1467822637od_a_a) (R2 tptp.set_Pr1948701895od_a_a) (Vs tptp.list_P1467822637od_a_a) (Ys2 tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ tptp.lenlex2038501170od_a_a R2))) (=> (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a Us) Xs2)) _let_1) (=> (= (@ tptp.size_s642698393od_a_a Vs) (@ tptp.size_s642698393od_a_a Ys2)) (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a (@ (@ tptp.append1574001858od_a_a Us) Vs)) (@ (@ tptp.append1574001858od_a_a Xs2) Ys2))) _let_1))))))
% 0.25/0.65 (assert (forall ((X3 tptp.product_prod_a_a) (Xa2 tptp.a) (Xb tptp.list_P1467822637od_a_a) (Y3 tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ tptp.produc575024326od_a_a Xa2))) (let ((_let_2 (@ tptp.produc600870406od_a_a X3))) (let ((_let_3 (@ tptp.accp_P1029463583od_a_a tptp.pair_co_path_rel_a))) (=> (= (@ (@ (@ tptp.pair_co_path_a X3) Xa2) Xb) Y3) (=> (@ _let_3 (@ _let_2 (@ _let_1 Xb))) (=> (=> (= Xb tptp.nil_Product_prod_a_a) (=> (= Y3 tptp.nil_Product_prod_a_a) (not (@ _let_3 (@ _let_2 (@ _let_1 tptp.nil_Product_prod_a_a)))))) (=> (forall ((E2 tptp.product_prod_a_a)) (let ((_let_1 (@ (@ tptp.cons_P1921020637od_a_a E2) tptp.nil_Product_prod_a_a))) (=> (= Xb _let_1) (=> (= Y3 _let_1) (not (@ (@ tptp.accp_P1029463583od_a_a tptp.pair_co_path_rel_a) (@ (@ tptp.produc600870406od_a_a X3) (@ (@ tptp.produc575024326od_a_a Xa2) _let_1)))))))) (not (forall ((U2 tptp.a) (V tptp.a)) (=> (= X3 (@ (@ tptp.product_Pair_a_a U2) V)) (forall ((E1 tptp.product_prod_a_a) (E22 tptp.product_prod_a_a) (Es tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ (@ tptp.cons_P1921020637od_a_a E22) Es))) (let ((_let_2 (@ tptp.cons_P1921020637od_a_a E1))) (let ((_let_3 (@ _let_2 _let_1))) (let ((_let_4 (@ tptp.product_Pair_a_a U2))) (let ((_let_5 (@ _let_4 V))) (let ((_let_6 (@ (@ tptp.pair_co_path_a _let_5) Xa2))) (let ((_let_7 (@ tptp.product_Pair_a_a Xa2))) (let ((_let_8 (@ tptp.product_Pair_a_a V))) (let ((_let_9 (and (= E1 (@ _let_8 Xa2)) (= E22 (@ _let_7 U2))))) (let ((_let_10 (@ _let_6 Es))) (let ((_let_11 (and (= E1 (@ _let_4 Xa2)) (= E22 (@ _let_7 V))))) (=> (= Xb _let_3) (=> (and (=> _let_11 (= Y3 (@ (@ tptp.cons_P1921020637od_a_a _let_5) _let_10))) (=> (not _let_11) (and (=> _let_9 (= Y3 (@ (@ tptp.cons_P1921020637od_a_a (@ _let_8 U2)) _let_10))) (=> (not _let_9) (= Y3 (@ _let_2 (@ _let_6 _let_1))))))) (not (@ (@ tptp.accp_P1029463583od_a_a tptp.pair_co_path_rel_a) (@ (@ tptp.produc600870406od_a_a _let_5) (@ (@ tptp.produc575024326od_a_a Xa2) _let_3))))))))))))))))))))))))))))))
% 0.25/0.65 (assert (forall ((U tptp.product_prod_a_a)) (= (@ (@ tptp.pair_p2140537249od_a_a U) tptp.nil_Pr1049924845od_a_a) (@ (@ tptp.cons_P1921020637od_a_a U) tptp.nil_Product_prod_a_a))))
% 0.25/0.65 (assert (forall ((E12 tptp.product_prod_a_a) (U tptp.a) (W2 tptp.a) (E23 tptp.product_prod_a_a) (V2 tptp.a) (Es2 tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ (@ tptp.cons_P1921020637od_a_a E23) Es2))) (let ((_let_2 (@ tptp.product_Pair_a_a U))) (let ((_let_3 (@ _let_2 V2))) (let ((_let_4 (@ (@ tptp.pair_co_path_a _let_3) W2))) (let ((_let_5 (@ tptp.cons_P1921020637od_a_a E12))) (let ((_let_6 (@ _let_4 (@ _let_5 _let_1)))) (let ((_let_7 (@ tptp.product_Pair_a_a W2))) (let ((_let_8 (@ tptp.product_Pair_a_a V2))) (let ((_let_9 (and (= E12 (@ _let_8 W2)) (= E23 (@ _let_7 U))))) (let ((_let_10 (@ _let_4 Es2))) (let ((_let_11 (and (= E12 (@ _let_2 W2)) (= E23 (@ _let_7 V2))))) (and (=> _let_11 (= _let_6 (@ (@ tptp.cons_P1921020637od_a_a _let_3) _let_10))) (=> (not _let_11) (and (=> _let_9 (= _let_6 (@ (@ tptp.cons_P1921020637od_a_a (@ _let_8 U)) _let_10))) (=> (not _let_9) (= _let_6 (@ _let_5 (@ _let_4 _let_1))))))))))))))))))))
% 0.25/0.65 (assert (forall ((Uw2 tptp.product_prod_a_a) (Ux2 tptp.a) (E tptp.product_prod_a_a)) (let ((_let_1 (@ (@ tptp.cons_P1921020637od_a_a E) tptp.nil_Product_prod_a_a))) (= (@ (@ (@ tptp.pair_co_path_a Uw2) Ux2) _let_1) _let_1))))
% 0.25/0.65 (assert (forall ((X3 tptp.product_prod_a_a) (Xa2 tptp.a) (Xb tptp.list_P1467822637od_a_a) (Y3 tptp.list_P1467822637od_a_a)) (=> (= (@ (@ (@ tptp.pair_co_path_a X3) Xa2) Xb) Y3) (=> (=> (= Xb tptp.nil_Product_prod_a_a) (not (= Y3 tptp.nil_Product_prod_a_a))) (=> (forall ((E2 tptp.product_prod_a_a)) (let ((_let_1 (@ (@ tptp.cons_P1921020637od_a_a E2) tptp.nil_Product_prod_a_a))) (=> (= Xb _let_1) (not (= Y3 _let_1))))) (not (forall ((U2 tptp.a) (V tptp.a)) (=> (= X3 (@ (@ tptp.product_Pair_a_a U2) V)) (forall ((E1 tptp.product_prod_a_a) (E22 tptp.product_prod_a_a) (Es tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ (@ tptp.cons_P1921020637od_a_a E22) Es))) (let ((_let_2 (@ tptp.product_Pair_a_a U2))) (let ((_let_3 (@ _let_2 V))) (let ((_let_4 (@ (@ tptp.pair_co_path_a _let_3) Xa2))) (let ((_let_5 (@ tptp.cons_P1921020637od_a_a E1))) (let ((_let_6 (@ tptp.product_Pair_a_a Xa2))) (let ((_let_7 (@ tptp.product_Pair_a_a V))) (let ((_let_8 (and (= E1 (@ _let_7 Xa2)) (= E22 (@ _let_6 U2))))) (let ((_let_9 (@ _let_4 Es))) (let ((_let_10 (and (= E1 (@ _let_2 Xa2)) (= E22 (@ _let_6 V))))) (=> (= Xb (@ _let_5 _let_1)) (not (and (=> _let_10 (= Y3 (@ (@ tptp.cons_P1921020637od_a_a _let_3) _let_9))) (=> (not _let_10) (and (=> _let_8 (= Y3 (@ (@ tptp.cons_P1921020637od_a_a (@ _let_7 U2)) _let_9))) (=> (not _let_8) (= Y3 (@ _let_5 (@ _let_4 _let_1))))))))))))))))))))))))))))
% 0.25/0.65 (assert (forall ((U tptp.a) (W2 tptp.a) (P3 tptp.list_P1467822637od_a_a) (V2 tptp.a)) (let ((_let_1 (@ tptp.product_Pair_a_a U))) (let ((_let_2 (@ _let_1 V2))) (let ((_let_3 (@ tptp.set_Product_prod_a_a2 P3))) (=> (not (@ (@ tptp.member449909584od_a_a (@ _let_1 W2)) _let_3)) (=> (not (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a V2) W2)) _let_3)) (= (@ (@ (@ tptp.pair_co_path_a _let_2) W2) (@ (@ (@ tptp.pair_sd_path_a _let_2) W2) P3)) P3))))))))
% 0.25/0.65 (assert (forall ((M tptp.product_prod_a_a) (Ms tptp.list_P1467822637od_a_a) (N tptp.product_prod_a_a) (Ns tptp.list_P1467822637od_a_a) (R tptp.set_Pr1948701895od_a_a)) (let ((_let_1 (@ tptp.lenlex2038501170od_a_a R))) (let ((_let_2 (@ tptp.size_s642698393od_a_a Ns))) (let ((_let_3 (@ tptp.size_s642698393od_a_a Ms))) (= (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a (@ (@ tptp.cons_P1921020637od_a_a M) Ms)) (@ (@ tptp.cons_P1921020637od_a_a N) Ns))) _let_1) (or (@ (@ tptp.ord_less_nat _let_3) _let_2) (and (= _let_3 _let_2) (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a M) N)) R)) (and (= M N) (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a Ms) Ns)) _let_1)))))))))
% 0.25/0.65 (assert (forall ((M tptp.a) (Ms tptp.list_a) (N tptp.a) (Ns tptp.list_a) (R tptp.set_Product_prod_a_a)) (let ((_let_1 (@ tptp.lenlex_a R))) (let ((_let_2 (@ tptp.size_size_list_a Ns))) (let ((_let_3 (@ tptp.size_size_list_a Ms))) (= (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a (@ (@ tptp.cons_a M) Ms)) (@ (@ tptp.cons_a N) Ns))) _let_1) (or (@ (@ tptp.ord_less_nat _let_3) _let_2) (and (= _let_3 _let_2) (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a M) N)) R)) (and (= M N) (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a Ms) Ns)) _let_1)))))))))
% 0.25/0.65 (assert (forall ((Y3 tptp.product_prod_a_a) (Ys2 tptp.list_P1467822637od_a_a) (Xs2 tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ tptp.set_li1284606018od_a_a (@ tptp.subseq2115548028od_a_a Xs2)))) (=> (@ (@ tptp.member1578987478od_a_a (@ (@ tptp.cons_P1921020637od_a_a Y3) Ys2)) _let_1) (@ (@ tptp.member1578987478od_a_a Ys2) _let_1)))))
% 0.25/0.65 (assert (forall ((X3 tptp.a) (Y3 tptp.a) (F (-> tptp.a tptp.nat)) (Fs tptp.list_a_nat)) (let ((_let_1 (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X3) Y3)))) (let ((_let_2 (@ F Y3))) (let ((_let_3 (@ F X3))) (= (@ _let_1 (@ tptp.measures_a (@ (@ tptp.cons_a_nat F) Fs))) (or (@ (@ tptp.ord_less_nat _let_3) _let_2) (and (= _let_3 _let_2) (@ _let_1 (@ tptp.measures_a Fs))))))))))
% 0.25/0.65 (assert (forall ((X3 tptp.list_P1467822637od_a_a) (Xa2 tptp.a) (Y3 tptp.a)) (=> (= (@ (@ tptp.invers1007791577list_a X3) Xa2) Y3) (=> (=> (= X3 tptp.nil_Product_prod_a_a) (not (= Y3 Xa2))) (not (forall ((Y4 tptp.a) (X6 tptp.a) (Xs4 tptp.list_P1467822637od_a_a)) (let ((_let_1 (= Xa2 X6))) (=> (= X3 (@ (@ tptp.cons_P1921020637od_a_a (@ (@ tptp.product_Pair_a_a Y4) X6)) Xs4)) (not (and (=> _let_1 (= Y3 Y4)) (=> (not _let_1) (= Y3 (@ (@ tptp.invers1007791577list_a Xs4) Xa2)))))))))))))
% 0.25/0.65 (assert (forall ((X3 tptp.a) (Y3 tptp.a)) (not (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X3) Y3)) (@ tptp.measures_a tptp.nil_a_nat)))))
% 0.25/0.65 (assert (forall ((X3 tptp.a) (X7 tptp.a) (Y5 tptp.a) (Xs2 tptp.list_P1467822637od_a_a)) (=> (not (= X3 X7)) (= (@ (@ tptp.invers1007791577list_a (@ (@ tptp.cons_P1921020637od_a_a (@ (@ tptp.product_Pair_a_a Y5) X7)) Xs2)) X3) (@ (@ tptp.invers1007791577list_a Xs2) X3)))))
% 0.25/0.65 (assert (forall ((X3 tptp.a) (X7 tptp.a) (Y3 tptp.a) (Xs2 tptp.list_P1467822637od_a_a)) (=> (= X3 X7) (= (@ (@ tptp.invers1007791577list_a (@ (@ tptp.cons_P1921020637od_a_a (@ (@ tptp.product_Pair_a_a Y3) X7)) Xs2)) X3) Y3))))
% 0.25/0.65 (assert (forall ((X3 tptp.a) (X7 tptp.a) (Y3 tptp.a) (Xs2 tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ (@ tptp.invers1007791577list_a (@ (@ tptp.cons_P1921020637od_a_a (@ (@ tptp.product_Pair_a_a Y3) X7)) Xs2)) X3))) (let ((_let_2 (= X3 X7))) (and (=> _let_2 (= _let_1 Y3)) (=> (not _let_2) (= _let_1 (@ (@ tptp.invers1007791577list_a Xs2) X3))))))))
% 0.25/0.65 (assert (forall ((F (-> tptp.a tptp.nat)) (X3 tptp.a) (Y3 tptp.a) (Fs tptp.list_a_nat)) (=> (@ (@ tptp.ord_less_nat (@ F X3)) (@ F Y3)) (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X3) Y3)) (@ tptp.measures_a (@ (@ tptp.cons_a_nat F) Fs))))))
% 0.25/0.65 (assert (forall ((Xs2 tptp.list_P1467822637od_a_a) (A4 tptp.set_a) (X3 tptp.a) (Y3 tptp.a)) (=> (@ (@ tptp.list_permutes_a Xs2) A4) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X3) Y3)) (@ tptp.set_Product_prod_a_a2 Xs2)) (= (@ (@ tptp.invers1007791577list_a Xs2) Y3) X3)))))
% 0.25/0.65 (assert (forall ((X3 tptp.a) (X7 tptp.a) (Y5 tptp.a) (Xs2 tptp.list_P1467822637od_a_a)) (=> (not (= X3 X7)) (= (@ (@ tptp.permut1422637723list_a (@ (@ tptp.cons_P1921020637od_a_a (@ (@ tptp.product_Pair_a_a X7) Y5)) Xs2)) X3) (@ (@ tptp.permut1422637723list_a Xs2) X3)))))
% 0.25/0.65 (assert (forall ((X3 tptp.a) (X7 tptp.a) (Y3 tptp.a) (Xs2 tptp.list_P1467822637od_a_a)) (=> (= X3 X7) (= (@ (@ tptp.permut1422637723list_a (@ (@ tptp.cons_P1921020637od_a_a (@ (@ tptp.product_Pair_a_a X7) Y3)) Xs2)) X3) Y3))))
% 0.25/0.65 (assert (forall ((Xs2 tptp.list_P1467822637od_a_a) (A4 tptp.set_a) (X3 tptp.a) (Y3 tptp.a)) (=> (@ (@ tptp.list_permutes_a Xs2) A4) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X3) Y3)) (@ tptp.set_Product_prod_a_a2 Xs2)) (= (@ (@ tptp.permut1422637723list_a Xs2) X3) Y3)))))
% 0.25/0.65 (assert (forall ((X3 tptp.a) (X7 tptp.a) (Y3 tptp.a) (Xs2 tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ (@ tptp.permut1422637723list_a (@ (@ tptp.cons_P1921020637od_a_a (@ (@ tptp.product_Pair_a_a X3) Y3)) Xs2)) X7))) (let ((_let_2 (= X3 X7))) (and (=> _let_2 (= _let_1 Y3)) (=> (not _let_2) (= _let_1 (@ (@ tptp.permut1422637723list_a Xs2) X7))))))))
% 0.25/0.65 (assert (forall ((X3 tptp.product_prod_a_a) (Xs2 tptp.list_P1467822637od_a_a)) (=> (not (@ (@ tptp.member449909584od_a_a X3) (@ tptp.set_Product_prod_a_a2 Xs2))) (= (@ (@ tptp.insert2123825731od_a_a X3) Xs2) (@ (@ tptp.cons_P1921020637od_a_a X3) Xs2)))))
% 0.25/0.65 (assert (forall ((X3 tptp.product_prod_a_a)) (= (@ (@ tptp.insert2123825731od_a_a X3) tptp.nil_Product_prod_a_a) (@ (@ tptp.cons_P1921020637od_a_a X3) tptp.nil_Product_prod_a_a))))
% 0.25/0.65 (assert (= tptp.insert2123825731od_a_a (lambda ((X tptp.product_prod_a_a) (Xs tptp.list_P1467822637od_a_a)) (@ (@ (@ tptp.if_lis321365491od_a_a (@ (@ tptp.member449909584od_a_a X) (@ tptp.set_Product_prod_a_a2 Xs))) Xs) (@ (@ tptp.cons_P1921020637od_a_a X) Xs)))))
% 0.25/0.65 (assert (forall ((Xss2 tptp.list_l1108175539od_a_a) (Ys2 tptp.list_P1467822637od_a_a) (Zs tptp.list_P1467822637od_a_a)) (let ((_let_1 (= Xss2 tptp.nil_li1885598003od_a_a))) (= (= (@ tptp.concat1878217064od_a_a Xss2) (@ (@ tptp.append1574001858od_a_a Ys2) Zs)) (and (=> _let_1 (and (= Ys2 tptp.nil_Product_prod_a_a) (= Zs tptp.nil_Product_prod_a_a))) (=> (not _let_1) (exists ((Xss1 tptp.list_l1108175539od_a_a) (Xs tptp.list_P1467822637od_a_a) (Xs6 tptp.list_P1467822637od_a_a) (Xss22 tptp.list_l1108175539od_a_a)) (and (= Xss2 (@ (@ tptp.append2141280328od_a_a Xss1) (@ (@ tptp.cons_l724116707od_a_a (@ (@ tptp.append1574001858od_a_a Xs) Xs6)) Xss22))) (= Ys2 (@ (@ tptp.append1574001858od_a_a (@ tptp.concat1878217064od_a_a Xss1)) Xs)) (= Zs (@ (@ tptp.append1574001858od_a_a Xs6) (@ tptp.concat1878217064od_a_a Xss22)))))))))))
% 0.25/0.65 (assert (forall ((X3 tptp.list_P1467822637od_a_a) (Xa2 tptp.a) (Y3 tptp.a)) (let ((_let_1 (@ tptp.accp_P941981633_a_a_a tptp.invers214109608_rel_a))) (=> (= (@ (@ tptp.invers1007791577list_a X3) Xa2) Y3) (=> (@ _let_1 (@ (@ tptp.produc998622632_a_a_a X3) Xa2)) (=> (=> (= X3 tptp.nil_Product_prod_a_a) (=> (= Y3 Xa2) (not (@ _let_1 (@ (@ tptp.produc998622632_a_a_a tptp.nil_Product_prod_a_a) Xa2))))) (not (forall ((Y4 tptp.a) (X6 tptp.a) (Xs4 tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ (@ tptp.cons_P1921020637od_a_a (@ (@ tptp.product_Pair_a_a Y4) X6)) Xs4))) (let ((_let_2 (= Xa2 X6))) (=> (= X3 _let_1) (=> (and (=> _let_2 (= Y3 Y4)) (=> (not _let_2) (= Y3 (@ (@ tptp.invers1007791577list_a Xs4) Xa2)))) (not (@ (@ tptp.accp_P941981633_a_a_a tptp.invers214109608_rel_a) (@ (@ tptp.produc998622632_a_a_a _let_1) Xa2)))))))))))))))
% 0.25/0.65 (assert (forall ((Xs2 tptp.list_l1108175539od_a_a) (Ys2 tptp.list_l1108175539od_a_a)) (= (@ tptp.concat1878217064od_a_a (@ (@ tptp.append2141280328od_a_a Xs2) Ys2)) (@ (@ tptp.append1574001858od_a_a (@ tptp.concat1878217064od_a_a Xs2)) (@ tptp.concat1878217064od_a_a Ys2)))))
% 0.25/0.65 (assert (forall ((X3 tptp.list_P1467822637od_a_a) (Xs2 tptp.list_l1108175539od_a_a)) (= (@ tptp.concat1878217064od_a_a (@ (@ tptp.cons_l724116707od_a_a X3) Xs2)) (@ (@ tptp.append1574001858od_a_a X3) (@ tptp.concat1878217064od_a_a Xs2)))))
% 0.25/0.65 (assert (forall ((Xss2 tptp.list_l1108175539od_a_a) (Ys2 tptp.list_P1467822637od_a_a) (Zs tptp.list_P1467822637od_a_a)) (=> (= (@ tptp.concat1878217064od_a_a Xss2) (@ (@ tptp.append1574001858od_a_a Ys2) Zs)) (=> (not (= Xss2 tptp.nil_li1885598003od_a_a)) (exists ((Xss12 tptp.list_l1108175539od_a_a) (Xs4 tptp.list_P1467822637od_a_a) (Xs3 tptp.list_P1467822637od_a_a) (Xss23 tptp.list_l1108175539od_a_a)) (and (= Xss2 (@ (@ tptp.append2141280328od_a_a Xss12) (@ (@ tptp.cons_l724116707od_a_a (@ (@ tptp.append1574001858od_a_a Xs4) Xs3)) Xss23))) (= Ys2 (@ (@ tptp.append1574001858od_a_a (@ tptp.concat1878217064od_a_a Xss12)) Xs4)) (= Zs (@ (@ tptp.append1574001858od_a_a Xs3) (@ tptp.concat1878217064od_a_a Xss23)))))))))
% 0.25/0.65 (assert (forall ((X1 tptp.list_P1467822637od_a_a) (X2 tptp.list_P1467822637od_a_a) (R tptp.set_Pr1948701895od_a_a) (P2 (-> tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a Bool))) (=> (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a X1) X2)) (@ tptp.listre2074280881od_a_a R)) (=> (@ (@ P2 tptp.nil_Product_prod_a_a) tptp.nil_Product_prod_a_a) (=> (forall ((X4 tptp.product_prod_a_a) (Y4 tptp.product_prod_a_a) (Xs4 tptp.list_P1467822637od_a_a) (Ys4 tptp.list_P1467822637od_a_a)) (=> (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a X4) Y4)) R) (=> (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a Xs4) Ys4)) (@ tptp.listre2074280881od_a_a R)) (=> (@ (@ P2 Xs4) Ys4) (@ (@ P2 (@ (@ tptp.cons_P1921020637od_a_a X4) Xs4)) (@ (@ tptp.cons_P1921020637od_a_a Y4) Ys4)))))) (@ (@ P2 X1) X2))))))
% 0.25/0.65 (assert (forall ((X1 tptp.list_a) (X2 tptp.list_a) (R tptp.set_Product_prod_a_a) (P2 (-> tptp.list_a tptp.list_a Bool))) (=> (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a X1) X2)) (@ tptp.listrel_a_a R)) (=> (@ (@ P2 tptp.nil_a) tptp.nil_a) (=> (forall ((X4 tptp.a) (Y4 tptp.a) (Xs4 tptp.list_a) (Ys4 tptp.list_a)) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X4) Y4)) R) (=> (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a Xs4) Ys4)) (@ tptp.listrel_a_a R)) (=> (@ (@ P2 Xs4) Ys4) (@ (@ P2 (@ (@ tptp.cons_a X4) Xs4)) (@ (@ tptp.cons_a Y4) Ys4)))))) (@ (@ P2 X1) X2))))))
% 0.25/0.65 (assert (forall ((X3 tptp.product_prod_a_a) (Y3 tptp.product_prod_a_a) (R tptp.set_Pr1948701895od_a_a) (Xs2 tptp.list_P1467822637od_a_a) (Ys2 tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ tptp.listre2074280881od_a_a R))) (=> (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a X3) Y3)) R) (=> (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a Xs2) Ys2)) _let_1) (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a (@ (@ tptp.cons_P1921020637od_a_a X3) Xs2)) (@ (@ tptp.cons_P1921020637od_a_a Y3) Ys2))) _let_1))))))
% 0.25/0.65 (assert (forall ((X3 tptp.a) (Y3 tptp.a) (R tptp.set_Product_prod_a_a) (Xs2 tptp.list_a) (Ys2 tptp.list_a)) (let ((_let_1 (@ tptp.listrel_a_a R))) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X3) Y3)) R) (=> (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a Xs2) Ys2)) _let_1) (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a (@ (@ tptp.cons_a X3) Xs2)) (@ (@ tptp.cons_a Y3) Ys2))) _let_1))))))
% 0.25/0.65 (assert (forall ((Y3 tptp.product_prod_a_a) (Ys2 tptp.list_P1467822637od_a_a) (Xs2 tptp.list_P1467822637od_a_a) (R tptp.set_Pr1948701895od_a_a)) (=> (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a (@ (@ tptp.cons_P1921020637od_a_a Y3) Ys2)) Xs2)) (@ tptp.listre2074280881od_a_a R)) (not (forall ((Y4 tptp.product_prod_a_a) (Ys4 tptp.list_P1467822637od_a_a)) (=> (= Xs2 (@ (@ tptp.cons_P1921020637od_a_a Y4) Ys4)) (=> (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a Y3) Y4)) R) (not (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a Ys2) Ys4)) (@ tptp.listre2074280881od_a_a R))))))))))
% 0.25/0.65 (assert (forall ((Y3 tptp.a) (Ys2 tptp.list_a) (Xs2 tptp.list_a) (R tptp.set_Product_prod_a_a)) (=> (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a (@ (@ tptp.cons_a Y3) Ys2)) Xs2)) (@ tptp.listrel_a_a R)) (not (forall ((Y4 tptp.a) (Ys4 tptp.list_a)) (=> (= Xs2 (@ (@ tptp.cons_a Y4) Ys4)) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a Y3) Y4)) R) (not (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a Ys2) Ys4)) (@ tptp.listrel_a_a R))))))))))
% 0.25/0.65 (assert (forall ((Xs2 tptp.list_P1467822637od_a_a) (Y3 tptp.product_prod_a_a) (Ys2 tptp.list_P1467822637od_a_a) (R tptp.set_Pr1948701895od_a_a)) (=> (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a Xs2) (@ (@ tptp.cons_P1921020637od_a_a Y3) Ys2))) (@ tptp.listre2074280881od_a_a R)) (not (forall ((X4 tptp.product_prod_a_a) (Xs4 tptp.list_P1467822637od_a_a)) (=> (= Xs2 (@ (@ tptp.cons_P1921020637od_a_a X4) Xs4)) (=> (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a X4) Y3)) R) (not (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a Xs4) Ys2)) (@ tptp.listre2074280881od_a_a R))))))))))
% 0.25/0.65 (assert (forall ((Xs2 tptp.list_a) (Y3 tptp.a) (Ys2 tptp.list_a) (R tptp.set_Product_prod_a_a)) (=> (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a Xs2) (@ (@ tptp.cons_a Y3) Ys2))) (@ tptp.listrel_a_a R)) (not (forall ((X4 tptp.a) (Xs4 tptp.list_a)) (=> (= Xs2 (@ (@ tptp.cons_a X4) Xs4)) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X4) Y3)) R) (not (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a Xs4) Ys2)) (@ tptp.listrel_a_a R))))))))))
% 0.25/0.65 (assert (forall ((A1 tptp.list_P1467822637od_a_a) (A22 tptp.list_P1467822637od_a_a) (R tptp.set_Pr1948701895od_a_a)) (=> (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a A1) A22)) (@ tptp.listre2074280881od_a_a R)) (=> (=> (= A1 tptp.nil_Product_prod_a_a) (not (= A22 tptp.nil_Product_prod_a_a))) (not (forall ((X4 tptp.product_prod_a_a) (Y4 tptp.product_prod_a_a) (Xs4 tptp.list_P1467822637od_a_a)) (=> (= A1 (@ (@ tptp.cons_P1921020637od_a_a X4) Xs4)) (forall ((Ys4 tptp.list_P1467822637od_a_a)) (=> (= A22 (@ (@ tptp.cons_P1921020637od_a_a Y4) Ys4)) (=> (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a X4) Y4)) R) (not (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a Xs4) Ys4)) (@ tptp.listre2074280881od_a_a R)))))))))))))
% 0.25/0.65 (assert (forall ((A1 tptp.list_a) (A22 tptp.list_a) (R tptp.set_Product_prod_a_a)) (=> (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a A1) A22)) (@ tptp.listrel_a_a R)) (=> (=> (= A1 tptp.nil_a) (not (= A22 tptp.nil_a))) (not (forall ((X4 tptp.a) (Y4 tptp.a) (Xs4 tptp.list_a)) (=> (= A1 (@ (@ tptp.cons_a X4) Xs4)) (forall ((Ys4 tptp.list_a)) (=> (= A22 (@ (@ tptp.cons_a Y4) Ys4)) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X4) Y4)) R) (not (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a Xs4) Ys4)) (@ tptp.listrel_a_a R)))))))))))))
% 0.25/0.65 (assert (forall ((A1 tptp.list_P1467822637od_a_a) (A22 tptp.list_P1467822637od_a_a) (R tptp.set_Pr1948701895od_a_a)) (= (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a A1) A22)) (@ tptp.listre2074280881od_a_a R)) (or (and (= A1 tptp.nil_Product_prod_a_a) (= A22 tptp.nil_Product_prod_a_a)) (exists ((X tptp.product_prod_a_a) (Y tptp.product_prod_a_a) (Xs tptp.list_P1467822637od_a_a) (Ys tptp.list_P1467822637od_a_a)) (and (= A1 (@ (@ tptp.cons_P1921020637od_a_a X) Xs)) (= A22 (@ (@ tptp.cons_P1921020637od_a_a Y) Ys)) (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a X) Y)) R) (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a Xs) Ys)) (@ tptp.listre2074280881od_a_a R))))))))
% 0.25/0.65 (assert (forall ((A1 tptp.list_a) (A22 tptp.list_a) (R tptp.set_Product_prod_a_a)) (= (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a A1) A22)) (@ tptp.listrel_a_a R)) (or (and (= A1 tptp.nil_a) (= A22 tptp.nil_a)) (exists ((X tptp.a) (Y tptp.a) (Xs tptp.list_a) (Ys tptp.list_a)) (and (= A1 (@ (@ tptp.cons_a X) Xs)) (= A22 (@ (@ tptp.cons_a Y) Ys)) (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X) Y)) R) (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a Xs) Ys)) (@ tptp.listrel_a_a R))))))))
% 1.01/1.28 (assert (forall ((P2 Bool)) (or (= P2 true) (= P2 false))))
% 1.01/1.28 (assert (forall ((X3 tptp.list_P1467822637od_a_a) (Y3 tptp.list_P1467822637od_a_a)) (= (@ (@ (@ tptp.if_lis321365491od_a_a false) X3) Y3) Y3)))
% 1.01/1.28 (assert (forall ((X3 tptp.list_P1467822637od_a_a) (Y3 tptp.list_P1467822637od_a_a)) (= (@ (@ (@ tptp.if_lis321365491od_a_a true) X3) Y3) X3)))
% 1.01/1.28 (assert (not (forall ((Xs4 tptp.list_P1467822637od_a_a) (X4 tptp.a) (Y4 tptp.a) (Ys4 tptp.list_P1467822637od_a_a)) (not (= tptp.es (@ (@ tptp.append1574001858od_a_a Xs4) (@ (@ tptp.cons_P1921020637od_a_a (@ (@ tptp.product_Pair_a_a X4) Y4)) (@ (@ tptp.cons_P1921020637od_a_a (@ (@ tptp.product_Pair_a_a Y4) X4)) Ys4))))))))
% 1.01/1.28 (set-info :filename cvc5---1.0.5_7160)
% 1.01/1.28 (check-sat-assuming ( true ))
% 1.01/1.28 ------- get file name : TPTP file name is ITP092^1
% 1.01/1.28 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_7160.smt2...
% 1.01/1.28 --- Run --ho-elim --full-saturate-quant at 10...
% 1.01/1.28 % SZS status Theorem for ITP092^1
% 1.01/1.28 % SZS output start Proof for ITP092^1
% 1.01/1.28 (
% 1.01/1.28 (let ((_let_1 (not (forall ((Xs4 tptp.list_P1467822637od_a_a) (X4 tptp.a) (Y4 tptp.a) (Ys4 tptp.list_P1467822637od_a_a)) (not (= tptp.es (@ (@ tptp.append1574001858od_a_a Xs4) (@ (@ tptp.cons_P1921020637od_a_a (@ (@ tptp.product_Pair_a_a X4) Y4)) (@ (@ tptp.cons_P1921020637od_a_a (@ (@ tptp.product_Pair_a_a Y4) X4)) Ys4))))))))) (let ((_let_2 (= tptp.insert2123825731od_a_a (lambda ((X tptp.product_prod_a_a) (Xs tptp.list_P1467822637od_a_a)) (@ (@ (@ tptp.if_lis321365491od_a_a (@ (@ tptp.member449909584od_a_a X) (@ tptp.set_Product_prod_a_a2 Xs))) Xs) (@ (@ tptp.cons_P1921020637od_a_a X) Xs)))))) (let ((_let_3 (= tptp.irrefl_a (lambda ((R5 tptp.set_Product_prod_a_a)) (forall ((A5 tptp.a)) (not (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a A5) A5)) R5))))))) (let ((_let_4 (= tptp.asym_a (lambda ((A5 tptp.set_Product_prod_a_a)) (exists ((R4 tptp.set_Product_prod_a_a)) (and (= A5 R4) (forall ((X tptp.a) (Y tptp.a)) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X) Y)) R4) (not (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a Y) X)) R4)))))))))) (let ((_let_5 (forall ((X3 tptp.product_prod_a_a) (Xs1 tptp.list_P1467822637od_a_a) (Ys2 tptp.list_P1467822637od_a_a) (Xs2 tptp.list_P1467822637od_a_a) (Zs tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ tptp.cons_P1921020637od_a_a X3))) (=> (= (@ _let_1 Xs1) Ys2) (=> (= Xs2 (@ (@ tptp.append1574001858od_a_a Xs1) Zs)) (= (@ _let_1 Xs2) (@ (@ tptp.append1574001858od_a_a Ys2) Zs)))))))) (let ((_let_6 (= tptp.kurato1072996284sing_a (lambda ((P tptp.list_P1467822637od_a_a)) (forall ((Xs tptp.list_P1467822637od_a_a) (X tptp.a) (Y tptp.a) (Ys tptp.list_P1467822637od_a_a)) (not (= P (@ (@ tptp.append1574001858od_a_a Xs) (@ (@ tptp.cons_P1921020637od_a_a (@ (@ tptp.product_Pair_a_a X) Y)) (@ (@ tptp.cons_P1921020637od_a_a (@ (@ tptp.product_Pair_a_a Y) X)) Ys)))))))))) (let ((_let_7 (= tptp.kurato292963650list_a (lambda ((P tptp.list_P601816365list_a)) (forall ((Xs tptp.list_P601816365list_a) (X tptp.list_a) (Y tptp.list_a) (Ys tptp.list_P601816365list_a)) (not (= P (@ (@ tptp.append750086082list_a Xs) (@ (@ tptp.cons_P2080942813list_a (@ (@ tptp.produc1448356631list_a X) Y)) (@ (@ tptp.cons_P2080942813list_a (@ (@ tptp.produc1448356631list_a Y) X)) Ys)))))))))) (let ((_let_8 (= tptp.kurato1404746725od_a_a (lambda ((P tptp.list_P1891567085od_a_a)) (forall ((Xs tptp.list_P1891567085od_a_a) (X tptp.product_prod_a_a) (Y tptp.product_prod_a_a) (Ys tptp.list_P1891567085od_a_a)) (not (= P (@ (@ tptp.append864718978od_a_a Xs) (@ (@ tptp.cons_P1070399645od_a_a (@ (@ tptp.produc1474507607od_a_a X) Y)) (@ (@ tptp.cons_P1070399645od_a_a (@ (@ tptp.produc1474507607od_a_a Y) X)) Ys)))))))))) (let ((_let_9 (@ tptp.kurato1072996284sing_a (@ (@ tptp.cons_P1921020637od_a_a tptp.e) tptp.es)))) (let ((_let_10 (ho_39 (ho_38 k_37 (ho_12 (ho_11 k_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_384) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_385)) (ho_39 (ho_38 k_37 (ho_12 (ho_11 k_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_385) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_384)) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_386)))) (let ((_let_11 (ho_39 (ho_41 k_40 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_383) _let_10))) (let ((_let_12 (= tptp.es _let_11))) (let ((_let_13 (ho_38 k_37 tptp.e))) (let ((_let_14 (ho_39 _let_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_383))) (let ((_let_15 (ho_39 (ho_41 k_40 _let_14) _let_10))) (let ((_let_16 (= (ho_39 _let_13 _let_11) _let_15))) (let ((_let_17 (= (ho_39 _let_13 tptp.es) _let_15))) (let ((_let_18 (forall ((Xs4 tptp.list_P1467822637od_a_a) (X4 tptp.a) (Y4 tptp.a) (Ys4 tptp.list_P1467822637od_a_a)) (not (= tptp.es (ho_39 (ho_41 k_40 Xs4) (ho_39 (ho_38 k_37 (ho_12 (ho_11 k_10 X4) Y4)) (ho_39 (ho_38 k_37 (ho_12 (ho_11 k_10 Y4) X4)) Ys4)))))))) (let ((_let_19 (not _let_18))) (let ((_let_20 (EQ_RESOLVE (ASSUME :args (_let_1)) (PREPROCESS :args ((= _let_1 _let_19)))))) (let ((_let_21 (or))) (let ((_let_22 (_let_12))) (let ((_let_23 (not _let_12))) (let ((_let_24 (forall ((X3 tptp.product_prod_a_a) (Xs1 tptp.list_P1467822637od_a_a) (Zs tptp.list_P1467822637od_a_a)) (let ((_let_1 (ho_38 k_37 X3))) (= (ho_39 _let_1 (ho_39 (ho_41 k_40 Xs1) Zs)) (ho_39 (ho_41 k_40 (ho_39 _let_1 Xs1)) Zs)))))) (let ((_let_25 (EQ_RESOLVE (ASSUME :args (_let_5)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((X3 tptp.product_prod_a_a) (Xs1 tptp.list_P1467822637od_a_a) (Zs tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ tptp.cons_P1921020637od_a_a X3))) (= (@ (@ tptp.append1574001858od_a_a (@ _let_1 Xs1)) Zs) (@ _let_1 (@ (@ tptp.append1574001858od_a_a Xs1) Zs))))) _let_24))))))) (let ((_let_26 (forall ((Xs tptp.list_P1467822637od_a_a) (X tptp.a) (Y tptp.a) (Ys tptp.list_P1467822637od_a_a)) (not (= (ho_39 (ho_41 k_40 Xs) (ho_39 (ho_38 k_37 (ho_12 (ho_11 k_10 X) Y)) (ho_39 (ho_38 k_37 (ho_12 (ho_11 k_10 Y) X)) Ys))) (ho_39 (ho_38 k_37 tptp.e) tptp.es)))))) (let ((_let_27 (not _let_17))) (let ((_let_28 (forall ((u |u_(-> tptp.list_a tptp.list_list_a tptp.list_list_a)|) (e |u_(-> tptp.list_list_a tptp.list_list_a)|) (i tptp.list_a)) (not (forall ((v |u_(-> tptp.list_a tptp.list_list_a tptp.list_list_a)|)) (not (forall ((ii tptp.list_a)) (= (ho_194 v ii) (ite (= i ii) e (ho_194 u ii)))))))))) (let ((_let_29 (forall ((x |u_(-> tptp.list_a tptp.list_list_a tptp.list_list_a)|) (y |u_(-> tptp.list_a tptp.list_list_a tptp.list_list_a)|)) (or (not (forall ((z tptp.list_a)) (= (ho_194 x z) (ho_194 y z)))) (= x y))))) (let ((_let_30 (forall ((u |u_(-> tptp.list_list_a tptp.list_list_a)|) (e tptp.list_list_a) (i tptp.list_list_a)) (not (forall ((v |u_(-> tptp.list_list_a tptp.list_list_a)|)) (not (forall ((ii tptp.list_list_a)) (= (ho_195 v ii) (ite (= i ii) e (ho_195 u ii)))))))))) (let ((_let_31 (forall ((x |u_(-> tptp.list_list_a tptp.list_list_a)|) (y |u_(-> tptp.list_list_a tptp.list_list_a)|)) (or (not (forall ((z tptp.list_list_a)) (= (ho_195 x z) (ho_195 y z)))) (= x y))))) (let ((_let_32 (forall ((u |u_(-> tptp.product_prod_a_a _u_(-> tptp.a tptp.nat)_ tptp.produc664688895_a_nat)|) (e |u_(-> _u_(-> tptp.a tptp.nat)_ tptp.produc664688895_a_nat)|) (i tptp.product_prod_a_a)) (not (forall ((v |u_(-> tptp.product_prod_a_a _u_(-> tptp.a tptp.nat)_ tptp.produc664688895_a_nat)|)) (not (forall ((ii tptp.product_prod_a_a)) (= (ho_277 v ii) (ite (= i ii) e (ho_277 u ii)))))))))) (let ((_let_33 (forall ((x |u_(-> tptp.product_prod_a_a _u_(-> tptp.a tptp.nat)_ tptp.produc664688895_a_nat)|) (y |u_(-> tptp.product_prod_a_a _u_(-> tptp.a tptp.nat)_ tptp.produc664688895_a_nat)|)) (or (not (forall ((z tptp.product_prod_a_a)) (= (ho_277 x z) (ho_277 y z)))) (= x y))))) (let ((_let_34 (forall ((u |u_(-> tptp.list_list_a tptp.list_list_a tptp.list_list_a)|) (e |u_(-> tptp.list_list_a tptp.list_list_a)|) (i tptp.list_list_a)) (not (forall ((v |u_(-> tptp.list_list_a tptp.list_list_a tptp.list_list_a)|)) (not (forall ((ii tptp.list_list_a)) (= (ho_197 v ii) (ite (= i ii) e (ho_197 u ii)))))))))) (let ((_let_35 (forall ((x |u_(-> tptp.list_list_a tptp.list_list_a tptp.list_list_a)|) (y |u_(-> tptp.list_list_a tptp.list_list_a tptp.list_list_a)|)) (or (not (forall ((z tptp.list_list_a)) (= (ho_197 x z) (ho_197 y z)))) (= x y))))) (let ((_let_36 (forall ((u |u_(-> tptp.produc1178641895_a_nat tptp.set_Pr1940702919_a_nat Bool)|) (e |u_(-> tptp.set_Pr1940702919_a_nat Bool)|) (i tptp.produc1178641895_a_nat)) (not (forall ((v |u_(-> tptp.produc1178641895_a_nat tptp.set_Pr1940702919_a_nat Bool)|)) (not (forall ((ii tptp.produc1178641895_a_nat)) (= (ho_189 v ii) (ite (= i ii) e (ho_189 u ii)))))))))) (let ((_let_37 (forall ((x |u_(-> tptp.produc1178641895_a_nat tptp.set_Pr1940702919_a_nat Bool)|) (y |u_(-> tptp.produc1178641895_a_nat tptp.set_Pr1940702919_a_nat Bool)|)) (or (not (forall ((z tptp.produc1178641895_a_nat)) (= (ho_189 x z) (ho_189 y z)))) (= x y))))) (let ((_let_38 (forall ((u |u_(-> _u_(-> tptp.a tptp.nat)_ _u_(-> tptp.a tptp.nat)_ tptp.produc1178641895_a_nat)|) (e |u_(-> _u_(-> tptp.a tptp.nat)_ tptp.produc1178641895_a_nat)|) (i |u_(-> tptp.a tptp.nat)|)) (not (forall ((v |u_(-> _u_(-> tptp.a tptp.nat)_ _u_(-> tptp.a tptp.nat)_ tptp.produc1178641895_a_nat)|)) (not (forall ((ii |u_(-> tptp.a tptp.nat)|)) (= (ho_186 v ii) (ite (= i ii) e (ho_186 u ii)))))))))) (let ((_let_39 (forall ((x |u_(-> _u_(-> tptp.a tptp.nat)_ _u_(-> tptp.a tptp.nat)_ tptp.produc1178641895_a_nat)|) (y |u_(-> _u_(-> tptp.a tptp.nat)_ _u_(-> tptp.a tptp.nat)_ tptp.produc1178641895_a_nat)|)) (or (not (forall ((z |u_(-> tptp.a tptp.nat)|)) (= (ho_186 x z) (ho_186 y z)))) (= x y))))) (let ((_let_40 (forall ((u |u_(-> tptp.a tptp.list_P1467822637od_a_a Bool)|) (e |u_(-> tptp.list_P1467822637od_a_a Bool)|) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.list_P1467822637od_a_a Bool)|)) (not (forall ((ii tptp.a)) (= (ho_337 v ii) (ite (= i ii) e (ho_337 u ii)))))))))) (let ((_let_41 (forall ((x |u_(-> tptp.a tptp.list_P1467822637od_a_a Bool)|) (y |u_(-> tptp.a tptp.list_P1467822637od_a_a Bool)|)) (or (not (forall ((z tptp.a)) (= (ho_337 x z) (ho_337 y z)))) (= x y))))) (let ((_let_42 (forall ((u |u_(-> _u_(-> tptp.a tptp.nat)_ tptp.produc1178641895_a_nat)|) (e tptp.produc1178641895_a_nat) (i |u_(-> tptp.a tptp.nat)|)) (not (forall ((v |u_(-> _u_(-> tptp.a tptp.nat)_ tptp.produc1178641895_a_nat)|)) (not (forall ((ii |u_(-> tptp.a tptp.nat)|)) (= (ho_187 v ii) (ite (= i ii) e (ho_187 u ii)))))))))) (let ((_let_43 (forall ((x |u_(-> _u_(-> tptp.a tptp.nat)_ tptp.produc1178641895_a_nat)|) (y |u_(-> _u_(-> tptp.a tptp.nat)_ tptp.produc1178641895_a_nat)|)) (or (not (forall ((z |u_(-> tptp.a tptp.nat)|)) (= (ho_187 x z) (ho_187 y z)))) (= x y))))) (let ((_let_44 (forall ((u |u_(-> tptp.list_P1467822637od_a_a tptp.set_a Bool)|) (e |u_(-> tptp.set_a Bool)|) (i tptp.list_P1467822637od_a_a)) (not (forall ((v |u_(-> tptp.list_P1467822637od_a_a tptp.set_a Bool)|)) (not (forall ((ii tptp.list_P1467822637od_a_a)) (= (ho_373 v ii) (ite (= i ii) e (ho_373 u ii)))))))))) (let ((_let_45 (forall ((x |u_(-> tptp.list_P1467822637od_a_a tptp.set_a Bool)|) (y |u_(-> tptp.list_P1467822637od_a_a tptp.set_a Bool)|)) (or (not (forall ((z tptp.list_P1467822637od_a_a)) (= (ho_373 x z) (ho_373 y z)))) (= x y))))) (let ((_let_46 (forall ((u |u_(-> tptp.set_Pr1940702919_a_nat Bool)|) (e Bool) (i tptp.set_Pr1940702919_a_nat)) (not (forall ((v |u_(-> tptp.set_Pr1940702919_a_nat Bool)|)) (not (forall ((ii tptp.set_Pr1940702919_a_nat)) (= (ho_190 v ii) (ite (= i ii) e (ho_190 u ii)))))))))) (let ((_let_47 (forall ((x |u_(-> tptp.set_Pr1940702919_a_nat Bool)|) (y |u_(-> tptp.set_Pr1940702919_a_nat Bool)|)) (or (not (forall ((z tptp.set_Pr1940702919_a_nat)) (= (ho_190 x z) (ho_190 y z)))) (= x y))))) (let ((_let_48 (forall ((u |u_(-> tptp.product_prod_a_a tptp.product_prod_a_a Bool)|) (e |u_(-> tptp.product_prod_a_a Bool)|) (i tptp.product_prod_a_a)) (not (forall ((v |u_(-> tptp.product_prod_a_a tptp.product_prod_a_a Bool)|)) (not (forall ((ii tptp.product_prod_a_a)) (= (ho_67 v ii) (ite (= i ii) e (ho_67 u ii)))))))))) (let ((_let_49 (forall ((x |u_(-> tptp.product_prod_a_a tptp.product_prod_a_a Bool)|) (y |u_(-> tptp.product_prod_a_a tptp.product_prod_a_a Bool)|)) (or (not (forall ((z tptp.product_prod_a_a)) (= (ho_67 x z) (ho_67 y z)))) (= x y))))) (let ((_let_50 (forall ((u |u_(-> tptp.produc1334933863_a_nat tptp.set_Pr753687879_a_nat Bool)|) (e |u_(-> tptp.set_Pr753687879_a_nat Bool)|) (i tptp.produc1334933863_a_nat)) (not (forall ((v |u_(-> tptp.produc1334933863_a_nat tptp.set_Pr753687879_a_nat Bool)|)) (not (forall ((ii tptp.produc1334933863_a_nat)) (= (ho_183 v ii) (ite (= i ii) e (ho_183 u ii)))))))))) (let ((_let_51 (forall ((x |u_(-> tptp.produc1334933863_a_nat tptp.set_Pr753687879_a_nat Bool)|) (y |u_(-> tptp.produc1334933863_a_nat tptp.set_Pr753687879_a_nat Bool)|)) (or (not (forall ((z tptp.produc1334933863_a_nat)) (= (ho_183 x z) (ho_183 y z)))) (= x y))))) (let ((_let_52 (forall ((u |u_(-> tptp.list_a_nat tptp.produc1334933863_a_nat)|) (e tptp.produc1334933863_a_nat) (i tptp.list_a_nat)) (not (forall ((v |u_(-> tptp.list_a_nat tptp.produc1334933863_a_nat)|)) (not (forall ((ii tptp.list_a_nat)) (= (ho_181 v ii) (ite (= i ii) e (ho_181 u ii)))))))))) (let ((_let_53 (forall ((x |u_(-> tptp.list_a_nat tptp.produc1334933863_a_nat)|) (y |u_(-> tptp.list_a_nat tptp.produc1334933863_a_nat)|)) (or (not (forall ((z tptp.list_a_nat)) (= (ho_181 x z) (ho_181 y z)))) (= x y))))) (let ((_let_54 (forall ((u |u_(-> tptp.set_Pr753687879_a_nat Bool)|) (e Bool) (i tptp.set_Pr753687879_a_nat)) (not (forall ((v |u_(-> tptp.set_Pr753687879_a_nat Bool)|)) (not (forall ((ii tptp.set_Pr753687879_a_nat)) (= (ho_184 v ii) (ite (= i ii) e (ho_184 u ii)))))))))) (let ((_let_55 (forall ((x |u_(-> tptp.set_Pr753687879_a_nat Bool)|) (y |u_(-> tptp.set_Pr753687879_a_nat Bool)|)) (or (not (forall ((z tptp.set_Pr753687879_a_nat)) (= (ho_184 x z) (ho_184 y z)))) (= x y))))) (let ((_let_56 (forall ((u |u_(-> tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a tptp.produc651658087od_a_a)|) (e |u_(-> tptp.list_P1467822637od_a_a tptp.produc651658087od_a_a)|) (i tptp.list_P1467822637od_a_a)) (not (forall ((v |u_(-> tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a tptp.produc651658087od_a_a)|)) (not (forall ((ii tptp.list_P1467822637od_a_a)) (= (ho_172 v ii) (ite (= i ii) e (ho_172 u ii)))))))))) (let ((_let_57 (forall ((x |u_(-> tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a tptp.produc651658087od_a_a)|) (y |u_(-> tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a tptp.produc651658087od_a_a)|)) (or (not (forall ((z tptp.list_P1467822637od_a_a)) (= (ho_172 x z) (ho_172 y z)))) (= x y))))) (let ((_let_58 (forall ((u |u_(-> tptp.list_l1108175539od_a_a tptp.list_P1175580892od_a_a)|) (e tptp.list_P1175580892od_a_a) (i tptp.list_l1108175539od_a_a)) (not (forall ((v |u_(-> tptp.list_l1108175539od_a_a tptp.list_P1175580892od_a_a)|)) (not (forall ((ii tptp.list_l1108175539od_a_a)) (= (ho_269 v ii) (ite (= i ii) e (ho_269 u ii)))))))))) (let ((_let_59 (forall ((x |u_(-> tptp.list_l1108175539od_a_a tptp.list_P1175580892od_a_a)|) (y |u_(-> tptp.list_l1108175539od_a_a tptp.list_P1175580892od_a_a)|)) (or (not (forall ((z tptp.list_l1108175539od_a_a)) (= (ho_269 x z) (ho_269 y z)))) (= x y))))) (let ((_let_60 (forall ((u |u_(-> tptp.list_P1467822637od_a_a tptp.produc651658087od_a_a)|) (e tptp.produc651658087od_a_a) (i tptp.list_P1467822637od_a_a)) (not (forall ((v |u_(-> tptp.list_P1467822637od_a_a tptp.produc651658087od_a_a)|)) (not (forall ((ii tptp.list_P1467822637od_a_a)) (= (ho_173 v ii) (ite (= i ii) e (ho_173 u ii)))))))))) (let ((_let_61 (forall ((x |u_(-> tptp.list_P1467822637od_a_a tptp.produc651658087od_a_a)|) (y |u_(-> tptp.list_P1467822637od_a_a tptp.produc651658087od_a_a)|)) (or (not (forall ((z tptp.list_P1467822637od_a_a)) (= (ho_173 x z) (ho_173 y z)))) (= x y))))) (let ((_let_62 (forall ((u |u_(-> tptp.list_l1108175539od_a_a tptp.list_l1108175539od_a_a tptp.produc657724903od_a_a)|) (e |u_(-> tptp.list_l1108175539od_a_a tptp.produc657724903od_a_a)|) (i tptp.list_l1108175539od_a_a)) (not (forall ((v |u_(-> tptp.list_l1108175539od_a_a tptp.list_l1108175539od_a_a tptp.produc657724903od_a_a)|)) (not (forall ((ii tptp.list_l1108175539od_a_a)) (= (ho_166 v ii) (ite (= i ii) e (ho_166 u ii)))))))))) (let ((_let_63 (forall ((x |u_(-> tptp.list_l1108175539od_a_a tptp.list_l1108175539od_a_a tptp.produc657724903od_a_a)|) (y |u_(-> tptp.list_l1108175539od_a_a tptp.list_l1108175539od_a_a tptp.produc657724903od_a_a)|)) (or (not (forall ((z tptp.list_l1108175539od_a_a)) (= (ho_166 x z) (ho_166 y z)))) (= x y))))) (let ((_let_64 (forall ((u |u_(-> tptp.set_Pr1971762695list_a tptp.produc864062247list_a Bool)|) (e |u_(-> tptp.produc864062247list_a Bool)|) (i tptp.set_Pr1971762695list_a)) (not (forall ((v |u_(-> tptp.set_Pr1971762695list_a tptp.produc864062247list_a Bool)|)) (not (forall ((ii tptp.set_Pr1971762695list_a)) (= (ho_32 v ii) (ite (= i ii) e (ho_32 u ii)))))))))) (let ((_let_65 (forall ((x |u_(-> tptp.set_Pr1971762695list_a tptp.produc864062247list_a Bool)|) (y |u_(-> tptp.set_Pr1971762695list_a tptp.produc864062247list_a Bool)|)) (or (not (forall ((z tptp.set_Pr1971762695list_a)) (= (ho_32 x z) (ho_32 y z)))) (= x y))))) (let ((_let_66 (forall ((u |u_(-> tptp.list_a_nat tptp.list_a_nat tptp.produc1334933863_a_nat)|) (e |u_(-> tptp.list_a_nat tptp.produc1334933863_a_nat)|) (i tptp.list_a_nat)) (not (forall ((v |u_(-> tptp.list_a_nat tptp.list_a_nat tptp.produc1334933863_a_nat)|)) (not (forall ((ii tptp.list_a_nat)) (= (ho_180 v ii) (ite (= i ii) e (ho_180 u ii)))))))))) (let ((_let_67 (forall ((x |u_(-> tptp.list_a_nat tptp.list_a_nat tptp.produc1334933863_a_nat)|) (y |u_(-> tptp.list_a_nat tptp.list_a_nat tptp.produc1334933863_a_nat)|)) (or (not (forall ((z tptp.list_a_nat)) (= (ho_180 x z) (ho_180 y z)))) (= x y))))) (let ((_let_68 (forall ((u |u_(-> tptp.set_Pr1239640519od_a_a Bool)|) (e Bool) (i tptp.set_Pr1239640519od_a_a)) (not (forall ((v |u_(-> tptp.set_Pr1239640519od_a_a Bool)|)) (not (forall ((ii tptp.set_Pr1239640519od_a_a)) (= (ho_170 v ii) (ite (= i ii) e (ho_170 u ii)))))))))) (let ((_let_69 (forall ((x |u_(-> tptp.set_Pr1239640519od_a_a Bool)|) (y |u_(-> tptp.set_Pr1239640519od_a_a Bool)|)) (or (not (forall ((z tptp.set_Pr1239640519od_a_a)) (= (ho_170 x z) (ho_170 y z)))) (= x y))))) (let ((_let_70 (forall ((u |u_(-> tptp.nat tptp.nat Bool)|) (e |u_(-> tptp.nat Bool)|) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.nat Bool)|)) (not (forall ((ii tptp.nat)) (= (ho_362 v ii) (ite (= i ii) e (ho_362 u ii)))))))))) (let ((_let_71 (forall ((x |u_(-> tptp.nat tptp.nat Bool)|) (y |u_(-> tptp.nat tptp.nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_362 x z) (ho_362 y z)))) (= x y))))) (let ((_let_72 (forall ((u |u_(-> tptp.produc1990712039od_a_a tptp.set_Pr1295299783od_a_a Bool)|) (e |u_(-> tptp.set_Pr1295299783od_a_a Bool)|) (i tptp.produc1990712039od_a_a)) (not (forall ((v |u_(-> tptp.produc1990712039od_a_a tptp.set_Pr1295299783od_a_a Bool)|)) (not (forall ((ii tptp.produc1990712039od_a_a)) (= (ho_161 v ii) (ite (= i ii) e (ho_161 u ii)))))))))) (let ((_let_73 (forall ((x |u_(-> tptp.produc1990712039od_a_a tptp.set_Pr1295299783od_a_a Bool)|) (y |u_(-> tptp.produc1990712039od_a_a tptp.set_Pr1295299783od_a_a Bool)|)) (or (not (forall ((z tptp.produc1990712039od_a_a)) (= (ho_161 x z) (ho_161 y z)))) (= x y))))) (let ((_let_74 (forall ((u |u_(-> tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a tptp.produc1990712039od_a_a)|) (e |u_(-> tptp.produc1572603623od_a_a tptp.produc1990712039od_a_a)|) (i tptp.produc1572603623od_a_a)) (not (forall ((v |u_(-> tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a tptp.produc1990712039od_a_a)|)) (not (forall ((ii tptp.produc1572603623od_a_a)) (= (ho_158 v ii) (ite (= i ii) e (ho_158 u ii)))))))))) (let ((_let_75 (forall ((x |u_(-> tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a tptp.produc1990712039od_a_a)|) (y |u_(-> tptp.produc1572603623od_a_a tptp.produc1572603623od_a_a tptp.produc1990712039od_a_a)|)) (or (not (forall ((z tptp.produc1572603623od_a_a)) (= (ho_158 x z) (ho_158 y z)))) (= x y))))) (let ((_let_76 (forall ((u |u_(-> tptp.set_Pr1295299783od_a_a tptp.set_Pr779272263od_a_a)|) (e tptp.set_Pr779272263od_a_a) (i tptp.set_Pr1295299783od_a_a)) (not (forall ((v |u_(-> tptp.set_Pr1295299783od_a_a tptp.set_Pr779272263od_a_a)|)) (not (forall ((ii tptp.set_Pr1295299783od_a_a)) (= (ho_150 v ii) (ite (= i ii) e (ho_150 u ii)))))))))) (let ((_let_77 (forall ((x |u_(-> tptp.set_Pr1295299783od_a_a tptp.set_Pr779272263od_a_a)|) (y |u_(-> tptp.set_Pr1295299783od_a_a tptp.set_Pr779272263od_a_a)|)) (or (not (forall ((z tptp.set_Pr1295299783od_a_a)) (= (ho_150 x z) (ho_150 y z)))) (= x y))))) (let ((_let_78 (forall ((u |u_(-> tptp.produc864062247list_a tptp.list_a Bool)|) (e |u_(-> tptp.list_a Bool)|) (i tptp.produc864062247list_a)) (not (forall ((v |u_(-> tptp.produc864062247list_a tptp.list_a Bool)|)) (not (forall ((ii tptp.produc864062247list_a)) (= (ho_301 v ii) (ite (= i ii) e (ho_301 u ii)))))))))) (let ((_let_79 (forall ((x |u_(-> tptp.produc864062247list_a tptp.list_a Bool)|) (y |u_(-> tptp.produc864062247list_a tptp.list_a Bool)|)) (or (not (forall ((z tptp.produc864062247list_a)) (= (ho_301 x z) (ho_301 y z)))) (= x y))))) (let ((_let_80 (forall ((u |u_(-> tptp.list_l1108175539od_a_a tptp.list_P1467822637od_a_a)|) (e tptp.list_P1467822637od_a_a) (i tptp.list_l1108175539od_a_a)) (not (forall ((v |u_(-> tptp.list_l1108175539od_a_a tptp.list_P1467822637od_a_a)|)) (not (forall ((ii tptp.list_l1108175539od_a_a)) (= (ho_148 v ii) (ite (= i ii) e (ho_148 u ii)))))))))) (let ((_let_81 (forall ((x |u_(-> tptp.list_l1108175539od_a_a tptp.list_P1467822637od_a_a)|) (y |u_(-> tptp.list_l1108175539od_a_a tptp.list_P1467822637od_a_a)|)) (or (not (forall ((z tptp.list_l1108175539od_a_a)) (= (ho_148 x z) (ho_148 y z)))) (= x y))))) (let ((_let_82 (forall ((u |u_(-> _u_(-> tptp.product_prod_a_a tptp.list_l1108175539od_a_a)_ tptp.list_P1467822637od_a_a tptp.list_l1108175539od_a_a)|) (e |u_(-> tptp.list_P1467822637od_a_a tptp.list_l1108175539od_a_a)|) (i |u_(-> tptp.product_prod_a_a tptp.list_l1108175539od_a_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.product_prod_a_a tptp.list_l1108175539od_a_a)_ tptp.list_P1467822637od_a_a tptp.list_l1108175539od_a_a)|)) (not (forall ((ii |u_(-> tptp.product_prod_a_a tptp.list_l1108175539od_a_a)|)) (= (ho_144 v ii) (ite (= i ii) e (ho_144 u ii)))))))))) (let ((_let_83 (forall ((x |u_(-> _u_(-> tptp.product_prod_a_a tptp.list_l1108175539od_a_a)_ tptp.list_P1467822637od_a_a tptp.list_l1108175539od_a_a)|) (y |u_(-> _u_(-> tptp.product_prod_a_a tptp.list_l1108175539od_a_a)_ tptp.list_P1467822637od_a_a tptp.list_l1108175539od_a_a)|)) (or (not (forall ((z |u_(-> tptp.product_prod_a_a tptp.list_l1108175539od_a_a)|)) (= (ho_144 x z) (ho_144 y z)))) (= x y))))) (let ((_let_84 (forall ((u |u_(-> _u_(-> _u_(-> tptp.a tptp.nat)_ tptp.list_P1467822637od_a_a)_ tptp.list_a_nat tptp.list_P1467822637od_a_a)|) (e |u_(-> tptp.list_a_nat tptp.list_P1467822637od_a_a)|) (i |u_(-> _u_(-> tptp.a tptp.nat)_ tptp.list_P1467822637od_a_a)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> tptp.a tptp.nat)_ tptp.list_P1467822637od_a_a)_ tptp.list_a_nat tptp.list_P1467822637od_a_a)|)) (not (forall ((ii |u_(-> _u_(-> tptp.a tptp.nat)_ tptp.list_P1467822637od_a_a)|)) (= (ho_141 v ii) (ite (= i ii) e (ho_141 u ii)))))))))) (let ((_let_85 (forall ((x |u_(-> _u_(-> _u_(-> tptp.a tptp.nat)_ tptp.list_P1467822637od_a_a)_ tptp.list_a_nat tptp.list_P1467822637od_a_a)|) (y |u_(-> _u_(-> _u_(-> tptp.a tptp.nat)_ tptp.list_P1467822637od_a_a)_ tptp.list_a_nat tptp.list_P1467822637od_a_a)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.a tptp.nat)_ tptp.list_P1467822637od_a_a)|)) (= (ho_141 x z) (ho_141 y z)))) (= x y))))) (let ((_let_86 (forall ((u |u_(-> _u_(-> tptp.list_P1467822637od_a_a tptp.list_a)_ tptp.list_l1108175539od_a_a tptp.list_a)|) (e |u_(-> tptp.list_l1108175539od_a_a tptp.list_a)|) (i |u_(-> tptp.list_P1467822637od_a_a tptp.list_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.list_P1467822637od_a_a tptp.list_a)_ tptp.list_l1108175539od_a_a tptp.list_a)|)) (not (forall ((ii |u_(-> tptp.list_P1467822637od_a_a tptp.list_a)|)) (= (ho_138 v ii) (ite (= i ii) e (ho_138 u ii)))))))))) (let ((_let_87 (forall ((x |u_(-> _u_(-> tptp.list_P1467822637od_a_a tptp.list_a)_ tptp.list_l1108175539od_a_a tptp.list_a)|) (y |u_(-> _u_(-> tptp.list_P1467822637od_a_a tptp.list_a)_ tptp.list_l1108175539od_a_a tptp.list_a)|)) (or (not (forall ((z |u_(-> tptp.list_P1467822637od_a_a tptp.list_a)|)) (= (ho_138 x z) (ho_138 y z)))) (= x y))))) (let ((_let_88 (forall ((u |u_(-> tptp.produc657167928_a_a_a Bool)|) (e Bool) (i tptp.produc657167928_a_a_a)) (not (forall ((v |u_(-> tptp.produc657167928_a_a_a Bool)|)) (not (forall ((ii tptp.produc657167928_a_a_a)) (= (ho_79 v ii) (ite (= i ii) e (ho_79 u ii)))))))))) (let ((_let_89 (forall ((x |u_(-> tptp.produc657167928_a_a_a Bool)|) (y |u_(-> tptp.produc657167928_a_a_a Bool)|)) (or (not (forall ((z tptp.produc657167928_a_a_a)) (= (ho_79 x z) (ho_79 y z)))) (= x y))))) (let ((_let_90 (forall ((u |u_(-> tptp.list_P1891567085od_a_a tptp.list_P1891567085od_a_a tptp.produc205693799od_a_a)|) (e |u_(-> tptp.list_P1891567085od_a_a tptp.produc205693799od_a_a)|) (i tptp.list_P1891567085od_a_a)) (not (forall ((v |u_(-> tptp.list_P1891567085od_a_a tptp.list_P1891567085od_a_a tptp.produc205693799od_a_a)|)) (not (forall ((ii tptp.list_P1891567085od_a_a)) (= (ho_152 v ii) (ite (= i ii) e (ho_152 u ii)))))))))) (let ((_let_91 (forall ((x |u_(-> tptp.list_P1891567085od_a_a tptp.list_P1891567085od_a_a tptp.produc205693799od_a_a)|) (y |u_(-> tptp.list_P1891567085od_a_a tptp.list_P1891567085od_a_a tptp.produc205693799od_a_a)|)) (or (not (forall ((z tptp.list_P1891567085od_a_a)) (= (ho_152 x z) (ho_152 y z)))) (= x y))))) (let ((_let_92 (forall ((u |u_(-> tptp.list_a tptp.list_l1108175539od_a_a)|) (e tptp.list_l1108175539od_a_a) (i tptp.list_a)) (not (forall ((v |u_(-> tptp.list_a tptp.list_l1108175539od_a_a)|)) (not (forall ((ii tptp.list_a)) (= (ho_136 v ii) (ite (= i ii) e (ho_136 u ii)))))))))) (let ((_let_93 (forall ((x |u_(-> tptp.list_a tptp.list_l1108175539od_a_a)|) (y |u_(-> tptp.list_a tptp.list_l1108175539od_a_a)|)) (or (not (forall ((z tptp.list_a)) (= (ho_136 x z) (ho_136 y z)))) (= x y))))) (let ((_let_94 (forall ((u |u_(-> tptp.set_Pr800560199od_a_a tptp.set_Pr1239640519od_a_a)|) (e tptp.set_Pr1239640519od_a_a) (i tptp.set_Pr800560199od_a_a)) (not (forall ((v |u_(-> tptp.set_Pr800560199od_a_a tptp.set_Pr1239640519od_a_a)|)) (not (forall ((ii tptp.set_Pr800560199od_a_a)) (= (ho_164 v ii) (ite (= i ii) e (ho_164 u ii)))))))))) (let ((_let_95 (forall ((x |u_(-> tptp.set_Pr800560199od_a_a tptp.set_Pr1239640519od_a_a)|) (y |u_(-> tptp.set_Pr800560199od_a_a tptp.set_Pr1239640519od_a_a)|)) (or (not (forall ((z tptp.set_Pr800560199od_a_a)) (= (ho_164 x z) (ho_164 y z)))) (= x y))))) (let ((_let_96 (forall ((u |u_(-> tptp.list_a_nat tptp.list_a)|) (e tptp.list_a) (i tptp.list_a_nat)) (not (forall ((v |u_(-> tptp.list_a_nat tptp.list_a)|)) (not (forall ((ii tptp.list_a_nat)) (= (ho_133 v ii) (ite (= i ii) e (ho_133 u ii)))))))))) (let ((_let_97 (forall ((x |u_(-> tptp.list_a_nat tptp.list_a)|) (y |u_(-> tptp.list_a_nat tptp.list_a)|)) (or (not (forall ((z tptp.list_a_nat)) (= (ho_133 x z) (ho_133 y z)))) (= x y))))) (let ((_let_98 (forall ((u |u_(-> tptp.product_prod_a_a tptp.list_a)|) (e tptp.list_a) (i tptp.product_prod_a_a)) (not (forall ((v |u_(-> tptp.product_prod_a_a tptp.list_a)|)) (not (forall ((ii tptp.product_prod_a_a)) (= (ho_91 v ii) (ite (= i ii) e (ho_91 u ii)))))))))) (let ((_let_99 (forall ((x |u_(-> tptp.product_prod_a_a tptp.list_a)|) (y |u_(-> tptp.product_prod_a_a tptp.list_a)|)) (or (not (forall ((z tptp.product_prod_a_a)) (= (ho_91 x z) (ho_91 y z)))) (= x y))))) (let ((_let_100 (forall ((u |u_(-> _u_(-> tptp.product_prod_a_a tptp.list_a)_ tptp.list_P1467822637od_a_a tptp.list_a)|) (e |u_(-> tptp.list_P1467822637od_a_a tptp.list_a)|) (i |u_(-> tptp.product_prod_a_a tptp.list_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.product_prod_a_a tptp.list_a)_ tptp.list_P1467822637od_a_a tptp.list_a)|)) (not (forall ((ii |u_(-> tptp.product_prod_a_a tptp.list_a)|)) (= (ho_127 v ii) (ite (= i ii) e (ho_127 u ii)))))))))) (let ((_let_101 (forall ((x |u_(-> _u_(-> tptp.product_prod_a_a tptp.list_a)_ tptp.list_P1467822637od_a_a tptp.list_a)|) (y |u_(-> _u_(-> tptp.product_prod_a_a tptp.list_a)_ tptp.list_P1467822637od_a_a tptp.list_a)|)) (or (not (forall ((z |u_(-> tptp.product_prod_a_a tptp.list_a)|)) (= (ho_127 x z) (ho_127 y z)))) (= x y))))) (let ((_let_102 (forall ((u |u_(-> _u_(-> tptp.a tptp.list_P1467822637od_a_a)_ tptp.list_P1467822637od_a_a)|) (e tptp.list_P1467822637od_a_a) (i |u_(-> tptp.a tptp.list_P1467822637od_a_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.a tptp.list_P1467822637od_a_a)_ tptp.list_P1467822637od_a_a)|)) (not (forall ((ii |u_(-> tptp.a tptp.list_P1467822637od_a_a)|)) (= (ho_98 v ii) (ite (= i ii) e (ho_98 u ii)))))))))) (let ((_let_103 (forall ((x |u_(-> _u_(-> tptp.a tptp.list_P1467822637od_a_a)_ tptp.list_P1467822637od_a_a)|) (y |u_(-> _u_(-> tptp.a tptp.list_P1467822637od_a_a)_ tptp.list_P1467822637od_a_a)|)) (or (not (forall ((z |u_(-> tptp.a tptp.list_P1467822637od_a_a)|)) (= (ho_98 x z) (ho_98 y z)))) (= x y))))) (let ((_let_104 (forall ((u |u_(-> _u_(-> tptp.product_prod_a_a tptp.list_P1467822637od_a_a)_ tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a)|) (e |u_(-> tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a)|) (i |u_(-> tptp.product_prod_a_a tptp.list_P1467822637od_a_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.product_prod_a_a tptp.list_P1467822637od_a_a)_ tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a)|)) (not (forall ((ii |u_(-> tptp.product_prod_a_a tptp.list_P1467822637od_a_a)|)) (= (ho_123 v ii) (ite (= i ii) e (ho_123 u ii)))))))))) (let ((_let_105 (forall ((x |u_(-> _u_(-> tptp.product_prod_a_a tptp.list_P1467822637od_a_a)_ tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a)|) (y |u_(-> _u_(-> tptp.product_prod_a_a tptp.list_P1467822637od_a_a)_ tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a)|)) (or (not (forall ((z |u_(-> tptp.product_prod_a_a tptp.list_P1467822637od_a_a)|)) (= (ho_123 x z) (ho_123 y z)))) (= x y))))) (let ((_let_106 (forall ((u |u_(-> _u_(-> tptp.a tptp.nat)_ tptp.product_prod_a_a_nat)|) (e tptp.product_prod_a_a_nat) (i |u_(-> tptp.a tptp.nat)|)) (not (forall ((v |u_(-> _u_(-> tptp.a tptp.nat)_ tptp.product_prod_a_a_nat)|)) (not (forall ((ii |u_(-> tptp.a tptp.nat)|)) (= (ho_242 v ii) (ite (= i ii) e (ho_242 u ii)))))))))) (let ((_let_107 (forall ((x |u_(-> _u_(-> tptp.a tptp.nat)_ tptp.product_prod_a_a_nat)|) (y |u_(-> _u_(-> tptp.a tptp.nat)_ tptp.product_prod_a_a_nat)|)) (or (not (forall ((z |u_(-> tptp.a tptp.nat)|)) (= (ho_242 x z) (ho_242 y z)))) (= x y))))) (let ((_let_108 (forall ((u |u_(-> _u_(-> _u_(-> tptp.a tptp.nat)_ tptp.list_a)_ tptp.list_a_nat tptp.list_a)|) (e |u_(-> tptp.list_a_nat tptp.list_a)|) (i |u_(-> _u_(-> tptp.a tptp.nat)_ tptp.list_a)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> tptp.a tptp.nat)_ tptp.list_a)_ tptp.list_a_nat tptp.list_a)|)) (not (forall ((ii |u_(-> _u_(-> tptp.a tptp.nat)_ tptp.list_a)|)) (= (ho_132 v ii) (ite (= i ii) e (ho_132 u ii)))))))))) (let ((_let_109 (forall ((x |u_(-> _u_(-> _u_(-> tptp.a tptp.nat)_ tptp.list_a)_ tptp.list_a_nat tptp.list_a)|) (y |u_(-> _u_(-> _u_(-> tptp.a tptp.nat)_ tptp.list_a)_ tptp.list_a_nat tptp.list_a)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.a tptp.nat)_ tptp.list_a)|)) (= (ho_132 x z) (ho_132 y z)))) (= x y))))) (let ((_let_110 (forall ((u |u_(-> _u_(-> tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a)_ tptp.list_P1467822637od_a_a)|) (e tptp.list_P1467822637od_a_a) (i |u_(-> tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a)_ tptp.list_P1467822637od_a_a)|)) (not (forall ((ii |u_(-> tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a)|)) (= (ho_121 v ii) (ite (= i ii) e (ho_121 u ii)))))))))) (let ((_let_111 (forall ((x |u_(-> _u_(-> tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a)_ tptp.list_P1467822637od_a_a)|) (y |u_(-> _u_(-> tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a)_ tptp.list_P1467822637od_a_a)|)) (or (not (forall ((z |u_(-> tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a)|)) (= (ho_121 x z) (ho_121 y z)))) (= x y))))) (let ((_let_112 (forall ((u |u_(-> tptp.a _u_(-> tptp.a tptp.nat)_ tptp.product_prod_a_a_nat)|) (e |u_(-> _u_(-> tptp.a tptp.nat)_ tptp.product_prod_a_a_nat)|) (i tptp.a)) (not (forall ((v |u_(-> tptp.a _u_(-> tptp.a tptp.nat)_ tptp.product_prod_a_a_nat)|)) (not (forall ((ii tptp.a)) (= (ho_241 v ii) (ite (= i ii) e (ho_241 u ii)))))))))) (let ((_let_113 (forall ((x |u_(-> tptp.a _u_(-> tptp.a tptp.nat)_ tptp.product_prod_a_a_nat)|) (y |u_(-> tptp.a _u_(-> tptp.a tptp.nat)_ tptp.product_prod_a_a_nat)|)) (or (not (forall ((z tptp.a)) (= (ho_241 x z) (ho_241 y z)))) (= x y))))) (let ((_let_114 (forall ((u |u_(-> tptp.product_prod_a_a tptp.list_l1108175539od_a_a)|) (e tptp.list_l1108175539od_a_a) (i tptp.product_prod_a_a)) (not (forall ((v |u_(-> tptp.product_prod_a_a tptp.list_l1108175539od_a_a)|)) (not (forall ((ii tptp.product_prod_a_a)) (= (ho_115 v ii) (ite (= i ii) e (ho_115 u ii)))))))))) (let ((_let_115 (forall ((x |u_(-> tptp.product_prod_a_a tptp.list_l1108175539od_a_a)|) (y |u_(-> tptp.product_prod_a_a tptp.list_l1108175539od_a_a)|)) (or (not (forall ((z tptp.product_prod_a_a)) (= (ho_115 x z) (ho_115 y z)))) (= x y))))) (let ((_let_116 (forall ((u |u_(-> tptp.a tptp.set_a Bool)|) (e |u_(-> tptp.set_a Bool)|) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.set_a Bool)|)) (not (forall ((ii tptp.a)) (= (ho_20 v ii) (ite (= i ii) e (ho_20 u ii)))))))))) (let ((_let_117 (forall ((x |u_(-> tptp.a tptp.set_a Bool)|) (y |u_(-> tptp.a tptp.set_a Bool)|)) (or (not (forall ((z tptp.a)) (= (ho_20 x z) (ho_20 y z)))) (= x y))))) (let ((_let_118 (forall ((u |u_(-> tptp.list_P1467822637od_a_a tptp.list_l1108175539od_a_a)|) (e tptp.list_l1108175539od_a_a) (i tptp.list_P1467822637od_a_a)) (not (forall ((v |u_(-> tptp.list_P1467822637od_a_a tptp.list_l1108175539od_a_a)|)) (not (forall ((ii tptp.list_P1467822637od_a_a)) (= (ho_145 v ii) (ite (= i ii) e (ho_145 u ii)))))))))) (let ((_let_119 (forall ((x |u_(-> tptp.list_P1467822637od_a_a tptp.list_l1108175539od_a_a)|) (y |u_(-> tptp.list_P1467822637od_a_a tptp.list_l1108175539od_a_a)|)) (or (not (forall ((z tptp.list_P1467822637od_a_a)) (= (ho_145 x z) (ho_145 y z)))) (= x y))))) (let ((_let_120 (forall ((u |u_(-> tptp.a tptp.product_prod_a_nat_a)|) (e tptp.product_prod_a_nat_a) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.product_prod_a_nat_a)|)) (not (forall ((ii tptp.a)) (= (ho_251 v ii) (ite (= i ii) e (ho_251 u ii)))))))))) (let ((_let_121 (forall ((x |u_(-> tptp.a tptp.product_prod_a_nat_a)|) (y |u_(-> tptp.a tptp.product_prod_a_nat_a)|)) (or (not (forall ((z tptp.a)) (= (ho_251 x z) (ho_251 y z)))) (= x y))))) (let ((_let_122 (forall ((u |u_(-> tptp.list_a_nat _u_(-> _u_(-> tptp.a tptp.nat)_ tptp.list_P1467822637od_a_a)_ tptp.list_P1467822637od_a_a)|) (e |u_(-> _u_(-> _u_(-> tptp.a tptp.nat)_ tptp.list_P1467822637od_a_a)_ tptp.list_P1467822637od_a_a)|) (i tptp.list_a_nat)) (not (forall ((v |u_(-> tptp.list_a_nat _u_(-> _u_(-> tptp.a tptp.nat)_ tptp.list_P1467822637od_a_a)_ tptp.list_P1467822637od_a_a)|)) (not (forall ((ii tptp.list_a_nat)) (= (ho_113 v ii) (ite (= i ii) e (ho_113 u ii)))))))))) (let ((_let_123 (forall ((x |u_(-> tptp.list_a_nat _u_(-> _u_(-> tptp.a tptp.nat)_ tptp.list_P1467822637od_a_a)_ tptp.list_P1467822637od_a_a)|) (y |u_(-> tptp.list_a_nat _u_(-> _u_(-> tptp.a tptp.nat)_ tptp.list_P1467822637od_a_a)_ tptp.list_P1467822637od_a_a)|)) (or (not (forall ((z tptp.list_a_nat)) (= (ho_113 x z) (ho_113 y z)))) (= x y))))) (let ((_let_124 (forall ((u |u_(-> _u_(-> _u_(-> tptp.a tptp.nat)_ tptp.list_P1467822637od_a_a)_ tptp.list_P1467822637od_a_a)|) (e tptp.list_P1467822637od_a_a) (i |u_(-> _u_(-> tptp.a tptp.nat)_ tptp.list_P1467822637od_a_a)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> tptp.a tptp.nat)_ tptp.list_P1467822637od_a_a)_ tptp.list_P1467822637od_a_a)|)) (not (forall ((ii |u_(-> _u_(-> tptp.a tptp.nat)_ tptp.list_P1467822637od_a_a)|)) (= (ho_114 v ii) (ite (= i ii) e (ho_114 u ii)))))))))) (let ((_let_125 (forall ((x |u_(-> _u_(-> _u_(-> tptp.a tptp.nat)_ tptp.list_P1467822637od_a_a)_ tptp.list_P1467822637od_a_a)|) (y |u_(-> _u_(-> _u_(-> tptp.a tptp.nat)_ tptp.list_P1467822637od_a_a)_ tptp.list_P1467822637od_a_a)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.a tptp.nat)_ tptp.list_P1467822637od_a_a)|)) (= (ho_114 x z) (ho_114 y z)))) (= x y))))) (let ((_let_126 (forall ((u |u_(-> _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a Bool)_ tptp.list_P1467822637od_a_a tptp.produc501911462od_a_a)|) (e |u_(-> tptp.list_P1467822637od_a_a tptp.produc501911462od_a_a)|) (i |u_(-> tptp.product_prod_a_a tptp.product_prod_a_a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a Bool)_ tptp.list_P1467822637od_a_a tptp.produc501911462od_a_a)|)) (not (forall ((ii |u_(-> tptp.product_prod_a_a tptp.product_prod_a_a Bool)|)) (= (ho_69 v ii) (ite (= i ii) e (ho_69 u ii)))))))))) (let ((_let_127 (forall ((x |u_(-> _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a Bool)_ tptp.list_P1467822637od_a_a tptp.produc501911462od_a_a)|) (y |u_(-> _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a Bool)_ tptp.list_P1467822637od_a_a tptp.produc501911462od_a_a)|)) (or (not (forall ((z |u_(-> tptp.product_prod_a_a tptp.product_prod_a_a Bool)|)) (= (ho_69 x z) (ho_69 y z)))) (= x y))))) (let ((_let_128 (forall ((u |u_(-> tptp.list_P305489470_a_a_a tptp.list_P305489470_a_a_a)|) (e tptp.list_P305489470_a_a_a) (i tptp.list_P305489470_a_a_a)) (not (forall ((v |u_(-> tptp.list_P305489470_a_a_a tptp.list_P305489470_a_a_a)|)) (not (forall ((ii tptp.list_P305489470_a_a_a)) (= (ho_266 v ii) (ite (= i ii) e (ho_266 u ii)))))))))) (let ((_let_129 (forall ((x |u_(-> tptp.list_P305489470_a_a_a tptp.list_P305489470_a_a_a)|) (y |u_(-> tptp.list_P305489470_a_a_a tptp.list_P305489470_a_a_a)|)) (or (not (forall ((z tptp.list_P305489470_a_a_a)) (= (ho_266 x z) (ho_266 y z)))) (= x y))))) (let ((_let_130 (forall ((u |u_(-> _u_(-> tptp.a tptp.nat)_ tptp.list_P1467822637od_a_a)|) (e tptp.list_P1467822637od_a_a) (i |u_(-> tptp.a tptp.nat)|)) (not (forall ((v |u_(-> _u_(-> tptp.a tptp.nat)_ tptp.list_P1467822637od_a_a)|)) (not (forall ((ii |u_(-> tptp.a tptp.nat)|)) (= (ho_111 v ii) (ite (= i ii) e (ho_111 u ii)))))))))) (let ((_let_131 (forall ((x |u_(-> _u_(-> tptp.a tptp.nat)_ tptp.list_P1467822637od_a_a)|) (y |u_(-> _u_(-> tptp.a tptp.nat)_ tptp.list_P1467822637od_a_a)|)) (or (not (forall ((z |u_(-> tptp.a tptp.nat)|)) (= (ho_111 x z) (ho_111 y z)))) (= x y))))) (let ((_let_132 (forall ((u |u_(-> tptp.produc864062247list_a tptp.set_Pr1971762695list_a Bool)|) (e |u_(-> tptp.set_Pr1971762695list_a Bool)|) (i tptp.produc864062247list_a)) (not (forall ((v |u_(-> tptp.produc864062247list_a tptp.set_Pr1971762695list_a Bool)|)) (not (forall ((ii tptp.produc864062247list_a)) (= (ho_35 v ii) (ite (= i ii) e (ho_35 u ii)))))))))) (let ((_let_133 (forall ((x |u_(-> tptp.produc864062247list_a tptp.set_Pr1971762695list_a Bool)|) (y |u_(-> tptp.produc864062247list_a tptp.set_Pr1971762695list_a Bool)|)) (or (not (forall ((z tptp.produc864062247list_a)) (= (ho_35 x z) (ho_35 y z)))) (= x y))))) (let ((_let_134 (forall ((u |u_(-> tptp.set_Pr1295299783od_a_a Bool)|) (e Bool) (i tptp.set_Pr1295299783od_a_a)) (not (forall ((v |u_(-> tptp.set_Pr1295299783od_a_a Bool)|)) (not (forall ((ii tptp.set_Pr1295299783od_a_a)) (= (ho_162 v ii) (ite (= i ii) e (ho_162 u ii)))))))))) (let ((_let_135 (forall ((x |u_(-> tptp.set_Pr1295299783od_a_a Bool)|) (y |u_(-> tptp.set_Pr1295299783od_a_a Bool)|)) (or (not (forall ((z tptp.set_Pr1295299783od_a_a)) (= (ho_162 x z) (ho_162 y z)))) (= x y))))) (let ((_let_136 (forall ((u |u_(-> tptp.list_l1108175539od_a_a _u_(-> tptp.list_P1467822637od_a_a tptp.list_a)_ tptp.list_a)|) (e |u_(-> _u_(-> tptp.list_P1467822637od_a_a tptp.list_a)_ tptp.list_a)|) (i tptp.list_l1108175539od_a_a)) (not (forall ((v |u_(-> tptp.list_l1108175539od_a_a _u_(-> tptp.list_P1467822637od_a_a tptp.list_a)_ tptp.list_a)|)) (not (forall ((ii tptp.list_l1108175539od_a_a)) (= (ho_109 v ii) (ite (= i ii) e (ho_109 u ii)))))))))) (let ((_let_137 (forall ((x |u_(-> tptp.list_l1108175539od_a_a _u_(-> tptp.list_P1467822637od_a_a tptp.list_a)_ tptp.list_a)|) (y |u_(-> tptp.list_l1108175539od_a_a _u_(-> tptp.list_P1467822637od_a_a tptp.list_a)_ tptp.list_a)|)) (or (not (forall ((z tptp.list_l1108175539od_a_a)) (= (ho_109 x z) (ho_109 y z)))) (= x y))))) (let ((_let_138 (forall ((u |u_(-> tptp.product_prod_a_a tptp.set_Product_prod_a_a Bool)|) (e |u_(-> tptp.set_Product_prod_a_a Bool)|) (i tptp.product_prod_a_a)) (not (forall ((v |u_(-> tptp.product_prod_a_a tptp.set_Product_prod_a_a Bool)|)) (not (forall ((ii tptp.product_prod_a_a)) (= (ho_14 v ii) (ite (= i ii) e (ho_14 u ii)))))))))) (let ((_let_139 (forall ((x |u_(-> tptp.product_prod_a_a tptp.set_Product_prod_a_a Bool)|) (y |u_(-> tptp.product_prod_a_a tptp.set_Product_prod_a_a Bool)|)) (or (not (forall ((z tptp.product_prod_a_a)) (= (ho_14 x z) (ho_14 y z)))) (= x y))))) (let ((_let_140 (forall ((u |u_(-> tptp.product_prod_a_a tptp.produc1572603623od_a_a)|) (e tptp.produc1572603623od_a_a) (i tptp.product_prod_a_a)) (not (forall ((v |u_(-> tptp.product_prod_a_a tptp.produc1572603623od_a_a)|)) (not (forall ((ii tptp.product_prod_a_a)) (= (ho_208 v ii) (ite (= i ii) e (ho_208 u ii)))))))))) (let ((_let_141 (forall ((x |u_(-> tptp.product_prod_a_a tptp.produc1572603623od_a_a)|) (y |u_(-> tptp.product_prod_a_a tptp.produc1572603623od_a_a)|)) (or (not (forall ((z tptp.product_prod_a_a)) (= (ho_208 x z) (ho_208 y z)))) (= x y))))) (let ((_let_142 (forall ((u |u_(-> tptp.list_P1467822637od_a_a tptp.list_a)|) (e tptp.list_a) (i tptp.list_P1467822637od_a_a)) (not (forall ((v |u_(-> tptp.list_P1467822637od_a_a tptp.list_a)|)) (not (forall ((ii tptp.list_P1467822637od_a_a)) (= (ho_107 v ii) (ite (= i ii) e (ho_107 u ii)))))))))) (let ((_let_143 (forall ((x |u_(-> tptp.list_P1467822637od_a_a tptp.list_a)|) (y |u_(-> tptp.list_P1467822637od_a_a tptp.list_a)|)) (or (not (forall ((z tptp.list_P1467822637od_a_a)) (= (ho_107 x z) (ho_107 y z)))) (= x y))))) (let ((_let_144 (forall ((u |u_(-> tptp.set_Pr779272263od_a_a Bool)|) (e Bool) (i tptp.set_Pr779272263od_a_a)) (not (forall ((v |u_(-> tptp.set_Pr779272263od_a_a Bool)|)) (not (forall ((ii tptp.set_Pr779272263od_a_a)) (= (ho_156 v ii) (ite (= i ii) e (ho_156 u ii)))))))))) (let ((_let_145 (forall ((x |u_(-> tptp.set_Pr779272263od_a_a Bool)|) (y |u_(-> tptp.set_Pr779272263od_a_a Bool)|)) (or (not (forall ((z tptp.set_Pr779272263od_a_a)) (= (ho_156 x z) (ho_156 y z)))) (= x y))))) (let ((_let_146 (forall ((u |u_(-> tptp.list_P1467822637od_a_a tptp.produc501911462od_a_a)|) (e tptp.produc501911462od_a_a) (i tptp.list_P1467822637od_a_a)) (not (forall ((v |u_(-> tptp.list_P1467822637od_a_a tptp.produc501911462od_a_a)|)) (not (forall ((ii tptp.list_P1467822637od_a_a)) (= (ho_70 v ii) (ite (= i ii) e (ho_70 u ii)))))))))) (let ((_let_147 (forall ((x |u_(-> tptp.list_P1467822637od_a_a tptp.produc501911462od_a_a)|) (y |u_(-> tptp.list_P1467822637od_a_a tptp.produc501911462od_a_a)|)) (or (not (forall ((z tptp.list_P1467822637od_a_a)) (= (ho_70 x z) (ho_70 y z)))) (= x y))))) (let ((_let_148 (forall ((u |u_(-> tptp.list_a _u_(-> tptp.a tptp.list_l1108175539od_a_a)_ tptp.list_l1108175539od_a_a)|) (e |u_(-> _u_(-> tptp.a tptp.list_l1108175539od_a_a)_ tptp.list_l1108175539od_a_a)|) (i tptp.list_a)) (not (forall ((v |u_(-> tptp.list_a _u_(-> tptp.a tptp.list_l1108175539od_a_a)_ tptp.list_l1108175539od_a_a)|)) (not (forall ((ii tptp.list_a)) (= (ho_105 v ii) (ite (= i ii) e (ho_105 u ii)))))))))) (let ((_let_149 (forall ((x |u_(-> tptp.list_a _u_(-> tptp.a tptp.list_l1108175539od_a_a)_ tptp.list_l1108175539od_a_a)|) (y |u_(-> tptp.list_a _u_(-> tptp.a tptp.list_l1108175539od_a_a)_ tptp.list_l1108175539od_a_a)|)) (or (not (forall ((z tptp.list_a)) (= (ho_105 x z) (ho_105 y z)))) (= x y))))) (let ((_let_150 (forall ((u |u_(-> _u_(-> tptp.a tptp.list_l1108175539od_a_a)_ tptp.list_l1108175539od_a_a)|) (e tptp.list_l1108175539od_a_a) (i |u_(-> tptp.a tptp.list_l1108175539od_a_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.a tptp.list_l1108175539od_a_a)_ tptp.list_l1108175539od_a_a)|)) (not (forall ((ii |u_(-> tptp.a tptp.list_l1108175539od_a_a)|)) (= (ho_106 v ii) (ite (= i ii) e (ho_106 u ii)))))))))) (let ((_let_151 (forall ((x |u_(-> _u_(-> tptp.a tptp.list_l1108175539od_a_a)_ tptp.list_l1108175539od_a_a)|) (y |u_(-> _u_(-> tptp.a tptp.list_l1108175539od_a_a)_ tptp.list_l1108175539od_a_a)|)) (or (not (forall ((z |u_(-> tptp.a tptp.list_l1108175539od_a_a)|)) (= (ho_106 x z) (ho_106 y z)))) (= x y))))) (let ((_let_152 (forall ((u |u_(-> tptp.list_P1467822637od_a_a tptp.list_a tptp.list_P319927492_a_a_a)|) (e |u_(-> tptp.list_a tptp.list_P319927492_a_a_a)|) (i tptp.list_P1467822637od_a_a)) (not (forall ((v |u_(-> tptp.list_P1467822637od_a_a tptp.list_a tptp.list_P319927492_a_a_a)|)) (not (forall ((ii tptp.list_P1467822637od_a_a)) (= (ho_220 v ii) (ite (= i ii) e (ho_220 u ii)))))))))) (let ((_let_153 (forall ((x |u_(-> tptp.list_P1467822637od_a_a tptp.list_a tptp.list_P319927492_a_a_a)|) (y |u_(-> tptp.list_P1467822637od_a_a tptp.list_a tptp.list_P319927492_a_a_a)|)) (or (not (forall ((z tptp.list_P1467822637od_a_a)) (= (ho_220 x z) (ho_220 y z)))) (= x y))))) (let ((_let_154 (forall ((u |u_(-> tptp.a tptp.list_l1108175539od_a_a)|) (e tptp.list_l1108175539od_a_a) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.list_l1108175539od_a_a)|)) (not (forall ((ii tptp.a)) (= (ho_103 v ii) (ite (= i ii) e (ho_103 u ii)))))))))) (let ((_let_155 (forall ((x |u_(-> tptp.a tptp.list_l1108175539od_a_a)|) (y |u_(-> tptp.a tptp.list_l1108175539od_a_a)|)) (or (not (forall ((z tptp.a)) (= (ho_103 x z) (ho_103 y z)))) (= x y))))) (let ((_let_156 (forall ((u |u_(-> tptp.list_a_nat _u_(-> _u_(-> tptp.a tptp.nat)_ tptp.list_a)_ tptp.list_a)|) (e |u_(-> _u_(-> _u_(-> tptp.a tptp.nat)_ tptp.list_a)_ tptp.list_a)|) (i tptp.list_a_nat)) (not (forall ((v |u_(-> tptp.list_a_nat _u_(-> _u_(-> tptp.a tptp.nat)_ tptp.list_a)_ tptp.list_a)|)) (not (forall ((ii tptp.list_a_nat)) (= (ho_101 v ii) (ite (= i ii) e (ho_101 u ii)))))))))) (let ((_let_157 (forall ((x |u_(-> tptp.list_a_nat _u_(-> _u_(-> tptp.a tptp.nat)_ tptp.list_a)_ tptp.list_a)|) (y |u_(-> tptp.list_a_nat _u_(-> _u_(-> tptp.a tptp.nat)_ tptp.list_a)_ tptp.list_a)|)) (or (not (forall ((z tptp.list_a_nat)) (= (ho_101 x z) (ho_101 y z)))) (= x y))))) (let ((_let_158 (forall ((u |u_(-> tptp.produc1572603623od_a_a tptp.set_Pr1948701895od_a_a Bool)|) (e |u_(-> tptp.set_Pr1948701895od_a_a Bool)|) (i tptp.produc1572603623od_a_a)) (not (forall ((v |u_(-> tptp.produc1572603623od_a_a tptp.set_Pr1948701895od_a_a Bool)|)) (not (forall ((ii tptp.produc1572603623od_a_a)) (= (ho_210 v ii) (ite (= i ii) e (ho_210 u ii)))))))))) (let ((_let_159 (forall ((x |u_(-> tptp.produc1572603623od_a_a tptp.set_Pr1948701895od_a_a Bool)|) (y |u_(-> tptp.produc1572603623od_a_a tptp.set_Pr1948701895od_a_a Bool)|)) (or (not (forall ((z tptp.produc1572603623od_a_a)) (= (ho_210 x z) (ho_210 y z)))) (= x y))))) (let ((_let_160 (forall ((u |u_(-> tptp.list_a _u_(-> tptp.a tptp.list_P1467822637od_a_a)_ tptp.list_P1467822637od_a_a)|) (e |u_(-> _u_(-> tptp.a tptp.list_P1467822637od_a_a)_ tptp.list_P1467822637od_a_a)|) (i tptp.list_a)) (not (forall ((v |u_(-> tptp.list_a _u_(-> tptp.a tptp.list_P1467822637od_a_a)_ tptp.list_P1467822637od_a_a)|)) (not (forall ((ii tptp.list_a)) (= (ho_97 v ii) (ite (= i ii) e (ho_97 u ii)))))))))) (let ((_let_161 (forall ((x |u_(-> tptp.list_a _u_(-> tptp.a tptp.list_P1467822637od_a_a)_ tptp.list_P1467822637od_a_a)|) (y |u_(-> tptp.list_a _u_(-> tptp.a tptp.list_P1467822637od_a_a)_ tptp.list_P1467822637od_a_a)|)) (or (not (forall ((z tptp.list_a)) (= (ho_97 x z) (ho_97 y z)))) (= x y))))) (let ((_let_162 (forall ((u |u_(-> _u_(-> tptp.a tptp.list_a)_ tptp.list_a tptp.list_a)|) (e |u_(-> tptp.list_a tptp.list_a)|) (i |u_(-> tptp.a tptp.list_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.a tptp.list_a)_ tptp.list_a tptp.list_a)|)) (not (forall ((ii |u_(-> tptp.a tptp.list_a)|)) (= (ho_125 v ii) (ite (= i ii) e (ho_125 u ii)))))))))) (let ((_let_163 (forall ((x |u_(-> _u_(-> tptp.a tptp.list_a)_ tptp.list_a tptp.list_a)|) (y |u_(-> _u_(-> tptp.a tptp.list_a)_ tptp.list_a tptp.list_a)|)) (or (not (forall ((z |u_(-> tptp.a tptp.list_a)|)) (= (ho_125 x z) (ho_125 y z)))) (= x y))))) (let ((_let_164 (forall ((u |u_(-> tptp.list_l1108175539od_a_a tptp.list_l1108175539od_a_a tptp.list_l1108175539od_a_a)|) (e |u_(-> tptp.list_l1108175539od_a_a tptp.list_l1108175539od_a_a)|) (i tptp.list_l1108175539od_a_a)) (not (forall ((v |u_(-> tptp.list_l1108175539od_a_a tptp.list_l1108175539od_a_a tptp.list_l1108175539od_a_a)|)) (not (forall ((ii tptp.list_l1108175539od_a_a)) (= (ho_49 v ii) (ite (= i ii) e (ho_49 u ii)))))))))) (let ((_let_165 (forall ((x |u_(-> tptp.list_l1108175539od_a_a tptp.list_l1108175539od_a_a tptp.list_l1108175539od_a_a)|) (y |u_(-> tptp.list_l1108175539od_a_a tptp.list_l1108175539od_a_a tptp.list_l1108175539od_a_a)|)) (or (not (forall ((z tptp.list_l1108175539od_a_a)) (= (ho_49 x z) (ho_49 y z)))) (= x y))))) (let ((_let_166 (forall ((u |u_(-> tptp.produc657724903od_a_a tptp.set_Pr1239640519od_a_a Bool)|) (e |u_(-> tptp.set_Pr1239640519od_a_a Bool)|) (i tptp.produc657724903od_a_a)) (not (forall ((v |u_(-> tptp.produc657724903od_a_a tptp.set_Pr1239640519od_a_a Bool)|)) (not (forall ((ii tptp.produc657724903od_a_a)) (= (ho_169 v ii) (ite (= i ii) e (ho_169 u ii)))))))))) (let ((_let_167 (forall ((x |u_(-> tptp.produc657724903od_a_a tptp.set_Pr1239640519od_a_a Bool)|) (y |u_(-> tptp.produc657724903od_a_a tptp.set_Pr1239640519od_a_a Bool)|)) (or (not (forall ((z tptp.produc657724903od_a_a)) (= (ho_169 x z) (ho_169 y z)))) (= x y))))) (let ((_let_168 (forall ((u |u_(-> tptp.list_P1891567085od_a_a tptp.list_P1891567085od_a_a tptp.list_P1891567085od_a_a)|) (e |u_(-> tptp.list_P1891567085od_a_a tptp.list_P1891567085od_a_a)|) (i tptp.list_P1891567085od_a_a)) (not (forall ((v |u_(-> tptp.list_P1891567085od_a_a tptp.list_P1891567085od_a_a tptp.list_P1891567085od_a_a)|)) (not (forall ((ii tptp.list_P1891567085od_a_a)) (= (ho_46 v ii) (ite (= i ii) e (ho_46 u ii)))))))))) (let ((_let_169 (forall ((x |u_(-> tptp.list_P1891567085od_a_a tptp.list_P1891567085od_a_a tptp.list_P1891567085od_a_a)|) (y |u_(-> tptp.list_P1891567085od_a_a tptp.list_P1891567085od_a_a tptp.list_P1891567085od_a_a)|)) (or (not (forall ((z tptp.list_P1891567085od_a_a)) (= (ho_46 x z) (ho_46 y z)))) (= x y))))) (let ((_let_170 (forall ((u |u_(-> tptp.list_P1467822637od_a_a tptp.list_l1108175539od_a_a tptp.list_l1108175539od_a_a)|) (e |u_(-> tptp.list_l1108175539od_a_a tptp.list_l1108175539od_a_a)|) (i tptp.list_P1467822637od_a_a)) (not (forall ((v |u_(-> tptp.list_P1467822637od_a_a tptp.list_l1108175539od_a_a tptp.list_l1108175539od_a_a)|)) (not (forall ((ii tptp.list_P1467822637od_a_a)) (= (ho_56 v ii) (ite (= i ii) e (ho_56 u ii)))))))))) (let ((_let_171 (forall ((x |u_(-> tptp.list_P1467822637od_a_a tptp.list_l1108175539od_a_a tptp.list_l1108175539od_a_a)|) (y |u_(-> tptp.list_P1467822637od_a_a tptp.list_l1108175539od_a_a tptp.list_l1108175539od_a_a)|)) (or (not (forall ((z tptp.list_P1467822637od_a_a)) (= (ho_56 x z) (ho_56 y z)))) (= x y))))) (let ((_let_172 (forall ((u |u_(-> tptp.list_P1891567085od_a_a tptp.list_P1891567085od_a_a)|) (e tptp.list_P1891567085od_a_a) (i tptp.list_P1891567085od_a_a)) (not (forall ((v |u_(-> tptp.list_P1891567085od_a_a tptp.list_P1891567085od_a_a)|)) (not (forall ((ii tptp.list_P1891567085od_a_a)) (= (ho_47 v ii) (ite (= i ii) e (ho_47 u ii)))))))))) (let ((_let_173 (forall ((x |u_(-> tptp.list_P1891567085od_a_a tptp.list_P1891567085od_a_a)|) (y |u_(-> tptp.list_P1891567085od_a_a tptp.list_P1891567085od_a_a)|)) (or (not (forall ((z tptp.list_P1891567085od_a_a)) (= (ho_47 x z) (ho_47 y z)))) (= x y))))) (let ((_let_174 (forall ((u |u_(-> _u_(-> tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a)_ tptp.list_l1108175539od_a_a tptp.list_P1467822637od_a_a)|) (e |u_(-> tptp.list_l1108175539od_a_a tptp.list_P1467822637od_a_a)|) (i |u_(-> tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a)_ tptp.list_l1108175539od_a_a tptp.list_P1467822637od_a_a)|)) (not (forall ((ii |u_(-> tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a)|)) (= (ho_147 v ii) (ite (= i ii) e (ho_147 u ii)))))))))) (let ((_let_175 (forall ((x |u_(-> _u_(-> tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a)_ tptp.list_l1108175539od_a_a tptp.list_P1467822637od_a_a)|) (y |u_(-> _u_(-> tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a)_ tptp.list_l1108175539od_a_a tptp.list_P1467822637od_a_a)|)) (or (not (forall ((z |u_(-> tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a)|)) (= (ho_147 x z) (ho_147 y z)))) (= x y))))) (let ((_let_176 (forall ((u |u_(-> tptp.product_prod_a_a Bool)|) (e Bool) (i tptp.product_prod_a_a)) (not (forall ((v |u_(-> tptp.product_prod_a_a Bool)|)) (not (forall ((ii tptp.product_prod_a_a)) (= (ho_30 v ii) (ite (= i ii) e (ho_30 u ii)))))))))) (let ((_let_177 (forall ((x |u_(-> tptp.product_prod_a_a Bool)|) (y |u_(-> tptp.product_prod_a_a Bool)|)) (or (not (forall ((z tptp.product_prod_a_a)) (= (ho_30 x z) (ho_30 y z)))) (= x y))))) (let ((_let_178 (forall ((u |u_(-> _u_(-> tptp.list_P1467822637od_a_a tptp.list_a)_ tptp.list_a)|) (e tptp.list_a) (i |u_(-> tptp.list_P1467822637od_a_a tptp.list_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.list_P1467822637od_a_a tptp.list_a)_ tptp.list_a)|)) (not (forall ((ii |u_(-> tptp.list_P1467822637od_a_a tptp.list_a)|)) (= (ho_110 v ii) (ite (= i ii) e (ho_110 u ii)))))))))) (let ((_let_179 (forall ((x |u_(-> _u_(-> tptp.list_P1467822637od_a_a tptp.list_a)_ tptp.list_a)|) (y |u_(-> _u_(-> tptp.list_P1467822637od_a_a tptp.list_a)_ tptp.list_a)|)) (or (not (forall ((z |u_(-> tptp.list_P1467822637od_a_a tptp.list_a)|)) (= (ho_110 x z) (ho_110 y z)))) (= x y))))) (let ((_let_180 (forall ((u |u_(-> tptp.product_prod_a_a tptp.a tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a)|) (e |u_(-> tptp.a tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a)|) (i tptp.product_prod_a_a)) (not (forall ((v |u_(-> tptp.product_prod_a_a tptp.a tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a)|)) (not (forall ((ii tptp.product_prod_a_a)) (= (ho_343 v ii) (ite (= i ii) e (ho_343 u ii)))))))))) (let ((_let_181 (forall ((x |u_(-> tptp.product_prod_a_a tptp.a tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a)|) (y |u_(-> tptp.product_prod_a_a tptp.a tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a)|)) (or (not (forall ((z tptp.product_prod_a_a)) (= (ho_343 x z) (ho_343 y z)))) (= x y))))) (let ((_let_182 (forall ((u |u_(-> _u_(-> tptp.a tptp.nat)_ tptp.list_a_nat tptp.list_a_nat)|) (e |u_(-> tptp.list_a_nat tptp.list_a_nat)|) (i |u_(-> tptp.a tptp.nat)|)) (not (forall ((v |u_(-> _u_(-> tptp.a tptp.nat)_ tptp.list_a_nat tptp.list_a_nat)|)) (not (forall ((ii |u_(-> tptp.a tptp.nat)|)) (= (ho_59 v ii) (ite (= i ii) e (ho_59 u ii)))))))))) (let ((_let_183 (forall ((x |u_(-> _u_(-> tptp.a tptp.nat)_ tptp.list_a_nat tptp.list_a_nat)|) (y |u_(-> _u_(-> tptp.a tptp.nat)_ tptp.list_a_nat tptp.list_a_nat)|)) (or (not (forall ((z |u_(-> tptp.a tptp.nat)|)) (= (ho_59 x z) (ho_59 y z)))) (= x y))))) (let ((_let_184 (forall ((u |u_(-> tptp.list_a Bool)|) (e Bool) (i tptp.list_a)) (not (forall ((v |u_(-> tptp.list_a Bool)|)) (not (forall ((ii tptp.list_a)) (= (ho_302 v ii) (ite (= i ii) e (ho_302 u ii)))))))))) (let ((_let_185 (forall ((x |u_(-> tptp.list_a Bool)|) (y |u_(-> tptp.list_a Bool)|)) (or (not (forall ((z tptp.list_a)) (= (ho_302 x z) (ho_302 y z)))) (= x y))))) (let ((_let_186 (forall ((u |u_(-> tptp.list_a tptp.list_a Bool)|) (e |u_(-> tptp.list_a Bool)|) (i tptp.list_a)) (not (forall ((v |u_(-> tptp.list_a tptp.list_a Bool)|)) (not (forall ((ii tptp.list_a)) (= (ho_381 v ii) (ite (= i ii) e (ho_381 u ii)))))))))) (let ((_let_187 (forall ((x |u_(-> tptp.list_a tptp.list_a Bool)|) (y |u_(-> tptp.list_a tptp.list_a Bool)|)) (or (not (forall ((z tptp.list_a)) (= (ho_381 x z) (ho_381 y z)))) (= x y))))) (let ((_let_188 (forall ((u |u_(-> tptp.product_prod_a_a tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a)|) (e |u_(-> tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a)|) (i tptp.product_prod_a_a)) (not (forall ((v |u_(-> tptp.product_prod_a_a tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a)|)) (not (forall ((ii tptp.product_prod_a_a)) (= (ho_38 v ii) (ite (= i ii) e (ho_38 u ii)))))))))) (let ((_let_189 (forall ((x |u_(-> tptp.product_prod_a_a tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a)|) (y |u_(-> tptp.product_prod_a_a tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a)|)) (or (not (forall ((z tptp.product_prod_a_a)) (= (ho_38 x z) (ho_38 y z)))) (= x y))))) (let ((_let_190 (forall ((u |u_(-> tptp.list_P601816365list_a tptp.list_P601816365list_a)|) (e tptp.list_P601816365list_a) (i tptp.list_P601816365list_a)) (not (forall ((v |u_(-> tptp.list_P601816365list_a tptp.list_P601816365list_a)|)) (not (forall ((ii tptp.list_P601816365list_a)) (= (ho_260 v ii) (ite (= i ii) e (ho_260 u ii)))))))))) (let ((_let_191 (forall ((x |u_(-> tptp.list_P601816365list_a tptp.list_P601816365list_a)|) (y |u_(-> tptp.list_P601816365list_a tptp.list_P601816365list_a)|)) (or (not (forall ((z tptp.list_P601816365list_a)) (= (ho_260 x z) (ho_260 y z)))) (= x y))))) (let ((_let_192 (forall ((u |u_(-> _u_(-> tptp.a tptp.nat)_ tptp.list_a)|) (e tptp.list_a) (i |u_(-> tptp.a tptp.nat)|)) (not (forall ((v |u_(-> _u_(-> tptp.a tptp.nat)_ tptp.list_a)|)) (not (forall ((ii |u_(-> tptp.a tptp.nat)|)) (= (ho_99 v ii) (ite (= i ii) e (ho_99 u ii)))))))))) (let ((_let_193 (forall ((x |u_(-> _u_(-> tptp.a tptp.nat)_ tptp.list_a)|) (y |u_(-> _u_(-> tptp.a tptp.nat)_ tptp.list_a)|)) (or (not (forall ((z |u_(-> tptp.a tptp.nat)|)) (= (ho_99 x z) (ho_99 y z)))) (= x y))))) (let ((_let_194 (forall ((u |u_(-> tptp.list_a tptp.list_P1467822637od_a_a)|) (e tptp.list_P1467822637od_a_a) (i tptp.list_a)) (not (forall ((v |u_(-> tptp.list_a tptp.list_P1467822637od_a_a)|)) (not (forall ((ii tptp.list_a)) (= (ho_130 v ii) (ite (= i ii) e (ho_130 u ii)))))))))) (let ((_let_195 (forall ((x |u_(-> tptp.list_a tptp.list_P1467822637od_a_a)|) (y |u_(-> tptp.list_a tptp.list_P1467822637od_a_a)|)) (or (not (forall ((z tptp.list_a)) (= (ho_130 x z) (ho_130 y z)))) (= x y))))) (let ((_let_196 (forall ((u |u_(-> tptp.a tptp.list_a tptp.list_a)|) (e |u_(-> tptp.list_a tptp.list_a)|) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.list_a tptp.list_a)|)) (not (forall ((ii tptp.a)) (= (ho_52 v ii) (ite (= i ii) e (ho_52 u ii)))))))))) (let ((_let_197 (forall ((x |u_(-> tptp.a tptp.list_a tptp.list_a)|) (y |u_(-> tptp.a tptp.list_a tptp.list_a)|)) (or (not (forall ((z tptp.a)) (= (ho_52 x z) (ho_52 y z)))) (= x y))))) (let ((_let_198 (forall ((u |u_(-> tptp.list_P1891567085od_a_a tptp.produc205693799od_a_a)|) (e tptp.produc205693799od_a_a) (i tptp.list_P1891567085od_a_a)) (not (forall ((v |u_(-> tptp.list_P1891567085od_a_a tptp.produc205693799od_a_a)|)) (not (forall ((ii tptp.list_P1891567085od_a_a)) (= (ho_153 v ii) (ite (= i ii) e (ho_153 u ii)))))))))) (let ((_let_199 (forall ((x |u_(-> tptp.list_P1891567085od_a_a tptp.produc205693799od_a_a)|) (y |u_(-> tptp.list_P1891567085od_a_a tptp.produc205693799od_a_a)|)) (or (not (forall ((z tptp.list_P1891567085od_a_a)) (= (ho_153 x z) (ho_153 y z)))) (= x y))))) (let ((_let_200 (forall ((u |u_(-> tptp.list_P1467822637od_a_a _u_(-> tptp.product_prod_a_a tptp.list_P1467822637od_a_a)_ tptp.list_P1467822637od_a_a)|) (e |u_(-> _u_(-> tptp.product_prod_a_a tptp.list_P1467822637od_a_a)_ tptp.list_P1467822637od_a_a)|) (i tptp.list_P1467822637od_a_a)) (not (forall ((v |u_(-> tptp.list_P1467822637od_a_a _u_(-> tptp.product_prod_a_a tptp.list_P1467822637od_a_a)_ tptp.list_P1467822637od_a_a)|)) (not (forall ((ii tptp.list_P1467822637od_a_a)) (= (ho_85 v ii) (ite (= i ii) e (ho_85 u ii)))))))))) (let ((_let_201 (forall ((x |u_(-> tptp.list_P1467822637od_a_a _u_(-> tptp.product_prod_a_a tptp.list_P1467822637od_a_a)_ tptp.list_P1467822637od_a_a)|) (y |u_(-> tptp.list_P1467822637od_a_a _u_(-> tptp.product_prod_a_a tptp.list_P1467822637od_a_a)_ tptp.list_P1467822637od_a_a)|)) (or (not (forall ((z tptp.list_P1467822637od_a_a)) (= (ho_85 x z) (ho_85 y z)))) (= x y))))) (let ((_let_202 (forall ((u |u_(-> tptp.list_l1108175539od_a_a tptp.list_a)|) (e tptp.list_a) (i tptp.list_l1108175539od_a_a)) (not (forall ((v |u_(-> tptp.list_l1108175539od_a_a tptp.list_a)|)) (not (forall ((ii tptp.list_l1108175539od_a_a)) (= (ho_139 v ii) (ite (= i ii) e (ho_139 u ii)))))))))) (let ((_let_203 (forall ((x |u_(-> tptp.list_l1108175539od_a_a tptp.list_a)|) (y |u_(-> tptp.list_l1108175539od_a_a tptp.list_a)|)) (or (not (forall ((z tptp.list_l1108175539od_a_a)) (= (ho_139 x z) (ho_139 y z)))) (= x y))))) (let ((_let_204 (forall ((u |u_(-> tptp.list_a_nat tptp.list_a_nat)|) (e tptp.list_a_nat) (i tptp.list_a_nat)) (not (forall ((v |u_(-> tptp.list_a_nat tptp.list_a_nat)|)) (not (forall ((ii tptp.list_a_nat)) (= (ho_60 v ii) (ite (= i ii) e (ho_60 u ii)))))))))) (let ((_let_205 (forall ((x |u_(-> tptp.list_a_nat tptp.list_a_nat)|) (y |u_(-> tptp.list_a_nat tptp.list_a_nat)|)) (or (not (forall ((z tptp.list_a_nat)) (= (ho_60 x z) (ho_60 y z)))) (= x y))))) (let ((_let_206 (forall ((u |u_(-> tptp.list_a_nat tptp.list_P1467822637od_a_a)|) (e tptp.list_P1467822637od_a_a) (i tptp.list_a_nat)) (not (forall ((v |u_(-> tptp.list_a_nat tptp.list_P1467822637od_a_a)|)) (not (forall ((ii tptp.list_a_nat)) (= (ho_142 v ii) (ite (= i ii) e (ho_142 u ii)))))))))) (let ((_let_207 (forall ((x |u_(-> tptp.list_a_nat tptp.list_P1467822637od_a_a)|) (y |u_(-> tptp.list_a_nat tptp.list_P1467822637od_a_a)|)) (or (not (forall ((z tptp.list_a_nat)) (= (ho_142 x z) (ho_142 y z)))) (= x y))))) (let ((_let_208 (forall ((u |u_(-> tptp.list_P1467822637od_a_a _u_(-> tptp.product_prod_a_a tptp.list_a)_ tptp.list_a)|) (e |u_(-> _u_(-> tptp.product_prod_a_a tptp.list_a)_ tptp.list_a)|) (i tptp.list_P1467822637od_a_a)) (not (forall ((v |u_(-> tptp.list_P1467822637od_a_a _u_(-> tptp.product_prod_a_a tptp.list_a)_ tptp.list_a)|)) (not (forall ((ii tptp.list_P1467822637od_a_a)) (= (ho_93 v ii) (ite (= i ii) e (ho_93 u ii)))))))))) (let ((_let_209 (forall ((x |u_(-> tptp.list_P1467822637od_a_a _u_(-> tptp.product_prod_a_a tptp.list_a)_ tptp.list_a)|) (y |u_(-> tptp.list_P1467822637od_a_a _u_(-> tptp.product_prod_a_a tptp.list_a)_ tptp.list_a)|)) (or (not (forall ((z tptp.list_P1467822637od_a_a)) (= (ho_93 x z) (ho_93 y z)))) (= x y))))) (let ((_let_210 (forall ((u |u_(-> tptp.produc1701253078od_a_a tptp.produc821581462od_a_a)|) (e tptp.produc821581462od_a_a) (i tptp.produc1701253078od_a_a)) (not (forall ((v |u_(-> tptp.produc1701253078od_a_a tptp.produc821581462od_a_a)|)) (not (forall ((ii tptp.produc1701253078od_a_a)) (= (ho_340 v ii) (ite (= i ii) e (ho_340 u ii)))))))))) (let ((_let_211 (forall ((x |u_(-> tptp.produc1701253078od_a_a tptp.produc821581462od_a_a)|) (y |u_(-> tptp.produc1701253078od_a_a tptp.produc821581462od_a_a)|)) (or (not (forall ((z tptp.produc1701253078od_a_a)) (= (ho_340 x z) (ho_340 y z)))) (= x y))))) (let ((_let_212 (forall ((u |u_(-> tptp.set_Product_prod_a_a Bool)|) (e Bool) (i tptp.set_Product_prod_a_a)) (not (forall ((v |u_(-> tptp.set_Product_prod_a_a Bool)|)) (not (forall ((ii tptp.set_Product_prod_a_a)) (= (ho_9 v ii) (ite (= i ii) e (ho_9 u ii)))))))))) (let ((_let_213 (forall ((x |u_(-> tptp.set_Product_prod_a_a Bool)|) (y |u_(-> tptp.set_Product_prod_a_a Bool)|)) (or (not (forall ((z tptp.set_Product_prod_a_a)) (= (ho_9 x z) (ho_9 y z)))) (= x y))))) (let ((_let_214 (forall ((u |u_(-> _u_(-> tptp.product_prod_a_a tptp.list_l1108175539od_a_a)_ tptp.list_l1108175539od_a_a)|) (e tptp.list_l1108175539od_a_a) (i |u_(-> tptp.product_prod_a_a tptp.list_l1108175539od_a_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.product_prod_a_a tptp.list_l1108175539od_a_a)_ tptp.list_l1108175539od_a_a)|)) (not (forall ((ii |u_(-> tptp.product_prod_a_a tptp.list_l1108175539od_a_a)|)) (= (ho_118 v ii) (ite (= i ii) e (ho_118 u ii)))))))))) (let ((_let_215 (forall ((x |u_(-> _u_(-> tptp.product_prod_a_a tptp.list_l1108175539od_a_a)_ tptp.list_l1108175539od_a_a)|) (y |u_(-> _u_(-> tptp.product_prod_a_a tptp.list_l1108175539od_a_a)_ tptp.list_l1108175539od_a_a)|)) (or (not (forall ((z |u_(-> tptp.product_prod_a_a tptp.list_l1108175539od_a_a)|)) (= (ho_118 x z) (ho_118 y z)))) (= x y))))) (let ((_let_216 (forall ((u |u_(-> tptp.list_P1467822637od_a_a tptp.a tptp.produc657167928_a_a_a)|) (e |u_(-> tptp.a tptp.produc657167928_a_a_a)|) (i tptp.list_P1467822637od_a_a)) (not (forall ((v |u_(-> tptp.list_P1467822637od_a_a tptp.a tptp.produc657167928_a_a_a)|)) (not (forall ((ii tptp.list_P1467822637od_a_a)) (= (ho_62 v ii) (ite (= i ii) e (ho_62 u ii)))))))))) (let ((_let_217 (forall ((x |u_(-> tptp.list_P1467822637od_a_a tptp.a tptp.produc657167928_a_a_a)|) (y |u_(-> tptp.list_P1467822637od_a_a tptp.a tptp.produc657167928_a_a_a)|)) (or (not (forall ((z tptp.list_P1467822637od_a_a)) (= (ho_62 x z) (ho_62 y z)))) (= x y))))) (let ((_let_218 (forall ((u |u_(-> tptp.list_a tptp.list_a)|) (e tptp.list_a) (i tptp.list_a)) (not (forall ((v |u_(-> tptp.list_a tptp.list_a)|)) (not (forall ((ii tptp.list_a)) (= (ho_44 v ii) (ite (= i ii) e (ho_44 u ii)))))))))) (let ((_let_219 (forall ((x |u_(-> tptp.list_a tptp.list_a)|) (y |u_(-> tptp.list_a tptp.list_a)|)) (or (not (forall ((z tptp.list_a)) (= (ho_44 x z) (ho_44 y z)))) (= x y))))) (let ((_let_220 (forall ((u |u_(-> _u_(-> tptp.a tptp.list_a)_ tptp.list_a)|) (e tptp.list_a) (i |u_(-> tptp.a tptp.list_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.a tptp.list_a)_ tptp.list_a)|)) (not (forall ((ii |u_(-> tptp.a tptp.list_a)|)) (= (ho_90 v ii) (ite (= i ii) e (ho_90 u ii)))))))))) (let ((_let_221 (forall ((x |u_(-> _u_(-> tptp.a tptp.list_a)_ tptp.list_a)|) (y |u_(-> _u_(-> tptp.a tptp.list_a)_ tptp.list_a)|)) (or (not (forall ((z |u_(-> tptp.a tptp.list_a)|)) (= (ho_90 x z) (ho_90 y z)))) (= x y))))) (let ((_let_222 (forall ((u |u_(-> tptp.set_li562223245od_a_a tptp.list_P1467822637od_a_a Bool)|) (e |u_(-> tptp.list_P1467822637od_a_a Bool)|) (i tptp.set_li562223245od_a_a)) (not (forall ((v |u_(-> tptp.set_li562223245od_a_a tptp.list_P1467822637od_a_a Bool)|)) (not (forall ((ii tptp.set_li562223245od_a_a)) (= (ho_23 v ii) (ite (= i ii) e (ho_23 u ii)))))))))) (let ((_let_223 (forall ((x |u_(-> tptp.set_li562223245od_a_a tptp.list_P1467822637od_a_a Bool)|) (y |u_(-> tptp.set_li562223245od_a_a tptp.list_P1467822637od_a_a Bool)|)) (or (not (forall ((z tptp.set_li562223245od_a_a)) (= (ho_23 x z) (ho_23 y z)))) (= x y))))) (let ((_let_224 (forall ((u |u_(-> tptp.product_prod_a_a tptp.a tptp.produc1016684094_a_a_a)|) (e |u_(-> tptp.a tptp.produc1016684094_a_a_a)|) (i tptp.product_prod_a_a)) (not (forall ((v |u_(-> tptp.product_prod_a_a tptp.a tptp.produc1016684094_a_a_a)|)) (not (forall ((ii tptp.product_prod_a_a)) (= (ho_223 v ii) (ite (= i ii) e (ho_223 u ii)))))))))) (let ((_let_225 (forall ((x |u_(-> tptp.product_prod_a_a tptp.a tptp.produc1016684094_a_a_a)|) (y |u_(-> tptp.product_prod_a_a tptp.a tptp.produc1016684094_a_a_a)|)) (or (not (forall ((z tptp.product_prod_a_a)) (= (ho_223 x z) (ho_223 y z)))) (= x y))))) (let ((_let_226 (forall ((u |u_(-> tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a)|) (e |u_(-> tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a)|) (i tptp.list_P1467822637od_a_a)) (not (forall ((v |u_(-> tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a)|)) (not (forall ((ii tptp.list_P1467822637od_a_a)) (= (ho_41 v ii) (ite (= i ii) e (ho_41 u ii)))))))))) (let ((_let_227 (forall ((x |u_(-> tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a)|) (y |u_(-> tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a)|)) (or (not (forall ((z tptp.list_P1467822637od_a_a)) (= (ho_41 x z) (ho_41 y z)))) (= x y))))) (let ((_let_228 (forall ((u |u_(-> tptp.a tptp.a tptp.product_prod_a_a)|) (e |u_(-> tptp.a tptp.product_prod_a_a)|) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.a tptp.product_prod_a_a)|)) (not (forall ((ii tptp.a)) (= (ho_11 v ii) (ite (= i ii) e (ho_11 u ii)))))))))) (let ((_let_229 (forall ((x |u_(-> tptp.a tptp.a tptp.product_prod_a_a)|) (y |u_(-> tptp.a tptp.a tptp.product_prod_a_a)|)) (or (not (forall ((z tptp.a)) (= (ho_11 x z) (ho_11 y z)))) (= x y))))) (let ((_let_230 (forall ((u |u_(-> tptp.set_Pr1742859527list_a Bool)|) (e Bool) (i tptp.set_Pr1742859527list_a)) (not (forall ((v |u_(-> tptp.set_Pr1742859527list_a Bool)|)) (not (forall ((ii tptp.set_Pr1742859527list_a)) (= (ho_203 v ii) (ite (= i ii) e (ho_203 u ii)))))))))) (let ((_let_231 (forall ((x |u_(-> tptp.set_Pr1742859527list_a Bool)|) (y |u_(-> tptp.set_Pr1742859527list_a Bool)|)) (or (not (forall ((z tptp.set_Pr1742859527list_a)) (= (ho_203 x z) (ho_203 y z)))) (= x y))))) (let ((_let_232 (forall ((u |u_(-> _u_(-> tptp.a tptp.nat)_ tptp.produc664688895_a_nat)|) (e tptp.produc664688895_a_nat) (i |u_(-> tptp.a tptp.nat)|)) (not (forall ((v |u_(-> _u_(-> tptp.a tptp.nat)_ tptp.produc664688895_a_nat)|)) (not (forall ((ii |u_(-> tptp.a tptp.nat)|)) (= (ho_278 v ii) (ite (= i ii) e (ho_278 u ii)))))))))) (let ((_let_233 (forall ((x |u_(-> _u_(-> tptp.a tptp.nat)_ tptp.produc664688895_a_nat)|) (y |u_(-> _u_(-> tptp.a tptp.nat)_ tptp.produc664688895_a_nat)|)) (or (not (forall ((z |u_(-> tptp.a tptp.nat)|)) (= (ho_278 x z) (ho_278 y z)))) (= x y))))) (let ((_let_234 (forall ((u |u_(-> tptp.set_Pr1971762695list_a Bool)|) (e Bool) (i tptp.set_Pr1971762695list_a)) (not (forall ((v |u_(-> tptp.set_Pr1971762695list_a Bool)|)) (not (forall ((ii tptp.set_Pr1971762695list_a)) (= (ho_36 v ii) (ite (= i ii) e (ho_36 u ii)))))))))) (let ((_let_235 (forall ((x |u_(-> tptp.set_Pr1971762695list_a Bool)|) (y |u_(-> tptp.set_Pr1971762695list_a Bool)|)) (or (not (forall ((z tptp.set_Pr1971762695list_a)) (= (ho_36 x z) (ho_36 y z)))) (= x y))))) (let ((_let_236 (forall ((u |u_(-> tptp.product_prod_a_a tptp.product_prod_a_a tptp.produc1572603623od_a_a)|) (e |u_(-> tptp.product_prod_a_a tptp.produc1572603623od_a_a)|) (i tptp.product_prod_a_a)) (not (forall ((v |u_(-> tptp.product_prod_a_a tptp.product_prod_a_a tptp.produc1572603623od_a_a)|)) (not (forall ((ii tptp.product_prod_a_a)) (= (ho_207 v ii) (ite (= i ii) e (ho_207 u ii)))))))))) (let ((_let_237 (forall ((x |u_(-> tptp.product_prod_a_a tptp.product_prod_a_a tptp.produc1572603623od_a_a)|) (y |u_(-> tptp.product_prod_a_a tptp.product_prod_a_a tptp.produc1572603623od_a_a)|)) (or (not (forall ((z tptp.product_prod_a_a)) (= (ho_207 x z) (ho_207 y z)))) (= x y))))) (let ((_let_238 (forall ((u |u_(-> tptp.produc864062247list_a Bool)|) (e Bool) (i tptp.produc864062247list_a)) (not (forall ((v |u_(-> tptp.produc864062247list_a Bool)|)) (not (forall ((ii tptp.produc864062247list_a)) (= (ho_33 v ii) (ite (= i ii) e (ho_33 u ii)))))))))) (let ((_let_239 (forall ((x |u_(-> tptp.produc864062247list_a Bool)|) (y |u_(-> tptp.produc864062247list_a Bool)|)) (or (not (forall ((z tptp.produc864062247list_a)) (= (ho_33 x z) (ho_33 y z)))) (= x y))))) (let ((_let_240 (forall ((u |u_(-> tptp.produc1572603623od_a_a tptp.list_P1891567085od_a_a tptp.list_P1891567085od_a_a)|) (e |u_(-> tptp.list_P1891567085od_a_a tptp.list_P1891567085od_a_a)|) (i tptp.produc1572603623od_a_a)) (not (forall ((v |u_(-> tptp.produc1572603623od_a_a tptp.list_P1891567085od_a_a tptp.list_P1891567085od_a_a)|)) (not (forall ((ii tptp.produc1572603623od_a_a)) (= (ho_54 v ii) (ite (= i ii) e (ho_54 u ii)))))))))) (let ((_let_241 (forall ((x |u_(-> tptp.produc1572603623od_a_a tptp.list_P1891567085od_a_a tptp.list_P1891567085od_a_a)|) (y |u_(-> tptp.produc1572603623od_a_a tptp.list_P1891567085od_a_a tptp.list_P1891567085od_a_a)|)) (or (not (forall ((z tptp.produc1572603623od_a_a)) (= (ho_54 x z) (ho_54 y z)))) (= x y))))) (let ((_let_242 (forall ((u |u_(-> tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a)|) (e tptp.list_P1467822637od_a_a) (i tptp.list_P1467822637od_a_a)) (not (forall ((v |u_(-> tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a)|)) (not (forall ((ii tptp.list_P1467822637od_a_a)) (= (ho_39 v ii) (ite (= i ii) e (ho_39 u ii)))))))))) (let ((_let_243 (forall ((x |u_(-> tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a)|) (y |u_(-> tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a)|)) (or (not (forall ((z tptp.list_P1467822637od_a_a)) (= (ho_39 x z) (ho_39 y z)))) (= x y))))) (let ((_let_244 (forall ((u |u_(-> tptp.list_P1467822637od_a_a _u_(-> tptp.product_prod_a_a tptp.list_l1108175539od_a_a)_ tptp.list_l1108175539od_a_a)|) (e |u_(-> _u_(-> tptp.product_prod_a_a tptp.list_l1108175539od_a_a)_ tptp.list_l1108175539od_a_a)|) (i tptp.list_P1467822637od_a_a)) (not (forall ((v |u_(-> tptp.list_P1467822637od_a_a _u_(-> tptp.product_prod_a_a tptp.list_l1108175539od_a_a)_ tptp.list_l1108175539od_a_a)|)) (not (forall ((ii tptp.list_P1467822637od_a_a)) (= (ho_117 v ii) (ite (= i ii) e (ho_117 u ii)))))))))) (let ((_let_245 (forall ((x |u_(-> tptp.list_P1467822637od_a_a _u_(-> tptp.product_prod_a_a tptp.list_l1108175539od_a_a)_ tptp.list_l1108175539od_a_a)|) (y |u_(-> tptp.list_P1467822637od_a_a _u_(-> tptp.product_prod_a_a tptp.list_l1108175539od_a_a)_ tptp.list_l1108175539od_a_a)|)) (or (not (forall ((z tptp.list_P1467822637od_a_a)) (= (ho_117 x z) (ho_117 y z)))) (= x y))))) (let ((_let_246 (forall ((u |u_(-> tptp.set_Product_prod_a_a tptp.product_prod_a_a Bool)|) (e |u_(-> tptp.product_prod_a_a Bool)|) (i tptp.set_Product_prod_a_a)) (not (forall ((v |u_(-> tptp.set_Product_prod_a_a tptp.product_prod_a_a Bool)|)) (not (forall ((ii tptp.set_Product_prod_a_a)) (= (ho_29 v ii) (ite (= i ii) e (ho_29 u ii)))))))))) (let ((_let_247 (forall ((x |u_(-> tptp.set_Product_prod_a_a tptp.product_prod_a_a Bool)|) (y |u_(-> tptp.set_Product_prod_a_a tptp.product_prod_a_a Bool)|)) (or (not (forall ((z tptp.set_Product_prod_a_a)) (= (ho_29 x z) (ho_29 y z)))) (= x y))))) (let ((_let_248 (forall ((u |u_(-> _u_(-> tptp.product_prod_a_a tptp.list_P1467822637od_a_a)_ tptp.list_P1467822637od_a_a)|) (e tptp.list_P1467822637od_a_a) (i |u_(-> tptp.product_prod_a_a tptp.list_P1467822637od_a_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.product_prod_a_a tptp.list_P1467822637od_a_a)_ tptp.list_P1467822637od_a_a)|)) (not (forall ((ii |u_(-> tptp.product_prod_a_a tptp.list_P1467822637od_a_a)|)) (= (ho_86 v ii) (ite (= i ii) e (ho_86 u ii)))))))))) (let ((_let_249 (forall ((x |u_(-> _u_(-> tptp.product_prod_a_a tptp.list_P1467822637od_a_a)_ tptp.list_P1467822637od_a_a)|) (y |u_(-> _u_(-> tptp.product_prod_a_a tptp.list_P1467822637od_a_a)_ tptp.list_P1467822637od_a_a)|)) (or (not (forall ((z |u_(-> tptp.product_prod_a_a tptp.list_P1467822637od_a_a)|)) (= (ho_86 x z) (ho_86 y z)))) (= x y))))) (let ((_let_250 (forall ((u |u_(-> tptp.produc864062247list_a tptp.list_P601816365list_a tptp.list_P601816365list_a)|) (e |u_(-> tptp.list_P601816365list_a tptp.list_P601816365list_a)|) (i tptp.produc864062247list_a)) (not (forall ((v |u_(-> tptp.produc864062247list_a tptp.list_P601816365list_a tptp.list_P601816365list_a)|)) (not (forall ((ii tptp.produc864062247list_a)) (= (ho_259 v ii) (ite (= i ii) e (ho_259 u ii)))))))))) (let ((_let_251 (forall ((x |u_(-> tptp.produc864062247list_a tptp.list_P601816365list_a tptp.list_P601816365list_a)|) (y |u_(-> tptp.produc864062247list_a tptp.list_P601816365list_a tptp.list_P601816365list_a)|)) (or (not (forall ((z tptp.produc864062247list_a)) (= (ho_259 x z) (ho_259 y z)))) (= x y))))) (let ((_let_252 (forall ((u |u_(-> tptp.a tptp.produc657167928_a_a_a tptp.produc1197928545_a_a_a)|) (e |u_(-> tptp.produc657167928_a_a_a tptp.produc1197928545_a_a_a)|) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.produc657167928_a_a_a tptp.produc1197928545_a_a_a)|)) (not (forall ((ii tptp.a)) (= (ho_72 v ii) (ite (= i ii) e (ho_72 u ii)))))))))) (let ((_let_253 (forall ((x |u_(-> tptp.a tptp.produc657167928_a_a_a tptp.produc1197928545_a_a_a)|) (y |u_(-> tptp.a tptp.produc657167928_a_a_a tptp.produc1197928545_a_a_a)|)) (or (not (forall ((z tptp.a)) (= (ho_72 x z) (ho_72 y z)))) (= x y))))) (let ((_let_254 (forall ((u |u_(-> tptp.set_Pr1971762695list_a tptp.set_Pr1742859527list_a)|) (e tptp.set_Pr1742859527list_a) (i tptp.set_Pr1971762695list_a)) (not (forall ((v |u_(-> tptp.set_Pr1971762695list_a tptp.set_Pr1742859527list_a)|)) (not (forall ((ii tptp.set_Pr1971762695list_a)) (= (ho_192 v ii) (ite (= i ii) e (ho_192 u ii)))))))))) (let ((_let_255 (forall ((x |u_(-> tptp.set_Pr1971762695list_a tptp.set_Pr1742859527list_a)|) (y |u_(-> tptp.set_Pr1971762695list_a tptp.set_Pr1742859527list_a)|)) (or (not (forall ((z tptp.set_Pr1971762695list_a)) (= (ho_192 x z) (ho_192 y z)))) (= x y))))) (let ((_let_256 (forall ((u |u_(-> tptp.list_l1108175539od_a_a tptp.list_l1108175539od_a_a)|) (e tptp.list_l1108175539od_a_a) (i tptp.list_l1108175539od_a_a)) (not (forall ((v |u_(-> tptp.list_l1108175539od_a_a tptp.list_l1108175539od_a_a)|)) (not (forall ((ii tptp.list_l1108175539od_a_a)) (= (ho_50 v ii) (ite (= i ii) e (ho_50 u ii)))))))))) (let ((_let_257 (forall ((x |u_(-> tptp.list_l1108175539od_a_a tptp.list_l1108175539od_a_a)|) (y |u_(-> tptp.list_l1108175539od_a_a tptp.list_l1108175539od_a_a)|)) (or (not (forall ((z tptp.list_l1108175539od_a_a)) (= (ho_50 x z) (ho_50 y z)))) (= x y))))) (let ((_let_258 (forall ((u |u_(-> tptp.produc657167928_a_a_a tptp.produc1197928545_a_a_a)|) (e tptp.produc1197928545_a_a_a) (i tptp.produc657167928_a_a_a)) (not (forall ((v |u_(-> tptp.produc657167928_a_a_a tptp.produc1197928545_a_a_a)|)) (not (forall ((ii tptp.produc657167928_a_a_a)) (= (ho_73 v ii) (ite (= i ii) e (ho_73 u ii)))))))))) (let ((_let_259 (forall ((x |u_(-> tptp.produc657167928_a_a_a tptp.produc1197928545_a_a_a)|) (y |u_(-> tptp.produc657167928_a_a_a tptp.produc1197928545_a_a_a)|)) (or (not (forall ((z tptp.produc657167928_a_a_a)) (= (ho_73 x z) (ho_73 y z)))) (= x y))))) (let ((_let_260 (forall ((u |u_(-> tptp.a tptp.list_a)|) (e tptp.list_a) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.list_a)|)) (not (forall ((ii tptp.a)) (= (ho_87 v ii) (ite (= i ii) e (ho_87 u ii)))))))))) (let ((_let_261 (forall ((x |u_(-> tptp.a tptp.list_a)|) (y |u_(-> tptp.a tptp.list_a)|)) (or (not (forall ((z tptp.a)) (= (ho_87 x z) (ho_87 y z)))) (= x y))))) (let ((_let_262 (forall ((u |u_(-> _u_(-> tptp.a tptp.list_l1108175539od_a_a)_ tptp.list_a tptp.list_l1108175539od_a_a)|) (e |u_(-> tptp.list_a tptp.list_l1108175539od_a_a)|) (i |u_(-> tptp.a tptp.list_l1108175539od_a_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.a tptp.list_l1108175539od_a_a)_ tptp.list_a tptp.list_l1108175539od_a_a)|)) (not (forall ((ii |u_(-> tptp.a tptp.list_l1108175539od_a_a)|)) (= (ho_135 v ii) (ite (= i ii) e (ho_135 u ii)))))))))) (let ((_let_263 (forall ((x |u_(-> _u_(-> tptp.a tptp.list_l1108175539od_a_a)_ tptp.list_a tptp.list_l1108175539od_a_a)|) (y |u_(-> _u_(-> tptp.a tptp.list_l1108175539od_a_a)_ tptp.list_a tptp.list_l1108175539od_a_a)|)) (or (not (forall ((z |u_(-> tptp.a tptp.list_l1108175539od_a_a)|)) (= (ho_135 x z) (ho_135 y z)))) (= x y))))) (let ((_let_264 (forall ((u |u_(-> tptp.produc1572603623od_a_a tptp.produc1990712039od_a_a)|) (e tptp.produc1990712039od_a_a) (i tptp.produc1572603623od_a_a)) (not (forall ((v |u_(-> tptp.produc1572603623od_a_a tptp.produc1990712039od_a_a)|)) (not (forall ((ii tptp.produc1572603623od_a_a)) (= (ho_159 v ii) (ite (= i ii) e (ho_159 u ii)))))))))) (let ((_let_265 (forall ((x |u_(-> tptp.produc1572603623od_a_a tptp.produc1990712039od_a_a)|) (y |u_(-> tptp.produc1572603623od_a_a tptp.produc1990712039od_a_a)|)) (or (not (forall ((z tptp.produc1572603623od_a_a)) (= (ho_159 x z) (ho_159 y z)))) (= x y))))) (let ((_let_266 (forall ((u |u_(-> tptp.list_P1891567085od_a_a tptp.list_P1467822637od_a_a)|) (e tptp.list_P1467822637od_a_a) (i tptp.list_P1891567085od_a_a)) (not (forall ((v |u_(-> tptp.list_P1891567085od_a_a tptp.list_P1467822637od_a_a)|)) (not (forall ((ii tptp.list_P1891567085od_a_a)) (= (ho_360 v ii) (ite (= i ii) e (ho_360 u ii)))))))))) (let ((_let_267 (forall ((x |u_(-> tptp.list_P1891567085od_a_a tptp.list_P1467822637od_a_a)|) (y |u_(-> tptp.list_P1891567085od_a_a tptp.list_P1467822637od_a_a)|)) (or (not (forall ((z tptp.list_P1891567085od_a_a)) (= (ho_360 x z) (ho_360 y z)))) (= x y))))) (let ((_let_268 (forall ((u |u_(-> tptp.list_P1467822637od_a_a Bool)|) (e Bool) (i tptp.list_P1467822637od_a_a)) (not (forall ((v |u_(-> tptp.list_P1467822637od_a_a Bool)|)) (not (forall ((ii tptp.list_P1467822637od_a_a)) (= (ho_24 v ii) (ite (= i ii) e (ho_24 u ii)))))))))) (let ((_let_269 (forall ((x |u_(-> tptp.list_P1467822637od_a_a Bool)|) (y |u_(-> tptp.list_P1467822637od_a_a Bool)|)) (or (not (forall ((z tptp.list_P1467822637od_a_a)) (= (ho_24 x z) (ho_24 y z)))) (= x y))))) (let ((_let_270 (forall ((u |u_(-> tptp.produc205693799od_a_a tptp.set_Pr779272263od_a_a Bool)|) (e |u_(-> tptp.set_Pr779272263od_a_a Bool)|) (i tptp.produc205693799od_a_a)) (not (forall ((v |u_(-> tptp.produc205693799od_a_a tptp.set_Pr779272263od_a_a Bool)|)) (not (forall ((ii tptp.produc205693799od_a_a)) (= (ho_155 v ii) (ite (= i ii) e (ho_155 u ii)))))))))) (let ((_let_271 (forall ((x |u_(-> tptp.produc205693799od_a_a tptp.set_Pr779272263od_a_a Bool)|) (y |u_(-> tptp.produc205693799od_a_a tptp.set_Pr779272263od_a_a Bool)|)) (or (not (forall ((z tptp.produc205693799od_a_a)) (= (ho_155 x z) (ho_155 y z)))) (= x y))))) (let ((_let_272 (forall ((u |u_(-> tptp.list_a tptp.list_a tptp.list_a)|) (e |u_(-> tptp.list_a tptp.list_a)|) (i tptp.list_a)) (not (forall ((v |u_(-> tptp.list_a tptp.list_a tptp.list_a)|)) (not (forall ((ii tptp.list_a)) (= (ho_43 v ii) (ite (= i ii) e (ho_43 u ii)))))))))) (let ((_let_273 (forall ((x |u_(-> tptp.list_a tptp.list_a tptp.list_a)|) (y |u_(-> tptp.list_a tptp.list_a tptp.list_a)|)) (or (not (forall ((z tptp.list_a)) (= (ho_43 x z) (ho_43 y z)))) (= x y))))) (let ((_let_274 (forall ((u |u_(-> _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a Bool)_ tptp.list_P1467822637od_a_a Bool)|) (e |u_(-> tptp.list_P1467822637od_a_a Bool)|) (i |u_(-> tptp.product_prod_a_a tptp.product_prod_a_a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a Bool)_ tptp.list_P1467822637od_a_a Bool)|)) (not (forall ((ii |u_(-> tptp.product_prod_a_a tptp.product_prod_a_a Bool)|)) (= (ho_335 v ii) (ite (= i ii) e (ho_335 u ii)))))))))) (let ((_let_275 (forall ((x |u_(-> _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a Bool)_ tptp.list_P1467822637od_a_a Bool)|) (y |u_(-> _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a Bool)_ tptp.list_P1467822637od_a_a Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_a_a tptp.product_prod_a_a Bool)|)) (= (ho_335 x z) (ho_335 y z)))) (= x y))))) (let ((_let_276 (forall ((u |u_(-> tptp.set_li562223245od_a_a Bool)|) (e Bool) (i tptp.set_li562223245od_a_a)) (not (forall ((v |u_(-> tptp.set_li562223245od_a_a Bool)|)) (not (forall ((ii tptp.set_li562223245od_a_a)) (= (ho_27 v ii) (ite (= i ii) e (ho_27 u ii)))))))))) (let ((_let_277 (forall ((x |u_(-> tptp.set_li562223245od_a_a Bool)|) (y |u_(-> tptp.set_li562223245od_a_a Bool)|)) (or (not (forall ((z tptp.set_li562223245od_a_a)) (= (ho_27 x z) (ho_27 y z)))) (= x y))))) (let ((_let_278 (forall ((u |u_(-> tptp.list_a _u_(-> tptp.a tptp.list_a)_ tptp.list_a)|) (e |u_(-> _u_(-> tptp.a tptp.list_a)_ tptp.list_a)|) (i tptp.list_a)) (not (forall ((v |u_(-> tptp.list_a _u_(-> tptp.a tptp.list_a)_ tptp.list_a)|)) (not (forall ((ii tptp.list_a)) (= (ho_89 v ii) (ite (= i ii) e (ho_89 u ii)))))))))) (let ((_let_279 (forall ((x |u_(-> tptp.list_a _u_(-> tptp.a tptp.list_a)_ tptp.list_a)|) (y |u_(-> tptp.list_a _u_(-> tptp.a tptp.list_a)_ tptp.list_a)|)) (or (not (forall ((z tptp.list_a)) (= (ho_89 x z) (ho_89 y z)))) (= x y))))) (let ((_let_280 (forall ((u |u_(-> tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a Bool)|) (e |u_(-> tptp.list_P1467822637od_a_a Bool)|) (i tptp.list_P1467822637od_a_a)) (not (forall ((v |u_(-> tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a Bool)|)) (not (forall ((ii tptp.list_P1467822637od_a_a)) (= (ho_332 v ii) (ite (= i ii) e (ho_332 u ii)))))))))) (let ((_let_281 (forall ((x |u_(-> tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a Bool)|) (y |u_(-> tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a Bool)|)) (or (not (forall ((z tptp.list_P1467822637od_a_a)) (= (ho_332 x z) (ho_332 y z)))) (= x y))))) (let ((_let_282 (forall ((u |u_(-> tptp.set_a Bool)|) (e Bool) (i tptp.set_a)) (not (forall ((v |u_(-> tptp.set_a Bool)|)) (not (forall ((ii tptp.set_a)) (= (ho_21 v ii) (ite (= i ii) e (ho_21 u ii)))))))))) (let ((_let_283 (forall ((x |u_(-> tptp.set_a Bool)|) (y |u_(-> tptp.set_a Bool)|)) (or (not (forall ((z tptp.set_a)) (= (ho_21 x z) (ho_21 y z)))) (= x y))))) (let ((_let_284 (forall ((u |u_(-> tptp.produc651658087od_a_a tptp.set_Pr800560199od_a_a Bool)|) (e |u_(-> tptp.set_Pr800560199od_a_a Bool)|) (i tptp.produc651658087od_a_a)) (not (forall ((v |u_(-> tptp.produc651658087od_a_a tptp.set_Pr800560199od_a_a Bool)|)) (not (forall ((ii tptp.produc651658087od_a_a)) (= (ho_175 v ii) (ite (= i ii) e (ho_175 u ii)))))))))) (let ((_let_285 (forall ((x |u_(-> tptp.produc651658087od_a_a tptp.set_Pr800560199od_a_a Bool)|) (y |u_(-> tptp.produc651658087od_a_a tptp.set_Pr800560199od_a_a Bool)|)) (or (not (forall ((z tptp.produc651658087od_a_a)) (= (ho_175 x z) (ho_175 y z)))) (= x y))))) (let ((_let_286 (forall ((u |u_(-> tptp.a tptp.nat)|) (e tptp.nat) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.nat)|)) (not (forall ((ii tptp.a)) (= (ho_57 v ii) (ite (= i ii) e (ho_57 u ii)))))))))) (let ((_let_287 (forall ((x |u_(-> tptp.a tptp.nat)|) (y |u_(-> tptp.a tptp.nat)|)) (or (not (forall ((z tptp.a)) (= (ho_57 x z) (ho_57 y z)))) (= x y))))) (let ((_let_288 (forall ((u |u_(-> _u_(-> tptp.product_prod_a_a tptp.list_a)_ tptp.list_a)|) (e tptp.list_a) (i |u_(-> tptp.product_prod_a_a tptp.list_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.product_prod_a_a tptp.list_a)_ tptp.list_a)|)) (not (forall ((ii |u_(-> tptp.product_prod_a_a tptp.list_a)|)) (= (ho_94 v ii) (ite (= i ii) e (ho_94 u ii)))))))))) (let ((_let_289 (forall ((x |u_(-> _u_(-> tptp.product_prod_a_a tptp.list_a)_ tptp.list_a)|) (y |u_(-> _u_(-> tptp.product_prod_a_a tptp.list_a)_ tptp.list_a)|)) (or (not (forall ((z |u_(-> tptp.product_prod_a_a tptp.list_a)|)) (= (ho_94 x z) (ho_94 y z)))) (= x y))))) (let ((_let_290 (forall ((u |u_(-> tptp.set_a tptp.a Bool)|) (e |u_(-> tptp.a Bool)|) (i tptp.set_a)) (not (forall ((v |u_(-> tptp.set_a tptp.a Bool)|)) (not (forall ((ii tptp.set_a)) (= (ho_17 v ii) (ite (= i ii) e (ho_17 u ii)))))))))) (let ((_let_291 (forall ((x |u_(-> tptp.set_a tptp.a Bool)|) (y |u_(-> tptp.set_a tptp.a Bool)|)) (or (not (forall ((z tptp.set_a)) (= (ho_17 x z) (ho_17 y z)))) (= x y))))) (let ((_let_292 (forall ((u |u_(-> tptp.a Bool)|) (e Bool) (i tptp.a)) (not (forall ((v |u_(-> tptp.a Bool)|)) (not (forall ((ii tptp.a)) (= (ho_18 v ii) (ite (= i ii) e (ho_18 u ii)))))))))) (let ((_let_293 (forall ((x |u_(-> tptp.a Bool)|) (y |u_(-> tptp.a Bool)|)) (or (not (forall ((z tptp.a)) (= (ho_18 x z) (ho_18 y z)))) (= x y))))) (let ((_let_294 (forall ((u |u_(-> tptp.a tptp.produc657167928_a_a_a)|) (e tptp.produc657167928_a_a_a) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.produc657167928_a_a_a)|)) (not (forall ((ii tptp.a)) (= (ho_63 v ii) (ite (= i ii) e (ho_63 u ii)))))))))) (let ((_let_295 (forall ((x |u_(-> tptp.a tptp.produc657167928_a_a_a)|) (y |u_(-> tptp.a tptp.produc657167928_a_a_a)|)) (or (not (forall ((z tptp.a)) (= (ho_63 x z) (ho_63 y z)))) (= x y))))) (let ((_let_296 (forall ((u |u_(-> tptp.list_l1108175539od_a_a _u_(-> tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a)_ tptp.list_P1467822637od_a_a)|) (e |u_(-> _u_(-> tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a)_ tptp.list_P1467822637od_a_a)|) (i tptp.list_l1108175539od_a_a)) (not (forall ((v |u_(-> tptp.list_l1108175539od_a_a _u_(-> tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a)_ tptp.list_P1467822637od_a_a)|)) (not (forall ((ii tptp.list_l1108175539od_a_a)) (= (ho_120 v ii) (ite (= i ii) e (ho_120 u ii)))))))))) (let ((_let_297 (forall ((x |u_(-> tptp.list_l1108175539od_a_a _u_(-> tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a)_ tptp.list_P1467822637od_a_a)|) (y |u_(-> tptp.list_l1108175539od_a_a _u_(-> tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a)_ tptp.list_P1467822637od_a_a)|)) (or (not (forall ((z tptp.list_l1108175539od_a_a)) (= (ho_120 x z) (ho_120 y z)))) (= x y))))) (let ((_let_298 (forall ((u |u_(-> tptp.set_Pr1940702919_a_nat tptp.set_Pr753687879_a_nat)|) (e tptp.set_Pr753687879_a_nat) (i tptp.set_Pr1940702919_a_nat)) (not (forall ((v |u_(-> tptp.set_Pr1940702919_a_nat tptp.set_Pr753687879_a_nat)|)) (not (forall ((ii tptp.set_Pr1940702919_a_nat)) (= (ho_178 v ii) (ite (= i ii) e (ho_178 u ii)))))))))) (let ((_let_299 (forall ((x |u_(-> tptp.set_Pr1940702919_a_nat tptp.set_Pr753687879_a_nat)|) (y |u_(-> tptp.set_Pr1940702919_a_nat tptp.set_Pr753687879_a_nat)|)) (or (not (forall ((z tptp.set_Pr1940702919_a_nat)) (= (ho_178 x z) (ho_178 y z)))) (= x y))))) (let ((_let_300 (forall ((u |u_(-> tptp.list_a tptp.produc864062247list_a)|) (e tptp.produc864062247list_a) (i tptp.list_a)) (not (forall ((v |u_(-> tptp.list_a tptp.produc864062247list_a)|)) (not (forall ((ii tptp.list_a)) (= (ho_66 v ii) (ite (= i ii) e (ho_66 u ii)))))))))) (let ((_let_301 (forall ((x |u_(-> tptp.list_a tptp.produc864062247list_a)|) (y |u_(-> tptp.list_a tptp.produc864062247list_a)|)) (or (not (forall ((z tptp.list_a)) (= (ho_66 x z) (ho_66 y z)))) (= x y))))) (let ((_let_302 (forall ((u |u_(-> tptp.set_Pr1948701895od_a_a tptp.set_Pr800560199od_a_a)|) (e tptp.set_Pr800560199od_a_a) (i tptp.set_Pr1948701895od_a_a)) (not (forall ((v |u_(-> tptp.set_Pr1948701895od_a_a tptp.set_Pr800560199od_a_a)|)) (not (forall ((ii tptp.set_Pr1948701895od_a_a)) (= (ho_205 v ii) (ite (= i ii) e (ho_205 u ii)))))))))) (let ((_let_303 (forall ((x |u_(-> tptp.set_Pr1948701895od_a_a tptp.set_Pr800560199od_a_a)|) (y |u_(-> tptp.set_Pr1948701895od_a_a tptp.set_Pr800560199od_a_a)|)) (or (not (forall ((z tptp.set_Pr1948701895od_a_a)) (= (ho_205 x z) (ho_205 y z)))) (= x y))))) (let ((_let_304 (forall ((u |u_(-> tptp.pair_p1891813445t_unit tptp.produc864062247list_a tptp.list_a Bool)|) (e |u_(-> tptp.produc864062247list_a tptp.list_a Bool)|) (i tptp.pair_p1891813445t_unit)) (not (forall ((v |u_(-> tptp.pair_p1891813445t_unit tptp.produc864062247list_a tptp.list_a Bool)|)) (not (forall ((ii tptp.pair_p1891813445t_unit)) (= (ho_300 v ii) (ite (= i ii) e (ho_300 u ii)))))))))) (let ((_let_305 (forall ((x |u_(-> tptp.pair_p1891813445t_unit tptp.produc864062247list_a tptp.list_a Bool)|) (y |u_(-> tptp.pair_p1891813445t_unit tptp.produc864062247list_a tptp.list_a Bool)|)) (or (not (forall ((z tptp.pair_p1891813445t_unit)) (= (ho_300 x z) (ho_300 y z)))) (= x y))))) (let ((_let_306 (forall ((u |u_(-> tptp.a tptp.product_prod_a_a)|) (e tptp.product_prod_a_a) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.product_prod_a_a)|)) (not (forall ((ii tptp.a)) (= (ho_12 v ii) (ite (= i ii) e (ho_12 u ii)))))))))) (let ((_let_307 (forall ((x |u_(-> tptp.a tptp.product_prod_a_a)|) (y |u_(-> tptp.a tptp.product_prod_a_a)|)) (or (not (forall ((z tptp.a)) (= (ho_12 x z) (ho_12 y z)))) (= x y))))) (let ((_let_308 (forall ((u |u_(-> tptp.list_a tptp.list_P319927492_a_a_a)|) (e tptp.list_P319927492_a_a_a) (i tptp.list_a)) (not (forall ((v |u_(-> tptp.list_a tptp.list_P319927492_a_a_a)|)) (not (forall ((ii tptp.list_a)) (= (ho_221 v ii) (ite (= i ii) e (ho_221 u ii)))))))))) (let ((_let_309 (forall ((x |u_(-> tptp.list_a tptp.list_P319927492_a_a_a)|) (y |u_(-> tptp.list_a tptp.list_P319927492_a_a_a)|)) (or (not (forall ((z tptp.list_a)) (= (ho_221 x z) (ho_221 y z)))) (= x y))))) (let ((_let_310 (forall ((u |u_(-> tptp.list_a tptp.list_a tptp.produc864062247list_a)|) (e |u_(-> tptp.list_a tptp.produc864062247list_a)|) (i tptp.list_a)) (not (forall ((v |u_(-> tptp.list_a tptp.list_a tptp.produc864062247list_a)|)) (not (forall ((ii tptp.list_a)) (= (ho_65 v ii) (ite (= i ii) e (ho_65 u ii)))))))))) (let ((_let_311 (forall ((x |u_(-> tptp.list_a tptp.list_a tptp.produc864062247list_a)|) (y |u_(-> tptp.list_a tptp.list_a tptp.produc864062247list_a)|)) (or (not (forall ((z tptp.list_a)) (= (ho_65 x z) (ho_65 y z)))) (= x y))))) (let ((_let_312 (forall ((u |u_(-> _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)_ tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a Bool)|) (e |u_(-> tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a Bool)|) (i |u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)_ tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a Bool)|)) (not (forall ((ii |u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)|)) (= (ho_334 v ii) (ite (= i ii) e (ho_334 u ii)))))))))) (let ((_let_313 (forall ((x |u_(-> _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)_ tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a Bool)|) (y |u_(-> _u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)_ tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)|)) (= (ho_334 x z) (ho_334 y z)))) (= x y))))) (let ((_let_314 (forall ((u |u_(-> tptp.set_Pr800560199od_a_a Bool)|) (e Bool) (i tptp.set_Pr800560199od_a_a)) (not (forall ((v |u_(-> tptp.set_Pr800560199od_a_a Bool)|)) (not (forall ((ii tptp.set_Pr800560199od_a_a)) (= (ho_176 v ii) (ite (= i ii) e (ho_176 u ii)))))))))) (let ((_let_315 (forall ((x |u_(-> tptp.set_Pr800560199od_a_a Bool)|) (y |u_(-> tptp.set_Pr800560199od_a_a Bool)|)) (or (not (forall ((z tptp.set_Pr800560199od_a_a)) (= (ho_176 x z) (ho_176 y z)))) (= x y))))) (let ((_let_316 (forall ((u |u_(-> tptp.list_a tptp.list_a_nat tptp.list_P576104046_a_nat)|) (e |u_(-> tptp.list_a_nat tptp.list_P576104046_a_nat)|) (i tptp.list_a)) (not (forall ((v |u_(-> tptp.list_a tptp.list_a_nat tptp.list_P576104046_a_nat)|)) (not (forall ((ii tptp.list_a)) (= (ho_238 v ii) (ite (= i ii) e (ho_238 u ii)))))))))) (let ((_let_317 (forall ((x |u_(-> tptp.list_a tptp.list_a_nat tptp.list_P576104046_a_nat)|) (y |u_(-> tptp.list_a tptp.list_a_nat tptp.list_P576104046_a_nat)|)) (or (not (forall ((z tptp.list_a)) (= (ho_238 x z) (ho_238 y z)))) (= x y))))) (let ((_let_318 (forall ((u |u_(-> tptp.list_P1467822637od_a_a tptp.produc1701253078od_a_a)|) (e tptp.produc1701253078od_a_a) (i tptp.list_P1467822637od_a_a)) (not (forall ((v |u_(-> tptp.list_P1467822637od_a_a tptp.produc1701253078od_a_a)|)) (not (forall ((ii tptp.list_P1467822637od_a_a)) (= (ho_76 v ii) (ite (= i ii) e (ho_76 u ii)))))))))) (let ((_let_319 (forall ((x |u_(-> tptp.list_P1467822637od_a_a tptp.produc1701253078od_a_a)|) (y |u_(-> tptp.list_P1467822637od_a_a tptp.produc1701253078od_a_a)|)) (or (not (forall ((z tptp.list_P1467822637od_a_a)) (= (ho_76 x z) (ho_76 y z)))) (= x y))))) (let ((_let_320 (forall ((u |u_(-> tptp.produc1701253078od_a_a Bool)|) (e Bool) (i tptp.produc1701253078od_a_a)) (not (forall ((v |u_(-> tptp.produc1701253078od_a_a Bool)|)) (not (forall ((ii tptp.produc1701253078od_a_a)) (= (ho_82 v ii) (ite (= i ii) e (ho_82 u ii)))))))))) (let ((_let_321 (forall ((x |u_(-> tptp.produc1701253078od_a_a Bool)|) (y |u_(-> tptp.produc1701253078od_a_a Bool)|)) (or (not (forall ((z tptp.produc1701253078od_a_a)) (= (ho_82 x z) (ho_82 y z)))) (= x y))))) (let ((_let_322 (forall ((u |u_(-> tptp.a tptp.list_P1467822637od_a_a tptp.produc1701253078od_a_a)|) (e |u_(-> tptp.list_P1467822637od_a_a tptp.produc1701253078od_a_a)|) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.list_P1467822637od_a_a tptp.produc1701253078od_a_a)|)) (not (forall ((ii tptp.a)) (= (ho_75 v ii) (ite (= i ii) e (ho_75 u ii)))))))))) (let ((_let_323 (forall ((x |u_(-> tptp.a tptp.list_P1467822637od_a_a tptp.produc1701253078od_a_a)|) (y |u_(-> tptp.a tptp.list_P1467822637od_a_a tptp.produc1701253078od_a_a)|)) (or (not (forall ((z tptp.a)) (= (ho_75 x z) (ho_75 y z)))) (= x y))))) (let ((_let_324 (forall ((u |u_(-> tptp.list_list_a tptp.produc403652391list_a)|) (e tptp.produc403652391list_a) (i tptp.list_list_a)) (not (forall ((v |u_(-> tptp.list_list_a tptp.produc403652391list_a)|)) (not (forall ((ii tptp.list_list_a)) (= (ho_200 v ii) (ite (= i ii) e (ho_200 u ii)))))))))) (let ((_let_325 (forall ((x |u_(-> tptp.list_list_a tptp.produc403652391list_a)|) (y |u_(-> tptp.list_list_a tptp.produc403652391list_a)|)) (or (not (forall ((z tptp.list_list_a)) (= (ho_200 x z) (ho_200 y z)))) (= x y))))) (let ((_let_326 (forall ((u |u_(-> _u_(-> tptp.a tptp.list_P1467822637od_a_a)_ tptp.list_a tptp.list_P1467822637od_a_a)|) (e |u_(-> tptp.list_a tptp.list_P1467822637od_a_a)|) (i |u_(-> tptp.a tptp.list_P1467822637od_a_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.a tptp.list_P1467822637od_a_a)_ tptp.list_a tptp.list_P1467822637od_a_a)|)) (not (forall ((ii |u_(-> tptp.a tptp.list_P1467822637od_a_a)|)) (= (ho_129 v ii) (ite (= i ii) e (ho_129 u ii)))))))))) (let ((_let_327 (forall ((x |u_(-> _u_(-> tptp.a tptp.list_P1467822637od_a_a)_ tptp.list_a tptp.list_P1467822637od_a_a)|) (y |u_(-> _u_(-> tptp.a tptp.list_P1467822637od_a_a)_ tptp.list_a tptp.list_P1467822637od_a_a)|)) (or (not (forall ((z |u_(-> tptp.a tptp.list_P1467822637od_a_a)|)) (= (ho_129 x z) (ho_129 y z)))) (= x y))))) (let ((_let_328 (forall ((u |u_(-> tptp.list_P1467822637od_a_a tptp.set_li562223245od_a_a Bool)|) (e |u_(-> tptp.set_li562223245od_a_a Bool)|) (i tptp.list_P1467822637od_a_a)) (not (forall ((v |u_(-> tptp.list_P1467822637od_a_a tptp.set_li562223245od_a_a Bool)|)) (not (forall ((ii tptp.list_P1467822637od_a_a)) (= (ho_26 v ii) (ite (= i ii) e (ho_26 u ii)))))))))) (let ((_let_329 (forall ((x |u_(-> tptp.list_P1467822637od_a_a tptp.set_li562223245od_a_a Bool)|) (y |u_(-> tptp.list_P1467822637od_a_a tptp.set_li562223245od_a_a Bool)|)) (or (not (forall ((z tptp.list_P1467822637od_a_a)) (= (ho_26 x z) (ho_26 y z)))) (= x y))))) (let ((_let_330 (forall ((u |u_(-> tptp.list_a_nat tptp.list_a_nat tptp.list_a_nat)|) (e |u_(-> tptp.list_a_nat tptp.list_a_nat)|) (i tptp.list_a_nat)) (not (forall ((v |u_(-> tptp.list_a_nat tptp.list_a_nat tptp.list_a_nat)|)) (not (forall ((ii tptp.list_a_nat)) (= (ho_78 v ii) (ite (= i ii) e (ho_78 u ii)))))))))) (let ((_let_331 (forall ((x |u_(-> tptp.list_a_nat tptp.list_a_nat tptp.list_a_nat)|) (y |u_(-> tptp.list_a_nat tptp.list_a_nat tptp.list_a_nat)|)) (or (not (forall ((z tptp.list_a_nat)) (= (ho_78 x z) (ho_78 y z)))) (= x y))))) (let ((_let_332 (forall ((u |u_(-> tptp.produc501911462od_a_a Bool)|) (e Bool) (i tptp.produc501911462od_a_a)) (not (forall ((v |u_(-> tptp.produc501911462od_a_a Bool)|)) (not (forall ((ii tptp.produc501911462od_a_a)) (= (ho_80 v ii) (ite (= i ii) e (ho_80 u ii)))))))))) (let ((_let_333 (forall ((x |u_(-> tptp.produc501911462od_a_a Bool)|) (y |u_(-> tptp.produc501911462od_a_a Bool)|)) (or (not (forall ((z tptp.produc501911462od_a_a)) (= (ho_80 x z) (ho_80 y z)))) (= x y))))) (let ((_let_334 (forall ((u |u_(-> tptp.produc1197928545_a_a_a Bool)|) (e Bool) (i tptp.produc1197928545_a_a_a)) (not (forall ((v |u_(-> tptp.produc1197928545_a_a_a Bool)|)) (not (forall ((ii tptp.produc1197928545_a_a_a)) (= (ho_81 v ii) (ite (= i ii) e (ho_81 u ii)))))))))) (let ((_let_335 (forall ((x |u_(-> tptp.produc1197928545_a_a_a Bool)|) (y |u_(-> tptp.produc1197928545_a_a_a Bool)|)) (or (not (forall ((z tptp.produc1197928545_a_a_a)) (= (ho_81 x z) (ho_81 y z)))) (= x y))))) (let ((_let_336 (forall ((u |u_(-> tptp.list_l1108175539od_a_a tptp.produc657724903od_a_a)|) (e tptp.produc657724903od_a_a) (i tptp.list_l1108175539od_a_a)) (not (forall ((v |u_(-> tptp.list_l1108175539od_a_a tptp.produc657724903od_a_a)|)) (not (forall ((ii tptp.list_l1108175539od_a_a)) (= (ho_167 v ii) (ite (= i ii) e (ho_167 u ii)))))))))) (let ((_let_337 (forall ((x |u_(-> tptp.list_l1108175539od_a_a tptp.produc657724903od_a_a)|) (y |u_(-> tptp.list_l1108175539od_a_a tptp.produc657724903od_a_a)|)) (or (not (forall ((z tptp.list_l1108175539od_a_a)) (= (ho_167 x z) (ho_167 y z)))) (= x y))))) (let ((_let_338 (forall ((u |u_(-> tptp.list_a tptp.list_a tptp.list_P1467822637od_a_a)|) (e |u_(-> tptp.list_a tptp.list_P1467822637od_a_a)|) (i tptp.list_a)) (not (forall ((v |u_(-> tptp.list_a tptp.list_a tptp.list_P1467822637od_a_a)|)) (not (forall ((ii tptp.list_a)) (= (ho_215 v ii) (ite (= i ii) e (ho_215 u ii)))))))))) (let ((_let_339 (forall ((x |u_(-> tptp.list_a tptp.list_a tptp.list_P1467822637od_a_a)|) (y |u_(-> tptp.list_a tptp.list_a tptp.list_P1467822637od_a_a)|)) (or (not (forall ((z tptp.list_a)) (= (ho_215 x z) (ho_215 y z)))) (= x y))))) (let ((_let_340 (forall ((u |u_(-> tptp.product_prod_a_a tptp.list_P1467822637od_a_a)|) (e tptp.list_P1467822637od_a_a) (i tptp.product_prod_a_a)) (not (forall ((v |u_(-> tptp.product_prod_a_a tptp.list_P1467822637od_a_a)|)) (not (forall ((ii tptp.product_prod_a_a)) (= (ho_83 v ii) (ite (= i ii) e (ho_83 u ii)))))))))) (let ((_let_341 (forall ((x |u_(-> tptp.product_prod_a_a tptp.list_P1467822637od_a_a)|) (y |u_(-> tptp.product_prod_a_a tptp.list_P1467822637od_a_a)|)) (or (not (forall ((z tptp.product_prod_a_a)) (= (ho_83 x z) (ho_83 y z)))) (= x y))))) (let ((_let_342 (forall ((u |u_(-> _u_(-> _u_(-> tptp.a tptp.nat)_ tptp.list_a)_ tptp.list_a)|) (e tptp.list_a) (i |u_(-> _u_(-> tptp.a tptp.nat)_ tptp.list_a)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> tptp.a tptp.nat)_ tptp.list_a)_ tptp.list_a)|)) (not (forall ((ii |u_(-> _u_(-> tptp.a tptp.nat)_ tptp.list_a)|)) (= (ho_102 v ii) (ite (= i ii) e (ho_102 u ii)))))))))) (let ((_let_343 (forall ((x |u_(-> _u_(-> _u_(-> tptp.a tptp.nat)_ tptp.list_a)_ tptp.list_a)|) (y |u_(-> _u_(-> _u_(-> tptp.a tptp.nat)_ tptp.list_a)_ tptp.list_a)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.a tptp.nat)_ tptp.list_a)|)) (= (ho_102 x z) (ho_102 y z)))) (= x y))))) (let ((_let_344 (forall ((u |u_(-> tptp.produc1572603623od_a_a Bool)|) (e Bool) (i tptp.produc1572603623od_a_a)) (not (forall ((v |u_(-> tptp.produc1572603623od_a_a Bool)|)) (not (forall ((ii tptp.produc1572603623od_a_a)) (= (ho_292 v ii) (ite (= i ii) e (ho_292 u ii)))))))))) (let ((_let_345 (forall ((x |u_(-> tptp.produc1572603623od_a_a Bool)|) (y |u_(-> tptp.produc1572603623od_a_a Bool)|)) (or (not (forall ((z tptp.produc1572603623od_a_a)) (= (ho_292 x z) (ho_292 y z)))) (= x y))))) (let ((_let_346 (forall ((u |u_(-> tptp.list_P1467822637od_a_a tptp.product_prod_a_a Bool)|) (e |u_(-> tptp.product_prod_a_a Bool)|) (i tptp.list_P1467822637od_a_a)) (not (forall ((v |u_(-> tptp.list_P1467822637od_a_a tptp.product_prod_a_a Bool)|)) (not (forall ((ii tptp.list_P1467822637od_a_a)) (= (ho_299 v ii) (ite (= i ii) e (ho_299 u ii)))))))))) (let ((_let_347 (forall ((x |u_(-> tptp.list_P1467822637od_a_a tptp.product_prod_a_a Bool)|) (y |u_(-> tptp.list_P1467822637od_a_a tptp.product_prod_a_a Bool)|)) (or (not (forall ((z tptp.list_P1467822637od_a_a)) (= (ho_299 x z) (ho_299 y z)))) (= x y))))) (let ((_let_348 (forall ((u |u_(-> tptp.a tptp.list_P1467822637od_a_a)|) (e tptp.list_P1467822637od_a_a) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.list_P1467822637od_a_a)|)) (not (forall ((ii tptp.a)) (= (ho_95 v ii) (ite (= i ii) e (ho_95 u ii)))))))))) (let ((_let_349 (forall ((x |u_(-> tptp.a tptp.list_P1467822637od_a_a)|) (y |u_(-> tptp.a tptp.list_P1467822637od_a_a)|)) (or (not (forall ((z tptp.a)) (= (ho_95 x z) (ho_95 y z)))) (= x y))))) (let ((_let_350 (forall ((u |u_(-> tptp.list_list_a tptp.list_list_a tptp.produc403652391list_a)|) (e |u_(-> tptp.list_list_a tptp.produc403652391list_a)|) (i tptp.list_list_a)) (not (forall ((v |u_(-> tptp.list_list_a tptp.list_list_a tptp.produc403652391list_a)|)) (not (forall ((ii tptp.list_list_a)) (= (ho_199 v ii) (ite (= i ii) e (ho_199 u ii)))))))))) (let ((_let_351 (forall ((x |u_(-> tptp.list_list_a tptp.list_list_a tptp.produc403652391list_a)|) (y |u_(-> tptp.list_list_a tptp.list_list_a tptp.produc403652391list_a)|)) (or (not (forall ((z tptp.list_list_a)) (= (ho_199 x z) (ho_199 y z)))) (= x y))))) (let ((_let_352 (forall ((u |u_(-> tptp.produc403652391list_a tptp.set_Pr1742859527list_a Bool)|) (e |u_(-> tptp.set_Pr1742859527list_a Bool)|) (i tptp.produc403652391list_a)) (not (forall ((v |u_(-> tptp.produc403652391list_a tptp.set_Pr1742859527list_a Bool)|)) (not (forall ((ii tptp.produc403652391list_a)) (= (ho_202 v ii) (ite (= i ii) e (ho_202 u ii)))))))))) (let ((_let_353 (forall ((x |u_(-> tptp.produc403652391list_a tptp.set_Pr1742859527list_a Bool)|) (y |u_(-> tptp.produc403652391list_a tptp.set_Pr1742859527list_a Bool)|)) (or (not (forall ((z tptp.produc403652391list_a)) (= (ho_202 x z) (ho_202 y z)))) (= x y))))) (let ((_let_354 (forall ((u |u_(-> tptp.set_Pr1948701895od_a_a Bool)|) (e Bool) (i tptp.set_Pr1948701895od_a_a)) (not (forall ((v |u_(-> tptp.set_Pr1948701895od_a_a Bool)|)) (not (forall ((ii tptp.set_Pr1948701895od_a_a)) (= (ho_211 v ii) (ite (= i ii) e (ho_211 u ii)))))))))) (let ((_let_355 (forall ((x |u_(-> tptp.set_Pr1948701895od_a_a Bool)|) (y |u_(-> tptp.set_Pr1948701895od_a_a Bool)|)) (or (not (forall ((z tptp.set_Pr1948701895od_a_a)) (= (ho_211 x z) (ho_211 y z)))) (= x y))))) (let ((_let_356 (forall ((u |u_(-> tptp.set_Product_prod_a_a tptp.set_Pr1971762695list_a)|) (e tptp.set_Pr1971762695list_a) (i tptp.set_Product_prod_a_a)) (not (forall ((v |u_(-> tptp.set_Product_prod_a_a tptp.set_Pr1971762695list_a)|)) (not (forall ((ii tptp.set_Product_prod_a_a)) (= (ho_213 v ii) (ite (= i ii) e (ho_213 u ii)))))))))) (let ((_let_357 (forall ((x |u_(-> tptp.set_Product_prod_a_a tptp.set_Pr1971762695list_a)|) (y |u_(-> tptp.set_Product_prod_a_a tptp.set_Pr1971762695list_a)|)) (or (not (forall ((z tptp.set_Product_prod_a_a)) (= (ho_213 x z) (ho_213 y z)))) (= x y))))) (let ((_let_358 (forall ((u |u_(-> tptp.list_P1467822637od_a_a tptp.list_P1891567085od_a_a)|) (e tptp.list_P1891567085od_a_a) (i tptp.list_P1467822637od_a_a)) (not (forall ((v |u_(-> tptp.list_P1467822637od_a_a tptp.list_P1891567085od_a_a)|)) (not (forall ((ii tptp.list_P1467822637od_a_a)) (= (ho_218 v ii) (ite (= i ii) e (ho_218 u ii)))))))))) (let ((_let_359 (forall ((x |u_(-> tptp.list_P1467822637od_a_a tptp.list_P1891567085od_a_a)|) (y |u_(-> tptp.list_P1467822637od_a_a tptp.list_P1891567085od_a_a)|)) (or (not (forall ((z tptp.list_P1467822637od_a_a)) (= (ho_218 x z) (ho_218 y z)))) (= x y))))) (let ((_let_360 (forall ((u |u_(-> tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a tptp.list_P1891567085od_a_a)|) (e |u_(-> tptp.list_P1467822637od_a_a tptp.list_P1891567085od_a_a)|) (i tptp.list_P1467822637od_a_a)) (not (forall ((v |u_(-> tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a tptp.list_P1891567085od_a_a)|)) (not (forall ((ii tptp.list_P1467822637od_a_a)) (= (ho_217 v ii) (ite (= i ii) e (ho_217 u ii)))))))))) (let ((_let_361 (forall ((x |u_(-> tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a tptp.list_P1891567085od_a_a)|) (y |u_(-> tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a tptp.list_P1891567085od_a_a)|)) (or (not (forall ((z tptp.list_P1467822637od_a_a)) (= (ho_217 x z) (ho_217 y z)))) (= x y))))) (let ((_let_362 (forall ((u |u_(-> tptp.list_P319927492_a_a_a tptp.list_P319927492_a_a_a)|) (e tptp.list_P319927492_a_a_a) (i tptp.list_P319927492_a_a_a)) (not (forall ((v |u_(-> tptp.list_P319927492_a_a_a tptp.list_P319927492_a_a_a)|)) (not (forall ((ii tptp.list_P319927492_a_a_a)) (= (ho_227 v ii) (ite (= i ii) e (ho_227 u ii)))))))))) (let ((_let_363 (forall ((x |u_(-> tptp.list_P319927492_a_a_a tptp.list_P319927492_a_a_a)|) (y |u_(-> tptp.list_P319927492_a_a_a tptp.list_P319927492_a_a_a)|)) (or (not (forall ((z tptp.list_P319927492_a_a_a)) (= (ho_227 x z) (ho_227 y z)))) (= x y))))) (let ((_let_364 (forall ((u |u_(-> tptp.a tptp.produc1016684094_a_a_a)|) (e tptp.produc1016684094_a_a_a) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.produc1016684094_a_a_a)|)) (not (forall ((ii tptp.a)) (= (ho_224 v ii) (ite (= i ii) e (ho_224 u ii)))))))))) (let ((_let_365 (forall ((x |u_(-> tptp.a tptp.produc1016684094_a_a_a)|) (y |u_(-> tptp.a tptp.produc1016684094_a_a_a)|)) (or (not (forall ((z tptp.a)) (= (ho_224 x z) (ho_224 y z)))) (= x y))))) (let ((_let_366 (forall ((u |u_(-> tptp.produc664688895_a_nat tptp.list_P1435957893_a_nat tptp.list_P1435957893_a_nat)|) (e |u_(-> tptp.list_P1435957893_a_nat tptp.list_P1435957893_a_nat)|) (i tptp.produc664688895_a_nat)) (not (forall ((v |u_(-> tptp.produc664688895_a_nat tptp.list_P1435957893_a_nat tptp.list_P1435957893_a_nat)|)) (not (forall ((ii tptp.produc664688895_a_nat)) (= (ho_280 v ii) (ite (= i ii) e (ho_280 u ii)))))))))) (let ((_let_367 (forall ((x |u_(-> tptp.produc664688895_a_nat tptp.list_P1435957893_a_nat tptp.list_P1435957893_a_nat)|) (y |u_(-> tptp.produc664688895_a_nat tptp.list_P1435957893_a_nat tptp.list_P1435957893_a_nat)|)) (or (not (forall ((z tptp.produc664688895_a_nat)) (= (ho_280 x z) (ho_280 y z)))) (= x y))))) (let ((_let_368 (forall ((u |u_(-> tptp.produc1016684094_a_a_a tptp.list_P319927492_a_a_a tptp.list_P319927492_a_a_a)|) (e |u_(-> tptp.list_P319927492_a_a_a tptp.list_P319927492_a_a_a)|) (i tptp.produc1016684094_a_a_a)) (not (forall ((v |u_(-> tptp.produc1016684094_a_a_a tptp.list_P319927492_a_a_a tptp.list_P319927492_a_a_a)|)) (not (forall ((ii tptp.produc1016684094_a_a_a)) (= (ho_226 v ii) (ite (= i ii) e (ho_226 u ii)))))))))) (let ((_let_369 (forall ((x |u_(-> tptp.produc1016684094_a_a_a tptp.list_P319927492_a_a_a tptp.list_P319927492_a_a_a)|) (y |u_(-> tptp.produc1016684094_a_a_a tptp.list_P319927492_a_a_a tptp.list_P319927492_a_a_a)|)) (or (not (forall ((z tptp.produc1016684094_a_a_a)) (= (ho_226 x z) (ho_226 y z)))) (= x y))))) (let ((_let_370 (forall ((u |u_(-> tptp.list_P1467822637od_a_a tptp.list_P1458844246od_a_a)|) (e tptp.list_P1458844246od_a_a) (i tptp.list_P1467822637od_a_a)) (not (forall ((v |u_(-> tptp.list_P1467822637od_a_a tptp.list_P1458844246od_a_a)|)) (not (forall ((ii tptp.list_P1467822637od_a_a)) (= (ho_230 v ii) (ite (= i ii) e (ho_230 u ii)))))))))) (let ((_let_371 (forall ((x |u_(-> tptp.list_P1467822637od_a_a tptp.list_P1458844246od_a_a)|) (y |u_(-> tptp.list_P1467822637od_a_a tptp.list_P1458844246od_a_a)|)) (or (not (forall ((z tptp.list_P1467822637od_a_a)) (= (ho_230 x z) (ho_230 y z)))) (= x y))))) (let ((_let_372 (forall ((u |u_(-> tptp.list_a tptp.list_P1467822637od_a_a tptp.list_P1458844246od_a_a)|) (e |u_(-> tptp.list_P1467822637od_a_a tptp.list_P1458844246od_a_a)|) (i tptp.list_a)) (not (forall ((v |u_(-> tptp.list_a tptp.list_P1467822637od_a_a tptp.list_P1458844246od_a_a)|)) (not (forall ((ii tptp.list_a)) (= (ho_229 v ii) (ite (= i ii) e (ho_229 u ii)))))))))) (let ((_let_373 (forall ((x |u_(-> tptp.list_a tptp.list_P1467822637od_a_a tptp.list_P1458844246od_a_a)|) (y |u_(-> tptp.list_a tptp.list_P1467822637od_a_a tptp.list_P1458844246od_a_a)|)) (or (not (forall ((z tptp.list_a)) (= (ho_229 x z) (ho_229 y z)))) (= x y))))) (let ((_let_374 (forall ((u |u_(-> tptp.list_P1458844246od_a_a tptp.list_P1458844246od_a_a)|) (e tptp.list_P1458844246od_a_a) (i tptp.list_P1458844246od_a_a)) (not (forall ((v |u_(-> tptp.list_P1458844246od_a_a tptp.list_P1458844246od_a_a)|)) (not (forall ((ii tptp.list_P1458844246od_a_a)) (= (ho_236 v ii) (ite (= i ii) e (ho_236 u ii)))))))))) (let ((_let_375 (forall ((x |u_(-> tptp.list_P1458844246od_a_a tptp.list_P1458844246od_a_a)|) (y |u_(-> tptp.list_P1458844246od_a_a tptp.list_P1458844246od_a_a)|)) (or (not (forall ((z tptp.list_P1458844246od_a_a)) (= (ho_236 x z) (ho_236 y z)))) (= x y))))) (let ((_let_376 (forall ((u |u_(-> tptp.product_prod_a_a tptp.produc1921647824od_a_a)|) (e tptp.produc1921647824od_a_a) (i tptp.product_prod_a_a)) (not (forall ((v |u_(-> tptp.product_prod_a_a tptp.produc1921647824od_a_a)|)) (not (forall ((ii tptp.product_prod_a_a)) (= (ho_233 v ii) (ite (= i ii) e (ho_233 u ii)))))))))) (let ((_let_377 (forall ((x |u_(-> tptp.product_prod_a_a tptp.produc1921647824od_a_a)|) (y |u_(-> tptp.product_prod_a_a tptp.produc1921647824od_a_a)|)) (or (not (forall ((z tptp.product_prod_a_a)) (= (ho_233 x z) (ho_233 y z)))) (= x y))))) (let ((_let_378 (forall ((u |u_(-> tptp.list_P1467822637od_a_a tptp.set_Product_prod_a_a)|) (e tptp.set_Product_prod_a_a) (i tptp.list_P1467822637od_a_a)) (not (forall ((v |u_(-> tptp.list_P1467822637od_a_a tptp.set_Product_prod_a_a)|)) (not (forall ((ii tptp.list_P1467822637od_a_a)) (= (ho_321 v ii) (ite (= i ii) e (ho_321 u ii)))))))))) (let ((_let_379 (forall ((x |u_(-> tptp.list_P1467822637od_a_a tptp.set_Product_prod_a_a)|) (y |u_(-> tptp.list_P1467822637od_a_a tptp.set_Product_prod_a_a)|)) (or (not (forall ((z tptp.list_P1467822637od_a_a)) (= (ho_321 x z) (ho_321 y z)))) (= x y))))) (let ((_let_380 (forall ((u |u_(-> tptp.a tptp.product_prod_a_a tptp.produc1921647824od_a_a)|) (e |u_(-> tptp.product_prod_a_a tptp.produc1921647824od_a_a)|) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.product_prod_a_a tptp.produc1921647824od_a_a)|)) (not (forall ((ii tptp.a)) (= (ho_232 v ii) (ite (= i ii) e (ho_232 u ii)))))))))) (let ((_let_381 (forall ((x |u_(-> tptp.a tptp.product_prod_a_a tptp.produc1921647824od_a_a)|) (y |u_(-> tptp.a tptp.product_prod_a_a tptp.produc1921647824od_a_a)|)) (or (not (forall ((z tptp.a)) (= (ho_232 x z) (ho_232 y z)))) (= x y))))) (let ((_let_382 (forall ((u |u_(-> tptp.produc1921647824od_a_a tptp.list_P1458844246od_a_a tptp.list_P1458844246od_a_a)|) (e |u_(-> tptp.list_P1458844246od_a_a tptp.list_P1458844246od_a_a)|) (i tptp.produc1921647824od_a_a)) (not (forall ((v |u_(-> tptp.produc1921647824od_a_a tptp.list_P1458844246od_a_a tptp.list_P1458844246od_a_a)|)) (not (forall ((ii tptp.produc1921647824od_a_a)) (= (ho_235 v ii) (ite (= i ii) e (ho_235 u ii)))))))))) (let ((_let_383 (forall ((x |u_(-> tptp.produc1921647824od_a_a tptp.list_P1458844246od_a_a tptp.list_P1458844246od_a_a)|) (y |u_(-> tptp.produc1921647824od_a_a tptp.list_P1458844246od_a_a tptp.list_P1458844246od_a_a)|)) (or (not (forall ((z tptp.produc1921647824od_a_a)) (= (ho_235 x z) (ho_235 y z)))) (= x y))))) (let ((_let_384 (forall ((u |u_(-> tptp.list_a_nat tptp.list_P576104046_a_nat)|) (e tptp.list_P576104046_a_nat) (i tptp.list_a_nat)) (not (forall ((v |u_(-> tptp.list_a_nat tptp.list_P576104046_a_nat)|)) (not (forall ((ii tptp.list_a_nat)) (= (ho_239 v ii) (ite (= i ii) e (ho_239 u ii)))))))))) (let ((_let_385 (forall ((x |u_(-> tptp.list_a_nat tptp.list_P576104046_a_nat)|) (y |u_(-> tptp.list_a_nat tptp.list_P576104046_a_nat)|)) (or (not (forall ((z tptp.list_a_nat)) (= (ho_239 x z) (ho_239 y z)))) (= x y))))) (let ((_let_386 (forall ((u |u_(-> tptp.list_P576104046_a_nat tptp.list_P576104046_a_nat)|) (e tptp.list_P576104046_a_nat) (i tptp.list_P576104046_a_nat)) (not (forall ((v |u_(-> tptp.list_P576104046_a_nat tptp.list_P576104046_a_nat)|)) (not (forall ((ii tptp.list_P576104046_a_nat)) (= (ho_245 v ii) (ite (= i ii) e (ho_245 u ii)))))))))) (let ((_let_387 (forall ((x |u_(-> tptp.list_P576104046_a_nat tptp.list_P576104046_a_nat)|) (y |u_(-> tptp.list_P576104046_a_nat tptp.list_P576104046_a_nat)|)) (or (not (forall ((z tptp.list_P576104046_a_nat)) (= (ho_245 x z) (ho_245 y z)))) (= x y))))) (let ((_let_388 (forall ((u |u_(-> tptp.product_prod_a_a_nat tptp.list_P576104046_a_nat tptp.list_P576104046_a_nat)|) (e |u_(-> tptp.list_P576104046_a_nat tptp.list_P576104046_a_nat)|) (i tptp.product_prod_a_a_nat)) (not (forall ((v |u_(-> tptp.product_prod_a_a_nat tptp.list_P576104046_a_nat tptp.list_P576104046_a_nat)|)) (not (forall ((ii tptp.product_prod_a_a_nat)) (= (ho_244 v ii) (ite (= i ii) e (ho_244 u ii)))))))))) (let ((_let_389 (forall ((x |u_(-> tptp.product_prod_a_a_nat tptp.list_P576104046_a_nat tptp.list_P576104046_a_nat)|) (y |u_(-> tptp.product_prod_a_a_nat tptp.list_P576104046_a_nat tptp.list_P576104046_a_nat)|)) (or (not (forall ((z tptp.product_prod_a_a_nat)) (= (ho_244 x z) (ho_244 y z)))) (= x y))))) (let ((_let_390 (forall ((u |u_(-> tptp.list_a tptp.list_P916011052_nat_a)|) (e tptp.list_P916011052_nat_a) (i tptp.list_a)) (not (forall ((v |u_(-> tptp.list_a tptp.list_P916011052_nat_a)|)) (not (forall ((ii tptp.list_a)) (= (ho_248 v ii) (ite (= i ii) e (ho_248 u ii)))))))))) (let ((_let_391 (forall ((x |u_(-> tptp.list_a tptp.list_P916011052_nat_a)|) (y |u_(-> tptp.list_a tptp.list_P916011052_nat_a)|)) (or (not (forall ((z tptp.list_a)) (= (ho_248 x z) (ho_248 y z)))) (= x y))))) (let ((_let_392 (forall ((u |u_(-> tptp.list_a_nat tptp.list_a tptp.list_P916011052_nat_a)|) (e |u_(-> tptp.list_a tptp.list_P916011052_nat_a)|) (i tptp.list_a_nat)) (not (forall ((v |u_(-> tptp.list_a_nat tptp.list_a tptp.list_P916011052_nat_a)|)) (not (forall ((ii tptp.list_a_nat)) (= (ho_247 v ii) (ite (= i ii) e (ho_247 u ii)))))))))) (let ((_let_393 (forall ((x |u_(-> tptp.list_a_nat tptp.list_a tptp.list_P916011052_nat_a)|) (y |u_(-> tptp.list_a_nat tptp.list_a tptp.list_P916011052_nat_a)|)) (or (not (forall ((z tptp.list_a_nat)) (= (ho_247 x z) (ho_247 y z)))) (= x y))))) (let ((_let_394 (forall ((u |u_(-> tptp.list_P916011052_nat_a tptp.list_P916011052_nat_a)|) (e tptp.list_P916011052_nat_a) (i tptp.list_P916011052_nat_a)) (not (forall ((v |u_(-> tptp.list_P916011052_nat_a tptp.list_P916011052_nat_a)|)) (not (forall ((ii tptp.list_P916011052_nat_a)) (= (ho_254 v ii) (ite (= i ii) e (ho_254 u ii)))))))))) (let ((_let_395 (forall ((x |u_(-> tptp.list_P916011052_nat_a tptp.list_P916011052_nat_a)|) (y |u_(-> tptp.list_P916011052_nat_a tptp.list_P916011052_nat_a)|)) (or (not (forall ((z tptp.list_P916011052_nat_a)) (= (ho_254 x z) (ho_254 y z)))) (= x y))))) (let ((_let_396 (forall ((u |u_(-> _u_(-> tptp.a tptp.nat)_ tptp.a tptp.product_prod_a_nat_a)|) (e |u_(-> tptp.a tptp.product_prod_a_nat_a)|) (i |u_(-> tptp.a tptp.nat)|)) (not (forall ((v |u_(-> _u_(-> tptp.a tptp.nat)_ tptp.a tptp.product_prod_a_nat_a)|)) (not (forall ((ii |u_(-> tptp.a tptp.nat)|)) (= (ho_250 v ii) (ite (= i ii) e (ho_250 u ii)))))))))) (let ((_let_397 (forall ((x |u_(-> _u_(-> tptp.a tptp.nat)_ tptp.a tptp.product_prod_a_nat_a)|) (y |u_(-> _u_(-> tptp.a tptp.nat)_ tptp.a tptp.product_prod_a_nat_a)|)) (or (not (forall ((z |u_(-> tptp.a tptp.nat)|)) (= (ho_250 x z) (ho_250 y z)))) (= x y))))) (let ((_let_398 (forall ((u |u_(-> tptp.product_prod_a_nat_a tptp.list_P916011052_nat_a tptp.list_P916011052_nat_a)|) (e |u_(-> tptp.list_P916011052_nat_a tptp.list_P916011052_nat_a)|) (i tptp.product_prod_a_nat_a)) (not (forall ((v |u_(-> tptp.product_prod_a_nat_a tptp.list_P916011052_nat_a tptp.list_P916011052_nat_a)|)) (not (forall ((ii tptp.product_prod_a_nat_a)) (= (ho_253 v ii) (ite (= i ii) e (ho_253 u ii)))))))))) (let ((_let_399 (forall ((x |u_(-> tptp.product_prod_a_nat_a tptp.list_P916011052_nat_a tptp.list_P916011052_nat_a)|) (y |u_(-> tptp.product_prod_a_nat_a tptp.list_P916011052_nat_a tptp.list_P916011052_nat_a)|)) (or (not (forall ((z tptp.product_prod_a_nat_a)) (= (ho_253 x z) (ho_253 y z)))) (= x y))))) (let ((_let_400 (forall ((u |u_(-> tptp.list_list_a tptp.list_P601816365list_a)|) (e tptp.list_P601816365list_a) (i tptp.list_list_a)) (not (forall ((v |u_(-> tptp.list_list_a tptp.list_P601816365list_a)|)) (not (forall ((ii tptp.list_list_a)) (= (ho_257 v ii) (ite (= i ii) e (ho_257 u ii)))))))))) (let ((_let_401 (forall ((x |u_(-> tptp.list_list_a tptp.list_P601816365list_a)|) (y |u_(-> tptp.list_list_a tptp.list_P601816365list_a)|)) (or (not (forall ((z tptp.list_list_a)) (= (ho_257 x z) (ho_257 y z)))) (= x y))))) (let ((_let_402 (forall ((u |u_(-> tptp.list_list_a tptp.list_list_a tptp.list_P601816365list_a)|) (e |u_(-> tptp.list_list_a tptp.list_P601816365list_a)|) (i tptp.list_list_a)) (not (forall ((v |u_(-> tptp.list_list_a tptp.list_list_a tptp.list_P601816365list_a)|)) (not (forall ((ii tptp.list_list_a)) (= (ho_256 v ii) (ite (= i ii) e (ho_256 u ii)))))))))) (let ((_let_403 (forall ((x |u_(-> tptp.list_list_a tptp.list_list_a tptp.list_P601816365list_a)|) (y |u_(-> tptp.list_list_a tptp.list_list_a tptp.list_P601816365list_a)|)) (or (not (forall ((z tptp.list_list_a)) (= (ho_256 x z) (ho_256 y z)))) (= x y))))) (let ((_let_404 (forall ((u |u_(-> tptp.list_a tptp.list_P305489470_a_a_a)|) (e tptp.list_P305489470_a_a_a) (i tptp.list_a)) (not (forall ((v |u_(-> tptp.list_a tptp.list_P305489470_a_a_a)|)) (not (forall ((ii tptp.list_a)) (= (ho_263 v ii) (ite (= i ii) e (ho_263 u ii)))))))))) (let ((_let_405 (forall ((x |u_(-> tptp.list_a tptp.list_P305489470_a_a_a)|) (y |u_(-> tptp.list_a tptp.list_P305489470_a_a_a)|)) (or (not (forall ((z tptp.list_a)) (= (ho_263 x z) (ho_263 y z)))) (= x y))))) (let ((_let_406 (forall ((u |u_(-> tptp.list_l1108175539od_a_a tptp.list_a tptp.list_P305489470_a_a_a)|) (e |u_(-> tptp.list_a tptp.list_P305489470_a_a_a)|) (i tptp.list_l1108175539od_a_a)) (not (forall ((v |u_(-> tptp.list_l1108175539od_a_a tptp.list_a tptp.list_P305489470_a_a_a)|)) (not (forall ((ii tptp.list_l1108175539od_a_a)) (= (ho_262 v ii) (ite (= i ii) e (ho_262 u ii)))))))))) (let ((_let_407 (forall ((x |u_(-> tptp.list_l1108175539od_a_a tptp.list_a tptp.list_P305489470_a_a_a)|) (y |u_(-> tptp.list_l1108175539od_a_a tptp.list_a tptp.list_P305489470_a_a_a)|)) (or (not (forall ((z tptp.list_l1108175539od_a_a)) (= (ho_262 x z) (ho_262 y z)))) (= x y))))) (let ((_let_408 (forall ((u |u_(-> tptp.produc657167928_a_a_a tptp.list_P305489470_a_a_a tptp.list_P305489470_a_a_a)|) (e |u_(-> tptp.list_P305489470_a_a_a tptp.list_P305489470_a_a_a)|) (i tptp.produc657167928_a_a_a)) (not (forall ((v |u_(-> tptp.produc657167928_a_a_a tptp.list_P305489470_a_a_a tptp.list_P305489470_a_a_a)|)) (not (forall ((ii tptp.produc657167928_a_a_a)) (= (ho_265 v ii) (ite (= i ii) e (ho_265 u ii)))))))))) (let ((_let_409 (forall ((x |u_(-> tptp.produc657167928_a_a_a tptp.list_P305489470_a_a_a tptp.list_P305489470_a_a_a)|) (y |u_(-> tptp.produc657167928_a_a_a tptp.list_P305489470_a_a_a tptp.list_P305489470_a_a_a)|)) (or (not (forall ((z tptp.produc657167928_a_a_a)) (= (ho_265 x z) (ho_265 y z)))) (= x y))))) (let ((_let_410 (forall ((u |u_(-> tptp.pair_p125712459t_unit tptp.product_prod_a_a tptp.a Bool)|) (e |u_(-> tptp.product_prod_a_a tptp.a Bool)|) (i tptp.pair_p125712459t_unit)) (not (forall ((v |u_(-> tptp.pair_p125712459t_unit tptp.product_prod_a_a tptp.a Bool)|)) (not (forall ((ii tptp.pair_p125712459t_unit)) (= (ho_303 v ii) (ite (= i ii) e (ho_303 u ii)))))))))) (let ((_let_411 (forall ((x |u_(-> tptp.pair_p125712459t_unit tptp.product_prod_a_a tptp.a Bool)|) (y |u_(-> tptp.pair_p125712459t_unit tptp.product_prod_a_a tptp.a Bool)|)) (or (not (forall ((z tptp.pair_p125712459t_unit)) (= (ho_303 x z) (ho_303 y z)))) (= x y))))) (let ((_let_412 (forall ((u |u_(-> tptp.list_a tptp.list_l1108175539od_a_a tptp.list_P1175580892od_a_a)|) (e |u_(-> tptp.list_l1108175539od_a_a tptp.list_P1175580892od_a_a)|) (i tptp.list_a)) (not (forall ((v |u_(-> tptp.list_a tptp.list_l1108175539od_a_a tptp.list_P1175580892od_a_a)|)) (not (forall ((ii tptp.list_a)) (= (ho_268 v ii) (ite (= i ii) e (ho_268 u ii)))))))))) (let ((_let_413 (forall ((x |u_(-> tptp.list_a tptp.list_l1108175539od_a_a tptp.list_P1175580892od_a_a)|) (y |u_(-> tptp.list_a tptp.list_l1108175539od_a_a tptp.list_P1175580892od_a_a)|)) (or (not (forall ((z tptp.list_a)) (= (ho_268 x z) (ho_268 y z)))) (= x y))))) (let ((_let_414 (forall ((u |u_(-> tptp.list_P1175580892od_a_a tptp.list_P1175580892od_a_a)|) (e tptp.list_P1175580892od_a_a) (i tptp.list_P1175580892od_a_a)) (not (forall ((v |u_(-> tptp.list_P1175580892od_a_a tptp.list_P1175580892od_a_a)|)) (not (forall ((ii tptp.list_P1175580892od_a_a)) (= (ho_272 v ii) (ite (= i ii) e (ho_272 u ii)))))))))) (let ((_let_415 (forall ((x |u_(-> tptp.list_P1175580892od_a_a tptp.list_P1175580892od_a_a)|) (y |u_(-> tptp.list_P1175580892od_a_a tptp.list_P1175580892od_a_a)|)) (or (not (forall ((z tptp.list_P1175580892od_a_a)) (= (ho_272 x z) (ho_272 y z)))) (= x y))))) (let ((_let_416 (forall ((u |u_(-> tptp.produc1701253078od_a_a tptp.list_P1175580892od_a_a tptp.list_P1175580892od_a_a)|) (e |u_(-> tptp.list_P1175580892od_a_a tptp.list_P1175580892od_a_a)|) (i tptp.produc1701253078od_a_a)) (not (forall ((v |u_(-> tptp.produc1701253078od_a_a tptp.list_P1175580892od_a_a tptp.list_P1175580892od_a_a)|)) (not (forall ((ii tptp.produc1701253078od_a_a)) (= (ho_271 v ii) (ite (= i ii) e (ho_271 u ii)))))))))) (let ((_let_417 (forall ((x |u_(-> tptp.produc1701253078od_a_a tptp.list_P1175580892od_a_a tptp.list_P1175580892od_a_a)|) (y |u_(-> tptp.produc1701253078od_a_a tptp.list_P1175580892od_a_a tptp.list_P1175580892od_a_a)|)) (or (not (forall ((z tptp.produc1701253078od_a_a)) (= (ho_271 x z) (ho_271 y z)))) (= x y))))) (let ((_let_418 (forall ((u |u_(-> tptp.product_prod_a_a tptp.a Bool)|) (e |u_(-> tptp.a Bool)|) (i tptp.product_prod_a_a)) (not (forall ((v |u_(-> tptp.product_prod_a_a tptp.a Bool)|)) (not (forall ((ii tptp.product_prod_a_a)) (= (ho_304 v ii) (ite (= i ii) e (ho_304 u ii)))))))))) (let ((_let_419 (forall ((x |u_(-> tptp.product_prod_a_a tptp.a Bool)|) (y |u_(-> tptp.product_prod_a_a tptp.a Bool)|)) (or (not (forall ((z tptp.product_prod_a_a)) (= (ho_304 x z) (ho_304 y z)))) (= x y))))) (let ((_let_420 (forall ((u |u_(-> tptp.list_a_nat tptp.list_P1435957893_a_nat)|) (e tptp.list_P1435957893_a_nat) (i tptp.list_a_nat)) (not (forall ((v |u_(-> tptp.list_a_nat tptp.list_P1435957893_a_nat)|)) (not (forall ((ii tptp.list_a_nat)) (= (ho_275 v ii) (ite (= i ii) e (ho_275 u ii)))))))))) (let ((_let_421 (forall ((x |u_(-> tptp.list_a_nat tptp.list_P1435957893_a_nat)|) (y |u_(-> tptp.list_a_nat tptp.list_P1435957893_a_nat)|)) (or (not (forall ((z tptp.list_a_nat)) (= (ho_275 x z) (ho_275 y z)))) (= x y))))) (let ((_let_422 (forall ((u |u_(-> tptp.list_P1467822637od_a_a tptp.list_a_nat tptp.list_P1435957893_a_nat)|) (e |u_(-> tptp.list_a_nat tptp.list_P1435957893_a_nat)|) (i tptp.list_P1467822637od_a_a)) (not (forall ((v |u_(-> tptp.list_P1467822637od_a_a tptp.list_a_nat tptp.list_P1435957893_a_nat)|)) (not (forall ((ii tptp.list_P1467822637od_a_a)) (= (ho_274 v ii) (ite (= i ii) e (ho_274 u ii)))))))))) (let ((_let_423 (forall ((x |u_(-> tptp.list_P1467822637od_a_a tptp.list_a_nat tptp.list_P1435957893_a_nat)|) (y |u_(-> tptp.list_P1467822637od_a_a tptp.list_a_nat tptp.list_P1435957893_a_nat)|)) (or (not (forall ((z tptp.list_P1467822637od_a_a)) (= (ho_274 x z) (ho_274 y z)))) (= x y))))) (let ((_let_424 (forall ((u |u_(-> tptp.a tptp.a)|) (e tptp.a) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.a)|)) (not (forall ((ii tptp.a)) (= (ho_371 v ii) (ite (= i ii) e (ho_371 u ii)))))))))) (let ((_let_425 (forall ((x |u_(-> tptp.a tptp.a)|) (y |u_(-> tptp.a tptp.a)|)) (or (not (forall ((z tptp.a)) (= (ho_371 x z) (ho_371 y z)))) (= x y))))) (let ((_let_426 (forall ((u |u_(-> tptp.list_P1435957893_a_nat tptp.list_P1435957893_a_nat)|) (e tptp.list_P1435957893_a_nat) (i tptp.list_P1435957893_a_nat)) (not (forall ((v |u_(-> tptp.list_P1435957893_a_nat tptp.list_P1435957893_a_nat)|)) (not (forall ((ii tptp.list_P1435957893_a_nat)) (= (ho_281 v ii) (ite (= i ii) e (ho_281 u ii)))))))))) (let ((_let_427 (forall ((x |u_(-> tptp.list_P1435957893_a_nat tptp.list_P1435957893_a_nat)|) (y |u_(-> tptp.list_P1435957893_a_nat tptp.list_P1435957893_a_nat)|)) (or (not (forall ((z tptp.list_P1435957893_a_nat)) (= (ho_281 x z) (ho_281 y z)))) (= x y))))) (let ((_let_428 (forall ((u |u_(-> tptp.list_a tptp.a Bool)|) (e |u_(-> tptp.a Bool)|) (i tptp.list_a)) (not (forall ((v |u_(-> tptp.list_a tptp.a Bool)|)) (not (forall ((ii tptp.list_a)) (= (ho_289 v ii) (ite (= i ii) e (ho_289 u ii)))))))))) (let ((_let_429 (forall ((x |u_(-> tptp.list_a tptp.a Bool)|) (y |u_(-> tptp.list_a tptp.a Bool)|)) (or (not (forall ((z tptp.list_a)) (= (ho_289 x z) (ho_289 y z)))) (= x y))))) (let ((_let_430 (forall ((u |u_(-> tptp.list_P1891567085od_a_a tptp.produc1572603623od_a_a Bool)|) (e |u_(-> tptp.produc1572603623od_a_a Bool)|) (i tptp.list_P1891567085od_a_a)) (not (forall ((v |u_(-> tptp.list_P1891567085od_a_a tptp.produc1572603623od_a_a Bool)|)) (not (forall ((ii tptp.list_P1891567085od_a_a)) (= (ho_291 v ii) (ite (= i ii) e (ho_291 u ii)))))))))) (let ((_let_431 (forall ((x |u_(-> tptp.list_P1891567085od_a_a tptp.produc1572603623od_a_a Bool)|) (y |u_(-> tptp.list_P1891567085od_a_a tptp.produc1572603623od_a_a Bool)|)) (or (not (forall ((z tptp.list_P1891567085od_a_a)) (= (ho_291 x z) (ho_291 y z)))) (= x y))))) (let ((_let_432 (forall ((u |u_(-> tptp.list_l1108175539od_a_a tptp.list_P1467822637od_a_a Bool)|) (e |u_(-> tptp.list_P1467822637od_a_a Bool)|) (i tptp.list_l1108175539od_a_a)) (not (forall ((v |u_(-> tptp.list_l1108175539od_a_a tptp.list_P1467822637od_a_a Bool)|)) (not (forall ((ii tptp.list_l1108175539od_a_a)) (= (ho_294 v ii) (ite (= i ii) e (ho_294 u ii)))))))))) (let ((_let_433 (forall ((x |u_(-> tptp.list_l1108175539od_a_a tptp.list_P1467822637od_a_a Bool)|) (y |u_(-> tptp.list_l1108175539od_a_a tptp.list_P1467822637od_a_a Bool)|)) (or (not (forall ((z tptp.list_l1108175539od_a_a)) (= (ho_294 x z) (ho_294 y z)))) (= x y))))) (let ((_let_434 (forall ((u |u_(-> _u_(-> tptp.a tptp.nat)_ Bool)|) (e Bool) (i |u_(-> tptp.a tptp.nat)|)) (not (forall ((v |u_(-> _u_(-> tptp.a tptp.nat)_ Bool)|)) (not (forall ((ii |u_(-> tptp.a tptp.nat)|)) (= (ho_297 v ii) (ite (= i ii) e (ho_297 u ii)))))))))) (let ((_let_435 (forall ((x |u_(-> _u_(-> tptp.a tptp.nat)_ Bool)|) (y |u_(-> _u_(-> tptp.a tptp.nat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.a tptp.nat)|)) (= (ho_297 x z) (ho_297 y z)))) (= x y))))) (let ((_let_436 (forall ((u |u_(-> tptp.list_a_nat _u_(-> tptp.a tptp.nat)_ Bool)|) (e |u_(-> _u_(-> tptp.a tptp.nat)_ Bool)|) (i tptp.list_a_nat)) (not (forall ((v |u_(-> tptp.list_a_nat _u_(-> tptp.a tptp.nat)_ Bool)|)) (not (forall ((ii tptp.list_a_nat)) (= (ho_296 v ii) (ite (= i ii) e (ho_296 u ii)))))))))) (let ((_let_437 (forall ((x |u_(-> tptp.list_a_nat _u_(-> tptp.a tptp.nat)_ Bool)|) (y |u_(-> tptp.list_a_nat _u_(-> tptp.a tptp.nat)_ Bool)|)) (or (not (forall ((z tptp.list_a_nat)) (= (ho_296 x z) (ho_296 y z)))) (= x y))))) (let ((_let_438 (forall ((u |u_(-> tptp.produc651658087od_a_a Bool)|) (e Bool) (i tptp.produc651658087od_a_a)) (not (forall ((v |u_(-> tptp.produc651658087od_a_a Bool)|)) (not (forall ((ii tptp.produc651658087od_a_a)) (= (ho_305 v ii) (ite (= i ii) e (ho_305 u ii)))))))))) (let ((_let_439 (forall ((x |u_(-> tptp.produc651658087od_a_a Bool)|) (y |u_(-> tptp.produc651658087od_a_a Bool)|)) (or (not (forall ((z tptp.produc651658087od_a_a)) (= (ho_305 x z) (ho_305 y z)))) (= x y))))) (let ((_let_440 (forall ((u |u_(-> _u_(-> tptp.produc651658087od_a_a Bool)_ tptp.set_Pr800560199od_a_a)|) (e tptp.set_Pr800560199od_a_a) (i |u_(-> tptp.produc651658087od_a_a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.produc651658087od_a_a Bool)_ tptp.set_Pr800560199od_a_a)|)) (not (forall ((ii |u_(-> tptp.produc651658087od_a_a Bool)|)) (= (ho_307 v ii) (ite (= i ii) e (ho_307 u ii)))))))))) (let ((_let_441 (forall ((x |u_(-> _u_(-> tptp.produc651658087od_a_a Bool)_ tptp.set_Pr800560199od_a_a)|) (y |u_(-> _u_(-> tptp.produc651658087od_a_a Bool)_ tptp.set_Pr800560199od_a_a)|)) (or (not (forall ((z |u_(-> tptp.produc651658087od_a_a Bool)|)) (= (ho_307 x z) (ho_307 y z)))) (= x y))))) (let ((_let_442 (forall ((u |u_(-> _u_(-> tptp.produc864062247list_a Bool)_ tptp.set_Pr1971762695list_a)|) (e tptp.set_Pr1971762695list_a) (i |u_(-> tptp.produc864062247list_a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.produc864062247list_a Bool)_ tptp.set_Pr1971762695list_a)|)) (not (forall ((ii |u_(-> tptp.produc864062247list_a Bool)|)) (= (ho_309 v ii) (ite (= i ii) e (ho_309 u ii)))))))))) (let ((_let_443 (forall ((x |u_(-> _u_(-> tptp.produc864062247list_a Bool)_ tptp.set_Pr1971762695list_a)|) (y |u_(-> _u_(-> tptp.produc864062247list_a Bool)_ tptp.set_Pr1971762695list_a)|)) (or (not (forall ((z |u_(-> tptp.produc864062247list_a Bool)|)) (= (ho_309 x z) (ho_309 y z)))) (= x y))))) (let ((_let_444 (forall ((u |u_(-> _u_(-> tptp.product_prod_a_a Bool)_ tptp.set_Product_prod_a_a)|) (e tptp.set_Product_prod_a_a) (i |u_(-> tptp.product_prod_a_a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.product_prod_a_a Bool)_ tptp.set_Product_prod_a_a)|)) (not (forall ((ii |u_(-> tptp.product_prod_a_a Bool)|)) (= (ho_311 v ii) (ite (= i ii) e (ho_311 u ii)))))))))) (let ((_let_445 (forall ((x |u_(-> _u_(-> tptp.product_prod_a_a Bool)_ tptp.set_Product_prod_a_a)|) (y |u_(-> _u_(-> tptp.product_prod_a_a Bool)_ tptp.set_Product_prod_a_a)|)) (or (not (forall ((z |u_(-> tptp.product_prod_a_a Bool)|)) (= (ho_311 x z) (ho_311 y z)))) (= x y))))) (let ((_let_446 (forall ((u |u_(-> _u_(-> tptp.list_P1467822637od_a_a Bool)_ tptp.set_li562223245od_a_a)|) (e tptp.set_li562223245od_a_a) (i |u_(-> tptp.list_P1467822637od_a_a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.list_P1467822637od_a_a Bool)_ tptp.set_li562223245od_a_a)|)) (not (forall ((ii |u_(-> tptp.list_P1467822637od_a_a Bool)|)) (= (ho_313 v ii) (ite (= i ii) e (ho_313 u ii)))))))))) (let ((_let_447 (forall ((x |u_(-> _u_(-> tptp.list_P1467822637od_a_a Bool)_ tptp.set_li562223245od_a_a)|) (y |u_(-> _u_(-> tptp.list_P1467822637od_a_a Bool)_ tptp.set_li562223245od_a_a)|)) (or (not (forall ((z |u_(-> tptp.list_P1467822637od_a_a Bool)|)) (= (ho_313 x z) (ho_313 y z)))) (= x y))))) (let ((_let_448 (forall ((u |u_(-> tptp.produc1016684094_a_a_a tptp.produc1912141786_a_a_a)|) (e tptp.produc1912141786_a_a_a) (i tptp.produc1016684094_a_a_a)) (not (forall ((v |u_(-> tptp.produc1016684094_a_a_a tptp.produc1912141786_a_a_a)|)) (not (forall ((ii tptp.produc1016684094_a_a_a)) (= (ho_318 v ii) (ite (= i ii) e (ho_318 u ii)))))))))) (let ((_let_449 (forall ((x |u_(-> tptp.produc1016684094_a_a_a tptp.produc1912141786_a_a_a)|) (y |u_(-> tptp.produc1016684094_a_a_a tptp.produc1912141786_a_a_a)|)) (or (not (forall ((z tptp.produc1016684094_a_a_a)) (= (ho_318 x z) (ho_318 y z)))) (= x y))))) (let ((_let_450 (forall ((u |u_(-> _u_(-> tptp.a Bool)_ tptp.set_a)|) (e tptp.set_a) (i |u_(-> tptp.a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.a Bool)_ tptp.set_a)|)) (not (forall ((ii |u_(-> tptp.a Bool)|)) (= (ho_315 v ii) (ite (= i ii) e (ho_315 u ii)))))))))) (let ((_let_451 (forall ((x |u_(-> _u_(-> tptp.a Bool)_ tptp.set_a)|) (y |u_(-> _u_(-> tptp.a Bool)_ tptp.set_a)|)) (or (not (forall ((z |u_(-> tptp.a Bool)|)) (= (ho_315 x z) (ho_315 y z)))) (= x y))))) (let ((_let_452 (forall ((u |u_(-> tptp.pair_p125712459t_unit tptp.produc1016684094_a_a_a tptp.produc1912141786_a_a_a)|) (e |u_(-> tptp.produc1016684094_a_a_a tptp.produc1912141786_a_a_a)|) (i tptp.pair_p125712459t_unit)) (not (forall ((v |u_(-> tptp.pair_p125712459t_unit tptp.produc1016684094_a_a_a tptp.produc1912141786_a_a_a)|)) (not (forall ((ii tptp.pair_p125712459t_unit)) (= (ho_317 v ii) (ite (= i ii) e (ho_317 u ii)))))))))) (let ((_let_453 (forall ((x |u_(-> tptp.pair_p125712459t_unit tptp.produc1016684094_a_a_a tptp.produc1912141786_a_a_a)|) (y |u_(-> tptp.pair_p125712459t_unit tptp.produc1016684094_a_a_a tptp.produc1912141786_a_a_a)|)) (or (not (forall ((z tptp.pair_p125712459t_unit)) (= (ho_317 x z) (ho_317 y z)))) (= x y))))) (let ((_let_454 (forall ((u |u_(-> tptp.list_a tptp.set_a)|) (e tptp.set_a) (i tptp.list_a)) (not (forall ((v |u_(-> tptp.list_a tptp.set_a)|)) (not (forall ((ii tptp.list_a)) (= (ho_323 v ii) (ite (= i ii) e (ho_323 u ii)))))))))) (let ((_let_455 (forall ((x |u_(-> tptp.list_a tptp.set_a)|) (y |u_(-> tptp.list_a tptp.set_a)|)) (or (not (forall ((z tptp.list_a)) (= (ho_323 x z) (ho_323 y z)))) (= x y))))) (let ((_let_456 (forall ((u |u_(-> tptp.list_a tptp.nat)|) (e tptp.nat) (i tptp.list_a)) (not (forall ((v |u_(-> tptp.list_a tptp.nat)|)) (not (forall ((ii tptp.list_a)) (= (ho_325 v ii) (ite (= i ii) e (ho_325 u ii)))))))))) (let ((_let_457 (forall ((x |u_(-> tptp.list_a tptp.nat)|) (y |u_(-> tptp.list_a tptp.nat)|)) (or (not (forall ((z tptp.list_a)) (= (ho_325 x z) (ho_325 y z)))) (= x y))))) (let ((_let_458 (forall ((u |u_(-> tptp.list_P1467822637od_a_a tptp.nat)|) (e tptp.nat) (i tptp.list_P1467822637od_a_a)) (not (forall ((v |u_(-> tptp.list_P1467822637od_a_a tptp.nat)|)) (not (forall ((ii tptp.list_P1467822637od_a_a)) (= (ho_327 v ii) (ite (= i ii) e (ho_327 u ii)))))))))) (let ((_let_459 (forall ((x |u_(-> tptp.list_P1467822637od_a_a tptp.nat)|) (y |u_(-> tptp.list_P1467822637od_a_a tptp.nat)|)) (or (not (forall ((z tptp.list_P1467822637od_a_a)) (= (ho_327 x z) (ho_327 y z)))) (= x y))))) (let ((_let_460 (forall ((u |u_(-> tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a Bool)|) (e |u_(-> tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a Bool)|) (i tptp.list_P1467822637od_a_a)) (not (forall ((v |u_(-> tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a Bool)|)) (not (forall ((ii tptp.list_P1467822637od_a_a)) (= (ho_331 v ii) (ite (= i ii) e (ho_331 u ii)))))))))) (let ((_let_461 (forall ((x |u_(-> tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a Bool)|) (y |u_(-> tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a Bool)|)) (or (not (forall ((z tptp.list_P1467822637od_a_a)) (= (ho_331 x z) (ho_331 y z)))) (= x y))))) (let ((_let_462 (forall ((u |u_(-> tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a Bool)|) (e |u_(-> tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a Bool)|) (i tptp.list_P1467822637od_a_a)) (not (forall ((v |u_(-> tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a Bool)|)) (not (forall ((ii tptp.list_P1467822637od_a_a)) (= (ho_330 v ii) (ite (= i ii) e (ho_330 u ii)))))))))) (let ((_let_463 (forall ((x |u_(-> tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a Bool)|) (y |u_(-> tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a Bool)|)) (or (not (forall ((z tptp.list_P1467822637od_a_a)) (= (ho_330 x z) (ho_330 y z)))) (= x y))))) (let ((_let_464 (forall ((u |u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)|) (e tptp.product_prod_a_a) (i tptp.product_prod_a_a)) (not (forall ((v |u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)|)) (not (forall ((ii tptp.product_prod_a_a)) (= (ho_333 v ii) (ite (= i ii) e (ho_333 u ii)))))))))) (let ((_let_465 (forall ((x |u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)|) (y |u_(-> tptp.product_prod_a_a tptp.product_prod_a_a)|)) (or (not (forall ((z tptp.product_prod_a_a)) (= (ho_333 x z) (ho_333 y z)))) (= x y))))) (let ((_let_466 (forall ((u |u_(-> tptp.product_prod_a_a tptp.a tptp.list_P1467822637od_a_a Bool)|) (e |u_(-> tptp.a tptp.list_P1467822637od_a_a Bool)|) (i tptp.product_prod_a_a)) (not (forall ((v |u_(-> tptp.product_prod_a_a tptp.a tptp.list_P1467822637od_a_a Bool)|)) (not (forall ((ii tptp.product_prod_a_a)) (= (ho_336 v ii) (ite (= i ii) e (ho_336 u ii)))))))))) (let ((_let_467 (forall ((x |u_(-> tptp.product_prod_a_a tptp.a tptp.list_P1467822637od_a_a Bool)|) (y |u_(-> tptp.product_prod_a_a tptp.a tptp.list_P1467822637od_a_a Bool)|)) (or (not (forall ((z tptp.product_prod_a_a)) (= (ho_336 x z) (ho_336 y z)))) (= x y))))) (let ((_let_468 (forall ((u |u_(-> tptp.list_P1467822637od_a_a tptp.a tptp.a)|) (e |u_(-> tptp.a tptp.a)|) (i tptp.list_P1467822637od_a_a)) (not (forall ((v |u_(-> tptp.list_P1467822637od_a_a tptp.a tptp.a)|)) (not (forall ((ii tptp.list_P1467822637od_a_a)) (= (ho_370 v ii) (ite (= i ii) e (ho_370 u ii)))))))))) (let ((_let_469 (forall ((x |u_(-> tptp.list_P1467822637od_a_a tptp.a tptp.a)|) (y |u_(-> tptp.list_P1467822637od_a_a tptp.a tptp.a)|)) (or (not (forall ((z tptp.list_P1467822637od_a_a)) (= (ho_370 x z) (ho_370 y z)))) (= x y))))) (let ((_let_470 (forall ((u |u_(-> tptp.product_prod_a_a tptp.produc1701253078od_a_a tptp.produc821581462od_a_a)|) (e |u_(-> tptp.produc1701253078od_a_a tptp.produc821581462od_a_a)|) (i tptp.product_prod_a_a)) (not (forall ((v |u_(-> tptp.product_prod_a_a tptp.produc1701253078od_a_a tptp.produc821581462od_a_a)|)) (not (forall ((ii tptp.product_prod_a_a)) (= (ho_339 v ii) (ite (= i ii) e (ho_339 u ii)))))))))) (let ((_let_471 (forall ((x |u_(-> tptp.product_prod_a_a tptp.produc1701253078od_a_a tptp.produc821581462od_a_a)|) (y |u_(-> tptp.product_prod_a_a tptp.produc1701253078od_a_a tptp.produc821581462od_a_a)|)) (or (not (forall ((z tptp.product_prod_a_a)) (= (ho_339 x z) (ho_339 y z)))) (= x y))))) (let ((_let_472 (forall ((u |u_(-> tptp.list_P1467822637od_a_a tptp.a Bool)|) (e |u_(-> tptp.a Bool)|) (i tptp.list_P1467822637od_a_a)) (not (forall ((v |u_(-> tptp.list_P1467822637od_a_a tptp.a Bool)|)) (not (forall ((ii tptp.list_P1467822637od_a_a)) (= (ho_341 v ii) (ite (= i ii) e (ho_341 u ii)))))))))) (let ((_let_473 (forall ((x |u_(-> tptp.list_P1467822637od_a_a tptp.a Bool)|) (y |u_(-> tptp.list_P1467822637od_a_a tptp.a Bool)|)) (or (not (forall ((z tptp.list_P1467822637od_a_a)) (= (ho_341 x z) (ho_341 y z)))) (= x y))))) (let ((_let_474 (forall ((u |u_(-> tptp.a tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a)|) (e |u_(-> tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a)|) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a)|)) (not (forall ((ii tptp.a)) (= (ho_344 v ii) (ite (= i ii) e (ho_344 u ii)))))))))) (let ((_let_475 (forall ((x |u_(-> tptp.a tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a)|) (y |u_(-> tptp.a tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a)|)) (or (not (forall ((z tptp.a)) (= (ho_344 x z) (ho_344 y z)))) (= x y))))) (let ((_let_476 (forall ((u |u_(-> Bool tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a)|) (e |u_(-> tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a)|) (i Bool)) (not (forall ((v |u_(-> Bool tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a)|)) (not (forall ((ii Bool)) (= (ho_346 v ii) (ite (= i ii) e (ho_346 u ii)))))))))) (let ((_let_477 (forall ((x |u_(-> Bool tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a)|) (y |u_(-> Bool tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a)|)) (or (not (forall ((z Bool)) (= (ho_346 x z) (ho_346 y z)))) (= x y))))) (let ((_let_478 (forall ((u |u_(-> tptp.set_Product_prod_a_a tptp.product_prod_a_a)|) (e tptp.product_prod_a_a) (i tptp.set_Product_prod_a_a)) (not (forall ((v |u_(-> tptp.set_Product_prod_a_a tptp.product_prod_a_a)|)) (not (forall ((ii tptp.set_Product_prod_a_a)) (= (ho_348 v ii) (ite (= i ii) e (ho_348 u ii)))))))))) (let ((_let_479 (forall ((x |u_(-> tptp.set_Product_prod_a_a tptp.product_prod_a_a)|) (y |u_(-> tptp.set_Product_prod_a_a tptp.product_prod_a_a)|)) (or (not (forall ((z tptp.set_Product_prod_a_a)) (= (ho_348 x z) (ho_348 y z)))) (= x y))))) (let ((_let_480 (forall ((u |u_(-> tptp.produc821581462od_a_a Bool)|) (e Bool) (i tptp.produc821581462od_a_a)) (not (forall ((v |u_(-> tptp.produc821581462od_a_a Bool)|)) (not (forall ((ii tptp.produc821581462od_a_a)) (= (ho_353 v ii) (ite (= i ii) e (ho_353 u ii)))))))))) (let ((_let_481 (forall ((x |u_(-> tptp.produc821581462od_a_a Bool)|) (y |u_(-> tptp.produc821581462od_a_a Bool)|)) (or (not (forall ((z tptp.produc821581462od_a_a)) (= (ho_353 x z) (ho_353 y z)))) (= x y))))) (let ((_let_482 (forall ((u |u_(-> tptp.produc821581462od_a_a tptp.produc821581462od_a_a Bool)|) (e |u_(-> tptp.produc821581462od_a_a Bool)|) (i tptp.produc821581462od_a_a)) (not (forall ((v |u_(-> tptp.produc821581462od_a_a tptp.produc821581462od_a_a Bool)|)) (not (forall ((ii tptp.produc821581462od_a_a)) (= (ho_350 v ii) (ite (= i ii) e (ho_350 u ii)))))))))) (let ((_let_483 (forall ((x |u_(-> tptp.produc821581462od_a_a tptp.produc821581462od_a_a Bool)|) (y |u_(-> tptp.produc821581462od_a_a tptp.produc821581462od_a_a Bool)|)) (or (not (forall ((z tptp.produc821581462od_a_a)) (= (ho_350 x z) (ho_350 y z)))) (= x y))))) (let ((_let_484 (forall ((u |u_(-> _u_(-> tptp.produc821581462od_a_a tptp.produc821581462od_a_a Bool)_ tptp.produc821581462od_a_a Bool)|) (e |u_(-> tptp.produc821581462od_a_a Bool)|) (i |u_(-> tptp.produc821581462od_a_a tptp.produc821581462od_a_a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.produc821581462od_a_a tptp.produc821581462od_a_a Bool)_ tptp.produc821581462od_a_a Bool)|)) (not (forall ((ii |u_(-> tptp.produc821581462od_a_a tptp.produc821581462od_a_a Bool)|)) (= (ho_352 v ii) (ite (= i ii) e (ho_352 u ii)))))))))) (let ((_let_485 (forall ((x |u_(-> _u_(-> tptp.produc821581462od_a_a tptp.produc821581462od_a_a Bool)_ tptp.produc821581462od_a_a Bool)|) (y |u_(-> _u_(-> tptp.produc821581462od_a_a tptp.produc821581462od_a_a Bool)_ tptp.produc821581462od_a_a Bool)|)) (or (not (forall ((z |u_(-> tptp.produc821581462od_a_a tptp.produc821581462od_a_a Bool)|)) (= (ho_352 x z) (ho_352 y z)))) (= x y))))) (let ((_let_486 (forall ((u |u_(-> tptp.product_prod_a_a tptp.list_P1891567085od_a_a tptp.list_P1467822637od_a_a)|) (e |u_(-> tptp.list_P1891567085od_a_a tptp.list_P1467822637od_a_a)|) (i tptp.product_prod_a_a)) (not (forall ((v |u_(-> tptp.product_prod_a_a tptp.list_P1891567085od_a_a tptp.list_P1467822637od_a_a)|)) (not (forall ((ii tptp.product_prod_a_a)) (= (ho_359 v ii) (ite (= i ii) e (ho_359 u ii)))))))))) (let ((_let_487 (forall ((x |u_(-> tptp.product_prod_a_a tptp.list_P1891567085od_a_a tptp.list_P1467822637od_a_a)|) (y |u_(-> tptp.product_prod_a_a tptp.list_P1891567085od_a_a tptp.list_P1467822637od_a_a)|)) (or (not (forall ((z tptp.product_prod_a_a)) (= (ho_359 x z) (ho_359 y z)))) (= x y))))) (let ((_let_488 (forall ((u |u_(-> tptp.nat Bool)|) (e Bool) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat Bool)|)) (not (forall ((ii tptp.nat)) (= (ho_363 v ii) (ite (= i ii) e (ho_363 u ii)))))))))) (let ((_let_489 (forall ((x |u_(-> tptp.nat Bool)|) (y |u_(-> tptp.nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_363 x z) (ho_363 y z)))) (= x y))))) (let ((_let_490 (forall ((u |u_(-> tptp.list_l1108175539od_a_a tptp.set_li562223245od_a_a)|) (e tptp.set_li562223245od_a_a) (i tptp.list_l1108175539od_a_a)) (not (forall ((v |u_(-> tptp.list_l1108175539od_a_a tptp.set_li562223245od_a_a)|)) (not (forall ((ii tptp.list_l1108175539od_a_a)) (= (ho_366 v ii) (ite (= i ii) e (ho_366 u ii)))))))))) (let ((_let_491 (forall ((x |u_(-> tptp.list_l1108175539od_a_a tptp.set_li562223245od_a_a)|) (y |u_(-> tptp.list_l1108175539od_a_a tptp.set_li562223245od_a_a)|)) (or (not (forall ((z tptp.list_l1108175539od_a_a)) (= (ho_366 x z) (ho_366 y z)))) (= x y))))) (let ((_let_492 (forall ((u |u_(-> tptp.list_a_nat tptp.set_Product_prod_a_a)|) (e tptp.set_Product_prod_a_a) (i tptp.list_a_nat)) (not (forall ((v |u_(-> tptp.list_a_nat tptp.set_Product_prod_a_a)|)) (not (forall ((ii tptp.list_a_nat)) (= (ho_368 v ii) (ite (= i ii) e (ho_368 u ii)))))))))) (let ((_let_493 (forall ((x |u_(-> tptp.list_a_nat tptp.set_Product_prod_a_a)|) (y |u_(-> tptp.list_a_nat tptp.set_Product_prod_a_a)|)) (or (not (forall ((z tptp.list_a_nat)) (= (ho_368 x z) (ho_368 y z)))) (= x y))))) (let ((_let_494 (forall ((u |u_(-> tptp.produc657167928_a_a_a tptp.produc657167928_a_a_a Bool)|) (e |u_(-> tptp.produc657167928_a_a_a Bool)|) (i tptp.produc657167928_a_a_a)) (not (forall ((v |u_(-> tptp.produc657167928_a_a_a tptp.produc657167928_a_a_a Bool)|)) (not (forall ((ii tptp.produc657167928_a_a_a)) (= (ho_377 v ii) (ite (= i ii) e (ho_377 u ii)))))))))) (let ((_let_495 (forall ((x |u_(-> tptp.produc657167928_a_a_a tptp.produc657167928_a_a_a Bool)|) (y |u_(-> tptp.produc657167928_a_a_a tptp.produc657167928_a_a_a Bool)|)) (or (not (forall ((z tptp.produc657167928_a_a_a)) (= (ho_377 x z) (ho_377 y z)))) (= x y))))) (let ((_let_496 (forall ((u |u_(-> _u_(-> tptp.produc657167928_a_a_a tptp.produc657167928_a_a_a Bool)_ tptp.produc657167928_a_a_a Bool)|) (e |u_(-> tptp.produc657167928_a_a_a Bool)|) (i |u_(-> tptp.produc657167928_a_a_a tptp.produc657167928_a_a_a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.produc657167928_a_a_a tptp.produc657167928_a_a_a Bool)_ tptp.produc657167928_a_a_a Bool)|)) (not (forall ((ii |u_(-> tptp.produc657167928_a_a_a tptp.produc657167928_a_a_a Bool)|)) (= (ho_379 v ii) (ite (= i ii) e (ho_379 u ii)))))))))) (let ((_let_497 (forall ((x |u_(-> _u_(-> tptp.produc657167928_a_a_a tptp.produc657167928_a_a_a Bool)_ tptp.produc657167928_a_a_a Bool)|) (y |u_(-> _u_(-> tptp.produc657167928_a_a_a tptp.produc657167928_a_a_a Bool)_ tptp.produc657167928_a_a_a Bool)|)) (or (not (forall ((z |u_(-> tptp.produc657167928_a_a_a tptp.produc657167928_a_a_a Bool)|)) (= (ho_379 x z) (ho_379 y z)))) (= x y))))) (let ((_let_498 (forall ((BOUND_VARIABLE_13015 tptp.set_Product_prod_a_a)) (= (ho_9 k_8 BOUND_VARIABLE_13015) (forall ((X tptp.a) (Y tptp.a)) (or (not (ho_9 (ho_14 k_13 (ho_12 (ho_11 k_10 X) Y)) BOUND_VARIABLE_13015)) (not (ho_9 (ho_14 k_13 (ho_12 (ho_11 k_10 Y) X)) BOUND_VARIABLE_13015)))))))) (let ((_let_499 (forall ((BOUND_VARIABLE_13004 tptp.set_Product_prod_a_a)) (= (ho_9 k_15 BOUND_VARIABLE_13004) (forall ((X tptp.a) (Y tptp.a)) (or (not (ho_9 (ho_14 k_13 (ho_12 (ho_11 k_10 X) Y)) BOUND_VARIABLE_13004)) (not (ho_9 (ho_14 k_13 (ho_12 (ho_11 k_10 Y) X)) BOUND_VARIABLE_13004)))))))) (let ((_let_500 (forall ((BOUND_VARIABLE_12996 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(Y21 tptp.list_P1467822637od_a_a) (Y22 tptp.list_l1108175539od_a_a)) (= (= (@ (@ tptp.cons_l724116707od_a_a X21) X22) (@ (@ tptp.cons_l724116707od_a_a Y21) Y22)) (and (= X21 Y21) (= X22 Y22)))) (forall ((X21 (-> tptp.a tptp.nat)) (X22 tptp.list_a_nat) (Y21 (-> tptp.a tptp.nat)) (Y22 tptp.list_a_nat)) (= (= (@ (@ tptp.cons_a_nat X21) X22) (@ (@ tptp.cons_a_nat Y21) Y22)) (and (= X21 Y21) (= X22 Y22)))) (forall ((X21 tptp.product_prod_a_a) (X22 tptp.list_P1467822637od_a_a) (Y21 tptp.product_prod_a_a) (Y22 tptp.list_P1467822637od_a_a)) (= (= (@ (@ tptp.cons_P1921020637od_a_a X21) X22) (@ (@ tptp.cons_P1921020637od_a_a Y21) Y22)) (and (= X21 Y21) (= X22 Y22)))) (forall ((X1 tptp.list_P1467822637od_a_a) (X2 tptp.a) (Y1 tptp.list_P1467822637od_a_a) (Y2 tptp.a)) (= (= (@ (@ tptp.produc998622632_a_a_a X1) X2) (@ (@ tptp.produc998622632_a_a_a Y1) Y2)) (and (= X1 Y1) (= X2 Y2)))) (forall ((X1 tptp.list_a) (X2 tptp.list_a) (Y1 tptp.list_a) (Y2 tptp.list_a)) (= (= (@ (@ tptp.produc1448356631list_a X1) X2) (@ (@ tptp.produc1448356631list_a Y1) Y2)) (and (= X1 Y1) (= X2 Y2)))) (forall ((X1 (-> tptp.product_prod_a_a tptp.product_prod_a_a Bool)) (X2 tptp.list_P1467822637od_a_a) (Y1 (-> tptp.product_prod_a_a tptp.product_prod_a_a Bool)) (Y2 tptp.list_P1467822637od_a_a)) (= (= (@ (@ tptp.produc214132118od_a_a X1) X2) (@ (@ tptp.produc214132118od_a_a Y1) Y2)) (and (= X1 Y1) (= X2 Y2)))) (forall ((X1 tptp.a) (X2 tptp.produc657167928_a_a_a) (Y1 tptp.a) (Y2 tptp.produc657167928_a_a_a)) (= (= (@ (@ tptp.produc1440321489_a_a_a X1) X2) (@ (@ tptp.produc1440321489_a_a_a Y1) Y2)) (and (= X1 Y1) (= X2 Y2)))) (forall ((X1 tptp.a) (X2 tptp.list_P1467822637od_a_a) (Y1 tptp.a) (Y2 tptp.list_P1467822637od_a_a)) (= (= (@ (@ tptp.produc575024326od_a_a X1) X2) (@ (@ tptp.produc575024326od_a_a Y1) Y2)) (and (= X1 Y1) (= X2 Y2)))) (forall ((X1 tptp.a) (X2 tptp.a) (Y1 tptp.a) (Y2 tptp.a)) (= (= (@ (@ tptp.product_Pair_a_a X1) X2) (@ (@ tptp.product_Pair_a_a Y1) Y2)) (and (= X1 Y1) (= X2 Y2)))) (forall ((A 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(Ys2 tptp.list_l1108175539od_a_a) (Xs2 tptp.list_l1108175539od_a_a) (Zs tptp.list_l1108175539od_a_a)) (let ((_let_1 (@ tptp.cons_l724116707od_a_a X3))) (=> (= (@ _let_1 Xs1) Ys2) (=> (= Xs2 (@ (@ tptp.append2141280328od_a_a Xs1) Zs)) (= (@ _let_1 Xs2) (@ (@ tptp.append2141280328od_a_a Ys2) Zs)))))) (forall ((X3 (-> tptp.a tptp.nat)) (Xs1 tptp.list_a_nat) (Ys2 tptp.list_a_nat) (Xs2 tptp.list_a_nat) (Zs tptp.list_a_nat)) (let ((_let_1 (@ tptp.cons_a_nat X3))) (=> (= (@ _let_1 Xs1) Ys2) (=> (= Xs2 (@ (@ tptp.append_a_nat Xs1) Zs)) (= (@ _let_1 Xs2) (@ (@ tptp.append_a_nat Ys2) Zs)))))) _let_5 (forall ((X3 tptp.a) (Xs2 tptp.list_a) (Ys2 tptp.list_a)) (let ((_let_1 (@ tptp.cons_a X3))) (= (@ (@ tptp.append_a (@ _let_1 Xs2)) Ys2) (@ _let_1 (@ (@ tptp.append_a Xs2) Ys2))))) (forall ((X3 tptp.produc1572603623od_a_a) (Xs2 tptp.list_P1891567085od_a_a) (Ys2 tptp.list_P1891567085od_a_a)) (let ((_let_1 (@ tptp.cons_P1070399645od_a_a X3))) (= (@ (@ tptp.append864718978od_a_a (@ _let_1 Xs2)) Ys2) (@ 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(@ tptp.append864718978od_a_a Xs2) Us2) Zs) (= Ys2 (@ _let_1 Ts)))))))) (forall ((Xs2 tptp.list_l1108175539od_a_a) (Ys2 tptp.list_l1108175539od_a_a) (Zs tptp.list_l1108175539od_a_a) (Ts tptp.list_l1108175539od_a_a)) (= (= (@ (@ tptp.append2141280328od_a_a Xs2) Ys2) (@ (@ tptp.append2141280328od_a_a Zs) Ts)) (exists ((Us2 tptp.list_l1108175539od_a_a)) (let ((_let_1 (@ tptp.append2141280328od_a_a Us2))) (or (and (= Xs2 (@ (@ tptp.append2141280328od_a_a Zs) Us2)) (= (@ _let_1 Ys2) Ts)) (and (= (@ (@ tptp.append2141280328od_a_a Xs2) Us2) Zs) (= Ys2 (@ _let_1 Ts)))))))) (forall ((Xs2 tptp.list_P1467822637od_a_a) (Ys2 tptp.list_P1467822637od_a_a) (Zs tptp.list_P1467822637od_a_a) (Ts tptp.list_P1467822637od_a_a)) (= (= (@ (@ tptp.append1574001858od_a_a Xs2) Ys2) (@ (@ tptp.append1574001858od_a_a Zs) Ts)) (exists ((Us2 tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ tptp.append1574001858od_a_a Us2))) (or (and (= Xs2 (@ (@ tptp.append1574001858od_a_a Zs) Us2)) (= (@ _let_1 Ys2) Ts)) (and (= (@ 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(Prod tptp.produc1701253078od_a_a)) (=> (forall ((A3 tptp.a) (B3 tptp.list_P1467822637od_a_a)) (@ P2 (@ (@ tptp.produc575024326od_a_a A3) B3))) (@ P2 Prod))) (forall ((P2 (-> tptp.product_prod_a_a Bool)) (Prod tptp.product_prod_a_a)) (=> (forall ((A3 tptp.a) (B3 tptp.a)) (@ P2 (@ (@ tptp.product_Pair_a_a A3) B3))) (@ P2 Prod))) (forall ((Y3 tptp.produc657167928_a_a_a)) (not (forall ((A3 tptp.list_P1467822637od_a_a) (B3 tptp.a)) (not (= Y3 (@ (@ tptp.produc998622632_a_a_a A3) B3)))))) (forall ((Y3 tptp.produc864062247list_a)) (not (forall ((A3 tptp.list_a) (B3 tptp.list_a)) (not (= Y3 (@ (@ tptp.produc1448356631list_a A3) B3)))))) (forall ((Y3 tptp.produc501911462od_a_a)) (not (forall ((A3 (-> tptp.product_prod_a_a tptp.product_prod_a_a Bool)) (B3 tptp.list_P1467822637od_a_a)) (not (= Y3 (@ (@ tptp.produc214132118od_a_a A3) B3)))))) (forall ((Y3 tptp.produc1197928545_a_a_a)) (not (forall ((A3 tptp.a) (B3 tptp.produc657167928_a_a_a)) (not (= Y3 (@ (@ tptp.produc1440321489_a_a_a A3) B3)))))) (forall ((Y3 tptp.produc1701253078od_a_a)) (not (forall ((A3 tptp.a) (B3 tptp.list_P1467822637od_a_a)) (not (= Y3 (@ (@ tptp.produc575024326od_a_a A3) B3)))))) (forall ((Y3 tptp.product_prod_a_a)) (not (forall ((A3 tptp.a) (B3 tptp.a)) (not (= Y3 (@ (@ tptp.product_Pair_a_a A3) B3)))))) (forall ((P2 (-> tptp.produc1197928545_a_a_a Bool)) (X3 tptp.produc1197928545_a_a_a)) (=> (forall ((A3 tptp.a) (B3 tptp.list_P1467822637od_a_a) (C2 tptp.a)) (@ P2 (@ (@ tptp.produc1440321489_a_a_a A3) (@ (@ tptp.produc998622632_a_a_a B3) C2)))) (@ P2 X3))) (forall ((Y3 tptp.produc1197928545_a_a_a)) (not (forall ((A3 tptp.a) (B3 tptp.list_P1467822637od_a_a) (C2 tptp.a)) (not (= Y3 (@ (@ tptp.produc1440321489_a_a_a A3) (@ (@ tptp.produc998622632_a_a_a B3) C2))))))) (forall ((A tptp.list_P1467822637od_a_a) (B tptp.a) (A2 tptp.list_P1467822637od_a_a) (B2 tptp.a)) (=> (= (@ (@ tptp.produc998622632_a_a_a A) B) (@ (@ tptp.produc998622632_a_a_a A2) B2)) (not (=> (= A A2) (not (= B B2)))))) (forall ((A 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tptp.bind_P1783625031od_a_a (@ (@ tptp.cons_P1921020637od_a_a X3) Xs2)) F) (@ (@ tptp.append1574001858od_a_a (@ F X3)) (@ (@ tptp.bind_P1783625031od_a_a Xs2) F)))) (forall ((X3 tptp.a) (Xs2 tptp.list_a) (F (-> tptp.a tptp.list_a))) (= (@ (@ tptp.bind_a_a (@ (@ tptp.cons_a X3) Xs2)) F) (@ (@ tptp.append_a (@ F X3)) (@ (@ tptp.bind_a_a Xs2) F)))) (forall ((X3 tptp.product_prod_a_a) (Xs2 tptp.list_P1467822637od_a_a) (F (-> tptp.product_prod_a_a tptp.list_a))) (= (@ (@ tptp.bind_P293964574_a_a_a (@ (@ tptp.cons_P1921020637od_a_a X3) Xs2)) F) (@ (@ tptp.append_a (@ F X3)) (@ (@ tptp.bind_P293964574_a_a_a Xs2) F)))) (forall ((X3 tptp.a) (Xs2 tptp.list_a) (F (-> tptp.a tptp.list_P1467822637od_a_a))) (= (@ (@ tptp.bind_a1679112752od_a_a (@ (@ tptp.cons_a X3) Xs2)) F) (@ (@ tptp.append1574001858od_a_a (@ F X3)) (@ (@ tptp.bind_a1679112752od_a_a Xs2) F)))) (forall ((X3 (-> tptp.a tptp.nat)) (Xs2 tptp.list_a_nat) (F (-> (-> tptp.a tptp.nat) tptp.list_a))) (= (@ (@ tptp.bind_a_nat_a (@ (@ 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Xs2))))) (forall ((F (-> tptp.product_prod_a_a tptp.list_a)) (X3 tptp.product_prod_a_a) (Xs2 tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ tptp.maps_P321755352_a_a_a F))) (= (@ _let_1 (@ (@ tptp.cons_P1921020637od_a_a X3) Xs2)) (@ (@ tptp.append_a (@ F X3)) (@ _let_1 Xs2))))) (forall ((F (-> tptp.a tptp.list_P1467822637od_a_a)) (X3 tptp.a) (Xs2 tptp.list_a)) (let ((_let_1 (@ tptp.maps_a1706903530od_a_a F))) (= (@ _let_1 (@ (@ tptp.cons_a X3) Xs2)) (@ (@ tptp.append1574001858od_a_a (@ F X3)) (@ _let_1 Xs2))))) (forall ((F (-> (-> tptp.a tptp.nat) tptp.list_a)) (X3 (-> tptp.a tptp.nat)) (Xs2 tptp.list_a_nat)) (let ((_let_1 (@ tptp.maps_a_nat_a F))) (= (@ _let_1 (@ (@ tptp.cons_a_nat X3) Xs2)) (@ (@ tptp.append_a (@ F X3)) (@ _let_1 Xs2))))) (forall ((F (-> tptp.a tptp.list_l1108175539od_a_a)) (X3 tptp.a) (Xs2 tptp.list_a)) (let ((_let_1 (@ tptp.maps_a667520880od_a_a F))) (= (@ _let_1 (@ (@ tptp.cons_a X3) Xs2)) (@ (@ tptp.append2141280328od_a_a (@ F X3)) (@ _let_1 Xs2))))) (forall ((F (-> tptp.list_P1467822637od_a_a tptp.list_a)) (X3 tptp.list_P1467822637od_a_a) (Xs2 tptp.list_l1108175539od_a_a)) (let ((_let_1 (@ tptp.maps_l1091119186_a_a_a F))) (= (@ _let_1 (@ (@ tptp.cons_l724116707od_a_a X3) Xs2)) (@ (@ tptp.append_a (@ F X3)) (@ _let_1 Xs2))))) (forall ((F (-> (-> tptp.a tptp.nat) tptp.list_P1467822637od_a_a)) (X3 (-> tptp.a tptp.nat)) (Xs2 tptp.list_a_nat)) (let ((_let_1 (@ tptp.maps_a836827497od_a_a F))) (= (@ _let_1 (@ (@ tptp.cons_a_nat X3) Xs2)) (@ (@ tptp.append1574001858od_a_a (@ F X3)) (@ _let_1 Xs2))))) (forall ((F (-> tptp.product_prod_a_a tptp.list_l1108175539od_a_a)) (X3 tptp.product_prod_a_a) (Xs2 tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ tptp.maps_P739084551od_a_a F))) (= (@ _let_1 (@ (@ tptp.cons_P1921020637od_a_a X3) Xs2)) (@ (@ tptp.append2141280328od_a_a (@ F X3)) (@ _let_1 Xs2))))) (forall ((F (-> tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a)) (X3 tptp.list_P1467822637od_a_a) (Xs2 tptp.list_l1108175539od_a_a)) (let ((_let_1 (@ tptp.maps_l1117535867od_a_a F))) (= (@ _let_1 (@ (@ tptp.cons_l724116707od_a_a X3) Xs2)) (@ (@ tptp.append1574001858od_a_a (@ F X3)) (@ _let_1 Xs2))))) (forall ((A tptp.produc1572603623od_a_a) (B tptp.produc1572603623od_a_a) (R tptp.set_Pr1295299783od_a_a) (U tptp.list_P1891567085od_a_a) (X3 tptp.list_P1891567085od_a_a) (Y3 tptp.list_P1891567085od_a_a)) (let ((_let_1 (@ tptp.append864718978od_a_a U))) (=> (@ (@ tptp.member1899387664od_a_a (@ (@ tptp.produc1935643479od_a_a A) B)) R) (@ (@ tptp.member1254757008od_a_a (@ (@ tptp.produc461662679od_a_a (@ _let_1 (@ (@ tptp.cons_P1070399645od_a_a A) X3))) (@ _let_1 (@ (@ tptp.cons_P1070399645od_a_a B) Y3)))) (@ tptp.lexord931792858od_a_a R))))) (forall ((A tptp.list_P1467822637od_a_a) (B tptp.list_P1467822637od_a_a) (R tptp.set_Pr800560199od_a_a) (U tptp.list_l1108175539od_a_a) (X3 tptp.list_l1108175539od_a_a) (Y3 tptp.list_l1108175539od_a_a)) (let ((_let_1 (@ tptp.append2141280328od_a_a U))) (=> (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a A) B)) R) (@ (@ tptp.member8108048od_a_a (@ (@ tptp.produc915218007od_a_a (@ _let_1 (@ (@ tptp.cons_l724116707od_a_a A) X3))) (@ _let_1 (@ (@ tptp.cons_l724116707od_a_a B) Y3)))) (@ tptp.lexord1284731808od_a_a R))))) (forall ((A (-> tptp.a tptp.nat)) (B (-> tptp.a tptp.nat)) (R tptp.set_Pr1940702919_a_nat) (U tptp.list_a_nat) (X3 tptp.list_a_nat) (Y3 tptp.list_a_nat)) (let ((_let_1 (@ tptp.append_a_nat U))) (=> (@ (@ tptp.member125757712_a_nat (@ (@ tptp.produc1569872215_a_nat A) B)) R) (@ (@ tptp.member688761744_a_nat (@ (@ tptp.produc1430747863_a_nat (@ _let_1 (@ (@ tptp.cons_a_nat A) X3))) (@ _let_1 (@ (@ tptp.cons_a_nat B) Y3)))) (@ tptp.lexord_a_nat R))))) (forall ((A tptp.list_a) (B tptp.list_a) (R tptp.set_Pr1971762695list_a) (U tptp.list_list_a) (X3 tptp.list_list_a) (Y3 tptp.list_list_a)) (let ((_let_1 (@ tptp.append_list_a U))) (=> (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a A) B)) R) (@ (@ tptp.member888406864list_a (@ (@ tptp.produc2583831list_a (@ _let_1 (@ (@ tptp.cons_list_a A) X3))) (@ _let_1 (@ (@ tptp.cons_list_a B) Y3)))) (@ tptp.lexord_list_a R))))) (forall ((A tptp.product_prod_a_a) (B tptp.product_prod_a_a) (R tptp.set_Pr1948701895od_a_a) (U tptp.list_P1467822637od_a_a) (X3 tptp.list_P1467822637od_a_a) (Y3 tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ tptp.append1574001858od_a_a U))) (=> (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a A) B)) R) (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a (@ _let_1 (@ (@ tptp.cons_P1921020637od_a_a A) X3))) (@ _let_1 (@ (@ tptp.cons_P1921020637od_a_a B) Y3)))) (@ tptp.lexord673907738od_a_a R))))) (forall ((A tptp.a) (B tptp.a) (R tptp.set_Product_prod_a_a) (U tptp.list_a) (X3 tptp.list_a) (Y3 tptp.list_a)) (let ((_let_1 (@ tptp.append_a U))) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a A) B)) R) (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a (@ _let_1 (@ (@ tptp.cons_a A) X3))) (@ _let_1 (@ (@ tptp.cons_a B) Y3)))) (@ tptp.lexord_a R))))) (forall ((X3 tptp.a) (Xs2 tptp.list_a) (Y3 tptp.a) (Ys2 tptp.list_a)) (= (@ (@ tptp.zip_a_a (@ (@ tptp.cons_a X3) Xs2)) (@ (@ tptp.cons_a Y3) Ys2)) (@ (@ tptp.cons_P1921020637od_a_a (@ (@ tptp.product_Pair_a_a X3) Y3)) (@ (@ tptp.zip_a_a Xs2) Ys2)))) (forall ((X3 tptp.product_prod_a_a) (Xs2 tptp.list_P1467822637od_a_a) (Y3 tptp.product_prod_a_a) (Ys2 tptp.list_P1467822637od_a_a)) (= (@ (@ tptp.zip_Pr792472183od_a_a (@ (@ tptp.cons_P1921020637od_a_a X3) Xs2)) (@ (@ tptp.cons_P1921020637od_a_a Y3) Ys2)) (@ (@ tptp.cons_P1070399645od_a_a (@ (@ tptp.produc1474507607od_a_a X3) Y3)) (@ (@ tptp.zip_Pr792472183od_a_a Xs2) Ys2)))) (forall ((X3 tptp.product_prod_a_a) (Xs2 tptp.list_P1467822637od_a_a) (Y3 tptp.a) (Ys2 tptp.list_a)) (= (@ (@ tptp.zip_Pr201224270_a_a_a (@ (@ tptp.cons_P1921020637od_a_a X3) Xs2)) (@ (@ tptp.cons_a Y3) Ys2)) (@ (@ tptp.cons_P86081012_a_a_a (@ (@ tptp.produc2061588782_a_a_a X3) Y3)) (@ (@ tptp.zip_Pr201224270_a_a_a Xs2) Ys2)))) (forall ((X3 tptp.a) (Xs2 tptp.list_a) (Y3 tptp.product_prod_a_a) (Ys2 tptp.list_P1467822637od_a_a)) (= (@ (@ tptp.zip_a_1586372448od_a_a (@ (@ tptp.cons_a X3) Xs2)) (@ (@ tptp.cons_P1921020637od_a_a Y3) Ys2)) (@ (@ tptp.cons_P991044742od_a_a (@ (@ tptp.produc1299253312od_a_a X3) Y3)) (@ (@ tptp.zip_a_1586372448od_a_a Xs2) Ys2)))) (forall ((X3 tptp.a) (Xs2 tptp.list_a) (Y3 (-> tptp.a tptp.nat)) (Ys2 tptp.list_a_nat)) (= (@ (@ tptp.zip_a_a_nat (@ (@ tptp.cons_a X3) Xs2)) (@ (@ tptp.cons_a_nat Y3) Ys2)) (@ (@ tptp.cons_P1915851550_a_nat (@ (@ tptp.product_Pair_a_a_nat X3) Y3)) (@ (@ tptp.zip_a_a_nat Xs2) Ys2)))) (forall ((X3 (-> tptp.a tptp.nat)) (Xs2 tptp.list_a_nat) (Y3 tptp.a) (Ys2 tptp.list_a)) (= (@ (@ tptp.zip_a_nat_a (@ (@ tptp.cons_a_nat X3) Xs2)) (@ (@ tptp.cons_a Y3) Ys2)) (@ (@ tptp.cons_P896312284_nat_a (@ (@ tptp.product_Pair_a_nat_a X3) Y3)) (@ (@ tptp.zip_a_nat_a Xs2) Ys2)))) (forall ((X3 tptp.list_a) (Xs2 tptp.list_list_a) (Y3 tptp.list_a) (Ys2 tptp.list_list_a)) (= (@ (@ tptp.zip_list_a_list_a (@ (@ tptp.cons_list_a X3) Xs2)) (@ (@ tptp.cons_list_a Y3) Ys2)) (@ (@ tptp.cons_P2080942813list_a (@ (@ tptp.produc1448356631list_a X3) Y3)) (@ (@ tptp.zip_list_a_list_a Xs2) Ys2)))) (forall ((X3 tptp.list_P1467822637od_a_a) (Xs2 tptp.list_l1108175539od_a_a) (Y3 tptp.a) (Ys2 tptp.list_a)) (= (@ (@ tptp.zip_li245157064_a_a_a (@ (@ tptp.cons_l724116707od_a_a X3) Xs2)) (@ (@ tptp.cons_a Y3) Ys2)) (@ (@ tptp.cons_P169173742_a_a_a (@ (@ tptp.produc998622632_a_a_a X3) Y3)) (@ (@ tptp.zip_li245157064_a_a_a Xs2) Ys2)))) (forall ((X3 tptp.a) (Xs2 tptp.list_a) (Y3 tptp.list_P1467822637od_a_a) (Ys2 tptp.list_l1108175539od_a_a)) (= (@ (@ tptp.zip_a_1969042406od_a_a (@ (@ tptp.cons_a X3) Xs2)) (@ (@ tptp.cons_l724116707od_a_a Y3) Ys2)) (@ (@ tptp.cons_P1213258892od_a_a (@ (@ tptp.produc575024326od_a_a X3) Y3)) (@ (@ tptp.zip_a_1969042406od_a_a Xs2) Ys2)))) (forall ((X3 tptp.product_prod_a_a) (Xs2 tptp.list_P1467822637od_a_a) (Y3 (-> tptp.a tptp.nat)) (Ys2 tptp.list_a_nat)) (= (@ (@ tptp.zip_Pr24086287_a_nat (@ (@ tptp.cons_P1921020637od_a_a X3) Xs2)) (@ (@ tptp.cons_a_nat Y3) Ys2)) (@ (@ tptp.cons_P659009461_a_nat (@ (@ tptp.produc825466863_a_nat X3) Y3)) (@ (@ tptp.zip_Pr24086287_a_nat Xs2) Ys2)))) (forall ((X3 tptp.produc1572603623od_a_a) (Y3 tptp.produc1572603623od_a_a) (R tptp.set_Pr1295299783od_a_a) (Xs2 tptp.list_P1891567085od_a_a) (Us tptp.list_P1891567085od_a_a) (Vs tptp.list_P1891567085od_a_a) (Ys2 tptp.list_P1891567085od_a_a)) (let ((_let_1 (@ tptp.append864718978od_a_a Us))) (=> (@ (@ tptp.member1899387664od_a_a (@ (@ tptp.produc1935643479od_a_a X3) Y3)) R) (=> (= Xs2 (@ _let_1 (@ (@ tptp.cons_P1070399645od_a_a X3) Vs))) (=> (= Ys2 (@ _let_1 (@ (@ tptp.cons_P1070399645od_a_a Y3) Vs))) (@ (@ tptp.member1254757008od_a_a (@ (@ tptp.produc461662679od_a_a Xs2) Ys2)) (@ tptp.listre1832537542od_a_a R))))))) (forall ((X3 tptp.list_P1467822637od_a_a) (Y3 tptp.list_P1467822637od_a_a) (R tptp.set_Pr800560199od_a_a) (Xs2 tptp.list_l1108175539od_a_a) (Us tptp.list_l1108175539od_a_a) (Vs tptp.list_l1108175539od_a_a) (Ys2 tptp.list_l1108175539od_a_a)) (let ((_let_1 (@ tptp.append2141280328od_a_a Us))) (=> (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a X3) Y3)) R) (=> (= Xs2 (@ _let_1 (@ (@ tptp.cons_l724116707od_a_a X3) Vs))) (=> (= Ys2 (@ _let_1 (@ (@ tptp.cons_l724116707od_a_a Y3) Vs))) (@ (@ tptp.member8108048od_a_a (@ (@ tptp.produc915218007od_a_a Xs2) Ys2)) (@ tptp.listre651914124od_a_a R))))))) (forall ((X3 (-> tptp.a tptp.nat)) (Y3 (-> tptp.a tptp.nat)) (R tptp.set_Pr1940702919_a_nat) (Xs2 tptp.list_a_nat) (Us tptp.list_a_nat) (Vs tptp.list_a_nat) (Ys2 tptp.list_a_nat)) (let ((_let_1 (@ tptp.append_a_nat Us))) (=> (@ (@ tptp.member125757712_a_nat (@ (@ tptp.produc1569872215_a_nat X3) Y3)) R) (=> (= Xs2 (@ _let_1 (@ (@ tptp.cons_a_nat X3) Vs))) (=> (= Ys2 (@ _let_1 (@ (@ tptp.cons_a_nat Y3) Vs))) (@ (@ tptp.member688761744_a_nat (@ (@ tptp.produc1430747863_a_nat Xs2) Ys2)) (@ tptp.listrel1_a_nat R))))))) (forall ((X3 tptp.list_a) (Y3 tptp.list_a) (R tptp.set_Pr1971762695list_a) (Xs2 tptp.list_list_a) (Us tptp.list_list_a) (Vs tptp.list_list_a) (Ys2 tptp.list_list_a)) (let ((_let_1 (@ tptp.append_list_a Us))) (=> (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a X3) Y3)) R) (=> (= Xs2 (@ _let_1 (@ (@ tptp.cons_list_a X3) Vs))) (=> (= Ys2 (@ _let_1 (@ (@ tptp.cons_list_a Y3) Vs))) (@ (@ tptp.member888406864list_a (@ (@ tptp.produc2583831list_a Xs2) Ys2)) (@ tptp.listrel1_list_a R))))))) (forall ((X3 tptp.product_prod_a_a) (Y3 tptp.product_prod_a_a) (R tptp.set_Pr1948701895od_a_a) (Xs2 tptp.list_P1467822637od_a_a) (Us tptp.list_P1467822637od_a_a) (Vs tptp.list_P1467822637od_a_a) (Ys2 tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ tptp.append1574001858od_a_a Us))) (=> (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a X3) Y3)) R) (=> (= Xs2 (@ _let_1 (@ (@ tptp.cons_P1921020637od_a_a X3) Vs))) (=> (= Ys2 (@ _let_1 (@ (@ tptp.cons_P1921020637od_a_a Y3) Vs))) (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a Xs2) Ys2)) (@ tptp.listre944824838od_a_a R))))))) (forall ((X3 tptp.a) (Y3 tptp.a) (R tptp.set_Product_prod_a_a) (Xs2 tptp.list_a) (Us tptp.list_a) (Vs tptp.list_a) (Ys2 tptp.list_a)) (let ((_let_1 (@ tptp.append_a Us))) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X3) Y3)) R) (=> (= Xs2 (@ _let_1 (@ (@ tptp.cons_a X3) Vs))) (=> (= Ys2 (@ _let_1 (@ (@ tptp.cons_a Y3) Vs))) (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a Xs2) Ys2)) (@ tptp.listrel1_a R))))))) (forall ((Xs2 tptp.list_P1891567085od_a_a) (Ys2 tptp.list_P1891567085od_a_a) (R tptp.set_Pr1295299783od_a_a)) (=> (@ (@ tptp.member1254757008od_a_a (@ (@ tptp.produc461662679od_a_a Xs2) Ys2)) (@ tptp.listre1832537542od_a_a R)) (not (forall ((X4 tptp.produc1572603623od_a_a) (Y4 tptp.produc1572603623od_a_a)) (=> (@ (@ tptp.member1899387664od_a_a (@ (@ tptp.produc1935643479od_a_a X4) Y4)) R) (forall ((Us3 tptp.list_P1891567085od_a_a) (Vs2 tptp.list_P1891567085od_a_a)) (let ((_let_1 (@ tptp.append864718978od_a_a Us3))) (=> (= Xs2 (@ _let_1 (@ (@ tptp.cons_P1070399645od_a_a X4) Vs2))) (not (= Ys2 (@ _let_1 (@ (@ tptp.cons_P1070399645od_a_a Y4) Vs2)))))))))))) (forall ((Xs2 tptp.list_l1108175539od_a_a) (Ys2 tptp.list_l1108175539od_a_a) (R tptp.set_Pr800560199od_a_a)) (=> (@ (@ tptp.member8108048od_a_a (@ (@ tptp.produc915218007od_a_a Xs2) Ys2)) (@ tptp.listre651914124od_a_a R)) (not (forall ((X4 tptp.list_P1467822637od_a_a) (Y4 tptp.list_P1467822637od_a_a)) (=> (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a X4) Y4)) R) (forall ((Us3 tptp.list_l1108175539od_a_a) (Vs2 tptp.list_l1108175539od_a_a)) (let ((_let_1 (@ tptp.append2141280328od_a_a Us3))) (=> (= Xs2 (@ _let_1 (@ (@ tptp.cons_l724116707od_a_a X4) Vs2))) (not (= Ys2 (@ _let_1 (@ (@ tptp.cons_l724116707od_a_a Y4) Vs2)))))))))))) (forall ((Xs2 tptp.list_a_nat) (Ys2 tptp.list_a_nat) (R tptp.set_Pr1940702919_a_nat)) (=> (@ (@ tptp.member688761744_a_nat (@ (@ tptp.produc1430747863_a_nat Xs2) Ys2)) (@ tptp.listrel1_a_nat R)) (not (forall ((X4 (-> tptp.a tptp.nat)) (Y4 (-> tptp.a tptp.nat))) (=> (@ (@ tptp.member125757712_a_nat (@ (@ tptp.produc1569872215_a_nat X4) Y4)) R) (forall ((Us3 tptp.list_a_nat) (Vs2 tptp.list_a_nat)) (let ((_let_1 (@ tptp.append_a_nat Us3))) (=> (= Xs2 (@ _let_1 (@ (@ tptp.cons_a_nat X4) Vs2))) (not (= Ys2 (@ _let_1 (@ (@ tptp.cons_a_nat Y4) Vs2)))))))))))) (forall ((Xs2 tptp.list_list_a) (Ys2 tptp.list_list_a) (R tptp.set_Pr1971762695list_a)) (=> (@ (@ tptp.member888406864list_a (@ (@ tptp.produc2583831list_a Xs2) Ys2)) (@ tptp.listrel1_list_a R)) (not (forall ((X4 tptp.list_a) (Y4 tptp.list_a)) (=> (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a X4) Y4)) R) (forall ((Us3 tptp.list_list_a) (Vs2 tptp.list_list_a)) (let ((_let_1 (@ tptp.append_list_a Us3))) (=> (= Xs2 (@ _let_1 (@ (@ tptp.cons_list_a X4) Vs2))) (not (= Ys2 (@ _let_1 (@ (@ tptp.cons_list_a Y4) Vs2)))))))))))) (forall ((Xs2 tptp.list_P1467822637od_a_a) (Ys2 tptp.list_P1467822637od_a_a) (R tptp.set_Pr1948701895od_a_a)) (=> (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a Xs2) Ys2)) (@ tptp.listre944824838od_a_a R)) (not (forall ((X4 tptp.product_prod_a_a) (Y4 tptp.product_prod_a_a)) (=> (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a X4) Y4)) R) (forall ((Us3 tptp.list_P1467822637od_a_a) (Vs2 tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ tptp.append1574001858od_a_a Us3))) (=> (= Xs2 (@ _let_1 (@ (@ tptp.cons_P1921020637od_a_a X4) Vs2))) (not (= Ys2 (@ _let_1 (@ (@ tptp.cons_P1921020637od_a_a Y4) Vs2)))))))))))) (forall ((Xs2 tptp.list_a) (Ys2 tptp.list_a) (R tptp.set_Product_prod_a_a)) (=> (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a Xs2) Ys2)) (@ tptp.listrel1_a R)) (not (forall ((X4 tptp.a) (Y4 tptp.a)) (=> (@ (@ tptp.member449909584od_a_a (@ (@ 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(@ (@ tptp.cons_a_nat X3) Xs2)) Y3) (or (= X3 Y3) (@ (@ tptp.member_a_nat Xs2) Y3)))) (forall ((X3 tptp.product_prod_a_a) (Xs2 tptp.list_P1467822637od_a_a) (Y3 tptp.product_prod_a_a)) (= (@ (@ tptp.member1112491458od_a_a (@ (@ tptp.cons_P1921020637od_a_a X3) Xs2)) Y3) (or (= X3 Y3) (@ (@ tptp.member1112491458od_a_a Xs2) Y3)))) (forall ((R tptp.list_P1467822637od_a_a) (S tptp.list_P1467822637od_a_a) (R2 tptp.set_Pr800560199od_a_a) (S2 tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ tptp.produc85179863od_a_a R))) (=> (@ (@ tptp.member1691432592od_a_a (@ _let_1 S)) R2) (=> (= S2 S) (@ (@ tptp.member1691432592od_a_a (@ _let_1 S2)) R2))))) (forall ((R tptp.list_P1467822637od_a_a) (S tptp.a) (R2 tptp.set_Pr1525541400_a_a_a) (S2 tptp.a)) (let ((_let_1 (@ tptp.produc998622632_a_a_a R))) (=> (@ (@ tptp.member430654177_a_a_a (@ _let_1 S)) R2) (=> (= S2 S) (@ (@ tptp.member430654177_a_a_a (@ _let_1 S2)) R2))))) (forall ((R tptp.list_a) (S tptp.list_a) (R2 tptp.set_Pr1971762695list_a) (S2 tptp.list_a)) (let ((_let_1 (@ tptp.produc1448356631list_a R))) (=> (@ (@ tptp.member1250517072list_a (@ _let_1 S)) R2) (=> (= S2 S) (@ (@ tptp.member1250517072list_a (@ _let_1 S2)) R2))))) (forall ((R (-> tptp.product_prod_a_a tptp.product_prod_a_a Bool)) (S tptp.list_P1467822637od_a_a) (R2 tptp.set_Pr727105414od_a_a) (S2 tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ tptp.produc214132118od_a_a R))) (=> (@ (@ tptp.member372644687od_a_a (@ _let_1 S)) R2) (=> (= S2 S) (@ (@ tptp.member372644687od_a_a (@ _let_1 S2)) R2))))) (forall ((R tptp.a) (S tptp.produc657167928_a_a_a) (R2 tptp.set_Pr110478017_a_a_a) (S2 tptp.produc657167928_a_a_a)) (let ((_let_1 (@ tptp.produc1440321489_a_a_a R))) (=> (@ (@ tptp.member1904151562_a_a_a (@ _let_1 S)) R2) (=> (= S2 S) (@ (@ tptp.member1904151562_a_a_a (@ _let_1 S2)) R2))))) (forall ((R tptp.a) (S tptp.list_P1467822637od_a_a) (R2 tptp.set_Pr248149174od_a_a) (S2 tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ tptp.produc575024326od_a_a R))) (=> (@ (@ tptp.member1474739327od_a_a (@ _let_1 S)) R2) (=> (= S2 S) (@ (@ tptp.member1474739327od_a_a (@ _let_1 S2)) R2))))) (forall ((R tptp.a) (S tptp.a) (R2 tptp.set_Product_prod_a_a) (S2 tptp.a)) (let ((_let_1 (@ tptp.product_Pair_a_a R))) (=> (@ (@ tptp.member449909584od_a_a (@ _let_1 S)) R2) (=> (= S2 S) (@ (@ tptp.member449909584od_a_a (@ _let_1 S2)) R2))))) (forall ((P2 (-> tptp.pair_p1891813445t_unit tptp.produc864062247list_a tptp.list_a Bool)) (A0 tptp.pair_p1891813445t_unit) (A1 tptp.produc864062247list_a) (A22 tptp.list_a)) (=> (forall ((G tptp.pair_p1891813445t_unit) (U2 tptp.list_a) (V tptp.list_a) (X_1 tptp.list_a)) (@ (@ (@ P2 G) (@ (@ tptp.produc1448356631list_a U2) V)) X_1)) (@ (@ (@ P2 A0) A1) A22))) (forall ((P2 (-> tptp.pair_p125712459t_unit tptp.product_prod_a_a tptp.a Bool)) (A0 tptp.pair_p125712459t_unit) (A1 tptp.product_prod_a_a) (A22 tptp.a)) (=> (forall ((G tptp.pair_p125712459t_unit) (U2 tptp.a) (V tptp.a) (X_1 tptp.a)) (@ (@ (@ P2 G) (@ (@ tptp.product_Pair_a_a U2) V)) X_1)) (@ (@ (@ P2 A0) A1) A22))) (forall ((X3 tptp.produc1572603623od_a_a) (Xs2 tptp.list_P1891567085od_a_a) (Y3 tptp.produc1572603623od_a_a) (Ys2 tptp.list_P1891567085od_a_a) (R tptp.set_Pr1295299783od_a_a)) (let ((_let_1 (@ tptp.listre1832537542od_a_a R))) (= (@ (@ tptp.member1254757008od_a_a (@ (@ tptp.produc461662679od_a_a (@ (@ tptp.cons_P1070399645od_a_a X3) Xs2)) (@ (@ tptp.cons_P1070399645od_a_a Y3) Ys2))) _let_1) (or (and (@ (@ tptp.member1899387664od_a_a (@ (@ tptp.produc1935643479od_a_a X3) Y3)) R) (= Xs2 Ys2)) (and (= X3 Y3) (@ (@ tptp.member1254757008od_a_a (@ (@ tptp.produc461662679od_a_a Xs2) Ys2)) _let_1)))))) (forall ((X3 tptp.list_P1467822637od_a_a) (Xs2 tptp.list_l1108175539od_a_a) (Y3 tptp.list_P1467822637od_a_a) (Ys2 tptp.list_l1108175539od_a_a) (R tptp.set_Pr800560199od_a_a)) (let ((_let_1 (@ tptp.listre651914124od_a_a R))) (= (@ (@ tptp.member8108048od_a_a (@ (@ tptp.produc915218007od_a_a (@ (@ tptp.cons_l724116707od_a_a X3) Xs2)) (@ (@ 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tptp.produc2583831list_a (@ (@ tptp.cons_list_a X3) Xs2)) (@ (@ tptp.cons_list_a Y3) Ys2))) _let_1) (or (and (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a X3) Y3)) R) (= Xs2 Ys2)) (and (= X3 Y3) (@ (@ tptp.member888406864list_a (@ (@ tptp.produc2583831list_a Xs2) Ys2)) _let_1)))))) (forall ((X3 tptp.product_prod_a_a) (Xs2 tptp.list_P1467822637od_a_a) (Y3 tptp.product_prod_a_a) (Ys2 tptp.list_P1467822637od_a_a) (R tptp.set_Pr1948701895od_a_a)) (let ((_let_1 (@ tptp.listre944824838od_a_a R))) (= (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a (@ (@ tptp.cons_P1921020637od_a_a X3) Xs2)) (@ (@ tptp.cons_P1921020637od_a_a Y3) Ys2))) _let_1) (or (and (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a X3) Y3)) R) (= Xs2 Ys2)) (and (= X3 Y3) (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a Xs2) Ys2)) _let_1)))))) (forall ((X3 tptp.a) (Xs2 tptp.list_a) (Y3 tptp.a) (Ys2 tptp.list_a) (R tptp.set_Product_prod_a_a)) (let ((_let_1 (@ tptp.listrel1_a R))) (= (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a (@ (@ tptp.cons_a X3) Xs2)) (@ (@ tptp.cons_a Y3) Ys2))) _let_1) (or (and (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X3) Y3)) R) (= Xs2 Ys2)) (and (= X3 Y3) (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a Xs2) Ys2)) _let_1)))))) (forall ((A tptp.produc1572603623od_a_a) (X3 tptp.list_P1891567085od_a_a) (B tptp.produc1572603623od_a_a) (Y3 tptp.list_P1891567085od_a_a) (R tptp.set_Pr1295299783od_a_a)) (let ((_let_1 (@ tptp.lexord931792858od_a_a R))) (= (@ (@ tptp.member1254757008od_a_a (@ (@ tptp.produc461662679od_a_a (@ (@ tptp.cons_P1070399645od_a_a A) X3)) (@ (@ tptp.cons_P1070399645od_a_a B) Y3))) _let_1) (or (@ (@ tptp.member1899387664od_a_a (@ (@ tptp.produc1935643479od_a_a A) B)) R) (and (= A B) (@ (@ tptp.member1254757008od_a_a (@ (@ tptp.produc461662679od_a_a X3) Y3)) _let_1)))))) (forall ((A tptp.list_P1467822637od_a_a) (X3 tptp.list_l1108175539od_a_a) (B tptp.list_P1467822637od_a_a) (Y3 tptp.list_l1108175539od_a_a) (R tptp.set_Pr800560199od_a_a)) (let ((_let_1 (@ tptp.lexord1284731808od_a_a R))) (= (@ (@ tptp.member8108048od_a_a (@ (@ tptp.produc915218007od_a_a (@ (@ tptp.cons_l724116707od_a_a A) X3)) (@ (@ tptp.cons_l724116707od_a_a B) Y3))) _let_1) (or (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a A) B)) R) (and (= A B) (@ (@ tptp.member8108048od_a_a (@ (@ tptp.produc915218007od_a_a X3) Y3)) _let_1)))))) (forall ((A (-> tptp.a tptp.nat)) (X3 tptp.list_a_nat) (B (-> tptp.a tptp.nat)) (Y3 tptp.list_a_nat) (R tptp.set_Pr1940702919_a_nat)) (let ((_let_1 (@ tptp.lexord_a_nat R))) (= (@ (@ tptp.member688761744_a_nat (@ (@ tptp.produc1430747863_a_nat (@ (@ tptp.cons_a_nat A) X3)) (@ (@ tptp.cons_a_nat B) Y3))) _let_1) (or (@ (@ tptp.member125757712_a_nat (@ (@ tptp.produc1569872215_a_nat A) B)) R) (and (= A B) (@ (@ tptp.member688761744_a_nat (@ (@ tptp.produc1430747863_a_nat X3) Y3)) _let_1)))))) (forall ((A tptp.list_a) (X3 tptp.list_list_a) (B tptp.list_a) (Y3 tptp.list_list_a) (R tptp.set_Pr1971762695list_a)) (let ((_let_1 (@ tptp.lexord_list_a R))) (= (@ (@ tptp.member888406864list_a (@ (@ tptp.produc2583831list_a (@ (@ tptp.cons_list_a A) X3)) (@ (@ tptp.cons_list_a B) Y3))) _let_1) (or (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a A) B)) R) (and (= A B) (@ (@ tptp.member888406864list_a (@ (@ tptp.produc2583831list_a X3) Y3)) _let_1)))))) (forall ((A tptp.product_prod_a_a) (X3 tptp.list_P1467822637od_a_a) (B tptp.product_prod_a_a) (Y3 tptp.list_P1467822637od_a_a) (R tptp.set_Pr1948701895od_a_a)) (let ((_let_1 (@ tptp.lexord673907738od_a_a R))) (= (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a (@ (@ tptp.cons_P1921020637od_a_a A) X3)) (@ (@ tptp.cons_P1921020637od_a_a B) Y3))) _let_1) (or (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a A) B)) R) (and (= A B) (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a X3) Y3)) _let_1)))))) (forall ((A tptp.a) (X3 tptp.list_a) (B tptp.a) (Y3 tptp.list_a) (R tptp.set_Product_prod_a_a)) (let ((_let_1 (@ tptp.lexord_a R))) (= (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a (@ (@ tptp.cons_a A) X3)) (@ (@ tptp.cons_a B) Y3))) _let_1) (or (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a A) B)) R) (and (= A B) (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a X3) Y3)) _let_1)))))) (forall ((Xs2 tptp.list_P1891567085od_a_a) (Ys2 tptp.list_P1891567085od_a_a) (R tptp.set_Pr1295299783od_a_a) (X3 tptp.produc1572603623od_a_a)) (let ((_let_1 (@ tptp.listre1832537542od_a_a R))) (let ((_let_2 (@ tptp.cons_P1070399645od_a_a X3))) (=> (@ (@ tptp.member1254757008od_a_a (@ (@ tptp.produc461662679od_a_a Xs2) Ys2)) _let_1) (@ (@ tptp.member1254757008od_a_a (@ (@ tptp.produc461662679od_a_a (@ _let_2 Xs2)) (@ _let_2 Ys2))) _let_1))))) (forall ((Xs2 tptp.list_l1108175539od_a_a) (Ys2 tptp.list_l1108175539od_a_a) (R tptp.set_Pr800560199od_a_a) (X3 tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ tptp.listre651914124od_a_a R))) (let ((_let_2 (@ tptp.cons_l724116707od_a_a X3))) (=> (@ (@ tptp.member8108048od_a_a (@ (@ tptp.produc915218007od_a_a Xs2) Ys2)) _let_1) (@ (@ tptp.member8108048od_a_a (@ (@ tptp.produc915218007od_a_a (@ _let_2 Xs2)) (@ _let_2 Ys2))) _let_1))))) (forall ((Xs2 tptp.list_a_nat) (Ys2 tptp.list_a_nat) (R tptp.set_Pr1940702919_a_nat) (X3 (-> tptp.a tptp.nat))) (let ((_let_1 (@ tptp.listrel1_a_nat R))) (let ((_let_2 (@ tptp.cons_a_nat X3))) (=> (@ (@ tptp.member688761744_a_nat (@ (@ tptp.produc1430747863_a_nat Xs2) Ys2)) _let_1) (@ (@ tptp.member688761744_a_nat (@ (@ tptp.produc1430747863_a_nat (@ _let_2 Xs2)) (@ _let_2 Ys2))) _let_1))))) (forall ((Xs2 tptp.list_a) (Ys2 tptp.list_a) (R tptp.set_Product_prod_a_a) (X3 tptp.a)) (let ((_let_1 (@ tptp.listrel1_a R))) (let ((_let_2 (@ tptp.cons_a X3))) (=> (@ (@ tptp.member1250517072list_a (@ (@ 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tptp.produc461662679od_a_a Us) Vs)) _let_1))) (@ (@ tptp.member1254757008od_a_a (@ (@ tptp.produc461662679od_a_a (@ (@ tptp.append864718978od_a_a Xs2) Us)) (@ (@ tptp.append864718978od_a_a Ys2) Vs))) _let_1)))) (forall ((Xs2 tptp.list_l1108175539od_a_a) (Ys2 tptp.list_l1108175539od_a_a) (R tptp.set_Pr800560199od_a_a) (Us tptp.list_l1108175539od_a_a) (Vs tptp.list_l1108175539od_a_a)) (let ((_let_1 (@ tptp.listre651914124od_a_a R))) (=> (or (and (@ (@ tptp.member8108048od_a_a (@ (@ tptp.produc915218007od_a_a Xs2) Ys2)) _let_1) (= Us Vs)) (and (= Xs2 Ys2) (@ (@ tptp.member8108048od_a_a (@ (@ tptp.produc915218007od_a_a Us) Vs)) _let_1))) (@ (@ tptp.member8108048od_a_a (@ (@ tptp.produc915218007od_a_a (@ (@ tptp.append2141280328od_a_a Xs2) Us)) (@ (@ tptp.append2141280328od_a_a Ys2) Vs))) _let_1)))) (forall ((Xs2 tptp.list_a) (Ys2 tptp.list_a) (R tptp.set_Product_prod_a_a) (Us tptp.list_a) (Vs tptp.list_a)) (let ((_let_1 (@ tptp.listrel1_a R))) (=> (or (and (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a Xs2) Ys2)) _let_1) (= Us Vs)) (and (= Xs2 Ys2) (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a Us) Vs)) _let_1))) (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a (@ (@ tptp.append_a Xs2) Us)) (@ (@ tptp.append_a Ys2) Vs))) _let_1)))) (forall ((Xs2 tptp.list_P1467822637od_a_a) (Ys2 tptp.list_P1467822637od_a_a) (R tptp.set_Pr1948701895od_a_a) (Us tptp.list_P1467822637od_a_a) (Vs tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ tptp.listre944824838od_a_a R))) (=> (or (and (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a Xs2) Ys2)) _let_1) (= Us Vs)) (and (= Xs2 Ys2) (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a Us) Vs)) _let_1))) (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a (@ (@ tptp.append1574001858od_a_a Xs2) Us)) (@ (@ tptp.append1574001858od_a_a Ys2) Vs))) _let_1)))) (forall ((R tptp.set_Pr800560199od_a_a) (X3 tptp.list_l1108175539od_a_a) (Y3 tptp.list_l1108175539od_a_a)) (let ((_let_1 (@ tptp.lexord1284731808od_a_a R))) (=> (forall ((A3 tptp.list_P1467822637od_a_a) (B3 tptp.list_P1467822637od_a_a)) (or (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a A3) B3)) R) (= A3 B3) (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a B3) A3)) R))) (or (@ (@ tptp.member8108048od_a_a (@ (@ tptp.produc915218007od_a_a X3) Y3)) _let_1) (= X3 Y3) (@ (@ tptp.member8108048od_a_a (@ (@ tptp.produc915218007od_a_a Y3) X3)) _let_1))))) (forall ((R tptp.set_Pr1948701895od_a_a) (X3 tptp.list_P1467822637od_a_a) (Y3 tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ tptp.lexord673907738od_a_a R))) (=> (forall ((A3 tptp.product_prod_a_a) (B3 tptp.product_prod_a_a)) (or (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a A3) B3)) R) (= A3 B3) (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a B3) A3)) R))) (or (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a X3) Y3)) _let_1) (= X3 Y3) (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a Y3) X3)) _let_1))))) (forall ((R tptp.set_Pr1971762695list_a) (X3 tptp.list_list_a) (Y3 tptp.list_list_a)) (let ((_let_1 (@ tptp.lexord_list_a R))) (=> (forall ((A3 tptp.list_a) (B3 tptp.list_a)) (or (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a A3) B3)) R) (= A3 B3) (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a B3) A3)) R))) (or (@ (@ tptp.member888406864list_a (@ (@ tptp.produc2583831list_a X3) Y3)) _let_1) (= X3 Y3) (@ (@ tptp.member888406864list_a (@ (@ tptp.produc2583831list_a Y3) X3)) _let_1))))) (forall ((R tptp.set_Product_prod_a_a) (X3 tptp.list_a) (Y3 tptp.list_a)) (let ((_let_1 (@ tptp.lexord_a R))) (=> (forall ((A3 tptp.a) (B3 tptp.a)) (or (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a A3) B3)) R) (= A3 B3) (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a B3) A3)) R))) (or (@ (@ tptp.member1250517072list_a (@ (@ 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((X tptp.produc864062247list_a)) (@ (@ tptp.member1250517072list_a X) A4))) A4)) (forall ((A4 tptp.set_Product_prod_a_a)) (= (@ tptp.collec645855634od_a_a (lambda ((X tptp.product_prod_a_a)) (@ (@ tptp.member449909584od_a_a X) A4))) A4)) (forall ((A4 tptp.set_li562223245od_a_a)) (= (@ tptp.collec1811041560od_a_a (lambda ((X tptp.list_P1467822637od_a_a)) (@ (@ tptp.member1578987478od_a_a X) A4))) A4)) (forall ((A4 tptp.set_a)) (= (@ tptp.collect_a (lambda ((X tptp.a)) (@ (@ tptp.member_a2 X) A4))) A4)) (forall ((R tptp.set_Product_prod_a_a) (Xs2 tptp.list_a)) (=> (forall ((X4 tptp.a)) (not (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X4) X4)) R))) (not (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a Xs2) Xs2)) (@ tptp.lexord_a R))))) (forall ((U tptp.list_P1467822637od_a_a) (V2 tptp.list_P1467822637od_a_a) (R tptp.set_Pr1948701895od_a_a) (X3 tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ tptp.lexord673907738od_a_a R))) (let ((_let_2 (@ tptp.append1574001858od_a_a X3))) (=> (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a U) V2)) _let_1) (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a (@ _let_2 U)) (@ _let_2 V2))) _let_1))))) (forall ((X3 tptp.product_prod_a_a) (Y3 tptp.product_prod_a_a) (R tptp.set_Pr1948701895od_a_a) (Xs2 tptp.list_P1467822637od_a_a)) (=> (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a X3) Y3)) R) (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a (@ (@ tptp.cons_P1921020637od_a_a X3) Xs2)) (@ (@ tptp.cons_P1921020637od_a_a Y3) Xs2))) (@ tptp.listre944824838od_a_a R)))) (forall ((X3 tptp.a) (Y3 tptp.a) (R tptp.set_Product_prod_a_a) (Xs2 tptp.list_a)) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X3) Y3)) R) (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a (@ (@ tptp.cons_a X3) Xs2)) (@ (@ tptp.cons_a Y3) Xs2))) (@ tptp.listrel1_a R)))) (forall ((X3 tptp.product_prod_a_a) (Xs2 tptp.list_P1467822637od_a_a) (Ys2 tptp.list_P1467822637od_a_a) (R tptp.set_Pr1948701895od_a_a)) (=> (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a (@ (@ tptp.cons_P1921020637od_a_a X3) Xs2)) Ys2)) (@ tptp.listre944824838od_a_a R)) (=> (forall ((Y4 tptp.product_prod_a_a)) (=> (= Ys2 (@ (@ tptp.cons_P1921020637od_a_a Y4) Xs2)) (not (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a X3) Y4)) R)))) (not (forall ((Zs2 tptp.list_P1467822637od_a_a)) (=> (= Ys2 (@ (@ tptp.cons_P1921020637od_a_a X3) Zs2)) (not (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a Xs2) Zs2)) (@ tptp.listre944824838od_a_a R))))))))) (forall ((X3 tptp.a) (Xs2 tptp.list_a) (Ys2 tptp.list_a) (R tptp.set_Product_prod_a_a)) (=> (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a (@ (@ tptp.cons_a X3) Xs2)) Ys2)) (@ tptp.listrel1_a R)) (=> (forall ((Y4 tptp.a)) (=> (= Ys2 (@ (@ tptp.cons_a Y4) Xs2)) (not (@ (@ tptp.member449909584od_a_a (@ (@ 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(@ (@ tptp.produc85179863od_a_a U) V2)) _let_1)))))) (forall ((X3 tptp.list_a) (U tptp.list_a) (V2 tptp.list_a) (R tptp.set_Product_prod_a_a)) (let ((_let_1 (@ tptp.lexord_a R))) (let ((_let_2 (@ tptp.append_a X3))) (=> (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a (@ _let_2 U)) (@ _let_2 V2))) _let_1) (=> (forall ((A3 tptp.a)) (not (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a A3) A3)) R))) (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a U) V2)) _let_1)))))) (forall ((Y3 tptp.list_P1467822637od_a_a) (X3 tptp.list_P1467822637od_a_a) (R tptp.set_Pr1948701895od_a_a)) (=> (exists ((B4 tptp.product_prod_a_a) (Z tptp.list_P1467822637od_a_a)) (= Y3 (@ (@ tptp.cons_P1921020637od_a_a B4) Z))) (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a X3) (@ (@ tptp.append1574001858od_a_a X3) Y3))) (@ tptp.lexord673907738od_a_a R)))) (forall ((Xs2 tptp.list_P1467822637od_a_a) (Ys2 tptp.list_P1467822637od_a_a) (Xy 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tptp.produc1912141786_a_a_a)) (not (forall ((G tptp.pair_p125712459t_unit) (U2 tptp.a) (V tptp.a) (W tptp.a)) (not (= X3 (@ (@ tptp.produc74075722_a_a_a G) (@ (@ tptp.produc2061588782_a_a_a (@ (@ tptp.product_Pair_a_a U2) V)) W))))))) (forall ((R tptp.set_Pr1948701895od_a_a) (Xs2 tptp.list_P1467822637od_a_a) (Ys2 tptp.list_P1467822637od_a_a) (Zs tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ tptp.lexord673907738od_a_a R))) (let ((_let_2 (@ tptp.append1574001858od_a_a Xs2))) (=> (@ tptp.irrefl76447196od_a_a R) (= (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a (@ _let_2 Ys2)) (@ _let_2 Zs))) _let_1) (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a Ys2) Zs)) _let_1)))))) (forall ((Xs2 tptp.list_P1467822637od_a_a) (X3 tptp.product_prod_a_a) (Ys2 tptp.list_P1467822637od_a_a) (Y3 tptp.product_prod_a_a) (R tptp.set_Pr1948701895od_a_a)) (let ((_let_1 (@ tptp.listre944824838od_a_a R))) (= (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a (@ (@ tptp.append1574001858od_a_a Xs2) (@ (@ tptp.cons_P1921020637od_a_a X3) tptp.nil_Product_prod_a_a))) (@ (@ tptp.append1574001858od_a_a Ys2) (@ (@ tptp.cons_P1921020637od_a_a Y3) tptp.nil_Product_prod_a_a)))) _let_1) (or (and (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a Xs2) Ys2)) _let_1) (= X3 Y3)) (and (= Xs2 Ys2) (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a X3) Y3)) R)))))) (forall ((Xs2 tptp.list_a) (X3 tptp.a) (Ys2 tptp.list_a) (Y3 tptp.a) (R tptp.set_Product_prod_a_a)) (let ((_let_1 (@ tptp.listrel1_a R))) (= (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a (@ (@ tptp.append_a Xs2) (@ (@ tptp.cons_a X3) tptp.nil_a))) (@ (@ tptp.append_a Ys2) (@ (@ tptp.cons_a Y3) tptp.nil_a)))) _let_1) (or (and (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a Xs2) Ys2)) _let_1) (= X3 Y3)) (and (= Xs2 Ys2) (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X3) Y3)) R)))))) (forall ((Y3 tptp.list_P1467822637od_a_a) (R tptp.set_Pr1948701895od_a_a)) (= (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a tptp.nil_Product_prod_a_a) Y3)) (@ tptp.lexord673907738od_a_a R)) (exists ((A5 tptp.product_prod_a_a) (X tptp.list_P1467822637od_a_a)) (= Y3 (@ (@ tptp.cons_P1921020637od_a_a A5) X))))) (forall ((Xs2 tptp.list_P1467822637od_a_a) (Ys2 tptp.list_P1467822637od_a_a) (Zs tptp.list_P1467822637od_a_a) (R tptp.set_Pr1948701895od_a_a)) (let ((_let_1 (@ tptp.lexord673907738od_a_a R))) (let ((_let_2 (@ tptp.append1574001858od_a_a Xs2))) (= (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a (@ _let_2 Ys2)) (@ _let_2 Zs))) _let_1) (or (exists ((X tptp.product_prod_a_a)) (and (@ (@ tptp.member449909584od_a_a X) (@ tptp.set_Product_prod_a_a2 Xs2)) (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a X) X)) R))) (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a Ys2) Zs)) _let_1)))))) (forall ((Xs2 tptp.list_a) (Ys2 tptp.list_a) (Zs tptp.list_a) (R tptp.set_Product_prod_a_a)) (let ((_let_1 (@ tptp.lexord_a R))) (let ((_let_2 (@ tptp.append_a Xs2))) (= (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a (@ _let_2 Ys2)) (@ _let_2 Zs))) _let_1) (or (exists ((X tptp.a)) (and (@ (@ tptp.member_a2 X) (@ tptp.set_a2 Xs2)) (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X) X)) R))) (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a Ys2) Zs)) _let_1)))))) (forall ((Xs2 tptp.list_a) (Us tptp.list_a) (Ys2 tptp.list_a) (Vs tptp.list_a)) (=> (= (@ tptp.size_size_list_a Xs2) (@ tptp.size_size_list_a Us)) (= (@ (@ tptp.zip_a_a (@ (@ tptp.append_a Xs2) Ys2)) (@ (@ tptp.append_a Us) Vs)) (@ (@ tptp.append1574001858od_a_a (@ (@ tptp.zip_a_a Xs2) Us)) (@ (@ tptp.zip_a_a Ys2) Vs))))) (forall ((Xs2 tptp.list_P1467822637od_a_a) (Us tptp.list_P1467822637od_a_a) (Ys2 tptp.list_P1467822637od_a_a) (Vs tptp.list_P1467822637od_a_a)) (=> (= (@ tptp.size_s642698393od_a_a Xs2) (@ tptp.size_s642698393od_a_a Us)) (= (@ (@ tptp.zip_Pr792472183od_a_a (@ (@ tptp.append1574001858od_a_a Xs2) Ys2)) (@ (@ tptp.append1574001858od_a_a Us) Vs)) (@ (@ tptp.append864718978od_a_a (@ (@ tptp.zip_Pr792472183od_a_a Xs2) Us)) (@ (@ tptp.zip_Pr792472183od_a_a Ys2) Vs))))) (forall ((R tptp.set_Pr1948701895od_a_a) (Xs2 tptp.list_P1467822637od_a_a) (Ys2 tptp.list_P1467822637od_a_a) (Zs tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ tptp.lex_Product_prod_a_a R))) (let ((_let_2 (@ tptp.append1574001858od_a_a Xs2))) (=> (forall ((X4 tptp.product_prod_a_a)) (not (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a X4) X4)) R))) (=> (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a (@ _let_2 Ys2)) (@ _let_2 Zs))) _let_1) (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a Ys2) Zs)) _let_1)))))) (forall ((R tptp.set_Product_prod_a_a) (Xs2 tptp.list_a) (Ys2 tptp.list_a) (Zs tptp.list_a)) (let ((_let_1 (@ tptp.lex_a R))) (let ((_let_2 (@ tptp.append_a Xs2))) (=> (forall ((X4 tptp.a)) (not (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X4) X4)) R))) (=> (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a (@ _let_2 Ys2)) (@ _let_2 Zs))) _let_1) (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a Ys2) Zs)) _let_1)))))) (forall ((R tptp.set_Pr1948701895od_a_a) (Xs2 tptp.list_P1467822637od_a_a) (Ys2 tptp.list_P1467822637od_a_a) (Zs tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ tptp.lex_Product_prod_a_a R))) (let ((_let_2 (@ tptp.append1574001858od_a_a Xs2))) (=> (forall ((X4 tptp.product_prod_a_a)) (not (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a X4) X4)) R))) (= (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a (@ _let_2 Ys2)) (@ _let_2 Zs))) _let_1) (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a Ys2) Zs)) _let_1)))))) (forall ((R tptp.set_Product_prod_a_a) (Xs2 tptp.list_a) (Ys2 tptp.list_a) (Zs tptp.list_a)) (let ((_let_1 (@ tptp.lex_a R))) (let ((_let_2 (@ tptp.append_a Xs2))) (=> (forall ((X4 tptp.a)) (not (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X4) X4)) R))) (= (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a (@ _let_2 Ys2)) (@ _let_2 Zs))) _let_1) (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a Ys2) Zs)) _let_1)))))) (forall ((A tptp.list_P1467822637od_a_a)) (= (@ (@ tptp.append1574001858od_a_a A) tptp.nil_Product_prod_a_a) A)) (forall ((Xs2 tptp.list_P1467822637od_a_a) (Ys2 tptp.list_P1467822637od_a_a)) (= (= (@ (@ tptp.append1574001858od_a_a Xs2) Ys2) tptp.nil_Product_prod_a_a) (and (= Xs2 tptp.nil_Product_prod_a_a) (= Ys2 tptp.nil_Product_prod_a_a)))) (forall ((Xs2 tptp.list_P1467822637od_a_a) (Ys2 tptp.list_P1467822637od_a_a)) (= (= tptp.nil_Product_prod_a_a (@ (@ tptp.append1574001858od_a_a Xs2) Ys2)) (and (= Xs2 tptp.nil_Product_prod_a_a) (= Ys2 tptp.nil_Product_prod_a_a)))) (forall ((Ys2 tptp.list_P1467822637od_a_a) (Xs2 tptp.list_P1467822637od_a_a)) (= (= Ys2 (@ (@ tptp.append1574001858od_a_a Xs2) Ys2)) (= Xs2 tptp.nil_Product_prod_a_a))) (forall ((Xs2 tptp.list_P1467822637od_a_a) (Ys2 tptp.list_P1467822637od_a_a)) (= (= (@ (@ tptp.append1574001858od_a_a Xs2) Ys2) Ys2) (= Xs2 tptp.nil_Product_prod_a_a))) (forall ((Xs2 tptp.list_P1467822637od_a_a) (Ys2 tptp.list_P1467822637od_a_a)) (= (= Xs2 (@ (@ tptp.append1574001858od_a_a Xs2) Ys2)) (= Ys2 tptp.nil_Product_prod_a_a))) (forall ((Xs2 tptp.list_P1467822637od_a_a) (Ys2 tptp.list_P1467822637od_a_a)) (= (= (@ (@ tptp.append1574001858od_a_a Xs2) Ys2) Xs2) (= Ys2 tptp.nil_Product_prod_a_a))) (forall ((Xs2 tptp.list_P1467822637od_a_a)) (= (@ (@ tptp.append1574001858od_a_a Xs2) tptp.nil_Product_prod_a_a) Xs2)) (forall ((Xs2 tptp.list_P1467822637od_a_a) (Ys2 tptp.list_P1467822637od_a_a) (Us tptp.list_P1467822637od_a_a) (Vs tptp.list_P1467822637od_a_a)) (=> (or (= (@ tptp.size_s642698393od_a_a Xs2) (@ tptp.size_s642698393od_a_a Ys2)) (= (@ tptp.size_s642698393od_a_a Us) (@ tptp.size_s642698393od_a_a Vs))) (= (= (@ (@ tptp.append1574001858od_a_a Xs2) Us) (@ (@ tptp.append1574001858od_a_a Ys2) Vs)) (and (= Xs2 Ys2) (= Us Vs))))) (forall ((Xs2 tptp.list_P1467822637od_a_a) (X3 tptp.product_prod_a_a) (Ys2 tptp.list_P1467822637od_a_a) (Y3 tptp.product_prod_a_a)) (= (= (@ (@ tptp.append1574001858od_a_a Xs2) (@ (@ tptp.cons_P1921020637od_a_a X3) tptp.nil_Product_prod_a_a)) (@ (@ tptp.append1574001858od_a_a Ys2) (@ (@ tptp.cons_P1921020637od_a_a Y3) tptp.nil_Product_prod_a_a))) (and (= Xs2 Ys2) (= X3 Y3)))) (forall ((X3 tptp.product_prod_a_a) (Xs2 tptp.list_P1467822637od_a_a) (Y3 tptp.product_prod_a_a) (Ys2 tptp.list_P1467822637od_a_a) (R tptp.set_Pr1948701895od_a_a)) (let ((_let_1 (@ tptp.lex_Product_prod_a_a R))) (= (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a (@ (@ tptp.cons_P1921020637od_a_a X3) Xs2)) (@ (@ tptp.cons_P1921020637od_a_a Y3) Ys2))) _let_1) (or (and (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a X3) Y3)) R) (= (@ tptp.size_s642698393od_a_a Xs2) (@ tptp.size_s642698393od_a_a Ys2))) (and (= X3 Y3) (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a Xs2) Ys2)) _let_1)))))) (forall ((X3 tptp.a) (Xs2 tptp.list_a) (Y3 tptp.a) (Ys2 tptp.list_a) (R tptp.set_Product_prod_a_a)) (let ((_let_1 (@ tptp.lex_a R))) (= (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a (@ (@ tptp.cons_a X3) Xs2)) (@ (@ tptp.cons_a Y3) Ys2))) _let_1) (or (and (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X3) Y3)) R) (= (@ tptp.size_size_list_a Xs2) (@ tptp.size_size_list_a Ys2))) (and (= X3 Y3) (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a Xs2) Ys2)) _let_1)))))) (forall ((Xs2 tptp.list_a) (Ys2 tptp.list_a) (X3 tptp.a)) (=> (= (@ tptp.size_size_list_a Xs2) (@ tptp.size_size_list_a Ys2)) (=> (@ (@ tptp.member_a2 X3) (@ tptp.set_a2 Xs2)) (not (forall ((Y4 tptp.a)) (not (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X3) Y4)) (@ tptp.set_Product_prod_a_a2 (@ (@ tptp.zip_a_a Xs2) Ys2))))))))) (forall ((Xs2 tptp.list_a) (Ys2 tptp.list_a) (Y3 tptp.a)) (=> (= (@ tptp.size_size_list_a Xs2) (@ tptp.size_size_list_a Ys2)) (=> (@ (@ tptp.member_a2 Y3) (@ tptp.set_a2 Ys2)) (not (forall ((X4 tptp.a)) (not (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X4) Y3)) (@ tptp.set_Product_prod_a_a2 (@ (@ tptp.zip_a_a Xs2) Ys2))))))))) (forall ((Xs2 tptp.list_P1467822637od_a_a) (Ys2 tptp.list_P1467822637od_a_a) (Zs tptp.list_P1467822637od_a_a) (Ws tptp.list_P1467822637od_a_a) (P2 (-> tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a Bool))) (let ((_let_1 (@ tptp.size_s642698393od_a_a Zs))) (let ((_let_2 (@ tptp.size_s642698393od_a_a Ys2))) (=> (= (@ tptp.size_s642698393od_a_a Xs2) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_s642698393od_a_a Ws)) (=> (@ (@ (@ (@ P2 tptp.nil_Product_prod_a_a) tptp.nil_Product_prod_a_a) tptp.nil_Product_prod_a_a) tptp.nil_Product_prod_a_a) (=> (forall ((X4 tptp.product_prod_a_a) (Xs4 tptp.list_P1467822637od_a_a) (Y4 tptp.product_prod_a_a) (Ys4 tptp.list_P1467822637od_a_a) (Z2 tptp.product_prod_a_a) (Zs2 tptp.list_P1467822637od_a_a) (W tptp.product_prod_a_a) (Ws2 tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ tptp.size_s642698393od_a_a Zs2))) (let ((_let_2 (@ tptp.size_s642698393od_a_a Ys4))) (=> (= (@ tptp.size_s642698393od_a_a Xs4) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_s642698393od_a_a Ws2)) (=> (@ (@ (@ (@ P2 Xs4) Ys4) Zs2) Ws2) (@ (@ (@ (@ P2 (@ (@ tptp.cons_P1921020637od_a_a X4) Xs4)) (@ (@ tptp.cons_P1921020637od_a_a Y4) Ys4)) (@ (@ tptp.cons_P1921020637od_a_a Z2) Zs2)) (@ (@ tptp.cons_P1921020637od_a_a W) Ws2))))))))) (@ (@ (@ (@ P2 Xs2) Ys2) Zs) Ws))))))))) (forall ((Xs2 tptp.list_P1467822637od_a_a) (Ys2 tptp.list_P1467822637od_a_a) (Zs tptp.list_P1467822637od_a_a) (P2 (-> tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a Bool))) (let ((_let_1 (@ tptp.size_s642698393od_a_a Ys2))) (=> (= (@ tptp.size_s642698393od_a_a Xs2) _let_1) (=> (= _let_1 (@ tptp.size_s642698393od_a_a Zs)) (=> (@ (@ (@ P2 tptp.nil_Product_prod_a_a) tptp.nil_Product_prod_a_a) tptp.nil_Product_prod_a_a) (=> (forall ((X4 tptp.product_prod_a_a) (Xs4 tptp.list_P1467822637od_a_a) (Y4 tptp.product_prod_a_a) (Ys4 tptp.list_P1467822637od_a_a) (Z2 tptp.product_prod_a_a) (Zs2 tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ tptp.size_s642698393od_a_a Ys4))) (=> (= (@ tptp.size_s642698393od_a_a Xs4) _let_1) (=> (= _let_1 (@ tptp.size_s642698393od_a_a Zs2)) (=> (@ (@ (@ P2 Xs4) Ys4) Zs2) (@ (@ (@ P2 (@ (@ tptp.cons_P1921020637od_a_a X4) Xs4)) (@ (@ tptp.cons_P1921020637od_a_a Y4) Ys4)) (@ (@ tptp.cons_P1921020637od_a_a Z2) Zs2))))))) (@ (@ (@ P2 Xs2) Ys2) Zs))))))) (forall ((Xs2 tptp.list_P1467822637od_a_a) (Ys2 tptp.list_P1467822637od_a_a) (P2 (-> tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a Bool))) (=> (= (@ tptp.size_s642698393od_a_a Xs2) (@ tptp.size_s642698393od_a_a Ys2)) (=> (@ (@ P2 tptp.nil_Product_prod_a_a) tptp.nil_Product_prod_a_a) (=> (forall ((X4 tptp.product_prod_a_a) (Xs4 tptp.list_P1467822637od_a_a) (Y4 tptp.product_prod_a_a) (Ys4 tptp.list_P1467822637od_a_a)) (=> (= (@ tptp.size_s642698393od_a_a Xs4) (@ tptp.size_s642698393od_a_a Ys4)) (=> (@ (@ P2 Xs4) Ys4) (@ (@ P2 (@ (@ tptp.cons_P1921020637od_a_a X4) Xs4)) (@ (@ tptp.cons_P1921020637od_a_a Y4) Ys4))))) (@ (@ P2 Xs2) Ys2))))) (forall ((X3 tptp.list_l1108175539od_a_a)) (=> (not (= X3 tptp.nil_li1885598003od_a_a)) (=> (forall ((Xss tptp.list_l1108175539od_a_a)) (not (= X3 (@ (@ tptp.cons_l724116707od_a_a tptp.nil_Product_prod_a_a) Xss)))) (not (forall ((X4 tptp.product_prod_a_a) (Xs4 tptp.list_P1467822637od_a_a) (Xss tptp.list_l1108175539od_a_a)) (not (= X3 (@ (@ tptp.cons_l724116707od_a_a (@ (@ tptp.cons_P1921020637od_a_a X4) Xs4)) Xss)))))))) (forall ((X3 tptp.a) (Y3 tptp.a) (Xs2 tptp.list_a) (Ys2 tptp.list_a)) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X3) Y3)) (@ tptp.set_Product_prod_a_a2 (@ (@ tptp.zip_a_a Xs2) Ys2))) (@ (@ tptp.member_a2 Y3) (@ tptp.set_a2 Ys2)))) (forall ((X3 tptp.a) (Y3 tptp.a) (Xs2 tptp.list_a) (Ys2 tptp.list_a)) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X3) Y3)) (@ tptp.set_Product_prod_a_a2 (@ (@ tptp.zip_a_a Xs2) Ys2))) (@ (@ tptp.member_a2 X3) (@ tptp.set_a2 Xs2)))) (forall ((X3 tptp.a) (Y3 tptp.a) (Xs2 tptp.list_a) (Ys2 tptp.list_a)) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X3) Y3)) (@ tptp.set_Product_prod_a_a2 (@ (@ tptp.zip_a_a Xs2) Ys2))) (not (=> (@ (@ tptp.member_a2 X3) (@ tptp.set_a2 Xs2)) (not (@ (@ tptp.member_a2 Y3) (@ tptp.set_a2 Ys2))))))) (forall ((A tptp.a) (B tptp.a) (Xs2 tptp.list_a)) (= (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a A) B)) (@ tptp.set_Product_prod_a_a2 (@ (@ tptp.zip_a_a Xs2) Xs2))) (and (@ (@ tptp.member_a2 A) 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(forall ((X3 tptp.product_prod_a_a) (Xs2 tptp.list_P1467822637od_a_a)) (= (@ (@ tptp.member449909584od_a_a X3) (@ tptp.set_Product_prod_a_a2 Xs2)) (exists ((Ys tptp.list_P1467822637od_a_a) (Zs3 tptp.list_P1467822637od_a_a)) (= Xs2 (@ (@ tptp.append1574001858od_a_a Ys) (@ (@ tptp.cons_P1921020637od_a_a X3) Zs3)))))) (forall ((X3 tptp.product_prod_a_a) (Xs2 tptp.list_P1467822637od_a_a) (Ys2 tptp.list_P1467822637od_a_a) (Xs5 tptp.list_P1467822637od_a_a) (Ys5 tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ tptp.cons_P1921020637od_a_a X3))) (let ((_let_2 (@ tptp.member449909584od_a_a X3))) (=> (not (@ _let_2 (@ tptp.set_Product_prod_a_a2 Xs2))) (=> (not (@ _let_2 (@ tptp.set_Product_prod_a_a2 Ys2))) (= (= (@ (@ tptp.append1574001858od_a_a Xs2) (@ _let_1 Ys2)) (@ (@ tptp.append1574001858od_a_a Xs5) (@ _let_1 Ys5))) (and (= Xs2 Xs5) (= Ys2 Ys5)))))))) (forall ((Xs2 tptp.list_P1467822637od_a_a) (P2 (-> tptp.product_prod_a_a Bool))) (=> (exists ((X5 tptp.product_prod_a_a)) (and (@ (@ 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tptp.product_prod_a_a)) (and (exists ((Zs2 tptp.list_P1467822637od_a_a)) (= Xs2 (@ (@ tptp.append1574001858od_a_a Ys4) (@ (@ tptp.cons_P1921020637od_a_a X4) Zs2)))) (@ P2 X4))))) (forall ((X3 tptp.product_prod_a_a) (Xs2 tptp.list_P1467822637od_a_a)) (=> (@ (@ tptp.member449909584od_a_a X3) (@ tptp.set_Product_prod_a_a2 Xs2)) (exists ((Ys4 tptp.list_P1467822637od_a_a) (Zs2 tptp.list_P1467822637od_a_a)) (and (= Xs2 (@ (@ tptp.append1574001858od_a_a Ys4) (@ (@ tptp.cons_P1921020637od_a_a X3) Zs2))) (not (@ (@ tptp.member449909584od_a_a X3) (@ tptp.set_Product_prod_a_a2 Zs2))))))) (forall ((X3 tptp.product_prod_a_a) (Xs2 tptp.list_P1467822637od_a_a)) (=> (@ (@ tptp.member449909584od_a_a X3) (@ tptp.set_Product_prod_a_a2 Xs2)) (exists ((Ys4 tptp.list_P1467822637od_a_a) (Zs2 tptp.list_P1467822637od_a_a)) (= Xs2 (@ (@ tptp.append1574001858od_a_a Ys4) (@ (@ tptp.cons_P1921020637od_a_a X3) Zs2)))))) (forall ((Xs2 tptp.list_P1467822637od_a_a) (P2 (-> tptp.list_P1467822637od_a_a Bool))) (=> (not 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tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ (@ tptp.cons_P1921020637od_a_a X3) Xs2))) (= (= _let_1 (@ (@ tptp.append1574001858od_a_a Ys2) Zs)) (or (and (= Ys2 tptp.nil_Product_prod_a_a) (= _let_1 Zs)) (exists ((Ys6 tptp.list_P1467822637od_a_a)) (and (= (@ (@ tptp.cons_P1921020637od_a_a X3) Ys6) Ys2) (= Xs2 (@ (@ tptp.append1574001858od_a_a Ys6) Zs)))))))) (forall ((Xs2 tptp.list_P1467822637od_a_a)) (=> (not (= Xs2 tptp.nil_Product_prod_a_a)) (not (forall ((Ys4 tptp.list_P1467822637od_a_a) (Y4 tptp.product_prod_a_a)) (not (= Xs2 (@ (@ tptp.append1574001858od_a_a Ys4) (@ (@ tptp.cons_P1921020637od_a_a Y4) tptp.nil_Product_prod_a_a)))))))) (forall ((P2 (-> tptp.list_P1467822637od_a_a Bool)) (Xs2 tptp.list_P1467822637od_a_a)) (=> (@ P2 tptp.nil_Product_prod_a_a) (=> (forall ((X4 tptp.product_prod_a_a) (Xs4 tptp.list_P1467822637od_a_a)) (=> (@ P2 Xs4) (@ P2 (@ (@ tptp.append1574001858od_a_a Xs4) (@ (@ tptp.cons_P1921020637od_a_a X4) tptp.nil_Product_prod_a_a))))) (@ P2 Xs2)))) (forall ((X3 tptp.produc651658087od_a_a)) (=> (forall ((Ys4 tptp.list_P1467822637od_a_a)) (not (= X3 (@ (@ tptp.produc85179863od_a_a tptp.nil_Product_prod_a_a) Ys4)))) (=> (forall ((Xs4 tptp.list_P1467822637od_a_a)) (not (= X3 (@ (@ tptp.produc85179863od_a_a Xs4) tptp.nil_Product_prod_a_a)))) (not (forall ((X4 tptp.product_prod_a_a) (Xs4 tptp.list_P1467822637od_a_a) (Y4 tptp.product_prod_a_a) (Ys4 tptp.list_P1467822637od_a_a)) (not (= X3 (@ (@ tptp.produc85179863od_a_a (@ (@ tptp.cons_P1921020637od_a_a X4) Xs4)) (@ (@ tptp.cons_P1921020637od_a_a Y4) Ys4))))))))) (forall ((P2 (-> tptp.product_prod_a_a tptp.a tptp.list_P1467822637od_a_a Bool)) (A0 tptp.product_prod_a_a) (A1 tptp.a) (A22 tptp.list_P1467822637od_a_a)) (=> (forall ((Uu tptp.product_prod_a_a) (Uv tptp.a)) (@ (@ (@ P2 Uu) Uv) tptp.nil_Product_prod_a_a)) (=> (forall ((U2 tptp.a) (V tptp.a) (W tptp.a) (E2 tptp.product_prod_a_a) (Es tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ (@ P2 (@ (@ tptp.product_Pair_a_a U2) V)) W))) (=> (@ _let_1 Es) (@ _let_1 (@ (@ tptp.cons_P1921020637od_a_a E2) Es))))) (@ (@ (@ P2 A0) A1) A22)))) (forall ((P2 (-> tptp.product_prod_a_a tptp.a tptp.list_P1467822637od_a_a Bool)) (A0 tptp.product_prod_a_a) (A1 tptp.a) (A22 tptp.list_P1467822637od_a_a)) (=> (forall ((Uu tptp.product_prod_a_a) (Uv tptp.a)) (@ (@ (@ P2 Uu) Uv) tptp.nil_Product_prod_a_a)) (=> (forall ((Uw tptp.product_prod_a_a) (Ux tptp.a) (E2 tptp.product_prod_a_a)) (@ (@ (@ P2 Uw) Ux) (@ (@ tptp.cons_P1921020637od_a_a E2) tptp.nil_Product_prod_a_a))) (=> (forall ((U2 tptp.a) (V tptp.a) (W tptp.a) (E1 tptp.product_prod_a_a) (E22 tptp.product_prod_a_a) (Es tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ (@ tptp.cons_P1921020637od_a_a E22) Es))) (let ((_let_2 (@ tptp.product_Pair_a_a U2))) (let ((_let_3 (@ (@ P2 (@ _let_2 V)) W))) (let ((_let_4 (@ tptp.product_Pair_a_a W))) (let ((_let_5 (and (= E1 (@ (@ tptp.product_Pair_a_a V) W)) (= E22 (@ _let_4 U2))))) (let ((_let_6 (and (= E1 (@ _let_2 W)) (= E22 (@ _let_4 V))))) (let ((_let_7 (not _let_6))) (let ((_let_8 (@ _let_3 Es))) (=> (=> _let_6 _let_8) (=> (=> _let_7 (=> _let_5 _let_8)) (=> (=> _let_7 (=> (not _let_5) (@ _let_3 _let_1))) (@ _let_3 (@ (@ tptp.cons_P1921020637od_a_a E1) _let_1)))))))))))))) (@ (@ (@ P2 A0) A1) A22))))) (forall ((X3 tptp.produc821581462od_a_a)) (=> (forall ((Uu tptp.product_prod_a_a) (Uv tptp.a)) (not (= X3 (@ (@ tptp.produc600870406od_a_a Uu) (@ (@ tptp.produc575024326od_a_a Uv) tptp.nil_Product_prod_a_a))))) (not (forall ((U2 tptp.a) (V tptp.a) (W tptp.a) (E2 tptp.product_prod_a_a) (Es tptp.list_P1467822637od_a_a)) (not (= X3 (@ (@ tptp.produc600870406od_a_a (@ (@ tptp.product_Pair_a_a U2) V)) (@ (@ tptp.produc575024326od_a_a W) (@ (@ tptp.cons_P1921020637od_a_a E2) Es))))))))) (forall ((X3 tptp.produc821581462od_a_a)) (=> (forall ((Uu tptp.product_prod_a_a) (Uv tptp.a)) (not (= X3 (@ (@ tptp.produc600870406od_a_a Uu) (@ (@ tptp.produc575024326od_a_a Uv) tptp.nil_Product_prod_a_a))))) (=> (forall ((Uw tptp.product_prod_a_a) (Ux tptp.a) (E2 tptp.product_prod_a_a)) (not (= X3 (@ (@ tptp.produc600870406od_a_a Uw) (@ (@ tptp.produc575024326od_a_a Ux) (@ (@ tptp.cons_P1921020637od_a_a E2) tptp.nil_Product_prod_a_a)))))) (not (forall ((U2 tptp.a) (V tptp.a) (W tptp.a) (E1 tptp.product_prod_a_a) (E22 tptp.product_prod_a_a) (Es tptp.list_P1467822637od_a_a)) (not (= X3 (@ (@ tptp.produc600870406od_a_a (@ (@ tptp.product_Pair_a_a U2) V)) (@ (@ tptp.produc575024326od_a_a W) (@ (@ tptp.cons_P1921020637od_a_a E1) (@ (@ tptp.cons_P1921020637od_a_a E22) Es))))))))))) (forall ((Ys2 tptp.list_P1467822637od_a_a) (Zs tptp.list_P1467822637od_a_a) (R tptp.set_Pr1948701895od_a_a) (Xs2 tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ tptp.lex_Product_prod_a_a R))) (let ((_let_2 (@ tptp.append1574001858od_a_a Xs2))) (=> (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a Ys2) Zs)) _let_1) (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a (@ _let_2 Ys2)) (@ _let_2 Zs))) _let_1))))) (forall ((E tptp.product_prod_a_a)) (@ tptp.kurato1072996284sing_a (@ (@ tptp.cons_P1921020637od_a_a E) tptp.nil_Product_prod_a_a))) (forall ((Xs2 tptp.list_a) (R tptp.set_Product_prod_a_a) (Ys2 tptp.list_a) (Zs tptp.list_a)) (let ((_let_1 (@ tptp.lexord_a R))) (let ((_let_2 (@ tptp.produc1448356631list_a Xs2))) (=> (forall ((X4 tptp.a) (Y4 tptp.a) (Z2 tptp.a)) (let ((_let_1 (@ tptp.product_Pair_a_a X4))) (=> (@ (@ tptp.member_a2 X4) (@ tptp.set_a2 Xs2)) (=> (@ (@ tptp.member449909584od_a_a (@ _let_1 Y4)) R) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a Y4) Z2)) R) (@ (@ tptp.member449909584od_a_a (@ _let_1 Z2)) R)))))) (=> (@ (@ tptp.member1250517072list_a (@ _let_2 Ys2)) _let_1) (=> (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a Ys2) Zs)) _let_1) (@ (@ tptp.member1250517072list_a (@ _let_2 Zs)) _let_1))))))) (forall ((Xs2 tptp.list_P1467822637od_a_a) (Zs tptp.list_P1467822637od_a_a) (Ys2 tptp.list_P1467822637od_a_a) (Qs tptp.list_P1467822637od_a_a) (R tptp.set_Pr1948701895od_a_a)) (let ((_let_1 (@ tptp.lexord673907738od_a_a R))) (=> (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a (@ (@ tptp.append1574001858od_a_a Xs2) Zs)) (@ (@ tptp.append1574001858od_a_a Ys2) Qs))) _let_1) (=> (not (= Xs2 Ys2)) (=> (= (@ tptp.size_s642698393od_a_a Xs2) (@ tptp.size_s642698393od_a_a Ys2)) (=> (= (@ tptp.size_s642698393od_a_a Zs) (@ tptp.size_s642698393od_a_a Qs)) (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a Xs2) Ys2)) _let_1))))))) (forall ((X3 tptp.produc651658087od_a_a)) (=> (forall ((Ys4 tptp.list_P1467822637od_a_a)) (not (= X3 (@ (@ tptp.produc85179863od_a_a tptp.nil_Product_prod_a_a) Ys4)))) (not (forall ((X4 tptp.product_prod_a_a) (Xs4 tptp.list_P1467822637od_a_a) (Ys4 tptp.list_P1467822637od_a_a)) (not (= X3 (@ (@ tptp.produc85179863od_a_a (@ (@ tptp.cons_P1921020637od_a_a X4) Xs4)) Ys4))))))) (forall ((X3 tptp.set_Product_prod_a_a) (P2 (-> tptp.set_Product_prod_a_a Bool))) (=> (@ tptp.asym_a X3) (=> (forall ((R3 tptp.set_Product_prod_a_a)) (=> (forall ((A6 tptp.a) (B4 tptp.a)) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a A6) B4)) R3) (not (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a B4) A6)) R3)))) (@ P2 R3))) (@ P2 X3)))) (forall ((R2 tptp.set_Product_prod_a_a)) (=> (forall ((A3 tptp.a) (B3 tptp.a)) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a A3) B3)) R2) (not (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a B3) A3)) R2)))) (@ tptp.asym_a R2))) _let_4 (forall ((A tptp.set_Product_prod_a_a)) (=> (@ tptp.asym_a A) (forall ((A6 tptp.a) (B4 tptp.a)) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a A6) B4)) A) (not (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a B4) A6)) A)))))) (= tptp.asym_a (lambda ((R4 tptp.set_Product_prod_a_a)) (forall ((X tptp.a) (Y tptp.a)) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X) Y)) R4) (not (@ (@ tptp.member449909584od_a_a (@ (@ 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(=> (forall ((Y4 tptp.a) (X6 tptp.a) (Xs4 tptp.list_P1467822637od_a_a) (X4 tptp.a)) (=> (=> (not (= X4 X6)) (@ (@ P2 Xs4) X4)) (@ (@ P2 (@ (@ tptp.cons_P1921020637od_a_a (@ (@ tptp.product_Pair_a_a Y4) X6)) Xs4)) X4))) (@ (@ P2 A0) A1)))) (forall ((U tptp.a) (V2 tptp.a) (W2 tptp.a) (E tptp.product_prod_a_a) (Es2 tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ tptp.product_Pair_a_a U))) (let ((_let_2 (@ _let_1 V2))) (let ((_let_3 (@ (@ tptp.pair_sd_path_a _let_2) W2))) (let ((_let_4 (@ tptp.cons_P1921020637od_a_a E))) (let ((_let_5 (@ tptp.product_Pair_a_a W2))) (let ((_let_6 (@ tptp.product_Pair_a_a V2))) (= (@ _let_3 (@ _let_4 Es2)) (@ (@ tptp.append1574001858od_a_a (@ (@ (@ tptp.if_lis321365491od_a_a (= E _let_2)) (@ (@ tptp.cons_P1921020637od_a_a (@ _let_1 W2)) (@ (@ tptp.cons_P1921020637od_a_a (@ _let_5 V2)) tptp.nil_Product_prod_a_a))) (@ (@ (@ tptp.if_lis321365491od_a_a (= E (@ _let_6 U))) (@ (@ tptp.cons_P1921020637od_a_a (@ _let_6 W2)) (@ (@ tptp.cons_P1921020637od_a_a (@ _let_5 U)) tptp.nil_Product_prod_a_a))) (@ _let_4 tptp.nil_Product_prod_a_a)))) (@ _let_3 Es2)))))))))) (forall ((X3 tptp.a) (Y3 tptp.a) (P3 tptp.list_P1467822637od_a_a) (W2 tptp.a)) (let ((_let_1 (@ (@ tptp.product_Pair_a_a X3) Y3))) (let ((_let_2 (@ tptp.set_Product_prod_a_a2 P3))) (=> (not (@ (@ tptp.member449909584od_a_a _let_1) _let_2)) (=> (not (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a Y3) X3)) _let_2)) (= (@ (@ (@ tptp.pair_sd_path_a _let_1) W2) P3) P3)))))) (forall ((X3 tptp.product_prod_a_a) (Xa2 tptp.a) (Xb tptp.list_P1467822637od_a_a) (Y3 tptp.list_P1467822637od_a_a)) (=> (= (@ (@ (@ tptp.pair_sd_path_a X3) Xa2) Xb) Y3) (=> (=> (= Xb tptp.nil_Product_prod_a_a) (not (= Y3 tptp.nil_Product_prod_a_a))) (not (forall ((U2 tptp.a) (V tptp.a)) (=> (= X3 (@ (@ tptp.product_Pair_a_a U2) V)) (forall ((E2 tptp.product_prod_a_a) (Es tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ tptp.product_Pair_a_a U2))) (let ((_let_2 (@ _let_1 V))) (let ((_let_3 (@ 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(let ((_let_2 (@ tptp.produc600870406od_a_a X3))) (let ((_let_3 (@ tptp.accp_P1029463583od_a_a tptp.pair_sd_path_rel_a))) (=> (= (@ (@ (@ tptp.pair_sd_path_a X3) Xa2) Xb) Y3) (=> (@ _let_3 (@ _let_2 (@ _let_1 Xb))) (=> (=> (= Xb tptp.nil_Product_prod_a_a) (=> (= Y3 tptp.nil_Product_prod_a_a) (not (@ _let_3 (@ _let_2 (@ _let_1 tptp.nil_Product_prod_a_a)))))) (not (forall ((U2 tptp.a) (V tptp.a)) (=> (= X3 (@ (@ tptp.product_Pair_a_a U2) V)) (forall ((E2 tptp.product_prod_a_a) (Es tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ tptp.cons_P1921020637od_a_a E2))) (let ((_let_2 (@ _let_1 Es))) (let ((_let_3 (@ tptp.product_Pair_a_a U2))) (let ((_let_4 (@ _let_3 V))) (let ((_let_5 (@ tptp.product_Pair_a_a Xa2))) (let ((_let_6 (@ tptp.product_Pair_a_a V))) (=> (= Xb _let_2) (=> (= Y3 (@ (@ tptp.append1574001858od_a_a (@ (@ (@ tptp.if_lis321365491od_a_a (= E2 _let_4)) (@ (@ tptp.cons_P1921020637od_a_a (@ _let_3 Xa2)) (@ (@ tptp.cons_P1921020637od_a_a (@ _let_5 V)) tptp.nil_Product_prod_a_a))) (@ (@ (@ tptp.if_lis321365491od_a_a (= E2 (@ _let_6 U2))) (@ (@ tptp.cons_P1921020637od_a_a (@ _let_6 Xa2)) (@ (@ tptp.cons_P1921020637od_a_a (@ _let_5 U2)) tptp.nil_Product_prod_a_a))) (@ _let_1 tptp.nil_Product_prod_a_a)))) (@ (@ (@ tptp.pair_sd_path_a _let_4) Xa2) Es))) (not (@ (@ tptp.accp_P1029463583od_a_a tptp.pair_sd_path_rel_a) (@ (@ tptp.produc600870406od_a_a _let_4) (@ (@ tptp.produc575024326od_a_a Xa2) _let_2))))))))))))))))))))))) (forall ((Y3 tptp.list_P1467822637od_a_a) (Ya tptp.list_P1467822637od_a_a)) (let ((_let_1 (not (= Ya tptp.nil_Product_prod_a_a)))) (let ((_let_2 (= Y3 tptp.nil_Product_prod_a_a))) (=> (=> _let_2 _let_1) (=> (=> _let_2 (forall ((X212 tptp.product_prod_a_a) (X222 tptp.list_P1467822637od_a_a)) (not (= Ya (@ (@ tptp.cons_P1921020637od_a_a X212) X222))))) (=> (=> (exists ((X212 tptp.product_prod_a_a) (X222 tptp.list_P1467822637od_a_a)) (= Y3 (@ (@ tptp.cons_P1921020637od_a_a X212) X222))) _let_1) (not (=> (exists ((X212 tptp.product_prod_a_a) (X222 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tptp.a) (Xb tptp.list_P1467822637od_a_a) (Y3 tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ tptp.produc575024326od_a_a Xa2))) (let ((_let_2 (@ tptp.produc600870406od_a_a X3))) (let ((_let_3 (@ tptp.accp_P1029463583od_a_a tptp.pair_co_path_rel_a))) (=> (= (@ (@ (@ tptp.pair_co_path_a X3) Xa2) Xb) Y3) (=> (@ _let_3 (@ _let_2 (@ _let_1 Xb))) (=> (=> (= Xb tptp.nil_Product_prod_a_a) (=> (= Y3 tptp.nil_Product_prod_a_a) (not (@ _let_3 (@ _let_2 (@ _let_1 tptp.nil_Product_prod_a_a)))))) (=> (forall ((E2 tptp.product_prod_a_a)) (let ((_let_1 (@ (@ tptp.cons_P1921020637od_a_a E2) tptp.nil_Product_prod_a_a))) (=> (= Xb _let_1) (=> (= Y3 _let_1) (not (@ (@ tptp.accp_P1029463583od_a_a tptp.pair_co_path_rel_a) (@ (@ tptp.produc600870406od_a_a X3) (@ (@ tptp.produc575024326od_a_a Xa2) _let_1)))))))) (not (forall ((U2 tptp.a) (V tptp.a)) (=> (= X3 (@ (@ tptp.product_Pair_a_a U2) V)) (forall ((E1 tptp.product_prod_a_a) (E22 tptp.product_prod_a_a) (Es tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ (@ tptp.cons_P1921020637od_a_a E22) Es))) (let ((_let_2 (@ tptp.cons_P1921020637od_a_a E1))) (let ((_let_3 (@ _let_2 _let_1))) (let ((_let_4 (@ tptp.product_Pair_a_a U2))) (let ((_let_5 (@ _let_4 V))) (let ((_let_6 (@ (@ tptp.pair_co_path_a _let_5) Xa2))) (let ((_let_7 (@ tptp.product_Pair_a_a Xa2))) (let ((_let_8 (@ tptp.product_Pair_a_a V))) (let ((_let_9 (and (= E1 (@ _let_8 Xa2)) (= E22 (@ _let_7 U2))))) (let ((_let_10 (@ _let_6 Es))) (let ((_let_11 (and (= E1 (@ _let_4 Xa2)) (= E22 (@ _let_7 V))))) (=> (= Xb _let_3) (=> (and (=> _let_11 (= Y3 (@ (@ tptp.cons_P1921020637od_a_a _let_5) _let_10))) (=> (not _let_11) (and (=> _let_9 (= Y3 (@ (@ tptp.cons_P1921020637od_a_a (@ _let_8 U2)) _let_10))) (=> (not _let_9) (= Y3 (@ _let_2 (@ _let_6 _let_1))))))) (not (@ (@ tptp.accp_P1029463583od_a_a tptp.pair_co_path_rel_a) (@ (@ tptp.produc600870406od_a_a _let_5) (@ (@ tptp.produc575024326od_a_a Xa2) _let_3))))))))))))))))))))))))))))) (forall ((U tptp.product_prod_a_a)) (= (@ (@ tptp.pair_p2140537249od_a_a U) tptp.nil_Pr1049924845od_a_a) (@ (@ tptp.cons_P1921020637od_a_a U) tptp.nil_Product_prod_a_a))) (forall ((E12 tptp.product_prod_a_a) (U tptp.a) (W2 tptp.a) (E23 tptp.product_prod_a_a) (V2 tptp.a) (Es2 tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ (@ tptp.cons_P1921020637od_a_a E23) Es2))) (let ((_let_2 (@ tptp.product_Pair_a_a U))) (let ((_let_3 (@ _let_2 V2))) (let ((_let_4 (@ (@ tptp.pair_co_path_a _let_3) W2))) (let ((_let_5 (@ tptp.cons_P1921020637od_a_a E12))) (let ((_let_6 (@ _let_4 (@ _let_5 _let_1)))) (let ((_let_7 (@ tptp.product_Pair_a_a W2))) (let ((_let_8 (@ tptp.product_Pair_a_a V2))) (let ((_let_9 (and (= E12 (@ _let_8 W2)) (= E23 (@ _let_7 U))))) (let ((_let_10 (@ _let_4 Es2))) (let ((_let_11 (and (= E12 (@ _let_2 W2)) (= E23 (@ _let_7 V2))))) (and (=> _let_11 (= _let_6 (@ (@ tptp.cons_P1921020637od_a_a _let_3) _let_10))) (=> (not _let_11) (and (=> _let_9 (= _let_6 (@ (@ tptp.cons_P1921020637od_a_a (@ _let_8 U)) _let_10))) (=> (not _let_9) (= _let_6 (@ _let_5 (@ _let_4 _let_1))))))))))))))))))) (forall ((Uw2 tptp.product_prod_a_a) (Ux2 tptp.a) (E tptp.product_prod_a_a)) (let ((_let_1 (@ (@ tptp.cons_P1921020637od_a_a E) tptp.nil_Product_prod_a_a))) (= (@ (@ (@ tptp.pair_co_path_a Uw2) Ux2) _let_1) _let_1))) (forall ((X3 tptp.product_prod_a_a) (Xa2 tptp.a) (Xb tptp.list_P1467822637od_a_a) (Y3 tptp.list_P1467822637od_a_a)) (=> (= (@ (@ (@ tptp.pair_co_path_a X3) Xa2) Xb) Y3) (=> (=> (= Xb tptp.nil_Product_prod_a_a) (not (= Y3 tptp.nil_Product_prod_a_a))) (=> (forall ((E2 tptp.product_prod_a_a)) (let ((_let_1 (@ (@ tptp.cons_P1921020637od_a_a E2) tptp.nil_Product_prod_a_a))) (=> (= Xb _let_1) (not (= Y3 _let_1))))) (not (forall ((U2 tptp.a) (V tptp.a)) (=> (= X3 (@ (@ tptp.product_Pair_a_a U2) V)) (forall ((E1 tptp.product_prod_a_a) (E22 tptp.product_prod_a_a) (Es tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ (@ tptp.cons_P1921020637od_a_a E22) Es))) (let ((_let_2 (@ tptp.product_Pair_a_a U2))) (let ((_let_3 (@ _let_2 V))) (let ((_let_4 (@ (@ tptp.pair_co_path_a _let_3) Xa2))) (let ((_let_5 (@ tptp.cons_P1921020637od_a_a E1))) (let ((_let_6 (@ tptp.product_Pair_a_a Xa2))) (let ((_let_7 (@ tptp.product_Pair_a_a V))) (let ((_let_8 (and (= E1 (@ _let_7 Xa2)) (= E22 (@ _let_6 U2))))) (let ((_let_9 (@ _let_4 Es))) (let ((_let_10 (and (= E1 (@ _let_2 Xa2)) (= E22 (@ _let_6 V))))) (=> (= Xb (@ _let_5 _let_1)) (not (and (=> _let_10 (= Y3 (@ (@ tptp.cons_P1921020637od_a_a _let_3) _let_9))) (=> (not _let_10) (and (=> _let_8 (= Y3 (@ (@ tptp.cons_P1921020637od_a_a (@ _let_7 U2)) _let_9))) (=> (not _let_8) (= Y3 (@ _let_5 (@ _let_4 _let_1))))))))))))))))))))))))))) (forall ((U tptp.a) (W2 tptp.a) (P3 tptp.list_P1467822637od_a_a) (V2 tptp.a)) (let ((_let_1 (@ tptp.product_Pair_a_a U))) (let ((_let_2 (@ _let_1 V2))) (let ((_let_3 (@ tptp.set_Product_prod_a_a2 P3))) (=> (not (@ (@ tptp.member449909584od_a_a (@ _let_1 W2)) _let_3)) (=> (not (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a V2) W2)) _let_3)) (= (@ (@ (@ tptp.pair_co_path_a _let_2) W2) (@ (@ (@ tptp.pair_sd_path_a _let_2) W2) P3)) P3))))))) (forall ((M tptp.product_prod_a_a) (Ms tptp.list_P1467822637od_a_a) (N tptp.product_prod_a_a) (Ns tptp.list_P1467822637od_a_a) (R tptp.set_Pr1948701895od_a_a)) (let ((_let_1 (@ tptp.lenlex2038501170od_a_a R))) (let ((_let_2 (@ tptp.size_s642698393od_a_a Ns))) (let ((_let_3 (@ tptp.size_s642698393od_a_a Ms))) (= (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a (@ (@ tptp.cons_P1921020637od_a_a M) Ms)) (@ (@ tptp.cons_P1921020637od_a_a N) Ns))) _let_1) (or (@ (@ tptp.ord_less_nat _let_3) _let_2) (and (= _let_3 _let_2) (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a M) N)) R)) (and (= M N) (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a Ms) Ns)) _let_1)))))))) (forall ((M tptp.a) (Ms tptp.list_a) (N tptp.a) (Ns tptp.list_a) (R tptp.set_Product_prod_a_a)) (let ((_let_1 (@ tptp.lenlex_a R))) (let ((_let_2 (@ tptp.size_size_list_a Ns))) (let ((_let_3 (@ tptp.size_size_list_a Ms))) (= (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a (@ (@ tptp.cons_a M) Ms)) (@ (@ tptp.cons_a N) Ns))) _let_1) (or (@ (@ tptp.ord_less_nat _let_3) _let_2) (and (= _let_3 _let_2) (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a M) N)) R)) (and (= M N) (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a Ms) Ns)) _let_1)))))))) (forall ((Y3 tptp.product_prod_a_a) (Ys2 tptp.list_P1467822637od_a_a) (Xs2 tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ tptp.set_li1284606018od_a_a (@ tptp.subseq2115548028od_a_a Xs2)))) (=> (@ (@ tptp.member1578987478od_a_a (@ (@ tptp.cons_P1921020637od_a_a Y3) Ys2)) _let_1) (@ (@ tptp.member1578987478od_a_a Ys2) _let_1)))) (forall ((X3 tptp.a) (Y3 tptp.a) (F (-> tptp.a tptp.nat)) (Fs tptp.list_a_nat)) (let ((_let_1 (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X3) Y3)))) (let ((_let_2 (@ F Y3))) (let ((_let_3 (@ F X3))) (= (@ _let_1 (@ tptp.measures_a (@ (@ tptp.cons_a_nat F) Fs))) (or (@ (@ tptp.ord_less_nat _let_3) _let_2) (and (= _let_3 _let_2) (@ _let_1 (@ tptp.measures_a Fs))))))))) (forall ((X3 tptp.list_P1467822637od_a_a) (Xa2 tptp.a) (Y3 tptp.a)) (=> (= (@ (@ tptp.invers1007791577list_a X3) Xa2) Y3) (=> (=> (= X3 tptp.nil_Product_prod_a_a) (not (= Y3 Xa2))) (not (forall ((Y4 tptp.a) (X6 tptp.a) (Xs4 tptp.list_P1467822637od_a_a)) (let ((_let_1 (= Xa2 X6))) (=> (= X3 (@ (@ tptp.cons_P1921020637od_a_a (@ (@ tptp.product_Pair_a_a Y4) X6)) Xs4)) (not (and (=> _let_1 (= Y3 Y4)) (=> (not _let_1) (= Y3 (@ (@ tptp.invers1007791577list_a Xs4) Xa2)))))))))))) (forall ((X3 tptp.a) (Y3 tptp.a)) (not (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X3) Y3)) (@ tptp.measures_a tptp.nil_a_nat)))) (forall ((X3 tptp.a) (X7 tptp.a) (Y5 tptp.a) (Xs2 tptp.list_P1467822637od_a_a)) (=> (not (= X3 X7)) (= (@ (@ tptp.invers1007791577list_a (@ (@ tptp.cons_P1921020637od_a_a (@ (@ tptp.product_Pair_a_a Y5) X7)) Xs2)) X3) (@ (@ 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tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X3) Y3)) (@ tptp.set_Product_prod_a_a2 Xs2)) (= (@ (@ tptp.invers1007791577list_a Xs2) Y3) X3)))) (forall ((X3 tptp.a) (X7 tptp.a) (Y5 tptp.a) (Xs2 tptp.list_P1467822637od_a_a)) (=> (not (= X3 X7)) (= (@ (@ tptp.permut1422637723list_a (@ (@ tptp.cons_P1921020637od_a_a (@ (@ tptp.product_Pair_a_a X7) Y5)) Xs2)) X3) (@ (@ tptp.permut1422637723list_a Xs2) X3)))) (forall ((X3 tptp.a) (X7 tptp.a) (Y3 tptp.a) (Xs2 tptp.list_P1467822637od_a_a)) (=> (= X3 X7) (= (@ (@ tptp.permut1422637723list_a (@ (@ tptp.cons_P1921020637od_a_a (@ (@ tptp.product_Pair_a_a X7) Y3)) Xs2)) X3) Y3))) (forall ((Xs2 tptp.list_P1467822637od_a_a) (A4 tptp.set_a) (X3 tptp.a) (Y3 tptp.a)) (=> (@ (@ tptp.list_permutes_a Xs2) A4) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X3) Y3)) (@ tptp.set_Product_prod_a_a2 Xs2)) (= (@ (@ tptp.permut1422637723list_a Xs2) X3) Y3)))) (forall ((X3 tptp.a) (X7 tptp.a) (Y3 tptp.a) (Xs2 tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ (@ tptp.permut1422637723list_a (@ (@ tptp.cons_P1921020637od_a_a (@ (@ tptp.product_Pair_a_a X3) Y3)) Xs2)) X7))) (let ((_let_2 (= X3 X7))) (and (=> _let_2 (= _let_1 Y3)) (=> (not _let_2) (= _let_1 (@ (@ tptp.permut1422637723list_a Xs2) X7))))))) (forall ((X3 tptp.product_prod_a_a) (Xs2 tptp.list_P1467822637od_a_a)) (=> (not (@ (@ tptp.member449909584od_a_a X3) (@ tptp.set_Product_prod_a_a2 Xs2))) (= (@ (@ tptp.insert2123825731od_a_a X3) Xs2) (@ (@ tptp.cons_P1921020637od_a_a X3) Xs2)))) (forall ((X3 tptp.product_prod_a_a)) (= (@ (@ tptp.insert2123825731od_a_a X3) tptp.nil_Product_prod_a_a) (@ (@ tptp.cons_P1921020637od_a_a X3) tptp.nil_Product_prod_a_a))) _let_2 (forall ((Xss2 tptp.list_l1108175539od_a_a) (Ys2 tptp.list_P1467822637od_a_a) (Zs tptp.list_P1467822637od_a_a)) (let ((_let_1 (= Xss2 tptp.nil_li1885598003od_a_a))) (= (= (@ tptp.concat1878217064od_a_a Xss2) (@ (@ tptp.append1574001858od_a_a Ys2) Zs)) (and (=> _let_1 (and (= Ys2 tptp.nil_Product_prod_a_a) (= Zs tptp.nil_Product_prod_a_a))) (=> (not _let_1) (exists ((Xss1 tptp.list_l1108175539od_a_a) (Xs tptp.list_P1467822637od_a_a) (Xs6 tptp.list_P1467822637od_a_a) (Xss22 tptp.list_l1108175539od_a_a)) (and (= Xss2 (@ (@ tptp.append2141280328od_a_a Xss1) (@ (@ tptp.cons_l724116707od_a_a (@ (@ tptp.append1574001858od_a_a Xs) Xs6)) Xss22))) (= Ys2 (@ (@ tptp.append1574001858od_a_a (@ tptp.concat1878217064od_a_a Xss1)) Xs)) (= Zs (@ (@ tptp.append1574001858od_a_a Xs6) (@ tptp.concat1878217064od_a_a Xss22)))))))))) (forall ((X3 tptp.list_P1467822637od_a_a) (Xa2 tptp.a) (Y3 tptp.a)) (let ((_let_1 (@ tptp.accp_P941981633_a_a_a tptp.invers214109608_rel_a))) (=> (= (@ (@ tptp.invers1007791577list_a X3) Xa2) Y3) (=> (@ _let_1 (@ (@ tptp.produc998622632_a_a_a X3) Xa2)) (=> (=> (= X3 tptp.nil_Product_prod_a_a) (=> (= Y3 Xa2) (not (@ _let_1 (@ (@ tptp.produc998622632_a_a_a tptp.nil_Product_prod_a_a) Xa2))))) (not (forall ((Y4 tptp.a) (X6 tptp.a) (Xs4 tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ (@ tptp.cons_P1921020637od_a_a (@ (@ tptp.product_Pair_a_a Y4) X6)) Xs4))) (let ((_let_2 (= Xa2 X6))) (=> (= X3 _let_1) (=> (and (=> _let_2 (= Y3 Y4)) (=> (not _let_2) (= Y3 (@ (@ tptp.invers1007791577list_a Xs4) Xa2)))) (not (@ (@ tptp.accp_P941981633_a_a_a tptp.invers214109608_rel_a) (@ (@ tptp.produc998622632_a_a_a _let_1) Xa2)))))))))))))) (forall ((Xs2 tptp.list_l1108175539od_a_a) (Ys2 tptp.list_l1108175539od_a_a)) (= (@ tptp.concat1878217064od_a_a (@ (@ tptp.append2141280328od_a_a Xs2) Ys2)) (@ (@ tptp.append1574001858od_a_a (@ tptp.concat1878217064od_a_a Xs2)) (@ tptp.concat1878217064od_a_a Ys2)))) (forall ((X3 tptp.list_P1467822637od_a_a) (Xs2 tptp.list_l1108175539od_a_a)) (= (@ tptp.concat1878217064od_a_a (@ (@ tptp.cons_l724116707od_a_a X3) Xs2)) (@ (@ tptp.append1574001858od_a_a X3) (@ tptp.concat1878217064od_a_a Xs2)))) (forall ((Xss2 tptp.list_l1108175539od_a_a) (Ys2 tptp.list_P1467822637od_a_a) (Zs tptp.list_P1467822637od_a_a)) (=> (= (@ tptp.concat1878217064od_a_a Xss2) (@ (@ tptp.append1574001858od_a_a Ys2) Zs)) (=> (not (= Xss2 tptp.nil_li1885598003od_a_a)) (exists ((Xss12 tptp.list_l1108175539od_a_a) (Xs4 tptp.list_P1467822637od_a_a) (Xs3 tptp.list_P1467822637od_a_a) (Xss23 tptp.list_l1108175539od_a_a)) (and (= Xss2 (@ (@ tptp.append2141280328od_a_a Xss12) (@ (@ tptp.cons_l724116707od_a_a (@ (@ tptp.append1574001858od_a_a Xs4) Xs3)) Xss23))) (= Ys2 (@ (@ tptp.append1574001858od_a_a (@ tptp.concat1878217064od_a_a Xss12)) Xs4)) (= Zs (@ (@ tptp.append1574001858od_a_a Xs3) (@ tptp.concat1878217064od_a_a Xss23)))))))) (forall ((X1 tptp.list_P1467822637od_a_a) (X2 tptp.list_P1467822637od_a_a) (R tptp.set_Pr1948701895od_a_a) (P2 (-> tptp.list_P1467822637od_a_a tptp.list_P1467822637od_a_a Bool))) (=> (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a X1) X2)) (@ tptp.listre2074280881od_a_a R)) (=> (@ (@ P2 tptp.nil_Product_prod_a_a) tptp.nil_Product_prod_a_a) (=> (forall ((X4 tptp.product_prod_a_a) (Y4 tptp.product_prod_a_a) (Xs4 tptp.list_P1467822637od_a_a) (Ys4 tptp.list_P1467822637od_a_a)) (=> (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a X4) Y4)) R) (=> (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a Xs4) Ys4)) (@ tptp.listre2074280881od_a_a R)) (=> (@ (@ P2 Xs4) Ys4) (@ (@ P2 (@ (@ tptp.cons_P1921020637od_a_a X4) Xs4)) (@ (@ tptp.cons_P1921020637od_a_a Y4) Ys4)))))) (@ (@ P2 X1) X2))))) (forall ((X1 tptp.list_a) (X2 tptp.list_a) (R tptp.set_Product_prod_a_a) (P2 (-> tptp.list_a tptp.list_a Bool))) (=> (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a X1) X2)) (@ tptp.listrel_a_a R)) (=> (@ (@ P2 tptp.nil_a) tptp.nil_a) (=> (forall ((X4 tptp.a) (Y4 tptp.a) (Xs4 tptp.list_a) (Ys4 tptp.list_a)) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X4) Y4)) R) (=> (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a Xs4) Ys4)) (@ tptp.listrel_a_a R)) (=> (@ (@ P2 Xs4) Ys4) (@ (@ P2 (@ (@ tptp.cons_a X4) Xs4)) (@ (@ tptp.cons_a Y4) Ys4)))))) (@ (@ P2 X1) X2))))) (forall ((X3 tptp.product_prod_a_a) (Y3 tptp.product_prod_a_a) (R tptp.set_Pr1948701895od_a_a) (Xs2 tptp.list_P1467822637od_a_a) (Ys2 tptp.list_P1467822637od_a_a)) (let ((_let_1 (@ tptp.listre2074280881od_a_a R))) (=> (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a X3) Y3)) R) (=> (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a Xs2) Ys2)) _let_1) (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a (@ (@ tptp.cons_P1921020637od_a_a X3) Xs2)) (@ (@ tptp.cons_P1921020637od_a_a Y3) Ys2))) _let_1))))) (forall ((X3 tptp.a) (Y3 tptp.a) (R tptp.set_Product_prod_a_a) (Xs2 tptp.list_a) (Ys2 tptp.list_a)) (let ((_let_1 (@ tptp.listrel_a_a R))) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X3) Y3)) R) (=> (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a Xs2) Ys2)) _let_1) (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a (@ (@ tptp.cons_a X3) Xs2)) (@ (@ tptp.cons_a Y3) Ys2))) _let_1))))) (forall ((Y3 tptp.product_prod_a_a) (Ys2 tptp.list_P1467822637od_a_a) (Xs2 tptp.list_P1467822637od_a_a) (R tptp.set_Pr1948701895od_a_a)) (=> (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a (@ (@ tptp.cons_P1921020637od_a_a Y3) Ys2)) Xs2)) (@ tptp.listre2074280881od_a_a R)) (not (forall ((Y4 tptp.product_prod_a_a) (Ys4 tptp.list_P1467822637od_a_a)) (=> (= Xs2 (@ (@ tptp.cons_P1921020637od_a_a Y4) Ys4)) (=> (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a Y3) Y4)) R) (not (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a Ys2) Ys4)) (@ tptp.listre2074280881od_a_a R))))))))) (forall ((Y3 tptp.a) (Ys2 tptp.list_a) (Xs2 tptp.list_a) (R tptp.set_Product_prod_a_a)) (=> (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a (@ (@ tptp.cons_a Y3) Ys2)) Xs2)) (@ tptp.listrel_a_a R)) (not (forall ((Y4 tptp.a) (Ys4 tptp.list_a)) (=> (= Xs2 (@ (@ tptp.cons_a Y4) Ys4)) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a Y3) Y4)) R) (not (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a Ys2) Ys4)) (@ tptp.listrel_a_a R))))))))) (forall ((Xs2 tptp.list_P1467822637od_a_a) (Y3 tptp.product_prod_a_a) (Ys2 tptp.list_P1467822637od_a_a) (R tptp.set_Pr1948701895od_a_a)) (=> (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a Xs2) (@ (@ tptp.cons_P1921020637od_a_a Y3) Ys2))) (@ tptp.listre2074280881od_a_a R)) (not (forall ((X4 tptp.product_prod_a_a) (Xs4 tptp.list_P1467822637od_a_a)) (=> (= Xs2 (@ (@ tptp.cons_P1921020637od_a_a X4) Xs4)) (=> (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a X4) Y3)) R) (not (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a Xs4) Ys2)) (@ tptp.listre2074280881od_a_a R))))))))) (forall ((Xs2 tptp.list_a) (Y3 tptp.a) (Ys2 tptp.list_a) (R tptp.set_Product_prod_a_a)) (=> (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a Xs2) (@ (@ tptp.cons_a Y3) Ys2))) (@ tptp.listrel_a_a R)) (not (forall ((X4 tptp.a) (Xs4 tptp.list_a)) (=> (= Xs2 (@ (@ tptp.cons_a X4) Xs4)) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X4) Y3)) R) (not (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a Xs4) Ys2)) (@ tptp.listrel_a_a R))))))))) (forall ((A1 tptp.list_P1467822637od_a_a) (A22 tptp.list_P1467822637od_a_a) (R tptp.set_Pr1948701895od_a_a)) (=> (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a A1) A22)) (@ tptp.listre2074280881od_a_a R)) (=> (=> (= A1 tptp.nil_Product_prod_a_a) (not (= A22 tptp.nil_Product_prod_a_a))) (not (forall ((X4 tptp.product_prod_a_a) (Y4 tptp.product_prod_a_a) (Xs4 tptp.list_P1467822637od_a_a)) (=> (= A1 (@ (@ tptp.cons_P1921020637od_a_a X4) Xs4)) (forall ((Ys4 tptp.list_P1467822637od_a_a)) (=> (= A22 (@ (@ tptp.cons_P1921020637od_a_a Y4) Ys4)) (=> (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a X4) Y4)) R) (not (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a Xs4) Ys4)) (@ tptp.listre2074280881od_a_a R)))))))))))) (forall ((A1 tptp.list_a) (A22 tptp.list_a) (R tptp.set_Product_prod_a_a)) (=> (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a A1) A22)) (@ tptp.listrel_a_a R)) (=> (=> (= A1 tptp.nil_a) (not (= A22 tptp.nil_a))) (not (forall ((X4 tptp.a) (Y4 tptp.a) (Xs4 tptp.list_a)) (=> (= A1 (@ (@ tptp.cons_a X4) Xs4)) (forall ((Ys4 tptp.list_a)) (=> (= A22 (@ (@ tptp.cons_a Y4) Ys4)) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X4) Y4)) R) (not (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a Xs4) Ys4)) (@ tptp.listrel_a_a R)))))))))))) (forall ((A1 tptp.list_P1467822637od_a_a) (A22 tptp.list_P1467822637od_a_a) (R tptp.set_Pr1948701895od_a_a)) (= (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a A1) A22)) (@ tptp.listre2074280881od_a_a R)) (or (and (= A1 tptp.nil_Product_prod_a_a) (= A22 tptp.nil_Product_prod_a_a)) (exists ((X tptp.product_prod_a_a) (Y tptp.product_prod_a_a) (Xs tptp.list_P1467822637od_a_a) (Ys tptp.list_P1467822637od_a_a)) (and (= A1 (@ (@ tptp.cons_P1921020637od_a_a X) Xs)) (= A22 (@ (@ tptp.cons_P1921020637od_a_a Y) Ys)) (@ (@ tptp.member2057358096od_a_a (@ (@ tptp.produc1474507607od_a_a X) Y)) R) (@ (@ tptp.member1691432592od_a_a (@ (@ tptp.produc85179863od_a_a Xs) Ys)) (@ tptp.listre2074280881od_a_a R))))))) (forall ((A1 tptp.list_a) (A22 tptp.list_a) (R tptp.set_Product_prod_a_a)) (= (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a A1) A22)) (@ tptp.listrel_a_a R)) (or (and (= A1 tptp.nil_a) (= A22 tptp.nil_a)) (exists ((X tptp.a) (Y tptp.a) (Xs tptp.list_a) (Ys tptp.list_a)) (and (= A1 (@ (@ tptp.cons_a X) Xs)) (= A22 (@ (@ tptp.cons_a Y) Ys)) (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X) Y)) R) (@ (@ tptp.member1250517072list_a (@ (@ tptp.produc1448356631list_a Xs) Ys)) (@ tptp.listrel_a_a R))))))) (forall ((P2 Bool)) (or (= P2 true) (= P2 false))) (forall ((X3 tptp.list_P1467822637od_a_a) (Y3 tptp.list_P1467822637od_a_a)) (= (@ (@ (@ tptp.if_lis321365491od_a_a false) X3) Y3) Y3)) (forall ((X3 tptp.list_P1467822637od_a_a) (Y3 tptp.list_P1467822637od_a_a)) (= (@ (@ (@ tptp.if_lis321365491od_a_a true) X3) Y3) X3)) _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 1.01/1.28 )
% 1.01/1.28 % SZS output end Proof for ITP092^1
% 1.01/1.28 % cvc5---1.0.5 exiting
% 1.01/1.28 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------