TSTP Solution File: ITP119^1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP119^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n009.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 03:18:23 EDT 2023
% Result : Theorem 0.44s 0.72s
% Output : Proof 0.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ITP119^1 : TPTP v8.1.2. Released v7.5.0.
% 0.07/0.12 % Command : do_cvc5 %s %d
% 0.12/0.31 % Computer : n009.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Sun Aug 27 16:36:20 EDT 2023
% 0.16/0.31 % CPUTime :
% 0.16/0.41 %----Proving TH0
% 0.16/0.42 %------------------------------------------------------------------------------
% 0.16/0.42 % File : ITP119^1 : TPTP v8.1.2. Released v7.5.0.
% 0.16/0.42 % Domain : Interactive Theorem Proving
% 0.16/0.42 % Problem : Sledgehammer Modular_Distrib_Lattice problem prob_144__3260118_1
% 0.16/0.42 % Version : Especial.
% 0.16/0.42 % English :
% 0.16/0.42
% 0.16/0.42 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.16/0.42 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.16/0.42 % Source : [Des21]
% 0.16/0.42 % Names : Modular_Distrib_Lattice/prob_144__3260118_1 [Des21]
% 0.16/0.42
% 0.16/0.42 % Status : ContradictoryAxioms
% 0.16/0.42 % Rating : 0.23 v8.1.0, 0.36 v7.5.0
% 0.16/0.42 % Syntax : Number of formulae : 425 ( 211 unt; 67 typ; 0 def)
% 0.16/0.42 % Number of atoms : 818 ( 483 equ; 0 cnn)
% 0.16/0.42 % Maximal formula atoms : 13 ( 2 avg)
% 0.16/0.42 % Number of connectives : 3280 ( 180 ~; 24 |; 99 &;2599 @)
% 0.16/0.42 % ( 0 <=>; 378 =>; 0 <=; 0 <~>)
% 0.16/0.42 % Maximal formula depth : 21 ( 6 avg)
% 0.16/0.42 % Number of types : 5 ( 4 usr)
% 0.16/0.42 % Number of type conns : 485 ( 485 >; 0 *; 0 +; 0 <<)
% 0.16/0.42 % Number of symbols : 65 ( 63 usr; 7 con; 0-6 aty)
% 0.16/0.42 % Number of variables : 1176 ( 18 ^;1063 !; 95 ?;1176 :)
% 0.16/0.42 % SPC : TH0_CAX_EQU_NAR
% 0.16/0.42
% 0.16/0.42 % Comments : This file was generated by Sledgehammer 2021-02-23 15:43:54.694
% 0.16/0.42 %------------------------------------------------------------------------------
% 0.16/0.42 % Could-be-implicit typings (4)
% 0.16/0.42 thf(ty_n_t__List__Olist_It__List__Olist_It__List__Olist_Itf__a_J_J_J,type,
% 0.16/0.42 list_list_list_a: $tType ).
% 0.16/0.42
% 0.16/0.42 thf(ty_n_t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 0.16/0.42 list_list_a: $tType ).
% 0.16/0.42
% 0.16/0.42 thf(ty_n_t__List__Olist_Itf__a_J,type,
% 0.16/0.42 list_a: $tType ).
% 0.16/0.42
% 0.16/0.42 thf(ty_n_tf__a,type,
% 0.16/0.42 a: $tType ).
% 0.16/0.42
% 0.16/0.42 % Explicit typings (63)
% 0.16/0.42 thf(sy_c_Finite__Set_Ocomp__fun__idem_001tf__a_001tf__a,type,
% 0.16/0.42 finite40241356em_a_a: ( a > a > a ) > $o ).
% 0.16/0.42
% 0.16/0.42 thf(sy_c_Groups_Oabel__semigroup_001t__List__Olist_Itf__a_J,type,
% 0.16/0.42 abel_s1075322906list_a: ( list_a > list_a > list_a ) > $o ).
% 0.16/0.42
% 0.16/0.42 thf(sy_c_Groups_Oabel__semigroup_001tf__a,type,
% 0.16/0.42 abel_semigroup_a: ( a > a > a ) > $o ).
% 0.16/0.42
% 0.16/0.42 thf(sy_c_Groups_Oabel__semigroup__axioms_001t__List__Olist_Itf__a_J,type,
% 0.16/0.42 abel_s374399671list_a: ( list_a > list_a > list_a ) > $o ).
% 0.16/0.42
% 0.16/0.42 thf(sy_c_Groups_Oabel__semigroup__axioms_001tf__a,type,
% 0.16/0.42 abel_s2117090225ioms_a: ( a > a > a ) > $o ).
% 0.16/0.42
% 0.16/0.42 thf(sy_c_Groups_Osemigroup_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 0.16/0.42 semigr656274520list_a: ( list_list_a > list_list_a > list_list_a ) > $o ).
% 0.16/0.42
% 0.16/0.42 thf(sy_c_Groups_Osemigroup_001t__List__Olist_Itf__a_J,type,
% 0.16/0.42 semigroup_list_a: ( list_a > list_a > list_a ) > $o ).
% 0.16/0.42
% 0.16/0.42 thf(sy_c_Groups_Osemigroup_001tf__a,type,
% 0.16/0.42 semigroup_a: ( a > a > a ) > $o ).
% 0.16/0.42
% 0.16/0.42 thf(sy_c_Lattices_Osemilattice_001tf__a,type,
% 0.16/0.42 semilattice_a: ( a > a > a ) > $o ).
% 0.16/0.42
% 0.16/0.42 thf(sy_c_Lattices_Osemilattice__axioms_001tf__a,type,
% 0.16/0.42 semilattice_axioms_a: ( a > a > a ) > $o ).
% 0.16/0.42
% 0.16/0.42 thf(sy_c_Lattices__Big_Osemilattice__set_001tf__a,type,
% 0.16/0.42 lattic1885654924_set_a: ( a > a > a ) > $o ).
% 0.16/0.42
% 0.16/0.42 thf(sy_c_List_Oappend_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 0.16/0.42 append_list_list_a: list_list_list_a > list_list_list_a > list_list_list_a ).
% 0.16/0.42
% 0.16/0.42 thf(sy_c_List_Oappend_001t__List__Olist_Itf__a_J,type,
% 0.16/0.42 append_list_a: list_list_a > list_list_a > list_list_a ).
% 0.16/0.42
% 0.16/0.42 thf(sy_c_List_Oappend_001tf__a,type,
% 0.16/0.42 append_a: list_a > list_a > list_a ).
% 0.16/0.42
% 0.16/0.42 thf(sy_c_List_Obind_001t__List__Olist_Itf__a_J_001t__List__Olist_Itf__a_J,type,
% 0.16/0.42 bind_list_a_list_a: list_list_a > ( list_a > list_list_a ) > list_list_a ).
% 0.16/0.42
% 0.16/0.42 thf(sy_c_List_Obind_001t__List__Olist_Itf__a_J_001tf__a,type,
% 0.16/0.42 bind_list_a_a: list_list_a > ( list_a > list_a ) > list_a ).
% 0.16/0.42
% 0.16/0.42 thf(sy_c_List_Obind_001tf__a_001t__List__Olist_Itf__a_J,type,
% 0.16/0.42 bind_a_list_a: list_a > ( a > list_list_a ) > list_list_a ).
% 0.16/0.42
% 0.16/0.42 thf(sy_c_List_Obind_001tf__a_001tf__a,type,
% 0.16/0.42 bind_a_a: list_a > ( a > list_a ) > list_a ).
% 0.16/0.42
% 0.16/0.42 thf(sy_c_List_Obutlast_001t__List__Olist_Itf__a_J,type,
% 0.16/0.42 butlast_list_a: list_list_a > list_list_a ).
% 0.16/0.42
% 0.16/0.42 thf(sy_c_List_Obutlast_001tf__a,type,
% 0.16/0.42 butlast_a: list_a > list_a ).
% 0.16/0.42
% 0.16/0.42 thf(sy_c_List_Oconcat_001t__List__Olist_Itf__a_J,type,
% 0.16/0.42 concat_list_a: list_list_list_a > list_list_a ).
% 0.16/0.42
% 0.16/0.42 thf(sy_c_List_Oconcat_001tf__a,type,
% 0.16/0.42 concat_a: list_list_a > list_a ).
% 0.16/0.42
% 0.16/0.42 thf(sy_c_List_Oinsert_001t__List__Olist_Itf__a_J,type,
% 0.16/0.42 insert_list_a: list_a > list_list_a > list_list_a ).
% 0.16/0.42
% 0.16/0.42 thf(sy_c_List_Oinsert_001tf__a,type,
% 0.16/0.42 insert_a: a > list_a > list_a ).
% 0.16/0.42
% 0.16/0.42 thf(sy_c_List_Olast_001t__List__Olist_Itf__a_J,type,
% 0.16/0.42 last_list_a: list_list_a > list_a ).
% 0.16/0.42
% 0.16/0.42 thf(sy_c_List_Olast_001tf__a,type,
% 0.16/0.42 last_a: list_a > a ).
% 0.16/0.42
% 0.16/0.42 thf(sy_c_List_Olist_OCons_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 0.16/0.42 cons_list_list_a: list_list_a > list_list_list_a > list_list_list_a ).
% 0.16/0.42
% 0.16/0.42 thf(sy_c_List_Olist_OCons_001t__List__Olist_Itf__a_J,type,
% 0.16/0.42 cons_list_a: list_a > list_list_a > list_list_a ).
% 0.16/0.42
% 0.16/0.42 thf(sy_c_List_Olist_OCons_001tf__a,type,
% 0.16/0.42 cons_a: a > list_a > list_a ).
% 0.16/0.42
% 0.16/0.42 thf(sy_c_List_Olist_ONil_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 0.16/0.42 nil_list_list_a: list_list_list_a ).
% 0.16/0.42
% 0.16/0.42 thf(sy_c_List_Olist_ONil_001t__List__Olist_Itf__a_J,type,
% 0.16/0.42 nil_list_a: list_list_a ).
% 0.16/0.42
% 0.16/0.42 thf(sy_c_List_Olist_ONil_001tf__a,type,
% 0.16/0.42 nil_a: list_a ).
% 0.16/0.42
% 0.16/0.42 thf(sy_c_List_Olist__ex1_001t__List__Olist_Itf__a_J,type,
% 0.16/0.42 list_ex1_list_a: ( list_a > $o ) > list_list_a > $o ).
% 0.16/0.42
% 0.16/0.42 thf(sy_c_List_Olist__ex1_001tf__a,type,
% 0.16/0.42 list_ex1_a: ( a > $o ) > list_a > $o ).
% 0.16/0.42
% 0.16/0.42 thf(sy_c_List_Omaps_001t__List__Olist_Itf__a_J_001t__List__Olist_Itf__a_J,type,
% 0.16/0.42 maps_list_a_list_a: ( list_a > list_list_a ) > list_list_a > list_list_a ).
% 0.16/0.42
% 0.16/0.42 thf(sy_c_List_Omaps_001t__List__Olist_Itf__a_J_001tf__a,type,
% 0.16/0.42 maps_list_a_a: ( list_a > list_a ) > list_list_a > list_a ).
% 0.16/0.42
% 0.16/0.42 thf(sy_c_List_Omaps_001tf__a_001t__List__Olist_Itf__a_J,type,
% 0.16/0.42 maps_a_list_a: ( a > list_list_a ) > list_a > list_list_a ).
% 0.16/0.42
% 0.16/0.42 thf(sy_c_List_Omaps_001tf__a_001tf__a,type,
% 0.16/0.42 maps_a_a: ( a > list_a ) > list_a > list_a ).
% 0.16/0.42
% 0.16/0.42 thf(sy_c_List_Oord_Olexordp_001t__List__Olist_Itf__a_J,type,
% 0.16/0.42 lexordp_list_a: ( list_a > list_a > $o ) > list_list_a > list_list_a > $o ).
% 0.16/0.42
% 0.16/0.42 thf(sy_c_List_Oord_Olexordp_001tf__a,type,
% 0.16/0.42 lexordp_a: ( a > a > $o ) > list_a > list_a > $o ).
% 0.16/0.42
% 0.16/0.42 thf(sy_c_List_Oord_Olexordp__eq_001t__List__Olist_Itf__a_J,type,
% 0.16/0.42 lexordp_eq_list_a: ( list_a > list_a > $o ) > list_list_a > list_list_a > $o ).
% 0.16/0.42
% 0.16/0.42 thf(sy_c_List_Oord_Olexordp__eq_001tf__a,type,
% 0.16/0.42 lexordp_eq_a: ( a > a > $o ) > list_a > list_a > $o ).
% 0.16/0.42
% 0.16/0.42 thf(sy_c_List_Oproduct__lists_001t__List__Olist_Itf__a_J,type,
% 0.16/0.42 product_lists_list_a: list_list_list_a > list_list_list_a ).
% 0.16/0.42
% 0.16/0.42 thf(sy_c_List_Oproduct__lists_001tf__a,type,
% 0.16/0.42 product_lists_a: list_list_a > list_list_a ).
% 0.16/0.42
% 0.16/0.42 thf(sy_c_List_Orotate1_001t__List__Olist_Itf__a_J,type,
% 0.16/0.42 rotate1_list_a: list_list_a > list_list_a ).
% 0.16/0.42
% 0.16/0.42 thf(sy_c_List_Orotate1_001tf__a,type,
% 0.16/0.42 rotate1_a: list_a > list_a ).
% 0.16/0.42
% 0.16/0.42 thf(sy_c_List_Osubseqs_001t__List__Olist_Itf__a_J,type,
% 0.16/0.42 subseqs_list_a: list_list_a > list_list_list_a ).
% 0.16/0.42
% 0.16/0.42 thf(sy_c_List_Osubseqs_001tf__a,type,
% 0.16/0.42 subseqs_a: list_a > list_list_a ).
% 0.16/0.42
% 0.16/0.42 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_OM5__lattice_001tf__a,type,
% 0.16/0.42 modula1376131916tice_a: ( a > a > a ) > ( a > a > $o ) > ( a > a > a ) > a > a > a > $o ).
% 0.16/0.42
% 0.16/0.42 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_ON5__lattice_001tf__a,type,
% 0.16/0.42 modula397570059tice_a: ( a > a > a ) > ( a > a > $o ) > ( a > a > a ) > a > a > a > $o ).
% 0.16/0.42
% 0.16/0.42 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Oa__aux_001tf__a,type,
% 0.16/0.42 modula17988509_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
% 0.16/0.42
% 0.16/0.42 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Ob__aux_001tf__a,type,
% 0.16/0.42 modula1373251614_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
% 0.16/0.42
% 0.16/0.42 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Oc__aux_001tf__a,type,
% 0.16/0.42 modula581031071_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
% 0.16/0.42
% 0.16/0.42 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Od__aux_001tf__a,type,
% 0.16/0.42 modula1936294176_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
% 0.16/0.42
% 0.16/0.42 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Oe__aux_001tf__a,type,
% 0.16/0.42 modula1144073633_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
% 0.16/0.42
% 0.16/0.42 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Ono__distrib_001tf__a,type,
% 0.16/0.42 modula1962211574trib_a: ( a > a > a ) > ( a > a > $o ) > ( a > a > a ) > a > a > a > $o ).
% 0.16/0.42
% 0.16/0.42 thf(sy_c_Relation_Otransp_001tf__a,type,
% 0.16/0.42 transp_a: ( a > a > $o ) > $o ).
% 0.16/0.42
% 0.16/0.42 thf(sy_v_a,type,
% 0.16/0.42 a2: a ).
% 0.16/0.42
% 0.16/0.42 thf(sy_v_b,type,
% 0.16/0.42 b: a ).
% 0.16/0.42
% 0.16/0.42 thf(sy_v_c,type,
% 0.16/0.42 c: a ).
% 0.16/0.42
% 0.16/0.42 thf(sy_v_inf,type,
% 0.16/0.42 inf: a > a > a ).
% 0.16/0.42
% 0.16/0.42 thf(sy_v_less,type,
% 0.16/0.42 less: a > a > $o ).
% 0.16/0.42
% 0.16/0.42 thf(sy_v_sup,type,
% 0.16/0.42 sup: a > a > a ).
% 0.16/0.42
% 0.16/0.42 % Relevant facts (352)
% 0.16/0.42 thf(fact_0_local_Odual__order_Oasym,axiom,
% 0.16/0.42 ! [B: a,A: a] :
% 0.16/0.42 ( ( less @ B @ A )
% 0.16/0.42 => ~ ( less @ A @ B ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.dual_order.asym
% 0.16/0.42 thf(fact_1_local_Odual__order_Ostrict__implies__not__eq,axiom,
% 0.16/0.42 ! [B: a,A: a] :
% 0.16/0.42 ( ( less @ B @ A )
% 0.16/0.42 => ( A != B ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.dual_order.strict_implies_not_eq
% 0.16/0.42 thf(fact_2_local_Odual__order_Ostrict__trans,axiom,
% 0.16/0.42 ! [B: a,A: a,C: a] :
% 0.16/0.42 ( ( less @ B @ A )
% 0.16/0.42 => ( ( less @ C @ B )
% 0.16/0.42 => ( less @ C @ A ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.dual_order.strict_trans
% 0.16/0.42 thf(fact_3_local_Oless__asym,axiom,
% 0.16/0.42 ! [X: a,Y: a] :
% 0.16/0.42 ( ( less @ X @ Y )
% 0.16/0.42 => ~ ( less @ Y @ X ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.less_asym
% 0.16/0.42 thf(fact_4_local_Oless__asym_H,axiom,
% 0.16/0.42 ! [A: a,B: a] :
% 0.16/0.42 ( ( less @ A @ B )
% 0.16/0.42 => ~ ( less @ B @ A ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.less_asym'
% 0.16/0.42 thf(fact_5_local_Oless__imp__neq,axiom,
% 0.16/0.42 ! [X: a,Y: a] :
% 0.16/0.42 ( ( less @ X @ Y )
% 0.16/0.42 => ( X != Y ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.less_imp_neq
% 0.16/0.42 thf(fact_6_local_Oless__imp__not__eq,axiom,
% 0.16/0.42 ! [X: a,Y: a] :
% 0.16/0.42 ( ( less @ X @ Y )
% 0.16/0.42 => ( X != Y ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.less_imp_not_eq
% 0.16/0.42 thf(fact_7_local_Oless__imp__not__eq2,axiom,
% 0.16/0.42 ! [X: a,Y: a] :
% 0.16/0.42 ( ( less @ X @ Y )
% 0.16/0.42 => ( Y != X ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.less_imp_not_eq2
% 0.16/0.42 thf(fact_8_local_Oless__imp__not__less,axiom,
% 0.16/0.42 ! [X: a,Y: a] :
% 0.16/0.42 ( ( less @ X @ Y )
% 0.16/0.42 => ~ ( less @ Y @ X ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.less_imp_not_less
% 0.16/0.42 thf(fact_9_local_Oless__imp__triv,axiom,
% 0.16/0.42 ! [X: a,Y: a,P: $o] :
% 0.16/0.42 ( ( less @ X @ Y )
% 0.16/0.42 => ( ( less @ Y @ X )
% 0.16/0.42 => P ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.less_imp_triv
% 0.16/0.42 thf(fact_10_local_Oless__irrefl,axiom,
% 0.16/0.42 ! [X: a] :
% 0.16/0.42 ~ ( less @ X @ X ) ).
% 0.16/0.42
% 0.16/0.42 % local.less_irrefl
% 0.16/0.42 thf(fact_11_local_Oless__not__sym,axiom,
% 0.16/0.42 ! [X: a,Y: a] :
% 0.16/0.42 ( ( less @ X @ Y )
% 0.16/0.42 => ~ ( less @ Y @ X ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.less_not_sym
% 0.16/0.42 thf(fact_12_local_Oless__trans,axiom,
% 0.16/0.42 ! [X: a,Y: a,Z: a] :
% 0.16/0.42 ( ( less @ X @ Y )
% 0.16/0.42 => ( ( less @ Y @ Z )
% 0.16/0.42 => ( less @ X @ Z ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.less_trans
% 0.16/0.42 thf(fact_13_local_Oord__eq__less__trans,axiom,
% 0.16/0.42 ! [A: a,B: a,C: a] :
% 0.16/0.42 ( ( A = B )
% 0.16/0.42 => ( ( less @ B @ C )
% 0.16/0.42 => ( less @ A @ C ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.ord_eq_less_trans
% 0.16/0.42 thf(fact_14_local_Oord__less__eq__trans,axiom,
% 0.16/0.42 ! [A: a,B: a,C: a] :
% 0.16/0.42 ( ( less @ A @ B )
% 0.16/0.42 => ( ( B = C )
% 0.16/0.42 => ( less @ A @ C ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.ord_less_eq_trans
% 0.16/0.42 thf(fact_15_local_Oorder_Oasym,axiom,
% 0.16/0.42 ! [A: a,B: a] :
% 0.16/0.42 ( ( less @ A @ B )
% 0.16/0.42 => ~ ( less @ B @ A ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.order.asym
% 0.16/0.42 thf(fact_16_local_Oorder_Oirrefl,axiom,
% 0.16/0.42 ! [A: a] :
% 0.16/0.42 ~ ( less @ A @ A ) ).
% 0.16/0.42
% 0.16/0.42 % local.order.irrefl
% 0.16/0.42 thf(fact_17_local_Oorder_Ostrict__implies__not__eq,axiom,
% 0.16/0.42 ! [A: a,B: a] :
% 0.16/0.42 ( ( less @ A @ B )
% 0.16/0.42 => ( A != B ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.order.strict_implies_not_eq
% 0.16/0.42 thf(fact_18_local_Oorder_Ostrict__trans,axiom,
% 0.16/0.42 ! [A: a,B: a,C: a] :
% 0.16/0.42 ( ( less @ A @ B )
% 0.16/0.42 => ( ( less @ B @ C )
% 0.16/0.42 => ( less @ A @ C ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.order.strict_trans
% 0.16/0.42 thf(fact_19_local_Oinf_Oassoc,axiom,
% 0.16/0.42 ! [A: a,B: a,C: a] :
% 0.16/0.42 ( ( inf @ ( inf @ A @ B ) @ C )
% 0.16/0.42 = ( inf @ A @ ( inf @ B @ C ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.inf.assoc
% 0.16/0.42 thf(fact_20_local_Oinf_Ocommute,axiom,
% 0.16/0.42 ! [A: a,B: a] :
% 0.16/0.42 ( ( inf @ A @ B )
% 0.16/0.42 = ( inf @ B @ A ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.inf.commute
% 0.16/0.42 thf(fact_21_local_Oinf_Oleft__commute,axiom,
% 0.16/0.42 ! [B: a,A: a,C: a] :
% 0.16/0.42 ( ( inf @ B @ ( inf @ A @ C ) )
% 0.16/0.42 = ( inf @ A @ ( inf @ B @ C ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.inf.left_commute
% 0.16/0.42 thf(fact_22_local_Oinf__assoc,axiom,
% 0.16/0.42 ! [X: a,Y: a,Z: a] :
% 0.16/0.42 ( ( inf @ ( inf @ X @ Y ) @ Z )
% 0.16/0.42 = ( inf @ X @ ( inf @ Y @ Z ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.inf_assoc
% 0.16/0.42 thf(fact_23_local_Oinf__commute,axiom,
% 0.16/0.42 ! [X: a,Y: a] :
% 0.16/0.42 ( ( inf @ X @ Y )
% 0.16/0.42 = ( inf @ Y @ X ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.inf_commute
% 0.16/0.42 thf(fact_24_local_Oinf__left__commute,axiom,
% 0.16/0.42 ! [X: a,Y: a,Z: a] :
% 0.16/0.42 ( ( inf @ X @ ( inf @ Y @ Z ) )
% 0.16/0.42 = ( inf @ Y @ ( inf @ X @ Z ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.inf_left_commute
% 0.16/0.42 thf(fact_25_local_Osup_Oassoc,axiom,
% 0.16/0.42 ! [A: a,B: a,C: a] :
% 0.16/0.42 ( ( sup @ ( sup @ A @ B ) @ C )
% 0.16/0.42 = ( sup @ A @ ( sup @ B @ C ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.sup.assoc
% 0.16/0.42 thf(fact_26_local_Osup_Ocommute,axiom,
% 0.16/0.42 ! [A: a,B: a] :
% 0.16/0.42 ( ( sup @ A @ B )
% 0.16/0.42 = ( sup @ B @ A ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.sup.commute
% 0.16/0.42 thf(fact_27_local_Osup_Oleft__commute,axiom,
% 0.16/0.42 ! [B: a,A: a,C: a] :
% 0.16/0.42 ( ( sup @ B @ ( sup @ A @ C ) )
% 0.16/0.42 = ( sup @ A @ ( sup @ B @ C ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.sup.left_commute
% 0.16/0.42 thf(fact_28_local_Osup__assoc,axiom,
% 0.16/0.42 ! [X: a,Y: a,Z: a] :
% 0.16/0.42 ( ( sup @ ( sup @ X @ Y ) @ Z )
% 0.16/0.42 = ( sup @ X @ ( sup @ Y @ Z ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.sup_assoc
% 0.16/0.42 thf(fact_29_local_Osup__commute,axiom,
% 0.16/0.42 ! [X: a,Y: a] :
% 0.16/0.42 ( ( sup @ X @ Y )
% 0.16/0.42 = ( sup @ Y @ X ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.sup_commute
% 0.16/0.42 thf(fact_30_local_Osup__left__commute,axiom,
% 0.16/0.42 ! [X: a,Y: a,Z: a] :
% 0.16/0.42 ( ( sup @ X @ ( sup @ Y @ Z ) )
% 0.16/0.42 = ( sup @ Y @ ( sup @ X @ Z ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.sup_left_commute
% 0.16/0.42 thf(fact_31_local_Oinf_Ostrict__boundedE,axiom,
% 0.16/0.42 ! [A: a,B: a,C: a] :
% 0.16/0.42 ( ( less @ A @ ( inf @ B @ C ) )
% 0.16/0.42 => ~ ( ( less @ A @ B )
% 0.16/0.42 => ~ ( less @ A @ C ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.inf.strict_boundedE
% 0.16/0.42 thf(fact_32_local_Oinf_Ostrict__coboundedI1,axiom,
% 0.16/0.42 ! [A: a,C: a,B: a] :
% 0.16/0.42 ( ( less @ A @ C )
% 0.16/0.42 => ( less @ ( inf @ A @ B ) @ C ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.inf.strict_coboundedI1
% 0.16/0.42 thf(fact_33_local_Oinf_Ostrict__coboundedI2,axiom,
% 0.16/0.42 ! [B: a,C: a,A: a] :
% 0.16/0.42 ( ( less @ B @ C )
% 0.16/0.42 => ( less @ ( inf @ A @ B ) @ C ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.inf.strict_coboundedI2
% 0.16/0.42 thf(fact_34_local_Oinf_Ostrict__order__iff,axiom,
% 0.16/0.42 ! [A: a,B: a] :
% 0.16/0.42 ( ( less @ A @ B )
% 0.16/0.42 = ( ( A
% 0.16/0.42 = ( inf @ A @ B ) )
% 0.16/0.42 & ( A != B ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.inf.strict_order_iff
% 0.16/0.42 thf(fact_35_local_Oless__infI1,axiom,
% 0.16/0.42 ! [A: a,X: a,B: a] :
% 0.16/0.42 ( ( less @ A @ X )
% 0.16/0.42 => ( less @ ( inf @ A @ B ) @ X ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.less_infI1
% 0.16/0.42 thf(fact_36_local_Oless__infI2,axiom,
% 0.16/0.42 ! [B: a,X: a,A: a] :
% 0.16/0.42 ( ( less @ B @ X )
% 0.16/0.42 => ( less @ ( inf @ A @ B ) @ X ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.less_infI2
% 0.16/0.42 thf(fact_37_local_Oless__supI1,axiom,
% 0.16/0.42 ! [X: a,A: a,B: a] :
% 0.16/0.42 ( ( less @ X @ A )
% 0.16/0.42 => ( less @ X @ ( sup @ A @ B ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.less_supI1
% 0.16/0.42 thf(fact_38_local_Oless__supI2,axiom,
% 0.16/0.42 ! [X: a,B: a,A: a] :
% 0.16/0.42 ( ( less @ X @ B )
% 0.16/0.42 => ( less @ X @ ( sup @ A @ B ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.less_supI2
% 0.16/0.42 thf(fact_39_local_Osup_Ostrict__boundedE,axiom,
% 0.16/0.42 ! [B: a,C: a,A: a] :
% 0.16/0.42 ( ( less @ ( sup @ B @ C ) @ A )
% 0.16/0.42 => ~ ( ( less @ B @ A )
% 0.16/0.42 => ~ ( less @ C @ A ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.sup.strict_boundedE
% 0.16/0.42 thf(fact_40_local_Osup_Ostrict__coboundedI1,axiom,
% 0.16/0.42 ! [C: a,A: a,B: a] :
% 0.16/0.42 ( ( less @ C @ A )
% 0.16/0.42 => ( less @ C @ ( sup @ A @ B ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.sup.strict_coboundedI1
% 0.16/0.42 thf(fact_41_local_Osup_Ostrict__coboundedI2,axiom,
% 0.16/0.42 ! [C: a,B: a,A: a] :
% 0.16/0.42 ( ( less @ C @ B )
% 0.16/0.42 => ( less @ C @ ( sup @ A @ B ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.sup.strict_coboundedI2
% 0.16/0.42 thf(fact_42_local_Osup_Ostrict__order__iff,axiom,
% 0.16/0.42 ! [B: a,A: a] :
% 0.16/0.42 ( ( less @ B @ A )
% 0.16/0.42 = ( ( A
% 0.16/0.42 = ( sup @ A @ B ) )
% 0.16/0.42 & ( A != B ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.sup.strict_order_iff
% 0.16/0.42 thf(fact_43_local_Odistrib__imp1,axiom,
% 0.16/0.42 ! [X: a,Y: a,Z: a] :
% 0.16/0.42 ( ! [X2: a,Y2: a,Z2: a] :
% 0.16/0.42 ( ( inf @ X2 @ ( sup @ Y2 @ Z2 ) )
% 0.16/0.42 = ( sup @ ( inf @ X2 @ Y2 ) @ ( inf @ X2 @ Z2 ) ) )
% 0.16/0.42 => ( ( sup @ X @ ( inf @ Y @ Z ) )
% 0.16/0.42 = ( inf @ ( sup @ X @ Y ) @ ( sup @ X @ Z ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.distrib_imp1
% 0.16/0.42 thf(fact_44_local_Odistrib__imp2,axiom,
% 0.16/0.42 ! [X: a,Y: a,Z: a] :
% 0.16/0.42 ( ! [X2: a,Y2: a,Z2: a] :
% 0.16/0.42 ( ( sup @ X2 @ ( inf @ Y2 @ Z2 ) )
% 0.16/0.42 = ( inf @ ( sup @ X2 @ Y2 ) @ ( sup @ X2 @ Z2 ) ) )
% 0.16/0.42 => ( ( inf @ X @ ( sup @ Y @ Z ) )
% 0.16/0.42 = ( sup @ ( inf @ X @ Y ) @ ( inf @ X @ Z ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.distrib_imp2
% 0.16/0.42 thf(fact_45_local_Oinf_Oidem,axiom,
% 0.16/0.42 ! [A: a] :
% 0.16/0.42 ( ( inf @ A @ A )
% 0.16/0.42 = A ) ).
% 0.16/0.42
% 0.16/0.42 % local.inf.idem
% 0.16/0.42 thf(fact_46_local_Oinf_Oleft__idem,axiom,
% 0.16/0.42 ! [A: a,B: a] :
% 0.16/0.42 ( ( inf @ A @ ( inf @ A @ B ) )
% 0.16/0.42 = ( inf @ A @ B ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.inf.left_idem
% 0.16/0.42 thf(fact_47_local_Oinf_Oright__idem,axiom,
% 0.16/0.42 ! [A: a,B: a] :
% 0.16/0.42 ( ( inf @ ( inf @ A @ B ) @ B )
% 0.16/0.42 = ( inf @ A @ B ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.inf.right_idem
% 0.16/0.42 thf(fact_48_local_Oinf__idem,axiom,
% 0.16/0.42 ! [X: a] :
% 0.16/0.42 ( ( inf @ X @ X )
% 0.16/0.42 = X ) ).
% 0.16/0.42
% 0.16/0.42 % local.inf_idem
% 0.16/0.42 thf(fact_49_local_Oinf__left__idem,axiom,
% 0.16/0.42 ! [X: a,Y: a] :
% 0.16/0.42 ( ( inf @ X @ ( inf @ X @ Y ) )
% 0.16/0.42 = ( inf @ X @ Y ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.inf_left_idem
% 0.16/0.42 thf(fact_50_local_Oinf__right__idem,axiom,
% 0.16/0.42 ! [X: a,Y: a] :
% 0.16/0.42 ( ( inf @ ( inf @ X @ Y ) @ Y )
% 0.16/0.42 = ( inf @ X @ Y ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.inf_right_idem
% 0.16/0.42 thf(fact_51_local_Osup_Oidem,axiom,
% 0.16/0.42 ! [A: a] :
% 0.16/0.42 ( ( sup @ A @ A )
% 0.16/0.42 = A ) ).
% 0.16/0.42
% 0.16/0.42 % local.sup.idem
% 0.16/0.42 thf(fact_52_local_Osup_Oleft__idem,axiom,
% 0.16/0.42 ! [A: a,B: a] :
% 0.16/0.42 ( ( sup @ A @ ( sup @ A @ B ) )
% 0.16/0.42 = ( sup @ A @ B ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.sup.left_idem
% 0.16/0.42 thf(fact_53_local_Osup_Oright__idem,axiom,
% 0.16/0.42 ! [A: a,B: a] :
% 0.16/0.42 ( ( sup @ ( sup @ A @ B ) @ B )
% 0.16/0.42 = ( sup @ A @ B ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.sup.right_idem
% 0.16/0.42 thf(fact_54_local_Osup__idem,axiom,
% 0.16/0.42 ! [X: a] :
% 0.16/0.42 ( ( sup @ X @ X )
% 0.16/0.42 = X ) ).
% 0.16/0.42
% 0.16/0.42 % local.sup_idem
% 0.16/0.42 thf(fact_55_local_Osup__left__idem,axiom,
% 0.16/0.42 ! [X: a,Y: a] :
% 0.16/0.42 ( ( sup @ X @ ( sup @ X @ Y ) )
% 0.16/0.42 = ( sup @ X @ Y ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.sup_left_idem
% 0.16/0.42 thf(fact_56_M5__lattice__def,axiom,
% 0.16/0.42 ! [A: a,B: a,C: a] :
% 0.16/0.42 ( ( modula1376131916tice_a @ inf @ less @ sup @ A @ B @ C )
% 0.16/0.42 = ( ( ( inf @ A @ B )
% 0.16/0.42 = ( inf @ B @ C ) )
% 0.16/0.42 & ( ( inf @ C @ A )
% 0.16/0.42 = ( inf @ B @ C ) )
% 0.16/0.42 & ( ( sup @ A @ B )
% 0.16/0.42 = ( sup @ B @ C ) )
% 0.16/0.42 & ( ( sup @ C @ A )
% 0.16/0.42 = ( sup @ B @ C ) )
% 0.16/0.42 & ( less @ ( inf @ A @ B ) @ ( sup @ A @ B ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % M5_lattice_def
% 0.16/0.42 thf(fact_57_N5__lattice__def,axiom,
% 0.16/0.42 ! [A: a,B: a,C: a] :
% 0.16/0.42 ( ( modula397570059tice_a @ inf @ less @ sup @ A @ B @ C )
% 0.16/0.42 = ( ( ( inf @ A @ C )
% 0.16/0.42 = ( inf @ B @ C ) )
% 0.16/0.42 & ( less @ A @ B )
% 0.16/0.42 & ( ( sup @ A @ C )
% 0.16/0.42 = ( sup @ B @ C ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % N5_lattice_def
% 0.16/0.42 thf(fact_58_no__distrib__def,axiom,
% 0.16/0.42 ! [A: a,B: a,C: a] :
% 0.16/0.42 ( ( modula1962211574trib_a @ inf @ less @ sup @ A @ B @ C )
% 0.16/0.42 = ( less @ ( sup @ ( inf @ A @ B ) @ ( inf @ C @ A ) ) @ ( inf @ A @ ( sup @ B @ C ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % no_distrib_def
% 0.16/0.42 thf(fact_59_local_Oinf__sup__absorb,axiom,
% 0.16/0.42 ! [X: a,Y: a] :
% 0.16/0.42 ( ( inf @ X @ ( sup @ X @ Y ) )
% 0.16/0.42 = X ) ).
% 0.16/0.42
% 0.16/0.42 % local.inf_sup_absorb
% 0.16/0.42 thf(fact_60_local_Osup__inf__absorb,axiom,
% 0.16/0.42 ! [X: a,Y: a] :
% 0.16/0.42 ( ( sup @ X @ ( inf @ X @ Y ) )
% 0.16/0.42 = X ) ).
% 0.16/0.42
% 0.16/0.42 % local.sup_inf_absorb
% 0.16/0.42 thf(fact_61_local_Oa__join__d,axiom,
% 0.16/0.42 ! [A: a,B: a,C: a] :
% 0.16/0.42 ( ( sup @ A @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) )
% 0.16/0.42 = ( sup @ A @ ( inf @ B @ C ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.a_join_d
% 0.16/0.42 thf(fact_62_local_Ob__join__d,axiom,
% 0.16/0.42 ! [B: a,A: a,C: a] :
% 0.16/0.42 ( ( sup @ B @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) )
% 0.16/0.42 = ( sup @ B @ ( inf @ C @ A ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.b_join_d
% 0.16/0.42 thf(fact_63_local_Od__aux__def,axiom,
% 0.16/0.42 ! [A: a,B: a,C: a] :
% 0.16/0.42 ( ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C )
% 0.16/0.42 = ( sup @ ( sup @ ( inf @ A @ B ) @ ( inf @ B @ C ) ) @ ( inf @ C @ A ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.d_aux_def
% 0.16/0.42 thf(fact_64_local_Od__b__c__a,axiom,
% 0.16/0.42 ! [B: a,C: a,A: a] :
% 0.16/0.42 ( ( modula1936294176_aux_a @ inf @ sup @ B @ C @ A )
% 0.16/0.42 = ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.d_b_c_a
% 0.16/0.42 thf(fact_65_local_Od__c__a__b,axiom,
% 0.16/0.42 ! [C: a,A: a,B: a] :
% 0.16/0.42 ( ( modula1936294176_aux_a @ inf @ sup @ C @ A @ B )
% 0.16/0.42 = ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.d_c_a_b
% 0.16/0.42 thf(fact_66_local_Oa__meet__e,axiom,
% 0.16/0.42 ! [A: a,B: a,C: a] :
% 0.16/0.42 ( ( inf @ A @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
% 0.16/0.42 = ( inf @ A @ ( sup @ B @ C ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.a_meet_e
% 0.16/0.42 thf(fact_67_local_Ob__meet__e,axiom,
% 0.16/0.42 ! [B: a,A: a,C: a] :
% 0.16/0.42 ( ( inf @ B @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
% 0.16/0.42 = ( inf @ B @ ( sup @ C @ A ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.b_meet_e
% 0.16/0.42 thf(fact_68_local_Oc__meet__e,axiom,
% 0.16/0.42 ! [C: a,A: a,B: a] :
% 0.16/0.42 ( ( inf @ C @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
% 0.16/0.42 = ( inf @ C @ ( sup @ A @ B ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.c_meet_e
% 0.16/0.42 thf(fact_69_local_Oe__aux__def,axiom,
% 0.16/0.42 ! [A: a,B: a,C: a] :
% 0.16/0.42 ( ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C )
% 0.16/0.42 = ( inf @ ( inf @ ( sup @ A @ B ) @ ( sup @ B @ C ) ) @ ( sup @ C @ A ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.e_aux_def
% 0.16/0.42 thf(fact_70_local_Oe__b__c__a,axiom,
% 0.16/0.42 ! [B: a,C: a,A: a] :
% 0.16/0.42 ( ( modula1144073633_aux_a @ inf @ sup @ B @ C @ A )
% 0.16/0.42 = ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.e_b_c_a
% 0.16/0.42 thf(fact_71_local_Oe__c__a__b,axiom,
% 0.16/0.42 ! [C: a,A: a,B: a] :
% 0.16/0.42 ( ( modula1144073633_aux_a @ inf @ sup @ C @ A @ B )
% 0.16/0.42 = ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.e_c_a_b
% 0.16/0.42 thf(fact_72_local_Ocomp__fun__idem__sup,axiom,
% 0.16/0.42 finite40241356em_a_a @ sup ).
% 0.16/0.42
% 0.16/0.42 % local.comp_fun_idem_sup
% 0.16/0.42 thf(fact_73_local_Ocomp__fun__idem__inf,axiom,
% 0.16/0.42 finite40241356em_a_a @ inf ).
% 0.16/0.42
% 0.16/0.42 % local.comp_fun_idem_inf
% 0.16/0.42 thf(fact_74_local_Oc__aux__def,axiom,
% 0.16/0.42 ! [A: a,B: a,C: a] :
% 0.16/0.42 ( ( modula581031071_aux_a @ inf @ sup @ A @ B @ C )
% 0.16/0.42 = ( sup @ ( inf @ C @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.c_aux_def
% 0.16/0.42 thf(fact_75_local_Ob__aux__def,axiom,
% 0.16/0.42 ! [A: a,B: a,C: a] :
% 0.16/0.42 ( ( modula1373251614_aux_a @ inf @ sup @ A @ B @ C )
% 0.16/0.42 = ( sup @ ( inf @ B @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.b_aux_def
% 0.16/0.42 thf(fact_76_local_Oa__aux__def,axiom,
% 0.16/0.42 ! [A: a,B: a,C: a] :
% 0.16/0.42 ( ( modula17988509_aux_a @ inf @ sup @ A @ B @ C )
% 0.16/0.42 = ( sup @ ( inf @ A @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.a_aux_def
% 0.16/0.42 thf(fact_77_lattice_Ono__distrib_Ocong,axiom,
% 0.16/0.42 modula1962211574trib_a = modula1962211574trib_a ).
% 0.16/0.42
% 0.16/0.42 % lattice.no_distrib.cong
% 0.16/0.42 thf(fact_78_lattice_ON5__lattice_Ocong,axiom,
% 0.16/0.42 modula397570059tice_a = modula397570059tice_a ).
% 0.16/0.42
% 0.16/0.42 % lattice.N5_lattice.cong
% 0.16/0.42 thf(fact_79_lattice_OM5__lattice_Ocong,axiom,
% 0.16/0.42 modula1376131916tice_a = modula1376131916tice_a ).
% 0.16/0.42
% 0.16/0.42 % lattice.M5_lattice.cong
% 0.16/0.42 thf(fact_80_lattice_Oe__aux_Ocong,axiom,
% 0.16/0.42 modula1144073633_aux_a = modula1144073633_aux_a ).
% 0.16/0.42
% 0.16/0.42 % lattice.e_aux.cong
% 0.16/0.42 thf(fact_81_lattice_Od__aux_Ocong,axiom,
% 0.16/0.42 modula1936294176_aux_a = modula1936294176_aux_a ).
% 0.16/0.42
% 0.16/0.42 % lattice.d_aux.cong
% 0.16/0.42 thf(fact_82_local_Oc__a,axiom,
% 0.16/0.42 ! [A: a,B: a,C: a] :
% 0.16/0.42 ( ( modula581031071_aux_a @ inf @ sup @ A @ B @ C )
% 0.16/0.42 = ( modula17988509_aux_a @ inf @ sup @ C @ A @ B ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.c_a
% 0.16/0.42 thf(fact_83_local_Ob__a,axiom,
% 0.16/0.42 ! [A: a,B: a,C: a] :
% 0.16/0.42 ( ( modula1373251614_aux_a @ inf @ sup @ A @ B @ C )
% 0.16/0.42 = ( modula17988509_aux_a @ inf @ sup @ B @ C @ A ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.b_a
% 0.16/0.42 thf(fact_84_local_Osup_Osemigroup__axioms,axiom,
% 0.16/0.42 semigroup_a @ sup ).
% 0.16/0.42
% 0.16/0.42 % local.sup.semigroup_axioms
% 0.16/0.42 thf(fact_85_local_Oinf_Osemigroup__axioms,axiom,
% 0.16/0.42 semigroup_a @ inf ).
% 0.16/0.42
% 0.16/0.42 % local.inf.semigroup_axioms
% 0.16/0.42 thf(fact_86_local_Osup_Osemilattice__axioms,axiom,
% 0.16/0.42 semilattice_a @ sup ).
% 0.16/0.42
% 0.16/0.42 % local.sup.semilattice_axioms
% 0.16/0.42 thf(fact_87_local_Oinf_Osemilattice__axioms,axiom,
% 0.16/0.42 semilattice_a @ inf ).
% 0.16/0.42
% 0.16/0.42 % local.inf.semilattice_axioms
% 0.16/0.42 thf(fact_88_lattice_Oa__aux_Ocong,axiom,
% 0.16/0.42 modula17988509_aux_a = modula17988509_aux_a ).
% 0.16/0.42
% 0.16/0.42 % lattice.a_aux.cong
% 0.16/0.42 thf(fact_89_lattice_Ob__aux_Ocong,axiom,
% 0.16/0.42 modula1373251614_aux_a = modula1373251614_aux_a ).
% 0.16/0.42
% 0.16/0.42 % lattice.b_aux.cong
% 0.16/0.42 thf(fact_90_lattice_Oc__aux_Ocong,axiom,
% 0.16/0.42 modula581031071_aux_a = modula581031071_aux_a ).
% 0.16/0.42
% 0.16/0.42 % lattice.c_aux.cong
% 0.16/0.42 thf(fact_91_local_Osup_Oabel__semigroup__axioms,axiom,
% 0.16/0.42 abel_semigroup_a @ sup ).
% 0.16/0.42
% 0.16/0.42 % local.sup.abel_semigroup_axioms
% 0.16/0.42 thf(fact_92_local_Oinf_Oabel__semigroup__axioms,axiom,
% 0.16/0.42 abel_semigroup_a @ inf ).
% 0.16/0.42
% 0.16/0.42 % local.inf.abel_semigroup_axioms
% 0.16/0.42 thf(fact_93_local_OSup__fin_Osemilattice__set__axioms,axiom,
% 0.16/0.42 lattic1885654924_set_a @ sup ).
% 0.16/0.42
% 0.16/0.42 % local.Sup_fin.semilattice_set_axioms
% 0.16/0.42 thf(fact_94_local_OInf__fin_Osemilattice__set__axioms,axiom,
% 0.16/0.42 lattic1885654924_set_a @ inf ).
% 0.16/0.42
% 0.16/0.42 % local.Inf_fin.semilattice_set_axioms
% 0.16/0.42 thf(fact_95_local_Olexordp__eq__refl,axiom,
% 0.16/0.42 ! [Xs: list_a] : ( lexordp_eq_a @ less @ Xs @ Xs ) ).
% 0.16/0.42
% 0.16/0.42 % local.lexordp_eq_refl
% 0.16/0.42 thf(fact_96_local_Olexordp__eq_ONil,axiom,
% 0.16/0.42 ! [Ys: list_a] : ( lexordp_eq_a @ less @ nil_a @ Ys ) ).
% 0.16/0.42
% 0.16/0.42 % local.lexordp_eq.Nil
% 0.16/0.42 thf(fact_97_abel__semigroup_Oaxioms_I1_J,axiom,
% 0.16/0.42 ! [F: list_a > list_a > list_a] :
% 0.16/0.42 ( ( abel_s1075322906list_a @ F )
% 0.16/0.42 => ( semigroup_list_a @ F ) ) ).
% 0.16/0.42
% 0.16/0.42 % abel_semigroup.axioms(1)
% 0.16/0.42 thf(fact_98_abel__semigroup_Oaxioms_I1_J,axiom,
% 0.16/0.42 ! [F: a > a > a] :
% 0.16/0.42 ( ( abel_semigroup_a @ F )
% 0.16/0.42 => ( semigroup_a @ F ) ) ).
% 0.16/0.42
% 0.16/0.42 % abel_semigroup.axioms(1)
% 0.16/0.42 thf(fact_99_semilattice__set_Oaxioms,axiom,
% 0.16/0.42 ! [F: a > a > a] :
% 0.16/0.42 ( ( lattic1885654924_set_a @ F )
% 0.16/0.42 => ( semilattice_a @ F ) ) ).
% 0.16/0.42
% 0.16/0.42 % semilattice_set.axioms
% 0.16/0.42 thf(fact_100_semilattice__set_Ointro,axiom,
% 0.16/0.42 ! [F: a > a > a] :
% 0.16/0.42 ( ( semilattice_a @ F )
% 0.16/0.42 => ( lattic1885654924_set_a @ F ) ) ).
% 0.16/0.42
% 0.16/0.42 % semilattice_set.intro
% 0.16/0.42 thf(fact_101_semilattice__set__def,axiom,
% 0.16/0.42 lattic1885654924_set_a = semilattice_a ).
% 0.16/0.42
% 0.16/0.42 % semilattice_set_def
% 0.16/0.42 thf(fact_102_local_Olexordp__eq__simps_I1_J,axiom,
% 0.16/0.42 ! [Ys: list_a] : ( lexordp_eq_a @ less @ nil_a @ Ys ) ).
% 0.16/0.42
% 0.16/0.42 % local.lexordp_eq_simps(1)
% 0.16/0.42 thf(fact_103_local_Olexordp__eq__simps_I2_J,axiom,
% 0.16/0.42 ! [Xs: list_a] :
% 0.16/0.42 ( ( lexordp_eq_a @ less @ Xs @ nil_a )
% 0.16/0.42 = ( Xs = nil_a ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.lexordp_eq_simps(2)
% 0.16/0.42 thf(fact_104_abel__semigroup_Oleft__commute,axiom,
% 0.16/0.42 ! [F: a > a > a,B: a,A: a,C: a] :
% 0.16/0.42 ( ( abel_semigroup_a @ F )
% 0.16/0.42 => ( ( F @ B @ ( F @ A @ C ) )
% 0.16/0.42 = ( F @ A @ ( F @ B @ C ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % abel_semigroup.left_commute
% 0.16/0.42 thf(fact_105_abel__semigroup_Ocommute,axiom,
% 0.16/0.42 ! [F: a > a > a,A: a,B: a] :
% 0.16/0.42 ( ( abel_semigroup_a @ F )
% 0.16/0.42 => ( ( F @ A @ B )
% 0.16/0.42 = ( F @ B @ A ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % abel_semigroup.commute
% 0.16/0.42 thf(fact_106_semigroup_Ointro,axiom,
% 0.16/0.42 ! [F: list_a > list_a > list_a] :
% 0.16/0.42 ( ! [A2: list_a,B2: list_a,C2: list_a] :
% 0.16/0.42 ( ( F @ ( F @ A2 @ B2 ) @ C2 )
% 0.16/0.42 = ( F @ A2 @ ( F @ B2 @ C2 ) ) )
% 0.16/0.42 => ( semigroup_list_a @ F ) ) ).
% 0.16/0.42
% 0.16/0.42 % semigroup.intro
% 0.16/0.42 thf(fact_107_semigroup_Ointro,axiom,
% 0.16/0.42 ! [F: a > a > a] :
% 0.16/0.42 ( ! [A2: a,B2: a,C2: a] :
% 0.16/0.42 ( ( F @ ( F @ A2 @ B2 ) @ C2 )
% 0.16/0.42 = ( F @ A2 @ ( F @ B2 @ C2 ) ) )
% 0.16/0.42 => ( semigroup_a @ F ) ) ).
% 0.16/0.42
% 0.16/0.42 % semigroup.intro
% 0.16/0.42 thf(fact_108_semigroup_Oassoc,axiom,
% 0.16/0.42 ! [F: list_a > list_a > list_a,A: list_a,B: list_a,C: list_a] :
% 0.16/0.42 ( ( semigroup_list_a @ F )
% 0.16/0.42 => ( ( F @ ( F @ A @ B ) @ C )
% 0.16/0.42 = ( F @ A @ ( F @ B @ C ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % semigroup.assoc
% 0.16/0.42 thf(fact_109_semigroup_Oassoc,axiom,
% 0.16/0.42 ! [F: a > a > a,A: a,B: a,C: a] :
% 0.16/0.42 ( ( semigroup_a @ F )
% 0.16/0.42 => ( ( F @ ( F @ A @ B ) @ C )
% 0.16/0.42 = ( F @ A @ ( F @ B @ C ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % semigroup.assoc
% 0.16/0.42 thf(fact_110_semigroup__def,axiom,
% 0.16/0.42 ( semigroup_list_a
% 0.16/0.42 = ( ^ [F2: list_a > list_a > list_a] :
% 0.16/0.42 ! [A3: list_a,B3: list_a,C3: list_a] :
% 0.16/0.42 ( ( F2 @ ( F2 @ A3 @ B3 ) @ C3 )
% 0.16/0.42 = ( F2 @ A3 @ ( F2 @ B3 @ C3 ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % semigroup_def
% 0.16/0.42 thf(fact_111_semigroup__def,axiom,
% 0.16/0.42 ( semigroup_a
% 0.16/0.42 = ( ^ [F2: a > a > a] :
% 0.16/0.42 ! [A3: a,B3: a,C3: a] :
% 0.16/0.42 ( ( F2 @ ( F2 @ A3 @ B3 ) @ C3 )
% 0.16/0.42 = ( F2 @ A3 @ ( F2 @ B3 @ C3 ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % semigroup_def
% 0.16/0.42 thf(fact_112_ord_Olexordp__eq__simps_I2_J,axiom,
% 0.16/0.42 ! [Less: list_a > list_a > $o,Xs: list_list_a] :
% 0.16/0.42 ( ( lexordp_eq_list_a @ Less @ Xs @ nil_list_a )
% 0.16/0.42 = ( Xs = nil_list_a ) ) ).
% 0.16/0.42
% 0.16/0.42 % ord.lexordp_eq_simps(2)
% 0.16/0.42 thf(fact_113_ord_Olexordp__eq__simps_I2_J,axiom,
% 0.16/0.42 ! [Less: a > a > $o,Xs: list_a] :
% 0.16/0.42 ( ( lexordp_eq_a @ Less @ Xs @ nil_a )
% 0.16/0.42 = ( Xs = nil_a ) ) ).
% 0.16/0.42
% 0.16/0.42 % ord.lexordp_eq_simps(2)
% 0.16/0.42 thf(fact_114_ord_Olexordp__eq__simps_I1_J,axiom,
% 0.16/0.42 ! [Less: list_a > list_a > $o,Ys: list_list_a] : ( lexordp_eq_list_a @ Less @ nil_list_a @ Ys ) ).
% 0.16/0.42
% 0.16/0.42 % ord.lexordp_eq_simps(1)
% 0.16/0.42 thf(fact_115_ord_Olexordp__eq__simps_I1_J,axiom,
% 0.16/0.42 ! [Less: a > a > $o,Ys: list_a] : ( lexordp_eq_a @ Less @ nil_a @ Ys ) ).
% 0.16/0.42
% 0.16/0.42 % ord.lexordp_eq_simps(1)
% 0.16/0.42 thf(fact_116_local_Olexordp__eq_Osimps,axiom,
% 0.16/0.42 ! [A1: list_a,A22: list_a] :
% 0.16/0.42 ( ( lexordp_eq_a @ less @ A1 @ A22 )
% 0.16/0.42 = ( ? [Ys2: list_a] :
% 0.16/0.42 ( ( A1 = nil_a )
% 0.16/0.42 & ( A22 = Ys2 ) )
% 0.16/0.42 | ? [X3: a,Y3: a,Xs2: list_a,Ys2: list_a] :
% 0.16/0.42 ( ( A1
% 0.16/0.42 = ( cons_a @ X3 @ Xs2 ) )
% 0.16/0.42 & ( A22
% 0.16/0.42 = ( cons_a @ Y3 @ Ys2 ) )
% 0.16/0.42 & ( less @ X3 @ Y3 ) )
% 0.16/0.42 | ? [X3: a,Y3: a,Xs2: list_a,Ys2: list_a] :
% 0.16/0.42 ( ( A1
% 0.16/0.42 = ( cons_a @ X3 @ Xs2 ) )
% 0.16/0.42 & ( A22
% 0.16/0.42 = ( cons_a @ Y3 @ Ys2 ) )
% 0.16/0.42 & ~ ( less @ X3 @ Y3 )
% 0.16/0.42 & ~ ( less @ Y3 @ X3 )
% 0.16/0.42 & ( lexordp_eq_a @ less @ Xs2 @ Ys2 ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.lexordp_eq.simps
% 0.16/0.42 thf(fact_117_local_Olexordp__eq_Oinducts,axiom,
% 0.16/0.42 ! [X1: list_a,X22: list_a,P: list_a > list_a > $o] :
% 0.16/0.42 ( ( lexordp_eq_a @ less @ X1 @ X22 )
% 0.16/0.42 => ( ! [X_1: list_a] : ( P @ nil_a @ X_1 )
% 0.16/0.42 => ( ! [X2: a,Y2: a,Xs3: list_a,Ys3: list_a] :
% 0.16/0.42 ( ( less @ X2 @ Y2 )
% 0.16/0.42 => ( P @ ( cons_a @ X2 @ Xs3 ) @ ( cons_a @ Y2 @ Ys3 ) ) )
% 0.16/0.42 => ( ! [X2: a,Y2: a,Xs3: list_a,Ys3: list_a] :
% 0.16/0.42 ( ~ ( less @ X2 @ Y2 )
% 0.16/0.42 => ( ~ ( less @ Y2 @ X2 )
% 0.16/0.42 => ( ( lexordp_eq_a @ less @ Xs3 @ Ys3 )
% 0.16/0.42 => ( ( P @ Xs3 @ Ys3 )
% 0.16/0.42 => ( P @ ( cons_a @ X2 @ Xs3 ) @ ( cons_a @ Y2 @ Ys3 ) ) ) ) ) )
% 0.16/0.42 => ( P @ X1 @ X22 ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.lexordp_eq.inducts
% 0.16/0.42 thf(fact_118_local_Olexordp__eq_Ocases,axiom,
% 0.16/0.42 ! [A1: list_a,A22: list_a] :
% 0.16/0.42 ( ( lexordp_eq_a @ less @ A1 @ A22 )
% 0.16/0.42 => ( ( A1 != nil_a )
% 0.16/0.42 => ( ! [X2: a] :
% 0.16/0.42 ( ? [Xs3: list_a] :
% 0.16/0.42 ( A1
% 0.16/0.42 = ( cons_a @ X2 @ Xs3 ) )
% 0.16/0.42 => ! [Y2: a] :
% 0.16/0.42 ( ? [Ys3: list_a] :
% 0.16/0.42 ( A22
% 0.16/0.42 = ( cons_a @ Y2 @ Ys3 ) )
% 0.16/0.42 => ~ ( less @ X2 @ Y2 ) ) )
% 0.16/0.42 => ~ ! [X2: a,Y2: a,Xs3: list_a] :
% 0.16/0.42 ( ( A1
% 0.16/0.42 = ( cons_a @ X2 @ Xs3 ) )
% 0.16/0.42 => ! [Ys3: list_a] :
% 0.16/0.42 ( ( A22
% 0.16/0.42 = ( cons_a @ Y2 @ Ys3 ) )
% 0.16/0.42 => ( ~ ( less @ X2 @ Y2 )
% 0.16/0.42 => ( ~ ( less @ Y2 @ X2 )
% 0.16/0.42 => ~ ( lexordp_eq_a @ less @ Xs3 @ Ys3 ) ) ) ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.lexordp_eq.cases
% 0.16/0.42 thf(fact_119_local_Olexordp__eq_OCons__eq,axiom,
% 0.16/0.42 ! [X: a,Y: a,Xs: list_a,Ys: list_a] :
% 0.16/0.42 ( ~ ( less @ X @ Y )
% 0.16/0.42 => ( ~ ( less @ Y @ X )
% 0.16/0.42 => ( ( lexordp_eq_a @ less @ Xs @ Ys )
% 0.16/0.42 => ( lexordp_eq_a @ less @ ( cons_a @ X @ Xs ) @ ( cons_a @ Y @ Ys ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.lexordp_eq.Cons_eq
% 0.16/0.42 thf(fact_120_local_Olexordp__eq_OCons,axiom,
% 0.16/0.42 ! [X: a,Y: a,Xs: list_a,Ys: list_a] :
% 0.16/0.42 ( ( less @ X @ Y )
% 0.16/0.42 => ( lexordp_eq_a @ less @ ( cons_a @ X @ Xs ) @ ( cons_a @ Y @ Ys ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.lexordp_eq.Cons
% 0.16/0.42 thf(fact_121_list_Oinject,axiom,
% 0.16/0.42 ! [X21: list_a,X222: list_list_a,Y21: list_a,Y22: list_list_a] :
% 0.16/0.42 ( ( ( cons_list_a @ X21 @ X222 )
% 0.16/0.42 = ( cons_list_a @ Y21 @ Y22 ) )
% 0.16/0.42 = ( ( X21 = Y21 )
% 0.16/0.42 & ( X222 = Y22 ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % list.inject
% 0.16/0.42 thf(fact_122_list_Oinject,axiom,
% 0.16/0.42 ! [X21: a,X222: list_a,Y21: a,Y22: list_a] :
% 0.16/0.42 ( ( ( cons_a @ X21 @ X222 )
% 0.16/0.42 = ( cons_a @ Y21 @ Y22 ) )
% 0.16/0.42 = ( ( X21 = Y21 )
% 0.16/0.42 & ( X222 = Y22 ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % list.inject
% 0.16/0.42 thf(fact_123_ord_Olexordp__eq__simps_I4_J,axiom,
% 0.16/0.42 ! [Less: list_a > list_a > $o,X: list_a,Xs: list_list_a,Y: list_a,Ys: list_list_a] :
% 0.16/0.42 ( ( lexordp_eq_list_a @ Less @ ( cons_list_a @ X @ Xs ) @ ( cons_list_a @ Y @ Ys ) )
% 0.16/0.42 = ( ( Less @ X @ Y )
% 0.16/0.42 | ( ~ ( Less @ Y @ X )
% 0.16/0.42 & ( lexordp_eq_list_a @ Less @ Xs @ Ys ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % ord.lexordp_eq_simps(4)
% 0.16/0.42 thf(fact_124_ord_Olexordp__eq__simps_I4_J,axiom,
% 0.16/0.42 ! [Less: a > a > $o,X: a,Xs: list_a,Y: a,Ys: list_a] :
% 0.16/0.42 ( ( lexordp_eq_a @ Less @ ( cons_a @ X @ Xs ) @ ( cons_a @ Y @ Ys ) )
% 0.16/0.42 = ( ( Less @ X @ Y )
% 0.16/0.42 | ( ~ ( Less @ Y @ X )
% 0.16/0.42 & ( lexordp_eq_a @ Less @ Xs @ Ys ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % ord.lexordp_eq_simps(4)
% 0.16/0.42 thf(fact_125_ord_Olexordp__eq__simps_I3_J,axiom,
% 0.16/0.42 ! [Less: list_a > list_a > $o,X: list_a,Xs: list_list_a] :
% 0.16/0.42 ~ ( lexordp_eq_list_a @ Less @ ( cons_list_a @ X @ Xs ) @ nil_list_a ) ).
% 0.16/0.42
% 0.16/0.42 % ord.lexordp_eq_simps(3)
% 0.16/0.42 thf(fact_126_ord_Olexordp__eq__simps_I3_J,axiom,
% 0.16/0.42 ! [Less: a > a > $o,X: a,Xs: list_a] :
% 0.16/0.42 ~ ( lexordp_eq_a @ Less @ ( cons_a @ X @ Xs ) @ nil_a ) ).
% 0.16/0.42
% 0.16/0.42 % ord.lexordp_eq_simps(3)
% 0.16/0.42 thf(fact_127_local_Olexordp__eq__simps_I4_J,axiom,
% 0.16/0.42 ! [X: a,Xs: list_a,Y: a,Ys: list_a] :
% 0.16/0.42 ( ( lexordp_eq_a @ less @ ( cons_a @ X @ Xs ) @ ( cons_a @ Y @ Ys ) )
% 0.16/0.42 = ( ( less @ X @ Y )
% 0.16/0.42 | ( ~ ( less @ Y @ X )
% 0.16/0.42 & ( lexordp_eq_a @ less @ Xs @ Ys ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.lexordp_eq_simps(4)
% 0.16/0.42 thf(fact_128_local_Olexordp__eq__simps_I3_J,axiom,
% 0.16/0.42 ! [X: a,Xs: list_a] :
% 0.16/0.42 ~ ( lexordp_eq_a @ less @ ( cons_a @ X @ Xs ) @ nil_a ) ).
% 0.16/0.42
% 0.16/0.42 % local.lexordp_eq_simps(3)
% 0.16/0.42 thf(fact_129_map__tailrec__rev_Oinduct,axiom,
% 0.16/0.42 ! [P: ( list_a > a ) > list_list_a > list_a > $o,A0: list_a > a,A1: list_list_a,A22: list_a] :
% 0.16/0.42 ( ! [F3: list_a > a,X_1: list_a] : ( P @ F3 @ nil_list_a @ X_1 )
% 0.16/0.42 => ( ! [F3: list_a > a,A2: list_a,As: list_list_a,Bs: list_a] :
% 0.16/0.42 ( ( P @ F3 @ As @ ( cons_a @ ( F3 @ A2 ) @ Bs ) )
% 0.16/0.42 => ( P @ F3 @ ( cons_list_a @ A2 @ As ) @ Bs ) )
% 0.16/0.42 => ( P @ A0 @ A1 @ A22 ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % map_tailrec_rev.induct
% 0.16/0.42 thf(fact_130_map__tailrec__rev_Oinduct,axiom,
% 0.16/0.42 ! [P: ( a > list_a ) > list_a > list_list_a > $o,A0: a > list_a,A1: list_a,A22: list_list_a] :
% 0.16/0.42 ( ! [F3: a > list_a,X_1: list_list_a] : ( P @ F3 @ nil_a @ X_1 )
% 0.16/0.42 => ( ! [F3: a > list_a,A2: a,As: list_a,Bs: list_list_a] :
% 0.16/0.42 ( ( P @ F3 @ As @ ( cons_list_a @ ( F3 @ A2 ) @ Bs ) )
% 0.16/0.42 => ( P @ F3 @ ( cons_a @ A2 @ As ) @ Bs ) )
% 0.16/0.42 => ( P @ A0 @ A1 @ A22 ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % map_tailrec_rev.induct
% 0.16/0.42 thf(fact_131_map__tailrec__rev_Oinduct,axiom,
% 0.16/0.42 ! [P: ( list_a > list_a ) > list_list_a > list_list_a > $o,A0: list_a > list_a,A1: list_list_a,A22: list_list_a] :
% 0.16/0.42 ( ! [F3: list_a > list_a,X_1: list_list_a] : ( P @ F3 @ nil_list_a @ X_1 )
% 0.16/0.42 => ( ! [F3: list_a > list_a,A2: list_a,As: list_list_a,Bs: list_list_a] :
% 0.16/0.42 ( ( P @ F3 @ As @ ( cons_list_a @ ( F3 @ A2 ) @ Bs ) )
% 0.16/0.42 => ( P @ F3 @ ( cons_list_a @ A2 @ As ) @ Bs ) )
% 0.16/0.42 => ( P @ A0 @ A1 @ A22 ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % map_tailrec_rev.induct
% 0.16/0.42 thf(fact_132_map__tailrec__rev_Oinduct,axiom,
% 0.16/0.42 ! [P: ( a > a ) > list_a > list_a > $o,A0: a > a,A1: list_a,A22: list_a] :
% 0.16/0.42 ( ! [F3: a > a,X_1: list_a] : ( P @ F3 @ nil_a @ X_1 )
% 0.16/0.42 => ( ! [F3: a > a,A2: a,As: list_a,Bs: list_a] :
% 0.16/0.42 ( ( P @ F3 @ As @ ( cons_a @ ( F3 @ A2 ) @ Bs ) )
% 0.16/0.42 => ( P @ F3 @ ( cons_a @ A2 @ As ) @ Bs ) )
% 0.16/0.42 => ( P @ A0 @ A1 @ A22 ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % map_tailrec_rev.induct
% 0.16/0.42 thf(fact_133_list__nonempty__induct,axiom,
% 0.16/0.42 ! [Xs: list_list_a,P: list_list_a > $o] :
% 0.16/0.42 ( ( Xs != nil_list_a )
% 0.16/0.42 => ( ! [X2: list_a] : ( P @ ( cons_list_a @ X2 @ nil_list_a ) )
% 0.16/0.42 => ( ! [X2: list_a,Xs3: list_list_a] :
% 0.16/0.42 ( ( Xs3 != nil_list_a )
% 0.16/0.42 => ( ( P @ Xs3 )
% 0.16/0.42 => ( P @ ( cons_list_a @ X2 @ Xs3 ) ) ) )
% 0.16/0.42 => ( P @ Xs ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % list_nonempty_induct
% 0.16/0.42 thf(fact_134_list__nonempty__induct,axiom,
% 0.16/0.42 ! [Xs: list_a,P: list_a > $o] :
% 0.16/0.42 ( ( Xs != nil_a )
% 0.16/0.42 => ( ! [X2: a] : ( P @ ( cons_a @ X2 @ nil_a ) )
% 0.16/0.42 => ( ! [X2: a,Xs3: list_a] :
% 0.16/0.42 ( ( Xs3 != nil_a )
% 0.16/0.42 => ( ( P @ Xs3 )
% 0.16/0.42 => ( P @ ( cons_a @ X2 @ Xs3 ) ) ) )
% 0.16/0.42 => ( P @ Xs ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % list_nonempty_induct
% 0.16/0.42 thf(fact_135_successively_Oinduct,axiom,
% 0.16/0.42 ! [P: ( list_a > list_a > $o ) > list_list_a > $o,A0: list_a > list_a > $o,A1: list_list_a] :
% 0.16/0.42 ( ! [P2: list_a > list_a > $o] : ( P @ P2 @ nil_list_a )
% 0.16/0.42 => ( ! [P2: list_a > list_a > $o,X2: list_a] : ( P @ P2 @ ( cons_list_a @ X2 @ nil_list_a ) )
% 0.16/0.42 => ( ! [P2: list_a > list_a > $o,X2: list_a,Y2: list_a,Xs3: list_list_a] :
% 0.16/0.42 ( ( P @ P2 @ ( cons_list_a @ Y2 @ Xs3 ) )
% 0.16/0.42 => ( P @ P2 @ ( cons_list_a @ X2 @ ( cons_list_a @ Y2 @ Xs3 ) ) ) )
% 0.16/0.42 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % successively.induct
% 0.16/0.42 thf(fact_136_successively_Oinduct,axiom,
% 0.16/0.42 ! [P: ( a > a > $o ) > list_a > $o,A0: a > a > $o,A1: list_a] :
% 0.16/0.42 ( ! [P2: a > a > $o] : ( P @ P2 @ nil_a )
% 0.16/0.42 => ( ! [P2: a > a > $o,X2: a] : ( P @ P2 @ ( cons_a @ X2 @ nil_a ) )
% 0.16/0.42 => ( ! [P2: a > a > $o,X2: a,Y2: a,Xs3: list_a] :
% 0.16/0.42 ( ( P @ P2 @ ( cons_a @ Y2 @ Xs3 ) )
% 0.16/0.42 => ( P @ P2 @ ( cons_a @ X2 @ ( cons_a @ Y2 @ Xs3 ) ) ) )
% 0.16/0.42 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % successively.induct
% 0.16/0.42 thf(fact_137_remdups__adj_Oinduct,axiom,
% 0.16/0.42 ! [P: list_list_a > $o,A0: list_list_a] :
% 0.16/0.42 ( ( P @ nil_list_a )
% 0.16/0.42 => ( ! [X2: list_a] : ( P @ ( cons_list_a @ X2 @ nil_list_a ) )
% 0.16/0.42 => ( ! [X2: list_a,Y2: list_a,Xs3: list_list_a] :
% 0.16/0.42 ( ( ( X2 = Y2 )
% 0.16/0.42 => ( P @ ( cons_list_a @ X2 @ Xs3 ) ) )
% 0.16/0.42 => ( ( ( X2 != Y2 )
% 0.16/0.42 => ( P @ ( cons_list_a @ Y2 @ Xs3 ) ) )
% 0.16/0.42 => ( P @ ( cons_list_a @ X2 @ ( cons_list_a @ Y2 @ Xs3 ) ) ) ) )
% 0.16/0.42 => ( P @ A0 ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % remdups_adj.induct
% 0.16/0.42 thf(fact_138_remdups__adj_Oinduct,axiom,
% 0.16/0.42 ! [P: list_a > $o,A0: list_a] :
% 0.16/0.42 ( ( P @ nil_a )
% 0.16/0.42 => ( ! [X2: a] : ( P @ ( cons_a @ X2 @ nil_a ) )
% 0.16/0.42 => ( ! [X2: a,Y2: a,Xs3: list_a] :
% 0.16/0.42 ( ( ( X2 = Y2 )
% 0.16/0.42 => ( P @ ( cons_a @ X2 @ Xs3 ) ) )
% 0.16/0.42 => ( ( ( X2 != Y2 )
% 0.16/0.42 => ( P @ ( cons_a @ Y2 @ Xs3 ) ) )
% 0.16/0.42 => ( P @ ( cons_a @ X2 @ ( cons_a @ Y2 @ Xs3 ) ) ) ) )
% 0.16/0.42 => ( P @ A0 ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % remdups_adj.induct
% 0.16/0.42 thf(fact_139_sorted__wrt_Oinduct,axiom,
% 0.16/0.42 ! [P: ( list_a > list_a > $o ) > list_list_a > $o,A0: list_a > list_a > $o,A1: list_list_a] :
% 0.16/0.42 ( ! [P2: list_a > list_a > $o] : ( P @ P2 @ nil_list_a )
% 0.16/0.42 => ( ! [P2: list_a > list_a > $o,X2: list_a,Ys3: list_list_a] :
% 0.16/0.42 ( ( P @ P2 @ Ys3 )
% 0.16/0.42 => ( P @ P2 @ ( cons_list_a @ X2 @ Ys3 ) ) )
% 0.16/0.42 => ( P @ A0 @ A1 ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % sorted_wrt.induct
% 0.16/0.42 thf(fact_140_sorted__wrt_Oinduct,axiom,
% 0.16/0.42 ! [P: ( a > a > $o ) > list_a > $o,A0: a > a > $o,A1: list_a] :
% 0.16/0.42 ( ! [P2: a > a > $o] : ( P @ P2 @ nil_a )
% 0.16/0.42 => ( ! [P2: a > a > $o,X2: a,Ys3: list_a] :
% 0.16/0.42 ( ( P @ P2 @ Ys3 )
% 0.16/0.42 => ( P @ P2 @ ( cons_a @ X2 @ Ys3 ) ) )
% 0.16/0.42 => ( P @ A0 @ A1 ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % sorted_wrt.induct
% 0.16/0.42 thf(fact_141_remdups__adj_Ocases,axiom,
% 0.16/0.42 ! [X: list_list_a] :
% 0.16/0.42 ( ( X != nil_list_a )
% 0.16/0.42 => ( ! [X2: list_a] :
% 0.16/0.42 ( X
% 0.16/0.42 != ( cons_list_a @ X2 @ nil_list_a ) )
% 0.16/0.42 => ~ ! [X2: list_a,Y2: list_a,Xs3: list_list_a] :
% 0.16/0.42 ( X
% 0.16/0.42 != ( cons_list_a @ X2 @ ( cons_list_a @ Y2 @ Xs3 ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % remdups_adj.cases
% 0.16/0.42 thf(fact_142_remdups__adj_Ocases,axiom,
% 0.16/0.42 ! [X: list_a] :
% 0.16/0.42 ( ( X != nil_a )
% 0.16/0.42 => ( ! [X2: a] :
% 0.16/0.42 ( X
% 0.16/0.42 != ( cons_a @ X2 @ nil_a ) )
% 0.16/0.42 => ~ ! [X2: a,Y2: a,Xs3: list_a] :
% 0.16/0.42 ( X
% 0.16/0.42 != ( cons_a @ X2 @ ( cons_a @ Y2 @ Xs3 ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % remdups_adj.cases
% 0.16/0.42 thf(fact_143_transpose_Ocases,axiom,
% 0.16/0.42 ! [X: list_list_list_a] :
% 0.16/0.42 ( ( X != nil_list_list_a )
% 0.16/0.42 => ( ! [Xss: list_list_list_a] :
% 0.16/0.42 ( X
% 0.16/0.42 != ( cons_list_list_a @ nil_list_a @ Xss ) )
% 0.16/0.42 => ~ ! [X2: list_a,Xs3: list_list_a,Xss: list_list_list_a] :
% 0.16/0.42 ( X
% 0.16/0.42 != ( cons_list_list_a @ ( cons_list_a @ X2 @ Xs3 ) @ Xss ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % transpose.cases
% 0.16/0.42 thf(fact_144_transpose_Ocases,axiom,
% 0.16/0.42 ! [X: list_list_a] :
% 0.16/0.42 ( ( X != nil_list_a )
% 0.16/0.42 => ( ! [Xss: list_list_a] :
% 0.16/0.42 ( X
% 0.16/0.42 != ( cons_list_a @ nil_a @ Xss ) )
% 0.16/0.42 => ~ ! [X2: a,Xs3: list_a,Xss: list_list_a] :
% 0.16/0.42 ( X
% 0.16/0.42 != ( cons_list_a @ ( cons_a @ X2 @ Xs3 ) @ Xss ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % transpose.cases
% 0.16/0.42 thf(fact_145_shuffles_Oinduct,axiom,
% 0.16/0.42 ! [P: list_list_a > list_list_a > $o,A0: list_list_a,A1: list_list_a] :
% 0.16/0.42 ( ! [X_1: list_list_a] : ( P @ nil_list_a @ X_1 )
% 0.16/0.42 => ( ! [Xs3: list_list_a] : ( P @ Xs3 @ nil_list_a )
% 0.16/0.42 => ( ! [X2: list_a,Xs3: list_list_a,Y2: list_a,Ys3: list_list_a] :
% 0.16/0.42 ( ( P @ Xs3 @ ( cons_list_a @ Y2 @ Ys3 ) )
% 0.16/0.42 => ( ( P @ ( cons_list_a @ X2 @ Xs3 ) @ Ys3 )
% 0.16/0.42 => ( P @ ( cons_list_a @ X2 @ Xs3 ) @ ( cons_list_a @ Y2 @ Ys3 ) ) ) )
% 0.16/0.42 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % shuffles.induct
% 0.16/0.42 thf(fact_146_shuffles_Oinduct,axiom,
% 0.16/0.42 ! [P: list_a > list_a > $o,A0: list_a,A1: list_a] :
% 0.16/0.42 ( ! [X_1: list_a] : ( P @ nil_a @ X_1 )
% 0.16/0.42 => ( ! [Xs3: list_a] : ( P @ Xs3 @ nil_a )
% 0.16/0.42 => ( ! [X2: a,Xs3: list_a,Y2: a,Ys3: list_a] :
% 0.16/0.42 ( ( P @ Xs3 @ ( cons_a @ Y2 @ Ys3 ) )
% 0.16/0.42 => ( ( P @ ( cons_a @ X2 @ Xs3 ) @ Ys3 )
% 0.16/0.42 => ( P @ ( cons_a @ X2 @ Xs3 ) @ ( cons_a @ Y2 @ Ys3 ) ) ) )
% 0.16/0.42 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % shuffles.induct
% 0.16/0.42 thf(fact_147_induct__list012,axiom,
% 0.16/0.42 ! [P: list_list_a > $o,Xs: list_list_a] :
% 0.16/0.42 ( ( P @ nil_list_a )
% 0.16/0.42 => ( ! [X2: list_a] : ( P @ ( cons_list_a @ X2 @ nil_list_a ) )
% 0.16/0.42 => ( ! [X2: list_a,Y2: list_a,Zs: list_list_a] :
% 0.16/0.42 ( ( P @ Zs )
% 0.16/0.42 => ( ( P @ ( cons_list_a @ Y2 @ Zs ) )
% 0.16/0.42 => ( P @ ( cons_list_a @ X2 @ ( cons_list_a @ Y2 @ Zs ) ) ) ) )
% 0.16/0.42 => ( P @ Xs ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % induct_list012
% 0.16/0.42 thf(fact_148_induct__list012,axiom,
% 0.16/0.42 ! [P: list_a > $o,Xs: list_a] :
% 0.16/0.42 ( ( P @ nil_a )
% 0.16/0.42 => ( ! [X2: a] : ( P @ ( cons_a @ X2 @ nil_a ) )
% 0.16/0.42 => ( ! [X2: a,Y2: a,Zs: list_a] :
% 0.16/0.42 ( ( P @ Zs )
% 0.16/0.42 => ( ( P @ ( cons_a @ Y2 @ Zs ) )
% 0.16/0.42 => ( P @ ( cons_a @ X2 @ ( cons_a @ Y2 @ Zs ) ) ) ) )
% 0.16/0.42 => ( P @ Xs ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % induct_list012
% 0.16/0.42 thf(fact_149_splice_Oinduct,axiom,
% 0.16/0.42 ! [P: list_list_a > list_list_a > $o,A0: list_list_a,A1: list_list_a] :
% 0.16/0.42 ( ! [X_1: list_list_a] : ( P @ nil_list_a @ X_1 )
% 0.16/0.42 => ( ! [X2: list_a,Xs3: list_list_a,Ys3: list_list_a] :
% 0.16/0.42 ( ( P @ Ys3 @ Xs3 )
% 0.16/0.42 => ( P @ ( cons_list_a @ X2 @ Xs3 ) @ Ys3 ) )
% 0.16/0.42 => ( P @ A0 @ A1 ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % splice.induct
% 0.16/0.42 thf(fact_150_splice_Oinduct,axiom,
% 0.16/0.42 ! [P: list_a > list_a > $o,A0: list_a,A1: list_a] :
% 0.16/0.42 ( ! [X_1: list_a] : ( P @ nil_a @ X_1 )
% 0.16/0.42 => ( ! [X2: a,Xs3: list_a,Ys3: list_a] :
% 0.16/0.42 ( ( P @ Ys3 @ Xs3 )
% 0.16/0.42 => ( P @ ( cons_a @ X2 @ Xs3 ) @ Ys3 ) )
% 0.16/0.42 => ( P @ A0 @ A1 ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % splice.induct
% 0.16/0.42 thf(fact_151_list__induct2_H,axiom,
% 0.16/0.42 ! [P: list_a > list_list_a > $o,Xs: list_a,Ys: list_list_a] :
% 0.16/0.42 ( ( P @ nil_a @ nil_list_a )
% 0.16/0.42 => ( ! [X2: a,Xs3: list_a] : ( P @ ( cons_a @ X2 @ Xs3 ) @ nil_list_a )
% 0.16/0.42 => ( ! [Y2: list_a,Ys3: list_list_a] : ( P @ nil_a @ ( cons_list_a @ Y2 @ Ys3 ) )
% 0.16/0.42 => ( ! [X2: a,Xs3: list_a,Y2: list_a,Ys3: list_list_a] :
% 0.16/0.42 ( ( P @ Xs3 @ Ys3 )
% 0.16/0.42 => ( P @ ( cons_a @ X2 @ Xs3 ) @ ( cons_list_a @ Y2 @ Ys3 ) ) )
% 0.16/0.42 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % list_induct2'
% 0.16/0.42 thf(fact_152_list__induct2_H,axiom,
% 0.16/0.42 ! [P: list_list_a > list_a > $o,Xs: list_list_a,Ys: list_a] :
% 0.16/0.42 ( ( P @ nil_list_a @ nil_a )
% 0.16/0.42 => ( ! [X2: list_a,Xs3: list_list_a] : ( P @ ( cons_list_a @ X2 @ Xs3 ) @ nil_a )
% 0.16/0.42 => ( ! [Y2: a,Ys3: list_a] : ( P @ nil_list_a @ ( cons_a @ Y2 @ Ys3 ) )
% 0.16/0.42 => ( ! [X2: list_a,Xs3: list_list_a,Y2: a,Ys3: list_a] :
% 0.16/0.42 ( ( P @ Xs3 @ Ys3 )
% 0.16/0.42 => ( P @ ( cons_list_a @ X2 @ Xs3 ) @ ( cons_a @ Y2 @ Ys3 ) ) )
% 0.16/0.42 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % list_induct2'
% 0.16/0.42 thf(fact_153_list__induct2_H,axiom,
% 0.16/0.42 ! [P: list_list_a > list_list_a > $o,Xs: list_list_a,Ys: list_list_a] :
% 0.16/0.42 ( ( P @ nil_list_a @ nil_list_a )
% 0.16/0.42 => ( ! [X2: list_a,Xs3: list_list_a] : ( P @ ( cons_list_a @ X2 @ Xs3 ) @ nil_list_a )
% 0.16/0.42 => ( ! [Y2: list_a,Ys3: list_list_a] : ( P @ nil_list_a @ ( cons_list_a @ Y2 @ Ys3 ) )
% 0.16/0.42 => ( ! [X2: list_a,Xs3: list_list_a,Y2: list_a,Ys3: list_list_a] :
% 0.16/0.42 ( ( P @ Xs3 @ Ys3 )
% 0.16/0.42 => ( P @ ( cons_list_a @ X2 @ Xs3 ) @ ( cons_list_a @ Y2 @ Ys3 ) ) )
% 0.16/0.42 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % list_induct2'
% 0.16/0.42 thf(fact_154_list__induct2_H,axiom,
% 0.16/0.42 ! [P: list_a > list_a > $o,Xs: list_a,Ys: list_a] :
% 0.16/0.42 ( ( P @ nil_a @ nil_a )
% 0.16/0.42 => ( ! [X2: a,Xs3: list_a] : ( P @ ( cons_a @ X2 @ Xs3 ) @ nil_a )
% 0.16/0.42 => ( ! [Y2: a,Ys3: list_a] : ( P @ nil_a @ ( cons_a @ Y2 @ Ys3 ) )
% 0.16/0.42 => ( ! [X2: a,Xs3: list_a,Y2: a,Ys3: list_a] :
% 0.16/0.42 ( ( P @ Xs3 @ Ys3 )
% 0.16/0.42 => ( P @ ( cons_a @ X2 @ Xs3 ) @ ( cons_a @ Y2 @ Ys3 ) ) )
% 0.16/0.42 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % list_induct2'
% 0.16/0.42 thf(fact_155_neq__Nil__conv,axiom,
% 0.16/0.42 ! [Xs: list_list_a] :
% 0.16/0.42 ( ( Xs != nil_list_a )
% 0.16/0.42 = ( ? [Y3: list_a,Ys2: list_list_a] :
% 0.16/0.42 ( Xs
% 0.16/0.42 = ( cons_list_a @ Y3 @ Ys2 ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % neq_Nil_conv
% 0.16/0.42 thf(fact_156_neq__Nil__conv,axiom,
% 0.16/0.42 ! [Xs: list_a] :
% 0.16/0.42 ( ( Xs != nil_a )
% 0.16/0.42 = ( ? [Y3: a,Ys2: list_a] :
% 0.16/0.42 ( Xs
% 0.16/0.42 = ( cons_a @ Y3 @ Ys2 ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % neq_Nil_conv
% 0.16/0.42 thf(fact_157_list_Oinducts,axiom,
% 0.16/0.42 ! [P: list_list_a > $o,List: list_list_a] :
% 0.16/0.42 ( ( P @ nil_list_a )
% 0.16/0.42 => ( ! [X12: list_a,X23: list_list_a] :
% 0.16/0.42 ( ( P @ X23 )
% 0.16/0.42 => ( P @ ( cons_list_a @ X12 @ X23 ) ) )
% 0.16/0.42 => ( P @ List ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % list.inducts
% 0.16/0.42 thf(fact_158_list_Oinducts,axiom,
% 0.16/0.42 ! [P: list_a > $o,List: list_a] :
% 0.16/0.42 ( ( P @ nil_a )
% 0.16/0.42 => ( ! [X12: a,X23: list_a] :
% 0.16/0.42 ( ( P @ X23 )
% 0.16/0.42 => ( P @ ( cons_a @ X12 @ X23 ) ) )
% 0.16/0.42 => ( P @ List ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % list.inducts
% 0.16/0.42 thf(fact_159_list_Oexhaust,axiom,
% 0.16/0.42 ! [Y: list_list_a] :
% 0.16/0.42 ( ( Y != nil_list_a )
% 0.16/0.42 => ~ ! [X212: list_a,X223: list_list_a] :
% 0.16/0.42 ( Y
% 0.16/0.42 != ( cons_list_a @ X212 @ X223 ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % list.exhaust
% 0.16/0.42 thf(fact_160_list_Oexhaust,axiom,
% 0.16/0.42 ! [Y: list_a] :
% 0.16/0.42 ( ( Y != nil_a )
% 0.16/0.42 => ~ ! [X212: a,X223: list_a] :
% 0.16/0.42 ( Y
% 0.16/0.42 != ( cons_a @ X212 @ X223 ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % list.exhaust
% 0.16/0.42 thf(fact_161_list_OdiscI,axiom,
% 0.16/0.42 ! [List: list_list_a,X21: list_a,X222: list_list_a] :
% 0.16/0.42 ( ( List
% 0.16/0.42 = ( cons_list_a @ X21 @ X222 ) )
% 0.16/0.42 => ( List != nil_list_a ) ) ).
% 0.16/0.42
% 0.16/0.42 % list.discI
% 0.16/0.42 thf(fact_162_list_OdiscI,axiom,
% 0.16/0.42 ! [List: list_a,X21: a,X222: list_a] :
% 0.16/0.42 ( ( List
% 0.16/0.42 = ( cons_a @ X21 @ X222 ) )
% 0.16/0.42 => ( List != nil_a ) ) ).
% 0.16/0.42
% 0.16/0.42 % list.discI
% 0.16/0.42 thf(fact_163_list_Odistinct_I1_J,axiom,
% 0.16/0.42 ! [X21: list_a,X222: list_list_a] :
% 0.16/0.42 ( nil_list_a
% 0.16/0.42 != ( cons_list_a @ X21 @ X222 ) ) ).
% 0.16/0.42
% 0.16/0.42 % list.distinct(1)
% 0.16/0.42 thf(fact_164_list_Odistinct_I1_J,axiom,
% 0.16/0.42 ! [X21: a,X222: list_a] :
% 0.16/0.42 ( nil_a
% 0.16/0.42 != ( cons_a @ X21 @ X222 ) ) ).
% 0.16/0.42
% 0.16/0.42 % list.distinct(1)
% 0.16/0.42 thf(fact_165_not__Cons__self2,axiom,
% 0.16/0.42 ! [X: list_a,Xs: list_list_a] :
% 0.16/0.42 ( ( cons_list_a @ X @ Xs )
% 0.16/0.42 != Xs ) ).
% 0.16/0.42
% 0.16/0.42 % not_Cons_self2
% 0.16/0.42 thf(fact_166_not__Cons__self2,axiom,
% 0.16/0.42 ! [X: a,Xs: list_a] :
% 0.16/0.42 ( ( cons_a @ X @ Xs )
% 0.16/0.42 != Xs ) ).
% 0.16/0.42
% 0.16/0.42 % not_Cons_self2
% 0.16/0.42 thf(fact_167_ord_Olexordp__eq_OCons__eq,axiom,
% 0.16/0.42 ! [Less: list_a > list_a > $o,X: list_a,Y: list_a,Xs: list_list_a,Ys: list_list_a] :
% 0.16/0.42 ( ~ ( Less @ X @ Y )
% 0.16/0.42 => ( ~ ( Less @ Y @ X )
% 0.16/0.42 => ( ( lexordp_eq_list_a @ Less @ Xs @ Ys )
% 0.16/0.42 => ( lexordp_eq_list_a @ Less @ ( cons_list_a @ X @ Xs ) @ ( cons_list_a @ Y @ Ys ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % ord.lexordp_eq.Cons_eq
% 0.16/0.42 thf(fact_168_ord_Olexordp__eq_OCons__eq,axiom,
% 0.16/0.42 ! [Less: a > a > $o,X: a,Y: a,Xs: list_a,Ys: list_a] :
% 0.16/0.42 ( ~ ( Less @ X @ Y )
% 0.16/0.42 => ( ~ ( Less @ Y @ X )
% 0.16/0.42 => ( ( lexordp_eq_a @ Less @ Xs @ Ys )
% 0.16/0.42 => ( lexordp_eq_a @ Less @ ( cons_a @ X @ Xs ) @ ( cons_a @ Y @ Ys ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % ord.lexordp_eq.Cons_eq
% 0.16/0.42 thf(fact_169_ord_Olexordp__eq_OCons,axiom,
% 0.16/0.42 ! [Less: list_a > list_a > $o,X: list_a,Y: list_a,Xs: list_list_a,Ys: list_list_a] :
% 0.16/0.42 ( ( Less @ X @ Y )
% 0.16/0.42 => ( lexordp_eq_list_a @ Less @ ( cons_list_a @ X @ Xs ) @ ( cons_list_a @ Y @ Ys ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % ord.lexordp_eq.Cons
% 0.16/0.42 thf(fact_170_ord_Olexordp__eq_OCons,axiom,
% 0.16/0.42 ! [Less: a > a > $o,X: a,Y: a,Xs: list_a,Ys: list_a] :
% 0.16/0.42 ( ( Less @ X @ Y )
% 0.16/0.42 => ( lexordp_eq_a @ Less @ ( cons_a @ X @ Xs ) @ ( cons_a @ Y @ Ys ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % ord.lexordp_eq.Cons
% 0.16/0.42 thf(fact_171_ord_Olexordp__eq_Oinducts,axiom,
% 0.16/0.42 ! [Less: list_a > list_a > $o,X1: list_list_a,X22: list_list_a,P: list_list_a > list_list_a > $o] :
% 0.16/0.42 ( ( lexordp_eq_list_a @ Less @ X1 @ X22 )
% 0.16/0.42 => ( ! [X_1: list_list_a] : ( P @ nil_list_a @ X_1 )
% 0.16/0.42 => ( ! [X2: list_a,Y2: list_a,Xs3: list_list_a,Ys3: list_list_a] :
% 0.16/0.42 ( ( Less @ X2 @ Y2 )
% 0.16/0.42 => ( P @ ( cons_list_a @ X2 @ Xs3 ) @ ( cons_list_a @ Y2 @ Ys3 ) ) )
% 0.16/0.42 => ( ! [X2: list_a,Y2: list_a,Xs3: list_list_a,Ys3: list_list_a] :
% 0.16/0.42 ( ~ ( Less @ X2 @ Y2 )
% 0.16/0.42 => ( ~ ( Less @ Y2 @ X2 )
% 0.16/0.42 => ( ( lexordp_eq_list_a @ Less @ Xs3 @ Ys3 )
% 0.16/0.42 => ( ( P @ Xs3 @ Ys3 )
% 0.16/0.42 => ( P @ ( cons_list_a @ X2 @ Xs3 ) @ ( cons_list_a @ Y2 @ Ys3 ) ) ) ) ) )
% 0.16/0.42 => ( P @ X1 @ X22 ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % ord.lexordp_eq.inducts
% 0.16/0.42 thf(fact_172_ord_Olexordp__eq_Oinducts,axiom,
% 0.16/0.42 ! [Less: a > a > $o,X1: list_a,X22: list_a,P: list_a > list_a > $o] :
% 0.16/0.42 ( ( lexordp_eq_a @ Less @ X1 @ X22 )
% 0.16/0.42 => ( ! [X_1: list_a] : ( P @ nil_a @ X_1 )
% 0.16/0.42 => ( ! [X2: a,Y2: a,Xs3: list_a,Ys3: list_a] :
% 0.16/0.42 ( ( Less @ X2 @ Y2 )
% 0.16/0.42 => ( P @ ( cons_a @ X2 @ Xs3 ) @ ( cons_a @ Y2 @ Ys3 ) ) )
% 0.16/0.42 => ( ! [X2: a,Y2: a,Xs3: list_a,Ys3: list_a] :
% 0.16/0.42 ( ~ ( Less @ X2 @ Y2 )
% 0.16/0.42 => ( ~ ( Less @ Y2 @ X2 )
% 0.16/0.42 => ( ( lexordp_eq_a @ Less @ Xs3 @ Ys3 )
% 0.16/0.42 => ( ( P @ Xs3 @ Ys3 )
% 0.16/0.42 => ( P @ ( cons_a @ X2 @ Xs3 ) @ ( cons_a @ Y2 @ Ys3 ) ) ) ) ) )
% 0.16/0.42 => ( P @ X1 @ X22 ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % ord.lexordp_eq.inducts
% 0.16/0.42 thf(fact_173_ord_Olexordp__eq_Osimps,axiom,
% 0.16/0.42 ( lexordp_eq_list_a
% 0.16/0.42 = ( ^ [Less2: list_a > list_a > $o,A12: list_list_a,A23: list_list_a] :
% 0.16/0.42 ( ? [Ys2: list_list_a] :
% 0.16/0.42 ( ( A12 = nil_list_a )
% 0.16/0.42 & ( A23 = Ys2 ) )
% 0.16/0.42 | ? [X3: list_a,Y3: list_a,Xs2: list_list_a,Ys2: list_list_a] :
% 0.16/0.42 ( ( A12
% 0.16/0.42 = ( cons_list_a @ X3 @ Xs2 ) )
% 0.16/0.42 & ( A23
% 0.16/0.42 = ( cons_list_a @ Y3 @ Ys2 ) )
% 0.16/0.42 & ( Less2 @ X3 @ Y3 ) )
% 0.16/0.42 | ? [X3: list_a,Y3: list_a,Xs2: list_list_a,Ys2: list_list_a] :
% 0.16/0.42 ( ( A12
% 0.16/0.42 = ( cons_list_a @ X3 @ Xs2 ) )
% 0.16/0.42 & ( A23
% 0.16/0.42 = ( cons_list_a @ Y3 @ Ys2 ) )
% 0.16/0.42 & ~ ( Less2 @ X3 @ Y3 )
% 0.16/0.42 & ~ ( Less2 @ Y3 @ X3 )
% 0.16/0.42 & ( lexordp_eq_list_a @ Less2 @ Xs2 @ Ys2 ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % ord.lexordp_eq.simps
% 0.16/0.42 thf(fact_174_ord_Olexordp__eq_Osimps,axiom,
% 0.16/0.42 ( lexordp_eq_a
% 0.16/0.42 = ( ^ [Less2: a > a > $o,A12: list_a,A23: list_a] :
% 0.16/0.42 ( ? [Ys2: list_a] :
% 0.16/0.42 ( ( A12 = nil_a )
% 0.16/0.42 & ( A23 = Ys2 ) )
% 0.16/0.42 | ? [X3: a,Y3: a,Xs2: list_a,Ys2: list_a] :
% 0.16/0.42 ( ( A12
% 0.16/0.42 = ( cons_a @ X3 @ Xs2 ) )
% 0.16/0.42 & ( A23
% 0.16/0.42 = ( cons_a @ Y3 @ Ys2 ) )
% 0.16/0.42 & ( Less2 @ X3 @ Y3 ) )
% 0.16/0.42 | ? [X3: a,Y3: a,Xs2: list_a,Ys2: list_a] :
% 0.16/0.42 ( ( A12
% 0.16/0.42 = ( cons_a @ X3 @ Xs2 ) )
% 0.16/0.42 & ( A23
% 0.16/0.42 = ( cons_a @ Y3 @ Ys2 ) )
% 0.16/0.42 & ~ ( Less2 @ X3 @ Y3 )
% 0.16/0.42 & ~ ( Less2 @ Y3 @ X3 )
% 0.16/0.42 & ( lexordp_eq_a @ Less2 @ Xs2 @ Ys2 ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % ord.lexordp_eq.simps
% 0.16/0.42 thf(fact_175_ord_Olexordp__eq_Ocases,axiom,
% 0.16/0.42 ! [Less: list_a > list_a > $o,A1: list_list_a,A22: list_list_a] :
% 0.16/0.42 ( ( lexordp_eq_list_a @ Less @ A1 @ A22 )
% 0.16/0.42 => ( ( A1 != nil_list_a )
% 0.16/0.42 => ( ! [X2: list_a] :
% 0.16/0.42 ( ? [Xs3: list_list_a] :
% 0.16/0.42 ( A1
% 0.16/0.42 = ( cons_list_a @ X2 @ Xs3 ) )
% 0.16/0.42 => ! [Y2: list_a] :
% 0.16/0.42 ( ? [Ys3: list_list_a] :
% 0.16/0.42 ( A22
% 0.16/0.42 = ( cons_list_a @ Y2 @ Ys3 ) )
% 0.16/0.42 => ~ ( Less @ X2 @ Y2 ) ) )
% 0.16/0.42 => ~ ! [X2: list_a,Y2: list_a,Xs3: list_list_a] :
% 0.16/0.42 ( ( A1
% 0.16/0.42 = ( cons_list_a @ X2 @ Xs3 ) )
% 0.16/0.42 => ! [Ys3: list_list_a] :
% 0.16/0.42 ( ( A22
% 0.16/0.42 = ( cons_list_a @ Y2 @ Ys3 ) )
% 0.16/0.42 => ( ~ ( Less @ X2 @ Y2 )
% 0.16/0.42 => ( ~ ( Less @ Y2 @ X2 )
% 0.16/0.42 => ~ ( lexordp_eq_list_a @ Less @ Xs3 @ Ys3 ) ) ) ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % ord.lexordp_eq.cases
% 0.16/0.42 thf(fact_176_ord_Olexordp__eq_Ocases,axiom,
% 0.16/0.42 ! [Less: a > a > $o,A1: list_a,A22: list_a] :
% 0.16/0.42 ( ( lexordp_eq_a @ Less @ A1 @ A22 )
% 0.16/0.42 => ( ( A1 != nil_a )
% 0.16/0.42 => ( ! [X2: a] :
% 0.16/0.42 ( ? [Xs3: list_a] :
% 0.16/0.42 ( A1
% 0.16/0.42 = ( cons_a @ X2 @ Xs3 ) )
% 0.16/0.42 => ! [Y2: a] :
% 0.16/0.42 ( ? [Ys3: list_a] :
% 0.16/0.42 ( A22
% 0.16/0.42 = ( cons_a @ Y2 @ Ys3 ) )
% 0.16/0.42 => ~ ( Less @ X2 @ Y2 ) ) )
% 0.16/0.42 => ~ ! [X2: a,Y2: a,Xs3: list_a] :
% 0.16/0.42 ( ( A1
% 0.16/0.42 = ( cons_a @ X2 @ Xs3 ) )
% 0.16/0.42 => ! [Ys3: list_a] :
% 0.16/0.42 ( ( A22
% 0.16/0.42 = ( cons_a @ Y2 @ Ys3 ) )
% 0.16/0.42 => ( ~ ( Less @ X2 @ Y2 )
% 0.16/0.42 => ( ~ ( Less @ Y2 @ X2 )
% 0.16/0.42 => ~ ( lexordp_eq_a @ Less @ Xs3 @ Ys3 ) ) ) ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % ord.lexordp_eq.cases
% 0.16/0.42 thf(fact_177_ord_Olexordp__eq_Ocong,axiom,
% 0.16/0.42 lexordp_eq_a = lexordp_eq_a ).
% 0.16/0.42
% 0.16/0.42 % ord.lexordp_eq.cong
% 0.16/0.42 thf(fact_178_ord_Olexordp__eq__refl,axiom,
% 0.16/0.42 ! [Less: a > a > $o,Xs: list_a] : ( lexordp_eq_a @ Less @ Xs @ Xs ) ).
% 0.16/0.42
% 0.16/0.42 % ord.lexordp_eq_refl
% 0.16/0.42 thf(fact_179_ord_Olexordp__eq_ONil,axiom,
% 0.16/0.42 ! [Less: list_a > list_a > $o,Ys: list_list_a] : ( lexordp_eq_list_a @ Less @ nil_list_a @ Ys ) ).
% 0.16/0.42
% 0.16/0.42 % ord.lexordp_eq.Nil
% 0.16/0.42 thf(fact_180_ord_Olexordp__eq_ONil,axiom,
% 0.16/0.42 ! [Less: a > a > $o,Ys: list_a] : ( lexordp_eq_a @ Less @ nil_a @ Ys ) ).
% 0.16/0.42
% 0.16/0.42 % ord.lexordp_eq.Nil
% 0.16/0.42 thf(fact_181_local_Olexordp_ONil,axiom,
% 0.16/0.42 ! [Y: a,Ys: list_a] : ( lexordp_a @ less @ nil_a @ ( cons_a @ Y @ Ys ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.lexordp.Nil
% 0.16/0.42 thf(fact_182_local_Olexordp_Ocases,axiom,
% 0.16/0.42 ! [A1: list_a,A22: list_a] :
% 0.16/0.42 ( ( lexordp_a @ less @ A1 @ A22 )
% 0.16/0.42 => ( ( ( A1 = nil_a )
% 0.16/0.42 => ! [Y2: a,Ys3: list_a] :
% 0.16/0.42 ( A22
% 0.16/0.42 != ( cons_a @ Y2 @ Ys3 ) ) )
% 0.16/0.42 => ( ! [X2: a] :
% 0.16/0.42 ( ? [Xs3: list_a] :
% 0.16/0.42 ( A1
% 0.16/0.42 = ( cons_a @ X2 @ Xs3 ) )
% 0.16/0.42 => ! [Y2: a] :
% 0.16/0.42 ( ? [Ys3: list_a] :
% 0.16/0.42 ( A22
% 0.16/0.42 = ( cons_a @ Y2 @ Ys3 ) )
% 0.16/0.42 => ~ ( less @ X2 @ Y2 ) ) )
% 0.16/0.42 => ~ ! [X2: a,Y2: a,Xs3: list_a] :
% 0.16/0.42 ( ( A1
% 0.16/0.42 = ( cons_a @ X2 @ Xs3 ) )
% 0.16/0.42 => ! [Ys3: list_a] :
% 0.16/0.42 ( ( A22
% 0.16/0.42 = ( cons_a @ Y2 @ Ys3 ) )
% 0.16/0.42 => ( ~ ( less @ X2 @ Y2 )
% 0.16/0.42 => ( ~ ( less @ Y2 @ X2 )
% 0.16/0.42 => ~ ( lexordp_a @ less @ Xs3 @ Ys3 ) ) ) ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.lexordp.cases
% 0.16/0.42 thf(fact_183_local_Olexordp_Oinducts,axiom,
% 0.16/0.42 ! [X1: list_a,X22: list_a,P: list_a > list_a > $o] :
% 0.16/0.42 ( ( lexordp_a @ less @ X1 @ X22 )
% 0.16/0.42 => ( ! [Y2: a,Ys3: list_a] : ( P @ nil_a @ ( cons_a @ Y2 @ Ys3 ) )
% 0.16/0.42 => ( ! [X2: a,Y2: a,Xs3: list_a,Ys3: list_a] :
% 0.16/0.42 ( ( less @ X2 @ Y2 )
% 0.16/0.42 => ( P @ ( cons_a @ X2 @ Xs3 ) @ ( cons_a @ Y2 @ Ys3 ) ) )
% 0.16/0.42 => ( ! [X2: a,Y2: a,Xs3: list_a,Ys3: list_a] :
% 0.16/0.42 ( ~ ( less @ X2 @ Y2 )
% 0.16/0.42 => ( ~ ( less @ Y2 @ X2 )
% 0.16/0.42 => ( ( lexordp_a @ less @ Xs3 @ Ys3 )
% 0.16/0.42 => ( ( P @ Xs3 @ Ys3 )
% 0.16/0.42 => ( P @ ( cons_a @ X2 @ Xs3 ) @ ( cons_a @ Y2 @ Ys3 ) ) ) ) ) )
% 0.16/0.42 => ( P @ X1 @ X22 ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.lexordp.inducts
% 0.16/0.42 thf(fact_184_local_Olexordp_Osimps,axiom,
% 0.16/0.42 ! [A1: list_a,A22: list_a] :
% 0.16/0.42 ( ( lexordp_a @ less @ A1 @ A22 )
% 0.16/0.42 = ( ? [Y3: a,Ys2: list_a] :
% 0.16/0.42 ( ( A1 = nil_a )
% 0.16/0.42 & ( A22
% 0.16/0.42 = ( cons_a @ Y3 @ Ys2 ) ) )
% 0.16/0.42 | ? [X3: a,Y3: a,Xs2: list_a,Ys2: list_a] :
% 0.16/0.42 ( ( A1
% 0.16/0.42 = ( cons_a @ X3 @ Xs2 ) )
% 0.16/0.42 & ( A22
% 0.16/0.42 = ( cons_a @ Y3 @ Ys2 ) )
% 0.16/0.42 & ( less @ X3 @ Y3 ) )
% 0.16/0.42 | ? [X3: a,Y3: a,Xs2: list_a,Ys2: list_a] :
% 0.16/0.42 ( ( A1
% 0.16/0.42 = ( cons_a @ X3 @ Xs2 ) )
% 0.16/0.42 & ( A22
% 0.16/0.42 = ( cons_a @ Y3 @ Ys2 ) )
% 0.16/0.42 & ~ ( less @ X3 @ Y3 )
% 0.16/0.42 & ~ ( less @ Y3 @ X3 )
% 0.16/0.42 & ( lexordp_a @ less @ Xs2 @ Ys2 ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.lexordp.simps
% 0.16/0.42 thf(fact_185_local_Olexordp__antisym,axiom,
% 0.16/0.42 ! [Xs: list_a,Ys: list_a] :
% 0.16/0.42 ( ( lexordp_a @ less @ Xs @ Ys )
% 0.16/0.42 => ~ ( lexordp_a @ less @ Ys @ Xs ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.lexordp_antisym
% 0.16/0.42 thf(fact_186_local_Olexordp__irreflexive,axiom,
% 0.16/0.42 ! [Xs: list_a] :
% 0.16/0.42 ( ! [X2: a] :
% 0.16/0.42 ~ ( less @ X2 @ X2 )
% 0.16/0.42 => ~ ( lexordp_a @ less @ Xs @ Xs ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.lexordp_irreflexive
% 0.16/0.42 thf(fact_187_local_Olexordp__irreflexive_H,axiom,
% 0.16/0.42 ! [Xs: list_a] :
% 0.16/0.42 ~ ( lexordp_a @ less @ Xs @ Xs ) ).
% 0.16/0.42
% 0.16/0.42 % local.lexordp_irreflexive'
% 0.16/0.42 thf(fact_188_local_Olexordp_OCons__eq,axiom,
% 0.16/0.42 ! [X: a,Y: a,Xs: list_a,Ys: list_a] :
% 0.16/0.42 ( ~ ( less @ X @ Y )
% 0.16/0.42 => ( ~ ( less @ Y @ X )
% 0.16/0.42 => ( ( lexordp_a @ less @ Xs @ Ys )
% 0.16/0.42 => ( lexordp_a @ less @ ( cons_a @ X @ Xs ) @ ( cons_a @ Y @ Ys ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.lexordp.Cons_eq
% 0.16/0.42 thf(fact_189_local_Olexordp_OCons,axiom,
% 0.16/0.42 ! [X: a,Y: a,Xs: list_a,Ys: list_a] :
% 0.16/0.42 ( ( less @ X @ Y )
% 0.16/0.42 => ( lexordp_a @ less @ ( cons_a @ X @ Xs ) @ ( cons_a @ Y @ Ys ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.lexordp.Cons
% 0.16/0.42 thf(fact_190_local_Olexordp__into__lexordp__eq,axiom,
% 0.16/0.42 ! [Xs: list_a,Ys: list_a] :
% 0.16/0.42 ( ( lexordp_a @ less @ Xs @ Ys )
% 0.16/0.42 => ( lexordp_eq_a @ less @ Xs @ Ys ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.lexordp_into_lexordp_eq
% 0.16/0.42 thf(fact_191_ord_Olexordp__simps_I3_J,axiom,
% 0.16/0.42 ! [Less: list_a > list_a > $o,X: list_a,Xs: list_list_a,Y: list_a,Ys: list_list_a] :
% 0.16/0.42 ( ( lexordp_list_a @ Less @ ( cons_list_a @ X @ Xs ) @ ( cons_list_a @ Y @ Ys ) )
% 0.16/0.42 = ( ( Less @ X @ Y )
% 0.16/0.42 | ( ~ ( Less @ Y @ X )
% 0.16/0.42 & ( lexordp_list_a @ Less @ Xs @ Ys ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % ord.lexordp_simps(3)
% 0.16/0.42 thf(fact_192_ord_Olexordp__simps_I3_J,axiom,
% 0.16/0.42 ! [Less: a > a > $o,X: a,Xs: list_a,Y: a,Ys: list_a] :
% 0.16/0.42 ( ( lexordp_a @ Less @ ( cons_a @ X @ Xs ) @ ( cons_a @ Y @ Ys ) )
% 0.16/0.42 = ( ( Less @ X @ Y )
% 0.16/0.42 | ( ~ ( Less @ Y @ X )
% 0.16/0.42 & ( lexordp_a @ Less @ Xs @ Ys ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % ord.lexordp_simps(3)
% 0.16/0.42 thf(fact_193_ord_Olexordp__simps_I2_J,axiom,
% 0.16/0.42 ! [Less: list_a > list_a > $o,Xs: list_list_a] :
% 0.16/0.42 ~ ( lexordp_list_a @ Less @ Xs @ nil_list_a ) ).
% 0.16/0.42
% 0.16/0.42 % ord.lexordp_simps(2)
% 0.16/0.42 thf(fact_194_ord_Olexordp__simps_I2_J,axiom,
% 0.16/0.42 ! [Less: a > a > $o,Xs: list_a] :
% 0.16/0.42 ~ ( lexordp_a @ Less @ Xs @ nil_a ) ).
% 0.16/0.42
% 0.16/0.42 % ord.lexordp_simps(2)
% 0.16/0.42 thf(fact_195_ord_Olexordp__simps_I1_J,axiom,
% 0.16/0.42 ! [Less: list_a > list_a > $o,Ys: list_list_a] :
% 0.16/0.42 ( ( lexordp_list_a @ Less @ nil_list_a @ Ys )
% 0.16/0.42 = ( Ys != nil_list_a ) ) ).
% 0.16/0.42
% 0.16/0.42 % ord.lexordp_simps(1)
% 0.16/0.42 thf(fact_196_ord_Olexordp__simps_I1_J,axiom,
% 0.16/0.42 ! [Less: a > a > $o,Ys: list_a] :
% 0.16/0.42 ( ( lexordp_a @ Less @ nil_a @ Ys )
% 0.16/0.42 = ( Ys != nil_a ) ) ).
% 0.16/0.42
% 0.16/0.42 % ord.lexordp_simps(1)
% 0.16/0.42 thf(fact_197_local_Olexordp__simps_I3_J,axiom,
% 0.16/0.42 ! [X: a,Xs: list_a,Y: a,Ys: list_a] :
% 0.16/0.42 ( ( lexordp_a @ less @ ( cons_a @ X @ Xs ) @ ( cons_a @ Y @ Ys ) )
% 0.16/0.42 = ( ( less @ X @ Y )
% 0.16/0.42 | ( ~ ( less @ Y @ X )
% 0.16/0.42 & ( lexordp_a @ less @ Xs @ Ys ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.lexordp_simps(3)
% 0.16/0.42 thf(fact_198_local_Olexordp__simps_I1_J,axiom,
% 0.16/0.42 ! [Ys: list_a] :
% 0.16/0.42 ( ( lexordp_a @ less @ nil_a @ Ys )
% 0.16/0.42 = ( Ys != nil_a ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.lexordp_simps(1)
% 0.16/0.42 thf(fact_199_local_Olexordp__simps_I2_J,axiom,
% 0.16/0.42 ! [Xs: list_a] :
% 0.16/0.42 ~ ( lexordp_a @ less @ Xs @ nil_a ) ).
% 0.16/0.42
% 0.16/0.42 % local.lexordp_simps(2)
% 0.16/0.42 thf(fact_200_ord_Olexordp_Ocong,axiom,
% 0.16/0.42 lexordp_a = lexordp_a ).
% 0.16/0.42
% 0.16/0.42 % ord.lexordp.cong
% 0.16/0.42 thf(fact_201_ord_Olexordp__irreflexive,axiom,
% 0.16/0.42 ! [Less: a > a > $o,Xs: list_a] :
% 0.16/0.42 ( ! [X2: a] :
% 0.16/0.42 ~ ( Less @ X2 @ X2 )
% 0.16/0.42 => ~ ( lexordp_a @ Less @ Xs @ Xs ) ) ).
% 0.16/0.42
% 0.16/0.42 % ord.lexordp_irreflexive
% 0.16/0.42 thf(fact_202_ord_Olexordp_OCons__eq,axiom,
% 0.16/0.42 ! [Less: list_a > list_a > $o,X: list_a,Y: list_a,Xs: list_list_a,Ys: list_list_a] :
% 0.16/0.42 ( ~ ( Less @ X @ Y )
% 0.16/0.42 => ( ~ ( Less @ Y @ X )
% 0.16/0.42 => ( ( lexordp_list_a @ Less @ Xs @ Ys )
% 0.16/0.42 => ( lexordp_list_a @ Less @ ( cons_list_a @ X @ Xs ) @ ( cons_list_a @ Y @ Ys ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % ord.lexordp.Cons_eq
% 0.16/0.42 thf(fact_203_ord_Olexordp_OCons__eq,axiom,
% 0.16/0.42 ! [Less: a > a > $o,X: a,Y: a,Xs: list_a,Ys: list_a] :
% 0.16/0.42 ( ~ ( Less @ X @ Y )
% 0.16/0.42 => ( ~ ( Less @ Y @ X )
% 0.16/0.42 => ( ( lexordp_a @ Less @ Xs @ Ys )
% 0.16/0.42 => ( lexordp_a @ Less @ ( cons_a @ X @ Xs ) @ ( cons_a @ Y @ Ys ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % ord.lexordp.Cons_eq
% 0.16/0.42 thf(fact_204_ord_Olexordp_OCons,axiom,
% 0.16/0.42 ! [Less: list_a > list_a > $o,X: list_a,Y: list_a,Xs: list_list_a,Ys: list_list_a] :
% 0.16/0.42 ( ( Less @ X @ Y )
% 0.16/0.42 => ( lexordp_list_a @ Less @ ( cons_list_a @ X @ Xs ) @ ( cons_list_a @ Y @ Ys ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % ord.lexordp.Cons
% 0.16/0.42 thf(fact_205_ord_Olexordp_OCons,axiom,
% 0.16/0.42 ! [Less: a > a > $o,X: a,Y: a,Xs: list_a,Ys: list_a] :
% 0.16/0.42 ( ( Less @ X @ Y )
% 0.16/0.42 => ( lexordp_a @ Less @ ( cons_a @ X @ Xs ) @ ( cons_a @ Y @ Ys ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % ord.lexordp.Cons
% 0.16/0.42 thf(fact_206_ord_Olexordp__into__lexordp__eq,axiom,
% 0.16/0.42 ! [Less: a > a > $o,Xs: list_a,Ys: list_a] :
% 0.16/0.42 ( ( lexordp_a @ Less @ Xs @ Ys )
% 0.16/0.42 => ( lexordp_eq_a @ Less @ Xs @ Ys ) ) ).
% 0.16/0.42
% 0.16/0.42 % ord.lexordp_into_lexordp_eq
% 0.16/0.42 thf(fact_207_ord_Olexordp_ONil,axiom,
% 0.16/0.42 ! [Less: list_a > list_a > $o,Y: list_a,Ys: list_list_a] : ( lexordp_list_a @ Less @ nil_list_a @ ( cons_list_a @ Y @ Ys ) ) ).
% 0.16/0.42
% 0.16/0.42 % ord.lexordp.Nil
% 0.16/0.42 thf(fact_208_ord_Olexordp_ONil,axiom,
% 0.16/0.42 ! [Less: a > a > $o,Y: a,Ys: list_a] : ( lexordp_a @ Less @ nil_a @ ( cons_a @ Y @ Ys ) ) ).
% 0.16/0.42
% 0.16/0.42 % ord.lexordp.Nil
% 0.16/0.42 thf(fact_209_ord_Olexordp_Ocases,axiom,
% 0.16/0.42 ! [Less: list_a > list_a > $o,A1: list_list_a,A22: list_list_a] :
% 0.16/0.42 ( ( lexordp_list_a @ Less @ A1 @ A22 )
% 0.16/0.42 => ( ( ( A1 = nil_list_a )
% 0.16/0.42 => ! [Y2: list_a,Ys3: list_list_a] :
% 0.16/0.42 ( A22
% 0.16/0.42 != ( cons_list_a @ Y2 @ Ys3 ) ) )
% 0.16/0.42 => ( ! [X2: list_a] :
% 0.16/0.42 ( ? [Xs3: list_list_a] :
% 0.16/0.42 ( A1
% 0.16/0.42 = ( cons_list_a @ X2 @ Xs3 ) )
% 0.16/0.42 => ! [Y2: list_a] :
% 0.16/0.42 ( ? [Ys3: list_list_a] :
% 0.16/0.42 ( A22
% 0.16/0.42 = ( cons_list_a @ Y2 @ Ys3 ) )
% 0.16/0.42 => ~ ( Less @ X2 @ Y2 ) ) )
% 0.16/0.42 => ~ ! [X2: list_a,Y2: list_a,Xs3: list_list_a] :
% 0.16/0.42 ( ( A1
% 0.16/0.42 = ( cons_list_a @ X2 @ Xs3 ) )
% 0.16/0.42 => ! [Ys3: list_list_a] :
% 0.16/0.42 ( ( A22
% 0.16/0.42 = ( cons_list_a @ Y2 @ Ys3 ) )
% 0.16/0.42 => ( ~ ( Less @ X2 @ Y2 )
% 0.16/0.42 => ( ~ ( Less @ Y2 @ X2 )
% 0.16/0.42 => ~ ( lexordp_list_a @ Less @ Xs3 @ Ys3 ) ) ) ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % ord.lexordp.cases
% 0.16/0.42 thf(fact_210_ord_Olexordp_Ocases,axiom,
% 0.16/0.42 ! [Less: a > a > $o,A1: list_a,A22: list_a] :
% 0.16/0.42 ( ( lexordp_a @ Less @ A1 @ A22 )
% 0.16/0.42 => ( ( ( A1 = nil_a )
% 0.16/0.42 => ! [Y2: a,Ys3: list_a] :
% 0.16/0.42 ( A22
% 0.16/0.42 != ( cons_a @ Y2 @ Ys3 ) ) )
% 0.16/0.42 => ( ! [X2: a] :
% 0.16/0.42 ( ? [Xs3: list_a] :
% 0.16/0.42 ( A1
% 0.16/0.42 = ( cons_a @ X2 @ Xs3 ) )
% 0.16/0.42 => ! [Y2: a] :
% 0.16/0.42 ( ? [Ys3: list_a] :
% 0.16/0.42 ( A22
% 0.16/0.42 = ( cons_a @ Y2 @ Ys3 ) )
% 0.16/0.42 => ~ ( Less @ X2 @ Y2 ) ) )
% 0.16/0.42 => ~ ! [X2: a,Y2: a,Xs3: list_a] :
% 0.16/0.42 ( ( A1
% 0.16/0.42 = ( cons_a @ X2 @ Xs3 ) )
% 0.16/0.42 => ! [Ys3: list_a] :
% 0.16/0.42 ( ( A22
% 0.16/0.42 = ( cons_a @ Y2 @ Ys3 ) )
% 0.16/0.42 => ( ~ ( Less @ X2 @ Y2 )
% 0.16/0.42 => ( ~ ( Less @ Y2 @ X2 )
% 0.16/0.42 => ~ ( lexordp_a @ Less @ Xs3 @ Ys3 ) ) ) ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % ord.lexordp.cases
% 0.16/0.42 thf(fact_211_ord_Olexordp_Osimps,axiom,
% 0.16/0.42 ( lexordp_list_a
% 0.16/0.42 = ( ^ [Less2: list_a > list_a > $o,A12: list_list_a,A23: list_list_a] :
% 0.16/0.42 ( ? [Y3: list_a,Ys2: list_list_a] :
% 0.16/0.42 ( ( A12 = nil_list_a )
% 0.16/0.42 & ( A23
% 0.16/0.42 = ( cons_list_a @ Y3 @ Ys2 ) ) )
% 0.16/0.42 | ? [X3: list_a,Y3: list_a,Xs2: list_list_a,Ys2: list_list_a] :
% 0.16/0.42 ( ( A12
% 0.16/0.42 = ( cons_list_a @ X3 @ Xs2 ) )
% 0.16/0.42 & ( A23
% 0.16/0.42 = ( cons_list_a @ Y3 @ Ys2 ) )
% 0.16/0.42 & ( Less2 @ X3 @ Y3 ) )
% 0.16/0.42 | ? [X3: list_a,Y3: list_a,Xs2: list_list_a,Ys2: list_list_a] :
% 0.16/0.42 ( ( A12
% 0.16/0.42 = ( cons_list_a @ X3 @ Xs2 ) )
% 0.16/0.42 & ( A23
% 0.16/0.42 = ( cons_list_a @ Y3 @ Ys2 ) )
% 0.16/0.42 & ~ ( Less2 @ X3 @ Y3 )
% 0.16/0.42 & ~ ( Less2 @ Y3 @ X3 )
% 0.16/0.42 & ( lexordp_list_a @ Less2 @ Xs2 @ Ys2 ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % ord.lexordp.simps
% 0.16/0.42 thf(fact_212_ord_Olexordp_Osimps,axiom,
% 0.16/0.42 ( lexordp_a
% 0.16/0.42 = ( ^ [Less2: a > a > $o,A12: list_a,A23: list_a] :
% 0.16/0.42 ( ? [Y3: a,Ys2: list_a] :
% 0.16/0.42 ( ( A12 = nil_a )
% 0.16/0.42 & ( A23
% 0.16/0.42 = ( cons_a @ Y3 @ Ys2 ) ) )
% 0.16/0.42 | ? [X3: a,Y3: a,Xs2: list_a,Ys2: list_a] :
% 0.16/0.42 ( ( A12
% 0.16/0.42 = ( cons_a @ X3 @ Xs2 ) )
% 0.16/0.42 & ( A23
% 0.16/0.42 = ( cons_a @ Y3 @ Ys2 ) )
% 0.16/0.42 & ( Less2 @ X3 @ Y3 ) )
% 0.16/0.42 | ? [X3: a,Y3: a,Xs2: list_a,Ys2: list_a] :
% 0.16/0.42 ( ( A12
% 0.16/0.42 = ( cons_a @ X3 @ Xs2 ) )
% 0.16/0.42 & ( A23
% 0.16/0.42 = ( cons_a @ Y3 @ Ys2 ) )
% 0.16/0.42 & ~ ( Less2 @ X3 @ Y3 )
% 0.16/0.42 & ~ ( Less2 @ Y3 @ X3 )
% 0.16/0.42 & ( lexordp_a @ Less2 @ Xs2 @ Ys2 ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % ord.lexordp.simps
% 0.16/0.42 thf(fact_213_ord_Olexordp_Oinducts,axiom,
% 0.16/0.42 ! [Less: list_a > list_a > $o,X1: list_list_a,X22: list_list_a,P: list_list_a > list_list_a > $o] :
% 0.16/0.42 ( ( lexordp_list_a @ Less @ X1 @ X22 )
% 0.16/0.42 => ( ! [Y2: list_a,Ys3: list_list_a] : ( P @ nil_list_a @ ( cons_list_a @ Y2 @ Ys3 ) )
% 0.16/0.42 => ( ! [X2: list_a,Y2: list_a,Xs3: list_list_a,Ys3: list_list_a] :
% 0.16/0.42 ( ( Less @ X2 @ Y2 )
% 0.16/0.42 => ( P @ ( cons_list_a @ X2 @ Xs3 ) @ ( cons_list_a @ Y2 @ Ys3 ) ) )
% 0.16/0.42 => ( ! [X2: list_a,Y2: list_a,Xs3: list_list_a,Ys3: list_list_a] :
% 0.16/0.42 ( ~ ( Less @ X2 @ Y2 )
% 0.16/0.42 => ( ~ ( Less @ Y2 @ X2 )
% 0.16/0.42 => ( ( lexordp_list_a @ Less @ Xs3 @ Ys3 )
% 0.16/0.42 => ( ( P @ Xs3 @ Ys3 )
% 0.16/0.42 => ( P @ ( cons_list_a @ X2 @ Xs3 ) @ ( cons_list_a @ Y2 @ Ys3 ) ) ) ) ) )
% 0.16/0.42 => ( P @ X1 @ X22 ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % ord.lexordp.inducts
% 0.16/0.42 thf(fact_214_ord_Olexordp_Oinducts,axiom,
% 0.16/0.42 ! [Less: a > a > $o,X1: list_a,X22: list_a,P: list_a > list_a > $o] :
% 0.16/0.42 ( ( lexordp_a @ Less @ X1 @ X22 )
% 0.16/0.42 => ( ! [Y2: a,Ys3: list_a] : ( P @ nil_a @ ( cons_a @ Y2 @ Ys3 ) )
% 0.16/0.42 => ( ! [X2: a,Y2: a,Xs3: list_a,Ys3: list_a] :
% 0.16/0.42 ( ( Less @ X2 @ Y2 )
% 0.16/0.42 => ( P @ ( cons_a @ X2 @ Xs3 ) @ ( cons_a @ Y2 @ Ys3 ) ) )
% 0.16/0.42 => ( ! [X2: a,Y2: a,Xs3: list_a,Ys3: list_a] :
% 0.16/0.42 ( ~ ( Less @ X2 @ Y2 )
% 0.16/0.42 => ( ~ ( Less @ Y2 @ X2 )
% 0.16/0.42 => ( ( lexordp_a @ Less @ Xs3 @ Ys3 )
% 0.16/0.42 => ( ( P @ Xs3 @ Ys3 )
% 0.16/0.42 => ( P @ ( cons_a @ X2 @ Xs3 ) @ ( cons_a @ Y2 @ Ys3 ) ) ) ) ) )
% 0.16/0.42 => ( P @ X1 @ X22 ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % ord.lexordp.inducts
% 0.16/0.42 thf(fact_215_local_Olexordp__append__rightI,axiom,
% 0.16/0.42 ! [Ys: list_a,Xs: list_a] :
% 0.16/0.42 ( ( Ys != nil_a )
% 0.16/0.42 => ( lexordp_a @ less @ Xs @ ( append_a @ Xs @ Ys ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.lexordp_append_rightI
% 0.16/0.42 thf(fact_216_local_Olexordp__append__left__rightI,axiom,
% 0.16/0.42 ! [X: a,Y: a,Us: list_a,Xs: list_a,Ys: list_a] :
% 0.16/0.42 ( ( less @ X @ Y )
% 0.16/0.42 => ( lexordp_a @ less @ ( append_a @ Us @ ( cons_a @ X @ Xs ) ) @ ( append_a @ Us @ ( cons_a @ Y @ Ys ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.lexordp_append_left_rightI
% 0.16/0.42 thf(fact_217_semilattice_Oaxioms_I1_J,axiom,
% 0.16/0.42 ! [F: a > a > a] :
% 0.16/0.42 ( ( semilattice_a @ F )
% 0.16/0.42 => ( abel_semigroup_a @ F ) ) ).
% 0.16/0.42
% 0.16/0.42 % semilattice.axioms(1)
% 0.16/0.42 thf(fact_218_local_Olexordp__append__leftD,axiom,
% 0.16/0.42 ! [Xs: list_a,Us: list_a,Vs: list_a] :
% 0.16/0.42 ( ( lexordp_a @ less @ ( append_a @ Xs @ Us ) @ ( append_a @ Xs @ Vs ) )
% 0.16/0.42 => ( ! [A2: a] :
% 0.16/0.42 ~ ( less @ A2 @ A2 )
% 0.16/0.42 => ( lexordp_a @ less @ Us @ Vs ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.lexordp_append_leftD
% 0.16/0.42 thf(fact_219_local_Olexordp__append__leftI,axiom,
% 0.16/0.42 ! [Us: list_a,Vs: list_a,Xs: list_a] :
% 0.16/0.42 ( ( lexordp_a @ less @ Us @ Vs )
% 0.16/0.42 => ( lexordp_a @ less @ ( append_a @ Xs @ Us ) @ ( append_a @ Xs @ Vs ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.lexordp_append_leftI
% 0.16/0.42 thf(fact_220_local_Olexordp__eq__pref,axiom,
% 0.16/0.42 ! [U: list_a,V: list_a] : ( lexordp_eq_a @ less @ U @ ( append_a @ U @ V ) ) ).
% 0.16/0.42
% 0.16/0.42 % local.lexordp_eq_pref
% 0.16/0.42 thf(fact_221_same__append__eq,axiom,
% 0.16/0.42 ! [Xs: list_list_a,Ys: list_list_a,Zs2: list_list_a] :
% 0.16/0.42 ( ( ( append_list_a @ Xs @ Ys )
% 0.16/0.42 = ( append_list_a @ Xs @ Zs2 ) )
% 0.16/0.42 = ( Ys = Zs2 ) ) ).
% 0.16/0.42
% 0.16/0.42 % same_append_eq
% 0.16/0.42 thf(fact_222_same__append__eq,axiom,
% 0.16/0.42 ! [Xs: list_a,Ys: list_a,Zs2: list_a] :
% 0.16/0.42 ( ( ( append_a @ Xs @ Ys )
% 0.16/0.42 = ( append_a @ Xs @ Zs2 ) )
% 0.16/0.42 = ( Ys = Zs2 ) ) ).
% 0.16/0.42
% 0.16/0.42 % same_append_eq
% 0.16/0.42 thf(fact_223_append__same__eq,axiom,
% 0.16/0.42 ! [Ys: list_list_a,Xs: list_list_a,Zs2: list_list_a] :
% 0.16/0.42 ( ( ( append_list_a @ Ys @ Xs )
% 0.16/0.42 = ( append_list_a @ Zs2 @ Xs ) )
% 0.16/0.42 = ( Ys = Zs2 ) ) ).
% 0.16/0.42
% 0.16/0.42 % append_same_eq
% 0.16/0.42 thf(fact_224_append__same__eq,axiom,
% 0.16/0.42 ! [Ys: list_a,Xs: list_a,Zs2: list_a] :
% 0.16/0.42 ( ( ( append_a @ Ys @ Xs )
% 0.16/0.42 = ( append_a @ Zs2 @ Xs ) )
% 0.16/0.42 = ( Ys = Zs2 ) ) ).
% 0.16/0.42
% 0.16/0.42 % append_same_eq
% 0.16/0.42 thf(fact_225_append__assoc,axiom,
% 0.16/0.42 ! [Xs: list_list_a,Ys: list_list_a,Zs2: list_list_a] :
% 0.16/0.42 ( ( append_list_a @ ( append_list_a @ Xs @ Ys ) @ Zs2 )
% 0.16/0.42 = ( append_list_a @ Xs @ ( append_list_a @ Ys @ Zs2 ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % append_assoc
% 0.16/0.42 thf(fact_226_append__assoc,axiom,
% 0.16/0.42 ! [Xs: list_a,Ys: list_a,Zs2: list_a] :
% 0.16/0.42 ( ( append_a @ ( append_a @ Xs @ Ys ) @ Zs2 )
% 0.16/0.42 = ( append_a @ Xs @ ( append_a @ Ys @ Zs2 ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % append_assoc
% 0.16/0.42 thf(fact_227_append_Oassoc,axiom,
% 0.16/0.42 ! [A: list_list_a,B: list_list_a,C: list_list_a] :
% 0.16/0.42 ( ( append_list_a @ ( append_list_a @ A @ B ) @ C )
% 0.16/0.42 = ( append_list_a @ A @ ( append_list_a @ B @ C ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % append.assoc
% 0.16/0.42 thf(fact_228_append_Oassoc,axiom,
% 0.16/0.42 ! [A: list_a,B: list_a,C: list_a] :
% 0.16/0.42 ( ( append_a @ ( append_a @ A @ B ) @ C )
% 0.16/0.42 = ( append_a @ A @ ( append_a @ B @ C ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % append.assoc
% 0.16/0.42 thf(fact_229_append_Oright__neutral,axiom,
% 0.16/0.42 ! [A: list_list_a] :
% 0.16/0.42 ( ( append_list_a @ A @ nil_list_a )
% 0.16/0.42 = A ) ).
% 0.16/0.42
% 0.16/0.42 % append.right_neutral
% 0.16/0.42 thf(fact_230_append_Oright__neutral,axiom,
% 0.16/0.42 ! [A: list_a] :
% 0.16/0.42 ( ( append_a @ A @ nil_a )
% 0.16/0.42 = A ) ).
% 0.16/0.42
% 0.16/0.42 % append.right_neutral
% 0.16/0.42 thf(fact_231_append__is__Nil__conv,axiom,
% 0.16/0.42 ! [Xs: list_list_a,Ys: list_list_a] :
% 0.16/0.42 ( ( ( append_list_a @ Xs @ Ys )
% 0.16/0.42 = nil_list_a )
% 0.16/0.42 = ( ( Xs = nil_list_a )
% 0.16/0.42 & ( Ys = nil_list_a ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % append_is_Nil_conv
% 0.16/0.42 thf(fact_232_append__is__Nil__conv,axiom,
% 0.16/0.42 ! [Xs: list_a,Ys: list_a] :
% 0.16/0.42 ( ( ( append_a @ Xs @ Ys )
% 0.16/0.42 = nil_a )
% 0.16/0.42 = ( ( Xs = nil_a )
% 0.16/0.42 & ( Ys = nil_a ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % append_is_Nil_conv
% 0.16/0.42 thf(fact_233_Nil__is__append__conv,axiom,
% 0.16/0.42 ! [Xs: list_list_a,Ys: list_list_a] :
% 0.16/0.42 ( ( nil_list_a
% 0.16/0.42 = ( append_list_a @ Xs @ Ys ) )
% 0.16/0.42 = ( ( Xs = nil_list_a )
% 0.16/0.42 & ( Ys = nil_list_a ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % Nil_is_append_conv
% 0.16/0.42 thf(fact_234_Nil__is__append__conv,axiom,
% 0.16/0.42 ! [Xs: list_a,Ys: list_a] :
% 0.16/0.42 ( ( nil_a
% 0.16/0.42 = ( append_a @ Xs @ Ys ) )
% 0.16/0.42 = ( ( Xs = nil_a )
% 0.16/0.42 & ( Ys = nil_a ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % Nil_is_append_conv
% 0.16/0.42 thf(fact_235_self__append__conv2,axiom,
% 0.16/0.42 ! [Ys: list_list_a,Xs: list_list_a] :
% 0.16/0.42 ( ( Ys
% 0.16/0.42 = ( append_list_a @ Xs @ Ys ) )
% 0.16/0.42 = ( Xs = nil_list_a ) ) ).
% 0.16/0.42
% 0.16/0.42 % self_append_conv2
% 0.16/0.42 thf(fact_236_self__append__conv2,axiom,
% 0.16/0.42 ! [Ys: list_a,Xs: list_a] :
% 0.16/0.42 ( ( Ys
% 0.16/0.42 = ( append_a @ Xs @ Ys ) )
% 0.16/0.42 = ( Xs = nil_a ) ) ).
% 0.16/0.42
% 0.16/0.42 % self_append_conv2
% 0.16/0.42 thf(fact_237_append__self__conv2,axiom,
% 0.16/0.42 ! [Xs: list_list_a,Ys: list_list_a] :
% 0.16/0.42 ( ( ( append_list_a @ Xs @ Ys )
% 0.16/0.42 = Ys )
% 0.16/0.42 = ( Xs = nil_list_a ) ) ).
% 0.16/0.42
% 0.16/0.42 % append_self_conv2
% 0.16/0.42 thf(fact_238_append__self__conv2,axiom,
% 0.16/0.42 ! [Xs: list_a,Ys: list_a] :
% 0.16/0.42 ( ( ( append_a @ Xs @ Ys )
% 0.16/0.42 = Ys )
% 0.16/0.42 = ( Xs = nil_a ) ) ).
% 0.16/0.42
% 0.16/0.42 % append_self_conv2
% 0.16/0.42 thf(fact_239_self__append__conv,axiom,
% 0.16/0.42 ! [Xs: list_list_a,Ys: list_list_a] :
% 0.16/0.42 ( ( Xs
% 0.16/0.42 = ( append_list_a @ Xs @ Ys ) )
% 0.16/0.42 = ( Ys = nil_list_a ) ) ).
% 0.16/0.42
% 0.16/0.42 % self_append_conv
% 0.16/0.42 thf(fact_240_self__append__conv,axiom,
% 0.16/0.42 ! [Xs: list_a,Ys: list_a] :
% 0.16/0.42 ( ( Xs
% 0.16/0.42 = ( append_a @ Xs @ Ys ) )
% 0.16/0.42 = ( Ys = nil_a ) ) ).
% 0.16/0.42
% 0.16/0.42 % self_append_conv
% 0.16/0.42 thf(fact_241_append__self__conv,axiom,
% 0.16/0.42 ! [Xs: list_list_a,Ys: list_list_a] :
% 0.16/0.42 ( ( ( append_list_a @ Xs @ Ys )
% 0.16/0.42 = Xs )
% 0.16/0.42 = ( Ys = nil_list_a ) ) ).
% 0.16/0.42
% 0.16/0.42 % append_self_conv
% 0.16/0.42 thf(fact_242_append__self__conv,axiom,
% 0.16/0.42 ! [Xs: list_a,Ys: list_a] :
% 0.16/0.42 ( ( ( append_a @ Xs @ Ys )
% 0.16/0.42 = Xs )
% 0.16/0.42 = ( Ys = nil_a ) ) ).
% 0.16/0.42
% 0.16/0.42 % append_self_conv
% 0.16/0.42 thf(fact_243_append__Nil2,axiom,
% 0.16/0.42 ! [Xs: list_list_a] :
% 0.16/0.42 ( ( append_list_a @ Xs @ nil_list_a )
% 0.16/0.42 = Xs ) ).
% 0.16/0.42
% 0.16/0.42 % append_Nil2
% 0.16/0.42 thf(fact_244_append__Nil2,axiom,
% 0.16/0.42 ! [Xs: list_a] :
% 0.16/0.42 ( ( append_a @ Xs @ nil_a )
% 0.16/0.42 = Xs ) ).
% 0.16/0.42
% 0.16/0.42 % append_Nil2
% 0.16/0.42 thf(fact_245_append1__eq__conv,axiom,
% 0.16/0.42 ! [Xs: list_list_a,X: list_a,Ys: list_list_a,Y: list_a] :
% 0.16/0.42 ( ( ( append_list_a @ Xs @ ( cons_list_a @ X @ nil_list_a ) )
% 0.16/0.42 = ( append_list_a @ Ys @ ( cons_list_a @ Y @ nil_list_a ) ) )
% 0.16/0.42 = ( ( Xs = Ys )
% 0.16/0.42 & ( X = Y ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % append1_eq_conv
% 0.16/0.42 thf(fact_246_append1__eq__conv,axiom,
% 0.16/0.42 ! [Xs: list_a,X: a,Ys: list_a,Y: a] :
% 0.16/0.42 ( ( ( append_a @ Xs @ ( cons_a @ X @ nil_a ) )
% 0.16/0.42 = ( append_a @ Ys @ ( cons_a @ Y @ nil_a ) ) )
% 0.16/0.42 = ( ( Xs = Ys )
% 0.16/0.42 & ( X = Y ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % append1_eq_conv
% 0.16/0.42 thf(fact_247_append_Oleft__neutral,axiom,
% 0.16/0.42 ! [A: list_list_a] :
% 0.16/0.42 ( ( append_list_a @ nil_list_a @ A )
% 0.16/0.42 = A ) ).
% 0.16/0.42
% 0.16/0.42 % append.left_neutral
% 0.16/0.42 thf(fact_248_append_Oleft__neutral,axiom,
% 0.16/0.42 ! [A: list_a] :
% 0.16/0.42 ( ( append_a @ nil_a @ A )
% 0.16/0.42 = A ) ).
% 0.16/0.42
% 0.16/0.42 % append.left_neutral
% 0.16/0.42 thf(fact_249_append__Nil,axiom,
% 0.16/0.42 ! [Ys: list_list_a] :
% 0.16/0.42 ( ( append_list_a @ nil_list_a @ Ys )
% 0.16/0.42 = Ys ) ).
% 0.16/0.42
% 0.16/0.42 % append_Nil
% 0.16/0.42 thf(fact_250_append__Nil,axiom,
% 0.16/0.42 ! [Ys: list_a] :
% 0.16/0.42 ( ( append_a @ nil_a @ Ys )
% 0.16/0.42 = Ys ) ).
% 0.16/0.42
% 0.16/0.42 % append_Nil
% 0.16/0.42 thf(fact_251_eq__Nil__appendI,axiom,
% 0.16/0.42 ! [Xs: list_list_a,Ys: list_list_a] :
% 0.16/0.42 ( ( Xs = Ys )
% 0.16/0.42 => ( Xs
% 0.16/0.42 = ( append_list_a @ nil_list_a @ Ys ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % eq_Nil_appendI
% 0.16/0.42 thf(fact_252_eq__Nil__appendI,axiom,
% 0.16/0.42 ! [Xs: list_a,Ys: list_a] :
% 0.16/0.42 ( ( Xs = Ys )
% 0.16/0.42 => ( Xs
% 0.16/0.42 = ( append_a @ nil_a @ Ys ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % eq_Nil_appendI
% 0.16/0.42 thf(fact_253_Cons__eq__appendI,axiom,
% 0.16/0.42 ! [X: list_a,Xs1: list_list_a,Ys: list_list_a,Xs: list_list_a,Zs2: list_list_a] :
% 0.16/0.42 ( ( ( cons_list_a @ X @ Xs1 )
% 0.16/0.42 = Ys )
% 0.16/0.42 => ( ( Xs
% 0.16/0.42 = ( append_list_a @ Xs1 @ Zs2 ) )
% 0.16/0.42 => ( ( cons_list_a @ X @ Xs )
% 0.16/0.42 = ( append_list_a @ Ys @ Zs2 ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % Cons_eq_appendI
% 0.16/0.42 thf(fact_254_Cons__eq__appendI,axiom,
% 0.16/0.42 ! [X: a,Xs1: list_a,Ys: list_a,Xs: list_a,Zs2: list_a] :
% 0.16/0.42 ( ( ( cons_a @ X @ Xs1 )
% 0.16/0.42 = Ys )
% 0.16/0.42 => ( ( Xs
% 0.16/0.42 = ( append_a @ Xs1 @ Zs2 ) )
% 0.16/0.42 => ( ( cons_a @ X @ Xs )
% 0.16/0.42 = ( append_a @ Ys @ Zs2 ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % Cons_eq_appendI
% 0.16/0.42 thf(fact_255_append__Cons,axiom,
% 0.16/0.42 ! [X: list_a,Xs: list_list_a,Ys: list_list_a] :
% 0.16/0.42 ( ( append_list_a @ ( cons_list_a @ X @ Xs ) @ Ys )
% 0.16/0.42 = ( cons_list_a @ X @ ( append_list_a @ Xs @ Ys ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % append_Cons
% 0.16/0.42 thf(fact_256_append__Cons,axiom,
% 0.16/0.42 ! [X: a,Xs: list_a,Ys: list_a] :
% 0.16/0.42 ( ( append_a @ ( cons_a @ X @ Xs ) @ Ys )
% 0.16/0.42 = ( cons_a @ X @ ( append_a @ Xs @ Ys ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % append_Cons
% 0.16/0.42 thf(fact_257_ord_Olexordp__append__leftD,axiom,
% 0.16/0.42 ! [Less: list_a > list_a > $o,Xs: list_list_a,Us: list_list_a,Vs: list_list_a] :
% 0.16/0.42 ( ( lexordp_list_a @ Less @ ( append_list_a @ Xs @ Us ) @ ( append_list_a @ Xs @ Vs ) )
% 0.16/0.42 => ( ! [A2: list_a] :
% 0.16/0.42 ~ ( Less @ A2 @ A2 )
% 0.16/0.42 => ( lexordp_list_a @ Less @ Us @ Vs ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % ord.lexordp_append_leftD
% 0.16/0.42 thf(fact_258_ord_Olexordp__append__leftD,axiom,
% 0.16/0.42 ! [Less: a > a > $o,Xs: list_a,Us: list_a,Vs: list_a] :
% 0.16/0.42 ( ( lexordp_a @ Less @ ( append_a @ Xs @ Us ) @ ( append_a @ Xs @ Vs ) )
% 0.16/0.42 => ( ! [A2: a] :
% 0.16/0.42 ~ ( Less @ A2 @ A2 )
% 0.16/0.42 => ( lexordp_a @ Less @ Us @ Vs ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % ord.lexordp_append_leftD
% 0.16/0.42 thf(fact_259_ord_Olexordp__append__leftI,axiom,
% 0.16/0.42 ! [Less: list_a > list_a > $o,Us: list_list_a,Vs: list_list_a,Xs: list_list_a] :
% 0.16/0.42 ( ( lexordp_list_a @ Less @ Us @ Vs )
% 0.16/0.42 => ( lexordp_list_a @ Less @ ( append_list_a @ Xs @ Us ) @ ( append_list_a @ Xs @ Vs ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % ord.lexordp_append_leftI
% 0.16/0.42 thf(fact_260_ord_Olexordp__append__leftI,axiom,
% 0.16/0.42 ! [Less: a > a > $o,Us: list_a,Vs: list_a,Xs: list_a] :
% 0.16/0.42 ( ( lexordp_a @ Less @ Us @ Vs )
% 0.16/0.42 => ( lexordp_a @ Less @ ( append_a @ Xs @ Us ) @ ( append_a @ Xs @ Vs ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % ord.lexordp_append_leftI
% 0.16/0.42 thf(fact_261_ord_Olexordp__eq__pref,axiom,
% 0.16/0.42 ! [Less: list_a > list_a > $o,U: list_list_a,V: list_list_a] : ( lexordp_eq_list_a @ Less @ U @ ( append_list_a @ U @ V ) ) ).
% 0.16/0.42
% 0.16/0.42 % ord.lexordp_eq_pref
% 0.16/0.42 thf(fact_262_ord_Olexordp__eq__pref,axiom,
% 0.16/0.42 ! [Less: a > a > $o,U: list_a,V: list_a] : ( lexordp_eq_a @ Less @ U @ ( append_a @ U @ V ) ) ).
% 0.16/0.42
% 0.16/0.42 % ord.lexordp_eq_pref
% 0.16/0.42 thf(fact_263_append__eq__append__conv2,axiom,
% 0.16/0.42 ! [Xs: list_list_a,Ys: list_list_a,Zs2: list_list_a,Ts: list_list_a] :
% 0.16/0.42 ( ( ( append_list_a @ Xs @ Ys )
% 0.16/0.42 = ( append_list_a @ Zs2 @ Ts ) )
% 0.16/0.42 = ( ? [Us2: list_list_a] :
% 0.16/0.42 ( ( ( Xs
% 0.16/0.42 = ( append_list_a @ Zs2 @ Us2 ) )
% 0.16/0.42 & ( ( append_list_a @ Us2 @ Ys )
% 0.16/0.42 = Ts ) )
% 0.16/0.42 | ( ( ( append_list_a @ Xs @ Us2 )
% 0.16/0.42 = Zs2 )
% 0.16/0.42 & ( Ys
% 0.16/0.42 = ( append_list_a @ Us2 @ Ts ) ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % append_eq_append_conv2
% 0.16/0.42 thf(fact_264_append__eq__append__conv2,axiom,
% 0.16/0.42 ! [Xs: list_a,Ys: list_a,Zs2: list_a,Ts: list_a] :
% 0.16/0.42 ( ( ( append_a @ Xs @ Ys )
% 0.16/0.42 = ( append_a @ Zs2 @ Ts ) )
% 0.16/0.42 = ( ? [Us2: list_a] :
% 0.16/0.42 ( ( ( Xs
% 0.16/0.42 = ( append_a @ Zs2 @ Us2 ) )
% 0.16/0.42 & ( ( append_a @ Us2 @ Ys )
% 0.16/0.42 = Ts ) )
% 0.16/0.42 | ( ( ( append_a @ Xs @ Us2 )
% 0.16/0.42 = Zs2 )
% 0.16/0.42 & ( Ys
% 0.16/0.42 = ( append_a @ Us2 @ Ts ) ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % append_eq_append_conv2
% 0.16/0.42 thf(fact_265_append__eq__appendI,axiom,
% 0.16/0.42 ! [Xs: list_list_a,Xs1: list_list_a,Zs2: list_list_a,Ys: list_list_a,Us: list_list_a] :
% 0.16/0.42 ( ( ( append_list_a @ Xs @ Xs1 )
% 0.16/0.42 = Zs2 )
% 0.16/0.42 => ( ( Ys
% 0.16/0.42 = ( append_list_a @ Xs1 @ Us ) )
% 0.16/0.42 => ( ( append_list_a @ Xs @ Ys )
% 0.16/0.42 = ( append_list_a @ Zs2 @ Us ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % append_eq_appendI
% 0.16/0.42 thf(fact_266_append__eq__appendI,axiom,
% 0.16/0.42 ! [Xs: list_a,Xs1: list_a,Zs2: list_a,Ys: list_a,Us: list_a] :
% 0.16/0.42 ( ( ( append_a @ Xs @ Xs1 )
% 0.16/0.42 = Zs2 )
% 0.16/0.42 => ( ( Ys
% 0.16/0.42 = ( append_a @ Xs1 @ Us ) )
% 0.16/0.42 => ( ( append_a @ Xs @ Ys )
% 0.16/0.42 = ( append_a @ Zs2 @ Us ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % append_eq_appendI
% 0.16/0.42 thf(fact_267_append_Osemigroup__axioms,axiom,
% 0.16/0.42 semigr656274520list_a @ append_list_a ).
% 0.16/0.42
% 0.16/0.42 % append.semigroup_axioms
% 0.16/0.42 thf(fact_268_append_Osemigroup__axioms,axiom,
% 0.16/0.42 semigroup_list_a @ append_a ).
% 0.16/0.42
% 0.16/0.42 % append.semigroup_axioms
% 0.16/0.42 thf(fact_269_rev__nonempty__induct,axiom,
% 0.16/0.42 ! [Xs: list_list_a,P: list_list_a > $o] :
% 0.16/0.42 ( ( Xs != nil_list_a )
% 0.16/0.42 => ( ! [X2: list_a] : ( P @ ( cons_list_a @ X2 @ nil_list_a ) )
% 0.16/0.42 => ( ! [X2: list_a,Xs3: list_list_a] :
% 0.16/0.42 ( ( Xs3 != nil_list_a )
% 0.16/0.42 => ( ( P @ Xs3 )
% 0.16/0.42 => ( P @ ( append_list_a @ Xs3 @ ( cons_list_a @ X2 @ nil_list_a ) ) ) ) )
% 0.16/0.42 => ( P @ Xs ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % rev_nonempty_induct
% 0.16/0.42 thf(fact_270_rev__nonempty__induct,axiom,
% 0.16/0.42 ! [Xs: list_a,P: list_a > $o] :
% 0.16/0.42 ( ( Xs != nil_a )
% 0.16/0.42 => ( ! [X2: a] : ( P @ ( cons_a @ X2 @ nil_a ) )
% 0.16/0.42 => ( ! [X2: a,Xs3: list_a] :
% 0.16/0.42 ( ( Xs3 != nil_a )
% 0.16/0.42 => ( ( P @ Xs3 )
% 0.16/0.42 => ( P @ ( append_a @ Xs3 @ ( cons_a @ X2 @ nil_a ) ) ) ) )
% 0.16/0.42 => ( P @ Xs ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % rev_nonempty_induct
% 0.16/0.42 thf(fact_271_append__eq__Cons__conv,axiom,
% 0.16/0.42 ! [Ys: list_list_a,Zs2: list_list_a,X: list_a,Xs: list_list_a] :
% 0.16/0.42 ( ( ( append_list_a @ Ys @ Zs2 )
% 0.16/0.42 = ( cons_list_a @ X @ Xs ) )
% 0.16/0.42 = ( ( ( Ys = nil_list_a )
% 0.16/0.42 & ( Zs2
% 0.16/0.42 = ( cons_list_a @ X @ Xs ) ) )
% 0.16/0.42 | ? [Ys4: list_list_a] :
% 0.16/0.42 ( ( Ys
% 0.16/0.42 = ( cons_list_a @ X @ Ys4 ) )
% 0.16/0.42 & ( ( append_list_a @ Ys4 @ Zs2 )
% 0.16/0.42 = Xs ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % append_eq_Cons_conv
% 0.16/0.42 thf(fact_272_append__eq__Cons__conv,axiom,
% 0.16/0.42 ! [Ys: list_a,Zs2: list_a,X: a,Xs: list_a] :
% 0.16/0.42 ( ( ( append_a @ Ys @ Zs2 )
% 0.16/0.42 = ( cons_a @ X @ Xs ) )
% 0.16/0.42 = ( ( ( Ys = nil_a )
% 0.16/0.42 & ( Zs2
% 0.16/0.42 = ( cons_a @ X @ Xs ) ) )
% 0.16/0.42 | ? [Ys4: list_a] :
% 0.16/0.42 ( ( Ys
% 0.16/0.42 = ( cons_a @ X @ Ys4 ) )
% 0.16/0.42 & ( ( append_a @ Ys4 @ Zs2 )
% 0.16/0.42 = Xs ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % append_eq_Cons_conv
% 0.16/0.42 thf(fact_273_Cons__eq__append__conv,axiom,
% 0.16/0.42 ! [X: list_a,Xs: list_list_a,Ys: list_list_a,Zs2: list_list_a] :
% 0.16/0.42 ( ( ( cons_list_a @ X @ Xs )
% 0.16/0.42 = ( append_list_a @ Ys @ Zs2 ) )
% 0.16/0.42 = ( ( ( Ys = nil_list_a )
% 0.16/0.42 & ( ( cons_list_a @ X @ Xs )
% 0.16/0.42 = Zs2 ) )
% 0.16/0.42 | ? [Ys4: list_list_a] :
% 0.16/0.42 ( ( ( cons_list_a @ X @ Ys4 )
% 0.16/0.42 = Ys )
% 0.16/0.42 & ( Xs
% 0.16/0.42 = ( append_list_a @ Ys4 @ Zs2 ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % Cons_eq_append_conv
% 0.16/0.42 thf(fact_274_Cons__eq__append__conv,axiom,
% 0.16/0.42 ! [X: a,Xs: list_a,Ys: list_a,Zs2: list_a] :
% 0.16/0.42 ( ( ( cons_a @ X @ Xs )
% 0.16/0.42 = ( append_a @ Ys @ Zs2 ) )
% 0.16/0.42 = ( ( ( Ys = nil_a )
% 0.16/0.42 & ( ( cons_a @ X @ Xs )
% 0.16/0.42 = Zs2 ) )
% 0.16/0.42 | ? [Ys4: list_a] :
% 0.16/0.42 ( ( ( cons_a @ X @ Ys4 )
% 0.16/0.42 = Ys )
% 0.16/0.42 & ( Xs
% 0.16/0.42 = ( append_a @ Ys4 @ Zs2 ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % Cons_eq_append_conv
% 0.16/0.42 thf(fact_275_rev__exhaust,axiom,
% 0.16/0.42 ! [Xs: list_list_a] :
% 0.16/0.42 ( ( Xs != nil_list_a )
% 0.16/0.42 => ~ ! [Ys3: list_list_a,Y2: list_a] :
% 0.16/0.42 ( Xs
% 0.16/0.42 != ( append_list_a @ Ys3 @ ( cons_list_a @ Y2 @ nil_list_a ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % rev_exhaust
% 0.16/0.42 thf(fact_276_rev__exhaust,axiom,
% 0.16/0.42 ! [Xs: list_a] :
% 0.16/0.42 ( ( Xs != nil_a )
% 0.16/0.42 => ~ ! [Ys3: list_a,Y2: a] :
% 0.16/0.42 ( Xs
% 0.16/0.42 != ( append_a @ Ys3 @ ( cons_a @ Y2 @ nil_a ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % rev_exhaust
% 0.16/0.42 thf(fact_277_rev__induct,axiom,
% 0.16/0.42 ! [P: list_list_a > $o,Xs: list_list_a] :
% 0.16/0.42 ( ( P @ nil_list_a )
% 0.16/0.42 => ( ! [X2: list_a,Xs3: list_list_a] :
% 0.16/0.42 ( ( P @ Xs3 )
% 0.16/0.42 => ( P @ ( append_list_a @ Xs3 @ ( cons_list_a @ X2 @ nil_list_a ) ) ) )
% 0.16/0.42 => ( P @ Xs ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % rev_induct
% 0.16/0.42 thf(fact_278_rev__induct,axiom,
% 0.16/0.42 ! [P: list_a > $o,Xs: list_a] :
% 0.16/0.42 ( ( P @ nil_a )
% 0.16/0.42 => ( ! [X2: a,Xs3: list_a] :
% 0.16/0.42 ( ( P @ Xs3 )
% 0.16/0.42 => ( P @ ( append_a @ Xs3 @ ( cons_a @ X2 @ nil_a ) ) ) )
% 0.16/0.42 => ( P @ Xs ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % rev_induct
% 0.16/0.42 thf(fact_279_ord_Olexordp__append__left__rightI,axiom,
% 0.16/0.42 ! [Less: list_a > list_a > $o,X: list_a,Y: list_a,Us: list_list_a,Xs: list_list_a,Ys: list_list_a] :
% 0.16/0.42 ( ( Less @ X @ Y )
% 0.16/0.42 => ( lexordp_list_a @ Less @ ( append_list_a @ Us @ ( cons_list_a @ X @ Xs ) ) @ ( append_list_a @ Us @ ( cons_list_a @ Y @ Ys ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % ord.lexordp_append_left_rightI
% 0.16/0.42 thf(fact_280_ord_Olexordp__append__left__rightI,axiom,
% 0.16/0.42 ! [Less: a > a > $o,X: a,Y: a,Us: list_a,Xs: list_a,Ys: list_a] :
% 0.16/0.42 ( ( Less @ X @ Y )
% 0.16/0.42 => ( lexordp_a @ Less @ ( append_a @ Us @ ( cons_a @ X @ Xs ) ) @ ( append_a @ Us @ ( cons_a @ Y @ Ys ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % ord.lexordp_append_left_rightI
% 0.16/0.42 thf(fact_281_ord_Olexordp__append__rightI,axiom,
% 0.16/0.42 ! [Ys: list_list_a,Less: list_a > list_a > $o,Xs: list_list_a] :
% 0.16/0.42 ( ( Ys != nil_list_a )
% 0.16/0.42 => ( lexordp_list_a @ Less @ Xs @ ( append_list_a @ Xs @ Ys ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % ord.lexordp_append_rightI
% 0.16/0.42 thf(fact_282_ord_Olexordp__append__rightI,axiom,
% 0.16/0.42 ! [Ys: list_a,Less: a > a > $o,Xs: list_a] :
% 0.16/0.42 ( ( Ys != nil_a )
% 0.16/0.42 => ( lexordp_a @ Less @ Xs @ ( append_a @ Xs @ Ys ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % ord.lexordp_append_rightI
% 0.16/0.42 thf(fact_283_semilattice_Oidem,axiom,
% 0.16/0.42 ! [F: a > a > a,A: a] :
% 0.16/0.42 ( ( semilattice_a @ F )
% 0.16/0.42 => ( ( F @ A @ A )
% 0.16/0.42 = A ) ) ).
% 0.16/0.42
% 0.16/0.42 % semilattice.idem
% 0.16/0.42 thf(fact_284_semilattice_Oleft__idem,axiom,
% 0.16/0.42 ! [F: a > a > a,A: a,B: a] :
% 0.16/0.42 ( ( semilattice_a @ F )
% 0.16/0.42 => ( ( F @ A @ ( F @ A @ B ) )
% 0.16/0.42 = ( F @ A @ B ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % semilattice.left_idem
% 0.16/0.42 thf(fact_285_semilattice_Oright__idem,axiom,
% 0.16/0.42 ! [F: a > a > a,A: a,B: a] :
% 0.16/0.42 ( ( semilattice_a @ F )
% 0.16/0.42 => ( ( F @ ( F @ A @ B ) @ B )
% 0.16/0.42 = ( F @ A @ B ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % semilattice.right_idem
% 0.16/0.42 thf(fact_286_product__lists_Osimps_I1_J,axiom,
% 0.16/0.42 ( ( product_lists_list_a @ nil_list_list_a )
% 0.16/0.42 = ( cons_list_list_a @ nil_list_a @ nil_list_list_a ) ) ).
% 0.16/0.42
% 0.16/0.42 % product_lists.simps(1)
% 0.16/0.42 thf(fact_287_product__lists_Osimps_I1_J,axiom,
% 0.16/0.42 ( ( product_lists_a @ nil_list_a )
% 0.16/0.42 = ( cons_list_a @ nil_a @ nil_list_a ) ) ).
% 0.16/0.42
% 0.16/0.42 % product_lists.simps(1)
% 0.16/0.42 thf(fact_288_bind__simps_I2_J,axiom,
% 0.16/0.42 ! [X: a,Xs: list_a,F: a > list_list_a] :
% 0.16/0.42 ( ( bind_a_list_a @ ( cons_a @ X @ Xs ) @ F )
% 0.16/0.42 = ( append_list_a @ ( F @ X ) @ ( bind_a_list_a @ Xs @ F ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % bind_simps(2)
% 0.16/0.42 thf(fact_289_bind__simps_I2_J,axiom,
% 0.16/0.42 ! [X: list_a,Xs: list_list_a,F: list_a > list_a] :
% 0.16/0.42 ( ( bind_list_a_a @ ( cons_list_a @ X @ Xs ) @ F )
% 0.16/0.42 = ( append_a @ ( F @ X ) @ ( bind_list_a_a @ Xs @ F ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % bind_simps(2)
% 0.16/0.42 thf(fact_290_bind__simps_I2_J,axiom,
% 0.16/0.42 ! [X: list_a,Xs: list_list_a,F: list_a > list_list_a] :
% 0.16/0.42 ( ( bind_list_a_list_a @ ( cons_list_a @ X @ Xs ) @ F )
% 0.16/0.42 = ( append_list_a @ ( F @ X ) @ ( bind_list_a_list_a @ Xs @ F ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % bind_simps(2)
% 0.16/0.42 thf(fact_291_bind__simps_I2_J,axiom,
% 0.16/0.42 ! [X: a,Xs: list_a,F: a > list_a] :
% 0.16/0.42 ( ( bind_a_a @ ( cons_a @ X @ Xs ) @ F )
% 0.16/0.42 = ( append_a @ ( F @ X ) @ ( bind_a_a @ Xs @ F ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % bind_simps(2)
% 0.16/0.42 thf(fact_292_bind__simps_I1_J,axiom,
% 0.16/0.42 ! [F: a > list_list_a] :
% 0.16/0.42 ( ( bind_a_list_a @ nil_a @ F )
% 0.16/0.42 = nil_list_a ) ).
% 0.16/0.42
% 0.16/0.42 % bind_simps(1)
% 0.16/0.42 thf(fact_293_bind__simps_I1_J,axiom,
% 0.16/0.42 ! [F: list_a > list_a] :
% 0.16/0.42 ( ( bind_list_a_a @ nil_list_a @ F )
% 0.16/0.42 = nil_a ) ).
% 0.16/0.42
% 0.16/0.42 % bind_simps(1)
% 0.16/0.42 thf(fact_294_bind__simps_I1_J,axiom,
% 0.16/0.42 ! [F: list_a > list_list_a] :
% 0.16/0.42 ( ( bind_list_a_list_a @ nil_list_a @ F )
% 0.16/0.42 = nil_list_a ) ).
% 0.16/0.42
% 0.16/0.42 % bind_simps(1)
% 0.16/0.42 thf(fact_295_bind__simps_I1_J,axiom,
% 0.16/0.42 ! [F: a > list_a] :
% 0.16/0.42 ( ( bind_a_a @ nil_a @ F )
% 0.16/0.42 = nil_a ) ).
% 0.16/0.42
% 0.16/0.42 % bind_simps(1)
% 0.16/0.42 thf(fact_296_abel__semigroup__def,axiom,
% 0.16/0.42 ( abel_s1075322906list_a
% 0.16/0.42 = ( ^ [F2: list_a > list_a > list_a] :
% 0.16/0.42 ( ( semigroup_list_a @ F2 )
% 0.16/0.42 & ( abel_s374399671list_a @ F2 ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % abel_semigroup_def
% 0.16/0.42 thf(fact_297_abel__semigroup__def,axiom,
% 0.16/0.42 ( abel_semigroup_a
% 0.16/0.42 = ( ^ [F2: a > a > a] :
% 0.16/0.42 ( ( semigroup_a @ F2 )
% 0.16/0.42 & ( abel_s2117090225ioms_a @ F2 ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % abel_semigroup_def
% 0.16/0.42 thf(fact_298_abel__semigroup_Ointro,axiom,
% 0.16/0.42 ! [F: list_a > list_a > list_a] :
% 0.16/0.42 ( ( semigroup_list_a @ F )
% 0.16/0.42 => ( ( abel_s374399671list_a @ F )
% 0.16/0.42 => ( abel_s1075322906list_a @ F ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % abel_semigroup.intro
% 0.16/0.42 thf(fact_299_abel__semigroup_Ointro,axiom,
% 0.16/0.42 ! [F: a > a > a] :
% 0.16/0.42 ( ( semigroup_a @ F )
% 0.16/0.42 => ( ( abel_s2117090225ioms_a @ F )
% 0.16/0.42 => ( abel_semigroup_a @ F ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % abel_semigroup.intro
% 0.16/0.42 thf(fact_300_abel__semigroup__axioms_Ointro,axiom,
% 0.16/0.42 ! [F: a > a > a] :
% 0.16/0.42 ( ! [A2: a,B2: a] :
% 0.16/0.42 ( ( F @ A2 @ B2 )
% 0.16/0.42 = ( F @ B2 @ A2 ) )
% 0.16/0.42 => ( abel_s2117090225ioms_a @ F ) ) ).
% 0.16/0.42
% 0.16/0.42 % abel_semigroup_axioms.intro
% 0.16/0.42 thf(fact_301_abel__semigroup__axioms__def,axiom,
% 0.16/0.42 ( abel_s2117090225ioms_a
% 0.16/0.42 = ( ^ [F2: a > a > a] :
% 0.16/0.42 ! [A3: a,B3: a] :
% 0.16/0.42 ( ( F2 @ A3 @ B3 )
% 0.16/0.42 = ( F2 @ B3 @ A3 ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % abel_semigroup_axioms_def
% 0.16/0.42 thf(fact_302_abel__semigroup_Oaxioms_I2_J,axiom,
% 0.16/0.42 ! [F: a > a > a] :
% 0.16/0.42 ( ( abel_semigroup_a @ F )
% 0.16/0.42 => ( abel_s2117090225ioms_a @ F ) ) ).
% 0.16/0.42
% 0.16/0.42 % abel_semigroup.axioms(2)
% 0.16/0.42 thf(fact_303_semilattice_Ointro,axiom,
% 0.16/0.42 ! [F: a > a > a] :
% 0.16/0.42 ( ( abel_semigroup_a @ F )
% 0.16/0.42 => ( ( semilattice_axioms_a @ F )
% 0.16/0.42 => ( semilattice_a @ F ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % semilattice.intro
% 0.16/0.42 thf(fact_304_semilattice__def,axiom,
% 0.16/0.42 ( semilattice_a
% 0.16/0.42 = ( ^ [F2: a > a > a] :
% 0.16/0.42 ( ( abel_semigroup_a @ F2 )
% 0.16/0.42 & ( semilattice_axioms_a @ F2 ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % semilattice_def
% 0.16/0.42 thf(fact_305_semilattice_Oaxioms_I2_J,axiom,
% 0.16/0.42 ! [F: a > a > a] :
% 0.16/0.42 ( ( semilattice_a @ F )
% 0.16/0.42 => ( semilattice_axioms_a @ F ) ) ).
% 0.16/0.42
% 0.16/0.42 % semilattice.axioms(2)
% 0.16/0.42 thf(fact_306_subseqs_Osimps_I1_J,axiom,
% 0.16/0.42 ( ( subseqs_list_a @ nil_list_a )
% 0.16/0.42 = ( cons_list_list_a @ nil_list_a @ nil_list_list_a ) ) ).
% 0.16/0.42
% 0.16/0.42 % subseqs.simps(1)
% 0.16/0.42 thf(fact_307_subseqs_Osimps_I1_J,axiom,
% 0.16/0.42 ( ( subseqs_a @ nil_a )
% 0.16/0.42 = ( cons_list_a @ nil_a @ nil_list_a ) ) ).
% 0.16/0.42
% 0.16/0.42 % subseqs.simps(1)
% 0.16/0.42 thf(fact_308_maps__simps_I1_J,axiom,
% 0.16/0.42 ! [F: a > list_list_a,X: a,Xs: list_a] :
% 0.16/0.42 ( ( maps_a_list_a @ F @ ( cons_a @ X @ Xs ) )
% 0.16/0.42 = ( append_list_a @ ( F @ X ) @ ( maps_a_list_a @ F @ Xs ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % maps_simps(1)
% 0.16/0.42 thf(fact_309_maps__simps_I1_J,axiom,
% 0.16/0.42 ! [F: list_a > list_a,X: list_a,Xs: list_list_a] :
% 0.16/0.42 ( ( maps_list_a_a @ F @ ( cons_list_a @ X @ Xs ) )
% 0.16/0.42 = ( append_a @ ( F @ X ) @ ( maps_list_a_a @ F @ Xs ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % maps_simps(1)
% 0.16/0.42 thf(fact_310_maps__simps_I1_J,axiom,
% 0.16/0.42 ! [F: list_a > list_list_a,X: list_a,Xs: list_list_a] :
% 0.16/0.42 ( ( maps_list_a_list_a @ F @ ( cons_list_a @ X @ Xs ) )
% 0.16/0.42 = ( append_list_a @ ( F @ X ) @ ( maps_list_a_list_a @ F @ Xs ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % maps_simps(1)
% 0.16/0.42 thf(fact_311_maps__simps_I1_J,axiom,
% 0.16/0.42 ! [F: a > list_a,X: a,Xs: list_a] :
% 0.16/0.42 ( ( maps_a_a @ F @ ( cons_a @ X @ Xs ) )
% 0.16/0.42 = ( append_a @ ( F @ X ) @ ( maps_a_a @ F @ Xs ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % maps_simps(1)
% 0.16/0.42 thf(fact_312_maps__simps_I2_J,axiom,
% 0.16/0.42 ! [F: a > list_list_a] :
% 0.16/0.42 ( ( maps_a_list_a @ F @ nil_a )
% 0.16/0.42 = nil_list_a ) ).
% 0.16/0.42
% 0.16/0.42 % maps_simps(2)
% 0.16/0.42 thf(fact_313_maps__simps_I2_J,axiom,
% 0.16/0.42 ! [F: list_a > list_a] :
% 0.16/0.42 ( ( maps_list_a_a @ F @ nil_list_a )
% 0.16/0.42 = nil_a ) ).
% 0.16/0.42
% 0.16/0.42 % maps_simps(2)
% 0.16/0.42 thf(fact_314_maps__simps_I2_J,axiom,
% 0.16/0.42 ! [F: list_a > list_list_a] :
% 0.16/0.42 ( ( maps_list_a_list_a @ F @ nil_list_a )
% 0.16/0.42 = nil_list_a ) ).
% 0.16/0.42
% 0.16/0.42 % maps_simps(2)
% 0.16/0.42 thf(fact_315_maps__simps_I2_J,axiom,
% 0.16/0.42 ! [F: a > list_a] :
% 0.16/0.42 ( ( maps_a_a @ F @ nil_a )
% 0.16/0.42 = nil_a ) ).
% 0.16/0.42
% 0.16/0.42 % maps_simps(2)
% 0.16/0.42 thf(fact_316_local_Otransp__less,axiom,
% 0.16/0.42 transp_a @ less ).
% 0.16/0.42
% 0.16/0.42 % local.transp_less
% 0.16/0.42 thf(fact_317_insert__Nil,axiom,
% 0.16/0.42 ! [X: list_a] :
% 0.16/0.42 ( ( insert_list_a @ X @ nil_list_a )
% 0.16/0.42 = ( cons_list_a @ X @ nil_list_a ) ) ).
% 0.16/0.42
% 0.16/0.42 % insert_Nil
% 0.16/0.42 thf(fact_318_insert__Nil,axiom,
% 0.16/0.42 ! [X: a] :
% 0.16/0.42 ( ( insert_a @ X @ nil_a )
% 0.16/0.42 = ( cons_a @ X @ nil_a ) ) ).
% 0.16/0.42
% 0.16/0.42 % insert_Nil
% 0.16/0.42 thf(fact_319_concat__eq__append__conv,axiom,
% 0.16/0.42 ! [Xss2: list_list_list_a,Ys: list_list_a,Zs2: list_list_a] :
% 0.16/0.42 ( ( ( concat_list_a @ Xss2 )
% 0.16/0.42 = ( append_list_a @ Ys @ Zs2 ) )
% 0.16/0.42 = ( ( ( Xss2 = nil_list_list_a )
% 0.16/0.42 => ( ( Ys = nil_list_a )
% 0.16/0.42 & ( Zs2 = nil_list_a ) ) )
% 0.16/0.42 & ( ( Xss2 != nil_list_list_a )
% 0.16/0.42 => ? [Xss1: list_list_list_a,Xs2: list_list_a,Xs4: list_list_a,Xss22: list_list_list_a] :
% 0.16/0.42 ( ( Xss2
% 0.16/0.42 = ( append_list_list_a @ Xss1 @ ( cons_list_list_a @ ( append_list_a @ Xs2 @ Xs4 ) @ Xss22 ) ) )
% 0.16/0.42 & ( Ys
% 0.16/0.42 = ( append_list_a @ ( concat_list_a @ Xss1 ) @ Xs2 ) )
% 0.16/0.42 & ( Zs2
% 0.16/0.42 = ( append_list_a @ Xs4 @ ( concat_list_a @ Xss22 ) ) ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % concat_eq_append_conv
% 0.16/0.42 thf(fact_320_concat__eq__append__conv,axiom,
% 0.16/0.42 ! [Xss2: list_list_a,Ys: list_a,Zs2: list_a] :
% 0.16/0.42 ( ( ( concat_a @ Xss2 )
% 0.16/0.42 = ( append_a @ Ys @ Zs2 ) )
% 0.16/0.42 = ( ( ( Xss2 = nil_list_a )
% 0.16/0.42 => ( ( Ys = nil_a )
% 0.16/0.42 & ( Zs2 = nil_a ) ) )
% 0.16/0.42 & ( ( Xss2 != nil_list_a )
% 0.16/0.42 => ? [Xss1: list_list_a,Xs2: list_a,Xs4: list_a,Xss22: list_list_a] :
% 0.16/0.42 ( ( Xss2
% 0.16/0.42 = ( append_list_a @ Xss1 @ ( cons_list_a @ ( append_a @ Xs2 @ Xs4 ) @ Xss22 ) ) )
% 0.16/0.42 & ( Ys
% 0.16/0.42 = ( append_a @ ( concat_a @ Xss1 ) @ Xs2 ) )
% 0.16/0.42 & ( Zs2
% 0.16/0.42 = ( append_a @ Xs4 @ ( concat_a @ Xss22 ) ) ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % concat_eq_append_conv
% 0.16/0.42 thf(fact_321_rotate1_Osimps_I2_J,axiom,
% 0.16/0.42 ! [X: list_a,Xs: list_list_a] :
% 0.16/0.42 ( ( rotate1_list_a @ ( cons_list_a @ X @ Xs ) )
% 0.16/0.42 = ( append_list_a @ Xs @ ( cons_list_a @ X @ nil_list_a ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % rotate1.simps(2)
% 0.16/0.42 thf(fact_322_rotate1_Osimps_I2_J,axiom,
% 0.16/0.42 ! [X: a,Xs: list_a] :
% 0.16/0.42 ( ( rotate1_a @ ( cons_a @ X @ Xs ) )
% 0.16/0.42 = ( append_a @ Xs @ ( cons_a @ X @ nil_a ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % rotate1.simps(2)
% 0.16/0.42 thf(fact_323_rotate1__is__Nil__conv,axiom,
% 0.16/0.42 ! [Xs: list_list_a] :
% 0.16/0.42 ( ( ( rotate1_list_a @ Xs )
% 0.16/0.42 = nil_list_a )
% 0.16/0.42 = ( Xs = nil_list_a ) ) ).
% 0.16/0.42
% 0.16/0.42 % rotate1_is_Nil_conv
% 0.16/0.42 thf(fact_324_rotate1__is__Nil__conv,axiom,
% 0.16/0.42 ! [Xs: list_a] :
% 0.16/0.42 ( ( ( rotate1_a @ Xs )
% 0.16/0.42 = nil_a )
% 0.16/0.42 = ( Xs = nil_a ) ) ).
% 0.16/0.42
% 0.16/0.42 % rotate1_is_Nil_conv
% 0.16/0.42 thf(fact_325_concat__append,axiom,
% 0.16/0.42 ! [Xs: list_list_list_a,Ys: list_list_list_a] :
% 0.16/0.42 ( ( concat_list_a @ ( append_list_list_a @ Xs @ Ys ) )
% 0.16/0.42 = ( append_list_a @ ( concat_list_a @ Xs ) @ ( concat_list_a @ Ys ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % concat_append
% 0.16/0.42 thf(fact_326_concat__append,axiom,
% 0.16/0.42 ! [Xs: list_list_a,Ys: list_list_a] :
% 0.16/0.42 ( ( concat_a @ ( append_list_a @ Xs @ Ys ) )
% 0.16/0.42 = ( append_a @ ( concat_a @ Xs ) @ ( concat_a @ Ys ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % concat_append
% 0.16/0.42 thf(fact_327_concat_Osimps_I1_J,axiom,
% 0.16/0.42 ( ( concat_list_a @ nil_list_list_a )
% 0.16/0.42 = nil_list_a ) ).
% 0.16/0.42
% 0.16/0.42 % concat.simps(1)
% 0.16/0.42 thf(fact_328_concat_Osimps_I1_J,axiom,
% 0.16/0.42 ( ( concat_a @ nil_list_a )
% 0.16/0.42 = nil_a ) ).
% 0.16/0.42
% 0.16/0.42 % concat.simps(1)
% 0.16/0.42 thf(fact_329_concat_Osimps_I2_J,axiom,
% 0.16/0.42 ! [X: list_list_a,Xs: list_list_list_a] :
% 0.16/0.42 ( ( concat_list_a @ ( cons_list_list_a @ X @ Xs ) )
% 0.16/0.42 = ( append_list_a @ X @ ( concat_list_a @ Xs ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % concat.simps(2)
% 0.16/0.42 thf(fact_330_concat_Osimps_I2_J,axiom,
% 0.16/0.42 ! [X: list_a,Xs: list_list_a] :
% 0.16/0.42 ( ( concat_a @ ( cons_list_a @ X @ Xs ) )
% 0.16/0.42 = ( append_a @ X @ ( concat_a @ Xs ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % concat.simps(2)
% 0.16/0.42 thf(fact_331_rotate1_Osimps_I1_J,axiom,
% 0.16/0.42 ( ( rotate1_list_a @ nil_list_a )
% 0.16/0.42 = nil_list_a ) ).
% 0.16/0.42
% 0.16/0.42 % rotate1.simps(1)
% 0.16/0.42 thf(fact_332_rotate1_Osimps_I1_J,axiom,
% 0.16/0.42 ( ( rotate1_a @ nil_a )
% 0.16/0.42 = nil_a ) ).
% 0.16/0.42
% 0.16/0.42 % rotate1.simps(1)
% 0.16/0.42 thf(fact_333_concat__eq__appendD,axiom,
% 0.16/0.42 ! [Xss2: list_list_list_a,Ys: list_list_a,Zs2: list_list_a] :
% 0.16/0.42 ( ( ( concat_list_a @ Xss2 )
% 0.16/0.42 = ( append_list_a @ Ys @ Zs2 ) )
% 0.16/0.42 => ( ( Xss2 != nil_list_list_a )
% 0.16/0.42 => ? [Xss12: list_list_list_a,Xs3: list_list_a,Xs5: list_list_a,Xss23: list_list_list_a] :
% 0.16/0.42 ( ( Xss2
% 0.16/0.42 = ( append_list_list_a @ Xss12 @ ( cons_list_list_a @ ( append_list_a @ Xs3 @ Xs5 ) @ Xss23 ) ) )
% 0.16/0.42 & ( Ys
% 0.16/0.42 = ( append_list_a @ ( concat_list_a @ Xss12 ) @ Xs3 ) )
% 0.16/0.42 & ( Zs2
% 0.16/0.42 = ( append_list_a @ Xs5 @ ( concat_list_a @ Xss23 ) ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % concat_eq_appendD
% 0.16/0.42 thf(fact_334_concat__eq__appendD,axiom,
% 0.16/0.42 ! [Xss2: list_list_a,Ys: list_a,Zs2: list_a] :
% 0.16/0.42 ( ( ( concat_a @ Xss2 )
% 0.16/0.42 = ( append_a @ Ys @ Zs2 ) )
% 0.16/0.42 => ( ( Xss2 != nil_list_a )
% 0.16/0.42 => ? [Xss12: list_list_a,Xs3: list_a,Xs5: list_a,Xss23: list_list_a] :
% 0.16/0.42 ( ( Xss2
% 0.16/0.42 = ( append_list_a @ Xss12 @ ( cons_list_a @ ( append_a @ Xs3 @ Xs5 ) @ Xss23 ) ) )
% 0.16/0.42 & ( Ys
% 0.16/0.42 = ( append_a @ ( concat_a @ Xss12 ) @ Xs3 ) )
% 0.16/0.42 & ( Zs2
% 0.16/0.42 = ( append_a @ Xs5 @ ( concat_a @ Xss23 ) ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % concat_eq_appendD
% 0.16/0.42 thf(fact_335_butlast__snoc,axiom,
% 0.16/0.42 ! [Xs: list_list_a,X: list_a] :
% 0.16/0.42 ( ( butlast_list_a @ ( append_list_a @ Xs @ ( cons_list_a @ X @ nil_list_a ) ) )
% 0.16/0.42 = Xs ) ).
% 0.16/0.42
% 0.16/0.42 % butlast_snoc
% 0.16/0.42 thf(fact_336_butlast__snoc,axiom,
% 0.16/0.42 ! [Xs: list_a,X: a] :
% 0.16/0.42 ( ( butlast_a @ ( append_a @ Xs @ ( cons_a @ X @ nil_a ) ) )
% 0.16/0.42 = Xs ) ).
% 0.16/0.42
% 0.16/0.42 % butlast_snoc
% 0.16/0.42 thf(fact_337_list__ex1__simps_I1_J,axiom,
% 0.16/0.42 ! [P: list_a > $o] :
% 0.16/0.42 ~ ( list_ex1_list_a @ P @ nil_list_a ) ).
% 0.16/0.42
% 0.16/0.42 % list_ex1_simps(1)
% 0.16/0.42 thf(fact_338_list__ex1__simps_I1_J,axiom,
% 0.16/0.42 ! [P: a > $o] :
% 0.16/0.42 ~ ( list_ex1_a @ P @ nil_a ) ).
% 0.16/0.42
% 0.16/0.42 % list_ex1_simps(1)
% 0.16/0.42 thf(fact_339_butlast__append,axiom,
% 0.16/0.42 ! [Ys: list_list_a,Xs: list_list_a] :
% 0.16/0.42 ( ( ( Ys = nil_list_a )
% 0.16/0.42 => ( ( butlast_list_a @ ( append_list_a @ Xs @ Ys ) )
% 0.16/0.42 = ( butlast_list_a @ Xs ) ) )
% 0.16/0.42 & ( ( Ys != nil_list_a )
% 0.16/0.42 => ( ( butlast_list_a @ ( append_list_a @ Xs @ Ys ) )
% 0.16/0.42 = ( append_list_a @ Xs @ ( butlast_list_a @ Ys ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % butlast_append
% 0.16/0.42 thf(fact_340_butlast__append,axiom,
% 0.16/0.42 ! [Ys: list_a,Xs: list_a] :
% 0.16/0.42 ( ( ( Ys = nil_a )
% 0.16/0.42 => ( ( butlast_a @ ( append_a @ Xs @ Ys ) )
% 0.16/0.42 = ( butlast_a @ Xs ) ) )
% 0.16/0.42 & ( ( Ys != nil_a )
% 0.16/0.42 => ( ( butlast_a @ ( append_a @ Xs @ Ys ) )
% 0.16/0.42 = ( append_a @ Xs @ ( butlast_a @ Ys ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % butlast_append
% 0.16/0.42 thf(fact_341_butlast_Osimps_I1_J,axiom,
% 0.16/0.42 ( ( butlast_list_a @ nil_list_a )
% 0.16/0.42 = nil_list_a ) ).
% 0.16/0.42
% 0.16/0.42 % butlast.simps(1)
% 0.16/0.42 thf(fact_342_butlast_Osimps_I1_J,axiom,
% 0.16/0.42 ( ( butlast_a @ nil_a )
% 0.16/0.42 = nil_a ) ).
% 0.16/0.42
% 0.16/0.42 % butlast.simps(1)
% 0.16/0.42 thf(fact_343_butlast_Osimps_I2_J,axiom,
% 0.16/0.42 ! [Xs: list_list_a,X: list_a] :
% 0.16/0.42 ( ( ( Xs = nil_list_a )
% 0.16/0.42 => ( ( butlast_list_a @ ( cons_list_a @ X @ Xs ) )
% 0.16/0.42 = nil_list_a ) )
% 0.16/0.42 & ( ( Xs != nil_list_a )
% 0.16/0.42 => ( ( butlast_list_a @ ( cons_list_a @ X @ Xs ) )
% 0.16/0.42 = ( cons_list_a @ X @ ( butlast_list_a @ Xs ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % butlast.simps(2)
% 0.16/0.42 thf(fact_344_butlast_Osimps_I2_J,axiom,
% 0.16/0.42 ! [Xs: list_a,X: a] :
% 0.16/0.42 ( ( ( Xs = nil_a )
% 0.16/0.42 => ( ( butlast_a @ ( cons_a @ X @ Xs ) )
% 0.16/0.42 = nil_a ) )
% 0.16/0.42 & ( ( Xs != nil_a )
% 0.16/0.42 => ( ( butlast_a @ ( cons_a @ X @ Xs ) )
% 0.16/0.42 = ( cons_a @ X @ ( butlast_a @ Xs ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 % butlast.simps(2)
% 0.16/0.42 thf(fact_345_append__butlast__last__id,axiom,
% 0.16/0.42 ! [Xs: list_list_a] :
% 0.16/0.42 ( ( Xs != nil_list_a )
% 0.16/0.42 => ( ( append_list_a @ ( butlast_list_a @ Xs ) @ ( cons_list_a @ ( last_list_a @ Xs ) @ nil_list_a ) )
% 0.16/0.42 = Xs ) ) ).
% 0.16/0.42
% 0.16/0.42 % append_butlast_last_id
% 0.16/0.42 thf(fact_346_append__butlast__last__id,axiom,
% 0.16/0.48 ! [Xs: list_a] :
% 0.16/0.48 ( ( Xs != nil_a )
% 0.16/0.48 => ( ( append_a @ ( butlast_a @ Xs ) @ ( cons_a @ ( last_a @ Xs ) @ nil_a ) )
% 0.16/0.48 = Xs ) ) ).
% 0.16/0.48
% 0.16/0.48 % append_butlast_last_id
% 0.16/0.48 thf(fact_347_snoc__eq__iff__butlast,axiom,
% 0.16/0.48 ! [Xs: list_list_a,X: list_a,Ys: list_list_a] :
% 0.16/0.48 ( ( ( append_list_a @ Xs @ ( cons_list_a @ X @ nil_list_a ) )
% 0.16/0.48 = Ys )
% 0.16/0.48 = ( ( Ys != nil_list_a )
% 0.16/0.48 & ( ( butlast_list_a @ Ys )
% 0.16/0.48 = Xs )
% 0.16/0.48 & ( ( last_list_a @ Ys )
% 0.16/0.48 = X ) ) ) ).
% 0.16/0.48
% 0.16/0.48 % snoc_eq_iff_butlast
% 0.16/0.48 thf(fact_348_snoc__eq__iff__butlast,axiom,
% 0.16/0.48 ! [Xs: list_a,X: a,Ys: list_a] :
% 0.16/0.48 ( ( ( append_a @ Xs @ ( cons_a @ X @ nil_a ) )
% 0.16/0.48 = Ys )
% 0.16/0.48 = ( ( Ys != nil_a )
% 0.16/0.48 & ( ( butlast_a @ Ys )
% 0.16/0.48 = Xs )
% 0.16/0.48 & ( ( last_a @ Ys )
% 0.16/0.48 = X ) ) ) ).
% 0.16/0.48
% 0.16/0.48 % snoc_eq_iff_butlast
% 0.16/0.48 thf(fact_349_last__appendR,axiom,
% 0.16/0.48 ! [Ys: list_list_a,Xs: list_list_a] :
% 0.16/0.48 ( ( Ys != nil_list_a )
% 0.16/0.48 => ( ( last_list_a @ ( append_list_a @ Xs @ Ys ) )
% 0.16/0.48 = ( last_list_a @ Ys ) ) ) ).
% 0.16/0.48
% 0.16/0.48 % last_appendR
% 0.16/0.48 thf(fact_350_last__appendR,axiom,
% 0.16/0.48 ! [Ys: list_a,Xs: list_a] :
% 0.16/0.48 ( ( Ys != nil_a )
% 0.16/0.48 => ( ( last_a @ ( append_a @ Xs @ Ys ) )
% 0.16/0.48 = ( last_a @ Ys ) ) ) ).
% 0.16/0.48
% 0.16/0.48 % last_appendR
% 0.16/0.48 thf(fact_351_last__appendL,axiom,
% 0.16/0.48 ! [Ys: list_a,Xs: list_a] :
% 0.16/0.48 ( ( Ys = nil_a )
% 0.16/0.48 => ( ( last_a @ ( append_a @ Xs @ Ys ) )
% 0.16/0.48 = ( last_a @ Xs ) ) ) ).
% 0.16/0.48
% 0.16/0.48 % last_appendL
% 0.16/0.48
% 0.16/0.48 % Conjectures (6)
% 0.16/0.48 thf(conj_0,hypothesis,
% 0.16/0.48 ( b
% 0.16/0.48 = ( inf @ b @ c ) ) ).
% 0.16/0.48
% 0.16/0.48 thf(conj_1,hypothesis,
% 0.16/0.48 ( ( inf @ c @ ( sup @ b @ c ) )
% 0.16/0.48 = b ) ).
% 0.16/0.48
% 0.16/0.48 thf(conj_2,hypothesis,
% 0.16/0.48 ( a2
% 0.16/0.48 = ( sup @ b @ c ) ) ).
% 0.16/0.48
% 0.16/0.48 thf(conj_3,hypothesis,
% 0.16/0.48 less @ b @ ( sup @ b @ c ) ).
% 0.16/0.48
% 0.16/0.48 thf(conj_4,hypothesis,
% 0.16/0.48 ( ( inf @ c @ ( sup @ b @ c ) )
% 0.16/0.48 = c ) ).
% 0.16/0.48
% 0.16/0.48 thf(conj_5,conjecture,
% 0.16/0.48 $false ).
% 0.16/0.48
% 0.16/0.48 %------------------------------------------------------------------------------
% 0.16/0.48 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.qniiFCHfyO/cvc5---1.0.5_32324.p...
% 0.16/0.48 (declare-sort $$unsorted 0)
% 0.16/0.48 (declare-sort tptp.list_list_list_a 0)
% 0.16/0.48 (declare-sort tptp.list_list_a 0)
% 0.16/0.48 (declare-sort tptp.list_a 0)
% 0.16/0.48 (declare-sort tptp.a 0)
% 0.16/0.48 (declare-fun tptp.finite40241356em_a_a ((-> tptp.a tptp.a tptp.a)) Bool)
% 0.16/0.48 (declare-fun tptp.abel_s1075322906list_a ((-> tptp.list_a tptp.list_a tptp.list_a)) Bool)
% 0.16/0.48 (declare-fun tptp.abel_semigroup_a ((-> tptp.a tptp.a tptp.a)) Bool)
% 0.16/0.48 (declare-fun tptp.abel_s374399671list_a ((-> tptp.list_a tptp.list_a tptp.list_a)) Bool)
% 0.16/0.48 (declare-fun tptp.abel_s2117090225ioms_a ((-> tptp.a tptp.a tptp.a)) Bool)
% 0.16/0.48 (declare-fun tptp.semigr656274520list_a ((-> tptp.list_list_a tptp.list_list_a tptp.list_list_a)) Bool)
% 0.16/0.48 (declare-fun tptp.semigroup_list_a ((-> tptp.list_a tptp.list_a tptp.list_a)) Bool)
% 0.16/0.48 (declare-fun tptp.semigroup_a ((-> tptp.a tptp.a tptp.a)) Bool)
% 0.16/0.48 (declare-fun tptp.semilattice_a ((-> tptp.a tptp.a tptp.a)) Bool)
% 0.16/0.48 (declare-fun tptp.semilattice_axioms_a ((-> tptp.a tptp.a tptp.a)) Bool)
% 0.16/0.48 (declare-fun tptp.lattic1885654924_set_a ((-> tptp.a tptp.a tptp.a)) Bool)
% 0.16/0.48 (declare-fun tptp.append_list_list_a (tptp.list_list_list_a tptp.list_list_list_a) tptp.list_list_list_a)
% 0.16/0.48 (declare-fun tptp.append_list_a (tptp.list_list_a tptp.list_list_a) tptp.list_list_a)
% 0.16/0.48 (declare-fun tptp.append_a (tptp.list_a tptp.list_a) tptp.list_a)
% 0.16/0.48 (declare-fun tptp.bind_list_a_list_a (tptp.list_list_a (-> tptp.list_a tptp.list_list_a)) tptp.list_list_a)
% 0.16/0.48 (declare-fun tptp.bind_list_a_a (tptp.list_list_a (-> tptp.list_a tptp.list_a)) tptp.list_a)
% 0.16/0.48 (declare-fun tptp.bind_a_list_a (tptp.list_a (-> tptp.a tptp.list_list_a)) tptp.list_list_a)
% 0.16/0.48 (declare-fun tptp.bind_a_a (tptp.list_a (-> tptp.a tptp.list_a)) tptp.list_a)
% 0.16/0.48 (declare-fun tptp.butlast_list_a (tptp.list_list_a) tptp.list_list_a)
% 0.16/0.48 (declare-fun tptp.butlast_a (tptp.list_a) tptp.list_a)
% 0.16/0.48 (declare-fun tptp.concat_list_a (tptp.list_list_list_a) tptp.list_list_a)
% 0.16/0.48 (declare-fun tptp.concat_a (tptp.list_list_a) tptp.list_a)
% 0.16/0.48 (declare-fun tptp.insert_list_a (tptp.list_a tptp.list_list_a) tptp.list_list_a)
% 0.16/0.48 (declare-fun tptp.insert_a (tptp.a tptp.list_a) tptp.list_a)
% 0.16/0.48 (declare-fun tptp.last_list_a (tptp.list_list_a) tptp.list_a)
% 0.16/0.48 (declare-fun tptp.last_a (tptp.list_a) tptp.a)
% 0.16/0.48 (declare-fun tptp.cons_list_list_a (tptp.list_list_a tptp.list_list_list_a) tptp.list_list_list_a)
% 0.16/0.48 (declare-fun tptp.cons_list_a (tptp.list_a tptp.list_list_a) tptp.list_list_a)
% 0.16/0.48 (declare-fun tptp.cons_a (tptp.a tptp.list_a) tptp.list_a)
% 0.16/0.48 (declare-fun tptp.nil_list_list_a () tptp.list_list_list_a)
% 0.16/0.48 (declare-fun tptp.nil_list_a () tptp.list_list_a)
% 0.16/0.48 (declare-fun tptp.nil_a () tptp.list_a)
% 0.16/0.48 (declare-fun tptp.list_ex1_list_a ((-> tptp.list_a Bool) tptp.list_list_a) Bool)
% 0.16/0.48 (declare-fun tptp.list_ex1_a ((-> tptp.a Bool) tptp.list_a) Bool)
% 0.16/0.48 (declare-fun tptp.maps_list_a_list_a ((-> tptp.list_a tptp.list_list_a) tptp.list_list_a) tptp.list_list_a)
% 0.16/0.48 (declare-fun tptp.maps_list_a_a ((-> tptp.list_a tptp.list_a) tptp.list_list_a) tptp.list_a)
% 0.16/0.48 (declare-fun tptp.maps_a_list_a ((-> tptp.a tptp.list_list_a) tptp.list_a) tptp.list_list_a)
% 0.16/0.48 (declare-fun tptp.maps_a_a ((-> tptp.a tptp.list_a) tptp.list_a) tptp.list_a)
% 0.16/0.48 (declare-fun tptp.lexordp_list_a ((-> tptp.list_a tptp.list_a Bool) tptp.list_list_a tptp.list_list_a) Bool)
% 0.16/0.48 (declare-fun tptp.lexordp_a ((-> tptp.a tptp.a Bool) tptp.list_a tptp.list_a) Bool)
% 0.16/0.48 (declare-fun tptp.lexordp_eq_list_a ((-> tptp.list_a tptp.list_a Bool) tptp.list_list_a tptp.list_list_a) Bool)
% 0.16/0.48 (declare-fun tptp.lexordp_eq_a ((-> tptp.a tptp.a Bool) tptp.list_a tptp.list_a) Bool)
% 0.16/0.48 (declare-fun tptp.product_lists_list_a (tptp.list_list_list_a) tptp.list_list_list_a)
% 0.16/0.48 (declare-fun tptp.product_lists_a (tptp.list_list_a) tptp.list_list_a)
% 0.16/0.48 (declare-fun tptp.rotate1_list_a (tptp.list_list_a) tptp.list_list_a)
% 0.16/0.48 (declare-fun tptp.rotate1_a (tptp.list_a) tptp.list_a)
% 0.16/0.48 (declare-fun tptp.subseqs_list_a (tptp.list_list_a) tptp.list_list_list_a)
% 0.16/0.48 (declare-fun tptp.subseqs_a (tptp.list_a) tptp.list_list_a)
% 0.16/0.48 (declare-fun tptp.modula1376131916tice_a ((-> tptp.a tptp.a tptp.a) (-> tptp.a tptp.a Bool) (-> tptp.a tptp.a tptp.a) tptp.a tptp.a tptp.a) Bool)
% 0.16/0.48 (declare-fun tptp.modula397570059tice_a ((-> tptp.a tptp.a tptp.a) (-> tptp.a tptp.a Bool) (-> tptp.a tptp.a tptp.a) tptp.a tptp.a tptp.a) Bool)
% 0.16/0.48 (declare-fun tptp.modula17988509_aux_a ((-> tptp.a tptp.a tptp.a) (-> tptp.a tptp.a tptp.a) tptp.a tptp.a tptp.a) tptp.a)
% 0.16/0.48 (declare-fun tptp.modula1373251614_aux_a ((-> tptp.a tptp.a tptp.a) (-> tptp.a tptp.a tptp.a) tptp.a tptp.a tptp.a) tptp.a)
% 0.16/0.48 (declare-fun tptp.modula581031071_aux_a ((-> tptp.a tptp.a tptp.a) (-> tptp.a tptp.a tptp.a) tptp.a tptp.a tptp.a) tptp.a)
% 0.16/0.48 (declare-fun tptp.modula1936294176_aux_a ((-> tptp.a tptp.a tptp.a) (-> tptp.a tptp.a tptp.a) tptp.a tptp.a tptp.a) tptp.a)
% 0.16/0.48 (declare-fun tptp.modula1144073633_aux_a ((-> tptp.a tptp.a tptp.a) (-> tptp.a tptp.a tptp.a) tptp.a tptp.a tptp.a) tptp.a)
% 0.16/0.48 (declare-fun tptp.modula1962211574trib_a ((-> tptp.a tptp.a tptp.a) (-> tptp.a tptp.a Bool) (-> tptp.a tptp.a tptp.a) tptp.a tptp.a tptp.a) Bool)
% 0.16/0.48 (declare-fun tptp.transp_a ((-> tptp.a tptp.a Bool)) Bool)
% 0.16/0.48 (declare-fun tptp.a2 () tptp.a)
% 0.16/0.48 (declare-fun tptp.b () tptp.a)
% 0.16/0.48 (declare-fun tptp.c () tptp.a)
% 0.16/0.48 (declare-fun tptp.inf (tptp.a tptp.a) tptp.a)
% 0.16/0.48 (declare-fun tptp.less (tptp.a tptp.a) Bool)
% 0.16/0.48 (declare-fun tptp.sup (tptp.a tptp.a) tptp.a)
% 0.16/0.48 (assert (forall ((B tptp.a) (A tptp.a)) (=> (@ (@ tptp.less B) A) (not (@ (@ tptp.less A) B)))))
% 0.16/0.48 (assert (forall ((B tptp.a) (A tptp.a)) (=> (@ (@ tptp.less B) A) (not (= A B)))))
% 0.16/0.48 (assert (forall ((B tptp.a) (A tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.less C))) (=> (@ (@ tptp.less B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 0.16/0.48 (assert (forall ((X tptp.a) (Y tptp.a)) (=> (@ (@ tptp.less X) Y) (not (@ (@ tptp.less Y) X)))))
% 0.16/0.48 (assert (forall ((A tptp.a) (B tptp.a)) (=> (@ (@ tptp.less A) B) (not (@ (@ tptp.less B) A)))))
% 0.16/0.48 (assert (forall ((X tptp.a) (Y tptp.a)) (=> (@ (@ tptp.less X) Y) (not (= X Y)))))
% 0.16/0.48 (assert (forall ((X tptp.a) (Y tptp.a)) (=> (@ (@ tptp.less X) Y) (not (= X Y)))))
% 0.16/0.48 (assert (forall ((X tptp.a) (Y tptp.a)) (=> (@ (@ tptp.less X) Y) (not (= Y X)))))
% 0.16/0.48 (assert (forall ((X tptp.a) (Y tptp.a)) (=> (@ (@ tptp.less X) Y) (not (@ (@ tptp.less Y) X)))))
% 0.16/0.48 (assert (forall ((X tptp.a) (Y tptp.a) (P Bool)) (=> (@ (@ tptp.less X) Y) (=> (@ (@ tptp.less Y) X) P))))
% 0.16/0.48 (assert (forall ((X tptp.a)) (not (@ (@ tptp.less X) X))))
% 0.16/0.48 (assert (forall ((X tptp.a) (Y tptp.a)) (=> (@ (@ tptp.less X) Y) (not (@ (@ tptp.less Y) X)))))
% 0.16/0.48 (assert (forall ((X tptp.a) (Y tptp.a) (Z tptp.a)) (let ((_let_1 (@ tptp.less X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.less Y) Z) (@ _let_1 Z))))))
% 0.16/0.48 (assert (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (=> (= A B) (=> (@ (@ tptp.less B) C) (@ (@ tptp.less A) C)))))
% 0.16/0.48 (assert (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.less A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 0.16/0.48 (assert (forall ((A tptp.a) (B tptp.a)) (=> (@ (@ tptp.less A) B) (not (@ (@ tptp.less B) A)))))
% 0.16/0.48 (assert (forall ((A tptp.a)) (not (@ (@ tptp.less A) A))))
% 0.16/0.48 (assert (forall ((A tptp.a) (B tptp.a)) (=> (@ (@ tptp.less A) B) (not (= A B)))))
% 0.16/0.48 (assert (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.less A))) (=> (@ _let_1 B) (=> (@ (@ tptp.less B) C) (@ _let_1 C))))))
% 0.16/0.48 (assert (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.inf A))) (= (@ (@ tptp.inf (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.inf B) C))))))
% 0.16/0.48 (assert (forall ((A tptp.a) (B tptp.a)) (= (@ (@ tptp.inf A) B) (@ (@ tptp.inf B) A))))
% 0.16/0.48 (assert (forall ((B tptp.a) (A tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.inf B))) (let ((_let_2 (@ tptp.inf A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 0.16/0.48 (assert (forall ((X tptp.a) (Y tptp.a) (Z tptp.a)) (let ((_let_1 (@ tptp.inf X))) (= (@ (@ tptp.inf (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.inf Y) Z))))))
% 0.16/0.48 (assert (forall ((X tptp.a) (Y tptp.a)) (= (@ (@ tptp.inf X) Y) (@ (@ tptp.inf Y) X))))
% 0.16/0.48 (assert (forall ((X tptp.a) (Y tptp.a) (Z tptp.a)) (let ((_let_1 (@ tptp.inf X))) (let ((_let_2 (@ tptp.inf Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 0.16/0.48 (assert (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.sup A))) (= (@ (@ tptp.sup (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.sup B) C))))))
% 0.16/0.48 (assert (forall ((A tptp.a) (B tptp.a)) (= (@ (@ tptp.sup A) B) (@ (@ tptp.sup B) A))))
% 0.16/0.48 (assert (forall ((B tptp.a) (A tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.sup B))) (let ((_let_2 (@ tptp.sup A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 0.16/0.48 (assert (forall ((X tptp.a) (Y tptp.a) (Z tptp.a)) (let ((_let_1 (@ tptp.sup X))) (= (@ (@ tptp.sup (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.sup Y) Z))))))
% 0.16/0.48 (assert (forall ((X tptp.a) (Y tptp.a)) (= (@ (@ tptp.sup X) Y) (@ (@ tptp.sup Y) X))))
% 0.16/0.48 (assert (forall ((X tptp.a) (Y tptp.a) (Z tptp.a)) (let ((_let_1 (@ tptp.sup X))) (let ((_let_2 (@ tptp.sup Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 0.16/0.48 (assert (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.less A))) (=> (@ _let_1 (@ (@ tptp.inf B) C)) (not (=> (@ _let_1 B) (not (@ _let_1 C))))))))
% 0.16/0.48 (assert (forall ((A tptp.a) (C tptp.a) (B tptp.a)) (=> (@ (@ tptp.less A) C) (@ (@ tptp.less (@ (@ tptp.inf A) B)) C))))
% 0.16/0.48 (assert (forall ((B tptp.a) (C tptp.a) (A tptp.a)) (=> (@ (@ tptp.less B) C) (@ (@ tptp.less (@ (@ tptp.inf A) B)) C))))
% 0.16/0.48 (assert (forall ((A tptp.a) (B tptp.a)) (= (@ (@ tptp.less A) B) (and (= A (@ (@ tptp.inf A) B)) (not (= A B))))))
% 0.16/0.48 (assert (forall ((A tptp.a) (X tptp.a) (B tptp.a)) (=> (@ (@ tptp.less A) X) (@ (@ tptp.less (@ (@ tptp.inf A) B)) X))))
% 0.16/0.48 (assert (forall ((B tptp.a) (X tptp.a) (A tptp.a)) (=> (@ (@ tptp.less B) X) (@ (@ tptp.less (@ (@ tptp.inf A) B)) X))))
% 0.16/0.48 (assert (forall ((X tptp.a) (A tptp.a) (B tptp.a)) (let ((_let_1 (@ tptp.less X))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup A) B))))))
% 0.16/0.48 (assert (forall ((X tptp.a) (B tptp.a) (A tptp.a)) (let ((_let_1 (@ tptp.less X))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup A) B))))))
% 0.16/0.48 (assert (forall ((B tptp.a) (C tptp.a) (A tptp.a)) (=> (@ (@ tptp.less (@ (@ tptp.sup B) C)) A) (not (=> (@ (@ tptp.less B) A) (not (@ (@ tptp.less C) A)))))))
% 0.16/0.48 (assert (forall ((C tptp.a) (A tptp.a) (B tptp.a)) (let ((_let_1 (@ tptp.less C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup A) B))))))
% 0.16/0.48 (assert (forall ((C tptp.a) (B tptp.a) (A tptp.a)) (let ((_let_1 (@ tptp.less C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup A) B))))))
% 0.16/0.48 (assert (forall ((B tptp.a) (A tptp.a)) (= (@ (@ tptp.less B) A) (and (= A (@ (@ tptp.sup A) B)) (not (= A B))))))
% 0.16/0.48 (assert (forall ((X tptp.a) (Y tptp.a) (Z tptp.a)) (let ((_let_1 (@ tptp.sup X))) (=> (forall ((X2 tptp.a) (Y2 tptp.a) (Z2 tptp.a)) (let ((_let_1 (@ tptp.inf X2))) (= (@ _let_1 (@ (@ tptp.sup Y2) Z2)) (@ (@ tptp.sup (@ _let_1 Y2)) (@ _let_1 Z2))))) (= (@ _let_1 (@ (@ tptp.inf Y) Z)) (@ (@ tptp.inf (@ _let_1 Y)) (@ _let_1 Z)))))))
% 0.16/0.48 (assert (forall ((X tptp.a) (Y tptp.a) (Z tptp.a)) (let ((_let_1 (@ tptp.inf X))) (=> (forall ((X2 tptp.a) (Y2 tptp.a) (Z2 tptp.a)) (let ((_let_1 (@ tptp.sup X2))) (= (@ _let_1 (@ (@ tptp.inf Y2) Z2)) (@ (@ tptp.inf (@ _let_1 Y2)) (@ _let_1 Z2))))) (= (@ _let_1 (@ (@ tptp.sup Y) Z)) (@ (@ tptp.sup (@ _let_1 Y)) (@ _let_1 Z)))))))
% 0.16/0.48 (assert (forall ((A tptp.a)) (= (@ (@ tptp.inf A) A) A)))
% 0.16/0.48 (assert (forall ((A tptp.a) (B tptp.a)) (let ((_let_1 (@ tptp.inf A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 0.16/0.48 (assert (forall ((A tptp.a) (B tptp.a)) (let ((_let_1 (@ (@ tptp.inf A) B))) (= (@ (@ tptp.inf _let_1) B) _let_1))))
% 0.16/0.48 (assert (forall ((X tptp.a)) (= (@ (@ tptp.inf X) X) X)))
% 0.16/0.48 (assert (forall ((X tptp.a) (Y tptp.a)) (let ((_let_1 (@ tptp.inf X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))))
% 0.16/0.48 (assert (forall ((X tptp.a) (Y tptp.a)) (let ((_let_1 (@ (@ tptp.inf X) Y))) (= (@ (@ tptp.inf _let_1) Y) _let_1))))
% 0.16/0.48 (assert (forall ((A tptp.a)) (= (@ (@ tptp.sup A) A) A)))
% 0.16/0.48 (assert (forall ((A tptp.a) (B tptp.a)) (let ((_let_1 (@ tptp.sup A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 0.16/0.48 (assert (forall ((A tptp.a) (B tptp.a)) (let ((_let_1 (@ (@ tptp.sup A) B))) (= (@ (@ tptp.sup _let_1) B) _let_1))))
% 0.16/0.48 (assert (forall ((X tptp.a)) (= (@ (@ tptp.sup X) X) X)))
% 0.16/0.48 (assert (forall ((X tptp.a) (Y tptp.a)) (let ((_let_1 (@ tptp.sup X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))))
% 0.16/0.48 (assert (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ (@ tptp.sup A) B))) (let ((_let_2 (@ (@ tptp.inf A) B))) (let ((_let_3 (@ (@ tptp.sup B) C))) (let ((_let_4 (@ (@ tptp.inf B) C))) (= (@ (@ (@ (@ (@ (@ tptp.modula1376131916tice_a tptp.inf) tptp.less) tptp.sup) A) B) C) (and (= _let_2 _let_4) (= (@ (@ tptp.inf C) A) _let_4) (= _let_1 _let_3) (= (@ (@ tptp.sup C) A) _let_3) (@ (@ tptp.less _let_2) _let_1)))))))))
% 0.16/0.48 (assert (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (= (@ (@ (@ (@ (@ (@ tptp.modula397570059tice_a tptp.inf) tptp.less) tptp.sup) A) B) C) (and (= (@ (@ tptp.inf A) C) (@ (@ tptp.inf B) C)) (@ (@ tptp.less A) B) (= (@ (@ tptp.sup A) C) (@ (@ tptp.sup B) C))))))
% 0.16/0.48 (assert (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.inf A))) (= (@ (@ (@ (@ (@ (@ tptp.modula1962211574trib_a tptp.inf) tptp.less) tptp.sup) A) B) C) (@ (@ tptp.less (@ (@ tptp.sup (@ _let_1 B)) (@ (@ tptp.inf C) A))) (@ _let_1 (@ (@ tptp.sup B) C)))))))
% 0.16/0.48 (assert (forall ((X tptp.a) (Y tptp.a)) (= (@ (@ tptp.inf X) (@ (@ tptp.sup X) Y)) X)))
% 0.16/0.48 (assert (forall ((X tptp.a) (Y tptp.a)) (= (@ (@ tptp.sup X) (@ (@ tptp.inf X) Y)) X)))
% 0.16/0.48 (assert (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.sup A))) (= (@ _let_1 (@ (@ (@ (@ (@ tptp.modula1936294176_aux_a tptp.inf) tptp.sup) A) B) C)) (@ _let_1 (@ (@ tptp.inf B) C))))))
% 0.16/0.48 (assert (forall ((B tptp.a) (A tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.sup B))) (= (@ _let_1 (@ (@ (@ (@ (@ tptp.modula1936294176_aux_a tptp.inf) tptp.sup) A) B) C)) (@ _let_1 (@ (@ tptp.inf C) A))))))
% 0.16/0.48 (assert (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (= (@ (@ (@ (@ (@ tptp.modula1936294176_aux_a tptp.inf) tptp.sup) A) B) C) (@ (@ tptp.sup (@ (@ tptp.sup (@ (@ tptp.inf A) B)) (@ (@ tptp.inf B) C))) (@ (@ tptp.inf C) A)))))
% 0.16/0.48 (assert (forall ((B tptp.a) (C tptp.a) (A tptp.a)) (let ((_let_1 (@ (@ tptp.modula1936294176_aux_a tptp.inf) tptp.sup))) (= (@ (@ (@ _let_1 B) C) A) (@ (@ (@ _let_1 A) B) C)))))
% 0.16/0.48 (assert (forall ((C tptp.a) (A tptp.a) (B tptp.a)) (let ((_let_1 (@ (@ tptp.modula1936294176_aux_a tptp.inf) tptp.sup))) (= (@ (@ (@ _let_1 C) A) B) (@ (@ (@ _let_1 A) B) C)))))
% 0.16/0.48 (assert (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.inf A))) (= (@ _let_1 (@ (@ (@ (@ (@ tptp.modula1144073633_aux_a tptp.inf) tptp.sup) A) B) C)) (@ _let_1 (@ (@ tptp.sup B) C))))))
% 0.16/0.48 (assert (forall ((B tptp.a) (A tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.inf B))) (= (@ _let_1 (@ (@ (@ (@ (@ tptp.modula1144073633_aux_a tptp.inf) tptp.sup) A) B) C)) (@ _let_1 (@ (@ tptp.sup C) A))))))
% 0.16/0.48 (assert (forall ((C tptp.a) (A tptp.a) (B tptp.a)) (let ((_let_1 (@ tptp.inf C))) (= (@ _let_1 (@ (@ (@ (@ (@ tptp.modula1144073633_aux_a tptp.inf) tptp.sup) A) B) C)) (@ _let_1 (@ (@ tptp.sup A) B))))))
% 0.16/0.48 (assert (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (= (@ (@ (@ (@ (@ tptp.modula1144073633_aux_a tptp.inf) tptp.sup) A) B) C) (@ (@ tptp.inf (@ (@ tptp.inf (@ (@ tptp.sup A) B)) (@ (@ tptp.sup B) C))) (@ (@ tptp.sup C) A)))))
% 0.16/0.48 (assert (forall ((B tptp.a) (C tptp.a) (A tptp.a)) (let ((_let_1 (@ (@ tptp.modula1144073633_aux_a tptp.inf) tptp.sup))) (= (@ (@ (@ _let_1 B) C) A) (@ (@ (@ _let_1 A) B) C)))))
% 0.16/0.48 (assert (forall ((C tptp.a) (A tptp.a) (B tptp.a)) (let ((_let_1 (@ (@ tptp.modula1144073633_aux_a tptp.inf) tptp.sup))) (= (@ (@ (@ _let_1 C) A) B) (@ (@ (@ _let_1 A) B) C)))))
% 0.16/0.48 (assert (@ tptp.finite40241356em_a_a tptp.sup))
% 0.16/0.48 (assert (@ tptp.finite40241356em_a_a tptp.inf))
% 0.16/0.48 (assert (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (= (@ (@ (@ (@ (@ tptp.modula581031071_aux_a tptp.inf) tptp.sup) A) B) C) (@ (@ tptp.sup (@ (@ tptp.inf C) (@ (@ (@ (@ (@ tptp.modula1144073633_aux_a tptp.inf) tptp.sup) A) B) C))) (@ (@ (@ (@ (@ tptp.modula1936294176_aux_a tptp.inf) tptp.sup) A) B) C)))))
% 0.16/0.48 (assert (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (= (@ (@ (@ (@ (@ tptp.modula1373251614_aux_a tptp.inf) tptp.sup) A) B) C) (@ (@ tptp.sup (@ (@ tptp.inf B) (@ (@ (@ (@ (@ tptp.modula1144073633_aux_a tptp.inf) tptp.sup) A) B) C))) (@ (@ (@ (@ (@ tptp.modula1936294176_aux_a tptp.inf) tptp.sup) A) B) C)))))
% 0.16/0.48 (assert (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (= (@ (@ (@ (@ (@ tptp.modula17988509_aux_a tptp.inf) tptp.sup) A) B) C) (@ (@ tptp.sup (@ (@ tptp.inf A) (@ (@ (@ (@ (@ tptp.modula1144073633_aux_a tptp.inf) tptp.sup) A) B) C))) (@ (@ (@ (@ (@ tptp.modula1936294176_aux_a tptp.inf) tptp.sup) A) B) C)))))
% 0.16/0.48 (assert (= tptp.modula1962211574trib_a tptp.modula1962211574trib_a))
% 0.16/0.48 (assert (= tptp.modula397570059tice_a tptp.modula397570059tice_a))
% 0.16/0.48 (assert (= tptp.modula1376131916tice_a tptp.modula1376131916tice_a))
% 0.16/0.48 (assert (= tptp.modula1144073633_aux_a tptp.modula1144073633_aux_a))
% 0.16/0.48 (assert (= tptp.modula1936294176_aux_a tptp.modula1936294176_aux_a))
% 0.16/0.48 (assert (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (= (@ (@ (@ (@ (@ tptp.modula581031071_aux_a tptp.inf) tptp.sup) A) B) C) (@ (@ (@ (@ (@ tptp.modula17988509_aux_a tptp.inf) tptp.sup) C) A) B))))
% 0.16/0.48 (assert (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (= (@ (@ (@ (@ (@ tptp.modula1373251614_aux_a tptp.inf) tptp.sup) A) B) C) (@ (@ (@ (@ (@ tptp.modula17988509_aux_a tptp.inf) tptp.sup) B) C) A))))
% 0.16/0.48 (assert (@ tptp.semigroup_a tptp.sup))
% 0.16/0.48 (assert (@ tptp.semigroup_a tptp.inf))
% 0.16/0.48 (assert (@ tptp.semilattice_a tptp.sup))
% 0.16/0.48 (assert (@ tptp.semilattice_a tptp.inf))
% 0.16/0.48 (assert (= tptp.modula17988509_aux_a tptp.modula17988509_aux_a))
% 0.16/0.48 (assert (= tptp.modula1373251614_aux_a tptp.modula1373251614_aux_a))
% 0.16/0.48 (assert (= tptp.modula581031071_aux_a tptp.modula581031071_aux_a))
% 0.16/0.48 (assert (@ tptp.abel_semigroup_a tptp.sup))
% 0.16/0.48 (assert (@ tptp.abel_semigroup_a tptp.inf))
% 0.16/0.48 (assert (@ tptp.lattic1885654924_set_a tptp.sup))
% 0.16/0.48 (assert (@ tptp.lattic1885654924_set_a tptp.inf))
% 0.16/0.48 (assert (forall ((Xs tptp.list_a)) (@ (@ (@ tptp.lexordp_eq_a tptp.less) Xs) Xs)))
% 0.16/0.48 (assert (forall ((Ys tptp.list_a)) (@ (@ (@ tptp.lexordp_eq_a tptp.less) tptp.nil_a) Ys)))
% 0.16/0.48 (assert (forall ((F (-> tptp.list_a tptp.list_a tptp.list_a))) (=> (@ tptp.abel_s1075322906list_a F) (@ tptp.semigroup_list_a F))))
% 0.16/0.48 (assert (forall ((F (-> tptp.a tptp.a tptp.a))) (=> (@ tptp.abel_semigroup_a F) (@ tptp.semigroup_a F))))
% 0.16/0.48 (assert (forall ((F (-> tptp.a tptp.a tptp.a))) (=> (@ tptp.lattic1885654924_set_a F) (@ tptp.semilattice_a F))))
% 0.16/0.48 (assert (forall ((F (-> tptp.a tptp.a tptp.a))) (=> (@ tptp.semilattice_a F) (@ tptp.lattic1885654924_set_a F))))
% 0.16/0.48 (assert (= tptp.lattic1885654924_set_a tptp.semilattice_a))
% 0.16/0.48 (assert (forall ((Ys tptp.list_a)) (@ (@ (@ tptp.lexordp_eq_a tptp.less) tptp.nil_a) Ys)))
% 0.16/0.48 (assert (forall ((Xs tptp.list_a)) (= (@ (@ (@ tptp.lexordp_eq_a tptp.less) Xs) tptp.nil_a) (= Xs tptp.nil_a))))
% 0.16/0.48 (assert (forall ((F (-> tptp.a tptp.a tptp.a)) (B tptp.a) (A tptp.a) (C tptp.a)) (let ((_let_1 (@ F B))) (let ((_let_2 (@ F A))) (=> (@ tptp.abel_semigroup_a F) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C))))))))
% 0.16/0.48 (assert (forall ((F (-> tptp.a tptp.a tptp.a)) (A tptp.a) (B tptp.a)) (=> (@ tptp.abel_semigroup_a F) (= (@ (@ F A) B) (@ (@ F B) A)))))
% 0.16/0.48 (assert (forall ((F (-> tptp.list_a tptp.list_a tptp.list_a))) (=> (forall ((A2 tptp.list_a) (B2 tptp.list_a) (C2 tptp.list_a)) (let ((_let_1 (@ F A2))) (= (@ (@ F (@ _let_1 B2)) C2) (@ _let_1 (@ (@ F B2) C2))))) (@ tptp.semigroup_list_a F))))
% 0.16/0.48 (assert (forall ((F (-> tptp.a tptp.a tptp.a))) (=> (forall ((A2 tptp.a) (B2 tptp.a) (C2 tptp.a)) (let ((_let_1 (@ F A2))) (= (@ (@ F (@ _let_1 B2)) C2) (@ _let_1 (@ (@ F B2) C2))))) (@ tptp.semigroup_a F))))
% 0.16/0.48 (assert (forall ((F (-> tptp.list_a tptp.list_a tptp.list_a)) (A tptp.list_a) (B tptp.list_a) (C tptp.list_a)) (let ((_let_1 (@ F A))) (=> (@ tptp.semigroup_list_a F) (= (@ (@ F (@ _let_1 B)) C) (@ _let_1 (@ (@ F B) C)))))))
% 0.16/0.48 (assert (forall ((F (-> tptp.a tptp.a tptp.a)) (A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ F A))) (=> (@ tptp.semigroup_a F) (= (@ (@ F (@ _let_1 B)) C) (@ _let_1 (@ (@ F B) C)))))))
% 0.16/0.48 (assert (= tptp.semigroup_list_a (lambda ((F2 (-> tptp.list_a tptp.list_a tptp.list_a))) (forall ((A3 tptp.list_a) (B3 tptp.list_a) (C3 tptp.list_a)) (let ((_let_1 (@ F2 A3))) (= (@ (@ F2 (@ _let_1 B3)) C3) (@ _let_1 (@ (@ F2 B3) C3))))))))
% 0.16/0.48 (assert (= tptp.semigroup_a (lambda ((F2 (-> tptp.a tptp.a tptp.a))) (forall ((A3 tptp.a) (B3 tptp.a) (C3 tptp.a)) (let ((_let_1 (@ F2 A3))) (= (@ (@ F2 (@ _let_1 B3)) C3) (@ _let_1 (@ (@ F2 B3) C3))))))))
% 0.16/0.48 (assert (forall ((Less (-> tptp.list_a tptp.list_a Bool)) (Xs tptp.list_list_a)) (= (@ (@ (@ tptp.lexordp_eq_list_a Less) Xs) tptp.nil_list_a) (= Xs tptp.nil_list_a))))
% 0.16/0.48 (assert (forall ((Less (-> tptp.a tptp.a Bool)) (Xs tptp.list_a)) (= (@ (@ (@ tptp.lexordp_eq_a Less) Xs) tptp.nil_a) (= Xs tptp.nil_a))))
% 0.16/0.48 (assert (forall ((Less (-> tptp.list_a tptp.list_a Bool)) (Ys tptp.list_list_a)) (@ (@ (@ tptp.lexordp_eq_list_a Less) tptp.nil_list_a) Ys)))
% 0.16/0.48 (assert (forall ((Less (-> tptp.a tptp.a Bool)) (Ys tptp.list_a)) (@ (@ (@ tptp.lexordp_eq_a Less) tptp.nil_a) Ys)))
% 0.16/0.48 (assert (forall ((A1 tptp.list_a) (A22 tptp.list_a)) (= (@ (@ (@ tptp.lexordp_eq_a tptp.less) A1) A22) (or (exists ((Ys2 tptp.list_a)) (and (= A1 tptp.nil_a) (= A22 Ys2))) (exists ((X3 tptp.a) (Y3 tptp.a) (Xs2 tptp.list_a) (Ys2 tptp.list_a)) (and (= A1 (@ (@ tptp.cons_a X3) Xs2)) (= A22 (@ (@ tptp.cons_a Y3) Ys2)) (@ (@ tptp.less X3) Y3))) (exists ((X3 tptp.a) (Y3 tptp.a) (Xs2 tptp.list_a) (Ys2 tptp.list_a)) (and (= A1 (@ (@ tptp.cons_a X3) Xs2)) (= A22 (@ (@ tptp.cons_a Y3) Ys2)) (not (@ (@ tptp.less X3) Y3)) (not (@ (@ tptp.less Y3) X3)) (@ (@ (@ tptp.lexordp_eq_a tptp.less) Xs2) Ys2)))))))
% 0.16/0.48 (assert (forall ((X1 tptp.list_a) (X22 tptp.list_a) (P (-> tptp.list_a tptp.list_a Bool))) (=> (@ (@ (@ tptp.lexordp_eq_a tptp.less) X1) X22) (=> (forall ((X_1 tptp.list_a)) (@ (@ P tptp.nil_a) X_1)) (=> (forall ((X2 tptp.a) (Y2 tptp.a) (Xs3 tptp.list_a) (Ys3 tptp.list_a)) (=> (@ (@ tptp.less X2) Y2) (@ (@ P (@ (@ tptp.cons_a X2) Xs3)) (@ (@ tptp.cons_a Y2) Ys3)))) (=> (forall ((X2 tptp.a) (Y2 tptp.a) (Xs3 tptp.list_a) (Ys3 tptp.list_a)) (=> (not (@ (@ tptp.less X2) Y2)) (=> (not (@ (@ tptp.less Y2) X2)) (=> (@ (@ (@ tptp.lexordp_eq_a tptp.less) Xs3) Ys3) (=> (@ (@ P Xs3) Ys3) (@ (@ P (@ (@ tptp.cons_a X2) Xs3)) (@ (@ tptp.cons_a Y2) Ys3))))))) (@ (@ P X1) X22)))))))
% 0.16/0.48 (assert (forall ((A1 tptp.list_a) (A22 tptp.list_a)) (=> (@ (@ (@ tptp.lexordp_eq_a tptp.less) A1) A22) (=> (not (= A1 tptp.nil_a)) (=> (forall ((X2 tptp.a)) (=> (exists ((Xs3 tptp.list_a)) (= A1 (@ (@ tptp.cons_a X2) Xs3))) (forall ((Y2 tptp.a)) (=> (exists ((Ys3 tptp.list_a)) (= A22 (@ (@ tptp.cons_a Y2) Ys3))) (not (@ (@ tptp.less X2) Y2)))))) (not (forall ((X2 tptp.a) (Y2 tptp.a) (Xs3 tptp.list_a)) (=> (= A1 (@ (@ tptp.cons_a X2) Xs3)) (forall ((Ys3 tptp.list_a)) (=> (= A22 (@ (@ tptp.cons_a Y2) Ys3)) (=> (not (@ (@ tptp.less X2) Y2)) (=> (not (@ (@ tptp.less Y2) X2)) (not (@ (@ (@ tptp.lexordp_eq_a tptp.less) Xs3) Ys3))))))))))))))
% 0.16/0.48 (assert (forall ((X tptp.a) (Y tptp.a) (Xs tptp.list_a) (Ys tptp.list_a)) (let ((_let_1 (@ tptp.lexordp_eq_a tptp.less))) (=> (not (@ (@ tptp.less X) Y)) (=> (not (@ (@ tptp.less Y) X)) (=> (@ (@ _let_1 Xs) Ys) (@ (@ _let_1 (@ (@ tptp.cons_a X) Xs)) (@ (@ tptp.cons_a Y) Ys))))))))
% 0.16/0.48 (assert (forall ((X tptp.a) (Y tptp.a) (Xs tptp.list_a) (Ys tptp.list_a)) (=> (@ (@ tptp.less X) Y) (@ (@ (@ tptp.lexordp_eq_a tptp.less) (@ (@ tptp.cons_a X) Xs)) (@ (@ tptp.cons_a Y) Ys)))))
% 0.16/0.48 (assert (forall ((X21 tptp.list_a) (X222 tptp.list_list_a) (Y21 tptp.list_a) (Y22 tptp.list_list_a)) (= (= (@ (@ tptp.cons_list_a X21) X222) (@ (@ tptp.cons_list_a Y21) Y22)) (and (= X21 Y21) (= X222 Y22)))))
% 0.16/0.48 (assert (forall ((X21 tptp.a) (X222 tptp.list_a) (Y21 tptp.a) (Y22 tptp.list_a)) (= (= (@ (@ tptp.cons_a X21) X222) (@ (@ tptp.cons_a Y21) Y22)) (and (= X21 Y21) (= X222 Y22)))))
% 0.16/0.48 (assert (forall ((Less (-> tptp.list_a tptp.list_a Bool)) (X tptp.list_a) (Xs tptp.list_list_a) (Y tptp.list_a) (Ys tptp.list_list_a)) (let ((_let_1 (@ tptp.lexordp_eq_list_a Less))) (= (@ (@ _let_1 (@ (@ tptp.cons_list_a X) Xs)) (@ (@ tptp.cons_list_a Y) Ys)) (or (@ (@ Less X) Y) (and (not (@ (@ Less Y) X)) (@ (@ _let_1 Xs) Ys)))))))
% 0.16/0.48 (assert (forall ((Less (-> tptp.a tptp.a Bool)) (X tptp.a) (Xs tptp.list_a) (Y tptp.a) (Ys tptp.list_a)) (let ((_let_1 (@ tptp.lexordp_eq_a Less))) (= (@ (@ _let_1 (@ (@ tptp.cons_a X) Xs)) (@ (@ tptp.cons_a Y) Ys)) (or (@ (@ Less X) Y) (and (not (@ (@ Less Y) X)) (@ (@ _let_1 Xs) Ys)))))))
% 0.16/0.48 (assert (forall ((Less (-> tptp.list_a tptp.list_a Bool)) (X tptp.list_a) (Xs tptp.list_list_a)) (not (@ (@ (@ tptp.lexordp_eq_list_a Less) (@ (@ tptp.cons_list_a X) Xs)) tptp.nil_list_a))))
% 0.16/0.48 (assert (forall ((Less (-> tptp.a tptp.a Bool)) (X tptp.a) (Xs tptp.list_a)) (not (@ (@ (@ tptp.lexordp_eq_a Less) (@ (@ tptp.cons_a X) Xs)) tptp.nil_a))))
% 0.16/0.48 (assert (forall ((X tptp.a) (Xs tptp.list_a) (Y tptp.a) (Ys tptp.list_a)) (let ((_let_1 (@ tptp.lexordp_eq_a tptp.less))) (= (@ (@ _let_1 (@ (@ tptp.cons_a X) Xs)) (@ (@ tptp.cons_a Y) Ys)) (or (@ (@ tptp.less X) Y) (and (not (@ (@ tptp.less Y) X)) (@ (@ _let_1 Xs) Ys)))))))
% 0.16/0.48 (assert (forall ((X tptp.a) (Xs tptp.list_a)) (not (@ (@ (@ tptp.lexordp_eq_a tptp.less) (@ (@ tptp.cons_a X) Xs)) tptp.nil_a))))
% 0.16/0.48 (assert (forall ((P (-> (-> tptp.list_a tptp.a) tptp.list_list_a tptp.list_a Bool)) (A0 (-> tptp.list_a tptp.a)) (A1 tptp.list_list_a) (A22 tptp.list_a)) (=> (forall ((F3 (-> tptp.list_a tptp.a)) (X_1 tptp.list_a)) (@ (@ (@ P F3) tptp.nil_list_a) X_1)) (=> (forall ((F3 (-> tptp.list_a tptp.a)) (A2 tptp.list_a) (As tptp.list_list_a) (Bs tptp.list_a)) (let ((_let_1 (@ P F3))) (=> (@ (@ _let_1 As) (@ (@ tptp.cons_a (@ F3 A2)) Bs)) (@ (@ _let_1 (@ (@ tptp.cons_list_a A2) As)) Bs)))) (@ (@ (@ P A0) A1) A22)))))
% 0.16/0.48 (assert (forall ((P (-> (-> tptp.a tptp.list_a) tptp.list_a tptp.list_list_a Bool)) (A0 (-> tptp.a tptp.list_a)) (A1 tptp.list_a) (A22 tptp.list_list_a)) (=> (forall ((F3 (-> tptp.a tptp.list_a)) (X_1 tptp.list_list_a)) (@ (@ (@ P F3) tptp.nil_a) X_1)) (=> (forall ((F3 (-> tptp.a tptp.list_a)) (A2 tptp.a) (As tptp.list_a) (Bs tptp.list_list_a)) (let ((_let_1 (@ P F3))) (=> (@ (@ _let_1 As) (@ (@ tptp.cons_list_a (@ F3 A2)) Bs)) (@ (@ _let_1 (@ (@ tptp.cons_a A2) As)) Bs)))) (@ (@ (@ P A0) A1) A22)))))
% 0.16/0.48 (assert (forall ((P (-> (-> tptp.list_a tptp.list_a) tptp.list_list_a tptp.list_list_a Bool)) (A0 (-> tptp.list_a tptp.list_a)) (A1 tptp.list_list_a) (A22 tptp.list_list_a)) (=> (forall ((F3 (-> tptp.list_a tptp.list_a)) (X_1 tptp.list_list_a)) (@ (@ (@ P F3) tptp.nil_list_a) X_1)) (=> (forall ((F3 (-> tptp.list_a tptp.list_a)) (A2 tptp.list_a) (As tptp.list_list_a) (Bs tptp.list_list_a)) (let ((_let_1 (@ P F3))) (=> (@ (@ _let_1 As) (@ (@ tptp.cons_list_a (@ F3 A2)) Bs)) (@ (@ _let_1 (@ (@ tptp.cons_list_a A2) As)) Bs)))) (@ (@ (@ P A0) A1) A22)))))
% 0.16/0.48 (assert (forall ((P (-> (-> tptp.a tptp.a) tptp.list_a tptp.list_a Bool)) (A0 (-> tptp.a tptp.a)) (A1 tptp.list_a) (A22 tptp.list_a)) (=> (forall ((F3 (-> tptp.a tptp.a)) (X_1 tptp.list_a)) (@ (@ (@ P F3) tptp.nil_a) X_1)) (=> (forall ((F3 (-> tptp.a tptp.a)) (A2 tptp.a) (As tptp.list_a) (Bs tptp.list_a)) (let ((_let_1 (@ P F3))) (=> (@ (@ _let_1 As) (@ (@ tptp.cons_a (@ F3 A2)) Bs)) (@ (@ _let_1 (@ (@ tptp.cons_a A2) As)) Bs)))) (@ (@ (@ P A0) A1) A22)))))
% 0.16/0.48 (assert (forall ((Xs tptp.list_list_a) (P (-> tptp.list_list_a Bool))) (=> (not (= Xs tptp.nil_list_a)) (=> (forall ((X2 tptp.list_a)) (@ P (@ (@ tptp.cons_list_a X2) tptp.nil_list_a))) (=> (forall ((X2 tptp.list_a) (Xs3 tptp.list_list_a)) (=> (not (= Xs3 tptp.nil_list_a)) (=> (@ P Xs3) (@ P (@ (@ tptp.cons_list_a X2) Xs3))))) (@ P Xs))))))
% 0.16/0.48 (assert (forall ((Xs tptp.list_a) (P (-> tptp.list_a Bool))) (=> (not (= Xs tptp.nil_a)) (=> (forall ((X2 tptp.a)) (@ P (@ (@ tptp.cons_a X2) tptp.nil_a))) (=> (forall ((X2 tptp.a) (Xs3 tptp.list_a)) (=> (not (= Xs3 tptp.nil_a)) (=> (@ P Xs3) (@ P (@ (@ tptp.cons_a X2) Xs3))))) (@ P Xs))))))
% 0.16/0.48 (assert (forall ((P (-> (-> tptp.list_a tptp.list_a Bool) tptp.list_list_a Bool)) (A0 (-> tptp.list_a tptp.list_a Bool)) (A1 tptp.list_list_a)) (=> (forall ((P2 (-> tptp.list_a tptp.list_a Bool))) (@ (@ P P2) tptp.nil_list_a)) (=> (forall ((P2 (-> tptp.list_a tptp.list_a Bool)) (X2 tptp.list_a)) (@ (@ P P2) (@ (@ tptp.cons_list_a X2) tptp.nil_list_a))) (=> (forall ((P2 (-> tptp.list_a tptp.list_a Bool)) (X2 tptp.list_a) (Y2 tptp.list_a) (Xs3 tptp.list_list_a)) (let ((_let_1 (@ (@ tptp.cons_list_a Y2) Xs3))) (let ((_let_2 (@ P P2))) (=> (@ _let_2 _let_1) (@ _let_2 (@ (@ tptp.cons_list_a X2) _let_1)))))) (@ (@ P A0) A1))))))
% 0.16/0.48 (assert (forall ((P (-> (-> tptp.a tptp.a Bool) tptp.list_a Bool)) (A0 (-> tptp.a tptp.a Bool)) (A1 tptp.list_a)) (=> (forall ((P2 (-> tptp.a tptp.a Bool))) (@ (@ P P2) tptp.nil_a)) (=> (forall ((P2 (-> tptp.a tptp.a Bool)) (X2 tptp.a)) (@ (@ P P2) (@ (@ tptp.cons_a X2) tptp.nil_a))) (=> (forall ((P2 (-> tptp.a tptp.a Bool)) (X2 tptp.a) (Y2 tptp.a) (Xs3 tptp.list_a)) (let ((_let_1 (@ (@ tptp.cons_a Y2) Xs3))) (let ((_let_2 (@ P P2))) (=> (@ _let_2 _let_1) (@ _let_2 (@ (@ tptp.cons_a X2) _let_1)))))) (@ (@ P A0) A1))))))
% 0.16/0.48 (assert (forall ((P (-> tptp.list_list_a Bool)) (A0 tptp.list_list_a)) (=> (@ P tptp.nil_list_a) (=> (forall ((X2 tptp.list_a)) (@ P (@ (@ tptp.cons_list_a X2) tptp.nil_list_a))) (=> (forall ((X2 tptp.list_a) (Y2 tptp.list_a) (Xs3 tptp.list_list_a)) (let ((_let_1 (@ (@ tptp.cons_list_a Y2) Xs3))) (let ((_let_2 (@ tptp.cons_list_a X2))) (let ((_let_3 (= X2 Y2))) (=> (=> _let_3 (@ P (@ _let_2 Xs3))) (=> (=> (not _let_3) (@ P _let_1)) (@ P (@ _let_2 _let_1)))))))) (@ P A0))))))
% 0.16/0.48 (assert (forall ((P (-> tptp.list_a Bool)) (A0 tptp.list_a)) (=> (@ P tptp.nil_a) (=> (forall ((X2 tptp.a)) (@ P (@ (@ tptp.cons_a X2) tptp.nil_a))) (=> (forall ((X2 tptp.a) (Y2 tptp.a) (Xs3 tptp.list_a)) (let ((_let_1 (@ (@ tptp.cons_a Y2) Xs3))) (let ((_let_2 (@ tptp.cons_a X2))) (let ((_let_3 (= X2 Y2))) (=> (=> _let_3 (@ P (@ _let_2 Xs3))) (=> (=> (not _let_3) (@ P _let_1)) (@ P (@ _let_2 _let_1)))))))) (@ P A0))))))
% 0.16/0.48 (assert (forall ((P (-> (-> tptp.list_a tptp.list_a Bool) tptp.list_list_a Bool)) (A0 (-> tptp.list_a tptp.list_a Bool)) (A1 tptp.list_list_a)) (=> (forall ((P2 (-> tptp.list_a tptp.list_a Bool))) (@ (@ P P2) tptp.nil_list_a)) (=> (forall ((P2 (-> tptp.list_a tptp.list_a Bool)) (X2 tptp.list_a) (Ys3 tptp.list_list_a)) (let ((_let_1 (@ P P2))) (=> (@ _let_1 Ys3) (@ _let_1 (@ (@ tptp.cons_list_a X2) Ys3))))) (@ (@ P A0) A1)))))
% 0.16/0.48 (assert (forall ((P (-> (-> tptp.a tptp.a Bool) tptp.list_a Bool)) (A0 (-> tptp.a tptp.a Bool)) (A1 tptp.list_a)) (=> (forall ((P2 (-> tptp.a tptp.a Bool))) (@ (@ P P2) tptp.nil_a)) (=> (forall ((P2 (-> tptp.a tptp.a Bool)) (X2 tptp.a) (Ys3 tptp.list_a)) (let ((_let_1 (@ P P2))) (=> (@ _let_1 Ys3) (@ _let_1 (@ (@ tptp.cons_a X2) Ys3))))) (@ (@ P A0) A1)))))
% 0.16/0.48 (assert (forall ((X tptp.list_list_a)) (=> (not (= X tptp.nil_list_a)) (=> (forall ((X2 tptp.list_a)) (not (= X (@ (@ tptp.cons_list_a X2) tptp.nil_list_a)))) (not (forall ((X2 tptp.list_a) (Y2 tptp.list_a) (Xs3 tptp.list_list_a)) (not (= X (@ (@ tptp.cons_list_a X2) (@ (@ tptp.cons_list_a Y2) Xs3))))))))))
% 0.16/0.48 (assert (forall ((X tptp.list_a)) (=> (not (= X tptp.nil_a)) (=> (forall ((X2 tptp.a)) (not (= X (@ (@ tptp.cons_a X2) tptp.nil_a)))) (not (forall ((X2 tptp.a) (Y2 tptp.a) (Xs3 tptp.list_a)) (not (= X (@ (@ tptp.cons_a X2) (@ (@ tptp.cons_a Y2) Xs3))))))))))
% 0.16/0.48 (assert (forall ((X tptp.list_list_list_a)) (=> (not (= X tptp.nil_list_list_a)) (=> (forall ((Xss tptp.list_list_list_a)) (not (= X (@ (@ tptp.cons_list_list_a tptp.nil_list_a) Xss)))) (not (forall ((X2 tptp.list_a) (Xs3 tptp.list_list_a) (Xss tptp.list_list_list_a)) (not (= X (@ (@ tptp.cons_list_list_a (@ (@ tptp.cons_list_a X2) Xs3)) Xss)))))))))
% 0.16/0.48 (assert (forall ((X tptp.list_list_a)) (=> (not (= X tptp.nil_list_a)) (=> (forall ((Xss tptp.list_list_a)) (not (= X (@ (@ tptp.cons_list_a tptp.nil_a) Xss)))) (not (forall ((X2 tptp.a) (Xs3 tptp.list_a) (Xss tptp.list_list_a)) (not (= X (@ (@ tptp.cons_list_a (@ (@ tptp.cons_a X2) Xs3)) Xss)))))))))
% 0.16/0.48 (assert (forall ((P (-> tptp.list_list_a tptp.list_list_a Bool)) (A0 tptp.list_list_a) (A1 tptp.list_list_a)) (=> (forall ((X_1 tptp.list_list_a)) (@ (@ P tptp.nil_list_a) X_1)) (=> (forall ((Xs3 tptp.list_list_a)) (@ (@ P Xs3) tptp.nil_list_a)) (=> (forall ((X2 tptp.list_a) (Xs3 tptp.list_list_a) (Y2 tptp.list_a) (Ys3 tptp.list_list_a)) (let ((_let_1 (@ (@ tptp.cons_list_a Y2) Ys3))) (let ((_let_2 (@ P (@ (@ tptp.cons_list_a X2) Xs3)))) (=> (@ (@ P Xs3) _let_1) (=> (@ _let_2 Ys3) (@ _let_2 _let_1)))))) (@ (@ P A0) A1))))))
% 0.16/0.48 (assert (forall ((P (-> tptp.list_a tptp.list_a Bool)) (A0 tptp.list_a) (A1 tptp.list_a)) (=> (forall ((X_1 tptp.list_a)) (@ (@ P tptp.nil_a) X_1)) (=> (forall ((Xs3 tptp.list_a)) (@ (@ P Xs3) tptp.nil_a)) (=> (forall ((X2 tptp.a) (Xs3 tptp.list_a) (Y2 tptp.a) (Ys3 tptp.list_a)) (let ((_let_1 (@ (@ tptp.cons_a Y2) Ys3))) (let ((_let_2 (@ P (@ (@ tptp.cons_a X2) Xs3)))) (=> (@ (@ P Xs3) _let_1) (=> (@ _let_2 Ys3) (@ _let_2 _let_1)))))) (@ (@ P A0) A1))))))
% 0.16/0.48 (assert (forall ((P (-> tptp.list_list_a Bool)) (Xs tptp.list_list_a)) (=> (@ P tptp.nil_list_a) (=> (forall ((X2 tptp.list_a)) (@ P (@ (@ tptp.cons_list_a X2) tptp.nil_list_a))) (=> (forall ((X2 tptp.list_a) (Y2 tptp.list_a) (Zs tptp.list_list_a)) (let ((_let_1 (@ (@ tptp.cons_list_a Y2) Zs))) (=> (@ P Zs) (=> (@ P _let_1) (@ P (@ (@ tptp.cons_list_a X2) _let_1)))))) (@ P Xs))))))
% 0.16/0.48 (assert (forall ((P (-> tptp.list_a Bool)) (Xs tptp.list_a)) (=> (@ P tptp.nil_a) (=> (forall ((X2 tptp.a)) (@ P (@ (@ tptp.cons_a X2) tptp.nil_a))) (=> (forall ((X2 tptp.a) (Y2 tptp.a) (Zs tptp.list_a)) (let ((_let_1 (@ (@ tptp.cons_a Y2) Zs))) (=> (@ P Zs) (=> (@ P _let_1) (@ P (@ (@ tptp.cons_a X2) _let_1)))))) (@ P Xs))))))
% 0.16/0.48 (assert (forall ((P (-> tptp.list_list_a tptp.list_list_a Bool)) (A0 tptp.list_list_a) (A1 tptp.list_list_a)) (=> (forall ((X_1 tptp.list_list_a)) (@ (@ P tptp.nil_list_a) X_1)) (=> (forall ((X2 tptp.list_a) (Xs3 tptp.list_list_a) (Ys3 tptp.list_list_a)) (=> (@ (@ P Ys3) Xs3) (@ (@ P (@ (@ tptp.cons_list_a X2) Xs3)) Ys3))) (@ (@ P A0) A1)))))
% 0.16/0.48 (assert (forall ((P (-> tptp.list_a tptp.list_a Bool)) (A0 tptp.list_a) (A1 tptp.list_a)) (=> (forall ((X_1 tptp.list_a)) (@ (@ P tptp.nil_a) X_1)) (=> (forall ((X2 tptp.a) (Xs3 tptp.list_a) (Ys3 tptp.list_a)) (=> (@ (@ P Ys3) Xs3) (@ (@ P (@ (@ tptp.cons_a X2) Xs3)) Ys3))) (@ (@ P A0) A1)))))
% 0.16/0.48 (assert (forall ((P (-> tptp.list_a tptp.list_list_a Bool)) (Xs tptp.list_a) (Ys tptp.list_list_a)) (=> (@ (@ P tptp.nil_a) tptp.nil_list_a) (=> (forall ((X2 tptp.a) (Xs3 tptp.list_a)) (@ (@ P (@ (@ tptp.cons_a X2) Xs3)) tptp.nil_list_a)) (=> (forall ((Y2 tptp.list_a) (Ys3 tptp.list_list_a)) (@ (@ P tptp.nil_a) (@ (@ tptp.cons_list_a Y2) Ys3))) (=> (forall ((X2 tptp.a) (Xs3 tptp.list_a) (Y2 tptp.list_a) (Ys3 tptp.list_list_a)) (=> (@ (@ P Xs3) Ys3) (@ (@ P (@ (@ tptp.cons_a X2) Xs3)) (@ (@ tptp.cons_list_a Y2) Ys3)))) (@ (@ P Xs) Ys)))))))
% 0.16/0.48 (assert (forall ((P (-> tptp.list_list_a tptp.list_a Bool)) (Xs tptp.list_list_a) (Ys tptp.list_a)) (=> (@ (@ P tptp.nil_list_a) tptp.nil_a) (=> (forall ((X2 tptp.list_a) (Xs3 tptp.list_list_a)) (@ (@ P (@ (@ tptp.cons_list_a X2) Xs3)) tptp.nil_a)) (=> (forall ((Y2 tptp.a) (Ys3 tptp.list_a)) (@ (@ P tptp.nil_list_a) (@ (@ tptp.cons_a Y2) Ys3))) (=> (forall ((X2 tptp.list_a) (Xs3 tptp.list_list_a) (Y2 tptp.a) (Ys3 tptp.list_a)) (=> (@ (@ P Xs3) Ys3) (@ (@ P (@ (@ tptp.cons_list_a X2) Xs3)) (@ (@ tptp.cons_a Y2) Ys3)))) (@ (@ P Xs) Ys)))))))
% 0.16/0.48 (assert (forall ((P (-> tptp.list_list_a tptp.list_list_a Bool)) (Xs tptp.list_list_a) (Ys tptp.list_list_a)) (=> (@ (@ P tptp.nil_list_a) tptp.nil_list_a) (=> (forall ((X2 tptp.list_a) (Xs3 tptp.list_list_a)) (@ (@ P (@ (@ tptp.cons_list_a X2) Xs3)) tptp.nil_list_a)) (=> (forall ((Y2 tptp.list_a) (Ys3 tptp.list_list_a)) (@ (@ P tptp.nil_list_a) (@ (@ tptp.cons_list_a Y2) Ys3))) (=> (forall ((X2 tptp.list_a) (Xs3 tptp.list_list_a) (Y2 tptp.list_a) (Ys3 tptp.list_list_a)) (=> (@ (@ P Xs3) Ys3) (@ (@ P (@ (@ tptp.cons_list_a X2) Xs3)) (@ (@ tptp.cons_list_a Y2) Ys3)))) (@ (@ P Xs) Ys)))))))
% 0.16/0.48 (assert (forall ((P (-> tptp.list_a tptp.list_a Bool)) (Xs tptp.list_a) (Ys tptp.list_a)) (=> (@ (@ P tptp.nil_a) tptp.nil_a) (=> (forall ((X2 tptp.a) (Xs3 tptp.list_a)) (@ (@ P (@ (@ tptp.cons_a X2) Xs3)) tptp.nil_a)) (=> (forall ((Y2 tptp.a) (Ys3 tptp.list_a)) (@ (@ P tptp.nil_a) (@ (@ tptp.cons_a Y2) Ys3))) (=> (forall ((X2 tptp.a) (Xs3 tptp.list_a) (Y2 tptp.a) (Ys3 tptp.list_a)) (=> (@ (@ P Xs3) Ys3) (@ (@ P (@ (@ tptp.cons_a X2) Xs3)) (@ (@ tptp.cons_a Y2) Ys3)))) (@ (@ P Xs) Ys)))))))
% 0.16/0.48 (assert (forall ((Xs tptp.list_list_a)) (= (not (= Xs tptp.nil_list_a)) (exists ((Y3 tptp.list_a) (Ys2 tptp.list_list_a)) (= Xs (@ (@ tptp.cons_list_a Y3) Ys2))))))
% 0.16/0.48 (assert (forall ((Xs tptp.list_a)) (= (not (= Xs tptp.nil_a)) (exists ((Y3 tptp.a) (Ys2 tptp.list_a)) (= Xs (@ (@ tptp.cons_a Y3) Ys2))))))
% 0.16/0.48 (assert (forall ((P (-> tptp.list_list_a Bool)) (List tptp.list_list_a)) (=> (@ P tptp.nil_list_a) (=> (forall ((X12 tptp.list_a) (X23 tptp.list_list_a)) (=> (@ P X23) (@ P (@ (@ tptp.cons_list_a X12) X23)))) (@ P List)))))
% 0.16/0.48 (assert (forall ((P (-> tptp.list_a Bool)) (List tptp.list_a)) (=> (@ P tptp.nil_a) (=> (forall ((X12 tptp.a) (X23 tptp.list_a)) (=> (@ P X23) (@ P (@ (@ tptp.cons_a X12) X23)))) (@ P List)))))
% 0.16/0.48 (assert (forall ((Y tptp.list_list_a)) (=> (not (= Y tptp.nil_list_a)) (not (forall ((X212 tptp.list_a) (X223 tptp.list_list_a)) (not (= Y (@ (@ tptp.cons_list_a X212) X223))))))))
% 0.16/0.48 (assert (forall ((Y tptp.list_a)) (=> (not (= Y tptp.nil_a)) (not (forall ((X212 tptp.a) (X223 tptp.list_a)) (not (= Y (@ (@ tptp.cons_a X212) X223))))))))
% 0.16/0.48 (assert (forall ((List tptp.list_list_a) (X21 tptp.list_a) (X222 tptp.list_list_a)) (=> (= List (@ (@ tptp.cons_list_a X21) X222)) (not (= List tptp.nil_list_a)))))
% 0.16/0.48 (assert (forall ((List tptp.list_a) (X21 tptp.a) (X222 tptp.list_a)) (=> (= List (@ (@ tptp.cons_a X21) X222)) (not (= List tptp.nil_a)))))
% 0.16/0.48 (assert (forall ((X21 tptp.list_a) (X222 tptp.list_list_a)) (not (= tptp.nil_list_a (@ (@ tptp.cons_list_a X21) X222)))))
% 0.16/0.48 (assert (forall ((X21 tptp.a) (X222 tptp.list_a)) (not (= tptp.nil_a (@ (@ tptp.cons_a X21) X222)))))
% 0.16/0.48 (assert (forall ((X tptp.list_a) (Xs tptp.list_list_a)) (not (= (@ (@ tptp.cons_list_a X) Xs) Xs))))
% 0.16/0.48 (assert (forall ((X tptp.a) (Xs tptp.list_a)) (not (= (@ (@ tptp.cons_a X) Xs) Xs))))
% 0.16/0.48 (assert (forall ((Less (-> tptp.list_a tptp.list_a Bool)) (X tptp.list_a) (Y tptp.list_a) (Xs tptp.list_list_a) (Ys tptp.list_list_a)) (let ((_let_1 (@ tptp.lexordp_eq_list_a Less))) (=> (not (@ (@ Less X) Y)) (=> (not (@ (@ Less Y) X)) (=> (@ (@ _let_1 Xs) Ys) (@ (@ _let_1 (@ (@ tptp.cons_list_a X) Xs)) (@ (@ tptp.cons_list_a Y) Ys))))))))
% 0.16/0.48 (assert (forall ((Less (-> tptp.a tptp.a Bool)) (X tptp.a) (Y tptp.a) (Xs tptp.list_a) (Ys tptp.list_a)) (let ((_let_1 (@ tptp.lexordp_eq_a Less))) (=> (not (@ (@ Less X) Y)) (=> (not (@ (@ Less Y) X)) (=> (@ (@ _let_1 Xs) Ys) (@ (@ _let_1 (@ (@ tptp.cons_a X) Xs)) (@ (@ tptp.cons_a Y) Ys))))))))
% 0.16/0.48 (assert (forall ((Less (-> tptp.list_a tptp.list_a Bool)) (X tptp.list_a) (Y tptp.list_a) (Xs tptp.list_list_a) (Ys tptp.list_list_a)) (=> (@ (@ Less X) Y) (@ (@ (@ tptp.lexordp_eq_list_a Less) (@ (@ tptp.cons_list_a X) Xs)) (@ (@ tptp.cons_list_a Y) Ys)))))
% 0.16/0.48 (assert (forall ((Less (-> tptp.a tptp.a Bool)) (X tptp.a) (Y tptp.a) (Xs tptp.list_a) (Ys tptp.list_a)) (=> (@ (@ Less X) Y) (@ (@ (@ tptp.lexordp_eq_a Less) (@ (@ tptp.cons_a X) Xs)) (@ (@ tptp.cons_a Y) Ys)))))
% 0.16/0.48 (assert (forall ((Less (-> tptp.list_a tptp.list_a Bool)) (X1 tptp.list_list_a) (X22 tptp.list_list_a) (P (-> tptp.list_list_a tptp.list_list_a Bool))) (=> (@ (@ (@ tptp.lexordp_eq_list_a Less) X1) X22) (=> (forall ((X_1 tptp.list_list_a)) (@ (@ P tptp.nil_list_a) X_1)) (=> (forall ((X2 tptp.list_a) (Y2 tptp.list_a) (Xs3 tptp.list_list_a) (Ys3 tptp.list_list_a)) (=> (@ (@ Less X2) Y2) (@ (@ P (@ (@ tptp.cons_list_a X2) Xs3)) (@ (@ tptp.cons_list_a Y2) Ys3)))) (=> (forall ((X2 tptp.list_a) (Y2 tptp.list_a) (Xs3 tptp.list_list_a) (Ys3 tptp.list_list_a)) (=> (not (@ (@ Less X2) Y2)) (=> (not (@ (@ Less Y2) X2)) (=> (@ (@ (@ tptp.lexordp_eq_list_a Less) Xs3) Ys3) (=> (@ (@ P Xs3) Ys3) (@ (@ P (@ (@ tptp.cons_list_a X2) Xs3)) (@ (@ tptp.cons_list_a Y2) Ys3))))))) (@ (@ P X1) X22)))))))
% 0.16/0.48 (assert (forall ((Less (-> tptp.a tptp.a Bool)) (X1 tptp.list_a) (X22 tptp.list_a) (P (-> tptp.list_a tptp.list_a Bool))) (=> (@ (@ (@ tptp.lexordp_eq_a Less) X1) X22) (=> (forall ((X_1 tptp.list_a)) (@ (@ P tptp.nil_a) X_1)) (=> (forall ((X2 tptp.a) (Y2 tptp.a) (Xs3 tptp.list_a) (Ys3 tptp.list_a)) (=> (@ (@ Less X2) Y2) (@ (@ P (@ (@ tptp.cons_a X2) Xs3)) (@ (@ tptp.cons_a Y2) Ys3)))) (=> (forall ((X2 tptp.a) (Y2 tptp.a) (Xs3 tptp.list_a) (Ys3 tptp.list_a)) (=> (not (@ (@ Less X2) Y2)) (=> (not (@ (@ Less Y2) X2)) (=> (@ (@ (@ tptp.lexordp_eq_a Less) Xs3) Ys3) (=> (@ (@ P Xs3) Ys3) (@ (@ P (@ (@ tptp.cons_a X2) Xs3)) (@ (@ tptp.cons_a Y2) Ys3))))))) (@ (@ P X1) X22)))))))
% 0.16/0.48 (assert (= tptp.lexordp_eq_list_a (lambda ((Less2 (-> tptp.list_a tptp.list_a Bool)) (A12 tptp.list_list_a) (A23 tptp.list_list_a)) (or (exists ((Ys2 tptp.list_list_a)) (and (= A12 tptp.nil_list_a) (= A23 Ys2))) (exists ((X3 tptp.list_a) (Y3 tptp.list_a) (Xs2 tptp.list_list_a) (Ys2 tptp.list_list_a)) (and (= A12 (@ (@ tptp.cons_list_a X3) Xs2)) (= A23 (@ (@ tptp.cons_list_a Y3) Ys2)) (@ (@ Less2 X3) Y3))) (exists ((X3 tptp.list_a) (Y3 tptp.list_a) (Xs2 tptp.list_list_a) (Ys2 tptp.list_list_a)) (and (= A12 (@ (@ tptp.cons_list_a X3) Xs2)) (= A23 (@ (@ tptp.cons_list_a Y3) Ys2)) (not (@ (@ Less2 X3) Y3)) (not (@ (@ Less2 Y3) X3)) (@ (@ (@ tptp.lexordp_eq_list_a Less2) Xs2) Ys2)))))))
% 0.16/0.48 (assert (= tptp.lexordp_eq_a (lambda ((Less2 (-> tptp.a tptp.a Bool)) (A12 tptp.list_a) (A23 tptp.list_a)) (or (exists ((Ys2 tptp.list_a)) (and (= A12 tptp.nil_a) (= A23 Ys2))) (exists ((X3 tptp.a) (Y3 tptp.a) (Xs2 tptp.list_a) (Ys2 tptp.list_a)) (and (= A12 (@ (@ tptp.cons_a X3) Xs2)) (= A23 (@ (@ tptp.cons_a Y3) Ys2)) (@ (@ Less2 X3) Y3))) (exists ((X3 tptp.a) (Y3 tptp.a) (Xs2 tptp.list_a) (Ys2 tptp.list_a)) (and (= A12 (@ (@ tptp.cons_a X3) Xs2)) (= A23 (@ (@ tptp.cons_a Y3) Ys2)) (not (@ (@ Less2 X3) Y3)) (not (@ (@ Less2 Y3) X3)) (@ (@ (@ tptp.lexordp_eq_a Less2) Xs2) Ys2)))))))
% 0.16/0.48 (assert (forall ((Less (-> tptp.list_a tptp.list_a Bool)) (A1 tptp.list_list_a) (A22 tptp.list_list_a)) (=> (@ (@ (@ tptp.lexordp_eq_list_a Less) A1) A22) (=> (not (= A1 tptp.nil_list_a)) (=> (forall ((X2 tptp.list_a)) (=> (exists ((Xs3 tptp.list_list_a)) (= A1 (@ (@ tptp.cons_list_a X2) Xs3))) (forall ((Y2 tptp.list_a)) (=> (exists ((Ys3 tptp.list_list_a)) (= A22 (@ (@ tptp.cons_list_a Y2) Ys3))) (not (@ (@ Less X2) Y2)))))) (not (forall ((X2 tptp.list_a) (Y2 tptp.list_a) (Xs3 tptp.list_list_a)) (=> (= A1 (@ (@ tptp.cons_list_a X2) Xs3)) (forall ((Ys3 tptp.list_list_a)) (=> (= A22 (@ (@ tptp.cons_list_a Y2) Ys3)) (=> (not (@ (@ Less X2) Y2)) (=> (not (@ (@ Less Y2) X2)) (not (@ (@ (@ tptp.lexordp_eq_list_a Less) Xs3) Ys3))))))))))))))
% 0.16/0.48 (assert (forall ((Less (-> tptp.a tptp.a Bool)) (A1 tptp.list_a) (A22 tptp.list_a)) (=> (@ (@ (@ tptp.lexordp_eq_a Less) A1) A22) (=> (not (= A1 tptp.nil_a)) (=> (forall ((X2 tptp.a)) (=> (exists ((Xs3 tptp.list_a)) (= A1 (@ (@ tptp.cons_a X2) Xs3))) (forall ((Y2 tptp.a)) (=> (exists ((Ys3 tptp.list_a)) (= A22 (@ (@ tptp.cons_a Y2) Ys3))) (not (@ (@ Less X2) Y2)))))) (not (forall ((X2 tptp.a) (Y2 tptp.a) (Xs3 tptp.list_a)) (=> (= A1 (@ (@ tptp.cons_a X2) Xs3)) (forall ((Ys3 tptp.list_a)) (=> (= A22 (@ (@ tptp.cons_a Y2) Ys3)) (=> (not (@ (@ Less X2) Y2)) (=> (not (@ (@ Less Y2) X2)) (not (@ (@ (@ tptp.lexordp_eq_a Less) Xs3) Ys3))))))))))))))
% 0.16/0.48 (assert (= tptp.lexordp_eq_a tptp.lexordp_eq_a))
% 0.16/0.48 (assert (forall ((Less (-> tptp.a tptp.a Bool)) (Xs tptp.list_a)) (@ (@ (@ tptp.lexordp_eq_a Less) Xs) Xs)))
% 0.16/0.48 (assert (forall ((Less (-> tptp.list_a tptp.list_a Bool)) (Ys tptp.list_list_a)) (@ (@ (@ tptp.lexordp_eq_list_a Less) tptp.nil_list_a) Ys)))
% 0.16/0.48 (assert (forall ((Less (-> tptp.a tptp.a Bool)) (Ys tptp.list_a)) (@ (@ (@ tptp.lexordp_eq_a Less) tptp.nil_a) Ys)))
% 0.16/0.48 (assert (forall ((Y tptp.a) (Ys tptp.list_a)) (@ (@ (@ tptp.lexordp_a tptp.less) tptp.nil_a) (@ (@ tptp.cons_a Y) Ys))))
% 0.16/0.48 (assert (forall ((A1 tptp.list_a) (A22 tptp.list_a)) (=> (@ (@ (@ tptp.lexordp_a tptp.less) A1) A22) (=> (=> (= A1 tptp.nil_a) (forall ((Y2 tptp.a) (Ys3 tptp.list_a)) (not (= A22 (@ (@ tptp.cons_a Y2) Ys3))))) (=> (forall ((X2 tptp.a)) (=> (exists ((Xs3 tptp.list_a)) (= A1 (@ (@ tptp.cons_a X2) Xs3))) (forall ((Y2 tptp.a)) (=> (exists ((Ys3 tptp.list_a)) (= A22 (@ (@ tptp.cons_a Y2) Ys3))) (not (@ (@ tptp.less X2) Y2)))))) (not (forall ((X2 tptp.a) (Y2 tptp.a) (Xs3 tptp.list_a)) (=> (= A1 (@ (@ tptp.cons_a X2) Xs3)) (forall ((Ys3 tptp.list_a)) (=> (= A22 (@ (@ tptp.cons_a Y2) Ys3)) (=> (not (@ (@ tptp.less X2) Y2)) (=> (not (@ (@ tptp.less Y2) X2)) (not (@ (@ (@ tptp.lexordp_a tptp.less) Xs3) Ys3))))))))))))))
% 0.16/0.48 (assert (forall ((X1 tptp.list_a) (X22 tptp.list_a) (P (-> tptp.list_a tptp.list_a Bool))) (=> (@ (@ (@ tptp.lexordp_a tptp.less) X1) X22) (=> (forall ((Y2 tptp.a) (Ys3 tptp.list_a)) (@ (@ P tptp.nil_a) (@ (@ tptp.cons_a Y2) Ys3))) (=> (forall ((X2 tptp.a) (Y2 tptp.a) (Xs3 tptp.list_a) (Ys3 tptp.list_a)) (=> (@ (@ tptp.less X2) Y2) (@ (@ P (@ (@ tptp.cons_a X2) Xs3)) (@ (@ tptp.cons_a Y2) Ys3)))) (=> (forall ((X2 tptp.a) (Y2 tptp.a) (Xs3 tptp.list_a) (Ys3 tptp.list_a)) (=> (not (@ (@ tptp.less X2) Y2)) (=> (not (@ (@ tptp.less Y2) X2)) (=> (@ (@ (@ tptp.lexordp_a tptp.less) Xs3) Ys3) (=> (@ (@ P Xs3) Ys3) (@ (@ P (@ (@ tptp.cons_a X2) Xs3)) (@ (@ tptp.cons_a Y2) Ys3))))))) (@ (@ P X1) X22)))))))
% 0.16/0.48 (assert (forall ((A1 tptp.list_a) (A22 tptp.list_a)) (= (@ (@ (@ tptp.lexordp_a tptp.less) A1) A22) (or (exists ((Y3 tptp.a) (Ys2 tptp.list_a)) (and (= A1 tptp.nil_a) (= A22 (@ (@ tptp.cons_a Y3) Ys2)))) (exists ((X3 tptp.a) (Y3 tptp.a) (Xs2 tptp.list_a) (Ys2 tptp.list_a)) (and (= A1 (@ (@ tptp.cons_a X3) Xs2)) (= A22 (@ (@ tptp.cons_a Y3) Ys2)) (@ (@ tptp.less X3) Y3))) (exists ((X3 tptp.a) (Y3 tptp.a) (Xs2 tptp.list_a) (Ys2 tptp.list_a)) (and (= A1 (@ (@ tptp.cons_a X3) Xs2)) (= A22 (@ (@ tptp.cons_a Y3) Ys2)) (not (@ (@ tptp.less X3) Y3)) (not (@ (@ tptp.less Y3) X3)) (@ (@ (@ tptp.lexordp_a tptp.less) Xs2) Ys2)))))))
% 0.16/0.48 (assert (forall ((Xs tptp.list_a) (Ys tptp.list_a)) (let ((_let_1 (@ tptp.lexordp_a tptp.less))) (=> (@ (@ _let_1 Xs) Ys) (not (@ (@ _let_1 Ys) Xs))))))
% 0.16/0.48 (assert (forall ((Xs tptp.list_a)) (=> (forall ((X2 tptp.a)) (not (@ (@ tptp.less X2) X2))) (not (@ (@ (@ tptp.lexordp_a tptp.less) Xs) Xs)))))
% 0.16/0.48 (assert (forall ((Xs tptp.list_a)) (not (@ (@ (@ tptp.lexordp_a tptp.less) Xs) Xs))))
% 0.16/0.48 (assert (forall ((X tptp.a) (Y tptp.a) (Xs tptp.list_a) (Ys tptp.list_a)) (let ((_let_1 (@ tptp.lexordp_a tptp.less))) (=> (not (@ (@ tptp.less X) Y)) (=> (not (@ (@ tptp.less Y) X)) (=> (@ (@ _let_1 Xs) Ys) (@ (@ _let_1 (@ (@ tptp.cons_a X) Xs)) (@ (@ tptp.cons_a Y) Ys))))))))
% 0.16/0.48 (assert (forall ((X tptp.a) (Y tptp.a) (Xs tptp.list_a) (Ys tptp.list_a)) (=> (@ (@ tptp.less X) Y) (@ (@ (@ tptp.lexordp_a tptp.less) (@ (@ tptp.cons_a X) Xs)) (@ (@ tptp.cons_a Y) Ys)))))
% 0.16/0.48 (assert (forall ((Xs tptp.list_a) (Ys tptp.list_a)) (=> (@ (@ (@ tptp.lexordp_a tptp.less) Xs) Ys) (@ (@ (@ tptp.lexordp_eq_a tptp.less) Xs) Ys))))
% 0.16/0.48 (assert (forall ((Less (-> tptp.list_a tptp.list_a Bool)) (X tptp.list_a) (Xs tptp.list_list_a) (Y tptp.list_a) (Ys tptp.list_list_a)) (let ((_let_1 (@ tptp.lexordp_list_a Less))) (= (@ (@ _let_1 (@ (@ tptp.cons_list_a X) Xs)) (@ (@ tptp.cons_list_a Y) Ys)) (or (@ (@ Less X) Y) (and (not (@ (@ Less Y) X)) (@ (@ _let_1 Xs) Ys)))))))
% 0.16/0.48 (assert (forall ((Less (-> tptp.a tptp.a Bool)) (X tptp.a) (Xs tptp.list_a) (Y tptp.a) (Ys tptp.list_a)) (let ((_let_1 (@ tptp.lexordp_a Less))) (= (@ (@ _let_1 (@ (@ tptp.cons_a X) Xs)) (@ (@ tptp.cons_a Y) Ys)) (or (@ (@ Less X) Y) (and (not (@ (@ Less Y) X)) (@ (@ _let_1 Xs) Ys)))))))
% 0.16/0.48 (assert (forall ((Less (-> tptp.list_a tptp.list_a Bool)) (Xs tptp.list_list_a)) (not (@ (@ (@ tptp.lexordp_list_a Less) Xs) tptp.nil_list_a))))
% 0.16/0.48 (assert (forall ((Less (-> tptp.a tptp.a Bool)) (Xs tptp.list_a)) (not (@ (@ (@ tptp.lexordp_a Less) Xs) tptp.nil_a))))
% 0.16/0.48 (assert (forall ((Less (-> tptp.list_a tptp.list_a Bool)) (Ys tptp.list_list_a)) (= (@ (@ (@ tptp.lexordp_list_a Less) tptp.nil_list_a) Ys) (not (= Ys tptp.nil_list_a)))))
% 0.16/0.48 (assert (forall ((Less (-> tptp.a tptp.a Bool)) (Ys tptp.list_a)) (= (@ (@ (@ tptp.lexordp_a Less) tptp.nil_a) Ys) (not (= Ys tptp.nil_a)))))
% 0.16/0.48 (assert (forall ((X tptp.a) (Xs tptp.list_a) (Y tptp.a) (Ys tptp.list_a)) (let ((_let_1 (@ tptp.lexordp_a tptp.less))) (= (@ (@ _let_1 (@ (@ tptp.cons_a X) Xs)) (@ (@ tptp.cons_a Y) Ys)) (or (@ (@ tptp.less X) Y) (and (not (@ (@ tptp.less Y) X)) (@ (@ _let_1 Xs) Ys)))))))
% 0.16/0.48 (assert (forall ((Ys tptp.list_a)) (= (@ (@ (@ tptp.lexordp_a tptp.less) tptp.nil_a) Ys) (not (= Ys tptp.nil_a)))))
% 0.16/0.48 (assert (forall ((Xs tptp.list_a)) (not (@ (@ (@ tptp.lexordp_a tptp.less) Xs) tptp.nil_a))))
% 0.16/0.48 (assert (= tptp.lexordp_a tptp.lexordp_a))
% 0.16/0.48 (assert (forall ((Less (-> tptp.a tptp.a Bool)) (Xs tptp.list_a)) (=> (forall ((X2 tptp.a)) (not (@ (@ Less X2) X2))) (not (@ (@ (@ tptp.lexordp_a Less) Xs) Xs)))))
% 0.16/0.48 (assert (forall ((Less (-> tptp.list_a tptp.list_a Bool)) (X tptp.list_a) (Y tptp.list_a) (Xs tptp.list_list_a) (Ys tptp.list_list_a)) (let ((_let_1 (@ tptp.lexordp_list_a Less))) (=> (not (@ (@ Less X) Y)) (=> (not (@ (@ Less Y) X)) (=> (@ (@ _let_1 Xs) Ys) (@ (@ _let_1 (@ (@ tptp.cons_list_a X) Xs)) (@ (@ tptp.cons_list_a Y) Ys))))))))
% 0.16/0.48 (assert (forall ((Less (-> tptp.a tptp.a Bool)) (X tptp.a) (Y tptp.a) (Xs tptp.list_a) (Ys tptp.list_a)) (let ((_let_1 (@ tptp.lexordp_a Less))) (=> (not (@ (@ Less X) Y)) (=> (not (@ (@ Less Y) X)) (=> (@ (@ _let_1 Xs) Ys) (@ (@ _let_1 (@ (@ tptp.cons_a X) Xs)) (@ (@ tptp.cons_a Y) Ys))))))))
% 0.16/0.48 (assert (forall ((Less (-> tptp.list_a tptp.list_a Bool)) (X tptp.list_a) (Y tptp.list_a) (Xs tptp.list_list_a) (Ys tptp.list_list_a)) (=> (@ (@ Less X) Y) (@ (@ (@ tptp.lexordp_list_a Less) (@ (@ tptp.cons_list_a X) Xs)) (@ (@ tptp.cons_list_a Y) Ys)))))
% 0.16/0.48 (assert (forall ((Less (-> tptp.a tptp.a Bool)) (X tptp.a) (Y tptp.a) (Xs tptp.list_a) (Ys tptp.list_a)) (=> (@ (@ Less X) Y) (@ (@ (@ tptp.lexordp_a Less) (@ (@ tptp.cons_a X) Xs)) (@ (@ tptp.cons_a Y) Ys)))))
% 0.16/0.48 (assert (forall ((Less (-> tptp.a tptp.a Bool)) (Xs tptp.list_a) (Ys tptp.list_a)) (=> (@ (@ (@ tptp.lexordp_a Less) Xs) Ys) (@ (@ (@ tptp.lexordp_eq_a Less) Xs) Ys))))
% 0.16/0.48 (assert (forall ((Less (-> tptp.list_a tptp.list_a Bool)) (Y tptp.list_a) (Ys tptp.list_list_a)) (@ (@ (@ tptp.lexordp_list_a Less) tptp.nil_list_a) (@ (@ tptp.cons_list_a Y) Ys))))
% 0.16/0.48 (assert (forall ((Less (-> tptp.a tptp.a Bool)) (Y tptp.a) (Ys tptp.list_a)) (@ (@ (@ tptp.lexordp_a Less) tptp.nil_a) (@ (@ tptp.cons_a Y) Ys))))
% 0.16/0.48 (assert (forall ((Less (-> tptp.list_a tptp.list_a Bool)) (A1 tptp.list_list_a) (A22 tptp.list_list_a)) (=> (@ (@ (@ tptp.lexordp_list_a Less) A1) A22) (=> (=> (= A1 tptp.nil_list_a) (forall ((Y2 tptp.list_a) (Ys3 tptp.list_list_a)) (not (= A22 (@ (@ tptp.cons_list_a Y2) Ys3))))) (=> (forall ((X2 tptp.list_a)) (=> (exists ((Xs3 tptp.list_list_a)) (= A1 (@ (@ tptp.cons_list_a X2) Xs3))) (forall ((Y2 tptp.list_a)) (=> (exists ((Ys3 tptp.list_list_a)) (= A22 (@ (@ tptp.cons_list_a Y2) Ys3))) (not (@ (@ Less X2) Y2)))))) (not (forall ((X2 tptp.list_a) (Y2 tptp.list_a) (Xs3 tptp.list_list_a)) (=> (= A1 (@ (@ tptp.cons_list_a X2) Xs3)) (forall ((Ys3 tptp.list_list_a)) (=> (= A22 (@ (@ tptp.cons_list_a Y2) Ys3)) (=> (not (@ (@ Less X2) Y2)) (=> (not (@ (@ Less Y2) X2)) (not (@ (@ (@ tptp.lexordp_list_a Less) Xs3) Ys3))))))))))))))
% 0.16/0.48 (assert (forall ((Less (-> tptp.a tptp.a Bool)) (A1 tptp.list_a) (A22 tptp.list_a)) (=> (@ (@ (@ tptp.lexordp_a Less) A1) A22) (=> (=> (= A1 tptp.nil_a) (forall ((Y2 tptp.a) (Ys3 tptp.list_a)) (not (= A22 (@ (@ tptp.cons_a Y2) Ys3))))) (=> (forall ((X2 tptp.a)) (=> (exists ((Xs3 tptp.list_a)) (= A1 (@ (@ tptp.cons_a X2) Xs3))) (forall ((Y2 tptp.a)) (=> (exists ((Ys3 tptp.list_a)) (= A22 (@ (@ tptp.cons_a Y2) Ys3))) (not (@ (@ Less X2) Y2)))))) (not (forall ((X2 tptp.a) (Y2 tptp.a) (Xs3 tptp.list_a)) (=> (= A1 (@ (@ tptp.cons_a X2) Xs3)) (forall ((Ys3 tptp.list_a)) (=> (= A22 (@ (@ tptp.cons_a Y2) Ys3)) (=> (not (@ (@ Less X2) Y2)) (=> (not (@ (@ Less Y2) X2)) (not (@ (@ (@ tptp.lexordp_a Less) Xs3) Ys3))))))))))))))
% 0.16/0.48 (assert (= tptp.lexordp_list_a (lambda ((Less2 (-> tptp.list_a tptp.list_a Bool)) (A12 tptp.list_list_a) (A23 tptp.list_list_a)) (or (exists ((Y3 tptp.list_a) (Ys2 tptp.list_list_a)) (and (= A12 tptp.nil_list_a) (= A23 (@ (@ tptp.cons_list_a Y3) Ys2)))) (exists ((X3 tptp.list_a) (Y3 tptp.list_a) (Xs2 tptp.list_list_a) (Ys2 tptp.list_list_a)) (and (= A12 (@ (@ tptp.cons_list_a X3) Xs2)) (= A23 (@ (@ tptp.cons_list_a Y3) Ys2)) (@ (@ Less2 X3) Y3))) (exists ((X3 tptp.list_a) (Y3 tptp.list_a) (Xs2 tptp.list_list_a) (Ys2 tptp.list_list_a)) (and (= A12 (@ (@ tptp.cons_list_a X3) Xs2)) (= A23 (@ (@ tptp.cons_list_a Y3) Ys2)) (not (@ (@ Less2 X3) Y3)) (not (@ (@ Less2 Y3) X3)) (@ (@ (@ tptp.lexordp_list_a Less2) Xs2) Ys2)))))))
% 0.16/0.48 (assert (= tptp.lexordp_a (lambda ((Less2 (-> tptp.a tptp.a Bool)) (A12 tptp.list_a) (A23 tptp.list_a)) (or (exists ((Y3 tptp.a) (Ys2 tptp.list_a)) (and (= A12 tptp.nil_a) (= A23 (@ (@ tptp.cons_a Y3) Ys2)))) (exists ((X3 tptp.a) (Y3 tptp.a) (Xs2 tptp.list_a) (Ys2 tptp.list_a)) (and (= A12 (@ (@ tptp.cons_a X3) Xs2)) (= A23 (@ (@ tptp.cons_a Y3) Ys2)) (@ (@ Less2 X3) Y3))) (exists ((X3 tptp.a) (Y3 tptp.a) (Xs2 tptp.list_a) (Ys2 tptp.list_a)) (and (= A12 (@ (@ tptp.cons_a X3) Xs2)) (= A23 (@ (@ tptp.cons_a Y3) Ys2)) (not (@ (@ Less2 X3) Y3)) (not (@ (@ Less2 Y3) X3)) (@ (@ (@ tptp.lexordp_a Less2) Xs2) Ys2)))))))
% 0.16/0.48 (assert (forall ((Less (-> tptp.list_a tptp.list_a Bool)) (X1 tptp.list_list_a) (X22 tptp.list_list_a) (P (-> tptp.list_list_a tptp.list_list_a Bool))) (=> (@ (@ (@ tptp.lexordp_list_a Less) X1) X22) (=> (forall ((Y2 tptp.list_a) (Ys3 tptp.list_list_a)) (@ (@ P tptp.nil_list_a) (@ (@ tptp.cons_list_a Y2) Ys3))) (=> (forall ((X2 tptp.list_a) (Y2 tptp.list_a) (Xs3 tptp.list_list_a) (Ys3 tptp.list_list_a)) (=> (@ (@ Less X2) Y2) (@ (@ P (@ (@ tptp.cons_list_a X2) Xs3)) (@ (@ tptp.cons_list_a Y2) Ys3)))) (=> (forall ((X2 tptp.list_a) (Y2 tptp.list_a) (Xs3 tptp.list_list_a) (Ys3 tptp.list_list_a)) (=> (not (@ (@ Less X2) Y2)) (=> (not (@ (@ Less Y2) X2)) (=> (@ (@ (@ tptp.lexordp_list_a Less) Xs3) Ys3) (=> (@ (@ P Xs3) Ys3) (@ (@ P (@ (@ tptp.cons_list_a X2) Xs3)) (@ (@ tptp.cons_list_a Y2) Ys3))))))) (@ (@ P X1) X22)))))))
% 0.16/0.48 (assert (forall ((Less (-> tptp.a tptp.a Bool)) (X1 tptp.list_a) (X22 tptp.list_a) (P (-> tptp.list_a tptp.list_a Bool))) (=> (@ (@ (@ tptp.lexordp_a Less) X1) X22) (=> (forall ((Y2 tptp.a) (Ys3 tptp.list_a)) (@ (@ P tptp.nil_a) (@ (@ tptp.cons_a Y2) Ys3))) (=> (forall ((X2 tptp.a) (Y2 tptp.a) (Xs3 tptp.list_a) (Ys3 tptp.list_a)) (=> (@ (@ Less X2) Y2) (@ (@ P (@ (@ tptp.cons_a X2) Xs3)) (@ (@ tptp.cons_a Y2) Ys3)))) (=> (forall ((X2 tptp.a) (Y2 tptp.a) (Xs3 tptp.list_a) (Ys3 tptp.list_a)) (=> (not (@ (@ Less X2) Y2)) (=> (not (@ (@ Less Y2) X2)) (=> (@ (@ (@ tptp.lexordp_a Less) Xs3) Ys3) (=> (@ (@ P Xs3) Ys3) (@ (@ P (@ (@ tptp.cons_a X2) Xs3)) (@ (@ tptp.cons_a Y2) Ys3))))))) (@ (@ P X1) X22)))))))
% 0.16/0.48 (assert (forall ((Ys tptp.list_a) (Xs tptp.list_a)) (=> (not (= Ys tptp.nil_a)) (@ (@ (@ tptp.lexordp_a tptp.less) Xs) (@ (@ tptp.append_a Xs) Ys)))))
% 0.16/0.48 (assert (forall ((X tptp.a) (Y tptp.a) (Us tptp.list_a) (Xs tptp.list_a) (Ys tptp.list_a)) (let ((_let_1 (@ tptp.append_a Us))) (=> (@ (@ tptp.less X) Y) (@ (@ (@ tptp.lexordp_a tptp.less) (@ _let_1 (@ (@ tptp.cons_a X) Xs))) (@ _let_1 (@ (@ tptp.cons_a Y) Ys)))))))
% 0.16/0.48 (assert (forall ((F (-> tptp.a tptp.a tptp.a))) (=> (@ tptp.semilattice_a F) (@ tptp.abel_semigroup_a F))))
% 0.16/0.48 (assert (forall ((Xs tptp.list_a) (Us tptp.list_a) (Vs tptp.list_a)) (let ((_let_1 (@ tptp.lexordp_a tptp.less))) (let ((_let_2 (@ tptp.append_a Xs))) (=> (@ (@ _let_1 (@ _let_2 Us)) (@ _let_2 Vs)) (=> (forall ((A2 tptp.a)) (not (@ (@ tptp.less A2) A2))) (@ (@ _let_1 Us) Vs)))))))
% 0.16/0.48 (assert (forall ((Us tptp.list_a) (Vs tptp.list_a) (Xs tptp.list_a)) (let ((_let_1 (@ tptp.append_a Xs))) (let ((_let_2 (@ tptp.lexordp_a tptp.less))) (=> (@ (@ _let_2 Us) Vs) (@ (@ _let_2 (@ _let_1 Us)) (@ _let_1 Vs)))))))
% 0.16/0.48 (assert (forall ((U tptp.list_a) (V tptp.list_a)) (@ (@ (@ tptp.lexordp_eq_a tptp.less) U) (@ (@ tptp.append_a U) V))))
% 0.16/0.48 (assert (forall ((Xs tptp.list_list_a) (Ys tptp.list_list_a) (Zs2 tptp.list_list_a)) (let ((_let_1 (@ tptp.append_list_a Xs))) (= (= (@ _let_1 Ys) (@ _let_1 Zs2)) (= Ys Zs2)))))
% 0.16/0.48 (assert (forall ((Xs tptp.list_a) (Ys tptp.list_a) (Zs2 tptp.list_a)) (let ((_let_1 (@ tptp.append_a Xs))) (= (= (@ _let_1 Ys) (@ _let_1 Zs2)) (= Ys Zs2)))))
% 0.16/0.48 (assert (forall ((Ys tptp.list_list_a) (Xs tptp.list_list_a) (Zs2 tptp.list_list_a)) (= (= (@ (@ tptp.append_list_a Ys) Xs) (@ (@ tptp.append_list_a Zs2) Xs)) (= Ys Zs2))))
% 0.16/0.48 (assert (forall ((Ys tptp.list_a) (Xs tptp.list_a) (Zs2 tptp.list_a)) (= (= (@ (@ tptp.append_a Ys) Xs) (@ (@ tptp.append_a Zs2) Xs)) (= Ys Zs2))))
% 0.16/0.48 (assert (forall ((Xs tptp.list_list_a) (Ys tptp.list_list_a) (Zs2 tptp.list_list_a)) (let ((_let_1 (@ tptp.append_list_a Xs))) (= (@ (@ tptp.append_list_a (@ _let_1 Ys)) Zs2) (@ _let_1 (@ (@ tptp.append_list_a Ys) Zs2))))))
% 0.16/0.48 (assert (forall ((Xs tptp.list_a) (Ys tptp.list_a) (Zs2 tptp.list_a)) (let ((_let_1 (@ tptp.append_a Xs))) (= (@ (@ tptp.append_a (@ _let_1 Ys)) Zs2) (@ _let_1 (@ (@ tptp.append_a Ys) Zs2))))))
% 0.16/0.48 (assert (forall ((A tptp.list_list_a) (B tptp.list_list_a) (C tptp.list_list_a)) (let ((_let_1 (@ tptp.append_list_a A))) (= (@ (@ tptp.append_list_a (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.append_list_a B) C))))))
% 0.16/0.48 (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))))))
% 0.16/0.48 (assert (forall ((A tptp.list_list_a)) (= (@ (@ tptp.append_list_a A) tptp.nil_list_a) A)))
% 0.16/0.48 (assert (forall ((A tptp.list_a)) (= (@ (@ tptp.append_a A) tptp.nil_a) A)))
% 0.16/0.48 (assert (forall ((Xs tptp.list_list_a) (Ys tptp.list_list_a)) (= (= (@ (@ tptp.append_list_a Xs) Ys) tptp.nil_list_a) (and (= Xs tptp.nil_list_a) (= Ys tptp.nil_list_a)))))
% 0.16/0.48 (assert (forall ((Xs tptp.list_a) (Ys tptp.list_a)) (= (= (@ (@ tptp.append_a Xs) Ys) tptp.nil_a) (and (= Xs tptp.nil_a) (= Ys tptp.nil_a)))))
% 0.16/0.48 (assert (forall ((Xs tptp.list_list_a) (Ys tptp.list_list_a)) (= (= tptp.nil_list_a (@ (@ tptp.append_list_a Xs) Ys)) (and (= Xs tptp.nil_list_a) (= Ys tptp.nil_list_a)))))
% 0.16/0.48 (assert (forall ((Xs tptp.list_a) (Ys tptp.list_a)) (= (= tptp.nil_a (@ (@ tptp.append_a Xs) Ys)) (and (= Xs tptp.nil_a) (= Ys tptp.nil_a)))))
% 0.16/0.48 (assert (forall ((Ys tptp.list_list_a) (Xs tptp.list_list_a)) (= (= Ys (@ (@ tptp.append_list_a Xs) Ys)) (= Xs tptp.nil_list_a))))
% 0.16/0.48 (assert (forall ((Ys tptp.list_a) (Xs tptp.list_a)) (= (= Ys (@ (@ tptp.append_a Xs) Ys)) (= Xs tptp.nil_a))))
% 0.16/0.48 (assert (forall ((Xs tptp.list_list_a) (Ys tptp.list_list_a)) (= (= (@ (@ tptp.append_list_a Xs) Ys) Ys) (= Xs tptp.nil_list_a))))
% 0.16/0.48 (assert (forall ((Xs tptp.list_a) (Ys tptp.list_a)) (= (= (@ (@ tptp.append_a Xs) Ys) Ys) (= Xs tptp.nil_a))))
% 0.16/0.48 (assert (forall ((Xs tptp.list_list_a) (Ys tptp.list_list_a)) (= (= Xs (@ (@ tptp.append_list_a Xs) Ys)) (= Ys tptp.nil_list_a))))
% 0.16/0.48 (assert (forall ((Xs tptp.list_a) (Ys tptp.list_a)) (= (= Xs (@ (@ tptp.append_a Xs) Ys)) (= Ys tptp.nil_a))))
% 0.16/0.48 (assert (forall ((Xs tptp.list_list_a) (Ys tptp.list_list_a)) (= (= (@ (@ tptp.append_list_a Xs) Ys) Xs) (= Ys tptp.nil_list_a))))
% 0.16/0.48 (assert (forall ((Xs tptp.list_a) (Ys tptp.list_a)) (= (= (@ (@ tptp.append_a Xs) Ys) Xs) (= Ys tptp.nil_a))))
% 0.16/0.48 (assert (forall ((Xs tptp.list_list_a)) (= (@ (@ tptp.append_list_a Xs) tptp.nil_list_a) Xs)))
% 0.16/0.48 (assert (forall ((Xs tptp.list_a)) (= (@ (@ tptp.append_a Xs) tptp.nil_a) Xs)))
% 0.16/0.48 (assert (forall ((Xs tptp.list_list_a) (X tptp.list_a) (Ys tptp.list_list_a) (Y tptp.list_a)) (= (= (@ (@ tptp.append_list_a Xs) (@ (@ tptp.cons_list_a X) tptp.nil_list_a)) (@ (@ tptp.append_list_a Ys) (@ (@ tptp.cons_list_a Y) tptp.nil_list_a))) (and (= Xs Ys) (= X Y)))))
% 0.16/0.48 (assert (forall ((Xs tptp.list_a) (X tptp.a) (Ys tptp.list_a) (Y tptp.a)) (= (= (@ (@ tptp.append_a Xs) (@ (@ tptp.cons_a X) tptp.nil_a)) (@ (@ tptp.append_a Ys) (@ (@ tptp.cons_a Y) tptp.nil_a))) (and (= Xs Ys) (= X Y)))))
% 0.16/0.48 (assert (forall ((A tptp.list_list_a)) (= (@ (@ tptp.append_list_a tptp.nil_list_a) A) A)))
% 0.16/0.48 (assert (forall ((A tptp.list_a)) (= (@ (@ tptp.append_a tptp.nil_a) A) A)))
% 0.16/0.48 (assert (forall ((Ys tptp.list_list_a)) (= (@ (@ tptp.append_list_a tptp.nil_list_a) Ys) Ys)))
% 0.16/0.48 (assert (forall ((Ys tptp.list_a)) (= (@ (@ tptp.append_a tptp.nil_a) Ys) Ys)))
% 0.16/0.48 (assert (forall ((Xs tptp.list_list_a) (Ys tptp.list_list_a)) (=> (= Xs Ys) (= Xs (@ (@ tptp.append_list_a tptp.nil_list_a) Ys)))))
% 0.16/0.48 (assert (forall ((Xs tptp.list_a) (Ys tptp.list_a)) (=> (= Xs Ys) (= Xs (@ (@ tptp.append_a tptp.nil_a) Ys)))))
% 0.16/0.48 (assert (forall ((X tptp.list_a) (Xs1 tptp.list_list_a) (Ys tptp.list_list_a) (Xs tptp.list_list_a) (Zs2 tptp.list_list_a)) (let ((_let_1 (@ tptp.cons_list_a X))) (=> (= (@ _let_1 Xs1) Ys) (=> (= Xs (@ (@ tptp.append_list_a Xs1) Zs2)) (= (@ _let_1 Xs) (@ (@ tptp.append_list_a Ys) Zs2)))))))
% 0.16/0.48 (assert (forall ((X tptp.a) (Xs1 tptp.list_a) (Ys tptp.list_a) (Xs tptp.list_a) (Zs2 tptp.list_a)) (let ((_let_1 (@ tptp.cons_a X))) (=> (= (@ _let_1 Xs1) Ys) (=> (= Xs (@ (@ tptp.append_a Xs1) Zs2)) (= (@ _let_1 Xs) (@ (@ tptp.append_a Ys) Zs2)))))))
% 0.16/0.48 (assert (forall ((X tptp.list_a) (Xs tptp.list_list_a) (Ys tptp.list_list_a)) (let ((_let_1 (@ tptp.cons_list_a X))) (= (@ (@ tptp.append_list_a (@ _let_1 Xs)) Ys) (@ _let_1 (@ (@ tptp.append_list_a Xs) Ys))))))
% 0.16/0.48 (assert (forall ((X tptp.a) (Xs tptp.list_a) (Ys tptp.list_a)) (let ((_let_1 (@ tptp.cons_a X))) (= (@ (@ tptp.append_a (@ _let_1 Xs)) Ys) (@ _let_1 (@ (@ tptp.append_a Xs) Ys))))))
% 0.16/0.48 (assert (forall ((Less (-> tptp.list_a tptp.list_a Bool)) (Xs tptp.list_list_a) (Us tptp.list_list_a) (Vs tptp.list_list_a)) (let ((_let_1 (@ tptp.lexordp_list_a Less))) (let ((_let_2 (@ tptp.append_list_a Xs))) (=> (@ (@ _let_1 (@ _let_2 Us)) (@ _let_2 Vs)) (=> (forall ((A2 tptp.list_a)) (not (@ (@ Less A2) A2))) (@ (@ _let_1 Us) Vs)))))))
% 0.16/0.48 (assert (forall ((Less (-> tptp.a tptp.a Bool)) (Xs tptp.list_a) (Us tptp.list_a) (Vs tptp.list_a)) (let ((_let_1 (@ tptp.lexordp_a Less))) (let ((_let_2 (@ tptp.append_a Xs))) (=> (@ (@ _let_1 (@ _let_2 Us)) (@ _let_2 Vs)) (=> (forall ((A2 tptp.a)) (not (@ (@ Less A2) A2))) (@ (@ _let_1 Us) Vs)))))))
% 0.16/0.48 (assert (forall ((Less (-> tptp.list_a tptp.list_a Bool)) (Us tptp.list_list_a) (Vs tptp.list_list_a) (Xs tptp.list_list_a)) (let ((_let_1 (@ tptp.append_list_a Xs))) (let ((_let_2 (@ tptp.lexordp_list_a Less))) (=> (@ (@ _let_2 Us) Vs) (@ (@ _let_2 (@ _let_1 Us)) (@ _let_1 Vs)))))))
% 0.16/0.48 (assert (forall ((Less (-> tptp.a tptp.a Bool)) (Us tptp.list_a) (Vs tptp.list_a) (Xs tptp.list_a)) (let ((_let_1 (@ tptp.append_a Xs))) (let ((_let_2 (@ tptp.lexordp_a Less))) (=> (@ (@ _let_2 Us) Vs) (@ (@ _let_2 (@ _let_1 Us)) (@ _let_1 Vs)))))))
% 0.16/0.48 (assert (forall ((Less (-> tptp.list_a tptp.list_a Bool)) (U tptp.list_list_a) (V tptp.list_list_a)) (@ (@ (@ tptp.lexordp_eq_list_a Less) U) (@ (@ tptp.append_list_a U) V))))
% 0.16/0.48 (assert (forall ((Less (-> tptp.a tptp.a Bool)) (U tptp.list_a) (V tptp.list_a)) (@ (@ (@ tptp.lexordp_eq_a Less) U) (@ (@ tptp.append_a U) V))))
% 0.16/0.48 (assert (forall ((Xs tptp.list_list_a) (Ys tptp.list_list_a) (Zs2 tptp.list_list_a) (Ts tptp.list_list_a)) (= (= (@ (@ tptp.append_list_a Xs) Ys) (@ (@ tptp.append_list_a Zs2) Ts)) (exists ((Us2 tptp.list_list_a)) (let ((_let_1 (@ tptp.append_list_a Us2))) (or (and (= Xs (@ (@ tptp.append_list_a Zs2) Us2)) (= (@ _let_1 Ys) Ts)) (and (= (@ (@ tptp.append_list_a Xs) Us2) Zs2) (= Ys (@ _let_1 Ts)))))))))
% 0.16/0.48 (assert (forall ((Xs tptp.list_a) (Ys tptp.list_a) (Zs2 tptp.list_a) (Ts tptp.list_a)) (= (= (@ (@ tptp.append_a Xs) Ys) (@ (@ tptp.append_a Zs2) Ts)) (exists ((Us2 tptp.list_a)) (let ((_let_1 (@ tptp.append_a Us2))) (or (and (= Xs (@ (@ tptp.append_a Zs2) Us2)) (= (@ _let_1 Ys) Ts)) (and (= (@ (@ tptp.append_a Xs) Us2) Zs2) (= Ys (@ _let_1 Ts)))))))))
% 0.16/0.48 (assert (forall ((Xs tptp.list_list_a) (Xs1 tptp.list_list_a) (Zs2 tptp.list_list_a) (Ys tptp.list_list_a) (Us tptp.list_list_a)) (let ((_let_1 (@ tptp.append_list_a Xs))) (=> (= (@ _let_1 Xs1) Zs2) (=> (= Ys (@ (@ tptp.append_list_a Xs1) Us)) (= (@ _let_1 Ys) (@ (@ tptp.append_list_a Zs2) Us)))))))
% 0.16/0.48 (assert (forall ((Xs tptp.list_a) (Xs1 tptp.list_a) (Zs2 tptp.list_a) (Ys tptp.list_a) (Us tptp.list_a)) (let ((_let_1 (@ tptp.append_a Xs))) (=> (= (@ _let_1 Xs1) Zs2) (=> (= Ys (@ (@ tptp.append_a Xs1) Us)) (= (@ _let_1 Ys) (@ (@ tptp.append_a Zs2) Us)))))))
% 0.16/0.48 (assert (@ tptp.semigr656274520list_a tptp.append_list_a))
% 0.16/0.48 (assert (@ tptp.semigroup_list_a tptp.append_a))
% 0.16/0.48 (assert (forall ((Xs tptp.list_list_a) (P (-> tptp.list_list_a Bool))) (=> (not (= Xs tptp.nil_list_a)) (=> (forall ((X2 tptp.list_a)) (@ P (@ (@ tptp.cons_list_a X2) tptp.nil_list_a))) (=> (forall ((X2 tptp.list_a) (Xs3 tptp.list_list_a)) (=> (not (= Xs3 tptp.nil_list_a)) (=> (@ P Xs3) (@ P (@ (@ tptp.append_list_a Xs3) (@ (@ tptp.cons_list_a X2) tptp.nil_list_a)))))) (@ P Xs))))))
% 0.16/0.48 (assert (forall ((Xs tptp.list_a) (P (-> tptp.list_a Bool))) (=> (not (= Xs tptp.nil_a)) (=> (forall ((X2 tptp.a)) (@ P (@ (@ tptp.cons_a X2) tptp.nil_a))) (=> (forall ((X2 tptp.a) (Xs3 tptp.list_a)) (=> (not (= Xs3 tptp.nil_a)) (=> (@ P Xs3) (@ P (@ (@ tptp.append_a Xs3) (@ (@ tptp.cons_a X2) tptp.nil_a)))))) (@ P Xs))))))
% 0.16/0.48 (assert (forall ((Ys tptp.list_list_a) (Zs2 tptp.list_list_a) (X tptp.list_a) (Xs tptp.list_list_a)) (let ((_let_1 (@ (@ tptp.cons_list_a X) Xs))) (= (= (@ (@ tptp.append_list_a Ys) Zs2) _let_1) (or (and (= Ys tptp.nil_list_a) (= Zs2 _let_1)) (exists ((Ys4 tptp.list_list_a)) (and (= Ys (@ (@ tptp.cons_list_a X) Ys4)) (= (@ (@ tptp.append_list_a Ys4) Zs2) Xs))))))))
% 0.16/0.48 (assert (forall ((Ys tptp.list_a) (Zs2 tptp.list_a) (X tptp.a) (Xs tptp.list_a)) (let ((_let_1 (@ (@ tptp.cons_a X) Xs))) (= (= (@ (@ tptp.append_a Ys) Zs2) _let_1) (or (and (= Ys tptp.nil_a) (= Zs2 _let_1)) (exists ((Ys4 tptp.list_a)) (and (= Ys (@ (@ tptp.cons_a X) Ys4)) (= (@ (@ tptp.append_a Ys4) Zs2) Xs))))))))
% 0.16/0.48 (assert (forall ((X tptp.list_a) (Xs tptp.list_list_a) (Ys tptp.list_list_a) (Zs2 tptp.list_list_a)) (let ((_let_1 (@ (@ tptp.cons_list_a X) Xs))) (= (= _let_1 (@ (@ tptp.append_list_a Ys) Zs2)) (or (and (= Ys tptp.nil_list_a) (= _let_1 Zs2)) (exists ((Ys4 tptp.list_list_a)) (and (= (@ (@ tptp.cons_list_a X) Ys4) Ys) (= Xs (@ (@ tptp.append_list_a Ys4) Zs2)))))))))
% 0.16/0.48 (assert (forall ((X tptp.a) (Xs tptp.list_a) (Ys tptp.list_a) (Zs2 tptp.list_a)) (let ((_let_1 (@ (@ tptp.cons_a X) Xs))) (= (= _let_1 (@ (@ tptp.append_a Ys) Zs2)) (or (and (= Ys tptp.nil_a) (= _let_1 Zs2)) (exists ((Ys4 tptp.list_a)) (and (= (@ (@ tptp.cons_a X) Ys4) Ys) (= Xs (@ (@ tptp.append_a Ys4) Zs2)))))))))
% 0.16/0.48 (assert (forall ((Xs tptp.list_list_a)) (=> (not (= Xs tptp.nil_list_a)) (not (forall ((Ys3 tptp.list_list_a) (Y2 tptp.list_a)) (not (= Xs (@ (@ tptp.append_list_a Ys3) (@ (@ tptp.cons_list_a Y2) tptp.nil_list_a)))))))))
% 0.16/0.48 (assert (forall ((Xs tptp.list_a)) (=> (not (= Xs tptp.nil_a)) (not (forall ((Ys3 tptp.list_a) (Y2 tptp.a)) (not (= Xs (@ (@ tptp.append_a Ys3) (@ (@ tptp.cons_a Y2) tptp.nil_a)))))))))
% 0.16/0.48 (assert (forall ((P (-> tptp.list_list_a Bool)) (Xs tptp.list_list_a)) (=> (@ P tptp.nil_list_a) (=> (forall ((X2 tptp.list_a) (Xs3 tptp.list_list_a)) (=> (@ P Xs3) (@ P (@ (@ tptp.append_list_a Xs3) (@ (@ tptp.cons_list_a X2) tptp.nil_list_a))))) (@ P Xs)))))
% 0.16/0.48 (assert (forall ((P (-> tptp.list_a Bool)) (Xs tptp.list_a)) (=> (@ P tptp.nil_a) (=> (forall ((X2 tptp.a) (Xs3 tptp.list_a)) (=> (@ P Xs3) (@ P (@ (@ tptp.append_a Xs3) (@ (@ tptp.cons_a X2) tptp.nil_a))))) (@ P Xs)))))
% 0.16/0.48 (assert (forall ((Less (-> tptp.list_a tptp.list_a Bool)) (X tptp.list_a) (Y tptp.list_a) (Us tptp.list_list_a) (Xs tptp.list_list_a) (Ys tptp.list_list_a)) (let ((_let_1 (@ tptp.append_list_a Us))) (=> (@ (@ Less X) Y) (@ (@ (@ tptp.lexordp_list_a Less) (@ _let_1 (@ (@ tptp.cons_list_a X) Xs))) (@ _let_1 (@ (@ tptp.cons_list_a Y) Ys)))))))
% 0.16/0.48 (assert (forall ((Less (-> tptp.a tptp.a Bool)) (X tptp.a) (Y tptp.a) (Us tptp.list_a) (Xs tptp.list_a) (Ys tptp.list_a)) (let ((_let_1 (@ tptp.append_a Us))) (=> (@ (@ Less X) Y) (@ (@ (@ tptp.lexordp_a Less) (@ _let_1 (@ (@ tptp.cons_a X) Xs))) (@ _let_1 (@ (@ tptp.cons_a Y) Ys)))))))
% 0.16/0.48 (assert (forall ((Ys tptp.list_list_a) (Less (-> tptp.list_a tptp.list_a Bool)) (Xs tptp.list_list_a)) (=> (not (= Ys tptp.nil_list_a)) (@ (@ (@ tptp.lexordp_list_a Less) Xs) (@ (@ tptp.append_list_a Xs) Ys)))))
% 0.16/0.48 (assert (forall ((Ys tptp.list_a) (Less (-> tptp.a tptp.a Bool)) (Xs tptp.list_a)) (=> (not (= Ys tptp.nil_a)) (@ (@ (@ tptp.lexordp_a Less) Xs) (@ (@ tptp.append_a Xs) Ys)))))
% 0.16/0.48 (assert (forall ((F (-> tptp.a tptp.a tptp.a)) (A tptp.a)) (=> (@ tptp.semilattice_a F) (= (@ (@ F A) A) A))))
% 0.16/0.48 (assert (forall ((F (-> tptp.a tptp.a tptp.a)) (A tptp.a) (B tptp.a)) (let ((_let_1 (@ F A))) (let ((_let_2 (@ _let_1 B))) (=> (@ tptp.semilattice_a F) (= (@ _let_1 _let_2) _let_2))))))
% 0.16/0.48 (assert (forall ((F (-> tptp.a tptp.a tptp.a)) (A tptp.a) (B tptp.a)) (let ((_let_1 (@ (@ F A) B))) (=> (@ tptp.semilattice_a F) (= (@ (@ F _let_1) B) _let_1)))))
% 0.16/0.48 (assert (= (@ tptp.product_lists_list_a tptp.nil_list_list_a) (@ (@ tptp.cons_list_list_a tptp.nil_list_a) tptp.nil_list_list_a)))
% 0.16/0.48 (assert (= (@ tptp.product_lists_a tptp.nil_list_a) (@ (@ tptp.cons_list_a tptp.nil_a) tptp.nil_list_a)))
% 0.16/0.48 (assert (forall ((X tptp.a) (Xs tptp.list_a) (F (-> tptp.a tptp.list_list_a))) (= (@ (@ tptp.bind_a_list_a (@ (@ tptp.cons_a X) Xs)) F) (@ (@ tptp.append_list_a (@ F X)) (@ (@ tptp.bind_a_list_a Xs) F)))))
% 0.16/0.48 (assert (forall ((X tptp.list_a) (Xs tptp.list_list_a) (F (-> tptp.list_a tptp.list_a))) (= (@ (@ tptp.bind_list_a_a (@ (@ tptp.cons_list_a X) Xs)) F) (@ (@ tptp.append_a (@ F X)) (@ (@ tptp.bind_list_a_a Xs) F)))))
% 0.16/0.48 (assert (forall ((X tptp.list_a) (Xs tptp.list_list_a) (F (-> tptp.list_a tptp.list_list_a))) (= (@ (@ tptp.bind_list_a_list_a (@ (@ tptp.cons_list_a X) Xs)) F) (@ (@ tptp.append_list_a (@ F X)) (@ (@ tptp.bind_list_a_list_a Xs) F)))))
% 0.16/0.48 (assert (forall ((X tptp.a) (Xs tptp.list_a) (F (-> tptp.a tptp.list_a))) (= (@ (@ tptp.bind_a_a (@ (@ tptp.cons_a X) Xs)) F) (@ (@ tptp.append_a (@ F X)) (@ (@ tptp.bind_a_a Xs) F)))))
% 0.16/0.48 (assert (forall ((F (-> tptp.a tptp.list_list_a))) (= (@ (@ tptp.bind_a_list_a tptp.nil_a) F) tptp.nil_list_a)))
% 0.16/0.48 (assert (forall ((F (-> tptp.list_a tptp.list_a))) (= (@ (@ tptp.bind_list_a_a tptp.nil_list_a) F) tptp.nil_a)))
% 0.16/0.48 (assert (forall ((F (-> tptp.list_a tptp.list_list_a))) (= (@ (@ tptp.bind_list_a_list_a tptp.nil_list_a) F) tptp.nil_list_a)))
% 0.16/0.48 (assert (forall ((F (-> tptp.a tptp.list_a))) (= (@ (@ tptp.bind_a_a tptp.nil_a) F) tptp.nil_a)))
% 0.16/0.48 (assert (= tptp.abel_s1075322906list_a (lambda ((F2 (-> tptp.list_a tptp.list_a tptp.list_a))) (and (@ tptp.semigroup_list_a F2) (@ tptp.abel_s374399671list_a F2)))))
% 0.16/0.48 (assert (= tptp.abel_semigroup_a (lambda ((F2 (-> tptp.a tptp.a tptp.a))) (and (@ tptp.semigroup_a F2) (@ tptp.abel_s2117090225ioms_a F2)))))
% 0.16/0.48 (assert (forall ((F (-> tptp.list_a tptp.list_a tptp.list_a))) (=> (@ tptp.semigroup_list_a F) (=> (@ tptp.abel_s374399671list_a F) (@ tptp.abel_s1075322906list_a F)))))
% 0.16/0.48 (assert (forall ((F (-> tptp.a tptp.a tptp.a))) (=> (@ tptp.semigroup_a F) (=> (@ tptp.abel_s2117090225ioms_a F) (@ tptp.abel_semigroup_a F)))))
% 0.16/0.48 (assert (forall ((F (-> tptp.a tptp.a tptp.a))) (=> (forall ((A2 tptp.a) (B2 tptp.a)) (= (@ (@ F A2) B2) (@ (@ F B2) A2))) (@ tptp.abel_s2117090225ioms_a F))))
% 0.16/0.48 (assert (= tptp.abel_s2117090225ioms_a (lambda ((F2 (-> tptp.a tptp.a tptp.a))) (forall ((A3 tptp.a) (B3 tptp.a)) (= (@ (@ F2 A3) B3) (@ (@ F2 B3) A3))))))
% 0.16/0.48 (assert (forall ((F (-> tptp.a tptp.a tptp.a))) (=> (@ tptp.abel_semigroup_a F) (@ tptp.abel_s2117090225ioms_a F))))
% 0.16/0.48 (assert (forall ((F (-> tptp.a tptp.a tptp.a))) (=> (@ tptp.abel_semigroup_a F) (=> (@ tptp.semilattice_axioms_a F) (@ tptp.semilattice_a F)))))
% 0.16/0.48 (assert (= tptp.semilattice_a (lambda ((F2 (-> tptp.a tptp.a tptp.a))) (and (@ tptp.abel_semigroup_a F2) (@ tptp.semilattice_axioms_a F2)))))
% 0.16/0.48 (assert (forall ((F (-> tptp.a tptp.a tptp.a))) (=> (@ tptp.semilattice_a F) (@ tptp.semilattice_axioms_a F))))
% 0.16/0.48 (assert (= (@ tptp.subseqs_list_a tptp.nil_list_a) (@ (@ tptp.cons_list_list_a tptp.nil_list_a) tptp.nil_list_list_a)))
% 0.16/0.48 (assert (= (@ tptp.subseqs_a tptp.nil_a) (@ (@ tptp.cons_list_a tptp.nil_a) tptp.nil_list_a)))
% 0.16/0.48 (assert (forall ((F (-> tptp.a tptp.list_list_a)) (X tptp.a) (Xs tptp.list_a)) (let ((_let_1 (@ tptp.maps_a_list_a F))) (= (@ _let_1 (@ (@ tptp.cons_a X) Xs)) (@ (@ tptp.append_list_a (@ F X)) (@ _let_1 Xs))))))
% 0.16/0.48 (assert (forall ((F (-> tptp.list_a tptp.list_a)) (X tptp.list_a) (Xs tptp.list_list_a)) (let ((_let_1 (@ tptp.maps_list_a_a F))) (= (@ _let_1 (@ (@ tptp.cons_list_a X) Xs)) (@ (@ tptp.append_a (@ F X)) (@ _let_1 Xs))))))
% 0.16/0.48 (assert (forall ((F (-> tptp.list_a tptp.list_list_a)) (X tptp.list_a) (Xs tptp.list_list_a)) (let ((_let_1 (@ tptp.maps_list_a_list_a F))) (= (@ _let_1 (@ (@ tptp.cons_list_a X) Xs)) (@ (@ tptp.append_list_a (@ F X)) (@ _let_1 Xs))))))
% 0.16/0.48 (assert (forall ((F (-> tptp.a tptp.list_a)) (X tptp.a) (Xs tptp.list_a)) (let ((_let_1 (@ tptp.maps_a_a F))) (= (@ _let_1 (@ (@ tptp.cons_a X) Xs)) (@ (@ tptp.append_a (@ F X)) (@ _let_1 Xs))))))
% 0.16/0.48 (assert (forall ((F (-> tptp.a tptp.list_list_a))) (= (@ (@ tptp.maps_a_list_a F) tptp.nil_a) tptp.nil_list_a)))
% 0.16/0.48 (assert (forall ((F (-> tptp.list_a tptp.list_a))) (= (@ (@ tptp.maps_list_a_a F) tptp.nil_list_a) tptp.nil_a)))
% 0.16/0.48 (assert (forall ((F (-> tptp.list_a tptp.list_list_a))) (= (@ (@ tptp.maps_list_a_list_a F) tptp.nil_list_a) tptp.nil_list_a)))
% 0.16/0.48 (assert (forall ((F (-> tptp.a tptp.list_a))) (= (@ (@ tptp.maps_a_a F) tptp.nil_a) tptp.nil_a)))
% 0.16/0.48 (assert (@ tptp.transp_a tptp.less))
% 0.16/0.48 (assert (forall ((X tptp.list_a)) (= (@ (@ tptp.insert_list_a X) tptp.nil_list_a) (@ (@ tptp.cons_list_a X) tptp.nil_list_a))))
% 0.16/0.48 (assert (forall ((X tptp.a)) (= (@ (@ tptp.insert_a X) tptp.nil_a) (@ (@ tptp.cons_a X) tptp.nil_a))))
% 0.16/0.48 (assert (forall ((Xss2 tptp.list_list_list_a) (Ys tptp.list_list_a) (Zs2 tptp.list_list_a)) (let ((_let_1 (= Xss2 tptp.nil_list_list_a))) (= (= (@ tptp.concat_list_a Xss2) (@ (@ tptp.append_list_a Ys) Zs2)) (and (=> _let_1 (and (= Ys tptp.nil_list_a) (= Zs2 tptp.nil_list_a))) (=> (not _let_1) (exists ((Xss1 tptp.list_list_list_a) (Xs2 tptp.list_list_a) (Xs4 tptp.list_list_a) (Xss22 tptp.list_list_list_a)) (and (= Xss2 (@ (@ tptp.append_list_list_a Xss1) (@ (@ tptp.cons_list_list_a (@ (@ tptp.append_list_a Xs2) Xs4)) Xss22))) (= Ys (@ (@ tptp.append_list_a (@ tptp.concat_list_a Xss1)) Xs2)) (= Zs2 (@ (@ tptp.append_list_a Xs4) (@ tptp.concat_list_a Xss22)))))))))))
% 0.16/0.48 (assert (forall ((Xss2 tptp.list_list_a) (Ys tptp.list_a) (Zs2 tptp.list_a)) (let ((_let_1 (= Xss2 tptp.nil_list_a))) (= (= (@ tptp.concat_a Xss2) (@ (@ tptp.append_a Ys) Zs2)) (and (=> _let_1 (and (= Ys tptp.nil_a) (= Zs2 tptp.nil_a))) (=> (not _let_1) (exists ((Xss1 tptp.list_list_a) (Xs2 tptp.list_a) (Xs4 tptp.list_a) (Xss22 tptp.list_list_a)) (and (= Xss2 (@ (@ tptp.append_list_a Xss1) (@ (@ tptp.cons_list_a (@ (@ tptp.append_a Xs2) Xs4)) Xss22))) (= Ys (@ (@ tptp.append_a (@ tptp.concat_a Xss1)) Xs2)) (= Zs2 (@ (@ tptp.append_a Xs4) (@ tptp.concat_a Xss22)))))))))))
% 0.16/0.48 (assert (forall ((X tptp.list_a) (Xs tptp.list_list_a)) (let ((_let_1 (@ tptp.cons_list_a X))) (= (@ tptp.rotate1_list_a (@ _let_1 Xs)) (@ (@ tptp.append_list_a Xs) (@ _let_1 tptp.nil_list_a))))))
% 0.16/0.48 (assert (forall ((X tptp.a) (Xs tptp.list_a)) (let ((_let_1 (@ tptp.cons_a X))) (= (@ tptp.rotate1_a (@ _let_1 Xs)) (@ (@ tptp.append_a Xs) (@ _let_1 tptp.nil_a))))))
% 0.16/0.48 (assert (forall ((Xs tptp.list_list_a)) (= (= (@ tptp.rotate1_list_a Xs) tptp.nil_list_a) (= Xs tptp.nil_list_a))))
% 0.16/0.48 (assert (forall ((Xs tptp.list_a)) (= (= (@ tptp.rotate1_a Xs) tptp.nil_a) (= Xs tptp.nil_a))))
% 0.16/0.48 (assert (forall ((Xs tptp.list_list_list_a) (Ys tptp.list_list_list_a)) (= (@ tptp.concat_list_a (@ (@ tptp.append_list_list_a Xs) Ys)) (@ (@ tptp.append_list_a (@ tptp.concat_list_a Xs)) (@ tptp.concat_list_a Ys)))))
% 0.16/0.48 (assert (forall ((Xs tptp.list_list_a) (Ys tptp.list_list_a)) (= (@ tptp.concat_a (@ (@ tptp.append_list_a Xs) Ys)) (@ (@ tptp.append_a (@ tptp.concat_a Xs)) (@ tptp.concat_a Ys)))))
% 0.16/0.48 (assert (= (@ tptp.concat_list_a tptp.nil_list_list_a) tptp.nil_list_a))
% 0.16/0.48 (assert (= (@ tptp.concat_a tptp.nil_list_a) tptp.nil_a))
% 0.16/0.48 (assert (forall ((X tptp.list_list_a) (Xs tptp.list_list_list_a)) (= (@ tptp.concat_list_a (@ (@ tptp.cons_list_list_a X) Xs)) (@ (@ tptp.append_list_a X) (@ tptp.concat_list_a Xs)))))
% 0.16/0.48 (assert (forall ((X tptp.list_a) (Xs tptp.list_list_a)) (= (@ tptp.concat_a (@ (@ tptp.cons_list_a X) Xs)) (@ (@ tptp.append_a X) (@ tptp.concat_a Xs)))))
% 0.16/0.48 (assert (= (@ tptp.rotate1_list_a tptp.nil_list_a) tptp.nil_list_a))
% 0.16/0.48 (assert (= (@ tptp.rotate1_a tptp.nil_a) tptp.nil_a))
% 0.16/0.48 (assert (forall ((Xss2 tptp.list_list_list_a) (Ys tptp.list_list_a) (Zs2 tptp.list_list_a)) (=> (= (@ tptp.concat_list_a Xss2) (@ (@ tptp.append_list_a Ys) Zs2)) (=> (not (= Xss2 tptp.nil_list_list_a)) (exists ((Xss12 tptp.list_list_list_a) (Xs3 tptp.list_list_a) (Xs5 tptp.list_list_a) (Xss23 tptp.list_list_list_a)) (and (= Xss2 (@ (@ tptp.append_list_list_a Xss12) (@ (@ tptp.cons_list_list_a (@ (@ tptp.append_list_a Xs3) Xs5)) Xss23))) (= Ys (@ (@ tptp.append_list_a (@ tptp.concat_list_a Xss12)) Xs3)) (= Zs2 (@ (@ tptp.append_list_a Xs5) (@ tptp.concat_list_a Xss23)))))))))
% 0.16/0.48 (assert (forall ((Xss2 tptp.list_list_a) (Ys tptp.list_a) (Zs2 tptp.list_a)) (=> (= (@ tptp.concat_a Xss2) (@ (@ tptp.append_a Ys) Zs2)) (=> (not (= Xss2 tptp.nil_list_a)) (exists ((Xss12 tptp.list_list_a) (Xs3 tptp.list_a) (Xs5 tptp.list_a) (Xss23 tptp.list_list_a)) (and (= Xss2 (@ (@ tptp.append_list_a Xss12) (@ (@ tptp.cons_list_a (@ (@ tptp.append_a Xs3) Xs5)) Xss23))) (= Ys (@ (@ tptp.append_a (@ tptp.concat_a Xss12)) Xs3)) (= Zs2 (@ (@ tptp.append_a Xs5) (@ tptp.concat_a Xss23)))))))))
% 0.16/0.48 (assert (forall ((Xs tptp.list_list_a) (X tptp.list_a)) (= (@ tptp.butlast_list_a (@ (@ tptp.append_list_a Xs) (@ (@ tptp.cons_list_a X) tptp.nil_list_a))) Xs)))
% 0.16/0.48 (assert (forall ((Xs tptp.list_a) (X tptp.a)) (= (@ tptp.butlast_a (@ (@ tptp.append_a Xs) (@ (@ tptp.cons_a X) tptp.nil_a))) Xs)))
% 0.16/0.48 (assert (forall ((P (-> tptp.list_a Bool))) (not (@ (@ tptp.list_ex1_list_a P) tptp.nil_list_a))))
% 0.16/0.48 (assert (forall ((P (-> tptp.a Bool))) (not (@ (@ tptp.list_ex1_a P) tptp.nil_a))))
% 0.16/0.48 (assert (forall ((Ys tptp.list_list_a) (Xs tptp.list_list_a)) (let ((_let_1 (@ tptp.append_list_a Xs))) (let ((_let_2 (@ tptp.butlast_list_a (@ _let_1 Ys)))) (let ((_let_3 (= Ys tptp.nil_list_a))) (and (=> _let_3 (= _let_2 (@ tptp.butlast_list_a Xs))) (=> (not _let_3) (= _let_2 (@ _let_1 (@ tptp.butlast_list_a Ys))))))))))
% 0.16/0.48 (assert (forall ((Ys tptp.list_a) (Xs tptp.list_a)) (let ((_let_1 (@ tptp.append_a Xs))) (let ((_let_2 (@ tptp.butlast_a (@ _let_1 Ys)))) (let ((_let_3 (= Ys tptp.nil_a))) (and (=> _let_3 (= _let_2 (@ tptp.butlast_a Xs))) (=> (not _let_3) (= _let_2 (@ _let_1 (@ tptp.butlast_a Ys))))))))))
% 0.16/0.48 (assert (= (@ tptp.butlast_list_a tptp.nil_list_a) tptp.nil_list_a))
% 0.16/0.48 (assert (= (@ tptp.butlast_a tptp.nil_a) tptp.nil_a))
% 0.16/0.48 (assert (forall ((Xs tptp.list_list_a) (X tptp.list_a)) (let ((_let_1 (@ tptp.cons_list_a X))) (let ((_let_2 (@ tptp.butlast_list_a (@ _let_1 Xs)))) (let ((_let_3 (= Xs tptp.nil_list_a))) (and (=> _let_3 (= _let_2 tptp.nil_list_a)) (=> (not _let_3) (= _let_2 (@ _let_1 (@ tptp.butlast_list_a Xs))))))))))
% 0.16/0.48 (assert (forall ((Xs tptp.list_a) (X tptp.a)) (let ((_let_1 (@ tptp.cons_a X))) (let ((_let_2 (@ tptp.butlast_a (@ _let_1 Xs)))) (let ((_let_3 (= Xs tptp.nil_a))) (and (=> _let_3 (= _let_2 tptp.nil_a)) (=> (not _let_3) (= _let_2 (@ _let_1 (@ tptp.butlast_a Xs))))))))))
% 0.16/0.48 (assert (forall ((Xs tptp.list_list_a)) (=> (not (= Xs tptp.nil_list_a)) (= (@ (@ tptp.append_list_a (@ tptp.butlast_list_a Xs)) (@ (@ tptp.cons_list_a (@ tptp.last_list_a Xs)) tptp.nil_list_a)) Xs))))
% 0.16/0.48 (assert (forall ((Xs tptp.list_a)) (=> (not (= Xs tptp.nil_a)) (= (@ (@ tptp.append_a (@ tptp.butlast_a Xs)) (@ (@ tptp.cons_a (@ tptp.last_a Xs)) tptp.nil_a)) Xs))))
% 0.16/0.48 (assert (forall ((Xs tptp.list_list_a) (X tptp.list_a) (Ys tptp.list_list_a)) (= (= (@ (@ tptp.append_list_a Xs) (@ (@ tptp.cons_list_a X) tptp.nil_list_a)) Ys) (and (not (= Ys tptp.nil_list_a)) (= (@ tptp.butlast_list_a Ys) Xs) (= (@ tptp.last_list_a Ys) X)))))
% 0.44/0.72 (assert (forall ((Xs tptp.list_a) (X tptp.a) (Ys tptp.list_a)) (= (= (@ (@ tptp.append_a Xs) (@ (@ tptp.cons_a X) tptp.nil_a)) Ys) (and (not (= Ys tptp.nil_a)) (= (@ tptp.butlast_a Ys) Xs) (= (@ tptp.last_a Ys) X)))))
% 0.44/0.72 (assert (forall ((Ys tptp.list_list_a) (Xs tptp.list_list_a)) (=> (not (= Ys tptp.nil_list_a)) (= (@ tptp.last_list_a (@ (@ tptp.append_list_a Xs) Ys)) (@ tptp.last_list_a Ys)))))
% 0.44/0.72 (assert (forall ((Ys tptp.list_a) (Xs tptp.list_a)) (=> (not (= Ys tptp.nil_a)) (= (@ tptp.last_a (@ (@ tptp.append_a Xs) Ys)) (@ tptp.last_a Ys)))))
% 0.44/0.72 (assert (forall ((Ys tptp.list_a) (Xs tptp.list_a)) (=> (= Ys tptp.nil_a) (= (@ tptp.last_a (@ (@ tptp.append_a Xs) Ys)) (@ tptp.last_a Xs)))))
% 0.44/0.72 (assert (= tptp.b (@ (@ tptp.inf tptp.b) tptp.c)))
% 0.44/0.72 (assert (= (@ (@ tptp.inf tptp.c) (@ (@ tptp.sup tptp.b) tptp.c)) tptp.b))
% 0.44/0.72 (assert (= tptp.a2 (@ (@ tptp.sup tptp.b) tptp.c)))
% 0.44/0.72 (assert (@ (@ tptp.less tptp.b) (@ (@ tptp.sup tptp.b) tptp.c)))
% 0.44/0.72 (assert (= (@ (@ tptp.inf tptp.c) (@ (@ tptp.sup tptp.b) tptp.c)) tptp.c))
% 0.44/0.72 (assert (not false))
% 0.44/0.72 (set-info :filename cvc5---1.0.5_32324)
% 0.44/0.72 (check-sat-assuming ( true ))
% 0.44/0.72 ------- get file name : TPTP file name is ITP119^1
% 0.44/0.72 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_32324.smt2...
% 0.44/0.72 --- Run --ho-elim --full-saturate-quant at 10...
% 0.44/0.72 % SZS status Theorem for ITP119^1
% 0.44/0.72 % SZS output start Proof for ITP119^1
% 0.44/0.72 (
% 0.44/0.72 (let ((_let_1 (@ (@ tptp.sup tptp.b) tptp.c))) (let ((_let_2 (@ (@ tptp.inf tptp.c) _let_1))) (let ((_let_3 (= _let_2 tptp.c))) (let ((_let_4 (@ (@ tptp.less tptp.b) _let_1))) (let ((_let_5 (= _let_2 tptp.b))) (let ((_let_6 (@ (@ tptp.cons_list_a tptp.nil_a) tptp.nil_list_a))) (let ((_let_7 (@ (@ tptp.cons_list_list_a tptp.nil_list_a) tptp.nil_list_list_a))) (let ((_let_8 (forall ((A tptp.a)) (= (@ (@ tptp.sup A) A) A)))) (let ((_let_9 (forall ((B tptp.a) (A tptp.a)) (=> (@ (@ tptp.less B) A) (not (@ (@ tptp.less A) B)))))) (let ((_let_10 (ho_34 k_36 tptp.b))) (let ((_let_11 (ho_35 _let_10 tptp.c))) (let ((_let_12 (ho_35 (ho_34 k_33 tptp.c) _let_11))) (let ((_let_13 (= tptp.b _let_12))) (let ((_let_14 (ho_11 (ho_6 k_32 tptp.b) _let_11))) (let ((_let_15 (= tptp.c _let_12))) (let ((_let_16 (= tptp.c (ho_35 (ho_34 k_36 tptp.c) tptp.c)))) (let ((_let_17 (ho_11 (ho_6 k_32 _let_11) tptp.b))) (let ((_let_18 (EQ_RESOLVE (ASSUME :args (_let_5)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (= tptp.b _let_2) _let_13))))))) (let ((_let_19 (EQ_RESOLVE (ASSUME :args (_let_4)) (PREPROCESS :args ((= _let_4 _let_14)))))) (let ((_let_20 (EQ_RESOLVE (ASSUME :args (_let_3)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (= tptp.c _let_2) _let_15))))))) (let ((_let_21 (forall ((A tptp.a)) (= A (ho_35 (ho_34 k_36 A) A))))) (let ((_let_22 (EQ_RESOLVE (ASSUME :args (_let_8)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((A tptp.a)) (= A (@ (@ tptp.sup A) A))) _let_21))))))) (let ((_let_23 (not _let_17))) (let ((_let_24 (not _let_14))) (let ((_let_25 (or _let_24 _let_23))) (let ((_let_26 (forall ((B tptp.a) (A tptp.a)) (or (not (ho_11 (ho_6 k_32 B) A)) (not (ho_11 (ho_6 k_32 A) B)))))) (let ((_let_27 (forall ((u |u_(-> tptp.list_a tptp.list_list_a Bool)|) (e |u_(-> tptp.list_list_a Bool)|) (i tptp.list_a)) (not (forall ((v |u_(-> tptp.list_a tptp.list_list_a Bool)|)) (not (forall ((ii tptp.list_a)) (= (ho_61 v ii) (ite (= i ii) e (ho_61 u ii)))))))))) (let ((_let_28 (forall ((x |u_(-> tptp.list_a tptp.list_list_a Bool)|) (y |u_(-> tptp.list_a tptp.list_list_a Bool)|)) (or (not (forall ((z tptp.list_a)) (= (ho_61 x z) (ho_61 y z)))) (= x y))))) (let ((_let_29 (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_88 v ii) (ite (= i ii) e (ho_88 u ii)))))))))) (let ((_let_30 (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_88 x z) (ho_88 y z)))) (= x y))))) (let ((_let_31 (forall ((u |u_(-> _u_(-> tptp.list_a tptp.a)_ tptp.list_list_a tptp.list_a Bool)|) (e |u_(-> tptp.list_list_a tptp.list_a Bool)|) (i |u_(-> tptp.list_a tptp.a)|)) (not (forall ((v |u_(-> _u_(-> tptp.list_a tptp.a)_ tptp.list_list_a tptp.list_a Bool)|)) (not (forall ((ii |u_(-> tptp.list_a tptp.a)|)) (= (ho_57 v ii) (ite (= i ii) e (ho_57 u ii)))))))))) (let ((_let_32 (forall ((x |u_(-> _u_(-> tptp.list_a tptp.a)_ tptp.list_list_a tptp.list_a Bool)|) (y |u_(-> _u_(-> tptp.list_a tptp.a)_ tptp.list_list_a tptp.list_a Bool)|)) (or (not (forall ((z |u_(-> tptp.list_a tptp.a)|)) (= (ho_57 x z) (ho_57 y z)))) (= x y))))) (let ((_let_33 (forall ((u |u_(-> tptp.list_a tptp.a)|) (e tptp.a) (i tptp.list_a)) (not (forall ((v |u_(-> tptp.list_a tptp.a)|)) (not (forall ((ii tptp.list_a)) (= (ho_56 v ii) (ite (= i ii) e (ho_56 u ii)))))))))) (let ((_let_34 (forall ((x |u_(-> tptp.list_a tptp.a)|) (y |u_(-> tptp.list_a tptp.a)|)) (or (not (forall ((z tptp.list_a)) (= (ho_56 x z) (ho_56 y z)))) (= x y))))) (let ((_let_35 (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_55 v ii) (ite (= i ii) e (ho_55 u ii)))))))))) (let ((_let_36 (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_55 x z) (ho_55 y z)))) (= x y))))) (let ((_let_37 (forall ((u |u_(-> _u_(-> tptp.list_a tptp.list_a)_ tptp.list_list_a tptp.list_a)|) (e |u_(-> tptp.list_list_a tptp.list_a)|) (i |u_(-> tptp.list_a tptp.list_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.list_a tptp.list_a)_ tptp.list_list_a tptp.list_a)|)) (not (forall ((ii |u_(-> tptp.list_a tptp.list_a)|)) (= (ho_98 v ii) (ite (= i ii) e (ho_98 u ii)))))))))) (let ((_let_38 (forall ((x |u_(-> _u_(-> tptp.list_a tptp.list_a)_ tptp.list_list_a tptp.list_a)|) (y |u_(-> _u_(-> tptp.list_a tptp.list_a)_ tptp.list_list_a tptp.list_a)|)) (or (not (forall ((z |u_(-> tptp.list_a tptp.list_a)|)) (= (ho_98 x z) (ho_98 y z)))) (= x y))))) (let ((_let_39 (forall ((u |u_(-> _u_(-> tptp.a tptp.a tptp.a)_ Bool)|) (e Bool) (i |u_(-> tptp.a tptp.a tptp.a)|)) (not (forall ((v |u_(-> _u_(-> tptp.a tptp.a tptp.a)_ Bool)|)) (not (forall ((ii |u_(-> tptp.a tptp.a tptp.a)|)) (= (ho_50 v ii) (ite (= i ii) e (ho_50 u ii)))))))))) (let ((_let_40 (forall ((x |u_(-> _u_(-> tptp.a tptp.a tptp.a)_ Bool)|) (y |u_(-> _u_(-> tptp.a tptp.a tptp.a)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.a tptp.a tptp.a)|)) (= (ho_50 x z) (ho_50 y z)))) (= x y))))) (let ((_let_41 (forall ((u |u_(-> tptp.a tptp.a tptp.a tptp.a)|) (e |u_(-> tptp.a tptp.a tptp.a)|) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.a tptp.a tptp.a)|)) (not (forall ((ii tptp.a)) (= (ho_47 v ii) (ite (= i ii) e (ho_47 u ii)))))))))) (let ((_let_42 (forall ((x |u_(-> tptp.a tptp.a tptp.a tptp.a)|) (y |u_(-> tptp.a tptp.a tptp.a tptp.a)|)) (or (not (forall ((z tptp.a)) (= (ho_47 x z) (ho_47 y z)))) (= x y))))) (let ((_let_43 (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_35 v ii) (ite (= i ii) e (ho_35 u ii)))))))))) (let ((_let_44 (forall ((x |u_(-> tptp.a tptp.a)|) (y |u_(-> tptp.a tptp.a)|)) (or (not (forall ((z tptp.a)) (= (ho_35 x z) (ho_35 y z)))) (= x y))))) (let ((_let_45 (forall ((u |u_(-> _u_(-> tptp.list_a tptp.list_list_a)_ tptp.list_list_a tptp.list_list_a)|) (e |u_(-> tptp.list_list_a tptp.list_list_a)|) (i |u_(-> tptp.list_a tptp.list_list_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.list_a tptp.list_list_a)_ tptp.list_list_a tptp.list_list_a)|)) (not (forall ((ii |u_(-> tptp.list_a tptp.list_list_a)|)) (= (ho_100 v ii) (ite (= i ii) e (ho_100 u ii)))))))))) (let ((_let_46 (forall ((x |u_(-> _u_(-> tptp.list_a tptp.list_list_a)_ tptp.list_list_a tptp.list_list_a)|) (y |u_(-> _u_(-> tptp.list_a tptp.list_list_a)_ tptp.list_list_a tptp.list_list_a)|)) (or (not (forall ((z |u_(-> tptp.list_a tptp.list_list_a)|)) (= (ho_100 x z) (ho_100 y z)))) (= x y))))) (let ((_let_47 (forall ((u |u_(-> _u_(-> tptp.a tptp.a tptp.a)_ tptp.a tptp.a tptp.a tptp.a)|) (e |u_(-> tptp.a tptp.a tptp.a tptp.a)|) (i |u_(-> tptp.a tptp.a tptp.a)|)) (not (forall ((v |u_(-> _u_(-> tptp.a tptp.a tptp.a)_ tptp.a tptp.a tptp.a tptp.a)|)) (not (forall ((ii |u_(-> tptp.a tptp.a tptp.a)|)) (= (ho_46 v ii) (ite (= i ii) e (ho_46 u ii)))))))))) (let ((_let_48 (forall ((x |u_(-> _u_(-> tptp.a tptp.a tptp.a)_ tptp.a tptp.a tptp.a tptp.a)|) (y |u_(-> _u_(-> tptp.a tptp.a tptp.a)_ tptp.a tptp.a tptp.a tptp.a)|)) (or (not (forall ((z |u_(-> tptp.a tptp.a tptp.a)|)) (= (ho_46 x z) (ho_46 y z)))) (= x y))))) (let ((_let_49 (forall ((u |u_(-> _u_(-> tptp.list_a tptp.list_a)_ tptp.list_list_a tptp.list_list_a Bool)|) (e |u_(-> tptp.list_list_a tptp.list_list_a Bool)|) (i |u_(-> tptp.list_a tptp.list_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.list_a tptp.list_a)_ tptp.list_list_a tptp.list_list_a Bool)|)) (not (forall ((ii |u_(-> tptp.list_a tptp.list_a)|)) (= (ho_62 v ii) (ite (= i ii) e (ho_62 u ii)))))))))) (let ((_let_50 (forall ((x |u_(-> _u_(-> tptp.list_a tptp.list_a)_ tptp.list_list_a tptp.list_list_a Bool)|) (y |u_(-> _u_(-> tptp.list_a tptp.list_a)_ tptp.list_list_a tptp.list_list_a Bool)|)) (or (not (forall ((z |u_(-> tptp.list_a tptp.list_a)|)) (= (ho_62 x z) (ho_62 y z)))) (= x y))))) (let ((_let_51 (forall ((u |u_(-> _u_(-> tptp.a Bool)_ tptp.list_a Bool)|) (e |u_(-> tptp.list_a Bool)|) (i |u_(-> tptp.a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.a Bool)_ tptp.list_a Bool)|)) (not (forall ((ii |u_(-> tptp.a Bool)|)) (= (ho_116 v ii) (ite (= i ii) e (ho_116 u ii)))))))))) (let ((_let_52 (forall ((x |u_(-> _u_(-> tptp.a Bool)_ tptp.list_a Bool)|) (y |u_(-> _u_(-> tptp.a Bool)_ tptp.list_a Bool)|)) (or (not (forall ((z |u_(-> tptp.a Bool)|)) (= (ho_116 x z) (ho_116 y z)))) (= x y))))) (let ((_let_53 (forall ((u |u_(-> tptp.list_list_a tptp.list_a Bool)|) (e |u_(-> tptp.list_a Bool)|) (i tptp.list_list_a)) (not (forall ((v |u_(-> tptp.list_list_a tptp.list_a Bool)|)) (not (forall ((ii tptp.list_list_a)) (= (ho_58 v ii) (ite (= i ii) e (ho_58 u ii)))))))))) (let ((_let_54 (forall ((x |u_(-> tptp.list_list_a tptp.list_a Bool)|) (y |u_(-> tptp.list_list_a tptp.list_a Bool)|)) (or (not (forall ((z tptp.list_list_a)) (= (ho_58 x z) (ho_58 y z)))) (= x y))))) (let ((_let_55 (forall ((u |u_(-> _u_(-> tptp.a tptp.a tptp.a)_ _u_(-> tptp.a tptp.a Bool)_ _u_(-> tptp.a tptp.a tptp.a)_ tptp.a tptp.a tptp.a Bool)|) (e |u_(-> _u_(-> tptp.a tptp.a Bool)_ _u_(-> tptp.a tptp.a tptp.a)_ tptp.a tptp.a tptp.a Bool)|) (i |u_(-> tptp.a tptp.a tptp.a)|)) (not (forall ((v |u_(-> _u_(-> tptp.a tptp.a tptp.a)_ _u_(-> tptp.a tptp.a Bool)_ _u_(-> tptp.a tptp.a tptp.a)_ tptp.a tptp.a tptp.a Bool)|)) (not (forall ((ii |u_(-> tptp.a tptp.a tptp.a)|)) (= (ho_38 v ii) (ite (= i ii) e (ho_38 u ii)))))))))) (let ((_let_56 (forall ((x |u_(-> _u_(-> tptp.a tptp.a tptp.a)_ _u_(-> tptp.a tptp.a Bool)_ _u_(-> tptp.a tptp.a tptp.a)_ tptp.a tptp.a tptp.a Bool)|) (y |u_(-> _u_(-> tptp.a tptp.a tptp.a)_ _u_(-> tptp.a tptp.a Bool)_ _u_(-> tptp.a tptp.a tptp.a)_ tptp.a tptp.a tptp.a Bool)|)) (or (not (forall ((z |u_(-> tptp.a tptp.a tptp.a)|)) (= (ho_38 x z) (ho_38 y z)))) (= x y))))) (let ((_let_57 (forall ((u |u_(-> tptp.list_list_a _u_(-> tptp.list_a tptp.list_a)_ tptp.list_a)|) (e |u_(-> _u_(-> tptp.list_a tptp.list_a)_ tptp.list_a)|) (i tptp.list_list_a)) (not (forall ((v |u_(-> tptp.list_list_a _u_(-> tptp.list_a tptp.list_a)_ tptp.list_a)|)) (not (forall ((ii tptp.list_list_a)) (= (ho_81 v ii) (ite (= i ii) e (ho_81 u ii)))))))))) (let ((_let_58 (forall ((x |u_(-> tptp.list_list_a _u_(-> tptp.list_a tptp.list_a)_ tptp.list_a)|) (y |u_(-> tptp.list_list_a _u_(-> tptp.list_a tptp.list_a)_ tptp.list_a)|)) (or (not (forall ((z tptp.list_list_a)) (= (ho_81 x z) (ho_81 y z)))) (= x y))))) (let ((_let_59 (forall ((u |u_(-> tptp.a tptp.a tptp.a Bool)|) (e |u_(-> tptp.a tptp.a Bool)|) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.a tptp.a Bool)|)) (not (forall ((ii tptp.a)) (= (ho_41 v ii) (ite (= i ii) e (ho_41 u ii)))))))))) (let ((_let_60 (forall ((x |u_(-> tptp.a tptp.a tptp.a Bool)|) (y |u_(-> tptp.a tptp.a tptp.a Bool)|)) (or (not (forall ((z tptp.a)) (= (ho_41 x z) (ho_41 y z)))) (= x y))))) (let ((_let_61 (forall ((u |u_(-> _u_(-> tptp.a tptp.a tptp.a)_ _u_(-> tptp.a tptp.a tptp.a)_ tptp.a tptp.a tptp.a tptp.a)|) (e |u_(-> _u_(-> tptp.a tptp.a tptp.a)_ tptp.a tptp.a tptp.a tptp.a)|) (i |u_(-> tptp.a tptp.a tptp.a)|)) (not (forall ((v |u_(-> _u_(-> tptp.a tptp.a tptp.a)_ _u_(-> tptp.a tptp.a tptp.a)_ tptp.a tptp.a tptp.a tptp.a)|)) (not (forall ((ii |u_(-> tptp.a tptp.a tptp.a)|)) (= (ho_45 v ii) (ite (= i ii) e (ho_45 u ii)))))))))) (let ((_let_62 (forall ((x |u_(-> _u_(-> tptp.a tptp.a tptp.a)_ _u_(-> tptp.a tptp.a tptp.a)_ tptp.a tptp.a tptp.a tptp.a)|) (y |u_(-> _u_(-> tptp.a tptp.a tptp.a)_ _u_(-> tptp.a tptp.a tptp.a)_ tptp.a tptp.a tptp.a tptp.a)|)) (or (not (forall ((z |u_(-> tptp.a tptp.a tptp.a)|)) (= (ho_45 x z) (ho_45 y z)))) (= x y))))) (let ((_let_63 (forall ((u |u_(-> tptp.list_a _u_(-> tptp.a tptp.list_list_a)_ tptp.list_list_a)|) (e |u_(-> _u_(-> tptp.a tptp.list_list_a)_ tptp.list_list_a)|) (i tptp.list_a)) (not (forall ((v |u_(-> tptp.list_a _u_(-> tptp.a tptp.list_list_a)_ tptp.list_list_a)|)) (not (forall ((ii tptp.list_a)) (= (ho_78 v ii) (ite (= i ii) e (ho_78 u ii)))))))))) (let ((_let_64 (forall ((x |u_(-> tptp.list_a _u_(-> tptp.a tptp.list_list_a)_ tptp.list_list_a)|) (y |u_(-> tptp.list_a _u_(-> tptp.a tptp.list_list_a)_ tptp.list_list_a)|)) (or (not (forall ((z tptp.list_a)) (= (ho_78 x z) (ho_78 y z)))) (= x y))))) (let ((_let_65 (forall ((u |u_(-> tptp.a tptp.a tptp.a)|) (e |u_(-> tptp.a tptp.a)|) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.a tptp.a)|)) (not (forall ((ii tptp.a)) (= (ho_34 v ii) (ite (= i ii) e (ho_34 u ii)))))))))) (let ((_let_66 (forall ((x |u_(-> tptp.a tptp.a tptp.a)|) (y |u_(-> tptp.a tptp.a tptp.a)|)) (or (not (forall ((z tptp.a)) (= (ho_34 x z) (ho_34 y z)))) (= x y))))) (let ((_let_67 (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_9 v ii) (ite (= i ii) e (ho_9 u ii)))))))))) (let ((_let_68 (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_9 x z) (ho_9 y z)))) (= x y))))) (let ((_let_69 (forall ((u |u_(-> _u_(-> tptp.list_a tptp.list_a Bool)_ tptp.list_list_a Bool)|) (e |u_(-> tptp.list_list_a Bool)|) (i |u_(-> tptp.list_a tptp.list_a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.list_a tptp.list_a Bool)_ tptp.list_list_a Bool)|)) (not (forall ((ii |u_(-> tptp.list_a tptp.list_a Bool)|)) (= (ho_64 v ii) (ite (= i ii) e (ho_64 u ii)))))))))) (let ((_let_70 (forall ((x |u_(-> _u_(-> tptp.list_a tptp.list_a Bool)_ tptp.list_list_a Bool)|) (y |u_(-> _u_(-> tptp.list_a tptp.list_a Bool)_ tptp.list_list_a Bool)|)) (or (not (forall ((z |u_(-> tptp.list_a tptp.list_a Bool)|)) (= (ho_64 x z) (ho_64 y z)))) (= x y))))) (let ((_let_71 (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_71 v ii) (ite (= i ii) e (ho_71 u ii)))))))))) (let ((_let_72 (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_71 x z) (ho_71 y z)))) (= x y))))) (let ((_let_73 (forall ((u |u_(-> _u_(-> tptp.a tptp.a tptp.a)_ tptp.a tptp.a tptp.a Bool)|) (e |u_(-> tptp.a tptp.a tptp.a Bool)|) (i |u_(-> tptp.a tptp.a tptp.a)|)) (not (forall ((v |u_(-> _u_(-> tptp.a tptp.a tptp.a)_ tptp.a tptp.a tptp.a Bool)|)) (not (forall ((ii |u_(-> tptp.a tptp.a tptp.a)|)) (= (ho_40 v ii) (ite (= i ii) e (ho_40 u ii)))))))))) (let ((_let_74 (forall ((x |u_(-> _u_(-> tptp.a tptp.a tptp.a)_ tptp.a tptp.a tptp.a Bool)|) (y |u_(-> _u_(-> tptp.a tptp.a tptp.a)_ tptp.a tptp.a tptp.a Bool)|)) (or (not (forall ((z |u_(-> tptp.a tptp.a tptp.a)|)) (= (ho_40 x z) (ho_40 y z)))) (= x y))))) (let ((_let_75 (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_13 v ii) (ite (= i ii) e (ho_13 u ii)))))))))) (let ((_let_76 (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_13 x z) (ho_13 y z)))) (= x y))))) (let ((_let_77 (forall ((u |u_(-> tptp.a tptp.a Bool)|) (e |u_(-> tptp.a Bool)|) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.a Bool)|)) (not (forall ((ii tptp.a)) (= (ho_6 v ii) (ite (= i ii) e (ho_6 u ii)))))))))) (let ((_let_78 (forall ((x |u_(-> tptp.a tptp.a Bool)|) (y |u_(-> tptp.a tptp.a Bool)|)) (or (not (forall ((z tptp.a)) (= (ho_6 x z) (ho_6 y z)))) (= x y))))) (let ((_let_79 (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_89 v ii) (ite (= i ii) e (ho_89 u ii)))))))))) (let ((_let_80 (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_89 x z) (ho_89 y z)))) (= x y))))) (let ((_let_81 (forall ((u |u_(-> _u_(-> tptp.a tptp.a Bool)_ tptp.list_a tptp.list_a Bool)|) (e |u_(-> tptp.list_a tptp.list_a Bool)|) (i |u_(-> tptp.a tptp.a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.a tptp.a Bool)_ tptp.list_a tptp.list_a Bool)|)) (not (forall ((ii |u_(-> tptp.a tptp.a Bool)|)) (= (ho_8 v ii) (ite (= i ii) e (ho_8 u ii)))))))))) (let ((_let_82 (forall ((x |u_(-> _u_(-> tptp.a tptp.a Bool)_ tptp.list_a tptp.list_a Bool)|) (y |u_(-> _u_(-> tptp.a tptp.a Bool)_ tptp.list_a tptp.list_a Bool)|)) (or (not (forall ((z |u_(-> tptp.a tptp.a Bool)|)) (= (ho_8 x z) (ho_8 y z)))) (= x y))))) (let ((_let_83 (forall ((u |u_(-> tptp.list_list_a tptp.list_list_a Bool)|) (e |u_(-> tptp.list_list_a Bool)|) (i tptp.list_list_a)) (not (forall ((v |u_(-> tptp.list_list_a tptp.list_list_a Bool)|)) (not (forall ((ii tptp.list_list_a)) (= (ho_22 v ii) (ite (= i ii) e (ho_22 u ii)))))))))) (let ((_let_84 (forall ((x |u_(-> tptp.list_list_a tptp.list_list_a Bool)|) (y |u_(-> tptp.list_list_a tptp.list_list_a Bool)|)) (or (not (forall ((z tptp.list_list_a)) (= (ho_22 x z) (ho_22 y z)))) (= x y))))) (let ((_let_85 (forall ((u |u_(-> tptp.a tptp.list_list_a)|) (e tptp.list_list_a) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.list_list_a)|)) (not (forall ((ii tptp.a)) (= (ho_76 v ii) (ite (= i ii) e (ho_76 u ii)))))))))) (let ((_let_86 (forall ((x |u_(-> tptp.a tptp.list_list_a)|) (y |u_(-> tptp.a tptp.list_list_a)|)) (or (not (forall ((z tptp.a)) (= (ho_76 x z) (ho_76 y z)))) (= x y))))) (let ((_let_87 (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_26 v ii) (ite (= i ii) e (ho_26 u ii)))))))))) (let ((_let_88 (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_26 x z) (ho_26 y z)))) (= x y))))) (let ((_let_89 (forall ((u |u_(-> tptp.a Bool)|) (e Bool) (i tptp.a)) (not (forall ((v |u_(-> tptp.a Bool)|)) (not (forall ((ii tptp.a)) (= (ho_11 v ii) (ite (= i ii) e (ho_11 u ii)))))))))) (let ((_let_90 (forall ((x |u_(-> tptp.a Bool)|) (y |u_(-> tptp.a Bool)|)) (or (not (forall ((z tptp.a)) (= (ho_11 x z) (ho_11 y z)))) (= x y))))) (let ((_let_91 (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_14 v ii) (ite (= i ii) e (ho_14 u ii)))))))))) (let ((_let_92 (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_14 x z) (ho_14 y z)))) (= x y))))) (let ((_let_93 (forall ((u |u_(-> _u_(-> tptp.a tptp.a Bool)_ _u_(-> tptp.a tptp.a tptp.a)_ tptp.a tptp.a tptp.a Bool)|) (e |u_(-> _u_(-> tptp.a tptp.a tptp.a)_ tptp.a tptp.a tptp.a Bool)|) (i |u_(-> tptp.a tptp.a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.a tptp.a Bool)_ _u_(-> tptp.a tptp.a tptp.a)_ tptp.a tptp.a tptp.a Bool)|)) (not (forall ((ii |u_(-> tptp.a tptp.a Bool)|)) (= (ho_39 v ii) (ite (= i ii) e (ho_39 u ii)))))))))) (let ((_let_94 (forall ((x |u_(-> _u_(-> tptp.a tptp.a Bool)_ _u_(-> tptp.a tptp.a tptp.a)_ tptp.a tptp.a tptp.a Bool)|) (y |u_(-> _u_(-> tptp.a tptp.a Bool)_ _u_(-> tptp.a tptp.a tptp.a)_ tptp.a tptp.a tptp.a Bool)|)) (or (not (forall ((z |u_(-> tptp.a tptp.a Bool)|)) (= (ho_39 x z) (ho_39 y z)))) (= x y))))) (let ((_let_95 (forall ((u |u_(-> tptp.list_list_list_a tptp.list_list_a)|) (e tptp.list_list_a) (i tptp.list_list_list_a)) (not (forall ((v |u_(-> tptp.list_list_list_a tptp.list_list_a)|)) (not (forall ((ii tptp.list_list_list_a)) (= (ho_16 v ii) (ite (= i ii) e (ho_16 u ii)))))))))) (let ((_let_96 (forall ((x |u_(-> tptp.list_list_list_a tptp.list_list_a)|) (y |u_(-> tptp.list_list_list_a tptp.list_list_a)|)) (or (not (forall ((z tptp.list_list_list_a)) (= (ho_16 x z) (ho_16 y z)))) (= x y))))) (let ((_let_97 (forall ((u |u_(-> tptp.list_list_a tptp.list_a)|) (e tptp.list_a) (i tptp.list_list_a)) (not (forall ((v |u_(-> tptp.list_list_a tptp.list_a)|)) (not (forall ((ii tptp.list_list_a)) (= (ho_18 v ii) (ite (= i ii) e (ho_18 u ii)))))))))) (let ((_let_98 (forall ((x |u_(-> tptp.list_list_a tptp.list_a)|) (y |u_(-> tptp.list_list_a tptp.list_a)|)) (or (not (forall ((z tptp.list_list_a)) (= (ho_18 x z) (ho_18 y z)))) (= x y))))) (let ((_let_99 (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_10 v ii) (ite (= i ii) e (ho_10 u ii)))))))))) (let ((_let_100 (forall ((x |u_(-> tptp.list_a Bool)|) (y |u_(-> tptp.list_a Bool)|)) (or (not (forall ((z tptp.list_a)) (= (ho_10 x z) (ho_10 y z)))) (= x y))))) (let ((_let_101 (forall ((u |u_(-> tptp.list_list_a Bool)|) (e Bool) (i tptp.list_list_a)) (not (forall ((v |u_(-> tptp.list_list_a Bool)|)) (not (forall ((ii tptp.list_list_a)) (= (ho_23 v ii) (ite (= i ii) e (ho_23 u ii)))))))))) (let ((_let_102 (forall ((x |u_(-> tptp.list_list_a Bool)|) (y |u_(-> tptp.list_list_a Bool)|)) (or (not (forall ((z tptp.list_list_a)) (= (ho_23 x z) (ho_23 y z)))) (= x y))))) (let ((_let_103 (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_25 v ii) (ite (= i ii) e (ho_25 u ii)))))))))) (let ((_let_104 (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_25 x z) (ho_25 y z)))) (= x y))))) (let ((_let_105 (forall ((u |u_(-> _u_(-> tptp.list_a tptp.list_a Bool)_ tptp.list_list_a tptp.list_list_a Bool)|) (e |u_(-> tptp.list_list_a tptp.list_list_a Bool)|) (i |u_(-> tptp.list_a tptp.list_a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.list_a tptp.list_a Bool)_ tptp.list_list_a tptp.list_list_a Bool)|)) (not (forall ((ii |u_(-> tptp.list_a tptp.list_a Bool)|)) (= (ho_21 v ii) (ite (= i ii) e (ho_21 u ii)))))))))) (let ((_let_106 (forall ((x |u_(-> _u_(-> tptp.list_a tptp.list_a Bool)_ tptp.list_list_a tptp.list_list_a Bool)|) (y |u_(-> _u_(-> tptp.list_a tptp.list_a Bool)_ tptp.list_list_a tptp.list_list_a Bool)|)) (or (not (forall ((z |u_(-> tptp.list_a tptp.list_a Bool)|)) (= (ho_21 x z) (ho_21 y z)))) (= x y))))) (let ((_let_107 (forall ((u |u_(-> _u_(-> tptp.list_list_a tptp.list_list_a tptp.list_list_a)_ Bool)|) (e Bool) (i |u_(-> tptp.list_list_a tptp.list_list_a tptp.list_list_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.list_list_a tptp.list_list_a tptp.list_list_a)_ Bool)|)) (not (forall ((ii |u_(-> tptp.list_list_a tptp.list_list_a tptp.list_list_a)|)) (= (ho_73 v ii) (ite (= i ii) e (ho_73 u ii)))))))))) (let ((_let_108 (forall ((x |u_(-> _u_(-> tptp.list_list_a tptp.list_list_a tptp.list_list_a)_ Bool)|) (y |u_(-> _u_(-> tptp.list_list_a tptp.list_list_a tptp.list_list_a)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.list_list_a tptp.list_list_a tptp.list_list_a)|)) (= (ho_73 x z) (ho_73 y z)))) (= x y))))) (let ((_let_109 (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_59 v ii) (ite (= i ii) e (ho_59 u ii)))))))))) (let ((_let_110 (forall ((x |u_(-> tptp.a tptp.list_a)|) (y |u_(-> tptp.a tptp.list_a)|)) (or (not (forall ((z tptp.a)) (= (ho_59 x z) (ho_59 y z)))) (= x y))))) (let ((_let_111 (forall ((u |u_(-> _u_(-> tptp.a tptp.list_a)_ tptp.list_a tptp.list_list_a Bool)|) (e |u_(-> tptp.list_a tptp.list_list_a Bool)|) (i |u_(-> tptp.a tptp.list_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.a tptp.list_a)_ tptp.list_a tptp.list_list_a Bool)|)) (not (forall ((ii |u_(-> tptp.a tptp.list_a)|)) (= (ho_60 v ii) (ite (= i ii) e (ho_60 u ii)))))))))) (let ((_let_112 (forall ((x |u_(-> _u_(-> tptp.a tptp.list_a)_ tptp.list_a tptp.list_list_a Bool)|) (y |u_(-> _u_(-> tptp.a tptp.list_a)_ tptp.list_a tptp.list_list_a Bool)|)) (or (not (forall ((z |u_(-> tptp.a tptp.list_a)|)) (= (ho_60 x z) (ho_60 y z)))) (= x y))))) (let ((_let_113 (forall ((u |u_(-> tptp.list_a tptp.list_list_a)|) (e tptp.list_list_a) (i tptp.list_a)) (not (forall ((v |u_(-> tptp.list_a tptp.list_list_a)|)) (not (forall ((ii tptp.list_a)) (= (ho_83 v ii) (ite (= i ii) e (ho_83 u ii)))))))))) (let ((_let_114 (forall ((x |u_(-> tptp.list_a tptp.list_list_a)|) (y |u_(-> tptp.list_a tptp.list_list_a)|)) (or (not (forall ((z tptp.list_a)) (= (ho_83 x z) (ho_83 y z)))) (= x y))))) (let ((_let_115 (forall ((u |u_(-> _u_(-> tptp.a tptp.a)_ tptp.list_a tptp.list_a Bool)|) (e |u_(-> tptp.list_a tptp.list_a Bool)|) (i |u_(-> tptp.a tptp.a)|)) (not (forall ((v |u_(-> _u_(-> tptp.a tptp.a)_ tptp.list_a tptp.list_a Bool)|)) (not (forall ((ii |u_(-> tptp.a tptp.a)|)) (= (ho_63 v ii) (ite (= i ii) e (ho_63 u ii)))))))))) (let ((_let_116 (forall ((x |u_(-> _u_(-> tptp.a tptp.a)_ tptp.list_a tptp.list_a Bool)|) (y |u_(-> _u_(-> tptp.a tptp.a)_ tptp.list_a tptp.list_a Bool)|)) (or (not (forall ((z |u_(-> tptp.a tptp.a)|)) (= (ho_63 x z) (ho_63 y z)))) (= x y))))) (let ((_let_117 (forall ((u |u_(-> _u_(-> tptp.a tptp.a Bool)_ Bool)|) (e Bool) (i |u_(-> tptp.a tptp.a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.a tptp.a Bool)_ Bool)|)) (not (forall ((ii |u_(-> tptp.a tptp.a Bool)|)) (= (ho_104 v ii) (ite (= i ii) e (ho_104 u ii)))))))))) (let ((_let_118 (forall ((x |u_(-> _u_(-> tptp.a tptp.a Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.a tptp.a Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.a tptp.a Bool)|)) (= (ho_104 x z) (ho_104 y z)))) (= x y))))) (let ((_let_119 (forall ((u |u_(-> _u_(-> tptp.a tptp.a Bool)_ tptp.list_a Bool)|) (e |u_(-> tptp.list_a Bool)|) (i |u_(-> tptp.a tptp.a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.a tptp.a Bool)_ tptp.list_a Bool)|)) (not (forall ((ii |u_(-> tptp.a tptp.a Bool)|)) (= (ho_65 v ii) (ite (= i ii) e (ho_65 u ii)))))))))) (let ((_let_120 (forall ((x |u_(-> _u_(-> tptp.a tptp.a Bool)_ tptp.list_a Bool)|) (y |u_(-> _u_(-> tptp.a tptp.a Bool)_ tptp.list_a Bool)|)) (or (not (forall ((z |u_(-> tptp.a tptp.a Bool)|)) (= (ho_65 x z) (ho_65 y z)))) (= x y))))) (let ((_let_121 (forall ((u |u_(-> tptp.list_list_a tptp.list_list_list_a tptp.list_list_list_a)|) (e |u_(-> tptp.list_list_list_a tptp.list_list_list_a)|) (i tptp.list_list_a)) (not (forall ((v |u_(-> tptp.list_list_a tptp.list_list_list_a tptp.list_list_list_a)|)) (not (forall ((ii tptp.list_list_a)) (= (ho_67 v ii) (ite (= i ii) e (ho_67 u ii)))))))))) (let ((_let_122 (forall ((x |u_(-> tptp.list_list_a tptp.list_list_list_a tptp.list_list_list_a)|) (y |u_(-> tptp.list_list_a tptp.list_list_list_a tptp.list_list_list_a)|)) (or (not (forall ((z tptp.list_list_a)) (= (ho_67 x z) (ho_67 y z)))) (= x y))))) (let ((_let_123 (forall ((u |u_(-> tptp.list_list_list_a tptp.list_list_list_a)|) (e tptp.list_list_list_a) (i tptp.list_list_list_a)) (not (forall ((v |u_(-> tptp.list_list_list_a tptp.list_list_list_a)|)) (not (forall ((ii tptp.list_list_list_a)) (= (ho_68 v ii) (ite (= i ii) e (ho_68 u ii)))))))))) (let ((_let_124 (forall ((x |u_(-> tptp.list_list_list_a tptp.list_list_list_a)|) (y |u_(-> tptp.list_list_list_a tptp.list_list_list_a)|)) (or (not (forall ((z tptp.list_list_list_a)) (= (ho_68 x z) (ho_68 y z)))) (= x y))))) (let ((_let_125 (forall ((u |u_(-> tptp.list_list_list_a tptp.list_list_list_a tptp.list_list_list_a)|) (e |u_(-> tptp.list_list_list_a tptp.list_list_list_a)|) (i tptp.list_list_list_a)) (not (forall ((v |u_(-> tptp.list_list_list_a tptp.list_list_list_a tptp.list_list_list_a)|)) (not (forall ((ii tptp.list_list_list_a)) (= (ho_108 v ii) (ite (= i ii) e (ho_108 u ii)))))))))) (let ((_let_126 (forall ((x |u_(-> tptp.list_list_list_a tptp.list_list_list_a tptp.list_list_list_a)|) (y |u_(-> tptp.list_list_list_a tptp.list_list_list_a tptp.list_list_list_a)|)) (or (not (forall ((z tptp.list_list_list_a)) (= (ho_108 x z) (ho_108 y z)))) (= x y))))) (let ((_let_127 (forall ((u |u_(-> _u_(-> tptp.a tptp.list_list_a)_ tptp.list_list_a)|) (e tptp.list_list_a) (i |u_(-> tptp.a tptp.list_list_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.a tptp.list_list_a)_ tptp.list_list_a)|)) (not (forall ((ii |u_(-> tptp.a tptp.list_list_a)|)) (= (ho_79 v ii) (ite (= i ii) e (ho_79 u ii)))))))))) (let ((_let_128 (forall ((x |u_(-> _u_(-> tptp.a tptp.list_list_a)_ tptp.list_list_a)|) (y |u_(-> _u_(-> tptp.a tptp.list_list_a)_ tptp.list_list_a)|)) (or (not (forall ((z |u_(-> tptp.a tptp.list_list_a)|)) (= (ho_79 x z) (ho_79 y z)))) (= x y))))) (let ((_let_129 (forall ((u |u_(-> _u_(-> tptp.list_a tptp.list_a)_ tptp.list_a)|) (e tptp.list_a) (i |u_(-> tptp.list_a tptp.list_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.list_a tptp.list_a)_ tptp.list_a)|)) (not (forall ((ii |u_(-> tptp.list_a tptp.list_a)|)) (= (ho_82 v ii) (ite (= i ii) e (ho_82 u ii)))))))))) (let ((_let_130 (forall ((x |u_(-> _u_(-> tptp.list_a tptp.list_a)_ tptp.list_a)|) (y |u_(-> _u_(-> tptp.list_a tptp.list_a)_ tptp.list_a)|)) (or (not (forall ((z |u_(-> tptp.list_a tptp.list_a)|)) (= (ho_82 x z) (ho_82 y z)))) (= x y))))) (let ((_let_131 (forall ((u |u_(-> _u_(-> tptp.list_a tptp.list_list_a)_ tptp.list_list_a)|) (e tptp.list_list_a) (i |u_(-> tptp.list_a tptp.list_list_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.list_a tptp.list_list_a)_ tptp.list_list_a)|)) (not (forall ((ii |u_(-> tptp.list_a tptp.list_list_a)|)) (= (ho_86 v ii) (ite (= i ii) e (ho_86 u ii)))))))))) (let ((_let_132 (forall ((x |u_(-> _u_(-> tptp.list_a tptp.list_list_a)_ tptp.list_list_a)|) (y |u_(-> _u_(-> tptp.list_a tptp.list_list_a)_ tptp.list_list_a)|)) (or (not (forall ((z |u_(-> tptp.list_a tptp.list_list_a)|)) (= (ho_86 x z) (ho_86 y z)))) (= x y))))) (let ((_let_133 (forall ((u |u_(-> _u_(-> tptp.list_a Bool)_ tptp.list_list_a Bool)|) (e |u_(-> tptp.list_list_a Bool)|) (i |u_(-> tptp.list_a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.list_a Bool)_ tptp.list_list_a Bool)|)) (not (forall ((ii |u_(-> tptp.list_a Bool)|)) (= (ho_114 v ii) (ite (= i ii) e (ho_114 u ii)))))))))) (let ((_let_134 (forall ((x |u_(-> _u_(-> tptp.list_a Bool)_ tptp.list_list_a Bool)|) (y |u_(-> _u_(-> tptp.list_a Bool)_ tptp.list_list_a Bool)|)) (or (not (forall ((z |u_(-> tptp.list_a Bool)|)) (= (ho_114 x z) (ho_114 y z)))) (= x y))))) (let ((_let_135 (forall ((u |u_(-> tptp.list_list_a _u_(-> tptp.list_a tptp.list_list_a)_ tptp.list_list_a)|) (e |u_(-> _u_(-> tptp.list_a tptp.list_list_a)_ tptp.list_list_a)|) (i tptp.list_list_a)) (not (forall ((v |u_(-> tptp.list_list_a _u_(-> tptp.list_a tptp.list_list_a)_ tptp.list_list_a)|)) (not (forall ((ii tptp.list_list_a)) (= (ho_85 v ii) (ite (= i ii) e (ho_85 u ii)))))))))) (let ((_let_136 (forall ((x |u_(-> tptp.list_list_a _u_(-> tptp.list_a tptp.list_list_a)_ tptp.list_list_a)|) (y |u_(-> tptp.list_list_a _u_(-> tptp.list_a tptp.list_list_a)_ tptp.list_list_a)|)) (or (not (forall ((z tptp.list_list_a)) (= (ho_85 x z) (ho_85 y z)))) (= x y))))) (let ((_let_137 (forall ((u |u_(-> tptp.list_list_a tptp.list_list_list_a)|) (e tptp.list_list_list_a) (i tptp.list_list_a)) (not (forall ((v |u_(-> tptp.list_list_a tptp.list_list_list_a)|)) (not (forall ((ii tptp.list_list_a)) (= (ho_93 v ii) (ite (= i ii) e (ho_93 u ii)))))))))) (let ((_let_138 (forall ((x |u_(-> tptp.list_list_a tptp.list_list_list_a)|) (y |u_(-> tptp.list_list_a tptp.list_list_list_a)|)) (or (not (forall ((z tptp.list_list_a)) (= (ho_93 x z) (ho_93 y z)))) (= x y))))) (let ((_let_139 (forall ((u |u_(-> _u_(-> tptp.list_a tptp.list_a tptp.list_a)_ Bool)|) (e Bool) (i |u_(-> tptp.list_a tptp.list_a tptp.list_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.list_a tptp.list_a tptp.list_a)_ Bool)|)) (not (forall ((ii |u_(-> tptp.list_a tptp.list_a tptp.list_a)|)) (= (ho_91 v ii) (ite (= i ii) e (ho_91 u ii)))))))))) (let ((_let_140 (forall ((x |u_(-> _u_(-> tptp.list_a tptp.list_a tptp.list_a)_ Bool)|) (y |u_(-> _u_(-> tptp.list_a tptp.list_a tptp.list_a)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.list_a tptp.list_a tptp.list_a)|)) (= (ho_91 x z) (ho_91 y z)))) (= x y))))) (let ((_let_141 (forall ((u |u_(-> _u_(-> tptp.a tptp.list_list_a)_ tptp.list_a tptp.list_list_a)|) (e |u_(-> tptp.list_a tptp.list_list_a)|) (i |u_(-> tptp.a tptp.list_list_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.a tptp.list_list_a)_ tptp.list_a tptp.list_list_a)|)) (not (forall ((ii |u_(-> tptp.a tptp.list_list_a)|)) (= (ho_96 v ii) (ite (= i ii) e (ho_96 u ii)))))))))) (let ((_let_142 (forall ((x |u_(-> _u_(-> tptp.a tptp.list_list_a)_ tptp.list_a tptp.list_list_a)|) (y |u_(-> _u_(-> tptp.a tptp.list_list_a)_ tptp.list_a tptp.list_list_a)|)) (or (not (forall ((z |u_(-> tptp.a tptp.list_list_a)|)) (= (ho_96 x z) (ho_96 y z)))) (= x y))))) (let ((_let_143 (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_102 v ii) (ite (= i ii) e (ho_102 u ii)))))))))) (let ((_let_144 (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_102 x z) (ho_102 y z)))) (= x y))))) (let ((_let_145 (forall ((BOUND_VARIABLE_11519 |u_(-> tptp.a tptp.a Bool)|) (BOUND_VARIABLE_11373 tptp.list_a) (BOUND_VARIABLE_11374 tptp.list_a)) (= (ho_10 (ho_9 (ho_8 k_19 BOUND_VARIABLE_11519) BOUND_VARIABLE_11373) BOUND_VARIABLE_11374) (or (and (= BOUND_VARIABLE_11373 (ho_18 k_17 (ho_16 k_15 tptp.nil_list_list_a))) (not (forall ((Y3 tptp.a) (Ys2 tptp.list_a)) (not (= BOUND_VARIABLE_11374 (ho_14 (ho_13 k_12 Y3) Ys2)))))) (not (forall ((X3 tptp.a) (Y3 tptp.a) (Xs2 tptp.list_a) (Ys2 tptp.list_a)) (or (not (= BOUND_VARIABLE_11373 (ho_14 (ho_13 k_12 X3) Xs2))) (not (= BOUND_VARIABLE_11374 (ho_14 (ho_13 k_12 Y3) Ys2))) (not (ho_11 (ho_6 BOUND_VARIABLE_11519 X3) Y3))))) (not (forall ((X3 tptp.a) (Y3 tptp.a) (Xs2 tptp.list_a) (Ys2 tptp.list_a)) (or (not (= BOUND_VARIABLE_11373 (ho_14 (ho_13 k_12 X3) Xs2))) (not (= BOUND_VARIABLE_11374 (ho_14 (ho_13 k_12 Y3) Ys2))) (ho_11 (ho_6 BOUND_VARIABLE_11519 X3) Y3) (ho_11 (ho_6 BOUND_VARIABLE_11519 Y3) X3) (not (ho_10 (ho_9 (ho_8 k_7 BOUND_VARIABLE_11519) Xs2) Ys2)))))))))) (let ((_let_146 (forall ((BOUND_VARIABLE_11605 |u_(-> tptp.list_a tptp.list_a Bool)|) (BOUND_VARIABLE_11333 tptp.list_list_a) (BOUND_VARIABLE_11334 tptp.list_list_a)) (= (ho_23 (ho_22 (ho_21 k_27 BOUND_VARIABLE_11605) BOUND_VARIABLE_11333) BOUND_VARIABLE_11334) (or (and (= BOUND_VARIABLE_11333 (ho_16 k_15 tptp.nil_list_list_a)) (not (forall ((Y3 tptp.list_a) (Ys2 tptp.list_list_a)) (not (= BOUND_VARIABLE_11334 (ho_26 (ho_25 k_24 Y3) Ys2)))))) (not (forall ((X3 tptp.list_a) (Y3 tptp.list_a) (Xs2 tptp.list_list_a) (Ys2 tptp.list_list_a)) (or (not (= BOUND_VARIABLE_11333 (ho_26 (ho_25 k_24 X3) Xs2))) (not (= BOUND_VARIABLE_11334 (ho_26 (ho_25 k_24 Y3) Ys2))) (not (ho_10 (ho_9 BOUND_VARIABLE_11605 X3) Y3))))) (not (forall ((X3 tptp.list_a) (Y3 tptp.list_a) (Xs2 tptp.list_list_a) (Ys2 tptp.list_list_a)) (or (not (= BOUND_VARIABLE_11333 (ho_26 (ho_25 k_24 X3) Xs2))) (not (= BOUND_VARIABLE_11334 (ho_26 (ho_25 k_24 Y3) Ys2))) (ho_10 (ho_9 BOUND_VARIABLE_11605 X3) Y3) (ho_10 (ho_9 BOUND_VARIABLE_11605 Y3) X3) (not (ho_23 (ho_22 (ho_21 k_20 BOUND_VARIABLE_11605) Xs2) Ys2)))))))))) (let ((_let_147 (forall ((BOUND_VARIABLE_11676 |u_(-> tptp.a tptp.a Bool)|) (BOUND_VARIABLE_11299 tptp.list_a) (BOUND_VARIABLE_11300 tptp.list_a)) (= (ho_10 (ho_9 (ho_8 k_29 BOUND_VARIABLE_11676) BOUND_VARIABLE_11299) BOUND_VARIABLE_11300) (or (= BOUND_VARIABLE_11299 (ho_18 k_17 (ho_16 k_15 tptp.nil_list_list_a))) (not (forall ((X3 tptp.a) (Y3 tptp.a) (Xs2 tptp.list_a) (Ys2 tptp.list_a)) (or (not (= BOUND_VARIABLE_11299 (ho_14 (ho_13 k_12 X3) Xs2))) (not (= BOUND_VARIABLE_11300 (ho_14 (ho_13 k_12 Y3) Ys2))) (not (ho_11 (ho_6 BOUND_VARIABLE_11676 X3) Y3))))) (not (forall ((X3 tptp.a) (Y3 tptp.a) (Xs2 tptp.list_a) (Ys2 tptp.list_a)) (or (not (= BOUND_VARIABLE_11299 (ho_14 (ho_13 k_12 X3) Xs2))) (not (= BOUND_VARIABLE_11300 (ho_14 (ho_13 k_12 Y3) Ys2))) (ho_11 (ho_6 BOUND_VARIABLE_11676 X3) Y3) (ho_11 (ho_6 BOUND_VARIABLE_11676 Y3) X3) (not (ho_10 (ho_9 (ho_8 k_28 BOUND_VARIABLE_11676) Xs2) Ys2)))))))))) (let ((_let_148 (forall ((BOUND_VARIABLE_11723 |u_(-> tptp.list_a tptp.list_a Bool)|) (BOUND_VARIABLE_11265 tptp.list_list_a) (BOUND_VARIABLE_11266 tptp.list_list_a)) (= (ho_23 (ho_22 (ho_21 k_31 BOUND_VARIABLE_11723) BOUND_VARIABLE_11265) BOUND_VARIABLE_11266) (or (= BOUND_VARIABLE_11265 (ho_16 k_15 tptp.nil_list_list_a)) (not (forall ((X3 tptp.list_a) (Y3 tptp.list_a) (Xs2 tptp.list_list_a) (Ys2 tptp.list_list_a)) (or (not (= BOUND_VARIABLE_11265 (ho_26 (ho_25 k_24 X3) Xs2))) (not (= BOUND_VARIABLE_11266 (ho_26 (ho_25 k_24 Y3) Ys2))) (not (ho_10 (ho_9 BOUND_VARIABLE_11723 X3) Y3))))) (not (forall ((X3 tptp.list_a) (Y3 tptp.list_a) (Xs2 tptp.list_list_a) (Ys2 tptp.list_list_a)) (or (not (= BOUND_VARIABLE_11265 (ho_26 (ho_25 k_24 X3) Xs2))) (not (= BOUND_VARIABLE_11266 (ho_26 (ho_25 k_24 Y3) Ys2))) (ho_10 (ho_9 BOUND_VARIABLE_11723 X3) Y3) (ho_10 (ho_9 BOUND_VARIABLE_11723 Y3) X3) (not (ho_23 (ho_22 (ho_21 k_30 BOUND_VARIABLE_11723) Xs2) Ys2)))))))))) (let ((_let_149 (forall ((BOUND_VARIABLE_11372 (-> tptp.a tptp.a Bool)) (BOUND_VARIABLE_11373 tptp.list_a) (BOUND_VARIABLE_11374 tptp.list_a)) (= (ll_5 BOUND_VARIABLE_11372 BOUND_VARIABLE_11373 BOUND_VARIABLE_11374) (or (and (= (@ tptp.concat_a (@ tptp.concat_list_a tptp.nil_list_list_a)) BOUND_VARIABLE_11373) (not (forall ((Y3 tptp.a) (Ys2 tptp.list_a)) (not (= (@ (@ tptp.cons_a Y3) Ys2) BOUND_VARIABLE_11374))))) (not (forall ((X3 tptp.a) (Y3 tptp.a) (Xs2 tptp.list_a) (Ys2 tptp.list_a)) (or (not (= (@ (@ tptp.cons_a X3) Xs2) BOUND_VARIABLE_11373)) (not (= (@ (@ tptp.cons_a Y3) Ys2) BOUND_VARIABLE_11374)) (not (@ (@ BOUND_VARIABLE_11372 X3) Y3))))) (not (forall ((X3 tptp.a) (Y3 tptp.a) (Xs2 tptp.list_a) (Ys2 tptp.list_a)) (or (not (= (@ (@ tptp.cons_a X3) Xs2) BOUND_VARIABLE_11373)) (not (= (@ (@ tptp.cons_a Y3) Ys2) BOUND_VARIABLE_11374)) (@ (@ BOUND_VARIABLE_11372 X3) Y3) (@ (@ BOUND_VARIABLE_11372 Y3) X3) (not (@ (@ (@ tptp.lexordp_a BOUND_VARIABLE_11372) Xs2) Ys2)))))))))) (let ((_let_150 (forall ((BOUND_VARIABLE_11332 (-> tptp.list_a tptp.list_a Bool)) (BOUND_VARIABLE_11333 tptp.list_list_a) (BOUND_VARIABLE_11334 tptp.list_list_a)) (= (ll_4 BOUND_VARIABLE_11332 BOUND_VARIABLE_11333 BOUND_VARIABLE_11334) (or (and (= (@ tptp.concat_list_a tptp.nil_list_list_a) BOUND_VARIABLE_11333) (not (forall ((Y3 tptp.list_a) (Ys2 tptp.list_list_a)) (not (= (@ (@ tptp.cons_list_a Y3) Ys2) BOUND_VARIABLE_11334))))) (not (forall ((X3 tptp.list_a) (Y3 tptp.list_a) (Xs2 tptp.list_list_a) (Ys2 tptp.list_list_a)) (or (not (= (@ (@ tptp.cons_list_a X3) Xs2) BOUND_VARIABLE_11333)) (not (= (@ (@ tptp.cons_list_a Y3) Ys2) BOUND_VARIABLE_11334)) (not (@ (@ BOUND_VARIABLE_11332 X3) Y3))))) (not (forall ((X3 tptp.list_a) (Y3 tptp.list_a) (Xs2 tptp.list_list_a) (Ys2 tptp.list_list_a)) (or (not (= (@ (@ tptp.cons_list_a X3) Xs2) BOUND_VARIABLE_11333)) (not (= (@ (@ tptp.cons_list_a Y3) Ys2) BOUND_VARIABLE_11334)) (@ (@ BOUND_VARIABLE_11332 X3) Y3) (@ (@ BOUND_VARIABLE_11332 Y3) X3) (not (@ (@ (@ tptp.lexordp_list_a BOUND_VARIABLE_11332) Xs2) Ys2)))))))))) (let ((_let_151 (forall ((BOUND_VARIABLE_11298 (-> tptp.a tptp.a Bool)) (BOUND_VARIABLE_11299 tptp.list_a) (BOUND_VARIABLE_11300 tptp.list_a)) (= (ll_3 BOUND_VARIABLE_11298 BOUND_VARIABLE_11299 BOUND_VARIABLE_11300) (or (= (@ tptp.concat_a (@ tptp.concat_list_a tptp.nil_list_list_a)) BOUND_VARIABLE_11299) (not (forall ((X3 tptp.a) (Y3 tptp.a) (Xs2 tptp.list_a) (Ys2 tptp.list_a)) (or (not (= (@ (@ tptp.cons_a X3) Xs2) BOUND_VARIABLE_11299)) (not (= (@ (@ tptp.cons_a Y3) Ys2) BOUND_VARIABLE_11300)) (not (@ (@ BOUND_VARIABLE_11298 X3) Y3))))) (not (forall ((X3 tptp.a) (Y3 tptp.a) (Xs2 tptp.list_a) (Ys2 tptp.list_a)) (or (not (= (@ (@ tptp.cons_a X3) Xs2) BOUND_VARIABLE_11299)) (not (= (@ (@ tptp.cons_a Y3) Ys2) BOUND_VARIABLE_11300)) (@ (@ BOUND_VARIABLE_11298 X3) Y3) (@ (@ BOUND_VARIABLE_11298 Y3) X3) (not (@ (@ (@ tptp.lexordp_eq_a BOUND_VARIABLE_11298) Xs2) Ys2)))))))))) (let ((_let_152 (forall ((BOUND_VARIABLE_11264 (-> tptp.list_a tptp.list_a Bool)) (BOUND_VARIABLE_11265 tptp.list_list_a) (BOUND_VARIABLE_11266 tptp.list_list_a)) (= (ll_2 BOUND_VARIABLE_11264 BOUND_VARIABLE_11265 BOUND_VARIABLE_11266) (or (= (@ tptp.concat_list_a tptp.nil_list_list_a) BOUND_VARIABLE_11265) (not (forall ((X3 tptp.list_a) (Y3 tptp.list_a) (Xs2 tptp.list_list_a) (Ys2 tptp.list_list_a)) (or (not (= (@ (@ tptp.cons_list_a X3) Xs2) BOUND_VARIABLE_11265)) (not (= (@ (@ tptp.cons_list_a Y3) Ys2) BOUND_VARIABLE_11266)) (not (@ (@ BOUND_VARIABLE_11264 X3) Y3))))) (not (forall ((X3 tptp.list_a) (Y3 tptp.list_a) (Xs2 tptp.list_list_a) (Ys2 tptp.list_list_a)) (or (not (= (@ (@ tptp.cons_list_a X3) Xs2) BOUND_VARIABLE_11265)) (not (= (@ (@ tptp.cons_list_a Y3) Ys2) BOUND_VARIABLE_11266)) (@ (@ BOUND_VARIABLE_11264 X3) Y3) (@ (@ BOUND_VARIABLE_11264 Y3) X3) (not (@ (@ (@ tptp.lexordp_eq_list_a BOUND_VARIABLE_11264) Xs2) Ys2)))))))))) (let ((_let_153 (and (forall ((B tptp.a) (A tptp.a)) (or (not (@ (@ tptp.less B) A)) (not (@ (@ tptp.less A) B)))) _let_152 _let_151 _let_150 _let_149))) (let ((_let_154 (_let_26))) (let ((_let_155 (ASSUME :args (_let_23)))) (let ((_let_156 (SYMM _let_20))) (let ((_let_157 (ASSUME :args (_let_16)))) (let ((_let_158 (APPLY_UF ho_35))) (let ((_let_159 (APPLY_UF ho_34))) (let ((_let_160 (TRANS _let_18 _let_156))) (let ((_let_161 (TRANS (CONG (CONG (REFL :args (k_33)) _let_160 :args _let_159) (REFL :args (_let_11)) :args _let_158) _let_156))) (let ((_let_162 (TRANS (CONG (REFL :args (_let_10)) (SYMM _let_161) :args _let_158) (CONG (CONG (REFL :args (k_36)) _let_160 :args _let_159) _let_161 :args _let_158) (SYMM _let_157) (SYMM _let_156) (SYMM _let_18)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_155 _let_20 _let_18 _let_157 _let_19) :args (_let_13 _let_14 _let_15 _let_16 _let_23)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_19)) (CONG (CONG (REFL :args (k_32)) (SYMM _let_162) :args (APPLY_UF ho_6)) _let_162 :args (APPLY_UF ho_11)) (FALSE_INTRO _let_155))) :args (_let_23 _let_15 _let_13 _let_16 _let_14)) :args ((not (and _let_13 _let_14 _let_15 _let_16 _let_23)) SB_LITERAL))) (CONG (REFL :args ((not _let_13))) (REFL :args (_let_24)) (REFL :args ((not _let_15))) (REFL :args ((not _let_16))) (MACRO_SR_PRED_INTRO :args ((= (not _let_23) _let_17))) :args (or))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_25)) :args ((or _let_24 _let_23 (not _let_25)))) _let_19 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_154) :args (tptp.b _let_11 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_154)) (AND_ELIM (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 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tptp.less C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup A) B))))) (forall ((C tptp.a) (B tptp.a) (A tptp.a)) (let ((_let_1 (@ tptp.less C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup A) B))))) (forall ((B tptp.a) (A tptp.a)) (= (@ (@ tptp.less B) A) (and (= A (@ (@ tptp.sup A) B)) (not (= A B))))) (forall ((X tptp.a) (Y tptp.a) (Z tptp.a)) (let ((_let_1 (@ tptp.sup X))) (=> (forall ((X2 tptp.a) (Y2 tptp.a) (Z2 tptp.a)) (let ((_let_1 (@ tptp.inf X2))) (= (@ _let_1 (@ (@ tptp.sup Y2) Z2)) (@ (@ tptp.sup (@ _let_1 Y2)) (@ _let_1 Z2))))) (= (@ _let_1 (@ (@ tptp.inf Y) Z)) (@ (@ tptp.inf (@ _let_1 Y)) (@ _let_1 Z)))))) (forall ((X tptp.a) (Y tptp.a) (Z tptp.a)) (let ((_let_1 (@ tptp.inf X))) (=> (forall ((X2 tptp.a) (Y2 tptp.a) (Z2 tptp.a)) (let ((_let_1 (@ tptp.sup X2))) (= (@ _let_1 (@ (@ tptp.inf Y2) Z2)) (@ (@ tptp.inf (@ _let_1 Y2)) (@ _let_1 Z2))))) (= (@ _let_1 (@ (@ tptp.sup Y) Z)) (@ (@ tptp.sup (@ _let_1 Y)) (@ _let_1 Z)))))) (forall ((A tptp.a)) (= (@ (@ tptp.inf A) A) A)) (forall ((A tptp.a) (B tptp.a)) (let ((_let_1 (@ tptp.inf A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))) (forall ((A tptp.a) (B tptp.a)) (let ((_let_1 (@ (@ tptp.inf A) B))) (= (@ (@ tptp.inf _let_1) B) _let_1))) (forall ((X tptp.a)) (= (@ (@ tptp.inf X) X) X)) (forall ((X tptp.a) (Y tptp.a)) (let ((_let_1 (@ tptp.inf X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))) (forall ((X tptp.a) (Y tptp.a)) (let ((_let_1 (@ (@ tptp.inf X) Y))) (= (@ (@ tptp.inf _let_1) Y) _let_1))) _let_8 (forall ((A tptp.a) (B tptp.a)) (let ((_let_1 (@ tptp.sup A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))) (forall ((A tptp.a) (B tptp.a)) (let ((_let_1 (@ (@ tptp.sup A) B))) (= (@ (@ tptp.sup _let_1) B) _let_1))) (forall ((X tptp.a)) (= (@ (@ tptp.sup X) X) X)) (forall ((X tptp.a) (Y tptp.a)) (let ((_let_1 (@ tptp.sup X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))) (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ (@ tptp.sup A) B))) (let ((_let_2 (@ (@ tptp.inf A) B))) (let ((_let_3 (@ (@ tptp.sup B) C))) (let ((_let_4 (@ (@ tptp.inf B) C))) (= (@ (@ (@ (@ (@ (@ tptp.modula1376131916tice_a tptp.inf) tptp.less) tptp.sup) A) B) C) (and (= _let_2 _let_4) (= (@ (@ tptp.inf C) A) _let_4) (= _let_1 _let_3) (= (@ (@ tptp.sup C) A) _let_3) (@ (@ tptp.less _let_2) _let_1)))))))) (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (= (@ (@ (@ (@ (@ (@ tptp.modula397570059tice_a tptp.inf) tptp.less) tptp.sup) A) B) C) (and (= (@ (@ tptp.inf A) C) (@ (@ tptp.inf B) C)) (@ (@ tptp.less A) B) (= (@ (@ tptp.sup A) C) (@ (@ tptp.sup B) C))))) (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.inf A))) (= (@ (@ (@ (@ (@ (@ tptp.modula1962211574trib_a tptp.inf) tptp.less) tptp.sup) A) B) C) (@ (@ tptp.less (@ (@ tptp.sup (@ _let_1 B)) (@ (@ tptp.inf C) A))) (@ _let_1 (@ (@ tptp.sup B) C)))))) (forall ((X tptp.a) (Y tptp.a)) (= (@ (@ tptp.inf X) (@ (@ tptp.sup X) Y)) X)) (forall ((X tptp.a) (Y tptp.a)) (= (@ (@ tptp.sup X) (@ (@ tptp.inf X) Y)) X)) (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.sup A))) (= (@ _let_1 (@ (@ (@ (@ (@ tptp.modula1936294176_aux_a tptp.inf) tptp.sup) A) B) C)) (@ _let_1 (@ (@ tptp.inf B) C))))) (forall ((B tptp.a) (A tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.sup B))) (= (@ _let_1 (@ (@ (@ (@ (@ tptp.modula1936294176_aux_a tptp.inf) tptp.sup) A) B) C)) (@ _let_1 (@ (@ tptp.inf C) A))))) (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (= (@ (@ (@ (@ (@ tptp.modula1936294176_aux_a tptp.inf) tptp.sup) A) B) C) (@ (@ tptp.sup (@ (@ tptp.sup (@ (@ tptp.inf A) B)) (@ (@ tptp.inf B) C))) (@ (@ tptp.inf C) A)))) (forall ((B tptp.a) (C tptp.a) (A tptp.a)) (let ((_let_1 (@ (@ tptp.modula1936294176_aux_a tptp.inf) tptp.sup))) (= (@ (@ (@ _let_1 B) C) A) (@ (@ (@ _let_1 A) B) C)))) (forall ((C tptp.a) (A tptp.a) (B tptp.a)) (let ((_let_1 (@ (@ tptp.modula1936294176_aux_a tptp.inf) tptp.sup))) (= (@ (@ (@ _let_1 C) A) B) (@ (@ (@ _let_1 A) B) C)))) (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.inf A))) (= (@ _let_1 (@ (@ (@ (@ (@ tptp.modula1144073633_aux_a tptp.inf) tptp.sup) A) B) C)) (@ _let_1 (@ (@ tptp.sup B) C))))) (forall ((B tptp.a) (A tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.inf B))) (= (@ _let_1 (@ (@ (@ (@ (@ tptp.modula1144073633_aux_a tptp.inf) tptp.sup) A) B) C)) (@ _let_1 (@ (@ tptp.sup C) A))))) (forall ((C tptp.a) (A tptp.a) (B tptp.a)) (let ((_let_1 (@ tptp.inf C))) (= (@ _let_1 (@ (@ (@ (@ (@ tptp.modula1144073633_aux_a tptp.inf) tptp.sup) A) B) C)) (@ _let_1 (@ (@ tptp.sup A) B))))) (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (= (@ (@ (@ (@ (@ tptp.modula1144073633_aux_a tptp.inf) tptp.sup) A) B) C) (@ (@ tptp.inf (@ (@ tptp.inf (@ (@ tptp.sup A) B)) (@ (@ tptp.sup B) C))) (@ (@ tptp.sup C) A)))) (forall ((B tptp.a) (C tptp.a) (A tptp.a)) (let ((_let_1 (@ (@ tptp.modula1144073633_aux_a tptp.inf) tptp.sup))) (= (@ (@ (@ _let_1 B) C) A) (@ (@ (@ _let_1 A) B) C)))) (forall ((C tptp.a) (A tptp.a) (B tptp.a)) (let ((_let_1 (@ (@ tptp.modula1144073633_aux_a tptp.inf) tptp.sup))) (= (@ (@ (@ _let_1 C) A) B) (@ (@ (@ _let_1 A) B) C)))) (@ tptp.finite40241356em_a_a tptp.sup) (@ tptp.finite40241356em_a_a tptp.inf) (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (= (@ (@ (@ (@ (@ tptp.modula581031071_aux_a tptp.inf) tptp.sup) A) B) C) (@ (@ tptp.sup (@ (@ tptp.inf C) (@ (@ (@ (@ (@ tptp.modula1144073633_aux_a tptp.inf) tptp.sup) A) B) C))) (@ (@ (@ (@ (@ tptp.modula1936294176_aux_a tptp.inf) tptp.sup) A) B) C)))) (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (= (@ (@ (@ (@ (@ tptp.modula1373251614_aux_a tptp.inf) tptp.sup) A) B) C) (@ (@ tptp.sup (@ (@ tptp.inf B) (@ (@ (@ (@ (@ tptp.modula1144073633_aux_a tptp.inf) tptp.sup) A) B) C))) (@ (@ (@ (@ (@ tptp.modula1936294176_aux_a tptp.inf) tptp.sup) A) B) C)))) (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (= (@ (@ (@ (@ (@ tptp.modula17988509_aux_a tptp.inf) tptp.sup) A) B) C) (@ (@ tptp.sup (@ (@ tptp.inf A) (@ (@ (@ (@ (@ tptp.modula1144073633_aux_a tptp.inf) tptp.sup) A) B) C))) (@ (@ (@ (@ (@ tptp.modula1936294176_aux_a tptp.inf) tptp.sup) A) B) C)))) (= tptp.modula1962211574trib_a tptp.modula1962211574trib_a) (= tptp.modula397570059tice_a tptp.modula397570059tice_a) (= tptp.modula1376131916tice_a tptp.modula1376131916tice_a) (= tptp.modula1144073633_aux_a tptp.modula1144073633_aux_a) (= tptp.modula1936294176_aux_a tptp.modula1936294176_aux_a) (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (= (@ (@ (@ (@ (@ tptp.modula581031071_aux_a tptp.inf) tptp.sup) A) B) C) (@ (@ (@ (@ (@ tptp.modula17988509_aux_a tptp.inf) tptp.sup) C) A) B))) (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (= (@ (@ (@ (@ (@ tptp.modula1373251614_aux_a tptp.inf) tptp.sup) A) B) C) (@ (@ (@ (@ (@ tptp.modula17988509_aux_a tptp.inf) tptp.sup) B) C) A))) (@ tptp.semigroup_a tptp.sup) (@ tptp.semigroup_a tptp.inf) (@ tptp.semilattice_a tptp.sup) (@ tptp.semilattice_a tptp.inf) (= tptp.modula17988509_aux_a tptp.modula17988509_aux_a) (= tptp.modula1373251614_aux_a tptp.modula1373251614_aux_a) (= tptp.modula581031071_aux_a tptp.modula581031071_aux_a) (@ tptp.abel_semigroup_a tptp.sup) (@ tptp.abel_semigroup_a tptp.inf) (@ tptp.lattic1885654924_set_a tptp.sup) (@ tptp.lattic1885654924_set_a tptp.inf) (forall ((Xs tptp.list_a)) (@ (@ (@ tptp.lexordp_eq_a tptp.less) Xs) Xs)) (forall ((Ys tptp.list_a)) (@ (@ (@ tptp.lexordp_eq_a tptp.less) tptp.nil_a) Ys)) (forall ((F (-> tptp.list_a tptp.list_a tptp.list_a))) (=> (@ tptp.abel_s1075322906list_a F) (@ tptp.semigroup_list_a F))) (forall ((F (-> tptp.a tptp.a tptp.a))) (=> (@ tptp.abel_semigroup_a F) (@ tptp.semigroup_a F))) (forall ((F (-> tptp.a tptp.a tptp.a))) (=> (@ tptp.lattic1885654924_set_a F) (@ tptp.semilattice_a F))) (forall ((F (-> tptp.a tptp.a tptp.a))) (=> (@ tptp.semilattice_a F) (@ tptp.lattic1885654924_set_a F))) (= tptp.lattic1885654924_set_a tptp.semilattice_a) (forall ((Ys tptp.list_a)) (@ (@ (@ tptp.lexordp_eq_a tptp.less) tptp.nil_a) Ys)) (forall ((Xs tptp.list_a)) (= (@ (@ (@ tptp.lexordp_eq_a tptp.less) Xs) tptp.nil_a) (= Xs tptp.nil_a))) (forall ((F (-> tptp.a tptp.a tptp.a)) (B tptp.a) (A tptp.a) (C tptp.a)) (let ((_let_1 (@ F B))) (let ((_let_2 (@ F A))) (=> (@ tptp.abel_semigroup_a F) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C))))))) (forall ((F (-> tptp.a tptp.a tptp.a)) (A tptp.a) (B tptp.a)) (=> (@ tptp.abel_semigroup_a F) (= (@ (@ F A) B) (@ (@ F B) A)))) (forall ((F (-> tptp.list_a tptp.list_a tptp.list_a))) (=> (forall ((A2 tptp.list_a) (B2 tptp.list_a) (C2 tptp.list_a)) (let ((_let_1 (@ F A2))) (= (@ (@ F (@ _let_1 B2)) C2) (@ _let_1 (@ (@ F B2) C2))))) (@ tptp.semigroup_list_a F))) (forall ((F (-> tptp.a tptp.a tptp.a))) (=> (forall ((A2 tptp.a) (B2 tptp.a) (C2 tptp.a)) (let ((_let_1 (@ F A2))) (= (@ (@ F (@ _let_1 B2)) C2) (@ _let_1 (@ (@ F B2) C2))))) (@ tptp.semigroup_a F))) (forall ((F (-> tptp.list_a tptp.list_a tptp.list_a)) (A tptp.list_a) (B tptp.list_a) (C tptp.list_a)) (let ((_let_1 (@ F A))) (=> (@ tptp.semigroup_list_a F) (= (@ (@ F (@ _let_1 B)) C) (@ _let_1 (@ (@ F B) C)))))) (forall ((F (-> tptp.a tptp.a tptp.a)) (A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ F A))) (=> (@ tptp.semigroup_a F) (= (@ (@ F (@ _let_1 B)) C) (@ _let_1 (@ (@ F B) C)))))) (= tptp.semigroup_list_a (lambda ((F2 (-> tptp.list_a tptp.list_a tptp.list_a))) (forall ((A3 tptp.list_a) (B3 tptp.list_a) (C3 tptp.list_a)) (let ((_let_1 (@ F2 A3))) (= (@ (@ F2 (@ _let_1 B3)) C3) (@ _let_1 (@ (@ F2 B3) C3))))))) (= tptp.semigroup_a (lambda ((F2 (-> tptp.a tptp.a tptp.a))) (forall ((A3 tptp.a) (B3 tptp.a) (C3 tptp.a)) (let ((_let_1 (@ F2 A3))) (= (@ (@ F2 (@ _let_1 B3)) C3) (@ _let_1 (@ (@ F2 B3) C3))))))) (forall ((Less (-> tptp.list_a tptp.list_a Bool)) (Xs tptp.list_list_a)) (= (@ (@ (@ tptp.lexordp_eq_list_a Less) Xs) tptp.nil_list_a) (= Xs tptp.nil_list_a))) (forall ((Less (-> tptp.a tptp.a Bool)) (Xs tptp.list_a)) (= (@ (@ (@ tptp.lexordp_eq_a Less) Xs) tptp.nil_a) (= Xs tptp.nil_a))) (forall ((Less (-> tptp.list_a tptp.list_a Bool)) (Ys tptp.list_list_a)) (@ (@ (@ tptp.lexordp_eq_list_a Less) tptp.nil_list_a) Ys)) (forall ((Less (-> tptp.a tptp.a Bool)) (Ys tptp.list_a)) (@ (@ (@ tptp.lexordp_eq_a Less) tptp.nil_a) Ys)) (forall ((A1 tptp.list_a) (A22 tptp.list_a)) (= (@ (@ (@ tptp.lexordp_eq_a tptp.less) A1) A22) (or (exists ((Ys2 tptp.list_a)) (and (= A1 tptp.nil_a) (= A22 Ys2))) (exists ((X3 tptp.a) (Y3 tptp.a) (Xs2 tptp.list_a) (Ys2 tptp.list_a)) (and (= A1 (@ (@ tptp.cons_a X3) Xs2)) (= A22 (@ (@ tptp.cons_a Y3) Ys2)) (@ (@ tptp.less X3) Y3))) (exists ((X3 tptp.a) (Y3 tptp.a) (Xs2 tptp.list_a) (Ys2 tptp.list_a)) (and (= A1 (@ (@ tptp.cons_a X3) Xs2)) (= A22 (@ (@ tptp.cons_a Y3) Ys2)) (not (@ (@ tptp.less X3) Y3)) (not (@ (@ tptp.less Y3) X3)) (@ (@ (@ tptp.lexordp_eq_a tptp.less) Xs2) Ys2)))))) (forall ((X1 tptp.list_a) (X22 tptp.list_a) (P (-> tptp.list_a tptp.list_a Bool))) (=> (@ (@ (@ tptp.lexordp_eq_a tptp.less) X1) X22) (=> (forall ((X_1 tptp.list_a)) (@ (@ P tptp.nil_a) X_1)) (=> (forall ((X2 tptp.a) (Y2 tptp.a) (Xs3 tptp.list_a) (Ys3 tptp.list_a)) (=> (@ (@ tptp.less X2) Y2) (@ (@ P (@ (@ tptp.cons_a X2) Xs3)) (@ (@ tptp.cons_a Y2) Ys3)))) (=> (forall ((X2 tptp.a) (Y2 tptp.a) (Xs3 tptp.list_a) (Ys3 tptp.list_a)) (=> (not (@ (@ tptp.less X2) Y2)) (=> (not (@ (@ tptp.less Y2) X2)) (=> (@ (@ (@ tptp.lexordp_eq_a tptp.less) Xs3) Ys3) (=> (@ (@ P Xs3) Ys3) (@ (@ P (@ (@ tptp.cons_a X2) Xs3)) (@ (@ tptp.cons_a Y2) Ys3))))))) (@ (@ P X1) X22)))))) (forall ((A1 tptp.list_a) (A22 tptp.list_a)) (=> (@ (@ (@ tptp.lexordp_eq_a tptp.less) A1) A22) (=> (not (= A1 tptp.nil_a)) (=> (forall ((X2 tptp.a)) (=> (exists ((Xs3 tptp.list_a)) (= A1 (@ (@ tptp.cons_a X2) Xs3))) (forall ((Y2 tptp.a)) (=> (exists ((Ys3 tptp.list_a)) (= A22 (@ (@ tptp.cons_a Y2) Ys3))) (not (@ (@ tptp.less X2) Y2)))))) (not (forall ((X2 tptp.a) (Y2 tptp.a) (Xs3 tptp.list_a)) (=> (= A1 (@ (@ tptp.cons_a X2) Xs3)) (forall ((Ys3 tptp.list_a)) (=> (= A22 (@ (@ tptp.cons_a Y2) Ys3)) (=> (not (@ (@ tptp.less X2) Y2)) (=> (not (@ (@ tptp.less Y2) X2)) (not (@ (@ (@ tptp.lexordp_eq_a tptp.less) Xs3) Ys3))))))))))))) (forall ((X tptp.a) (Y tptp.a) (Xs tptp.list_a) (Ys tptp.list_a)) (let ((_let_1 (@ tptp.lexordp_eq_a tptp.less))) (=> (not (@ (@ tptp.less X) Y)) (=> (not (@ (@ tptp.less Y) X)) (=> (@ (@ _let_1 Xs) Ys) (@ (@ _let_1 (@ (@ tptp.cons_a X) Xs)) (@ (@ tptp.cons_a Y) Ys))))))) (forall ((X tptp.a) (Y tptp.a) (Xs tptp.list_a) (Ys tptp.list_a)) (=> (@ (@ tptp.less X) Y) (@ (@ (@ tptp.lexordp_eq_a tptp.less) (@ (@ tptp.cons_a X) Xs)) (@ (@ tptp.cons_a Y) Ys)))) (forall ((X21 tptp.list_a) (X222 tptp.list_list_a) (Y21 tptp.list_a) (Y22 tptp.list_list_a)) (= (= (@ (@ tptp.cons_list_a X21) X222) (@ (@ tptp.cons_list_a Y21) Y22)) (and (= X21 Y21) (= X222 Y22)))) (forall ((X21 tptp.a) (X222 tptp.list_a) (Y21 tptp.a) (Y22 tptp.list_a)) (= (= (@ (@ tptp.cons_a X21) X222) (@ (@ tptp.cons_a Y21) Y22)) (and (= X21 Y21) (= X222 Y22)))) (forall ((Less (-> tptp.list_a tptp.list_a Bool)) (X tptp.list_a) (Xs tptp.list_list_a) (Y tptp.list_a) (Ys tptp.list_list_a)) (let ((_let_1 (@ tptp.lexordp_eq_list_a Less))) (= (@ (@ _let_1 (@ (@ tptp.cons_list_a X) Xs)) (@ (@ tptp.cons_list_a Y) Ys)) (or (@ (@ Less X) Y) (and (not (@ (@ Less Y) X)) (@ (@ _let_1 Xs) Ys)))))) (forall ((Less (-> tptp.a tptp.a Bool)) (X tptp.a) (Xs tptp.list_a) (Y tptp.a) (Ys tptp.list_a)) (let ((_let_1 (@ tptp.lexordp_eq_a Less))) (= (@ (@ _let_1 (@ (@ tptp.cons_a X) Xs)) (@ (@ tptp.cons_a Y) Ys)) (or (@ (@ Less X) Y) (and (not (@ (@ Less Y) X)) (@ (@ _let_1 Xs) Ys)))))) (forall ((Less (-> tptp.list_a tptp.list_a Bool)) (X tptp.list_a) (Xs tptp.list_list_a)) (not (@ (@ (@ tptp.lexordp_eq_list_a Less) (@ (@ tptp.cons_list_a X) Xs)) tptp.nil_list_a))) (forall ((Less (-> tptp.a tptp.a Bool)) (X tptp.a) (Xs tptp.list_a)) (not (@ (@ (@ tptp.lexordp_eq_a Less) (@ (@ tptp.cons_a X) Xs)) tptp.nil_a))) (forall ((X tptp.a) (Xs tptp.list_a) (Y tptp.a) (Ys tptp.list_a)) (let ((_let_1 (@ tptp.lexordp_eq_a tptp.less))) (= (@ (@ _let_1 (@ (@ tptp.cons_a X) Xs)) (@ (@ tptp.cons_a Y) Ys)) (or (@ (@ tptp.less X) Y) (and (not (@ (@ tptp.less Y) X)) (@ (@ _let_1 Xs) Ys)))))) (forall ((X tptp.a) (Xs tptp.list_a)) (not (@ (@ (@ tptp.lexordp_eq_a tptp.less) (@ (@ tptp.cons_a X) Xs)) tptp.nil_a))) (forall ((P (-> (-> tptp.list_a tptp.a) tptp.list_list_a tptp.list_a Bool)) (A0 (-> tptp.list_a tptp.a)) (A1 tptp.list_list_a) (A22 tptp.list_a)) (=> (forall ((F3 (-> tptp.list_a tptp.a)) (X_1 tptp.list_a)) (@ (@ (@ P F3) tptp.nil_list_a) X_1)) (=> (forall ((F3 (-> tptp.list_a tptp.a)) (A2 tptp.list_a) (As tptp.list_list_a) (Bs tptp.list_a)) (let ((_let_1 (@ P F3))) (=> (@ (@ _let_1 As) (@ (@ tptp.cons_a (@ F3 A2)) Bs)) (@ (@ _let_1 (@ (@ tptp.cons_list_a A2) As)) Bs)))) (@ (@ (@ P A0) A1) A22)))) (forall ((P (-> (-> tptp.a tptp.list_a) tptp.list_a tptp.list_list_a Bool)) (A0 (-> tptp.a tptp.list_a)) (A1 tptp.list_a) (A22 tptp.list_list_a)) (=> (forall ((F3 (-> tptp.a tptp.list_a)) (X_1 tptp.list_list_a)) (@ (@ (@ P F3) tptp.nil_a) X_1)) (=> (forall ((F3 (-> tptp.a tptp.list_a)) (A2 tptp.a) (As tptp.list_a) (Bs tptp.list_list_a)) (let ((_let_1 (@ P F3))) (=> (@ (@ _let_1 As) (@ (@ tptp.cons_list_a (@ F3 A2)) Bs)) (@ (@ _let_1 (@ (@ tptp.cons_a A2) As)) Bs)))) (@ (@ (@ P A0) A1) A22)))) (forall ((P (-> (-> tptp.list_a tptp.list_a) tptp.list_list_a tptp.list_list_a Bool)) (A0 (-> tptp.list_a tptp.list_a)) (A1 tptp.list_list_a) (A22 tptp.list_list_a)) (=> (forall ((F3 (-> tptp.list_a tptp.list_a)) (X_1 tptp.list_list_a)) (@ (@ (@ P F3) tptp.nil_list_a) X_1)) (=> (forall ((F3 (-> tptp.list_a tptp.list_a)) (A2 tptp.list_a) (As tptp.list_list_a) (Bs tptp.list_list_a)) (let ((_let_1 (@ P F3))) (=> (@ (@ _let_1 As) (@ (@ tptp.cons_list_a (@ F3 A2)) Bs)) (@ (@ _let_1 (@ (@ tptp.cons_list_a A2) As)) Bs)))) (@ (@ (@ P A0) A1) A22)))) (forall ((P (-> (-> tptp.a tptp.a) tptp.list_a tptp.list_a Bool)) (A0 (-> tptp.a tptp.a)) (A1 tptp.list_a) (A22 tptp.list_a)) (=> (forall ((F3 (-> tptp.a tptp.a)) (X_1 tptp.list_a)) (@ (@ (@ P F3) tptp.nil_a) X_1)) (=> (forall ((F3 (-> tptp.a tptp.a)) (A2 tptp.a) (As tptp.list_a) (Bs tptp.list_a)) (let ((_let_1 (@ P F3))) (=> (@ (@ _let_1 As) (@ (@ tptp.cons_a (@ F3 A2)) Bs)) (@ (@ _let_1 (@ (@ tptp.cons_a A2) As)) Bs)))) (@ (@ (@ P A0) A1) A22)))) (forall ((Xs tptp.list_list_a) (P (-> tptp.list_list_a Bool))) (=> (not (= Xs tptp.nil_list_a)) (=> (forall ((X2 tptp.list_a)) (@ P (@ (@ tptp.cons_list_a X2) tptp.nil_list_a))) (=> (forall ((X2 tptp.list_a) (Xs3 tptp.list_list_a)) (=> (not (= Xs3 tptp.nil_list_a)) (=> (@ P Xs3) (@ P (@ (@ tptp.cons_list_a X2) Xs3))))) (@ P Xs))))) (forall ((Xs tptp.list_a) (P (-> tptp.list_a Bool))) (=> (not (= Xs tptp.nil_a)) (=> (forall ((X2 tptp.a)) (@ P (@ (@ tptp.cons_a X2) tptp.nil_a))) (=> (forall ((X2 tptp.a) (Xs3 tptp.list_a)) (=> (not (= Xs3 tptp.nil_a)) (=> (@ P Xs3) (@ P (@ (@ tptp.cons_a X2) Xs3))))) (@ P Xs))))) (forall ((P (-> (-> tptp.list_a tptp.list_a Bool) tptp.list_list_a Bool)) (A0 (-> tptp.list_a tptp.list_a Bool)) (A1 tptp.list_list_a)) (=> (forall ((P2 (-> tptp.list_a tptp.list_a Bool))) (@ (@ P P2) tptp.nil_list_a)) (=> (forall ((P2 (-> tptp.list_a tptp.list_a Bool)) (X2 tptp.list_a)) (@ (@ P P2) (@ (@ tptp.cons_list_a X2) tptp.nil_list_a))) (=> (forall ((P2 (-> tptp.list_a tptp.list_a Bool)) (X2 tptp.list_a) (Y2 tptp.list_a) (Xs3 tptp.list_list_a)) (let ((_let_1 (@ (@ tptp.cons_list_a Y2) Xs3))) (let ((_let_2 (@ P P2))) (=> (@ _let_2 _let_1) (@ _let_2 (@ (@ tptp.cons_list_a X2) _let_1)))))) (@ (@ P A0) A1))))) (forall ((P (-> (-> tptp.a tptp.a Bool) tptp.list_a Bool)) (A0 (-> tptp.a tptp.a Bool)) (A1 tptp.list_a)) (=> (forall ((P2 (-> tptp.a tptp.a Bool))) (@ (@ P P2) tptp.nil_a)) (=> (forall ((P2 (-> tptp.a tptp.a Bool)) (X2 tptp.a)) (@ (@ P P2) (@ (@ tptp.cons_a X2) tptp.nil_a))) (=> (forall ((P2 (-> tptp.a tptp.a Bool)) (X2 tptp.a) (Y2 tptp.a) (Xs3 tptp.list_a)) (let ((_let_1 (@ (@ tptp.cons_a Y2) Xs3))) (let ((_let_2 (@ P P2))) (=> (@ _let_2 _let_1) (@ _let_2 (@ (@ tptp.cons_a X2) _let_1)))))) (@ (@ P A0) A1))))) (forall ((P (-> tptp.list_list_a Bool)) (A0 tptp.list_list_a)) (=> (@ P tptp.nil_list_a) (=> (forall ((X2 tptp.list_a)) (@ P (@ (@ tptp.cons_list_a X2) tptp.nil_list_a))) (=> (forall ((X2 tptp.list_a) (Y2 tptp.list_a) (Xs3 tptp.list_list_a)) (let ((_let_1 (@ (@ tptp.cons_list_a Y2) Xs3))) (let ((_let_2 (@ tptp.cons_list_a X2))) (let ((_let_3 (= X2 Y2))) (=> (=> _let_3 (@ P (@ _let_2 Xs3))) (=> (=> (not _let_3) (@ P _let_1)) (@ P (@ _let_2 _let_1)))))))) (@ P A0))))) (forall ((P (-> tptp.list_a Bool)) (A0 tptp.list_a)) (=> (@ P tptp.nil_a) (=> (forall ((X2 tptp.a)) (@ P (@ (@ tptp.cons_a X2) tptp.nil_a))) (=> (forall ((X2 tptp.a) (Y2 tptp.a) (Xs3 tptp.list_a)) (let ((_let_1 (@ (@ tptp.cons_a Y2) Xs3))) (let ((_let_2 (@ tptp.cons_a X2))) (let ((_let_3 (= X2 Y2))) (=> (=> _let_3 (@ P (@ _let_2 Xs3))) (=> (=> (not _let_3) (@ P _let_1)) (@ P (@ _let_2 _let_1)))))))) (@ P A0))))) (forall ((P (-> (-> tptp.list_a tptp.list_a Bool) tptp.list_list_a Bool)) (A0 (-> tptp.list_a tptp.list_a Bool)) (A1 tptp.list_list_a)) (=> (forall ((P2 (-> tptp.list_a tptp.list_a Bool))) (@ (@ P P2) tptp.nil_list_a)) (=> (forall ((P2 (-> tptp.list_a tptp.list_a Bool)) (X2 tptp.list_a) (Ys3 tptp.list_list_a)) (let ((_let_1 (@ P P2))) (=> (@ _let_1 Ys3) (@ _let_1 (@ (@ tptp.cons_list_a X2) Ys3))))) (@ (@ P A0) A1)))) (forall ((P (-> (-> tptp.a tptp.a Bool) tptp.list_a Bool)) (A0 (-> tptp.a tptp.a Bool)) (A1 tptp.list_a)) (=> (forall ((P2 (-> tptp.a tptp.a Bool))) (@ (@ P P2) tptp.nil_a)) (=> (forall ((P2 (-> tptp.a tptp.a Bool)) (X2 tptp.a) (Ys3 tptp.list_a)) (let ((_let_1 (@ P P2))) (=> (@ _let_1 Ys3) (@ _let_1 (@ (@ tptp.cons_a X2) Ys3))))) (@ (@ P A0) A1)))) (forall ((X tptp.list_list_a)) (=> (not (= X tptp.nil_list_a)) (=> (forall ((X2 tptp.list_a)) (not (= X (@ (@ tptp.cons_list_a X2) tptp.nil_list_a)))) (not (forall ((X2 tptp.list_a) (Y2 tptp.list_a) (Xs3 tptp.list_list_a)) (not (= X (@ (@ tptp.cons_list_a X2) (@ (@ tptp.cons_list_a Y2) Xs3))))))))) (forall ((X tptp.list_a)) (=> (not (= X tptp.nil_a)) (=> (forall ((X2 tptp.a)) (not (= X (@ (@ tptp.cons_a X2) tptp.nil_a)))) (not (forall ((X2 tptp.a) (Y2 tptp.a) (Xs3 tptp.list_a)) (not (= X (@ (@ tptp.cons_a X2) (@ (@ tptp.cons_a Y2) Xs3))))))))) (forall ((X tptp.list_list_list_a)) (=> (not (= X tptp.nil_list_list_a)) (=> (forall ((Xss tptp.list_list_list_a)) (not (= X (@ (@ tptp.cons_list_list_a tptp.nil_list_a) Xss)))) (not (forall ((X2 tptp.list_a) (Xs3 tptp.list_list_a) (Xss tptp.list_list_list_a)) (not (= X (@ (@ tptp.cons_list_list_a (@ (@ tptp.cons_list_a X2) Xs3)) Xss)))))))) (forall ((X tptp.list_list_a)) (=> (not (= X tptp.nil_list_a)) (=> (forall ((Xss tptp.list_list_a)) (not (= X (@ (@ tptp.cons_list_a tptp.nil_a) Xss)))) (not (forall ((X2 tptp.a) (Xs3 tptp.list_a) (Xss tptp.list_list_a)) (not (= X (@ (@ tptp.cons_list_a (@ (@ tptp.cons_a X2) Xs3)) Xss)))))))) (forall ((P (-> tptp.list_list_a tptp.list_list_a Bool)) (A0 tptp.list_list_a) (A1 tptp.list_list_a)) (=> (forall ((X_1 tptp.list_list_a)) (@ (@ P tptp.nil_list_a) X_1)) (=> (forall ((Xs3 tptp.list_list_a)) (@ (@ P Xs3) tptp.nil_list_a)) (=> (forall ((X2 tptp.list_a) (Xs3 tptp.list_list_a) (Y2 tptp.list_a) (Ys3 tptp.list_list_a)) (let ((_let_1 (@ (@ tptp.cons_list_a Y2) Ys3))) (let ((_let_2 (@ P (@ (@ tptp.cons_list_a X2) Xs3)))) (=> (@ (@ P Xs3) _let_1) (=> (@ _let_2 Ys3) (@ _let_2 _let_1)))))) (@ (@ P A0) A1))))) (forall ((P (-> tptp.list_a tptp.list_a Bool)) (A0 tptp.list_a) (A1 tptp.list_a)) (=> (forall ((X_1 tptp.list_a)) (@ (@ P tptp.nil_a) X_1)) (=> (forall ((Xs3 tptp.list_a)) (@ (@ P Xs3) tptp.nil_a)) (=> (forall ((X2 tptp.a) (Xs3 tptp.list_a) (Y2 tptp.a) (Ys3 tptp.list_a)) (let ((_let_1 (@ (@ tptp.cons_a Y2) Ys3))) (let ((_let_2 (@ P (@ (@ tptp.cons_a X2) Xs3)))) (=> (@ (@ P Xs3) _let_1) (=> (@ _let_2 Ys3) (@ _let_2 _let_1)))))) (@ (@ P A0) A1))))) (forall ((P (-> tptp.list_list_a Bool)) (Xs tptp.list_list_a)) (=> (@ P tptp.nil_list_a) (=> (forall ((X2 tptp.list_a)) (@ P (@ (@ tptp.cons_list_a X2) tptp.nil_list_a))) (=> (forall ((X2 tptp.list_a) (Y2 tptp.list_a) (Zs tptp.list_list_a)) (let ((_let_1 (@ (@ tptp.cons_list_a Y2) Zs))) (=> (@ P Zs) (=> (@ P _let_1) (@ P (@ (@ tptp.cons_list_a X2) _let_1)))))) (@ P Xs))))) (forall ((P (-> tptp.list_a Bool)) (Xs tptp.list_a)) (=> (@ P tptp.nil_a) (=> (forall ((X2 tptp.a)) (@ P (@ (@ tptp.cons_a X2) tptp.nil_a))) (=> (forall ((X2 tptp.a) (Y2 tptp.a) (Zs tptp.list_a)) (let ((_let_1 (@ (@ tptp.cons_a Y2) Zs))) (=> (@ P Zs) (=> (@ P _let_1) (@ P (@ (@ tptp.cons_a X2) _let_1)))))) (@ P Xs))))) (forall ((P (-> tptp.list_list_a tptp.list_list_a Bool)) (A0 tptp.list_list_a) (A1 tptp.list_list_a)) (=> (forall ((X_1 tptp.list_list_a)) (@ (@ P tptp.nil_list_a) X_1)) (=> (forall ((X2 tptp.list_a) (Xs3 tptp.list_list_a) (Ys3 tptp.list_list_a)) (=> (@ (@ P Ys3) Xs3) (@ (@ P (@ (@ tptp.cons_list_a X2) Xs3)) Ys3))) (@ (@ P A0) A1)))) (forall ((P (-> tptp.list_a tptp.list_a Bool)) (A0 tptp.list_a) (A1 tptp.list_a)) (=> (forall ((X_1 tptp.list_a)) (@ (@ P tptp.nil_a) X_1)) (=> (forall ((X2 tptp.a) (Xs3 tptp.list_a) (Ys3 tptp.list_a)) (=> (@ (@ P Ys3) Xs3) (@ (@ P (@ (@ tptp.cons_a X2) Xs3)) Ys3))) (@ (@ P A0) A1)))) (forall ((P (-> tptp.list_a tptp.list_list_a Bool)) (Xs tptp.list_a) (Ys tptp.list_list_a)) (=> (@ (@ P tptp.nil_a) tptp.nil_list_a) (=> (forall ((X2 tptp.a) (Xs3 tptp.list_a)) (@ (@ P (@ (@ tptp.cons_a X2) Xs3)) tptp.nil_list_a)) (=> (forall ((Y2 tptp.list_a) (Ys3 tptp.list_list_a)) (@ (@ P tptp.nil_a) (@ (@ tptp.cons_list_a Y2) Ys3))) (=> (forall ((X2 tptp.a) (Xs3 tptp.list_a) (Y2 tptp.list_a) (Ys3 tptp.list_list_a)) (=> (@ (@ P Xs3) Ys3) (@ (@ P (@ (@ tptp.cons_a X2) Xs3)) (@ (@ tptp.cons_list_a Y2) Ys3)))) (@ (@ P Xs) Ys)))))) (forall ((P (-> tptp.list_list_a tptp.list_a Bool)) (Xs tptp.list_list_a) (Ys tptp.list_a)) (=> (@ (@ P tptp.nil_list_a) tptp.nil_a) (=> (forall ((X2 tptp.list_a) (Xs3 tptp.list_list_a)) (@ (@ P (@ (@ tptp.cons_list_a X2) Xs3)) tptp.nil_a)) (=> (forall ((Y2 tptp.a) (Ys3 tptp.list_a)) (@ (@ P tptp.nil_list_a) (@ (@ tptp.cons_a Y2) Ys3))) (=> (forall ((X2 tptp.list_a) (Xs3 tptp.list_list_a) (Y2 tptp.a) (Ys3 tptp.list_a)) (=> (@ (@ P Xs3) Ys3) (@ (@ P (@ (@ tptp.cons_list_a X2) Xs3)) (@ (@ tptp.cons_a Y2) Ys3)))) (@ (@ P Xs) Ys)))))) (forall ((P (-> tptp.list_list_a tptp.list_list_a Bool)) (Xs tptp.list_list_a) (Ys tptp.list_list_a)) (=> (@ (@ P tptp.nil_list_a) tptp.nil_list_a) (=> (forall ((X2 tptp.list_a) (Xs3 tptp.list_list_a)) (@ (@ P (@ (@ tptp.cons_list_a X2) Xs3)) tptp.nil_list_a)) (=> (forall ((Y2 tptp.list_a) (Ys3 tptp.list_list_a)) (@ (@ P tptp.nil_list_a) (@ (@ tptp.cons_list_a Y2) Ys3))) (=> (forall ((X2 tptp.list_a) (Xs3 tptp.list_list_a) (Y2 tptp.list_a) (Ys3 tptp.list_list_a)) (=> (@ (@ P Xs3) Ys3) (@ (@ P (@ (@ tptp.cons_list_a X2) Xs3)) (@ (@ tptp.cons_list_a Y2) Ys3)))) (@ (@ P Xs) Ys)))))) (forall ((P (-> tptp.list_a tptp.list_a Bool)) (Xs tptp.list_a) (Ys tptp.list_a)) (=> (@ (@ P tptp.nil_a) tptp.nil_a) (=> (forall ((X2 tptp.a) (Xs3 tptp.list_a)) (@ (@ P (@ (@ tptp.cons_a X2) Xs3)) tptp.nil_a)) (=> (forall ((Y2 tptp.a) (Ys3 tptp.list_a)) (@ (@ P tptp.nil_a) (@ (@ tptp.cons_a Y2) Ys3))) (=> (forall ((X2 tptp.a) (Xs3 tptp.list_a) (Y2 tptp.a) (Ys3 tptp.list_a)) (=> (@ (@ P Xs3) Ys3) (@ (@ P (@ (@ tptp.cons_a X2) Xs3)) (@ (@ tptp.cons_a Y2) Ys3)))) (@ (@ P Xs) Ys)))))) (forall ((Xs tptp.list_list_a)) (= (not (= Xs tptp.nil_list_a)) (exists ((Y3 tptp.list_a) (Ys2 tptp.list_list_a)) (= Xs (@ (@ tptp.cons_list_a Y3) Ys2))))) (forall ((Xs tptp.list_a)) (= (not (= Xs tptp.nil_a)) (exists ((Y3 tptp.a) (Ys2 tptp.list_a)) (= Xs (@ (@ tptp.cons_a Y3) Ys2))))) (forall ((P (-> tptp.list_list_a Bool)) (List tptp.list_list_a)) (=> (@ P tptp.nil_list_a) (=> (forall ((X12 tptp.list_a) (X23 tptp.list_list_a)) (=> (@ P X23) (@ P (@ (@ tptp.cons_list_a X12) X23)))) (@ P List)))) (forall ((P (-> tptp.list_a Bool)) (List tptp.list_a)) (=> (@ P tptp.nil_a) (=> (forall ((X12 tptp.a) (X23 tptp.list_a)) (=> (@ P X23) (@ P (@ (@ tptp.cons_a X12) X23)))) (@ P List)))) (forall ((Y tptp.list_list_a)) (=> (not (= Y tptp.nil_list_a)) (not (forall ((X212 tptp.list_a) (X223 tptp.list_list_a)) (not (= Y (@ (@ tptp.cons_list_a X212) X223))))))) (forall ((Y tptp.list_a)) (=> (not (= Y tptp.nil_a)) (not (forall ((X212 tptp.a) (X223 tptp.list_a)) (not (= Y (@ (@ tptp.cons_a X212) X223))))))) (forall ((List tptp.list_list_a) (X21 tptp.list_a) (X222 tptp.list_list_a)) (=> (= List (@ (@ tptp.cons_list_a X21) X222)) (not (= List tptp.nil_list_a)))) (forall ((List tptp.list_a) (X21 tptp.a) (X222 tptp.list_a)) (=> (= List (@ (@ tptp.cons_a X21) X222)) (not (= List tptp.nil_a)))) (forall ((X21 tptp.list_a) (X222 tptp.list_list_a)) (not (= tptp.nil_list_a (@ (@ tptp.cons_list_a X21) X222)))) (forall ((X21 tptp.a) (X222 tptp.list_a)) (not (= tptp.nil_a (@ (@ tptp.cons_a X21) X222)))) (forall ((X tptp.list_a) (Xs tptp.list_list_a)) (not (= (@ (@ tptp.cons_list_a X) Xs) Xs))) (forall ((X tptp.a) (Xs tptp.list_a)) (not (= (@ (@ tptp.cons_a X) Xs) Xs))) (forall ((Less (-> tptp.list_a tptp.list_a Bool)) (X tptp.list_a) (Y tptp.list_a) (Xs tptp.list_list_a) (Ys tptp.list_list_a)) (let ((_let_1 (@ tptp.lexordp_eq_list_a Less))) (=> (not (@ (@ Less X) Y)) (=> (not (@ (@ Less Y) X)) (=> (@ (@ _let_1 Xs) Ys) (@ (@ _let_1 (@ (@ tptp.cons_list_a X) Xs)) (@ (@ tptp.cons_list_a Y) Ys))))))) (forall ((Less (-> tptp.a tptp.a Bool)) (X tptp.a) (Y tptp.a) (Xs tptp.list_a) (Ys tptp.list_a)) (let ((_let_1 (@ tptp.lexordp_eq_a Less))) (=> (not (@ (@ Less X) Y)) (=> (not (@ (@ Less Y) X)) (=> (@ (@ _let_1 Xs) Ys) (@ (@ _let_1 (@ (@ tptp.cons_a X) Xs)) (@ (@ tptp.cons_a Y) Ys))))))) (forall ((Less (-> tptp.list_a tptp.list_a Bool)) (X tptp.list_a) (Y tptp.list_a) (Xs tptp.list_list_a) (Ys tptp.list_list_a)) (=> (@ (@ Less X) Y) (@ (@ (@ tptp.lexordp_eq_list_a Less) (@ (@ tptp.cons_list_a X) Xs)) (@ (@ tptp.cons_list_a Y) Ys)))) (forall ((Less (-> tptp.a tptp.a Bool)) (X tptp.a) (Y tptp.a) (Xs tptp.list_a) (Ys tptp.list_a)) (=> (@ (@ Less X) Y) (@ (@ (@ tptp.lexordp_eq_a Less) (@ (@ tptp.cons_a X) Xs)) (@ (@ tptp.cons_a Y) Ys)))) (forall ((Less (-> tptp.list_a tptp.list_a Bool)) (X1 tptp.list_list_a) (X22 tptp.list_list_a) (P (-> tptp.list_list_a tptp.list_list_a Bool))) (=> (@ (@ (@ tptp.lexordp_eq_list_a Less) X1) X22) (=> (forall ((X_1 tptp.list_list_a)) (@ (@ P tptp.nil_list_a) X_1)) (=> (forall ((X2 tptp.list_a) (Y2 tptp.list_a) (Xs3 tptp.list_list_a) (Ys3 tptp.list_list_a)) (=> (@ (@ Less X2) Y2) (@ (@ P (@ (@ tptp.cons_list_a X2) Xs3)) (@ (@ tptp.cons_list_a Y2) Ys3)))) (=> (forall ((X2 tptp.list_a) (Y2 tptp.list_a) (Xs3 tptp.list_list_a) (Ys3 tptp.list_list_a)) (=> (not (@ (@ Less X2) Y2)) (=> (not (@ (@ Less Y2) X2)) (=> (@ (@ (@ tptp.lexordp_eq_list_a Less) Xs3) Ys3) (=> (@ (@ P Xs3) Ys3) (@ (@ P (@ (@ tptp.cons_list_a X2) Xs3)) (@ (@ tptp.cons_list_a Y2) Ys3))))))) (@ (@ P X1) X22)))))) (forall ((Less (-> tptp.a tptp.a Bool)) (X1 tptp.list_a) (X22 tptp.list_a) (P (-> tptp.list_a tptp.list_a Bool))) (=> (@ (@ (@ tptp.lexordp_eq_a Less) X1) X22) (=> (forall ((X_1 tptp.list_a)) (@ (@ P tptp.nil_a) X_1)) (=> (forall ((X2 tptp.a) (Y2 tptp.a) (Xs3 tptp.list_a) (Ys3 tptp.list_a)) (=> (@ (@ Less X2) Y2) (@ (@ P (@ (@ tptp.cons_a X2) Xs3)) (@ (@ tptp.cons_a Y2) Ys3)))) (=> (forall ((X2 tptp.a) (Y2 tptp.a) (Xs3 tptp.list_a) (Ys3 tptp.list_a)) (=> (not (@ (@ Less X2) Y2)) (=> (not (@ (@ Less Y2) X2)) (=> (@ (@ (@ tptp.lexordp_eq_a Less) Xs3) Ys3) (=> (@ (@ P Xs3) Ys3) (@ (@ P (@ (@ tptp.cons_a X2) Xs3)) (@ (@ tptp.cons_a Y2) Ys3))))))) (@ (@ P X1) X22)))))) (= tptp.lexordp_eq_list_a (lambda ((Less2 (-> tptp.list_a tptp.list_a Bool)) (A12 tptp.list_list_a) (A23 tptp.list_list_a)) (or (exists ((Ys2 tptp.list_list_a)) (and (= A12 tptp.nil_list_a) (= A23 Ys2))) (exists ((X3 tptp.list_a) (Y3 tptp.list_a) (Xs2 tptp.list_list_a) (Ys2 tptp.list_list_a)) (and (= A12 (@ (@ tptp.cons_list_a X3) Xs2)) (= A23 (@ (@ tptp.cons_list_a Y3) Ys2)) (@ (@ Less2 X3) Y3))) (exists ((X3 tptp.list_a) (Y3 tptp.list_a) (Xs2 tptp.list_list_a) (Ys2 tptp.list_list_a)) (and (= A12 (@ (@ tptp.cons_list_a X3) Xs2)) (= A23 (@ (@ tptp.cons_list_a Y3) Ys2)) (not (@ (@ Less2 X3) Y3)) (not (@ (@ Less2 Y3) X3)) (@ (@ (@ tptp.lexordp_eq_list_a Less2) Xs2) Ys2)))))) (= tptp.lexordp_eq_a (lambda ((Less2 (-> tptp.a tptp.a Bool)) (A12 tptp.list_a) (A23 tptp.list_a)) (or (exists ((Ys2 tptp.list_a)) (and (= A12 tptp.nil_a) (= A23 Ys2))) (exists ((X3 tptp.a) (Y3 tptp.a) (Xs2 tptp.list_a) (Ys2 tptp.list_a)) (and (= A12 (@ (@ tptp.cons_a X3) Xs2)) (= A23 (@ (@ tptp.cons_a Y3) Ys2)) (@ (@ Less2 X3) Y3))) (exists ((X3 tptp.a) (Y3 tptp.a) (Xs2 tptp.list_a) (Ys2 tptp.list_a)) (and (= A12 (@ (@ tptp.cons_a X3) Xs2)) (= A23 (@ (@ tptp.cons_a Y3) Ys2)) (not (@ (@ Less2 X3) Y3)) (not (@ (@ Less2 Y3) X3)) (@ (@ (@ tptp.lexordp_eq_a Less2) Xs2) Ys2)))))) (forall ((Less (-> tptp.list_a tptp.list_a Bool)) (A1 tptp.list_list_a) (A22 tptp.list_list_a)) (=> (@ (@ (@ tptp.lexordp_eq_list_a Less) A1) A22) (=> (not (= A1 tptp.nil_list_a)) (=> (forall ((X2 tptp.list_a)) (=> (exists ((Xs3 tptp.list_list_a)) (= A1 (@ (@ tptp.cons_list_a X2) Xs3))) (forall ((Y2 tptp.list_a)) (=> (exists ((Ys3 tptp.list_list_a)) (= A22 (@ (@ tptp.cons_list_a Y2) Ys3))) (not (@ (@ Less X2) Y2)))))) (not (forall ((X2 tptp.list_a) (Y2 tptp.list_a) (Xs3 tptp.list_list_a)) (=> (= A1 (@ (@ tptp.cons_list_a X2) Xs3)) (forall ((Ys3 tptp.list_list_a)) (=> (= A22 (@ (@ tptp.cons_list_a Y2) Ys3)) (=> (not (@ (@ Less X2) Y2)) (=> (not (@ (@ Less Y2) X2)) (not (@ (@ (@ tptp.lexordp_eq_list_a Less) Xs3) Ys3))))))))))))) (forall ((Less (-> tptp.a tptp.a Bool)) (A1 tptp.list_a) (A22 tptp.list_a)) (=> (@ (@ (@ tptp.lexordp_eq_a Less) A1) A22) (=> (not (= A1 tptp.nil_a)) (=> (forall ((X2 tptp.a)) (=> (exists ((Xs3 tptp.list_a)) (= A1 (@ (@ tptp.cons_a X2) Xs3))) (forall ((Y2 tptp.a)) (=> (exists ((Ys3 tptp.list_a)) (= A22 (@ (@ tptp.cons_a Y2) Ys3))) (not (@ (@ Less X2) Y2)))))) (not (forall ((X2 tptp.a) (Y2 tptp.a) (Xs3 tptp.list_a)) (=> (= A1 (@ (@ tptp.cons_a X2) Xs3)) (forall ((Ys3 tptp.list_a)) (=> (= A22 (@ (@ tptp.cons_a Y2) Ys3)) (=> (not (@ (@ Less X2) Y2)) (=> (not (@ (@ Less Y2) X2)) (not (@ (@ (@ tptp.lexordp_eq_a Less) Xs3) Ys3))))))))))))) (= tptp.lexordp_eq_a tptp.lexordp_eq_a) (forall ((Less (-> tptp.a tptp.a Bool)) (Xs tptp.list_a)) (@ (@ (@ tptp.lexordp_eq_a Less) Xs) Xs)) (forall ((Less (-> tptp.list_a tptp.list_a Bool)) (Ys tptp.list_list_a)) (@ (@ (@ tptp.lexordp_eq_list_a Less) tptp.nil_list_a) Ys)) (forall ((Less (-> tptp.a tptp.a Bool)) (Ys tptp.list_a)) (@ (@ (@ tptp.lexordp_eq_a Less) tptp.nil_a) Ys)) (forall ((Y tptp.a) (Ys tptp.list_a)) (@ (@ (@ tptp.lexordp_a tptp.less) tptp.nil_a) (@ (@ tptp.cons_a Y) Ys))) (forall ((A1 tptp.list_a) (A22 tptp.list_a)) (=> (@ (@ (@ tptp.lexordp_a tptp.less) A1) A22) (=> (=> (= A1 tptp.nil_a) (forall ((Y2 tptp.a) (Ys3 tptp.list_a)) (not (= A22 (@ (@ tptp.cons_a Y2) Ys3))))) (=> (forall ((X2 tptp.a)) (=> (exists ((Xs3 tptp.list_a)) (= A1 (@ (@ tptp.cons_a X2) Xs3))) (forall ((Y2 tptp.a)) (=> (exists ((Ys3 tptp.list_a)) (= A22 (@ (@ tptp.cons_a Y2) Ys3))) (not (@ (@ tptp.less X2) Y2)))))) (not (forall ((X2 tptp.a) (Y2 tptp.a) (Xs3 tptp.list_a)) (=> (= A1 (@ (@ tptp.cons_a X2) Xs3)) (forall ((Ys3 tptp.list_a)) (=> (= A22 (@ (@ tptp.cons_a Y2) Ys3)) (=> (not (@ (@ tptp.less X2) Y2)) (=> (not (@ (@ tptp.less Y2) X2)) (not (@ (@ (@ tptp.lexordp_a tptp.less) Xs3) Ys3))))))))))))) (forall ((X1 tptp.list_a) (X22 tptp.list_a) (P (-> tptp.list_a tptp.list_a Bool))) (=> (@ (@ (@ tptp.lexordp_a tptp.less) X1) X22) (=> (forall ((Y2 tptp.a) (Ys3 tptp.list_a)) (@ (@ P tptp.nil_a) (@ (@ tptp.cons_a Y2) Ys3))) (=> (forall ((X2 tptp.a) (Y2 tptp.a) (Xs3 tptp.list_a) (Ys3 tptp.list_a)) (=> (@ (@ tptp.less X2) Y2) (@ (@ P (@ (@ tptp.cons_a X2) Xs3)) (@ (@ tptp.cons_a Y2) Ys3)))) (=> (forall ((X2 tptp.a) (Y2 tptp.a) (Xs3 tptp.list_a) (Ys3 tptp.list_a)) (=> (not (@ (@ tptp.less X2) Y2)) (=> (not (@ (@ tptp.less Y2) X2)) (=> (@ (@ (@ tptp.lexordp_a tptp.less) Xs3) Ys3) (=> (@ (@ P Xs3) Ys3) (@ (@ P (@ (@ tptp.cons_a X2) Xs3)) (@ (@ tptp.cons_a Y2) Ys3))))))) (@ (@ P X1) X22)))))) (forall ((A1 tptp.list_a) (A22 tptp.list_a)) (= (@ (@ (@ tptp.lexordp_a tptp.less) A1) A22) (or (exists ((Y3 tptp.a) (Ys2 tptp.list_a)) (and (= A1 tptp.nil_a) (= A22 (@ (@ tptp.cons_a Y3) Ys2)))) (exists ((X3 tptp.a) (Y3 tptp.a) (Xs2 tptp.list_a) (Ys2 tptp.list_a)) (and (= A1 (@ (@ tptp.cons_a X3) Xs2)) (= A22 (@ (@ tptp.cons_a Y3) Ys2)) (@ (@ tptp.less X3) Y3))) (exists ((X3 tptp.a) (Y3 tptp.a) (Xs2 tptp.list_a) (Ys2 tptp.list_a)) (and (= A1 (@ (@ tptp.cons_a X3) Xs2)) (= A22 (@ (@ tptp.cons_a Y3) Ys2)) (not (@ (@ tptp.less X3) Y3)) (not (@ (@ tptp.less Y3) X3)) (@ (@ (@ tptp.lexordp_a tptp.less) Xs2) Ys2)))))) (forall ((Xs tptp.list_a) (Ys tptp.list_a)) (let ((_let_1 (@ tptp.lexordp_a tptp.less))) (=> (@ (@ _let_1 Xs) Ys) (not (@ (@ _let_1 Ys) Xs))))) (forall ((Xs tptp.list_a)) (=> (forall ((X2 tptp.a)) (not (@ (@ tptp.less X2) X2))) (not (@ (@ (@ tptp.lexordp_a tptp.less) Xs) Xs)))) (forall ((Xs tptp.list_a)) (not (@ (@ (@ tptp.lexordp_a tptp.less) Xs) Xs))) (forall ((X tptp.a) (Y tptp.a) (Xs tptp.list_a) (Ys tptp.list_a)) (let ((_let_1 (@ tptp.lexordp_a tptp.less))) (=> (not (@ (@ tptp.less X) Y)) (=> (not (@ (@ tptp.less Y) X)) (=> (@ (@ _let_1 Xs) Ys) (@ (@ _let_1 (@ (@ tptp.cons_a X) Xs)) (@ (@ tptp.cons_a Y) Ys))))))) (forall ((X tptp.a) (Y tptp.a) (Xs tptp.list_a) (Ys tptp.list_a)) (=> (@ (@ tptp.less X) Y) (@ (@ (@ tptp.lexordp_a tptp.less) (@ (@ tptp.cons_a X) Xs)) (@ (@ tptp.cons_a Y) Ys)))) (forall ((Xs tptp.list_a) (Ys tptp.list_a)) (=> (@ (@ (@ tptp.lexordp_a tptp.less) Xs) Ys) (@ (@ (@ tptp.lexordp_eq_a tptp.less) Xs) Ys))) (forall ((Less (-> tptp.list_a tptp.list_a Bool)) (X tptp.list_a) (Xs tptp.list_list_a) (Y tptp.list_a) (Ys tptp.list_list_a)) (let ((_let_1 (@ tptp.lexordp_list_a Less))) (= (@ (@ _let_1 (@ (@ tptp.cons_list_a X) Xs)) (@ (@ tptp.cons_list_a Y) Ys)) (or (@ (@ Less X) Y) (and (not (@ (@ Less Y) X)) (@ (@ _let_1 Xs) Ys)))))) (forall ((Less (-> tptp.a tptp.a Bool)) (X tptp.a) (Xs tptp.list_a) (Y tptp.a) (Ys tptp.list_a)) (let ((_let_1 (@ tptp.lexordp_a Less))) (= (@ (@ _let_1 (@ (@ tptp.cons_a X) Xs)) (@ (@ tptp.cons_a Y) Ys)) (or (@ (@ Less X) Y) (and (not (@ (@ Less Y) X)) (@ (@ _let_1 Xs) Ys)))))) (forall ((Less (-> tptp.list_a tptp.list_a Bool)) (Xs tptp.list_list_a)) (not (@ (@ (@ tptp.lexordp_list_a Less) Xs) tptp.nil_list_a))) (forall ((Less (-> tptp.a tptp.a Bool)) (Xs tptp.list_a)) (not (@ (@ (@ tptp.lexordp_a Less) Xs) tptp.nil_a))) (forall ((Less (-> tptp.list_a tptp.list_a Bool)) (Ys tptp.list_list_a)) (= (@ (@ (@ tptp.lexordp_list_a Less) tptp.nil_list_a) Ys) (not (= Ys tptp.nil_list_a)))) (forall ((Less (-> tptp.a tptp.a Bool)) (Ys tptp.list_a)) (= (@ (@ (@ tptp.lexordp_a Less) tptp.nil_a) Ys) (not (= Ys tptp.nil_a)))) (forall ((X tptp.a) (Xs tptp.list_a) (Y tptp.a) (Ys tptp.list_a)) (let ((_let_1 (@ tptp.lexordp_a tptp.less))) (= (@ (@ _let_1 (@ (@ tptp.cons_a X) Xs)) (@ (@ tptp.cons_a Y) Ys)) (or (@ (@ tptp.less X) Y) (and (not (@ (@ tptp.less Y) X)) (@ (@ _let_1 Xs) Ys)))))) (forall ((Ys tptp.list_a)) (= (@ (@ (@ tptp.lexordp_a tptp.less) tptp.nil_a) Ys) (not (= Ys tptp.nil_a)))) (forall ((Xs tptp.list_a)) (not (@ (@ (@ tptp.lexordp_a tptp.less) Xs) tptp.nil_a))) (= tptp.lexordp_a tptp.lexordp_a) (forall ((Less (-> tptp.a tptp.a Bool)) (Xs tptp.list_a)) (=> (forall ((X2 tptp.a)) (not (@ (@ Less X2) X2))) (not (@ (@ (@ tptp.lexordp_a Less) Xs) Xs)))) (forall ((Less (-> tptp.list_a tptp.list_a Bool)) (X tptp.list_a) (Y tptp.list_a) (Xs tptp.list_list_a) (Ys tptp.list_list_a)) (let ((_let_1 (@ tptp.lexordp_list_a Less))) (=> (not (@ (@ Less X) Y)) (=> (not (@ (@ Less Y) X)) (=> (@ (@ _let_1 Xs) Ys) (@ (@ _let_1 (@ (@ tptp.cons_list_a X) Xs)) (@ (@ tptp.cons_list_a Y) Ys))))))) (forall ((Less (-> tptp.a tptp.a Bool)) (X tptp.a) (Y tptp.a) (Xs tptp.list_a) (Ys tptp.list_a)) (let ((_let_1 (@ tptp.lexordp_a Less))) (=> (not (@ (@ Less X) Y)) (=> (not (@ (@ Less Y) X)) (=> (@ (@ _let_1 Xs) Ys) (@ (@ _let_1 (@ (@ tptp.cons_a X) Xs)) (@ (@ tptp.cons_a Y) Ys))))))) (forall ((Less (-> tptp.list_a tptp.list_a Bool)) (X tptp.list_a) (Y tptp.list_a) (Xs tptp.list_list_a) (Ys tptp.list_list_a)) (=> (@ (@ Less X) Y) (@ (@ (@ tptp.lexordp_list_a Less) (@ (@ tptp.cons_list_a X) Xs)) (@ (@ tptp.cons_list_a Y) Ys)))) (forall ((Less (-> tptp.a tptp.a Bool)) (X tptp.a) (Y tptp.a) (Xs tptp.list_a) (Ys tptp.list_a)) (=> (@ (@ Less X) Y) (@ (@ (@ tptp.lexordp_a Less) (@ (@ tptp.cons_a X) Xs)) (@ (@ tptp.cons_a Y) Ys)))) (forall ((Less (-> tptp.a tptp.a Bool)) (Xs tptp.list_a) (Ys tptp.list_a)) (=> (@ (@ (@ tptp.lexordp_a Less) Xs) Ys) (@ (@ (@ tptp.lexordp_eq_a Less) Xs) Ys))) (forall ((Less (-> tptp.list_a tptp.list_a Bool)) (Y tptp.list_a) (Ys tptp.list_list_a)) (@ (@ (@ tptp.lexordp_list_a Less) tptp.nil_list_a) (@ (@ tptp.cons_list_a Y) Ys))) (forall ((Less (-> tptp.a tptp.a Bool)) (Y tptp.a) (Ys tptp.list_a)) (@ (@ (@ tptp.lexordp_a Less) tptp.nil_a) (@ (@ tptp.cons_a Y) Ys))) (forall ((Less (-> tptp.list_a tptp.list_a Bool)) (A1 tptp.list_list_a) (A22 tptp.list_list_a)) (=> (@ (@ (@ tptp.lexordp_list_a Less) A1) A22) (=> (=> (= A1 tptp.nil_list_a) (forall ((Y2 tptp.list_a) (Ys3 tptp.list_list_a)) (not (= A22 (@ (@ tptp.cons_list_a Y2) Ys3))))) (=> (forall ((X2 tptp.list_a)) (=> (exists ((Xs3 tptp.list_list_a)) (= A1 (@ (@ tptp.cons_list_a X2) Xs3))) (forall ((Y2 tptp.list_a)) (=> (exists ((Ys3 tptp.list_list_a)) (= A22 (@ (@ tptp.cons_list_a Y2) Ys3))) (not (@ (@ Less X2) Y2)))))) (not (forall ((X2 tptp.list_a) (Y2 tptp.list_a) (Xs3 tptp.list_list_a)) (=> (= A1 (@ (@ tptp.cons_list_a X2) Xs3)) (forall ((Ys3 tptp.list_list_a)) (=> (= A22 (@ (@ tptp.cons_list_a Y2) Ys3)) (=> (not (@ (@ Less X2) Y2)) (=> (not (@ (@ Less Y2) X2)) (not (@ (@ (@ tptp.lexordp_list_a Less) Xs3) Ys3))))))))))))) (forall ((Less (-> tptp.a tptp.a Bool)) (A1 tptp.list_a) (A22 tptp.list_a)) (=> (@ (@ (@ tptp.lexordp_a Less) A1) A22) (=> (=> (= A1 tptp.nil_a) (forall ((Y2 tptp.a) (Ys3 tptp.list_a)) (not (= A22 (@ (@ tptp.cons_a Y2) Ys3))))) (=> (forall ((X2 tptp.a)) (=> (exists ((Xs3 tptp.list_a)) (= A1 (@ (@ tptp.cons_a X2) Xs3))) (forall ((Y2 tptp.a)) (=> (exists ((Ys3 tptp.list_a)) (= A22 (@ (@ tptp.cons_a Y2) Ys3))) (not (@ (@ Less X2) Y2)))))) (not (forall ((X2 tptp.a) (Y2 tptp.a) (Xs3 tptp.list_a)) (=> (= A1 (@ (@ tptp.cons_a X2) Xs3)) (forall ((Ys3 tptp.list_a)) (=> (= A22 (@ (@ tptp.cons_a Y2) Ys3)) (=> (not (@ (@ Less X2) Y2)) (=> (not (@ (@ Less Y2) X2)) (not (@ (@ (@ tptp.lexordp_a Less) Xs3) Ys3))))))))))))) (= tptp.lexordp_list_a (lambda ((Less2 (-> tptp.list_a tptp.list_a Bool)) (A12 tptp.list_list_a) (A23 tptp.list_list_a)) (or (exists ((Y3 tptp.list_a) (Ys2 tptp.list_list_a)) (and (= A12 tptp.nil_list_a) (= A23 (@ (@ tptp.cons_list_a Y3) Ys2)))) (exists ((X3 tptp.list_a) (Y3 tptp.list_a) (Xs2 tptp.list_list_a) (Ys2 tptp.list_list_a)) (and (= A12 (@ (@ tptp.cons_list_a X3) Xs2)) (= A23 (@ (@ tptp.cons_list_a Y3) Ys2)) (@ (@ Less2 X3) Y3))) (exists ((X3 tptp.list_a) (Y3 tptp.list_a) (Xs2 tptp.list_list_a) (Ys2 tptp.list_list_a)) (and (= A12 (@ (@ tptp.cons_list_a X3) Xs2)) (= A23 (@ (@ tptp.cons_list_a Y3) Ys2)) (not (@ (@ Less2 X3) Y3)) (not (@ (@ Less2 Y3) X3)) (@ (@ (@ tptp.lexordp_list_a Less2) Xs2) Ys2)))))) (= tptp.lexordp_a (lambda ((Less2 (-> tptp.a tptp.a Bool)) (A12 tptp.list_a) (A23 tptp.list_a)) (or (exists ((Y3 tptp.a) (Ys2 tptp.list_a)) (and (= A12 tptp.nil_a) (= A23 (@ (@ tptp.cons_a Y3) Ys2)))) (exists ((X3 tptp.a) (Y3 tptp.a) (Xs2 tptp.list_a) (Ys2 tptp.list_a)) (and (= A12 (@ (@ tptp.cons_a X3) Xs2)) (= A23 (@ (@ tptp.cons_a Y3) Ys2)) (@ (@ Less2 X3) Y3))) (exists ((X3 tptp.a) (Y3 tptp.a) (Xs2 tptp.list_a) (Ys2 tptp.list_a)) (and (= A12 (@ (@ tptp.cons_a X3) Xs2)) (= A23 (@ (@ tptp.cons_a Y3) Ys2)) (not (@ (@ Less2 X3) Y3)) (not (@ (@ Less2 Y3) X3)) (@ (@ (@ tptp.lexordp_a Less2) Xs2) Ys2)))))) (forall ((Less (-> tptp.list_a tptp.list_a Bool)) (X1 tptp.list_list_a) (X22 tptp.list_list_a) (P (-> tptp.list_list_a tptp.list_list_a Bool))) (=> (@ (@ (@ tptp.lexordp_list_a Less) X1) X22) (=> (forall ((Y2 tptp.list_a) (Ys3 tptp.list_list_a)) (@ (@ P tptp.nil_list_a) (@ (@ tptp.cons_list_a Y2) Ys3))) (=> (forall ((X2 tptp.list_a) (Y2 tptp.list_a) (Xs3 tptp.list_list_a) (Ys3 tptp.list_list_a)) (=> (@ (@ Less X2) Y2) (@ (@ P (@ (@ tptp.cons_list_a X2) Xs3)) (@ (@ tptp.cons_list_a Y2) Ys3)))) (=> (forall ((X2 tptp.list_a) (Y2 tptp.list_a) (Xs3 tptp.list_list_a) (Ys3 tptp.list_list_a)) (=> (not (@ (@ Less X2) Y2)) (=> (not (@ (@ Less Y2) X2)) (=> (@ (@ (@ tptp.lexordp_list_a Less) Xs3) Ys3) (=> (@ (@ P Xs3) Ys3) (@ (@ P (@ (@ tptp.cons_list_a X2) Xs3)) (@ (@ tptp.cons_list_a Y2) Ys3))))))) (@ (@ P X1) X22)))))) (forall ((Less (-> tptp.a tptp.a Bool)) (X1 tptp.list_a) (X22 tptp.list_a) (P (-> tptp.list_a tptp.list_a Bool))) (=> (@ (@ (@ tptp.lexordp_a Less) X1) X22) (=> (forall ((Y2 tptp.a) (Ys3 tptp.list_a)) (@ (@ P tptp.nil_a) (@ (@ tptp.cons_a Y2) Ys3))) (=> (forall ((X2 tptp.a) (Y2 tptp.a) (Xs3 tptp.list_a) (Ys3 tptp.list_a)) (=> (@ (@ Less X2) Y2) (@ (@ P (@ (@ tptp.cons_a X2) Xs3)) (@ (@ tptp.cons_a Y2) Ys3)))) (=> (forall ((X2 tptp.a) (Y2 tptp.a) (Xs3 tptp.list_a) (Ys3 tptp.list_a)) (=> (not (@ (@ Less X2) Y2)) (=> (not (@ (@ Less Y2) X2)) (=> (@ (@ (@ tptp.lexordp_a Less) Xs3) Ys3) (=> (@ (@ P Xs3) Ys3) (@ (@ P (@ (@ tptp.cons_a X2) Xs3)) (@ (@ tptp.cons_a Y2) Ys3))))))) (@ (@ P X1) X22)))))) (forall ((Ys tptp.list_a) (Xs tptp.list_a)) (=> (not (= Ys tptp.nil_a)) (@ (@ (@ tptp.lexordp_a tptp.less) Xs) (@ (@ tptp.append_a Xs) Ys)))) (forall ((X tptp.a) (Y tptp.a) (Us tptp.list_a) (Xs tptp.list_a) (Ys tptp.list_a)) (let ((_let_1 (@ tptp.append_a Us))) (=> (@ (@ tptp.less X) Y) (@ (@ (@ tptp.lexordp_a tptp.less) (@ _let_1 (@ (@ tptp.cons_a X) Xs))) (@ _let_1 (@ (@ tptp.cons_a Y) Ys)))))) (forall ((F (-> tptp.a tptp.a tptp.a))) (=> (@ tptp.semilattice_a F) (@ tptp.abel_semigroup_a F))) (forall ((Xs tptp.list_a) (Us tptp.list_a) (Vs tptp.list_a)) (let ((_let_1 (@ tptp.lexordp_a tptp.less))) (let ((_let_2 (@ tptp.append_a Xs))) (=> (@ (@ _let_1 (@ _let_2 Us)) (@ _let_2 Vs)) (=> (forall ((A2 tptp.a)) (not (@ (@ tptp.less A2) A2))) (@ (@ _let_1 Us) Vs)))))) (forall ((Us tptp.list_a) (Vs tptp.list_a) (Xs tptp.list_a)) (let ((_let_1 (@ tptp.append_a Xs))) (let ((_let_2 (@ tptp.lexordp_a tptp.less))) (=> (@ (@ _let_2 Us) Vs) (@ (@ _let_2 (@ _let_1 Us)) (@ _let_1 Vs)))))) (forall ((U tptp.list_a) (V tptp.list_a)) (@ (@ (@ tptp.lexordp_eq_a tptp.less) U) (@ (@ tptp.append_a U) V))) (forall ((Xs tptp.list_list_a) (Ys tptp.list_list_a) (Zs2 tptp.list_list_a)) (let ((_let_1 (@ tptp.append_list_a Xs))) (= (= (@ _let_1 Ys) (@ _let_1 Zs2)) (= Ys Zs2)))) (forall ((Xs tptp.list_a) (Ys tptp.list_a) (Zs2 tptp.list_a)) (let ((_let_1 (@ tptp.append_a Xs))) (= (= (@ _let_1 Ys) (@ _let_1 Zs2)) (= Ys Zs2)))) (forall ((Ys tptp.list_list_a) (Xs tptp.list_list_a) (Zs2 tptp.list_list_a)) (= (= (@ (@ tptp.append_list_a Ys) Xs) (@ (@ tptp.append_list_a Zs2) Xs)) (= Ys Zs2))) (forall ((Ys tptp.list_a) (Xs tptp.list_a) (Zs2 tptp.list_a)) (= (= (@ (@ tptp.append_a Ys) Xs) (@ (@ tptp.append_a Zs2) Xs)) (= Ys Zs2))) (forall ((Xs tptp.list_list_a) (Ys tptp.list_list_a) (Zs2 tptp.list_list_a)) (let ((_let_1 (@ tptp.append_list_a Xs))) (= (@ (@ tptp.append_list_a (@ _let_1 Ys)) Zs2) (@ _let_1 (@ (@ tptp.append_list_a Ys) Zs2))))) (forall ((Xs tptp.list_a) (Ys tptp.list_a) (Zs2 tptp.list_a)) (let ((_let_1 (@ tptp.append_a Xs))) (= (@ (@ tptp.append_a (@ _let_1 Ys)) Zs2) (@ _let_1 (@ (@ tptp.append_a Ys) Zs2))))) (forall ((A tptp.list_list_a) (B tptp.list_list_a) (C tptp.list_list_a)) (let ((_let_1 (@ tptp.append_list_a A))) (= (@ (@ tptp.append_list_a (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.append_list_a B) C))))) (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))))) (forall ((A tptp.list_list_a)) (= (@ (@ tptp.append_list_a A) tptp.nil_list_a) A)) (forall ((A tptp.list_a)) (= (@ (@ tptp.append_a A) tptp.nil_a) A)) (forall ((Xs tptp.list_list_a) (Ys tptp.list_list_a)) (= (= (@ (@ tptp.append_list_a Xs) Ys) tptp.nil_list_a) (and (= Xs tptp.nil_list_a) (= Ys tptp.nil_list_a)))) (forall ((Xs tptp.list_a) (Ys tptp.list_a)) (= (= (@ (@ tptp.append_a Xs) Ys) tptp.nil_a) (and (= Xs tptp.nil_a) (= Ys tptp.nil_a)))) (forall ((Xs tptp.list_list_a) (Ys tptp.list_list_a)) (= (= tptp.nil_list_a (@ (@ tptp.append_list_a Xs) Ys)) (and (= Xs tptp.nil_list_a) (= Ys tptp.nil_list_a)))) (forall ((Xs tptp.list_a) (Ys tptp.list_a)) (= (= tptp.nil_a (@ (@ tptp.append_a Xs) Ys)) (and (= Xs tptp.nil_a) (= Ys tptp.nil_a)))) (forall ((Ys tptp.list_list_a) (Xs tptp.list_list_a)) (= (= Ys (@ (@ tptp.append_list_a Xs) Ys)) (= Xs tptp.nil_list_a))) (forall ((Ys tptp.list_a) (Xs tptp.list_a)) (= (= Ys (@ (@ tptp.append_a Xs) Ys)) (= Xs tptp.nil_a))) (forall ((Xs tptp.list_list_a) (Ys tptp.list_list_a)) (= (= (@ (@ tptp.append_list_a Xs) Ys) Ys) (= Xs tptp.nil_list_a))) (forall ((Xs tptp.list_a) (Ys tptp.list_a)) (= (= (@ (@ tptp.append_a Xs) Ys) Ys) (= Xs tptp.nil_a))) (forall ((Xs tptp.list_list_a) (Ys tptp.list_list_a)) (= (= Xs (@ (@ tptp.append_list_a Xs) Ys)) (= Ys tptp.nil_list_a))) (forall ((Xs tptp.list_a) (Ys tptp.list_a)) (= (= Xs (@ (@ tptp.append_a Xs) Ys)) (= Ys tptp.nil_a))) (forall ((Xs tptp.list_list_a) (Ys tptp.list_list_a)) (= (= (@ (@ tptp.append_list_a Xs) Ys) Xs) (= Ys tptp.nil_list_a))) (forall ((Xs tptp.list_a) (Ys tptp.list_a)) (= (= (@ (@ tptp.append_a Xs) Ys) Xs) (= Ys tptp.nil_a))) (forall ((Xs tptp.list_list_a)) (= (@ (@ tptp.append_list_a Xs) tptp.nil_list_a) Xs)) (forall ((Xs tptp.list_a)) (= (@ (@ tptp.append_a Xs) tptp.nil_a) Xs)) (forall ((Xs tptp.list_list_a) (X tptp.list_a) (Ys tptp.list_list_a) (Y tptp.list_a)) (= (= (@ (@ tptp.append_list_a Xs) (@ (@ tptp.cons_list_a X) tptp.nil_list_a)) (@ (@ tptp.append_list_a Ys) (@ (@ tptp.cons_list_a Y) tptp.nil_list_a))) (and (= Xs Ys) (= X Y)))) (forall ((Xs tptp.list_a) (X tptp.a) (Ys tptp.list_a) (Y tptp.a)) (= (= (@ (@ tptp.append_a Xs) (@ (@ tptp.cons_a X) tptp.nil_a)) (@ (@ tptp.append_a Ys) (@ (@ tptp.cons_a Y) tptp.nil_a))) (and (= Xs Ys) (= X Y)))) (forall ((A tptp.list_list_a)) (= (@ (@ tptp.append_list_a tptp.nil_list_a) A) A)) (forall ((A tptp.list_a)) (= (@ (@ tptp.append_a tptp.nil_a) A) A)) (forall ((Ys tptp.list_list_a)) (= (@ (@ tptp.append_list_a tptp.nil_list_a) Ys) Ys)) (forall ((Ys tptp.list_a)) (= (@ (@ tptp.append_a tptp.nil_a) Ys) Ys)) (forall ((Xs tptp.list_list_a) (Ys tptp.list_list_a)) (=> (= Xs Ys) (= Xs (@ (@ tptp.append_list_a tptp.nil_list_a) Ys)))) (forall ((Xs tptp.list_a) (Ys tptp.list_a)) (=> (= Xs Ys) (= Xs (@ (@ tptp.append_a tptp.nil_a) Ys)))) (forall ((X tptp.list_a) (Xs1 tptp.list_list_a) (Ys tptp.list_list_a) (Xs tptp.list_list_a) (Zs2 tptp.list_list_a)) (let ((_let_1 (@ tptp.cons_list_a X))) (=> (= (@ _let_1 Xs1) Ys) (=> (= Xs (@ (@ tptp.append_list_a Xs1) Zs2)) (= (@ _let_1 Xs) (@ (@ tptp.append_list_a Ys) Zs2)))))) (forall ((X tptp.a) (Xs1 tptp.list_a) (Ys tptp.list_a) (Xs tptp.list_a) (Zs2 tptp.list_a)) (let ((_let_1 (@ tptp.cons_a X))) (=> (= (@ _let_1 Xs1) Ys) (=> (= Xs (@ (@ tptp.append_a Xs1) Zs2)) (= (@ _let_1 Xs) (@ (@ tptp.append_a Ys) Zs2)))))) (forall ((X tptp.list_a) (Xs tptp.list_list_a) (Ys tptp.list_list_a)) (let ((_let_1 (@ tptp.cons_list_a X))) (= (@ (@ tptp.append_list_a (@ _let_1 Xs)) Ys) (@ _let_1 (@ (@ tptp.append_list_a Xs) Ys))))) (forall ((X tptp.a) (Xs tptp.list_a) (Ys tptp.list_a)) (let ((_let_1 (@ tptp.cons_a X))) (= (@ (@ tptp.append_a (@ _let_1 Xs)) Ys) (@ _let_1 (@ (@ tptp.append_a Xs) Ys))))) (forall ((Less (-> tptp.list_a tptp.list_a Bool)) (Xs tptp.list_list_a) (Us tptp.list_list_a) (Vs tptp.list_list_a)) (let ((_let_1 (@ tptp.lexordp_list_a Less))) (let ((_let_2 (@ tptp.append_list_a Xs))) (=> (@ (@ _let_1 (@ _let_2 Us)) (@ _let_2 Vs)) (=> (forall ((A2 tptp.list_a)) (not (@ (@ Less A2) A2))) (@ (@ _let_1 Us) Vs)))))) (forall ((Less (-> tptp.a tptp.a Bool)) (Xs tptp.list_a) (Us tptp.list_a) (Vs tptp.list_a)) (let ((_let_1 (@ tptp.lexordp_a Less))) (let ((_let_2 (@ tptp.append_a Xs))) (=> (@ (@ _let_1 (@ _let_2 Us)) (@ _let_2 Vs)) (=> (forall ((A2 tptp.a)) (not (@ (@ Less A2) A2))) (@ (@ _let_1 Us) Vs)))))) (forall ((Less (-> tptp.list_a tptp.list_a Bool)) (Us tptp.list_list_a) (Vs tptp.list_list_a) (Xs tptp.list_list_a)) (let ((_let_1 (@ tptp.append_list_a Xs))) (let ((_let_2 (@ tptp.lexordp_list_a Less))) (=> (@ (@ _let_2 Us) Vs) (@ (@ _let_2 (@ _let_1 Us)) (@ _let_1 Vs)))))) (forall ((Less (-> tptp.a tptp.a Bool)) (Us tptp.list_a) (Vs tptp.list_a) (Xs tptp.list_a)) (let ((_let_1 (@ tptp.append_a Xs))) (let ((_let_2 (@ tptp.lexordp_a Less))) (=> (@ (@ _let_2 Us) Vs) (@ (@ _let_2 (@ _let_1 Us)) (@ _let_1 Vs)))))) (forall ((Less (-> tptp.list_a tptp.list_a Bool)) (U tptp.list_list_a) (V tptp.list_list_a)) (@ (@ (@ tptp.lexordp_eq_list_a Less) U) (@ (@ tptp.append_list_a U) V))) (forall ((Less (-> tptp.a tptp.a Bool)) (U tptp.list_a) (V tptp.list_a)) (@ (@ (@ tptp.lexordp_eq_a Less) U) (@ (@ tptp.append_a U) V))) (forall ((Xs tptp.list_list_a) (Ys tptp.list_list_a) (Zs2 tptp.list_list_a) (Ts tptp.list_list_a)) (= (= (@ (@ tptp.append_list_a Xs) Ys) (@ (@ tptp.append_list_a Zs2) Ts)) (exists ((Us2 tptp.list_list_a)) (let ((_let_1 (@ tptp.append_list_a Us2))) (or (and (= Xs (@ (@ tptp.append_list_a Zs2) Us2)) (= (@ _let_1 Ys) Ts)) (and (= (@ (@ tptp.append_list_a Xs) Us2) Zs2) (= Ys (@ _let_1 Ts)))))))) (forall ((Xs tptp.list_a) (Ys tptp.list_a) (Zs2 tptp.list_a) (Ts tptp.list_a)) (= (= (@ (@ tptp.append_a Xs) Ys) (@ (@ tptp.append_a Zs2) Ts)) (exists ((Us2 tptp.list_a)) (let ((_let_1 (@ tptp.append_a Us2))) (or (and (= Xs (@ (@ tptp.append_a Zs2) Us2)) (= (@ _let_1 Ys) Ts)) (and (= (@ (@ tptp.append_a Xs) Us2) Zs2) (= Ys (@ _let_1 Ts)))))))) (forall ((Xs tptp.list_list_a) (Xs1 tptp.list_list_a) (Zs2 tptp.list_list_a) (Ys tptp.list_list_a) (Us tptp.list_list_a)) (let ((_let_1 (@ tptp.append_list_a Xs))) (=> (= (@ _let_1 Xs1) Zs2) (=> (= Ys (@ (@ tptp.append_list_a Xs1) Us)) (= (@ _let_1 Ys) (@ (@ tptp.append_list_a Zs2) Us)))))) (forall ((Xs tptp.list_a) (Xs1 tptp.list_a) (Zs2 tptp.list_a) (Ys tptp.list_a) (Us tptp.list_a)) (let ((_let_1 (@ tptp.append_a Xs))) (=> (= (@ _let_1 Xs1) Zs2) (=> (= Ys (@ (@ tptp.append_a Xs1) Us)) (= (@ _let_1 Ys) (@ (@ tptp.append_a Zs2) Us)))))) (@ tptp.semigr656274520list_a tptp.append_list_a) (@ tptp.semigroup_list_a tptp.append_a) (forall ((Xs tptp.list_list_a) (P (-> tptp.list_list_a Bool))) (=> (not (= Xs tptp.nil_list_a)) (=> (forall ((X2 tptp.list_a)) (@ P (@ (@ tptp.cons_list_a X2) tptp.nil_list_a))) (=> (forall ((X2 tptp.list_a) (Xs3 tptp.list_list_a)) (=> (not (= Xs3 tptp.nil_list_a)) (=> (@ P Xs3) (@ P (@ (@ tptp.append_list_a Xs3) (@ (@ tptp.cons_list_a X2) tptp.nil_list_a)))))) (@ P Xs))))) (forall ((Xs tptp.list_a) (P (-> tptp.list_a Bool))) (=> (not (= Xs tptp.nil_a)) (=> (forall ((X2 tptp.a)) (@ P (@ (@ tptp.cons_a X2) tptp.nil_a))) (=> (forall ((X2 tptp.a) (Xs3 tptp.list_a)) (=> (not (= Xs3 tptp.nil_a)) (=> (@ P Xs3) (@ P (@ (@ tptp.append_a Xs3) (@ (@ tptp.cons_a X2) tptp.nil_a)))))) (@ P Xs))))) (forall ((Ys tptp.list_list_a) (Zs2 tptp.list_list_a) (X tptp.list_a) (Xs tptp.list_list_a)) (let ((_let_1 (@ (@ tptp.cons_list_a X) Xs))) (= (= (@ (@ tptp.append_list_a Ys) Zs2) _let_1) (or (and (= Ys tptp.nil_list_a) (= Zs2 _let_1)) (exists ((Ys4 tptp.list_list_a)) (and (= Ys (@ (@ tptp.cons_list_a X) Ys4)) (= (@ (@ tptp.append_list_a Ys4) Zs2) Xs))))))) (forall ((Ys tptp.list_a) (Zs2 tptp.list_a) (X tptp.a) (Xs tptp.list_a)) (let ((_let_1 (@ (@ tptp.cons_a X) Xs))) (= (= (@ (@ tptp.append_a Ys) Zs2) _let_1) (or (and (= Ys tptp.nil_a) (= Zs2 _let_1)) (exists ((Ys4 tptp.list_a)) (and (= Ys (@ (@ tptp.cons_a X) Ys4)) (= (@ (@ tptp.append_a Ys4) Zs2) Xs))))))) (forall ((X tptp.list_a) (Xs tptp.list_list_a) (Ys tptp.list_list_a) (Zs2 tptp.list_list_a)) (let ((_let_1 (@ (@ tptp.cons_list_a X) Xs))) (= (= _let_1 (@ (@ tptp.append_list_a Ys) Zs2)) (or (and (= Ys tptp.nil_list_a) (= _let_1 Zs2)) (exists ((Ys4 tptp.list_list_a)) (and (= (@ (@ tptp.cons_list_a X) Ys4) Ys) (= Xs (@ (@ tptp.append_list_a Ys4) Zs2)))))))) (forall ((X tptp.a) (Xs tptp.list_a) (Ys tptp.list_a) (Zs2 tptp.list_a)) (let ((_let_1 (@ (@ tptp.cons_a X) Xs))) (= (= _let_1 (@ (@ tptp.append_a Ys) Zs2)) (or (and (= Ys tptp.nil_a) (= _let_1 Zs2)) (exists ((Ys4 tptp.list_a)) (and (= (@ (@ tptp.cons_a X) Ys4) Ys) (= Xs (@ (@ tptp.append_a Ys4) Zs2)))))))) (forall ((Xs tptp.list_list_a)) (=> (not (= Xs tptp.nil_list_a)) (not (forall ((Ys3 tptp.list_list_a) (Y2 tptp.list_a)) (not (= Xs (@ (@ tptp.append_list_a Ys3) (@ (@ tptp.cons_list_a Y2) tptp.nil_list_a)))))))) (forall ((Xs tptp.list_a)) (=> (not (= Xs tptp.nil_a)) (not (forall ((Ys3 tptp.list_a) (Y2 tptp.a)) (not (= Xs (@ (@ tptp.append_a Ys3) (@ (@ tptp.cons_a Y2) tptp.nil_a)))))))) (forall ((P (-> tptp.list_list_a Bool)) (Xs tptp.list_list_a)) (=> (@ P tptp.nil_list_a) (=> (forall ((X2 tptp.list_a) (Xs3 tptp.list_list_a)) (=> (@ P Xs3) (@ P (@ (@ tptp.append_list_a Xs3) (@ (@ tptp.cons_list_a X2) tptp.nil_list_a))))) (@ P Xs)))) (forall ((P (-> tptp.list_a Bool)) (Xs tptp.list_a)) (=> (@ P tptp.nil_a) (=> (forall ((X2 tptp.a) (Xs3 tptp.list_a)) (=> (@ P Xs3) (@ P (@ (@ tptp.append_a Xs3) (@ (@ tptp.cons_a X2) tptp.nil_a))))) (@ P Xs)))) (forall ((Less (-> tptp.list_a tptp.list_a Bool)) (X tptp.list_a) (Y tptp.list_a) (Us tptp.list_list_a) (Xs tptp.list_list_a) (Ys tptp.list_list_a)) (let ((_let_1 (@ tptp.append_list_a Us))) (=> (@ (@ Less X) Y) (@ (@ (@ tptp.lexordp_list_a Less) (@ _let_1 (@ (@ tptp.cons_list_a X) Xs))) (@ _let_1 (@ (@ tptp.cons_list_a Y) Ys)))))) (forall ((Less (-> tptp.a tptp.a Bool)) (X tptp.a) (Y tptp.a) (Us tptp.list_a) (Xs tptp.list_a) (Ys tptp.list_a)) (let ((_let_1 (@ tptp.append_a Us))) (=> (@ (@ Less X) Y) (@ (@ (@ tptp.lexordp_a Less) (@ _let_1 (@ (@ tptp.cons_a X) Xs))) (@ _let_1 (@ (@ tptp.cons_a Y) Ys)))))) (forall ((Ys tptp.list_list_a) (Less (-> tptp.list_a tptp.list_a Bool)) (Xs tptp.list_list_a)) (=> (not (= Ys tptp.nil_list_a)) (@ (@ (@ tptp.lexordp_list_a Less) Xs) (@ (@ tptp.append_list_a Xs) Ys)))) (forall ((Ys tptp.list_a) (Less (-> tptp.a tptp.a Bool)) (Xs tptp.list_a)) (=> (not (= Ys tptp.nil_a)) (@ (@ (@ tptp.lexordp_a Less) Xs) (@ (@ tptp.append_a Xs) Ys)))) (forall ((F (-> tptp.a tptp.a tptp.a)) (A tptp.a)) (=> (@ tptp.semilattice_a F) (= (@ (@ F A) A) A))) (forall ((F (-> tptp.a tptp.a tptp.a)) (A tptp.a) (B tptp.a)) (let ((_let_1 (@ F A))) (let ((_let_2 (@ _let_1 B))) (=> (@ tptp.semilattice_a F) (= (@ _let_1 _let_2) _let_2))))) (forall ((F (-> tptp.a tptp.a tptp.a)) (A tptp.a) (B tptp.a)) (let ((_let_1 (@ (@ F A) B))) (=> (@ tptp.semilattice_a F) (= (@ (@ F _let_1) B) _let_1)))) (= (@ tptp.product_lists_list_a tptp.nil_list_list_a) _let_7) (= (@ tptp.product_lists_a tptp.nil_list_a) _let_6) (forall ((X tptp.a) (Xs tptp.list_a) (F (-> tptp.a tptp.list_list_a))) (= (@ (@ tptp.bind_a_list_a (@ (@ tptp.cons_a X) Xs)) F) (@ (@ tptp.append_list_a (@ F X)) (@ (@ tptp.bind_a_list_a Xs) F)))) (forall ((X tptp.list_a) (Xs tptp.list_list_a) (F (-> tptp.list_a tptp.list_a))) (= (@ (@ tptp.bind_list_a_a (@ (@ tptp.cons_list_a X) Xs)) F) (@ (@ tptp.append_a (@ F X)) (@ (@ tptp.bind_list_a_a Xs) F)))) (forall ((X tptp.list_a) (Xs tptp.list_list_a) (F (-> tptp.list_a tptp.list_list_a))) (= (@ (@ tptp.bind_list_a_list_a (@ (@ tptp.cons_list_a X) Xs)) F) (@ (@ tptp.append_list_a (@ F X)) (@ (@ tptp.bind_list_a_list_a Xs) F)))) (forall ((X tptp.a) (Xs tptp.list_a) (F (-> tptp.a tptp.list_a))) (= (@ (@ tptp.bind_a_a (@ (@ tptp.cons_a X) Xs)) F) (@ (@ tptp.append_a (@ F X)) (@ (@ tptp.bind_a_a Xs) F)))) (forall ((F (-> tptp.a tptp.list_list_a))) (= (@ (@ tptp.bind_a_list_a tptp.nil_a) F) tptp.nil_list_a)) (forall ((F (-> tptp.list_a tptp.list_a))) (= (@ (@ tptp.bind_list_a_a tptp.nil_list_a) F) tptp.nil_a)) (forall ((F (-> tptp.list_a tptp.list_list_a))) (= (@ (@ tptp.bind_list_a_list_a tptp.nil_list_a) F) tptp.nil_list_a)) (forall ((F (-> tptp.a tptp.list_a))) (= (@ (@ tptp.bind_a_a tptp.nil_a) F) tptp.nil_a)) (= tptp.abel_s1075322906list_a (lambda ((F2 (-> tptp.list_a tptp.list_a tptp.list_a))) (and (@ tptp.semigroup_list_a F2) (@ tptp.abel_s374399671list_a F2)))) (= tptp.abel_semigroup_a (lambda ((F2 (-> tptp.a tptp.a tptp.a))) (and (@ tptp.semigroup_a F2) (@ tptp.abel_s2117090225ioms_a F2)))) (forall ((F (-> tptp.list_a tptp.list_a tptp.list_a))) (=> (@ tptp.semigroup_list_a F) (=> (@ tptp.abel_s374399671list_a F) (@ tptp.abel_s1075322906list_a F)))) (forall ((F (-> tptp.a tptp.a tptp.a))) (=> (@ tptp.semigroup_a F) (=> (@ tptp.abel_s2117090225ioms_a F) (@ tptp.abel_semigroup_a F)))) (forall ((F (-> tptp.a tptp.a tptp.a))) (=> (forall ((A2 tptp.a) (B2 tptp.a)) (= (@ (@ F A2) B2) (@ (@ F B2) A2))) (@ tptp.abel_s2117090225ioms_a F))) (= tptp.abel_s2117090225ioms_a (lambda ((F2 (-> tptp.a tptp.a tptp.a))) (forall ((A3 tptp.a) (B3 tptp.a)) (= (@ (@ F2 A3) B3) (@ (@ F2 B3) A3))))) (forall ((F (-> tptp.a tptp.a tptp.a))) (=> (@ tptp.abel_semigroup_a F) (@ tptp.abel_s2117090225ioms_a F))) (forall ((F (-> tptp.a tptp.a tptp.a))) (=> (@ tptp.abel_semigroup_a F) (=> (@ tptp.semilattice_axioms_a F) (@ tptp.semilattice_a F)))) (= tptp.semilattice_a (lambda ((F2 (-> tptp.a tptp.a tptp.a))) (and (@ tptp.abel_semigroup_a F2) (@ tptp.semilattice_axioms_a F2)))) (forall ((F (-> tptp.a tptp.a tptp.a))) (=> (@ tptp.semilattice_a F) (@ tptp.semilattice_axioms_a F))) (= (@ tptp.subseqs_list_a tptp.nil_list_a) _let_7) (= (@ tptp.subseqs_a tptp.nil_a) _let_6) (forall ((F (-> tptp.a tptp.list_list_a)) (X tptp.a) (Xs tptp.list_a)) (let ((_let_1 (@ tptp.maps_a_list_a F))) (= (@ _let_1 (@ (@ tptp.cons_a X) Xs)) (@ (@ tptp.append_list_a (@ F X)) (@ _let_1 Xs))))) (forall ((F (-> tptp.list_a tptp.list_a)) (X tptp.list_a) (Xs tptp.list_list_a)) (let ((_let_1 (@ tptp.maps_list_a_a F))) (= (@ _let_1 (@ (@ tptp.cons_list_a X) Xs)) (@ (@ tptp.append_a (@ F X)) (@ _let_1 Xs))))) (forall ((F (-> tptp.list_a tptp.list_list_a)) (X tptp.list_a) (Xs tptp.list_list_a)) (let ((_let_1 (@ tptp.maps_list_a_list_a F))) (= (@ _let_1 (@ (@ tptp.cons_list_a X) Xs)) (@ (@ tptp.append_list_a (@ F X)) (@ _let_1 Xs))))) (forall ((F (-> tptp.a tptp.list_a)) (X tptp.a) (Xs tptp.list_a)) (let ((_let_1 (@ tptp.maps_a_a F))) (= (@ _let_1 (@ (@ tptp.cons_a X) Xs)) (@ (@ tptp.append_a (@ F X)) (@ _let_1 Xs))))) (forall ((F (-> tptp.a tptp.list_list_a))) (= (@ (@ tptp.maps_a_list_a F) tptp.nil_a) tptp.nil_list_a)) (forall ((F (-> tptp.list_a tptp.list_a))) (= (@ (@ tptp.maps_list_a_a F) tptp.nil_list_a) tptp.nil_a)) (forall ((F (-> tptp.list_a tptp.list_list_a))) (= (@ (@ tptp.maps_list_a_list_a F) tptp.nil_list_a) tptp.nil_list_a)) (forall ((F (-> tptp.a tptp.list_a))) (= (@ (@ tptp.maps_a_a F) tptp.nil_a) tptp.nil_a)) (@ tptp.transp_a tptp.less) (forall ((X tptp.list_a)) (= (@ (@ tptp.insert_list_a X) tptp.nil_list_a) (@ (@ tptp.cons_list_a X) tptp.nil_list_a))) (forall ((X tptp.a)) (= (@ (@ tptp.insert_a X) tptp.nil_a) (@ (@ tptp.cons_a X) tptp.nil_a))) (forall ((Xss2 tptp.list_list_list_a) (Ys tptp.list_list_a) (Zs2 tptp.list_list_a)) (let ((_let_1 (= Xss2 tptp.nil_list_list_a))) (= (= (@ tptp.concat_list_a Xss2) (@ (@ tptp.append_list_a Ys) Zs2)) (and (=> _let_1 (and (= Ys tptp.nil_list_a) (= Zs2 tptp.nil_list_a))) (=> (not _let_1) (exists ((Xss1 tptp.list_list_list_a) (Xs2 tptp.list_list_a) (Xs4 tptp.list_list_a) (Xss22 tptp.list_list_list_a)) (and (= Xss2 (@ (@ tptp.append_list_list_a Xss1) (@ (@ tptp.cons_list_list_a (@ (@ tptp.append_list_a Xs2) Xs4)) Xss22))) (= Ys (@ (@ tptp.append_list_a (@ tptp.concat_list_a Xss1)) Xs2)) (= Zs2 (@ (@ tptp.append_list_a Xs4) (@ tptp.concat_list_a Xss22)))))))))) (forall ((Xss2 tptp.list_list_a) (Ys tptp.list_a) (Zs2 tptp.list_a)) (let ((_let_1 (= Xss2 tptp.nil_list_a))) (= (= (@ tptp.concat_a Xss2) (@ (@ tptp.append_a Ys) Zs2)) (and (=> _let_1 (and (= Ys tptp.nil_a) (= Zs2 tptp.nil_a))) (=> (not _let_1) (exists ((Xss1 tptp.list_list_a) (Xs2 tptp.list_a) (Xs4 tptp.list_a) (Xss22 tptp.list_list_a)) (and (= Xss2 (@ (@ tptp.append_list_a Xss1) (@ (@ tptp.cons_list_a (@ (@ tptp.append_a Xs2) Xs4)) Xss22))) (= Ys (@ (@ tptp.append_a (@ tptp.concat_a Xss1)) Xs2)) (= Zs2 (@ (@ tptp.append_a Xs4) (@ tptp.concat_a Xss22)))))))))) (forall ((X tptp.list_a) (Xs tptp.list_list_a)) (let ((_let_1 (@ tptp.cons_list_a X))) (= (@ tptp.rotate1_list_a (@ _let_1 Xs)) (@ (@ tptp.append_list_a Xs) (@ _let_1 tptp.nil_list_a))))) (forall ((X tptp.a) (Xs tptp.list_a)) (let ((_let_1 (@ tptp.cons_a X))) (= (@ tptp.rotate1_a (@ _let_1 Xs)) (@ (@ tptp.append_a Xs) (@ _let_1 tptp.nil_a))))) (forall ((Xs tptp.list_list_a)) (= (= (@ tptp.rotate1_list_a Xs) tptp.nil_list_a) (= Xs tptp.nil_list_a))) (forall ((Xs tptp.list_a)) (= (= (@ tptp.rotate1_a Xs) tptp.nil_a) (= Xs tptp.nil_a))) (forall ((Xs tptp.list_list_list_a) (Ys tptp.list_list_list_a)) (= (@ tptp.concat_list_a (@ (@ tptp.append_list_list_a Xs) Ys)) (@ (@ tptp.append_list_a (@ tptp.concat_list_a Xs)) (@ tptp.concat_list_a Ys)))) (forall ((Xs tptp.list_list_a) (Ys tptp.list_list_a)) (= (@ tptp.concat_a (@ (@ tptp.append_list_a Xs) Ys)) (@ (@ tptp.append_a (@ tptp.concat_a Xs)) (@ tptp.concat_a Ys)))) (= (@ tptp.concat_list_a tptp.nil_list_list_a) tptp.nil_list_a) (= (@ tptp.concat_a tptp.nil_list_a) tptp.nil_a) (forall ((X tptp.list_list_a) (Xs tptp.list_list_list_a)) (= (@ tptp.concat_list_a (@ (@ tptp.cons_list_list_a X) Xs)) (@ (@ tptp.append_list_a X) (@ tptp.concat_list_a Xs)))) (forall ((X tptp.list_a) (Xs tptp.list_list_a)) (= (@ tptp.concat_a (@ (@ tptp.cons_list_a X) Xs)) (@ (@ tptp.append_a X) (@ tptp.concat_a Xs)))) (= (@ tptp.rotate1_list_a tptp.nil_list_a) tptp.nil_list_a) (= (@ tptp.rotate1_a tptp.nil_a) tptp.nil_a) (forall ((Xss2 tptp.list_list_list_a) (Ys tptp.list_list_a) (Zs2 tptp.list_list_a)) (=> (= (@ tptp.concat_list_a Xss2) (@ (@ tptp.append_list_a Ys) Zs2)) (=> (not (= Xss2 tptp.nil_list_list_a)) (exists ((Xss12 tptp.list_list_list_a) (Xs3 tptp.list_list_a) (Xs5 tptp.list_list_a) (Xss23 tptp.list_list_list_a)) (and (= Xss2 (@ (@ tptp.append_list_list_a Xss12) (@ (@ tptp.cons_list_list_a (@ (@ tptp.append_list_a Xs3) Xs5)) Xss23))) (= Ys (@ (@ tptp.append_list_a (@ tptp.concat_list_a Xss12)) Xs3)) (= Zs2 (@ (@ tptp.append_list_a Xs5) (@ tptp.concat_list_a Xss23)))))))) (forall ((Xss2 tptp.list_list_a) (Ys tptp.list_a) (Zs2 tptp.list_a)) (=> (= (@ tptp.concat_a Xss2) (@ (@ tptp.append_a Ys) Zs2)) (=> (not (= Xss2 tptp.nil_list_a)) (exists ((Xss12 tptp.list_list_a) (Xs3 tptp.list_a) (Xs5 tptp.list_a) (Xss23 tptp.list_list_a)) (and (= Xss2 (@ (@ tptp.append_list_a Xss12) (@ (@ tptp.cons_list_a (@ (@ tptp.append_a Xs3) Xs5)) Xss23))) (= Ys (@ (@ tptp.append_a (@ tptp.concat_a Xss12)) Xs3)) (= Zs2 (@ (@ tptp.append_a Xs5) (@ tptp.concat_a Xss23)))))))) (forall ((Xs tptp.list_list_a) (X tptp.list_a)) (= (@ tptp.butlast_list_a (@ (@ tptp.append_list_a Xs) (@ (@ tptp.cons_list_a X) tptp.nil_list_a))) Xs)) (forall ((Xs tptp.list_a) (X tptp.a)) (= (@ tptp.butlast_a (@ (@ tptp.append_a Xs) (@ (@ tptp.cons_a X) tptp.nil_a))) Xs)) (forall ((P (-> tptp.list_a Bool))) (not (@ (@ tptp.list_ex1_list_a P) tptp.nil_list_a))) (forall ((P (-> tptp.a Bool))) (not (@ (@ tptp.list_ex1_a P) tptp.nil_a))) (forall ((Ys tptp.list_list_a) (Xs tptp.list_list_a)) (let ((_let_1 (@ tptp.append_list_a Xs))) (let ((_let_2 (@ tptp.butlast_list_a (@ _let_1 Ys)))) (let ((_let_3 (= Ys tptp.nil_list_a))) (and (=> _let_3 (= _let_2 (@ tptp.butlast_list_a Xs))) (=> (not _let_3) (= _let_2 (@ _let_1 (@ tptp.butlast_list_a Ys))))))))) (forall ((Ys tptp.list_a) (Xs tptp.list_a)) (let ((_let_1 (@ tptp.append_a Xs))) (let ((_let_2 (@ tptp.butlast_a (@ _let_1 Ys)))) (let ((_let_3 (= Ys tptp.nil_a))) (and (=> _let_3 (= _let_2 (@ tptp.butlast_a Xs))) (=> (not _let_3) (= _let_2 (@ _let_1 (@ tptp.butlast_a Ys))))))))) (= (@ tptp.butlast_list_a tptp.nil_list_a) tptp.nil_list_a) (= (@ tptp.butlast_a tptp.nil_a) tptp.nil_a) (forall ((Xs tptp.list_list_a) (X tptp.list_a)) (let ((_let_1 (@ tptp.cons_list_a X))) (let ((_let_2 (@ tptp.butlast_list_a (@ _let_1 Xs)))) (let ((_let_3 (= Xs tptp.nil_list_a))) (and (=> _let_3 (= _let_2 tptp.nil_list_a)) (=> (not _let_3) (= _let_2 (@ _let_1 (@ tptp.butlast_list_a Xs))))))))) (forall ((Xs tptp.list_a) (X tptp.a)) (let ((_let_1 (@ tptp.cons_a X))) (let ((_let_2 (@ tptp.butlast_a (@ _let_1 Xs)))) (let ((_let_3 (= Xs tptp.nil_a))) (and (=> _let_3 (= _let_2 tptp.nil_a)) (=> (not _let_3) (= _let_2 (@ _let_1 (@ tptp.butlast_a Xs))))))))) (forall ((Xs tptp.list_list_a)) (=> (not (= Xs tptp.nil_list_a)) (= (@ (@ tptp.append_list_a (@ tptp.butlast_list_a Xs)) (@ (@ tptp.cons_list_a (@ tptp.last_list_a Xs)) tptp.nil_list_a)) Xs))) (forall ((Xs tptp.list_a)) (=> (not (= Xs tptp.nil_a)) (= (@ (@ tptp.append_a (@ tptp.butlast_a Xs)) (@ (@ tptp.cons_a (@ tptp.last_a Xs)) tptp.nil_a)) Xs))) (forall ((Xs tptp.list_list_a) (X tptp.list_a) (Ys tptp.list_list_a)) (= (= (@ (@ tptp.append_list_a Xs) (@ (@ tptp.cons_list_a X) tptp.nil_list_a)) Ys) (and (not (= Ys tptp.nil_list_a)) (= (@ tptp.butlast_list_a Ys) Xs) (= (@ tptp.last_list_a Ys) X)))) (forall ((Xs tptp.list_a) (X tptp.a) (Ys tptp.list_a)) (= (= (@ (@ tptp.append_a Xs) (@ (@ tptp.cons_a X) tptp.nil_a)) Ys) (and (not (= Ys tptp.nil_a)) (= (@ tptp.butlast_a Ys) Xs) (= (@ tptp.last_a Ys) X)))) (forall ((Ys tptp.list_list_a) (Xs tptp.list_list_a)) (=> (not (= Ys tptp.nil_list_a)) (= (@ tptp.last_list_a (@ (@ tptp.append_list_a Xs) Ys)) (@ tptp.last_list_a Ys)))) (forall ((Ys tptp.list_a) (Xs tptp.list_a)) (=> (not (= Ys tptp.nil_a)) (= (@ tptp.last_a (@ (@ tptp.append_a Xs) Ys)) (@ tptp.last_a Ys)))) (forall ((Ys tptp.list_a) (Xs tptp.list_a)) (=> (= Ys tptp.nil_a) (= (@ tptp.last_a (@ (@ tptp.append_a Xs) Ys)) (@ tptp.last_a Xs)))) (= tptp.b (@ (@ tptp.inf tptp.b) tptp.c)) _let_5 (= tptp.a2 _let_1) _let_4 _let_3 (not false) true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.54/0.72 )
% 0.54/0.72 % SZS output end Proof for ITP119^1
% 0.54/0.72 % cvc5---1.0.5 exiting
% 0.54/0.72 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------