%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP092^2 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:55:29 AM UTC 2026
% Result : Theorem 63.00s 10.29s
% Output : Refutation 63.00s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP092^2 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.14/0.34 % Computer : n029.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Feb 24 08:26:14 EST 2026
% 0.14/0.34 % CPUTime :
% 0.14/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.31/0.46 ---- Original DTF file ---
% 0.31/0.46 thf(spec,logic,$$dhol).
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 % File : ITP092^2 : TPTP v9.2.1. Released v7.5.0.
% 0.31/0.46 % Domain : Interactive Theorem Proving
% 0.31/0.46 % Problem : Sledgehammer Kuratowski problem prob_158__5524402_1
% 0.31/0.46 % Version : Especial.
% 0.31/0.46 % English :
% 0.31/0.46
% 0.31/0.46 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.31/0.46 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.31/0.46 % Source : [Des21]
% 0.31/0.46 % Names : Kuratowski/prob_158__5524402_1 [Des21]
% 0.31/0.46
% 0.31/0.46 % Status : Theorem
% 0.31/0.46 % Rating : 0.67 v8.1.0, 0.75 v7.5.0
% 0.31/0.46 % Syntax : Number of formulae : 322 ( 119 unt; 55 typ; 0 def)
% 0.31/0.46 % Number of atoms : 749 ( 473 equ; 0 cnn)
% 0.31/0.46 % Maximal formula atoms : 26 ( 2 avg)
% 0.31/0.46 % Number of connectives : 8153 ( 211 ~; 22 |; 91 &;7441 @)
% 0.31/0.46 % ( 0 <=>; 388 =>; 0 <=; 0 <~>)
% 0.31/0.46 % Maximal formula depth : 34 ( 10 avg)
% 0.31/0.46 % Number of types : 4 ( 3 usr)
% 0.31/0.46 % Number of type conns : 234 ( 234 >; 0 *; 0 +; 0 <<)
% 0.31/0.46 % Number of symbols : 55 ( 52 usr; 4 con; 0-5 aty)
% 0.31/0.46 % Number of variables : 1498 ( 7 ^;1363 !; 72 ?;1498 :)
% 0.31/0.46 % ( 56 !>; 0 ?*; 0 @-; 0 @+)
% 0.31/0.46 % SPC : TH1_THM_EQU_NAR
% 0.31/0.46
% 0.31/0.46 % Comments : This file was generated by Sledgehammer 2021-02-23 16:29:25.897
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 % Could-be-implicit typings (7)
% 0.31/0.46 thf(ty_t_Pair__Digraph_Opair__pre__digraph_Opair__pre__digraph__ext,type,
% 0.31/0.46 pair_p1731315293ph_ext: $tType > $tType > $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_t_Product__Type_Ounit,type,
% 0.31/0.46 product_unit: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_t_Product__Type_Oprod,type,
% 0.31/0.46 product_prod: $tType > $tType > $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_t_List_Olist,type,
% 0.31/0.46 list: $tType > $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_t_Set_Oset,type,
% 0.31/0.46 set: $tType > $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_t_Nat_Onat,type,
% 0.31/0.46 nat: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_tf_a,type,
% 0.31/0.46 a: $tType ).
% 0.31/0.46
% 0.31/0.46 % Explicit typings (48)
% 0.31/0.46 thf(sy_cl_HOL_Otype,type,
% 0.31/0.46 type:
% 0.31/0.46 !>[A: $tType] : $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_cl_Orderings_Oord,type,
% 0.31/0.46 ord:
% 0.31/0.46 !>[A: $tType] : $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_cl_Orderings_Olinorder,type,
% 0.31/0.46 linorder:
% 0.31/0.46 !>[A: $tType] : $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Groups_Ozero__class_Ozero,type,
% 0.31/0.46 zero_zero:
% 0.31/0.46 !>[A: $tType] : A ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_If,type,
% 0.31/0.46 if:
% 0.31/0.46 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Kuratowski__Mirabelle__hkvioyikiw_Oprogressing,type,
% 0.31/0.46 kurato990191779essing:
% 0.31/0.46 !>[A: $tType] : ( ( list @ ( product_prod @ A @ A ) ) > $o ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_List_Oappend,type,
% 0.31/0.46 append:
% 0.31/0.46 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > ( list @ A ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_List_Obind,type,
% 0.31/0.46 bind:
% 0.31/0.46 !>[A: $tType,B: $tType] : ( ( list @ A ) > ( A > ( list @ B ) ) > ( list @ B ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_List_Oconcat,type,
% 0.31/0.46 concat:
% 0.31/0.46 !>[A: $tType] : ( ( list @ ( list @ A ) ) > ( list @ A ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_List_Oinsert,type,
% 0.31/0.46 insert:
% 0.31/0.46 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_List_Olenlex,type,
% 0.31/0.46 lenlex:
% 0.31/0.46 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > ( set @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_List_Olex,type,
% 0.31/0.46 lex:
% 0.31/0.46 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > ( set @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_List_Olexord,type,
% 0.31/0.46 lexord:
% 0.31/0.46 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > ( set @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_List_Olist_OCons,type,
% 0.31/0.46 cons:
% 0.31/0.46 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_List_Olist_ONil,type,
% 0.31/0.46 nil:
% 0.31/0.46 !>[A: $tType] : ( list @ A ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_List_Olist_Oset,type,
% 0.31/0.46 set2:
% 0.31/0.46 !>[A: $tType] : ( ( list @ A ) > ( set @ A ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_List_Olistrel,type,
% 0.31/0.46 listrel:
% 0.31/0.46 !>[A: $tType,B: $tType] : ( ( set @ ( product_prod @ A @ B ) ) > ( set @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_List_Olistrel1,type,
% 0.31/0.46 listrel1:
% 0.31/0.46 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > ( set @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_List_Omaps,type,
% 0.31/0.46 maps:
% 0.31/0.46 !>[A: $tType,B: $tType] : ( ( A > ( list @ B ) ) > ( list @ A ) > ( list @ B ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_List_Omeasures,type,
% 0.31/0.46 measures:
% 0.31/0.46 !>[A: $tType] : ( ( list @ ( A > nat ) ) > ( set @ ( product_prod @ A @ A ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_List_Omember,type,
% 0.31/0.46 member:
% 0.31/0.46 !>[A: $tType] : ( ( list @ A ) > A > $o ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_List_On__lists,type,
% 0.31/0.46 n_lists:
% 0.31/0.46 !>[A: $tType] : ( nat > ( list @ A ) > ( list @ ( list @ A ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_List_Oproduct__lists,type,
% 0.31/0.46 product_lists:
% 0.31/0.46 !>[A: $tType] : ( ( list @ ( list @ A ) ) > ( list @ ( list @ A ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_List_Osubseqs,type,
% 0.31/0.46 subseqs:
% 0.31/0.46 !>[A: $tType] : ( ( list @ A ) > ( list @ ( list @ A ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_List_Ozip,type,
% 0.31/0.46 zip:
% 0.31/0.46 !>[A: $tType,B: $tType] : ( ( list @ A ) > ( list @ B ) > ( list @ ( product_prod @ A @ B ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Multiset_Olinorder__class_Opart,type,
% 0.31/0.46 linorder_part:
% 0.31/0.46 !>[B: $tType,A: $tType] : ( ( B > A ) > A > ( list @ B ) > ( product_prod @ ( list @ B ) @ ( product_prod @ ( list @ B ) @ ( list @ B ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Nat_Osize__class_Osize,type,
% 0.31/0.46 size_size:
% 0.31/0.46 !>[A: $tType] : ( A > nat ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Orderings_Oord__class_Oless,type,
% 0.31/0.46 ord_less:
% 0.31/0.46 !>[A: $tType] : ( A > A > $o ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Pair__Digraph_Oco__path,type,
% 0.31/0.46 pair_co_path:
% 0.31/0.46 !>[A: $tType] : ( ( product_prod @ A @ A ) > A > ( list @ ( product_prod @ A @ A ) ) > ( list @ ( product_prod @ A @ A ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Pair__Digraph_Oco__path__rel,type,
% 0.31/0.46 pair_co_path_rel:
% 0.31/0.46 !>[A: $tType] : ( ( product_prod @ ( product_prod @ A @ A ) @ ( product_prod @ A @ ( list @ ( product_prod @ A @ A ) ) ) ) > ( product_prod @ ( product_prod @ A @ A ) @ ( product_prod @ A @ ( list @ ( product_prod @ A @ A ) ) ) ) > $o ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Pair__Digraph_Opawalk__verts,type,
% 0.31/0.46 pair_pawalk_verts:
% 0.31/0.46 !>[A: $tType] : ( A > ( list @ ( product_prod @ A @ A ) ) > ( list @ A ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Pair__Digraph_Osd__path,type,
% 0.31/0.46 pair_sd_path:
% 0.31/0.46 !>[A: $tType] : ( ( product_prod @ A @ A ) > A > ( list @ ( product_prod @ A @ A ) ) > ( list @ ( product_prod @ A @ A ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Pair__Digraph_Osd__path__rel,type,
% 0.31/0.46 pair_sd_path_rel:
% 0.31/0.46 !>[A: $tType] : ( ( product_prod @ ( product_prod @ A @ A ) @ ( product_prod @ A @ ( list @ ( product_prod @ A @ A ) ) ) ) > ( product_prod @ ( product_prod @ A @ A ) @ ( product_prod @ A @ ( list @ ( product_prod @ A @ A ) ) ) ) > $o ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Permutations_Oinverse__permutation__of__list,type,
% 0.31/0.46 invers965609412f_list:
% 0.31/0.46 !>[A: $tType] : ( ( list @ ( product_prod @ A @ A ) ) > A > A ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Permutations_Oinverse__permutation__of__list__rel,type,
% 0.31/0.46 invers1507583541st_rel:
% 0.31/0.46 !>[A: $tType] : ( ( product_prod @ ( list @ ( product_prod @ A @ A ) ) @ A ) > ( product_prod @ ( list @ ( product_prod @ A @ A ) ) @ A ) > $o ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Permutations_Olist__permutes,type,
% 0.31/0.46 list_permutes:
% 0.31/0.46 !>[A: $tType] : ( ( list @ ( product_prod @ A @ A ) ) > ( set @ A ) > $o ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Permutations_Opermutation__of__list,type,
% 0.31/0.46 permutation_of_list:
% 0.31/0.46 !>[A: $tType] : ( ( list @ ( product_prod @ A @ A ) ) > A > A ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Product__Type_OPair,type,
% 0.31/0.46 product_Pair:
% 0.31/0.46 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Product__Type_Ointernal__case__prod,type,
% 0.31/0.46 produc2004651681e_prod:
% 0.31/0.46 !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > ( product_prod @ A @ B ) > C ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod,type,
% 0.31/0.46 product_rec_prod:
% 0.31/0.46 !>[A: $tType,B: $tType,T: $tType] : ( ( A > B > T ) > ( product_prod @ A @ B ) > T ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Relation_Oasym,type,
% 0.31/0.46 asym:
% 0.31/0.46 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > $o ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Relation_Oirrefl,type,
% 0.31/0.46 irrefl:
% 0.31/0.46 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > $o ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Set_OCollect,type,
% 0.31/0.46 collect:
% 0.31/0.46 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Set_Othe__elem,type,
% 0.31/0.46 the_elem:
% 0.31/0.46 !>[A: $tType] : ( ( set @ A ) > A ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Wellfounded_Oaccp,type,
% 0.31/0.46 accp:
% 0.31/0.46 !>[A: $tType] : ( ( A > A > $o ) > A > $o ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_member,type,
% 0.31/0.46 member2:
% 0.31/0.46 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_v_e,type,
% 0.31/0.46 e: product_prod @ a @ a ).
% 0.31/0.46
% 0.31/0.46 thf(sy_v_es,type,
% 0.31/0.46 es: list @ ( product_prod @ a @ a ) ).
% 0.31/0.46
% 0.31/0.46 % Relevant facts (255)
% 0.31/0.46 thf(fact_0_assms,axiom,
% 0.31/0.46 kurato990191779essing @ a @ ( cons @ ( product_prod @ a @ a ) @ e @ es ) ).
% 0.31/0.46
% 0.31/0.46 % assms
% 0.31/0.46 thf(fact_1_progressing__def,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( kurato990191779essing @ A )
% 0.31/0.46 = ( ^ [P: list @ ( product_prod @ A @ A )] :
% 0.31/0.46 ! [Xs: list @ ( product_prod @ A @ A ),X: A,Y: A,Ys: list @ ( product_prod @ A @ A )] :
% 0.31/0.46 ( P
% 0.31/0.46 != ( append @ ( product_prod @ A @ A ) @ Xs @ ( cons @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y ) @ ( cons @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y @ X ) @ Ys ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % progressing_def
% 0.31/0.46 thf(fact_2_append_Oassoc,axiom,
% 0.31/0.46 ! [A: $tType,A2: list @ A,B2: list @ A,C2: list @ A] :
% 0.31/0.46 ( ( append @ A @ ( append @ A @ A2 @ B2 ) @ C2 )
% 0.31/0.46 = ( append @ A @ A2 @ ( append @ A @ B2 @ C2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % append.assoc
% 0.31/0.46 thf(fact_3_append__assoc,axiom,
% 0.31/0.46 ! [A: $tType,Xs2: list @ A,Ys2: list @ A,Zs: list @ A] :
% 0.31/0.46 ( ( append @ A @ ( append @ A @ Xs2 @ Ys2 ) @ Zs )
% 0.31/0.46 = ( append @ A @ Xs2 @ ( append @ A @ Ys2 @ Zs ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % append_assoc
% 0.31/0.46 thf(fact_4_append__same__eq,axiom,
% 0.31/0.46 ! [A: $tType,Ys2: list @ A,Xs2: list @ A,Zs: list @ A] :
% 0.31/0.46 ( ( ( append @ A @ Ys2 @ Xs2 )
% 0.31/0.46 = ( append @ A @ Zs @ Xs2 ) )
% 0.31/0.46 = ( Ys2 = Zs ) ) ).
% 0.31/0.46
% 0.31/0.46 % append_same_eq
% 0.31/0.46 thf(fact_5_same__append__eq,axiom,
% 0.31/0.46 ! [A: $tType,Xs2: list @ A,Ys2: list @ A,Zs: list @ A] :
% 0.31/0.46 ( ( ( append @ A @ Xs2 @ Ys2 )
% 0.31/0.46 = ( append @ A @ Xs2 @ Zs ) )
% 0.31/0.46 = ( Ys2 = Zs ) ) ).
% 0.31/0.46
% 0.31/0.46 % same_append_eq
% 0.31/0.46 thf(fact_6_list_Oinject,axiom,
% 0.31/0.46 ! [A: $tType,X21: A,X22: list @ A,Y21: A,Y22: list @ A] :
% 0.31/0.46 ( ( ( cons @ A @ X21 @ X22 )
% 0.31/0.46 = ( cons @ A @ Y21 @ Y22 ) )
% 0.31/0.46 = ( ( X21 = Y21 )
% 0.31/0.46 & ( X22 = Y22 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % list.inject
% 0.31/0.46 thf(fact_7_prod_Oinject,axiom,
% 0.31/0.46 ! [A: $tType,B: $tType,X1: A,X2: B,Y1: A,Y2: B] :
% 0.31/0.46 ( ( ( product_Pair @ A @ B @ X1 @ X2 )
% 0.31/0.46 = ( product_Pair @ A @ B @ Y1 @ Y2 ) )
% 0.31/0.46 = ( ( X1 = Y1 )
% 0.31/0.46 & ( X2 = Y2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % prod.inject
% 0.31/0.46 thf(fact_8_old_Oprod_Oinject,axiom,
% 0.31/0.46 ! [A: $tType,B: $tType,A2: A,B2: B,A3: A,B3: B] :
% 0.31/0.46 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 0.31/0.46 = ( product_Pair @ A @ B @ A3 @ B3 ) )
% 0.31/0.46 = ( ( A2 = A3 )
% 0.31/0.46 & ( B2 = B3 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % old.prod.inject
% 0.31/0.46 thf(fact_9_Cons__eq__appendI,axiom,
% 0.31/0.46 ! [A: $tType,X3: A,Xs1: list @ A,Ys2: list @ A,Xs2: list @ A,Zs: list @ A] :
% 0.31/0.46 ( ( ( cons @ A @ X3 @ Xs1 )
% 0.31/0.46 = Ys2 )
% 0.31/0.46 => ( ( Xs2
% 0.31/0.46 = ( append @ A @ Xs1 @ Zs ) )
% 0.31/0.46 => ( ( cons @ A @ X3 @ Xs2 )
% 0.31/0.46 = ( append @ A @ Ys2 @ Zs ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Cons_eq_appendI
% 0.31/0.46 thf(fact_10_append__Cons,axiom,
% 0.31/0.46 ! [A: $tType,X3: A,Xs2: list @ A,Ys2: list @ A] :
% 0.31/0.46 ( ( append @ A @ ( cons @ A @ X3 @ Xs2 ) @ Ys2 )
% 0.31/0.46 = ( cons @ A @ X3 @ ( append @ A @ Xs2 @ Ys2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % append_Cons
% 0.31/0.46 thf(fact_11_append__eq__appendI,axiom,
% 0.31/0.46 ! [A: $tType,Xs2: list @ A,Xs1: list @ A,Zs: list @ A,Ys2: list @ A,Us: list @ A] :
% 0.31/0.46 ( ( ( append @ A @ Xs2 @ Xs1 )
% 0.31/0.46 = Zs )
% 0.31/0.46 => ( ( Ys2
% 0.31/0.46 = ( append @ A @ Xs1 @ Us ) )
% 0.31/0.46 => ( ( append @ A @ Xs2 @ Ys2 )
% 0.31/0.46 = ( append @ A @ Zs @ Us ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % append_eq_appendI
% 0.31/0.46 thf(fact_12_append__eq__append__conv2,axiom,
% 0.31/0.46 ! [A: $tType,Xs2: list @ A,Ys2: list @ A,Zs: list @ A,Ts: list @ A] :
% 0.31/0.46 ( ( ( append @ A @ Xs2 @ Ys2 )
% 0.31/0.46 = ( append @ A @ Zs @ Ts ) )
% 0.31/0.46 = ( ? [Us2: list @ A] :
% 0.31/0.46 ( ( ( Xs2
% 0.31/0.46 = ( append @ A @ Zs @ Us2 ) )
% 0.31/0.46 & ( ( append @ A @ Us2 @ Ys2 )
% 0.31/0.46 = Ts ) )
% 0.31/0.46 | ( ( ( append @ A @ Xs2 @ Us2 )
% 0.31/0.46 = Zs )
% 0.31/0.46 & ( Ys2
% 0.31/0.46 = ( append @ A @ Us2 @ Ts ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % append_eq_append_conv2
% 0.31/0.46 thf(fact_13_old_Oprod_Oinducts,axiom,
% 0.31/0.46 ! [B: $tType,A: $tType,P2: ( product_prod @ A @ B ) > $o,Prod: product_prod @ A @ B] :
% 0.31/0.46 ( ! [A4: A,B4: B] : ( P2 @ ( product_Pair @ A @ B @ A4 @ B4 ) )
% 0.31/0.46 => ( P2 @ Prod ) ) ).
% 0.31/0.46
% 0.31/0.46 % old.prod.inducts
% 0.31/0.46 thf(fact_14_old_Oprod_Oexhaust,axiom,
% 0.31/0.46 ! [A: $tType,B: $tType,Y3: product_prod @ A @ B] :
% 0.31/0.46 ~ ! [A4: A,B4: B] :
% 0.31/0.46 ( Y3
% 0.31/0.46 != ( product_Pair @ A @ B @ A4 @ B4 ) ) ).
% 0.31/0.46
% 0.31/0.46 % old.prod.exhaust
% 0.31/0.46 thf(fact_15_prod__induct7,axiom,
% 0.31/0.46 ! [G: $tType,F: $tType,E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P2: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) ) )] :
% 0.31/0.46 ( ! [A4: A,B4: B,C3: C,D2: D,E2: E,F2: F,G2: G] : ( P2 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) @ C3 @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F @ G ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F @ G ) @ E2 @ ( product_Pair @ F @ G @ F2 @ G2 ) ) ) ) ) ) )
% 0.31/0.46 => ( P2 @ X3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % prod_induct7
% 0.31/0.46 thf(fact_16_prod__induct6,axiom,
% 0.31/0.46 ! [F: $tType,E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P2: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) )] :
% 0.31/0.46 ( ! [A4: A,B4: B,C3: C,D2: D,E2: E,F2: F] : ( P2 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) @ C3 @ ( product_Pair @ D @ ( product_prod @ E @ F ) @ D2 @ ( product_Pair @ E @ F @ E2 @ F2 ) ) ) ) ) )
% 0.31/0.46 => ( P2 @ X3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % prod_induct6
% 0.31/0.46 thf(fact_17_prod__induct5,axiom,
% 0.31/0.46 ! [E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P2: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) )] :
% 0.31/0.46 ( ! [A4: A,B4: B,C3: C,D2: D,E2: E] : ( P2 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ E ) @ C3 @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) )
% 0.31/0.46 => ( P2 @ X3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % prod_induct5
% 0.31/0.46 thf(fact_18_prod__induct4,axiom,
% 0.31/0.46 ! [D: $tType,C: $tType,B: $tType,A: $tType,P2: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 0.31/0.46 ( ! [A4: A,B4: B,C3: C,D2: D] : ( P2 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B4 @ ( product_Pair @ C @ D @ C3 @ D2 ) ) ) )
% 0.31/0.46 => ( P2 @ X3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % prod_induct4
% 0.31/0.46 thf(fact_19_prod__induct3,axiom,
% 0.31/0.46 ! [C: $tType,B: $tType,A: $tType,P2: ( product_prod @ A @ ( product_prod @ B @ C ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ C )] :
% 0.31/0.46 ( ! [A4: A,B4: B,C3: C] : ( P2 @ ( product_Pair @ A @ ( product_prod @ B @ C ) @ A4 @ ( product_Pair @ B @ C @ B4 @ C3 ) ) )
% 0.31/0.46 => ( P2 @ X3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % prod_induct3
% 0.31/0.46 thf(fact_20_prod__cases7,axiom,
% 0.31/0.46 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,F: $tType,G: $tType,Y3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) ) )] :
% 0.31/0.46 ~ ! [A4: A,B4: B,C3: C,D2: D,E2: E,F2: F,G2: G] :
% 0.31/0.46 ( Y3
% 0.31/0.46 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) @ C3 @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F @ G ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F @ G ) @ E2 @ ( product_Pair @ F @ G @ F2 @ G2 ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % prod_cases7
% 0.31/0.46 thf(fact_21_prod__cases6,axiom,
% 0.31/0.46 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,F: $tType,Y3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) )] :
% 0.31/0.46 ~ ! [A4: A,B4: B,C3: C,D2: D,E2: E,F2: F] :
% 0.31/0.46 ( Y3
% 0.31/0.46 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) @ C3 @ ( product_Pair @ D @ ( product_prod @ E @ F ) @ D2 @ ( product_Pair @ E @ F @ E2 @ F2 ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % prod_cases6
% 0.31/0.46 thf(fact_22_prod__cases5,axiom,
% 0.31/0.46 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,Y3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) )] :
% 0.31/0.46 ~ ! [A4: A,B4: B,C3: C,D2: D,E2: E] :
% 0.31/0.46 ( Y3
% 0.31/0.46 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ E ) @ C3 @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % prod_cases5
% 0.31/0.46 thf(fact_23_prod__cases4,axiom,
% 0.31/0.46 ! [A: $tType,B: $tType,C: $tType,D: $tType,Y3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 0.31/0.46 ~ ! [A4: A,B4: B,C3: C,D2: D] :
% 0.31/0.46 ( Y3
% 0.31/0.46 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B4 @ ( product_Pair @ C @ D @ C3 @ D2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % prod_cases4
% 0.31/0.46 thf(fact_24_prod__cases3,axiom,
% 0.31/0.46 ! [A: $tType,B: $tType,C: $tType,Y3: product_prod @ A @ ( product_prod @ B @ C )] :
% 0.31/0.46 ~ ! [A4: A,B4: B,C3: C] :
% 0.31/0.46 ( Y3
% 0.31/0.46 != ( product_Pair @ A @ ( product_prod @ B @ C ) @ A4 @ ( product_Pair @ B @ C @ B4 @ C3 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % prod_cases3
% 0.31/0.46 thf(fact_25_Pair__inject,axiom,
% 0.31/0.46 ! [A: $tType,B: $tType,A2: A,B2: B,A3: A,B3: B] :
% 0.31/0.46 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 0.31/0.46 = ( product_Pair @ A @ B @ A3 @ B3 ) )
% 0.31/0.46 => ~ ( ( A2 = A3 )
% 0.31/0.46 => ( B2 != B3 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Pair_inject
% 0.31/0.46 thf(fact_26_prod__cases,axiom,
% 0.31/0.46 ! [B: $tType,A: $tType,P2: ( product_prod @ A @ B ) > $o,P3: product_prod @ A @ B] :
% 0.31/0.46 ( ! [A4: A,B4: B] : ( P2 @ ( product_Pair @ A @ B @ A4 @ B4 ) )
% 0.31/0.46 => ( P2 @ P3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % prod_cases
% 0.31/0.46 thf(fact_27_surj__pair,axiom,
% 0.31/0.46 ! [A: $tType,B: $tType,P3: product_prod @ A @ B] :
% 0.31/0.46 ? [X4: A,Y4: B] :
% 0.31/0.46 ( P3
% 0.31/0.46 = ( product_Pair @ A @ B @ X4 @ Y4 ) ) ).
% 0.31/0.46
% 0.31/0.46 % surj_pair
% 0.31/0.46 thf(fact_28_not__Cons__self2,axiom,
% 0.31/0.46 ! [A: $tType,X3: A,Xs2: list @ A] :
% 0.31/0.46 ( ( cons @ A @ X3 @ Xs2 )
% 0.31/0.46 != Xs2 ) ).
% 0.31/0.46
% 0.31/0.46 % not_Cons_self2
% 0.31/0.46 thf(fact_29_old_Oprod_Orec,axiom,
% 0.31/0.46 ! [A: $tType,T: $tType,B: $tType,F1: A > B > T,A2: A,B2: B] :
% 0.31/0.46 ( ( product_rec_prod @ A @ B @ T @ F1 @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 0.31/0.46 = ( F1 @ A2 @ B2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % old.prod.rec
% 0.31/0.46 thf(fact_30_bind__simps_I2_J,axiom,
% 0.31/0.46 ! [A: $tType,B: $tType,X3: B,Xs2: list @ B,F3: B > ( list @ A )] :
% 0.31/0.46 ( ( bind @ B @ A @ ( cons @ B @ X3 @ Xs2 ) @ F3 )
% 0.31/0.46 = ( append @ A @ ( F3 @ X3 ) @ ( bind @ B @ A @ Xs2 @ F3 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % bind_simps(2)
% 0.31/0.46 thf(fact_31_maps__simps_I1_J,axiom,
% 0.31/0.46 ! [A: $tType,B: $tType,F3: B > ( list @ A ),X3: B,Xs2: list @ B] :
% 0.31/0.46 ( ( maps @ B @ A @ F3 @ ( cons @ B @ X3 @ Xs2 ) )
% 0.31/0.46 = ( append @ A @ ( F3 @ X3 ) @ ( maps @ B @ A @ F3 @ Xs2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % maps_simps(1)
% 0.31/0.46 thf(fact_32_internal__case__prod__conv,axiom,
% 0.31/0.46 ! [B: $tType,A: $tType,C: $tType,C2: B > C > A,A2: B,B2: C] :
% 0.31/0.46 ( ( produc2004651681e_prod @ B @ C @ A @ C2 @ ( product_Pair @ B @ C @ A2 @ B2 ) )
% 0.31/0.46 = ( C2 @ A2 @ B2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % internal_case_prod_conv
% 0.31/0.46 thf(fact_33_lexord__append__left__rightI,axiom,
% 0.31/0.46 ! [A: $tType,A2: A,B2: A,R: set @ ( product_prod @ A @ A ),U: list @ A,X3: list @ A,Y3: list @ A] :
% 0.31/0.46 ( ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ R )
% 0.31/0.46 => ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ U @ ( cons @ A @ A2 @ X3 ) ) @ ( append @ A @ U @ ( cons @ A @ B2 @ Y3 ) ) ) @ ( lexord @ A @ R ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lexord_append_left_rightI
% 0.31/0.46 thf(fact_34_zip__Cons__Cons,axiom,
% 0.31/0.46 ! [A: $tType,B: $tType,X3: A,Xs2: list @ A,Y3: B,Ys2: list @ B] :
% 0.31/0.46 ( ( zip @ A @ B @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ B @ Y3 @ Ys2 ) )
% 0.31/0.46 = ( cons @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X3 @ Y3 ) @ ( zip @ A @ B @ Xs2 @ Ys2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % zip_Cons_Cons
% 0.31/0.46 thf(fact_35_listrel1I,axiom,
% 0.31/0.46 ! [A: $tType,X3: A,Y3: A,R: set @ ( product_prod @ A @ A ),Xs2: list @ A,Us: list @ A,Vs: list @ A,Ys2: list @ A] :
% 0.31/0.46 ( ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X3 @ Y3 ) @ R )
% 0.31/0.46 => ( ( Xs2
% 0.31/0.46 = ( append @ A @ Us @ ( cons @ A @ X3 @ Vs ) ) )
% 0.31/0.46 => ( ( Ys2
% 0.31/0.46 = ( append @ A @ Us @ ( cons @ A @ Y3 @ Vs ) ) )
% 0.31/0.46 => ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs2 @ Ys2 ) @ ( listrel1 @ A @ R ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % listrel1I
% 0.31/0.46 thf(fact_36_listrel1E,axiom,
% 0.31/0.46 ! [A: $tType,Xs2: list @ A,Ys2: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.31/0.46 ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs2 @ Ys2 ) @ ( listrel1 @ A @ R ) )
% 0.31/0.46 => ~ ! [X4: A,Y4: A] :
% 0.31/0.46 ( ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X4 @ Y4 ) @ R )
% 0.31/0.46 => ! [Us3: list @ A,Vs2: list @ A] :
% 0.31/0.46 ( ( Xs2
% 0.31/0.46 = ( append @ A @ Us3 @ ( cons @ A @ X4 @ Vs2 ) ) )
% 0.31/0.46 => ( Ys2
% 0.31/0.46 != ( append @ A @ Us3 @ ( cons @ A @ Y4 @ Vs2 ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % listrel1E
% 0.31/0.46 thf(fact_37_member__rec_I1_J,axiom,
% 0.31/0.46 ! [A: $tType,X3: A,Xs2: list @ A,Y3: A] :
% 0.31/0.46 ( ( member @ A @ ( cons @ A @ X3 @ Xs2 ) @ Y3 )
% 0.31/0.46 = ( ( X3 = Y3 )
% 0.31/0.46 | ( member @ A @ Xs2 @ Y3 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % member_rec(1)
% 0.31/0.46 thf(fact_38_ssubst__Pair__rhs,axiom,
% 0.31/0.46 ! [B: $tType,A: $tType,R: A,S: B,R2: set @ ( product_prod @ A @ B ),S2: B] :
% 0.31/0.46 ( ( member2 @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ R @ S ) @ R2 )
% 0.31/0.46 => ( ( S2 = S )
% 0.31/0.46 => ( member2 @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ R @ S2 ) @ R2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % ssubst_Pair_rhs
% 0.31/0.46 thf(fact_39_subdivide_Oinduct,axiom,
% 0.31/0.46 ! [A: $tType,P2: ( pair_p1731315293ph_ext @ A @ product_unit ) > ( product_prod @ A @ A ) > A > $o,A0: pair_p1731315293ph_ext @ A @ product_unit,A1: product_prod @ A @ A,A22: A] :
% 0.31/0.46 ( ! [G3: pair_p1731315293ph_ext @ A @ product_unit,U2: A,V: A,X_1: A] : ( P2 @ G3 @ ( product_Pair @ A @ A @ U2 @ V ) @ X_1 )
% 0.31/0.46 => ( P2 @ A0 @ A1 @ A22 ) ) ).
% 0.31/0.46
% 0.31/0.46 % subdivide.induct
% 0.31/0.46 thf(fact_40_Cons__listrel1__Cons,axiom,
% 0.31/0.46 ! [A: $tType,X3: A,Xs2: list @ A,Y3: A,Ys2: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.31/0.46 ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ A @ Y3 @ Ys2 ) ) @ ( listrel1 @ A @ R ) )
% 0.31/0.46 = ( ( ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X3 @ Y3 ) @ R )
% 0.31/0.46 & ( Xs2 = Ys2 ) )
% 0.31/0.46 | ( ( X3 = Y3 )
% 0.31/0.46 & ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs2 @ Ys2 ) @ ( listrel1 @ A @ R ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Cons_listrel1_Cons
% 0.31/0.46 thf(fact_41_lexord__cons__cons,axiom,
% 0.31/0.46 ! [A: $tType,A2: A,X3: list @ A,B2: A,Y3: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.31/0.46 ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ A2 @ X3 ) @ ( cons @ A @ B2 @ Y3 ) ) @ ( lexord @ A @ R ) )
% 0.31/0.46 = ( ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ R )
% 0.31/0.46 | ( ( A2 = B2 )
% 0.31/0.46 & ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ X3 @ Y3 ) @ ( lexord @ A @ R ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lexord_cons_cons
% 0.31/0.46 thf(fact_42_listrel1I2,axiom,
% 0.31/0.46 ! [A: $tType,Xs2: list @ A,Ys2: list @ A,R: set @ ( product_prod @ A @ A ),X3: A] :
% 0.31/0.46 ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs2 @ Ys2 ) @ ( listrel1 @ A @ R ) )
% 0.31/0.46 => ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ A @ X3 @ Ys2 ) ) @ ( listrel1 @ A @ R ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % listrel1I2
% 0.31/0.46 thf(fact_43_append__listrel1I,axiom,
% 0.31/0.46 ! [A: $tType,Xs2: list @ A,Ys2: list @ A,R: set @ ( product_prod @ A @ A ),Us: list @ A,Vs: list @ A] :
% 0.31/0.46 ( ( ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs2 @ Ys2 ) @ ( listrel1 @ A @ R ) )
% 0.31/0.46 & ( Us = Vs ) )
% 0.31/0.46 | ( ( Xs2 = Ys2 )
% 0.31/0.46 & ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Us @ Vs ) @ ( listrel1 @ A @ R ) ) ) )
% 0.31/0.46 => ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ Xs2 @ Us ) @ ( append @ A @ Ys2 @ Vs ) ) @ ( listrel1 @ A @ R ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % append_listrel1I
% 0.31/0.46 thf(fact_44_lexord__linear,axiom,
% 0.31/0.46 ! [A: $tType,R: set @ ( product_prod @ A @ A ),X3: list @ A,Y3: list @ A] :
% 0.31/0.46 ( ! [A4: A,B4: A] :
% 0.31/0.46 ( ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A4 @ B4 ) @ R )
% 0.31/0.46 | ( A4 = B4 )
% 0.31/0.46 | ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ B4 @ A4 ) @ R ) )
% 0.31/0.46 => ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ X3 @ Y3 ) @ ( lexord @ A @ R ) )
% 0.31/0.46 | ( X3 = Y3 )
% 0.31/0.46 | ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Y3 @ X3 ) @ ( lexord @ A @ R ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lexord_linear
% 0.31/0.46 thf(fact_45_mem__Collect__eq,axiom,
% 0.31/0.46 ! [A: $tType,A2: A,P2: A > $o] :
% 0.31/0.46 ( ( member2 @ A @ A2 @ ( collect @ A @ P2 ) )
% 0.31/0.46 = ( P2 @ A2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % mem_Collect_eq
% 0.31/0.46 thf(fact_46_Collect__mem__eq,axiom,
% 0.31/0.46 ! [A: $tType,A5: set @ A] :
% 0.31/0.46 ( ( collect @ A
% 0.31/0.46 @ ^ [X: A] : ( member2 @ A @ X @ A5 ) )
% 0.31/0.46 = A5 ) ).
% 0.31/0.46
% 0.31/0.46 % Collect_mem_eq
% 0.31/0.46 thf(fact_47_Collect__cong,axiom,
% 0.31/0.46 ! [A: $tType,P2: A > $o,Q: A > $o] :
% 0.31/0.46 ( ! [X4: A] :
% 0.31/0.46 ( ( P2 @ X4 )
% 0.31/0.46 = ( Q @ X4 ) )
% 0.31/0.46 => ( ( collect @ A @ P2 )
% 0.31/0.46 = ( collect @ A @ Q ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Collect_cong
% 0.31/0.46 thf(fact_48_lexord__irreflexive,axiom,
% 0.31/0.46 ! [A: $tType,R: set @ ( product_prod @ A @ A ),Xs2: list @ A] :
% 0.31/0.46 ( ! [X4: A] :
% 0.31/0.46 ~ ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X4 @ X4 ) @ R )
% 0.31/0.46 => ~ ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs2 @ Xs2 ) @ ( lexord @ A @ R ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lexord_irreflexive
% 0.31/0.46 thf(fact_49_lexord__append__leftI,axiom,
% 0.31/0.46 ! [A: $tType,U: list @ A,V2: list @ A,R: set @ ( product_prod @ A @ A ),X3: list @ A] :
% 0.31/0.46 ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ U @ V2 ) @ ( lexord @ A @ R ) )
% 0.31/0.46 => ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ X3 @ U ) @ ( append @ A @ X3 @ V2 ) ) @ ( lexord @ A @ R ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lexord_append_leftI
% 0.31/0.46 thf(fact_50_listrel1I1,axiom,
% 0.31/0.46 ! [A: $tType,X3: A,Y3: A,R: set @ ( product_prod @ A @ A ),Xs2: list @ A] :
% 0.31/0.46 ( ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X3 @ Y3 ) @ R )
% 0.31/0.46 => ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ A @ Y3 @ Xs2 ) ) @ ( listrel1 @ A @ R ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % listrel1I1
% 0.31/0.46 thf(fact_51_Cons__listrel1E1,axiom,
% 0.31/0.46 ! [A: $tType,X3: A,Xs2: list @ A,Ys2: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.31/0.46 ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X3 @ Xs2 ) @ Ys2 ) @ ( listrel1 @ A @ R ) )
% 0.31/0.46 => ( ! [Y4: A] :
% 0.31/0.46 ( ( Ys2
% 0.31/0.46 = ( cons @ A @ Y4 @ Xs2 ) )
% 0.31/0.46 => ~ ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X3 @ Y4 ) @ R ) )
% 0.31/0.46 => ~ ! [Zs2: list @ A] :
% 0.31/0.46 ( ( Ys2
% 0.31/0.46 = ( cons @ A @ X3 @ Zs2 ) )
% 0.31/0.46 => ~ ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs2 @ Zs2 ) @ ( listrel1 @ A @ R ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Cons_listrel1E1
% 0.31/0.46 thf(fact_52_Cons__listrel1E2,axiom,
% 0.31/0.46 ! [A: $tType,Xs2: list @ A,Y3: A,Ys2: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.31/0.46 ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs2 @ ( cons @ A @ Y3 @ Ys2 ) ) @ ( listrel1 @ A @ R ) )
% 0.31/0.46 => ( ! [X4: A] :
% 0.31/0.46 ( ( Xs2
% 0.31/0.46 = ( cons @ A @ X4 @ Ys2 ) )
% 0.31/0.46 => ~ ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X4 @ Y3 ) @ R ) )
% 0.31/0.46 => ~ ! [Zs2: list @ A] :
% 0.31/0.46 ( ( Xs2
% 0.31/0.46 = ( cons @ A @ Y3 @ Zs2 ) )
% 0.31/0.46 => ~ ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Zs2 @ Ys2 ) @ ( listrel1 @ A @ R ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Cons_listrel1E2
% 0.31/0.46 thf(fact_53_lexord__append__leftD,axiom,
% 0.31/0.46 ! [A: $tType,X3: list @ A,U: list @ A,V2: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.31/0.46 ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ X3 @ U ) @ ( append @ A @ X3 @ V2 ) ) @ ( lexord @ A @ R ) )
% 0.31/0.46 => ( ! [A4: A] :
% 0.31/0.46 ~ ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A4 @ A4 ) @ R )
% 0.31/0.46 => ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ U @ V2 ) @ ( lexord @ A @ R ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lexord_append_leftD
% 0.31/0.46 thf(fact_54_lexord__append__rightI,axiom,
% 0.31/0.46 ! [A: $tType,Y3: list @ A,X3: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.31/0.46 ( ? [B5: A,Z: list @ A] :
% 0.31/0.46 ( Y3
% 0.31/0.46 = ( cons @ A @ B5 @ Z ) )
% 0.31/0.46 => ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ X3 @ ( append @ A @ X3 @ Y3 ) ) @ ( lexord @ A @ R ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lexord_append_rightI
% 0.31/0.46 thf(fact_55_zip__eq__ConsE,axiom,
% 0.31/0.46 ! [A: $tType,B: $tType,Xs2: list @ A,Ys2: list @ B,Xy: product_prod @ A @ B,Xys: list @ ( product_prod @ A @ B )] :
% 0.31/0.46 ( ( ( zip @ A @ B @ Xs2 @ Ys2 )
% 0.31/0.46 = ( cons @ ( product_prod @ A @ B ) @ Xy @ Xys ) )
% 0.31/0.46 => ~ ! [X4: A,Xs3: list @ A] :
% 0.31/0.46 ( ( Xs2
% 0.31/0.46 = ( cons @ A @ X4 @ Xs3 ) )
% 0.31/0.46 => ! [Y4: B,Ys3: list @ B] :
% 0.31/0.46 ( ( Ys2
% 0.31/0.46 = ( cons @ B @ Y4 @ Ys3 ) )
% 0.31/0.46 => ( ( Xy
% 0.31/0.46 = ( product_Pair @ A @ B @ X4 @ Y4 ) )
% 0.31/0.46 => ( Xys
% 0.31/0.46 != ( zip @ A @ B @ Xs3 @ Ys3 ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % zip_eq_ConsE
% 0.31/0.46 thf(fact_56_subdivide_Ocases,axiom,
% 0.31/0.46 ! [A: $tType,X3: product_prod @ ( pair_p1731315293ph_ext @ A @ product_unit ) @ ( product_prod @ ( product_prod @ A @ A ) @ A )] :
% 0.31/0.46 ~ ! [G3: pair_p1731315293ph_ext @ A @ product_unit,U2: A,V: A,W: A] :
% 0.31/0.46 ( X3
% 0.31/0.46 != ( product_Pair @ ( pair_p1731315293ph_ext @ A @ product_unit ) @ ( product_prod @ ( product_prod @ A @ A ) @ A ) @ G3 @ ( product_Pair @ ( product_prod @ A @ A ) @ A @ ( product_Pair @ A @ A @ U2 @ V ) @ W ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % subdivide.cases
% 0.31/0.46 thf(fact_57_lexord__same__pref__if__irrefl,axiom,
% 0.31/0.46 ! [A: $tType,R: set @ ( product_prod @ A @ A ),Xs2: list @ A,Ys2: list @ A,Zs: list @ A] :
% 0.31/0.46 ( ( irrefl @ A @ R )
% 0.31/0.46 => ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ Xs2 @ Ys2 ) @ ( append @ A @ Xs2 @ Zs ) ) @ ( lexord @ A @ R ) )
% 0.31/0.46 = ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Ys2 @ Zs ) @ ( lexord @ A @ R ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lexord_same_pref_if_irrefl
% 0.31/0.46 thf(fact_58_snoc__listrel1__snoc__iff,axiom,
% 0.31/0.46 ! [A: $tType,Xs2: list @ A,X3: A,Ys2: list @ A,Y3: A,R: set @ ( product_prod @ A @ A )] :
% 0.31/0.46 ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ Xs2 @ ( cons @ A @ X3 @ ( nil @ A ) ) ) @ ( append @ A @ Ys2 @ ( cons @ A @ Y3 @ ( nil @ A ) ) ) ) @ ( listrel1 @ A @ R ) )
% 0.31/0.46 = ( ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs2 @ Ys2 ) @ ( listrel1 @ A @ R ) )
% 0.31/0.46 & ( X3 = Y3 ) )
% 0.31/0.46 | ( ( Xs2 = Ys2 )
% 0.31/0.46 & ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X3 @ Y3 ) @ R ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % snoc_listrel1_snoc_iff
% 0.31/0.46 thf(fact_59_lexord__Nil__left,axiom,
% 0.31/0.46 ! [A: $tType,Y3: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.31/0.46 ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( nil @ A ) @ Y3 ) @ ( lexord @ A @ R ) )
% 0.31/0.46 = ( ? [A6: A,X: list @ A] :
% 0.31/0.46 ( Y3
% 0.31/0.46 = ( cons @ A @ A6 @ X ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lexord_Nil_left
% 0.31/0.46 thf(fact_60_lexord__same__pref__iff,axiom,
% 0.31/0.46 ! [A: $tType,Xs2: list @ A,Ys2: list @ A,Zs: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.31/0.46 ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ Xs2 @ Ys2 ) @ ( append @ A @ Xs2 @ Zs ) ) @ ( lexord @ A @ R ) )
% 0.31/0.46 = ( ? [X: A] :
% 0.31/0.46 ( ( member2 @ A @ X @ ( set2 @ A @ Xs2 ) )
% 0.31/0.46 & ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ X ) @ R ) )
% 0.31/0.46 | ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Ys2 @ Zs ) @ ( lexord @ A @ R ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lexord_same_pref_iff
% 0.31/0.46 thf(fact_61_zip__append,axiom,
% 0.31/0.46 ! [A: $tType,B: $tType,Xs2: list @ A,Us: list @ B,Ys2: list @ A,Vs: list @ B] :
% 0.31/0.46 ( ( ( size_size @ ( list @ A ) @ Xs2 )
% 0.31/0.46 = ( size_size @ ( list @ B ) @ Us ) )
% 0.31/0.46 => ( ( zip @ A @ B @ ( append @ A @ Xs2 @ Ys2 ) @ ( append @ B @ Us @ Vs ) )
% 0.31/0.46 = ( append @ ( product_prod @ A @ B ) @ ( zip @ A @ B @ Xs2 @ Us ) @ ( zip @ A @ B @ Ys2 @ Vs ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % zip_append
% 0.31/0.46 thf(fact_62_lex__append__leftD,axiom,
% 0.31/0.46 ! [A: $tType,R: set @ ( product_prod @ A @ A ),Xs2: list @ A,Ys2: list @ A,Zs: list @ A] :
% 0.31/0.46 ( ! [X4: A] :
% 0.31/0.46 ~ ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X4 @ X4 ) @ R )
% 0.31/0.46 => ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ Xs2 @ Ys2 ) @ ( append @ A @ Xs2 @ Zs ) ) @ ( lex @ A @ R ) )
% 0.31/0.46 => ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Ys2 @ Zs ) @ ( lex @ A @ R ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lex_append_leftD
% 0.31/0.46 thf(fact_63_lex__append__left__iff,axiom,
% 0.31/0.46 ! [A: $tType,R: set @ ( product_prod @ A @ A ),Xs2: list @ A,Ys2: list @ A,Zs: list @ A] :
% 0.31/0.46 ( ! [X4: A] :
% 0.31/0.46 ~ ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X4 @ X4 ) @ R )
% 0.31/0.46 => ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ Xs2 @ Ys2 ) @ ( append @ A @ Xs2 @ Zs ) ) @ ( lex @ A @ R ) )
% 0.31/0.46 = ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Ys2 @ Zs ) @ ( lex @ A @ R ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lex_append_left_iff
% 0.31/0.46 thf(fact_64_lexord__asymmetric,axiom,
% 0.31/0.46 ! [A: $tType,R2: set @ ( product_prod @ A @ A ),A2: list @ A,B2: list @ A] :
% 0.31/0.46 ( ( asym @ A @ R2 )
% 0.31/0.46 => ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ A2 @ B2 ) @ ( lexord @ A @ R2 ) )
% 0.31/0.46 => ~ ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ B2 @ A2 ) @ ( lexord @ A @ R2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lexord_asymmetric
% 0.31/0.46 thf(fact_65_append_Oright__neutral,axiom,
% 0.31/0.46 ! [A: $tType,A2: list @ A] :
% 0.31/0.46 ( ( append @ A @ A2 @ ( nil @ A ) )
% 0.31/0.46 = A2 ) ).
% 0.31/0.46
% 0.31/0.46 % append.right_neutral
% 0.31/0.46 thf(fact_66_append__is__Nil__conv,axiom,
% 0.31/0.46 ! [A: $tType,Xs2: list @ A,Ys2: list @ A] :
% 0.31/0.46 ( ( ( append @ A @ Xs2 @ Ys2 )
% 0.31/0.46 = ( nil @ A ) )
% 0.31/0.46 = ( ( Xs2
% 0.31/0.46 = ( nil @ A ) )
% 0.31/0.46 & ( Ys2
% 0.31/0.46 = ( nil @ A ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % append_is_Nil_conv
% 0.31/0.46 thf(fact_67_Nil__is__append__conv,axiom,
% 0.31/0.46 ! [A: $tType,Xs2: list @ A,Ys2: list @ A] :
% 0.31/0.46 ( ( ( nil @ A )
% 0.31/0.46 = ( append @ A @ Xs2 @ Ys2 ) )
% 0.31/0.46 = ( ( Xs2
% 0.31/0.46 = ( nil @ A ) )
% 0.31/0.46 & ( Ys2
% 0.31/0.46 = ( nil @ A ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Nil_is_append_conv
% 0.31/0.46 thf(fact_68_self__append__conv2,axiom,
% 0.31/0.46 ! [A: $tType,Ys2: list @ A,Xs2: list @ A] :
% 0.31/0.46 ( ( Ys2
% 0.31/0.46 = ( append @ A @ Xs2 @ Ys2 ) )
% 0.31/0.46 = ( Xs2
% 0.31/0.46 = ( nil @ A ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % self_append_conv2
% 0.31/0.46 thf(fact_69_append__self__conv2,axiom,
% 0.31/0.46 ! [A: $tType,Xs2: list @ A,Ys2: list @ A] :
% 0.31/0.46 ( ( ( append @ A @ Xs2 @ Ys2 )
% 0.31/0.46 = Ys2 )
% 0.31/0.46 = ( Xs2
% 0.31/0.46 = ( nil @ A ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % append_self_conv2
% 0.31/0.46 thf(fact_70_self__append__conv,axiom,
% 0.31/0.46 ! [A: $tType,Xs2: list @ A,Ys2: list @ A] :
% 0.31/0.46 ( ( Xs2
% 0.31/0.46 = ( append @ A @ Xs2 @ Ys2 ) )
% 0.31/0.46 = ( Ys2
% 0.31/0.46 = ( nil @ A ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % self_append_conv
% 0.31/0.46 thf(fact_71_append__self__conv,axiom,
% 0.31/0.46 ! [A: $tType,Xs2: list @ A,Ys2: list @ A] :
% 0.31/0.46 ( ( ( append @ A @ Xs2 @ Ys2 )
% 0.31/0.46 = Xs2 )
% 0.31/0.46 = ( Ys2
% 0.31/0.46 = ( nil @ A ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % append_self_conv
% 0.31/0.46 thf(fact_72_append__Nil2,axiom,
% 0.31/0.46 ! [A: $tType,Xs2: list @ A] :
% 0.31/0.46 ( ( append @ A @ Xs2 @ ( nil @ A ) )
% 0.31/0.46 = Xs2 ) ).
% 0.31/0.46
% 0.31/0.46 % append_Nil2
% 0.31/0.46 thf(fact_73_append__eq__append__conv,axiom,
% 0.31/0.46 ! [A: $tType,Xs2: list @ A,Ys2: list @ A,Us: list @ A,Vs: list @ A] :
% 0.31/0.46 ( ( ( ( size_size @ ( list @ A ) @ Xs2 )
% 0.31/0.46 = ( size_size @ ( list @ A ) @ Ys2 ) )
% 0.31/0.46 | ( ( size_size @ ( list @ A ) @ Us )
% 0.31/0.46 = ( size_size @ ( list @ A ) @ Vs ) ) )
% 0.31/0.46 => ( ( ( append @ A @ Xs2 @ Us )
% 0.31/0.46 = ( append @ A @ Ys2 @ Vs ) )
% 0.31/0.46 = ( ( Xs2 = Ys2 )
% 0.31/0.46 & ( Us = Vs ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % append_eq_append_conv
% 0.31/0.46 thf(fact_74_zip__Nil,axiom,
% 0.31/0.46 ! [B: $tType,A: $tType,Ys2: list @ B] :
% 0.31/0.46 ( ( zip @ A @ B @ ( nil @ A ) @ Ys2 )
% 0.31/0.46 = ( nil @ ( product_prod @ A @ B ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % zip_Nil
% 0.31/0.46 thf(fact_75_bind__simps_I1_J,axiom,
% 0.31/0.46 ! [B: $tType,A: $tType,F3: B > ( list @ A )] :
% 0.31/0.46 ( ( bind @ B @ A @ ( nil @ B ) @ F3 )
% 0.31/0.46 = ( nil @ A ) ) ).
% 0.31/0.46
% 0.31/0.46 % bind_simps(1)
% 0.31/0.46 thf(fact_76_append1__eq__conv,axiom,
% 0.31/0.46 ! [A: $tType,Xs2: list @ A,X3: A,Ys2: list @ A,Y3: A] :
% 0.31/0.46 ( ( ( append @ A @ Xs2 @ ( cons @ A @ X3 @ ( nil @ A ) ) )
% 0.31/0.46 = ( append @ A @ Ys2 @ ( cons @ A @ Y3 @ ( nil @ A ) ) ) )
% 0.31/0.46 = ( ( Xs2 = Ys2 )
% 0.31/0.46 & ( X3 = Y3 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % append1_eq_conv
% 0.31/0.46 thf(fact_77_Cons__in__lex,axiom,
% 0.31/0.46 ! [A: $tType,X3: A,Xs2: list @ A,Y3: A,Ys2: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.31/0.46 ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ A @ Y3 @ Ys2 ) ) @ ( lex @ A @ R ) )
% 0.31/0.46 = ( ( ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X3 @ Y3 ) @ R )
% 0.31/0.46 & ( ( size_size @ ( list @ A ) @ Xs2 )
% 0.31/0.46 = ( size_size @ ( list @ A ) @ Ys2 ) ) )
% 0.31/0.46 | ( ( X3 = Y3 )
% 0.31/0.46 & ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs2 @ Ys2 ) @ ( lex @ A @ R ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Cons_in_lex
% 0.31/0.46 thf(fact_78_zip_Osimps_I1_J,axiom,
% 0.31/0.46 ! [B: $tType,A: $tType,Xs2: list @ A] :
% 0.31/0.46 ( ( zip @ A @ B @ Xs2 @ ( nil @ B ) )
% 0.31/0.46 = ( nil @ ( product_prod @ A @ B ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % zip.simps(1)
% 0.31/0.46 thf(fact_79_Nil__notin__lex,axiom,
% 0.31/0.46 ! [A: $tType,Ys2: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.31/0.46 ~ ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( nil @ A ) @ Ys2 ) @ ( lex @ A @ R ) ) ).
% 0.31/0.46
% 0.31/0.46 % Nil_notin_lex
% 0.31/0.46 thf(fact_80_Nil2__notin__lex,axiom,
% 0.31/0.46 ! [A: $tType,Xs2: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.31/0.46 ~ ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs2 @ ( nil @ A ) ) @ ( lex @ A @ R ) ) ).
% 0.31/0.46
% 0.31/0.46 % Nil2_notin_lex
% 0.31/0.46 thf(fact_81_zip__eq__Nil__iff,axiom,
% 0.31/0.46 ! [A: $tType,B: $tType,Xs2: list @ A,Ys2: list @ B] :
% 0.31/0.46 ( ( ( zip @ A @ B @ Xs2 @ Ys2 )
% 0.31/0.46 = ( nil @ ( product_prod @ A @ B ) ) )
% 0.31/0.46 = ( ( Xs2
% 0.31/0.46 = ( nil @ A ) )
% 0.31/0.46 | ( Ys2
% 0.31/0.46 = ( nil @ B ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % zip_eq_Nil_iff
% 0.31/0.46 thf(fact_82_in__set__impl__in__set__zip1,axiom,
% 0.31/0.46 ! [A: $tType,B: $tType,Xs2: list @ A,Ys2: list @ B,X3: A] :
% 0.31/0.46 ( ( ( size_size @ ( list @ A ) @ Xs2 )
% 0.31/0.46 = ( size_size @ ( list @ B ) @ Ys2 ) )
% 0.31/0.46 => ( ( member2 @ A @ X3 @ ( set2 @ A @ Xs2 ) )
% 0.31/0.46 => ~ ! [Y4: B] :
% 0.31/0.46 ~ ( member2 @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X3 @ Y4 ) @ ( set2 @ ( product_prod @ A @ B ) @ ( zip @ A @ B @ Xs2 @ Ys2 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % in_set_impl_in_set_zip1
% 0.31/0.46 thf(fact_83_in__set__impl__in__set__zip2,axiom,
% 0.31/0.46 ! [A: $tType,B: $tType,Xs2: list @ A,Ys2: list @ B,Y3: B] :
% 0.31/0.46 ( ( ( size_size @ ( list @ A ) @ Xs2 )
% 0.31/0.46 = ( size_size @ ( list @ B ) @ Ys2 ) )
% 0.31/0.46 => ( ( member2 @ B @ Y3 @ ( set2 @ B @ Ys2 ) )
% 0.31/0.46 => ~ ! [X4: A] :
% 0.31/0.46 ~ ( member2 @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X4 @ Y3 ) @ ( set2 @ ( product_prod @ A @ B ) @ ( zip @ A @ B @ Xs2 @ Ys2 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % in_set_impl_in_set_zip2
% 0.31/0.46 thf(fact_84_list__induct4,axiom,
% 0.31/0.46 ! [C: $tType,A: $tType,B: $tType,D: $tType,Xs2: list @ A,Ys2: list @ B,Zs: list @ C,Ws: list @ D,P2: ( list @ A ) > ( list @ B ) > ( list @ C ) > ( list @ D ) > $o] :
% 0.31/0.46 ( ( ( size_size @ ( list @ A ) @ Xs2 )
% 0.31/0.46 = ( size_size @ ( list @ B ) @ Ys2 ) )
% 0.31/0.46 => ( ( ( size_size @ ( list @ B ) @ Ys2 )
% 0.31/0.46 = ( size_size @ ( list @ C ) @ Zs ) )
% 0.31/0.46 => ( ( ( size_size @ ( list @ C ) @ Zs )
% 0.31/0.46 = ( size_size @ ( list @ D ) @ Ws ) )
% 0.31/0.46 => ( ( P2 @ ( nil @ A ) @ ( nil @ B ) @ ( nil @ C ) @ ( nil @ D ) )
% 0.31/0.46 => ( ! [X4: A,Xs4: list @ A,Y4: B,Ys4: list @ B,Z2: C,Zs2: list @ C,W: D,Ws2: list @ D] :
% 0.31/0.46 ( ( ( size_size @ ( list @ A ) @ Xs4 )
% 0.31/0.46 = ( size_size @ ( list @ B ) @ Ys4 ) )
% 0.31/0.46 => ( ( ( size_size @ ( list @ B ) @ Ys4 )
% 0.31/0.46 = ( size_size @ ( list @ C ) @ Zs2 ) )
% 0.31/0.46 => ( ( ( size_size @ ( list @ C ) @ Zs2 )
% 0.31/0.46 = ( size_size @ ( list @ D ) @ Ws2 ) )
% 0.31/0.46 => ( ( P2 @ Xs4 @ Ys4 @ Zs2 @ Ws2 )
% 0.31/0.46 => ( P2 @ ( cons @ A @ X4 @ Xs4 ) @ ( cons @ B @ Y4 @ Ys4 ) @ ( cons @ C @ Z2 @ Zs2 ) @ ( cons @ D @ W @ Ws2 ) ) ) ) ) )
% 0.31/0.46 => ( P2 @ Xs2 @ Ys2 @ Zs @ Ws ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % list_induct4
% 0.31/0.46 thf(fact_85_list__induct3,axiom,
% 0.31/0.46 ! [B: $tType,A: $tType,C: $tType,Xs2: list @ A,Ys2: list @ B,Zs: list @ C,P2: ( list @ A ) > ( list @ B ) > ( list @ C ) > $o] :
% 0.31/0.46 ( ( ( size_size @ ( list @ A ) @ Xs2 )
% 0.31/0.46 = ( size_size @ ( list @ B ) @ Ys2 ) )
% 0.31/0.46 => ( ( ( size_size @ ( list @ B ) @ Ys2 )
% 0.31/0.46 = ( size_size @ ( list @ C ) @ Zs ) )
% 0.31/0.46 => ( ( P2 @ ( nil @ A ) @ ( nil @ B ) @ ( nil @ C ) )
% 0.31/0.46 => ( ! [X4: A,Xs4: list @ A,Y4: B,Ys4: list @ B,Z2: C,Zs2: list @ C] :
% 0.31/0.46 ( ( ( size_size @ ( list @ A ) @ Xs4 )
% 0.31/0.46 = ( size_size @ ( list @ B ) @ Ys4 ) )
% 0.31/0.46 => ( ( ( size_size @ ( list @ B ) @ Ys4 )
% 0.31/0.46 = ( size_size @ ( list @ C ) @ Zs2 ) )
% 0.31/0.46 => ( ( P2 @ Xs4 @ Ys4 @ Zs2 )
% 0.31/0.46 => ( P2 @ ( cons @ A @ X4 @ Xs4 ) @ ( cons @ B @ Y4 @ Ys4 ) @ ( cons @ C @ Z2 @ Zs2 ) ) ) ) )
% 0.31/0.46 => ( P2 @ Xs2 @ Ys2 @ Zs ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % list_induct3
% 0.31/0.46 thf(fact_86_list__induct2,axiom,
% 0.31/0.46 ! [A: $tType,B: $tType,Xs2: list @ A,Ys2: list @ B,P2: ( list @ A ) > ( list @ B ) > $o] :
% 0.31/0.46 ( ( ( size_size @ ( list @ A ) @ Xs2 )
% 0.31/0.46 = ( size_size @ ( list @ B ) @ Ys2 ) )
% 0.31/0.46 => ( ( P2 @ ( nil @ A ) @ ( nil @ B ) )
% 0.31/0.46 => ( ! [X4: A,Xs4: list @ A,Y4: B,Ys4: list @ B] :
% 0.31/0.46 ( ( ( size_size @ ( list @ A ) @ Xs4 )
% 0.31/0.46 = ( size_size @ ( list @ B ) @ Ys4 ) )
% 0.31/0.46 => ( ( P2 @ Xs4 @ Ys4 )
% 0.31/0.46 => ( P2 @ ( cons @ A @ X4 @ Xs4 ) @ ( cons @ B @ Y4 @ Ys4 ) ) ) )
% 0.31/0.46 => ( P2 @ Xs2 @ Ys2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % list_induct2
% 0.31/0.46 thf(fact_87_transpose_Ocases,axiom,
% 0.31/0.46 ! [A: $tType,X3: list @ ( list @ A )] :
% 0.31/0.46 ( ( X3
% 0.31/0.46 != ( nil @ ( list @ A ) ) )
% 0.31/0.46 => ( ! [Xss: list @ ( list @ A )] :
% 0.31/0.46 ( X3
% 0.31/0.46 != ( cons @ ( list @ A ) @ ( nil @ A ) @ Xss ) )
% 0.31/0.46 => ~ ! [X4: A,Xs4: list @ A,Xss: list @ ( list @ A )] :
% 0.31/0.46 ( X3
% 0.31/0.46 != ( cons @ ( list @ A ) @ ( cons @ A @ X4 @ Xs4 ) @ Xss ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % transpose.cases
% 0.31/0.46 thf(fact_88_neq__if__length__neq,axiom,
% 0.31/0.46 ! [A: $tType,Xs2: list @ A,Ys2: list @ A] :
% 0.31/0.46 ( ( ( size_size @ ( list @ A ) @ Xs2 )
% 0.31/0.46 != ( size_size @ ( list @ A ) @ Ys2 ) )
% 0.31/0.46 => ( Xs2 != Ys2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % neq_if_length_neq
% 0.31/0.46 thf(fact_89_Ex__list__of__length,axiom,
% 0.31/0.46 ! [A: $tType,N: nat] :
% 0.31/0.46 ? [Xs4: list @ A] :
% 0.31/0.46 ( ( size_size @ ( list @ A ) @ Xs4 )
% 0.31/0.46 = N ) ).
% 0.31/0.46
% 0.31/0.46 % Ex_list_of_length
% 0.31/0.46 thf(fact_90_irrefl__lex,axiom,
% 0.31/0.46 ! [A: $tType,R: set @ ( product_prod @ A @ A )] :
% 0.31/0.46 ( ( irrefl @ A @ R )
% 0.31/0.46 => ( irrefl @ ( list @ A ) @ ( lex @ A @ R ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % irrefl_lex
% 0.31/0.46 thf(fact_91_asym__lex,axiom,
% 0.31/0.46 ! [A: $tType,R2: set @ ( product_prod @ A @ A )] :
% 0.31/0.46 ( ( asym @ A @ R2 )
% 0.31/0.46 => ( asym @ ( list @ A ) @ ( lex @ A @ R2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % asym_lex
% 0.31/0.46 thf(fact_92_lexl__not__refl,axiom,
% 0.31/0.46 ! [A: $tType,R: set @ ( product_prod @ A @ A ),X3: list @ A] :
% 0.31/0.46 ( ( irrefl @ A @ R )
% 0.31/0.46 => ~ ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ X3 @ X3 ) @ ( lex @ A @ R ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lexl_not_refl
% 0.31/0.46 thf(fact_93_lexord__irrefl,axiom,
% 0.31/0.46 ! [A: $tType,R2: set @ ( product_prod @ A @ A )] :
% 0.31/0.46 ( ( irrefl @ A @ R2 )
% 0.31/0.46 => ( irrefl @ ( list @ A ) @ ( lexord @ A @ R2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lexord_irrefl
% 0.31/0.46 thf(fact_94_lexord__asym,axiom,
% 0.31/0.46 ! [A: $tType,R2: set @ ( product_prod @ A @ A )] :
% 0.31/0.46 ( ( asym @ A @ R2 )
% 0.31/0.46 => ( asym @ ( list @ A ) @ ( lexord @ A @ R2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lexord_asym
% 0.31/0.46 thf(fact_95_set__zip__rightD,axiom,
% 0.31/0.46 ! [A: $tType,B: $tType,X3: A,Y3: B,Xs2: list @ A,Ys2: list @ B] :
% 0.31/0.46 ( ( member2 @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X3 @ Y3 ) @ ( set2 @ ( product_prod @ A @ B ) @ ( zip @ A @ B @ Xs2 @ Ys2 ) ) )
% 0.31/0.46 => ( member2 @ B @ Y3 @ ( set2 @ B @ Ys2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % set_zip_rightD
% 0.31/0.46 thf(fact_96_set__zip__leftD,axiom,
% 0.31/0.46 ! [B: $tType,A: $tType,X3: A,Y3: B,Xs2: list @ A,Ys2: list @ B] :
% 0.31/0.46 ( ( member2 @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X3 @ Y3 ) @ ( set2 @ ( product_prod @ A @ B ) @ ( zip @ A @ B @ Xs2 @ Ys2 ) ) )
% 0.31/0.46 => ( member2 @ A @ X3 @ ( set2 @ A @ Xs2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % set_zip_leftD
% 0.31/0.46 thf(fact_97_in__set__zipE,axiom,
% 0.31/0.46 ! [A: $tType,B: $tType,X3: A,Y3: B,Xs2: list @ A,Ys2: list @ B] :
% 0.31/0.46 ( ( member2 @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X3 @ Y3 ) @ ( set2 @ ( product_prod @ A @ B ) @ ( zip @ A @ B @ Xs2 @ Ys2 ) ) )
% 0.31/0.46 => ~ ( ( member2 @ A @ X3 @ ( set2 @ A @ Xs2 ) )
% 0.31/0.46 => ~ ( member2 @ B @ Y3 @ ( set2 @ B @ Ys2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % in_set_zipE
% 0.31/0.46 thf(fact_98_zip__same,axiom,
% 0.31/0.46 ! [A: $tType,A2: A,B2: A,Xs2: list @ A] :
% 0.31/0.46 ( ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ ( set2 @ ( product_prod @ A @ A ) @ ( zip @ A @ A @ Xs2 @ Xs2 ) ) )
% 0.31/0.46 = ( ( member2 @ A @ A2 @ ( set2 @ A @ Xs2 ) )
% 0.31/0.46 & ( A2 = B2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % zip_same
% 0.31/0.46 thf(fact_99_same__length__different,axiom,
% 0.31/0.46 ! [A: $tType,Xs2: list @ A,Ys2: list @ A] :
% 0.31/0.46 ( ( Xs2 != Ys2 )
% 0.31/0.46 => ( ( ( size_size @ ( list @ A ) @ Xs2 )
% 0.31/0.46 = ( size_size @ ( list @ A ) @ Ys2 ) )
% 0.31/0.46 => ? [Pre: list @ A,X4: A,Xs3: list @ A,Y4: A,Ys3: list @ A] :
% 0.31/0.46 ( ( X4 != Y4 )
% 0.31/0.46 & ( Xs2
% 0.31/0.46 = ( append @ A @ Pre @ ( append @ A @ ( cons @ A @ X4 @ ( nil @ A ) ) @ Xs3 ) ) )
% 0.31/0.46 & ( Ys2
% 0.31/0.46 = ( append @ A @ Pre @ ( append @ A @ ( cons @ A @ Y4 @ ( nil @ A ) ) @ Ys3 ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % same_length_different
% 0.31/0.46 thf(fact_100_list_Oset__cases,axiom,
% 0.31/0.46 ! [A: $tType,E3: A,A2: list @ A] :
% 0.31/0.46 ( ( member2 @ A @ E3 @ ( set2 @ A @ A2 ) )
% 0.31/0.46 => ( ! [Z22: list @ A] :
% 0.31/0.46 ( A2
% 0.31/0.46 != ( cons @ A @ E3 @ Z22 ) )
% 0.31/0.46 => ~ ! [Z1: A,Z22: list @ A] :
% 0.31/0.46 ( ( A2
% 0.31/0.46 = ( cons @ A @ Z1 @ Z22 ) )
% 0.31/0.46 => ~ ( member2 @ A @ E3 @ ( set2 @ A @ Z22 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % list.set_cases
% 0.31/0.46 thf(fact_101_set__ConsD,axiom,
% 0.31/0.46 ! [A: $tType,Y3: A,X3: A,Xs2: list @ A] :
% 0.31/0.46 ( ( member2 @ A @ Y3 @ ( set2 @ A @ ( cons @ A @ X3 @ Xs2 ) ) )
% 0.31/0.46 => ( ( Y3 = X3 )
% 0.31/0.46 | ( member2 @ A @ Y3 @ ( set2 @ A @ Xs2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % set_ConsD
% 0.31/0.46 thf(fact_102_list_Oset__intros_I1_J,axiom,
% 0.31/0.46 ! [A: $tType,X21: A,X22: list @ A] : ( member2 @ A @ X21 @ ( set2 @ A @ ( cons @ A @ X21 @ X22 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % list.set_intros(1)
% 0.31/0.46 thf(fact_103_list_Oset__intros_I2_J,axiom,
% 0.31/0.46 ! [A: $tType,Y3: A,X22: list @ A,X21: A] :
% 0.31/0.46 ( ( member2 @ A @ Y3 @ ( set2 @ A @ X22 ) )
% 0.31/0.46 => ( member2 @ A @ Y3 @ ( set2 @ A @ ( cons @ A @ X21 @ X22 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % list.set_intros(2)
% 0.31/0.46 thf(fact_104_lex__append__rightI,axiom,
% 0.31/0.46 ! [A: $tType,Xs2: list @ A,Ys2: list @ A,R: set @ ( product_prod @ A @ A ),Vs: list @ A,Us: list @ A] :
% 0.31/0.46 ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs2 @ Ys2 ) @ ( lex @ A @ R ) )
% 0.31/0.46 => ( ( ( size_size @ ( list @ A ) @ Vs )
% 0.31/0.46 = ( size_size @ ( list @ A ) @ Us ) )
% 0.31/0.46 => ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ Xs2 @ Us ) @ ( append @ A @ Ys2 @ Vs ) ) @ ( lex @ A @ R ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lex_append_rightI
% 0.31/0.46 thf(fact_105_sorted__wrt_Ocases,axiom,
% 0.31/0.46 ! [A: $tType,X3: product_prod @ ( A > A > $o ) @ ( list @ A )] :
% 0.31/0.46 ( ! [P4: A > A > $o] :
% 0.31/0.46 ( X3
% 0.31/0.46 != ( product_Pair @ ( A > A > $o ) @ ( list @ A ) @ P4 @ ( nil @ A ) ) )
% 0.31/0.46 => ~ ! [P4: A > A > $o,X4: A,Ys4: list @ A] :
% 0.31/0.46 ( X3
% 0.31/0.46 != ( product_Pair @ ( A > A > $o ) @ ( list @ A ) @ P4 @ ( cons @ A @ X4 @ Ys4 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % sorted_wrt.cases
% 0.31/0.46 thf(fact_106_arg__min__list_Ocases,axiom,
% 0.31/0.46 ! [B: $tType,A: $tType] :
% 0.31/0.46 ( ( linorder @ B )
% 0.31/0.46 => ! [X3: product_prod @ ( A > B ) @ ( list @ A )] :
% 0.31/0.46 ( ! [F2: A > B,X4: A] :
% 0.31/0.46 ( X3
% 0.31/0.46 != ( product_Pair @ ( A > B ) @ ( list @ A ) @ F2 @ ( cons @ A @ X4 @ ( nil @ A ) ) ) )
% 0.31/0.46 => ( ! [F2: A > B,X4: A,Y4: A,Zs2: list @ A] :
% 0.31/0.46 ( X3
% 0.31/0.46 != ( product_Pair @ ( A > B ) @ ( list @ A ) @ F2 @ ( cons @ A @ X4 @ ( cons @ A @ Y4 @ Zs2 ) ) ) )
% 0.31/0.46 => ~ ! [A4: A > B] :
% 0.31/0.46 ( X3
% 0.31/0.46 != ( product_Pair @ ( A > B ) @ ( list @ A ) @ A4 @ ( nil @ A ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % arg_min_list.cases
% 0.31/0.46 thf(fact_107_successively_Ocases,axiom,
% 0.31/0.46 ! [A: $tType,X3: product_prod @ ( A > A > $o ) @ ( list @ A )] :
% 0.31/0.46 ( ! [P4: A > A > $o] :
% 0.31/0.46 ( X3
% 0.31/0.46 != ( product_Pair @ ( A > A > $o ) @ ( list @ A ) @ P4 @ ( nil @ A ) ) )
% 0.31/0.46 => ( ! [P4: A > A > $o,X4: A] :
% 0.31/0.46 ( X3
% 0.31/0.46 != ( product_Pair @ ( A > A > $o ) @ ( list @ A ) @ P4 @ ( cons @ A @ X4 @ ( nil @ A ) ) ) )
% 0.31/0.46 => ~ ! [P4: A > A > $o,X4: A,Y4: A,Xs4: list @ A] :
% 0.31/0.46 ( X3
% 0.31/0.46 != ( product_Pair @ ( A > A > $o ) @ ( list @ A ) @ P4 @ ( cons @ A @ X4 @ ( cons @ A @ Y4 @ Xs4 ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % successively.cases
% 0.31/0.46 thf(fact_108_strict__sorted_Oinduct,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( linorder @ A )
% 0.31/0.46 => ! [P2: ( list @ A ) > $o,A0: list @ A] :
% 0.31/0.46 ( ( P2 @ ( nil @ A ) )
% 0.31/0.46 => ( ! [X4: A,Ys4: list @ A] :
% 0.31/0.46 ( ( P2 @ Ys4 )
% 0.31/0.46 => ( P2 @ ( cons @ A @ X4 @ Ys4 ) ) )
% 0.31/0.46 => ( P2 @ A0 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % strict_sorted.induct
% 0.31/0.46 thf(fact_109_strict__sorted_Ocases,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( linorder @ A )
% 0.31/0.46 => ! [X3: list @ A] :
% 0.31/0.46 ( ( X3
% 0.31/0.46 != ( nil @ A ) )
% 0.31/0.46 => ~ ! [X4: A,Ys4: list @ A] :
% 0.31/0.46 ( X3
% 0.31/0.46 != ( cons @ A @ X4 @ Ys4 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % strict_sorted.cases
% 0.31/0.46 thf(fact_110_map__tailrec__rev_Oinduct,axiom,
% 0.31/0.46 ! [A: $tType,B: $tType,P2: ( A > B ) > ( list @ A ) > ( list @ B ) > $o,A0: A > B,A1: list @ A,A22: list @ B] :
% 0.31/0.46 ( ! [F2: A > B,X_1: list @ B] : ( P2 @ F2 @ ( nil @ A ) @ X_1 )
% 0.31/0.46 => ( ! [F2: A > B,A4: A,As: list @ A,Bs: list @ B] :
% 0.31/0.46 ( ( P2 @ F2 @ As @ ( cons @ B @ ( F2 @ A4 ) @ Bs ) )
% 0.31/0.46 => ( P2 @ F2 @ ( cons @ A @ A4 @ As ) @ Bs ) )
% 0.31/0.46 => ( P2 @ A0 @ A1 @ A22 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % map_tailrec_rev.induct
% 0.31/0.46 thf(fact_111_list__nonempty__induct,axiom,
% 0.31/0.46 ! [A: $tType,Xs2: list @ A,P2: ( list @ A ) > $o] :
% 0.31/0.46 ( ( Xs2
% 0.31/0.46 != ( nil @ A ) )
% 0.31/0.46 => ( ! [X4: A] : ( P2 @ ( cons @ A @ X4 @ ( nil @ A ) ) )
% 0.31/0.46 => ( ! [X4: A,Xs4: list @ A] :
% 0.31/0.46 ( ( Xs4
% 0.31/0.46 != ( nil @ A ) )
% 0.31/0.46 => ( ( P2 @ Xs4 )
% 0.31/0.46 => ( P2 @ ( cons @ A @ X4 @ Xs4 ) ) ) )
% 0.31/0.46 => ( P2 @ Xs2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % list_nonempty_induct
% 0.31/0.46 thf(fact_112_successively_Oinduct,axiom,
% 0.31/0.46 ! [A: $tType,P2: ( A > A > $o ) > ( list @ A ) > $o,A0: A > A > $o,A1: list @ A] :
% 0.31/0.46 ( ! [P4: A > A > $o] : ( P2 @ P4 @ ( nil @ A ) )
% 0.31/0.46 => ( ! [P4: A > A > $o,X4: A] : ( P2 @ P4 @ ( cons @ A @ X4 @ ( nil @ A ) ) )
% 0.31/0.46 => ( ! [P4: A > A > $o,X4: A,Y4: A,Xs4: list @ A] :
% 0.31/0.46 ( ( P2 @ P4 @ ( cons @ A @ Y4 @ Xs4 ) )
% 0.31/0.46 => ( P2 @ P4 @ ( cons @ A @ X4 @ ( cons @ A @ Y4 @ Xs4 ) ) ) )
% 0.31/0.46 => ( P2 @ A0 @ A1 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % successively.induct
% 0.31/0.46 thf(fact_113_arg__min__list_Oinduct,axiom,
% 0.31/0.46 ! [B: $tType,A: $tType] :
% 0.31/0.46 ( ( linorder @ B )
% 0.31/0.46 => ! [P2: ( A > B ) > ( list @ A ) > $o,A0: A > B,A1: list @ A] :
% 0.31/0.46 ( ! [F2: A > B,X4: A] : ( P2 @ F2 @ ( cons @ A @ X4 @ ( nil @ A ) ) )
% 0.31/0.46 => ( ! [F2: A > B,X4: A,Y4: A,Zs2: list @ A] :
% 0.31/0.46 ( ( P2 @ F2 @ ( cons @ A @ Y4 @ Zs2 ) )
% 0.31/0.46 => ( P2 @ F2 @ ( cons @ A @ X4 @ ( cons @ A @ Y4 @ Zs2 ) ) ) )
% 0.31/0.46 => ( ! [A4: A > B] : ( P2 @ A4 @ ( nil @ A ) )
% 0.31/0.46 => ( P2 @ A0 @ A1 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % arg_min_list.induct
% 0.31/0.46 thf(fact_114_remdups__adj_Oinduct,axiom,
% 0.31/0.46 ! [A: $tType,P2: ( list @ A ) > $o,A0: list @ A] :
% 0.31/0.46 ( ( P2 @ ( nil @ A ) )
% 0.31/0.46 => ( ! [X4: A] : ( P2 @ ( cons @ A @ X4 @ ( nil @ A ) ) )
% 0.31/0.46 => ( ! [X4: A,Y4: A,Xs4: list @ A] :
% 0.31/0.46 ( ( ( X4 = Y4 )
% 0.31/0.46 => ( P2 @ ( cons @ A @ X4 @ Xs4 ) ) )
% 0.31/0.46 => ( ( ( X4 != Y4 )
% 0.31/0.46 => ( P2 @ ( cons @ A @ Y4 @ Xs4 ) ) )
% 0.31/0.46 => ( P2 @ ( cons @ A @ X4 @ ( cons @ A @ Y4 @ Xs4 ) ) ) ) )
% 0.31/0.46 => ( P2 @ A0 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % remdups_adj.induct
% 0.31/0.46 thf(fact_115_sorted__wrt_Oinduct,axiom,
% 0.31/0.46 ! [A: $tType,P2: ( A > A > $o ) > ( list @ A ) > $o,A0: A > A > $o,A1: list @ A] :
% 0.31/0.46 ( ! [P4: A > A > $o] : ( P2 @ P4 @ ( nil @ A ) )
% 0.31/0.46 => ( ! [P4: A > A > $o,X4: A,Ys4: list @ A] :
% 0.31/0.46 ( ( P2 @ P4 @ Ys4 )
% 0.31/0.46 => ( P2 @ P4 @ ( cons @ A @ X4 @ Ys4 ) ) )
% 0.31/0.46 => ( P2 @ A0 @ A1 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % sorted_wrt.induct
% 0.31/0.46 thf(fact_116_remdups__adj_Ocases,axiom,
% 0.31/0.46 ! [A: $tType,X3: list @ A] :
% 0.31/0.46 ( ( X3
% 0.31/0.46 != ( nil @ A ) )
% 0.31/0.46 => ( ! [X4: A] :
% 0.31/0.46 ( X3
% 0.31/0.46 != ( cons @ A @ X4 @ ( nil @ A ) ) )
% 0.31/0.46 => ~ ! [X4: A,Y4: A,Xs4: list @ A] :
% 0.31/0.46 ( X3
% 0.31/0.46 != ( cons @ A @ X4 @ ( cons @ A @ Y4 @ Xs4 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % remdups_adj.cases
% 0.31/0.46 thf(fact_117_shuffles_Oinduct,axiom,
% 0.31/0.46 ! [A: $tType,P2: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 0.31/0.46 ( ! [X_1: list @ A] : ( P2 @ ( nil @ A ) @ X_1 )
% 0.31/0.46 => ( ! [Xs4: list @ A] : ( P2 @ Xs4 @ ( nil @ A ) )
% 0.31/0.46 => ( ! [X4: A,Xs4: list @ A,Y4: A,Ys4: list @ A] :
% 0.31/0.46 ( ( P2 @ Xs4 @ ( cons @ A @ Y4 @ Ys4 ) )
% 0.31/0.46 => ( ( P2 @ ( cons @ A @ X4 @ Xs4 ) @ Ys4 )
% 0.31/0.46 => ( P2 @ ( cons @ A @ X4 @ Xs4 ) @ ( cons @ A @ Y4 @ Ys4 ) ) ) )
% 0.31/0.46 => ( P2 @ A0 @ A1 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % shuffles.induct
% 0.31/0.46 thf(fact_118_min__list_Oinduct,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( ord @ A )
% 0.31/0.46 => ! [P2: ( list @ A ) > $o,A0: list @ A] :
% 0.31/0.46 ( ! [X4: A,Xs4: list @ A] :
% 0.31/0.46 ( ! [X212: A,X222: list @ A] :
% 0.31/0.46 ( ( Xs4
% 0.31/0.46 = ( cons @ A @ X212 @ X222 ) )
% 0.31/0.46 => ( P2 @ Xs4 ) )
% 0.31/0.46 => ( P2 @ ( cons @ A @ X4 @ Xs4 ) ) )
% 0.31/0.46 => ( ( P2 @ ( nil @ A ) )
% 0.31/0.46 => ( P2 @ A0 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % min_list.induct
% 0.31/0.46 thf(fact_119_min__list_Ocases,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( ord @ A )
% 0.31/0.46 => ! [X3: list @ A] :
% 0.31/0.46 ( ! [X4: A,Xs4: list @ A] :
% 0.31/0.46 ( X3
% 0.31/0.46 != ( cons @ A @ X4 @ Xs4 ) )
% 0.31/0.46 => ( X3
% 0.31/0.46 = ( nil @ A ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % min_list.cases
% 0.31/0.46 thf(fact_120_induct__list012,axiom,
% 0.31/0.46 ! [A: $tType,P2: ( list @ A ) > $o,Xs2: list @ A] :
% 0.31/0.46 ( ( P2 @ ( nil @ A ) )
% 0.31/0.46 => ( ! [X4: A] : ( P2 @ ( cons @ A @ X4 @ ( nil @ A ) ) )
% 0.31/0.46 => ( ! [X4: A,Y4: A,Zs2: list @ A] :
% 0.31/0.46 ( ( P2 @ Zs2 )
% 0.31/0.46 => ( ( P2 @ ( cons @ A @ Y4 @ Zs2 ) )
% 0.31/0.46 => ( P2 @ ( cons @ A @ X4 @ ( cons @ A @ Y4 @ Zs2 ) ) ) ) )
% 0.31/0.46 => ( P2 @ Xs2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % induct_list012
% 0.31/0.46 thf(fact_121_splice_Oinduct,axiom,
% 0.31/0.46 ! [A: $tType,P2: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 0.31/0.46 ( ! [X_1: list @ A] : ( P2 @ ( nil @ A ) @ X_1 )
% 0.31/0.46 => ( ! [X4: A,Xs4: list @ A,Ys4: list @ A] :
% 0.31/0.46 ( ( P2 @ Ys4 @ Xs4 )
% 0.31/0.46 => ( P2 @ ( cons @ A @ X4 @ Xs4 ) @ Ys4 ) )
% 0.31/0.46 => ( P2 @ A0 @ A1 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % splice.induct
% 0.31/0.46 thf(fact_122_list__induct2_H,axiom,
% 0.31/0.46 ! [A: $tType,B: $tType,P2: ( list @ A ) > ( list @ B ) > $o,Xs2: list @ A,Ys2: list @ B] :
% 0.31/0.46 ( ( P2 @ ( nil @ A ) @ ( nil @ B ) )
% 0.31/0.46 => ( ! [X4: A,Xs4: list @ A] : ( P2 @ ( cons @ A @ X4 @ Xs4 ) @ ( nil @ B ) )
% 0.31/0.46 => ( ! [Y4: B,Ys4: list @ B] : ( P2 @ ( nil @ A ) @ ( cons @ B @ Y4 @ Ys4 ) )
% 0.31/0.46 => ( ! [X4: A,Xs4: list @ A,Y4: B,Ys4: list @ B] :
% 0.31/0.46 ( ( P2 @ Xs4 @ Ys4 )
% 0.31/0.46 => ( P2 @ ( cons @ A @ X4 @ Xs4 ) @ ( cons @ B @ Y4 @ Ys4 ) ) )
% 0.31/0.46 => ( P2 @ Xs2 @ Ys2 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % list_induct2'
% 0.31/0.46 thf(fact_123_neq__Nil__conv,axiom,
% 0.31/0.46 ! [A: $tType,Xs2: list @ A] :
% 0.31/0.46 ( ( Xs2
% 0.31/0.46 != ( nil @ A ) )
% 0.31/0.46 = ( ? [Y: A,Ys: list @ A] :
% 0.31/0.46 ( Xs2
% 0.31/0.46 = ( cons @ A @ Y @ Ys ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % neq_Nil_conv
% 0.31/0.46 thf(fact_124_list_Oinducts,axiom,
% 0.31/0.46 ! [A: $tType,P2: ( list @ A ) > $o,List: list @ A] :
% 0.31/0.46 ( ( P2 @ ( nil @ A ) )
% 0.31/0.46 => ( ! [X12: A,X23: list @ A] :
% 0.31/0.46 ( ( P2 @ X23 )
% 0.31/0.46 => ( P2 @ ( cons @ A @ X12 @ X23 ) ) )
% 0.31/0.46 => ( P2 @ List ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % list.inducts
% 0.31/0.46 thf(fact_125_list_Oexhaust,axiom,
% 0.31/0.46 ! [A: $tType,Y3: list @ A] :
% 0.31/0.46 ( ( Y3
% 0.31/0.46 != ( nil @ A ) )
% 0.31/0.46 => ~ ! [X213: A,X223: list @ A] :
% 0.31/0.46 ( Y3
% 0.31/0.46 != ( cons @ A @ X213 @ X223 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % list.exhaust
% 0.31/0.46 thf(fact_126_list_OdiscI,axiom,
% 0.31/0.46 ! [A: $tType,List: list @ A,X21: A,X22: list @ A] :
% 0.31/0.46 ( ( List
% 0.31/0.46 = ( cons @ A @ X21 @ X22 ) )
% 0.31/0.46 => ( List
% 0.31/0.46 != ( nil @ A ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % list.discI
% 0.31/0.46 thf(fact_127_list_Odistinct_I1_J,axiom,
% 0.31/0.46 ! [A: $tType,X21: A,X22: list @ A] :
% 0.31/0.46 ( ( nil @ A )
% 0.31/0.46 != ( cons @ A @ X21 @ X22 ) ) ).
% 0.31/0.46
% 0.31/0.46 % list.distinct(1)
% 0.31/0.46 thf(fact_128_append_Oleft__neutral,axiom,
% 0.31/0.46 ! [A: $tType,A2: list @ A] :
% 0.31/0.46 ( ( append @ A @ ( nil @ A ) @ A2 )
% 0.31/0.46 = A2 ) ).
% 0.31/0.46
% 0.31/0.46 % append.left_neutral
% 0.31/0.46 thf(fact_129_append__Nil,axiom,
% 0.31/0.46 ! [A: $tType,Ys2: list @ A] :
% 0.31/0.46 ( ( append @ A @ ( nil @ A ) @ Ys2 )
% 0.31/0.46 = Ys2 ) ).
% 0.31/0.46
% 0.31/0.46 % append_Nil
% 0.31/0.46 thf(fact_130_eq__Nil__appendI,axiom,
% 0.31/0.46 ! [A: $tType,Xs2: list @ A,Ys2: list @ A] :
% 0.31/0.46 ( ( Xs2 = Ys2 )
% 0.31/0.46 => ( Xs2
% 0.31/0.46 = ( append @ A @ ( nil @ A ) @ Ys2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % eq_Nil_appendI
% 0.31/0.46 thf(fact_131_lexord__lex,axiom,
% 0.31/0.46 ! [A: $tType,X3: list @ A,Y3: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.31/0.46 ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ X3 @ Y3 ) @ ( lex @ A @ R ) )
% 0.31/0.46 = ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ X3 @ Y3 ) @ ( lexord @ A @ R ) )
% 0.31/0.46 & ( ( size_size @ ( list @ A ) @ X3 )
% 0.31/0.46 = ( size_size @ ( list @ A ) @ Y3 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lexord_lex
% 0.31/0.46 thf(fact_132_pcas_Ocases,axiom,
% 0.31/0.46 ! [A: $tType,X3: product_prod @ A @ ( product_prod @ ( list @ ( product_prod @ A @ A ) ) @ A )] :
% 0.31/0.46 ( ! [U2: A,V: A] :
% 0.31/0.46 ( X3
% 0.31/0.46 != ( product_Pair @ A @ ( product_prod @ ( list @ ( product_prod @ A @ A ) ) @ A ) @ U2 @ ( product_Pair @ ( list @ ( product_prod @ A @ A ) ) @ A @ ( nil @ ( product_prod @ A @ A ) ) @ V ) ) )
% 0.31/0.46 => ~ ! [U2: A,E2: product_prod @ A @ A,Es: list @ ( product_prod @ A @ A ),V: A] :
% 0.31/0.46 ( X3
% 0.31/0.46 != ( product_Pair @ A @ ( product_prod @ ( list @ ( product_prod @ A @ A ) ) @ A ) @ U2 @ ( product_Pair @ ( list @ ( product_prod @ A @ A ) ) @ A @ ( cons @ ( product_prod @ A @ A ) @ E2 @ Es ) @ V ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % pcas.cases
% 0.31/0.46 thf(fact_133_list__bind__cong,axiom,
% 0.31/0.46 ! [B: $tType,A: $tType,Xs2: list @ A,Ys2: list @ A,F3: A > ( list @ B ),G4: A > ( list @ B )] :
% 0.31/0.46 ( ( Xs2 = Ys2 )
% 0.31/0.46 => ( ! [X4: A] :
% 0.31/0.46 ( ( member2 @ A @ X4 @ ( set2 @ A @ Xs2 ) )
% 0.31/0.46 => ( ( F3 @ X4 )
% 0.31/0.46 = ( G4 @ X4 ) ) )
% 0.31/0.46 => ( ( bind @ A @ B @ Xs2 @ F3 )
% 0.31/0.46 = ( bind @ A @ B @ Ys2 @ G4 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % list_bind_cong
% 0.31/0.46 thf(fact_134_in__set__member,axiom,
% 0.31/0.46 ! [A: $tType,X3: A,Xs2: list @ A] :
% 0.31/0.46 ( ( member2 @ A @ X3 @ ( set2 @ A @ Xs2 ) )
% 0.31/0.46 = ( member @ A @ Xs2 @ X3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % in_set_member
% 0.31/0.46 thf(fact_135_maps__simps_I2_J,axiom,
% 0.31/0.46 ! [B: $tType,A: $tType,F3: B > ( list @ A )] :
% 0.31/0.46 ( ( maps @ B @ A @ F3 @ ( nil @ B ) )
% 0.31/0.46 = ( nil @ A ) ) ).
% 0.31/0.46
% 0.31/0.46 % maps_simps(2)
% 0.31/0.46 thf(fact_136_member__rec_I2_J,axiom,
% 0.31/0.46 ! [A: $tType,Y3: A] :
% 0.31/0.46 ~ ( member @ A @ ( nil @ A ) @ Y3 ) ).
% 0.31/0.46
% 0.31/0.46 % member_rec(2)
% 0.31/0.46 thf(fact_137_progressing__Nil,axiom,
% 0.31/0.46 ! [A: $tType] : ( kurato990191779essing @ A @ ( nil @ ( product_prod @ A @ A ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % progressing_Nil
% 0.31/0.46 thf(fact_138_split__list__first__prop__iff,axiom,
% 0.31/0.46 ! [A: $tType,Xs2: list @ A,P2: A > $o] :
% 0.31/0.46 ( ( ? [X: A] :
% 0.31/0.46 ( ( member2 @ A @ X @ ( set2 @ A @ Xs2 ) )
% 0.31/0.46 & ( P2 @ X ) ) )
% 0.31/0.46 = ( ? [Ys: list @ A,X: A] :
% 0.31/0.46 ( ? [Zs3: list @ A] :
% 0.31/0.46 ( Xs2
% 0.31/0.46 = ( append @ A @ Ys @ ( cons @ A @ X @ Zs3 ) ) )
% 0.31/0.46 & ( P2 @ X )
% 0.31/0.46 & ! [Y: A] :
% 0.31/0.46 ( ( member2 @ A @ Y @ ( set2 @ A @ Ys ) )
% 0.31/0.46 => ~ ( P2 @ Y ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % split_list_first_prop_iff
% 0.31/0.46 thf(fact_139_split__list__last__prop__iff,axiom,
% 0.31/0.46 ! [A: $tType,Xs2: list @ A,P2: A > $o] :
% 0.31/0.46 ( ( ? [X: A] :
% 0.31/0.46 ( ( member2 @ A @ X @ ( set2 @ A @ Xs2 ) )
% 0.31/0.46 & ( P2 @ X ) ) )
% 0.31/0.46 = ( ? [Ys: list @ A,X: A,Zs3: list @ A] :
% 0.31/0.46 ( ( Xs2
% 0.31/0.46 = ( append @ A @ Ys @ ( cons @ A @ X @ Zs3 ) ) )
% 0.31/0.46 & ( P2 @ X )
% 0.31/0.46 & ! [Y: A] :
% 0.31/0.46 ( ( member2 @ A @ Y @ ( set2 @ A @ Zs3 ) )
% 0.31/0.46 => ~ ( P2 @ Y ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % split_list_last_prop_iff
% 0.31/0.46 thf(fact_140_in__set__conv__decomp__first,axiom,
% 0.31/0.46 ! [A: $tType,X3: A,Xs2: list @ A] :
% 0.31/0.46 ( ( member2 @ A @ X3 @ ( set2 @ A @ Xs2 ) )
% 0.31/0.46 = ( ? [Ys: list @ A,Zs3: list @ A] :
% 0.31/0.46 ( ( Xs2
% 0.31/0.46 = ( append @ A @ Ys @ ( cons @ A @ X3 @ Zs3 ) ) )
% 0.31/0.46 & ~ ( member2 @ A @ X3 @ ( set2 @ A @ Ys ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % in_set_conv_decomp_first
% 0.31/0.46 thf(fact_141_in__set__conv__decomp__last,axiom,
% 0.31/0.46 ! [A: $tType,X3: A,Xs2: list @ A] :
% 0.31/0.46 ( ( member2 @ A @ X3 @ ( set2 @ A @ Xs2 ) )
% 0.31/0.46 = ( ? [Ys: list @ A,Zs3: list @ A] :
% 0.31/0.46 ( ( Xs2
% 0.31/0.46 = ( append @ A @ Ys @ ( cons @ A @ X3 @ Zs3 ) ) )
% 0.31/0.46 & ~ ( member2 @ A @ X3 @ ( set2 @ A @ Zs3 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % in_set_conv_decomp_last
% 0.31/0.46 thf(fact_142_split__list__first__propE,axiom,
% 0.31/0.46 ! [A: $tType,Xs2: list @ A,P2: A > $o] :
% 0.31/0.46 ( ? [X5: A] :
% 0.31/0.46 ( ( member2 @ A @ X5 @ ( set2 @ A @ Xs2 ) )
% 0.31/0.46 & ( P2 @ X5 ) )
% 0.31/0.46 => ~ ! [Ys4: list @ A,X4: A] :
% 0.31/0.46 ( ? [Zs2: list @ A] :
% 0.31/0.46 ( Xs2
% 0.31/0.46 = ( append @ A @ Ys4 @ ( cons @ A @ X4 @ Zs2 ) ) )
% 0.31/0.46 => ( ( P2 @ X4 )
% 0.31/0.46 => ~ ! [Xa: A] :
% 0.31/0.46 ( ( member2 @ A @ Xa @ ( set2 @ A @ Ys4 ) )
% 0.31/0.46 => ~ ( P2 @ Xa ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % split_list_first_propE
% 0.31/0.46 thf(fact_143_split__list__last__propE,axiom,
% 0.31/0.46 ! [A: $tType,Xs2: list @ A,P2: A > $o] :
% 0.31/0.46 ( ? [X5: A] :
% 0.31/0.46 ( ( member2 @ A @ X5 @ ( set2 @ A @ Xs2 ) )
% 0.31/0.46 & ( P2 @ X5 ) )
% 0.31/0.46 => ~ ! [Ys4: list @ A,X4: A,Zs2: list @ A] :
% 0.31/0.46 ( ( Xs2
% 0.31/0.46 = ( append @ A @ Ys4 @ ( cons @ A @ X4 @ Zs2 ) ) )
% 0.31/0.46 => ( ( P2 @ X4 )
% 0.31/0.46 => ~ ! [Xa: A] :
% 0.31/0.46 ( ( member2 @ A @ Xa @ ( set2 @ A @ Zs2 ) )
% 0.31/0.46 => ~ ( P2 @ Xa ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % split_list_last_propE
% 0.31/0.46 thf(fact_144_split__list__first__prop,axiom,
% 0.31/0.46 ! [A: $tType,Xs2: list @ A,P2: A > $o] :
% 0.31/0.46 ( ? [X5: A] :
% 0.31/0.46 ( ( member2 @ A @ X5 @ ( set2 @ A @ Xs2 ) )
% 0.31/0.46 & ( P2 @ X5 ) )
% 0.31/0.46 => ? [Ys4: list @ A,X4: A] :
% 0.31/0.46 ( ? [Zs2: list @ A] :
% 0.31/0.46 ( Xs2
% 0.31/0.46 = ( append @ A @ Ys4 @ ( cons @ A @ X4 @ Zs2 ) ) )
% 0.31/0.46 & ( P2 @ X4 )
% 0.31/0.46 & ! [Xa: A] :
% 0.31/0.46 ( ( member2 @ A @ Xa @ ( set2 @ A @ Ys4 ) )
% 0.31/0.46 => ~ ( P2 @ Xa ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % split_list_first_prop
% 0.31/0.46 thf(fact_145_split__list__last__prop,axiom,
% 0.31/0.46 ! [A: $tType,Xs2: list @ A,P2: A > $o] :
% 0.31/0.46 ( ? [X5: A] :
% 0.31/0.46 ( ( member2 @ A @ X5 @ ( set2 @ A @ Xs2 ) )
% 0.31/0.46 & ( P2 @ X5 ) )
% 0.31/0.46 => ? [Ys4: list @ A,X4: A,Zs2: list @ A] :
% 0.31/0.46 ( ( Xs2
% 0.31/0.46 = ( append @ A @ Ys4 @ ( cons @ A @ X4 @ Zs2 ) ) )
% 0.31/0.46 & ( P2 @ X4 )
% 0.31/0.46 & ! [Xa: A] :
% 0.31/0.46 ( ( member2 @ A @ Xa @ ( set2 @ A @ Zs2 ) )
% 0.31/0.46 => ~ ( P2 @ Xa ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % split_list_last_prop
% 0.31/0.46 thf(fact_146_in__set__conv__decomp,axiom,
% 0.31/0.46 ! [A: $tType,X3: A,Xs2: list @ A] :
% 0.31/0.46 ( ( member2 @ A @ X3 @ ( set2 @ A @ Xs2 ) )
% 0.31/0.46 = ( ? [Ys: list @ A,Zs3: list @ A] :
% 0.31/0.46 ( Xs2
% 0.31/0.46 = ( append @ A @ Ys @ ( cons @ A @ X3 @ Zs3 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % in_set_conv_decomp
% 0.31/0.46 thf(fact_147_append__Cons__eq__iff,axiom,
% 0.31/0.46 ! [A: $tType,X3: A,Xs2: list @ A,Ys2: list @ A,Xs5: list @ A,Ys5: list @ A] :
% 0.31/0.46 ( ~ ( member2 @ A @ X3 @ ( set2 @ A @ Xs2 ) )
% 0.31/0.46 => ( ~ ( member2 @ A @ X3 @ ( set2 @ A @ Ys2 ) )
% 0.31/0.46 => ( ( ( append @ A @ Xs2 @ ( cons @ A @ X3 @ Ys2 ) )
% 0.31/0.46 = ( append @ A @ Xs5 @ ( cons @ A @ X3 @ Ys5 ) ) )
% 0.31/0.46 = ( ( Xs2 = Xs5 )
% 0.31/0.46 & ( Ys2 = Ys5 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % append_Cons_eq_iff
% 0.31/0.46 thf(fact_148_split__list__propE,axiom,
% 0.31/0.46 ! [A: $tType,Xs2: list @ A,P2: A > $o] :
% 0.31/0.46 ( ? [X5: A] :
% 0.31/0.46 ( ( member2 @ A @ X5 @ ( set2 @ A @ Xs2 ) )
% 0.31/0.46 & ( P2 @ X5 ) )
% 0.31/0.46 => ~ ! [Ys4: list @ A,X4: A] :
% 0.31/0.46 ( ? [Zs2: list @ A] :
% 0.31/0.46 ( Xs2
% 0.31/0.46 = ( append @ A @ Ys4 @ ( cons @ A @ X4 @ Zs2 ) ) )
% 0.31/0.46 => ~ ( P2 @ X4 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % split_list_propE
% 0.31/0.46 thf(fact_149_split__list__first,axiom,
% 0.31/0.46 ! [A: $tType,X3: A,Xs2: list @ A] :
% 0.31/0.46 ( ( member2 @ A @ X3 @ ( set2 @ A @ Xs2 ) )
% 0.31/0.46 => ? [Ys4: list @ A,Zs2: list @ A] :
% 0.31/0.46 ( ( Xs2
% 0.31/0.46 = ( append @ A @ Ys4 @ ( cons @ A @ X3 @ Zs2 ) ) )
% 0.31/0.46 & ~ ( member2 @ A @ X3 @ ( set2 @ A @ Ys4 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % split_list_first
% 0.31/0.46 thf(fact_150_split__list__prop,axiom,
% 0.31/0.46 ! [A: $tType,Xs2: list @ A,P2: A > $o] :
% 0.31/0.46 ( ? [X5: A] :
% 0.31/0.46 ( ( member2 @ A @ X5 @ ( set2 @ A @ Xs2 ) )
% 0.31/0.46 & ( P2 @ X5 ) )
% 0.31/0.46 => ? [Ys4: list @ A,X4: A] :
% 0.31/0.46 ( ? [Zs2: list @ A] :
% 0.31/0.46 ( Xs2
% 0.31/0.46 = ( append @ A @ Ys4 @ ( cons @ A @ X4 @ Zs2 ) ) )
% 0.31/0.46 & ( P2 @ X4 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % split_list_prop
% 0.31/0.46 thf(fact_151_split__list__last,axiom,
% 0.31/0.46 ! [A: $tType,X3: A,Xs2: list @ A] :
% 0.31/0.46 ( ( member2 @ A @ X3 @ ( set2 @ A @ Xs2 ) )
% 0.31/0.46 => ? [Ys4: list @ A,Zs2: list @ A] :
% 0.31/0.46 ( ( Xs2
% 0.31/0.46 = ( append @ A @ Ys4 @ ( cons @ A @ X3 @ Zs2 ) ) )
% 0.31/0.46 & ~ ( member2 @ A @ X3 @ ( set2 @ A @ Zs2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % split_list_last
% 0.31/0.46 thf(fact_152_split__list,axiom,
% 0.31/0.46 ! [A: $tType,X3: A,Xs2: list @ A] :
% 0.31/0.46 ( ( member2 @ A @ X3 @ ( set2 @ A @ Xs2 ) )
% 0.31/0.46 => ? [Ys4: list @ A,Zs2: list @ A] :
% 0.31/0.46 ( Xs2
% 0.31/0.46 = ( append @ A @ Ys4 @ ( cons @ A @ X3 @ Zs2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % split_list
% 0.31/0.46 thf(fact_153_rev__nonempty__induct,axiom,
% 0.31/0.46 ! [A: $tType,Xs2: list @ A,P2: ( list @ A ) > $o] :
% 0.31/0.46 ( ( Xs2
% 0.31/0.46 != ( nil @ A ) )
% 0.31/0.46 => ( ! [X4: A] : ( P2 @ ( cons @ A @ X4 @ ( nil @ A ) ) )
% 0.31/0.46 => ( ! [X4: A,Xs4: list @ A] :
% 0.31/0.46 ( ( Xs4
% 0.31/0.46 != ( nil @ A ) )
% 0.31/0.46 => ( ( P2 @ Xs4 )
% 0.31/0.46 => ( P2 @ ( append @ A @ Xs4 @ ( cons @ A @ X4 @ ( nil @ A ) ) ) ) ) )
% 0.31/0.46 => ( P2 @ Xs2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % rev_nonempty_induct
% 0.31/0.46 thf(fact_154_append__eq__Cons__conv,axiom,
% 0.31/0.46 ! [A: $tType,Ys2: list @ A,Zs: list @ A,X3: A,Xs2: list @ A] :
% 0.31/0.46 ( ( ( append @ A @ Ys2 @ Zs )
% 0.31/0.46 = ( cons @ A @ X3 @ Xs2 ) )
% 0.31/0.46 = ( ( ( Ys2
% 0.31/0.46 = ( nil @ A ) )
% 0.31/0.46 & ( Zs
% 0.31/0.46 = ( cons @ A @ X3 @ Xs2 ) ) )
% 0.31/0.46 | ? [Ys6: list @ A] :
% 0.31/0.46 ( ( Ys2
% 0.31/0.46 = ( cons @ A @ X3 @ Ys6 ) )
% 0.31/0.46 & ( ( append @ A @ Ys6 @ Zs )
% 0.31/0.46 = Xs2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % append_eq_Cons_conv
% 0.31/0.46 thf(fact_155_Cons__eq__append__conv,axiom,
% 0.31/0.46 ! [A: $tType,X3: A,Xs2: list @ A,Ys2: list @ A,Zs: list @ A] :
% 0.31/0.46 ( ( ( cons @ A @ X3 @ Xs2 )
% 0.31/0.46 = ( append @ A @ Ys2 @ Zs ) )
% 0.31/0.46 = ( ( ( Ys2
% 0.31/0.46 = ( nil @ A ) )
% 0.31/0.46 & ( ( cons @ A @ X3 @ Xs2 )
% 0.31/0.46 = Zs ) )
% 0.31/0.46 | ? [Ys6: list @ A] :
% 0.31/0.46 ( ( ( cons @ A @ X3 @ Ys6 )
% 0.31/0.46 = Ys2 )
% 0.31/0.46 & ( Xs2
% 0.31/0.46 = ( append @ A @ Ys6 @ Zs ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Cons_eq_append_conv
% 0.31/0.46 thf(fact_156_rev__exhaust,axiom,
% 0.31/0.46 ! [A: $tType,Xs2: list @ A] :
% 0.31/0.46 ( ( Xs2
% 0.31/0.46 != ( nil @ A ) )
% 0.31/0.46 => ~ ! [Ys4: list @ A,Y4: A] :
% 0.31/0.46 ( Xs2
% 0.31/0.46 != ( append @ A @ Ys4 @ ( cons @ A @ Y4 @ ( nil @ A ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % rev_exhaust
% 0.31/0.46 thf(fact_157_rev__induct,axiom,
% 0.31/0.46 ! [A: $tType,P2: ( list @ A ) > $o,Xs2: list @ A] :
% 0.31/0.46 ( ( P2 @ ( nil @ A ) )
% 0.31/0.46 => ( ! [X4: A,Xs4: list @ A] :
% 0.31/0.46 ( ( P2 @ Xs4 )
% 0.31/0.46 => ( P2 @ ( append @ A @ Xs4 @ ( cons @ A @ X4 @ ( nil @ A ) ) ) ) )
% 0.31/0.46 => ( P2 @ Xs2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % rev_induct
% 0.31/0.46 thf(fact_158_shuffles_Ocases,axiom,
% 0.31/0.46 ! [A: $tType,X3: product_prod @ ( list @ A ) @ ( list @ A )] :
% 0.31/0.46 ( ! [Ys4: list @ A] :
% 0.31/0.46 ( X3
% 0.31/0.46 != ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( nil @ A ) @ Ys4 ) )
% 0.31/0.46 => ( ! [Xs4: list @ A] :
% 0.31/0.46 ( X3
% 0.31/0.46 != ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs4 @ ( nil @ A ) ) )
% 0.31/0.46 => ~ ! [X4: A,Xs4: list @ A,Y4: A,Ys4: list @ A] :
% 0.31/0.46 ( X3
% 0.31/0.46 != ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X4 @ Xs4 ) @ ( cons @ A @ Y4 @ Ys4 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % shuffles.cases
% 0.31/0.46 thf(fact_159_map__tailrec__rev_Ocases,axiom,
% 0.31/0.46 ! [A: $tType,B: $tType,X3: product_prod @ ( A > B ) @ ( product_prod @ ( list @ A ) @ ( list @ B ) )] :
% 0.31/0.46 ( ! [F2: A > B,Bs: list @ B] :
% 0.31/0.46 ( X3
% 0.31/0.46 != ( product_Pair @ ( A > B ) @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ F2 @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ ( nil @ A ) @ Bs ) ) )
% 0.31/0.46 => ~ ! [F2: A > B,A4: A,As: list @ A,Bs: list @ B] :
% 0.31/0.46 ( X3
% 0.31/0.46 != ( product_Pair @ ( A > B ) @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ F2 @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ ( cons @ A @ A4 @ As ) @ Bs ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % map_tailrec_rev.cases
% 0.31/0.46 thf(fact_160_sd__path_Oinduct,axiom,
% 0.31/0.46 ! [A: $tType,P2: ( product_prod @ A @ A ) > A > ( list @ ( product_prod @ A @ A ) ) > $o,A0: product_prod @ A @ A,A1: A,A22: list @ ( product_prod @ A @ A )] :
% 0.31/0.46 ( ! [Uu: product_prod @ A @ A,Uv: A] : ( P2 @ Uu @ Uv @ ( nil @ ( product_prod @ A @ A ) ) )
% 0.31/0.46 => ( ! [U2: A,V: A,W: A,E2: product_prod @ A @ A,Es: list @ ( product_prod @ A @ A )] :
% 0.31/0.46 ( ( P2 @ ( product_Pair @ A @ A @ U2 @ V ) @ W @ Es )
% 0.31/0.46 => ( P2 @ ( product_Pair @ A @ A @ U2 @ V ) @ W @ ( cons @ ( product_prod @ A @ A ) @ E2 @ Es ) ) )
% 0.31/0.46 => ( P2 @ A0 @ A1 @ A22 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % sd_path.induct
% 0.31/0.46 thf(fact_161_co__path_Oinduct,axiom,
% 0.31/0.46 ! [A: $tType,P2: ( product_prod @ A @ A ) > A > ( list @ ( product_prod @ A @ A ) ) > $o,A0: product_prod @ A @ A,A1: A,A22: list @ ( product_prod @ A @ A )] :
% 0.31/0.46 ( ! [Uu: product_prod @ A @ A,Uv: A] : ( P2 @ Uu @ Uv @ ( nil @ ( product_prod @ A @ A ) ) )
% 0.31/0.46 => ( ! [Uw: product_prod @ A @ A,Ux: A,E2: product_prod @ A @ A] : ( P2 @ Uw @ Ux @ ( cons @ ( product_prod @ A @ A ) @ E2 @ ( nil @ ( product_prod @ A @ A ) ) ) )
% 0.31/0.46 => ( ! [U2: A,V: A,W: A,E1: product_prod @ A @ A,E22: product_prod @ A @ A,Es: list @ ( product_prod @ A @ A )] :
% 0.31/0.46 ( ( ( ( E1
% 0.31/0.46 = ( product_Pair @ A @ A @ U2 @ W ) )
% 0.31/0.46 & ( E22
% 0.31/0.46 = ( product_Pair @ A @ A @ W @ V ) ) )
% 0.31/0.46 => ( P2 @ ( product_Pair @ A @ A @ U2 @ V ) @ W @ Es ) )
% 0.31/0.46 => ( ( ~ ( ( E1
% 0.31/0.46 = ( product_Pair @ A @ A @ U2 @ W ) )
% 0.31/0.46 & ( E22
% 0.31/0.46 = ( product_Pair @ A @ A @ W @ V ) ) )
% 0.31/0.46 => ( ( ( E1
% 0.31/0.46 = ( product_Pair @ A @ A @ V @ W ) )
% 0.31/0.46 & ( E22
% 0.31/0.46 = ( product_Pair @ A @ A @ W @ U2 ) ) )
% 0.31/0.46 => ( P2 @ ( product_Pair @ A @ A @ U2 @ V ) @ W @ Es ) ) )
% 0.31/0.46 => ( ( ~ ( ( E1
% 0.31/0.46 = ( product_Pair @ A @ A @ U2 @ W ) )
% 0.31/0.46 & ( E22
% 0.31/0.46 = ( product_Pair @ A @ A @ W @ V ) ) )
% 0.31/0.46 => ( ~ ( ( E1
% 0.31/0.46 = ( product_Pair @ A @ A @ V @ W ) )
% 0.31/0.46 & ( E22
% 0.31/0.46 = ( product_Pair @ A @ A @ W @ U2 ) ) )
% 0.31/0.46 => ( P2 @ ( product_Pair @ A @ A @ U2 @ V ) @ W @ ( cons @ ( product_prod @ A @ A ) @ E22 @ Es ) ) ) )
% 0.31/0.46 => ( P2 @ ( product_Pair @ A @ A @ U2 @ V ) @ W @ ( cons @ ( product_prod @ A @ A ) @ E1 @ ( cons @ ( product_prod @ A @ A ) @ E22 @ Es ) ) ) ) ) )
% 0.31/0.46 => ( P2 @ A0 @ A1 @ A22 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % co_path.induct
% 0.31/0.46 thf(fact_162_sd__path_Ocases,axiom,
% 0.31/0.46 ! [A: $tType,X3: product_prod @ ( product_prod @ A @ A ) @ ( product_prod @ A @ ( list @ ( product_prod @ A @ A ) ) )] :
% 0.31/0.46 ( ! [Uu: product_prod @ A @ A,Uv: A] :
% 0.31/0.46 ( X3
% 0.31/0.46 != ( product_Pair @ ( product_prod @ A @ A ) @ ( product_prod @ A @ ( list @ ( product_prod @ A @ A ) ) ) @ Uu @ ( product_Pair @ A @ ( list @ ( product_prod @ A @ A ) ) @ Uv @ ( nil @ ( product_prod @ A @ A ) ) ) ) )
% 0.31/0.46 => ~ ! [U2: A,V: A,W: A,E2: product_prod @ A @ A,Es: list @ ( product_prod @ A @ A )] :
% 0.31/0.46 ( X3
% 0.31/0.46 != ( product_Pair @ ( product_prod @ A @ A ) @ ( product_prod @ A @ ( list @ ( product_prod @ A @ A ) ) ) @ ( product_Pair @ A @ A @ U2 @ V ) @ ( product_Pair @ A @ ( list @ ( product_prod @ A @ A ) ) @ W @ ( cons @ ( product_prod @ A @ A ) @ E2 @ Es ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % sd_path.cases
% 0.31/0.46 thf(fact_163_co__path_Ocases,axiom,
% 0.31/0.46 ! [A: $tType,X3: product_prod @ ( product_prod @ A @ A ) @ ( product_prod @ A @ ( list @ ( product_prod @ A @ A ) ) )] :
% 0.31/0.46 ( ! [Uu: product_prod @ A @ A,Uv: A] :
% 0.31/0.46 ( X3
% 0.31/0.46 != ( product_Pair @ ( product_prod @ A @ A ) @ ( product_prod @ A @ ( list @ ( product_prod @ A @ A ) ) ) @ Uu @ ( product_Pair @ A @ ( list @ ( product_prod @ A @ A ) ) @ Uv @ ( nil @ ( product_prod @ A @ A ) ) ) ) )
% 0.31/0.46 => ( ! [Uw: product_prod @ A @ A,Ux: A,E2: product_prod @ A @ A] :
% 0.31/0.46 ( X3
% 0.31/0.46 != ( product_Pair @ ( product_prod @ A @ A ) @ ( product_prod @ A @ ( list @ ( product_prod @ A @ A ) ) ) @ Uw @ ( product_Pair @ A @ ( list @ ( product_prod @ A @ A ) ) @ Ux @ ( cons @ ( product_prod @ A @ A ) @ E2 @ ( nil @ ( product_prod @ A @ A ) ) ) ) ) )
% 0.31/0.46 => ~ ! [U2: A,V: A,W: A,E1: product_prod @ A @ A,E22: product_prod @ A @ A,Es: list @ ( product_prod @ A @ A )] :
% 0.31/0.46 ( X3
% 0.31/0.46 != ( product_Pair @ ( product_prod @ A @ A ) @ ( product_prod @ A @ ( list @ ( product_prod @ A @ A ) ) ) @ ( product_Pair @ A @ A @ U2 @ V ) @ ( product_Pair @ A @ ( list @ ( product_prod @ A @ A ) ) @ W @ ( cons @ ( product_prod @ A @ A ) @ E1 @ ( cons @ ( product_prod @ A @ A ) @ E22 @ Es ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % co_path.cases
% 0.31/0.46 thf(fact_164_listrel1__eq__len,axiom,
% 0.31/0.46 ! [A: $tType,Xs2: list @ A,Ys2: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.31/0.46 ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs2 @ Ys2 ) @ ( listrel1 @ A @ R ) )
% 0.31/0.46 => ( ( size_size @ ( list @ A ) @ Xs2 )
% 0.31/0.46 = ( size_size @ ( list @ A ) @ Ys2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % listrel1_eq_len
% 0.31/0.46 thf(fact_165_not__listrel1__Nil,axiom,
% 0.31/0.46 ! [A: $tType,Xs2: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.31/0.46 ~ ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs2 @ ( nil @ A ) ) @ ( listrel1 @ A @ R ) ) ).
% 0.31/0.46
% 0.31/0.46 % not_listrel1_Nil
% 0.31/0.46 thf(fact_166_not__Nil__listrel1,axiom,
% 0.31/0.46 ! [A: $tType,Xs2: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.31/0.46 ~ ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( nil @ A ) @ Xs2 ) @ ( listrel1 @ A @ R ) ) ).
% 0.31/0.46
% 0.31/0.46 % not_Nil_listrel1
% 0.31/0.46 thf(fact_167_lexord__Nil__right,axiom,
% 0.31/0.46 ! [A: $tType,X3: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.31/0.46 ~ ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ X3 @ ( nil @ A ) ) @ ( lexord @ A @ R ) ) ).
% 0.31/0.46
% 0.31/0.46 % lexord_Nil_right
% 0.31/0.46 thf(fact_168_lex__append__leftI,axiom,
% 0.31/0.46 ! [A: $tType,Ys2: list @ A,Zs: list @ A,R: set @ ( product_prod @ A @ A ),Xs2: list @ A] :
% 0.31/0.46 ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Ys2 @ Zs ) @ ( lex @ A @ R ) )
% 0.31/0.46 => ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ Xs2 @ Ys2 ) @ ( append @ A @ Xs2 @ Zs ) ) @ ( lex @ A @ R ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lex_append_leftI
% 0.31/0.46 thf(fact_169_progressing__single,axiom,
% 0.31/0.46 ! [A: $tType,E3: product_prod @ A @ A] : ( kurato990191779essing @ A @ ( cons @ ( product_prod @ A @ A ) @ E3 @ ( nil @ ( product_prod @ A @ A ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % progressing_single
% 0.31/0.46 thf(fact_170_lexord__partial__trans,axiom,
% 0.31/0.46 ! [A: $tType,Xs2: list @ A,R: set @ ( product_prod @ A @ A ),Ys2: list @ A,Zs: list @ A] :
% 0.31/0.46 ( ! [X4: A,Y4: A,Z2: A] :
% 0.31/0.46 ( ( member2 @ A @ X4 @ ( set2 @ A @ Xs2 ) )
% 0.31/0.46 => ( ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X4 @ Y4 ) @ R )
% 0.31/0.46 => ( ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y4 @ Z2 ) @ R )
% 0.31/0.46 => ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X4 @ Z2 ) @ R ) ) ) )
% 0.31/0.46 => ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs2 @ Ys2 ) @ ( lexord @ A @ R ) )
% 0.31/0.46 => ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Ys2 @ Zs ) @ ( lexord @ A @ R ) )
% 0.31/0.46 => ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs2 @ Zs ) @ ( lexord @ A @ R ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lexord_partial_trans
% 0.31/0.46 thf(fact_171_lexord__sufE,axiom,
% 0.31/0.46 ! [A: $tType,Xs2: list @ A,Zs: list @ A,Ys2: list @ A,Qs: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.31/0.46 ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ Xs2 @ Zs ) @ ( append @ A @ Ys2 @ Qs ) ) @ ( lexord @ A @ R ) )
% 0.31/0.46 => ( ( Xs2 != Ys2 )
% 0.31/0.46 => ( ( ( size_size @ ( list @ A ) @ Xs2 )
% 0.31/0.46 = ( size_size @ ( list @ A ) @ Ys2 ) )
% 0.31/0.46 => ( ( ( size_size @ ( list @ A ) @ Zs )
% 0.31/0.46 = ( size_size @ ( list @ A ) @ Qs ) )
% 0.31/0.46 => ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs2 @ Ys2 ) @ ( lexord @ A @ R ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lexord_sufE
% 0.31/0.46 thf(fact_172_subset__eq__mset__impl_Ocases,axiom,
% 0.31/0.46 ! [A: $tType,X3: product_prod @ ( list @ A ) @ ( list @ A )] :
% 0.31/0.46 ( ! [Ys4: list @ A] :
% 0.31/0.46 ( X3
% 0.31/0.46 != ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( nil @ A ) @ Ys4 ) )
% 0.31/0.46 => ~ ! [X4: A,Xs4: list @ A,Ys4: list @ A] :
% 0.31/0.46 ( X3
% 0.31/0.46 != ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X4 @ Xs4 ) @ Ys4 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % subset_eq_mset_impl.cases
% 0.31/0.46 thf(fact_173_pre__digraph_Ocas_Ocases,axiom,
% 0.31/0.46 ! [B: $tType,A: $tType,X3: product_prod @ A @ ( product_prod @ ( list @ B ) @ A )] :
% 0.31/0.46 ( ! [U2: A,V: A] :
% 0.31/0.46 ( X3
% 0.31/0.46 != ( product_Pair @ A @ ( product_prod @ ( list @ B ) @ A ) @ U2 @ ( product_Pair @ ( list @ B ) @ A @ ( nil @ B ) @ V ) ) )
% 0.31/0.46 => ~ ! [U2: A,E2: B,Es: list @ B,V: A] :
% 0.31/0.46 ( X3
% 0.31/0.46 != ( product_Pair @ A @ ( product_prod @ ( list @ B ) @ A ) @ U2 @ ( product_Pair @ ( list @ B ) @ A @ ( cons @ B @ E2 @ Es ) @ V ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % pre_digraph.cas.cases
% 0.31/0.46 thf(fact_174_asym_Oinducts,axiom,
% 0.31/0.46 ! [A: $tType,X3: set @ ( product_prod @ A @ A ),P2: ( set @ ( product_prod @ A @ A ) ) > $o] :
% 0.31/0.46 ( ( asym @ A @ X3 )
% 0.31/0.46 => ( ! [R3: set @ ( product_prod @ A @ A )] :
% 0.31/0.46 ( ! [A7: A,B5: A] :
% 0.31/0.46 ( ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A7 @ B5 ) @ R3 )
% 0.31/0.46 => ~ ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ B5 @ A7 ) @ R3 ) )
% 0.31/0.46 => ( P2 @ R3 ) )
% 0.31/0.46 => ( P2 @ X3 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % asym.inducts
% 0.31/0.46 thf(fact_175_asym_Ointros,axiom,
% 0.31/0.46 ! [A: $tType,R2: set @ ( product_prod @ A @ A )] :
% 0.31/0.46 ( ! [A4: A,B4: A] :
% 0.31/0.46 ( ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A4 @ B4 ) @ R2 )
% 0.31/0.46 => ~ ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ B4 @ A4 ) @ R2 ) )
% 0.31/0.46 => ( asym @ A @ R2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % asym.intros
% 0.31/0.46 thf(fact_176_asym_Osimps,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( asym @ A )
% 0.31/0.46 = ( ^ [A6: set @ ( product_prod @ A @ A )] :
% 0.31/0.46 ? [R4: set @ ( product_prod @ A @ A )] :
% 0.31/0.46 ( ( A6 = R4 )
% 0.31/0.46 & ! [X: A,Y: A] :
% 0.31/0.46 ( ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y ) @ R4 )
% 0.31/0.46 => ~ ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y @ X ) @ R4 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % asym.simps
% 0.31/0.46 thf(fact_177_asym_Ocases,axiom,
% 0.31/0.46 ! [A: $tType,A2: set @ ( product_prod @ A @ A )] :
% 0.31/0.46 ( ( asym @ A @ A2 )
% 0.31/0.46 => ! [A7: A,B5: A] :
% 0.31/0.46 ( ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A7 @ B5 ) @ A2 )
% 0.31/0.46 => ~ ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ B5 @ A7 ) @ A2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % asym.cases
% 0.31/0.46 thf(fact_178_asym__iff,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( asym @ A )
% 0.31/0.46 = ( ^ [R4: set @ ( product_prod @ A @ A )] :
% 0.31/0.46 ! [X: A,Y: A] :
% 0.31/0.46 ( ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y ) @ R4 )
% 0.31/0.46 => ~ ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y @ X ) @ R4 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % asym_iff
% 0.31/0.46 thf(fact_179_irreflI,axiom,
% 0.31/0.46 ! [A: $tType,R2: set @ ( product_prod @ A @ A )] :
% 0.31/0.46 ( ! [A4: A] :
% 0.31/0.46 ~ ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A4 @ A4 ) @ R2 )
% 0.31/0.46 => ( irrefl @ A @ R2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % irreflI
% 0.31/0.46 thf(fact_180_irrefl__def,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( irrefl @ A )
% 0.31/0.46 = ( ^ [R5: set @ ( product_prod @ A @ A )] :
% 0.31/0.46 ! [A6: A] :
% 0.31/0.46 ~ ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A6 @ A6 ) @ R5 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % irrefl_def
% 0.31/0.46 thf(fact_181_asymD,axiom,
% 0.31/0.46 ! [A: $tType,R2: set @ ( product_prod @ A @ A ),X3: A,Y3: A] :
% 0.31/0.46 ( ( asym @ A @ R2 )
% 0.31/0.46 => ( ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X3 @ Y3 ) @ R2 )
% 0.31/0.46 => ~ ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y3 @ X3 ) @ R2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % asymD
% 0.31/0.46 thf(fact_182_inverse__permutation__of__list_Ocases,axiom,
% 0.31/0.46 ! [A: $tType,X3: product_prod @ ( list @ ( product_prod @ A @ A ) ) @ A] :
% 0.31/0.46 ( ! [X4: A] :
% 0.31/0.46 ( X3
% 0.31/0.46 != ( product_Pair @ ( list @ ( product_prod @ A @ A ) ) @ A @ ( nil @ ( product_prod @ A @ A ) ) @ X4 ) )
% 0.31/0.46 => ~ ! [Y4: A,X6: A,Xs4: list @ ( product_prod @ A @ A ),X4: A] :
% 0.31/0.46 ( X3
% 0.31/0.46 != ( product_Pair @ ( list @ ( product_prod @ A @ A ) ) @ A @ ( cons @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y4 @ X6 ) @ Xs4 ) @ X4 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % inverse_permutation_of_list.cases
% 0.31/0.46 thf(fact_183_inverse__permutation__of__list_Oinduct,axiom,
% 0.31/0.46 ! [A: $tType,P2: ( list @ ( product_prod @ A @ A ) ) > A > $o,A0: list @ ( product_prod @ A @ A ),A1: A] :
% 0.31/0.46 ( ! [X_1: A] : ( P2 @ ( nil @ ( product_prod @ A @ A ) ) @ X_1 )
% 0.31/0.46 => ( ! [Y4: A,X6: A,Xs4: list @ ( product_prod @ A @ A ),X4: A] :
% 0.31/0.46 ( ( ( X4 != X6 )
% 0.31/0.46 => ( P2 @ Xs4 @ X4 ) )
% 0.31/0.46 => ( P2 @ ( cons @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y4 @ X6 ) @ Xs4 ) @ X4 ) )
% 0.31/0.46 => ( P2 @ A0 @ A1 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % inverse_permutation_of_list.induct
% 0.31/0.46 thf(fact_184_sd__path_Osimps_I2_J,axiom,
% 0.31/0.46 ! [A: $tType,U: A,V2: A,W2: A,E3: product_prod @ A @ A,Es2: list @ ( product_prod @ A @ A )] :
% 0.31/0.46 ( ( pair_sd_path @ A @ ( product_Pair @ A @ A @ U @ V2 ) @ W2 @ ( cons @ ( product_prod @ A @ A ) @ E3 @ Es2 ) )
% 0.31/0.46 = ( append @ ( product_prod @ A @ A )
% 0.31/0.46 @ ( if @ ( list @ ( product_prod @ A @ A ) )
% 0.31/0.46 @ ( E3
% 0.31/0.46 = ( product_Pair @ A @ A @ U @ V2 ) )
% 0.31/0.46 @ ( cons @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ U @ W2 ) @ ( cons @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ W2 @ V2 ) @ ( nil @ ( product_prod @ A @ A ) ) ) )
% 0.31/0.46 @ ( if @ ( list @ ( product_prod @ A @ A ) )
% 0.31/0.46 @ ( E3
% 0.31/0.46 = ( product_Pair @ A @ A @ V2 @ U ) )
% 0.31/0.46 @ ( cons @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ V2 @ W2 ) @ ( cons @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ W2 @ U ) @ ( nil @ ( product_prod @ A @ A ) ) ) )
% 0.31/0.46 @ ( cons @ ( product_prod @ A @ A ) @ E3 @ ( nil @ ( product_prod @ A @ A ) ) ) ) )
% 0.31/0.46 @ ( pair_sd_path @ A @ ( product_Pair @ A @ A @ U @ V2 ) @ W2 @ Es2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % sd_path.simps(2)
% 0.31/0.46 thf(fact_185_sd__path_Osimps_I1_J,axiom,
% 0.31/0.46 ! [A: $tType,Uu2: product_prod @ A @ A,Uv2: A] :
% 0.31/0.46 ( ( pair_sd_path @ A @ Uu2 @ Uv2 @ ( nil @ ( product_prod @ A @ A ) ) )
% 0.31/0.46 = ( nil @ ( product_prod @ A @ A ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % sd_path.simps(1)
% 0.31/0.46 thf(fact_186_sd__path__id,axiom,
% 0.31/0.46 ! [A: $tType,X3: A,Y3: A,P3: list @ ( product_prod @ A @ A ),W2: A] :
% 0.31/0.46 ( ~ ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X3 @ Y3 ) @ ( set2 @ ( product_prod @ A @ A ) @ P3 ) )
% 0.31/0.46 => ( ~ ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y3 @ X3 ) @ ( set2 @ ( product_prod @ A @ A ) @ P3 ) )
% 0.31/0.46 => ( ( pair_sd_path @ A @ ( product_Pair @ A @ A @ X3 @ Y3 ) @ W2 @ P3 )
% 0.31/0.46 = P3 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % sd_path_id
% 0.31/0.46 thf(fact_187_sd__path_Oelims,axiom,
% 0.31/0.46 ! [A: $tType,X3: product_prod @ A @ A,Xa2: A,Xb: list @ ( product_prod @ A @ A ),Y3: list @ ( product_prod @ A @ A )] :
% 0.31/0.46 ( ( ( pair_sd_path @ A @ X3 @ Xa2 @ Xb )
% 0.31/0.46 = Y3 )
% 0.31/0.46 => ( ( ( Xb
% 0.31/0.46 = ( nil @ ( product_prod @ A @ A ) ) )
% 0.31/0.46 => ( Y3
% 0.31/0.46 != ( nil @ ( product_prod @ A @ A ) ) ) )
% 0.31/0.46 => ~ ! [U2: A,V: A] :
% 0.31/0.46 ( ( X3
% 0.31/0.46 = ( product_Pair @ A @ A @ U2 @ V ) )
% 0.31/0.46 => ! [E2: product_prod @ A @ A,Es: list @ ( product_prod @ A @ A )] :
% 0.31/0.46 ( ( Xb
% 0.31/0.46 = ( cons @ ( product_prod @ A @ A ) @ E2 @ Es ) )
% 0.31/0.46 => ( Y3
% 0.31/0.46 != ( append @ ( product_prod @ A @ A )
% 0.31/0.46 @ ( if @ ( list @ ( product_prod @ A @ A ) )
% 0.31/0.46 @ ( E2
% 0.31/0.46 = ( product_Pair @ A @ A @ U2 @ V ) )
% 0.31/0.46 @ ( cons @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ U2 @ Xa2 ) @ ( cons @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Xa2 @ V ) @ ( nil @ ( product_prod @ A @ A ) ) ) )
% 0.31/0.46 @ ( if @ ( list @ ( product_prod @ A @ A ) )
% 0.31/0.46 @ ( E2
% 0.31/0.46 = ( product_Pair @ A @ A @ V @ U2 ) )
% 0.31/0.46 @ ( cons @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ V @ Xa2 ) @ ( cons @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Xa2 @ U2 ) @ ( nil @ ( product_prod @ A @ A ) ) ) )
% 0.31/0.46 @ ( cons @ ( product_prod @ A @ A ) @ E2 @ ( nil @ ( product_prod @ A @ A ) ) ) ) )
% 0.31/0.46 @ ( pair_sd_path @ A @ ( product_Pair @ A @ A @ U2 @ V ) @ Xa2 @ Es ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % sd_path.elims
% 0.31/0.46 thf(fact_188_the__elem__set,axiom,
% 0.31/0.46 ! [A: $tType,X3: A] :
% 0.31/0.46 ( ( the_elem @ A @ ( set2 @ A @ ( cons @ A @ X3 @ ( nil @ A ) ) ) )
% 0.31/0.46 = X3 ) ).
% 0.31/0.46
% 0.31/0.46 % the_elem_set
% 0.31/0.46 thf(fact_189_sd__path_Opelims,axiom,
% 0.31/0.46 ! [A: $tType,X3: product_prod @ A @ A,Xa2: A,Xb: list @ ( product_prod @ A @ A ),Y3: list @ ( product_prod @ A @ A )] :
% 0.31/0.46 ( ( ( pair_sd_path @ A @ X3 @ Xa2 @ Xb )
% 0.31/0.46 = Y3 )
% 0.31/0.46 => ( ( accp @ ( product_prod @ ( product_prod @ A @ A ) @ ( product_prod @ A @ ( list @ ( product_prod @ A @ A ) ) ) ) @ ( pair_sd_path_rel @ A ) @ ( product_Pair @ ( product_prod @ A @ A ) @ ( product_prod @ A @ ( list @ ( product_prod @ A @ A ) ) ) @ X3 @ ( product_Pair @ A @ ( list @ ( product_prod @ A @ A ) ) @ Xa2 @ Xb ) ) )
% 0.31/0.46 => ( ( ( Xb
% 0.31/0.46 = ( nil @ ( product_prod @ A @ A ) ) )
% 0.31/0.46 => ( ( Y3
% 0.31/0.46 = ( nil @ ( product_prod @ A @ A ) ) )
% 0.31/0.46 => ~ ( accp @ ( product_prod @ ( product_prod @ A @ A ) @ ( product_prod @ A @ ( list @ ( product_prod @ A @ A ) ) ) ) @ ( pair_sd_path_rel @ A ) @ ( product_Pair @ ( product_prod @ A @ A ) @ ( product_prod @ A @ ( list @ ( product_prod @ A @ A ) ) ) @ X3 @ ( product_Pair @ A @ ( list @ ( product_prod @ A @ A ) ) @ Xa2 @ ( nil @ ( product_prod @ A @ A ) ) ) ) ) ) )
% 0.31/0.46 => ~ ! [U2: A,V: A] :
% 0.31/0.46 ( ( X3
% 0.31/0.46 = ( product_Pair @ A @ A @ U2 @ V ) )
% 0.31/0.46 => ! [E2: product_prod @ A @ A,Es: list @ ( product_prod @ A @ A )] :
% 0.31/0.46 ( ( Xb
% 0.31/0.46 = ( cons @ ( product_prod @ A @ A ) @ E2 @ Es ) )
% 0.31/0.46 => ( ( Y3
% 0.31/0.46 = ( append @ ( product_prod @ A @ A )
% 0.31/0.46 @ ( if @ ( list @ ( product_prod @ A @ A ) )
% 0.31/0.46 @ ( E2
% 0.31/0.46 = ( product_Pair @ A @ A @ U2 @ V ) )
% 0.31/0.46 @ ( cons @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ U2 @ Xa2 ) @ ( cons @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Xa2 @ V ) @ ( nil @ ( product_prod @ A @ A ) ) ) )
% 0.31/0.46 @ ( if @ ( list @ ( product_prod @ A @ A ) )
% 0.31/0.46 @ ( E2
% 0.31/0.46 = ( product_Pair @ A @ A @ V @ U2 ) )
% 0.31/0.46 @ ( cons @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ V @ Xa2 ) @ ( cons @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Xa2 @ U2 ) @ ( nil @ ( product_prod @ A @ A ) ) ) )
% 0.31/0.46 @ ( cons @ ( product_prod @ A @ A ) @ E2 @ ( nil @ ( product_prod @ A @ A ) ) ) ) )
% 0.31/0.46 @ ( pair_sd_path @ A @ ( product_Pair @ A @ A @ U2 @ V ) @ Xa2 @ Es ) ) )
% 0.31/0.46 => ~ ( accp @ ( product_prod @ ( product_prod @ A @ A ) @ ( product_prod @ A @ ( list @ ( product_prod @ A @ A ) ) ) ) @ ( pair_sd_path_rel @ A ) @ ( product_Pair @ ( product_prod @ A @ A ) @ ( product_prod @ A @ ( list @ ( product_prod @ A @ A ) ) ) @ ( product_Pair @ A @ A @ U2 @ V ) @ ( product_Pair @ A @ ( list @ ( product_prod @ A @ A ) ) @ Xa2 @ ( cons @ ( product_prod @ A @ A ) @ E2 @ Es ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % sd_path.pelims
% 0.31/0.46 thf(fact_190_list__exhaust2,axiom,
% 0.31/0.46 ! [A: $tType,B: $tType,Y3: list @ A,Ya: list @ B] :
% 0.31/0.46 ( ( ( Y3
% 0.31/0.46 = ( nil @ A ) )
% 0.31/0.46 => ( Ya
% 0.31/0.46 != ( nil @ B ) ) )
% 0.31/0.46 => ( ( ( Y3
% 0.31/0.46 = ( nil @ A ) )
% 0.31/0.46 => ! [X213: B,X223: list @ B] :
% 0.31/0.46 ( Ya
% 0.31/0.46 != ( cons @ B @ X213 @ X223 ) ) )
% 0.31/0.46 => ( ( ? [X213: A,X223: list @ A] :
% 0.31/0.46 ( Y3
% 0.31/0.46 = ( cons @ A @ X213 @ X223 ) )
% 0.31/0.46 => ( Ya
% 0.31/0.46 != ( nil @ B ) ) )
% 0.31/0.46 => ~ ( ? [X213: A,X223: list @ A] :
% 0.31/0.46 ( Y3
% 0.31/0.46 = ( cons @ A @ X213 @ X223 ) )
% 0.31/0.46 => ! [X21a: B,X22a: list @ B] :
% 0.31/0.46 ( Ya
% 0.31/0.46 != ( cons @ B @ X21a @ X22a ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % list_exhaust2
% 0.31/0.46 thf(fact_191_list__exhaust__NSC,axiom,
% 0.31/0.46 ! [A: $tType,Xs2: list @ A] :
% 0.31/0.46 ( ( Xs2
% 0.31/0.46 != ( nil @ A ) )
% 0.31/0.46 => ( ! [X4: A] :
% 0.31/0.46 ( Xs2
% 0.31/0.46 != ( cons @ A @ X4 @ ( nil @ A ) ) )
% 0.31/0.46 => ~ ! [X4: A,Y4: A,Ys4: list @ A] :
% 0.31/0.46 ( Xs2
% 0.31/0.46 != ( cons @ A @ X4 @ ( cons @ A @ Y4 @ Ys4 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % list_exhaust_NSC
% 0.31/0.46 thf(fact_192_product__lists_Osimps_I1_J,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( product_lists @ A @ ( nil @ ( list @ A ) ) )
% 0.31/0.46 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % product_lists.simps(1)
% 0.31/0.46 thf(fact_193_lenlex__append2,axiom,
% 0.31/0.46 ! [A: $tType,R2: set @ ( product_prod @ A @ A ),Us: list @ A,Xs2: list @ A,Ys2: list @ A] :
% 0.31/0.46 ( ( irrefl @ A @ R2 )
% 0.31/0.46 => ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ Us @ Xs2 ) @ ( append @ A @ Us @ Ys2 ) ) @ ( lenlex @ A @ R2 ) )
% 0.31/0.46 = ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs2 @ Ys2 ) @ ( lenlex @ A @ R2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lenlex_append2
% 0.31/0.46 thf(fact_194_Nil__lenlex__iff1,axiom,
% 0.31/0.46 ! [A: $tType,Ns: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.31/0.46 ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( nil @ A ) @ Ns ) @ ( lenlex @ A @ R ) )
% 0.31/0.46 = ( Ns
% 0.31/0.46 != ( nil @ A ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Nil_lenlex_iff1
% 0.31/0.46 thf(fact_195_in__set__product__lists__length,axiom,
% 0.31/0.46 ! [A: $tType,Xs2: list @ A,Xss2: list @ ( list @ A )] :
% 0.31/0.46 ( ( member2 @ ( list @ A ) @ Xs2 @ ( set2 @ ( list @ A ) @ ( product_lists @ A @ Xss2 ) ) )
% 0.31/0.46 => ( ( size_size @ ( list @ A ) @ Xs2 )
% 0.31/0.46 = ( size_size @ ( list @ ( list @ A ) ) @ Xss2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % in_set_product_lists_length
% 0.31/0.46 thf(fact_196_lenlex__irreflexive,axiom,
% 0.31/0.46 ! [A: $tType,R: set @ ( product_prod @ A @ A ),Xs2: list @ A] :
% 0.31/0.46 ( ! [X4: A] :
% 0.31/0.46 ~ ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X4 @ X4 ) @ R )
% 0.31/0.46 => ~ ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs2 @ Xs2 ) @ ( lenlex @ A @ R ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lenlex_irreflexive
% 0.31/0.46 thf(fact_197_Nil__lenlex__iff2,axiom,
% 0.31/0.46 ! [A: $tType,Ns: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.31/0.46 ~ ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Ns @ ( nil @ A ) ) @ ( lenlex @ A @ R ) ) ).
% 0.31/0.46
% 0.31/0.46 % Nil_lenlex_iff2
% 0.31/0.46 thf(fact_198_lenlex__append1,axiom,
% 0.31/0.46 ! [A: $tType,Us: list @ A,Xs2: list @ A,R2: set @ ( product_prod @ A @ A ),Vs: list @ A,Ys2: list @ A] :
% 0.31/0.46 ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Us @ Xs2 ) @ ( lenlex @ A @ R2 ) )
% 0.31/0.46 => ( ( ( size_size @ ( list @ A ) @ Vs )
% 0.31/0.46 = ( size_size @ ( list @ A ) @ Ys2 ) )
% 0.31/0.46 => ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ Us @ Vs ) @ ( append @ A @ Xs2 @ Ys2 ) ) @ ( lenlex @ A @ R2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % lenlex_append1
% 0.31/0.46 thf(fact_199_asym__lenlex,axiom,
% 0.31/0.46 ! [A: $tType,R2: set @ ( product_prod @ A @ A )] :
% 0.31/0.46 ( ( asym @ A @ R2 )
% 0.31/0.46 => ( asym @ ( list @ A ) @ ( lenlex @ A @ R2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % asym_lenlex
% 0.31/0.46 thf(fact_200_co__path_Opelims,axiom,
% 0.31/0.46 ! [A: $tType,X3: product_prod @ A @ A,Xa2: A,Xb: list @ ( product_prod @ A @ A ),Y3: list @ ( product_prod @ A @ A )] :
% 0.31/0.46 ( ( ( pair_co_path @ A @ X3 @ Xa2 @ Xb )
% 0.31/0.46 = Y3 )
% 0.31/0.46 => ( ( accp @ ( product_prod @ ( product_prod @ A @ A ) @ ( product_prod @ A @ ( list @ ( product_prod @ A @ A ) ) ) ) @ ( pair_co_path_rel @ A ) @ ( product_Pair @ ( product_prod @ A @ A ) @ ( product_prod @ A @ ( list @ ( product_prod @ A @ A ) ) ) @ X3 @ ( product_Pair @ A @ ( list @ ( product_prod @ A @ A ) ) @ Xa2 @ Xb ) ) )
% 0.31/0.46 => ( ( ( Xb
% 0.31/0.46 = ( nil @ ( product_prod @ A @ A ) ) )
% 0.31/0.46 => ( ( Y3
% 0.31/0.46 = ( nil @ ( product_prod @ A @ A ) ) )
% 0.31/0.46 => ~ ( accp @ ( product_prod @ ( product_prod @ A @ A ) @ ( product_prod @ A @ ( list @ ( product_prod @ A @ A ) ) ) ) @ ( pair_co_path_rel @ A ) @ ( product_Pair @ ( product_prod @ A @ A ) @ ( product_prod @ A @ ( list @ ( product_prod @ A @ A ) ) ) @ X3 @ ( product_Pair @ A @ ( list @ ( product_prod @ A @ A ) ) @ Xa2 @ ( nil @ ( product_prod @ A @ A ) ) ) ) ) ) )
% 0.31/0.46 => ( ! [E2: product_prod @ A @ A] :
% 0.31/0.46 ( ( Xb
% 0.31/0.46 = ( cons @ ( product_prod @ A @ A ) @ E2 @ ( nil @ ( product_prod @ A @ A ) ) ) )
% 0.31/0.46 => ( ( Y3
% 0.31/0.46 = ( cons @ ( product_prod @ A @ A ) @ E2 @ ( nil @ ( product_prod @ A @ A ) ) ) )
% 0.31/0.46 => ~ ( accp @ ( product_prod @ ( product_prod @ A @ A ) @ ( product_prod @ A @ ( list @ ( product_prod @ A @ A ) ) ) ) @ ( pair_co_path_rel @ A ) @ ( product_Pair @ ( product_prod @ A @ A ) @ ( product_prod @ A @ ( list @ ( product_prod @ A @ A ) ) ) @ X3 @ ( product_Pair @ A @ ( list @ ( product_prod @ A @ A ) ) @ Xa2 @ ( cons @ ( product_prod @ A @ A ) @ E2 @ ( nil @ ( product_prod @ A @ A ) ) ) ) ) ) ) )
% 0.31/0.46 => ~ ! [U2: A,V: A] :
% 0.31/0.46 ( ( X3
% 0.31/0.46 = ( product_Pair @ A @ A @ U2 @ V ) )
% 0.31/0.46 => ! [E1: product_prod @ A @ A,E22: product_prod @ A @ A,Es: list @ ( product_prod @ A @ A )] :
% 0.31/0.46 ( ( Xb
% 0.31/0.46 = ( cons @ ( product_prod @ A @ A ) @ E1 @ ( cons @ ( product_prod @ A @ A ) @ E22 @ Es ) ) )
% 0.31/0.46 => ( ( ( ( ( E1
% 0.31/0.46 = ( product_Pair @ A @ A @ U2 @ Xa2 ) )
% 0.31/0.46 & ( E22
% 0.31/0.46 = ( product_Pair @ A @ A @ Xa2 @ V ) ) )
% 0.31/0.46 => ( Y3
% 0.31/0.46 = ( cons @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ U2 @ V ) @ ( pair_co_path @ A @ ( product_Pair @ A @ A @ U2 @ V ) @ Xa2 @ Es ) ) ) )
% 0.31/0.46 & ( ~ ( ( E1
% 0.31/0.46 = ( product_Pair @ A @ A @ U2 @ Xa2 ) )
% 0.31/0.46 & ( E22
% 0.31/0.46 = ( product_Pair @ A @ A @ Xa2 @ V ) ) )
% 0.31/0.46 => ( ( ( ( E1
% 0.31/0.46 = ( product_Pair @ A @ A @ V @ Xa2 ) )
% 0.31/0.46 & ( E22
% 0.31/0.46 = ( product_Pair @ A @ A @ Xa2 @ U2 ) ) )
% 0.31/0.46 => ( Y3
% 0.31/0.46 = ( cons @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ V @ U2 ) @ ( pair_co_path @ A @ ( product_Pair @ A @ A @ U2 @ V ) @ Xa2 @ Es ) ) ) )
% 0.31/0.46 & ( ~ ( ( E1
% 0.31/0.46 = ( product_Pair @ A @ A @ V @ Xa2 ) )
% 0.31/0.46 & ( E22
% 0.31/0.46 = ( product_Pair @ A @ A @ Xa2 @ U2 ) ) )
% 0.31/0.46 => ( Y3
% 0.31/0.46 = ( cons @ ( product_prod @ A @ A ) @ E1 @ ( pair_co_path @ A @ ( product_Pair @ A @ A @ U2 @ V ) @ Xa2 @ ( cons @ ( product_prod @ A @ A ) @ E22 @ Es ) ) ) ) ) ) ) )
% 0.31/0.46 => ~ ( accp @ ( product_prod @ ( product_prod @ A @ A ) @ ( product_prod @ A @ ( list @ ( product_prod @ A @ A ) ) ) ) @ ( pair_co_path_rel @ A ) @ ( product_Pair @ ( product_prod @ A @ A ) @ ( product_prod @ A @ ( list @ ( product_prod @ A @ A ) ) ) @ ( product_Pair @ A @ A @ U2 @ V ) @ ( product_Pair @ A @ ( list @ ( product_prod @ A @ A ) ) @ Xa2 @ ( cons @ ( product_prod @ A @ A ) @ E1 @ ( cons @ ( product_prod @ A @ A ) @ E22 @ Es ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % co_path.pelims
% 0.31/0.46 thf(fact_201_pawalk__verts_Osimps_I1_J,axiom,
% 0.31/0.46 ! [A: $tType,U: A] :
% 0.31/0.46 ( ( pair_pawalk_verts @ A @ U @ ( nil @ ( product_prod @ A @ A ) ) )
% 0.31/0.46 = ( cons @ A @ U @ ( nil @ A ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % pawalk_verts.simps(1)
% 0.31/0.46 thf(fact_202_co__path__nonempty,axiom,
% 0.31/0.46 ! [A: $tType,E3: product_prod @ A @ A,W2: A,P3: list @ ( product_prod @ A @ A )] :
% 0.31/0.46 ( ( ( pair_co_path @ A @ E3 @ W2 @ P3 )
% 0.31/0.46 = ( nil @ ( product_prod @ A @ A ) ) )
% 0.31/0.46 = ( P3
% 0.31/0.46 = ( nil @ ( product_prod @ A @ A ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % co_path_nonempty
% 0.31/0.46 thf(fact_203_co__path_Osimps_I1_J,axiom,
% 0.31/0.46 ! [A: $tType,Uu2: product_prod @ A @ A,Uv2: A] :
% 0.31/0.46 ( ( pair_co_path @ A @ Uu2 @ Uv2 @ ( nil @ ( product_prod @ A @ A ) ) )
% 0.31/0.46 = ( nil @ ( product_prod @ A @ A ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % co_path.simps(1)
% 0.31/0.46 thf(fact_204_co__path_Osimps_I3_J,axiom,
% 0.31/0.46 ! [A: $tType,E12: product_prod @ A @ A,U: A,W2: A,E23: product_prod @ A @ A,V2: A,Es2: list @ ( product_prod @ A @ A )] :
% 0.31/0.46 ( ( ( ( E12
% 0.31/0.46 = ( product_Pair @ A @ A @ U @ W2 ) )
% 0.31/0.46 & ( E23
% 0.31/0.46 = ( product_Pair @ A @ A @ W2 @ V2 ) ) )
% 0.31/0.46 => ( ( pair_co_path @ A @ ( product_Pair @ A @ A @ U @ V2 ) @ W2 @ ( cons @ ( product_prod @ A @ A ) @ E12 @ ( cons @ ( product_prod @ A @ A ) @ E23 @ Es2 ) ) )
% 0.31/0.46 = ( cons @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ U @ V2 ) @ ( pair_co_path @ A @ ( product_Pair @ A @ A @ U @ V2 ) @ W2 @ Es2 ) ) ) )
% 0.31/0.46 & ( ~ ( ( E12
% 0.31/0.46 = ( product_Pair @ A @ A @ U @ W2 ) )
% 0.31/0.46 & ( E23
% 0.31/0.46 = ( product_Pair @ A @ A @ W2 @ V2 ) ) )
% 0.31/0.46 => ( ( ( ( E12
% 0.31/0.46 = ( product_Pair @ A @ A @ V2 @ W2 ) )
% 0.31/0.46 & ( E23
% 0.31/0.46 = ( product_Pair @ A @ A @ W2 @ U ) ) )
% 0.31/0.46 => ( ( pair_co_path @ A @ ( product_Pair @ A @ A @ U @ V2 ) @ W2 @ ( cons @ ( product_prod @ A @ A ) @ E12 @ ( cons @ ( product_prod @ A @ A ) @ E23 @ Es2 ) ) )
% 0.31/0.46 = ( cons @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ V2 @ U ) @ ( pair_co_path @ A @ ( product_Pair @ A @ A @ U @ V2 ) @ W2 @ Es2 ) ) ) )
% 0.31/0.46 & ( ~ ( ( E12
% 0.31/0.46 = ( product_Pair @ A @ A @ V2 @ W2 ) )
% 0.31/0.46 & ( E23
% 0.31/0.46 = ( product_Pair @ A @ A @ W2 @ U ) ) )
% 0.31/0.46 => ( ( pair_co_path @ A @ ( product_Pair @ A @ A @ U @ V2 ) @ W2 @ ( cons @ ( product_prod @ A @ A ) @ E12 @ ( cons @ ( product_prod @ A @ A ) @ E23 @ Es2 ) ) )
% 0.31/0.46 = ( cons @ ( product_prod @ A @ A ) @ E12 @ ( pair_co_path @ A @ ( product_Pair @ A @ A @ U @ V2 ) @ W2 @ ( cons @ ( product_prod @ A @ A ) @ E23 @ Es2 ) ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % co_path.simps(3)
% 0.31/0.46 thf(fact_205_co__path_Osimps_I2_J,axiom,
% 0.31/0.46 ! [A: $tType,Uw2: product_prod @ A @ A,Ux2: A,E3: product_prod @ A @ A] :
% 0.31/0.46 ( ( pair_co_path @ A @ Uw2 @ Ux2 @ ( cons @ ( product_prod @ A @ A ) @ E3 @ ( nil @ ( product_prod @ A @ A ) ) ) )
% 0.31/0.46 = ( cons @ ( product_prod @ A @ A ) @ E3 @ ( nil @ ( product_prod @ A @ A ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % co_path.simps(2)
% 0.31/0.46 thf(fact_206_co__path_Oelims,axiom,
% 0.31/0.46 ! [A: $tType,X3: product_prod @ A @ A,Xa2: A,Xb: list @ ( product_prod @ A @ A ),Y3: list @ ( product_prod @ A @ A )] :
% 0.31/0.46 ( ( ( pair_co_path @ A @ X3 @ Xa2 @ Xb )
% 0.31/0.46 = Y3 )
% 0.31/0.46 => ( ( ( Xb
% 0.31/0.46 = ( nil @ ( product_prod @ A @ A ) ) )
% 0.31/0.46 => ( Y3
% 0.31/0.46 != ( nil @ ( product_prod @ A @ A ) ) ) )
% 0.31/0.46 => ( ! [E2: product_prod @ A @ A] :
% 0.31/0.46 ( ( Xb
% 0.31/0.46 = ( cons @ ( product_prod @ A @ A ) @ E2 @ ( nil @ ( product_prod @ A @ A ) ) ) )
% 0.31/0.46 => ( Y3
% 0.31/0.46 != ( cons @ ( product_prod @ A @ A ) @ E2 @ ( nil @ ( product_prod @ A @ A ) ) ) ) )
% 0.31/0.46 => ~ ! [U2: A,V: A] :
% 0.31/0.46 ( ( X3
% 0.31/0.46 = ( product_Pair @ A @ A @ U2 @ V ) )
% 0.31/0.46 => ! [E1: product_prod @ A @ A,E22: product_prod @ A @ A,Es: list @ ( product_prod @ A @ A )] :
% 0.31/0.46 ( ( Xb
% 0.31/0.46 = ( cons @ ( product_prod @ A @ A ) @ E1 @ ( cons @ ( product_prod @ A @ A ) @ E22 @ Es ) ) )
% 0.31/0.46 => ~ ( ( ( ( E1
% 0.31/0.46 = ( product_Pair @ A @ A @ U2 @ Xa2 ) )
% 0.31/0.46 & ( E22
% 0.31/0.46 = ( product_Pair @ A @ A @ Xa2 @ V ) ) )
% 0.31/0.46 => ( Y3
% 0.31/0.46 = ( cons @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ U2 @ V ) @ ( pair_co_path @ A @ ( product_Pair @ A @ A @ U2 @ V ) @ Xa2 @ Es ) ) ) )
% 0.31/0.46 & ( ~ ( ( E1
% 0.31/0.46 = ( product_Pair @ A @ A @ U2 @ Xa2 ) )
% 0.31/0.46 & ( E22
% 0.31/0.46 = ( product_Pair @ A @ A @ Xa2 @ V ) ) )
% 0.31/0.46 => ( ( ( ( E1
% 0.31/0.46 = ( product_Pair @ A @ A @ V @ Xa2 ) )
% 0.31/0.46 & ( E22
% 0.31/0.46 = ( product_Pair @ A @ A @ Xa2 @ U2 ) ) )
% 0.31/0.46 => ( Y3
% 0.31/0.46 = ( cons @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ V @ U2 ) @ ( pair_co_path @ A @ ( product_Pair @ A @ A @ U2 @ V ) @ Xa2 @ Es ) ) ) )
% 0.31/0.46 & ( ~ ( ( E1
% 0.31/0.46 = ( product_Pair @ A @ A @ V @ Xa2 ) )
% 0.31/0.46 & ( E22
% 0.31/0.46 = ( product_Pair @ A @ A @ Xa2 @ U2 ) ) )
% 0.31/0.46 => ( Y3
% 0.31/0.46 = ( cons @ ( product_prod @ A @ A ) @ E1 @ ( pair_co_path @ A @ ( product_Pair @ A @ A @ U2 @ V ) @ Xa2 @ ( cons @ ( product_prod @ A @ A ) @ E22 @ Es ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % co_path.elims
% 0.31/0.46 thf(fact_207_co__sd__id,axiom,
% 0.31/0.46 ! [A: $tType,U: A,W2: A,P3: list @ ( product_prod @ A @ A ),V2: A] :
% 0.31/0.46 ( ~ ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ U @ W2 ) @ ( set2 @ ( product_prod @ A @ A ) @ P3 ) )
% 0.31/0.46 => ( ~ ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ V2 @ W2 ) @ ( set2 @ ( product_prod @ A @ A ) @ P3 ) )
% 0.31/0.46 => ( ( pair_co_path @ A @ ( product_Pair @ A @ A @ U @ V2 ) @ W2 @ ( pair_sd_path @ A @ ( product_Pair @ A @ A @ U @ V2 ) @ W2 @ P3 ) )
% 0.31/0.46 = P3 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % co_sd_id
% 0.31/0.46 thf(fact_208_subseqs_Osimps_I1_J,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( subseqs @ A @ ( nil @ A ) )
% 0.31/0.46 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % subseqs.simps(1)
% 0.31/0.46 thf(fact_209_Cons__lenlex__iff,axiom,
% 0.31/0.46 ! [A: $tType,M: A,Ms: list @ A,N: A,Ns: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.31/0.46 ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ M @ Ms ) @ ( cons @ A @ N @ Ns ) ) @ ( lenlex @ A @ R ) )
% 0.31/0.46 = ( ( ord_less @ nat @ ( size_size @ ( list @ A ) @ Ms ) @ ( size_size @ ( list @ A ) @ Ns ) )
% 0.31/0.46 | ( ( ( size_size @ ( list @ A ) @ Ms )
% 0.31/0.46 = ( size_size @ ( list @ A ) @ Ns ) )
% 0.31/0.46 & ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ M @ N ) @ R ) )
% 0.31/0.46 | ( ( M = N )
% 0.31/0.46 & ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Ms @ Ns ) @ ( lenlex @ A @ R ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Cons_lenlex_iff
% 0.31/0.46 thf(fact_210_length__induct,axiom,
% 0.31/0.46 ! [A: $tType,P2: ( list @ A ) > $o,Xs2: list @ A] :
% 0.31/0.46 ( ! [Xs4: list @ A] :
% 0.31/0.46 ( ! [Ys7: list @ A] :
% 0.31/0.46 ( ( ord_less @ nat @ ( size_size @ ( list @ A ) @ Ys7 ) @ ( size_size @ ( list @ A ) @ Xs4 ) )
% 0.31/0.46 => ( P2 @ Ys7 ) )
% 0.31/0.46 => ( P2 @ Xs4 ) )
% 0.31/0.46 => ( P2 @ Xs2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % length_induct
% 0.31/0.46 thf(fact_211_subseqs__refl,axiom,
% 0.31/0.46 ! [A: $tType,Xs2: list @ A] : ( member2 @ ( list @ A ) @ Xs2 @ ( set2 @ ( list @ A ) @ ( subseqs @ A @ Xs2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % subseqs_refl
% 0.31/0.46 thf(fact_212_Cons__in__subseqsD,axiom,
% 0.31/0.46 ! [A: $tType,Y3: A,Ys2: list @ A,Xs2: list @ A] :
% 0.31/0.46 ( ( member2 @ ( list @ A ) @ ( cons @ A @ Y3 @ Ys2 ) @ ( set2 @ ( list @ A ) @ ( subseqs @ A @ Xs2 ) ) )
% 0.31/0.46 => ( member2 @ ( list @ A ) @ Ys2 @ ( set2 @ ( list @ A ) @ ( subseqs @ A @ Xs2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Cons_in_subseqsD
% 0.31/0.46 thf(fact_213_in__measures_I2_J,axiom,
% 0.31/0.46 ! [A: $tType,X3: A,Y3: A,F3: A > nat,Fs: list @ ( A > nat )] :
% 0.31/0.46 ( ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X3 @ Y3 ) @ ( measures @ A @ ( cons @ ( A > nat ) @ F3 @ Fs ) ) )
% 0.31/0.46 = ( ( ord_less @ nat @ ( F3 @ X3 ) @ ( F3 @ Y3 ) )
% 0.31/0.46 | ( ( ( F3 @ X3 )
% 0.31/0.46 = ( F3 @ Y3 ) )
% 0.31/0.46 & ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X3 @ Y3 ) @ ( measures @ A @ Fs ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % in_measures(2)
% 0.31/0.46 thf(fact_214_inverse__permutation__of__list_Oelims,axiom,
% 0.31/0.46 ! [A: $tType,X3: list @ ( product_prod @ A @ A ),Xa2: A,Y3: A] :
% 0.31/0.46 ( ( ( invers965609412f_list @ A @ X3 @ Xa2 )
% 0.31/0.46 = Y3 )
% 0.31/0.46 => ( ( ( X3
% 0.31/0.46 = ( nil @ ( product_prod @ A @ A ) ) )
% 0.31/0.46 => ( Y3 != Xa2 ) )
% 0.31/0.46 => ~ ! [Y4: A,X6: A,Xs4: list @ ( product_prod @ A @ A )] :
% 0.31/0.46 ( ( X3
% 0.31/0.46 = ( cons @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y4 @ X6 ) @ Xs4 ) )
% 0.31/0.46 => ~ ( ( ( Xa2 = X6 )
% 0.31/0.46 => ( Y3 = Y4 ) )
% 0.31/0.46 & ( ( Xa2 != X6 )
% 0.31/0.46 => ( Y3
% 0.31/0.46 = ( invers965609412f_list @ A @ Xs4 @ Xa2 ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % inverse_permutation_of_list.elims
% 0.31/0.46 thf(fact_215_in__measures_I1_J,axiom,
% 0.31/0.46 ! [A: $tType,X3: A,Y3: A] :
% 0.31/0.46 ~ ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X3 @ Y3 ) @ ( measures @ A @ ( nil @ ( A > nat ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % in_measures(1)
% 0.31/0.46 thf(fact_216_eval__inverse__permutation__of__list_I3_J,axiom,
% 0.31/0.46 ! [A: $tType,X3: A,X7: A,Y5: A,Xs2: list @ ( product_prod @ A @ A )] :
% 0.31/0.46 ( ( X3 != X7 )
% 0.31/0.46 => ( ( invers965609412f_list @ A @ ( cons @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y5 @ X7 ) @ Xs2 ) @ X3 )
% 0.31/0.46 = ( invers965609412f_list @ A @ Xs2 @ X3 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % eval_inverse_permutation_of_list(3)
% 0.31/0.46 thf(fact_217_eval__inverse__permutation__of__list_I2_J,axiom,
% 0.31/0.46 ! [A: $tType,X3: A,X7: A,Y3: A,Xs2: list @ ( product_prod @ A @ A )] :
% 0.31/0.46 ( ( X3 = X7 )
% 0.31/0.46 => ( ( invers965609412f_list @ A @ ( cons @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y3 @ X7 ) @ Xs2 ) @ X3 )
% 0.31/0.46 = Y3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % eval_inverse_permutation_of_list(2)
% 0.31/0.46 thf(fact_218_inverse__permutation__of__list_Osimps_I1_J,axiom,
% 0.31/0.46 ! [A: $tType,X3: A] :
% 0.31/0.46 ( ( invers965609412f_list @ A @ ( nil @ ( product_prod @ A @ A ) ) @ X3 )
% 0.31/0.46 = X3 ) ).
% 0.31/0.46
% 0.31/0.46 % inverse_permutation_of_list.simps(1)
% 0.31/0.46 thf(fact_219_inverse__permutation__of__list_Osimps_I2_J,axiom,
% 0.31/0.46 ! [A: $tType,X3: A,X7: A,Y3: A,Xs2: list @ ( product_prod @ A @ A )] :
% 0.31/0.46 ( ( ( X3 = X7 )
% 0.31/0.46 => ( ( invers965609412f_list @ A @ ( cons @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y3 @ X7 ) @ Xs2 ) @ X3 )
% 0.31/0.46 = Y3 ) )
% 0.31/0.46 & ( ( X3 != X7 )
% 0.31/0.46 => ( ( invers965609412f_list @ A @ ( cons @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y3 @ X7 ) @ Xs2 ) @ X3 )
% 0.31/0.46 = ( invers965609412f_list @ A @ Xs2 @ X3 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % inverse_permutation_of_list.simps(2)
% 0.31/0.46 thf(fact_220_measures__less,axiom,
% 0.31/0.46 ! [A: $tType,F3: A > nat,X3: A,Y3: A,Fs: list @ ( A > nat )] :
% 0.31/0.46 ( ( ord_less @ nat @ ( F3 @ X3 ) @ ( F3 @ Y3 ) )
% 0.31/0.46 => ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X3 @ Y3 ) @ ( measures @ A @ ( cons @ ( A > nat ) @ F3 @ Fs ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % measures_less
% 0.31/0.46 thf(fact_221_inverse__permutation__of__list__unique,axiom,
% 0.31/0.46 ! [A: $tType,Xs2: list @ ( product_prod @ A @ A ),A5: set @ A,X3: A,Y3: A] :
% 0.31/0.46 ( ( list_permutes @ A @ Xs2 @ A5 )
% 0.31/0.46 => ( ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X3 @ Y3 ) @ ( set2 @ ( product_prod @ A @ A ) @ Xs2 ) )
% 0.31/0.46 => ( ( invers965609412f_list @ A @ Xs2 @ Y3 )
% 0.31/0.46 = X3 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % inverse_permutation_of_list_unique
% 0.31/0.46 thf(fact_222_eval__permutation__of__list_I3_J,axiom,
% 0.31/0.46 ! [A: $tType,X3: A,X7: A,Y5: A,Xs2: list @ ( product_prod @ A @ A )] :
% 0.31/0.46 ( ( X3 != X7 )
% 0.31/0.46 => ( ( permutation_of_list @ A @ ( cons @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X7 @ Y5 ) @ Xs2 ) @ X3 )
% 0.31/0.46 = ( permutation_of_list @ A @ Xs2 @ X3 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % eval_permutation_of_list(3)
% 0.31/0.46 thf(fact_223_eval__permutation__of__list_I1_J,axiom,
% 0.31/0.46 ! [A: $tType,X3: A] :
% 0.31/0.46 ( ( permutation_of_list @ A @ ( nil @ ( product_prod @ A @ A ) ) @ X3 )
% 0.31/0.46 = X3 ) ).
% 0.31/0.46
% 0.31/0.46 % eval_permutation_of_list(1)
% 0.31/0.46 thf(fact_224_eval__permutation__of__list_I2_J,axiom,
% 0.31/0.46 ! [A: $tType,X3: A,X7: A,Y3: A,Xs2: list @ ( product_prod @ A @ A )] :
% 0.31/0.46 ( ( X3 = X7 )
% 0.31/0.46 => ( ( permutation_of_list @ A @ ( cons @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X7 @ Y3 ) @ Xs2 ) @ X3 )
% 0.31/0.46 = Y3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % eval_permutation_of_list(2)
% 0.31/0.46 thf(fact_225_permutation__of__list__unique,axiom,
% 0.31/0.46 ! [A: $tType,Xs2: list @ ( product_prod @ A @ A ),A5: set @ A,X3: A,Y3: A] :
% 0.31/0.46 ( ( list_permutes @ A @ Xs2 @ A5 )
% 0.31/0.46 => ( ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X3 @ Y3 ) @ ( set2 @ ( product_prod @ A @ A ) @ Xs2 ) )
% 0.31/0.46 => ( ( permutation_of_list @ A @ Xs2 @ X3 )
% 0.31/0.46 = Y3 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % permutation_of_list_unique
% 0.31/0.46 thf(fact_226_permutation__of__list__Cons,axiom,
% 0.31/0.46 ! [A: $tType,X3: A,X7: A,Y3: A,Xs2: list @ ( product_prod @ A @ A )] :
% 0.31/0.46 ( ( ( X3 = X7 )
% 0.31/0.46 => ( ( permutation_of_list @ A @ ( cons @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X3 @ Y3 ) @ Xs2 ) @ X7 )
% 0.31/0.46 = Y3 ) )
% 0.31/0.46 & ( ( X3 != X7 )
% 0.31/0.46 => ( ( permutation_of_list @ A @ ( cons @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X3 @ Y3 ) @ Xs2 ) @ X7 )
% 0.31/0.46 = ( permutation_of_list @ A @ Xs2 @ X7 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % permutation_of_list_Cons
% 0.31/0.46 thf(fact_227_part__code_I1_J,axiom,
% 0.31/0.46 ! [A: $tType,B: $tType] :
% 0.31/0.46 ( ( linorder @ A )
% 0.31/0.46 => ! [F3: B > A,Pivot: A] :
% 0.31/0.46 ( ( linorder_part @ B @ A @ F3 @ Pivot @ ( nil @ B ) )
% 0.31/0.46 = ( product_Pair @ ( list @ B ) @ ( product_prod @ ( list @ B ) @ ( list @ B ) ) @ ( nil @ B ) @ ( product_Pair @ ( list @ B ) @ ( list @ B ) @ ( nil @ B ) @ ( nil @ B ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % part_code(1)
% 0.31/0.46 thf(fact_228_not__in__set__insert,axiom,
% 0.31/0.46 ! [A: $tType,X3: A,Xs2: list @ A] :
% 0.31/0.46 ( ~ ( member2 @ A @ X3 @ ( set2 @ A @ Xs2 ) )
% 0.31/0.46 => ( ( insert @ A @ X3 @ Xs2 )
% 0.31/0.46 = ( cons @ A @ X3 @ Xs2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % not_in_set_insert
% 0.31/0.46 thf(fact_229_in__set__insert,axiom,
% 0.31/0.46 ! [A: $tType,X3: A,Xs2: list @ A] :
% 0.31/0.46 ( ( member2 @ A @ X3 @ ( set2 @ A @ Xs2 ) )
% 0.31/0.46 => ( ( insert @ A @ X3 @ Xs2 )
% 0.31/0.46 = Xs2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % in_set_insert
% 0.31/0.46 thf(fact_230_insert__Nil,axiom,
% 0.31/0.46 ! [A: $tType,X3: A] :
% 0.31/0.46 ( ( insert @ A @ X3 @ ( nil @ A ) )
% 0.31/0.46 = ( cons @ A @ X3 @ ( nil @ A ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % insert_Nil
% 0.31/0.46 thf(fact_231_List_Oinsert__def,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( insert @ A )
% 0.31/0.46 = ( ^ [X: A,Xs: list @ A] : ( if @ ( list @ A ) @ ( member2 @ A @ X @ ( set2 @ A @ Xs ) ) @ Xs @ ( cons @ A @ X @ Xs ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % List.insert_def
% 0.31/0.46 thf(fact_232_concat__eq__append__conv,axiom,
% 0.31/0.46 ! [A: $tType,Xss2: list @ ( list @ A ),Ys2: list @ A,Zs: list @ A] :
% 0.31/0.46 ( ( ( concat @ A @ Xss2 )
% 0.31/0.46 = ( append @ A @ Ys2 @ Zs ) )
% 0.31/0.46 = ( ( ( Xss2
% 0.31/0.46 = ( nil @ ( list @ A ) ) )
% 0.31/0.46 => ( ( Ys2
% 0.31/0.46 = ( nil @ A ) )
% 0.31/0.46 & ( Zs
% 0.31/0.46 = ( nil @ A ) ) ) )
% 0.31/0.46 & ( ( Xss2
% 0.31/0.46 != ( nil @ ( list @ A ) ) )
% 0.31/0.46 => ? [Xss1: list @ ( list @ A ),Xs: list @ A,Xs6: list @ A,Xss22: list @ ( list @ A )] :
% 0.31/0.46 ( ( Xss2
% 0.31/0.46 = ( append @ ( list @ A ) @ Xss1 @ ( cons @ ( list @ A ) @ ( append @ A @ Xs @ Xs6 ) @ Xss22 ) ) )
% 0.31/0.46 & ( Ys2
% 0.31/0.46 = ( append @ A @ ( concat @ A @ Xss1 ) @ Xs ) )
% 0.31/0.46 & ( Zs
% 0.31/0.46 = ( append @ A @ Xs6 @ ( concat @ A @ Xss22 ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % concat_eq_append_conv
% 0.31/0.46 thf(fact_233_inverse__permutation__of__list_Opelims,axiom,
% 0.31/0.46 ! [A: $tType,X3: list @ ( product_prod @ A @ A ),Xa2: A,Y3: A] :
% 0.31/0.46 ( ( ( invers965609412f_list @ A @ X3 @ Xa2 )
% 0.31/0.46 = Y3 )
% 0.31/0.46 => ( ( accp @ ( product_prod @ ( list @ ( product_prod @ A @ A ) ) @ A ) @ ( invers1507583541st_rel @ A ) @ ( product_Pair @ ( list @ ( product_prod @ A @ A ) ) @ A @ X3 @ Xa2 ) )
% 0.31/0.46 => ( ( ( X3
% 0.31/0.46 = ( nil @ ( product_prod @ A @ A ) ) )
% 0.31/0.46 => ( ( Y3 = Xa2 )
% 0.31/0.46 => ~ ( accp @ ( product_prod @ ( list @ ( product_prod @ A @ A ) ) @ A ) @ ( invers1507583541st_rel @ A ) @ ( product_Pair @ ( list @ ( product_prod @ A @ A ) ) @ A @ ( nil @ ( product_prod @ A @ A ) ) @ Xa2 ) ) ) )
% 0.31/0.46 => ~ ! [Y4: A,X6: A,Xs4: list @ ( product_prod @ A @ A )] :
% 0.31/0.46 ( ( X3
% 0.31/0.46 = ( cons @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y4 @ X6 ) @ Xs4 ) )
% 0.31/0.46 => ( ( ( ( Xa2 = X6 )
% 0.31/0.46 => ( Y3 = Y4 ) )
% 0.31/0.46 & ( ( Xa2 != X6 )
% 0.31/0.46 => ( Y3
% 0.31/0.46 = ( invers965609412f_list @ A @ Xs4 @ Xa2 ) ) ) )
% 0.31/0.46 => ~ ( accp @ ( product_prod @ ( list @ ( product_prod @ A @ A ) ) @ A ) @ ( invers1507583541st_rel @ A ) @ ( product_Pair @ ( list @ ( product_prod @ A @ A ) ) @ A @ ( cons @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y4 @ X6 ) @ Xs4 ) @ Xa2 ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % inverse_permutation_of_list.pelims
% 0.31/0.46 thf(fact_234_Nil__eq__concat__conv,axiom,
% 0.31/0.46 ! [A: $tType,Xss2: list @ ( list @ A )] :
% 0.31/0.46 ( ( ( nil @ A )
% 0.31/0.46 = ( concat @ A @ Xss2 ) )
% 0.31/0.46 = ( ! [X: list @ A] :
% 0.31/0.46 ( ( member2 @ ( list @ A ) @ X @ ( set2 @ ( list @ A ) @ Xss2 ) )
% 0.31/0.46 => ( X
% 0.31/0.46 = ( nil @ A ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Nil_eq_concat_conv
% 0.31/0.46 thf(fact_235_concat__eq__Nil__conv,axiom,
% 0.31/0.46 ! [A: $tType,Xss2: list @ ( list @ A )] :
% 0.31/0.46 ( ( ( concat @ A @ Xss2 )
% 0.31/0.46 = ( nil @ A ) )
% 0.31/0.46 = ( ! [X: list @ A] :
% 0.31/0.46 ( ( member2 @ ( list @ A ) @ X @ ( set2 @ ( list @ A ) @ Xss2 ) )
% 0.31/0.46 => ( X
% 0.31/0.46 = ( nil @ A ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % concat_eq_Nil_conv
% 0.31/0.46 thf(fact_236_concat__append,axiom,
% 0.31/0.46 ! [A: $tType,Xs2: list @ ( list @ A ),Ys2: list @ ( list @ A )] :
% 0.31/0.46 ( ( concat @ A @ ( append @ ( list @ A ) @ Xs2 @ Ys2 ) )
% 0.31/0.46 = ( append @ A @ ( concat @ A @ Xs2 ) @ ( concat @ A @ Ys2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % concat_append
% 0.31/0.46 thf(fact_237_concat_Osimps_I2_J,axiom,
% 0.31/0.46 ! [A: $tType,X3: list @ A,Xs2: list @ ( list @ A )] :
% 0.31/0.46 ( ( concat @ A @ ( cons @ ( list @ A ) @ X3 @ Xs2 ) )
% 0.31/0.46 = ( append @ A @ X3 @ ( concat @ A @ Xs2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % concat.simps(2)
% 0.31/0.46 thf(fact_238_concat_Osimps_I1_J,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( concat @ A @ ( nil @ ( list @ A ) ) )
% 0.31/0.46 = ( nil @ A ) ) ).
% 0.31/0.46
% 0.31/0.46 % concat.simps(1)
% 0.31/0.46 thf(fact_239_concat__eq__appendD,axiom,
% 0.31/0.46 ! [A: $tType,Xss2: list @ ( list @ A ),Ys2: list @ A,Zs: list @ A] :
% 0.31/0.46 ( ( ( concat @ A @ Xss2 )
% 0.31/0.46 = ( append @ A @ Ys2 @ Zs ) )
% 0.31/0.46 => ( ( Xss2
% 0.31/0.46 != ( nil @ ( list @ A ) ) )
% 0.31/0.46 => ? [Xss12: list @ ( list @ A ),Xs4: list @ A,Xs3: list @ A,Xss23: list @ ( list @ A )] :
% 0.31/0.46 ( ( Xss2
% 0.31/0.46 = ( append @ ( list @ A ) @ Xss12 @ ( cons @ ( list @ A ) @ ( append @ A @ Xs4 @ Xs3 ) @ Xss23 ) ) )
% 0.31/0.46 & ( Ys2
% 0.31/0.46 = ( append @ A @ ( concat @ A @ Xss12 ) @ Xs4 ) )
% 0.31/0.46 & ( Zs
% 0.31/0.46 = ( append @ A @ Xs3 @ ( concat @ A @ Xss23 ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % concat_eq_appendD
% 0.31/0.46 thf(fact_240_length__n__lists__elem,axiom,
% 0.31/0.46 ! [A: $tType,Ys2: list @ A,N: nat,Xs2: list @ A] :
% 0.31/0.46 ( ( member2 @ ( list @ A ) @ Ys2 @ ( set2 @ ( list @ A ) @ ( n_lists @ A @ N @ Xs2 ) ) )
% 0.31/0.46 => ( ( size_size @ ( list @ A ) @ Ys2 )
% 0.31/0.46 = N ) ) ).
% 0.31/0.46
% 0.31/0.46 % length_n_lists_elem
% 0.31/0.46 thf(fact_241_listrel_Oinducts,axiom,
% 0.31/0.46 ! [A: $tType,B: $tType,X1: list @ A,X2: list @ B,R: set @ ( product_prod @ A @ B ),P2: ( list @ A ) > ( list @ B ) > $o] :
% 0.31/0.46 ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ X1 @ X2 ) @ ( listrel @ A @ B @ R ) )
% 0.31/0.46 => ( ( P2 @ ( nil @ A ) @ ( nil @ B ) )
% 0.31/0.46 => ( ! [X4: A,Y4: B,Xs4: list @ A,Ys4: list @ B] :
% 0.31/0.46 ( ( member2 @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X4 @ Y4 ) @ R )
% 0.31/0.46 => ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ Xs4 @ Ys4 ) @ ( listrel @ A @ B @ R ) )
% 0.31/0.46 => ( ( P2 @ Xs4 @ Ys4 )
% 0.31/0.46 => ( P2 @ ( cons @ A @ X4 @ Xs4 ) @ ( cons @ B @ Y4 @ Ys4 ) ) ) ) )
% 0.31/0.46 => ( P2 @ X1 @ X2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % listrel.inducts
% 0.31/0.46 thf(fact_242_listrel__eq__len,axiom,
% 0.31/0.46 ! [A: $tType,B: $tType,Xs2: list @ A,Ys2: list @ B,R: set @ ( product_prod @ A @ B )] :
% 0.31/0.46 ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ Xs2 @ Ys2 ) @ ( listrel @ A @ B @ R ) )
% 0.31/0.46 => ( ( size_size @ ( list @ A ) @ Xs2 )
% 0.31/0.46 = ( size_size @ ( list @ B ) @ Ys2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % listrel_eq_len
% 0.31/0.46 thf(fact_243_listrel_ONil,axiom,
% 0.31/0.46 ! [B: $tType,A: $tType,R: set @ ( product_prod @ A @ B )] : ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ ( nil @ A ) @ ( nil @ B ) ) @ ( listrel @ A @ B @ R ) ) ).
% 0.31/0.46
% 0.31/0.46 % listrel.Nil
% 0.31/0.46 thf(fact_244_listrel__Nil1,axiom,
% 0.31/0.46 ! [A: $tType,B: $tType,Xs2: list @ B,R: set @ ( product_prod @ A @ B )] :
% 0.31/0.46 ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ ( nil @ A ) @ Xs2 ) @ ( listrel @ A @ B @ R ) )
% 0.31/0.46 => ( Xs2
% 0.31/0.46 = ( nil @ B ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % listrel_Nil1
% 0.31/0.46 thf(fact_245_listrel__Nil2,axiom,
% 0.31/0.46 ! [B: $tType,A: $tType,Xs2: list @ A,R: set @ ( product_prod @ A @ B )] :
% 0.31/0.46 ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ Xs2 @ ( nil @ B ) ) @ ( listrel @ A @ B @ R ) )
% 0.31/0.46 => ( Xs2
% 0.31/0.46 = ( nil @ A ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % listrel_Nil2
% 0.31/0.46 thf(fact_246_listrel_OCons,axiom,
% 0.31/0.46 ! [B: $tType,A: $tType,X3: A,Y3: B,R: set @ ( product_prod @ A @ B ),Xs2: list @ A,Ys2: list @ B] :
% 0.31/0.46 ( ( member2 @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X3 @ Y3 ) @ R )
% 0.31/0.46 => ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ Xs2 @ Ys2 ) @ ( listrel @ A @ B @ R ) )
% 0.31/0.46 => ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ B @ Y3 @ Ys2 ) ) @ ( listrel @ A @ B @ R ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % listrel.Cons
% 0.31/0.46 thf(fact_247_listrel__Cons1,axiom,
% 0.31/0.46 ! [B: $tType,A: $tType,Y3: A,Ys2: list @ A,Xs2: list @ B,R: set @ ( product_prod @ A @ B )] :
% 0.31/0.46 ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ ( cons @ A @ Y3 @ Ys2 ) @ Xs2 ) @ ( listrel @ A @ B @ R ) )
% 0.31/0.46 => ~ ! [Y4: B,Ys4: list @ B] :
% 0.31/0.46 ( ( Xs2
% 0.31/0.46 = ( cons @ B @ Y4 @ Ys4 ) )
% 0.31/0.46 => ( ( member2 @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ Y3 @ Y4 ) @ R )
% 0.31/0.46 => ~ ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ Ys2 @ Ys4 ) @ ( listrel @ A @ B @ R ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % listrel_Cons1
% 0.31/0.46 thf(fact_248_listrel__Cons2,axiom,
% 0.31/0.46 ! [B: $tType,A: $tType,Xs2: list @ A,Y3: B,Ys2: list @ B,R: set @ ( product_prod @ A @ B )] :
% 0.31/0.46 ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ Xs2 @ ( cons @ B @ Y3 @ Ys2 ) ) @ ( listrel @ A @ B @ R ) )
% 0.31/0.46 => ~ ! [X4: A,Xs4: list @ A] :
% 0.31/0.46 ( ( Xs2
% 0.31/0.46 = ( cons @ A @ X4 @ Xs4 ) )
% 0.31/0.46 => ( ( member2 @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X4 @ Y3 ) @ R )
% 0.31/0.46 => ~ ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ Xs4 @ Ys2 ) @ ( listrel @ A @ B @ R ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % listrel_Cons2
% 0.31/0.46 thf(fact_249_listrel_Ocases,axiom,
% 0.31/0.46 ! [B: $tType,A: $tType,A1: list @ A,A22: list @ B,R: set @ ( product_prod @ A @ B )] :
% 0.31/0.46 ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ A1 @ A22 ) @ ( listrel @ A @ B @ R ) )
% 0.31/0.46 => ( ( ( A1
% 0.31/0.46 = ( nil @ A ) )
% 0.31/0.46 => ( A22
% 0.31/0.46 != ( nil @ B ) ) )
% 0.31/0.46 => ~ ! [X4: A,Y4: B,Xs4: list @ A] :
% 0.31/0.46 ( ( A1
% 0.31/0.46 = ( cons @ A @ X4 @ Xs4 ) )
% 0.31/0.46 => ! [Ys4: list @ B] :
% 0.31/0.46 ( ( A22
% 0.31/0.46 = ( cons @ B @ Y4 @ Ys4 ) )
% 0.31/0.46 => ( ( member2 @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X4 @ Y4 ) @ R )
% 0.31/0.46 => ~ ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ Xs4 @ Ys4 ) @ ( listrel @ A @ B @ R ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % listrel.cases
% 0.31/0.46 thf(fact_250_listrel_Osimps,axiom,
% 0.31/0.46 ! [B: $tType,A: $tType,A1: list @ A,A22: list @ B,R: set @ ( product_prod @ A @ B )] :
% 0.31/0.46 ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ A1 @ A22 ) @ ( listrel @ A @ B @ R ) )
% 0.31/0.46 = ( ( ( A1
% 0.31/0.46 = ( nil @ A ) )
% 0.31/0.46 & ( A22
% 0.31/0.46 = ( nil @ B ) ) )
% 0.31/0.46 | ? [X: A,Y: B,Xs: list @ A,Ys: list @ B] :
% 0.31/0.46 ( ( A1
% 0.31/0.46 = ( cons @ A @ X @ Xs ) )
% 0.31/0.46 & ( A22
% 0.31/0.46 = ( cons @ B @ Y @ Ys ) )
% 0.31/0.46 & ( member2 @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X @ Y ) @ R )
% 0.31/0.46 & ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ Xs @ Ys ) @ ( listrel @ A @ B @ R ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % listrel.simps
% 0.31/0.46 thf(fact_251_n__lists__Nil,axiom,
% 0.31/0.46 ! [A: $tType,N: nat] :
% 0.31/0.46 ( ( ( N
% 0.31/0.46 = ( zero_zero @ nat ) )
% 0.31/0.46 => ( ( n_lists @ A @ N @ ( nil @ A ) )
% 0.31/0.46 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) )
% 0.31/0.46 & ( ( N
% 0.31/0.46 != ( zero_zero @ nat ) )
% 0.31/0.46 => ( ( n_lists @ A @ N @ ( nil @ A ) )
% 0.31/0.46 = ( nil @ ( list @ A ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % n_lists_Nil
% 0.31/0.46 thf(fact_252_n__lists_Osimps_I1_J,axiom,
% 0.31/0.46 ! [A: $tType,Xs2: list @ A] :
% 0.31/0.46 ( ( n_lists @ A @ ( zero_zero @ nat ) @ Xs2 )
% 0.31/0.46 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % n_lists.simps(1)
% 0.31/0.46 thf(fact_253_length__0__conv,axiom,
% 0.31/0.46 ! [A: $tType,Xs2: list @ A] :
% 0.31/0.46 ( ( ( size_size @ ( list @ A ) @ Xs2 )
% 0.31/0.46 = ( zero_zero @ nat ) )
% 0.31/0.46 = ( Xs2
% 0.31/0.46 = ( nil @ A ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % length_0_conv
% 0.31/0.46 thf(fact_254_length__greater__0__conv,axiom,
% 0.31/0.46 ! [A: $tType,Xs2: list @ A] :
% 0.31/0.46 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( size_size @ ( list @ A ) @ Xs2 ) )
% 0.31/0.46 = ( Xs2
% 0.31/0.46 != ( nil @ A ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % length_greater_0_conv
% 0.31/0.46
% 0.31/0.46 % Type constructors (8)
% 0.31/0.46 thf(tcon_fun___Orderings_Oord,axiom,
% 0.31/0.46 ! [A8: $tType,A9: $tType] :
% 0.31/0.46 ( ( ord @ A9 )
% 0.31/0.46 => ( ord @ ( A8 > A9 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 0.31/0.46 linorder @ nat ).
% 0.31/0.46
% 0.31/0.46 thf(tcon_Nat_Onat___Orderings_Oord_1,axiom,
% 0.31/0.46 ord @ nat ).
% 0.31/0.46
% 0.31/0.46 thf(tcon_Set_Oset___Orderings_Oord_2,axiom,
% 0.31/0.46 ! [A8: $tType] : ( ord @ ( set @ A8 ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(tcon_HOL_Obool___Orderings_Olinorder_3,axiom,
% 0.31/0.46 linorder @ $o ).
% 0.31/0.46
% 0.31/0.46 thf(tcon_HOL_Obool___Orderings_Oord_4,axiom,
% 0.31/0.46 ord @ $o ).
% 0.31/0.46
% 0.31/0.46 thf(tcon_Product__Type_Ounit___Orderings_Olinorder_5,axiom,
% 0.31/0.46 linorder @ product_unit ).
% 0.31/0.46
% 0.31/0.46 thf(tcon_Product__Type_Ounit___Orderings_Oord_6,axiom,
% 0.31/0.46 ord @ product_unit ).
% 0.31/0.46
% 0.31/0.46 % Helper facts (3)
% 0.31/0.46 thf(help_If_3_1_T,axiom,
% 0.31/0.46 ! [P2: $o] :
% 0.31/0.46 ( ( P2 = $true )
% 0.31/0.46 | ( P2 = $false ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(help_If_2_1_T,axiom,
% 0.31/0.46 ! [A: $tType,X3: A,Y3: A] :
% 0.31/0.46 ( ( if @ A @ $false @ X3 @ Y3 )
% 0.31/0.46 = Y3 ) ).
% 0.31/0.46
% 0.31/0.46 thf(help_If_1_1_T,axiom,
% 0.31/0.46 ! [A: $tType,X3: A,Y3: A] :
% 0.31/0.46 ( ( if @ A @ $true @ X3 @ Y3 )
% 0.31/0.46 = X3 ) ).
% 0.31/0.46
% 0.31/0.46 % Conjectures (1)
% 0.31/0.46 thf(conj_0,conjecture,
% 0.31/0.46 ! [Xs4: list @ ( product_prod @ a @ a ),X4: a,Y4: a,Ys4: list @ ( product_prod @ a @ a )] :
% 0.31/0.46 ( es
% 0.31/0.46 != ( append @ ( product_prod @ a @ a ) @ Xs4 @ ( cons @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ X4 @ Y4 ) @ ( cons @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ Y4 @ X4 ) @ Ys4 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 ------------------------
% 2.92/1.57 ---- Embedded in THF ---
% 2.92/1.57 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.92/1.57 %%% Generated on Tue Feb 24 08:26:15 EST 2026
% 2.92/1.57 %%% using '$$dhol' embedding, version 1.3.0.
% 2.92/1.57 %%% Logic specification used:
% 2.92/1.57 %%% thf(spec, logic, $$dhol).
% 2.92/1.57
% 2.92/1.57 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.eKA1rT9gZb/DTF2DTF9790.p
% 2.92/1.57 thf(ty_t_Pair__Digraph_Opair__pre__digraph_Opair__pre__digraph__ext, type, pair_p1731315293ph_ext: ($tType > ($tType > $tType))).
% 2.92/1.57 thf(ty_t_Product__Type_Ounit, type, product_unit: $tType).
% 2.92/1.57 thf(ty_t_Product__Type_Oprod, type, product_prod: ($tType > ($tType > $tType))).
% 2.92/1.57 thf(ty_t_List_Olist, type, list: ($tType > $tType)).
% 2.92/1.57 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 2.92/1.57 thf(ty_t_Nat_Onat, type, nat: $tType).
% 2.92/1.57 thf(ty_tf_a, type, a: $tType).
% 2.92/1.57 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: ($o))).
% 2.92/1.57 thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: ($o))).
% 2.92/1.57 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: ($o))).
% 2.92/1.57 thf(sy_c_Groups_Ozero__class_Ozero, type, zero_zero: (!> [A:$tType]: (A))).
% 2.92/1.57 thf(sy_c_If, type, if: (!> [A:$tType]: (($o > (A > (A > A)))))).
% 2.92/1.57 thf(sy_c_Kuratowski__Mirabelle__hkvioyikiw_Oprogressing, type, kurato990191779essing: (!> [A:$tType]: (((list @ ((product_prod @ A) @ A)) > $o)))).
% 2.92/1.57 thf(sy_c_List_Oappend, type, append: (!> [A:$tType]: (((list @ A) > ((list @ A) > (list @ A)))))).
% 2.92/1.57 thf(sy_c_List_Obind, type, bind: (!> [A:$tType,B:$tType]: (((list @ A) > ((A > (list @ B)) > (list @ B)))))).
% 2.92/1.57 thf(sy_c_List_Oconcat, type, concat: (!> [A:$tType]: (((list @ (list @ A)) > (list @ A))))).
% 2.92/1.57 thf(sy_c_List_Oinsert, type, insert: (!> [A:$tType]: ((A > ((list @ A) > (list @ A)))))).
% 2.92/1.57 thf(sy_c_List_Olenlex, type, lenlex: (!> [A:$tType]: (((set @ ((product_prod @ A) @ A)) > (set @ ((product_prod @ (list @ A)) @ (list @ A))))))).
% 2.92/1.57 thf(sy_c_List_Olex, type, lex: (!> [A:$tType]: (((set @ ((product_prod @ A) @ A)) > (set @ ((product_prod @ (list @ A)) @ (list @ A))))))).
% 2.92/1.57 thf(sy_c_List_Olexord, type, lexord: (!> [A:$tType]: (((set @ ((product_prod @ A) @ A)) > (set @ ((product_prod @ (list @ A)) @ (list @ A))))))).
% 2.92/1.57 thf(sy_c_List_Olist_OCons, type, cons: (!> [A:$tType]: ((A > ((list @ A) > (list @ A)))))).
% 2.92/1.57 thf(sy_c_List_Olist_ONil, type, nil: (!> [A:$tType]: ((list @ A)))).
% 2.92/1.57 thf(sy_c_List_Olist_Oset, type, set2: (!> [A:$tType]: (((list @ A) > (set @ A))))).
% 2.92/1.57 thf(sy_c_List_Olistrel, type, listrel: (!> [A:$tType,B:$tType]: (((set @ ((product_prod @ A) @ B)) > (set @ ((product_prod @ (list @ A)) @ (list @ B))))))).
% 2.92/1.57 thf(sy_c_List_Olistrel1, type, listrel1: (!> [A:$tType]: (((set @ ((product_prod @ A) @ A)) > (set @ ((product_prod @ (list @ A)) @ (list @ A))))))).
% 2.92/1.57 thf(sy_c_List_Omaps, type, maps: (!> [A:$tType,B:$tType]: (((A > (list @ B)) > ((list @ A) > (list @ B)))))).
% 2.92/1.57 thf(sy_c_List_Omeasures, type, measures: (!> [A:$tType]: (((list @ (A > nat)) > (set @ ((product_prod @ A) @ A)))))).
% 2.92/1.57 thf(sy_c_List_Omember, type, member: (!> [A:$tType]: (((list @ A) > (A > $o))))).
% 2.92/1.57 thf(sy_c_List_On__lists, type, n_lists: (!> [A:$tType]: ((nat > ((list @ A) > (list @ (list @ A))))))).
% 2.92/1.57 thf(sy_c_List_Oproduct__lists, type, product_lists: (!> [A:$tType]: (((list @ (list @ A)) > (list @ (list @ A)))))).
% 2.92/1.57 thf(sy_c_List_Osubseqs, type, subseqs: (!> [A:$tType]: (((list @ A) > (list @ (list @ A)))))).
% 2.92/1.57 thf(sy_c_List_Ozip, type, zip: (!> [A:$tType,B:$tType]: (((list @ A) > ((list @ B) > (list @ ((product_prod @ A) @ B))))))).
% 2.92/1.57 thf(sy_c_Multiset_Olinorder__class_Opart, type, linorder_part: (!> [B:$tType,A:$tType]: (((B > A) > (A > ((list @ B) > ((product_prod @ (list @ B)) @ ((product_prod @ (list @ B)) @ (list @ B))))))))).
% 2.92/1.57 thf(sy_c_Nat_Osize__class_Osize, type, size_size: (!> [A:$tType]: ((A > nat)))).
% 2.92/1.57 thf(sy_c_Orderings_Oord__class_Oless, type, ord_less: (!> [A:$tType]: ((A > (A > $o))))).
% 2.92/1.57 thf(sy_c_Pair__Digraph_Oco__path, type, pair_co_path: (!> [A:$tType]: ((((product_prod @ A) @ A) > (A > ((list @ ((product_prod @ A) @ A)) > (list @ ((product_prod @ A) @ A)))))))).
% 2.92/1.57 thf(sy_c_Pair__Digraph_Oco__path__rel, type, pair_co_path_rel: (!> [A:$tType]: ((((product_prod @ ((product_prod @ A) @ A)) @ ((product_prod @ A) @ (list @ ((product_prod @ A) @ A)))) > (((product_prod @ ((product_prod @ A) @ A)) @ ((product_prod @ A) @ (list @ ((product_prod @ A) @ A)))) > $o))))).
% 2.92/1.57 thf(sy_c_Pair__Digraph_Opawalk__verts, type, pair_pawalk_verts: (!> [A:$tType]: ((A > ((list @ ((product_prod @ A) @ A)) > (list @ A)))))).
% 2.92/1.57 thf(sy_c_Pair__Digraph_Osd__path, type, pair_sd_path: (!> [A:$tType]: ((((product_prod @ A) @ A) > (A > ((list @ ((product_prod @ A) @ A)) > (list @ ((product_prod @ A) @ A)))))))).
% 2.92/1.57 thf(sy_c_Pair__Digraph_Osd__path__rel, type, pair_sd_path_rel: (!> [A:$tType]: ((((product_prod @ ((product_prod @ A) @ A)) @ ((product_prod @ A) @ (list @ ((product_prod @ A) @ A)))) > (((product_prod @ ((product_prod @ A) @ A)) @ ((product_prod @ A) @ (list @ ((product_prod @ A) @ A)))) > $o))))).
% 2.92/1.57 thf(sy_c_Permutations_Oinverse__permutation__of__list, type, invers965609412f_list: (!> [A:$tType]: (((list @ ((product_prod @ A) @ A)) > (A > A))))).
% 2.92/1.57 thf(sy_c_Permutations_Oinverse__permutation__of__list__rel, type, invers1507583541st_rel: (!> [A:$tType]: ((((product_prod @ (list @ ((product_prod @ A) @ A))) @ A) > (((product_prod @ (list @ ((product_prod @ A) @ A))) @ A) > $o))))).
% 2.92/1.57 thf(sy_c_Permutations_Olist__permutes, type, list_permutes: (!> [A:$tType]: (((list @ ((product_prod @ A) @ A)) > ((set @ A) > $o))))).
% 2.92/1.57 thf(sy_c_Permutations_Opermutation__of__list, type, permutation_of_list: (!> [A:$tType]: (((list @ ((product_prod @ A) @ A)) > (A > A))))).
% 2.92/1.57 thf(sy_c_Product__Type_OPair, type, product_Pair: (!> [A:$tType,B:$tType]: ((A > (B > ((product_prod @ A) @ B)))))).
% 2.92/1.57 thf(sy_c_Product__Type_Ointernal__case__prod, type, produc2004651681e_prod: (!> [A:$tType,B:$tType,C:$tType]: (((A > (B > C)) > (((product_prod @ A) @ B) > C))))).
% 2.92/1.57 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod, type, product_rec_prod: (!> [A:$tType,B:$tType,T:$tType]: (((A > (B > T)) > (((product_prod @ A) @ B) > T))))).
% 2.92/1.57 thf(sy_c_Relation_Oasym, type, asym: (!> [A:$tType]: (((set @ ((product_prod @ A) @ A)) > $o)))).
% 2.92/1.57 thf(sy_c_Relation_Oirrefl, type, irrefl: (!> [A:$tType]: (((set @ ((product_prod @ A) @ A)) > $o)))).
% 2.92/1.57 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 2.92/1.57 thf(sy_c_Set_Othe__elem, type, the_elem: (!> [A:$tType]: (((set @ A) > A)))).
% 2.92/1.57 thf(sy_c_Wellfounded_Oaccp, type, accp: (!> [A:$tType]: (((A > (A > $o)) > (A > $o))))).
% 2.92/1.57 thf(sy_c_member, type, member2: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 2.92/1.57 thf(sy_v_e, type, e: ((product_prod @ a) @ a)).
% 2.92/1.57 thf(sy_v_es, type, es: (list @ ((product_prod @ a) @ a))).
% 2.92/1.57 thf(fact_0_assms, axiom, ((kurato990191779essing @ a) @ (((cons @ ((product_prod @ a) @ a)) @ e) @ es))).
% 2.92/1.57 thf(fact_1_progressing__def, axiom, (! [A:$tType]: (((kurato990191779essing @ A) = (^ [P:(list @ ((product_prod @ A) @ A))]: ((! [Xs:(list @ ((product_prod @ A) @ A)),X:A,Y:A,Ys:(list @ ((product_prod @ A) @ A))]: ((P != (((append @ ((product_prod @ A) @ A)) @ Xs) @ (((cons @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X) @ Y)) @ (((cons @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Y) @ X)) @ Ys)))))))))))).
% 2.92/1.57 thf(fact_2_append_Oassoc, axiom, (! [A:$tType,A2:(list @ A),B2:(list @ A),C2:(list @ A)]: (((((append @ A) @ (((append @ A) @ A2) @ B2)) @ C2) = (((append @ A) @ A2) @ (((append @ A) @ B2) @ C2)))))).
% 2.92/1.57 thf(fact_3_append__assoc, axiom, (! [A:$tType,Xs2:(list @ A),Ys2:(list @ A),Zs:(list @ A)]: (((((append @ A) @ (((append @ A) @ Xs2) @ Ys2)) @ Zs) = (((append @ A) @ Xs2) @ (((append @ A) @ Ys2) @ Zs)))))).
% 2.92/1.57 thf(fact_4_append__same__eq, axiom, (! [A:$tType,Ys2:(list @ A),Xs2:(list @ A),Zs:(list @ A)]: ((((((append @ A) @ Ys2) @ Xs2) = (((append @ A) @ Zs) @ Xs2)) = (Ys2 = Zs))))).
% 2.92/1.57 thf(fact_5_same__append__eq, axiom, (! [A:$tType,Xs2:(list @ A),Ys2:(list @ A),Zs:(list @ A)]: ((((((append @ A) @ Xs2) @ Ys2) = (((append @ A) @ Xs2) @ Zs)) = (Ys2 = Zs))))).
% 2.92/1.57 thf(fact_6_list_Oinject, axiom, (! [A:$tType,X21:A,X22:(list @ A),Y21:A,Y22:(list @ A)]: ((((((cons @ A) @ X21) @ X22) = (((cons @ A) @ Y21) @ Y22)) = ((X21 = Y21) & (X22 = Y22)))))).
% 2.92/1.57 thf(fact_7_prod_Oinject, axiom, (! [A:$tType,B:$tType,X1:A,X2:B,Y1:A,Y2:B]: (((((((product_Pair @ A) @ B) @ X1) @ X2) = ((((product_Pair @ A) @ B) @ Y1) @ Y2)) = ((X1 = Y1) & (X2 = Y2)))))).
% 2.92/1.57 thf(fact_8_old_Oprod_Oinject, axiom, (! [A:$tType,B:$tType,A2:A,B2:B,A3:A,B3:B]: (((((((product_Pair @ A) @ B) @ A2) @ B2) = ((((product_Pair @ A) @ B) @ A3) @ B3)) = ((A2 = A3) & (B2 = B3)))))).
% 2.92/1.57 thf(fact_9_Cons__eq__appendI, axiom, (! [A:$tType,X3:A,Xs1:(list @ A),Ys2:(list @ A),Xs2:(list @ A),Zs:(list @ A)]: ((((((cons @ A) @ X3) @ Xs1) = Ys2) => ((Xs2 = (((append @ A) @ Xs1) @ Zs)) => ((((cons @ A) @ X3) @ Xs2) = (((append @ A) @ Ys2) @ Zs))))))).
% 2.92/1.57 thf(fact_10_append__Cons, axiom, (! [A:$tType,X3:A,Xs2:(list @ A),Ys2:(list @ A)]: (((((append @ A) @ (((cons @ A) @ X3) @ Xs2)) @ Ys2) = (((cons @ A) @ X3) @ (((append @ A) @ Xs2) @ Ys2)))))).
% 2.92/1.57 thf(fact_11_append__eq__appendI, axiom, (! [A:$tType,Xs2:(list @ A),Xs1:(list @ A),Zs:(list @ A),Ys2:(list @ A),Us:(list @ A)]: ((((((append @ A) @ Xs2) @ Xs1) = Zs) => ((Ys2 = (((append @ A) @ Xs1) @ Us)) => ((((append @ A) @ Xs2) @ Ys2) = (((append @ A) @ Zs) @ Us))))))).
% 2.92/1.57 thf(fact_12_append__eq__append__conv2, axiom, (! [A:$tType,Xs2:(list @ A),Ys2:(list @ A),Zs:(list @ A),Ts:(list @ A)]: ((((((append @ A) @ Xs2) @ Ys2) = (((append @ A) @ Zs) @ Ts)) = (? [Us2:(list @ A)]: ((((Xs2 = (((append @ A) @ Zs) @ Us2)) & ((((append @ A) @ Us2) @ Ys2) = Ts)) | (((((append @ A) @ Xs2) @ Us2) = Zs) & (Ys2 = (((append @ A) @ Us2) @ Ts)))))))))).
% 2.92/1.57 thf(fact_13_old_Oprod_Oinducts, axiom, (! [B:$tType,A:$tType,P2:(((product_prod @ A) @ B) > $o),Prod:((product_prod @ A) @ B)]: (((! [A4:A,B4:B]: ((P2 @ ((((product_Pair @ A) @ B) @ A4) @ B4)))) => (P2 @ Prod))))).
% 2.92/1.57 thf(fact_14_old_Oprod_Oexhaust, axiom, (! [A:$tType,B:$tType,Y3:((product_prod @ A) @ B)]: ((~ ((! [A4:A,B4:B]: ((Y3 != ((((product_Pair @ A) @ B) @ A4) @ B4))))))))).
% 2.92/1.57 thf(fact_15_prod__induct7, axiom, (! [G:$tType,F:$tType,E:$tType,D:$tType,C:$tType,B:$tType,A:$tType,P2:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F) @ G)))))) > $o),X3:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F) @ G))))))]: (((! [A4:A,B4:B,C3:C,D2:D,E2:E,F2:F,G2:G]: ((P2 @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F) @ G)))))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F) @ G))))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F) @ G)))) @ C3) @ ((((product_Pair @ D) @ ((product_prod @ E) @ ((product_prod @ F) @ G))) @ D2) @ ((((product_Pair @ E) @ ((product_prod @ F) @ G)) @ E2) @ ((((product_Pair @ F) @ G) @ F2) @ G2))))))))) => (P2 @ X3))))).
% 2.92/1.57 thf(fact_16_prod__induct6, axiom, (! [F:$tType,E:$tType,D:$tType,C:$tType,B:$tType,A:$tType,P2:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F))))) > $o),X3:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F)))))]: (((! [A4:A,B4:B,C3:C,D2:D,E2:E,F2:F]: ((P2 @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F))))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F)))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F))) @ C3) @ ((((product_Pair @ D) @ ((product_prod @ E) @ F)) @ D2) @ ((((product_Pair @ E) @ F) @ E2) @ F2)))))))) => (P2 @ X3))))).
% 2.92/1.57 thf(fact_17_prod__induct5, axiom, (! [E:$tType,D:$tType,C:$tType,B:$tType,A:$tType,P2:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E)))) > $o),X3:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E))))]: (((! [A4:A,B4:B,C3:C,D2:D,E2:E]: ((P2 @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E)))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ E)) @ C3) @ ((((product_Pair @ D) @ E) @ D2) @ E2))))))) => (P2 @ X3))))).
% 2.92/1.57 thf(fact_18_prod__induct4, axiom, (! [D:$tType,C:$tType,B:$tType,A:$tType,P2:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D))) > $o),X3:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D)))]: (((! [A4:A,B4:B,C3:C,D2:D]: ((P2 @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C) @ D)) @ B4) @ ((((product_Pair @ C) @ D) @ C3) @ D2)))))) => (P2 @ X3))))).
% 2.92/1.57 thf(fact_19_prod__induct3, axiom, (! [C:$tType,B:$tType,A:$tType,P2:(((product_prod @ A) @ ((product_prod @ B) @ C)) > $o),X3:((product_prod @ A) @ ((product_prod @ B) @ C))]: (((! [A4:A,B4:B,C3:C]: ((P2 @ ((((product_Pair @ A) @ ((product_prod @ B) @ C)) @ A4) @ ((((product_Pair @ B) @ C) @ B4) @ C3))))) => (P2 @ X3))))).
% 2.92/1.57 thf(fact_20_prod__cases7, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,E:$tType,F:$tType,G:$tType,Y3:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F) @ G))))))]: ((~ ((! [A4:A,B4:B,C3:C,D2:D,E2:E,F2:F,G2:G]: ((Y3 != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F) @ G)))))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F) @ G))))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F) @ G)))) @ C3) @ ((((product_Pair @ D) @ ((product_prod @ E) @ ((product_prod @ F) @ G))) @ D2) @ ((((product_Pair @ E) @ ((product_prod @ F) @ G)) @ E2) @ ((((product_Pair @ F) @ G) @ F2) @ G2)))))))))))))).
% 2.92/1.57 thf(fact_21_prod__cases6, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,E:$tType,F:$tType,Y3:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F)))))]: ((~ ((! [A4:A,B4:B,C3:C,D2:D,E2:E,F2:F]: ((Y3 != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F))))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F)))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F))) @ C3) @ ((((product_Pair @ D) @ ((product_prod @ E) @ F)) @ D2) @ ((((product_Pair @ E) @ F) @ E2) @ F2))))))))))))).
% 2.92/1.57 thf(fact_22_prod__cases5, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,E:$tType,Y3:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E))))]: ((~ ((! [A4:A,B4:B,C3:C,D2:D,E2:E]: ((Y3 != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E)))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ E)) @ C3) @ ((((product_Pair @ D) @ E) @ D2) @ E2)))))))))))).
% 2.92/1.57 thf(fact_23_prod__cases4, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,Y3:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D)))]: ((~ ((! [A4:A,B4:B,C3:C,D2:D]: ((Y3 != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C) @ D)) @ B4) @ ((((product_Pair @ C) @ D) @ C3) @ D2))))))))))).
% 2.92/1.57 thf(fact_24_prod__cases3, axiom, (! [A:$tType,B:$tType,C:$tType,Y3:((product_prod @ A) @ ((product_prod @ B) @ C))]: ((~ ((! [A4:A,B4:B,C3:C]: ((Y3 != ((((product_Pair @ A) @ ((product_prod @ B) @ C)) @ A4) @ ((((product_Pair @ B) @ C) @ B4) @ C3)))))))))).
% 2.92/1.57 thf(fact_25_Pair__inject, axiom, (! [A:$tType,B:$tType,A2:A,B2:B,A3:A,B3:B]: (((((((product_Pair @ A) @ B) @ A2) @ B2) = ((((product_Pair @ A) @ B) @ A3) @ B3)) => (~ (((A2 = A3) => (B2 != B3)))))))).
% 2.92/1.57 thf(fact_26_prod__cases, axiom, (! [B:$tType,A:$tType,P2:(((product_prod @ A) @ B) > $o),P3:((product_prod @ A) @ B)]: (((! [A4:A,B4:B]: ((P2 @ ((((product_Pair @ A) @ B) @ A4) @ B4)))) => (P2 @ P3))))).
% 2.92/1.57 thf(fact_27_surj__pair, axiom, (! [A:$tType,B:$tType,P3:((product_prod @ A) @ B)]: ((? [X4:A,Y4:B]: ((P3 = ((((product_Pair @ A) @ B) @ X4) @ Y4))))))).
% 2.92/1.57 thf(fact_28_not__Cons__self2, axiom, (! [A:$tType,X3:A,Xs2:(list @ A)]: (((((cons @ A) @ X3) @ Xs2) != Xs2)))).
% 2.92/1.57 thf(fact_29_old_Oprod_Orec, axiom, (! [A:$tType,T:$tType,B:$tType,F1:(A > (B > T)),A2:A,B2:B]: (((((((product_rec_prod @ A) @ B) @ T) @ F1) @ ((((product_Pair @ A) @ B) @ A2) @ B2)) = ((F1 @ A2) @ B2))))).
% 2.92/1.57 thf(fact_30_bind__simps_I2_J, axiom, (! [A:$tType,B:$tType,X3:B,Xs2:(list @ B),F3:(B > (list @ A))]: ((((((bind @ B) @ A) @ (((cons @ B) @ X3) @ Xs2)) @ F3) = (((append @ A) @ (F3 @ X3)) @ ((((bind @ B) @ A) @ Xs2) @ F3)))))).
% 2.92/1.57 thf(fact_31_maps__simps_I1_J, axiom, (! [A:$tType,B:$tType,F3:(B > (list @ A)),X3:B,Xs2:(list @ B)]: ((((((maps @ B) @ A) @ F3) @ (((cons @ B) @ X3) @ Xs2)) = (((append @ A) @ (F3 @ X3)) @ ((((maps @ B) @ A) @ F3) @ Xs2)))))).
% 2.92/1.57 thf(fact_32_internal__case__prod__conv, axiom, (! [B:$tType,A:$tType,C:$tType,C2:(B > (C > A)),A2:B,B2:C]: (((((((produc2004651681e_prod @ B) @ C) @ A) @ C2) @ ((((product_Pair @ B) @ C) @ A2) @ B2)) = ((C2 @ A2) @ B2))))).
% 2.92/1.57 thf(fact_33_lexord__append__left__rightI, axiom, (! [A:$tType,A2:A,B2:A,R:(set @ ((product_prod @ A) @ A)),U:(list @ A),X3:(list @ A),Y3:(list @ A)]: (((((member2 @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A2) @ B2)) @ R) => (((member2 @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((append @ A) @ U) @ (((cons @ A) @ A2) @ X3))) @ (((append @ A) @ U) @ (((cons @ A) @ B2) @ Y3)))) @ ((lexord @ A) @ R)))))).
% 2.92/1.57 thf(fact_34_zip__Cons__Cons, axiom, (! [A:$tType,B:$tType,X3:A,Xs2:(list @ A),Y3:B,Ys2:(list @ B)]: ((((((zip @ A) @ B) @ (((cons @ A) @ X3) @ Xs2)) @ (((cons @ B) @ Y3) @ Ys2)) = (((cons @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X3) @ Y3)) @ ((((zip @ A) @ B) @ Xs2) @ Ys2)))))).
% 2.92/1.57 thf(fact_35_listrel1I, axiom, (! [A:$tType,X3:A,Y3:A,R:(set @ ((product_prod @ A) @ A)),Xs2:(list @ A),Us:(list @ A),Vs:(list @ A),Ys2:(list @ A)]: (((((member2 @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X3) @ Y3)) @ R) => ((Xs2 = (((append @ A) @ Us) @ (((cons @ A) @ X3) @ Vs))) => ((Ys2 = (((append @ A) @ Us) @ (((cons @ A) @ Y3) @ Vs))) => (((member2 @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Xs2) @ Ys2)) @ ((listrel1 @ A) @ R)))))))).
% 2.92/1.57 thf(fact_36_listrel1E, axiom, (! [A:$tType,Xs2:(list @ A),Ys2:(list @ A),R:(set @ ((product_prod @ A) @ A))]: (((((member2 @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Xs2) @ Ys2)) @ ((listrel1 @ A) @ R)) => (~ ((! [X4:A,Y4:A]: (((((member2 @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X4) @ Y4)) @ R) => (! [Us3:(list @ A),Vs2:(list @ A)]: (((Xs2 = (((append @ A) @ Us3) @ (((cons @ A) @ X4) @ Vs2))) => (Ys2 != (((append @ A) @ Us3) @ (((cons @ A) @ Y4) @ Vs2))))))))))))))).
% 2.92/1.57 thf(fact_37_member__rec_I1_J, axiom, (! [A:$tType,X3:A,Xs2:(list @ A),Y3:A]: (((((member @ A) @ (((cons @ A) @ X3) @ Xs2)) @ Y3) = ((X3 = Y3) | (((member @ A) @ Xs2) @ Y3)))))).
% 2.92/1.57 thf(fact_38_ssubst__Pair__rhs, axiom, (! [B:$tType,A:$tType,R:A,S:B,R2:(set @ ((product_prod @ A) @ B)),S2:B]: (((((member2 @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ R) @ S)) @ R2) => ((S2 = S) => (((member2 @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ R) @ S2)) @ R2)))))).
% 2.92/1.57 thf(fact_39_subdivide_Oinduct, axiom, (! [A:$tType,P2:(((pair_p1731315293ph_ext @ A) @ product_unit) > (((product_prod @ A) @ A) > (A > $o))),A0:((pair_p1731315293ph_ext @ A) @ product_unit),A1:((product_prod @ A) @ A),A22:A]: (((! [G3:((pair_p1731315293ph_ext @ A) @ product_unit),U2:A,V:A,X_1:A]: ((((P2 @ G3) @ ((((product_Pair @ A) @ A) @ U2) @ V)) @ X_1))) => (((P2 @ A0) @ A1) @ A22))))).
% 2.92/1.57 thf(fact_40_Cons__listrel1__Cons, axiom, (! [A:$tType,X3:A,Xs2:(list @ A),Y3:A,Ys2:(list @ A),R:(set @ ((product_prod @ A) @ A))]: (((((member2 @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((cons @ A) @ X3) @ Xs2)) @ (((cons @ A) @ Y3) @ Ys2))) @ ((listrel1 @ A) @ R)) = (((((member2 @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X3) @ Y3)) @ R) & (Xs2 = Ys2)) | ((X3 = Y3) & (((member2 @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Xs2) @ Ys2)) @ ((listrel1 @ A) @ R)))))))).
% 2.92/1.57 thf(fact_41_lexord__cons__cons, axiom, (! [A:$tType,A2:A,X3:(list @ A),B2:A,Y3:(list @ A),R:(set @ ((product_prod @ A) @ A))]: (((((member2 @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((cons @ A) @ A2) @ X3)) @ (((cons @ A) @ B2) @ Y3))) @ ((lexord @ A) @ R)) = ((((member2 @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A2) @ B2)) @ R) | ((A2 = B2) & (((member2 @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ X3) @ Y3)) @ ((lexord @ A) @ R)))))))).
% 2.92/1.57 thf(fact_42_listrel1I2, axiom, (! [A:$tType,Xs2:(list @ A),Ys2:(list @ A),R:(set @ ((product_prod @ A) @ A)),X3:A]: (((((member2 @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Xs2) @ Ys2)) @ ((listrel1 @ A) @ R)) => (((member2 @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((cons @ A) @ X3) @ Xs2)) @ (((cons @ A) @ X3) @ Ys2))) @ ((listrel1 @ A) @ R)))))).
% 2.92/1.57 thf(fact_43_append__listrel1I, axiom, (! [A:$tType,Xs2:(list @ A),Ys2:(list @ A),R:(set @ ((product_prod @ A) @ A)),Us:(list @ A),Vs:(list @ A)]: (((((((member2 @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Xs2) @ Ys2)) @ ((listrel1 @ A) @ R)) & (Us = Vs)) | ((Xs2 = Ys2) & (((member2 @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Us) @ Vs)) @ ((listrel1 @ A) @ R)))) => (((member2 @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((append @ A) @ Xs2) @ Us)) @ (((append @ A) @ Ys2) @ Vs))) @ ((listrel1 @ A) @ R)))))).
% 2.92/1.57 thf(fact_44_lexord__linear, axiom, (! [A:$tType,R:(set @ ((product_prod @ A) @ A)),X3:(list @ A),Y3:(list @ A)]: (((! [A4:A,B4:A]: (((((member2 @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A4) @ B4)) @ R) | ((A4 = B4) | (((member2 @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ B4) @ A4)) @ R))))) => ((((member2 @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ X3) @ Y3)) @ ((lexord @ A) @ R)) | ((X3 = Y3) | (((member2 @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Y3) @ X3)) @ ((lexord @ A) @ R)))))))).
% 2.92/1.57 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P2:(A > $o)]: (((((member2 @ A) @ A2) @ ((collect @ A) @ P2)) = (P2 @ A2))))).
% 2.92/1.57 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A5:(set @ A)]: ((((collect @ A) @ (^ [X:A]: ((((member2 @ A) @ X) @ A5)))) = A5)))).
% 2.92/1.57 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P2:(A > $o),Q:(A > $o)]: (((! [X4:A]: (((P2 @ X4) = (Q @ X4)))) => (((collect @ A) @ P2) = ((collect @ A) @ Q)))))).
% 2.92/1.57 thf(fact_48_lexord__irreflexive, axiom, (! [A:$tType,R:(set @ ((product_prod @ A) @ A)),Xs2:(list @ A)]: (((! [X4:A]: ((~ ((((member2 @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X4) @ X4)) @ R))))) => (~ ((((member2 @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Xs2) @ Xs2)) @ ((lexord @ A) @ R)))))))).
% 2.92/1.57 thf(fact_49_lexord__append__leftI, axiom, (! [A:$tType,U:(list @ A),V2:(list @ A),R:(set @ ((product_prod @ A) @ A)),X3:(list @ A)]: (((((member2 @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ U) @ V2)) @ ((lexord @ A) @ R)) => (((member2 @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((append @ A) @ X3) @ U)) @ (((append @ A) @ X3) @ V2))) @ ((lexord @ A) @ R)))))).
% 2.92/1.57 thf(fact_50_listrel1I1, axiom, (! [A:$tType,X3:A,Y3:A,R:(set @ ((product_prod @ A) @ A)),Xs2:(list @ A)]: (((((member2 @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X3) @ Y3)) @ R) => (((member2 @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((cons @ A) @ X3) @ Xs2)) @ (((cons @ A) @ Y3) @ Xs2))) @ ((listrel1 @ A) @ R)))))).
% 2.92/1.57 thf(fact_51_Cons__listrel1E1, axiom, (! [A:$tType,X3:A,Xs2:(list @ A),Ys2:(list @ A),R:(set @ ((product_prod @ A) @ A))]: (((((member2 @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((cons @ A) @ X3) @ Xs2)) @ Ys2)) @ ((listrel1 @ A) @ R)) => ((! [Y4:A]: (((Ys2 = (((cons @ A) @ Y4) @ Xs2)) => (~ ((((member2 @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X3) @ Y4)) @ R)))))) => (~ ((! [Zs2:(list @ A)]: (((Ys2 = (((cons @ A) @ X3) @ Zs2)) => (~ ((((member2 @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Xs2) @ Zs2)) @ ((listrel1 @ A) @ R)))))))))))))).
% 2.92/1.57 thf(fact_52_Cons__listrel1E2, axiom, (! [A:$tType,Xs2:(list @ A),Y3:A,Ys2:(list @ A),R:(set @ ((product_prod @ A) @ A))]: (((((member2 @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Xs2) @ (((cons @ A) @ Y3) @ Ys2))) @ ((listrel1 @ A) @ R)) => ((! [X4:A]: (((Xs2 = (((cons @ A) @ X4) @ Ys2)) => (~ ((((member2 @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X4) @ Y3)) @ R)))))) => (~ ((! [Zs2:(list @ A)]: (((Xs2 = (((cons @ A) @ Y3) @ Zs2)) => (~ ((((member2 @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Zs2) @ Ys2)) @ ((listrel1 @ A) @ R)))))))))))))).
% 2.92/1.57 thf(fact_53_lexord__append__leftD, axiom, (! [A:$tType,X3:(list @ A),U:(list @ A),V2:(list @ A),R:(set @ ((product_prod @ A) @ A))]: (((((member2 @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((append @ A) @ X3) @ U)) @ (((append @ A) @ X3) @ V2))) @ ((lexord @ A) @ R)) => ((! [A4:A]: ((~ ((((member2 @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A4) @ A4)) @ R))))) => (((member2 @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ U) @ V2)) @ ((lexord @ A) @ R))))))).
% 2.92/1.57 thf(fact_54_lexord__append__rightI, axiom, (! [A:$tType,Y3:(list @ A),X3:(list @ A),R:(set @ ((product_prod @ A) @ A))]: (((? [B5:A,Z:(list @ A)]: ((Y3 = (((cons @ A) @ B5) @ Z)))) => (((member2 @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ X3) @ (((append @ A) @ X3) @ Y3))) @ ((lexord @ A) @ R)))))).
% 2.92/1.57 thf(fact_55_zip__eq__ConsE, axiom, (! [A:$tType,B:$tType,Xs2:(list @ A),Ys2:(list @ B),Xy:((product_prod @ A) @ B),Xys:(list @ ((product_prod @ A) @ B))]: (((((((zip @ A) @ B) @ Xs2) @ Ys2) = (((cons @ ((product_prod @ A) @ B)) @ Xy) @ Xys)) => (~ ((! [X4:A,Xs3:(list @ A)]: (((Xs2 = (((cons @ A) @ X4) @ Xs3)) => (! [Y4:B,Ys3:(list @ B)]: (((Ys2 = (((cons @ B) @ Y4) @ Ys3)) => ((Xy = ((((product_Pair @ A) @ B) @ X4) @ Y4)) => (Xys != ((((zip @ A) @ B) @ Xs3) @ Ys3))))))))))))))).
% 2.92/1.57 thf(fact_56_subdivide_Ocases, axiom, (! [A:$tType,X3:((product_prod @ ((pair_p1731315293ph_ext @ A) @ product_unit)) @ ((product_prod @ ((product_prod @ A) @ A)) @ A))]: ((~ ((! [G3:((pair_p1731315293ph_ext @ A) @ product_unit),U2:A,V:A,W:A]: ((X3 != ((((product_Pair @ ((pair_p1731315293ph_ext @ A) @ product_unit)) @ ((product_prod @ ((product_prod @ A) @ A)) @ A)) @ G3) @ ((((product_Pair @ ((product_prod @ A) @ A)) @ A) @ ((((product_Pair @ A) @ A) @ U2) @ V)) @ W)))))))))).
% 2.92/1.57 thf(fact_57_lexord__same__pref__if__irrefl, axiom, (! [A:$tType,R:(set @ ((product_prod @ A) @ A)),Xs2:(list @ A),Ys2:(list @ A),Zs:(list @ A)]: ((((irrefl @ A) @ R) => ((((member2 @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((append @ A) @ Xs2) @ Ys2)) @ (((append @ A) @ Xs2) @ Zs))) @ ((lexord @ A) @ R)) = (((member2 @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Ys2) @ Zs)) @ ((lexord @ A) @ R))))))).
% 2.92/1.57 thf(fact_58_snoc__listrel1__snoc__iff, axiom, (! [A:$tType,Xs2:(list @ A),X3:A,Ys2:(list @ A),Y3:A,R:(set @ ((product_prod @ A) @ A))]: (((((member2 @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((append @ A) @ Xs2) @ (((cons @ A) @ X3) @ (nil @ A)))) @ (((append @ A) @ Ys2) @ (((cons @ A) @ Y3) @ (nil @ A))))) @ ((listrel1 @ A) @ R)) = (((((member2 @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Xs2) @ Ys2)) @ ((listrel1 @ A) @ R)) & (X3 = Y3)) | ((Xs2 = Ys2) & (((member2 @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X3) @ Y3)) @ R))))))).
% 2.92/1.57 thf(fact_59_lexord__Nil__left, axiom, (! [A:$tType,Y3:(list @ A),R:(set @ ((product_prod @ A) @ A))]: (((((member2 @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ (nil @ A)) @ Y3)) @ ((lexord @ A) @ R)) = (? [A6:A,X:(list @ A)]: ((Y3 = (((cons @ A) @ A6) @ X)))))))).
% 2.92/1.57 thf(fact_60_lexord__same__pref__iff, axiom, (! [A:$tType,Xs2:(list @ A),Ys2:(list @ A),Zs:(list @ A),R:(set @ ((product_prod @ A) @ A))]: (((((member2 @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((append @ A) @ Xs2) @ Ys2)) @ (((append @ A) @ Xs2) @ Zs))) @ ((lexord @ A) @ R)) = ((? [X:A]: (((((member2 @ A) @ X) @ ((set2 @ A) @ Xs2)) & (((member2 @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X) @ X)) @ R)))) | (((member2 @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Ys2) @ Zs)) @ ((lexord @ A) @ R))))))).
% 2.92/1.57 thf(fact_61_zip__append, axiom, (! [A:$tType,B:$tType,Xs2:(list @ A),Us:(list @ B),Ys2:(list @ A),Vs:(list @ B)]: (((((size_size @ (list @ A)) @ Xs2) = ((size_size @ (list @ B)) @ Us)) => (((((zip @ A) @ B) @ (((append @ A) @ Xs2) @ Ys2)) @ (((append @ B) @ Us) @ Vs)) = (((append @ ((product_prod @ A) @ B)) @ ((((zip @ A) @ B) @ Xs2) @ Us)) @ ((((zip @ A) @ B) @ Ys2) @ Vs))))))).
% 2.92/1.57 thf(fact_62_lex__append__leftD, axiom, (! [A:$tType,R:(set @ ((product_prod @ A) @ A)),Xs2:(list @ A),Ys2:(list @ A),Zs:(list @ A)]: (((! [X4:A]: ((~ ((((member2 @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X4) @ X4)) @ R))))) => ((((member2 @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((append @ A) @ Xs2) @ Ys2)) @ (((append @ A) @ Xs2) @ Zs))) @ ((lex @ A) @ R)) => (((member2 @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Ys2) @ Zs)) @ ((lex @ A) @ R))))))).
% 2.92/1.57 thf(fact_63_lex__append__left__iff, axiom, (! [A:$tType,R:(set @ ((product_prod @ A) @ A)),Xs2:(list @ A),Ys2:(list @ A),Zs:(list @ A)]: (((! [X4:A]: ((~ ((((member2 @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X4) @ X4)) @ R))))) => ((((member2 @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((append @ A) @ Xs2) @ Ys2)) @ (((append @ A) @ Xs2) @ Zs))) @ ((lex @ A) @ R)) = (((member2 @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Ys2) @ Zs)) @ ((lex @ A) @ R))))))).
% 2.92/1.57 thf(fact_64_lexord__asymmetric, axiom, (! [A:$tType,R2:(set @ ((product_prod @ A) @ A)),A2:(list @ A),B2:(list @ A)]: ((((asym @ A) @ R2) => ((((member2 @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ A2) @ B2)) @ ((lexord @ A) @ R2)) => (~ ((((member2 @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ B2) @ A2)) @ ((lexord @ A) @ R2))))))))).
% 2.92/1.57 thf(fact_65_append_Oright__neutral, axiom, (! [A:$tType,A2:(list @ A)]: (((((append @ A) @ A2) @ (nil @ A)) = A2)))).
% 2.92/1.57 thf(fact_66_append__is__Nil__conv, axiom, (! [A:$tType,Xs2:(list @ A),Ys2:(list @ A)]: ((((((append @ A) @ Xs2) @ Ys2) = (nil @ A)) = ((Xs2 = (nil @ A)) & (Ys2 = (nil @ A))))))).
% 2.92/1.57 thf(fact_67_Nil__is__append__conv, axiom, (! [A:$tType,Xs2:(list @ A),Ys2:(list @ A)]: ((((nil @ A) = (((append @ A) @ Xs2) @ Ys2)) = ((Xs2 = (nil @ A)) & (Ys2 = (nil @ A))))))).
% 2.92/1.57 thf(fact_68_self__append__conv2, axiom, (! [A:$tType,Ys2:(list @ A),Xs2:(list @ A)]: (((Ys2 = (((append @ A) @ Xs2) @ Ys2)) = (Xs2 = (nil @ A)))))).
% 2.92/1.57 thf(fact_69_append__self__conv2, axiom, (! [A:$tType,Xs2:(list @ A),Ys2:(list @ A)]: ((((((append @ A) @ Xs2) @ Ys2) = Ys2) = (Xs2 = (nil @ A)))))).
% 2.92/1.57 thf(fact_70_self__append__conv, axiom, (! [A:$tType,Xs2:(list @ A),Ys2:(list @ A)]: (((Xs2 = (((append @ A) @ Xs2) @ Ys2)) = (Ys2 = (nil @ A)))))).
% 2.92/1.57 thf(fact_71_append__self__conv, axiom, (! [A:$tType,Xs2:(list @ A),Ys2:(list @ A)]: ((((((append @ A) @ Xs2) @ Ys2) = Xs2) = (Ys2 = (nil @ A)))))).
% 2.92/1.57 thf(fact_72_append__Nil2, axiom, (! [A:$tType,Xs2:(list @ A)]: (((((append @ A) @ Xs2) @ (nil @ A)) = Xs2)))).
% 2.92/1.57 thf(fact_73_append__eq__append__conv, axiom, (! [A:$tType,Xs2:(list @ A),Ys2:(list @ A),Us:(list @ A),Vs:(list @ A)]: ((((((size_size @ (list @ A)) @ Xs2) = ((size_size @ (list @ A)) @ Ys2)) | (((size_size @ (list @ A)) @ Us) = ((size_size @ (list @ A)) @ Vs))) => (((((append @ A) @ Xs2) @ Us) = (((append @ A) @ Ys2) @ Vs)) = ((Xs2 = Ys2) & (Us = Vs))))))).
% 2.92/1.57 thf(fact_74_zip__Nil, axiom, (! [B:$tType,A:$tType,Ys2:(list @ B)]: ((((((zip @ A) @ B) @ (nil @ A)) @ Ys2) = (nil @ ((product_prod @ A) @ B)))))).
% 2.92/1.57 thf(fact_75_bind__simps_I1_J, axiom, (! [B:$tType,A:$tType,F3:(B > (list @ A))]: ((((((bind @ B) @ A) @ (nil @ B)) @ F3) = (nil @ A))))).
% 2.92/1.57 thf(fact_76_append1__eq__conv, axiom, (! [A:$tType,Xs2:(list @ A),X3:A,Ys2:(list @ A),Y3:A]: ((((((append @ A) @ Xs2) @ (((cons @ A) @ X3) @ (nil @ A))) = (((append @ A) @ Ys2) @ (((cons @ A) @ Y3) @ (nil @ A)))) = ((Xs2 = Ys2) & (X3 = Y3)))))).
% 2.92/1.57 thf(fact_77_Cons__in__lex, axiom, (! [A:$tType,X3:A,Xs2:(list @ A),Y3:A,Ys2:(list @ A),R:(set @ ((product_prod @ A) @ A))]: (((((member2 @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((cons @ A) @ X3) @ Xs2)) @ (((cons @ A) @ Y3) @ Ys2))) @ ((lex @ A) @ R)) = (((((member2 @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X3) @ Y3)) @ R) & (((size_size @ (list @ A)) @ Xs2) = ((size_size @ (list @ A)) @ Ys2))) | ((X3 = Y3) & (((member2 @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Xs2) @ Ys2)) @ ((lex @ A) @ R)))))))).
% 2.92/1.57 thf(fact_78_zip_Osimps_I1_J, axiom, (! [B:$tType,A:$tType,Xs2:(list @ A)]: ((((((zip @ A) @ B) @ Xs2) @ (nil @ B)) = (nil @ ((product_prod @ A) @ B)))))).
% 2.92/1.57 thf(fact_79_Nil__notin__lex, axiom, (! [A:$tType,Ys2:(list @ A),R:(set @ ((product_prod @ A) @ A))]: ((~ ((((member2 @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ (nil @ A)) @ Ys2)) @ ((lex @ A) @ R))))))).
% 2.92/1.57 thf(fact_80_Nil2__notin__lex, axiom, (! [A:$tType,Xs2:(list @ A),R:(set @ ((product_prod @ A) @ A))]: ((~ ((((member2 @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Xs2) @ (nil @ A))) @ ((lex @ A) @ R))))))).
% 2.92/1.57 thf(fact_81_zip__eq__Nil__iff, axiom, (! [A:$tType,B:$tType,Xs2:(list @ A),Ys2:(list @ B)]: (((((((zip @ A) @ B) @ Xs2) @ Ys2) = (nil @ ((product_prod @ A) @ B))) = ((Xs2 = (nil @ A)) | (Ys2 = (nil @ B))))))).
% 2.92/1.57 thf(fact_82_in__set__impl__in__set__zip1, axiom, (! [A:$tType,B:$tType,Xs2:(list @ A),Ys2:(list @ B),X3:A]: (((((size_size @ (list @ A)) @ Xs2) = ((size_size @ (list @ B)) @ Ys2)) => ((((member2 @ A) @ X3) @ ((set2 @ A) @ Xs2)) => (~ ((! [Y4:B]: ((~ ((((member2 @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X3) @ Y4)) @ ((set2 @ ((product_prod @ A) @ B)) @ ((((zip @ A) @ B) @ Xs2) @ Ys2)))))))))))))).
% 2.92/1.57 thf(fact_83_in__set__impl__in__set__zip2, axiom, (! [A:$tType,B:$tType,Xs2:(list @ A),Ys2:(list @ B),Y3:B]: (((((size_size @ (list @ A)) @ Xs2) = ((size_size @ (list @ B)) @ Ys2)) => ((((member2 @ B) @ Y3) @ ((set2 @ B) @ Ys2)) => (~ ((! [X4:A]: ((~ ((((member2 @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X4) @ Y3)) @ ((set2 @ ((product_prod @ A) @ B)) @ ((((zip @ A) @ B) @ Xs2) @ Ys2)))))))))))))).
% 2.92/1.57 thf(fact_84_list__induct4, axiom, (! [C:$tType,A:$tType,B:$tType,D:$tType,Xs2:(list @ A),Ys2:(list @ B),Zs:(list @ C),Ws:(list @ D),P2:((list @ A) > ((list @ B) > ((list @ C) > ((list @ D) > $o))))]: (((((size_size @ (list @ A)) @ Xs2) = ((size_size @ (list @ B)) @ Ys2)) => ((((size_size @ (list @ B)) @ Ys2) = ((size_size @ (list @ C)) @ Zs)) => ((((size_size @ (list @ C)) @ Zs) = ((size_size @ (list @ D)) @ Ws)) => (((((P2 @ (nil @ A)) @ (nil @ B)) @ (nil @ C)) @ (nil @ D)) => ((! [X4:A,Xs4:(list @ A),Y4:B,Ys4:(list @ B),Z2:C,Zs2:(list @ C),W:D,Ws2:(list @ D)]: (((((size_size @ (list @ A)) @ Xs4) = ((size_size @ (list @ B)) @ Ys4)) => ((((size_size @ (list @ B)) @ Ys4) = ((size_size @ (list @ C)) @ Zs2)) => ((((size_size @ (list @ C)) @ Zs2) = ((size_size @ (list @ D)) @ Ws2)) => (((((P2 @ Xs4) @ Ys4) @ Zs2) @ Ws2) => ((((P2 @ (((cons @ A) @ X4) @ Xs4)) @ (((cons @ B) @ Y4) @ Ys4)) @ (((cons @ C) @ Z2) @ Zs2)) @ (((cons @ D) @ W) @ Ws2)))))))) => ((((P2 @ Xs2) @ Ys2) @ Zs) @ Ws))))))))).
% 2.92/1.57 thf(fact_85_list__induct3, axiom, (! [B:$tType,A:$tType,C:$tType,Xs2:(list @ A),Ys2:(list @ B),Zs:(list @ C),P2:((list @ A) > ((list @ B) > ((list @ C) > $o)))]: (((((size_size @ (list @ A)) @ Xs2) = ((size_size @ (list @ B)) @ Ys2)) => ((((size_size @ (list @ B)) @ Ys2) = ((size_size @ (list @ C)) @ Zs)) => ((((P2 @ (nil @ A)) @ (nil @ B)) @ (nil @ C)) => ((! [X4:A,Xs4:(list @ A),Y4:B,Ys4:(list @ B),Z2:C,Zs2:(list @ C)]: (((((size_size @ (list @ A)) @ Xs4) = ((size_size @ (list @ B)) @ Ys4)) => ((((size_size @ (list @ B)) @ Ys4) = ((size_size @ (list @ C)) @ Zs2)) => ((((P2 @ Xs4) @ Ys4) @ Zs2) => (((P2 @ (((cons @ A) @ X4) @ Xs4)) @ (((cons @ B) @ Y4) @ Ys4)) @ (((cons @ C) @ Z2) @ Zs2))))))) => (((P2 @ Xs2) @ Ys2) @ Zs)))))))).
% 2.92/1.57 thf(fact_86_list__induct2, axiom, (! [A:$tType,B:$tType,Xs2:(list @ A),Ys2:(list @ B),P2:((list @ A) > ((list @ B) > $o))]: (((((size_size @ (list @ A)) @ Xs2) = ((size_size @ (list @ B)) @ Ys2)) => (((P2 @ (nil @ A)) @ (nil @ B)) => ((! [X4:A,Xs4:(list @ A),Y4:B,Ys4:(list @ B)]: (((((size_size @ (list @ A)) @ Xs4) = ((size_size @ (list @ B)) @ Ys4)) => (((P2 @ Xs4) @ Ys4) => ((P2 @ (((cons @ A) @ X4) @ Xs4)) @ (((cons @ B) @ Y4) @ Ys4)))))) => ((P2 @ Xs2) @ Ys2))))))).
% 2.92/1.57 thf(fact_87_transpose_Ocases, axiom, (! [A:$tType,X3:(list @ (list @ A))]: (((X3 != (nil @ (list @ A))) => ((! [Xss:(list @ (list @ A))]: ((X3 != (((cons @ (list @ A)) @ (nil @ A)) @ Xss)))) => (~ ((! [X4:A,Xs4:(list @ A),Xss:(list @ (list @ A))]: ((X3 != (((cons @ (list @ A)) @ (((cons @ A) @ X4) @ Xs4)) @ Xss))))))))))).
% 2.92/1.57 thf(fact_88_neq__if__length__neq, axiom, (! [A:$tType,Xs2:(list @ A),Ys2:(list @ A)]: (((((size_size @ (list @ A)) @ Xs2) != ((size_size @ (list @ A)) @ Ys2)) => (Xs2 != Ys2))))).
% 2.92/1.57 thf(fact_89_Ex__list__of__length, axiom, (! [A:$tType,N:nat]: ((? [Xs4:(list @ A)]: ((((size_size @ (list @ A)) @ Xs4) = N)))))).
% 2.92/1.57 thf(fact_90_irrefl__lex, axiom, (! [A:$tType,R:(set @ ((product_prod @ A) @ A))]: ((((irrefl @ A) @ R) => ((irrefl @ (list @ A)) @ ((lex @ A) @ R)))))).
% 2.92/1.57 thf(fact_91_asym__lex, axiom, (! [A:$tType,R2:(set @ ((product_prod @ A) @ A))]: ((((asym @ A) @ R2) => ((asym @ (list @ A)) @ ((lex @ A) @ R2)))))).
% 2.92/1.57 thf(fact_92_lexl__not__refl, axiom, (! [A:$tType,R:(set @ ((product_prod @ A) @ A)),X3:(list @ A)]: ((((irrefl @ A) @ R) => (~ ((((member2 @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ X3) @ X3)) @ ((lex @ A) @ R)))))))).
% 2.92/1.57 thf(fact_93_lexord__irrefl, axiom, (! [A:$tType,R2:(set @ ((product_prod @ A) @ A))]: ((((irrefl @ A) @ R2) => ((irrefl @ (list @ A)) @ ((lexord @ A) @ R2)))))).
% 2.92/1.57 thf(fact_94_lexord__asym, axiom, (! [A:$tType,R2:(set @ ((product_prod @ A) @ A))]: ((((asym @ A) @ R2) => ((asym @ (list @ A)) @ ((lexord @ A) @ R2)))))).
% 2.92/1.57 thf(fact_95_set__zip__rightD, axiom, (! [A:$tType,B:$tType,X3:A,Y3:B,Xs2:(list @ A),Ys2:(list @ B)]: (((((member2 @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X3) @ Y3)) @ ((set2 @ ((product_prod @ A) @ B)) @ ((((zip @ A) @ B) @ Xs2) @ Ys2))) => (((member2 @ B) @ Y3) @ ((set2 @ B) @ Ys2)))))).
% 2.92/1.57 thf(fact_96_set__zip__leftD, axiom, (! [B:$tType,A:$tType,X3:A,Y3:B,Xs2:(list @ A),Ys2:(list @ B)]: (((((member2 @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X3) @ Y3)) @ ((set2 @ ((product_prod @ A) @ B)) @ ((((zip @ A) @ B) @ Xs2) @ Ys2))) => (((member2 @ A) @ X3) @ ((set2 @ A) @ Xs2)))))).
% 2.92/1.57 thf(fact_97_in__set__zipE, axiom, (! [A:$tType,B:$tType,X3:A,Y3:B,Xs2:(list @ A),Ys2:(list @ B)]: (((((member2 @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X3) @ Y3)) @ ((set2 @ ((product_prod @ A) @ B)) @ ((((zip @ A) @ B) @ Xs2) @ Ys2))) => (~ (((((member2 @ A) @ X3) @ ((set2 @ A) @ Xs2)) => (~ ((((member2 @ B) @ Y3) @ ((set2 @ B) @ Ys2))))))))))).
% 2.92/1.57 thf(fact_98_zip__same, axiom, (! [A:$tType,A2:A,B2:A,Xs2:(list @ A)]: (((((member2 @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A2) @ B2)) @ ((set2 @ ((product_prod @ A) @ A)) @ ((((zip @ A) @ A) @ Xs2) @ Xs2))) = ((((member2 @ A) @ A2) @ ((set2 @ A) @ Xs2)) & (A2 = B2)))))).
% 2.92/1.57 thf(fact_99_same__length__different, axiom, (! [A:$tType,Xs2:(list @ A),Ys2:(list @ A)]: (((Xs2 != Ys2) => ((((size_size @ (list @ A)) @ Xs2) = ((size_size @ (list @ A)) @ Ys2)) => (? [Pre:(list @ A),X4:A,Xs3:(list @ A),Y4:A,Ys3:(list @ A)]: (((X4 != Y4) & ((Xs2 = (((append @ A) @ Pre) @ (((append @ A) @ (((cons @ A) @ X4) @ (nil @ A))) @ Xs3))) & (Ys2 = (((append @ A) @ Pre) @ (((append @ A) @ (((cons @ A) @ Y4) @ (nil @ A))) @ Ys3)))))))))))).
% 2.92/1.57 thf(fact_100_list_Oset__cases, axiom, (! [A:$tType,E3:A,A2:(list @ A)]: (((((member2 @ A) @ E3) @ ((set2 @ A) @ A2)) => ((! [Z22:(list @ A)]: ((A2 != (((cons @ A) @ E3) @ Z22)))) => (~ ((! [Z1:A,Z22:(list @ A)]: (((A2 = (((cons @ A) @ Z1) @ Z22)) => (~ ((((member2 @ A) @ E3) @ ((set2 @ A) @ Z22)))))))))))))).
% 2.92/1.57 thf(fact_101_set__ConsD, axiom, (! [A:$tType,Y3:A,X3:A,Xs2:(list @ A)]: (((((member2 @ A) @ Y3) @ ((set2 @ A) @ (((cons @ A) @ X3) @ Xs2))) => ((Y3 = X3) | (((member2 @ A) @ Y3) @ ((set2 @ A) @ Xs2))))))).
% 2.92/1.57 thf(fact_102_list_Oset__intros_I1_J, axiom, (! [A:$tType,X21:A,X22:(list @ A)]: ((((member2 @ A) @ X21) @ ((set2 @ A) @ (((cons @ A) @ X21) @ X22)))))).
% 2.92/1.57 thf(fact_103_list_Oset__intros_I2_J, axiom, (! [A:$tType,Y3:A,X22:(list @ A),X21:A]: (((((member2 @ A) @ Y3) @ ((set2 @ A) @ X22)) => (((member2 @ A) @ Y3) @ ((set2 @ A) @ (((cons @ A) @ X21) @ X22))))))).
% 2.92/1.57 thf(fact_104_lex__append__rightI, axiom, (! [A:$tType,Xs2:(list @ A),Ys2:(list @ A),R:(set @ ((product_prod @ A) @ A)),Vs:(list @ A),Us:(list @ A)]: (((((member2 @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Xs2) @ Ys2)) @ ((lex @ A) @ R)) => ((((size_size @ (list @ A)) @ Vs) = ((size_size @ (list @ A)) @ Us)) => (((member2 @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((append @ A) @ Xs2) @ Us)) @ (((append @ A) @ Ys2) @ Vs))) @ ((lex @ A) @ R))))))).
% 2.92/1.57 thf(fact_105_sorted__wrt_Ocases, axiom, (! [A:$tType,X3:((product_prod @ (A > (A > $o))) @ (list @ A))]: (((! [P4:(A > (A > $o))]: ((X3 != ((((product_Pair @ (A > (A > $o))) @ (list @ A)) @ P4) @ (nil @ A))))) => (~ ((! [P4:(A > (A > $o)),X4:A,Ys4:(list @ A)]: ((X3 != ((((product_Pair @ (A > (A > $o))) @ (list @ A)) @ P4) @ (((cons @ A) @ X4) @ Ys4))))))))))).
% 2.92/1.57 thf(fact_106_arg__min__list_Ocases, axiom, (! [B:$tType,A:$tType]: (((linorder @ B) => (! [X3:((product_prod @ (A > B)) @ (list @ A))]: (((! [F2:(A > B),X4:A]: ((X3 != ((((product_Pair @ (A > B)) @ (list @ A)) @ F2) @ (((cons @ A) @ X4) @ (nil @ A)))))) => ((! [F2:(A > B),X4:A,Y4:A,Zs2:(list @ A)]: ((X3 != ((((product_Pair @ (A > B)) @ (list @ A)) @ F2) @ (((cons @ A) @ X4) @ (((cons @ A) @ Y4) @ Zs2)))))) => (~ ((! [A4:(A > B)]: ((X3 != ((((product_Pair @ (A > B)) @ (list @ A)) @ A4) @ (nil @ A))))))))))))))).
% 2.92/1.57 thf(fact_107_successively_Ocases, axiom, (! [A:$tType,X3:((product_prod @ (A > (A > $o))) @ (list @ A))]: (((! [P4:(A > (A > $o))]: ((X3 != ((((product_Pair @ (A > (A > $o))) @ (list @ A)) @ P4) @ (nil @ A))))) => ((! [P4:(A > (A > $o)),X4:A]: ((X3 != ((((product_Pair @ (A > (A > $o))) @ (list @ A)) @ P4) @ (((cons @ A) @ X4) @ (nil @ A)))))) => (~ ((! [P4:(A > (A > $o)),X4:A,Y4:A,Xs4:(list @ A)]: ((X3 != ((((product_Pair @ (A > (A > $o))) @ (list @ A)) @ P4) @ (((cons @ A) @ X4) @ (((cons @ A) @ Y4) @ Xs4))))))))))))).
% 2.92/1.57 thf(fact_108_strict__sorted_Oinduct, axiom, (! [A:$tType]: (((linorder @ A) => (! [P2:((list @ A) > $o),A0:(list @ A)]: (((P2 @ (nil @ A)) => ((! [X4:A,Ys4:(list @ A)]: (((P2 @ Ys4) => (P2 @ (((cons @ A) @ X4) @ Ys4))))) => (P2 @ A0))))))))).
% 2.92/1.57 thf(fact_109_strict__sorted_Ocases, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:(list @ A)]: (((X3 != (nil @ A)) => (~ ((! [X4:A,Ys4:(list @ A)]: ((X3 != (((cons @ A) @ X4) @ Ys4))))))))))))).
% 2.92/1.57 thf(fact_110_map__tailrec__rev_Oinduct, axiom, (! [A:$tType,B:$tType,P2:((A > B) > ((list @ A) > ((list @ B) > $o))),A0:(A > B),A1:(list @ A),A22:(list @ B)]: (((! [F2:(A > B),X_1:(list @ B)]: ((((P2 @ F2) @ (nil @ A)) @ X_1))) => ((! [F2:(A > B),A4:A,As:(list @ A),Bs:(list @ B)]: (((((P2 @ F2) @ As) @ (((cons @ B) @ (F2 @ A4)) @ Bs)) => (((P2 @ F2) @ (((cons @ A) @ A4) @ As)) @ Bs)))) => (((P2 @ A0) @ A1) @ A22)))))).
% 2.92/1.57 thf(fact_111_list__nonempty__induct, axiom, (! [A:$tType,Xs2:(list @ A),P2:((list @ A) > $o)]: (((Xs2 != (nil @ A)) => ((! [X4:A]: ((P2 @ (((cons @ A) @ X4) @ (nil @ A))))) => ((! [X4:A,Xs4:(list @ A)]: (((Xs4 != (nil @ A)) => ((P2 @ Xs4) => (P2 @ (((cons @ A) @ X4) @ Xs4)))))) => (P2 @ Xs2))))))).
% 2.92/1.57 thf(fact_112_successively_Oinduct, axiom, (! [A:$tType,P2:((A > (A > $o)) > ((list @ A) > $o)),A0:(A > (A > $o)),A1:(list @ A)]: (((! [P4:(A > (A > $o))]: (((P2 @ P4) @ (nil @ A)))) => ((! [P4:(A > (A > $o)),X4:A]: (((P2 @ P4) @ (((cons @ A) @ X4) @ (nil @ A))))) => ((! [P4:(A > (A > $o)),X4:A,Y4:A,Xs4:(list @ A)]: ((((P2 @ P4) @ (((cons @ A) @ Y4) @ Xs4)) => ((P2 @ P4) @ (((cons @ A) @ X4) @ (((cons @ A) @ Y4) @ Xs4)))))) => ((P2 @ A0) @ A1))))))).
% 2.92/1.57 thf(fact_113_arg__min__list_Oinduct, axiom, (! [B:$tType,A:$tType]: (((linorder @ B) => (! [P2:((A > B) > ((list @ A) > $o)),A0:(A > B),A1:(list @ A)]: (((! [F2:(A > B),X4:A]: (((P2 @ F2) @ (((cons @ A) @ X4) @ (nil @ A))))) => ((! [F2:(A > B),X4:A,Y4:A,Zs2:(list @ A)]: ((((P2 @ F2) @ (((cons @ A) @ Y4) @ Zs2)) => ((P2 @ F2) @ (((cons @ A) @ X4) @ (((cons @ A) @ Y4) @ Zs2)))))) => ((! [A4:(A > B)]: (((P2 @ A4) @ (nil @ A)))) => ((P2 @ A0) @ A1)))))))))).
% 2.92/1.57 thf(fact_114_remdups__adj_Oinduct, axiom, (! [A:$tType,P2:((list @ A) > $o),A0:(list @ A)]: (((P2 @ (nil @ A)) => ((! [X4:A]: ((P2 @ (((cons @ A) @ X4) @ (nil @ A))))) => ((! [X4:A,Y4:A,Xs4:(list @ A)]: ((((X4 = Y4) => (P2 @ (((cons @ A) @ X4) @ Xs4))) => (((X4 != Y4) => (P2 @ (((cons @ A) @ Y4) @ Xs4))) => (P2 @ (((cons @ A) @ X4) @ (((cons @ A) @ Y4) @ Xs4))))))) => (P2 @ A0))))))).
% 2.92/1.57 thf(fact_115_sorted__wrt_Oinduct, axiom, (! [A:$tType,P2:((A > (A > $o)) > ((list @ A) > $o)),A0:(A > (A > $o)),A1:(list @ A)]: (((! [P4:(A > (A > $o))]: (((P2 @ P4) @ (nil @ A)))) => ((! [P4:(A > (A > $o)),X4:A,Ys4:(list @ A)]: ((((P2 @ P4) @ Ys4) => ((P2 @ P4) @ (((cons @ A) @ X4) @ Ys4))))) => ((P2 @ A0) @ A1)))))).
% 2.92/1.57 thf(fact_116_remdups__adj_Ocases, axiom, (! [A:$tType,X3:(list @ A)]: (((X3 != (nil @ A)) => ((! [X4:A]: ((X3 != (((cons @ A) @ X4) @ (nil @ A))))) => (~ ((! [X4:A,Y4:A,Xs4:(list @ A)]: ((X3 != (((cons @ A) @ X4) @ (((cons @ A) @ Y4) @ Xs4)))))))))))).
% 2.92/1.57 thf(fact_117_shuffles_Oinduct, axiom, (! [A:$tType,P2:((list @ A) > ((list @ A) > $o)),A0:(list @ A),A1:(list @ A)]: (((! [X_1:(list @ A)]: (((P2 @ (nil @ A)) @ X_1))) => ((! [Xs4:(list @ A)]: (((P2 @ Xs4) @ (nil @ A)))) => ((! [X4:A,Xs4:(list @ A),Y4:A,Ys4:(list @ A)]: ((((P2 @ Xs4) @ (((cons @ A) @ Y4) @ Ys4)) => (((P2 @ (((cons @ A) @ X4) @ Xs4)) @ Ys4) => ((P2 @ (((cons @ A) @ X4) @ Xs4)) @ (((cons @ A) @ Y4) @ Ys4)))))) => ((P2 @ A0) @ A1))))))).
% 2.92/1.57 thf(fact_118_min__list_Oinduct, axiom, (! [A:$tType]: (((ord @ A) => (! [P2:((list @ A) > $o),A0:(list @ A)]: (((! [X4:A,Xs4:(list @ A)]: (((! [X212:A,X222:(list @ A)]: (((Xs4 = (((cons @ A) @ X212) @ X222)) => (P2 @ Xs4)))) => (P2 @ (((cons @ A) @ X4) @ Xs4))))) => ((P2 @ (nil @ A)) => (P2 @ A0))))))))).
% 2.92/1.57 thf(fact_119_min__list_Ocases, axiom, (! [A:$tType]: (((ord @ A) => (! [X3:(list @ A)]: (((! [X4:A,Xs4:(list @ A)]: ((X3 != (((cons @ A) @ X4) @ Xs4)))) => (X3 = (nil @ A))))))))).
% 2.92/1.57 thf(fact_120_induct__list012, axiom, (! [A:$tType,P2:((list @ A) > $o),Xs2:(list @ A)]: (((P2 @ (nil @ A)) => ((! [X4:A]: ((P2 @ (((cons @ A) @ X4) @ (nil @ A))))) => ((! [X4:A,Y4:A,Zs2:(list @ A)]: (((P2 @ Zs2) => ((P2 @ (((cons @ A) @ Y4) @ Zs2)) => (P2 @ (((cons @ A) @ X4) @ (((cons @ A) @ Y4) @ Zs2))))))) => (P2 @ Xs2))))))).
% 2.92/1.57 thf(fact_121_splice_Oinduct, axiom, (! [A:$tType,P2:((list @ A) > ((list @ A) > $o)),A0:(list @ A),A1:(list @ A)]: (((! [X_1:(list @ A)]: (((P2 @ (nil @ A)) @ X_1))) => ((! [X4:A,Xs4:(list @ A),Ys4:(list @ A)]: ((((P2 @ Ys4) @ Xs4) => ((P2 @ (((cons @ A) @ X4) @ Xs4)) @ Ys4)))) => ((P2 @ A0) @ A1)))))).
% 2.92/1.57 thf(fact_122_list__induct2_H, axiom, (! [A:$tType,B:$tType,P2:((list @ A) > ((list @ B) > $o)),Xs2:(list @ A),Ys2:(list @ B)]: ((((P2 @ (nil @ A)) @ (nil @ B)) => ((! [X4:A,Xs4:(list @ A)]: (((P2 @ (((cons @ A) @ X4) @ Xs4)) @ (nil @ B)))) => ((! [Y4:B,Ys4:(list @ B)]: (((P2 @ (nil @ A)) @ (((cons @ B) @ Y4) @ Ys4)))) => ((! [X4:A,Xs4:(list @ A),Y4:B,Ys4:(list @ B)]: ((((P2 @ Xs4) @ Ys4) => ((P2 @ (((cons @ A) @ X4) @ Xs4)) @ (((cons @ B) @ Y4) @ Ys4))))) => ((P2 @ Xs2) @ Ys2)))))))).
% 2.92/1.57 thf(fact_123_neq__Nil__conv, axiom, (! [A:$tType,Xs2:(list @ A)]: (((Xs2 != (nil @ A)) = (? [Y:A,Ys:(list @ A)]: ((Xs2 = (((cons @ A) @ Y) @ Ys)))))))).
% 2.92/1.57 thf(fact_124_list_Oinducts, axiom, (! [A:$tType,P2:((list @ A) > $o),List:(list @ A)]: (((P2 @ (nil @ A)) => ((! [X12:A,X23:(list @ A)]: (((P2 @ X23) => (P2 @ (((cons @ A) @ X12) @ X23))))) => (P2 @ List)))))).
% 2.92/1.57 thf(fact_125_list_Oexhaust, axiom, (! [A:$tType,Y3:(list @ A)]: (((Y3 != (nil @ A)) => (~ ((! [X213:A,X223:(list @ A)]: ((Y3 != (((cons @ A) @ X213) @ X223)))))))))).
% 2.92/1.57 thf(fact_126_list_OdiscI, axiom, (! [A:$tType,List:(list @ A),X21:A,X22:(list @ A)]: (((List = (((cons @ A) @ X21) @ X22)) => (List != (nil @ A)))))).
% 2.92/1.57 thf(fact_127_list_Odistinct_I1_J, axiom, (! [A:$tType,X21:A,X22:(list @ A)]: (((nil @ A) != (((cons @ A) @ X21) @ X22))))).
% 2.92/1.57 thf(fact_128_append_Oleft__neutral, axiom, (! [A:$tType,A2:(list @ A)]: (((((append @ A) @ (nil @ A)) @ A2) = A2)))).
% 2.92/1.57 thf(fact_129_append__Nil, axiom, (! [A:$tType,Ys2:(list @ A)]: (((((append @ A) @ (nil @ A)) @ Ys2) = Ys2)))).
% 2.92/1.57 thf(fact_130_eq__Nil__appendI, axiom, (! [A:$tType,Xs2:(list @ A),Ys2:(list @ A)]: (((Xs2 = Ys2) => (Xs2 = (((append @ A) @ (nil @ A)) @ Ys2)))))).
% 2.92/1.57 thf(fact_131_lexord__lex, axiom, (! [A:$tType,X3:(list @ A),Y3:(list @ A),R:(set @ ((product_prod @ A) @ A))]: (((((member2 @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ X3) @ Y3)) @ ((lex @ A) @ R)) = ((((member2 @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ X3) @ Y3)) @ ((lexord @ A) @ R)) & (((size_size @ (list @ A)) @ X3) = ((size_size @ (list @ A)) @ Y3))))))).
% 2.92/1.57 thf(fact_132_pcas_Ocases, axiom, (! [A:$tType,X3:((product_prod @ A) @ ((product_prod @ (list @ ((product_prod @ A) @ A))) @ A))]: (((! [U2:A,V:A]: ((X3 != ((((product_Pair @ A) @ ((product_prod @ (list @ ((product_prod @ A) @ A))) @ A)) @ U2) @ ((((product_Pair @ (list @ ((product_prod @ A) @ A))) @ A) @ (nil @ ((product_prod @ A) @ A))) @ V))))) => (~ ((! [U2:A,E2:((product_prod @ A) @ A),Es:(list @ ((product_prod @ A) @ A)),V:A]: ((X3 != ((((product_Pair @ A) @ ((product_prod @ (list @ ((product_prod @ A) @ A))) @ A)) @ U2) @ ((((product_Pair @ (list @ ((product_prod @ A) @ A))) @ A) @ (((cons @ ((product_prod @ A) @ A)) @ E2) @ Es)) @ V))))))))))).
% 2.92/1.57 thf(fact_133_list__bind__cong, axiom, (! [B:$tType,A:$tType,Xs2:(list @ A),Ys2:(list @ A),F3:(A > (list @ B)),G4:(A > (list @ B))]: (((Xs2 = Ys2) => ((! [X4:A]: (((((member2 @ A) @ X4) @ ((set2 @ A) @ Xs2)) => ((F3 @ X4) = (G4 @ X4))))) => (((((bind @ A) @ B) @ Xs2) @ F3) = ((((bind @ A) @ B) @ Ys2) @ G4))))))).
% 2.92/1.57 thf(fact_134_in__set__member, axiom, (! [A:$tType,X3:A,Xs2:(list @ A)]: (((((member2 @ A) @ X3) @ ((set2 @ A) @ Xs2)) = (((member @ A) @ Xs2) @ X3))))).
% 2.92/1.57 thf(fact_135_maps__simps_I2_J, axiom, (! [B:$tType,A:$tType,F3:(B > (list @ A))]: ((((((maps @ B) @ A) @ F3) @ (nil @ B)) = (nil @ A))))).
% 2.92/1.57 thf(fact_136_member__rec_I2_J, axiom, (! [A:$tType,Y3:A]: ((~ ((((member @ A) @ (nil @ A)) @ Y3)))))).
% 2.92/1.57 thf(fact_137_progressing__Nil, axiom, (! [A:$tType]: (((kurato990191779essing @ A) @ (nil @ ((product_prod @ A) @ A)))))).
% 2.92/1.57 thf(fact_138_split__list__first__prop__iff, axiom, (! [A:$tType,Xs2:(list @ A),P2:(A > $o)]: (((? [X:A]: (((((member2 @ A) @ X) @ ((set2 @ A) @ Xs2)) & (P2 @ X)))) = (? [Ys:(list @ A),X:A]: (((? [Zs3:(list @ A)]: ((Xs2 = (((append @ A) @ Ys) @ (((cons @ A) @ X) @ Zs3))))) & ((P2 @ X) & (! [Y:A]: (((((member2 @ A) @ Y) @ ((set2 @ A) @ Ys)) => (~ ((P2 @ Y)))))))))))))).
% 2.92/1.57 thf(fact_139_split__list__last__prop__iff, axiom, (! [A:$tType,Xs2:(list @ A),P2:(A > $o)]: (((? [X:A]: (((((member2 @ A) @ X) @ ((set2 @ A) @ Xs2)) & (P2 @ X)))) = (? [Ys:(list @ A),X:A,Zs3:(list @ A)]: (((Xs2 = (((append @ A) @ Ys) @ (((cons @ A) @ X) @ Zs3))) & ((P2 @ X) & (! [Y:A]: (((((member2 @ A) @ Y) @ ((set2 @ A) @ Zs3)) => (~ ((P2 @ Y)))))))))))))).
% 2.92/1.57 thf(fact_140_in__set__conv__decomp__first, axiom, (! [A:$tType,X3:A,Xs2:(list @ A)]: (((((member2 @ A) @ X3) @ ((set2 @ A) @ Xs2)) = (? [Ys:(list @ A),Zs3:(list @ A)]: (((Xs2 = (((append @ A) @ Ys) @ (((cons @ A) @ X3) @ Zs3))) & (~ ((((member2 @ A) @ X3) @ ((set2 @ A) @ Ys))))))))))).
% 2.92/1.57 thf(fact_141_in__set__conv__decomp__last, axiom, (! [A:$tType,X3:A,Xs2:(list @ A)]: (((((member2 @ A) @ X3) @ ((set2 @ A) @ Xs2)) = (? [Ys:(list @ A),Zs3:(list @ A)]: (((Xs2 = (((append @ A) @ Ys) @ (((cons @ A) @ X3) @ Zs3))) & (~ ((((member2 @ A) @ X3) @ ((set2 @ A) @ Zs3))))))))))).
% 2.92/1.57 thf(fact_142_split__list__first__propE, axiom, (! [A:$tType,Xs2:(list @ A),P2:(A > $o)]: (((? [X5:A]: (((((member2 @ A) @ X5) @ ((set2 @ A) @ Xs2)) & (P2 @ X5)))) => (~ ((! [Ys4:(list @ A),X4:A]: (((? [Zs2:(list @ A)]: ((Xs2 = (((append @ A) @ Ys4) @ (((cons @ A) @ X4) @ Zs2))))) => ((P2 @ X4) => (~ ((! [Xa:A]: (((((member2 @ A) @ Xa) @ ((set2 @ A) @ Ys4)) => (~ ((P2 @ Xa)))))))))))))))))).
% 2.92/1.57 thf(fact_143_split__list__last__propE, axiom, (! [A:$tType,Xs2:(list @ A),P2:(A > $o)]: (((? [X5:A]: (((((member2 @ A) @ X5) @ ((set2 @ A) @ Xs2)) & (P2 @ X5)))) => (~ ((! [Ys4:(list @ A),X4:A,Zs2:(list @ A)]: (((Xs2 = (((append @ A) @ Ys4) @ (((cons @ A) @ X4) @ Zs2))) => ((P2 @ X4) => (~ ((! [Xa:A]: (((((member2 @ A) @ Xa) @ ((set2 @ A) @ Zs2)) => (~ ((P2 @ Xa)))))))))))))))))).
% 2.92/1.57 thf(fact_144_split__list__first__prop, axiom, (! [A:$tType,Xs2:(list @ A),P2:(A > $o)]: (((? [X5:A]: (((((member2 @ A) @ X5) @ ((set2 @ A) @ Xs2)) & (P2 @ X5)))) => (? [Ys4:(list @ A),X4:A]: (((? [Zs2:(list @ A)]: ((Xs2 = (((append @ A) @ Ys4) @ (((cons @ A) @ X4) @ Zs2))))) & ((P2 @ X4) & (! [Xa:A]: (((((member2 @ A) @ Xa) @ ((set2 @ A) @ Ys4)) => (~ ((P2 @ Xa)))))))))))))).
% 2.92/1.57 thf(fact_145_split__list__last__prop, axiom, (! [A:$tType,Xs2:(list @ A),P2:(A > $o)]: (((? [X5:A]: (((((member2 @ A) @ X5) @ ((set2 @ A) @ Xs2)) & (P2 @ X5)))) => (? [Ys4:(list @ A),X4:A,Zs2:(list @ A)]: (((Xs2 = (((append @ A) @ Ys4) @ (((cons @ A) @ X4) @ Zs2))) & ((P2 @ X4) & (! [Xa:A]: (((((member2 @ A) @ Xa) @ ((set2 @ A) @ Zs2)) => (~ ((P2 @ Xa)))))))))))))).
% 2.92/1.57 thf(fact_146_in__set__conv__decomp, axiom, (! [A:$tType,X3:A,Xs2:(list @ A)]: (((((member2 @ A) @ X3) @ ((set2 @ A) @ Xs2)) = (? [Ys:(list @ A),Zs3:(list @ A)]: ((Xs2 = (((append @ A) @ Ys) @ (((cons @ A) @ X3) @ Zs3))))))))).
% 2.92/1.57 thf(fact_147_append__Cons__eq__iff, axiom, (! [A:$tType,X3:A,Xs2:(list @ A),Ys2:(list @ A),Xs5:(list @ A),Ys5:(list @ A)]: (((~ ((((member2 @ A) @ X3) @ ((set2 @ A) @ Xs2)))) => ((~ ((((member2 @ A) @ X3) @ ((set2 @ A) @ Ys2)))) => (((((append @ A) @ Xs2) @ (((cons @ A) @ X3) @ Ys2)) = (((append @ A) @ Xs5) @ (((cons @ A) @ X3) @ Ys5))) = ((Xs2 = Xs5) & (Ys2 = Ys5)))))))).
% 2.92/1.57 thf(fact_148_split__list__propE, axiom, (! [A:$tType,Xs2:(list @ A),P2:(A > $o)]: (((? [X5:A]: (((((member2 @ A) @ X5) @ ((set2 @ A) @ Xs2)) & (P2 @ X5)))) => (~ ((! [Ys4:(list @ A),X4:A]: (((? [Zs2:(list @ A)]: ((Xs2 = (((append @ A) @ Ys4) @ (((cons @ A) @ X4) @ Zs2))))) => (~ ((P2 @ X4)))))))))))).
% 2.92/1.57 thf(fact_149_split__list__first, axiom, (! [A:$tType,X3:A,Xs2:(list @ A)]: (((((member2 @ A) @ X3) @ ((set2 @ A) @ Xs2)) => (? [Ys4:(list @ A),Zs2:(list @ A)]: (((Xs2 = (((append @ A) @ Ys4) @ (((cons @ A) @ X3) @ Zs2))) & (~ ((((member2 @ A) @ X3) @ ((set2 @ A) @ Ys4))))))))))).
% 2.92/1.57 thf(fact_150_split__list__prop, axiom, (! [A:$tType,Xs2:(list @ A),P2:(A > $o)]: (((? [X5:A]: (((((member2 @ A) @ X5) @ ((set2 @ A) @ Xs2)) & (P2 @ X5)))) => (? [Ys4:(list @ A),X4:A]: (((? [Zs2:(list @ A)]: ((Xs2 = (((append @ A) @ Ys4) @ (((cons @ A) @ X4) @ Zs2))))) & (P2 @ X4)))))))).
% 2.92/1.57 thf(fact_151_split__list__last, axiom, (! [A:$tType,X3:A,Xs2:(list @ A)]: (((((member2 @ A) @ X3) @ ((set2 @ A) @ Xs2)) => (? [Ys4:(list @ A),Zs2:(list @ A)]: (((Xs2 = (((append @ A) @ Ys4) @ (((cons @ A) @ X3) @ Zs2))) & (~ ((((member2 @ A) @ X3) @ ((set2 @ A) @ Zs2))))))))))).
% 2.92/1.57 thf(fact_152_split__list, axiom, (! [A:$tType,X3:A,Xs2:(list @ A)]: (((((member2 @ A) @ X3) @ ((set2 @ A) @ Xs2)) => (? [Ys4:(list @ A),Zs2:(list @ A)]: ((Xs2 = (((append @ A) @ Ys4) @ (((cons @ A) @ X3) @ Zs2))))))))).
% 2.92/1.57 thf(fact_153_rev__nonempty__induct, axiom, (! [A:$tType,Xs2:(list @ A),P2:((list @ A) > $o)]: (((Xs2 != (nil @ A)) => ((! [X4:A]: ((P2 @ (((cons @ A) @ X4) @ (nil @ A))))) => ((! [X4:A,Xs4:(list @ A)]: (((Xs4 != (nil @ A)) => ((P2 @ Xs4) => (P2 @ (((append @ A) @ Xs4) @ (((cons @ A) @ X4) @ (nil @ A)))))))) => (P2 @ Xs2))))))).
% 2.92/1.57 thf(fact_154_append__eq__Cons__conv, axiom, (! [A:$tType,Ys2:(list @ A),Zs:(list @ A),X3:A,Xs2:(list @ A)]: ((((((append @ A) @ Ys2) @ Zs) = (((cons @ A) @ X3) @ Xs2)) = (((Ys2 = (nil @ A)) & (Zs = (((cons @ A) @ X3) @ Xs2))) | (? [Ys6:(list @ A)]: (((Ys2 = (((cons @ A) @ X3) @ Ys6)) & ((((append @ A) @ Ys6) @ Zs) = Xs2))))))))).
% 2.92/1.57 thf(fact_155_Cons__eq__append__conv, axiom, (! [A:$tType,X3:A,Xs2:(list @ A),Ys2:(list @ A),Zs:(list @ A)]: ((((((cons @ A) @ X3) @ Xs2) = (((append @ A) @ Ys2) @ Zs)) = (((Ys2 = (nil @ A)) & ((((cons @ A) @ X3) @ Xs2) = Zs)) | (? [Ys6:(list @ A)]: ((((((cons @ A) @ X3) @ Ys6) = Ys2) & (Xs2 = (((append @ A) @ Ys6) @ Zs)))))))))).
% 2.92/1.57 thf(fact_156_rev__exhaust, axiom, (! [A:$tType,Xs2:(list @ A)]: (((Xs2 != (nil @ A)) => (~ ((! [Ys4:(list @ A),Y4:A]: ((Xs2 != (((append @ A) @ Ys4) @ (((cons @ A) @ Y4) @ (nil @ A)))))))))))).
% 2.92/1.57 thf(fact_157_rev__induct, axiom, (! [A:$tType,P2:((list @ A) > $o),Xs2:(list @ A)]: (((P2 @ (nil @ A)) => ((! [X4:A,Xs4:(list @ A)]: (((P2 @ Xs4) => (P2 @ (((append @ A) @ Xs4) @ (((cons @ A) @ X4) @ (nil @ A))))))) => (P2 @ Xs2)))))).
% 2.92/1.57 thf(fact_158_shuffles_Ocases, axiom, (! [A:$tType,X3:((product_prod @ (list @ A)) @ (list @ A))]: (((! [Ys4:(list @ A)]: ((X3 != ((((product_Pair @ (list @ A)) @ (list @ A)) @ (nil @ A)) @ Ys4)))) => ((! [Xs4:(list @ A)]: ((X3 != ((((product_Pair @ (list @ A)) @ (list @ A)) @ Xs4) @ (nil @ A))))) => (~ ((! [X4:A,Xs4:(list @ A),Y4:A,Ys4:(list @ A)]: ((X3 != ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((cons @ A) @ X4) @ Xs4)) @ (((cons @ A) @ Y4) @ Ys4)))))))))))).
% 2.92/1.57 thf(fact_159_map__tailrec__rev_Ocases, axiom, (! [A:$tType,B:$tType,X3:((product_prod @ (A > B)) @ ((product_prod @ (list @ A)) @ (list @ B)))]: (((! [F2:(A > B),Bs:(list @ B)]: ((X3 != ((((product_Pair @ (A > B)) @ ((product_prod @ (list @ A)) @ (list @ B))) @ F2) @ ((((product_Pair @ (list @ A)) @ (list @ B)) @ (nil @ A)) @ Bs))))) => (~ ((! [F2:(A > B),A4:A,As:(list @ A),Bs:(list @ B)]: ((X3 != ((((product_Pair @ (A > B)) @ ((product_prod @ (list @ A)) @ (list @ B))) @ F2) @ ((((product_Pair @ (list @ A)) @ (list @ B)) @ (((cons @ A) @ A4) @ As)) @ Bs))))))))))).
% 2.92/1.57 thf(fact_160_sd__path_Oinduct, axiom, (! [A:$tType,P2:(((product_prod @ A) @ A) > (A > ((list @ ((product_prod @ A) @ A)) > $o))),A0:((product_prod @ A) @ A),A1:A,A22:(list @ ((product_prod @ A) @ A))]: (((! [Uu:((product_prod @ A) @ A),Uv:A]: ((((P2 @ Uu) @ Uv) @ (nil @ ((product_prod @ A) @ A))))) => ((! [U2:A,V:A,W:A,E2:((product_prod @ A) @ A),Es:(list @ ((product_prod @ A) @ A))]: (((((P2 @ ((((product_Pair @ A) @ A) @ U2) @ V)) @ W) @ Es) => (((P2 @ ((((product_Pair @ A) @ A) @ U2) @ V)) @ W) @ (((cons @ ((product_prod @ A) @ A)) @ E2) @ Es))))) => (((P2 @ A0) @ A1) @ A22)))))).
% 2.92/1.57 thf(fact_161_co__path_Oinduct, axiom, (! [A:$tType,P2:(((product_prod @ A) @ A) > (A > ((list @ ((product_prod @ A) @ A)) > $o))),A0:((product_prod @ A) @ A),A1:A,A22:(list @ ((product_prod @ A) @ A))]: (((! [Uu:((product_prod @ A) @ A),Uv:A]: ((((P2 @ Uu) @ Uv) @ (nil @ ((product_prod @ A) @ A))))) => ((! [Uw:((product_prod @ A) @ A),Ux:A,E2:((product_prod @ A) @ A)]: ((((P2 @ Uw) @ Ux) @ (((cons @ ((product_prod @ A) @ A)) @ E2) @ (nil @ ((product_prod @ A) @ A)))))) => ((! [U2:A,V:A,W:A,E1:((product_prod @ A) @ A),E22:((product_prod @ A) @ A),Es:(list @ ((product_prod @ A) @ A))]: (((((E1 = ((((product_Pair @ A) @ A) @ U2) @ W)) & (E22 = ((((product_Pair @ A) @ A) @ W) @ V))) => (((P2 @ ((((product_Pair @ A) @ A) @ U2) @ V)) @ W) @ Es)) => (((~ (((E1 = ((((product_Pair @ A) @ A) @ U2) @ W)) & (E22 = ((((product_Pair @ A) @ A) @ W) @ V))))) => (((E1 = ((((product_Pair @ A) @ A) @ V) @ W)) & (E22 = ((((product_Pair @ A) @ A) @ W) @ U2))) => (((P2 @ ((((product_Pair @ A) @ A) @ U2) @ V)) @ W) @ Es))) => (((~ (((E1 = ((((product_Pair @ A) @ A) @ U2) @ W)) & (E22 = ((((product_Pair @ A) @ A) @ W) @ V))))) => ((~ (((E1 = ((((product_Pair @ A) @ A) @ V) @ W)) & (E22 = ((((product_Pair @ A) @ A) @ W) @ U2))))) => (((P2 @ ((((product_Pair @ A) @ A) @ U2) @ V)) @ W) @ (((cons @ ((product_prod @ A) @ A)) @ E22) @ Es)))) => (((P2 @ ((((product_Pair @ A) @ A) @ U2) @ V)) @ W) @ (((cons @ ((product_prod @ A) @ A)) @ E1) @ (((cons @ ((product_prod @ A) @ A)) @ E22) @ Es)))))))) => (((P2 @ A0) @ A1) @ A22))))))).
% 2.92/1.57 thf(fact_162_sd__path_Ocases, axiom, (! [A:$tType,X3:((product_prod @ ((product_prod @ A) @ A)) @ ((product_prod @ A) @ (list @ ((product_prod @ A) @ A))))]: (((! [Uu:((product_prod @ A) @ A),Uv:A]: ((X3 != ((((product_Pair @ ((product_prod @ A) @ A)) @ ((product_prod @ A) @ (list @ ((product_prod @ A) @ A)))) @ Uu) @ ((((product_Pair @ A) @ (list @ ((product_prod @ A) @ A))) @ Uv) @ (nil @ ((product_prod @ A) @ A))))))) => (~ ((! [U2:A,V:A,W:A,E2:((product_prod @ A) @ A),Es:(list @ ((product_prod @ A) @ A))]: ((X3 != ((((product_Pair @ ((product_prod @ A) @ A)) @ ((product_prod @ A) @ (list @ ((product_prod @ A) @ A)))) @ ((((product_Pair @ A) @ A) @ U2) @ V)) @ ((((product_Pair @ A) @ (list @ ((product_prod @ A) @ A))) @ W) @ (((cons @ ((product_prod @ A) @ A)) @ E2) @ Es)))))))))))).
% 2.92/1.57 thf(fact_163_co__path_Ocases, axiom, (! [A:$tType,X3:((product_prod @ ((product_prod @ A) @ A)) @ ((product_prod @ A) @ (list @ ((product_prod @ A) @ A))))]: (((! [Uu:((product_prod @ A) @ A),Uv:A]: ((X3 != ((((product_Pair @ ((product_prod @ A) @ A)) @ ((product_prod @ A) @ (list @ ((product_prod @ A) @ A)))) @ Uu) @ ((((product_Pair @ A) @ (list @ ((product_prod @ A) @ A))) @ Uv) @ (nil @ ((product_prod @ A) @ A))))))) => ((! [Uw:((product_prod @ A) @ A),Ux:A,E2:((product_prod @ A) @ A)]: ((X3 != ((((product_Pair @ ((product_prod @ A) @ A)) @ ((product_prod @ A) @ (list @ ((product_prod @ A) @ A)))) @ Uw) @ ((((product_Pair @ A) @ (list @ ((product_prod @ A) @ A))) @ Ux) @ (((cons @ ((product_prod @ A) @ A)) @ E2) @ (nil @ ((product_prod @ A) @ A)))))))) => (~ ((! [U2:A,V:A,W:A,E1:((product_prod @ A) @ A),E22:((product_prod @ A) @ A),Es:(list @ ((product_prod @ A) @ A))]: ((X3 != ((((product_Pair @ ((product_prod @ A) @ A)) @ ((product_prod @ A) @ (list @ ((product_prod @ A) @ A)))) @ ((((product_Pair @ A) @ A) @ U2) @ V)) @ ((((product_Pair @ A) @ (list @ ((product_prod @ A) @ A))) @ W) @ (((cons @ ((product_prod @ A) @ A)) @ E1) @ (((cons @ ((product_prod @ A) @ A)) @ E22) @ Es)))))))))))))).
% 2.92/1.57 thf(fact_164_listrel1__eq__len, axiom, (! [A:$tType,Xs2:(list @ A),Ys2:(list @ A),R:(set @ ((product_prod @ A) @ A))]: (((((member2 @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Xs2) @ Ys2)) @ ((listrel1 @ A) @ R)) => (((size_size @ (list @ A)) @ Xs2) = ((size_size @ (list @ A)) @ Ys2)))))).
% 2.92/1.57 thf(fact_165_not__listrel1__Nil, axiom, (! [A:$tType,Xs2:(list @ A),R:(set @ ((product_prod @ A) @ A))]: ((~ ((((member2 @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Xs2) @ (nil @ A))) @ ((listrel1 @ A) @ R))))))).
% 2.92/1.57 thf(fact_166_not__Nil__listrel1, axiom, (! [A:$tType,Xs2:(list @ A),R:(set @ ((product_prod @ A) @ A))]: ((~ ((((member2 @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ (nil @ A)) @ Xs2)) @ ((listrel1 @ A) @ R))))))).
% 2.92/1.57 thf(fact_167_lexord__Nil__right, axiom, (! [A:$tType,X3:(list @ A),R:(set @ ((product_prod @ A) @ A))]: ((~ ((((member2 @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ X3) @ (nil @ A))) @ ((lexord @ A) @ R))))))).
% 2.92/1.57 thf(fact_168_lex__append__leftI, axiom, (! [A:$tType,Ys2:(list @ A),Zs:(list @ A),R:(set @ ((product_prod @ A) @ A)),Xs2:(list @ A)]: (((((member2 @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Ys2) @ Zs)) @ ((lex @ A) @ R)) => (((member2 @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((append @ A) @ Xs2) @ Ys2)) @ (((append @ A) @ Xs2) @ Zs))) @ ((lex @ A) @ R)))))).
% 2.92/1.57 thf(fact_169_progressing__single, axiom, (! [A:$tType,E3:((product_prod @ A) @ A)]: (((kurato990191779essing @ A) @ (((cons @ ((product_prod @ A) @ A)) @ E3) @ (nil @ ((product_prod @ A) @ A))))))).
% 2.92/1.57 thf(fact_170_lexord__partial__trans, axiom, (! [A:$tType,Xs2:(list @ A),R:(set @ ((product_prod @ A) @ A)),Ys2:(list @ A),Zs:(list @ A)]: (((! [X4:A,Y4:A,Z2:A]: (((((member2 @ A) @ X4) @ ((set2 @ A) @ Xs2)) => ((((member2 @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X4) @ Y4)) @ R) => ((((member2 @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Y4) @ Z2)) @ R) => (((member2 @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X4) @ Z2)) @ R)))))) => ((((member2 @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Xs2) @ Ys2)) @ ((lexord @ A) @ R)) => ((((member2 @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Ys2) @ Zs)) @ ((lexord @ A) @ R)) => (((member2 @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Xs2) @ Zs)) @ ((lexord @ A) @ R)))))))).
% 2.92/1.57 thf(fact_171_lexord__sufE, axiom, (! [A:$tType,Xs2:(list @ A),Zs:(list @ A),Ys2:(list @ A),Qs:(list @ A),R:(set @ ((product_prod @ A) @ A))]: (((((member2 @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((append @ A) @ Xs2) @ Zs)) @ (((append @ A) @ Ys2) @ Qs))) @ ((lexord @ A) @ R)) => ((Xs2 != Ys2) => ((((size_size @ (list @ A)) @ Xs2) = ((size_size @ (list @ A)) @ Ys2)) => ((((size_size @ (list @ A)) @ Zs) = ((size_size @ (list @ A)) @ Qs)) => (((member2 @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Xs2) @ Ys2)) @ ((lexord @ A) @ R))))))))).
% 2.92/1.57 thf(fact_172_subset__eq__mset__impl_Ocases, axiom, (! [A:$tType,X3:((product_prod @ (list @ A)) @ (list @ A))]: (((! [Ys4:(list @ A)]: ((X3 != ((((product_Pair @ (list @ A)) @ (list @ A)) @ (nil @ A)) @ Ys4)))) => (~ ((! [X4:A,Xs4:(list @ A),Ys4:(list @ A)]: ((X3 != ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((cons @ A) @ X4) @ Xs4)) @ Ys4)))))))))).
% 2.92/1.57 thf(fact_173_pre__digraph_Ocas_Ocases, axiom, (! [B:$tType,A:$tType,X3:((product_prod @ A) @ ((product_prod @ (list @ B)) @ A))]: (((! [U2:A,V:A]: ((X3 != ((((product_Pair @ A) @ ((product_prod @ (list @ B)) @ A)) @ U2) @ ((((product_Pair @ (list @ B)) @ A) @ (nil @ B)) @ V))))) => (~ ((! [U2:A,E2:B,Es:(list @ B),V:A]: ((X3 != ((((product_Pair @ A) @ ((product_prod @ (list @ B)) @ A)) @ U2) @ ((((product_Pair @ (list @ B)) @ A) @ (((cons @ B) @ E2) @ Es)) @ V))))))))))).
% 2.92/1.57 thf(fact_174_asym_Oinducts, axiom, (! [A:$tType,X3:(set @ ((product_prod @ A) @ A)),P2:((set @ ((product_prod @ A) @ A)) > $o)]: ((((asym @ A) @ X3) => ((! [R3:(set @ ((product_prod @ A) @ A))]: (((! [A7:A,B5:A]: (((((member2 @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A7) @ B5)) @ R3) => (~ ((((member2 @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ B5) @ A7)) @ R3)))))) => (P2 @ R3)))) => (P2 @ X3)))))).
% 2.92/1.57 thf(fact_175_asym_Ointros, axiom, (! [A:$tType,R2:(set @ ((product_prod @ A) @ A))]: (((! [A4:A,B4:A]: (((((member2 @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A4) @ B4)) @ R2) => (~ ((((member2 @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ B4) @ A4)) @ R2)))))) => ((asym @ A) @ R2))))).
% 2.92/1.57 thf(fact_176_asym_Osimps, axiom, (! [A:$tType]: (((asym @ A) = (^ [A6:(set @ ((product_prod @ A) @ A))]: ((? [R4:(set @ ((product_prod @ A) @ A))]: (((A6 = R4) & (! [X:A,Y:A]: (((((member2 @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X) @ Y)) @ R4) => (~ ((((member2 @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Y) @ X)) @ R4))))))))))))))).
% 2.92/1.57 thf(fact_177_asym_Ocases, axiom, (! [A:$tType,A2:(set @ ((product_prod @ A) @ A))]: ((((asym @ A) @ A2) => (! [A7:A,B5:A]: (((((member2 @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A7) @ B5)) @ A2) => (~ ((((member2 @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ B5) @ A7)) @ A2)))))))))).
% 2.92/1.57 thf(fact_178_asym__iff, axiom, (! [A:$tType]: (((asym @ A) = (^ [R4:(set @ ((product_prod @ A) @ A))]: ((! [X:A,Y:A]: (((((member2 @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X) @ Y)) @ R4) => (~ ((((member2 @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Y) @ X)) @ R4)))))))))))).
% 2.92/1.57 thf(fact_179_irreflI, axiom, (! [A:$tType,R2:(set @ ((product_prod @ A) @ A))]: (((! [A4:A]: ((~ ((((member2 @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A4) @ A4)) @ R2))))) => ((irrefl @ A) @ R2))))).
% 2.92/1.57 thf(fact_180_irrefl__def, axiom, (! [A:$tType]: (((irrefl @ A) = (^ [R5:(set @ ((product_prod @ A) @ A))]: ((! [A6:A]: ((~ ((((member2 @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A6) @ A6)) @ R5))))))))))).
% 2.92/1.57 thf(fact_181_asymD, axiom, (! [A:$tType,R2:(set @ ((product_prod @ A) @ A)),X3:A,Y3:A]: ((((asym @ A) @ R2) => ((((member2 @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X3) @ Y3)) @ R2) => (~ ((((member2 @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Y3) @ X3)) @ R2)))))))).
% 2.92/1.57 thf(fact_182_inverse__permutation__of__list_Ocases, axiom, (! [A:$tType,X3:((product_prod @ (list @ ((product_prod @ A) @ A))) @ A)]: (((! [X4:A]: ((X3 != ((((product_Pair @ (list @ ((product_prod @ A) @ A))) @ A) @ (nil @ ((product_prod @ A) @ A))) @ X4)))) => (~ ((! [Y4:A,X6:A,Xs4:(list @ ((product_prod @ A) @ A)),X4:A]: ((X3 != ((((product_Pair @ (list @ ((product_prod @ A) @ A))) @ A) @ (((cons @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Y4) @ X6)) @ Xs4)) @ X4)))))))))).
% 2.92/1.57 thf(fact_183_inverse__permutation__of__list_Oinduct, axiom, (! [A:$tType,P2:((list @ ((product_prod @ A) @ A)) > (A > $o)),A0:(list @ ((product_prod @ A) @ A)),A1:A]: (((! [X_1:A]: (((P2 @ (nil @ ((product_prod @ A) @ A))) @ X_1))) => ((! [Y4:A,X6:A,Xs4:(list @ ((product_prod @ A) @ A)),X4:A]: ((((X4 != X6) => ((P2 @ Xs4) @ X4)) => ((P2 @ (((cons @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Y4) @ X6)) @ Xs4)) @ X4)))) => ((P2 @ A0) @ A1)))))).
% 2.92/1.57 thf(fact_184_sd__path_Osimps_I2_J, axiom, (! [A:$tType,U:A,V2:A,W2:A,E3:((product_prod @ A) @ A),Es2:(list @ ((product_prod @ A) @ A))]: ((((((pair_sd_path @ A) @ ((((product_Pair @ A) @ A) @ U) @ V2)) @ W2) @ (((cons @ ((product_prod @ A) @ A)) @ E3) @ Es2)) = (((append @ ((product_prod @ A) @ A)) @ ((((if @ (list @ ((product_prod @ A) @ A))) @ (E3 = ((((product_Pair @ A) @ A) @ U) @ V2))) @ (((cons @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ U) @ W2)) @ (((cons @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ W2) @ V2)) @ (nil @ ((product_prod @ A) @ A))))) @ ((((if @ (list @ ((product_prod @ A) @ A))) @ (E3 = ((((product_Pair @ A) @ A) @ V2) @ U))) @ (((cons @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ V2) @ W2)) @ (((cons @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ W2) @ U)) @ (nil @ ((product_prod @ A) @ A))))) @ (((cons @ ((product_prod @ A) @ A)) @ E3) @ (nil @ ((product_prod @ A) @ A)))))) @ ((((pair_sd_path @ A) @ ((((product_Pair @ A) @ A) @ U) @ V2)) @ W2) @ Es2)))))).
% 2.92/1.57 thf(fact_185_sd__path_Osimps_I1_J, axiom, (! [A:$tType,Uu2:((product_prod @ A) @ A),Uv2:A]: ((((((pair_sd_path @ A) @ Uu2) @ Uv2) @ (nil @ ((product_prod @ A) @ A))) = (nil @ ((product_prod @ A) @ A)))))).
% 2.92/1.57 thf(fact_186_sd__path__id, axiom, (! [A:$tType,X3:A,Y3:A,P3:(list @ ((product_prod @ A) @ A)),W2:A]: (((~ ((((member2 @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X3) @ Y3)) @ ((set2 @ ((product_prod @ A) @ A)) @ P3)))) => ((~ ((((member2 @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Y3) @ X3)) @ ((set2 @ ((product_prod @ A) @ A)) @ P3)))) => (((((pair_sd_path @ A) @ ((((product_Pair @ A) @ A) @ X3) @ Y3)) @ W2) @ P3) = P3)))))).
% 2.92/1.57 thf(fact_187_sd__path_Oelims, axiom, (! [A:$tType,X3:((product_prod @ A) @ A),Xa2:A,Xb:(list @ ((product_prod @ A) @ A)),Y3:(list @ ((product_prod @ A) @ A))]: (((((((pair_sd_path @ A) @ X3) @ Xa2) @ Xb) = Y3) => (((Xb = (nil @ ((product_prod @ A) @ A))) => (Y3 != (nil @ ((product_prod @ A) @ A)))) => (~ ((! [U2:A,V:A]: (((X3 = ((((product_Pair @ A) @ A) @ U2) @ V)) => (! [E2:((product_prod @ A) @ A),Es:(list @ ((product_prod @ A) @ A))]: (((Xb = (((cons @ ((product_prod @ A) @ A)) @ E2) @ Es)) => (Y3 != (((append @ ((product_prod @ A) @ A)) @ ((((if @ (list @ ((product_prod @ A) @ A))) @ (E2 = ((((product_Pair @ A) @ A) @ U2) @ V))) @ (((cons @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ U2) @ Xa2)) @ (((cons @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Xa2) @ V)) @ (nil @ ((product_prod @ A) @ A))))) @ ((((if @ (list @ ((product_prod @ A) @ A))) @ (E2 = ((((product_Pair @ A) @ A) @ V) @ U2))) @ (((cons @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ V) @ Xa2)) @ (((cons @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Xa2) @ U2)) @ (nil @ ((product_prod @ A) @ A))))) @ (((cons @ ((product_prod @ A) @ A)) @ E2) @ (nil @ ((product_prod @ A) @ A)))))) @ ((((pair_sd_path @ A) @ ((((product_Pair @ A) @ A) @ U2) @ V)) @ Xa2) @ Es)))))))))))))))).
% 2.92/1.57 thf(fact_188_the__elem__set, axiom, (! [A:$tType,X3:A]: ((((the_elem @ A) @ ((set2 @ A) @ (((cons @ A) @ X3) @ (nil @ A)))) = X3)))).
% 2.92/1.57 thf(fact_189_sd__path_Opelims, axiom, (! [A:$tType,X3:((product_prod @ A) @ A),Xa2:A,Xb:(list @ ((product_prod @ A) @ A)),Y3:(list @ ((product_prod @ A) @ A))]: (((((((pair_sd_path @ A) @ X3) @ Xa2) @ Xb) = Y3) => ((((accp @ ((product_prod @ ((product_prod @ A) @ A)) @ ((product_prod @ A) @ (list @ ((product_prod @ A) @ A))))) @ (pair_sd_path_rel @ A)) @ ((((product_Pair @ ((product_prod @ A) @ A)) @ ((product_prod @ A) @ (list @ ((product_prod @ A) @ A)))) @ X3) @ ((((product_Pair @ A) @ (list @ ((product_prod @ A) @ A))) @ Xa2) @ Xb))) => (((Xb = (nil @ ((product_prod @ A) @ A))) => ((Y3 = (nil @ ((product_prod @ A) @ A))) => (~ ((((accp @ ((product_prod @ ((product_prod @ A) @ A)) @ ((product_prod @ A) @ (list @ ((product_prod @ A) @ A))))) @ (pair_sd_path_rel @ A)) @ ((((product_Pair @ ((product_prod @ A) @ A)) @ ((product_prod @ A) @ (list @ ((product_prod @ A) @ A)))) @ X3) @ ((((product_Pair @ A) @ (list @ ((product_prod @ A) @ A))) @ Xa2) @ (nil @ ((product_prod @ A) @ A))))))))) => (~ ((! [U2:A,V:A]: (((X3 = ((((product_Pair @ A) @ A) @ U2) @ V)) => (! [E2:((product_prod @ A) @ A),Es:(list @ ((product_prod @ A) @ A))]: (((Xb = (((cons @ ((product_prod @ A) @ A)) @ E2) @ Es)) => ((Y3 = (((append @ ((product_prod @ A) @ A)) @ ((((if @ (list @ ((product_prod @ A) @ A))) @ (E2 = ((((product_Pair @ A) @ A) @ U2) @ V))) @ (((cons @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ U2) @ Xa2)) @ (((cons @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Xa2) @ V)) @ (nil @ ((product_prod @ A) @ A))))) @ ((((if @ (list @ ((product_prod @ A) @ A))) @ (E2 = ((((product_Pair @ A) @ A) @ V) @ U2))) @ (((cons @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ V) @ Xa2)) @ (((cons @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Xa2) @ U2)) @ (nil @ ((product_prod @ A) @ A))))) @ (((cons @ ((product_prod @ A) @ A)) @ E2) @ (nil @ ((product_prod @ A) @ A)))))) @ ((((pair_sd_path @ A) @ ((((product_Pair @ A) @ A) @ U2) @ V)) @ Xa2) @ Es))) => (~ ((((accp @ ((product_prod @ ((product_prod @ A) @ A)) @ ((product_prod @ A) @ (list @ ((product_prod @ A) @ A))))) @ (pair_sd_path_rel @ A)) @ ((((product_Pair @ ((product_prod @ A) @ A)) @ ((product_prod @ A) @ (list @ ((product_prod @ A) @ A)))) @ ((((product_Pair @ A) @ A) @ U2) @ V)) @ ((((product_Pair @ A) @ (list @ ((product_prod @ A) @ A))) @ Xa2) @ (((cons @ ((product_prod @ A) @ A)) @ E2) @ Es))))))))))))))))))))).
% 2.92/1.57 thf(fact_190_list__exhaust2, axiom, (! [A:$tType,B:$tType,Y3:(list @ A),Ya:(list @ B)]: ((((Y3 = (nil @ A)) => (Ya != (nil @ B))) => (((Y3 = (nil @ A)) => (! [X213:B,X223:(list @ B)]: ((Ya != (((cons @ B) @ X213) @ X223))))) => (((? [X213:A,X223:(list @ A)]: ((Y3 = (((cons @ A) @ X213) @ X223)))) => (Ya != (nil @ B))) => (~ (((? [X213:A,X223:(list @ A)]: ((Y3 = (((cons @ A) @ X213) @ X223)))) => (! [X21a:B,X22a:(list @ B)]: ((Ya != (((cons @ B) @ X21a) @ X22a))))))))))))).
% 2.92/1.57 thf(fact_191_list__exhaust__NSC, axiom, (! [A:$tType,Xs2:(list @ A)]: (((Xs2 != (nil @ A)) => ((! [X4:A]: ((Xs2 != (((cons @ A) @ X4) @ (nil @ A))))) => (~ ((! [X4:A,Y4:A,Ys4:(list @ A)]: ((Xs2 != (((cons @ A) @ X4) @ (((cons @ A) @ Y4) @ Ys4)))))))))))).
% 2.92/1.57 thf(fact_192_product__lists_Osimps_I1_J, axiom, (! [A:$tType]: ((((product_lists @ A) @ (nil @ (list @ A))) = (((cons @ (list @ A)) @ (nil @ A)) @ (nil @ (list @ A))))))).
% 2.92/1.57 thf(fact_193_lenlex__append2, axiom, (! [A:$tType,R2:(set @ ((product_prod @ A) @ A)),Us:(list @ A),Xs2:(list @ A),Ys2:(list @ A)]: ((((irrefl @ A) @ R2) => ((((member2 @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((append @ A) @ Us) @ Xs2)) @ (((append @ A) @ Us) @ Ys2))) @ ((lenlex @ A) @ R2)) = (((member2 @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Xs2) @ Ys2)) @ ((lenlex @ A) @ R2))))))).
% 2.92/1.57 thf(fact_194_Nil__lenlex__iff1, axiom, (! [A:$tType,Ns:(list @ A),R:(set @ ((product_prod @ A) @ A))]: (((((member2 @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ (nil @ A)) @ Ns)) @ ((lenlex @ A) @ R)) = (Ns != (nil @ A)))))).
% 2.92/1.57 thf(fact_195_in__set__product__lists__length, axiom, (! [A:$tType,Xs2:(list @ A),Xss2:(list @ (list @ A))]: (((((member2 @ (list @ A)) @ Xs2) @ ((set2 @ (list @ A)) @ ((product_lists @ A) @ Xss2))) => (((size_size @ (list @ A)) @ Xs2) = ((size_size @ (list @ (list @ A))) @ Xss2)))))).
% 2.92/1.57 thf(fact_196_lenlex__irreflexive, axiom, (! [A:$tType,R:(set @ ((product_prod @ A) @ A)),Xs2:(list @ A)]: (((! [X4:A]: ((~ ((((member2 @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X4) @ X4)) @ R))))) => (~ ((((member2 @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Xs2) @ Xs2)) @ ((lenlex @ A) @ R)))))))).
% 2.92/1.57 thf(fact_197_Nil__lenlex__iff2, axiom, (! [A:$tType,Ns:(list @ A),R:(set @ ((product_prod @ A) @ A))]: ((~ ((((member2 @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Ns) @ (nil @ A))) @ ((lenlex @ A) @ R))))))).
% 2.92/1.57 thf(fact_198_lenlex__append1, axiom, (! [A:$tType,Us:(list @ A),Xs2:(list @ A),R2:(set @ ((product_prod @ A) @ A)),Vs:(list @ A),Ys2:(list @ A)]: (((((member2 @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Us) @ Xs2)) @ ((lenlex @ A) @ R2)) => ((((size_size @ (list @ A)) @ Vs) = ((size_size @ (list @ A)) @ Ys2)) => (((member2 @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((append @ A) @ Us) @ Vs)) @ (((append @ A) @ Xs2) @ Ys2))) @ ((lenlex @ A) @ R2))))))).
% 2.92/1.57 thf(fact_199_asym__lenlex, axiom, (! [A:$tType,R2:(set @ ((product_prod @ A) @ A))]: ((((asym @ A) @ R2) => ((asym @ (list @ A)) @ ((lenlex @ A) @ R2)))))).
% 2.92/1.57 thf(fact_200_co__path_Opelims, axiom, (! [A:$tType,X3:((product_prod @ A) @ A),Xa2:A,Xb:(list @ ((product_prod @ A) @ A)),Y3:(list @ ((product_prod @ A) @ A))]: (((((((pair_co_path @ A) @ X3) @ Xa2) @ Xb) = Y3) => ((((accp @ ((product_prod @ ((product_prod @ A) @ A)) @ ((product_prod @ A) @ (list @ ((product_prod @ A) @ A))))) @ (pair_co_path_rel @ A)) @ ((((product_Pair @ ((product_prod @ A) @ A)) @ ((product_prod @ A) @ (list @ ((product_prod @ A) @ A)))) @ X3) @ ((((product_Pair @ A) @ (list @ ((product_prod @ A) @ A))) @ Xa2) @ Xb))) => (((Xb = (nil @ ((product_prod @ A) @ A))) => ((Y3 = (nil @ ((product_prod @ A) @ A))) => (~ ((((accp @ ((product_prod @ ((product_prod @ A) @ A)) @ ((product_prod @ A) @ (list @ ((product_prod @ A) @ A))))) @ (pair_co_path_rel @ A)) @ ((((product_Pair @ ((product_prod @ A) @ A)) @ ((product_prod @ A) @ (list @ ((product_prod @ A) @ A)))) @ X3) @ ((((product_Pair @ A) @ (list @ ((product_prod @ A) @ A))) @ Xa2) @ (nil @ ((product_prod @ A) @ A))))))))) => ((! [E2:((product_prod @ A) @ A)]: (((Xb = (((cons @ ((product_prod @ A) @ A)) @ E2) @ (nil @ ((product_prod @ A) @ A)))) => ((Y3 = (((cons @ ((product_prod @ A) @ A)) @ E2) @ (nil @ ((product_prod @ A) @ A)))) => (~ ((((accp @ ((product_prod @ ((product_prod @ A) @ A)) @ ((product_prod @ A) @ (list @ ((product_prod @ A) @ A))))) @ (pair_co_path_rel @ A)) @ ((((product_Pair @ ((product_prod @ A) @ A)) @ ((product_prod @ A) @ (list @ ((product_prod @ A) @ A)))) @ X3) @ ((((product_Pair @ A) @ (list @ ((product_prod @ A) @ A))) @ Xa2) @ (((cons @ ((product_prod @ A) @ A)) @ E2) @ (nil @ ((product_prod @ A) @ A)))))))))))) => (~ ((! [U2:A,V:A]: (((X3 = ((((product_Pair @ A) @ A) @ U2) @ V)) => (! [E1:((product_prod @ A) @ A),E22:((product_prod @ A) @ A),Es:(list @ ((product_prod @ A) @ A))]: (((Xb = (((cons @ ((product_prod @ A) @ A)) @ E1) @ (((cons @ ((product_prod @ A) @ A)) @ E22) @ Es))) => (((((E1 = ((((product_Pair @ A) @ A) @ U2) @ Xa2)) & (E22 = ((((product_Pair @ A) @ A) @ Xa2) @ V))) => (Y3 = (((cons @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ U2) @ V)) @ ((((pair_co_path @ A) @ ((((product_Pair @ A) @ A) @ U2) @ V)) @ Xa2) @ Es)))) & ((~ (((E1 = ((((product_Pair @ A) @ A) @ U2) @ Xa2)) & (E22 = ((((product_Pair @ A) @ A) @ Xa2) @ V))))) => ((((E1 = ((((product_Pair @ A) @ A) @ V) @ Xa2)) & (E22 = ((((product_Pair @ A) @ A) @ Xa2) @ U2))) => (Y3 = (((cons @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ V) @ U2)) @ ((((pair_co_path @ A) @ ((((product_Pair @ A) @ A) @ U2) @ V)) @ Xa2) @ Es)))) & ((~ (((E1 = ((((product_Pair @ A) @ A) @ V) @ Xa2)) & (E22 = ((((product_Pair @ A) @ A) @ Xa2) @ U2))))) => (Y3 = (((cons @ ((product_prod @ A) @ A)) @ E1) @ ((((pair_co_path @ A) @ ((((product_Pair @ A) @ A) @ U2) @ V)) @ Xa2) @ (((cons @ ((product_prod @ A) @ A)) @ E22) @ Es)))))))) => (~ ((((accp @ ((product_prod @ ((product_prod @ A) @ A)) @ ((product_prod @ A) @ (list @ ((product_prod @ A) @ A))))) @ (pair_co_path_rel @ A)) @ ((((product_Pair @ ((product_prod @ A) @ A)) @ ((product_prod @ A) @ (list @ ((product_prod @ A) @ A)))) @ ((((product_Pair @ A) @ A) @ U2) @ V)) @ ((((product_Pair @ A) @ (list @ ((product_prod @ A) @ A))) @ Xa2) @ (((cons @ ((product_prod @ A) @ A)) @ E1) @ (((cons @ ((product_prod @ A) @ A)) @ E22) @ Es))))))))))))))))))))))).
% 2.92/1.57 thf(fact_201_pawalk__verts_Osimps_I1_J, axiom, (! [A:$tType,U:A]: (((((pair_pawalk_verts @ A) @ U) @ (nil @ ((product_prod @ A) @ A))) = (((cons @ A) @ U) @ (nil @ A)))))).
% 2.92/1.57 thf(fact_202_co__path__nonempty, axiom, (! [A:$tType,E3:((product_prod @ A) @ A),W2:A,P3:(list @ ((product_prod @ A) @ A))]: (((((((pair_co_path @ A) @ E3) @ W2) @ P3) = (nil @ ((product_prod @ A) @ A))) = (P3 = (nil @ ((product_prod @ A) @ A))))))).
% 2.92/1.57 thf(fact_203_co__path_Osimps_I1_J, axiom, (! [A:$tType,Uu2:((product_prod @ A) @ A),Uv2:A]: ((((((pair_co_path @ A) @ Uu2) @ Uv2) @ (nil @ ((product_prod @ A) @ A))) = (nil @ ((product_prod @ A) @ A)))))).
% 2.92/1.57 thf(fact_204_co__path_Osimps_I3_J, axiom, (! [A:$tType,E12:((product_prod @ A) @ A),U:A,W2:A,E23:((product_prod @ A) @ A),V2:A,Es2:(list @ ((product_prod @ A) @ A))]: (((((E12 = ((((product_Pair @ A) @ A) @ U) @ W2)) & (E23 = ((((product_Pair @ A) @ A) @ W2) @ V2))) => (((((pair_co_path @ A) @ ((((product_Pair @ A) @ A) @ U) @ V2)) @ W2) @ (((cons @ ((product_prod @ A) @ A)) @ E12) @ (((cons @ ((product_prod @ A) @ A)) @ E23) @ Es2))) = (((cons @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ U) @ V2)) @ ((((pair_co_path @ A) @ ((((product_Pair @ A) @ A) @ U) @ V2)) @ W2) @ Es2)))) & ((~ (((E12 = ((((product_Pair @ A) @ A) @ U) @ W2)) & (E23 = ((((product_Pair @ A) @ A) @ W2) @ V2))))) => ((((E12 = ((((product_Pair @ A) @ A) @ V2) @ W2)) & (E23 = ((((product_Pair @ A) @ A) @ W2) @ U))) => (((((pair_co_path @ A) @ ((((product_Pair @ A) @ A) @ U) @ V2)) @ W2) @ (((cons @ ((product_prod @ A) @ A)) @ E12) @ (((cons @ ((product_prod @ A) @ A)) @ E23) @ Es2))) = (((cons @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ V2) @ U)) @ ((((pair_co_path @ A) @ ((((product_Pair @ A) @ A) @ U) @ V2)) @ W2) @ Es2)))) & ((~ (((E12 = ((((product_Pair @ A) @ A) @ V2) @ W2)) & (E23 = ((((product_Pair @ A) @ A) @ W2) @ U))))) => (((((pair_co_path @ A) @ ((((product_Pair @ A) @ A) @ U) @ V2)) @ W2) @ (((cons @ ((product_prod @ A) @ A)) @ E12) @ (((cons @ ((product_prod @ A) @ A)) @ E23) @ Es2))) = (((cons @ ((product_prod @ A) @ A)) @ E12) @ ((((pair_co_path @ A) @ ((((product_Pair @ A) @ A) @ U) @ V2)) @ W2) @ (((cons @ ((product_prod @ A) @ A)) @ E23) @ Es2))))))))))).
% 2.92/1.57 thf(fact_205_co__path_Osimps_I2_J, axiom, (! [A:$tType,Uw2:((product_prod @ A) @ A),Ux2:A,E3:((product_prod @ A) @ A)]: ((((((pair_co_path @ A) @ Uw2) @ Ux2) @ (((cons @ ((product_prod @ A) @ A)) @ E3) @ (nil @ ((product_prod @ A) @ A)))) = (((cons @ ((product_prod @ A) @ A)) @ E3) @ (nil @ ((product_prod @ A) @ A))))))).
% 2.92/1.57 thf(fact_206_co__path_Oelims, axiom, (! [A:$tType,X3:((product_prod @ A) @ A),Xa2:A,Xb:(list @ ((product_prod @ A) @ A)),Y3:(list @ ((product_prod @ A) @ A))]: (((((((pair_co_path @ A) @ X3) @ Xa2) @ Xb) = Y3) => (((Xb = (nil @ ((product_prod @ A) @ A))) => (Y3 != (nil @ ((product_prod @ A) @ A)))) => ((! [E2:((product_prod @ A) @ A)]: (((Xb = (((cons @ ((product_prod @ A) @ A)) @ E2) @ (nil @ ((product_prod @ A) @ A)))) => (Y3 != (((cons @ ((product_prod @ A) @ A)) @ E2) @ (nil @ ((product_prod @ A) @ A))))))) => (~ ((! [U2:A,V:A]: (((X3 = ((((product_Pair @ A) @ A) @ U2) @ V)) => (! [E1:((product_prod @ A) @ A),E22:((product_prod @ A) @ A),Es:(list @ ((product_prod @ A) @ A))]: (((Xb = (((cons @ ((product_prod @ A) @ A)) @ E1) @ (((cons @ ((product_prod @ A) @ A)) @ E22) @ Es))) => (~ (((((E1 = ((((product_Pair @ A) @ A) @ U2) @ Xa2)) & (E22 = ((((product_Pair @ A) @ A) @ Xa2) @ V))) => (Y3 = (((cons @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ U2) @ V)) @ ((((pair_co_path @ A) @ ((((product_Pair @ A) @ A) @ U2) @ V)) @ Xa2) @ Es)))) & ((~ (((E1 = ((((product_Pair @ A) @ A) @ U2) @ Xa2)) & (E22 = ((((product_Pair @ A) @ A) @ Xa2) @ V))))) => ((((E1 = ((((product_Pair @ A) @ A) @ V) @ Xa2)) & (E22 = ((((product_Pair @ A) @ A) @ Xa2) @ U2))) => (Y3 = (((cons @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ V) @ U2)) @ ((((pair_co_path @ A) @ ((((product_Pair @ A) @ A) @ U2) @ V)) @ Xa2) @ Es)))) & ((~ (((E1 = ((((product_Pair @ A) @ A) @ V) @ Xa2)) & (E22 = ((((product_Pair @ A) @ A) @ Xa2) @ U2))))) => (Y3 = (((cons @ ((product_prod @ A) @ A)) @ E1) @ ((((pair_co_path @ A) @ ((((product_Pair @ A) @ A) @ U2) @ V)) @ Xa2) @ (((cons @ ((product_prod @ A) @ A)) @ E22) @ Es)))))))))))))))))))))))).
% 2.92/1.57 thf(fact_207_co__sd__id, axiom, (! [A:$tType,U:A,W2:A,P3:(list @ ((product_prod @ A) @ A)),V2:A]: (((~ ((((member2 @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ U) @ W2)) @ ((set2 @ ((product_prod @ A) @ A)) @ P3)))) => ((~ ((((member2 @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ V2) @ W2)) @ ((set2 @ ((product_prod @ A) @ A)) @ P3)))) => (((((pair_co_path @ A) @ ((((product_Pair @ A) @ A) @ U) @ V2)) @ W2) @ ((((pair_sd_path @ A) @ ((((product_Pair @ A) @ A) @ U) @ V2)) @ W2) @ P3)) = P3)))))).
% 2.92/1.57 thf(fact_208_subseqs_Osimps_I1_J, axiom, (! [A:$tType]: ((((subseqs @ A) @ (nil @ A)) = (((cons @ (list @ A)) @ (nil @ A)) @ (nil @ (list @ A))))))).
% 2.92/1.57 thf(fact_209_Cons__lenlex__iff, axiom, (! [A:$tType,M:A,Ms:(list @ A),N:A,Ns:(list @ A),R:(set @ ((product_prod @ A) @ A))]: (((((member2 @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((cons @ A) @ M) @ Ms)) @ (((cons @ A) @ N) @ Ns))) @ ((lenlex @ A) @ R)) = ((((ord_less @ nat) @ ((size_size @ (list @ A)) @ Ms)) @ ((size_size @ (list @ A)) @ Ns)) | (((((size_size @ (list @ A)) @ Ms) = ((size_size @ (list @ A)) @ Ns)) & (((member2 @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ M) @ N)) @ R)) | ((M = N) & (((member2 @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Ms) @ Ns)) @ ((lenlex @ A) @ R))))))))).
% 2.92/1.57 thf(fact_210_length__induct, axiom, (! [A:$tType,P2:((list @ A) > $o),Xs2:(list @ A)]: (((! [Xs4:(list @ A)]: (((! [Ys7:(list @ A)]: (((((ord_less @ nat) @ ((size_size @ (list @ A)) @ Ys7)) @ ((size_size @ (list @ A)) @ Xs4)) => (P2 @ Ys7)))) => (P2 @ Xs4)))) => (P2 @ Xs2))))).
% 2.92/1.57 thf(fact_211_subseqs__refl, axiom, (! [A:$tType,Xs2:(list @ A)]: ((((member2 @ (list @ A)) @ Xs2) @ ((set2 @ (list @ A)) @ ((subseqs @ A) @ Xs2)))))).
% 2.92/1.57 thf(fact_212_Cons__in__subseqsD, axiom, (! [A:$tType,Y3:A,Ys2:(list @ A),Xs2:(list @ A)]: (((((member2 @ (list @ A)) @ (((cons @ A) @ Y3) @ Ys2)) @ ((set2 @ (list @ A)) @ ((subseqs @ A) @ Xs2))) => (((member2 @ (list @ A)) @ Ys2) @ ((set2 @ (list @ A)) @ ((subseqs @ A) @ Xs2))))))).
% 2.92/1.57 thf(fact_213_in__measures_I2_J, axiom, (! [A:$tType,X3:A,Y3:A,F3:(A > nat),Fs:(list @ (A > nat))]: (((((member2 @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X3) @ Y3)) @ ((measures @ A) @ (((cons @ (A > nat)) @ F3) @ Fs))) = ((((ord_less @ nat) @ (F3 @ X3)) @ (F3 @ Y3)) | (((F3 @ X3) = (F3 @ Y3)) & (((member2 @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X3) @ Y3)) @ ((measures @ A) @ Fs)))))))).
% 2.92/1.57 thf(fact_214_inverse__permutation__of__list_Oelims, axiom, (! [A:$tType,X3:(list @ ((product_prod @ A) @ A)),Xa2:A,Y3:A]: ((((((invers965609412f_list @ A) @ X3) @ Xa2) = Y3) => (((X3 = (nil @ ((product_prod @ A) @ A))) => (Y3 != Xa2)) => (~ ((! [Y4:A,X6:A,Xs4:(list @ ((product_prod @ A) @ A))]: (((X3 = (((cons @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Y4) @ X6)) @ Xs4)) => (~ ((((Xa2 = X6) => (Y3 = Y4)) & ((Xa2 != X6) => (Y3 = (((invers965609412f_list @ A) @ Xs4) @ Xa2)))))))))))))))).
% 2.92/1.57 thf(fact_215_in__measures_I1_J, axiom, (! [A:$tType,X3:A,Y3:A]: ((~ ((((member2 @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X3) @ Y3)) @ ((measures @ A) @ (nil @ (A > nat))))))))).
% 2.92/1.57 thf(fact_216_eval__inverse__permutation__of__list_I3_J, axiom, (! [A:$tType,X3:A,X7:A,Y5:A,Xs2:(list @ ((product_prod @ A) @ A))]: (((X3 != X7) => ((((invers965609412f_list @ A) @ (((cons @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Y5) @ X7)) @ Xs2)) @ X3) = (((invers965609412f_list @ A) @ Xs2) @ X3)))))).
% 2.92/1.57 thf(fact_217_eval__inverse__permutation__of__list_I2_J, axiom, (! [A:$tType,X3:A,X7:A,Y3:A,Xs2:(list @ ((product_prod @ A) @ A))]: (((X3 = X7) => ((((invers965609412f_list @ A) @ (((cons @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Y3) @ X7)) @ Xs2)) @ X3) = Y3))))).
% 2.92/1.57 thf(fact_218_inverse__permutation__of__list_Osimps_I1_J, axiom, (! [A:$tType,X3:A]: (((((invers965609412f_list @ A) @ (nil @ ((product_prod @ A) @ A))) @ X3) = X3)))).
% 2.92/1.57 thf(fact_219_inverse__permutation__of__list_Osimps_I2_J, axiom, (! [A:$tType,X3:A,X7:A,Y3:A,Xs2:(list @ ((product_prod @ A) @ A))]: ((((X3 = X7) => ((((invers965609412f_list @ A) @ (((cons @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Y3) @ X7)) @ Xs2)) @ X3) = Y3)) & ((X3 != X7) => ((((invers965609412f_list @ A) @ (((cons @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Y3) @ X7)) @ Xs2)) @ X3) = (((invers965609412f_list @ A) @ Xs2) @ X3))))))).
% 2.92/1.57 thf(fact_220_measures__less, axiom, (! [A:$tType,F3:(A > nat),X3:A,Y3:A,Fs:(list @ (A > nat))]: (((((ord_less @ nat) @ (F3 @ X3)) @ (F3 @ Y3)) => (((member2 @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X3) @ Y3)) @ ((measures @ A) @ (((cons @ (A > nat)) @ F3) @ Fs))))))).
% 2.92/1.57 thf(fact_221_inverse__permutation__of__list__unique, axiom, (! [A:$tType,Xs2:(list @ ((product_prod @ A) @ A)),A5:(set @ A),X3:A,Y3:A]: (((((list_permutes @ A) @ Xs2) @ A5) => ((((member2 @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X3) @ Y3)) @ ((set2 @ ((product_prod @ A) @ A)) @ Xs2)) => ((((invers965609412f_list @ A) @ Xs2) @ Y3) = X3)))))).
% 2.92/1.57 thf(fact_222_eval__permutation__of__list_I3_J, axiom, (! [A:$tType,X3:A,X7:A,Y5:A,Xs2:(list @ ((product_prod @ A) @ A))]: (((X3 != X7) => ((((permutation_of_list @ A) @ (((cons @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X7) @ Y5)) @ Xs2)) @ X3) = (((permutation_of_list @ A) @ Xs2) @ X3)))))).
% 2.92/1.57 thf(fact_223_eval__permutation__of__list_I1_J, axiom, (! [A:$tType,X3:A]: (((((permutation_of_list @ A) @ (nil @ ((product_prod @ A) @ A))) @ X3) = X3)))).
% 2.92/1.57 thf(fact_224_eval__permutation__of__list_I2_J, axiom, (! [A:$tType,X3:A,X7:A,Y3:A,Xs2:(list @ ((product_prod @ A) @ A))]: (((X3 = X7) => ((((permutation_of_list @ A) @ (((cons @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X7) @ Y3)) @ Xs2)) @ X3) = Y3))))).
% 2.92/1.57 thf(fact_225_permutation__of__list__unique, axiom, (! [A:$tType,Xs2:(list @ ((product_prod @ A) @ A)),A5:(set @ A),X3:A,Y3:A]: (((((list_permutes @ A) @ Xs2) @ A5) => ((((member2 @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X3) @ Y3)) @ ((set2 @ ((product_prod @ A) @ A)) @ Xs2)) => ((((permutation_of_list @ A) @ Xs2) @ X3) = Y3)))))).
% 2.92/1.57 thf(fact_226_permutation__of__list__Cons, axiom, (! [A:$tType,X3:A,X7:A,Y3:A,Xs2:(list @ ((product_prod @ A) @ A))]: ((((X3 = X7) => ((((permutation_of_list @ A) @ (((cons @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X3) @ Y3)) @ Xs2)) @ X7) = Y3)) & ((X3 != X7) => ((((permutation_of_list @ A) @ (((cons @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X3) @ Y3)) @ Xs2)) @ X7) = (((permutation_of_list @ A) @ Xs2) @ X7))))))).
% 2.92/1.57 thf(fact_227_part__code_I1_J, axiom, (! [A:$tType,B:$tType]: (((linorder @ A) => (! [F3:(B > A),Pivot:A]: (((((((linorder_part @ B) @ A) @ F3) @ Pivot) @ (nil @ B)) = ((((product_Pair @ (list @ B)) @ ((product_prod @ (list @ B)) @ (list @ B))) @ (nil @ B)) @ ((((product_Pair @ (list @ B)) @ (list @ B)) @ (nil @ B)) @ (nil @ B)))))))))).
% 2.92/1.57 thf(fact_228_not__in__set__insert, axiom, (! [A:$tType,X3:A,Xs2:(list @ A)]: (((~ ((((member2 @ A) @ X3) @ ((set2 @ A) @ Xs2)))) => ((((insert @ A) @ X3) @ Xs2) = (((cons @ A) @ X3) @ Xs2)))))).
% 2.92/1.57 thf(fact_229_in__set__insert, axiom, (! [A:$tType,X3:A,Xs2:(list @ A)]: (((((member2 @ A) @ X3) @ ((set2 @ A) @ Xs2)) => ((((insert @ A) @ X3) @ Xs2) = Xs2))))).
% 2.92/1.57 thf(fact_230_insert__Nil, axiom, (! [A:$tType,X3:A]: (((((insert @ A) @ X3) @ (nil @ A)) = (((cons @ A) @ X3) @ (nil @ A)))))).
% 2.92/1.57 thf(fact_231_List_Oinsert__def, axiom, (! [A:$tType]: (((insert @ A) = (^ [X:A,Xs:(list @ A)]: (((((if @ (list @ A)) @ (((member2 @ A) @ X) @ ((set2 @ A) @ Xs))) @ Xs) @ (((cons @ A) @ X) @ Xs)))))))).
% 2.92/1.57 thf(fact_232_concat__eq__append__conv, axiom, (! [A:$tType,Xss2:(list @ (list @ A)),Ys2:(list @ A),Zs:(list @ A)]: (((((concat @ A) @ Xss2) = (((append @ A) @ Ys2) @ Zs)) = (((Xss2 = (nil @ (list @ A))) => ((Ys2 = (nil @ A)) & (Zs = (nil @ A)))) & ((Xss2 != (nil @ (list @ A))) => (? [Xss1:(list @ (list @ A)),Xs:(list @ A),Xs6:(list @ A),Xss22:(list @ (list @ A))]: (((Xss2 = (((append @ (list @ A)) @ Xss1) @ (((cons @ (list @ A)) @ (((append @ A) @ Xs) @ Xs6)) @ Xss22))) & ((Ys2 = (((append @ A) @ ((concat @ A) @ Xss1)) @ Xs)) & (Zs = (((append @ A) @ Xs6) @ ((concat @ A) @ Xss22))))))))))))).
% 2.92/1.57 thf(fact_233_inverse__permutation__of__list_Opelims, axiom, (! [A:$tType,X3:(list @ ((product_prod @ A) @ A)),Xa2:A,Y3:A]: ((((((invers965609412f_list @ A) @ X3) @ Xa2) = Y3) => ((((accp @ ((product_prod @ (list @ ((product_prod @ A) @ A))) @ A)) @ (invers1507583541st_rel @ A)) @ ((((product_Pair @ (list @ ((product_prod @ A) @ A))) @ A) @ X3) @ Xa2)) => (((X3 = (nil @ ((product_prod @ A) @ A))) => ((Y3 = Xa2) => (~ ((((accp @ ((product_prod @ (list @ ((product_prod @ A) @ A))) @ A)) @ (invers1507583541st_rel @ A)) @ ((((product_Pair @ (list @ ((product_prod @ A) @ A))) @ A) @ (nil @ ((product_prod @ A) @ A))) @ Xa2)))))) => (~ ((! [Y4:A,X6:A,Xs4:(list @ ((product_prod @ A) @ A))]: (((X3 = (((cons @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Y4) @ X6)) @ Xs4)) => ((((Xa2 = X6) => (Y3 = Y4)) & ((Xa2 != X6) => (Y3 = (((invers965609412f_list @ A) @ Xs4) @ Xa2)))) => (~ ((((accp @ ((product_prod @ (list @ ((product_prod @ A) @ A))) @ A)) @ (invers1507583541st_rel @ A)) @ ((((product_Pair @ (list @ ((product_prod @ A) @ A))) @ A) @ (((cons @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Y4) @ X6)) @ Xs4)) @ Xa2)))))))))))))))).
% 2.92/1.57 thf(fact_234_Nil__eq__concat__conv, axiom, (! [A:$tType,Xss2:(list @ (list @ A))]: ((((nil @ A) = ((concat @ A) @ Xss2)) = (! [X:(list @ A)]: (((((member2 @ (list @ A)) @ X) @ ((set2 @ (list @ A)) @ Xss2)) => (X = (nil @ A))))))))).
% 2.92/1.57 thf(fact_235_concat__eq__Nil__conv, axiom, (! [A:$tType,Xss2:(list @ (list @ A))]: (((((concat @ A) @ Xss2) = (nil @ A)) = (! [X:(list @ A)]: (((((member2 @ (list @ A)) @ X) @ ((set2 @ (list @ A)) @ Xss2)) => (X = (nil @ A))))))))).
% 2.92/1.57 thf(fact_236_concat__append, axiom, (! [A:$tType,Xs2:(list @ (list @ A)),Ys2:(list @ (list @ A))]: ((((concat @ A) @ (((append @ (list @ A)) @ Xs2) @ Ys2)) = (((append @ A) @ ((concat @ A) @ Xs2)) @ ((concat @ A) @ Ys2)))))).
% 2.92/1.57 thf(fact_237_concat_Osimps_I2_J, axiom, (! [A:$tType,X3:(list @ A),Xs2:(list @ (list @ A))]: ((((concat @ A) @ (((cons @ (list @ A)) @ X3) @ Xs2)) = (((append @ A) @ X3) @ ((concat @ A) @ Xs2)))))).
% 2.92/1.57 thf(fact_238_concat_Osimps_I1_J, axiom, (! [A:$tType]: ((((concat @ A) @ (nil @ (list @ A))) = (nil @ A))))).
% 2.92/1.57 thf(fact_239_concat__eq__appendD, axiom, (! [A:$tType,Xss2:(list @ (list @ A)),Ys2:(list @ A),Zs:(list @ A)]: (((((concat @ A) @ Xss2) = (((append @ A) @ Ys2) @ Zs)) => ((Xss2 != (nil @ (list @ A))) => (? [Xss12:(list @ (list @ A)),Xs4:(list @ A),Xs3:(list @ A),Xss23:(list @ (list @ A))]: (((Xss2 = (((append @ (list @ A)) @ Xss12) @ (((cons @ (list @ A)) @ (((append @ A) @ Xs4) @ Xs3)) @ Xss23))) & ((Ys2 = (((append @ A) @ ((concat @ A) @ Xss12)) @ Xs4)) & (Zs = (((append @ A) @ Xs3) @ ((concat @ A) @ Xss23)))))))))))).
% 2.92/1.57 thf(fact_240_length__n__lists__elem, axiom, (! [A:$tType,Ys2:(list @ A),N:nat,Xs2:(list @ A)]: (((((member2 @ (list @ A)) @ Ys2) @ ((set2 @ (list @ A)) @ (((n_lists @ A) @ N) @ Xs2))) => (((size_size @ (list @ A)) @ Ys2) = N))))).
% 2.92/1.57 thf(fact_241_listrel_Oinducts, axiom, (! [A:$tType,B:$tType,X1:(list @ A),X2:(list @ B),R:(set @ ((product_prod @ A) @ B)),P2:((list @ A) > ((list @ B) > $o))]: (((((member2 @ ((product_prod @ (list @ A)) @ (list @ B))) @ ((((product_Pair @ (list @ A)) @ (list @ B)) @ X1) @ X2)) @ (((listrel @ A) @ B) @ R)) => (((P2 @ (nil @ A)) @ (nil @ B)) => ((! [X4:A,Y4:B,Xs4:(list @ A),Ys4:(list @ B)]: (((((member2 @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X4) @ Y4)) @ R) => ((((member2 @ ((product_prod @ (list @ A)) @ (list @ B))) @ ((((product_Pair @ (list @ A)) @ (list @ B)) @ Xs4) @ Ys4)) @ (((listrel @ A) @ B) @ R)) => (((P2 @ Xs4) @ Ys4) => ((P2 @ (((cons @ A) @ X4) @ Xs4)) @ (((cons @ B) @ Y4) @ Ys4))))))) => ((P2 @ X1) @ X2))))))).
% 2.92/1.57 thf(fact_242_listrel__eq__len, axiom, (! [A:$tType,B:$tType,Xs2:(list @ A),Ys2:(list @ B),R:(set @ ((product_prod @ A) @ B))]: (((((member2 @ ((product_prod @ (list @ A)) @ (list @ B))) @ ((((product_Pair @ (list @ A)) @ (list @ B)) @ Xs2) @ Ys2)) @ (((listrel @ A) @ B) @ R)) => (((size_size @ (list @ A)) @ Xs2) = ((size_size @ (list @ B)) @ Ys2)))))).
% 2.92/1.57 thf(fact_243_listrel_ONil, axiom, (! [B:$tType,A:$tType,R:(set @ ((product_prod @ A) @ B))]: ((((member2 @ ((product_prod @ (list @ A)) @ (list @ B))) @ ((((product_Pair @ (list @ A)) @ (list @ B)) @ (nil @ A)) @ (nil @ B))) @ (((listrel @ A) @ B) @ R))))).
% 2.92/1.57 thf(fact_244_listrel__Nil1, axiom, (! [A:$tType,B:$tType,Xs2:(list @ B),R:(set @ ((product_prod @ A) @ B))]: (((((member2 @ ((product_prod @ (list @ A)) @ (list @ B))) @ ((((product_Pair @ (list @ A)) @ (list @ B)) @ (nil @ A)) @ Xs2)) @ (((listrel @ A) @ B) @ R)) => (Xs2 = (nil @ B)))))).
% 2.92/1.57 thf(fact_245_listrel__Nil2, axiom, (! [B:$tType,A:$tType,Xs2:(list @ A),R:(set @ ((product_prod @ A) @ B))]: (((((member2 @ ((product_prod @ (list @ A)) @ (list @ B))) @ ((((product_Pair @ (list @ A)) @ (list @ B)) @ Xs2) @ (nil @ B))) @ (((listrel @ A) @ B) @ R)) => (Xs2 = (nil @ A)))))).
% 2.92/1.57 thf(fact_246_listrel_OCons, axiom, (! [B:$tType,A:$tType,X3:A,Y3:B,R:(set @ ((product_prod @ A) @ B)),Xs2:(list @ A),Ys2:(list @ B)]: (((((member2 @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X3) @ Y3)) @ R) => ((((member2 @ ((product_prod @ (list @ A)) @ (list @ B))) @ ((((product_Pair @ (list @ A)) @ (list @ B)) @ Xs2) @ Ys2)) @ (((listrel @ A) @ B) @ R)) => (((member2 @ ((product_prod @ (list @ A)) @ (list @ B))) @ ((((product_Pair @ (list @ A)) @ (list @ B)) @ (((cons @ A) @ X3) @ Xs2)) @ (((cons @ B) @ Y3) @ Ys2))) @ (((listrel @ A) @ B) @ R))))))).
% 2.92/1.57 thf(fact_247_listrel__Cons1, axiom, (! [B:$tType,A:$tType,Y3:A,Ys2:(list @ A),Xs2:(list @ B),R:(set @ ((product_prod @ A) @ B))]: (((((member2 @ ((product_prod @ (list @ A)) @ (list @ B))) @ ((((product_Pair @ (list @ A)) @ (list @ B)) @ (((cons @ A) @ Y3) @ Ys2)) @ Xs2)) @ (((listrel @ A) @ B) @ R)) => (~ ((! [Y4:B,Ys4:(list @ B)]: (((Xs2 = (((cons @ B) @ Y4) @ Ys4)) => ((((member2 @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ Y3) @ Y4)) @ R) => (~ ((((member2 @ ((product_prod @ (list @ A)) @ (list @ B))) @ ((((product_Pair @ (list @ A)) @ (list @ B)) @ Ys2) @ Ys4)) @ (((listrel @ A) @ B) @ R)))))))))))))).
% 2.92/1.57 thf(fact_248_listrel__Cons2, axiom, (! [B:$tType,A:$tType,Xs2:(list @ A),Y3:B,Ys2:(list @ B),R:(set @ ((product_prod @ A) @ B))]: (((((member2 @ ((product_prod @ (list @ A)) @ (list @ B))) @ ((((product_Pair @ (list @ A)) @ (list @ B)) @ Xs2) @ (((cons @ B) @ Y3) @ Ys2))) @ (((listrel @ A) @ B) @ R)) => (~ ((! [X4:A,Xs4:(list @ A)]: (((Xs2 = (((cons @ A) @ X4) @ Xs4)) => ((((member2 @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X4) @ Y3)) @ R) => (~ ((((member2 @ ((product_prod @ (list @ A)) @ (list @ B))) @ ((((product_Pair @ (list @ A)) @ (list @ B)) @ Xs4) @ Ys2)) @ (((listrel @ A) @ B) @ R)))))))))))))).
% 2.92/1.57 thf(fact_249_listrel_Ocases, axiom, (! [B:$tType,A:$tType,A1:(list @ A),A22:(list @ B),R:(set @ ((product_prod @ A) @ B))]: (((((member2 @ ((product_prod @ (list @ A)) @ (list @ B))) @ ((((product_Pair @ (list @ A)) @ (list @ B)) @ A1) @ A22)) @ (((listrel @ A) @ B) @ R)) => (((A1 = (nil @ A)) => (A22 != (nil @ B))) => (~ ((! [X4:A,Y4:B,Xs4:(list @ A)]: (((A1 = (((cons @ A) @ X4) @ Xs4)) => (! [Ys4:(list @ B)]: (((A22 = (((cons @ B) @ Y4) @ Ys4)) => ((((member2 @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X4) @ Y4)) @ R) => (~ ((((member2 @ ((product_prod @ (list @ A)) @ (list @ B))) @ ((((product_Pair @ (list @ A)) @ (list @ B)) @ Xs4) @ Ys4)) @ (((listrel @ A) @ B) @ R)))))))))))))))))).
% 2.92/1.57 thf(fact_250_listrel_Osimps, axiom, (! [B:$tType,A:$tType,A1:(list @ A),A22:(list @ B),R:(set @ ((product_prod @ A) @ B))]: (((((member2 @ ((product_prod @ (list @ A)) @ (list @ B))) @ ((((product_Pair @ (list @ A)) @ (list @ B)) @ A1) @ A22)) @ (((listrel @ A) @ B) @ R)) = (((A1 = (nil @ A)) & (A22 = (nil @ B))) | (? [X:A,Y:B,Xs:(list @ A),Ys:(list @ B)]: (((A1 = (((cons @ A) @ X) @ Xs)) & ((A22 = (((cons @ B) @ Y) @ Ys)) & ((((member2 @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X) @ Y)) @ R) & (((member2 @ ((product_prod @ (list @ A)) @ (list @ B))) @ ((((product_Pair @ (list @ A)) @ (list @ B)) @ Xs) @ Ys)) @ (((listrel @ A) @ B) @ R)))))))))))).
% 2.92/1.57 thf(fact_251_n__lists__Nil, axiom, (! [A:$tType,N:nat]: ((((N = (zero_zero @ nat)) => ((((n_lists @ A) @ N) @ (nil @ A)) = (((cons @ (list @ A)) @ (nil @ A)) @ (nil @ (list @ A))))) & ((N != (zero_zero @ nat)) => ((((n_lists @ A) @ N) @ (nil @ A)) = (nil @ (list @ A)))))))).
% 2.92/1.57 thf(fact_252_n__lists_Osimps_I1_J, axiom, (! [A:$tType,Xs2:(list @ A)]: (((((n_lists @ A) @ (zero_zero @ nat)) @ Xs2) = (((cons @ (list @ A)) @ (nil @ A)) @ (nil @ (list @ A))))))).
% 2.92/1.57 thf(fact_253_length__0__conv, axiom, (! [A:$tType,Xs2:(list @ A)]: (((((size_size @ (list @ A)) @ Xs2) = (zero_zero @ nat)) = (Xs2 = (nil @ A)))))).
% 2.92/1.57 thf(fact_254_length__greater__0__conv, axiom, (! [A:$tType,Xs2:(list @ A)]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ ((size_size @ (list @ A)) @ Xs2)) = (Xs2 != (nil @ A)))))).
% 2.92/1.57 thf(tcon_fun___Orderings_Oord, axiom, (! [A8:$tType,A9:$tType]: (((ord @ A9) => (ord @ (A8 > A9)))))).
% 2.92/1.57 thf(tcon_Nat_Onat___Orderings_Olinorder, axiom, (linorder @ nat)).
% 2.92/1.57 thf(tcon_Nat_Onat___Orderings_Oord_1, axiom, (ord @ nat)).
% 2.92/1.57 thf(tcon_Set_Oset___Orderings_Oord_2, axiom, (! [A8:$tType]: ((ord @ (set @ A8))))).
% 2.92/1.57 thf(tcon_HOL_Obool___Orderings_Olinorder_3, axiom, (linorder @ $o)).
% 2.92/1.57 thf(tcon_HOL_Obool___Orderings_Oord_4, axiom, (ord @ $o)).
% 2.92/1.57 thf(tcon_Product__Type_Ounit___Orderings_Olinorder_5, axiom, (linorder @ product_unit)).
% 2.92/1.57 thf(tcon_Product__Type_Ounit___Orderings_Oord_6, axiom, (ord @ product_unit)).
% 2.92/1.57 thf(help_If_3_1_T, axiom, (! [P2:$o]: (((P2 = $true) | (P2 = $false))))).
% 2.92/1.57 thf(help_If_2_1_T, axiom, (! [A:$tType,X3:A,Y3:A]: ((((((if @ A) @ $false) @ X3) @ Y3) = Y3)))).
% 2.92/1.57 thf(help_If_1_1_T, axiom, (! [A:$tType,X3:A,Y3:A]: ((((((if @ A) @ $true) @ X3) @ Y3) = X3)))).
% 2.92/1.57 thf(conj_0, conjecture, (! [Xs4:(list @ ((product_prod @ a) @ a)),X4:a,Y4:a,Ys4:(list @ ((product_prod @ a) @ a))]: ((es != (((append @ ((product_prod @ a) @ a)) @ Xs4) @ (((cons @ ((product_prod @ a) @ a)) @ ((((product_Pair @ a) @ a) @ X4) @ Y4)) @ (((cons @ ((product_prod @ a) @ a)) @ ((((product_Pair @ a) @ a) @ Y4) @ X4)) @ Ys4))))))).
% 2.92/1.57 % SZS output end ListOfTHF for /export/starexec/sandbox2/tmp/tmp.eKA1rT9gZb/DTF2DTF9790.p
% 2.92/1.57 ------------------------
% 3.12/1.62 ---- Cleaned THF ---
% 3.12/1.62 thf(ty_t_Pair__Digraph_Opair__pre__digraph_Opair__pre__digraph__ext,type,
% 3.12/1.62 pair_p1731315293ph_ext: $tType > $tType > $tType ).
% 3.12/1.62
% 3.12/1.62 thf(ty_t_Product__Type_Ounit,type,
% 3.12/1.62 product_unit: $tType ).
% 3.12/1.62
% 3.12/1.62 thf(ty_t_Product__Type_Oprod,type,
% 3.12/1.62 product_prod: $tType > $tType > $tType ).
% 3.12/1.62
% 3.12/1.62 thf(ty_t_List_Olist,type,
% 3.12/1.62 list: $tType > $tType ).
% 3.12/1.62
% 3.12/1.62 thf(ty_t_Set_Oset,type,
% 3.12/1.62 set: $tType > $tType ).
% 3.12/1.62
% 3.12/1.62 thf(ty_t_Nat_Onat,type,
% 3.12/1.62 nat: $tType ).
% 3.12/1.62
% 3.12/1.62 thf(ty_tf_a,type,
% 3.12/1.62 a: $tType ).
% 3.12/1.62
% 3.12/1.62 thf(sy_cl_HOL_Otype,type,
% 3.12/1.62 type:
% 3.12/1.62 !>[A: $tType] : $o ).
% 3.12/1.62
% 3.12/1.62 thf(sy_cl_Orderings_Oord,type,
% 3.12/1.62 ord:
% 3.12/1.62 !>[A: $tType] : $o ).
% 3.12/1.62
% 3.12/1.62 thf(sy_cl_Orderings_Olinorder,type,
% 3.12/1.62 linorder:
% 3.12/1.62 !>[A: $tType] : $o ).
% 3.12/1.62
% 3.12/1.62 thf(sy_c_Groups_Ozero__class_Ozero,type,
% 3.12/1.62 zero_zero:
% 3.12/1.62 !>[A: $tType] : A ).
% 3.12/1.62
% 3.12/1.62 thf(sy_c_If,type,
% 3.12/1.62 if:
% 3.12/1.62 !>[A: $tType] : ( $o > A > A > A ) ).
% 3.12/1.62
% 3.12/1.62 thf(sy_c_Kuratowski__Mirabelle__hkvioyikiw_Oprogressing,type,
% 3.12/1.62 kurato990191779essing:
% 3.12/1.62 !>[A: $tType] : ( ( list @ ( product_prod @ A @ A ) ) > $o ) ).
% 3.12/1.62
% 3.12/1.62 thf(sy_c_List_Oappend,type,
% 3.12/1.62 append:
% 3.12/1.62 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > ( list @ A ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(sy_c_List_Obind,type,
% 3.12/1.62 bind:
% 3.12/1.62 !>[A: $tType,B: $tType] : ( ( list @ A ) > ( A > ( list @ B ) ) > ( list @ B ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(sy_c_List_Oconcat,type,
% 3.12/1.62 concat:
% 3.12/1.62 !>[A: $tType] : ( ( list @ ( list @ A ) ) > ( list @ A ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(sy_c_List_Oinsert,type,
% 3.12/1.62 insert:
% 3.12/1.62 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(sy_c_List_Olenlex,type,
% 3.12/1.62 lenlex:
% 3.12/1.62 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > ( set @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(sy_c_List_Olex,type,
% 3.12/1.62 lex:
% 3.12/1.62 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > ( set @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(sy_c_List_Olexord,type,
% 3.12/1.62 lexord:
% 3.12/1.62 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > ( set @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(sy_c_List_Olist_OCons,type,
% 3.12/1.62 cons:
% 3.12/1.62 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(sy_c_List_Olist_ONil,type,
% 3.12/1.62 nil:
% 3.12/1.62 !>[A: $tType] : ( list @ A ) ).
% 3.12/1.62
% 3.12/1.62 thf(sy_c_List_Olist_Oset,type,
% 3.12/1.62 set2:
% 3.12/1.62 !>[A: $tType] : ( ( list @ A ) > ( set @ A ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(sy_c_List_Olistrel,type,
% 3.12/1.62 listrel:
% 3.12/1.62 !>[A: $tType,B: $tType] : ( ( set @ ( product_prod @ A @ B ) ) > ( set @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(sy_c_List_Olistrel1,type,
% 3.12/1.62 listrel1:
% 3.12/1.62 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > ( set @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(sy_c_List_Omaps,type,
% 3.12/1.62 maps:
% 3.12/1.62 !>[A: $tType,B: $tType] : ( ( A > ( list @ B ) ) > ( list @ A ) > ( list @ B ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(sy_c_List_Omeasures,type,
% 3.12/1.62 measures:
% 3.12/1.62 !>[A: $tType] : ( ( list @ ( A > nat ) ) > ( set @ ( product_prod @ A @ A ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(sy_c_List_Omember,type,
% 3.12/1.62 member:
% 3.12/1.62 !>[A: $tType] : ( ( list @ A ) > A > $o ) ).
% 3.12/1.62
% 3.12/1.62 thf(sy_c_List_On__lists,type,
% 3.12/1.62 n_lists:
% 3.12/1.62 !>[A: $tType] : ( nat > ( list @ A ) > ( list @ ( list @ A ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(sy_c_List_Oproduct__lists,type,
% 3.12/1.62 product_lists:
% 3.12/1.62 !>[A: $tType] : ( ( list @ ( list @ A ) ) > ( list @ ( list @ A ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(sy_c_List_Osubseqs,type,
% 3.12/1.62 subseqs:
% 3.12/1.62 !>[A: $tType] : ( ( list @ A ) > ( list @ ( list @ A ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(sy_c_List_Ozip,type,
% 3.12/1.62 zip:
% 3.12/1.62 !>[A: $tType,B: $tType] : ( ( list @ A ) > ( list @ B ) > ( list @ ( product_prod @ A @ B ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(sy_c_Multiset_Olinorder__class_Opart,type,
% 3.12/1.62 linorder_part:
% 3.12/1.62 !>[B: $tType,A: $tType] : ( ( B > A ) > A > ( list @ B ) > ( product_prod @ ( list @ B ) @ ( product_prod @ ( list @ B ) @ ( list @ B ) ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(sy_c_Nat_Osize__class_Osize,type,
% 3.12/1.62 size_size:
% 3.12/1.62 !>[A: $tType] : ( A > nat ) ).
% 3.12/1.62
% 3.12/1.62 thf(sy_c_Orderings_Oord__class_Oless,type,
% 3.12/1.62 ord_less:
% 3.12/1.62 !>[A: $tType] : ( A > A > $o ) ).
% 3.12/1.62
% 3.12/1.62 thf(sy_c_Pair__Digraph_Oco__path,type,
% 3.12/1.62 pair_co_path:
% 3.12/1.62 !>[A: $tType] : ( ( product_prod @ A @ A ) > A > ( list @ ( product_prod @ A @ A ) ) > ( list @ ( product_prod @ A @ A ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(sy_c_Pair__Digraph_Oco__path__rel,type,
% 3.12/1.62 pair_co_path_rel:
% 3.12/1.62 !>[A: $tType] : ( ( product_prod @ ( product_prod @ A @ A ) @ ( product_prod @ A @ ( list @ ( product_prod @ A @ A ) ) ) ) > ( product_prod @ ( product_prod @ A @ A ) @ ( product_prod @ A @ ( list @ ( product_prod @ A @ A ) ) ) ) > $o ) ).
% 3.12/1.62
% 3.12/1.62 thf(sy_c_Pair__Digraph_Opawalk__verts,type,
% 3.12/1.62 pair_pawalk_verts:
% 3.12/1.62 !>[A: $tType] : ( A > ( list @ ( product_prod @ A @ A ) ) > ( list @ A ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(sy_c_Pair__Digraph_Osd__path,type,
% 3.12/1.62 pair_sd_path:
% 3.12/1.62 !>[A: $tType] : ( ( product_prod @ A @ A ) > A > ( list @ ( product_prod @ A @ A ) ) > ( list @ ( product_prod @ A @ A ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(sy_c_Pair__Digraph_Osd__path__rel,type,
% 3.12/1.62 pair_sd_path_rel:
% 3.12/1.62 !>[A: $tType] : ( ( product_prod @ ( product_prod @ A @ A ) @ ( product_prod @ A @ ( list @ ( product_prod @ A @ A ) ) ) ) > ( product_prod @ ( product_prod @ A @ A ) @ ( product_prod @ A @ ( list @ ( product_prod @ A @ A ) ) ) ) > $o ) ).
% 3.12/1.62
% 3.12/1.62 thf(sy_c_Permutations_Oinverse__permutation__of__list,type,
% 3.12/1.62 invers965609412f_list:
% 3.12/1.62 !>[A: $tType] : ( ( list @ ( product_prod @ A @ A ) ) > A > A ) ).
% 3.12/1.62
% 3.12/1.62 thf(sy_c_Permutations_Oinverse__permutation__of__list__rel,type,
% 3.12/1.62 invers1507583541st_rel:
% 3.12/1.62 !>[A: $tType] : ( ( product_prod @ ( list @ ( product_prod @ A @ A ) ) @ A ) > ( product_prod @ ( list @ ( product_prod @ A @ A ) ) @ A ) > $o ) ).
% 3.12/1.62
% 3.12/1.62 thf(sy_c_Permutations_Olist__permutes,type,
% 3.12/1.62 list_permutes:
% 3.12/1.62 !>[A: $tType] : ( ( list @ ( product_prod @ A @ A ) ) > ( set @ A ) > $o ) ).
% 3.12/1.62
% 3.12/1.62 thf(sy_c_Permutations_Opermutation__of__list,type,
% 3.12/1.62 permutation_of_list:
% 3.12/1.62 !>[A: $tType] : ( ( list @ ( product_prod @ A @ A ) ) > A > A ) ).
% 3.12/1.62
% 3.12/1.62 thf(sy_c_Product__Type_OPair,type,
% 3.12/1.62 product_Pair:
% 3.12/1.62 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(sy_c_Product__Type_Ointernal__case__prod,type,
% 3.12/1.62 produc2004651681e_prod:
% 3.12/1.62 !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > ( product_prod @ A @ B ) > C ) ).
% 3.12/1.62
% 3.12/1.62 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod,type,
% 3.12/1.62 product_rec_prod:
% 3.12/1.62 !>[A: $tType,B: $tType,T: $tType] : ( ( A > B > T ) > ( product_prod @ A @ B ) > T ) ).
% 3.12/1.62
% 3.12/1.62 thf(sy_c_Relation_Oasym,type,
% 3.12/1.62 asym:
% 3.12/1.62 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > $o ) ).
% 3.12/1.62
% 3.12/1.62 thf(sy_c_Relation_Oirrefl,type,
% 3.12/1.62 irrefl:
% 3.12/1.62 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > $o ) ).
% 3.12/1.62
% 3.12/1.62 thf(sy_c_Set_OCollect,type,
% 3.12/1.62 collect:
% 3.12/1.62 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(sy_c_Set_Othe__elem,type,
% 3.12/1.62 the_elem:
% 3.12/1.62 !>[A: $tType] : ( ( set @ A ) > A ) ).
% 3.12/1.62
% 3.12/1.62 thf(sy_c_Wellfounded_Oaccp,type,
% 3.12/1.62 accp:
% 3.12/1.62 !>[A: $tType] : ( ( A > A > $o ) > A > $o ) ).
% 3.12/1.62
% 3.12/1.62 thf(sy_c_member,type,
% 3.12/1.62 member2:
% 3.12/1.62 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 3.12/1.62
% 3.12/1.62 thf(sy_v_e,type,
% 3.12/1.62 e: product_prod @ a @ a ).
% 3.12/1.62
% 3.12/1.62 thf(sy_v_es,type,
% 3.12/1.62 es: list @ ( product_prod @ a @ a ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_0_assms,axiom,
% 3.12/1.62 kurato990191779essing @ a @ ( cons @ ( product_prod @ a @ a ) @ e @ es ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_1_progressing__def,axiom,
% 3.12/1.62 ! [A: $tType] :
% 3.12/1.62 ( ( kurato990191779essing @ A )
% 3.12/1.62 = ( ^ [P: list @ ( product_prod @ A @ A )] :
% 3.12/1.62 ! [Xs: list @ ( product_prod @ A @ A ),X: A,Y: A,Ys: list @ ( product_prod @ A @ A )] :
% 3.12/1.62 ( P
% 3.12/1.62 != ( append @ ( product_prod @ A @ A ) @ Xs @ ( cons @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y ) @ ( cons @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y @ X ) @ Ys ) ) ) ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_2_append_Oassoc,axiom,
% 3.12/1.62 ! [A: $tType,A2: list @ A,B2: list @ A,C2: list @ A] :
% 3.12/1.62 ( ( append @ A @ ( append @ A @ A2 @ B2 ) @ C2 )
% 3.12/1.62 = ( append @ A @ A2 @ ( append @ A @ B2 @ C2 ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_3_append__assoc,axiom,
% 3.12/1.62 ! [A: $tType,Xs2: list @ A,Ys2: list @ A,Zs: list @ A] :
% 3.12/1.62 ( ( append @ A @ ( append @ A @ Xs2 @ Ys2 ) @ Zs )
% 3.12/1.62 = ( append @ A @ Xs2 @ ( append @ A @ Ys2 @ Zs ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_4_append__same__eq,axiom,
% 3.12/1.62 ! [A: $tType,Ys2: list @ A,Xs2: list @ A,Zs: list @ A] :
% 3.12/1.62 ( ( ( append @ A @ Ys2 @ Xs2 )
% 3.12/1.62 = ( append @ A @ Zs @ Xs2 ) )
% 3.12/1.62 = ( Ys2 = Zs ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_5_same__append__eq,axiom,
% 3.12/1.62 ! [A: $tType,Xs2: list @ A,Ys2: list @ A,Zs: list @ A] :
% 3.12/1.62 ( ( ( append @ A @ Xs2 @ Ys2 )
% 3.12/1.62 = ( append @ A @ Xs2 @ Zs ) )
% 3.12/1.62 = ( Ys2 = Zs ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_6_list_Oinject,axiom,
% 3.12/1.62 ! [A: $tType,X21: A,X22: list @ A,Y21: A,Y22: list @ A] :
% 3.12/1.62 ( ( ( cons @ A @ X21 @ X22 )
% 3.12/1.62 = ( cons @ A @ Y21 @ Y22 ) )
% 3.12/1.62 = ( ( X21 = Y21 )
% 3.12/1.62 & ( X22 = Y22 ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_7_prod_Oinject,axiom,
% 3.12/1.62 ! [A: $tType,B: $tType,X1: A,X2: B,Y1: A,Y2: B] :
% 3.12/1.62 ( ( ( product_Pair @ A @ B @ X1 @ X2 )
% 3.12/1.62 = ( product_Pair @ A @ B @ Y1 @ Y2 ) )
% 3.12/1.62 = ( ( X1 = Y1 )
% 3.12/1.62 & ( X2 = Y2 ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_8_old_Oprod_Oinject,axiom,
% 3.12/1.62 ! [A: $tType,B: $tType,A2: A,B2: B,A3: A,B3: B] :
% 3.12/1.62 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 3.12/1.62 = ( product_Pair @ A @ B @ A3 @ B3 ) )
% 3.12/1.62 = ( ( A2 = A3 )
% 3.12/1.62 & ( B2 = B3 ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_9_Cons__eq__appendI,axiom,
% 3.12/1.62 ! [A: $tType,X3: A,Xs1: list @ A,Ys2: list @ A,Xs2: list @ A,Zs: list @ A] :
% 3.12/1.62 ( ( ( cons @ A @ X3 @ Xs1 )
% 3.12/1.62 = Ys2 )
% 3.12/1.62 => ( ( Xs2
% 3.12/1.62 = ( append @ A @ Xs1 @ Zs ) )
% 3.12/1.62 => ( ( cons @ A @ X3 @ Xs2 )
% 3.12/1.62 = ( append @ A @ Ys2 @ Zs ) ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_10_append__Cons,axiom,
% 3.12/1.62 ! [A: $tType,X3: A,Xs2: list @ A,Ys2: list @ A] :
% 3.12/1.62 ( ( append @ A @ ( cons @ A @ X3 @ Xs2 ) @ Ys2 )
% 3.12/1.62 = ( cons @ A @ X3 @ ( append @ A @ Xs2 @ Ys2 ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_11_append__eq__appendI,axiom,
% 3.12/1.62 ! [A: $tType,Xs2: list @ A,Xs1: list @ A,Zs: list @ A,Ys2: list @ A,Us: list @ A] :
% 3.12/1.62 ( ( ( append @ A @ Xs2 @ Xs1 )
% 3.12/1.62 = Zs )
% 3.12/1.62 => ( ( Ys2
% 3.12/1.62 = ( append @ A @ Xs1 @ Us ) )
% 3.12/1.62 => ( ( append @ A @ Xs2 @ Ys2 )
% 3.12/1.62 = ( append @ A @ Zs @ Us ) ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_12_append__eq__append__conv2,axiom,
% 3.12/1.62 ! [A: $tType,Xs2: list @ A,Ys2: list @ A,Zs: list @ A,Ts: list @ A] :
% 3.12/1.62 ( ( ( append @ A @ Xs2 @ Ys2 )
% 3.12/1.62 = ( append @ A @ Zs @ Ts ) )
% 3.12/1.62 = ( ? [Us2: list @ A] :
% 3.12/1.62 ( ( ( Xs2
% 3.12/1.62 = ( append @ A @ Zs @ Us2 ) )
% 3.12/1.62 & ( ( append @ A @ Us2 @ Ys2 )
% 3.12/1.62 = Ts ) )
% 3.12/1.62 | ( ( ( append @ A @ Xs2 @ Us2 )
% 3.12/1.62 = Zs )
% 3.12/1.62 & ( Ys2
% 3.12/1.62 = ( append @ A @ Us2 @ Ts ) ) ) ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_13_old_Oprod_Oinducts,axiom,
% 3.12/1.62 ! [B: $tType,A: $tType,P2: ( product_prod @ A @ B ) > $o,Prod: product_prod @ A @ B] :
% 3.12/1.62 ( ! [A4: A,B4: B] : ( P2 @ ( product_Pair @ A @ B @ A4 @ B4 ) )
% 3.12/1.62 => ( P2 @ Prod ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_14_old_Oprod_Oexhaust,axiom,
% 3.12/1.62 ! [A: $tType,B: $tType,Y3: product_prod @ A @ B] :
% 3.12/1.62 ~ ! [A4: A,B4: B] :
% 3.12/1.62 ( Y3
% 3.12/1.62 != ( product_Pair @ A @ B @ A4 @ B4 ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_15_prod__induct7,axiom,
% 3.12/1.62 ! [G: $tType,F: $tType,E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P2: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) ) )] :
% 3.12/1.62 ( ! [A4: A,B4: B,C3: C,D2: D,E2: E,F2: F,G2: G] : ( P2 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) @ C3 @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F @ G ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F @ G ) @ E2 @ ( product_Pair @ F @ G @ F2 @ G2 ) ) ) ) ) ) )
% 3.12/1.62 => ( P2 @ X3 ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_16_prod__induct6,axiom,
% 3.12/1.62 ! [F: $tType,E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P2: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) )] :
% 3.12/1.62 ( ! [A4: A,B4: B,C3: C,D2: D,E2: E,F2: F] : ( P2 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) @ C3 @ ( product_Pair @ D @ ( product_prod @ E @ F ) @ D2 @ ( product_Pair @ E @ F @ E2 @ F2 ) ) ) ) ) )
% 3.12/1.62 => ( P2 @ X3 ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_17_prod__induct5,axiom,
% 3.12/1.62 ! [E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P2: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) )] :
% 3.12/1.62 ( ! [A4: A,B4: B,C3: C,D2: D,E2: E] : ( P2 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ E ) @ C3 @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) )
% 3.12/1.62 => ( P2 @ X3 ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_18_prod__induct4,axiom,
% 3.12/1.62 ! [D: $tType,C: $tType,B: $tType,A: $tType,P2: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 3.12/1.62 ( ! [A4: A,B4: B,C3: C,D2: D] : ( P2 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B4 @ ( product_Pair @ C @ D @ C3 @ D2 ) ) ) )
% 3.12/1.62 => ( P2 @ X3 ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_19_prod__induct3,axiom,
% 3.12/1.62 ! [C: $tType,B: $tType,A: $tType,P2: ( product_prod @ A @ ( product_prod @ B @ C ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ C )] :
% 3.12/1.62 ( ! [A4: A,B4: B,C3: C] : ( P2 @ ( product_Pair @ A @ ( product_prod @ B @ C ) @ A4 @ ( product_Pair @ B @ C @ B4 @ C3 ) ) )
% 3.12/1.62 => ( P2 @ X3 ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_20_prod__cases7,axiom,
% 3.12/1.62 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,F: $tType,G: $tType,Y3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) ) )] :
% 3.12/1.62 ~ ! [A4: A,B4: B,C3: C,D2: D,E2: E,F2: F,G2: G] :
% 3.12/1.62 ( Y3
% 3.12/1.62 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) @ C3 @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F @ G ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F @ G ) @ E2 @ ( product_Pair @ F @ G @ F2 @ G2 ) ) ) ) ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_21_prod__cases6,axiom,
% 3.12/1.62 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,F: $tType,Y3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) )] :
% 3.12/1.62 ~ ! [A4: A,B4: B,C3: C,D2: D,E2: E,F2: F] :
% 3.12/1.62 ( Y3
% 3.12/1.62 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) @ C3 @ ( product_Pair @ D @ ( product_prod @ E @ F ) @ D2 @ ( product_Pair @ E @ F @ E2 @ F2 ) ) ) ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_22_prod__cases5,axiom,
% 3.12/1.62 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,Y3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) )] :
% 3.12/1.62 ~ ! [A4: A,B4: B,C3: C,D2: D,E2: E] :
% 3.12/1.62 ( Y3
% 3.12/1.62 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ E ) @ C3 @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_23_prod__cases4,axiom,
% 3.12/1.62 ! [A: $tType,B: $tType,C: $tType,D: $tType,Y3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 3.12/1.62 ~ ! [A4: A,B4: B,C3: C,D2: D] :
% 3.12/1.62 ( Y3
% 3.12/1.62 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B4 @ ( product_Pair @ C @ D @ C3 @ D2 ) ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_24_prod__cases3,axiom,
% 3.12/1.62 ! [A: $tType,B: $tType,C: $tType,Y3: product_prod @ A @ ( product_prod @ B @ C )] :
% 3.12/1.62 ~ ! [A4: A,B4: B,C3: C] :
% 3.12/1.62 ( Y3
% 3.12/1.62 != ( product_Pair @ A @ ( product_prod @ B @ C ) @ A4 @ ( product_Pair @ B @ C @ B4 @ C3 ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_25_Pair__inject,axiom,
% 3.12/1.62 ! [A: $tType,B: $tType,A2: A,B2: B,A3: A,B3: B] :
% 3.12/1.62 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 3.12/1.62 = ( product_Pair @ A @ B @ A3 @ B3 ) )
% 3.12/1.62 => ~ ( ( A2 = A3 )
% 3.12/1.62 => ( B2 != B3 ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_26_prod__cases,axiom,
% 3.12/1.62 ! [B: $tType,A: $tType,P2: ( product_prod @ A @ B ) > $o,P3: product_prod @ A @ B] :
% 3.12/1.62 ( ! [A4: A,B4: B] : ( P2 @ ( product_Pair @ A @ B @ A4 @ B4 ) )
% 3.12/1.62 => ( P2 @ P3 ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_27_surj__pair,axiom,
% 3.12/1.62 ! [A: $tType,B: $tType,P3: product_prod @ A @ B] :
% 3.12/1.62 ? [X4: A,Y4: B] :
% 3.12/1.62 ( P3
% 3.12/1.62 = ( product_Pair @ A @ B @ X4 @ Y4 ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_28_not__Cons__self2,axiom,
% 3.12/1.62 ! [A: $tType,X3: A,Xs2: list @ A] :
% 3.12/1.62 ( ( cons @ A @ X3 @ Xs2 )
% 3.12/1.62 != Xs2 ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_29_old_Oprod_Orec,axiom,
% 3.12/1.62 ! [A: $tType,T: $tType,B: $tType,F1: A > B > T,A2: A,B2: B] :
% 3.12/1.62 ( ( product_rec_prod @ A @ B @ T @ F1 @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 3.12/1.62 = ( F1 @ A2 @ B2 ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_30_bind__simps_I2_J,axiom,
% 3.12/1.62 ! [A: $tType,B: $tType,X3: B,Xs2: list @ B,F3: B > ( list @ A )] :
% 3.12/1.62 ( ( bind @ B @ A @ ( cons @ B @ X3 @ Xs2 ) @ F3 )
% 3.12/1.62 = ( append @ A @ ( F3 @ X3 ) @ ( bind @ B @ A @ Xs2 @ F3 ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_31_maps__simps_I1_J,axiom,
% 3.12/1.62 ! [A: $tType,B: $tType,F3: B > ( list @ A ),X3: B,Xs2: list @ B] :
% 3.12/1.62 ( ( maps @ B @ A @ F3 @ ( cons @ B @ X3 @ Xs2 ) )
% 3.12/1.62 = ( append @ A @ ( F3 @ X3 ) @ ( maps @ B @ A @ F3 @ Xs2 ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_32_internal__case__prod__conv,axiom,
% 3.12/1.62 ! [B: $tType,A: $tType,C: $tType,C2: B > C > A,A2: B,B2: C] :
% 3.12/1.62 ( ( produc2004651681e_prod @ B @ C @ A @ C2 @ ( product_Pair @ B @ C @ A2 @ B2 ) )
% 3.12/1.62 = ( C2 @ A2 @ B2 ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_33_lexord__append__left__rightI,axiom,
% 3.12/1.62 ! [A: $tType,A2: A,B2: A,R: set @ ( product_prod @ A @ A ),U: list @ A,X3: list @ A,Y3: list @ A] :
% 3.12/1.62 ( ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ R )
% 3.12/1.62 => ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ U @ ( cons @ A @ A2 @ X3 ) ) @ ( append @ A @ U @ ( cons @ A @ B2 @ Y3 ) ) ) @ ( lexord @ A @ R ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_34_zip__Cons__Cons,axiom,
% 3.12/1.62 ! [A: $tType,B: $tType,X3: A,Xs2: list @ A,Y3: B,Ys2: list @ B] :
% 3.12/1.62 ( ( zip @ A @ B @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ B @ Y3 @ Ys2 ) )
% 3.12/1.62 = ( cons @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X3 @ Y3 ) @ ( zip @ A @ B @ Xs2 @ Ys2 ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_35_listrel1I,axiom,
% 3.12/1.62 ! [A: $tType,X3: A,Y3: A,R: set @ ( product_prod @ A @ A ),Xs2: list @ A,Us: list @ A,Vs: list @ A,Ys2: list @ A] :
% 3.12/1.62 ( ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X3 @ Y3 ) @ R )
% 3.12/1.62 => ( ( Xs2
% 3.12/1.62 = ( append @ A @ Us @ ( cons @ A @ X3 @ Vs ) ) )
% 3.12/1.62 => ( ( Ys2
% 3.12/1.62 = ( append @ A @ Us @ ( cons @ A @ Y3 @ Vs ) ) )
% 3.12/1.62 => ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs2 @ Ys2 ) @ ( listrel1 @ A @ R ) ) ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_36_listrel1E,axiom,
% 3.12/1.62 ! [A: $tType,Xs2: list @ A,Ys2: list @ A,R: set @ ( product_prod @ A @ A )] :
% 3.12/1.62 ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs2 @ Ys2 ) @ ( listrel1 @ A @ R ) )
% 3.12/1.62 => ~ ! [X4: A,Y4: A] :
% 3.12/1.62 ( ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X4 @ Y4 ) @ R )
% 3.12/1.62 => ! [Us3: list @ A,Vs2: list @ A] :
% 3.12/1.62 ( ( Xs2
% 3.12/1.62 = ( append @ A @ Us3 @ ( cons @ A @ X4 @ Vs2 ) ) )
% 3.12/1.62 => ( Ys2
% 3.12/1.62 != ( append @ A @ Us3 @ ( cons @ A @ Y4 @ Vs2 ) ) ) ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_37_member__rec_I1_J,axiom,
% 3.12/1.62 ! [A: $tType,X3: A,Xs2: list @ A,Y3: A] :
% 3.12/1.62 ( ( member @ A @ ( cons @ A @ X3 @ Xs2 ) @ Y3 )
% 3.12/1.62 = ( ( X3 = Y3 )
% 3.12/1.62 | ( member @ A @ Xs2 @ Y3 ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_38_ssubst__Pair__rhs,axiom,
% 3.12/1.62 ! [B: $tType,A: $tType,R: A,S: B,R2: set @ ( product_prod @ A @ B ),S2: B] :
% 3.12/1.62 ( ( member2 @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ R @ S ) @ R2 )
% 3.12/1.62 => ( ( S2 = S )
% 3.12/1.62 => ( member2 @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ R @ S2 ) @ R2 ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_39_subdivide_Oinduct,axiom,
% 3.12/1.62 ! [A: $tType,P2: ( pair_p1731315293ph_ext @ A @ product_unit ) > ( product_prod @ A @ A ) > A > $o,A0: pair_p1731315293ph_ext @ A @ product_unit,A1: product_prod @ A @ A,A22: A] :
% 3.12/1.62 ( ! [G3: pair_p1731315293ph_ext @ A @ product_unit,U2: A,V: A,X_1: A] : ( P2 @ G3 @ ( product_Pair @ A @ A @ U2 @ V ) @ X_1 )
% 3.12/1.62 => ( P2 @ A0 @ A1 @ A22 ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_40_Cons__listrel1__Cons,axiom,
% 3.12/1.62 ! [A: $tType,X3: A,Xs2: list @ A,Y3: A,Ys2: list @ A,R: set @ ( product_prod @ A @ A )] :
% 3.12/1.62 ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ A @ Y3 @ Ys2 ) ) @ ( listrel1 @ A @ R ) )
% 3.12/1.62 = ( ( ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X3 @ Y3 ) @ R )
% 3.12/1.62 & ( Xs2 = Ys2 ) )
% 3.12/1.62 | ( ( X3 = Y3 )
% 3.12/1.62 & ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs2 @ Ys2 ) @ ( listrel1 @ A @ R ) ) ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_41_lexord__cons__cons,axiom,
% 3.12/1.62 ! [A: $tType,A2: A,X3: list @ A,B2: A,Y3: list @ A,R: set @ ( product_prod @ A @ A )] :
% 3.12/1.62 ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ A2 @ X3 ) @ ( cons @ A @ B2 @ Y3 ) ) @ ( lexord @ A @ R ) )
% 3.12/1.62 = ( ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ R )
% 3.12/1.62 | ( ( A2 = B2 )
% 3.12/1.62 & ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ X3 @ Y3 ) @ ( lexord @ A @ R ) ) ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_42_listrel1I2,axiom,
% 3.12/1.62 ! [A: $tType,Xs2: list @ A,Ys2: list @ A,R: set @ ( product_prod @ A @ A ),X3: A] :
% 3.12/1.62 ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs2 @ Ys2 ) @ ( listrel1 @ A @ R ) )
% 3.12/1.62 => ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ A @ X3 @ Ys2 ) ) @ ( listrel1 @ A @ R ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_43_append__listrel1I,axiom,
% 3.12/1.62 ! [A: $tType,Xs2: list @ A,Ys2: list @ A,R: set @ ( product_prod @ A @ A ),Us: list @ A,Vs: list @ A] :
% 3.12/1.62 ( ( ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs2 @ Ys2 ) @ ( listrel1 @ A @ R ) )
% 3.12/1.62 & ( Us = Vs ) )
% 3.12/1.62 | ( ( Xs2 = Ys2 )
% 3.12/1.62 & ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Us @ Vs ) @ ( listrel1 @ A @ R ) ) ) )
% 3.12/1.62 => ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ Xs2 @ Us ) @ ( append @ A @ Ys2 @ Vs ) ) @ ( listrel1 @ A @ R ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_44_lexord__linear,axiom,
% 3.12/1.62 ! [A: $tType,R: set @ ( product_prod @ A @ A ),X3: list @ A,Y3: list @ A] :
% 3.12/1.62 ( ! [A4: A,B4: A] :
% 3.12/1.62 ( ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A4 @ B4 ) @ R )
% 3.12/1.62 | ( A4 = B4 )
% 3.12/1.62 | ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ B4 @ A4 ) @ R ) )
% 3.12/1.62 => ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ X3 @ Y3 ) @ ( lexord @ A @ R ) )
% 3.12/1.62 | ( X3 = Y3 )
% 3.12/1.62 | ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Y3 @ X3 ) @ ( lexord @ A @ R ) ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_45_mem__Collect__eq,axiom,
% 3.12/1.62 ! [A: $tType,A2: A,P2: A > $o] :
% 3.12/1.62 ( ( member2 @ A @ A2 @ ( collect @ A @ P2 ) )
% 3.12/1.62 = ( P2 @ A2 ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_46_Collect__mem__eq,axiom,
% 3.12/1.62 ! [A: $tType,A5: set @ A] :
% 3.12/1.62 ( ( collect @ A
% 3.12/1.62 @ ^ [X: A] : ( member2 @ A @ X @ A5 ) )
% 3.12/1.62 = A5 ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_47_Collect__cong,axiom,
% 3.12/1.62 ! [A: $tType,P2: A > $o,Q: A > $o] :
% 3.12/1.62 ( ! [X4: A] :
% 3.12/1.62 ( ( P2 @ X4 )
% 3.12/1.62 = ( Q @ X4 ) )
% 3.12/1.62 => ( ( collect @ A @ P2 )
% 3.12/1.62 = ( collect @ A @ Q ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_48_lexord__irreflexive,axiom,
% 3.12/1.62 ! [A: $tType,R: set @ ( product_prod @ A @ A ),Xs2: list @ A] :
% 3.12/1.62 ( ! [X4: A] :
% 3.12/1.62 ~ ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X4 @ X4 ) @ R )
% 3.12/1.62 => ~ ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs2 @ Xs2 ) @ ( lexord @ A @ R ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_49_lexord__append__leftI,axiom,
% 3.12/1.62 ! [A: $tType,U: list @ A,V2: list @ A,R: set @ ( product_prod @ A @ A ),X3: list @ A] :
% 3.12/1.62 ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ U @ V2 ) @ ( lexord @ A @ R ) )
% 3.12/1.62 => ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ X3 @ U ) @ ( append @ A @ X3 @ V2 ) ) @ ( lexord @ A @ R ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_50_listrel1I1,axiom,
% 3.12/1.62 ! [A: $tType,X3: A,Y3: A,R: set @ ( product_prod @ A @ A ),Xs2: list @ A] :
% 3.12/1.62 ( ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X3 @ Y3 ) @ R )
% 3.12/1.62 => ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ A @ Y3 @ Xs2 ) ) @ ( listrel1 @ A @ R ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_51_Cons__listrel1E1,axiom,
% 3.12/1.62 ! [A: $tType,X3: A,Xs2: list @ A,Ys2: list @ A,R: set @ ( product_prod @ A @ A )] :
% 3.12/1.62 ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X3 @ Xs2 ) @ Ys2 ) @ ( listrel1 @ A @ R ) )
% 3.12/1.62 => ( ! [Y4: A] :
% 3.12/1.62 ( ( Ys2
% 3.12/1.62 = ( cons @ A @ Y4 @ Xs2 ) )
% 3.12/1.62 => ~ ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X3 @ Y4 ) @ R ) )
% 3.12/1.62 => ~ ! [Zs2: list @ A] :
% 3.12/1.62 ( ( Ys2
% 3.12/1.62 = ( cons @ A @ X3 @ Zs2 ) )
% 3.12/1.62 => ~ ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs2 @ Zs2 ) @ ( listrel1 @ A @ R ) ) ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_52_Cons__listrel1E2,axiom,
% 3.12/1.62 ! [A: $tType,Xs2: list @ A,Y3: A,Ys2: list @ A,R: set @ ( product_prod @ A @ A )] :
% 3.12/1.62 ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs2 @ ( cons @ A @ Y3 @ Ys2 ) ) @ ( listrel1 @ A @ R ) )
% 3.12/1.62 => ( ! [X4: A] :
% 3.12/1.62 ( ( Xs2
% 3.12/1.62 = ( cons @ A @ X4 @ Ys2 ) )
% 3.12/1.62 => ~ ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X4 @ Y3 ) @ R ) )
% 3.12/1.62 => ~ ! [Zs2: list @ A] :
% 3.12/1.62 ( ( Xs2
% 3.12/1.62 = ( cons @ A @ Y3 @ Zs2 ) )
% 3.12/1.62 => ~ ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Zs2 @ Ys2 ) @ ( listrel1 @ A @ R ) ) ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_53_lexord__append__leftD,axiom,
% 3.12/1.62 ! [A: $tType,X3: list @ A,U: list @ A,V2: list @ A,R: set @ ( product_prod @ A @ A )] :
% 3.12/1.62 ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ X3 @ U ) @ ( append @ A @ X3 @ V2 ) ) @ ( lexord @ A @ R ) )
% 3.12/1.62 => ( ! [A4: A] :
% 3.12/1.62 ~ ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A4 @ A4 ) @ R )
% 3.12/1.62 => ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ U @ V2 ) @ ( lexord @ A @ R ) ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_54_lexord__append__rightI,axiom,
% 3.12/1.62 ! [A: $tType,Y3: list @ A,X3: list @ A,R: set @ ( product_prod @ A @ A )] :
% 3.12/1.62 ( ? [B5: A,Z: list @ A] :
% 3.12/1.62 ( Y3
% 3.12/1.62 = ( cons @ A @ B5 @ Z ) )
% 3.12/1.62 => ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ X3 @ ( append @ A @ X3 @ Y3 ) ) @ ( lexord @ A @ R ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_55_zip__eq__ConsE,axiom,
% 3.12/1.62 ! [A: $tType,B: $tType,Xs2: list @ A,Ys2: list @ B,Xy: product_prod @ A @ B,Xys: list @ ( product_prod @ A @ B )] :
% 3.12/1.62 ( ( ( zip @ A @ B @ Xs2 @ Ys2 )
% 3.12/1.62 = ( cons @ ( product_prod @ A @ B ) @ Xy @ Xys ) )
% 3.12/1.62 => ~ ! [X4: A,Xs3: list @ A] :
% 3.12/1.62 ( ( Xs2
% 3.12/1.62 = ( cons @ A @ X4 @ Xs3 ) )
% 3.12/1.62 => ! [Y4: B,Ys3: list @ B] :
% 3.12/1.62 ( ( Ys2
% 3.12/1.62 = ( cons @ B @ Y4 @ Ys3 ) )
% 3.12/1.62 => ( ( Xy
% 3.12/1.62 = ( product_Pair @ A @ B @ X4 @ Y4 ) )
% 3.12/1.62 => ( Xys
% 3.12/1.62 != ( zip @ A @ B @ Xs3 @ Ys3 ) ) ) ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_56_subdivide_Ocases,axiom,
% 3.12/1.62 ! [A: $tType,X3: product_prod @ ( pair_p1731315293ph_ext @ A @ product_unit ) @ ( product_prod @ ( product_prod @ A @ A ) @ A )] :
% 3.12/1.62 ~ ! [G3: pair_p1731315293ph_ext @ A @ product_unit,U2: A,V: A,W: A] :
% 3.12/1.62 ( X3
% 3.12/1.62 != ( product_Pair @ ( pair_p1731315293ph_ext @ A @ product_unit ) @ ( product_prod @ ( product_prod @ A @ A ) @ A ) @ G3 @ ( product_Pair @ ( product_prod @ A @ A ) @ A @ ( product_Pair @ A @ A @ U2 @ V ) @ W ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_57_lexord__same__pref__if__irrefl,axiom,
% 3.12/1.62 ! [A: $tType,R: set @ ( product_prod @ A @ A ),Xs2: list @ A,Ys2: list @ A,Zs: list @ A] :
% 3.12/1.62 ( ( irrefl @ A @ R )
% 3.12/1.62 => ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ Xs2 @ Ys2 ) @ ( append @ A @ Xs2 @ Zs ) ) @ ( lexord @ A @ R ) )
% 3.12/1.62 = ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Ys2 @ Zs ) @ ( lexord @ A @ R ) ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_58_snoc__listrel1__snoc__iff,axiom,
% 3.12/1.62 ! [A: $tType,Xs2: list @ A,X3: A,Ys2: list @ A,Y3: A,R: set @ ( product_prod @ A @ A )] :
% 3.12/1.62 ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ Xs2 @ ( cons @ A @ X3 @ ( nil @ A ) ) ) @ ( append @ A @ Ys2 @ ( cons @ A @ Y3 @ ( nil @ A ) ) ) ) @ ( listrel1 @ A @ R ) )
% 3.12/1.62 = ( ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs2 @ Ys2 ) @ ( listrel1 @ A @ R ) )
% 3.12/1.62 & ( X3 = Y3 ) )
% 3.12/1.62 | ( ( Xs2 = Ys2 )
% 3.12/1.62 & ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X3 @ Y3 ) @ R ) ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_59_lexord__Nil__left,axiom,
% 3.12/1.62 ! [A: $tType,Y3: list @ A,R: set @ ( product_prod @ A @ A )] :
% 3.12/1.62 ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( nil @ A ) @ Y3 ) @ ( lexord @ A @ R ) )
% 3.12/1.62 = ( ? [A6: A,X: list @ A] :
% 3.12/1.62 ( Y3
% 3.12/1.62 = ( cons @ A @ A6 @ X ) ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_60_lexord__same__pref__iff,axiom,
% 3.12/1.62 ! [A: $tType,Xs2: list @ A,Ys2: list @ A,Zs: list @ A,R: set @ ( product_prod @ A @ A )] :
% 3.12/1.62 ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ Xs2 @ Ys2 ) @ ( append @ A @ Xs2 @ Zs ) ) @ ( lexord @ A @ R ) )
% 3.12/1.62 = ( ? [X: A] :
% 3.12/1.62 ( ( member2 @ A @ X @ ( set2 @ A @ Xs2 ) )
% 3.12/1.62 & ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ X ) @ R ) )
% 3.12/1.62 | ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Ys2 @ Zs ) @ ( lexord @ A @ R ) ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_61_zip__append,axiom,
% 3.12/1.62 ! [A: $tType,B: $tType,Xs2: list @ A,Us: list @ B,Ys2: list @ A,Vs: list @ B] :
% 3.12/1.62 ( ( ( size_size @ ( list @ A ) @ Xs2 )
% 3.12/1.62 = ( size_size @ ( list @ B ) @ Us ) )
% 3.12/1.62 => ( ( zip @ A @ B @ ( append @ A @ Xs2 @ Ys2 ) @ ( append @ B @ Us @ Vs ) )
% 3.12/1.62 = ( append @ ( product_prod @ A @ B ) @ ( zip @ A @ B @ Xs2 @ Us ) @ ( zip @ A @ B @ Ys2 @ Vs ) ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_62_lex__append__leftD,axiom,
% 3.12/1.62 ! [A: $tType,R: set @ ( product_prod @ A @ A ),Xs2: list @ A,Ys2: list @ A,Zs: list @ A] :
% 3.12/1.62 ( ! [X4: A] :
% 3.12/1.62 ~ ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X4 @ X4 ) @ R )
% 3.12/1.62 => ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ Xs2 @ Ys2 ) @ ( append @ A @ Xs2 @ Zs ) ) @ ( lex @ A @ R ) )
% 3.12/1.62 => ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Ys2 @ Zs ) @ ( lex @ A @ R ) ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_63_lex__append__left__iff,axiom,
% 3.12/1.62 ! [A: $tType,R: set @ ( product_prod @ A @ A ),Xs2: list @ A,Ys2: list @ A,Zs: list @ A] :
% 3.12/1.62 ( ! [X4: A] :
% 3.12/1.62 ~ ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X4 @ X4 ) @ R )
% 3.12/1.62 => ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ Xs2 @ Ys2 ) @ ( append @ A @ Xs2 @ Zs ) ) @ ( lex @ A @ R ) )
% 3.12/1.62 = ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Ys2 @ Zs ) @ ( lex @ A @ R ) ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_64_lexord__asymmetric,axiom,
% 3.12/1.62 ! [A: $tType,R2: set @ ( product_prod @ A @ A ),A2: list @ A,B2: list @ A] :
% 3.12/1.62 ( ( asym @ A @ R2 )
% 3.12/1.62 => ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ A2 @ B2 ) @ ( lexord @ A @ R2 ) )
% 3.12/1.62 => ~ ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ B2 @ A2 ) @ ( lexord @ A @ R2 ) ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_65_append_Oright__neutral,axiom,
% 3.12/1.62 ! [A: $tType,A2: list @ A] :
% 3.12/1.62 ( ( append @ A @ A2 @ ( nil @ A ) )
% 3.12/1.62 = A2 ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_66_append__is__Nil__conv,axiom,
% 3.12/1.62 ! [A: $tType,Xs2: list @ A,Ys2: list @ A] :
% 3.12/1.62 ( ( ( append @ A @ Xs2 @ Ys2 )
% 3.12/1.62 = ( nil @ A ) )
% 3.12/1.62 = ( ( Xs2
% 3.12/1.62 = ( nil @ A ) )
% 3.12/1.62 & ( Ys2
% 3.12/1.62 = ( nil @ A ) ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_67_Nil__is__append__conv,axiom,
% 3.12/1.62 ! [A: $tType,Xs2: list @ A,Ys2: list @ A] :
% 3.12/1.62 ( ( ( nil @ A )
% 3.12/1.62 = ( append @ A @ Xs2 @ Ys2 ) )
% 3.12/1.62 = ( ( Xs2
% 3.12/1.62 = ( nil @ A ) )
% 3.12/1.62 & ( Ys2
% 3.12/1.62 = ( nil @ A ) ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_68_self__append__conv2,axiom,
% 3.12/1.62 ! [A: $tType,Ys2: list @ A,Xs2: list @ A] :
% 3.12/1.62 ( ( Ys2
% 3.12/1.62 = ( append @ A @ Xs2 @ Ys2 ) )
% 3.12/1.62 = ( Xs2
% 3.12/1.62 = ( nil @ A ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_69_append__self__conv2,axiom,
% 3.12/1.62 ! [A: $tType,Xs2: list @ A,Ys2: list @ A] :
% 3.12/1.62 ( ( ( append @ A @ Xs2 @ Ys2 )
% 3.12/1.62 = Ys2 )
% 3.12/1.62 = ( Xs2
% 3.12/1.62 = ( nil @ A ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_70_self__append__conv,axiom,
% 3.12/1.62 ! [A: $tType,Xs2: list @ A,Ys2: list @ A] :
% 3.12/1.62 ( ( Xs2
% 3.12/1.62 = ( append @ A @ Xs2 @ Ys2 ) )
% 3.12/1.62 = ( Ys2
% 3.12/1.62 = ( nil @ A ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_71_append__self__conv,axiom,
% 3.12/1.62 ! [A: $tType,Xs2: list @ A,Ys2: list @ A] :
% 3.12/1.62 ( ( ( append @ A @ Xs2 @ Ys2 )
% 3.12/1.62 = Xs2 )
% 3.12/1.62 = ( Ys2
% 3.12/1.62 = ( nil @ A ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_72_append__Nil2,axiom,
% 3.12/1.62 ! [A: $tType,Xs2: list @ A] :
% 3.12/1.62 ( ( append @ A @ Xs2 @ ( nil @ A ) )
% 3.12/1.62 = Xs2 ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_73_append__eq__append__conv,axiom,
% 3.12/1.62 ! [A: $tType,Xs2: list @ A,Ys2: list @ A,Us: list @ A,Vs: list @ A] :
% 3.12/1.62 ( ( ( ( size_size @ ( list @ A ) @ Xs2 )
% 3.12/1.62 = ( size_size @ ( list @ A ) @ Ys2 ) )
% 3.12/1.62 | ( ( size_size @ ( list @ A ) @ Us )
% 3.12/1.62 = ( size_size @ ( list @ A ) @ Vs ) ) )
% 3.12/1.62 => ( ( ( append @ A @ Xs2 @ Us )
% 3.12/1.62 = ( append @ A @ Ys2 @ Vs ) )
% 3.12/1.62 = ( ( Xs2 = Ys2 )
% 3.12/1.62 & ( Us = Vs ) ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_74_zip__Nil,axiom,
% 3.12/1.62 ! [B: $tType,A: $tType,Ys2: list @ B] :
% 3.12/1.62 ( ( zip @ A @ B @ ( nil @ A ) @ Ys2 )
% 3.12/1.62 = ( nil @ ( product_prod @ A @ B ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_75_bind__simps_I1_J,axiom,
% 3.12/1.62 ! [B: $tType,A: $tType,F3: B > ( list @ A )] :
% 3.12/1.62 ( ( bind @ B @ A @ ( nil @ B ) @ F3 )
% 3.12/1.62 = ( nil @ A ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_76_append1__eq__conv,axiom,
% 3.12/1.62 ! [A: $tType,Xs2: list @ A,X3: A,Ys2: list @ A,Y3: A] :
% 3.12/1.62 ( ( ( append @ A @ Xs2 @ ( cons @ A @ X3 @ ( nil @ A ) ) )
% 3.12/1.62 = ( append @ A @ Ys2 @ ( cons @ A @ Y3 @ ( nil @ A ) ) ) )
% 3.12/1.62 = ( ( Xs2 = Ys2 )
% 3.12/1.62 & ( X3 = Y3 ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_77_Cons__in__lex,axiom,
% 3.12/1.62 ! [A: $tType,X3: A,Xs2: list @ A,Y3: A,Ys2: list @ A,R: set @ ( product_prod @ A @ A )] :
% 3.12/1.62 ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ A @ Y3 @ Ys2 ) ) @ ( lex @ A @ R ) )
% 3.12/1.62 = ( ( ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X3 @ Y3 ) @ R )
% 3.12/1.62 & ( ( size_size @ ( list @ A ) @ Xs2 )
% 3.12/1.62 = ( size_size @ ( list @ A ) @ Ys2 ) ) )
% 3.12/1.62 | ( ( X3 = Y3 )
% 3.12/1.62 & ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs2 @ Ys2 ) @ ( lex @ A @ R ) ) ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_78_zip_Osimps_I1_J,axiom,
% 3.12/1.62 ! [B: $tType,A: $tType,Xs2: list @ A] :
% 3.12/1.62 ( ( zip @ A @ B @ Xs2 @ ( nil @ B ) )
% 3.12/1.62 = ( nil @ ( product_prod @ A @ B ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_79_Nil__notin__lex,axiom,
% 3.12/1.62 ! [A: $tType,Ys2: list @ A,R: set @ ( product_prod @ A @ A )] :
% 3.12/1.62 ~ ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( nil @ A ) @ Ys2 ) @ ( lex @ A @ R ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_80_Nil2__notin__lex,axiom,
% 3.12/1.62 ! [A: $tType,Xs2: list @ A,R: set @ ( product_prod @ A @ A )] :
% 3.12/1.62 ~ ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs2 @ ( nil @ A ) ) @ ( lex @ A @ R ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_81_zip__eq__Nil__iff,axiom,
% 3.12/1.62 ! [A: $tType,B: $tType,Xs2: list @ A,Ys2: list @ B] :
% 3.12/1.62 ( ( ( zip @ A @ B @ Xs2 @ Ys2 )
% 3.12/1.62 = ( nil @ ( product_prod @ A @ B ) ) )
% 3.12/1.62 = ( ( Xs2
% 3.12/1.62 = ( nil @ A ) )
% 3.12/1.62 | ( Ys2
% 3.12/1.62 = ( nil @ B ) ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_82_in__set__impl__in__set__zip1,axiom,
% 3.12/1.62 ! [A: $tType,B: $tType,Xs2: list @ A,Ys2: list @ B,X3: A] :
% 3.12/1.62 ( ( ( size_size @ ( list @ A ) @ Xs2 )
% 3.12/1.62 = ( size_size @ ( list @ B ) @ Ys2 ) )
% 3.12/1.62 => ( ( member2 @ A @ X3 @ ( set2 @ A @ Xs2 ) )
% 3.12/1.62 => ~ ! [Y4: B] :
% 3.12/1.62 ~ ( member2 @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X3 @ Y4 ) @ ( set2 @ ( product_prod @ A @ B ) @ ( zip @ A @ B @ Xs2 @ Ys2 ) ) ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_83_in__set__impl__in__set__zip2,axiom,
% 3.12/1.62 ! [A: $tType,B: $tType,Xs2: list @ A,Ys2: list @ B,Y3: B] :
% 3.12/1.62 ( ( ( size_size @ ( list @ A ) @ Xs2 )
% 3.12/1.62 = ( size_size @ ( list @ B ) @ Ys2 ) )
% 3.12/1.62 => ( ( member2 @ B @ Y3 @ ( set2 @ B @ Ys2 ) )
% 3.12/1.62 => ~ ! [X4: A] :
% 3.12/1.62 ~ ( member2 @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X4 @ Y3 ) @ ( set2 @ ( product_prod @ A @ B ) @ ( zip @ A @ B @ Xs2 @ Ys2 ) ) ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_84_list__induct4,axiom,
% 3.12/1.62 ! [C: $tType,A: $tType,B: $tType,D: $tType,Xs2: list @ A,Ys2: list @ B,Zs: list @ C,Ws: list @ D,P2: ( list @ A ) > ( list @ B ) > ( list @ C ) > ( list @ D ) > $o] :
% 3.12/1.62 ( ( ( size_size @ ( list @ A ) @ Xs2 )
% 3.12/1.62 = ( size_size @ ( list @ B ) @ Ys2 ) )
% 3.12/1.62 => ( ( ( size_size @ ( list @ B ) @ Ys2 )
% 3.12/1.62 = ( size_size @ ( list @ C ) @ Zs ) )
% 3.12/1.62 => ( ( ( size_size @ ( list @ C ) @ Zs )
% 3.12/1.62 = ( size_size @ ( list @ D ) @ Ws ) )
% 3.12/1.62 => ( ( P2 @ ( nil @ A ) @ ( nil @ B ) @ ( nil @ C ) @ ( nil @ D ) )
% 3.12/1.62 => ( ! [X4: A,Xs4: list @ A,Y4: B,Ys4: list @ B,Z2: C,Zs2: list @ C,W: D,Ws2: list @ D] :
% 3.12/1.62 ( ( ( size_size @ ( list @ A ) @ Xs4 )
% 3.12/1.62 = ( size_size @ ( list @ B ) @ Ys4 ) )
% 3.12/1.62 => ( ( ( size_size @ ( list @ B ) @ Ys4 )
% 3.12/1.62 = ( size_size @ ( list @ C ) @ Zs2 ) )
% 3.12/1.62 => ( ( ( size_size @ ( list @ C ) @ Zs2 )
% 3.12/1.62 = ( size_size @ ( list @ D ) @ Ws2 ) )
% 3.12/1.62 => ( ( P2 @ Xs4 @ Ys4 @ Zs2 @ Ws2 )
% 3.12/1.62 => ( P2 @ ( cons @ A @ X4 @ Xs4 ) @ ( cons @ B @ Y4 @ Ys4 ) @ ( cons @ C @ Z2 @ Zs2 ) @ ( cons @ D @ W @ Ws2 ) ) ) ) ) )
% 3.12/1.62 => ( P2 @ Xs2 @ Ys2 @ Zs @ Ws ) ) ) ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_85_list__induct3,axiom,
% 3.12/1.62 ! [B: $tType,A: $tType,C: $tType,Xs2: list @ A,Ys2: list @ B,Zs: list @ C,P2: ( list @ A ) > ( list @ B ) > ( list @ C ) > $o] :
% 3.12/1.62 ( ( ( size_size @ ( list @ A ) @ Xs2 )
% 3.12/1.62 = ( size_size @ ( list @ B ) @ Ys2 ) )
% 3.12/1.62 => ( ( ( size_size @ ( list @ B ) @ Ys2 )
% 3.12/1.62 = ( size_size @ ( list @ C ) @ Zs ) )
% 3.12/1.62 => ( ( P2 @ ( nil @ A ) @ ( nil @ B ) @ ( nil @ C ) )
% 3.12/1.62 => ( ! [X4: A,Xs4: list @ A,Y4: B,Ys4: list @ B,Z2: C,Zs2: list @ C] :
% 3.12/1.62 ( ( ( size_size @ ( list @ A ) @ Xs4 )
% 3.12/1.62 = ( size_size @ ( list @ B ) @ Ys4 ) )
% 3.12/1.62 => ( ( ( size_size @ ( list @ B ) @ Ys4 )
% 3.12/1.62 = ( size_size @ ( list @ C ) @ Zs2 ) )
% 3.12/1.62 => ( ( P2 @ Xs4 @ Ys4 @ Zs2 )
% 3.12/1.62 => ( P2 @ ( cons @ A @ X4 @ Xs4 ) @ ( cons @ B @ Y4 @ Ys4 ) @ ( cons @ C @ Z2 @ Zs2 ) ) ) ) )
% 3.12/1.62 => ( P2 @ Xs2 @ Ys2 @ Zs ) ) ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_86_list__induct2,axiom,
% 3.12/1.62 ! [A: $tType,B: $tType,Xs2: list @ A,Ys2: list @ B,P2: ( list @ A ) > ( list @ B ) > $o] :
% 3.12/1.62 ( ( ( size_size @ ( list @ A ) @ Xs2 )
% 3.12/1.62 = ( size_size @ ( list @ B ) @ Ys2 ) )
% 3.12/1.62 => ( ( P2 @ ( nil @ A ) @ ( nil @ B ) )
% 3.12/1.62 => ( ! [X4: A,Xs4: list @ A,Y4: B,Ys4: list @ B] :
% 3.12/1.62 ( ( ( size_size @ ( list @ A ) @ Xs4 )
% 3.12/1.62 = ( size_size @ ( list @ B ) @ Ys4 ) )
% 3.12/1.62 => ( ( P2 @ Xs4 @ Ys4 )
% 3.12/1.62 => ( P2 @ ( cons @ A @ X4 @ Xs4 ) @ ( cons @ B @ Y4 @ Ys4 ) ) ) )
% 3.12/1.62 => ( P2 @ Xs2 @ Ys2 ) ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_87_transpose_Ocases,axiom,
% 3.12/1.62 ! [A: $tType,X3: list @ ( list @ A )] :
% 3.12/1.62 ( ( X3
% 3.12/1.62 != ( nil @ ( list @ A ) ) )
% 3.12/1.62 => ( ! [Xss: list @ ( list @ A )] :
% 3.12/1.62 ( X3
% 3.12/1.62 != ( cons @ ( list @ A ) @ ( nil @ A ) @ Xss ) )
% 3.12/1.62 => ~ ! [X4: A,Xs4: list @ A,Xss: list @ ( list @ A )] :
% 3.12/1.62 ( X3
% 3.12/1.62 != ( cons @ ( list @ A ) @ ( cons @ A @ X4 @ Xs4 ) @ Xss ) ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_88_neq__if__length__neq,axiom,
% 3.12/1.62 ! [A: $tType,Xs2: list @ A,Ys2: list @ A] :
% 3.12/1.62 ( ( ( size_size @ ( list @ A ) @ Xs2 )
% 3.12/1.62 != ( size_size @ ( list @ A ) @ Ys2 ) )
% 3.12/1.62 => ( Xs2 != Ys2 ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_89_Ex__list__of__length,axiom,
% 3.12/1.62 ! [A: $tType,N: nat] :
% 3.12/1.62 ? [Xs4: list @ A] :
% 3.12/1.62 ( ( size_size @ ( list @ A ) @ Xs4 )
% 3.12/1.62 = N ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_90_irrefl__lex,axiom,
% 3.12/1.62 ! [A: $tType,R: set @ ( product_prod @ A @ A )] :
% 3.12/1.62 ( ( irrefl @ A @ R )
% 3.12/1.62 => ( irrefl @ ( list @ A ) @ ( lex @ A @ R ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_91_asym__lex,axiom,
% 3.12/1.62 ! [A: $tType,R2: set @ ( product_prod @ A @ A )] :
% 3.12/1.62 ( ( asym @ A @ R2 )
% 3.12/1.62 => ( asym @ ( list @ A ) @ ( lex @ A @ R2 ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_92_lexl__not__refl,axiom,
% 3.12/1.62 ! [A: $tType,R: set @ ( product_prod @ A @ A ),X3: list @ A] :
% 3.12/1.62 ( ( irrefl @ A @ R )
% 3.12/1.62 => ~ ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ X3 @ X3 ) @ ( lex @ A @ R ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_93_lexord__irrefl,axiom,
% 3.12/1.62 ! [A: $tType,R2: set @ ( product_prod @ A @ A )] :
% 3.12/1.62 ( ( irrefl @ A @ R2 )
% 3.12/1.62 => ( irrefl @ ( list @ A ) @ ( lexord @ A @ R2 ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_94_lexord__asym,axiom,
% 3.12/1.62 ! [A: $tType,R2: set @ ( product_prod @ A @ A )] :
% 3.12/1.62 ( ( asym @ A @ R2 )
% 3.12/1.62 => ( asym @ ( list @ A ) @ ( lexord @ A @ R2 ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_95_set__zip__rightD,axiom,
% 3.12/1.62 ! [A: $tType,B: $tType,X3: A,Y3: B,Xs2: list @ A,Ys2: list @ B] :
% 3.12/1.62 ( ( member2 @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X3 @ Y3 ) @ ( set2 @ ( product_prod @ A @ B ) @ ( zip @ A @ B @ Xs2 @ Ys2 ) ) )
% 3.12/1.62 => ( member2 @ B @ Y3 @ ( set2 @ B @ Ys2 ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_96_set__zip__leftD,axiom,
% 3.12/1.62 ! [B: $tType,A: $tType,X3: A,Y3: B,Xs2: list @ A,Ys2: list @ B] :
% 3.12/1.62 ( ( member2 @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X3 @ Y3 ) @ ( set2 @ ( product_prod @ A @ B ) @ ( zip @ A @ B @ Xs2 @ Ys2 ) ) )
% 3.12/1.62 => ( member2 @ A @ X3 @ ( set2 @ A @ Xs2 ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_97_in__set__zipE,axiom,
% 3.12/1.62 ! [A: $tType,B: $tType,X3: A,Y3: B,Xs2: list @ A,Ys2: list @ B] :
% 3.12/1.62 ( ( member2 @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X3 @ Y3 ) @ ( set2 @ ( product_prod @ A @ B ) @ ( zip @ A @ B @ Xs2 @ Ys2 ) ) )
% 3.12/1.62 => ~ ( ( member2 @ A @ X3 @ ( set2 @ A @ Xs2 ) )
% 3.12/1.62 => ~ ( member2 @ B @ Y3 @ ( set2 @ B @ Ys2 ) ) ) ) ).
% 3.12/1.62
% 3.12/1.62 thf(fact_98_zip__same,axiom,
% 3.12/1.62 ! [A: $tType,A2: A,B2: A,Xs2: list @ A] :
% 3.12/1.62 ( ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ ( set2 @ ( product_prod @ A @ A ) @ ( zip @ A @ A @ Xs2 @ Xs2 ) ) )
% 3.12/1.62 = ( ( member2 @ A @ A2 @ ( set2 @ A @ Xs2 ) )
% 3.12/1.63 & ( A2 = B2 ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_99_same__length__different,axiom,
% 3.12/1.63 ! [A: $tType,Xs2: list @ A,Ys2: list @ A] :
% 3.12/1.63 ( ( Xs2 != Ys2 )
% 3.12/1.63 => ( ( ( size_size @ ( list @ A ) @ Xs2 )
% 3.12/1.63 = ( size_size @ ( list @ A ) @ Ys2 ) )
% 3.12/1.63 => ? [Pre: list @ A,X4: A,Xs3: list @ A,Y4: A,Ys3: list @ A] :
% 3.12/1.63 ( ( X4 != Y4 )
% 3.12/1.63 & ( Xs2
% 3.12/1.63 = ( append @ A @ Pre @ ( append @ A @ ( cons @ A @ X4 @ ( nil @ A ) ) @ Xs3 ) ) )
% 3.12/1.63 & ( Ys2
% 3.12/1.63 = ( append @ A @ Pre @ ( append @ A @ ( cons @ A @ Y4 @ ( nil @ A ) ) @ Ys3 ) ) ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_100_list_Oset__cases,axiom,
% 3.12/1.63 ! [A: $tType,E3: A,A2: list @ A] :
% 3.12/1.63 ( ( member2 @ A @ E3 @ ( set2 @ A @ A2 ) )
% 3.12/1.63 => ( ! [Z22: list @ A] :
% 3.12/1.63 ( A2
% 3.12/1.63 != ( cons @ A @ E3 @ Z22 ) )
% 3.12/1.63 => ~ ! [Z1: A,Z22: list @ A] :
% 3.12/1.63 ( ( A2
% 3.12/1.63 = ( cons @ A @ Z1 @ Z22 ) )
% 3.12/1.63 => ~ ( member2 @ A @ E3 @ ( set2 @ A @ Z22 ) ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_101_set__ConsD,axiom,
% 3.12/1.63 ! [A: $tType,Y3: A,X3: A,Xs2: list @ A] :
% 3.12/1.63 ( ( member2 @ A @ Y3 @ ( set2 @ A @ ( cons @ A @ X3 @ Xs2 ) ) )
% 3.12/1.63 => ( ( Y3 = X3 )
% 3.12/1.63 | ( member2 @ A @ Y3 @ ( set2 @ A @ Xs2 ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_102_list_Oset__intros_I1_J,axiom,
% 3.12/1.63 ! [A: $tType,X21: A,X22: list @ A] : ( member2 @ A @ X21 @ ( set2 @ A @ ( cons @ A @ X21 @ X22 ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_103_list_Oset__intros_I2_J,axiom,
% 3.12/1.63 ! [A: $tType,Y3: A,X22: list @ A,X21: A] :
% 3.12/1.63 ( ( member2 @ A @ Y3 @ ( set2 @ A @ X22 ) )
% 3.12/1.63 => ( member2 @ A @ Y3 @ ( set2 @ A @ ( cons @ A @ X21 @ X22 ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_104_lex__append__rightI,axiom,
% 3.12/1.63 ! [A: $tType,Xs2: list @ A,Ys2: list @ A,R: set @ ( product_prod @ A @ A ),Vs: list @ A,Us: list @ A] :
% 3.12/1.63 ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs2 @ Ys2 ) @ ( lex @ A @ R ) )
% 3.12/1.63 => ( ( ( size_size @ ( list @ A ) @ Vs )
% 3.12/1.63 = ( size_size @ ( list @ A ) @ Us ) )
% 3.12/1.63 => ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ Xs2 @ Us ) @ ( append @ A @ Ys2 @ Vs ) ) @ ( lex @ A @ R ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_105_sorted__wrt_Ocases,axiom,
% 3.12/1.63 ! [A: $tType,X3: product_prod @ ( A > A > $o ) @ ( list @ A )] :
% 3.12/1.63 ( ! [P4: A > A > $o] :
% 3.12/1.63 ( X3
% 3.12/1.63 != ( product_Pair @ ( A > A > $o ) @ ( list @ A ) @ P4 @ ( nil @ A ) ) )
% 3.12/1.63 => ~ ! [P4: A > A > $o,X4: A,Ys4: list @ A] :
% 3.12/1.63 ( X3
% 3.12/1.63 != ( product_Pair @ ( A > A > $o ) @ ( list @ A ) @ P4 @ ( cons @ A @ X4 @ Ys4 ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_106_arg__min__list_Ocases,axiom,
% 3.12/1.63 ! [B: $tType,A: $tType] :
% 3.12/1.63 ( ( linorder @ B )
% 3.12/1.63 => ! [X3: product_prod @ ( A > B ) @ ( list @ A )] :
% 3.12/1.63 ( ! [F2: A > B,X4: A] :
% 3.12/1.63 ( X3
% 3.12/1.63 != ( product_Pair @ ( A > B ) @ ( list @ A ) @ F2 @ ( cons @ A @ X4 @ ( nil @ A ) ) ) )
% 3.12/1.63 => ( ! [F2: A > B,X4: A,Y4: A,Zs2: list @ A] :
% 3.12/1.63 ( X3
% 3.12/1.63 != ( product_Pair @ ( A > B ) @ ( list @ A ) @ F2 @ ( cons @ A @ X4 @ ( cons @ A @ Y4 @ Zs2 ) ) ) )
% 3.12/1.63 => ~ ! [A4: A > B] :
% 3.12/1.63 ( X3
% 3.12/1.63 != ( product_Pair @ ( A > B ) @ ( list @ A ) @ A4 @ ( nil @ A ) ) ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_107_successively_Ocases,axiom,
% 3.12/1.63 ! [A: $tType,X3: product_prod @ ( A > A > $o ) @ ( list @ A )] :
% 3.12/1.63 ( ! [P4: A > A > $o] :
% 3.12/1.63 ( X3
% 3.12/1.63 != ( product_Pair @ ( A > A > $o ) @ ( list @ A ) @ P4 @ ( nil @ A ) ) )
% 3.12/1.63 => ( ! [P4: A > A > $o,X4: A] :
% 3.12/1.63 ( X3
% 3.12/1.63 != ( product_Pair @ ( A > A > $o ) @ ( list @ A ) @ P4 @ ( cons @ A @ X4 @ ( nil @ A ) ) ) )
% 3.12/1.63 => ~ ! [P4: A > A > $o,X4: A,Y4: A,Xs4: list @ A] :
% 3.12/1.63 ( X3
% 3.12/1.63 != ( product_Pair @ ( A > A > $o ) @ ( list @ A ) @ P4 @ ( cons @ A @ X4 @ ( cons @ A @ Y4 @ Xs4 ) ) ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_108_strict__sorted_Oinduct,axiom,
% 3.12/1.63 ! [A: $tType] :
% 3.12/1.63 ( ( linorder @ A )
% 3.12/1.63 => ! [P2: ( list @ A ) > $o,A0: list @ A] :
% 3.12/1.63 ( ( P2 @ ( nil @ A ) )
% 3.12/1.63 => ( ! [X4: A,Ys4: list @ A] :
% 3.12/1.63 ( ( P2 @ Ys4 )
% 3.12/1.63 => ( P2 @ ( cons @ A @ X4 @ Ys4 ) ) )
% 3.12/1.63 => ( P2 @ A0 ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_109_strict__sorted_Ocases,axiom,
% 3.12/1.63 ! [A: $tType] :
% 3.12/1.63 ( ( linorder @ A )
% 3.12/1.63 => ! [X3: list @ A] :
% 3.12/1.63 ( ( X3
% 3.12/1.63 != ( nil @ A ) )
% 3.12/1.63 => ~ ! [X4: A,Ys4: list @ A] :
% 3.12/1.63 ( X3
% 3.12/1.63 != ( cons @ A @ X4 @ Ys4 ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_110_map__tailrec__rev_Oinduct,axiom,
% 3.12/1.63 ! [A: $tType,B: $tType,P2: ( A > B ) > ( list @ A ) > ( list @ B ) > $o,A0: A > B,A1: list @ A,A22: list @ B] :
% 3.12/1.63 ( ! [F2: A > B,X_1: list @ B] : ( P2 @ F2 @ ( nil @ A ) @ X_1 )
% 3.12/1.63 => ( ! [F2: A > B,A4: A,As: list @ A,Bs: list @ B] :
% 3.12/1.63 ( ( P2 @ F2 @ As @ ( cons @ B @ ( F2 @ A4 ) @ Bs ) )
% 3.12/1.63 => ( P2 @ F2 @ ( cons @ A @ A4 @ As ) @ Bs ) )
% 3.12/1.63 => ( P2 @ A0 @ A1 @ A22 ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_111_list__nonempty__induct,axiom,
% 3.12/1.63 ! [A: $tType,Xs2: list @ A,P2: ( list @ A ) > $o] :
% 3.12/1.63 ( ( Xs2
% 3.12/1.63 != ( nil @ A ) )
% 3.12/1.63 => ( ! [X4: A] : ( P2 @ ( cons @ A @ X4 @ ( nil @ A ) ) )
% 3.12/1.63 => ( ! [X4: A,Xs4: list @ A] :
% 3.12/1.63 ( ( Xs4
% 3.12/1.63 != ( nil @ A ) )
% 3.12/1.63 => ( ( P2 @ Xs4 )
% 3.12/1.63 => ( P2 @ ( cons @ A @ X4 @ Xs4 ) ) ) )
% 3.12/1.63 => ( P2 @ Xs2 ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_112_successively_Oinduct,axiom,
% 3.12/1.63 ! [A: $tType,P2: ( A > A > $o ) > ( list @ A ) > $o,A0: A > A > $o,A1: list @ A] :
% 3.12/1.63 ( ! [P4: A > A > $o] : ( P2 @ P4 @ ( nil @ A ) )
% 3.12/1.63 => ( ! [P4: A > A > $o,X4: A] : ( P2 @ P4 @ ( cons @ A @ X4 @ ( nil @ A ) ) )
% 3.12/1.63 => ( ! [P4: A > A > $o,X4: A,Y4: A,Xs4: list @ A] :
% 3.12/1.63 ( ( P2 @ P4 @ ( cons @ A @ Y4 @ Xs4 ) )
% 3.12/1.63 => ( P2 @ P4 @ ( cons @ A @ X4 @ ( cons @ A @ Y4 @ Xs4 ) ) ) )
% 3.12/1.63 => ( P2 @ A0 @ A1 ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_113_arg__min__list_Oinduct,axiom,
% 3.12/1.63 ! [B: $tType,A: $tType] :
% 3.12/1.63 ( ( linorder @ B )
% 3.12/1.63 => ! [P2: ( A > B ) > ( list @ A ) > $o,A0: A > B,A1: list @ A] :
% 3.12/1.63 ( ! [F2: A > B,X4: A] : ( P2 @ F2 @ ( cons @ A @ X4 @ ( nil @ A ) ) )
% 3.12/1.63 => ( ! [F2: A > B,X4: A,Y4: A,Zs2: list @ A] :
% 3.12/1.63 ( ( P2 @ F2 @ ( cons @ A @ Y4 @ Zs2 ) )
% 3.12/1.63 => ( P2 @ F2 @ ( cons @ A @ X4 @ ( cons @ A @ Y4 @ Zs2 ) ) ) )
% 3.12/1.63 => ( ! [A4: A > B] : ( P2 @ A4 @ ( nil @ A ) )
% 3.12/1.63 => ( P2 @ A0 @ A1 ) ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_114_remdups__adj_Oinduct,axiom,
% 3.12/1.63 ! [A: $tType,P2: ( list @ A ) > $o,A0: list @ A] :
% 3.12/1.63 ( ( P2 @ ( nil @ A ) )
% 3.12/1.63 => ( ! [X4: A] : ( P2 @ ( cons @ A @ X4 @ ( nil @ A ) ) )
% 3.12/1.63 => ( ! [X4: A,Y4: A,Xs4: list @ A] :
% 3.12/1.63 ( ( ( X4 = Y4 )
% 3.12/1.63 => ( P2 @ ( cons @ A @ X4 @ Xs4 ) ) )
% 3.12/1.63 => ( ( ( X4 != Y4 )
% 3.12/1.63 => ( P2 @ ( cons @ A @ Y4 @ Xs4 ) ) )
% 3.12/1.63 => ( P2 @ ( cons @ A @ X4 @ ( cons @ A @ Y4 @ Xs4 ) ) ) ) )
% 3.12/1.63 => ( P2 @ A0 ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_115_sorted__wrt_Oinduct,axiom,
% 3.12/1.63 ! [A: $tType,P2: ( A > A > $o ) > ( list @ A ) > $o,A0: A > A > $o,A1: list @ A] :
% 3.12/1.63 ( ! [P4: A > A > $o] : ( P2 @ P4 @ ( nil @ A ) )
% 3.12/1.63 => ( ! [P4: A > A > $o,X4: A,Ys4: list @ A] :
% 3.12/1.63 ( ( P2 @ P4 @ Ys4 )
% 3.12/1.63 => ( P2 @ P4 @ ( cons @ A @ X4 @ Ys4 ) ) )
% 3.12/1.63 => ( P2 @ A0 @ A1 ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_116_remdups__adj_Ocases,axiom,
% 3.12/1.63 ! [A: $tType,X3: list @ A] :
% 3.12/1.63 ( ( X3
% 3.12/1.63 != ( nil @ A ) )
% 3.12/1.63 => ( ! [X4: A] :
% 3.12/1.63 ( X3
% 3.12/1.63 != ( cons @ A @ X4 @ ( nil @ A ) ) )
% 3.12/1.63 => ~ ! [X4: A,Y4: A,Xs4: list @ A] :
% 3.12/1.63 ( X3
% 3.12/1.63 != ( cons @ A @ X4 @ ( cons @ A @ Y4 @ Xs4 ) ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_117_shuffles_Oinduct,axiom,
% 3.12/1.63 ! [A: $tType,P2: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 3.12/1.63 ( ! [X_1: list @ A] : ( P2 @ ( nil @ A ) @ X_1 )
% 3.12/1.63 => ( ! [Xs4: list @ A] : ( P2 @ Xs4 @ ( nil @ A ) )
% 3.12/1.63 => ( ! [X4: A,Xs4: list @ A,Y4: A,Ys4: list @ A] :
% 3.12/1.63 ( ( P2 @ Xs4 @ ( cons @ A @ Y4 @ Ys4 ) )
% 3.12/1.63 => ( ( P2 @ ( cons @ A @ X4 @ Xs4 ) @ Ys4 )
% 3.12/1.63 => ( P2 @ ( cons @ A @ X4 @ Xs4 ) @ ( cons @ A @ Y4 @ Ys4 ) ) ) )
% 3.12/1.63 => ( P2 @ A0 @ A1 ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_118_min__list_Oinduct,axiom,
% 3.12/1.63 ! [A: $tType] :
% 3.12/1.63 ( ( ord @ A )
% 3.12/1.63 => ! [P2: ( list @ A ) > $o,A0: list @ A] :
% 3.12/1.63 ( ! [X4: A,Xs4: list @ A] :
% 3.12/1.63 ( ! [X212: A,X222: list @ A] :
% 3.12/1.63 ( ( Xs4
% 3.12/1.63 = ( cons @ A @ X212 @ X222 ) )
% 3.12/1.63 => ( P2 @ Xs4 ) )
% 3.12/1.63 => ( P2 @ ( cons @ A @ X4 @ Xs4 ) ) )
% 3.12/1.63 => ( ( P2 @ ( nil @ A ) )
% 3.12/1.63 => ( P2 @ A0 ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_119_min__list_Ocases,axiom,
% 3.12/1.63 ! [A: $tType] :
% 3.12/1.63 ( ( ord @ A )
% 3.12/1.63 => ! [X3: list @ A] :
% 3.12/1.63 ( ! [X4: A,Xs4: list @ A] :
% 3.12/1.63 ( X3
% 3.12/1.63 != ( cons @ A @ X4 @ Xs4 ) )
% 3.12/1.63 => ( X3
% 3.12/1.63 = ( nil @ A ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_120_induct__list012,axiom,
% 3.12/1.63 ! [A: $tType,P2: ( list @ A ) > $o,Xs2: list @ A] :
% 3.12/1.63 ( ( P2 @ ( nil @ A ) )
% 3.12/1.63 => ( ! [X4: A] : ( P2 @ ( cons @ A @ X4 @ ( nil @ A ) ) )
% 3.12/1.63 => ( ! [X4: A,Y4: A,Zs2: list @ A] :
% 3.12/1.63 ( ( P2 @ Zs2 )
% 3.12/1.63 => ( ( P2 @ ( cons @ A @ Y4 @ Zs2 ) )
% 3.12/1.63 => ( P2 @ ( cons @ A @ X4 @ ( cons @ A @ Y4 @ Zs2 ) ) ) ) )
% 3.12/1.63 => ( P2 @ Xs2 ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_121_splice_Oinduct,axiom,
% 3.12/1.63 ! [A: $tType,P2: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 3.12/1.63 ( ! [X_1: list @ A] : ( P2 @ ( nil @ A ) @ X_1 )
% 3.12/1.63 => ( ! [X4: A,Xs4: list @ A,Ys4: list @ A] :
% 3.12/1.63 ( ( P2 @ Ys4 @ Xs4 )
% 3.12/1.63 => ( P2 @ ( cons @ A @ X4 @ Xs4 ) @ Ys4 ) )
% 3.12/1.63 => ( P2 @ A0 @ A1 ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_122_list__induct2_H,axiom,
% 3.12/1.63 ! [A: $tType,B: $tType,P2: ( list @ A ) > ( list @ B ) > $o,Xs2: list @ A,Ys2: list @ B] :
% 3.12/1.63 ( ( P2 @ ( nil @ A ) @ ( nil @ B ) )
% 3.12/1.63 => ( ! [X4: A,Xs4: list @ A] : ( P2 @ ( cons @ A @ X4 @ Xs4 ) @ ( nil @ B ) )
% 3.12/1.63 => ( ! [Y4: B,Ys4: list @ B] : ( P2 @ ( nil @ A ) @ ( cons @ B @ Y4 @ Ys4 ) )
% 3.12/1.63 => ( ! [X4: A,Xs4: list @ A,Y4: B,Ys4: list @ B] :
% 3.12/1.63 ( ( P2 @ Xs4 @ Ys4 )
% 3.12/1.63 => ( P2 @ ( cons @ A @ X4 @ Xs4 ) @ ( cons @ B @ Y4 @ Ys4 ) ) )
% 3.12/1.63 => ( P2 @ Xs2 @ Ys2 ) ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_123_neq__Nil__conv,axiom,
% 3.12/1.63 ! [A: $tType,Xs2: list @ A] :
% 3.12/1.63 ( ( Xs2
% 3.12/1.63 != ( nil @ A ) )
% 3.12/1.63 = ( ? [Y: A,Ys: list @ A] :
% 3.12/1.63 ( Xs2
% 3.12/1.63 = ( cons @ A @ Y @ Ys ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_124_list_Oinducts,axiom,
% 3.12/1.63 ! [A: $tType,P2: ( list @ A ) > $o,List: list @ A] :
% 3.12/1.63 ( ( P2 @ ( nil @ A ) )
% 3.12/1.63 => ( ! [X12: A,X23: list @ A] :
% 3.12/1.63 ( ( P2 @ X23 )
% 3.12/1.63 => ( P2 @ ( cons @ A @ X12 @ X23 ) ) )
% 3.12/1.63 => ( P2 @ List ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_125_list_Oexhaust,axiom,
% 3.12/1.63 ! [A: $tType,Y3: list @ A] :
% 3.12/1.63 ( ( Y3
% 3.12/1.63 != ( nil @ A ) )
% 3.12/1.63 => ~ ! [X213: A,X223: list @ A] :
% 3.12/1.63 ( Y3
% 3.12/1.63 != ( cons @ A @ X213 @ X223 ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_126_list_OdiscI,axiom,
% 3.12/1.63 ! [A: $tType,List: list @ A,X21: A,X22: list @ A] :
% 3.12/1.63 ( ( List
% 3.12/1.63 = ( cons @ A @ X21 @ X22 ) )
% 3.12/1.63 => ( List
% 3.12/1.63 != ( nil @ A ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_127_list_Odistinct_I1_J,axiom,
% 3.12/1.63 ! [A: $tType,X21: A,X22: list @ A] :
% 3.12/1.63 ( ( nil @ A )
% 3.12/1.63 != ( cons @ A @ X21 @ X22 ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_128_append_Oleft__neutral,axiom,
% 3.12/1.63 ! [A: $tType,A2: list @ A] :
% 3.12/1.63 ( ( append @ A @ ( nil @ A ) @ A2 )
% 3.12/1.63 = A2 ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_129_append__Nil,axiom,
% 3.12/1.63 ! [A: $tType,Ys2: list @ A] :
% 3.12/1.63 ( ( append @ A @ ( nil @ A ) @ Ys2 )
% 3.12/1.63 = Ys2 ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_130_eq__Nil__appendI,axiom,
% 3.12/1.63 ! [A: $tType,Xs2: list @ A,Ys2: list @ A] :
% 3.12/1.63 ( ( Xs2 = Ys2 )
% 3.12/1.63 => ( Xs2
% 3.12/1.63 = ( append @ A @ ( nil @ A ) @ Ys2 ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_131_lexord__lex,axiom,
% 3.12/1.63 ! [A: $tType,X3: list @ A,Y3: list @ A,R: set @ ( product_prod @ A @ A )] :
% 3.12/1.63 ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ X3 @ Y3 ) @ ( lex @ A @ R ) )
% 3.12/1.63 = ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ X3 @ Y3 ) @ ( lexord @ A @ R ) )
% 3.12/1.63 & ( ( size_size @ ( list @ A ) @ X3 )
% 3.12/1.63 = ( size_size @ ( list @ A ) @ Y3 ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_132_pcas_Ocases,axiom,
% 3.12/1.63 ! [A: $tType,X3: product_prod @ A @ ( product_prod @ ( list @ ( product_prod @ A @ A ) ) @ A )] :
% 3.12/1.63 ( ! [U2: A,V: A] :
% 3.12/1.63 ( X3
% 3.12/1.63 != ( product_Pair @ A @ ( product_prod @ ( list @ ( product_prod @ A @ A ) ) @ A ) @ U2 @ ( product_Pair @ ( list @ ( product_prod @ A @ A ) ) @ A @ ( nil @ ( product_prod @ A @ A ) ) @ V ) ) )
% 3.12/1.63 => ~ ! [U2: A,E2: product_prod @ A @ A,Es: list @ ( product_prod @ A @ A ),V: A] :
% 3.12/1.63 ( X3
% 3.12/1.63 != ( product_Pair @ A @ ( product_prod @ ( list @ ( product_prod @ A @ A ) ) @ A ) @ U2 @ ( product_Pair @ ( list @ ( product_prod @ A @ A ) ) @ A @ ( cons @ ( product_prod @ A @ A ) @ E2 @ Es ) @ V ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_133_list__bind__cong,axiom,
% 3.12/1.63 ! [B: $tType,A: $tType,Xs2: list @ A,Ys2: list @ A,F3: A > ( list @ B ),G4: A > ( list @ B )] :
% 3.12/1.63 ( ( Xs2 = Ys2 )
% 3.12/1.63 => ( ! [X4: A] :
% 3.12/1.63 ( ( member2 @ A @ X4 @ ( set2 @ A @ Xs2 ) )
% 3.12/1.63 => ( ( F3 @ X4 )
% 3.12/1.63 = ( G4 @ X4 ) ) )
% 3.12/1.63 => ( ( bind @ A @ B @ Xs2 @ F3 )
% 3.12/1.63 = ( bind @ A @ B @ Ys2 @ G4 ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_134_in__set__member,axiom,
% 3.12/1.63 ! [A: $tType,X3: A,Xs2: list @ A] :
% 3.12/1.63 ( ( member2 @ A @ X3 @ ( set2 @ A @ Xs2 ) )
% 3.12/1.63 = ( member @ A @ Xs2 @ X3 ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_135_maps__simps_I2_J,axiom,
% 3.12/1.63 ! [B: $tType,A: $tType,F3: B > ( list @ A )] :
% 3.12/1.63 ( ( maps @ B @ A @ F3 @ ( nil @ B ) )
% 3.12/1.63 = ( nil @ A ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_136_member__rec_I2_J,axiom,
% 3.12/1.63 ! [A: $tType,Y3: A] :
% 3.12/1.63 ~ ( member @ A @ ( nil @ A ) @ Y3 ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_137_progressing__Nil,axiom,
% 3.12/1.63 ! [A: $tType] : ( kurato990191779essing @ A @ ( nil @ ( product_prod @ A @ A ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_138_split__list__first__prop__iff,axiom,
% 3.12/1.63 ! [A: $tType,Xs2: list @ A,P2: A > $o] :
% 3.12/1.63 ( ( ? [X: A] :
% 3.12/1.63 ( ( member2 @ A @ X @ ( set2 @ A @ Xs2 ) )
% 3.12/1.63 & ( P2 @ X ) ) )
% 3.12/1.63 = ( ? [Ys: list @ A,X: A] :
% 3.12/1.63 ( ? [Zs3: list @ A] :
% 3.12/1.63 ( Xs2
% 3.12/1.63 = ( append @ A @ Ys @ ( cons @ A @ X @ Zs3 ) ) )
% 3.12/1.63 & ( P2 @ X )
% 3.12/1.63 & ! [Y: A] :
% 3.12/1.63 ( ( member2 @ A @ Y @ ( set2 @ A @ Ys ) )
% 3.12/1.63 => ~ ( P2 @ Y ) ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_139_split__list__last__prop__iff,axiom,
% 3.12/1.63 ! [A: $tType,Xs2: list @ A,P2: A > $o] :
% 3.12/1.63 ( ( ? [X: A] :
% 3.12/1.63 ( ( member2 @ A @ X @ ( set2 @ A @ Xs2 ) )
% 3.12/1.63 & ( P2 @ X ) ) )
% 3.12/1.63 = ( ? [Ys: list @ A,X: A,Zs3: list @ A] :
% 3.12/1.63 ( ( Xs2
% 3.12/1.63 = ( append @ A @ Ys @ ( cons @ A @ X @ Zs3 ) ) )
% 3.12/1.63 & ( P2 @ X )
% 3.12/1.63 & ! [Y: A] :
% 3.12/1.63 ( ( member2 @ A @ Y @ ( set2 @ A @ Zs3 ) )
% 3.12/1.63 => ~ ( P2 @ Y ) ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_140_in__set__conv__decomp__first,axiom,
% 3.12/1.63 ! [A: $tType,X3: A,Xs2: list @ A] :
% 3.12/1.63 ( ( member2 @ A @ X3 @ ( set2 @ A @ Xs2 ) )
% 3.12/1.63 = ( ? [Ys: list @ A,Zs3: list @ A] :
% 3.12/1.63 ( ( Xs2
% 3.12/1.63 = ( append @ A @ Ys @ ( cons @ A @ X3 @ Zs3 ) ) )
% 3.12/1.63 & ~ ( member2 @ A @ X3 @ ( set2 @ A @ Ys ) ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_141_in__set__conv__decomp__last,axiom,
% 3.12/1.63 ! [A: $tType,X3: A,Xs2: list @ A] :
% 3.12/1.63 ( ( member2 @ A @ X3 @ ( set2 @ A @ Xs2 ) )
% 3.12/1.63 = ( ? [Ys: list @ A,Zs3: list @ A] :
% 3.12/1.63 ( ( Xs2
% 3.12/1.63 = ( append @ A @ Ys @ ( cons @ A @ X3 @ Zs3 ) ) )
% 3.12/1.63 & ~ ( member2 @ A @ X3 @ ( set2 @ A @ Zs3 ) ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_142_split__list__first__propE,axiom,
% 3.12/1.63 ! [A: $tType,Xs2: list @ A,P2: A > $o] :
% 3.12/1.63 ( ? [X5: A] :
% 3.12/1.63 ( ( member2 @ A @ X5 @ ( set2 @ A @ Xs2 ) )
% 3.12/1.63 & ( P2 @ X5 ) )
% 3.12/1.63 => ~ ! [Ys4: list @ A,X4: A] :
% 3.12/1.63 ( ? [Zs2: list @ A] :
% 3.12/1.63 ( Xs2
% 3.12/1.63 = ( append @ A @ Ys4 @ ( cons @ A @ X4 @ Zs2 ) ) )
% 3.12/1.63 => ( ( P2 @ X4 )
% 3.12/1.63 => ~ ! [Xa: A] :
% 3.12/1.63 ( ( member2 @ A @ Xa @ ( set2 @ A @ Ys4 ) )
% 3.12/1.63 => ~ ( P2 @ Xa ) ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_143_split__list__last__propE,axiom,
% 3.12/1.63 ! [A: $tType,Xs2: list @ A,P2: A > $o] :
% 3.12/1.63 ( ? [X5: A] :
% 3.12/1.63 ( ( member2 @ A @ X5 @ ( set2 @ A @ Xs2 ) )
% 3.12/1.63 & ( P2 @ X5 ) )
% 3.12/1.63 => ~ ! [Ys4: list @ A,X4: A,Zs2: list @ A] :
% 3.12/1.63 ( ( Xs2
% 3.12/1.63 = ( append @ A @ Ys4 @ ( cons @ A @ X4 @ Zs2 ) ) )
% 3.12/1.63 => ( ( P2 @ X4 )
% 3.12/1.63 => ~ ! [Xa: A] :
% 3.12/1.63 ( ( member2 @ A @ Xa @ ( set2 @ A @ Zs2 ) )
% 3.12/1.63 => ~ ( P2 @ Xa ) ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_144_split__list__first__prop,axiom,
% 3.12/1.63 ! [A: $tType,Xs2: list @ A,P2: A > $o] :
% 3.12/1.63 ( ? [X5: A] :
% 3.12/1.63 ( ( member2 @ A @ X5 @ ( set2 @ A @ Xs2 ) )
% 3.12/1.63 & ( P2 @ X5 ) )
% 3.12/1.63 => ? [Ys4: list @ A,X4: A] :
% 3.12/1.63 ( ? [Zs2: list @ A] :
% 3.12/1.63 ( Xs2
% 3.12/1.63 = ( append @ A @ Ys4 @ ( cons @ A @ X4 @ Zs2 ) ) )
% 3.12/1.63 & ( P2 @ X4 )
% 3.12/1.63 & ! [Xa: A] :
% 3.12/1.63 ( ( member2 @ A @ Xa @ ( set2 @ A @ Ys4 ) )
% 3.12/1.63 => ~ ( P2 @ Xa ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_145_split__list__last__prop,axiom,
% 3.12/1.63 ! [A: $tType,Xs2: list @ A,P2: A > $o] :
% 3.12/1.63 ( ? [X5: A] :
% 3.12/1.63 ( ( member2 @ A @ X5 @ ( set2 @ A @ Xs2 ) )
% 3.12/1.63 & ( P2 @ X5 ) )
% 3.12/1.63 => ? [Ys4: list @ A,X4: A,Zs2: list @ A] :
% 3.12/1.63 ( ( Xs2
% 3.12/1.63 = ( append @ A @ Ys4 @ ( cons @ A @ X4 @ Zs2 ) ) )
% 3.12/1.63 & ( P2 @ X4 )
% 3.12/1.63 & ! [Xa: A] :
% 3.12/1.63 ( ( member2 @ A @ Xa @ ( set2 @ A @ Zs2 ) )
% 3.12/1.63 => ~ ( P2 @ Xa ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_146_in__set__conv__decomp,axiom,
% 3.12/1.63 ! [A: $tType,X3: A,Xs2: list @ A] :
% 3.12/1.63 ( ( member2 @ A @ X3 @ ( set2 @ A @ Xs2 ) )
% 3.12/1.63 = ( ? [Ys: list @ A,Zs3: list @ A] :
% 3.12/1.63 ( Xs2
% 3.12/1.63 = ( append @ A @ Ys @ ( cons @ A @ X3 @ Zs3 ) ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_147_append__Cons__eq__iff,axiom,
% 3.12/1.63 ! [A: $tType,X3: A,Xs2: list @ A,Ys2: list @ A,Xs5: list @ A,Ys5: list @ A] :
% 3.12/1.63 ( ~ ( member2 @ A @ X3 @ ( set2 @ A @ Xs2 ) )
% 3.12/1.63 => ( ~ ( member2 @ A @ X3 @ ( set2 @ A @ Ys2 ) )
% 3.12/1.63 => ( ( ( append @ A @ Xs2 @ ( cons @ A @ X3 @ Ys2 ) )
% 3.12/1.63 = ( append @ A @ Xs5 @ ( cons @ A @ X3 @ Ys5 ) ) )
% 3.12/1.63 = ( ( Xs2 = Xs5 )
% 3.12/1.63 & ( Ys2 = Ys5 ) ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_148_split__list__propE,axiom,
% 3.12/1.63 ! [A: $tType,Xs2: list @ A,P2: A > $o] :
% 3.12/1.63 ( ? [X5: A] :
% 3.12/1.63 ( ( member2 @ A @ X5 @ ( set2 @ A @ Xs2 ) )
% 3.12/1.63 & ( P2 @ X5 ) )
% 3.12/1.63 => ~ ! [Ys4: list @ A,X4: A] :
% 3.12/1.63 ( ? [Zs2: list @ A] :
% 3.12/1.63 ( Xs2
% 3.12/1.63 = ( append @ A @ Ys4 @ ( cons @ A @ X4 @ Zs2 ) ) )
% 3.12/1.63 => ~ ( P2 @ X4 ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_149_split__list__first,axiom,
% 3.12/1.63 ! [A: $tType,X3: A,Xs2: list @ A] :
% 3.12/1.63 ( ( member2 @ A @ X3 @ ( set2 @ A @ Xs2 ) )
% 3.12/1.63 => ? [Ys4: list @ A,Zs2: list @ A] :
% 3.12/1.63 ( ( Xs2
% 3.12/1.63 = ( append @ A @ Ys4 @ ( cons @ A @ X3 @ Zs2 ) ) )
% 3.12/1.63 & ~ ( member2 @ A @ X3 @ ( set2 @ A @ Ys4 ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_150_split__list__prop,axiom,
% 3.12/1.63 ! [A: $tType,Xs2: list @ A,P2: A > $o] :
% 3.12/1.63 ( ? [X5: A] :
% 3.12/1.63 ( ( member2 @ A @ X5 @ ( set2 @ A @ Xs2 ) )
% 3.12/1.63 & ( P2 @ X5 ) )
% 3.12/1.63 => ? [Ys4: list @ A,X4: A] :
% 3.12/1.63 ( ? [Zs2: list @ A] :
% 3.12/1.63 ( Xs2
% 3.12/1.63 = ( append @ A @ Ys4 @ ( cons @ A @ X4 @ Zs2 ) ) )
% 3.12/1.63 & ( P2 @ X4 ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_151_split__list__last,axiom,
% 3.12/1.63 ! [A: $tType,X3: A,Xs2: list @ A] :
% 3.12/1.63 ( ( member2 @ A @ X3 @ ( set2 @ A @ Xs2 ) )
% 3.12/1.63 => ? [Ys4: list @ A,Zs2: list @ A] :
% 3.12/1.63 ( ( Xs2
% 3.12/1.63 = ( append @ A @ Ys4 @ ( cons @ A @ X3 @ Zs2 ) ) )
% 3.12/1.63 & ~ ( member2 @ A @ X3 @ ( set2 @ A @ Zs2 ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_152_split__list,axiom,
% 3.12/1.63 ! [A: $tType,X3: A,Xs2: list @ A] :
% 3.12/1.63 ( ( member2 @ A @ X3 @ ( set2 @ A @ Xs2 ) )
% 3.12/1.63 => ? [Ys4: list @ A,Zs2: list @ A] :
% 3.12/1.63 ( Xs2
% 3.12/1.63 = ( append @ A @ Ys4 @ ( cons @ A @ X3 @ Zs2 ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_153_rev__nonempty__induct,axiom,
% 3.12/1.63 ! [A: $tType,Xs2: list @ A,P2: ( list @ A ) > $o] :
% 3.12/1.63 ( ( Xs2
% 3.12/1.63 != ( nil @ A ) )
% 3.12/1.63 => ( ! [X4: A] : ( P2 @ ( cons @ A @ X4 @ ( nil @ A ) ) )
% 3.12/1.63 => ( ! [X4: A,Xs4: list @ A] :
% 3.12/1.63 ( ( Xs4
% 3.12/1.63 != ( nil @ A ) )
% 3.12/1.63 => ( ( P2 @ Xs4 )
% 3.12/1.63 => ( P2 @ ( append @ A @ Xs4 @ ( cons @ A @ X4 @ ( nil @ A ) ) ) ) ) )
% 3.12/1.63 => ( P2 @ Xs2 ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_154_append__eq__Cons__conv,axiom,
% 3.12/1.63 ! [A: $tType,Ys2: list @ A,Zs: list @ A,X3: A,Xs2: list @ A] :
% 3.12/1.63 ( ( ( append @ A @ Ys2 @ Zs )
% 3.12/1.63 = ( cons @ A @ X3 @ Xs2 ) )
% 3.12/1.63 = ( ( ( Ys2
% 3.12/1.63 = ( nil @ A ) )
% 3.12/1.63 & ( Zs
% 3.12/1.63 = ( cons @ A @ X3 @ Xs2 ) ) )
% 3.12/1.63 | ? [Ys6: list @ A] :
% 3.12/1.63 ( ( Ys2
% 3.12/1.63 = ( cons @ A @ X3 @ Ys6 ) )
% 3.12/1.63 & ( ( append @ A @ Ys6 @ Zs )
% 3.12/1.63 = Xs2 ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_155_Cons__eq__append__conv,axiom,
% 3.12/1.63 ! [A: $tType,X3: A,Xs2: list @ A,Ys2: list @ A,Zs: list @ A] :
% 3.12/1.63 ( ( ( cons @ A @ X3 @ Xs2 )
% 3.12/1.63 = ( append @ A @ Ys2 @ Zs ) )
% 3.12/1.63 = ( ( ( Ys2
% 3.12/1.63 = ( nil @ A ) )
% 3.12/1.63 & ( ( cons @ A @ X3 @ Xs2 )
% 3.12/1.63 = Zs ) )
% 3.12/1.63 | ? [Ys6: list @ A] :
% 3.12/1.63 ( ( ( cons @ A @ X3 @ Ys6 )
% 3.12/1.63 = Ys2 )
% 3.12/1.63 & ( Xs2
% 3.12/1.63 = ( append @ A @ Ys6 @ Zs ) ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_156_rev__exhaust,axiom,
% 3.12/1.63 ! [A: $tType,Xs2: list @ A] :
% 3.12/1.63 ( ( Xs2
% 3.12/1.63 != ( nil @ A ) )
% 3.12/1.63 => ~ ! [Ys4: list @ A,Y4: A] :
% 3.12/1.63 ( Xs2
% 3.12/1.63 != ( append @ A @ Ys4 @ ( cons @ A @ Y4 @ ( nil @ A ) ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_157_rev__induct,axiom,
% 3.12/1.63 ! [A: $tType,P2: ( list @ A ) > $o,Xs2: list @ A] :
% 3.12/1.63 ( ( P2 @ ( nil @ A ) )
% 3.12/1.63 => ( ! [X4: A,Xs4: list @ A] :
% 3.12/1.63 ( ( P2 @ Xs4 )
% 3.12/1.63 => ( P2 @ ( append @ A @ Xs4 @ ( cons @ A @ X4 @ ( nil @ A ) ) ) ) )
% 3.12/1.63 => ( P2 @ Xs2 ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_158_shuffles_Ocases,axiom,
% 3.12/1.63 ! [A: $tType,X3: product_prod @ ( list @ A ) @ ( list @ A )] :
% 3.12/1.63 ( ! [Ys4: list @ A] :
% 3.12/1.63 ( X3
% 3.12/1.63 != ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( nil @ A ) @ Ys4 ) )
% 3.12/1.63 => ( ! [Xs4: list @ A] :
% 3.12/1.63 ( X3
% 3.12/1.63 != ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs4 @ ( nil @ A ) ) )
% 3.12/1.63 => ~ ! [X4: A,Xs4: list @ A,Y4: A,Ys4: list @ A] :
% 3.12/1.63 ( X3
% 3.12/1.63 != ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X4 @ Xs4 ) @ ( cons @ A @ Y4 @ Ys4 ) ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_159_map__tailrec__rev_Ocases,axiom,
% 3.12/1.63 ! [A: $tType,B: $tType,X3: product_prod @ ( A > B ) @ ( product_prod @ ( list @ A ) @ ( list @ B ) )] :
% 3.12/1.63 ( ! [F2: A > B,Bs: list @ B] :
% 3.12/1.63 ( X3
% 3.12/1.63 != ( product_Pair @ ( A > B ) @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ F2 @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ ( nil @ A ) @ Bs ) ) )
% 3.12/1.63 => ~ ! [F2: A > B,A4: A,As: list @ A,Bs: list @ B] :
% 3.12/1.63 ( X3
% 3.12/1.63 != ( product_Pair @ ( A > B ) @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ F2 @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ ( cons @ A @ A4 @ As ) @ Bs ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_160_sd__path_Oinduct,axiom,
% 3.12/1.63 ! [A: $tType,P2: ( product_prod @ A @ A ) > A > ( list @ ( product_prod @ A @ A ) ) > $o,A0: product_prod @ A @ A,A1: A,A22: list @ ( product_prod @ A @ A )] :
% 3.12/1.63 ( ! [Uu: product_prod @ A @ A,Uv: A] : ( P2 @ Uu @ Uv @ ( nil @ ( product_prod @ A @ A ) ) )
% 3.12/1.63 => ( ! [U2: A,V: A,W: A,E2: product_prod @ A @ A,Es: list @ ( product_prod @ A @ A )] :
% 3.12/1.63 ( ( P2 @ ( product_Pair @ A @ A @ U2 @ V ) @ W @ Es )
% 3.12/1.63 => ( P2 @ ( product_Pair @ A @ A @ U2 @ V ) @ W @ ( cons @ ( product_prod @ A @ A ) @ E2 @ Es ) ) )
% 3.12/1.63 => ( P2 @ A0 @ A1 @ A22 ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_161_co__path_Oinduct,axiom,
% 3.12/1.63 ! [A: $tType,P2: ( product_prod @ A @ A ) > A > ( list @ ( product_prod @ A @ A ) ) > $o,A0: product_prod @ A @ A,A1: A,A22: list @ ( product_prod @ A @ A )] :
% 3.12/1.63 ( ! [Uu: product_prod @ A @ A,Uv: A] : ( P2 @ Uu @ Uv @ ( nil @ ( product_prod @ A @ A ) ) )
% 3.12/1.63 => ( ! [Uw: product_prod @ A @ A,Ux: A,E2: product_prod @ A @ A] : ( P2 @ Uw @ Ux @ ( cons @ ( product_prod @ A @ A ) @ E2 @ ( nil @ ( product_prod @ A @ A ) ) ) )
% 3.12/1.63 => ( ! [U2: A,V: A,W: A,E1: product_prod @ A @ A,E22: product_prod @ A @ A,Es: list @ ( product_prod @ A @ A )] :
% 3.12/1.63 ( ( ( ( E1
% 3.12/1.63 = ( product_Pair @ A @ A @ U2 @ W ) )
% 3.12/1.63 & ( E22
% 3.12/1.63 = ( product_Pair @ A @ A @ W @ V ) ) )
% 3.12/1.63 => ( P2 @ ( product_Pair @ A @ A @ U2 @ V ) @ W @ Es ) )
% 3.12/1.63 => ( ( ~ ( ( E1
% 3.12/1.63 = ( product_Pair @ A @ A @ U2 @ W ) )
% 3.12/1.63 & ( E22
% 3.12/1.63 = ( product_Pair @ A @ A @ W @ V ) ) )
% 3.12/1.63 => ( ( ( E1
% 3.12/1.63 = ( product_Pair @ A @ A @ V @ W ) )
% 3.12/1.63 & ( E22
% 3.12/1.63 = ( product_Pair @ A @ A @ W @ U2 ) ) )
% 3.12/1.63 => ( P2 @ ( product_Pair @ A @ A @ U2 @ V ) @ W @ Es ) ) )
% 3.12/1.63 => ( ( ~ ( ( E1
% 3.12/1.63 = ( product_Pair @ A @ A @ U2 @ W ) )
% 3.12/1.63 & ( E22
% 3.12/1.63 = ( product_Pair @ A @ A @ W @ V ) ) )
% 3.12/1.63 => ( ~ ( ( E1
% 3.12/1.63 = ( product_Pair @ A @ A @ V @ W ) )
% 3.12/1.63 & ( E22
% 3.12/1.63 = ( product_Pair @ A @ A @ W @ U2 ) ) )
% 3.12/1.63 => ( P2 @ ( product_Pair @ A @ A @ U2 @ V ) @ W @ ( cons @ ( product_prod @ A @ A ) @ E22 @ Es ) ) ) )
% 3.12/1.63 => ( P2 @ ( product_Pair @ A @ A @ U2 @ V ) @ W @ ( cons @ ( product_prod @ A @ A ) @ E1 @ ( cons @ ( product_prod @ A @ A ) @ E22 @ Es ) ) ) ) ) )
% 3.12/1.63 => ( P2 @ A0 @ A1 @ A22 ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_162_sd__path_Ocases,axiom,
% 3.12/1.63 ! [A: $tType,X3: product_prod @ ( product_prod @ A @ A ) @ ( product_prod @ A @ ( list @ ( product_prod @ A @ A ) ) )] :
% 3.12/1.63 ( ! [Uu: product_prod @ A @ A,Uv: A] :
% 3.12/1.63 ( X3
% 3.12/1.63 != ( product_Pair @ ( product_prod @ A @ A ) @ ( product_prod @ A @ ( list @ ( product_prod @ A @ A ) ) ) @ Uu @ ( product_Pair @ A @ ( list @ ( product_prod @ A @ A ) ) @ Uv @ ( nil @ ( product_prod @ A @ A ) ) ) ) )
% 3.12/1.63 => ~ ! [U2: A,V: A,W: A,E2: product_prod @ A @ A,Es: list @ ( product_prod @ A @ A )] :
% 3.12/1.63 ( X3
% 3.12/1.63 != ( product_Pair @ ( product_prod @ A @ A ) @ ( product_prod @ A @ ( list @ ( product_prod @ A @ A ) ) ) @ ( product_Pair @ A @ A @ U2 @ V ) @ ( product_Pair @ A @ ( list @ ( product_prod @ A @ A ) ) @ W @ ( cons @ ( product_prod @ A @ A ) @ E2 @ Es ) ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_163_co__path_Ocases,axiom,
% 3.12/1.63 ! [A: $tType,X3: product_prod @ ( product_prod @ A @ A ) @ ( product_prod @ A @ ( list @ ( product_prod @ A @ A ) ) )] :
% 3.12/1.63 ( ! [Uu: product_prod @ A @ A,Uv: A] :
% 3.12/1.63 ( X3
% 3.12/1.63 != ( product_Pair @ ( product_prod @ A @ A ) @ ( product_prod @ A @ ( list @ ( product_prod @ A @ A ) ) ) @ Uu @ ( product_Pair @ A @ ( list @ ( product_prod @ A @ A ) ) @ Uv @ ( nil @ ( product_prod @ A @ A ) ) ) ) )
% 3.12/1.63 => ( ! [Uw: product_prod @ A @ A,Ux: A,E2: product_prod @ A @ A] :
% 3.12/1.63 ( X3
% 3.12/1.63 != ( product_Pair @ ( product_prod @ A @ A ) @ ( product_prod @ A @ ( list @ ( product_prod @ A @ A ) ) ) @ Uw @ ( product_Pair @ A @ ( list @ ( product_prod @ A @ A ) ) @ Ux @ ( cons @ ( product_prod @ A @ A ) @ E2 @ ( nil @ ( product_prod @ A @ A ) ) ) ) ) )
% 3.12/1.63 => ~ ! [U2: A,V: A,W: A,E1: product_prod @ A @ A,E22: product_prod @ A @ A,Es: list @ ( product_prod @ A @ A )] :
% 3.12/1.63 ( X3
% 3.12/1.63 != ( product_Pair @ ( product_prod @ A @ A ) @ ( product_prod @ A @ ( list @ ( product_prod @ A @ A ) ) ) @ ( product_Pair @ A @ A @ U2 @ V ) @ ( product_Pair @ A @ ( list @ ( product_prod @ A @ A ) ) @ W @ ( cons @ ( product_prod @ A @ A ) @ E1 @ ( cons @ ( product_prod @ A @ A ) @ E22 @ Es ) ) ) ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_164_listrel1__eq__len,axiom,
% 3.12/1.63 ! [A: $tType,Xs2: list @ A,Ys2: list @ A,R: set @ ( product_prod @ A @ A )] :
% 3.12/1.63 ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs2 @ Ys2 ) @ ( listrel1 @ A @ R ) )
% 3.12/1.63 => ( ( size_size @ ( list @ A ) @ Xs2 )
% 3.12/1.63 = ( size_size @ ( list @ A ) @ Ys2 ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_165_not__listrel1__Nil,axiom,
% 3.12/1.63 ! [A: $tType,Xs2: list @ A,R: set @ ( product_prod @ A @ A )] :
% 3.12/1.63 ~ ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs2 @ ( nil @ A ) ) @ ( listrel1 @ A @ R ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_166_not__Nil__listrel1,axiom,
% 3.12/1.63 ! [A: $tType,Xs2: list @ A,R: set @ ( product_prod @ A @ A )] :
% 3.12/1.63 ~ ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( nil @ A ) @ Xs2 ) @ ( listrel1 @ A @ R ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_167_lexord__Nil__right,axiom,
% 3.12/1.63 ! [A: $tType,X3: list @ A,R: set @ ( product_prod @ A @ A )] :
% 3.12/1.63 ~ ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ X3 @ ( nil @ A ) ) @ ( lexord @ A @ R ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_168_lex__append__leftI,axiom,
% 3.12/1.63 ! [A: $tType,Ys2: list @ A,Zs: list @ A,R: set @ ( product_prod @ A @ A ),Xs2: list @ A] :
% 3.12/1.63 ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Ys2 @ Zs ) @ ( lex @ A @ R ) )
% 3.12/1.63 => ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ Xs2 @ Ys2 ) @ ( append @ A @ Xs2 @ Zs ) ) @ ( lex @ A @ R ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_169_progressing__single,axiom,
% 3.12/1.63 ! [A: $tType,E3: product_prod @ A @ A] : ( kurato990191779essing @ A @ ( cons @ ( product_prod @ A @ A ) @ E3 @ ( nil @ ( product_prod @ A @ A ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_170_lexord__partial__trans,axiom,
% 3.12/1.63 ! [A: $tType,Xs2: list @ A,R: set @ ( product_prod @ A @ A ),Ys2: list @ A,Zs: list @ A] :
% 3.12/1.63 ( ! [X4: A,Y4: A,Z2: A] :
% 3.12/1.63 ( ( member2 @ A @ X4 @ ( set2 @ A @ Xs2 ) )
% 3.12/1.63 => ( ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X4 @ Y4 ) @ R )
% 3.12/1.63 => ( ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y4 @ Z2 ) @ R )
% 3.12/1.63 => ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X4 @ Z2 ) @ R ) ) ) )
% 3.12/1.63 => ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs2 @ Ys2 ) @ ( lexord @ A @ R ) )
% 3.12/1.63 => ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Ys2 @ Zs ) @ ( lexord @ A @ R ) )
% 3.12/1.63 => ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs2 @ Zs ) @ ( lexord @ A @ R ) ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_171_lexord__sufE,axiom,
% 3.12/1.63 ! [A: $tType,Xs2: list @ A,Zs: list @ A,Ys2: list @ A,Qs: list @ A,R: set @ ( product_prod @ A @ A )] :
% 3.12/1.63 ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ Xs2 @ Zs ) @ ( append @ A @ Ys2 @ Qs ) ) @ ( lexord @ A @ R ) )
% 3.12/1.63 => ( ( Xs2 != Ys2 )
% 3.12/1.63 => ( ( ( size_size @ ( list @ A ) @ Xs2 )
% 3.12/1.63 = ( size_size @ ( list @ A ) @ Ys2 ) )
% 3.12/1.63 => ( ( ( size_size @ ( list @ A ) @ Zs )
% 3.12/1.63 = ( size_size @ ( list @ A ) @ Qs ) )
% 3.12/1.63 => ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs2 @ Ys2 ) @ ( lexord @ A @ R ) ) ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_172_subset__eq__mset__impl_Ocases,axiom,
% 3.12/1.63 ! [A: $tType,X3: product_prod @ ( list @ A ) @ ( list @ A )] :
% 3.12/1.63 ( ! [Ys4: list @ A] :
% 3.12/1.63 ( X3
% 3.12/1.63 != ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( nil @ A ) @ Ys4 ) )
% 3.12/1.63 => ~ ! [X4: A,Xs4: list @ A,Ys4: list @ A] :
% 3.12/1.63 ( X3
% 3.12/1.63 != ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X4 @ Xs4 ) @ Ys4 ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_173_pre__digraph_Ocas_Ocases,axiom,
% 3.12/1.63 ! [B: $tType,A: $tType,X3: product_prod @ A @ ( product_prod @ ( list @ B ) @ A )] :
% 3.12/1.63 ( ! [U2: A,V: A] :
% 3.12/1.63 ( X3
% 3.12/1.63 != ( product_Pair @ A @ ( product_prod @ ( list @ B ) @ A ) @ U2 @ ( product_Pair @ ( list @ B ) @ A @ ( nil @ B ) @ V ) ) )
% 3.12/1.63 => ~ ! [U2: A,E2: B,Es: list @ B,V: A] :
% 3.12/1.63 ( X3
% 3.12/1.63 != ( product_Pair @ A @ ( product_prod @ ( list @ B ) @ A ) @ U2 @ ( product_Pair @ ( list @ B ) @ A @ ( cons @ B @ E2 @ Es ) @ V ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_174_asym_Oinducts,axiom,
% 3.12/1.63 ! [A: $tType,X3: set @ ( product_prod @ A @ A ),P2: ( set @ ( product_prod @ A @ A ) ) > $o] :
% 3.12/1.63 ( ( asym @ A @ X3 )
% 3.12/1.63 => ( ! [R3: set @ ( product_prod @ A @ A )] :
% 3.12/1.63 ( ! [A7: A,B5: A] :
% 3.12/1.63 ( ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A7 @ B5 ) @ R3 )
% 3.12/1.63 => ~ ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ B5 @ A7 ) @ R3 ) )
% 3.12/1.63 => ( P2 @ R3 ) )
% 3.12/1.63 => ( P2 @ X3 ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_175_asym_Ointros,axiom,
% 3.12/1.63 ! [A: $tType,R2: set @ ( product_prod @ A @ A )] :
% 3.12/1.63 ( ! [A4: A,B4: A] :
% 3.12/1.63 ( ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A4 @ B4 ) @ R2 )
% 3.12/1.63 => ~ ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ B4 @ A4 ) @ R2 ) )
% 3.12/1.63 => ( asym @ A @ R2 ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_176_asym_Osimps,axiom,
% 3.12/1.63 ! [A: $tType] :
% 3.12/1.63 ( ( asym @ A )
% 3.12/1.63 = ( ^ [A6: set @ ( product_prod @ A @ A )] :
% 3.12/1.63 ? [R4: set @ ( product_prod @ A @ A )] :
% 3.12/1.63 ( ( A6 = R4 )
% 3.12/1.63 & ! [X: A,Y: A] :
% 3.12/1.63 ( ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y ) @ R4 )
% 3.12/1.63 => ~ ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y @ X ) @ R4 ) ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_177_asym_Ocases,axiom,
% 3.12/1.63 ! [A: $tType,A2: set @ ( product_prod @ A @ A )] :
% 3.12/1.63 ( ( asym @ A @ A2 )
% 3.12/1.63 => ! [A7: A,B5: A] :
% 3.12/1.63 ( ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A7 @ B5 ) @ A2 )
% 3.12/1.63 => ~ ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ B5 @ A7 ) @ A2 ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_178_asym__iff,axiom,
% 3.12/1.63 ! [A: $tType] :
% 3.12/1.63 ( ( asym @ A )
% 3.12/1.63 = ( ^ [R4: set @ ( product_prod @ A @ A )] :
% 3.12/1.63 ! [X: A,Y: A] :
% 3.12/1.63 ( ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y ) @ R4 )
% 3.12/1.63 => ~ ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y @ X ) @ R4 ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_179_irreflI,axiom,
% 3.12/1.63 ! [A: $tType,R2: set @ ( product_prod @ A @ A )] :
% 3.12/1.63 ( ! [A4: A] :
% 3.12/1.63 ~ ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A4 @ A4 ) @ R2 )
% 3.12/1.63 => ( irrefl @ A @ R2 ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_180_irrefl__def,axiom,
% 3.12/1.63 ! [A: $tType] :
% 3.12/1.63 ( ( irrefl @ A )
% 3.12/1.63 = ( ^ [R5: set @ ( product_prod @ A @ A )] :
% 3.12/1.63 ! [A6: A] :
% 3.12/1.63 ~ ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A6 @ A6 ) @ R5 ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_181_asymD,axiom,
% 3.12/1.63 ! [A: $tType,R2: set @ ( product_prod @ A @ A ),X3: A,Y3: A] :
% 3.12/1.63 ( ( asym @ A @ R2 )
% 3.12/1.63 => ( ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X3 @ Y3 ) @ R2 )
% 3.12/1.63 => ~ ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y3 @ X3 ) @ R2 ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_182_inverse__permutation__of__list_Ocases,axiom,
% 3.12/1.63 ! [A: $tType,X3: product_prod @ ( list @ ( product_prod @ A @ A ) ) @ A] :
% 3.12/1.63 ( ! [X4: A] :
% 3.12/1.63 ( X3
% 3.12/1.63 != ( product_Pair @ ( list @ ( product_prod @ A @ A ) ) @ A @ ( nil @ ( product_prod @ A @ A ) ) @ X4 ) )
% 3.12/1.63 => ~ ! [Y4: A,X6: A,Xs4: list @ ( product_prod @ A @ A ),X4: A] :
% 3.12/1.63 ( X3
% 3.12/1.63 != ( product_Pair @ ( list @ ( product_prod @ A @ A ) ) @ A @ ( cons @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y4 @ X6 ) @ Xs4 ) @ X4 ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_183_inverse__permutation__of__list_Oinduct,axiom,
% 3.12/1.63 ! [A: $tType,P2: ( list @ ( product_prod @ A @ A ) ) > A > $o,A0: list @ ( product_prod @ A @ A ),A1: A] :
% 3.12/1.63 ( ! [X_1: A] : ( P2 @ ( nil @ ( product_prod @ A @ A ) ) @ X_1 )
% 3.12/1.63 => ( ! [Y4: A,X6: A,Xs4: list @ ( product_prod @ A @ A ),X4: A] :
% 3.12/1.63 ( ( ( X4 != X6 )
% 3.12/1.63 => ( P2 @ Xs4 @ X4 ) )
% 3.12/1.63 => ( P2 @ ( cons @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y4 @ X6 ) @ Xs4 ) @ X4 ) )
% 3.12/1.63 => ( P2 @ A0 @ A1 ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_184_sd__path_Osimps_I2_J,axiom,
% 3.12/1.63 ! [A: $tType,U: A,V2: A,W2: A,E3: product_prod @ A @ A,Es2: list @ ( product_prod @ A @ A )] :
% 3.12/1.63 ( ( pair_sd_path @ A @ ( product_Pair @ A @ A @ U @ V2 ) @ W2 @ ( cons @ ( product_prod @ A @ A ) @ E3 @ Es2 ) )
% 3.12/1.63 = ( append @ ( product_prod @ A @ A )
% 3.12/1.63 @ ( if @ ( list @ ( product_prod @ A @ A ) )
% 3.12/1.63 @ ( E3
% 3.12/1.63 = ( product_Pair @ A @ A @ U @ V2 ) )
% 3.12/1.63 @ ( cons @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ U @ W2 ) @ ( cons @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ W2 @ V2 ) @ ( nil @ ( product_prod @ A @ A ) ) ) )
% 3.12/1.63 @ ( if @ ( list @ ( product_prod @ A @ A ) )
% 3.12/1.63 @ ( E3
% 3.12/1.63 = ( product_Pair @ A @ A @ V2 @ U ) )
% 3.12/1.63 @ ( cons @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ V2 @ W2 ) @ ( cons @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ W2 @ U ) @ ( nil @ ( product_prod @ A @ A ) ) ) )
% 3.12/1.63 @ ( cons @ ( product_prod @ A @ A ) @ E3 @ ( nil @ ( product_prod @ A @ A ) ) ) ) )
% 3.12/1.63 @ ( pair_sd_path @ A @ ( product_Pair @ A @ A @ U @ V2 ) @ W2 @ Es2 ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_185_sd__path_Osimps_I1_J,axiom,
% 3.12/1.63 ! [A: $tType,Uu2: product_prod @ A @ A,Uv2: A] :
% 3.12/1.63 ( ( pair_sd_path @ A @ Uu2 @ Uv2 @ ( nil @ ( product_prod @ A @ A ) ) )
% 3.12/1.63 = ( nil @ ( product_prod @ A @ A ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_186_sd__path__id,axiom,
% 3.12/1.63 ! [A: $tType,X3: A,Y3: A,P3: list @ ( product_prod @ A @ A ),W2: A] :
% 3.12/1.63 ( ~ ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X3 @ Y3 ) @ ( set2 @ ( product_prod @ A @ A ) @ P3 ) )
% 3.12/1.63 => ( ~ ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y3 @ X3 ) @ ( set2 @ ( product_prod @ A @ A ) @ P3 ) )
% 3.12/1.63 => ( ( pair_sd_path @ A @ ( product_Pair @ A @ A @ X3 @ Y3 ) @ W2 @ P3 )
% 3.12/1.63 = P3 ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_187_sd__path_Oelims,axiom,
% 3.12/1.63 ! [A: $tType,X3: product_prod @ A @ A,Xa2: A,Xb: list @ ( product_prod @ A @ A ),Y3: list @ ( product_prod @ A @ A )] :
% 3.12/1.63 ( ( ( pair_sd_path @ A @ X3 @ Xa2 @ Xb )
% 3.12/1.63 = Y3 )
% 3.12/1.63 => ( ( ( Xb
% 3.12/1.63 = ( nil @ ( product_prod @ A @ A ) ) )
% 3.12/1.63 => ( Y3
% 3.12/1.63 != ( nil @ ( product_prod @ A @ A ) ) ) )
% 3.12/1.63 => ~ ! [U2: A,V: A] :
% 3.12/1.63 ( ( X3
% 3.12/1.63 = ( product_Pair @ A @ A @ U2 @ V ) )
% 3.12/1.63 => ! [E2: product_prod @ A @ A,Es: list @ ( product_prod @ A @ A )] :
% 3.12/1.63 ( ( Xb
% 3.12/1.63 = ( cons @ ( product_prod @ A @ A ) @ E2 @ Es ) )
% 3.12/1.63 => ( Y3
% 3.12/1.63 != ( append @ ( product_prod @ A @ A )
% 3.12/1.63 @ ( if @ ( list @ ( product_prod @ A @ A ) )
% 3.12/1.63 @ ( E2
% 3.12/1.63 = ( product_Pair @ A @ A @ U2 @ V ) )
% 3.12/1.63 @ ( cons @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ U2 @ Xa2 ) @ ( cons @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Xa2 @ V ) @ ( nil @ ( product_prod @ A @ A ) ) ) )
% 3.12/1.63 @ ( if @ ( list @ ( product_prod @ A @ A ) )
% 3.12/1.63 @ ( E2
% 3.12/1.63 = ( product_Pair @ A @ A @ V @ U2 ) )
% 3.12/1.63 @ ( cons @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ V @ Xa2 ) @ ( cons @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Xa2 @ U2 ) @ ( nil @ ( product_prod @ A @ A ) ) ) )
% 3.12/1.63 @ ( cons @ ( product_prod @ A @ A ) @ E2 @ ( nil @ ( product_prod @ A @ A ) ) ) ) )
% 3.12/1.63 @ ( pair_sd_path @ A @ ( product_Pair @ A @ A @ U2 @ V ) @ Xa2 @ Es ) ) ) ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_188_the__elem__set,axiom,
% 3.12/1.63 ! [A: $tType,X3: A] :
% 3.12/1.63 ( ( the_elem @ A @ ( set2 @ A @ ( cons @ A @ X3 @ ( nil @ A ) ) ) )
% 3.12/1.63 = X3 ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_189_sd__path_Opelims,axiom,
% 3.12/1.63 ! [A: $tType,X3: product_prod @ A @ A,Xa2: A,Xb: list @ ( product_prod @ A @ A ),Y3: list @ ( product_prod @ A @ A )] :
% 3.12/1.63 ( ( ( pair_sd_path @ A @ X3 @ Xa2 @ Xb )
% 3.12/1.63 = Y3 )
% 3.12/1.63 => ( ( accp @ ( product_prod @ ( product_prod @ A @ A ) @ ( product_prod @ A @ ( list @ ( product_prod @ A @ A ) ) ) ) @ ( pair_sd_path_rel @ A ) @ ( product_Pair @ ( product_prod @ A @ A ) @ ( product_prod @ A @ ( list @ ( product_prod @ A @ A ) ) ) @ X3 @ ( product_Pair @ A @ ( list @ ( product_prod @ A @ A ) ) @ Xa2 @ Xb ) ) )
% 3.12/1.63 => ( ( ( Xb
% 3.12/1.63 = ( nil @ ( product_prod @ A @ A ) ) )
% 3.12/1.63 => ( ( Y3
% 3.12/1.63 = ( nil @ ( product_prod @ A @ A ) ) )
% 3.12/1.63 => ~ ( accp @ ( product_prod @ ( product_prod @ A @ A ) @ ( product_prod @ A @ ( list @ ( product_prod @ A @ A ) ) ) ) @ ( pair_sd_path_rel @ A ) @ ( product_Pair @ ( product_prod @ A @ A ) @ ( product_prod @ A @ ( list @ ( product_prod @ A @ A ) ) ) @ X3 @ ( product_Pair @ A @ ( list @ ( product_prod @ A @ A ) ) @ Xa2 @ ( nil @ ( product_prod @ A @ A ) ) ) ) ) ) )
% 3.12/1.63 => ~ ! [U2: A,V: A] :
% 3.12/1.63 ( ( X3
% 3.12/1.63 = ( product_Pair @ A @ A @ U2 @ V ) )
% 3.12/1.63 => ! [E2: product_prod @ A @ A,Es: list @ ( product_prod @ A @ A )] :
% 3.12/1.63 ( ( Xb
% 3.12/1.63 = ( cons @ ( product_prod @ A @ A ) @ E2 @ Es ) )
% 3.12/1.63 => ( ( Y3
% 3.12/1.63 = ( append @ ( product_prod @ A @ A )
% 3.12/1.63 @ ( if @ ( list @ ( product_prod @ A @ A ) )
% 3.12/1.63 @ ( E2
% 3.12/1.63 = ( product_Pair @ A @ A @ U2 @ V ) )
% 3.12/1.63 @ ( cons @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ U2 @ Xa2 ) @ ( cons @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Xa2 @ V ) @ ( nil @ ( product_prod @ A @ A ) ) ) )
% 3.12/1.63 @ ( if @ ( list @ ( product_prod @ A @ A ) )
% 3.12/1.63 @ ( E2
% 3.12/1.63 = ( product_Pair @ A @ A @ V @ U2 ) )
% 3.12/1.63 @ ( cons @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ V @ Xa2 ) @ ( cons @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Xa2 @ U2 ) @ ( nil @ ( product_prod @ A @ A ) ) ) )
% 3.12/1.63 @ ( cons @ ( product_prod @ A @ A ) @ E2 @ ( nil @ ( product_prod @ A @ A ) ) ) ) )
% 3.12/1.63 @ ( pair_sd_path @ A @ ( product_Pair @ A @ A @ U2 @ V ) @ Xa2 @ Es ) ) )
% 3.12/1.63 => ~ ( accp @ ( product_prod @ ( product_prod @ A @ A ) @ ( product_prod @ A @ ( list @ ( product_prod @ A @ A ) ) ) ) @ ( pair_sd_path_rel @ A ) @ ( product_Pair @ ( product_prod @ A @ A ) @ ( product_prod @ A @ ( list @ ( product_prod @ A @ A ) ) ) @ ( product_Pair @ A @ A @ U2 @ V ) @ ( product_Pair @ A @ ( list @ ( product_prod @ A @ A ) ) @ Xa2 @ ( cons @ ( product_prod @ A @ A ) @ E2 @ Es ) ) ) ) ) ) ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_190_list__exhaust2,axiom,
% 3.12/1.63 ! [A: $tType,B: $tType,Y3: list @ A,Ya: list @ B] :
% 3.12/1.63 ( ( ( Y3
% 3.12/1.63 = ( nil @ A ) )
% 3.12/1.63 => ( Ya
% 3.12/1.63 != ( nil @ B ) ) )
% 3.12/1.63 => ( ( ( Y3
% 3.12/1.63 = ( nil @ A ) )
% 3.12/1.63 => ! [X213: B,X223: list @ B] :
% 3.12/1.63 ( Ya
% 3.12/1.63 != ( cons @ B @ X213 @ X223 ) ) )
% 3.12/1.63 => ( ( ? [X213: A,X223: list @ A] :
% 3.12/1.63 ( Y3
% 3.12/1.63 = ( cons @ A @ X213 @ X223 ) )
% 3.12/1.63 => ( Ya
% 3.12/1.63 != ( nil @ B ) ) )
% 3.12/1.63 => ~ ( ? [X213: A,X223: list @ A] :
% 3.12/1.63 ( Y3
% 3.12/1.63 = ( cons @ A @ X213 @ X223 ) )
% 3.12/1.63 => ! [X21a: B,X22a: list @ B] :
% 3.12/1.63 ( Ya
% 3.12/1.63 != ( cons @ B @ X21a @ X22a ) ) ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_191_list__exhaust__NSC,axiom,
% 3.12/1.63 ! [A: $tType,Xs2: list @ A] :
% 3.12/1.63 ( ( Xs2
% 3.12/1.63 != ( nil @ A ) )
% 3.12/1.63 => ( ! [X4: A] :
% 3.12/1.63 ( Xs2
% 3.12/1.63 != ( cons @ A @ X4 @ ( nil @ A ) ) )
% 3.12/1.63 => ~ ! [X4: A,Y4: A,Ys4: list @ A] :
% 3.12/1.63 ( Xs2
% 3.12/1.63 != ( cons @ A @ X4 @ ( cons @ A @ Y4 @ Ys4 ) ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_192_product__lists_Osimps_I1_J,axiom,
% 3.12/1.63 ! [A: $tType] :
% 3.12/1.63 ( ( product_lists @ A @ ( nil @ ( list @ A ) ) )
% 3.12/1.63 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_193_lenlex__append2,axiom,
% 3.12/1.63 ! [A: $tType,R2: set @ ( product_prod @ A @ A ),Us: list @ A,Xs2: list @ A,Ys2: list @ A] :
% 3.12/1.63 ( ( irrefl @ A @ R2 )
% 3.12/1.63 => ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ Us @ Xs2 ) @ ( append @ A @ Us @ Ys2 ) ) @ ( lenlex @ A @ R2 ) )
% 3.12/1.63 = ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs2 @ Ys2 ) @ ( lenlex @ A @ R2 ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_194_Nil__lenlex__iff1,axiom,
% 3.12/1.63 ! [A: $tType,Ns: list @ A,R: set @ ( product_prod @ A @ A )] :
% 3.12/1.63 ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( nil @ A ) @ Ns ) @ ( lenlex @ A @ R ) )
% 3.12/1.63 = ( Ns
% 3.12/1.63 != ( nil @ A ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_195_in__set__product__lists__length,axiom,
% 3.12/1.63 ! [A: $tType,Xs2: list @ A,Xss2: list @ ( list @ A )] :
% 3.12/1.63 ( ( member2 @ ( list @ A ) @ Xs2 @ ( set2 @ ( list @ A ) @ ( product_lists @ A @ Xss2 ) ) )
% 3.12/1.63 => ( ( size_size @ ( list @ A ) @ Xs2 )
% 3.12/1.63 = ( size_size @ ( list @ ( list @ A ) ) @ Xss2 ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_196_lenlex__irreflexive,axiom,
% 3.12/1.63 ! [A: $tType,R: set @ ( product_prod @ A @ A ),Xs2: list @ A] :
% 3.12/1.63 ( ! [X4: A] :
% 3.12/1.63 ~ ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X4 @ X4 ) @ R )
% 3.12/1.63 => ~ ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs2 @ Xs2 ) @ ( lenlex @ A @ R ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_197_Nil__lenlex__iff2,axiom,
% 3.12/1.63 ! [A: $tType,Ns: list @ A,R: set @ ( product_prod @ A @ A )] :
% 3.12/1.63 ~ ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Ns @ ( nil @ A ) ) @ ( lenlex @ A @ R ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_198_lenlex__append1,axiom,
% 3.12/1.63 ! [A: $tType,Us: list @ A,Xs2: list @ A,R2: set @ ( product_prod @ A @ A ),Vs: list @ A,Ys2: list @ A] :
% 3.12/1.63 ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Us @ Xs2 ) @ ( lenlex @ A @ R2 ) )
% 3.12/1.63 => ( ( ( size_size @ ( list @ A ) @ Vs )
% 3.12/1.63 = ( size_size @ ( list @ A ) @ Ys2 ) )
% 3.12/1.63 => ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ Us @ Vs ) @ ( append @ A @ Xs2 @ Ys2 ) ) @ ( lenlex @ A @ R2 ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_199_asym__lenlex,axiom,
% 3.12/1.63 ! [A: $tType,R2: set @ ( product_prod @ A @ A )] :
% 3.12/1.63 ( ( asym @ A @ R2 )
% 3.12/1.63 => ( asym @ ( list @ A ) @ ( lenlex @ A @ R2 ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_200_co__path_Opelims,axiom,
% 3.12/1.63 ! [A: $tType,X3: product_prod @ A @ A,Xa2: A,Xb: list @ ( product_prod @ A @ A ),Y3: list @ ( product_prod @ A @ A )] :
% 3.12/1.63 ( ( ( pair_co_path @ A @ X3 @ Xa2 @ Xb )
% 3.12/1.63 = Y3 )
% 3.12/1.63 => ( ( accp @ ( product_prod @ ( product_prod @ A @ A ) @ ( product_prod @ A @ ( list @ ( product_prod @ A @ A ) ) ) ) @ ( pair_co_path_rel @ A ) @ ( product_Pair @ ( product_prod @ A @ A ) @ ( product_prod @ A @ ( list @ ( product_prod @ A @ A ) ) ) @ X3 @ ( product_Pair @ A @ ( list @ ( product_prod @ A @ A ) ) @ Xa2 @ Xb ) ) )
% 3.12/1.63 => ( ( ( Xb
% 3.12/1.63 = ( nil @ ( product_prod @ A @ A ) ) )
% 3.12/1.63 => ( ( Y3
% 3.12/1.63 = ( nil @ ( product_prod @ A @ A ) ) )
% 3.12/1.63 => ~ ( accp @ ( product_prod @ ( product_prod @ A @ A ) @ ( product_prod @ A @ ( list @ ( product_prod @ A @ A ) ) ) ) @ ( pair_co_path_rel @ A ) @ ( product_Pair @ ( product_prod @ A @ A ) @ ( product_prod @ A @ ( list @ ( product_prod @ A @ A ) ) ) @ X3 @ ( product_Pair @ A @ ( list @ ( product_prod @ A @ A ) ) @ Xa2 @ ( nil @ ( product_prod @ A @ A ) ) ) ) ) ) )
% 3.12/1.63 => ( ! [E2: product_prod @ A @ A] :
% 3.12/1.63 ( ( Xb
% 3.12/1.63 = ( cons @ ( product_prod @ A @ A ) @ E2 @ ( nil @ ( product_prod @ A @ A ) ) ) )
% 3.12/1.63 => ( ( Y3
% 3.12/1.63 = ( cons @ ( product_prod @ A @ A ) @ E2 @ ( nil @ ( product_prod @ A @ A ) ) ) )
% 3.12/1.63 => ~ ( accp @ ( product_prod @ ( product_prod @ A @ A ) @ ( product_prod @ A @ ( list @ ( product_prod @ A @ A ) ) ) ) @ ( pair_co_path_rel @ A ) @ ( product_Pair @ ( product_prod @ A @ A ) @ ( product_prod @ A @ ( list @ ( product_prod @ A @ A ) ) ) @ X3 @ ( product_Pair @ A @ ( list @ ( product_prod @ A @ A ) ) @ Xa2 @ ( cons @ ( product_prod @ A @ A ) @ E2 @ ( nil @ ( product_prod @ A @ A ) ) ) ) ) ) ) )
% 3.12/1.63 => ~ ! [U2: A,V: A] :
% 3.12/1.63 ( ( X3
% 3.12/1.63 = ( product_Pair @ A @ A @ U2 @ V ) )
% 3.12/1.63 => ! [E1: product_prod @ A @ A,E22: product_prod @ A @ A,Es: list @ ( product_prod @ A @ A )] :
% 3.12/1.63 ( ( Xb
% 3.12/1.63 = ( cons @ ( product_prod @ A @ A ) @ E1 @ ( cons @ ( product_prod @ A @ A ) @ E22 @ Es ) ) )
% 3.12/1.63 => ( ( ( ( ( E1
% 3.12/1.63 = ( product_Pair @ A @ A @ U2 @ Xa2 ) )
% 3.12/1.63 & ( E22
% 3.12/1.63 = ( product_Pair @ A @ A @ Xa2 @ V ) ) )
% 3.12/1.63 => ( Y3
% 3.12/1.63 = ( cons @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ U2 @ V ) @ ( pair_co_path @ A @ ( product_Pair @ A @ A @ U2 @ V ) @ Xa2 @ Es ) ) ) )
% 3.12/1.63 & ( ~ ( ( E1
% 3.12/1.63 = ( product_Pair @ A @ A @ U2 @ Xa2 ) )
% 3.12/1.63 & ( E22
% 3.12/1.63 = ( product_Pair @ A @ A @ Xa2 @ V ) ) )
% 3.12/1.63 => ( ( ( ( E1
% 3.12/1.63 = ( product_Pair @ A @ A @ V @ Xa2 ) )
% 3.12/1.63 & ( E22
% 3.12/1.63 = ( product_Pair @ A @ A @ Xa2 @ U2 ) ) )
% 3.12/1.63 => ( Y3
% 3.12/1.63 = ( cons @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ V @ U2 ) @ ( pair_co_path @ A @ ( product_Pair @ A @ A @ U2 @ V ) @ Xa2 @ Es ) ) ) )
% 3.12/1.63 & ( ~ ( ( E1
% 3.12/1.63 = ( product_Pair @ A @ A @ V @ Xa2 ) )
% 3.12/1.63 & ( E22
% 3.12/1.63 = ( product_Pair @ A @ A @ Xa2 @ U2 ) ) )
% 3.12/1.63 => ( Y3
% 3.12/1.63 = ( cons @ ( product_prod @ A @ A ) @ E1 @ ( pair_co_path @ A @ ( product_Pair @ A @ A @ U2 @ V ) @ Xa2 @ ( cons @ ( product_prod @ A @ A ) @ E22 @ Es ) ) ) ) ) ) ) )
% 3.12/1.63 => ~ ( accp @ ( product_prod @ ( product_prod @ A @ A ) @ ( product_prod @ A @ ( list @ ( product_prod @ A @ A ) ) ) ) @ ( pair_co_path_rel @ A ) @ ( product_Pair @ ( product_prod @ A @ A ) @ ( product_prod @ A @ ( list @ ( product_prod @ A @ A ) ) ) @ ( product_Pair @ A @ A @ U2 @ V ) @ ( product_Pair @ A @ ( list @ ( product_prod @ A @ A ) ) @ Xa2 @ ( cons @ ( product_prod @ A @ A ) @ E1 @ ( cons @ ( product_prod @ A @ A ) @ E22 @ Es ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_201_pawalk__verts_Osimps_I1_J,axiom,
% 3.12/1.63 ! [A: $tType,U: A] :
% 3.12/1.63 ( ( pair_pawalk_verts @ A @ U @ ( nil @ ( product_prod @ A @ A ) ) )
% 3.12/1.63 = ( cons @ A @ U @ ( nil @ A ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_202_co__path__nonempty,axiom,
% 3.12/1.63 ! [A: $tType,E3: product_prod @ A @ A,W2: A,P3: list @ ( product_prod @ A @ A )] :
% 3.12/1.63 ( ( ( pair_co_path @ A @ E3 @ W2 @ P3 )
% 3.12/1.63 = ( nil @ ( product_prod @ A @ A ) ) )
% 3.12/1.63 = ( P3
% 3.12/1.63 = ( nil @ ( product_prod @ A @ A ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_203_co__path_Osimps_I1_J,axiom,
% 3.12/1.63 ! [A: $tType,Uu2: product_prod @ A @ A,Uv2: A] :
% 3.12/1.63 ( ( pair_co_path @ A @ Uu2 @ Uv2 @ ( nil @ ( product_prod @ A @ A ) ) )
% 3.12/1.63 = ( nil @ ( product_prod @ A @ A ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_204_co__path_Osimps_I3_J,axiom,
% 3.12/1.63 ! [A: $tType,E12: product_prod @ A @ A,U: A,W2: A,E23: product_prod @ A @ A,V2: A,Es2: list @ ( product_prod @ A @ A )] :
% 3.12/1.63 ( ( ( ( E12
% 3.12/1.63 = ( product_Pair @ A @ A @ U @ W2 ) )
% 3.12/1.63 & ( E23
% 3.12/1.63 = ( product_Pair @ A @ A @ W2 @ V2 ) ) )
% 3.12/1.63 => ( ( pair_co_path @ A @ ( product_Pair @ A @ A @ U @ V2 ) @ W2 @ ( cons @ ( product_prod @ A @ A ) @ E12 @ ( cons @ ( product_prod @ A @ A ) @ E23 @ Es2 ) ) )
% 3.12/1.63 = ( cons @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ U @ V2 ) @ ( pair_co_path @ A @ ( product_Pair @ A @ A @ U @ V2 ) @ W2 @ Es2 ) ) ) )
% 3.12/1.63 & ( ~ ( ( E12
% 3.12/1.63 = ( product_Pair @ A @ A @ U @ W2 ) )
% 3.12/1.63 & ( E23
% 3.12/1.63 = ( product_Pair @ A @ A @ W2 @ V2 ) ) )
% 3.12/1.63 => ( ( ( ( E12
% 3.12/1.63 = ( product_Pair @ A @ A @ V2 @ W2 ) )
% 3.12/1.63 & ( E23
% 3.12/1.63 = ( product_Pair @ A @ A @ W2 @ U ) ) )
% 3.12/1.63 => ( ( pair_co_path @ A @ ( product_Pair @ A @ A @ U @ V2 ) @ W2 @ ( cons @ ( product_prod @ A @ A ) @ E12 @ ( cons @ ( product_prod @ A @ A ) @ E23 @ Es2 ) ) )
% 3.12/1.63 = ( cons @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ V2 @ U ) @ ( pair_co_path @ A @ ( product_Pair @ A @ A @ U @ V2 ) @ W2 @ Es2 ) ) ) )
% 3.12/1.63 & ( ~ ( ( E12
% 3.12/1.63 = ( product_Pair @ A @ A @ V2 @ W2 ) )
% 3.12/1.63 & ( E23
% 3.12/1.63 = ( product_Pair @ A @ A @ W2 @ U ) ) )
% 3.12/1.63 => ( ( pair_co_path @ A @ ( product_Pair @ A @ A @ U @ V2 ) @ W2 @ ( cons @ ( product_prod @ A @ A ) @ E12 @ ( cons @ ( product_prod @ A @ A ) @ E23 @ Es2 ) ) )
% 3.12/1.63 = ( cons @ ( product_prod @ A @ A ) @ E12 @ ( pair_co_path @ A @ ( product_Pair @ A @ A @ U @ V2 ) @ W2 @ ( cons @ ( product_prod @ A @ A ) @ E23 @ Es2 ) ) ) ) ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_205_co__path_Osimps_I2_J,axiom,
% 3.12/1.63 ! [A: $tType,Uw2: product_prod @ A @ A,Ux2: A,E3: product_prod @ A @ A] :
% 3.12/1.63 ( ( pair_co_path @ A @ Uw2 @ Ux2 @ ( cons @ ( product_prod @ A @ A ) @ E3 @ ( nil @ ( product_prod @ A @ A ) ) ) )
% 3.12/1.63 = ( cons @ ( product_prod @ A @ A ) @ E3 @ ( nil @ ( product_prod @ A @ A ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_206_co__path_Oelims,axiom,
% 3.12/1.63 ! [A: $tType,X3: product_prod @ A @ A,Xa2: A,Xb: list @ ( product_prod @ A @ A ),Y3: list @ ( product_prod @ A @ A )] :
% 3.12/1.63 ( ( ( pair_co_path @ A @ X3 @ Xa2 @ Xb )
% 3.12/1.63 = Y3 )
% 3.12/1.63 => ( ( ( Xb
% 3.12/1.63 = ( nil @ ( product_prod @ A @ A ) ) )
% 3.12/1.63 => ( Y3
% 3.12/1.63 != ( nil @ ( product_prod @ A @ A ) ) ) )
% 3.12/1.63 => ( ! [E2: product_prod @ A @ A] :
% 3.12/1.63 ( ( Xb
% 3.12/1.63 = ( cons @ ( product_prod @ A @ A ) @ E2 @ ( nil @ ( product_prod @ A @ A ) ) ) )
% 3.12/1.63 => ( Y3
% 3.12/1.63 != ( cons @ ( product_prod @ A @ A ) @ E2 @ ( nil @ ( product_prod @ A @ A ) ) ) ) )
% 3.12/1.63 => ~ ! [U2: A,V: A] :
% 3.12/1.63 ( ( X3
% 3.12/1.63 = ( product_Pair @ A @ A @ U2 @ V ) )
% 3.12/1.63 => ! [E1: product_prod @ A @ A,E22: product_prod @ A @ A,Es: list @ ( product_prod @ A @ A )] :
% 3.12/1.63 ( ( Xb
% 3.12/1.63 = ( cons @ ( product_prod @ A @ A ) @ E1 @ ( cons @ ( product_prod @ A @ A ) @ E22 @ Es ) ) )
% 3.12/1.63 => ~ ( ( ( ( E1
% 3.12/1.63 = ( product_Pair @ A @ A @ U2 @ Xa2 ) )
% 3.12/1.63 & ( E22
% 3.12/1.63 = ( product_Pair @ A @ A @ Xa2 @ V ) ) )
% 3.12/1.63 => ( Y3
% 3.12/1.63 = ( cons @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ U2 @ V ) @ ( pair_co_path @ A @ ( product_Pair @ A @ A @ U2 @ V ) @ Xa2 @ Es ) ) ) )
% 3.12/1.63 & ( ~ ( ( E1
% 3.12/1.63 = ( product_Pair @ A @ A @ U2 @ Xa2 ) )
% 3.12/1.63 & ( E22
% 3.12/1.63 = ( product_Pair @ A @ A @ Xa2 @ V ) ) )
% 3.12/1.63 => ( ( ( ( E1
% 3.12/1.63 = ( product_Pair @ A @ A @ V @ Xa2 ) )
% 3.12/1.63 & ( E22
% 3.12/1.63 = ( product_Pair @ A @ A @ Xa2 @ U2 ) ) )
% 3.12/1.63 => ( Y3
% 3.12/1.63 = ( cons @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ V @ U2 ) @ ( pair_co_path @ A @ ( product_Pair @ A @ A @ U2 @ V ) @ Xa2 @ Es ) ) ) )
% 3.12/1.63 & ( ~ ( ( E1
% 3.12/1.63 = ( product_Pair @ A @ A @ V @ Xa2 ) )
% 3.12/1.63 & ( E22
% 3.12/1.63 = ( product_Pair @ A @ A @ Xa2 @ U2 ) ) )
% 3.12/1.63 => ( Y3
% 3.12/1.63 = ( cons @ ( product_prod @ A @ A ) @ E1 @ ( pair_co_path @ A @ ( product_Pair @ A @ A @ U2 @ V ) @ Xa2 @ ( cons @ ( product_prod @ A @ A ) @ E22 @ Es ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_207_co__sd__id,axiom,
% 3.12/1.63 ! [A: $tType,U: A,W2: A,P3: list @ ( product_prod @ A @ A ),V2: A] :
% 3.12/1.63 ( ~ ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ U @ W2 ) @ ( set2 @ ( product_prod @ A @ A ) @ P3 ) )
% 3.12/1.63 => ( ~ ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ V2 @ W2 ) @ ( set2 @ ( product_prod @ A @ A ) @ P3 ) )
% 3.12/1.63 => ( ( pair_co_path @ A @ ( product_Pair @ A @ A @ U @ V2 ) @ W2 @ ( pair_sd_path @ A @ ( product_Pair @ A @ A @ U @ V2 ) @ W2 @ P3 ) )
% 3.12/1.63 = P3 ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_208_subseqs_Osimps_I1_J,axiom,
% 3.12/1.63 ! [A: $tType] :
% 3.12/1.63 ( ( subseqs @ A @ ( nil @ A ) )
% 3.12/1.63 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_209_Cons__lenlex__iff,axiom,
% 3.12/1.63 ! [A: $tType,M: A,Ms: list @ A,N: A,Ns: list @ A,R: set @ ( product_prod @ A @ A )] :
% 3.12/1.63 ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ M @ Ms ) @ ( cons @ A @ N @ Ns ) ) @ ( lenlex @ A @ R ) )
% 3.12/1.63 = ( ( ord_less @ nat @ ( size_size @ ( list @ A ) @ Ms ) @ ( size_size @ ( list @ A ) @ Ns ) )
% 3.12/1.63 | ( ( ( size_size @ ( list @ A ) @ Ms )
% 3.12/1.63 = ( size_size @ ( list @ A ) @ Ns ) )
% 3.12/1.63 & ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ M @ N ) @ R ) )
% 3.12/1.63 | ( ( M = N )
% 3.12/1.63 & ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Ms @ Ns ) @ ( lenlex @ A @ R ) ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_210_length__induct,axiom,
% 3.12/1.63 ! [A: $tType,P2: ( list @ A ) > $o,Xs2: list @ A] :
% 3.12/1.63 ( ! [Xs4: list @ A] :
% 3.12/1.63 ( ! [Ys7: list @ A] :
% 3.12/1.63 ( ( ord_less @ nat @ ( size_size @ ( list @ A ) @ Ys7 ) @ ( size_size @ ( list @ A ) @ Xs4 ) )
% 3.12/1.63 => ( P2 @ Ys7 ) )
% 3.12/1.63 => ( P2 @ Xs4 ) )
% 3.12/1.63 => ( P2 @ Xs2 ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_211_subseqs__refl,axiom,
% 3.12/1.63 ! [A: $tType,Xs2: list @ A] : ( member2 @ ( list @ A ) @ Xs2 @ ( set2 @ ( list @ A ) @ ( subseqs @ A @ Xs2 ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_212_Cons__in__subseqsD,axiom,
% 3.12/1.63 ! [A: $tType,Y3: A,Ys2: list @ A,Xs2: list @ A] :
% 3.12/1.63 ( ( member2 @ ( list @ A ) @ ( cons @ A @ Y3 @ Ys2 ) @ ( set2 @ ( list @ A ) @ ( subseqs @ A @ Xs2 ) ) )
% 3.12/1.63 => ( member2 @ ( list @ A ) @ Ys2 @ ( set2 @ ( list @ A ) @ ( subseqs @ A @ Xs2 ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_213_in__measures_I2_J,axiom,
% 3.12/1.63 ! [A: $tType,X3: A,Y3: A,F3: A > nat,Fs: list @ ( A > nat )] :
% 3.12/1.63 ( ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X3 @ Y3 ) @ ( measures @ A @ ( cons @ ( A > nat ) @ F3 @ Fs ) ) )
% 3.12/1.63 = ( ( ord_less @ nat @ ( F3 @ X3 ) @ ( F3 @ Y3 ) )
% 3.12/1.63 | ( ( ( F3 @ X3 )
% 3.12/1.63 = ( F3 @ Y3 ) )
% 3.12/1.63 & ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X3 @ Y3 ) @ ( measures @ A @ Fs ) ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_214_inverse__permutation__of__list_Oelims,axiom,
% 3.12/1.63 ! [A: $tType,X3: list @ ( product_prod @ A @ A ),Xa2: A,Y3: A] :
% 3.12/1.63 ( ( ( invers965609412f_list @ A @ X3 @ Xa2 )
% 3.12/1.63 = Y3 )
% 3.12/1.63 => ( ( ( X3
% 3.12/1.63 = ( nil @ ( product_prod @ A @ A ) ) )
% 3.12/1.63 => ( Y3 != Xa2 ) )
% 3.12/1.63 => ~ ! [Y4: A,X6: A,Xs4: list @ ( product_prod @ A @ A )] :
% 3.12/1.63 ( ( X3
% 3.12/1.63 = ( cons @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y4 @ X6 ) @ Xs4 ) )
% 3.12/1.63 => ~ ( ( ( Xa2 = X6 )
% 3.12/1.63 => ( Y3 = Y4 ) )
% 3.12/1.63 & ( ( Xa2 != X6 )
% 3.12/1.63 => ( Y3
% 3.12/1.63 = ( invers965609412f_list @ A @ Xs4 @ Xa2 ) ) ) ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_215_in__measures_I1_J,axiom,
% 3.12/1.63 ! [A: $tType,X3: A,Y3: A] :
% 3.12/1.63 ~ ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X3 @ Y3 ) @ ( measures @ A @ ( nil @ ( A > nat ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_216_eval__inverse__permutation__of__list_I3_J,axiom,
% 3.12/1.63 ! [A: $tType,X3: A,X7: A,Y5: A,Xs2: list @ ( product_prod @ A @ A )] :
% 3.12/1.63 ( ( X3 != X7 )
% 3.12/1.63 => ( ( invers965609412f_list @ A @ ( cons @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y5 @ X7 ) @ Xs2 ) @ X3 )
% 3.12/1.63 = ( invers965609412f_list @ A @ Xs2 @ X3 ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_217_eval__inverse__permutation__of__list_I2_J,axiom,
% 3.12/1.63 ! [A: $tType,X3: A,X7: A,Y3: A,Xs2: list @ ( product_prod @ A @ A )] :
% 3.12/1.63 ( ( X3 = X7 )
% 3.12/1.63 => ( ( invers965609412f_list @ A @ ( cons @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y3 @ X7 ) @ Xs2 ) @ X3 )
% 3.12/1.63 = Y3 ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_218_inverse__permutation__of__list_Osimps_I1_J,axiom,
% 3.12/1.63 ! [A: $tType,X3: A] :
% 3.12/1.63 ( ( invers965609412f_list @ A @ ( nil @ ( product_prod @ A @ A ) ) @ X3 )
% 3.12/1.63 = X3 ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_219_inverse__permutation__of__list_Osimps_I2_J,axiom,
% 3.12/1.63 ! [A: $tType,X3: A,X7: A,Y3: A,Xs2: list @ ( product_prod @ A @ A )] :
% 3.12/1.63 ( ( ( X3 = X7 )
% 3.12/1.63 => ( ( invers965609412f_list @ A @ ( cons @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y3 @ X7 ) @ Xs2 ) @ X3 )
% 3.12/1.63 = Y3 ) )
% 3.12/1.63 & ( ( X3 != X7 )
% 3.12/1.63 => ( ( invers965609412f_list @ A @ ( cons @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y3 @ X7 ) @ Xs2 ) @ X3 )
% 3.12/1.63 = ( invers965609412f_list @ A @ Xs2 @ X3 ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_220_measures__less,axiom,
% 3.12/1.63 ! [A: $tType,F3: A > nat,X3: A,Y3: A,Fs: list @ ( A > nat )] :
% 3.12/1.63 ( ( ord_less @ nat @ ( F3 @ X3 ) @ ( F3 @ Y3 ) )
% 3.12/1.63 => ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X3 @ Y3 ) @ ( measures @ A @ ( cons @ ( A > nat ) @ F3 @ Fs ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_221_inverse__permutation__of__list__unique,axiom,
% 3.12/1.63 ! [A: $tType,Xs2: list @ ( product_prod @ A @ A ),A5: set @ A,X3: A,Y3: A] :
% 3.12/1.63 ( ( list_permutes @ A @ Xs2 @ A5 )
% 3.12/1.63 => ( ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X3 @ Y3 ) @ ( set2 @ ( product_prod @ A @ A ) @ Xs2 ) )
% 3.12/1.63 => ( ( invers965609412f_list @ A @ Xs2 @ Y3 )
% 3.12/1.63 = X3 ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_222_eval__permutation__of__list_I3_J,axiom,
% 3.12/1.63 ! [A: $tType,X3: A,X7: A,Y5: A,Xs2: list @ ( product_prod @ A @ A )] :
% 3.12/1.63 ( ( X3 != X7 )
% 3.12/1.63 => ( ( permutation_of_list @ A @ ( cons @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X7 @ Y5 ) @ Xs2 ) @ X3 )
% 3.12/1.63 = ( permutation_of_list @ A @ Xs2 @ X3 ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_223_eval__permutation__of__list_I1_J,axiom,
% 3.12/1.63 ! [A: $tType,X3: A] :
% 3.12/1.63 ( ( permutation_of_list @ A @ ( nil @ ( product_prod @ A @ A ) ) @ X3 )
% 3.12/1.63 = X3 ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_224_eval__permutation__of__list_I2_J,axiom,
% 3.12/1.63 ! [A: $tType,X3: A,X7: A,Y3: A,Xs2: list @ ( product_prod @ A @ A )] :
% 3.12/1.63 ( ( X3 = X7 )
% 3.12/1.63 => ( ( permutation_of_list @ A @ ( cons @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X7 @ Y3 ) @ Xs2 ) @ X3 )
% 3.12/1.63 = Y3 ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_225_permutation__of__list__unique,axiom,
% 3.12/1.63 ! [A: $tType,Xs2: list @ ( product_prod @ A @ A ),A5: set @ A,X3: A,Y3: A] :
% 3.12/1.63 ( ( list_permutes @ A @ Xs2 @ A5 )
% 3.12/1.63 => ( ( member2 @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X3 @ Y3 ) @ ( set2 @ ( product_prod @ A @ A ) @ Xs2 ) )
% 3.12/1.63 => ( ( permutation_of_list @ A @ Xs2 @ X3 )
% 3.12/1.63 = Y3 ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_226_permutation__of__list__Cons,axiom,
% 3.12/1.63 ! [A: $tType,X3: A,X7: A,Y3: A,Xs2: list @ ( product_prod @ A @ A )] :
% 3.12/1.63 ( ( ( X3 = X7 )
% 3.12/1.63 => ( ( permutation_of_list @ A @ ( cons @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X3 @ Y3 ) @ Xs2 ) @ X7 )
% 3.12/1.63 = Y3 ) )
% 3.12/1.63 & ( ( X3 != X7 )
% 3.12/1.63 => ( ( permutation_of_list @ A @ ( cons @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X3 @ Y3 ) @ Xs2 ) @ X7 )
% 3.12/1.63 = ( permutation_of_list @ A @ Xs2 @ X7 ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_227_part__code_I1_J,axiom,
% 3.12/1.63 ! [A: $tType,B: $tType] :
% 3.12/1.63 ( ( linorder @ A )
% 3.12/1.63 => ! [F3: B > A,Pivot: A] :
% 3.12/1.63 ( ( linorder_part @ B @ A @ F3 @ Pivot @ ( nil @ B ) )
% 3.12/1.63 = ( product_Pair @ ( list @ B ) @ ( product_prod @ ( list @ B ) @ ( list @ B ) ) @ ( nil @ B ) @ ( product_Pair @ ( list @ B ) @ ( list @ B ) @ ( nil @ B ) @ ( nil @ B ) ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_228_not__in__set__insert,axiom,
% 3.12/1.63 ! [A: $tType,X3: A,Xs2: list @ A] :
% 3.12/1.63 ( ~ ( member2 @ A @ X3 @ ( set2 @ A @ Xs2 ) )
% 3.12/1.63 => ( ( insert @ A @ X3 @ Xs2 )
% 3.12/1.63 = ( cons @ A @ X3 @ Xs2 ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_229_in__set__insert,axiom,
% 3.12/1.63 ! [A: $tType,X3: A,Xs2: list @ A] :
% 3.12/1.63 ( ( member2 @ A @ X3 @ ( set2 @ A @ Xs2 ) )
% 3.12/1.63 => ( ( insert @ A @ X3 @ Xs2 )
% 3.12/1.63 = Xs2 ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_230_insert__Nil,axiom,
% 3.12/1.63 ! [A: $tType,X3: A] :
% 3.12/1.63 ( ( insert @ A @ X3 @ ( nil @ A ) )
% 3.12/1.63 = ( cons @ A @ X3 @ ( nil @ A ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_231_List_Oinsert__def,axiom,
% 3.12/1.63 ! [A: $tType] :
% 3.12/1.63 ( ( insert @ A )
% 3.12/1.63 = ( ^ [X: A,Xs: list @ A] : ( if @ ( list @ A ) @ ( member2 @ A @ X @ ( set2 @ A @ Xs ) ) @ Xs @ ( cons @ A @ X @ Xs ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_232_concat__eq__append__conv,axiom,
% 3.12/1.63 ! [A: $tType,Xss2: list @ ( list @ A ),Ys2: list @ A,Zs: list @ A] :
% 3.12/1.63 ( ( ( concat @ A @ Xss2 )
% 3.12/1.63 = ( append @ A @ Ys2 @ Zs ) )
% 3.12/1.63 = ( ( ( Xss2
% 3.12/1.63 = ( nil @ ( list @ A ) ) )
% 3.12/1.63 => ( ( Ys2
% 3.12/1.63 = ( nil @ A ) )
% 3.12/1.63 & ( Zs
% 3.12/1.63 = ( nil @ A ) ) ) )
% 3.12/1.63 & ( ( Xss2
% 3.12/1.63 != ( nil @ ( list @ A ) ) )
% 3.12/1.63 => ? [Xss1: list @ ( list @ A ),Xs: list @ A,Xs6: list @ A,Xss22: list @ ( list @ A )] :
% 3.12/1.63 ( ( Xss2
% 3.12/1.63 = ( append @ ( list @ A ) @ Xss1 @ ( cons @ ( list @ A ) @ ( append @ A @ Xs @ Xs6 ) @ Xss22 ) ) )
% 3.12/1.63 & ( Ys2
% 3.12/1.63 = ( append @ A @ ( concat @ A @ Xss1 ) @ Xs ) )
% 3.12/1.63 & ( Zs
% 3.12/1.63 = ( append @ A @ Xs6 @ ( concat @ A @ Xss22 ) ) ) ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_233_inverse__permutation__of__list_Opelims,axiom,
% 3.12/1.63 ! [A: $tType,X3: list @ ( product_prod @ A @ A ),Xa2: A,Y3: A] :
% 3.12/1.63 ( ( ( invers965609412f_list @ A @ X3 @ Xa2 )
% 3.12/1.63 = Y3 )
% 3.12/1.63 => ( ( accp @ ( product_prod @ ( list @ ( product_prod @ A @ A ) ) @ A ) @ ( invers1507583541st_rel @ A ) @ ( product_Pair @ ( list @ ( product_prod @ A @ A ) ) @ A @ X3 @ Xa2 ) )
% 3.12/1.63 => ( ( ( X3
% 3.12/1.63 = ( nil @ ( product_prod @ A @ A ) ) )
% 3.12/1.63 => ( ( Y3 = Xa2 )
% 3.12/1.63 => ~ ( accp @ ( product_prod @ ( list @ ( product_prod @ A @ A ) ) @ A ) @ ( invers1507583541st_rel @ A ) @ ( product_Pair @ ( list @ ( product_prod @ A @ A ) ) @ A @ ( nil @ ( product_prod @ A @ A ) ) @ Xa2 ) ) ) )
% 3.12/1.63 => ~ ! [Y4: A,X6: A,Xs4: list @ ( product_prod @ A @ A )] :
% 3.12/1.63 ( ( X3
% 3.12/1.63 = ( cons @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y4 @ X6 ) @ Xs4 ) )
% 3.12/1.63 => ( ( ( ( Xa2 = X6 )
% 3.12/1.63 => ( Y3 = Y4 ) )
% 3.12/1.63 & ( ( Xa2 != X6 )
% 3.12/1.63 => ( Y3
% 3.12/1.63 = ( invers965609412f_list @ A @ Xs4 @ Xa2 ) ) ) )
% 3.12/1.63 => ~ ( accp @ ( product_prod @ ( list @ ( product_prod @ A @ A ) ) @ A ) @ ( invers1507583541st_rel @ A ) @ ( product_Pair @ ( list @ ( product_prod @ A @ A ) ) @ A @ ( cons @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y4 @ X6 ) @ Xs4 ) @ Xa2 ) ) ) ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_234_Nil__eq__concat__conv,axiom,
% 3.12/1.63 ! [A: $tType,Xss2: list @ ( list @ A )] :
% 3.12/1.63 ( ( ( nil @ A )
% 3.12/1.63 = ( concat @ A @ Xss2 ) )
% 3.12/1.63 = ( ! [X: list @ A] :
% 3.12/1.63 ( ( member2 @ ( list @ A ) @ X @ ( set2 @ ( list @ A ) @ Xss2 ) )
% 3.12/1.63 => ( X
% 3.12/1.63 = ( nil @ A ) ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_235_concat__eq__Nil__conv,axiom,
% 3.12/1.63 ! [A: $tType,Xss2: list @ ( list @ A )] :
% 3.12/1.63 ( ( ( concat @ A @ Xss2 )
% 3.12/1.63 = ( nil @ A ) )
% 3.12/1.63 = ( ! [X: list @ A] :
% 3.12/1.63 ( ( member2 @ ( list @ A ) @ X @ ( set2 @ ( list @ A ) @ Xss2 ) )
% 3.12/1.63 => ( X
% 3.12/1.63 = ( nil @ A ) ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_236_concat__append,axiom,
% 3.12/1.63 ! [A: $tType,Xs2: list @ ( list @ A ),Ys2: list @ ( list @ A )] :
% 3.12/1.63 ( ( concat @ A @ ( append @ ( list @ A ) @ Xs2 @ Ys2 ) )
% 3.12/1.63 = ( append @ A @ ( concat @ A @ Xs2 ) @ ( concat @ A @ Ys2 ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_237_concat_Osimps_I2_J,axiom,
% 3.12/1.63 ! [A: $tType,X3: list @ A,Xs2: list @ ( list @ A )] :
% 3.12/1.63 ( ( concat @ A @ ( cons @ ( list @ A ) @ X3 @ Xs2 ) )
% 3.12/1.63 = ( append @ A @ X3 @ ( concat @ A @ Xs2 ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_238_concat_Osimps_I1_J,axiom,
% 3.12/1.63 ! [A: $tType] :
% 3.12/1.63 ( ( concat @ A @ ( nil @ ( list @ A ) ) )
% 3.12/1.63 = ( nil @ A ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_239_concat__eq__appendD,axiom,
% 3.12/1.63 ! [A: $tType,Xss2: list @ ( list @ A ),Ys2: list @ A,Zs: list @ A] :
% 3.12/1.63 ( ( ( concat @ A @ Xss2 )
% 3.12/1.63 = ( append @ A @ Ys2 @ Zs ) )
% 3.12/1.63 => ( ( Xss2
% 3.12/1.63 != ( nil @ ( list @ A ) ) )
% 3.12/1.63 => ? [Xss12: list @ ( list @ A ),Xs4: list @ A,Xs3: list @ A,Xss23: list @ ( list @ A )] :
% 3.12/1.63 ( ( Xss2
% 3.12/1.63 = ( append @ ( list @ A ) @ Xss12 @ ( cons @ ( list @ A ) @ ( append @ A @ Xs4 @ Xs3 ) @ Xss23 ) ) )
% 3.12/1.63 & ( Ys2
% 3.12/1.63 = ( append @ A @ ( concat @ A @ Xss12 ) @ Xs4 ) )
% 3.12/1.63 & ( Zs
% 3.12/1.63 = ( append @ A @ Xs3 @ ( concat @ A @ Xss23 ) ) ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_240_length__n__lists__elem,axiom,
% 3.12/1.63 ! [A: $tType,Ys2: list @ A,N: nat,Xs2: list @ A] :
% 3.12/1.63 ( ( member2 @ ( list @ A ) @ Ys2 @ ( set2 @ ( list @ A ) @ ( n_lists @ A @ N @ Xs2 ) ) )
% 3.12/1.63 => ( ( size_size @ ( list @ A ) @ Ys2 )
% 3.12/1.63 = N ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_241_listrel_Oinducts,axiom,
% 3.12/1.63 ! [A: $tType,B: $tType,X1: list @ A,X2: list @ B,R: set @ ( product_prod @ A @ B ),P2: ( list @ A ) > ( list @ B ) > $o] :
% 3.12/1.63 ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ X1 @ X2 ) @ ( listrel @ A @ B @ R ) )
% 3.12/1.63 => ( ( P2 @ ( nil @ A ) @ ( nil @ B ) )
% 3.12/1.63 => ( ! [X4: A,Y4: B,Xs4: list @ A,Ys4: list @ B] :
% 3.12/1.63 ( ( member2 @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X4 @ Y4 ) @ R )
% 3.12/1.63 => ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ Xs4 @ Ys4 ) @ ( listrel @ A @ B @ R ) )
% 3.12/1.63 => ( ( P2 @ Xs4 @ Ys4 )
% 3.12/1.63 => ( P2 @ ( cons @ A @ X4 @ Xs4 ) @ ( cons @ B @ Y4 @ Ys4 ) ) ) ) )
% 3.12/1.63 => ( P2 @ X1 @ X2 ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_242_listrel__eq__len,axiom,
% 3.12/1.63 ! [A: $tType,B: $tType,Xs2: list @ A,Ys2: list @ B,R: set @ ( product_prod @ A @ B )] :
% 3.12/1.63 ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ Xs2 @ Ys2 ) @ ( listrel @ A @ B @ R ) )
% 3.12/1.63 => ( ( size_size @ ( list @ A ) @ Xs2 )
% 3.12/1.63 = ( size_size @ ( list @ B ) @ Ys2 ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_243_listrel_ONil,axiom,
% 3.12/1.63 ! [B: $tType,A: $tType,R: set @ ( product_prod @ A @ B )] : ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ ( nil @ A ) @ ( nil @ B ) ) @ ( listrel @ A @ B @ R ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_244_listrel__Nil1,axiom,
% 3.12/1.63 ! [A: $tType,B: $tType,Xs2: list @ B,R: set @ ( product_prod @ A @ B )] :
% 3.12/1.63 ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ ( nil @ A ) @ Xs2 ) @ ( listrel @ A @ B @ R ) )
% 3.12/1.63 => ( Xs2
% 3.12/1.63 = ( nil @ B ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_245_listrel__Nil2,axiom,
% 3.12/1.63 ! [B: $tType,A: $tType,Xs2: list @ A,R: set @ ( product_prod @ A @ B )] :
% 3.12/1.63 ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ Xs2 @ ( nil @ B ) ) @ ( listrel @ A @ B @ R ) )
% 3.12/1.63 => ( Xs2
% 3.12/1.63 = ( nil @ A ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_246_listrel_OCons,axiom,
% 3.12/1.63 ! [B: $tType,A: $tType,X3: A,Y3: B,R: set @ ( product_prod @ A @ B ),Xs2: list @ A,Ys2: list @ B] :
% 3.12/1.63 ( ( member2 @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X3 @ Y3 ) @ R )
% 3.12/1.63 => ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ Xs2 @ Ys2 ) @ ( listrel @ A @ B @ R ) )
% 3.12/1.63 => ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ B @ Y3 @ Ys2 ) ) @ ( listrel @ A @ B @ R ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_247_listrel__Cons1,axiom,
% 3.12/1.63 ! [B: $tType,A: $tType,Y3: A,Ys2: list @ A,Xs2: list @ B,R: set @ ( product_prod @ A @ B )] :
% 3.12/1.63 ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ ( cons @ A @ Y3 @ Ys2 ) @ Xs2 ) @ ( listrel @ A @ B @ R ) )
% 3.12/1.63 => ~ ! [Y4: B,Ys4: list @ B] :
% 3.12/1.63 ( ( Xs2
% 3.12/1.63 = ( cons @ B @ Y4 @ Ys4 ) )
% 3.12/1.63 => ( ( member2 @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ Y3 @ Y4 ) @ R )
% 3.12/1.63 => ~ ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ Ys2 @ Ys4 ) @ ( listrel @ A @ B @ R ) ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_248_listrel__Cons2,axiom,
% 3.12/1.63 ! [B: $tType,A: $tType,Xs2: list @ A,Y3: B,Ys2: list @ B,R: set @ ( product_prod @ A @ B )] :
% 3.12/1.63 ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ Xs2 @ ( cons @ B @ Y3 @ Ys2 ) ) @ ( listrel @ A @ B @ R ) )
% 3.12/1.63 => ~ ! [X4: A,Xs4: list @ A] :
% 3.12/1.63 ( ( Xs2
% 3.12/1.63 = ( cons @ A @ X4 @ Xs4 ) )
% 3.12/1.63 => ( ( member2 @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X4 @ Y3 ) @ R )
% 3.12/1.63 => ~ ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ Xs4 @ Ys2 ) @ ( listrel @ A @ B @ R ) ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_249_listrel_Ocases,axiom,
% 3.12/1.63 ! [B: $tType,A: $tType,A1: list @ A,A22: list @ B,R: set @ ( product_prod @ A @ B )] :
% 3.12/1.63 ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ A1 @ A22 ) @ ( listrel @ A @ B @ R ) )
% 3.12/1.63 => ( ( ( A1
% 3.12/1.63 = ( nil @ A ) )
% 3.12/1.63 => ( A22
% 3.12/1.63 != ( nil @ B ) ) )
% 3.12/1.63 => ~ ! [X4: A,Y4: B,Xs4: list @ A] :
% 3.12/1.63 ( ( A1
% 3.12/1.63 = ( cons @ A @ X4 @ Xs4 ) )
% 3.12/1.63 => ! [Ys4: list @ B] :
% 3.12/1.63 ( ( A22
% 3.12/1.63 = ( cons @ B @ Y4 @ Ys4 ) )
% 3.12/1.63 => ( ( member2 @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X4 @ Y4 ) @ R )
% 3.12/1.63 => ~ ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ Xs4 @ Ys4 ) @ ( listrel @ A @ B @ R ) ) ) ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_250_listrel_Osimps,axiom,
% 3.12/1.63 ! [B: $tType,A: $tType,A1: list @ A,A22: list @ B,R: set @ ( product_prod @ A @ B )] :
% 3.12/1.63 ( ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ A1 @ A22 ) @ ( listrel @ A @ B @ R ) )
% 3.12/1.63 = ( ( ( A1
% 3.12/1.63 = ( nil @ A ) )
% 3.12/1.63 & ( A22
% 3.12/1.63 = ( nil @ B ) ) )
% 3.12/1.63 | ? [X: A,Y: B,Xs: list @ A,Ys: list @ B] :
% 3.12/1.63 ( ( A1
% 3.12/1.63 = ( cons @ A @ X @ Xs ) )
% 3.12/1.63 & ( A22
% 3.12/1.63 = ( cons @ B @ Y @ Ys ) )
% 3.12/1.63 & ( member2 @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X @ Y ) @ R )
% 3.12/1.63 & ( member2 @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ Xs @ Ys ) @ ( listrel @ A @ B @ R ) ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_251_n__lists__Nil,axiom,
% 3.12/1.63 ! [A: $tType,N: nat] :
% 3.12/1.63 ( ( ( N
% 3.12/1.63 = ( zero_zero @ nat ) )
% 3.12/1.63 => ( ( n_lists @ A @ N @ ( nil @ A ) )
% 3.12/1.63 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) )
% 3.12/1.63 & ( ( N
% 3.12/1.63 != ( zero_zero @ nat ) )
% 3.12/1.63 => ( ( n_lists @ A @ N @ ( nil @ A ) )
% 3.12/1.63 = ( nil @ ( list @ A ) ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_252_n__lists_Osimps_I1_J,axiom,
% 3.12/1.63 ! [A: $tType,Xs2: list @ A] :
% 3.12/1.63 ( ( n_lists @ A @ ( zero_zero @ nat ) @ Xs2 )
% 3.12/1.63 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_253_length__0__conv,axiom,
% 3.12/1.63 ! [A: $tType,Xs2: list @ A] :
% 3.12/1.63 ( ( ( size_size @ ( list @ A ) @ Xs2 )
% 3.12/1.63 = ( zero_zero @ nat ) )
% 3.12/1.63 = ( Xs2
% 3.12/1.63 = ( nil @ A ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(fact_254_length__greater__0__conv,axiom,
% 3.12/1.63 ! [A: $tType,Xs2: list @ A] :
% 3.12/1.63 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( size_size @ ( list @ A ) @ Xs2 ) )
% 3.12/1.63 = ( Xs2
% 3.12/1.63 != ( nil @ A ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(tcon_fun___Orderings_Oord,axiom,
% 3.12/1.63 ! [A8: $tType,A9: $tType] :
% 3.12/1.63 ( ( ord @ A9 )
% 3.12/1.63 => ( ord @ ( A8 > A9 ) ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 3.12/1.63 linorder @ nat ).
% 3.12/1.63
% 3.12/1.63 thf(tcon_Nat_Onat___Orderings_Oord_1,axiom,
% 3.12/1.63 ord @ nat ).
% 3.12/1.63
% 3.12/1.63 thf(tcon_Set_Oset___Orderings_Oord_2,axiom,
% 3.12/1.63 ! [A8: $tType] : ( ord @ ( set @ A8 ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(tcon_HOL_Obool___Orderings_Olinorder_3,axiom,
% 3.12/1.63 linorder @ $o ).
% 3.12/1.63
% 3.12/1.63 thf(tcon_HOL_Obool___Orderings_Oord_4,axiom,
% 3.12/1.63 ord @ $o ).
% 3.12/1.63
% 3.12/1.63 thf(tcon_Product__Type_Ounit___Orderings_Olinorder_5,axiom,
% 3.12/1.63 linorder @ product_unit ).
% 3.12/1.63
% 3.12/1.63 thf(tcon_Product__Type_Ounit___Orderings_Oord_6,axiom,
% 3.12/1.63 ord @ product_unit ).
% 3.12/1.63
% 3.12/1.63 thf(help_If_3_1_T,axiom,
% 3.12/1.63 ! [P2: $o] :
% 3.12/1.63 ( ( P2 = $true )
% 3.12/1.63 | ( P2 = $false ) ) ).
% 3.12/1.63
% 3.12/1.63 thf(help_If_2_1_T,axiom,
% 3.12/1.63 ! [A: $tType,X3: A,Y3: A] :
% 3.12/1.63 ( ( if @ A @ $false @ X3 @ Y3 )
% 3.12/1.63 = Y3 ) ).
% 3.12/1.63
% 3.12/1.63 thf(help_If_1_1_T,axiom,
% 3.12/1.63 ! [A: $tType,X3: A,Y3: A] :
% 3.12/1.63 ( ( if @ A @ $true @ X3 @ Y3 )
% 3.12/1.63 = X3 ) ).
% 3.12/1.63
% 3.12/1.63 thf(conj_0,conjecture,
% 3.12/1.63 ! [Xs4: list @ ( product_prod @ a @ a ),X4: a,Y4: a,Ys4: list @ ( product_prod @ a @ a )] :
% 3.12/1.63 ( es
% 3.12/1.63 != ( append @ ( product_prod @ a @ a ) @ Xs4 @ ( cons @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ X4 @ Y4 ) @ ( cons @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ Y4 @ X4 ) @ Ys4 ) ) ) ) ).
% 3.12/1.63 ------------------------
% 3.12/1.66 % (9956)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_9790 for (2999ds/183Mi)
% 3.12/1.66 % (9961)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_9790 for (2999ds/275Mi)
% 3.12/1.66 % (9960)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_9790 for (2999ds/2Mi)
% 3.12/1.66 % (9958)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_9790 for (2999ds/27Mi)
% 3.12/1.66 % (9959)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_9790 for (2999ds/2Mi)
% 3.12/1.66 % (9962)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_9790 for (2999ds/18Mi)
% 3.12/1.66 % (9959)Instruction limit reached!
% 3.12/1.66 % (9959)------------------------------
% 3.12/1.66 % (9959)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.66 % (9959)Termination reason: Unknown
% 3.12/1.66 % (9959)Termination phase: shuffling
% 3.12/1.66
% 3.12/1.66 % (9959)Memory used [KB]: 1407
% 3.12/1.66 % (9959)Time elapsed: 0.002 s
% 3.12/1.66 % (9959)Instructions burned: 2 (million)
% 3.12/1.66 % (9959)------------------------------
% 3.12/1.66 % (9959)------------------------------
% 3.12/1.66 % (9960)Instruction limit reached!
% 3.12/1.66 % (9960)------------------------------
% 3.12/1.66 % (9960)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.66 % (9960)Termination reason: Unknown
% 3.12/1.66 % (9960)Termination phase: shuffling
% 3.12/1.66
% 3.12/1.66 % (9960)Memory used [KB]: 1535
% 3.12/1.66 % (9960)Time elapsed: 0.003 s
% 3.12/1.66 % (9960)Instructions burned: 5 (million)
% 3.12/1.66 % (9960)------------------------------
% 3.12/1.66 % (9960)------------------------------
% 3.12/1.66 % (9957)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_9790 for (2999ds/4Mi)
% 3.12/1.66 % (9962)Instruction limit reached!
% 3.12/1.66 % (9962)------------------------------
% 3.12/1.66 % (9962)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.66 % (9962)Termination reason: Unknown
% 3.12/1.66 % (9962)Termination phase: shuffling
% 3.12/1.66
% 3.12/1.66 % (9962)Memory used [KB]: 1791
% 3.12/1.66 % (9962)Time elapsed: 0.008 s
% 3.12/1.66 % (9962)Instructions burned: 20 (million)
% 3.12/1.66 % (9962)------------------------------
% 3.12/1.66 % (9962)------------------------------
% 3.12/1.66 % (9957)Instruction limit reached!
% 3.12/1.66 % (9957)------------------------------
% 3.12/1.66 % (9957)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.66 % (9957)Termination reason: Unknown
% 3.12/1.66 % (9957)Termination phase: shuffling
% 3.12/1.66
% 3.12/1.66 % (9957)Memory used [KB]: 1535
% 3.12/1.66 % (9957)Time elapsed: 0.004 s
% 3.12/1.66 % (9957)Instructions burned: 4 (million)
% 3.12/1.66 % (9957)------------------------------
% 3.12/1.66 % (9957)------------------------------
% 3.12/1.67 % (9958)Instruction limit reached!
% 3.12/1.67 % (9958)------------------------------
% 3.12/1.67 % (9958)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.67 % (9958)Termination reason: Unknown
% 3.12/1.67 % (9958)Termination phase: shuffling
% 3.12/1.67
% 3.12/1.67 % (9958)Memory used [KB]: 1918
% 3.12/1.67 % (9958)Time elapsed: 0.011 s
% 3.12/1.67 % (9958)Instructions burned: 28 (million)
% 3.12/1.67 % (9958)------------------------------
% 3.12/1.67 % (9958)------------------------------
% 3.12/1.67 % (9964)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_9790 for (2999ds/37Mi)
% 3.12/1.67 % (9963)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_9790 for (2999ds/3Mi)
% 3.12/1.67 % (9963)Instruction limit reached!
% 3.12/1.67 % (9963)------------------------------
% 3.12/1.67 % (9963)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.67 % (9963)Termination reason: Unknown
% 3.12/1.67 % (9963)Termination phase: shuffling
% 3.12/1.67
% 3.12/1.67 % (9963)Memory used [KB]: 1407
% 3.12/1.67 % (9963)Time elapsed: 0.003 s
% 3.12/1.67 % (9963)Instructions burned: 4 (million)
% 3.12/1.67 % (9963)------------------------------
% 3.12/1.67 % (9963)------------------------------
% 3.12/1.67 % (9965)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_9790 for (2999ds/15Mi)
% 3.12/1.68 % (9967)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_9790 for (2999ds/1041Mi)
% 3.12/1.68 % (9964)Instruction limit reached!
% 3.12/1.68 % (9964)------------------------------
% 3.12/1.68 % (9964)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.68 % (9964)Termination reason: Unknown
% 3.12/1.68 % (9964)Termination phase: shuffling
% 3.12/1.68
% 3.12/1.68 % (9964)Memory used [KB]: 2174
% 3.12/1.68 % (9964)Time elapsed: 0.011 s
% 3.12/1.68 % (9964)Instructions burned: 37 (million)
% 3.12/1.68 % (9964)------------------------------
% 3.12/1.68 % (9964)------------------------------
% 3.12/1.68 % (9965)Instruction limit reached!
% 3.12/1.68 % (9965)------------------------------
% 3.12/1.68 % (9965)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.68 % (9965)Termination reason: Unknown
% 3.12/1.68 % (9965)Termination phase: shuffling
% 3.12/1.68
% 3.12/1.68 % (9965)Memory used [KB]: 1791
% 3.12/1.68 % (9965)Time elapsed: 0.006 s
% 3.12/1.68 % (9965)Instructions burned: 15 (million)
% 3.12/1.68 % (9965)------------------------------
% 3.12/1.68 % (9965)------------------------------
% 3.12/1.68 % (9968)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_9790 for (2999ds/7Mi)
% 3.12/1.68 % (9968)Instruction limit reached!
% 3.12/1.68 % (9968)------------------------------
% 3.12/1.68 % (9968)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.68 % (9968)Termination reason: Unknown
% 3.12/1.68 % (9968)Termination phase: shuffling
% 3.12/1.68
% 3.12/1.68 % (9968)Memory used [KB]: 1535
% 3.12/1.68 % (9968)Time elapsed: 0.004 s
% 3.12/1.68 % (9968)Instructions burned: 9 (million)
% 3.12/1.68 % (9968)------------------------------
% 3.12/1.68 % (9968)------------------------------
% 3.12/1.68 % (9966)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_9790 for (2999ds/3Mi)
% 3.12/1.68 % (9966)Instruction limit reached!
% 3.12/1.68 % (9966)------------------------------
% 3.12/1.68 % (9966)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.68 % (9966)Termination reason: Unknown
% 3.12/1.68 % (9966)Termination phase: shuffling
% 3.12/1.68
% 3.12/1.68 % (9966)Memory used [KB]: 1407
% 3.12/1.68 % (9966)Time elapsed: 0.004 s
% 3.12/1.68 % (9966)Instructions burned: 3 (million)
% 3.12/1.68 % (9966)------------------------------
% 3.12/1.68 % (9966)------------------------------
% 3.12/1.69 % (9970)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_9790 for (2999ds/16Mi)
% 3.12/1.69 % (9971)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_9790 for (2999ds/3Mi)
% 3.12/1.69 % (9971)Instruction limit reached!
% 3.12/1.69 % (9971)------------------------------
% 3.12/1.69 % (9971)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.69 % (9971)Termination reason: Unknown
% 3.12/1.69 % (9971)Termination phase: shuffling
% 3.12/1.69
% 3.12/1.69 % (9971)Memory used [KB]: 1535
% 3.12/1.69 % (9971)Time elapsed: 0.003 s
% 3.12/1.69 % (9971)Instructions burned: 5 (million)
% 3.12/1.69 % (9971)------------------------------
% 3.12/1.69 % (9971)------------------------------
% 3.12/1.69 % (9974)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_9790 for (2999ds/3Mi)
% 3.12/1.69 % (9974)Instruction limit reached!
% 3.12/1.69 % (9974)------------------------------
% 3.12/1.69 % (9974)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.69 % (9974)Termination reason: Unknown
% 3.12/1.69 % (9974)Termination phase: shuffling
% 3.12/1.69
% 3.12/1.69 % (9974)Memory used [KB]: 1407
% 3.12/1.69 % (9974)Time elapsed: 0.002 s
% 3.12/1.69 % (9974)Instructions burned: 3 (million)
% 3.12/1.69 % (9974)------------------------------
% 3.12/1.69 % (9974)------------------------------
% 3.12/1.69 % (9970)Instruction limit reached!
% 3.12/1.69 % (9970)------------------------------
% 3.12/1.69 % (9970)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.69 % (9970)Termination reason: Unknown
% 3.12/1.69 % (9970)Termination phase: shuffling
% 3.12/1.69
% 3.12/1.69 % (9970)Memory used [KB]: 1791
% 3.12/1.69 % (9970)Time elapsed: 0.007 s
% 3.12/1.69 % (9970)Instructions burned: 18 (million)
% 3.12/1.69 % (9970)------------------------------
% 3.12/1.69 % (9970)------------------------------
% 3.12/1.69 % (9961)Refutation not found, incomplete strategy
% 3.12/1.69 % (9961)------------------------------
% 3.12/1.69 % (9961)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.69 % (9961)Termination reason: Refutation not found, incomplete strategy
% 3.12/1.69
% 3.12/1.69
% 3.12/1.69 % (9961)Memory used [KB]: 7547
% 3.12/1.69 % (9961)Time elapsed: 0.039 s
% 3.12/1.69 % (9961)Instructions burned: 124 (million)
% 3.12/1.69 % (9961)------------------------------
% 3.12/1.69 % (9961)------------------------------
% 3.18/1.70 % (9978)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_9790 for (2999ds/3Mi)
% 3.18/1.70 % (9978)Instruction limit reached!
% 3.18/1.70 % (9978)------------------------------
% 3.18/1.70 % (9978)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.70 % (9978)Termination reason: Unknown
% 3.18/1.70 % (9978)Termination phase: shuffling
% 3.18/1.70
% 3.18/1.70 % (9978)Memory used [KB]: 1535
% 3.18/1.70 % (9978)Time elapsed: 0.003 s
% 3.18/1.70 % (9978)Instructions burned: 5 (million)
% 3.18/1.70 % (9978)------------------------------
% 3.18/1.70 % (9978)------------------------------
% 3.18/1.70 % (9980)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_9790 for (2999ds/4Mi)
% 3.18/1.70 % (9975)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_9790 for (2999ds/7Mi)
% 3.18/1.70 % (9981)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_9790 for (2999ds/18Mi)
% 3.18/1.70 % (9980)Instruction limit reached!
% 3.18/1.70 % (9980)------------------------------
% 3.18/1.70 % (9980)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.70 % (9980)Termination reason: Unknown
% 3.18/1.70 % (9980)Termination phase: shuffling
% 3.18/1.70
% 3.18/1.70 % (9980)Memory used [KB]: 1535
% 3.18/1.70 % (9980)Time elapsed: 0.003 s
% 3.18/1.70 % (9980)Instructions burned: 5 (million)
% 3.18/1.70 % (9980)------------------------------
% 3.18/1.70 % (9980)------------------------------
% 3.18/1.70 % (9984)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_9790 for (2999ds/710Mi)
% 3.18/1.71 % (9975)Instruction limit reached!
% 3.18/1.71 % (9975)------------------------------
% 3.18/1.71 % (9975)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.71 % (9975)Termination reason: Unknown
% 3.18/1.71 % (9975)Termination phase: shuffling
% 3.18/1.71
% 3.18/1.71 % (9975)Memory used [KB]: 1663
% 3.18/1.71 % (9975)Time elapsed: 0.007 s
% 3.18/1.71 % (9975)Instructions burned: 8 (million)
% 3.18/1.71 % (9975)------------------------------
% 3.18/1.71 % (9975)------------------------------
% 3.18/1.71 % (9981)Instruction limit reached!
% 3.18/1.71 % (9981)------------------------------
% 3.18/1.71 % (9981)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.71 % (9981)Termination reason: Unknown
% 3.18/1.71 % (9981)Termination phase: shuffling
% 3.18/1.71
% 3.18/1.71 % (9981)Memory used [KB]: 1791
% 3.18/1.71 % (9981)Time elapsed: 0.008 s
% 3.18/1.71 % (9981)Instructions burned: 20 (million)
% 3.18/1.71 % (9981)------------------------------
% 3.18/1.71 % (9981)------------------------------
% 3.18/1.71 % (9956)Instruction limit reached!
% 3.18/1.71 % (9956)------------------------------
% 3.18/1.71 % (9956)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.71 % (9956)Termination reason: Unknown
% 3.18/1.71 % (9956)Termination phase: Saturation
% 3.18/1.71
% 3.18/1.71 % (9956)Memory used [KB]: 7547
% 3.18/1.71 % (9956)Time elapsed: 0.055 s
% 3.18/1.71 % (9956)Instructions burned: 186 (million)
% 3.18/1.71 % (9956)------------------------------
% 3.18/1.71 % (9956)------------------------------
% 3.18/1.71 % (9987)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_9790 for (2999ds/6Mi)
% 3.18/1.71 % (9987)Instruction limit reached!
% 3.18/1.71 % (9987)------------------------------
% 3.18/1.71 % (9987)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.71 % (9987)Termination reason: Unknown
% 3.18/1.71 % (9987)Termination phase: shuffling
% 3.18/1.71
% 3.18/1.71 % (9987)Memory used [KB]: 1535
% 3.18/1.71 % (9987)Time elapsed: 0.003 s
% 3.18/1.71 % (9987)Instructions burned: 6 (million)
% 3.18/1.71 % (9987)------------------------------
% 3.18/1.71 % (9987)------------------------------
% 3.18/1.71 % (9988)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_9790 for (2999ds/902Mi)
% 3.18/1.72 % (9993)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_9790 for (2999ds/5Mi)
% 3.18/1.72 % (9994)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_9790 for (2999ds/6Mi)
% 3.18/1.72 % (9993)Instruction limit reached!
% 3.18/1.72 % (9993)------------------------------
% 3.18/1.72 % (9993)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.72 % (9993)Termination reason: Unknown
% 3.18/1.72 % (9993)Termination phase: shuffling
% 3.18/1.72
% 3.18/1.72 % (9993)Memory used [KB]: 1535
% 3.18/1.72 % (9993)Time elapsed: 0.003 s
% 3.18/1.72 % (9993)Instructions burned: 6 (million)
% 3.18/1.72 % (9993)------------------------------
% 3.18/1.72 % (9993)------------------------------
% 3.18/1.72 % (9994)Instruction limit reached!
% 3.18/1.72 % (9994)------------------------------
% 3.18/1.72 % (9994)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.72 % (9994)Termination reason: Unknown
% 3.18/1.72 % (9994)Termination phase: shuffling
% 3.18/1.72
% 3.18/1.72 % (9994)Memory used [KB]: 1535
% 3.18/1.72 % (9994)Time elapsed: 0.003 s
% 3.18/1.72 % (9994)Instructions burned: 6 (million)
% 3.18/1.72 % (9994)------------------------------
% 3.18/1.72 % (9994)------------------------------
% 3.18/1.72 % (9996)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_9790 for (2999ds/377Mi)
% 3.18/1.72 % (9991)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_9790 for (2999ds/21Mi)
% 3.18/1.73 % (10001)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_9790 for (2999ds/779Mi)
% 3.18/1.73 % (10002)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_9790 for (2999ds/19Mi)
% 3.18/1.74 % (9991)Instruction limit reached!
% 3.18/1.74 % (9991)------------------------------
% 3.18/1.74 % (9991)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.74 % (9991)Termination reason: Unknown
% 3.18/1.74 % (9991)Termination phase: shuffling
% 3.18/1.74
% 3.18/1.74 % (9991)Memory used [KB]: 1791
% 3.18/1.74 % (9991)Time elapsed: 0.014 s
% 3.18/1.74 % (9991)Instructions burned: 22 (million)
% 3.18/1.74 % (9991)------------------------------
% 3.18/1.74 % (9991)------------------------------
% 3.18/1.74 % (10002)Instruction limit reached!
% 3.18/1.74 % (10002)------------------------------
% 3.18/1.74 % (10002)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.74 % (10002)Termination reason: Unknown
% 3.18/1.74 % (10002)Termination phase: shuffling
% 3.18/1.74
% 3.18/1.74 % (10002)Memory used [KB]: 1918
% 3.18/1.74 % (10002)Time elapsed: 0.007 s
% 3.18/1.74 % (10002)Instructions burned: 21 (million)
% 3.18/1.74 % (10002)------------------------------
% 3.18/1.74 % (10002)------------------------------
% 3.18/1.75 % (10008)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_9790 for (2999ds/879Mi)
% 3.18/1.75 % (10009)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_9790 for (2999ds/17Mi)
% 3.18/1.75 % (10009)Instruction limit reached!
% 3.18/1.75 % (10009)------------------------------
% 3.18/1.75 % (10009)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.75 % (10009)Termination reason: Unknown
% 3.18/1.75 % (10009)Termination phase: shuffling
% 3.18/1.75
% 3.18/1.75 % (10009)Memory used [KB]: 1791
% 3.18/1.75 % (10009)Time elapsed: 0.007 s
% 3.18/1.75 % (10009)Instructions burned: 17 (million)
% 3.18/1.75 % (10009)------------------------------
% 3.18/1.75 % (10009)------------------------------
% 3.18/1.76 % (10017)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_9790 for (2998ds/3Mi)
% 3.18/1.76 % (10017)Instruction limit reached!
% 3.18/1.76 % (10017)------------------------------
% 3.18/1.76 % (10017)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.76 % (10017)Termination reason: Unknown
% 3.18/1.76 % (10017)Termination phase: shuffling
% 3.18/1.76
% 3.18/1.76 % (10017)Memory used [KB]: 1407
% 3.18/1.76 % (10017)Time elapsed: 0.002 s
% 3.18/1.76 % (10017)Instructions burned: 3 (million)
% 3.18/1.76 % (10017)------------------------------
% 3.18/1.76 % (10017)------------------------------
% 3.18/1.77 % (10024)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_9790 for (2998ds/30Mi)
% 3.18/1.78 % (10024)Instruction limit reached!
% 3.18/1.78 % (10024)------------------------------
% 3.18/1.78 % (10024)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.78 % (10024)Termination reason: Unknown
% 3.18/1.78 % (10024)Termination phase: shuffling
% 3.18/1.78
% 3.18/1.78 % (10024)Memory used [KB]: 1918
% 3.18/1.78 % (10024)Time elapsed: 0.011 s
% 3.18/1.78 % (10024)Instructions burned: 30 (million)
% 3.18/1.78 % (10024)------------------------------
% 3.18/1.78 % (10024)------------------------------
% 3.18/1.79 % (10032)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_9790 for (2998ds/127Mi)
% 3.18/1.83 % (10032)Instruction limit reached!
% 3.18/1.83 % (10032)------------------------------
% 3.18/1.83 % (10032)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.83 % (10032)Termination reason: Unknown
% 3.18/1.83 % (10032)Termination phase: Property scanning
% 3.18/1.83
% 3.18/1.83 % (10032)Memory used [KB]: 2942
% 3.18/1.83 % (10032)Time elapsed: 0.041 s
% 3.18/1.83 % (10032)Instructions burned: 129 (million)
% 3.18/1.83 % (10032)------------------------------
% 3.18/1.83 % (10032)------------------------------
% 3.18/1.84 % (10048)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_9790 for (2997ds/100Mi)
% 3.18/1.84 % (9996)Instruction limit reached!
% 3.18/1.84 % (9996)------------------------------
% 3.18/1.84 % (9996)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.84 % (9996)Termination reason: Unknown
% 3.18/1.84 % (9996)Termination phase: Saturation
% 3.18/1.84
% 3.18/1.84 % (9996)Memory used [KB]: 8827
% 3.18/1.84 % (9996)Time elapsed: 0.125 s
% 3.18/1.84 % (9996)Instructions burned: 377 (million)
% 3.18/1.84 % (9996)------------------------------
% 3.18/1.84 % (9996)------------------------------
% 3.18/1.85 % (10057)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_9790 for (2997ds/3Mi)
% 3.18/1.86 % (10057)Instruction limit reached!
% 3.18/1.86 % (10057)------------------------------
% 3.18/1.86 % (10057)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.86 % (10057)Termination reason: Unknown
% 3.18/1.86 % (10057)Termination phase: shuffling
% 3.18/1.86
% 3.18/1.86 % (10057)Memory used [KB]: 1535
% 3.18/1.86 % (10057)Time elapsed: 0.002 s
% 3.18/1.86 % (10057)Instructions burned: 3 (million)
% 3.18/1.86 % (10057)------------------------------
% 3.18/1.86 % (10057)------------------------------
% 3.18/1.87 % (10058)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_9790 for (2997ds/20Mi)
% 3.18/1.87 % (10048)Instruction limit reached!
% 3.18/1.87 % (10048)------------------------------
% 3.18/1.87 % (10048)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.87 % (10048)Termination reason: Unknown
% 3.18/1.87 % (10048)Termination phase: Property scanning
% 3.18/1.87
% 3.18/1.87 % (10048)Memory used [KB]: 2686
% 3.18/1.87 % (10048)Time elapsed: 0.028 s
% 3.18/1.87 % (10048)Instructions burned: 100 (million)
% 3.18/1.87 % (10048)------------------------------
% 3.18/1.87 % (10048)------------------------------
% 3.18/1.87 % (10058)Instruction limit reached!
% 3.18/1.87 % (10058)------------------------------
% 3.18/1.87 % (10058)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.87 % (10058)Termination reason: Unknown
% 3.18/1.87 % (10058)Termination phase: shuffling
% 3.18/1.87
% 3.18/1.87 % (10058)Memory used [KB]: 1791
% 3.18/1.87 % (10058)Time elapsed: 0.008 s
% 3.18/1.87 % (10058)Instructions burned: 20 (million)
% 3.18/1.87 % (10058)------------------------------
% 3.18/1.87 % (10058)------------------------------
% 3.18/1.88 % (10067)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_9790 for (2997ds/86Mi)
% 3.18/1.88 % (10071)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_9790 for (2997ds/107Mi)
% 3.18/1.90 % (10067)Instruction limit reached!
% 3.18/1.90 % (10067)------------------------------
% 3.18/1.90 % (10067)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.90 % (10067)Termination reason: Unknown
% 3.18/1.90 % (10067)Termination phase: Preprocessing 3
% 3.18/1.90
% 3.18/1.90 % (10067)Memory used [KB]: 2686
% 3.18/1.90 % (10067)Time elapsed: 0.028 s
% 3.18/1.90 % (10067)Instructions burned: 88 (million)
% 3.18/1.90 % (10067)------------------------------
% 3.18/1.90 % (10067)------------------------------
% 3.18/1.91 % (10081)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_9790 for (2997ds/39Mi)
% 3.18/1.91 % (10071)Instruction limit reached!
% 3.18/1.91 % (10071)------------------------------
% 3.18/1.91 % (10071)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.91 % (10071)Termination reason: Unknown
% 3.18/1.91 % (10071)Termination phase: Property scanning
% 3.18/1.91
% 3.18/1.91 % (10071)Memory used [KB]: 2686
% 3.18/1.91 % (10071)Time elapsed: 0.033 s
% 3.18/1.91 % (10071)Instructions burned: 108 (million)
% 3.18/1.91 % (10071)------------------------------
% 3.18/1.91 % (10071)------------------------------
% 3.18/1.92 % (10092)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_9790 for (2997ds/448Mi)
% 3.18/1.92 % (10081)Instruction limit reached!
% 3.18/1.92 % (10081)------------------------------
% 3.18/1.92 % (10081)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.92 % (10081)Termination reason: Unknown
% 3.18/1.92 % (10081)Termination phase: shuffling
% 3.18/1.92
% 3.18/1.92 % (10081)Memory used [KB]: 2174
% 3.18/1.92 % (10081)Time elapsed: 0.012 s
% 3.18/1.92 % (10081)Instructions burned: 40 (million)
% 3.18/1.92 % (10081)------------------------------
% 3.18/1.92 % (10081)------------------------------
% 3.18/1.93 % (9984)Instruction limit reached!
% 3.18/1.93 % (9984)------------------------------
% 3.18/1.93 % (9984)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.93 % (9984)Termination reason: Unknown
% 3.18/1.93 % (9984)Termination phase: Saturation
% 3.18/1.93
% 3.18/1.93 % (9984)Memory used [KB]: 8315
% 3.18/1.93 % (9984)Time elapsed: 0.223 s
% 3.18/1.93 % (9984)Instructions burned: 711 (million)
% 3.18/1.93 % (9984)------------------------------
% 3.18/1.93 % (9984)------------------------------
% 3.18/1.93 % (10099)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_9790 for (2997ds/46Mi)
% 3.18/1.94 % (10101)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_9790 for (2997ds/98Mi)
% 3.18/1.95 % (10099)Instruction limit reached!
% 3.18/1.95 % (10099)------------------------------
% 3.18/1.95 % (10099)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.95 % (10099)Termination reason: Unknown
% 3.18/1.95 % (10099)Termination phase: Property scanning
% 3.18/1.95
% 3.18/1.95 % (10099)Memory used [KB]: 2046
% 3.18/1.95 % (10099)Time elapsed: 0.016 s
% 3.18/1.95 % (10099)Instructions burned: 48 (million)
% 3.18/1.95 % (10099)------------------------------
% 3.18/1.95 % (10099)------------------------------
% 3.18/1.96 % (10109)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_9790 for (2996ds/507Mi)
% 3.18/1.96 % (10101)Instruction limit reached!
% 3.18/1.96 % (10101)------------------------------
% 3.18/1.96 % (10101)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.96 % (10101)Termination reason: Unknown
% 3.18/1.96 % (10101)Termination phase: Property scanning
% 3.18/1.96
% 3.18/1.96 % (10101)Memory used [KB]: 2686
% 3.18/1.96 % (10101)Time elapsed: 0.027 s
% 3.18/1.96 % (10101)Instructions burned: 98 (million)
% 3.18/1.96 % (10101)------------------------------
% 3.18/1.96 % (10101)------------------------------
% 3.18/1.96 % (10001)Instruction limit reached!
% 3.18/1.96 % (10001)------------------------------
% 3.18/1.96 % (10001)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.96 % (10001)Termination reason: Unknown
% 3.18/1.96 % (10001)Termination phase: Saturation
% 3.18/1.96
% 3.18/1.96 % (10001)Memory used [KB]: 8955
% 3.18/1.96 % (10001)Time elapsed: 0.257 s
% 3.18/1.96 % (10001)Instructions burned: 780 (million)
% 3.18/1.96 % (10001)------------------------------
% 3.18/1.96 % (10001)------------------------------
% 3.18/1.97 % (10120)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_9790 for (2996ds/149Mi)
% 3.18/1.97 % (10122)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_9790 for (2996ds/39Mi)
% 3.18/1.97 % (9988)Instruction limit reached!
% 3.18/1.97 % (9988)------------------------------
% 3.18/1.97 % (9988)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.97 % (9988)Termination reason: Unknown
% 3.18/1.97 % (9988)Termination phase: Saturation
% 3.18/1.97
% 3.18/1.97 % (9988)Memory used [KB]: 9594
% 3.18/1.97 % (9988)Time elapsed: 0.264 s
% 3.18/1.97 % (9988)Instructions burned: 904 (million)
% 3.18/1.97 % (9988)------------------------------
% 3.18/1.97 % (9988)------------------------------
% 3.18/1.98 % (10127)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_9790 for (2996ds/6Mi)
% 3.18/1.99 % (10127)Instruction limit reached!
% 3.18/1.99 % (10127)------------------------------
% 3.18/1.99 % (10127)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.99 % (10127)Termination reason: Unknown
% 3.18/1.99 % (10127)Termination phase: shuffling
% 3.18/1.99
% 3.18/1.99 % (10127)Memory used [KB]: 1535
% 3.18/1.99 % (10127)Time elapsed: 0.003 s
% 3.18/1.99 % (10127)Instructions burned: 7 (million)
% 3.18/1.99 % (10127)------------------------------
% 3.18/1.99 % (10127)------------------------------
% 3.18/1.99 % (10122)Instruction limit reached!
% 3.18/1.99 % (10122)------------------------------
% 3.18/1.99 % (10122)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.99 % (10122)Termination reason: Unknown
% 3.18/1.99 % (10122)Termination phase: Property scanning
% 3.18/1.99
% 3.18/1.99 % (10122)Memory used [KB]: 2046
% 3.18/1.99 % (10122)Time elapsed: 0.014 s
% 3.18/1.99 % (10122)Instructions burned: 40 (million)
% 3.18/1.99 % (10122)------------------------------
% 3.18/1.99 % (10122)------------------------------
% 3.18/2.00 % (10131)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_9790 for (2996ds/1087Mi)
% 3.18/2.00 % (10132)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_9790 for (2996ds/47Mi)
% 3.18/2.00 % (9967)Instruction limit reached!
% 3.18/2.00 % (9967)------------------------------
% 3.18/2.00 % (9967)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/2.00 % (9967)Termination reason: Unknown
% 3.18/2.00 % (9967)Termination phase: Saturation
% 3.18/2.00
% 3.18/2.00 % (9967)Memory used [KB]: 10362
% 3.18/2.00 % (9967)Time elapsed: 0.329 s
% 3.18/2.00 % (9967)Instructions burned: 1042 (million)
% 3.18/2.00 % (9967)------------------------------
% 3.18/2.00 % (9967)------------------------------
% 3.18/2.01 % (10008)Instruction limit reached!
% 3.18/2.01 % (10008)------------------------------
% 3.18/2.01 % (10008)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/2.01 % (10008)Termination reason: Unknown
% 3.18/2.01 % (10008)Termination phase: Saturation
% 3.18/2.01
% 3.18/2.01 % (10008)Memory used [KB]: 8443
% 3.18/2.01 % (10008)Time elapsed: 0.285 s
% 3.18/2.01 % (10008)Instructions burned: 881 (million)
% 3.18/2.01 % (10008)------------------------------
% 3.18/2.01 % (10008)------------------------------
% 5.70/2.01 % (10132)Instruction limit reached!
% 5.70/2.01 % (10132)------------------------------
% 5.70/2.01 % (10132)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.70/2.01 % (10132)Termination reason: Unknown
% 5.70/2.01 % (10132)Termination phase: Property scanning
% 5.70/2.01
% 5.70/2.01 % (10132)Memory used [KB]: 2046
% 5.70/2.01 % (10132)Time elapsed: 0.017 s
% 5.70/2.01 % (10132)Instructions burned: 50 (million)
% 5.70/2.01 % (10132)------------------------------
% 5.70/2.01 % (10132)------------------------------
% 5.70/2.01 % (10143)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_9790 for (2996ds/44Mi)
% 5.70/2.01 % (10120)Instruction limit reached!
% 5.70/2.01 % (10120)------------------------------
% 5.70/2.01 % (10120)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.70/2.01 % (10120)Termination reason: Unknown
% 5.70/2.01 % (10120)Termination phase: Property scanning
% 5.70/2.01
% 5.70/2.01 % (10120)Memory used [KB]: 2942
% 5.70/2.01 % (10120)Time elapsed: 0.044 s
% 5.70/2.01 % (10120)Instructions burned: 151 (million)
% 5.70/2.01 % (10120)------------------------------
% 5.70/2.01 % (10120)------------------------------
% 5.70/2.02 % (10146)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_9790 for (2996ds/432Mi)
% 5.70/2.02 % (10148)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_9790 for (2996ds/62Mi)
% 5.70/2.02 % (10149)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_9790 for (2996ds/31Mi)
% 5.70/2.03 % (10143)Instruction limit reached!
% 5.70/2.03 % (10143)------------------------------
% 5.70/2.03 % (10143)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.70/2.03 % (10143)Termination reason: Unknown
% 5.70/2.03 % (10143)Termination phase: shuffling
% 5.70/2.03
% 5.70/2.03 % (10143)Memory used [KB]: 2302
% 5.70/2.03 % (10143)Time elapsed: 0.014 s
% 5.70/2.03 % (10143)Instructions burned: 46 (million)
% 5.70/2.03 % (10143)------------------------------
% 5.70/2.03 % (10143)------------------------------
% 5.70/2.03 % (10149)Instruction limit reached!
% 5.70/2.03 % (10149)------------------------------
% 5.70/2.03 % (10149)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.70/2.03 % (10149)Termination reason: Unknown
% 5.70/2.03 % (10149)Termination phase: shuffling
% 5.70/2.03
% 5.70/2.03 % (10149)Memory used [KB]: 2046
% 5.70/2.03 % (10149)Time elapsed: 0.012 s
% 5.70/2.03 % (10149)Instructions burned: 33 (million)
% 5.70/2.03 % (10149)------------------------------
% 5.70/2.03 % (10149)------------------------------
% 5.70/2.04 % (10155)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_9790 for (2996ds/96Mi)
% 5.70/2.04 % (10148)Instruction limit reached!
% 5.70/2.04 % (10148)------------------------------
% 5.70/2.04 % (10148)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.70/2.04 % (10148)Termination reason: Unknown
% 5.70/2.04 % (10148)Termination phase: shuffling
% 5.70/2.04
% 5.70/2.04 % (10148)Memory used [KB]: 2686
% 5.70/2.04 % (10148)Time elapsed: 0.019 s
% 5.70/2.04 % (10148)Instructions burned: 65 (million)
% 5.70/2.04 % (10148)------------------------------
% 5.70/2.04 % (10148)------------------------------
% 5.70/2.04 % (10158)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_9790 for (2995ds/453Mi)
% 5.70/2.05 % (10160)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_9790 for (2995ds/71Mi)
% 5.70/2.07 % (10155)Instruction limit reached!
% 5.70/2.07 % (10155)------------------------------
% 5.70/2.07 % (10155)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.70/2.07 % (10155)Termination reason: Unknown
% 5.70/2.07 % (10155)Termination phase: Preprocessing 3
% 5.70/2.07
% 5.70/2.07 % (10155)Memory used [KB]: 2814
% 5.70/2.07 % (10155)Time elapsed: 0.031 s
% 5.70/2.07 % (10155)Instructions burned: 98 (million)
% 5.70/2.07 % (10155)------------------------------
% 5.70/2.07 % (10155)------------------------------
% 5.70/2.07 % (10160)Instruction limit reached!
% 5.70/2.07 % (10160)------------------------------
% 5.70/2.07 % (10160)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.70/2.07 % (10160)Termination reason: Unknown
% 5.70/2.07 % (10160)Termination phase: Preprocessing 1
% 5.70/2.07
% 5.70/2.07 % (10160)Memory used [KB]: 2302
% 5.70/2.07 % (10160)Time elapsed: 0.024 s
% 5.70/2.07 % (10160)Instructions burned: 73 (million)
% 5.70/2.07 % (10160)------------------------------
% 5.70/2.07 % (10160)------------------------------
% 5.70/2.08 % (10168)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_9790 for (2995ds/83Mi)
% 5.70/2.08 % (10172)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_9790 for (2995ds/11Mi)
% 5.70/2.09 % (10172)Instruction limit reached!
% 5.70/2.09 % (10172)------------------------------
% 5.70/2.09 % (10172)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.70/2.09 % (10172)Termination reason: Unknown
% 5.70/2.09 % (10172)Termination phase: shuffling
% 5.70/2.09
% 5.70/2.09 % (10172)Memory used [KB]: 1663
% 5.70/2.09 % (10172)Time elapsed: 0.005 s
% 5.70/2.09 % (10172)Instructions burned: 12 (million)
% 5.70/2.09 % (10172)------------------------------
% 5.70/2.09 % (10172)------------------------------
% 5.70/2.09 % (10179)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_9790 for (2995ds/41Mi)
% 5.70/2.10 % (10092)Instruction limit reached!
% 5.70/2.10 % (10092)------------------------------
% 5.70/2.10 % (10092)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.70/2.10 % (10092)Termination reason: Unknown
% 5.70/2.10 % (10092)Termination phase: Saturation
% 5.70/2.10
% 5.70/2.10 % (10092)Memory used [KB]: 9083
% 5.70/2.10 % (10092)Time elapsed: 0.173 s
% 5.70/2.10 % (10092)Instructions burned: 450 (million)
% 5.70/2.10 % (10092)------------------------------
% 5.70/2.10 % (10092)------------------------------
% 5.70/2.10 % (10168)Instruction limit reached!
% 5.70/2.10 % (10168)------------------------------
% 5.70/2.10 % (10168)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.70/2.10 % (10168)Termination reason: Unknown
% 5.70/2.10 % (10168)Termination phase: Preprocessing 3
% 5.70/2.10
% 5.70/2.10 % (10168)Memory used [KB]: 2430
% 5.70/2.10 % (10168)Time elapsed: 0.027 s
% 5.70/2.10 % (10168)Instructions burned: 84 (million)
% 5.70/2.10 % (10168)------------------------------
% 5.70/2.10 % (10168)------------------------------
% 5.70/2.10 % (10109)Instruction limit reached!
% 5.70/2.10 % (10109)------------------------------
% 5.70/2.10 % (10109)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.70/2.10 % (10109)Termination reason: Unknown
% 5.70/2.10 % (10109)Termination phase: Saturation
% 5.70/2.10
% 5.70/2.10 % (10109)Memory used [KB]: 9594
% 5.70/2.10 % (10109)Time elapsed: 0.146 s
% 5.70/2.10 % (10109)Instructions burned: 509 (million)
% 5.70/2.10 % (10109)------------------------------
% 5.70/2.10 % (10109)------------------------------
% 5.70/2.11 % (10179)Instruction limit reached!
% 5.70/2.11 % (10179)------------------------------
% 5.70/2.11 % (10179)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.70/2.11 % (10179)Termination reason: Unknown
% 5.70/2.11 % (10179)Termination phase: shuffling
% 5.70/2.11
% 5.70/2.11 % (10179)Memory used [KB]: 2302
% 5.70/2.11 % (10179)Time elapsed: 0.013 s
% 5.70/2.11 % (10179)Instructions burned: 43 (million)
% 5.70/2.11 % (10179)------------------------------
% 5.70/2.11 % (10179)------------------------------
% 5.70/2.11 % (10183)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_9790 for (2995ds/6Mi)
% 5.70/2.11 % (10183)Instruction limit reached!
% 5.70/2.11 % (10183)------------------------------
% 5.70/2.11 % (10183)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.70/2.11 % (10183)Termination reason: Unknown
% 5.70/2.11 % (10183)Termination phase: shuffling
% 5.70/2.11
% 5.70/2.11 % (10183)Memory used [KB]: 1535
% 5.70/2.11 % (10183)Time elapsed: 0.004 s
% 5.70/2.11 % (10183)Instructions burned: 6 (million)
% 5.70/2.11 % (10183)------------------------------
% 5.70/2.11 % (10183)------------------------------
% 5.70/2.11 % (10186)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_9790 for (2995ds/150Mi)
% 6.24/2.11 % (10187)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_9790 for (2995ds/343Mi)
% 6.24/2.12 % (10189)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_9790 for (2995ds/109Mi)
% 6.24/2.12 % (10190)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_9790 for (2995ds/253Mi)
% 6.24/2.15 % (10146)Instruction limit reached!
% 6.24/2.15 % (10146)------------------------------
% 6.24/2.15 % (10146)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.24/2.15 % (10146)Termination reason: Unknown
% 6.24/2.15 % (10146)Termination phase: Saturation
% 6.24/2.15
% 6.24/2.15 % (10146)Memory used [KB]: 4093
% 6.24/2.15 % (10146)Time elapsed: 0.131 s
% 6.24/2.15 % (10146)Instructions burned: 432 (million)
% 6.24/2.15 % (10146)------------------------------
% 6.24/2.15 % (10146)------------------------------
% 6.24/2.15 % (10189)Instruction limit reached!
% 6.24/2.15 % (10189)------------------------------
% 6.24/2.15 % (10189)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.24/2.15 % (10189)Termination reason: Unknown
% 6.24/2.15 % (10189)Termination phase: Property scanning
% 6.24/2.15
% 6.24/2.15 % (10189)Memory used [KB]: 2814
% 6.24/2.15 % (10189)Time elapsed: 0.035 s
% 6.24/2.15 % (10189)Instructions burned: 110 (million)
% 6.24/2.15 % (10189)------------------------------
% 6.24/2.15 % (10189)------------------------------
% 6.24/2.16 % (10186)Instruction limit reached!
% 6.24/2.16 % (10186)------------------------------
% 6.24/2.16 % (10186)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.24/2.16 % (10186)Termination reason: Unknown
% 6.24/2.16 % (10186)Termination phase: Property scanning
% 6.24/2.16
% 6.24/2.16 % (10186)Memory used [KB]: 3198
% 6.24/2.16 % (10186)Time elapsed: 0.046 s
% 6.24/2.16 % (10186)Instructions burned: 153 (million)
% 6.24/2.16 % (10186)------------------------------
% 6.24/2.16 % (10186)------------------------------
% 6.24/2.16 % (10204)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_9790 for (2994ds/140Mi)
% 6.24/2.16 % (10207)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_9790 for (2994ds/614Mi)
% 6.24/2.17 % (10210)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_9790 for (2994ds/202Mi)
% 6.24/2.17 % (10158)Instruction limit reached!
% 6.24/2.17 % (10158)------------------------------
% 6.24/2.17 % (10158)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.24/2.17 % (10158)Termination reason: Unknown
% 6.24/2.17 % (10158)Termination phase: Saturation
% 6.24/2.17
% 6.24/2.17 % (10158)Memory used [KB]: 8699
% 6.24/2.17 % (10158)Time elapsed: 0.129 s
% 6.24/2.17 % (10158)Instructions burned: 453 (million)
% 6.24/2.17 % (10158)------------------------------
% 6.24/2.17 % (10158)------------------------------
% 6.24/2.17 % (10190)Refutation not found, incomplete strategy
% 6.24/2.17 % (10190)------------------------------
% 6.24/2.17 % (10190)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.24/2.17 % (10190)Termination reason: Refutation not found, incomplete strategy
% 6.24/2.17
% 6.24/2.17
% 6.24/2.17 % (10190)Memory used [KB]: 7931
% 6.24/2.17 % (10190)Time elapsed: 0.054 s
% 6.24/2.17 % (10190)Instructions burned: 159 (million)
% 6.24/2.17 % (10190)------------------------------
% 6.24/2.17 % (10190)------------------------------
% 6.24/2.18 % (10215)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on DTF2THF_9790 for (2994ds/283Mi)
% 6.24/2.19 % (10214)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_9790 for (2994ds/339Mi)
% 6.75/2.20 % (10204)Instruction limit reached!
% 6.75/2.20 % (10204)------------------------------
% 6.75/2.20 % (10204)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.75/2.20 % (10204)Termination reason: Unknown
% 6.75/2.20 % (10204)Termination phase: Saturation
% 6.75/2.20
% 6.75/2.20 % (10204)Memory used [KB]: 7547
% 6.75/2.20 % (10204)Time elapsed: 0.067 s
% 6.75/2.20 % (10204)Instructions burned: 142 (million)
% 6.75/2.20 % (10204)------------------------------
% 6.75/2.20 % (10204)------------------------------
% 6.75/2.21 % (10234)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_9790 for (2994ds/134Mi)
% 6.75/2.22 % (10187)Instruction limit reached!
% 6.75/2.22 % (10187)------------------------------
% 6.75/2.22 % (10187)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.75/2.22 % (10187)Termination reason: Unknown
% 6.75/2.22 % (10187)Termination phase: Saturation
% 6.75/2.22
% 6.75/2.22 % (10187)Memory used [KB]: 8187
% 6.75/2.22 % (10187)Time elapsed: 0.108 s
% 6.75/2.22 % (10187)Instructions burned: 343 (million)
% 6.75/2.22 % (10187)------------------------------
% 6.75/2.22 % (10187)------------------------------
% 6.75/2.23 % (10210)Instruction limit reached!
% 6.75/2.23 % (10210)------------------------------
% 6.75/2.23 % (10210)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.75/2.23 % (10210)Termination reason: Unknown
% 6.75/2.23 % (10210)Termination phase: Saturation
% 6.75/2.23
% 6.75/2.23 % (10210)Memory used [KB]: 8315
% 6.75/2.23 % (10210)Time elapsed: 0.062 s
% 6.75/2.23 % (10210)Instructions burned: 204 (million)
% 6.75/2.23 % (10210)------------------------------
% 6.75/2.23 % (10210)------------------------------
% 6.75/2.23 % (10247)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_9790 for (2994ds/298Mi)
% 6.75/2.24 % (10251)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_9790 for (2993ds/192Mi)
% 6.75/2.25 % (10234)Instruction limit reached!
% 6.75/2.25 % (10234)------------------------------
% 6.75/2.25 % (10234)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.75/2.25 % (10234)Termination reason: Unknown
% 6.75/2.25 % (10234)Termination phase: Property scanning
% 6.75/2.25
% 6.75/2.25 % (10234)Memory used [KB]: 3070
% 6.75/2.25 % (10234)Time elapsed: 0.040 s
% 6.75/2.25 % (10234)Instructions burned: 134 (million)
% 6.75/2.25 % (10234)------------------------------
% 6.75/2.25 % (10234)------------------------------
% 6.75/2.26 % (10259)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_9790 for (2993ds/258Mi)
% 6.75/2.27 % (10215)Instruction limit reached!
% 6.75/2.27 % (10215)------------------------------
% 6.75/2.27 % (10215)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.75/2.27 % (10215)Termination reason: Unknown
% 6.75/2.27 % (10215)Termination phase: Saturation
% 6.75/2.27
% 6.75/2.27 % (10215)Memory used [KB]: 7803
% 6.75/2.27 % (10215)Time elapsed: 0.114 s
% 6.75/2.27 % (10215)Instructions burned: 285 (million)
% 6.75/2.27 % (10215)------------------------------
% 6.75/2.27 % (10215)------------------------------
% 6.75/2.28 % (10260)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_9790 for (2993ds/90Mi)
% 6.75/2.29 % (10251)Instruction limit reached!
% 6.75/2.29 % (10251)------------------------------
% 6.75/2.29 % (10251)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.75/2.29 % (10251)Termination reason: Unknown
% 6.75/2.29 % (10251)Termination phase: Saturation
% 6.75/2.29
% 6.75/2.29 % (10251)Memory used [KB]: 3198
% 6.75/2.29 % (10251)Time elapsed: 0.057 s
% 6.75/2.29 % (10251)Instructions burned: 193 (million)
% 6.75/2.29 % (10251)------------------------------
% 6.75/2.29 % (10251)------------------------------
% 7.31/2.30 % (10214)Instruction limit reached!
% 7.31/2.30 % (10214)------------------------------
% 7.31/2.30 % (10214)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.31/2.30 % (10214)Termination reason: Unknown
% 7.31/2.30 % (10214)Termination phase: Saturation
% 7.31/2.30
% 7.31/2.30 % (10214)Memory used [KB]: 7931
% 7.31/2.30 % (10214)Time elapsed: 0.113 s
% 7.31/2.30 % (10214)Instructions burned: 340 (million)
% 7.31/2.30 % (10214)------------------------------
% 7.31/2.30 % (10214)------------------------------
% 7.31/2.30 % (10261)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_9790 for (2993ds/231Mi)
% 7.31/2.31 % (10262)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on DTF2THF_9790 for (2993ds/458Mi)
% 7.31/2.31 % (10247)Instruction limit reached!
% 7.31/2.31 % (10247)------------------------------
% 7.31/2.31 % (10247)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.31/2.31 % (10247)Termination reason: Unknown
% 7.31/2.31 % (10247)Termination phase: Saturation
% 7.31/2.31
% 7.31/2.31 % (10247)Memory used [KB]: 8443
% 7.31/2.31 % (10247)Time elapsed: 0.084 s
% 7.31/2.31 % (10247)Instructions burned: 300 (million)
% 7.31/2.31 % (10247)------------------------------
% 7.31/2.31 % (10247)------------------------------
% 7.31/2.31 % (10260)Instruction limit reached!
% 7.31/2.31 % (10260)------------------------------
% 7.31/2.31 % (10260)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.31/2.31 % (10260)Termination reason: Unknown
% 7.31/2.31 % (10260)Termination phase: Preprocessing 3
% 7.31/2.31
% 7.31/2.31 % (10260)Memory used [KB]: 2814
% 7.31/2.31 % (10260)Time elapsed: 0.032 s
% 7.31/2.31 % (10260)Instructions burned: 91 (million)
% 7.31/2.31 % (10260)------------------------------
% 7.31/2.31 % (10260)------------------------------
% 7.31/2.32 % (10263)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_9790 for (2993ds/31Mi)
% 7.31/2.32 % (10264)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on DTF2THF_9790 for (2993ds/297Mi)
% 7.31/2.33 % (10263)Instruction limit reached!
% 7.31/2.33 % (10263)------------------------------
% 7.31/2.33 % (10263)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.31/2.33 % (10263)Termination reason: Unknown
% 7.31/2.33 % (10263)Termination phase: shuffling
% 7.31/2.33
% 7.31/2.33 % (10263)Memory used [KB]: 1918
% 7.31/2.33 % (10263)Time elapsed: 0.011 s
% 7.31/2.33 % (10263)Instructions burned: 31 (million)
% 7.31/2.33 % (10263)------------------------------
% 7.31/2.33 % (10263)------------------------------
% 7.31/2.33 % (10131)Instruction limit reached!
% 7.31/2.33 % (10131)------------------------------
% 7.31/2.33 % (10131)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.31/2.33 % (10131)Termination reason: Unknown
% 7.31/2.33 % (10131)Termination phase: Saturation
% 7.31/2.33
% 7.31/2.33 % (10131)Memory used [KB]: 9978
% 7.31/2.33 % (10131)Time elapsed: 0.337 s
% 7.31/2.33 % (10131)Instructions burned: 1087 (million)
% 7.31/2.33 % (10131)------------------------------
% 7.31/2.33 % (10131)------------------------------
% 7.31/2.34 % (10259)Instruction limit reached!
% 7.31/2.34 % (10259)------------------------------
% 7.31/2.34 % (10259)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.31/2.34 % (10259)Termination reason: Unknown
% 7.31/2.34 % (10259)Termination phase: Saturation
% 7.31/2.34
% 7.31/2.34 % (10259)Memory used [KB]: 7675
% 7.31/2.34 % (10259)Time elapsed: 0.079 s
% 7.31/2.34 % (10259)Instructions burned: 258 (million)
% 7.31/2.34 % (10259)------------------------------
% 7.31/2.34 % (10259)------------------------------
% 7.31/2.34 % (10265)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on DTF2THF_9790 for (2992ds/987Mi)
% 7.31/2.34 % (10266)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on DTF2THF_9790 for (2992ds/182Mi)
% 7.31/2.34 % (10207)Instruction limit reached!
% 7.31/2.34 % (10207)------------------------------
% 7.31/2.34 % (10207)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.31/2.34 % (10207)Termination reason: Unknown
% 7.31/2.34 % (10207)Termination phase: Saturation
% 7.31/2.34
% 7.31/2.34 % (10207)Memory used [KB]: 8699
% 7.31/2.34 % (10207)Time elapsed: 0.206 s
% 7.31/2.34 % (10207)Instructions burned: 617 (million)
% 7.31/2.34 % (10207)------------------------------
% 7.31/2.34 % (10207)------------------------------
% 7.31/2.35 % (10267)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on DTF2THF_9790 for (2992ds/182Mi)
% 7.31/2.35 % (10268)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on DTF2THF_9790 for (2992ds/154Mi)
% 7.31/2.36 % (10261)Instruction limit reached!
% 7.31/2.36 % (10261)------------------------------
% 7.31/2.36 % (10261)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.31/2.36 % (10261)Termination reason: Unknown
% 7.31/2.36 % (10261)Termination phase: Property scanning
% 7.31/2.36
% 7.31/2.36 % (10261)Memory used [KB]: 2942
% 7.31/2.36 % (10261)Time elapsed: 0.063 s
% 7.31/2.36 % (10261)Instructions burned: 231 (million)
% 7.31/2.36 % (10261)------------------------------
% 7.31/2.36 % (10261)------------------------------
% 7.31/2.37 % (10269)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on DTF2THF_9790 for (2992ds/79Mi)
% 7.31/2.39 % (10266)Instruction limit reached!
% 7.31/2.39 % (10266)------------------------------
% 7.31/2.39 % (10266)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.31/2.39 % (10266)Termination reason: Unknown
% 7.31/2.39 % (10266)Termination phase: Function definition elimination
% 7.31/2.39
% 7.31/2.39 % (10266)Memory used [KB]: 2942
% 7.31/2.39 % (10266)Time elapsed: 0.052 s
% 7.31/2.39 % (10266)Instructions burned: 184 (million)
% 7.31/2.39 % (10266)------------------------------
% 7.31/2.39 % (10266)------------------------------
% 7.31/2.40 % (10268)Instruction limit reached!
% 7.31/2.40 % (10268)------------------------------
% 7.31/2.40 % (10268)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.31/2.40 % (10268)Termination reason: Unknown
% 7.31/2.40 % (10268)Termination phase: Property scanning
% 7.31/2.40
% 7.31/2.40 % (10268)Memory used [KB]: 2942
% 7.31/2.40 % (10268)Time elapsed: 0.044 s
% 7.31/2.40 % (10268)Instructions burned: 155 (million)
% 7.31/2.40 % (10268)------------------------------
% 7.31/2.40 % (10268)------------------------------
% 8.05/2.40 % (10269)Instruction limit reached!
% 8.05/2.40 % (10269)------------------------------
% 8.05/2.40 % (10269)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.05/2.40 % (10269)Termination reason: Unknown
% 8.05/2.40 % (10269)Termination phase: Preprocessing 3
% 8.05/2.40
% 8.05/2.40 % (10269)Memory used [KB]: 2686
% 8.05/2.40 % (10269)Time elapsed: 0.026 s
% 8.05/2.40 % (10269)Instructions burned: 81 (million)
% 8.05/2.40 % (10269)------------------------------
% 8.05/2.40 % (10269)------------------------------
% 8.05/2.40 % (10267)Instruction limit reached!
% 8.05/2.40 % (10267)------------------------------
% 8.05/2.40 % (10267)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.05/2.40 % (10267)Termination reason: Unknown
% 8.05/2.40 % (10267)Termination phase: Property scanning
% 8.05/2.40
% 8.05/2.40 % (10267)Memory used [KB]: 3198
% 8.05/2.40 % (10267)Time elapsed: 0.054 s
% 8.05/2.40 % (10267)Instructions burned: 185 (million)
% 8.05/2.40 % (10267)------------------------------
% 8.05/2.40 % (10267)------------------------------
% 8.05/2.40 % (10270)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on DTF2THF_9790 for (2992ds/216Mi)
% 8.05/2.41 % (10271)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_9790 for (2992ds/114Mi)
% 8.05/2.41 % (10272)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on DTF2THF_9790 for (2992ds/922Mi)
% 8.05/2.41 % (10273)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on DTF2THF_9790 for (2992ds/182Mi)
% 8.05/2.41 % (10264)Instruction limit reached!
% 8.05/2.41 % (10264)------------------------------
% 8.05/2.41 % (10264)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.05/2.41 % (10264)Termination reason: Unknown
% 8.05/2.41 % (10264)Termination phase: Saturation
% 8.05/2.41
% 8.05/2.41 % (10264)Memory used [KB]: 7803
% 8.05/2.41 % (10264)Time elapsed: 0.093 s
% 8.05/2.41 % (10264)Instructions burned: 298 (million)
% 8.05/2.41 % (10264)------------------------------
% 8.05/2.41 % (10264)------------------------------
% 8.05/2.42 % (10274)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on DTF2THF_9790 for (2992ds/164Mi)
% 8.05/2.44 % (10271)Instruction limit reached!
% 8.05/2.44 % (10271)------------------------------
% 8.05/2.44 % (10271)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.05/2.44 % (10271)Termination reason: Unknown
% 8.05/2.44 % (10271)Termination phase: Property scanning
% 8.05/2.44
% 8.05/2.44 % (10271)Memory used [KB]: 2942
% 8.05/2.44 % (10271)Time elapsed: 0.037 s
% 8.05/2.44 % (10271)Instructions burned: 117 (million)
% 8.05/2.44 % (10271)------------------------------
% 8.05/2.44 % (10271)------------------------------
% 8.05/2.45 % (10262)Instruction limit reached!
% 8.05/2.45 % (10262)------------------------------
% 8.05/2.45 % (10262)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.05/2.45 % (10262)Termination reason: Unknown
% 8.05/2.45 % (10262)Termination phase: Saturation
% 8.05/2.45
% 8.05/2.45 % (10262)Memory used [KB]: 8955
% 8.05/2.45 % (10262)Time elapsed: 0.138 s
% 8.05/2.45 % (10262)Instructions burned: 460 (million)
% 8.05/2.45 % (10262)------------------------------
% 8.05/2.45 % (10262)------------------------------
% 8.05/2.45 % (10275)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on DTF2THF_9790 for (2991ds/50Mi)
% 8.05/2.46 % (10276)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_9790 for (2991ds/368Mi)
% 8.05/2.46 % (10273)Instruction limit reached!
% 8.05/2.46 % (10273)------------------------------
% 8.05/2.46 % (10273)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.05/2.46 % (10273)Termination reason: Unknown
% 8.05/2.46 % (10273)Termination phase: Saturation
% 8.05/2.46
% 8.05/2.46 % (10273)Memory used [KB]: 2942
% 8.05/2.46 % (10273)Time elapsed: 0.051 s
% 8.05/2.46 % (10273)Instructions burned: 182 (million)
% 8.05/2.46 % (10273)------------------------------
% 8.05/2.46 % (10273)------------------------------
% 8.05/2.46 % (10270)Instruction limit reached!
% 8.05/2.46 % (10270)------------------------------
% 8.05/2.46 % (10270)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.05/2.46 % (10270)Termination reason: Unknown
% 8.05/2.46 % (10270)Termination phase: Saturation
% 8.05/2.46
% 8.05/2.46 % (10270)Memory used [KB]: 7675
% 8.05/2.46 % (10270)Time elapsed: 0.062 s
% 8.05/2.46 % (10270)Instructions burned: 219 (million)
% 8.05/2.46 % (10270)------------------------------
% 8.05/2.46 % (10270)------------------------------
% 8.05/2.47 % (10275)Instruction limit reached!
% 8.05/2.47 % (10275)------------------------------
% 8.05/2.47 % (10275)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.05/2.47 % (10275)Termination reason: Unknown
% 8.05/2.47 % (10275)Termination phase: shuffling
% 8.05/2.47
% 8.05/2.47 % (10275)Memory used [KB]: 2430
% 8.05/2.47 % (10275)Time elapsed: 0.016 s
% 8.05/2.47 % (10275)Instructions burned: 53 (million)
% 8.05/2.47 % (10275)------------------------------
% 8.05/2.47 % (10275)------------------------------
% 8.05/2.47 % (10277)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on DTF2THF_9790 for (2991ds/1021Mi)
% 8.05/2.47 % (10274)Instruction limit reached!
% 8.05/2.47 % (10274)------------------------------
% 8.05/2.47 % (10274)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.05/2.47 % (10274)Termination reason: Unknown
% 8.05/2.47 % (10274)Termination phase: Saturation
% 8.05/2.47
% 8.05/2.47 % (10274)Memory used [KB]: 2814
% 8.05/2.47 % (10274)Time elapsed: 0.047 s
% 8.05/2.47 % (10274)Instructions burned: 164 (million)
% 8.05/2.47 % (10274)------------------------------
% 8.05/2.47 % (10274)------------------------------
% 8.05/2.47 % (10278)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on DTF2THF_9790 for (2991ds/267Mi)
% 8.05/2.48 % (10279)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on DTF2THF_9790 for (2991ds/204Mi)
% 8.05/2.48 % (10280)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_9790 for (2991ds/26Mi)
% 8.05/2.49 % (10280)Instruction limit reached!
% 8.05/2.49 % (10280)------------------------------
% 8.05/2.49 % (10280)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.05/2.49 % (10280)Termination reason: Unknown
% 8.05/2.49 % (10280)Termination phase: shuffling
% 8.05/2.49
% 8.05/2.49 % (10280)Memory used [KB]: 2046
% 8.05/2.49 % (10280)Time elapsed: 0.009 s
% 8.05/2.49 % (10280)Instructions burned: 29 (million)
% 8.05/2.49 % (10280)------------------------------
% 8.05/2.49 % (10280)------------------------------
% 8.71/2.50 % (10281)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on DTF2THF_9790 for (2991ds/53Mi)
% 8.71/2.51 % (10281)Instruction limit reached!
% 8.71/2.51 % (10281)------------------------------
% 8.71/2.51 % (10281)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.71/2.51 % (10281)Termination reason: Unknown
% 8.71/2.51 % (10281)Termination phase: shuffling
% 8.71/2.51
% 8.71/2.51 % (10281)Memory used [KB]: 2430
% 8.71/2.51 % (10281)Time elapsed: 0.017 s
% 8.71/2.51 % (10281)Instructions burned: 55 (million)
% 8.71/2.51 % (10281)------------------------------
% 8.71/2.51 % (10281)------------------------------
% 8.71/2.52 % (10282)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on DTF2THF_9790 for (2991ds/4436Mi)
% 8.71/2.53 % (10279)Instruction limit reached!
% 8.71/2.53 % (10279)------------------------------
% 8.71/2.53 % (10279)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.71/2.53 % (10279)Termination reason: Unknown
% 8.71/2.53 % (10279)Termination phase: Saturation
% 8.71/2.53
% 8.71/2.53 % (10279)Memory used [KB]: 7547
% 8.71/2.53 % (10279)Time elapsed: 0.060 s
% 8.71/2.53 % (10279)Instructions burned: 206 (million)
% 8.71/2.53 % (10279)------------------------------
% 8.71/2.53 % (10279)------------------------------
% 8.71/2.54 % (10283)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on DTF2THF_9790 for (2991ds/1539Mi)
% 8.71/2.55 % (10278)Instruction limit reached!
% 8.71/2.55 % (10278)------------------------------
% 8.71/2.55 % (10278)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.71/2.55 % (10278)Termination reason: Unknown
% 8.71/2.55 % (10278)Termination phase: Saturation
% 8.71/2.55
% 8.71/2.55 % (10278)Memory used [KB]: 7803
% 8.71/2.55 % (10278)Time elapsed: 0.078 s
% 8.71/2.55 % (10278)Instructions burned: 268 (million)
% 8.71/2.55 % (10278)------------------------------
% 8.71/2.55 % (10278)------------------------------
% 8.71/2.56 % (10284)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=408:si=on:rtra=on_0 on DTF2THF_9790 for (2990ds/408Mi)
% 8.71/2.57 % (10276)Instruction limit reached!
% 8.71/2.57 % (10276)------------------------------
% 8.71/2.57 % (10276)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.71/2.57 % (10276)Termination reason: Unknown
% 8.71/2.57 % (10276)Termination phase: Saturation
% 8.71/2.57
% 8.71/2.57 % (10276)Memory used [KB]: 8315
% 8.71/2.57 % (10276)Time elapsed: 0.110 s
% 8.71/2.57 % (10276)Instructions burned: 369 (million)
% 8.71/2.57 % (10276)------------------------------
% 8.71/2.57 % (10276)------------------------------
% 8.71/2.58 % (10285)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=5205:si=on:rtra=on_0 on DTF2THF_9790 for (2990ds/5205Mi)
% 9.02/2.64 % (10265)Instruction limit reached!
% 9.02/2.64 % (10265)------------------------------
% 9.02/2.64 % (10265)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.02/2.64 % (10265)Termination reason: Unknown
% 9.02/2.64 % (10265)Termination phase: Saturation
% 9.02/2.64
% 9.02/2.64 % (10265)Memory used [KB]: 9594
% 9.02/2.64 % (10265)Time elapsed: 0.297 s
% 9.02/2.64 % (10265)Instructions burned: 988 (million)
% 9.02/2.64 % (10265)------------------------------
% 9.02/2.64 % (10265)------------------------------
% 9.02/2.65 % (10286)dis+1010_1:4_au=on:av=off:cbe=off:nwc=10.0:s2a=on:s2at=3.0:sd=2:ss=axioms:st=5.0:i=1913:si=on:rtra=on_0 on DTF2THF_9790 for (2990ds/1913Mi)
% 9.02/2.68 % (10284)Instruction limit reached!
% 9.02/2.68 % (10284)------------------------------
% 9.02/2.68 % (10284)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.02/2.68 % (10284)Termination reason: Unknown
% 9.02/2.68 % (10284)Termination phase: Saturation
% 9.02/2.68
% 9.02/2.68 % (10284)Memory used [KB]: 9466
% 9.02/2.68 % (10284)Time elapsed: 0.118 s
% 9.02/2.68 % (10284)Instructions burned: 408 (million)
% 9.02/2.68 % (10284)------------------------------
% 9.02/2.68 % (10284)------------------------------
% 9.02/2.69 % (10287)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on DTF2THF_9790 for (2989ds/4350Mi)
% 9.02/2.69 % (10272)Instruction limit reached!
% 9.02/2.69 % (10272)------------------------------
% 9.02/2.69 % (10272)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.02/2.69 % (10272)Termination reason: Unknown
% 9.02/2.69 % (10272)Termination phase: Saturation
% 9.02/2.69
% 9.02/2.69 % (10272)Memory used [KB]: 9210
% 9.02/2.69 % (10272)Time elapsed: 0.288 s
% 9.02/2.69 % (10272)Instructions burned: 923 (million)
% 9.02/2.69 % (10272)------------------------------
% 9.02/2.69 % (10272)------------------------------
% 9.75/2.70 % (10288)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_9790 for (2989ds/68Mi)
% 9.75/2.72 % (10288)Instruction limit reached!
% 9.75/2.72 % (10288)------------------------------
% 9.75/2.72 % (10288)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.75/2.72 % (10288)Termination reason: Unknown
% 9.75/2.72 % (10288)Termination phase: SInE selection
% 9.75/2.72
% 9.75/2.72 % (10288)Memory used [KB]: 2046
% 9.75/2.72 % (10288)Time elapsed: 0.022 s
% 9.75/2.72 % (10288)Instructions burned: 69 (million)
% 9.75/2.72 % (10288)------------------------------
% 9.75/2.72 % (10288)------------------------------
% 9.75/2.73 % (10289)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on DTF2THF_9790 for (2989ds/358Mi)
% 9.75/2.77 % (10277)Instruction limit reached!
% 9.75/2.77 % (10277)------------------------------
% 9.75/2.77 % (10277)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.75/2.77 % (10277)Termination reason: Unknown
% 9.75/2.77 % (10277)Termination phase: Saturation
% 9.75/2.77
% 9.75/2.77 % (10277)Memory used [KB]: 10362
% 9.75/2.77 % (10277)Time elapsed: 0.305 s
% 9.75/2.77 % (10277)Instructions burned: 1023 (million)
% 9.75/2.77 % (10277)------------------------------
% 9.75/2.77 % (10277)------------------------------
% 9.75/2.78 % (10290)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_9790 for (2988ds/31Mi)
% 9.75/2.79 % (10290)Instruction limit reached!
% 9.75/2.79 % (10290)------------------------------
% 9.75/2.79 % (10290)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.75/2.79 % (10290)Termination reason: Unknown
% 9.75/2.79 % (10290)Termination phase: shuffling
% 9.75/2.79
% 9.75/2.79 % (10290)Memory used [KB]: 1918
% 9.75/2.79 % (10290)Time elapsed: 0.012 s
% 9.75/2.79 % (10290)Instructions burned: 33 (million)
% 9.75/2.79 % (10290)------------------------------
% 9.75/2.79 % (10290)------------------------------
% 10.12/2.80 % (10291)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_9790 for (2988ds/279Mi)
% 10.12/2.84 % (10289)Instruction limit reached!
% 10.12/2.84 % (10289)------------------------------
% 10.12/2.84 % (10289)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.12/2.84 % (10289)Termination reason: Unknown
% 10.12/2.84 % (10289)Termination phase: Saturation
% 10.12/2.84
% 10.12/2.84 % (10289)Memory used [KB]: 8059
% 10.12/2.84 % (10289)Time elapsed: 0.110 s
% 10.12/2.84 % (10289)Instructions burned: 359 (million)
% 10.12/2.84 % (10289)------------------------------
% 10.12/2.84 % (10289)------------------------------
% 10.12/2.85 % (10291)Refutation not found, incomplete strategy
% 10.12/2.85 % (10291)------------------------------
% 10.12/2.85 % (10291)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.12/2.85 % (10291)Termination reason: Refutation not found, incomplete strategy
% 10.12/2.85
% 10.12/2.85
% 10.12/2.85 % (10291)Memory used [KB]: 7419
% 10.12/2.85 % (10291)Time elapsed: 0.048 s
% 10.12/2.85 % (10291)Instructions burned: 168 (million)
% 10.12/2.85 % (10291)------------------------------
% 10.12/2.85 % (10291)------------------------------
% 10.12/2.85 % (10292)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_9790 for (2987ds/258Mi)
% 10.12/2.86 % (10293)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_9790 for (2987ds/26Mi)
% 10.12/2.87 % (10293)Instruction limit reached!
% 10.12/2.87 % (10293)------------------------------
% 10.12/2.87 % (10293)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.12/2.87 % (10293)Termination reason: Unknown
% 10.12/2.87 % (10293)Termination phase: shuffling
% 10.12/2.87
% 10.12/2.87 % (10293)Memory used [KB]: 2046
% 10.12/2.87 % (10293)Time elapsed: 0.009 s
% 10.12/2.87 % (10293)Instructions burned: 27 (million)
% 10.12/2.87 % (10293)------------------------------
% 10.12/2.87 % (10293)------------------------------
% 10.12/2.88 % (10294)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=995:si=on:rtra=on_0 on DTF2THF_9790 for (2987ds/995Mi)
% 10.33/2.93 % (10292)Instruction limit reached!
% 10.33/2.93 % (10292)------------------------------
% 10.33/2.93 % (10292)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.33/2.93 % (10292)Termination reason: Unknown
% 10.33/2.93 % (10292)Termination phase: Saturation
% 10.33/2.93
% 10.33/2.93 % (10292)Memory used [KB]: 8059
% 10.33/2.93 % (10292)Time elapsed: 0.075 s
% 10.33/2.93 % (10292)Instructions burned: 260 (million)
% 10.33/2.93 % (10292)------------------------------
% 10.33/2.93 % (10292)------------------------------
% 10.33/2.94 % (10295)dis+10_1:8_amm=sco:cbe=off:hflw=5:hfsq=on:hfsqc=14:hfsql=off:hfsqr=4,1:hud=5:ile=on:lma=on:nm=2:ntd=on:prag=on:sac=on:sp=frequency:i=373:si=on:rtra=on_0 on DTF2THF_9790 for (2987ds/373Mi)
% 10.33/3.00 % (10283)Instruction limit reached!
% 10.33/3.00 % (10283)------------------------------
% 10.33/3.00 % (10283)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.33/3.00 % (10283)Termination reason: Unknown
% 10.33/3.00 % (10283)Termination phase: Saturation
% 10.33/3.00
% 10.33/3.00 % (10283)Memory used [KB]: 12920
% 10.33/3.00 % (10283)Time elapsed: 0.458 s
% 10.33/3.00 % (10283)Instructions burned: 1541 (million)
% 10.33/3.00 % (10283)------------------------------
% 10.33/3.00 % (10283)------------------------------
% 12.68/3.01 % (10296)lrs+1010_1:128_au=on:cnfonf=lazy_pi_sigma_gen:hflw=4:hfsq=on:hfsqc=20:hfsql=off:i=253:si=on:rtra=on_0 on DTF2THF_9790 for (2986ds/253Mi)
% 12.68/3.05 % (10295)Instruction limit reached!
% 12.68/3.05 % (10295)------------------------------
% 12.68/3.05 % (10295)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.68/3.05 % (10295)Termination reason: Unknown
% 12.68/3.05 % (10295)Termination phase: Saturation
% 12.68/3.05
% 12.68/3.05 % (10295)Memory used [KB]: 8699
% 12.68/3.05 % (10295)Time elapsed: 0.133 s
% 12.68/3.05 % (10295)Instructions burned: 373 (million)
% 12.68/3.05 % (10295)------------------------------
% 12.68/3.05 % (10295)------------------------------
% 12.68/3.06 % (10297)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=832:si=on:rtra=on_0 on DTF2THF_9790 for (2985ds/832Mi)
% 12.68/3.08 % (10296)Instruction limit reached!
% 12.68/3.08 % (10296)------------------------------
% 12.68/3.08 % (10296)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.68/3.08 % (10296)Termination reason: Unknown
% 12.68/3.08 % (10296)Termination phase: Saturation
% 12.68/3.08
% 12.68/3.08 % (10296)Memory used [KB]: 7803
% 12.68/3.08 % (10296)Time elapsed: 0.071 s
% 12.68/3.08 % (10296)Instructions burned: 255 (million)
% 12.68/3.08 % (10296)------------------------------
% 12.68/3.08 % (10296)------------------------------
% 12.68/3.09 % (10298)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=668:si=on:rtra=on_0 on DTF2THF_9790 for (2985ds/668Mi)
% 13.32/3.16 % (10294)Instruction limit reached!
% 13.32/3.16 % (10294)------------------------------
% 13.32/3.16 % (10294)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.32/3.16 % (10294)Termination reason: Unknown
% 13.32/3.16 % (10294)Termination phase: Saturation
% 13.32/3.16
% 13.32/3.16 % (10294)Memory used [KB]: 9850
% 13.32/3.16 % (10294)Time elapsed: 0.284 s
% 13.32/3.16 % (10294)Instructions burned: 995 (million)
% 13.32/3.16 % (10294)------------------------------
% 13.32/3.16 % (10294)------------------------------
% 13.32/3.17 % (10299)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=40:si=on:rtra=on_0 on DTF2THF_9790 for (2984ds/40Mi)
% 13.32/3.18 % (10299)Instruction limit reached!
% 13.32/3.18 % (10299)------------------------------
% 13.32/3.18 % (10299)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.32/3.18 % (10299)Termination reason: Unknown
% 13.32/3.18 % (10299)Termination phase: shuffling
% 13.32/3.18
% 13.32/3.18 % (10299)Memory used [KB]: 2174
% 13.32/3.18 % (10299)Time elapsed: 0.013 s
% 13.32/3.18 % (10299)Instructions burned: 42 (million)
% 13.32/3.18 % (10299)------------------------------
% 13.32/3.18 % (10299)------------------------------
% 13.32/3.19 % (10300)lrs+1010_1:1_cnfonf=lazy_pi_sigma_gen:fd=off:ntd=on:sd=1:sgt=32:sos=on:ss=axioms:i=294:si=on:rtra=on_0 on DTF2THF_9790 for (2984ds/294Mi)
% 13.74/3.23 % (10286)Instruction limit reached!
% 13.74/3.23 % (10286)------------------------------
% 13.74/3.23 % (10286)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.74/3.23 % (10286)Termination reason: Unknown
% 13.74/3.23 % (10286)Termination phase: Saturation
% 13.74/3.23
% 13.74/3.23 % (10286)Memory used [KB]: 4221
% 13.74/3.23 % (10286)Time elapsed: 0.581 s
% 13.74/3.23 % (10286)Instructions burned: 1915 (million)
% 13.74/3.23 % (10286)------------------------------
% 13.74/3.23 % (10286)------------------------------
% 13.74/3.24 % (10301)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on DTF2THF_9790 for (2983ds/187Mi)
% 13.74/3.27 % (10300)Instruction limit reached!
% 13.74/3.27 % (10300)------------------------------
% 13.74/3.27 % (10300)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.74/3.27 % (10300)Termination reason: Unknown
% 13.74/3.27 % (10300)Termination phase: Saturation
% 13.74/3.27
% 13.74/3.27 % (10300)Memory used [KB]: 7675
% 13.74/3.27 % (10300)Time elapsed: 0.084 s
% 13.74/3.27 % (10300)Instructions burned: 297 (million)
% 13.74/3.27 % (10300)------------------------------
% 13.74/3.27 % (10300)------------------------------
% 13.74/3.28 % (10298)Instruction limit reached!
% 13.74/3.28 % (10298)------------------------------
% 13.74/3.28 % (10298)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.74/3.28 % (10298)Termination reason: Unknown
% 13.74/3.28 % (10298)Termination phase: Saturation
% 13.74/3.28
% 13.74/3.28 % (10298)Memory used [KB]: 13816
% 13.74/3.28 % (10298)Time elapsed: 0.191 s
% 13.74/3.28 % (10298)Instructions burned: 670 (million)
% 13.74/3.28 % (10298)------------------------------
% 13.74/3.28 % (10298)------------------------------
% 13.74/3.28 % (10302)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_9790 for (2983ds/371Mi)
% 13.74/3.29 % (10303)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_9790 for (2983ds/1827Mi)
% 13.74/3.29 % (10301)Instruction limit reached!
% 13.74/3.29 % (10301)------------------------------
% 13.74/3.29 % (10301)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.74/3.29 % (10301)Termination reason: Unknown
% 13.74/3.29 % (10301)Termination phase: Saturation
% 13.74/3.29
% 13.74/3.29 % (10301)Memory used [KB]: 7547
% 13.74/3.29 % (10301)Time elapsed: 0.056 s
% 13.74/3.29 % (10301)Instructions burned: 189 (million)
% 13.74/3.29 % (10301)------------------------------
% 13.74/3.29 % (10301)------------------------------
% 14.42/3.30 % (10304)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=70:si=on:rtra=on_0 on DTF2THF_9790 for (2983ds/70Mi)
% 14.42/3.30 % (10297)Instruction limit reached!
% 14.42/3.30 % (10297)------------------------------
% 14.42/3.30 % (10297)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.42/3.30 % (10297)Termination reason: Unknown
% 14.42/3.30 % (10297)Termination phase: Saturation
% 14.42/3.30
% 14.42/3.30 % (10297)Memory used [KB]: 9850
% 14.42/3.30 % (10297)Time elapsed: 0.249 s
% 14.42/3.30 % (10297)Instructions burned: 834 (million)
% 14.42/3.30 % (10297)------------------------------
% 14.42/3.30 % (10297)------------------------------
% 14.42/3.31 % (10305)lrs+10_1:20_bd=off:cnfonf=lazy_not_be_gen:fe=axiom:hud=10:ins=1:nm=20:prag=on:sos=on:i=316:si=on:rtra=on_0 on DTF2THF_9790 for (2983ds/316Mi)
% 14.42/3.32 % (10304)Instruction limit reached!
% 14.42/3.32 % (10304)------------------------------
% 14.42/3.32 % (10304)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.42/3.32 % (10304)Termination reason: Unknown
% 14.42/3.32 % (10304)Termination phase: Property scanning
% 14.42/3.32
% 14.42/3.32 % (10304)Memory used [KB]: 2686
% 14.42/3.32 % (10304)Time elapsed: 0.021 s
% 14.42/3.32 % (10304)Instructions burned: 71 (million)
% 14.42/3.32 % (10304)------------------------------
% 14.42/3.32 % (10304)------------------------------
% 14.42/3.33 % (10306)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=932:si=on:rtra=on_0 on DTF2THF_9790 for (2983ds/932Mi)
% 15.01/3.40 % (10305)Instruction limit reached!
% 15.01/3.40 % (10305)------------------------------
% 15.01/3.40 % (10305)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.01/3.40 % (10305)Termination reason: Unknown
% 15.01/3.40 % (10305)Termination phase: Saturation
% 15.01/3.40
% 15.01/3.40 % (10305)Memory used [KB]: 3965
% 15.01/3.40 % (10305)Time elapsed: 0.089 s
% 15.01/3.40 % (10305)Instructions burned: 317 (million)
% 15.01/3.40 % (10305)------------------------------
% 15.01/3.40 % (10305)------------------------------
% 15.01/3.40 % (10302)Instruction limit reached!
% 15.01/3.40 % (10302)------------------------------
% 15.01/3.40 % (10302)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.01/3.40 % (10302)Termination reason: Unknown
% 15.01/3.40 % (10302)Termination phase: Saturation
% 15.01/3.40
% 15.01/3.40 % (10302)Memory used [KB]: 8187
% 15.01/3.40 % (10302)Time elapsed: 0.119 s
% 15.01/3.40 % (10302)Instructions burned: 372 (million)
% 15.01/3.40 % (10302)------------------------------
% 15.01/3.40 % (10302)------------------------------
% 15.01/3.41 % (10307)lrs+1010_1:128_au=on:bd=preordered:cnfonf=lazy_pi_sigma_gen:plsq=on:plsqc=1:plsqr=32,1:sos=all:sp=occurrence:i=4714:si=on:rtra=on_0 on DTF2THF_9790 for (2982ds/4714Mi)
% 15.01/3.41 % (10308)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=8250:si=on:rtra=on_0 on DTF2THF_9790 for (2982ds/8250Mi)
% 15.54/3.53 % (10307)Refutation not found, incomplete strategy
% 15.54/3.53 % (10307)------------------------------
% 15.54/3.53 % (10307)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.54/3.53 % (10307)Termination reason: Refutation not found, incomplete strategy
% 15.54/3.53
% 15.54/3.53
% 15.54/3.53 % (10307)Memory used [KB]: 8955
% 15.54/3.53 % (10307)Time elapsed: 0.119 s
% 15.54/3.53 % (10307)Instructions burned: 420 (million)
% 15.54/3.53 % (10307)------------------------------
% 15.54/3.53 % (10307)------------------------------
% 15.54/3.54 % (10309)lrs+1002_1:1_apa=on:cnfonf=off:fd=off:flr=on:hud=1:lcm=reverse:prag=on:sd=1:sos=on:ss=axioms:i=770:si=on:rtra=on_0 on DTF2THF_9790 for (2980ds/770Mi)
% 15.54/3.57 % (10309)Refutation not found, incomplete strategy
% 15.54/3.57 % (10309)------------------------------
% 15.54/3.57 % (10309)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.54/3.57 % (10309)Termination reason: Refutation not found, incomplete strategy
% 15.54/3.57
% 15.54/3.57
% 15.54/3.57 % (10309)Memory used [KB]: 7419
% 15.54/3.57 % (10309)Time elapsed: 0.032 s
% 15.54/3.57 % (10309)Instructions burned: 101 (million)
% 15.54/3.57 % (10309)------------------------------
% 15.54/3.57 % (10309)------------------------------
% 15.54/3.58 % (10310)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_9790 for (2980ds/794Mi)
% 16.01/3.60 % (10306)Instruction limit reached!
% 16.01/3.60 % (10306)------------------------------
% 16.01/3.60 % (10306)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.01/3.60 % (10306)Termination reason: Unknown
% 16.01/3.60 % (10306)Termination phase: Saturation
% 16.01/3.60
% 16.01/3.60 % (10306)Memory used [KB]: 11257
% 16.01/3.60 % (10306)Time elapsed: 0.274 s
% 16.01/3.60 % (10306)Instructions burned: 932 (million)
% 16.01/3.60 % (10306)------------------------------
% 16.01/3.60 % (10306)------------------------------
% 16.01/3.61 % (10311)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_9790 for (2980ds/464Mi)
% 16.60/3.76 % (10311)Instruction limit reached!
% 16.60/3.76 % (10311)------------------------------
% 16.60/3.76 % (10311)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.60/3.76 % (10311)Termination reason: Unknown
% 16.60/3.76 % (10311)Termination phase: Saturation
% 16.60/3.76
% 16.60/3.76 % (10311)Memory used [KB]: 8571
% 16.60/3.76 % (10311)Time elapsed: 0.147 s
% 16.60/3.76 % (10311)Instructions burned: 466 (million)
% 16.60/3.76 % (10311)------------------------------
% 16.60/3.76 % (10311)------------------------------
% 16.60/3.77 % (10312)ott+21_1:3_avsq=on:bd=off:cnfonf=lazy_gen:fe=off:hud=10:ixr=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=1376:si=on:rtra=on_0 on DTF2THF_9790 for (2978ds/1376Mi)
% 17.05/3.82 % (10310)Instruction limit reached!
% 17.05/3.82 % (10310)------------------------------
% 17.05/3.82 % (10310)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.05/3.82 % (10310)Termination reason: Unknown
% 17.05/3.82 % (10310)Termination phase: Saturation
% 17.05/3.82
% 17.05/3.82 % (10310)Memory used [KB]: 6524
% 17.05/3.82 % (10310)Time elapsed: 0.244 s
% 17.05/3.82 % (10310)Instructions burned: 796 (million)
% 17.05/3.82 % (10310)------------------------------
% 17.05/3.82 % (10310)------------------------------
% 17.05/3.83 % (10313)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_9790 for (2978ds/906Mi)
% 17.05/3.87 % (10303)Instruction limit reached!
% 17.05/3.87 % (10303)------------------------------
% 17.05/3.87 % (10303)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.05/3.87 % (10303)Termination reason: Unknown
% 17.05/3.87 % (10303)Termination phase: Saturation
% 17.05/3.87
% 17.05/3.87 % (10303)Memory used [KB]: 11001
% 17.05/3.87 % (10303)Time elapsed: 0.579 s
% 17.05/3.87 % (10303)Instructions burned: 1828 (million)
% 17.05/3.87 % (10303)------------------------------
% 17.05/3.87 % (10303)------------------------------
% 17.05/3.87 % (10282)Instruction limit reached!
% 17.05/3.87 % (10282)------------------------------
% 17.05/3.87 % (10282)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.05/3.87 % (10282)Termination reason: Unknown
% 17.05/3.87 % (10282)Termination phase: Saturation
% 17.05/3.87
% 17.05/3.87 % (10282)Memory used [KB]: 14328
% 17.05/3.87 % (10282)Time elapsed: 1.349 s
% 17.05/3.87 % (10282)Instructions burned: 4436 (million)
% 17.05/3.87 % (10282)------------------------------
% 17.05/3.87 % (10282)------------------------------
% 17.05/3.88 % (10314)lrs+1002_1:16_bd=off:e2e=on:fde=unused:kws=precedence:sac=on:sos=on:ss=axioms:i=434:si=on:rtra=on_0 on DTF2THF_9790 for (2977ds/434Mi)
% 17.05/3.88 % (10315)lrs+10_5:4_cnfonf=conj_eager:fe=axiom:hflw=5:hfsq=on:hfsqc=10:hfsql=off:hud=10:plsq=on:sgt=5:spb=goal_then_units:ss=axioms:i=865:si=on:rtra=on_0 on DTF2THF_9790 for (2977ds/865Mi)
% 18.19/3.92 % (10314)Refutation not found, incomplete strategy
% 18.19/3.92 % (10314)------------------------------
% 18.19/3.92 % (10314)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.19/3.92 % (10314)Termination reason: Refutation not found, incomplete strategy
% 18.19/3.92
% 18.19/3.92
% 18.19/3.92 % (10314)Memory used [KB]: 7419
% 18.19/3.92 % (10314)Time elapsed: 0.039 s
% 18.19/3.92 % (10314)Instructions burned: 123 (million)
% 18.19/3.92 % (10314)------------------------------
% 18.19/3.92 % (10314)------------------------------
% 18.19/3.93 % (10316)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=593:si=on:rtra=on_0 on DTF2THF_9790 for (2977ds/593Mi)
% 18.19/3.93 % (10287)Instruction limit reached!
% 18.19/3.93 % (10287)------------------------------
% 18.19/3.93 % (10287)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.19/3.93 % (10287)Termination reason: Unknown
% 18.19/3.93 % (10287)Termination phase: Saturation
% 18.19/3.93
% 18.19/3.93 % (10287)Memory used [KB]: 13304
% 18.19/3.93 % (10287)Time elapsed: 1.248 s
% 18.19/3.93 % (10287)Instructions burned: 4352 (million)
% 18.19/3.93 % (10287)------------------------------
% 18.19/3.93 % (10287)------------------------------
% 18.19/3.94 % (10317)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_9790 for (2976ds/443Mi)
% 19.78/4.08 % (10317)Instruction limit reached!
% 19.78/4.08 % (10317)------------------------------
% 19.78/4.08 % (10317)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.78/4.08 % (10317)Termination reason: Unknown
% 19.78/4.08 % (10317)Termination phase: Saturation
% 19.78/4.08
% 19.78/4.08 % (10317)Memory used [KB]: 8187
% 19.78/4.08 % (10317)Time elapsed: 0.134 s
% 19.78/4.08 % (10317)Instructions burned: 444 (million)
% 19.78/4.08 % (10317)------------------------------
% 19.78/4.08 % (10317)------------------------------
% 19.78/4.09 % (10318)dis+10_1:1_atotf=0.1:cbe=off:sd=3:ss=axioms:st=2.0:i=594:si=on:rtra=on_0 on DTF2THF_9790 for (2975ds/594Mi)
% 19.78/4.09 % (10316)Instruction limit reached!
% 19.78/4.09 % (10316)------------------------------
% 19.78/4.09 % (10316)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.78/4.09 % (10316)Termination reason: Unknown
% 19.78/4.09 % (10316)Termination phase: Saturation
% 19.78/4.09
% 19.78/4.09 % (10316)Memory used [KB]: 9722
% 19.78/4.09 % (10316)Time elapsed: 0.162 s
% 19.78/4.09 % (10316)Instructions burned: 595 (million)
% 19.78/4.09 % (10316)------------------------------
% 19.78/4.09 % (10316)------------------------------
% 19.78/4.10 % (10319)ott+10_1:1024_anc=none:bd=off:e2e=on:fde=none:fsr=off:hud=10:ixr=off:nm=4:nwc=5.0:spb=goal:i=327:si=on:rtra=on_0 on DTF2THF_9790 for (2975ds/327Mi)
% 20.43/4.13 % (10315)Instruction limit reached!
% 20.43/4.13 % (10315)------------------------------
% 20.43/4.13 % (10315)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.43/4.13 % (10315)Termination reason: Unknown
% 20.43/4.13 % (10315)Termination phase: Saturation
% 20.43/4.13
% 20.43/4.13 % (10315)Memory used [KB]: 9594
% 20.43/4.13 % (10315)Time elapsed: 0.251 s
% 20.43/4.13 % (10315)Instructions burned: 867 (million)
% 20.43/4.13 % (10315)------------------------------
% 20.43/4.13 % (10315)------------------------------
% 20.43/4.14 % (10320)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=5411:si=on:rtra=on_0 on DTF2THF_9790 for (2974ds/5411Mi)
% 20.43/4.16 % (10313)Instruction limit reached!
% 20.43/4.16 % (10313)------------------------------
% 20.43/4.16 % (10313)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.43/4.16 % (10313)Termination reason: Unknown
% 20.43/4.16 % (10313)Termination phase: Saturation
% 20.43/4.16
% 20.43/4.16 % (10313)Memory used [KB]: 12920
% 20.43/4.16 % (10313)Time elapsed: 0.324 s
% 20.43/4.16 % (10313)Instructions burned: 906 (million)
% 20.43/4.16 % (10313)------------------------------
% 20.43/4.16 % (10313)------------------------------
% 20.43/4.17 % (10321)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=1762:si=on:rtra=on_0 on DTF2THF_9790 for (2974ds/1762Mi)
% 20.43/4.18 % (10320)Refutation not found, incomplete strategy
% 20.43/4.18 % (10320)------------------------------
% 20.43/4.18 % (10320)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.43/4.18 % (10320)Termination reason: Refutation not found, incomplete strategy
% 20.43/4.18
% 20.43/4.18
% 20.43/4.18 % (10320)Memory used [KB]: 7419
% 20.43/4.18 % (10320)Time elapsed: 0.039 s
% 20.43/4.18 % (10320)Instructions burned: 125 (million)
% 20.43/4.18 % (10320)------------------------------
% 20.43/4.18 % (10320)------------------------------
% 20.43/4.18 % (10312)Instruction limit reached!
% 20.43/4.18 % (10312)------------------------------
% 20.43/4.18 % (10312)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.43/4.18 % (10312)Termination reason: Unknown
% 20.43/4.18 % (10312)Termination phase: Saturation
% 20.43/4.18
% 20.43/4.18 % (10312)Memory used [KB]: 14583
% 20.43/4.18 % (10312)Time elapsed: 0.416 s
% 20.43/4.18 % (10312)Instructions burned: 1378 (million)
% 20.43/4.18 % (10312)------------------------------
% 20.43/4.18 % (10312)------------------------------
% 20.43/4.19 % (10322)dis+1003_1:64_cha=on:cnfonf=lazy_gen:hud=9:nwc=8.0:prag=on:i=96:si=on:rtra=on_0 on DTF2THF_9790 for (2974ds/96Mi)
% 20.43/4.19 % (10323)lrs+21_1:1_hud=5:kws=inv_frequency:nm=16:nwc=2.0:prag=on:sos=on:ss=axioms:i=503:si=on:rtra=on_0 on DTF2THF_9790 for (2974ds/503Mi)
% 20.43/4.20 % (10319)Instruction limit reached!
% 20.43/4.20 % (10319)------------------------------
% 20.43/4.20 % (10319)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.43/4.20 % (10319)Termination reason: Unknown
% 20.43/4.20 % (10319)Termination phase: Saturation
% 20.43/4.20
% 20.43/4.20 % (10319)Memory used [KB]: 8571
% 20.43/4.20 % (10319)Time elapsed: 0.099 s
% 20.43/4.20 % (10319)Instructions burned: 329 (million)
% 20.43/4.20 % (10319)------------------------------
% 20.43/4.20 % (10319)------------------------------
% 20.86/4.21 % (10324)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_9790 for (2974ds/90Mi)
% 20.86/4.21 % (10285)Instruction limit reached!
% 20.86/4.21 % (10285)------------------------------
% 20.86/4.21 % (10285)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.86/4.21 % (10285)Termination reason: Unknown
% 20.86/4.21 % (10285)Termination phase: Saturation
% 20.86/4.21
% 20.86/4.21 % (10285)Memory used [KB]: 15223
% 20.86/4.21 % (10285)Time elapsed: 1.633 s
% 20.86/4.21 % (10285)Instructions burned: 5206 (million)
% 20.86/4.21 % (10285)------------------------------
% 20.86/4.21 % (10285)------------------------------
% 20.86/4.22 % (10322)Instruction limit reached!
% 20.86/4.22 % (10322)------------------------------
% 20.86/4.22 % (10322)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.86/4.22 % (10322)Termination reason: Unknown
% 20.86/4.22 % (10322)Termination phase: Property scanning
% 20.86/4.22
% 20.86/4.22 % (10322)Memory used [KB]: 2686
% 20.86/4.22 % (10322)Time elapsed: 0.028 s
% 20.86/4.22 % (10322)Instructions burned: 97 (million)
% 20.86/4.22 % (10322)------------------------------
% 20.86/4.22 % (10322)------------------------------
% 20.86/4.22 % (10325)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_9790 for (2974ds/593Mi)
% 20.86/4.23 % (10326)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=1512:si=on:rtra=on_0 on DTF2THF_9790 for (2974ds/1512Mi)
% 20.86/4.23 % (10324)Instruction limit reached!
% 20.86/4.23 % (10324)------------------------------
% 20.86/4.23 % (10324)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.86/4.23 % (10324)Termination reason: Unknown
% 20.86/4.23 % (10324)Termination phase: Preprocessing 3
% 20.86/4.23
% 20.86/4.23 % (10324)Memory used [KB]: 2814
% 20.86/4.23 % (10324)Time elapsed: 0.030 s
% 20.86/4.23 % (10324)Instructions burned: 93 (million)
% 20.86/4.23 % (10324)------------------------------
% 20.86/4.23 % (10324)------------------------------
% 20.86/4.24 % (10323)Refutation not found, incomplete strategy
% 20.86/4.24 % (10323)------------------------------
% 20.86/4.24 % (10323)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.86/4.24 % (10323)Termination reason: Refutation not found, incomplete strategy
% 20.86/4.24
% 20.86/4.24
% 20.86/4.24 % (10323)Memory used [KB]: 7803
% 20.86/4.24 % (10323)Time elapsed: 0.045 s
% 20.86/4.24 % (10323)Instructions burned: 147 (million)
% 20.86/4.24 % (10323)------------------------------
% 20.86/4.24 % (10323)------------------------------
% 20.86/4.24 % (10327)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_9790 for (2973ds/569Mi)
% 20.86/4.25 % (10328)ott+1002_1:1_bd=off:cnfonf=off:e2e=on:fd=off:fe=axiom:hud=5:prag=on:sos=on:i=501:si=on:rtra=on_0 on DTF2THF_9790 for (2973ds/501Mi)
% 20.86/4.27 % (10318)Instruction limit reached!
% 20.86/4.27 % (10318)------------------------------
% 20.86/4.27 % (10318)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.86/4.27 % (10318)Termination reason: Unknown
% 20.86/4.27 % (10318)Termination phase: Saturation
% 20.86/4.27
% 20.86/4.27 % (10318)Memory used [KB]: 7931
% 20.86/4.27 % (10318)Time elapsed: 0.184 s
% 20.86/4.27 % (10318)Instructions burned: 595 (million)
% 20.86/4.27 % (10318)------------------------------
% 20.86/4.27 % (10318)------------------------------
% 20.86/4.28 % (10329)lrs+1010_1:3_cnfonf=conj_eager:fsr=off:prag=on:sd=4:sgt=10:ss=axioms:i=562:si=on:rtra=on_0 on DTF2THF_9790 for (2973ds/562Mi)
% 21.32/4.39 % (10328)Refutation not found, incomplete strategy
% 21.32/4.39 % (10328)------------------------------
% 21.32/4.39 % (10328)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.32/4.39 % (10328)Termination reason: Refutation not found, incomplete strategy
% 21.32/4.39
% 21.32/4.39
% 21.32/4.39 % (10328)Memory used [KB]: 11001
% 21.32/4.39 % (10328)Time elapsed: 0.145 s
% 21.32/4.39 % (10328)Instructions burned: 495 (million)
% 21.32/4.39 % (10328)------------------------------
% 21.32/4.39 % (10328)------------------------------
% 21.57/4.40 % (10325)Instruction limit reached!
% 21.57/4.40 % (10325)------------------------------
% 21.57/4.40 % (10325)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.57/4.40 % (10325)Termination reason: Unknown
% 21.57/4.40 % (10325)Termination phase: Saturation
% 21.57/4.40
% 21.57/4.40 % (10325)Memory used [KB]: 9338
% 21.57/4.40 % (10325)Time elapsed: 0.180 s
% 21.57/4.40 % (10325)Instructions burned: 594 (million)
% 21.57/4.40 % (10325)------------------------------
% 21.57/4.40 % (10325)------------------------------
% 21.57/4.40 % (10327)Instruction limit reached!
% 21.57/4.40 % (10327)------------------------------
% 21.57/4.40 % (10327)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.57/4.40 % (10327)Termination reason: Unknown
% 21.57/4.40 % (10327)Termination phase: Saturation
% 21.57/4.40
% 21.57/4.40 % (10327)Memory used [KB]: 7803
% 21.57/4.40 % (10327)Time elapsed: 0.159 s
% 21.57/4.40 % (10327)Instructions burned: 569 (million)
% 21.57/4.40 % (10327)------------------------------
% 21.57/4.40 % (10327)------------------------------
% 21.57/4.40 % (10330)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_9790 for (2972ds/406Mi)
% 21.57/4.41 % (10331)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_9790 for (2972ds/582Mi)
% 21.57/4.41 % (10332)lrs+2_1:1_au=on:bd=off:bsr=unit_only:sd=2:sgt=32:sos=all:ss=axioms:i=456:si=on:rtra=on_0 on DTF2THF_9790 for (2972ds/456Mi)
% 21.57/4.45 % (10329)Instruction limit reached!
% 21.57/4.45 % (10329)------------------------------
% 21.57/4.45 % (10329)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.57/4.45 % (10329)Termination reason: Unknown
% 21.57/4.45 % (10329)Termination phase: Saturation
% 21.57/4.45
% 21.57/4.45 % (10329)Memory used [KB]: 9083
% 21.57/4.45 % (10329)Time elapsed: 0.170 s
% 21.57/4.45 % (10329)Instructions burned: 564 (million)
% 21.57/4.45 % (10329)------------------------------
% 21.57/4.45 % (10329)------------------------------
% 21.57/4.46 % (10333)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_9790 for (2971ds/393Mi)
% 22.20/4.52 % (10330)Instruction limit reached!
% 22.20/4.52 % (10330)------------------------------
% 22.20/4.52 % (10330)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.20/4.52 % (10330)Termination reason: Unknown
% 22.20/4.52 % (10330)Termination phase: Saturation
% 22.20/4.52
% 22.20/4.52 % (10330)Memory used [KB]: 8955
% 22.20/4.52 % (10330)Time elapsed: 0.122 s
% 22.20/4.52 % (10330)Instructions burned: 408 (million)
% 22.20/4.52 % (10330)------------------------------
% 22.20/4.52 % (10330)------------------------------
% 22.20/4.54 % (10334)lrs+1010_1:6_au=on:cnfonf=conj_eager:nwc=10.0:pe=on:prag=on:s2a=on:ss=axioms:st=1.5:i=1335:si=on:rtra=on_0 on DTF2THF_9790 for (2971ds/1335Mi)
% 22.20/4.55 % (10332)Instruction limit reached!
% 22.20/4.55 % (10332)------------------------------
% 22.20/4.55 % (10332)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.20/4.55 % (10332)Termination reason: Unknown
% 22.20/4.55 % (10332)Termination phase: Saturation
% 22.20/4.55
% 22.20/4.55 % (10332)Memory used [KB]: 8315
% 22.20/4.55 % (10332)Time elapsed: 0.137 s
% 22.20/4.55 % (10332)Instructions burned: 458 (million)
% 22.20/4.55 % (10332)------------------------------
% 22.20/4.55 % (10332)------------------------------
% 22.20/4.56 % (10335)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=3373:si=on:rtra=on_0 on DTF2THF_9790 for (2970ds/3373Mi)
% 22.20/4.56 % (10333)Instruction limit reached!
% 22.20/4.56 % (10333)------------------------------
% 22.20/4.56 % (10333)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.20/4.56 % (10333)Termination reason: Unknown
% 22.20/4.56 % (10333)Termination phase: Saturation
% 22.20/4.56
% 22.20/4.56 % (10333)Memory used [KB]: 7803
% 22.20/4.56 % (10333)Time elapsed: 0.107 s
% 22.20/4.56 % (10333)Instructions burned: 394 (million)
% 22.20/4.56 % (10333)------------------------------
% 22.20/4.56 % (10333)------------------------------
% 22.20/4.57 % (10336)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_9790 for (2970ds/474Mi)
% 22.20/4.59 % (10331)Instruction limit reached!
% 22.20/4.59 % (10331)------------------------------
% 22.20/4.59 % (10331)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.20/4.59 % (10331)Termination reason: Unknown
% 22.20/4.59 % (10331)Termination phase: Saturation
% 22.20/4.59
% 22.20/4.59 % (10331)Memory used [KB]: 8955
% 22.20/4.59 % (10331)Time elapsed: 0.181 s
% 22.20/4.59 % (10331)Instructions burned: 585 (million)
% 22.20/4.59 % (10331)------------------------------
% 22.20/4.59 % (10331)------------------------------
% 22.20/4.60 % (10337)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_9790 for (2970ds/157Mi)
% 22.88/4.64 % (10337)Instruction limit reached!
% 22.88/4.64 % (10337)------------------------------
% 22.88/4.64 % (10337)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.88/4.64 % (10337)Termination reason: Unknown
% 22.88/4.64 % (10337)Termination phase: Property scanning
% 22.88/4.64
% 22.88/4.64 % (10337)Memory used [KB]: 2942
% 22.88/4.64 % (10337)Time elapsed: 0.044 s
% 22.88/4.64 % (10337)Instructions burned: 157 (million)
% 22.88/4.64 % (10337)------------------------------
% 22.88/4.64 % (10337)------------------------------
% 22.88/4.65 % (10338)dis+1010_1:1_amm=off:cs=on:kws=precedence:nwc=10.0:piset=all:s2a=on:sac=on:sp=unary_frequency:spb=goal:ss=axioms:st=3.0:i=590:si=on:rtra=on_0 on DTF2THF_9790 for (2970ds/590Mi)
% 22.88/4.65 % (10321)Instruction limit reached!
% 22.88/4.65 % (10321)------------------------------
% 22.88/4.65 % (10321)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.88/4.65 % (10321)Termination reason: Unknown
% 22.88/4.65 % (10321)Termination phase: Saturation
% 22.88/4.65
% 22.88/4.65 % (10321)Memory used [KB]: 10362
% 22.88/4.65 % (10321)Time elapsed: 0.486 s
% 22.88/4.65 % (10321)Instructions burned: 1765 (million)
% 22.88/4.65 % (10321)------------------------------
% 22.88/4.65 % (10321)------------------------------
% 22.88/4.66 % (10339)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_9790 for (2969ds/104Mi)
% 22.88/4.69 % (10326)Instruction limit reached!
% 22.88/4.69 % (10326)------------------------------
% 22.88/4.69 % (10326)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.88/4.69 % (10326)Termination reason: Unknown
% 22.88/4.69 % (10326)Termination phase: Saturation
% 22.88/4.69
% 22.88/4.69 % (10326)Memory used [KB]: 11129
% 22.88/4.69 % (10326)Time elapsed: 0.462 s
% 22.88/4.69 % (10326)Instructions burned: 1512 (million)
% 22.88/4.69 % (10326)------------------------------
% 22.88/4.69 % (10326)------------------------------
% 22.88/4.69 % (10339)Instruction limit reached!
% 22.88/4.69 % (10339)------------------------------
% 22.88/4.69 % (10339)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.88/4.69 % (10339)Termination reason: Unknown
% 22.88/4.69 % (10339)Termination phase: Property scanning
% 22.88/4.69
% 22.88/4.69 % (10339)Memory used [KB]: 2942
% 22.88/4.69 % (10339)Time elapsed: 0.033 s
% 22.88/4.69 % (10339)Instructions burned: 106 (million)
% 22.88/4.69 % (10339)------------------------------
% 22.88/4.69 % (10339)------------------------------
% 24.06/4.70 % (10340)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_9790 for (2969ds/414Mi)
% 24.06/4.70 % (10341)dis+10_1:1_av=off:bsd=on:bsr=unit_only:fd=off:hud=8:nm=16:prag=on:i=715:si=on:rtra=on_0 on DTF2THF_9790 for (2969ds/715Mi)
% 24.06/4.71 % (10336)Instruction limit reached!
% 24.06/4.71 % (10336)------------------------------
% 24.06/4.71 % (10336)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.06/4.71 % (10336)Termination reason: Unknown
% 24.06/4.71 % (10336)Termination phase: Saturation
% 24.06/4.71
% 24.06/4.71 % (10336)Memory used [KB]: 8443
% 24.06/4.71 % (10336)Time elapsed: 0.139 s
% 24.06/4.71 % (10336)Instructions burned: 476 (million)
% 24.06/4.71 % (10336)------------------------------
% 24.06/4.71 % (10336)------------------------------
% 24.06/4.72 % (10342)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=961:si=on:rtra=on_0 on DTF2THF_9790 for (2969ds/961Mi)
% 24.30/4.81 % (10340)Instruction limit reached!
% 24.30/4.81 % (10340)------------------------------
% 24.30/4.81 % (10340)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.30/4.81 % (10340)Termination reason: Unknown
% 24.30/4.81 % (10340)Termination phase: Saturation
% 24.30/4.81
% 24.30/4.81 % (10340)Memory used [KB]: 8699
% 24.30/4.81 % (10340)Time elapsed: 0.115 s
% 24.30/4.81 % (10340)Instructions burned: 417 (million)
% 24.30/4.81 % (10340)------------------------------
% 24.30/4.81 % (10340)------------------------------
% 24.30/4.81 % (10338)Instruction limit reached!
% 24.30/4.81 % (10338)------------------------------
% 24.30/4.81 % (10338)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.30/4.81 % (10338)Termination reason: Unknown
% 24.30/4.81 % (10338)Termination phase: Saturation
% 24.30/4.81
% 24.30/4.81 % (10338)Memory used [KB]: 8187
% 24.30/4.81 % (10338)Time elapsed: 0.166 s
% 24.30/4.81 % (10338)Instructions burned: 590 (million)
% 24.30/4.81 % (10338)------------------------------
% 24.30/4.81 % (10338)------------------------------
% 24.30/4.82 % (10343)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=1213:si=on:rtra=on_0 on DTF2THF_9790 for (2968ds/1213Mi)
% 24.30/4.82 % (10344)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_9790 for (2968ds/1979Mi)
% 24.71/4.92 % (10341)Instruction limit reached!
% 24.71/4.92 % (10341)------------------------------
% 24.71/4.92 % (10341)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.71/4.92 % (10341)Termination reason: Unknown
% 24.71/4.92 % (10341)Termination phase: Saturation
% 24.71/4.92
% 24.71/4.92 % (10341)Memory used [KB]: 4477
% 24.71/4.92 % (10341)Time elapsed: 0.238 s
% 24.71/4.92 % (10341)Instructions burned: 715 (million)
% 24.71/4.92 % (10341)------------------------------
% 24.71/4.92 % (10341)------------------------------
% 24.71/4.93 % (10345)dis+1002_1:1_amm=off:au=on:bsd=on:cbe=off:cnfonf=lazy_gen:sp=unary_frequency:i=481:si=on:rtra=on_0 on DTF2THF_9790 for (2967ds/481Mi)
% 24.71/4.93 % (10334)Instruction limit reached!
% 24.71/4.93 % (10334)------------------------------
% 24.71/4.93 % (10334)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.71/4.93 % (10334)Termination reason: Unknown
% 24.71/4.93 % (10334)Termination phase: Saturation
% 24.71/4.93
% 24.71/4.93 % (10334)Memory used [KB]: 9466
% 24.71/4.93 % (10334)Time elapsed: 0.396 s
% 24.71/4.93 % (10334)Instructions burned: 1336 (million)
% 24.71/4.93 % (10334)------------------------------
% 24.71/4.93 % (10334)------------------------------
% 24.71/4.94 % (10346)dis+10_8:1_apa=on:cnfonf=off:e2e=on:plsq=on:plsqc=1:plsqr=32,1:ss=axioms:i=783:si=on:rtra=on_0 on DTF2THF_9790 for (2966ds/783Mi)
% 24.71/5.01 % (10342)Instruction limit reached!
% 24.71/5.01 % (10342)------------------------------
% 24.71/5.01 % (10342)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.71/5.01 % (10342)Termination reason: Unknown
% 24.71/5.01 % (10342)Termination phase: Saturation
% 24.71/5.01
% 24.71/5.01 % (10342)Memory used [KB]: 9083
% 24.71/5.01 % (10342)Time elapsed: 0.293 s
% 24.71/5.01 % (10342)Instructions burned: 961 (million)
% 24.71/5.01 % (10342)------------------------------
% 24.71/5.01 % (10342)------------------------------
% 24.71/5.02 % (10347)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=432:si=on:rtra=on_0 on DTF2THF_9790 for (2966ds/432Mi)
% 26.79/5.07 % (10345)Instruction limit reached!
% 26.79/5.07 % (10345)------------------------------
% 26.79/5.07 % (10345)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.79/5.07 % (10345)Termination reason: Unknown
% 26.79/5.07 % (10345)Termination phase: Saturation
% 26.79/5.07
% 26.79/5.07 % (10345)Memory used [KB]: 7931
% 26.79/5.07 % (10345)Time elapsed: 0.144 s
% 26.79/5.07 % (10345)Instructions burned: 483 (million)
% 26.79/5.07 % (10345)------------------------------
% 26.79/5.07 % (10345)------------------------------
% 26.79/5.08 % (10348)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=1670:si=on:rtra=on_0 on DTF2THF_9790 for (2965ds/1670Mi)
% 27.37/5.16 % (10347)Instruction limit reached!
% 27.37/5.16 % (10347)------------------------------
% 27.37/5.16 % (10347)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.37/5.16 % (10347)Termination reason: Unknown
% 27.37/5.16 % (10347)Termination phase: Saturation
% 27.37/5.16
% 27.37/5.16 % (10347)Memory used [KB]: 8059
% 27.37/5.16 % (10347)Time elapsed: 0.134 s
% 27.37/5.16 % (10347)Instructions burned: 434 (million)
% 27.37/5.16 % (10347)------------------------------
% 27.37/5.16 % (10347)------------------------------
% 27.37/5.17 % (10349)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_9790 for (2964ds/90Mi)
% 27.37/5.17 % (10346)Instruction limit reached!
% 27.37/5.17 % (10346)------------------------------
% 27.37/5.17 % (10346)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.37/5.17 % (10346)Termination reason: Unknown
% 27.37/5.17 % (10346)Termination phase: Saturation
% 27.37/5.17
% 27.37/5.17 % (10346)Memory used [KB]: 9978
% 27.37/5.17 % (10346)Time elapsed: 0.230 s
% 27.37/5.17 % (10346)Instructions burned: 785 (million)
% 27.37/5.17 % (10346)------------------------------
% 27.37/5.17 % (10346)------------------------------
% 27.37/5.18 % (10350)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_9790 for (2964ds/346Mi)
% 27.37/5.19 % (10343)Instruction limit reached!
% 27.37/5.19 % (10343)------------------------------
% 27.37/5.19 % (10343)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.37/5.19 % (10343)Termination reason: Unknown
% 27.37/5.19 % (10343)Termination phase: Saturation
% 27.37/5.19
% 27.37/5.19 % (10343)Memory used [KB]: 11257
% 27.37/5.19 % (10343)Time elapsed: 0.367 s
% 27.37/5.19 % (10343)Instructions burned: 1214 (million)
% 27.37/5.19 % (10343)------------------------------
% 27.37/5.19 % (10343)------------------------------
% 27.37/5.19 % (10349)Instruction limit reached!
% 27.37/5.19 % (10349)------------------------------
% 27.37/5.19 % (10349)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.37/5.19 % (10349)Termination reason: Unknown
% 27.37/5.19 % (10349)Termination phase: Preprocessing 3
% 27.37/5.19
% 27.37/5.19 % (10349)Memory used [KB]: 2686
% 27.37/5.19 % (10349)Time elapsed: 0.029 s
% 27.37/5.19 % (10349)Instructions burned: 91 (million)
% 27.37/5.19 % (10349)------------------------------
% 27.37/5.19 % (10349)------------------------------
% 27.37/5.20 % (10351)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=401:si=on:rtra=on_0 on DTF2THF_9790 for (2964ds/401Mi)
% 27.91/5.20 % (10352)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on DTF2THF_9790 for (2964ds/6454Mi)
% 27.91/5.28 % (10350)Instruction limit reached!
% 27.91/5.28 % (10350)------------------------------
% 27.91/5.28 % (10350)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.91/5.28 % (10350)Termination reason: Unknown
% 27.91/5.28 % (10350)Termination phase: Saturation
% 27.91/5.28
% 27.91/5.28 % (10350)Memory used [KB]: 7931
% 27.91/5.28 % (10350)Time elapsed: 0.105 s
% 27.91/5.28 % (10350)Instructions burned: 348 (million)
% 27.91/5.28 % (10350)------------------------------
% 27.91/5.28 % (10350)------------------------------
% 27.91/5.29 % (10353)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:kws=arity:prag=on:i=283:si=on:rtra=on_0 on DTF2THF_9790 for (2963ds/283Mi)
% 28.31/5.31 % (10351)Instruction limit reached!
% 28.31/5.31 % (10351)------------------------------
% 28.31/5.31 % (10351)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.31/5.31 % (10351)Termination reason: Unknown
% 28.31/5.31 % (10351)Termination phase: Saturation
% 28.31/5.31
% 28.31/5.31 % (10351)Memory used [KB]: 9083
% 28.31/5.31 % (10351)Time elapsed: 0.113 s
% 28.31/5.31 % (10351)Instructions burned: 402 (million)
% 28.31/5.31 % (10351)------------------------------
% 28.31/5.31 % (10351)------------------------------
% 28.31/5.32 % (10354)ott+10_1:1_aac=none:apa=on:au=on:cnfonf=off:ntd=on:nwc=12.0:sos=on:i=865:si=on:rtra=on_0 on DTF2THF_9790 for (2963ds/865Mi)
% 28.31/5.38 % (10353)Instruction limit reached!
% 28.31/5.38 % (10353)------------------------------
% 28.31/5.38 % (10353)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.31/5.38 % (10353)Termination reason: Unknown
% 28.31/5.38 % (10353)Termination phase: Saturation
% 28.31/5.38
% 28.31/5.38 % (10353)Memory used [KB]: 8187
% 28.31/5.38 % (10353)Time elapsed: 0.086 s
% 28.31/5.38 % (10353)Instructions burned: 284 (million)
% 28.31/5.38 % (10353)------------------------------
% 28.31/5.38 % (10353)------------------------------
% 28.31/5.39 % (10355)lrs+1002_3:4_au=on:av=off:cnfonf=off:fd=off:fsr=off:ins=2:sd=1:sos=on:ss=axioms:i=4528:si=on:rtra=on_0 on DTF2THF_9790 for (2962ds/4528Mi)
% 28.83/5.42 % (10355)Refutation not found, incomplete strategy
% 28.83/5.42 % (10355)------------------------------
% 28.83/5.42 % (10355)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.83/5.42 % (10355)Termination reason: Refutation not found, incomplete strategy
% 28.83/5.42
% 28.83/5.42
% 28.83/5.42 % (10355)Memory used [KB]: 2814
% 28.83/5.42 % (10355)Time elapsed: 0.032 s
% 28.83/5.42 % (10355)Instructions burned: 98 (million)
% 28.83/5.42 % (10355)------------------------------
% 28.83/5.42 % (10355)------------------------------
% 28.83/5.42 % (10344)Instruction limit reached!
% 28.83/5.42 % (10344)------------------------------
% 28.83/5.42 % (10344)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.83/5.42 % (10344)Termination reason: Unknown
% 28.83/5.42 % (10344)Termination phase: Saturation
% 28.83/5.42
% 28.83/5.42 % (10344)Memory used [KB]: 10106
% 28.83/5.42 % (10344)Time elapsed: 0.598 s
% 28.83/5.42 % (10344)Instructions burned: 1980 (million)
% 28.83/5.42 % (10344)------------------------------
% 28.83/5.42 % (10344)------------------------------
% 28.83/5.43 % (10356)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=1001:si=on:rtra=on_0 on DTF2THF_9790 for (2962ds/1001Mi)
% 28.83/5.43 % (10357)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on DTF2THF_9790 for (2962ds/102Mi)
% 28.83/5.46 % (10357)Instruction limit reached!
% 28.83/5.46 % (10357)------------------------------
% 28.83/5.46 % (10357)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.83/5.46 % (10357)Termination reason: Unknown
% 28.83/5.46 % (10357)Termination phase: Property scanning
% 28.83/5.46
% 28.83/5.46 % (10357)Memory used [KB]: 2686
% 28.83/5.46 % (10357)Time elapsed: 0.029 s
% 28.83/5.46 % (10357)Instructions burned: 105 (million)
% 28.83/5.46 % (10357)------------------------------
% 28.83/5.46 % (10357)------------------------------
% 28.83/5.47 % (10358)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on DTF2THF_9790 for (2961ds/952Mi)
% 29.17/5.55 % (10335)Instruction limit reached!
% 29.17/5.55 % (10335)------------------------------
% 29.17/5.55 % (10335)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.17/5.55 % (10335)Termination reason: Unknown
% 29.17/5.55 % (10335)Termination phase: Saturation
% 29.17/5.55
% 29.17/5.55 % (10335)Memory used [KB]: 11513
% 29.17/5.55 % (10335)Time elapsed: 0.993 s
% 29.17/5.55 % (10335)Instructions burned: 3375 (million)
% 29.17/5.55 % (10335)------------------------------
% 29.17/5.55 % (10335)------------------------------
% 29.17/5.56 % (10359)lrs+1010_1:1024_add=large:c=on:cbe=off:cnfonf=lazy_gen:fde=none:nm=30:piset=and:sac=on:uhcvi=on:i=578:si=on:rtra=on_0 on DTF2THF_9790 for (2960ds/578Mi)
% 29.17/5.56 % (10348)Instruction limit reached!
% 29.17/5.56 % (10348)------------------------------
% 29.17/5.56 % (10348)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.17/5.56 % (10348)Termination reason: Unknown
% 29.17/5.56 % (10348)Termination phase: Saturation
% 29.17/5.56
% 29.17/5.56 % (10348)Memory used [KB]: 11769
% 29.17/5.56 % (10348)Time elapsed: 0.481 s
% 29.17/5.56 % (10348)Instructions burned: 1670 (million)
% 29.17/5.56 % (10348)------------------------------
% 29.17/5.56 % (10348)------------------------------
% 29.17/5.57 % (10354)Instruction limit reached!
% 29.17/5.57 % (10354)------------------------------
% 29.17/5.57 % (10354)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.17/5.57 % (10354)Termination reason: Unknown
% 29.17/5.57 % (10354)Termination phase: Saturation
% 29.17/5.57
% 29.17/5.57 % (10354)Memory used [KB]: 10874
% 29.17/5.57 % (10354)Time elapsed: 0.252 s
% 29.17/5.57 % (10354)Instructions burned: 866 (million)
% 29.17/5.57 % (10354)------------------------------
% 29.17/5.57 % (10354)------------------------------
% 29.17/5.57 % (10360)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on DTF2THF_9790 for (2960ds/643Mi)
% 29.17/5.58 % (10361)lrs+1010_1:1_cnfonf=off:ntd=on:nwc=3.0:s2a=on:sp=const_frequency:i=865:si=on:rtra=on_0 on DTF2THF_9790 for (2960ds/865Mi)
% 30.16/5.72 % (10356)Instruction limit reached!
% 30.16/5.72 % (10356)------------------------------
% 30.16/5.72 % (10356)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.16/5.72 % (10356)Termination reason: Unknown
% 30.16/5.72 % (10356)Termination phase: Saturation
% 30.16/5.72
% 30.16/5.72 % (10356)Memory used [KB]: 9210
% 30.16/5.72 % (10356)Time elapsed: 0.315 s
% 30.16/5.72 % (10356)Instructions burned: 1003 (million)
% 30.16/5.72 % (10356)------------------------------
% 30.16/5.72 % (10356)------------------------------
% 30.16/5.73 % (10359)Instruction limit reached!
% 30.16/5.73 % (10359)------------------------------
% 30.16/5.73 % (10359)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.16/5.73 % (10359)Termination reason: Unknown
% 30.16/5.73 % (10359)Termination phase: Saturation
% 30.16/5.73
% 30.16/5.73 % (10359)Memory used [KB]: 9338
% 30.16/5.73 % (10359)Time elapsed: 0.168 s
% 30.16/5.73 % (10359)Instructions burned: 581 (million)
% 30.16/5.73 % (10359)------------------------------
% 30.16/5.73 % (10359)------------------------------
% 30.16/5.73 % (10362)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on DTF2THF_9790 for (2959ds/1174Mi)
% 30.16/5.74 % (10363)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=644:si=on:rtra=on_0 on DTF2THF_9790 for (2958ds/644Mi)
% 30.16/5.75 % (10360)Instruction limit reached!
% 30.16/5.75 % (10360)------------------------------
% 30.16/5.75 % (10360)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.16/5.75 % (10360)Termination reason: Unknown
% 30.16/5.75 % (10360)Termination phase: Saturation
% 30.16/5.75
% 30.16/5.75 % (10360)Memory used [KB]: 11001
% 30.16/5.75 % (10360)Time elapsed: 0.186 s
% 30.16/5.75 % (10360)Instructions burned: 645 (million)
% 30.16/5.75 % (10360)------------------------------
% 30.16/5.75 % (10360)------------------------------
% 30.16/5.76 % (10358)Instruction limit reached!
% 30.16/5.76 % (10358)------------------------------
% 30.16/5.76 % (10358)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.16/5.76 % (10358)Termination reason: Unknown
% 30.16/5.76 % (10358)Termination phase: Saturation
% 30.16/5.76
% 30.16/5.76 % (10358)Memory used [KB]: 10618
% 30.16/5.76 % (10358)Time elapsed: 0.290 s
% 30.16/5.76 % (10358)Instructions burned: 952 (million)
% 30.16/5.76 % (10358)------------------------------
% 30.16/5.76 % (10358)------------------------------
% 30.16/5.76 % (10364)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on DTF2THF_9790 for (2958ds/1201Mi)
% 30.16/5.77 % (10365)lrs+1666_1:64_cnfonf=lazy_simp:hud=5:plsq=on:plsql=on:plsqr=152565,524288:tnu=2:i=1046:si=on:rtra=on_0 on DTF2THF_9790 for (2958ds/1046Mi)
% 31.24/5.85 % (10361)Instruction limit reached!
% 31.24/5.85 % (10361)------------------------------
% 31.24/5.85 % (10361)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.24/5.85 % (10361)Termination reason: Unknown
% 31.24/5.85 % (10361)Termination phase: Saturation
% 31.24/5.85
% 31.24/5.85 % (10361)Memory used [KB]: 10618
% 31.24/5.85 % (10361)Time elapsed: 0.267 s
% 31.24/5.85 % (10361)Instructions burned: 866 (million)
% 31.24/5.85 % (10361)------------------------------
% 31.24/5.85 % (10361)------------------------------
% 31.24/5.86 % (10366)lrs+1010_1:1_c=on:cnfonf=lazy_simp:fsr=off:hud=5:kws=arity:nm=32:plsq=on:plsqc=1:plsqr=642,29:prag=on:i=222:si=on:rtra=on_0 on DTF2THF_9790 for (2957ds/222Mi)
% 31.63/5.92 % (10366)Instruction limit reached!
% 31.63/5.92 % (10366)------------------------------
% 31.63/5.92 % (10366)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.63/5.92 % (10366)Termination reason: Unknown
% 31.63/5.92 % (10366)Termination phase: Saturation
% 31.63/5.92
% 31.63/5.92 % (10366)Memory used [KB]: 7547
% 31.63/5.92 % (10366)Time elapsed: 0.063 s
% 31.63/5.92 % (10366)Instructions burned: 222 (million)
% 31.63/5.92 % (10366)------------------------------
% 31.63/5.92 % (10366)------------------------------
% 31.63/5.93 % (10367)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_9790 for (2957ds/68Mi)
% 31.63/5.93 % (10363)Instruction limit reached!
% 31.63/5.93 % (10363)------------------------------
% 31.63/5.93 % (10363)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.63/5.93 % (10363)Termination reason: Unknown
% 31.63/5.93 % (10363)Termination phase: Saturation
% 31.63/5.93
% 31.63/5.93 % (10363)Memory used [KB]: 11641
% 31.63/5.93 % (10363)Time elapsed: 0.193 s
% 31.63/5.93 % (10363)Instructions burned: 644 (million)
% 31.63/5.93 % (10363)------------------------------
% 31.63/5.93 % (10363)------------------------------
% 31.63/5.94 % (10368)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=454:si=on:rtra=on_0 on DTF2THF_9790 for (2956ds/454Mi)
% 31.63/5.94 % (10308)Instruction limit reached!
% 31.63/5.94 % (10308)------------------------------
% 31.63/5.94 % (10308)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.63/5.94 % (10308)Termination reason: Unknown
% 31.63/5.94 % (10308)Termination phase: Saturation
% 31.63/5.94
% 31.63/5.94 % (10308)Memory used [KB]: 16502
% 31.63/5.94 % (10308)Time elapsed: 2.533 s
% 31.63/5.94 % (10308)Instructions burned: 8252 (million)
% 31.63/5.94 % (10308)------------------------------
% 31.63/5.94 % (10308)------------------------------
% 31.63/5.95 % (10367)Instruction limit reached!
% 31.63/5.95 % (10367)------------------------------
% 31.63/5.95 % (10367)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.63/5.95 % (10367)Termination reason: Unknown
% 31.63/5.95 % (10367)Termination phase: SInE selection
% 31.63/5.95
% 31.63/5.95 % (10367)Memory used [KB]: 2046
% 31.63/5.95 % (10367)Time elapsed: 0.022 s
% 31.63/5.95 % (10367)Instructions burned: 70 (million)
% 31.63/5.95 % (10367)------------------------------
% 31.63/5.95 % (10367)------------------------------
% 31.63/5.95 % (10369)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on DTF2THF_9790 for (2956ds/360Mi)
% 31.63/5.96 % (10370)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_9790 for (2956ds/157Mi)
% 31.63/6.00 % (10370)Instruction limit reached!
% 31.63/6.00 % (10370)------------------------------
% 31.63/6.00 % (10370)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.63/6.00 % (10370)Termination reason: Unknown
% 31.63/6.00 % (10370)Termination phase: Property scanning
% 31.63/6.00
% 31.63/6.00 % (10370)Memory used [KB]: 2942
% 31.63/6.00 % (10370)Time elapsed: 0.046 s
% 31.63/6.00 % (10370)Instructions burned: 159 (million)
% 31.63/6.00 % (10370)------------------------------
% 31.63/6.00 % (10370)------------------------------
% 31.63/6.01 % (10371)ott+1004_1:24_anc=none:cbe=off:cnfonf=lazy_not_gen:fe=off:piset=not:prag=on:rp=on:i=5061:si=on:rtra=on_0 on DTF2THF_9790 for (2956ds/5061Mi)
% 33.81/6.05 % (10369)Instruction limit reached!
% 33.81/6.05 % (10369)------------------------------
% 33.81/6.05 % (10369)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.81/6.05 % (10369)Termination reason: Unknown
% 33.81/6.05 % (10369)Termination phase: Saturation
% 33.81/6.05
% 33.81/6.05 % (10369)Memory used [KB]: 8699
% 33.81/6.05 % (10369)Time elapsed: 0.101 s
% 33.81/6.05 % (10369)Instructions burned: 363 (million)
% 33.81/6.05 % (10369)------------------------------
% 33.81/6.05 % (10369)------------------------------
% 33.81/6.06 % (10372)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=2401:si=on:rtra=on_0 on DTF2THF_9790 for (2955ds/2401Mi)
% 33.81/6.07 % (10368)Instruction limit reached!
% 33.81/6.07 % (10368)------------------------------
% 33.81/6.07 % (10368)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.81/6.07 % (10368)Termination reason: Unknown
% 33.81/6.07 % (10368)Termination phase: Saturation
% 33.81/6.07
% 33.81/6.07 % (10368)Memory used [KB]: 13304
% 33.81/6.07 % (10368)Time elapsed: 0.131 s
% 33.81/6.07 % (10368)Instructions burned: 456 (million)
% 33.81/6.07 % (10368)------------------------------
% 33.81/6.07 % (10368)------------------------------
% 33.81/6.07 % (10365)Instruction limit reached!
% 33.81/6.07 % (10365)------------------------------
% 33.81/6.07 % (10365)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.81/6.07 % (10365)Termination reason: Unknown
% 33.81/6.07 % (10365)Termination phase: Saturation
% 33.81/6.07
% 33.81/6.07 % (10365)Memory used [KB]: 9722
% 33.81/6.07 % (10365)Time elapsed: 0.305 s
% 33.81/6.07 % (10365)Instructions burned: 1047 (million)
% 33.81/6.07 % (10365)------------------------------
% 33.81/6.07 % (10365)------------------------------
% 33.81/6.08 % (10373)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=5798:si=on:rtra=on_0 on DTF2THF_9790 for (2955ds/5798Mi)
% 33.81/6.08 % (10374)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_9790 for (2955ds/346Mi)
% 33.81/6.08 % (10362)Instruction limit reached!
% 33.81/6.08 % (10362)------------------------------
% 33.81/6.08 % (10362)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.81/6.08 % (10362)Termination reason: Unknown
% 33.81/6.08 % (10362)Termination phase: Saturation
% 33.81/6.08
% 33.81/6.08 % (10362)Memory used [KB]: 11897
% 33.81/6.08 % (10362)Time elapsed: 0.354 s
% 33.81/6.08 % (10362)Instructions burned: 1174 (million)
% 33.81/6.08 % (10362)------------------------------
% 33.81/6.08 % (10362)------------------------------
% 33.81/6.09 % (10375)lrs+1002_1:1_av=off:bd=off:bet=on:e2e=on:fde=unused:fe=off:plsq=on:prag=on:sos=on:i=1321:si=on:rtra=on_0 on DTF2THF_9790 for (2955ds/1321Mi)
% 33.81/6.10 % (10364)Instruction limit reached!
% 33.81/6.10 % (10364)------------------------------
% 33.81/6.10 % (10364)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.81/6.10 % (10364)Termination reason: Unknown
% 33.81/6.10 % (10364)Termination phase: Saturation
% 33.81/6.10
% 33.81/6.10 % (10364)Memory used [KB]: 9850
% 33.81/6.10 % (10364)Time elapsed: 0.339 s
% 33.81/6.10 % (10364)Instructions burned: 1203 (million)
% 33.81/6.10 % (10364)------------------------------
% 33.81/6.10 % (10364)------------------------------
% 33.81/6.11 % (10376)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:i=1312:si=on:rtra=on_0 on DTF2THF_9790 for (2955ds/1312Mi)
% 34.23/6.18 % (10374)Instruction limit reached!
% 34.23/6.18 % (10374)------------------------------
% 34.23/6.18 % (10374)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.23/6.18 % (10374)Termination reason: Unknown
% 34.23/6.18 % (10374)Termination phase: Saturation
% 34.23/6.18
% 34.23/6.18 % (10374)Memory used [KB]: 7931
% 34.23/6.18 % (10374)Time elapsed: 0.102 s
% 34.23/6.18 % (10374)Instructions burned: 348 (million)
% 34.23/6.18 % (10374)------------------------------
% 34.23/6.18 % (10374)------------------------------
% 34.23/6.19 % (10377)ott+2_8:1_add=large:c=on:cnfonf=off:e2e=on:er=filter:hud=5:plsq=on:plsqr=1,1:ss=axioms:i=672:si=on:rtra=on_0 on DTF2THF_9790 for (2954ds/672Mi)
% 34.63/6.40 % (10377)Instruction limit reached!
% 34.63/6.40 % (10377)------------------------------
% 34.63/6.40 % (10377)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.63/6.40 % (10377)Termination reason: Unknown
% 34.63/6.40 % (10377)Termination phase: Saturation
% 34.63/6.40
% 34.63/6.40 % (10377)Memory used [KB]: 9083
% 34.63/6.40 % (10377)Time elapsed: 0.208 s
% 34.63/6.40 % (10377)Instructions burned: 674 (million)
% 34.63/6.40 % (10377)------------------------------
% 34.63/6.40 % (10377)------------------------------
% 34.63/6.41 % (10378)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=1897:si=on:rtra=on_0 on DTF2THF_9790 for (2952ds/1897Mi)
% 34.63/6.46 % (10378)Refutation not found, incomplete strategy
% 34.63/6.46 % (10378)------------------------------
% 34.63/6.46 % (10378)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.63/6.46 % (10378)Termination reason: Refutation not found, incomplete strategy
% 34.63/6.46
% 34.63/6.46
% 34.63/6.46 % (10378)Memory used [KB]: 7931
% 34.63/6.46 % (10378)Time elapsed: 0.051 s
% 34.63/6.46 % (10378)Instructions burned: 158 (million)
% 34.63/6.46 % (10378)------------------------------
% 34.63/6.46 % (10378)------------------------------
% 34.63/6.47 % (10379)lrs+10_1:40_av=off:fde=unused:ntd=on:plsq=on:plsqc=2:plsqr=411915,1048576:sp=unary_frequency:tgt=full:i=1202:si=on:rtra=on_0 on DTF2THF_9790 for (2951ds/1202Mi)
% 34.63/6.47 % (10375)Instruction limit reached!
% 34.63/6.47 % (10375)------------------------------
% 34.63/6.47 % (10375)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.63/6.47 % (10375)Termination reason: Unknown
% 34.63/6.47 % (10375)Termination phase: Saturation
% 34.63/6.47
% 34.63/6.47 % (10375)Memory used [KB]: 8827
% 34.63/6.47 % (10375)Time elapsed: 0.381 s
% 34.63/6.47 % (10375)Instructions burned: 1323 (million)
% 34.63/6.47 % (10375)------------------------------
% 34.63/6.47 % (10375)------------------------------
% 34.63/6.48 % (10380)dis+21_1:1_au=on:cnfonf=lazy_pi_sigma_gen:hfsq=on:hfsqc=40:hfsqr=8,1:ntd=on:sos=on:sp=occurrence:ss=axioms:i=1493:si=on:rtra=on_0 on DTF2THF_9790 for (2951ds/1493Mi)
% 34.63/6.49 % (10376)Instruction limit reached!
% 34.63/6.49 % (10376)------------------------------
% 34.63/6.49 % (10376)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.63/6.49 % (10376)Termination reason: Unknown
% 34.63/6.49 % (10376)Termination phase: Saturation
% 34.63/6.49
% 34.63/6.49 % (10376)Memory used [KB]: 9850
% 34.63/6.49 % (10376)Time elapsed: 0.378 s
% 34.63/6.49 % (10376)Instructions burned: 1313 (million)
% 34.63/6.49 % (10376)------------------------------
% 34.63/6.49 % (10376)------------------------------
% 35.78/6.50 % (10381)dis+1010_3:1_av=off:fde=unused:hud=10:nwc=10.0:s2a=on:ss=axioms:i=7679:si=on:rtra=on_0 on DTF2THF_9790 for (2951ds/7679Mi)
% 35.78/6.53 % (10380)Refutation not found, incomplete strategy
% 35.78/6.53 % (10380)------------------------------
% 35.78/6.53 % (10380)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.78/6.53 % (10380)Termination reason: Refutation not found, incomplete strategy
% 35.78/6.53
% 35.78/6.53
% 35.78/6.53 % (10380)Memory used [KB]: 7547
% 35.78/6.53 % (10380)Time elapsed: 0.050 s
% 35.78/6.53 % (10380)Instructions burned: 180 (million)
% 35.78/6.53 % (10380)------------------------------
% 35.78/6.53 % (10380)------------------------------
% 35.78/6.54 % (10382)lrs+2_1:1024_anc=all:cnfonf=off:cs=on:e2e=on:nm=20:s2at=1.5:slsq=on:slsqr=1,2:spb=goal:i=340:si=on:rtra=on_0 on DTF2THF_9790 for (2951ds/340Mi)
% 35.94/6.64 % (10382)Instruction limit reached!
% 35.94/6.64 % (10382)------------------------------
% 35.94/6.64 % (10382)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.94/6.64 % (10382)Termination reason: Unknown
% 35.94/6.64 % (10382)Termination phase: Saturation
% 35.94/6.64
% 35.94/6.64 % (10382)Memory used [KB]: 8827
% 35.94/6.64 % (10382)Time elapsed: 0.097 s
% 35.94/6.64 % (10382)Instructions burned: 342 (million)
% 35.94/6.64 % (10382)------------------------------
% 35.94/6.64 % (10382)------------------------------
% 35.94/6.65 % (10383)dis+1002_1:1_acc=model:au=on:nwc=5.0:sd=5:ss=axioms:st=2.5:i=3672:si=on:rtra=on_0 on DTF2THF_9790 for (2950ds/3672Mi)
% 36.15/6.79 % (10372)Instruction limit reached!
% 36.15/6.79 % (10372)------------------------------
% 36.15/6.79 % (10372)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.15/6.79 % (10372)Termination reason: Unknown
% 36.15/6.79 % (10372)Termination phase: Saturation
% 36.15/6.79
% 36.15/6.79 % (10372)Memory used [KB]: 7803
% 36.15/6.79 % (10372)Time elapsed: 0.727 s
% 36.15/6.79 % (10372)Instructions burned: 2404 (million)
% 36.15/6.79 % (10372)------------------------------
% 36.15/6.79 % (10372)------------------------------
% 37.00/6.80 % (10384)dis-1002_3:1_acc=model:bd=off:bsd=on:bsdmm=1:cnfonf=lazy_not_be_gen:fd=off:fe=off:ntd=on:nwc=10.0:piset=equals:plsq=on:plsqc=1:plsqr=32,1:sp=const_max:uhcvi=on:i=1535:si=on:rtra=on_0 on DTF2THF_9790 for (2948ds/1535Mi)
% 37.00/6.83 % (10379)Instruction limit reached!
% 37.00/6.83 % (10379)------------------------------
% 37.00/6.83 % (10379)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.00/6.83 % (10379)Termination reason: Unknown
% 37.00/6.83 % (10379)Termination phase: Saturation
% 37.00/6.83
% 37.00/6.83 % (10379)Memory used [KB]: 6780
% 37.00/6.83 % (10379)Time elapsed: 0.365 s
% 37.00/6.83 % (10379)Instructions burned: 1202 (million)
% 37.00/6.83 % (10379)------------------------------
% 37.00/6.83 % (10379)------------------------------
% 37.00/6.84 % (10385)dis+10_16:1_hud=1:plsq=on:plsqc=1:plsqr=32,1:prag=on:sd=1:sgt=64:ss=axioms:i=4637:si=on:rtra=on_0 on DTF2THF_9790 for (2948ds/4637Mi)
% 37.48/7.00 % (10352)Instruction limit reached!
% 37.48/7.00 % (10352)------------------------------
% 37.48/7.00 % (10352)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.48/7.00 % (10352)Termination reason: Unknown
% 37.48/7.00 % (10352)Termination phase: Saturation
% 37.48/7.00
% 37.48/7.00 % (10352)Memory used [KB]: 11001
% 37.48/7.00 % (10352)Time elapsed: 1.797 s
% 37.48/7.00 % (10352)Instructions burned: 6454 (million)
% 37.48/7.00 % (10352)------------------------------
% 37.48/7.00 % (10352)------------------------------
% 37.48/7.02 % (10386)lrs+10_1:1_fde=unused:prag=on:sd=2:sgt=32:ss=axioms:i=3174:si=on:rtra=on_0 on DTF2THF_9790 for (2946ds/3174Mi)
% 41.90/7.25 % (10384)Instruction limit reached!
% 41.90/7.25 % (10384)------------------------------
% 41.90/7.25 % (10384)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.90/7.25 % (10384)Termination reason: Unknown
% 41.90/7.25 % (10384)Termination phase: Saturation
% 41.90/7.25
% 41.90/7.25 % (10384)Memory used [KB]: 12537
% 41.90/7.25 % (10384)Time elapsed: 0.452 s
% 41.90/7.25 % (10384)Instructions burned: 1537 (million)
% 41.90/7.25 % (10384)------------------------------
% 41.90/7.25 % (10384)------------------------------
% 41.90/7.26 % (10387)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_9790 for (2943ds/307Mi)
% 42.47/7.35 % (10387)Instruction limit reached!
% 42.47/7.35 % (10387)------------------------------
% 42.47/7.35 % (10387)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.47/7.35 % (10387)Termination reason: Unknown
% 42.47/7.35 % (10387)Termination phase: Saturation
% 42.47/7.35
% 42.47/7.35 % (10387)Memory used [KB]: 8443
% 42.47/7.35 % (10387)Time elapsed: 0.085 s
% 42.47/7.35 % (10387)Instructions burned: 309 (million)
% 42.47/7.35 % (10387)------------------------------
% 42.47/7.35 % (10387)------------------------------
% 42.47/7.36 % (10388)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=3619:si=on:rtra=on_0 on DTF2THF_9790 for (2942ds/3619Mi)
% 43.07/7.43 % (10383)Instruction limit reached!
% 43.07/7.43 % (10383)------------------------------
% 43.07/7.43 % (10383)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.07/7.43 % (10383)Termination reason: Unknown
% 43.07/7.43 % (10383)Termination phase: Saturation
% 43.07/7.43
% 43.07/7.43 % (10383)Memory used [KB]: 9466
% 43.07/7.43 % (10383)Time elapsed: 0.779 s
% 43.07/7.43 % (10383)Instructions burned: 3676 (million)
% 43.07/7.43 % (10383)------------------------------
% 43.07/7.43 % (10383)------------------------------
% 43.07/7.44 % (10389)lrs+1002_1:1_au=on:cbe=off:fde=none:ins=1:sp=const_max:i=2325:si=on:rtra=on_0 on DTF2THF_9790 for (2941ds/2325Mi)
% 43.07/7.46 % (10371)Instruction limit reached!
% 43.07/7.46 % (10371)------------------------------
% 43.07/7.46 % (10371)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.07/7.46 % (10371)Termination reason: Unknown
% 43.07/7.46 % (10371)Termination phase: Saturation
% 43.07/7.46
% 43.07/7.46 % (10371)Memory used [KB]: 13816
% 43.07/7.46 % (10371)Time elapsed: 1.452 s
% 43.07/7.46 % (10371)Instructions burned: 5062 (million)
% 43.07/7.46 % (10371)------------------------------
% 43.07/7.46 % (10371)------------------------------
% 43.07/7.47 % (10390)dis+1002_1:1_au=on:sac=on:sd=5:slsq=on:slsqr=1,4:ss=axioms:st=2.0:i=2341:si=on:rtra=on_0 on DTF2THF_9790 for (2941ds/2341Mi)
% 44.07/7.79 % (10373)Instruction limit reached!
% 44.07/7.79 % (10373)------------------------------
% 44.07/7.79 % (10373)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.07/7.79 % (10373)Termination reason: Unknown
% 44.07/7.79 % (10373)Termination phase: Saturation
% 44.07/7.79
% 44.07/7.79 % (10373)Memory used [KB]: 14072
% 44.07/7.79 % (10373)Time elapsed: 1.709 s
% 44.07/7.79 % (10373)Instructions burned: 5799 (million)
% 44.07/7.79 % (10373)------------------------------
% 44.07/7.79 % (10373)------------------------------
% 44.07/7.80 % (10391)lrs+1010_1:16_apa=on:bsd=on:cnfonf=off:hud=10:sac=on:sos=on:ss=axioms:i=7257:si=on:rtra=on_0 on DTF2THF_9790 for (2938ds/7257Mi)
% 44.37/7.85 % (10391)Refutation not found, incomplete strategy
% 44.37/7.85 % (10391)------------------------------
% 44.37/7.85 % (10391)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.37/7.85 % (10391)Termination reason: Refutation not found, incomplete strategy
% 44.37/7.85
% 44.37/7.85
% 44.37/7.85 % (10391)Memory used [KB]: 8059
% 44.37/7.85 % (10391)Time elapsed: 0.052 s
% 44.37/7.85 % (10391)Instructions burned: 159 (million)
% 44.37/7.85 % (10391)------------------------------
% 44.37/7.85 % (10391)------------------------------
% 44.37/7.86 % (10392)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=3710:si=on:rtra=on_0 on DTF2THF_9790 for (2937ds/3710Mi)
% 44.63/7.96 % (10389)Refutation not found, non-redundant clauses discarded% (10389)------------------------------
% 44.63/7.96 % (10389)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.63/7.96 % (10389)Termination reason: Refutation not found, non-redundant clauses discarded
% 44.63/7.96
% 44.63/7.96 % (10389)Memory used [KB]: 11641
% 44.63/7.96 % (10389)Time elapsed: 0.522 s
% 44.63/7.96 % (10389)Instructions burned: 1762 (million)
% 44.63/7.96 % (10389)------------------------------
% 44.63/7.96 % (10389)------------------------------
% 44.63/7.97 % (10393)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=326:si=on:rtra=on_0 on DTF2THF_9790 for (2936ds/326Mi)
% 44.63/7.97 % (10386)Instruction limit reached!
% 44.63/7.97 % (10386)------------------------------
% 44.63/7.97 % (10386)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.63/7.97 % (10386)Termination reason: Unknown
% 44.63/7.97 % (10386)Termination phase: Saturation
% 44.63/7.97
% 44.63/7.97 % (10386)Memory used [KB]: 13944
% 44.63/7.97 % (10386)Time elapsed: 0.952 s
% 44.63/7.97 % (10386)Instructions burned: 3174 (million)
% 44.63/7.97 % (10386)------------------------------
% 44.63/7.97 % (10386)------------------------------
% 44.63/7.98 % (10394)lrs+1010_1:64_au=on:c=on:e2e=on:flr=on:hfsq=on:hfsql=off:hfsqr=4,1:ins=1:ntd=on:sp=occurrence:i=1100:si=on:rtra=on_0 on DTF2THF_9790 for (2936ds/1100Mi)
% 47.85/8.07 % (10393)Instruction limit reached!
% 47.85/8.07 % (10393)------------------------------
% 47.85/8.07 % (10393)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.85/8.07 % (10393)Termination reason: Unknown
% 47.85/8.07 % (10393)Termination phase: Saturation
% 47.85/8.07
% 47.85/8.07 % (10393)Memory used [KB]: 7931
% 47.85/8.07 % (10393)Time elapsed: 0.102 s
% 47.85/8.07 % (10393)Instructions burned: 326 (million)
% 47.85/8.07 % (10393)------------------------------
% 47.85/8.07 % (10393)------------------------------
% 47.85/8.08 % (10395)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_9790 for (2935ds/406Mi)
% 47.85/8.11 % (10390)Instruction limit reached!
% 47.85/8.11 % (10390)------------------------------
% 47.85/8.11 % (10390)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.85/8.11 % (10390)Termination reason: Unknown
% 47.85/8.11 % (10390)Termination phase: Saturation
% 47.85/8.11
% 47.85/8.11 % (10390)Memory used [KB]: 8443
% 47.85/8.11 % (10390)Time elapsed: 0.636 s
% 47.85/8.11 % (10390)Instructions burned: 2345 (million)
% 47.85/8.11 % (10390)------------------------------
% 47.85/8.11 % (10390)------------------------------
% 47.85/8.12 % (10396)dis+1010_1:1_aac=none:bd=preordered:e2e=on:fde=none:fe=axiom:nm=16:nwc=10.0:prag=on:i=1871:si=on:rtra=on_0 on DTF2THF_9790 for (2935ds/1871Mi)
% 48.90/8.20 % (10395)Instruction limit reached!
% 48.90/8.20 % (10395)------------------------------
% 48.90/8.20 % (10395)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.90/8.20 % (10395)Termination reason: Unknown
% 48.90/8.20 % (10395)Termination phase: Saturation
% 48.90/8.20
% 48.90/8.20 % (10395)Memory used [KB]: 8955
% 48.90/8.20 % (10395)Time elapsed: 0.121 s
% 48.90/8.20 % (10395)Instructions burned: 406 (million)
% 48.90/8.20 % (10395)------------------------------
% 48.90/8.20 % (10395)------------------------------
% 48.90/8.21 % (10397)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1194:si=on:rtra=on_0 on DTF2THF_9790 for (2934ds/1194Mi)
% 48.90/8.22 % (10385)Instruction limit reached!
% 48.90/8.22 % (10385)------------------------------
% 48.90/8.22 % (10385)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.90/8.22 % (10385)Termination reason: Unknown
% 48.90/8.22 % (10385)Termination phase: Saturation
% 48.90/8.22
% 48.90/8.22 % (10385)Memory used [KB]: 13816
% 48.90/8.22 % (10385)Time elapsed: 1.376 s
% 48.90/8.22 % (10385)Instructions burned: 4638 (million)
% 48.90/8.22 % (10385)------------------------------
% 48.90/8.22 % (10385)------------------------------
% 48.90/8.23 % (10398)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_9790 for (2934ds/474Mi)
% 49.46/8.31 % (10394)Instruction limit reached!
% 49.46/8.31 % (10394)------------------------------
% 49.46/8.31 % (10394)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.46/8.31 % (10394)Termination reason: Unknown
% 49.46/8.31 % (10394)Termination phase: Saturation
% 49.46/8.31
% 49.46/8.31 % (10394)Memory used [KB]: 12281
% 49.46/8.31 % (10394)Time elapsed: 0.335 s
% 49.46/8.31 % (10394)Instructions burned: 1103 (million)
% 49.46/8.31 % (10394)------------------------------
% 49.46/8.31 % (10394)------------------------------
% 49.46/8.33 % (10399)dis+1010_1:1_au=on:cnfonf=lazy_gen:ins=3:plsq=on:plsqc=1:plsqr=15142123,262144:sp=reverse_arity:i=3115:si=on:rtra=on_0 on DTF2THF_9790 for (2933ds/3115Mi)
% 49.46/8.37 % (10398)Instruction limit reached!
% 49.46/8.37 % (10398)------------------------------
% 49.46/8.37 % (10398)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.46/8.37 % (10398)Termination reason: Unknown
% 49.46/8.37 % (10398)Termination phase: Saturation
% 49.46/8.37
% 49.46/8.37 % (10398)Memory used [KB]: 8443
% 49.46/8.37 % (10398)Time elapsed: 0.162 s
% 49.46/8.37 % (10398)Instructions burned: 476 (million)
% 49.46/8.37 % (10398)------------------------------
% 49.46/8.37 % (10398)------------------------------
% 49.46/8.38 % (10400)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=831:si=on:rtra=on_0 on DTF2THF_9790 for (2932ds/831Mi)
% 49.46/8.40 % (10388)Instruction limit reached!
% 49.46/8.40 % (10388)------------------------------
% 49.46/8.40 % (10388)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.46/8.40 % (10388)Termination reason: Unknown
% 49.46/8.40 % (10388)Termination phase: Saturation
% 49.46/8.40
% 49.46/8.40 % (10388)Memory used [KB]: 11385
% 49.46/8.40 % (10388)Time elapsed: 1.041 s
% 49.46/8.40 % (10388)Instructions burned: 3621 (million)
% 49.46/8.40 % (10388)------------------------------
% 49.46/8.40 % (10388)------------------------------
% 49.95/8.41 % (10401)dis+1666_14:1_cnfonf=lazy_gen:fe=off:hud=10:piset=all_but_not_eq:prag=on:sp=const_max:i=1188:si=on:rtra=on_0 on DTF2THF_9790 for (2932ds/1188Mi)
% 50.15/8.57 % (10397)Instruction limit reached!
% 50.15/8.57 % (10397)------------------------------
% 50.15/8.57 % (10397)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.15/8.57 % (10397)Termination reason: Unknown
% 50.15/8.57 % (10397)Termination phase: Saturation
% 50.15/8.57
% 50.15/8.57 % (10397)Memory used [KB]: 10490
% 50.15/8.57 % (10397)Time elapsed: 0.381 s
% 50.15/8.57 % (10397)Instructions burned: 1194 (million)
% 50.15/8.57 % (10397)------------------------------
% 50.15/8.57 % (10397)------------------------------
% 50.15/8.58 % (10402)ott+1010_1:20_cnfonf=lazy_pi_sigma_gen:fe=axiom:plsq=on:plsqc=2:plsqr=32,1:sac=on:sos=all:i=2868:si=on:rtra=on_0 on DTF2THF_9790 for (2930ds/2868Mi)
% 50.72/8.62 % (10400)Instruction limit reached!
% 50.72/8.62 % (10400)------------------------------
% 50.72/8.62 % (10400)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.72/8.62 % (10400)Termination reason: Unknown
% 50.72/8.62 % (10400)Termination phase: Saturation
% 50.72/8.62
% 50.72/8.62 % (10400)Memory used [KB]: 11129
% 50.72/8.62 % (10400)Time elapsed: 0.250 s
% 50.72/8.62 % (10400)Instructions burned: 832 (million)
% 50.72/8.62 % (10400)------------------------------
% 50.72/8.62 % (10400)------------------------------
% 50.72/8.63 % (10403)dis+10_1:4_atotf=0.1:avsq=on:bsr=unit_only:e2e=on:sd=1:sp=const_max:ss=axioms:i=1516:si=on:rtra=on_0 on DTF2THF_9790 for (2930ds/1516Mi)
% 50.72/8.69 % (10396)Instruction limit reached!
% 50.72/8.69 % (10396)------------------------------
% 50.72/8.69 % (10396)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.72/8.69 % (10396)Termination reason: Unknown
% 50.72/8.69 % (10396)Termination phase: Saturation
% 50.72/8.69
% 50.72/8.69 % (10396)Memory used [KB]: 11897
% 50.72/8.69 % (10396)Time elapsed: 0.596 s
% 50.72/8.69 % (10396)Instructions burned: 1873 (million)
% 50.72/8.69 % (10396)------------------------------
% 50.72/8.69 % (10396)------------------------------
% 51.76/8.70 % (10404)lrs+1002_1:20_afp=1000:au=on:bsd=on:cnfonf=lazy_not_gen_be_off:sos=all:sp=const_max:i=2321:si=on:rtra=on_0 on DTF2THF_9790 for (2929ds/2321Mi)
% 51.76/8.72 % (10402)Refutation not found, incomplete strategy
% 51.76/8.72 % (10402)------------------------------
% 51.76/8.72 % (10402)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.76/8.72 % (10402)Termination reason: Refutation not found, incomplete strategy
% 51.76/8.72
% 51.76/8.72
% 51.76/8.72 % (10402)Memory used [KB]: 9210
% 51.76/8.72 % (10402)Time elapsed: 0.167 s
% 51.76/8.72 % (10402)Instructions burned: 524 (million)
% 51.76/8.72 % (10402)------------------------------
% 51.76/8.72 % (10402)------------------------------
% 51.76/8.73 % (10405)dis+1010_1:1_au=on:bd=off:bsd=on:ixr=off:sp=const_max:i=2812:si=on:rtra=on_0 on DTF2THF_9790 for (2929ds/2812Mi)
% 51.76/8.76 % (10381)Instruction limit reached!
% 51.76/8.76 % (10381)------------------------------
% 51.76/8.76 % (10381)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.76/8.76 % (10381)Termination reason: Unknown
% 51.76/8.76 % (10381)Termination phase: Saturation
% 51.76/8.76
% 51.76/8.76 % (10381)Memory used [KB]: 14967
% 51.76/8.76 % (10381)Time elapsed: 2.265 s
% 51.76/8.76 % (10381)Instructions burned: 7682 (million)
% 51.76/8.76 % (10381)------------------------------
% 51.76/8.76 % (10381)------------------------------
% 51.76/8.77 % (10401)Instruction limit reached!
% 51.76/8.77 % (10401)------------------------------
% 51.76/8.77 % (10401)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.76/8.77 % (10401)Termination reason: Unknown
% 51.76/8.77 % (10401)Termination phase: Saturation
% 51.76/8.77
% 51.76/8.77 % (10401)Memory used [KB]: 9850
% 51.76/8.77 % (10401)Time elapsed: 0.392 s
% 51.76/8.77 % (10401)Instructions burned: 1190 (million)
% 51.76/8.77 % (10401)------------------------------
% 51.76/8.77 % (10401)------------------------------
% 51.76/8.77 % (10406)dis+1002_8:1_bd=off:sd=1:sgt=16:ss=axioms:i=4604:si=on:rtra=on_0 on DTF2THF_9790 for (2928ds/4604Mi)
% 51.76/8.78 % (10407)ott+1002_1:4_c=on:chr=on:cnfonf=lazy_not_be_gen:hud=10:nm=10:piset=all_but_not_eq:rp=on:spb=goal:uhcvi=on:i=2678:si=on:rtra=on_0 on DTF2THF_9790 for (2928ds/2678Mi)
% 52.48/8.81 % (10404)Refutation not found, incomplete strategy
% 52.48/8.81 % (10404)------------------------------
% 52.48/8.81 % (10404)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 52.48/8.81 % (10404)Termination reason: Refutation not found, incomplete strategy
% 52.48/8.81
% 52.48/8.81
% 52.48/8.81 % (10404)Memory used [KB]: 9083
% 52.48/8.81 % (10404)Time elapsed: 0.108 s
% 52.48/8.81 % (10404)Instructions burned: 394 (million)
% 52.48/8.81 % (10404)------------------------------
% 52.48/8.81 % (10404)------------------------------
% 52.48/8.82 % (10408)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on DTF2THF_9790 for (2928ds/643Mi)
% 52.69/8.94 % (10392)Instruction limit reached!
% 52.69/8.94 % (10392)------------------------------
% 52.69/8.94 % (10392)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 52.69/8.94 % (10392)Termination reason: Unknown
% 52.69/8.94 % (10392)Termination phase: Saturation
% 52.69/8.94
% 52.69/8.94 % (10392)Memory used [KB]: 19573
% 52.69/8.94 % (10392)Time elapsed: 1.085 s
% 52.69/8.94 % (10392)Instructions burned: 3710 (million)
% 52.69/8.94 % (10392)------------------------------
% 52.69/8.94 % (10392)------------------------------
% 52.69/8.95 % (10409)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=458:si=on:rtra=on_0 on DTF2THF_9790 for (2926ds/458Mi)
% 52.69/9.00 % (10408)Instruction limit reached!
% 52.69/9.00 % (10408)------------------------------
% 52.69/9.00 % (10408)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 52.69/9.00 % (10408)Termination reason: Unknown
% 52.69/9.00 % (10408)Termination phase: Saturation
% 52.69/9.00
% 52.69/9.00 % (10408)Memory used [KB]: 11129
% 52.69/9.00 % (10408)Time elapsed: 0.179 s
% 52.69/9.00 % (10408)Instructions burned: 643 (million)
% 52.69/9.00 % (10408)------------------------------
% 52.69/9.00 % (10408)------------------------------
% 52.69/9.01 % (10410)lrs+1010_1:1_anc=all_dependent:apa=on:au=on:bd=off:c=on:cnfonf=off:ntd=on:i=2546:si=on:rtra=on_0 on DTF2THF_9790 for (2926ds/2546Mi)
% 54.87/9.07 % (10403)Instruction limit reached!
% 54.87/9.07 % (10403)------------------------------
% 54.87/9.07 % (10403)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 54.87/9.07 % (10403)Termination reason: Unknown
% 54.87/9.07 % (10403)Termination phase: Saturation
% 54.87/9.07
% 54.87/9.07 % (10403)Memory used [KB]: 9083
% 54.87/9.07 % (10403)Time elapsed: 0.465 s
% 54.87/9.07 % (10403)Instructions burned: 1519 (million)
% 54.87/9.07 % (10403)------------------------------
% 54.87/9.07 % (10403)------------------------------
% 54.87/9.08 % (10411)dis+21_1:1_acc=model:au=on:cnfonf=lazy_gen:ins=2:plsq=on:plsqc=1:plsqr=32,1:i=1432:si=on:rtra=on_0 on DTF2THF_9790 for (2925ds/1432Mi)
% 54.87/9.08 % (10409)Instruction limit reached!
% 54.87/9.08 % (10409)------------------------------
% 54.87/9.08 % (10409)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 54.87/9.08 % (10409)Termination reason: Unknown
% 54.87/9.08 % (10409)Termination phase: Saturation
% 54.87/9.08
% 54.87/9.08 % (10409)Memory used [KB]: 8699
% 54.87/9.08 % (10409)Time elapsed: 0.132 s
% 54.87/9.08 % (10409)Instructions burned: 460 (million)
% 54.87/9.08 % (10409)------------------------------
% 54.87/9.08 % (10409)------------------------------
% 54.87/9.09 % (10412)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=386:si=on:rtra=on_0 on DTF2THF_9790 for (2925ds/386Mi)
% 55.41/9.20 % (10412)Instruction limit reached!
% 55.41/9.20 % (10412)------------------------------
% 55.41/9.20 % (10412)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.41/9.20 % (10412)Termination reason: Unknown
% 55.41/9.20 % (10412)Termination phase: Saturation
% 55.41/9.20
% 55.41/9.20 % (10412)Memory used [KB]: 8699
% 55.41/9.20 % (10412)Time elapsed: 0.105 s
% 55.41/9.20 % (10412)Instructions burned: 386 (million)
% 55.41/9.20 % (10412)------------------------------
% 55.41/9.20 % (10412)------------------------------
% 55.71/9.21 % (10413)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on DTF2THF_9790 for (2924ds/360Mi)
% 55.71/9.26 % (10399)Instruction limit reached!
% 55.71/9.26 % (10399)------------------------------
% 55.71/9.26 % (10399)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.71/9.26 % (10399)Termination reason: Unknown
% 55.71/9.26 % (10399)Termination phase: Saturation
% 55.71/9.26
% 55.71/9.26 % (10399)Memory used [KB]: 12537
% 55.71/9.26 % (10399)Time elapsed: 0.954 s
% 55.71/9.26 % (10399)Instructions burned: 3117 (million)
% 55.71/9.26 % (10399)------------------------------
% 55.71/9.26 % (10399)------------------------------
% 55.71/9.27 % (10414)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=5446:si=on:rtra=on_0 on DTF2THF_9790 for (2923ds/5446Mi)
% 56.20/9.31 % (10413)Instruction limit reached!
% 56.20/9.31 % (10413)------------------------------
% 56.20/9.31 % (10413)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.20/9.31 % (10413)Termination reason: Unknown
% 56.20/9.31 % (10413)Termination phase: Saturation
% 56.20/9.31
% 56.20/9.31 % (10413)Memory used [KB]: 8699
% 56.20/9.31 % (10413)Time elapsed: 0.100 s
% 56.20/9.31 % (10413)Instructions burned: 361 (million)
% 56.20/9.31 % (10413)------------------------------
% 56.20/9.31 % (10413)------------------------------
% 56.20/9.32 % (10415)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=2573:si=on:rtra=on_0 on DTF2THF_9790 for (2923ds/2573Mi)
% 56.92/9.52 % (10411)Instruction limit reached!
% 56.92/9.52 % (10411)------------------------------
% 56.92/9.52 % (10411)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.92/9.52 % (10411)Termination reason: Unknown
% 56.92/9.52 % (10411)Termination phase: Saturation
% 56.92/9.52
% 56.92/9.52 % (10411)Memory used [KB]: 10490
% 56.92/9.52 % (10411)Time elapsed: 0.439 s
% 56.92/9.52 % (10411)Instructions burned: 1433 (million)
% 56.92/9.52 % (10411)------------------------------
% 56.92/9.52 % (10411)------------------------------
% 56.92/9.53 % (10416)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=2655:si=on:rtra=on_0 on DTF2THF_9790 for (2921ds/2655Mi)
% 56.92/9.55 % (10407)Instruction limit reached!
% 56.92/9.55 % (10407)------------------------------
% 56.92/9.55 % (10407)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.92/9.55 % (10407)Termination reason: Unknown
% 56.92/9.55 % (10407)Termination phase: Saturation
% 56.92/9.55
% 56.92/9.55 % (10407)Memory used [KB]: 12792
% 56.92/9.55 % (10407)Time elapsed: 0.770 s
% 56.92/9.55 % (10407)Instructions burned: 2678 (million)
% 56.92/9.55 % (10407)------------------------------
% 56.92/9.55 % (10407)------------------------------
% 56.92/9.56 % (10417)dis+1002_16:1_apa=on:au=on:av=off:cnfonf=off:e2e=on:nm=0:nwc=10.0:i=2781:si=on:rtra=on_0 on DTF2THF_9790 for (2920ds/2781Mi)
% 57.62/9.60 % (10405)Instruction limit reached!
% 57.62/9.60 % (10405)------------------------------
% 57.62/9.60 % (10405)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.62/9.60 % (10405)Termination reason: Unknown
% 57.62/9.60 % (10405)Termination phase: Saturation
% 57.62/9.60
% 57.62/9.60 % (10405)Memory used [KB]: 11129
% 57.62/9.60 % (10405)Time elapsed: 0.871 s
% 57.62/9.60 % (10405)Instructions burned: 2812 (million)
% 57.62/9.60 % (10405)------------------------------
% 57.62/9.60 % (10405)------------------------------
% 57.62/9.61 % (10418)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_9790 for (2920ds/307Mi)
% 57.62/9.70 % (10418)Instruction limit reached!
% 57.62/9.70 % (10418)------------------------------
% 57.62/9.70 % (10418)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.62/9.70 % (10418)Termination reason: Unknown
% 57.62/9.70 % (10418)Termination phase: Saturation
% 57.62/9.70
% 57.62/9.70 % (10418)Memory used [KB]: 8443
% 57.62/9.70 % (10418)Time elapsed: 0.085 s
% 57.62/9.70 % (10418)Instructions burned: 309 (million)
% 57.62/9.70 % (10418)------------------------------
% 57.62/9.70 % (10418)------------------------------
% 57.83/9.71 % (10419)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=1548:si=on:rtra=on_0 on DTF2THF_9790 for (2919ds/1548Mi)
% 57.83/9.79 % (10410)Instruction limit reached!
% 57.83/9.79 % (10410)------------------------------
% 57.83/9.79 % (10410)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.83/9.79 % (10410)Termination reason: Unknown
% 57.83/9.79 % (10410)Termination phase: Saturation
% 57.83/9.79
% 57.83/9.79 % (10410)Memory used [KB]: 11257
% 57.83/9.79 % (10410)Time elapsed: 0.784 s
% 57.83/9.79 % (10410)Instructions burned: 2546 (million)
% 57.83/9.79 % (10410)------------------------------
% 57.83/9.79 % (10410)------------------------------
% 58.73/9.80 % (10420)lrs+10_1:3_alpa=true:hud=3:ins=1:ntd=on:plsq=on:plsqc=1:plsqr=32,1:prag=on:s2a=on:s2agt=10:i=5214:si=on:rtra=on_0 on DTF2THF_9790 for (2918ds/5214Mi)
% 61.89/10.10 % (10415)Instruction limit reached!
% 61.89/10.10 % (10415)------------------------------
% 61.89/10.10 % (10415)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 61.89/10.10 % (10415)Termination reason: Unknown
% 61.89/10.10 % (10415)Termination phase: Saturation
% 61.89/10.10
% 61.89/10.10 % (10415)Memory used [KB]: 11129
% 61.89/10.10 % (10415)Time elapsed: 0.788 s
% 61.89/10.10 % (10415)Instructions burned: 2574 (million)
% 61.89/10.10 % (10415)------------------------------
% 61.89/10.10 % (10415)------------------------------
% 61.89/10.11 % (10421)dis+21_1:1_aac=none:bsr=on:nwc=3.0:s2a=on:i=3201:si=on:rtra=on_0 on DTF2THF_9790 for (2915ds/3201Mi)
% 62.61/10.14 % (10406)Instruction limit reached!
% 62.61/10.14 % (10406)------------------------------
% 62.61/10.14 % (10406)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 62.61/10.14 % (10406)Termination reason: Unknown
% 62.61/10.14 % (10406)Termination phase: Saturation
% 62.61/10.14
% 62.61/10.14 % (10406)Memory used [KB]: 17270
% 62.61/10.14 % (10406)Time elapsed: 1.367 s
% 62.61/10.14 % (10406)Instructions burned: 4607 (million)
% 62.61/10.14 % (10406)------------------------------
% 62.61/10.14 % (10406)------------------------------
% 62.61/10.15 % (10422)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=454:si=on:rtra=on_0 on DTF2THF_9790 for (2914ds/454Mi)
% 62.61/10.17 % (10419)Instruction limit reached!
% 62.61/10.17 % (10419)------------------------------
% 62.61/10.17 % (10419)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 62.61/10.17 % (10419)Termination reason: Unknown
% 62.61/10.17 % (10419)Termination phase: Saturation
% 62.61/10.17
% 62.61/10.17 % (10419)Memory used [KB]: 9850
% 62.61/10.17 % (10419)Time elapsed: 0.470 s
% 62.61/10.17 % (10419)Instructions burned: 1551 (million)
% 62.61/10.17 % (10419)------------------------------
% 62.61/10.17 % (10419)------------------------------
% 62.61/10.18 % (10423)lrs+1002_1:32_au=on:ins=2:nm=16:ntd=on:piset=all_but_not_eq:sp=occurrence:i=3049:si=on:rtra=on_0 on DTF2THF_9790 for (2914ds/3049Mi)
% 63.00/10.28 % (10422)Instruction limit reached!
% 63.00/10.28 % (10422)------------------------------
% 63.00/10.28 % (10422)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.00/10.28 % (10422)Termination reason: Unknown
% 63.00/10.28 % (10422)Termination phase: Saturation
% 63.00/10.28
% 63.00/10.28 % (10422)Memory used [KB]: 12153
% 63.00/10.28 % (10422)Time elapsed: 0.128 s
% 63.00/10.28 % (10422)Instructions burned: 457 (million)
% 63.00/10.28 % (10422)------------------------------
% 63.00/10.28 % (10422)------------------------------
% 63.00/10.29 % (10420)First to succeed.
% 63.00/10.29 % (10424)lrs+1010_1:1_bd=preordered:cnfonf=off:e2e=on:kws=inv_precedence:lwlo=on:sd=2:ss=axioms:i=7311:si=on:rtra=on_0 on DTF2THF_9790 for (2913ds/7311Mi)
% 63.00/10.29 % (10420)Refutation found. Thanks to Tanya!
% 63.00/10.29 % SZS status Theorem for DTF2THF_9790
% 63.00/10.29 % SZS output start Proof for DTF2THF_9790
% 63.00/10.29 thf(type_def_6, type, product_prod: ($tType * $tType) > $tType).
% 63.00/10.29 thf(type_def_7, type, list: ($tType) > $tType).
% 63.00/10.29 thf(type_def_8, type, set: ($tType) > $tType).
% 63.00/10.29 thf(type_def_9, type, nat: $tType).
% 63.00/10.29 thf(type_def_10, type, a: $tType).
% 63.00/10.29 thf(type_def_11, type, product_unit: $tType).
% 63.00/10.29 thf(type_def_12, type, pair_p1731315293ph_ext: ($tType * $tType) > $tType).
% 63.00/10.29 thf(func_def_0, type, pair_p1731315293ph_ext: ($tType * $tType) > $tType).
% 63.00/10.29 thf(func_def_1, type, product_unit: $tType).
% 63.00/10.29 thf(func_def_2, type, product_prod: ($tType * $tType) > $tType).
% 63.00/10.29 thf(func_def_3, type, list: ($tType) > $tType).
% 63.00/10.29 thf(func_def_4, type, set: ($tType) > $tType).
% 63.00/10.29 thf(func_def_5, type, nat: $tType).
% 63.00/10.29 thf(func_def_6, type, a: $tType).
% 63.00/10.29 thf(func_def_7, type, type: !>[X0: $tType]:($o)).
% 63.00/10.29 thf(func_def_8, type, ord: !>[X0: $tType]:($o)).
% 63.00/10.29 thf(func_def_9, type, linorder: !>[X0: $tType]:($o)).
% 63.00/10.29 thf(func_def_10, type, zero_zero: !>[X0: $tType]:(X0)).
% 63.00/10.29 thf(func_def_11, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 63.00/10.29 thf(func_def_12, type, kurato990191779essing: !>[X0: $tType]:(list @ product_prod @ X0 @ X0 > $o)).
% 63.00/10.29 thf(func_def_13, type, append: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 63.00/10.29 thf(func_def_14, type, bind: !>[X0: $tType, X1: $tType]:(list @ X0 > (X0 > list @ X1) > list @ X1)).
% 63.00/10.29 thf(func_def_15, type, concat: !>[X0: $tType]:(list @ list @ X0 > list @ X0)).
% 63.00/10.29 thf(func_def_16, type, insert: !>[X0: $tType]:(X0 > list @ X0 > list @ X0)).
% 63.00/10.29 thf(func_def_17, type, lenlex: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > set @ product_prod @ list @ X0 @ list @ X0)).
% 63.00/10.29 thf(func_def_18, type, lex: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > set @ product_prod @ list @ X0 @ list @ X0)).
% 63.00/10.29 thf(func_def_19, type, lexord: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > set @ product_prod @ list @ X0 @ list @ X0)).
% 63.00/10.29 thf(func_def_20, type, cons: !>[X0: $tType]:(X0 > list @ X0 > list @ X0)).
% 63.00/10.29 thf(func_def_21, type, nil: !>[X0: $tType]:(list @ X0)).
% 63.00/10.29 thf(func_def_22, type, set2: !>[X0: $tType]:(list @ X0 > set @ X0)).
% 63.00/10.29 thf(func_def_23, type, listrel: !>[X0: $tType, X1: $tType]:(set @ product_prod @ X0 @ X1 > set @ product_prod @ list @ X0 @ list @ X1)).
% 63.00/10.29 thf(func_def_24, type, listrel1: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > set @ product_prod @ list @ X0 @ list @ X0)).
% 63.00/10.29 thf(func_def_25, type, maps: !>[X0: $tType, X1: $tType]:((X0 > list @ X1) > list @ X0 > list @ X1)).
% 63.00/10.29 thf(func_def_26, type, measures: !>[X0: $tType]:(list @ (X0 > nat) > set @ product_prod @ X0 @ X0)).
% 63.00/10.29 thf(func_def_27, type, member: !>[X0: $tType]:(list @ X0 > X0 > $o)).
% 63.00/10.29 thf(func_def_28, type, n_lists: !>[X0: $tType]:(nat > list @ X0 > list @ list @ X0)).
% 63.00/10.29 thf(func_def_29, type, product_lists: !>[X0: $tType]:(list @ list @ X0 > list @ list @ X0)).
% 63.00/10.29 thf(func_def_30, type, subseqs: !>[X0: $tType]:(list @ X0 > list @ list @ X0)).
% 63.00/10.29 thf(func_def_31, type, zip: !>[X0: $tType, X1: $tType]:(list @ X0 > list @ X1 > list @ product_prod @ X0 @ X1)).
% 63.00/10.29 thf(func_def_32, type, linorder_part: !>[X0: $tType, X1: $tType]:((X0 > X1) > X1 > list @ X0 > product_prod @ list @ X0 @ product_prod @ list @ X0 @ list @ X0)).
% 63.00/10.29 thf(func_def_33, type, size_size: !>[X0: $tType]:(X0 > nat)).
% 63.00/10.29 thf(func_def_34, type, ord_less: !>[X0: $tType]:(X0 > X0 > $o)).
% 63.00/10.29 thf(func_def_35, type, pair_co_path: !>[X0: $tType]:(product_prod @ X0 @ X0 > X0 > list @ product_prod @ X0 @ X0 > list @ product_prod @ X0 @ X0)).
% 63.00/10.29 thf(func_def_36, type, pair_co_path_rel: !>[X0: $tType]:(product_prod @ product_prod @ X0 @ X0 @ product_prod @ X0 @ list @ product_prod @ X0 @ X0 > product_prod @ product_prod @ X0 @ X0 @ product_prod @ X0 @ list @ product_prod @ X0 @ X0 > $o)).
% 63.00/10.29 thf(func_def_37, type, pair_pawalk_verts: !>[X0: $tType]:(X0 > list @ product_prod @ X0 @ X0 > list @ X0)).
% 63.00/10.29 thf(func_def_38, type, pair_sd_path: !>[X0: $tType]:(product_prod @ X0 @ X0 > X0 > list @ product_prod @ X0 @ X0 > list @ product_prod @ X0 @ X0)).
% 63.00/10.29 thf(func_def_39, type, pair_sd_path_rel: !>[X0: $tType]:(product_prod @ product_prod @ X0 @ X0 @ product_prod @ X0 @ list @ product_prod @ X0 @ X0 > product_prod @ product_prod @ X0 @ X0 @ product_prod @ X0 @ list @ product_prod @ X0 @ X0 > $o)).
% 63.00/10.29 thf(func_def_40, type, invers965609412f_list: !>[X0: $tType]:(list @ product_prod @ X0 @ X0 > X0 > X0)).
% 63.00/10.29 thf(func_def_41, type, invers1507583541st_rel: !>[X0: $tType]:(product_prod @ list @ product_prod @ X0 @ X0 @ X0 > product_prod @ list @ product_prod @ X0 @ X0 @ X0 > $o)).
% 63.00/10.29 thf(func_def_42, type, list_permutes: !>[X0: $tType]:(list @ product_prod @ X0 @ X0 > set @ X0 > $o)).
% 63.00/10.29 thf(func_def_43, type, permutation_of_list: !>[X0: $tType]:(list @ product_prod @ X0 @ X0 > X0 > X0)).
% 63.00/10.29 thf(func_def_44, type, product_Pair: !>[X0: $tType, X1: $tType]:(X0 > X1 > product_prod @ X0 @ X1)).
% 63.00/10.29 thf(func_def_45, type, produc2004651681e_prod: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2)).
% 63.00/10.29 thf(func_def_46, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2)).
% 63.00/10.29 thf(func_def_47, type, asym: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > $o)).
% 63.00/10.29 thf(func_def_48, type, irrefl: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > $o)).
% 63.00/10.29 thf(func_def_49, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 63.00/10.29 thf(func_def_50, type, the_elem: !>[X0: $tType]:(set @ X0 > X0)).
% 63.00/10.29 thf(func_def_51, type, accp: !>[X0: $tType]:((X0 > X0 > $o) > X0 > $o)).
% 63.00/10.29 thf(func_def_52, type, member2: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 63.00/10.29 thf(func_def_53, type, e: product_prod @ a @ a).
% 63.00/10.29 thf(func_def_54, type, es: list @ product_prod @ a @ a).
% 63.00/10.29 thf(func_def_71, type, sP0: !>[X0: $tType]:(list @ product_prod @ X0 @ X0 > X0 > X0 > X0 > list @ product_prod @ X0 @ X0 > $o)).
% 63.00/10.29 thf(func_def_72, type, sP1: !>[X0: $tType, X1: $tType]:(list @ X1 > list @ X0 > $o)).
% 63.00/10.29 thf(func_def_73, type, sP2: !>[X0: $tType]:(product_prod @ X0 @ X0 > list @ product_prod @ X0 @ X0 > X0 > list @ product_prod @ X0 @ X0 > $o)).
% 63.00/10.29 thf(func_def_74, type, sP3: !>[X0: $tType]:(list @ product_prod @ X0 @ X0 > X0 > X0 > $o)).
% 63.00/10.29 thf(func_def_75, type, sP4: !>[X0: $tType]:(product_prod @ X0 @ X0 > X0 > X0 > X0 > product_prod @ X0 @ X0 > list @ product_prod @ X0 @ X0 > list @ product_prod @ X0 @ X0 > $o)).
% 63.00/10.29 thf(func_def_76, type, sP5: !>[X0: $tType]:(product_prod @ X0 @ X0 > list @ product_prod @ X0 @ X0 > X0 > list @ product_prod @ X0 @ X0 > $o)).
% 63.00/10.29 thf(func_def_77, type, sP6: !>[X0: $tType]:(list @ product_prod @ X0 @ X0 > list @ product_prod @ X0 @ X0 > product_prod @ X0 @ X0 > X0 > $o)).
% 63.00/10.29 thf(func_def_78, type, sK7: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ list @ X0 > list @ list @ X0)).
% 63.00/10.29 thf(func_def_79, type, sK8: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ list @ X0 > list @ X0)).
% 63.00/10.29 thf(func_def_80, type, sK9: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ list @ X0 > list @ X0)).
% 63.00/10.29 thf(func_def_81, type, sK10: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ list @ X0 > list @ list @ X0)).
% 63.00/10.29 thf(func_def_82, type, sK11: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 63.00/10.29 thf(func_def_83, type, sK12: !>[X0: $tType]:((X0 > $o) > list @ X0 > X0)).
% 63.00/10.29 thf(func_def_84, type, sK13: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 63.00/10.29 thf(func_def_85, type, sK14: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X1)).
% 63.00/10.29 thf(func_def_86, type, sK15: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X1)).
% 63.00/10.29 thf(func_def_87, type, sK16: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X0)).
% 63.00/10.29 thf(func_def_88, type, sK17: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X0)).
% 63.00/10.29 thf(func_def_89, type, sK18: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X0)).
% 63.00/10.29 thf(func_def_90, type, sK19: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X0)).
% 63.00/10.29 thf(func_def_91, type, sK20: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X1)).
% 63.00/10.29 thf(func_def_92, type, sK21: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X1)).
% 63.00/10.29 thf(func_def_93, type, sK22: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X0)).
% 63.00/10.29 thf(func_def_94, type, sK23: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X1)).
% 63.00/10.29 thf(func_def_95, type, sK24: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X2)).
% 63.00/10.29 thf(func_def_96, type, sK25: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X3)).
% 63.00/10.29 thf(func_def_97, type, sK26: !>[X0: $tType]:(product_prod @ (X0 > X0 > $o) @ list @ X0 > X0 > X0 > $o)).
% 63.00/10.29 thf(func_def_98, type, sK27: !>[X0: $tType]:(product_prod @ (X0 > X0 > $o) @ list @ X0 > X0 > X0 > $o)).
% 63.00/10.29 thf(func_def_99, type, sK28: !>[X0: $tType]:(product_prod @ (X0 > X0 > $o) @ list @ X0 > X0)).
% 63.00/10.29 thf(func_def_100, type, sK29: !>[X0: $tType]:(product_prod @ (X0 > X0 > $o) @ list @ X0 > list @ X0)).
% 63.00/10.29 thf(func_def_101, type, sK30: !>[X0: $tType]:(nat > list @ X0)).
% 63.00/10.29 thf(func_def_102, type, sK31: !>[X0: $tType]:(product_prod @ (X0 > X0 > $o) @ list @ X0 > X0 > X0 > $o)).
% 63.00/10.29 thf(func_def_103, type, sK32: !>[X0: $tType]:(product_prod @ (X0 > X0 > $o) @ list @ X0 > X0 > X0 > $o)).
% 63.00/10.29 thf(func_def_104, type, sK33: !>[X0: $tType]:(product_prod @ (X0 > X0 > $o) @ list @ X0 > X0)).
% 63.00/10.29 thf(func_def_105, type, sK34: !>[X0: $tType]:(product_prod @ (X0 > X0 > $o) @ list @ X0 > X0)).
% 63.00/10.29 thf(func_def_106, type, sK35: !>[X0: $tType]:(product_prod @ (X0 > X0 > $o) @ list @ X0 > list @ X0)).
% 63.00/10.29 thf(func_def_107, type, sK36: !>[X0: $tType]:(product_prod @ (X0 > X0 > $o) @ list @ X0 > X0 > X0 > $o)).
% 63.00/10.29 thf(func_def_108, type, sK37: !>[X0: $tType]:(product_prod @ (X0 > X0 > $o) @ list @ X0 > X0)).
% 63.00/10.29 thf(func_def_109, type, sK38: !>[X0: $tType]:(product_prod @ pair_p1731315293ph_ext @ X0 @ product_unit @ product_prod @ product_prod @ X0 @ X0 @ X0 > pair_p1731315293ph_ext @ X0 @ product_unit)).
% 63.00/10.29 thf(func_def_110, type, sK39: !>[X0: $tType]:(product_prod @ pair_p1731315293ph_ext @ X0 @ product_unit @ product_prod @ product_prod @ X0 @ X0 @ X0 > X0)).
% 63.00/10.29 thf(func_def_111, type, sK40: !>[X0: $tType]:(product_prod @ pair_p1731315293ph_ext @ X0 @ product_unit @ product_prod @ product_prod @ X0 @ X0 @ X0 > X0)).
% 63.00/10.29 thf(func_def_112, type, sK41: !>[X0: $tType]:(product_prod @ pair_p1731315293ph_ext @ X0 @ product_unit @ product_prod @ product_prod @ X0 @ X0 @ X0 > X0)).
% 63.00/10.29 thf(func_def_113, type, sK42: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 63.00/10.29 thf(func_def_114, type, sK43: !>[X0: $tType]:(list @ X0 > list @ X0 > X0)).
% 63.00/10.29 thf(func_def_115, type, sK44: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 63.00/10.29 thf(func_def_116, type, sK45: !>[X0: $tType]:(list @ X0 > list @ X0 > X0)).
% 63.00/10.29 thf(func_def_117, type, sK46: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 63.00/10.29 thf(func_def_118, type, sK47: !>[X0: $tType]:(list @ product_prod @ X0 @ X0 > X0 > X0 > X0 > list @ product_prod @ X0 @ X0 > product_prod @ X0 @ X0)).
% 63.00/10.29 thf(func_def_119, type, sK48: !>[X0: $tType]:(list @ product_prod @ X0 @ X0 > X0 > X0 > X0 > list @ product_prod @ X0 @ X0 > product_prod @ X0 @ X0)).
% 63.00/10.29 thf(func_def_120, type, sK49: !>[X0: $tType]:(list @ product_prod @ X0 @ X0 > X0 > X0 > X0 > list @ product_prod @ X0 @ X0 > list @ product_prod @ X0 @ X0)).
% 63.00/10.29 thf(func_def_121, type, sK50: !>[X0: $tType]:(list @ product_prod @ X0 @ X0 > list @ product_prod @ X0 @ X0 > product_prod @ X0 @ X0)).
% 63.00/10.29 thf(func_def_122, type, sK51: !>[X0: $tType]:(list @ product_prod @ X0 @ X0 > list @ product_prod @ X0 @ X0 > X0 > product_prod @ X0 @ X0 > X0)).
% 63.00/10.29 thf(func_def_123, type, sK52: !>[X0: $tType]:(list @ product_prod @ X0 @ X0 > list @ product_prod @ X0 @ X0 > X0 > product_prod @ X0 @ X0 > X0)).
% 63.00/10.29 thf(func_def_124, type, sK53: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X5)).
% 63.00/10.29 thf(func_def_125, type, sK54: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4)).
% 63.00/10.29 thf(func_def_126, type, sK55: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3)).
% 63.00/10.29 thf(func_def_127, type, sK56: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 63.00/10.29 thf(func_def_128, type, sK57: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 63.00/10.29 thf(func_def_129, type, sK58: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 63.00/10.29 thf(func_def_130, type, sK59: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3)).
% 63.00/10.29 thf(func_def_131, type, sK60: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 63.00/10.29 thf(func_def_132, type, sK61: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 63.00/10.29 thf(func_def_133, type, sK62: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 63.00/10.29 thf(func_def_134, type, sK63: !>[X0: $tType]:(product_prod @ list @ product_prod @ X0 @ X0 @ X0 > X0)).
% 63.00/10.29 thf(func_def_135, type, sK64: !>[X0: $tType]:(product_prod @ list @ product_prod @ X0 @ X0 @ X0 > X0)).
% 63.00/10.29 thf(func_def_136, type, sK65: !>[X0: $tType]:(product_prod @ list @ product_prod @ X0 @ X0 @ X0 > X0)).
% 63.00/10.29 thf(func_def_137, type, sK66: !>[X0: $tType]:(product_prod @ list @ product_prod @ X0 @ X0 @ X0 > list @ product_prod @ X0 @ X0)).
% 63.00/10.29 thf(func_def_138, type, sK67: !>[X0: $tType]:(product_prod @ list @ product_prod @ X0 @ X0 @ X0 > X0)).
% 63.00/10.29 thf(func_def_139, type, sK68: !>[X0: $tType]:(product_prod @ product_prod @ X0 @ X0 @ product_prod @ X0 @ list @ product_prod @ X0 @ X0 > product_prod @ X0 @ X0)).
% 63.00/10.29 thf(func_def_140, type, sK69: !>[X0: $tType]:(product_prod @ product_prod @ X0 @ X0 @ product_prod @ X0 @ list @ product_prod @ X0 @ X0 > X0)).
% 63.00/10.29 thf(func_def_141, type, sK70: !>[X0: $tType]:(product_prod @ product_prod @ X0 @ X0 @ product_prod @ X0 @ list @ product_prod @ X0 @ X0 > X0)).
% 63.00/10.29 thf(func_def_142, type, sK71: !>[X0: $tType]:(product_prod @ product_prod @ X0 @ X0 @ product_prod @ X0 @ list @ product_prod @ X0 @ X0 > X0)).
% 63.00/10.29 thf(func_def_143, type, sK72: !>[X0: $tType]:(product_prod @ product_prod @ X0 @ X0 @ product_prod @ X0 @ list @ product_prod @ X0 @ X0 > X0)).
% 63.00/10.29 thf(func_def_144, type, sK73: !>[X0: $tType]:(product_prod @ product_prod @ X0 @ X0 @ product_prod @ X0 @ list @ product_prod @ X0 @ X0 > product_prod @ X0 @ X0)).
% 63.00/10.29 thf(func_def_145, type, sK74: !>[X0: $tType]:(product_prod @ product_prod @ X0 @ X0 @ product_prod @ X0 @ list @ product_prod @ X0 @ X0 > list @ product_prod @ X0 @ X0)).
% 63.00/10.29 thf(func_def_146, type, sK75: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 63.00/10.29 thf(func_def_147, type, sK76: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 63.00/10.29 thf(func_def_148, type, sK77: !>[X0: $tType, X1: $tType]:(set @ product_prod @ X1 @ X0 > list @ X0 > list @ X1 > X1 > X0)).
% 63.00/10.29 thf(func_def_149, type, sK78: !>[X0: $tType, X1: $tType]:(set @ product_prod @ X1 @ X0 > list @ X0 > list @ X1 > X1 > list @ X0)).
% 63.00/10.29 thf(func_def_150, type, sK79: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > list @ X0 > X0 > list @ X0 > list @ X0)).
% 63.00/10.29 thf(func_def_151, type, sK80: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > list @ X0 > X0 > list @ X0 > X0)).
% 63.00/10.29 thf(func_def_152, type, sK81: !>[X0: $tType]:((pair_p1731315293ph_ext @ X0 @ product_unit > product_prod @ X0 @ X0 > X0 > $o) > pair_p1731315293ph_ext @ X0 @ product_unit)).
% 63.00/10.29 thf(func_def_153, type, sK82: !>[X0: $tType]:((pair_p1731315293ph_ext @ X0 @ product_unit > product_prod @ X0 @ X0 > X0 > $o) > X0)).
% 63.00/10.29 thf(func_def_154, type, sK83: !>[X0: $tType]:((pair_p1731315293ph_ext @ X0 @ product_unit > product_prod @ X0 @ X0 > X0 > $o) > X0)).
% 63.00/10.29 thf(func_def_155, type, sK84: !>[X0: $tType]:((pair_p1731315293ph_ext @ X0 @ product_unit > product_prod @ X0 @ X0 > X0 > $o) > X0)).
% 63.00/10.29 thf(func_def_156, type, sK85: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 63.00/10.29 thf(func_def_157, type, sK86: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 63.00/10.29 thf(func_def_158, type, sK87: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 63.00/10.29 thf(func_def_159, type, sK88: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 63.00/10.29 thf(func_def_160, type, sK89: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 63.00/10.29 thf(func_def_161, type, sK90: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 63.00/10.29 thf(func_def_162, type, sK91: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 63.00/10.29 thf(func_def_163, type, sK92: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 63.00/10.29 thf(func_def_164, type, sK93: !>[X0: $tType]:(list @ X0 > X0)).
% 63.00/10.29 thf(func_def_165, type, sK94: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 63.00/10.29 thf(func_def_166, type, sK95: !>[X0: $tType, X1: $tType, X2: $tType]:((list @ X1 > list @ X0 > list @ X2 > $o) > X1)).
% 63.00/10.29 thf(func_def_167, type, sK96: !>[X0: $tType, X1: $tType, X2: $tType]:((list @ X1 > list @ X0 > list @ X2 > $o) > list @ X1)).
% 63.00/10.29 thf(func_def_168, type, sK97: !>[X0: $tType, X1: $tType, X2: $tType]:((list @ X1 > list @ X0 > list @ X2 > $o) > X0)).
% 63.00/10.29 thf(func_def_169, type, sK98: !>[X0: $tType, X1: $tType, X2: $tType]:((list @ X1 > list @ X0 > list @ X2 > $o) > list @ X0)).
% 63.00/10.29 thf(func_def_170, type, sK99: !>[X0: $tType, X1: $tType, X2: $tType]:((list @ X1 > list @ X0 > list @ X2 > $o) > X2)).
% 63.00/10.29 thf(func_def_171, type, sK100: !>[X0: $tType, X1: $tType, X2: $tType]:((list @ X1 > list @ X0 > list @ X2 > $o) > list @ X2)).
% 63.00/10.29 thf(func_def_172, type, sK101: !>[X0: $tType, X1: $tType]:(product_prod @ (X1 > X0) @ list @ X1 > X1 > X0)).
% 63.00/10.29 thf(func_def_173, type, sK102: !>[X0: $tType, X1: $tType]:(product_prod @ (X1 > X0) @ list @ X1 > X1)).
% 63.00/10.29 thf(func_def_174, type, sK103: !>[X0: $tType, X1: $tType]:(product_prod @ (X1 > X0) @ list @ X1 > X1 > X0)).
% 63.00/10.29 thf(func_def_175, type, sK104: !>[X0: $tType, X1: $tType]:(product_prod @ (X1 > X0) @ list @ X1 > X1 > X0)).
% 63.00/10.29 thf(func_def_176, type, sK105: !>[X0: $tType, X1: $tType]:(product_prod @ (X1 > X0) @ list @ X1 > X1)).
% 63.00/10.29 thf(func_def_177, type, sK106: !>[X0: $tType, X1: $tType]:(product_prod @ (X1 > X0) @ list @ X1 > X1)).
% 63.00/10.29 thf(func_def_178, type, sK107: !>[X0: $tType, X1: $tType]:(product_prod @ (X1 > X0) @ list @ X1 > list @ X1)).
% 63.00/10.29 thf(func_def_179, type, sK108: !>[X0: $tType, X1: $tType]:(product_prod @ (X0 > X1) @ product_prod @ list @ X0 @ list @ X1 > X0 > X1)).
% 63.00/10.29 thf(func_def_180, type, sK109: !>[X0: $tType, X1: $tType]:(product_prod @ (X0 > X1) @ product_prod @ list @ X0 @ list @ X1 > list @ X1)).
% 63.00/10.29 thf(func_def_181, type, sK110: !>[X0: $tType, X1: $tType]:(product_prod @ (X0 > X1) @ product_prod @ list @ X0 @ list @ X1 > X0 > X1)).
% 63.00/10.29 thf(func_def_182, type, sK111: !>[X0: $tType, X1: $tType]:(product_prod @ (X0 > X1) @ product_prod @ list @ X0 @ list @ X1 > X0)).
% 63.00/10.29 thf(func_def_183, type, sK112: !>[X0: $tType, X1: $tType]:(product_prod @ (X0 > X1) @ product_prod @ list @ X0 @ list @ X1 > list @ X0)).
% 63.00/10.29 thf(func_def_184, type, sK113: !>[X0: $tType, X1: $tType]:(product_prod @ (X0 > X1) @ product_prod @ list @ X0 @ list @ X1 > list @ X1)).
% 63.00/10.29 thf(func_def_185, type, sK114: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > set @ product_prod @ X0 @ X1 > X0)).
% 63.00/10.29 thf(func_def_186, type, sK115: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > set @ product_prod @ X0 @ X1 > X1)).
% 63.00/10.29 thf(func_def_187, type, sK116: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > set @ product_prod @ X0 @ X1 > list @ X0)).
% 63.00/10.29 thf(func_def_188, type, sK117: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > set @ product_prod @ X0 @ X1 > list @ X1)).
% 63.00/10.29 thf(func_def_189, type, sK118: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X0)).
% 63.00/10.29 thf(func_def_190, type, sK119: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X1)).
% 63.00/10.29 thf(func_def_191, type, sK120: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X2)).
% 63.00/10.29 thf(func_def_192, type, sK121: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X3)).
% 63.00/10.29 thf(func_def_193, type, sK122: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X4)).
% 63.00/10.29 thf(func_def_194, type, sK123: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X5)).
% 63.00/10.29 thf(func_def_195, type, sK124: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X6)).
% 63.00/10.29 thf(func_def_196, type, sK125: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0)).
% 63.00/10.29 thf(func_def_197, type, sK126: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0)).
% 63.00/10.29 thf(func_def_198, type, sK127: !>[X0: $tType]:(list @ X0 > X0)).
% 63.00/10.29 thf(func_def_199, type, sK128: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 63.00/10.29 thf(func_def_200, type, sK129: !>[X0: $tType]:(list @ X0 > X0)).
% 63.00/10.29 thf(func_def_201, type, sK130: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 63.00/10.29 thf(func_def_202, type, sK131: !>[X0: $tType]:(list @ X0 > X0)).
% 63.00/10.29 thf(func_def_203, type, sK132: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 63.00/10.29 thf(func_def_204, type, sK133: !>[X0: $tType]:(list @ X0 > X0)).
% 63.00/10.29 thf(func_def_205, type, sK134: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 63.00/10.29 thf(func_def_206, type, sK135: !>[X0: $tType]:((product_prod @ X0 @ X0 > X0 > list @ product_prod @ X0 @ X0 > $o) > product_prod @ X0 @ X0)).
% 63.00/10.29 thf(func_def_207, type, sK136: !>[X0: $tType]:((product_prod @ X0 @ X0 > X0 > list @ product_prod @ X0 @ X0 > $o) > X0)).
% 63.00/10.29 thf(func_def_208, type, sK137: !>[X0: $tType]:((product_prod @ X0 @ X0 > X0 > list @ product_prod @ X0 @ X0 > $o) > product_prod @ X0 @ X0)).
% 63.00/10.29 thf(func_def_209, type, sK138: !>[X0: $tType]:((product_prod @ X0 @ X0 > X0 > list @ product_prod @ X0 @ X0 > $o) > X0)).
% 63.00/10.29 thf(func_def_210, type, sK139: !>[X0: $tType]:((product_prod @ X0 @ X0 > X0 > list @ product_prod @ X0 @ X0 > $o) > product_prod @ X0 @ X0)).
% 63.00/10.29 thf(func_def_211, type, sK140: !>[X0: $tType]:((product_prod @ X0 @ X0 > X0 > list @ product_prod @ X0 @ X0 > $o) > X0)).
% 63.00/10.29 thf(func_def_212, type, sK141: !>[X0: $tType]:((product_prod @ X0 @ X0 > X0 > list @ product_prod @ X0 @ X0 > $o) > X0)).
% 63.00/10.29 thf(func_def_213, type, sK142: !>[X0: $tType]:((product_prod @ X0 @ X0 > X0 > list @ product_prod @ X0 @ X0 > $o) > X0)).
% 63.00/10.29 thf(func_def_214, type, sK143: !>[X0: $tType]:((product_prod @ X0 @ X0 > X0 > list @ product_prod @ X0 @ X0 > $o) > product_prod @ X0 @ X0)).
% 63.00/10.29 thf(func_def_215, type, sK144: !>[X0: $tType]:((product_prod @ X0 @ X0 > X0 > list @ product_prod @ X0 @ X0 > $o) > product_prod @ X0 @ X0)).
% 63.00/10.29 thf(func_def_216, type, sK145: !>[X0: $tType]:((product_prod @ X0 @ X0 > X0 > list @ product_prod @ X0 @ X0 > $o) > list @ product_prod @ X0 @ X0)).
% 63.00/10.29 thf(func_def_217, type, sK146: !>[X0: $tType, X1: $tType]:(list @ product_prod @ X0 @ X1 > product_prod @ X0 @ X1 > list @ X1 > list @ X0 > X0)).
% 63.00/10.29 thf(func_def_218, type, sK147: !>[X0: $tType, X1: $tType]:(list @ product_prod @ X0 @ X1 > product_prod @ X0 @ X1 > list @ X1 > list @ X0 > list @ X0)).
% 63.00/10.29 thf(func_def_219, type, sK148: !>[X0: $tType, X1: $tType]:(list @ product_prod @ X0 @ X1 > product_prod @ X0 @ X1 > list @ X1 > list @ X0 > X1)).
% 63.00/10.29 thf(func_def_220, type, sK149: !>[X0: $tType, X1: $tType]:(list @ product_prod @ X0 @ X1 > product_prod @ X0 @ X1 > list @ X1 > list @ X0 > list @ X1)).
% 63.00/10.29 thf(func_def_221, type, sK150: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4)).
% 63.00/10.29 thf(func_def_222, type, sK151: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3)).
% 63.00/10.29 thf(func_def_223, type, sK152: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 63.00/10.29 thf(func_def_224, type, sK153: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 63.00/10.29 thf(func_def_225, type, sK154: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 63.00/10.29 thf(func_def_226, type, sK155: !>[X0: $tType, X1: $tType]:(((X1 > X0) > list @ X1 > $o) > X1 > X0)).
% 63.00/10.29 thf(func_def_227, type, sK156: !>[X0: $tType, X1: $tType]:(((X1 > X0) > list @ X1 > $o) > X1)).
% 63.00/10.29 thf(func_def_228, type, sK157: !>[X0: $tType, X1: $tType]:(((X1 > X0) > list @ X1 > $o) > X1)).
% 63.00/10.29 thf(func_def_229, type, sK158: !>[X0: $tType, X1: $tType]:(((X1 > X0) > list @ X1 > $o) > list @ X1)).
% 63.00/10.29 thf(func_def_230, type, sK159: !>[X0: $tType, X1: $tType]:(((X1 > X0) > list @ X1 > $o) > X1 > X0)).
% 63.00/10.29 thf(func_def_231, type, sK160: !>[X0: $tType, X1: $tType]:(((X1 > X0) > list @ X1 > $o) > X1 > X0)).
% 63.00/10.29 thf(func_def_232, type, sK161: !>[X0: $tType, X1: $tType]:(((X1 > X0) > list @ X1 > $o) > X1)).
% 63.00/10.29 thf(func_def_233, type, sK162: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X0)).
% 63.00/10.29 thf(func_def_234, type, sK163: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X1)).
% 63.00/10.29 thf(func_def_235, type, sK164: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X2)).
% 63.00/10.29 thf(func_def_236, type, sK165: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X3)).
% 63.00/10.29 thf(func_def_237, type, sK166: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X4)).
% 63.00/10.29 thf(func_def_238, type, sK167: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X5)).
% 63.00/10.29 thf(func_def_239, type, sK168: !>[X0: $tType]:(product_prod @ X0 @ X0 > list @ product_prod @ X0 @ X0 > X0 > list @ product_prod @ X0 @ X0 > X0)).
% 63.00/10.29 thf(func_def_240, type, sK169: !>[X0: $tType]:(product_prod @ X0 @ X0 > list @ product_prod @ X0 @ X0 > X0 > list @ product_prod @ X0 @ X0 > X0)).
% 63.00/10.29 thf(func_def_241, type, sK170: !>[X0: $tType]:(product_prod @ X0 @ X0 > list @ product_prod @ X0 @ X0 > X0 > list @ product_prod @ X0 @ X0 > product_prod @ X0 @ X0)).
% 63.00/10.29 thf(func_def_242, type, sK171: !>[X0: $tType]:(product_prod @ X0 @ X0 > list @ product_prod @ X0 @ X0 > X0 > list @ product_prod @ X0 @ X0 > list @ product_prod @ X0 @ X0)).
% 63.00/10.29 thf(func_def_243, type, sK172: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 63.00/10.29 thf(func_def_244, type, sK173: !>[X0: $tType]:((X0 > $o) > list @ X0 > X0)).
% 63.00/10.29 thf(func_def_245, type, sK174: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 63.00/10.29 thf(func_def_246, type, sK175: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > list @ X0 > list @ X0 > X0 > X0)).
% 63.00/10.29 thf(func_def_247, type, sK176: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > list @ X0 > list @ X0 > X0 > list @ X0)).
% 63.00/10.29 thf(func_def_248, type, sK177: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X1)).
% 63.00/10.29 thf(func_def_249, type, sK178: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X0)).
% 63.00/10.29 thf(func_def_250, type, sK179: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 63.00/10.29 thf(func_def_251, type, sK180: !>[X0: $tType]:(list @ X0 > X0)).
% 63.00/10.29 thf(func_def_252, type, sK181: !>[X0: $tType]:(list @ X0 > X0)).
% 63.00/10.29 thf(func_def_253, type, sK182: !>[X0: $tType]:(list @ X0 > X0)).
% 63.00/10.29 thf(func_def_254, type, sK183: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 63.00/10.29 thf(func_def_255, type, sK184: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((list @ X1 > list @ X2 > list @ X0 > list @ X3 > $o) > X1)).
% 63.00/10.29 thf(func_def_256, type, sK185: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((list @ X1 > list @ X2 > list @ X0 > list @ X3 > $o) > list @ X1)).
% 63.00/10.29 thf(func_def_257, type, sK186: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((list @ X1 > list @ X2 > list @ X0 > list @ X3 > $o) > X2)).
% 63.00/10.29 thf(func_def_258, type, sK187: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((list @ X1 > list @ X2 > list @ X0 > list @ X3 > $o) > list @ X2)).
% 63.00/10.29 thf(func_def_259, type, sK188: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((list @ X1 > list @ X2 > list @ X0 > list @ X3 > $o) > X0)).
% 63.00/10.29 thf(func_def_260, type, sK189: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((list @ X1 > list @ X2 > list @ X0 > list @ X3 > $o) > list @ X0)).
% 63.00/10.29 thf(func_def_261, type, sK190: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((list @ X1 > list @ X2 > list @ X0 > list @ X3 > $o) > X3)).
% 63.00/10.29 thf(func_def_262, type, sK191: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((list @ X1 > list @ X2 > list @ X0 > list @ X3 > $o) > list @ X3)).
% 63.00/10.29 thf(func_def_263, type, sK192: !>[X0: $tType, X1: $tType]:(set @ product_prod @ X1 @ X0 > list @ X0 > X0 > list @ X1 > X1)).
% 63.00/10.29 thf(func_def_264, type, sK193: !>[X0: $tType, X1: $tType]:(set @ product_prod @ X1 @ X0 > list @ X0 > X0 > list @ X1 > list @ X1)).
% 63.00/10.29 thf(func_def_265, type, sK194: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0)).
% 63.00/10.29 thf(func_def_266, type, sK195: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 63.00/10.29 thf(func_def_267, type, sK196: !>[X0: $tType]:((X0 > $o) > list @ X0 > X0)).
% 63.00/10.29 thf(func_def_268, type, sK197: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 63.00/10.29 thf(func_def_269, type, sK198: !>[X0: $tType, X1: $tType]:(product_prod @ X1 @ product_prod @ list @ X0 @ X1 > X1)).
% 63.00/10.29 thf(func_def_270, type, sK199: !>[X0: $tType, X1: $tType]:(product_prod @ X1 @ product_prod @ list @ X0 @ X1 > X0)).
% 63.00/10.29 thf(func_def_271, type, sK200: !>[X0: $tType, X1: $tType]:(product_prod @ X1 @ product_prod @ list @ X0 @ X1 > list @ X0)).
% 63.00/10.29 thf(func_def_272, type, sK201: !>[X0: $tType, X1: $tType]:(product_prod @ X1 @ product_prod @ list @ X0 @ X1 > X1)).
% 63.00/10.29 thf(func_def_273, type, sK202: !>[X0: $tType, X1: $tType]:(product_prod @ X1 @ product_prod @ list @ X0 @ X1 > X1)).
% 63.00/10.29 thf(func_def_274, type, sK203: !>[X0: $tType, X1: $tType]:(product_prod @ X1 @ product_prod @ list @ X0 @ X1 > X1)).
% 63.00/10.29 thf(func_def_275, type, sK204: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X0)).
% 63.00/10.29 thf(func_def_276, type, sK205: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X1)).
% 63.00/10.29 thf(func_def_277, type, sK206: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > list @ X0 > X0)).
% 63.00/10.29 thf(func_def_278, type, sK207: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > list @ X0 > X0)).
% 63.00/10.29 thf(func_def_279, type, sK208: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > list @ X0 > X0)).
% 63.00/10.29 thf(func_def_280, type, sK209: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0)).
% 63.00/10.29 thf(func_def_281, type, sK210: !>[X0: $tType]:(X0 > X0 > list @ product_prod @ X0 @ X0 > X0)).
% 63.00/10.29 thf(func_def_282, type, sK211: !>[X0: $tType]:(X0 > X0 > list @ product_prod @ X0 @ X0 > X0)).
% 63.00/10.29 thf(func_def_283, type, sK212: !>[X0: $tType]:(X0 > X0 > list @ product_prod @ X0 @ X0 > list @ product_prod @ X0 @ X0)).
% 63.00/10.29 thf(func_def_284, type, sK213: !>[X0: $tType, X1: $tType]:(X1 > list @ X1 > list @ X0 > X0)).
% 63.00/10.29 thf(func_def_285, type, sK214: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0)).
% 63.00/10.29 thf(func_def_286, type, sK215: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X0)).
% 63.00/10.29 thf(func_def_287, type, sK216: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X1)).
% 63.00/10.29 thf(func_def_288, type, sK217: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X2)).
% 63.00/10.29 thf(func_def_289, type, sK218: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X3)).
% 63.00/10.29 thf(func_def_290, type, sK219: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X4)).
% 63.00/10.29 thf(func_def_291, type, sK220: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 63.00/10.29 thf(func_def_292, type, sK221: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 63.00/10.29 thf(func_def_293, type, sK222: list @ product_prod @ a @ a).
% 63.00/10.29 thf(func_def_294, type, sK223: a).
% 63.00/10.29 thf(func_def_295, type, sK224: a).
% 63.00/10.29 thf(func_def_296, type, sK225: list @ product_prod @ a @ a).
% 63.00/10.29 thf(func_def_297, type, sK226: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0)).
% 63.00/10.29 thf(func_def_298, type, sK227: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 63.00/10.29 thf(func_def_299, type, sK228: !>[X0: $tType]:((X0 > $o) > list @ X0 > X0)).
% 63.00/10.29 thf(func_def_300, type, sK229: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 63.00/10.29 thf(func_def_301, type, sK230: !>[X0: $tType]:((product_prod @ X0 @ X0 > X0 > list @ product_prod @ X0 @ X0 > $o) > X0)).
% 63.00/10.29 thf(func_def_302, type, sK231: !>[X0: $tType]:((product_prod @ X0 @ X0 > X0 > list @ product_prod @ X0 @ X0 > $o) > X0)).
% 63.00/10.29 thf(func_def_303, type, sK232: !>[X0: $tType]:((product_prod @ X0 @ X0 > X0 > list @ product_prod @ X0 @ X0 > $o) > X0)).
% 63.00/10.29 thf(func_def_304, type, sK233: !>[X0: $tType]:((product_prod @ X0 @ X0 > X0 > list @ product_prod @ X0 @ X0 > $o) > product_prod @ X0 @ X0)).
% 63.00/10.29 thf(func_def_305, type, sK234: !>[X0: $tType]:((product_prod @ X0 @ X0 > X0 > list @ product_prod @ X0 @ X0 > $o) > list @ product_prod @ X0 @ X0)).
% 63.00/10.29 thf(func_def_306, type, sK235: !>[X0: $tType]:((product_prod @ X0 @ X0 > X0 > list @ product_prod @ X0 @ X0 > $o) > product_prod @ X0 @ X0)).
% 63.00/10.29 thf(func_def_307, type, sK236: !>[X0: $tType]:((product_prod @ X0 @ X0 > X0 > list @ product_prod @ X0 @ X0 > $o) > X0)).
% 63.00/10.29 thf(func_def_308, type, sK237: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 63.00/10.29 thf(func_def_309, type, sK238: !>[X0: $tType]:(list @ list @ X0 > list @ list @ X0)).
% 63.00/10.29 thf(func_def_310, type, sK239: !>[X0: $tType]:(list @ list @ X0 > X0)).
% 63.00/10.29 thf(func_def_311, type, sK240: !>[X0: $tType]:(list @ list @ X0 > list @ X0)).
% 63.00/10.29 thf(func_def_312, type, sK241: !>[X0: $tType]:(list @ list @ X0 > list @ list @ X0)).
% 63.00/10.29 thf(func_def_313, type, sK242: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 63.00/10.29 thf(func_def_314, type, sK243: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 63.00/10.29 thf(func_def_315, type, sK244: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 63.00/10.29 thf(func_def_316, type, sK245: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 63.00/10.29 thf(func_def_317, type, sK246: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 63.00/10.29 thf(func_def_318, type, sK247: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 63.00/10.29 thf(func_def_319, type, sK248: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X0)).
% 63.00/10.29 thf(func_def_320, type, sK249: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X0)).
% 63.00/10.29 thf(func_def_321, type, sK250: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X1)).
% 63.00/10.29 thf(func_def_322, type, sK251: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X1)).
% 63.00/10.29 thf(func_def_323, type, sK252: !>[X0: $tType]:(product_prod @ product_prod @ X0 @ X0 @ product_prod @ X0 @ list @ product_prod @ X0 @ X0 > X0)).
% 63.00/10.29 thf(func_def_324, type, sK253: !>[X0: $tType]:(product_prod @ product_prod @ X0 @ X0 @ product_prod @ X0 @ list @ product_prod @ X0 @ X0 > X0)).
% 63.00/10.29 thf(func_def_325, type, sK254: !>[X0: $tType]:(product_prod @ product_prod @ X0 @ X0 @ product_prod @ X0 @ list @ product_prod @ X0 @ X0 > X0)).
% 63.00/10.29 thf(func_def_326, type, sK255: !>[X0: $tType]:(product_prod @ product_prod @ X0 @ X0 @ product_prod @ X0 @ list @ product_prod @ X0 @ X0 > product_prod @ X0 @ X0)).
% 63.00/10.29 thf(func_def_327, type, sK256: !>[X0: $tType]:(product_prod @ product_prod @ X0 @ X0 @ product_prod @ X0 @ list @ product_prod @ X0 @ X0 > product_prod @ X0 @ X0)).
% 63.00/10.29 thf(func_def_328, type, sK257: !>[X0: $tType]:(product_prod @ product_prod @ X0 @ X0 @ product_prod @ X0 @ list @ product_prod @ X0 @ X0 > list @ product_prod @ X0 @ X0)).
% 63.00/10.29 thf(func_def_329, type, sK258: !>[X0: $tType]:(product_prod @ product_prod @ X0 @ X0 @ product_prod @ X0 @ list @ product_prod @ X0 @ X0 > product_prod @ X0 @ X0)).
% 63.00/10.29 thf(func_def_330, type, sK259: !>[X0: $tType]:(product_prod @ product_prod @ X0 @ X0 @ product_prod @ X0 @ list @ product_prod @ X0 @ X0 > X0)).
% 63.00/10.29 thf(func_def_331, type, sK260: !>[X0: $tType]:(product_prod @ product_prod @ X0 @ X0 @ product_prod @ X0 @ list @ product_prod @ X0 @ X0 > product_prod @ X0 @ X0)).
% 63.00/10.29 thf(func_def_332, type, sK261: !>[X0: $tType]:(product_prod @ product_prod @ X0 @ X0 @ product_prod @ X0 @ list @ product_prod @ X0 @ X0 > product_prod @ X0 @ X0)).
% 63.00/10.29 thf(func_def_333, type, sK262: !>[X0: $tType]:(product_prod @ product_prod @ X0 @ X0 @ product_prod @ X0 @ list @ product_prod @ X0 @ X0 > X0)).
% 63.00/10.29 thf(func_def_334, type, sK263: !>[X0: $tType]:(list @ product_prod @ X0 @ X0 > X0 > X0 > X0)).
% 63.00/10.29 thf(func_def_335, type, sK264: !>[X0: $tType]:(list @ product_prod @ X0 @ X0 > X0 > X0 > X0)).
% 63.00/10.29 thf(func_def_336, type, sK265: !>[X0: $tType]:(list @ product_prod @ X0 @ X0 > X0 > X0 > list @ product_prod @ X0 @ X0)).
% 63.00/10.29 thf(func_def_337, type, sK266: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > X0 > X1)).
% 63.00/10.29 thf(func_def_338, type, sK267: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > X0)).
% 63.00/10.29 thf(func_def_339, type, sK268: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > list @ X0)).
% 63.00/10.29 thf(func_def_340, type, sK269: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > list @ X1)).
% 63.00/10.29 thf(func_def_341, type, sK270: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > X0 > X1)).
% 63.00/10.29 thf(func_def_342, type, sK271: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > list @ X1)).
% 63.00/10.29 thf(func_def_343, type, sK272: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o)).
% 63.00/10.29 thf(func_def_344, type, sK273: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0)).
% 63.00/10.29 thf(func_def_345, type, sK274: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > list @ X0)).
% 63.00/10.29 thf(func_def_346, type, sK275: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o)).
% 63.00/10.29 thf(func_def_347, type, sK276: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 63.00/10.29 thf(func_def_348, type, sK277: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 63.00/10.29 thf(func_def_349, type, sK278: !>[X0: $tType]:(list @ product_prod @ X0 @ X0 > list @ product_prod @ X0 @ X0 > product_prod @ X0 @ X0 > X0 > product_prod @ X0 @ X0)).
% 63.00/10.29 thf(func_def_350, type, sK279: !>[X0: $tType]:(product_prod @ X0 @ X0 > list @ product_prod @ X0 @ X0 > X0 > list @ product_prod @ X0 @ X0 > X0)).
% 63.00/10.29 thf(func_def_351, type, sK280: !>[X0: $tType]:(product_prod @ X0 @ X0 > list @ product_prod @ X0 @ X0 > X0 > list @ product_prod @ X0 @ X0 > X0)).
% 63.00/10.29 thf(func_def_352, type, sK281: !>[X0: $tType]:(product_prod @ X0 @ X0 > list @ product_prod @ X0 @ X0 > X0 > list @ product_prod @ X0 @ X0 > product_prod @ X0 @ X0)).
% 63.00/10.29 thf(func_def_353, type, sK282: !>[X0: $tType]:(product_prod @ X0 @ X0 > list @ product_prod @ X0 @ X0 > X0 > list @ product_prod @ X0 @ X0 > product_prod @ X0 @ X0)).
% 63.00/10.29 thf(func_def_354, type, sK283: !>[X0: $tType]:(product_prod @ X0 @ X0 > list @ product_prod @ X0 @ X0 > X0 > list @ product_prod @ X0 @ X0 > list @ product_prod @ X0 @ X0)).
% 63.00/10.29 thf(func_def_355, type, sK284: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > $o) > set @ product_prod @ X0 @ X0)).
% 63.00/10.29 thf(func_def_356, type, sK285: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 63.00/10.29 thf(func_def_357, type, sK286: !>[X0: $tType]:(list @ X0 > X0 > X0)).
% 63.00/10.29 thf(func_def_358, type, sK287: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 63.00/10.29 thf(func_def_359, type, sK288: !>[X0: $tType]:(list @ X0 > X0)).
% 63.00/10.29 thf(func_def_360, type, sK289: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 63.00/10.29 thf(func_def_361, type, sK290: !>[X0: $tType]:(product_prod @ list @ X0 @ list @ X0 > list @ X0)).
% 63.00/10.29 thf(func_def_362, type, sK291: !>[X0: $tType]:(product_prod @ list @ X0 @ list @ X0 > X0)).
% 63.00/10.29 thf(func_def_363, type, sK292: !>[X0: $tType]:(product_prod @ list @ X0 @ list @ X0 > list @ X0)).
% 63.00/10.29 thf(func_def_364, type, sK293: !>[X0: $tType]:(product_prod @ list @ X0 @ list @ X0 > list @ X0)).
% 63.00/10.29 thf(func_def_365, type, sK294: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X1)).
% 63.00/10.29 thf(func_def_366, type, sK295: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X0)).
% 63.00/10.29 thf(func_def_367, type, sK296: !>[X0: $tType]:(list @ product_prod @ X0 @ X0 > list @ product_prod @ X0 @ X0 > X0 > product_prod @ X0 @ X0 > X0)).
% 63.00/10.29 thf(func_def_368, type, sK297: !>[X0: $tType]:(list @ product_prod @ X0 @ X0 > list @ product_prod @ X0 @ X0 > X0 > product_prod @ X0 @ X0 > X0)).
% 63.00/10.29 thf(func_def_369, type, sK298: !>[X0: $tType]:(list @ product_prod @ X0 @ X0 > list @ product_prod @ X0 @ X0 > X0 > product_prod @ X0 @ X0 > product_prod @ X0 @ X0)).
% 63.00/10.29 thf(func_def_370, type, sK299: !>[X0: $tType]:(list @ product_prod @ X0 @ X0 > list @ product_prod @ X0 @ X0 > X0 > product_prod @ X0 @ X0 > list @ product_prod @ X0 @ X0)).
% 63.00/10.29 thf(func_def_371, type, sK300: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o)).
% 63.00/10.29 thf(func_def_372, type, sK301: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0)).
% 63.00/10.29 thf(func_def_373, type, sK302: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0)).
% 63.00/10.29 thf(func_def_374, type, sK303: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > list @ X0)).
% 63.00/10.29 thf(func_def_375, type, sK304: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o)).
% 63.00/10.29 thf(func_def_376, type, sK305: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o)).
% 63.00/10.29 thf(func_def_377, type, sK306: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0)).
% 63.00/10.29 thf(func_def_378, type, sK307: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 63.00/10.29 thf(func_def_379, type, sK308: !>[X0: $tType]:((X0 > $o) > list @ X0 > X0)).
% 63.00/10.29 thf(func_def_380, type, sK309: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 63.00/10.29 thf(func_def_381, type, sK310: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0)).
% 63.00/10.29 thf(func_def_382, type, sK311: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0)).
% 63.00/10.29 thf(func_def_383, type, sK312: !>[X0: $tType]:((list @ product_prod @ X0 @ X0 > X0 > $o) > X0)).
% 63.00/10.29 thf(func_def_384, type, sK313: !>[X0: $tType]:((list @ product_prod @ X0 @ X0 > X0 > $o) > X0)).
% 63.00/10.29 thf(func_def_385, type, sK314: !>[X0: $tType]:((list @ product_prod @ X0 @ X0 > X0 > $o) > list @ product_prod @ X0 @ X0)).
% 63.00/10.29 thf(func_def_386, type, sK315: !>[X0: $tType]:((list @ product_prod @ X0 @ X0 > X0 > $o) > X0)).
% 63.00/10.29 thf(func_def_387, type, sK316: !>[X0: $tType]:((list @ product_prod @ X0 @ X0 > X0 > $o) > X0)).
% 63.00/10.29 thf(func_def_388, type, sK317: !>[X0: $tType, X1: $tType]:((X1 > list @ X0) > (X1 > list @ X0) > list @ X1 > X1)).
% 63.00/10.29 thf(func_def_389, type, sK318: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X6)).
% 63.00/10.29 thf(func_def_390, type, sK319: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X5)).
% 63.00/10.29 thf(func_def_391, type, sK320: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4)).
% 63.00/10.29 thf(func_def_392, type, sK321: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3)).
% 63.00/10.29 thf(func_def_393, type, sK322: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 63.00/10.29 thf(func_def_394, type, sK323: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 63.00/10.29 thf(func_def_395, type, sK324: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 63.00/10.29 thf(func_def_396, type, sK325: !>[X0: $tType]:(list @ X0 > X0)).
% 63.00/10.29 thf(func_def_397, type, sK326: !>[X0: $tType]:(list @ X0 > X0)).
% 63.00/10.29 thf(func_def_398, type, sK327: !>[X0: $tType]:(list @ X0 > X0)).
% 63.00/10.29 thf(func_def_399, type, sK328: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 63.00/10.29 thf(func_def_400, type, sK329: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0)).
% 63.00/10.29 thf(func_def_401, type, sK330: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > list @ X0 > list @ X0 > X0)).
% 63.00/10.29 thf(func_def_402, type, sK331: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > list @ X0 > list @ X0 > X0)).
% 63.00/10.29 thf(func_def_403, type, sK332: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > list @ X0 > list @ X0 > list @ X0)).
% 63.00/10.29 thf(func_def_404, type, sK333: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > list @ X0 > list @ X0 > list @ X0)).
% 63.00/10.29 thf(func_def_405, type, sK334: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 63.00/10.29 thf(func_def_406, type, sK335: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 63.00/10.29 thf(func_def_407, type, sK336: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 63.00/10.29 thf(func_def_408, type, sK337: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 63.00/10.29 thf(func_def_409, type, sK338: !>[X0: $tType, X1: $tType]:(set @ product_prod @ X1 @ X0 > list @ X0 > list @ X1 > X1)).
% 63.00/10.29 thf(func_def_410, type, sK339: !>[X0: $tType, X1: $tType]:(set @ product_prod @ X1 @ X0 > list @ X0 > list @ X1 > X0)).
% 63.00/10.29 thf(func_def_411, type, sK340: !>[X0: $tType, X1: $tType]:(set @ product_prod @ X1 @ X0 > list @ X0 > list @ X1 > list @ X1)).
% 63.00/10.29 thf(func_def_412, type, sK341: !>[X0: $tType, X1: $tType]:(set @ product_prod @ X1 @ X0 > list @ X0 > list @ X1 > list @ X0)).
% 63.00/10.29 thf(func_def_413, type, sK342: !>[X0: $tType]:(list @ X0 > X0)).
% 63.00/10.29 thf(func_def_414, type, sK343: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 63.00/10.29 thf(func_def_415, type, sK344: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 63.00/10.29 thf(func_def_416, type, sK345: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 63.00/10.29 thf(func_def_417, type, sK346: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 63.00/10.29 thf(func_def_418, type, sK347: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 63.00/10.29 thf(func_def_419, type, sK348: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 63.00/10.29 thf(func_def_420, type, sK349: !>[X0: $tType]:(product_prod @ list @ X0 @ list @ X0 > X0)).
% 63.00/10.29 thf(func_def_421, type, sK350: !>[X0: $tType]:(product_prod @ list @ X0 @ list @ X0 > list @ X0)).
% 63.00/10.29 thf(func_def_422, type, sK351: !>[X0: $tType]:(product_prod @ list @ X0 @ list @ X0 > X0)).
% 63.00/10.29 thf(func_def_423, type, sK352: !>[X0: $tType]:(product_prod @ list @ X0 @ list @ X0 > list @ X0)).
% 63.00/10.29 thf(func_def_424, type, sK353: !>[X0: $tType]:(product_prod @ list @ X0 @ list @ X0 > list @ X0)).
% 63.00/10.29 thf(func_def_425, type, sK354: !>[X0: $tType]:(product_prod @ list @ X0 @ list @ X0 > list @ X0)).
% 63.00/10.29 thf(func_def_426, type, sK355: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 63.00/10.29 thf(func_def_427, type, sK356: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 63.00/10.29 thf(func_def_428, type, sK357: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 63.00/10.29 thf(func_def_429, type, sK358: !>[X0: $tType]:(list @ X0 > X0)).
% 63.00/10.29 thf(func_def_430, type, sK359: !>[X0: $tType]:(product_prod @ X0 @ product_prod @ list @ product_prod @ X0 @ X0 @ X0 > X0)).
% 63.00/10.29 thf(func_def_431, type, sK360: !>[X0: $tType]:(product_prod @ X0 @ product_prod @ list @ product_prod @ X0 @ X0 @ X0 > product_prod @ X0 @ X0)).
% 63.00/10.29 thf(func_def_432, type, sK361: !>[X0: $tType]:(product_prod @ X0 @ product_prod @ list @ product_prod @ X0 @ X0 @ X0 > list @ product_prod @ X0 @ X0)).
% 63.00/10.29 thf(func_def_433, type, sK362: !>[X0: $tType]:(product_prod @ X0 @ product_prod @ list @ product_prod @ X0 @ X0 @ X0 > X0)).
% 63.00/10.29 thf(func_def_434, type, sK363: !>[X0: $tType]:(product_prod @ X0 @ product_prod @ list @ product_prod @ X0 @ X0 @ X0 > X0)).
% 63.00/10.29 thf(func_def_435, type, sK364: !>[X0: $tType]:(product_prod @ X0 @ product_prod @ list @ product_prod @ X0 @ X0 @ X0 > X0)).
% 63.00/10.29 thf(func_def_436, type, sK365: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ product_prod @ X1 @ X2 > X0)).
% 63.00/10.29 thf(func_def_437, type, sK366: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ product_prod @ X1 @ X2 > X1)).
% 63.00/10.29 thf(func_def_438, type, sK367: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ product_prod @ X1 @ X2 > X2)).
% 63.00/10.29 thf(func_def_439, type, sK368: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X0)).
% 63.00/10.29 thf(func_def_440, type, sK369: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X1)).
% 63.00/10.29 thf(func_def_441, type, sK370: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 63.00/10.29 thf(func_def_442, type, sK371: !>[X0: $tType]:((X0 > $o) > list @ X0 > X0)).
% 63.00/10.29 thf(func_def_443, type, sK372: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 63.00/10.29 thf(func_def_444, type, sK373: !>[X0: $tType, X1: $tType]:(X0 > list @ X1 > list @ X0 > X1)).
% 63.00/10.29 thf(func_def_445, type, sK374: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 63.00/10.29 thf(func_def_446, type, sK375: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 63.00/10.29 thf(func_def_447, type, sK376: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 63.00/10.29 thf(func_def_448, type, sK377: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 63.00/10.29 thf(func_def_449, type, sK378: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 63.00/10.29 thf(func_def_450, type, sK379: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 63.00/10.29 thf(func_def_451, type, sK380: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 63.00/10.29 thf(func_def_452, type, sK381: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 63.00/10.29 thf(func_def_453, type, sK382: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 63.00/10.29 thf(func_def_454, type, sK383: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 63.00/10.29 thf(func_def_455, type, sK384: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0)).
% 63.00/10.29 thf(func_def_456, type, sP385: $o > $o).
% 63.00/10.29 thf(func_def_457, type, sP386: $o > $o).
% 63.00/10.29 thf(func_def_458, type, sP387: $o > $o).
% 63.00/10.29 thf(func_def_459, type, sP388: $o > $o).
% 63.00/10.29 thf(func_def_460, type, sP389: $o > $o).
% 63.00/10.29 thf(func_def_461, type, sP390: $o > $o).
% 63.00/10.29 thf(func_def_462, type, sP391: $o > $o).
% 63.00/10.29 thf(func_def_463, type, sP392: $o > $o).
% 63.00/10.29 thf(func_def_464, type, sP393: $o > $o).
% 63.00/10.29 thf(func_def_465, type, sP394: $o > $o).
% 63.00/10.29 thf(func_def_466, type, sP395: $o > $o).
% 63.00/10.29 thf(func_def_467, type, sP396: $o > $o).
% 63.00/10.29 thf(func_def_468, type, sP397: $o > $o).
% 63.00/10.29 thf(func_def_469, type, sP398: $o > $o).
% 63.00/10.29 thf(func_def_470, type, sP399: $o > $o).
% 63.00/10.29 thf(func_def_471, type, sP400: $o > $o).
% 63.00/10.29 thf(func_def_472, type, sP401: $o > $o).
% 63.00/10.29 thf(func_def_473, type, sP402: $o > $o).
% 63.00/10.29 thf(func_def_474, type, sP403: $o > $o).
% 63.00/10.29 thf(func_def_475, type, sP404: $o > $o).
% 63.00/10.29 thf(func_def_476, type, sP405: $o > $o).
% 63.00/10.29 thf(func_def_477, type, sP406: $o > $o).
% 63.00/10.29 thf(func_def_478, type, sP407: $o > $o).
% 63.00/10.29 thf(func_def_479, type, sP408: $o > $o).
% 63.00/10.29 thf(func_def_480, type, sP409: $o > $o).
% 63.00/10.29 thf(func_def_481, type, sP410: $o > $o).
% 63.00/10.29 thf(func_def_482, type, sP411: $o > $o).
% 63.00/10.29 thf(func_def_483, type, sP412: $o > $o).
% 63.00/10.29 thf(func_def_484, type, sP413: $o > $o).
% 63.00/10.29 thf(func_def_485, type, sP414: $o > $o).
% 63.00/10.29 thf(func_def_486, type, sP415: $o > $o).
% 63.00/10.29 thf(func_def_487, type, sP416: $o > $o).
% 63.00/10.29 thf(func_def_488, type, sP417: $o > $o).
% 63.00/10.29 thf(func_def_489, type, sP418: $o > $o).
% 63.00/10.29 thf(func_def_490, type, sP419: $o > $o).
% 63.00/10.29 thf(func_def_491, type, sP420: $o > $o).
% 63.00/10.29 thf(func_def_492, type, sP421: $o > $o).
% 63.00/10.29 thf(func_def_493, type, sP422: $o > $o).
% 63.00/10.29 thf(func_def_494, type, sP423: $o > $o).
% 63.00/10.29 thf(func_def_495, type, sP424: $o > $o).
% 63.00/10.29 thf(func_def_496, type, sP425: $o > $o).
% 63.00/10.29 thf(func_def_497, type, sP426: $o > $o).
% 63.00/10.29 thf(func_def_498, type, sP427: $o > $o).
% 63.00/10.29 thf(func_def_499, type, sP428: $o > $o).
% 63.00/10.29 thf(func_def_500, type, sP429: $o > $o).
% 63.00/10.29 thf(func_def_501, type, sP430: $o > $o).
% 63.00/10.29 thf(func_def_502, type, sP431: $o > $o).
% 63.00/10.29 thf(func_def_503, type, sP432: $o > $o).
% 63.00/10.29 thf(func_def_504, type, sP433: $o > $o).
% 63.00/10.29 thf(func_def_505, type, sP434: $o > $o).
% 63.00/10.29 thf(func_def_506, type, sP435: $o > $o).
% 63.00/10.29 thf(func_def_507, type, sP436: $o > $o).
% 63.00/10.29 thf(func_def_508, type, sP437: $o > $o).
% 63.00/10.29 thf(func_def_509, type, sP438: $o > $o).
% 63.00/10.29 thf(func_def_510, type, sP439: $o > $o).
% 63.00/10.29 thf(func_def_511, type, sP440: $o > $o).
% 63.00/10.29 thf(func_def_512, type, sP441: $o > $o).
% 63.00/10.29 thf(func_def_513, type, sP442: $o > $o).
% 63.00/10.29 thf(func_def_514, type, sP443: $o > $o).
% 63.00/10.29 thf(func_def_515, type, sP444: $o > $o).
% 63.00/10.29 thf(func_def_516, type, sP445: $o > $o).
% 63.00/10.29 thf(func_def_517, type, sP446: $o > $o).
% 63.00/10.29 thf(func_def_518, type, sP447: $o > $o).
% 63.00/10.29 thf(func_def_519, type, sP448: $o > $o).
% 63.00/10.29 thf(func_def_520, type, sP449: $o > $o).
% 63.00/10.29 thf(func_def_521, type, sP450: $o > $o).
% 63.00/10.29 thf(func_def_522, type, sP451: $o > $o).
% 63.00/10.29 thf(func_def_523, type, sP452: $o > $o).
% 63.00/10.29 thf(func_def_524, type, sP453: $o > $o).
% 63.00/10.29 thf(func_def_525, type, sP454: $o > $o).
% 63.00/10.29 thf(func_def_526, type, sP455: $o > $o).
% 63.00/10.29 thf(func_def_527, type, sP456: $o > $o).
% 63.00/10.29 thf(func_def_528, type, sP457: $o > $o).
% 63.00/10.29 thf(func_def_529, type, sP458: $o > $o).
% 63.00/10.29 thf(func_def_530, type, sP459: $o > $o).
% 63.00/10.29 thf(func_def_531, type, sP460: $o > $o).
% 63.00/10.29 thf(func_def_532, type, sP461: $o > $o).
% 63.00/10.29 thf(func_def_533, type, sP462: $o > $o).
% 63.00/10.29 thf(func_def_534, type, sP463: $o > $o).
% 63.00/10.29 thf(func_def_535, type, sP464: $o > $o).
% 63.00/10.29 thf(func_def_536, type, sP465: $o > $o).
% 63.00/10.29 thf(func_def_537, type, sP466: $o > $o).
% 63.00/10.29 thf(func_def_538, type, sP467: $o > $o).
% 63.00/10.29 thf(func_def_539, type, sP468: $o > $o).
% 63.00/10.29 thf(func_def_540, type, sP469: $o > $o).
% 63.00/10.29 thf(func_def_541, type, sP470: $o > $o).
% 63.00/10.29 thf(func_def_542, type, sP471: $o > $o).
% 63.00/10.29 thf(func_def_543, type, sP472: $o > $o).
% 63.00/10.29 thf(func_def_544, type, sP473: $o > $o).
% 63.00/10.29 thf(func_def_545, type, sP474: $o > $o).
% 63.00/10.29 thf(func_def_546, type, sP475: $o > $o).
% 63.00/10.29 thf(func_def_547, type, sP476: $o > $o).
% 63.00/10.29 thf(func_def_548, type, sP477: $o > $o).
% 63.00/10.29 thf(func_def_549, type, sP478: $o > $o).
% 63.00/10.29 thf(func_def_550, type, sP479: $o > $o).
% 63.00/10.29 thf(func_def_551, type, sP480: $o > $o).
% 63.00/10.29 thf(func_def_552, type, sP481: $o > $o).
% 63.00/10.29 thf(func_def_553, type, sP482: $o > $o).
% 63.00/10.29 thf(func_def_554, type, sP483: $o > $o).
% 63.00/10.29 thf(func_def_555, type, sP484: $o > $o).
% 63.00/10.29 thf(func_def_556, type, sP485: $o > $o).
% 63.00/10.29 thf(func_def_557, type, sP486: $o > $o).
% 63.00/10.29 thf(func_def_558, type, sP487: $o > $o).
% 63.00/10.29 thf(func_def_559, type, sP488: $o > $o).
% 63.00/10.29 thf(func_def_560, type, sP489: $o > $o).
% 63.00/10.29 thf(func_def_561, type, sP490: $o > $o).
% 63.00/10.29 thf(func_def_562, type, sP491: $o > $o).
% 63.00/10.29 thf(func_def_563, type, sP492: $o > $o).
% 63.00/10.29 thf(func_def_564, type, sP493: $o > $o).
% 63.00/10.29 thf(func_def_565, type, sP494: $o > $o).
% 63.00/10.29 thf(func_def_566, type, sP495: $o > $o).
% 63.00/10.29 thf(func_def_567, type, sP496: $o > $o).
% 63.00/10.29 thf(func_def_568, type, sP497: $o > $o).
% 63.00/10.29 thf(func_def_569, type, sP498: $o > $o).
% 63.00/10.29 thf(func_def_570, type, sP499: $o > $o).
% 63.00/10.29 thf(func_def_571, type, sP500: $o > $o).
% 63.00/10.29 thf(func_def_572, type, sP501: $o > $o).
% 63.00/10.29 thf(func_def_573, type, sP502: $o > $o).
% 63.00/10.29 thf(func_def_574, type, sP503: $o > $o).
% 63.00/10.29 thf(func_def_575, type, sP504: $o > $o).
% 63.00/10.29 thf(func_def_576, type, sP505: $o > $o).
% 63.00/10.29 thf(func_def_577, type, sP506: $o > $o).
% 63.00/10.29 thf(func_def_578, type, sP507: $o > $o).
% 63.00/10.29 thf(func_def_579, type, sP508: $o > $o).
% 63.00/10.29 thf(func_def_580, type, sP509: $o > $o).
% 63.00/10.29 thf(func_def_581, type, sP510: $o > $o).
% 63.00/10.29 thf(func_def_582, type, sP511: $o > $o).
% 63.00/10.29 thf(func_def_583, type, sP512: $o > $o).
% 63.00/10.29 thf(func_def_584, type, sP513: $o > $o).
% 63.00/10.29 thf(func_def_585, type, sP514: $o > $o).
% 63.00/10.29 thf(func_def_586, type, sP515: $o > $o).
% 63.00/10.29 thf(func_def_587, type, sP516: $o > $o).
% 63.00/10.29 thf(func_def_588, type, sP517: $o > $o).
% 63.00/10.29 thf(func_def_589, type, sP518: $o > $o).
% 63.00/10.29 thf(func_def_590, type, sP519: $o > $o).
% 63.00/10.29 thf(func_def_591, type, sP520: $o > $o).
% 63.00/10.29 thf(func_def_592, type, sP521: $o > $o).
% 63.00/10.29 thf(func_def_593, type, sP522: $o > $o).
% 63.00/10.29 thf(func_def_594, type, sP523: $o > $o).
% 63.00/10.29 thf(func_def_595, type, sP524: $o > $o).
% 63.00/10.29 thf(func_def_596, type, sP525: $o > $o).
% 63.00/10.29 thf(func_def_597, type, sP526: $o > $o).
% 63.00/10.29 thf(func_def_598, type, sP527: $o > $o).
% 63.00/10.29 thf(func_def_599, type, sP528: $o > $o).
% 63.00/10.29 thf(func_def_600, type, sP529: $o > $o).
% 63.00/10.29 thf(func_def_601, type, sP530: $o > $o).
% 63.00/10.29 thf(func_def_602, type, sP531: $o > $o).
% 63.00/10.29 thf(func_def_603, type, sP532: $o > $o).
% 63.00/10.29 thf(func_def_604, type, sP533: $o > $o).
% 63.00/10.29 thf(func_def_605, type, sP534: $o > $o).
% 63.00/10.29 thf(func_def_606, type, sP535: $o > $o).
% 63.00/10.29 thf(func_def_607, type, sP536: $o > $o).
% 63.00/10.29 thf(func_def_608, type, sP537: $o > $o).
% 63.00/10.29 thf(func_def_609, type, sP538: $o > $o).
% 63.00/10.29 thf(func_def_610, type, sP539: $o > $o).
% 63.00/10.29 thf(func_def_611, type, sP540: $o > $o).
% 63.00/10.29 thf(func_def_612, type, sP541: $o > $o).
% 63.00/10.29 thf(func_def_613, type, sP542: $o > $o).
% 63.00/10.29 thf(func_def_614, type, sP543: $o > $o).
% 63.00/10.29 thf(func_def_615, type, sP544: $o > $o).
% 63.00/10.29 thf(func_def_616, type, sP545: $o > $o).
% 63.00/10.29 thf(func_def_617, type, sP546: $o > $o).
% 63.00/10.29 thf(func_def_618, type, sP547: $o > $o).
% 63.00/10.29 thf(func_def_619, type, sP548: $o > $o).
% 63.00/10.29 thf(func_def_620, type, sP549: $o > $o).
% 63.00/10.29 thf(func_def_621, type, sP550: $o > $o).
% 63.00/10.29 thf(func_def_622, type, sP551: $o > $o).
% 63.00/10.29 thf(func_def_623, type, sP552: $o > $o).
% 63.00/10.29 thf(func_def_624, type, sP553: $o > $o).
% 63.00/10.29 thf(func_def_625, type, sP554: $o > $o).
% 63.00/10.29 thf(func_def_626, type, sP555: $o > $o).
% 63.00/10.29 thf(func_def_627, type, sP556: $o > $o).
% 63.00/10.29 thf(func_def_628, type, sP557: $o > $o).
% 63.00/10.29 thf(func_def_629, type, sP558: $o > $o).
% 63.00/10.29 thf(func_def_630, type, sP559: $o > $o).
% 63.00/10.29 thf(func_def_631, type, sP560: $o > $o).
% 63.00/10.29 thf(func_def_632, type, sP561: $o > $o).
% 63.00/10.29 thf(func_def_633, type, sP562: $o > $o).
% 63.00/10.29 thf(func_def_634, type, sP563: $o > $o).
% 63.00/10.29 thf(func_def_635, type, sP564: $o > $o).
% 63.00/10.29 thf(func_def_636, type, sP565: $o > $o).
% 63.00/10.29 thf(func_def_637, type, sP566: $o > $o).
% 63.00/10.29 thf(func_def_638, type, sP567: $o > $o).
% 63.00/10.29 thf(func_def_639, type, sP568: $o > $o).
% 63.00/10.29 thf(func_def_640, type, sP569: $o > $o).
% 63.00/10.29 thf(func_def_641, type, sP570: $o > $o).
% 63.00/10.29 thf(func_def_642, type, sP571: $o > $o).
% 63.00/10.29 thf(func_def_643, type, sP572: $o > $o).
% 63.00/10.29 thf(func_def_644, type, sP573: $o > $o).
% 63.00/10.29 thf(func_def_645, type, sP574: $o > $o).
% 63.00/10.29 thf(func_def_646, type, sP575: $o > $o).
% 63.00/10.29 thf(func_def_647, type, sP576: $o > $o).
% 63.00/10.29 thf(func_def_648, type, sP577: $o > $o).
% 63.00/10.29 thf(func_def_649, type, sP578: $o > $o).
% 63.00/10.29 thf(func_def_650, type, sP579: $o > $o).
% 63.00/10.29 thf(func_def_651, type, sP580: $o > $o).
% 63.00/10.29 thf(func_def_652, type, sP581: $o > $o).
% 63.00/10.29 thf(func_def_653, type, sP582: $o > $o).
% 63.00/10.29 thf(func_def_654, type, sP583: $o > $o).
% 63.00/10.29 thf(func_def_655, type, sP584: $o > $o).
% 63.00/10.29 thf(func_def_656, type, sP585: $o > $o).
% 63.00/10.29 thf(func_def_657, type, sP586: $o > $o).
% 63.00/10.29 thf(func_def_658, type, sP587: $o > $o).
% 63.00/10.29 thf(func_def_659, type, sP588: $o > $o).
% 63.00/10.29 thf(func_def_660, type, sP589: $o > $o).
% 63.00/10.29 thf(func_def_661, type, sP590: $o > $o).
% 63.00/10.29 thf(func_def_662, type, sP591: $o > $o).
% 63.00/10.29 thf(func_def_663, type, sP592: $o > $o).
% 63.00/10.29 thf(func_def_664, type, sP593: $o > $o).
% 63.00/10.29 thf(func_def_665, type, sP594: $o > $o).
% 63.00/10.29 thf(func_def_666, type, sP595: $o > $o).
% 63.00/10.29 thf(func_def_667, type, sP596: $o > $o).
% 63.00/10.29 thf(func_def_668, type, sP597: $o > $o).
% 63.00/10.29 thf(func_def_669, type, sP598: $o > $o).
% 63.00/10.29 thf(func_def_670, type, sP599: $o > $o).
% 63.00/10.29 thf(func_def_671, type, sP600: $o > $o).
% 63.00/10.29 thf(func_def_672, type, sP601: $o > $o).
% 63.00/10.29 thf(func_def_673, type, sP602: $o > $o).
% 63.00/10.29 thf(func_def_674, type, sP603: $o > $o).
% 63.00/10.29 thf(func_def_675, type, sP604: $o > $o).
% 63.00/10.29 thf(func_def_676, type, sP605: $o > $o).
% 63.00/10.29 thf(func_def_677, type, sP606: $o > $o).
% 63.00/10.29 thf(func_def_678, type, sP607: $o > $o).
% 63.00/10.29 thf(func_def_679, type, sP608: $o > $o).
% 63.00/10.29 thf(func_def_680, type, sP609: $o > $o).
% 63.00/10.29 thf(func_def_681, type, sP610: $o > $o).
% 63.00/10.29 thf(func_def_682, type, sP611: $o > $o).
% 63.00/10.29 thf(func_def_683, type, sP612: $o > $o).
% 63.00/10.29 thf(func_def_684, type, sP613: $o > $o).
% 63.00/10.29 thf(func_def_685, type, sP614: $o > $o).
% 63.00/10.29 thf(func_def_686, type, sP615: $o > $o).
% 63.00/10.29 thf(func_def_687, type, sP616: $o > $o).
% 63.00/10.29 thf(func_def_688, type, sP617: $o > $o).
% 63.00/10.29 thf(func_def_689, type, sP618: $o > $o).
% 63.00/10.29 thf(func_def_690, type, sP619: $o > $o).
% 63.00/10.29 thf(func_def_691, type, sP620: nat > $o).
% 63.00/10.29 thf(func_def_692, type, sP621: $o > $o).
% 63.00/10.29 thf(func_def_693, type, sP622: $o > $o).
% 63.00/10.29 thf(func_def_694, type, sP623: $o > $o).
% 63.00/10.29 thf(func_def_695, type, sP624: $o > $o).
% 63.00/10.29 thf(func_def_696, type, sP625: $o > $o).
% 63.00/10.29 thf(func_def_697, type, sP626: $o > $o).
% 63.00/10.29 thf(func_def_698, type, sP627: $o > $o).
% 63.00/10.29 thf(func_def_699, type, sP628: $o > $o).
% 63.00/10.29 thf(func_def_700, type, sP629: $o > $o).
% 63.00/10.29 thf(func_def_701, type, sP630: $o > $o).
% 63.00/10.29 thf(func_def_702, type, sP631: $o > $o).
% 63.00/10.29 thf(func_def_703, type, sP632: $o > $o).
% 63.00/10.29 thf(func_def_704, type, sP633: $o > $o).
% 63.00/10.29 thf(func_def_705, type, sP634: $o > $o).
% 63.00/10.29 thf(func_def_706, type, sP635: $o > $o).
% 63.00/10.29 thf(func_def_707, type, sP636: $o > $o).
% 63.00/10.29 thf(func_def_708, type, sP637: $o > $o).
% 63.00/10.29 thf(func_def_709, type, sP638: $o > $o).
% 63.00/10.29 thf(func_def_710, type, sP639: $o > $o).
% 63.00/10.29 thf(func_def_711, type, sP640: $o > $o).
% 63.00/10.29 thf(func_def_712, type, sP641: $o > $o).
% 63.00/10.29 thf(func_def_713, type, sP642: $o > $o).
% 63.00/10.29 thf(func_def_714, type, sP643: $o > $o).
% 63.00/10.29 thf(func_def_715, type, sP644: $o > $o).
% 63.00/10.29 thf(func_def_716, type, sP645: $o > $o).
% 63.00/10.29 thf(func_def_717, type, sP646: $o > $o).
% 63.00/10.29 thf(func_def_718, type, sP647: $o > $o).
% 63.00/10.29 thf(func_def_719, type, sP648: $o > $o).
% 63.00/10.29 thf(func_def_720, type, sP649: $o > $o).
% 63.00/10.29 thf(func_def_721, type, sP650: $o > $o).
% 63.00/10.29 thf(func_def_722, type, sP651: $o > $o).
% 63.00/10.29 thf(func_def_723, type, sP652: $o > $o).
% 63.00/10.29 thf(func_def_724, type, sP653: $o > $o).
% 63.00/10.29 thf(func_def_725, type, sP654: $o > $o).
% 63.00/10.29 thf(func_def_726, type, sP655: $o > $o).
% 63.00/10.29 thf(func_def_727, type, sP656: $o > $o).
% 63.00/10.29 thf(func_def_728, type, sP657: $o > $o).
% 63.00/10.29 thf(func_def_729, type, sP658: $o > $o).
% 63.00/10.29 thf(func_def_730, type, sP659: $o > $o).
% 63.00/10.29 thf(func_def_731, type, sP660: $o > $o).
% 63.00/10.29 thf(func_def_732, type, sP661: $o > $o).
% 63.00/10.29 thf(func_def_733, type, sP662: $o > $o).
% 63.00/10.29 thf(func_def_734, type, sP663: $o > $o).
% 63.00/10.29 thf(func_def_735, type, sP664: $o > $o).
% 63.00/10.29 thf(func_def_736, type, sP665: $o > $o).
% 63.00/10.29 thf(func_def_737, type, sP666: $o > $o).
% 63.00/10.29 thf(func_def_738, type, sP667: $o > $o).
% 63.00/10.29 thf(func_def_739, type, sP668: $o > $o).
% 63.00/10.29 thf(func_def_740, type, sP669: $o > $o).
% 63.00/10.29 thf(func_def_741, type, sP670: $o > $o).
% 63.00/10.29 thf(func_def_742, type, sP671: $o > $o).
% 63.00/10.29 thf(func_def_743, type, sP672: $o > $o).
% 63.00/10.29 thf(func_def_744, type, sP673: $o > $o).
% 63.00/10.29 thf(func_def_745, type, sP674: $o > $o).
% 63.00/10.29 thf(func_def_746, type, sP675: $o > $o).
% 63.00/10.29 thf(func_def_747, type, sP676: $o > $o).
% 63.00/10.29 thf(func_def_748, type, sP677: $o > $o).
% 63.00/10.29 thf(func_def_749, type, sP678: $o > $o).
% 63.00/10.29 thf(func_def_750, type, sP679: $o > $o).
% 63.00/10.29 thf(func_def_751, type, sP680: $o > $o).
% 63.00/10.29 thf(func_def_752, type, sP681: $o > $o).
% 63.00/10.29 thf(func_def_753, type, sP682: $o > $o).
% 63.00/10.29 thf(func_def_754, type, sP683: $o > $o).
% 63.00/10.29 thf(func_def_755, type, sP684: $o > $o).
% 63.00/10.29 thf(func_def_756, type, sP685: $o > $o).
% 63.00/10.29 thf(func_def_757, type, sP686: $o > $o).
% 63.00/10.29 thf(func_def_758, type, sP687: $o > $o).
% 63.00/10.29 thf(func_def_759, type, sP688: $o > $o).
% 63.00/10.29 thf(func_def_760, type, sP689: $o > $o).
% 63.00/10.29 thf(func_def_761, type, sP690: $o > $o).
% 63.00/10.29 thf(func_def_762, type, sP691: $o > $o).
% 63.00/10.29 thf(func_def_763, type, sP692: $o > $o).
% 63.00/10.29 thf(func_def_764, type, sP693: $o > $o).
% 63.00/10.29 thf(func_def_765, type, sP694: $o > $o).
% 63.00/10.29 thf(func_def_766, type, sP695: $o > $o).
% 63.00/10.29 thf(func_def_767, type, sP696: $o > $o).
% 63.00/10.29 thf(func_def_768, type, sP697: $o > $o).
% 63.00/10.29 thf(func_def_769, type, sP698: $o > $o).
% 63.00/10.29 thf(func_def_770, type, sP699: $o > $o).
% 63.00/10.29 thf(func_def_771, type, sP700: $o > $o).
% 63.00/10.29 thf(func_def_772, type, sP701: $o > $o).
% 63.00/10.29 thf(func_def_773, type, sP702: $o > $o).
% 63.00/10.29 thf(func_def_774, type, sP703: $o > $o).
% 63.00/10.29 thf(func_def_775, type, sP704: $o > $o).
% 63.00/10.29 thf(func_def_776, type, sP705: $o > $o).
% 63.00/10.29 thf(func_def_777, type, sP706: $o > $o).
% 63.00/10.29 thf(func_def_778, type, sP707: $o > $o).
% 63.00/10.29 thf(func_def_779, type, sP708: $o > $o).
% 63.00/10.29 thf(func_def_780, type, sP709: $o > $o).
% 63.00/10.29 thf(func_def_781, type, sP710: $o > $o).
% 63.00/10.29 thf(func_def_782, type, sP711: $o > $o).
% 63.00/10.29 thf(func_def_783, type, sP712: $o > $o).
% 63.00/10.29 thf(func_def_784, type, sP713: $o > $o).
% 63.00/10.29 thf(func_def_785, type, sP714: $o > $o).
% 63.00/10.29 thf(func_def_786, type, sP715: $o > $o).
% 63.00/10.29 thf(func_def_787, type, sP716: $o > $o).
% 63.00/10.29 thf(func_def_788, type, sP717: $o > $o).
% 63.00/10.29 thf(func_def_790, type, sK719: !>[X0: $tType]:(list @ X0 > (X0 > $o) > X0)).
% 63.00/10.29 thf(func_def_791, type, sK720: !>[X0: $tType]:((X0 > $o) > list @ X0 > X0)).
% 63.00/10.29 thf(func_def_792, type, sK721: !>[X0: $tType]:((X0 > $o) > list @ X0 > X0)).
% 63.00/10.29 thf(func_def_793, type, sK722: !>[X0: $tType]:(list @ X0 > (X0 > $o) > X0)).
% 63.00/10.29 thf(func_def_794, type, sK723: !>[X0: $tType]:(list @ X0 > (X0 > $o) > list @ X0)).
% 63.00/10.29 thf(func_def_795, type, sK724: !>[X0: $tType]:(list @ X0 > (X0 > $o) > list @ X0)).
% 63.00/10.29 thf(func_def_796, type, sK725: !>[X0: $tType]:(X0 > list @ X0 > list @ X0)).
% 63.00/10.29 thf(func_def_797, type, sK726: !>[X0: $tType]:(X0 > list @ X0 > list @ X0)).
% 63.00/10.29 thf(func_def_798, type, sK727: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0 > list @ X0 > list @ X0)).
% 63.00/10.29 thf(func_def_799, type, sK728: !>[X0: $tType, X1: $tType]:(list @ X0 > set @ product_prod @ X1 @ X0 > list @ X1 > list @ X0)).
% 63.00/10.29 thf(func_def_800, type, sK729: !>[X0: $tType, X1: $tType]:(list @ X0 > set @ product_prod @ X1 @ X0 > list @ X1 > list @ X1)).
% 63.00/10.29 thf(func_def_801, type, sK730: !>[X0: $tType, X1: $tType]:(list @ X0 > set @ product_prod @ X1 @ X0 > list @ X1 > X0)).
% 63.00/10.29 thf(func_def_802, type, sK731: !>[X0: $tType, X1: $tType]:(list @ X0 > set @ product_prod @ X1 @ X0 > list @ X1 > X1)).
% 63.00/10.29 thf(func_def_803, type, sK732: !>[X0: $tType, X1: $tType]:(list @ X0 > set @ product_prod @ X1 @ X0 > list @ X1 > list @ X1)).
% 63.00/10.29 thf(func_def_804, type, sK733: !>[X0: $tType, X1: $tType]:(list @ X0 > set @ product_prod @ X1 @ X0 > list @ X1 > X0)).
% 63.00/10.29 thf(func_def_805, type, sK734: !>[X0: $tType, X1: $tType]:(list @ X0 > set @ product_prod @ X1 @ X0 > list @ X1 > X1)).
% 63.00/10.29 thf(func_def_806, type, sK735: !>[X0: $tType]:(list @ list @ X0 > list @ X0)).
% 63.00/10.29 thf(func_def_807, type, sK736: !>[X0: $tType]:(list @ list @ X0 > list @ X0 > list @ X0 > list @ list @ X0)).
% 63.00/10.29 thf(func_def_808, type, sK737: !>[X0: $tType]:(list @ list @ X0 > list @ X0 > list @ X0 > list @ X0)).
% 63.00/10.29 thf(func_def_809, type, sK738: !>[X0: $tType]:(list @ list @ X0 > list @ X0 > list @ X0 > list @ X0)).
% 63.00/10.29 thf(func_def_810, type, sK739: !>[X0: $tType]:(list @ list @ X0 > list @ X0 > list @ X0 > list @ list @ X0)).
% 63.00/10.29 thf(func_def_811, type, sK740: !>[X0: $tType]:(list @ list @ X0 > list @ X0)).
% 63.00/10.29 thf(func_def_812, type, sK741: !>[X0: $tType]:(list @ X0 > list @ X0 > X0 > list @ X0 > list @ X0)).
% 63.00/10.29 thf(func_def_813, type, sK742: !>[X0: $tType]:(list @ X0 > list @ X0 > X0 > list @ X0 > list @ X0)).
% 63.00/10.29 thf(func_def_814, type, sK743: !>[X0: $tType]:(X0 > list @ X0 > list @ X0)).
% 63.00/10.29 thf(func_def_815, type, sK744: !>[X0: $tType]:(X0 > list @ X0 > list @ X0)).
% 63.00/10.29 thf(func_def_816, type, sK745: !>[X0: $tType]:(list @ X0 > set @ product_prod @ X0 @ X0 > X0)).
% 63.00/10.29 thf(func_def_817, type, sK746: !>[X0: $tType]:(X0 > list @ X0 > list @ X0 > list @ X0 > list @ X0)).
% 63.00/10.29 thf(func_def_818, type, sK747: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 63.00/10.29 thf(func_def_819, type, sK748: !>[X0: $tType]:(list @ X0 > X0)).
% 63.00/10.29 thf(func_def_820, type, sK749: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 63.00/10.29 thf(func_def_821, type, sK750: !>[X0: $tType]:(list @ X0 > X0)).
% 63.00/10.29 thf(func_def_822, type, sK751: !>[X0: $tType]:(list @ X0 > (X0 > $o) > list @ X0)).
% 63.00/10.29 thf(func_def_823, type, sK752: !>[X0: $tType]:(list @ X0 > (X0 > $o) > X0)).
% 63.00/10.29 thf(func_def_824, type, sK753: !>[X0: $tType]:(list @ X0 > (X0 > $o) > list @ X0)).
% 63.00/10.29 thf(func_def_825, type, sK754: !>[X0: $tType]:(list @ X0 > (X0 > $o) > X0)).
% 63.00/10.29 thf(func_def_826, type, sK755: !>[X0: $tType]:((X0 > $o) > list @ X0 > X0)).
% 63.00/10.29 thf(func_def_827, type, sK756: !>[X0: $tType]:((X0 > $o) > list @ X0 > X0)).
% 63.00/10.29 thf(func_def_828, type, sK757: !>[X0: $tType]:(X0 > list @ X0 > list @ X0)).
% 63.00/10.29 thf(func_def_829, type, sK758: !>[X0: $tType]:(X0 > list @ X0 > list @ X0)).
% 63.00/10.29 thf(func_def_830, type, ph759: !>[X0: $tType]:(X0)).
% 63.00/10.29 thf(f3751,plain,(
% 63.00/10.29 $false),
% 63.00/10.29 inference(equality_resolution,[status(thm)],[f3262])).
% 63.00/10.29 thf(f3262,plain,(
% 63.00/10.29 ( ! [X2 : a,X3 : a,X0 : product_prod @ a @ a,X1 : list @ product_prod @ a @ a,X4 : list @ product_prod @ a @ a] : (((cons @ product_prod @ a @ a @ e @ (append @ product_prod @ a @ a @ sK222 @ (cons @ product_prod @ a @ a @ (product_Pair @ a @ a @ sK223 @ sK224) @ (cons @ product_prod @ a @ a @ (product_Pair @ a @ a @ sK224 @ sK223) @ sK225)))) != (cons @ product_prod @ a @ a @ X0 @ (append @ product_prod @ a @ a @ X1 @ (cons @ product_prod @ a @ a @ (product_Pair @ a @ a @ X2 @ X3) @ (cons @ product_prod @ a @ a @ (product_Pair @ a @ a @ X3 @ X2) @ X4)))))) )),
% 63.00/10.29 inference(superposition,[status(thm)],[f2593,f1535])).
% 63.00/10.29 thf(f1535,plain,(
% 63.00/10.29 ( ! [X0 : $tType,X2 : list @ X0,X3 : list @ X0,X1 : X0] : (((cons @ X0 @ X1 @ (append @ X0 @ X2 @ X3)) = (append @ X0 @ (cons @ X0 @ X1 @ X2) @ X3))) )),
% 63.00/10.29 inference(cnf_transformation,[status(thm)],[f669])).
% 63.00/10.29 thf(f669,plain,(
% 63.00/10.29 ! [X0 : $tType,X1 : X0,X2 : list @ X0,X3 : list @ X0] : ((cons @ X0 @ X1 @ (append @ X0 @ X2 @ X3)) = (append @ X0 @ (cons @ X0 @ X1 @ X2) @ X3))),
% 63.00/10.29 inference(rectify,[status(thm)],[f11])).
% 63.00/10.29 thf(f11,axiom,(
% 63.00/10.29 ! [X0 : $tType,X25 : X0,X12 : list @ X0,X13 : list @ X0] : ((append @ X0 @ (cons @ X0 @ X25 @ X12) @ X13) = (cons @ X0 @ X25 @ (append @ X0 @ X12 @ X13)))),
% 63.00/10.29 file('/export/starexec/sandbox2/tmp/tmp.eKA1rT9gZb/DTF2THF_9790.p',fact_10_append__Cons)).
% 63.00/10.29 thf(f2593,plain,(
% 63.00/10.29 ( ! [X2 : a,X3 : a,X1 : list @ product_prod @ a @ a,X4 : list @ product_prod @ a @ a] : (((cons @ product_prod @ a @ a @ e @ (append @ product_prod @ a @ a @ sK222 @ (cons @ product_prod @ a @ a @ (product_Pair @ a @ a @ sK223 @ sK224) @ (cons @ product_prod @ a @ a @ (product_Pair @ a @ a @ sK224 @ sK223) @ sK225)))) != (append @ product_prod @ a @ a @ X4 @ (cons @ product_prod @ a @ a @ (product_Pair @ a @ a @ X3 @ X2) @ (cons @ product_prod @ a @ a @ (product_Pair @ a @ a @ X2 @ X3) @ X1))))) )),
% 63.00/10.29 inference(equality_proxy_clausification,[status(thm)],[f2592])).
% 63.00/10.29 thf(f2592,plain,(
% 63.00/10.29 ( ! [X2 : a,X3 : a,X1 : list @ product_prod @ a @ a,X4 : list @ product_prod @ a @ a] : ((((append @ product_prod @ a @ a @ X4 @ (cons @ product_prod @ a @ a @ (product_Pair @ a @ a @ X3 @ X2) @ (cons @ product_prod @ a @ a @ (product_Pair @ a @ a @ X2 @ X3) @ X1))) = (cons @ product_prod @ a @ a @ e @ (append @ product_prod @ a @ a @ sK222 @ (cons @ product_prod @ a @ a @ (product_Pair @ a @ a @ sK223 @ sK224) @ (cons @ product_prod @ a @ a @ (product_Pair @ a @ a @ sK224 @ sK223) @ sK225))))) = $false)) )),
% 63.00/10.29 inference(not_proxy_clausification,[status(thm)],[f2591])).
% 63.00/10.29 thf(f2591,plain,(
% 63.00/10.29 ( ! [X2 : a,X3 : a,X1 : list @ product_prod @ a @ a,X4 : list @ product_prod @ a @ a] : (($true = (~ ((append @ product_prod @ a @ a @ X4 @ (cons @ product_prod @ a @ a @ (product_Pair @ a @ a @ X3 @ X2) @ (cons @ product_prod @ a @ a @ (product_Pair @ a @ a @ X2 @ X3) @ X1))) = (cons @ product_prod @ a @ a @ e @ (append @ product_prod @ a @ a @ sK222 @ (cons @ product_prod @ a @ a @ (product_Pair @ a @ a @ sK223 @ sK224) @ (cons @ product_prod @ a @ a @ (product_Pair @ a @ a @ sK224 @ sK223) @ sK225)))))))) )),
% 63.00/10.29 inference(beta_eta_normalization,[status(thm)],[f2590])).
% 63.00/10.29 thf(f2590,plain,(
% 63.00/10.29 ( ! [X2 : a,X3 : a,X1 : list @ product_prod @ a @ a,X4 : list @ product_prod @ a @ a] : (($true = ((^[Y0 : list @ product_prod @ a @ a]: (~ ((append @ product_prod @ a @ a @ Y0 @ (cons @ product_prod @ a @ a @ (product_Pair @ a @ a @ X3 @ X2) @ (cons @ product_prod @ a @ a @ (product_Pair @ a @ a @ X2 @ X3) @ X1))) = (cons @ product_prod @ a @ a @ e @ (append @ product_prod @ a @ a @ sK222 @ (cons @ product_prod @ a @ a @ (product_Pair @ a @ a @ sK223 @ sK224) @ (cons @ product_prod @ a @ a @ (product_Pair @ a @ a @ sK224 @ sK223) @ sK225))))))) @ X4))) )),
% 63.00/10.29 inference(pi_clausification,[status(thm)],[f2589])).
% 63.00/10.29 thf(f2589,plain,(
% 63.00/10.29 ( ! [X2 : a,X3 : a,X1 : list @ product_prod @ a @ a] : (($true = (!! @ list @ product_prod @ a @ a @ (^[Y0 : list @ product_prod @ a @ a]: (~ ((append @ product_prod @ a @ a @ Y0 @ (cons @ product_prod @ a @ a @ (product_Pair @ a @ a @ X3 @ X2) @ (cons @ product_prod @ a @ a @ (product_Pair @ a @ a @ X2 @ X3) @ X1))) = (cons @ product_prod @ a @ a @ e @ (append @ product_prod @ a @ a @ sK222 @ (cons @ product_prod @ a @ a @ (product_Pair @ a @ a @ sK223 @ sK224) @ (cons @ product_prod @ a @ a @ (product_Pair @ a @ a @ sK224 @ sK223) @ sK225)))))))))) )),
% 63.00/10.29 inference(beta_eta_normalization,[status(thm)],[f2588])).
% 63.00/10.29 thf(f2588,plain,(
% 63.00/10.29 ( ! [X2 : a,X3 : a,X1 : list @ product_prod @ a @ a] : (($true = ((^[Y0 : a]: (!! @ list @ product_prod @ a @ a @ (^[Y1 : list @ product_prod @ a @ a]: (~ ((append @ product_prod @ a @ a @ Y1 @ (cons @ product_prod @ a @ a @ (product_Pair @ a @ a @ Y0 @ X2) @ (cons @ product_prod @ a @ a @ (product_Pair @ a @ a @ X2 @ Y0) @ X1))) = (cons @ product_prod @ a @ a @ e @ (append @ product_prod @ a @ a @ sK222 @ (cons @ product_prod @ a @ a @ (product_Pair @ a @ a @ sK223 @ sK224) @ (cons @ product_prod @ a @ a @ (product_Pair @ a @ a @ sK224 @ sK223) @ sK225))))))))) @ X3))) )),
% 63.00/10.29 inference(pi_clausification,[status(thm)],[f2587])).
% 63.00/10.29 thf(f2587,plain,(
% 63.00/10.29 ( ! [X2 : a,X1 : list @ product_prod @ a @ a] : (($true = (!! @ a @ (^[Y0 : a]: (!! @ list @ product_prod @ a @ a @ (^[Y1 : list @ product_prod @ a @ a]: (~ ((append @ product_prod @ a @ a @ Y1 @ (cons @ product_prod @ a @ a @ (product_Pair @ a @ a @ Y0 @ X2) @ (cons @ product_prod @ a @ a @ (product_Pair @ a @ a @ X2 @ Y0) @ X1))) = (cons @ product_prod @ a @ a @ e @ (append @ product_prod @ a @ a @ sK222 @ (cons @ product_prod @ a @ a @ (product_Pair @ a @ a @ sK223 @ sK224) @ (cons @ product_prod @ a @ a @ (product_Pair @ a @ a @ sK224 @ sK223) @ sK225)))))))))))) )),
% 63.00/10.29 inference(beta_eta_normalization,[status(thm)],[f2586])).
% 63.00/10.29 thf(f2586,plain,(
% 63.00/10.29 ( ! [X2 : a,X1 : list @ product_prod @ a @ a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ list @ product_prod @ a @ a @ (^[Y2 : list @ product_prod @ a @ a]: (~ ((append @ product_prod @ a @ a @ Y2 @ (cons @ product_prod @ a @ a @ (product_Pair @ a @ a @ Y1 @ Y0) @ (cons @ product_prod @ a @ a @ (product_Pair @ a @ a @ Y0 @ Y1) @ X1))) = (cons @ product_prod @ a @ a @ e @ (append @ product_prod @ a @ a @ sK222 @ (cons @ product_prod @ a @ a @ (product_Pair @ a @ a @ sK223 @ sK224) @ (cons @ product_prod @ a @ a @ (product_Pair @ a @ a @ sK224 @ sK223) @ sK225))))))))))) @ X2))) )),
% 63.00/10.29 inference(pi_clausification,[status(thm)],[f2585])).
% 63.00/10.29 thf(f2585,plain,(
% 63.00/10.29 ( ! [X1 : list @ product_prod @ a @ a] : (($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ list @ product_prod @ a @ a @ (^[Y2 : list @ product_prod @ a @ a]: (~ ((append @ product_prod @ a @ a @ Y2 @ (cons @ product_prod @ a @ a @ (product_Pair @ a @ a @ Y1 @ Y0) @ (cons @ product_prod @ a @ a @ (product_Pair @ a @ a @ Y0 @ Y1) @ X1))) = (cons @ product_prod @ a @ a @ e @ (append @ product_prod @ a @ a @ sK222 @ (cons @ product_prod @ a @ a @ (product_Pair @ a @ a @ sK223 @ sK224) @ (cons @ product_prod @ a @ a @ (product_Pair @ a @ a @ sK224 @ sK223) @ sK225)))))))))))))) )),
% 63.00/10.29 inference(beta_eta_normalization,[status(thm)],[f2584])).
% 63.00/10.29 thf(f2584,plain,(
% 63.00/10.29 ( ! [X1 : list @ product_prod @ a @ a] : (($true = ((^[Y0 : list @ product_prod @ a @ a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ list @ product_prod @ a @ a @ (^[Y3 : list @ product_prod @ a @ a]: (~ ((append @ product_prod @ a @ a @ Y3 @ (cons @ product_prod @ a @ a @ (product_Pair @ a @ a @ Y2 @ Y1) @ (cons @ product_prod @ a @ a @ (product_Pair @ a @ a @ Y1 @ Y2) @ Y0))) = (cons @ product_prod @ a @ a @ e @ (append @ product_prod @ a @ a @ sK222 @ (cons @ product_prod @ a @ a @ (product_Pair @ a @ a @ sK223 @ sK224) @ (cons @ product_prod @ a @ a @ (product_Pair @ a @ a @ sK224 @ sK223) @ sK225))))))))))))) @ X1))) )),
% 63.00/10.29 inference(pi_clausification,[status(thm)],[f2583])).
% 63.00/10.29 thf(f2583,plain,(
% 63.00/10.29 ($true = (!! @ list @ product_prod @ a @ a @ (^[Y0 : list @ product_prod @ a @ a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ list @ product_prod @ a @ a @ (^[Y3 : list @ product_prod @ a @ a]: (~ ((append @ product_prod @ a @ a @ Y3 @ (cons @ product_prod @ a @ a @ (product_Pair @ a @ a @ Y2 @ Y1) @ (cons @ product_prod @ a @ a @ (product_Pair @ a @ a @ Y1 @ Y2) @ Y0))) = (cons @ product_prod @ a @ a @ e @ (append @ product_prod @ a @ a @ sK222 @ (cons @ product_prod @ a @ a @ (product_Pair @ a @ a @ sK223 @ sK224) @ (cons @ product_prod @ a @ a @ (product_Pair @ a @ a @ sK224 @ sK223) @ sK225)))))))))))))))),
% 63.00/10.29 inference(beta_eta_normalization,[status(thm)],[f1747])).
% 63.00/10.29 thf(f1747,plain,(
% 63.00/10.29 ($true = ((^[Y0 : list @ product_prod @ a @ a]: (!! @ list @ product_prod @ a @ a @ (^[Y1 : list @ product_prod @ a @ a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ list @ product_prod @ a @ a @ (^[Y4 : list @ product_prod @ a @ a]: (~ ((append @ product_prod @ a @ a @ Y4 @ (cons @ product_prod @ a @ a @ (product_Pair @ a @ a @ Y3 @ Y2) @ (cons @ product_prod @ a @ a @ (product_Pair @ a @ a @ Y2 @ Y3) @ Y1))) = Y0))))))))))) @ (cons @ product_prod @ a @ a @ e @ (append @ product_prod @ a @ a @ sK222 @ (cons @ product_prod @ a @ a @ (product_Pair @ a @ a @ sK223 @ sK224) @ (cons @ product_prod @ a @ a @ (product_Pair @ a @ a @ sK224 @ sK223) @ sK225))))))),
% 63.00/10.29 inference(definition_unfolding,[status(thm)],[f1570,f1457,f1553])).
% 63.00/10.29 thf(f1553,plain,(
% 63.00/10.29 (es = (append @ product_prod @ a @ a @ sK222 @ (cons @ product_prod @ a @ a @ (product_Pair @ a @ a @ sK223 @ sK224) @ (cons @ product_prod @ a @ a @ (product_Pair @ a @ a @ sK224 @ sK223) @ sK225))))),
% 63.00/10.29 inference(cnf_transformation,[status(thm)],[f1161])).
% 63.00/10.29 thf(f1161,plain,(
% 63.00/10.29 (es = (append @ product_prod @ a @ a @ sK222 @ (cons @ product_prod @ a @ a @ (product_Pair @ a @ a @ sK223 @ sK224) @ (cons @ product_prod @ a @ a @ (product_Pair @ a @ a @ sK224 @ sK223) @ sK225))))),
% 63.00/10.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK222,sK223,sK224,sK225])],[f841,f1160])).
% 63.00/10.29 thf(f1160,plain,(
% 63.00/10.29 ? [X0 : list @ product_prod @ a @ a,X1 : a,X2 : a,X3 : list @ product_prod @ a @ a] : (es = (append @ product_prod @ a @ a @ X0 @ (cons @ product_prod @ a @ a @ (product_Pair @ a @ a @ X1 @ X2) @ (cons @ product_prod @ a @ a @ (product_Pair @ a @ a @ X2 @ X1) @ X3)))) => (es = (append @ product_prod @ a @ a @ sK222 @ (cons @ product_prod @ a @ a @ (product_Pair @ a @ a @ sK223 @ sK224) @ (cons @ product_prod @ a @ a @ (product_Pair @ a @ a @ sK224 @ sK223) @ sK225))))),
% 63.00/10.29 introduced(definition,[],[choice_axiom])).
% 63.00/10.29 thf(f841,plain,(
% 63.00/10.29 ? [X0 : list @ product_prod @ a @ a,X1 : a,X2 : a,X3 : list @ product_prod @ a @ a] : (es = (append @ product_prod @ a @ a @ X0 @ (cons @ product_prod @ a @ a @ (product_Pair @ a @ a @ X1 @ X2) @ (cons @ product_prod @ a @ a @ (product_Pair @ a @ a @ X2 @ X1) @ X3))))),
% 63.00/10.29 inference(ennf_transformation,[status(thm)],[f671])).
% 63.00/10.29 thf(f671,plain,(
% 63.00/10.29 ~! [X0 : list @ product_prod @ a @ a,X1 : a,X2 : a,X3 : list @ product_prod @ a @ a] : (es != (append @ product_prod @ a @ a @ X0 @ (cons @ product_prod @ a @ a @ (product_Pair @ a @ a @ X1 @ X2) @ (cons @ product_prod @ a @ a @ (product_Pair @ a @ a @ X2 @ X1) @ X3))))),
% 63.00/10.29 inference(rectify,[status(thm)],[f268])).
% 63.00/10.29 thf(f268,negated_conjecture,(
% 63.00/10.29 ~! [X77 : list @ product_prod @ a @ a,X45 : a,X46 : a,X78 : list @ product_prod @ a @ a] : (es != (append @ product_prod @ a @ a @ X77 @ (cons @ product_prod @ a @ a @ (product_Pair @ a @ a @ X45 @ X46) @ (cons @ product_prod @ a @ a @ (product_Pair @ a @ a @ X46 @ X45) @ X78))))),
% 63.00/10.29 inference(negated_conjecture,[status(cth)],[f267])).
% 63.00/10.29 thf(f267,conjecture,(
% 63.00/10.29 ! [X77 : list @ product_prod @ a @ a,X45 : a,X46 : a,X78 : list @ product_prod @ a @ a] : (es != (append @ product_prod @ a @ a @ X77 @ (cons @ product_prod @ a @ a @ (product_Pair @ a @ a @ X45 @ X46) @ (cons @ product_prod @ a @ a @ (product_Pair @ a @ a @ X46 @ X45) @ X78))))),
% 63.00/10.29 file('/export/starexec/sandbox2/tmp/tmp.eKA1rT9gZb/DTF2THF_9790.p',conj_0)).
% 63.00/10.29 thf(f1457,plain,(
% 63.00/10.29 ( ! [X0 : $tType] : ((kurato990191779essing @ X0 = (^[Y0 : list @ product_prod @ X0 @ X0]: (!! @ list @ product_prod @ X0 @ X0 @ (^[Y1 : list @ product_prod @ X0 @ X0]: (!! @ X0 @ (^[Y2 : X0]: (!! @ X0 @ (^[Y3 : X0]: (!! @ list @ product_prod @ X0 @ X0 @ (^[Y4 : list @ product_prod @ X0 @ X0]: (~ ((append @ product_prod @ X0 @ X0 @ Y4 @ (cons @ product_prod @ X0 @ X0 @ (product_Pair @ X0 @ X0 @ Y3 @ Y2) @ (cons @ product_prod @ X0 @ X0 @ (product_Pair @ X0 @ X0 @ Y2 @ Y3) @ Y1))) = Y0))))))))))))) )),
% 63.00/10.29 inference(cnf_transformation,[status(thm)],[f539])).
% 63.00/10.29 thf(f539,plain,(
% 63.00/10.29 ! [X0 : $tType] : (kurato990191779essing @ X0 = (^[Y0 : list @ product_prod @ X0 @ X0]: (!! @ list @ product_prod @ X0 @ X0 @ (^[Y1 : list @ product_prod @ X0 @ X0]: (!! @ X0 @ (^[Y2 : X0]: (!! @ X0 @ (^[Y3 : X0]: (!! @ list @ product_prod @ X0 @ X0 @ (^[Y4 : list @ product_prod @ X0 @ X0]: (~ ((append @ product_prod @ X0 @ X0 @ Y4 @ (cons @ product_prod @ X0 @ X0 @ (product_Pair @ X0 @ X0 @ Y3 @ Y2) @ (cons @ product_prod @ X0 @ X0 @ (product_Pair @ X0 @ X0 @ Y2 @ Y3) @ Y1))) = Y0))))))))))))),
% 63.00/10.29 inference(fool_elimination,[status(thm)],[f538])).
% 63.00/10.29 thf(f538,plain,(
% 63.00/10.29 ! [X0 : $tType] : ((^[X1 : list @ product_prod @ X0 @ X0] : (! [X2 : list @ product_prod @ X0 @ X0,X3 : X0,X4 : X0,X5 : list @ product_prod @ X0 @ X0] : ((append @ product_prod @ X0 @ X0 @ X2 @ (cons @ product_prod @ X0 @ X0 @ (product_Pair @ X0 @ X0 @ X3 @ X4) @ (cons @ product_prod @ X0 @ X0 @ (product_Pair @ X0 @ X0 @ X4 @ X3) @ X5))) != X1))) = kurato990191779essing @ X0)),
% 63.00/10.29 inference(rectify,[status(thm)],[f2])).
% 63.00/10.29 thf(f2,axiom,(
% 63.00/10.29 ! [X0 : $tType] : ((^[X4 : list @ product_prod @ X0 @ X0] : (! [X5 : list @ product_prod @ X0 @ X0,X6 : X0,X7 : X0,X8 : list @ product_prod @ X0 @ X0] : ((append @ product_prod @ X0 @ X0 @ X5 @ (cons @ product_prod @ X0 @ X0 @ (product_Pair @ X0 @ X0 @ X6 @ X7) @ (cons @ product_prod @ X0 @ X0 @ (product_Pair @ X0 @ X0 @ X7 @ X6) @ X8))) != X4))) = kurato990191779essing @ X0)),
% 63.00/10.29 file('/export/starexec/sandbox2/tmp/tmp.eKA1rT9gZb/DTF2THF_9790.p',fact_1_progressing__def)).
% 63.00/10.29 thf(f1570,plain,(
% 63.00/10.29 ((kurato990191779essing @ a @ (cons @ product_prod @ a @ a @ e @ es)) = $true)),
% 63.00/10.29 inference(cnf_transformation,[status(thm)],[f351])).
% 63.00/10.29 thf(f351,plain,(
% 63.00/10.29 ((kurato990191779essing @ a @ (cons @ product_prod @ a @ a @ e @ es)) = $true)),
% 63.00/10.29 inference(fool_elimination,[status(thm)],[f350])).
% 63.00/10.29 thf(f350,plain,(
% 63.00/10.29 (kurato990191779essing @ a @ (cons @ product_prod @ a @ a @ e @ es))),
% 63.00/10.29 inference(rectify,[status(thm)],[f1])).
% 63.00/10.29 thf(f1,axiom,(
% 63.00/10.29 (kurato990191779essing @ a @ (cons @ product_prod @ a @ a @ e @ es))),
% 63.00/10.29 file('/export/starexec/sandbox2/tmp/tmp.eKA1rT9gZb/DTF2THF_9790.p',fact_0_assms)).
% 63.00/10.29 % SZS output end Proof for DTF2THF_9790
% 63.00/10.29 % (10420)------------------------------
% 63.00/10.29 % (10420)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.00/10.29 % (10420)Termination reason: Refutation
% 63.00/10.29
% 63.00/10.29 % (10420)Memory used [KB]: 14072
% 63.00/10.29 % (10420)Time elapsed: 0.492 s
% 63.00/10.29 % (10420)Instructions burned: 1618 (million)
% 63.00/10.29 % (10420)------------------------------
% 63.00/10.29 % (10420)------------------------------
% 63.00/10.29 % (9955)Success in time 8.668 s
%------------------------------------------------------------------------------