%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP029^2 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n020.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 08:54:59 AM UTC 2026
% Result : ContradictoryAxioms 2.92s 1.74s
% Output : Refutation 2.92s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP029^2 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n020.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 08:23:57 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.47 ---- Original DTF file ---
% 0.30/0.47 thf(spec,logic,$$dhol).
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 % File : ITP029^2 : TPTP v9.2.1. Released v7.5.0.
% 0.30/0.47 % Domain : Interactive Theorem Proving
% 0.30/0.47 % Problem : Sledgehammer BinaryTree problem prob_163__3251696_1
% 0.30/0.47 % Version : Especial.
% 0.30/0.47 % English :
% 0.30/0.47
% 0.30/0.47 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.30/0.47 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.30/0.47 % Source : [Des21]
% 0.30/0.47 % Names : BinaryTree/prob_163__3251696_1 [Des21]
% 0.30/0.47
% 0.30/0.47 % Status : ContradictoryAxioms
% 0.30/0.47 % Rating : 0.33 v8.1.0, 0.50 v7.5.0
% 0.30/0.47 % Syntax : Number of formulae : 347 ( 136 unt; 54 typ; 0 def)
% 0.30/0.47 % Number of atoms : 802 ( 284 equ; 0 cnn)
% 0.30/0.47 % Maximal formula atoms : 13 ( 2 avg)
% 0.30/0.47 % Number of connectives : 3296 ( 86 ~; 31 |; 60 &;2752 @)
% 0.30/0.47 % ( 0 <=>; 367 =>; 0 <=; 0 <~>)
% 0.30/0.47 % Maximal formula depth : 18 ( 7 avg)
% 0.30/0.47 % Number of types : 3 ( 2 usr)
% 0.30/0.47 % Number of type conns : 204 ( 204 >; 0 *; 0 +; 0 <<)
% 0.30/0.47 % Number of symbols : 55 ( 52 usr; 7 con; 0-6 aty)
% 0.30/0.47 % Number of variables : 1031 ( 91 ^; 847 !; 46 ?;1031 :)
% 0.30/0.47 % ( 47 !>; 0 ?*; 0 @-; 0 @+)
% 0.30/0.47 % SPC : TH1_THM_EQU_NAR
% 0.30/0.47
% 0.30/0.47 % Comments : This file was generated by Sledgehammer 2021-02-23 16:15:27.169
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 % Could-be-implicit typings (4)
% 0.30/0.47 thf(ty_t_BinaryTree__Mirabelle__pchhvghoao_OTree,type,
% 0.30/0.47 binary1291135688e_Tree: $tType > $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_t_Set_Oset,type,
% 0.30/0.47 set: $tType > $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_t_Int_Oint,type,
% 0.30/0.47 int: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_tf_a,type,
% 0.30/0.47 a: $tType ).
% 0.30/0.47
% 0.30/0.47 % Explicit typings (50)
% 0.30/0.47 thf(sy_cl_Lattices_Obounded__lattice,type,
% 0.30/0.47 bounded_lattice:
% 0.30/0.47 !>[A: $tType] : $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_cl_HOL_Otype,type,
% 0.30/0.47 type:
% 0.30/0.47 !>[A: $tType] : $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_cl_Orderings_Obot,type,
% 0.30/0.47 bot:
% 0.30/0.47 !>[A: $tType] : $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_cl_Orderings_Oord,type,
% 0.30/0.47 ord:
% 0.30/0.47 !>[A: $tType] : $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_cl_Orderings_Oorder,type,
% 0.30/0.47 order:
% 0.30/0.47 !>[A: $tType] : $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_cl_Orderings_Ono__bot,type,
% 0.30/0.47 no_bot:
% 0.30/0.47 !>[A: $tType] : $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_cl_Orderings_Ono__top,type,
% 0.30/0.47 no_top:
% 0.30/0.47 !>[A: $tType] : $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_cl_Orderings_Olinorder,type,
% 0.30/0.47 linorder:
% 0.30/0.47 !>[A: $tType] : $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_cl_Orderings_Opreorder,type,
% 0.30/0.47 preorder:
% 0.30/0.47 !>[A: $tType] : $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_cl_Orderings_Oorder__bot,type,
% 0.30/0.47 order_bot:
% 0.30/0.47 !>[A: $tType] : $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_cl_Orderings_Owellorder,type,
% 0.30/0.47 wellorder:
% 0.30/0.47 !>[A: $tType] : $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_cl_Orderings_Odense__order,type,
% 0.30/0.47 dense_order:
% 0.30/0.47 !>[A: $tType] : $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_cl_Rings_Olinordered__idom,type,
% 0.30/0.47 linordered_idom:
% 0.30/0.47 !>[A: $tType] : $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_cl_Fields_Olinordered__field,type,
% 0.30/0.47 linordered_field:
% 0.30/0.47 !>[A: $tType] : $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_cl_Lattices_Osemilattice__sup,type,
% 0.30/0.47 semilattice_sup:
% 0.30/0.47 !>[A: $tType] : $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_cl_Lattices_Obounded__semilattice__sup__bot,type,
% 0.30/0.47 bounde1808546759up_bot:
% 0.30/0.47 !>[A: $tType] : $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_cl_Conditionally__Complete__Lattices_Olinear__continuum,type,
% 0.30/0.47 condit1656338222tinuum:
% 0.30/0.47 !>[A: $tType] : $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_BinaryTree__Mirabelle__pchhvghoao_OTree_OT,type,
% 0.30/0.47 binary210054475elle_T:
% 0.30/0.47 !>[A: $tType] : ( ( binary1291135688e_Tree @ A ) > A > ( binary1291135688e_Tree @ A ) > ( binary1291135688e_Tree @ A ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_BinaryTree__Mirabelle__pchhvghoao_OTree_OTip,type,
% 0.30/0.47 binary1746293266le_Tip:
% 0.30/0.47 !>[A: $tType] : ( binary1291135688e_Tree @ A ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_BinaryTree__Mirabelle__pchhvghoao_OTree_Ocase__Tree,type,
% 0.30/0.47 binary536355927e_Tree:
% 0.30/0.47 !>[B: $tType,A: $tType] : ( B > ( ( binary1291135688e_Tree @ A ) > A > ( binary1291135688e_Tree @ A ) > B ) > ( binary1291135688e_Tree @ A ) > B ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_BinaryTree__Mirabelle__pchhvghoao_OTree_Orec__Tree,type,
% 0.30/0.47 binary1929596613c_Tree:
% 0.30/0.47 !>[C: $tType,A: $tType] : ( C > ( ( binary1291135688e_Tree @ A ) > A > ( binary1291135688e_Tree @ A ) > C > C > C ) > ( binary1291135688e_Tree @ A ) > C ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_BinaryTree__Mirabelle__pchhvghoao_OTree_Oset__Tree,type,
% 0.30/0.47 binary2130109271t_Tree:
% 0.30/0.47 !>[A: $tType] : ( ( binary1291135688e_Tree @ A ) > ( set @ A ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_BinaryTree__Mirabelle__pchhvghoao_Oeqs,type,
% 0.30/0.47 binary64540844le_eqs:
% 0.30/0.47 !>[A: $tType] : ( ( A > int ) > A > ( set @ A ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_BinaryTree__Mirabelle__pchhvghoao_OsetOf,type,
% 0.30/0.47 binary1653327646_setOf:
% 0.30/0.47 !>[A: $tType] : ( ( binary1291135688e_Tree @ A ) > ( set @ A ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_BinaryTree__Mirabelle__pchhvghoao_OsortedTree,type,
% 0.30/0.47 binary1610619414edTree:
% 0.30/0.47 !>[A: $tType] : ( ( A > int ) > ( binary1291135688e_Tree @ A ) > $o ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_BinaryTree__Mirabelle__pchhvghoao_Osorted__distinct__pred,type,
% 0.30/0.47 binary231205461t_pred:
% 0.30/0.47 !>[A: $tType] : ( ( A > int ) > A > A > ( binary1291135688e_Tree @ A ) > $o ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_HOL_OThe,type,
% 0.30/0.47 the:
% 0.30/0.47 !>[A: $tType] : ( ( A > $o ) > A ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_If,type,
% 0.30/0.47 if:
% 0.30/0.47 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Lattices_Osemilattice__neutr,type,
% 0.30/0.47 semilattice_neutr:
% 0.30/0.47 !>[A: $tType] : ( ( A > A > A ) > A > $o ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Lattices_Osup__class_Osup,type,
% 0.30/0.47 sup_sup:
% 0.30/0.47 !>[A: $tType] : ( A > A > A ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Orderings_Obot__class_Obot,type,
% 0.30/0.47 bot_bot:
% 0.30/0.47 !>[A: $tType] : A ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Orderings_Oord__class_Oless,type,
% 0.30/0.47 ord_less:
% 0.30/0.47 !>[A: $tType] : ( A > A > $o ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.30/0.47 ord_less_eq:
% 0.30/0.47 !>[A: $tType] : ( A > A > $o ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Relation_OPowp,type,
% 0.30/0.47 powp:
% 0.30/0.47 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) > $o ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Relation_Oinv__imagep,type,
% 0.30/0.47 inv_imagep:
% 0.30/0.47 !>[B: $tType,A: $tType] : ( ( B > B > $o ) > ( A > B ) > A > A > $o ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Set_OCollect,type,
% 0.30/0.47 collect:
% 0.30/0.47 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Set_OPow,type,
% 0.30/0.47 pow:
% 0.30/0.47 !>[A: $tType] : ( ( set @ A ) > ( set @ ( set @ A ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Set_Oinsert,type,
% 0.30/0.47 insert:
% 0.30/0.47 !>[A: $tType] : ( A > ( set @ A ) > ( set @ A ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Set_Ois__empty,type,
% 0.30/0.47 is_empty:
% 0.30/0.47 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Set_Ois__singleton,type,
% 0.30/0.47 is_singleton:
% 0.30/0.47 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Set_Othe__elem,type,
% 0.30/0.47 the_elem:
% 0.30/0.47 !>[A: $tType] : ( ( set @ A ) > A ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Zorn_Ochains,type,
% 0.30/0.47 chains:
% 0.30/0.47 !>[A: $tType] : ( ( set @ ( set @ A ) ) > ( set @ ( set @ ( set @ A ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Zorn_Opred__on_Ochain,type,
% 0.30/0.47 pred_chain:
% 0.30/0.47 !>[A: $tType] : ( ( set @ A ) > ( A > A > $o ) > ( set @ A ) > $o ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_member,type,
% 0.30/0.47 member:
% 0.30/0.47 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_v_a,type,
% 0.30/0.47 a2: a ).
% 0.30/0.47
% 0.30/0.47 thf(sy_v_b,type,
% 0.30/0.47 b: a ).
% 0.30/0.47
% 0.30/0.47 thf(sy_v_h,type,
% 0.30/0.47 h: a > int ).
% 0.30/0.47
% 0.30/0.47 thf(sy_v_t1____,type,
% 0.30/0.47 t1: binary1291135688e_Tree @ a ).
% 0.30/0.47
% 0.30/0.47 thf(sy_v_t2____,type,
% 0.30/0.47 t2: binary1291135688e_Tree @ a ).
% 0.30/0.47
% 0.30/0.47 thf(sy_v_x____,type,
% 0.30/0.47 x: a ).
% 0.30/0.47
% 0.30/0.47 % Relevant facts (256)
% 0.30/0.47 thf(fact_0_hahb,axiom,
% 0.30/0.47 ( ( h @ a2 )
% 0.30/0.47 = ( h @ b ) ) ).
% 0.30/0.47
% 0.30/0.47 % hahb
% 0.30/0.47 thf(fact_1__092_060open_062h_Ab_A_060_Ah_Aa_092_060close_062,axiom,
% 0.30/0.47 ord_less @ int @ ( h @ b ) @ ( h @ a2 ) ).
% 0.30/0.47
% 0.30/0.47 % \<open>h b < h a\<close>
% 0.30/0.47 thf(fact_2__092_060open_062a_A_061_Ax_A_092_060Longrightarrow_062_Aa_A_061_Ab_092_060close_062,axiom,
% 0.30/0.47 ( ( a2 = x )
% 0.30/0.47 => ( a2 = b ) ) ).
% 0.30/0.47
% 0.30/0.47 % \<open>a = x \<Longrightarrow> a = b\<close>
% 0.30/0.47 thf(fact_3_adef1,axiom,
% 0.30/0.47 member @ a @ a2 @ ( binary1653327646_setOf @ a @ t2 ) ).
% 0.30/0.47
% 0.30/0.47 % adef1
% 0.30/0.47 thf(fact_4_bdef1,axiom,
% 0.30/0.47 member @ a @ b @ ( binary1653327646_setOf @ a @ t1 ) ).
% 0.30/0.47
% 0.30/0.47 % bdef1
% 0.30/0.47 thf(fact_5__092_060open_062a_A_092_060in_062_AsetOf_At1_A_092_060Longrightarrow_062_Aa_A_061_Ab_092_060close_062,axiom,
% 0.30/0.47 ( ( member @ a @ a2 @ ( binary1653327646_setOf @ a @ t1 ) )
% 0.30/0.47 => ( a2 = b ) ) ).
% 0.30/0.47
% 0.30/0.47 % \<open>a \<in> setOf t1 \<Longrightarrow> a = b\<close>
% 0.30/0.47 thf(fact_6_o1,axiom,
% 0.30/0.47 ord_less @ int @ ( h @ b ) @ ( h @ x ) ).
% 0.30/0.47
% 0.30/0.47 % o1
% 0.30/0.47 thf(fact_7_o2,axiom,
% 0.30/0.47 ord_less @ int @ ( h @ x ) @ ( h @ a2 ) ).
% 0.30/0.47
% 0.30/0.47 % o2
% 0.30/0.47 thf(fact_8_h2,axiom,
% 0.30/0.47 binary231205461t_pred @ a @ h @ a2 @ b @ t2 ).
% 0.30/0.47
% 0.30/0.47 % h2
% 0.30/0.47 thf(fact_9_h1,axiom,
% 0.30/0.47 binary231205461t_pred @ a @ h @ a2 @ b @ t1 ).
% 0.30/0.47
% 0.30/0.47 % h1
% 0.30/0.47 thf(fact_10__092_060open_062sorted__distinct__pred_Ah_Aa_Ab_ATip_092_060close_062,axiom,
% 0.30/0.47 binary231205461t_pred @ a @ h @ a2 @ b @ ( binary1746293266le_Tip @ a ) ).
% 0.30/0.47
% 0.30/0.47 % \<open>sorted_distinct_pred h a b Tip\<close>
% 0.30/0.47 thf(fact_11_calculation,axiom,
% 0.30/0.47 ( ( member @ a @ b @ ( binary1653327646_setOf @ a @ t1 ) )
% 0.30/0.47 | ( b = x )
% 0.30/0.47 | ( member @ a @ b @ ( binary1653327646_setOf @ a @ t2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % calculation
% 0.30/0.47 thf(fact_12__092_060open_062a_A_092_060in_062_AsetOf_At1_A_092_060or_062_Aa_A_061_Ax_A_092_060or_062_Aa_A_092_060in_062_AsetOf_At2_092_060close_062,axiom,
% 0.30/0.47 ( ( member @ a @ a2 @ ( binary1653327646_setOf @ a @ t1 ) )
% 0.30/0.47 | ( a2 = x )
% 0.30/0.47 | ( member @ a @ a2 @ ( binary1653327646_setOf @ a @ t2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % \<open>a \<in> setOf t1 \<or> a = x \<or> a \<in> setOf t2\<close>
% 0.30/0.47 thf(fact_13_bdef,axiom,
% 0.30/0.47 member @ a @ b @ ( binary1653327646_setOf @ a @ ( binary210054475elle_T @ a @ t1 @ x @ t2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % bdef
% 0.30/0.47 thf(fact_14_Tree_Oinject,axiom,
% 0.30/0.47 ! [A: $tType,X21: binary1291135688e_Tree @ A,X22: A,X23: binary1291135688e_Tree @ A,Y21: binary1291135688e_Tree @ A,Y22: A,Y23: binary1291135688e_Tree @ A] :
% 0.30/0.47 ( ( ( binary210054475elle_T @ A @ X21 @ X22 @ X23 )
% 0.30/0.47 = ( binary210054475elle_T @ A @ Y21 @ Y22 @ Y23 ) )
% 0.30/0.47 = ( ( X21 = Y21 )
% 0.30/0.47 & ( X22 = Y22 )
% 0.30/0.47 & ( X23 = Y23 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Tree.inject
% 0.30/0.47 thf(fact_15_adef,axiom,
% 0.30/0.47 member @ a @ a2 @ ( binary1653327646_setOf @ a @ ( binary210054475elle_T @ a @ t1 @ x @ t2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % adef
% 0.30/0.47 thf(fact_16_s,axiom,
% 0.30/0.47 binary1610619414edTree @ a @ h @ ( binary210054475elle_T @ a @ t1 @ x @ t2 ) ).
% 0.30/0.47
% 0.30/0.47 % s
% 0.30/0.47 thf(fact_17_Tree_Odistinct_I1_J,axiom,
% 0.30/0.47 ! [A: $tType,X21: binary1291135688e_Tree @ A,X22: A,X23: binary1291135688e_Tree @ A] :
% 0.30/0.47 ( ( binary1746293266le_Tip @ A )
% 0.30/0.47 != ( binary210054475elle_T @ A @ X21 @ X22 @ X23 ) ) ).
% 0.30/0.47
% 0.30/0.47 % Tree.distinct(1)
% 0.30/0.47 thf(fact_18_Tree_Oinduct,axiom,
% 0.30/0.47 ! [A: $tType,P: ( binary1291135688e_Tree @ A ) > $o,Tree: binary1291135688e_Tree @ A] :
% 0.30/0.47 ( ( P @ ( binary1746293266le_Tip @ A ) )
% 0.30/0.47 => ( ! [X1: binary1291135688e_Tree @ A,X2: A,X3: binary1291135688e_Tree @ A] :
% 0.30/0.47 ( ( P @ X1 )
% 0.30/0.47 => ( ( P @ X3 )
% 0.30/0.47 => ( P @ ( binary210054475elle_T @ A @ X1 @ X2 @ X3 ) ) ) )
% 0.30/0.47 => ( P @ Tree ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Tree.induct
% 0.30/0.47 thf(fact_19_Tree_Oexhaust,axiom,
% 0.30/0.47 ! [A: $tType,Y: binary1291135688e_Tree @ A] :
% 0.30/0.47 ( ( Y
% 0.30/0.47 != ( binary1746293266le_Tip @ A ) )
% 0.30/0.47 => ~ ! [X212: binary1291135688e_Tree @ A,X222: A,X232: binary1291135688e_Tree @ A] :
% 0.30/0.47 ( Y
% 0.30/0.47 != ( binary210054475elle_T @ A @ X212 @ X222 @ X232 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Tree.exhaust
% 0.30/0.47 thf(fact_20_s2,axiom,
% 0.30/0.47 binary1610619414edTree @ a @ h @ t2 ).
% 0.30/0.47
% 0.30/0.47 % s2
% 0.30/0.47 thf(fact_21_s1,axiom,
% 0.30/0.47 binary1610619414edTree @ a @ h @ t1 ).
% 0.30/0.47
% 0.30/0.47 % s1
% 0.30/0.47 thf(fact_22_sortedTree_Osimps_I2_J,axiom,
% 0.30/0.47 ! [A: $tType,H: A > int,T1: binary1291135688e_Tree @ A,X: A,T2: binary1291135688e_Tree @ A] :
% 0.30/0.47 ( ( binary1610619414edTree @ A @ H @ ( binary210054475elle_T @ A @ T1 @ X @ T2 ) )
% 0.30/0.47 = ( ( binary1610619414edTree @ A @ H @ T1 )
% 0.30/0.47 & ! [X4: A] :
% 0.30/0.47 ( ( member @ A @ X4 @ ( binary1653327646_setOf @ A @ T1 ) )
% 0.30/0.47 => ( ord_less @ int @ ( H @ X4 ) @ ( H @ X ) ) )
% 0.30/0.47 & ! [X4: A] :
% 0.30/0.47 ( ( member @ A @ X4 @ ( binary1653327646_setOf @ A @ T2 ) )
% 0.30/0.47 => ( ord_less @ int @ ( H @ X ) @ ( H @ X4 ) ) )
% 0.30/0.47 & ( binary1610619414edTree @ A @ H @ T2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % sortedTree.simps(2)
% 0.30/0.47 thf(fact_23_sorted__distinct__pred__def,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( binary231205461t_pred @ A )
% 0.30/0.47 = ( ^ [H2: A > int,A2: A,B2: A,T: binary1291135688e_Tree @ A] :
% 0.30/0.47 ( ( ( binary1610619414edTree @ A @ H2 @ T )
% 0.30/0.47 & ( member @ A @ A2 @ ( binary1653327646_setOf @ A @ T ) )
% 0.30/0.47 & ( member @ A @ B2 @ ( binary1653327646_setOf @ A @ T ) )
% 0.30/0.47 & ( ( H2 @ A2 )
% 0.30/0.47 = ( H2 @ B2 ) ) )
% 0.30/0.47 => ( A2 = B2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % sorted_distinct_pred_def
% 0.30/0.47 thf(fact_24_eqs__def,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( binary64540844le_eqs @ A )
% 0.30/0.47 = ( ^ [H2: A > int,X4: A] :
% 0.30/0.47 ( collect @ A
% 0.30/0.47 @ ^ [Y2: A] :
% 0.30/0.47 ( ( H2 @ Y2 )
% 0.30/0.47 = ( H2 @ X4 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % eqs_def
% 0.30/0.47 thf(fact_25_minf_I11_J,axiom,
% 0.30/0.47 ! [C: $tType,D: $tType] :
% 0.30/0.47 ( ( ord @ C )
% 0.30/0.47 => ! [F: D] :
% 0.30/0.47 ? [Z: C] :
% 0.30/0.47 ! [X5: C] :
% 0.30/0.47 ( ( ord_less @ C @ X5 @ Z )
% 0.30/0.47 => ( F = F ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % minf(11)
% 0.30/0.47 thf(fact_26_minf_I7_J,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ! [T3: A] :
% 0.30/0.47 ? [Z: A] :
% 0.30/0.47 ! [X5: A] :
% 0.30/0.47 ( ( ord_less @ A @ X5 @ Z )
% 0.30/0.47 => ~ ( ord_less @ A @ T3 @ X5 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % minf(7)
% 0.30/0.47 thf(fact_27_minf_I5_J,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ! [T3: A] :
% 0.30/0.47 ? [Z: A] :
% 0.30/0.47 ! [X5: A] :
% 0.30/0.47 ( ( ord_less @ A @ X5 @ Z )
% 0.30/0.47 => ( ord_less @ A @ X5 @ T3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % minf(5)
% 0.30/0.47 thf(fact_28_minf_I4_J,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ! [T3: A] :
% 0.30/0.47 ? [Z: A] :
% 0.30/0.47 ! [X5: A] :
% 0.30/0.47 ( ( ord_less @ A @ X5 @ Z )
% 0.30/0.47 => ( X5 != T3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % minf(4)
% 0.30/0.47 thf(fact_29_minf_I3_J,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ! [T3: A] :
% 0.30/0.47 ? [Z: A] :
% 0.30/0.47 ! [X5: A] :
% 0.30/0.47 ( ( ord_less @ A @ X5 @ Z )
% 0.30/0.47 => ( X5 != T3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % minf(3)
% 0.30/0.47 thf(fact_30_minf_I2_J,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ! [P: A > $o,P2: A > $o,Q: A > $o,Q2: A > $o] :
% 0.30/0.47 ( ? [Z2: A] :
% 0.30/0.47 ! [X6: A] :
% 0.30/0.47 ( ( ord_less @ A @ X6 @ Z2 )
% 0.30/0.47 => ( ( P @ X6 )
% 0.30/0.47 = ( P2 @ X6 ) ) )
% 0.30/0.47 => ( ? [Z2: A] :
% 0.30/0.47 ! [X6: A] :
% 0.30/0.47 ( ( ord_less @ A @ X6 @ Z2 )
% 0.30/0.47 => ( ( Q @ X6 )
% 0.30/0.47 = ( Q2 @ X6 ) ) )
% 0.30/0.47 => ? [Z: A] :
% 0.30/0.47 ! [X5: A] :
% 0.30/0.47 ( ( ord_less @ A @ X5 @ Z )
% 0.30/0.47 => ( ( ( P @ X5 )
% 0.30/0.47 | ( Q @ X5 ) )
% 0.30/0.47 = ( ( P2 @ X5 )
% 0.30/0.47 | ( Q2 @ X5 ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % minf(2)
% 0.30/0.47 thf(fact_31_sortLemmaR,axiom,
% 0.30/0.47 ! [A: $tType,H: A > int,T1: binary1291135688e_Tree @ A,X: A,T2: binary1291135688e_Tree @ A] :
% 0.30/0.47 ( ( binary1610619414edTree @ A @ H @ ( binary210054475elle_T @ A @ T1 @ X @ T2 ) )
% 0.30/0.47 => ( binary1610619414edTree @ A @ H @ T2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % sortLemmaR
% 0.30/0.47 thf(fact_32_sortLemmaL,axiom,
% 0.30/0.47 ! [A: $tType,H: A > int,T1: binary1291135688e_Tree @ A,X: A,T2: binary1291135688e_Tree @ A] :
% 0.30/0.47 ( ( binary1610619414edTree @ A @ H @ ( binary210054475elle_T @ A @ T1 @ X @ T2 ) )
% 0.30/0.47 => ( binary1610619414edTree @ A @ H @ T1 ) ) ).
% 0.30/0.47
% 0.30/0.47 % sortLemmaL
% 0.30/0.47 thf(fact_33_sortedTree_Osimps_I1_J,axiom,
% 0.30/0.47 ! [A: $tType,H: A > int] : ( binary1610619414edTree @ A @ H @ ( binary1746293266le_Tip @ A ) ) ).
% 0.30/0.47
% 0.30/0.47 % sortedTree.simps(1)
% 0.30/0.47 thf(fact_34_pinf_I1_J,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ! [P: A > $o,P2: A > $o,Q: A > $o,Q2: A > $o] :
% 0.30/0.47 ( ? [Z2: A] :
% 0.30/0.47 ! [X6: A] :
% 0.30/0.47 ( ( ord_less @ A @ Z2 @ X6 )
% 0.30/0.47 => ( ( P @ X6 )
% 0.30/0.47 = ( P2 @ X6 ) ) )
% 0.30/0.47 => ( ? [Z2: A] :
% 0.30/0.47 ! [X6: A] :
% 0.30/0.47 ( ( ord_less @ A @ Z2 @ X6 )
% 0.30/0.47 => ( ( Q @ X6 )
% 0.30/0.47 = ( Q2 @ X6 ) ) )
% 0.30/0.47 => ? [Z: A] :
% 0.30/0.47 ! [X5: A] :
% 0.30/0.47 ( ( ord_less @ A @ Z @ X5 )
% 0.30/0.47 => ( ( ( P @ X5 )
% 0.30/0.47 & ( Q @ X5 ) )
% 0.30/0.47 = ( ( P2 @ X5 )
% 0.30/0.47 & ( Q2 @ X5 ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % pinf(1)
% 0.30/0.47 thf(fact_35_pinf_I2_J,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ! [P: A > $o,P2: A > $o,Q: A > $o,Q2: A > $o] :
% 0.30/0.47 ( ? [Z2: A] :
% 0.30/0.47 ! [X6: A] :
% 0.30/0.47 ( ( ord_less @ A @ Z2 @ X6 )
% 0.30/0.47 => ( ( P @ X6 )
% 0.30/0.47 = ( P2 @ X6 ) ) )
% 0.30/0.47 => ( ? [Z2: A] :
% 0.30/0.47 ! [X6: A] :
% 0.30/0.47 ( ( ord_less @ A @ Z2 @ X6 )
% 0.30/0.47 => ( ( Q @ X6 )
% 0.30/0.47 = ( Q2 @ X6 ) ) )
% 0.30/0.47 => ? [Z: A] :
% 0.30/0.47 ! [X5: A] :
% 0.30/0.47 ( ( ord_less @ A @ Z @ X5 )
% 0.30/0.47 => ( ( ( P @ X5 )
% 0.30/0.47 | ( Q @ X5 ) )
% 0.30/0.47 = ( ( P2 @ X5 )
% 0.30/0.47 | ( Q2 @ X5 ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % pinf(2)
% 0.30/0.47 thf(fact_36_pinf_I3_J,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ! [T3: A] :
% 0.30/0.47 ? [Z: A] :
% 0.30/0.47 ! [X5: A] :
% 0.30/0.47 ( ( ord_less @ A @ Z @ X5 )
% 0.30/0.47 => ( X5 != T3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % pinf(3)
% 0.30/0.47 thf(fact_37_pinf_I4_J,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ! [T3: A] :
% 0.30/0.47 ? [Z: A] :
% 0.30/0.47 ! [X5: A] :
% 0.30/0.47 ( ( ord_less @ A @ Z @ X5 )
% 0.30/0.47 => ( X5 != T3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % pinf(4)
% 0.30/0.47 thf(fact_38_pinf_I5_J,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ! [T3: A] :
% 0.30/0.47 ? [Z: A] :
% 0.30/0.47 ! [X5: A] :
% 0.30/0.47 ( ( ord_less @ A @ Z @ X5 )
% 0.30/0.47 => ~ ( ord_less @ A @ X5 @ T3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % pinf(5)
% 0.30/0.47 thf(fact_39_pinf_I7_J,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ! [T3: A] :
% 0.30/0.47 ? [Z: A] :
% 0.30/0.47 ! [X5: A] :
% 0.30/0.47 ( ( ord_less @ A @ Z @ X5 )
% 0.30/0.47 => ( ord_less @ A @ T3 @ X5 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % pinf(7)
% 0.30/0.47 thf(fact_40_pinf_I11_J,axiom,
% 0.30/0.47 ! [C: $tType,D: $tType] :
% 0.30/0.47 ( ( ord @ C )
% 0.30/0.47 => ! [F: D] :
% 0.30/0.47 ? [Z: C] :
% 0.30/0.47 ! [X5: C] :
% 0.30/0.47 ( ( ord_less @ C @ Z @ X5 )
% 0.30/0.47 => ( F = F ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % pinf(11)
% 0.30/0.47 thf(fact_41_minf_I1_J,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ! [P: A > $o,P2: A > $o,Q: A > $o,Q2: A > $o] :
% 0.30/0.47 ( ? [Z2: A] :
% 0.30/0.47 ! [X6: A] :
% 0.30/0.47 ( ( ord_less @ A @ X6 @ Z2 )
% 0.30/0.47 => ( ( P @ X6 )
% 0.30/0.47 = ( P2 @ X6 ) ) )
% 0.30/0.47 => ( ? [Z2: A] :
% 0.30/0.47 ! [X6: A] :
% 0.30/0.47 ( ( ord_less @ A @ X6 @ Z2 )
% 0.30/0.47 => ( ( Q @ X6 )
% 0.30/0.47 = ( Q2 @ X6 ) ) )
% 0.30/0.47 => ? [Z: A] :
% 0.30/0.47 ! [X5: A] :
% 0.30/0.47 ( ( ord_less @ A @ X5 @ Z )
% 0.30/0.47 => ( ( ( P @ X5 )
% 0.30/0.47 & ( Q @ X5 ) )
% 0.30/0.47 = ( ( P2 @ X5 )
% 0.30/0.47 & ( Q2 @ X5 ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % minf(1)
% 0.30/0.47 thf(fact_42_ex__gt__or__lt,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( condit1656338222tinuum @ A )
% 0.30/0.47 => ! [A3: A] :
% 0.30/0.47 ? [B3: A] :
% 0.30/0.47 ( ( ord_less @ A @ A3 @ B3 )
% 0.30/0.47 | ( ord_less @ A @ B3 @ A3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % ex_gt_or_lt
% 0.30/0.47 thf(fact_43_linorder__neqE__linordered__idom,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linordered_idom @ A )
% 0.30/0.47 => ! [X: A,Y: A] :
% 0.30/0.47 ( ( X != Y )
% 0.30/0.47 => ( ~ ( ord_less @ A @ X @ Y )
% 0.30/0.47 => ( ord_less @ A @ Y @ X ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % linorder_neqE_linordered_idom
% 0.30/0.47 thf(fact_44_dual__order_Ostrict__implies__not__eq,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( order @ A )
% 0.30/0.47 => ! [B4: A,A3: A] :
% 0.30/0.47 ( ( ord_less @ A @ B4 @ A3 )
% 0.30/0.47 => ( A3 != B4 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % dual_order.strict_implies_not_eq
% 0.30/0.47 thf(fact_45_mem__Collect__eq,axiom,
% 0.30/0.47 ! [A: $tType,A3: A,P: A > $o] :
% 0.30/0.47 ( ( member @ A @ A3 @ ( collect @ A @ P ) )
% 0.30/0.47 = ( P @ A3 ) ) ).
% 0.30/0.47
% 0.30/0.47 % mem_Collect_eq
% 0.30/0.47 thf(fact_46_Collect__mem__eq,axiom,
% 0.30/0.47 ! [A: $tType,A4: set @ A] :
% 0.30/0.47 ( ( collect @ A
% 0.30/0.47 @ ^ [X4: A] : ( member @ A @ X4 @ A4 ) )
% 0.30/0.47 = A4 ) ).
% 0.30/0.47
% 0.30/0.47 % Collect_mem_eq
% 0.30/0.47 thf(fact_47_Collect__cong,axiom,
% 0.30/0.47 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.30/0.47 ( ! [X6: A] :
% 0.30/0.47 ( ( P @ X6 )
% 0.30/0.47 = ( Q @ X6 ) )
% 0.30/0.47 => ( ( collect @ A @ P )
% 0.30/0.47 = ( collect @ A @ Q ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Collect_cong
% 0.30/0.47 thf(fact_48_ext,axiom,
% 0.30/0.47 ! [B: $tType,A: $tType,F2: A > B,G: A > B] :
% 0.30/0.47 ( ! [X6: A] :
% 0.30/0.47 ( ( F2 @ X6 )
% 0.30/0.47 = ( G @ X6 ) )
% 0.30/0.47 => ( F2 = G ) ) ).
% 0.30/0.47
% 0.30/0.47 % ext
% 0.30/0.47 thf(fact_49_linordered__field__no__ub,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linordered_field @ A )
% 0.30/0.47 => ! [X5: A] :
% 0.30/0.47 ? [X_1: A] : ( ord_less @ A @ X5 @ X_1 ) ) ).
% 0.30/0.47
% 0.30/0.47 % linordered_field_no_ub
% 0.30/0.47 thf(fact_50_linordered__field__no__lb,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linordered_field @ A )
% 0.30/0.47 => ! [X5: A] :
% 0.30/0.47 ? [Y3: A] : ( ord_less @ A @ Y3 @ X5 ) ) ).
% 0.30/0.47
% 0.30/0.47 % linordered_field_no_lb
% 0.30/0.47 thf(fact_51_order_Ostrict__implies__not__eq,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( order @ A )
% 0.30/0.47 => ! [A3: A,B4: A] :
% 0.30/0.47 ( ( ord_less @ A @ A3 @ B4 )
% 0.30/0.47 => ( A3 != B4 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % order.strict_implies_not_eq
% 0.30/0.47 thf(fact_52_dependent__wellorder__choice,axiom,
% 0.30/0.47 ! [B: $tType,A: $tType] :
% 0.30/0.47 ( ( wellorder @ A )
% 0.30/0.47 => ! [P: ( A > B ) > A > B > $o] :
% 0.30/0.47 ( ! [R: B,F3: A > B,G2: A > B,X6: A] :
% 0.30/0.47 ( ! [Y4: A] :
% 0.30/0.47 ( ( ord_less @ A @ Y4 @ X6 )
% 0.30/0.47 => ( ( F3 @ Y4 )
% 0.30/0.47 = ( G2 @ Y4 ) ) )
% 0.30/0.47 => ( ( P @ F3 @ X6 @ R )
% 0.30/0.47 = ( P @ G2 @ X6 @ R ) ) )
% 0.30/0.47 => ( ! [X6: A,F3: A > B] :
% 0.30/0.47 ( ! [Y4: A] :
% 0.30/0.47 ( ( ord_less @ A @ Y4 @ X6 )
% 0.30/0.47 => ( P @ F3 @ Y4 @ ( F3 @ Y4 ) ) )
% 0.30/0.47 => ? [X_12: B] : ( P @ F3 @ X6 @ X_12 ) )
% 0.30/0.47 => ? [F3: A > B] :
% 0.30/0.47 ! [X5: A] : ( P @ F3 @ X5 @ ( F3 @ X5 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % dependent_wellorder_choice
% 0.30/0.47 thf(fact_53_not__less__iff__gr__or__eq,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ! [X: A,Y: A] :
% 0.30/0.47 ( ( ~ ( ord_less @ A @ X @ Y ) )
% 0.30/0.47 = ( ( ord_less @ A @ Y @ X )
% 0.30/0.47 | ( X = Y ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % not_less_iff_gr_or_eq
% 0.30/0.47 thf(fact_54_dual__order_Ostrict__trans,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( order @ A )
% 0.30/0.47 => ! [B4: A,A3: A,C2: A] :
% 0.30/0.47 ( ( ord_less @ A @ B4 @ A3 )
% 0.30/0.47 => ( ( ord_less @ A @ C2 @ B4 )
% 0.30/0.47 => ( ord_less @ A @ C2 @ A3 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % dual_order.strict_trans
% 0.30/0.47 thf(fact_55_ord__eq__less__subst,axiom,
% 0.30/0.47 ! [A: $tType,B: $tType] :
% 0.30/0.47 ( ( ( ord @ B )
% 0.30/0.47 & ( ord @ A ) )
% 0.30/0.47 => ! [A3: A,F2: B > A,B4: B,C2: B] :
% 0.30/0.47 ( ( A3
% 0.30/0.47 = ( F2 @ B4 ) )
% 0.30/0.47 => ( ( ord_less @ B @ B4 @ C2 )
% 0.30/0.47 => ( ! [X6: B,Y3: B] :
% 0.30/0.47 ( ( ord_less @ B @ X6 @ Y3 )
% 0.30/0.47 => ( ord_less @ A @ ( F2 @ X6 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.47 => ( ord_less @ A @ A3 @ ( F2 @ C2 ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % ord_eq_less_subst
% 0.30/0.47 thf(fact_56_ord__less__eq__subst,axiom,
% 0.30/0.47 ! [A: $tType,B: $tType] :
% 0.30/0.47 ( ( ( ord @ B )
% 0.30/0.47 & ( ord @ A ) )
% 0.30/0.47 => ! [A3: A,B4: A,F2: A > B,C2: B] :
% 0.30/0.47 ( ( ord_less @ A @ A3 @ B4 )
% 0.30/0.47 => ( ( ( F2 @ B4 )
% 0.30/0.47 = C2 )
% 0.30/0.47 => ( ! [X6: A,Y3: A] :
% 0.30/0.47 ( ( ord_less @ A @ X6 @ Y3 )
% 0.30/0.47 => ( ord_less @ B @ ( F2 @ X6 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.47 => ( ord_less @ B @ ( F2 @ A3 ) @ C2 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % ord_less_eq_subst
% 0.30/0.47 thf(fact_57_order__less__subst1,axiom,
% 0.30/0.47 ! [A: $tType,B: $tType] :
% 0.30/0.47 ( ( ( order @ B )
% 0.30/0.47 & ( order @ A ) )
% 0.30/0.47 => ! [A3: A,F2: B > A,B4: B,C2: B] :
% 0.30/0.47 ( ( ord_less @ A @ A3 @ ( F2 @ B4 ) )
% 0.30/0.47 => ( ( ord_less @ B @ B4 @ C2 )
% 0.30/0.47 => ( ! [X6: B,Y3: B] :
% 0.30/0.47 ( ( ord_less @ B @ X6 @ Y3 )
% 0.30/0.47 => ( ord_less @ A @ ( F2 @ X6 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.47 => ( ord_less @ A @ A3 @ ( F2 @ C2 ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % order_less_subst1
% 0.30/0.47 thf(fact_58_order__less__subst2,axiom,
% 0.30/0.47 ! [A: $tType,C: $tType] :
% 0.30/0.47 ( ( ( order @ C )
% 0.30/0.47 & ( order @ A ) )
% 0.30/0.47 => ! [A3: A,B4: A,F2: A > C,C2: C] :
% 0.30/0.47 ( ( ord_less @ A @ A3 @ B4 )
% 0.30/0.47 => ( ( ord_less @ C @ ( F2 @ B4 ) @ C2 )
% 0.30/0.47 => ( ! [X6: A,Y3: A] :
% 0.30/0.47 ( ( ord_less @ A @ X6 @ Y3 )
% 0.30/0.47 => ( ord_less @ C @ ( F2 @ X6 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.47 => ( ord_less @ C @ ( F2 @ A3 ) @ C2 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % order_less_subst2
% 0.30/0.47 thf(fact_59_lt__ex,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( no_bot @ A )
% 0.30/0.47 => ! [X: A] :
% 0.30/0.47 ? [Y3: A] : ( ord_less @ A @ Y3 @ X ) ) ).
% 0.30/0.47
% 0.30/0.47 % lt_ex
% 0.30/0.47 thf(fact_60_gt__ex,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( no_top @ A )
% 0.30/0.47 => ! [X: A] :
% 0.30/0.47 ? [X_1: A] : ( ord_less @ A @ X @ X_1 ) ) ).
% 0.30/0.47
% 0.30/0.47 % gt_ex
% 0.30/0.47 thf(fact_61_neqE,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ! [X: A,Y: A] :
% 0.30/0.47 ( ( X != Y )
% 0.30/0.47 => ( ~ ( ord_less @ A @ X @ Y )
% 0.30/0.47 => ( ord_less @ A @ Y @ X ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % neqE
% 0.30/0.47 thf(fact_62_neq__iff,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ! [X: A,Y: A] :
% 0.30/0.47 ( ( X != Y )
% 0.30/0.47 = ( ( ord_less @ A @ X @ Y )
% 0.30/0.47 | ( ord_less @ A @ Y @ X ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % neq_iff
% 0.30/0.47 thf(fact_63_order_Oasym,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( order @ A )
% 0.30/0.47 => ! [A3: A,B4: A] :
% 0.30/0.47 ( ( ord_less @ A @ A3 @ B4 )
% 0.30/0.47 => ~ ( ord_less @ A @ B4 @ A3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % order.asym
% 0.30/0.47 thf(fact_64_dense,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( dense_order @ A )
% 0.30/0.47 => ! [X: A,Y: A] :
% 0.30/0.47 ( ( ord_less @ A @ X @ Y )
% 0.30/0.47 => ? [Z: A] :
% 0.30/0.47 ( ( ord_less @ A @ X @ Z )
% 0.30/0.47 & ( ord_less @ A @ Z @ Y ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % dense
% 0.30/0.47 thf(fact_65_less__imp__neq,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( order @ A )
% 0.30/0.47 => ! [X: A,Y: A] :
% 0.30/0.47 ( ( ord_less @ A @ X @ Y )
% 0.30/0.47 => ( X != Y ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % less_imp_neq
% 0.30/0.47 thf(fact_66_less__asym,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( preorder @ A )
% 0.30/0.47 => ! [X: A,Y: A] :
% 0.30/0.47 ( ( ord_less @ A @ X @ Y )
% 0.30/0.47 => ~ ( ord_less @ A @ Y @ X ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % less_asym
% 0.30/0.47 thf(fact_67_less__asym_H,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( preorder @ A )
% 0.30/0.47 => ! [A3: A,B4: A] :
% 0.30/0.47 ( ( ord_less @ A @ A3 @ B4 )
% 0.30/0.47 => ~ ( ord_less @ A @ B4 @ A3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % less_asym'
% 0.30/0.47 thf(fact_68_less__trans,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( preorder @ A )
% 0.30/0.47 => ! [X: A,Y: A,Z3: A] :
% 0.30/0.47 ( ( ord_less @ A @ X @ Y )
% 0.30/0.47 => ( ( ord_less @ A @ Y @ Z3 )
% 0.30/0.47 => ( ord_less @ A @ X @ Z3 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % less_trans
% 0.30/0.47 thf(fact_69_less__linear,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ! [X: A,Y: A] :
% 0.30/0.47 ( ( ord_less @ A @ X @ Y )
% 0.30/0.47 | ( X = Y )
% 0.30/0.47 | ( ord_less @ A @ Y @ X ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % less_linear
% 0.30/0.47 thf(fact_70_less__irrefl,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( preorder @ A )
% 0.30/0.47 => ! [X: A] :
% 0.30/0.47 ~ ( ord_less @ A @ X @ X ) ) ).
% 0.30/0.47
% 0.30/0.47 % less_irrefl
% 0.30/0.47 thf(fact_71_ord__eq__less__trans,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( ord @ A )
% 0.30/0.47 => ! [A3: A,B4: A,C2: A] :
% 0.30/0.47 ( ( A3 = B4 )
% 0.30/0.47 => ( ( ord_less @ A @ B4 @ C2 )
% 0.30/0.47 => ( ord_less @ A @ A3 @ C2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % ord_eq_less_trans
% 0.30/0.47 thf(fact_72_ord__less__eq__trans,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( ord @ A )
% 0.30/0.47 => ! [A3: A,B4: A,C2: A] :
% 0.30/0.47 ( ( ord_less @ A @ A3 @ B4 )
% 0.30/0.47 => ( ( B4 = C2 )
% 0.30/0.47 => ( ord_less @ A @ A3 @ C2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % ord_less_eq_trans
% 0.30/0.47 thf(fact_73_dual__order_Oasym,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( order @ A )
% 0.30/0.47 => ! [B4: A,A3: A] :
% 0.30/0.47 ( ( ord_less @ A @ B4 @ A3 )
% 0.30/0.47 => ~ ( ord_less @ A @ A3 @ B4 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % dual_order.asym
% 0.30/0.47 thf(fact_74_less__imp__not__eq,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( order @ A )
% 0.30/0.47 => ! [X: A,Y: A] :
% 0.30/0.47 ( ( ord_less @ A @ X @ Y )
% 0.30/0.47 => ( X != Y ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % less_imp_not_eq
% 0.30/0.47 thf(fact_75_less__not__sym,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( preorder @ A )
% 0.30/0.47 => ! [X: A,Y: A] :
% 0.30/0.47 ( ( ord_less @ A @ X @ Y )
% 0.30/0.47 => ~ ( ord_less @ A @ Y @ X ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % less_not_sym
% 0.30/0.47 thf(fact_76_less__induct,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( wellorder @ A )
% 0.30/0.47 => ! [P: A > $o,A3: A] :
% 0.30/0.47 ( ! [X6: A] :
% 0.30/0.47 ( ! [Y4: A] :
% 0.30/0.47 ( ( ord_less @ A @ Y4 @ X6 )
% 0.30/0.47 => ( P @ Y4 ) )
% 0.30/0.47 => ( P @ X6 ) )
% 0.30/0.47 => ( P @ A3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % less_induct
% 0.30/0.47 thf(fact_77_antisym__conv3,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ! [Y: A,X: A] :
% 0.30/0.47 ( ~ ( ord_less @ A @ Y @ X )
% 0.30/0.47 => ( ( ~ ( ord_less @ A @ X @ Y ) )
% 0.30/0.47 = ( X = Y ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % antisym_conv3
% 0.30/0.47 thf(fact_78_less__imp__not__eq2,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( order @ A )
% 0.30/0.47 => ! [X: A,Y: A] :
% 0.30/0.47 ( ( ord_less @ A @ X @ Y )
% 0.30/0.47 => ( Y != X ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % less_imp_not_eq2
% 0.30/0.47 thf(fact_79_less__imp__triv,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( preorder @ A )
% 0.30/0.47 => ! [X: A,Y: A,P: $o] :
% 0.30/0.47 ( ( ord_less @ A @ X @ Y )
% 0.30/0.47 => ( ( ord_less @ A @ Y @ X )
% 0.30/0.47 => P ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % less_imp_triv
% 0.30/0.47 thf(fact_80_linorder__cases,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ! [X: A,Y: A] :
% 0.30/0.47 ( ~ ( ord_less @ A @ X @ Y )
% 0.30/0.47 => ( ( X != Y )
% 0.30/0.47 => ( ord_less @ A @ Y @ X ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % linorder_cases
% 0.30/0.47 thf(fact_81_dual__order_Oirrefl,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( order @ A )
% 0.30/0.47 => ! [A3: A] :
% 0.30/0.47 ~ ( ord_less @ A @ A3 @ A3 ) ) ).
% 0.30/0.47
% 0.30/0.47 % dual_order.irrefl
% 0.30/0.47 thf(fact_82_order_Ostrict__trans,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( order @ A )
% 0.30/0.47 => ! [A3: A,B4: A,C2: A] :
% 0.30/0.47 ( ( ord_less @ A @ A3 @ B4 )
% 0.30/0.47 => ( ( ord_less @ A @ B4 @ C2 )
% 0.30/0.47 => ( ord_less @ A @ A3 @ C2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % order.strict_trans
% 0.30/0.47 thf(fact_83_less__imp__not__less,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( preorder @ A )
% 0.30/0.47 => ! [X: A,Y: A] :
% 0.30/0.47 ( ( ord_less @ A @ X @ Y )
% 0.30/0.47 => ~ ( ord_less @ A @ Y @ X ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % less_imp_not_less
% 0.30/0.47 thf(fact_84_exists__least__iff,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( wellorder @ A )
% 0.30/0.47 => ( ( ^ [P3: A > $o] :
% 0.30/0.47 ? [X7: A] : ( P3 @ X7 ) )
% 0.30/0.47 = ( ^ [P4: A > $o] :
% 0.30/0.47 ? [N: A] :
% 0.30/0.47 ( ( P4 @ N )
% 0.30/0.47 & ! [M: A] :
% 0.30/0.47 ( ( ord_less @ A @ M @ N )
% 0.30/0.47 => ~ ( P4 @ M ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % exists_least_iff
% 0.30/0.47 thf(fact_85_linorder__less__wlog,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ! [P: A > A > $o,A3: A,B4: A] :
% 0.30/0.47 ( ! [A5: A,B3: A] :
% 0.30/0.47 ( ( ord_less @ A @ A5 @ B3 )
% 0.30/0.47 => ( P @ A5 @ B3 ) )
% 0.30/0.47 => ( ! [A5: A] : ( P @ A5 @ A5 )
% 0.30/0.47 => ( ! [A5: A,B3: A] :
% 0.30/0.47 ( ( P @ B3 @ A5 )
% 0.30/0.47 => ( P @ A5 @ B3 ) )
% 0.30/0.47 => ( P @ A3 @ B4 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % linorder_less_wlog
% 0.30/0.47 thf(fact_86_verit__comp__simplify1_I1_J,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( order @ A )
% 0.30/0.47 => ! [A3: A] :
% 0.30/0.47 ~ ( ord_less @ A @ A3 @ A3 ) ) ).
% 0.30/0.47
% 0.30/0.47 % verit_comp_simplify1(1)
% 0.30/0.47 thf(fact_87_measure__induct,axiom,
% 0.30/0.47 ! [B: $tType,A: $tType] :
% 0.30/0.47 ( ( wellorder @ B )
% 0.30/0.47 => ! [F2: A > B,P: A > $o,A3: A] :
% 0.30/0.47 ( ! [X6: A] :
% 0.30/0.47 ( ! [Y4: A] :
% 0.30/0.47 ( ( ord_less @ B @ ( F2 @ Y4 ) @ ( F2 @ X6 ) )
% 0.30/0.47 => ( P @ Y4 ) )
% 0.30/0.47 => ( P @ X6 ) )
% 0.30/0.47 => ( P @ A3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % measure_induct
% 0.30/0.47 thf(fact_88_measure__induct__rule,axiom,
% 0.30/0.47 ! [B: $tType,A: $tType] :
% 0.30/0.47 ( ( wellorder @ B )
% 0.30/0.47 => ! [F2: A > B,P: A > $o,A3: A] :
% 0.30/0.47 ( ! [X6: A] :
% 0.30/0.47 ( ! [Y4: A] :
% 0.30/0.47 ( ( ord_less @ B @ ( F2 @ Y4 ) @ ( F2 @ X6 ) )
% 0.30/0.47 => ( P @ Y4 ) )
% 0.30/0.47 => ( P @ X6 ) )
% 0.30/0.47 => ( P @ A3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % measure_induct_rule
% 0.30/0.47 thf(fact_89_Tree_Osimps_I4_J,axiom,
% 0.30/0.47 ! [A: $tType,B: $tType,F1: B,F22: ( binary1291135688e_Tree @ A ) > A > ( binary1291135688e_Tree @ A ) > B] :
% 0.30/0.47 ( ( binary536355927e_Tree @ B @ A @ F1 @ F22 @ ( binary1746293266le_Tip @ A ) )
% 0.30/0.47 = F1 ) ).
% 0.30/0.47
% 0.30/0.47 % Tree.simps(4)
% 0.30/0.47 thf(fact_90_Tree_Osimps_I5_J,axiom,
% 0.30/0.47 ! [B: $tType,A: $tType,F1: B,F22: ( binary1291135688e_Tree @ A ) > A > ( binary1291135688e_Tree @ A ) > B,X21: binary1291135688e_Tree @ A,X22: A,X23: binary1291135688e_Tree @ A] :
% 0.30/0.47 ( ( binary536355927e_Tree @ B @ A @ F1 @ F22 @ ( binary210054475elle_T @ A @ X21 @ X22 @ X23 ) )
% 0.30/0.47 = ( F22 @ X21 @ X22 @ X23 ) ) ).
% 0.30/0.47
% 0.30/0.47 % Tree.simps(5)
% 0.30/0.47 thf(fact_91_setOf_Osimps_I1_J,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( binary1653327646_setOf @ A @ ( binary1746293266le_Tip @ A ) )
% 0.30/0.47 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % setOf.simps(1)
% 0.30/0.47 thf(fact_92_Tree_Osimps_I6_J,axiom,
% 0.30/0.47 ! [A: $tType,C: $tType,F1: C,F22: ( binary1291135688e_Tree @ A ) > A > ( binary1291135688e_Tree @ A ) > C > C > C] :
% 0.30/0.47 ( ( binary1929596613c_Tree @ C @ A @ F1 @ F22 @ ( binary1746293266le_Tip @ A ) )
% 0.30/0.47 = F1 ) ).
% 0.30/0.47
% 0.30/0.47 % Tree.simps(6)
% 0.30/0.47 thf(fact_93_Tree_Osimps_I7_J,axiom,
% 0.30/0.47 ! [C: $tType,A: $tType,F1: C,F22: ( binary1291135688e_Tree @ A ) > A > ( binary1291135688e_Tree @ A ) > C > C > C,X21: binary1291135688e_Tree @ A,X22: A,X23: binary1291135688e_Tree @ A] :
% 0.30/0.47 ( ( binary1929596613c_Tree @ C @ A @ F1 @ F22 @ ( binary210054475elle_T @ A @ X21 @ X22 @ X23 ) )
% 0.30/0.47 = ( F22 @ X21 @ X22 @ X23 @ ( binary1929596613c_Tree @ C @ A @ F1 @ F22 @ X21 ) @ ( binary1929596613c_Tree @ C @ A @ F1 @ F22 @ X23 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Tree.simps(7)
% 0.30/0.47 thf(fact_94_bot__apply,axiom,
% 0.30/0.47 ! [C: $tType,D: $tType] :
% 0.30/0.47 ( ( bot @ C )
% 0.30/0.47 => ( ( bot_bot @ ( D > C ) )
% 0.30/0.47 = ( ^ [X4: D] : ( bot_bot @ C ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % bot_apply
% 0.30/0.47 thf(fact_95_bot__fun__def,axiom,
% 0.30/0.47 ! [B: $tType,A: $tType] :
% 0.30/0.47 ( ( bot @ B )
% 0.30/0.47 => ( ( bot_bot @ ( A > B ) )
% 0.30/0.47 = ( ^ [X4: A] : ( bot_bot @ B ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % bot_fun_def
% 0.30/0.47 thf(fact_96_bot_Oextremum__strict,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( order_bot @ A )
% 0.30/0.47 => ! [A3: A] :
% 0.30/0.47 ~ ( ord_less @ A @ A3 @ ( bot_bot @ A ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % bot.extremum_strict
% 0.30/0.47 thf(fact_97_bot_Onot__eq__extremum,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( order_bot @ A )
% 0.30/0.47 => ! [A3: A] :
% 0.30/0.47 ( ( A3
% 0.30/0.47 != ( bot_bot @ A ) )
% 0.30/0.47 = ( ord_less @ A @ ( bot_bot @ A ) @ A3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % bot.not_eq_extremum
% 0.30/0.47 thf(fact_98_Tree_Ocase__distrib,axiom,
% 0.30/0.47 ! [C: $tType,B: $tType,A: $tType,H: B > C,F1: B,F22: ( binary1291135688e_Tree @ A ) > A > ( binary1291135688e_Tree @ A ) > B,Tree: binary1291135688e_Tree @ A] :
% 0.30/0.47 ( ( H @ ( binary536355927e_Tree @ B @ A @ F1 @ F22 @ Tree ) )
% 0.30/0.47 = ( binary536355927e_Tree @ C @ A @ ( H @ F1 )
% 0.30/0.47 @ ^ [X12: binary1291135688e_Tree @ A,X24: A,X32: binary1291135688e_Tree @ A] : ( H @ ( F22 @ X12 @ X24 @ X32 ) )
% 0.30/0.47 @ Tree ) ) ).
% 0.30/0.47
% 0.30/0.47 % Tree.case_distrib
% 0.30/0.47 thf(fact_99_empty__Collect__eq,axiom,
% 0.30/0.47 ! [A: $tType,P: A > $o] :
% 0.30/0.47 ( ( ( bot_bot @ ( set @ A ) )
% 0.30/0.47 = ( collect @ A @ P ) )
% 0.30/0.47 = ( ! [X4: A] :
% 0.30/0.47 ~ ( P @ X4 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % empty_Collect_eq
% 0.30/0.47 thf(fact_100_Collect__empty__eq,axiom,
% 0.30/0.47 ! [A: $tType,P: A > $o] :
% 0.30/0.47 ( ( ( collect @ A @ P )
% 0.30/0.47 = ( bot_bot @ ( set @ A ) ) )
% 0.30/0.47 = ( ! [X4: A] :
% 0.30/0.47 ~ ( P @ X4 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Collect_empty_eq
% 0.30/0.47 thf(fact_101_all__not__in__conv,axiom,
% 0.30/0.47 ! [A: $tType,A4: set @ A] :
% 0.30/0.47 ( ( ! [X4: A] :
% 0.30/0.47 ~ ( member @ A @ X4 @ A4 ) )
% 0.30/0.47 = ( A4
% 0.30/0.47 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % all_not_in_conv
% 0.30/0.47 thf(fact_102_empty__iff,axiom,
% 0.30/0.47 ! [A: $tType,C2: A] :
% 0.30/0.47 ~ ( member @ A @ C2 @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % empty_iff
% 0.30/0.47 thf(fact_103_empty__def,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( bot_bot @ ( set @ A ) )
% 0.30/0.47 = ( collect @ A
% 0.30/0.47 @ ^ [X4: A] : $false ) ) ).
% 0.30/0.47
% 0.30/0.47 % empty_def
% 0.30/0.47 thf(fact_104_bot__set__def,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( bot_bot @ ( set @ A ) )
% 0.30/0.47 = ( collect @ A @ ( bot_bot @ ( A > $o ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % bot_set_def
% 0.30/0.47 thf(fact_105_not__psubset__empty,axiom,
% 0.30/0.47 ! [A: $tType,A4: set @ A] :
% 0.30/0.47 ~ ( ord_less @ ( set @ A ) @ A4 @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % not_psubset_empty
% 0.30/0.47 thf(fact_106_emptyE,axiom,
% 0.30/0.47 ! [A: $tType,A3: A] :
% 0.30/0.47 ~ ( member @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % emptyE
% 0.30/0.47 thf(fact_107_equals0D,axiom,
% 0.30/0.47 ! [A: $tType,A4: set @ A,A3: A] :
% 0.30/0.47 ( ( A4
% 0.30/0.47 = ( bot_bot @ ( set @ A ) ) )
% 0.30/0.47 => ~ ( member @ A @ A3 @ A4 ) ) ).
% 0.30/0.47
% 0.30/0.47 % equals0D
% 0.30/0.47 thf(fact_108_equals0I,axiom,
% 0.30/0.47 ! [A: $tType,A4: set @ A] :
% 0.30/0.47 ( ! [Y3: A] :
% 0.30/0.47 ~ ( member @ A @ Y3 @ A4 )
% 0.30/0.47 => ( A4
% 0.30/0.47 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % equals0I
% 0.30/0.47 thf(fact_109_ex__in__conv,axiom,
% 0.30/0.47 ! [A: $tType,A4: set @ A] :
% 0.30/0.47 ( ( ? [X4: A] : ( member @ A @ X4 @ A4 ) )
% 0.30/0.47 = ( A4
% 0.30/0.47 != ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % ex_in_conv
% 0.30/0.47 thf(fact_110_Set_Ois__empty__def,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( is_empty @ A )
% 0.30/0.47 = ( ^ [A6: set @ A] :
% 0.30/0.47 ( A6
% 0.30/0.47 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Set.is_empty_def
% 0.30/0.47 thf(fact_111_Collect__empty__eq__bot,axiom,
% 0.30/0.47 ! [A: $tType,P: A > $o] :
% 0.30/0.47 ( ( ( collect @ A @ P )
% 0.30/0.47 = ( bot_bot @ ( set @ A ) ) )
% 0.30/0.47 = ( P
% 0.30/0.47 = ( bot_bot @ ( A > $o ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Collect_empty_eq_bot
% 0.30/0.47 thf(fact_112_bot__empty__eq,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( bot_bot @ ( A > $o ) )
% 0.30/0.47 = ( ^ [X4: A] : ( member @ A @ X4 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % bot_empty_eq
% 0.30/0.47 thf(fact_113_Tree_Osimps_I14_J,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( binary2130109271t_Tree @ A @ ( binary1746293266le_Tip @ A ) )
% 0.30/0.47 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Tree.simps(14)
% 0.30/0.47 thf(fact_114_is__singletonI_H,axiom,
% 0.30/0.47 ! [A: $tType,A4: set @ A] :
% 0.30/0.47 ( ( A4
% 0.30/0.47 != ( bot_bot @ ( set @ A ) ) )
% 0.30/0.47 => ( ! [X6: A,Y3: A] :
% 0.30/0.47 ( ( member @ A @ X6 @ A4 )
% 0.30/0.47 => ( ( member @ A @ Y3 @ A4 )
% 0.30/0.47 => ( X6 = Y3 ) ) )
% 0.30/0.47 => ( is_singleton @ A @ A4 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % is_singletonI'
% 0.30/0.47 thf(fact_115_psubsetD,axiom,
% 0.30/0.47 ! [A: $tType,A4: set @ A,B5: set @ A,C2: A] :
% 0.30/0.47 ( ( ord_less @ ( set @ A ) @ A4 @ B5 )
% 0.30/0.47 => ( ( member @ A @ C2 @ A4 )
% 0.30/0.47 => ( member @ A @ C2 @ B5 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % psubsetD
% 0.30/0.47 thf(fact_116_less__set__def,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( ord_less @ ( set @ A ) )
% 0.30/0.47 = ( ^ [A6: set @ A,B6: set @ A] :
% 0.30/0.47 ( ord_less @ ( A > $o )
% 0.30/0.47 @ ^ [X4: A] : ( member @ A @ X4 @ A6 )
% 0.30/0.47 @ ^ [X4: A] : ( member @ A @ X4 @ B6 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % less_set_def
% 0.30/0.47 thf(fact_117_psubset__trans,axiom,
% 0.30/0.47 ! [A: $tType,A4: set @ A,B5: set @ A,C3: set @ A] :
% 0.30/0.47 ( ( ord_less @ ( set @ A ) @ A4 @ B5 )
% 0.30/0.47 => ( ( ord_less @ ( set @ A ) @ B5 @ C3 )
% 0.30/0.47 => ( ord_less @ ( set @ A ) @ A4 @ C3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % psubset_trans
% 0.30/0.47 thf(fact_118_Tree_Oset__cases,axiom,
% 0.30/0.47 ! [A: $tType,E: A,A3: binary1291135688e_Tree @ A] :
% 0.30/0.47 ( ( member @ A @ E @ ( binary2130109271t_Tree @ A @ A3 ) )
% 0.30/0.47 => ( ! [Z1: binary1291135688e_Tree @ A] :
% 0.30/0.47 ( ? [Z22: A,Z32: binary1291135688e_Tree @ A] :
% 0.30/0.47 ( A3
% 0.30/0.47 = ( binary210054475elle_T @ A @ Z1 @ Z22 @ Z32 ) )
% 0.30/0.47 => ~ ( member @ A @ E @ ( binary2130109271t_Tree @ A @ Z1 ) ) )
% 0.30/0.47 => ( ! [Z1: binary1291135688e_Tree @ A,Z32: binary1291135688e_Tree @ A] :
% 0.30/0.47 ( A3
% 0.30/0.47 != ( binary210054475elle_T @ A @ Z1 @ E @ Z32 ) )
% 0.30/0.47 => ~ ! [Z1: binary1291135688e_Tree @ A,Z22: A,Z32: binary1291135688e_Tree @ A] :
% 0.30/0.47 ( ( A3
% 0.30/0.47 = ( binary210054475elle_T @ A @ Z1 @ Z22 @ Z32 ) )
% 0.30/0.47 => ~ ( member @ A @ E @ ( binary2130109271t_Tree @ A @ Z32 ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Tree.set_cases
% 0.30/0.47 thf(fact_119_Tree_Oset__intros_I1_J,axiom,
% 0.30/0.47 ! [A: $tType,Y: A,X21: binary1291135688e_Tree @ A,X22: A,X23: binary1291135688e_Tree @ A] :
% 0.30/0.47 ( ( member @ A @ Y @ ( binary2130109271t_Tree @ A @ X21 ) )
% 0.30/0.47 => ( member @ A @ Y @ ( binary2130109271t_Tree @ A @ ( binary210054475elle_T @ A @ X21 @ X22 @ X23 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Tree.set_intros(1)
% 0.30/0.47 thf(fact_120_Tree_Oset__intros_I2_J,axiom,
% 0.30/0.47 ! [A: $tType,X22: A,X21: binary1291135688e_Tree @ A,X23: binary1291135688e_Tree @ A] : ( member @ A @ X22 @ ( binary2130109271t_Tree @ A @ ( binary210054475elle_T @ A @ X21 @ X22 @ X23 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Tree.set_intros(2)
% 0.30/0.47 thf(fact_121_Tree_Oset__intros_I3_J,axiom,
% 0.30/0.47 ! [A: $tType,Ya: A,X23: binary1291135688e_Tree @ A,X21: binary1291135688e_Tree @ A,X22: A] :
% 0.30/0.47 ( ( member @ A @ Ya @ ( binary2130109271t_Tree @ A @ X23 ) )
% 0.30/0.47 => ( member @ A @ Ya @ ( binary2130109271t_Tree @ A @ ( binary210054475elle_T @ A @ X21 @ X22 @ X23 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Tree.set_intros(3)
% 0.30/0.47 thf(fact_122_is__singletonI,axiom,
% 0.30/0.47 ! [A: $tType,X: A] : ( is_singleton @ A @ ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % is_singletonI
% 0.30/0.47 thf(fact_123_is__singleton__def,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( is_singleton @ A )
% 0.30/0.47 = ( ^ [A6: set @ A] :
% 0.30/0.47 ? [X4: A] :
% 0.30/0.47 ( A6
% 0.30/0.47 = ( insert @ A @ X4 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % is_singleton_def
% 0.30/0.47 thf(fact_124_is__singletonE,axiom,
% 0.30/0.47 ! [A: $tType,A4: set @ A] :
% 0.30/0.47 ( ( is_singleton @ A @ A4 )
% 0.30/0.47 => ~ ! [X6: A] :
% 0.30/0.47 ( A4
% 0.30/0.47 != ( insert @ A @ X6 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % is_singletonE
% 0.30/0.47 thf(fact_125_inv__imagep__def,axiom,
% 0.30/0.47 ! [A: $tType,B: $tType] :
% 0.30/0.47 ( ( inv_imagep @ B @ A )
% 0.30/0.47 = ( ^ [R2: B > B > $o,F4: A > B,X4: A,Y2: A] : ( R2 @ ( F4 @ X4 ) @ ( F4 @ Y2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % inv_imagep_def
% 0.30/0.47 thf(fact_126_insert__absorb2,axiom,
% 0.30/0.47 ! [A: $tType,X: A,A4: set @ A] :
% 0.30/0.47 ( ( insert @ A @ X @ ( insert @ A @ X @ A4 ) )
% 0.30/0.47 = ( insert @ A @ X @ A4 ) ) ).
% 0.30/0.47
% 0.30/0.47 % insert_absorb2
% 0.30/0.47 thf(fact_127_insert__iff,axiom,
% 0.30/0.47 ! [A: $tType,A3: A,B4: A,A4: set @ A] :
% 0.30/0.47 ( ( member @ A @ A3 @ ( insert @ A @ B4 @ A4 ) )
% 0.30/0.47 = ( ( A3 = B4 )
% 0.30/0.47 | ( member @ A @ A3 @ A4 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % insert_iff
% 0.30/0.47 thf(fact_128_insertCI,axiom,
% 0.30/0.47 ! [A: $tType,A3: A,B5: set @ A,B4: A] :
% 0.30/0.47 ( ( ~ ( member @ A @ A3 @ B5 )
% 0.30/0.47 => ( A3 = B4 ) )
% 0.30/0.47 => ( member @ A @ A3 @ ( insert @ A @ B4 @ B5 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % insertCI
% 0.30/0.47 thf(fact_129_singletonI,axiom,
% 0.30/0.47 ! [A: $tType,A3: A] : ( member @ A @ A3 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % singletonI
% 0.30/0.47 thf(fact_130_singleton__conv,axiom,
% 0.30/0.47 ! [A: $tType,A3: A] :
% 0.30/0.47 ( ( collect @ A
% 0.30/0.47 @ ^ [X4: A] : ( X4 = A3 ) )
% 0.30/0.47 = ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % singleton_conv
% 0.30/0.47 thf(fact_131_singleton__conv2,axiom,
% 0.30/0.47 ! [A: $tType,A3: A] :
% 0.30/0.47 ( ( collect @ A
% 0.30/0.47 @ ( ^ [Y5: A,Z4: A] : ( Y5 = Z4 )
% 0.30/0.47 @ A3 ) )
% 0.30/0.47 = ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % singleton_conv2
% 0.30/0.47 thf(fact_132_singleton__inject,axiom,
% 0.30/0.47 ! [A: $tType,A3: A,B4: A] :
% 0.30/0.47 ( ( ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) )
% 0.30/0.47 = ( insert @ A @ B4 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.47 => ( A3 = B4 ) ) ).
% 0.30/0.47
% 0.30/0.47 % singleton_inject
% 0.30/0.47 thf(fact_133_insert__not__empty,axiom,
% 0.30/0.47 ! [A: $tType,A3: A,A4: set @ A] :
% 0.30/0.47 ( ( insert @ A @ A3 @ A4 )
% 0.30/0.47 != ( bot_bot @ ( set @ A ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % insert_not_empty
% 0.30/0.47 thf(fact_134_doubleton__eq__iff,axiom,
% 0.30/0.47 ! [A: $tType,A3: A,B4: A,C2: A,D2: A] :
% 0.30/0.47 ( ( ( insert @ A @ A3 @ ( insert @ A @ B4 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.47 = ( insert @ A @ C2 @ ( insert @ A @ D2 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.30/0.47 = ( ( ( A3 = C2 )
% 0.30/0.47 & ( B4 = D2 ) )
% 0.30/0.47 | ( ( A3 = D2 )
% 0.30/0.47 & ( B4 = C2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % doubleton_eq_iff
% 0.30/0.47 thf(fact_135_singleton__iff,axiom,
% 0.30/0.47 ! [A: $tType,B4: A,A3: A] :
% 0.30/0.47 ( ( member @ A @ B4 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.47 = ( B4 = A3 ) ) ).
% 0.30/0.47
% 0.30/0.47 % singleton_iff
% 0.30/0.47 thf(fact_136_singletonD,axiom,
% 0.30/0.47 ! [A: $tType,B4: A,A3: A] :
% 0.30/0.47 ( ( member @ A @ B4 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.47 => ( B4 = A3 ) ) ).
% 0.30/0.47
% 0.30/0.47 % singletonD
% 0.30/0.47 thf(fact_137_insert__compr,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( insert @ A )
% 0.30/0.47 = ( ^ [A2: A,B6: set @ A] :
% 0.30/0.47 ( collect @ A
% 0.30/0.47 @ ^ [X4: A] :
% 0.30/0.47 ( ( X4 = A2 )
% 0.30/0.47 | ( member @ A @ X4 @ B6 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % insert_compr
% 0.30/0.47 thf(fact_138_insert__Collect,axiom,
% 0.30/0.47 ! [A: $tType,A3: A,P: A > $o] :
% 0.30/0.47 ( ( insert @ A @ A3 @ ( collect @ A @ P ) )
% 0.30/0.47 = ( collect @ A
% 0.30/0.47 @ ^ [U: A] :
% 0.30/0.47 ( ( U != A3 )
% 0.30/0.47 => ( P @ U ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % insert_Collect
% 0.30/0.47 thf(fact_139_mk__disjoint__insert,axiom,
% 0.30/0.47 ! [A: $tType,A3: A,A4: set @ A] :
% 0.30/0.47 ( ( member @ A @ A3 @ A4 )
% 0.30/0.47 => ? [B7: set @ A] :
% 0.30/0.47 ( ( A4
% 0.30/0.47 = ( insert @ A @ A3 @ B7 ) )
% 0.30/0.47 & ~ ( member @ A @ A3 @ B7 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % mk_disjoint_insert
% 0.30/0.47 thf(fact_140_insert__commute,axiom,
% 0.30/0.47 ! [A: $tType,X: A,Y: A,A4: set @ A] :
% 0.30/0.47 ( ( insert @ A @ X @ ( insert @ A @ Y @ A4 ) )
% 0.30/0.47 = ( insert @ A @ Y @ ( insert @ A @ X @ A4 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % insert_commute
% 0.30/0.47 thf(fact_141_insert__eq__iff,axiom,
% 0.30/0.47 ! [A: $tType,A3: A,A4: set @ A,B4: A,B5: set @ A] :
% 0.30/0.47 ( ~ ( member @ A @ A3 @ A4 )
% 0.30/0.47 => ( ~ ( member @ A @ B4 @ B5 )
% 0.30/0.47 => ( ( ( insert @ A @ A3 @ A4 )
% 0.30/0.47 = ( insert @ A @ B4 @ B5 ) )
% 0.30/0.47 = ( ( ( A3 = B4 )
% 0.30/0.47 => ( A4 = B5 ) )
% 0.30/0.47 & ( ( A3 != B4 )
% 0.30/0.47 => ? [C4: set @ A] :
% 0.30/0.47 ( ( A4
% 0.30/0.47 = ( insert @ A @ B4 @ C4 ) )
% 0.30/0.47 & ~ ( member @ A @ B4 @ C4 )
% 0.30/0.47 & ( B5
% 0.30/0.47 = ( insert @ A @ A3 @ C4 ) )
% 0.30/0.47 & ~ ( member @ A @ A3 @ C4 ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % insert_eq_iff
% 0.30/0.47 thf(fact_142_insert__absorb,axiom,
% 0.30/0.47 ! [A: $tType,A3: A,A4: set @ A] :
% 0.30/0.47 ( ( member @ A @ A3 @ A4 )
% 0.30/0.47 => ( ( insert @ A @ A3 @ A4 )
% 0.30/0.47 = A4 ) ) ).
% 0.30/0.47
% 0.30/0.47 % insert_absorb
% 0.30/0.47 thf(fact_143_insert__ident,axiom,
% 0.30/0.47 ! [A: $tType,X: A,A4: set @ A,B5: set @ A] :
% 0.30/0.47 ( ~ ( member @ A @ X @ A4 )
% 0.30/0.47 => ( ~ ( member @ A @ X @ B5 )
% 0.30/0.47 => ( ( ( insert @ A @ X @ A4 )
% 0.30/0.47 = ( insert @ A @ X @ B5 ) )
% 0.30/0.47 = ( A4 = B5 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % insert_ident
% 0.30/0.47 thf(fact_144_Set_Oset__insert,axiom,
% 0.30/0.47 ! [A: $tType,X: A,A4: set @ A] :
% 0.30/0.47 ( ( member @ A @ X @ A4 )
% 0.30/0.47 => ~ ! [B7: set @ A] :
% 0.30/0.47 ( ( A4
% 0.30/0.47 = ( insert @ A @ X @ B7 ) )
% 0.30/0.47 => ( member @ A @ X @ B7 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Set.set_insert
% 0.30/0.47 thf(fact_145_insertI2,axiom,
% 0.30/0.47 ! [A: $tType,A3: A,B5: set @ A,B4: A] :
% 0.30/0.47 ( ( member @ A @ A3 @ B5 )
% 0.30/0.47 => ( member @ A @ A3 @ ( insert @ A @ B4 @ B5 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % insertI2
% 0.30/0.47 thf(fact_146_insertI1,axiom,
% 0.30/0.47 ! [A: $tType,A3: A,B5: set @ A] : ( member @ A @ A3 @ ( insert @ A @ A3 @ B5 ) ) ).
% 0.30/0.47
% 0.30/0.47 % insertI1
% 0.30/0.47 thf(fact_147_insertE,axiom,
% 0.30/0.47 ! [A: $tType,A3: A,B4: A,A4: set @ A] :
% 0.30/0.47 ( ( member @ A @ A3 @ ( insert @ A @ B4 @ A4 ) )
% 0.30/0.47 => ( ( A3 != B4 )
% 0.30/0.47 => ( member @ A @ A3 @ A4 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % insertE
% 0.30/0.47 thf(fact_148_Collect__conv__if,axiom,
% 0.30/0.47 ! [A: $tType,P: A > $o,A3: A] :
% 0.30/0.47 ( ( ( P @ A3 )
% 0.30/0.47 => ( ( collect @ A
% 0.30/0.47 @ ^ [X4: A] :
% 0.30/0.47 ( ( X4 = A3 )
% 0.30/0.47 & ( P @ X4 ) ) )
% 0.30/0.47 = ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.30/0.47 & ( ~ ( P @ A3 )
% 0.30/0.47 => ( ( collect @ A
% 0.30/0.47 @ ^ [X4: A] :
% 0.30/0.47 ( ( X4 = A3 )
% 0.30/0.47 & ( P @ X4 ) ) )
% 0.30/0.47 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Collect_conv_if
% 0.30/0.47 thf(fact_149_Collect__conv__if2,axiom,
% 0.30/0.47 ! [A: $tType,P: A > $o,A3: A] :
% 0.30/0.47 ( ( ( P @ A3 )
% 0.30/0.47 => ( ( collect @ A
% 0.30/0.47 @ ^ [X4: A] :
% 0.30/0.47 ( ( A3 = X4 )
% 0.30/0.47 & ( P @ X4 ) ) )
% 0.30/0.47 = ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.30/0.47 & ( ~ ( P @ A3 )
% 0.30/0.47 => ( ( collect @ A
% 0.30/0.47 @ ^ [X4: A] :
% 0.30/0.47 ( ( A3 = X4 )
% 0.30/0.47 & ( P @ X4 ) ) )
% 0.30/0.47 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Collect_conv_if2
% 0.30/0.47 thf(fact_150_is__singleton__the__elem,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( is_singleton @ A )
% 0.30/0.47 = ( ^ [A6: set @ A] :
% 0.30/0.47 ( A6
% 0.30/0.47 = ( insert @ A @ ( the_elem @ A @ A6 ) @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % is_singleton_the_elem
% 0.30/0.47 thf(fact_151_the__elem__eq,axiom,
% 0.30/0.47 ! [A: $tType,X: A] :
% 0.30/0.47 ( ( the_elem @ A @ ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.47 = X ) ).
% 0.30/0.47
% 0.30/0.47 % the_elem_eq
% 0.30/0.47 thf(fact_152_setOf_Osimps_I2_J,axiom,
% 0.30/0.47 ! [A: $tType,T1: binary1291135688e_Tree @ A,X: A,T2: binary1291135688e_Tree @ A] :
% 0.30/0.47 ( ( binary1653327646_setOf @ A @ ( binary210054475elle_T @ A @ T1 @ X @ T2 ) )
% 0.30/0.47 = ( sup_sup @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ ( binary1653327646_setOf @ A @ T1 ) @ ( binary1653327646_setOf @ A @ T2 ) ) @ ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % setOf.simps(2)
% 0.30/0.47 thf(fact_153_Tree_Osimps_I15_J,axiom,
% 0.30/0.47 ! [A: $tType,X21: binary1291135688e_Tree @ A,X22: A,X23: binary1291135688e_Tree @ A] :
% 0.30/0.47 ( ( binary2130109271t_Tree @ A @ ( binary210054475elle_T @ A @ X21 @ X22 @ X23 ) )
% 0.30/0.47 = ( sup_sup @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ ( binary2130109271t_Tree @ A @ X21 ) @ ( insert @ A @ X22 @ ( bot_bot @ ( set @ A ) ) ) ) @ ( binary2130109271t_Tree @ A @ X23 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Tree.simps(15)
% 0.30/0.47 thf(fact_154_UnCI,axiom,
% 0.30/0.47 ! [A: $tType,C2: A,B5: set @ A,A4: set @ A] :
% 0.30/0.47 ( ( ~ ( member @ A @ C2 @ B5 )
% 0.30/0.47 => ( member @ A @ C2 @ A4 ) )
% 0.30/0.47 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % UnCI
% 0.30/0.47 thf(fact_155_Un__iff,axiom,
% 0.30/0.47 ! [A: $tType,C2: A,A4: set @ A,B5: set @ A] :
% 0.30/0.47 ( ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) )
% 0.30/0.47 = ( ( member @ A @ C2 @ A4 )
% 0.30/0.47 | ( member @ A @ C2 @ B5 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Un_iff
% 0.30/0.47 thf(fact_156_Un__empty,axiom,
% 0.30/0.47 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 0.30/0.47 ( ( ( sup_sup @ ( set @ A ) @ A4 @ B5 )
% 0.30/0.47 = ( bot_bot @ ( set @ A ) ) )
% 0.30/0.47 = ( ( A4
% 0.30/0.47 = ( bot_bot @ ( set @ A ) ) )
% 0.30/0.47 & ( B5
% 0.30/0.47 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Un_empty
% 0.30/0.47 thf(fact_157_Un__insert__right,axiom,
% 0.30/0.47 ! [A: $tType,A4: set @ A,A3: A,B5: set @ A] :
% 0.30/0.47 ( ( sup_sup @ ( set @ A ) @ A4 @ ( insert @ A @ A3 @ B5 ) )
% 0.30/0.47 = ( insert @ A @ A3 @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Un_insert_right
% 0.30/0.47 thf(fact_158_Un__insert__left,axiom,
% 0.30/0.47 ! [A: $tType,A3: A,B5: set @ A,C3: set @ A] :
% 0.30/0.47 ( ( sup_sup @ ( set @ A ) @ ( insert @ A @ A3 @ B5 ) @ C3 )
% 0.30/0.47 = ( insert @ A @ A3 @ ( sup_sup @ ( set @ A ) @ B5 @ C3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Un_insert_left
% 0.30/0.47 thf(fact_159_UnE,axiom,
% 0.30/0.47 ! [A: $tType,C2: A,A4: set @ A,B5: set @ A] :
% 0.30/0.47 ( ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) )
% 0.30/0.47 => ( ~ ( member @ A @ C2 @ A4 )
% 0.30/0.47 => ( member @ A @ C2 @ B5 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % UnE
% 0.30/0.47 thf(fact_160_UnI1,axiom,
% 0.30/0.47 ! [A: $tType,C2: A,A4: set @ A,B5: set @ A] :
% 0.30/0.47 ( ( member @ A @ C2 @ A4 )
% 0.30/0.47 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % UnI1
% 0.30/0.47 thf(fact_161_UnI2,axiom,
% 0.30/0.47 ! [A: $tType,C2: A,B5: set @ A,A4: set @ A] :
% 0.30/0.47 ( ( member @ A @ C2 @ B5 )
% 0.30/0.47 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % UnI2
% 0.30/0.47 thf(fact_162_bex__Un,axiom,
% 0.30/0.47 ! [A: $tType,A4: set @ A,B5: set @ A,P: A > $o] :
% 0.30/0.47 ( ( ? [X4: A] :
% 0.30/0.47 ( ( member @ A @ X4 @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) )
% 0.30/0.47 & ( P @ X4 ) ) )
% 0.30/0.47 = ( ? [X4: A] :
% 0.30/0.47 ( ( member @ A @ X4 @ A4 )
% 0.30/0.47 & ( P @ X4 ) )
% 0.30/0.47 | ? [X4: A] :
% 0.30/0.47 ( ( member @ A @ X4 @ B5 )
% 0.30/0.47 & ( P @ X4 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % bex_Un
% 0.30/0.47 thf(fact_163_ball__Un,axiom,
% 0.30/0.47 ! [A: $tType,A4: set @ A,B5: set @ A,P: A > $o] :
% 0.30/0.47 ( ( ! [X4: A] :
% 0.30/0.47 ( ( member @ A @ X4 @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) )
% 0.30/0.47 => ( P @ X4 ) ) )
% 0.30/0.47 = ( ! [X4: A] :
% 0.30/0.47 ( ( member @ A @ X4 @ A4 )
% 0.30/0.47 => ( P @ X4 ) )
% 0.30/0.47 & ! [X4: A] :
% 0.30/0.47 ( ( member @ A @ X4 @ B5 )
% 0.30/0.47 => ( P @ X4 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % ball_Un
% 0.30/0.47 thf(fact_164_Un__assoc,axiom,
% 0.30/0.47 ! [A: $tType,A4: set @ A,B5: set @ A,C3: set @ A] :
% 0.30/0.47 ( ( sup_sup @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) @ C3 )
% 0.30/0.47 = ( sup_sup @ ( set @ A ) @ A4 @ ( sup_sup @ ( set @ A ) @ B5 @ C3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Un_assoc
% 0.30/0.47 thf(fact_165_Un__absorb,axiom,
% 0.30/0.47 ! [A: $tType,A4: set @ A] :
% 0.30/0.47 ( ( sup_sup @ ( set @ A ) @ A4 @ A4 )
% 0.30/0.47 = A4 ) ).
% 0.30/0.47
% 0.30/0.47 % Un_absorb
% 0.30/0.47 thf(fact_166_Un__commute,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( sup_sup @ ( set @ A ) )
% 0.30/0.47 = ( ^ [A6: set @ A,B6: set @ A] : ( sup_sup @ ( set @ A ) @ B6 @ A6 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Un_commute
% 0.30/0.47 thf(fact_167_Un__left__absorb,axiom,
% 0.30/0.47 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 0.30/0.47 ( ( sup_sup @ ( set @ A ) @ A4 @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) )
% 0.30/0.47 = ( sup_sup @ ( set @ A ) @ A4 @ B5 ) ) ).
% 0.30/0.47
% 0.30/0.47 % Un_left_absorb
% 0.30/0.47 thf(fact_168_Un__left__commute,axiom,
% 0.30/0.47 ! [A: $tType,A4: set @ A,B5: set @ A,C3: set @ A] :
% 0.30/0.47 ( ( sup_sup @ ( set @ A ) @ A4 @ ( sup_sup @ ( set @ A ) @ B5 @ C3 ) )
% 0.30/0.47 = ( sup_sup @ ( set @ A ) @ B5 @ ( sup_sup @ ( set @ A ) @ A4 @ C3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Un_left_commute
% 0.30/0.47 thf(fact_169_Collect__disj__eq,axiom,
% 0.30/0.47 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.30/0.47 ( ( collect @ A
% 0.30/0.47 @ ^ [X4: A] :
% 0.30/0.47 ( ( P @ X4 )
% 0.30/0.47 | ( Q @ X4 ) ) )
% 0.30/0.47 = ( sup_sup @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Collect_disj_eq
% 0.30/0.47 thf(fact_170_Un__def,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( sup_sup @ ( set @ A ) )
% 0.30/0.47 = ( ^ [A6: set @ A,B6: set @ A] :
% 0.30/0.47 ( collect @ A
% 0.30/0.47 @ ^ [X4: A] :
% 0.30/0.47 ( ( member @ A @ X4 @ A6 )
% 0.30/0.47 | ( member @ A @ X4 @ B6 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Un_def
% 0.30/0.47 thf(fact_171_Un__empty__left,axiom,
% 0.30/0.47 ! [A: $tType,B5: set @ A] :
% 0.30/0.47 ( ( sup_sup @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ B5 )
% 0.30/0.47 = B5 ) ).
% 0.30/0.47
% 0.30/0.47 % Un_empty_left
% 0.30/0.47 thf(fact_172_Un__empty__right,axiom,
% 0.30/0.47 ! [A: $tType,A4: set @ A] :
% 0.30/0.47 ( ( sup_sup @ ( set @ A ) @ A4 @ ( bot_bot @ ( set @ A ) ) )
% 0.30/0.47 = A4 ) ).
% 0.30/0.47
% 0.30/0.47 % Un_empty_right
% 0.30/0.47 thf(fact_173_insert__def,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( insert @ A )
% 0.30/0.47 = ( ^ [A2: A] :
% 0.30/0.47 ( sup_sup @ ( set @ A )
% 0.30/0.47 @ ( collect @ A
% 0.30/0.47 @ ^ [X4: A] : ( X4 = A2 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % insert_def
% 0.30/0.47 thf(fact_174_insert__is__Un,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( insert @ A )
% 0.30/0.47 = ( ^ [A2: A] : ( sup_sup @ ( set @ A ) @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % insert_is_Un
% 0.30/0.47 thf(fact_175_Un__singleton__iff,axiom,
% 0.30/0.47 ! [A: $tType,A4: set @ A,B5: set @ A,X: A] :
% 0.30/0.47 ( ( ( sup_sup @ ( set @ A ) @ A4 @ B5 )
% 0.30/0.47 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.47 = ( ( ( A4
% 0.30/0.47 = ( bot_bot @ ( set @ A ) ) )
% 0.30/0.47 & ( B5
% 0.30/0.47 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.30/0.47 | ( ( A4
% 0.30/0.47 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.47 & ( B5
% 0.30/0.47 = ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.47 | ( ( A4
% 0.30/0.47 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.47 & ( B5
% 0.30/0.47 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Un_singleton_iff
% 0.30/0.47 thf(fact_176_singleton__Un__iff,axiom,
% 0.30/0.47 ! [A: $tType,X: A,A4: set @ A,B5: set @ A] :
% 0.30/0.47 ( ( ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) )
% 0.30/0.47 = ( sup_sup @ ( set @ A ) @ A4 @ B5 ) )
% 0.30/0.47 = ( ( ( A4
% 0.30/0.47 = ( bot_bot @ ( set @ A ) ) )
% 0.30/0.47 & ( B5
% 0.30/0.47 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.30/0.47 | ( ( A4
% 0.30/0.47 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.47 & ( B5
% 0.30/0.47 = ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.47 | ( ( A4
% 0.30/0.47 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.47 & ( B5
% 0.30/0.47 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % singleton_Un_iff
% 0.30/0.47 thf(fact_177_sup__bot__left,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( bounde1808546759up_bot @ A )
% 0.30/0.47 => ! [X: A] :
% 0.30/0.47 ( ( sup_sup @ A @ ( bot_bot @ A ) @ X )
% 0.30/0.47 = X ) ) ).
% 0.30/0.47
% 0.30/0.47 % sup_bot_left
% 0.30/0.47 thf(fact_178_sup__bot__right,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( bounde1808546759up_bot @ A )
% 0.30/0.47 => ! [X: A] :
% 0.30/0.47 ( ( sup_sup @ A @ X @ ( bot_bot @ A ) )
% 0.30/0.47 = X ) ) ).
% 0.30/0.47
% 0.30/0.47 % sup_bot_right
% 0.30/0.47 thf(fact_179_bot__eq__sup__iff,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( bounde1808546759up_bot @ A )
% 0.30/0.47 => ! [X: A,Y: A] :
% 0.30/0.47 ( ( ( bot_bot @ A )
% 0.30/0.47 = ( sup_sup @ A @ X @ Y ) )
% 0.30/0.47 = ( ( X
% 0.30/0.47 = ( bot_bot @ A ) )
% 0.30/0.47 & ( Y
% 0.30/0.47 = ( bot_bot @ A ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % bot_eq_sup_iff
% 0.30/0.47 thf(fact_180_sup__bot_Oright__neutral,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( bounde1808546759up_bot @ A )
% 0.30/0.47 => ! [A3: A] :
% 0.30/0.47 ( ( sup_sup @ A @ A3 @ ( bot_bot @ A ) )
% 0.30/0.47 = A3 ) ) ).
% 0.30/0.47
% 0.30/0.47 % sup_bot.right_neutral
% 0.30/0.47 thf(fact_181_sup__bot_Oneutr__eq__iff,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( bounde1808546759up_bot @ A )
% 0.30/0.47 => ! [A3: A,B4: A] :
% 0.30/0.47 ( ( ( bot_bot @ A )
% 0.30/0.47 = ( sup_sup @ A @ A3 @ B4 ) )
% 0.30/0.47 = ( ( A3
% 0.30/0.47 = ( bot_bot @ A ) )
% 0.30/0.47 & ( B4
% 0.30/0.47 = ( bot_bot @ A ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % sup_bot.neutr_eq_iff
% 0.30/0.47 thf(fact_182_sup__bot_Oleft__neutral,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( bounde1808546759up_bot @ A )
% 0.30/0.47 => ! [A3: A] :
% 0.30/0.47 ( ( sup_sup @ A @ ( bot_bot @ A ) @ A3 )
% 0.30/0.47 = A3 ) ) ).
% 0.30/0.47
% 0.30/0.47 % sup_bot.left_neutral
% 0.30/0.47 thf(fact_183_sup__bot_Oeq__neutr__iff,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( bounde1808546759up_bot @ A )
% 0.30/0.47 => ! [A3: A,B4: A] :
% 0.30/0.47 ( ( ( sup_sup @ A @ A3 @ B4 )
% 0.30/0.47 = ( bot_bot @ A ) )
% 0.30/0.47 = ( ( A3
% 0.30/0.47 = ( bot_bot @ A ) )
% 0.30/0.47 & ( B4
% 0.30/0.47 = ( bot_bot @ A ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % sup_bot.eq_neutr_iff
% 0.30/0.47 thf(fact_184_sup__eq__bot__iff,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( bounde1808546759up_bot @ A )
% 0.30/0.47 => ! [X: A,Y: A] :
% 0.30/0.47 ( ( ( sup_sup @ A @ X @ Y )
% 0.30/0.47 = ( bot_bot @ A ) )
% 0.30/0.47 = ( ( X
% 0.30/0.47 = ( bot_bot @ A ) )
% 0.30/0.47 & ( Y
% 0.30/0.47 = ( bot_bot @ A ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % sup_eq_bot_iff
% 0.30/0.47 thf(fact_185_sup__set__def,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( sup_sup @ ( set @ A ) )
% 0.30/0.47 = ( ^ [A6: set @ A,B6: set @ A] :
% 0.30/0.47 ( collect @ A
% 0.30/0.47 @ ( sup_sup @ ( A > $o )
% 0.30/0.47 @ ^ [X4: A] : ( member @ A @ X4 @ A6 )
% 0.30/0.47 @ ^ [X4: A] : ( member @ A @ X4 @ B6 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % sup_set_def
% 0.30/0.47 thf(fact_186_sup__Un__eq,axiom,
% 0.30/0.47 ! [A: $tType,R3: set @ A,S: set @ A] :
% 0.30/0.47 ( ( sup_sup @ ( A > $o )
% 0.30/0.47 @ ^ [X4: A] : ( member @ A @ X4 @ R3 )
% 0.30/0.47 @ ^ [X4: A] : ( member @ A @ X4 @ S ) )
% 0.30/0.47 = ( ^ [X4: A] : ( member @ A @ X4 @ ( sup_sup @ ( set @ A ) @ R3 @ S ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % sup_Un_eq
% 0.30/0.47 thf(fact_187_sup_Ostrict__coboundedI2,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( semilattice_sup @ A )
% 0.30/0.47 => ! [C2: A,B4: A,A3: A] :
% 0.30/0.47 ( ( ord_less @ A @ C2 @ B4 )
% 0.30/0.47 => ( ord_less @ A @ C2 @ ( sup_sup @ A @ A3 @ B4 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % sup.strict_coboundedI2
% 0.30/0.47 thf(fact_188_sup_Ostrict__coboundedI1,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( semilattice_sup @ A )
% 0.30/0.47 => ! [C2: A,A3: A,B4: A] :
% 0.30/0.47 ( ( ord_less @ A @ C2 @ A3 )
% 0.30/0.47 => ( ord_less @ A @ C2 @ ( sup_sup @ A @ A3 @ B4 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % sup.strict_coboundedI1
% 0.30/0.47 thf(fact_189_sup_Ostrict__order__iff,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( semilattice_sup @ A )
% 0.30/0.47 => ( ( ord_less @ A )
% 0.30/0.47 = ( ^ [B2: A,A2: A] :
% 0.30/0.47 ( ( A2
% 0.30/0.47 = ( sup_sup @ A @ A2 @ B2 ) )
% 0.30/0.47 & ( A2 != B2 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % sup.strict_order_iff
% 0.30/0.47 thf(fact_190_sup_Ostrict__boundedE,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( semilattice_sup @ A )
% 0.30/0.47 => ! [B4: A,C2: A,A3: A] :
% 0.30/0.47 ( ( ord_less @ A @ ( sup_sup @ A @ B4 @ C2 ) @ A3 )
% 0.30/0.47 => ~ ( ( ord_less @ A @ B4 @ A3 )
% 0.30/0.47 => ~ ( ord_less @ A @ C2 @ A3 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % sup.strict_boundedE
% 0.30/0.47 thf(fact_191_less__supI2,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( semilattice_sup @ A )
% 0.30/0.47 => ! [X: A,B4: A,A3: A] :
% 0.30/0.47 ( ( ord_less @ A @ X @ B4 )
% 0.30/0.47 => ( ord_less @ A @ X @ ( sup_sup @ A @ A3 @ B4 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % less_supI2
% 0.30/0.47 thf(fact_192_less__supI1,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( semilattice_sup @ A )
% 0.30/0.47 => ! [X: A,A3: A,B4: A] :
% 0.30/0.47 ( ( ord_less @ A @ X @ A3 )
% 0.30/0.47 => ( ord_less @ A @ X @ ( sup_sup @ A @ A3 @ B4 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % less_supI1
% 0.30/0.47 thf(fact_193_the__elem__def,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( the_elem @ A )
% 0.30/0.47 = ( ^ [X8: set @ A] :
% 0.30/0.47 ( the @ A
% 0.30/0.47 @ ^ [X4: A] :
% 0.30/0.47 ( X8
% 0.30/0.47 = ( insert @ A @ X4 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % the_elem_def
% 0.30/0.47 thf(fact_194_pred__on_Ochain__extend,axiom,
% 0.30/0.47 ! [A: $tType,A4: set @ A,P: A > A > $o,C3: set @ A,Z3: A] :
% 0.30/0.47 ( ( pred_chain @ A @ A4 @ P @ C3 )
% 0.30/0.47 => ( ( member @ A @ Z3 @ A4 )
% 0.30/0.47 => ( ! [X6: A] :
% 0.30/0.47 ( ( member @ A @ X6 @ C3 )
% 0.30/0.47 => ( sup_sup @ ( A > A > $o ) @ P
% 0.30/0.47 @ ^ [Y5: A,Z4: A] : ( Y5 = Z4 )
% 0.30/0.47 @ X6
% 0.30/0.47 @ Z3 ) )
% 0.30/0.47 => ( pred_chain @ A @ A4 @ P @ ( sup_sup @ ( set @ A ) @ ( insert @ A @ Z3 @ ( bot_bot @ ( set @ A ) ) ) @ C3 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % pred_on.chain_extend
% 0.30/0.47 thf(fact_195_sup__bot_Osemilattice__neutr__axioms,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( bounde1808546759up_bot @ A )
% 0.30/0.47 => ( semilattice_neutr @ A @ ( sup_sup @ A ) @ ( bot_bot @ A ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % sup_bot.semilattice_neutr_axioms
% 0.30/0.47 thf(fact_196_subset_Ochain__extend,axiom,
% 0.30/0.47 ! [A: $tType,A4: set @ ( set @ A ),C3: set @ ( set @ A ),Z3: set @ A] :
% 0.30/0.47 ( ( pred_chain @ ( set @ A ) @ A4 @ ( ord_less @ ( set @ A ) ) @ C3 )
% 0.30/0.47 => ( ( member @ ( set @ A ) @ Z3 @ A4 )
% 0.30/0.47 => ( ! [X6: set @ A] :
% 0.30/0.47 ( ( member @ ( set @ A ) @ X6 @ C3 )
% 0.30/0.47 => ( sup_sup @ ( ( set @ A ) > ( set @ A ) > $o ) @ ( ord_less @ ( set @ A ) )
% 0.30/0.47 @ ^ [Y5: set @ A,Z4: set @ A] : ( Y5 = Z4 )
% 0.30/0.47 @ X6
% 0.30/0.47 @ Z3 ) )
% 0.30/0.47 => ( pred_chain @ ( set @ A ) @ A4 @ ( ord_less @ ( set @ A ) ) @ ( sup_sup @ ( set @ ( set @ A ) ) @ ( insert @ ( set @ A ) @ Z3 @ ( bot_bot @ ( set @ ( set @ A ) ) ) ) @ C3 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % subset.chain_extend
% 0.30/0.47 thf(fact_197_subset_Ochain__total,axiom,
% 0.30/0.47 ! [A: $tType,A4: set @ ( set @ A ),C3: set @ ( set @ A ),X: set @ A,Y: set @ A] :
% 0.30/0.47 ( ( pred_chain @ ( set @ A ) @ A4 @ ( ord_less @ ( set @ A ) ) @ C3 )
% 0.30/0.47 => ( ( member @ ( set @ A ) @ X @ C3 )
% 0.30/0.47 => ( ( member @ ( set @ A ) @ Y @ C3 )
% 0.30/0.47 => ( ( sup_sup @ ( ( set @ A ) > ( set @ A ) > $o ) @ ( ord_less @ ( set @ A ) )
% 0.30/0.47 @ ^ [Y5: set @ A,Z4: set @ A] : ( Y5 = Z4 )
% 0.30/0.47 @ X
% 0.30/0.47 @ Y )
% 0.30/0.47 | ( sup_sup @ ( ( set @ A ) > ( set @ A ) > $o ) @ ( ord_less @ ( set @ A ) )
% 0.30/0.47 @ ^ [Y5: set @ A,Z4: set @ A] : ( Y5 = Z4 )
% 0.30/0.47 @ Y
% 0.30/0.47 @ X ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % subset.chain_total
% 0.30/0.47 thf(fact_198_pred__on_Ochain__total,axiom,
% 0.30/0.47 ! [A: $tType,A4: set @ A,P: A > A > $o,C3: set @ A,X: A,Y: A] :
% 0.30/0.47 ( ( pred_chain @ A @ A4 @ P @ C3 )
% 0.30/0.47 => ( ( member @ A @ X @ C3 )
% 0.30/0.47 => ( ( member @ A @ Y @ C3 )
% 0.30/0.47 => ( ( sup_sup @ ( A > A > $o ) @ P
% 0.30/0.47 @ ^ [Y5: A,Z4: A] : ( Y5 = Z4 )
% 0.30/0.47 @ X
% 0.30/0.47 @ Y )
% 0.30/0.47 | ( sup_sup @ ( A > A > $o ) @ P
% 0.30/0.47 @ ^ [Y5: A,Z4: A] : ( Y5 = Z4 )
% 0.30/0.47 @ Y
% 0.30/0.47 @ X ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % pred_on.chain_total
% 0.30/0.47 thf(fact_199_subset_Ochain__empty,axiom,
% 0.30/0.47 ! [A: $tType,A4: set @ ( set @ A )] : ( pred_chain @ ( set @ A ) @ A4 @ ( ord_less @ ( set @ A ) ) @ ( bot_bot @ ( set @ ( set @ A ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % subset.chain_empty
% 0.30/0.47 thf(fact_200_pred__on_Ochain__empty,axiom,
% 0.30/0.47 ! [A: $tType,A4: set @ A,P: A > A > $o] : ( pred_chain @ A @ A4 @ P @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % pred_on.chain_empty
% 0.30/0.47 thf(fact_201_chain__mono,axiom,
% 0.30/0.47 ! [A: $tType,A4: set @ A,P: A > A > $o,Q: A > A > $o,C3: set @ A] :
% 0.30/0.47 ( ! [X6: A,Y3: A] :
% 0.30/0.47 ( ( member @ A @ X6 @ A4 )
% 0.30/0.48 => ( ( member @ A @ Y3 @ A4 )
% 0.30/0.48 => ( ( P @ X6 @ Y3 )
% 0.30/0.48 => ( Q @ X6 @ Y3 ) ) ) )
% 0.30/0.48 => ( ( pred_chain @ A @ A4 @ P @ C3 )
% 0.30/0.48 => ( pred_chain @ A @ A4 @ Q @ C3 ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % chain_mono
% 0.30/0.48 thf(fact_202_pred__on_Ochain_Ocong,axiom,
% 0.30/0.48 ! [A: $tType] :
% 0.30/0.48 ( ( pred_chain @ A )
% 0.30/0.48 = ( pred_chain @ A ) ) ).
% 0.30/0.48
% 0.30/0.48 % pred_on.chain.cong
% 0.30/0.48 thf(fact_203_the__equality,axiom,
% 0.30/0.48 ! [A: $tType,P: A > $o,A3: A] :
% 0.30/0.48 ( ( P @ A3 )
% 0.30/0.48 => ( ! [X6: A] :
% 0.30/0.48 ( ( P @ X6 )
% 0.30/0.48 => ( X6 = A3 ) )
% 0.30/0.48 => ( ( the @ A @ P )
% 0.30/0.48 = A3 ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % the_equality
% 0.30/0.48 thf(fact_204_the__eq__trivial,axiom,
% 0.30/0.48 ! [A: $tType,A3: A] :
% 0.30/0.48 ( ( the @ A
% 0.30/0.48 @ ^ [X4: A] : ( X4 = A3 ) )
% 0.30/0.48 = A3 ) ).
% 0.30/0.48
% 0.30/0.48 % the_eq_trivial
% 0.30/0.48 thf(fact_205_the__sym__eq__trivial,axiom,
% 0.30/0.48 ! [A: $tType,X: A] :
% 0.30/0.48 ( ( the @ A
% 0.30/0.48 @ ( ^ [Y5: A,Z4: A] : ( Y5 = Z4 )
% 0.30/0.48 @ X ) )
% 0.30/0.48 = X ) ).
% 0.30/0.48
% 0.30/0.48 % the_sym_eq_trivial
% 0.30/0.48 thf(fact_206_the1__equality,axiom,
% 0.30/0.48 ! [A: $tType,P: A > $o,A3: A] :
% 0.30/0.48 ( ? [X5: A] :
% 0.30/0.48 ( ( P @ X5 )
% 0.30/0.48 & ! [Y3: A] :
% 0.30/0.48 ( ( P @ Y3 )
% 0.30/0.48 => ( Y3 = X5 ) ) )
% 0.30/0.48 => ( ( P @ A3 )
% 0.30/0.48 => ( ( the @ A @ P )
% 0.30/0.48 = A3 ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % the1_equality
% 0.30/0.48 thf(fact_207_the1I2,axiom,
% 0.30/0.48 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.30/0.48 ( ? [X5: A] :
% 0.30/0.48 ( ( P @ X5 )
% 0.30/0.48 & ! [Y3: A] :
% 0.30/0.48 ( ( P @ Y3 )
% 0.30/0.48 => ( Y3 = X5 ) ) )
% 0.30/0.48 => ( ! [X6: A] :
% 0.30/0.48 ( ( P @ X6 )
% 0.30/0.48 => ( Q @ X6 ) )
% 0.30/0.48 => ( Q @ ( the @ A @ P ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % the1I2
% 0.30/0.48 thf(fact_208_If__def,axiom,
% 0.30/0.48 ! [A: $tType] :
% 0.30/0.48 ( ( if @ A )
% 0.30/0.48 = ( ^ [P4: $o,X4: A,Y2: A] :
% 0.30/0.48 ( the @ A
% 0.30/0.48 @ ^ [Z5: A] :
% 0.30/0.48 ( ( P4
% 0.30/0.48 => ( Z5 = X4 ) )
% 0.30/0.48 & ( ~ P4
% 0.30/0.48 => ( Z5 = Y2 ) ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % If_def
% 0.30/0.48 thf(fact_209_theI2,axiom,
% 0.30/0.48 ! [A: $tType,P: A > $o,A3: A,Q: A > $o] :
% 0.30/0.48 ( ( P @ A3 )
% 0.30/0.48 => ( ! [X6: A] :
% 0.30/0.48 ( ( P @ X6 )
% 0.30/0.48 => ( X6 = A3 ) )
% 0.30/0.48 => ( ! [X6: A] :
% 0.30/0.48 ( ( P @ X6 )
% 0.30/0.48 => ( Q @ X6 ) )
% 0.30/0.48 => ( Q @ ( the @ A @ P ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % theI2
% 0.30/0.48 thf(fact_210_theI_H,axiom,
% 0.30/0.48 ! [A: $tType,P: A > $o] :
% 0.30/0.48 ( ? [X5: A] :
% 0.30/0.48 ( ( P @ X5 )
% 0.30/0.48 & ! [Y3: A] :
% 0.30/0.48 ( ( P @ Y3 )
% 0.30/0.48 => ( Y3 = X5 ) ) )
% 0.30/0.48 => ( P @ ( the @ A @ P ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % theI'
% 0.30/0.48 thf(fact_211_theI,axiom,
% 0.30/0.48 ! [A: $tType,P: A > $o,A3: A] :
% 0.30/0.48 ( ( P @ A3 )
% 0.30/0.48 => ( ! [X6: A] :
% 0.30/0.48 ( ( P @ X6 )
% 0.30/0.48 => ( X6 = A3 ) )
% 0.30/0.48 => ( P @ ( the @ A @ P ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % theI
% 0.30/0.48 thf(fact_212_chains__alt__def,axiom,
% 0.30/0.48 ! [A: $tType] :
% 0.30/0.48 ( ( chains @ A )
% 0.30/0.48 = ( ^ [A6: set @ ( set @ A )] : ( collect @ ( set @ ( set @ A ) ) @ ( pred_chain @ ( set @ A ) @ A6 @ ( ord_less @ ( set @ A ) ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % chains_alt_def
% 0.30/0.48 thf(fact_213_Pow__empty,axiom,
% 0.30/0.48 ! [A: $tType] :
% 0.30/0.48 ( ( pow @ A @ ( bot_bot @ ( set @ A ) ) )
% 0.30/0.48 = ( insert @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ ( bot_bot @ ( set @ ( set @ A ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % Pow_empty
% 0.30/0.48 thf(fact_214_Pow__singleton__iff,axiom,
% 0.30/0.48 ! [A: $tType,X9: set @ A,Y6: set @ A] :
% 0.30/0.48 ( ( ( pow @ A @ X9 )
% 0.30/0.48 = ( insert @ ( set @ A ) @ Y6 @ ( bot_bot @ ( set @ ( set @ A ) ) ) ) )
% 0.30/0.48 = ( ( X9
% 0.30/0.48 = ( bot_bot @ ( set @ A ) ) )
% 0.30/0.48 & ( Y6
% 0.30/0.48 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % Pow_singleton_iff
% 0.30/0.48 thf(fact_215_Pow__not__empty,axiom,
% 0.30/0.48 ! [A: $tType,A4: set @ A] :
% 0.30/0.48 ( ( pow @ A @ A4 )
% 0.30/0.48 != ( bot_bot @ ( set @ ( set @ A ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % Pow_not_empty
% 0.30/0.48 thf(fact_216_Pow__bottom,axiom,
% 0.30/0.48 ! [A: $tType,B5: set @ A] : ( member @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ ( pow @ A @ B5 ) ) ).
% 0.30/0.48
% 0.30/0.48 % Pow_bottom
% 0.30/0.48 thf(fact_217_Pow__top,axiom,
% 0.30/0.48 ! [A: $tType,A4: set @ A] : ( member @ ( set @ A ) @ A4 @ ( pow @ A @ A4 ) ) ).
% 0.30/0.48
% 0.30/0.48 % Pow_top
% 0.30/0.48 thf(fact_218_chains__extend,axiom,
% 0.30/0.48 ! [A: $tType,C2: set @ ( set @ A ),S: set @ ( set @ A ),Z3: set @ A] :
% 0.30/0.48 ( ( member @ ( set @ ( set @ A ) ) @ C2 @ ( chains @ A @ S ) )
% 0.30/0.48 => ( ( member @ ( set @ A ) @ Z3 @ S )
% 0.30/0.48 => ( ! [X6: set @ A] :
% 0.30/0.48 ( ( member @ ( set @ A ) @ X6 @ C2 )
% 0.30/0.48 => ( ord_less_eq @ ( set @ A ) @ X6 @ Z3 ) )
% 0.30/0.48 => ( member @ ( set @ ( set @ A ) ) @ ( sup_sup @ ( set @ ( set @ A ) ) @ ( insert @ ( set @ A ) @ Z3 @ ( bot_bot @ ( set @ ( set @ A ) ) ) ) @ C2 ) @ ( chains @ A @ S ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % chains_extend
% 0.30/0.48 thf(fact_219_Powp__Pow__eq,axiom,
% 0.30/0.48 ! [A: $tType,A4: set @ A] :
% 0.30/0.48 ( ( powp @ A
% 0.30/0.48 @ ^ [X4: A] : ( member @ A @ X4 @ A4 ) )
% 0.30/0.48 = ( ^ [X4: set @ A] : ( member @ ( set @ A ) @ X4 @ ( pow @ A @ A4 ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % Powp_Pow_eq
% 0.30/0.48 thf(fact_220_order__refl,axiom,
% 0.30/0.48 ! [A: $tType] :
% 0.30/0.48 ( ( preorder @ A )
% 0.30/0.48 => ! [X: A] : ( ord_less_eq @ A @ X @ X ) ) ).
% 0.30/0.48
% 0.30/0.48 % order_refl
% 0.30/0.48 thf(fact_221_subset__antisym,axiom,
% 0.30/0.48 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 0.30/0.48 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 0.30/0.48 => ( ( ord_less_eq @ ( set @ A ) @ B5 @ A4 )
% 0.30/0.48 => ( A4 = B5 ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % subset_antisym
% 0.30/0.48 thf(fact_222_subsetI,axiom,
% 0.30/0.48 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 0.30/0.48 ( ! [X6: A] :
% 0.30/0.48 ( ( member @ A @ X6 @ A4 )
% 0.30/0.48 => ( member @ A @ X6 @ B5 ) )
% 0.30/0.48 => ( ord_less_eq @ ( set @ A ) @ A4 @ B5 ) ) ).
% 0.30/0.48
% 0.30/0.48 % subsetI
% 0.30/0.48 thf(fact_223_empty__subsetI,axiom,
% 0.30/0.48 ! [A: $tType,A4: set @ A] : ( ord_less_eq @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ A4 ) ).
% 0.30/0.48
% 0.30/0.48 % empty_subsetI
% 0.30/0.48 thf(fact_224_subset__empty,axiom,
% 0.30/0.48 ! [A: $tType,A4: set @ A] :
% 0.30/0.48 ( ( ord_less_eq @ ( set @ A ) @ A4 @ ( bot_bot @ ( set @ A ) ) )
% 0.30/0.48 = ( A4
% 0.30/0.48 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % subset_empty
% 0.30/0.48 thf(fact_225_insert__subset,axiom,
% 0.30/0.48 ! [A: $tType,X: A,A4: set @ A,B5: set @ A] :
% 0.30/0.48 ( ( ord_less_eq @ ( set @ A ) @ ( insert @ A @ X @ A4 ) @ B5 )
% 0.30/0.48 = ( ( member @ A @ X @ B5 )
% 0.30/0.48 & ( ord_less_eq @ ( set @ A ) @ A4 @ B5 ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % insert_subset
% 0.30/0.48 thf(fact_226_Un__subset__iff,axiom,
% 0.30/0.48 ! [A: $tType,A4: set @ A,B5: set @ A,C3: set @ A] :
% 0.30/0.48 ( ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) @ C3 )
% 0.30/0.48 = ( ( ord_less_eq @ ( set @ A ) @ A4 @ C3 )
% 0.30/0.48 & ( ord_less_eq @ ( set @ A ) @ B5 @ C3 ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % Un_subset_iff
% 0.30/0.48 thf(fact_227_psubsetI,axiom,
% 0.30/0.48 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 0.30/0.48 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 0.30/0.48 => ( ( A4 != B5 )
% 0.30/0.48 => ( ord_less @ ( set @ A ) @ A4 @ B5 ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % psubsetI
% 0.30/0.48 thf(fact_228_PowI,axiom,
% 0.30/0.48 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 0.30/0.48 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 0.30/0.48 => ( member @ ( set @ A ) @ A4 @ ( pow @ A @ B5 ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % PowI
% 0.30/0.48 thf(fact_229_Pow__iff,axiom,
% 0.30/0.48 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 0.30/0.48 ( ( member @ ( set @ A ) @ A4 @ ( pow @ A @ B5 ) )
% 0.30/0.48 = ( ord_less_eq @ ( set @ A ) @ A4 @ B5 ) ) ).
% 0.30/0.48
% 0.30/0.48 % Pow_iff
% 0.30/0.48 thf(fact_230_singleton__insert__inj__eq,axiom,
% 0.30/0.48 ! [A: $tType,B4: A,A3: A,A4: set @ A] :
% 0.30/0.48 ( ( ( insert @ A @ B4 @ ( bot_bot @ ( set @ A ) ) )
% 0.30/0.48 = ( insert @ A @ A3 @ A4 ) )
% 0.30/0.48 = ( ( A3 = B4 )
% 0.30/0.48 & ( ord_less_eq @ ( set @ A ) @ A4 @ ( insert @ A @ B4 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % singleton_insert_inj_eq
% 0.30/0.48 thf(fact_231_singleton__insert__inj__eq_H,axiom,
% 0.30/0.48 ! [A: $tType,A3: A,A4: set @ A,B4: A] :
% 0.30/0.48 ( ( ( insert @ A @ A3 @ A4 )
% 0.30/0.48 = ( insert @ A @ B4 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.48 = ( ( A3 = B4 )
% 0.30/0.48 & ( ord_less_eq @ ( set @ A ) @ A4 @ ( insert @ A @ B4 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % singleton_insert_inj_eq'
% 0.30/0.48 thf(fact_232_PowD,axiom,
% 0.30/0.48 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 0.30/0.48 ( ( member @ ( set @ A ) @ A4 @ ( pow @ A @ B5 ) )
% 0.30/0.48 => ( ord_less_eq @ ( set @ A ) @ A4 @ B5 ) ) ).
% 0.30/0.48
% 0.30/0.48 % PowD
% 0.30/0.48 thf(fact_233_Pow__mono,axiom,
% 0.30/0.48 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 0.30/0.48 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 0.30/0.48 => ( ord_less_eq @ ( set @ ( set @ A ) ) @ ( pow @ A @ A4 ) @ ( pow @ A @ B5 ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % Pow_mono
% 0.30/0.48 thf(fact_234_Pow__def,axiom,
% 0.30/0.48 ! [A: $tType] :
% 0.30/0.48 ( ( pow @ A )
% 0.30/0.48 = ( ^ [A6: set @ A] :
% 0.30/0.48 ( collect @ ( set @ A )
% 0.30/0.48 @ ^ [B6: set @ A] : ( ord_less_eq @ ( set @ A ) @ B6 @ A6 ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % Pow_def
% 0.30/0.48 thf(fact_235_chainsD,axiom,
% 0.30/0.48 ! [A: $tType,C2: set @ ( set @ A ),S: set @ ( set @ A ),X: set @ A,Y: set @ A] :
% 0.30/0.48 ( ( member @ ( set @ ( set @ A ) ) @ C2 @ ( chains @ A @ S ) )
% 0.30/0.48 => ( ( member @ ( set @ A ) @ X @ C2 )
% 0.30/0.48 => ( ( member @ ( set @ A ) @ Y @ C2 )
% 0.30/0.48 => ( ( ord_less_eq @ ( set @ A ) @ X @ Y )
% 0.30/0.48 | ( ord_less_eq @ ( set @ A ) @ Y @ X ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % chainsD
% 0.30/0.48 thf(fact_236_chainsD2,axiom,
% 0.30/0.48 ! [A: $tType,C2: set @ ( set @ A ),S: set @ ( set @ A )] :
% 0.30/0.48 ( ( member @ ( set @ ( set @ A ) ) @ C2 @ ( chains @ A @ S ) )
% 0.30/0.48 => ( ord_less_eq @ ( set @ ( set @ A ) ) @ C2 @ S ) ) ).
% 0.30/0.48
% 0.30/0.48 % chainsD2
% 0.30/0.48 thf(fact_237_Zorn__Lemma2,axiom,
% 0.30/0.48 ! [A: $tType,A4: set @ ( set @ A )] :
% 0.30/0.48 ( ! [X6: set @ ( set @ A )] :
% 0.30/0.48 ( ( member @ ( set @ ( set @ A ) ) @ X6 @ ( chains @ A @ A4 ) )
% 0.30/0.48 => ? [Xa: set @ A] :
% 0.30/0.48 ( ( member @ ( set @ A ) @ Xa @ A4 )
% 0.30/0.48 & ! [Xb: set @ A] :
% 0.30/0.48 ( ( member @ ( set @ A ) @ Xb @ X6 )
% 0.30/0.48 => ( ord_less_eq @ ( set @ A ) @ Xb @ Xa ) ) ) )
% 0.30/0.48 => ? [X6: set @ A] :
% 0.30/0.48 ( ( member @ ( set @ A ) @ X6 @ A4 )
% 0.30/0.48 & ! [Xa: set @ A] :
% 0.30/0.48 ( ( member @ ( set @ A ) @ Xa @ A4 )
% 0.30/0.48 => ( ( ord_less_eq @ ( set @ A ) @ X6 @ Xa )
% 0.30/0.48 => ( Xa = X6 ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % Zorn_Lemma2
% 0.30/0.48 thf(fact_238_verit__la__disequality,axiom,
% 0.30/0.48 ! [A: $tType] :
% 0.30/0.48 ( ( linorder @ A )
% 0.30/0.48 => ! [A3: A,B4: A] :
% 0.30/0.48 ( ( A3 = B4 )
% 0.30/0.48 | ~ ( ord_less_eq @ A @ A3 @ B4 )
% 0.30/0.48 | ~ ( ord_less_eq @ A @ B4 @ A3 ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % verit_la_disequality
% 0.30/0.48 thf(fact_239_dual__order_Oantisym,axiom,
% 0.30/0.48 ! [A: $tType] :
% 0.30/0.48 ( ( order @ A )
% 0.30/0.48 => ! [B4: A,A3: A] :
% 0.30/0.48 ( ( ord_less_eq @ A @ B4 @ A3 )
% 0.30/0.48 => ( ( ord_less_eq @ A @ A3 @ B4 )
% 0.30/0.48 => ( A3 = B4 ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % dual_order.antisym
% 0.30/0.48 thf(fact_240_dual__order_Oeq__iff,axiom,
% 0.30/0.48 ! [A: $tType] :
% 0.30/0.48 ( ( order @ A )
% 0.30/0.48 => ( ( ^ [Y5: A,Z4: A] : ( Y5 = Z4 ) )
% 0.30/0.48 = ( ^ [A2: A,B2: A] :
% 0.30/0.48 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.30/0.48 & ( ord_less_eq @ A @ A2 @ B2 ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % dual_order.eq_iff
% 0.30/0.48 thf(fact_241_dual__order_Otrans,axiom,
% 0.30/0.48 ! [A: $tType] :
% 0.30/0.48 ( ( order @ A )
% 0.30/0.48 => ! [B4: A,A3: A,C2: A] :
% 0.30/0.48 ( ( ord_less_eq @ A @ B4 @ A3 )
% 0.30/0.48 => ( ( ord_less_eq @ A @ C2 @ B4 )
% 0.30/0.48 => ( ord_less_eq @ A @ C2 @ A3 ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % dual_order.trans
% 0.30/0.48 thf(fact_242_linorder__wlog,axiom,
% 0.30/0.48 ! [A: $tType] :
% 0.30/0.48 ( ( linorder @ A )
% 0.30/0.48 => ! [P: A > A > $o,A3: A,B4: A] :
% 0.30/0.48 ( ! [A5: A,B3: A] :
% 0.30/0.48 ( ( ord_less_eq @ A @ A5 @ B3 )
% 0.30/0.48 => ( P @ A5 @ B3 ) )
% 0.30/0.48 => ( ! [A5: A,B3: A] :
% 0.30/0.48 ( ( P @ B3 @ A5 )
% 0.30/0.48 => ( P @ A5 @ B3 ) )
% 0.30/0.48 => ( P @ A3 @ B4 ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % linorder_wlog
% 0.30/0.48 thf(fact_243_dual__order_Orefl,axiom,
% 0.30/0.48 ! [A: $tType] :
% 0.30/0.48 ( ( order @ A )
% 0.30/0.48 => ! [A3: A] : ( ord_less_eq @ A @ A3 @ A3 ) ) ).
% 0.30/0.48
% 0.30/0.48 % dual_order.refl
% 0.30/0.48 thf(fact_244_order__trans,axiom,
% 0.30/0.48 ! [A: $tType] :
% 0.30/0.48 ( ( preorder @ A )
% 0.30/0.48 => ! [X: A,Y: A,Z3: A] :
% 0.30/0.48 ( ( ord_less_eq @ A @ X @ Y )
% 0.30/0.48 => ( ( ord_less_eq @ A @ Y @ Z3 )
% 0.30/0.48 => ( ord_less_eq @ A @ X @ Z3 ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % order_trans
% 0.30/0.48 thf(fact_245_order__class_Oorder_Oantisym,axiom,
% 0.30/0.48 ! [A: $tType] :
% 0.30/0.48 ( ( order @ A )
% 0.30/0.48 => ! [A3: A,B4: A] :
% 0.30/0.48 ( ( ord_less_eq @ A @ A3 @ B4 )
% 0.30/0.48 => ( ( ord_less_eq @ A @ B4 @ A3 )
% 0.30/0.48 => ( A3 = B4 ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % order_class.order.antisym
% 0.30/0.48 thf(fact_246_ord__le__eq__trans,axiom,
% 0.30/0.48 ! [A: $tType] :
% 0.30/0.48 ( ( ord @ A )
% 0.30/0.48 => ! [A3: A,B4: A,C2: A] :
% 0.30/0.48 ( ( ord_less_eq @ A @ A3 @ B4 )
% 0.30/0.48 => ( ( B4 = C2 )
% 0.30/0.48 => ( ord_less_eq @ A @ A3 @ C2 ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % ord_le_eq_trans
% 0.30/0.48 thf(fact_247_ord__eq__le__trans,axiom,
% 0.30/0.48 ! [A: $tType] :
% 0.30/0.48 ( ( ord @ A )
% 0.30/0.48 => ! [A3: A,B4: A,C2: A] :
% 0.30/0.48 ( ( A3 = B4 )
% 0.30/0.48 => ( ( ord_less_eq @ A @ B4 @ C2 )
% 0.30/0.48 => ( ord_less_eq @ A @ A3 @ C2 ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % ord_eq_le_trans
% 0.30/0.48 thf(fact_248_order__class_Oorder_Oeq__iff,axiom,
% 0.30/0.48 ! [A: $tType] :
% 0.30/0.48 ( ( order @ A )
% 0.30/0.48 => ( ( ^ [Y5: A,Z4: A] : ( Y5 = Z4 ) )
% 0.30/0.48 = ( ^ [A2: A,B2: A] :
% 0.30/0.48 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.30/0.48 & ( ord_less_eq @ A @ B2 @ A2 ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % order_class.order.eq_iff
% 0.30/0.48 thf(fact_249_antisym__conv,axiom,
% 0.30/0.48 ! [A: $tType] :
% 0.30/0.48 ( ( order @ A )
% 0.30/0.48 => ! [Y: A,X: A] :
% 0.30/0.48 ( ( ord_less_eq @ A @ Y @ X )
% 0.30/0.48 => ( ( ord_less_eq @ A @ X @ Y )
% 0.30/0.48 = ( X = Y ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % antisym_conv
% 0.30/0.48 thf(fact_250_le__cases3,axiom,
% 0.30/0.48 ! [A: $tType] :
% 0.30/0.48 ( ( linorder @ A )
% 0.30/0.48 => ! [X: A,Y: A,Z3: A] :
% 0.30/0.48 ( ( ( ord_less_eq @ A @ X @ Y )
% 0.30/0.48 => ~ ( ord_less_eq @ A @ Y @ Z3 ) )
% 0.30/0.48 => ( ( ( ord_less_eq @ A @ Y @ X )
% 0.30/0.48 => ~ ( ord_less_eq @ A @ X @ Z3 ) )
% 0.30/0.48 => ( ( ( ord_less_eq @ A @ X @ Z3 )
% 0.30/0.48 => ~ ( ord_less_eq @ A @ Z3 @ Y ) )
% 0.30/0.48 => ( ( ( ord_less_eq @ A @ Z3 @ Y )
% 0.30/0.48 => ~ ( ord_less_eq @ A @ Y @ X ) )
% 0.30/0.48 => ( ( ( ord_less_eq @ A @ Y @ Z3 )
% 0.30/0.48 => ~ ( ord_less_eq @ A @ Z3 @ X ) )
% 0.30/0.48 => ~ ( ( ord_less_eq @ A @ Z3 @ X )
% 0.30/0.48 => ~ ( ord_less_eq @ A @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % le_cases3
% 0.30/0.48 thf(fact_251_order_Otrans,axiom,
% 0.30/0.48 ! [A: $tType] :
% 0.30/0.48 ( ( order @ A )
% 0.30/0.48 => ! [A3: A,B4: A,C2: A] :
% 0.30/0.48 ( ( ord_less_eq @ A @ A3 @ B4 )
% 0.30/0.48 => ( ( ord_less_eq @ A @ B4 @ C2 )
% 0.30/0.48 => ( ord_less_eq @ A @ A3 @ C2 ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % order.trans
% 0.30/0.48 thf(fact_252_le__cases,axiom,
% 0.30/0.48 ! [A: $tType] :
% 0.30/0.48 ( ( linorder @ A )
% 0.30/0.48 => ! [X: A,Y: A] :
% 0.30/0.48 ( ~ ( ord_less_eq @ A @ X @ Y )
% 0.30/0.48 => ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % le_cases
% 0.30/0.48 thf(fact_253_eq__refl,axiom,
% 0.30/0.48 ! [A: $tType] :
% 0.30/0.48 ( ( preorder @ A )
% 0.30/0.48 => ! [X: A,Y: A] :
% 0.30/0.48 ( ( X = Y )
% 0.30/0.48 => ( ord_less_eq @ A @ X @ Y ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % eq_refl
% 0.30/0.48 thf(fact_254_linear,axiom,
% 0.30/0.48 ! [A: $tType] :
% 0.30/0.48 ( ( linorder @ A )
% 0.30/0.48 => ! [X: A,Y: A] :
% 0.30/0.48 ( ( ord_less_eq @ A @ X @ Y )
% 0.30/0.48 | ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % linear
% 0.30/0.48 thf(fact_255_antisym,axiom,
% 0.30/0.48 ! [A: $tType] :
% 0.30/0.48 ( ( order @ A )
% 0.30/0.48 => ! [X: A,Y: A] :
% 0.30/0.48 ( ( ord_less_eq @ A @ X @ Y )
% 0.30/0.48 => ( ( ord_less_eq @ A @ Y @ X )
% 0.30/0.48 => ( X = Y ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % antisym
% 0.30/0.48
% 0.30/0.48 % Type constructors (33)
% 0.30/0.48 thf(tcon_HOL_Obool___Lattices_Obounded__lattice,axiom,
% 0.30/0.48 bounded_lattice @ $o ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1,axiom,
% 0.30/0.48 ! [A7: $tType] : ( bounded_lattice @ ( set @ A7 ) ) ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_fun___Lattices_Obounded__lattice_2,axiom,
% 0.30/0.48 ! [A7: $tType,A8: $tType] :
% 0.30/0.48 ( ( bounded_lattice @ A8 )
% 0.30/0.48 => ( bounded_lattice @ ( A7 > A8 ) ) ) ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_fun___Lattices_Obounded__semilattice__sup__bot,axiom,
% 0.30/0.48 ! [A7: $tType,A8: $tType] :
% 0.30/0.48 ( ( bounded_lattice @ A8 )
% 0.30/0.48 => ( bounde1808546759up_bot @ ( A7 > A8 ) ) ) ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_fun___Lattices_Osemilattice__sup,axiom,
% 0.30/0.48 ! [A7: $tType,A8: $tType] :
% 0.30/0.48 ( ( semilattice_sup @ A8 )
% 0.30/0.48 => ( semilattice_sup @ ( A7 > A8 ) ) ) ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_fun___Orderings_Oorder__bot,axiom,
% 0.30/0.48 ! [A7: $tType,A8: $tType] :
% 0.30/0.48 ( ( order_bot @ A8 )
% 0.30/0.48 => ( order_bot @ ( A7 > A8 ) ) ) ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.30/0.48 ! [A7: $tType,A8: $tType] :
% 0.30/0.48 ( ( preorder @ A8 )
% 0.30/0.48 => ( preorder @ ( A7 > A8 ) ) ) ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.30/0.48 ! [A7: $tType,A8: $tType] :
% 0.30/0.48 ( ( order @ A8 )
% 0.30/0.48 => ( order @ ( A7 > A8 ) ) ) ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_fun___Orderings_Oord,axiom,
% 0.30/0.48 ! [A7: $tType,A8: $tType] :
% 0.30/0.48 ( ( ord @ A8 )
% 0.30/0.48 => ( ord @ ( A7 > A8 ) ) ) ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_fun___Orderings_Obot,axiom,
% 0.30/0.48 ! [A7: $tType,A8: $tType] :
% 0.30/0.48 ( ( bot @ A8 )
% 0.30/0.48 => ( bot @ ( A7 > A8 ) ) ) ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_Int_Oint___Lattices_Osemilattice__sup_3,axiom,
% 0.30/0.48 semilattice_sup @ int ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_Int_Oint___Rings_Olinordered__idom,axiom,
% 0.30/0.48 linordered_idom @ int ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_Int_Oint___Orderings_Opreorder_4,axiom,
% 0.30/0.48 preorder @ int ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_Int_Oint___Orderings_Olinorder,axiom,
% 0.30/0.48 linorder @ int ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_Int_Oint___Orderings_Ono__top,axiom,
% 0.30/0.48 no_top @ int ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_Int_Oint___Orderings_Ono__bot,axiom,
% 0.30/0.48 no_bot @ int ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_Int_Oint___Orderings_Oorder_5,axiom,
% 0.30/0.48 order @ int ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_Int_Oint___Orderings_Oord_6,axiom,
% 0.30/0.48 ord @ int ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_Set_Oset___Lattices_Obounded__semilattice__sup__bot_7,axiom,
% 0.30/0.48 ! [A7: $tType] : ( bounde1808546759up_bot @ ( set @ A7 ) ) ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_Set_Oset___Lattices_Osemilattice__sup_8,axiom,
% 0.30/0.48 ! [A7: $tType] : ( semilattice_sup @ ( set @ A7 ) ) ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_Set_Oset___Orderings_Oorder__bot_9,axiom,
% 0.30/0.48 ! [A7: $tType] : ( order_bot @ ( set @ A7 ) ) ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_Set_Oset___Orderings_Opreorder_10,axiom,
% 0.30/0.48 ! [A7: $tType] : ( preorder @ ( set @ A7 ) ) ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_Set_Oset___Orderings_Oorder_11,axiom,
% 0.30/0.48 ! [A7: $tType] : ( order @ ( set @ A7 ) ) ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_Set_Oset___Orderings_Oord_12,axiom,
% 0.30/0.48 ! [A7: $tType] : ( ord @ ( set @ A7 ) ) ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_Set_Oset___Orderings_Obot_13,axiom,
% 0.30/0.48 ! [A7: $tType] : ( bot @ ( set @ A7 ) ) ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_HOL_Obool___Lattices_Obounded__semilattice__sup__bot_14,axiom,
% 0.30/0.48 bounde1808546759up_bot @ $o ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_HOL_Obool___Lattices_Osemilattice__sup_15,axiom,
% 0.30/0.48 semilattice_sup @ $o ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_HOL_Obool___Orderings_Oorder__bot_16,axiom,
% 0.30/0.48 order_bot @ $o ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_HOL_Obool___Orderings_Opreorder_17,axiom,
% 0.30/0.48 preorder @ $o ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_HOL_Obool___Orderings_Olinorder_18,axiom,
% 0.30/0.48 linorder @ $o ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_HOL_Obool___Orderings_Oorder_19,axiom,
% 0.30/0.48 order @ $o ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_HOL_Obool___Orderings_Oord_20,axiom,
% 0.30/0.48 ord @ $o ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_HOL_Obool___Orderings_Obot_21,axiom,
% 0.30/0.48 bot @ $o ).
% 0.30/0.48
% 0.30/0.48 % Helper facts (3)
% 0.30/0.48 thf(help_If_3_1_T,axiom,
% 0.30/0.48 ! [P: $o] :
% 0.30/0.48 ( ( P = $true )
% 0.30/0.48 | ( P = $false ) ) ).
% 0.30/0.48
% 0.30/0.48 thf(help_If_2_1_T,axiom,
% 0.30/0.48 ! [A: $tType,X: A,Y: A] :
% 0.30/0.48 ( ( if @ A @ $false @ X @ Y )
% 0.30/0.48 = Y ) ).
% 0.30/0.48
% 0.30/0.48 thf(help_If_1_1_T,axiom,
% 0.30/0.48 ! [A: $tType,X: A,Y: A] :
% 0.30/0.48 ( ( if @ A @ $true @ X @ Y )
% 0.30/0.48 = X ) ).
% 0.30/0.48
% 0.30/0.48 % Conjectures (1)
% 0.30/0.48 thf(conj_0,conjecture,
% 0.30/0.48 a2 = b ).
% 0.30/0.48
% 0.30/0.48 %------------------------------------------------------------------------------
% 0.30/0.48 ------------------------
% 2.75/1.54 ---- Embedded in THF ---
% 2.75/1.54 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.75/1.54 %%% Generated on Tue Feb 24 08:23:58 EST 2026
% 2.75/1.54 %%% using '$$dhol' embedding, version 1.3.0.
% 2.75/1.54 %%% Logic specification used:
% 2.75/1.54 %%% thf(spec, logic, $$dhol).
% 2.75/1.54
% 2.75/1.54 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.YQ97kakufk/DTF2DTF26539.p
% 2.75/1.54 thf(ty_t_BinaryTree__Mirabelle__pchhvghoao_OTree, type, binary1291135688e_Tree: ($tType > $tType)).
% 2.75/1.54 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 2.75/1.54 thf(ty_t_Int_Oint, type, int: $tType).
% 2.75/1.54 thf(ty_tf_a, type, a: $tType).
% 2.75/1.54 thf(sy_cl_Lattices_Obounded__lattice, type, bounded_lattice: (!> [A:$tType]: ($o))).
% 2.75/1.54 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: ($o))).
% 2.75/1.54 thf(sy_cl_Orderings_Obot, type, bot: (!> [A:$tType]: ($o))).
% 2.75/1.54 thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: ($o))).
% 2.75/1.54 thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: ($o))).
% 2.75/1.54 thf(sy_cl_Orderings_Ono__bot, type, no_bot: (!> [A:$tType]: ($o))).
% 2.75/1.54 thf(sy_cl_Orderings_Ono__top, type, no_top: (!> [A:$tType]: ($o))).
% 2.75/1.54 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: ($o))).
% 2.75/1.54 thf(sy_cl_Orderings_Opreorder, type, preorder: (!> [A:$tType]: ($o))).
% 2.75/1.54 thf(sy_cl_Orderings_Oorder__bot, type, order_bot: (!> [A:$tType]: ($o))).
% 2.75/1.54 thf(sy_cl_Orderings_Owellorder, type, wellorder: (!> [A:$tType]: ($o))).
% 2.75/1.54 thf(sy_cl_Orderings_Odense__order, type, dense_order: (!> [A:$tType]: ($o))).
% 2.75/1.54 thf(sy_cl_Rings_Olinordered__idom, type, linordered_idom: (!> [A:$tType]: ($o))).
% 2.75/1.54 thf(sy_cl_Fields_Olinordered__field, type, linordered_field: (!> [A:$tType]: ($o))).
% 2.75/1.54 thf(sy_cl_Lattices_Osemilattice__sup, type, semilattice_sup: (!> [A:$tType]: ($o))).
% 2.75/1.54 thf(sy_cl_Lattices_Obounded__semilattice__sup__bot, type, bounde1808546759up_bot: (!> [A:$tType]: ($o))).
% 2.75/1.54 thf(sy_cl_Conditionally__Complete__Lattices_Olinear__continuum, type, condit1656338222tinuum: (!> [A:$tType]: ($o))).
% 2.75/1.54 thf(sy_c_BinaryTree__Mirabelle__pchhvghoao_OTree_OT, type, binary210054475elle_T: (!> [A:$tType]: (((binary1291135688e_Tree @ A) > (A > ((binary1291135688e_Tree @ A) > (binary1291135688e_Tree @ A))))))).
% 2.75/1.54 thf(sy_c_BinaryTree__Mirabelle__pchhvghoao_OTree_OTip, type, binary1746293266le_Tip: (!> [A:$tType]: ((binary1291135688e_Tree @ A)))).
% 2.75/1.54 thf(sy_c_BinaryTree__Mirabelle__pchhvghoao_OTree_Ocase__Tree, type, binary536355927e_Tree: (!> [B:$tType,A:$tType]: ((B > (((binary1291135688e_Tree @ A) > (A > ((binary1291135688e_Tree @ A) > B))) > ((binary1291135688e_Tree @ A) > B)))))).
% 2.75/1.54 thf(sy_c_BinaryTree__Mirabelle__pchhvghoao_OTree_Orec__Tree, type, binary1929596613c_Tree: (!> [C:$tType,A:$tType]: ((C > (((binary1291135688e_Tree @ A) > (A > ((binary1291135688e_Tree @ A) > (C > (C > C))))) > ((binary1291135688e_Tree @ A) > C)))))).
% 2.75/1.54 thf(sy_c_BinaryTree__Mirabelle__pchhvghoao_OTree_Oset__Tree, type, binary2130109271t_Tree: (!> [A:$tType]: (((binary1291135688e_Tree @ A) > (set @ A))))).
% 2.75/1.54 thf(sy_c_BinaryTree__Mirabelle__pchhvghoao_Oeqs, type, binary64540844le_eqs: (!> [A:$tType]: (((A > int) > (A > (set @ A)))))).
% 2.75/1.54 thf(sy_c_BinaryTree__Mirabelle__pchhvghoao_OsetOf, type, binary1653327646_setOf: (!> [A:$tType]: (((binary1291135688e_Tree @ A) > (set @ A))))).
% 2.75/1.54 thf(sy_c_BinaryTree__Mirabelle__pchhvghoao_OsortedTree, type, binary1610619414edTree: (!> [A:$tType]: (((A > int) > ((binary1291135688e_Tree @ A) > $o))))).
% 2.75/1.54 thf(sy_c_BinaryTree__Mirabelle__pchhvghoao_Osorted__distinct__pred, type, binary231205461t_pred: (!> [A:$tType]: (((A > int) > (A > (A > ((binary1291135688e_Tree @ A) > $o))))))).
% 2.75/1.54 thf(sy_c_HOL_OThe, type, the: (!> [A:$tType]: (((A > $o) > A)))).
% 2.75/1.54 thf(sy_c_If, type, if: (!> [A:$tType]: (($o > (A > (A > A)))))).
% 2.75/1.54 thf(sy_c_Lattices_Osemilattice__neutr, type, semilattice_neutr: (!> [A:$tType]: (((A > (A > A)) > (A > $o))))).
% 2.75/1.54 thf(sy_c_Lattices_Osup__class_Osup, type, sup_sup: (!> [A:$tType]: ((A > (A > A))))).
% 2.75/1.54 thf(sy_c_Orderings_Obot__class_Obot, type, bot_bot: (!> [A:$tType]: (A))).
% 2.75/1.54 thf(sy_c_Orderings_Oord__class_Oless, type, ord_less: (!> [A:$tType]: ((A > (A > $o))))).
% 2.75/1.54 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 2.75/1.54 thf(sy_c_Relation_OPowp, type, powp: (!> [A:$tType]: (((A > $o) > ((set @ A) > $o))))).
% 2.75/1.54 thf(sy_c_Relation_Oinv__imagep, type, inv_imagep: (!> [B:$tType,A:$tType]: (((B > (B > $o)) > ((A > B) > (A > (A > $o))))))).
% 2.75/1.54 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 2.75/1.54 thf(sy_c_Set_OPow, type, pow: (!> [A:$tType]: (((set @ A) > (set @ (set @ A)))))).
% 2.75/1.54 thf(sy_c_Set_Oinsert, type, insert: (!> [A:$tType]: ((A > ((set @ A) > (set @ A)))))).
% 2.75/1.54 thf(sy_c_Set_Ois__empty, type, is_empty: (!> [A:$tType]: (((set @ A) > $o)))).
% 2.75/1.54 thf(sy_c_Set_Ois__singleton, type, is_singleton: (!> [A:$tType]: (((set @ A) > $o)))).
% 2.75/1.54 thf(sy_c_Set_Othe__elem, type, the_elem: (!> [A:$tType]: (((set @ A) > A)))).
% 2.75/1.54 thf(sy_c_Zorn_Ochains, type, chains: (!> [A:$tType]: (((set @ (set @ A)) > (set @ (set @ (set @ A))))))).
% 2.75/1.54 thf(sy_c_Zorn_Opred__on_Ochain, type, pred_chain: (!> [A:$tType]: (((set @ A) > ((A > (A > $o)) > ((set @ A) > $o)))))).
% 2.75/1.54 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 2.75/1.54 thf(sy_v_a, type, a2: a).
% 2.75/1.54 thf(sy_v_b, type, b: a).
% 2.75/1.54 thf(sy_v_h, type, h: (a > int)).
% 2.75/1.54 thf(sy_v_t1____, type, t1: (binary1291135688e_Tree @ a)).
% 2.75/1.54 thf(sy_v_t2____, type, t2: (binary1291135688e_Tree @ a)).
% 2.75/1.54 thf(sy_v_x____, type, x: a).
% 2.75/1.54 thf(fact_0_hahb, axiom, ((h @ a2) = (h @ b))).
% 2.75/1.54 thf(fact_1__092_060open_062h_Ab_A_060_Ah_Aa_092_060close_062, axiom, (((ord_less @ int) @ (h @ b)) @ (h @ a2))).
% 2.75/1.54 thf(fact_2__092_060open_062a_A_061_Ax_A_092_060Longrightarrow_062_Aa_A_061_Ab_092_060close_062, axiom, ((a2 = x) => (a2 = b))).
% 2.75/1.54 thf(fact_3_adef1, axiom, (((member @ a) @ a2) @ ((binary1653327646_setOf @ a) @ t2))).
% 2.75/1.54 thf(fact_4_bdef1, axiom, (((member @ a) @ b) @ ((binary1653327646_setOf @ a) @ t1))).
% 2.75/1.54 thf(fact_5__092_060open_062a_A_092_060in_062_AsetOf_At1_A_092_060Longrightarrow_062_Aa_A_061_Ab_092_060close_062, axiom, ((((member @ a) @ a2) @ ((binary1653327646_setOf @ a) @ t1)) => (a2 = b))).
% 2.75/1.54 thf(fact_6_o1, axiom, (((ord_less @ int) @ (h @ b)) @ (h @ x))).
% 2.75/1.54 thf(fact_7_o2, axiom, (((ord_less @ int) @ (h @ x)) @ (h @ a2))).
% 2.75/1.54 thf(fact_8_h2, axiom, (((((binary231205461t_pred @ a) @ h) @ a2) @ b) @ t2)).
% 2.75/1.54 thf(fact_9_h1, axiom, (((((binary231205461t_pred @ a) @ h) @ a2) @ b) @ t1)).
% 2.75/1.54 thf(fact_10__092_060open_062sorted__distinct__pred_Ah_Aa_Ab_ATip_092_060close_062, axiom, (((((binary231205461t_pred @ a) @ h) @ a2) @ b) @ (binary1746293266le_Tip @ a))).
% 2.75/1.54 thf(fact_11_calculation, axiom, ((((member @ a) @ b) @ ((binary1653327646_setOf @ a) @ t1)) | ((b = x) | (((member @ a) @ b) @ ((binary1653327646_setOf @ a) @ t2))))).
% 2.75/1.54 thf(fact_12__092_060open_062a_A_092_060in_062_AsetOf_At1_A_092_060or_062_Aa_A_061_Ax_A_092_060or_062_Aa_A_092_060in_062_AsetOf_At2_092_060close_062, axiom, ((((member @ a) @ a2) @ ((binary1653327646_setOf @ a) @ t1)) | ((a2 = x) | (((member @ a) @ a2) @ ((binary1653327646_setOf @ a) @ t2))))).
% 2.75/1.54 thf(fact_13_bdef, axiom, (((member @ a) @ b) @ ((binary1653327646_setOf @ a) @ ((((binary210054475elle_T @ a) @ t1) @ x) @ t2)))).
% 2.75/1.54 thf(fact_14_Tree_Oinject, axiom, (! [A:$tType,X21:(binary1291135688e_Tree @ A),X22:A,X23:(binary1291135688e_Tree @ A),Y21:(binary1291135688e_Tree @ A),Y22:A,Y23:(binary1291135688e_Tree @ A)]: (((((((binary210054475elle_T @ A) @ X21) @ X22) @ X23) = ((((binary210054475elle_T @ A) @ Y21) @ Y22) @ Y23)) = ((X21 = Y21) & ((X22 = Y22) & (X23 = Y23))))))).
% 2.75/1.54 thf(fact_15_adef, axiom, (((member @ a) @ a2) @ ((binary1653327646_setOf @ a) @ ((((binary210054475elle_T @ a) @ t1) @ x) @ t2)))).
% 2.75/1.54 thf(fact_16_s, axiom, (((binary1610619414edTree @ a) @ h) @ ((((binary210054475elle_T @ a) @ t1) @ x) @ t2))).
% 2.75/1.54 thf(fact_17_Tree_Odistinct_I1_J, axiom, (! [A:$tType,X21:(binary1291135688e_Tree @ A),X22:A,X23:(binary1291135688e_Tree @ A)]: (((binary1746293266le_Tip @ A) != ((((binary210054475elle_T @ A) @ X21) @ X22) @ X23))))).
% 2.75/1.54 thf(fact_18_Tree_Oinduct, axiom, (! [A:$tType,P:((binary1291135688e_Tree @ A) > $o),Tree:(binary1291135688e_Tree @ A)]: (((P @ (binary1746293266le_Tip @ A)) => ((! [X1:(binary1291135688e_Tree @ A),X2:A,X3:(binary1291135688e_Tree @ A)]: (((P @ X1) => ((P @ X3) => (P @ ((((binary210054475elle_T @ A) @ X1) @ X2) @ X3)))))) => (P @ Tree)))))).
% 2.75/1.54 thf(fact_19_Tree_Oexhaust, axiom, (! [A:$tType,Y:(binary1291135688e_Tree @ A)]: (((Y != (binary1746293266le_Tip @ A)) => (~ ((! [X212:(binary1291135688e_Tree @ A),X222:A,X232:(binary1291135688e_Tree @ A)]: ((Y != ((((binary210054475elle_T @ A) @ X212) @ X222) @ X232)))))))))).
% 2.75/1.54 thf(fact_20_s2, axiom, (((binary1610619414edTree @ a) @ h) @ t2)).
% 2.75/1.54 thf(fact_21_s1, axiom, (((binary1610619414edTree @ a) @ h) @ t1)).
% 2.75/1.54 thf(fact_22_sortedTree_Osimps_I2_J, axiom, (! [A:$tType,H:(A > int),T1:(binary1291135688e_Tree @ A),X:A,T2:(binary1291135688e_Tree @ A)]: (((((binary1610619414edTree @ A) @ H) @ ((((binary210054475elle_T @ A) @ T1) @ X) @ T2)) = ((((binary1610619414edTree @ A) @ H) @ T1) & ((! [X4:A]: (((((member @ A) @ X4) @ ((binary1653327646_setOf @ A) @ T1)) => (((ord_less @ int) @ (H @ X4)) @ (H @ X))))) & ((! [X4:A]: (((((member @ A) @ X4) @ ((binary1653327646_setOf @ A) @ T2)) => (((ord_less @ int) @ (H @ X)) @ (H @ X4))))) & (((binary1610619414edTree @ A) @ H) @ T2)))))))).
% 2.75/1.54 thf(fact_23_sorted__distinct__pred__def, axiom, (! [A:$tType]: (((binary231205461t_pred @ A) = (^ [H2:(A > int),A2:A,B2:A,T:(binary1291135688e_Tree @ A)]: ((((((binary1610619414edTree @ A) @ H2) @ T) & ((((member @ A) @ A2) @ ((binary1653327646_setOf @ A) @ T)) & ((((member @ A) @ B2) @ ((binary1653327646_setOf @ A) @ T)) & ((H2 @ A2) = (H2 @ B2))))) => (A2 = B2)))))))).
% 2.75/1.54 thf(fact_24_eqs__def, axiom, (! [A:$tType]: (((binary64540844le_eqs @ A) = (^ [H2:(A > int),X4:A]: (((collect @ A) @ (^ [Y2:A]: (((H2 @ Y2) = (H2 @ X4))))))))))).
% 2.75/1.54 thf(fact_25_minf_I11_J, axiom, (! [C:$tType,D:$tType]: (((ord @ C) => (! [F:D]: ((? [Z:C]: ((! [X5:C]: (((((ord_less @ C) @ X5) @ Z) => (F = F)))))))))))).
% 2.75/1.54 thf(fact_26_minf_I7_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [T3:A]: ((? [Z:A]: ((! [X5:A]: (((((ord_less @ A) @ X5) @ Z) => (~ ((((ord_less @ A) @ T3) @ X5)))))))))))))).
% 2.75/1.54 thf(fact_27_minf_I5_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [T3:A]: ((? [Z:A]: ((! [X5:A]: (((((ord_less @ A) @ X5) @ Z) => (((ord_less @ A) @ X5) @ T3)))))))))))).
% 2.75/1.54 thf(fact_28_minf_I4_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [T3:A]: ((? [Z:A]: ((! [X5:A]: (((((ord_less @ A) @ X5) @ Z) => (X5 != T3)))))))))))).
% 2.75/1.54 thf(fact_29_minf_I3_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [T3:A]: ((? [Z:A]: ((! [X5:A]: (((((ord_less @ A) @ X5) @ Z) => (X5 != T3)))))))))))).
% 2.75/1.54 thf(fact_30_minf_I2_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:(A > $o),P2:(A > $o),Q:(A > $o),Q2:(A > $o)]: (((? [Z2:A]: ((! [X6:A]: (((((ord_less @ A) @ X6) @ Z2) => ((P @ X6) = (P2 @ X6))))))) => ((? [Z2:A]: ((! [X6:A]: (((((ord_less @ A) @ X6) @ Z2) => ((Q @ X6) = (Q2 @ X6))))))) => (? [Z:A]: ((! [X5:A]: (((((ord_less @ A) @ X5) @ Z) => (((P @ X5) | (Q @ X5)) = ((P2 @ X5) | (Q2 @ X5)))))))))))))))).
% 2.75/1.54 thf(fact_31_sortLemmaR, axiom, (! [A:$tType,H:(A > int),T1:(binary1291135688e_Tree @ A),X:A,T2:(binary1291135688e_Tree @ A)]: (((((binary1610619414edTree @ A) @ H) @ ((((binary210054475elle_T @ A) @ T1) @ X) @ T2)) => (((binary1610619414edTree @ A) @ H) @ T2))))).
% 2.75/1.54 thf(fact_32_sortLemmaL, axiom, (! [A:$tType,H:(A > int),T1:(binary1291135688e_Tree @ A),X:A,T2:(binary1291135688e_Tree @ A)]: (((((binary1610619414edTree @ A) @ H) @ ((((binary210054475elle_T @ A) @ T1) @ X) @ T2)) => (((binary1610619414edTree @ A) @ H) @ T1))))).
% 2.75/1.54 thf(fact_33_sortedTree_Osimps_I1_J, axiom, (! [A:$tType,H:(A > int)]: ((((binary1610619414edTree @ A) @ H) @ (binary1746293266le_Tip @ A))))).
% 2.75/1.54 thf(fact_34_pinf_I1_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:(A > $o),P2:(A > $o),Q:(A > $o),Q2:(A > $o)]: (((? [Z2:A]: ((! [X6:A]: (((((ord_less @ A) @ Z2) @ X6) => ((P @ X6) = (P2 @ X6))))))) => ((? [Z2:A]: ((! [X6:A]: (((((ord_less @ A) @ Z2) @ X6) => ((Q @ X6) = (Q2 @ X6))))))) => (? [Z:A]: ((! [X5:A]: (((((ord_less @ A) @ Z) @ X5) => (((P @ X5) & (Q @ X5)) = ((P2 @ X5) & (Q2 @ X5)))))))))))))))).
% 2.75/1.54 thf(fact_35_pinf_I2_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:(A > $o),P2:(A > $o),Q:(A > $o),Q2:(A > $o)]: (((? [Z2:A]: ((! [X6:A]: (((((ord_less @ A) @ Z2) @ X6) => ((P @ X6) = (P2 @ X6))))))) => ((? [Z2:A]: ((! [X6:A]: (((((ord_less @ A) @ Z2) @ X6) => ((Q @ X6) = (Q2 @ X6))))))) => (? [Z:A]: ((! [X5:A]: (((((ord_less @ A) @ Z) @ X5) => (((P @ X5) | (Q @ X5)) = ((P2 @ X5) | (Q2 @ X5)))))))))))))))).
% 2.75/1.54 thf(fact_36_pinf_I3_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [T3:A]: ((? [Z:A]: ((! [X5:A]: (((((ord_less @ A) @ Z) @ X5) => (X5 != T3)))))))))))).
% 2.75/1.54 thf(fact_37_pinf_I4_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [T3:A]: ((? [Z:A]: ((! [X5:A]: (((((ord_less @ A) @ Z) @ X5) => (X5 != T3)))))))))))).
% 2.75/1.54 thf(fact_38_pinf_I5_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [T3:A]: ((? [Z:A]: ((! [X5:A]: (((((ord_less @ A) @ Z) @ X5) => (~ ((((ord_less @ A) @ X5) @ T3)))))))))))))).
% 2.75/1.54 thf(fact_39_pinf_I7_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [T3:A]: ((? [Z:A]: ((! [X5:A]: (((((ord_less @ A) @ Z) @ X5) => (((ord_less @ A) @ T3) @ X5)))))))))))).
% 2.75/1.54 thf(fact_40_pinf_I11_J, axiom, (! [C:$tType,D:$tType]: (((ord @ C) => (! [F:D]: ((? [Z:C]: ((! [X5:C]: (((((ord_less @ C) @ Z) @ X5) => (F = F)))))))))))).
% 2.75/1.54 thf(fact_41_minf_I1_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:(A > $o),P2:(A > $o),Q:(A > $o),Q2:(A > $o)]: (((? [Z2:A]: ((! [X6:A]: (((((ord_less @ A) @ X6) @ Z2) => ((P @ X6) = (P2 @ X6))))))) => ((? [Z2:A]: ((! [X6:A]: (((((ord_less @ A) @ X6) @ Z2) => ((Q @ X6) = (Q2 @ X6))))))) => (? [Z:A]: ((! [X5:A]: (((((ord_less @ A) @ X5) @ Z) => (((P @ X5) & (Q @ X5)) = ((P2 @ X5) & (Q2 @ X5)))))))))))))))).
% 2.75/1.54 thf(fact_42_ex__gt__or__lt, axiom, (! [A:$tType]: (((condit1656338222tinuum @ A) => (! [A3:A]: ((? [B3:A]: (((((ord_less @ A) @ A3) @ B3) | (((ord_less @ A) @ B3) @ A3)))))))))).
% 2.75/1.54 thf(fact_43_linorder__neqE__linordered__idom, axiom, (! [A:$tType]: (((linordered_idom @ A) => (! [X:A,Y:A]: (((X != Y) => ((~ ((((ord_less @ A) @ X) @ Y))) => (((ord_less @ A) @ Y) @ X))))))))).
% 2.75/1.54 thf(fact_44_dual__order_Ostrict__implies__not__eq, axiom, (! [A:$tType]: (((order @ A) => (! [B4:A,A3:A]: (((((ord_less @ A) @ B4) @ A3) => (A3 != B4)))))))).
% 2.75/1.54 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A3:A,P:(A > $o)]: (((((member @ A) @ A3) @ ((collect @ A) @ P)) = (P @ A3))))).
% 2.75/1.54 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A4:(set @ A)]: ((((collect @ A) @ (^ [X4:A]: ((((member @ A) @ X4) @ A4)))) = A4)))).
% 2.75/1.54 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X6:A]: (((P @ X6) = (Q @ X6)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 2.75/1.54 thf(fact_48_ext, axiom, (! [B:$tType,A:$tType,F2:(A > B),G:(A > B)]: (((! [X6:A]: (((F2 @ X6) = (G @ X6)))) => (F2 = G))))).
% 2.75/1.54 thf(fact_49_linordered__field__no__ub, axiom, (! [A:$tType]: (((linordered_field @ A) => (! [X5:A]: ((? [X_1:A]: ((((ord_less @ A) @ X5) @ X_1))))))))).
% 2.75/1.54 thf(fact_50_linordered__field__no__lb, axiom, (! [A:$tType]: (((linordered_field @ A) => (! [X5:A]: ((? [Y3:A]: ((((ord_less @ A) @ Y3) @ X5))))))))).
% 2.75/1.54 thf(fact_51_order_Ostrict__implies__not__eq, axiom, (! [A:$tType]: (((order @ A) => (! [A3:A,B4:A]: (((((ord_less @ A) @ A3) @ B4) => (A3 != B4)))))))).
% 2.75/1.54 thf(fact_52_dependent__wellorder__choice, axiom, (! [B:$tType,A:$tType]: (((wellorder @ A) => (! [P:((A > B) > (A > (B > $o)))]: (((! [R:B,F3:(A > B),G2:(A > B),X6:A]: (((! [Y4:A]: (((((ord_less @ A) @ Y4) @ X6) => ((F3 @ Y4) = (G2 @ Y4))))) => ((((P @ F3) @ X6) @ R) = (((P @ G2) @ X6) @ R))))) => ((! [X6:A,F3:(A > B)]: (((! [Y4:A]: (((((ord_less @ A) @ Y4) @ X6) => (((P @ F3) @ Y4) @ (F3 @ Y4))))) => (? [X_12:B]: ((((P @ F3) @ X6) @ X_12)))))) => (? [F3:(A > B)]: ((! [X5:A]: ((((P @ F3) @ X5) @ (F3 @ X5)))))))))))))).
% 2.75/1.55 thf(fact_53_not__less__iff__gr__or__eq, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:A,Y:A]: (((~ ((((ord_less @ A) @ X) @ Y))) = ((((ord_less @ A) @ Y) @ X) | (X = Y))))))))).
% 2.75/1.55 thf(fact_54_dual__order_Ostrict__trans, axiom, (! [A:$tType]: (((order @ A) => (! [B4:A,A3:A,C2:A]: (((((ord_less @ A) @ B4) @ A3) => ((((ord_less @ A) @ C2) @ B4) => (((ord_less @ A) @ C2) @ A3))))))))).
% 2.75/1.55 thf(fact_55_ord__eq__less__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A3:A,F2:(B > A),B4:B,C2:B]: (((A3 = (F2 @ B4)) => ((((ord_less @ B) @ B4) @ C2) => ((! [X6:B,Y3:B]: (((((ord_less @ B) @ X6) @ Y3) => (((ord_less @ A) @ (F2 @ X6)) @ (F2 @ Y3))))) => (((ord_less @ A) @ A3) @ (F2 @ C2))))))))))).
% 2.75/1.55 thf(fact_56_ord__less__eq__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A3:A,B4:A,F2:(A > B),C2:B]: (((((ord_less @ A) @ A3) @ B4) => (((F2 @ B4) = C2) => ((! [X6:A,Y3:A]: (((((ord_less @ A) @ X6) @ Y3) => (((ord_less @ B) @ (F2 @ X6)) @ (F2 @ Y3))))) => (((ord_less @ B) @ (F2 @ A3)) @ C2)))))))))).
% 2.75/1.55 thf(fact_57_order__less__subst1, axiom, (! [A:$tType,B:$tType]: ((((order @ B) & (order @ A)) => (! [A3:A,F2:(B > A),B4:B,C2:B]: (((((ord_less @ A) @ A3) @ (F2 @ B4)) => ((((ord_less @ B) @ B4) @ C2) => ((! [X6:B,Y3:B]: (((((ord_less @ B) @ X6) @ Y3) => (((ord_less @ A) @ (F2 @ X6)) @ (F2 @ Y3))))) => (((ord_less @ A) @ A3) @ (F2 @ C2))))))))))).
% 2.75/1.55 thf(fact_58_order__less__subst2, axiom, (! [A:$tType,C:$tType]: ((((order @ C) & (order @ A)) => (! [A3:A,B4:A,F2:(A > C),C2:C]: (((((ord_less @ A) @ A3) @ B4) => ((((ord_less @ C) @ (F2 @ B4)) @ C2) => ((! [X6:A,Y3:A]: (((((ord_less @ A) @ X6) @ Y3) => (((ord_less @ C) @ (F2 @ X6)) @ (F2 @ Y3))))) => (((ord_less @ C) @ (F2 @ A3)) @ C2)))))))))).
% 2.75/1.55 thf(fact_59_lt__ex, axiom, (! [A:$tType]: (((no_bot @ A) => (! [X:A]: ((? [Y3:A]: ((((ord_less @ A) @ Y3) @ X))))))))).
% 2.75/1.55 thf(fact_60_gt__ex, axiom, (! [A:$tType]: (((no_top @ A) => (! [X:A]: ((? [X_1:A]: ((((ord_less @ A) @ X) @ X_1))))))))).
% 2.75/1.55 thf(fact_61_neqE, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:A,Y:A]: (((X != Y) => ((~ ((((ord_less @ A) @ X) @ Y))) => (((ord_less @ A) @ Y) @ X))))))))).
% 2.75/1.55 thf(fact_62_neq__iff, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:A,Y:A]: (((X != Y) = ((((ord_less @ A) @ X) @ Y) | (((ord_less @ A) @ Y) @ X))))))))).
% 2.75/1.55 thf(fact_63_order_Oasym, axiom, (! [A:$tType]: (((order @ A) => (! [A3:A,B4:A]: (((((ord_less @ A) @ A3) @ B4) => (~ ((((ord_less @ A) @ B4) @ A3)))))))))).
% 2.75/1.55 thf(fact_64_dense, axiom, (! [A:$tType]: (((dense_order @ A) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) => (? [Z:A]: (((((ord_less @ A) @ X) @ Z) & (((ord_less @ A) @ Z) @ Y))))))))))).
% 2.75/1.55 thf(fact_65_less__imp__neq, axiom, (! [A:$tType]: (((order @ A) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) => (X != Y)))))))).
% 2.75/1.55 thf(fact_66_less__asym, axiom, (! [A:$tType]: (((preorder @ A) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) => (~ ((((ord_less @ A) @ Y) @ X)))))))))).
% 2.75/1.55 thf(fact_67_less__asym_H, axiom, (! [A:$tType]: (((preorder @ A) => (! [A3:A,B4:A]: (((((ord_less @ A) @ A3) @ B4) => (~ ((((ord_less @ A) @ B4) @ A3)))))))))).
% 2.75/1.55 thf(fact_68_less__trans, axiom, (! [A:$tType]: (((preorder @ A) => (! [X:A,Y:A,Z3:A]: (((((ord_less @ A) @ X) @ Y) => ((((ord_less @ A) @ Y) @ Z3) => (((ord_less @ A) @ X) @ Z3))))))))).
% 2.75/1.55 thf(fact_69_less__linear, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) | ((X = Y) | (((ord_less @ A) @ Y) @ X))))))))).
% 2.75/1.55 thf(fact_70_less__irrefl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X:A]: ((~ ((((ord_less @ A) @ X) @ X))))))))).
% 2.75/1.55 thf(fact_71_ord__eq__less__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A3:A,B4:A,C2:A]: (((A3 = B4) => ((((ord_less @ A) @ B4) @ C2) => (((ord_less @ A) @ A3) @ C2))))))))).
% 2.75/1.55 thf(fact_72_ord__less__eq__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A3:A,B4:A,C2:A]: (((((ord_less @ A) @ A3) @ B4) => ((B4 = C2) => (((ord_less @ A) @ A3) @ C2))))))))).
% 2.75/1.55 thf(fact_73_dual__order_Oasym, axiom, (! [A:$tType]: (((order @ A) => (! [B4:A,A3:A]: (((((ord_less @ A) @ B4) @ A3) => (~ ((((ord_less @ A) @ A3) @ B4)))))))))).
% 2.75/1.55 thf(fact_74_less__imp__not__eq, axiom, (! [A:$tType]: (((order @ A) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) => (X != Y)))))))).
% 2.75/1.55 thf(fact_75_less__not__sym, axiom, (! [A:$tType]: (((preorder @ A) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) => (~ ((((ord_less @ A) @ Y) @ X)))))))))).
% 2.75/1.55 thf(fact_76_less__induct, axiom, (! [A:$tType]: (((wellorder @ A) => (! [P:(A > $o),A3:A]: (((! [X6:A]: (((! [Y4:A]: (((((ord_less @ A) @ Y4) @ X6) => (P @ Y4)))) => (P @ X6)))) => (P @ A3)))))))).
% 2.75/1.55 thf(fact_77_antisym__conv3, axiom, (! [A:$tType]: (((linorder @ A) => (! [Y:A,X:A]: (((~ ((((ord_less @ A) @ Y) @ X))) => ((~ ((((ord_less @ A) @ X) @ Y))) = (X = Y))))))))).
% 2.75/1.55 thf(fact_78_less__imp__not__eq2, axiom, (! [A:$tType]: (((order @ A) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) => (Y != X)))))))).
% 2.75/1.55 thf(fact_79_less__imp__triv, axiom, (! [A:$tType]: (((preorder @ A) => (! [X:A,Y:A,P:$o]: (((((ord_less @ A) @ X) @ Y) => ((((ord_less @ A) @ Y) @ X) => P)))))))).
% 2.75/1.55 thf(fact_80_linorder__cases, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:A,Y:A]: (((~ ((((ord_less @ A) @ X) @ Y))) => ((X != Y) => (((ord_less @ A) @ Y) @ X))))))))).
% 2.75/1.55 thf(fact_81_dual__order_Oirrefl, axiom, (! [A:$tType]: (((order @ A) => (! [A3:A]: ((~ ((((ord_less @ A) @ A3) @ A3))))))))).
% 2.75/1.55 thf(fact_82_order_Ostrict__trans, axiom, (! [A:$tType]: (((order @ A) => (! [A3:A,B4:A,C2:A]: (((((ord_less @ A) @ A3) @ B4) => ((((ord_less @ A) @ B4) @ C2) => (((ord_less @ A) @ A3) @ C2))))))))).
% 2.75/1.55 thf(fact_83_less__imp__not__less, axiom, (! [A:$tType]: (((preorder @ A) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) => (~ ((((ord_less @ A) @ Y) @ X)))))))))).
% 2.75/1.55 thf(fact_84_exists__least__iff, axiom, (! [A:$tType]: (((wellorder @ A) => ((^ [P3:(A > $o)]: ((? [X7:A]: ((P3 @ X7))))) = (^ [P4:(A > $o)]: ((? [N:A]: (((P4 @ N) & (! [M:A]: (((((ord_less @ A) @ M) @ N) => (~ ((P4 @ M)))))))))))))))).
% 2.75/1.55 thf(fact_85_linorder__less__wlog, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:(A > (A > $o)),A3:A,B4:A]: (((! [A5:A,B3:A]: (((((ord_less @ A) @ A5) @ B3) => ((P @ A5) @ B3)))) => ((! [A5:A]: (((P @ A5) @ A5))) => ((! [A5:A,B3:A]: ((((P @ B3) @ A5) => ((P @ A5) @ B3)))) => ((P @ A3) @ B4)))))))))).
% 2.75/1.55 thf(fact_86_verit__comp__simplify1_I1_J, axiom, (! [A:$tType]: (((order @ A) => (! [A3:A]: ((~ ((((ord_less @ A) @ A3) @ A3))))))))).
% 2.75/1.55 thf(fact_87_measure__induct, axiom, (! [B:$tType,A:$tType]: (((wellorder @ B) => (! [F2:(A > B),P:(A > $o),A3:A]: (((! [X6:A]: (((! [Y4:A]: (((((ord_less @ B) @ (F2 @ Y4)) @ (F2 @ X6)) => (P @ Y4)))) => (P @ X6)))) => (P @ A3)))))))).
% 2.75/1.55 thf(fact_88_measure__induct__rule, axiom, (! [B:$tType,A:$tType]: (((wellorder @ B) => (! [F2:(A > B),P:(A > $o),A3:A]: (((! [X6:A]: (((! [Y4:A]: (((((ord_less @ B) @ (F2 @ Y4)) @ (F2 @ X6)) => (P @ Y4)))) => (P @ X6)))) => (P @ A3)))))))).
% 2.75/1.55 thf(fact_89_Tree_Osimps_I4_J, axiom, (! [A:$tType,B:$tType,F1:B,F22:((binary1291135688e_Tree @ A) > (A > ((binary1291135688e_Tree @ A) > B)))]: (((((((binary536355927e_Tree @ B) @ A) @ F1) @ F22) @ (binary1746293266le_Tip @ A)) = F1)))).
% 2.75/1.55 thf(fact_90_Tree_Osimps_I5_J, axiom, (! [B:$tType,A:$tType,F1:B,F22:((binary1291135688e_Tree @ A) > (A > ((binary1291135688e_Tree @ A) > B))),X21:(binary1291135688e_Tree @ A),X22:A,X23:(binary1291135688e_Tree @ A)]: (((((((binary536355927e_Tree @ B) @ A) @ F1) @ F22) @ ((((binary210054475elle_T @ A) @ X21) @ X22) @ X23)) = (((F22 @ X21) @ X22) @ X23))))).
% 2.75/1.55 thf(fact_91_setOf_Osimps_I1_J, axiom, (! [A:$tType]: ((((binary1653327646_setOf @ A) @ (binary1746293266le_Tip @ A)) = (bot_bot @ (set @ A)))))).
% 2.75/1.55 thf(fact_92_Tree_Osimps_I6_J, axiom, (! [A:$tType,C:$tType,F1:C,F22:((binary1291135688e_Tree @ A) > (A > ((binary1291135688e_Tree @ A) > (C > (C > C)))))]: (((((((binary1929596613c_Tree @ C) @ A) @ F1) @ F22) @ (binary1746293266le_Tip @ A)) = F1)))).
% 2.75/1.55 thf(fact_93_Tree_Osimps_I7_J, axiom, (! [C:$tType,A:$tType,F1:C,F22:((binary1291135688e_Tree @ A) > (A > ((binary1291135688e_Tree @ A) > (C > (C > C))))),X21:(binary1291135688e_Tree @ A),X22:A,X23:(binary1291135688e_Tree @ A)]: (((((((binary1929596613c_Tree @ C) @ A) @ F1) @ F22) @ ((((binary210054475elle_T @ A) @ X21) @ X22) @ X23)) = (((((F22 @ X21) @ X22) @ X23) @ (((((binary1929596613c_Tree @ C) @ A) @ F1) @ F22) @ X21)) @ (((((binary1929596613c_Tree @ C) @ A) @ F1) @ F22) @ X23)))))).
% 2.75/1.55 thf(fact_94_bot__apply, axiom, (! [C:$tType,D:$tType]: (((bot @ C) => ((bot_bot @ (D > C)) = (^ [X4:D]: ((bot_bot @ C)))))))).
% 2.75/1.55 thf(fact_95_bot__fun__def, axiom, (! [B:$tType,A:$tType]: (((bot @ B) => ((bot_bot @ (A > B)) = (^ [X4:A]: ((bot_bot @ B)))))))).
% 2.75/1.55 thf(fact_96_bot_Oextremum__strict, axiom, (! [A:$tType]: (((order_bot @ A) => (! [A3:A]: ((~ ((((ord_less @ A) @ A3) @ (bot_bot @ A)))))))))).
% 2.75/1.55 thf(fact_97_bot_Onot__eq__extremum, axiom, (! [A:$tType]: (((order_bot @ A) => (! [A3:A]: (((A3 != (bot_bot @ A)) = (((ord_less @ A) @ (bot_bot @ A)) @ A3)))))))).
% 2.75/1.55 thf(fact_98_Tree_Ocase__distrib, axiom, (! [C:$tType,B:$tType,A:$tType,H:(B > C),F1:B,F22:((binary1291135688e_Tree @ A) > (A > ((binary1291135688e_Tree @ A) > B))),Tree:(binary1291135688e_Tree @ A)]: (((H @ (((((binary536355927e_Tree @ B) @ A) @ F1) @ F22) @ Tree)) = (((((binary536355927e_Tree @ C) @ A) @ (H @ F1)) @ (^ [X12:(binary1291135688e_Tree @ A),X24:A,X32:(binary1291135688e_Tree @ A)]: ((H @ (((F22 @ X12) @ X24) @ X32))))) @ Tree))))).
% 2.75/1.55 thf(fact_99_empty__Collect__eq, axiom, (! [A:$tType,P:(A > $o)]: ((((bot_bot @ (set @ A)) = ((collect @ A) @ P)) = (! [X4:A]: ((~ ((P @ X4))))))))).
% 2.75/1.55 thf(fact_100_Collect__empty__eq, axiom, (! [A:$tType,P:(A > $o)]: (((((collect @ A) @ P) = (bot_bot @ (set @ A))) = (! [X4:A]: ((~ ((P @ X4))))))))).
% 2.75/1.55 thf(fact_101_all__not__in__conv, axiom, (! [A:$tType,A4:(set @ A)]: (((! [X4:A]: ((~ ((((member @ A) @ X4) @ A4))))) = (A4 = (bot_bot @ (set @ A))))))).
% 2.75/1.55 thf(fact_102_empty__iff, axiom, (! [A:$tType,C2:A]: ((~ ((((member @ A) @ C2) @ (bot_bot @ (set @ A)))))))).
% 2.75/1.55 thf(fact_103_empty__def, axiom, (! [A:$tType]: (((bot_bot @ (set @ A)) = ((collect @ A) @ (^ [X4:A]: ($false))))))).
% 2.75/1.55 thf(fact_104_bot__set__def, axiom, (! [A:$tType]: (((bot_bot @ (set @ A)) = ((collect @ A) @ (bot_bot @ (A > $o))))))).
% 2.75/1.55 thf(fact_105_not__psubset__empty, axiom, (! [A:$tType,A4:(set @ A)]: ((~ ((((ord_less @ (set @ A)) @ A4) @ (bot_bot @ (set @ A)))))))).
% 2.75/1.55 thf(fact_106_emptyE, axiom, (! [A:$tType,A3:A]: ((~ ((((member @ A) @ A3) @ (bot_bot @ (set @ A)))))))).
% 2.75/1.55 thf(fact_107_equals0D, axiom, (! [A:$tType,A4:(set @ A),A3:A]: (((A4 = (bot_bot @ (set @ A))) => (~ ((((member @ A) @ A3) @ A4))))))).
% 2.75/1.55 thf(fact_108_equals0I, axiom, (! [A:$tType,A4:(set @ A)]: (((! [Y3:A]: ((~ ((((member @ A) @ Y3) @ A4))))) => (A4 = (bot_bot @ (set @ A))))))).
% 2.75/1.55 thf(fact_109_ex__in__conv, axiom, (! [A:$tType,A4:(set @ A)]: (((? [X4:A]: ((((member @ A) @ X4) @ A4))) = (A4 != (bot_bot @ (set @ A))))))).
% 2.75/1.55 thf(fact_110_Set_Ois__empty__def, axiom, (! [A:$tType]: (((is_empty @ A) = (^ [A6:(set @ A)]: ((A6 = (bot_bot @ (set @ A))))))))).
% 2.75/1.55 thf(fact_111_Collect__empty__eq__bot, axiom, (! [A:$tType,P:(A > $o)]: (((((collect @ A) @ P) = (bot_bot @ (set @ A))) = (P = (bot_bot @ (A > $o))))))).
% 2.75/1.55 thf(fact_112_bot__empty__eq, axiom, (! [A:$tType]: (((bot_bot @ (A > $o)) = (^ [X4:A]: ((((member @ A) @ X4) @ (bot_bot @ (set @ A))))))))).
% 2.75/1.55 thf(fact_113_Tree_Osimps_I14_J, axiom, (! [A:$tType]: ((((binary2130109271t_Tree @ A) @ (binary1746293266le_Tip @ A)) = (bot_bot @ (set @ A)))))).
% 2.75/1.55 thf(fact_114_is__singletonI_H, axiom, (! [A:$tType,A4:(set @ A)]: (((A4 != (bot_bot @ (set @ A))) => ((! [X6:A,Y3:A]: (((((member @ A) @ X6) @ A4) => ((((member @ A) @ Y3) @ A4) => (X6 = Y3))))) => ((is_singleton @ A) @ A4)))))).
% 2.75/1.55 thf(fact_115_psubsetD, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A),C2:A]: (((((ord_less @ (set @ A)) @ A4) @ B5) => ((((member @ A) @ C2) @ A4) => (((member @ A) @ C2) @ B5)))))).
% 2.75/1.55 thf(fact_116_less__set__def, axiom, (! [A:$tType]: (((ord_less @ (set @ A)) = (^ [A6:(set @ A),B6:(set @ A)]: ((((ord_less @ (A > $o)) @ (^ [X4:A]: ((((member @ A) @ X4) @ A6)))) @ (^ [X4:A]: ((((member @ A) @ X4) @ B6)))))))))).
% 2.75/1.55 thf(fact_117_psubset__trans, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A),C3:(set @ A)]: (((((ord_less @ (set @ A)) @ A4) @ B5) => ((((ord_less @ (set @ A)) @ B5) @ C3) => (((ord_less @ (set @ A)) @ A4) @ C3)))))).
% 2.75/1.55 thf(fact_118_Tree_Oset__cases, axiom, (! [A:$tType,E:A,A3:(binary1291135688e_Tree @ A)]: (((((member @ A) @ E) @ ((binary2130109271t_Tree @ A) @ A3)) => ((! [Z1:(binary1291135688e_Tree @ A)]: (((? [Z22:A,Z32:(binary1291135688e_Tree @ A)]: ((A3 = ((((binary210054475elle_T @ A) @ Z1) @ Z22) @ Z32)))) => (~ ((((member @ A) @ E) @ ((binary2130109271t_Tree @ A) @ Z1))))))) => ((! [Z1:(binary1291135688e_Tree @ A),Z32:(binary1291135688e_Tree @ A)]: ((A3 != ((((binary210054475elle_T @ A) @ Z1) @ E) @ Z32)))) => (~ ((! [Z1:(binary1291135688e_Tree @ A),Z22:A,Z32:(binary1291135688e_Tree @ A)]: (((A3 = ((((binary210054475elle_T @ A) @ Z1) @ Z22) @ Z32)) => (~ ((((member @ A) @ E) @ ((binary2130109271t_Tree @ A) @ Z32))))))))))))))).
% 2.75/1.55 thf(fact_119_Tree_Oset__intros_I1_J, axiom, (! [A:$tType,Y:A,X21:(binary1291135688e_Tree @ A),X22:A,X23:(binary1291135688e_Tree @ A)]: (((((member @ A) @ Y) @ ((binary2130109271t_Tree @ A) @ X21)) => (((member @ A) @ Y) @ ((binary2130109271t_Tree @ A) @ ((((binary210054475elle_T @ A) @ X21) @ X22) @ X23))))))).
% 2.75/1.55 thf(fact_120_Tree_Oset__intros_I2_J, axiom, (! [A:$tType,X22:A,X21:(binary1291135688e_Tree @ A),X23:(binary1291135688e_Tree @ A)]: ((((member @ A) @ X22) @ ((binary2130109271t_Tree @ A) @ ((((binary210054475elle_T @ A) @ X21) @ X22) @ X23)))))).
% 2.75/1.55 thf(fact_121_Tree_Oset__intros_I3_J, axiom, (! [A:$tType,Ya:A,X23:(binary1291135688e_Tree @ A),X21:(binary1291135688e_Tree @ A),X22:A]: (((((member @ A) @ Ya) @ ((binary2130109271t_Tree @ A) @ X23)) => (((member @ A) @ Ya) @ ((binary2130109271t_Tree @ A) @ ((((binary210054475elle_T @ A) @ X21) @ X22) @ X23))))))).
% 2.75/1.55 thf(fact_122_is__singletonI, axiom, (! [A:$tType,X:A]: (((is_singleton @ A) @ (((insert @ A) @ X) @ (bot_bot @ (set @ A))))))).
% 2.75/1.55 thf(fact_123_is__singleton__def, axiom, (! [A:$tType]: (((is_singleton @ A) = (^ [A6:(set @ A)]: ((? [X4:A]: ((A6 = (((insert @ A) @ X4) @ (bot_bot @ (set @ A)))))))))))).
% 2.75/1.55 thf(fact_124_is__singletonE, axiom, (! [A:$tType,A4:(set @ A)]: ((((is_singleton @ A) @ A4) => (~ ((! [X6:A]: ((A4 != (((insert @ A) @ X6) @ (bot_bot @ (set @ A)))))))))))).
% 2.75/1.55 thf(fact_125_inv__imagep__def, axiom, (! [A:$tType,B:$tType]: ((((inv_imagep @ B) @ A) = (^ [R2:(B > (B > $o)),F4:(A > B),X4:A,Y2:A]: (((R2 @ (F4 @ X4)) @ (F4 @ Y2)))))))).
% 2.75/1.55 thf(fact_126_insert__absorb2, axiom, (! [A:$tType,X:A,A4:(set @ A)]: (((((insert @ A) @ X) @ (((insert @ A) @ X) @ A4)) = (((insert @ A) @ X) @ A4))))).
% 2.75/1.55 thf(fact_127_insert__iff, axiom, (! [A:$tType,A3:A,B4:A,A4:(set @ A)]: (((((member @ A) @ A3) @ (((insert @ A) @ B4) @ A4)) = ((A3 = B4) | (((member @ A) @ A3) @ A4)))))).
% 2.75/1.55 thf(fact_128_insertCI, axiom, (! [A:$tType,A3:A,B5:(set @ A),B4:A]: ((((~ ((((member @ A) @ A3) @ B5))) => (A3 = B4)) => (((member @ A) @ A3) @ (((insert @ A) @ B4) @ B5)))))).
% 2.75/1.55 thf(fact_129_singletonI, axiom, (! [A:$tType,A3:A]: ((((member @ A) @ A3) @ (((insert @ A) @ A3) @ (bot_bot @ (set @ A))))))).
% 2.75/1.55 thf(fact_130_singleton__conv, axiom, (! [A:$tType,A3:A]: ((((collect @ A) @ (^ [X4:A]: ((X4 = A3)))) = (((insert @ A) @ A3) @ (bot_bot @ (set @ A))))))).
% 2.75/1.55 thf(fact_131_singleton__conv2, axiom, (! [A:$tType,A3:A]: ((((collect @ A) @ ((^ [Y5:A,Z4:A]: ((Y5 = Z4))) @ A3)) = (((insert @ A) @ A3) @ (bot_bot @ (set @ A))))))).
% 2.75/1.55 thf(fact_132_singleton__inject, axiom, (! [A:$tType,A3:A,B4:A]: ((((((insert @ A) @ A3) @ (bot_bot @ (set @ A))) = (((insert @ A) @ B4) @ (bot_bot @ (set @ A)))) => (A3 = B4))))).
% 2.75/1.55 thf(fact_133_insert__not__empty, axiom, (! [A:$tType,A3:A,A4:(set @ A)]: (((((insert @ A) @ A3) @ A4) != (bot_bot @ (set @ A)))))).
% 2.75/1.55 thf(fact_134_doubleton__eq__iff, axiom, (! [A:$tType,A3:A,B4:A,C2:A,D2:A]: ((((((insert @ A) @ A3) @ (((insert @ A) @ B4) @ (bot_bot @ (set @ A)))) = (((insert @ A) @ C2) @ (((insert @ A) @ D2) @ (bot_bot @ (set @ A))))) = (((A3 = C2) & (B4 = D2)) | ((A3 = D2) & (B4 = C2))))))).
% 2.75/1.55 thf(fact_135_singleton__iff, axiom, (! [A:$tType,B4:A,A3:A]: (((((member @ A) @ B4) @ (((insert @ A) @ A3) @ (bot_bot @ (set @ A)))) = (B4 = A3))))).
% 2.75/1.55 thf(fact_136_singletonD, axiom, (! [A:$tType,B4:A,A3:A]: (((((member @ A) @ B4) @ (((insert @ A) @ A3) @ (bot_bot @ (set @ A)))) => (B4 = A3))))).
% 2.75/1.55 thf(fact_137_insert__compr, axiom, (! [A:$tType]: (((insert @ A) = (^ [A2:A,B6:(set @ A)]: (((collect @ A) @ (^ [X4:A]: (((X4 = A2) | (((member @ A) @ X4) @ B6))))))))))).
% 2.75/1.55 thf(fact_138_insert__Collect, axiom, (! [A:$tType,A3:A,P:(A > $o)]: (((((insert @ A) @ A3) @ ((collect @ A) @ P)) = ((collect @ A) @ (^ [U:A]: (((U != A3) => (P @ U))))))))).
% 2.75/1.55 thf(fact_139_mk__disjoint__insert, axiom, (! [A:$tType,A3:A,A4:(set @ A)]: (((((member @ A) @ A3) @ A4) => (? [B7:(set @ A)]: (((A4 = (((insert @ A) @ A3) @ B7)) & (~ ((((member @ A) @ A3) @ B7)))))))))).
% 2.75/1.55 thf(fact_140_insert__commute, axiom, (! [A:$tType,X:A,Y:A,A4:(set @ A)]: (((((insert @ A) @ X) @ (((insert @ A) @ Y) @ A4)) = (((insert @ A) @ Y) @ (((insert @ A) @ X) @ A4)))))).
% 2.75/1.55 thf(fact_141_insert__eq__iff, axiom, (! [A:$tType,A3:A,A4:(set @ A),B4:A,B5:(set @ A)]: (((~ ((((member @ A) @ A3) @ A4))) => ((~ ((((member @ A) @ B4) @ B5))) => (((((insert @ A) @ A3) @ A4) = (((insert @ A) @ B4) @ B5)) = (((A3 = B4) => (A4 = B5)) & ((A3 != B4) => (? [C4:(set @ A)]: (((A4 = (((insert @ A) @ B4) @ C4)) & ((~ ((((member @ A) @ B4) @ C4))) & ((B5 = (((insert @ A) @ A3) @ C4)) & (~ ((((member @ A) @ A3) @ C4)))))))))))))))).
% 2.75/1.55 thf(fact_142_insert__absorb, axiom, (! [A:$tType,A3:A,A4:(set @ A)]: (((((member @ A) @ A3) @ A4) => ((((insert @ A) @ A3) @ A4) = A4))))).
% 2.75/1.55 thf(fact_143_insert__ident, axiom, (! [A:$tType,X:A,A4:(set @ A),B5:(set @ A)]: (((~ ((((member @ A) @ X) @ A4))) => ((~ ((((member @ A) @ X) @ B5))) => (((((insert @ A) @ X) @ A4) = (((insert @ A) @ X) @ B5)) = (A4 = B5))))))).
% 2.75/1.55 thf(fact_144_Set_Oset__insert, axiom, (! [A:$tType,X:A,A4:(set @ A)]: (((((member @ A) @ X) @ A4) => (~ ((! [B7:(set @ A)]: (((A4 = (((insert @ A) @ X) @ B7)) => (((member @ A) @ X) @ B7)))))))))).
% 2.75/1.55 thf(fact_145_insertI2, axiom, (! [A:$tType,A3:A,B5:(set @ A),B4:A]: (((((member @ A) @ A3) @ B5) => (((member @ A) @ A3) @ (((insert @ A) @ B4) @ B5)))))).
% 2.75/1.55 thf(fact_146_insertI1, axiom, (! [A:$tType,A3:A,B5:(set @ A)]: ((((member @ A) @ A3) @ (((insert @ A) @ A3) @ B5))))).
% 2.75/1.55 thf(fact_147_insertE, axiom, (! [A:$tType,A3:A,B4:A,A4:(set @ A)]: (((((member @ A) @ A3) @ (((insert @ A) @ B4) @ A4)) => ((A3 != B4) => (((member @ A) @ A3) @ A4)))))).
% 2.75/1.55 thf(fact_148_Collect__conv__if, axiom, (! [A:$tType,P:(A > $o),A3:A]: ((((P @ A3) => (((collect @ A) @ (^ [X4:A]: (((X4 = A3) & (P @ X4))))) = (((insert @ A) @ A3) @ (bot_bot @ (set @ A))))) & ((~ ((P @ A3))) => (((collect @ A) @ (^ [X4:A]: (((X4 = A3) & (P @ X4))))) = (bot_bot @ (set @ A)))))))).
% 2.75/1.55 thf(fact_149_Collect__conv__if2, axiom, (! [A:$tType,P:(A > $o),A3:A]: ((((P @ A3) => (((collect @ A) @ (^ [X4:A]: (((A3 = X4) & (P @ X4))))) = (((insert @ A) @ A3) @ (bot_bot @ (set @ A))))) & ((~ ((P @ A3))) => (((collect @ A) @ (^ [X4:A]: (((A3 = X4) & (P @ X4))))) = (bot_bot @ (set @ A)))))))).
% 2.75/1.55 thf(fact_150_is__singleton__the__elem, axiom, (! [A:$tType]: (((is_singleton @ A) = (^ [A6:(set @ A)]: ((A6 = (((insert @ A) @ ((the_elem @ A) @ A6)) @ (bot_bot @ (set @ A)))))))))).
% 2.75/1.55 thf(fact_151_the__elem__eq, axiom, (! [A:$tType,X:A]: ((((the_elem @ A) @ (((insert @ A) @ X) @ (bot_bot @ (set @ A)))) = X)))).
% 2.75/1.55 thf(fact_152_setOf_Osimps_I2_J, axiom, (! [A:$tType,T1:(binary1291135688e_Tree @ A),X:A,T2:(binary1291135688e_Tree @ A)]: ((((binary1653327646_setOf @ A) @ ((((binary210054475elle_T @ A) @ T1) @ X) @ T2)) = (((sup_sup @ (set @ A)) @ (((sup_sup @ (set @ A)) @ ((binary1653327646_setOf @ A) @ T1)) @ ((binary1653327646_setOf @ A) @ T2))) @ (((insert @ A) @ X) @ (bot_bot @ (set @ A)))))))).
% 2.75/1.55 thf(fact_153_Tree_Osimps_I15_J, axiom, (! [A:$tType,X21:(binary1291135688e_Tree @ A),X22:A,X23:(binary1291135688e_Tree @ A)]: ((((binary2130109271t_Tree @ A) @ ((((binary210054475elle_T @ A) @ X21) @ X22) @ X23)) = (((sup_sup @ (set @ A)) @ (((sup_sup @ (set @ A)) @ ((binary2130109271t_Tree @ A) @ X21)) @ (((insert @ A) @ X22) @ (bot_bot @ (set @ A))))) @ ((binary2130109271t_Tree @ A) @ X23)))))).
% 2.75/1.55 thf(fact_154_UnCI, axiom, (! [A:$tType,C2:A,B5:(set @ A),A4:(set @ A)]: ((((~ ((((member @ A) @ C2) @ B5))) => (((member @ A) @ C2) @ A4)) => (((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A4) @ B5)))))).
% 2.75/1.55 thf(fact_155_Un__iff, axiom, (! [A:$tType,C2:A,A4:(set @ A),B5:(set @ A)]: (((((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A4) @ B5)) = ((((member @ A) @ C2) @ A4) | (((member @ A) @ C2) @ B5)))))).
% 2.75/1.55 thf(fact_156_Un__empty, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A)]: ((((((sup_sup @ (set @ A)) @ A4) @ B5) = (bot_bot @ (set @ A))) = ((A4 = (bot_bot @ (set @ A))) & (B5 = (bot_bot @ (set @ A)))))))).
% 2.75/1.55 thf(fact_157_Un__insert__right, axiom, (! [A:$tType,A4:(set @ A),A3:A,B5:(set @ A)]: (((((sup_sup @ (set @ A)) @ A4) @ (((insert @ A) @ A3) @ B5)) = (((insert @ A) @ A3) @ (((sup_sup @ (set @ A)) @ A4) @ B5)))))).
% 2.75/1.55 thf(fact_158_Un__insert__left, axiom, (! [A:$tType,A3:A,B5:(set @ A),C3:(set @ A)]: (((((sup_sup @ (set @ A)) @ (((insert @ A) @ A3) @ B5)) @ C3) = (((insert @ A) @ A3) @ (((sup_sup @ (set @ A)) @ B5) @ C3)))))).
% 2.75/1.55 thf(fact_159_UnE, axiom, (! [A:$tType,C2:A,A4:(set @ A),B5:(set @ A)]: (((((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A4) @ B5)) => ((~ ((((member @ A) @ C2) @ A4))) => (((member @ A) @ C2) @ B5)))))).
% 2.75/1.55 thf(fact_160_UnI1, axiom, (! [A:$tType,C2:A,A4:(set @ A),B5:(set @ A)]: (((((member @ A) @ C2) @ A4) => (((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A4) @ B5)))))).
% 2.75/1.55 thf(fact_161_UnI2, axiom, (! [A:$tType,C2:A,B5:(set @ A),A4:(set @ A)]: (((((member @ A) @ C2) @ B5) => (((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A4) @ B5)))))).
% 2.75/1.55 thf(fact_162_bex__Un, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A),P:(A > $o)]: (((? [X4:A]: (((((member @ A) @ X4) @ (((sup_sup @ (set @ A)) @ A4) @ B5)) & (P @ X4)))) = ((? [X4:A]: (((((member @ A) @ X4) @ A4) & (P @ X4)))) | (? [X4:A]: (((((member @ A) @ X4) @ B5) & (P @ X4))))))))).
% 2.75/1.55 thf(fact_163_ball__Un, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A),P:(A > $o)]: (((! [X4:A]: (((((member @ A) @ X4) @ (((sup_sup @ (set @ A)) @ A4) @ B5)) => (P @ X4)))) = ((! [X4:A]: (((((member @ A) @ X4) @ A4) => (P @ X4)))) & (! [X4:A]: (((((member @ A) @ X4) @ B5) => (P @ X4))))))))).
% 2.75/1.55 thf(fact_164_Un__assoc, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A),C3:(set @ A)]: (((((sup_sup @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A4) @ B5)) @ C3) = (((sup_sup @ (set @ A)) @ A4) @ (((sup_sup @ (set @ A)) @ B5) @ C3)))))).
% 2.75/1.55 thf(fact_165_Un__absorb, axiom, (! [A:$tType,A4:(set @ A)]: (((((sup_sup @ (set @ A)) @ A4) @ A4) = A4)))).
% 2.75/1.55 thf(fact_166_Un__commute, axiom, (! [A:$tType]: (((sup_sup @ (set @ A)) = (^ [A6:(set @ A),B6:(set @ A)]: ((((sup_sup @ (set @ A)) @ B6) @ A6))))))).
% 2.75/1.55 thf(fact_167_Un__left__absorb, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A)]: (((((sup_sup @ (set @ A)) @ A4) @ (((sup_sup @ (set @ A)) @ A4) @ B5)) = (((sup_sup @ (set @ A)) @ A4) @ B5))))).
% 2.75/1.55 thf(fact_168_Un__left__commute, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A),C3:(set @ A)]: (((((sup_sup @ (set @ A)) @ A4) @ (((sup_sup @ (set @ A)) @ B5) @ C3)) = (((sup_sup @ (set @ A)) @ B5) @ (((sup_sup @ (set @ A)) @ A4) @ C3)))))).
% 2.75/1.55 thf(fact_169_Collect__disj__eq, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: ((((collect @ A) @ (^ [X4:A]: (((P @ X4) | (Q @ X4))))) = (((sup_sup @ (set @ A)) @ ((collect @ A) @ P)) @ ((collect @ A) @ Q)))))).
% 2.75/1.55 thf(fact_170_Un__def, axiom, (! [A:$tType]: (((sup_sup @ (set @ A)) = (^ [A6:(set @ A),B6:(set @ A)]: (((collect @ A) @ (^ [X4:A]: (((((member @ A) @ X4) @ A6) | (((member @ A) @ X4) @ B6))))))))))).
% 2.75/1.55 thf(fact_171_Un__empty__left, axiom, (! [A:$tType,B5:(set @ A)]: (((((sup_sup @ (set @ A)) @ (bot_bot @ (set @ A))) @ B5) = B5)))).
% 2.75/1.55 thf(fact_172_Un__empty__right, axiom, (! [A:$tType,A4:(set @ A)]: (((((sup_sup @ (set @ A)) @ A4) @ (bot_bot @ (set @ A))) = A4)))).
% 2.75/1.55 thf(fact_173_insert__def, axiom, (! [A:$tType]: (((insert @ A) = (^ [A2:A]: (((sup_sup @ (set @ A)) @ ((collect @ A) @ (^ [X4:A]: ((X4 = A2))))))))))).
% 2.75/1.55 thf(fact_174_insert__is__Un, axiom, (! [A:$tType]: (((insert @ A) = (^ [A2:A]: (((sup_sup @ (set @ A)) @ (((insert @ A) @ A2) @ (bot_bot @ (set @ A)))))))))).
% 2.75/1.55 thf(fact_175_Un__singleton__iff, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A),X:A]: ((((((sup_sup @ (set @ A)) @ A4) @ B5) = (((insert @ A) @ X) @ (bot_bot @ (set @ A)))) = (((A4 = (bot_bot @ (set @ A))) & (B5 = (((insert @ A) @ X) @ (bot_bot @ (set @ A))))) | (((A4 = (((insert @ A) @ X) @ (bot_bot @ (set @ A)))) & (B5 = (bot_bot @ (set @ A)))) | ((A4 = (((insert @ A) @ X) @ (bot_bot @ (set @ A)))) & (B5 = (((insert @ A) @ X) @ (bot_bot @ (set @ A))))))))))).
% 2.75/1.55 thf(fact_176_singleton__Un__iff, axiom, (! [A:$tType,X:A,A4:(set @ A),B5:(set @ A)]: ((((((insert @ A) @ X) @ (bot_bot @ (set @ A))) = (((sup_sup @ (set @ A)) @ A4) @ B5)) = (((A4 = (bot_bot @ (set @ A))) & (B5 = (((insert @ A) @ X) @ (bot_bot @ (set @ A))))) | (((A4 = (((insert @ A) @ X) @ (bot_bot @ (set @ A)))) & (B5 = (bot_bot @ (set @ A)))) | ((A4 = (((insert @ A) @ X) @ (bot_bot @ (set @ A)))) & (B5 = (((insert @ A) @ X) @ (bot_bot @ (set @ A))))))))))).
% 2.75/1.55 thf(fact_177_sup__bot__left, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [X:A]: (((((sup_sup @ A) @ (bot_bot @ A)) @ X) = X))))))).
% 2.75/1.55 thf(fact_178_sup__bot__right, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [X:A]: (((((sup_sup @ A) @ X) @ (bot_bot @ A)) = X))))))).
% 2.75/1.55 thf(fact_179_bot__eq__sup__iff, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [X:A,Y:A]: ((((bot_bot @ A) = (((sup_sup @ A) @ X) @ Y)) = ((X = (bot_bot @ A)) & (Y = (bot_bot @ A)))))))))).
% 2.75/1.55 thf(fact_180_sup__bot_Oright__neutral, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [A3:A]: (((((sup_sup @ A) @ A3) @ (bot_bot @ A)) = A3))))))).
% 2.75/1.55 thf(fact_181_sup__bot_Oneutr__eq__iff, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [A3:A,B4:A]: ((((bot_bot @ A) = (((sup_sup @ A) @ A3) @ B4)) = ((A3 = (bot_bot @ A)) & (B4 = (bot_bot @ A)))))))))).
% 2.75/1.55 thf(fact_182_sup__bot_Oleft__neutral, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [A3:A]: (((((sup_sup @ A) @ (bot_bot @ A)) @ A3) = A3))))))).
% 2.75/1.55 thf(fact_183_sup__bot_Oeq__neutr__iff, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [A3:A,B4:A]: ((((((sup_sup @ A) @ A3) @ B4) = (bot_bot @ A)) = ((A3 = (bot_bot @ A)) & (B4 = (bot_bot @ A)))))))))).
% 2.75/1.55 thf(fact_184_sup__eq__bot__iff, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [X:A,Y:A]: ((((((sup_sup @ A) @ X) @ Y) = (bot_bot @ A)) = ((X = (bot_bot @ A)) & (Y = (bot_bot @ A)))))))))).
% 2.75/1.55 thf(fact_185_sup__set__def, axiom, (! [A:$tType]: (((sup_sup @ (set @ A)) = (^ [A6:(set @ A),B6:(set @ A)]: (((collect @ A) @ (((sup_sup @ (A > $o)) @ (^ [X4:A]: ((((member @ A) @ X4) @ A6)))) @ (^ [X4:A]: ((((member @ A) @ X4) @ B6))))))))))).
% 2.75/1.55 thf(fact_186_sup__Un__eq, axiom, (! [A:$tType,R3:(set @ A),S:(set @ A)]: (((((sup_sup @ (A > $o)) @ (^ [X4:A]: ((((member @ A) @ X4) @ R3)))) @ (^ [X4:A]: ((((member @ A) @ X4) @ S)))) = (^ [X4:A]: ((((member @ A) @ X4) @ (((sup_sup @ (set @ A)) @ R3) @ S)))))))).
% 2.75/1.55 thf(fact_187_sup_Ostrict__coboundedI2, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [C2:A,B4:A,A3:A]: (((((ord_less @ A) @ C2) @ B4) => (((ord_less @ A) @ C2) @ (((sup_sup @ A) @ A3) @ B4))))))))).
% 2.75/1.55 thf(fact_188_sup_Ostrict__coboundedI1, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [C2:A,A3:A,B4:A]: (((((ord_less @ A) @ C2) @ A3) => (((ord_less @ A) @ C2) @ (((sup_sup @ A) @ A3) @ B4))))))))).
% 2.75/1.55 thf(fact_189_sup_Ostrict__order__iff, axiom, (! [A:$tType]: (((semilattice_sup @ A) => ((ord_less @ A) = (^ [B2:A,A2:A]: (((A2 = (((sup_sup @ A) @ A2) @ B2)) & (A2 != B2))))))))).
% 2.75/1.55 thf(fact_190_sup_Ostrict__boundedE, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [B4:A,C2:A,A3:A]: (((((ord_less @ A) @ (((sup_sup @ A) @ B4) @ C2)) @ A3) => (~ (((((ord_less @ A) @ B4) @ A3) => (~ ((((ord_less @ A) @ C2) @ A3))))))))))))).
% 2.75/1.55 thf(fact_191_less__supI2, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [X:A,B4:A,A3:A]: (((((ord_less @ A) @ X) @ B4) => (((ord_less @ A) @ X) @ (((sup_sup @ A) @ A3) @ B4))))))))).
% 2.75/1.55 thf(fact_192_less__supI1, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [X:A,A3:A,B4:A]: (((((ord_less @ A) @ X) @ A3) => (((ord_less @ A) @ X) @ (((sup_sup @ A) @ A3) @ B4))))))))).
% 2.75/1.55 thf(fact_193_the__elem__def, axiom, (! [A:$tType]: (((the_elem @ A) = (^ [X8:(set @ A)]: (((the @ A) @ (^ [X4:A]: ((X8 = (((insert @ A) @ X4) @ (bot_bot @ (set @ A))))))))))))).
% 2.75/1.55 thf(fact_194_pred__on_Ochain__extend, axiom, (! [A:$tType,A4:(set @ A),P:(A > (A > $o)),C3:(set @ A),Z3:A]: ((((((pred_chain @ A) @ A4) @ P) @ C3) => ((((member @ A) @ Z3) @ A4) => ((! [X6:A]: (((((member @ A) @ X6) @ C3) => (((((sup_sup @ (A > (A > $o))) @ P) @ (^ [Y5:A,Z4:A]: ((Y5 = Z4)))) @ X6) @ Z3)))) => ((((pred_chain @ A) @ A4) @ P) @ (((sup_sup @ (set @ A)) @ (((insert @ A) @ Z3) @ (bot_bot @ (set @ A)))) @ C3)))))))).
% 2.75/1.55 thf(fact_195_sup__bot_Osemilattice__neutr__axioms, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (((semilattice_neutr @ A) @ (sup_sup @ A)) @ (bot_bot @ A)))))).
% 2.75/1.55 thf(fact_196_subset_Ochain__extend, axiom, (! [A:$tType,A4:(set @ (set @ A)),C3:(set @ (set @ A)),Z3:(set @ A)]: ((((((pred_chain @ (set @ A)) @ A4) @ (ord_less @ (set @ A))) @ C3) => ((((member @ (set @ A)) @ Z3) @ A4) => ((! [X6:(set @ A)]: (((((member @ (set @ A)) @ X6) @ C3) => (((((sup_sup @ ((set @ A) > ((set @ A) > $o))) @ (ord_less @ (set @ A))) @ (^ [Y5:(set @ A),Z4:(set @ A)]: ((Y5 = Z4)))) @ X6) @ Z3)))) => ((((pred_chain @ (set @ A)) @ A4) @ (ord_less @ (set @ A))) @ (((sup_sup @ (set @ (set @ A))) @ (((insert @ (set @ A)) @ Z3) @ (bot_bot @ (set @ (set @ A))))) @ C3)))))))).
% 2.75/1.55 thf(fact_197_subset_Ochain__total, axiom, (! [A:$tType,A4:(set @ (set @ A)),C3:(set @ (set @ A)),X:(set @ A),Y:(set @ A)]: ((((((pred_chain @ (set @ A)) @ A4) @ (ord_less @ (set @ A))) @ C3) => ((((member @ (set @ A)) @ X) @ C3) => ((((member @ (set @ A)) @ Y) @ C3) => ((((((sup_sup @ ((set @ A) > ((set @ A) > $o))) @ (ord_less @ (set @ A))) @ (^ [Y5:(set @ A),Z4:(set @ A)]: ((Y5 = Z4)))) @ X) @ Y) | (((((sup_sup @ ((set @ A) > ((set @ A) > $o))) @ (ord_less @ (set @ A))) @ (^ [Y5:(set @ A),Z4:(set @ A)]: ((Y5 = Z4)))) @ Y) @ X)))))))).
% 2.75/1.55 thf(fact_198_pred__on_Ochain__total, axiom, (! [A:$tType,A4:(set @ A),P:(A > (A > $o)),C3:(set @ A),X:A,Y:A]: ((((((pred_chain @ A) @ A4) @ P) @ C3) => ((((member @ A) @ X) @ C3) => ((((member @ A) @ Y) @ C3) => ((((((sup_sup @ (A > (A > $o))) @ P) @ (^ [Y5:A,Z4:A]: ((Y5 = Z4)))) @ X) @ Y) | (((((sup_sup @ (A > (A > $o))) @ P) @ (^ [Y5:A,Z4:A]: ((Y5 = Z4)))) @ Y) @ X)))))))).
% 2.75/1.55 thf(fact_199_subset_Ochain__empty, axiom, (! [A:$tType,A4:(set @ (set @ A))]: (((((pred_chain @ (set @ A)) @ A4) @ (ord_less @ (set @ A))) @ (bot_bot @ (set @ (set @ A))))))).
% 2.75/1.55 thf(fact_200_pred__on_Ochain__empty, axiom, (! [A:$tType,A4:(set @ A),P:(A > (A > $o))]: (((((pred_chain @ A) @ A4) @ P) @ (bot_bot @ (set @ A)))))).
% 2.75/1.55 thf(fact_201_chain__mono, axiom, (! [A:$tType,A4:(set @ A),P:(A > (A > $o)),Q:(A > (A > $o)),C3:(set @ A)]: (((! [X6:A,Y3:A]: (((((member @ A) @ X6) @ A4) => ((((member @ A) @ Y3) @ A4) => (((P @ X6) @ Y3) => ((Q @ X6) @ Y3)))))) => (((((pred_chain @ A) @ A4) @ P) @ C3) => ((((pred_chain @ A) @ A4) @ Q) @ C3)))))).
% 2.75/1.55 thf(fact_202_pred__on_Ochain_Ocong, axiom, (! [A:$tType]: (((pred_chain @ A) = (pred_chain @ A))))).
% 2.75/1.55 thf(fact_203_the__equality, axiom, (! [A:$tType,P:(A > $o),A3:A]: (((P @ A3) => ((! [X6:A]: (((P @ X6) => (X6 = A3)))) => (((the @ A) @ P) = A3)))))).
% 2.75/1.55 thf(fact_204_the__eq__trivial, axiom, (! [A:$tType,A3:A]: ((((the @ A) @ (^ [X4:A]: ((X4 = A3)))) = A3)))).
% 2.75/1.55 thf(fact_205_the__sym__eq__trivial, axiom, (! [A:$tType,X:A]: ((((the @ A) @ ((^ [Y5:A,Z4:A]: ((Y5 = Z4))) @ X)) = X)))).
% 2.75/1.55 thf(fact_206_the1__equality, axiom, (! [A:$tType,P:(A > $o),A3:A]: (((? [X5:A]: (((P @ X5) & (! [Y3:A]: (((P @ Y3) => (Y3 = X5))))))) => ((P @ A3) => (((the @ A) @ P) = A3)))))).
% 2.75/1.55 thf(fact_207_the1I2, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((? [X5:A]: (((P @ X5) & (! [Y3:A]: (((P @ Y3) => (Y3 = X5))))))) => ((! [X6:A]: (((P @ X6) => (Q @ X6)))) => (Q @ ((the @ A) @ P))))))).
% 2.75/1.55 thf(fact_208_If__def, axiom, (! [A:$tType]: (((if @ A) = (^ [P4:$o,X4:A,Y2:A]: (((the @ A) @ (^ [Z5:A]: (((P4 => (Z5 = X4)) & ((~ (P4)) => (Z5 = Y2)))))))))))).
% 2.75/1.55 thf(fact_209_theI2, axiom, (! [A:$tType,P:(A > $o),A3:A,Q:(A > $o)]: (((P @ A3) => ((! [X6:A]: (((P @ X6) => (X6 = A3)))) => ((! [X6:A]: (((P @ X6) => (Q @ X6)))) => (Q @ ((the @ A) @ P)))))))).
% 2.75/1.55 thf(fact_210_theI_H, axiom, (! [A:$tType,P:(A > $o)]: (((? [X5:A]: (((P @ X5) & (! [Y3:A]: (((P @ Y3) => (Y3 = X5))))))) => (P @ ((the @ A) @ P)))))).
% 2.75/1.55 thf(fact_211_theI, axiom, (! [A:$tType,P:(A > $o),A3:A]: (((P @ A3) => ((! [X6:A]: (((P @ X6) => (X6 = A3)))) => (P @ ((the @ A) @ P))))))).
% 2.75/1.55 thf(fact_212_chains__alt__def, axiom, (! [A:$tType]: (((chains @ A) = (^ [A6:(set @ (set @ A))]: (((collect @ (set @ (set @ A))) @ (((pred_chain @ (set @ A)) @ A6) @ (ord_less @ (set @ A)))))))))).
% 2.75/1.55 thf(fact_213_Pow__empty, axiom, (! [A:$tType]: ((((pow @ A) @ (bot_bot @ (set @ A))) = (((insert @ (set @ A)) @ (bot_bot @ (set @ A))) @ (bot_bot @ (set @ (set @ A)))))))).
% 2.75/1.55 thf(fact_214_Pow__singleton__iff, axiom, (! [A:$tType,X9:(set @ A),Y6:(set @ A)]: (((((pow @ A) @ X9) = (((insert @ (set @ A)) @ Y6) @ (bot_bot @ (set @ (set @ A))))) = ((X9 = (bot_bot @ (set @ A))) & (Y6 = (bot_bot @ (set @ A)))))))).
% 2.75/1.55 thf(fact_215_Pow__not__empty, axiom, (! [A:$tType,A4:(set @ A)]: ((((pow @ A) @ A4) != (bot_bot @ (set @ (set @ A))))))).
% 2.75/1.55 thf(fact_216_Pow__bottom, axiom, (! [A:$tType,B5:(set @ A)]: ((((member @ (set @ A)) @ (bot_bot @ (set @ A))) @ ((pow @ A) @ B5))))).
% 2.75/1.55 thf(fact_217_Pow__top, axiom, (! [A:$tType,A4:(set @ A)]: ((((member @ (set @ A)) @ A4) @ ((pow @ A) @ A4))))).
% 2.75/1.55 thf(fact_218_chains__extend, axiom, (! [A:$tType,C2:(set @ (set @ A)),S:(set @ (set @ A)),Z3:(set @ A)]: (((((member @ (set @ (set @ A))) @ C2) @ ((chains @ A) @ S)) => ((((member @ (set @ A)) @ Z3) @ S) => ((! [X6:(set @ A)]: (((((member @ (set @ A)) @ X6) @ C2) => (((ord_less_eq @ (set @ A)) @ X6) @ Z3)))) => (((member @ (set @ (set @ A))) @ (((sup_sup @ (set @ (set @ A))) @ (((insert @ (set @ A)) @ Z3) @ (bot_bot @ (set @ (set @ A))))) @ C2)) @ ((chains @ A) @ S)))))))).
% 2.75/1.55 thf(fact_219_Powp__Pow__eq, axiom, (! [A:$tType,A4:(set @ A)]: ((((powp @ A) @ (^ [X4:A]: ((((member @ A) @ X4) @ A4)))) = (^ [X4:(set @ A)]: ((((member @ (set @ A)) @ X4) @ ((pow @ A) @ A4)))))))).
% 2.75/1.55 thf(fact_220_order__refl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X:A]: ((((ord_less_eq @ A) @ X) @ X))))))).
% 2.75/1.55 thf(fact_221_subset__antisym, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A4) @ B5) => ((((ord_less_eq @ (set @ A)) @ B5) @ A4) => (A4 = B5)))))).
% 2.75/1.55 thf(fact_222_subsetI, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A)]: (((! [X6:A]: (((((member @ A) @ X6) @ A4) => (((member @ A) @ X6) @ B5)))) => (((ord_less_eq @ (set @ A)) @ A4) @ B5))))).
% 2.75/1.55 thf(fact_223_empty__subsetI, axiom, (! [A:$tType,A4:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ (bot_bot @ (set @ A))) @ A4)))).
% 2.75/1.55 thf(fact_224_subset__empty, axiom, (! [A:$tType,A4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A4) @ (bot_bot @ (set @ A))) = (A4 = (bot_bot @ (set @ A))))))).
% 2.75/1.55 thf(fact_225_insert__subset, axiom, (! [A:$tType,X:A,A4:(set @ A),B5:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ (((insert @ A) @ X) @ A4)) @ B5) = ((((member @ A) @ X) @ B5) & (((ord_less_eq @ (set @ A)) @ A4) @ B5)))))).
% 2.75/1.55 thf(fact_226_Un__subset__iff, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A),C3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A4) @ B5)) @ C3) = ((((ord_less_eq @ (set @ A)) @ A4) @ C3) & (((ord_less_eq @ (set @ A)) @ B5) @ C3)))))).
% 2.75/1.55 thf(fact_227_psubsetI, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A4) @ B5) => ((A4 != B5) => (((ord_less @ (set @ A)) @ A4) @ B5)))))).
% 2.75/1.55 thf(fact_228_PowI, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A4) @ B5) => (((member @ (set @ A)) @ A4) @ ((pow @ A) @ B5)))))).
% 2.75/1.55 thf(fact_229_Pow__iff, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A)]: (((((member @ (set @ A)) @ A4) @ ((pow @ A) @ B5)) = (((ord_less_eq @ (set @ A)) @ A4) @ B5))))).
% 2.75/1.55 thf(fact_230_singleton__insert__inj__eq, axiom, (! [A:$tType,B4:A,A3:A,A4:(set @ A)]: ((((((insert @ A) @ B4) @ (bot_bot @ (set @ A))) = (((insert @ A) @ A3) @ A4)) = ((A3 = B4) & (((ord_less_eq @ (set @ A)) @ A4) @ (((insert @ A) @ B4) @ (bot_bot @ (set @ A))))))))).
% 2.75/1.55 thf(fact_231_singleton__insert__inj__eq_H, axiom, (! [A:$tType,A3:A,A4:(set @ A),B4:A]: ((((((insert @ A) @ A3) @ A4) = (((insert @ A) @ B4) @ (bot_bot @ (set @ A)))) = ((A3 = B4) & (((ord_less_eq @ (set @ A)) @ A4) @ (((insert @ A) @ B4) @ (bot_bot @ (set @ A))))))))).
% 2.75/1.55 thf(fact_232_PowD, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A)]: (((((member @ (set @ A)) @ A4) @ ((pow @ A) @ B5)) => (((ord_less_eq @ (set @ A)) @ A4) @ B5))))).
% 2.75/1.55 thf(fact_233_Pow__mono, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A4) @ B5) => (((ord_less_eq @ (set @ (set @ A))) @ ((pow @ A) @ A4)) @ ((pow @ A) @ B5)))))).
% 2.75/1.55 thf(fact_234_Pow__def, axiom, (! [A:$tType]: (((pow @ A) = (^ [A6:(set @ A)]: (((collect @ (set @ A)) @ (^ [B6:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ B6) @ A6)))))))))).
% 2.75/1.55 thf(fact_235_chainsD, axiom, (! [A:$tType,C2:(set @ (set @ A)),S:(set @ (set @ A)),X:(set @ A),Y:(set @ A)]: (((((member @ (set @ (set @ A))) @ C2) @ ((chains @ A) @ S)) => ((((member @ (set @ A)) @ X) @ C2) => ((((member @ (set @ A)) @ Y) @ C2) => ((((ord_less_eq @ (set @ A)) @ X) @ Y) | (((ord_less_eq @ (set @ A)) @ Y) @ X)))))))).
% 2.75/1.55 thf(fact_236_chainsD2, axiom, (! [A:$tType,C2:(set @ (set @ A)),S:(set @ (set @ A))]: (((((member @ (set @ (set @ A))) @ C2) @ ((chains @ A) @ S)) => (((ord_less_eq @ (set @ (set @ A))) @ C2) @ S))))).
% 2.75/1.55 thf(fact_237_Zorn__Lemma2, axiom, (! [A:$tType,A4:(set @ (set @ A))]: (((! [X6:(set @ (set @ A))]: (((((member @ (set @ (set @ A))) @ X6) @ ((chains @ A) @ A4)) => (? [Xa:(set @ A)]: (((((member @ (set @ A)) @ Xa) @ A4) & (! [Xb:(set @ A)]: (((((member @ (set @ A)) @ Xb) @ X6) => (((ord_less_eq @ (set @ A)) @ Xb) @ Xa)))))))))) => (? [X6:(set @ A)]: (((((member @ (set @ A)) @ X6) @ A4) & (! [Xa:(set @ A)]: (((((member @ (set @ A)) @ Xa) @ A4) => ((((ord_less_eq @ (set @ A)) @ X6) @ Xa) => (Xa = X6)))))))))))).
% 2.75/1.55 thf(fact_238_verit__la__disequality, axiom, (! [A:$tType]: (((linorder @ A) => (! [A3:A,B4:A]: (((A3 = B4) | ((~ ((((ord_less_eq @ A) @ A3) @ B4))) | (~ ((((ord_less_eq @ A) @ B4) @ A3))))))))))).
% 2.75/1.55 thf(fact_239_dual__order_Oantisym, axiom, (! [A:$tType]: (((order @ A) => (! [B4:A,A3:A]: (((((ord_less_eq @ A) @ B4) @ A3) => ((((ord_less_eq @ A) @ A3) @ B4) => (A3 = B4))))))))).
% 2.75/1.55 thf(fact_240_dual__order_Oeq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y5:A,Z4:A]: ((Y5 = Z4))) = (^ [A2:A,B2:A]: (((((ord_less_eq @ A) @ B2) @ A2) & (((ord_less_eq @ A) @ A2) @ B2))))))))).
% 2.75/1.55 thf(fact_241_dual__order_Otrans, axiom, (! [A:$tType]: (((order @ A) => (! [B4:A,A3:A,C2:A]: (((((ord_less_eq @ A) @ B4) @ A3) => ((((ord_less_eq @ A) @ C2) @ B4) => (((ord_less_eq @ A) @ C2) @ A3))))))))).
% 2.75/1.55 thf(fact_242_linorder__wlog, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:(A > (A > $o)),A3:A,B4:A]: (((! [A5:A,B3:A]: (((((ord_less_eq @ A) @ A5) @ B3) => ((P @ A5) @ B3)))) => ((! [A5:A,B3:A]: ((((P @ B3) @ A5) => ((P @ A5) @ B3)))) => ((P @ A3) @ B4))))))))).
% 2.75/1.55 thf(fact_243_dual__order_Orefl, axiom, (! [A:$tType]: (((order @ A) => (! [A3:A]: ((((ord_less_eq @ A) @ A3) @ A3))))))).
% 2.75/1.55 thf(fact_244_order__trans, axiom, (! [A:$tType]: (((preorder @ A) => (! [X:A,Y:A,Z3:A]: (((((ord_less_eq @ A) @ X) @ Y) => ((((ord_less_eq @ A) @ Y) @ Z3) => (((ord_less_eq @ A) @ X) @ Z3))))))))).
% 2.75/1.55 thf(fact_245_order__class_Oorder_Oantisym, axiom, (! [A:$tType]: (((order @ A) => (! [A3:A,B4:A]: (((((ord_less_eq @ A) @ A3) @ B4) => ((((ord_less_eq @ A) @ B4) @ A3) => (A3 = B4))))))))).
% 2.75/1.55 thf(fact_246_ord__le__eq__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A3:A,B4:A,C2:A]: (((((ord_less_eq @ A) @ A3) @ B4) => ((B4 = C2) => (((ord_less_eq @ A) @ A3) @ C2))))))))).
% 2.75/1.55 thf(fact_247_ord__eq__le__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A3:A,B4:A,C2:A]: (((A3 = B4) => ((((ord_less_eq @ A) @ B4) @ C2) => (((ord_less_eq @ A) @ A3) @ C2))))))))).
% 2.75/1.55 thf(fact_248_order__class_Oorder_Oeq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y5:A,Z4:A]: ((Y5 = Z4))) = (^ [A2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ B2) & (((ord_less_eq @ A) @ B2) @ A2))))))))).
% 2.75/1.55 thf(fact_249_antisym__conv, axiom, (! [A:$tType]: (((order @ A) => (! [Y:A,X:A]: (((((ord_less_eq @ A) @ Y) @ X) => ((((ord_less_eq @ A) @ X) @ Y) = (X = Y))))))))).
% 2.75/1.55 thf(fact_250_le__cases3, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:A,Y:A,Z3:A]: ((((((ord_less_eq @ A) @ X) @ Y) => (~ ((((ord_less_eq @ A) @ Y) @ Z3)))) => (((((ord_less_eq @ A) @ Y) @ X) => (~ ((((ord_less_eq @ A) @ X) @ Z3)))) => (((((ord_less_eq @ A) @ X) @ Z3) => (~ ((((ord_less_eq @ A) @ Z3) @ Y)))) => (((((ord_less_eq @ A) @ Z3) @ Y) => (~ ((((ord_less_eq @ A) @ Y) @ X)))) => (((((ord_less_eq @ A) @ Y) @ Z3) => (~ ((((ord_less_eq @ A) @ Z3) @ X)))) => (~ (((((ord_less_eq @ A) @ Z3) @ X) => (~ ((((ord_less_eq @ A) @ X) @ Y))))))))))))))))).
% 2.75/1.55 thf(fact_251_order_Otrans, axiom, (! [A:$tType]: (((order @ A) => (! [A3:A,B4:A,C2:A]: (((((ord_less_eq @ A) @ A3) @ B4) => ((((ord_less_eq @ A) @ B4) @ C2) => (((ord_less_eq @ A) @ A3) @ C2))))))))).
% 2.75/1.55 thf(fact_252_le__cases, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:A,Y:A]: (((~ ((((ord_less_eq @ A) @ X) @ Y))) => (((ord_less_eq @ A) @ Y) @ X)))))))).
% 2.75/1.55 thf(fact_253_eq__refl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X:A,Y:A]: (((X = Y) => (((ord_less_eq @ A) @ X) @ Y)))))))).
% 2.75/1.55 thf(fact_254_linear, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:A,Y:A]: (((((ord_less_eq @ A) @ X) @ Y) | (((ord_less_eq @ A) @ Y) @ X)))))))).
% 2.75/1.55 thf(fact_255_antisym, axiom, (! [A:$tType]: (((order @ A) => (! [X:A,Y:A]: (((((ord_less_eq @ A) @ X) @ Y) => ((((ord_less_eq @ A) @ Y) @ X) => (X = Y))))))))).
% 2.75/1.55 thf(tcon_HOL_Obool___Lattices_Obounded__lattice, axiom, (bounded_lattice @ $o)).
% 2.75/1.55 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1, axiom, (! [A7:$tType]: ((bounded_lattice @ (set @ A7))))).
% 2.75/1.55 thf(tcon_fun___Lattices_Obounded__lattice_2, axiom, (! [A7:$tType,A8:$tType]: (((bounded_lattice @ A8) => (bounded_lattice @ (A7 > A8)))))).
% 2.75/1.55 thf(tcon_fun___Lattices_Obounded__semilattice__sup__bot, axiom, (! [A7:$tType,A8:$tType]: (((bounded_lattice @ A8) => (bounde1808546759up_bot @ (A7 > A8)))))).
% 2.75/1.55 thf(tcon_fun___Lattices_Osemilattice__sup, axiom, (! [A7:$tType,A8:$tType]: (((semilattice_sup @ A8) => (semilattice_sup @ (A7 > A8)))))).
% 2.75/1.55 thf(tcon_fun___Orderings_Oorder__bot, axiom, (! [A7:$tType,A8:$tType]: (((order_bot @ A8) => (order_bot @ (A7 > A8)))))).
% 2.75/1.55 thf(tcon_fun___Orderings_Opreorder, axiom, (! [A7:$tType,A8:$tType]: (((preorder @ A8) => (preorder @ (A7 > A8)))))).
% 2.75/1.55 thf(tcon_fun___Orderings_Oorder, axiom, (! [A7:$tType,A8:$tType]: (((order @ A8) => (order @ (A7 > A8)))))).
% 2.75/1.55 thf(tcon_fun___Orderings_Oord, axiom, (! [A7:$tType,A8:$tType]: (((ord @ A8) => (ord @ (A7 > A8)))))).
% 2.75/1.55 thf(tcon_fun___Orderings_Obot, axiom, (! [A7:$tType,A8:$tType]: (((bot @ A8) => (bot @ (A7 > A8)))))).
% 2.75/1.55 thf(tcon_Int_Oint___Lattices_Osemilattice__sup_3, axiom, (semilattice_sup @ int)).
% 2.75/1.55 thf(tcon_Int_Oint___Rings_Olinordered__idom, axiom, (linordered_idom @ int)).
% 2.75/1.55 thf(tcon_Int_Oint___Orderings_Opreorder_4, axiom, (preorder @ int)).
% 2.75/1.55 thf(tcon_Int_Oint___Orderings_Olinorder, axiom, (linorder @ int)).
% 2.75/1.55 thf(tcon_Int_Oint___Orderings_Ono__top, axiom, (no_top @ int)).
% 2.75/1.55 thf(tcon_Int_Oint___Orderings_Ono__bot, axiom, (no_bot @ int)).
% 2.75/1.55 thf(tcon_Int_Oint___Orderings_Oorder_5, axiom, (order @ int)).
% 2.75/1.55 thf(tcon_Int_Oint___Orderings_Oord_6, axiom, (ord @ int)).
% 2.75/1.55 thf(tcon_Set_Oset___Lattices_Obounded__semilattice__sup__bot_7, axiom, (! [A7:$tType]: ((bounde1808546759up_bot @ (set @ A7))))).
% 2.75/1.55 thf(tcon_Set_Oset___Lattices_Osemilattice__sup_8, axiom, (! [A7:$tType]: ((semilattice_sup @ (set @ A7))))).
% 2.75/1.55 thf(tcon_Set_Oset___Orderings_Oorder__bot_9, axiom, (! [A7:$tType]: ((order_bot @ (set @ A7))))).
% 2.75/1.55 thf(tcon_Set_Oset___Orderings_Opreorder_10, axiom, (! [A7:$tType]: ((preorder @ (set @ A7))))).
% 2.75/1.55 thf(tcon_Set_Oset___Orderings_Oorder_11, axiom, (! [A7:$tType]: ((order @ (set @ A7))))).
% 2.75/1.55 thf(tcon_Set_Oset___Orderings_Oord_12, axiom, (! [A7:$tType]: ((ord @ (set @ A7))))).
% 2.75/1.55 thf(tcon_Set_Oset___Orderings_Obot_13, axiom, (! [A7:$tType]: ((bot @ (set @ A7))))).
% 2.75/1.55 thf(tcon_HOL_Obool___Lattices_Obounded__semilattice__sup__bot_14, axiom, (bounde1808546759up_bot @ $o)).
% 2.75/1.55 thf(tcon_HOL_Obool___Lattices_Osemilattice__sup_15, axiom, (semilattice_sup @ $o)).
% 2.75/1.55 thf(tcon_HOL_Obool___Orderings_Oorder__bot_16, axiom, (order_bot @ $o)).
% 2.75/1.55 thf(tcon_HOL_Obool___Orderings_Opreorder_17, axiom, (preorder @ $o)).
% 2.75/1.55 thf(tcon_HOL_Obool___Orderings_Olinorder_18, axiom, (linorder @ $o)).
% 2.75/1.55 thf(tcon_HOL_Obool___Orderings_Oorder_19, axiom, (order @ $o)).
% 2.75/1.55 thf(tcon_HOL_Obool___Orderings_Oord_20, axiom, (ord @ $o)).
% 2.75/1.55 thf(tcon_HOL_Obool___Orderings_Obot_21, axiom, (bot @ $o)).
% 2.75/1.55 thf(help_If_3_1_T, axiom, (! [P:$o]: (((P = $true) | (P = $false))))).
% 2.75/1.55 thf(help_If_2_1_T, axiom, (! [A:$tType,X:A,Y:A]: ((((((if @ A) @ $false) @ X) @ Y) = Y)))).
% 2.75/1.55 thf(help_If_1_1_T, axiom, (! [A:$tType,X:A,Y:A]: ((((((if @ A) @ $true) @ X) @ Y) = X)))).
% 2.75/1.55 thf(conj_0, conjecture, (a2 = b)).
% 2.75/1.55 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.YQ97kakufk/DTF2DTF26539.p
% 2.75/1.55 ------------------------
% 2.75/1.57 ---- Cleaned THF ---
% 2.75/1.57 thf(ty_t_BinaryTree__Mirabelle__pchhvghoao_OTree,type,
% 2.75/1.57 binary1291135688e_Tree: $tType > $tType ).
% 2.75/1.57
% 2.75/1.57 thf(ty_t_Set_Oset,type,
% 2.75/1.57 set: $tType > $tType ).
% 2.75/1.57
% 2.75/1.57 thf(ty_t_Int_Oint,type,
% 2.75/1.57 int: $tType ).
% 2.75/1.57
% 2.75/1.57 thf(ty_tf_a,type,
% 2.75/1.57 a: $tType ).
% 2.75/1.57
% 2.75/1.57 thf(sy_cl_Lattices_Obounded__lattice,type,
% 2.75/1.57 bounded_lattice:
% 2.75/1.57 !>[A: $tType] : $o ).
% 2.75/1.57
% 2.75/1.57 thf(sy_cl_HOL_Otype,type,
% 2.75/1.57 type:
% 2.75/1.57 !>[A: $tType] : $o ).
% 2.75/1.57
% 2.75/1.57 thf(sy_cl_Orderings_Obot,type,
% 2.75/1.57 bot:
% 2.75/1.57 !>[A: $tType] : $o ).
% 2.75/1.57
% 2.75/1.57 thf(sy_cl_Orderings_Oord,type,
% 2.75/1.57 ord:
% 2.75/1.57 !>[A: $tType] : $o ).
% 2.75/1.57
% 2.75/1.57 thf(sy_cl_Orderings_Oorder,type,
% 2.75/1.57 order:
% 2.75/1.57 !>[A: $tType] : $o ).
% 2.75/1.57
% 2.75/1.57 thf(sy_cl_Orderings_Ono__bot,type,
% 2.75/1.57 no_bot:
% 2.75/1.57 !>[A: $tType] : $o ).
% 2.75/1.57
% 2.75/1.57 thf(sy_cl_Orderings_Ono__top,type,
% 2.75/1.57 no_top:
% 2.75/1.57 !>[A: $tType] : $o ).
% 2.75/1.57
% 2.75/1.57 thf(sy_cl_Orderings_Olinorder,type,
% 2.75/1.57 linorder:
% 2.75/1.57 !>[A: $tType] : $o ).
% 2.75/1.57
% 2.75/1.57 thf(sy_cl_Orderings_Opreorder,type,
% 2.75/1.57 preorder:
% 2.75/1.57 !>[A: $tType] : $o ).
% 2.75/1.57
% 2.75/1.57 thf(sy_cl_Orderings_Oorder__bot,type,
% 2.75/1.57 order_bot:
% 2.75/1.57 !>[A: $tType] : $o ).
% 2.75/1.57
% 2.75/1.57 thf(sy_cl_Orderings_Owellorder,type,
% 2.75/1.57 wellorder:
% 2.75/1.57 !>[A: $tType] : $o ).
% 2.75/1.57
% 2.75/1.57 thf(sy_cl_Orderings_Odense__order,type,
% 2.75/1.57 dense_order:
% 2.75/1.57 !>[A: $tType] : $o ).
% 2.75/1.57
% 2.75/1.57 thf(sy_cl_Rings_Olinordered__idom,type,
% 2.75/1.57 linordered_idom:
% 2.75/1.57 !>[A: $tType] : $o ).
% 2.75/1.57
% 2.75/1.57 thf(sy_cl_Fields_Olinordered__field,type,
% 2.75/1.57 linordered_field:
% 2.75/1.57 !>[A: $tType] : $o ).
% 2.75/1.57
% 2.75/1.57 thf(sy_cl_Lattices_Osemilattice__sup,type,
% 2.75/1.57 semilattice_sup:
% 2.75/1.57 !>[A: $tType] : $o ).
% 2.75/1.57
% 2.75/1.57 thf(sy_cl_Lattices_Obounded__semilattice__sup__bot,type,
% 2.75/1.57 bounde1808546759up_bot:
% 2.75/1.57 !>[A: $tType] : $o ).
% 2.75/1.57
% 2.75/1.57 thf(sy_cl_Conditionally__Complete__Lattices_Olinear__continuum,type,
% 2.75/1.57 condit1656338222tinuum:
% 2.75/1.57 !>[A: $tType] : $o ).
% 2.75/1.57
% 2.75/1.57 thf(sy_c_BinaryTree__Mirabelle__pchhvghoao_OTree_OT,type,
% 2.75/1.57 binary210054475elle_T:
% 2.75/1.57 !>[A: $tType] : ( ( binary1291135688e_Tree @ A ) > A > ( binary1291135688e_Tree @ A ) > ( binary1291135688e_Tree @ A ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(sy_c_BinaryTree__Mirabelle__pchhvghoao_OTree_OTip,type,
% 2.75/1.57 binary1746293266le_Tip:
% 2.75/1.57 !>[A: $tType] : ( binary1291135688e_Tree @ A ) ).
% 2.75/1.57
% 2.75/1.57 thf(sy_c_BinaryTree__Mirabelle__pchhvghoao_OTree_Ocase__Tree,type,
% 2.75/1.57 binary536355927e_Tree:
% 2.75/1.57 !>[B: $tType,A: $tType] : ( B > ( ( binary1291135688e_Tree @ A ) > A > ( binary1291135688e_Tree @ A ) > B ) > ( binary1291135688e_Tree @ A ) > B ) ).
% 2.75/1.57
% 2.75/1.57 thf(sy_c_BinaryTree__Mirabelle__pchhvghoao_OTree_Orec__Tree,type,
% 2.75/1.57 binary1929596613c_Tree:
% 2.75/1.57 !>[C: $tType,A: $tType] : ( C > ( ( binary1291135688e_Tree @ A ) > A > ( binary1291135688e_Tree @ A ) > C > C > C ) > ( binary1291135688e_Tree @ A ) > C ) ).
% 2.75/1.57
% 2.75/1.57 thf(sy_c_BinaryTree__Mirabelle__pchhvghoao_OTree_Oset__Tree,type,
% 2.75/1.57 binary2130109271t_Tree:
% 2.75/1.57 !>[A: $tType] : ( ( binary1291135688e_Tree @ A ) > ( set @ A ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(sy_c_BinaryTree__Mirabelle__pchhvghoao_Oeqs,type,
% 2.75/1.57 binary64540844le_eqs:
% 2.75/1.57 !>[A: $tType] : ( ( A > int ) > A > ( set @ A ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(sy_c_BinaryTree__Mirabelle__pchhvghoao_OsetOf,type,
% 2.75/1.57 binary1653327646_setOf:
% 2.75/1.57 !>[A: $tType] : ( ( binary1291135688e_Tree @ A ) > ( set @ A ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(sy_c_BinaryTree__Mirabelle__pchhvghoao_OsortedTree,type,
% 2.75/1.57 binary1610619414edTree:
% 2.75/1.57 !>[A: $tType] : ( ( A > int ) > ( binary1291135688e_Tree @ A ) > $o ) ).
% 2.75/1.57
% 2.75/1.57 thf(sy_c_BinaryTree__Mirabelle__pchhvghoao_Osorted__distinct__pred,type,
% 2.75/1.57 binary231205461t_pred:
% 2.75/1.57 !>[A: $tType] : ( ( A > int ) > A > A > ( binary1291135688e_Tree @ A ) > $o ) ).
% 2.75/1.57
% 2.75/1.57 thf(sy_c_HOL_OThe,type,
% 2.75/1.57 the:
% 2.75/1.57 !>[A: $tType] : ( ( A > $o ) > A ) ).
% 2.75/1.57
% 2.75/1.57 thf(sy_c_If,type,
% 2.75/1.57 if:
% 2.75/1.57 !>[A: $tType] : ( $o > A > A > A ) ).
% 2.75/1.57
% 2.75/1.57 thf(sy_c_Lattices_Osemilattice__neutr,type,
% 2.75/1.57 semilattice_neutr:
% 2.75/1.57 !>[A: $tType] : ( ( A > A > A ) > A > $o ) ).
% 2.75/1.57
% 2.75/1.57 thf(sy_c_Lattices_Osup__class_Osup,type,
% 2.75/1.57 sup_sup:
% 2.75/1.57 !>[A: $tType] : ( A > A > A ) ).
% 2.75/1.57
% 2.75/1.57 thf(sy_c_Orderings_Obot__class_Obot,type,
% 2.75/1.57 bot_bot:
% 2.75/1.57 !>[A: $tType] : A ).
% 2.75/1.57
% 2.75/1.57 thf(sy_c_Orderings_Oord__class_Oless,type,
% 2.75/1.57 ord_less:
% 2.75/1.57 !>[A: $tType] : ( A > A > $o ) ).
% 2.75/1.57
% 2.75/1.57 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 2.75/1.57 ord_less_eq:
% 2.75/1.57 !>[A: $tType] : ( A > A > $o ) ).
% 2.75/1.57
% 2.75/1.57 thf(sy_c_Relation_OPowp,type,
% 2.75/1.57 powp:
% 2.75/1.57 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) > $o ) ).
% 2.75/1.57
% 2.75/1.57 thf(sy_c_Relation_Oinv__imagep,type,
% 2.75/1.57 inv_imagep:
% 2.75/1.57 !>[B: $tType,A: $tType] : ( ( B > B > $o ) > ( A > B ) > A > A > $o ) ).
% 2.75/1.57
% 2.75/1.57 thf(sy_c_Set_OCollect,type,
% 2.75/1.57 collect:
% 2.75/1.57 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(sy_c_Set_OPow,type,
% 2.75/1.57 pow:
% 2.75/1.57 !>[A: $tType] : ( ( set @ A ) > ( set @ ( set @ A ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(sy_c_Set_Oinsert,type,
% 2.75/1.57 insert:
% 2.75/1.57 !>[A: $tType] : ( A > ( set @ A ) > ( set @ A ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(sy_c_Set_Ois__empty,type,
% 2.75/1.57 is_empty:
% 2.75/1.57 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 2.75/1.57
% 2.75/1.57 thf(sy_c_Set_Ois__singleton,type,
% 2.75/1.57 is_singleton:
% 2.75/1.57 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 2.75/1.57
% 2.75/1.57 thf(sy_c_Set_Othe__elem,type,
% 2.75/1.57 the_elem:
% 2.75/1.57 !>[A: $tType] : ( ( set @ A ) > A ) ).
% 2.75/1.57
% 2.75/1.57 thf(sy_c_Zorn_Ochains,type,
% 2.75/1.57 chains:
% 2.75/1.57 !>[A: $tType] : ( ( set @ ( set @ A ) ) > ( set @ ( set @ ( set @ A ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(sy_c_Zorn_Opred__on_Ochain,type,
% 2.75/1.57 pred_chain:
% 2.75/1.57 !>[A: $tType] : ( ( set @ A ) > ( A > A > $o ) > ( set @ A ) > $o ) ).
% 2.75/1.57
% 2.75/1.57 thf(sy_c_member,type,
% 2.75/1.57 member:
% 2.75/1.57 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 2.75/1.57
% 2.75/1.57 thf(sy_v_a,type,
% 2.75/1.57 a2: a ).
% 2.75/1.57
% 2.75/1.57 thf(sy_v_b,type,
% 2.75/1.57 b: a ).
% 2.75/1.57
% 2.75/1.57 thf(sy_v_h,type,
% 2.75/1.57 h: a > int ).
% 2.75/1.57
% 2.75/1.57 thf(sy_v_t1____,type,
% 2.75/1.57 t1: binary1291135688e_Tree @ a ).
% 2.75/1.57
% 2.75/1.57 thf(sy_v_t2____,type,
% 2.75/1.57 t2: binary1291135688e_Tree @ a ).
% 2.75/1.57
% 2.75/1.57 thf(sy_v_x____,type,
% 2.75/1.57 x: a ).
% 2.75/1.57
% 2.75/1.57 thf(fact_0_hahb,axiom,
% 2.75/1.57 ( ( h @ a2 )
% 2.75/1.57 = ( h @ b ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_1__092_060open_062h_Ab_A_060_Ah_Aa_092_060close_062,axiom,
% 2.75/1.57 ord_less @ int @ ( h @ b ) @ ( h @ a2 ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_2__092_060open_062a_A_061_Ax_A_092_060Longrightarrow_062_Aa_A_061_Ab_092_060close_062,axiom,
% 2.75/1.57 ( ( a2 = x )
% 2.75/1.57 => ( a2 = b ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_3_adef1,axiom,
% 2.75/1.57 member @ a @ a2 @ ( binary1653327646_setOf @ a @ t2 ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_4_bdef1,axiom,
% 2.75/1.57 member @ a @ b @ ( binary1653327646_setOf @ a @ t1 ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_5__092_060open_062a_A_092_060in_062_AsetOf_At1_A_092_060Longrightarrow_062_Aa_A_061_Ab_092_060close_062,axiom,
% 2.75/1.57 ( ( member @ a @ a2 @ ( binary1653327646_setOf @ a @ t1 ) )
% 2.75/1.57 => ( a2 = b ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_6_o1,axiom,
% 2.75/1.57 ord_less @ int @ ( h @ b ) @ ( h @ x ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_7_o2,axiom,
% 2.75/1.57 ord_less @ int @ ( h @ x ) @ ( h @ a2 ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_8_h2,axiom,
% 2.75/1.57 binary231205461t_pred @ a @ h @ a2 @ b @ t2 ).
% 2.75/1.57
% 2.75/1.57 thf(fact_9_h1,axiom,
% 2.75/1.57 binary231205461t_pred @ a @ h @ a2 @ b @ t1 ).
% 2.75/1.57
% 2.75/1.57 thf(fact_10__092_060open_062sorted__distinct__pred_Ah_Aa_Ab_ATip_092_060close_062,axiom,
% 2.75/1.57 binary231205461t_pred @ a @ h @ a2 @ b @ ( binary1746293266le_Tip @ a ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_11_calculation,axiom,
% 2.75/1.57 ( ( member @ a @ b @ ( binary1653327646_setOf @ a @ t1 ) )
% 2.75/1.57 | ( b = x )
% 2.75/1.57 | ( member @ a @ b @ ( binary1653327646_setOf @ a @ t2 ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_12__092_060open_062a_A_092_060in_062_AsetOf_At1_A_092_060or_062_Aa_A_061_Ax_A_092_060or_062_Aa_A_092_060in_062_AsetOf_At2_092_060close_062,axiom,
% 2.75/1.57 ( ( member @ a @ a2 @ ( binary1653327646_setOf @ a @ t1 ) )
% 2.75/1.57 | ( a2 = x )
% 2.75/1.57 | ( member @ a @ a2 @ ( binary1653327646_setOf @ a @ t2 ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_13_bdef,axiom,
% 2.75/1.57 member @ a @ b @ ( binary1653327646_setOf @ a @ ( binary210054475elle_T @ a @ t1 @ x @ t2 ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_14_Tree_Oinject,axiom,
% 2.75/1.57 ! [A: $tType,X21: binary1291135688e_Tree @ A,X22: A,X23: binary1291135688e_Tree @ A,Y21: binary1291135688e_Tree @ A,Y22: A,Y23: binary1291135688e_Tree @ A] :
% 2.75/1.57 ( ( ( binary210054475elle_T @ A @ X21 @ X22 @ X23 )
% 2.75/1.57 = ( binary210054475elle_T @ A @ Y21 @ Y22 @ Y23 ) )
% 2.75/1.57 = ( ( X21 = Y21 )
% 2.75/1.57 & ( X22 = Y22 )
% 2.75/1.57 & ( X23 = Y23 ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_15_adef,axiom,
% 2.75/1.57 member @ a @ a2 @ ( binary1653327646_setOf @ a @ ( binary210054475elle_T @ a @ t1 @ x @ t2 ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_16_s,axiom,
% 2.75/1.57 binary1610619414edTree @ a @ h @ ( binary210054475elle_T @ a @ t1 @ x @ t2 ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_17_Tree_Odistinct_I1_J,axiom,
% 2.75/1.57 ! [A: $tType,X21: binary1291135688e_Tree @ A,X22: A,X23: binary1291135688e_Tree @ A] :
% 2.75/1.57 ( ( binary1746293266le_Tip @ A )
% 2.75/1.57 != ( binary210054475elle_T @ A @ X21 @ X22 @ X23 ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_18_Tree_Oinduct,axiom,
% 2.75/1.57 ! [A: $tType,P: ( binary1291135688e_Tree @ A ) > $o,Tree: binary1291135688e_Tree @ A] :
% 2.75/1.57 ( ( P @ ( binary1746293266le_Tip @ A ) )
% 2.75/1.57 => ( ! [X1: binary1291135688e_Tree @ A,X2: A,X3: binary1291135688e_Tree @ A] :
% 2.75/1.57 ( ( P @ X1 )
% 2.75/1.57 => ( ( P @ X3 )
% 2.75/1.57 => ( P @ ( binary210054475elle_T @ A @ X1 @ X2 @ X3 ) ) ) )
% 2.75/1.57 => ( P @ Tree ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_19_Tree_Oexhaust,axiom,
% 2.75/1.57 ! [A: $tType,Y: binary1291135688e_Tree @ A] :
% 2.75/1.57 ( ( Y
% 2.75/1.57 != ( binary1746293266le_Tip @ A ) )
% 2.75/1.57 => ~ ! [X212: binary1291135688e_Tree @ A,X222: A,X232: binary1291135688e_Tree @ A] :
% 2.75/1.57 ( Y
% 2.75/1.57 != ( binary210054475elle_T @ A @ X212 @ X222 @ X232 ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_20_s2,axiom,
% 2.75/1.57 binary1610619414edTree @ a @ h @ t2 ).
% 2.75/1.57
% 2.75/1.57 thf(fact_21_s1,axiom,
% 2.75/1.57 binary1610619414edTree @ a @ h @ t1 ).
% 2.75/1.57
% 2.75/1.57 thf(fact_22_sortedTree_Osimps_I2_J,axiom,
% 2.75/1.57 ! [A: $tType,H: A > int,T1: binary1291135688e_Tree @ A,X: A,T2: binary1291135688e_Tree @ A] :
% 2.75/1.57 ( ( binary1610619414edTree @ A @ H @ ( binary210054475elle_T @ A @ T1 @ X @ T2 ) )
% 2.75/1.57 = ( ( binary1610619414edTree @ A @ H @ T1 )
% 2.75/1.57 & ! [X4: A] :
% 2.75/1.57 ( ( member @ A @ X4 @ ( binary1653327646_setOf @ A @ T1 ) )
% 2.75/1.57 => ( ord_less @ int @ ( H @ X4 ) @ ( H @ X ) ) )
% 2.75/1.57 & ! [X4: A] :
% 2.75/1.57 ( ( member @ A @ X4 @ ( binary1653327646_setOf @ A @ T2 ) )
% 2.75/1.57 => ( ord_less @ int @ ( H @ X ) @ ( H @ X4 ) ) )
% 2.75/1.57 & ( binary1610619414edTree @ A @ H @ T2 ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_23_sorted__distinct__pred__def,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( binary231205461t_pred @ A )
% 2.75/1.57 = ( ^ [H2: A > int,A2: A,B2: A,T: binary1291135688e_Tree @ A] :
% 2.75/1.57 ( ( ( binary1610619414edTree @ A @ H2 @ T )
% 2.75/1.57 & ( member @ A @ A2 @ ( binary1653327646_setOf @ A @ T ) )
% 2.75/1.57 & ( member @ A @ B2 @ ( binary1653327646_setOf @ A @ T ) )
% 2.75/1.57 & ( ( H2 @ A2 )
% 2.75/1.57 = ( H2 @ B2 ) ) )
% 2.75/1.57 => ( A2 = B2 ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_24_eqs__def,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( binary64540844le_eqs @ A )
% 2.75/1.57 = ( ^ [H2: A > int,X4: A] :
% 2.75/1.57 ( collect @ A
% 2.75/1.57 @ ^ [Y2: A] :
% 2.75/1.57 ( ( H2 @ Y2 )
% 2.75/1.57 = ( H2 @ X4 ) ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_25_minf_I11_J,axiom,
% 2.75/1.57 ! [C: $tType,D: $tType] :
% 2.75/1.57 ( ( ord @ C )
% 2.75/1.57 => ! [F: D] :
% 2.75/1.57 ? [Z: C] :
% 2.75/1.57 ! [X5: C] :
% 2.75/1.57 ( ( ord_less @ C @ X5 @ Z )
% 2.75/1.57 => ( F = F ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_26_minf_I7_J,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( linorder @ A )
% 2.75/1.57 => ! [T3: A] :
% 2.75/1.57 ? [Z: A] :
% 2.75/1.57 ! [X5: A] :
% 2.75/1.57 ( ( ord_less @ A @ X5 @ Z )
% 2.75/1.57 => ~ ( ord_less @ A @ T3 @ X5 ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_27_minf_I5_J,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( linorder @ A )
% 2.75/1.57 => ! [T3: A] :
% 2.75/1.57 ? [Z: A] :
% 2.75/1.57 ! [X5: A] :
% 2.75/1.57 ( ( ord_less @ A @ X5 @ Z )
% 2.75/1.57 => ( ord_less @ A @ X5 @ T3 ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_28_minf_I4_J,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( linorder @ A )
% 2.75/1.57 => ! [T3: A] :
% 2.75/1.57 ? [Z: A] :
% 2.75/1.57 ! [X5: A] :
% 2.75/1.57 ( ( ord_less @ A @ X5 @ Z )
% 2.75/1.57 => ( X5 != T3 ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_29_minf_I3_J,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( linorder @ A )
% 2.75/1.57 => ! [T3: A] :
% 2.75/1.57 ? [Z: A] :
% 2.75/1.57 ! [X5: A] :
% 2.75/1.57 ( ( ord_less @ A @ X5 @ Z )
% 2.75/1.57 => ( X5 != T3 ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_30_minf_I2_J,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( linorder @ A )
% 2.75/1.57 => ! [P: A > $o,P2: A > $o,Q: A > $o,Q2: A > $o] :
% 2.75/1.57 ( ? [Z2: A] :
% 2.75/1.57 ! [X6: A] :
% 2.75/1.57 ( ( ord_less @ A @ X6 @ Z2 )
% 2.75/1.57 => ( ( P @ X6 )
% 2.75/1.57 = ( P2 @ X6 ) ) )
% 2.75/1.57 => ( ? [Z2: A] :
% 2.75/1.57 ! [X6: A] :
% 2.75/1.57 ( ( ord_less @ A @ X6 @ Z2 )
% 2.75/1.57 => ( ( Q @ X6 )
% 2.75/1.57 = ( Q2 @ X6 ) ) )
% 2.75/1.57 => ? [Z: A] :
% 2.75/1.57 ! [X5: A] :
% 2.75/1.57 ( ( ord_less @ A @ X5 @ Z )
% 2.75/1.57 => ( ( ( P @ X5 )
% 2.75/1.57 | ( Q @ X5 ) )
% 2.75/1.57 = ( ( P2 @ X5 )
% 2.75/1.57 | ( Q2 @ X5 ) ) ) ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_31_sortLemmaR,axiom,
% 2.75/1.57 ! [A: $tType,H: A > int,T1: binary1291135688e_Tree @ A,X: A,T2: binary1291135688e_Tree @ A] :
% 2.75/1.57 ( ( binary1610619414edTree @ A @ H @ ( binary210054475elle_T @ A @ T1 @ X @ T2 ) )
% 2.75/1.57 => ( binary1610619414edTree @ A @ H @ T2 ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_32_sortLemmaL,axiom,
% 2.75/1.57 ! [A: $tType,H: A > int,T1: binary1291135688e_Tree @ A,X: A,T2: binary1291135688e_Tree @ A] :
% 2.75/1.57 ( ( binary1610619414edTree @ A @ H @ ( binary210054475elle_T @ A @ T1 @ X @ T2 ) )
% 2.75/1.57 => ( binary1610619414edTree @ A @ H @ T1 ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_33_sortedTree_Osimps_I1_J,axiom,
% 2.75/1.57 ! [A: $tType,H: A > int] : ( binary1610619414edTree @ A @ H @ ( binary1746293266le_Tip @ A ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_34_pinf_I1_J,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( linorder @ A )
% 2.75/1.57 => ! [P: A > $o,P2: A > $o,Q: A > $o,Q2: A > $o] :
% 2.75/1.57 ( ? [Z2: A] :
% 2.75/1.57 ! [X6: A] :
% 2.75/1.57 ( ( ord_less @ A @ Z2 @ X6 )
% 2.75/1.57 => ( ( P @ X6 )
% 2.75/1.57 = ( P2 @ X6 ) ) )
% 2.75/1.57 => ( ? [Z2: A] :
% 2.75/1.57 ! [X6: A] :
% 2.75/1.57 ( ( ord_less @ A @ Z2 @ X6 )
% 2.75/1.57 => ( ( Q @ X6 )
% 2.75/1.57 = ( Q2 @ X6 ) ) )
% 2.75/1.57 => ? [Z: A] :
% 2.75/1.57 ! [X5: A] :
% 2.75/1.57 ( ( ord_less @ A @ Z @ X5 )
% 2.75/1.57 => ( ( ( P @ X5 )
% 2.75/1.57 & ( Q @ X5 ) )
% 2.75/1.57 = ( ( P2 @ X5 )
% 2.75/1.57 & ( Q2 @ X5 ) ) ) ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_35_pinf_I2_J,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( linorder @ A )
% 2.75/1.57 => ! [P: A > $o,P2: A > $o,Q: A > $o,Q2: A > $o] :
% 2.75/1.57 ( ? [Z2: A] :
% 2.75/1.57 ! [X6: A] :
% 2.75/1.57 ( ( ord_less @ A @ Z2 @ X6 )
% 2.75/1.57 => ( ( P @ X6 )
% 2.75/1.57 = ( P2 @ X6 ) ) )
% 2.75/1.57 => ( ? [Z2: A] :
% 2.75/1.57 ! [X6: A] :
% 2.75/1.57 ( ( ord_less @ A @ Z2 @ X6 )
% 2.75/1.57 => ( ( Q @ X6 )
% 2.75/1.57 = ( Q2 @ X6 ) ) )
% 2.75/1.57 => ? [Z: A] :
% 2.75/1.57 ! [X5: A] :
% 2.75/1.57 ( ( ord_less @ A @ Z @ X5 )
% 2.75/1.57 => ( ( ( P @ X5 )
% 2.75/1.57 | ( Q @ X5 ) )
% 2.75/1.57 = ( ( P2 @ X5 )
% 2.75/1.57 | ( Q2 @ X5 ) ) ) ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_36_pinf_I3_J,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( linorder @ A )
% 2.75/1.57 => ! [T3: A] :
% 2.75/1.57 ? [Z: A] :
% 2.75/1.57 ! [X5: A] :
% 2.75/1.57 ( ( ord_less @ A @ Z @ X5 )
% 2.75/1.57 => ( X5 != T3 ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_37_pinf_I4_J,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( linorder @ A )
% 2.75/1.57 => ! [T3: A] :
% 2.75/1.57 ? [Z: A] :
% 2.75/1.57 ! [X5: A] :
% 2.75/1.57 ( ( ord_less @ A @ Z @ X5 )
% 2.75/1.57 => ( X5 != T3 ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_38_pinf_I5_J,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( linorder @ A )
% 2.75/1.57 => ! [T3: A] :
% 2.75/1.57 ? [Z: A] :
% 2.75/1.57 ! [X5: A] :
% 2.75/1.57 ( ( ord_less @ A @ Z @ X5 )
% 2.75/1.57 => ~ ( ord_less @ A @ X5 @ T3 ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_39_pinf_I7_J,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( linorder @ A )
% 2.75/1.57 => ! [T3: A] :
% 2.75/1.57 ? [Z: A] :
% 2.75/1.57 ! [X5: A] :
% 2.75/1.57 ( ( ord_less @ A @ Z @ X5 )
% 2.75/1.57 => ( ord_less @ A @ T3 @ X5 ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_40_pinf_I11_J,axiom,
% 2.75/1.57 ! [C: $tType,D: $tType] :
% 2.75/1.57 ( ( ord @ C )
% 2.75/1.57 => ! [F: D] :
% 2.75/1.57 ? [Z: C] :
% 2.75/1.57 ! [X5: C] :
% 2.75/1.57 ( ( ord_less @ C @ Z @ X5 )
% 2.75/1.57 => ( F = F ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_41_minf_I1_J,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( linorder @ A )
% 2.75/1.57 => ! [P: A > $o,P2: A > $o,Q: A > $o,Q2: A > $o] :
% 2.75/1.57 ( ? [Z2: A] :
% 2.75/1.57 ! [X6: A] :
% 2.75/1.57 ( ( ord_less @ A @ X6 @ Z2 )
% 2.75/1.57 => ( ( P @ X6 )
% 2.75/1.57 = ( P2 @ X6 ) ) )
% 2.75/1.57 => ( ? [Z2: A] :
% 2.75/1.57 ! [X6: A] :
% 2.75/1.57 ( ( ord_less @ A @ X6 @ Z2 )
% 2.75/1.57 => ( ( Q @ X6 )
% 2.75/1.57 = ( Q2 @ X6 ) ) )
% 2.75/1.57 => ? [Z: A] :
% 2.75/1.57 ! [X5: A] :
% 2.75/1.57 ( ( ord_less @ A @ X5 @ Z )
% 2.75/1.57 => ( ( ( P @ X5 )
% 2.75/1.57 & ( Q @ X5 ) )
% 2.75/1.57 = ( ( P2 @ X5 )
% 2.75/1.57 & ( Q2 @ X5 ) ) ) ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_42_ex__gt__or__lt,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( condit1656338222tinuum @ A )
% 2.75/1.57 => ! [A3: A] :
% 2.75/1.57 ? [B3: A] :
% 2.75/1.57 ( ( ord_less @ A @ A3 @ B3 )
% 2.75/1.57 | ( ord_less @ A @ B3 @ A3 ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_43_linorder__neqE__linordered__idom,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( linordered_idom @ A )
% 2.75/1.57 => ! [X: A,Y: A] :
% 2.75/1.57 ( ( X != Y )
% 2.75/1.57 => ( ~ ( ord_less @ A @ X @ Y )
% 2.75/1.57 => ( ord_less @ A @ Y @ X ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_44_dual__order_Ostrict__implies__not__eq,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( order @ A )
% 2.75/1.57 => ! [B4: A,A3: A] :
% 2.75/1.57 ( ( ord_less @ A @ B4 @ A3 )
% 2.75/1.57 => ( A3 != B4 ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_45_mem__Collect__eq,axiom,
% 2.75/1.57 ! [A: $tType,A3: A,P: A > $o] :
% 2.75/1.57 ( ( member @ A @ A3 @ ( collect @ A @ P ) )
% 2.75/1.57 = ( P @ A3 ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_46_Collect__mem__eq,axiom,
% 2.75/1.57 ! [A: $tType,A4: set @ A] :
% 2.75/1.57 ( ( collect @ A
% 2.75/1.57 @ ^ [X4: A] : ( member @ A @ X4 @ A4 ) )
% 2.75/1.57 = A4 ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_47_Collect__cong,axiom,
% 2.75/1.57 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.75/1.57 ( ! [X6: A] :
% 2.75/1.57 ( ( P @ X6 )
% 2.75/1.57 = ( Q @ X6 ) )
% 2.75/1.57 => ( ( collect @ A @ P )
% 2.75/1.57 = ( collect @ A @ Q ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_48_ext,axiom,
% 2.75/1.57 ! [B: $tType,A: $tType,F2: A > B,G: A > B] :
% 2.75/1.57 ( ! [X6: A] :
% 2.75/1.57 ( ( F2 @ X6 )
% 2.75/1.57 = ( G @ X6 ) )
% 2.75/1.57 => ( F2 = G ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_49_linordered__field__no__ub,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( linordered_field @ A )
% 2.75/1.57 => ! [X5: A] :
% 2.75/1.57 ? [X_1: A] : ( ord_less @ A @ X5 @ X_1 ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_50_linordered__field__no__lb,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( linordered_field @ A )
% 2.75/1.57 => ! [X5: A] :
% 2.75/1.57 ? [Y3: A] : ( ord_less @ A @ Y3 @ X5 ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_51_order_Ostrict__implies__not__eq,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( order @ A )
% 2.75/1.57 => ! [A3: A,B4: A] :
% 2.75/1.57 ( ( ord_less @ A @ A3 @ B4 )
% 2.75/1.57 => ( A3 != B4 ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_52_dependent__wellorder__choice,axiom,
% 2.75/1.57 ! [B: $tType,A: $tType] :
% 2.75/1.57 ( ( wellorder @ A )
% 2.75/1.57 => ! [P: ( A > B ) > A > B > $o] :
% 2.75/1.57 ( ! [R: B,F3: A > B,G2: A > B,X6: A] :
% 2.75/1.57 ( ! [Y4: A] :
% 2.75/1.57 ( ( ord_less @ A @ Y4 @ X6 )
% 2.75/1.57 => ( ( F3 @ Y4 )
% 2.75/1.57 = ( G2 @ Y4 ) ) )
% 2.75/1.57 => ( ( P @ F3 @ X6 @ R )
% 2.75/1.57 = ( P @ G2 @ X6 @ R ) ) )
% 2.75/1.57 => ( ! [X6: A,F3: A > B] :
% 2.75/1.57 ( ! [Y4: A] :
% 2.75/1.57 ( ( ord_less @ A @ Y4 @ X6 )
% 2.75/1.57 => ( P @ F3 @ Y4 @ ( F3 @ Y4 ) ) )
% 2.75/1.57 => ? [X_12: B] : ( P @ F3 @ X6 @ X_12 ) )
% 2.75/1.57 => ? [F3: A > B] :
% 2.75/1.57 ! [X5: A] : ( P @ F3 @ X5 @ ( F3 @ X5 ) ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_53_not__less__iff__gr__or__eq,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( linorder @ A )
% 2.75/1.57 => ! [X: A,Y: A] :
% 2.75/1.57 ( ( ~ ( ord_less @ A @ X @ Y ) )
% 2.75/1.57 = ( ( ord_less @ A @ Y @ X )
% 2.75/1.57 | ( X = Y ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_54_dual__order_Ostrict__trans,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( order @ A )
% 2.75/1.57 => ! [B4: A,A3: A,C2: A] :
% 2.75/1.57 ( ( ord_less @ A @ B4 @ A3 )
% 2.75/1.57 => ( ( ord_less @ A @ C2 @ B4 )
% 2.75/1.57 => ( ord_less @ A @ C2 @ A3 ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_55_ord__eq__less__subst,axiom,
% 2.75/1.57 ! [A: $tType,B: $tType] :
% 2.75/1.57 ( ( ( ord @ B )
% 2.75/1.57 & ( ord @ A ) )
% 2.75/1.57 => ! [A3: A,F2: B > A,B4: B,C2: B] :
% 2.75/1.57 ( ( A3
% 2.75/1.57 = ( F2 @ B4 ) )
% 2.75/1.57 => ( ( ord_less @ B @ B4 @ C2 )
% 2.75/1.57 => ( ! [X6: B,Y3: B] :
% 2.75/1.57 ( ( ord_less @ B @ X6 @ Y3 )
% 2.75/1.57 => ( ord_less @ A @ ( F2 @ X6 ) @ ( F2 @ Y3 ) ) )
% 2.75/1.57 => ( ord_less @ A @ A3 @ ( F2 @ C2 ) ) ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_56_ord__less__eq__subst,axiom,
% 2.75/1.57 ! [A: $tType,B: $tType] :
% 2.75/1.57 ( ( ( ord @ B )
% 2.75/1.57 & ( ord @ A ) )
% 2.75/1.57 => ! [A3: A,B4: A,F2: A > B,C2: B] :
% 2.75/1.57 ( ( ord_less @ A @ A3 @ B4 )
% 2.75/1.57 => ( ( ( F2 @ B4 )
% 2.75/1.57 = C2 )
% 2.75/1.57 => ( ! [X6: A,Y3: A] :
% 2.75/1.57 ( ( ord_less @ A @ X6 @ Y3 )
% 2.75/1.57 => ( ord_less @ B @ ( F2 @ X6 ) @ ( F2 @ Y3 ) ) )
% 2.75/1.57 => ( ord_less @ B @ ( F2 @ A3 ) @ C2 ) ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_57_order__less__subst1,axiom,
% 2.75/1.57 ! [A: $tType,B: $tType] :
% 2.75/1.57 ( ( ( order @ B )
% 2.75/1.57 & ( order @ A ) )
% 2.75/1.57 => ! [A3: A,F2: B > A,B4: B,C2: B] :
% 2.75/1.57 ( ( ord_less @ A @ A3 @ ( F2 @ B4 ) )
% 2.75/1.57 => ( ( ord_less @ B @ B4 @ C2 )
% 2.75/1.57 => ( ! [X6: B,Y3: B] :
% 2.75/1.57 ( ( ord_less @ B @ X6 @ Y3 )
% 2.75/1.57 => ( ord_less @ A @ ( F2 @ X6 ) @ ( F2 @ Y3 ) ) )
% 2.75/1.57 => ( ord_less @ A @ A3 @ ( F2 @ C2 ) ) ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_58_order__less__subst2,axiom,
% 2.75/1.57 ! [A: $tType,C: $tType] :
% 2.75/1.57 ( ( ( order @ C )
% 2.75/1.57 & ( order @ A ) )
% 2.75/1.57 => ! [A3: A,B4: A,F2: A > C,C2: C] :
% 2.75/1.57 ( ( ord_less @ A @ A3 @ B4 )
% 2.75/1.57 => ( ( ord_less @ C @ ( F2 @ B4 ) @ C2 )
% 2.75/1.57 => ( ! [X6: A,Y3: A] :
% 2.75/1.57 ( ( ord_less @ A @ X6 @ Y3 )
% 2.75/1.57 => ( ord_less @ C @ ( F2 @ X6 ) @ ( F2 @ Y3 ) ) )
% 2.75/1.57 => ( ord_less @ C @ ( F2 @ A3 ) @ C2 ) ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_59_lt__ex,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( no_bot @ A )
% 2.75/1.57 => ! [X: A] :
% 2.75/1.57 ? [Y3: A] : ( ord_less @ A @ Y3 @ X ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_60_gt__ex,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( no_top @ A )
% 2.75/1.57 => ! [X: A] :
% 2.75/1.57 ? [X_1: A] : ( ord_less @ A @ X @ X_1 ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_61_neqE,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( linorder @ A )
% 2.75/1.57 => ! [X: A,Y: A] :
% 2.75/1.57 ( ( X != Y )
% 2.75/1.57 => ( ~ ( ord_less @ A @ X @ Y )
% 2.75/1.57 => ( ord_less @ A @ Y @ X ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_62_neq__iff,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( linorder @ A )
% 2.75/1.57 => ! [X: A,Y: A] :
% 2.75/1.57 ( ( X != Y )
% 2.75/1.57 = ( ( ord_less @ A @ X @ Y )
% 2.75/1.57 | ( ord_less @ A @ Y @ X ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_63_order_Oasym,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( order @ A )
% 2.75/1.57 => ! [A3: A,B4: A] :
% 2.75/1.57 ( ( ord_less @ A @ A3 @ B4 )
% 2.75/1.57 => ~ ( ord_less @ A @ B4 @ A3 ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_64_dense,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( dense_order @ A )
% 2.75/1.57 => ! [X: A,Y: A] :
% 2.75/1.57 ( ( ord_less @ A @ X @ Y )
% 2.75/1.57 => ? [Z: A] :
% 2.75/1.57 ( ( ord_less @ A @ X @ Z )
% 2.75/1.57 & ( ord_less @ A @ Z @ Y ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_65_less__imp__neq,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( order @ A )
% 2.75/1.57 => ! [X: A,Y: A] :
% 2.75/1.57 ( ( ord_less @ A @ X @ Y )
% 2.75/1.57 => ( X != Y ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_66_less__asym,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( preorder @ A )
% 2.75/1.57 => ! [X: A,Y: A] :
% 2.75/1.57 ( ( ord_less @ A @ X @ Y )
% 2.75/1.57 => ~ ( ord_less @ A @ Y @ X ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_67_less__asym_H,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( preorder @ A )
% 2.75/1.57 => ! [A3: A,B4: A] :
% 2.75/1.57 ( ( ord_less @ A @ A3 @ B4 )
% 2.75/1.57 => ~ ( ord_less @ A @ B4 @ A3 ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_68_less__trans,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( preorder @ A )
% 2.75/1.57 => ! [X: A,Y: A,Z3: A] :
% 2.75/1.57 ( ( ord_less @ A @ X @ Y )
% 2.75/1.57 => ( ( ord_less @ A @ Y @ Z3 )
% 2.75/1.57 => ( ord_less @ A @ X @ Z3 ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_69_less__linear,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( linorder @ A )
% 2.75/1.57 => ! [X: A,Y: A] :
% 2.75/1.57 ( ( ord_less @ A @ X @ Y )
% 2.75/1.57 | ( X = Y )
% 2.75/1.57 | ( ord_less @ A @ Y @ X ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_70_less__irrefl,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( preorder @ A )
% 2.75/1.57 => ! [X: A] :
% 2.75/1.57 ~ ( ord_less @ A @ X @ X ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_71_ord__eq__less__trans,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( ord @ A )
% 2.75/1.57 => ! [A3: A,B4: A,C2: A] :
% 2.75/1.57 ( ( A3 = B4 )
% 2.75/1.57 => ( ( ord_less @ A @ B4 @ C2 )
% 2.75/1.57 => ( ord_less @ A @ A3 @ C2 ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_72_ord__less__eq__trans,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( ord @ A )
% 2.75/1.57 => ! [A3: A,B4: A,C2: A] :
% 2.75/1.57 ( ( ord_less @ A @ A3 @ B4 )
% 2.75/1.57 => ( ( B4 = C2 )
% 2.75/1.57 => ( ord_less @ A @ A3 @ C2 ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_73_dual__order_Oasym,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( order @ A )
% 2.75/1.57 => ! [B4: A,A3: A] :
% 2.75/1.57 ( ( ord_less @ A @ B4 @ A3 )
% 2.75/1.57 => ~ ( ord_less @ A @ A3 @ B4 ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_74_less__imp__not__eq,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( order @ A )
% 2.75/1.57 => ! [X: A,Y: A] :
% 2.75/1.57 ( ( ord_less @ A @ X @ Y )
% 2.75/1.57 => ( X != Y ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_75_less__not__sym,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( preorder @ A )
% 2.75/1.57 => ! [X: A,Y: A] :
% 2.75/1.57 ( ( ord_less @ A @ X @ Y )
% 2.75/1.57 => ~ ( ord_less @ A @ Y @ X ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_76_less__induct,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( wellorder @ A )
% 2.75/1.57 => ! [P: A > $o,A3: A] :
% 2.75/1.57 ( ! [X6: A] :
% 2.75/1.57 ( ! [Y4: A] :
% 2.75/1.57 ( ( ord_less @ A @ Y4 @ X6 )
% 2.75/1.57 => ( P @ Y4 ) )
% 2.75/1.57 => ( P @ X6 ) )
% 2.75/1.57 => ( P @ A3 ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_77_antisym__conv3,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( linorder @ A )
% 2.75/1.57 => ! [Y: A,X: A] :
% 2.75/1.57 ( ~ ( ord_less @ A @ Y @ X )
% 2.75/1.57 => ( ( ~ ( ord_less @ A @ X @ Y ) )
% 2.75/1.57 = ( X = Y ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_78_less__imp__not__eq2,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( order @ A )
% 2.75/1.57 => ! [X: A,Y: A] :
% 2.75/1.57 ( ( ord_less @ A @ X @ Y )
% 2.75/1.57 => ( Y != X ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_79_less__imp__triv,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( preorder @ A )
% 2.75/1.57 => ! [X: A,Y: A,P: $o] :
% 2.75/1.57 ( ( ord_less @ A @ X @ Y )
% 2.75/1.57 => ( ( ord_less @ A @ Y @ X )
% 2.75/1.57 => P ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_80_linorder__cases,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( linorder @ A )
% 2.75/1.57 => ! [X: A,Y: A] :
% 2.75/1.57 ( ~ ( ord_less @ A @ X @ Y )
% 2.75/1.57 => ( ( X != Y )
% 2.75/1.57 => ( ord_less @ A @ Y @ X ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_81_dual__order_Oirrefl,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( order @ A )
% 2.75/1.57 => ! [A3: A] :
% 2.75/1.57 ~ ( ord_less @ A @ A3 @ A3 ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_82_order_Ostrict__trans,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( order @ A )
% 2.75/1.57 => ! [A3: A,B4: A,C2: A] :
% 2.75/1.57 ( ( ord_less @ A @ A3 @ B4 )
% 2.75/1.57 => ( ( ord_less @ A @ B4 @ C2 )
% 2.75/1.57 => ( ord_less @ A @ A3 @ C2 ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_83_less__imp__not__less,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( preorder @ A )
% 2.75/1.57 => ! [X: A,Y: A] :
% 2.75/1.57 ( ( ord_less @ A @ X @ Y )
% 2.75/1.57 => ~ ( ord_less @ A @ Y @ X ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_84_exists__least__iff,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( wellorder @ A )
% 2.75/1.57 => ( ( ^ [P3: A > $o] :
% 2.75/1.57 ? [X7: A] : ( P3 @ X7 ) )
% 2.75/1.57 = ( ^ [P4: A > $o] :
% 2.75/1.57 ? [N: A] :
% 2.75/1.57 ( ( P4 @ N )
% 2.75/1.57 & ! [M: A] :
% 2.75/1.57 ( ( ord_less @ A @ M @ N )
% 2.75/1.57 => ~ ( P4 @ M ) ) ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_85_linorder__less__wlog,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( linorder @ A )
% 2.75/1.57 => ! [P: A > A > $o,A3: A,B4: A] :
% 2.75/1.57 ( ! [A5: A,B3: A] :
% 2.75/1.57 ( ( ord_less @ A @ A5 @ B3 )
% 2.75/1.57 => ( P @ A5 @ B3 ) )
% 2.75/1.57 => ( ! [A5: A] : ( P @ A5 @ A5 )
% 2.75/1.57 => ( ! [A5: A,B3: A] :
% 2.75/1.57 ( ( P @ B3 @ A5 )
% 2.75/1.57 => ( P @ A5 @ B3 ) )
% 2.75/1.57 => ( P @ A3 @ B4 ) ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_86_verit__comp__simplify1_I1_J,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( order @ A )
% 2.75/1.57 => ! [A3: A] :
% 2.75/1.57 ~ ( ord_less @ A @ A3 @ A3 ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_87_measure__induct,axiom,
% 2.75/1.57 ! [B: $tType,A: $tType] :
% 2.75/1.57 ( ( wellorder @ B )
% 2.75/1.57 => ! [F2: A > B,P: A > $o,A3: A] :
% 2.75/1.57 ( ! [X6: A] :
% 2.75/1.57 ( ! [Y4: A] :
% 2.75/1.57 ( ( ord_less @ B @ ( F2 @ Y4 ) @ ( F2 @ X6 ) )
% 2.75/1.57 => ( P @ Y4 ) )
% 2.75/1.57 => ( P @ X6 ) )
% 2.75/1.57 => ( P @ A3 ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_88_measure__induct__rule,axiom,
% 2.75/1.57 ! [B: $tType,A: $tType] :
% 2.75/1.57 ( ( wellorder @ B )
% 2.75/1.57 => ! [F2: A > B,P: A > $o,A3: A] :
% 2.75/1.57 ( ! [X6: A] :
% 2.75/1.57 ( ! [Y4: A] :
% 2.75/1.57 ( ( ord_less @ B @ ( F2 @ Y4 ) @ ( F2 @ X6 ) )
% 2.75/1.57 => ( P @ Y4 ) )
% 2.75/1.57 => ( P @ X6 ) )
% 2.75/1.57 => ( P @ A3 ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_89_Tree_Osimps_I4_J,axiom,
% 2.75/1.57 ! [A: $tType,B: $tType,F1: B,F22: ( binary1291135688e_Tree @ A ) > A > ( binary1291135688e_Tree @ A ) > B] :
% 2.75/1.57 ( ( binary536355927e_Tree @ B @ A @ F1 @ F22 @ ( binary1746293266le_Tip @ A ) )
% 2.75/1.57 = F1 ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_90_Tree_Osimps_I5_J,axiom,
% 2.75/1.57 ! [B: $tType,A: $tType,F1: B,F22: ( binary1291135688e_Tree @ A ) > A > ( binary1291135688e_Tree @ A ) > B,X21: binary1291135688e_Tree @ A,X22: A,X23: binary1291135688e_Tree @ A] :
% 2.75/1.57 ( ( binary536355927e_Tree @ B @ A @ F1 @ F22 @ ( binary210054475elle_T @ A @ X21 @ X22 @ X23 ) )
% 2.75/1.57 = ( F22 @ X21 @ X22 @ X23 ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_91_setOf_Osimps_I1_J,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( binary1653327646_setOf @ A @ ( binary1746293266le_Tip @ A ) )
% 2.75/1.57 = ( bot_bot @ ( set @ A ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_92_Tree_Osimps_I6_J,axiom,
% 2.75/1.57 ! [A: $tType,C: $tType,F1: C,F22: ( binary1291135688e_Tree @ A ) > A > ( binary1291135688e_Tree @ A ) > C > C > C] :
% 2.75/1.57 ( ( binary1929596613c_Tree @ C @ A @ F1 @ F22 @ ( binary1746293266le_Tip @ A ) )
% 2.75/1.57 = F1 ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_93_Tree_Osimps_I7_J,axiom,
% 2.75/1.57 ! [C: $tType,A: $tType,F1: C,F22: ( binary1291135688e_Tree @ A ) > A > ( binary1291135688e_Tree @ A ) > C > C > C,X21: binary1291135688e_Tree @ A,X22: A,X23: binary1291135688e_Tree @ A] :
% 2.75/1.57 ( ( binary1929596613c_Tree @ C @ A @ F1 @ F22 @ ( binary210054475elle_T @ A @ X21 @ X22 @ X23 ) )
% 2.75/1.57 = ( F22 @ X21 @ X22 @ X23 @ ( binary1929596613c_Tree @ C @ A @ F1 @ F22 @ X21 ) @ ( binary1929596613c_Tree @ C @ A @ F1 @ F22 @ X23 ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_94_bot__apply,axiom,
% 2.75/1.57 ! [C: $tType,D: $tType] :
% 2.75/1.57 ( ( bot @ C )
% 2.75/1.57 => ( ( bot_bot @ ( D > C ) )
% 2.75/1.57 = ( ^ [X4: D] : ( bot_bot @ C ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_95_bot__fun__def,axiom,
% 2.75/1.57 ! [B: $tType,A: $tType] :
% 2.75/1.57 ( ( bot @ B )
% 2.75/1.57 => ( ( bot_bot @ ( A > B ) )
% 2.75/1.57 = ( ^ [X4: A] : ( bot_bot @ B ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_96_bot_Oextremum__strict,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( order_bot @ A )
% 2.75/1.57 => ! [A3: A] :
% 2.75/1.57 ~ ( ord_less @ A @ A3 @ ( bot_bot @ A ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_97_bot_Onot__eq__extremum,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( order_bot @ A )
% 2.75/1.57 => ! [A3: A] :
% 2.75/1.57 ( ( A3
% 2.75/1.57 != ( bot_bot @ A ) )
% 2.75/1.57 = ( ord_less @ A @ ( bot_bot @ A ) @ A3 ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_98_Tree_Ocase__distrib,axiom,
% 2.75/1.57 ! [C: $tType,B: $tType,A: $tType,H: B > C,F1: B,F22: ( binary1291135688e_Tree @ A ) > A > ( binary1291135688e_Tree @ A ) > B,Tree: binary1291135688e_Tree @ A] :
% 2.75/1.57 ( ( H @ ( binary536355927e_Tree @ B @ A @ F1 @ F22 @ Tree ) )
% 2.75/1.57 = ( binary536355927e_Tree @ C @ A @ ( H @ F1 )
% 2.75/1.57 @ ^ [X12: binary1291135688e_Tree @ A,X24: A,X32: binary1291135688e_Tree @ A] : ( H @ ( F22 @ X12 @ X24 @ X32 ) )
% 2.75/1.57 @ Tree ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_99_empty__Collect__eq,axiom,
% 2.75/1.57 ! [A: $tType,P: A > $o] :
% 2.75/1.57 ( ( ( bot_bot @ ( set @ A ) )
% 2.75/1.57 = ( collect @ A @ P ) )
% 2.75/1.57 = ( ! [X4: A] :
% 2.75/1.57 ~ ( P @ X4 ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_100_Collect__empty__eq,axiom,
% 2.75/1.57 ! [A: $tType,P: A > $o] :
% 2.75/1.57 ( ( ( collect @ A @ P )
% 2.75/1.57 = ( bot_bot @ ( set @ A ) ) )
% 2.75/1.57 = ( ! [X4: A] :
% 2.75/1.57 ~ ( P @ X4 ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_101_all__not__in__conv,axiom,
% 2.75/1.57 ! [A: $tType,A4: set @ A] :
% 2.75/1.57 ( ( ! [X4: A] :
% 2.75/1.57 ~ ( member @ A @ X4 @ A4 ) )
% 2.75/1.57 = ( A4
% 2.75/1.57 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_102_empty__iff,axiom,
% 2.75/1.57 ! [A: $tType,C2: A] :
% 2.75/1.57 ~ ( member @ A @ C2 @ ( bot_bot @ ( set @ A ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_103_empty__def,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( bot_bot @ ( set @ A ) )
% 2.75/1.57 = ( collect @ A
% 2.75/1.57 @ ^ [X4: A] : $false ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_104_bot__set__def,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( bot_bot @ ( set @ A ) )
% 2.75/1.57 = ( collect @ A @ ( bot_bot @ ( A > $o ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_105_not__psubset__empty,axiom,
% 2.75/1.57 ! [A: $tType,A4: set @ A] :
% 2.75/1.57 ~ ( ord_less @ ( set @ A ) @ A4 @ ( bot_bot @ ( set @ A ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_106_emptyE,axiom,
% 2.75/1.57 ! [A: $tType,A3: A] :
% 2.75/1.57 ~ ( member @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_107_equals0D,axiom,
% 2.75/1.57 ! [A: $tType,A4: set @ A,A3: A] :
% 2.75/1.57 ( ( A4
% 2.75/1.57 = ( bot_bot @ ( set @ A ) ) )
% 2.75/1.57 => ~ ( member @ A @ A3 @ A4 ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_108_equals0I,axiom,
% 2.75/1.57 ! [A: $tType,A4: set @ A] :
% 2.75/1.57 ( ! [Y3: A] :
% 2.75/1.57 ~ ( member @ A @ Y3 @ A4 )
% 2.75/1.57 => ( A4
% 2.75/1.57 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_109_ex__in__conv,axiom,
% 2.75/1.57 ! [A: $tType,A4: set @ A] :
% 2.75/1.57 ( ( ? [X4: A] : ( member @ A @ X4 @ A4 ) )
% 2.75/1.57 = ( A4
% 2.75/1.57 != ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_110_Set_Ois__empty__def,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( is_empty @ A )
% 2.75/1.57 = ( ^ [A6: set @ A] :
% 2.75/1.57 ( A6
% 2.75/1.57 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_111_Collect__empty__eq__bot,axiom,
% 2.75/1.57 ! [A: $tType,P: A > $o] :
% 2.75/1.57 ( ( ( collect @ A @ P )
% 2.75/1.57 = ( bot_bot @ ( set @ A ) ) )
% 2.75/1.57 = ( P
% 2.75/1.57 = ( bot_bot @ ( A > $o ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_112_bot__empty__eq,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( bot_bot @ ( A > $o ) )
% 2.75/1.57 = ( ^ [X4: A] : ( member @ A @ X4 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_113_Tree_Osimps_I14_J,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( binary2130109271t_Tree @ A @ ( binary1746293266le_Tip @ A ) )
% 2.75/1.57 = ( bot_bot @ ( set @ A ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_114_is__singletonI_H,axiom,
% 2.75/1.57 ! [A: $tType,A4: set @ A] :
% 2.75/1.57 ( ( A4
% 2.75/1.57 != ( bot_bot @ ( set @ A ) ) )
% 2.75/1.57 => ( ! [X6: A,Y3: A] :
% 2.75/1.57 ( ( member @ A @ X6 @ A4 )
% 2.75/1.57 => ( ( member @ A @ Y3 @ A4 )
% 2.75/1.57 => ( X6 = Y3 ) ) )
% 2.75/1.57 => ( is_singleton @ A @ A4 ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_115_psubsetD,axiom,
% 2.75/1.57 ! [A: $tType,A4: set @ A,B5: set @ A,C2: A] :
% 2.75/1.57 ( ( ord_less @ ( set @ A ) @ A4 @ B5 )
% 2.75/1.57 => ( ( member @ A @ C2 @ A4 )
% 2.75/1.57 => ( member @ A @ C2 @ B5 ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_116_less__set__def,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( ord_less @ ( set @ A ) )
% 2.75/1.57 = ( ^ [A6: set @ A,B6: set @ A] :
% 2.75/1.57 ( ord_less @ ( A > $o )
% 2.75/1.57 @ ^ [X4: A] : ( member @ A @ X4 @ A6 )
% 2.75/1.57 @ ^ [X4: A] : ( member @ A @ X4 @ B6 ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_117_psubset__trans,axiom,
% 2.75/1.57 ! [A: $tType,A4: set @ A,B5: set @ A,C3: set @ A] :
% 2.75/1.57 ( ( ord_less @ ( set @ A ) @ A4 @ B5 )
% 2.75/1.57 => ( ( ord_less @ ( set @ A ) @ B5 @ C3 )
% 2.75/1.57 => ( ord_less @ ( set @ A ) @ A4 @ C3 ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_118_Tree_Oset__cases,axiom,
% 2.75/1.57 ! [A: $tType,E: A,A3: binary1291135688e_Tree @ A] :
% 2.75/1.57 ( ( member @ A @ E @ ( binary2130109271t_Tree @ A @ A3 ) )
% 2.75/1.57 => ( ! [Z1: binary1291135688e_Tree @ A] :
% 2.75/1.57 ( ? [Z22: A,Z32: binary1291135688e_Tree @ A] :
% 2.75/1.57 ( A3
% 2.75/1.57 = ( binary210054475elle_T @ A @ Z1 @ Z22 @ Z32 ) )
% 2.75/1.57 => ~ ( member @ A @ E @ ( binary2130109271t_Tree @ A @ Z1 ) ) )
% 2.75/1.57 => ( ! [Z1: binary1291135688e_Tree @ A,Z32: binary1291135688e_Tree @ A] :
% 2.75/1.57 ( A3
% 2.75/1.57 != ( binary210054475elle_T @ A @ Z1 @ E @ Z32 ) )
% 2.75/1.57 => ~ ! [Z1: binary1291135688e_Tree @ A,Z22: A,Z32: binary1291135688e_Tree @ A] :
% 2.75/1.57 ( ( A3
% 2.75/1.57 = ( binary210054475elle_T @ A @ Z1 @ Z22 @ Z32 ) )
% 2.75/1.57 => ~ ( member @ A @ E @ ( binary2130109271t_Tree @ A @ Z32 ) ) ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_119_Tree_Oset__intros_I1_J,axiom,
% 2.75/1.57 ! [A: $tType,Y: A,X21: binary1291135688e_Tree @ A,X22: A,X23: binary1291135688e_Tree @ A] :
% 2.75/1.57 ( ( member @ A @ Y @ ( binary2130109271t_Tree @ A @ X21 ) )
% 2.75/1.57 => ( member @ A @ Y @ ( binary2130109271t_Tree @ A @ ( binary210054475elle_T @ A @ X21 @ X22 @ X23 ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_120_Tree_Oset__intros_I2_J,axiom,
% 2.75/1.57 ! [A: $tType,X22: A,X21: binary1291135688e_Tree @ A,X23: binary1291135688e_Tree @ A] : ( member @ A @ X22 @ ( binary2130109271t_Tree @ A @ ( binary210054475elle_T @ A @ X21 @ X22 @ X23 ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_121_Tree_Oset__intros_I3_J,axiom,
% 2.75/1.57 ! [A: $tType,Ya: A,X23: binary1291135688e_Tree @ A,X21: binary1291135688e_Tree @ A,X22: A] :
% 2.75/1.57 ( ( member @ A @ Ya @ ( binary2130109271t_Tree @ A @ X23 ) )
% 2.75/1.57 => ( member @ A @ Ya @ ( binary2130109271t_Tree @ A @ ( binary210054475elle_T @ A @ X21 @ X22 @ X23 ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_122_is__singletonI,axiom,
% 2.75/1.57 ! [A: $tType,X: A] : ( is_singleton @ A @ ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_123_is__singleton__def,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( is_singleton @ A )
% 2.75/1.57 = ( ^ [A6: set @ A] :
% 2.75/1.57 ? [X4: A] :
% 2.75/1.57 ( A6
% 2.75/1.57 = ( insert @ A @ X4 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_124_is__singletonE,axiom,
% 2.75/1.57 ! [A: $tType,A4: set @ A] :
% 2.75/1.57 ( ( is_singleton @ A @ A4 )
% 2.75/1.57 => ~ ! [X6: A] :
% 2.75/1.57 ( A4
% 2.75/1.57 != ( insert @ A @ X6 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_125_inv__imagep__def,axiom,
% 2.75/1.57 ! [A: $tType,B: $tType] :
% 2.75/1.57 ( ( inv_imagep @ B @ A )
% 2.75/1.57 = ( ^ [R2: B > B > $o,F4: A > B,X4: A,Y2: A] : ( R2 @ ( F4 @ X4 ) @ ( F4 @ Y2 ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_126_insert__absorb2,axiom,
% 2.75/1.57 ! [A: $tType,X: A,A4: set @ A] :
% 2.75/1.57 ( ( insert @ A @ X @ ( insert @ A @ X @ A4 ) )
% 2.75/1.57 = ( insert @ A @ X @ A4 ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_127_insert__iff,axiom,
% 2.75/1.57 ! [A: $tType,A3: A,B4: A,A4: set @ A] :
% 2.75/1.57 ( ( member @ A @ A3 @ ( insert @ A @ B4 @ A4 ) )
% 2.75/1.57 = ( ( A3 = B4 )
% 2.75/1.57 | ( member @ A @ A3 @ A4 ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_128_insertCI,axiom,
% 2.75/1.57 ! [A: $tType,A3: A,B5: set @ A,B4: A] :
% 2.75/1.57 ( ( ~ ( member @ A @ A3 @ B5 )
% 2.75/1.57 => ( A3 = B4 ) )
% 2.75/1.57 => ( member @ A @ A3 @ ( insert @ A @ B4 @ B5 ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_129_singletonI,axiom,
% 2.75/1.57 ! [A: $tType,A3: A] : ( member @ A @ A3 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_130_singleton__conv,axiom,
% 2.75/1.57 ! [A: $tType,A3: A] :
% 2.75/1.57 ( ( collect @ A
% 2.75/1.57 @ ^ [X4: A] : ( X4 = A3 ) )
% 2.75/1.57 = ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_131_singleton__conv2,axiom,
% 2.75/1.57 ! [A: $tType,A3: A] :
% 2.75/1.57 ( ( collect @ A
% 2.75/1.57 @ ( ^ [Y5: A,Z4: A] : ( Y5 = Z4 )
% 2.75/1.57 @ A3 ) )
% 2.75/1.57 = ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_132_singleton__inject,axiom,
% 2.75/1.57 ! [A: $tType,A3: A,B4: A] :
% 2.75/1.57 ( ( ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) )
% 2.75/1.57 = ( insert @ A @ B4 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.75/1.57 => ( A3 = B4 ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_133_insert__not__empty,axiom,
% 2.75/1.57 ! [A: $tType,A3: A,A4: set @ A] :
% 2.75/1.57 ( ( insert @ A @ A3 @ A4 )
% 2.75/1.57 != ( bot_bot @ ( set @ A ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_134_doubleton__eq__iff,axiom,
% 2.75/1.57 ! [A: $tType,A3: A,B4: A,C2: A,D2: A] :
% 2.75/1.57 ( ( ( insert @ A @ A3 @ ( insert @ A @ B4 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.75/1.57 = ( insert @ A @ C2 @ ( insert @ A @ D2 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 2.75/1.57 = ( ( ( A3 = C2 )
% 2.75/1.57 & ( B4 = D2 ) )
% 2.75/1.57 | ( ( A3 = D2 )
% 2.75/1.57 & ( B4 = C2 ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_135_singleton__iff,axiom,
% 2.75/1.57 ! [A: $tType,B4: A,A3: A] :
% 2.75/1.57 ( ( member @ A @ B4 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.75/1.57 = ( B4 = A3 ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_136_singletonD,axiom,
% 2.75/1.57 ! [A: $tType,B4: A,A3: A] :
% 2.75/1.57 ( ( member @ A @ B4 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.75/1.57 => ( B4 = A3 ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_137_insert__compr,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( insert @ A )
% 2.75/1.57 = ( ^ [A2: A,B6: set @ A] :
% 2.75/1.57 ( collect @ A
% 2.75/1.57 @ ^ [X4: A] :
% 2.75/1.57 ( ( X4 = A2 )
% 2.75/1.57 | ( member @ A @ X4 @ B6 ) ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_138_insert__Collect,axiom,
% 2.75/1.57 ! [A: $tType,A3: A,P: A > $o] :
% 2.75/1.57 ( ( insert @ A @ A3 @ ( collect @ A @ P ) )
% 2.75/1.57 = ( collect @ A
% 2.75/1.57 @ ^ [U: A] :
% 2.75/1.57 ( ( U != A3 )
% 2.75/1.57 => ( P @ U ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_139_mk__disjoint__insert,axiom,
% 2.75/1.57 ! [A: $tType,A3: A,A4: set @ A] :
% 2.75/1.57 ( ( member @ A @ A3 @ A4 )
% 2.75/1.57 => ? [B7: set @ A] :
% 2.75/1.57 ( ( A4
% 2.75/1.57 = ( insert @ A @ A3 @ B7 ) )
% 2.75/1.57 & ~ ( member @ A @ A3 @ B7 ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_140_insert__commute,axiom,
% 2.75/1.57 ! [A: $tType,X: A,Y: A,A4: set @ A] :
% 2.75/1.57 ( ( insert @ A @ X @ ( insert @ A @ Y @ A4 ) )
% 2.75/1.57 = ( insert @ A @ Y @ ( insert @ A @ X @ A4 ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_141_insert__eq__iff,axiom,
% 2.75/1.57 ! [A: $tType,A3: A,A4: set @ A,B4: A,B5: set @ A] :
% 2.75/1.57 ( ~ ( member @ A @ A3 @ A4 )
% 2.75/1.57 => ( ~ ( member @ A @ B4 @ B5 )
% 2.75/1.57 => ( ( ( insert @ A @ A3 @ A4 )
% 2.75/1.57 = ( insert @ A @ B4 @ B5 ) )
% 2.75/1.57 = ( ( ( A3 = B4 )
% 2.75/1.57 => ( A4 = B5 ) )
% 2.75/1.57 & ( ( A3 != B4 )
% 2.75/1.57 => ? [C4: set @ A] :
% 2.75/1.57 ( ( A4
% 2.75/1.57 = ( insert @ A @ B4 @ C4 ) )
% 2.75/1.57 & ~ ( member @ A @ B4 @ C4 )
% 2.75/1.57 & ( B5
% 2.75/1.57 = ( insert @ A @ A3 @ C4 ) )
% 2.75/1.57 & ~ ( member @ A @ A3 @ C4 ) ) ) ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_142_insert__absorb,axiom,
% 2.75/1.57 ! [A: $tType,A3: A,A4: set @ A] :
% 2.75/1.57 ( ( member @ A @ A3 @ A4 )
% 2.75/1.57 => ( ( insert @ A @ A3 @ A4 )
% 2.75/1.57 = A4 ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_143_insert__ident,axiom,
% 2.75/1.57 ! [A: $tType,X: A,A4: set @ A,B5: set @ A] :
% 2.75/1.57 ( ~ ( member @ A @ X @ A4 )
% 2.75/1.57 => ( ~ ( member @ A @ X @ B5 )
% 2.75/1.57 => ( ( ( insert @ A @ X @ A4 )
% 2.75/1.57 = ( insert @ A @ X @ B5 ) )
% 2.75/1.57 = ( A4 = B5 ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_144_Set_Oset__insert,axiom,
% 2.75/1.57 ! [A: $tType,X: A,A4: set @ A] :
% 2.75/1.57 ( ( member @ A @ X @ A4 )
% 2.75/1.57 => ~ ! [B7: set @ A] :
% 2.75/1.57 ( ( A4
% 2.75/1.57 = ( insert @ A @ X @ B7 ) )
% 2.75/1.57 => ( member @ A @ X @ B7 ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_145_insertI2,axiom,
% 2.75/1.57 ! [A: $tType,A3: A,B5: set @ A,B4: A] :
% 2.75/1.57 ( ( member @ A @ A3 @ B5 )
% 2.75/1.57 => ( member @ A @ A3 @ ( insert @ A @ B4 @ B5 ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_146_insertI1,axiom,
% 2.75/1.57 ! [A: $tType,A3: A,B5: set @ A] : ( member @ A @ A3 @ ( insert @ A @ A3 @ B5 ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_147_insertE,axiom,
% 2.75/1.57 ! [A: $tType,A3: A,B4: A,A4: set @ A] :
% 2.75/1.57 ( ( member @ A @ A3 @ ( insert @ A @ B4 @ A4 ) )
% 2.75/1.57 => ( ( A3 != B4 )
% 2.75/1.57 => ( member @ A @ A3 @ A4 ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_148_Collect__conv__if,axiom,
% 2.75/1.57 ! [A: $tType,P: A > $o,A3: A] :
% 2.75/1.57 ( ( ( P @ A3 )
% 2.75/1.57 => ( ( collect @ A
% 2.75/1.57 @ ^ [X4: A] :
% 2.75/1.57 ( ( X4 = A3 )
% 2.75/1.57 & ( P @ X4 ) ) )
% 2.75/1.57 = ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 2.75/1.57 & ( ~ ( P @ A3 )
% 2.75/1.57 => ( ( collect @ A
% 2.75/1.57 @ ^ [X4: A] :
% 2.75/1.57 ( ( X4 = A3 )
% 2.75/1.57 & ( P @ X4 ) ) )
% 2.75/1.57 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_149_Collect__conv__if2,axiom,
% 2.75/1.57 ! [A: $tType,P: A > $o,A3: A] :
% 2.75/1.57 ( ( ( P @ A3 )
% 2.75/1.57 => ( ( collect @ A
% 2.75/1.57 @ ^ [X4: A] :
% 2.75/1.57 ( ( A3 = X4 )
% 2.75/1.57 & ( P @ X4 ) ) )
% 2.75/1.57 = ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 2.75/1.57 & ( ~ ( P @ A3 )
% 2.75/1.57 => ( ( collect @ A
% 2.75/1.57 @ ^ [X4: A] :
% 2.75/1.57 ( ( A3 = X4 )
% 2.75/1.57 & ( P @ X4 ) ) )
% 2.75/1.57 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_150_is__singleton__the__elem,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( is_singleton @ A )
% 2.75/1.57 = ( ^ [A6: set @ A] :
% 2.75/1.57 ( A6
% 2.75/1.57 = ( insert @ A @ ( the_elem @ A @ A6 ) @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_151_the__elem__eq,axiom,
% 2.75/1.57 ! [A: $tType,X: A] :
% 2.75/1.57 ( ( the_elem @ A @ ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 2.75/1.57 = X ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_152_setOf_Osimps_I2_J,axiom,
% 2.75/1.57 ! [A: $tType,T1: binary1291135688e_Tree @ A,X: A,T2: binary1291135688e_Tree @ A] :
% 2.75/1.57 ( ( binary1653327646_setOf @ A @ ( binary210054475elle_T @ A @ T1 @ X @ T2 ) )
% 2.75/1.57 = ( sup_sup @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ ( binary1653327646_setOf @ A @ T1 ) @ ( binary1653327646_setOf @ A @ T2 ) ) @ ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_153_Tree_Osimps_I15_J,axiom,
% 2.75/1.57 ! [A: $tType,X21: binary1291135688e_Tree @ A,X22: A,X23: binary1291135688e_Tree @ A] :
% 2.75/1.57 ( ( binary2130109271t_Tree @ A @ ( binary210054475elle_T @ A @ X21 @ X22 @ X23 ) )
% 2.75/1.57 = ( sup_sup @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ ( binary2130109271t_Tree @ A @ X21 ) @ ( insert @ A @ X22 @ ( bot_bot @ ( set @ A ) ) ) ) @ ( binary2130109271t_Tree @ A @ X23 ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_154_UnCI,axiom,
% 2.75/1.57 ! [A: $tType,C2: A,B5: set @ A,A4: set @ A] :
% 2.75/1.57 ( ( ~ ( member @ A @ C2 @ B5 )
% 2.75/1.57 => ( member @ A @ C2 @ A4 ) )
% 2.75/1.57 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_155_Un__iff,axiom,
% 2.75/1.57 ! [A: $tType,C2: A,A4: set @ A,B5: set @ A] :
% 2.75/1.57 ( ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) )
% 2.75/1.57 = ( ( member @ A @ C2 @ A4 )
% 2.75/1.57 | ( member @ A @ C2 @ B5 ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_156_Un__empty,axiom,
% 2.75/1.57 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 2.75/1.57 ( ( ( sup_sup @ ( set @ A ) @ A4 @ B5 )
% 2.75/1.57 = ( bot_bot @ ( set @ A ) ) )
% 2.75/1.57 = ( ( A4
% 2.75/1.57 = ( bot_bot @ ( set @ A ) ) )
% 2.75/1.57 & ( B5
% 2.75/1.57 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_157_Un__insert__right,axiom,
% 2.75/1.57 ! [A: $tType,A4: set @ A,A3: A,B5: set @ A] :
% 2.75/1.57 ( ( sup_sup @ ( set @ A ) @ A4 @ ( insert @ A @ A3 @ B5 ) )
% 2.75/1.57 = ( insert @ A @ A3 @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_158_Un__insert__left,axiom,
% 2.75/1.57 ! [A: $tType,A3: A,B5: set @ A,C3: set @ A] :
% 2.75/1.57 ( ( sup_sup @ ( set @ A ) @ ( insert @ A @ A3 @ B5 ) @ C3 )
% 2.75/1.57 = ( insert @ A @ A3 @ ( sup_sup @ ( set @ A ) @ B5 @ C3 ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_159_UnE,axiom,
% 2.75/1.57 ! [A: $tType,C2: A,A4: set @ A,B5: set @ A] :
% 2.75/1.57 ( ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) )
% 2.75/1.57 => ( ~ ( member @ A @ C2 @ A4 )
% 2.75/1.57 => ( member @ A @ C2 @ B5 ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_160_UnI1,axiom,
% 2.75/1.57 ! [A: $tType,C2: A,A4: set @ A,B5: set @ A] :
% 2.75/1.57 ( ( member @ A @ C2 @ A4 )
% 2.75/1.57 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_161_UnI2,axiom,
% 2.75/1.57 ! [A: $tType,C2: A,B5: set @ A,A4: set @ A] :
% 2.75/1.57 ( ( member @ A @ C2 @ B5 )
% 2.75/1.57 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_162_bex__Un,axiom,
% 2.75/1.57 ! [A: $tType,A4: set @ A,B5: set @ A,P: A > $o] :
% 2.75/1.57 ( ( ? [X4: A] :
% 2.75/1.57 ( ( member @ A @ X4 @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) )
% 2.75/1.57 & ( P @ X4 ) ) )
% 2.75/1.57 = ( ? [X4: A] :
% 2.75/1.57 ( ( member @ A @ X4 @ A4 )
% 2.75/1.57 & ( P @ X4 ) )
% 2.75/1.57 | ? [X4: A] :
% 2.75/1.57 ( ( member @ A @ X4 @ B5 )
% 2.75/1.57 & ( P @ X4 ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_163_ball__Un,axiom,
% 2.75/1.57 ! [A: $tType,A4: set @ A,B5: set @ A,P: A > $o] :
% 2.75/1.57 ( ( ! [X4: A] :
% 2.75/1.57 ( ( member @ A @ X4 @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) )
% 2.75/1.57 => ( P @ X4 ) ) )
% 2.75/1.57 = ( ! [X4: A] :
% 2.75/1.57 ( ( member @ A @ X4 @ A4 )
% 2.75/1.57 => ( P @ X4 ) )
% 2.75/1.57 & ! [X4: A] :
% 2.75/1.57 ( ( member @ A @ X4 @ B5 )
% 2.75/1.57 => ( P @ X4 ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_164_Un__assoc,axiom,
% 2.75/1.57 ! [A: $tType,A4: set @ A,B5: set @ A,C3: set @ A] :
% 2.75/1.57 ( ( sup_sup @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) @ C3 )
% 2.75/1.57 = ( sup_sup @ ( set @ A ) @ A4 @ ( sup_sup @ ( set @ A ) @ B5 @ C3 ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_165_Un__absorb,axiom,
% 2.75/1.57 ! [A: $tType,A4: set @ A] :
% 2.75/1.57 ( ( sup_sup @ ( set @ A ) @ A4 @ A4 )
% 2.75/1.57 = A4 ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_166_Un__commute,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( sup_sup @ ( set @ A ) )
% 2.75/1.57 = ( ^ [A6: set @ A,B6: set @ A] : ( sup_sup @ ( set @ A ) @ B6 @ A6 ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_167_Un__left__absorb,axiom,
% 2.75/1.57 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 2.75/1.57 ( ( sup_sup @ ( set @ A ) @ A4 @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) )
% 2.75/1.57 = ( sup_sup @ ( set @ A ) @ A4 @ B5 ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_168_Un__left__commute,axiom,
% 2.75/1.57 ! [A: $tType,A4: set @ A,B5: set @ A,C3: set @ A] :
% 2.75/1.57 ( ( sup_sup @ ( set @ A ) @ A4 @ ( sup_sup @ ( set @ A ) @ B5 @ C3 ) )
% 2.75/1.57 = ( sup_sup @ ( set @ A ) @ B5 @ ( sup_sup @ ( set @ A ) @ A4 @ C3 ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_169_Collect__disj__eq,axiom,
% 2.75/1.57 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.75/1.57 ( ( collect @ A
% 2.75/1.57 @ ^ [X4: A] :
% 2.75/1.57 ( ( P @ X4 )
% 2.75/1.57 | ( Q @ X4 ) ) )
% 2.75/1.57 = ( sup_sup @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_170_Un__def,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( sup_sup @ ( set @ A ) )
% 2.75/1.57 = ( ^ [A6: set @ A,B6: set @ A] :
% 2.75/1.57 ( collect @ A
% 2.75/1.57 @ ^ [X4: A] :
% 2.75/1.57 ( ( member @ A @ X4 @ A6 )
% 2.75/1.57 | ( member @ A @ X4 @ B6 ) ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_171_Un__empty__left,axiom,
% 2.75/1.57 ! [A: $tType,B5: set @ A] :
% 2.75/1.57 ( ( sup_sup @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ B5 )
% 2.75/1.57 = B5 ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_172_Un__empty__right,axiom,
% 2.75/1.57 ! [A: $tType,A4: set @ A] :
% 2.75/1.57 ( ( sup_sup @ ( set @ A ) @ A4 @ ( bot_bot @ ( set @ A ) ) )
% 2.75/1.57 = A4 ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_173_insert__def,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( insert @ A )
% 2.75/1.57 = ( ^ [A2: A] :
% 2.75/1.57 ( sup_sup @ ( set @ A )
% 2.75/1.57 @ ( collect @ A
% 2.75/1.57 @ ^ [X4: A] : ( X4 = A2 ) ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_174_insert__is__Un,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( insert @ A )
% 2.75/1.57 = ( ^ [A2: A] : ( sup_sup @ ( set @ A ) @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_175_Un__singleton__iff,axiom,
% 2.75/1.57 ! [A: $tType,A4: set @ A,B5: set @ A,X: A] :
% 2.75/1.57 ( ( ( sup_sup @ ( set @ A ) @ A4 @ B5 )
% 2.75/1.57 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 2.75/1.57 = ( ( ( A4
% 2.75/1.57 = ( bot_bot @ ( set @ A ) ) )
% 2.75/1.57 & ( B5
% 2.75/1.57 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) )
% 2.75/1.57 | ( ( A4
% 2.75/1.57 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 2.75/1.57 & ( B5
% 2.75/1.57 = ( bot_bot @ ( set @ A ) ) ) )
% 2.75/1.57 | ( ( A4
% 2.75/1.57 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 2.75/1.57 & ( B5
% 2.75/1.57 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_176_singleton__Un__iff,axiom,
% 2.75/1.57 ! [A: $tType,X: A,A4: set @ A,B5: set @ A] :
% 2.75/1.57 ( ( ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) )
% 2.75/1.57 = ( sup_sup @ ( set @ A ) @ A4 @ B5 ) )
% 2.75/1.57 = ( ( ( A4
% 2.75/1.57 = ( bot_bot @ ( set @ A ) ) )
% 2.75/1.57 & ( B5
% 2.75/1.57 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) )
% 2.75/1.57 | ( ( A4
% 2.75/1.57 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 2.75/1.57 & ( B5
% 2.75/1.57 = ( bot_bot @ ( set @ A ) ) ) )
% 2.75/1.57 | ( ( A4
% 2.75/1.57 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 2.75/1.57 & ( B5
% 2.75/1.57 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_177_sup__bot__left,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( bounde1808546759up_bot @ A )
% 2.75/1.57 => ! [X: A] :
% 2.75/1.57 ( ( sup_sup @ A @ ( bot_bot @ A ) @ X )
% 2.75/1.57 = X ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_178_sup__bot__right,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( bounde1808546759up_bot @ A )
% 2.75/1.57 => ! [X: A] :
% 2.75/1.57 ( ( sup_sup @ A @ X @ ( bot_bot @ A ) )
% 2.75/1.57 = X ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_179_bot__eq__sup__iff,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( bounde1808546759up_bot @ A )
% 2.75/1.57 => ! [X: A,Y: A] :
% 2.75/1.57 ( ( ( bot_bot @ A )
% 2.75/1.57 = ( sup_sup @ A @ X @ Y ) )
% 2.75/1.57 = ( ( X
% 2.75/1.57 = ( bot_bot @ A ) )
% 2.75/1.57 & ( Y
% 2.75/1.57 = ( bot_bot @ A ) ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_180_sup__bot_Oright__neutral,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( bounde1808546759up_bot @ A )
% 2.75/1.57 => ! [A3: A] :
% 2.75/1.57 ( ( sup_sup @ A @ A3 @ ( bot_bot @ A ) )
% 2.75/1.57 = A3 ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_181_sup__bot_Oneutr__eq__iff,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( bounde1808546759up_bot @ A )
% 2.75/1.57 => ! [A3: A,B4: A] :
% 2.75/1.57 ( ( ( bot_bot @ A )
% 2.75/1.57 = ( sup_sup @ A @ A3 @ B4 ) )
% 2.75/1.57 = ( ( A3
% 2.75/1.57 = ( bot_bot @ A ) )
% 2.75/1.57 & ( B4
% 2.75/1.57 = ( bot_bot @ A ) ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_182_sup__bot_Oleft__neutral,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( bounde1808546759up_bot @ A )
% 2.75/1.57 => ! [A3: A] :
% 2.75/1.57 ( ( sup_sup @ A @ ( bot_bot @ A ) @ A3 )
% 2.75/1.57 = A3 ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_183_sup__bot_Oeq__neutr__iff,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( bounde1808546759up_bot @ A )
% 2.75/1.57 => ! [A3: A,B4: A] :
% 2.75/1.57 ( ( ( sup_sup @ A @ A3 @ B4 )
% 2.75/1.57 = ( bot_bot @ A ) )
% 2.75/1.57 = ( ( A3
% 2.75/1.57 = ( bot_bot @ A ) )
% 2.75/1.57 & ( B4
% 2.75/1.57 = ( bot_bot @ A ) ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_184_sup__eq__bot__iff,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( bounde1808546759up_bot @ A )
% 2.75/1.57 => ! [X: A,Y: A] :
% 2.75/1.57 ( ( ( sup_sup @ A @ X @ Y )
% 2.75/1.57 = ( bot_bot @ A ) )
% 2.75/1.57 = ( ( X
% 2.75/1.57 = ( bot_bot @ A ) )
% 2.75/1.57 & ( Y
% 2.75/1.57 = ( bot_bot @ A ) ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_185_sup__set__def,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( sup_sup @ ( set @ A ) )
% 2.75/1.57 = ( ^ [A6: set @ A,B6: set @ A] :
% 2.75/1.57 ( collect @ A
% 2.75/1.57 @ ( sup_sup @ ( A > $o )
% 2.75/1.57 @ ^ [X4: A] : ( member @ A @ X4 @ A6 )
% 2.75/1.57 @ ^ [X4: A] : ( member @ A @ X4 @ B6 ) ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_186_sup__Un__eq,axiom,
% 2.75/1.57 ! [A: $tType,R3: set @ A,S: set @ A] :
% 2.75/1.57 ( ( sup_sup @ ( A > $o )
% 2.75/1.57 @ ^ [X4: A] : ( member @ A @ X4 @ R3 )
% 2.75/1.57 @ ^ [X4: A] : ( member @ A @ X4 @ S ) )
% 2.75/1.57 = ( ^ [X4: A] : ( member @ A @ X4 @ ( sup_sup @ ( set @ A ) @ R3 @ S ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_187_sup_Ostrict__coboundedI2,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( semilattice_sup @ A )
% 2.75/1.57 => ! [C2: A,B4: A,A3: A] :
% 2.75/1.57 ( ( ord_less @ A @ C2 @ B4 )
% 2.75/1.57 => ( ord_less @ A @ C2 @ ( sup_sup @ A @ A3 @ B4 ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_188_sup_Ostrict__coboundedI1,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( semilattice_sup @ A )
% 2.75/1.57 => ! [C2: A,A3: A,B4: A] :
% 2.75/1.57 ( ( ord_less @ A @ C2 @ A3 )
% 2.75/1.57 => ( ord_less @ A @ C2 @ ( sup_sup @ A @ A3 @ B4 ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_189_sup_Ostrict__order__iff,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( semilattice_sup @ A )
% 2.75/1.57 => ( ( ord_less @ A )
% 2.75/1.57 = ( ^ [B2: A,A2: A] :
% 2.75/1.57 ( ( A2
% 2.75/1.57 = ( sup_sup @ A @ A2 @ B2 ) )
% 2.75/1.57 & ( A2 != B2 ) ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_190_sup_Ostrict__boundedE,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( semilattice_sup @ A )
% 2.75/1.57 => ! [B4: A,C2: A,A3: A] :
% 2.75/1.57 ( ( ord_less @ A @ ( sup_sup @ A @ B4 @ C2 ) @ A3 )
% 2.75/1.57 => ~ ( ( ord_less @ A @ B4 @ A3 )
% 2.75/1.57 => ~ ( ord_less @ A @ C2 @ A3 ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_191_less__supI2,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( semilattice_sup @ A )
% 2.75/1.57 => ! [X: A,B4: A,A3: A] :
% 2.75/1.57 ( ( ord_less @ A @ X @ B4 )
% 2.75/1.57 => ( ord_less @ A @ X @ ( sup_sup @ A @ A3 @ B4 ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_192_less__supI1,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( semilattice_sup @ A )
% 2.75/1.57 => ! [X: A,A3: A,B4: A] :
% 2.75/1.57 ( ( ord_less @ A @ X @ A3 )
% 2.75/1.57 => ( ord_less @ A @ X @ ( sup_sup @ A @ A3 @ B4 ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_193_the__elem__def,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( the_elem @ A )
% 2.75/1.57 = ( ^ [X8: set @ A] :
% 2.75/1.57 ( the @ A
% 2.75/1.57 @ ^ [X4: A] :
% 2.75/1.57 ( X8
% 2.75/1.57 = ( insert @ A @ X4 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_194_pred__on_Ochain__extend,axiom,
% 2.75/1.57 ! [A: $tType,A4: set @ A,P: A > A > $o,C3: set @ A,Z3: A] :
% 2.75/1.57 ( ( pred_chain @ A @ A4 @ P @ C3 )
% 2.75/1.57 => ( ( member @ A @ Z3 @ A4 )
% 2.75/1.57 => ( ! [X6: A] :
% 2.75/1.57 ( ( member @ A @ X6 @ C3 )
% 2.75/1.57 => ( sup_sup @ ( A > A > $o ) @ P
% 2.75/1.57 @ ^ [Y5: A,Z4: A] : ( Y5 = Z4 )
% 2.75/1.57 @ X6
% 2.75/1.57 @ Z3 ) )
% 2.75/1.57 => ( pred_chain @ A @ A4 @ P @ ( sup_sup @ ( set @ A ) @ ( insert @ A @ Z3 @ ( bot_bot @ ( set @ A ) ) ) @ C3 ) ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_195_sup__bot_Osemilattice__neutr__axioms,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( bounde1808546759up_bot @ A )
% 2.75/1.57 => ( semilattice_neutr @ A @ ( sup_sup @ A ) @ ( bot_bot @ A ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_196_subset_Ochain__extend,axiom,
% 2.75/1.57 ! [A: $tType,A4: set @ ( set @ A ),C3: set @ ( set @ A ),Z3: set @ A] :
% 2.75/1.57 ( ( pred_chain @ ( set @ A ) @ A4 @ ( ord_less @ ( set @ A ) ) @ C3 )
% 2.75/1.57 => ( ( member @ ( set @ A ) @ Z3 @ A4 )
% 2.75/1.57 => ( ! [X6: set @ A] :
% 2.75/1.57 ( ( member @ ( set @ A ) @ X6 @ C3 )
% 2.75/1.57 => ( sup_sup @ ( ( set @ A ) > ( set @ A ) > $o ) @ ( ord_less @ ( set @ A ) )
% 2.75/1.57 @ ^ [Y5: set @ A,Z4: set @ A] : ( Y5 = Z4 )
% 2.75/1.57 @ X6
% 2.75/1.57 @ Z3 ) )
% 2.75/1.57 => ( pred_chain @ ( set @ A ) @ A4 @ ( ord_less @ ( set @ A ) ) @ ( sup_sup @ ( set @ ( set @ A ) ) @ ( insert @ ( set @ A ) @ Z3 @ ( bot_bot @ ( set @ ( set @ A ) ) ) ) @ C3 ) ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_197_subset_Ochain__total,axiom,
% 2.75/1.57 ! [A: $tType,A4: set @ ( set @ A ),C3: set @ ( set @ A ),X: set @ A,Y: set @ A] :
% 2.75/1.57 ( ( pred_chain @ ( set @ A ) @ A4 @ ( ord_less @ ( set @ A ) ) @ C3 )
% 2.75/1.57 => ( ( member @ ( set @ A ) @ X @ C3 )
% 2.75/1.57 => ( ( member @ ( set @ A ) @ Y @ C3 )
% 2.75/1.57 => ( ( sup_sup @ ( ( set @ A ) > ( set @ A ) > $o ) @ ( ord_less @ ( set @ A ) )
% 2.75/1.57 @ ^ [Y5: set @ A,Z4: set @ A] : ( Y5 = Z4 )
% 2.75/1.57 @ X
% 2.75/1.57 @ Y )
% 2.75/1.57 | ( sup_sup @ ( ( set @ A ) > ( set @ A ) > $o ) @ ( ord_less @ ( set @ A ) )
% 2.75/1.57 @ ^ [Y5: set @ A,Z4: set @ A] : ( Y5 = Z4 )
% 2.75/1.57 @ Y
% 2.75/1.57 @ X ) ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_198_pred__on_Ochain__total,axiom,
% 2.75/1.57 ! [A: $tType,A4: set @ A,P: A > A > $o,C3: set @ A,X: A,Y: A] :
% 2.75/1.57 ( ( pred_chain @ A @ A4 @ P @ C3 )
% 2.75/1.57 => ( ( member @ A @ X @ C3 )
% 2.75/1.57 => ( ( member @ A @ Y @ C3 )
% 2.75/1.57 => ( ( sup_sup @ ( A > A > $o ) @ P
% 2.75/1.57 @ ^ [Y5: A,Z4: A] : ( Y5 = Z4 )
% 2.75/1.57 @ X
% 2.75/1.57 @ Y )
% 2.75/1.57 | ( sup_sup @ ( A > A > $o ) @ P
% 2.75/1.57 @ ^ [Y5: A,Z4: A] : ( Y5 = Z4 )
% 2.75/1.57 @ Y
% 2.75/1.57 @ X ) ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_199_subset_Ochain__empty,axiom,
% 2.75/1.57 ! [A: $tType,A4: set @ ( set @ A )] : ( pred_chain @ ( set @ A ) @ A4 @ ( ord_less @ ( set @ A ) ) @ ( bot_bot @ ( set @ ( set @ A ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_200_pred__on_Ochain__empty,axiom,
% 2.75/1.57 ! [A: $tType,A4: set @ A,P: A > A > $o] : ( pred_chain @ A @ A4 @ P @ ( bot_bot @ ( set @ A ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_201_chain__mono,axiom,
% 2.75/1.57 ! [A: $tType,A4: set @ A,P: A > A > $o,Q: A > A > $o,C3: set @ A] :
% 2.75/1.57 ( ! [X6: A,Y3: A] :
% 2.75/1.57 ( ( member @ A @ X6 @ A4 )
% 2.75/1.57 => ( ( member @ A @ Y3 @ A4 )
% 2.75/1.57 => ( ( P @ X6 @ Y3 )
% 2.75/1.57 => ( Q @ X6 @ Y3 ) ) ) )
% 2.75/1.57 => ( ( pred_chain @ A @ A4 @ P @ C3 )
% 2.75/1.57 => ( pred_chain @ A @ A4 @ Q @ C3 ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_202_pred__on_Ochain_Ocong,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( pred_chain @ A )
% 2.75/1.57 = ( pred_chain @ A ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_203_the__equality,axiom,
% 2.75/1.57 ! [A: $tType,P: A > $o,A3: A] :
% 2.75/1.57 ( ( P @ A3 )
% 2.75/1.57 => ( ! [X6: A] :
% 2.75/1.57 ( ( P @ X6 )
% 2.75/1.57 => ( X6 = A3 ) )
% 2.75/1.57 => ( ( the @ A @ P )
% 2.75/1.57 = A3 ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_204_the__eq__trivial,axiom,
% 2.75/1.57 ! [A: $tType,A3: A] :
% 2.75/1.57 ( ( the @ A
% 2.75/1.57 @ ^ [X4: A] : ( X4 = A3 ) )
% 2.75/1.57 = A3 ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_205_the__sym__eq__trivial,axiom,
% 2.75/1.57 ! [A: $tType,X: A] :
% 2.75/1.57 ( ( the @ A
% 2.75/1.57 @ ( ^ [Y5: A,Z4: A] : ( Y5 = Z4 )
% 2.75/1.57 @ X ) )
% 2.75/1.57 = X ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_206_the1__equality,axiom,
% 2.75/1.57 ! [A: $tType,P: A > $o,A3: A] :
% 2.75/1.57 ( ? [X5: A] :
% 2.75/1.57 ( ( P @ X5 )
% 2.75/1.57 & ! [Y3: A] :
% 2.75/1.57 ( ( P @ Y3 )
% 2.75/1.57 => ( Y3 = X5 ) ) )
% 2.75/1.57 => ( ( P @ A3 )
% 2.75/1.57 => ( ( the @ A @ P )
% 2.75/1.57 = A3 ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_207_the1I2,axiom,
% 2.75/1.57 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.75/1.57 ( ? [X5: A] :
% 2.75/1.57 ( ( P @ X5 )
% 2.75/1.57 & ! [Y3: A] :
% 2.75/1.57 ( ( P @ Y3 )
% 2.75/1.57 => ( Y3 = X5 ) ) )
% 2.75/1.57 => ( ! [X6: A] :
% 2.75/1.57 ( ( P @ X6 )
% 2.75/1.57 => ( Q @ X6 ) )
% 2.75/1.57 => ( Q @ ( the @ A @ P ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_208_If__def,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( if @ A )
% 2.75/1.57 = ( ^ [P4: $o,X4: A,Y2: A] :
% 2.75/1.57 ( the @ A
% 2.75/1.57 @ ^ [Z5: A] :
% 2.75/1.57 ( ( P4
% 2.75/1.57 => ( Z5 = X4 ) )
% 2.75/1.57 & ( ~ P4
% 2.75/1.57 => ( Z5 = Y2 ) ) ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_209_theI2,axiom,
% 2.75/1.57 ! [A: $tType,P: A > $o,A3: A,Q: A > $o] :
% 2.75/1.57 ( ( P @ A3 )
% 2.75/1.57 => ( ! [X6: A] :
% 2.75/1.57 ( ( P @ X6 )
% 2.75/1.57 => ( X6 = A3 ) )
% 2.75/1.57 => ( ! [X6: A] :
% 2.75/1.57 ( ( P @ X6 )
% 2.75/1.57 => ( Q @ X6 ) )
% 2.75/1.57 => ( Q @ ( the @ A @ P ) ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_210_theI_H,axiom,
% 2.75/1.57 ! [A: $tType,P: A > $o] :
% 2.75/1.57 ( ? [X5: A] :
% 2.75/1.57 ( ( P @ X5 )
% 2.75/1.57 & ! [Y3: A] :
% 2.75/1.57 ( ( P @ Y3 )
% 2.75/1.57 => ( Y3 = X5 ) ) )
% 2.75/1.57 => ( P @ ( the @ A @ P ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_211_theI,axiom,
% 2.75/1.57 ! [A: $tType,P: A > $o,A3: A] :
% 2.75/1.57 ( ( P @ A3 )
% 2.75/1.57 => ( ! [X6: A] :
% 2.75/1.57 ( ( P @ X6 )
% 2.75/1.57 => ( X6 = A3 ) )
% 2.75/1.57 => ( P @ ( the @ A @ P ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_212_chains__alt__def,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( chains @ A )
% 2.75/1.57 = ( ^ [A6: set @ ( set @ A )] : ( collect @ ( set @ ( set @ A ) ) @ ( pred_chain @ ( set @ A ) @ A6 @ ( ord_less @ ( set @ A ) ) ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_213_Pow__empty,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( pow @ A @ ( bot_bot @ ( set @ A ) ) )
% 2.75/1.57 = ( insert @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ ( bot_bot @ ( set @ ( set @ A ) ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_214_Pow__singleton__iff,axiom,
% 2.75/1.57 ! [A: $tType,X9: set @ A,Y6: set @ A] :
% 2.75/1.57 ( ( ( pow @ A @ X9 )
% 2.75/1.57 = ( insert @ ( set @ A ) @ Y6 @ ( bot_bot @ ( set @ ( set @ A ) ) ) ) )
% 2.75/1.57 = ( ( X9
% 2.75/1.57 = ( bot_bot @ ( set @ A ) ) )
% 2.75/1.57 & ( Y6
% 2.75/1.57 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_215_Pow__not__empty,axiom,
% 2.75/1.57 ! [A: $tType,A4: set @ A] :
% 2.75/1.57 ( ( pow @ A @ A4 )
% 2.75/1.57 != ( bot_bot @ ( set @ ( set @ A ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_216_Pow__bottom,axiom,
% 2.75/1.57 ! [A: $tType,B5: set @ A] : ( member @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ ( pow @ A @ B5 ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_217_Pow__top,axiom,
% 2.75/1.57 ! [A: $tType,A4: set @ A] : ( member @ ( set @ A ) @ A4 @ ( pow @ A @ A4 ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_218_chains__extend,axiom,
% 2.75/1.57 ! [A: $tType,C2: set @ ( set @ A ),S: set @ ( set @ A ),Z3: set @ A] :
% 2.75/1.57 ( ( member @ ( set @ ( set @ A ) ) @ C2 @ ( chains @ A @ S ) )
% 2.75/1.57 => ( ( member @ ( set @ A ) @ Z3 @ S )
% 2.75/1.57 => ( ! [X6: set @ A] :
% 2.75/1.57 ( ( member @ ( set @ A ) @ X6 @ C2 )
% 2.75/1.57 => ( ord_less_eq @ ( set @ A ) @ X6 @ Z3 ) )
% 2.75/1.57 => ( member @ ( set @ ( set @ A ) ) @ ( sup_sup @ ( set @ ( set @ A ) ) @ ( insert @ ( set @ A ) @ Z3 @ ( bot_bot @ ( set @ ( set @ A ) ) ) ) @ C2 ) @ ( chains @ A @ S ) ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_219_Powp__Pow__eq,axiom,
% 2.75/1.57 ! [A: $tType,A4: set @ A] :
% 2.75/1.57 ( ( powp @ A
% 2.75/1.57 @ ^ [X4: A] : ( member @ A @ X4 @ A4 ) )
% 2.75/1.57 = ( ^ [X4: set @ A] : ( member @ ( set @ A ) @ X4 @ ( pow @ A @ A4 ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_220_order__refl,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( preorder @ A )
% 2.75/1.57 => ! [X: A] : ( ord_less_eq @ A @ X @ X ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_221_subset__antisym,axiom,
% 2.75/1.57 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 2.75/1.57 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 2.75/1.57 => ( ( ord_less_eq @ ( set @ A ) @ B5 @ A4 )
% 2.75/1.57 => ( A4 = B5 ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_222_subsetI,axiom,
% 2.75/1.57 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 2.75/1.57 ( ! [X6: A] :
% 2.75/1.57 ( ( member @ A @ X6 @ A4 )
% 2.75/1.57 => ( member @ A @ X6 @ B5 ) )
% 2.75/1.57 => ( ord_less_eq @ ( set @ A ) @ A4 @ B5 ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_223_empty__subsetI,axiom,
% 2.75/1.57 ! [A: $tType,A4: set @ A] : ( ord_less_eq @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ A4 ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_224_subset__empty,axiom,
% 2.75/1.57 ! [A: $tType,A4: set @ A] :
% 2.75/1.57 ( ( ord_less_eq @ ( set @ A ) @ A4 @ ( bot_bot @ ( set @ A ) ) )
% 2.75/1.57 = ( A4
% 2.75/1.57 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_225_insert__subset,axiom,
% 2.75/1.57 ! [A: $tType,X: A,A4: set @ A,B5: set @ A] :
% 2.75/1.57 ( ( ord_less_eq @ ( set @ A ) @ ( insert @ A @ X @ A4 ) @ B5 )
% 2.75/1.57 = ( ( member @ A @ X @ B5 )
% 2.75/1.57 & ( ord_less_eq @ ( set @ A ) @ A4 @ B5 ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_226_Un__subset__iff,axiom,
% 2.75/1.57 ! [A: $tType,A4: set @ A,B5: set @ A,C3: set @ A] :
% 2.75/1.57 ( ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) @ C3 )
% 2.75/1.57 = ( ( ord_less_eq @ ( set @ A ) @ A4 @ C3 )
% 2.75/1.57 & ( ord_less_eq @ ( set @ A ) @ B5 @ C3 ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_227_psubsetI,axiom,
% 2.75/1.57 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 2.75/1.57 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 2.75/1.57 => ( ( A4 != B5 )
% 2.75/1.57 => ( ord_less @ ( set @ A ) @ A4 @ B5 ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_228_PowI,axiom,
% 2.75/1.57 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 2.75/1.57 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 2.75/1.57 => ( member @ ( set @ A ) @ A4 @ ( pow @ A @ B5 ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_229_Pow__iff,axiom,
% 2.75/1.57 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 2.75/1.57 ( ( member @ ( set @ A ) @ A4 @ ( pow @ A @ B5 ) )
% 2.75/1.57 = ( ord_less_eq @ ( set @ A ) @ A4 @ B5 ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_230_singleton__insert__inj__eq,axiom,
% 2.75/1.57 ! [A: $tType,B4: A,A3: A,A4: set @ A] :
% 2.75/1.57 ( ( ( insert @ A @ B4 @ ( bot_bot @ ( set @ A ) ) )
% 2.75/1.57 = ( insert @ A @ A3 @ A4 ) )
% 2.75/1.57 = ( ( A3 = B4 )
% 2.75/1.57 & ( ord_less_eq @ ( set @ A ) @ A4 @ ( insert @ A @ B4 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_231_singleton__insert__inj__eq_H,axiom,
% 2.75/1.57 ! [A: $tType,A3: A,A4: set @ A,B4: A] :
% 2.75/1.57 ( ( ( insert @ A @ A3 @ A4 )
% 2.75/1.57 = ( insert @ A @ B4 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.75/1.57 = ( ( A3 = B4 )
% 2.75/1.57 & ( ord_less_eq @ ( set @ A ) @ A4 @ ( insert @ A @ B4 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_232_PowD,axiom,
% 2.75/1.57 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 2.75/1.57 ( ( member @ ( set @ A ) @ A4 @ ( pow @ A @ B5 ) )
% 2.75/1.57 => ( ord_less_eq @ ( set @ A ) @ A4 @ B5 ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_233_Pow__mono,axiom,
% 2.75/1.57 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 2.75/1.57 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 2.75/1.57 => ( ord_less_eq @ ( set @ ( set @ A ) ) @ ( pow @ A @ A4 ) @ ( pow @ A @ B5 ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_234_Pow__def,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( pow @ A )
% 2.75/1.57 = ( ^ [A6: set @ A] :
% 2.75/1.57 ( collect @ ( set @ A )
% 2.75/1.57 @ ^ [B6: set @ A] : ( ord_less_eq @ ( set @ A ) @ B6 @ A6 ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_235_chainsD,axiom,
% 2.75/1.57 ! [A: $tType,C2: set @ ( set @ A ),S: set @ ( set @ A ),X: set @ A,Y: set @ A] :
% 2.75/1.57 ( ( member @ ( set @ ( set @ A ) ) @ C2 @ ( chains @ A @ S ) )
% 2.75/1.57 => ( ( member @ ( set @ A ) @ X @ C2 )
% 2.75/1.57 => ( ( member @ ( set @ A ) @ Y @ C2 )
% 2.75/1.57 => ( ( ord_less_eq @ ( set @ A ) @ X @ Y )
% 2.75/1.57 | ( ord_less_eq @ ( set @ A ) @ Y @ X ) ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_236_chainsD2,axiom,
% 2.75/1.57 ! [A: $tType,C2: set @ ( set @ A ),S: set @ ( set @ A )] :
% 2.75/1.57 ( ( member @ ( set @ ( set @ A ) ) @ C2 @ ( chains @ A @ S ) )
% 2.75/1.57 => ( ord_less_eq @ ( set @ ( set @ A ) ) @ C2 @ S ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_237_Zorn__Lemma2,axiom,
% 2.75/1.57 ! [A: $tType,A4: set @ ( set @ A )] :
% 2.75/1.57 ( ! [X6: set @ ( set @ A )] :
% 2.75/1.57 ( ( member @ ( set @ ( set @ A ) ) @ X6 @ ( chains @ A @ A4 ) )
% 2.75/1.57 => ? [Xa: set @ A] :
% 2.75/1.57 ( ( member @ ( set @ A ) @ Xa @ A4 )
% 2.75/1.57 & ! [Xb: set @ A] :
% 2.75/1.57 ( ( member @ ( set @ A ) @ Xb @ X6 )
% 2.75/1.57 => ( ord_less_eq @ ( set @ A ) @ Xb @ Xa ) ) ) )
% 2.75/1.57 => ? [X6: set @ A] :
% 2.75/1.57 ( ( member @ ( set @ A ) @ X6 @ A4 )
% 2.75/1.57 & ! [Xa: set @ A] :
% 2.75/1.57 ( ( member @ ( set @ A ) @ Xa @ A4 )
% 2.75/1.57 => ( ( ord_less_eq @ ( set @ A ) @ X6 @ Xa )
% 2.75/1.57 => ( Xa = X6 ) ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_238_verit__la__disequality,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( linorder @ A )
% 2.75/1.57 => ! [A3: A,B4: A] :
% 2.75/1.57 ( ( A3 = B4 )
% 2.75/1.57 | ~ ( ord_less_eq @ A @ A3 @ B4 )
% 2.75/1.57 | ~ ( ord_less_eq @ A @ B4 @ A3 ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_239_dual__order_Oantisym,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( order @ A )
% 2.75/1.57 => ! [B4: A,A3: A] :
% 2.75/1.57 ( ( ord_less_eq @ A @ B4 @ A3 )
% 2.75/1.57 => ( ( ord_less_eq @ A @ A3 @ B4 )
% 2.75/1.57 => ( A3 = B4 ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_240_dual__order_Oeq__iff,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( order @ A )
% 2.75/1.57 => ( ( ^ [Y5: A,Z4: A] : ( Y5 = Z4 ) )
% 2.75/1.57 = ( ^ [A2: A,B2: A] :
% 2.75/1.57 ( ( ord_less_eq @ A @ B2 @ A2 )
% 2.75/1.57 & ( ord_less_eq @ A @ A2 @ B2 ) ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_241_dual__order_Otrans,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( order @ A )
% 2.75/1.57 => ! [B4: A,A3: A,C2: A] :
% 2.75/1.57 ( ( ord_less_eq @ A @ B4 @ A3 )
% 2.75/1.57 => ( ( ord_less_eq @ A @ C2 @ B4 )
% 2.75/1.57 => ( ord_less_eq @ A @ C2 @ A3 ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_242_linorder__wlog,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( linorder @ A )
% 2.75/1.57 => ! [P: A > A > $o,A3: A,B4: A] :
% 2.75/1.57 ( ! [A5: A,B3: A] :
% 2.75/1.57 ( ( ord_less_eq @ A @ A5 @ B3 )
% 2.75/1.57 => ( P @ A5 @ B3 ) )
% 2.75/1.57 => ( ! [A5: A,B3: A] :
% 2.75/1.57 ( ( P @ B3 @ A5 )
% 2.75/1.57 => ( P @ A5 @ B3 ) )
% 2.75/1.57 => ( P @ A3 @ B4 ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_243_dual__order_Orefl,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( order @ A )
% 2.75/1.57 => ! [A3: A] : ( ord_less_eq @ A @ A3 @ A3 ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_244_order__trans,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( preorder @ A )
% 2.75/1.57 => ! [X: A,Y: A,Z3: A] :
% 2.75/1.57 ( ( ord_less_eq @ A @ X @ Y )
% 2.75/1.57 => ( ( ord_less_eq @ A @ Y @ Z3 )
% 2.75/1.57 => ( ord_less_eq @ A @ X @ Z3 ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_245_order__class_Oorder_Oantisym,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( order @ A )
% 2.75/1.57 => ! [A3: A,B4: A] :
% 2.75/1.57 ( ( ord_less_eq @ A @ A3 @ B4 )
% 2.75/1.57 => ( ( ord_less_eq @ A @ B4 @ A3 )
% 2.75/1.57 => ( A3 = B4 ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_246_ord__le__eq__trans,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( ord @ A )
% 2.75/1.57 => ! [A3: A,B4: A,C2: A] :
% 2.75/1.57 ( ( ord_less_eq @ A @ A3 @ B4 )
% 2.75/1.57 => ( ( B4 = C2 )
% 2.75/1.57 => ( ord_less_eq @ A @ A3 @ C2 ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_247_ord__eq__le__trans,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( ord @ A )
% 2.75/1.57 => ! [A3: A,B4: A,C2: A] :
% 2.75/1.57 ( ( A3 = B4 )
% 2.75/1.57 => ( ( ord_less_eq @ A @ B4 @ C2 )
% 2.75/1.57 => ( ord_less_eq @ A @ A3 @ C2 ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_248_order__class_Oorder_Oeq__iff,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( order @ A )
% 2.75/1.57 => ( ( ^ [Y5: A,Z4: A] : ( Y5 = Z4 ) )
% 2.75/1.57 = ( ^ [A2: A,B2: A] :
% 2.75/1.57 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.75/1.57 & ( ord_less_eq @ A @ B2 @ A2 ) ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_249_antisym__conv,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( order @ A )
% 2.75/1.57 => ! [Y: A,X: A] :
% 2.75/1.57 ( ( ord_less_eq @ A @ Y @ X )
% 2.75/1.57 => ( ( ord_less_eq @ A @ X @ Y )
% 2.75/1.57 = ( X = Y ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_250_le__cases3,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( linorder @ A )
% 2.75/1.57 => ! [X: A,Y: A,Z3: A] :
% 2.75/1.57 ( ( ( ord_less_eq @ A @ X @ Y )
% 2.75/1.57 => ~ ( ord_less_eq @ A @ Y @ Z3 ) )
% 2.75/1.57 => ( ( ( ord_less_eq @ A @ Y @ X )
% 2.75/1.57 => ~ ( ord_less_eq @ A @ X @ Z3 ) )
% 2.75/1.57 => ( ( ( ord_less_eq @ A @ X @ Z3 )
% 2.75/1.57 => ~ ( ord_less_eq @ A @ Z3 @ Y ) )
% 2.75/1.57 => ( ( ( ord_less_eq @ A @ Z3 @ Y )
% 2.75/1.57 => ~ ( ord_less_eq @ A @ Y @ X ) )
% 2.75/1.57 => ( ( ( ord_less_eq @ A @ Y @ Z3 )
% 2.75/1.57 => ~ ( ord_less_eq @ A @ Z3 @ X ) )
% 2.75/1.57 => ~ ( ( ord_less_eq @ A @ Z3 @ X )
% 2.75/1.57 => ~ ( ord_less_eq @ A @ X @ Y ) ) ) ) ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_251_order_Otrans,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( order @ A )
% 2.75/1.57 => ! [A3: A,B4: A,C2: A] :
% 2.75/1.57 ( ( ord_less_eq @ A @ A3 @ B4 )
% 2.75/1.57 => ( ( ord_less_eq @ A @ B4 @ C2 )
% 2.75/1.57 => ( ord_less_eq @ A @ A3 @ C2 ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_252_le__cases,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( linorder @ A )
% 2.75/1.57 => ! [X: A,Y: A] :
% 2.75/1.57 ( ~ ( ord_less_eq @ A @ X @ Y )
% 2.75/1.57 => ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_253_eq__refl,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( preorder @ A )
% 2.75/1.57 => ! [X: A,Y: A] :
% 2.75/1.57 ( ( X = Y )
% 2.75/1.57 => ( ord_less_eq @ A @ X @ Y ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_254_linear,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( linorder @ A )
% 2.75/1.57 => ! [X: A,Y: A] :
% 2.75/1.57 ( ( ord_less_eq @ A @ X @ Y )
% 2.75/1.57 | ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(fact_255_antisym,axiom,
% 2.75/1.57 ! [A: $tType] :
% 2.75/1.57 ( ( order @ A )
% 2.75/1.57 => ! [X: A,Y: A] :
% 2.75/1.57 ( ( ord_less_eq @ A @ X @ Y )
% 2.75/1.57 => ( ( ord_less_eq @ A @ Y @ X )
% 2.75/1.57 => ( X = Y ) ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(tcon_HOL_Obool___Lattices_Obounded__lattice,axiom,
% 2.75/1.57 bounded_lattice @ $o ).
% 2.75/1.57
% 2.75/1.57 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1,axiom,
% 2.75/1.57 ! [A7: $tType] : ( bounded_lattice @ ( set @ A7 ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(tcon_fun___Lattices_Obounded__lattice_2,axiom,
% 2.75/1.57 ! [A7: $tType,A8: $tType] :
% 2.75/1.57 ( ( bounded_lattice @ A8 )
% 2.75/1.57 => ( bounded_lattice @ ( A7 > A8 ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(tcon_fun___Lattices_Obounded__semilattice__sup__bot,axiom,
% 2.75/1.57 ! [A7: $tType,A8: $tType] :
% 2.75/1.57 ( ( bounded_lattice @ A8 )
% 2.75/1.57 => ( bounde1808546759up_bot @ ( A7 > A8 ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(tcon_fun___Lattices_Osemilattice__sup,axiom,
% 2.75/1.57 ! [A7: $tType,A8: $tType] :
% 2.75/1.57 ( ( semilattice_sup @ A8 )
% 2.75/1.57 => ( semilattice_sup @ ( A7 > A8 ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(tcon_fun___Orderings_Oorder__bot,axiom,
% 2.75/1.57 ! [A7: $tType,A8: $tType] :
% 2.75/1.57 ( ( order_bot @ A8 )
% 2.75/1.57 => ( order_bot @ ( A7 > A8 ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(tcon_fun___Orderings_Opreorder,axiom,
% 2.75/1.57 ! [A7: $tType,A8: $tType] :
% 2.75/1.57 ( ( preorder @ A8 )
% 2.75/1.57 => ( preorder @ ( A7 > A8 ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(tcon_fun___Orderings_Oorder,axiom,
% 2.75/1.57 ! [A7: $tType,A8: $tType] :
% 2.75/1.57 ( ( order @ A8 )
% 2.75/1.57 => ( order @ ( A7 > A8 ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(tcon_fun___Orderings_Oord,axiom,
% 2.75/1.57 ! [A7: $tType,A8: $tType] :
% 2.75/1.57 ( ( ord @ A8 )
% 2.75/1.57 => ( ord @ ( A7 > A8 ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(tcon_fun___Orderings_Obot,axiom,
% 2.75/1.57 ! [A7: $tType,A8: $tType] :
% 2.75/1.57 ( ( bot @ A8 )
% 2.75/1.57 => ( bot @ ( A7 > A8 ) ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(tcon_Int_Oint___Lattices_Osemilattice__sup_3,axiom,
% 2.75/1.57 semilattice_sup @ int ).
% 2.75/1.57
% 2.75/1.57 thf(tcon_Int_Oint___Rings_Olinordered__idom,axiom,
% 2.75/1.57 linordered_idom @ int ).
% 2.75/1.57
% 2.75/1.57 thf(tcon_Int_Oint___Orderings_Opreorder_4,axiom,
% 2.75/1.57 preorder @ int ).
% 2.75/1.57
% 2.75/1.57 thf(tcon_Int_Oint___Orderings_Olinorder,axiom,
% 2.75/1.57 linorder @ int ).
% 2.75/1.57
% 2.75/1.57 thf(tcon_Int_Oint___Orderings_Ono__top,axiom,
% 2.75/1.57 no_top @ int ).
% 2.75/1.57
% 2.75/1.57 thf(tcon_Int_Oint___Orderings_Ono__bot,axiom,
% 2.75/1.57 no_bot @ int ).
% 2.75/1.57
% 2.75/1.57 thf(tcon_Int_Oint___Orderings_Oorder_5,axiom,
% 2.75/1.57 order @ int ).
% 2.75/1.57
% 2.75/1.57 thf(tcon_Int_Oint___Orderings_Oord_6,axiom,
% 2.75/1.57 ord @ int ).
% 2.75/1.57
% 2.75/1.57 thf(tcon_Set_Oset___Lattices_Obounded__semilattice__sup__bot_7,axiom,
% 2.75/1.57 ! [A7: $tType] : ( bounde1808546759up_bot @ ( set @ A7 ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(tcon_Set_Oset___Lattices_Osemilattice__sup_8,axiom,
% 2.75/1.57 ! [A7: $tType] : ( semilattice_sup @ ( set @ A7 ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(tcon_Set_Oset___Orderings_Oorder__bot_9,axiom,
% 2.75/1.57 ! [A7: $tType] : ( order_bot @ ( set @ A7 ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(tcon_Set_Oset___Orderings_Opreorder_10,axiom,
% 2.75/1.57 ! [A7: $tType] : ( preorder @ ( set @ A7 ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(tcon_Set_Oset___Orderings_Oorder_11,axiom,
% 2.75/1.57 ! [A7: $tType] : ( order @ ( set @ A7 ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(tcon_Set_Oset___Orderings_Oord_12,axiom,
% 2.75/1.57 ! [A7: $tType] : ( ord @ ( set @ A7 ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(tcon_Set_Oset___Orderings_Obot_13,axiom,
% 2.75/1.57 ! [A7: $tType] : ( bot @ ( set @ A7 ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(tcon_HOL_Obool___Lattices_Obounded__semilattice__sup__bot_14,axiom,
% 2.75/1.57 bounde1808546759up_bot @ $o ).
% 2.75/1.57
% 2.75/1.57 thf(tcon_HOL_Obool___Lattices_Osemilattice__sup_15,axiom,
% 2.75/1.57 semilattice_sup @ $o ).
% 2.75/1.57
% 2.75/1.57 thf(tcon_HOL_Obool___Orderings_Oorder__bot_16,axiom,
% 2.75/1.57 order_bot @ $o ).
% 2.75/1.57
% 2.75/1.57 thf(tcon_HOL_Obool___Orderings_Opreorder_17,axiom,
% 2.75/1.57 preorder @ $o ).
% 2.75/1.57
% 2.75/1.57 thf(tcon_HOL_Obool___Orderings_Olinorder_18,axiom,
% 2.75/1.57 linorder @ $o ).
% 2.75/1.57
% 2.75/1.57 thf(tcon_HOL_Obool___Orderings_Oorder_19,axiom,
% 2.75/1.57 order @ $o ).
% 2.75/1.57
% 2.75/1.57 thf(tcon_HOL_Obool___Orderings_Oord_20,axiom,
% 2.75/1.57 ord @ $o ).
% 2.75/1.57
% 2.75/1.57 thf(tcon_HOL_Obool___Orderings_Obot_21,axiom,
% 2.75/1.57 bot @ $o ).
% 2.75/1.57
% 2.75/1.57 thf(help_If_3_1_T,axiom,
% 2.75/1.57 ! [P: $o] :
% 2.75/1.57 ( ( P = $true )
% 2.75/1.57 | ( P = $false ) ) ).
% 2.75/1.57
% 2.75/1.57 thf(help_If_2_1_T,axiom,
% 2.75/1.57 ! [A: $tType,X: A,Y: A] :
% 2.75/1.57 ( ( if @ A @ $false @ X @ Y )
% 2.75/1.57 = Y ) ).
% 2.75/1.57
% 2.75/1.57 thf(help_If_1_1_T,axiom,
% 2.75/1.57 ! [A: $tType,X: A,Y: A] :
% 2.75/1.57 ( ( if @ A @ $true @ X @ Y )
% 2.75/1.57 = X ) ).
% 2.75/1.57
% 2.75/1.57 thf(conj_0,conjecture,
% 2.75/1.57 a2 = b ).
% 2.75/1.57 ------------------------
% 2.75/1.59 % (26656)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_26539 for (2999ds/183Mi)
% 2.75/1.59 % (26662)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_26539 for (2999ds/18Mi)
% 2.75/1.59 % (26657)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_26539 for (2999ds/4Mi)
% 2.75/1.59 % (26658)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_26539 for (2999ds/27Mi)
% 2.75/1.59 % (26657)Instruction limit reached!
% 2.75/1.59 % (26657)------------------------------
% 2.75/1.59 % (26657)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.59 % (26657)Termination reason: Unknown
% 2.75/1.59 % (26657)Termination phase: shuffling
% 2.75/1.59
% 2.75/1.59 % (26657)Memory used [KB]: 1407
% 2.75/1.59 % (26657)Time elapsed: 0.003 s
% 2.75/1.59 % (26657)Instructions burned: 6 (million)
% 2.75/1.59 % (26657)------------------------------
% 2.75/1.59 % (26657)------------------------------
% 2.75/1.59 % (26662)Instruction limit reached!
% 2.75/1.59 % (26662)------------------------------
% 2.75/1.59 % (26662)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.59 % (26662)Termination reason: Unknown
% 2.75/1.59 % (26662)Termination phase: shuffling
% 2.75/1.59
% 2.75/1.59 % (26662)Memory used [KB]: 1663
% 2.75/1.59 % (26662)Time elapsed: 0.007 s
% 2.75/1.59 % (26662)Instructions burned: 18 (million)
% 2.75/1.59 % (26662)------------------------------
% 2.75/1.59 % (26662)------------------------------
% 2.75/1.60 % (26659)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_26539 for (2999ds/2Mi)
% 2.75/1.60 % (26659)Instruction limit reached!
% 2.75/1.60 % (26659)------------------------------
% 2.75/1.60 % (26659)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.60 % (26659)Termination reason: Unknown
% 2.92/1.60 % (26659)Termination phase: shuffling
% 2.92/1.60
% 2.92/1.60 % (26659)Memory used [KB]: 1279
% 2.92/1.60 % (26659)Time elapsed: 0.003 s
% 2.92/1.60 % (26659)Instructions burned: 2 (million)
% 2.92/1.60 % (26659)------------------------------
% 2.92/1.60 % (26659)------------------------------
% 2.92/1.60 % (26661)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_26539 for (2999ds/275Mi)
% 2.92/1.60 % (26660)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_26539 for (2999ds/2Mi)
% 2.92/1.60 % (26658)Instruction limit reached!
% 2.92/1.60 % (26658)------------------------------
% 2.92/1.60 % (26658)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.60 % (26658)Termination reason: Unknown
% 2.92/1.60 % (26658)Termination phase: Property scanning
% 2.92/1.60
% 2.92/1.60 % (26658)Memory used [KB]: 1791
% 2.92/1.60 % (26658)Time elapsed: 0.010 s
% 2.92/1.60 % (26658)Instructions burned: 27 (million)
% 2.92/1.60 % (26658)------------------------------
% 2.92/1.60 % (26658)------------------------------
% 2.92/1.60 % (26660)Instruction limit reached!
% 2.92/1.60 % (26660)------------------------------
% 2.92/1.60 % (26660)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.60 % (26660)Termination reason: Unknown
% 2.92/1.60 % (26660)Termination phase: shuffling
% 2.92/1.60
% 2.92/1.60 % (26660)Memory used [KB]: 1407
% 2.92/1.60 % (26660)Time elapsed: 0.004 s
% 2.92/1.60 % (26660)Instructions burned: 2 (million)
% 2.92/1.60 % (26660)------------------------------
% 2.92/1.60 % (26660)------------------------------
% 2.92/1.60 % (26663)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_26539 for (2999ds/3Mi)
% 2.92/1.60 % (26663)Instruction limit reached!
% 2.92/1.60 % (26663)------------------------------
% 2.92/1.60 % (26663)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.60 % (26663)Termination reason: Unknown
% 2.92/1.60 % (26663)Termination phase: shuffling
% 2.92/1.60
% 2.92/1.60 % (26663)Memory used [KB]: 1407
% 2.92/1.60 % (26663)Time elapsed: 0.003 s
% 2.92/1.60 % (26663)Instructions burned: 3 (million)
% 2.92/1.60 % (26663)------------------------------
% 2.92/1.60 % (26663)------------------------------
% 2.92/1.60 % (26664)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_26539 for (2999ds/37Mi)
% 2.92/1.61 % (26666)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_26539 for (2999ds/3Mi)
% 2.92/1.61 % (26666)Instruction limit reached!
% 2.92/1.61 % (26666)------------------------------
% 2.92/1.61 % (26666)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.61 % (26666)Termination reason: Unknown
% 2.92/1.61 % (26666)Termination phase: shuffling
% 2.92/1.61
% 2.92/1.61 % (26666)Memory used [KB]: 1407
% 2.92/1.61 % (26666)Time elapsed: 0.003 s
% 2.92/1.61 % (26666)Instructions burned: 3 (million)
% 2.92/1.61 % (26666)------------------------------
% 2.92/1.61 % (26666)------------------------------
% 2.92/1.61 % (26668)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_26539 for (2999ds/7Mi)
% 2.92/1.61 % (26665)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_26539 for (2999ds/15Mi)
% 2.92/1.61 % (26664)Instruction limit reached!
% 2.92/1.61 % (26664)------------------------------
% 2.92/1.61 % (26664)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.61 % (26664)Termination reason: Unknown
% 2.92/1.61 % (26664)Termination phase: Property scanning
% 2.92/1.61
% 2.92/1.61 % (26664)Memory used [KB]: 2046
% 2.92/1.61 % (26664)Time elapsed: 0.011 s
% 2.92/1.61 % (26664)Instructions burned: 37 (million)
% 2.92/1.61 % (26664)------------------------------
% 2.92/1.61 % (26664)------------------------------
% 2.92/1.62 % (26668)Instruction limit reached!
% 2.92/1.62 % (26668)------------------------------
% 2.92/1.62 % (26668)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.62 % (26668)Termination reason: Unknown
% 2.92/1.62 % (26668)Termination phase: shuffling
% 2.92/1.62
% 2.92/1.62 % (26668)Memory used [KB]: 1535
% 2.92/1.62 % (26668)Time elapsed: 0.005 s
% 2.92/1.62 % (26668)Instructions burned: 9 (million)
% 2.92/1.62 % (26668)------------------------------
% 2.92/1.62 % (26668)------------------------------
% 2.92/1.62 % (26661)Refutation not found, incomplete strategy
% 2.92/1.62 % (26661)------------------------------
% 2.92/1.62 % (26661)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.62 % (26661)Termination reason: Refutation not found, incomplete strategy
% 2.92/1.62
% 2.92/1.62
% 2.92/1.62 % (26667)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_26539 for (2999ds/1041Mi)
% 2.92/1.62 % (26661)Memory used [KB]: 6268
% 2.92/1.62 % (26661)Time elapsed: 0.022 s
% 2.92/1.62 % (26661)Instructions burned: 32 (million)
% 2.92/1.62 % (26661)------------------------------
% 2.92/1.62 % (26661)------------------------------
% 2.92/1.62 % (26669)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_26539 for (2999ds/16Mi)
% 2.92/1.62 % (26665)Instruction limit reached!
% 2.92/1.62 % (26665)------------------------------
% 2.92/1.62 % (26665)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.62 % (26665)Termination reason: Unknown
% 2.92/1.62 % (26665)Termination phase: shuffling
% 2.92/1.62
% 2.92/1.62 % (26665)Memory used [KB]: 1663
% 2.92/1.62 % (26665)Time elapsed: 0.009 s
% 2.92/1.62 % (26665)Instructions burned: 15 (million)
% 2.92/1.62 % (26665)------------------------------
% 2.92/1.62 % (26665)------------------------------
% 2.92/1.62 % (26670)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_26539 for (2999ds/3Mi)
% 2.92/1.62 % (26670)Instruction limit reached!
% 2.92/1.62 % (26670)------------------------------
% 2.92/1.62 % (26670)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.62 % (26670)Termination reason: Unknown
% 2.92/1.62 % (26670)Termination phase: shuffling
% 2.92/1.62
% 2.92/1.62 % (26670)Memory used [KB]: 1407
% 2.92/1.62 % (26670)Time elapsed: 0.002 s
% 2.92/1.62 % (26670)Instructions burned: 3 (million)
% 2.92/1.62 % (26670)------------------------------
% 2.92/1.62 % (26670)------------------------------
% 2.92/1.63 % (26669)Instruction limit reached!
% 2.92/1.63 % (26669)------------------------------
% 2.92/1.63 % (26669)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.63 % (26669)Termination reason: Unknown
% 2.92/1.63 % (26669)Termination phase: shuffling
% 2.92/1.63
% 2.92/1.63 % (26669)Memory used [KB]: 1663
% 2.92/1.63 % (26669)Time elapsed: 0.007 s
% 2.92/1.63 % (26669)Instructions burned: 16 (million)
% 2.92/1.63 % (26669)------------------------------
% 2.92/1.63 % (26669)------------------------------
% 2.92/1.63 % (26676)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_26539 for (2999ds/3Mi)
% 2.92/1.63 % (26672)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_26539 for (2999ds/3Mi)
% 2.92/1.63 % (26675)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_26539 for (2999ds/7Mi)
% 2.92/1.63 % (26676)Instruction limit reached!
% 2.92/1.63 % (26676)------------------------------
% 2.92/1.63 % (26676)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.63 % (26676)Termination reason: Unknown
% 2.92/1.63 % (26676)Termination phase: shuffling
% 2.92/1.63
% 2.92/1.63 % (26676)Memory used [KB]: 1407
% 2.92/1.63 % (26676)Time elapsed: 0.003 s
% 2.92/1.63 % (26676)Instructions burned: 5 (million)
% 2.92/1.63 % (26676)------------------------------
% 2.92/1.63 % (26676)------------------------------
% 2.92/1.63 % (26677)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_26539 for (2999ds/4Mi)
% 2.92/1.63 % (26672)Instruction limit reached!
% 2.92/1.63 % (26672)------------------------------
% 2.92/1.63 % (26672)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.63 % (26672)Termination reason: Unknown
% 2.92/1.63 % (26672)Termination phase: shuffling
% 2.92/1.63
% 2.92/1.63 % (26672)Memory used [KB]: 1407
% 2.92/1.63 % (26672)Time elapsed: 0.004 s
% 2.92/1.63 % (26672)Instructions burned: 3 (million)
% 2.92/1.63 % (26672)------------------------------
% 2.92/1.63 % (26672)------------------------------
% 2.92/1.64 % (26677)Instruction limit reached!
% 2.92/1.64 % (26677)------------------------------
% 2.92/1.64 % (26677)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.64 % (26677)Termination reason: Unknown
% 2.92/1.64 % (26677)Termination phase: shuffling
% 2.92/1.64
% 2.92/1.64 % (26677)Memory used [KB]: 1407
% 2.92/1.64 % (26677)Time elapsed: 0.003 s
% 2.92/1.64 % (26677)Instructions burned: 6 (million)
% 2.92/1.64 % (26677)------------------------------
% 2.92/1.64 % (26677)------------------------------
% 2.92/1.64 % (26675)Instruction limit reached!
% 2.92/1.64 % (26675)------------------------------
% 2.92/1.64 % (26675)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.64 % (26675)Termination reason: Unknown
% 2.92/1.64 % (26675)Termination phase: shuffling
% 2.92/1.64
% 2.92/1.64 % (26675)Memory used [KB]: 1407
% 2.92/1.64 % (26675)Time elapsed: 0.004 s
% 2.92/1.64 % (26675)Instructions burned: 7 (million)
% 2.92/1.64 % (26675)------------------------------
% 2.92/1.64 % (26675)------------------------------
% 2.92/1.64 % (26678)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_26539 for (2999ds/18Mi)
% 2.92/1.64 % (26656)Instruction limit reached!
% 2.92/1.64 % (26656)------------------------------
% 2.92/1.64 % (26656)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.64 % (26656)Termination reason: Unknown
% 2.92/1.64 % (26656)Termination phase: Saturation
% 2.92/1.64
% 2.92/1.64 % (26656)Memory used [KB]: 7164
% 2.92/1.64 % (26656)Time elapsed: 0.055 s
% 2.92/1.64 % (26656)Instructions burned: 185 (million)
% 2.92/1.64 % (26656)------------------------------
% 2.92/1.64 % (26656)------------------------------
% 2.92/1.64 % (26679)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_26539 for (2999ds/710Mi)
% 2.92/1.64 % (26678)Instruction limit reached!
% 2.92/1.64 % (26678)------------------------------
% 2.92/1.64 % (26678)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.64 % (26678)Termination reason: Unknown
% 2.92/1.64 % (26678)Termination phase: shuffling
% 2.92/1.64
% 2.92/1.64 % (26678)Memory used [KB]: 1663
% 2.92/1.64 % (26678)Time elapsed: 0.010 s
% 2.92/1.64 % (26678)Instructions burned: 19 (million)
% 2.92/1.64 % (26678)------------------------------
% 2.92/1.64 % (26678)------------------------------
% 2.92/1.65 % (26681)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_26539 for (2999ds/902Mi)
% 2.92/1.65 % (26682)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_26539 for (2999ds/21Mi)
% 2.92/1.65 % (26680)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_26539 for (2999ds/6Mi)
% 2.92/1.65 % (26691)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_26539 for (2999ds/5Mi)
% 2.92/1.65 % (26691)Instruction limit reached!
% 2.92/1.65 % (26691)------------------------------
% 2.92/1.65 % (26691)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.65 % (26691)Termination reason: Unknown
% 2.92/1.65 % (26691)Termination phase: shuffling
% 2.92/1.65
% 2.92/1.65 % (26691)Memory used [KB]: 1407
% 2.92/1.65 % (26691)Time elapsed: 0.003 s
% 2.92/1.65 % (26691)Instructions burned: 6 (million)
% 2.92/1.65 % (26691)------------------------------
% 2.92/1.65 % (26691)------------------------------
% 2.92/1.65 % (26680)Instruction limit reached!
% 2.92/1.65 % (26680)------------------------------
% 2.92/1.65 % (26680)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.65 % (26680)Termination reason: Unknown
% 2.92/1.65 % (26680)Termination phase: shuffling
% 2.92/1.65
% 2.92/1.65 % (26680)Memory used [KB]: 1407
% 2.92/1.65 % (26680)Time elapsed: 0.005 s
% 2.92/1.65 % (26680)Instructions burned: 6 (million)
% 2.92/1.65 % (26680)------------------------------
% 2.92/1.65 % (26680)------------------------------
% 2.92/1.66 % (26696)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_26539 for (2999ds/6Mi)
% 2.92/1.66 % (26682)Instruction limit reached!
% 2.92/1.66 % (26682)------------------------------
% 2.92/1.66 % (26682)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.66 % (26682)Termination reason: Unknown
% 2.92/1.66 % (26682)Termination phase: shuffling
% 2.92/1.66
% 2.92/1.66 % (26682)Memory used [KB]: 1791
% 2.92/1.66 % (26682)Time elapsed: 0.009 s
% 2.92/1.66 % (26682)Instructions burned: 22 (million)
% 2.92/1.66 % (26682)------------------------------
% 2.92/1.66 % (26682)------------------------------
% 2.92/1.66 % (26679)Refutation not found, incomplete strategy
% 2.92/1.66 % (26679)------------------------------
% 2.92/1.66 % (26679)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.66 % (26679)Termination reason: Refutation not found, incomplete strategy
% 2.92/1.66
% 2.92/1.66
% 2.92/1.66 % (26679)Memory used [KB]: 6268
% 2.92/1.66 % (26679)Time elapsed: 0.012 s
% 2.92/1.66 % (26679)Instructions burned: 31 (million)
% 2.92/1.66 % (26679)------------------------------
% 2.92/1.66 % (26679)------------------------------
% 2.92/1.66 % (26696)Instruction limit reached!
% 2.92/1.66 % (26696)------------------------------
% 2.92/1.66 % (26696)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.66 % (26696)Termination reason: Unknown
% 2.92/1.66 % (26696)Termination phase: shuffling
% 2.92/1.66
% 2.92/1.66 % (26696)Memory used [KB]: 1407
% 2.92/1.66 % (26696)Time elapsed: 0.003 s
% 2.92/1.66 % (26696)Instructions burned: 7 (million)
% 2.92/1.66 % (26696)------------------------------
% 2.92/1.66 % (26696)------------------------------
% 2.92/1.66 % (26699)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_26539 for (2999ds/377Mi)
% 2.92/1.66 % (26700)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_26539 for (2999ds/779Mi)
% 2.92/1.67 % (26701)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_26539 for (2999ds/19Mi)
% 2.92/1.67 % (26702)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_26539 for (2999ds/879Mi)
% 2.92/1.67 % (26703)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_26539 for (2999ds/17Mi)
% 2.92/1.67 % (26701)Instruction limit reached!
% 2.92/1.67 % (26701)------------------------------
% 2.92/1.67 % (26701)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.67 % (26701)Termination reason: Unknown
% 2.92/1.67 % (26701)Termination phase: shuffling
% 2.92/1.67
% 2.92/1.67 % (26701)Memory used [KB]: 1663
% 2.92/1.67 % (26701)Time elapsed: 0.008 s
% 2.92/1.67 % (26701)Instructions burned: 21 (million)
% 2.92/1.67 % (26701)------------------------------
% 2.92/1.67 % (26701)------------------------------
% 2.92/1.67 % (26703)Instruction limit reached!
% 2.92/1.67 % (26703)------------------------------
% 2.92/1.67 % (26703)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.67 % (26703)Termination reason: Unknown
% 2.92/1.67 % (26703)Termination phase: shuffling
% 2.92/1.67
% 2.92/1.67 % (26703)Memory used [KB]: 1663
% 2.92/1.67 % (26703)Time elapsed: 0.008 s
% 2.92/1.67 % (26703)Instructions burned: 17 (million)
% 2.92/1.67 % (26703)------------------------------
% 2.92/1.67 % (26703)------------------------------
% 2.92/1.68 % (26702)Refutation not found, incomplete strategy
% 2.92/1.68 % (26702)------------------------------
% 2.92/1.68 % (26702)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.68 % (26702)Termination reason: Refutation not found, incomplete strategy
% 2.92/1.68
% 2.92/1.68
% 2.92/1.68 % (26702)Memory used [KB]: 6396
% 2.92/1.68 % (26702)Time elapsed: 0.016 s
% 2.92/1.68 % (26702)Instructions burned: 41 (million)
% 2.92/1.68 % (26702)------------------------------
% 2.92/1.68 % (26702)------------------------------
% 2.92/1.68 % (26681)Refutation not found, incomplete strategy
% 2.92/1.68 % (26681)------------------------------
% 2.92/1.68 % (26681)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.68 % (26681)Termination reason: Refutation not found, incomplete strategy
% 2.92/1.68
% 2.92/1.68
% 2.92/1.68 % (26681)Memory used [KB]: 7164
% 2.92/1.68 % (26681)Time elapsed: 0.037 s
% 2.92/1.68 % (26681)Instructions burned: 122 (million)
% 2.92/1.68 % (26704)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_26539 for (2999ds/3Mi)
% 2.92/1.68 % (26681)------------------------------
% 2.92/1.68 % (26681)------------------------------
% 2.92/1.68 % (26704)Instruction limit reached!
% 2.92/1.68 % (26704)------------------------------
% 2.92/1.68 % (26704)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.68 % (26704)Termination reason: Unknown
% 2.92/1.68 % (26704)Termination phase: shuffling
% 2.92/1.68
% 2.92/1.68 % (26704)Memory used [KB]: 1279
% 2.92/1.68 % (26704)Time elapsed: 0.003 s
% 2.92/1.68 % (26704)Instructions burned: 3 (million)
% 2.92/1.68 % (26704)------------------------------
% 2.92/1.68 % (26704)------------------------------
% 2.92/1.68 % (26705)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_26539 for (2999ds/30Mi)
% 2.92/1.69 % (26707)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_26539 for (2999ds/100Mi)
% 2.92/1.69 % (26706)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_26539 for (2999ds/127Mi)
% 2.92/1.69 % (26708)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_26539 for (2999ds/3Mi)
% 2.92/1.69 % (26705)Instruction limit reached!
% 2.92/1.69 % (26705)------------------------------
% 2.92/1.69 % (26705)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.69 % (26705)Termination reason: Unknown
% 2.92/1.69 % (26705)Termination phase: Property scanning
% 2.92/1.69
% 2.92/1.69 % (26705)Memory used [KB]: 1791
% 2.92/1.69 % (26705)Time elapsed: 0.011 s
% 2.92/1.69 % (26705)Instructions burned: 30 (million)
% 2.92/1.69 % (26705)------------------------------
% 2.92/1.69 % (26705)------------------------------
% 2.92/1.69 % (26708)Instruction limit reached!
% 2.92/1.69 % (26708)------------------------------
% 2.92/1.69 % (26708)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.69 % (26708)Termination reason: Unknown
% 2.92/1.69 % (26708)Termination phase: shuffling
% 2.92/1.69
% 2.92/1.69 % (26708)Memory used [KB]: 1407
% 2.92/1.69 % (26708)Time elapsed: 0.003 s
% 2.92/1.69 % (26708)Instructions burned: 3 (million)
% 2.92/1.69 % (26708)------------------------------
% 2.92/1.69 % (26708)------------------------------
% 2.92/1.70 % (26709)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_26539 for (2998ds/20Mi)
% 2.92/1.70 % (26710)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_26539 for (2998ds/86Mi)
% 2.92/1.71 % (26709)Instruction limit reached!
% 2.92/1.71 % (26709)------------------------------
% 2.92/1.71 % (26709)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.71 % (26709)Termination reason: Unknown
% 2.92/1.71 % (26709)Termination phase: Property scanning
% 2.92/1.71
% 2.92/1.71 % (26709)Memory used [KB]: 1791
% 2.92/1.71 % (26709)Time elapsed: 0.009 s
% 2.92/1.71 % (26709)Instructions burned: 22 (million)
% 2.92/1.71 % (26709)------------------------------
% 2.92/1.71 % (26709)------------------------------
% 2.92/1.72 % (26707)Instruction limit reached!
% 2.92/1.72 % (26707)------------------------------
% 2.92/1.72 % (26707)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.72 % (26707)Termination reason: Unknown
% 2.92/1.72 % (26707)Termination phase: Saturation
% 2.92/1.72
% 2.92/1.72 % (26707)Memory used [KB]: 6780
% 2.92/1.72 % (26707)Time elapsed: 0.028 s
% 2.92/1.72 % (26707)Instructions burned: 102 (million)
% 2.92/1.72 % (26707)------------------------------
% 2.92/1.72 % (26707)------------------------------
% 2.92/1.72 % (26711)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_26539 for (2998ds/107Mi)
% 2.92/1.73 % (26712)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_26539 for (2998ds/39Mi)
% 2.92/1.73 % (26710)Instruction limit reached!
% 2.92/1.73 % (26710)------------------------------
% 2.92/1.73 % (26710)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.73 % (26710)Termination reason: Unknown
% 2.92/1.73 % (26710)Termination phase: Property scanning
% 2.92/1.73
% 2.92/1.73 % (26710)Memory used [KB]: 2302
% 2.92/1.73 % (26710)Time elapsed: 0.029 s
% 2.92/1.73 % (26710)Instructions burned: 86 (million)
% 2.92/1.73 % (26710)------------------------------
% 2.92/1.73 % (26710)------------------------------
% 2.92/1.73 % (26706)Instruction limit reached!
% 2.92/1.73 % (26706)------------------------------
% 2.92/1.73 % (26706)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.73 % (26706)Termination reason: Unknown
% 2.92/1.73 % (26706)Termination phase: Saturation
% 2.92/1.73
% 2.92/1.73 % (26706)Memory used [KB]: 6780
% 2.92/1.73 % (26706)Time elapsed: 0.042 s
% 2.92/1.73 % (26706)Instructions burned: 129 (million)
% 2.92/1.73 % (26706)------------------------------
% 2.92/1.73 % (26706)------------------------------
% 2.92/1.74 % (26700)First to succeed.
% 2.92/1.74 % (26700)Refutation found. Thanks to Tanya!
% 2.92/1.74 % SZS status ContradictoryAxioms for DTF2THF_26539
% 2.92/1.74 % SZS output start Proof for DTF2THF_26539
% 2.92/1.74 thf(type_def_5, type, binary1291135688e_Tree: ($tType) > $tType).
% 2.92/1.74 thf(type_def_7, type, set: ($tType) > $tType).
% 2.92/1.74 thf(type_def_8, type, int: $tType).
% 2.92/1.74 thf(type_def_9, type, a: $tType).
% 2.92/1.74 thf(func_def_0, type, binary1291135688e_Tree: ($tType) > $tType).
% 2.92/1.74 thf(func_def_1, type, set: ($tType) > $tType).
% 2.92/1.74 thf(func_def_2, type, int: $tType).
% 2.92/1.74 thf(func_def_3, type, a: $tType).
% 2.92/1.74 thf(func_def_4, type, bounded_lattice: !>[X0: $tType]:($o)).
% 2.92/1.74 thf(func_def_5, type, type: !>[X0: $tType]:($o)).
% 2.92/1.74 thf(func_def_6, type, bot: !>[X0: $tType]:($o)).
% 2.92/1.74 thf(func_def_7, type, ord: !>[X0: $tType]:($o)).
% 2.92/1.74 thf(func_def_8, type, order: !>[X0: $tType]:($o)).
% 2.92/1.74 thf(func_def_9, type, no_bot: !>[X0: $tType]:($o)).
% 2.92/1.74 thf(func_def_10, type, no_top: !>[X0: $tType]:($o)).
% 2.92/1.74 thf(func_def_11, type, linorder: !>[X0: $tType]:($o)).
% 2.92/1.74 thf(func_def_12, type, preorder: !>[X0: $tType]:($o)).
% 2.92/1.74 thf(func_def_13, type, order_bot: !>[X0: $tType]:($o)).
% 2.92/1.74 thf(func_def_14, type, wellorder: !>[X0: $tType]:($o)).
% 2.92/1.74 thf(func_def_15, type, dense_order: !>[X0: $tType]:($o)).
% 2.92/1.74 thf(func_def_16, type, linordered_idom: !>[X0: $tType]:($o)).
% 2.92/1.74 thf(func_def_17, type, linordered_field: !>[X0: $tType]:($o)).
% 2.92/1.74 thf(func_def_18, type, semilattice_sup: !>[X0: $tType]:($o)).
% 2.92/1.74 thf(func_def_19, type, bounde1808546759up_bot: !>[X0: $tType]:($o)).
% 2.92/1.74 thf(func_def_20, type, condit1656338222tinuum: !>[X0: $tType]:($o)).
% 2.92/1.74 thf(func_def_21, type, binary210054475elle_T: !>[X0: $tType]:(binary1291135688e_Tree @ X0 > X0 > binary1291135688e_Tree @ X0 > binary1291135688e_Tree @ X0)).
% 2.92/1.74 thf(func_def_22, type, binary1746293266le_Tip: !>[X0: $tType]:(binary1291135688e_Tree @ X0)).
% 2.92/1.74 thf(func_def_23, type, binary536355927e_Tree: !>[X0: $tType, X1: $tType]:(X0 > (binary1291135688e_Tree @ X1 > X1 > binary1291135688e_Tree @ X1 > X0) > binary1291135688e_Tree @ X1 > X0)).
% 2.92/1.74 thf(func_def_24, type, binary1929596613c_Tree: !>[X0: $tType, X1: $tType]:(X0 > (binary1291135688e_Tree @ X1 > X1 > binary1291135688e_Tree @ X1 > X0 > X0 > X0) > binary1291135688e_Tree @ X1 > X0)).
% 2.92/1.74 thf(func_def_25, type, binary2130109271t_Tree: !>[X0: $tType]:(binary1291135688e_Tree @ X0 > set @ X0)).
% 2.92/1.74 thf(func_def_26, type, binary64540844le_eqs: !>[X0: $tType]:((X0 > int) > X0 > set @ X0)).
% 2.92/1.74 thf(func_def_27, type, binary1653327646_setOf: !>[X0: $tType]:(binary1291135688e_Tree @ X0 > set @ X0)).
% 2.92/1.74 thf(func_def_28, type, binary1610619414edTree: !>[X0: $tType]:((X0 > int) > binary1291135688e_Tree @ X0 > $o)).
% 2.92/1.74 thf(func_def_29, type, binary231205461t_pred: !>[X0: $tType]:((X0 > int) > X0 > X0 > binary1291135688e_Tree @ X0 > $o)).
% 2.92/1.74 thf(func_def_30, type, the: !>[X0: $tType]:((X0 > $o) > X0)).
% 2.92/1.74 thf(func_def_31, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 2.92/1.74 thf(func_def_32, type, semilattice_neutr: !>[X0: $tType]:((X0 > X0 > X0) > X0 > $o)).
% 2.92/1.74 thf(func_def_33, type, sup_sup: !>[X0: $tType]:(X0 > X0 > X0)).
% 2.92/1.74 thf(func_def_34, type, bot_bot: !>[X0: $tType]:(X0)).
% 2.92/1.74 thf(func_def_35, type, ord_less: !>[X0: $tType]:(X0 > X0 > $o)).
% 2.92/1.74 thf(func_def_36, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 2.92/1.74 thf(func_def_37, type, powp: !>[X0: $tType]:((X0 > $o) > set @ X0 > $o)).
% 2.92/1.74 thf(func_def_38, type, inv_imagep: !>[X0: $tType, X1: $tType]:((X0 > X0 > $o) > (X1 > X0) > X1 > X1 > $o)).
% 2.92/1.74 thf(func_def_39, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 2.92/1.74 thf(func_def_40, type, pow: !>[X0: $tType]:(set @ X0 > set @ set @ X0)).
% 2.92/1.74 thf(func_def_41, type, insert: !>[X0: $tType]:(X0 > set @ X0 > set @ X0)).
% 2.92/1.74 thf(func_def_42, type, is_empty: !>[X0: $tType]:(set @ X0 > $o)).
% 2.92/1.74 thf(func_def_43, type, is_singleton: !>[X0: $tType]:(set @ X0 > $o)).
% 2.92/1.74 thf(func_def_44, type, the_elem: !>[X0: $tType]:(set @ X0 > X0)).
% 2.92/1.74 thf(func_def_45, type, chains: !>[X0: $tType]:(set @ set @ X0 > set @ set @ set @ X0)).
% 2.92/1.74 thf(func_def_46, type, pred_chain: !>[X0: $tType]:(set @ X0 > (X0 > X0 > $o) > set @ X0 > $o)).
% 2.92/1.74 thf(func_def_47, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 2.92/1.74 thf(func_def_48, type, a2: a).
% 2.92/1.74 thf(func_def_49, type, b: a).
% 2.92/1.74 thf(func_def_50, type, h: a > int).
% 2.92/1.74 thf(func_def_51, type, t1: binary1291135688e_Tree @ a).
% 2.92/1.74 thf(func_def_52, type, t2: binary1291135688e_Tree @ a).
% 2.92/1.74 thf(func_def_53, type, x: a).
% 2.92/1.74 thf(func_def_72, type, sK1: !>[X0: $tType]:(binary1291135688e_Tree @ X0 > X0 > (X0 > int) > X0)).
% 2.92/1.74 thf(func_def_73, type, sK2: !>[X0: $tType]:(binary1291135688e_Tree @ X0 > (X0 > int) > X0 > X0)).
% 2.92/1.74 thf(func_def_74, type, sK3: !>[X0: $tType]:((X0 > $o) > X0)).
% 2.92/1.74 thf(func_def_75, type, sK4: !>[X0: $tType]:(X0 > X0)).
% 2.92/1.74 thf(func_def_76, type, sK5: !>[X0: $tType]:(set @ X0 > X0)).
% 2.92/1.74 thf(func_def_77, type, sK6: !>[X0: $tType]:((X0 > $o) > set @ X0 > X0)).
% 2.92/1.74 thf(func_def_78, type, sK7: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 2.92/1.74 thf(func_def_79, type, sK8: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 2.92/1.74 thf(func_def_80, type, sK9: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 2.92/1.74 thf(func_def_81, type, sK10: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 2.92/1.74 thf(func_def_82, type, sK11: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 2.92/1.74 thf(func_def_83, type, sK12: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 2.92/1.74 thf(func_def_84, type, sK13: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 2.92/1.74 thf(func_def_85, type, sK14: !>[X0: $tType]:(binary1291135688e_Tree @ X0 > binary1291135688e_Tree @ X0)).
% 2.92/1.74 thf(func_def_86, type, sK15: !>[X0: $tType]:(binary1291135688e_Tree @ X0 > X0)).
% 2.92/1.74 thf(func_def_87, type, sK16: !>[X0: $tType]:(binary1291135688e_Tree @ X0 > binary1291135688e_Tree @ X0)).
% 2.92/1.74 thf(func_def_88, type, sK17: !>[X0: $tType]:(X0 > X0)).
% 2.92/1.74 thf(func_def_89, type, sK18: !>[X0: $tType]:(set @ X0 > set @ X0 > X0)).
% 2.92/1.74 thf(func_def_90, type, sK19: !>[X0: $tType]:(set @ X0 > X0 > set @ X0)).
% 2.92/1.74 thf(func_def_91, type, sK20: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 2.92/1.74 thf(func_def_92, type, sK21: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 2.92/1.74 thf(func_def_93, type, sK22: !>[X0: $tType]:(X0 > X0)).
% 2.92/1.74 thf(func_def_94, type, sK23: !>[X0: $tType]:((X0 > $o) > set @ X0 > X0)).
% 2.92/1.74 thf(func_def_95, type, sK24: !>[X0: $tType]:((X0 > $o) > set @ X0 > X0)).
% 2.92/1.74 thf(func_def_96, type, sK25: !>[X0: $tType]:(X0)).
% 2.92/1.74 thf(func_def_97, type, sK26: !>[X0: $tType]:(X0 > X0)).
% 2.92/1.74 thf(func_def_98, type, sK27: !>[X0: $tType]:(set @ X0 > X0 > set @ X0)).
% 2.92/1.74 thf(func_def_99, type, sK28: !>[X0: $tType]:(X0 > X0)).
% 2.92/1.74 thf(func_def_100, type, sK29: !>[X0: $tType]:((binary1291135688e_Tree @ X0 > $o) > binary1291135688e_Tree @ X0)).
% 2.92/1.74 thf(func_def_101, type, sK30: !>[X0: $tType]:((binary1291135688e_Tree @ X0 > $o) > X0)).
% 2.92/1.74 thf(func_def_102, type, sK31: !>[X0: $tType]:((binary1291135688e_Tree @ X0 > $o) > binary1291135688e_Tree @ X0)).
% 2.92/1.74 thf(func_def_103, type, sK32: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 2.92/1.74 thf(func_def_104, type, sK33: !>[X0: $tType]:(set @ X0 > X0)).
% 2.92/1.74 thf(func_def_105, type, sK34: !>[X0: $tType]:(set @ X0 > X0 > set @ X0 > X0 > set @ X0)).
% 2.92/1.74 thf(func_def_106, type, sK35: !>[X0: $tType]:(X0 > X0)).
% 2.92/1.74 thf(func_def_107, type, sK36: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 2.92/1.74 thf(func_def_108, type, sK37: !>[X0: $tType]:(binary1291135688e_Tree @ X0 > X0 > binary1291135688e_Tree @ X0)).
% 2.92/1.74 thf(func_def_109, type, sK38: !>[X0: $tType]:(binary1291135688e_Tree @ X0 > X0 > binary1291135688e_Tree @ X0)).
% 2.92/1.74 thf(func_def_110, type, sK39: !>[X0: $tType]:(binary1291135688e_Tree @ X0 > X0 > binary1291135688e_Tree @ X0)).
% 2.92/1.74 thf(func_def_111, type, sK40: !>[X0: $tType]:(binary1291135688e_Tree @ X0 > X0 > X0)).
% 2.92/1.74 thf(func_def_112, type, sK41: !>[X0: $tType]:(binary1291135688e_Tree @ X0 > X0 > binary1291135688e_Tree @ X0)).
% 2.92/1.74 thf(func_def_113, type, sK42: !>[X0: $tType]:(binary1291135688e_Tree @ X0 > X0 > binary1291135688e_Tree @ X0)).
% 2.92/1.74 thf(func_def_114, type, sK43: !>[X0: $tType]:(binary1291135688e_Tree @ X0 > X0 > binary1291135688e_Tree @ X0)).
% 2.92/1.74 thf(func_def_115, type, sK44: !>[X0: $tType]:(binary1291135688e_Tree @ X0 > X0 > X0)).
% 2.92/1.74 thf(f3121,plain,(
% 2.92/1.74 $false),
% 2.92/1.74 inference(trivial_inequality_removal,[status(thm)],[f3119])).
% 2.92/1.74 thf(f3119,plain,(
% 2.92/1.74 ($true = $false)),
% 2.92/1.74 inference(backward_demodulation,[status(thm)],[f1147,f3113])).
% 2.92/1.74 thf(f3113,plain,(
% 2.92/1.74 (order @ int = $false)),
% 2.92/1.74 inference(trivial_inequality_removal,[status(thm)],[f3109])).
% 2.92/1.74 thf(f3109,plain,(
% 2.92/1.74 ((h @ a2) != (h @ a2)) | ($true = $false) | (order @ int = $false)),
% 2.92/1.74 inference(superposition,[status(thm)],[f3095,f1368])).
% 2.92/1.74 thf(f1368,plain,(
% 2.92/1.74 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (((ord_less @ X0 @ X2 @ X1) = $false) | (order @ X0 = $false) | (X1 != X2)) )),
% 2.92/1.74 inference(equality_proxy_clausification,[status(thm)],[f1367])).
% 2.92/1.74 thf(f1367,plain,(
% 2.92/1.74 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((order @ X0 = $false) | ((X2 = X1) = $false) | ((ord_less @ X0 @ X2 @ X1) = $false)) )),
% 2.92/1.74 inference(not_proxy_clausification,[status(thm)],[f1366])).
% 2.92/1.74 thf(f1366,plain,(
% 2.92/1.74 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = (~ (X2 = X1))) | (order @ X0 = $false) | ((ord_less @ X0 @ X2 @ X1) = $false)) )),
% 2.92/1.74 inference(binary_proxy_clausification,[status(thm)],[f1365])).
% 2.92/1.74 thf(f1365,plain,(
% 2.92/1.74 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((order @ X0 = $false) | (((ord_less @ X0 @ X2 @ X1) => (~ (X2 = X1))) = $true)) )),
% 2.92/1.74 inference(beta_eta_normalization,[status(thm)],[f1364])).
% 2.92/1.74 thf(f1364,plain,(
% 2.92/1.74 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((order @ X0 = $false) | (((^[Y0 : X0]: ((ord_less @ X0 @ Y0 @ X1) => (~ (Y0 = X1)))) @ X2) = $true)) )),
% 2.92/1.74 inference(pi_clausification,[status(thm)],[f1363])).
% 2.92/1.74 thf(f1363,plain,(
% 2.92/1.74 ( ! [X0 : $tType,X1 : X0] : (($true = (!! @ X0 @ (^[Y0 : X0]: ((ord_less @ X0 @ Y0 @ X1) => (~ (Y0 = X1)))))) | (order @ X0 = $false)) )),
% 2.92/1.74 inference(beta_eta_normalization,[status(thm)],[f1362])).
% 2.92/1.74 thf(f1362,plain,(
% 2.92/1.74 ( ! [X0 : $tType,X1 : X0] : ((order @ X0 = $false) | ($true = ((^[Y0 : X0]: (!! @ X0 @ (^[Y1 : X0]: ((ord_less @ X0 @ Y1 @ Y0) => (~ (Y1 = Y0)))))) @ X1))) )),
% 2.92/1.74 inference(pi_clausification,[status(thm)],[f1361])).
% 2.92/1.74 thf(f1361,plain,(
% 2.92/1.74 ( ! [X0 : $tType] : ((order @ X0 = $false) | ((!! @ X0 @ (^[Y0 : X0]: (!! @ X0 @ (^[Y1 : X0]: ((ord_less @ X0 @ Y1 @ Y0) => (~ (Y1 = Y0))))))) = $true)) )),
% 2.92/1.74 inference(binary_proxy_clausification,[status(thm)],[f1058])).
% 2.92/1.74 thf(f1058,plain,(
% 2.92/1.74 ( ! [X0 : $tType] : (($true = (order @ X0 => (!! @ X0 @ (^[Y0 : X0]: (!! @ X0 @ (^[Y1 : X0]: ((ord_less @ X0 @ Y1 @ Y0) => (~ (Y1 = Y0)))))))))) )),
% 2.92/1.74 inference(cnf_transformation,[status(thm)],[f1006])).
% 2.92/1.74 thf(f1006,plain,(
% 2.92/1.74 ! [X0 : $tType] : ($true = (order @ X0 => (!! @ X0 @ (^[Y0 : X0]: (!! @ X0 @ (^[Y1 : X0]: ((ord_less @ X0 @ Y1 @ Y0) => (~ (Y1 = Y0)))))))))),
% 2.92/1.74 inference(closure,[status(thm)],[f372])).
% 2.92/1.74 thf(f372,plain,(
% 2.92/1.74 ( ! [X0 : $tType] : (($true = (order @ X0 => (!! @ X0 @ (^[Y0 : X0]: (!! @ X0 @ (^[Y1 : X0]: ((ord_less @ X0 @ Y1 @ Y0) => (~ (Y1 = Y0)))))))))) )),
% 2.92/1.74 inference(fool_elimination,[status(thm)],[f371])).
% 2.92/1.74 thf(f371,plain,(
% 2.92/1.74 ! [X0 : $tType] : (order @ X0 => ! [X1 : X0,X2 : X0] : ((ord_less @ X0 @ X1 @ X2) => (X1 != X2)))),
% 2.92/1.74 inference(rectify,[status(thm)],[f52])).
% 2.92/1.74 thf(f52,axiom,(
% 2.92/1.74 ! [X0 : $tType] : (order @ X0 => ! [X38 : X0,X40 : X0] : ((ord_less @ X0 @ X38 @ X40) => (X38 != X40)))),
% 2.92/1.74 file('/export/starexec/sandbox/tmp/tmp.YQ97kakufk/DTF2THF_26539.p',fact_51_order_Ostrict__implies__not__eq)).
% 2.92/1.74 thf(f3095,plain,(
% 2.92/1.74 ((ord_less @ int @ (h @ a2) @ (h @ a2)) = $true)),
% 2.92/1.74 inference(forward_demodulation,[status(thm)],[f1113,f1140])).
% 2.92/1.74 thf(f1140,plain,(
% 2.92/1.74 ((h @ a2) = (h @ b))),
% 2.92/1.74 inference(cnf_transformation,[status(thm)],[f471])).
% 2.92/1.74 thf(f471,plain,(
% 2.92/1.74 ((h @ a2) = (h @ b))),
% 2.92/1.74 inference(fool_elimination,[status(thm)],[f1])).
% 2.92/1.74 thf(f1,axiom,(
% 2.92/1.74 ((h @ a2) = (h @ b))),
% 2.92/1.74 file('/export/starexec/sandbox/tmp/tmp.YQ97kakufk/DTF2THF_26539.p',fact_0_hahb)).
% 2.92/1.74 thf(f1113,plain,(
% 2.92/1.74 ((ord_less @ int @ (h @ b) @ (h @ a2)) = $true)),
% 2.92/1.74 inference(cnf_transformation,[status(thm)],[f319])).
% 2.92/1.74 thf(f319,plain,(
% 2.92/1.74 ((ord_less @ int @ (h @ b) @ (h @ a2)) = $true)),
% 2.92/1.74 inference(fool_elimination,[status(thm)],[f318])).
% 2.92/1.74 thf(f318,plain,(
% 2.92/1.74 (ord_less @ int @ (h @ b) @ (h @ a2))),
% 2.92/1.74 inference(rectify,[status(thm)],[f2])).
% 2.92/1.74 thf(f2,axiom,(
% 2.92/1.74 (ord_less @ int @ (h @ b) @ (h @ a2))),
% 2.92/1.74 file('/export/starexec/sandbox/tmp/tmp.YQ97kakufk/DTF2THF_26539.p',fact_1__092_060open_062h_Ab_A_060_Ah_Aa_092_060close_062)).
% 2.92/1.74 thf(f1147,plain,(
% 2.92/1.74 (order @ int = $true)),
% 2.92/1.74 inference(cnf_transformation,[status(thm)],[f349])).
% 2.92/1.74 thf(f349,plain,(
% 2.92/1.74 (order @ int = $true)),
% 2.92/1.74 inference(fool_elimination,[status(thm)],[f348])).
% 2.92/1.74 thf(f348,plain,(
% 2.92/1.74 order @ int),
% 2.92/1.74 inference(rectify,[status(thm)],[f273])).
% 2.92/1.74 thf(f273,axiom,(
% 2.92/1.74 order @ int),
% 2.92/1.74 file('/export/starexec/sandbox/tmp/tmp.YQ97kakufk/DTF2THF_26539.p',tcon_Int_Oint___Orderings_Oorder_5)).
% 2.92/1.74 % SZS output end Proof for DTF2THF_26539
% 2.92/1.74 % (26700)------------------------------
% 2.92/1.74 % (26700)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.74 % (26700)Termination reason: Refutation
% 2.92/1.74
% 2.92/1.74 % (26700)Memory used [KB]: 7547
% 2.92/1.74 % (26700)Time elapsed: 0.075 s
% 2.92/1.74 % (26700)Instructions burned: 244 (million)
% 2.92/1.74 % (26700)------------------------------
% 2.92/1.74 % (26700)------------------------------
% 2.92/1.74 % (26655)Success in time 0.167 s
%------------------------------------------------------------------------------