TSTP Solution File: ITP070^1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP070^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 03:17:57 EDT 2023
% Result : Theorem 0.67s 0.87s
% Output : Proof 0.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.15 % Problem : ITP070^1 : TPTP v8.1.2. Released v7.5.0.
% 0.12/0.17 % Command : do_cvc5 %s %d
% 0.18/0.38 % Computer : n015.cluster.edu
% 0.18/0.38 % Model : x86_64 x86_64
% 0.18/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.38 % Memory : 8042.1875MB
% 0.18/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.38 % CPULimit : 300
% 0.18/0.38 % WCLimit : 300
% 0.18/0.38 % DateTime : Sun Aug 27 12:51:09 EDT 2023
% 0.18/0.38 % CPUTime :
% 0.25/0.55 %----Proving TH0
% 0.25/0.56 %------------------------------------------------------------------------------
% 0.25/0.56 % File : ITP070^1 : TPTP v8.1.2. Released v7.5.0.
% 0.25/0.56 % Domain : Interactive Theorem Proving
% 0.25/0.56 % Problem : Sledgehammer HeapImperative problem prob_824__5349520_1
% 0.25/0.56 % Version : Especial.
% 0.25/0.56 % English :
% 0.25/0.56
% 0.25/0.56 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.25/0.56 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.25/0.56 % Source : [Des21]
% 0.25/0.56 % Names : HeapImperative/prob_824__5349520_1 [Des21]
% 0.25/0.56
% 0.25/0.56 % Status : Theorem
% 0.25/0.56 % Rating : 0.31 v8.1.0, 0.27 v7.5.0
% 0.25/0.56 % Syntax : Number of formulae : 269 ( 98 unt; 54 typ; 0 def)
% 0.25/0.56 % Number of atoms : 653 ( 280 equ; 0 cnn)
% 0.25/0.56 % Maximal formula atoms : 12 ( 3 avg)
% 0.25/0.56 % Number of connectives : 2679 ( 90 ~; 7 |; 54 &;2166 @)
% 0.25/0.56 % ( 0 <=>; 362 =>; 0 <=; 0 <~>)
% 0.25/0.56 % Maximal formula depth : 25 ( 8 avg)
% 0.25/0.56 % Number of types : 8 ( 7 usr)
% 0.25/0.56 % Number of type conns : 343 ( 343 >; 0 *; 0 +; 0 <<)
% 0.25/0.56 % Number of symbols : 50 ( 47 usr; 11 con; 0-6 aty)
% 0.25/0.56 % Number of variables : 852 ( 52 ^; 787 !; 13 ?; 852 :)
% 0.25/0.56 % SPC : TH0_THM_EQU_NAR
% 0.25/0.56
% 0.25/0.56 % Comments : This file was generated by Sledgehammer 2021-02-23 15:31:22.775
% 0.25/0.56 %------------------------------------------------------------------------------
% 0.25/0.56 % Could-be-implicit typings (7)
% 0.25/0.56 thf(ty_n_t__Product____Type__Oprod_It__Heap__OTree_Itf__a_J_Mt__List__Olist_Itf__a_J_J,type,
% 0.25/0.56 produc768687417list_a: $tType ).
% 0.25/0.56
% 0.25/0.56 thf(ty_n_t__Product____Type__Oprod_Itf__a_Mt__Heap__OTree_Itf__a_J_J,type,
% 0.25/0.56 produc143150363Tree_a: $tType ).
% 0.25/0.56
% 0.25/0.56 thf(ty_n_t__Multiset__Omultiset_Itf__a_J,type,
% 0.25/0.56 multiset_a: $tType ).
% 0.25/0.56
% 0.25/0.56 thf(ty_n_t__List__Olist_Itf__a_J,type,
% 0.25/0.56 list_a: $tType ).
% 0.25/0.56
% 0.25/0.56 thf(ty_n_t__Heap__OTree_Itf__a_J,type,
% 0.25/0.56 tree_a: $tType ).
% 0.25/0.56
% 0.25/0.56 thf(ty_n_t__Set__Oset_Itf__a_J,type,
% 0.25/0.56 set_a: $tType ).
% 0.25/0.56
% 0.25/0.56 thf(ty_n_tf__a,type,
% 0.25/0.56 a: $tType ).
% 0.25/0.56
% 0.25/0.56 % Explicit typings (47)
% 0.25/0.56 thf(sy_c_Groups_Oplus__class_Oplus_001t__Multiset__Omultiset_Itf__a_J,type,
% 0.25/0.56 plus_plus_multiset_a: multiset_a > multiset_a > multiset_a ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Groups_Ozero__class_Ozero_001t__Multiset__Omultiset_Itf__a_J,type,
% 0.25/0.56 zero_zero_multiset_a: multiset_a ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_HeapImperative__Mirabelle__ksbqzsoydx_Oheapify_001tf__a,type,
% 0.25/0.56 heapIm970322378pify_a: tree_a > tree_a ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_HeapImperative__Mirabelle__ksbqzsoydx_Ohs__is__empty_001tf__a,type,
% 0.25/0.56 heapIm229596386mpty_a: tree_a > $o ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_HeapImperative__Mirabelle__ksbqzsoydx_Ohs__of__list_001tf__a,type,
% 0.25/0.56 heapIm1057938560list_a: list_a > tree_a ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_HeapImperative__Mirabelle__ksbqzsoydx_Oleft_001tf__a,type,
% 0.25/0.56 heapIm1140443833left_a: tree_a > tree_a ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_HeapImperative__Mirabelle__ksbqzsoydx_Oof__list__tree_001tf__a,type,
% 0.25/0.56 heapIm1637418125tree_a: list_a > tree_a ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_HeapImperative__Mirabelle__ksbqzsoydx_OremoveLeaf_001tf__a,type,
% 0.25/0.56 heapIm837449470Leaf_a: tree_a > produc143150363Tree_a ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_HeapImperative__Mirabelle__ksbqzsoydx_Oright_001tf__a,type,
% 0.25/0.56 heapIm1257206334ight_a: tree_a > tree_a ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_HeapImperative__Mirabelle__ksbqzsoydx_OsiftDown_001tf__a,type,
% 0.25/0.56 heapIm1091024090Down_a: tree_a > tree_a ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Heap_OHeap_001t__Heap__OTree_Itf__a_J_001tf__a,type,
% 0.25/0.56 heap_Tree_a_a: tree_a > ( tree_a > $o ) > ( list_a > tree_a ) > ( tree_a > multiset_a ) > ( tree_a > tree_a ) > ( tree_a > produc143150363Tree_a ) > $o ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Heap_OHeap__axioms_001t__Heap__OTree_Itf__a_J_001tf__a,type,
% 0.25/0.56 heap_axioms_Tree_a_a: ( tree_a > $o ) > ( list_a > tree_a ) > ( tree_a > multiset_a ) > ( tree_a > tree_a ) > ( tree_a > produc143150363Tree_a ) > $o ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Heap_OTree_OE_001tf__a,type,
% 0.25/0.56 e_a: tree_a ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Heap_OTree_OT_001tf__a,type,
% 0.25/0.56 t_a: a > tree_a > tree_a > tree_a ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Heap_Oin__tree_001tf__a,type,
% 0.25/0.56 in_tree_a: a > tree_a > $o ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Heap_Ois__heap_001tf__a,type,
% 0.25/0.56 is_heap_a: tree_a > $o ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Heap_Omultiset_001tf__a,type,
% 0.25/0.56 multiset_a2: tree_a > multiset_a ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Heap_Oval_001tf__a,type,
% 0.25/0.56 val_a: tree_a > a ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Lattices__Big_Olinorder__class_OMax_001tf__a,type,
% 0.25/0.56 lattic146396397_Max_a: set_a > a ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_List_Olist_OCons_001tf__a,type,
% 0.25/0.56 cons_a: a > list_a > list_a ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Multiset_Oadd__mset_001tf__a,type,
% 0.25/0.56 add_mset_a: a > multiset_a > multiset_a ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Multiset_Ois__empty_001tf__a,type,
% 0.25/0.56 is_empty_a: multiset_a > $o ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Multiset_Oset__mset_001tf__a,type,
% 0.25/0.56 set_mset_a: multiset_a > set_a ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Multiset_Osubseteq__mset_001tf__a,type,
% 0.25/0.56 subseteq_mset_a: multiset_a > multiset_a > $o ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_Eo_M_062_I_Eo_Mtf__a_J_J,type,
% 0.25/0.56 ord_less_eq_o_o_a: ( $o > $o > a ) > ( $o > $o > a ) > $o ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_Eo_Mtf__a_J,type,
% 0.25/0.56 ord_less_eq_o_a: ( $o > a ) > ( $o > a ) > $o ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Multiset__Omultiset_Itf__a_J,type,
% 0.25/0.56 ord_le1199012836iset_a: multiset_a > multiset_a > $o ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__a_J,type,
% 0.25/0.56 ord_less_eq_set_a: set_a > set_a > $o ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Orderings_Oord__class_Oless__eq_001tf__a,type,
% 0.25/0.56 ord_less_eq_a: a > a > $o ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Orderings_Oorder__class_OGreatest_001_062_I_Eo_Mtf__a_J,type,
% 0.25/0.56 order_Greatest_o_a: ( ( $o > a ) > $o ) > $o > a ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Orderings_Oorder__class_OGreatest_001tf__a,type,
% 0.25/0.56 order_Greatest_a: ( a > $o ) > a ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Product__Type_OPair_001t__Heap__OTree_Itf__a_J_001t__List__Olist_Itf__a_J,type,
% 0.25/0.56 produc1352981801list_a: tree_a > list_a > produc768687417list_a ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Product__Type_OPair_001tf__a_001t__Heap__OTree_Itf__a_J,type,
% 0.25/0.56 produc686083979Tree_a: a > tree_a > produc143150363Tree_a ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_RemoveMax_OCollection_Oset_001t__Heap__OTree_Itf__a_J_001tf__a,type,
% 0.25/0.56 set_Tree_a_a: ( tree_a > multiset_a ) > tree_a > set_a ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_RemoveMax_ORemoveMax_001t__Heap__OTree_Itf__a_J_001tf__a,type,
% 0.25/0.56 removeMax_Tree_a_a: tree_a > ( tree_a > $o ) > ( list_a > tree_a ) > ( tree_a > multiset_a ) > ( tree_a > produc143150363Tree_a ) > ( tree_a > $o ) > $o ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_RemoveMax_ORemoveMax_Ossort_H_001t__Heap__OTree_Itf__a_J_001tf__a,type,
% 0.25/0.56 ssort_Tree_a_a: ( tree_a > $o ) > ( tree_a > produc143150363Tree_a ) > tree_a > list_a > list_a ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_RemoveMax_ORemoveMax_Ossort_H__dom_001t__Heap__OTree_Itf__a_J_001tf__a,type,
% 0.25/0.56 ssort_dom_Tree_a_a: ( tree_a > $o ) > ( tree_a > produc143150363Tree_a ) > produc768687417list_a > $o ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_RemoveMax_ORemoveMax__axioms_001t__Heap__OTree_Itf__a_J_001tf__a,type,
% 0.25/0.56 remove301631099ee_a_a: ( tree_a > $o ) > ( list_a > tree_a ) > ( tree_a > multiset_a ) > ( tree_a > produc143150363Tree_a ) > ( tree_a > $o ) > $o ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_Set_OCollect_001tf__a,type,
% 0.25/0.56 collect_a: ( a > $o ) > set_a ).
% 0.25/0.56
% 0.25/0.56 thf(sy_c_member_001tf__a,type,
% 0.25/0.56 member_a: a > set_a > $o ).
% 0.25/0.56
% 0.25/0.56 thf(sy_v_l1____,type,
% 0.25/0.56 l1: tree_a ).
% 0.25/0.56
% 0.25/0.56 thf(sy_v_l2____,type,
% 0.25/0.56 l2: tree_a ).
% 0.25/0.56
% 0.25/0.56 thf(sy_v_r1____,type,
% 0.25/0.56 r1: tree_a ).
% 0.25/0.56
% 0.25/0.56 thf(sy_v_r2____,type,
% 0.25/0.56 r2: tree_a ).
% 0.25/0.56
% 0.25/0.56 thf(sy_v_v1____,type,
% 0.25/0.56 v1: a ).
% 0.25/0.56
% 0.25/0.56 thf(sy_v_v2____,type,
% 0.25/0.56 v2: a ).
% 0.25/0.56
% 0.25/0.56 thf(sy_v_v____,type,
% 0.25/0.56 v: a ).
% 0.25/0.56
% 0.25/0.56 % Relevant facts (214)
% 0.25/0.56 thf(fact_0__092_060open_062v2_A_092_060le_062_Av1_092_060close_062,axiom,
% 0.25/0.56 ord_less_eq_a @ v2 @ v1 ).
% 0.25/0.56
% 0.25/0.56 % \<open>v2 \<le> v1\<close>
% 0.25/0.56 thf(fact_1_True,axiom,
% 0.25/0.56 ord_less_eq_a @ v1 @ v ).
% 0.25/0.56
% 0.25/0.56 % True
% 0.25/0.56 thf(fact_2__C5__2_Ohyps_C_I2_J,axiom,
% 0.25/0.56 ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ v2 @ l2 @ r2 ) ) @ ( val_a @ ( t_a @ v1 @ l1 @ r1 ) ) )
% 0.25/0.56 => ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ v2 @ l2 @ r2 ) ) @ v )
% 0.25/0.56 => ( ( multiset_a2 @ ( heapIm1091024090Down_a @ ( t_a @ v @ ( heapIm1140443833left_a @ ( t_a @ v2 @ l2 @ r2 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ v2 @ l2 @ r2 ) ) ) ) )
% 0.25/0.56 = ( multiset_a2 @ ( t_a @ v @ ( heapIm1140443833left_a @ ( t_a @ v2 @ l2 @ r2 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ v2 @ l2 @ r2 ) ) ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % "5_2.hyps"(2)
% 0.25/0.56 thf(fact_3__C5__2_Ohyps_C_I1_J,axiom,
% 0.25/0.56 ( ( ord_less_eq_a @ ( val_a @ ( t_a @ v2 @ l2 @ r2 ) ) @ ( val_a @ ( t_a @ v1 @ l1 @ r1 ) ) )
% 0.25/0.56 => ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ v1 @ l1 @ r1 ) ) @ v )
% 0.25/0.56 => ( ( multiset_a2 @ ( heapIm1091024090Down_a @ ( t_a @ v @ ( heapIm1140443833left_a @ ( t_a @ v1 @ l1 @ r1 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ v1 @ l1 @ r1 ) ) ) ) )
% 0.25/0.56 = ( multiset_a2 @ ( t_a @ v @ ( heapIm1140443833left_a @ ( t_a @ v1 @ l1 @ r1 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ v1 @ l1 @ r1 ) ) ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % "5_2.hyps"(1)
% 0.25/0.56 thf(fact_4_siftDown__Node,axiom,
% 0.25/0.56 ! [T: tree_a,V: a,L: tree_a,R: tree_a] :
% 0.25/0.56 ( ( T
% 0.25/0.56 = ( t_a @ V @ L @ R ) )
% 0.25/0.56 => ? [L2: tree_a,V2: a,R2: tree_a] :
% 0.25/0.56 ( ( ( heapIm1091024090Down_a @ T )
% 0.25/0.56 = ( t_a @ V2 @ L2 @ R2 ) )
% 0.25/0.56 & ( ord_less_eq_a @ V @ V2 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % siftDown_Node
% 0.25/0.56 thf(fact_5_Tree_Oinject,axiom,
% 0.25/0.56 ! [X21: a,X22: tree_a,X23: tree_a,Y21: a,Y22: tree_a,Y23: tree_a] :
% 0.25/0.56 ( ( ( t_a @ X21 @ X22 @ X23 )
% 0.25/0.56 = ( t_a @ Y21 @ Y22 @ Y23 ) )
% 0.25/0.56 = ( ( X21 = Y21 )
% 0.25/0.56 & ( X22 = Y22 )
% 0.25/0.56 & ( X23 = Y23 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % Tree.inject
% 0.25/0.56 thf(fact_6_heapify_Osimps_I2_J,axiom,
% 0.25/0.56 ! [V: a,L: tree_a,R: tree_a] :
% 0.25/0.56 ( ( heapIm970322378pify_a @ ( t_a @ V @ L @ R ) )
% 0.25/0.56 = ( heapIm1091024090Down_a @ ( t_a @ V @ ( heapIm970322378pify_a @ L ) @ ( heapIm970322378pify_a @ R ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % heapify.simps(2)
% 0.25/0.56 thf(fact_7_siftDown__heap__is__heap,axiom,
% 0.25/0.56 ! [L: tree_a,R: tree_a,T: tree_a,V: a] :
% 0.25/0.56 ( ( is_heap_a @ L )
% 0.25/0.56 => ( ( is_heap_a @ R )
% 0.25/0.56 => ( ( T
% 0.25/0.56 = ( t_a @ V @ L @ R ) )
% 0.25/0.56 => ( is_heap_a @ ( heapIm1091024090Down_a @ T ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % siftDown_heap_is_heap
% 0.25/0.56 thf(fact_8_siftDown__in__tree__set,axiom,
% 0.25/0.56 ( in_tree_a
% 0.25/0.56 = ( ^ [V3: a,T2: tree_a] : ( in_tree_a @ V3 @ ( heapIm1091024090Down_a @ T2 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % siftDown_in_tree_set
% 0.25/0.56 thf(fact_9_left_Osimps,axiom,
% 0.25/0.56 ! [V: a,L: tree_a,R: tree_a] :
% 0.25/0.56 ( ( heapIm1140443833left_a @ ( t_a @ V @ L @ R ) )
% 0.25/0.56 = L ) ).
% 0.25/0.56
% 0.25/0.56 % left.simps
% 0.25/0.56 thf(fact_10_right_Osimps,axiom,
% 0.25/0.56 ! [V: a,L: tree_a,R: tree_a] :
% 0.25/0.56 ( ( heapIm1257206334ight_a @ ( t_a @ V @ L @ R ) )
% 0.25/0.56 = R ) ).
% 0.25/0.56
% 0.25/0.56 % right.simps
% 0.25/0.56 thf(fact_11_siftDown_Osimps_I2_J,axiom,
% 0.25/0.56 ! [V: a] :
% 0.25/0.56 ( ( heapIm1091024090Down_a @ ( t_a @ V @ e_a @ e_a ) )
% 0.25/0.56 = ( t_a @ V @ e_a @ e_a ) ) ).
% 0.25/0.56
% 0.25/0.56 % siftDown.simps(2)
% 0.25/0.56 thf(fact_12_siftDown_Osimps_I1_J,axiom,
% 0.25/0.56 ( ( heapIm1091024090Down_a @ e_a )
% 0.25/0.56 = e_a ) ).
% 0.25/0.56
% 0.25/0.56 % siftDown.simps(1)
% 0.25/0.56 thf(fact_13_in__tree_Osimps_I1_J,axiom,
% 0.25/0.56 ! [V: a] :
% 0.25/0.56 ~ ( in_tree_a @ V @ e_a ) ).
% 0.25/0.56
% 0.25/0.56 % in_tree.simps(1)
% 0.25/0.56 thf(fact_14_is__heap_Osimps_I6_J,axiom,
% 0.25/0.56 ! [V: a,Vd: a,Ve: tree_a,Vf: tree_a,Va: a,Vb: tree_a,Vc: tree_a] :
% 0.25/0.56 ( ( is_heap_a @ ( t_a @ V @ ( t_a @ Vd @ Ve @ Vf ) @ ( t_a @ Va @ Vb @ Vc ) ) )
% 0.25/0.56 = ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Va @ Vb @ Vc ) ) @ V )
% 0.25/0.56 & ( is_heap_a @ ( t_a @ Va @ Vb @ Vc ) )
% 0.25/0.56 & ( ord_less_eq_a @ ( val_a @ ( t_a @ Vd @ Ve @ Vf ) ) @ V )
% 0.25/0.56 & ( is_heap_a @ ( t_a @ Vd @ Ve @ Vf ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % is_heap.simps(6)
% 0.25/0.56 thf(fact_15_is__heap_Osimps_I5_J,axiom,
% 0.25/0.56 ! [V: a,Va: a,Vb: tree_a,Vc: tree_a,Vd: a,Ve: tree_a,Vf: tree_a] :
% 0.25/0.56 ( ( is_heap_a @ ( t_a @ V @ ( t_a @ Va @ Vb @ Vc ) @ ( t_a @ Vd @ Ve @ Vf ) ) )
% 0.25/0.56 = ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Vd @ Ve @ Vf ) ) @ V )
% 0.25/0.56 & ( is_heap_a @ ( t_a @ Vd @ Ve @ Vf ) )
% 0.25/0.56 & ( ord_less_eq_a @ ( val_a @ ( t_a @ Va @ Vb @ Vc ) ) @ V )
% 0.25/0.56 & ( is_heap_a @ ( t_a @ Va @ Vb @ Vc ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % is_heap.simps(5)
% 0.25/0.56 thf(fact_16_is__heap_Osimps_I4_J,axiom,
% 0.25/0.56 ! [V: a,Va: a,Vb: tree_a,Vc: tree_a] :
% 0.25/0.56 ( ( is_heap_a @ ( t_a @ V @ ( t_a @ Va @ Vb @ Vc ) @ e_a ) )
% 0.25/0.56 = ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Va @ Vb @ Vc ) ) @ V )
% 0.25/0.56 & ( is_heap_a @ ( t_a @ Va @ Vb @ Vc ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % is_heap.simps(4)
% 0.25/0.56 thf(fact_17_is__heap_Osimps_I3_J,axiom,
% 0.25/0.56 ! [V: a,Va: a,Vb: tree_a,Vc: tree_a] :
% 0.25/0.56 ( ( is_heap_a @ ( t_a @ V @ e_a @ ( t_a @ Va @ Vb @ Vc ) ) )
% 0.25/0.56 = ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Va @ Vb @ Vc ) ) @ V )
% 0.25/0.56 & ( is_heap_a @ ( t_a @ Va @ Vb @ Vc ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % is_heap.simps(3)
% 0.25/0.56 thf(fact_18_is__heap_Osimps_I2_J,axiom,
% 0.25/0.56 ! [V: a] : ( is_heap_a @ ( t_a @ V @ e_a @ e_a ) ) ).
% 0.25/0.56
% 0.25/0.56 % is_heap.simps(2)
% 0.25/0.56 thf(fact_19_is__heap_Osimps_I1_J,axiom,
% 0.25/0.56 is_heap_a @ e_a ).
% 0.25/0.56
% 0.25/0.56 % is_heap.simps(1)
% 0.25/0.56 thf(fact_20_heapify_Osimps_I1_J,axiom,
% 0.25/0.56 ( ( heapIm970322378pify_a @ e_a )
% 0.25/0.56 = e_a ) ).
% 0.25/0.56
% 0.25/0.56 % heapify.simps(1)
% 0.25/0.56 thf(fact_21_is__heap__max,axiom,
% 0.25/0.56 ! [V: a,T: tree_a] :
% 0.25/0.56 ( ( in_tree_a @ V @ T )
% 0.25/0.56 => ( ( is_heap_a @ T )
% 0.25/0.56 => ( ord_less_eq_a @ V @ ( val_a @ T ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % is_heap_max
% 0.25/0.56 thf(fact_22_heapify__heap__is__heap,axiom,
% 0.25/0.56 ! [T: tree_a] : ( is_heap_a @ ( heapIm970322378pify_a @ T ) ) ).
% 0.25/0.56
% 0.25/0.56 % heapify_heap_is_heap
% 0.25/0.56 thf(fact_23_siftDown__in__tree,axiom,
% 0.25/0.56 ! [T: tree_a] :
% 0.25/0.56 ( ( T != e_a )
% 0.25/0.56 => ( in_tree_a @ ( val_a @ ( heapIm1091024090Down_a @ T ) ) @ T ) ) ).
% 0.25/0.56
% 0.25/0.56 % siftDown_in_tree
% 0.25/0.56 thf(fact_24_is__heap_Ocases,axiom,
% 0.25/0.56 ! [X: tree_a] :
% 0.25/0.56 ( ( X != e_a )
% 0.25/0.56 => ( ! [V4: a] :
% 0.25/0.56 ( X
% 0.25/0.56 != ( t_a @ V4 @ e_a @ e_a ) )
% 0.25/0.56 => ( ! [V4: a,Va2: a,Vb2: tree_a,Vc2: tree_a] :
% 0.25/0.56 ( X
% 0.25/0.56 != ( t_a @ V4 @ e_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 0.25/0.56 => ( ! [V4: a,Va2: a,Vb2: tree_a,Vc2: tree_a] :
% 0.25/0.56 ( X
% 0.25/0.56 != ( t_a @ V4 @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ e_a ) )
% 0.25/0.56 => ~ ! [V4: a,Va2: a,Vb2: tree_a,Vc2: tree_a,Vd2: a,Ve2: tree_a,Vf2: tree_a] :
% 0.25/0.56 ( X
% 0.25/0.56 != ( t_a @ V4 @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % is_heap.cases
% 0.25/0.56 thf(fact_25_Tree_Oexhaust,axiom,
% 0.25/0.56 ! [Y: tree_a] :
% 0.25/0.56 ( ( Y != e_a )
% 0.25/0.56 => ~ ! [X212: a,X222: tree_a,X232: tree_a] :
% 0.25/0.56 ( Y
% 0.25/0.56 != ( t_a @ X212 @ X222 @ X232 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % Tree.exhaust
% 0.25/0.56 thf(fact_26_Tree_Oinduct,axiom,
% 0.25/0.56 ! [P: tree_a > $o,Tree: tree_a] :
% 0.25/0.56 ( ( P @ e_a )
% 0.25/0.56 => ( ! [X1: a,X2: tree_a,X3: tree_a] :
% 0.25/0.56 ( ( P @ X2 )
% 0.25/0.56 => ( ( P @ X3 )
% 0.25/0.56 => ( P @ ( t_a @ X1 @ X2 @ X3 ) ) ) )
% 0.25/0.56 => ( P @ Tree ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % Tree.induct
% 0.25/0.56 thf(fact_27_Tree_Odistinct_I1_J,axiom,
% 0.25/0.56 ! [X21: a,X22: tree_a,X23: tree_a] :
% 0.25/0.56 ( e_a
% 0.25/0.56 != ( t_a @ X21 @ X22 @ X23 ) ) ).
% 0.25/0.56
% 0.25/0.56 % Tree.distinct(1)
% 0.25/0.56 thf(fact_28_siftDown_Osimps_I3_J,axiom,
% 0.25/0.56 ! [Va: a,Vb: tree_a,Vc: tree_a,V: a] :
% 0.25/0.56 ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Va @ Vb @ Vc ) ) @ V )
% 0.25/0.56 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ ( t_a @ Va @ Vb @ Vc ) @ e_a ) )
% 0.25/0.56 = ( t_a @ V @ ( t_a @ Va @ Vb @ Vc ) @ e_a ) ) )
% 0.25/0.56 & ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ Va @ Vb @ Vc ) ) @ V )
% 0.25/0.56 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ ( t_a @ Va @ Vb @ Vc ) @ e_a ) )
% 0.25/0.56 = ( t_a @ ( val_a @ ( t_a @ Va @ Vb @ Vc ) ) @ ( heapIm1091024090Down_a @ ( t_a @ V @ ( heapIm1140443833left_a @ ( t_a @ Va @ Vb @ Vc ) ) @ ( heapIm1257206334ight_a @ ( t_a @ Va @ Vb @ Vc ) ) ) ) @ e_a ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % siftDown.simps(3)
% 0.25/0.56 thf(fact_29_siftDown_Osimps_I4_J,axiom,
% 0.25/0.56 ! [Va: a,Vb: tree_a,Vc: tree_a,V: a] :
% 0.25/0.56 ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Va @ Vb @ Vc ) ) @ V )
% 0.25/0.56 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ e_a @ ( t_a @ Va @ Vb @ Vc ) ) )
% 0.25/0.56 = ( t_a @ V @ e_a @ ( t_a @ Va @ Vb @ Vc ) ) ) )
% 0.25/0.56 & ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ Va @ Vb @ Vc ) ) @ V )
% 0.25/0.56 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ e_a @ ( t_a @ Va @ Vb @ Vc ) ) )
% 0.25/0.56 = ( t_a @ ( val_a @ ( t_a @ Va @ Vb @ Vc ) ) @ e_a @ ( heapIm1091024090Down_a @ ( t_a @ V @ ( heapIm1140443833left_a @ ( t_a @ Va @ Vb @ Vc ) ) @ ( heapIm1257206334ight_a @ ( t_a @ Va @ Vb @ Vc ) ) ) ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % siftDown.simps(4)
% 0.25/0.56 thf(fact_30_val_Osimps,axiom,
% 0.25/0.56 ! [V: a,Uu: tree_a,Uv: tree_a] :
% 0.25/0.56 ( ( val_a @ ( t_a @ V @ Uu @ Uv ) )
% 0.25/0.56 = V ) ).
% 0.25/0.56
% 0.25/0.56 % val.simps
% 0.25/0.56 thf(fact_31_siftDown_Osimps_I5_J,axiom,
% 0.25/0.56 ! [Vd: a,Ve: tree_a,Vf: tree_a,Va: a,Vb: tree_a,Vc: tree_a,V: a] :
% 0.25/0.56 ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Vd @ Ve @ Vf ) ) @ ( val_a @ ( t_a @ Va @ Vb @ Vc ) ) )
% 0.25/0.56 => ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Va @ Vb @ Vc ) ) @ V )
% 0.25/0.56 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ ( t_a @ Va @ Vb @ Vc ) @ ( t_a @ Vd @ Ve @ Vf ) ) )
% 0.25/0.56 = ( t_a @ V @ ( t_a @ Va @ Vb @ Vc ) @ ( t_a @ Vd @ Ve @ Vf ) ) ) )
% 0.25/0.56 & ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ Va @ Vb @ Vc ) ) @ V )
% 0.25/0.56 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ ( t_a @ Va @ Vb @ Vc ) @ ( t_a @ Vd @ Ve @ Vf ) ) )
% 0.25/0.56 = ( t_a @ ( val_a @ ( t_a @ Va @ Vb @ Vc ) ) @ ( heapIm1091024090Down_a @ ( t_a @ V @ ( heapIm1140443833left_a @ ( t_a @ Va @ Vb @ Vc ) ) @ ( heapIm1257206334ight_a @ ( t_a @ Va @ Vb @ Vc ) ) ) ) @ ( t_a @ Vd @ Ve @ Vf ) ) ) ) ) )
% 0.25/0.56 & ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ Vd @ Ve @ Vf ) ) @ ( val_a @ ( t_a @ Va @ Vb @ Vc ) ) )
% 0.25/0.56 => ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Vd @ Ve @ Vf ) ) @ V )
% 0.25/0.56 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ ( t_a @ Va @ Vb @ Vc ) @ ( t_a @ Vd @ Ve @ Vf ) ) )
% 0.25/0.56 = ( t_a @ V @ ( t_a @ Va @ Vb @ Vc ) @ ( t_a @ Vd @ Ve @ Vf ) ) ) )
% 0.25/0.56 & ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ Vd @ Ve @ Vf ) ) @ V )
% 0.25/0.56 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ ( t_a @ Va @ Vb @ Vc ) @ ( t_a @ Vd @ Ve @ Vf ) ) )
% 0.25/0.56 = ( t_a @ ( val_a @ ( t_a @ Vd @ Ve @ Vf ) ) @ ( t_a @ Va @ Vb @ Vc ) @ ( heapIm1091024090Down_a @ ( t_a @ V @ ( heapIm1140443833left_a @ ( t_a @ Vd @ Ve @ Vf ) ) @ ( heapIm1257206334ight_a @ ( t_a @ Vd @ Ve @ Vf ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % siftDown.simps(5)
% 0.25/0.56 thf(fact_32_siftDown_Osimps_I6_J,axiom,
% 0.25/0.56 ! [Va: a,Vb: tree_a,Vc: tree_a,Vd: a,Ve: tree_a,Vf: tree_a,V: a] :
% 0.25/0.56 ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Va @ Vb @ Vc ) ) @ ( val_a @ ( t_a @ Vd @ Ve @ Vf ) ) )
% 0.25/0.56 => ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Vd @ Ve @ Vf ) ) @ V )
% 0.25/0.56 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ ( t_a @ Vd @ Ve @ Vf ) @ ( t_a @ Va @ Vb @ Vc ) ) )
% 0.25/0.56 = ( t_a @ V @ ( t_a @ Vd @ Ve @ Vf ) @ ( t_a @ Va @ Vb @ Vc ) ) ) )
% 0.25/0.56 & ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ Vd @ Ve @ Vf ) ) @ V )
% 0.25/0.56 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ ( t_a @ Vd @ Ve @ Vf ) @ ( t_a @ Va @ Vb @ Vc ) ) )
% 0.25/0.56 = ( t_a @ ( val_a @ ( t_a @ Vd @ Ve @ Vf ) ) @ ( heapIm1091024090Down_a @ ( t_a @ V @ ( heapIm1140443833left_a @ ( t_a @ Vd @ Ve @ Vf ) ) @ ( heapIm1257206334ight_a @ ( t_a @ Vd @ Ve @ Vf ) ) ) ) @ ( t_a @ Va @ Vb @ Vc ) ) ) ) ) )
% 0.25/0.56 & ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ Va @ Vb @ Vc ) ) @ ( val_a @ ( t_a @ Vd @ Ve @ Vf ) ) )
% 0.25/0.56 => ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Va @ Vb @ Vc ) ) @ V )
% 0.25/0.56 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ ( t_a @ Vd @ Ve @ Vf ) @ ( t_a @ Va @ Vb @ Vc ) ) )
% 0.25/0.56 = ( t_a @ V @ ( t_a @ Vd @ Ve @ Vf ) @ ( t_a @ Va @ Vb @ Vc ) ) ) )
% 0.25/0.56 & ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ Va @ Vb @ Vc ) ) @ V )
% 0.25/0.56 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ ( t_a @ Vd @ Ve @ Vf ) @ ( t_a @ Va @ Vb @ Vc ) ) )
% 0.25/0.56 = ( t_a @ ( val_a @ ( t_a @ Va @ Vb @ Vc ) ) @ ( t_a @ Vd @ Ve @ Vf ) @ ( heapIm1091024090Down_a @ ( t_a @ V @ ( heapIm1140443833left_a @ ( t_a @ Va @ Vb @ Vc ) ) @ ( heapIm1257206334ight_a @ ( t_a @ Va @ Vb @ Vc ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % siftDown.simps(6)
% 0.25/0.56 thf(fact_33_in__tree_Osimps_I2_J,axiom,
% 0.25/0.56 ! [V: a,V5: a,L: tree_a,R: tree_a] :
% 0.25/0.56 ( ( in_tree_a @ V @ ( t_a @ V5 @ L @ R ) )
% 0.25/0.56 = ( ( V = V5 )
% 0.25/0.56 | ( in_tree_a @ V @ L )
% 0.25/0.56 | ( in_tree_a @ V @ R ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % in_tree.simps(2)
% 0.25/0.56 thf(fact_34_removeLeaf_Oinduct,axiom,
% 0.25/0.56 ! [P: tree_a > $o,A0: tree_a] :
% 0.25/0.56 ( ! [V4: a] : ( P @ ( t_a @ V4 @ e_a @ e_a ) )
% 0.25/0.56 => ( ! [V4: a,Va2: a,Vb2: tree_a,Vc2: tree_a] :
% 0.25/0.56 ( ( P @ ( t_a @ Va2 @ Vb2 @ Vc2 ) )
% 0.25/0.56 => ( ( P @ ( t_a @ Va2 @ Vb2 @ Vc2 ) )
% 0.25/0.56 => ( P @ ( t_a @ V4 @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ e_a ) ) ) )
% 0.25/0.56 => ( ! [V4: a,Va2: a,Vb2: tree_a,Vc2: tree_a] :
% 0.25/0.56 ( ( P @ ( t_a @ Va2 @ Vb2 @ Vc2 ) )
% 0.25/0.56 => ( ( P @ ( t_a @ Va2 @ Vb2 @ Vc2 ) )
% 0.25/0.56 => ( P @ ( t_a @ V4 @ e_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) ) )
% 0.25/0.56 => ( ! [V4: a,Va2: a,Vb2: tree_a,Vc2: tree_a,Vd2: a,Ve2: tree_a,Vf2: tree_a] :
% 0.25/0.56 ( ( P @ ( t_a @ Va2 @ Vb2 @ Vc2 ) )
% 0.25/0.56 => ( ( P @ ( t_a @ Va2 @ Vb2 @ Vc2 ) )
% 0.25/0.56 => ( P @ ( t_a @ V4 @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) ) ) )
% 0.25/0.56 => ( ! [V4: a,Vd2: a,Ve2: tree_a,Vf2: tree_a,Va2: a,Vb2: tree_a,Vc2: tree_a] :
% 0.25/0.56 ( ( P @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) )
% 0.25/0.56 => ( ( P @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) )
% 0.25/0.56 => ( P @ ( t_a @ V4 @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) ) )
% 0.25/0.56 => ( ( P @ e_a )
% 0.25/0.56 => ( P @ A0 ) ) ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % removeLeaf.induct
% 0.25/0.56 thf(fact_35_removeLeaf_Ocases,axiom,
% 0.25/0.56 ! [X: tree_a] :
% 0.25/0.56 ( ! [V4: a] :
% 0.25/0.56 ( X
% 0.25/0.56 != ( t_a @ V4 @ e_a @ e_a ) )
% 0.25/0.56 => ( ! [V4: a,Va2: a,Vb2: tree_a,Vc2: tree_a] :
% 0.25/0.56 ( X
% 0.25/0.56 != ( t_a @ V4 @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ e_a ) )
% 0.25/0.56 => ( ! [V4: a,Va2: a,Vb2: tree_a,Vc2: tree_a] :
% 0.25/0.56 ( X
% 0.25/0.56 != ( t_a @ V4 @ e_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 0.25/0.56 => ( ! [V4: a,Va2: a,Vb2: tree_a,Vc2: tree_a,Vd2: a,Ve2: tree_a,Vf2: tree_a] :
% 0.25/0.56 ( X
% 0.25/0.56 != ( t_a @ V4 @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) )
% 0.25/0.56 => ( ! [V4: a,Vd2: a,Ve2: tree_a,Vf2: tree_a,Va2: a,Vb2: tree_a,Vc2: tree_a] :
% 0.25/0.56 ( X
% 0.25/0.56 != ( t_a @ V4 @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 0.25/0.56 => ( X = e_a ) ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % removeLeaf.cases
% 0.25/0.56 thf(fact_36_siftDown_Ocases,axiom,
% 0.25/0.56 ! [X: tree_a] :
% 0.25/0.56 ( ( X != e_a )
% 0.25/0.56 => ( ! [V4: a] :
% 0.25/0.56 ( X
% 0.25/0.56 != ( t_a @ V4 @ e_a @ e_a ) )
% 0.25/0.56 => ( ! [V4: a,Va2: a,Vb2: tree_a,Vc2: tree_a] :
% 0.25/0.56 ( X
% 0.25/0.56 != ( t_a @ V4 @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ e_a ) )
% 0.25/0.56 => ( ! [V4: a,Va2: a,Vb2: tree_a,Vc2: tree_a] :
% 0.25/0.56 ( X
% 0.25/0.56 != ( t_a @ V4 @ e_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 0.25/0.56 => ~ ! [V4: a,Va2: a,Vb2: tree_a,Vc2: tree_a,Vd2: a,Ve2: tree_a,Vf2: tree_a] :
% 0.25/0.56 ( X
% 0.25/0.56 != ( t_a @ V4 @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % siftDown.cases
% 0.25/0.56 thf(fact_37_hs__is__empty__def,axiom,
% 0.25/0.56 ( heapIm229596386mpty_a
% 0.25/0.56 = ( ^ [T2: tree_a] : ( T2 = e_a ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % hs_is_empty_def
% 0.25/0.56 thf(fact_38_order__refl,axiom,
% 0.25/0.56 ! [X: $o > a] : ( ord_less_eq_o_a @ X @ X ) ).
% 0.25/0.56
% 0.25/0.56 % order_refl
% 0.25/0.56 thf(fact_39_order__refl,axiom,
% 0.25/0.56 ! [X: a] : ( ord_less_eq_a @ X @ X ) ).
% 0.25/0.56
% 0.25/0.56 % order_refl
% 0.25/0.56 thf(fact_40_heap__top__geq,axiom,
% 0.25/0.56 ! [A: a,T: tree_a] :
% 0.25/0.56 ( ( member_a @ A @ ( set_mset_a @ ( multiset_a2 @ T ) ) )
% 0.25/0.56 => ( ( is_heap_a @ T )
% 0.25/0.56 => ( ord_less_eq_a @ A @ ( val_a @ T ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % heap_top_geq
% 0.25/0.56 thf(fact_41_hs__of__list__def,axiom,
% 0.25/0.56 ( heapIm1057938560list_a
% 0.25/0.56 = ( ^ [L3: list_a] : ( heapIm970322378pify_a @ ( heapIm1637418125tree_a @ L3 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % hs_of_list_def
% 0.25/0.56 thf(fact_42_mem__Collect__eq,axiom,
% 0.25/0.56 ! [A: a,P: a > $o] :
% 0.25/0.56 ( ( member_a @ A @ ( collect_a @ P ) )
% 0.25/0.56 = ( P @ A ) ) ).
% 0.25/0.56
% 0.25/0.56 % mem_Collect_eq
% 0.25/0.56 thf(fact_43_Collect__mem__eq,axiom,
% 0.25/0.56 ! [A2: set_a] :
% 0.25/0.56 ( ( collect_a
% 0.25/0.56 @ ^ [X4: a] : ( member_a @ X4 @ A2 ) )
% 0.25/0.56 = A2 ) ).
% 0.25/0.56
% 0.25/0.56 % Collect_mem_eq
% 0.25/0.56 thf(fact_44_le__funD,axiom,
% 0.25/0.56 ! [F: $o > a,G: $o > a,X: $o] :
% 0.25/0.56 ( ( ord_less_eq_o_a @ F @ G )
% 0.25/0.56 => ( ord_less_eq_a @ ( F @ X ) @ ( G @ X ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % le_funD
% 0.25/0.56 thf(fact_45_le__funE,axiom,
% 0.25/0.56 ! [F: $o > a,G: $o > a,X: $o] :
% 0.25/0.56 ( ( ord_less_eq_o_a @ F @ G )
% 0.25/0.56 => ( ord_less_eq_a @ ( F @ X ) @ ( G @ X ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % le_funE
% 0.25/0.56 thf(fact_46_le__funI,axiom,
% 0.25/0.56 ! [F: $o > a,G: $o > a] :
% 0.25/0.56 ( ! [X5: $o] : ( ord_less_eq_a @ ( F @ X5 ) @ ( G @ X5 ) )
% 0.25/0.56 => ( ord_less_eq_o_a @ F @ G ) ) ).
% 0.25/0.56
% 0.25/0.56 % le_funI
% 0.25/0.56 thf(fact_47_le__fun__def,axiom,
% 0.25/0.56 ( ord_less_eq_o_a
% 0.25/0.56 = ( ^ [F2: $o > a,G2: $o > a] :
% 0.25/0.56 ! [X4: $o] : ( ord_less_eq_a @ ( F2 @ X4 ) @ ( G2 @ X4 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % le_fun_def
% 0.25/0.56 thf(fact_48_order__subst1,axiom,
% 0.25/0.56 ! [A: a,F: ( $o > a ) > a,B: $o > a,C: $o > a] :
% 0.25/0.56 ( ( ord_less_eq_a @ A @ ( F @ B ) )
% 0.25/0.56 => ( ( ord_less_eq_o_a @ B @ C )
% 0.25/0.56 => ( ! [X5: $o > a,Y2: $o > a] :
% 0.25/0.56 ( ( ord_less_eq_o_a @ X5 @ Y2 )
% 0.25/0.56 => ( ord_less_eq_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.25/0.56 => ( ord_less_eq_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order_subst1
% 0.25/0.56 thf(fact_49_order__subst1,axiom,
% 0.25/0.56 ! [A: $o > a,F: a > $o > a,B: a,C: a] :
% 0.25/0.56 ( ( ord_less_eq_o_a @ A @ ( F @ B ) )
% 0.25/0.56 => ( ( ord_less_eq_a @ B @ C )
% 0.25/0.56 => ( ! [X5: a,Y2: a] :
% 0.25/0.56 ( ( ord_less_eq_a @ X5 @ Y2 )
% 0.25/0.56 => ( ord_less_eq_o_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.25/0.56 => ( ord_less_eq_o_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order_subst1
% 0.25/0.56 thf(fact_50_order__subst1,axiom,
% 0.25/0.56 ! [A: $o > a,F: ( $o > a ) > $o > a,B: $o > a,C: $o > a] :
% 0.25/0.56 ( ( ord_less_eq_o_a @ A @ ( F @ B ) )
% 0.25/0.56 => ( ( ord_less_eq_o_a @ B @ C )
% 0.25/0.56 => ( ! [X5: $o > a,Y2: $o > a] :
% 0.25/0.56 ( ( ord_less_eq_o_a @ X5 @ Y2 )
% 0.25/0.56 => ( ord_less_eq_o_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.25/0.56 => ( ord_less_eq_o_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order_subst1
% 0.25/0.56 thf(fact_51_order__subst1,axiom,
% 0.25/0.56 ! [A: a,F: a > a,B: a,C: a] :
% 0.25/0.56 ( ( ord_less_eq_a @ A @ ( F @ B ) )
% 0.25/0.56 => ( ( ord_less_eq_a @ B @ C )
% 0.25/0.56 => ( ! [X5: a,Y2: a] :
% 0.25/0.56 ( ( ord_less_eq_a @ X5 @ Y2 )
% 0.25/0.56 => ( ord_less_eq_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.25/0.56 => ( ord_less_eq_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order_subst1
% 0.25/0.56 thf(fact_52_order__subst2,axiom,
% 0.25/0.56 ! [A: a,B: a,F: a > $o > a,C: $o > a] :
% 0.25/0.56 ( ( ord_less_eq_a @ A @ B )
% 0.25/0.56 => ( ( ord_less_eq_o_a @ ( F @ B ) @ C )
% 0.25/0.56 => ( ! [X5: a,Y2: a] :
% 0.25/0.56 ( ( ord_less_eq_a @ X5 @ Y2 )
% 0.25/0.56 => ( ord_less_eq_o_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.25/0.56 => ( ord_less_eq_o_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order_subst2
% 0.25/0.56 thf(fact_53_order__subst2,axiom,
% 0.25/0.56 ! [A: $o > a,B: $o > a,F: ( $o > a ) > a,C: a] :
% 0.25/0.56 ( ( ord_less_eq_o_a @ A @ B )
% 0.25/0.56 => ( ( ord_less_eq_a @ ( F @ B ) @ C )
% 0.25/0.56 => ( ! [X5: $o > a,Y2: $o > a] :
% 0.25/0.56 ( ( ord_less_eq_o_a @ X5 @ Y2 )
% 0.25/0.56 => ( ord_less_eq_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.25/0.56 => ( ord_less_eq_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order_subst2
% 0.25/0.56 thf(fact_54_order__subst2,axiom,
% 0.25/0.56 ! [A: $o > a,B: $o > a,F: ( $o > a ) > $o > a,C: $o > a] :
% 0.25/0.56 ( ( ord_less_eq_o_a @ A @ B )
% 0.25/0.56 => ( ( ord_less_eq_o_a @ ( F @ B ) @ C )
% 0.25/0.56 => ( ! [X5: $o > a,Y2: $o > a] :
% 0.25/0.56 ( ( ord_less_eq_o_a @ X5 @ Y2 )
% 0.25/0.56 => ( ord_less_eq_o_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.25/0.56 => ( ord_less_eq_o_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order_subst2
% 0.25/0.56 thf(fact_55_order__subst2,axiom,
% 0.25/0.56 ! [A: a,B: a,F: a > a,C: a] :
% 0.25/0.56 ( ( ord_less_eq_a @ A @ B )
% 0.25/0.56 => ( ( ord_less_eq_a @ ( F @ B ) @ C )
% 0.25/0.56 => ( ! [X5: a,Y2: a] :
% 0.25/0.56 ( ( ord_less_eq_a @ X5 @ Y2 )
% 0.25/0.56 => ( ord_less_eq_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.25/0.56 => ( ord_less_eq_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order_subst2
% 0.25/0.56 thf(fact_56_dual__order_Oantisym,axiom,
% 0.25/0.56 ! [B: $o > a,A: $o > a] :
% 0.25/0.56 ( ( ord_less_eq_o_a @ B @ A )
% 0.25/0.56 => ( ( ord_less_eq_o_a @ A @ B )
% 0.25/0.56 => ( A = B ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % dual_order.antisym
% 0.25/0.56 thf(fact_57_dual__order_Oantisym,axiom,
% 0.25/0.56 ! [B: a,A: a] :
% 0.25/0.56 ( ( ord_less_eq_a @ B @ A )
% 0.25/0.56 => ( ( ord_less_eq_a @ A @ B )
% 0.25/0.56 => ( A = B ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % dual_order.antisym
% 0.25/0.56 thf(fact_58_dual__order_Oeq__iff,axiom,
% 0.25/0.56 ( ( ^ [Y3: $o > a,Z: $o > a] : ( Y3 = Z ) )
% 0.25/0.56 = ( ^ [A3: $o > a,B2: $o > a] :
% 0.25/0.56 ( ( ord_less_eq_o_a @ B2 @ A3 )
% 0.25/0.56 & ( ord_less_eq_o_a @ A3 @ B2 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % dual_order.eq_iff
% 0.25/0.56 thf(fact_59_dual__order_Oeq__iff,axiom,
% 0.25/0.56 ( ( ^ [Y3: a,Z: a] : ( Y3 = Z ) )
% 0.25/0.56 = ( ^ [A3: a,B2: a] :
% 0.25/0.56 ( ( ord_less_eq_a @ B2 @ A3 )
% 0.25/0.56 & ( ord_less_eq_a @ A3 @ B2 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % dual_order.eq_iff
% 0.25/0.56 thf(fact_60_dual__order_Otrans,axiom,
% 0.25/0.56 ! [B: $o > a,A: $o > a,C: $o > a] :
% 0.25/0.56 ( ( ord_less_eq_o_a @ B @ A )
% 0.25/0.56 => ( ( ord_less_eq_o_a @ C @ B )
% 0.25/0.56 => ( ord_less_eq_o_a @ C @ A ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % dual_order.trans
% 0.25/0.56 thf(fact_61_dual__order_Otrans,axiom,
% 0.25/0.56 ! [B: a,A: a,C: a] :
% 0.25/0.56 ( ( ord_less_eq_a @ B @ A )
% 0.25/0.56 => ( ( ord_less_eq_a @ C @ B )
% 0.25/0.56 => ( ord_less_eq_a @ C @ A ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % dual_order.trans
% 0.25/0.56 thf(fact_62_linorder__wlog,axiom,
% 0.25/0.56 ! [P: a > a > $o,A: a,B: a] :
% 0.25/0.56 ( ! [A4: a,B3: a] :
% 0.25/0.56 ( ( ord_less_eq_a @ A4 @ B3 )
% 0.25/0.56 => ( P @ A4 @ B3 ) )
% 0.25/0.56 => ( ! [A4: a,B3: a] :
% 0.25/0.56 ( ( P @ B3 @ A4 )
% 0.25/0.56 => ( P @ A4 @ B3 ) )
% 0.25/0.56 => ( P @ A @ B ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % linorder_wlog
% 0.25/0.56 thf(fact_63_dual__order_Orefl,axiom,
% 0.25/0.56 ! [A: $o > a] : ( ord_less_eq_o_a @ A @ A ) ).
% 0.25/0.56
% 0.25/0.56 % dual_order.refl
% 0.25/0.56 thf(fact_64_dual__order_Orefl,axiom,
% 0.25/0.56 ! [A: a] : ( ord_less_eq_a @ A @ A ) ).
% 0.25/0.56
% 0.25/0.56 % dual_order.refl
% 0.25/0.56 thf(fact_65_order__trans,axiom,
% 0.25/0.56 ! [X: $o > a,Y: $o > a,Z2: $o > a] :
% 0.25/0.56 ( ( ord_less_eq_o_a @ X @ Y )
% 0.25/0.56 => ( ( ord_less_eq_o_a @ Y @ Z2 )
% 0.25/0.56 => ( ord_less_eq_o_a @ X @ Z2 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order_trans
% 0.25/0.56 thf(fact_66_order__trans,axiom,
% 0.25/0.56 ! [X: a,Y: a,Z2: a] :
% 0.25/0.56 ( ( ord_less_eq_a @ X @ Y )
% 0.25/0.56 => ( ( ord_less_eq_a @ Y @ Z2 )
% 0.25/0.56 => ( ord_less_eq_a @ X @ Z2 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order_trans
% 0.25/0.56 thf(fact_67_order__class_Oorder_Oantisym,axiom,
% 0.25/0.56 ! [A: $o > a,B: $o > a] :
% 0.25/0.56 ( ( ord_less_eq_o_a @ A @ B )
% 0.25/0.56 => ( ( ord_less_eq_o_a @ B @ A )
% 0.25/0.56 => ( A = B ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order_class.order.antisym
% 0.25/0.56 thf(fact_68_order__class_Oorder_Oantisym,axiom,
% 0.25/0.56 ! [A: a,B: a] :
% 0.25/0.56 ( ( ord_less_eq_a @ A @ B )
% 0.25/0.56 => ( ( ord_less_eq_a @ B @ A )
% 0.25/0.56 => ( A = B ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order_class.order.antisym
% 0.25/0.56 thf(fact_69_ord__le__eq__trans,axiom,
% 0.25/0.56 ! [A: $o > a,B: $o > a,C: $o > a] :
% 0.25/0.56 ( ( ord_less_eq_o_a @ A @ B )
% 0.25/0.56 => ( ( B = C )
% 0.25/0.56 => ( ord_less_eq_o_a @ A @ C ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % ord_le_eq_trans
% 0.25/0.56 thf(fact_70_ord__le__eq__trans,axiom,
% 0.25/0.56 ! [A: a,B: a,C: a] :
% 0.25/0.56 ( ( ord_less_eq_a @ A @ B )
% 0.25/0.56 => ( ( B = C )
% 0.25/0.56 => ( ord_less_eq_a @ A @ C ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % ord_le_eq_trans
% 0.25/0.56 thf(fact_71_ord__eq__le__trans,axiom,
% 0.25/0.56 ! [A: $o > a,B: $o > a,C: $o > a] :
% 0.25/0.56 ( ( A = B )
% 0.25/0.56 => ( ( ord_less_eq_o_a @ B @ C )
% 0.25/0.56 => ( ord_less_eq_o_a @ A @ C ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % ord_eq_le_trans
% 0.25/0.56 thf(fact_72_ord__eq__le__trans,axiom,
% 0.25/0.56 ! [A: a,B: a,C: a] :
% 0.25/0.56 ( ( A = B )
% 0.25/0.56 => ( ( ord_less_eq_a @ B @ C )
% 0.25/0.56 => ( ord_less_eq_a @ A @ C ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % ord_eq_le_trans
% 0.25/0.56 thf(fact_73_order__class_Oorder_Oeq__iff,axiom,
% 0.25/0.56 ( ( ^ [Y3: $o > a,Z: $o > a] : ( Y3 = Z ) )
% 0.25/0.56 = ( ^ [A3: $o > a,B2: $o > a] :
% 0.25/0.56 ( ( ord_less_eq_o_a @ A3 @ B2 )
% 0.25/0.56 & ( ord_less_eq_o_a @ B2 @ A3 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order_class.order.eq_iff
% 0.25/0.56 thf(fact_74_order__class_Oorder_Oeq__iff,axiom,
% 0.25/0.56 ( ( ^ [Y3: a,Z: a] : ( Y3 = Z ) )
% 0.25/0.56 = ( ^ [A3: a,B2: a] :
% 0.25/0.56 ( ( ord_less_eq_a @ A3 @ B2 )
% 0.25/0.56 & ( ord_less_eq_a @ B2 @ A3 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order_class.order.eq_iff
% 0.25/0.56 thf(fact_75_antisym__conv,axiom,
% 0.25/0.56 ! [Y: $o > a,X: $o > a] :
% 0.25/0.56 ( ( ord_less_eq_o_a @ Y @ X )
% 0.25/0.56 => ( ( ord_less_eq_o_a @ X @ Y )
% 0.25/0.56 = ( X = Y ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % antisym_conv
% 0.25/0.56 thf(fact_76_antisym__conv,axiom,
% 0.25/0.56 ! [Y: a,X: a] :
% 0.25/0.56 ( ( ord_less_eq_a @ Y @ X )
% 0.25/0.56 => ( ( ord_less_eq_a @ X @ Y )
% 0.25/0.56 = ( X = Y ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % antisym_conv
% 0.25/0.56 thf(fact_77_le__cases3,axiom,
% 0.25/0.56 ! [X: a,Y: a,Z2: a] :
% 0.25/0.56 ( ( ( ord_less_eq_a @ X @ Y )
% 0.25/0.56 => ~ ( ord_less_eq_a @ Y @ Z2 ) )
% 0.25/0.56 => ( ( ( ord_less_eq_a @ Y @ X )
% 0.25/0.56 => ~ ( ord_less_eq_a @ X @ Z2 ) )
% 0.25/0.56 => ( ( ( ord_less_eq_a @ X @ Z2 )
% 0.25/0.56 => ~ ( ord_less_eq_a @ Z2 @ Y ) )
% 0.25/0.56 => ( ( ( ord_less_eq_a @ Z2 @ Y )
% 0.25/0.56 => ~ ( ord_less_eq_a @ Y @ X ) )
% 0.25/0.56 => ( ( ( ord_less_eq_a @ Y @ Z2 )
% 0.25/0.56 => ~ ( ord_less_eq_a @ Z2 @ X ) )
% 0.25/0.56 => ~ ( ( ord_less_eq_a @ Z2 @ X )
% 0.25/0.56 => ~ ( ord_less_eq_a @ X @ Y ) ) ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % le_cases3
% 0.25/0.56 thf(fact_78_order_Otrans,axiom,
% 0.25/0.56 ! [A: $o > a,B: $o > a,C: $o > a] :
% 0.25/0.56 ( ( ord_less_eq_o_a @ A @ B )
% 0.25/0.56 => ( ( ord_less_eq_o_a @ B @ C )
% 0.25/0.56 => ( ord_less_eq_o_a @ A @ C ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order.trans
% 0.25/0.56 thf(fact_79_order_Otrans,axiom,
% 0.25/0.56 ! [A: a,B: a,C: a] :
% 0.25/0.56 ( ( ord_less_eq_a @ A @ B )
% 0.25/0.56 => ( ( ord_less_eq_a @ B @ C )
% 0.25/0.56 => ( ord_less_eq_a @ A @ C ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order.trans
% 0.25/0.56 thf(fact_80_le__cases,axiom,
% 0.25/0.56 ! [X: a,Y: a] :
% 0.25/0.56 ( ~ ( ord_less_eq_a @ X @ Y )
% 0.25/0.56 => ( ord_less_eq_a @ Y @ X ) ) ).
% 0.25/0.56
% 0.25/0.56 % le_cases
% 0.25/0.56 thf(fact_81_eq__refl,axiom,
% 0.25/0.56 ! [X: $o > a,Y: $o > a] :
% 0.25/0.56 ( ( X = Y )
% 0.25/0.56 => ( ord_less_eq_o_a @ X @ Y ) ) ).
% 0.25/0.56
% 0.25/0.56 % eq_refl
% 0.25/0.56 thf(fact_82_eq__refl,axiom,
% 0.25/0.56 ! [X: a,Y: a] :
% 0.25/0.56 ( ( X = Y )
% 0.25/0.56 => ( ord_less_eq_a @ X @ Y ) ) ).
% 0.25/0.56
% 0.25/0.56 % eq_refl
% 0.25/0.56 thf(fact_83_linear,axiom,
% 0.25/0.56 ! [X: a,Y: a] :
% 0.25/0.56 ( ( ord_less_eq_a @ X @ Y )
% 0.25/0.56 | ( ord_less_eq_a @ Y @ X ) ) ).
% 0.25/0.56
% 0.25/0.56 % linear
% 0.25/0.56 thf(fact_84_antisym,axiom,
% 0.25/0.56 ! [X: $o > a,Y: $o > a] :
% 0.25/0.56 ( ( ord_less_eq_o_a @ X @ Y )
% 0.25/0.56 => ( ( ord_less_eq_o_a @ Y @ X )
% 0.25/0.56 => ( X = Y ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % antisym
% 0.25/0.56 thf(fact_85_antisym,axiom,
% 0.25/0.56 ! [X: a,Y: a] :
% 0.25/0.56 ( ( ord_less_eq_a @ X @ Y )
% 0.25/0.56 => ( ( ord_less_eq_a @ Y @ X )
% 0.25/0.56 => ( X = Y ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % antisym
% 0.25/0.56 thf(fact_86_eq__iff,axiom,
% 0.25/0.56 ( ( ^ [Y3: $o > a,Z: $o > a] : ( Y3 = Z ) )
% 0.25/0.56 = ( ^ [X4: $o > a,Y4: $o > a] :
% 0.25/0.56 ( ( ord_less_eq_o_a @ X4 @ Y4 )
% 0.25/0.56 & ( ord_less_eq_o_a @ Y4 @ X4 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % eq_iff
% 0.25/0.56 thf(fact_87_eq__iff,axiom,
% 0.25/0.56 ( ( ^ [Y3: a,Z: a] : ( Y3 = Z ) )
% 0.25/0.56 = ( ^ [X4: a,Y4: a] :
% 0.25/0.56 ( ( ord_less_eq_a @ X4 @ Y4 )
% 0.25/0.56 & ( ord_less_eq_a @ Y4 @ X4 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % eq_iff
% 0.25/0.56 thf(fact_88_ord__le__eq__subst,axiom,
% 0.25/0.56 ! [A: a,B: a,F: a > $o > a,C: $o > a] :
% 0.25/0.56 ( ( ord_less_eq_a @ A @ B )
% 0.25/0.56 => ( ( ( F @ B )
% 0.25/0.56 = C )
% 0.25/0.56 => ( ! [X5: a,Y2: a] :
% 0.25/0.56 ( ( ord_less_eq_a @ X5 @ Y2 )
% 0.25/0.56 => ( ord_less_eq_o_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.25/0.56 => ( ord_less_eq_o_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % ord_le_eq_subst
% 0.25/0.56 thf(fact_89_ord__le__eq__subst,axiom,
% 0.25/0.56 ! [A: $o > a,B: $o > a,F: ( $o > a ) > a,C: a] :
% 0.25/0.56 ( ( ord_less_eq_o_a @ A @ B )
% 0.25/0.56 => ( ( ( F @ B )
% 0.25/0.56 = C )
% 0.25/0.56 => ( ! [X5: $o > a,Y2: $o > a] :
% 0.25/0.56 ( ( ord_less_eq_o_a @ X5 @ Y2 )
% 0.25/0.56 => ( ord_less_eq_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.25/0.56 => ( ord_less_eq_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % ord_le_eq_subst
% 0.25/0.56 thf(fact_90_ord__le__eq__subst,axiom,
% 0.25/0.56 ! [A: $o > a,B: $o > a,F: ( $o > a ) > $o > a,C: $o > a] :
% 0.25/0.56 ( ( ord_less_eq_o_a @ A @ B )
% 0.25/0.56 => ( ( ( F @ B )
% 0.25/0.56 = C )
% 0.25/0.56 => ( ! [X5: $o > a,Y2: $o > a] :
% 0.25/0.56 ( ( ord_less_eq_o_a @ X5 @ Y2 )
% 0.25/0.56 => ( ord_less_eq_o_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.25/0.56 => ( ord_less_eq_o_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % ord_le_eq_subst
% 0.25/0.56 thf(fact_91_ord__le__eq__subst,axiom,
% 0.25/0.56 ! [A: a,B: a,F: a > a,C: a] :
% 0.25/0.56 ( ( ord_less_eq_a @ A @ B )
% 0.25/0.56 => ( ( ( F @ B )
% 0.25/0.56 = C )
% 0.25/0.56 => ( ! [X5: a,Y2: a] :
% 0.25/0.56 ( ( ord_less_eq_a @ X5 @ Y2 )
% 0.25/0.56 => ( ord_less_eq_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.25/0.56 => ( ord_less_eq_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % ord_le_eq_subst
% 0.25/0.56 thf(fact_92_ord__eq__le__subst,axiom,
% 0.25/0.56 ! [A: $o > a,F: a > $o > a,B: a,C: a] :
% 0.25/0.56 ( ( A
% 0.25/0.56 = ( F @ B ) )
% 0.25/0.56 => ( ( ord_less_eq_a @ B @ C )
% 0.25/0.56 => ( ! [X5: a,Y2: a] :
% 0.25/0.56 ( ( ord_less_eq_a @ X5 @ Y2 )
% 0.25/0.56 => ( ord_less_eq_o_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.25/0.56 => ( ord_less_eq_o_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % ord_eq_le_subst
% 0.25/0.56 thf(fact_93_ord__eq__le__subst,axiom,
% 0.25/0.56 ! [A: a,F: ( $o > a ) > a,B: $o > a,C: $o > a] :
% 0.25/0.56 ( ( A
% 0.25/0.56 = ( F @ B ) )
% 0.25/0.56 => ( ( ord_less_eq_o_a @ B @ C )
% 0.25/0.56 => ( ! [X5: $o > a,Y2: $o > a] :
% 0.25/0.56 ( ( ord_less_eq_o_a @ X5 @ Y2 )
% 0.25/0.56 => ( ord_less_eq_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.25/0.56 => ( ord_less_eq_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % ord_eq_le_subst
% 0.25/0.56 thf(fact_94_ord__eq__le__subst,axiom,
% 0.25/0.56 ! [A: $o > a,F: ( $o > a ) > $o > a,B: $o > a,C: $o > a] :
% 0.25/0.56 ( ( A
% 0.25/0.56 = ( F @ B ) )
% 0.25/0.56 => ( ( ord_less_eq_o_a @ B @ C )
% 0.25/0.56 => ( ! [X5: $o > a,Y2: $o > a] :
% 0.25/0.56 ( ( ord_less_eq_o_a @ X5 @ Y2 )
% 0.25/0.56 => ( ord_less_eq_o_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.25/0.56 => ( ord_less_eq_o_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % ord_eq_le_subst
% 0.25/0.56 thf(fact_95_ord__eq__le__subst,axiom,
% 0.25/0.56 ! [A: a,F: a > a,B: a,C: a] :
% 0.25/0.56 ( ( A
% 0.25/0.56 = ( F @ B ) )
% 0.25/0.56 => ( ( ord_less_eq_a @ B @ C )
% 0.25/0.56 => ( ! [X5: a,Y2: a] :
% 0.25/0.56 ( ( ord_less_eq_a @ X5 @ Y2 )
% 0.25/0.56 => ( ord_less_eq_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.25/0.56 => ( ord_less_eq_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % ord_eq_le_subst
% 0.25/0.56 thf(fact_96_heap__top__max,axiom,
% 0.25/0.56 ! [T: tree_a] :
% 0.25/0.56 ( ( T != e_a )
% 0.25/0.56 => ( ( is_heap_a @ T )
% 0.25/0.56 => ( ( val_a @ T )
% 0.25/0.56 = ( lattic146396397_Max_a @ ( set_mset_a @ ( multiset_a2 @ T ) ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % heap_top_max
% 0.25/0.56 thf(fact_97_of__list__tree_Osimps_I2_J,axiom,
% 0.25/0.56 ! [V: a,Tail: list_a] :
% 0.25/0.56 ( ( heapIm1637418125tree_a @ ( cons_a @ V @ Tail ) )
% 0.25/0.56 = ( t_a @ V @ ( heapIm1637418125tree_a @ Tail ) @ e_a ) ) ).
% 0.25/0.56
% 0.25/0.56 % of_list_tree.simps(2)
% 0.25/0.56 thf(fact_98_Greatest__equality,axiom,
% 0.25/0.56 ! [P: ( $o > a ) > $o,X: $o > a] :
% 0.25/0.56 ( ( P @ X )
% 0.25/0.56 => ( ! [Y2: $o > a] :
% 0.25/0.56 ( ( P @ Y2 )
% 0.25/0.56 => ( ord_less_eq_o_a @ Y2 @ X ) )
% 0.25/0.56 => ( ( order_Greatest_o_a @ P )
% 0.25/0.56 = X ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % Greatest_equality
% 0.25/0.56 thf(fact_99_Greatest__equality,axiom,
% 0.25/0.56 ! [P: a > $o,X: a] :
% 0.25/0.56 ( ( P @ X )
% 0.25/0.56 => ( ! [Y2: a] :
% 0.25/0.56 ( ( P @ Y2 )
% 0.25/0.56 => ( ord_less_eq_a @ Y2 @ X ) )
% 0.25/0.56 => ( ( order_Greatest_a @ P )
% 0.25/0.56 = X ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % Greatest_equality
% 0.25/0.56 thf(fact_100_GreatestI2__order,axiom,
% 0.25/0.56 ! [P: ( $o > a ) > $o,X: $o > a,Q: ( $o > a ) > $o] :
% 0.25/0.56 ( ( P @ X )
% 0.25/0.56 => ( ! [Y2: $o > a] :
% 0.25/0.56 ( ( P @ Y2 )
% 0.25/0.56 => ( ord_less_eq_o_a @ Y2 @ X ) )
% 0.25/0.56 => ( ! [X5: $o > a] :
% 0.25/0.56 ( ( P @ X5 )
% 0.25/0.56 => ( ! [Y5: $o > a] :
% 0.25/0.56 ( ( P @ Y5 )
% 0.25/0.56 => ( ord_less_eq_o_a @ Y5 @ X5 ) )
% 0.25/0.56 => ( Q @ X5 ) ) )
% 0.25/0.56 => ( Q @ ( order_Greatest_o_a @ P ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % GreatestI2_order
% 0.25/0.56 thf(fact_101_GreatestI2__order,axiom,
% 0.25/0.56 ! [P: a > $o,X: a,Q: a > $o] :
% 0.25/0.56 ( ( P @ X )
% 0.25/0.56 => ( ! [Y2: a] :
% 0.25/0.56 ( ( P @ Y2 )
% 0.25/0.56 => ( ord_less_eq_a @ Y2 @ X ) )
% 0.25/0.56 => ( ! [X5: a] :
% 0.25/0.56 ( ( P @ X5 )
% 0.25/0.56 => ( ! [Y5: a] :
% 0.25/0.56 ( ( P @ Y5 )
% 0.25/0.56 => ( ord_less_eq_a @ Y5 @ X5 ) )
% 0.25/0.56 => ( Q @ X5 ) ) )
% 0.25/0.56 => ( Q @ ( order_Greatest_a @ P ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % GreatestI2_order
% 0.25/0.56 thf(fact_102_le__rel__bool__arg__iff,axiom,
% 0.25/0.56 ( ord_less_eq_o_o_a
% 0.25/0.56 = ( ^ [X6: $o > $o > a,Y6: $o > $o > a] :
% 0.25/0.56 ( ( ord_less_eq_o_a @ ( X6 @ $false ) @ ( Y6 @ $false ) )
% 0.25/0.56 & ( ord_less_eq_o_a @ ( X6 @ $true ) @ ( Y6 @ $true ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % le_rel_bool_arg_iff
% 0.25/0.56 thf(fact_103_le__rel__bool__arg__iff,axiom,
% 0.25/0.56 ( ord_less_eq_o_a
% 0.25/0.56 = ( ^ [X6: $o > a,Y6: $o > a] :
% 0.25/0.56 ( ( ord_less_eq_a @ ( X6 @ $false ) @ ( Y6 @ $false ) )
% 0.25/0.56 & ( ord_less_eq_a @ ( X6 @ $true ) @ ( Y6 @ $true ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % le_rel_bool_arg_iff
% 0.25/0.56 thf(fact_104_verit__la__disequality,axiom,
% 0.25/0.56 ! [A: a,B: a] :
% 0.25/0.56 ( ( A = B )
% 0.25/0.56 | ~ ( ord_less_eq_a @ A @ B )
% 0.25/0.56 | ~ ( ord_less_eq_a @ B @ A ) ) ).
% 0.25/0.56
% 0.25/0.56 % verit_la_disequality
% 0.25/0.56 thf(fact_105_list_Oinject,axiom,
% 0.25/0.56 ! [X21: a,X22: list_a,Y21: a,Y22: list_a] :
% 0.25/0.56 ( ( ( cons_a @ X21 @ X22 )
% 0.25/0.56 = ( cons_a @ Y21 @ Y22 ) )
% 0.25/0.56 = ( ( X21 = Y21 )
% 0.25/0.56 & ( X22 = Y22 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % list.inject
% 0.25/0.56 thf(fact_106_not__Cons__self2,axiom,
% 0.25/0.56 ! [X: a,Xs: list_a] :
% 0.25/0.56 ( ( cons_a @ X @ Xs )
% 0.25/0.56 != Xs ) ).
% 0.25/0.56
% 0.25/0.56 % not_Cons_self2
% 0.25/0.56 thf(fact_107_Heap__axioms__def,axiom,
% 0.25/0.56 ( heap_axioms_Tree_a_a
% 0.25/0.56 = ( ^ [Is_empty: tree_a > $o,Of_list: list_a > tree_a,Multiset: tree_a > multiset_a,As_tree: tree_a > tree_a,Remove_max: tree_a > produc143150363Tree_a] :
% 0.25/0.56 ( ! [L3: tree_a] :
% 0.25/0.56 ( ( Multiset @ L3 )
% 0.25/0.56 = ( multiset_a2 @ ( As_tree @ L3 ) ) )
% 0.25/0.56 & ! [I: list_a] : ( is_heap_a @ ( As_tree @ ( Of_list @ I ) ) )
% 0.25/0.56 & ! [T2: tree_a] :
% 0.25/0.56 ( ( ( As_tree @ T2 )
% 0.25/0.56 = e_a )
% 0.25/0.56 = ( Is_empty @ T2 ) )
% 0.25/0.56 & ! [L3: tree_a,M: a,L4: tree_a] :
% 0.25/0.56 ( ~ ( Is_empty @ L3 )
% 0.25/0.56 => ( ( ( produc686083979Tree_a @ M @ L4 )
% 0.25/0.56 = ( Remove_max @ L3 ) )
% 0.25/0.56 => ( ( add_mset_a @ M @ ( Multiset @ L4 ) )
% 0.25/0.56 = ( Multiset @ L3 ) ) ) )
% 0.25/0.56 & ! [L3: tree_a,M: a,L4: tree_a] :
% 0.25/0.56 ( ~ ( Is_empty @ L3 )
% 0.25/0.56 => ( ( is_heap_a @ ( As_tree @ L3 ) )
% 0.25/0.56 => ( ( ( produc686083979Tree_a @ M @ L4 )
% 0.25/0.56 = ( Remove_max @ L3 ) )
% 0.25/0.56 => ( is_heap_a @ ( As_tree @ L4 ) ) ) ) )
% 0.25/0.56 & ! [T2: tree_a,M: a,T3: tree_a] :
% 0.25/0.56 ( ~ ( Is_empty @ T2 )
% 0.25/0.56 => ( ( ( produc686083979Tree_a @ M @ T3 )
% 0.25/0.56 = ( Remove_max @ T2 ) )
% 0.25/0.56 => ( M
% 0.25/0.56 = ( val_a @ ( As_tree @ T2 ) ) ) ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % Heap_axioms_def
% 0.25/0.56 thf(fact_108_Heap__axioms_Ointro,axiom,
% 0.25/0.56 ! [Multiset2: tree_a > multiset_a,As_tree2: tree_a > tree_a,Of_list2: list_a > tree_a,Is_empty2: tree_a > $o,Remove_max2: tree_a > produc143150363Tree_a] :
% 0.25/0.56 ( ! [L5: tree_a] :
% 0.25/0.56 ( ( Multiset2 @ L5 )
% 0.25/0.56 = ( multiset_a2 @ ( As_tree2 @ L5 ) ) )
% 0.25/0.56 => ( ! [I2: list_a] : ( is_heap_a @ ( As_tree2 @ ( Of_list2 @ I2 ) ) )
% 0.25/0.56 => ( ! [T4: tree_a] :
% 0.25/0.56 ( ( ( As_tree2 @ T4 )
% 0.25/0.56 = e_a )
% 0.25/0.56 = ( Is_empty2 @ T4 ) )
% 0.25/0.56 => ( ! [L5: tree_a,M2: a,L2: tree_a] :
% 0.25/0.56 ( ~ ( Is_empty2 @ L5 )
% 0.25/0.56 => ( ( ( produc686083979Tree_a @ M2 @ L2 )
% 0.25/0.56 = ( Remove_max2 @ L5 ) )
% 0.25/0.56 => ( ( add_mset_a @ M2 @ ( Multiset2 @ L2 ) )
% 0.25/0.56 = ( Multiset2 @ L5 ) ) ) )
% 0.25/0.56 => ( ! [L5: tree_a,M2: a,L2: tree_a] :
% 0.25/0.56 ( ~ ( Is_empty2 @ L5 )
% 0.25/0.56 => ( ( is_heap_a @ ( As_tree2 @ L5 ) )
% 0.25/0.56 => ( ( ( produc686083979Tree_a @ M2 @ L2 )
% 0.25/0.56 = ( Remove_max2 @ L5 ) )
% 0.25/0.56 => ( is_heap_a @ ( As_tree2 @ L2 ) ) ) ) )
% 0.25/0.56 => ( ! [T4: tree_a,M2: a,T5: tree_a] :
% 0.25/0.56 ( ~ ( Is_empty2 @ T4 )
% 0.25/0.56 => ( ( ( produc686083979Tree_a @ M2 @ T5 )
% 0.25/0.56 = ( Remove_max2 @ T4 ) )
% 0.25/0.56 => ( M2
% 0.25/0.56 = ( val_a @ ( As_tree2 @ T4 ) ) ) ) )
% 0.25/0.56 => ( heap_axioms_Tree_a_a @ Is_empty2 @ Of_list2 @ Multiset2 @ As_tree2 @ Remove_max2 ) ) ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % Heap_axioms.intro
% 0.25/0.56 thf(fact_109_Heap_Oremove__max__multiset_H,axiom,
% 0.25/0.56 ! [Empty: tree_a,Is_empty2: tree_a > $o,Of_list2: list_a > tree_a,Multiset2: tree_a > multiset_a,As_tree2: tree_a > tree_a,Remove_max2: tree_a > produc143150363Tree_a,L: tree_a,M3: a,L6: tree_a] :
% 0.25/0.56 ( ( heap_Tree_a_a @ Empty @ Is_empty2 @ Of_list2 @ Multiset2 @ As_tree2 @ Remove_max2 )
% 0.25/0.56 => ( ~ ( Is_empty2 @ L )
% 0.25/0.56 => ( ( ( produc686083979Tree_a @ M3 @ L6 )
% 0.25/0.56 = ( Remove_max2 @ L ) )
% 0.25/0.56 => ( ( add_mset_a @ M3 @ ( Multiset2 @ L6 ) )
% 0.25/0.56 = ( Multiset2 @ L ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % Heap.remove_max_multiset'
% 0.25/0.56 thf(fact_110_Heap_Oremove__max__val,axiom,
% 0.25/0.56 ! [Empty: tree_a,Is_empty2: tree_a > $o,Of_list2: list_a > tree_a,Multiset2: tree_a > multiset_a,As_tree2: tree_a > tree_a,Remove_max2: tree_a > produc143150363Tree_a,T: tree_a,M3: a,T6: tree_a] :
% 0.25/0.56 ( ( heap_Tree_a_a @ Empty @ Is_empty2 @ Of_list2 @ Multiset2 @ As_tree2 @ Remove_max2 )
% 0.25/0.56 => ( ~ ( Is_empty2 @ T )
% 0.25/0.56 => ( ( ( produc686083979Tree_a @ M3 @ T6 )
% 0.25/0.56 = ( Remove_max2 @ T ) )
% 0.25/0.56 => ( M3
% 0.25/0.56 = ( val_a @ ( As_tree2 @ T ) ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % Heap.remove_max_val
% 0.25/0.56 thf(fact_111_Heap_Oremove__max__is__heap,axiom,
% 0.25/0.56 ! [Empty: tree_a,Is_empty2: tree_a > $o,Of_list2: list_a > tree_a,Multiset2: tree_a > multiset_a,As_tree2: tree_a > tree_a,Remove_max2: tree_a > produc143150363Tree_a,L: tree_a,M3: a,L6: tree_a] :
% 0.25/0.56 ( ( heap_Tree_a_a @ Empty @ Is_empty2 @ Of_list2 @ Multiset2 @ As_tree2 @ Remove_max2 )
% 0.25/0.56 => ( ~ ( Is_empty2 @ L )
% 0.25/0.56 => ( ( is_heap_a @ ( As_tree2 @ L ) )
% 0.25/0.56 => ( ( ( produc686083979Tree_a @ M3 @ L6 )
% 0.25/0.56 = ( Remove_max2 @ L ) )
% 0.25/0.56 => ( is_heap_a @ ( As_tree2 @ L6 ) ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % Heap.remove_max_is_heap
% 0.25/0.56 thf(fact_112_multi__self__add__other__not__self,axiom,
% 0.25/0.56 ! [M4: multiset_a,X: a] :
% 0.25/0.56 ( M4
% 0.25/0.56 != ( add_mset_a @ X @ M4 ) ) ).
% 0.25/0.56
% 0.25/0.56 % multi_self_add_other_not_self
% 0.25/0.56 thf(fact_113_add__mset__add__mset__same__iff,axiom,
% 0.25/0.56 ! [A: a,A2: multiset_a,B4: multiset_a] :
% 0.25/0.56 ( ( ( add_mset_a @ A @ A2 )
% 0.25/0.56 = ( add_mset_a @ A @ B4 ) )
% 0.25/0.56 = ( A2 = B4 ) ) ).
% 0.25/0.56
% 0.25/0.56 % add_mset_add_mset_same_iff
% 0.25/0.56 thf(fact_114_old_Oprod_Oinject,axiom,
% 0.25/0.56 ! [A: a,B: tree_a,A5: a,B5: tree_a] :
% 0.25/0.56 ( ( ( produc686083979Tree_a @ A @ B )
% 0.25/0.56 = ( produc686083979Tree_a @ A5 @ B5 ) )
% 0.25/0.56 = ( ( A = A5 )
% 0.25/0.56 & ( B = B5 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % old.prod.inject
% 0.25/0.56 thf(fact_115_prod_Oinject,axiom,
% 0.25/0.56 ! [X12: a,X24: tree_a,Y1: a,Y24: tree_a] :
% 0.25/0.56 ( ( ( produc686083979Tree_a @ X12 @ X24 )
% 0.25/0.56 = ( produc686083979Tree_a @ Y1 @ Y24 ) )
% 0.25/0.56 = ( ( X12 = Y1 )
% 0.25/0.56 & ( X24 = Y24 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % prod.inject
% 0.25/0.56 thf(fact_116_mset__add,axiom,
% 0.25/0.56 ! [A: a,A2: multiset_a] :
% 0.25/0.56 ( ( member_a @ A @ ( set_mset_a @ A2 ) )
% 0.25/0.56 => ~ ! [B6: multiset_a] :
% 0.25/0.56 ( A2
% 0.25/0.56 != ( add_mset_a @ A @ B6 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mset_add
% 0.25/0.56 thf(fact_117_multi__member__split,axiom,
% 0.25/0.56 ! [X: a,M4: multiset_a] :
% 0.25/0.56 ( ( member_a @ X @ ( set_mset_a @ M4 ) )
% 0.25/0.56 => ? [A6: multiset_a] :
% 0.25/0.56 ( M4
% 0.25/0.56 = ( add_mset_a @ X @ A6 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % multi_member_split
% 0.25/0.56 thf(fact_118_surj__pair,axiom,
% 0.25/0.56 ! [P2: produc143150363Tree_a] :
% 0.25/0.56 ? [X5: a,Y2: tree_a] :
% 0.25/0.56 ( P2
% 0.25/0.56 = ( produc686083979Tree_a @ X5 @ Y2 ) ) ).
% 0.25/0.56
% 0.25/0.56 % surj_pair
% 0.25/0.56 thf(fact_119_prod__cases,axiom,
% 0.25/0.56 ! [P: produc143150363Tree_a > $o,P2: produc143150363Tree_a] :
% 0.25/0.56 ( ! [A4: a,B3: tree_a] : ( P @ ( produc686083979Tree_a @ A4 @ B3 ) )
% 0.25/0.56 => ( P @ P2 ) ) ).
% 0.25/0.56
% 0.25/0.56 % prod_cases
% 0.25/0.56 thf(fact_120_Pair__inject,axiom,
% 0.25/0.56 ! [A: a,B: tree_a,A5: a,B5: tree_a] :
% 0.25/0.56 ( ( ( produc686083979Tree_a @ A @ B )
% 0.25/0.56 = ( produc686083979Tree_a @ A5 @ B5 ) )
% 0.25/0.56 => ~ ( ( A = A5 )
% 0.25/0.56 => ( B != B5 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % Pair_inject
% 0.25/0.56 thf(fact_121_old_Oprod_Oexhaust,axiom,
% 0.25/0.56 ! [Y: produc143150363Tree_a] :
% 0.25/0.56 ~ ! [A4: a,B3: tree_a] :
% 0.25/0.56 ( Y
% 0.25/0.56 != ( produc686083979Tree_a @ A4 @ B3 ) ) ).
% 0.25/0.56
% 0.25/0.56 % old.prod.exhaust
% 0.25/0.56 thf(fact_122_old_Oprod_Oinducts,axiom,
% 0.25/0.56 ! [P: produc143150363Tree_a > $o,Prod: produc143150363Tree_a] :
% 0.25/0.56 ( ! [A4: a,B3: tree_a] : ( P @ ( produc686083979Tree_a @ A4 @ B3 ) )
% 0.25/0.56 => ( P @ Prod ) ) ).
% 0.25/0.56
% 0.25/0.56 % old.prod.inducts
% 0.25/0.56 thf(fact_123_add__eq__conv__ex,axiom,
% 0.25/0.56 ! [A: a,M4: multiset_a,B: a,N: multiset_a] :
% 0.25/0.56 ( ( ( add_mset_a @ A @ M4 )
% 0.25/0.56 = ( add_mset_a @ B @ N ) )
% 0.25/0.56 = ( ( ( M4 = N )
% 0.25/0.56 & ( A = B ) )
% 0.25/0.56 | ? [K: multiset_a] :
% 0.25/0.56 ( ( M4
% 0.25/0.56 = ( add_mset_a @ B @ K ) )
% 0.25/0.56 & ( N
% 0.25/0.56 = ( add_mset_a @ A @ K ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % add_eq_conv_ex
% 0.25/0.56 thf(fact_124_add__mset__commute,axiom,
% 0.25/0.56 ! [X: a,Y: a,M4: multiset_a] :
% 0.25/0.56 ( ( add_mset_a @ X @ ( add_mset_a @ Y @ M4 ) )
% 0.25/0.56 = ( add_mset_a @ Y @ ( add_mset_a @ X @ M4 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % add_mset_commute
% 0.25/0.56 thf(fact_125_union__single__eq__member,axiom,
% 0.25/0.56 ! [X: a,M4: multiset_a,N: multiset_a] :
% 0.25/0.56 ( ( ( add_mset_a @ X @ M4 )
% 0.25/0.56 = N )
% 0.25/0.56 => ( member_a @ X @ ( set_mset_a @ N ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % union_single_eq_member
% 0.25/0.56 thf(fact_126_insert__noteq__member,axiom,
% 0.25/0.56 ! [B: a,B4: multiset_a,C: a,C2: multiset_a] :
% 0.25/0.56 ( ( ( add_mset_a @ B @ B4 )
% 0.25/0.56 = ( add_mset_a @ C @ C2 ) )
% 0.25/0.56 => ( ( B != C )
% 0.25/0.56 => ( member_a @ C @ ( set_mset_a @ B4 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % insert_noteq_member
% 0.25/0.56 thf(fact_127_removeLeaf_Osimps_I1_J,axiom,
% 0.25/0.56 ! [V: a] :
% 0.25/0.56 ( ( heapIm837449470Leaf_a @ ( t_a @ V @ e_a @ e_a ) )
% 0.25/0.56 = ( produc686083979Tree_a @ V @ e_a ) ) ).
% 0.25/0.56
% 0.25/0.56 % removeLeaf.simps(1)
% 0.25/0.56 thf(fact_128_RemoveMax__axioms__def,axiom,
% 0.25/0.56 ( remove301631099ee_a_a
% 0.25/0.56 = ( ^ [Is_empty: tree_a > $o,Of_list: list_a > tree_a,Multiset: tree_a > multiset_a,Remove_max: tree_a > produc143150363Tree_a,Inv: tree_a > $o] :
% 0.25/0.56 ( ! [X4: list_a] : ( Inv @ ( Of_list @ X4 ) )
% 0.25/0.56 & ! [L3: tree_a,M: a,L4: tree_a] :
% 0.25/0.56 ( ~ ( Is_empty @ L3 )
% 0.25/0.56 => ( ( Inv @ L3 )
% 0.25/0.56 => ( ( ( produc686083979Tree_a @ M @ L4 )
% 0.25/0.56 = ( Remove_max @ L3 ) )
% 0.25/0.56 => ( M
% 0.25/0.56 = ( lattic146396397_Max_a @ ( set_Tree_a_a @ Multiset @ L3 ) ) ) ) ) )
% 0.25/0.56 & ! [L3: tree_a,M: a,L4: tree_a] :
% 0.25/0.56 ( ~ ( Is_empty @ L3 )
% 0.25/0.56 => ( ( Inv @ L3 )
% 0.25/0.56 => ( ( ( produc686083979Tree_a @ M @ L4 )
% 0.25/0.56 = ( Remove_max @ L3 ) )
% 0.25/0.56 => ( ( add_mset_a @ M @ ( Multiset @ L4 ) )
% 0.25/0.56 = ( Multiset @ L3 ) ) ) ) )
% 0.25/0.56 & ! [L3: tree_a,M: a,L4: tree_a] :
% 0.25/0.56 ( ~ ( Is_empty @ L3 )
% 0.25/0.56 => ( ( Inv @ L3 )
% 0.25/0.56 => ( ( ( produc686083979Tree_a @ M @ L4 )
% 0.25/0.56 = ( Remove_max @ L3 ) )
% 0.25/0.56 => ( Inv @ L4 ) ) ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % RemoveMax_axioms_def
% 0.25/0.56 thf(fact_129_RemoveMax__axioms_Ointro,axiom,
% 0.25/0.56 ! [Inv2: tree_a > $o,Of_list2: list_a > tree_a,Is_empty2: tree_a > $o,Remove_max2: tree_a > produc143150363Tree_a,Multiset2: tree_a > multiset_a] :
% 0.25/0.56 ( ! [X5: list_a] : ( Inv2 @ ( Of_list2 @ X5 ) )
% 0.25/0.56 => ( ! [L5: tree_a,M2: a,L2: tree_a] :
% 0.25/0.56 ( ~ ( Is_empty2 @ L5 )
% 0.25/0.56 => ( ( Inv2 @ L5 )
% 0.25/0.56 => ( ( ( produc686083979Tree_a @ M2 @ L2 )
% 0.25/0.56 = ( Remove_max2 @ L5 ) )
% 0.25/0.56 => ( M2
% 0.25/0.56 = ( lattic146396397_Max_a @ ( set_Tree_a_a @ Multiset2 @ L5 ) ) ) ) ) )
% 0.25/0.56 => ( ! [L5: tree_a,M2: a,L2: tree_a] :
% 0.25/0.56 ( ~ ( Is_empty2 @ L5 )
% 0.25/0.56 => ( ( Inv2 @ L5 )
% 0.25/0.56 => ( ( ( produc686083979Tree_a @ M2 @ L2 )
% 0.25/0.56 = ( Remove_max2 @ L5 ) )
% 0.25/0.56 => ( ( add_mset_a @ M2 @ ( Multiset2 @ L2 ) )
% 0.25/0.56 = ( Multiset2 @ L5 ) ) ) ) )
% 0.25/0.56 => ( ! [L5: tree_a,M2: a,L2: tree_a] :
% 0.25/0.56 ( ~ ( Is_empty2 @ L5 )
% 0.25/0.56 => ( ( Inv2 @ L5 )
% 0.25/0.56 => ( ( ( produc686083979Tree_a @ M2 @ L2 )
% 0.25/0.56 = ( Remove_max2 @ L5 ) )
% 0.25/0.56 => ( Inv2 @ L2 ) ) ) )
% 0.25/0.56 => ( remove301631099ee_a_a @ Is_empty2 @ Of_list2 @ Multiset2 @ Remove_max2 @ Inv2 ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % RemoveMax_axioms.intro
% 0.25/0.56 thf(fact_130_RemoveMax_Oremove__max__max,axiom,
% 0.25/0.56 ! [Empty: tree_a,Is_empty2: tree_a > $o,Of_list2: list_a > tree_a,Multiset2: tree_a > multiset_a,Remove_max2: tree_a > produc143150363Tree_a,Inv2: tree_a > $o,L: tree_a,M3: a,L6: tree_a] :
% 0.25/0.56 ( ( removeMax_Tree_a_a @ Empty @ Is_empty2 @ Of_list2 @ Multiset2 @ Remove_max2 @ Inv2 )
% 0.25/0.56 => ( ~ ( Is_empty2 @ L )
% 0.25/0.56 => ( ( Inv2 @ L )
% 0.25/0.56 => ( ( ( produc686083979Tree_a @ M3 @ L6 )
% 0.25/0.56 = ( Remove_max2 @ L ) )
% 0.25/0.56 => ( M3
% 0.25/0.56 = ( lattic146396397_Max_a @ ( set_Tree_a_a @ Multiset2 @ L ) ) ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % RemoveMax.remove_max_max
% 0.25/0.56 thf(fact_131_multiset__induct__max,axiom,
% 0.25/0.56 ! [P: multiset_a > $o,M4: multiset_a] :
% 0.25/0.56 ( ( P @ zero_zero_multiset_a )
% 0.25/0.56 => ( ! [X5: a,M5: multiset_a] :
% 0.25/0.56 ( ( P @ M5 )
% 0.25/0.56 => ( ! [Xa: a] :
% 0.25/0.56 ( ( member_a @ Xa @ ( set_mset_a @ M5 ) )
% 0.25/0.56 => ( ord_less_eq_a @ Xa @ X5 ) )
% 0.25/0.56 => ( P @ ( add_mset_a @ X5 @ M5 ) ) ) )
% 0.25/0.56 => ( P @ M4 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % multiset_induct_max
% 0.25/0.56 thf(fact_132_add__mset__eq__singleton__iff,axiom,
% 0.25/0.56 ! [X: a,M4: multiset_a,Y: a] :
% 0.25/0.56 ( ( ( add_mset_a @ X @ M4 )
% 0.25/0.56 = ( add_mset_a @ Y @ zero_zero_multiset_a ) )
% 0.25/0.56 = ( ( M4 = zero_zero_multiset_a )
% 0.25/0.56 & ( X = Y ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % add_mset_eq_singleton_iff
% 0.25/0.56 thf(fact_133_single__eq__add__mset,axiom,
% 0.25/0.56 ! [A: a,B: a,M4: multiset_a] :
% 0.25/0.56 ( ( ( add_mset_a @ A @ zero_zero_multiset_a )
% 0.25/0.56 = ( add_mset_a @ B @ M4 ) )
% 0.25/0.56 = ( ( B = A )
% 0.25/0.56 & ( M4 = zero_zero_multiset_a ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % single_eq_add_mset
% 0.25/0.56 thf(fact_134_add__mset__eq__single,axiom,
% 0.25/0.56 ! [B: a,M4: multiset_a,A: a] :
% 0.25/0.56 ( ( ( add_mset_a @ B @ M4 )
% 0.25/0.56 = ( add_mset_a @ A @ zero_zero_multiset_a ) )
% 0.25/0.56 = ( ( B = A )
% 0.25/0.56 & ( M4 = zero_zero_multiset_a ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % add_mset_eq_single
% 0.25/0.56 thf(fact_135_single__eq__single,axiom,
% 0.25/0.56 ! [A: a,B: a] :
% 0.25/0.56 ( ( ( add_mset_a @ A @ zero_zero_multiset_a )
% 0.25/0.56 = ( add_mset_a @ B @ zero_zero_multiset_a ) )
% 0.25/0.56 = ( A = B ) ) ).
% 0.25/0.56
% 0.25/0.56 % single_eq_single
% 0.25/0.56 thf(fact_136_multiset__cases,axiom,
% 0.25/0.56 ! [M4: multiset_a] :
% 0.25/0.56 ( ( M4 != zero_zero_multiset_a )
% 0.25/0.56 => ~ ! [X5: a,N2: multiset_a] :
% 0.25/0.56 ( M4
% 0.25/0.56 != ( add_mset_a @ X5 @ N2 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % multiset_cases
% 0.25/0.56 thf(fact_137_multiset__induct,axiom,
% 0.25/0.56 ! [P: multiset_a > $o,M4: multiset_a] :
% 0.25/0.56 ( ( P @ zero_zero_multiset_a )
% 0.25/0.56 => ( ! [X5: a,M5: multiset_a] :
% 0.25/0.56 ( ( P @ M5 )
% 0.25/0.56 => ( P @ ( add_mset_a @ X5 @ M5 ) ) )
% 0.25/0.56 => ( P @ M4 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % multiset_induct
% 0.25/0.56 thf(fact_138_multiset__induct2,axiom,
% 0.25/0.56 ! [P: multiset_a > multiset_a > $o,M4: multiset_a,N: multiset_a] :
% 0.25/0.56 ( ( P @ zero_zero_multiset_a @ zero_zero_multiset_a )
% 0.25/0.56 => ( ! [A4: a,M5: multiset_a,N2: multiset_a] :
% 0.25/0.56 ( ( P @ M5 @ N2 )
% 0.25/0.56 => ( P @ ( add_mset_a @ A4 @ M5 ) @ N2 ) )
% 0.25/0.56 => ( ! [A4: a,M5: multiset_a,N2: multiset_a] :
% 0.25/0.56 ( ( P @ M5 @ N2 )
% 0.25/0.56 => ( P @ M5 @ ( add_mset_a @ A4 @ N2 ) ) )
% 0.25/0.56 => ( P @ M4 @ N ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % multiset_induct2
% 0.25/0.56 thf(fact_139_empty__not__add__mset,axiom,
% 0.25/0.56 ! [A: a,A2: multiset_a] :
% 0.25/0.56 ( zero_zero_multiset_a
% 0.25/0.56 != ( add_mset_a @ A @ A2 ) ) ).
% 0.25/0.56
% 0.25/0.56 % empty_not_add_mset
% 0.25/0.56 thf(fact_140_multi__nonempty__split,axiom,
% 0.25/0.56 ! [M4: multiset_a] :
% 0.25/0.56 ( ( M4 != zero_zero_multiset_a )
% 0.25/0.56 => ? [A6: multiset_a,A4: a] :
% 0.25/0.56 ( M4
% 0.25/0.56 = ( add_mset_a @ A4 @ A6 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % multi_nonempty_split
% 0.25/0.56 thf(fact_141_multiset__nonemptyE,axiom,
% 0.25/0.56 ! [A2: multiset_a] :
% 0.25/0.56 ( ( A2 != zero_zero_multiset_a )
% 0.25/0.56 => ~ ! [X5: a] :
% 0.25/0.56 ~ ( member_a @ X5 @ ( set_mset_a @ A2 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % multiset_nonemptyE
% 0.25/0.56 thf(fact_142_RemoveMax_Oremove__max__inv,axiom,
% 0.25/0.56 ! [Empty: tree_a,Is_empty2: tree_a > $o,Of_list2: list_a > tree_a,Multiset2: tree_a > multiset_a,Remove_max2: tree_a > produc143150363Tree_a,Inv2: tree_a > $o,L: tree_a,M3: a,L6: tree_a] :
% 0.25/0.56 ( ( removeMax_Tree_a_a @ Empty @ Is_empty2 @ Of_list2 @ Multiset2 @ Remove_max2 @ Inv2 )
% 0.25/0.56 => ( ~ ( Is_empty2 @ L )
% 0.25/0.56 => ( ( Inv2 @ L )
% 0.25/0.56 => ( ( ( produc686083979Tree_a @ M3 @ L6 )
% 0.25/0.56 = ( Remove_max2 @ L ) )
% 0.25/0.56 => ( Inv2 @ L6 ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % RemoveMax.remove_max_inv
% 0.25/0.56 thf(fact_143_multi__member__last,axiom,
% 0.25/0.56 ! [X: a] : ( member_a @ X @ ( set_mset_a @ ( add_mset_a @ X @ zero_zero_multiset_a ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % multi_member_last
% 0.25/0.56 thf(fact_144_RemoveMax_Oremove__max__multiset,axiom,
% 0.25/0.56 ! [Empty: tree_a,Is_empty2: tree_a > $o,Of_list2: list_a > tree_a,Multiset2: tree_a > multiset_a,Remove_max2: tree_a > produc143150363Tree_a,Inv2: tree_a > $o,L: tree_a,M3: a,L6: tree_a] :
% 0.25/0.56 ( ( removeMax_Tree_a_a @ Empty @ Is_empty2 @ Of_list2 @ Multiset2 @ Remove_max2 @ Inv2 )
% 0.25/0.56 => ( ~ ( Is_empty2 @ L )
% 0.25/0.56 => ( ( Inv2 @ L )
% 0.25/0.56 => ( ( ( produc686083979Tree_a @ M3 @ L6 )
% 0.25/0.56 = ( Remove_max2 @ L ) )
% 0.25/0.56 => ( ( add_mset_a @ M3 @ ( Multiset2 @ L6 ) )
% 0.25/0.56 = ( Multiset2 @ L ) ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % RemoveMax.remove_max_multiset
% 0.25/0.56 thf(fact_145_multiset_Osimps_I1_J,axiom,
% 0.25/0.56 ( ( multiset_a2 @ e_a )
% 0.25/0.56 = zero_zero_multiset_a ) ).
% 0.25/0.56
% 0.25/0.56 % multiset.simps(1)
% 0.25/0.56 thf(fact_146_multiset__induct__min,axiom,
% 0.25/0.56 ! [P: multiset_a > $o,M4: multiset_a] :
% 0.25/0.56 ( ( P @ zero_zero_multiset_a )
% 0.25/0.56 => ( ! [X5: a,M5: multiset_a] :
% 0.25/0.56 ( ( P @ M5 )
% 0.25/0.56 => ( ! [Xa: a] :
% 0.25/0.56 ( ( member_a @ Xa @ ( set_mset_a @ M5 ) )
% 0.25/0.56 => ( ord_less_eq_a @ X5 @ Xa ) )
% 0.25/0.56 => ( P @ ( add_mset_a @ X5 @ M5 ) ) ) )
% 0.25/0.56 => ( P @ M4 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % multiset_induct_min
% 0.25/0.56 thf(fact_147_Multiset_Ois__empty__def,axiom,
% 0.25/0.56 ( is_empty_a
% 0.25/0.56 = ( ^ [A7: multiset_a] : ( A7 = zero_zero_multiset_a ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % Multiset.is_empty_def
% 0.25/0.56 thf(fact_148_RemoveMax_Ossort_HInduct,axiom,
% 0.25/0.56 ! [Empty: tree_a,Is_empty2: tree_a > $o,Of_list2: list_a > tree_a,Multiset2: tree_a > multiset_a,Remove_max2: tree_a > produc143150363Tree_a,Inv2: tree_a > $o,L: tree_a,P: tree_a > list_a > $o,Sl: list_a] :
% 0.25/0.56 ( ( removeMax_Tree_a_a @ Empty @ Is_empty2 @ Of_list2 @ Multiset2 @ Remove_max2 @ Inv2 )
% 0.25/0.56 => ( ( Inv2 @ L )
% 0.25/0.56 => ( ( P @ L @ Sl )
% 0.25/0.56 => ( ! [L5: tree_a,Sl2: list_a,M2: a,L2: tree_a] :
% 0.25/0.56 ( ~ ( Is_empty2 @ L5 )
% 0.25/0.56 => ( ( Inv2 @ L5 )
% 0.25/0.56 => ( ( ( produc686083979Tree_a @ M2 @ L2 )
% 0.25/0.56 = ( Remove_max2 @ L5 ) )
% 0.25/0.56 => ( ( P @ L5 @ Sl2 )
% 0.25/0.56 => ( P @ L2 @ ( cons_a @ M2 @ Sl2 ) ) ) ) ) )
% 0.25/0.56 => ( P @ Empty @ ( ssort_Tree_a_a @ Is_empty2 @ Remove_max2 @ L @ Sl ) ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % RemoveMax.ssort'Induct
% 0.25/0.56 thf(fact_149_RemoveMax_Ossort_H__dom_Ocases,axiom,
% 0.25/0.56 ! [Empty: tree_a,Is_empty2: tree_a > $o,Of_list2: list_a > tree_a,Multiset2: tree_a > multiset_a,Remove_max2: tree_a > produc143150363Tree_a,Inv2: tree_a > $o,A: produc768687417list_a] :
% 0.25/0.56 ( ( removeMax_Tree_a_a @ Empty @ Is_empty2 @ Of_list2 @ Multiset2 @ Remove_max2 @ Inv2 )
% 0.25/0.56 => ( ( ssort_dom_Tree_a_a @ Is_empty2 @ Remove_max2 @ A )
% 0.25/0.56 => ~ ! [L5: tree_a,Sl2: list_a] :
% 0.25/0.56 ( ( A
% 0.25/0.56 = ( produc1352981801list_a @ L5 @ Sl2 ) )
% 0.25/0.56 => ~ ( ~ ( Is_empty2 @ L5 )
% 0.25/0.56 => ! [M6: a,L7: tree_a] :
% 0.25/0.56 ( ( ( produc686083979Tree_a @ M6 @ L7 )
% 0.25/0.56 = ( Remove_max2 @ L5 ) )
% 0.25/0.56 => ( ssort_dom_Tree_a_a @ Is_empty2 @ Remove_max2 @ ( produc1352981801list_a @ L7 @ ( cons_a @ M6 @ Sl2 ) ) ) ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % RemoveMax.ssort'_dom.cases
% 0.25/0.56 thf(fact_150_RemoveMax_Ossort_H__dom_Osimps,axiom,
% 0.25/0.56 ! [Empty: tree_a,Is_empty2: tree_a > $o,Of_list2: list_a > tree_a,Multiset2: tree_a > multiset_a,Remove_max2: tree_a > produc143150363Tree_a,Inv2: tree_a > $o,A: produc768687417list_a] :
% 0.25/0.56 ( ( removeMax_Tree_a_a @ Empty @ Is_empty2 @ Of_list2 @ Multiset2 @ Remove_max2 @ Inv2 )
% 0.25/0.56 => ( ( ssort_dom_Tree_a_a @ Is_empty2 @ Remove_max2 @ A )
% 0.25/0.56 = ( ? [L3: tree_a,Sl3: list_a] :
% 0.25/0.56 ( ( A
% 0.25/0.56 = ( produc1352981801list_a @ L3 @ Sl3 ) )
% 0.25/0.56 & ! [X4: a,Y4: tree_a] :
% 0.25/0.56 ( ~ ( Is_empty2 @ L3 )
% 0.25/0.56 => ( ( ( produc686083979Tree_a @ X4 @ Y4 )
% 0.25/0.56 = ( Remove_max2 @ L3 ) )
% 0.25/0.56 => ( ssort_dom_Tree_a_a @ Is_empty2 @ Remove_max2 @ ( produc1352981801list_a @ Y4 @ ( cons_a @ X4 @ Sl3 ) ) ) ) ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % RemoveMax.ssort'_dom.simps
% 0.25/0.56 thf(fact_151_RemoveMax_Ossort_H__dom_Oinducts,axiom,
% 0.25/0.56 ! [Empty: tree_a,Is_empty2: tree_a > $o,Of_list2: list_a > tree_a,Multiset2: tree_a > multiset_a,Remove_max2: tree_a > produc143150363Tree_a,Inv2: tree_a > $o,X: produc768687417list_a,P: produc768687417list_a > $o] :
% 0.25/0.56 ( ( removeMax_Tree_a_a @ Empty @ Is_empty2 @ Of_list2 @ Multiset2 @ Remove_max2 @ Inv2 )
% 0.25/0.56 => ( ( ssort_dom_Tree_a_a @ Is_empty2 @ Remove_max2 @ X )
% 0.25/0.56 => ( ! [L5: tree_a,Sl2: list_a] :
% 0.25/0.56 ( ! [M6: a,L7: tree_a] :
% 0.25/0.56 ( ~ ( Is_empty2 @ L5 )
% 0.25/0.56 => ( ( ( produc686083979Tree_a @ M6 @ L7 )
% 0.25/0.56 = ( Remove_max2 @ L5 ) )
% 0.25/0.56 => ( ssort_dom_Tree_a_a @ Is_empty2 @ Remove_max2 @ ( produc1352981801list_a @ L7 @ ( cons_a @ M6 @ Sl2 ) ) ) ) )
% 0.25/0.56 => ( ! [M6: a,L7: tree_a] :
% 0.25/0.56 ( ~ ( Is_empty2 @ L5 )
% 0.25/0.56 => ( ( ( produc686083979Tree_a @ M6 @ L7 )
% 0.25/0.56 = ( Remove_max2 @ L5 ) )
% 0.25/0.56 => ( P @ ( produc1352981801list_a @ L7 @ ( cons_a @ M6 @ Sl2 ) ) ) ) )
% 0.25/0.56 => ( P @ ( produc1352981801list_a @ L5 @ Sl2 ) ) ) )
% 0.25/0.56 => ( P @ X ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % RemoveMax.ssort'_dom.inducts
% 0.25/0.56 thf(fact_152_RemoveMax_Ossort_H__dom_Ointros,axiom,
% 0.25/0.56 ! [Empty: tree_a,Is_empty2: tree_a > $o,Of_list2: list_a > tree_a,Multiset2: tree_a > multiset_a,Remove_max2: tree_a > produc143150363Tree_a,Inv2: tree_a > $o,L: tree_a,Sl: list_a] :
% 0.25/0.56 ( ( removeMax_Tree_a_a @ Empty @ Is_empty2 @ Of_list2 @ Multiset2 @ Remove_max2 @ Inv2 )
% 0.25/0.56 => ( ! [M2: a,L2: tree_a] :
% 0.25/0.56 ( ~ ( Is_empty2 @ L )
% 0.25/0.56 => ( ( ( produc686083979Tree_a @ M2 @ L2 )
% 0.25/0.56 = ( Remove_max2 @ L ) )
% 0.25/0.56 => ( ssort_dom_Tree_a_a @ Is_empty2 @ Remove_max2 @ ( produc1352981801list_a @ L2 @ ( cons_a @ M2 @ Sl ) ) ) ) )
% 0.25/0.56 => ( ssort_dom_Tree_a_a @ Is_empty2 @ Remove_max2 @ ( produc1352981801list_a @ L @ Sl ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % RemoveMax.ssort'_dom.intros
% 0.25/0.56 thf(fact_153_multiset_Osimps_I2_J,axiom,
% 0.25/0.56 ! [V: a,L: tree_a,R: tree_a] :
% 0.25/0.56 ( ( multiset_a2 @ ( t_a @ V @ L @ R ) )
% 0.25/0.56 = ( plus_plus_multiset_a @ ( plus_plus_multiset_a @ ( multiset_a2 @ L ) @ ( add_mset_a @ V @ zero_zero_multiset_a ) ) @ ( multiset_a2 @ R ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % multiset.simps(2)
% 0.25/0.56 thf(fact_154_single__subset__iff,axiom,
% 0.25/0.56 ! [A: a,M4: multiset_a] :
% 0.25/0.56 ( ( subseteq_mset_a @ ( add_mset_a @ A @ zero_zero_multiset_a ) @ M4 )
% 0.25/0.56 = ( member_a @ A @ ( set_mset_a @ M4 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % single_subset_iff
% 0.25/0.56 thf(fact_155_subset__mset_Obot_Oextremum__unique,axiom,
% 0.25/0.56 ! [A: multiset_a] :
% 0.25/0.56 ( ( subseteq_mset_a @ A @ zero_zero_multiset_a )
% 0.25/0.56 = ( A = zero_zero_multiset_a ) ) ).
% 0.25/0.56
% 0.25/0.56 % subset_mset.bot.extremum_unique
% 0.25/0.56 thf(fact_156_subset__mset_Ole__zero__eq,axiom,
% 0.25/0.56 ! [N3: multiset_a] :
% 0.25/0.56 ( ( subseteq_mset_a @ N3 @ zero_zero_multiset_a )
% 0.25/0.56 = ( N3 = zero_zero_multiset_a ) ) ).
% 0.25/0.56
% 0.25/0.56 % subset_mset.le_zero_eq
% 0.25/0.56 thf(fact_157_subset__mset_Oadd__le__cancel__left,axiom,
% 0.25/0.56 ! [C: multiset_a,A: multiset_a,B: multiset_a] :
% 0.25/0.56 ( ( subseteq_mset_a @ ( plus_plus_multiset_a @ C @ A ) @ ( plus_plus_multiset_a @ C @ B ) )
% 0.25/0.56 = ( subseteq_mset_a @ A @ B ) ) ).
% 0.25/0.56
% 0.25/0.56 % subset_mset.add_le_cancel_left
% 0.25/0.56 thf(fact_158_subset__mset_Oadd__le__cancel__right,axiom,
% 0.25/0.56 ! [A: multiset_a,C: multiset_a,B: multiset_a] :
% 0.25/0.56 ( ( subseteq_mset_a @ ( plus_plus_multiset_a @ A @ C ) @ ( plus_plus_multiset_a @ B @ C ) )
% 0.25/0.56 = ( subseteq_mset_a @ A @ B ) ) ).
% 0.25/0.56
% 0.25/0.56 % subset_mset.add_le_cancel_right
% 0.25/0.56 thf(fact_159_mset__subset__eq__mono__add__left__cancel,axiom,
% 0.25/0.56 ! [C2: multiset_a,A2: multiset_a,B4: multiset_a] :
% 0.25/0.56 ( ( subseteq_mset_a @ ( plus_plus_multiset_a @ C2 @ A2 ) @ ( plus_plus_multiset_a @ C2 @ B4 ) )
% 0.25/0.56 = ( subseteq_mset_a @ A2 @ B4 ) ) ).
% 0.25/0.56
% 0.25/0.56 % mset_subset_eq_mono_add_left_cancel
% 0.25/0.56 thf(fact_160_mset__subset__eq__mono__add__right__cancel,axiom,
% 0.25/0.56 ! [A2: multiset_a,C2: multiset_a,B4: multiset_a] :
% 0.25/0.56 ( ( subseteq_mset_a @ ( plus_plus_multiset_a @ A2 @ C2 ) @ ( plus_plus_multiset_a @ B4 @ C2 ) )
% 0.25/0.56 = ( subseteq_mset_a @ A2 @ B4 ) ) ).
% 0.25/0.56
% 0.25/0.56 % mset_subset_eq_mono_add_right_cancel
% 0.25/0.56 thf(fact_161_subset__mset_Ozero__eq__add__iff__both__eq__0,axiom,
% 0.25/0.56 ! [X: multiset_a,Y: multiset_a] :
% 0.25/0.56 ( ( zero_zero_multiset_a
% 0.25/0.56 = ( plus_plus_multiset_a @ X @ Y ) )
% 0.25/0.56 = ( ( X = zero_zero_multiset_a )
% 0.25/0.56 & ( Y = zero_zero_multiset_a ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % subset_mset.zero_eq_add_iff_both_eq_0
% 0.25/0.56 thf(fact_162_subset__mset_Oadd__eq__0__iff__both__eq__0,axiom,
% 0.25/0.56 ! [X: multiset_a,Y: multiset_a] :
% 0.25/0.56 ( ( ( plus_plus_multiset_a @ X @ Y )
% 0.25/0.56 = zero_zero_multiset_a )
% 0.25/0.56 = ( ( X = zero_zero_multiset_a )
% 0.25/0.56 & ( Y = zero_zero_multiset_a ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % subset_mset.add_eq_0_iff_both_eq_0
% 0.25/0.56 thf(fact_163_union__eq__empty,axiom,
% 0.25/0.56 ! [M4: multiset_a,N: multiset_a] :
% 0.25/0.56 ( ( ( plus_plus_multiset_a @ M4 @ N )
% 0.25/0.56 = zero_zero_multiset_a )
% 0.25/0.56 = ( ( M4 = zero_zero_multiset_a )
% 0.25/0.56 & ( N = zero_zero_multiset_a ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % union_eq_empty
% 0.25/0.56 thf(fact_164_empty__eq__union,axiom,
% 0.25/0.56 ! [M4: multiset_a,N: multiset_a] :
% 0.25/0.56 ( ( zero_zero_multiset_a
% 0.25/0.56 = ( plus_plus_multiset_a @ M4 @ N ) )
% 0.25/0.56 = ( ( M4 = zero_zero_multiset_a )
% 0.25/0.56 & ( N = zero_zero_multiset_a ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % empty_eq_union
% 0.25/0.56 thf(fact_165_union__mset__add__mset__right,axiom,
% 0.25/0.56 ! [A2: multiset_a,A: a,B4: multiset_a] :
% 0.25/0.56 ( ( plus_plus_multiset_a @ A2 @ ( add_mset_a @ A @ B4 ) )
% 0.25/0.56 = ( add_mset_a @ A @ ( plus_plus_multiset_a @ A2 @ B4 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % union_mset_add_mset_right
% 0.25/0.56 thf(fact_166_union__mset__add__mset__left,axiom,
% 0.25/0.56 ! [A: a,A2: multiset_a,B4: multiset_a] :
% 0.25/0.56 ( ( plus_plus_multiset_a @ ( add_mset_a @ A @ A2 ) @ B4 )
% 0.25/0.56 = ( add_mset_a @ A @ ( plus_plus_multiset_a @ A2 @ B4 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % union_mset_add_mset_left
% 0.25/0.56 thf(fact_167_subset__mset_Oadd__le__same__cancel1,axiom,
% 0.25/0.56 ! [B: multiset_a,A: multiset_a] :
% 0.25/0.56 ( ( subseteq_mset_a @ ( plus_plus_multiset_a @ B @ A ) @ B )
% 0.25/0.56 = ( subseteq_mset_a @ A @ zero_zero_multiset_a ) ) ).
% 0.25/0.56
% 0.25/0.56 % subset_mset.add_le_same_cancel1
% 0.25/0.56 thf(fact_168_subset__mset_Oadd__le__same__cancel2,axiom,
% 0.25/0.56 ! [A: multiset_a,B: multiset_a] :
% 0.25/0.56 ( ( subseteq_mset_a @ ( plus_plus_multiset_a @ A @ B ) @ B )
% 0.25/0.56 = ( subseteq_mset_a @ A @ zero_zero_multiset_a ) ) ).
% 0.25/0.56
% 0.25/0.56 % subset_mset.add_le_same_cancel2
% 0.25/0.56 thf(fact_169_subset__mset_Ole__add__same__cancel1,axiom,
% 0.25/0.56 ! [A: multiset_a,B: multiset_a] :
% 0.25/0.56 ( ( subseteq_mset_a @ A @ ( plus_plus_multiset_a @ A @ B ) )
% 0.25/0.56 = ( subseteq_mset_a @ zero_zero_multiset_a @ B ) ) ).
% 0.25/0.56
% 0.25/0.56 % subset_mset.le_add_same_cancel1
% 0.25/0.56 thf(fact_170_subset__mset_Ole__add__same__cancel2,axiom,
% 0.25/0.56 ! [A: multiset_a,B: multiset_a] :
% 0.25/0.56 ( ( subseteq_mset_a @ A @ ( plus_plus_multiset_a @ B @ A ) )
% 0.25/0.56 = ( subseteq_mset_a @ zero_zero_multiset_a @ B ) ) ).
% 0.25/0.56
% 0.25/0.56 % subset_mset.le_add_same_cancel2
% 0.25/0.56 thf(fact_171_add__mset__subseteq__single__iff,axiom,
% 0.25/0.56 ! [A: a,M4: multiset_a,B: a] :
% 0.25/0.56 ( ( subseteq_mset_a @ ( add_mset_a @ A @ M4 ) @ ( add_mset_a @ B @ zero_zero_multiset_a ) )
% 0.25/0.56 = ( ( M4 = zero_zero_multiset_a )
% 0.25/0.56 & ( A = B ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % add_mset_subseteq_single_iff
% 0.25/0.56 thf(fact_172_union__assoc,axiom,
% 0.25/0.56 ! [M4: multiset_a,N: multiset_a,K2: multiset_a] :
% 0.25/0.56 ( ( plus_plus_multiset_a @ ( plus_plus_multiset_a @ M4 @ N ) @ K2 )
% 0.25/0.56 = ( plus_plus_multiset_a @ M4 @ ( plus_plus_multiset_a @ N @ K2 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % union_assoc
% 0.25/0.56 thf(fact_173_union__lcomm,axiom,
% 0.25/0.56 ! [M4: multiset_a,N: multiset_a,K2: multiset_a] :
% 0.25/0.56 ( ( plus_plus_multiset_a @ M4 @ ( plus_plus_multiset_a @ N @ K2 ) )
% 0.25/0.56 = ( plus_plus_multiset_a @ N @ ( plus_plus_multiset_a @ M4 @ K2 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % union_lcomm
% 0.25/0.56 thf(fact_174_union__commute,axiom,
% 0.25/0.56 ( plus_plus_multiset_a
% 0.25/0.56 = ( ^ [M7: multiset_a,N4: multiset_a] : ( plus_plus_multiset_a @ N4 @ M7 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % union_commute
% 0.25/0.56 thf(fact_175_union__left__cancel,axiom,
% 0.25/0.56 ! [K2: multiset_a,M4: multiset_a,N: multiset_a] :
% 0.25/0.56 ( ( ( plus_plus_multiset_a @ K2 @ M4 )
% 0.25/0.56 = ( plus_plus_multiset_a @ K2 @ N ) )
% 0.25/0.56 = ( M4 = N ) ) ).
% 0.25/0.56
% 0.25/0.56 % union_left_cancel
% 0.25/0.56 thf(fact_176_union__right__cancel,axiom,
% 0.25/0.56 ! [M4: multiset_a,K2: multiset_a,N: multiset_a] :
% 0.25/0.56 ( ( ( plus_plus_multiset_a @ M4 @ K2 )
% 0.25/0.56 = ( plus_plus_multiset_a @ N @ K2 ) )
% 0.25/0.56 = ( M4 = N ) ) ).
% 0.25/0.56
% 0.25/0.56 % union_right_cancel
% 0.25/0.56 thf(fact_177_subset__mset_Oadd__mono,axiom,
% 0.25/0.56 ! [A: multiset_a,B: multiset_a,C: multiset_a,D: multiset_a] :
% 0.25/0.56 ( ( subseteq_mset_a @ A @ B )
% 0.25/0.56 => ( ( subseteq_mset_a @ C @ D )
% 0.25/0.56 => ( subseteq_mset_a @ ( plus_plus_multiset_a @ A @ C ) @ ( plus_plus_multiset_a @ B @ D ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % subset_mset.add_mono
% 0.25/0.56 thf(fact_178_subset__mset_Oless__eqE,axiom,
% 0.25/0.56 ! [A: multiset_a,B: multiset_a] :
% 0.25/0.56 ( ( subseteq_mset_a @ A @ B )
% 0.25/0.56 => ~ ! [C3: multiset_a] :
% 0.25/0.56 ( B
% 0.25/0.56 != ( plus_plus_multiset_a @ A @ C3 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % subset_mset.less_eqE
% 0.25/0.56 thf(fact_179_subset__mset_Ole__iff__add,axiom,
% 0.25/0.56 ( subseteq_mset_a
% 0.25/0.56 = ( ^ [A3: multiset_a,B2: multiset_a] :
% 0.25/0.56 ? [C4: multiset_a] :
% 0.25/0.56 ( B2
% 0.25/0.56 = ( plus_plus_multiset_a @ A3 @ C4 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % subset_mset.le_iff_add
% 0.25/0.56 thf(fact_180_mset__subset__eq__add__left,axiom,
% 0.25/0.56 ! [A2: multiset_a,B4: multiset_a] : ( subseteq_mset_a @ A2 @ ( plus_plus_multiset_a @ A2 @ B4 ) ) ).
% 0.25/0.56
% 0.25/0.56 % mset_subset_eq_add_left
% 0.25/0.56 thf(fact_181_mset__subset__eq__mono__add,axiom,
% 0.25/0.56 ! [A2: multiset_a,B4: multiset_a,C2: multiset_a,D2: multiset_a] :
% 0.25/0.56 ( ( subseteq_mset_a @ A2 @ B4 )
% 0.25/0.56 => ( ( subseteq_mset_a @ C2 @ D2 )
% 0.25/0.56 => ( subseteq_mset_a @ ( plus_plus_multiset_a @ A2 @ C2 ) @ ( plus_plus_multiset_a @ B4 @ D2 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mset_subset_eq_mono_add
% 0.25/0.56 thf(fact_182_mset__subset__eq__add__right,axiom,
% 0.25/0.56 ! [B4: multiset_a,A2: multiset_a] : ( subseteq_mset_a @ B4 @ ( plus_plus_multiset_a @ A2 @ B4 ) ) ).
% 0.25/0.56
% 0.25/0.56 % mset_subset_eq_add_right
% 0.25/0.56 thf(fact_183_multi__union__self__other__eq,axiom,
% 0.25/0.56 ! [A2: multiset_a,X7: multiset_a,Y7: multiset_a] :
% 0.25/0.56 ( ( ( plus_plus_multiset_a @ A2 @ X7 )
% 0.25/0.56 = ( plus_plus_multiset_a @ A2 @ Y7 ) )
% 0.25/0.56 => ( X7 = Y7 ) ) ).
% 0.25/0.56
% 0.25/0.56 % multi_union_self_other_eq
% 0.25/0.56 thf(fact_184_subset__mset_Oadd__left__mono,axiom,
% 0.25/0.56 ! [A: multiset_a,B: multiset_a,C: multiset_a] :
% 0.25/0.56 ( ( subseteq_mset_a @ A @ B )
% 0.25/0.56 => ( subseteq_mset_a @ ( plus_plus_multiset_a @ C @ A ) @ ( plus_plus_multiset_a @ C @ B ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % subset_mset.add_left_mono
% 0.25/0.56 thf(fact_185_mset__subset__eq__exists__conv,axiom,
% 0.25/0.56 ( subseteq_mset_a
% 0.25/0.56 = ( ^ [A7: multiset_a,B7: multiset_a] :
% 0.25/0.56 ? [C5: multiset_a] :
% 0.25/0.56 ( B7
% 0.25/0.56 = ( plus_plus_multiset_a @ A7 @ C5 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mset_subset_eq_exists_conv
% 0.25/0.56 thf(fact_186_subset__mset_Oadd__right__mono,axiom,
% 0.25/0.56 ! [A: multiset_a,B: multiset_a,C: multiset_a] :
% 0.25/0.56 ( ( subseteq_mset_a @ A @ B )
% 0.25/0.56 => ( subseteq_mset_a @ ( plus_plus_multiset_a @ A @ C ) @ ( plus_plus_multiset_a @ B @ C ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % subset_mset.add_right_mono
% 0.25/0.56 thf(fact_187_subset__mset_Oadd__le__imp__le__left,axiom,
% 0.25/0.56 ! [C: multiset_a,A: multiset_a,B: multiset_a] :
% 0.25/0.56 ( ( subseteq_mset_a @ ( plus_plus_multiset_a @ C @ A ) @ ( plus_plus_multiset_a @ C @ B ) )
% 0.25/0.56 => ( subseteq_mset_a @ A @ B ) ) ).
% 0.25/0.56
% 0.25/0.56 % subset_mset.add_le_imp_le_left
% 0.25/0.56 thf(fact_188_subset__mset_Oadd__le__imp__le__right,axiom,
% 0.25/0.56 ! [A: multiset_a,C: multiset_a,B: multiset_a] :
% 0.25/0.56 ( ( subseteq_mset_a @ ( plus_plus_multiset_a @ A @ C ) @ ( plus_plus_multiset_a @ B @ C ) )
% 0.25/0.56 => ( subseteq_mset_a @ A @ B ) ) ).
% 0.25/0.56
% 0.25/0.56 % subset_mset.add_le_imp_le_right
% 0.25/0.56 thf(fact_189_union__iff,axiom,
% 0.25/0.56 ! [A: a,A2: multiset_a,B4: multiset_a] :
% 0.25/0.56 ( ( member_a @ A @ ( set_mset_a @ ( plus_plus_multiset_a @ A2 @ B4 ) ) )
% 0.25/0.56 = ( ( member_a @ A @ ( set_mset_a @ A2 ) )
% 0.25/0.56 | ( member_a @ A @ ( set_mset_a @ B4 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % union_iff
% 0.25/0.56 thf(fact_190_mset__subset__eqD,axiom,
% 0.25/0.56 ! [A2: multiset_a,B4: multiset_a,X: a] :
% 0.25/0.56 ( ( subseteq_mset_a @ A2 @ B4 )
% 0.25/0.56 => ( ( member_a @ X @ ( set_mset_a @ A2 ) )
% 0.25/0.56 => ( member_a @ X @ ( set_mset_a @ B4 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mset_subset_eqD
% 0.25/0.56 thf(fact_191_set__mset__mono,axiom,
% 0.25/0.56 ! [A2: multiset_a,B4: multiset_a] :
% 0.25/0.56 ( ( subseteq_mset_a @ A2 @ B4 )
% 0.25/0.56 => ( ord_less_eq_set_a @ ( set_mset_a @ A2 ) @ ( set_mset_a @ B4 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % set_mset_mono
% 0.25/0.56 thf(fact_192_mset__subset__eq__add__mset__cancel,axiom,
% 0.25/0.56 ! [A: a,A2: multiset_a,B4: multiset_a] :
% 0.25/0.56 ( ( subseteq_mset_a @ ( add_mset_a @ A @ A2 ) @ ( add_mset_a @ A @ B4 ) )
% 0.25/0.56 = ( subseteq_mset_a @ A2 @ B4 ) ) ).
% 0.25/0.56
% 0.25/0.56 % mset_subset_eq_add_mset_cancel
% 0.25/0.56 thf(fact_193_add__mono__thms__linordered__semiring_I3_J,axiom,
% 0.25/0.56 ! [I3: multiset_a,J: multiset_a,K3: multiset_a,L: multiset_a] :
% 0.25/0.56 ( ( ( ord_le1199012836iset_a @ I3 @ J )
% 0.25/0.56 & ( K3 = L ) )
% 0.25/0.56 => ( ord_le1199012836iset_a @ ( plus_plus_multiset_a @ I3 @ K3 ) @ ( plus_plus_multiset_a @ J @ L ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % add_mono_thms_linordered_semiring(3)
% 0.25/0.56 thf(fact_194_add__mono__thms__linordered__semiring_I2_J,axiom,
% 0.25/0.56 ! [I3: multiset_a,J: multiset_a,K3: multiset_a,L: multiset_a] :
% 0.25/0.56 ( ( ( I3 = J )
% 0.25/0.56 & ( ord_le1199012836iset_a @ K3 @ L ) )
% 0.25/0.56 => ( ord_le1199012836iset_a @ ( plus_plus_multiset_a @ I3 @ K3 ) @ ( plus_plus_multiset_a @ J @ L ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % add_mono_thms_linordered_semiring(2)
% 0.25/0.56 thf(fact_195_add__mono__thms__linordered__semiring_I1_J,axiom,
% 0.25/0.56 ! [I3: multiset_a,J: multiset_a,K3: multiset_a,L: multiset_a] :
% 0.25/0.56 ( ( ( ord_le1199012836iset_a @ I3 @ J )
% 0.25/0.56 & ( ord_le1199012836iset_a @ K3 @ L ) )
% 0.25/0.56 => ( ord_le1199012836iset_a @ ( plus_plus_multiset_a @ I3 @ K3 ) @ ( plus_plus_multiset_a @ J @ L ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % add_mono_thms_linordered_semiring(1)
% 0.25/0.56 thf(fact_196_add__mono,axiom,
% 0.25/0.56 ! [A: multiset_a,B: multiset_a,C: multiset_a,D: multiset_a] :
% 0.25/0.56 ( ( ord_le1199012836iset_a @ A @ B )
% 0.25/0.56 => ( ( ord_le1199012836iset_a @ C @ D )
% 0.25/0.56 => ( ord_le1199012836iset_a @ ( plus_plus_multiset_a @ A @ C ) @ ( plus_plus_multiset_a @ B @ D ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % add_mono
% 0.25/0.56 thf(fact_197_add__left__mono,axiom,
% 0.25/0.56 ! [A: multiset_a,B: multiset_a,C: multiset_a] :
% 0.25/0.56 ( ( ord_le1199012836iset_a @ A @ B )
% 0.25/0.56 => ( ord_le1199012836iset_a @ ( plus_plus_multiset_a @ C @ A ) @ ( plus_plus_multiset_a @ C @ B ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % add_left_mono
% 0.25/0.56 thf(fact_198_add__right__mono,axiom,
% 0.25/0.56 ! [A: multiset_a,B: multiset_a,C: multiset_a] :
% 0.25/0.56 ( ( ord_le1199012836iset_a @ A @ B )
% 0.25/0.56 => ( ord_le1199012836iset_a @ ( plus_plus_multiset_a @ A @ C ) @ ( plus_plus_multiset_a @ B @ C ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % add_right_mono
% 0.25/0.56 thf(fact_199_empty__neutral_I2_J,axiom,
% 0.25/0.56 ! [X: multiset_a] :
% 0.25/0.56 ( ( plus_plus_multiset_a @ X @ zero_zero_multiset_a )
% 0.25/0.56 = X ) ).
% 0.25/0.56
% 0.25/0.56 % empty_neutral(2)
% 0.25/0.56 thf(fact_200_empty__neutral_I1_J,axiom,
% 0.25/0.56 ! [X: multiset_a] :
% 0.25/0.56 ( ( plus_plus_multiset_a @ zero_zero_multiset_a @ X )
% 0.25/0.56 = X ) ).
% 0.25/0.56
% 0.25/0.56 % empty_neutral(1)
% 0.25/0.56 thf(fact_201_empty__le,axiom,
% 0.25/0.56 ! [A2: multiset_a] : ( subseteq_mset_a @ zero_zero_multiset_a @ A2 ) ).
% 0.25/0.56
% 0.25/0.56 % empty_le
% 0.25/0.56 thf(fact_202_subset__mset_Ozero__le,axiom,
% 0.25/0.56 ! [X: multiset_a] : ( subseteq_mset_a @ zero_zero_multiset_a @ X ) ).
% 0.25/0.56
% 0.25/0.56 % subset_mset.zero_le
% 0.25/0.56 thf(fact_203_subset__mset_Obot_Oextremum,axiom,
% 0.25/0.56 ! [A: multiset_a] : ( subseteq_mset_a @ zero_zero_multiset_a @ A ) ).
% 0.25/0.56
% 0.25/0.56 % subset_mset.bot.extremum
% 0.25/0.56 thf(fact_204_subset__mset_Oadd__decreasing,axiom,
% 0.25/0.56 ! [A: multiset_a,C: multiset_a,B: multiset_a] :
% 0.25/0.56 ( ( subseteq_mset_a @ A @ zero_zero_multiset_a )
% 0.25/0.56 => ( ( subseteq_mset_a @ C @ B )
% 0.25/0.56 => ( subseteq_mset_a @ ( plus_plus_multiset_a @ A @ C ) @ B ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % subset_mset.add_decreasing
% 0.25/0.56 thf(fact_205_subset__mset_Oadd__increasing,axiom,
% 0.25/0.56 ! [A: multiset_a,B: multiset_a,C: multiset_a] :
% 0.25/0.56 ( ( subseteq_mset_a @ zero_zero_multiset_a @ A )
% 0.25/0.56 => ( ( subseteq_mset_a @ B @ C )
% 0.25/0.62 => ( subseteq_mset_a @ B @ ( plus_plus_multiset_a @ A @ C ) ) ) ) ).
% 0.25/0.62
% 0.25/0.62 % subset_mset.add_increasing
% 0.25/0.62 thf(fact_206_subset__mset_Oadd__decreasing2,axiom,
% 0.25/0.62 ! [C: multiset_a,A: multiset_a,B: multiset_a] :
% 0.25/0.62 ( ( subseteq_mset_a @ C @ zero_zero_multiset_a )
% 0.25/0.62 => ( ( subseteq_mset_a @ A @ B )
% 0.25/0.62 => ( subseteq_mset_a @ ( plus_plus_multiset_a @ A @ C ) @ B ) ) ) ).
% 0.25/0.62
% 0.25/0.62 % subset_mset.add_decreasing2
% 0.25/0.62 thf(fact_207_subset__mset_Oadd__increasing2,axiom,
% 0.25/0.62 ! [C: multiset_a,B: multiset_a,A: multiset_a] :
% 0.25/0.62 ( ( subseteq_mset_a @ zero_zero_multiset_a @ C )
% 0.25/0.62 => ( ( subseteq_mset_a @ B @ A )
% 0.25/0.62 => ( subseteq_mset_a @ B @ ( plus_plus_multiset_a @ A @ C ) ) ) ) ).
% 0.25/0.62
% 0.25/0.62 % subset_mset.add_increasing2
% 0.25/0.62 thf(fact_208_subset__mset_Oadd__nonneg__nonneg,axiom,
% 0.25/0.62 ! [A: multiset_a,B: multiset_a] :
% 0.25/0.62 ( ( subseteq_mset_a @ zero_zero_multiset_a @ A )
% 0.25/0.62 => ( ( subseteq_mset_a @ zero_zero_multiset_a @ B )
% 0.25/0.62 => ( subseteq_mset_a @ zero_zero_multiset_a @ ( plus_plus_multiset_a @ A @ B ) ) ) ) ).
% 0.25/0.62
% 0.25/0.62 % subset_mset.add_nonneg_nonneg
% 0.25/0.62 thf(fact_209_subset__mset_Oadd__nonpos__nonpos,axiom,
% 0.25/0.62 ! [A: multiset_a,B: multiset_a] :
% 0.25/0.62 ( ( subseteq_mset_a @ A @ zero_zero_multiset_a )
% 0.25/0.62 => ( ( subseteq_mset_a @ B @ zero_zero_multiset_a )
% 0.25/0.62 => ( subseteq_mset_a @ ( plus_plus_multiset_a @ A @ B ) @ zero_zero_multiset_a ) ) ) ).
% 0.25/0.62
% 0.25/0.62 % subset_mset.add_nonpos_nonpos
% 0.25/0.62 thf(fact_210_subset__mset_Oadd__nonneg__eq__0__iff,axiom,
% 0.25/0.62 ! [X: multiset_a,Y: multiset_a] :
% 0.25/0.62 ( ( subseteq_mset_a @ zero_zero_multiset_a @ X )
% 0.25/0.62 => ( ( subseteq_mset_a @ zero_zero_multiset_a @ Y )
% 0.25/0.62 => ( ( ( plus_plus_multiset_a @ X @ Y )
% 0.25/0.62 = zero_zero_multiset_a )
% 0.25/0.62 = ( ( X = zero_zero_multiset_a )
% 0.25/0.62 & ( Y = zero_zero_multiset_a ) ) ) ) ) ).
% 0.25/0.62
% 0.25/0.62 % subset_mset.add_nonneg_eq_0_iff
% 0.25/0.62 thf(fact_211_subset__mset_Oadd__nonpos__eq__0__iff,axiom,
% 0.25/0.62 ! [X: multiset_a,Y: multiset_a] :
% 0.25/0.62 ( ( subseteq_mset_a @ X @ zero_zero_multiset_a )
% 0.25/0.62 => ( ( subseteq_mset_a @ Y @ zero_zero_multiset_a )
% 0.25/0.62 => ( ( ( plus_plus_multiset_a @ X @ Y )
% 0.25/0.62 = zero_zero_multiset_a )
% 0.25/0.62 = ( ( X = zero_zero_multiset_a )
% 0.25/0.62 & ( Y = zero_zero_multiset_a ) ) ) ) ) ).
% 0.25/0.62
% 0.25/0.62 % subset_mset.add_nonpos_eq_0_iff
% 0.25/0.62 thf(fact_212_subset__mset_Obot_Oextremum__uniqueI,axiom,
% 0.25/0.62 ! [A: multiset_a] :
% 0.25/0.62 ( ( subseteq_mset_a @ A @ zero_zero_multiset_a )
% 0.25/0.62 => ( A = zero_zero_multiset_a ) ) ).
% 0.25/0.62
% 0.25/0.62 % subset_mset.bot.extremum_uniqueI
% 0.25/0.62 thf(fact_213_verit__sum__simplify,axiom,
% 0.25/0.62 ! [A: multiset_a] :
% 0.25/0.62 ( ( plus_plus_multiset_a @ A @ zero_zero_multiset_a )
% 0.25/0.62 = A ) ).
% 0.25/0.62
% 0.25/0.62 % verit_sum_simplify
% 0.25/0.62
% 0.25/0.62 % Conjectures (1)
% 0.25/0.62 thf(conj_0,conjecture,
% 0.25/0.62 ( ( multiset_a2 @ ( heapIm1091024090Down_a @ ( t_a @ v @ ( t_a @ v1 @ l1 @ r1 ) @ ( t_a @ v2 @ l2 @ r2 ) ) ) )
% 0.25/0.62 = ( multiset_a2 @ ( t_a @ v @ ( t_a @ v1 @ l1 @ r1 ) @ ( t_a @ v2 @ l2 @ r2 ) ) ) ) ).
% 0.25/0.62
% 0.25/0.62 %------------------------------------------------------------------------------
% 0.25/0.62 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.JAAyaUOIEg/cvc5---1.0.5_25347.p...
% 0.25/0.62 (declare-sort $$unsorted 0)
% 0.25/0.63 (declare-sort tptp.produc768687417list_a 0)
% 0.25/0.63 (declare-sort tptp.produc143150363Tree_a 0)
% 0.25/0.63 (declare-sort tptp.multiset_a 0)
% 0.25/0.63 (declare-sort tptp.list_a 0)
% 0.25/0.63 (declare-sort tptp.tree_a 0)
% 0.25/0.63 (declare-sort tptp.set_a 0)
% 0.25/0.63 (declare-sort tptp.a 0)
% 0.25/0.63 (declare-fun tptp.plus_plus_multiset_a (tptp.multiset_a tptp.multiset_a) tptp.multiset_a)
% 0.25/0.63 (declare-fun tptp.zero_zero_multiset_a () tptp.multiset_a)
% 0.25/0.63 (declare-fun tptp.heapIm970322378pify_a (tptp.tree_a) tptp.tree_a)
% 0.25/0.63 (declare-fun tptp.heapIm229596386mpty_a (tptp.tree_a) Bool)
% 0.25/0.63 (declare-fun tptp.heapIm1057938560list_a (tptp.list_a) tptp.tree_a)
% 0.25/0.63 (declare-fun tptp.heapIm1140443833left_a (tptp.tree_a) tptp.tree_a)
% 0.25/0.63 (declare-fun tptp.heapIm1637418125tree_a (tptp.list_a) tptp.tree_a)
% 0.25/0.63 (declare-fun tptp.heapIm837449470Leaf_a (tptp.tree_a) tptp.produc143150363Tree_a)
% 0.25/0.63 (declare-fun tptp.heapIm1257206334ight_a (tptp.tree_a) tptp.tree_a)
% 0.25/0.63 (declare-fun tptp.heapIm1091024090Down_a (tptp.tree_a) tptp.tree_a)
% 0.25/0.63 (declare-fun tptp.heap_Tree_a_a (tptp.tree_a (-> tptp.tree_a Bool) (-> tptp.list_a tptp.tree_a) (-> tptp.tree_a tptp.multiset_a) (-> tptp.tree_a tptp.tree_a) (-> tptp.tree_a tptp.produc143150363Tree_a)) Bool)
% 0.25/0.63 (declare-fun tptp.heap_axioms_Tree_a_a ((-> tptp.tree_a Bool) (-> tptp.list_a tptp.tree_a) (-> tptp.tree_a tptp.multiset_a) (-> tptp.tree_a tptp.tree_a) (-> tptp.tree_a tptp.produc143150363Tree_a)) Bool)
% 0.25/0.63 (declare-fun tptp.e_a () tptp.tree_a)
% 0.25/0.63 (declare-fun tptp.t_a (tptp.a tptp.tree_a tptp.tree_a) tptp.tree_a)
% 0.25/0.63 (declare-fun tptp.in_tree_a (tptp.a tptp.tree_a) Bool)
% 0.25/0.63 (declare-fun tptp.is_heap_a (tptp.tree_a) Bool)
% 0.25/0.63 (declare-fun tptp.multiset_a2 (tptp.tree_a) tptp.multiset_a)
% 0.25/0.63 (declare-fun tptp.val_a (tptp.tree_a) tptp.a)
% 0.25/0.63 (declare-fun tptp.lattic146396397_Max_a (tptp.set_a) tptp.a)
% 0.25/0.63 (declare-fun tptp.cons_a (tptp.a tptp.list_a) tptp.list_a)
% 0.25/0.63 (declare-fun tptp.add_mset_a (tptp.a tptp.multiset_a) tptp.multiset_a)
% 0.25/0.63 (declare-fun tptp.is_empty_a (tptp.multiset_a) Bool)
% 0.25/0.63 (declare-fun tptp.set_mset_a (tptp.multiset_a) tptp.set_a)
% 0.25/0.63 (declare-fun tptp.subseteq_mset_a (tptp.multiset_a tptp.multiset_a) Bool)
% 0.25/0.63 (declare-fun tptp.ord_less_eq_o_o_a ((-> Bool Bool tptp.a) (-> Bool Bool tptp.a)) Bool)
% 0.25/0.63 (declare-fun tptp.ord_less_eq_o_a ((-> Bool tptp.a) (-> Bool tptp.a)) Bool)
% 0.25/0.63 (declare-fun tptp.ord_le1199012836iset_a (tptp.multiset_a tptp.multiset_a) Bool)
% 0.25/0.63 (declare-fun tptp.ord_less_eq_set_a (tptp.set_a tptp.set_a) Bool)
% 0.25/0.63 (declare-fun tptp.ord_less_eq_a (tptp.a tptp.a) Bool)
% 0.25/0.63 (declare-fun tptp.order_Greatest_o_a ((-> (-> Bool tptp.a) Bool) Bool) tptp.a)
% 0.25/0.63 (declare-fun tptp.order_Greatest_a ((-> tptp.a Bool)) tptp.a)
% 0.25/0.63 (declare-fun tptp.produc1352981801list_a (tptp.tree_a tptp.list_a) tptp.produc768687417list_a)
% 0.25/0.63 (declare-fun tptp.produc686083979Tree_a (tptp.a tptp.tree_a) tptp.produc143150363Tree_a)
% 0.25/0.63 (declare-fun tptp.set_Tree_a_a ((-> tptp.tree_a tptp.multiset_a) tptp.tree_a) tptp.set_a)
% 0.25/0.63 (declare-fun tptp.removeMax_Tree_a_a (tptp.tree_a (-> tptp.tree_a Bool) (-> tptp.list_a tptp.tree_a) (-> tptp.tree_a tptp.multiset_a) (-> tptp.tree_a tptp.produc143150363Tree_a) (-> tptp.tree_a Bool)) Bool)
% 0.25/0.63 (declare-fun tptp.ssort_Tree_a_a ((-> tptp.tree_a Bool) (-> tptp.tree_a tptp.produc143150363Tree_a) tptp.tree_a tptp.list_a) tptp.list_a)
% 0.25/0.63 (declare-fun tptp.ssort_dom_Tree_a_a ((-> tptp.tree_a Bool) (-> tptp.tree_a tptp.produc143150363Tree_a) tptp.produc768687417list_a) Bool)
% 0.25/0.63 (declare-fun tptp.remove301631099ee_a_a ((-> tptp.tree_a Bool) (-> tptp.list_a tptp.tree_a) (-> tptp.tree_a tptp.multiset_a) (-> tptp.tree_a tptp.produc143150363Tree_a) (-> tptp.tree_a Bool)) Bool)
% 0.25/0.63 (declare-fun tptp.collect_a ((-> tptp.a Bool)) tptp.set_a)
% 0.25/0.63 (declare-fun tptp.member_a (tptp.a tptp.set_a) Bool)
% 0.25/0.63 (declare-fun tptp.l1 () tptp.tree_a)
% 0.25/0.63 (declare-fun tptp.l2 () tptp.tree_a)
% 0.25/0.63 (declare-fun tptp.r1 () tptp.tree_a)
% 0.25/0.63 (declare-fun tptp.r2 () tptp.tree_a)
% 0.25/0.63 (declare-fun tptp.v1 () tptp.a)
% 0.25/0.63 (declare-fun tptp.v2 () tptp.a)
% 0.25/0.63 (declare-fun tptp.v () tptp.a)
% 0.25/0.63 (assert (@ (@ tptp.ord_less_eq_a tptp.v2) tptp.v1))
% 0.25/0.63 (assert (@ (@ tptp.ord_less_eq_a tptp.v1) tptp.v))
% 0.25/0.63 (assert (let ((_let_1 (@ (@ (@ tptp.t_a tptp.v2) tptp.l2) tptp.r2))) (let ((_let_2 (@ (@ (@ tptp.t_a tptp.v) (@ tptp.heapIm1140443833left_a _let_1)) (@ tptp.heapIm1257206334ight_a _let_1)))) (let ((_let_3 (@ tptp.ord_less_eq_a (@ tptp.val_a _let_1)))) (=> (not (@ _let_3 (@ tptp.val_a (@ (@ (@ tptp.t_a tptp.v1) tptp.l1) tptp.r1)))) (=> (not (@ _let_3 tptp.v)) (= (@ tptp.multiset_a2 (@ tptp.heapIm1091024090Down_a _let_2)) (@ tptp.multiset_a2 _let_2))))))))
% 0.25/0.63 (assert (let ((_let_1 (@ (@ (@ tptp.t_a tptp.v1) tptp.l1) tptp.r1))) (let ((_let_2 (@ (@ (@ tptp.t_a tptp.v) (@ tptp.heapIm1140443833left_a _let_1)) (@ tptp.heapIm1257206334ight_a _let_1)))) (let ((_let_3 (@ tptp.val_a _let_1))) (=> (@ (@ tptp.ord_less_eq_a (@ tptp.val_a (@ (@ (@ tptp.t_a tptp.v2) tptp.l2) tptp.r2))) _let_3) (=> (not (@ (@ tptp.ord_less_eq_a _let_3) tptp.v)) (= (@ tptp.multiset_a2 (@ tptp.heapIm1091024090Down_a _let_2)) (@ tptp.multiset_a2 _let_2))))))))
% 0.25/0.63 (assert (forall ((T tptp.tree_a) (V tptp.a) (L tptp.tree_a) (R tptp.tree_a)) (=> (= T (@ (@ (@ tptp.t_a V) L) R)) (exists ((L2 tptp.tree_a) (V2 tptp.a) (R2 tptp.tree_a)) (and (= (@ tptp.heapIm1091024090Down_a T) (@ (@ (@ tptp.t_a V2) L2) R2)) (@ (@ tptp.ord_less_eq_a V) V2))))))
% 0.25/0.63 (assert (forall ((X21 tptp.a) (X22 tptp.tree_a) (X23 tptp.tree_a) (Y21 tptp.a) (Y22 tptp.tree_a) (Y23 tptp.tree_a)) (= (= (@ (@ (@ tptp.t_a X21) X22) X23) (@ (@ (@ tptp.t_a Y21) Y22) Y23)) (and (= X21 Y21) (= X22 Y22) (= X23 Y23)))))
% 0.25/0.63 (assert (forall ((V tptp.a) (L tptp.tree_a) (R tptp.tree_a)) (let ((_let_1 (@ tptp.t_a V))) (= (@ tptp.heapIm970322378pify_a (@ (@ _let_1 L) R)) (@ tptp.heapIm1091024090Down_a (@ (@ _let_1 (@ tptp.heapIm970322378pify_a L)) (@ tptp.heapIm970322378pify_a R)))))))
% 0.25/0.63 (assert (forall ((L tptp.tree_a) (R tptp.tree_a) (T tptp.tree_a) (V tptp.a)) (=> (@ tptp.is_heap_a L) (=> (@ tptp.is_heap_a R) (=> (= T (@ (@ (@ tptp.t_a V) L) R)) (@ tptp.is_heap_a (@ tptp.heapIm1091024090Down_a T)))))))
% 0.25/0.63 (assert (= tptp.in_tree_a (lambda ((V3 tptp.a) (T2 tptp.tree_a)) (@ (@ tptp.in_tree_a V3) (@ tptp.heapIm1091024090Down_a T2)))))
% 0.25/0.63 (assert (forall ((V tptp.a) (L tptp.tree_a) (R tptp.tree_a)) (= (@ tptp.heapIm1140443833left_a (@ (@ (@ tptp.t_a V) L) R)) L)))
% 0.25/0.63 (assert (forall ((V tptp.a) (L tptp.tree_a) (R tptp.tree_a)) (= (@ tptp.heapIm1257206334ight_a (@ (@ (@ tptp.t_a V) L) R)) R)))
% 0.25/0.63 (assert (forall ((V tptp.a)) (let ((_let_1 (@ (@ (@ tptp.t_a V) tptp.e_a) tptp.e_a))) (= (@ tptp.heapIm1091024090Down_a _let_1) _let_1))))
% 0.25/0.63 (assert (= (@ tptp.heapIm1091024090Down_a tptp.e_a) tptp.e_a))
% 0.25/0.63 (assert (forall ((V tptp.a)) (not (@ (@ tptp.in_tree_a V) tptp.e_a))))
% 0.25/0.63 (assert (forall ((V tptp.a) (Vd tptp.a) (Ve tptp.tree_a) (Vf tptp.tree_a) (Va tptp.a) (Vb tptp.tree_a) (Vc tptp.tree_a)) (let ((_let_1 (@ (@ (@ tptp.t_a Vd) Ve) Vf))) (let ((_let_2 (@ (@ (@ tptp.t_a Va) Vb) Vc))) (= (@ tptp.is_heap_a (@ (@ (@ tptp.t_a V) _let_1) _let_2)) (and (@ (@ tptp.ord_less_eq_a (@ tptp.val_a _let_2)) V) (@ tptp.is_heap_a _let_2) (@ (@ tptp.ord_less_eq_a (@ tptp.val_a _let_1)) V) (@ tptp.is_heap_a _let_1)))))))
% 0.25/0.63 (assert (forall ((V tptp.a) (Va tptp.a) (Vb tptp.tree_a) (Vc tptp.tree_a) (Vd tptp.a) (Ve tptp.tree_a) (Vf tptp.tree_a)) (let ((_let_1 (@ (@ (@ tptp.t_a Va) Vb) Vc))) (let ((_let_2 (@ (@ (@ tptp.t_a Vd) Ve) Vf))) (= (@ tptp.is_heap_a (@ (@ (@ tptp.t_a V) _let_1) _let_2)) (and (@ (@ tptp.ord_less_eq_a (@ tptp.val_a _let_2)) V) (@ tptp.is_heap_a _let_2) (@ (@ tptp.ord_less_eq_a (@ tptp.val_a _let_1)) V) (@ tptp.is_heap_a _let_1)))))))
% 0.25/0.63 (assert (forall ((V tptp.a) (Va tptp.a) (Vb tptp.tree_a) (Vc tptp.tree_a)) (let ((_let_1 (@ (@ (@ tptp.t_a Va) Vb) Vc))) (= (@ tptp.is_heap_a (@ (@ (@ tptp.t_a V) _let_1) tptp.e_a)) (and (@ (@ tptp.ord_less_eq_a (@ tptp.val_a _let_1)) V) (@ tptp.is_heap_a _let_1))))))
% 0.25/0.63 (assert (forall ((V tptp.a) (Va tptp.a) (Vb tptp.tree_a) (Vc tptp.tree_a)) (let ((_let_1 (@ (@ (@ tptp.t_a Va) Vb) Vc))) (= (@ tptp.is_heap_a (@ (@ (@ tptp.t_a V) tptp.e_a) _let_1)) (and (@ (@ tptp.ord_less_eq_a (@ tptp.val_a _let_1)) V) (@ tptp.is_heap_a _let_1))))))
% 0.25/0.63 (assert (forall ((V tptp.a)) (@ tptp.is_heap_a (@ (@ (@ tptp.t_a V) tptp.e_a) tptp.e_a))))
% 0.25/0.63 (assert (@ tptp.is_heap_a tptp.e_a))
% 0.25/0.63 (assert (= (@ tptp.heapIm970322378pify_a tptp.e_a) tptp.e_a))
% 0.25/0.63 (assert (forall ((V tptp.a) (T tptp.tree_a)) (=> (@ (@ tptp.in_tree_a V) T) (=> (@ tptp.is_heap_a T) (@ (@ tptp.ord_less_eq_a V) (@ tptp.val_a T))))))
% 0.25/0.63 (assert (forall ((T tptp.tree_a)) (@ tptp.is_heap_a (@ tptp.heapIm970322378pify_a T))))
% 0.25/0.63 (assert (forall ((T tptp.tree_a)) (=> (not (= T tptp.e_a)) (@ (@ tptp.in_tree_a (@ tptp.val_a (@ tptp.heapIm1091024090Down_a T))) T))))
% 0.25/0.63 (assert (forall ((X tptp.tree_a)) (=> (not (= X tptp.e_a)) (=> (forall ((V4 tptp.a)) (not (= X (@ (@ (@ tptp.t_a V4) tptp.e_a) tptp.e_a)))) (=> (forall ((V4 tptp.a) (Va2 tptp.a) (Vb2 tptp.tree_a) (Vc2 tptp.tree_a)) (not (= X (@ (@ (@ tptp.t_a V4) tptp.e_a) (@ (@ (@ tptp.t_a Va2) Vb2) Vc2))))) (=> (forall ((V4 tptp.a) (Va2 tptp.a) (Vb2 tptp.tree_a) (Vc2 tptp.tree_a)) (not (= X (@ (@ (@ tptp.t_a V4) (@ (@ (@ tptp.t_a Va2) Vb2) Vc2)) tptp.e_a)))) (not (forall ((V4 tptp.a) (Va2 tptp.a) (Vb2 tptp.tree_a) (Vc2 tptp.tree_a) (Vd2 tptp.a) (Ve2 tptp.tree_a) (Vf2 tptp.tree_a)) (not (= X (@ (@ (@ tptp.t_a V4) (@ (@ (@ tptp.t_a Va2) Vb2) Vc2)) (@ (@ (@ tptp.t_a Vd2) Ve2) Vf2))))))))))))
% 0.25/0.63 (assert (forall ((Y tptp.tree_a)) (=> (not (= Y tptp.e_a)) (not (forall ((X212 tptp.a) (X222 tptp.tree_a) (X232 tptp.tree_a)) (not (= Y (@ (@ (@ tptp.t_a X212) X222) X232))))))))
% 0.25/0.63 (assert (forall ((P (-> tptp.tree_a Bool)) (Tree tptp.tree_a)) (=> (@ P tptp.e_a) (=> (forall ((X1 tptp.a) (X2 tptp.tree_a) (X3 tptp.tree_a)) (=> (@ P X2) (=> (@ P X3) (@ P (@ (@ (@ tptp.t_a X1) X2) X3))))) (@ P Tree)))))
% 0.25/0.63 (assert (forall ((X21 tptp.a) (X22 tptp.tree_a) (X23 tptp.tree_a)) (not (= tptp.e_a (@ (@ (@ tptp.t_a X21) X22) X23)))))
% 0.25/0.63 (assert (forall ((Va tptp.a) (Vb tptp.tree_a) (Vc tptp.tree_a) (V tptp.a)) (let ((_let_1 (@ (@ (@ tptp.t_a Va) Vb) Vc))) (let ((_let_2 (@ tptp.t_a V))) (let ((_let_3 (@ tptp.val_a _let_1))) (let ((_let_4 (@ (@ _let_2 _let_1) tptp.e_a))) (let ((_let_5 (@ tptp.heapIm1091024090Down_a _let_4))) (let ((_let_6 (@ (@ tptp.ord_less_eq_a _let_3) V))) (and (=> _let_6 (= _let_5 _let_4)) (=> (not _let_6) (= _let_5 (@ (@ (@ tptp.t_a _let_3) (@ tptp.heapIm1091024090Down_a (@ (@ _let_2 (@ tptp.heapIm1140443833left_a _let_1)) (@ tptp.heapIm1257206334ight_a _let_1)))) tptp.e_a))))))))))))
% 0.25/0.63 (assert (forall ((Va tptp.a) (Vb tptp.tree_a) (Vc tptp.tree_a) (V tptp.a)) (let ((_let_1 (@ (@ (@ tptp.t_a Va) Vb) Vc))) (let ((_let_2 (@ tptp.t_a V))) (let ((_let_3 (@ tptp.val_a _let_1))) (let ((_let_4 (@ (@ _let_2 tptp.e_a) _let_1))) (let ((_let_5 (@ tptp.heapIm1091024090Down_a _let_4))) (let ((_let_6 (@ (@ tptp.ord_less_eq_a _let_3) V))) (and (=> _let_6 (= _let_5 _let_4)) (=> (not _let_6) (= _let_5 (@ (@ (@ tptp.t_a _let_3) tptp.e_a) (@ tptp.heapIm1091024090Down_a (@ (@ _let_2 (@ tptp.heapIm1140443833left_a _let_1)) (@ tptp.heapIm1257206334ight_a _let_1)))))))))))))))
% 0.25/0.63 (assert (forall ((V tptp.a) (Uu tptp.tree_a) (Uv tptp.tree_a)) (= (@ tptp.val_a (@ (@ (@ tptp.t_a V) Uu) Uv)) V)))
% 0.25/0.63 (assert (forall ((Vd tptp.a) (Ve tptp.tree_a) (Vf tptp.tree_a) (Va tptp.a) (Vb tptp.tree_a) (Vc tptp.tree_a) (V tptp.a)) (let ((_let_1 (@ (@ (@ tptp.t_a Vd) Ve) Vf))) (let ((_let_2 (@ tptp.t_a V))) (let ((_let_3 (@ (@ (@ tptp.t_a Va) Vb) Vc))) (let ((_let_4 (@ tptp.val_a _let_1))) (let ((_let_5 (@ (@ _let_2 _let_3) _let_1))) (let ((_let_6 (@ tptp.heapIm1091024090Down_a _let_5))) (let ((_let_7 (@ tptp.ord_less_eq_a _let_4))) (let ((_let_8 (@ _let_7 V))) (let ((_let_9 (= _let_6 _let_5))) (let ((_let_10 (@ tptp.val_a _let_3))) (let ((_let_11 (@ _let_7 _let_10))) (let ((_let_12 (@ (@ tptp.ord_less_eq_a _let_10) V))) (and (=> _let_11 (and (=> _let_12 _let_9) (=> (not _let_12) (= _let_6 (@ (@ (@ tptp.t_a _let_10) (@ tptp.heapIm1091024090Down_a (@ (@ _let_2 (@ tptp.heapIm1140443833left_a _let_3)) (@ tptp.heapIm1257206334ight_a _let_3)))) _let_1))))) (=> (not _let_11) (and (=> _let_8 _let_9) (=> (not _let_8) (= _let_6 (@ (@ (@ tptp.t_a _let_4) _let_3) (@ tptp.heapIm1091024090Down_a (@ (@ _let_2 (@ tptp.heapIm1140443833left_a _let_1)) (@ tptp.heapIm1257206334ight_a _let_1)))))))))))))))))))))))
% 0.25/0.63 (assert (forall ((Va tptp.a) (Vb tptp.tree_a) (Vc tptp.tree_a) (Vd tptp.a) (Ve tptp.tree_a) (Vf tptp.tree_a) (V tptp.a)) (let ((_let_1 (@ (@ (@ tptp.t_a Va) Vb) Vc))) (let ((_let_2 (@ tptp.t_a V))) (let ((_let_3 (@ (@ (@ tptp.t_a Vd) Ve) Vf))) (let ((_let_4 (@ tptp.val_a _let_1))) (let ((_let_5 (@ (@ _let_2 _let_3) _let_1))) (let ((_let_6 (@ tptp.heapIm1091024090Down_a _let_5))) (let ((_let_7 (@ tptp.ord_less_eq_a _let_4))) (let ((_let_8 (@ _let_7 V))) (let ((_let_9 (= _let_6 _let_5))) (let ((_let_10 (@ tptp.val_a _let_3))) (let ((_let_11 (@ _let_7 _let_10))) (let ((_let_12 (@ (@ tptp.ord_less_eq_a _let_10) V))) (and (=> _let_11 (and (=> _let_12 _let_9) (=> (not _let_12) (= _let_6 (@ (@ (@ tptp.t_a _let_10) (@ tptp.heapIm1091024090Down_a (@ (@ _let_2 (@ tptp.heapIm1140443833left_a _let_3)) (@ tptp.heapIm1257206334ight_a _let_3)))) _let_1))))) (=> (not _let_11) (and (=> _let_8 _let_9) (=> (not _let_8) (= _let_6 (@ (@ (@ tptp.t_a _let_4) _let_3) (@ tptp.heapIm1091024090Down_a (@ (@ _let_2 (@ tptp.heapIm1140443833left_a _let_1)) (@ tptp.heapIm1257206334ight_a _let_1)))))))))))))))))))))))
% 0.25/0.63 (assert (forall ((V tptp.a) (V5 tptp.a) (L tptp.tree_a) (R tptp.tree_a)) (let ((_let_1 (@ tptp.in_tree_a V))) (= (@ _let_1 (@ (@ (@ tptp.t_a V5) L) R)) (or (= V V5) (@ _let_1 L) (@ _let_1 R))))))
% 0.25/0.63 (assert (forall ((P (-> tptp.tree_a Bool)) (A0 tptp.tree_a)) (=> (forall ((V4 tptp.a)) (@ P (@ (@ (@ tptp.t_a V4) tptp.e_a) tptp.e_a))) (=> (forall ((V4 tptp.a) (Va2 tptp.a) (Vb2 tptp.tree_a) (Vc2 tptp.tree_a)) (let ((_let_1 (@ (@ (@ tptp.t_a Va2) Vb2) Vc2))) (let ((_let_2 (@ P _let_1))) (=> _let_2 (=> _let_2 (@ P (@ (@ (@ tptp.t_a V4) _let_1) tptp.e_a))))))) (=> (forall ((V4 tptp.a) (Va2 tptp.a) (Vb2 tptp.tree_a) (Vc2 tptp.tree_a)) (let ((_let_1 (@ (@ (@ tptp.t_a Va2) Vb2) Vc2))) (let ((_let_2 (@ P _let_1))) (=> _let_2 (=> _let_2 (@ P (@ (@ (@ tptp.t_a V4) tptp.e_a) _let_1))))))) (=> (forall ((V4 tptp.a) (Va2 tptp.a) (Vb2 tptp.tree_a) (Vc2 tptp.tree_a) (Vd2 tptp.a) (Ve2 tptp.tree_a) (Vf2 tptp.tree_a)) (let ((_let_1 (@ (@ (@ tptp.t_a Va2) Vb2) Vc2))) (let ((_let_2 (@ P _let_1))) (=> _let_2 (=> _let_2 (@ P (@ (@ (@ tptp.t_a V4) _let_1) (@ (@ (@ tptp.t_a Vd2) Ve2) Vf2)))))))) (=> (forall ((V4 tptp.a) (Vd2 tptp.a) (Ve2 tptp.tree_a) (Vf2 tptp.tree_a) (Va2 tptp.a) (Vb2 tptp.tree_a) (Vc2 tptp.tree_a)) (let ((_let_1 (@ (@ (@ tptp.t_a Vd2) Ve2) Vf2))) (let ((_let_2 (@ P _let_1))) (=> _let_2 (=> _let_2 (@ P (@ (@ (@ tptp.t_a V4) _let_1) (@ (@ (@ tptp.t_a Va2) Vb2) Vc2)))))))) (=> (@ P tptp.e_a) (@ P A0)))))))))
% 0.25/0.63 (assert (forall ((X tptp.tree_a)) (=> (forall ((V4 tptp.a)) (not (= X (@ (@ (@ tptp.t_a V4) tptp.e_a) tptp.e_a)))) (=> (forall ((V4 tptp.a) (Va2 tptp.a) (Vb2 tptp.tree_a) (Vc2 tptp.tree_a)) (not (= X (@ (@ (@ tptp.t_a V4) (@ (@ (@ tptp.t_a Va2) Vb2) Vc2)) tptp.e_a)))) (=> (forall ((V4 tptp.a) (Va2 tptp.a) (Vb2 tptp.tree_a) (Vc2 tptp.tree_a)) (not (= X (@ (@ (@ tptp.t_a V4) tptp.e_a) (@ (@ (@ tptp.t_a Va2) Vb2) Vc2))))) (=> (forall ((V4 tptp.a) (Va2 tptp.a) (Vb2 tptp.tree_a) (Vc2 tptp.tree_a) (Vd2 tptp.a) (Ve2 tptp.tree_a) (Vf2 tptp.tree_a)) (not (= X (@ (@ (@ tptp.t_a V4) (@ (@ (@ tptp.t_a Va2) Vb2) Vc2)) (@ (@ (@ tptp.t_a Vd2) Ve2) Vf2))))) (=> (forall ((V4 tptp.a) (Vd2 tptp.a) (Ve2 tptp.tree_a) (Vf2 tptp.tree_a) (Va2 tptp.a) (Vb2 tptp.tree_a) (Vc2 tptp.tree_a)) (not (= X (@ (@ (@ tptp.t_a V4) (@ (@ (@ tptp.t_a Vd2) Ve2) Vf2)) (@ (@ (@ tptp.t_a Va2) Vb2) Vc2))))) (= X tptp.e_a))))))))
% 0.25/0.63 (assert (forall ((X tptp.tree_a)) (=> (not (= X tptp.e_a)) (=> (forall ((V4 tptp.a)) (not (= X (@ (@ (@ tptp.t_a V4) tptp.e_a) tptp.e_a)))) (=> (forall ((V4 tptp.a) (Va2 tptp.a) (Vb2 tptp.tree_a) (Vc2 tptp.tree_a)) (not (= X (@ (@ (@ tptp.t_a V4) (@ (@ (@ tptp.t_a Va2) Vb2) Vc2)) tptp.e_a)))) (=> (forall ((V4 tptp.a) (Va2 tptp.a) (Vb2 tptp.tree_a) (Vc2 tptp.tree_a)) (not (= X (@ (@ (@ tptp.t_a V4) tptp.e_a) (@ (@ (@ tptp.t_a Va2) Vb2) Vc2))))) (not (forall ((V4 tptp.a) (Va2 tptp.a) (Vb2 tptp.tree_a) (Vc2 tptp.tree_a) (Vd2 tptp.a) (Ve2 tptp.tree_a) (Vf2 tptp.tree_a)) (not (= X (@ (@ (@ tptp.t_a V4) (@ (@ (@ tptp.t_a Va2) Vb2) Vc2)) (@ (@ (@ tptp.t_a Vd2) Ve2) Vf2))))))))))))
% 0.25/0.63 (assert (= tptp.heapIm229596386mpty_a (lambda ((T2 tptp.tree_a)) (= T2 tptp.e_a))))
% 0.25/0.63 (assert (forall ((X (-> Bool tptp.a))) (@ (@ tptp.ord_less_eq_o_a X) X)))
% 0.25/0.63 (assert (forall ((X tptp.a)) (@ (@ tptp.ord_less_eq_a X) X)))
% 0.25/0.63 (assert (forall ((A tptp.a) (T tptp.tree_a)) (=> (@ (@ tptp.member_a A) (@ tptp.set_mset_a (@ tptp.multiset_a2 T))) (=> (@ tptp.is_heap_a T) (@ (@ tptp.ord_less_eq_a A) (@ tptp.val_a T))))))
% 0.25/0.63 (assert (= tptp.heapIm1057938560list_a (lambda ((L3 tptp.list_a)) (@ tptp.heapIm970322378pify_a (@ tptp.heapIm1637418125tree_a L3)))))
% 0.25/0.63 (assert (forall ((A tptp.a) (P (-> tptp.a Bool))) (= (@ (@ tptp.member_a A) (@ tptp.collect_a P)) (@ P A))))
% 0.25/0.63 (assert (forall ((A2 tptp.set_a)) (= (@ tptp.collect_a (lambda ((X4 tptp.a)) (@ (@ tptp.member_a X4) A2))) A2)))
% 0.25/0.63 (assert (forall ((F (-> Bool tptp.a)) (G (-> Bool tptp.a)) (X Bool)) (=> (@ (@ tptp.ord_less_eq_o_a F) G) (@ (@ tptp.ord_less_eq_a (@ F X)) (@ G X)))))
% 0.25/0.63 (assert (forall ((F (-> Bool tptp.a)) (G (-> Bool tptp.a)) (X Bool)) (=> (@ (@ tptp.ord_less_eq_o_a F) G) (@ (@ tptp.ord_less_eq_a (@ F X)) (@ G X)))))
% 0.25/0.63 (assert (forall ((F (-> Bool tptp.a)) (G (-> Bool tptp.a))) (=> (forall ((X5 Bool)) (@ (@ tptp.ord_less_eq_a (@ F X5)) (@ G X5))) (@ (@ tptp.ord_less_eq_o_a F) G))))
% 0.25/0.63 (assert (= tptp.ord_less_eq_o_a (lambda ((F2 (-> Bool tptp.a)) (G2 (-> Bool tptp.a))) (forall ((X4 Bool)) (@ (@ tptp.ord_less_eq_a (@ F2 X4)) (@ G2 X4))))))
% 0.25/0.63 (assert (forall ((A tptp.a) (F (-> (-> Bool tptp.a) tptp.a)) (B (-> Bool tptp.a)) (C (-> Bool tptp.a))) (let ((_let_1 (@ tptp.ord_less_eq_a A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_o_a B) C) (=> (forall ((X5 (-> Bool tptp.a)) (Y2 (-> Bool tptp.a))) (=> (@ (@ tptp.ord_less_eq_o_a X5) Y2) (@ (@ tptp.ord_less_eq_a (@ F X5)) (@ F Y2)))) (@ _let_1 (@ F C))))))))
% 0.25/0.63 (assert (forall ((A (-> Bool tptp.a)) (F (-> tptp.a Bool tptp.a)) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.ord_less_eq_o_a A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_a B) C) (=> (forall ((X5 tptp.a) (Y2 tptp.a)) (=> (@ (@ tptp.ord_less_eq_a X5) Y2) (@ (@ tptp.ord_less_eq_o_a (@ F X5)) (@ F Y2)))) (@ _let_1 (@ F C))))))))
% 0.25/0.63 (assert (forall ((A (-> Bool tptp.a)) (F (-> (-> Bool tptp.a) Bool tptp.a)) (B (-> Bool tptp.a)) (C (-> Bool tptp.a))) (let ((_let_1 (@ tptp.ord_less_eq_o_a A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_o_a B) C) (=> (forall ((X5 (-> Bool tptp.a)) (Y2 (-> Bool tptp.a))) (=> (@ (@ tptp.ord_less_eq_o_a X5) Y2) (@ (@ tptp.ord_less_eq_o_a (@ F X5)) (@ F Y2)))) (@ _let_1 (@ F C))))))))
% 0.25/0.63 (assert (forall ((A tptp.a) (F (-> tptp.a tptp.a)) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.ord_less_eq_a A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_a B) C) (=> (forall ((X5 tptp.a) (Y2 tptp.a)) (=> (@ (@ tptp.ord_less_eq_a X5) Y2) (@ (@ tptp.ord_less_eq_a (@ F X5)) (@ F Y2)))) (@ _let_1 (@ F C))))))))
% 0.25/0.63 (assert (forall ((A tptp.a) (B tptp.a) (F (-> tptp.a Bool tptp.a)) (C (-> Bool tptp.a))) (=> (@ (@ tptp.ord_less_eq_a A) B) (=> (@ (@ tptp.ord_less_eq_o_a (@ F B)) C) (=> (forall ((X5 tptp.a) (Y2 tptp.a)) (=> (@ (@ tptp.ord_less_eq_a X5) Y2) (@ (@ tptp.ord_less_eq_o_a (@ F X5)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_o_a (@ F A)) C))))))
% 0.25/0.63 (assert (forall ((A (-> Bool tptp.a)) (B (-> Bool tptp.a)) (F (-> (-> Bool tptp.a) tptp.a)) (C tptp.a)) (=> (@ (@ tptp.ord_less_eq_o_a A) B) (=> (@ (@ tptp.ord_less_eq_a (@ F B)) C) (=> (forall ((X5 (-> Bool tptp.a)) (Y2 (-> Bool tptp.a))) (=> (@ (@ tptp.ord_less_eq_o_a X5) Y2) (@ (@ tptp.ord_less_eq_a (@ F X5)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_a (@ F A)) C))))))
% 0.25/0.63 (assert (forall ((A (-> Bool tptp.a)) (B (-> Bool tptp.a)) (F (-> (-> Bool tptp.a) Bool tptp.a)) (C (-> Bool tptp.a))) (=> (@ (@ tptp.ord_less_eq_o_a A) B) (=> (@ (@ tptp.ord_less_eq_o_a (@ F B)) C) (=> (forall ((X5 (-> Bool tptp.a)) (Y2 (-> Bool tptp.a))) (=> (@ (@ tptp.ord_less_eq_o_a X5) Y2) (@ (@ tptp.ord_less_eq_o_a (@ F X5)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_o_a (@ F A)) C))))))
% 0.25/0.63 (assert (forall ((A tptp.a) (B tptp.a) (F (-> tptp.a tptp.a)) (C tptp.a)) (=> (@ (@ tptp.ord_less_eq_a A) B) (=> (@ (@ tptp.ord_less_eq_a (@ F B)) C) (=> (forall ((X5 tptp.a) (Y2 tptp.a)) (=> (@ (@ tptp.ord_less_eq_a X5) Y2) (@ (@ tptp.ord_less_eq_a (@ F X5)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_a (@ F A)) C))))))
% 0.25/0.63 (assert (forall ((B (-> Bool tptp.a)) (A (-> Bool tptp.a))) (=> (@ (@ tptp.ord_less_eq_o_a B) A) (=> (@ (@ tptp.ord_less_eq_o_a A) B) (= A B)))))
% 0.25/0.63 (assert (forall ((B tptp.a) (A tptp.a)) (=> (@ (@ tptp.ord_less_eq_a B) A) (=> (@ (@ tptp.ord_less_eq_a A) B) (= A B)))))
% 0.25/0.63 (assert (= (lambda ((Y3 (-> Bool tptp.a)) (Z (-> Bool tptp.a))) (= Y3 Z)) (lambda ((A3 (-> Bool tptp.a)) (B2 (-> Bool tptp.a))) (and (@ (@ tptp.ord_less_eq_o_a B2) A3) (@ (@ tptp.ord_less_eq_o_a A3) B2)))))
% 0.25/0.63 (assert (= (lambda ((Y3 tptp.a) (Z tptp.a)) (= Y3 Z)) (lambda ((A3 tptp.a) (B2 tptp.a)) (and (@ (@ tptp.ord_less_eq_a B2) A3) (@ (@ tptp.ord_less_eq_a A3) B2)))))
% 0.25/0.63 (assert (forall ((B (-> Bool tptp.a)) (A (-> Bool tptp.a)) (C (-> Bool tptp.a))) (let ((_let_1 (@ tptp.ord_less_eq_o_a C))) (=> (@ (@ tptp.ord_less_eq_o_a B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 0.25/0.63 (assert (forall ((B tptp.a) (A tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.ord_less_eq_a C))) (=> (@ (@ tptp.ord_less_eq_a B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 0.25/0.63 (assert (forall ((P (-> tptp.a tptp.a Bool)) (A tptp.a) (B tptp.a)) (=> (forall ((A4 tptp.a) (B3 tptp.a)) (=> (@ (@ tptp.ord_less_eq_a A4) B3) (@ (@ P A4) B3))) (=> (forall ((A4 tptp.a) (B3 tptp.a)) (=> (@ (@ P B3) A4) (@ (@ P A4) B3))) (@ (@ P A) B)))))
% 0.25/0.63 (assert (forall ((A (-> Bool tptp.a))) (@ (@ tptp.ord_less_eq_o_a A) A)))
% 0.25/0.63 (assert (forall ((A tptp.a)) (@ (@ tptp.ord_less_eq_a A) A)))
% 0.25/0.63 (assert (forall ((X (-> Bool tptp.a)) (Y (-> Bool tptp.a)) (Z2 (-> Bool tptp.a))) (let ((_let_1 (@ tptp.ord_less_eq_o_a X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_o_a Y) Z2) (@ _let_1 Z2))))))
% 0.25/0.63 (assert (forall ((X tptp.a) (Y tptp.a) (Z2 tptp.a)) (let ((_let_1 (@ tptp.ord_less_eq_a X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_a Y) Z2) (@ _let_1 Z2))))))
% 0.25/0.63 (assert (forall ((A (-> Bool tptp.a)) (B (-> Bool tptp.a))) (=> (@ (@ tptp.ord_less_eq_o_a A) B) (=> (@ (@ tptp.ord_less_eq_o_a B) A) (= A B)))))
% 0.25/0.63 (assert (forall ((A tptp.a) (B tptp.a)) (=> (@ (@ tptp.ord_less_eq_a A) B) (=> (@ (@ tptp.ord_less_eq_a B) A) (= A B)))))
% 0.25/0.63 (assert (forall ((A (-> Bool tptp.a)) (B (-> Bool tptp.a)) (C (-> Bool tptp.a))) (let ((_let_1 (@ tptp.ord_less_eq_o_a A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 0.25/0.63 (assert (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.ord_less_eq_a A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 0.25/0.63 (assert (forall ((A (-> Bool tptp.a)) (B (-> Bool tptp.a)) (C (-> Bool tptp.a))) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_o_a B) C) (@ (@ tptp.ord_less_eq_o_a A) C)))))
% 0.25/0.63 (assert (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_a B) C) (@ (@ tptp.ord_less_eq_a A) C)))))
% 0.25/0.63 (assert (= (lambda ((Y3 (-> Bool tptp.a)) (Z (-> Bool tptp.a))) (= Y3 Z)) (lambda ((A3 (-> Bool tptp.a)) (B2 (-> Bool tptp.a))) (and (@ (@ tptp.ord_less_eq_o_a A3) B2) (@ (@ tptp.ord_less_eq_o_a B2) A3)))))
% 0.25/0.63 (assert (= (lambda ((Y3 tptp.a) (Z tptp.a)) (= Y3 Z)) (lambda ((A3 tptp.a) (B2 tptp.a)) (and (@ (@ tptp.ord_less_eq_a A3) B2) (@ (@ tptp.ord_less_eq_a B2) A3)))))
% 0.25/0.63 (assert (forall ((Y (-> Bool tptp.a)) (X (-> Bool tptp.a))) (=> (@ (@ tptp.ord_less_eq_o_a Y) X) (= (@ (@ tptp.ord_less_eq_o_a X) Y) (= X Y)))))
% 0.25/0.63 (assert (forall ((Y tptp.a) (X tptp.a)) (=> (@ (@ tptp.ord_less_eq_a Y) X) (= (@ (@ tptp.ord_less_eq_a X) Y) (= X Y)))))
% 0.25/0.63 (assert (forall ((X tptp.a) (Y tptp.a) (Z2 tptp.a)) (let ((_let_1 (@ tptp.ord_less_eq_a X))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ tptp.ord_less_eq_a Z2))) (let ((_let_4 (@ _let_3 X))) (let ((_let_5 (@ tptp.ord_less_eq_a Y))) (let ((_let_6 (@ _let_5 Z2))) (let ((_let_7 (@ _let_5 X))) (let ((_let_8 (@ _let_3 Y))) (let ((_let_9 (@ _let_1 Z2))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))))
% 0.25/0.63 (assert (forall ((A (-> Bool tptp.a)) (B (-> Bool tptp.a)) (C (-> Bool tptp.a))) (let ((_let_1 (@ tptp.ord_less_eq_o_a A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_o_a B) C) (@ _let_1 C))))))
% 0.25/0.63 (assert (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.ord_less_eq_a A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_a B) C) (@ _let_1 C))))))
% 0.25/0.63 (assert (forall ((X tptp.a) (Y tptp.a)) (=> (not (@ (@ tptp.ord_less_eq_a X) Y)) (@ (@ tptp.ord_less_eq_a Y) X))))
% 0.25/0.63 (assert (forall ((X (-> Bool tptp.a)) (Y (-> Bool tptp.a))) (=> (= X Y) (@ (@ tptp.ord_less_eq_o_a X) Y))))
% 0.25/0.63 (assert (forall ((X tptp.a) (Y tptp.a)) (=> (= X Y) (@ (@ tptp.ord_less_eq_a X) Y))))
% 0.25/0.63 (assert (forall ((X tptp.a) (Y tptp.a)) (or (@ (@ tptp.ord_less_eq_a X) Y) (@ (@ tptp.ord_less_eq_a Y) X))))
% 0.25/0.63 (assert (forall ((X (-> Bool tptp.a)) (Y (-> Bool tptp.a))) (=> (@ (@ tptp.ord_less_eq_o_a X) Y) (=> (@ (@ tptp.ord_less_eq_o_a Y) X) (= X Y)))))
% 0.25/0.63 (assert (forall ((X tptp.a) (Y tptp.a)) (=> (@ (@ tptp.ord_less_eq_a X) Y) (=> (@ (@ tptp.ord_less_eq_a Y) X) (= X Y)))))
% 0.25/0.63 (assert (= (lambda ((Y3 (-> Bool tptp.a)) (Z (-> Bool tptp.a))) (= Y3 Z)) (lambda ((X4 (-> Bool tptp.a)) (Y4 (-> Bool tptp.a))) (and (@ (@ tptp.ord_less_eq_o_a X4) Y4) (@ (@ tptp.ord_less_eq_o_a Y4) X4)))))
% 0.25/0.63 (assert (= (lambda ((Y3 tptp.a) (Z tptp.a)) (= Y3 Z)) (lambda ((X4 tptp.a) (Y4 tptp.a)) (and (@ (@ tptp.ord_less_eq_a X4) Y4) (@ (@ tptp.ord_less_eq_a Y4) X4)))))
% 0.25/0.63 (assert (forall ((A tptp.a) (B tptp.a) (F (-> tptp.a Bool tptp.a)) (C (-> Bool tptp.a))) (=> (@ (@ tptp.ord_less_eq_a A) B) (=> (= (@ F B) C) (=> (forall ((X5 tptp.a) (Y2 tptp.a)) (=> (@ (@ tptp.ord_less_eq_a X5) Y2) (@ (@ tptp.ord_less_eq_o_a (@ F X5)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_o_a (@ F A)) C))))))
% 0.25/0.63 (assert (forall ((A (-> Bool tptp.a)) (B (-> Bool tptp.a)) (F (-> (-> Bool tptp.a) tptp.a)) (C tptp.a)) (=> (@ (@ tptp.ord_less_eq_o_a A) B) (=> (= (@ F B) C) (=> (forall ((X5 (-> Bool tptp.a)) (Y2 (-> Bool tptp.a))) (=> (@ (@ tptp.ord_less_eq_o_a X5) Y2) (@ (@ tptp.ord_less_eq_a (@ F X5)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_a (@ F A)) C))))))
% 0.25/0.63 (assert (forall ((A (-> Bool tptp.a)) (B (-> Bool tptp.a)) (F (-> (-> Bool tptp.a) Bool tptp.a)) (C (-> Bool tptp.a))) (=> (@ (@ tptp.ord_less_eq_o_a A) B) (=> (= (@ F B) C) (=> (forall ((X5 (-> Bool tptp.a)) (Y2 (-> Bool tptp.a))) (=> (@ (@ tptp.ord_less_eq_o_a X5) Y2) (@ (@ tptp.ord_less_eq_o_a (@ F X5)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_o_a (@ F A)) C))))))
% 0.25/0.63 (assert (forall ((A tptp.a) (B tptp.a) (F (-> tptp.a tptp.a)) (C tptp.a)) (=> (@ (@ tptp.ord_less_eq_a A) B) (=> (= (@ F B) C) (=> (forall ((X5 tptp.a) (Y2 tptp.a)) (=> (@ (@ tptp.ord_less_eq_a X5) Y2) (@ (@ tptp.ord_less_eq_a (@ F X5)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_a (@ F A)) C))))))
% 0.25/0.63 (assert (forall ((A (-> Bool tptp.a)) (F (-> tptp.a Bool tptp.a)) (B tptp.a) (C tptp.a)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_a B) C) (=> (forall ((X5 tptp.a) (Y2 tptp.a)) (=> (@ (@ tptp.ord_less_eq_a X5) Y2) (@ (@ tptp.ord_less_eq_o_a (@ F X5)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_o_a A) (@ F C)))))))
% 0.25/0.63 (assert (forall ((A tptp.a) (F (-> (-> Bool tptp.a) tptp.a)) (B (-> Bool tptp.a)) (C (-> Bool tptp.a))) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_o_a B) C) (=> (forall ((X5 (-> Bool tptp.a)) (Y2 (-> Bool tptp.a))) (=> (@ (@ tptp.ord_less_eq_o_a X5) Y2) (@ (@ tptp.ord_less_eq_a (@ F X5)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_a A) (@ F C)))))))
% 0.25/0.63 (assert (forall ((A (-> Bool tptp.a)) (F (-> (-> Bool tptp.a) Bool tptp.a)) (B (-> Bool tptp.a)) (C (-> Bool tptp.a))) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_o_a B) C) (=> (forall ((X5 (-> Bool tptp.a)) (Y2 (-> Bool tptp.a))) (=> (@ (@ tptp.ord_less_eq_o_a X5) Y2) (@ (@ tptp.ord_less_eq_o_a (@ F X5)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_o_a A) (@ F C)))))))
% 0.25/0.63 (assert (forall ((A tptp.a) (F (-> tptp.a tptp.a)) (B tptp.a) (C tptp.a)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_a B) C) (=> (forall ((X5 tptp.a) (Y2 tptp.a)) (=> (@ (@ tptp.ord_less_eq_a X5) Y2) (@ (@ tptp.ord_less_eq_a (@ F X5)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_a A) (@ F C)))))))
% 0.25/0.63 (assert (forall ((T tptp.tree_a)) (=> (not (= T tptp.e_a)) (=> (@ tptp.is_heap_a T) (= (@ tptp.val_a T) (@ tptp.lattic146396397_Max_a (@ tptp.set_mset_a (@ tptp.multiset_a2 T))))))))
% 0.25/0.63 (assert (forall ((V tptp.a) (Tail tptp.list_a)) (= (@ tptp.heapIm1637418125tree_a (@ (@ tptp.cons_a V) Tail)) (@ (@ (@ tptp.t_a V) (@ tptp.heapIm1637418125tree_a Tail)) tptp.e_a))))
% 0.25/0.63 (assert (forall ((P (-> (-> Bool tptp.a) Bool)) (X (-> Bool tptp.a))) (=> (@ P X) (=> (forall ((Y2 (-> Bool tptp.a))) (=> (@ P Y2) (@ (@ tptp.ord_less_eq_o_a Y2) X))) (= (@ tptp.order_Greatest_o_a P) X)))))
% 0.25/0.63 (assert (forall ((P (-> tptp.a Bool)) (X tptp.a)) (=> (@ P X) (=> (forall ((Y2 tptp.a)) (=> (@ P Y2) (@ (@ tptp.ord_less_eq_a Y2) X))) (= (@ tptp.order_Greatest_a P) X)))))
% 0.25/0.63 (assert (forall ((P (-> (-> Bool tptp.a) Bool)) (X (-> Bool tptp.a)) (Q (-> (-> Bool tptp.a) Bool))) (=> (@ P X) (=> (forall ((Y2 (-> Bool tptp.a))) (=> (@ P Y2) (@ (@ tptp.ord_less_eq_o_a Y2) X))) (=> (forall ((X5 (-> Bool tptp.a))) (=> (@ P X5) (=> (forall ((Y5 (-> Bool tptp.a))) (=> (@ P Y5) (@ (@ tptp.ord_less_eq_o_a Y5) X5))) (@ Q X5)))) (@ Q (@ tptp.order_Greatest_o_a P)))))))
% 0.25/0.63 (assert (forall ((P (-> tptp.a Bool)) (X tptp.a) (Q (-> tptp.a Bool))) (=> (@ P X) (=> (forall ((Y2 tptp.a)) (=> (@ P Y2) (@ (@ tptp.ord_less_eq_a Y2) X))) (=> (forall ((X5 tptp.a)) (=> (@ P X5) (=> (forall ((Y5 tptp.a)) (=> (@ P Y5) (@ (@ tptp.ord_less_eq_a Y5) X5))) (@ Q X5)))) (@ Q (@ tptp.order_Greatest_a P)))))))
% 0.25/0.63 (assert (= tptp.ord_less_eq_o_o_a (lambda ((X6 (-> Bool Bool tptp.a)) (Y6 (-> Bool Bool tptp.a))) (and (@ (@ tptp.ord_less_eq_o_a (@ X6 false)) (@ Y6 false)) (@ (@ tptp.ord_less_eq_o_a (@ X6 true)) (@ Y6 true))))))
% 0.25/0.63 (assert (= tptp.ord_less_eq_o_a (lambda ((X6 (-> Bool tptp.a)) (Y6 (-> Bool tptp.a))) (and (@ (@ tptp.ord_less_eq_a (@ X6 false)) (@ Y6 false)) (@ (@ tptp.ord_less_eq_a (@ X6 true)) (@ Y6 true))))))
% 0.25/0.63 (assert (forall ((A tptp.a) (B tptp.a)) (or (= A B) (not (@ (@ tptp.ord_less_eq_a A) B)) (not (@ (@ tptp.ord_less_eq_a B) A)))))
% 0.25/0.63 (assert (forall ((X21 tptp.a) (X22 tptp.list_a) (Y21 tptp.a) (Y22 tptp.list_a)) (= (= (@ (@ tptp.cons_a X21) X22) (@ (@ tptp.cons_a Y21) Y22)) (and (= X21 Y21) (= X22 Y22)))))
% 0.25/0.63 (assert (forall ((X tptp.a) (Xs tptp.list_a)) (not (= (@ (@ tptp.cons_a X) Xs) Xs))))
% 0.25/0.63 (assert (= tptp.heap_axioms_Tree_a_a (lambda ((Is_empty (-> tptp.tree_a Bool)) (Of_list (-> tptp.list_a tptp.tree_a)) (Multiset (-> tptp.tree_a tptp.multiset_a)) (As_tree (-> tptp.tree_a tptp.tree_a)) (Remove_max (-> tptp.tree_a tptp.produc143150363Tree_a))) (and (forall ((L3 tptp.tree_a)) (= (@ Multiset L3) (@ tptp.multiset_a2 (@ As_tree L3)))) (forall ((I tptp.list_a)) (@ tptp.is_heap_a (@ As_tree (@ Of_list I)))) (forall ((T2 tptp.tree_a)) (= (= (@ As_tree T2) tptp.e_a) (@ Is_empty T2))) (forall ((L3 tptp.tree_a) (M tptp.a) (L4 tptp.tree_a)) (=> (not (@ Is_empty L3)) (=> (= (@ (@ tptp.produc686083979Tree_a M) L4) (@ Remove_max L3)) (= (@ (@ tptp.add_mset_a M) (@ Multiset L4)) (@ Multiset L3))))) (forall ((L3 tptp.tree_a) (M tptp.a) (L4 tptp.tree_a)) (=> (not (@ Is_empty L3)) (=> (@ tptp.is_heap_a (@ As_tree L3)) (=> (= (@ (@ tptp.produc686083979Tree_a M) L4) (@ Remove_max L3)) (@ tptp.is_heap_a (@ As_tree L4)))))) (forall ((T2 tptp.tree_a) (M tptp.a) (T3 tptp.tree_a)) (=> (not (@ Is_empty T2)) (=> (= (@ (@ tptp.produc686083979Tree_a M) T3) (@ Remove_max T2)) (= M (@ tptp.val_a (@ As_tree T2))))))))))
% 0.25/0.63 (assert (forall ((Multiset2 (-> tptp.tree_a tptp.multiset_a)) (As_tree2 (-> tptp.tree_a tptp.tree_a)) (Of_list2 (-> tptp.list_a tptp.tree_a)) (Is_empty2 (-> tptp.tree_a Bool)) (Remove_max2 (-> tptp.tree_a tptp.produc143150363Tree_a))) (=> (forall ((L5 tptp.tree_a)) (= (@ Multiset2 L5) (@ tptp.multiset_a2 (@ As_tree2 L5)))) (=> (forall ((I2 tptp.list_a)) (@ tptp.is_heap_a (@ As_tree2 (@ Of_list2 I2)))) (=> (forall ((T4 tptp.tree_a)) (= (= (@ As_tree2 T4) tptp.e_a) (@ Is_empty2 T4))) (=> (forall ((L5 tptp.tree_a) (M2 tptp.a) (L2 tptp.tree_a)) (=> (not (@ Is_empty2 L5)) (=> (= (@ (@ tptp.produc686083979Tree_a M2) L2) (@ Remove_max2 L5)) (= (@ (@ tptp.add_mset_a M2) (@ Multiset2 L2)) (@ Multiset2 L5))))) (=> (forall ((L5 tptp.tree_a) (M2 tptp.a) (L2 tptp.tree_a)) (=> (not (@ Is_empty2 L5)) (=> (@ tptp.is_heap_a (@ As_tree2 L5)) (=> (= (@ (@ tptp.produc686083979Tree_a M2) L2) (@ Remove_max2 L5)) (@ tptp.is_heap_a (@ As_tree2 L2)))))) (=> (forall ((T4 tptp.tree_a) (M2 tptp.a) (T5 tptp.tree_a)) (=> (not (@ Is_empty2 T4)) (=> (= (@ (@ tptp.produc686083979Tree_a M2) T5) (@ Remove_max2 T4)) (= M2 (@ tptp.val_a (@ As_tree2 T4)))))) (@ (@ (@ (@ (@ tptp.heap_axioms_Tree_a_a Is_empty2) Of_list2) Multiset2) As_tree2) Remove_max2)))))))))
% 0.25/0.63 (assert (forall ((Empty tptp.tree_a) (Is_empty2 (-> tptp.tree_a Bool)) (Of_list2 (-> tptp.list_a tptp.tree_a)) (Multiset2 (-> tptp.tree_a tptp.multiset_a)) (As_tree2 (-> tptp.tree_a tptp.tree_a)) (Remove_max2 (-> tptp.tree_a tptp.produc143150363Tree_a)) (L tptp.tree_a) (M3 tptp.a) (L6 tptp.tree_a)) (=> (@ (@ (@ (@ (@ (@ tptp.heap_Tree_a_a Empty) Is_empty2) Of_list2) Multiset2) As_tree2) Remove_max2) (=> (not (@ Is_empty2 L)) (=> (= (@ (@ tptp.produc686083979Tree_a M3) L6) (@ Remove_max2 L)) (= (@ (@ tptp.add_mset_a M3) (@ Multiset2 L6)) (@ Multiset2 L)))))))
% 0.25/0.63 (assert (forall ((Empty tptp.tree_a) (Is_empty2 (-> tptp.tree_a Bool)) (Of_list2 (-> tptp.list_a tptp.tree_a)) (Multiset2 (-> tptp.tree_a tptp.multiset_a)) (As_tree2 (-> tptp.tree_a tptp.tree_a)) (Remove_max2 (-> tptp.tree_a tptp.produc143150363Tree_a)) (T tptp.tree_a) (M3 tptp.a) (T6 tptp.tree_a)) (=> (@ (@ (@ (@ (@ (@ tptp.heap_Tree_a_a Empty) Is_empty2) Of_list2) Multiset2) As_tree2) Remove_max2) (=> (not (@ Is_empty2 T)) (=> (= (@ (@ tptp.produc686083979Tree_a M3) T6) (@ Remove_max2 T)) (= M3 (@ tptp.val_a (@ As_tree2 T))))))))
% 0.25/0.63 (assert (forall ((Empty tptp.tree_a) (Is_empty2 (-> tptp.tree_a Bool)) (Of_list2 (-> tptp.list_a tptp.tree_a)) (Multiset2 (-> tptp.tree_a tptp.multiset_a)) (As_tree2 (-> tptp.tree_a tptp.tree_a)) (Remove_max2 (-> tptp.tree_a tptp.produc143150363Tree_a)) (L tptp.tree_a) (M3 tptp.a) (L6 tptp.tree_a)) (=> (@ (@ (@ (@ (@ (@ tptp.heap_Tree_a_a Empty) Is_empty2) Of_list2) Multiset2) As_tree2) Remove_max2) (=> (not (@ Is_empty2 L)) (=> (@ tptp.is_heap_a (@ As_tree2 L)) (=> (= (@ (@ tptp.produc686083979Tree_a M3) L6) (@ Remove_max2 L)) (@ tptp.is_heap_a (@ As_tree2 L6))))))))
% 0.25/0.63 (assert (forall ((M4 tptp.multiset_a) (X tptp.a)) (not (= M4 (@ (@ tptp.add_mset_a X) M4)))))
% 0.25/0.63 (assert (forall ((A tptp.a) (A2 tptp.multiset_a) (B4 tptp.multiset_a)) (let ((_let_1 (@ tptp.add_mset_a A))) (= (= (@ _let_1 A2) (@ _let_1 B4)) (= A2 B4)))))
% 0.25/0.63 (assert (forall ((A tptp.a) (B tptp.tree_a) (A5 tptp.a) (B5 tptp.tree_a)) (= (= (@ (@ tptp.produc686083979Tree_a A) B) (@ (@ tptp.produc686083979Tree_a A5) B5)) (and (= A A5) (= B B5)))))
% 0.25/0.63 (assert (forall ((X12 tptp.a) (X24 tptp.tree_a) (Y1 tptp.a) (Y24 tptp.tree_a)) (= (= (@ (@ tptp.produc686083979Tree_a X12) X24) (@ (@ tptp.produc686083979Tree_a Y1) Y24)) (and (= X12 Y1) (= X24 Y24)))))
% 0.25/0.63 (assert (forall ((A tptp.a) (A2 tptp.multiset_a)) (=> (@ (@ tptp.member_a A) (@ tptp.set_mset_a A2)) (not (forall ((B6 tptp.multiset_a)) (not (= A2 (@ (@ tptp.add_mset_a A) B6))))))))
% 0.25/0.63 (assert (forall ((X tptp.a) (M4 tptp.multiset_a)) (=> (@ (@ tptp.member_a X) (@ tptp.set_mset_a M4)) (exists ((A6 tptp.multiset_a)) (= M4 (@ (@ tptp.add_mset_a X) A6))))))
% 0.25/0.63 (assert (forall ((P2 tptp.produc143150363Tree_a)) (exists ((X5 tptp.a) (Y2 tptp.tree_a)) (= P2 (@ (@ tptp.produc686083979Tree_a X5) Y2)))))
% 0.25/0.63 (assert (forall ((P (-> tptp.produc143150363Tree_a Bool)) (P2 tptp.produc143150363Tree_a)) (=> (forall ((A4 tptp.a) (B3 tptp.tree_a)) (@ P (@ (@ tptp.produc686083979Tree_a A4) B3))) (@ P P2))))
% 0.25/0.63 (assert (forall ((A tptp.a) (B tptp.tree_a) (A5 tptp.a) (B5 tptp.tree_a)) (=> (= (@ (@ tptp.produc686083979Tree_a A) B) (@ (@ tptp.produc686083979Tree_a A5) B5)) (not (=> (= A A5) (not (= B B5)))))))
% 0.25/0.63 (assert (forall ((Y tptp.produc143150363Tree_a)) (not (forall ((A4 tptp.a) (B3 tptp.tree_a)) (not (= Y (@ (@ tptp.produc686083979Tree_a A4) B3)))))))
% 0.25/0.63 (assert (forall ((P (-> tptp.produc143150363Tree_a Bool)) (Prod tptp.produc143150363Tree_a)) (=> (forall ((A4 tptp.a) (B3 tptp.tree_a)) (@ P (@ (@ tptp.produc686083979Tree_a A4) B3))) (@ P Prod))))
% 0.25/0.63 (assert (forall ((A tptp.a) (M4 tptp.multiset_a) (B tptp.a) (N tptp.multiset_a)) (= (= (@ (@ tptp.add_mset_a A) M4) (@ (@ tptp.add_mset_a B) N)) (or (and (= M4 N) (= A B)) (exists ((K tptp.multiset_a)) (and (= M4 (@ (@ tptp.add_mset_a B) K)) (= N (@ (@ tptp.add_mset_a A) K))))))))
% 0.25/0.63 (assert (forall ((X tptp.a) (Y tptp.a) (M4 tptp.multiset_a)) (let ((_let_1 (@ tptp.add_mset_a X))) (let ((_let_2 (@ tptp.add_mset_a Y))) (= (@ _let_1 (@ _let_2 M4)) (@ _let_2 (@ _let_1 M4)))))))
% 0.25/0.63 (assert (forall ((X tptp.a) (M4 tptp.multiset_a) (N tptp.multiset_a)) (=> (= (@ (@ tptp.add_mset_a X) M4) N) (@ (@ tptp.member_a X) (@ tptp.set_mset_a N)))))
% 0.25/0.63 (assert (forall ((B tptp.a) (B4 tptp.multiset_a) (C tptp.a) (C2 tptp.multiset_a)) (=> (= (@ (@ tptp.add_mset_a B) B4) (@ (@ tptp.add_mset_a C) C2)) (=> (not (= B C)) (@ (@ tptp.member_a C) (@ tptp.set_mset_a B4))))))
% 0.25/0.63 (assert (forall ((V tptp.a)) (= (@ tptp.heapIm837449470Leaf_a (@ (@ (@ tptp.t_a V) tptp.e_a) tptp.e_a)) (@ (@ tptp.produc686083979Tree_a V) tptp.e_a))))
% 0.25/0.63 (assert (= tptp.remove301631099ee_a_a (lambda ((Is_empty (-> tptp.tree_a Bool)) (Of_list (-> tptp.list_a tptp.tree_a)) (Multiset (-> tptp.tree_a tptp.multiset_a)) (Remove_max (-> tptp.tree_a tptp.produc143150363Tree_a)) (Inv (-> tptp.tree_a Bool))) (and (forall ((X4 tptp.list_a)) (@ Inv (@ Of_list X4))) (forall ((L3 tptp.tree_a) (M tptp.a) (L4 tptp.tree_a)) (=> (not (@ Is_empty L3)) (=> (@ Inv L3) (=> (= (@ (@ tptp.produc686083979Tree_a M) L4) (@ Remove_max L3)) (= M (@ tptp.lattic146396397_Max_a (@ (@ tptp.set_Tree_a_a Multiset) L3))))))) (forall ((L3 tptp.tree_a) (M tptp.a) (L4 tptp.tree_a)) (=> (not (@ Is_empty L3)) (=> (@ Inv L3) (=> (= (@ (@ tptp.produc686083979Tree_a M) L4) (@ Remove_max L3)) (= (@ (@ tptp.add_mset_a M) (@ Multiset L4)) (@ Multiset L3)))))) (forall ((L3 tptp.tree_a) (M tptp.a) (L4 tptp.tree_a)) (=> (not (@ Is_empty L3)) (=> (@ Inv L3) (=> (= (@ (@ tptp.produc686083979Tree_a M) L4) (@ Remove_max L3)) (@ Inv L4)))))))))
% 0.25/0.63 (assert (forall ((Inv2 (-> tptp.tree_a Bool)) (Of_list2 (-> tptp.list_a tptp.tree_a)) (Is_empty2 (-> tptp.tree_a Bool)) (Remove_max2 (-> tptp.tree_a tptp.produc143150363Tree_a)) (Multiset2 (-> tptp.tree_a tptp.multiset_a))) (=> (forall ((X5 tptp.list_a)) (@ Inv2 (@ Of_list2 X5))) (=> (forall ((L5 tptp.tree_a) (M2 tptp.a) (L2 tptp.tree_a)) (=> (not (@ Is_empty2 L5)) (=> (@ Inv2 L5) (=> (= (@ (@ tptp.produc686083979Tree_a M2) L2) (@ Remove_max2 L5)) (= M2 (@ tptp.lattic146396397_Max_a (@ (@ tptp.set_Tree_a_a Multiset2) L5))))))) (=> (forall ((L5 tptp.tree_a) (M2 tptp.a) (L2 tptp.tree_a)) (=> (not (@ Is_empty2 L5)) (=> (@ Inv2 L5) (=> (= (@ (@ tptp.produc686083979Tree_a M2) L2) (@ Remove_max2 L5)) (= (@ (@ tptp.add_mset_a M2) (@ Multiset2 L2)) (@ Multiset2 L5)))))) (=> (forall ((L5 tptp.tree_a) (M2 tptp.a) (L2 tptp.tree_a)) (=> (not (@ Is_empty2 L5)) (=> (@ Inv2 L5) (=> (= (@ (@ tptp.produc686083979Tree_a M2) L2) (@ Remove_max2 L5)) (@ Inv2 L2))))) (@ (@ (@ (@ (@ tptp.remove301631099ee_a_a Is_empty2) Of_list2) Multiset2) Remove_max2) Inv2)))))))
% 0.25/0.63 (assert (forall ((Empty tptp.tree_a) (Is_empty2 (-> tptp.tree_a Bool)) (Of_list2 (-> tptp.list_a tptp.tree_a)) (Multiset2 (-> tptp.tree_a tptp.multiset_a)) (Remove_max2 (-> tptp.tree_a tptp.produc143150363Tree_a)) (Inv2 (-> tptp.tree_a Bool)) (L tptp.tree_a) (M3 tptp.a) (L6 tptp.tree_a)) (=> (@ (@ (@ (@ (@ (@ tptp.removeMax_Tree_a_a Empty) Is_empty2) Of_list2) Multiset2) Remove_max2) Inv2) (=> (not (@ Is_empty2 L)) (=> (@ Inv2 L) (=> (= (@ (@ tptp.produc686083979Tree_a M3) L6) (@ Remove_max2 L)) (= M3 (@ tptp.lattic146396397_Max_a (@ (@ tptp.set_Tree_a_a Multiset2) L)))))))))
% 0.25/0.63 (assert (forall ((P (-> tptp.multiset_a Bool)) (M4 tptp.multiset_a)) (=> (@ P tptp.zero_zero_multiset_a) (=> (forall ((X5 tptp.a) (M5 tptp.multiset_a)) (=> (@ P M5) (=> (forall ((Xa tptp.a)) (=> (@ (@ tptp.member_a Xa) (@ tptp.set_mset_a M5)) (@ (@ tptp.ord_less_eq_a Xa) X5))) (@ P (@ (@ tptp.add_mset_a X5) M5))))) (@ P M4)))))
% 0.25/0.63 (assert (forall ((X tptp.a) (M4 tptp.multiset_a) (Y tptp.a)) (= (= (@ (@ tptp.add_mset_a X) M4) (@ (@ tptp.add_mset_a Y) tptp.zero_zero_multiset_a)) (and (= M4 tptp.zero_zero_multiset_a) (= X Y)))))
% 0.25/0.63 (assert (forall ((A tptp.a) (B tptp.a) (M4 tptp.multiset_a)) (= (= (@ (@ tptp.add_mset_a A) tptp.zero_zero_multiset_a) (@ (@ tptp.add_mset_a B) M4)) (and (= B A) (= M4 tptp.zero_zero_multiset_a)))))
% 0.25/0.63 (assert (forall ((B tptp.a) (M4 tptp.multiset_a) (A tptp.a)) (= (= (@ (@ tptp.add_mset_a B) M4) (@ (@ tptp.add_mset_a A) tptp.zero_zero_multiset_a)) (and (= B A) (= M4 tptp.zero_zero_multiset_a)))))
% 0.25/0.63 (assert (forall ((A tptp.a) (B tptp.a)) (= (= (@ (@ tptp.add_mset_a A) tptp.zero_zero_multiset_a) (@ (@ tptp.add_mset_a B) tptp.zero_zero_multiset_a)) (= A B))))
% 0.25/0.63 (assert (forall ((M4 tptp.multiset_a)) (=> (not (= M4 tptp.zero_zero_multiset_a)) (not (forall ((X5 tptp.a) (N2 tptp.multiset_a)) (not (= M4 (@ (@ tptp.add_mset_a X5) N2))))))))
% 0.25/0.63 (assert (forall ((P (-> tptp.multiset_a Bool)) (M4 tptp.multiset_a)) (=> (@ P tptp.zero_zero_multiset_a) (=> (forall ((X5 tptp.a) (M5 tptp.multiset_a)) (=> (@ P M5) (@ P (@ (@ tptp.add_mset_a X5) M5)))) (@ P M4)))))
% 0.25/0.63 (assert (forall ((P (-> tptp.multiset_a tptp.multiset_a Bool)) (M4 tptp.multiset_a) (N tptp.multiset_a)) (=> (@ (@ P tptp.zero_zero_multiset_a) tptp.zero_zero_multiset_a) (=> (forall ((A4 tptp.a) (M5 tptp.multiset_a) (N2 tptp.multiset_a)) (=> (@ (@ P M5) N2) (@ (@ P (@ (@ tptp.add_mset_a A4) M5)) N2))) (=> (forall ((A4 tptp.a) (M5 tptp.multiset_a) (N2 tptp.multiset_a)) (let ((_let_1 (@ P M5))) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.add_mset_a A4) N2))))) (@ (@ P M4) N))))))
% 0.25/0.63 (assert (forall ((A tptp.a) (A2 tptp.multiset_a)) (not (= tptp.zero_zero_multiset_a (@ (@ tptp.add_mset_a A) A2)))))
% 0.25/0.63 (assert (forall ((M4 tptp.multiset_a)) (=> (not (= M4 tptp.zero_zero_multiset_a)) (exists ((A6 tptp.multiset_a) (A4 tptp.a)) (= M4 (@ (@ tptp.add_mset_a A4) A6))))))
% 0.25/0.63 (assert (forall ((A2 tptp.multiset_a)) (=> (not (= A2 tptp.zero_zero_multiset_a)) (not (forall ((X5 tptp.a)) (not (@ (@ tptp.member_a X5) (@ tptp.set_mset_a A2))))))))
% 0.25/0.63 (assert (forall ((Empty tptp.tree_a) (Is_empty2 (-> tptp.tree_a Bool)) (Of_list2 (-> tptp.list_a tptp.tree_a)) (Multiset2 (-> tptp.tree_a tptp.multiset_a)) (Remove_max2 (-> tptp.tree_a tptp.produc143150363Tree_a)) (Inv2 (-> tptp.tree_a Bool)) (L tptp.tree_a) (M3 tptp.a) (L6 tptp.tree_a)) (=> (@ (@ (@ (@ (@ (@ tptp.removeMax_Tree_a_a Empty) Is_empty2) Of_list2) Multiset2) Remove_max2) Inv2) (=> (not (@ Is_empty2 L)) (=> (@ Inv2 L) (=> (= (@ (@ tptp.produc686083979Tree_a M3) L6) (@ Remove_max2 L)) (@ Inv2 L6)))))))
% 0.25/0.63 (assert (forall ((X tptp.a)) (@ (@ tptp.member_a X) (@ tptp.set_mset_a (@ (@ tptp.add_mset_a X) tptp.zero_zero_multiset_a)))))
% 0.25/0.63 (assert (forall ((Empty tptp.tree_a) (Is_empty2 (-> tptp.tree_a Bool)) (Of_list2 (-> tptp.list_a tptp.tree_a)) (Multiset2 (-> tptp.tree_a tptp.multiset_a)) (Remove_max2 (-> tptp.tree_a tptp.produc143150363Tree_a)) (Inv2 (-> tptp.tree_a Bool)) (L tptp.tree_a) (M3 tptp.a) (L6 tptp.tree_a)) (=> (@ (@ (@ (@ (@ (@ tptp.removeMax_Tree_a_a Empty) Is_empty2) Of_list2) Multiset2) Remove_max2) Inv2) (=> (not (@ Is_empty2 L)) (=> (@ Inv2 L) (=> (= (@ (@ tptp.produc686083979Tree_a M3) L6) (@ Remove_max2 L)) (= (@ (@ tptp.add_mset_a M3) (@ Multiset2 L6)) (@ Multiset2 L))))))))
% 0.25/0.63 (assert (= (@ tptp.multiset_a2 tptp.e_a) tptp.zero_zero_multiset_a))
% 0.25/0.63 (assert (forall ((P (-> tptp.multiset_a Bool)) (M4 tptp.multiset_a)) (=> (@ P tptp.zero_zero_multiset_a) (=> (forall ((X5 tptp.a) (M5 tptp.multiset_a)) (=> (@ P M5) (=> (forall ((Xa tptp.a)) (=> (@ (@ tptp.member_a Xa) (@ tptp.set_mset_a M5)) (@ (@ tptp.ord_less_eq_a X5) Xa))) (@ P (@ (@ tptp.add_mset_a X5) M5))))) (@ P M4)))))
% 0.25/0.63 (assert (= tptp.is_empty_a (lambda ((A7 tptp.multiset_a)) (= A7 tptp.zero_zero_multiset_a))))
% 0.25/0.63 (assert (forall ((Empty tptp.tree_a) (Is_empty2 (-> tptp.tree_a Bool)) (Of_list2 (-> tptp.list_a tptp.tree_a)) (Multiset2 (-> tptp.tree_a tptp.multiset_a)) (Remove_max2 (-> tptp.tree_a tptp.produc143150363Tree_a)) (Inv2 (-> tptp.tree_a Bool)) (L tptp.tree_a) (P (-> tptp.tree_a tptp.list_a Bool)) (Sl tptp.list_a)) (=> (@ (@ (@ (@ (@ (@ tptp.removeMax_Tree_a_a Empty) Is_empty2) Of_list2) Multiset2) Remove_max2) Inv2) (=> (@ Inv2 L) (=> (@ (@ P L) Sl) (=> (forall ((L5 tptp.tree_a) (Sl2 tptp.list_a) (M2 tptp.a) (L2 tptp.tree_a)) (=> (not (@ Is_empty2 L5)) (=> (@ Inv2 L5) (=> (= (@ (@ tptp.produc686083979Tree_a M2) L2) (@ Remove_max2 L5)) (=> (@ (@ P L5) Sl2) (@ (@ P L2) (@ (@ tptp.cons_a M2) Sl2))))))) (@ (@ P Empty) (@ (@ (@ (@ tptp.ssort_Tree_a_a Is_empty2) Remove_max2) L) Sl))))))))
% 0.25/0.63 (assert (forall ((Empty tptp.tree_a) (Is_empty2 (-> tptp.tree_a Bool)) (Of_list2 (-> tptp.list_a tptp.tree_a)) (Multiset2 (-> tptp.tree_a tptp.multiset_a)) (Remove_max2 (-> tptp.tree_a tptp.produc143150363Tree_a)) (Inv2 (-> tptp.tree_a Bool)) (A tptp.produc768687417list_a)) (=> (@ (@ (@ (@ (@ (@ tptp.removeMax_Tree_a_a Empty) Is_empty2) Of_list2) Multiset2) Remove_max2) Inv2) (=> (@ (@ (@ tptp.ssort_dom_Tree_a_a Is_empty2) Remove_max2) A) (not (forall ((L5 tptp.tree_a) (Sl2 tptp.list_a)) (=> (= A (@ (@ tptp.produc1352981801list_a L5) Sl2)) (not (=> (not (@ Is_empty2 L5)) (forall ((M6 tptp.a) (L7 tptp.tree_a)) (=> (= (@ (@ tptp.produc686083979Tree_a M6) L7) (@ Remove_max2 L5)) (@ (@ (@ tptp.ssort_dom_Tree_a_a Is_empty2) Remove_max2) (@ (@ tptp.produc1352981801list_a L7) (@ (@ tptp.cons_a M6) Sl2))))))))))))))
% 0.25/0.63 (assert (forall ((Empty tptp.tree_a) (Is_empty2 (-> tptp.tree_a Bool)) (Of_list2 (-> tptp.list_a tptp.tree_a)) (Multiset2 (-> tptp.tree_a tptp.multiset_a)) (Remove_max2 (-> tptp.tree_a tptp.produc143150363Tree_a)) (Inv2 (-> tptp.tree_a Bool)) (A tptp.produc768687417list_a)) (=> (@ (@ (@ (@ (@ (@ tptp.removeMax_Tree_a_a Empty) Is_empty2) Of_list2) Multiset2) Remove_max2) Inv2) (= (@ (@ (@ tptp.ssort_dom_Tree_a_a Is_empty2) Remove_max2) A) (exists ((L3 tptp.tree_a) (Sl3 tptp.list_a)) (and (= A (@ (@ tptp.produc1352981801list_a L3) Sl3)) (forall ((X4 tptp.a) (Y4 tptp.tree_a)) (=> (not (@ Is_empty2 L3)) (=> (= (@ (@ tptp.produc686083979Tree_a X4) Y4) (@ Remove_max2 L3)) (@ (@ (@ tptp.ssort_dom_Tree_a_a Is_empty2) Remove_max2) (@ (@ tptp.produc1352981801list_a Y4) (@ (@ tptp.cons_a X4) Sl3))))))))))))
% 0.25/0.63 (assert (forall ((Empty tptp.tree_a) (Is_empty2 (-> tptp.tree_a Bool)) (Of_list2 (-> tptp.list_a tptp.tree_a)) (Multiset2 (-> tptp.tree_a tptp.multiset_a)) (Remove_max2 (-> tptp.tree_a tptp.produc143150363Tree_a)) (Inv2 (-> tptp.tree_a Bool)) (X tptp.produc768687417list_a) (P (-> tptp.produc768687417list_a Bool))) (=> (@ (@ (@ (@ (@ (@ tptp.removeMax_Tree_a_a Empty) Is_empty2) Of_list2) Multiset2) Remove_max2) Inv2) (=> (@ (@ (@ tptp.ssort_dom_Tree_a_a Is_empty2) Remove_max2) X) (=> (forall ((L5 tptp.tree_a) (Sl2 tptp.list_a)) (=> (forall ((M6 tptp.a) (L7 tptp.tree_a)) (=> (not (@ Is_empty2 L5)) (=> (= (@ (@ tptp.produc686083979Tree_a M6) L7) (@ Remove_max2 L5)) (@ (@ (@ tptp.ssort_dom_Tree_a_a Is_empty2) Remove_max2) (@ (@ tptp.produc1352981801list_a L7) (@ (@ tptp.cons_a M6) Sl2)))))) (=> (forall ((M6 tptp.a) (L7 tptp.tree_a)) (=> (not (@ Is_empty2 L5)) (=> (= (@ (@ tptp.produc686083979Tree_a M6) L7) (@ Remove_max2 L5)) (@ P (@ (@ tptp.produc1352981801list_a L7) (@ (@ tptp.cons_a M6) Sl2)))))) (@ P (@ (@ tptp.produc1352981801list_a L5) Sl2))))) (@ P X))))))
% 0.25/0.63 (assert (forall ((Empty tptp.tree_a) (Is_empty2 (-> tptp.tree_a Bool)) (Of_list2 (-> tptp.list_a tptp.tree_a)) (Multiset2 (-> tptp.tree_a tptp.multiset_a)) (Remove_max2 (-> tptp.tree_a tptp.produc143150363Tree_a)) (Inv2 (-> tptp.tree_a Bool)) (L tptp.tree_a) (Sl tptp.list_a)) (=> (@ (@ (@ (@ (@ (@ tptp.removeMax_Tree_a_a Empty) Is_empty2) Of_list2) Multiset2) Remove_max2) Inv2) (=> (forall ((M2 tptp.a) (L2 tptp.tree_a)) (=> (not (@ Is_empty2 L)) (=> (= (@ (@ tptp.produc686083979Tree_a M2) L2) (@ Remove_max2 L)) (@ (@ (@ tptp.ssort_dom_Tree_a_a Is_empty2) Remove_max2) (@ (@ tptp.produc1352981801list_a L2) (@ (@ tptp.cons_a M2) Sl)))))) (@ (@ (@ tptp.ssort_dom_Tree_a_a Is_empty2) Remove_max2) (@ (@ tptp.produc1352981801list_a L) Sl))))))
% 0.25/0.63 (assert (forall ((V tptp.a) (L tptp.tree_a) (R tptp.tree_a)) (= (@ tptp.multiset_a2 (@ (@ (@ tptp.t_a V) L) R)) (@ (@ tptp.plus_plus_multiset_a (@ (@ tptp.plus_plus_multiset_a (@ tptp.multiset_a2 L)) (@ (@ tptp.add_mset_a V) tptp.zero_zero_multiset_a))) (@ tptp.multiset_a2 R)))))
% 0.25/0.63 (assert (forall ((A tptp.a) (M4 tptp.multiset_a)) (= (@ (@ tptp.subseteq_mset_a (@ (@ tptp.add_mset_a A) tptp.zero_zero_multiset_a)) M4) (@ (@ tptp.member_a A) (@ tptp.set_mset_a M4)))))
% 0.25/0.63 (assert (forall ((A tptp.multiset_a)) (= (@ (@ tptp.subseteq_mset_a A) tptp.zero_zero_multiset_a) (= A tptp.zero_zero_multiset_a))))
% 0.25/0.63 (assert (forall ((N3 tptp.multiset_a)) (= (@ (@ tptp.subseteq_mset_a N3) tptp.zero_zero_multiset_a) (= N3 tptp.zero_zero_multiset_a))))
% 0.25/0.63 (assert (forall ((C tptp.multiset_a) (A tptp.multiset_a) (B tptp.multiset_a)) (let ((_let_1 (@ tptp.plus_plus_multiset_a C))) (= (@ (@ tptp.subseteq_mset_a (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.subseteq_mset_a A) B)))))
% 0.25/0.63 (assert (forall ((A tptp.multiset_a) (C tptp.multiset_a) (B tptp.multiset_a)) (= (@ (@ tptp.subseteq_mset_a (@ (@ tptp.plus_plus_multiset_a A) C)) (@ (@ tptp.plus_plus_multiset_a B) C)) (@ (@ tptp.subseteq_mset_a A) B))))
% 0.25/0.63 (assert (forall ((C2 tptp.multiset_a) (A2 tptp.multiset_a) (B4 tptp.multiset_a)) (let ((_let_1 (@ tptp.plus_plus_multiset_a C2))) (= (@ (@ tptp.subseteq_mset_a (@ _let_1 A2)) (@ _let_1 B4)) (@ (@ tptp.subseteq_mset_a A2) B4)))))
% 0.25/0.63 (assert (forall ((A2 tptp.multiset_a) (C2 tptp.multiset_a) (B4 tptp.multiset_a)) (= (@ (@ tptp.subseteq_mset_a (@ (@ tptp.plus_plus_multiset_a A2) C2)) (@ (@ tptp.plus_plus_multiset_a B4) C2)) (@ (@ tptp.subseteq_mset_a A2) B4))))
% 0.25/0.63 (assert (forall ((X tptp.multiset_a) (Y tptp.multiset_a)) (= (= tptp.zero_zero_multiset_a (@ (@ tptp.plus_plus_multiset_a X) Y)) (and (= X tptp.zero_zero_multiset_a) (= Y tptp.zero_zero_multiset_a)))))
% 0.25/0.63 (assert (forall ((X tptp.multiset_a) (Y tptp.multiset_a)) (= (= (@ (@ tptp.plus_plus_multiset_a X) Y) tptp.zero_zero_multiset_a) (and (= X tptp.zero_zero_multiset_a) (= Y tptp.zero_zero_multiset_a)))))
% 0.25/0.63 (assert (forall ((M4 tptp.multiset_a) (N tptp.multiset_a)) (= (= (@ (@ tptp.plus_plus_multiset_a M4) N) tptp.zero_zero_multiset_a) (and (= M4 tptp.zero_zero_multiset_a) (= N tptp.zero_zero_multiset_a)))))
% 0.25/0.63 (assert (forall ((M4 tptp.multiset_a) (N tptp.multiset_a)) (= (= tptp.zero_zero_multiset_a (@ (@ tptp.plus_plus_multiset_a M4) N)) (and (= M4 tptp.zero_zero_multiset_a) (= N tptp.zero_zero_multiset_a)))))
% 0.25/0.63 (assert (forall ((A2 tptp.multiset_a) (A tptp.a) (B4 tptp.multiset_a)) (let ((_let_1 (@ tptp.plus_plus_multiset_a A2))) (let ((_let_2 (@ tptp.add_mset_a A))) (= (@ _let_1 (@ _let_2 B4)) (@ _let_2 (@ _let_1 B4)))))))
% 0.25/0.63 (assert (forall ((A tptp.a) (A2 tptp.multiset_a) (B4 tptp.multiset_a)) (let ((_let_1 (@ tptp.add_mset_a A))) (= (@ (@ tptp.plus_plus_multiset_a (@ _let_1 A2)) B4) (@ _let_1 (@ (@ tptp.plus_plus_multiset_a A2) B4))))))
% 0.25/0.63 (assert (forall ((B tptp.multiset_a) (A tptp.multiset_a)) (= (@ (@ tptp.subseteq_mset_a (@ (@ tptp.plus_plus_multiset_a B) A)) B) (@ (@ tptp.subseteq_mset_a A) tptp.zero_zero_multiset_a))))
% 0.25/0.63 (assert (forall ((A tptp.multiset_a) (B tptp.multiset_a)) (= (@ (@ tptp.subseteq_mset_a (@ (@ tptp.plus_plus_multiset_a A) B)) B) (@ (@ tptp.subseteq_mset_a A) tptp.zero_zero_multiset_a))))
% 0.25/0.63 (assert (forall ((A tptp.multiset_a) (B tptp.multiset_a)) (= (@ (@ tptp.subseteq_mset_a A) (@ (@ tptp.plus_plus_multiset_a A) B)) (@ (@ tptp.subseteq_mset_a tptp.zero_zero_multiset_a) B))))
% 0.25/0.63 (assert (forall ((A tptp.multiset_a) (B tptp.multiset_a)) (= (@ (@ tptp.subseteq_mset_a A) (@ (@ tptp.plus_plus_multiset_a B) A)) (@ (@ tptp.subseteq_mset_a tptp.zero_zero_multiset_a) B))))
% 0.25/0.63 (assert (forall ((A tptp.a) (M4 tptp.multiset_a) (B tptp.a)) (= (@ (@ tptp.subseteq_mset_a (@ (@ tptp.add_mset_a A) M4)) (@ (@ tptp.add_mset_a B) tptp.zero_zero_multiset_a)) (and (= M4 tptp.zero_zero_multiset_a) (= A B)))))
% 0.25/0.63 (assert (forall ((M4 tptp.multiset_a) (N tptp.multiset_a) (K2 tptp.multiset_a)) (let ((_let_1 (@ tptp.plus_plus_multiset_a M4))) (= (@ (@ tptp.plus_plus_multiset_a (@ _let_1 N)) K2) (@ _let_1 (@ (@ tptp.plus_plus_multiset_a N) K2))))))
% 0.25/0.63 (assert (forall ((M4 tptp.multiset_a) (N tptp.multiset_a) (K2 tptp.multiset_a)) (let ((_let_1 (@ tptp.plus_plus_multiset_a M4))) (let ((_let_2 (@ tptp.plus_plus_multiset_a N))) (= (@ _let_1 (@ _let_2 K2)) (@ _let_2 (@ _let_1 K2)))))))
% 0.25/0.63 (assert (= tptp.plus_plus_multiset_a (lambda ((M7 tptp.multiset_a) (N4 tptp.multiset_a)) (@ (@ tptp.plus_plus_multiset_a N4) M7))))
% 0.25/0.63 (assert (forall ((K2 tptp.multiset_a) (M4 tptp.multiset_a) (N tptp.multiset_a)) (let ((_let_1 (@ tptp.plus_plus_multiset_a K2))) (= (= (@ _let_1 M4) (@ _let_1 N)) (= M4 N)))))
% 0.25/0.63 (assert (forall ((M4 tptp.multiset_a) (K2 tptp.multiset_a) (N tptp.multiset_a)) (= (= (@ (@ tptp.plus_plus_multiset_a M4) K2) (@ (@ tptp.plus_plus_multiset_a N) K2)) (= M4 N))))
% 0.25/0.63 (assert (forall ((A tptp.multiset_a) (B tptp.multiset_a) (C tptp.multiset_a) (D tptp.multiset_a)) (=> (@ (@ tptp.subseteq_mset_a A) B) (=> (@ (@ tptp.subseteq_mset_a C) D) (@ (@ tptp.subseteq_mset_a (@ (@ tptp.plus_plus_multiset_a A) C)) (@ (@ tptp.plus_plus_multiset_a B) D))))))
% 0.25/0.63 (assert (forall ((A tptp.multiset_a) (B tptp.multiset_a)) (=> (@ (@ tptp.subseteq_mset_a A) B) (not (forall ((C3 tptp.multiset_a)) (not (= B (@ (@ tptp.plus_plus_multiset_a A) C3))))))))
% 0.25/0.63 (assert (= tptp.subseteq_mset_a (lambda ((A3 tptp.multiset_a) (B2 tptp.multiset_a)) (exists ((C4 tptp.multiset_a)) (= B2 (@ (@ tptp.plus_plus_multiset_a A3) C4))))))
% 0.25/0.63 (assert (forall ((A2 tptp.multiset_a) (B4 tptp.multiset_a)) (@ (@ tptp.subseteq_mset_a A2) (@ (@ tptp.plus_plus_multiset_a A2) B4))))
% 0.25/0.63 (assert (forall ((A2 tptp.multiset_a) (B4 tptp.multiset_a) (C2 tptp.multiset_a) (D2 tptp.multiset_a)) (=> (@ (@ tptp.subseteq_mset_a A2) B4) (=> (@ (@ tptp.subseteq_mset_a C2) D2) (@ (@ tptp.subseteq_mset_a (@ (@ tptp.plus_plus_multiset_a A2) C2)) (@ (@ tptp.plus_plus_multiset_a B4) D2))))))
% 0.25/0.63 (assert (forall ((B4 tptp.multiset_a) (A2 tptp.multiset_a)) (@ (@ tptp.subseteq_mset_a B4) (@ (@ tptp.plus_plus_multiset_a A2) B4))))
% 0.25/0.63 (assert (forall ((A2 tptp.multiset_a) (X7 tptp.multiset_a) (Y7 tptp.multiset_a)) (let ((_let_1 (@ tptp.plus_plus_multiset_a A2))) (=> (= (@ _let_1 X7) (@ _let_1 Y7)) (= X7 Y7)))))
% 0.25/0.63 (assert (forall ((A tptp.multiset_a) (B tptp.multiset_a) (C tptp.multiset_a)) (let ((_let_1 (@ tptp.plus_plus_multiset_a C))) (=> (@ (@ tptp.subseteq_mset_a A) B) (@ (@ tptp.subseteq_mset_a (@ _let_1 A)) (@ _let_1 B))))))
% 0.25/0.63 (assert (= tptp.subseteq_mset_a (lambda ((A7 tptp.multiset_a) (B7 tptp.multiset_a)) (exists ((C5 tptp.multiset_a)) (= B7 (@ (@ tptp.plus_plus_multiset_a A7) C5))))))
% 0.25/0.63 (assert (forall ((A tptp.multiset_a) (B tptp.multiset_a) (C tptp.multiset_a)) (=> (@ (@ tptp.subseteq_mset_a A) B) (@ (@ tptp.subseteq_mset_a (@ (@ tptp.plus_plus_multiset_a A) C)) (@ (@ tptp.plus_plus_multiset_a B) C)))))
% 0.25/0.63 (assert (forall ((C tptp.multiset_a) (A tptp.multiset_a) (B tptp.multiset_a)) (let ((_let_1 (@ tptp.plus_plus_multiset_a C))) (=> (@ (@ tptp.subseteq_mset_a (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.subseteq_mset_a A) B)))))
% 0.25/0.63 (assert (forall ((A tptp.multiset_a) (C tptp.multiset_a) (B tptp.multiset_a)) (=> (@ (@ tptp.subseteq_mset_a (@ (@ tptp.plus_plus_multiset_a A) C)) (@ (@ tptp.plus_plus_multiset_a B) C)) (@ (@ tptp.subseteq_mset_a A) B))))
% 0.25/0.63 (assert (forall ((A tptp.a) (A2 tptp.multiset_a) (B4 tptp.multiset_a)) (let ((_let_1 (@ tptp.member_a A))) (= (@ _let_1 (@ tptp.set_mset_a (@ (@ tptp.plus_plus_multiset_a A2) B4))) (or (@ _let_1 (@ tptp.set_mset_a A2)) (@ _let_1 (@ tptp.set_mset_a B4)))))))
% 0.25/0.63 (assert (forall ((A2 tptp.multiset_a) (B4 tptp.multiset_a) (X tptp.a)) (let ((_let_1 (@ tptp.member_a X))) (=> (@ (@ tptp.subseteq_mset_a A2) B4) (=> (@ _let_1 (@ tptp.set_mset_a A2)) (@ _let_1 (@ tptp.set_mset_a B4)))))))
% 0.25/0.63 (assert (forall ((A2 tptp.multiset_a) (B4 tptp.multiset_a)) (=> (@ (@ tptp.subseteq_mset_a A2) B4) (@ (@ tptp.ord_less_eq_set_a (@ tptp.set_mset_a A2)) (@ tptp.set_mset_a B4)))))
% 0.25/0.63 (assert (forall ((A tptp.a) (A2 tptp.multiset_a) (B4 tptp.multiset_a)) (let ((_let_1 (@ tptp.add_mset_a A))) (= (@ (@ tptp.subseteq_mset_a (@ _let_1 A2)) (@ _let_1 B4)) (@ (@ tptp.subseteq_mset_a A2) B4)))))
% 0.25/0.63 (assert (forall ((I3 tptp.multiset_a) (J tptp.multiset_a) (K3 tptp.multiset_a) (L tptp.multiset_a)) (=> (and (@ (@ tptp.ord_le1199012836iset_a I3) J) (= K3 L)) (@ (@ tptp.ord_le1199012836iset_a (@ (@ tptp.plus_plus_multiset_a I3) K3)) (@ (@ tptp.plus_plus_multiset_a J) L)))))
% 0.25/0.63 (assert (forall ((I3 tptp.multiset_a) (J tptp.multiset_a) (K3 tptp.multiset_a) (L tptp.multiset_a)) (=> (and (= I3 J) (@ (@ tptp.ord_le1199012836iset_a K3) L)) (@ (@ tptp.ord_le1199012836iset_a (@ (@ tptp.plus_plus_multiset_a I3) K3)) (@ (@ tptp.plus_plus_multiset_a J) L)))))
% 0.25/0.63 (assert (forall ((I3 tptp.multiset_a) (J tptp.multiset_a) (K3 tptp.multiset_a) (L tptp.multiset_a)) (=> (and (@ (@ tptp.ord_le1199012836iset_a I3) J) (@ (@ tptp.ord_le1199012836iset_a K3) L)) (@ (@ tptp.ord_le1199012836iset_a (@ (@ tptp.plus_plus_multiset_a I3) K3)) (@ (@ tptp.plus_plus_multiset_a J) L)))))
% 0.25/0.63 (assert (forall ((A tptp.multiset_a) (B tptp.multiset_a) (C tptp.multiset_a) (D tptp.multiset_a)) (=> (@ (@ tptp.ord_le1199012836iset_a A) B) (=> (@ (@ tptp.ord_le1199012836iset_a C) D) (@ (@ tptp.ord_le1199012836iset_a (@ (@ tptp.plus_plus_multiset_a A) C)) (@ (@ tptp.plus_plus_multiset_a B) D))))))
% 0.25/0.63 (assert (forall ((A tptp.multiset_a) (B tptp.multiset_a) (C tptp.multiset_a)) (let ((_let_1 (@ tptp.plus_plus_multiset_a C))) (=> (@ (@ tptp.ord_le1199012836iset_a A) B) (@ (@ tptp.ord_le1199012836iset_a (@ _let_1 A)) (@ _let_1 B))))))
% 0.25/0.63 (assert (forall ((A tptp.multiset_a) (B tptp.multiset_a) (C tptp.multiset_a)) (=> (@ (@ tptp.ord_le1199012836iset_a A) B) (@ (@ tptp.ord_le1199012836iset_a (@ (@ tptp.plus_plus_multiset_a A) C)) (@ (@ tptp.plus_plus_multiset_a B) C)))))
% 0.25/0.63 (assert (forall ((X tptp.multiset_a)) (= (@ (@ tptp.plus_plus_multiset_a X) tptp.zero_zero_multiset_a) X)))
% 0.25/0.63 (assert (forall ((X tptp.multiset_a)) (= (@ (@ tptp.plus_plus_multiset_a tptp.zero_zero_multiset_a) X) X)))
% 0.67/0.87 (assert (forall ((A2 tptp.multiset_a)) (@ (@ tptp.subseteq_mset_a tptp.zero_zero_multiset_a) A2)))
% 0.67/0.87 (assert (forall ((X tptp.multiset_a)) (@ (@ tptp.subseteq_mset_a tptp.zero_zero_multiset_a) X)))
% 0.67/0.87 (assert (forall ((A tptp.multiset_a)) (@ (@ tptp.subseteq_mset_a tptp.zero_zero_multiset_a) A)))
% 0.67/0.87 (assert (forall ((A tptp.multiset_a) (C tptp.multiset_a) (B tptp.multiset_a)) (=> (@ (@ tptp.subseteq_mset_a A) tptp.zero_zero_multiset_a) (=> (@ (@ tptp.subseteq_mset_a C) B) (@ (@ tptp.subseteq_mset_a (@ (@ tptp.plus_plus_multiset_a A) C)) B)))))
% 0.67/0.87 (assert (forall ((A tptp.multiset_a) (B tptp.multiset_a) (C tptp.multiset_a)) (let ((_let_1 (@ tptp.subseteq_mset_a B))) (=> (@ (@ tptp.subseteq_mset_a tptp.zero_zero_multiset_a) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_multiset_a A) C)))))))
% 0.67/0.87 (assert (forall ((C tptp.multiset_a) (A tptp.multiset_a) (B tptp.multiset_a)) (=> (@ (@ tptp.subseteq_mset_a C) tptp.zero_zero_multiset_a) (=> (@ (@ tptp.subseteq_mset_a A) B) (@ (@ tptp.subseteq_mset_a (@ (@ tptp.plus_plus_multiset_a A) C)) B)))))
% 0.67/0.87 (assert (forall ((C tptp.multiset_a) (B tptp.multiset_a) (A tptp.multiset_a)) (let ((_let_1 (@ tptp.subseteq_mset_a B))) (=> (@ (@ tptp.subseteq_mset_a tptp.zero_zero_multiset_a) C) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.plus_plus_multiset_a A) C)))))))
% 0.67/0.87 (assert (forall ((A tptp.multiset_a) (B tptp.multiset_a)) (let ((_let_1 (@ tptp.subseteq_mset_a tptp.zero_zero_multiset_a))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_multiset_a A) B)))))))
% 0.67/0.87 (assert (forall ((A tptp.multiset_a) (B tptp.multiset_a)) (=> (@ (@ tptp.subseteq_mset_a A) tptp.zero_zero_multiset_a) (=> (@ (@ tptp.subseteq_mset_a B) tptp.zero_zero_multiset_a) (@ (@ tptp.subseteq_mset_a (@ (@ tptp.plus_plus_multiset_a A) B)) tptp.zero_zero_multiset_a)))))
% 0.67/0.87 (assert (forall ((X tptp.multiset_a) (Y tptp.multiset_a)) (let ((_let_1 (@ tptp.subseteq_mset_a tptp.zero_zero_multiset_a))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_multiset_a X) Y) tptp.zero_zero_multiset_a) (and (= X tptp.zero_zero_multiset_a) (= Y tptp.zero_zero_multiset_a))))))))
% 0.67/0.87 (assert (forall ((X tptp.multiset_a) (Y tptp.multiset_a)) (=> (@ (@ tptp.subseteq_mset_a X) tptp.zero_zero_multiset_a) (=> (@ (@ tptp.subseteq_mset_a Y) tptp.zero_zero_multiset_a) (= (= (@ (@ tptp.plus_plus_multiset_a X) Y) tptp.zero_zero_multiset_a) (and (= X tptp.zero_zero_multiset_a) (= Y tptp.zero_zero_multiset_a)))))))
% 0.67/0.87 (assert (forall ((A tptp.multiset_a)) (=> (@ (@ tptp.subseteq_mset_a A) tptp.zero_zero_multiset_a) (= A tptp.zero_zero_multiset_a))))
% 0.67/0.87 (assert (forall ((A tptp.multiset_a)) (= (@ (@ tptp.plus_plus_multiset_a A) tptp.zero_zero_multiset_a) A)))
% 0.67/0.87 (assert (let ((_let_1 (@ (@ (@ tptp.t_a tptp.v) (@ (@ (@ tptp.t_a tptp.v1) tptp.l1) tptp.r1)) (@ (@ (@ tptp.t_a tptp.v2) tptp.l2) tptp.r2)))) (not (= (@ tptp.multiset_a2 (@ tptp.heapIm1091024090Down_a _let_1)) (@ tptp.multiset_a2 _let_1)))))
% 0.67/0.87 (set-info :filename cvc5---1.0.5_25347)
% 0.67/0.87 (check-sat-assuming ( true ))
% 0.67/0.87 ------- get file name : TPTP file name is ITP070^1
% 0.67/0.87 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_25347.smt2...
% 0.67/0.87 --- Run --ho-elim --full-saturate-quant at 10...
% 0.67/0.87 % SZS status Theorem for ITP070^1
% 0.67/0.87 % SZS output start Proof for ITP070^1
% 0.67/0.87 (
% 0.67/0.87 (let ((_let_1 (@ (@ (@ tptp.t_a tptp.v2) tptp.l2) tptp.r2))) (let ((_let_2 (@ (@ (@ tptp.t_a tptp.v1) tptp.l1) tptp.r1))) (let ((_let_3 (@ tptp.t_a tptp.v))) (let ((_let_4 (@ (@ _let_3 _let_2) _let_1))) (let ((_let_5 (not (= (@ tptp.multiset_a2 (@ tptp.heapIm1091024090Down_a _let_4)) (@ tptp.multiset_a2 _let_4))))) (let ((_let_6 (forall ((Vd tptp.a) (Ve tptp.tree_a) (Vf tptp.tree_a) (Va tptp.a) (Vb tptp.tree_a) (Vc tptp.tree_a) (V tptp.a)) (let ((_let_1 (@ (@ (@ tptp.t_a Vd) Ve) Vf))) (let ((_let_2 (@ tptp.t_a V))) (let ((_let_3 (@ (@ (@ tptp.t_a Va) Vb) Vc))) (let ((_let_4 (@ tptp.val_a _let_1))) (let ((_let_5 (@ (@ _let_2 _let_3) _let_1))) (let ((_let_6 (@ tptp.heapIm1091024090Down_a _let_5))) (let ((_let_7 (@ tptp.ord_less_eq_a _let_4))) (let ((_let_8 (@ _let_7 V))) (let ((_let_9 (= _let_6 _let_5))) (let ((_let_10 (@ tptp.val_a _let_3))) (let ((_let_11 (@ _let_7 _let_10))) (let ((_let_12 (@ (@ tptp.ord_less_eq_a _let_10) V))) (and (=> _let_11 (and (=> _let_12 _let_9) (=> (not _let_12) (= _let_6 (@ (@ (@ tptp.t_a _let_10) (@ tptp.heapIm1091024090Down_a (@ (@ _let_2 (@ tptp.heapIm1140443833left_a _let_3)) (@ tptp.heapIm1257206334ight_a _let_3)))) _let_1))))) (=> (not _let_11) (and (=> _let_8 _let_9) (=> (not _let_8) (= _let_6 (@ (@ (@ tptp.t_a _let_4) _let_3) (@ tptp.heapIm1091024090Down_a (@ (@ _let_2 (@ tptp.heapIm1140443833left_a _let_1)) (@ tptp.heapIm1257206334ight_a _let_1)))))))))))))))))))))))) (let ((_let_7 (forall ((V tptp.a) (Uu tptp.tree_a) (Uv tptp.tree_a)) (= (@ tptp.val_a (@ (@ (@ tptp.t_a V) Uu) Uv)) V)))) (let ((_let_8 (@ (@ _let_3 (@ tptp.heapIm1140443833left_a _let_2)) (@ tptp.heapIm1257206334ight_a _let_2)))) (let ((_let_9 (@ tptp.val_a _let_2))) (let ((_let_10 (@ tptp.ord_less_eq_a (@ tptp.val_a _let_1)))) (let ((_let_11 (@ _let_10 _let_9))) (let ((_let_12 (@ (@ _let_3 (@ tptp.heapIm1140443833left_a _let_1)) (@ tptp.heapIm1257206334ight_a _let_1)))) (let ((_let_13 (@ (@ tptp.ord_less_eq_a tptp.v1) tptp.v))) (let ((_let_14 (@ (@ tptp.ord_less_eq_a tptp.v2) tptp.v1))) (let ((_let_15 (ho_58 (ho_62 (ho_61 k_60 tptp.v2) tptp.l2) tptp.r2))) (let ((_let_16 (ho_58 (ho_62 (ho_61 k_60 tptp.v1) tptp.l1) tptp.r1))) (let ((_let_17 (ho_61 k_60 tptp.v))) (let ((_let_18 (ho_58 (ho_62 _let_17 _let_16) _let_15))) (let ((_let_19 (ho_58 k_57 _let_18))) (let ((_let_20 (= (ho_66 k_65 _let_18) (ho_66 k_65 _let_19)))) (let ((_let_21 (= _let_18 _let_19))) (let ((_let_22 (ho_68 k_67 _let_16))) (let ((_let_23 (ho_35 (ho_34 k_33 _let_22) tptp.v))) (let ((_let_24 (not _let_23))) (let ((_let_25 (or _let_24 _let_21))) (let ((_let_26 (and _let_25 (or _let_23 (= _let_19 (ho_58 (ho_62 (ho_61 k_60 _let_22) (ho_58 k_57 (ho_58 (ho_62 _let_17 (ho_58 k_64 _let_16)) (ho_58 k_63 _let_16)))) _let_15)))))) (let ((_let_27 (ho_68 k_67 _let_15))) (let ((_let_28 (ho_35 (ho_34 k_33 _let_27) _let_22))) (let ((_let_29 (not _let_28))) (let ((_let_30 (or _let_29 _let_26))) (let ((_let_31 (forall ((BOUND_VARIABLE_4861 tptp.a) (BOUND_VARIABLE_4863 tptp.tree_a) (BOUND_VARIABLE_4865 tptp.tree_a) (BOUND_VARIABLE_4867 tptp.a) (BOUND_VARIABLE_4869 tptp.tree_a) (BOUND_VARIABLE_4871 tptp.tree_a) (BOUND_VARIABLE_4873 tptp.a)) (let ((_let_1 (ho_58 (ho_62 (ho_61 k_60 BOUND_VARIABLE_4861) BOUND_VARIABLE_4863) BOUND_VARIABLE_4865))) (let ((_let_2 (ho_58 (ho_62 (ho_61 k_60 BOUND_VARIABLE_4867) BOUND_VARIABLE_4869) BOUND_VARIABLE_4871))) (let ((_let_3 (ho_61 k_60 BOUND_VARIABLE_4873))) (let ((_let_4 (ho_58 (ho_62 _let_3 _let_2) _let_1))) (let ((_let_5 (ho_58 k_57 _let_4))) (let ((_let_6 (ho_68 k_67 _let_2))) (let ((_let_7 (ho_35 (ho_34 k_33 _let_6) BOUND_VARIABLE_4873))) (or (not (ho_35 (ho_34 k_33 (ho_68 k_67 _let_1)) _let_6)) (and (or (not _let_7) (= _let_4 _let_5)) (or _let_7 (= (ho_58 (ho_62 (ho_61 k_60 _let_6) (ho_58 k_57 (ho_58 (ho_62 _let_3 (ho_58 k_64 _let_2)) (ho_58 k_63 _let_2)))) _let_1) _let_5)))))))))))))) (let ((_let_32 (0))) (let ((_let_33 (_let_31))) (let ((_let_34 (= tptp.v1 _let_22))) (let ((_let_35 (= tptp.v2 _let_27))) (let ((_let_36 (ho_35 (ho_34 k_33 tptp.v2) tptp.v1))) (let ((_let_37 (forall ((V tptp.a) (Uu tptp.tree_a) (Uv tptp.tree_a)) (= V (ho_68 k_67 (ho_58 (ho_62 (ho_61 k_60 V) Uu) Uv)))))) (let ((_let_38 (EQ_RESOLVE (ASSUME :args (_let_7)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((V tptp.a) (Uu tptp.tree_a) (Uv tptp.tree_a)) (= V (@ tptp.val_a (@ (@ (@ tptp.t_a V) Uu) Uv)))) _let_37))))))) (let ((_let_39 (_let_37))) (let ((_let_40 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_38 :args (tptp.v1 tptp.l1 tptp.r1 QUANTIFIERS_INST_CBQI_PROP)) :args _let_39)) _let_38 :args (_let_34 false _let_37)))) (let ((_let_41 (forall ((u |u_(-> _u_(-> tptp.tree_a Bool)_ _u_(-> tptp.tree_a tptp.produc143150363Tree_a)_ tptp.produc768687417list_a Bool)|) (e |u_(-> _u_(-> tptp.tree_a tptp.produc143150363Tree_a)_ tptp.produc768687417list_a Bool)|) (i |u_(-> tptp.tree_a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.tree_a Bool)_ _u_(-> tptp.tree_a tptp.produc143150363Tree_a)_ tptp.produc768687417list_a Bool)|)) (not (forall ((ii |u_(-> tptp.tree_a Bool)|)) (= (ho_124 v ii) (ite (= i ii) e (ho_124 u ii)))))))))) (let ((_let_42 (forall ((x |u_(-> _u_(-> tptp.tree_a Bool)_ _u_(-> tptp.tree_a tptp.produc143150363Tree_a)_ tptp.produc768687417list_a Bool)|) (y |u_(-> _u_(-> tptp.tree_a Bool)_ _u_(-> tptp.tree_a tptp.produc143150363Tree_a)_ tptp.produc768687417list_a Bool)|)) (or (not (forall ((z |u_(-> tptp.tree_a Bool)|)) (= (ho_124 x z) (ho_124 y z)))) (= x y))))) (let ((_let_43 (forall ((u |u_(-> tptp.produc768687417list_a Bool)|) (e Bool) (i tptp.produc768687417list_a)) (not (forall ((v |u_(-> tptp.produc768687417list_a Bool)|)) (not (forall ((ii tptp.produc768687417list_a)) (= (ho_126 v ii) (ite (= i ii) e (ho_126 u ii)))))))))) (let ((_let_44 (forall ((x |u_(-> tptp.produc768687417list_a Bool)|) (y |u_(-> tptp.produc768687417list_a Bool)|)) (or (not (forall ((z tptp.produc768687417list_a)) (= (ho_126 x z) (ho_126 y z)))) (= x y))))) (let ((_let_45 (forall ((u |u_(-> tptp.tree_a tptp.list_a tptp.produc768687417list_a)|) (e |u_(-> tptp.list_a tptp.produc768687417list_a)|) (i tptp.tree_a)) (not (forall ((v |u_(-> tptp.tree_a tptp.list_a tptp.produc768687417list_a)|)) (not (forall ((ii tptp.tree_a)) (= (ho_121 v ii) (ite (= i ii) e (ho_121 u ii)))))))))) (let ((_let_46 (forall ((x |u_(-> tptp.tree_a tptp.list_a tptp.produc768687417list_a)|) (y |u_(-> tptp.tree_a tptp.list_a tptp.produc768687417list_a)|)) (or (not (forall ((z tptp.tree_a)) (= (ho_121 x z) (ho_121 y z)))) (= x y))))) (let ((_let_47 (forall ((u |u_(-> _u_(-> tptp.tree_a tptp.tree_a)_ _u_(-> tptp.tree_a tptp.produc143150363Tree_a)_ Bool)|) (e |u_(-> _u_(-> tptp.tree_a tptp.produc143150363Tree_a)_ Bool)|) (i |u_(-> tptp.tree_a tptp.tree_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.tree_a tptp.tree_a)_ _u_(-> tptp.tree_a tptp.produc143150363Tree_a)_ Bool)|)) (not (forall ((ii |u_(-> tptp.tree_a tptp.tree_a)|)) (= (ho_100 v ii) (ite (= i ii) e (ho_100 u ii)))))))))) (let ((_let_48 (forall ((x |u_(-> _u_(-> tptp.tree_a tptp.tree_a)_ _u_(-> tptp.tree_a tptp.produc143150363Tree_a)_ Bool)|) (y |u_(-> _u_(-> tptp.tree_a tptp.tree_a)_ _u_(-> tptp.tree_a tptp.produc143150363Tree_a)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.tree_a tptp.tree_a)|)) (= (ho_100 x z) (ho_100 y z)))) (= x y))))) (let ((_let_49 (forall ((u |u_(-> tptp.list_a tptp.produc768687417list_a)|) (e tptp.produc768687417list_a) (i tptp.list_a)) (not (forall ((v |u_(-> tptp.list_a tptp.produc768687417list_a)|)) (not (forall ((ii tptp.list_a)) (= (ho_122 v ii) (ite (= i ii) e (ho_122 u ii)))))))))) (let ((_let_50 (forall ((x |u_(-> tptp.list_a tptp.produc768687417list_a)|) (y |u_(-> tptp.list_a tptp.produc768687417list_a)|)) (or (not (forall ((z tptp.list_a)) (= (ho_122 x z) (ho_122 y z)))) (= x y))))) (let ((_let_51 (forall ((u |u_(-> tptp.tree_a tptp.list_a Bool)|) (e |u_(-> tptp.list_a Bool)|) (i tptp.tree_a)) (not (forall ((v |u_(-> tptp.tree_a tptp.list_a Bool)|)) (not (forall ((ii tptp.tree_a)) (= (ho_118 v ii) (ite (= i ii) e (ho_118 u ii)))))))))) (let ((_let_52 (forall ((x |u_(-> tptp.tree_a tptp.list_a Bool)|) (y |u_(-> tptp.tree_a tptp.list_a Bool)|)) (or (not (forall ((z tptp.tree_a)) (= (ho_118 x z) (ho_118 y z)))) (= x y))))) (let ((_let_53 (forall ((u |u_(-> tptp.list_a Bool)|) (e Bool) (i tptp.list_a)) (not (forall ((v |u_(-> tptp.list_a Bool)|)) (not (forall ((ii tptp.list_a)) (= (ho_119 v ii) (ite (= i ii) e (ho_119 u ii)))))))))) (let ((_let_54 (forall ((x |u_(-> tptp.list_a Bool)|) (y |u_(-> tptp.list_a Bool)|)) (or (not (forall ((z tptp.list_a)) (= (ho_119 x z) (ho_119 y z)))) (= x y))))) (let ((_let_55 (forall ((u |u_(-> tptp.list_a tptp.list_a)|) (e tptp.list_a) (i tptp.list_a)) (not (forall ((v |u_(-> tptp.list_a tptp.list_a)|)) (not (forall ((ii tptp.list_a)) (= (ho_85 v ii) (ite (= i ii) e (ho_85 u ii)))))))))) (let ((_let_56 (forall ((x |u_(-> tptp.list_a tptp.list_a)|) (y |u_(-> tptp.list_a tptp.list_a)|)) (or (not (forall ((z tptp.list_a)) (= (ho_85 x z) (ho_85 y z)))) (= x y))))) (let ((_let_57 (forall ((u |u_(-> _u_(-> tptp.tree_a tptp.produc143150363Tree_a)_ tptp.tree_a tptp.list_a tptp.list_a)|) (e |u_(-> tptp.tree_a tptp.list_a tptp.list_a)|) (i |u_(-> tptp.tree_a tptp.produc143150363Tree_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.tree_a tptp.produc143150363Tree_a)_ tptp.tree_a tptp.list_a tptp.list_a)|)) (not (forall ((ii |u_(-> tptp.tree_a tptp.produc143150363Tree_a)|)) (= (ho_116 v ii) (ite (= i ii) e (ho_116 u ii)))))))))) (let ((_let_58 (forall ((x |u_(-> _u_(-> tptp.tree_a tptp.produc143150363Tree_a)_ tptp.tree_a tptp.list_a tptp.list_a)|) (y |u_(-> _u_(-> tptp.tree_a tptp.produc143150363Tree_a)_ tptp.tree_a tptp.list_a tptp.list_a)|)) (or (not (forall ((z |u_(-> tptp.tree_a tptp.produc143150363Tree_a)|)) (= (ho_116 x z) (ho_116 y z)))) (= x y))))) (let ((_let_59 (forall ((u |u_(-> tptp.tree_a tptp.list_a tptp.list_a)|) (e |u_(-> tptp.list_a tptp.list_a)|) (i tptp.tree_a)) (not (forall ((v |u_(-> tptp.tree_a tptp.list_a tptp.list_a)|)) (not (forall ((ii tptp.tree_a)) (= (ho_117 v ii) (ite (= i ii) e (ho_117 u ii)))))))))) (let ((_let_60 (forall ((x |u_(-> tptp.tree_a tptp.list_a tptp.list_a)|) (y |u_(-> tptp.tree_a tptp.list_a tptp.list_a)|)) (or (not (forall ((z tptp.tree_a)) (= (ho_117 x z) (ho_117 y z)))) (= x y))))) (let ((_let_61 (forall ((u |u_(-> _u_(-> tptp.list_a tptp.tree_a)_ _u_(-> tptp.tree_a tptp.multiset_a)_ _u_(-> tptp.tree_a tptp.produc143150363Tree_a)_ _u_(-> tptp.tree_a Bool)_ Bool)|) (e |u_(-> _u_(-> tptp.tree_a tptp.multiset_a)_ _u_(-> tptp.tree_a tptp.produc143150363Tree_a)_ _u_(-> tptp.tree_a Bool)_ Bool)|) (i |u_(-> tptp.list_a tptp.tree_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.list_a tptp.tree_a)_ _u_(-> tptp.tree_a tptp.multiset_a)_ _u_(-> tptp.tree_a tptp.produc143150363Tree_a)_ _u_(-> tptp.tree_a Bool)_ Bool)|)) (not (forall ((ii |u_(-> tptp.list_a tptp.tree_a)|)) (= (ho_110 v ii) (ite (= i ii) e (ho_110 u ii)))))))))) (let ((_let_62 (forall ((x |u_(-> _u_(-> tptp.list_a tptp.tree_a)_ _u_(-> tptp.tree_a tptp.multiset_a)_ _u_(-> tptp.tree_a tptp.produc143150363Tree_a)_ _u_(-> tptp.tree_a Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.list_a tptp.tree_a)_ _u_(-> tptp.tree_a tptp.multiset_a)_ _u_(-> tptp.tree_a tptp.produc143150363Tree_a)_ _u_(-> tptp.tree_a Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.list_a tptp.tree_a)|)) (= (ho_110 x z) (ho_110 y z)))) (= x y))))) (let ((_let_63 (forall ((u |u_(-> _u_(-> tptp.tree_a Bool)_ Bool)|) (e Bool) (i |u_(-> tptp.tree_a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.tree_a Bool)_ Bool)|)) (not (forall ((ii |u_(-> tptp.tree_a Bool)|)) (= (ho_113 v ii) (ite (= i ii) e (ho_113 u ii)))))))))) (let ((_let_64 (forall ((x |u_(-> _u_(-> tptp.tree_a Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.tree_a Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.tree_a Bool)|)) (= (ho_113 x z) (ho_113 y z)))) (= x y))))) (let ((_let_65 (forall ((u |u_(-> tptp.tree_a _u_(-> tptp.tree_a Bool)_ _u_(-> tptp.list_a tptp.tree_a)_ _u_(-> tptp.tree_a tptp.multiset_a)_ _u_(-> tptp.tree_a tptp.tree_a)_ _u_(-> tptp.tree_a tptp.produc143150363Tree_a)_ Bool)|) (e |u_(-> _u_(-> tptp.tree_a Bool)_ _u_(-> tptp.list_a tptp.tree_a)_ _u_(-> tptp.tree_a tptp.multiset_a)_ _u_(-> tptp.tree_a tptp.tree_a)_ _u_(-> tptp.tree_a tptp.produc143150363Tree_a)_ Bool)|) (i tptp.tree_a)) (not (forall ((v |u_(-> tptp.tree_a _u_(-> tptp.tree_a Bool)_ _u_(-> tptp.list_a tptp.tree_a)_ _u_(-> tptp.tree_a tptp.multiset_a)_ _u_(-> tptp.tree_a tptp.tree_a)_ _u_(-> tptp.tree_a tptp.produc143150363Tree_a)_ Bool)|)) (not (forall ((ii tptp.tree_a)) (= (ho_96 v ii) (ite (= i ii) e (ho_96 u ii)))))))))) (let ((_let_66 (forall ((x |u_(-> tptp.tree_a _u_(-> tptp.tree_a Bool)_ _u_(-> tptp.list_a tptp.tree_a)_ _u_(-> tptp.tree_a tptp.multiset_a)_ _u_(-> tptp.tree_a tptp.tree_a)_ _u_(-> tptp.tree_a tptp.produc143150363Tree_a)_ Bool)|) (y |u_(-> tptp.tree_a _u_(-> tptp.tree_a Bool)_ _u_(-> tptp.list_a tptp.tree_a)_ _u_(-> tptp.tree_a tptp.multiset_a)_ _u_(-> tptp.tree_a tptp.tree_a)_ _u_(-> tptp.tree_a tptp.produc143150363Tree_a)_ Bool)|)) (or (not (forall ((z tptp.tree_a)) (= (ho_96 x z) (ho_96 y z)))) (= x y))))) (let ((_let_67 (forall ((u |u_(-> _u_(-> tptp.tree_a Bool)_ _u_(-> tptp.list_a tptp.tree_a)_ _u_(-> tptp.tree_a tptp.multiset_a)_ _u_(-> tptp.tree_a tptp.tree_a)_ _u_(-> tptp.tree_a tptp.produc143150363Tree_a)_ Bool)|) (e |u_(-> _u_(-> tptp.list_a tptp.tree_a)_ _u_(-> tptp.tree_a tptp.multiset_a)_ _u_(-> tptp.tree_a tptp.tree_a)_ _u_(-> tptp.tree_a tptp.produc143150363Tree_a)_ Bool)|) (i |u_(-> tptp.tree_a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.tree_a Bool)_ _u_(-> tptp.list_a tptp.tree_a)_ _u_(-> tptp.tree_a tptp.multiset_a)_ _u_(-> tptp.tree_a tptp.tree_a)_ _u_(-> tptp.tree_a tptp.produc143150363Tree_a)_ Bool)|)) (not (forall ((ii |u_(-> tptp.tree_a Bool)|)) (= (ho_97 v ii) (ite (= i ii) e (ho_97 u ii)))))))))) (let ((_let_68 (forall ((x |u_(-> _u_(-> tptp.tree_a Bool)_ _u_(-> tptp.list_a tptp.tree_a)_ _u_(-> tptp.tree_a tptp.multiset_a)_ _u_(-> tptp.tree_a tptp.tree_a)_ _u_(-> tptp.tree_a tptp.produc143150363Tree_a)_ Bool)|) (y |u_(-> _u_(-> tptp.tree_a Bool)_ _u_(-> tptp.list_a tptp.tree_a)_ _u_(-> tptp.tree_a tptp.multiset_a)_ _u_(-> tptp.tree_a tptp.tree_a)_ _u_(-> tptp.tree_a tptp.produc143150363Tree_a)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.tree_a Bool)|)) (= (ho_97 x z) (ho_97 y z)))) (= x y))))) (let ((_let_69 (forall ((u |u_(-> _u_(-> tptp.list_a tptp.tree_a)_ _u_(-> tptp.tree_a tptp.multiset_a)_ _u_(-> tptp.tree_a tptp.tree_a)_ _u_(-> tptp.tree_a tptp.produc143150363Tree_a)_ Bool)|) (e |u_(-> _u_(-> tptp.tree_a tptp.multiset_a)_ _u_(-> tptp.tree_a tptp.tree_a)_ _u_(-> tptp.tree_a tptp.produc143150363Tree_a)_ Bool)|) (i |u_(-> tptp.list_a tptp.tree_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.list_a tptp.tree_a)_ _u_(-> tptp.tree_a tptp.multiset_a)_ _u_(-> tptp.tree_a tptp.tree_a)_ _u_(-> tptp.tree_a tptp.produc143150363Tree_a)_ Bool)|)) (not (forall ((ii |u_(-> tptp.list_a tptp.tree_a)|)) (= (ho_98 v ii) (ite (= i ii) e (ho_98 u ii)))))))))) (let ((_let_70 (forall ((x |u_(-> _u_(-> tptp.list_a tptp.tree_a)_ _u_(-> tptp.tree_a tptp.multiset_a)_ _u_(-> tptp.tree_a tptp.tree_a)_ _u_(-> tptp.tree_a tptp.produc143150363Tree_a)_ Bool)|) (y |u_(-> _u_(-> tptp.list_a tptp.tree_a)_ _u_(-> tptp.tree_a tptp.multiset_a)_ _u_(-> tptp.tree_a tptp.tree_a)_ _u_(-> tptp.tree_a tptp.produc143150363Tree_a)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.list_a tptp.tree_a)|)) (= (ho_98 x z) (ho_98 y z)))) (= x y))))) (let ((_let_71 (forall ((u |u_(-> _u_(-> tptp.tree_a tptp.produc143150363Tree_a)_ Bool)|) (e Bool) (i |u_(-> tptp.tree_a tptp.produc143150363Tree_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.tree_a tptp.produc143150363Tree_a)_ Bool)|)) (not (forall ((ii |u_(-> tptp.tree_a tptp.produc143150363Tree_a)|)) (= (ho_101 v ii) (ite (= i ii) e (ho_101 u ii)))))))))) (let ((_let_72 (forall ((x |u_(-> _u_(-> tptp.tree_a tptp.produc143150363Tree_a)_ Bool)|) (y |u_(-> _u_(-> tptp.tree_a tptp.produc143150363Tree_a)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.tree_a tptp.produc143150363Tree_a)|)) (= (ho_101 x z) (ho_101 y z)))) (= x y))))) (let ((_let_73 (forall ((u |u_(-> tptp.a tptp.tree_a tptp.produc143150363Tree_a)|) (e |u_(-> tptp.tree_a tptp.produc143150363Tree_a)|) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.tree_a tptp.produc143150363Tree_a)|)) (not (forall ((ii tptp.a)) (= (ho_92 v ii) (ite (= i ii) e (ho_92 u ii)))))))))) (let ((_let_74 (forall ((x |u_(-> tptp.a tptp.tree_a tptp.produc143150363Tree_a)|) (y |u_(-> tptp.a tptp.tree_a tptp.produc143150363Tree_a)|)) (or (not (forall ((z tptp.a)) (= (ho_92 x z) (ho_92 y z)))) (= x y))))) (let ((_let_75 (forall ((u |u_(-> _u_(-> tptp.a Bool)_ tptp.a)|) (e tptp.a) (i |u_(-> tptp.a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.a Bool)_ tptp.a)|)) (not (forall ((ii |u_(-> tptp.a Bool)|)) (= (ho_89 v ii) (ite (= i ii) e (ho_89 u ii)))))))))) (let ((_let_76 (forall ((x |u_(-> _u_(-> tptp.a Bool)_ tptp.a)|) (y |u_(-> _u_(-> tptp.a Bool)_ tptp.a)|)) (or (not (forall ((z |u_(-> tptp.a Bool)|)) (= (ho_89 x z) (ho_89 y z)))) (= x y))))) (let ((_let_77 (forall ((u |u_(-> _u_(-> tptp.tree_a tptp.multiset_a)_ _u_(-> tptp.tree_a tptp.tree_a)_ _u_(-> tptp.tree_a tptp.produc143150363Tree_a)_ Bool)|) (e |u_(-> _u_(-> tptp.tree_a tptp.tree_a)_ _u_(-> tptp.tree_a tptp.produc143150363Tree_a)_ Bool)|) (i |u_(-> tptp.tree_a tptp.multiset_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.tree_a tptp.multiset_a)_ _u_(-> tptp.tree_a tptp.tree_a)_ _u_(-> tptp.tree_a tptp.produc143150363Tree_a)_ Bool)|)) (not (forall ((ii |u_(-> tptp.tree_a tptp.multiset_a)|)) (= (ho_99 v ii) (ite (= i ii) e (ho_99 u ii)))))))))) (let ((_let_78 (forall ((x |u_(-> _u_(-> tptp.tree_a tptp.multiset_a)_ _u_(-> tptp.tree_a tptp.tree_a)_ _u_(-> tptp.tree_a tptp.produc143150363Tree_a)_ Bool)|) (y |u_(-> _u_(-> tptp.tree_a tptp.multiset_a)_ _u_(-> tptp.tree_a tptp.tree_a)_ _u_(-> tptp.tree_a tptp.produc143150363Tree_a)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.tree_a tptp.multiset_a)|)) (= (ho_99 x z) (ho_99 y z)))) (= x y))))) (let ((_let_79 (forall ((u |u_(-> _u_(-> _u_(-> Bool tptp.a)_ Bool)_ Bool tptp.a)|) (e |u_(-> Bool tptp.a)|) (i |u_(-> _u_(-> Bool tptp.a)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> Bool tptp.a)_ Bool)_ Bool tptp.a)|)) (not (forall ((ii |u_(-> _u_(-> Bool tptp.a)_ Bool)|)) (= (ho_87 v ii) (ite (= i ii) e (ho_87 u ii)))))))))) (let ((_let_80 (forall ((x |u_(-> _u_(-> _u_(-> Bool tptp.a)_ Bool)_ Bool tptp.a)|) (y |u_(-> _u_(-> _u_(-> Bool tptp.a)_ Bool)_ Bool tptp.a)|)) (or (not (forall ((z |u_(-> _u_(-> Bool tptp.a)_ Bool)|)) (= (ho_87 x z) (ho_87 y z)))) (= x y))))) (let ((_let_81 (forall ((u |u_(-> tptp.multiset_a Bool)|) (e Bool) (i tptp.multiset_a)) (not (forall ((v |u_(-> tptp.multiset_a Bool)|)) (not (forall ((ii tptp.multiset_a)) (= (ho_23 v ii) (ite (= i ii) e (ho_23 u ii)))))))))) (let ((_let_82 (forall ((x |u_(-> tptp.multiset_a Bool)|) (y |u_(-> tptp.multiset_a Bool)|)) (or (not (forall ((z tptp.multiset_a)) (= (ho_23 x z) (ho_23 y z)))) (= x y))))) (let ((_let_83 (forall ((u |u_(-> _u_(-> tptp.tree_a tptp.produc143150363Tree_a)_ tptp.produc768687417list_a Bool)|) (e |u_(-> tptp.produc768687417list_a Bool)|) (i |u_(-> tptp.tree_a tptp.produc143150363Tree_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.tree_a tptp.produc143150363Tree_a)_ tptp.produc768687417list_a Bool)|)) (not (forall ((ii |u_(-> tptp.tree_a tptp.produc143150363Tree_a)|)) (= (ho_125 v ii) (ite (= i ii) e (ho_125 u ii)))))))))) (let ((_let_84 (forall ((x |u_(-> _u_(-> tptp.tree_a tptp.produc143150363Tree_a)_ tptp.produc768687417list_a Bool)|) (y |u_(-> _u_(-> tptp.tree_a tptp.produc143150363Tree_a)_ tptp.produc768687417list_a Bool)|)) (or (not (forall ((z |u_(-> tptp.tree_a tptp.produc143150363Tree_a)|)) (= (ho_125 x z) (ho_125 y z)))) (= x y))))) (let ((_let_85 (forall ((u |u_(-> tptp.tree_a tptp.tree_a tptp.tree_a)|) (e |u_(-> tptp.tree_a tptp.tree_a)|) (i tptp.tree_a)) (not (forall ((v |u_(-> tptp.tree_a tptp.tree_a tptp.tree_a)|)) (not (forall ((ii tptp.tree_a)) (= (ho_62 v ii) (ite (= i ii) e (ho_62 u ii)))))))))) (let ((_let_86 (forall ((x |u_(-> tptp.tree_a tptp.tree_a tptp.tree_a)|) (y |u_(-> tptp.tree_a tptp.tree_a tptp.tree_a)|)) (or (not (forall ((z tptp.tree_a)) (= (ho_62 x z) (ho_62 y z)))) (= x y))))) (let ((_let_87 (forall ((u |u_(-> tptp.a tptp.a Bool)|) (e |u_(-> tptp.a Bool)|) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.a Bool)|)) (not (forall ((ii tptp.a)) (= (ho_34 v ii) (ite (= i ii) e (ho_34 u ii)))))))))) (let ((_let_88 (forall ((x |u_(-> tptp.a tptp.a Bool)|) (y |u_(-> tptp.a tptp.a Bool)|)) (or (not (forall ((z tptp.a)) (= (ho_34 x z) (ho_34 y z)))) (= x y))))) (let ((_let_89 (forall ((u |u_(-> tptp.a tptp.tree_a tptp.tree_a tptp.tree_a)|) (e |u_(-> tptp.tree_a tptp.tree_a tptp.tree_a)|) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.tree_a tptp.tree_a tptp.tree_a)|)) (not (forall ((ii tptp.a)) (= (ho_61 v ii) (ite (= i ii) e (ho_61 u ii)))))))))) (let ((_let_90 (forall ((x |u_(-> tptp.a tptp.tree_a tptp.tree_a tptp.tree_a)|) (y |u_(-> tptp.a tptp.tree_a tptp.tree_a tptp.tree_a)|)) (or (not (forall ((z tptp.a)) (= (ho_61 x z) (ho_61 y z)))) (= x y))))) (let ((_let_91 (forall ((u |u_(-> _u_(-> Bool tptp.a)_ _u_(-> Bool tptp.a)_ Bool)|) (e |u_(-> _u_(-> Bool tptp.a)_ Bool)|) (i |u_(-> Bool tptp.a)|)) (not (forall ((v |u_(-> _u_(-> Bool tptp.a)_ _u_(-> Bool tptp.a)_ Bool)|)) (not (forall ((ii |u_(-> Bool tptp.a)|)) (= (ho_31 v ii) (ite (= i ii) e (ho_31 u ii)))))))))) (let ((_let_92 (forall ((x |u_(-> _u_(-> Bool tptp.a)_ _u_(-> Bool tptp.a)_ Bool)|) (y |u_(-> _u_(-> Bool tptp.a)_ _u_(-> Bool tptp.a)_ Bool)|)) (or (not (forall ((z |u_(-> Bool tptp.a)|)) (= (ho_31 x z) (ho_31 y z)))) (= x y))))) (let ((_let_93 (forall ((u |u_(-> tptp.tree_a _u_(-> tptp.tree_a Bool)_ _u_(-> tptp.list_a tptp.tree_a)_ _u_(-> tptp.tree_a tptp.multiset_a)_ _u_(-> tptp.tree_a tptp.produc143150363Tree_a)_ _u_(-> tptp.tree_a Bool)_ Bool)|) (e |u_(-> _u_(-> tptp.tree_a Bool)_ _u_(-> tptp.list_a tptp.tree_a)_ _u_(-> tptp.tree_a tptp.multiset_a)_ _u_(-> tptp.tree_a tptp.produc143150363Tree_a)_ _u_(-> tptp.tree_a Bool)_ Bool)|) (i tptp.tree_a)) (not (forall ((v |u_(-> tptp.tree_a _u_(-> tptp.tree_a Bool)_ _u_(-> tptp.list_a tptp.tree_a)_ _u_(-> tptp.tree_a tptp.multiset_a)_ _u_(-> tptp.tree_a tptp.produc143150363Tree_a)_ _u_(-> tptp.tree_a Bool)_ Bool)|)) (not (forall ((ii tptp.tree_a)) (= (ho_108 v ii) (ite (= i ii) e (ho_108 u ii)))))))))) (let ((_let_94 (forall ((x |u_(-> tptp.tree_a _u_(-> tptp.tree_a Bool)_ _u_(-> tptp.list_a tptp.tree_a)_ _u_(-> tptp.tree_a tptp.multiset_a)_ _u_(-> tptp.tree_a tptp.produc143150363Tree_a)_ _u_(-> tptp.tree_a Bool)_ Bool)|) (y |u_(-> tptp.tree_a _u_(-> tptp.tree_a Bool)_ _u_(-> tptp.list_a tptp.tree_a)_ _u_(-> tptp.tree_a tptp.multiset_a)_ _u_(-> tptp.tree_a tptp.produc143150363Tree_a)_ _u_(-> tptp.tree_a Bool)_ Bool)|)) (or (not (forall ((z tptp.tree_a)) (= (ho_108 x z) (ho_108 y z)))) (= x y))))) (let ((_let_95 (forall ((u |u_(-> tptp.tree_a Bool)|) (e Bool) (i tptp.tree_a)) (not (forall ((v |u_(-> tptp.tree_a Bool)|)) (not (forall ((ii tptp.tree_a)) (= (ho_56 v ii) (ite (= i ii) e (ho_56 u ii)))))))))) (let ((_let_96 (forall ((x |u_(-> tptp.tree_a Bool)|) (y |u_(-> tptp.tree_a Bool)|)) (or (not (forall ((z tptp.tree_a)) (= (ho_56 x z) (ho_56 y z)))) (= x y))))) (let ((_let_97 (forall ((u |u_(-> _u_(-> tptp.tree_a tptp.produc143150363Tree_a)_ _u_(-> tptp.tree_a Bool)_ Bool)|) (e |u_(-> _u_(-> tptp.tree_a Bool)_ Bool)|) (i |u_(-> tptp.tree_a tptp.produc143150363Tree_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.tree_a tptp.produc143150363Tree_a)_ _u_(-> tptp.tree_a Bool)_ Bool)|)) (not (forall ((ii |u_(-> tptp.tree_a tptp.produc143150363Tree_a)|)) (= (ho_112 v ii) (ite (= i ii) e (ho_112 u ii)))))))))) (let ((_let_98 (forall ((x |u_(-> _u_(-> tptp.tree_a tptp.produc143150363Tree_a)_ _u_(-> tptp.tree_a Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.tree_a tptp.produc143150363Tree_a)_ _u_(-> tptp.tree_a Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.tree_a tptp.produc143150363Tree_a)|)) (= (ho_112 x z) (ho_112 y z)))) (= x y))))) (let ((_let_99 (forall ((u |u_(-> tptp.tree_a tptp.set_a)|) (e tptp.set_a) (i tptp.tree_a)) (not (forall ((v |u_(-> tptp.tree_a tptp.set_a)|)) (not (forall ((ii tptp.tree_a)) (= (ho_106 v ii) (ite (= i ii) e (ho_106 u ii)))))))))) (let ((_let_100 (forall ((x |u_(-> tptp.tree_a tptp.set_a)|) (y |u_(-> tptp.tree_a tptp.set_a)|)) (or (not (forall ((z tptp.tree_a)) (= (ho_106 x z) (ho_106 y z)))) (= x y))))) (let ((_let_101 (forall ((u |u_(-> tptp.a tptp.tree_a Bool)|) (e |u_(-> tptp.tree_a Bool)|) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.tree_a Bool)|)) (not (forall ((ii tptp.a)) (= (ho_55 v ii) (ite (= i ii) e (ho_55 u ii)))))))))) (let ((_let_102 (forall ((x |u_(-> tptp.a tptp.tree_a Bool)|) (y |u_(-> tptp.a tptp.tree_a Bool)|)) (or (not (forall ((z tptp.a)) (= (ho_55 x z) (ho_55 y z)))) (= x y))))) (let ((_let_103 (forall ((u |u_(-> Bool tptp.a)|) (e tptp.a) (i Bool)) (not (forall ((v |u_(-> Bool tptp.a)|)) (not (forall ((ii Bool)) (= (ho_29 v ii) (ite (= i ii) e (ho_29 u ii)))))))))) (let ((_let_104 (forall ((x |u_(-> Bool tptp.a)|) (y |u_(-> Bool tptp.a)|)) (or (not (forall ((z Bool)) (= (ho_29 x z) (ho_29 y z)))) (= x y))))) (let ((_let_105 (forall ((u |u_(-> tptp.set_a Bool)|) (e Bool) (i tptp.set_a)) (not (forall ((v |u_(-> tptp.set_a Bool)|)) (not (forall ((ii tptp.set_a)) (= (ho_53 v ii) (ite (= i ii) e (ho_53 u ii)))))))))) (let ((_let_106 (forall ((x |u_(-> tptp.set_a Bool)|) (y |u_(-> tptp.set_a Bool)|)) (or (not (forall ((z tptp.set_a)) (= (ho_53 x z) (ho_53 y z)))) (= x y))))) (let ((_let_107 (forall ((u |u_(-> _u_(-> Bool tptp.a)_ Bool)|) (e Bool) (i |u_(-> Bool tptp.a)|)) (not (forall ((v |u_(-> _u_(-> Bool tptp.a)_ Bool)|)) (not (forall ((ii |u_(-> Bool tptp.a)|)) (= (ho_32 v ii) (ite (= i ii) e (ho_32 u ii)))))))))) (let ((_let_108 (forall ((x |u_(-> _u_(-> Bool tptp.a)_ Bool)|) (y |u_(-> _u_(-> Bool tptp.a)_ Bool)|)) (or (not (forall ((z |u_(-> Bool tptp.a)|)) (= (ho_32 x z) (ho_32 y z)))) (= x y))))) (let ((_let_109 (forall ((u |u_(-> tptp.a tptp.set_a Bool)|) (e |u_(-> tptp.set_a Bool)|) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.set_a Bool)|)) (not (forall ((ii tptp.a)) (= (ho_52 v ii) (ite (= i ii) e (ho_52 u ii)))))))))) (let ((_let_110 (forall ((x |u_(-> tptp.a tptp.set_a Bool)|) (y |u_(-> tptp.a tptp.set_a Bool)|)) (or (not (forall ((z tptp.a)) (= (ho_52 x z) (ho_52 y z)))) (= x y))))) (let ((_let_111 (forall ((u |u_(-> tptp.tree_a tptp.multiset_a)|) (e tptp.multiset_a) (i tptp.tree_a)) (not (forall ((v |u_(-> tptp.tree_a tptp.multiset_a)|)) (not (forall ((ii tptp.tree_a)) (= (ho_66 v ii) (ite (= i ii) e (ho_66 u ii)))))))))) (let ((_let_112 (forall ((x |u_(-> tptp.tree_a tptp.multiset_a)|) (y |u_(-> tptp.tree_a tptp.multiset_a)|)) (or (not (forall ((z tptp.tree_a)) (= (ho_66 x z) (ho_66 y z)))) (= x y))))) (let ((_let_113 (forall ((u |u_(-> tptp.a tptp.multiset_a tptp.multiset_a)|) (e |u_(-> tptp.multiset_a tptp.multiset_a)|) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.multiset_a tptp.multiset_a)|)) (not (forall ((ii tptp.a)) (= (ho_94 v ii) (ite (= i ii) e (ho_94 u ii)))))))))) (let ((_let_114 (forall ((x |u_(-> tptp.a tptp.multiset_a tptp.multiset_a)|) (y |u_(-> tptp.a tptp.multiset_a tptp.multiset_a)|)) (or (not (forall ((z tptp.a)) (= (ho_94 x z) (ho_94 y z)))) (= x y))))) (let ((_let_115 (forall ((u |u_(-> tptp.set_a tptp.a Bool)|) (e |u_(-> tptp.a Bool)|) (i tptp.set_a)) (not (forall ((v |u_(-> tptp.set_a tptp.a Bool)|)) (not (forall ((ii tptp.set_a)) (= (ho_50 v ii) (ite (= i ii) e (ho_50 u ii)))))))))) (let ((_let_116 (forall ((x |u_(-> tptp.set_a tptp.a Bool)|) (y |u_(-> tptp.set_a tptp.a Bool)|)) (or (not (forall ((z tptp.set_a)) (= (ho_50 x z) (ho_50 y z)))) (= x y))))) (let ((_let_117 (forall ((u |u_(-> tptp.list_a tptp.tree_a)|) (e tptp.tree_a) (i tptp.list_a)) (not (forall ((v |u_(-> tptp.list_a tptp.tree_a)|)) (not (forall ((ii tptp.list_a)) (= (ho_82 v ii) (ite (= i ii) e (ho_82 u ii)))))))))) (let ((_let_118 (forall ((x |u_(-> tptp.list_a tptp.tree_a)|) (y |u_(-> tptp.list_a tptp.tree_a)|)) (or (not (forall ((z tptp.list_a)) (= (ho_82 x z) (ho_82 y z)))) (= x y))))) (let ((_let_119 (forall ((u |u_(-> tptp.a Bool)|) (e Bool) (i tptp.a)) (not (forall ((v |u_(-> tptp.a Bool)|)) (not (forall ((ii tptp.a)) (= (ho_35 v ii) (ite (= i ii) e (ho_35 u ii)))))))))) (let ((_let_120 (forall ((x |u_(-> tptp.a Bool)|) (y |u_(-> tptp.a Bool)|)) (or (not (forall ((z tptp.a)) (= (ho_35 x z) (ho_35 y z)))) (= x y))))) (let ((_let_121 (forall ((u |u_(-> _u_(-> tptp.tree_a tptp.multiset_a)_ _u_(-> tptp.tree_a tptp.produc143150363Tree_a)_ _u_(-> tptp.tree_a Bool)_ Bool)|) (e |u_(-> _u_(-> tptp.tree_a tptp.produc143150363Tree_a)_ _u_(-> tptp.tree_a Bool)_ Bool)|) (i |u_(-> tptp.tree_a tptp.multiset_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.tree_a tptp.multiset_a)_ _u_(-> tptp.tree_a tptp.produc143150363Tree_a)_ _u_(-> tptp.tree_a Bool)_ Bool)|)) (not (forall ((ii |u_(-> tptp.tree_a tptp.multiset_a)|)) (= (ho_111 v ii) (ite (= i ii) e (ho_111 u ii)))))))))) (let ((_let_122 (forall ((x |u_(-> _u_(-> tptp.tree_a tptp.multiset_a)_ _u_(-> tptp.tree_a tptp.produc143150363Tree_a)_ _u_(-> tptp.tree_a Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.tree_a tptp.multiset_a)_ _u_(-> tptp.tree_a tptp.produc143150363Tree_a)_ _u_(-> tptp.tree_a Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.tree_a tptp.multiset_a)|)) (= (ho_111 x z) (ho_111 y z)))) (= x y))))) (let ((_let_123 (forall ((u |u_(-> _u_(-> Bool tptp.a)_ tptp.a)|) (e tptp.a) (i |u_(-> Bool tptp.a)|)) (not (forall ((v |u_(-> _u_(-> Bool tptp.a)_ tptp.a)|)) (not (forall ((ii |u_(-> Bool tptp.a)|)) (= (ho_75 v ii) (ite (= i ii) e (ho_75 u ii)))))))))) (let ((_let_124 (forall ((x |u_(-> _u_(-> Bool tptp.a)_ tptp.a)|) (y |u_(-> _u_(-> Bool tptp.a)_ tptp.a)|)) (or (not (forall ((z |u_(-> Bool tptp.a)|)) (= (ho_75 x z) (ho_75 y z)))) (= x y))))) (let ((_let_125 (forall ((u |u_(-> tptp.tree_a tptp.produc143150363Tree_a)|) (e tptp.produc143150363Tree_a) (i tptp.tree_a)) (not (forall ((v |u_(-> tptp.tree_a tptp.produc143150363Tree_a)|)) (not (forall ((ii tptp.tree_a)) (= (ho_90 v ii) (ite (= i ii) e (ho_90 u ii)))))))))) (let ((_let_126 (forall ((x |u_(-> tptp.tree_a tptp.produc143150363Tree_a)|) (y |u_(-> tptp.tree_a tptp.produc143150363Tree_a)|)) (or (not (forall ((z tptp.tree_a)) (= (ho_90 x z) (ho_90 y z)))) (= x y))))) (let ((_let_127 (forall ((u |u_(-> tptp.multiset_a tptp.multiset_a)|) (e tptp.multiset_a) (i tptp.multiset_a)) (not (forall ((v |u_(-> tptp.multiset_a tptp.multiset_a)|)) (not (forall ((ii tptp.multiset_a)) (= (ho_26 v ii) (ite (= i ii) e (ho_26 u ii)))))))))) (let ((_let_128 (forall ((x |u_(-> tptp.multiset_a tptp.multiset_a)|) (y |u_(-> tptp.multiset_a tptp.multiset_a)|)) (or (not (forall ((z tptp.multiset_a)) (= (ho_26 x z) (ho_26 y z)))) (= x y))))) (let ((_let_129 (forall ((u |u_(-> tptp.multiset_a tptp.multiset_a tptp.multiset_a)|) (e |u_(-> tptp.multiset_a tptp.multiset_a)|) (i tptp.multiset_a)) (not (forall ((v |u_(-> tptp.multiset_a tptp.multiset_a tptp.multiset_a)|)) (not (forall ((ii tptp.multiset_a)) (= (ho_25 v ii) (ite (= i ii) e (ho_25 u ii)))))))))) (let ((_let_130 (forall ((x |u_(-> tptp.multiset_a tptp.multiset_a tptp.multiset_a)|) (y |u_(-> tptp.multiset_a tptp.multiset_a tptp.multiset_a)|)) (or (not (forall ((z tptp.multiset_a)) (= (ho_25 x z) (ho_25 y z)))) (= x y))))) (let ((_let_131 (forall ((u |u_(-> tptp.set_a tptp.a)|) (e tptp.a) (i tptp.set_a)) (not (forall ((v |u_(-> tptp.set_a tptp.a)|)) (not (forall ((ii tptp.set_a)) (= (ho_80 v ii) (ite (= i ii) e (ho_80 u ii)))))))))) (let ((_let_132 (forall ((x |u_(-> tptp.set_a tptp.a)|) (y |u_(-> tptp.set_a tptp.a)|)) (or (not (forall ((z tptp.set_a)) (= (ho_80 x z) (ho_80 y z)))) (= x y))))) (let ((_let_133 (forall ((u |u_(-> _u_(-> tptp.tree_a tptp.multiset_a)_ tptp.tree_a tptp.set_a)|) (e |u_(-> tptp.tree_a tptp.set_a)|) (i |u_(-> tptp.tree_a tptp.multiset_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.tree_a tptp.multiset_a)_ tptp.tree_a tptp.set_a)|)) (not (forall ((ii |u_(-> tptp.tree_a tptp.multiset_a)|)) (= (ho_105 v ii) (ite (= i ii) e (ho_105 u ii)))))))))) (let ((_let_134 (forall ((x |u_(-> _u_(-> tptp.tree_a tptp.multiset_a)_ tptp.tree_a tptp.set_a)|) (y |u_(-> _u_(-> tptp.tree_a tptp.multiset_a)_ tptp.tree_a tptp.set_a)|)) (or (not (forall ((z |u_(-> tptp.tree_a tptp.multiset_a)|)) (= (ho_105 x z) (ho_105 y z)))) (= x y))))) (let ((_let_135 (forall ((u |u_(-> tptp.tree_a tptp.tree_a)|) (e tptp.tree_a) (i tptp.tree_a)) (not (forall ((v |u_(-> tptp.tree_a tptp.tree_a)|)) (not (forall ((ii tptp.tree_a)) (= (ho_58 v ii) (ite (= i ii) e (ho_58 u ii)))))))))) (let ((_let_136 (forall ((x |u_(-> tptp.tree_a tptp.tree_a)|) (y |u_(-> tptp.tree_a tptp.tree_a)|)) (or (not (forall ((z tptp.tree_a)) (= (ho_58 x z) (ho_58 y z)))) (= x y))))) (let ((_let_137 (forall ((u |u_(-> tptp.multiset_a tptp.multiset_a Bool)|) (e |u_(-> tptp.multiset_a Bool)|) (i tptp.multiset_a)) (not (forall ((v |u_(-> tptp.multiset_a tptp.multiset_a Bool)|)) (not (forall ((ii tptp.multiset_a)) (= (ho_22 v ii) (ite (= i ii) e (ho_22 u ii)))))))))) (let ((_let_138 (forall ((x |u_(-> tptp.multiset_a tptp.multiset_a Bool)|) (y |u_(-> tptp.multiset_a tptp.multiset_a Bool)|)) (or (not (forall ((z tptp.multiset_a)) (= (ho_22 x z) (ho_22 y z)))) (= x y))))) (let ((_let_139 (forall ((u |u_(-> tptp.a Bool tptp.a)|) (e |u_(-> Bool tptp.a)|) (i tptp.a)) (not (forall ((v |u_(-> tptp.a Bool tptp.a)|)) (not (forall ((ii tptp.a)) (= (ho_76 v ii) (ite (= i ii) e (ho_76 u ii)))))))))) (let ((_let_140 (forall ((x |u_(-> tptp.a Bool tptp.a)|) (y |u_(-> tptp.a Bool tptp.a)|)) (or (not (forall ((z tptp.a)) (= (ho_76 x z) (ho_76 y z)))) (= x y))))) (let ((_let_141 (forall ((u |u_(-> _u_(-> Bool tptp.a)_ Bool tptp.a)|) (e |u_(-> Bool tptp.a)|) (i |u_(-> Bool tptp.a)|)) (not (forall ((v |u_(-> _u_(-> Bool tptp.a)_ Bool tptp.a)|)) (not (forall ((ii |u_(-> Bool tptp.a)|)) (= (ho_77 v ii) (ite (= i ii) e (ho_77 u ii)))))))))) (let ((_let_142 (forall ((x |u_(-> _u_(-> Bool tptp.a)_ Bool tptp.a)|) (y |u_(-> _u_(-> Bool tptp.a)_ Bool tptp.a)|)) (or (not (forall ((z |u_(-> Bool tptp.a)|)) (= (ho_77 x z) (ho_77 y z)))) (= x y))))) (let ((_let_143 (forall ((u |u_(-> tptp.tree_a tptp.a)|) (e tptp.a) (i tptp.tree_a)) (not (forall ((v |u_(-> tptp.tree_a tptp.a)|)) (not (forall ((ii tptp.tree_a)) (= (ho_68 v ii) (ite (= i ii) e (ho_68 u ii)))))))))) (let ((_let_144 (forall ((x |u_(-> tptp.tree_a tptp.a)|) (y |u_(-> tptp.tree_a tptp.a)|)) (or (not (forall ((z tptp.tree_a)) (= (ho_68 x z) (ho_68 y z)))) (= x y))))) (let ((_let_145 (forall ((u |u_(-> tptp.multiset_a tptp.set_a)|) (e tptp.set_a) (i tptp.multiset_a)) (not (forall ((v |u_(-> tptp.multiset_a tptp.set_a)|)) (not (forall ((ii tptp.multiset_a)) (= (ho_72 v ii) (ite (= i ii) e (ho_72 u ii)))))))))) (let ((_let_146 (forall ((x |u_(-> tptp.multiset_a tptp.set_a)|) (y |u_(-> tptp.multiset_a tptp.set_a)|)) (or (not (forall ((z tptp.multiset_a)) (= (ho_72 x z) (ho_72 y z)))) (= x y))))) (let ((_let_147 (forall ((u |u_(-> _u_(-> tptp.a Bool)_ tptp.set_a)|) (e tptp.set_a) (i |u_(-> tptp.a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.a Bool)_ tptp.set_a)|)) (not (forall ((ii |u_(-> tptp.a Bool)|)) (= (ho_74 v ii) (ite (= i ii) e (ho_74 u ii)))))))))) (let ((_let_148 (forall ((x |u_(-> _u_(-> tptp.a Bool)_ tptp.set_a)|) (y |u_(-> _u_(-> tptp.a Bool)_ tptp.set_a)|)) (or (not (forall ((z |u_(-> tptp.a Bool)|)) (= (ho_74 x z) (ho_74 y z)))) (= x y))))) (let ((_let_149 (forall ((u |u_(-> _u_(-> tptp.tree_a Bool)_ _u_(-> tptp.list_a tptp.tree_a)_ _u_(-> tptp.tree_a tptp.multiset_a)_ _u_(-> tptp.tree_a tptp.produc143150363Tree_a)_ _u_(-> tptp.tree_a Bool)_ Bool)|) (e |u_(-> _u_(-> tptp.list_a tptp.tree_a)_ _u_(-> tptp.tree_a tptp.multiset_a)_ _u_(-> tptp.tree_a tptp.produc143150363Tree_a)_ _u_(-> tptp.tree_a Bool)_ Bool)|) (i |u_(-> tptp.tree_a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.tree_a Bool)_ _u_(-> tptp.list_a tptp.tree_a)_ _u_(-> tptp.tree_a tptp.multiset_a)_ _u_(-> tptp.tree_a tptp.produc143150363Tree_a)_ _u_(-> tptp.tree_a Bool)_ Bool)|)) (not (forall ((ii |u_(-> tptp.tree_a Bool)|)) (= (ho_109 v ii) (ite (= i ii) e (ho_109 u ii)))))))))) (let ((_let_150 (forall ((x |u_(-> _u_(-> tptp.tree_a Bool)_ _u_(-> tptp.list_a tptp.tree_a)_ _u_(-> tptp.tree_a tptp.multiset_a)_ _u_(-> tptp.tree_a tptp.produc143150363Tree_a)_ _u_(-> tptp.tree_a Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.tree_a Bool)_ _u_(-> tptp.list_a tptp.tree_a)_ _u_(-> tptp.tree_a tptp.multiset_a)_ _u_(-> tptp.tree_a tptp.produc143150363Tree_a)_ _u_(-> tptp.tree_a Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.tree_a Bool)|)) (= (ho_109 x z) (ho_109 y z)))) (= x y))))) (let ((_let_151 (forall ((u |u_(-> tptp.a tptp.a)|) (e tptp.a) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.a)|)) (not (forall ((ii tptp.a)) (= (ho_78 v ii) (ite (= i ii) e (ho_78 u ii)))))))))) (let ((_let_152 (forall ((x |u_(-> tptp.a tptp.a)|) (y |u_(-> tptp.a tptp.a)|)) (or (not (forall ((z tptp.a)) (= (ho_78 x z) (ho_78 y z)))) (= x y))))) (let ((_let_153 (forall ((u |u_(-> tptp.a tptp.list_a tptp.list_a)|) (e |u_(-> tptp.list_a tptp.list_a)|) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.list_a tptp.list_a)|)) (not (forall ((ii tptp.a)) (= (ho_84 v ii) (ite (= i ii) e (ho_84 u ii)))))))))) (let ((_let_154 (forall ((x |u_(-> tptp.a tptp.list_a tptp.list_a)|) (y |u_(-> tptp.a tptp.list_a tptp.list_a)|)) (or (not (forall ((z tptp.a)) (= (ho_84 x z) (ho_84 y z)))) (= x y))))) (let ((_let_155 (forall ((u |u_(-> _u_(-> tptp.tree_a Bool)_ _u_(-> tptp.tree_a tptp.produc143150363Tree_a)_ tptp.tree_a tptp.list_a tptp.list_a)|) (e |u_(-> _u_(-> tptp.tree_a tptp.produc143150363Tree_a)_ tptp.tree_a tptp.list_a tptp.list_a)|) (i |u_(-> tptp.tree_a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.tree_a Bool)_ _u_(-> tptp.tree_a tptp.produc143150363Tree_a)_ tptp.tree_a tptp.list_a tptp.list_a)|)) (not (forall ((ii |u_(-> tptp.tree_a Bool)|)) (= (ho_115 v ii) (ite (= i ii) e (ho_115 u ii)))))))))) (let ((_let_156 (forall ((x |u_(-> _u_(-> tptp.tree_a Bool)_ _u_(-> tptp.tree_a tptp.produc143150363Tree_a)_ tptp.tree_a tptp.list_a tptp.list_a)|) (y |u_(-> _u_(-> tptp.tree_a Bool)_ _u_(-> tptp.tree_a tptp.produc143150363Tree_a)_ tptp.tree_a tptp.list_a tptp.list_a)|)) (or (not (forall ((z |u_(-> tptp.tree_a Bool)|)) (= (ho_115 x z) (ho_115 y z)))) (= x y))))) (let ((_let_157 (forall ((u |u_(-> tptp.produc143150363Tree_a Bool)|) (e Bool) (i tptp.produc143150363Tree_a)) (not (forall ((v |u_(-> tptp.produc143150363Tree_a Bool)|)) (not (forall ((ii tptp.produc143150363Tree_a)) (= (ho_102 v ii) (ite (= i ii) e (ho_102 u ii)))))))))) (let ((_let_158 (forall ((x |u_(-> tptp.produc143150363Tree_a Bool)|) (y |u_(-> tptp.produc143150363Tree_a Bool)|)) (or (not (forall ((z tptp.produc143150363Tree_a)) (= (ho_102 x z) (ho_102 y z)))) (= x y))))) (let ((_let_159 (forall ((u |u_(-> tptp.set_a tptp.set_a Bool)|) (e |u_(-> tptp.set_a Bool)|) (i tptp.set_a)) (not (forall ((v |u_(-> tptp.set_a tptp.set_a Bool)|)) (not (forall ((ii tptp.set_a)) (= (ho_128 v ii) (ite (= i ii) e (ho_128 u ii)))))))))) (let ((_let_160 (forall ((x |u_(-> tptp.set_a tptp.set_a Bool)|) (y |u_(-> tptp.set_a tptp.set_a Bool)|)) (or (not (forall ((z tptp.set_a)) (= (ho_128 x z) (ho_128 y z)))) (= x y))))) (let ((_let_161 (forall ((BOUND_VARIABLE_10105 tptp.multiset_a) (BOUND_VARIABLE_10106 tptp.multiset_a)) (= (ho_23 (ho_22 k_21 BOUND_VARIABLE_10105) BOUND_VARIABLE_10106) (not (forall ((C4 tptp.multiset_a)) (not (= BOUND_VARIABLE_10106 (ho_26 (ho_25 k_24 BOUND_VARIABLE_10105) C4))))))))) (let ((_let_162 (forall ((BOUND_VARIABLE_10093 tptp.multiset_a) (BOUND_VARIABLE_10094 tptp.multiset_a)) (= (ho_23 (ho_22 k_27 BOUND_VARIABLE_10093) BOUND_VARIABLE_10094) (not (forall ((C5 tptp.multiset_a)) (not (= BOUND_VARIABLE_10094 (ho_26 (ho_25 k_24 BOUND_VARIABLE_10093) C5))))))))) (let ((_let_163 (forall ((BOUND_VARIABLE_10085 tptp.multiset_a) (BOUND_VARIABLE_10086 tptp.multiset_a)) (= (ho_26 (ho_25 k_28 BOUND_VARIABLE_10085) BOUND_VARIABLE_10086) (ho_26 (ho_25 k_24 BOUND_VARIABLE_10086) BOUND_VARIABLE_10085))))) (let ((_let_164 (forall ((BOUND_VARIABLE_10213 |u_(-> Bool tptp.a)|) (BOUND_VARIABLE_10210 |u_(-> Bool tptp.a)|)) (= (ho_32 (ho_31 k_30 BOUND_VARIABLE_10213) BOUND_VARIABLE_10210) (forall ((X4 Bool)) (ho_35 (ho_34 k_33 (ho_29 BOUND_VARIABLE_10213 X4)) (ho_29 BOUND_VARIABLE_10210 X4))))))) (let ((_let_165 (forall ((BOUND_VARIABLE_10243 |u_(-> Bool tptp.a)|) (BOUND_VARIABLE_10242 |u_(-> Bool tptp.a)|)) (= (ho_32 (ho_31 k_36 BOUND_VARIABLE_10243) BOUND_VARIABLE_10242) (and (ho_35 (ho_34 k_33 (ho_29 BOUND_VARIABLE_10243 false)) (ho_29 BOUND_VARIABLE_10242 false)) (ho_35 (ho_34 k_33 (ho_29 BOUND_VARIABLE_10243 true)) (ho_29 BOUND_VARIABLE_10242 true))))))) (let ((_let_166 (forall ((BOUND_VARIABLE_10052 tptp.a) (BOUND_VARIABLE_10053 tptp.a)) (= (= BOUND_VARIABLE_10052 BOUND_VARIABLE_10053) (ho_35 (ho_34 k_37 BOUND_VARIABLE_10052) BOUND_VARIABLE_10053))))) (let ((_let_167 (forall ((BOUND_VARIABLE_10041 tptp.a) (BOUND_VARIABLE_10042 tptp.a)) (= (ho_35 (ho_34 k_38 BOUND_VARIABLE_10041) BOUND_VARIABLE_10042) (and (ho_35 (ho_34 k_33 BOUND_VARIABLE_10041) BOUND_VARIABLE_10042) (ho_35 (ho_34 k_33 BOUND_VARIABLE_10042) BOUND_VARIABLE_10041)))))) (let ((_let_168 (forall ((BOUND_VARIABLE_10281 |u_(-> Bool tptp.a)|) (BOUND_VARIABLE_10280 |u_(-> Bool tptp.a)|)) (= (ho_32 (ho_31 k_39 BOUND_VARIABLE_10281) BOUND_VARIABLE_10280) (= BOUND_VARIABLE_10280 BOUND_VARIABLE_10281))))) (let ((_let_169 (forall ((BOUND_VARIABLE_10292 |u_(-> Bool tptp.a)|) (BOUND_VARIABLE_10291 |u_(-> Bool tptp.a)|)) (= (ho_32 (ho_31 k_40 BOUND_VARIABLE_10292) BOUND_VARIABLE_10291) (and (forall ((X4 Bool)) (ho_35 (ho_34 k_33 (ho_29 BOUND_VARIABLE_10292 X4)) (ho_29 BOUND_VARIABLE_10291 X4))) (forall ((X4 Bool)) (ho_35 (ho_34 k_33 (ho_29 BOUND_VARIABLE_10291 X4)) (ho_29 BOUND_VARIABLE_10292 X4)))))))) (let ((_let_170 (forall ((BOUND_VARIABLE_10012 tptp.a) (BOUND_VARIABLE_10013 tptp.a)) (= (= BOUND_VARIABLE_10012 BOUND_VARIABLE_10013) (ho_35 (ho_34 k_41 BOUND_VARIABLE_10012) BOUND_VARIABLE_10013))))) (let ((_let_171 (forall ((BOUND_VARIABLE_10001 tptp.a) (BOUND_VARIABLE_10002 tptp.a)) (= (ho_35 (ho_34 k_42 BOUND_VARIABLE_10001) BOUND_VARIABLE_10002) (and (ho_35 (ho_34 k_33 BOUND_VARIABLE_10001) BOUND_VARIABLE_10002) (ho_35 (ho_34 k_33 BOUND_VARIABLE_10002) BOUND_VARIABLE_10001)))))) (let ((_let_172 (forall ((BOUND_VARIABLE_10330 |u_(-> Bool tptp.a)|) (BOUND_VARIABLE_10329 |u_(-> Bool tptp.a)|)) (= (ho_32 (ho_31 k_43 BOUND_VARIABLE_10330) BOUND_VARIABLE_10329) (= BOUND_VARIABLE_10329 BOUND_VARIABLE_10330))))) (let ((_let_173 (forall ((BOUND_VARIABLE_10341 |u_(-> Bool tptp.a)|) (BOUND_VARIABLE_10340 |u_(-> Bool tptp.a)|)) (= (ho_32 (ho_31 k_44 BOUND_VARIABLE_10341) BOUND_VARIABLE_10340) (and (forall ((X4 Bool)) (ho_35 (ho_34 k_33 (ho_29 BOUND_VARIABLE_10341 X4)) (ho_29 BOUND_VARIABLE_10340 X4))) (forall ((X4 Bool)) (ho_35 (ho_34 k_33 (ho_29 BOUND_VARIABLE_10340 X4)) (ho_29 BOUND_VARIABLE_10341 X4)))))))) (let ((_let_174 (forall ((BOUND_VARIABLE_9972 tptp.a) (BOUND_VARIABLE_9973 tptp.a)) (= (= BOUND_VARIABLE_9972 BOUND_VARIABLE_9973) (ho_35 (ho_34 k_45 BOUND_VARIABLE_9972) BOUND_VARIABLE_9973))))) (let ((_let_175 (forall ((BOUND_VARIABLE_9961 tptp.a) (BOUND_VARIABLE_9962 tptp.a)) (= (ho_35 (ho_34 k_46 BOUND_VARIABLE_9961) BOUND_VARIABLE_9962) (and (ho_35 (ho_34 k_33 BOUND_VARIABLE_9962) BOUND_VARIABLE_9961) (ho_35 (ho_34 k_33 BOUND_VARIABLE_9961) BOUND_VARIABLE_9962)))))) (let ((_let_176 (forall ((BOUND_VARIABLE_10379 |u_(-> Bool tptp.a)|) (BOUND_VARIABLE_10378 |u_(-> Bool tptp.a)|)) (= (ho_32 (ho_31 k_47 BOUND_VARIABLE_10379) BOUND_VARIABLE_10378) (= BOUND_VARIABLE_10378 BOUND_VARIABLE_10379))))) (let ((_let_177 (forall ((BOUND_VARIABLE_10390 |u_(-> Bool tptp.a)|) (BOUND_VARIABLE_10389 |u_(-> Bool tptp.a)|)) (= (ho_32 (ho_31 k_48 BOUND_VARIABLE_10390) BOUND_VARIABLE_10389) (and (forall ((X4 Bool)) (ho_35 (ho_34 k_33 (ho_29 BOUND_VARIABLE_10389 X4)) (ho_29 BOUND_VARIABLE_10390 X4))) (forall ((X4 Bool)) (ho_35 (ho_34 k_33 (ho_29 BOUND_VARIABLE_10390 X4)) (ho_29 BOUND_VARIABLE_10389 X4)))))))) (let ((_let_178 (forall ((BOUND_VARIABLE_9931 tptp.set_a) (BOUND_VARIABLE_9932 tptp.a)) (= (ho_35 (ho_50 k_49 BOUND_VARIABLE_9931) BOUND_VARIABLE_9932) (ho_53 (ho_52 k_51 BOUND_VARIABLE_9932) BOUND_VARIABLE_9931))))) (let ((_let_179 (forall ((BOUND_VARIABLE_9922 tptp.a) (BOUND_VARIABLE_9923 tptp.tree_a)) (= (ho_56 (ho_55 k_54 BOUND_VARIABLE_9922) BOUND_VARIABLE_9923) (ho_56 (ho_55 k_59 BOUND_VARIABLE_9922) (ho_58 k_57 BOUND_VARIABLE_9923)))))) (let ((_let_180 (forall ((BOUND_VARIABLE_10105 tptp.multiset_a) (BOUND_VARIABLE_10106 tptp.multiset_a)) (= (not (forall ((C4 tptp.multiset_a)) (not (= BOUND_VARIABLE_10106 (@ (@ tptp.plus_plus_multiset_a BOUND_VARIABLE_10105) C4))))) (ll_20 BOUND_VARIABLE_10105 BOUND_VARIABLE_10106))))) (let ((_let_181 (forall ((BOUND_VARIABLE_10093 tptp.multiset_a) (BOUND_VARIABLE_10094 tptp.multiset_a)) (= (not (forall ((C5 tptp.multiset_a)) (not (= BOUND_VARIABLE_10094 (@ (@ tptp.plus_plus_multiset_a BOUND_VARIABLE_10093) C5))))) (ll_19 BOUND_VARIABLE_10093 BOUND_VARIABLE_10094))))) (let ((_let_182 (forall ((BOUND_VARIABLE_10085 tptp.multiset_a) (BOUND_VARIABLE_10086 tptp.multiset_a)) (= (@ (@ tptp.plus_plus_multiset_a BOUND_VARIABLE_10086) BOUND_VARIABLE_10085) (ll_18 BOUND_VARIABLE_10085 BOUND_VARIABLE_10086))))) (let ((_let_183 (forall ((BOUND_VARIABLE_10074 (-> Bool tptp.a)) (BOUND_VARIABLE_10075 (-> Bool tptp.a))) (= (forall ((X4 Bool)) (@ (@ tptp.ord_less_eq_a (@ BOUND_VARIABLE_10074 X4)) (@ BOUND_VARIABLE_10075 X4))) (ll_17 BOUND_VARIABLE_10074 BOUND_VARIABLE_10075))))) (let ((_let_184 (forall ((BOUND_VARIABLE_10059 (-> Bool tptp.a)) (BOUND_VARIABLE_10060 (-> Bool tptp.a))) (= (and (@ (@ tptp.ord_less_eq_a (@ BOUND_VARIABLE_10059 false)) (@ 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_let_121 _let_120 _let_119 _let_118 _let_117 _let_116 _let_115 _let_114 _let_113 _let_112 _let_111 _let_110 _let_109 _let_108 _let_107 _let_106 _let_105 _let_104 _let_103 _let_102 _let_101 _let_100 _let_99 _let_98 _let_97 _let_96 _let_95 _let_94 _let_93 _let_92 _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69 _let_68 _let_67 _let_66 _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 _let_43 _let_42 _let_41)))) :args ((and _let_36 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 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(ho_58 (ho_62 _let_3 _let_2) _let_1))) (let ((_let_5 (ho_58 k_57 _let_4))) (let ((_let_6 (ho_68 k_67 _let_1))) (let ((_let_7 (ho_34 k_33 _let_6))) (let ((_let_8 (ho_35 _let_7 BOUND_VARIABLE_4921))) (or (ho_35 _let_7 (ho_68 k_67 _let_2)) (and (or (not _let_8) (= _let_4 _let_5)) (or _let_8 (= (ho_58 (ho_62 (ho_61 k_60 _let_6) _let_2) (ho_58 k_57 (ho_58 (ho_62 _let_3 (ho_58 k_64 _let_1)) (ho_58 k_63 _let_1)))) _let_5))))))))))))))))))) :args _let_32) :args (_let_30 false _let_31)) :args (_let_26 false _let_28 false _let_30)) :args (_let_25 false _let_26)) :args (_let_21 false _let_23 false _let_25)) (EQ_RESOLVE (ASSUME :args (_let_5)) (PREPROCESS :args ((= _let_5 (not _let_20))))) :args (false false _let_21 true _let_20)) :args (_let_14 _let_13 (=> (not _let_11) (=> (not (@ _let_10 tptp.v)) (= (@ tptp.multiset_a2 (@ tptp.heapIm1091024090Down_a _let_12)) (@ tptp.multiset_a2 _let_12)))) (=> _let_11 (=> (not (@ (@ tptp.ord_less_eq_a _let_9) tptp.v)) (= (@ tptp.multiset_a2 (@ tptp.heapIm1091024090Down_a _let_8)) (@ tptp.multiset_a2 _let_8)))) (forall ((T tptp.tree_a) (V tptp.a) (L tptp.tree_a) (R tptp.tree_a)) (=> (= T (@ (@ (@ tptp.t_a V) L) R)) (exists ((L2 tptp.tree_a) (V2 tptp.a) (R2 tptp.tree_a)) (and (= (@ tptp.heapIm1091024090Down_a T) (@ (@ (@ tptp.t_a V2) L2) R2)) (@ (@ tptp.ord_less_eq_a V) V2))))) (forall ((X21 tptp.a) (X22 tptp.tree_a) (X23 tptp.tree_a) (Y21 tptp.a) (Y22 tptp.tree_a) (Y23 tptp.tree_a)) (= (= (@ (@ (@ tptp.t_a X21) X22) X23) (@ (@ (@ tptp.t_a Y21) Y22) Y23)) (and (= X21 Y21) (= X22 Y22) (= X23 Y23)))) (forall ((V tptp.a) (L tptp.tree_a) (R tptp.tree_a)) (let ((_let_1 (@ tptp.t_a V))) (= (@ tptp.heapIm970322378pify_a (@ (@ _let_1 L) R)) (@ tptp.heapIm1091024090Down_a (@ (@ _let_1 (@ tptp.heapIm970322378pify_a L)) (@ tptp.heapIm970322378pify_a R)))))) (forall ((L tptp.tree_a) (R tptp.tree_a) (T tptp.tree_a) (V tptp.a)) (=> (@ tptp.is_heap_a L) (=> (@ tptp.is_heap_a R) (=> (= T (@ (@ (@ tptp.t_a V) L) R)) (@ tptp.is_heap_a (@ tptp.heapIm1091024090Down_a T)))))) (= tptp.in_tree_a (lambda ((V3 tptp.a) (T2 tptp.tree_a)) (@ (@ tptp.in_tree_a V3) (@ tptp.heapIm1091024090Down_a T2)))) (forall ((V tptp.a) (L tptp.tree_a) (R tptp.tree_a)) (= (@ tptp.heapIm1140443833left_a (@ (@ (@ tptp.t_a V) L) R)) L)) (forall ((V tptp.a) (L tptp.tree_a) (R tptp.tree_a)) (= (@ tptp.heapIm1257206334ight_a (@ (@ (@ tptp.t_a V) L) R)) R)) (forall ((V tptp.a)) (let ((_let_1 (@ (@ (@ tptp.t_a V) tptp.e_a) tptp.e_a))) (= (@ tptp.heapIm1091024090Down_a _let_1) _let_1))) (= (@ tptp.heapIm1091024090Down_a tptp.e_a) tptp.e_a) (forall ((V tptp.a)) (not (@ (@ tptp.in_tree_a V) tptp.e_a))) (forall ((V tptp.a) (Vd tptp.a) (Ve tptp.tree_a) (Vf tptp.tree_a) (Va tptp.a) (Vb tptp.tree_a) (Vc tptp.tree_a)) (let ((_let_1 (@ (@ (@ tptp.t_a Vd) Ve) Vf))) (let ((_let_2 (@ (@ (@ tptp.t_a Va) Vb) Vc))) (= (@ tptp.is_heap_a (@ (@ (@ tptp.t_a V) _let_1) _let_2)) (and (@ (@ tptp.ord_less_eq_a (@ tptp.val_a _let_2)) V) (@ tptp.is_heap_a _let_2) (@ (@ tptp.ord_less_eq_a (@ tptp.val_a _let_1)) V) (@ tptp.is_heap_a _let_1)))))) (forall ((V tptp.a) (Va tptp.a) (Vb tptp.tree_a) (Vc tptp.tree_a) (Vd tptp.a) (Ve tptp.tree_a) (Vf tptp.tree_a)) (let ((_let_1 (@ (@ (@ tptp.t_a Va) Vb) Vc))) (let ((_let_2 (@ (@ (@ tptp.t_a Vd) Ve) Vf))) (= (@ tptp.is_heap_a (@ (@ (@ tptp.t_a V) _let_1) _let_2)) (and (@ (@ tptp.ord_less_eq_a (@ tptp.val_a _let_2)) V) (@ tptp.is_heap_a _let_2) (@ (@ tptp.ord_less_eq_a (@ tptp.val_a _let_1)) V) (@ tptp.is_heap_a _let_1)))))) (forall ((V tptp.a) (Va tptp.a) (Vb tptp.tree_a) (Vc tptp.tree_a)) (let ((_let_1 (@ (@ (@ tptp.t_a Va) Vb) Vc))) (= (@ tptp.is_heap_a (@ (@ (@ tptp.t_a V) _let_1) tptp.e_a)) (and (@ (@ tptp.ord_less_eq_a (@ tptp.val_a _let_1)) V) (@ tptp.is_heap_a _let_1))))) (forall ((V tptp.a) (Va tptp.a) (Vb tptp.tree_a) (Vc tptp.tree_a)) (let ((_let_1 (@ (@ (@ tptp.t_a Va) Vb) Vc))) (= (@ tptp.is_heap_a (@ (@ (@ tptp.t_a V) tptp.e_a) _let_1)) (and (@ (@ tptp.ord_less_eq_a (@ tptp.val_a _let_1)) V) (@ tptp.is_heap_a _let_1))))) (forall ((V tptp.a)) (@ tptp.is_heap_a (@ (@ (@ tptp.t_a V) tptp.e_a) tptp.e_a))) (@ tptp.is_heap_a tptp.e_a) (= (@ tptp.heapIm970322378pify_a tptp.e_a) tptp.e_a) (forall ((V tptp.a) (T tptp.tree_a)) (=> (@ (@ tptp.in_tree_a V) T) (=> (@ tptp.is_heap_a T) (@ (@ tptp.ord_less_eq_a V) (@ tptp.val_a T))))) (forall ((T tptp.tree_a)) (@ tptp.is_heap_a (@ tptp.heapIm970322378pify_a T))) (forall ((T tptp.tree_a)) (=> (not (= T tptp.e_a)) (@ (@ tptp.in_tree_a (@ tptp.val_a (@ tptp.heapIm1091024090Down_a T))) T))) (forall ((X tptp.tree_a)) (=> (not (= X tptp.e_a)) (=> (forall ((V4 tptp.a)) (not (= X (@ (@ (@ tptp.t_a V4) tptp.e_a) tptp.e_a)))) (=> (forall ((V4 tptp.a) (Va2 tptp.a) (Vb2 tptp.tree_a) (Vc2 tptp.tree_a)) (not (= X (@ (@ (@ tptp.t_a V4) tptp.e_a) (@ (@ (@ tptp.t_a Va2) Vb2) Vc2))))) (=> (forall ((V4 tptp.a) (Va2 tptp.a) (Vb2 tptp.tree_a) (Vc2 tptp.tree_a)) (not (= X (@ (@ (@ tptp.t_a V4) (@ (@ (@ tptp.t_a Va2) Vb2) Vc2)) tptp.e_a)))) (not (forall ((V4 tptp.a) (Va2 tptp.a) (Vb2 tptp.tree_a) (Vc2 tptp.tree_a) (Vd2 tptp.a) (Ve2 tptp.tree_a) (Vf2 tptp.tree_a)) (not (= X (@ (@ (@ tptp.t_a V4) (@ (@ (@ tptp.t_a Va2) Vb2) Vc2)) (@ (@ (@ tptp.t_a Vd2) Ve2) Vf2))))))))))) (forall ((Y tptp.tree_a)) (=> (not (= Y tptp.e_a)) (not (forall ((X212 tptp.a) (X222 tptp.tree_a) (X232 tptp.tree_a)) (not (= Y (@ (@ (@ tptp.t_a X212) X222) X232))))))) (forall ((P (-> tptp.tree_a Bool)) (Tree tptp.tree_a)) (=> (@ P tptp.e_a) (=> (forall ((X1 tptp.a) (X2 tptp.tree_a) (X3 tptp.tree_a)) (=> (@ P X2) (=> (@ P X3) (@ P (@ (@ (@ tptp.t_a X1) X2) X3))))) (@ P Tree)))) (forall ((X21 tptp.a) (X22 tptp.tree_a) (X23 tptp.tree_a)) (not (= tptp.e_a (@ (@ (@ tptp.t_a X21) X22) X23)))) (forall ((Va tptp.a) (Vb tptp.tree_a) (Vc tptp.tree_a) (V tptp.a)) (let ((_let_1 (@ (@ (@ tptp.t_a Va) Vb) Vc))) (let ((_let_2 (@ tptp.t_a V))) (let ((_let_3 (@ tptp.val_a _let_1))) (let ((_let_4 (@ (@ _let_2 _let_1) tptp.e_a))) (let ((_let_5 (@ tptp.heapIm1091024090Down_a _let_4))) (let ((_let_6 (@ (@ tptp.ord_less_eq_a _let_3) V))) (and (=> _let_6 (= _let_5 _let_4)) (=> (not _let_6) (= _let_5 (@ (@ (@ tptp.t_a _let_3) (@ tptp.heapIm1091024090Down_a (@ (@ _let_2 (@ tptp.heapIm1140443833left_a _let_1)) (@ tptp.heapIm1257206334ight_a _let_1)))) tptp.e_a))))))))))) (forall ((Va tptp.a) (Vb tptp.tree_a) (Vc tptp.tree_a) (V tptp.a)) (let ((_let_1 (@ (@ (@ tptp.t_a Va) Vb) Vc))) (let ((_let_2 (@ tptp.t_a V))) (let ((_let_3 (@ tptp.val_a _let_1))) (let ((_let_4 (@ (@ _let_2 tptp.e_a) _let_1))) (let ((_let_5 (@ tptp.heapIm1091024090Down_a _let_4))) (let ((_let_6 (@ (@ tptp.ord_less_eq_a _let_3) V))) (and (=> _let_6 (= _let_5 _let_4)) (=> (not _let_6) (= _let_5 (@ (@ (@ tptp.t_a _let_3) tptp.e_a) (@ tptp.heapIm1091024090Down_a (@ (@ _let_2 (@ tptp.heapIm1140443833left_a _let_1)) (@ tptp.heapIm1257206334ight_a _let_1)))))))))))))) _let_7 _let_6 (forall ((Va tptp.a) (Vb tptp.tree_a) (Vc tptp.tree_a) (Vd tptp.a) (Ve tptp.tree_a) (Vf tptp.tree_a) (V tptp.a)) (let ((_let_1 (@ (@ (@ tptp.t_a Va) Vb) Vc))) (let ((_let_2 (@ tptp.t_a V))) (let ((_let_3 (@ (@ (@ tptp.t_a Vd) Ve) Vf))) (let ((_let_4 (@ tptp.val_a _let_1))) (let ((_let_5 (@ (@ _let_2 _let_3) _let_1))) (let ((_let_6 (@ tptp.heapIm1091024090Down_a _let_5))) (let ((_let_7 (@ tptp.ord_less_eq_a _let_4))) (let ((_let_8 (@ _let_7 V))) (let ((_let_9 (= _let_6 _let_5))) (let ((_let_10 (@ tptp.val_a _let_3))) (let ((_let_11 (@ _let_7 _let_10))) (let ((_let_12 (@ (@ tptp.ord_less_eq_a _let_10) V))) (and (=> _let_11 (and (=> _let_12 _let_9) (=> (not _let_12) (= _let_6 (@ (@ (@ tptp.t_a _let_10) (@ tptp.heapIm1091024090Down_a (@ (@ _let_2 (@ tptp.heapIm1140443833left_a _let_3)) (@ tptp.heapIm1257206334ight_a _let_3)))) _let_1))))) (=> (not _let_11) (and (=> _let_8 _let_9) (=> (not _let_8) (= _let_6 (@ (@ (@ tptp.t_a _let_4) _let_3) (@ tptp.heapIm1091024090Down_a (@ (@ _let_2 (@ tptp.heapIm1140443833left_a _let_1)) (@ tptp.heapIm1257206334ight_a _let_1)))))))))))))))))))))) (forall ((V tptp.a) (V5 tptp.a) (L tptp.tree_a) (R tptp.tree_a)) (let ((_let_1 (@ tptp.in_tree_a V))) (= (@ _let_1 (@ (@ (@ tptp.t_a V5) L) R)) (or (= V V5) (@ _let_1 L) (@ _let_1 R))))) (forall ((P (-> tptp.tree_a Bool)) (A0 tptp.tree_a)) (=> (forall ((V4 tptp.a)) (@ P (@ (@ (@ tptp.t_a V4) tptp.e_a) tptp.e_a))) (=> (forall ((V4 tptp.a) (Va2 tptp.a) (Vb2 tptp.tree_a) (Vc2 tptp.tree_a)) (let ((_let_1 (@ (@ (@ tptp.t_a Va2) Vb2) Vc2))) (let ((_let_2 (@ P _let_1))) (=> _let_2 (=> _let_2 (@ P (@ (@ (@ tptp.t_a V4) _let_1) tptp.e_a))))))) (=> (forall ((V4 tptp.a) (Va2 tptp.a) (Vb2 tptp.tree_a) (Vc2 tptp.tree_a)) (let ((_let_1 (@ (@ (@ tptp.t_a Va2) Vb2) Vc2))) (let ((_let_2 (@ P _let_1))) (=> _let_2 (=> _let_2 (@ P (@ (@ (@ tptp.t_a V4) tptp.e_a) _let_1))))))) (=> (forall ((V4 tptp.a) (Va2 tptp.a) (Vb2 tptp.tree_a) (Vc2 tptp.tree_a) (Vd2 tptp.a) (Ve2 tptp.tree_a) (Vf2 tptp.tree_a)) (let ((_let_1 (@ (@ (@ tptp.t_a Va2) Vb2) Vc2))) (let ((_let_2 (@ P _let_1))) (=> _let_2 (=> _let_2 (@ P (@ (@ (@ tptp.t_a V4) _let_1) (@ (@ (@ tptp.t_a Vd2) Ve2) Vf2)))))))) (=> (forall ((V4 tptp.a) (Vd2 tptp.a) (Ve2 tptp.tree_a) (Vf2 tptp.tree_a) (Va2 tptp.a) (Vb2 tptp.tree_a) (Vc2 tptp.tree_a)) (let ((_let_1 (@ (@ (@ tptp.t_a Vd2) Ve2) Vf2))) (let ((_let_2 (@ P _let_1))) (=> _let_2 (=> _let_2 (@ P (@ (@ (@ tptp.t_a V4) _let_1) (@ (@ (@ tptp.t_a Va2) Vb2) Vc2)))))))) (=> (@ P tptp.e_a) (@ P A0)))))))) (forall ((X tptp.tree_a)) (=> (forall ((V4 tptp.a)) (not (= X (@ (@ (@ tptp.t_a V4) tptp.e_a) tptp.e_a)))) (=> (forall ((V4 tptp.a) (Va2 tptp.a) (Vb2 tptp.tree_a) (Vc2 tptp.tree_a)) (not (= X (@ (@ (@ tptp.t_a V4) (@ (@ (@ tptp.t_a Va2) Vb2) Vc2)) tptp.e_a)))) (=> (forall ((V4 tptp.a) (Va2 tptp.a) (Vb2 tptp.tree_a) (Vc2 tptp.tree_a)) (not (= X (@ (@ (@ tptp.t_a V4) tptp.e_a) (@ (@ (@ tptp.t_a Va2) Vb2) Vc2))))) (=> (forall ((V4 tptp.a) (Va2 tptp.a) (Vb2 tptp.tree_a) (Vc2 tptp.tree_a) (Vd2 tptp.a) (Ve2 tptp.tree_a) (Vf2 tptp.tree_a)) (not (= X (@ (@ (@ tptp.t_a V4) (@ (@ (@ tptp.t_a Va2) Vb2) Vc2)) (@ (@ (@ tptp.t_a Vd2) Ve2) Vf2))))) (=> (forall ((V4 tptp.a) (Vd2 tptp.a) (Ve2 tptp.tree_a) (Vf2 tptp.tree_a) (Va2 tptp.a) (Vb2 tptp.tree_a) (Vc2 tptp.tree_a)) (not (= X (@ (@ (@ tptp.t_a V4) (@ (@ (@ tptp.t_a Vd2) Ve2) Vf2)) (@ (@ (@ tptp.t_a Va2) Vb2) Vc2))))) (= X tptp.e_a))))))) (forall ((X tptp.tree_a)) (=> (not (= X tptp.e_a)) (=> (forall ((V4 tptp.a)) (not (= X (@ (@ (@ tptp.t_a V4) tptp.e_a) tptp.e_a)))) (=> (forall ((V4 tptp.a) (Va2 tptp.a) (Vb2 tptp.tree_a) (Vc2 tptp.tree_a)) (not (= X (@ (@ (@ tptp.t_a V4) (@ (@ (@ tptp.t_a Va2) Vb2) Vc2)) tptp.e_a)))) (=> (forall ((V4 tptp.a) (Va2 tptp.a) (Vb2 tptp.tree_a) (Vc2 tptp.tree_a)) (not (= X (@ (@ (@ tptp.t_a V4) tptp.e_a) (@ (@ (@ tptp.t_a Va2) Vb2) Vc2))))) (not (forall ((V4 tptp.a) (Va2 tptp.a) (Vb2 tptp.tree_a) (Vc2 tptp.tree_a) (Vd2 tptp.a) (Ve2 tptp.tree_a) (Vf2 tptp.tree_a)) (not (= X (@ (@ (@ tptp.t_a V4) (@ (@ (@ tptp.t_a Va2) Vb2) Vc2)) (@ (@ (@ tptp.t_a Vd2) Ve2) Vf2))))))))))) (= tptp.heapIm229596386mpty_a (lambda ((T2 tptp.tree_a)) (= T2 tptp.e_a))) (forall ((X (-> Bool tptp.a))) (@ (@ tptp.ord_less_eq_o_a X) X)) (forall ((X tptp.a)) (@ (@ tptp.ord_less_eq_a X) X)) (forall ((A tptp.a) (T tptp.tree_a)) (=> (@ (@ tptp.member_a A) (@ tptp.set_mset_a (@ tptp.multiset_a2 T))) (=> (@ tptp.is_heap_a T) (@ (@ tptp.ord_less_eq_a A) (@ tptp.val_a T))))) (= tptp.heapIm1057938560list_a (lambda ((L3 tptp.list_a)) (@ tptp.heapIm970322378pify_a (@ tptp.heapIm1637418125tree_a L3)))) (forall ((A tptp.a) (P (-> tptp.a Bool))) (= (@ (@ tptp.member_a A) (@ tptp.collect_a P)) (@ P A))) (forall ((A2 tptp.set_a)) (= (@ tptp.collect_a (lambda ((X4 tptp.a)) (@ (@ tptp.member_a X4) A2))) A2)) (forall ((F (-> Bool tptp.a)) (G (-> Bool tptp.a)) (X Bool)) (=> (@ (@ tptp.ord_less_eq_o_a F) G) (@ (@ tptp.ord_less_eq_a (@ F X)) (@ G X)))) (forall ((F (-> Bool tptp.a)) (G (-> Bool tptp.a)) (X Bool)) (=> (@ (@ tptp.ord_less_eq_o_a F) G) (@ (@ tptp.ord_less_eq_a (@ F X)) (@ G X)))) (forall ((F (-> Bool tptp.a)) (G (-> Bool tptp.a))) (=> (forall ((X5 Bool)) (@ (@ tptp.ord_less_eq_a (@ F X5)) (@ G X5))) (@ (@ tptp.ord_less_eq_o_a F) G))) (= tptp.ord_less_eq_o_a (lambda ((F2 (-> Bool tptp.a)) (G2 (-> Bool tptp.a))) (forall ((X4 Bool)) (@ (@ tptp.ord_less_eq_a (@ F2 X4)) (@ G2 X4))))) (forall ((A tptp.a) (F (-> (-> Bool tptp.a) tptp.a)) (B (-> Bool tptp.a)) (C (-> Bool tptp.a))) (let ((_let_1 (@ tptp.ord_less_eq_a A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_o_a B) C) (=> (forall ((X5 (-> Bool tptp.a)) (Y2 (-> Bool tptp.a))) (=> (@ (@ tptp.ord_less_eq_o_a X5) Y2) (@ (@ tptp.ord_less_eq_a (@ F X5)) (@ F Y2)))) (@ _let_1 (@ F C))))))) (forall ((A (-> Bool tptp.a)) (F (-> tptp.a Bool tptp.a)) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.ord_less_eq_o_a A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_a B) C) (=> (forall ((X5 tptp.a) (Y2 tptp.a)) (=> (@ (@ tptp.ord_less_eq_a X5) Y2) (@ (@ tptp.ord_less_eq_o_a (@ F X5)) (@ F Y2)))) (@ _let_1 (@ F C))))))) (forall ((A (-> Bool tptp.a)) (F (-> (-> Bool tptp.a) Bool tptp.a)) (B (-> Bool tptp.a)) (C (-> Bool tptp.a))) (let ((_let_1 (@ tptp.ord_less_eq_o_a A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_o_a B) C) (=> (forall ((X5 (-> Bool tptp.a)) (Y2 (-> Bool tptp.a))) (=> (@ (@ tptp.ord_less_eq_o_a X5) Y2) (@ (@ tptp.ord_less_eq_o_a (@ F X5)) (@ F Y2)))) (@ _let_1 (@ F C))))))) (forall ((A tptp.a) (F (-> tptp.a tptp.a)) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.ord_less_eq_a A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_a B) C) (=> (forall ((X5 tptp.a) (Y2 tptp.a)) (=> (@ (@ tptp.ord_less_eq_a X5) Y2) (@ (@ tptp.ord_less_eq_a (@ F X5)) (@ F Y2)))) (@ _let_1 (@ F C))))))) (forall ((A tptp.a) (B tptp.a) (F (-> tptp.a Bool tptp.a)) (C (-> Bool tptp.a))) (=> (@ (@ tptp.ord_less_eq_a A) B) (=> (@ (@ tptp.ord_less_eq_o_a (@ F B)) C) (=> (forall ((X5 tptp.a) (Y2 tptp.a)) (=> (@ (@ tptp.ord_less_eq_a X5) Y2) (@ (@ tptp.ord_less_eq_o_a (@ F X5)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_o_a (@ F A)) C))))) (forall ((A (-> Bool tptp.a)) (B (-> Bool tptp.a)) (F (-> (-> Bool tptp.a) tptp.a)) (C tptp.a)) (=> (@ (@ tptp.ord_less_eq_o_a A) B) (=> (@ (@ tptp.ord_less_eq_a (@ F B)) C) (=> (forall ((X5 (-> Bool tptp.a)) (Y2 (-> Bool tptp.a))) (=> (@ (@ tptp.ord_less_eq_o_a X5) Y2) (@ (@ tptp.ord_less_eq_a (@ F X5)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_a (@ F A)) C))))) (forall ((A (-> Bool tptp.a)) (B (-> Bool tptp.a)) (F (-> (-> Bool tptp.a) Bool tptp.a)) (C (-> Bool tptp.a))) (=> (@ (@ tptp.ord_less_eq_o_a A) B) (=> (@ (@ tptp.ord_less_eq_o_a (@ F B)) C) (=> (forall ((X5 (-> Bool tptp.a)) (Y2 (-> Bool tptp.a))) (=> (@ (@ tptp.ord_less_eq_o_a X5) Y2) (@ (@ tptp.ord_less_eq_o_a (@ F X5)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_o_a (@ F A)) C))))) (forall ((A tptp.a) (B tptp.a) (F (-> tptp.a tptp.a)) (C tptp.a)) (=> (@ (@ tptp.ord_less_eq_a A) B) (=> (@ (@ tptp.ord_less_eq_a (@ F B)) C) (=> (forall ((X5 tptp.a) (Y2 tptp.a)) (=> (@ (@ tptp.ord_less_eq_a X5) Y2) (@ (@ tptp.ord_less_eq_a (@ F X5)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_a (@ F A)) C))))) (forall ((B (-> Bool tptp.a)) (A (-> Bool tptp.a))) (=> (@ (@ tptp.ord_less_eq_o_a B) A) (=> (@ (@ tptp.ord_less_eq_o_a A) B) (= A B)))) (forall ((B tptp.a) (A tptp.a)) (=> (@ (@ tptp.ord_less_eq_a B) A) (=> (@ (@ tptp.ord_less_eq_a A) B) (= A B)))) (= (lambda ((Y3 (-> Bool tptp.a)) (Z (-> Bool tptp.a))) (= Y3 Z)) (lambda ((A3 (-> Bool tptp.a)) (B2 (-> Bool tptp.a))) (and (@ (@ tptp.ord_less_eq_o_a B2) A3) (@ (@ tptp.ord_less_eq_o_a A3) B2)))) (= (lambda ((Y3 tptp.a) (Z tptp.a)) (= Y3 Z)) (lambda ((A3 tptp.a) (B2 tptp.a)) (and (@ (@ tptp.ord_less_eq_a B2) A3) (@ (@ tptp.ord_less_eq_a A3) B2)))) (forall ((B (-> Bool tptp.a)) (A (-> Bool tptp.a)) (C (-> Bool tptp.a))) (let ((_let_1 (@ tptp.ord_less_eq_o_a C))) (=> (@ (@ tptp.ord_less_eq_o_a B) A) (=> (@ _let_1 B) (@ _let_1 A))))) (forall ((B tptp.a) (A tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.ord_less_eq_a C))) (=> (@ (@ tptp.ord_less_eq_a B) A) (=> (@ _let_1 B) (@ _let_1 A))))) (forall ((P (-> tptp.a tptp.a Bool)) (A tptp.a) (B tptp.a)) (=> (forall ((A4 tptp.a) (B3 tptp.a)) (=> (@ (@ tptp.ord_less_eq_a A4) B3) (@ (@ P A4) B3))) (=> (forall ((A4 tptp.a) (B3 tptp.a)) (=> (@ (@ P B3) A4) (@ (@ P A4) B3))) (@ (@ P A) B)))) (forall ((A (-> Bool tptp.a))) (@ (@ tptp.ord_less_eq_o_a A) A)) (forall ((A tptp.a)) (@ (@ tptp.ord_less_eq_a A) A)) (forall ((X (-> Bool tptp.a)) (Y (-> Bool tptp.a)) (Z2 (-> Bool tptp.a))) (let ((_let_1 (@ tptp.ord_less_eq_o_a X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_o_a Y) Z2) (@ _let_1 Z2))))) (forall ((X tptp.a) (Y tptp.a) (Z2 tptp.a)) (let ((_let_1 (@ tptp.ord_less_eq_a X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_a Y) Z2) (@ _let_1 Z2))))) (forall ((A (-> Bool tptp.a)) (B (-> Bool tptp.a))) (=> (@ (@ tptp.ord_less_eq_o_a A) B) (=> (@ (@ tptp.ord_less_eq_o_a B) A) (= A B)))) (forall ((A tptp.a) (B tptp.a)) (=> (@ (@ tptp.ord_less_eq_a A) B) (=> (@ (@ tptp.ord_less_eq_a B) A) (= A B)))) (forall ((A (-> Bool tptp.a)) (B (-> Bool tptp.a)) (C (-> Bool tptp.a))) (let ((_let_1 (@ tptp.ord_less_eq_o_a A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))) (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.ord_less_eq_a A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))) (forall ((A (-> Bool tptp.a)) (B (-> Bool tptp.a)) (C (-> Bool tptp.a))) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_o_a B) C) (@ (@ tptp.ord_less_eq_o_a A) C)))) (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_a B) C) (@ (@ tptp.ord_less_eq_a A) C)))) (= (lambda ((Y3 (-> Bool tptp.a)) (Z (-> Bool tptp.a))) (= Y3 Z)) (lambda ((A3 (-> Bool tptp.a)) (B2 (-> Bool tptp.a))) (and (@ (@ tptp.ord_less_eq_o_a A3) B2) (@ (@ tptp.ord_less_eq_o_a B2) A3)))) (= (lambda ((Y3 tptp.a) (Z tptp.a)) (= Y3 Z)) (lambda ((A3 tptp.a) (B2 tptp.a)) (and (@ (@ tptp.ord_less_eq_a A3) B2) (@ (@ tptp.ord_less_eq_a B2) A3)))) (forall ((Y (-> Bool tptp.a)) (X (-> Bool tptp.a))) (=> (@ (@ tptp.ord_less_eq_o_a Y) X) (= (@ (@ tptp.ord_less_eq_o_a X) Y) (= X Y)))) (forall ((Y tptp.a) (X tptp.a)) (=> (@ (@ tptp.ord_less_eq_a Y) X) (= (@ (@ tptp.ord_less_eq_a X) Y) (= X Y)))) (forall ((X tptp.a) (Y tptp.a) (Z2 tptp.a)) (let ((_let_1 (@ tptp.ord_less_eq_a X))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ tptp.ord_less_eq_a Z2))) (let ((_let_4 (@ _let_3 X))) (let ((_let_5 (@ tptp.ord_less_eq_a Y))) (let ((_let_6 (@ _let_5 Z2))) (let ((_let_7 (@ _let_5 X))) (let ((_let_8 (@ _let_3 Y))) (let ((_let_9 (@ _let_1 Z2))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))) (forall ((A (-> Bool tptp.a)) (B (-> Bool tptp.a)) (C (-> Bool tptp.a))) (let ((_let_1 (@ tptp.ord_less_eq_o_a A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_o_a B) C) (@ _let_1 C))))) (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.ord_less_eq_a A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_a B) C) (@ _let_1 C))))) (forall ((X tptp.a) (Y tptp.a)) (=> (not (@ (@ tptp.ord_less_eq_a X) Y)) (@ (@ tptp.ord_less_eq_a Y) X))) (forall ((X (-> Bool tptp.a)) (Y (-> Bool tptp.a))) (=> (= X Y) (@ (@ tptp.ord_less_eq_o_a X) Y))) (forall ((X tptp.a) (Y tptp.a)) (=> (= X Y) (@ (@ tptp.ord_less_eq_a X) Y))) (forall ((X tptp.a) (Y tptp.a)) (or (@ (@ tptp.ord_less_eq_a X) Y) (@ (@ tptp.ord_less_eq_a Y) X))) (forall ((X (-> Bool tptp.a)) (Y (-> Bool tptp.a))) (=> (@ (@ tptp.ord_less_eq_o_a X) Y) (=> (@ (@ tptp.ord_less_eq_o_a Y) X) (= X Y)))) (forall ((X tptp.a) (Y tptp.a)) (=> (@ (@ tptp.ord_less_eq_a X) Y) (=> (@ (@ tptp.ord_less_eq_a Y) X) (= X Y)))) (= (lambda ((Y3 (-> Bool tptp.a)) (Z (-> Bool tptp.a))) (= Y3 Z)) (lambda ((X4 (-> Bool tptp.a)) (Y4 (-> Bool tptp.a))) (and (@ (@ tptp.ord_less_eq_o_a X4) Y4) (@ (@ tptp.ord_less_eq_o_a Y4) X4)))) (= (lambda ((Y3 tptp.a) (Z tptp.a)) (= Y3 Z)) (lambda ((X4 tptp.a) (Y4 tptp.a)) (and (@ (@ tptp.ord_less_eq_a X4) Y4) (@ (@ tptp.ord_less_eq_a Y4) X4)))) (forall ((A tptp.a) (B tptp.a) (F (-> tptp.a Bool tptp.a)) (C (-> Bool tptp.a))) (=> (@ (@ tptp.ord_less_eq_a A) B) (=> (= (@ F B) C) (=> (forall ((X5 tptp.a) (Y2 tptp.a)) (=> (@ (@ tptp.ord_less_eq_a X5) Y2) (@ (@ tptp.ord_less_eq_o_a (@ F X5)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_o_a (@ F A)) C))))) (forall ((A (-> Bool tptp.a)) (B (-> Bool tptp.a)) (F (-> (-> Bool tptp.a) tptp.a)) (C tptp.a)) (=> (@ (@ tptp.ord_less_eq_o_a A) B) (=> (= (@ F B) C) (=> (forall ((X5 (-> Bool tptp.a)) (Y2 (-> Bool tptp.a))) (=> (@ (@ tptp.ord_less_eq_o_a X5) Y2) (@ (@ tptp.ord_less_eq_a (@ F X5)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_a (@ F A)) C))))) (forall ((A (-> Bool tptp.a)) (B (-> Bool tptp.a)) (F (-> (-> Bool tptp.a) Bool tptp.a)) (C (-> Bool tptp.a))) (=> (@ (@ tptp.ord_less_eq_o_a A) B) (=> (= (@ F B) C) (=> (forall ((X5 (-> Bool tptp.a)) (Y2 (-> Bool tptp.a))) (=> (@ (@ tptp.ord_less_eq_o_a X5) Y2) (@ (@ tptp.ord_less_eq_o_a (@ F X5)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_o_a (@ F A)) C))))) (forall ((A tptp.a) (B tptp.a) (F (-> tptp.a tptp.a)) (C tptp.a)) (=> (@ (@ tptp.ord_less_eq_a A) B) (=> (= (@ F B) C) (=> (forall ((X5 tptp.a) (Y2 tptp.a)) (=> (@ (@ tptp.ord_less_eq_a X5) Y2) (@ (@ tptp.ord_less_eq_a (@ F X5)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_a (@ F A)) C))))) (forall ((A (-> Bool tptp.a)) (F (-> tptp.a Bool tptp.a)) (B tptp.a) (C tptp.a)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_a B) C) (=> (forall ((X5 tptp.a) (Y2 tptp.a)) (=> (@ (@ tptp.ord_less_eq_a X5) Y2) (@ (@ tptp.ord_less_eq_o_a (@ F X5)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_o_a A) (@ F C)))))) (forall ((A tptp.a) (F (-> (-> Bool tptp.a) tptp.a)) (B (-> Bool tptp.a)) (C (-> Bool tptp.a))) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_o_a B) C) (=> (forall ((X5 (-> Bool tptp.a)) (Y2 (-> Bool tptp.a))) (=> (@ (@ tptp.ord_less_eq_o_a X5) Y2) (@ (@ tptp.ord_less_eq_a (@ F X5)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_a A) (@ F C)))))) (forall ((A (-> Bool tptp.a)) (F (-> (-> Bool tptp.a) Bool tptp.a)) (B (-> Bool tptp.a)) (C (-> Bool tptp.a))) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_o_a B) C) (=> (forall ((X5 (-> Bool tptp.a)) (Y2 (-> Bool tptp.a))) (=> (@ (@ tptp.ord_less_eq_o_a X5) Y2) (@ (@ tptp.ord_less_eq_o_a (@ F X5)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_o_a A) (@ F C)))))) (forall ((A tptp.a) (F (-> tptp.a tptp.a)) (B tptp.a) (C tptp.a)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_a B) C) (=> (forall ((X5 tptp.a) (Y2 tptp.a)) (=> (@ (@ tptp.ord_less_eq_a X5) Y2) (@ (@ tptp.ord_less_eq_a (@ F X5)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_a A) (@ F C)))))) (forall ((T tptp.tree_a)) (=> (not (= T tptp.e_a)) (=> (@ tptp.is_heap_a T) (= (@ tptp.val_a T) (@ tptp.lattic146396397_Max_a (@ tptp.set_mset_a (@ tptp.multiset_a2 T))))))) (forall ((V tptp.a) (Tail tptp.list_a)) (= (@ tptp.heapIm1637418125tree_a (@ (@ tptp.cons_a V) Tail)) (@ (@ (@ tptp.t_a V) (@ tptp.heapIm1637418125tree_a Tail)) tptp.e_a))) (forall ((P (-> (-> Bool tptp.a) Bool)) (X (-> Bool tptp.a))) (=> (@ P X) (=> (forall ((Y2 (-> Bool tptp.a))) (=> (@ P Y2) (@ (@ tptp.ord_less_eq_o_a Y2) X))) (= (@ tptp.order_Greatest_o_a P) X)))) (forall ((P (-> tptp.a Bool)) (X tptp.a)) (=> (@ P X) (=> (forall ((Y2 tptp.a)) (=> (@ P Y2) (@ (@ tptp.ord_less_eq_a Y2) X))) (= (@ tptp.order_Greatest_a P) X)))) (forall ((P (-> (-> Bool tptp.a) Bool)) (X (-> Bool tptp.a)) (Q (-> (-> Bool tptp.a) Bool))) (=> (@ P X) (=> (forall ((Y2 (-> Bool tptp.a))) (=> (@ P Y2) (@ (@ tptp.ord_less_eq_o_a Y2) X))) (=> (forall ((X5 (-> Bool tptp.a))) (=> (@ P X5) (=> (forall ((Y5 (-> Bool tptp.a))) (=> (@ P Y5) (@ (@ tptp.ord_less_eq_o_a Y5) X5))) (@ Q X5)))) (@ Q (@ tptp.order_Greatest_o_a P)))))) (forall ((P (-> tptp.a Bool)) (X tptp.a) (Q (-> tptp.a Bool))) (=> (@ P X) (=> (forall ((Y2 tptp.a)) (=> (@ P Y2) (@ (@ tptp.ord_less_eq_a Y2) X))) (=> (forall ((X5 tptp.a)) (=> (@ P X5) (=> (forall ((Y5 tptp.a)) (=> (@ P Y5) (@ (@ tptp.ord_less_eq_a Y5) X5))) (@ Q X5)))) (@ Q (@ tptp.order_Greatest_a P)))))) (= tptp.ord_less_eq_o_o_a (lambda ((X6 (-> Bool Bool tptp.a)) (Y6 (-> Bool Bool tptp.a))) (and (@ (@ tptp.ord_less_eq_o_a (@ X6 false)) (@ Y6 false)) (@ (@ tptp.ord_less_eq_o_a (@ X6 true)) (@ Y6 true))))) (= tptp.ord_less_eq_o_a (lambda ((X6 (-> Bool tptp.a)) (Y6 (-> Bool tptp.a))) (and (@ (@ tptp.ord_less_eq_a (@ X6 false)) (@ Y6 false)) (@ (@ tptp.ord_less_eq_a (@ X6 true)) (@ Y6 true))))) (forall ((A tptp.a) (B tptp.a)) (or (= A B) (not (@ (@ tptp.ord_less_eq_a A) B)) (not (@ (@ tptp.ord_less_eq_a B) A)))) (forall ((X21 tptp.a) (X22 tptp.list_a) (Y21 tptp.a) (Y22 tptp.list_a)) (= (= (@ (@ tptp.cons_a X21) X22) (@ (@ tptp.cons_a Y21) Y22)) (and (= X21 Y21) (= X22 Y22)))) (forall ((X tptp.a) (Xs tptp.list_a)) (not (= (@ (@ tptp.cons_a X) Xs) Xs))) (= tptp.heap_axioms_Tree_a_a (lambda ((Is_empty (-> tptp.tree_a Bool)) (Of_list (-> tptp.list_a tptp.tree_a)) (Multiset (-> tptp.tree_a tptp.multiset_a)) (As_tree (-> tptp.tree_a tptp.tree_a)) (Remove_max (-> tptp.tree_a tptp.produc143150363Tree_a))) (and (forall ((L3 tptp.tree_a)) (= (@ Multiset L3) (@ tptp.multiset_a2 (@ As_tree L3)))) (forall ((I tptp.list_a)) (@ tptp.is_heap_a (@ As_tree (@ Of_list I)))) (forall ((T2 tptp.tree_a)) (= (= (@ As_tree T2) tptp.e_a) (@ Is_empty T2))) (forall ((L3 tptp.tree_a) (M tptp.a) (L4 tptp.tree_a)) (=> (not (@ Is_empty L3)) (=> (= (@ (@ tptp.produc686083979Tree_a M) L4) (@ Remove_max L3)) (= (@ (@ tptp.add_mset_a M) (@ Multiset L4)) (@ Multiset L3))))) (forall ((L3 tptp.tree_a) (M tptp.a) (L4 tptp.tree_a)) (=> (not (@ Is_empty L3)) (=> (@ tptp.is_heap_a (@ As_tree L3)) (=> (= (@ (@ tptp.produc686083979Tree_a M) L4) (@ Remove_max L3)) (@ tptp.is_heap_a (@ As_tree L4)))))) (forall ((T2 tptp.tree_a) (M tptp.a) (T3 tptp.tree_a)) (=> (not (@ Is_empty T2)) (=> (= (@ (@ tptp.produc686083979Tree_a M) T3) (@ Remove_max T2)) (= M (@ tptp.val_a (@ As_tree T2))))))))) (forall ((Multiset2 (-> tptp.tree_a tptp.multiset_a)) (As_tree2 (-> tptp.tree_a tptp.tree_a)) (Of_list2 (-> tptp.list_a tptp.tree_a)) (Is_empty2 (-> tptp.tree_a Bool)) (Remove_max2 (-> tptp.tree_a tptp.produc143150363Tree_a))) (=> (forall ((L5 tptp.tree_a)) (= (@ Multiset2 L5) (@ tptp.multiset_a2 (@ As_tree2 L5)))) (=> (forall ((I2 tptp.list_a)) (@ tptp.is_heap_a (@ As_tree2 (@ Of_list2 I2)))) (=> (forall ((T4 tptp.tree_a)) (= (= (@ As_tree2 T4) tptp.e_a) (@ Is_empty2 T4))) (=> (forall ((L5 tptp.tree_a) (M2 tptp.a) (L2 tptp.tree_a)) (=> (not (@ Is_empty2 L5)) (=> (= (@ (@ tptp.produc686083979Tree_a M2) L2) (@ Remove_max2 L5)) (= (@ (@ tptp.add_mset_a M2) (@ Multiset2 L2)) (@ Multiset2 L5))))) (=> (forall ((L5 tptp.tree_a) (M2 tptp.a) (L2 tptp.tree_a)) (=> (not (@ Is_empty2 L5)) (=> (@ tptp.is_heap_a (@ As_tree2 L5)) (=> (= (@ (@ tptp.produc686083979Tree_a M2) L2) (@ Remove_max2 L5)) (@ tptp.is_heap_a (@ As_tree2 L2)))))) (=> (forall ((T4 tptp.tree_a) (M2 tptp.a) (T5 tptp.tree_a)) (=> (not (@ Is_empty2 T4)) (=> (= (@ (@ tptp.produc686083979Tree_a M2) T5) (@ Remove_max2 T4)) (= M2 (@ tptp.val_a (@ As_tree2 T4)))))) (@ (@ (@ (@ (@ tptp.heap_axioms_Tree_a_a Is_empty2) Of_list2) Multiset2) As_tree2) Remove_max2)))))))) (forall ((Empty tptp.tree_a) (Is_empty2 (-> tptp.tree_a Bool)) (Of_list2 (-> tptp.list_a tptp.tree_a)) (Multiset2 (-> tptp.tree_a tptp.multiset_a)) (As_tree2 (-> tptp.tree_a tptp.tree_a)) (Remove_max2 (-> tptp.tree_a tptp.produc143150363Tree_a)) (L tptp.tree_a) (M3 tptp.a) (L6 tptp.tree_a)) (=> (@ (@ (@ (@ (@ (@ tptp.heap_Tree_a_a Empty) Is_empty2) Of_list2) Multiset2) As_tree2) Remove_max2) (=> (not (@ Is_empty2 L)) (=> (= (@ (@ tptp.produc686083979Tree_a M3) L6) (@ Remove_max2 L)) (= (@ (@ tptp.add_mset_a M3) (@ Multiset2 L6)) (@ Multiset2 L)))))) (forall ((Empty tptp.tree_a) (Is_empty2 (-> tptp.tree_a Bool)) (Of_list2 (-> tptp.list_a tptp.tree_a)) (Multiset2 (-> tptp.tree_a tptp.multiset_a)) (As_tree2 (-> tptp.tree_a tptp.tree_a)) (Remove_max2 (-> tptp.tree_a tptp.produc143150363Tree_a)) (T tptp.tree_a) (M3 tptp.a) (T6 tptp.tree_a)) (=> (@ (@ (@ (@ (@ (@ tptp.heap_Tree_a_a Empty) Is_empty2) Of_list2) Multiset2) As_tree2) Remove_max2) (=> (not (@ Is_empty2 T)) (=> (= (@ (@ tptp.produc686083979Tree_a M3) T6) (@ Remove_max2 T)) (= M3 (@ tptp.val_a (@ As_tree2 T))))))) (forall ((Empty tptp.tree_a) (Is_empty2 (-> tptp.tree_a Bool)) (Of_list2 (-> tptp.list_a tptp.tree_a)) (Multiset2 (-> tptp.tree_a tptp.multiset_a)) (As_tree2 (-> tptp.tree_a tptp.tree_a)) (Remove_max2 (-> tptp.tree_a tptp.produc143150363Tree_a)) (L tptp.tree_a) (M3 tptp.a) (L6 tptp.tree_a)) (=> (@ (@ (@ (@ (@ (@ tptp.heap_Tree_a_a Empty) Is_empty2) Of_list2) Multiset2) As_tree2) Remove_max2) (=> (not (@ Is_empty2 L)) (=> (@ tptp.is_heap_a (@ As_tree2 L)) (=> (= (@ (@ tptp.produc686083979Tree_a M3) L6) (@ Remove_max2 L)) (@ tptp.is_heap_a (@ As_tree2 L6))))))) (forall ((M4 tptp.multiset_a) (X tptp.a)) (not (= M4 (@ (@ tptp.add_mset_a X) M4)))) (forall ((A tptp.a) (A2 tptp.multiset_a) (B4 tptp.multiset_a)) (let ((_let_1 (@ tptp.add_mset_a A))) (= (= (@ _let_1 A2) (@ _let_1 B4)) (= A2 B4)))) (forall ((A tptp.a) (B tptp.tree_a) (A5 tptp.a) (B5 tptp.tree_a)) (= (= (@ (@ tptp.produc686083979Tree_a A) B) (@ (@ tptp.produc686083979Tree_a A5) B5)) (and (= A A5) (= B B5)))) (forall ((X12 tptp.a) (X24 tptp.tree_a) (Y1 tptp.a) (Y24 tptp.tree_a)) (= (= (@ (@ tptp.produc686083979Tree_a X12) X24) (@ (@ tptp.produc686083979Tree_a Y1) Y24)) (and (= X12 Y1) (= X24 Y24)))) (forall ((A tptp.a) (A2 tptp.multiset_a)) (=> (@ (@ tptp.member_a A) (@ tptp.set_mset_a A2)) (not (forall ((B6 tptp.multiset_a)) (not (= A2 (@ (@ tptp.add_mset_a A) B6))))))) (forall ((X tptp.a) (M4 tptp.multiset_a)) (=> (@ (@ tptp.member_a X) (@ tptp.set_mset_a M4)) (exists ((A6 tptp.multiset_a)) (= M4 (@ (@ tptp.add_mset_a X) A6))))) (forall ((P2 tptp.produc143150363Tree_a)) (exists ((X5 tptp.a) (Y2 tptp.tree_a)) (= P2 (@ (@ tptp.produc686083979Tree_a X5) Y2)))) (forall ((P (-> tptp.produc143150363Tree_a Bool)) (P2 tptp.produc143150363Tree_a)) (=> (forall ((A4 tptp.a) (B3 tptp.tree_a)) (@ P (@ (@ tptp.produc686083979Tree_a A4) B3))) (@ P P2))) (forall ((A tptp.a) (B tptp.tree_a) (A5 tptp.a) (B5 tptp.tree_a)) (=> (= (@ (@ tptp.produc686083979Tree_a A) B) (@ (@ tptp.produc686083979Tree_a A5) B5)) (not (=> (= A A5) (not (= B B5)))))) (forall ((Y tptp.produc143150363Tree_a)) (not (forall ((A4 tptp.a) (B3 tptp.tree_a)) (not (= Y (@ (@ tptp.produc686083979Tree_a A4) B3)))))) (forall ((P (-> tptp.produc143150363Tree_a Bool)) (Prod tptp.produc143150363Tree_a)) (=> (forall ((A4 tptp.a) (B3 tptp.tree_a)) (@ P (@ (@ tptp.produc686083979Tree_a A4) B3))) (@ P Prod))) (forall ((A tptp.a) (M4 tptp.multiset_a) (B tptp.a) (N tptp.multiset_a)) (= (= (@ (@ tptp.add_mset_a A) M4) (@ (@ tptp.add_mset_a B) N)) (or (and (= M4 N) (= A B)) (exists ((K tptp.multiset_a)) (and (= M4 (@ (@ tptp.add_mset_a B) K)) (= N (@ (@ tptp.add_mset_a A) K))))))) (forall ((X tptp.a) (Y tptp.a) (M4 tptp.multiset_a)) (let ((_let_1 (@ tptp.add_mset_a X))) (let ((_let_2 (@ tptp.add_mset_a Y))) (= (@ _let_1 (@ _let_2 M4)) (@ _let_2 (@ _let_1 M4)))))) (forall ((X tptp.a) (M4 tptp.multiset_a) (N tptp.multiset_a)) (=> (= (@ (@ tptp.add_mset_a X) M4) N) (@ (@ tptp.member_a X) (@ tptp.set_mset_a N)))) (forall ((B tptp.a) (B4 tptp.multiset_a) (C tptp.a) (C2 tptp.multiset_a)) (=> (= (@ (@ tptp.add_mset_a B) B4) (@ (@ tptp.add_mset_a C) C2)) (=> (not (= B C)) (@ (@ tptp.member_a C) (@ tptp.set_mset_a B4))))) (forall ((V tptp.a)) (= (@ tptp.heapIm837449470Leaf_a (@ (@ (@ tptp.t_a V) tptp.e_a) tptp.e_a)) (@ (@ tptp.produc686083979Tree_a V) tptp.e_a))) (= tptp.remove301631099ee_a_a (lambda ((Is_empty (-> tptp.tree_a Bool)) (Of_list (-> tptp.list_a tptp.tree_a)) (Multiset (-> tptp.tree_a tptp.multiset_a)) (Remove_max (-> tptp.tree_a tptp.produc143150363Tree_a)) (Inv (-> tptp.tree_a Bool))) (and (forall ((X4 tptp.list_a)) (@ Inv (@ Of_list X4))) (forall ((L3 tptp.tree_a) (M tptp.a) (L4 tptp.tree_a)) (=> (not (@ Is_empty L3)) (=> (@ Inv L3) (=> (= (@ (@ tptp.produc686083979Tree_a M) L4) (@ Remove_max L3)) (= M (@ tptp.lattic146396397_Max_a (@ (@ tptp.set_Tree_a_a Multiset) L3))))))) (forall ((L3 tptp.tree_a) (M tptp.a) (L4 tptp.tree_a)) (=> (not (@ Is_empty L3)) (=> (@ Inv L3) (=> (= (@ (@ tptp.produc686083979Tree_a M) L4) (@ Remove_max L3)) (= (@ (@ tptp.add_mset_a M) (@ Multiset L4)) (@ Multiset L3)))))) (forall ((L3 tptp.tree_a) (M tptp.a) (L4 tptp.tree_a)) (=> (not (@ Is_empty L3)) (=> (@ Inv L3) (=> (= (@ (@ tptp.produc686083979Tree_a M) L4) (@ Remove_max L3)) (@ Inv L4)))))))) (forall ((Inv2 (-> tptp.tree_a Bool)) (Of_list2 (-> tptp.list_a tptp.tree_a)) (Is_empty2 (-> tptp.tree_a Bool)) (Remove_max2 (-> tptp.tree_a tptp.produc143150363Tree_a)) (Multiset2 (-> tptp.tree_a tptp.multiset_a))) (=> (forall ((X5 tptp.list_a)) (@ Inv2 (@ Of_list2 X5))) (=> (forall ((L5 tptp.tree_a) (M2 tptp.a) (L2 tptp.tree_a)) (=> (not (@ Is_empty2 L5)) (=> (@ Inv2 L5) (=> (= (@ (@ tptp.produc686083979Tree_a M2) L2) (@ Remove_max2 L5)) (= M2 (@ tptp.lattic146396397_Max_a (@ (@ tptp.set_Tree_a_a Multiset2) L5))))))) (=> (forall ((L5 tptp.tree_a) (M2 tptp.a) (L2 tptp.tree_a)) (=> (not (@ Is_empty2 L5)) (=> (@ Inv2 L5) (=> (= (@ (@ tptp.produc686083979Tree_a M2) L2) (@ Remove_max2 L5)) (= (@ (@ tptp.add_mset_a M2) (@ Multiset2 L2)) (@ Multiset2 L5)))))) (=> (forall ((L5 tptp.tree_a) (M2 tptp.a) (L2 tptp.tree_a)) (=> (not (@ Is_empty2 L5)) (=> (@ Inv2 L5) (=> (= (@ (@ tptp.produc686083979Tree_a M2) L2) (@ Remove_max2 L5)) (@ Inv2 L2))))) (@ (@ (@ (@ (@ tptp.remove301631099ee_a_a Is_empty2) Of_list2) Multiset2) Remove_max2) Inv2)))))) (forall ((Empty tptp.tree_a) (Is_empty2 (-> tptp.tree_a Bool)) (Of_list2 (-> tptp.list_a tptp.tree_a)) (Multiset2 (-> tptp.tree_a tptp.multiset_a)) (Remove_max2 (-> tptp.tree_a tptp.produc143150363Tree_a)) (Inv2 (-> tptp.tree_a Bool)) (L tptp.tree_a) (M3 tptp.a) (L6 tptp.tree_a)) (=> (@ (@ (@ (@ (@ (@ tptp.removeMax_Tree_a_a Empty) Is_empty2) Of_list2) Multiset2) Remove_max2) Inv2) (=> (not (@ Is_empty2 L)) (=> (@ Inv2 L) (=> (= (@ (@ tptp.produc686083979Tree_a M3) L6) (@ Remove_max2 L)) (= M3 (@ tptp.lattic146396397_Max_a (@ (@ tptp.set_Tree_a_a Multiset2) L)))))))) (forall ((P (-> tptp.multiset_a Bool)) (M4 tptp.multiset_a)) (=> (@ P tptp.zero_zero_multiset_a) (=> (forall ((X5 tptp.a) (M5 tptp.multiset_a)) (=> (@ P M5) (=> (forall ((Xa tptp.a)) (=> (@ (@ tptp.member_a Xa) (@ tptp.set_mset_a M5)) (@ (@ tptp.ord_less_eq_a Xa) X5))) (@ P (@ (@ tptp.add_mset_a X5) M5))))) (@ P M4)))) (forall ((X tptp.a) (M4 tptp.multiset_a) (Y tptp.a)) (= (= (@ (@ tptp.add_mset_a X) M4) (@ (@ tptp.add_mset_a Y) tptp.zero_zero_multiset_a)) (and (= M4 tptp.zero_zero_multiset_a) (= X Y)))) (forall ((A tptp.a) (B tptp.a) (M4 tptp.multiset_a)) (= (= (@ (@ tptp.add_mset_a A) tptp.zero_zero_multiset_a) (@ (@ tptp.add_mset_a B) M4)) (and (= B A) (= M4 tptp.zero_zero_multiset_a)))) (forall ((B tptp.a) (M4 tptp.multiset_a) (A tptp.a)) (= (= (@ (@ tptp.add_mset_a B) M4) (@ (@ tptp.add_mset_a A) tptp.zero_zero_multiset_a)) (and (= B A) (= M4 tptp.zero_zero_multiset_a)))) (forall ((A tptp.a) (B tptp.a)) (= (= (@ (@ tptp.add_mset_a A) tptp.zero_zero_multiset_a) (@ (@ tptp.add_mset_a B) tptp.zero_zero_multiset_a)) (= A B))) (forall ((M4 tptp.multiset_a)) (=> (not (= M4 tptp.zero_zero_multiset_a)) (not (forall ((X5 tptp.a) (N2 tptp.multiset_a)) (not (= M4 (@ (@ tptp.add_mset_a X5) N2))))))) (forall ((P (-> tptp.multiset_a Bool)) (M4 tptp.multiset_a)) (=> (@ P tptp.zero_zero_multiset_a) (=> (forall ((X5 tptp.a) (M5 tptp.multiset_a)) (=> (@ P M5) (@ P (@ (@ tptp.add_mset_a X5) M5)))) (@ P M4)))) (forall ((P (-> tptp.multiset_a tptp.multiset_a Bool)) (M4 tptp.multiset_a) (N tptp.multiset_a)) (=> (@ (@ P tptp.zero_zero_multiset_a) tptp.zero_zero_multiset_a) (=> (forall ((A4 tptp.a) (M5 tptp.multiset_a) (N2 tptp.multiset_a)) (=> (@ (@ P M5) N2) (@ (@ P (@ (@ tptp.add_mset_a A4) M5)) N2))) (=> (forall ((A4 tptp.a) (M5 tptp.multiset_a) (N2 tptp.multiset_a)) (let ((_let_1 (@ P M5))) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.add_mset_a A4) N2))))) (@ (@ P M4) N))))) (forall ((A tptp.a) (A2 tptp.multiset_a)) (not (= tptp.zero_zero_multiset_a (@ (@ tptp.add_mset_a A) A2)))) (forall ((M4 tptp.multiset_a)) (=> (not (= M4 tptp.zero_zero_multiset_a)) (exists ((A6 tptp.multiset_a) (A4 tptp.a)) (= M4 (@ (@ tptp.add_mset_a A4) A6))))) (forall ((A2 tptp.multiset_a)) (=> (not (= A2 tptp.zero_zero_multiset_a)) (not (forall ((X5 tptp.a)) (not (@ (@ tptp.member_a X5) (@ tptp.set_mset_a A2))))))) (forall ((Empty tptp.tree_a) (Is_empty2 (-> tptp.tree_a Bool)) (Of_list2 (-> tptp.list_a tptp.tree_a)) (Multiset2 (-> tptp.tree_a tptp.multiset_a)) (Remove_max2 (-> tptp.tree_a tptp.produc143150363Tree_a)) (Inv2 (-> tptp.tree_a Bool)) (L tptp.tree_a) (M3 tptp.a) (L6 tptp.tree_a)) (=> (@ (@ (@ (@ (@ (@ tptp.removeMax_Tree_a_a Empty) Is_empty2) Of_list2) Multiset2) Remove_max2) Inv2) (=> (not (@ Is_empty2 L)) (=> (@ Inv2 L) (=> (= (@ (@ tptp.produc686083979Tree_a M3) L6) (@ Remove_max2 L)) (@ Inv2 L6)))))) (forall ((X tptp.a)) (@ (@ tptp.member_a X) (@ tptp.set_mset_a (@ (@ tptp.add_mset_a X) tptp.zero_zero_multiset_a)))) (forall ((Empty tptp.tree_a) (Is_empty2 (-> tptp.tree_a Bool)) (Of_list2 (-> tptp.list_a tptp.tree_a)) (Multiset2 (-> tptp.tree_a tptp.multiset_a)) (Remove_max2 (-> tptp.tree_a tptp.produc143150363Tree_a)) (Inv2 (-> tptp.tree_a Bool)) (L tptp.tree_a) (M3 tptp.a) (L6 tptp.tree_a)) (=> (@ (@ (@ (@ (@ (@ tptp.removeMax_Tree_a_a Empty) Is_empty2) Of_list2) Multiset2) Remove_max2) Inv2) (=> (not (@ Is_empty2 L)) (=> (@ Inv2 L) (=> (= (@ (@ tptp.produc686083979Tree_a M3) L6) (@ Remove_max2 L)) (= (@ (@ tptp.add_mset_a M3) (@ Multiset2 L6)) (@ Multiset2 L))))))) (= (@ tptp.multiset_a2 tptp.e_a) tptp.zero_zero_multiset_a) (forall ((P (-> tptp.multiset_a Bool)) (M4 tptp.multiset_a)) (=> (@ P tptp.zero_zero_multiset_a) (=> (forall ((X5 tptp.a) (M5 tptp.multiset_a)) (=> (@ P M5) (=> (forall ((Xa tptp.a)) (=> (@ (@ tptp.member_a Xa) (@ tptp.set_mset_a M5)) (@ (@ tptp.ord_less_eq_a X5) Xa))) (@ P (@ (@ tptp.add_mset_a X5) M5))))) (@ P M4)))) (= tptp.is_empty_a (lambda ((A7 tptp.multiset_a)) (= A7 tptp.zero_zero_multiset_a))) (forall ((Empty tptp.tree_a) (Is_empty2 (-> tptp.tree_a Bool)) (Of_list2 (-> tptp.list_a tptp.tree_a)) (Multiset2 (-> tptp.tree_a tptp.multiset_a)) (Remove_max2 (-> tptp.tree_a tptp.produc143150363Tree_a)) (Inv2 (-> tptp.tree_a Bool)) (L tptp.tree_a) (P (-> tptp.tree_a tptp.list_a Bool)) (Sl tptp.list_a)) (=> (@ (@ (@ (@ (@ (@ tptp.removeMax_Tree_a_a Empty) Is_empty2) Of_list2) Multiset2) Remove_max2) Inv2) (=> (@ Inv2 L) (=> (@ (@ P L) Sl) (=> (forall ((L5 tptp.tree_a) (Sl2 tptp.list_a) (M2 tptp.a) (L2 tptp.tree_a)) (=> (not (@ Is_empty2 L5)) (=> (@ Inv2 L5) (=> (= (@ (@ tptp.produc686083979Tree_a M2) L2) (@ Remove_max2 L5)) (=> (@ (@ P L5) Sl2) (@ (@ P L2) (@ (@ tptp.cons_a M2) Sl2))))))) (@ (@ P Empty) (@ (@ (@ (@ tptp.ssort_Tree_a_a Is_empty2) Remove_max2) L) Sl))))))) (forall ((Empty tptp.tree_a) (Is_empty2 (-> tptp.tree_a Bool)) (Of_list2 (-> tptp.list_a tptp.tree_a)) (Multiset2 (-> tptp.tree_a tptp.multiset_a)) (Remove_max2 (-> tptp.tree_a tptp.produc143150363Tree_a)) (Inv2 (-> tptp.tree_a Bool)) (A tptp.produc768687417list_a)) (=> (@ (@ (@ (@ (@ (@ tptp.removeMax_Tree_a_a Empty) Is_empty2) Of_list2) Multiset2) Remove_max2) Inv2) (=> (@ (@ (@ tptp.ssort_dom_Tree_a_a Is_empty2) Remove_max2) A) (not (forall ((L5 tptp.tree_a) (Sl2 tptp.list_a)) (=> (= A (@ (@ tptp.produc1352981801list_a L5) Sl2)) (not (=> (not (@ Is_empty2 L5)) (forall ((M6 tptp.a) (L7 tptp.tree_a)) (=> (= (@ (@ tptp.produc686083979Tree_a M6) L7) (@ Remove_max2 L5)) (@ (@ (@ tptp.ssort_dom_Tree_a_a Is_empty2) Remove_max2) (@ (@ tptp.produc1352981801list_a L7) (@ (@ tptp.cons_a M6) Sl2))))))))))))) (forall ((Empty tptp.tree_a) (Is_empty2 (-> tptp.tree_a Bool)) (Of_list2 (-> tptp.list_a tptp.tree_a)) (Multiset2 (-> tptp.tree_a tptp.multiset_a)) (Remove_max2 (-> tptp.tree_a tptp.produc143150363Tree_a)) (Inv2 (-> tptp.tree_a Bool)) (A tptp.produc768687417list_a)) (=> (@ (@ (@ (@ (@ (@ tptp.removeMax_Tree_a_a Empty) Is_empty2) Of_list2) Multiset2) Remove_max2) Inv2) (= (@ (@ (@ tptp.ssort_dom_Tree_a_a Is_empty2) Remove_max2) A) (exists ((L3 tptp.tree_a) (Sl3 tptp.list_a)) (and (= A (@ (@ tptp.produc1352981801list_a L3) Sl3)) (forall ((X4 tptp.a) (Y4 tptp.tree_a)) (=> (not (@ Is_empty2 L3)) (=> (= (@ (@ tptp.produc686083979Tree_a X4) Y4) (@ Remove_max2 L3)) (@ (@ (@ tptp.ssort_dom_Tree_a_a Is_empty2) Remove_max2) (@ (@ tptp.produc1352981801list_a Y4) (@ (@ tptp.cons_a X4) Sl3))))))))))) (forall ((Empty tptp.tree_a) (Is_empty2 (-> tptp.tree_a Bool)) (Of_list2 (-> tptp.list_a tptp.tree_a)) (Multiset2 (-> tptp.tree_a tptp.multiset_a)) (Remove_max2 (-> tptp.tree_a tptp.produc143150363Tree_a)) (Inv2 (-> tptp.tree_a Bool)) (X tptp.produc768687417list_a) (P (-> tptp.produc768687417list_a Bool))) (=> (@ (@ (@ (@ (@ (@ tptp.removeMax_Tree_a_a Empty) Is_empty2) Of_list2) Multiset2) Remove_max2) Inv2) (=> (@ (@ (@ tptp.ssort_dom_Tree_a_a Is_empty2) Remove_max2) X) (=> (forall ((L5 tptp.tree_a) (Sl2 tptp.list_a)) (=> (forall ((M6 tptp.a) (L7 tptp.tree_a)) (=> (not (@ Is_empty2 L5)) (=> (= (@ (@ tptp.produc686083979Tree_a M6) L7) (@ Remove_max2 L5)) (@ (@ (@ tptp.ssort_dom_Tree_a_a Is_empty2) Remove_max2) (@ (@ tptp.produc1352981801list_a L7) (@ (@ tptp.cons_a M6) Sl2)))))) (=> (forall ((M6 tptp.a) (L7 tptp.tree_a)) (=> (not (@ Is_empty2 L5)) (=> (= (@ (@ tptp.produc686083979Tree_a M6) L7) (@ Remove_max2 L5)) (@ P (@ (@ tptp.produc1352981801list_a L7) (@ (@ tptp.cons_a M6) Sl2)))))) (@ P (@ (@ tptp.produc1352981801list_a L5) Sl2))))) (@ P X))))) (forall ((Empty tptp.tree_a) (Is_empty2 (-> tptp.tree_a Bool)) (Of_list2 (-> tptp.list_a tptp.tree_a)) (Multiset2 (-> tptp.tree_a tptp.multiset_a)) (Remove_max2 (-> tptp.tree_a tptp.produc143150363Tree_a)) (Inv2 (-> tptp.tree_a Bool)) (L tptp.tree_a) (Sl tptp.list_a)) (=> (@ (@ (@ (@ (@ (@ tptp.removeMax_Tree_a_a Empty) Is_empty2) Of_list2) Multiset2) Remove_max2) Inv2) (=> (forall ((M2 tptp.a) (L2 tptp.tree_a)) (=> (not (@ Is_empty2 L)) (=> (= (@ (@ tptp.produc686083979Tree_a M2) L2) (@ Remove_max2 L)) (@ (@ (@ tptp.ssort_dom_Tree_a_a Is_empty2) Remove_max2) (@ (@ tptp.produc1352981801list_a L2) (@ (@ tptp.cons_a M2) Sl)))))) (@ (@ (@ tptp.ssort_dom_Tree_a_a Is_empty2) Remove_max2) (@ (@ tptp.produc1352981801list_a L) Sl))))) (forall ((V tptp.a) (L tptp.tree_a) (R tptp.tree_a)) (= (@ tptp.multiset_a2 (@ (@ (@ tptp.t_a V) L) R)) (@ (@ tptp.plus_plus_multiset_a (@ (@ tptp.plus_plus_multiset_a (@ tptp.multiset_a2 L)) (@ (@ tptp.add_mset_a V) tptp.zero_zero_multiset_a))) (@ tptp.multiset_a2 R)))) (forall ((A tptp.a) (M4 tptp.multiset_a)) (= (@ (@ tptp.subseteq_mset_a (@ (@ tptp.add_mset_a A) tptp.zero_zero_multiset_a)) M4) (@ (@ tptp.member_a A) (@ tptp.set_mset_a M4)))) (forall ((A tptp.multiset_a)) (= (@ (@ tptp.subseteq_mset_a A) tptp.zero_zero_multiset_a) (= A tptp.zero_zero_multiset_a))) (forall ((N3 tptp.multiset_a)) (= (@ (@ tptp.subseteq_mset_a N3) tptp.zero_zero_multiset_a) (= N3 tptp.zero_zero_multiset_a))) (forall ((C tptp.multiset_a) (A tptp.multiset_a) (B tptp.multiset_a)) (let ((_let_1 (@ tptp.plus_plus_multiset_a C))) (= (@ (@ tptp.subseteq_mset_a (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.subseteq_mset_a A) B)))) (forall ((A tptp.multiset_a) (C tptp.multiset_a) (B tptp.multiset_a)) (= (@ (@ tptp.subseteq_mset_a (@ (@ tptp.plus_plus_multiset_a A) C)) (@ (@ tptp.plus_plus_multiset_a B) C)) (@ (@ tptp.subseteq_mset_a A) B))) (forall ((C2 tptp.multiset_a) (A2 tptp.multiset_a) (B4 tptp.multiset_a)) (let ((_let_1 (@ tptp.plus_plus_multiset_a C2))) (= (@ (@ tptp.subseteq_mset_a (@ _let_1 A2)) (@ _let_1 B4)) (@ (@ tptp.subseteq_mset_a A2) B4)))) (forall ((A2 tptp.multiset_a) (C2 tptp.multiset_a) (B4 tptp.multiset_a)) (= (@ (@ tptp.subseteq_mset_a (@ (@ tptp.plus_plus_multiset_a A2) C2)) (@ (@ tptp.plus_plus_multiset_a B4) C2)) (@ (@ tptp.subseteq_mset_a A2) B4))) (forall ((X tptp.multiset_a) (Y tptp.multiset_a)) (= (= tptp.zero_zero_multiset_a (@ (@ tptp.plus_plus_multiset_a X) Y)) (and (= X tptp.zero_zero_multiset_a) (= Y tptp.zero_zero_multiset_a)))) (forall ((X tptp.multiset_a) (Y tptp.multiset_a)) (= (= (@ (@ tptp.plus_plus_multiset_a X) Y) tptp.zero_zero_multiset_a) (and (= X tptp.zero_zero_multiset_a) (= Y tptp.zero_zero_multiset_a)))) (forall ((M4 tptp.multiset_a) (N tptp.multiset_a)) (= (= (@ (@ tptp.plus_plus_multiset_a M4) N) tptp.zero_zero_multiset_a) (and (= M4 tptp.zero_zero_multiset_a) (= N tptp.zero_zero_multiset_a)))) (forall ((M4 tptp.multiset_a) (N tptp.multiset_a)) (= (= tptp.zero_zero_multiset_a (@ (@ tptp.plus_plus_multiset_a M4) N)) (and (= M4 tptp.zero_zero_multiset_a) (= N tptp.zero_zero_multiset_a)))) (forall ((A2 tptp.multiset_a) (A tptp.a) (B4 tptp.multiset_a)) (let ((_let_1 (@ tptp.plus_plus_multiset_a A2))) (let ((_let_2 (@ tptp.add_mset_a A))) (= (@ _let_1 (@ _let_2 B4)) (@ _let_2 (@ _let_1 B4)))))) (forall ((A tptp.a) (A2 tptp.multiset_a) (B4 tptp.multiset_a)) (let ((_let_1 (@ tptp.add_mset_a A))) (= (@ (@ tptp.plus_plus_multiset_a (@ _let_1 A2)) B4) (@ _let_1 (@ (@ tptp.plus_plus_multiset_a A2) B4))))) (forall ((B tptp.multiset_a) (A tptp.multiset_a)) (= (@ (@ tptp.subseteq_mset_a (@ (@ tptp.plus_plus_multiset_a B) A)) B) (@ (@ tptp.subseteq_mset_a A) tptp.zero_zero_multiset_a))) (forall ((A tptp.multiset_a) (B tptp.multiset_a)) (= (@ (@ tptp.subseteq_mset_a (@ (@ tptp.plus_plus_multiset_a A) B)) B) (@ (@ tptp.subseteq_mset_a A) tptp.zero_zero_multiset_a))) (forall ((A tptp.multiset_a) (B tptp.multiset_a)) (= (@ (@ tptp.subseteq_mset_a A) (@ (@ tptp.plus_plus_multiset_a A) B)) (@ (@ tptp.subseteq_mset_a tptp.zero_zero_multiset_a) B))) (forall ((A tptp.multiset_a) (B tptp.multiset_a)) (= (@ (@ tptp.subseteq_mset_a A) (@ (@ tptp.plus_plus_multiset_a B) A)) (@ (@ tptp.subseteq_mset_a tptp.zero_zero_multiset_a) B))) (forall ((A tptp.a) (M4 tptp.multiset_a) (B tptp.a)) (= (@ (@ tptp.subseteq_mset_a (@ (@ tptp.add_mset_a A) M4)) (@ (@ tptp.add_mset_a B) tptp.zero_zero_multiset_a)) (and (= M4 tptp.zero_zero_multiset_a) (= A B)))) (forall ((M4 tptp.multiset_a) (N tptp.multiset_a) (K2 tptp.multiset_a)) (let ((_let_1 (@ tptp.plus_plus_multiset_a M4))) (= (@ (@ tptp.plus_plus_multiset_a (@ _let_1 N)) K2) (@ _let_1 (@ (@ tptp.plus_plus_multiset_a N) K2))))) (forall ((M4 tptp.multiset_a) (N tptp.multiset_a) (K2 tptp.multiset_a)) (let ((_let_1 (@ tptp.plus_plus_multiset_a M4))) (let ((_let_2 (@ tptp.plus_plus_multiset_a N))) (= (@ _let_1 (@ _let_2 K2)) (@ _let_2 (@ _let_1 K2)))))) (= tptp.plus_plus_multiset_a (lambda ((M7 tptp.multiset_a) (N4 tptp.multiset_a)) (@ (@ tptp.plus_plus_multiset_a N4) M7))) (forall ((K2 tptp.multiset_a) (M4 tptp.multiset_a) (N tptp.multiset_a)) (let ((_let_1 (@ tptp.plus_plus_multiset_a K2))) (= (= (@ _let_1 M4) (@ _let_1 N)) (= M4 N)))) (forall ((M4 tptp.multiset_a) (K2 tptp.multiset_a) (N tptp.multiset_a)) (= (= (@ (@ tptp.plus_plus_multiset_a M4) K2) (@ (@ tptp.plus_plus_multiset_a N) K2)) (= M4 N))) (forall ((A tptp.multiset_a) (B tptp.multiset_a) (C tptp.multiset_a) (D tptp.multiset_a)) (=> (@ (@ tptp.subseteq_mset_a A) B) (=> (@ (@ tptp.subseteq_mset_a C) D) (@ (@ tptp.subseteq_mset_a (@ (@ tptp.plus_plus_multiset_a A) C)) (@ (@ tptp.plus_plus_multiset_a B) D))))) (forall ((A tptp.multiset_a) (B tptp.multiset_a)) (=> (@ (@ tptp.subseteq_mset_a A) B) (not (forall ((C3 tptp.multiset_a)) (not (= B (@ (@ tptp.plus_plus_multiset_a A) C3))))))) (= tptp.subseteq_mset_a (lambda ((A3 tptp.multiset_a) (B2 tptp.multiset_a)) (exists ((C4 tptp.multiset_a)) (= B2 (@ (@ tptp.plus_plus_multiset_a A3) C4))))) (forall ((A2 tptp.multiset_a) (B4 tptp.multiset_a)) (@ (@ tptp.subseteq_mset_a A2) (@ (@ tptp.plus_plus_multiset_a A2) B4))) (forall ((A2 tptp.multiset_a) (B4 tptp.multiset_a) (C2 tptp.multiset_a) (D2 tptp.multiset_a)) (=> (@ (@ tptp.subseteq_mset_a A2) B4) (=> (@ (@ tptp.subseteq_mset_a C2) D2) (@ (@ tptp.subseteq_mset_a (@ (@ tptp.plus_plus_multiset_a A2) C2)) (@ (@ tptp.plus_plus_multiset_a B4) D2))))) (forall ((B4 tptp.multiset_a) (A2 tptp.multiset_a)) (@ (@ tptp.subseteq_mset_a B4) (@ (@ tptp.plus_plus_multiset_a A2) B4))) (forall ((A2 tptp.multiset_a) (X7 tptp.multiset_a) (Y7 tptp.multiset_a)) (let ((_let_1 (@ tptp.plus_plus_multiset_a A2))) (=> (= (@ _let_1 X7) (@ _let_1 Y7)) (= X7 Y7)))) (forall ((A tptp.multiset_a) (B tptp.multiset_a) (C tptp.multiset_a)) (let ((_let_1 (@ tptp.plus_plus_multiset_a C))) (=> (@ (@ tptp.subseteq_mset_a A) B) (@ (@ tptp.subseteq_mset_a (@ _let_1 A)) (@ _let_1 B))))) (= tptp.subseteq_mset_a (lambda ((A7 tptp.multiset_a) (B7 tptp.multiset_a)) (exists ((C5 tptp.multiset_a)) (= B7 (@ (@ tptp.plus_plus_multiset_a A7) C5))))) (forall ((A tptp.multiset_a) (B tptp.multiset_a) (C tptp.multiset_a)) (=> (@ (@ tptp.subseteq_mset_a A) B) (@ (@ tptp.subseteq_mset_a (@ (@ tptp.plus_plus_multiset_a A) C)) (@ (@ tptp.plus_plus_multiset_a B) C)))) (forall ((C tptp.multiset_a) (A tptp.multiset_a) (B tptp.multiset_a)) (let ((_let_1 (@ tptp.plus_plus_multiset_a C))) (=> (@ (@ tptp.subseteq_mset_a (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.subseteq_mset_a A) B)))) (forall ((A tptp.multiset_a) (C tptp.multiset_a) (B tptp.multiset_a)) (=> (@ (@ tptp.subseteq_mset_a (@ (@ tptp.plus_plus_multiset_a A) C)) (@ (@ tptp.plus_plus_multiset_a B) C)) (@ (@ tptp.subseteq_mset_a A) B))) (forall ((A tptp.a) (A2 tptp.multiset_a) (B4 tptp.multiset_a)) (let ((_let_1 (@ tptp.member_a A))) (= (@ _let_1 (@ tptp.set_mset_a (@ (@ tptp.plus_plus_multiset_a A2) B4))) (or (@ _let_1 (@ tptp.set_mset_a A2)) (@ _let_1 (@ tptp.set_mset_a B4)))))) (forall ((A2 tptp.multiset_a) (B4 tptp.multiset_a) (X tptp.a)) (let ((_let_1 (@ tptp.member_a X))) (=> (@ (@ tptp.subseteq_mset_a A2) B4) (=> (@ _let_1 (@ tptp.set_mset_a A2)) (@ _let_1 (@ tptp.set_mset_a B4)))))) (forall ((A2 tptp.multiset_a) (B4 tptp.multiset_a)) (=> (@ (@ tptp.subseteq_mset_a A2) B4) (@ (@ tptp.ord_less_eq_set_a (@ tptp.set_mset_a A2)) (@ tptp.set_mset_a B4)))) (forall ((A tptp.a) (A2 tptp.multiset_a) (B4 tptp.multiset_a)) (let ((_let_1 (@ tptp.add_mset_a A))) (= (@ (@ tptp.subseteq_mset_a (@ _let_1 A2)) (@ _let_1 B4)) (@ (@ tptp.subseteq_mset_a A2) B4)))) (forall ((I3 tptp.multiset_a) (J tptp.multiset_a) (K3 tptp.multiset_a) (L tptp.multiset_a)) (=> (and (@ (@ tptp.ord_le1199012836iset_a I3) J) (= K3 L)) (@ (@ tptp.ord_le1199012836iset_a (@ (@ tptp.plus_plus_multiset_a I3) K3)) (@ (@ tptp.plus_plus_multiset_a J) L)))) (forall ((I3 tptp.multiset_a) (J tptp.multiset_a) (K3 tptp.multiset_a) (L tptp.multiset_a)) (=> (and (= I3 J) (@ (@ tptp.ord_le1199012836iset_a K3) L)) (@ (@ tptp.ord_le1199012836iset_a (@ (@ tptp.plus_plus_multiset_a I3) K3)) (@ (@ tptp.plus_plus_multiset_a J) L)))) (forall ((I3 tptp.multiset_a) (J tptp.multiset_a) (K3 tptp.multiset_a) (L tptp.multiset_a)) (=> (and (@ (@ tptp.ord_le1199012836iset_a I3) J) (@ (@ tptp.ord_le1199012836iset_a K3) L)) (@ (@ tptp.ord_le1199012836iset_a (@ (@ tptp.plus_plus_multiset_a I3) K3)) (@ (@ tptp.plus_plus_multiset_a J) L)))) (forall ((A tptp.multiset_a) (B tptp.multiset_a) (C tptp.multiset_a) (D tptp.multiset_a)) (=> (@ (@ tptp.ord_le1199012836iset_a A) B) (=> (@ (@ tptp.ord_le1199012836iset_a C) D) (@ (@ tptp.ord_le1199012836iset_a (@ (@ tptp.plus_plus_multiset_a A) C)) (@ (@ tptp.plus_plus_multiset_a B) D))))) (forall ((A tptp.multiset_a) (B tptp.multiset_a) (C tptp.multiset_a)) (let ((_let_1 (@ tptp.plus_plus_multiset_a C))) (=> (@ (@ tptp.ord_le1199012836iset_a A) B) (@ (@ tptp.ord_le1199012836iset_a (@ _let_1 A)) (@ _let_1 B))))) (forall ((A tptp.multiset_a) (B tptp.multiset_a) (C tptp.multiset_a)) (=> (@ (@ tptp.ord_le1199012836iset_a A) B) (@ (@ tptp.ord_le1199012836iset_a (@ (@ tptp.plus_plus_multiset_a A) C)) (@ (@ tptp.plus_plus_multiset_a B) C)))) (forall ((X tptp.multiset_a)) (= (@ (@ tptp.plus_plus_multiset_a X) tptp.zero_zero_multiset_a) X)) (forall ((X tptp.multiset_a)) (= (@ (@ tptp.plus_plus_multiset_a tptp.zero_zero_multiset_a) X) X)) (forall ((A2 tptp.multiset_a)) (@ (@ tptp.subseteq_mset_a tptp.zero_zero_multiset_a) A2)) (forall ((X tptp.multiset_a)) (@ (@ tptp.subseteq_mset_a tptp.zero_zero_multiset_a) X)) (forall ((A tptp.multiset_a)) (@ (@ tptp.subseteq_mset_a tptp.zero_zero_multiset_a) A)) (forall ((A tptp.multiset_a) (C tptp.multiset_a) (B tptp.multiset_a)) (=> (@ (@ tptp.subseteq_mset_a A) tptp.zero_zero_multiset_a) (=> (@ (@ tptp.subseteq_mset_a C) B) (@ (@ tptp.subseteq_mset_a (@ (@ tptp.plus_plus_multiset_a A) C)) B)))) (forall ((A tptp.multiset_a) (B tptp.multiset_a) (C tptp.multiset_a)) (let ((_let_1 (@ tptp.subseteq_mset_a B))) (=> (@ (@ tptp.subseteq_mset_a tptp.zero_zero_multiset_a) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_multiset_a A) C)))))) (forall ((C tptp.multiset_a) (A tptp.multiset_a) (B tptp.multiset_a)) (=> (@ (@ tptp.subseteq_mset_a C) tptp.zero_zero_multiset_a) (=> (@ (@ tptp.subseteq_mset_a A) B) (@ (@ tptp.subseteq_mset_a (@ (@ tptp.plus_plus_multiset_a A) C)) B)))) (forall ((C tptp.multiset_a) (B tptp.multiset_a) (A tptp.multiset_a)) (let ((_let_1 (@ tptp.subseteq_mset_a B))) (=> (@ (@ tptp.subseteq_mset_a tptp.zero_zero_multiset_a) C) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.plus_plus_multiset_a A) C)))))) (forall ((A tptp.multiset_a) (B tptp.multiset_a)) (let ((_let_1 (@ tptp.subseteq_mset_a tptp.zero_zero_multiset_a))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_multiset_a A) B)))))) (forall ((A tptp.multiset_a) (B tptp.multiset_a)) (=> (@ (@ tptp.subseteq_mset_a A) tptp.zero_zero_multiset_a) (=> (@ (@ tptp.subseteq_mset_a B) tptp.zero_zero_multiset_a) (@ (@ tptp.subseteq_mset_a (@ (@ tptp.plus_plus_multiset_a A) B)) tptp.zero_zero_multiset_a)))) (forall ((X tptp.multiset_a) (Y tptp.multiset_a)) (let ((_let_1 (@ tptp.subseteq_mset_a tptp.zero_zero_multiset_a))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_multiset_a X) Y) tptp.zero_zero_multiset_a) (and (= X tptp.zero_zero_multiset_a) (= Y tptp.zero_zero_multiset_a))))))) (forall ((X tptp.multiset_a) (Y tptp.multiset_a)) (=> (@ (@ tptp.subseteq_mset_a X) tptp.zero_zero_multiset_a) (=> (@ (@ tptp.subseteq_mset_a Y) tptp.zero_zero_multiset_a) (= (= (@ (@ tptp.plus_plus_multiset_a X) Y) tptp.zero_zero_multiset_a) (and (= X tptp.zero_zero_multiset_a) (= Y tptp.zero_zero_multiset_a)))))) (forall ((A tptp.multiset_a)) (=> (@ (@ tptp.subseteq_mset_a A) tptp.zero_zero_multiset_a) (= A tptp.zero_zero_multiset_a))) (forall ((A tptp.multiset_a)) (= (@ (@ tptp.plus_plus_multiset_a A) tptp.zero_zero_multiset_a) A)) _let_5 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.67/0.88 )
% 0.67/0.88 % SZS output end Proof for ITP070^1
% 0.67/0.88 % cvc5---1.0.5 exiting
% 0.74/0.88 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------