TSTP Solution File: ITP068^1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP068^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n028.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 03:17:56 EDT 2023
% Result : Theorem 0.23s 0.79s
% Output : Proof 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.15 % Problem : ITP068^1 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.16 % Command : do_cvc5 %s %d
% 0.16/0.37 % Computer : n028.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Sun Aug 27 14:13:38 EDT 2023
% 0.22/0.37 % CPUTime :
% 0.23/0.53 %----Proving TH0
% 0.23/0.54 %------------------------------------------------------------------------------
% 0.23/0.54 % File : ITP068^1 : TPTP v8.1.2. Released v7.5.0.
% 0.23/0.54 % Domain : Interactive Theorem Proving
% 0.23/0.54 % Problem : Sledgehammer HeapImperative problem prob_383__5342344_1
% 0.23/0.54 % Version : Especial.
% 0.23/0.54 % English :
% 0.23/0.54
% 0.23/0.54 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.23/0.54 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.23/0.54 % Source : [Des21]
% 0.23/0.54 % Names : HeapImperative/prob_383__5342344_1 [Des21]
% 0.23/0.54
% 0.23/0.54 % Status : Theorem
% 0.23/0.54 % Rating : 0.38 v8.1.0, 0.36 v7.5.0
% 0.23/0.54 % Syntax : Number of formulae : 240 ( 77 unt; 64 typ; 0 def)
% 0.23/0.54 % Number of atoms : 543 ( 193 equ; 0 cnn)
% 0.23/0.54 % Maximal formula atoms : 12 ( 3 avg)
% 0.23/0.54 % Number of connectives : 2155 ( 59 ~; 11 |; 53 &;1759 @)
% 0.23/0.54 % ( 0 <=>; 273 =>; 0 <=; 0 <~>)
% 0.23/0.54 % Maximal formula depth : 22 ( 8 avg)
% 0.23/0.54 % Number of types : 11 ( 10 usr)
% 0.23/0.54 % Number of type conns : 278 ( 278 >; 0 *; 0 +; 0 <<)
% 0.23/0.54 % Number of symbols : 57 ( 54 usr; 15 con; 0-3 aty)
% 0.23/0.54 % Number of variables : 630 ( 43 ^; 569 !; 18 ?; 630 :)
% 0.23/0.54 % SPC : TH0_THM_EQU_NAR
% 0.23/0.54
% 0.23/0.54 % Comments : This file was generated by Sledgehammer 2021-02-23 15:30:28.993
% 0.23/0.54 %------------------------------------------------------------------------------
% 0.23/0.54 % Could-be-implicit typings (10)
% 0.23/0.54 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Multiset__Omultiset_Itf__a_J_Mt__Multiset__Omultiset_Itf__a_J_J_J,type,
% 0.23/0.54 set_Pr158363655iset_a: $tType ).
% 0.23/0.54
% 0.23/0.54 thf(ty_n_t__Product____Type__Oprod_It__Multiset__Omultiset_Itf__a_J_Mt__Multiset__Omultiset_Itf__a_J_J,type,
% 0.23/0.54 produc1127127335iset_a: $tType ).
% 0.23/0.54
% 0.23/0.54 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J,type,
% 0.23/0.54 set_Product_prod_a_a: $tType ).
% 0.23/0.54
% 0.23/0.54 thf(ty_n_t__Multiset__Omultiset_It__Multiset__Omultiset_Itf__a_J_J,type,
% 0.23/0.54 multiset_multiset_a: $tType ).
% 0.23/0.54
% 0.23/0.54 thf(ty_n_t__Set__Oset_It__Multiset__Omultiset_Itf__a_J_J,type,
% 0.23/0.54 set_multiset_a: $tType ).
% 0.23/0.54
% 0.23/0.54 thf(ty_n_t__Product____Type__Oprod_Itf__a_Mtf__a_J,type,
% 0.23/0.54 product_prod_a_a: $tType ).
% 0.23/0.54
% 0.23/0.54 thf(ty_n_t__Multiset__Omultiset_Itf__a_J,type,
% 0.23/0.54 multiset_a: $tType ).
% 0.23/0.54
% 0.23/0.54 thf(ty_n_t__Heap__OTree_Itf__a_J,type,
% 0.23/0.54 tree_a: $tType ).
% 0.23/0.54
% 0.23/0.54 thf(ty_n_t__Set__Oset_Itf__a_J,type,
% 0.23/0.54 set_a: $tType ).
% 0.23/0.54
% 0.23/0.54 thf(ty_n_tf__a,type,
% 0.23/0.54 a: $tType ).
% 0.23/0.54
% 0.23/0.54 % Explicit typings (54)
% 0.23/0.54 thf(sy_c_Groups_Oplus__class_Oplus_001t__Multiset__Omultiset_Itf__a_J,type,
% 0.23/0.54 plus_plus_multiset_a: multiset_a > multiset_a > multiset_a ).
% 0.23/0.54
% 0.23/0.54 thf(sy_c_Groups_Ozero__class_Ozero_001t__Multiset__Omultiset_Itf__a_J,type,
% 0.23/0.54 zero_zero_multiset_a: multiset_a ).
% 0.23/0.54
% 0.23/0.54 thf(sy_c_HOL_ONO__MATCH_001t__Multiset__Omultiset_Itf__a_J_001t__Multiset__Omultiset_Itf__a_J,type,
% 0.23/0.54 nO_MAT1617603563iset_a: multiset_a > multiset_a > $o ).
% 0.23/0.54
% 0.23/0.54 thf(sy_c_HeapImperative__Mirabelle__ksbqzsoydx_Oleft_001tf__a,type,
% 0.23/0.54 heapIm1140443833left_a: tree_a > tree_a ).
% 0.23/0.54
% 0.23/0.54 thf(sy_c_HeapImperative__Mirabelle__ksbqzsoydx_Oright_001tf__a,type,
% 0.23/0.54 heapIm1257206334ight_a: tree_a > tree_a ).
% 0.23/0.54
% 0.23/0.54 thf(sy_c_HeapImperative__Mirabelle__ksbqzsoydx_OsiftDown_001tf__a,type,
% 0.23/0.54 heapIm1091024090Down_a: tree_a > tree_a ).
% 0.23/0.54
% 0.23/0.54 thf(sy_c_Heap_OTree_OE_001tf__a,type,
% 0.23/0.54 e_a: tree_a ).
% 0.23/0.54
% 0.23/0.54 thf(sy_c_Heap_OTree_OT_001tf__a,type,
% 0.23/0.54 t_a: a > tree_a > tree_a > tree_a ).
% 0.23/0.54
% 0.23/0.54 thf(sy_c_Heap_OTree_Orel__Tree_001tf__a_001tf__a,type,
% 0.23/0.54 rel_Tree_a_a: ( a > a > $o ) > tree_a > tree_a > $o ).
% 0.23/0.54
% 0.23/0.54 thf(sy_c_Heap_Oin__tree_001tf__a,type,
% 0.23/0.54 in_tree_a: a > tree_a > $o ).
% 0.23/0.54
% 0.23/0.54 thf(sy_c_Heap_Ois__heap_001tf__a,type,
% 0.23/0.54 is_heap_a: tree_a > $o ).
% 0.23/0.54
% 0.23/0.54 thf(sy_c_Heap_Omultiset_001tf__a,type,
% 0.23/0.54 multiset_a2: tree_a > multiset_a ).
% 0.23/0.54
% 0.23/0.54 thf(sy_c_Heap_Oval_001tf__a,type,
% 0.23/0.54 val_a: tree_a > a ).
% 0.23/0.54
% 0.23/0.54 thf(sy_c_Lattices__Big_Olinorder__class_OMax_001tf__a,type,
% 0.23/0.54 lattic146396397_Max_a: set_a > a ).
% 0.23/0.54
% 0.23/0.54 thf(sy_c_Multiset_Oadd__mset_001tf__a,type,
% 0.23/0.54 add_mset_a: a > multiset_a > multiset_a ).
% 0.23/0.54
% 0.23/0.54 thf(sy_c_Multiset_Ocomm__monoid__add_Osum__mset_001t__Multiset__Omultiset_Itf__a_J,type,
% 0.23/0.54 comm_m315775925iset_a: ( multiset_a > multiset_a > multiset_a ) > multiset_a > multiset_multiset_a > multiset_a ).
% 0.23/0.54
% 0.23/0.54 thf(sy_c_Multiset_Ofold__mset_001t__Multiset__Omultiset_Itf__a_J_001t__Multiset__Omultiset_Itf__a_J,type,
% 0.23/0.54 fold_m382157835iset_a: ( multiset_a > multiset_a > multiset_a ) > multiset_a > multiset_multiset_a > multiset_a ).
% 0.23/0.54
% 0.23/0.54 thf(sy_c_Multiset_Ofold__mset_001tf__a_001t__Multiset__Omultiset_Itf__a_J,type,
% 0.23/0.54 fold_m364285649iset_a: ( a > multiset_a > multiset_a ) > multiset_a > multiset_a > multiset_a ).
% 0.23/0.54
% 0.23/0.54 thf(sy_c_Multiset_Oimage__mset_001tf__a_001t__Multiset__Omultiset_Itf__a_J,type,
% 0.23/0.54 image_929116801iset_a: ( a > multiset_a ) > multiset_a > multiset_multiset_a ).
% 0.23/0.54
% 0.23/0.54 thf(sy_c_Multiset_Oimage__mset_001tf__a_001tf__a,type,
% 0.23/0.54 image_mset_a_a: ( a > a ) > multiset_a > multiset_a ).
% 0.23/0.54
% 0.23/0.54 thf(sy_c_Multiset_Omult1_001tf__a,type,
% 0.23/0.54 mult1_a: set_Product_prod_a_a > set_Pr158363655iset_a ).
% 0.23/0.54
% 0.23/0.54 thf(sy_c_Multiset_Omult_001tf__a,type,
% 0.23/0.54 mult_a: set_Product_prod_a_a > set_Pr158363655iset_a ).
% 0.23/0.54
% 0.23/0.54 thf(sy_c_Multiset_Oset__mset_001t__Multiset__Omultiset_Itf__a_J,type,
% 0.23/0.54 set_mset_multiset_a: multiset_multiset_a > set_multiset_a ).
% 0.23/0.54
% 0.23/0.54 thf(sy_c_Multiset_Oset__mset_001tf__a,type,
% 0.23/0.54 set_mset_a: multiset_a > set_a ).
% 0.23/0.54
% 0.23/0.54 thf(sy_c_Multiset_Osubseteq__mset_001tf__a,type,
% 0.23/0.54 subseteq_mset_a: multiset_a > multiset_a > $o ).
% 0.23/0.54
% 0.23/0.54 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_Eo_M_062_I_Eo_Mtf__a_J_J,type,
% 0.23/0.54 ord_less_eq_o_o_a: ( $o > $o > a ) > ( $o > $o > a ) > $o ).
% 0.23/0.54
% 0.23/0.54 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_Eo_Mtf__a_J,type,
% 0.23/0.54 ord_less_eq_o_a: ( $o > a ) > ( $o > a ) > $o ).
% 0.23/0.54
% 0.23/0.54 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Heap__OTree_Itf__a_J_M_062_It__Heap__OTree_Itf__a_J_M_Eo_J_J,type,
% 0.23/0.54 ord_le1530450702ee_a_o: ( tree_a > tree_a > $o ) > ( tree_a > tree_a > $o ) > $o ).
% 0.23/0.54
% 0.23/0.54 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_Itf__a_M_062_Itf__a_M_Eo_J_J,type,
% 0.23/0.54 ord_less_eq_a_a_o: ( a > a > $o ) > ( a > a > $o ) > $o ).
% 0.23/0.54
% 0.23/0.54 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Multiset__Omultiset_Itf__a_J,type,
% 0.23/0.54 ord_le1199012836iset_a: multiset_a > multiset_a > $o ).
% 0.23/0.54
% 0.23/0.54 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__a_J,type,
% 0.23/0.54 ord_less_eq_set_a: set_a > set_a > $o ).
% 0.23/0.54
% 0.23/0.54 thf(sy_c_Orderings_Oord__class_Oless__eq_001tf__a,type,
% 0.23/0.54 ord_less_eq_a: a > a > $o ).
% 0.23/0.54
% 0.23/0.54 thf(sy_c_Orderings_Oorder__class_OGreatest_001_062_I_Eo_Mtf__a_J,type,
% 0.23/0.54 order_Greatest_o_a: ( ( $o > a ) > $o ) > $o > a ).
% 0.23/0.54
% 0.23/0.54 thf(sy_c_Orderings_Oorder__class_OGreatest_001tf__a,type,
% 0.23/0.54 order_Greatest_a: ( a > $o ) > a ).
% 0.23/0.54
% 0.23/0.54 thf(sy_c_Product__Type_OPair_001t__Multiset__Omultiset_Itf__a_J_001t__Multiset__Omultiset_Itf__a_J,type,
% 0.23/0.54 produc2037245207iset_a: multiset_a > multiset_a > produc1127127335iset_a ).
% 0.23/0.54
% 0.23/0.54 thf(sy_c_Product__Type_OPair_001tf__a_001tf__a,type,
% 0.23/0.54 product_Pair_a_a: a > a > product_prod_a_a ).
% 0.23/0.54
% 0.23/0.54 thf(sy_c_Relation_Oirrefl_001tf__a,type,
% 0.23/0.54 irrefl_a: set_Product_prod_a_a > $o ).
% 0.23/0.54
% 0.23/0.54 thf(sy_c_Relation_Otrans_001tf__a,type,
% 0.23/0.54 trans_a: set_Product_prod_a_a > $o ).
% 0.23/0.54
% 0.23/0.54 thf(sy_c_Set_OCollect_001tf__a,type,
% 0.23/0.54 collect_a: ( a > $o ) > set_a ).
% 0.23/0.54
% 0.23/0.54 thf(sy_c_member_001t__Multiset__Omultiset_Itf__a_J,type,
% 0.23/0.54 member_multiset_a: multiset_a > set_multiset_a > $o ).
% 0.23/0.54
% 0.23/0.54 thf(sy_c_member_001t__Product____Type__Oprod_It__Multiset__Omultiset_Itf__a_J_Mt__Multiset__Omultiset_Itf__a_J_J,type,
% 0.23/0.54 member340150864iset_a: produc1127127335iset_a > set_Pr158363655iset_a > $o ).
% 0.23/0.54
% 0.23/0.54 thf(sy_c_member_001t__Product____Type__Oprod_Itf__a_Mtf__a_J,type,
% 0.23/0.54 member449909584od_a_a: product_prod_a_a > set_Product_prod_a_a > $o ).
% 0.23/0.54
% 0.23/0.54 thf(sy_c_member_001tf__a,type,
% 0.23/0.54 member_a: a > set_a > $o ).
% 0.23/0.54
% 0.23/0.54 thf(sy_v_l,type,
% 0.23/0.54 l: tree_a ).
% 0.23/0.54
% 0.23/0.54 thf(sy_v_l1____,type,
% 0.23/0.54 l1: tree_a ).
% 0.23/0.54
% 0.23/0.54 thf(sy_v_la____,type,
% 0.23/0.54 la: tree_a ).
% 0.23/0.54
% 0.23/0.54 thf(sy_v_r,type,
% 0.23/0.54 r: tree_a ).
% 0.23/0.54
% 0.23/0.54 thf(sy_v_r1____,type,
% 0.23/0.54 r1: tree_a ).
% 0.23/0.54
% 0.23/0.54 thf(sy_v_ra____,type,
% 0.23/0.54 ra: tree_a ).
% 0.23/0.54
% 0.23/0.54 thf(sy_v_t,type,
% 0.23/0.54 t: tree_a ).
% 0.23/0.54
% 0.23/0.54 thf(sy_v_v,type,
% 0.23/0.54 v: a ).
% 0.23/0.54
% 0.23/0.54 thf(sy_v_v1____,type,
% 0.23/0.54 v1: a ).
% 0.23/0.54
% 0.23/0.54 thf(sy_v_v2____,type,
% 0.23/0.54 v2: a ).
% 0.23/0.54
% 0.23/0.54 thf(sy_v_va____,type,
% 0.23/0.54 va: a ).
% 0.23/0.54
% 0.23/0.54 % Relevant facts (175)
% 0.23/0.54 thf(fact_0__C4_Oprems_C_I2_J,axiom,
% 0.23/0.54 is_heap_a @ ra ).
% 0.23/0.54
% 0.23/0.54 % "4.prems"(2)
% 0.23/0.54 thf(fact_1__C4_Oprems_C_I1_J,axiom,
% 0.23/0.54 is_heap_a @ la ).
% 0.23/0.54
% 0.23/0.54 % "4.prems"(1)
% 0.23/0.54 thf(fact_2_assms_I2_J,axiom,
% 0.23/0.54 is_heap_a @ r ).
% 0.23/0.54
% 0.23/0.54 % assms(2)
% 0.23/0.54 thf(fact_3_assms_I1_J,axiom,
% 0.23/0.54 is_heap_a @ l ).
% 0.23/0.54
% 0.23/0.54 % assms(1)
% 0.23/0.54 thf(fact_4_True,axiom,
% 0.23/0.54 ord_less_eq_a @ v1 @ v2 ).
% 0.23/0.54
% 0.23/0.54 % True
% 0.23/0.54 thf(fact_5__C4_Oprems_C_I3_J,axiom,
% 0.23/0.54 ( ( t_a @ v2 @ e_a @ ( t_a @ v1 @ l1 @ r1 ) )
% 0.23/0.54 = ( t_a @ va @ la @ ra ) ) ).
% 0.23/0.54
% 0.23/0.54 % "4.prems"(3)
% 0.23/0.54 thf(fact_6_siftDown_Osimps_I2_J,axiom,
% 0.23/0.54 ! [V: a] :
% 0.23/0.54 ( ( heapIm1091024090Down_a @ ( t_a @ V @ e_a @ e_a ) )
% 0.23/0.54 = ( t_a @ V @ e_a @ e_a ) ) ).
% 0.23/0.54
% 0.23/0.54 % siftDown.simps(2)
% 0.23/0.54 thf(fact_7_siftDown_Osimps_I1_J,axiom,
% 0.23/0.54 ( ( heapIm1091024090Down_a @ e_a )
% 0.23/0.54 = e_a ) ).
% 0.23/0.54
% 0.23/0.54 % siftDown.simps(1)
% 0.23/0.54 thf(fact_8_siftDown_Ocases,axiom,
% 0.23/0.54 ! [X: tree_a] :
% 0.23/0.54 ( ( X != e_a )
% 0.23/0.54 => ( ! [V2: a] :
% 0.23/0.54 ( X
% 0.23/0.54 != ( t_a @ V2 @ e_a @ e_a ) )
% 0.23/0.54 => ( ! [V2: a,Va: a,Vb: tree_a,Vc: tree_a] :
% 0.23/0.54 ( X
% 0.23/0.54 != ( t_a @ V2 @ ( t_a @ Va @ Vb @ Vc ) @ e_a ) )
% 0.23/0.54 => ( ! [V2: a,Va: a,Vb: tree_a,Vc: tree_a] :
% 0.23/0.54 ( X
% 0.23/0.54 != ( t_a @ V2 @ e_a @ ( t_a @ Va @ Vb @ Vc ) ) )
% 0.23/0.54 => ~ ! [V2: a,Va: a,Vb: tree_a,Vc: tree_a,Vd: a,Ve: tree_a,Vf: tree_a] :
% 0.23/0.54 ( X
% 0.23/0.54 != ( t_a @ V2 @ ( t_a @ Va @ Vb @ Vc ) @ ( t_a @ Vd @ Ve @ Vf ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % siftDown.cases
% 0.23/0.54 thf(fact_9_assms_I3_J,axiom,
% 0.23/0.54 ( t
% 0.23/0.54 = ( t_a @ v @ l @ r ) ) ).
% 0.23/0.54
% 0.23/0.54 % assms(3)
% 0.23/0.54 thf(fact_10_is__heap_Osimps_I2_J,axiom,
% 0.23/0.54 ! [V: a] : ( is_heap_a @ ( t_a @ V @ e_a @ e_a ) ) ).
% 0.23/0.54
% 0.23/0.54 % is_heap.simps(2)
% 0.23/0.54 thf(fact_11_siftDown__Node,axiom,
% 0.23/0.54 ! [T: tree_a,V: a,L: tree_a,R: tree_a] :
% 0.23/0.54 ( ( T
% 0.23/0.54 = ( t_a @ V @ L @ R ) )
% 0.23/0.54 => ? [L2: tree_a,V3: a,R2: tree_a] :
% 0.23/0.54 ( ( ( heapIm1091024090Down_a @ T )
% 0.23/0.54 = ( t_a @ V3 @ L2 @ R2 ) )
% 0.23/0.54 & ( ord_less_eq_a @ V @ V3 ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % siftDown_Node
% 0.23/0.54 thf(fact_12__C4_Ohyps_C,axiom,
% 0.23/0.54 ! [L: tree_a,R: tree_a,V: a] :
% 0.23/0.54 ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ v1 @ l1 @ r1 ) ) @ v2 )
% 0.23/0.54 => ( ( is_heap_a @ L )
% 0.23/0.54 => ( ( is_heap_a @ R )
% 0.23/0.54 => ( ( ( t_a @ v2 @ ( heapIm1140443833left_a @ ( t_a @ v1 @ l1 @ r1 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ v1 @ l1 @ r1 ) ) )
% 0.23/0.54 = ( t_a @ V @ L @ R ) )
% 0.23/0.54 => ( is_heap_a @ ( heapIm1091024090Down_a @ ( t_a @ v2 @ ( heapIm1140443833left_a @ ( t_a @ v1 @ l1 @ r1 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ v1 @ l1 @ r1 ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % "4.hyps"
% 0.23/0.54 thf(fact_13_Tree_Oinject,axiom,
% 0.23/0.54 ! [X21: a,X22: tree_a,X23: tree_a,Y21: a,Y22: tree_a,Y23: tree_a] :
% 0.23/0.54 ( ( ( t_a @ X21 @ X22 @ X23 )
% 0.23/0.54 = ( t_a @ Y21 @ Y22 @ Y23 ) )
% 0.23/0.54 = ( ( X21 = Y21 )
% 0.23/0.54 & ( X22 = Y22 )
% 0.23/0.54 & ( X23 = Y23 ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % Tree.inject
% 0.23/0.54 thf(fact_14_is__heap_Osimps_I1_J,axiom,
% 0.23/0.54 is_heap_a @ e_a ).
% 0.23/0.54
% 0.23/0.54 % is_heap.simps(1)
% 0.23/0.54 thf(fact_15_Tree_Odistinct_I1_J,axiom,
% 0.23/0.54 ! [X21: a,X22: tree_a,X23: tree_a] :
% 0.23/0.54 ( e_a
% 0.23/0.54 != ( t_a @ X21 @ X22 @ X23 ) ) ).
% 0.23/0.54
% 0.23/0.54 % Tree.distinct(1)
% 0.23/0.54 thf(fact_16_Tree_Oinduct,axiom,
% 0.23/0.54 ! [P: tree_a > $o,Tree: tree_a] :
% 0.23/0.54 ( ( P @ e_a )
% 0.23/0.54 => ( ! [X1: a,X2: tree_a,X3: tree_a] :
% 0.23/0.54 ( ( P @ X2 )
% 0.23/0.54 => ( ( P @ X3 )
% 0.23/0.54 => ( P @ ( t_a @ X1 @ X2 @ X3 ) ) ) )
% 0.23/0.54 => ( P @ Tree ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % Tree.induct
% 0.23/0.54 thf(fact_17_Tree_Oexhaust,axiom,
% 0.23/0.54 ! [Y: tree_a] :
% 0.23/0.54 ( ( Y != e_a )
% 0.23/0.54 => ~ ! [X212: a,X222: tree_a,X232: tree_a] :
% 0.23/0.54 ( Y
% 0.23/0.54 != ( t_a @ X212 @ X222 @ X232 ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % Tree.exhaust
% 0.23/0.54 thf(fact_18_is__heap_Ocases,axiom,
% 0.23/0.54 ! [X: tree_a] :
% 0.23/0.54 ( ( X != e_a )
% 0.23/0.54 => ( ! [V2: a] :
% 0.23/0.54 ( X
% 0.23/0.54 != ( t_a @ V2 @ e_a @ e_a ) )
% 0.23/0.54 => ( ! [V2: a,Va: a,Vb: tree_a,Vc: tree_a] :
% 0.23/0.54 ( X
% 0.23/0.54 != ( t_a @ V2 @ e_a @ ( t_a @ Va @ Vb @ Vc ) ) )
% 0.23/0.54 => ( ! [V2: a,Va: a,Vb: tree_a,Vc: tree_a] :
% 0.23/0.54 ( X
% 0.23/0.54 != ( t_a @ V2 @ ( t_a @ Va @ Vb @ Vc ) @ e_a ) )
% 0.23/0.54 => ~ ! [V2: a,Va: a,Vb: tree_a,Vc: tree_a,Vd: a,Ve: tree_a,Vf: tree_a] :
% 0.23/0.54 ( X
% 0.23/0.54 != ( t_a @ V2 @ ( t_a @ Va @ Vb @ Vc ) @ ( t_a @ Vd @ Ve @ Vf ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % is_heap.cases
% 0.23/0.54 thf(fact_19_siftDown__in__tree__set,axiom,
% 0.23/0.54 ( in_tree_a
% 0.23/0.54 = ( ^ [V4: a,T2: tree_a] : ( in_tree_a @ V4 @ ( heapIm1091024090Down_a @ T2 ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % siftDown_in_tree_set
% 0.23/0.54 thf(fact_20_left_Osimps,axiom,
% 0.23/0.54 ! [V: a,L: tree_a,R: tree_a] :
% 0.23/0.54 ( ( heapIm1140443833left_a @ ( t_a @ V @ L @ R ) )
% 0.23/0.54 = L ) ).
% 0.23/0.54
% 0.23/0.54 % left.simps
% 0.23/0.54 thf(fact_21_is__heap__max,axiom,
% 0.23/0.54 ! [V: a,T: tree_a] :
% 0.23/0.54 ( ( in_tree_a @ V @ T )
% 0.23/0.54 => ( ( is_heap_a @ T )
% 0.23/0.54 => ( ord_less_eq_a @ V @ ( val_a @ T ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % is_heap_max
% 0.23/0.54 thf(fact_22_val_Osimps,axiom,
% 0.23/0.54 ! [V: a,Uu: tree_a,Uv: tree_a] :
% 0.23/0.54 ( ( val_a @ ( t_a @ V @ Uu @ Uv ) )
% 0.23/0.54 = V ) ).
% 0.23/0.54
% 0.23/0.54 % val.simps
% 0.23/0.54 thf(fact_23_in__tree_Osimps_I2_J,axiom,
% 0.23/0.54 ! [V: a,V5: a,L: tree_a,R: tree_a] :
% 0.23/0.54 ( ( in_tree_a @ V @ ( t_a @ V5 @ L @ R ) )
% 0.23/0.54 = ( ( V = V5 )
% 0.23/0.54 | ( in_tree_a @ V @ L )
% 0.23/0.54 | ( in_tree_a @ V @ R ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % in_tree.simps(2)
% 0.23/0.54 thf(fact_24_siftDown_Osimps_I5_J,axiom,
% 0.23/0.54 ! [Vd2: a,Ve2: tree_a,Vf2: tree_a,Va2: a,Vb2: tree_a,Vc2: tree_a,V: a] :
% 0.23/0.54 ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 0.23/0.54 => ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 0.23/0.54 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) )
% 0.23/0.54 = ( t_a @ V @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) ) )
% 0.23/0.54 & ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 0.23/0.54 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) )
% 0.23/0.54 = ( t_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ ( heapIm1091024090Down_a @ ( t_a @ V @ ( heapIm1140443833left_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) ) @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) ) ) ) )
% 0.23/0.54 & ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 0.23/0.54 => ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ V )
% 0.23/0.54 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) )
% 0.23/0.54 = ( t_a @ V @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) ) )
% 0.23/0.54 & ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ V )
% 0.23/0.54 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) )
% 0.23/0.54 = ( t_a @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ ( heapIm1091024090Down_a @ ( t_a @ V @ ( heapIm1140443833left_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % siftDown.simps(5)
% 0.23/0.54 thf(fact_25_siftDown_Osimps_I6_J,axiom,
% 0.23/0.54 ! [Va2: a,Vb2: tree_a,Vc2: tree_a,Vd2: a,Ve2: tree_a,Vf2: tree_a,V: a] :
% 0.23/0.54 ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) )
% 0.23/0.54 => ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ V )
% 0.23/0.54 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 0.23/0.54 = ( t_a @ V @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) )
% 0.23/0.54 & ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ V )
% 0.23/0.54 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 0.23/0.54 = ( t_a @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ ( heapIm1091024090Down_a @ ( t_a @ V @ ( heapIm1140443833left_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) ) ) @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) )
% 0.23/0.54 & ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) )
% 0.23/0.54 => ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 0.23/0.54 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 0.23/0.54 = ( t_a @ V @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) )
% 0.23/0.54 & ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 0.23/0.54 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 0.23/0.54 = ( t_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) @ ( heapIm1091024090Down_a @ ( t_a @ V @ ( heapIm1140443833left_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % siftDown.simps(6)
% 0.23/0.54 thf(fact_26_in__tree_Osimps_I1_J,axiom,
% 0.23/0.54 ! [V: a] :
% 0.23/0.54 ~ ( in_tree_a @ V @ e_a ) ).
% 0.23/0.54
% 0.23/0.54 % in_tree.simps(1)
% 0.23/0.54 thf(fact_27_is__heap_Osimps_I5_J,axiom,
% 0.23/0.54 ! [V: a,Va2: a,Vb2: tree_a,Vc2: tree_a,Vd2: a,Ve2: tree_a,Vf2: tree_a] :
% 0.23/0.54 ( ( is_heap_a @ ( t_a @ V @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) )
% 0.23/0.54 = ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ V )
% 0.23/0.54 & ( is_heap_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) )
% 0.23/0.54 & ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 0.23/0.54 & ( is_heap_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % is_heap.simps(5)
% 0.23/0.54 thf(fact_28_is__heap_Osimps_I6_J,axiom,
% 0.23/0.54 ! [V: a,Vd2: a,Ve2: tree_a,Vf2: tree_a,Va2: a,Vb2: tree_a,Vc2: tree_a] :
% 0.23/0.54 ( ( is_heap_a @ ( t_a @ V @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 0.23/0.54 = ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 0.23/0.54 & ( is_heap_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) )
% 0.23/0.54 & ( ord_less_eq_a @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ V )
% 0.23/0.54 & ( is_heap_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % is_heap.simps(6)
% 0.23/0.54 thf(fact_29_siftDown_Osimps_I3_J,axiom,
% 0.23/0.54 ! [Va2: a,Vb2: tree_a,Vc2: tree_a,V: a] :
% 0.23/0.54 ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 0.23/0.54 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ e_a ) )
% 0.23/0.54 = ( t_a @ V @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ e_a ) ) )
% 0.23/0.54 & ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 0.23/0.54 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ e_a ) )
% 0.23/0.54 = ( t_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ ( heapIm1091024090Down_a @ ( t_a @ V @ ( heapIm1140443833left_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) ) @ e_a ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % siftDown.simps(3)
% 0.23/0.54 thf(fact_30_siftDown_Osimps_I4_J,axiom,
% 0.23/0.54 ! [Va2: a,Vb2: tree_a,Vc2: tree_a,V: a] :
% 0.23/0.54 ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 0.23/0.54 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ e_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 0.23/0.54 = ( t_a @ V @ e_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) )
% 0.23/0.54 & ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 0.23/0.54 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ e_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 0.23/0.54 = ( t_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ e_a @ ( heapIm1091024090Down_a @ ( t_a @ V @ ( heapIm1140443833left_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % siftDown.simps(4)
% 0.23/0.54 thf(fact_31_siftDown__in__tree,axiom,
% 0.23/0.54 ! [T: tree_a] :
% 0.23/0.54 ( ( T != e_a )
% 0.23/0.54 => ( in_tree_a @ ( val_a @ ( heapIm1091024090Down_a @ T ) ) @ T ) ) ).
% 0.23/0.54
% 0.23/0.54 % siftDown_in_tree
% 0.23/0.54 thf(fact_32_is__heap_Osimps_I3_J,axiom,
% 0.23/0.54 ! [V: a,Va2: a,Vb2: tree_a,Vc2: tree_a] :
% 0.23/0.54 ( ( is_heap_a @ ( t_a @ V @ e_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 0.23/0.54 = ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 0.23/0.54 & ( is_heap_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % is_heap.simps(3)
% 0.23/0.54 thf(fact_33_is__heap_Osimps_I4_J,axiom,
% 0.23/0.54 ! [V: a,Va2: a,Vb2: tree_a,Vc2: tree_a] :
% 0.23/0.54 ( ( is_heap_a @ ( t_a @ V @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ e_a ) )
% 0.23/0.54 = ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 0.23/0.54 & ( is_heap_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % is_heap.simps(4)
% 0.23/0.54 thf(fact_34_right_Osimps,axiom,
% 0.23/0.54 ! [V: a,L: tree_a,R: tree_a] :
% 0.23/0.54 ( ( heapIm1257206334ight_a @ ( t_a @ V @ L @ R ) )
% 0.23/0.54 = R ) ).
% 0.23/0.54
% 0.23/0.54 % right.simps
% 0.23/0.54 thf(fact_35_order__refl,axiom,
% 0.23/0.54 ! [X: $o > a] : ( ord_less_eq_o_a @ X @ X ) ).
% 0.23/0.54
% 0.23/0.54 % order_refl
% 0.23/0.54 thf(fact_36_order__refl,axiom,
% 0.23/0.54 ! [X: a] : ( ord_less_eq_a @ X @ X ) ).
% 0.23/0.54
% 0.23/0.54 % order_refl
% 0.23/0.54 thf(fact_37_le__funD,axiom,
% 0.23/0.54 ! [F: $o > a,G: $o > a,X: $o] :
% 0.23/0.54 ( ( ord_less_eq_o_a @ F @ G )
% 0.23/0.54 => ( ord_less_eq_a @ ( F @ X ) @ ( G @ X ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % le_funD
% 0.23/0.54 thf(fact_38_le__funE,axiom,
% 0.23/0.54 ! [F: $o > a,G: $o > a,X: $o] :
% 0.23/0.54 ( ( ord_less_eq_o_a @ F @ G )
% 0.23/0.54 => ( ord_less_eq_a @ ( F @ X ) @ ( G @ X ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % le_funE
% 0.23/0.54 thf(fact_39_le__funI,axiom,
% 0.23/0.54 ! [F: $o > a,G: $o > a] :
% 0.23/0.54 ( ! [X4: $o] : ( ord_less_eq_a @ ( F @ X4 ) @ ( G @ X4 ) )
% 0.23/0.54 => ( ord_less_eq_o_a @ F @ G ) ) ).
% 0.23/0.54
% 0.23/0.54 % le_funI
% 0.23/0.54 thf(fact_40_le__fun__def,axiom,
% 0.23/0.54 ( ord_less_eq_o_a
% 0.23/0.54 = ( ^ [F2: $o > a,G2: $o > a] :
% 0.23/0.54 ! [X5: $o] : ( ord_less_eq_a @ ( F2 @ X5 ) @ ( G2 @ X5 ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % le_fun_def
% 0.23/0.54 thf(fact_41_order__subst1,axiom,
% 0.23/0.54 ! [A: a,F: ( $o > a ) > a,B: $o > a,C: $o > a] :
% 0.23/0.54 ( ( ord_less_eq_a @ A @ ( F @ B ) )
% 0.23/0.54 => ( ( ord_less_eq_o_a @ B @ C )
% 0.23/0.54 => ( ! [X4: $o > a,Y2: $o > a] :
% 0.23/0.54 ( ( ord_less_eq_o_a @ X4 @ Y2 )
% 0.23/0.54 => ( ord_less_eq_a @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.23/0.54 => ( ord_less_eq_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % order_subst1
% 0.23/0.54 thf(fact_42_order__subst1,axiom,
% 0.23/0.54 ! [A: $o > a,F: a > $o > a,B: a,C: a] :
% 0.23/0.54 ( ( ord_less_eq_o_a @ A @ ( F @ B ) )
% 0.23/0.54 => ( ( ord_less_eq_a @ B @ C )
% 0.23/0.54 => ( ! [X4: a,Y2: a] :
% 0.23/0.54 ( ( ord_less_eq_a @ X4 @ Y2 )
% 0.23/0.54 => ( ord_less_eq_o_a @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.23/0.54 => ( ord_less_eq_o_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % order_subst1
% 0.23/0.54 thf(fact_43_order__subst1,axiom,
% 0.23/0.54 ! [A: $o > a,F: ( $o > a ) > $o > a,B: $o > a,C: $o > a] :
% 0.23/0.54 ( ( ord_less_eq_o_a @ A @ ( F @ B ) )
% 0.23/0.54 => ( ( ord_less_eq_o_a @ B @ C )
% 0.23/0.54 => ( ! [X4: $o > a,Y2: $o > a] :
% 0.23/0.54 ( ( ord_less_eq_o_a @ X4 @ Y2 )
% 0.23/0.54 => ( ord_less_eq_o_a @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.23/0.54 => ( ord_less_eq_o_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % order_subst1
% 0.23/0.54 thf(fact_44_order__subst1,axiom,
% 0.23/0.54 ! [A: a,F: a > a,B: a,C: a] :
% 0.23/0.54 ( ( ord_less_eq_a @ A @ ( F @ B ) )
% 0.23/0.54 => ( ( ord_less_eq_a @ B @ C )
% 0.23/0.54 => ( ! [X4: a,Y2: a] :
% 0.23/0.54 ( ( ord_less_eq_a @ X4 @ Y2 )
% 0.23/0.54 => ( ord_less_eq_a @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.23/0.54 => ( ord_less_eq_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % order_subst1
% 0.23/0.54 thf(fact_45_order__subst2,axiom,
% 0.23/0.54 ! [A: a,B: a,F: a > $o > a,C: $o > a] :
% 0.23/0.54 ( ( ord_less_eq_a @ A @ B )
% 0.23/0.54 => ( ( ord_less_eq_o_a @ ( F @ B ) @ C )
% 0.23/0.54 => ( ! [X4: a,Y2: a] :
% 0.23/0.54 ( ( ord_less_eq_a @ X4 @ Y2 )
% 0.23/0.54 => ( ord_less_eq_o_a @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.23/0.54 => ( ord_less_eq_o_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % order_subst2
% 0.23/0.54 thf(fact_46_order__subst2,axiom,
% 0.23/0.54 ! [A: $o > a,B: $o > a,F: ( $o > a ) > a,C: a] :
% 0.23/0.54 ( ( ord_less_eq_o_a @ A @ B )
% 0.23/0.54 => ( ( ord_less_eq_a @ ( F @ B ) @ C )
% 0.23/0.54 => ( ! [X4: $o > a,Y2: $o > a] :
% 0.23/0.54 ( ( ord_less_eq_o_a @ X4 @ Y2 )
% 0.23/0.54 => ( ord_less_eq_a @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.23/0.54 => ( ord_less_eq_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % order_subst2
% 0.23/0.54 thf(fact_47_order__subst2,axiom,
% 0.23/0.54 ! [A: $o > a,B: $o > a,F: ( $o > a ) > $o > a,C: $o > a] :
% 0.23/0.54 ( ( ord_less_eq_o_a @ A @ B )
% 0.23/0.54 => ( ( ord_less_eq_o_a @ ( F @ B ) @ C )
% 0.23/0.54 => ( ! [X4: $o > a,Y2: $o > a] :
% 0.23/0.54 ( ( ord_less_eq_o_a @ X4 @ Y2 )
% 0.23/0.54 => ( ord_less_eq_o_a @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.23/0.54 => ( ord_less_eq_o_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % order_subst2
% 0.23/0.54 thf(fact_48_order__subst2,axiom,
% 0.23/0.54 ! [A: a,B: a,F: a > a,C: a] :
% 0.23/0.54 ( ( ord_less_eq_a @ A @ B )
% 0.23/0.54 => ( ( ord_less_eq_a @ ( F @ B ) @ C )
% 0.23/0.54 => ( ! [X4: a,Y2: a] :
% 0.23/0.54 ( ( ord_less_eq_a @ X4 @ Y2 )
% 0.23/0.54 => ( ord_less_eq_a @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.23/0.54 => ( ord_less_eq_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % order_subst2
% 0.23/0.54 thf(fact_49_verit__la__disequality,axiom,
% 0.23/0.54 ! [A: a,B: a] :
% 0.23/0.54 ( ( A = B )
% 0.23/0.54 | ~ ( ord_less_eq_a @ A @ B )
% 0.23/0.54 | ~ ( ord_less_eq_a @ B @ A ) ) ).
% 0.23/0.54
% 0.23/0.54 % verit_la_disequality
% 0.23/0.54 thf(fact_50_ord__eq__le__subst,axiom,
% 0.23/0.54 ! [A: $o > a,F: a > $o > a,B: a,C: a] :
% 0.23/0.54 ( ( A
% 0.23/0.54 = ( F @ B ) )
% 0.23/0.54 => ( ( ord_less_eq_a @ B @ C )
% 0.23/0.54 => ( ! [X4: a,Y2: a] :
% 0.23/0.54 ( ( ord_less_eq_a @ X4 @ Y2 )
% 0.23/0.54 => ( ord_less_eq_o_a @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.23/0.54 => ( ord_less_eq_o_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % ord_eq_le_subst
% 0.23/0.54 thf(fact_51_ord__eq__le__subst,axiom,
% 0.23/0.54 ! [A: a,F: ( $o > a ) > a,B: $o > a,C: $o > a] :
% 0.23/0.54 ( ( A
% 0.23/0.54 = ( F @ B ) )
% 0.23/0.54 => ( ( ord_less_eq_o_a @ B @ C )
% 0.23/0.54 => ( ! [X4: $o > a,Y2: $o > a] :
% 0.23/0.54 ( ( ord_less_eq_o_a @ X4 @ Y2 )
% 0.23/0.54 => ( ord_less_eq_a @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.23/0.54 => ( ord_less_eq_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % ord_eq_le_subst
% 0.23/0.54 thf(fact_52_ord__eq__le__subst,axiom,
% 0.23/0.54 ! [A: $o > a,F: ( $o > a ) > $o > a,B: $o > a,C: $o > a] :
% 0.23/0.54 ( ( A
% 0.23/0.54 = ( F @ B ) )
% 0.23/0.54 => ( ( ord_less_eq_o_a @ B @ C )
% 0.23/0.54 => ( ! [X4: $o > a,Y2: $o > a] :
% 0.23/0.54 ( ( ord_less_eq_o_a @ X4 @ Y2 )
% 0.23/0.54 => ( ord_less_eq_o_a @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.23/0.54 => ( ord_less_eq_o_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % ord_eq_le_subst
% 0.23/0.54 thf(fact_53_ord__eq__le__subst,axiom,
% 0.23/0.54 ! [A: a,F: a > a,B: a,C: a] :
% 0.23/0.54 ( ( A
% 0.23/0.54 = ( F @ B ) )
% 0.23/0.54 => ( ( ord_less_eq_a @ B @ C )
% 0.23/0.54 => ( ! [X4: a,Y2: a] :
% 0.23/0.54 ( ( ord_less_eq_a @ X4 @ Y2 )
% 0.23/0.54 => ( ord_less_eq_a @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.23/0.54 => ( ord_less_eq_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % ord_eq_le_subst
% 0.23/0.54 thf(fact_54_ord__le__eq__subst,axiom,
% 0.23/0.54 ! [A: a,B: a,F: a > $o > a,C: $o > a] :
% 0.23/0.54 ( ( ord_less_eq_a @ A @ B )
% 0.23/0.54 => ( ( ( F @ B )
% 0.23/0.54 = C )
% 0.23/0.54 => ( ! [X4: a,Y2: a] :
% 0.23/0.54 ( ( ord_less_eq_a @ X4 @ Y2 )
% 0.23/0.54 => ( ord_less_eq_o_a @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.23/0.54 => ( ord_less_eq_o_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % ord_le_eq_subst
% 0.23/0.54 thf(fact_55_ord__le__eq__subst,axiom,
% 0.23/0.54 ! [A: $o > a,B: $o > a,F: ( $o > a ) > a,C: a] :
% 0.23/0.54 ( ( ord_less_eq_o_a @ A @ B )
% 0.23/0.54 => ( ( ( F @ B )
% 0.23/0.54 = C )
% 0.23/0.54 => ( ! [X4: $o > a,Y2: $o > a] :
% 0.23/0.54 ( ( ord_less_eq_o_a @ X4 @ Y2 )
% 0.23/0.54 => ( ord_less_eq_a @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.23/0.54 => ( ord_less_eq_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % ord_le_eq_subst
% 0.23/0.54 thf(fact_56_ord__le__eq__subst,axiom,
% 0.23/0.54 ! [A: $o > a,B: $o > a,F: ( $o > a ) > $o > a,C: $o > a] :
% 0.23/0.54 ( ( ord_less_eq_o_a @ A @ B )
% 0.23/0.54 => ( ( ( F @ B )
% 0.23/0.54 = C )
% 0.23/0.54 => ( ! [X4: $o > a,Y2: $o > a] :
% 0.23/0.54 ( ( ord_less_eq_o_a @ X4 @ Y2 )
% 0.23/0.54 => ( ord_less_eq_o_a @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.23/0.54 => ( ord_less_eq_o_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % ord_le_eq_subst
% 0.23/0.54 thf(fact_57_ord__le__eq__subst,axiom,
% 0.23/0.54 ! [A: a,B: a,F: a > a,C: a] :
% 0.23/0.54 ( ( ord_less_eq_a @ A @ B )
% 0.23/0.54 => ( ( ( F @ B )
% 0.23/0.54 = C )
% 0.23/0.54 => ( ! [X4: a,Y2: a] :
% 0.23/0.54 ( ( ord_less_eq_a @ X4 @ Y2 )
% 0.23/0.54 => ( ord_less_eq_a @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.23/0.54 => ( ord_less_eq_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % ord_le_eq_subst
% 0.23/0.54 thf(fact_58_mem__Collect__eq,axiom,
% 0.23/0.54 ! [A: a,P: a > $o] :
% 0.23/0.54 ( ( member_a @ A @ ( collect_a @ P ) )
% 0.23/0.54 = ( P @ A ) ) ).
% 0.23/0.54
% 0.23/0.54 % mem_Collect_eq
% 0.23/0.54 thf(fact_59_Collect__mem__eq,axiom,
% 0.23/0.54 ! [A2: set_a] :
% 0.23/0.54 ( ( collect_a
% 0.23/0.54 @ ^ [X5: a] : ( member_a @ X5 @ A2 ) )
% 0.23/0.54 = A2 ) ).
% 0.23/0.54
% 0.23/0.54 % Collect_mem_eq
% 0.23/0.54 thf(fact_60_dual__order_Oantisym,axiom,
% 0.23/0.54 ! [B: $o > a,A: $o > a] :
% 0.23/0.54 ( ( ord_less_eq_o_a @ B @ A )
% 0.23/0.54 => ( ( ord_less_eq_o_a @ A @ B )
% 0.23/0.54 => ( A = B ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % dual_order.antisym
% 0.23/0.54 thf(fact_61_dual__order_Oantisym,axiom,
% 0.23/0.54 ! [B: a,A: a] :
% 0.23/0.54 ( ( ord_less_eq_a @ B @ A )
% 0.23/0.54 => ( ( ord_less_eq_a @ A @ B )
% 0.23/0.54 => ( A = B ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % dual_order.antisym
% 0.23/0.54 thf(fact_62_dual__order_Oeq__iff,axiom,
% 0.23/0.54 ( ( ^ [Y3: $o > a,Z: $o > a] : ( Y3 = Z ) )
% 0.23/0.54 = ( ^ [A3: $o > a,B2: $o > a] :
% 0.23/0.54 ( ( ord_less_eq_o_a @ B2 @ A3 )
% 0.23/0.54 & ( ord_less_eq_o_a @ A3 @ B2 ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % dual_order.eq_iff
% 0.23/0.54 thf(fact_63_dual__order_Oeq__iff,axiom,
% 0.23/0.54 ( ( ^ [Y3: a,Z: a] : ( Y3 = Z ) )
% 0.23/0.54 = ( ^ [A3: a,B2: a] :
% 0.23/0.54 ( ( ord_less_eq_a @ B2 @ A3 )
% 0.23/0.54 & ( ord_less_eq_a @ A3 @ B2 ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % dual_order.eq_iff
% 0.23/0.54 thf(fact_64_dual__order_Otrans,axiom,
% 0.23/0.54 ! [B: $o > a,A: $o > a,C: $o > a] :
% 0.23/0.54 ( ( ord_less_eq_o_a @ B @ A )
% 0.23/0.54 => ( ( ord_less_eq_o_a @ C @ B )
% 0.23/0.54 => ( ord_less_eq_o_a @ C @ A ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % dual_order.trans
% 0.23/0.54 thf(fact_65_dual__order_Otrans,axiom,
% 0.23/0.54 ! [B: a,A: a,C: a] :
% 0.23/0.54 ( ( ord_less_eq_a @ B @ A )
% 0.23/0.54 => ( ( ord_less_eq_a @ C @ B )
% 0.23/0.54 => ( ord_less_eq_a @ C @ A ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % dual_order.trans
% 0.23/0.54 thf(fact_66_linorder__wlog,axiom,
% 0.23/0.54 ! [P: a > a > $o,A: a,B: a] :
% 0.23/0.54 ( ! [A4: a,B3: a] :
% 0.23/0.54 ( ( ord_less_eq_a @ A4 @ B3 )
% 0.23/0.54 => ( P @ A4 @ B3 ) )
% 0.23/0.54 => ( ! [A4: a,B3: a] :
% 0.23/0.54 ( ( P @ B3 @ A4 )
% 0.23/0.54 => ( P @ A4 @ B3 ) )
% 0.23/0.54 => ( P @ A @ B ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % linorder_wlog
% 0.23/0.54 thf(fact_67_dual__order_Orefl,axiom,
% 0.23/0.54 ! [A: $o > a] : ( ord_less_eq_o_a @ A @ A ) ).
% 0.23/0.54
% 0.23/0.54 % dual_order.refl
% 0.23/0.54 thf(fact_68_dual__order_Orefl,axiom,
% 0.23/0.54 ! [A: a] : ( ord_less_eq_a @ A @ A ) ).
% 0.23/0.54
% 0.23/0.54 % dual_order.refl
% 0.23/0.54 thf(fact_69_order__trans,axiom,
% 0.23/0.54 ! [X: $o > a,Y: $o > a,Z2: $o > a] :
% 0.23/0.54 ( ( ord_less_eq_o_a @ X @ Y )
% 0.23/0.54 => ( ( ord_less_eq_o_a @ Y @ Z2 )
% 0.23/0.54 => ( ord_less_eq_o_a @ X @ Z2 ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % order_trans
% 0.23/0.54 thf(fact_70_order__trans,axiom,
% 0.23/0.54 ! [X: a,Y: a,Z2: a] :
% 0.23/0.54 ( ( ord_less_eq_a @ X @ Y )
% 0.23/0.54 => ( ( ord_less_eq_a @ Y @ Z2 )
% 0.23/0.54 => ( ord_less_eq_a @ X @ Z2 ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % order_trans
% 0.23/0.54 thf(fact_71_order__class_Oorder_Oantisym,axiom,
% 0.23/0.54 ! [A: $o > a,B: $o > a] :
% 0.23/0.54 ( ( ord_less_eq_o_a @ A @ B )
% 0.23/0.54 => ( ( ord_less_eq_o_a @ B @ A )
% 0.23/0.54 => ( A = B ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % order_class.order.antisym
% 0.23/0.54 thf(fact_72_order__class_Oorder_Oantisym,axiom,
% 0.23/0.54 ! [A: a,B: a] :
% 0.23/0.54 ( ( ord_less_eq_a @ A @ B )
% 0.23/0.54 => ( ( ord_less_eq_a @ B @ A )
% 0.23/0.54 => ( A = B ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % order_class.order.antisym
% 0.23/0.54 thf(fact_73_ord__le__eq__trans,axiom,
% 0.23/0.54 ! [A: $o > a,B: $o > a,C: $o > a] :
% 0.23/0.54 ( ( ord_less_eq_o_a @ A @ B )
% 0.23/0.54 => ( ( B = C )
% 0.23/0.54 => ( ord_less_eq_o_a @ A @ C ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % ord_le_eq_trans
% 0.23/0.54 thf(fact_74_ord__le__eq__trans,axiom,
% 0.23/0.54 ! [A: a,B: a,C: a] :
% 0.23/0.54 ( ( ord_less_eq_a @ A @ B )
% 0.23/0.54 => ( ( B = C )
% 0.23/0.54 => ( ord_less_eq_a @ A @ C ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % ord_le_eq_trans
% 0.23/0.54 thf(fact_75_ord__eq__le__trans,axiom,
% 0.23/0.54 ! [A: $o > a,B: $o > a,C: $o > a] :
% 0.23/0.54 ( ( A = B )
% 0.23/0.54 => ( ( ord_less_eq_o_a @ B @ C )
% 0.23/0.54 => ( ord_less_eq_o_a @ A @ C ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % ord_eq_le_trans
% 0.23/0.54 thf(fact_76_ord__eq__le__trans,axiom,
% 0.23/0.54 ! [A: a,B: a,C: a] :
% 0.23/0.54 ( ( A = B )
% 0.23/0.54 => ( ( ord_less_eq_a @ B @ C )
% 0.23/0.54 => ( ord_less_eq_a @ A @ C ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % ord_eq_le_trans
% 0.23/0.54 thf(fact_77_order__class_Oorder_Oeq__iff,axiom,
% 0.23/0.54 ( ( ^ [Y3: $o > a,Z: $o > a] : ( Y3 = Z ) )
% 0.23/0.54 = ( ^ [A3: $o > a,B2: $o > a] :
% 0.23/0.54 ( ( ord_less_eq_o_a @ A3 @ B2 )
% 0.23/0.54 & ( ord_less_eq_o_a @ B2 @ A3 ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % order_class.order.eq_iff
% 0.23/0.54 thf(fact_78_order__class_Oorder_Oeq__iff,axiom,
% 0.23/0.54 ( ( ^ [Y3: a,Z: a] : ( Y3 = Z ) )
% 0.23/0.54 = ( ^ [A3: a,B2: a] :
% 0.23/0.54 ( ( ord_less_eq_a @ A3 @ B2 )
% 0.23/0.54 & ( ord_less_eq_a @ B2 @ A3 ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % order_class.order.eq_iff
% 0.23/0.54 thf(fact_79_antisym__conv,axiom,
% 0.23/0.54 ! [Y: $o > a,X: $o > a] :
% 0.23/0.54 ( ( ord_less_eq_o_a @ Y @ X )
% 0.23/0.54 => ( ( ord_less_eq_o_a @ X @ Y )
% 0.23/0.54 = ( X = Y ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % antisym_conv
% 0.23/0.54 thf(fact_80_antisym__conv,axiom,
% 0.23/0.54 ! [Y: a,X: a] :
% 0.23/0.54 ( ( ord_less_eq_a @ Y @ X )
% 0.23/0.54 => ( ( ord_less_eq_a @ X @ Y )
% 0.23/0.54 = ( X = Y ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % antisym_conv
% 0.23/0.54 thf(fact_81_le__cases3,axiom,
% 0.23/0.54 ! [X: a,Y: a,Z2: a] :
% 0.23/0.54 ( ( ( ord_less_eq_a @ X @ Y )
% 0.23/0.54 => ~ ( ord_less_eq_a @ Y @ Z2 ) )
% 0.23/0.54 => ( ( ( ord_less_eq_a @ Y @ X )
% 0.23/0.54 => ~ ( ord_less_eq_a @ X @ Z2 ) )
% 0.23/0.54 => ( ( ( ord_less_eq_a @ X @ Z2 )
% 0.23/0.54 => ~ ( ord_less_eq_a @ Z2 @ Y ) )
% 0.23/0.54 => ( ( ( ord_less_eq_a @ Z2 @ Y )
% 0.23/0.54 => ~ ( ord_less_eq_a @ Y @ X ) )
% 0.23/0.54 => ( ( ( ord_less_eq_a @ Y @ Z2 )
% 0.23/0.54 => ~ ( ord_less_eq_a @ Z2 @ X ) )
% 0.23/0.54 => ~ ( ( ord_less_eq_a @ Z2 @ X )
% 0.23/0.54 => ~ ( ord_less_eq_a @ X @ Y ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % le_cases3
% 0.23/0.54 thf(fact_82_order_Otrans,axiom,
% 0.23/0.54 ! [A: $o > a,B: $o > a,C: $o > a] :
% 0.23/0.54 ( ( ord_less_eq_o_a @ A @ B )
% 0.23/0.54 => ( ( ord_less_eq_o_a @ B @ C )
% 0.23/0.54 => ( ord_less_eq_o_a @ A @ C ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % order.trans
% 0.23/0.54 thf(fact_83_order_Otrans,axiom,
% 0.23/0.54 ! [A: a,B: a,C: a] :
% 0.23/0.54 ( ( ord_less_eq_a @ A @ B )
% 0.23/0.54 => ( ( ord_less_eq_a @ B @ C )
% 0.23/0.54 => ( ord_less_eq_a @ A @ C ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % order.trans
% 0.23/0.54 thf(fact_84_le__cases,axiom,
% 0.23/0.54 ! [X: a,Y: a] :
% 0.23/0.54 ( ~ ( ord_less_eq_a @ X @ Y )
% 0.23/0.54 => ( ord_less_eq_a @ Y @ X ) ) ).
% 0.23/0.54
% 0.23/0.54 % le_cases
% 0.23/0.54 thf(fact_85_eq__refl,axiom,
% 0.23/0.54 ! [X: $o > a,Y: $o > a] :
% 0.23/0.54 ( ( X = Y )
% 0.23/0.54 => ( ord_less_eq_o_a @ X @ Y ) ) ).
% 0.23/0.54
% 0.23/0.54 % eq_refl
% 0.23/0.54 thf(fact_86_eq__refl,axiom,
% 0.23/0.54 ! [X: a,Y: a] :
% 0.23/0.54 ( ( X = Y )
% 0.23/0.54 => ( ord_less_eq_a @ X @ Y ) ) ).
% 0.23/0.54
% 0.23/0.54 % eq_refl
% 0.23/0.54 thf(fact_87_linear,axiom,
% 0.23/0.54 ! [X: a,Y: a] :
% 0.23/0.54 ( ( ord_less_eq_a @ X @ Y )
% 0.23/0.54 | ( ord_less_eq_a @ Y @ X ) ) ).
% 0.23/0.54
% 0.23/0.54 % linear
% 0.23/0.54 thf(fact_88_antisym,axiom,
% 0.23/0.54 ! [X: $o > a,Y: $o > a] :
% 0.23/0.54 ( ( ord_less_eq_o_a @ X @ Y )
% 0.23/0.54 => ( ( ord_less_eq_o_a @ Y @ X )
% 0.23/0.54 => ( X = Y ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % antisym
% 0.23/0.54 thf(fact_89_antisym,axiom,
% 0.23/0.54 ! [X: a,Y: a] :
% 0.23/0.54 ( ( ord_less_eq_a @ X @ Y )
% 0.23/0.54 => ( ( ord_less_eq_a @ Y @ X )
% 0.23/0.54 => ( X = Y ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % antisym
% 0.23/0.54 thf(fact_90_eq__iff,axiom,
% 0.23/0.54 ( ( ^ [Y3: $o > a,Z: $o > a] : ( Y3 = Z ) )
% 0.23/0.54 = ( ^ [X5: $o > a,Y4: $o > a] :
% 0.23/0.54 ( ( ord_less_eq_o_a @ X5 @ Y4 )
% 0.23/0.54 & ( ord_less_eq_o_a @ Y4 @ X5 ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % eq_iff
% 0.23/0.54 thf(fact_91_eq__iff,axiom,
% 0.23/0.54 ( ( ^ [Y3: a,Z: a] : ( Y3 = Z ) )
% 0.23/0.54 = ( ^ [X5: a,Y4: a] :
% 0.23/0.54 ( ( ord_less_eq_a @ X5 @ Y4 )
% 0.23/0.54 & ( ord_less_eq_a @ Y4 @ X5 ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % eq_iff
% 0.23/0.54 thf(fact_92_Greatest__equality,axiom,
% 0.23/0.54 ! [P: ( $o > a ) > $o,X: $o > a] :
% 0.23/0.54 ( ( P @ X )
% 0.23/0.54 => ( ! [Y2: $o > a] :
% 0.23/0.54 ( ( P @ Y2 )
% 0.23/0.54 => ( ord_less_eq_o_a @ Y2 @ X ) )
% 0.23/0.54 => ( ( order_Greatest_o_a @ P )
% 0.23/0.54 = X ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % Greatest_equality
% 0.23/0.54 thf(fact_93_Greatest__equality,axiom,
% 0.23/0.54 ! [P: a > $o,X: a] :
% 0.23/0.54 ( ( P @ X )
% 0.23/0.54 => ( ! [Y2: a] :
% 0.23/0.54 ( ( P @ Y2 )
% 0.23/0.54 => ( ord_less_eq_a @ Y2 @ X ) )
% 0.23/0.54 => ( ( order_Greatest_a @ P )
% 0.23/0.54 = X ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % Greatest_equality
% 0.23/0.54 thf(fact_94_GreatestI2__order,axiom,
% 0.23/0.54 ! [P: ( $o > a ) > $o,X: $o > a,Q: ( $o > a ) > $o] :
% 0.23/0.54 ( ( P @ X )
% 0.23/0.54 => ( ! [Y2: $o > a] :
% 0.23/0.54 ( ( P @ Y2 )
% 0.23/0.54 => ( ord_less_eq_o_a @ Y2 @ X ) )
% 0.23/0.54 => ( ! [X4: $o > a] :
% 0.23/0.54 ( ( P @ X4 )
% 0.23/0.54 => ( ! [Y5: $o > a] :
% 0.23/0.54 ( ( P @ Y5 )
% 0.23/0.54 => ( ord_less_eq_o_a @ Y5 @ X4 ) )
% 0.23/0.54 => ( Q @ X4 ) ) )
% 0.23/0.54 => ( Q @ ( order_Greatest_o_a @ P ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % GreatestI2_order
% 0.23/0.54 thf(fact_95_GreatestI2__order,axiom,
% 0.23/0.54 ! [P: a > $o,X: a,Q: a > $o] :
% 0.23/0.54 ( ( P @ X )
% 0.23/0.54 => ( ! [Y2: a] :
% 0.23/0.54 ( ( P @ Y2 )
% 0.23/0.54 => ( ord_less_eq_a @ Y2 @ X ) )
% 0.23/0.54 => ( ! [X4: a] :
% 0.23/0.54 ( ( P @ X4 )
% 0.23/0.54 => ( ! [Y5: a] :
% 0.23/0.54 ( ( P @ Y5 )
% 0.23/0.54 => ( ord_less_eq_a @ Y5 @ X4 ) )
% 0.23/0.54 => ( Q @ X4 ) ) )
% 0.23/0.54 => ( Q @ ( order_Greatest_a @ P ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % GreatestI2_order
% 0.23/0.54 thf(fact_96_le__rel__bool__arg__iff,axiom,
% 0.23/0.54 ( ord_less_eq_o_o_a
% 0.23/0.54 = ( ^ [X6: $o > $o > a,Y6: $o > $o > a] :
% 0.23/0.54 ( ( ord_less_eq_o_a @ ( X6 @ $false ) @ ( Y6 @ $false ) )
% 0.23/0.54 & ( ord_less_eq_o_a @ ( X6 @ $true ) @ ( Y6 @ $true ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % le_rel_bool_arg_iff
% 0.23/0.54 thf(fact_97_le__rel__bool__arg__iff,axiom,
% 0.23/0.54 ( ord_less_eq_o_a
% 0.23/0.54 = ( ^ [X6: $o > a,Y6: $o > a] :
% 0.23/0.54 ( ( ord_less_eq_a @ ( X6 @ $false ) @ ( Y6 @ $false ) )
% 0.23/0.54 & ( ord_less_eq_a @ ( X6 @ $true ) @ ( Y6 @ $true ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % le_rel_bool_arg_iff
% 0.23/0.54 thf(fact_98_Tree_Orel__induct,axiom,
% 0.23/0.54 ! [R3: a > a > $o,X: tree_a,Y: tree_a,Q: tree_a > tree_a > $o] :
% 0.23/0.54 ( ( rel_Tree_a_a @ R3 @ X @ Y )
% 0.23/0.54 => ( ( Q @ e_a @ e_a )
% 0.23/0.54 => ( ! [A21: a,A22: tree_a,A23: tree_a,B21: a,B22: tree_a,B23: tree_a] :
% 0.23/0.54 ( ( R3 @ A21 @ B21 )
% 0.23/0.54 => ( ( Q @ A22 @ B22 )
% 0.23/0.54 => ( ( Q @ A23 @ B23 )
% 0.23/0.54 => ( Q @ ( t_a @ A21 @ A22 @ A23 ) @ ( t_a @ B21 @ B22 @ B23 ) ) ) ) )
% 0.23/0.54 => ( Q @ X @ Y ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % Tree.rel_induct
% 0.23/0.54 thf(fact_99_Tree_Orel__mono,axiom,
% 0.23/0.54 ! [R3: a > a > $o,Ra: a > a > $o] :
% 0.23/0.54 ( ( ord_less_eq_a_a_o @ R3 @ Ra )
% 0.23/0.54 => ( ord_le1530450702ee_a_o @ ( rel_Tree_a_a @ R3 ) @ ( rel_Tree_a_a @ Ra ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % Tree.rel_mono
% 0.23/0.54 thf(fact_100_Tree_Orel__eq,axiom,
% 0.23/0.54 ( ( rel_Tree_a_a
% 0.23/0.54 @ ^ [Y3: a,Z: a] : ( Y3 = Z ) )
% 0.23/0.54 = ( ^ [Y3: tree_a,Z: tree_a] : ( Y3 = Z ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % Tree.rel_eq
% 0.23/0.54 thf(fact_101_Tree_Orel__refl,axiom,
% 0.23/0.54 ! [Ra: a > a > $o,X: tree_a] :
% 0.23/0.54 ( ! [X4: a] : ( Ra @ X4 @ X4 )
% 0.23/0.54 => ( rel_Tree_a_a @ Ra @ X @ X ) ) ).
% 0.23/0.54
% 0.23/0.54 % Tree.rel_refl
% 0.23/0.54 thf(fact_102_Tree_Orel__inject_I2_J,axiom,
% 0.23/0.54 ! [R3: a > a > $o,X21: a,X22: tree_a,X23: tree_a,Y21: a,Y22: tree_a,Y23: tree_a] :
% 0.23/0.54 ( ( rel_Tree_a_a @ R3 @ ( t_a @ X21 @ X22 @ X23 ) @ ( t_a @ Y21 @ Y22 @ Y23 ) )
% 0.23/0.54 = ( ( R3 @ X21 @ Y21 )
% 0.23/0.54 & ( rel_Tree_a_a @ R3 @ X22 @ Y22 )
% 0.23/0.54 & ( rel_Tree_a_a @ R3 @ X23 @ Y23 ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % Tree.rel_inject(2)
% 0.23/0.54 thf(fact_103_Tree_Orel__intros_I2_J,axiom,
% 0.23/0.54 ! [R3: a > a > $o,X21: a,Y21: a,X22: tree_a,Y22: tree_a,X23: tree_a,Y23: tree_a] :
% 0.23/0.54 ( ( R3 @ X21 @ Y21 )
% 0.23/0.54 => ( ( rel_Tree_a_a @ R3 @ X22 @ Y22 )
% 0.23/0.54 => ( ( rel_Tree_a_a @ R3 @ X23 @ Y23 )
% 0.23/0.54 => ( rel_Tree_a_a @ R3 @ ( t_a @ X21 @ X22 @ X23 ) @ ( t_a @ Y21 @ Y22 @ Y23 ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % Tree.rel_intros(2)
% 0.23/0.54 thf(fact_104_Tree_Octr__transfer_I1_J,axiom,
% 0.23/0.54 ! [R3: a > a > $o] : ( rel_Tree_a_a @ R3 @ e_a @ e_a ) ).
% 0.23/0.54
% 0.23/0.54 % Tree.ctr_transfer(1)
% 0.23/0.54 thf(fact_105_Tree_Orel__distinct_I2_J,axiom,
% 0.23/0.54 ! [R3: a > a > $o,Y21: a,Y22: tree_a,Y23: tree_a] :
% 0.23/0.54 ~ ( rel_Tree_a_a @ R3 @ ( t_a @ Y21 @ Y22 @ Y23 ) @ e_a ) ).
% 0.23/0.54
% 0.23/0.54 % Tree.rel_distinct(2)
% 0.23/0.54 thf(fact_106_Tree_Orel__distinct_I1_J,axiom,
% 0.23/0.54 ! [R3: a > a > $o,Y21: a,Y22: tree_a,Y23: tree_a] :
% 0.23/0.54 ~ ( rel_Tree_a_a @ R3 @ e_a @ ( t_a @ Y21 @ Y22 @ Y23 ) ) ).
% 0.23/0.54
% 0.23/0.54 % Tree.rel_distinct(1)
% 0.23/0.54 thf(fact_107_Tree_Orel__cases,axiom,
% 0.23/0.54 ! [R3: a > a > $o,A: tree_a,B: tree_a] :
% 0.23/0.54 ( ( rel_Tree_a_a @ R3 @ A @ B )
% 0.23/0.54 => ( ( ( A = e_a )
% 0.23/0.54 => ( B != e_a ) )
% 0.23/0.54 => ~ ! [X1: a,X2: tree_a,X3: tree_a] :
% 0.23/0.54 ( ( A
% 0.23/0.54 = ( t_a @ X1 @ X2 @ X3 ) )
% 0.23/0.54 => ! [Y1: a,Y24: tree_a,Y32: tree_a] :
% 0.23/0.54 ( ( B
% 0.23/0.54 = ( t_a @ Y1 @ Y24 @ Y32 ) )
% 0.23/0.54 => ( ( R3 @ X1 @ Y1 )
% 0.23/0.54 => ( ( rel_Tree_a_a @ R3 @ X2 @ Y24 )
% 0.23/0.54 => ~ ( rel_Tree_a_a @ R3 @ X3 @ Y32 ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % Tree.rel_cases
% 0.23/0.54 thf(fact_108_heap__top__geq,axiom,
% 0.23/0.54 ! [A: a,T: tree_a] :
% 0.23/0.54 ( ( member_a @ A @ ( set_mset_a @ ( multiset_a2 @ T ) ) )
% 0.23/0.54 => ( ( is_heap_a @ T )
% 0.23/0.54 => ( ord_less_eq_a @ A @ ( val_a @ T ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % heap_top_geq
% 0.23/0.54 thf(fact_109_add__mset__add__mset__same__iff,axiom,
% 0.23/0.54 ! [A: a,A2: multiset_a,B4: multiset_a] :
% 0.23/0.54 ( ( ( add_mset_a @ A @ A2 )
% 0.23/0.54 = ( add_mset_a @ A @ B4 ) )
% 0.23/0.54 = ( A2 = B4 ) ) ).
% 0.23/0.54
% 0.23/0.54 % add_mset_add_mset_same_iff
% 0.23/0.54 thf(fact_110_multi__self__add__other__not__self,axiom,
% 0.23/0.54 ! [M: multiset_a,X: a] :
% 0.23/0.54 ( M
% 0.23/0.54 != ( add_mset_a @ X @ M ) ) ).
% 0.23/0.54
% 0.23/0.54 % multi_self_add_other_not_self
% 0.23/0.54 thf(fact_111_mset__add,axiom,
% 0.23/0.54 ! [A: a,A2: multiset_a] :
% 0.23/0.54 ( ( member_a @ A @ ( set_mset_a @ A2 ) )
% 0.23/0.54 => ~ ! [B5: multiset_a] :
% 0.23/0.54 ( A2
% 0.23/0.54 != ( add_mset_a @ A @ B5 ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % mset_add
% 0.23/0.54 thf(fact_112_multi__member__split,axiom,
% 0.23/0.54 ! [X: a,M: multiset_a] :
% 0.23/0.54 ( ( member_a @ X @ ( set_mset_a @ M ) )
% 0.23/0.54 => ? [A5: multiset_a] :
% 0.23/0.54 ( M
% 0.23/0.54 = ( add_mset_a @ X @ A5 ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % multi_member_split
% 0.23/0.54 thf(fact_113_add__mset__commute,axiom,
% 0.23/0.54 ! [X: a,Y: a,M: multiset_a] :
% 0.23/0.54 ( ( add_mset_a @ X @ ( add_mset_a @ Y @ M ) )
% 0.23/0.54 = ( add_mset_a @ Y @ ( add_mset_a @ X @ M ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % add_mset_commute
% 0.23/0.54 thf(fact_114_add__eq__conv__ex,axiom,
% 0.23/0.54 ! [A: a,M: multiset_a,B: a,N: multiset_a] :
% 0.23/0.54 ( ( ( add_mset_a @ A @ M )
% 0.23/0.54 = ( add_mset_a @ B @ N ) )
% 0.23/0.54 = ( ( ( M = N )
% 0.23/0.54 & ( A = B ) )
% 0.23/0.54 | ? [K: multiset_a] :
% 0.23/0.54 ( ( M
% 0.23/0.54 = ( add_mset_a @ B @ K ) )
% 0.23/0.54 & ( N
% 0.23/0.54 = ( add_mset_a @ A @ K ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % add_eq_conv_ex
% 0.23/0.54 thf(fact_115_union__single__eq__member,axiom,
% 0.23/0.54 ! [X: a,M: multiset_a,N: multiset_a] :
% 0.23/0.54 ( ( ( add_mset_a @ X @ M )
% 0.23/0.54 = N )
% 0.23/0.54 => ( member_a @ X @ ( set_mset_a @ N ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % union_single_eq_member
% 0.23/0.54 thf(fact_116_insert__noteq__member,axiom,
% 0.23/0.54 ! [B: a,B4: multiset_a,C: a,C2: multiset_a] :
% 0.23/0.54 ( ( ( add_mset_a @ B @ B4 )
% 0.23/0.54 = ( add_mset_a @ C @ C2 ) )
% 0.23/0.54 => ( ( B != C )
% 0.23/0.54 => ( member_a @ C @ ( set_mset_a @ B4 ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % insert_noteq_member
% 0.23/0.54 thf(fact_117_heap__top__max,axiom,
% 0.23/0.54 ! [T: tree_a] :
% 0.23/0.54 ( ( T != e_a )
% 0.23/0.54 => ( ( is_heap_a @ T )
% 0.23/0.54 => ( ( val_a @ T )
% 0.23/0.54 = ( lattic146396397_Max_a @ ( set_mset_a @ ( multiset_a2 @ T ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % heap_top_max
% 0.23/0.54 thf(fact_118_multiset__induct__max,axiom,
% 0.23/0.54 ! [P: multiset_a > $o,M: multiset_a] :
% 0.23/0.54 ( ( P @ zero_zero_multiset_a )
% 0.23/0.54 => ( ! [X4: a,M2: multiset_a] :
% 0.23/0.54 ( ( P @ M2 )
% 0.23/0.54 => ( ! [Xa: a] :
% 0.23/0.54 ( ( member_a @ Xa @ ( set_mset_a @ M2 ) )
% 0.23/0.54 => ( ord_less_eq_a @ Xa @ X4 ) )
% 0.23/0.54 => ( P @ ( add_mset_a @ X4 @ M2 ) ) ) )
% 0.23/0.54 => ( P @ M ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % multiset_induct_max
% 0.23/0.54 thf(fact_119_multiset__induct__min,axiom,
% 0.23/0.54 ! [P: multiset_a > $o,M: multiset_a] :
% 0.23/0.54 ( ( P @ zero_zero_multiset_a )
% 0.23/0.54 => ( ! [X4: a,M2: multiset_a] :
% 0.23/0.54 ( ( P @ M2 )
% 0.23/0.54 => ( ! [Xa: a] :
% 0.23/0.54 ( ( member_a @ Xa @ ( set_mset_a @ M2 ) )
% 0.23/0.54 => ( ord_less_eq_a @ X4 @ Xa ) )
% 0.23/0.54 => ( P @ ( add_mset_a @ X4 @ M2 ) ) ) )
% 0.23/0.54 => ( P @ M ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % multiset_induct_min
% 0.23/0.54 thf(fact_120_add__mset__eq__singleton__iff,axiom,
% 0.23/0.54 ! [X: a,M: multiset_a,Y: a] :
% 0.23/0.54 ( ( ( add_mset_a @ X @ M )
% 0.23/0.54 = ( add_mset_a @ Y @ zero_zero_multiset_a ) )
% 0.23/0.54 = ( ( M = zero_zero_multiset_a )
% 0.23/0.54 & ( X = Y ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % add_mset_eq_singleton_iff
% 0.23/0.54 thf(fact_121_single__eq__add__mset,axiom,
% 0.23/0.54 ! [A: a,B: a,M: multiset_a] :
% 0.23/0.54 ( ( ( add_mset_a @ A @ zero_zero_multiset_a )
% 0.23/0.54 = ( add_mset_a @ B @ M ) )
% 0.23/0.54 = ( ( B = A )
% 0.23/0.54 & ( M = zero_zero_multiset_a ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % single_eq_add_mset
% 0.23/0.54 thf(fact_122_add__mset__eq__single,axiom,
% 0.23/0.54 ! [B: a,M: multiset_a,A: a] :
% 0.23/0.54 ( ( ( add_mset_a @ B @ M )
% 0.23/0.54 = ( add_mset_a @ A @ zero_zero_multiset_a ) )
% 0.23/0.54 = ( ( B = A )
% 0.23/0.54 & ( M = zero_zero_multiset_a ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % add_mset_eq_single
% 0.23/0.54 thf(fact_123_single__eq__single,axiom,
% 0.23/0.54 ! [A: a,B: a] :
% 0.23/0.54 ( ( ( add_mset_a @ A @ zero_zero_multiset_a )
% 0.23/0.54 = ( add_mset_a @ B @ zero_zero_multiset_a ) )
% 0.23/0.54 = ( A = B ) ) ).
% 0.23/0.54
% 0.23/0.54 % single_eq_single
% 0.23/0.54 thf(fact_124_multiset__cases,axiom,
% 0.23/0.54 ! [M: multiset_a] :
% 0.23/0.54 ( ( M != zero_zero_multiset_a )
% 0.23/0.54 => ~ ! [X4: a,N2: multiset_a] :
% 0.23/0.54 ( M
% 0.23/0.54 != ( add_mset_a @ X4 @ N2 ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % multiset_cases
% 0.23/0.54 thf(fact_125_multiset__induct,axiom,
% 0.23/0.54 ! [P: multiset_a > $o,M: multiset_a] :
% 0.23/0.54 ( ( P @ zero_zero_multiset_a )
% 0.23/0.54 => ( ! [X4: a,M2: multiset_a] :
% 0.23/0.54 ( ( P @ M2 )
% 0.23/0.54 => ( P @ ( add_mset_a @ X4 @ M2 ) ) )
% 0.23/0.54 => ( P @ M ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % multiset_induct
% 0.23/0.54 thf(fact_126_multiset__induct2,axiom,
% 0.23/0.54 ! [P: multiset_a > multiset_a > $o,M: multiset_a,N: multiset_a] :
% 0.23/0.54 ( ( P @ zero_zero_multiset_a @ zero_zero_multiset_a )
% 0.23/0.54 => ( ! [A4: a,M2: multiset_a,N2: multiset_a] :
% 0.23/0.54 ( ( P @ M2 @ N2 )
% 0.23/0.54 => ( P @ ( add_mset_a @ A4 @ M2 ) @ N2 ) )
% 0.23/0.54 => ( ! [A4: a,M2: multiset_a,N2: multiset_a] :
% 0.23/0.54 ( ( P @ M2 @ N2 )
% 0.23/0.54 => ( P @ M2 @ ( add_mset_a @ A4 @ N2 ) ) )
% 0.23/0.54 => ( P @ M @ N ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % multiset_induct2
% 0.23/0.54 thf(fact_127_empty__not__add__mset,axiom,
% 0.23/0.54 ! [A: a,A2: multiset_a] :
% 0.23/0.54 ( zero_zero_multiset_a
% 0.23/0.54 != ( add_mset_a @ A @ A2 ) ) ).
% 0.23/0.54
% 0.23/0.54 % empty_not_add_mset
% 0.23/0.54 thf(fact_128_multiset__nonemptyE,axiom,
% 0.23/0.54 ! [A2: multiset_a] :
% 0.23/0.54 ( ( A2 != zero_zero_multiset_a )
% 0.23/0.54 => ~ ! [X4: a] :
% 0.23/0.54 ~ ( member_a @ X4 @ ( set_mset_a @ A2 ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % multiset_nonemptyE
% 0.23/0.54 thf(fact_129_multi__nonempty__split,axiom,
% 0.23/0.54 ! [M: multiset_a] :
% 0.23/0.54 ( ( M != zero_zero_multiset_a )
% 0.23/0.54 => ? [A5: multiset_a,A4: a] :
% 0.23/0.54 ( M
% 0.23/0.54 = ( add_mset_a @ A4 @ A5 ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % multi_nonempty_split
% 0.23/0.54 thf(fact_130_multi__member__last,axiom,
% 0.23/0.54 ! [X: a] : ( member_a @ X @ ( set_mset_a @ ( add_mset_a @ X @ zero_zero_multiset_a ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % multi_member_last
% 0.23/0.54 thf(fact_131_multiset_Osimps_I1_J,axiom,
% 0.23/0.54 ( ( multiset_a2 @ e_a )
% 0.23/0.54 = zero_zero_multiset_a ) ).
% 0.23/0.54
% 0.23/0.54 % multiset.simps(1)
% 0.23/0.54 thf(fact_132_multiset_Osimps_I2_J,axiom,
% 0.23/0.54 ! [V: a,L: tree_a,R: tree_a] :
% 0.23/0.54 ( ( multiset_a2 @ ( t_a @ V @ L @ R ) )
% 0.23/0.54 = ( plus_plus_multiset_a @ ( plus_plus_multiset_a @ ( multiset_a2 @ L ) @ ( add_mset_a @ V @ zero_zero_multiset_a ) ) @ ( multiset_a2 @ R ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % multiset.simps(2)
% 0.23/0.54 thf(fact_133_single__subset__iff,axiom,
% 0.23/0.54 ! [A: a,M: multiset_a] :
% 0.23/0.54 ( ( subseteq_mset_a @ ( add_mset_a @ A @ zero_zero_multiset_a ) @ M )
% 0.23/0.54 = ( member_a @ A @ ( set_mset_a @ M ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % single_subset_iff
% 0.23/0.54 thf(fact_134_union__mset__add__mset__left,axiom,
% 0.23/0.54 ! [A: a,A2: multiset_a,B4: multiset_a] :
% 0.23/0.54 ( ( plus_plus_multiset_a @ ( add_mset_a @ A @ A2 ) @ B4 )
% 0.23/0.54 = ( add_mset_a @ A @ ( plus_plus_multiset_a @ A2 @ B4 ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % union_mset_add_mset_left
% 0.23/0.54 thf(fact_135_union__mset__add__mset__right,axiom,
% 0.23/0.54 ! [A2: multiset_a,A: a,B4: multiset_a] :
% 0.23/0.54 ( ( plus_plus_multiset_a @ A2 @ ( add_mset_a @ A @ B4 ) )
% 0.23/0.54 = ( add_mset_a @ A @ ( plus_plus_multiset_a @ A2 @ B4 ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % union_mset_add_mset_right
% 0.23/0.54 thf(fact_136_add__mset__subseteq__single__iff,axiom,
% 0.23/0.54 ! [A: a,M: multiset_a,B: a] :
% 0.23/0.54 ( ( subseteq_mset_a @ ( add_mset_a @ A @ M ) @ ( add_mset_a @ B @ zero_zero_multiset_a ) )
% 0.23/0.54 = ( ( M = zero_zero_multiset_a )
% 0.23/0.54 & ( A = B ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % add_mset_subseteq_single_iff
% 0.23/0.54 thf(fact_137_verit__sum__simplify,axiom,
% 0.23/0.54 ! [A: multiset_a] :
% 0.23/0.54 ( ( plus_plus_multiset_a @ A @ zero_zero_multiset_a )
% 0.23/0.54 = A ) ).
% 0.23/0.54
% 0.23/0.54 % verit_sum_simplify
% 0.23/0.54 thf(fact_138_add__mono__thms__linordered__semiring_I3_J,axiom,
% 0.23/0.54 ! [I: multiset_a,J: multiset_a,K2: multiset_a,L: multiset_a] :
% 0.23/0.54 ( ( ( ord_le1199012836iset_a @ I @ J )
% 0.23/0.54 & ( K2 = L ) )
% 0.23/0.54 => ( ord_le1199012836iset_a @ ( plus_plus_multiset_a @ I @ K2 ) @ ( plus_plus_multiset_a @ J @ L ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % add_mono_thms_linordered_semiring(3)
% 0.23/0.54 thf(fact_139_add__mono__thms__linordered__semiring_I2_J,axiom,
% 0.23/0.54 ! [I: multiset_a,J: multiset_a,K2: multiset_a,L: multiset_a] :
% 0.23/0.54 ( ( ( I = J )
% 0.23/0.54 & ( ord_le1199012836iset_a @ K2 @ L ) )
% 0.23/0.54 => ( ord_le1199012836iset_a @ ( plus_plus_multiset_a @ I @ K2 ) @ ( plus_plus_multiset_a @ J @ L ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % add_mono_thms_linordered_semiring(2)
% 0.23/0.54 thf(fact_140_add__mono__thms__linordered__semiring_I1_J,axiom,
% 0.23/0.54 ! [I: multiset_a,J: multiset_a,K2: multiset_a,L: multiset_a] :
% 0.23/0.54 ( ( ( ord_le1199012836iset_a @ I @ J )
% 0.23/0.54 & ( ord_le1199012836iset_a @ K2 @ L ) )
% 0.23/0.54 => ( ord_le1199012836iset_a @ ( plus_plus_multiset_a @ I @ K2 ) @ ( plus_plus_multiset_a @ J @ L ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % add_mono_thms_linordered_semiring(1)
% 0.23/0.54 thf(fact_141_add__mono,axiom,
% 0.23/0.54 ! [A: multiset_a,B: multiset_a,C: multiset_a,D: multiset_a] :
% 0.23/0.54 ( ( ord_le1199012836iset_a @ A @ B )
% 0.23/0.54 => ( ( ord_le1199012836iset_a @ C @ D )
% 0.23/0.54 => ( ord_le1199012836iset_a @ ( plus_plus_multiset_a @ A @ C ) @ ( plus_plus_multiset_a @ B @ D ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % add_mono
% 0.23/0.54 thf(fact_142_add__left__mono,axiom,
% 0.23/0.54 ! [A: multiset_a,B: multiset_a,C: multiset_a] :
% 0.23/0.54 ( ( ord_le1199012836iset_a @ A @ B )
% 0.23/0.54 => ( ord_le1199012836iset_a @ ( plus_plus_multiset_a @ C @ A ) @ ( plus_plus_multiset_a @ C @ B ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % add_left_mono
% 0.23/0.54 thf(fact_143_add__right__mono,axiom,
% 0.23/0.54 ! [A: multiset_a,B: multiset_a,C: multiset_a] :
% 0.23/0.54 ( ( ord_le1199012836iset_a @ A @ B )
% 0.23/0.54 => ( ord_le1199012836iset_a @ ( plus_plus_multiset_a @ A @ C ) @ ( plus_plus_multiset_a @ B @ C ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % add_right_mono
% 0.23/0.54 thf(fact_144_union__iff,axiom,
% 0.23/0.54 ! [A: a,A2: multiset_a,B4: multiset_a] :
% 0.23/0.54 ( ( member_a @ A @ ( set_mset_a @ ( plus_plus_multiset_a @ A2 @ B4 ) ) )
% 0.23/0.54 = ( ( member_a @ A @ ( set_mset_a @ A2 ) )
% 0.23/0.54 | ( member_a @ A @ ( set_mset_a @ B4 ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % union_iff
% 0.23/0.54 thf(fact_145_mset__subset__eqD,axiom,
% 0.23/0.54 ! [A2: multiset_a,B4: multiset_a,X: a] :
% 0.23/0.54 ( ( subseteq_mset_a @ A2 @ B4 )
% 0.23/0.54 => ( ( member_a @ X @ ( set_mset_a @ A2 ) )
% 0.23/0.54 => ( member_a @ X @ ( set_mset_a @ B4 ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % mset_subset_eqD
% 0.23/0.54 thf(fact_146_mset__subset__eq__add__mset__cancel,axiom,
% 0.23/0.54 ! [A: a,A2: multiset_a,B4: multiset_a] :
% 0.23/0.54 ( ( subseteq_mset_a @ ( add_mset_a @ A @ A2 ) @ ( add_mset_a @ A @ B4 ) )
% 0.23/0.54 = ( subseteq_mset_a @ A2 @ B4 ) ) ).
% 0.23/0.54
% 0.23/0.54 % mset_subset_eq_add_mset_cancel
% 0.23/0.54 thf(fact_147_set__mset__mono,axiom,
% 0.23/0.54 ! [A2: multiset_a,B4: multiset_a] :
% 0.23/0.54 ( ( subseteq_mset_a @ A2 @ B4 )
% 0.23/0.54 => ( ord_less_eq_set_a @ ( set_mset_a @ A2 ) @ ( set_mset_a @ B4 ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % set_mset_mono
% 0.23/0.54 thf(fact_148_single__is__union,axiom,
% 0.23/0.54 ! [A: a,M: multiset_a,N: multiset_a] :
% 0.23/0.54 ( ( ( add_mset_a @ A @ zero_zero_multiset_a )
% 0.23/0.54 = ( plus_plus_multiset_a @ M @ N ) )
% 0.23/0.54 = ( ( ( ( add_mset_a @ A @ zero_zero_multiset_a )
% 0.23/0.54 = M )
% 0.23/0.54 & ( N = zero_zero_multiset_a ) )
% 0.23/0.54 | ( ( M = zero_zero_multiset_a )
% 0.23/0.54 & ( ( add_mset_a @ A @ zero_zero_multiset_a )
% 0.23/0.54 = N ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % single_is_union
% 0.23/0.54 thf(fact_149_union__is__single,axiom,
% 0.23/0.54 ! [M: multiset_a,N: multiset_a,A: a] :
% 0.23/0.54 ( ( ( plus_plus_multiset_a @ M @ N )
% 0.23/0.54 = ( add_mset_a @ A @ zero_zero_multiset_a ) )
% 0.23/0.54 = ( ( ( M
% 0.23/0.54 = ( add_mset_a @ A @ zero_zero_multiset_a ) )
% 0.23/0.54 & ( N = zero_zero_multiset_a ) )
% 0.23/0.54 | ( ( M = zero_zero_multiset_a )
% 0.23/0.54 & ( N
% 0.23/0.54 = ( add_mset_a @ A @ zero_zero_multiset_a ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % union_is_single
% 0.23/0.54 thf(fact_150_add__mset__add__single,axiom,
% 0.23/0.54 ( add_mset_a
% 0.23/0.54 = ( ^ [A3: a,A6: multiset_a] : ( plus_plus_multiset_a @ A6 @ ( add_mset_a @ A3 @ zero_zero_multiset_a ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % add_mset_add_single
% 0.23/0.54 thf(fact_151_multi__subset__induct,axiom,
% 0.23/0.54 ! [F3: multiset_a,A2: multiset_a,P: multiset_a > $o] :
% 0.23/0.54 ( ( subseteq_mset_a @ F3 @ A2 )
% 0.23/0.54 => ( ( P @ zero_zero_multiset_a )
% 0.23/0.54 => ( ! [A4: a,F4: multiset_a] :
% 0.23/0.54 ( ( member_a @ A4 @ ( set_mset_a @ A2 ) )
% 0.23/0.54 => ( ( P @ F4 )
% 0.23/0.54 => ( P @ ( add_mset_a @ A4 @ F4 ) ) ) )
% 0.23/0.54 => ( P @ F3 ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % multi_subset_induct
% 0.23/0.54 thf(fact_152_mset__subset__eq__single,axiom,
% 0.23/0.54 ! [A: a,B4: multiset_a] :
% 0.23/0.54 ( ( member_a @ A @ ( set_mset_a @ B4 ) )
% 0.23/0.54 => ( subseteq_mset_a @ ( add_mset_a @ A @ zero_zero_multiset_a ) @ B4 ) ) ).
% 0.23/0.54
% 0.23/0.54 % mset_subset_eq_single
% 0.23/0.54 thf(fact_153_multi__member__skip,axiom,
% 0.23/0.54 ! [X: a,XS: multiset_a,Y: a] :
% 0.23/0.54 ( ( member_a @ X @ ( set_mset_a @ XS ) )
% 0.23/0.54 => ( member_a @ X @ ( set_mset_a @ ( plus_plus_multiset_a @ ( add_mset_a @ Y @ zero_zero_multiset_a ) @ XS ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % multi_member_skip
% 0.23/0.54 thf(fact_154_multi__member__this,axiom,
% 0.23/0.54 ! [X: a,XS: multiset_a] : ( member_a @ X @ ( set_mset_a @ ( plus_plus_multiset_a @ ( add_mset_a @ X @ zero_zero_multiset_a ) @ XS ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % multi_member_this
% 0.23/0.54 thf(fact_155_mult1E,axiom,
% 0.23/0.54 ! [N: multiset_a,M: multiset_a,R: set_Product_prod_a_a] :
% 0.23/0.54 ( ( member340150864iset_a @ ( produc2037245207iset_a @ N @ M ) @ ( mult1_a @ R ) )
% 0.23/0.54 => ~ ! [A4: a,M0: multiset_a] :
% 0.23/0.54 ( ( M
% 0.23/0.54 = ( add_mset_a @ A4 @ M0 ) )
% 0.23/0.54 => ! [K3: multiset_a] :
% 0.23/0.54 ( ( N
% 0.23/0.54 = ( plus_plus_multiset_a @ M0 @ K3 ) )
% 0.23/0.54 => ~ ! [B6: a] :
% 0.23/0.54 ( ( member_a @ B6 @ ( set_mset_a @ K3 ) )
% 0.23/0.54 => ( member449909584od_a_a @ ( product_Pair_a_a @ B6 @ A4 ) @ R ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % mult1E
% 0.23/0.54 thf(fact_156_mult1I,axiom,
% 0.23/0.54 ! [M: multiset_a,A: a,M02: multiset_a,N: multiset_a,K4: multiset_a,R: set_Product_prod_a_a] :
% 0.23/0.54 ( ( M
% 0.23/0.54 = ( add_mset_a @ A @ M02 ) )
% 0.23/0.54 => ( ( N
% 0.23/0.54 = ( plus_plus_multiset_a @ M02 @ K4 ) )
% 0.23/0.54 => ( ! [B3: a] :
% 0.23/0.54 ( ( member_a @ B3 @ ( set_mset_a @ K4 ) )
% 0.23/0.54 => ( member449909584od_a_a @ ( product_Pair_a_a @ B3 @ A ) @ R ) )
% 0.23/0.54 => ( member340150864iset_a @ ( produc2037245207iset_a @ N @ M ) @ ( mult1_a @ R ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % mult1I
% 0.23/0.54 thf(fact_157_less__add,axiom,
% 0.23/0.54 ! [N: multiset_a,A: a,M02: multiset_a,R: set_Product_prod_a_a] :
% 0.23/0.54 ( ( member340150864iset_a @ ( produc2037245207iset_a @ N @ ( add_mset_a @ A @ M02 ) ) @ ( mult1_a @ R ) )
% 0.23/0.54 => ( ? [M2: multiset_a] :
% 0.23/0.54 ( ( member340150864iset_a @ ( produc2037245207iset_a @ M2 @ M02 ) @ ( mult1_a @ R ) )
% 0.23/0.54 & ( N
% 0.23/0.54 = ( add_mset_a @ A @ M2 ) ) )
% 0.23/0.54 | ? [K3: multiset_a] :
% 0.23/0.54 ( ! [B6: a] :
% 0.23/0.54 ( ( member_a @ B6 @ ( set_mset_a @ K3 ) )
% 0.23/0.54 => ( member449909584od_a_a @ ( product_Pair_a_a @ B6 @ A ) @ R ) )
% 0.23/0.54 & ( N
% 0.23/0.54 = ( plus_plus_multiset_a @ M02 @ K3 ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % less_add
% 0.23/0.54 thf(fact_158_subsetI,axiom,
% 0.23/0.54 ! [A2: set_a,B4: set_a] :
% 0.23/0.54 ( ! [X4: a] :
% 0.23/0.54 ( ( member_a @ X4 @ A2 )
% 0.23/0.54 => ( member_a @ X4 @ B4 ) )
% 0.23/0.54 => ( ord_less_eq_set_a @ A2 @ B4 ) ) ).
% 0.23/0.54
% 0.23/0.54 % subsetI
% 0.23/0.54 thf(fact_159_in__mono,axiom,
% 0.23/0.54 ! [A2: set_a,B4: set_a,X: a] :
% 0.23/0.54 ( ( ord_less_eq_set_a @ A2 @ B4 )
% 0.23/0.54 => ( ( member_a @ X @ A2 )
% 0.23/0.54 => ( member_a @ X @ B4 ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % in_mono
% 0.23/0.54 thf(fact_160_subsetD,axiom,
% 0.23/0.54 ! [A2: set_a,B4: set_a,C: a] :
% 0.23/0.54 ( ( ord_less_eq_set_a @ A2 @ B4 )
% 0.23/0.54 => ( ( member_a @ C @ A2 )
% 0.23/0.54 => ( member_a @ C @ B4 ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % subsetD
% 0.23/0.54 thf(fact_161_subset__eq,axiom,
% 0.23/0.54 ( ord_less_eq_set_a
% 0.23/0.54 = ( ^ [A6: set_a,B7: set_a] :
% 0.23/0.54 ! [X5: a] :
% 0.23/0.54 ( ( member_a @ X5 @ A6 )
% 0.23/0.54 => ( member_a @ X5 @ B7 ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % subset_eq
% 0.23/0.54 thf(fact_162_subset__iff,axiom,
% 0.23/0.54 ( ord_less_eq_set_a
% 0.23/0.54 = ( ^ [A6: set_a,B7: set_a] :
% 0.23/0.54 ! [T2: a] :
% 0.23/0.54 ( ( member_a @ T2 @ A6 )
% 0.23/0.54 => ( member_a @ T2 @ B7 ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % subset_iff
% 0.23/0.54 thf(fact_163_one__step__implies__mult,axiom,
% 0.23/0.54 ! [J2: multiset_a,K4: multiset_a,R: set_Product_prod_a_a,I2: multiset_a] :
% 0.23/0.54 ( ( J2 != zero_zero_multiset_a )
% 0.23/0.54 => ( ! [X4: a] :
% 0.23/0.54 ( ( member_a @ X4 @ ( set_mset_a @ K4 ) )
% 0.23/0.54 => ? [Xa: a] :
% 0.23/0.54 ( ( member_a @ Xa @ ( set_mset_a @ J2 ) )
% 0.23/0.54 & ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Xa ) @ R ) ) )
% 0.23/0.54 => ( member340150864iset_a @ ( produc2037245207iset_a @ ( plus_plus_multiset_a @ I2 @ K4 ) @ ( plus_plus_multiset_a @ I2 @ J2 ) ) @ ( mult_a @ R ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % one_step_implies_mult
% 0.23/0.54 thf(fact_164_mult__implies__one__step,axiom,
% 0.23/0.54 ! [R: set_Product_prod_a_a,M: multiset_a,N: multiset_a] :
% 0.23/0.54 ( ( trans_a @ R )
% 0.23/0.54 => ( ( member340150864iset_a @ ( produc2037245207iset_a @ M @ N ) @ ( mult_a @ R ) )
% 0.23/0.54 => ? [I3: multiset_a,J3: multiset_a] :
% 0.23/0.54 ( ( N
% 0.23/0.54 = ( plus_plus_multiset_a @ I3 @ J3 ) )
% 0.23/0.54 & ? [K3: multiset_a] :
% 0.23/0.54 ( ( M
% 0.23/0.54 = ( plus_plus_multiset_a @ I3 @ K3 ) )
% 0.23/0.54 & ( J3 != zero_zero_multiset_a )
% 0.23/0.54 & ! [X7: a] :
% 0.23/0.54 ( ( member_a @ X7 @ ( set_mset_a @ K3 ) )
% 0.23/0.54 => ? [Xa2: a] :
% 0.23/0.54 ( ( member_a @ Xa2 @ ( set_mset_a @ J3 ) )
% 0.23/0.54 & ( member449909584od_a_a @ ( product_Pair_a_a @ X7 @ Xa2 ) @ R ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % mult_implies_one_step
% 0.23/0.54 thf(fact_165_subset__mset_Osum__mset__0__iff,axiom,
% 0.23/0.54 ! [M: multiset_multiset_a] :
% 0.23/0.54 ( ( ( comm_m315775925iset_a @ plus_plus_multiset_a @ zero_zero_multiset_a @ M )
% 0.23/0.54 = zero_zero_multiset_a )
% 0.23/0.54 = ( ! [X5: multiset_a] :
% 0.23/0.54 ( ( member_multiset_a @ X5 @ ( set_mset_multiset_a @ M ) )
% 0.23/0.54 => ( X5 = zero_zero_multiset_a ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % subset_mset.sum_mset_0_iff
% 0.23/0.54 thf(fact_166_mult__cancel__add__mset,axiom,
% 0.23/0.54 ! [S: set_Product_prod_a_a,Uu: a,X8: multiset_a,Y7: multiset_a] :
% 0.23/0.54 ( ( trans_a @ S )
% 0.23/0.54 => ( ( irrefl_a @ S )
% 0.23/0.54 => ( ( member340150864iset_a @ ( produc2037245207iset_a @ ( add_mset_a @ Uu @ X8 ) @ ( add_mset_a @ Uu @ Y7 ) ) @ ( mult_a @ S ) )
% 0.23/0.54 = ( member340150864iset_a @ ( produc2037245207iset_a @ X8 @ Y7 ) @ ( mult_a @ S ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % mult_cancel_add_mset
% 0.23/0.54 thf(fact_167_in__mset__fold__plus__iff,axiom,
% 0.23/0.54 ! [X: a,M: multiset_a,NN: multiset_multiset_a] :
% 0.23/0.54 ( ( member_a @ X @ ( set_mset_a @ ( fold_m382157835iset_a @ plus_plus_multiset_a @ M @ NN ) ) )
% 0.23/0.54 = ( ( member_a @ X @ ( set_mset_a @ M ) )
% 0.23/0.54 | ? [N3: multiset_a] :
% 0.23/0.54 ( ( member_multiset_a @ N3 @ ( set_mset_multiset_a @ NN ) )
% 0.23/0.54 & ( member_a @ X @ ( set_mset_a @ N3 ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % in_mset_fold_plus_iff
% 0.23/0.54 thf(fact_168_union__fold__mset__add__mset,axiom,
% 0.23/0.54 ( plus_plus_multiset_a
% 0.23/0.54 = ( fold_m364285649iset_a @ add_mset_a ) ) ).
% 0.23/0.54
% 0.23/0.54 % union_fold_mset_add_mset
% 0.23/0.54 thf(fact_169_add__mset__replicate__mset__safe,axiom,
% 0.23/0.54 ! [M: multiset_a,A: a] :
% 0.23/0.54 ( ( nO_MAT1617603563iset_a @ zero_zero_multiset_a @ M )
% 0.23/0.54 => ( ( add_mset_a @ A @ M )
% 0.23/0.54 = ( plus_plus_multiset_a @ ( add_mset_a @ A @ zero_zero_multiset_a ) @ M ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % add_mset_replicate_mset_safe
% 0.23/0.54 thf(fact_170_subset__mset_Osum__mset__mono,axiom,
% 0.23/0.54 ! [K4: multiset_a,F: a > multiset_a,G: a > multiset_a] :
% 0.23/0.59 ( ! [I4: a] :
% 0.23/0.59 ( ( member_a @ I4 @ ( set_mset_a @ K4 ) )
% 0.23/0.59 => ( subseteq_mset_a @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 0.23/0.59 => ( subseteq_mset_a @ ( comm_m315775925iset_a @ plus_plus_multiset_a @ zero_zero_multiset_a @ ( image_929116801iset_a @ F @ K4 ) ) @ ( comm_m315775925iset_a @ plus_plus_multiset_a @ zero_zero_multiset_a @ ( image_929116801iset_a @ G @ K4 ) ) ) ) ).
% 0.23/0.59
% 0.23/0.59 % subset_mset.sum_mset_mono
% 0.23/0.59 thf(fact_171_image__mset__add__mset,axiom,
% 0.23/0.59 ! [F: a > a,A: a,M: multiset_a] :
% 0.23/0.59 ( ( image_mset_a_a @ F @ ( add_mset_a @ A @ M ) )
% 0.23/0.59 = ( add_mset_a @ ( F @ A ) @ ( image_mset_a_a @ F @ M ) ) ) ).
% 0.23/0.59
% 0.23/0.59 % image_mset_add_mset
% 0.23/0.59 thf(fact_172_msed__map__invR,axiom,
% 0.23/0.59 ! [F: a > a,M: multiset_a,B: a,N: multiset_a] :
% 0.23/0.59 ( ( ( image_mset_a_a @ F @ M )
% 0.23/0.59 = ( add_mset_a @ B @ N ) )
% 0.23/0.59 => ? [M1: multiset_a,A4: a] :
% 0.23/0.59 ( ( M
% 0.23/0.59 = ( add_mset_a @ A4 @ M1 ) )
% 0.23/0.59 & ( ( F @ A4 )
% 0.23/0.59 = B )
% 0.23/0.59 & ( ( image_mset_a_a @ F @ M1 )
% 0.23/0.59 = N ) ) ) ).
% 0.23/0.59
% 0.23/0.59 % msed_map_invR
% 0.23/0.59 thf(fact_173_msed__map__invL,axiom,
% 0.23/0.59 ! [F: a > a,A: a,M: multiset_a,N: multiset_a] :
% 0.23/0.59 ( ( ( image_mset_a_a @ F @ ( add_mset_a @ A @ M ) )
% 0.23/0.59 = N )
% 0.23/0.59 => ? [N1: multiset_a] :
% 0.23/0.59 ( ( N
% 0.23/0.59 = ( add_mset_a @ ( F @ A ) @ N1 ) )
% 0.23/0.59 & ( ( image_mset_a_a @ F @ M )
% 0.23/0.59 = N1 ) ) ) ).
% 0.23/0.59
% 0.23/0.59 % msed_map_invL
% 0.23/0.59 thf(fact_174_image__mset__single,axiom,
% 0.23/0.59 ! [F: a > a,X: a] :
% 0.23/0.59 ( ( image_mset_a_a @ F @ ( add_mset_a @ X @ zero_zero_multiset_a ) )
% 0.23/0.59 = ( add_mset_a @ ( F @ X ) @ zero_zero_multiset_a ) ) ).
% 0.23/0.59
% 0.23/0.59 % image_mset_single
% 0.23/0.59
% 0.23/0.59 % Conjectures (1)
% 0.23/0.59 thf(conj_0,conjecture,
% 0.23/0.59 is_heap_a @ ( heapIm1091024090Down_a @ ( t_a @ v2 @ e_a @ ( t_a @ v1 @ l1 @ r1 ) ) ) ).
% 0.23/0.59
% 0.23/0.59 %------------------------------------------------------------------------------
% 0.23/0.59 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.Y2lsIPk9Zd/cvc5---1.0.5_20824.p...
% 0.23/0.59 (declare-sort $$unsorted 0)
% 0.23/0.59 (declare-sort tptp.set_Pr158363655iset_a 0)
% 0.23/0.59 (declare-sort tptp.produc1127127335iset_a 0)
% 0.23/0.59 (declare-sort tptp.set_Product_prod_a_a 0)
% 0.23/0.59 (declare-sort tptp.multiset_multiset_a 0)
% 0.23/0.59 (declare-sort tptp.set_multiset_a 0)
% 0.23/0.59 (declare-sort tptp.product_prod_a_a 0)
% 0.23/0.59 (declare-sort tptp.multiset_a 0)
% 0.23/0.59 (declare-sort tptp.tree_a 0)
% 0.23/0.59 (declare-sort tptp.set_a 0)
% 0.23/0.59 (declare-sort tptp.a 0)
% 0.23/0.59 (declare-fun tptp.plus_plus_multiset_a (tptp.multiset_a tptp.multiset_a) tptp.multiset_a)
% 0.23/0.59 (declare-fun tptp.zero_zero_multiset_a () tptp.multiset_a)
% 0.23/0.59 (declare-fun tptp.nO_MAT1617603563iset_a (tptp.multiset_a tptp.multiset_a) Bool)
% 0.23/0.59 (declare-fun tptp.heapIm1140443833left_a (tptp.tree_a) tptp.tree_a)
% 0.23/0.59 (declare-fun tptp.heapIm1257206334ight_a (tptp.tree_a) tptp.tree_a)
% 0.23/0.59 (declare-fun tptp.heapIm1091024090Down_a (tptp.tree_a) tptp.tree_a)
% 0.23/0.59 (declare-fun tptp.e_a () tptp.tree_a)
% 0.23/0.59 (declare-fun tptp.t_a (tptp.a tptp.tree_a tptp.tree_a) tptp.tree_a)
% 0.23/0.59 (declare-fun tptp.rel_Tree_a_a ((-> tptp.a tptp.a Bool) tptp.tree_a tptp.tree_a) Bool)
% 0.23/0.59 (declare-fun tptp.in_tree_a (tptp.a tptp.tree_a) Bool)
% 0.23/0.59 (declare-fun tptp.is_heap_a (tptp.tree_a) Bool)
% 0.23/0.59 (declare-fun tptp.multiset_a2 (tptp.tree_a) tptp.multiset_a)
% 0.23/0.59 (declare-fun tptp.val_a (tptp.tree_a) tptp.a)
% 0.23/0.59 (declare-fun tptp.lattic146396397_Max_a (tptp.set_a) tptp.a)
% 0.23/0.59 (declare-fun tptp.add_mset_a (tptp.a tptp.multiset_a) tptp.multiset_a)
% 0.23/0.59 (declare-fun tptp.comm_m315775925iset_a ((-> tptp.multiset_a tptp.multiset_a tptp.multiset_a) tptp.multiset_a tptp.multiset_multiset_a) tptp.multiset_a)
% 0.23/0.59 (declare-fun tptp.fold_m382157835iset_a ((-> tptp.multiset_a tptp.multiset_a tptp.multiset_a) tptp.multiset_a tptp.multiset_multiset_a) tptp.multiset_a)
% 0.23/0.59 (declare-fun tptp.fold_m364285649iset_a ((-> tptp.a tptp.multiset_a tptp.multiset_a) tptp.multiset_a tptp.multiset_a) tptp.multiset_a)
% 0.23/0.59 (declare-fun tptp.image_929116801iset_a ((-> tptp.a tptp.multiset_a) tptp.multiset_a) tptp.multiset_multiset_a)
% 0.23/0.59 (declare-fun tptp.image_mset_a_a ((-> tptp.a tptp.a) tptp.multiset_a) tptp.multiset_a)
% 0.23/0.59 (declare-fun tptp.mult1_a (tptp.set_Product_prod_a_a) tptp.set_Pr158363655iset_a)
% 0.23/0.59 (declare-fun tptp.mult_a (tptp.set_Product_prod_a_a) tptp.set_Pr158363655iset_a)
% 0.23/0.59 (declare-fun tptp.set_mset_multiset_a (tptp.multiset_multiset_a) tptp.set_multiset_a)
% 0.23/0.59 (declare-fun tptp.set_mset_a (tptp.multiset_a) tptp.set_a)
% 0.23/0.59 (declare-fun tptp.subseteq_mset_a (tptp.multiset_a tptp.multiset_a) Bool)
% 0.23/0.59 (declare-fun tptp.ord_less_eq_o_o_a ((-> Bool Bool tptp.a) (-> Bool Bool tptp.a)) Bool)
% 0.23/0.59 (declare-fun tptp.ord_less_eq_o_a ((-> Bool tptp.a) (-> Bool tptp.a)) Bool)
% 0.23/0.59 (declare-fun tptp.ord_le1530450702ee_a_o ((-> tptp.tree_a tptp.tree_a Bool) (-> tptp.tree_a tptp.tree_a Bool)) Bool)
% 0.23/0.59 (declare-fun tptp.ord_less_eq_a_a_o ((-> tptp.a tptp.a Bool) (-> tptp.a tptp.a Bool)) Bool)
% 0.23/0.59 (declare-fun tptp.ord_le1199012836iset_a (tptp.multiset_a tptp.multiset_a) Bool)
% 0.23/0.59 (declare-fun tptp.ord_less_eq_set_a (tptp.set_a tptp.set_a) Bool)
% 0.23/0.59 (declare-fun tptp.ord_less_eq_a (tptp.a tptp.a) Bool)
% 0.23/0.59 (declare-fun tptp.order_Greatest_o_a ((-> (-> Bool tptp.a) Bool) Bool) tptp.a)
% 0.23/0.59 (declare-fun tptp.order_Greatest_a ((-> tptp.a Bool)) tptp.a)
% 0.23/0.59 (declare-fun tptp.produc2037245207iset_a (tptp.multiset_a tptp.multiset_a) tptp.produc1127127335iset_a)
% 0.23/0.59 (declare-fun tptp.product_Pair_a_a (tptp.a tptp.a) tptp.product_prod_a_a)
% 0.23/0.59 (declare-fun tptp.irrefl_a (tptp.set_Product_prod_a_a) Bool)
% 0.23/0.59 (declare-fun tptp.trans_a (tptp.set_Product_prod_a_a) Bool)
% 0.23/0.59 (declare-fun tptp.collect_a ((-> tptp.a Bool)) tptp.set_a)
% 0.23/0.59 (declare-fun tptp.member_multiset_a (tptp.multiset_a tptp.set_multiset_a) Bool)
% 0.23/0.59 (declare-fun tptp.member340150864iset_a (tptp.produc1127127335iset_a tptp.set_Pr158363655iset_a) Bool)
% 0.23/0.59 (declare-fun tptp.member449909584od_a_a (tptp.product_prod_a_a tptp.set_Product_prod_a_a) Bool)
% 0.23/0.59 (declare-fun tptp.member_a (tptp.a tptp.set_a) Bool)
% 0.23/0.59 (declare-fun tptp.l () tptp.tree_a)
% 0.23/0.59 (declare-fun tptp.l1 () tptp.tree_a)
% 0.23/0.59 (declare-fun tptp.la () tptp.tree_a)
% 0.23/0.59 (declare-fun tptp.r () tptp.tree_a)
% 0.23/0.59 (declare-fun tptp.r1 () tptp.tree_a)
% 0.23/0.59 (declare-fun tptp.ra () tptp.tree_a)
% 0.23/0.59 (declare-fun tptp.t () tptp.tree_a)
% 0.23/0.59 (declare-fun tptp.v () tptp.a)
% 0.23/0.59 (declare-fun tptp.v1 () tptp.a)
% 0.23/0.59 (declare-fun tptp.v2 () tptp.a)
% 0.23/0.59 (declare-fun tptp.va () tptp.a)
% 0.23/0.59 (assert (@ tptp.is_heap_a tptp.ra))
% 0.23/0.59 (assert (@ tptp.is_heap_a tptp.la))
% 0.23/0.59 (assert (@ tptp.is_heap_a tptp.r))
% 0.23/0.59 (assert (@ tptp.is_heap_a tptp.l))
% 0.23/0.59 (assert (@ (@ tptp.ord_less_eq_a tptp.v1) tptp.v2))
% 0.23/0.59 (assert (= (@ (@ (@ tptp.t_a tptp.v2) tptp.e_a) (@ (@ (@ tptp.t_a tptp.v1) tptp.l1) tptp.r1)) (@ (@ (@ tptp.t_a tptp.va) tptp.la) tptp.ra)))
% 0.23/0.59 (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))))
% 0.23/0.59 (assert (= (@ tptp.heapIm1091024090Down_a tptp.e_a) tptp.e_a))
% 0.23/0.59 (assert (forall ((X tptp.tree_a)) (=> (not (= X tptp.e_a)) (=> (forall ((V2 tptp.a)) (not (= X (@ (@ (@ tptp.t_a V2) tptp.e_a) tptp.e_a)))) (=> (forall ((V2 tptp.a) (Va tptp.a) (Vb tptp.tree_a) (Vc tptp.tree_a)) (not (= X (@ (@ (@ tptp.t_a V2) (@ (@ (@ tptp.t_a Va) Vb) Vc)) tptp.e_a)))) (=> (forall ((V2 tptp.a) (Va tptp.a) (Vb tptp.tree_a) (Vc tptp.tree_a)) (not (= X (@ (@ (@ tptp.t_a V2) tptp.e_a) (@ (@ (@ tptp.t_a Va) Vb) Vc))))) (not (forall ((V2 tptp.a) (Va tptp.a) (Vb tptp.tree_a) (Vc tptp.tree_a) (Vd tptp.a) (Ve tptp.tree_a) (Vf tptp.tree_a)) (not (= X (@ (@ (@ tptp.t_a V2) (@ (@ (@ tptp.t_a Va) Vb) Vc)) (@ (@ (@ tptp.t_a Vd) Ve) Vf))))))))))))
% 0.23/0.59 (assert (= tptp.t (@ (@ (@ tptp.t_a tptp.v) tptp.l) tptp.r)))
% 0.23/0.59 (assert (forall ((V tptp.a)) (@ tptp.is_heap_a (@ (@ (@ tptp.t_a V) tptp.e_a) tptp.e_a))))
% 0.23/0.59 (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) (V3 tptp.a) (R2 tptp.tree_a)) (and (= (@ tptp.heapIm1091024090Down_a T) (@ (@ (@ tptp.t_a V3) L2) R2)) (@ (@ tptp.ord_less_eq_a V) V3))))))
% 0.23/0.59 (assert (forall ((L tptp.tree_a) (R tptp.tree_a) (V tptp.a)) (let ((_let_1 (@ (@ (@ tptp.t_a tptp.v1) tptp.l1) tptp.r1))) (let ((_let_2 (@ (@ (@ tptp.t_a tptp.v2) (@ tptp.heapIm1140443833left_a _let_1)) (@ tptp.heapIm1257206334ight_a _let_1)))) (=> (not (@ (@ tptp.ord_less_eq_a (@ tptp.val_a _let_1)) tptp.v2)) (=> (@ tptp.is_heap_a L) (=> (@ tptp.is_heap_a R) (=> (= _let_2 (@ (@ (@ tptp.t_a V) L) R)) (@ tptp.is_heap_a (@ tptp.heapIm1091024090Down_a _let_2))))))))))
% 0.23/0.59 (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)))))
% 0.23/0.59 (assert (@ tptp.is_heap_a tptp.e_a))
% 0.23/0.59 (assert (forall ((X21 tptp.a) (X22 tptp.tree_a) (X23 tptp.tree_a)) (not (= tptp.e_a (@ (@ (@ tptp.t_a X21) X22) X23)))))
% 0.23/0.59 (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)))))
% 0.23/0.59 (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))))))))
% 0.23/0.59 (assert (forall ((X tptp.tree_a)) (=> (not (= X tptp.e_a)) (=> (forall ((V2 tptp.a)) (not (= X (@ (@ (@ tptp.t_a V2) tptp.e_a) tptp.e_a)))) (=> (forall ((V2 tptp.a) (Va tptp.a) (Vb tptp.tree_a) (Vc tptp.tree_a)) (not (= X (@ (@ (@ tptp.t_a V2) tptp.e_a) (@ (@ (@ tptp.t_a Va) Vb) Vc))))) (=> (forall ((V2 tptp.a) (Va tptp.a) (Vb tptp.tree_a) (Vc tptp.tree_a)) (not (= X (@ (@ (@ tptp.t_a V2) (@ (@ (@ tptp.t_a Va) Vb) Vc)) tptp.e_a)))) (not (forall ((V2 tptp.a) (Va tptp.a) (Vb tptp.tree_a) (Vc tptp.tree_a) (Vd tptp.a) (Ve tptp.tree_a) (Vf tptp.tree_a)) (not (= X (@ (@ (@ tptp.t_a V2) (@ (@ (@ tptp.t_a Va) Vb) Vc)) (@ (@ (@ tptp.t_a Vd) Ve) Vf))))))))))))
% 0.23/0.59 (assert (= tptp.in_tree_a (lambda ((V4 tptp.a) (T2 tptp.tree_a)) (@ (@ tptp.in_tree_a V4) (@ tptp.heapIm1091024090Down_a T2)))))
% 0.23/0.59 (assert (forall ((V tptp.a) (L tptp.tree_a) (R tptp.tree_a)) (= (@ tptp.heapIm1140443833left_a (@ (@ (@ tptp.t_a V) L) R)) L)))
% 0.23/0.59 (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))))))
% 0.23/0.59 (assert (forall ((V tptp.a) (Uu tptp.tree_a) (Uv tptp.tree_a)) (= (@ tptp.val_a (@ (@ (@ tptp.t_a V) Uu) Uv)) V)))
% 0.23/0.59 (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))))))
% 0.23/0.59 (assert (forall ((Vd2 tptp.a) (Ve2 tptp.tree_a) (Vf2 tptp.tree_a) (Va2 tptp.a) (Vb2 tptp.tree_a) (Vc2 tptp.tree_a) (V tptp.a)) (let ((_let_1 (@ (@ (@ tptp.t_a Vd2) Ve2) Vf2))) (let ((_let_2 (@ tptp.t_a V))) (let ((_let_3 (@ (@ (@ tptp.t_a Va2) Vb2) Vc2))) (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)))))))))))))))))))))))
% 0.23/0.59 (assert (forall ((Va2 tptp.a) (Vb2 tptp.tree_a) (Vc2 tptp.tree_a) (Vd2 tptp.a) (Ve2 tptp.tree_a) (Vf2 tptp.tree_a) (V tptp.a)) (let ((_let_1 (@ (@ (@ tptp.t_a Va2) Vb2) Vc2))) (let ((_let_2 (@ tptp.t_a V))) (let ((_let_3 (@ (@ (@ tptp.t_a Vd2) Ve2) Vf2))) (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)))))))))))))))))))))))
% 0.23/0.59 (assert (forall ((V tptp.a)) (not (@ (@ tptp.in_tree_a V) tptp.e_a))))
% 0.23/0.59 (assert (forall ((V 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 (@ (@ (@ tptp.t_a Vd2) Ve2) Vf2))) (= (@ 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)))))))
% 0.23/0.59 (assert (forall ((V 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 (@ (@ (@ tptp.t_a Va2) Vb2) Vc2))) (= (@ 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)))))))
% 0.23/0.59 (assert (forall ((Va2 tptp.a) (Vb2 tptp.tree_a) (Vc2 tptp.tree_a) (V tptp.a)) (let ((_let_1 (@ (@ (@ tptp.t_a Va2) Vb2) Vc2))) (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))))))))))))
% 0.23/0.59 (assert (forall ((Va2 tptp.a) (Vb2 tptp.tree_a) (Vc2 tptp.tree_a) (V tptp.a)) (let ((_let_1 (@ (@ (@ tptp.t_a Va2) Vb2) Vc2))) (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)))))))))))))))
% 0.23/0.59 (assert (forall ((T tptp.tree_a)) (=> (not (= T tptp.e_a)) (@ (@ tptp.in_tree_a (@ tptp.val_a (@ tptp.heapIm1091024090Down_a T))) T))))
% 0.23/0.59 (assert (forall ((V tptp.a) (Va2 tptp.a) (Vb2 tptp.tree_a) (Vc2 tptp.tree_a)) (let ((_let_1 (@ (@ (@ tptp.t_a Va2) Vb2) Vc2))) (= (@ 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))))))
% 0.23/0.59 (assert (forall ((V tptp.a) (Va2 tptp.a) (Vb2 tptp.tree_a) (Vc2 tptp.tree_a)) (let ((_let_1 (@ (@ (@ tptp.t_a Va2) Vb2) Vc2))) (= (@ 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))))))
% 0.23/0.59 (assert (forall ((V tptp.a) (L tptp.tree_a) (R tptp.tree_a)) (= (@ tptp.heapIm1257206334ight_a (@ (@ (@ tptp.t_a V) L) R)) R)))
% 0.23/0.59 (assert (forall ((X (-> Bool tptp.a))) (@ (@ tptp.ord_less_eq_o_a X) X)))
% 0.23/0.59 (assert (forall ((X tptp.a)) (@ (@ tptp.ord_less_eq_a X) X)))
% 0.23/0.59 (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)))))
% 0.23/0.59 (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)))))
% 0.23/0.59 (assert (forall ((F (-> Bool tptp.a)) (G (-> Bool tptp.a))) (=> (forall ((X4 Bool)) (@ (@ tptp.ord_less_eq_a (@ F X4)) (@ G X4))) (@ (@ tptp.ord_less_eq_o_a F) G))))
% 0.23/0.59 (assert (= tptp.ord_less_eq_o_a (lambda ((F2 (-> Bool tptp.a)) (G2 (-> Bool tptp.a))) (forall ((X5 Bool)) (@ (@ tptp.ord_less_eq_a (@ F2 X5)) (@ G2 X5))))))
% 0.23/0.59 (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 ((X4 (-> Bool tptp.a)) (Y2 (-> Bool tptp.a))) (=> (@ (@ tptp.ord_less_eq_o_a X4) Y2) (@ (@ tptp.ord_less_eq_a (@ F X4)) (@ F Y2)))) (@ _let_1 (@ F C))))))))
% 0.23/0.59 (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 ((X4 tptp.a) (Y2 tptp.a)) (=> (@ (@ tptp.ord_less_eq_a X4) Y2) (@ (@ tptp.ord_less_eq_o_a (@ F X4)) (@ F Y2)))) (@ _let_1 (@ F C))))))))
% 0.23/0.59 (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 ((X4 (-> Bool tptp.a)) (Y2 (-> Bool tptp.a))) (=> (@ (@ tptp.ord_less_eq_o_a X4) Y2) (@ (@ tptp.ord_less_eq_o_a (@ F X4)) (@ F Y2)))) (@ _let_1 (@ F C))))))))
% 0.23/0.59 (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 ((X4 tptp.a) (Y2 tptp.a)) (=> (@ (@ tptp.ord_less_eq_a X4) Y2) (@ (@ tptp.ord_less_eq_a (@ F X4)) (@ F Y2)))) (@ _let_1 (@ F C))))))))
% 0.23/0.59 (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 ((X4 tptp.a) (Y2 tptp.a)) (=> (@ (@ tptp.ord_less_eq_a X4) Y2) (@ (@ tptp.ord_less_eq_o_a (@ F X4)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_o_a (@ F A)) C))))))
% 0.23/0.59 (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 ((X4 (-> Bool tptp.a)) (Y2 (-> Bool tptp.a))) (=> (@ (@ tptp.ord_less_eq_o_a X4) Y2) (@ (@ tptp.ord_less_eq_a (@ F X4)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_a (@ F A)) C))))))
% 0.23/0.59 (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 ((X4 (-> Bool tptp.a)) (Y2 (-> Bool tptp.a))) (=> (@ (@ tptp.ord_less_eq_o_a X4) Y2) (@ (@ tptp.ord_less_eq_o_a (@ F X4)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_o_a (@ F A)) C))))))
% 0.23/0.59 (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 ((X4 tptp.a) (Y2 tptp.a)) (=> (@ (@ tptp.ord_less_eq_a X4) Y2) (@ (@ tptp.ord_less_eq_a (@ F X4)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_a (@ F A)) C))))))
% 0.23/0.59 (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)))))
% 0.23/0.59 (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 ((X4 tptp.a) (Y2 tptp.a)) (=> (@ (@ tptp.ord_less_eq_a X4) Y2) (@ (@ tptp.ord_less_eq_o_a (@ F X4)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_o_a A) (@ F C)))))))
% 0.23/0.59 (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 ((X4 (-> Bool tptp.a)) (Y2 (-> Bool tptp.a))) (=> (@ (@ tptp.ord_less_eq_o_a X4) Y2) (@ (@ tptp.ord_less_eq_a (@ F X4)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_a A) (@ F C)))))))
% 0.23/0.59 (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 ((X4 (-> Bool tptp.a)) (Y2 (-> Bool tptp.a))) (=> (@ (@ tptp.ord_less_eq_o_a X4) Y2) (@ (@ tptp.ord_less_eq_o_a (@ F X4)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_o_a A) (@ F C)))))))
% 0.23/0.59 (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 ((X4 tptp.a) (Y2 tptp.a)) (=> (@ (@ tptp.ord_less_eq_a X4) Y2) (@ (@ tptp.ord_less_eq_a (@ F X4)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_a A) (@ F C)))))))
% 0.23/0.59 (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 ((X4 tptp.a) (Y2 tptp.a)) (=> (@ (@ tptp.ord_less_eq_a X4) Y2) (@ (@ tptp.ord_less_eq_o_a (@ F X4)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_o_a (@ F A)) C))))))
% 0.23/0.59 (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 ((X4 (-> Bool tptp.a)) (Y2 (-> Bool tptp.a))) (=> (@ (@ tptp.ord_less_eq_o_a X4) Y2) (@ (@ tptp.ord_less_eq_a (@ F X4)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_a (@ F A)) C))))))
% 0.23/0.59 (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 ((X4 (-> Bool tptp.a)) (Y2 (-> Bool tptp.a))) (=> (@ (@ tptp.ord_less_eq_o_a X4) Y2) (@ (@ tptp.ord_less_eq_o_a (@ F X4)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_o_a (@ F A)) C))))))
% 0.23/0.59 (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 ((X4 tptp.a) (Y2 tptp.a)) (=> (@ (@ tptp.ord_less_eq_a X4) Y2) (@ (@ tptp.ord_less_eq_a (@ F X4)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_a (@ F A)) C))))))
% 0.23/0.59 (assert (forall ((A tptp.a) (P (-> tptp.a Bool))) (= (@ (@ tptp.member_a A) (@ tptp.collect_a P)) (@ P A))))
% 0.23/0.59 (assert (forall ((A2 tptp.set_a)) (= (@ tptp.collect_a (lambda ((X5 tptp.a)) (@ (@ tptp.member_a X5) A2))) A2)))
% 0.23/0.59 (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)))))
% 0.23/0.59 (assert (forall ((B tptp.a) (A tptp.a)) (=> (@ (@ tptp.ord_less_eq_a B) A) (=> (@ (@ tptp.ord_less_eq_a A) B) (= A B)))))
% 0.23/0.59 (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)))))
% 0.23/0.59 (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)))))
% 0.23/0.59 (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))))))
% 0.23/0.59 (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))))))
% 0.23/0.59 (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)))))
% 0.23/0.59 (assert (forall ((A (-> Bool tptp.a))) (@ (@ tptp.ord_less_eq_o_a A) A)))
% 0.23/0.59 (assert (forall ((A tptp.a)) (@ (@ tptp.ord_less_eq_a A) A)))
% 0.23/0.59 (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))))))
% 0.23/0.59 (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))))))
% 0.23/0.59 (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)))))
% 0.23/0.59 (assert (forall ((A tptp.a) (B tptp.a)) (=> (@ (@ tptp.ord_less_eq_a A) B) (=> (@ (@ tptp.ord_less_eq_a B) A) (= A B)))))
% 0.23/0.59 (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))))))
% 0.23/0.59 (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))))))
% 0.23/0.59 (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)))))
% 0.23/0.59 (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)))))
% 0.23/0.59 (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)))))
% 0.23/0.59 (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)))))
% 0.23/0.59 (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)))))
% 0.23/0.59 (assert (forall ((Y tptp.a) (X tptp.a)) (=> (@ (@ tptp.ord_less_eq_a Y) X) (= (@ (@ tptp.ord_less_eq_a X) Y) (= X Y)))))
% 0.23/0.59 (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)))))))))))))))))))
% 0.23/0.59 (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))))))
% 0.23/0.59 (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))))))
% 0.23/0.59 (assert (forall ((X tptp.a) (Y tptp.a)) (=> (not (@ (@ tptp.ord_less_eq_a X) Y)) (@ (@ tptp.ord_less_eq_a Y) X))))
% 0.23/0.59 (assert (forall ((X (-> Bool tptp.a)) (Y (-> Bool tptp.a))) (=> (= X Y) (@ (@ tptp.ord_less_eq_o_a X) Y))))
% 0.23/0.59 (assert (forall ((X tptp.a) (Y tptp.a)) (=> (= X Y) (@ (@ tptp.ord_less_eq_a X) Y))))
% 0.23/0.59 (assert (forall ((X tptp.a) (Y tptp.a)) (or (@ (@ tptp.ord_less_eq_a X) Y) (@ (@ tptp.ord_less_eq_a Y) X))))
% 0.23/0.59 (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)))))
% 0.23/0.59 (assert (forall ((X tptp.a) (Y tptp.a)) (=> (@ (@ tptp.ord_less_eq_a X) Y) (=> (@ (@ tptp.ord_less_eq_a Y) X) (= X Y)))))
% 0.23/0.59 (assert (= (lambda ((Y3 (-> Bool tptp.a)) (Z (-> Bool tptp.a))) (= Y3 Z)) (lambda ((X5 (-> Bool tptp.a)) (Y4 (-> Bool tptp.a))) (and (@ (@ tptp.ord_less_eq_o_a X5) Y4) (@ (@ tptp.ord_less_eq_o_a Y4) X5)))))
% 0.23/0.59 (assert (= (lambda ((Y3 tptp.a) (Z tptp.a)) (= Y3 Z)) (lambda ((X5 tptp.a) (Y4 tptp.a)) (and (@ (@ tptp.ord_less_eq_a X5) Y4) (@ (@ tptp.ord_less_eq_a Y4) X5)))))
% 0.23/0.59 (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)))))
% 0.23/0.59 (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)))))
% 0.23/0.59 (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 ((X4 (-> Bool tptp.a))) (=> (@ P X4) (=> (forall ((Y5 (-> Bool tptp.a))) (=> (@ P Y5) (@ (@ tptp.ord_less_eq_o_a Y5) X4))) (@ Q X4)))) (@ Q (@ tptp.order_Greatest_o_a P)))))))
% 0.23/0.59 (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 ((X4 tptp.a)) (=> (@ P X4) (=> (forall ((Y5 tptp.a)) (=> (@ P Y5) (@ (@ tptp.ord_less_eq_a Y5) X4))) (@ Q X4)))) (@ Q (@ tptp.order_Greatest_a P)))))))
% 0.23/0.59 (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))))))
% 0.23/0.59 (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))))))
% 0.23/0.59 (assert (forall ((R3 (-> tptp.a tptp.a Bool)) (X tptp.tree_a) (Y tptp.tree_a) (Q (-> tptp.tree_a tptp.tree_a Bool))) (=> (@ (@ (@ tptp.rel_Tree_a_a R3) X) Y) (=> (@ (@ Q tptp.e_a) tptp.e_a) (=> (forall ((A21 tptp.a) (A22 tptp.tree_a) (A23 tptp.tree_a) (B21 tptp.a) (B22 tptp.tree_a) (B23 tptp.tree_a)) (=> (@ (@ R3 A21) B21) (=> (@ (@ Q A22) B22) (=> (@ (@ Q A23) B23) (@ (@ Q (@ (@ (@ tptp.t_a A21) A22) A23)) (@ (@ (@ tptp.t_a B21) B22) B23)))))) (@ (@ Q X) Y))))))
% 0.23/0.59 (assert (forall ((R3 (-> tptp.a tptp.a Bool)) (Ra (-> tptp.a tptp.a Bool))) (=> (@ (@ tptp.ord_less_eq_a_a_o R3) Ra) (@ (@ tptp.ord_le1530450702ee_a_o (@ tptp.rel_Tree_a_a R3)) (@ tptp.rel_Tree_a_a Ra)))))
% 0.23/0.59 (assert (= (@ tptp.rel_Tree_a_a (lambda ((Y3 tptp.a) (Z tptp.a)) (= Y3 Z))) (lambda ((Y3 tptp.tree_a) (Z tptp.tree_a)) (= Y3 Z))))
% 0.23/0.59 (assert (forall ((Ra (-> tptp.a tptp.a Bool)) (X tptp.tree_a)) (=> (forall ((X4 tptp.a)) (@ (@ Ra X4) X4)) (@ (@ (@ tptp.rel_Tree_a_a Ra) X) X))))
% 0.23/0.59 (assert (forall ((R3 (-> tptp.a tptp.a Bool)) (X21 tptp.a) (X22 tptp.tree_a) (X23 tptp.tree_a) (Y21 tptp.a) (Y22 tptp.tree_a) (Y23 tptp.tree_a)) (let ((_let_1 (@ tptp.rel_Tree_a_a R3))) (= (@ (@ _let_1 (@ (@ (@ tptp.t_a X21) X22) X23)) (@ (@ (@ tptp.t_a Y21) Y22) Y23)) (and (@ (@ R3 X21) Y21) (@ (@ _let_1 X22) Y22) (@ (@ _let_1 X23) Y23))))))
% 0.23/0.59 (assert (forall ((R3 (-> tptp.a tptp.a Bool)) (X21 tptp.a) (Y21 tptp.a) (X22 tptp.tree_a) (Y22 tptp.tree_a) (X23 tptp.tree_a) (Y23 tptp.tree_a)) (let ((_let_1 (@ tptp.rel_Tree_a_a R3))) (=> (@ (@ R3 X21) Y21) (=> (@ (@ _let_1 X22) Y22) (=> (@ (@ _let_1 X23) Y23) (@ (@ _let_1 (@ (@ (@ tptp.t_a X21) X22) X23)) (@ (@ (@ tptp.t_a Y21) Y22) Y23))))))))
% 0.23/0.59 (assert (forall ((R3 (-> tptp.a tptp.a Bool))) (@ (@ (@ tptp.rel_Tree_a_a R3) tptp.e_a) tptp.e_a)))
% 0.23/0.59 (assert (forall ((R3 (-> tptp.a tptp.a Bool)) (Y21 tptp.a) (Y22 tptp.tree_a) (Y23 tptp.tree_a)) (not (@ (@ (@ tptp.rel_Tree_a_a R3) (@ (@ (@ tptp.t_a Y21) Y22) Y23)) tptp.e_a))))
% 0.23/0.59 (assert (forall ((R3 (-> tptp.a tptp.a Bool)) (Y21 tptp.a) (Y22 tptp.tree_a) (Y23 tptp.tree_a)) (not (@ (@ (@ tptp.rel_Tree_a_a R3) tptp.e_a) (@ (@ (@ tptp.t_a Y21) Y22) Y23)))))
% 0.23/0.59 (assert (forall ((R3 (-> tptp.a tptp.a Bool)) (A tptp.tree_a) (B tptp.tree_a)) (=> (@ (@ (@ tptp.rel_Tree_a_a R3) A) B) (=> (=> (= A tptp.e_a) (not (= B tptp.e_a))) (not (forall ((X1 tptp.a) (X2 tptp.tree_a) (X3 tptp.tree_a)) (=> (= A (@ (@ (@ tptp.t_a X1) X2) X3)) (forall ((Y1 tptp.a) (Y24 tptp.tree_a) (Y32 tptp.tree_a)) (let ((_let_1 (@ tptp.rel_Tree_a_a R3))) (=> (= B (@ (@ (@ tptp.t_a Y1) Y24) Y32)) (=> (@ (@ R3 X1) Y1) (=> (@ (@ _let_1 X2) Y24) (not (@ (@ _let_1 X3) Y32))))))))))))))
% 0.23/0.59 (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))))))
% 0.23/0.59 (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)))))
% 0.23/0.59 (assert (forall ((M tptp.multiset_a) (X tptp.a)) (not (= M (@ (@ tptp.add_mset_a X) M)))))
% 0.23/0.59 (assert (forall ((A tptp.a) (A2 tptp.multiset_a)) (=> (@ (@ tptp.member_a A) (@ tptp.set_mset_a A2)) (not (forall ((B5 tptp.multiset_a)) (not (= A2 (@ (@ tptp.add_mset_a A) B5))))))))
% 0.23/0.59 (assert (forall ((X tptp.a) (M tptp.multiset_a)) (=> (@ (@ tptp.member_a X) (@ tptp.set_mset_a M)) (exists ((A5 tptp.multiset_a)) (= M (@ (@ tptp.add_mset_a X) A5))))))
% 0.23/0.59 (assert (forall ((X tptp.a) (Y tptp.a) (M tptp.multiset_a)) (let ((_let_1 (@ tptp.add_mset_a X))) (let ((_let_2 (@ tptp.add_mset_a Y))) (= (@ _let_1 (@ _let_2 M)) (@ _let_2 (@ _let_1 M)))))))
% 0.23/0.59 (assert (forall ((A tptp.a) (M tptp.multiset_a) (B tptp.a) (N tptp.multiset_a)) (= (= (@ (@ tptp.add_mset_a A) M) (@ (@ tptp.add_mset_a B) N)) (or (and (= M N) (= A B)) (exists ((K tptp.multiset_a)) (and (= M (@ (@ tptp.add_mset_a B) K)) (= N (@ (@ tptp.add_mset_a A) K))))))))
% 0.23/0.59 (assert (forall ((X tptp.a) (M tptp.multiset_a) (N tptp.multiset_a)) (=> (= (@ (@ tptp.add_mset_a X) M) N) (@ (@ tptp.member_a X) (@ tptp.set_mset_a N)))))
% 0.23/0.59 (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))))))
% 0.23/0.59 (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))))))))
% 0.23/0.59 (assert (forall ((P (-> tptp.multiset_a Bool)) (M tptp.multiset_a)) (=> (@ P tptp.zero_zero_multiset_a) (=> (forall ((X4 tptp.a) (M2 tptp.multiset_a)) (=> (@ P M2) (=> (forall ((Xa tptp.a)) (=> (@ (@ tptp.member_a Xa) (@ tptp.set_mset_a M2)) (@ (@ tptp.ord_less_eq_a Xa) X4))) (@ P (@ (@ tptp.add_mset_a X4) M2))))) (@ P M)))))
% 0.23/0.59 (assert (forall ((P (-> tptp.multiset_a Bool)) (M tptp.multiset_a)) (=> (@ P tptp.zero_zero_multiset_a) (=> (forall ((X4 tptp.a) (M2 tptp.multiset_a)) (=> (@ P M2) (=> (forall ((Xa tptp.a)) (=> (@ (@ tptp.member_a Xa) (@ tptp.set_mset_a M2)) (@ (@ tptp.ord_less_eq_a X4) Xa))) (@ P (@ (@ tptp.add_mset_a X4) M2))))) (@ P M)))))
% 0.23/0.59 (assert (forall ((X tptp.a) (M tptp.multiset_a) (Y tptp.a)) (= (= (@ (@ tptp.add_mset_a X) M) (@ (@ tptp.add_mset_a Y) tptp.zero_zero_multiset_a)) (and (= M tptp.zero_zero_multiset_a) (= X Y)))))
% 0.23/0.59 (assert (forall ((A tptp.a) (B tptp.a) (M tptp.multiset_a)) (= (= (@ (@ tptp.add_mset_a A) tptp.zero_zero_multiset_a) (@ (@ tptp.add_mset_a B) M)) (and (= B A) (= M tptp.zero_zero_multiset_a)))))
% 0.23/0.59 (assert (forall ((B tptp.a) (M tptp.multiset_a) (A tptp.a)) (= (= (@ (@ tptp.add_mset_a B) M) (@ (@ tptp.add_mset_a A) tptp.zero_zero_multiset_a)) (and (= B A) (= M tptp.zero_zero_multiset_a)))))
% 0.23/0.59 (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))))
% 0.23/0.59 (assert (forall ((M tptp.multiset_a)) (=> (not (= M tptp.zero_zero_multiset_a)) (not (forall ((X4 tptp.a) (N2 tptp.multiset_a)) (not (= M (@ (@ tptp.add_mset_a X4) N2))))))))
% 0.23/0.59 (assert (forall ((P (-> tptp.multiset_a Bool)) (M tptp.multiset_a)) (=> (@ P tptp.zero_zero_multiset_a) (=> (forall ((X4 tptp.a) (M2 tptp.multiset_a)) (=> (@ P M2) (@ P (@ (@ tptp.add_mset_a X4) M2)))) (@ P M)))))
% 0.23/0.59 (assert (forall ((P (-> tptp.multiset_a tptp.multiset_a Bool)) (M tptp.multiset_a) (N tptp.multiset_a)) (=> (@ (@ P tptp.zero_zero_multiset_a) tptp.zero_zero_multiset_a) (=> (forall ((A4 tptp.a) (M2 tptp.multiset_a) (N2 tptp.multiset_a)) (=> (@ (@ P M2) N2) (@ (@ P (@ (@ tptp.add_mset_a A4) M2)) N2))) (=> (forall ((A4 tptp.a) (M2 tptp.multiset_a) (N2 tptp.multiset_a)) (let ((_let_1 (@ P M2))) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.add_mset_a A4) N2))))) (@ (@ P M) N))))))
% 0.23/0.59 (assert (forall ((A tptp.a) (A2 tptp.multiset_a)) (not (= tptp.zero_zero_multiset_a (@ (@ tptp.add_mset_a A) A2)))))
% 0.23/0.59 (assert (forall ((A2 tptp.multiset_a)) (=> (not (= A2 tptp.zero_zero_multiset_a)) (not (forall ((X4 tptp.a)) (not (@ (@ tptp.member_a X4) (@ tptp.set_mset_a A2))))))))
% 0.23/0.59 (assert (forall ((M tptp.multiset_a)) (=> (not (= M tptp.zero_zero_multiset_a)) (exists ((A5 tptp.multiset_a) (A4 tptp.a)) (= M (@ (@ tptp.add_mset_a A4) A5))))))
% 0.23/0.59 (assert (forall ((X tptp.a)) (@ (@ tptp.member_a X) (@ tptp.set_mset_a (@ (@ tptp.add_mset_a X) tptp.zero_zero_multiset_a)))))
% 0.23/0.59 (assert (= (@ tptp.multiset_a2 tptp.e_a) tptp.zero_zero_multiset_a))
% 0.23/0.59 (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)))))
% 0.23/0.59 (assert (forall ((A tptp.a) (M tptp.multiset_a)) (= (@ (@ tptp.subseteq_mset_a (@ (@ tptp.add_mset_a A) tptp.zero_zero_multiset_a)) M) (@ (@ tptp.member_a A) (@ tptp.set_mset_a M)))))
% 0.23/0.59 (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))))))
% 0.23/0.59 (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)))))))
% 0.23/0.59 (assert (forall ((A tptp.a) (M tptp.multiset_a) (B tptp.a)) (= (@ (@ tptp.subseteq_mset_a (@ (@ tptp.add_mset_a A) M)) (@ (@ tptp.add_mset_a B) tptp.zero_zero_multiset_a)) (and (= M tptp.zero_zero_multiset_a) (= A B)))))
% 0.23/0.59 (assert (forall ((A tptp.multiset_a)) (= (@ (@ tptp.plus_plus_multiset_a A) tptp.zero_zero_multiset_a) A)))
% 0.23/0.59 (assert (forall ((I tptp.multiset_a) (J tptp.multiset_a) (K2 tptp.multiset_a) (L tptp.multiset_a)) (=> (and (@ (@ tptp.ord_le1199012836iset_a I) J) (= K2 L)) (@ (@ tptp.ord_le1199012836iset_a (@ (@ tptp.plus_plus_multiset_a I) K2)) (@ (@ tptp.plus_plus_multiset_a J) L)))))
% 0.23/0.59 (assert (forall ((I tptp.multiset_a) (J tptp.multiset_a) (K2 tptp.multiset_a) (L tptp.multiset_a)) (=> (and (= I J) (@ (@ tptp.ord_le1199012836iset_a K2) L)) (@ (@ tptp.ord_le1199012836iset_a (@ (@ tptp.plus_plus_multiset_a I) K2)) (@ (@ tptp.plus_plus_multiset_a J) L)))))
% 0.23/0.59 (assert (forall ((I tptp.multiset_a) (J tptp.multiset_a) (K2 tptp.multiset_a) (L tptp.multiset_a)) (=> (and (@ (@ tptp.ord_le1199012836iset_a I) J) (@ (@ tptp.ord_le1199012836iset_a K2) L)) (@ (@ tptp.ord_le1199012836iset_a (@ (@ tptp.plus_plus_multiset_a I) K2)) (@ (@ tptp.plus_plus_multiset_a J) L)))))
% 0.23/0.59 (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))))))
% 0.23/0.59 (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))))))
% 0.23/0.59 (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)))))
% 0.23/0.59 (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)))))))
% 0.23/0.59 (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)))))))
% 0.23/0.59 (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)))))
% 0.23/0.59 (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)))))
% 0.23/0.59 (assert (forall ((A tptp.a) (M tptp.multiset_a) (N tptp.multiset_a)) (let ((_let_1 (@ (@ tptp.add_mset_a A) tptp.zero_zero_multiset_a))) (= (= _let_1 (@ (@ tptp.plus_plus_multiset_a M) N)) (or (and (= _let_1 M) (= N tptp.zero_zero_multiset_a)) (and (= M tptp.zero_zero_multiset_a) (= _let_1 N)))))))
% 0.23/0.59 (assert (forall ((M tptp.multiset_a) (N tptp.multiset_a) (A tptp.a)) (let ((_let_1 (@ (@ tptp.add_mset_a A) tptp.zero_zero_multiset_a))) (= (= (@ (@ tptp.plus_plus_multiset_a M) N) _let_1) (or (and (= M _let_1) (= N tptp.zero_zero_multiset_a)) (and (= M tptp.zero_zero_multiset_a) (= N _let_1)))))))
% 0.23/0.59 (assert (= tptp.add_mset_a (lambda ((A3 tptp.a) (A6 tptp.multiset_a)) (@ (@ tptp.plus_plus_multiset_a A6) (@ (@ tptp.add_mset_a A3) tptp.zero_zero_multiset_a)))))
% 0.23/0.59 (assert (forall ((F3 tptp.multiset_a) (A2 tptp.multiset_a) (P (-> tptp.multiset_a Bool))) (=> (@ (@ tptp.subseteq_mset_a F3) A2) (=> (@ P tptp.zero_zero_multiset_a) (=> (forall ((A4 tptp.a) (F4 tptp.multiset_a)) (=> (@ (@ tptp.member_a A4) (@ tptp.set_mset_a A2)) (=> (@ P F4) (@ P (@ (@ tptp.add_mset_a A4) F4))))) (@ P F3))))))
% 0.23/0.59 (assert (forall ((A tptp.a) (B4 tptp.multiset_a)) (=> (@ (@ tptp.member_a A) (@ tptp.set_mset_a B4)) (@ (@ tptp.subseteq_mset_a (@ (@ tptp.add_mset_a A) tptp.zero_zero_multiset_a)) B4))))
% 0.23/0.59 (assert (forall ((X tptp.a) (XS tptp.multiset_a) (Y tptp.a)) (let ((_let_1 (@ tptp.member_a X))) (=> (@ _let_1 (@ tptp.set_mset_a XS)) (@ _let_1 (@ tptp.set_mset_a (@ (@ tptp.plus_plus_multiset_a (@ (@ tptp.add_mset_a Y) tptp.zero_zero_multiset_a)) XS)))))))
% 0.23/0.59 (assert (forall ((X tptp.a) (XS tptp.multiset_a)) (@ (@ tptp.member_a X) (@ tptp.set_mset_a (@ (@ tptp.plus_plus_multiset_a (@ (@ tptp.add_mset_a X) tptp.zero_zero_multiset_a)) XS)))))
% 0.23/0.59 (assert (forall ((N tptp.multiset_a) (M tptp.multiset_a) (R tptp.set_Product_prod_a_a)) (=> (@ (@ tptp.member340150864iset_a (@ (@ tptp.produc2037245207iset_a N) M)) (@ tptp.mult1_a R)) (not (forall ((A4 tptp.a) (M0 tptp.multiset_a)) (=> (= M (@ (@ tptp.add_mset_a A4) M0)) (forall ((K3 tptp.multiset_a)) (=> (= N (@ (@ tptp.plus_plus_multiset_a M0) K3)) (not (forall ((B6 tptp.a)) (=> (@ (@ tptp.member_a B6) (@ tptp.set_mset_a K3)) (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a B6) A4)) R))))))))))))
% 0.23/0.59 (assert (forall ((M tptp.multiset_a) (A tptp.a) (M02 tptp.multiset_a) (N tptp.multiset_a) (K4 tptp.multiset_a) (R tptp.set_Product_prod_a_a)) (=> (= M (@ (@ tptp.add_mset_a A) M02)) (=> (= N (@ (@ tptp.plus_plus_multiset_a M02) K4)) (=> (forall ((B3 tptp.a)) (=> (@ (@ tptp.member_a B3) (@ tptp.set_mset_a K4)) (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a B3) A)) R))) (@ (@ tptp.member340150864iset_a (@ (@ tptp.produc2037245207iset_a N) M)) (@ tptp.mult1_a R)))))))
% 0.23/0.59 (assert (forall ((N tptp.multiset_a) (A tptp.a) (M02 tptp.multiset_a) (R tptp.set_Product_prod_a_a)) (=> (@ (@ tptp.member340150864iset_a (@ (@ tptp.produc2037245207iset_a N) (@ (@ tptp.add_mset_a A) M02))) (@ tptp.mult1_a R)) (or (exists ((M2 tptp.multiset_a)) (and (@ (@ tptp.member340150864iset_a (@ (@ tptp.produc2037245207iset_a M2) M02)) (@ tptp.mult1_a R)) (= N (@ (@ tptp.add_mset_a A) M2)))) (exists ((K3 tptp.multiset_a)) (and (forall ((B6 tptp.a)) (=> (@ (@ tptp.member_a B6) (@ tptp.set_mset_a K3)) (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a B6) A)) R))) (= N (@ (@ tptp.plus_plus_multiset_a M02) K3))))))))
% 0.23/0.59 (assert (forall ((A2 tptp.set_a) (B4 tptp.set_a)) (=> (forall ((X4 tptp.a)) (let ((_let_1 (@ tptp.member_a X4))) (=> (@ _let_1 A2) (@ _let_1 B4)))) (@ (@ tptp.ord_less_eq_set_a A2) B4))))
% 0.23/0.59 (assert (forall ((A2 tptp.set_a) (B4 tptp.set_a) (X tptp.a)) (let ((_let_1 (@ tptp.member_a X))) (=> (@ (@ tptp.ord_less_eq_set_a A2) B4) (=> (@ _let_1 A2) (@ _let_1 B4))))))
% 0.23/0.59 (assert (forall ((A2 tptp.set_a) (B4 tptp.set_a) (C tptp.a)) (let ((_let_1 (@ tptp.member_a C))) (=> (@ (@ tptp.ord_less_eq_set_a A2) B4) (=> (@ _let_1 A2) (@ _let_1 B4))))))
% 0.23/0.59 (assert (= tptp.ord_less_eq_set_a (lambda ((A6 tptp.set_a) (B7 tptp.set_a)) (forall ((X5 tptp.a)) (let ((_let_1 (@ tptp.member_a X5))) (=> (@ _let_1 A6) (@ _let_1 B7)))))))
% 0.23/0.59 (assert (= tptp.ord_less_eq_set_a (lambda ((A6 tptp.set_a) (B7 tptp.set_a)) (forall ((T2 tptp.a)) (let ((_let_1 (@ tptp.member_a T2))) (=> (@ _let_1 A6) (@ _let_1 B7)))))))
% 0.23/0.59 (assert (forall ((J2 tptp.multiset_a) (K4 tptp.multiset_a) (R tptp.set_Product_prod_a_a) (I2 tptp.multiset_a)) (let ((_let_1 (@ tptp.plus_plus_multiset_a I2))) (=> (not (= J2 tptp.zero_zero_multiset_a)) (=> (forall ((X4 tptp.a)) (=> (@ (@ tptp.member_a X4) (@ tptp.set_mset_a K4)) (exists ((Xa tptp.a)) (and (@ (@ tptp.member_a Xa) (@ tptp.set_mset_a J2)) (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X4) Xa)) R))))) (@ (@ tptp.member340150864iset_a (@ (@ tptp.produc2037245207iset_a (@ _let_1 K4)) (@ _let_1 J2))) (@ tptp.mult_a R)))))))
% 0.23/0.59 (assert (forall ((R tptp.set_Product_prod_a_a) (M tptp.multiset_a) (N tptp.multiset_a)) (=> (@ tptp.trans_a R) (=> (@ (@ tptp.member340150864iset_a (@ (@ tptp.produc2037245207iset_a M) N)) (@ tptp.mult_a R)) (exists ((I3 tptp.multiset_a) (J3 tptp.multiset_a)) (and (= N (@ (@ tptp.plus_plus_multiset_a I3) J3)) (exists ((K3 tptp.multiset_a)) (and (= M (@ (@ tptp.plus_plus_multiset_a I3) K3)) (not (= J3 tptp.zero_zero_multiset_a)) (forall ((X7 tptp.a)) (=> (@ (@ tptp.member_a X7) (@ tptp.set_mset_a K3)) (exists ((Xa2 tptp.a)) (and (@ (@ tptp.member_a Xa2) (@ tptp.set_mset_a J3)) (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X7) Xa2)) R)))))))))))))
% 0.23/0.79 (assert (forall ((M tptp.multiset_multiset_a)) (= (= (@ (@ (@ tptp.comm_m315775925iset_a tptp.plus_plus_multiset_a) tptp.zero_zero_multiset_a) M) tptp.zero_zero_multiset_a) (forall ((X5 tptp.multiset_a)) (=> (@ (@ tptp.member_multiset_a X5) (@ tptp.set_mset_multiset_a M)) (= X5 tptp.zero_zero_multiset_a))))))
% 0.23/0.79 (assert (forall ((S tptp.set_Product_prod_a_a) (Uu tptp.a) (X8 tptp.multiset_a) (Y7 tptp.multiset_a)) (let ((_let_1 (@ tptp.mult_a S))) (let ((_let_2 (@ tptp.add_mset_a Uu))) (=> (@ tptp.trans_a S) (=> (@ tptp.irrefl_a S) (= (@ (@ tptp.member340150864iset_a (@ (@ tptp.produc2037245207iset_a (@ _let_2 X8)) (@ _let_2 Y7))) _let_1) (@ (@ tptp.member340150864iset_a (@ (@ tptp.produc2037245207iset_a X8) Y7)) _let_1))))))))
% 0.23/0.79 (assert (forall ((X tptp.a) (M tptp.multiset_a) (NN tptp.multiset_multiset_a)) (let ((_let_1 (@ tptp.member_a X))) (= (@ _let_1 (@ tptp.set_mset_a (@ (@ (@ tptp.fold_m382157835iset_a tptp.plus_plus_multiset_a) M) NN))) (or (@ _let_1 (@ tptp.set_mset_a M)) (exists ((N3 tptp.multiset_a)) (and (@ (@ tptp.member_multiset_a N3) (@ tptp.set_mset_multiset_a NN)) (@ (@ tptp.member_a X) (@ tptp.set_mset_a N3)))))))))
% 0.23/0.79 (assert (= tptp.plus_plus_multiset_a (@ tptp.fold_m364285649iset_a tptp.add_mset_a)))
% 0.23/0.79 (assert (forall ((M tptp.multiset_a) (A tptp.a)) (let ((_let_1 (@ tptp.add_mset_a A))) (=> (@ (@ tptp.nO_MAT1617603563iset_a tptp.zero_zero_multiset_a) M) (= (@ _let_1 M) (@ (@ tptp.plus_plus_multiset_a (@ _let_1 tptp.zero_zero_multiset_a)) M))))))
% 0.23/0.79 (assert (forall ((K4 tptp.multiset_a) (F (-> tptp.a tptp.multiset_a)) (G (-> tptp.a tptp.multiset_a))) (let ((_let_1 (@ (@ tptp.comm_m315775925iset_a tptp.plus_plus_multiset_a) tptp.zero_zero_multiset_a))) (=> (forall ((I4 tptp.a)) (=> (@ (@ tptp.member_a I4) (@ tptp.set_mset_a K4)) (@ (@ tptp.subseteq_mset_a (@ F I4)) (@ G I4)))) (@ (@ tptp.subseteq_mset_a (@ _let_1 (@ (@ tptp.image_929116801iset_a F) K4))) (@ _let_1 (@ (@ tptp.image_929116801iset_a G) K4)))))))
% 0.23/0.79 (assert (forall ((F (-> tptp.a tptp.a)) (A tptp.a) (M tptp.multiset_a)) (let ((_let_1 (@ tptp.image_mset_a_a F))) (= (@ _let_1 (@ (@ tptp.add_mset_a A) M)) (@ (@ tptp.add_mset_a (@ F A)) (@ _let_1 M))))))
% 0.23/0.79 (assert (forall ((F (-> tptp.a tptp.a)) (M tptp.multiset_a) (B tptp.a) (N tptp.multiset_a)) (=> (= (@ (@ tptp.image_mset_a_a F) M) (@ (@ tptp.add_mset_a B) N)) (exists ((M1 tptp.multiset_a) (A4 tptp.a)) (and (= M (@ (@ tptp.add_mset_a A4) M1)) (= (@ F A4) B) (= (@ (@ tptp.image_mset_a_a F) M1) N))))))
% 0.23/0.79 (assert (forall ((F (-> tptp.a tptp.a)) (A tptp.a) (M tptp.multiset_a) (N tptp.multiset_a)) (=> (= (@ (@ tptp.image_mset_a_a F) (@ (@ tptp.add_mset_a A) M)) N) (exists ((N1 tptp.multiset_a)) (and (= N (@ (@ tptp.add_mset_a (@ F A)) N1)) (= (@ (@ tptp.image_mset_a_a F) M) N1))))))
% 0.23/0.79 (assert (forall ((F (-> tptp.a tptp.a)) (X tptp.a)) (= (@ (@ tptp.image_mset_a_a F) (@ (@ tptp.add_mset_a X) tptp.zero_zero_multiset_a)) (@ (@ tptp.add_mset_a (@ F X)) tptp.zero_zero_multiset_a))))
% 0.23/0.79 (assert (not (@ tptp.is_heap_a (@ tptp.heapIm1091024090Down_a (@ (@ (@ tptp.t_a tptp.v2) tptp.e_a) (@ (@ (@ tptp.t_a tptp.v1) tptp.l1) tptp.r1))))))
% 0.23/0.79 (set-info :filename cvc5---1.0.5_20824)
% 0.23/0.79 (check-sat-assuming ( true ))
% 0.23/0.79 ------- get file name : TPTP file name is ITP068^1
% 0.23/0.79 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_20824.smt2...
% 0.23/0.79 --- Run --ho-elim --full-saturate-quant at 10...
% 0.23/0.79 % SZS status Theorem for ITP068^1
% 0.23/0.79 % SZS output start Proof for ITP068^1
% 0.23/0.79 (
% 0.23/0.79 (let ((_let_1 (@ (@ (@ tptp.t_a tptp.v2) tptp.e_a) (@ (@ (@ tptp.t_a tptp.v1) tptp.l1) tptp.r1)))) (let ((_let_2 (not (@ tptp.is_heap_a (@ tptp.heapIm1091024090Down_a _let_1))))) (let ((_let_3 (forall ((V tptp.a) (Va2 tptp.a) (Vb2 tptp.tree_a) (Vc2 tptp.tree_a)) (let ((_let_1 (@ (@ (@ tptp.t_a Va2) Vb2) Vc2))) (= (@ 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))))))) (let ((_let_4 (forall ((Va2 tptp.a) (Vb2 tptp.tree_a) (Vc2 tptp.tree_a) (V tptp.a)) (let ((_let_1 (@ (@ (@ tptp.t_a Va2) Vb2) Vc2))) (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 ((_let_5 (forall ((V tptp.a) (Uu tptp.tree_a) (Uv tptp.tree_a)) (= (@ tptp.val_a (@ (@ (@ tptp.t_a V) Uu) Uv)) V)))) (let ((_let_6 (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)))))) (let ((_let_7 (= _let_1 (@ (@ (@ tptp.t_a tptp.va) tptp.la) tptp.ra)))) (let ((_let_8 (@ (@ tptp.ord_less_eq_a tptp.v1) tptp.v2))) (let ((_let_9 (@ tptp.is_heap_a tptp.ra))) (let ((_let_10 (ho_67 (ho_72 (ho_71 k_70 tptp.v1) tptp.l1) tptp.r1))) (let ((_let_11 (ho_67 (ho_72 (ho_71 k_70 tptp.v2) tptp.e_a) _let_10))) (let ((_let_12 (ho_43 k_69 _let_11))) (let ((_let_13 (ho_43 k_69 _let_10))) (let ((_let_14 (ho_76 k_75 _let_10))) (let ((_let_15 (ho_40 (ho_39 k_48 _let_14) tptp.v2))) (let ((_let_16 (and _let_15 _let_13))) (let ((_let_17 (= _let_16 _let_12))) (let ((_let_18 (ho_67 k_66 _let_11))) (let ((_let_19 (= _let_11 _let_18))) (let ((_let_20 (ho_43 k_69 _let_18))) (let ((_let_21 (not _let_12))) (let ((_let_22 (not _let_15))) (let ((_let_23 (or _let_22 _let_19))) (let ((_let_24 (forall ((BOUND_VARIABLE_4135 tptp.a) (BOUND_VARIABLE_4137 tptp.tree_a) (BOUND_VARIABLE_4139 tptp.tree_a) (BOUND_VARIABLE_4141 tptp.a)) (let ((_let_1 (ho_67 (ho_72 (ho_71 k_70 BOUND_VARIABLE_4135) BOUND_VARIABLE_4137) BOUND_VARIABLE_4139))) (let ((_let_2 (ho_67 (ho_72 (ho_71 k_70 BOUND_VARIABLE_4141) tptp.e_a) _let_1))) (or (not (ho_40 (ho_39 k_48 (ho_76 k_75 _let_1)) BOUND_VARIABLE_4141)) (= _let_2 (ho_67 k_66 _let_2)))))))) (let ((_let_25 (0))) (let ((_let_26 (_let_24))) (let ((_let_27 (= tptp.v1 _let_14))) (let ((_let_28 (ho_40 (ho_39 k_48 tptp.v1) tptp.v2))) (let ((_let_29 (forall ((V tptp.a) (Uu tptp.tree_a) (Uv tptp.tree_a)) (= V (ho_76 k_75 (ho_67 (ho_72 (ho_71 k_70 V) Uu) Uv)))))) (let ((_let_30 (EQ_RESOLVE (ASSUME :args (_let_5)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_5 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_29))))))) (let ((_let_31 (EQ_RESOLVE (ASSUME :args (_let_8)) (PREPROCESS :args ((= _let_8 _let_28)))))) (let ((_let_32 (and _let_28 _let_27))) (let ((_let_33 (_let_28 _let_27))) (let ((_let_34 (ASSUME :args (_let_27)))) (let ((_let_35 (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_32)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_31 _let_34) (SCOPE (TRUE_ELIM (TRANS (CONG (CONG (REFL :args (k_48)) (SYMM _let_34) :args (APPLY_UF ho_39)) (REFL :args (tptp.v2)) :args (APPLY_UF ho_40)) (TRUE_INTRO _let_31))) :args _let_33)) :args _let_33)) :args (true _let_32)) :args ((or _let_15 (not _let_28) (not _let_27)))) _let_31 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_30 :args (tptp.v1 tptp.l1 tptp.r1 QUANTIFIERS_INST_CBQI_PROP)) :args (_let_29))) _let_30 :args (_let_27 false _let_29)) :args (_let_15 false _let_28 false _let_27)))) (let ((_let_36 (not _let_20))) (let ((_let_37 (EQ_RESOLVE (ASSUME :args (_let_2)) (PREPROCESS :args ((= _let_2 _let_36)))))) (let ((_let_38 (and _let_36 _let_19))) (let ((_let_39 (_let_36 _let_19))) (let ((_let_40 (APPLY_UF ho_43))) (let ((_let_41 (ASSUME :args (_let_19)))) (let ((_let_42 (REFL :args (k_69)))) (let ((_let_43 (= tptp.ra _let_10))) (let ((_let_44 (ho_43 k_69 tptp.ra))) (let ((_let_45 (and (= tptp.v2 tptp.va) (= tptp.e_a tptp.la) _let_43))) (let ((_let_46 (= (ho_67 (ho_72 (ho_71 k_70 tptp.va) tptp.la) tptp.ra) _let_11))) (let ((_let_47 (= _let_46 _let_45))) (let ((_let_48 (forall ((X21 tptp.a) (X22 tptp.tree_a) (X23 tptp.tree_a) (Y21 tptp.a) (Y22 tptp.tree_a) (Y23 tptp.tree_a)) (= (and (= X21 Y21) (= X22 Y22) (= X23 Y23)) (= (ho_67 (ho_72 (ho_71 k_70 Y21) Y22) Y23) (ho_67 (ho_72 (ho_71 k_70 X21) X22) X23)))))) (let ((_let_49 (EQ_RESOLVE (ASSUME :args (_let_6)) (PREPROCESS :args ((= _let_6 _let_48)))))) (let ((_let_50 (forall ((u |u_(-> _u_(-> tptp.a tptp.a Bool)_ tptp.tree_a tptp.tree_a Bool)|) (e |u_(-> tptp.tree_a tptp.tree_a Bool)|) (i |u_(-> tptp.a tptp.a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.a tptp.a Bool)_ tptp.tree_a tptp.tree_a Bool)|)) (not (forall ((ii |u_(-> tptp.a tptp.a Bool)|)) (= (ho_88 v ii) (ite (= i ii) e (ho_88 u ii)))))))))) (let ((_let_51 (forall ((x |u_(-> _u_(-> tptp.a tptp.a Bool)_ tptp.tree_a tptp.tree_a Bool)|) (y |u_(-> _u_(-> tptp.a tptp.a Bool)_ tptp.tree_a tptp.tree_a Bool)|)) (or (not (forall ((z |u_(-> tptp.a tptp.a Bool)|)) (= (ho_88 x z) (ho_88 y z)))) (= x y))))) (let ((_let_52 (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_25 v ii) (ite (= i ii) e (ho_25 u ii)))))))))) (let ((_let_53 (forall ((x |u_(-> tptp.set_a Bool)|) (y |u_(-> tptp.set_a Bool)|)) (or (not (forall ((z tptp.set_a)) (= (ho_25 x z) (ho_25 y z)))) (= x y))))) (let ((_let_54 (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_31 v ii) (ite (= i ii) e (ho_31 u ii)))))))))) (let ((_let_55 (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_31 x z) (ho_31 y z)))) (= x y))))) (let ((_let_56 (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_86 v ii) (ite (= i ii) e (ho_86 u ii)))))))))) (let ((_let_57 (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_86 x z) (ho_86 y z)))) (= x y))))) (let ((_let_58 (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_63 v ii) (ite (= i ii) e (ho_63 u ii)))))))))) (let ((_let_59 (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_63 x z) (ho_63 y z)))) (= x y))))) (let ((_let_60 (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_84 v ii) (ite (= i ii) e (ho_84 u ii)))))))))) (let ((_let_61 (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_84 x z) (ho_84 y z)))) (= x y))))) (let ((_let_62 (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_100 v ii) (ite (= i ii) e (ho_100 u ii)))))))))) (let ((_let_63 (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_100 x z) (ho_100 y z)))) (= x y))))) (let ((_let_64 (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_82 v ii) (ite (= i ii) e (ho_82 u ii)))))))))) (let ((_let_65 (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_82 x z) (ho_82 y z)))) (= x y))))) (let ((_let_66 (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_65 v ii) (ite (= i ii) e (ho_65 u ii)))))))))) (let ((_let_67 (forall ((x |u_(-> tptp.a tptp.tree_a Bool)|) (y |u_(-> tptp.a tptp.tree_a Bool)|)) (or (not (forall ((z tptp.a)) (= (ho_65 x z) (ho_65 y z)))) (= x y))))) (let ((_let_68 (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_79 v ii) (ite (= i ii) e (ho_79 u ii)))))))))) (let ((_let_69 (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_79 x z) (ho_79 y z)))) (= x y))))) (let ((_let_70 (forall ((u |u_(-> _u_(-> tptp.multiset_a tptp.multiset_a tptp.multiset_a)_ tptp.multiset_a tptp.multiset_multiset_a tptp.multiset_a)|) (e |u_(-> tptp.multiset_a tptp.multiset_multiset_a tptp.multiset_a)|) (i |u_(-> tptp.multiset_a tptp.multiset_a tptp.multiset_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.multiset_a tptp.multiset_a tptp.multiset_a)_ tptp.multiset_a tptp.multiset_multiset_a tptp.multiset_a)|)) (not (forall ((ii |u_(-> tptp.multiset_a tptp.multiset_a tptp.multiset_a)|)) (= (ho_120 v ii) (ite (= i ii) e (ho_120 u ii)))))))))) (let ((_let_71 (forall ((x |u_(-> _u_(-> tptp.multiset_a tptp.multiset_a tptp.multiset_a)_ tptp.multiset_a tptp.multiset_multiset_a tptp.multiset_a)|) (y |u_(-> _u_(-> tptp.multiset_a tptp.multiset_a tptp.multiset_a)_ tptp.multiset_a tptp.multiset_multiset_a tptp.multiset_a)|)) (or (not (forall ((z |u_(-> tptp.multiset_a tptp.multiset_a tptp.multiset_a)|)) (= (ho_120 x z) (ho_120 y z)))) (= x y))))) (let ((_let_72 (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_77 v ii) (ite (= i ii) e (ho_77 u ii)))))))))) (let ((_let_73 (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_77 x z) (ho_77 y z)))) (= x y))))) (let ((_let_74 (forall ((u |u_(-> _u_(-> tptp.a tptp.multiset_a tptp.multiset_a)_ tptp.multiset_a tptp.multiset_a tptp.multiset_a)|) (e |u_(-> tptp.multiset_a tptp.multiset_a tptp.multiset_a)|) (i |u_(-> tptp.a tptp.multiset_a tptp.multiset_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.a tptp.multiset_a tptp.multiset_a)_ tptp.multiset_a tptp.multiset_a tptp.multiset_a)|)) (not (forall ((ii |u_(-> tptp.a tptp.multiset_a tptp.multiset_a)|)) (= (ho_36 v ii) (ite (= i ii) e (ho_36 u ii)))))))))) (let ((_let_75 (forall ((x |u_(-> _u_(-> tptp.a tptp.multiset_a tptp.multiset_a)_ tptp.multiset_a tptp.multiset_a tptp.multiset_a)|) (y |u_(-> _u_(-> tptp.a tptp.multiset_a tptp.multiset_a)_ tptp.multiset_a tptp.multiset_a tptp.multiset_a)|)) (or (not (forall ((z |u_(-> tptp.a tptp.multiset_a tptp.multiset_a)|)) (= (ho_36 x z) (ho_36 y z)))) (= x y))))) (let ((_let_76 (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_71 v ii) (ite (= i ii) e (ho_71 u ii)))))))))) (let ((_let_77 (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_71 x z) (ho_71 y z)))) (= x y))))) (let ((_let_78 (forall ((u |u_(-> tptp.a tptp.a tptp.product_prod_a_a)|) (e |u_(-> tptp.a tptp.product_prod_a_a)|) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.a tptp.product_prod_a_a)|)) (not (forall ((ii tptp.a)) (= (ho_104 v ii) (ite (= i ii) e (ho_104 u ii)))))))))) (let ((_let_79 (forall ((x |u_(-> tptp.a tptp.a tptp.product_prod_a_a)|) (y |u_(-> tptp.a tptp.a tptp.product_prod_a_a)|)) (or (not (forall ((z tptp.a)) (= (ho_104 x z) (ho_104 y z)))) (= x y))))) (let ((_let_80 (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_67 v ii) (ite (= i ii) e (ho_67 u ii)))))))))) (let ((_let_81 (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_67 x z) (ho_67 y z)))) (= x y))))) (let ((_let_82 (forall ((u |u_(-> tptp.a Bool)|) (e Bool) (i tptp.a)) (not (forall ((v |u_(-> tptp.a Bool)|)) (not (forall ((ii tptp.a)) (= (ho_40 v ii) (ite (= i ii) e (ho_40 u ii)))))))))) (let ((_let_83 (forall ((x |u_(-> tptp.a Bool)|) (y |u_(-> tptp.a Bool)|)) (or (not (forall ((z tptp.a)) (= (ho_40 x z) (ho_40 y z)))) (= x y))))) (let ((_let_84 (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_76 v ii) (ite (= i ii) e (ho_76 u ii)))))))))) (let ((_let_85 (forall ((x |u_(-> tptp.tree_a tptp.a)|) (y |u_(-> tptp.tree_a tptp.a)|)) (or (not (forall ((z tptp.tree_a)) (= (ho_76 x z) (ho_76 y z)))) (= x y))))) (let ((_let_86 (forall ((u |u_(-> tptp.product_prod_a_a tptp.set_Product_prod_a_a Bool)|) (e |u_(-> tptp.set_Product_prod_a_a Bool)|) (i tptp.product_prod_a_a)) (not (forall ((v |u_(-> tptp.product_prod_a_a tptp.set_Product_prod_a_a Bool)|)) (not (forall ((ii tptp.product_prod_a_a)) (= (ho_107 v ii) (ite (= i ii) e (ho_107 u ii)))))))))) (let ((_let_87 (forall ((x |u_(-> tptp.product_prod_a_a tptp.set_Product_prod_a_a Bool)|) (y |u_(-> tptp.product_prod_a_a tptp.set_Product_prod_a_a Bool)|)) (or (not (forall ((z tptp.product_prod_a_a)) (= (ho_107 x z) (ho_107 y z)))) (= x y))))) (let ((_let_88 (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_46 v ii) (ite (= i ii) e (ho_46 u ii)))))))))) (let ((_let_89 (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_46 x z) (ho_46 y z)))) (= x y))))) (let ((_let_90 (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_47 v ii) (ite (= i ii) e (ho_47 u ii)))))))))) (let ((_let_91 (forall ((x |u_(-> _u_(-> Bool tptp.a)_ Bool)|) (y |u_(-> _u_(-> Bool tptp.a)_ Bool)|)) (or (not (forall ((z |u_(-> Bool tptp.a)|)) (= (ho_47 x z) (ho_47 y z)))) (= x y))))) (let ((_let_92 (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_33 v ii) (ite (= i ii) e (ho_33 u ii)))))))))) (let ((_let_93 (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_33 x z) (ho_33 y z)))) (= x y))))) (let ((_let_94 (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_99 v ii) (ite (= i ii) e (ho_99 u ii)))))))))) (let ((_let_95 (forall ((x |u_(-> tptp.multiset_a Bool)|) (y |u_(-> tptp.multiset_a Bool)|)) (or (not (forall ((z tptp.multiset_a)) (= (ho_99 x z) (ho_99 y z)))) (= x y))))) (let ((_let_96 (forall ((u |u_(-> tptp.produc1127127335iset_a tptp.set_Pr158363655iset_a Bool)|) (e |u_(-> tptp.set_Pr158363655iset_a Bool)|) (i tptp.produc1127127335iset_a)) (not (forall ((v |u_(-> tptp.produc1127127335iset_a tptp.set_Pr158363655iset_a Bool)|)) (not (forall ((ii tptp.produc1127127335iset_a)) (= (ho_115 v ii) (ite (= i ii) e (ho_115 u ii)))))))))) (let ((_let_97 (forall ((x |u_(-> tptp.produc1127127335iset_a tptp.set_Pr158363655iset_a Bool)|) (y |u_(-> tptp.produc1127127335iset_a tptp.set_Pr158363655iset_a Bool)|)) (or (not (forall ((z tptp.produc1127127335iset_a)) (= (ho_115 x z) (ho_115 y z)))) (= x y))))) (let ((_let_98 (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_27 v ii) (ite (= i ii) e (ho_27 u ii)))))))))) (let ((_let_99 (forall ((x |u_(-> tptp.a tptp.set_a Bool)|) (y |u_(-> tptp.a tptp.set_a Bool)|)) (or (not (forall ((z tptp.a)) (= (ho_27 x z) (ho_27 y z)))) (= x y))))) (let ((_let_100 (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_98 v ii) (ite (= i ii) e (ho_98 u ii)))))))))) (let ((_let_101 (forall ((x |u_(-> tptp.set_a tptp.a)|) (y |u_(-> tptp.set_a tptp.a)|)) (or (not (forall ((z tptp.set_a)) (= (ho_98 x z) (ho_98 y z)))) (= x y))))) (let ((_let_102 (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_78 v ii) (ite (= i ii) e (ho_78 u ii)))))))))) (let ((_let_103 (forall ((x |u_(-> tptp.a Bool tptp.a)|) (y |u_(-> tptp.a Bool tptp.a)|)) (or (not (forall ((z tptp.a)) (= (ho_78 x z) (ho_78 y z)))) (= x y))))) (let ((_let_104 (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_24 v ii) (ite (= i ii) e (ho_24 u ii)))))))))) (let ((_let_105 (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_24 x z) (ho_24 y z)))) (= x y))))) (let ((_let_106 (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_43 v ii) (ite (= i ii) e (ho_43 u ii)))))))))) (let ((_let_107 (forall ((x |u_(-> tptp.tree_a Bool)|) (y |u_(-> tptp.tree_a Bool)|)) (or (not (forall ((z tptp.tree_a)) (= (ho_43 x z) (ho_43 y z)))) (= x y))))) (let ((_let_108 (forall ((u |u_(-> tptp.multiset_a tptp.set_multiset_a Bool)|) (e |u_(-> tptp.set_multiset_a Bool)|) (i tptp.multiset_a)) (not (forall ((v |u_(-> tptp.multiset_a tptp.set_multiset_a Bool)|)) (not (forall ((ii tptp.multiset_a)) (= (ho_126 v ii) (ite (= i ii) e (ho_126 u ii)))))))))) (let ((_let_109 (forall ((x |u_(-> tptp.multiset_a tptp.set_multiset_a Bool)|) (y |u_(-> tptp.multiset_a tptp.set_multiset_a Bool)|)) (or (not (forall ((z tptp.multiset_a)) (= (ho_126 x z) (ho_126 y z)))) (= x y))))) (let ((_let_110 (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_30 v ii) (ite (= i ii) e (ho_30 u ii)))))))))) (let ((_let_111 (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_30 x z) (ho_30 y z)))) (= x y))))) (let ((_let_112 (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_80 v ii) (ite (= i ii) e (ho_80 u ii)))))))))) (let ((_let_113 (forall ((x |u_(-> tptp.a tptp.a)|) (y |u_(-> tptp.a tptp.a)|)) (or (not (forall ((z tptp.a)) (= (ho_80 x z) (ho_80 y z)))) (= x y))))) (let ((_let_114 (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_39 v ii) (ite (= i ii) e (ho_39 u ii)))))))))) (let ((_let_115 (forall ((x |u_(-> tptp.a tptp.a Bool)|) (y |u_(-> tptp.a tptp.a Bool)|)) (or (not (forall ((z tptp.a)) (= (ho_39 x z) (ho_39 y z)))) (= x y))))) (let ((_let_116 (forall ((u |u_(-> _u_(-> tptp.tree_a tptp.tree_a Bool)_ Bool)|) (e Bool) (i |u_(-> tptp.tree_a tptp.tree_a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.tree_a tptp.tree_a Bool)_ Bool)|)) (not (forall ((ii |u_(-> tptp.tree_a tptp.tree_a Bool)|)) (= (ho_91 v ii) (ite (= i ii) e (ho_91 u ii)))))))))) (let ((_let_117 (forall ((x |u_(-> _u_(-> tptp.tree_a tptp.tree_a Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.tree_a tptp.tree_a Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.tree_a tptp.tree_a Bool)|)) (= (ho_91 x z) (ho_91 y z)))) (= x y))))) (let ((_let_118 (forall ((u |u_(-> tptp.set_Product_prod_a_a Bool)|) (e Bool) (i tptp.set_Product_prod_a_a)) (not (forall ((v |u_(-> tptp.set_Product_prod_a_a Bool)|)) (not (forall ((ii tptp.set_Product_prod_a_a)) (= (ho_108 v ii) (ite (= i ii) e (ho_108 u ii)))))))))) (let ((_let_119 (forall ((x |u_(-> tptp.set_Product_prod_a_a Bool)|) (y |u_(-> tptp.set_Product_prod_a_a Bool)|)) (or (not (forall ((z tptp.set_Product_prod_a_a)) (= (ho_108 x z) (ho_108 y z)))) (= x y))))) (let ((_let_120 (forall ((u |u_(-> tptp.a tptp.product_prod_a_a)|) (e tptp.product_prod_a_a) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.product_prod_a_a)|)) (not (forall ((ii tptp.a)) (= (ho_105 v ii) (ite (= i ii) e (ho_105 u ii)))))))))) (let ((_let_121 (forall ((x |u_(-> tptp.a tptp.product_prod_a_a)|) (y |u_(-> tptp.a tptp.product_prod_a_a)|)) (or (not (forall ((z tptp.a)) (= (ho_105 x z) (ho_105 y z)))) (= x y))))) (let ((_let_122 (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_37 v ii) (ite (= i ii) e (ho_37 u ii)))))))))) (let ((_let_123 (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_37 x z) (ho_37 y z)))) (= x y))))) (let ((_let_124 (forall ((u |u_(-> tptp.tree_a tptp.tree_a Bool)|) (e |u_(-> tptp.tree_a Bool)|) (i tptp.tree_a)) (not (forall ((v |u_(-> tptp.tree_a tptp.tree_a Bool)|)) (not (forall ((ii tptp.tree_a)) (= (ho_42 v ii) (ite (= i ii) e (ho_42 u ii)))))))))) (let ((_let_125 (forall ((x |u_(-> tptp.tree_a tptp.tree_a Bool)|) (y |u_(-> tptp.tree_a tptp.tree_a Bool)|)) (or (not (forall ((z tptp.tree_a)) (= (ho_42 x z) (ho_42 y z)))) (= x y))))) (let ((_let_126 (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_72 v ii) (ite (= i ii) e (ho_72 u ii)))))))))) (let ((_let_127 (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_72 x z) (ho_72 y z)))) (= x y))))) (let ((_let_128 (forall ((u |u_(-> Bool tptp.a)|) (e tptp.a) (i Bool)) (not (forall ((v |u_(-> Bool tptp.a)|)) (not (forall ((ii Bool)) (= (ho_44 v ii) (ite (= i ii) e (ho_44 u ii)))))))))) (let ((_let_129 (forall ((x |u_(-> Bool tptp.a)|) (y |u_(-> Bool tptp.a)|)) (or (not (forall ((z Bool)) (= (ho_44 x z) (ho_44 y z)))) (= x y))))) (let ((_let_130 (forall ((u |u_(-> tptp.multiset_a tptp.multiset_multiset_a)|) (e tptp.multiset_multiset_a) (i tptp.multiset_a)) (not (forall ((v |u_(-> tptp.multiset_a tptp.multiset_multiset_a)|)) (not (forall ((ii tptp.multiset_a)) (= (ho_134 v ii) (ite (= i ii) e (ho_134 u ii)))))))))) (let ((_let_131 (forall ((x |u_(-> tptp.multiset_a tptp.multiset_multiset_a)|) (y |u_(-> tptp.multiset_a tptp.multiset_multiset_a)|)) (or (not (forall ((z tptp.multiset_a)) (= (ho_134 x z) (ho_134 y z)))) (= x y))))) (let ((_let_132 (forall ((u |u_(-> _u_(-> tptp.tree_a tptp.tree_a Bool)_ _u_(-> tptp.tree_a tptp.tree_a Bool)_ Bool)|) (e |u_(-> _u_(-> tptp.tree_a tptp.tree_a Bool)_ Bool)|) (i |u_(-> tptp.tree_a tptp.tree_a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.tree_a tptp.tree_a Bool)_ _u_(-> tptp.tree_a tptp.tree_a Bool)_ Bool)|)) (not (forall ((ii |u_(-> tptp.tree_a tptp.tree_a Bool)|)) (= (ho_90 v ii) (ite (= i ii) e (ho_90 u ii)))))))))) (let ((_let_133 (forall ((x |u_(-> _u_(-> tptp.tree_a tptp.tree_a Bool)_ _u_(-> tptp.tree_a tptp.tree_a Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.tree_a tptp.tree_a Bool)_ _u_(-> tptp.tree_a tptp.tree_a Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.tree_a tptp.tree_a Bool)|)) (= (ho_90 x z) (ho_90 y z)))) (= x y))))) (let ((_let_134 (forall ((u |u_(-> _u_(-> tptp.a tptp.a Bool)_ Bool)|) (e Bool) (i |u_(-> tptp.a tptp.a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.a tptp.a Bool)_ Bool)|)) (not (forall ((ii |u_(-> tptp.a tptp.a Bool)|)) (= (ho_94 v ii) (ite (= i ii) e (ho_94 u ii)))))))))) (let ((_let_135 (forall ((x |u_(-> _u_(-> tptp.a tptp.a Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.a tptp.a Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.a tptp.a Bool)|)) (= (ho_94 x z) (ho_94 y z)))) (= x y))))) (let ((_let_136 (forall ((u |u_(-> tptp.multiset_a tptp.multiset_a tptp.produc1127127335iset_a)|) (e |u_(-> tptp.multiset_a tptp.produc1127127335iset_a)|) (i tptp.multiset_a)) (not (forall ((v |u_(-> tptp.multiset_a tptp.multiset_a tptp.produc1127127335iset_a)|)) (not (forall ((ii tptp.multiset_a)) (= (ho_112 v ii) (ite (= i ii) e (ho_112 u ii)))))))))) (let ((_let_137 (forall ((x |u_(-> tptp.multiset_a tptp.multiset_a tptp.produc1127127335iset_a)|) (y |u_(-> tptp.multiset_a tptp.multiset_a tptp.produc1127127335iset_a)|)) (or (not (forall ((z tptp.multiset_a)) (= (ho_112 x z) (ho_112 y z)))) (= x y))))) (let ((_let_138 (forall ((u |u_(-> _u_(-> tptp.a tptp.a Bool)_ _u_(-> tptp.a tptp.a Bool)_ Bool)|) (e |u_(-> _u_(-> tptp.a tptp.a Bool)_ Bool)|) (i |u_(-> tptp.a tptp.a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.a tptp.a Bool)_ _u_(-> tptp.a tptp.a Bool)_ Bool)|)) (not (forall ((ii |u_(-> tptp.a tptp.a Bool)|)) (= (ho_93 v ii) (ite (= i ii) e (ho_93 u ii)))))))))) (let ((_let_139 (forall ((x |u_(-> _u_(-> tptp.a tptp.a Bool)_ _u_(-> tptp.a tptp.a Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.a tptp.a Bool)_ _u_(-> tptp.a tptp.a Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.a tptp.a Bool)|)) (= (ho_93 x z) (ho_93 y z)))) (= x y))))) (let ((_let_140 (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_96 v ii) (ite (= i ii) e (ho_96 u ii)))))))))) (let ((_let_141 (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_96 x z) (ho_96 y z)))) (= x y))))) (let ((_let_142 (forall ((u |u_(-> tptp.set_Product_prod_a_a tptp.set_Pr158363655iset_a)|) (e tptp.set_Pr158363655iset_a) (i tptp.set_Product_prod_a_a)) (not (forall ((v |u_(-> tptp.set_Product_prod_a_a tptp.set_Pr158363655iset_a)|)) (not (forall ((ii tptp.set_Product_prod_a_a)) (= (ho_110 v ii) (ite (= i ii) e (ho_110 u ii)))))))))) (let ((_let_143 (forall ((x |u_(-> tptp.set_Product_prod_a_a tptp.set_Pr158363655iset_a)|) (y |u_(-> tptp.set_Product_prod_a_a tptp.set_Pr158363655iset_a)|)) (or (not (forall ((z tptp.set_Product_prod_a_a)) (= (ho_110 x z) (ho_110 y z)))) (= x y))))) (let ((_let_144 (forall ((u |u_(-> tptp.set_Pr158363655iset_a Bool)|) (e Bool) (i tptp.set_Pr158363655iset_a)) (not (forall ((v |u_(-> tptp.set_Pr158363655iset_a Bool)|)) (not (forall ((ii tptp.set_Pr158363655iset_a)) (= (ho_116 v ii) (ite (= i ii) e (ho_116 u ii)))))))))) (let ((_let_145 (forall ((x |u_(-> tptp.set_Pr158363655iset_a Bool)|) (y |u_(-> tptp.set_Pr158363655iset_a Bool)|)) (or (not (forall ((z tptp.set_Pr158363655iset_a)) (= (ho_116 x z) (ho_116 y z)))) (= x y))))) (let ((_let_146 (forall ((u |u_(-> tptp.multiset_a tptp.produc1127127335iset_a)|) (e tptp.produc1127127335iset_a) (i tptp.multiset_a)) (not (forall ((v |u_(-> tptp.multiset_a tptp.produc1127127335iset_a)|)) (not (forall ((ii tptp.multiset_a)) (= (ho_113 v ii) (ite (= i ii) e (ho_113 u ii)))))))))) (let ((_let_147 (forall ((x |u_(-> tptp.multiset_a tptp.produc1127127335iset_a)|) (y |u_(-> tptp.multiset_a tptp.produc1127127335iset_a)|)) (or (not (forall ((z tptp.multiset_a)) (= (ho_113 x z) (ho_113 y z)))) (= x y))))) (let ((_let_148 (forall ((u |u_(-> tptp.multiset_multiset_a tptp.multiset_a)|) (e tptp.multiset_a) (i tptp.multiset_multiset_a)) (not (forall ((v |u_(-> tptp.multiset_multiset_a tptp.multiset_a)|)) (not (forall ((ii tptp.multiset_multiset_a)) (= (ho_122 v ii) (ite (= i ii) e (ho_122 u ii)))))))))) (let ((_let_149 (forall ((x |u_(-> tptp.multiset_multiset_a tptp.multiset_a)|) (y |u_(-> tptp.multiset_multiset_a tptp.multiset_a)|)) (or (not (forall ((z tptp.multiset_multiset_a)) (= (ho_122 x z) (ho_122 y z)))) (= x y))))) (let ((_let_150 (forall ((u |u_(-> tptp.multiset_a tptp.multiset_multiset_a tptp.multiset_a)|) (e |u_(-> tptp.multiset_multiset_a tptp.multiset_a)|) (i tptp.multiset_a)) (not (forall ((v |u_(-> tptp.multiset_a tptp.multiset_multiset_a tptp.multiset_a)|)) (not (forall ((ii tptp.multiset_a)) (= (ho_121 v ii) (ite (= i ii) e (ho_121 u ii)))))))))) (let ((_let_151 (forall ((x |u_(-> tptp.multiset_a tptp.multiset_multiset_a tptp.multiset_a)|) (y |u_(-> tptp.multiset_a tptp.multiset_multiset_a tptp.multiset_a)|)) (or (not (forall ((z tptp.multiset_a)) (= (ho_121 x z) (ho_121 y z)))) (= x y))))) (let ((_let_152 (forall ((u |u_(-> tptp.multiset_multiset_a tptp.set_multiset_a)|) (e tptp.set_multiset_a) (i tptp.multiset_multiset_a)) (not (forall ((v |u_(-> tptp.multiset_multiset_a tptp.set_multiset_a)|)) (not (forall ((ii tptp.multiset_multiset_a)) (= (ho_124 v ii) (ite (= i ii) e (ho_124 u ii)))))))))) (let ((_let_153 (forall ((x |u_(-> tptp.multiset_multiset_a tptp.set_multiset_a)|) (y |u_(-> tptp.multiset_multiset_a tptp.set_multiset_a)|)) (or (not (forall ((z tptp.multiset_multiset_a)) (= (ho_124 x z) (ho_124 y z)))) (= x y))))) (let ((_let_154 (forall ((u |u_(-> tptp.set_multiset_a Bool)|) (e Bool) (i tptp.set_multiset_a)) (not (forall ((v |u_(-> tptp.set_multiset_a Bool)|)) (not (forall ((ii tptp.set_multiset_a)) (= (ho_127 v ii) (ite (= i ii) e (ho_127 u ii)))))))))) (let ((_let_155 (forall ((x |u_(-> tptp.set_multiset_a Bool)|) (y |u_(-> tptp.set_multiset_a Bool)|)) (or (not (forall ((z tptp.set_multiset_a)) (= (ho_127 x z) (ho_127 y z)))) (= x y))))) (let ((_let_156 (forall ((u |u_(-> tptp.a tptp.multiset_a)|) (e tptp.multiset_a) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.multiset_a)|)) (not (forall ((ii tptp.a)) (= (ho_131 v ii) (ite (= i ii) e (ho_131 u ii)))))))))) (let ((_let_157 (forall ((x |u_(-> tptp.a tptp.multiset_a)|) (y |u_(-> tptp.a tptp.multiset_a)|)) (or (not (forall ((z tptp.a)) (= (ho_131 x z) (ho_131 y z)))) (= x y))))) (let ((_let_158 (forall ((u |u_(-> _u_(-> tptp.a tptp.multiset_a)_ tptp.multiset_a tptp.multiset_multiset_a)|) (e |u_(-> tptp.multiset_a tptp.multiset_multiset_a)|) (i |u_(-> tptp.a tptp.multiset_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.a tptp.multiset_a)_ tptp.multiset_a tptp.multiset_multiset_a)|)) (not (forall ((ii |u_(-> tptp.a tptp.multiset_a)|)) (= (ho_133 v ii) (ite (= i ii) e (ho_133 u ii)))))))))) (let ((_let_159 (forall ((x |u_(-> _u_(-> tptp.a tptp.multiset_a)_ tptp.multiset_a tptp.multiset_multiset_a)|) (y |u_(-> _u_(-> tptp.a tptp.multiset_a)_ tptp.multiset_a tptp.multiset_multiset_a)|)) (or (not (forall ((z |u_(-> tptp.a tptp.multiset_a)|)) (= (ho_133 x z) (ho_133 y z)))) (= x y))))) (let ((_let_160 (forall ((u |u_(-> _u_(-> tptp.a tptp.a)_ tptp.multiset_a tptp.multiset_a)|) (e |u_(-> tptp.multiset_a tptp.multiset_a)|) (i |u_(-> tptp.a tptp.a)|)) (not (forall ((v |u_(-> _u_(-> tptp.a tptp.a)_ tptp.multiset_a tptp.multiset_a)|)) (not (forall ((ii |u_(-> tptp.a tptp.a)|)) (= (ho_136 v ii) (ite (= i ii) e (ho_136 u ii)))))))))) (let ((_let_161 (forall ((x |u_(-> _u_(-> tptp.a tptp.a)_ tptp.multiset_a tptp.multiset_a)|) (y |u_(-> _u_(-> tptp.a tptp.a)_ tptp.multiset_a tptp.multiset_a)|)) (or (not (forall ((z |u_(-> tptp.a tptp.a)|)) (= (ho_136 x z) (ho_136 y z)))) (= x y))))) (let ((_let_162 (forall ((BOUND_VARIABLE_7624 tptp.set_a) (BOUND_VARIABLE_7625 tptp.set_a)) (= (ho_25 (ho_24 k_23 BOUND_VARIABLE_7624) BOUND_VARIABLE_7625) (forall ((X5 tptp.a)) (let ((_let_1 (ho_27 k_26 X5))) (or (not (ho_25 _let_1 BOUND_VARIABLE_7624)) (ho_25 _let_1 BOUND_VARIABLE_7625)))))))) (let ((_let_163 (forall ((BOUND_VARIABLE_7613 tptp.set_a) (BOUND_VARIABLE_7614 tptp.set_a)) (= (ho_25 (ho_24 k_28 BOUND_VARIABLE_7613) BOUND_VARIABLE_7614) (forall ((T2 tptp.a)) (let ((_let_1 (ho_27 k_26 T2))) (or (not (ho_25 _let_1 BOUND_VARIABLE_7613)) (ho_25 _let_1 BOUND_VARIABLE_7614)))))))) (let ((_let_164 (forall ((BOUND_VARIABLE_7603 tptp.a) (BOUND_VARIABLE_7604 tptp.multiset_a)) (= (ho_31 (ho_30 k_29 BOUND_VARIABLE_7603) BOUND_VARIABLE_7604) (ho_31 (ho_37 (ho_36 k_35 k_34) BOUND_VARIABLE_7604) (ho_31 (ho_30 k_34 BOUND_VARIABLE_7603) (ho_33 k_32 tptp.e_a))))))) (let ((_let_165 (forall ((BOUND_VARIABLE_7596 tptp.a) (BOUND_VARIABLE_7597 tptp.a)) (= (= BOUND_VARIABLE_7596 BOUND_VARIABLE_7597) (ho_40 (ho_39 k_38 BOUND_VARIABLE_7596) BOUND_VARIABLE_7597))))) (let ((_let_166 (forall ((BOUND_VARIABLE_7589 tptp.tree_a) (BOUND_VARIABLE_7590 tptp.tree_a)) (= (= BOUND_VARIABLE_7589 BOUND_VARIABLE_7590) (ho_43 (ho_42 k_41 BOUND_VARIABLE_7589) BOUND_VARIABLE_7590))))) (let ((_let_167 (forall ((BOUND_VARIABLE_7781 |u_(-> Bool tptp.a)|) (BOUND_VARIABLE_7778 |u_(-> Bool tptp.a)|)) (= (ho_47 (ho_46 k_45 BOUND_VARIABLE_7781) BOUND_VARIABLE_7778) (forall ((X5 Bool)) (ho_40 (ho_39 k_48 (ho_44 BOUND_VARIABLE_7781 X5)) (ho_44 BOUND_VARIABLE_7778 X5))))))) (let ((_let_168 (forall ((BOUND_VARIABLE_7805 |u_(-> Bool tptp.a)|) (BOUND_VARIABLE_7804 |u_(-> Bool tptp.a)|)) (= (ho_47 (ho_46 k_49 BOUND_VARIABLE_7805) BOUND_VARIABLE_7804) (and (ho_40 (ho_39 k_48 (ho_44 BOUND_VARIABLE_7805 false)) (ho_44 BOUND_VARIABLE_7804 false)) (ho_40 (ho_39 k_48 (ho_44 BOUND_VARIABLE_7805 true)) (ho_44 BOUND_VARIABLE_7804 true))))))) (let ((_let_169 (forall ((BOUND_VARIABLE_7556 tptp.a) (BOUND_VARIABLE_7557 tptp.a)) (= (= BOUND_VARIABLE_7556 BOUND_VARIABLE_7557) (ho_40 (ho_39 k_50 BOUND_VARIABLE_7556) BOUND_VARIABLE_7557))))) (let ((_let_170 (forall ((BOUND_VARIABLE_7545 tptp.a) (BOUND_VARIABLE_7546 tptp.a)) (= (ho_40 (ho_39 k_51 BOUND_VARIABLE_7545) BOUND_VARIABLE_7546) (and (ho_40 (ho_39 k_48 BOUND_VARIABLE_7545) BOUND_VARIABLE_7546) (ho_40 (ho_39 k_48 BOUND_VARIABLE_7546) BOUND_VARIABLE_7545)))))) (let ((_let_171 (forall ((BOUND_VARIABLE_7843 |u_(-> Bool tptp.a)|) (BOUND_VARIABLE_7842 |u_(-> Bool tptp.a)|)) (= (ho_47 (ho_46 k_52 BOUND_VARIABLE_7843) BOUND_VARIABLE_7842) (= BOUND_VARIABLE_7842 BOUND_VARIABLE_7843))))) (let ((_let_172 (forall ((BOUND_VARIABLE_7854 |u_(-> Bool tptp.a)|) (BOUND_VARIABLE_7853 |u_(-> Bool tptp.a)|)) (= (ho_47 (ho_46 k_53 BOUND_VARIABLE_7854) BOUND_VARIABLE_7853) (and (forall ((X5 Bool)) (ho_40 (ho_39 k_48 (ho_44 BOUND_VARIABLE_7854 X5)) (ho_44 BOUND_VARIABLE_7853 X5))) (forall ((X5 Bool)) (ho_40 (ho_39 k_48 (ho_44 BOUND_VARIABLE_7853 X5)) (ho_44 BOUND_VARIABLE_7854 X5)))))))) (let ((_let_173 (forall ((BOUND_VARIABLE_7516 tptp.a) (BOUND_VARIABLE_7517 tptp.a)) (= (= BOUND_VARIABLE_7516 BOUND_VARIABLE_7517) (ho_40 (ho_39 k_54 BOUND_VARIABLE_7516) BOUND_VARIABLE_7517))))) (let ((_let_174 (forall ((BOUND_VARIABLE_7505 tptp.a) (BOUND_VARIABLE_7506 tptp.a)) (= (ho_40 (ho_39 k_55 BOUND_VARIABLE_7505) BOUND_VARIABLE_7506) (and (ho_40 (ho_39 k_48 BOUND_VARIABLE_7505) BOUND_VARIABLE_7506) (ho_40 (ho_39 k_48 BOUND_VARIABLE_7506) BOUND_VARIABLE_7505)))))) (let ((_let_175 (forall ((BOUND_VARIABLE_7892 |u_(-> Bool tptp.a)|) (BOUND_VARIABLE_7891 |u_(-> Bool tptp.a)|)) (= (ho_47 (ho_46 k_56 BOUND_VARIABLE_7892) BOUND_VARIABLE_7891) (= BOUND_VARIABLE_7891 BOUND_VARIABLE_7892))))) (let ((_let_176 (forall ((BOUND_VARIABLE_7903 |u_(-> Bool tptp.a)|) (BOUND_VARIABLE_7902 |u_(-> Bool tptp.a)|)) (= (ho_47 (ho_46 k_57 BOUND_VARIABLE_7903) BOUND_VARIABLE_7902) (and (forall ((X5 Bool)) (ho_40 (ho_39 k_48 (ho_44 BOUND_VARIABLE_7903 X5)) (ho_44 BOUND_VARIABLE_7902 X5))) (forall ((X5 Bool)) (ho_40 (ho_39 k_48 (ho_44 BOUND_VARIABLE_7902 X5)) (ho_44 BOUND_VARIABLE_7903 X5)))))))) (let ((_let_177 (forall ((BOUND_VARIABLE_7476 tptp.a) (BOUND_VARIABLE_7477 tptp.a)) (= (= BOUND_VARIABLE_7476 BOUND_VARIABLE_7477) (ho_40 (ho_39 k_58 BOUND_VARIABLE_7476) BOUND_VARIABLE_7477))))) (let ((_let_178 (forall ((BOUND_VARIABLE_7465 tptp.a) (BOUND_VARIABLE_7466 tptp.a)) (= (ho_40 (ho_39 k_59 BOUND_VARIABLE_7465) BOUND_VARIABLE_7466) (and (ho_40 (ho_39 k_48 BOUND_VARIABLE_7466) BOUND_VARIABLE_7465) (ho_40 (ho_39 k_48 BOUND_VARIABLE_7465) BOUND_VARIABLE_7466)))))) (let ((_let_179 (forall ((BOUND_VARIABLE_7941 |u_(-> Bool tptp.a)|) (BOUND_VARIABLE_7940 |u_(-> Bool tptp.a)|)) (= (ho_47 (ho_46 k_60 BOUND_VARIABLE_7941) BOUND_VARIABLE_7940) (= BOUND_VARIABLE_7940 BOUND_VARIABLE_7941))))) (let ((_let_180 (forall ((BOUND_VARIABLE_7952 |u_(-> Bool tptp.a)|) (BOUND_VARIABLE_7951 |u_(-> Bool tptp.a)|)) (= (ho_47 (ho_46 k_61 BOUND_VARIABLE_7952) BOUND_VARIABLE_7951) (and (forall ((X5 Bool)) (ho_40 (ho_39 k_48 (ho_44 BOUND_VARIABLE_7951 X5)) (ho_44 BOUND_VARIABLE_7952 X5))) (forall ((X5 Bool)) (ho_40 (ho_39 k_48 (ho_44 BOUND_VARIABLE_7952 X5)) (ho_44 BOUND_VARIABLE_7951 X5)))))))) (let ((_let_181 (forall ((BOUND_VARIABLE_7435 tptp.set_a) (BOUND_VARIABLE_7436 tptp.a)) (= (ho_40 (ho_63 k_62 BOUND_VARIABLE_7435) BOUND_VARIABLE_7436) (ho_25 (ho_27 k_26 BOUND_VARIABLE_7436) BOUND_VARIABLE_7435))))) (let ((_let_182 (forall ((BOUND_VARIABLE_7426 tptp.a) (BOUND_VARIABLE_7427 tptp.tree_a)) (= (ho_43 (ho_65 k_64 BOUND_VARIABLE_7426) BOUND_VARIABLE_7427) (ho_43 (ho_65 k_68 BOUND_VARIABLE_7426) (ho_67 k_66 BOUND_VARIABLE_7427)))))) (let ((_let_183 (forall ((BOUND_VARIABLE_7624 tptp.set_a) (BOUND_VARIABLE_7625 tptp.set_a)) (= (forall ((X5 tptp.a)) (let ((_let_1 (@ tptp.member_a X5))) (or (not (@ _let_1 BOUND_VARIABLE_7624)) (@ _let_1 BOUND_VARIABLE_7625)))) (ll_22 BOUND_VARIABLE_7624 BOUND_VARIABLE_7625))))) (let ((_let_184 (forall ((BOUND_VARIABLE_7613 tptp.set_a) (BOUND_VARIABLE_7614 tptp.set_a)) (= (forall ((T2 tptp.a)) (let ((_let_1 (@ tptp.member_a T2))) (or (not (@ _let_1 BOUND_VARIABLE_7613)) (@ _let_1 BOUND_VARIABLE_7614)))) (ll_21 BOUND_VARIABLE_7613 BOUND_VARIABLE_7614))))) (let ((_let_185 (forall ((BOUND_VARIABLE_7603 tptp.a) (BOUND_VARIABLE_7604 tptp.multiset_a)) (= (@ (@ (@ tptp.fold_m364285649iset_a tptp.add_mset_a) BOUND_VARIABLE_7604) (@ (@ tptp.add_mset_a BOUND_VARIABLE_7603) (@ tptp.multiset_a2 tptp.e_a))) (ll_20 BOUND_VARIABLE_7603 BOUND_VARIABLE_7604))))) (let ((_let_186 (forall ((BOUND_VARIABLE_7596 tptp.a) (BOUND_VARIABLE_7597 tptp.a)) (= (= BOUND_VARIABLE_7596 BOUND_VARIABLE_7597) (ll_19 BOUND_VARIABLE_7596 BOUND_VARIABLE_7597))))) (let ((_let_187 (forall ((BOUND_VARIABLE_7589 tptp.tree_a) (BOUND_VARIABLE_7590 tptp.tree_a)) (= (= BOUND_VARIABLE_7589 BOUND_VARIABLE_7590) (ll_18 BOUND_VARIABLE_7589 BOUND_VARIABLE_7590))))) (let ((_let_188 (forall ((BOUND_VARIABLE_7578 (-> Bool tptp.a)) (BOUND_VARIABLE_7579 (-> Bool tptp.a))) (= (forall ((X5 Bool)) (@ (@ tptp.ord_less_eq_a (@ BOUND_VARIABLE_7578 X5)) (@ BOUND_VARIABLE_7579 X5))) (ll_17 BOUND_VARIABLE_7578 BOUND_VARIABLE_7579))))) (let ((_let_189 (forall ((BOUND_VARIABLE_7563 (-> Bool tptp.a)) (BOUND_VARIABLE_7564 (-> Bool tptp.a))) (= (and (@ (@ tptp.ord_less_eq_a (@ BOUND_VARIABLE_7563 false)) (@ BOUND_VARIABLE_7564 false)) (@ (@ tptp.ord_less_eq_a (@ BOUND_VARIABLE_7563 true)) (@ BOUND_VARIABLE_7564 true))) (ll_16 BOUND_VARIABLE_7563 BOUND_VARIABLE_7564))))) (let ((_let_190 (forall ((BOUND_VARIABLE_7556 tptp.a) (BOUND_VARIABLE_7557 tptp.a)) (= (= BOUND_VARIABLE_7556 BOUND_VARIABLE_7557) (ll_15 BOUND_VARIABLE_7556 BOUND_VARIABLE_7557))))) (let ((_let_191 (forall ((BOUND_VARIABLE_7545 tptp.a) (BOUND_VARIABLE_7546 tptp.a)) (= (and (@ (@ tptp.ord_less_eq_a BOUND_VARIABLE_7545) BOUND_VARIABLE_7546) (@ (@ tptp.ord_less_eq_a BOUND_VARIABLE_7546) BOUND_VARIABLE_7545)) (ll_14 BOUND_VARIABLE_7545 BOUND_VARIABLE_7546))))) (let ((_let_192 (forall ((BOUND_VARIABLE_7538 (-> Bool tptp.a)) (BOUND_VARIABLE_7539 (-> Bool tptp.a))) (= (= BOUND_VARIABLE_7538 BOUND_VARIABLE_7539) (ll_13 BOUND_VARIABLE_7538 BOUND_VARIABLE_7539))))) (let ((_let_193 (forall ((BOUND_VARIABLE_7523 (-> Bool tptp.a)) (BOUND_VARIABLE_7524 (-> Bool tptp.a))) (= (and (forall ((X5 Bool)) (@ (@ tptp.ord_less_eq_a (@ BOUND_VARIABLE_7523 X5)) (@ BOUND_VARIABLE_7524 X5))) (forall ((X5 Bool)) (@ (@ tptp.ord_less_eq_a (@ BOUND_VARIABLE_7524 X5)) (@ BOUND_VARIABLE_7523 X5)))) (ll_12 BOUND_VARIABLE_7523 BOUND_VARIABLE_7524))))) (let ((_let_194 (forall ((BOUND_VARIABLE_7516 tptp.a) (BOUND_VARIABLE_7517 tptp.a)) (= (= BOUND_VARIABLE_7516 BOUND_VARIABLE_7517) (ll_11 BOUND_VARIABLE_7516 BOUND_VARIABLE_7517))))) (let ((_let_195 (forall ((BOUND_VARIABLE_7505 tptp.a) (BOUND_VARIABLE_7506 tptp.a)) (= (and (@ (@ tptp.ord_less_eq_a BOUND_VARIABLE_7505) BOUND_VARIABLE_7506) (@ (@ tptp.ord_less_eq_a BOUND_VARIABLE_7506) BOUND_VARIABLE_7505)) (ll_10 BOUND_VARIABLE_7505 BOUND_VARIABLE_7506))))) (let ((_let_196 (forall ((BOUND_VARIABLE_7498 (-> Bool tptp.a)) (BOUND_VARIABLE_7499 (-> Bool tptp.a))) (= (= BOUND_VARIABLE_7498 BOUND_VARIABLE_7499) (ll_9 BOUND_VARIABLE_7498 BOUND_VARIABLE_7499))))) (let ((_let_197 (forall ((BOUND_VARIABLE_7483 (-> Bool tptp.a)) (BOUND_VARIABLE_7484 (-> Bool tptp.a))) (= (and (forall ((X5 Bool)) (@ (@ tptp.ord_less_eq_a (@ BOUND_VARIABLE_7483 X5)) (@ BOUND_VARIABLE_7484 X5))) (forall ((X5 Bool)) (@ (@ tptp.ord_less_eq_a (@ BOUND_VARIABLE_7484 X5)) (@ BOUND_VARIABLE_7483 X5)))) (ll_8 BOUND_VARIABLE_7483 BOUND_VARIABLE_7484))))) (let ((_let_198 (forall ((BOUND_VARIABLE_7476 tptp.a) (BOUND_VARIABLE_7477 tptp.a)) (= (= BOUND_VARIABLE_7476 BOUND_VARIABLE_7477) (ll_7 BOUND_VARIABLE_7476 BOUND_VARIABLE_7477))))) (let ((_let_199 (forall ((BOUND_VARIABLE_7465 tptp.a) (BOUND_VARIABLE_7466 tptp.a)) (= (and (@ (@ tptp.ord_less_eq_a BOUND_VARIABLE_7466) BOUND_VARIABLE_7465) (@ (@ tptp.ord_less_eq_a BOUND_VARIABLE_7465) BOUND_VARIABLE_7466)) (ll_6 BOUND_VARIABLE_7465 BOUND_VARIABLE_7466))))) (let ((_let_200 (forall ((BOUND_VARIABLE_7458 (-> Bool tptp.a)) (BOUND_VARIABLE_7459 (-> Bool tptp.a))) (= (= BOUND_VARIABLE_7458 BOUND_VARIABLE_7459) (ll_5 BOUND_VARIABLE_7458 BOUND_VARIABLE_7459))))) (let ((_let_201 (forall ((BOUND_VARIABLE_7443 (-> Bool tptp.a)) (BOUND_VARIABLE_7444 (-> Bool tptp.a))) (= (and (forall ((X5 Bool)) (@ (@ tptp.ord_less_eq_a (@ BOUND_VARIABLE_7444 X5)) (@ BOUND_VARIABLE_7443 X5))) (forall ((X5 Bool)) (@ (@ tptp.ord_less_eq_a (@ BOUND_VARIABLE_7443 X5)) (@ BOUND_VARIABLE_7444 X5)))) (ll_4 BOUND_VARIABLE_7443 BOUND_VARIABLE_7444))))) (let ((_let_202 (forall ((BOUND_VARIABLE_7435 tptp.set_a) (BOUND_VARIABLE_7436 tptp.a)) (= (@ (@ tptp.member_a BOUND_VARIABLE_7436) BOUND_VARIABLE_7435) (ll_3 BOUND_VARIABLE_7435 BOUND_VARIABLE_7436))))) (let ((_let_203 (forall ((BOUND_VARIABLE_7426 tptp.a) (BOUND_VARIABLE_7427 tptp.tree_a)) (= (@ (@ tptp.in_tree_a BOUND_VARIABLE_7426) (@ tptp.heapIm1091024090Down_a BOUND_VARIABLE_7427)) (ll_2 BOUND_VARIABLE_7426 BOUND_VARIABLE_7427))))) (let ((_let_204 (and _let_9 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183))) (let ((_let_205 (and _let_44 _let_43))) (let ((_let_206 (_let_44 _let_43))) (let ((_let_207 (ASSUME :args (_let_44)))) (let ((_let_208 (ASSUME :args (_let_43)))) (let ((_let_209 (forall ((V tptp.a) (Va2 tptp.a) (Vb2 tptp.tree_a) (Vc2 tptp.tree_a)) (let ((_let_1 (ho_67 (ho_72 (ho_71 k_70 Va2) Vb2) Vc2))) (= (and (ho_40 (ho_39 k_48 (ho_76 k_75 _let_1)) V) (ho_43 k_69 _let_1)) (ho_43 k_69 (ho_67 (ho_72 (ho_71 k_70 V) tptp.e_a) _let_1))))))) (let ((_let_210 (EQ_RESOLVE (ASSUME :args (_let_3)) (PREPROCESS :args ((= _let_3 _let_209)))))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_17)) :args ((or _let_12 (not _let_16) (not _let_17)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_210 :args (tptp.v2 tptp.v1 tptp.l1 tptp.r1 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_209))) _let_210 :args (_let_17 false _let_209)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_16)) :args ((or _let_22 _let_16 (not _let_13)))) _let_35 (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_205)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_207 _let_208) (SCOPE (TRUE_ELIM (TRANS (CONG _let_42 (SYMM _let_208) :args _let_40) (TRUE_INTRO _let_207))) :args _let_206)) :args _let_206)) :args (true _let_205)) (AND_ELIM (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (MACRO_SR_PRED_TRANSFORM (AND_INTRO (ASSUME :args (_let_9)) (PREPROCESS :args ((and _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183)))) :args (_let_204)) (PREPROCESS :args ((= _let_204 (and _let_44 _let_182 _let_181 _let_180 _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))))) (PREPROCESS :args ((and _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 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _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)))) :args ((and _let_44 _let_182 _let_181 _let_180 _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 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _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))) :args _let_25) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_45 2)) :args ((or _let_43 (not _let_45)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_47)) :args ((or (not _let_46) _let_45 (not _let_47)))) (EQ_RESOLVE (ASSUME :args (_let_7)) (PREPROCESS :args ((= _let_7 _let_46)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_49 :args (tptp.v2 tptp.e_a _let_10 tptp.va tptp.la tptp.ra QUANTIFIERS_INST_CBQI_PROP)) :args (_let_48)))) _let_49 :args (_let_47 false _let_48)) :args (_let_45 false _let_46 false _let_47)) :args (_let_43 false _let_45)) :args (_let_13 false _let_44 false _let_43)) :args (_let_16 false _let_15 false _let_13)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_38)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_37 _let_41) (SCOPE (FALSE_ELIM (TRANS (CONG _let_42 (SYMM (SYMM _let_41)) :args _let_40) (FALSE_INTRO _let_37))) :args _let_39)) :args _let_39)) :args (true _let_38)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_36) _let_20))) (REFL :args ((not _let_19))) (REFL :args (_let_21)) :args (or))) _let_37 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_23)) :args ((or _let_22 _let_19 (not _let_23)))) _let_35 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_26) :args (tptp.v1 tptp.l1 tptp.r1 tptp.v2 QUANTIFIERS_INST_CBQI_PROP)) :args _let_26)) (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_4)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (and (forall ((BOUND_VARIABLE_4135 tptp.a) (BOUND_VARIABLE_4137 tptp.tree_a) (BOUND_VARIABLE_4139 tptp.tree_a) (BOUND_VARIABLE_4141 tptp.a)) (let ((_let_1 (@ (@ (@ tptp.t_a BOUND_VARIABLE_4135) BOUND_VARIABLE_4137) BOUND_VARIABLE_4139))) (let ((_let_2 (@ (@ (@ tptp.t_a BOUND_VARIABLE_4141) tptp.e_a) _let_1))) (or (not (@ (@ tptp.ord_less_eq_a (@ tptp.val_a _let_1)) BOUND_VARIABLE_4141)) (= _let_2 (@ tptp.heapIm1091024090Down_a _let_2)))))) (forall ((BOUND_VARIABLE_4158 tptp.a) (BOUND_VARIABLE_4160 tptp.tree_a) (BOUND_VARIABLE_4162 tptp.tree_a) (BOUND_VARIABLE_4164 tptp.a)) (let ((_let_1 (@ (@ (@ tptp.t_a BOUND_VARIABLE_4158) BOUND_VARIABLE_4160) BOUND_VARIABLE_4162))) (let ((_let_2 (@ tptp.t_a BOUND_VARIABLE_4164))) (let ((_let_3 (@ tptp.val_a _let_1))) (or (@ (@ tptp.ord_less_eq_a _let_3) BOUND_VARIABLE_4164) (= (@ tptp.heapIm1091024090Down_a (@ (@ _let_2 tptp.e_a) _let_1)) (@ (@ (@ tptp.t_a _let_3) tptp.e_a) (@ tptp.heapIm1091024090Down_a (@ (@ _let_2 (@ tptp.heapIm1140443833left_a _let_1)) (@ tptp.heapIm1257206334ight_a _let_1))))))))))) (and _let_24 (forall ((BOUND_VARIABLE_4158 tptp.a) (BOUND_VARIABLE_4160 tptp.tree_a) (BOUND_VARIABLE_4162 tptp.tree_a) (BOUND_VARIABLE_4164 tptp.a)) (let ((_let_1 (ho_67 (ho_72 (ho_71 k_70 BOUND_VARIABLE_4158) BOUND_VARIABLE_4160) BOUND_VARIABLE_4162))) (let ((_let_2 (ho_71 k_70 BOUND_VARIABLE_4164))) (let ((_let_3 (ho_76 k_75 _let_1))) (or (ho_40 (ho_39 k_48 _let_3) BOUND_VARIABLE_4164) (= (ho_67 (ho_72 (ho_71 k_70 _let_3) tptp.e_a) (ho_67 k_66 (ho_67 (ho_72 _let_2 (ho_67 k_74 _let_1)) (ho_67 k_73 _let_1)))) (ho_67 k_66 (ho_67 (ho_72 _let_2 tptp.e_a) _let_1)))))))))))))) :args _let_25) :args (_let_23 false _let_24)) :args (_let_19 false _let_15 false _let_23)) :args (_let_21 true _let_20 false _let_19)) :args (false false _let_17 false _let_16 true _let_12)) :args (_let_9 (@ tptp.is_heap_a tptp.la) (@ tptp.is_heap_a tptp.r) (@ tptp.is_heap_a tptp.l) _let_8 _let_7 (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 ((X tptp.tree_a)) (=> (not (= X tptp.e_a)) (=> (forall ((V2 tptp.a)) (not (= X (@ (@ (@ tptp.t_a V2) tptp.e_a) tptp.e_a)))) (=> (forall ((V2 tptp.a) (Va tptp.a) (Vb tptp.tree_a) (Vc tptp.tree_a)) (not (= X (@ (@ (@ tptp.t_a V2) (@ (@ (@ tptp.t_a Va) Vb) Vc)) tptp.e_a)))) (=> (forall ((V2 tptp.a) (Va tptp.a) (Vb tptp.tree_a) (Vc tptp.tree_a)) (not (= X (@ (@ (@ tptp.t_a V2) tptp.e_a) (@ (@ (@ tptp.t_a Va) Vb) Vc))))) (not (forall ((V2 tptp.a) (Va tptp.a) (Vb tptp.tree_a) (Vc tptp.tree_a) (Vd tptp.a) (Ve tptp.tree_a) (Vf tptp.tree_a)) (not (= X (@ (@ (@ tptp.t_a V2) (@ (@ (@ tptp.t_a Va) Vb) Vc)) (@ (@ (@ tptp.t_a Vd) Ve) Vf))))))))))) (= tptp.t (@ (@ (@ tptp.t_a tptp.v) tptp.l) tptp.r)) (forall ((V tptp.a)) (@ tptp.is_heap_a (@ (@ (@ tptp.t_a V) tptp.e_a) tptp.e_a))) (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) (V3 tptp.a) (R2 tptp.tree_a)) (and (= (@ tptp.heapIm1091024090Down_a T) (@ (@ (@ tptp.t_a V3) L2) R2)) (@ (@ tptp.ord_less_eq_a V) V3))))) (forall ((L tptp.tree_a) (R tptp.tree_a) (V tptp.a)) (let ((_let_1 (@ (@ (@ tptp.t_a tptp.v1) tptp.l1) tptp.r1))) (let ((_let_2 (@ (@ (@ tptp.t_a tptp.v2) (@ tptp.heapIm1140443833left_a _let_1)) (@ tptp.heapIm1257206334ight_a _let_1)))) (=> (not (@ (@ tptp.ord_less_eq_a (@ tptp.val_a _let_1)) tptp.v2)) (=> (@ tptp.is_heap_a L) (=> (@ tptp.is_heap_a R) (=> (= _let_2 (@ (@ (@ tptp.t_a V) L) R)) (@ tptp.is_heap_a (@ tptp.heapIm1091024090Down_a _let_2))))))))) _let_6 (@ tptp.is_heap_a tptp.e_a) (forall ((X21 tptp.a) (X22 tptp.tree_a) (X23 tptp.tree_a)) (not (= tptp.e_a (@ (@ (@ tptp.t_a X21) X22) X23)))) (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 ((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 ((X tptp.tree_a)) (=> (not (= X tptp.e_a)) (=> (forall ((V2 tptp.a)) (not (= X (@ (@ (@ tptp.t_a V2) tptp.e_a) tptp.e_a)))) (=> (forall ((V2 tptp.a) (Va tptp.a) (Vb tptp.tree_a) (Vc tptp.tree_a)) (not (= X (@ (@ (@ tptp.t_a V2) tptp.e_a) (@ (@ (@ tptp.t_a Va) Vb) Vc))))) (=> (forall ((V2 tptp.a) (Va tptp.a) (Vb tptp.tree_a) (Vc tptp.tree_a)) (not (= X (@ (@ (@ tptp.t_a V2) (@ (@ (@ tptp.t_a Va) Vb) Vc)) tptp.e_a)))) (not (forall ((V2 tptp.a) (Va tptp.a) (Vb tptp.tree_a) (Vc tptp.tree_a) (Vd tptp.a) (Ve tptp.tree_a) (Vf tptp.tree_a)) (not (= X (@ (@ (@ tptp.t_a V2) (@ (@ (@ tptp.t_a Va) Vb) Vc)) (@ (@ (@ tptp.t_a Vd) Ve) Vf))))))))))) (= tptp.in_tree_a (lambda ((V4 tptp.a) (T2 tptp.tree_a)) (@ (@ tptp.in_tree_a V4) (@ tptp.heapIm1091024090Down_a T2)))) (forall ((V tptp.a) (L tptp.tree_a) (R tptp.tree_a)) (= (@ 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(@ tptp.heapIm1091024090Down_a (@ (@ _let_2 (@ tptp.heapIm1140443833left_a _let_1)) (@ tptp.heapIm1257206334ight_a _let_1)))) tptp.e_a))))))))))) _let_4 (forall ((T tptp.tree_a)) (=> (not (= T tptp.e_a)) (@ (@ tptp.in_tree_a (@ tptp.val_a (@ tptp.heapIm1091024090Down_a T))) T))) _let_3 (forall ((V tptp.a) (Va2 tptp.a) (Vb2 tptp.tree_a) (Vc2 tptp.tree_a)) (let ((_let_1 (@ (@ (@ tptp.t_a Va2) Vb2) Vc2))) (= (@ 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) (L tptp.tree_a) (R tptp.tree_a)) (= (@ tptp.heapIm1257206334ight_a (@ (@ (@ tptp.t_a V) L) R)) R)) (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 ((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 ((X4 Bool)) (@ (@ tptp.ord_less_eq_a (@ F X4)) (@ G X4))) (@ (@ tptp.ord_less_eq_o_a F) G))) (= tptp.ord_less_eq_o_a (lambda ((F2 (-> Bool tptp.a)) (G2 (-> Bool tptp.a))) (forall ((X5 Bool)) (@ (@ tptp.ord_less_eq_a (@ F2 X5)) (@ G2 X5))))) (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 ((X4 (-> Bool tptp.a)) (Y2 (-> Bool tptp.a))) (=> (@ (@ tptp.ord_less_eq_o_a X4) Y2) (@ (@ tptp.ord_less_eq_a (@ F X4)) (@ 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 ((X4 tptp.a) (Y2 tptp.a)) (=> (@ (@ tptp.ord_less_eq_a X4) Y2) (@ (@ tptp.ord_less_eq_o_a (@ F X4)) (@ 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 ((X4 (-> Bool tptp.a)) (Y2 (-> Bool tptp.a))) (=> (@ (@ tptp.ord_less_eq_o_a X4) Y2) (@ (@ tptp.ord_less_eq_o_a (@ F X4)) (@ 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 ((X4 tptp.a) (Y2 tptp.a)) (=> (@ (@ tptp.ord_less_eq_a X4) Y2) (@ (@ tptp.ord_less_eq_a (@ F X4)) (@ 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 ((X4 tptp.a) (Y2 tptp.a)) (=> (@ (@ tptp.ord_less_eq_a X4) Y2) (@ (@ tptp.ord_less_eq_o_a (@ F X4)) (@ 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 ((X4 (-> Bool tptp.a)) (Y2 (-> Bool tptp.a))) (=> (@ (@ tptp.ord_less_eq_o_a X4) Y2) (@ (@ tptp.ord_less_eq_a (@ F X4)) (@ 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 ((X4 (-> Bool tptp.a)) (Y2 (-> Bool tptp.a))) (=> (@ (@ tptp.ord_less_eq_o_a X4) Y2) (@ (@ tptp.ord_less_eq_o_a (@ F X4)) (@ 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 ((X4 tptp.a) (Y2 tptp.a)) (=> (@ (@ tptp.ord_less_eq_a X4) Y2) (@ (@ tptp.ord_less_eq_a (@ F X4)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_a (@ F A)) C))))) (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 ((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 ((X4 tptp.a) (Y2 tptp.a)) (=> (@ (@ tptp.ord_less_eq_a X4) Y2) (@ (@ tptp.ord_less_eq_o_a (@ F X4)) (@ 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 ((X4 (-> Bool tptp.a)) (Y2 (-> Bool tptp.a))) (=> (@ (@ tptp.ord_less_eq_o_a X4) Y2) (@ (@ tptp.ord_less_eq_a (@ F X4)) (@ 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 ((X4 (-> Bool tptp.a)) (Y2 (-> Bool tptp.a))) (=> (@ (@ tptp.ord_less_eq_o_a X4) Y2) (@ (@ tptp.ord_less_eq_o_a (@ F X4)) (@ 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 ((X4 tptp.a) (Y2 tptp.a)) (=> (@ (@ tptp.ord_less_eq_a X4) Y2) (@ (@ tptp.ord_less_eq_a (@ F X4)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_a A) (@ 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) (=> (= (@ F B) C) (=> (forall ((X4 tptp.a) (Y2 tptp.a)) (=> (@ (@ tptp.ord_less_eq_a X4) Y2) (@ (@ tptp.ord_less_eq_o_a (@ F X4)) (@ 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 ((X4 (-> Bool tptp.a)) (Y2 (-> Bool tptp.a))) (=> (@ (@ tptp.ord_less_eq_o_a X4) Y2) (@ (@ tptp.ord_less_eq_a (@ F X4)) (@ 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 ((X4 (-> Bool tptp.a)) (Y2 (-> Bool tptp.a))) (=> (@ (@ tptp.ord_less_eq_o_a X4) Y2) (@ (@ tptp.ord_less_eq_o_a (@ F X4)) (@ 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 ((X4 tptp.a) (Y2 tptp.a)) (=> (@ (@ tptp.ord_less_eq_a X4) Y2) (@ (@ tptp.ord_less_eq_a (@ F X4)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_a (@ F A)) C))))) (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 ((X5 tptp.a)) (@ (@ tptp.member_a X5) A2))) A2)) (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 ((X5 (-> Bool tptp.a)) (Y4 (-> Bool tptp.a))) (and (@ (@ tptp.ord_less_eq_o_a X5) Y4) (@ (@ tptp.ord_less_eq_o_a Y4) X5)))) (= (lambda ((Y3 tptp.a) (Z tptp.a)) (= Y3 Z)) (lambda ((X5 tptp.a) (Y4 tptp.a)) (and (@ (@ tptp.ord_less_eq_a X5) Y4) (@ (@ tptp.ord_less_eq_a Y4) X5)))) (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 ((X4 (-> Bool tptp.a))) (=> (@ P X4) (=> (forall ((Y5 (-> Bool tptp.a))) (=> (@ P Y5) (@ (@ tptp.ord_less_eq_o_a Y5) X4))) (@ Q X4)))) (@ 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 ((X4 tptp.a)) (=> (@ P X4) (=> (forall ((Y5 tptp.a)) (=> (@ P Y5) (@ (@ tptp.ord_less_eq_a Y5) X4))) (@ Q X4)))) (@ 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 ((R3 (-> tptp.a tptp.a Bool)) (X tptp.tree_a) (Y tptp.tree_a) (Q (-> tptp.tree_a tptp.tree_a Bool))) (=> (@ (@ (@ tptp.rel_Tree_a_a R3) X) Y) (=> (@ (@ Q tptp.e_a) tptp.e_a) (=> (forall ((A21 tptp.a) (A22 tptp.tree_a) (A23 tptp.tree_a) (B21 tptp.a) (B22 tptp.tree_a) (B23 tptp.tree_a)) (=> (@ (@ R3 A21) B21) (=> (@ (@ Q A22) B22) (=> (@ (@ Q A23) B23) (@ (@ Q (@ (@ (@ tptp.t_a A21) A22) A23)) (@ (@ (@ tptp.t_a B21) B22) B23)))))) (@ (@ Q X) Y))))) (forall ((R3 (-> tptp.a tptp.a Bool)) (Ra (-> tptp.a tptp.a Bool))) (=> (@ (@ tptp.ord_less_eq_a_a_o R3) Ra) (@ (@ tptp.ord_le1530450702ee_a_o (@ tptp.rel_Tree_a_a R3)) (@ tptp.rel_Tree_a_a Ra)))) (= (@ tptp.rel_Tree_a_a (lambda ((Y3 tptp.a) (Z tptp.a)) (= Y3 Z))) (lambda ((Y3 tptp.tree_a) (Z tptp.tree_a)) (= Y3 Z))) (forall ((Ra (-> tptp.a tptp.a Bool)) (X tptp.tree_a)) (=> (forall ((X4 tptp.a)) (@ (@ Ra X4) X4)) (@ (@ (@ tptp.rel_Tree_a_a Ra) X) X))) (forall ((R3 (-> tptp.a tptp.a Bool)) (X21 tptp.a) (X22 tptp.tree_a) (X23 tptp.tree_a) (Y21 tptp.a) (Y22 tptp.tree_a) (Y23 tptp.tree_a)) (let ((_let_1 (@ tptp.rel_Tree_a_a R3))) (= (@ (@ _let_1 (@ (@ (@ tptp.t_a X21) X22) X23)) (@ (@ (@ tptp.t_a Y21) Y22) Y23)) (and (@ (@ R3 X21) Y21) (@ (@ _let_1 X22) Y22) (@ (@ _let_1 X23) Y23))))) (forall ((R3 (-> tptp.a tptp.a Bool)) (X21 tptp.a) (Y21 tptp.a) (X22 tptp.tree_a) (Y22 tptp.tree_a) (X23 tptp.tree_a) (Y23 tptp.tree_a)) (let ((_let_1 (@ tptp.rel_Tree_a_a R3))) (=> (@ (@ R3 X21) Y21) (=> (@ (@ _let_1 X22) Y22) (=> (@ (@ _let_1 X23) Y23) (@ (@ _let_1 (@ (@ (@ tptp.t_a X21) X22) X23)) (@ (@ (@ tptp.t_a Y21) Y22) Y23))))))) (forall ((R3 (-> tptp.a tptp.a Bool))) (@ (@ (@ tptp.rel_Tree_a_a R3) tptp.e_a) tptp.e_a)) (forall ((R3 (-> tptp.a tptp.a Bool)) (Y21 tptp.a) (Y22 tptp.tree_a) (Y23 tptp.tree_a)) (not (@ (@ (@ tptp.rel_Tree_a_a R3) (@ (@ (@ tptp.t_a Y21) Y22) Y23)) tptp.e_a))) (forall ((R3 (-> tptp.a tptp.a Bool)) (Y21 tptp.a) (Y22 tptp.tree_a) (Y23 tptp.tree_a)) (not (@ (@ (@ tptp.rel_Tree_a_a R3) tptp.e_a) (@ (@ (@ tptp.t_a Y21) Y22) Y23)))) (forall ((R3 (-> tptp.a tptp.a Bool)) (A tptp.tree_a) (B tptp.tree_a)) (=> (@ (@ (@ tptp.rel_Tree_a_a R3) A) B) (=> (=> (= A tptp.e_a) (not (= B tptp.e_a))) (not (forall ((X1 tptp.a) (X2 tptp.tree_a) (X3 tptp.tree_a)) (=> (= A (@ (@ (@ tptp.t_a X1) X2) X3)) (forall ((Y1 tptp.a) (Y24 tptp.tree_a) (Y32 tptp.tree_a)) (let ((_let_1 (@ tptp.rel_Tree_a_a R3))) (=> (= B (@ (@ (@ tptp.t_a Y1) Y24) Y32)) (=> (@ (@ R3 X1) Y1) (=> (@ (@ _let_1 X2) Y24) (not (@ (@ _let_1 X3) Y32))))))))))))) (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))))) (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 ((M tptp.multiset_a) (X tptp.a)) (not (= M (@ (@ tptp.add_mset_a X) M)))) (forall ((A tptp.a) (A2 tptp.multiset_a)) (=> (@ (@ tptp.member_a A) (@ tptp.set_mset_a A2)) (not (forall ((B5 tptp.multiset_a)) (not (= A2 (@ (@ tptp.add_mset_a A) B5))))))) (forall ((X tptp.a) (M tptp.multiset_a)) (=> (@ (@ tptp.member_a X) (@ tptp.set_mset_a M)) (exists ((A5 tptp.multiset_a)) (= M (@ (@ tptp.add_mset_a X) A5))))) (forall ((X tptp.a) (Y tptp.a) (M tptp.multiset_a)) (let ((_let_1 (@ tptp.add_mset_a X))) (let ((_let_2 (@ tptp.add_mset_a Y))) (= (@ _let_1 (@ _let_2 M)) (@ _let_2 (@ _let_1 M)))))) (forall ((A tptp.a) (M tptp.multiset_a) (B tptp.a) (N tptp.multiset_a)) (= (= (@ (@ tptp.add_mset_a A) M) (@ (@ tptp.add_mset_a B) N)) (or (and (= M N) (= A B)) (exists ((K tptp.multiset_a)) (and (= M (@ (@ tptp.add_mset_a B) K)) (= N (@ (@ tptp.add_mset_a A) K))))))) (forall ((X tptp.a) (M tptp.multiset_a) (N tptp.multiset_a)) (=> (= (@ (@ tptp.add_mset_a X) M) 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 ((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 ((P (-> tptp.multiset_a Bool)) (M tptp.multiset_a)) (=> (@ P tptp.zero_zero_multiset_a) (=> (forall ((X4 tptp.a) (M2 tptp.multiset_a)) (=> (@ P M2) (=> (forall ((Xa tptp.a)) (=> (@ (@ tptp.member_a Xa) (@ tptp.set_mset_a M2)) (@ (@ tptp.ord_less_eq_a Xa) X4))) (@ P (@ (@ tptp.add_mset_a X4) M2))))) (@ P M)))) (forall ((P (-> tptp.multiset_a Bool)) (M tptp.multiset_a)) (=> (@ P tptp.zero_zero_multiset_a) (=> (forall ((X4 tptp.a) (M2 tptp.multiset_a)) (=> (@ P M2) (=> (forall ((Xa tptp.a)) (=> (@ (@ tptp.member_a Xa) (@ tptp.set_mset_a M2)) (@ (@ tptp.ord_less_eq_a X4) Xa))) (@ P (@ (@ tptp.add_mset_a X4) M2))))) (@ P M)))) (forall ((X tptp.a) (M tptp.multiset_a) (Y tptp.a)) (= (= (@ (@ tptp.add_mset_a X) M) (@ (@ tptp.add_mset_a Y) tptp.zero_zero_multiset_a)) (and (= M tptp.zero_zero_multiset_a) (= X Y)))) (forall ((A tptp.a) (B tptp.a) (M tptp.multiset_a)) (= (= (@ (@ tptp.add_mset_a A) tptp.zero_zero_multiset_a) (@ (@ tptp.add_mset_a B) M)) (and (= B A) (= M tptp.zero_zero_multiset_a)))) (forall ((B tptp.a) (M tptp.multiset_a) (A tptp.a)) (= (= (@ (@ tptp.add_mset_a B) M) (@ (@ tptp.add_mset_a A) tptp.zero_zero_multiset_a)) (and (= B A) (= M 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 ((M tptp.multiset_a)) (=> (not (= M tptp.zero_zero_multiset_a)) (not (forall ((X4 tptp.a) (N2 tptp.multiset_a)) (not (= M (@ (@ tptp.add_mset_a X4) N2))))))) (forall ((P (-> tptp.multiset_a Bool)) (M tptp.multiset_a)) (=> (@ P tptp.zero_zero_multiset_a) (=> (forall ((X4 tptp.a) (M2 tptp.multiset_a)) (=> (@ P M2) (@ P (@ (@ tptp.add_mset_a X4) M2)))) (@ P M)))) (forall ((P (-> tptp.multiset_a tptp.multiset_a Bool)) (M tptp.multiset_a) (N tptp.multiset_a)) (=> (@ (@ P tptp.zero_zero_multiset_a) tptp.zero_zero_multiset_a) (=> (forall ((A4 tptp.a) (M2 tptp.multiset_a) (N2 tptp.multiset_a)) (=> (@ (@ P M2) N2) (@ (@ P (@ (@ tptp.add_mset_a A4) M2)) N2))) (=> (forall ((A4 tptp.a) (M2 tptp.multiset_a) (N2 tptp.multiset_a)) (let ((_let_1 (@ P M2))) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.add_mset_a A4) N2))))) (@ (@ P M) N))))) (forall ((A tptp.a) (A2 tptp.multiset_a)) (not (= tptp.zero_zero_multiset_a (@ (@ tptp.add_mset_a A) A2)))) (forall ((A2 tptp.multiset_a)) (=> (not (= A2 tptp.zero_zero_multiset_a)) (not (forall ((X4 tptp.a)) (not (@ (@ tptp.member_a X4) (@ tptp.set_mset_a A2))))))) (forall ((M tptp.multiset_a)) (=> (not (= M tptp.zero_zero_multiset_a)) (exists ((A5 tptp.multiset_a) (A4 tptp.a)) (= M (@ (@ tptp.add_mset_a A4) A5))))) (forall ((X tptp.a)) (@ (@ tptp.member_a X) (@ tptp.set_mset_a (@ (@ tptp.add_mset_a X) tptp.zero_zero_multiset_a)))) (= (@ tptp.multiset_a2 tptp.e_a) tptp.zero_zero_multiset_a) (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) (M tptp.multiset_a)) (= (@ (@ tptp.subseteq_mset_a (@ (@ tptp.add_mset_a A) tptp.zero_zero_multiset_a)) M) (@ (@ tptp.member_a A) (@ tptp.set_mset_a M)))) (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 ((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) (M tptp.multiset_a) (B tptp.a)) (= (@ (@ tptp.subseteq_mset_a (@ (@ tptp.add_mset_a A) M)) (@ (@ tptp.add_mset_a B) tptp.zero_zero_multiset_a)) (and (= M tptp.zero_zero_multiset_a) (= A B)))) (forall ((A tptp.multiset_a)) (= (@ (@ tptp.plus_plus_multiset_a A) tptp.zero_zero_multiset_a) A)) (forall ((I tptp.multiset_a) (J tptp.multiset_a) (K2 tptp.multiset_a) (L tptp.multiset_a)) (=> (and (@ (@ tptp.ord_le1199012836iset_a I) J) (= K2 L)) (@ (@ tptp.ord_le1199012836iset_a (@ (@ tptp.plus_plus_multiset_a I) K2)) (@ (@ tptp.plus_plus_multiset_a J) L)))) (forall ((I tptp.multiset_a) (J tptp.multiset_a) (K2 tptp.multiset_a) (L tptp.multiset_a)) (=> (and (= I J) (@ (@ tptp.ord_le1199012836iset_a K2) L)) (@ (@ tptp.ord_le1199012836iset_a (@ (@ tptp.plus_plus_multiset_a I) K2)) (@ (@ tptp.plus_plus_multiset_a J) L)))) (forall ((I tptp.multiset_a) (J tptp.multiset_a) (K2 tptp.multiset_a) (L tptp.multiset_a)) (=> (and (@ (@ tptp.ord_le1199012836iset_a I) J) (@ (@ tptp.ord_le1199012836iset_a K2) L)) (@ (@ tptp.ord_le1199012836iset_a (@ (@ tptp.plus_plus_multiset_a I) K2)) (@ (@ 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 ((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 ((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 ((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) (M tptp.multiset_a) (N tptp.multiset_a)) (let ((_let_1 (@ (@ tptp.add_mset_a A) tptp.zero_zero_multiset_a))) (= (= _let_1 (@ (@ tptp.plus_plus_multiset_a M) N)) (or (and (= _let_1 M) (= N tptp.zero_zero_multiset_a)) (and (= M tptp.zero_zero_multiset_a) (= _let_1 N)))))) (forall ((M tptp.multiset_a) (N tptp.multiset_a) (A tptp.a)) (let ((_let_1 (@ (@ tptp.add_mset_a A) tptp.zero_zero_multiset_a))) (= (= (@ (@ tptp.plus_plus_multiset_a M) N) _let_1) (or (and (= M _let_1) (= N tptp.zero_zero_multiset_a)) (and (= M tptp.zero_zero_multiset_a) (= N _let_1)))))) (= tptp.add_mset_a (lambda ((A3 tptp.a) (A6 tptp.multiset_a)) (@ (@ tptp.plus_plus_multiset_a A6) (@ (@ tptp.add_mset_a A3) tptp.zero_zero_multiset_a)))) (forall ((F3 tptp.multiset_a) (A2 tptp.multiset_a) (P (-> tptp.multiset_a Bool))) (=> (@ (@ tptp.subseteq_mset_a F3) A2) (=> (@ P tptp.zero_zero_multiset_a) (=> (forall ((A4 tptp.a) (F4 tptp.multiset_a)) (=> (@ (@ tptp.member_a A4) (@ tptp.set_mset_a A2)) (=> (@ P F4) (@ P (@ (@ tptp.add_mset_a A4) F4))))) (@ P F3))))) (forall ((A tptp.a) (B4 tptp.multiset_a)) (=> (@ (@ tptp.member_a A) (@ tptp.set_mset_a B4)) (@ (@ tptp.subseteq_mset_a (@ (@ tptp.add_mset_a A) tptp.zero_zero_multiset_a)) B4))) (forall ((X tptp.a) (XS tptp.multiset_a) (Y tptp.a)) (let ((_let_1 (@ tptp.member_a X))) (=> (@ _let_1 (@ tptp.set_mset_a XS)) (@ _let_1 (@ tptp.set_mset_a (@ (@ tptp.plus_plus_multiset_a (@ (@ tptp.add_mset_a Y) tptp.zero_zero_multiset_a)) XS)))))) (forall ((X tptp.a) (XS tptp.multiset_a)) (@ (@ tptp.member_a X) (@ tptp.set_mset_a (@ (@ tptp.plus_plus_multiset_a (@ (@ tptp.add_mset_a X) tptp.zero_zero_multiset_a)) XS)))) (forall ((N tptp.multiset_a) (M tptp.multiset_a) (R tptp.set_Product_prod_a_a)) (=> (@ (@ tptp.member340150864iset_a (@ (@ tptp.produc2037245207iset_a N) M)) (@ tptp.mult1_a R)) (not (forall ((A4 tptp.a) (M0 tptp.multiset_a)) (=> (= M (@ (@ tptp.add_mset_a A4) M0)) (forall ((K3 tptp.multiset_a)) (=> (= N (@ (@ tptp.plus_plus_multiset_a M0) K3)) (not (forall ((B6 tptp.a)) (=> (@ (@ tptp.member_a B6) (@ tptp.set_mset_a K3)) (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a B6) A4)) R))))))))))) (forall ((M tptp.multiset_a) (A tptp.a) (M02 tptp.multiset_a) (N tptp.multiset_a) (K4 tptp.multiset_a) (R tptp.set_Product_prod_a_a)) (=> (= M (@ (@ tptp.add_mset_a A) M02)) (=> (= N (@ (@ tptp.plus_plus_multiset_a M02) K4)) (=> (forall ((B3 tptp.a)) (=> (@ (@ tptp.member_a B3) (@ tptp.set_mset_a K4)) (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a B3) A)) R))) (@ (@ tptp.member340150864iset_a (@ (@ tptp.produc2037245207iset_a N) M)) (@ tptp.mult1_a R)))))) (forall ((N tptp.multiset_a) (A tptp.a) (M02 tptp.multiset_a) (R tptp.set_Product_prod_a_a)) (=> (@ (@ tptp.member340150864iset_a (@ (@ tptp.produc2037245207iset_a N) (@ (@ tptp.add_mset_a A) M02))) (@ tptp.mult1_a R)) (or (exists ((M2 tptp.multiset_a)) (and (@ (@ tptp.member340150864iset_a (@ (@ tptp.produc2037245207iset_a M2) M02)) (@ tptp.mult1_a R)) (= N (@ (@ tptp.add_mset_a A) M2)))) (exists ((K3 tptp.multiset_a)) (and (forall ((B6 tptp.a)) (=> (@ (@ tptp.member_a B6) (@ tptp.set_mset_a K3)) (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a B6) A)) R))) (= N (@ (@ tptp.plus_plus_multiset_a M02) K3))))))) (forall ((A2 tptp.set_a) (B4 tptp.set_a)) (=> (forall ((X4 tptp.a)) (let ((_let_1 (@ tptp.member_a X4))) (=> (@ _let_1 A2) (@ _let_1 B4)))) (@ (@ tptp.ord_less_eq_set_a A2) B4))) (forall ((A2 tptp.set_a) (B4 tptp.set_a) (X tptp.a)) (let ((_let_1 (@ tptp.member_a X))) (=> (@ (@ tptp.ord_less_eq_set_a A2) B4) (=> (@ _let_1 A2) (@ _let_1 B4))))) (forall ((A2 tptp.set_a) (B4 tptp.set_a) (C tptp.a)) (let ((_let_1 (@ tptp.member_a C))) (=> (@ (@ tptp.ord_less_eq_set_a A2) B4) (=> (@ _let_1 A2) (@ _let_1 B4))))) (= tptp.ord_less_eq_set_a (lambda ((A6 tptp.set_a) (B7 tptp.set_a)) (forall ((X5 tptp.a)) (let ((_let_1 (@ tptp.member_a X5))) (=> (@ _let_1 A6) (@ _let_1 B7)))))) (= tptp.ord_less_eq_set_a (lambda ((A6 tptp.set_a) (B7 tptp.set_a)) (forall ((T2 tptp.a)) (let ((_let_1 (@ tptp.member_a T2))) (=> (@ _let_1 A6) (@ _let_1 B7)))))) (forall ((J2 tptp.multiset_a) (K4 tptp.multiset_a) (R tptp.set_Product_prod_a_a) (I2 tptp.multiset_a)) (let ((_let_1 (@ tptp.plus_plus_multiset_a I2))) (=> (not (= J2 tptp.zero_zero_multiset_a)) (=> (forall ((X4 tptp.a)) (=> (@ (@ tptp.member_a X4) (@ tptp.set_mset_a K4)) (exists ((Xa tptp.a)) (and (@ (@ tptp.member_a Xa) (@ tptp.set_mset_a J2)) (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X4) Xa)) R))))) (@ (@ tptp.member340150864iset_a (@ (@ tptp.produc2037245207iset_a (@ _let_1 K4)) (@ _let_1 J2))) (@ tptp.mult_a R)))))) (forall ((R tptp.set_Product_prod_a_a) (M tptp.multiset_a) (N tptp.multiset_a)) (=> (@ tptp.trans_a R) (=> (@ (@ tptp.member340150864iset_a (@ (@ tptp.produc2037245207iset_a M) N)) (@ tptp.mult_a R)) (exists ((I3 tptp.multiset_a) (J3 tptp.multiset_a)) (and (= N (@ (@ tptp.plus_plus_multiset_a I3) J3)) (exists ((K3 tptp.multiset_a)) (and (= M (@ (@ tptp.plus_plus_multiset_a I3) K3)) (not (= J3 tptp.zero_zero_multiset_a)) (forall ((X7 tptp.a)) (=> (@ (@ tptp.member_a X7) (@ tptp.set_mset_a K3)) (exists ((Xa2 tptp.a)) (and (@ (@ tptp.member_a Xa2) (@ tptp.set_mset_a J3)) (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X7) Xa2)) R)))))))))))) (forall ((M tptp.multiset_multiset_a)) (= (= (@ (@ (@ tptp.comm_m315775925iset_a tptp.plus_plus_multiset_a) tptp.zero_zero_multiset_a) M) tptp.zero_zero_multiset_a) (forall ((X5 tptp.multiset_a)) (=> (@ (@ tptp.member_multiset_a X5) (@ tptp.set_mset_multiset_a M)) (= X5 tptp.zero_zero_multiset_a))))) (forall ((S tptp.set_Product_prod_a_a) (Uu tptp.a) (X8 tptp.multiset_a) (Y7 tptp.multiset_a)) (let ((_let_1 (@ tptp.mult_a S))) (let ((_let_2 (@ tptp.add_mset_a Uu))) (=> (@ tptp.trans_a S) (=> (@ tptp.irrefl_a S) (= (@ (@ tptp.member340150864iset_a (@ (@ tptp.produc2037245207iset_a (@ _let_2 X8)) (@ _let_2 Y7))) _let_1) (@ (@ tptp.member340150864iset_a (@ (@ tptp.produc2037245207iset_a X8) Y7)) _let_1))))))) (forall ((X tptp.a) (M tptp.multiset_a) (NN tptp.multiset_multiset_a)) (let ((_let_1 (@ tptp.member_a X))) (= (@ _let_1 (@ tptp.set_mset_a (@ (@ (@ tptp.fold_m382157835iset_a tptp.plus_plus_multiset_a) M) NN))) (or (@ _let_1 (@ tptp.set_mset_a M)) (exists ((N3 tptp.multiset_a)) (and (@ (@ tptp.member_multiset_a N3) (@ tptp.set_mset_multiset_a NN)) (@ (@ tptp.member_a X) (@ tptp.set_mset_a N3)))))))) (= tptp.plus_plus_multiset_a (@ tptp.fold_m364285649iset_a tptp.add_mset_a)) (forall ((M tptp.multiset_a) (A tptp.a)) (let ((_let_1 (@ tptp.add_mset_a A))) (=> (@ (@ tptp.nO_MAT1617603563iset_a tptp.zero_zero_multiset_a) M) (= (@ _let_1 M) (@ (@ tptp.plus_plus_multiset_a (@ _let_1 tptp.zero_zero_multiset_a)) M))))) (forall ((K4 tptp.multiset_a) (F (-> tptp.a tptp.multiset_a)) (G (-> tptp.a tptp.multiset_a))) (let ((_let_1 (@ (@ tptp.comm_m315775925iset_a tptp.plus_plus_multiset_a) tptp.zero_zero_multiset_a))) (=> (forall ((I4 tptp.a)) (=> (@ (@ tptp.member_a I4) (@ tptp.set_mset_a K4)) (@ (@ tptp.subseteq_mset_a (@ F I4)) (@ G I4)))) (@ (@ tptp.subseteq_mset_a (@ _let_1 (@ (@ tptp.image_929116801iset_a F) K4))) (@ _let_1 (@ (@ tptp.image_929116801iset_a G) K4)))))) (forall ((F (-> tptp.a tptp.a)) (A tptp.a) (M tptp.multiset_a)) (let ((_let_1 (@ tptp.image_mset_a_a F))) (= (@ _let_1 (@ (@ tptp.add_mset_a A) M)) (@ (@ tptp.add_mset_a (@ F A)) (@ _let_1 M))))) (forall ((F (-> tptp.a tptp.a)) (M tptp.multiset_a) (B tptp.a) (N tptp.multiset_a)) (=> (= (@ (@ tptp.image_mset_a_a F) M) (@ (@ tptp.add_mset_a B) N)) (exists ((M1 tptp.multiset_a) (A4 tptp.a)) (and (= M (@ (@ tptp.add_mset_a A4) M1)) (= (@ F A4) B) (= (@ (@ tptp.image_mset_a_a F) M1) N))))) (forall ((F (-> tptp.a tptp.a)) (A tptp.a) (M tptp.multiset_a) (N tptp.multiset_a)) (=> (= (@ (@ tptp.image_mset_a_a F) (@ (@ tptp.add_mset_a A) M)) N) (exists ((N1 tptp.multiset_a)) (and (= N (@ (@ tptp.add_mset_a (@ F A)) N1)) (= (@ (@ tptp.image_mset_a_a F) M) N1))))) (forall ((F (-> tptp.a tptp.a)) (X tptp.a)) (= (@ (@ tptp.image_mset_a_a F) (@ (@ tptp.add_mset_a X) tptp.zero_zero_multiset_a)) (@ (@ tptp.add_mset_a (@ F X)) tptp.zero_zero_multiset_a))) _let_2 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.23/0.79 )
% 0.23/0.79 % SZS output end Proof for ITP068^1
% 0.23/0.79 % cvc5---1.0.5 exiting
% 0.23/0.80 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------