TSTP Solution File: ITP079^1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP079^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 03:18:02 EDT 2023
% Result : Theorem 0.83s 1.05s
% Output : Proof 0.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.17 % Problem : ITP079^1 : TPTP v8.1.2. Released v7.5.0.
% 0.12/0.18 % Command : do_cvc5 %s %d
% 0.18/0.39 % Computer : n022.cluster.edu
% 0.18/0.39 % Model : x86_64 x86_64
% 0.18/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.39 % Memory : 8042.1875MB
% 0.18/0.39 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.39 % CPULimit : 300
% 0.18/0.39 % WCLimit : 300
% 0.18/0.39 % DateTime : Sun Aug 27 10:42:54 EDT 2023
% 0.18/0.39 % CPUTime :
% 0.26/0.57 %----Proving TH0
% 0.26/0.58 %------------------------------------------------------------------------------
% 0.26/0.58 % File : ITP079^1 : TPTP v8.1.2. Released v7.5.0.
% 0.26/0.58 % Domain : Interactive Theorem Proving
% 0.26/0.58 % Problem : Sledgehammer Irreducible problem prob_209__6623758_1
% 0.26/0.58 % Version : Especial.
% 0.26/0.58 % English :
% 0.26/0.58
% 0.26/0.58 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.26/0.58 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.26/0.58 % Source : [Des21]
% 0.26/0.58 % Names : Irreducible/prob_209__6623758_1 [Des21]
% 0.26/0.58
% 0.26/0.58 % Status : Theorem
% 0.26/0.58 % Rating : 0.23 v8.1.0, 0.27 v7.5.0
% 0.26/0.58 % Syntax : Number of formulae : 437 ( 125 unt; 77 typ; 0 def)
% 0.26/0.58 % Number of atoms : 1207 ( 255 equ; 0 cnn)
% 0.26/0.58 % Maximal formula atoms : 12 ( 3 avg)
% 0.26/0.58 % Number of connectives : 3030 ( 50 ~; 19 |; 37 &;2359 @)
% 0.26/0.58 % ( 0 <=>; 565 =>; 0 <=; 0 <~>)
% 0.26/0.58 % Maximal formula depth : 16 ( 7 avg)
% 0.26/0.58 % Number of types : 5 ( 4 usr)
% 0.26/0.58 % Number of type conns : 567 ( 567 >; 0 *; 0 +; 0 <<)
% 0.26/0.58 % Number of symbols : 76 ( 73 usr; 4 con; 0-4 aty)
% 0.26/0.58 % Number of variables : 1151 ( 131 ^;1020 !; 0 ?;1151 :)
% 0.26/0.58 % SPC : TH0_THM_EQU_NAR
% 0.26/0.58
% 0.26/0.58 % Comments : This file was generated by Sledgehammer 2021-02-23 15:36:10.728
% 0.26/0.58 %------------------------------------------------------------------------------
% 0.26/0.58 % Could-be-implicit typings (4)
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% 0.26/0.58
% 0.26/0.58 thf(sy_c_Set__Interval_Oord__class_OatMost_001tf__val,type,
% 0.26/0.58 set_ord_atMost_val: val > set_val ).
% 0.26/0.58
% 0.26/0.58 thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001tf__val,type,
% 0.26/0.58 set_or2126567818an_val: val > val > set_val ).
% 0.26/0.58
% 0.26/0.58 thf(sy_c_Set__Interval_Oord__class_OgreaterThan_001tf__val,type,
% 0.26/0.58 set_or1288365508an_val: val > set_val ).
% 0.26/0.58
% 0.26/0.58 thf(sy_c_Set__Interval_Oord__class_OlessThan_001tf__val,type,
% 0.26/0.58 set_ord_lessThan_val: val > set_val ).
% 0.26/0.58
% 0.26/0.58 thf(sy_c_member_001t__Set__Oset_Itf__val_J,type,
% 0.26/0.58 member_set_val: set_val > set_set_val > $o ).
% 0.26/0.58
% 0.26/0.58 thf(sy_c_member_001tf__val,type,
% 0.26/0.58 member_val: val > set_val > $o ).
% 0.26/0.58
% 0.26/0.58 thf(sy_v_P,type,
% 0.26/0.58 p: set_val ).
% 0.26/0.58
% 0.26/0.58 thf(sy_v_scc,type,
% 0.26/0.58 scc: set_val ).
% 0.26/0.58
% 0.26/0.58 % Relevant facts (350)
% 0.26/0.58 thf(fact_0__092_060open_062_092_060And_062x_O_Ax_A_092_060in_062_Ascc_A_092_060Longrightarrow_062_Ax_A_092_060in_062_AP_092_060close_062,axiom,
% 0.26/0.58 ! [X: val] :
% 0.26/0.58 ( ( member_val @ X @ scc )
% 0.26/0.58 => ( member_val @ X @ p ) ) ).
% 0.26/0.58
% 0.26/0.58 % \<open>\<And>x. x \<in> scc \<Longrightarrow> x \<in> P\<close>
% 0.26/0.58 thf(fact_1_subsetI,axiom,
% 0.26/0.58 ! [A: set_set_val,B: set_set_val] :
% 0.26/0.58 ( ! [X2: set_val] :
% 0.26/0.58 ( ( member_set_val @ X2 @ A )
% 0.26/0.58 => ( member_set_val @ X2 @ B ) )
% 0.26/0.58 => ( ord_le1742111550et_val @ A @ B ) ) ).
% 0.26/0.58
% 0.26/0.58 % subsetI
% 0.26/0.58 thf(fact_2_subsetI,axiom,
% 0.26/0.58 ! [A: set_val,B: set_val] :
% 0.26/0.58 ( ! [X2: val] :
% 0.26/0.58 ( ( member_val @ X2 @ A )
% 0.26/0.58 => ( member_val @ X2 @ B ) )
% 0.26/0.58 => ( ord_less_eq_set_val @ A @ B ) ) ).
% 0.26/0.58
% 0.26/0.58 % subsetI
% 0.26/0.58 thf(fact_3_subset__antisym,axiom,
% 0.26/0.58 ! [A: set_set_val,B: set_set_val] :
% 0.26/0.58 ( ( ord_le1742111550et_val @ A @ B )
% 0.26/0.58 => ( ( ord_le1742111550et_val @ B @ A )
% 0.26/0.58 => ( A = B ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % subset_antisym
% 0.26/0.58 thf(fact_4_subset__antisym,axiom,
% 0.26/0.58 ! [A: set_val,B: set_val] :
% 0.26/0.58 ( ( ord_less_eq_set_val @ A @ B )
% 0.26/0.58 => ( ( ord_less_eq_set_val @ B @ A )
% 0.26/0.58 => ( A = B ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % subset_antisym
% 0.26/0.58 thf(fact_5_order__mono__setup_Orefl,axiom,
% 0.26/0.58 ! [X: $o > set_val] : ( ord_le994826475et_val @ X @ X ) ).
% 0.26/0.58
% 0.26/0.58 % order_mono_setup.refl
% 0.26/0.58 thf(fact_6_order__mono__setup_Orefl,axiom,
% 0.26/0.58 ! [X: val] : ( ord_less_eq_val @ X @ X ) ).
% 0.26/0.58
% 0.26/0.58 % order_mono_setup.refl
% 0.26/0.58 thf(fact_7_order__mono__setup_Orefl,axiom,
% 0.26/0.58 ! [X: set_set_val] : ( ord_le1742111550et_val @ X @ X ) ).
% 0.26/0.58
% 0.26/0.58 % order_mono_setup.refl
% 0.26/0.58 thf(fact_8_order__mono__setup_Orefl,axiom,
% 0.26/0.58 ! [X: set_val] : ( ord_less_eq_set_val @ X @ X ) ).
% 0.26/0.58
% 0.26/0.58 % order_mono_setup.refl
% 0.26/0.58 thf(fact_9_relprop__triggers_I6_J,axiom,
% 0.26/0.58 ! [R: set_set_val,R2: set_set_val] :
% 0.26/0.58 ( ( ord_le1742111550et_val @ R @ R2 )
% 0.26/0.58 => ( ord_le1742111550et_val @ R @ R2 ) ) ).
% 0.26/0.58
% 0.26/0.58 % relprop_triggers(6)
% 0.26/0.58 thf(fact_10_relprop__triggers_I6_J,axiom,
% 0.26/0.58 ! [R: set_val,R2: set_val] :
% 0.26/0.58 ( ( ord_less_eq_set_val @ R @ R2 )
% 0.26/0.58 => ( ord_less_eq_set_val @ R @ R2 ) ) ).
% 0.26/0.58
% 0.26/0.58 % relprop_triggers(6)
% 0.26/0.58 thf(fact_11_in__mono,axiom,
% 0.26/0.58 ! [A: set_set_val,B: set_set_val,X: set_val] :
% 0.26/0.58 ( ( ord_le1742111550et_val @ A @ B )
% 0.26/0.58 => ( ( member_set_val @ X @ A )
% 0.26/0.58 => ( member_set_val @ X @ B ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % in_mono
% 0.26/0.58 thf(fact_12_in__mono,axiom,
% 0.26/0.58 ! [A: set_val,B: set_val,X: val] :
% 0.26/0.58 ( ( ord_less_eq_set_val @ A @ B )
% 0.26/0.58 => ( ( member_val @ X @ A )
% 0.26/0.58 => ( member_val @ X @ B ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % in_mono
% 0.26/0.58 thf(fact_13_subsetD,axiom,
% 0.26/0.58 ! [A: set_set_val,B: set_set_val,C: set_val] :
% 0.26/0.58 ( ( ord_le1742111550et_val @ A @ B )
% 0.26/0.58 => ( ( member_set_val @ C @ A )
% 0.26/0.58 => ( member_set_val @ C @ B ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % subsetD
% 0.26/0.58 thf(fact_14_subsetD,axiom,
% 0.26/0.58 ! [A: set_val,B: set_val,C: val] :
% 0.26/0.58 ( ( ord_less_eq_set_val @ A @ B )
% 0.26/0.58 => ( ( member_val @ C @ A )
% 0.26/0.58 => ( member_val @ C @ B ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % subsetD
% 0.26/0.58 thf(fact_15_equalityE,axiom,
% 0.26/0.58 ! [A: set_set_val,B: set_set_val] :
% 0.26/0.58 ( ( A = B )
% 0.26/0.58 => ~ ( ( ord_le1742111550et_val @ A @ B )
% 0.26/0.58 => ~ ( ord_le1742111550et_val @ B @ A ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % equalityE
% 0.26/0.58 thf(fact_16_equalityE,axiom,
% 0.26/0.58 ! [A: set_val,B: set_val] :
% 0.26/0.58 ( ( A = B )
% 0.26/0.58 => ~ ( ( ord_less_eq_set_val @ A @ B )
% 0.26/0.58 => ~ ( ord_less_eq_set_val @ B @ A ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % equalityE
% 0.26/0.58 thf(fact_17_subset__eq,axiom,
% 0.26/0.58 ( ord_le1742111550et_val
% 0.26/0.58 = ( ^ [A2: set_set_val,B2: set_set_val] :
% 0.26/0.58 ! [X3: set_val] :
% 0.26/0.58 ( ( member_set_val @ X3 @ A2 )
% 0.26/0.58 => ( member_set_val @ X3 @ B2 ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % subset_eq
% 0.26/0.58 thf(fact_18_subset__eq,axiom,
% 0.26/0.58 ( ord_less_eq_set_val
% 0.26/0.58 = ( ^ [A2: set_val,B2: set_val] :
% 0.26/0.58 ! [X3: val] :
% 0.26/0.58 ( ( member_val @ X3 @ A2 )
% 0.26/0.58 => ( member_val @ X3 @ B2 ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % subset_eq
% 0.26/0.58 thf(fact_19_equalityD1,axiom,
% 0.26/0.58 ! [A: set_set_val,B: set_set_val] :
% 0.26/0.58 ( ( A = B )
% 0.26/0.58 => ( ord_le1742111550et_val @ A @ B ) ) ).
% 0.26/0.58
% 0.26/0.58 % equalityD1
% 0.26/0.58 thf(fact_20_equalityD1,axiom,
% 0.26/0.58 ! [A: set_val,B: set_val] :
% 0.26/0.58 ( ( A = B )
% 0.26/0.58 => ( ord_less_eq_set_val @ A @ B ) ) ).
% 0.26/0.58
% 0.26/0.58 % equalityD1
% 0.26/0.58 thf(fact_21_equalityD2,axiom,
% 0.26/0.58 ! [A: set_set_val,B: set_set_val] :
% 0.26/0.58 ( ( A = B )
% 0.26/0.58 => ( ord_le1742111550et_val @ B @ A ) ) ).
% 0.26/0.58
% 0.26/0.58 % equalityD2
% 0.26/0.58 thf(fact_22_equalityD2,axiom,
% 0.26/0.58 ! [A: set_val,B: set_val] :
% 0.26/0.58 ( ( A = B )
% 0.26/0.58 => ( ord_less_eq_set_val @ B @ A ) ) ).
% 0.26/0.58
% 0.26/0.58 % equalityD2
% 0.26/0.58 thf(fact_23_subset__iff,axiom,
% 0.26/0.58 ( ord_le1742111550et_val
% 0.26/0.58 = ( ^ [A2: set_set_val,B2: set_set_val] :
% 0.26/0.58 ! [T: set_val] :
% 0.26/0.58 ( ( member_set_val @ T @ A2 )
% 0.26/0.58 => ( member_set_val @ T @ B2 ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % subset_iff
% 0.26/0.58 thf(fact_24_subset__iff,axiom,
% 0.26/0.58 ( ord_less_eq_set_val
% 0.26/0.58 = ( ^ [A2: set_val,B2: set_val] :
% 0.26/0.58 ! [T: val] :
% 0.26/0.58 ( ( member_val @ T @ A2 )
% 0.26/0.58 => ( member_val @ T @ B2 ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % subset_iff
% 0.26/0.58 thf(fact_25_subset__refl,axiom,
% 0.26/0.58 ! [A: set_set_val] : ( ord_le1742111550et_val @ A @ A ) ).
% 0.26/0.58
% 0.26/0.58 % subset_refl
% 0.26/0.58 thf(fact_26_subset__refl,axiom,
% 0.26/0.58 ! [A: set_val] : ( ord_less_eq_set_val @ A @ A ) ).
% 0.26/0.58
% 0.26/0.58 % subset_refl
% 0.26/0.58 thf(fact_27_order__mono__setup_Omono__if,axiom,
% 0.26/0.58 ! [T2: $o > set_val,T3: $o > set_val,E: $o > set_val,E2: $o > set_val,B3: $o] :
% 0.26/0.58 ( ( ord_le994826475et_val @ T2 @ T3 )
% 0.26/0.58 => ( ( ord_le994826475et_val @ E @ E2 )
% 0.26/0.58 => ( ord_le994826475et_val @ ( if_o_set_val @ B3 @ T2 @ E ) @ ( if_o_set_val @ B3 @ T3 @ E2 ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % order_mono_setup.mono_if
% 0.26/0.58 thf(fact_28_order__mono__setup_Omono__if,axiom,
% 0.26/0.58 ! [T2: val,T3: val,E: val,E2: val,B3: $o] :
% 0.26/0.58 ( ( ord_less_eq_val @ T2 @ T3 )
% 0.26/0.58 => ( ( ord_less_eq_val @ E @ E2 )
% 0.26/0.58 => ( ord_less_eq_val @ ( if_val @ B3 @ T2 @ E ) @ ( if_val @ B3 @ T3 @ E2 ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % order_mono_setup.mono_if
% 0.26/0.58 thf(fact_29_order__mono__setup_Omono__if,axiom,
% 0.26/0.58 ! [T2: set_set_val,T3: set_set_val,E: set_set_val,E2: set_set_val,B3: $o] :
% 0.26/0.58 ( ( ord_le1742111550et_val @ T2 @ T3 )
% 0.26/0.58 => ( ( ord_le1742111550et_val @ E @ E2 )
% 0.26/0.58 => ( ord_le1742111550et_val @ ( if_set_set_val @ B3 @ T2 @ E ) @ ( if_set_set_val @ B3 @ T3 @ E2 ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % order_mono_setup.mono_if
% 0.26/0.58 thf(fact_30_order__mono__setup_Omono__if,axiom,
% 0.26/0.58 ! [T2: set_val,T3: set_val,E: set_val,E2: set_val,B3: $o] :
% 0.26/0.58 ( ( ord_less_eq_set_val @ T2 @ T3 )
% 0.26/0.58 => ( ( ord_less_eq_set_val @ E @ E2 )
% 0.26/0.58 => ( ord_less_eq_set_val @ ( if_set_val @ B3 @ T2 @ E ) @ ( if_set_val @ B3 @ T3 @ E2 ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % order_mono_setup.mono_if
% 0.26/0.58 thf(fact_31_Collect__mono__iff,axiom,
% 0.26/0.58 ! [P: set_val > $o,Q: set_val > $o] :
% 0.26/0.58 ( ( ord_le1742111550et_val @ ( collect_set_val @ P ) @ ( collect_set_val @ Q ) )
% 0.26/0.58 = ( ! [X3: set_val] :
% 0.26/0.58 ( ( P @ X3 )
% 0.26/0.58 => ( Q @ X3 ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % Collect_mono_iff
% 0.26/0.58 thf(fact_32_Collect__mono__iff,axiom,
% 0.26/0.58 ! [P: val > $o,Q: val > $o] :
% 0.26/0.58 ( ( ord_less_eq_set_val @ ( collect_val @ P ) @ ( collect_val @ Q ) )
% 0.26/0.58 = ( ! [X3: val] :
% 0.26/0.58 ( ( P @ X3 )
% 0.26/0.58 => ( Q @ X3 ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % Collect_mono_iff
% 0.26/0.58 thf(fact_33_set__eq__subset,axiom,
% 0.26/0.58 ( ( ^ [Y: set_set_val,Z: set_set_val] : ( Y = Z ) )
% 0.26/0.58 = ( ^ [A2: set_set_val,B2: set_set_val] :
% 0.26/0.58 ( ( ord_le1742111550et_val @ A2 @ B2 )
% 0.26/0.58 & ( ord_le1742111550et_val @ B2 @ A2 ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % set_eq_subset
% 0.26/0.58 thf(fact_34_set__eq__subset,axiom,
% 0.26/0.58 ( ( ^ [Y: set_val,Z: set_val] : ( Y = Z ) )
% 0.26/0.58 = ( ^ [A2: set_val,B2: set_val] :
% 0.26/0.58 ( ( ord_less_eq_set_val @ A2 @ B2 )
% 0.26/0.58 & ( ord_less_eq_set_val @ B2 @ A2 ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % set_eq_subset
% 0.26/0.58 thf(fact_35_subset__trans,axiom,
% 0.26/0.58 ! [A: set_set_val,B: set_set_val,C2: set_set_val] :
% 0.26/0.58 ( ( ord_le1742111550et_val @ A @ B )
% 0.26/0.58 => ( ( ord_le1742111550et_val @ B @ C2 )
% 0.26/0.58 => ( ord_le1742111550et_val @ A @ C2 ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % subset_trans
% 0.26/0.58 thf(fact_36_subset__trans,axiom,
% 0.26/0.58 ! [A: set_val,B: set_val,C2: set_val] :
% 0.26/0.58 ( ( ord_less_eq_set_val @ A @ B )
% 0.26/0.58 => ( ( ord_less_eq_set_val @ B @ C2 )
% 0.26/0.58 => ( ord_less_eq_set_val @ A @ C2 ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % subset_trans
% 0.26/0.58 thf(fact_37_Collect__mono,axiom,
% 0.26/0.58 ! [P: set_val > $o,Q: set_val > $o] :
% 0.26/0.58 ( ! [X2: set_val] :
% 0.26/0.58 ( ( P @ X2 )
% 0.26/0.58 => ( Q @ X2 ) )
% 0.26/0.58 => ( ord_le1742111550et_val @ ( collect_set_val @ P ) @ ( collect_set_val @ Q ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % Collect_mono
% 0.26/0.58 thf(fact_38_Collect__mono,axiom,
% 0.26/0.58 ! [P: val > $o,Q: val > $o] :
% 0.26/0.58 ( ! [X2: val] :
% 0.26/0.58 ( ( P @ X2 )
% 0.26/0.58 => ( Q @ X2 ) )
% 0.26/0.58 => ( ord_less_eq_set_val @ ( collect_val @ P ) @ ( collect_val @ Q ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % Collect_mono
% 0.26/0.58 thf(fact_39_subset__Collect__conv,axiom,
% 0.26/0.58 ! [S: set_set_val,P: set_val > $o] :
% 0.26/0.58 ( ( ord_le1742111550et_val @ S @ ( collect_set_val @ P ) )
% 0.26/0.58 = ( ! [X3: set_val] :
% 0.26/0.58 ( ( member_set_val @ X3 @ S )
% 0.26/0.58 => ( P @ X3 ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % subset_Collect_conv
% 0.26/0.58 thf(fact_40_subset__Collect__conv,axiom,
% 0.26/0.58 ! [S: set_val,P: val > $o] :
% 0.26/0.58 ( ( ord_less_eq_set_val @ S @ ( collect_val @ P ) )
% 0.26/0.58 = ( ! [X3: val] :
% 0.26/0.58 ( ( member_val @ X3 @ S )
% 0.26/0.58 => ( P @ X3 ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % subset_Collect_conv
% 0.26/0.58 thf(fact_41_dual__order_Oantisym,axiom,
% 0.26/0.58 ! [B3: $o > set_val,A3: $o > set_val] :
% 0.26/0.58 ( ( ord_le994826475et_val @ B3 @ A3 )
% 0.26/0.58 => ( ( ord_le994826475et_val @ A3 @ B3 )
% 0.26/0.58 => ( A3 = B3 ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % dual_order.antisym
% 0.26/0.58 thf(fact_42_dual__order_Oantisym,axiom,
% 0.26/0.58 ! [B3: val,A3: val] :
% 0.26/0.58 ( ( ord_less_eq_val @ B3 @ A3 )
% 0.26/0.58 => ( ( ord_less_eq_val @ A3 @ B3 )
% 0.26/0.58 => ( A3 = B3 ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % dual_order.antisym
% 0.26/0.58 thf(fact_43_dual__order_Oantisym,axiom,
% 0.26/0.58 ! [B3: set_set_val,A3: set_set_val] :
% 0.26/0.58 ( ( ord_le1742111550et_val @ B3 @ A3 )
% 0.26/0.58 => ( ( ord_le1742111550et_val @ A3 @ B3 )
% 0.26/0.58 => ( A3 = B3 ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % dual_order.antisym
% 0.26/0.58 thf(fact_44_dual__order_Oantisym,axiom,
% 0.26/0.58 ! [B3: set_val,A3: set_val] :
% 0.26/0.58 ( ( ord_less_eq_set_val @ B3 @ A3 )
% 0.26/0.58 => ( ( ord_less_eq_set_val @ A3 @ B3 )
% 0.26/0.58 => ( A3 = B3 ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % dual_order.antisym
% 0.26/0.58 thf(fact_45_dual__order_Oeq__iff,axiom,
% 0.26/0.58 ( ( ^ [Y: $o > set_val,Z: $o > set_val] : ( Y = Z ) )
% 0.26/0.58 = ( ^ [A4: $o > set_val,B4: $o > set_val] :
% 0.26/0.58 ( ( ord_le994826475et_val @ B4 @ A4 )
% 0.26/0.58 & ( ord_le994826475et_val @ A4 @ B4 ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % dual_order.eq_iff
% 0.26/0.58 thf(fact_46_dual__order_Oeq__iff,axiom,
% 0.26/0.58 ( ( ^ [Y: val,Z: val] : ( Y = Z ) )
% 0.26/0.58 = ( ^ [A4: val,B4: val] :
% 0.26/0.58 ( ( ord_less_eq_val @ B4 @ A4 )
% 0.26/0.58 & ( ord_less_eq_val @ A4 @ B4 ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % dual_order.eq_iff
% 0.26/0.58 thf(fact_47_dual__order_Oeq__iff,axiom,
% 0.26/0.58 ( ( ^ [Y: set_set_val,Z: set_set_val] : ( Y = Z ) )
% 0.26/0.58 = ( ^ [A4: set_set_val,B4: set_set_val] :
% 0.26/0.58 ( ( ord_le1742111550et_val @ B4 @ A4 )
% 0.26/0.58 & ( ord_le1742111550et_val @ A4 @ B4 ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % dual_order.eq_iff
% 0.26/0.58 thf(fact_48_dual__order_Oeq__iff,axiom,
% 0.26/0.58 ( ( ^ [Y: set_val,Z: set_val] : ( Y = Z ) )
% 0.26/0.58 = ( ^ [A4: set_val,B4: set_val] :
% 0.26/0.58 ( ( ord_less_eq_set_val @ B4 @ A4 )
% 0.26/0.58 & ( ord_less_eq_set_val @ A4 @ B4 ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % dual_order.eq_iff
% 0.26/0.58 thf(fact_49_dual__order_Otrans,axiom,
% 0.26/0.58 ! [B3: $o > set_val,A3: $o > set_val,C: $o > set_val] :
% 0.26/0.58 ( ( ord_le994826475et_val @ B3 @ A3 )
% 0.26/0.58 => ( ( ord_le994826475et_val @ C @ B3 )
% 0.26/0.58 => ( ord_le994826475et_val @ C @ A3 ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % dual_order.trans
% 0.26/0.58 thf(fact_50_dual__order_Otrans,axiom,
% 0.26/0.58 ! [B3: val,A3: val,C: val] :
% 0.26/0.58 ( ( ord_less_eq_val @ B3 @ A3 )
% 0.26/0.58 => ( ( ord_less_eq_val @ C @ B3 )
% 0.26/0.58 => ( ord_less_eq_val @ C @ A3 ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % dual_order.trans
% 0.26/0.58 thf(fact_51_dual__order_Otrans,axiom,
% 0.26/0.58 ! [B3: set_set_val,A3: set_set_val,C: set_set_val] :
% 0.26/0.58 ( ( ord_le1742111550et_val @ B3 @ A3 )
% 0.26/0.58 => ( ( ord_le1742111550et_val @ C @ B3 )
% 0.26/0.58 => ( ord_le1742111550et_val @ C @ A3 ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % dual_order.trans
% 0.26/0.58 thf(fact_52_dual__order_Otrans,axiom,
% 0.26/0.58 ! [B3: set_val,A3: set_val,C: set_val] :
% 0.26/0.58 ( ( ord_less_eq_set_val @ B3 @ A3 )
% 0.26/0.58 => ( ( ord_less_eq_set_val @ C @ B3 )
% 0.26/0.58 => ( ord_less_eq_set_val @ C @ A3 ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % dual_order.trans
% 0.26/0.58 thf(fact_53_linorder__wlog,axiom,
% 0.26/0.58 ! [P: val > val > $o,A3: val,B3: val] :
% 0.26/0.58 ( ! [A5: val,B5: val] :
% 0.26/0.58 ( ( ord_less_eq_val @ A5 @ B5 )
% 0.26/0.58 => ( P @ A5 @ B5 ) )
% 0.26/0.58 => ( ! [A5: val,B5: val] :
% 0.26/0.58 ( ( P @ B5 @ A5 )
% 0.26/0.58 => ( P @ A5 @ B5 ) )
% 0.26/0.58 => ( P @ A3 @ B3 ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % linorder_wlog
% 0.26/0.58 thf(fact_54_dual__order_Orefl,axiom,
% 0.26/0.58 ! [A3: $o > set_val] : ( ord_le994826475et_val @ A3 @ A3 ) ).
% 0.26/0.58
% 0.26/0.58 % dual_order.refl
% 0.26/0.58 thf(fact_55_dual__order_Orefl,axiom,
% 0.26/0.58 ! [A3: val] : ( ord_less_eq_val @ A3 @ A3 ) ).
% 0.26/0.58
% 0.26/0.58 % dual_order.refl
% 0.26/0.58 thf(fact_56_dual__order_Orefl,axiom,
% 0.26/0.58 ! [A3: set_set_val] : ( ord_le1742111550et_val @ A3 @ A3 ) ).
% 0.26/0.58
% 0.26/0.58 % dual_order.refl
% 0.26/0.58 thf(fact_57_dual__order_Orefl,axiom,
% 0.26/0.58 ! [A3: set_val] : ( ord_less_eq_set_val @ A3 @ A3 ) ).
% 0.26/0.58
% 0.26/0.58 % dual_order.refl
% 0.26/0.58 thf(fact_58_order__trans,axiom,
% 0.26/0.58 ! [X: $o > set_val,Y2: $o > set_val,Z2: $o > set_val] :
% 0.26/0.58 ( ( ord_le994826475et_val @ X @ Y2 )
% 0.26/0.58 => ( ( ord_le994826475et_val @ Y2 @ Z2 )
% 0.26/0.58 => ( ord_le994826475et_val @ X @ Z2 ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % order_trans
% 0.26/0.58 thf(fact_59_order__trans,axiom,
% 0.26/0.58 ! [X: val,Y2: val,Z2: val] :
% 0.26/0.58 ( ( ord_less_eq_val @ X @ Y2 )
% 0.26/0.58 => ( ( ord_less_eq_val @ Y2 @ Z2 )
% 0.26/0.58 => ( ord_less_eq_val @ X @ Z2 ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % order_trans
% 0.26/0.58 thf(fact_60_order__trans,axiom,
% 0.26/0.58 ! [X: set_set_val,Y2: set_set_val,Z2: set_set_val] :
% 0.26/0.58 ( ( ord_le1742111550et_val @ X @ Y2 )
% 0.26/0.58 => ( ( ord_le1742111550et_val @ Y2 @ Z2 )
% 0.26/0.58 => ( ord_le1742111550et_val @ X @ Z2 ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % order_trans
% 0.26/0.58 thf(fact_61_order__trans,axiom,
% 0.26/0.58 ! [X: set_val,Y2: set_val,Z2: set_val] :
% 0.26/0.58 ( ( ord_less_eq_set_val @ X @ Y2 )
% 0.26/0.58 => ( ( ord_less_eq_set_val @ Y2 @ Z2 )
% 0.26/0.58 => ( ord_less_eq_set_val @ X @ Z2 ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % order_trans
% 0.26/0.58 thf(fact_62_order__class_Oorder_Oantisym,axiom,
% 0.26/0.58 ! [A3: $o > set_val,B3: $o > set_val] :
% 0.26/0.58 ( ( ord_le994826475et_val @ A3 @ B3 )
% 0.26/0.58 => ( ( ord_le994826475et_val @ B3 @ A3 )
% 0.26/0.58 => ( A3 = B3 ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % order_class.order.antisym
% 0.26/0.58 thf(fact_63_order__class_Oorder_Oantisym,axiom,
% 0.26/0.58 ! [A3: val,B3: val] :
% 0.26/0.58 ( ( ord_less_eq_val @ A3 @ B3 )
% 0.26/0.58 => ( ( ord_less_eq_val @ B3 @ A3 )
% 0.26/0.58 => ( A3 = B3 ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % order_class.order.antisym
% 0.26/0.58 thf(fact_64_order__class_Oorder_Oantisym,axiom,
% 0.26/0.58 ! [A3: set_set_val,B3: set_set_val] :
% 0.26/0.58 ( ( ord_le1742111550et_val @ A3 @ B3 )
% 0.26/0.58 => ( ( ord_le1742111550et_val @ B3 @ A3 )
% 0.26/0.58 => ( A3 = B3 ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % order_class.order.antisym
% 0.26/0.58 thf(fact_65_order__class_Oorder_Oantisym,axiom,
% 0.26/0.58 ! [A3: set_val,B3: set_val] :
% 0.26/0.58 ( ( ord_less_eq_set_val @ A3 @ B3 )
% 0.26/0.58 => ( ( ord_less_eq_set_val @ B3 @ A3 )
% 0.26/0.58 => ( A3 = B3 ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % order_class.order.antisym
% 0.26/0.58 thf(fact_66_ord__le__eq__trans,axiom,
% 0.26/0.58 ! [A3: $o > set_val,B3: $o > set_val,C: $o > set_val] :
% 0.26/0.58 ( ( ord_le994826475et_val @ A3 @ B3 )
% 0.26/0.58 => ( ( B3 = C )
% 0.26/0.58 => ( ord_le994826475et_val @ A3 @ C ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % ord_le_eq_trans
% 0.26/0.58 thf(fact_67_ord__le__eq__trans,axiom,
% 0.26/0.58 ! [A3: val,B3: val,C: val] :
% 0.26/0.58 ( ( ord_less_eq_val @ A3 @ B3 )
% 0.26/0.58 => ( ( B3 = C )
% 0.26/0.58 => ( ord_less_eq_val @ A3 @ C ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % ord_le_eq_trans
% 0.26/0.58 thf(fact_68_ord__le__eq__trans,axiom,
% 0.26/0.58 ! [A3: set_set_val,B3: set_set_val,C: set_set_val] :
% 0.26/0.58 ( ( ord_le1742111550et_val @ A3 @ B3 )
% 0.26/0.58 => ( ( B3 = C )
% 0.26/0.58 => ( ord_le1742111550et_val @ A3 @ C ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % ord_le_eq_trans
% 0.26/0.58 thf(fact_69_ord__le__eq__trans,axiom,
% 0.26/0.58 ! [A3: set_val,B3: set_val,C: set_val] :
% 0.26/0.58 ( ( ord_less_eq_set_val @ A3 @ B3 )
% 0.26/0.58 => ( ( B3 = C )
% 0.26/0.58 => ( ord_less_eq_set_val @ A3 @ C ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % ord_le_eq_trans
% 0.26/0.58 thf(fact_70_le__funD,axiom,
% 0.26/0.58 ! [F: $o > set_val,G: $o > set_val,X: $o] :
% 0.26/0.58 ( ( ord_le994826475et_val @ F @ G )
% 0.26/0.58 => ( ord_less_eq_set_val @ ( F @ X ) @ ( G @ X ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % le_funD
% 0.26/0.58 thf(fact_71_le__funE,axiom,
% 0.26/0.58 ! [F: $o > set_val,G: $o > set_val,X: $o] :
% 0.26/0.58 ( ( ord_le994826475et_val @ F @ G )
% 0.26/0.58 => ( ord_less_eq_set_val @ ( F @ X ) @ ( G @ X ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % le_funE
% 0.26/0.58 thf(fact_72_le__funI,axiom,
% 0.26/0.58 ! [F: $o > set_val,G: $o > set_val] :
% 0.26/0.58 ( ! [X2: $o] : ( ord_less_eq_set_val @ ( F @ X2 ) @ ( G @ X2 ) )
% 0.26/0.58 => ( ord_le994826475et_val @ F @ G ) ) ).
% 0.26/0.58
% 0.26/0.58 % le_funI
% 0.26/0.58 thf(fact_73_le__fun__def,axiom,
% 0.26/0.58 ( ord_le994826475et_val
% 0.26/0.58 = ( ^ [F2: $o > set_val,G2: $o > set_val] :
% 0.26/0.58 ! [X3: $o] : ( ord_less_eq_set_val @ ( F2 @ X3 ) @ ( G2 @ X3 ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % le_fun_def
% 0.26/0.58 thf(fact_74_order__subst1,axiom,
% 0.26/0.58 ! [A3: set_val,F: set_val > set_val,B3: set_val,C: set_val] :
% 0.26/0.58 ( ( ord_less_eq_set_val @ A3 @ ( F @ B3 ) )
% 0.26/0.58 => ( ( ord_less_eq_set_val @ B3 @ C )
% 0.26/0.58 => ( ! [X2: set_val,Y3: set_val] :
% 0.26/0.58 ( ( ord_less_eq_set_val @ X2 @ Y3 )
% 0.26/0.58 => ( ord_less_eq_set_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.26/0.58 => ( ord_less_eq_set_val @ A3 @ ( F @ C ) ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % order_subst1
% 0.26/0.58 thf(fact_75_order__subst1,axiom,
% 0.26/0.58 ! [A3: val,F: val > val,B3: val,C: val] :
% 0.26/0.58 ( ( ord_less_eq_val @ A3 @ ( F @ B3 ) )
% 0.26/0.58 => ( ( ord_less_eq_val @ B3 @ C )
% 0.26/0.58 => ( ! [X2: val,Y3: val] :
% 0.26/0.58 ( ( ord_less_eq_val @ X2 @ Y3 )
% 0.26/0.58 => ( ord_less_eq_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.26/0.58 => ( ord_less_eq_val @ A3 @ ( F @ C ) ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % order_subst1
% 0.26/0.58 thf(fact_76_order__subst1,axiom,
% 0.26/0.58 ! [A3: set_val,F: val > set_val,B3: val,C: val] :
% 0.26/0.58 ( ( ord_less_eq_set_val @ A3 @ ( F @ B3 ) )
% 0.26/0.58 => ( ( ord_less_eq_val @ B3 @ C )
% 0.26/0.58 => ( ! [X2: val,Y3: val] :
% 0.26/0.58 ( ( ord_less_eq_val @ X2 @ Y3 )
% 0.26/0.58 => ( ord_less_eq_set_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.26/0.58 => ( ord_less_eq_set_val @ A3 @ ( F @ C ) ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % order_subst1
% 0.26/0.58 thf(fact_77_order__subst1,axiom,
% 0.26/0.58 ! [A3: val,F: set_val > val,B3: set_val,C: set_val] :
% 0.26/0.58 ( ( ord_less_eq_val @ A3 @ ( F @ B3 ) )
% 0.26/0.58 => ( ( ord_less_eq_set_val @ B3 @ C )
% 0.26/0.58 => ( ! [X2: set_val,Y3: set_val] :
% 0.26/0.58 ( ( ord_less_eq_set_val @ X2 @ Y3 )
% 0.26/0.58 => ( ord_less_eq_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.26/0.58 => ( ord_less_eq_val @ A3 @ ( F @ C ) ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % order_subst1
% 0.26/0.58 thf(fact_78_order__subst1,axiom,
% 0.26/0.58 ! [A3: val,F: set_set_val > val,B3: set_set_val,C: set_set_val] :
% 0.26/0.58 ( ( ord_less_eq_val @ A3 @ ( F @ B3 ) )
% 0.26/0.58 => ( ( ord_le1742111550et_val @ B3 @ C )
% 0.26/0.58 => ( ! [X2: set_set_val,Y3: set_set_val] :
% 0.26/0.58 ( ( ord_le1742111550et_val @ X2 @ Y3 )
% 0.26/0.58 => ( ord_less_eq_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.26/0.58 => ( ord_less_eq_val @ A3 @ ( F @ C ) ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % order_subst1
% 0.26/0.58 thf(fact_79_order__subst1,axiom,
% 0.26/0.58 ! [A3: set_set_val,F: val > set_set_val,B3: val,C: val] :
% 0.26/0.58 ( ( ord_le1742111550et_val @ A3 @ ( F @ B3 ) )
% 0.26/0.58 => ( ( ord_less_eq_val @ B3 @ C )
% 0.26/0.58 => ( ! [X2: val,Y3: val] :
% 0.26/0.58 ( ( ord_less_eq_val @ X2 @ Y3 )
% 0.26/0.58 => ( ord_le1742111550et_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.26/0.58 => ( ord_le1742111550et_val @ A3 @ ( F @ C ) ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % order_subst1
% 0.26/0.58 thf(fact_80_order__subst1,axiom,
% 0.26/0.58 ! [A3: set_val,F: set_set_val > set_val,B3: set_set_val,C: set_set_val] :
% 0.26/0.58 ( ( ord_less_eq_set_val @ A3 @ ( F @ B3 ) )
% 0.26/0.58 => ( ( ord_le1742111550et_val @ B3 @ C )
% 0.26/0.58 => ( ! [X2: set_set_val,Y3: set_set_val] :
% 0.26/0.58 ( ( ord_le1742111550et_val @ X2 @ Y3 )
% 0.26/0.58 => ( ord_less_eq_set_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.26/0.58 => ( ord_less_eq_set_val @ A3 @ ( F @ C ) ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % order_subst1
% 0.26/0.58 thf(fact_81_order__subst1,axiom,
% 0.26/0.58 ! [A3: $o > set_val,F: val > $o > set_val,B3: val,C: val] :
% 0.26/0.58 ( ( ord_le994826475et_val @ A3 @ ( F @ B3 ) )
% 0.26/0.58 => ( ( ord_less_eq_val @ B3 @ C )
% 0.26/0.58 => ( ! [X2: val,Y3: val] :
% 0.26/0.58 ( ( ord_less_eq_val @ X2 @ Y3 )
% 0.26/0.58 => ( ord_le994826475et_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.26/0.58 => ( ord_le994826475et_val @ A3 @ ( F @ C ) ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % order_subst1
% 0.26/0.58 thf(fact_82_order__subst1,axiom,
% 0.26/0.58 ! [A3: val,F: ( $o > set_val ) > val,B3: $o > set_val,C: $o > set_val] :
% 0.26/0.58 ( ( ord_less_eq_val @ A3 @ ( F @ B3 ) )
% 0.26/0.58 => ( ( ord_le994826475et_val @ B3 @ C )
% 0.26/0.58 => ( ! [X2: $o > set_val,Y3: $o > set_val] :
% 0.26/0.58 ( ( ord_le994826475et_val @ X2 @ Y3 )
% 0.26/0.58 => ( ord_less_eq_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.26/0.58 => ( ord_less_eq_val @ A3 @ ( F @ C ) ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % order_subst1
% 0.26/0.58 thf(fact_83_order__subst1,axiom,
% 0.26/0.58 ! [A3: set_set_val,F: set_val > set_set_val,B3: set_val,C: set_val] :
% 0.26/0.58 ( ( ord_le1742111550et_val @ A3 @ ( F @ B3 ) )
% 0.26/0.58 => ( ( ord_less_eq_set_val @ B3 @ C )
% 0.26/0.58 => ( ! [X2: set_val,Y3: set_val] :
% 0.26/0.58 ( ( ord_less_eq_set_val @ X2 @ Y3 )
% 0.26/0.58 => ( ord_le1742111550et_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.26/0.58 => ( ord_le1742111550et_val @ A3 @ ( F @ C ) ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % order_subst1
% 0.26/0.58 thf(fact_84_order__subst2,axiom,
% 0.26/0.58 ! [A3: set_val,B3: set_val,F: set_val > set_val,C: set_val] :
% 0.26/0.58 ( ( ord_less_eq_set_val @ A3 @ B3 )
% 0.26/0.58 => ( ( ord_less_eq_set_val @ ( F @ B3 ) @ C )
% 0.26/0.58 => ( ! [X2: set_val,Y3: set_val] :
% 0.26/0.58 ( ( ord_less_eq_set_val @ X2 @ Y3 )
% 0.26/0.58 => ( ord_less_eq_set_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.26/0.58 => ( ord_less_eq_set_val @ ( F @ A3 ) @ C ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % order_subst2
% 0.26/0.58 thf(fact_85_order__subst2,axiom,
% 0.26/0.58 ! [A3: val,B3: val,F: val > val,C: val] :
% 0.26/0.58 ( ( ord_less_eq_val @ A3 @ B3 )
% 0.26/0.58 => ( ( ord_less_eq_val @ ( F @ B3 ) @ C )
% 0.26/0.58 => ( ! [X2: val,Y3: val] :
% 0.26/0.58 ( ( ord_less_eq_val @ X2 @ Y3 )
% 0.26/0.58 => ( ord_less_eq_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.26/0.58 => ( ord_less_eq_val @ ( F @ A3 ) @ C ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % order_subst2
% 0.26/0.58 thf(fact_86_order__subst2,axiom,
% 0.26/0.58 ! [A3: set_val,B3: set_val,F: set_val > val,C: val] :
% 0.26/0.58 ( ( ord_less_eq_set_val @ A3 @ B3 )
% 0.26/0.58 => ( ( ord_less_eq_val @ ( F @ B3 ) @ C )
% 0.26/0.58 => ( ! [X2: set_val,Y3: set_val] :
% 0.26/0.58 ( ( ord_less_eq_set_val @ X2 @ Y3 )
% 0.26/0.58 => ( ord_less_eq_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.26/0.58 => ( ord_less_eq_val @ ( F @ A3 ) @ C ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % order_subst2
% 0.26/0.58 thf(fact_87_order__subst2,axiom,
% 0.26/0.58 ! [A3: val,B3: val,F: val > set_val,C: set_val] :
% 0.26/0.58 ( ( ord_less_eq_val @ A3 @ B3 )
% 0.26/0.58 => ( ( ord_less_eq_set_val @ ( F @ B3 ) @ C )
% 0.26/0.58 => ( ! [X2: val,Y3: val] :
% 0.26/0.58 ( ( ord_less_eq_val @ X2 @ Y3 )
% 0.26/0.58 => ( ord_less_eq_set_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.26/0.58 => ( ord_less_eq_set_val @ ( F @ A3 ) @ C ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % order_subst2
% 0.26/0.58 thf(fact_88_order__subst2,axiom,
% 0.26/0.58 ! [A3: val,B3: val,F: val > set_set_val,C: set_set_val] :
% 0.26/0.58 ( ( ord_less_eq_val @ A3 @ B3 )
% 0.26/0.58 => ( ( ord_le1742111550et_val @ ( F @ B3 ) @ C )
% 0.26/0.58 => ( ! [X2: val,Y3: val] :
% 0.26/0.58 ( ( ord_less_eq_val @ X2 @ Y3 )
% 0.26/0.58 => ( ord_le1742111550et_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.26/0.58 => ( ord_le1742111550et_val @ ( F @ A3 ) @ C ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % order_subst2
% 0.26/0.58 thf(fact_89_order__subst2,axiom,
% 0.26/0.58 ! [A3: set_set_val,B3: set_set_val,F: set_set_val > val,C: val] :
% 0.26/0.58 ( ( ord_le1742111550et_val @ A3 @ B3 )
% 0.26/0.58 => ( ( ord_less_eq_val @ ( F @ B3 ) @ C )
% 0.26/0.58 => ( ! [X2: set_set_val,Y3: set_set_val] :
% 0.26/0.58 ( ( ord_le1742111550et_val @ X2 @ Y3 )
% 0.26/0.58 => ( ord_less_eq_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.26/0.58 => ( ord_less_eq_val @ ( F @ A3 ) @ C ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % order_subst2
% 0.26/0.58 thf(fact_90_order__subst2,axiom,
% 0.26/0.58 ! [A3: set_val,B3: set_val,F: set_val > set_set_val,C: set_set_val] :
% 0.26/0.58 ( ( ord_less_eq_set_val @ A3 @ B3 )
% 0.26/0.58 => ( ( ord_le1742111550et_val @ ( F @ B3 ) @ C )
% 0.26/0.58 => ( ! [X2: set_val,Y3: set_val] :
% 0.26/0.58 ( ( ord_less_eq_set_val @ X2 @ Y3 )
% 0.26/0.58 => ( ord_le1742111550et_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.26/0.58 => ( ord_le1742111550et_val @ ( F @ A3 ) @ C ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % order_subst2
% 0.26/0.58 thf(fact_91_order__subst2,axiom,
% 0.26/0.58 ! [A3: $o > set_val,B3: $o > set_val,F: ( $o > set_val ) > val,C: val] :
% 0.26/0.58 ( ( ord_le994826475et_val @ A3 @ B3 )
% 0.26/0.58 => ( ( ord_less_eq_val @ ( F @ B3 ) @ C )
% 0.26/0.58 => ( ! [X2: $o > set_val,Y3: $o > set_val] :
% 0.26/0.58 ( ( ord_le994826475et_val @ X2 @ Y3 )
% 0.26/0.58 => ( ord_less_eq_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.26/0.58 => ( ord_less_eq_val @ ( F @ A3 ) @ C ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % order_subst2
% 0.26/0.58 thf(fact_92_order__subst2,axiom,
% 0.26/0.58 ! [A3: val,B3: val,F: val > $o > set_val,C: $o > set_val] :
% 0.26/0.58 ( ( ord_less_eq_val @ A3 @ B3 )
% 0.26/0.58 => ( ( ord_le994826475et_val @ ( F @ B3 ) @ C )
% 0.26/0.58 => ( ! [X2: val,Y3: val] :
% 0.26/0.58 ( ( ord_less_eq_val @ X2 @ Y3 )
% 0.26/0.58 => ( ord_le994826475et_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.26/0.58 => ( ord_le994826475et_val @ ( F @ A3 ) @ C ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % order_subst2
% 0.26/0.58 thf(fact_93_order__subst2,axiom,
% 0.26/0.58 ! [A3: set_set_val,B3: set_set_val,F: set_set_val > set_val,C: set_val] :
% 0.26/0.58 ( ( ord_le1742111550et_val @ A3 @ B3 )
% 0.26/0.58 => ( ( ord_less_eq_set_val @ ( F @ B3 ) @ C )
% 0.26/0.58 => ( ! [X2: set_set_val,Y3: set_set_val] :
% 0.26/0.58 ( ( ord_le1742111550et_val @ X2 @ Y3 )
% 0.26/0.58 => ( ord_less_eq_set_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.26/0.58 => ( ord_less_eq_set_val @ ( F @ A3 ) @ C ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % order_subst2
% 0.26/0.58 thf(fact_94_ord__eq__le__eq__trans,axiom,
% 0.26/0.58 ! [A3: $o > set_val,B3: $o > set_val,C: $o > set_val,D: $o > set_val] :
% 0.26/0.58 ( ( A3 = B3 )
% 0.26/0.58 => ( ( ord_le994826475et_val @ B3 @ C )
% 0.26/0.58 => ( ( C = D )
% 0.26/0.58 => ( ord_le994826475et_val @ A3 @ D ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % ord_eq_le_eq_trans
% 0.26/0.58 thf(fact_95_ord__eq__le__eq__trans,axiom,
% 0.26/0.58 ! [A3: val,B3: val,C: val,D: val] :
% 0.26/0.58 ( ( A3 = B3 )
% 0.26/0.58 => ( ( ord_less_eq_val @ B3 @ C )
% 0.26/0.58 => ( ( C = D )
% 0.26/0.58 => ( ord_less_eq_val @ A3 @ D ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % ord_eq_le_eq_trans
% 0.26/0.58 thf(fact_96_ord__eq__le__eq__trans,axiom,
% 0.26/0.58 ! [A3: set_set_val,B3: set_set_val,C: set_set_val,D: set_set_val] :
% 0.26/0.58 ( ( A3 = B3 )
% 0.26/0.58 => ( ( ord_le1742111550et_val @ B3 @ C )
% 0.26/0.58 => ( ( C = D )
% 0.26/0.58 => ( ord_le1742111550et_val @ A3 @ D ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % ord_eq_le_eq_trans
% 0.26/0.58 thf(fact_97_ord__eq__le__eq__trans,axiom,
% 0.26/0.58 ! [A3: set_val,B3: set_val,C: set_val,D: set_val] :
% 0.26/0.58 ( ( A3 = B3 )
% 0.26/0.58 => ( ( ord_less_eq_set_val @ B3 @ C )
% 0.26/0.58 => ( ( C = D )
% 0.26/0.58 => ( ord_less_eq_set_val @ A3 @ D ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % ord_eq_le_eq_trans
% 0.26/0.58 thf(fact_98_ord__eq__le__subst,axiom,
% 0.26/0.58 ! [A3: set_val,F: set_val > set_val,B3: set_val,C: set_val] :
% 0.26/0.58 ( ( A3
% 0.26/0.58 = ( F @ B3 ) )
% 0.26/0.58 => ( ( ord_less_eq_set_val @ B3 @ C )
% 0.26/0.58 => ( ! [X2: set_val,Y3: set_val] :
% 0.26/0.58 ( ( ord_less_eq_set_val @ X2 @ Y3 )
% 0.26/0.58 => ( ord_less_eq_set_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.26/0.58 => ( ord_less_eq_set_val @ A3 @ ( F @ C ) ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % ord_eq_le_subst
% 0.26/0.58 thf(fact_99_ord__eq__le__subst,axiom,
% 0.26/0.58 ! [A3: val,F: val > val,B3: val,C: val] :
% 0.26/0.58 ( ( A3
% 0.26/0.58 = ( F @ B3 ) )
% 0.26/0.58 => ( ( ord_less_eq_val @ B3 @ C )
% 0.26/0.58 => ( ! [X2: val,Y3: val] :
% 0.26/0.58 ( ( ord_less_eq_val @ X2 @ Y3 )
% 0.26/0.58 => ( ord_less_eq_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.26/0.58 => ( ord_less_eq_val @ A3 @ ( F @ C ) ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % ord_eq_le_subst
% 0.26/0.58 thf(fact_100_ord__eq__le__subst,axiom,
% 0.26/0.58 ! [A3: val,F: set_val > val,B3: set_val,C: set_val] :
% 0.26/0.58 ( ( A3
% 0.26/0.58 = ( F @ B3 ) )
% 0.26/0.58 => ( ( ord_less_eq_set_val @ B3 @ C )
% 0.26/0.58 => ( ! [X2: set_val,Y3: set_val] :
% 0.26/0.58 ( ( ord_less_eq_set_val @ X2 @ Y3 )
% 0.26/0.58 => ( ord_less_eq_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.26/0.58 => ( ord_less_eq_val @ A3 @ ( F @ C ) ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % ord_eq_le_subst
% 0.26/0.58 thf(fact_101_ord__eq__le__subst,axiom,
% 0.26/0.58 ! [A3: set_val,F: val > set_val,B3: val,C: val] :
% 0.26/0.58 ( ( A3
% 0.26/0.58 = ( F @ B3 ) )
% 0.26/0.58 => ( ( ord_less_eq_val @ B3 @ C )
% 0.26/0.58 => ( ! [X2: val,Y3: val] :
% 0.26/0.58 ( ( ord_less_eq_val @ X2 @ Y3 )
% 0.26/0.58 => ( ord_less_eq_set_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.26/0.58 => ( ord_less_eq_set_val @ A3 @ ( F @ C ) ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % ord_eq_le_subst
% 0.26/0.58 thf(fact_102_ord__eq__le__subst,axiom,
% 0.26/0.58 ! [A3: set_set_val,F: val > set_set_val,B3: val,C: val] :
% 0.26/0.58 ( ( A3
% 0.26/0.58 = ( F @ B3 ) )
% 0.26/0.58 => ( ( ord_less_eq_val @ B3 @ C )
% 0.26/0.58 => ( ! [X2: val,Y3: val] :
% 0.26/0.58 ( ( ord_less_eq_val @ X2 @ Y3 )
% 0.26/0.58 => ( ord_le1742111550et_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.26/0.58 => ( ord_le1742111550et_val @ A3 @ ( F @ C ) ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % ord_eq_le_subst
% 0.26/0.58 thf(fact_103_ord__eq__le__subst,axiom,
% 0.26/0.58 ! [A3: val,F: set_set_val > val,B3: set_set_val,C: set_set_val] :
% 0.26/0.58 ( ( A3
% 0.26/0.58 = ( F @ B3 ) )
% 0.26/0.58 => ( ( ord_le1742111550et_val @ B3 @ C )
% 0.26/0.58 => ( ! [X2: set_set_val,Y3: set_set_val] :
% 0.26/0.58 ( ( ord_le1742111550et_val @ X2 @ Y3 )
% 0.26/0.58 => ( ord_less_eq_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.26/0.58 => ( ord_less_eq_val @ A3 @ ( F @ C ) ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % ord_eq_le_subst
% 0.26/0.58 thf(fact_104_ord__eq__le__subst,axiom,
% 0.26/0.58 ! [A3: set_set_val,F: set_val > set_set_val,B3: set_val,C: set_val] :
% 0.26/0.58 ( ( A3
% 0.26/0.58 = ( F @ B3 ) )
% 0.26/0.58 => ( ( ord_less_eq_set_val @ B3 @ C )
% 0.26/0.58 => ( ! [X2: set_val,Y3: set_val] :
% 0.26/0.58 ( ( ord_less_eq_set_val @ X2 @ Y3 )
% 0.26/0.58 => ( ord_le1742111550et_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.26/0.58 => ( ord_le1742111550et_val @ A3 @ ( F @ C ) ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % ord_eq_le_subst
% 0.26/0.58 thf(fact_105_ord__eq__le__subst,axiom,
% 0.26/0.58 ! [A3: val,F: ( $o > set_val ) > val,B3: $o > set_val,C: $o > set_val] :
% 0.26/0.58 ( ( A3
% 0.26/0.58 = ( F @ B3 ) )
% 0.26/0.58 => ( ( ord_le994826475et_val @ B3 @ C )
% 0.26/0.58 => ( ! [X2: $o > set_val,Y3: $o > set_val] :
% 0.26/0.58 ( ( ord_le994826475et_val @ X2 @ Y3 )
% 0.26/0.58 => ( ord_less_eq_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.26/0.58 => ( ord_less_eq_val @ A3 @ ( F @ C ) ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % ord_eq_le_subst
% 0.26/0.58 thf(fact_106_ord__eq__le__subst,axiom,
% 0.26/0.58 ! [A3: $o > set_val,F: val > $o > set_val,B3: val,C: val] :
% 0.26/0.58 ( ( A3
% 0.26/0.58 = ( F @ B3 ) )
% 0.26/0.58 => ( ( ord_less_eq_val @ B3 @ C )
% 0.26/0.58 => ( ! [X2: val,Y3: val] :
% 0.26/0.58 ( ( ord_less_eq_val @ X2 @ Y3 )
% 0.26/0.58 => ( ord_le994826475et_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.26/0.58 => ( ord_le994826475et_val @ A3 @ ( F @ C ) ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % ord_eq_le_subst
% 0.26/0.58 thf(fact_107_ord__eq__le__subst,axiom,
% 0.26/0.58 ! [A3: set_val,F: set_set_val > set_val,B3: set_set_val,C: set_set_val] :
% 0.26/0.58 ( ( A3
% 0.26/0.58 = ( F @ B3 ) )
% 0.26/0.58 => ( ( ord_le1742111550et_val @ B3 @ C )
% 0.26/0.58 => ( ! [X2: set_set_val,Y3: set_set_val] :
% 0.26/0.58 ( ( ord_le1742111550et_val @ X2 @ Y3 )
% 0.26/0.58 => ( ord_less_eq_set_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.26/0.58 => ( ord_less_eq_set_val @ A3 @ ( F @ C ) ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % ord_eq_le_subst
% 0.26/0.58 thf(fact_108_ord__le__eq__subst,axiom,
% 0.26/0.58 ! [A3: set_val,B3: set_val,F: set_val > set_val,C: set_val] :
% 0.26/0.58 ( ( ord_less_eq_set_val @ A3 @ B3 )
% 0.26/0.58 => ( ( ( F @ B3 )
% 0.26/0.58 = C )
% 0.26/0.58 => ( ! [X2: set_val,Y3: set_val] :
% 0.26/0.58 ( ( ord_less_eq_set_val @ X2 @ Y3 )
% 0.26/0.58 => ( ord_less_eq_set_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.26/0.58 => ( ord_less_eq_set_val @ ( F @ A3 ) @ C ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % ord_le_eq_subst
% 0.26/0.58 thf(fact_109_ord__le__eq__subst,axiom,
% 0.26/0.58 ! [A3: val,B3: val,F: val > val,C: val] :
% 0.26/0.58 ( ( ord_less_eq_val @ A3 @ B3 )
% 0.26/0.58 => ( ( ( F @ B3 )
% 0.26/0.58 = C )
% 0.26/0.58 => ( ! [X2: val,Y3: val] :
% 0.26/0.58 ( ( ord_less_eq_val @ X2 @ Y3 )
% 0.26/0.58 => ( ord_less_eq_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.26/0.58 => ( ord_less_eq_val @ ( F @ A3 ) @ C ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % ord_le_eq_subst
% 0.26/0.58 thf(fact_110_ord__le__eq__subst,axiom,
% 0.26/0.58 ! [A3: set_val,B3: set_val,F: set_val > val,C: val] :
% 0.26/0.58 ( ( ord_less_eq_set_val @ A3 @ B3 )
% 0.26/0.58 => ( ( ( F @ B3 )
% 0.26/0.58 = C )
% 0.26/0.58 => ( ! [X2: set_val,Y3: set_val] :
% 0.26/0.58 ( ( ord_less_eq_set_val @ X2 @ Y3 )
% 0.26/0.58 => ( ord_less_eq_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.26/0.58 => ( ord_less_eq_val @ ( F @ A3 ) @ C ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % ord_le_eq_subst
% 0.26/0.58 thf(fact_111_ord__le__eq__subst,axiom,
% 0.26/0.58 ! [A3: val,B3: val,F: val > set_val,C: set_val] :
% 0.26/0.58 ( ( ord_less_eq_val @ A3 @ B3 )
% 0.26/0.58 => ( ( ( F @ B3 )
% 0.26/0.58 = C )
% 0.26/0.58 => ( ! [X2: val,Y3: val] :
% 0.26/0.58 ( ( ord_less_eq_val @ X2 @ Y3 )
% 0.26/0.58 => ( ord_less_eq_set_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.26/0.58 => ( ord_less_eq_set_val @ ( F @ A3 ) @ C ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % ord_le_eq_subst
% 0.26/0.58 thf(fact_112_ord__le__eq__subst,axiom,
% 0.26/0.58 ! [A3: val,B3: val,F: val > set_set_val,C: set_set_val] :
% 0.26/0.58 ( ( ord_less_eq_val @ A3 @ B3 )
% 0.26/0.58 => ( ( ( F @ B3 )
% 0.26/0.58 = C )
% 0.26/0.58 => ( ! [X2: val,Y3: val] :
% 0.26/0.58 ( ( ord_less_eq_val @ X2 @ Y3 )
% 0.26/0.58 => ( ord_le1742111550et_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.26/0.58 => ( ord_le1742111550et_val @ ( F @ A3 ) @ C ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % ord_le_eq_subst
% 0.26/0.58 thf(fact_113_ord__le__eq__subst,axiom,
% 0.26/0.58 ! [A3: set_set_val,B3: set_set_val,F: set_set_val > val,C: val] :
% 0.26/0.58 ( ( ord_le1742111550et_val @ A3 @ B3 )
% 0.26/0.58 => ( ( ( F @ B3 )
% 0.26/0.58 = C )
% 0.26/0.58 => ( ! [X2: set_set_val,Y3: set_set_val] :
% 0.26/0.58 ( ( ord_le1742111550et_val @ X2 @ Y3 )
% 0.26/0.58 => ( ord_less_eq_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.26/0.58 => ( ord_less_eq_val @ ( F @ A3 ) @ C ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % ord_le_eq_subst
% 0.26/0.58 thf(fact_114_ord__le__eq__subst,axiom,
% 0.26/0.58 ! [A3: set_val,B3: set_val,F: set_val > set_set_val,C: set_set_val] :
% 0.26/0.58 ( ( ord_less_eq_set_val @ A3 @ B3 )
% 0.26/0.58 => ( ( ( F @ B3 )
% 0.26/0.58 = C )
% 0.26/0.58 => ( ! [X2: set_val,Y3: set_val] :
% 0.26/0.58 ( ( ord_less_eq_set_val @ X2 @ Y3 )
% 0.26/0.58 => ( ord_le1742111550et_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.26/0.58 => ( ord_le1742111550et_val @ ( F @ A3 ) @ C ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % ord_le_eq_subst
% 0.26/0.58 thf(fact_115_ord__le__eq__subst,axiom,
% 0.26/0.58 ! [A3: $o > set_val,B3: $o > set_val,F: ( $o > set_val ) > val,C: val] :
% 0.26/0.58 ( ( ord_le994826475et_val @ A3 @ B3 )
% 0.26/0.58 => ( ( ( F @ B3 )
% 0.26/0.58 = C )
% 0.26/0.58 => ( ! [X2: $o > set_val,Y3: $o > set_val] :
% 0.26/0.58 ( ( ord_le994826475et_val @ X2 @ Y3 )
% 0.26/0.58 => ( ord_less_eq_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.26/0.58 => ( ord_less_eq_val @ ( F @ A3 ) @ C ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % ord_le_eq_subst
% 0.26/0.58 thf(fact_116_ord__le__eq__subst,axiom,
% 0.26/0.58 ! [A3: val,B3: val,F: val > $o > set_val,C: $o > set_val] :
% 0.26/0.58 ( ( ord_less_eq_val @ A3 @ B3 )
% 0.26/0.58 => ( ( ( F @ B3 )
% 0.26/0.58 = C )
% 0.26/0.58 => ( ! [X2: val,Y3: val] :
% 0.26/0.58 ( ( ord_less_eq_val @ X2 @ Y3 )
% 0.26/0.58 => ( ord_le994826475et_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.26/0.58 => ( ord_le994826475et_val @ ( F @ A3 ) @ C ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % ord_le_eq_subst
% 0.26/0.58 thf(fact_117_ord__le__eq__subst,axiom,
% 0.26/0.58 ! [A3: set_set_val,B3: set_set_val,F: set_set_val > set_val,C: set_val] :
% 0.26/0.58 ( ( ord_le1742111550et_val @ A3 @ B3 )
% 0.26/0.58 => ( ( ( F @ B3 )
% 0.26/0.58 = C )
% 0.26/0.58 => ( ! [X2: set_set_val,Y3: set_set_val] :
% 0.26/0.58 ( ( ord_le1742111550et_val @ X2 @ Y3 )
% 0.26/0.58 => ( ord_less_eq_set_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.26/0.58 => ( ord_less_eq_set_val @ ( F @ A3 ) @ C ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % ord_le_eq_subst
% 0.26/0.58 thf(fact_118_eq__iff,axiom,
% 0.26/0.58 ( ( ^ [Y: $o > set_val,Z: $o > set_val] : ( Y = Z ) )
% 0.26/0.58 = ( ^ [X3: $o > set_val,Y4: $o > set_val] :
% 0.26/0.58 ( ( ord_le994826475et_val @ X3 @ Y4 )
% 0.26/0.58 & ( ord_le994826475et_val @ Y4 @ X3 ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % eq_iff
% 0.26/0.58 thf(fact_119_eq__iff,axiom,
% 0.26/0.58 ( ( ^ [Y: val,Z: val] : ( Y = Z ) )
% 0.26/0.58 = ( ^ [X3: val,Y4: val] :
% 0.26/0.58 ( ( ord_less_eq_val @ X3 @ Y4 )
% 0.26/0.58 & ( ord_less_eq_val @ Y4 @ X3 ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % eq_iff
% 0.26/0.58 thf(fact_120_eq__iff,axiom,
% 0.26/0.58 ( ( ^ [Y: set_set_val,Z: set_set_val] : ( Y = Z ) )
% 0.26/0.58 = ( ^ [X3: set_set_val,Y4: set_set_val] :
% 0.26/0.58 ( ( ord_le1742111550et_val @ X3 @ Y4 )
% 0.26/0.58 & ( ord_le1742111550et_val @ Y4 @ X3 ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % eq_iff
% 0.26/0.58 thf(fact_121_eq__iff,axiom,
% 0.26/0.58 ( ( ^ [Y: set_val,Z: set_val] : ( Y = Z ) )
% 0.26/0.58 = ( ^ [X3: set_val,Y4: set_val] :
% 0.26/0.58 ( ( ord_less_eq_set_val @ X3 @ Y4 )
% 0.26/0.58 & ( ord_less_eq_set_val @ Y4 @ X3 ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % eq_iff
% 0.26/0.58 thf(fact_122_antisym,axiom,
% 0.26/0.58 ! [X: $o > set_val,Y2: $o > set_val] :
% 0.26/0.58 ( ( ord_le994826475et_val @ X @ Y2 )
% 0.26/0.58 => ( ( ord_le994826475et_val @ Y2 @ X )
% 0.26/0.58 => ( X = Y2 ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % antisym
% 0.26/0.58 thf(fact_123_antisym,axiom,
% 0.26/0.58 ! [X: val,Y2: val] :
% 0.26/0.58 ( ( ord_less_eq_val @ X @ Y2 )
% 0.26/0.58 => ( ( ord_less_eq_val @ Y2 @ X )
% 0.26/0.58 => ( X = Y2 ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % antisym
% 0.26/0.58 thf(fact_124_antisym,axiom,
% 0.26/0.58 ! [X: set_set_val,Y2: set_set_val] :
% 0.26/0.58 ( ( ord_le1742111550et_val @ X @ Y2 )
% 0.26/0.58 => ( ( ord_le1742111550et_val @ Y2 @ X )
% 0.26/0.58 => ( X = Y2 ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % antisym
% 0.26/0.58 thf(fact_125_antisym,axiom,
% 0.26/0.58 ! [X: set_val,Y2: set_val] :
% 0.26/0.58 ( ( ord_less_eq_set_val @ X @ Y2 )
% 0.26/0.58 => ( ( ord_less_eq_set_val @ Y2 @ X )
% 0.26/0.58 => ( X = Y2 ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % antisym
% 0.26/0.58 thf(fact_126_linear,axiom,
% 0.26/0.58 ! [X: val,Y2: val] :
% 0.26/0.58 ( ( ord_less_eq_val @ X @ Y2 )
% 0.26/0.58 | ( ord_less_eq_val @ Y2 @ X ) ) ).
% 0.26/0.58
% 0.26/0.58 % linear
% 0.26/0.58 thf(fact_127_eq__refl,axiom,
% 0.26/0.58 ! [X: $o > set_val,Y2: $o > set_val] :
% 0.26/0.58 ( ( X = Y2 )
% 0.26/0.58 => ( ord_le994826475et_val @ X @ Y2 ) ) ).
% 0.26/0.58
% 0.26/0.58 % eq_refl
% 0.26/0.58 thf(fact_128_eq__refl,axiom,
% 0.26/0.58 ! [X: val,Y2: val] :
% 0.26/0.58 ( ( X = Y2 )
% 0.26/0.58 => ( ord_less_eq_val @ X @ Y2 ) ) ).
% 0.26/0.58
% 0.26/0.58 % eq_refl
% 0.26/0.58 thf(fact_129_eq__refl,axiom,
% 0.26/0.58 ! [X: set_set_val,Y2: set_set_val] :
% 0.26/0.58 ( ( X = Y2 )
% 0.26/0.58 => ( ord_le1742111550et_val @ X @ Y2 ) ) ).
% 0.26/0.58
% 0.26/0.58 % eq_refl
% 0.26/0.58 thf(fact_130_eq__refl,axiom,
% 0.26/0.58 ! [X: set_val,Y2: set_val] :
% 0.26/0.58 ( ( X = Y2 )
% 0.26/0.58 => ( ord_less_eq_set_val @ X @ Y2 ) ) ).
% 0.26/0.58
% 0.26/0.58 % eq_refl
% 0.26/0.58 thf(fact_131_le__cases,axiom,
% 0.26/0.58 ! [X: val,Y2: val] :
% 0.26/0.58 ( ~ ( ord_less_eq_val @ X @ Y2 )
% 0.26/0.58 => ( ord_less_eq_val @ Y2 @ X ) ) ).
% 0.26/0.58
% 0.26/0.58 % le_cases
% 0.26/0.58 thf(fact_132_order_Otrans,axiom,
% 0.26/0.58 ! [A3: $o > set_val,B3: $o > set_val,C: $o > set_val] :
% 0.26/0.58 ( ( ord_le994826475et_val @ A3 @ B3 )
% 0.26/0.58 => ( ( ord_le994826475et_val @ B3 @ C )
% 0.26/0.58 => ( ord_le994826475et_val @ A3 @ C ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % order.trans
% 0.26/0.58 thf(fact_133_order_Otrans,axiom,
% 0.26/0.58 ! [A3: val,B3: val,C: val] :
% 0.26/0.58 ( ( ord_less_eq_val @ A3 @ B3 )
% 0.26/0.58 => ( ( ord_less_eq_val @ B3 @ C )
% 0.26/0.58 => ( ord_less_eq_val @ A3 @ C ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % order.trans
% 0.26/0.58 thf(fact_134_order_Otrans,axiom,
% 0.26/0.58 ! [A3: set_set_val,B3: set_set_val,C: set_set_val] :
% 0.26/0.58 ( ( ord_le1742111550et_val @ A3 @ B3 )
% 0.26/0.58 => ( ( ord_le1742111550et_val @ B3 @ C )
% 0.26/0.58 => ( ord_le1742111550et_val @ A3 @ C ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % order.trans
% 0.26/0.58 thf(fact_135_order_Otrans,axiom,
% 0.26/0.58 ! [A3: set_val,B3: set_val,C: set_val] :
% 0.26/0.58 ( ( ord_less_eq_set_val @ A3 @ B3 )
% 0.26/0.58 => ( ( ord_less_eq_set_val @ B3 @ C )
% 0.26/0.58 => ( ord_less_eq_set_val @ A3 @ C ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % order.trans
% 0.26/0.58 thf(fact_136_mem__Collect__eq,axiom,
% 0.26/0.58 ! [A3: set_val,P: set_val > $o] :
% 0.26/0.58 ( ( member_set_val @ A3 @ ( collect_set_val @ P ) )
% 0.26/0.58 = ( P @ A3 ) ) ).
% 0.26/0.58
% 0.26/0.58 % mem_Collect_eq
% 0.26/0.58 thf(fact_137_mem__Collect__eq,axiom,
% 0.26/0.58 ! [A3: val,P: val > $o] :
% 0.26/0.58 ( ( member_val @ A3 @ ( collect_val @ P ) )
% 0.26/0.58 = ( P @ A3 ) ) ).
% 0.26/0.58
% 0.26/0.58 % mem_Collect_eq
% 0.26/0.58 thf(fact_138_Collect__mem__eq,axiom,
% 0.26/0.58 ! [A: set_set_val] :
% 0.26/0.58 ( ( collect_set_val
% 0.26/0.58 @ ^ [X3: set_val] : ( member_set_val @ X3 @ A ) )
% 0.26/0.58 = A ) ).
% 0.26/0.58
% 0.26/0.58 % Collect_mem_eq
% 0.26/0.58 thf(fact_139_Collect__mem__eq,axiom,
% 0.26/0.58 ! [A: set_val] :
% 0.26/0.58 ( ( collect_val
% 0.26/0.58 @ ^ [X3: val] : ( member_val @ X3 @ A ) )
% 0.26/0.58 = A ) ).
% 0.26/0.58
% 0.26/0.58 % Collect_mem_eq
% 0.26/0.58 thf(fact_140_Collect__cong,axiom,
% 0.26/0.58 ! [P: val > $o,Q: val > $o] :
% 0.26/0.58 ( ! [X2: val] :
% 0.26/0.58 ( ( P @ X2 )
% 0.26/0.58 = ( Q @ X2 ) )
% 0.26/0.58 => ( ( collect_val @ P )
% 0.26/0.58 = ( collect_val @ Q ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % Collect_cong
% 0.26/0.58 thf(fact_141_le__cases3,axiom,
% 0.26/0.58 ! [X: val,Y2: val,Z2: val] :
% 0.26/0.58 ( ( ( ord_less_eq_val @ X @ Y2 )
% 0.26/0.58 => ~ ( ord_less_eq_val @ Y2 @ Z2 ) )
% 0.26/0.58 => ( ( ( ord_less_eq_val @ Y2 @ X )
% 0.26/0.58 => ~ ( ord_less_eq_val @ X @ Z2 ) )
% 0.26/0.58 => ( ( ( ord_less_eq_val @ X @ Z2 )
% 0.26/0.58 => ~ ( ord_less_eq_val @ Z2 @ Y2 ) )
% 0.26/0.58 => ( ( ( ord_less_eq_val @ Z2 @ Y2 )
% 0.26/0.58 => ~ ( ord_less_eq_val @ Y2 @ X ) )
% 0.26/0.58 => ( ( ( ord_less_eq_val @ Y2 @ Z2 )
% 0.26/0.58 => ~ ( ord_less_eq_val @ Z2 @ X ) )
% 0.26/0.58 => ~ ( ( ord_less_eq_val @ Z2 @ X )
% 0.26/0.58 => ~ ( ord_less_eq_val @ X @ Y2 ) ) ) ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % le_cases3
% 0.26/0.58 thf(fact_142_antisym__conv,axiom,
% 0.26/0.58 ! [Y2: $o > set_val,X: $o > set_val] :
% 0.26/0.58 ( ( ord_le994826475et_val @ Y2 @ X )
% 0.26/0.58 => ( ( ord_le994826475et_val @ X @ Y2 )
% 0.26/0.58 = ( X = Y2 ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % antisym_conv
% 0.26/0.58 thf(fact_143_antisym__conv,axiom,
% 0.26/0.58 ! [Y2: val,X: val] :
% 0.26/0.58 ( ( ord_less_eq_val @ Y2 @ X )
% 0.26/0.58 => ( ( ord_less_eq_val @ X @ Y2 )
% 0.26/0.58 = ( X = Y2 ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % antisym_conv
% 0.26/0.58 thf(fact_144_antisym__conv,axiom,
% 0.26/0.58 ! [Y2: set_set_val,X: set_set_val] :
% 0.26/0.58 ( ( ord_le1742111550et_val @ Y2 @ X )
% 0.26/0.58 => ( ( ord_le1742111550et_val @ X @ Y2 )
% 0.26/0.58 = ( X = Y2 ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % antisym_conv
% 0.26/0.58 thf(fact_145_antisym__conv,axiom,
% 0.26/0.58 ! [Y2: set_val,X: set_val] :
% 0.26/0.58 ( ( ord_less_eq_set_val @ Y2 @ X )
% 0.26/0.58 => ( ( ord_less_eq_set_val @ X @ Y2 )
% 0.26/0.58 = ( X = Y2 ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % antisym_conv
% 0.26/0.58 thf(fact_146_order__class_Oorder_Oeq__iff,axiom,
% 0.26/0.58 ( ( ^ [Y: $o > set_val,Z: $o > set_val] : ( Y = Z ) )
% 0.26/0.58 = ( ^ [A4: $o > set_val,B4: $o > set_val] :
% 0.26/0.58 ( ( ord_le994826475et_val @ A4 @ B4 )
% 0.26/0.58 & ( ord_le994826475et_val @ B4 @ A4 ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % order_class.order.eq_iff
% 0.26/0.58 thf(fact_147_order__class_Oorder_Oeq__iff,axiom,
% 0.26/0.58 ( ( ^ [Y: val,Z: val] : ( Y = Z ) )
% 0.26/0.58 = ( ^ [A4: val,B4: val] :
% 0.26/0.58 ( ( ord_less_eq_val @ A4 @ B4 )
% 0.26/0.58 & ( ord_less_eq_val @ B4 @ A4 ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % order_class.order.eq_iff
% 0.26/0.58 thf(fact_148_order__class_Oorder_Oeq__iff,axiom,
% 0.26/0.58 ( ( ^ [Y: set_set_val,Z: set_set_val] : ( Y = Z ) )
% 0.26/0.58 = ( ^ [A4: set_set_val,B4: set_set_val] :
% 0.26/0.58 ( ( ord_le1742111550et_val @ A4 @ B4 )
% 0.26/0.58 & ( ord_le1742111550et_val @ B4 @ A4 ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % order_class.order.eq_iff
% 0.26/0.58 thf(fact_149_order__class_Oorder_Oeq__iff,axiom,
% 0.26/0.58 ( ( ^ [Y: set_val,Z: set_val] : ( Y = Z ) )
% 0.26/0.58 = ( ^ [A4: set_val,B4: set_val] :
% 0.26/0.58 ( ( ord_less_eq_set_val @ A4 @ B4 )
% 0.26/0.58 & ( ord_less_eq_set_val @ B4 @ A4 ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % order_class.order.eq_iff
% 0.26/0.58 thf(fact_150_ord__eq__le__trans,axiom,
% 0.26/0.58 ! [A3: $o > set_val,B3: $o > set_val,C: $o > set_val] :
% 0.26/0.58 ( ( A3 = B3 )
% 0.26/0.58 => ( ( ord_le994826475et_val @ B3 @ C )
% 0.26/0.58 => ( ord_le994826475et_val @ A3 @ C ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % ord_eq_le_trans
% 0.26/0.58 thf(fact_151_ord__eq__le__trans,axiom,
% 0.26/0.58 ! [A3: val,B3: val,C: val] :
% 0.26/0.58 ( ( A3 = B3 )
% 0.26/0.58 => ( ( ord_less_eq_val @ B3 @ C )
% 0.26/0.58 => ( ord_less_eq_val @ A3 @ C ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % ord_eq_le_trans
% 0.26/0.58 thf(fact_152_ord__eq__le__trans,axiom,
% 0.26/0.58 ! [A3: set_set_val,B3: set_set_val,C: set_set_val] :
% 0.26/0.58 ( ( A3 = B3 )
% 0.26/0.58 => ( ( ord_le1742111550et_val @ B3 @ C )
% 0.26/0.58 => ( ord_le1742111550et_val @ A3 @ C ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % ord_eq_le_trans
% 0.26/0.58 thf(fact_153_ord__eq__le__trans,axiom,
% 0.26/0.58 ! [A3: set_val,B3: set_val,C: set_val] :
% 0.26/0.58 ( ( A3 = B3 )
% 0.26/0.58 => ( ( ord_less_eq_set_val @ B3 @ C )
% 0.26/0.58 => ( ord_less_eq_set_val @ A3 @ C ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % ord_eq_le_trans
% 0.26/0.58 thf(fact_154_GreatestI2__order,axiom,
% 0.26/0.58 ! [P: ( $o > set_val ) > $o,X: $o > set_val,Q: ( $o > set_val ) > $o] :
% 0.26/0.58 ( ( P @ X )
% 0.26/0.58 => ( ! [Y3: $o > set_val] :
% 0.26/0.58 ( ( P @ Y3 )
% 0.26/0.58 => ( ord_le994826475et_val @ Y3 @ X ) )
% 0.26/0.58 => ( ! [X2: $o > set_val] :
% 0.26/0.58 ( ( P @ X2 )
% 0.26/0.58 => ( ! [Y5: $o > set_val] :
% 0.26/0.58 ( ( P @ Y5 )
% 0.26/0.58 => ( ord_le994826475et_val @ Y5 @ X2 ) )
% 0.26/0.58 => ( Q @ X2 ) ) )
% 0.26/0.58 => ( Q @ ( order_985126002et_val @ P ) ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % GreatestI2_order
% 0.26/0.58 thf(fact_155_GreatestI2__order,axiom,
% 0.26/0.58 ! [P: val > $o,X: val,Q: val > $o] :
% 0.26/0.58 ( ( P @ X )
% 0.26/0.58 => ( ! [Y3: val] :
% 0.26/0.58 ( ( P @ Y3 )
% 0.26/0.58 => ( ord_less_eq_val @ Y3 @ X ) )
% 0.26/0.58 => ( ! [X2: val] :
% 0.26/0.58 ( ( P @ X2 )
% 0.26/0.58 => ( ! [Y5: val] :
% 0.26/0.58 ( ( P @ Y5 )
% 0.26/0.58 => ( ord_less_eq_val @ Y5 @ X2 ) )
% 0.26/0.58 => ( Q @ X2 ) ) )
% 0.26/0.58 => ( Q @ ( order_Greatest_val @ P ) ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % GreatestI2_order
% 0.26/0.58 thf(fact_156_GreatestI2__order,axiom,
% 0.26/0.58 ! [P: set_set_val > $o,X: set_set_val,Q: set_set_val > $o] :
% 0.26/0.58 ( ( P @ X )
% 0.26/0.58 => ( ! [Y3: set_set_val] :
% 0.26/0.58 ( ( P @ Y3 )
% 0.26/0.58 => ( ord_le1742111550et_val @ Y3 @ X ) )
% 0.26/0.58 => ( ! [X2: set_set_val] :
% 0.26/0.58 ( ( P @ X2 )
% 0.26/0.58 => ( ! [Y5: set_set_val] :
% 0.26/0.58 ( ( P @ Y5 )
% 0.26/0.58 => ( ord_le1742111550et_val @ Y5 @ X2 ) )
% 0.26/0.58 => ( Q @ X2 ) ) )
% 0.26/0.58 => ( Q @ ( order_544136439et_val @ P ) ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % GreatestI2_order
% 0.26/0.58 thf(fact_157_GreatestI2__order,axiom,
% 0.26/0.58 ! [P: set_val > $o,X: set_val,Q: set_val > $o] :
% 0.26/0.58 ( ( P @ X )
% 0.26/0.58 => ( ! [Y3: set_val] :
% 0.26/0.58 ( ( P @ Y3 )
% 0.26/0.58 => ( ord_less_eq_set_val @ Y3 @ X ) )
% 0.26/0.58 => ( ! [X2: set_val] :
% 0.26/0.58 ( ( P @ X2 )
% 0.26/0.58 => ( ! [Y5: set_val] :
% 0.26/0.58 ( ( P @ Y5 )
% 0.26/0.58 => ( ord_less_eq_set_val @ Y5 @ X2 ) )
% 0.26/0.58 => ( Q @ X2 ) ) )
% 0.26/0.58 => ( Q @ ( order_1960465943et_val @ P ) ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % GreatestI2_order
% 0.26/0.58 thf(fact_158_Greatest__equality,axiom,
% 0.26/0.58 ! [P: ( $o > set_val ) > $o,X: $o > set_val] :
% 0.26/0.58 ( ( P @ X )
% 0.26/0.58 => ( ! [Y3: $o > set_val] :
% 0.26/0.58 ( ( P @ Y3 )
% 0.26/0.58 => ( ord_le994826475et_val @ Y3 @ X ) )
% 0.26/0.58 => ( ( order_985126002et_val @ P )
% 0.26/0.58 = X ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % Greatest_equality
% 0.26/0.58 thf(fact_159_Greatest__equality,axiom,
% 0.26/0.58 ! [P: val > $o,X: val] :
% 0.26/0.58 ( ( P @ X )
% 0.26/0.58 => ( ! [Y3: val] :
% 0.26/0.58 ( ( P @ Y3 )
% 0.26/0.58 => ( ord_less_eq_val @ Y3 @ X ) )
% 0.26/0.58 => ( ( order_Greatest_val @ P )
% 0.26/0.58 = X ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % Greatest_equality
% 0.26/0.58 thf(fact_160_Greatest__equality,axiom,
% 0.26/0.58 ! [P: set_set_val > $o,X: set_set_val] :
% 0.26/0.58 ( ( P @ X )
% 0.26/0.58 => ( ! [Y3: set_set_val] :
% 0.26/0.58 ( ( P @ Y3 )
% 0.26/0.58 => ( ord_le1742111550et_val @ Y3 @ X ) )
% 0.26/0.58 => ( ( order_544136439et_val @ P )
% 0.26/0.58 = X ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % Greatest_equality
% 0.26/0.58 thf(fact_161_Greatest__equality,axiom,
% 0.26/0.58 ! [P: set_val > $o,X: set_val] :
% 0.26/0.58 ( ( P @ X )
% 0.26/0.58 => ( ! [Y3: set_val] :
% 0.26/0.58 ( ( P @ Y3 )
% 0.26/0.58 => ( ord_less_eq_set_val @ Y3 @ X ) )
% 0.26/0.58 => ( ( order_1960465943et_val @ P )
% 0.26/0.58 = X ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % Greatest_equality
% 0.26/0.58 thf(fact_162_Refine__Misc_Oif__mono,axiom,
% 0.26/0.59 ! [B3: $o,M1: $o > set_val,M12: $o > set_val,M2: $o > set_val,M22: $o > set_val] :
% 0.26/0.59 ( ( B3
% 0.26/0.59 => ( ord_le994826475et_val @ M1 @ M12 ) )
% 0.26/0.59 => ( ( ~ B3
% 0.26/0.59 => ( ord_le994826475et_val @ M2 @ M22 ) )
% 0.26/0.59 => ( ord_le994826475et_val @ ( if_o_set_val @ B3 @ M1 @ M2 ) @ ( if_o_set_val @ B3 @ M12 @ M22 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Refine_Misc.if_mono
% 0.26/0.59 thf(fact_163_Refine__Misc_Oif__mono,axiom,
% 0.26/0.59 ! [B3: $o,M1: val,M12: val,M2: val,M22: val] :
% 0.26/0.59 ( ( B3
% 0.26/0.59 => ( ord_less_eq_val @ M1 @ M12 ) )
% 0.26/0.59 => ( ( ~ B3
% 0.26/0.59 => ( ord_less_eq_val @ M2 @ M22 ) )
% 0.26/0.59 => ( ord_less_eq_val @ ( if_val @ B3 @ M1 @ M2 ) @ ( if_val @ B3 @ M12 @ M22 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Refine_Misc.if_mono
% 0.26/0.59 thf(fact_164_Refine__Misc_Oif__mono,axiom,
% 0.26/0.59 ! [B3: $o,M1: set_set_val,M12: set_set_val,M2: set_set_val,M22: set_set_val] :
% 0.26/0.59 ( ( B3
% 0.26/0.59 => ( ord_le1742111550et_val @ M1 @ M12 ) )
% 0.26/0.59 => ( ( ~ B3
% 0.26/0.59 => ( ord_le1742111550et_val @ M2 @ M22 ) )
% 0.26/0.59 => ( ord_le1742111550et_val @ ( if_set_set_val @ B3 @ M1 @ M2 ) @ ( if_set_set_val @ B3 @ M12 @ M22 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Refine_Misc.if_mono
% 0.26/0.59 thf(fact_165_Refine__Misc_Oif__mono,axiom,
% 0.26/0.59 ! [B3: $o,M1: set_val,M12: set_val,M2: set_val,M22: set_val] :
% 0.26/0.59 ( ( B3
% 0.26/0.59 => ( ord_less_eq_set_val @ M1 @ M12 ) )
% 0.26/0.59 => ( ( ~ B3
% 0.26/0.59 => ( ord_less_eq_set_val @ M2 @ M22 ) )
% 0.26/0.59 => ( ord_less_eq_set_val @ ( if_set_val @ B3 @ M1 @ M2 ) @ ( if_set_val @ B3 @ M12 @ M22 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Refine_Misc.if_mono
% 0.26/0.59 thf(fact_166_lhs__step__If,axiom,
% 0.26/0.59 ! [B3: $o,T2: $o > set_val,M: $o > set_val,E: $o > set_val] :
% 0.26/0.59 ( ( B3
% 0.26/0.59 => ( ord_le994826475et_val @ T2 @ M ) )
% 0.26/0.59 => ( ( ~ B3
% 0.26/0.59 => ( ord_le994826475et_val @ E @ M ) )
% 0.26/0.59 => ( ord_le994826475et_val @ ( if_o_set_val @ B3 @ T2 @ E ) @ M ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % lhs_step_If
% 0.26/0.59 thf(fact_167_lhs__step__If,axiom,
% 0.26/0.59 ! [B3: $o,T2: val,M: val,E: val] :
% 0.26/0.59 ( ( B3
% 0.26/0.59 => ( ord_less_eq_val @ T2 @ M ) )
% 0.26/0.59 => ( ( ~ B3
% 0.26/0.59 => ( ord_less_eq_val @ E @ M ) )
% 0.26/0.59 => ( ord_less_eq_val @ ( if_val @ B3 @ T2 @ E ) @ M ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % lhs_step_If
% 0.26/0.59 thf(fact_168_lhs__step__If,axiom,
% 0.26/0.59 ! [B3: $o,T2: set_set_val,M: set_set_val,E: set_set_val] :
% 0.26/0.59 ( ( B3
% 0.26/0.59 => ( ord_le1742111550et_val @ T2 @ M ) )
% 0.26/0.59 => ( ( ~ B3
% 0.26/0.59 => ( ord_le1742111550et_val @ E @ M ) )
% 0.26/0.59 => ( ord_le1742111550et_val @ ( if_set_set_val @ B3 @ T2 @ E ) @ M ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % lhs_step_If
% 0.26/0.59 thf(fact_169_lhs__step__If,axiom,
% 0.26/0.59 ! [B3: $o,T2: set_val,M: set_val,E: set_val] :
% 0.26/0.59 ( ( B3
% 0.26/0.59 => ( ord_less_eq_set_val @ T2 @ M ) )
% 0.26/0.59 => ( ( ~ B3
% 0.26/0.59 => ( ord_less_eq_set_val @ E @ M ) )
% 0.26/0.59 => ( ord_less_eq_set_val @ ( if_set_val @ B3 @ T2 @ E ) @ M ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % lhs_step_If
% 0.26/0.59 thf(fact_170_verit__la__disequality,axiom,
% 0.26/0.59 ! [A3: val,B3: val] :
% 0.26/0.59 ( ( A3 = B3 )
% 0.26/0.59 | ~ ( ord_less_eq_val @ A3 @ B3 )
% 0.26/0.59 | ~ ( ord_less_eq_val @ B3 @ A3 ) ) ).
% 0.26/0.59
% 0.26/0.59 % verit_la_disequality
% 0.26/0.59 thf(fact_171_le__rel__bool__arg__iff,axiom,
% 0.26/0.59 ( ord_le1441829300et_val
% 0.26/0.59 = ( ^ [X4: $o > $o > set_val,Y6: $o > $o > set_val] :
% 0.26/0.59 ( ( ord_le994826475et_val @ ( X4 @ $false ) @ ( Y6 @ $false ) )
% 0.26/0.59 & ( ord_le994826475et_val @ ( X4 @ $true ) @ ( Y6 @ $true ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % le_rel_bool_arg_iff
% 0.26/0.59 thf(fact_172_le__rel__bool__arg__iff,axiom,
% 0.26/0.59 ( ord_less_eq_o_val
% 0.26/0.59 = ( ^ [X4: $o > val,Y6: $o > val] :
% 0.26/0.59 ( ( ord_less_eq_val @ ( X4 @ $false ) @ ( Y6 @ $false ) )
% 0.26/0.59 & ( ord_less_eq_val @ ( X4 @ $true ) @ ( Y6 @ $true ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % le_rel_bool_arg_iff
% 0.26/0.59 thf(fact_173_le__rel__bool__arg__iff,axiom,
% 0.26/0.59 ( ord_le936627147et_val
% 0.26/0.59 = ( ^ [X4: $o > set_set_val,Y6: $o > set_set_val] :
% 0.26/0.59 ( ( ord_le1742111550et_val @ ( X4 @ $false ) @ ( Y6 @ $false ) )
% 0.26/0.59 & ( ord_le1742111550et_val @ ( X4 @ $true ) @ ( Y6 @ $true ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % le_rel_bool_arg_iff
% 0.26/0.59 thf(fact_174_le__rel__bool__arg__iff,axiom,
% 0.26/0.59 ( ord_le994826475et_val
% 0.26/0.59 = ( ^ [X4: $o > set_val,Y6: $o > set_val] :
% 0.26/0.59 ( ( ord_less_eq_set_val @ ( X4 @ $false ) @ ( Y6 @ $false ) )
% 0.26/0.59 & ( ord_less_eq_set_val @ ( X4 @ $true ) @ ( Y6 @ $true ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % le_rel_bool_arg_iff
% 0.26/0.59 thf(fact_175_antimonoD,axiom,
% 0.26/0.59 ! [F: set_val > set_val,X: set_val,Y2: set_val] :
% 0.26/0.59 ( ( order_1719375026et_val @ F )
% 0.26/0.59 => ( ( ord_less_eq_set_val @ X @ Y2 )
% 0.26/0.59 => ( ord_less_eq_set_val @ ( F @ Y2 ) @ ( F @ X ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % antimonoD
% 0.26/0.59 thf(fact_176_antimonoD,axiom,
% 0.26/0.59 ! [F: val > val,X: val,Y2: val] :
% 0.26/0.59 ( ( order_1689798834al_val @ F )
% 0.26/0.59 => ( ( ord_less_eq_val @ X @ Y2 )
% 0.26/0.59 => ( ord_less_eq_val @ ( F @ Y2 ) @ ( F @ X ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % antimonoD
% 0.26/0.59 thf(fact_177_antimonoD,axiom,
% 0.26/0.59 ! [F: set_val > val,X: set_val,Y2: set_val] :
% 0.26/0.59 ( ( order_1375876562al_val @ F )
% 0.26/0.59 => ( ( ord_less_eq_set_val @ X @ Y2 )
% 0.26/0.59 => ( ord_less_eq_val @ ( F @ Y2 ) @ ( F @ X ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % antimonoD
% 0.26/0.59 thf(fact_178_antimonoD,axiom,
% 0.26/0.59 ! [F: val > set_val,X: val,Y2: val] :
% 0.26/0.59 ( ( order_1484138386et_val @ F )
% 0.26/0.59 => ( ( ord_less_eq_val @ X @ Y2 )
% 0.26/0.59 => ( ord_less_eq_set_val @ ( F @ Y2 ) @ ( F @ X ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % antimonoD
% 0.26/0.59 thf(fact_179_antimonoD,axiom,
% 0.26/0.59 ! [F: val > set_set_val,X: val,Y2: val] :
% 0.26/0.59 ( ( order_1945059954et_val @ F )
% 0.26/0.59 => ( ( ord_less_eq_val @ X @ Y2 )
% 0.26/0.59 => ( ord_le1742111550et_val @ ( F @ Y2 ) @ ( F @ X ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % antimonoD
% 0.26/0.59 thf(fact_180_antimonoD,axiom,
% 0.26/0.59 ! [F: set_set_val > val,X: set_set_val,Y2: set_set_val] :
% 0.26/0.59 ( ( order_1520822002al_val @ F )
% 0.26/0.59 => ( ( ord_le1742111550et_val @ X @ Y2 )
% 0.26/0.59 => ( ord_less_eq_val @ ( F @ Y2 ) @ ( F @ X ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % antimonoD
% 0.26/0.59 thf(fact_181_antimonoD,axiom,
% 0.26/0.59 ! [F: set_val > set_set_val,X: set_val,Y2: set_val] :
% 0.26/0.59 ( ( order_1957703570et_val @ F )
% 0.26/0.59 => ( ( ord_less_eq_set_val @ X @ Y2 )
% 0.26/0.59 => ( ord_le1742111550et_val @ ( F @ Y2 ) @ ( F @ X ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % antimonoD
% 0.26/0.59 thf(fact_182_antimonoD,axiom,
% 0.26/0.59 ! [F: ( $o > set_val ) > val,X: $o > set_val,Y2: $o > set_val] :
% 0.26/0.59 ( ( order_23236447al_val @ F )
% 0.26/0.59 => ( ( ord_le994826475et_val @ X @ Y2 )
% 0.26/0.59 => ( ord_less_eq_val @ ( F @ Y2 ) @ ( F @ X ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % antimonoD
% 0.26/0.59 thf(fact_183_antimonoD,axiom,
% 0.26/0.59 ! [F: val > $o > set_val,X: val,Y2: val] :
% 0.26/0.59 ( ( order_255079095et_val @ F )
% 0.26/0.59 => ( ( ord_less_eq_val @ X @ Y2 )
% 0.26/0.59 => ( ord_le994826475et_val @ ( F @ Y2 ) @ ( F @ X ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % antimonoD
% 0.26/0.59 thf(fact_184_antimonoD,axiom,
% 0.26/0.59 ! [F: set_set_val > set_val,X: set_set_val,Y2: set_set_val] :
% 0.26/0.59 ( ( order_650823122et_val @ F )
% 0.26/0.59 => ( ( ord_le1742111550et_val @ X @ Y2 )
% 0.26/0.59 => ( ord_less_eq_set_val @ ( F @ Y2 ) @ ( F @ X ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % antimonoD
% 0.26/0.59 thf(fact_185_antimonoE,axiom,
% 0.26/0.59 ! [F: set_val > set_val,X: set_val,Y2: set_val] :
% 0.26/0.59 ( ( order_1719375026et_val @ F )
% 0.26/0.59 => ( ( ord_less_eq_set_val @ X @ Y2 )
% 0.26/0.59 => ( ord_less_eq_set_val @ ( F @ Y2 ) @ ( F @ X ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % antimonoE
% 0.26/0.59 thf(fact_186_antimonoE,axiom,
% 0.26/0.59 ! [F: val > val,X: val,Y2: val] :
% 0.26/0.59 ( ( order_1689798834al_val @ F )
% 0.26/0.59 => ( ( ord_less_eq_val @ X @ Y2 )
% 0.26/0.59 => ( ord_less_eq_val @ ( F @ Y2 ) @ ( F @ X ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % antimonoE
% 0.26/0.59 thf(fact_187_antimonoE,axiom,
% 0.26/0.59 ! [F: set_val > val,X: set_val,Y2: set_val] :
% 0.26/0.59 ( ( order_1375876562al_val @ F )
% 0.26/0.59 => ( ( ord_less_eq_set_val @ X @ Y2 )
% 0.26/0.59 => ( ord_less_eq_val @ ( F @ Y2 ) @ ( F @ X ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % antimonoE
% 0.26/0.59 thf(fact_188_antimonoE,axiom,
% 0.26/0.59 ! [F: val > set_val,X: val,Y2: val] :
% 0.26/0.59 ( ( order_1484138386et_val @ F )
% 0.26/0.59 => ( ( ord_less_eq_val @ X @ Y2 )
% 0.26/0.59 => ( ord_less_eq_set_val @ ( F @ Y2 ) @ ( F @ X ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % antimonoE
% 0.26/0.59 thf(fact_189_antimonoE,axiom,
% 0.26/0.59 ! [F: val > set_set_val,X: val,Y2: val] :
% 0.26/0.59 ( ( order_1945059954et_val @ F )
% 0.26/0.59 => ( ( ord_less_eq_val @ X @ Y2 )
% 0.26/0.59 => ( ord_le1742111550et_val @ ( F @ Y2 ) @ ( F @ X ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % antimonoE
% 0.26/0.59 thf(fact_190_antimonoE,axiom,
% 0.26/0.59 ! [F: set_set_val > val,X: set_set_val,Y2: set_set_val] :
% 0.26/0.59 ( ( order_1520822002al_val @ F )
% 0.26/0.59 => ( ( ord_le1742111550et_val @ X @ Y2 )
% 0.26/0.59 => ( ord_less_eq_val @ ( F @ Y2 ) @ ( F @ X ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % antimonoE
% 0.26/0.59 thf(fact_191_antimonoE,axiom,
% 0.26/0.59 ! [F: set_val > set_set_val,X: set_val,Y2: set_val] :
% 0.26/0.59 ( ( order_1957703570et_val @ F )
% 0.26/0.59 => ( ( ord_less_eq_set_val @ X @ Y2 )
% 0.26/0.59 => ( ord_le1742111550et_val @ ( F @ Y2 ) @ ( F @ X ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % antimonoE
% 0.26/0.59 thf(fact_192_antimonoE,axiom,
% 0.26/0.59 ! [F: ( $o > set_val ) > val,X: $o > set_val,Y2: $o > set_val] :
% 0.26/0.59 ( ( order_23236447al_val @ F )
% 0.26/0.59 => ( ( ord_le994826475et_val @ X @ Y2 )
% 0.26/0.59 => ( ord_less_eq_val @ ( F @ Y2 ) @ ( F @ X ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % antimonoE
% 0.26/0.59 thf(fact_193_antimonoE,axiom,
% 0.26/0.59 ! [F: val > $o > set_val,X: val,Y2: val] :
% 0.26/0.59 ( ( order_255079095et_val @ F )
% 0.26/0.59 => ( ( ord_less_eq_val @ X @ Y2 )
% 0.26/0.59 => ( ord_le994826475et_val @ ( F @ Y2 ) @ ( F @ X ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % antimonoE
% 0.26/0.59 thf(fact_194_antimonoE,axiom,
% 0.26/0.59 ! [F: set_set_val > set_val,X: set_set_val,Y2: set_set_val] :
% 0.26/0.59 ( ( order_650823122et_val @ F )
% 0.26/0.59 => ( ( ord_le1742111550et_val @ X @ Y2 )
% 0.26/0.59 => ( ord_less_eq_set_val @ ( F @ Y2 ) @ ( F @ X ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % antimonoE
% 0.26/0.59 thf(fact_195_antimono__def,axiom,
% 0.26/0.59 ( order_1719375026et_val
% 0.26/0.59 = ( ^ [F2: set_val > set_val] :
% 0.26/0.59 ! [X3: set_val,Y4: set_val] :
% 0.26/0.59 ( ( ord_less_eq_set_val @ X3 @ Y4 )
% 0.26/0.59 => ( ord_less_eq_set_val @ ( F2 @ Y4 ) @ ( F2 @ X3 ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % antimono_def
% 0.26/0.59 thf(fact_196_antimono__def,axiom,
% 0.26/0.59 ( order_1689798834al_val
% 0.26/0.59 = ( ^ [F2: val > val] :
% 0.26/0.59 ! [X3: val,Y4: val] :
% 0.26/0.59 ( ( ord_less_eq_val @ X3 @ Y4 )
% 0.26/0.59 => ( ord_less_eq_val @ ( F2 @ Y4 ) @ ( F2 @ X3 ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % antimono_def
% 0.26/0.59 thf(fact_197_antimono__def,axiom,
% 0.26/0.59 ( order_1375876562al_val
% 0.26/0.59 = ( ^ [F2: set_val > val] :
% 0.26/0.59 ! [X3: set_val,Y4: set_val] :
% 0.26/0.59 ( ( ord_less_eq_set_val @ X3 @ Y4 )
% 0.26/0.59 => ( ord_less_eq_val @ ( F2 @ Y4 ) @ ( F2 @ X3 ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % antimono_def
% 0.26/0.59 thf(fact_198_antimono__def,axiom,
% 0.26/0.59 ( order_1484138386et_val
% 0.26/0.59 = ( ^ [F2: val > set_val] :
% 0.26/0.59 ! [X3: val,Y4: val] :
% 0.26/0.59 ( ( ord_less_eq_val @ X3 @ Y4 )
% 0.26/0.59 => ( ord_less_eq_set_val @ ( F2 @ Y4 ) @ ( F2 @ X3 ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % antimono_def
% 0.26/0.59 thf(fact_199_antimono__def,axiom,
% 0.26/0.59 ( order_1945059954et_val
% 0.26/0.59 = ( ^ [F2: val > set_set_val] :
% 0.26/0.59 ! [X3: val,Y4: val] :
% 0.26/0.59 ( ( ord_less_eq_val @ X3 @ Y4 )
% 0.26/0.59 => ( ord_le1742111550et_val @ ( F2 @ Y4 ) @ ( F2 @ X3 ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % antimono_def
% 0.26/0.59 thf(fact_200_antimono__def,axiom,
% 0.26/0.59 ( order_1520822002al_val
% 0.26/0.59 = ( ^ [F2: set_set_val > val] :
% 0.26/0.59 ! [X3: set_set_val,Y4: set_set_val] :
% 0.26/0.59 ( ( ord_le1742111550et_val @ X3 @ Y4 )
% 0.26/0.59 => ( ord_less_eq_val @ ( F2 @ Y4 ) @ ( F2 @ X3 ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % antimono_def
% 0.26/0.59 thf(fact_201_antimono__def,axiom,
% 0.26/0.59 ( order_1957703570et_val
% 0.26/0.59 = ( ^ [F2: set_val > set_set_val] :
% 0.26/0.59 ! [X3: set_val,Y4: set_val] :
% 0.26/0.59 ( ( ord_less_eq_set_val @ X3 @ Y4 )
% 0.26/0.59 => ( ord_le1742111550et_val @ ( F2 @ Y4 ) @ ( F2 @ X3 ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % antimono_def
% 0.26/0.59 thf(fact_202_antimono__def,axiom,
% 0.26/0.59 ( order_23236447al_val
% 0.26/0.59 = ( ^ [F2: ( $o > set_val ) > val] :
% 0.26/0.59 ! [X3: $o > set_val,Y4: $o > set_val] :
% 0.26/0.59 ( ( ord_le994826475et_val @ X3 @ Y4 )
% 0.26/0.59 => ( ord_less_eq_val @ ( F2 @ Y4 ) @ ( F2 @ X3 ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % antimono_def
% 0.26/0.59 thf(fact_203_antimono__def,axiom,
% 0.26/0.59 ( order_255079095et_val
% 0.26/0.59 = ( ^ [F2: val > $o > set_val] :
% 0.26/0.59 ! [X3: val,Y4: val] :
% 0.26/0.59 ( ( ord_less_eq_val @ X3 @ Y4 )
% 0.26/0.59 => ( ord_le994826475et_val @ ( F2 @ Y4 ) @ ( F2 @ X3 ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % antimono_def
% 0.26/0.59 thf(fact_204_antimono__def,axiom,
% 0.26/0.59 ( order_650823122et_val
% 0.26/0.59 = ( ^ [F2: set_set_val > set_val] :
% 0.26/0.59 ! [X3: set_set_val,Y4: set_set_val] :
% 0.26/0.59 ( ( ord_le1742111550et_val @ X3 @ Y4 )
% 0.26/0.59 => ( ord_less_eq_set_val @ ( F2 @ Y4 ) @ ( F2 @ X3 ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % antimono_def
% 0.26/0.59 thf(fact_205_antimonoI,axiom,
% 0.26/0.59 ! [F: set_val > set_val] :
% 0.26/0.59 ( ! [X2: set_val,Y3: set_val] :
% 0.26/0.59 ( ( ord_less_eq_set_val @ X2 @ Y3 )
% 0.26/0.59 => ( ord_less_eq_set_val @ ( F @ Y3 ) @ ( F @ X2 ) ) )
% 0.26/0.59 => ( order_1719375026et_val @ F ) ) ).
% 0.26/0.59
% 0.26/0.59 % antimonoI
% 0.26/0.59 thf(fact_206_antimonoI,axiom,
% 0.26/0.59 ! [F: val > val] :
% 0.26/0.59 ( ! [X2: val,Y3: val] :
% 0.26/0.59 ( ( ord_less_eq_val @ X2 @ Y3 )
% 0.26/0.59 => ( ord_less_eq_val @ ( F @ Y3 ) @ ( F @ X2 ) ) )
% 0.26/0.59 => ( order_1689798834al_val @ F ) ) ).
% 0.26/0.59
% 0.26/0.59 % antimonoI
% 0.26/0.59 thf(fact_207_antimonoI,axiom,
% 0.26/0.59 ! [F: set_val > val] :
% 0.26/0.59 ( ! [X2: set_val,Y3: set_val] :
% 0.26/0.59 ( ( ord_less_eq_set_val @ X2 @ Y3 )
% 0.26/0.59 => ( ord_less_eq_val @ ( F @ Y3 ) @ ( F @ X2 ) ) )
% 0.26/0.59 => ( order_1375876562al_val @ F ) ) ).
% 0.26/0.59
% 0.26/0.59 % antimonoI
% 0.26/0.59 thf(fact_208_antimonoI,axiom,
% 0.26/0.59 ! [F: val > set_val] :
% 0.26/0.59 ( ! [X2: val,Y3: val] :
% 0.26/0.59 ( ( ord_less_eq_val @ X2 @ Y3 )
% 0.26/0.59 => ( ord_less_eq_set_val @ ( F @ Y3 ) @ ( F @ X2 ) ) )
% 0.26/0.59 => ( order_1484138386et_val @ F ) ) ).
% 0.26/0.59
% 0.26/0.59 % antimonoI
% 0.26/0.59 thf(fact_209_antimonoI,axiom,
% 0.26/0.59 ! [F: val > set_set_val] :
% 0.26/0.59 ( ! [X2: val,Y3: val] :
% 0.26/0.59 ( ( ord_less_eq_val @ X2 @ Y3 )
% 0.26/0.59 => ( ord_le1742111550et_val @ ( F @ Y3 ) @ ( F @ X2 ) ) )
% 0.26/0.59 => ( order_1945059954et_val @ F ) ) ).
% 0.26/0.59
% 0.26/0.59 % antimonoI
% 0.26/0.59 thf(fact_210_antimonoI,axiom,
% 0.26/0.59 ! [F: set_set_val > val] :
% 0.26/0.59 ( ! [X2: set_set_val,Y3: set_set_val] :
% 0.26/0.59 ( ( ord_le1742111550et_val @ X2 @ Y3 )
% 0.26/0.59 => ( ord_less_eq_val @ ( F @ Y3 ) @ ( F @ X2 ) ) )
% 0.26/0.59 => ( order_1520822002al_val @ F ) ) ).
% 0.26/0.59
% 0.26/0.59 % antimonoI
% 0.26/0.59 thf(fact_211_antimonoI,axiom,
% 0.26/0.59 ! [F: set_val > set_set_val] :
% 0.26/0.59 ( ! [X2: set_val,Y3: set_val] :
% 0.26/0.59 ( ( ord_less_eq_set_val @ X2 @ Y3 )
% 0.26/0.59 => ( ord_le1742111550et_val @ ( F @ Y3 ) @ ( F @ X2 ) ) )
% 0.26/0.59 => ( order_1957703570et_val @ F ) ) ).
% 0.26/0.59
% 0.26/0.59 % antimonoI
% 0.26/0.59 thf(fact_212_antimonoI,axiom,
% 0.26/0.59 ! [F: ( $o > set_val ) > val] :
% 0.26/0.59 ( ! [X2: $o > set_val,Y3: $o > set_val] :
% 0.26/0.59 ( ( ord_le994826475et_val @ X2 @ Y3 )
% 0.26/0.59 => ( ord_less_eq_val @ ( F @ Y3 ) @ ( F @ X2 ) ) )
% 0.26/0.59 => ( order_23236447al_val @ F ) ) ).
% 0.26/0.59
% 0.26/0.59 % antimonoI
% 0.26/0.59 thf(fact_213_antimonoI,axiom,
% 0.26/0.59 ! [F: val > $o > set_val] :
% 0.26/0.59 ( ! [X2: val,Y3: val] :
% 0.26/0.59 ( ( ord_less_eq_val @ X2 @ Y3 )
% 0.26/0.59 => ( ord_le994826475et_val @ ( F @ Y3 ) @ ( F @ X2 ) ) )
% 0.26/0.59 => ( order_255079095et_val @ F ) ) ).
% 0.26/0.59
% 0.26/0.59 % antimonoI
% 0.26/0.59 thf(fact_214_antimonoI,axiom,
% 0.26/0.59 ! [F: set_set_val > set_val] :
% 0.26/0.59 ( ! [X2: set_set_val,Y3: set_set_val] :
% 0.26/0.59 ( ( ord_le1742111550et_val @ X2 @ Y3 )
% 0.26/0.59 => ( ord_less_eq_set_val @ ( F @ Y3 ) @ ( F @ X2 ) ) )
% 0.26/0.59 => ( order_650823122et_val @ F ) ) ).
% 0.26/0.59
% 0.26/0.59 % antimonoI
% 0.26/0.59 thf(fact_215_order__mono__setup_Omono__setup__loc__axioms,axiom,
% 0.26/0.59 refine16560100et_val @ ord_le994826475et_val ).
% 0.26/0.59
% 0.26/0.59 % order_mono_setup.mono_setup_loc_axioms
% 0.26/0.59 thf(fact_216_order__mono__setup_Omono__setup__loc__axioms,axiom,
% 0.26/0.59 refine67622213oc_val @ ord_less_eq_val ).
% 0.26/0.59
% 0.26/0.59 % order_mono_setup.mono_setup_loc_axioms
% 0.26/0.59 thf(fact_217_order__mono__setup_Omono__setup__loc__axioms,axiom,
% 0.26/0.59 refine1506227973et_val @ ord_le1742111550et_val ).
% 0.26/0.59
% 0.26/0.59 % order_mono_setup.mono_setup_loc_axioms
% 0.26/0.59 thf(fact_218_order__mono__setup_Omono__setup__loc__axioms,axiom,
% 0.26/0.59 refine275900453et_val @ ord_less_eq_set_val ).
% 0.26/0.59
% 0.26/0.59 % order_mono_setup.mono_setup_loc_axioms
% 0.26/0.59 thf(fact_219_galois__connection_O_092_060gamma_062_092_060alpha_062__infl,axiom,
% 0.26/0.59 ! [Alpha: set_val > set_val,Gamma: set_val > set_val,X: set_val] :
% 0.26/0.59 ( ( refine1929691018et_val @ Alpha @ Gamma )
% 0.26/0.59 => ( ord_less_eq_set_val @ X @ ( Gamma @ ( Alpha @ X ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % galois_connection.\<gamma>\<alpha>_infl
% 0.26/0.59 thf(fact_220_galois__connection_O_092_060alpha_062_092_060gamma_062__defl,axiom,
% 0.26/0.59 ! [Alpha: set_val > set_val,Gamma: set_val > set_val,X: set_val] :
% 0.26/0.59 ( ( refine1929691018et_val @ Alpha @ Gamma )
% 0.26/0.59 => ( ord_less_eq_set_val @ ( Alpha @ ( Gamma @ X ) ) @ X ) ) ).
% 0.26/0.59
% 0.26/0.59 % galois_connection.\<alpha>\<gamma>_defl
% 0.26/0.59 thf(fact_221_galois__connection_Ogalois,axiom,
% 0.26/0.59 ! [Alpha: set_val > $o > set_val,Gamma: ( $o > set_val ) > set_val,C: set_val,A3: $o > set_val] :
% 0.26/0.59 ( ( refine51544255et_val @ Alpha @ Gamma )
% 0.26/0.59 => ( ( ord_less_eq_set_val @ C @ ( Gamma @ A3 ) )
% 0.26/0.59 = ( ord_le994826475et_val @ ( Alpha @ C ) @ A3 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % galois_connection.galois
% 0.26/0.59 thf(fact_222_galois__connection_Ogalois,axiom,
% 0.26/0.59 ! [Alpha: set_val > set_set_val,Gamma: set_set_val > set_val,C: set_val,A3: set_set_val] :
% 0.26/0.59 ( ( refine1315043946et_val @ Alpha @ Gamma )
% 0.26/0.59 => ( ( ord_less_eq_set_val @ C @ ( Gamma @ A3 ) )
% 0.26/0.59 = ( ord_le1742111550et_val @ ( Alpha @ C ) @ A3 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % galois_connection.galois
% 0.26/0.59 thf(fact_223_galois__connection_Ogalois,axiom,
% 0.26/0.59 ! [Alpha: ( $o > set_val ) > set_val,Gamma: set_val > $o > set_val,C: $o > set_val,A3: set_val] :
% 0.26/0.59 ( ( refine1948536167et_val @ Alpha @ Gamma )
% 0.26/0.59 => ( ( ord_le994826475et_val @ C @ ( Gamma @ A3 ) )
% 0.26/0.59 = ( ord_less_eq_set_val @ ( Alpha @ C ) @ A3 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % galois_connection.galois
% 0.26/0.59 thf(fact_224_galois__connection_Ogalois,axiom,
% 0.26/0.59 ! [Alpha: ( $o > set_val ) > $o > set_val,Gamma: ( $o > set_val ) > $o > set_val,C: $o > set_val,A3: $o > set_val] :
% 0.26/0.59 ( ( refine1924899106et_val @ Alpha @ Gamma )
% 0.26/0.59 => ( ( ord_le994826475et_val @ C @ ( Gamma @ A3 ) )
% 0.26/0.59 = ( ord_le994826475et_val @ ( Alpha @ C ) @ A3 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % galois_connection.galois
% 0.26/0.59 thf(fact_225_galois__connection_Ogalois,axiom,
% 0.26/0.59 ! [Alpha: ( $o > set_val ) > set_set_val,Gamma: set_set_val > $o > set_val,C: $o > set_val,A3: set_set_val] :
% 0.26/0.59 ( ( refine1169396807et_val @ Alpha @ Gamma )
% 0.26/0.59 => ( ( ord_le994826475et_val @ C @ ( Gamma @ A3 ) )
% 0.26/0.59 = ( ord_le1742111550et_val @ ( Alpha @ C ) @ A3 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % galois_connection.galois
% 0.26/0.59 thf(fact_226_galois__connection_Ogalois,axiom,
% 0.26/0.59 ! [Alpha: set_set_val > set_val,Gamma: set_val > set_set_val,C: set_set_val,A3: set_val] :
% 0.26/0.59 ( ( refine8163498et_val @ Alpha @ Gamma )
% 0.26/0.59 => ( ( ord_le1742111550et_val @ C @ ( Gamma @ A3 ) )
% 0.26/0.59 = ( ord_less_eq_set_val @ ( Alpha @ C ) @ A3 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % galois_connection.galois
% 0.26/0.59 thf(fact_227_galois__connection_Ogalois,axiom,
% 0.26/0.59 ! [Alpha: set_set_val > $o > set_val,Gamma: ( $o > set_val ) > set_set_val,C: set_set_val,A3: $o > set_val] :
% 0.26/0.59 ( ( refine86398879et_val @ Alpha @ Gamma )
% 0.26/0.59 => ( ( ord_le1742111550et_val @ C @ ( Gamma @ A3 ) )
% 0.26/0.59 = ( ord_le994826475et_val @ ( Alpha @ C ) @ A3 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % galois_connection.galois
% 0.26/0.59 thf(fact_228_galois__connection_Ogalois,axiom,
% 0.26/0.59 ! [Alpha: set_set_val > set_set_val,Gamma: set_set_val > set_set_val,C: set_set_val,A3: set_set_val] :
% 0.26/0.59 ( ( refine855985034et_val @ Alpha @ Gamma )
% 0.26/0.59 => ( ( ord_le1742111550et_val @ C @ ( Gamma @ A3 ) )
% 0.26/0.59 = ( ord_le1742111550et_val @ ( Alpha @ C ) @ A3 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % galois_connection.galois
% 0.26/0.59 thf(fact_229_galois__connection_Ogalois,axiom,
% 0.26/0.59 ! [Alpha: set_val > set_val,Gamma: set_val > set_val,C: set_val,A3: set_val] :
% 0.26/0.59 ( ( refine1929691018et_val @ Alpha @ Gamma )
% 0.26/0.59 => ( ( ord_less_eq_set_val @ C @ ( Gamma @ A3 ) )
% 0.26/0.59 = ( ord_less_eq_set_val @ ( Alpha @ C ) @ A3 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % galois_connection.galois
% 0.26/0.59 thf(fact_230_galois__connection_Ointro,axiom,
% 0.26/0.59 ! [Gamma: ( $o > set_val ) > set_val,Alpha: set_val > $o > set_val] :
% 0.26/0.59 ( ! [C3: set_val,A5: $o > set_val] :
% 0.26/0.59 ( ( ord_less_eq_set_val @ C3 @ ( Gamma @ A5 ) )
% 0.26/0.59 = ( ord_le994826475et_val @ ( Alpha @ C3 ) @ A5 ) )
% 0.26/0.59 => ( refine51544255et_val @ Alpha @ Gamma ) ) ).
% 0.26/0.59
% 0.26/0.59 % galois_connection.intro
% 0.26/0.59 thf(fact_231_galois__connection_Ointro,axiom,
% 0.26/0.59 ! [Gamma: set_set_val > set_val,Alpha: set_val > set_set_val] :
% 0.26/0.59 ( ! [C3: set_val,A5: set_set_val] :
% 0.26/0.59 ( ( ord_less_eq_set_val @ C3 @ ( Gamma @ A5 ) )
% 0.26/0.59 = ( ord_le1742111550et_val @ ( Alpha @ C3 ) @ A5 ) )
% 0.26/0.59 => ( refine1315043946et_val @ Alpha @ Gamma ) ) ).
% 0.26/0.59
% 0.26/0.59 % galois_connection.intro
% 0.26/0.59 thf(fact_232_galois__connection_Ointro,axiom,
% 0.26/0.59 ! [Gamma: set_val > $o > set_val,Alpha: ( $o > set_val ) > set_val] :
% 0.26/0.59 ( ! [C3: $o > set_val,A5: set_val] :
% 0.26/0.59 ( ( ord_le994826475et_val @ C3 @ ( Gamma @ A5 ) )
% 0.26/0.59 = ( ord_less_eq_set_val @ ( Alpha @ C3 ) @ A5 ) )
% 0.26/0.59 => ( refine1948536167et_val @ Alpha @ Gamma ) ) ).
% 0.26/0.59
% 0.26/0.59 % galois_connection.intro
% 0.26/0.59 thf(fact_233_galois__connection_Ointro,axiom,
% 0.26/0.59 ! [Gamma: ( $o > set_val ) > $o > set_val,Alpha: ( $o > set_val ) > $o > set_val] :
% 0.26/0.59 ( ! [C3: $o > set_val,A5: $o > set_val] :
% 0.26/0.59 ( ( ord_le994826475et_val @ C3 @ ( Gamma @ A5 ) )
% 0.26/0.59 = ( ord_le994826475et_val @ ( Alpha @ C3 ) @ A5 ) )
% 0.26/0.59 => ( refine1924899106et_val @ Alpha @ Gamma ) ) ).
% 0.26/0.59
% 0.26/0.59 % galois_connection.intro
% 0.26/0.59 thf(fact_234_galois__connection_Ointro,axiom,
% 0.26/0.59 ! [Gamma: set_set_val > $o > set_val,Alpha: ( $o > set_val ) > set_set_val] :
% 0.26/0.59 ( ! [C3: $o > set_val,A5: set_set_val] :
% 0.26/0.59 ( ( ord_le994826475et_val @ C3 @ ( Gamma @ A5 ) )
% 0.26/0.59 = ( ord_le1742111550et_val @ ( Alpha @ C3 ) @ A5 ) )
% 0.26/0.59 => ( refine1169396807et_val @ Alpha @ Gamma ) ) ).
% 0.26/0.59
% 0.26/0.59 % galois_connection.intro
% 0.26/0.59 thf(fact_235_galois__connection_Ointro,axiom,
% 0.26/0.59 ! [Gamma: set_val > set_set_val,Alpha: set_set_val > set_val] :
% 0.26/0.59 ( ! [C3: set_set_val,A5: set_val] :
% 0.26/0.59 ( ( ord_le1742111550et_val @ C3 @ ( Gamma @ A5 ) )
% 0.26/0.59 = ( ord_less_eq_set_val @ ( Alpha @ C3 ) @ A5 ) )
% 0.26/0.59 => ( refine8163498et_val @ Alpha @ Gamma ) ) ).
% 0.26/0.59
% 0.26/0.59 % galois_connection.intro
% 0.26/0.59 thf(fact_236_galois__connection_Ointro,axiom,
% 0.26/0.59 ! [Gamma: ( $o > set_val ) > set_set_val,Alpha: set_set_val > $o > set_val] :
% 0.26/0.59 ( ! [C3: set_set_val,A5: $o > set_val] :
% 0.26/0.59 ( ( ord_le1742111550et_val @ C3 @ ( Gamma @ A5 ) )
% 0.26/0.59 = ( ord_le994826475et_val @ ( Alpha @ C3 ) @ A5 ) )
% 0.26/0.59 => ( refine86398879et_val @ Alpha @ Gamma ) ) ).
% 0.26/0.59
% 0.26/0.59 % galois_connection.intro
% 0.26/0.59 thf(fact_237_galois__connection_Ointro,axiom,
% 0.26/0.59 ! [Gamma: set_set_val > set_set_val,Alpha: set_set_val > set_set_val] :
% 0.26/0.59 ( ! [C3: set_set_val,A5: set_set_val] :
% 0.26/0.59 ( ( ord_le1742111550et_val @ C3 @ ( Gamma @ A5 ) )
% 0.26/0.59 = ( ord_le1742111550et_val @ ( Alpha @ C3 ) @ A5 ) )
% 0.26/0.59 => ( refine855985034et_val @ Alpha @ Gamma ) ) ).
% 0.26/0.59
% 0.26/0.59 % galois_connection.intro
% 0.26/0.59 thf(fact_238_galois__connection_Ointro,axiom,
% 0.26/0.59 ! [Gamma: set_val > set_val,Alpha: set_val > set_val] :
% 0.26/0.59 ( ! [C3: set_val,A5: set_val] :
% 0.26/0.59 ( ( ord_less_eq_set_val @ C3 @ ( Gamma @ A5 ) )
% 0.26/0.59 = ( ord_less_eq_set_val @ ( Alpha @ C3 ) @ A5 ) )
% 0.26/0.59 => ( refine1929691018et_val @ Alpha @ Gamma ) ) ).
% 0.26/0.59
% 0.26/0.59 % galois_connection.intro
% 0.26/0.59 thf(fact_239_galois__connection__def,axiom,
% 0.26/0.59 ( refine51544255et_val
% 0.26/0.59 = ( ^ [Alpha2: set_val > $o > set_val,Gamma2: ( $o > set_val ) > set_val] :
% 0.26/0.59 ! [C4: set_val,A4: $o > set_val] :
% 0.26/0.59 ( ( ord_less_eq_set_val @ C4 @ ( Gamma2 @ A4 ) )
% 0.26/0.59 = ( ord_le994826475et_val @ ( Alpha2 @ C4 ) @ A4 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % galois_connection_def
% 0.26/0.59 thf(fact_240_galois__connection__def,axiom,
% 0.26/0.59 ( refine1315043946et_val
% 0.26/0.59 = ( ^ [Alpha2: set_val > set_set_val,Gamma2: set_set_val > set_val] :
% 0.26/0.59 ! [C4: set_val,A4: set_set_val] :
% 0.26/0.59 ( ( ord_less_eq_set_val @ C4 @ ( Gamma2 @ A4 ) )
% 0.26/0.59 = ( ord_le1742111550et_val @ ( Alpha2 @ C4 ) @ A4 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % galois_connection_def
% 0.26/0.59 thf(fact_241_galois__connection__def,axiom,
% 0.26/0.59 ( refine1948536167et_val
% 0.26/0.59 = ( ^ [Alpha2: ( $o > set_val ) > set_val,Gamma2: set_val > $o > set_val] :
% 0.26/0.59 ! [C4: $o > set_val,A4: set_val] :
% 0.26/0.59 ( ( ord_le994826475et_val @ C4 @ ( Gamma2 @ A4 ) )
% 0.26/0.59 = ( ord_less_eq_set_val @ ( Alpha2 @ C4 ) @ A4 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % galois_connection_def
% 0.26/0.59 thf(fact_242_galois__connection__def,axiom,
% 0.26/0.59 ( refine1924899106et_val
% 0.26/0.59 = ( ^ [Alpha2: ( $o > set_val ) > $o > set_val,Gamma2: ( $o > set_val ) > $o > set_val] :
% 0.26/0.59 ! [C4: $o > set_val,A4: $o > set_val] :
% 0.26/0.59 ( ( ord_le994826475et_val @ C4 @ ( Gamma2 @ A4 ) )
% 0.26/0.59 = ( ord_le994826475et_val @ ( Alpha2 @ C4 ) @ A4 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % galois_connection_def
% 0.26/0.59 thf(fact_243_galois__connection__def,axiom,
% 0.26/0.59 ( refine1169396807et_val
% 0.26/0.59 = ( ^ [Alpha2: ( $o > set_val ) > set_set_val,Gamma2: set_set_val > $o > set_val] :
% 0.26/0.59 ! [C4: $o > set_val,A4: set_set_val] :
% 0.26/0.59 ( ( ord_le994826475et_val @ C4 @ ( Gamma2 @ A4 ) )
% 0.26/0.59 = ( ord_le1742111550et_val @ ( Alpha2 @ C4 ) @ A4 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % galois_connection_def
% 0.26/0.59 thf(fact_244_galois__connection__def,axiom,
% 0.26/0.59 ( refine8163498et_val
% 0.26/0.59 = ( ^ [Alpha2: set_set_val > set_val,Gamma2: set_val > set_set_val] :
% 0.26/0.59 ! [C4: set_set_val,A4: set_val] :
% 0.26/0.59 ( ( ord_le1742111550et_val @ C4 @ ( Gamma2 @ A4 ) )
% 0.26/0.59 = ( ord_less_eq_set_val @ ( Alpha2 @ C4 ) @ A4 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % galois_connection_def
% 0.26/0.59 thf(fact_245_galois__connection__def,axiom,
% 0.26/0.59 ( refine86398879et_val
% 0.26/0.59 = ( ^ [Alpha2: set_set_val > $o > set_val,Gamma2: ( $o > set_val ) > set_set_val] :
% 0.26/0.59 ! [C4: set_set_val,A4: $o > set_val] :
% 0.26/0.59 ( ( ord_le1742111550et_val @ C4 @ ( Gamma2 @ A4 ) )
% 0.26/0.59 = ( ord_le994826475et_val @ ( Alpha2 @ C4 ) @ A4 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % galois_connection_def
% 0.26/0.59 thf(fact_246_galois__connection__def,axiom,
% 0.26/0.59 ( refine855985034et_val
% 0.26/0.59 = ( ^ [Alpha2: set_set_val > set_set_val,Gamma2: set_set_val > set_set_val] :
% 0.26/0.59 ! [C4: set_set_val,A4: set_set_val] :
% 0.26/0.59 ( ( ord_le1742111550et_val @ C4 @ ( Gamma2 @ A4 ) )
% 0.26/0.59 = ( ord_le1742111550et_val @ ( Alpha2 @ C4 ) @ A4 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % galois_connection_def
% 0.26/0.59 thf(fact_247_galois__connection__def,axiom,
% 0.26/0.59 ( refine1929691018et_val
% 0.26/0.59 = ( ^ [Alpha2: set_val > set_val,Gamma2: set_val > set_val] :
% 0.26/0.59 ! [C4: set_val,A4: set_val] :
% 0.26/0.59 ( ( ord_less_eq_set_val @ C4 @ ( Gamma2 @ A4 ) )
% 0.26/0.59 = ( ord_less_eq_set_val @ ( Alpha2 @ C4 ) @ A4 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % galois_connection_def
% 0.26/0.59 thf(fact_248_mono__setup__loc__def,axiom,
% 0.26/0.59 ( refine275900453et_val
% 0.26/0.59 = ( ^ [Le: set_val > set_val > $o] :
% 0.26/0.59 ! [X3: set_val] : ( Le @ X3 @ X3 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % mono_setup_loc_def
% 0.26/0.59 thf(fact_249_mono__setup__loc_Orefl,axiom,
% 0.26/0.59 ! [Le2: set_val > set_val > $o,X: set_val] :
% 0.26/0.59 ( ( refine275900453et_val @ Le2 )
% 0.26/0.59 => ( Le2 @ X @ X ) ) ).
% 0.26/0.59
% 0.26/0.59 % mono_setup_loc.refl
% 0.26/0.59 thf(fact_250_mono__setup__loc_Ointro,axiom,
% 0.26/0.59 ! [Le2: set_val > set_val > $o] :
% 0.26/0.59 ( ! [X2: set_val] : ( Le2 @ X2 @ X2 )
% 0.26/0.59 => ( refine275900453et_val @ Le2 ) ) ).
% 0.26/0.59
% 0.26/0.59 % mono_setup_loc.intro
% 0.26/0.59 thf(fact_251_mono__setup__loc_Omono__if,axiom,
% 0.26/0.59 ! [Le2: set_val > set_val > $o,T2: set_val,T3: set_val,E: set_val,E2: set_val,B3: $o] :
% 0.26/0.59 ( ( refine275900453et_val @ Le2 )
% 0.26/0.59 => ( ( Le2 @ T2 @ T3 )
% 0.26/0.59 => ( ( Le2 @ E @ E2 )
% 0.26/0.59 => ( Le2 @ ( if_set_val @ B3 @ T2 @ E ) @ ( if_set_val @ B3 @ T3 @ E2 ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % mono_setup_loc.mono_if
% 0.26/0.59 thf(fact_252_galois__connection_Oinf__dist___092_060alpha_062,axiom,
% 0.26/0.59 ! [Alpha: set_val > set_val,Gamma: set_val > set_val] :
% 0.26/0.59 ( ( refine1929691018et_val @ Alpha @ Gamma )
% 0.26/0.59 => ( refine2057434761et_val @ Alpha ) ) ).
% 0.26/0.59
% 0.26/0.59 % galois_connection.inf_dist_\<alpha>
% 0.26/0.59 thf(fact_253_strict__mono__less__eq,axiom,
% 0.26/0.59 ! [F: val > set_val,X: val,Y2: val] :
% 0.26/0.59 ( ( order_99134233et_val @ F )
% 0.26/0.59 => ( ( ord_less_eq_set_val @ ( F @ X ) @ ( F @ Y2 ) )
% 0.26/0.59 = ( ord_less_eq_val @ X @ Y2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % strict_mono_less_eq
% 0.26/0.59 thf(fact_254_strict__mono__less__eq,axiom,
% 0.26/0.59 ! [F: val > $o > set_val,X: val,Y2: val] :
% 0.26/0.59 ( ( order_1205732848et_val @ F )
% 0.26/0.59 => ( ( ord_le994826475et_val @ ( F @ X ) @ ( F @ Y2 ) )
% 0.26/0.59 = ( ord_less_eq_val @ X @ Y2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % strict_mono_less_eq
% 0.26/0.59 thf(fact_255_strict__mono__less__eq,axiom,
% 0.26/0.59 ! [F: val > val,X: val,Y2: val] :
% 0.26/0.59 ( ( order_1139042361al_val @ F )
% 0.26/0.59 => ( ( ord_less_eq_val @ ( F @ X ) @ ( F @ Y2 ) )
% 0.26/0.59 = ( ord_less_eq_val @ X @ Y2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % strict_mono_less_eq
% 0.26/0.59 thf(fact_256_strict__mono__less__eq,axiom,
% 0.26/0.59 ! [F: val > set_set_val,X: val,Y2: val] :
% 0.26/0.59 ( ( order_68692473et_val @ F )
% 0.26/0.59 => ( ( ord_le1742111550et_val @ ( F @ X ) @ ( F @ Y2 ) )
% 0.26/0.59 = ( ord_less_eq_val @ X @ Y2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % strict_mono_less_eq
% 0.26/0.59 thf(fact_257_greaterThan__subset__iff,axiom,
% 0.26/0.59 ! [X: val,Y2: val] :
% 0.26/0.59 ( ( ord_less_eq_set_val @ ( set_or1288365508an_val @ X ) @ ( set_or1288365508an_val @ Y2 ) )
% 0.26/0.59 = ( ord_less_eq_val @ Y2 @ X ) ) ).
% 0.26/0.59
% 0.26/0.59 % greaterThan_subset_iff
% 0.26/0.59 thf(fact_258_START__REFINEG__TRANSFER,axiom,
% 0.26/0.59 ! [D: $o > set_val,C: $o > set_val,A3: $o > set_val] :
% 0.26/0.59 ( ( refine1593386065et_val @ D @ C )
% 0.26/0.59 => ( ( ord_le994826475et_val @ C @ A3 )
% 0.26/0.59 => ( ( refine511606705et_val @ C @ D )
% 0.26/0.59 => ( ord_le994826475et_val @ D @ A3 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % START_REFINEG_TRANSFER
% 0.26/0.59 thf(fact_259_START__REFINEG__TRANSFER,axiom,
% 0.26/0.59 ! [D: val,C: val,A3: val] :
% 0.26/0.59 ( ( refine2021912633al_val @ D @ C )
% 0.26/0.59 => ( ( ord_less_eq_val @ C @ A3 )
% 0.26/0.59 => ( ( refine403244856MP_val @ C @ D )
% 0.26/0.59 => ( ord_less_eq_val @ D @ A3 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % START_REFINEG_TRANSFER
% 0.26/0.59 thf(fact_260_START__REFINEG__TRANSFER,axiom,
% 0.26/0.59 ! [D: set_set_val,C: set_set_val,A3: set_set_val] :
% 0.26/0.59 ( ( refine1034950713et_val @ D @ C )
% 0.26/0.59 => ( ( ord_le1742111550et_val @ C @ A3 )
% 0.26/0.59 => ( ( refine1908789496et_val @ C @ D )
% 0.26/0.59 => ( ord_le1742111550et_val @ D @ A3 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % START_REFINEG_TRANSFER
% 0.26/0.59 thf(fact_261_START__REFINEG__TRANSFER,axiom,
% 0.26/0.59 ! [D: set_val,C: set_val,A3: set_val] :
% 0.26/0.59 ( ( refine654574649et_val @ D @ C )
% 0.26/0.59 => ( ( ord_less_eq_set_val @ C @ A3 )
% 0.26/0.59 => ( ( refine1893322264et_val @ C @ D )
% 0.26/0.59 => ( ord_less_eq_set_val @ D @ A3 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % START_REFINEG_TRANSFER
% 0.26/0.59 thf(fact_262_lessThan__subset__iff,axiom,
% 0.26/0.59 ! [X: val,Y2: val] :
% 0.26/0.59 ( ( ord_less_eq_set_val @ ( set_ord_lessThan_val @ X ) @ ( set_ord_lessThan_val @ Y2 ) )
% 0.26/0.59 = ( ord_less_eq_val @ X @ Y2 ) ) ).
% 0.26/0.59
% 0.26/0.59 % lessThan_subset_iff
% 0.26/0.59 thf(fact_263_atLeast__subset__iff,axiom,
% 0.26/0.59 ! [X: set_set_val,Y2: set_set_val] :
% 0.26/0.59 ( ( ord_le1135847966et_val @ ( set_or1337784553et_val @ X ) @ ( set_or1337784553et_val @ Y2 ) )
% 0.26/0.59 = ( ord_le1742111550et_val @ Y2 @ X ) ) ).
% 0.26/0.59
% 0.26/0.59 % atLeast_subset_iff
% 0.26/0.59 thf(fact_264_atLeast__subset__iff,axiom,
% 0.26/0.59 ! [X: set_val,Y2: set_val] :
% 0.26/0.59 ( ( ord_le1742111550et_val @ ( set_or650197513et_val @ X ) @ ( set_or650197513et_val @ Y2 ) )
% 0.26/0.59 = ( ord_less_eq_set_val @ Y2 @ X ) ) ).
% 0.26/0.59
% 0.26/0.59 % atLeast_subset_iff
% 0.26/0.59 thf(fact_265_atLeast__subset__iff,axiom,
% 0.26/0.59 ! [X: val,Y2: val] :
% 0.26/0.59 ( ( ord_less_eq_set_val @ ( set_ord_atLeast_val @ X ) @ ( set_ord_atLeast_val @ Y2 ) )
% 0.26/0.59 = ( ord_less_eq_val @ Y2 @ X ) ) ).
% 0.26/0.59
% 0.26/0.59 % atLeast_subset_iff
% 0.26/0.59 thf(fact_266_atLeast__iff,axiom,
% 0.26/0.59 ! [I: val,K: val] :
% 0.26/0.59 ( ( member_val @ I @ ( set_ord_atLeast_val @ K ) )
% 0.26/0.59 = ( ord_less_eq_val @ K @ I ) ) ).
% 0.26/0.59
% 0.26/0.59 % atLeast_iff
% 0.26/0.59 thf(fact_267_atLeast__iff,axiom,
% 0.26/0.59 ! [I: set_val,K: set_val] :
% 0.26/0.59 ( ( member_set_val @ I @ ( set_or650197513et_val @ K ) )
% 0.26/0.59 = ( ord_less_eq_set_val @ K @ I ) ) ).
% 0.26/0.59
% 0.26/0.59 % atLeast_iff
% 0.26/0.59 thf(fact_268_Ioi__le__Ico,axiom,
% 0.26/0.59 ! [A3: val] : ( ord_less_eq_set_val @ ( set_or1288365508an_val @ A3 ) @ ( set_ord_atLeast_val @ A3 ) ) ).
% 0.26/0.59
% 0.26/0.59 % Ioi_le_Ico
% 0.26/0.59 thf(fact_269_Ici__subset__Ioi__iff,axiom,
% 0.26/0.59 ! [A3: val,B3: val] :
% 0.26/0.59 ( ( ord_less_eq_set_val @ ( set_ord_atLeast_val @ A3 ) @ ( set_or1288365508an_val @ B3 ) )
% 0.26/0.59 = ( ord_less_val @ B3 @ A3 ) ) ).
% 0.26/0.59
% 0.26/0.59 % Ici_subset_Ioi_iff
% 0.26/0.59 thf(fact_270_Icc__subset__Ici__iff,axiom,
% 0.26/0.59 ! [L: set_val,H: set_val,L2: set_val] :
% 0.26/0.59 ( ( ord_le1742111550et_val @ ( set_or1554624499et_val @ L @ H ) @ ( set_or650197513et_val @ L2 ) )
% 0.26/0.59 = ( ~ ( ord_less_eq_set_val @ L @ H )
% 0.26/0.59 | ( ord_less_eq_set_val @ L2 @ L ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Icc_subset_Ici_iff
% 0.26/0.59 thf(fact_271_Icc__subset__Ici__iff,axiom,
% 0.26/0.59 ! [L: val,H: val,L2: val] :
% 0.26/0.59 ( ( ord_less_eq_set_val @ ( set_or18208019st_val @ L @ H ) @ ( set_ord_atLeast_val @ L2 ) )
% 0.26/0.59 = ( ~ ( ord_less_eq_val @ L @ H )
% 0.26/0.59 | ( ord_less_eq_val @ L2 @ L ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Icc_subset_Ici_iff
% 0.26/0.59 thf(fact_272_atMost__subset__iff,axiom,
% 0.26/0.59 ! [X: set_val,Y2: set_val] :
% 0.26/0.59 ( ( ord_le1742111550et_val @ ( set_or867701765et_val @ X ) @ ( set_or867701765et_val @ Y2 ) )
% 0.26/0.59 = ( ord_less_eq_set_val @ X @ Y2 ) ) ).
% 0.26/0.59
% 0.26/0.59 % atMost_subset_iff
% 0.26/0.59 thf(fact_273_atMost__subset__iff,axiom,
% 0.26/0.59 ! [X: val,Y2: val] :
% 0.26/0.59 ( ( ord_less_eq_set_val @ ( set_ord_atMost_val @ X ) @ ( set_ord_atMost_val @ Y2 ) )
% 0.26/0.59 = ( ord_less_eq_val @ X @ Y2 ) ) ).
% 0.26/0.59
% 0.26/0.59 % atMost_subset_iff
% 0.26/0.59 thf(fact_274_psubsetI,axiom,
% 0.26/0.59 ! [A: set_val,B: set_val] :
% 0.26/0.59 ( ( ord_less_eq_set_val @ A @ B )
% 0.26/0.59 => ( ( A != B )
% 0.26/0.59 => ( ord_less_set_val @ A @ B ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % psubsetI
% 0.26/0.59 thf(fact_275_ComplI,axiom,
% 0.26/0.59 ! [C: val,A: set_val] :
% 0.26/0.59 ( ~ ( member_val @ C @ A )
% 0.26/0.59 => ( member_val @ C @ ( uminus1961393973et_val @ A ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % ComplI
% 0.26/0.59 thf(fact_276_Compl__iff,axiom,
% 0.26/0.59 ! [C: val,A: set_val] :
% 0.26/0.59 ( ( member_val @ C @ ( uminus1961393973et_val @ A ) )
% 0.26/0.59 = ( ~ ( member_val @ C @ A ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Compl_iff
% 0.26/0.59 thf(fact_277_atLeastAtMost__iff,axiom,
% 0.26/0.59 ! [I: val,L: val,U: val] :
% 0.26/0.59 ( ( member_val @ I @ ( set_or18208019st_val @ L @ U ) )
% 0.26/0.59 = ( ( ord_less_eq_val @ L @ I )
% 0.26/0.59 & ( ord_less_eq_val @ I @ U ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % atLeastAtMost_iff
% 0.26/0.59 thf(fact_278_atLeastAtMost__iff,axiom,
% 0.26/0.59 ! [I: set_val,L: set_val,U: set_val] :
% 0.26/0.59 ( ( member_set_val @ I @ ( set_or1554624499et_val @ L @ U ) )
% 0.26/0.59 = ( ( ord_less_eq_set_val @ L @ I )
% 0.26/0.59 & ( ord_less_eq_set_val @ I @ U ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % atLeastAtMost_iff
% 0.26/0.59 thf(fact_279_Icc__eq__Icc,axiom,
% 0.26/0.59 ! [L: set_val,H: set_val,L2: set_val,H2: set_val] :
% 0.26/0.59 ( ( ( set_or1554624499et_val @ L @ H )
% 0.26/0.59 = ( set_or1554624499et_val @ L2 @ H2 ) )
% 0.26/0.59 = ( ( ( L = L2 )
% 0.26/0.59 & ( H = H2 ) )
% 0.26/0.59 | ( ~ ( ord_less_eq_set_val @ L @ H )
% 0.26/0.59 & ~ ( ord_less_eq_set_val @ L2 @ H2 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Icc_eq_Icc
% 0.26/0.59 thf(fact_280_atMost__iff,axiom,
% 0.26/0.59 ! [I: val,K: val] :
% 0.26/0.59 ( ( member_val @ I @ ( set_ord_atMost_val @ K ) )
% 0.26/0.59 = ( ord_less_eq_val @ I @ K ) ) ).
% 0.26/0.59
% 0.26/0.59 % atMost_iff
% 0.26/0.59 thf(fact_281_atMost__iff,axiom,
% 0.26/0.59 ! [I: set_val,K: set_val] :
% 0.26/0.59 ( ( member_set_val @ I @ ( set_or867701765et_val @ K ) )
% 0.26/0.59 = ( ord_less_eq_set_val @ I @ K ) ) ).
% 0.26/0.59
% 0.26/0.59 % atMost_iff
% 0.26/0.59 thf(fact_282_lessThan__iff,axiom,
% 0.26/0.59 ! [I: val,K: val] :
% 0.26/0.59 ( ( member_val @ I @ ( set_ord_lessThan_val @ K ) )
% 0.26/0.59 = ( ord_less_val @ I @ K ) ) ).
% 0.26/0.59
% 0.26/0.59 % lessThan_iff
% 0.26/0.59 thf(fact_283_Compl__anti__mono,axiom,
% 0.26/0.59 ! [A: set_val,B: set_val] :
% 0.26/0.59 ( ( ord_less_eq_set_val @ A @ B )
% 0.26/0.59 => ( ord_less_eq_set_val @ ( uminus1961393973et_val @ B ) @ ( uminus1961393973et_val @ A ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Compl_anti_mono
% 0.26/0.59 thf(fact_284_Compl__subset__Compl__iff,axiom,
% 0.26/0.59 ! [A: set_val,B: set_val] :
% 0.26/0.59 ( ( ord_less_eq_set_val @ ( uminus1961393973et_val @ A ) @ ( uminus1961393973et_val @ B ) )
% 0.26/0.59 = ( ord_less_eq_set_val @ B @ A ) ) ).
% 0.26/0.59
% 0.26/0.59 % Compl_subset_Compl_iff
% 0.26/0.59 thf(fact_285_greaterThan__iff,axiom,
% 0.26/0.59 ! [I: val,K: val] :
% 0.26/0.59 ( ( member_val @ I @ ( set_or1288365508an_val @ K ) )
% 0.26/0.59 = ( ord_less_val @ K @ I ) ) ).
% 0.26/0.59
% 0.26/0.59 % greaterThan_iff
% 0.26/0.59 thf(fact_286_atLeastatMost__subset__iff,axiom,
% 0.26/0.59 ! [A3: set_val,B3: set_val,C: set_val,D: set_val] :
% 0.26/0.59 ( ( ord_le1742111550et_val @ ( set_or1554624499et_val @ A3 @ B3 ) @ ( set_or1554624499et_val @ C @ D ) )
% 0.26/0.59 = ( ~ ( ord_less_eq_set_val @ A3 @ B3 )
% 0.26/0.59 | ( ( ord_less_eq_set_val @ C @ A3 )
% 0.26/0.59 & ( ord_less_eq_set_val @ B3 @ D ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % atLeastatMost_subset_iff
% 0.26/0.59 thf(fact_287_atLeastatMost__subset__iff,axiom,
% 0.26/0.59 ! [A3: val,B3: val,C: val,D: val] :
% 0.26/0.59 ( ( ord_less_eq_set_val @ ( set_or18208019st_val @ A3 @ B3 ) @ ( set_or18208019st_val @ C @ D ) )
% 0.26/0.59 = ( ~ ( ord_less_eq_val @ A3 @ B3 )
% 0.26/0.59 | ( ( ord_less_eq_val @ C @ A3 )
% 0.26/0.59 & ( ord_less_eq_val @ B3 @ D ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % atLeastatMost_subset_iff
% 0.26/0.59 thf(fact_288_Icc__subset__Iic__iff,axiom,
% 0.26/0.59 ! [L: set_val,H: set_val,H2: set_val] :
% 0.26/0.59 ( ( ord_le1742111550et_val @ ( set_or1554624499et_val @ L @ H ) @ ( set_or867701765et_val @ H2 ) )
% 0.26/0.59 = ( ~ ( ord_less_eq_set_val @ L @ H )
% 0.26/0.59 | ( ord_less_eq_set_val @ H @ H2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Icc_subset_Iic_iff
% 0.26/0.59 thf(fact_289_Icc__subset__Iic__iff,axiom,
% 0.26/0.59 ! [L: val,H: val,H2: val] :
% 0.26/0.59 ( ( ord_less_eq_set_val @ ( set_or18208019st_val @ L @ H ) @ ( set_ord_atMost_val @ H2 ) )
% 0.26/0.59 = ( ~ ( ord_less_eq_val @ L @ H )
% 0.26/0.59 | ( ord_less_eq_val @ H @ H2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Icc_subset_Iic_iff
% 0.26/0.59 thf(fact_290_atLeastatMost__psubset__iff,axiom,
% 0.26/0.59 ! [A3: set_val,B3: set_val,C: set_val,D: set_val] :
% 0.26/0.59 ( ( ord_less_set_set_val @ ( set_or1554624499et_val @ A3 @ B3 ) @ ( set_or1554624499et_val @ C @ D ) )
% 0.26/0.59 = ( ( ~ ( ord_less_eq_set_val @ A3 @ B3 )
% 0.26/0.59 | ( ( ord_less_eq_set_val @ C @ A3 )
% 0.26/0.59 & ( ord_less_eq_set_val @ B3 @ D )
% 0.26/0.59 & ( ( ord_less_set_val @ C @ A3 )
% 0.26/0.59 | ( ord_less_set_val @ B3 @ D ) ) ) )
% 0.26/0.59 & ( ord_less_eq_set_val @ C @ D ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % atLeastatMost_psubset_iff
% 0.26/0.59 thf(fact_291_ComplD,axiom,
% 0.26/0.59 ! [C: val,A: set_val] :
% 0.26/0.59 ( ( member_val @ C @ ( uminus1961393973et_val @ A ) )
% 0.26/0.59 => ~ ( member_val @ C @ A ) ) ).
% 0.26/0.59
% 0.26/0.59 % ComplD
% 0.26/0.59 thf(fact_292_Iic__subset__Iio__iff,axiom,
% 0.26/0.59 ! [A3: val,B3: val] :
% 0.26/0.59 ( ( ord_less_eq_set_val @ ( set_ord_atMost_val @ A3 ) @ ( set_ord_lessThan_val @ B3 ) )
% 0.26/0.59 = ( ord_less_val @ A3 @ B3 ) ) ).
% 0.26/0.59
% 0.26/0.59 % Iic_subset_Iio_iff
% 0.26/0.59 thf(fact_293_leD,axiom,
% 0.26/0.59 ! [Y2: set_val,X: set_val] :
% 0.26/0.59 ( ( ord_less_eq_set_val @ Y2 @ X )
% 0.26/0.59 => ~ ( ord_less_set_val @ X @ Y2 ) ) ).
% 0.26/0.59
% 0.26/0.59 % leD
% 0.26/0.59 thf(fact_294_le__less,axiom,
% 0.26/0.59 ( ord_less_eq_set_val
% 0.26/0.59 = ( ^ [X3: set_val,Y4: set_val] :
% 0.26/0.59 ( ( ord_less_set_val @ X3 @ Y4 )
% 0.26/0.59 | ( X3 = Y4 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % le_less
% 0.26/0.59 thf(fact_295_less__le,axiom,
% 0.26/0.59 ( ord_less_set_val
% 0.26/0.59 = ( ^ [X3: set_val,Y4: set_val] :
% 0.26/0.59 ( ( ord_less_eq_set_val @ X3 @ Y4 )
% 0.26/0.59 & ( X3 != Y4 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % less_le
% 0.26/0.59 thf(fact_296_order__le__less__subst2,axiom,
% 0.26/0.59 ! [A3: set_val,B3: set_val,F: set_val > set_val,C: set_val] :
% 0.26/0.59 ( ( ord_less_eq_set_val @ A3 @ B3 )
% 0.26/0.59 => ( ( ord_less_set_val @ ( F @ B3 ) @ C )
% 0.26/0.59 => ( ! [X2: set_val,Y3: set_val] :
% 0.26/0.59 ( ( ord_less_eq_set_val @ X2 @ Y3 )
% 0.26/0.59 => ( ord_less_eq_set_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.26/0.59 => ( ord_less_set_val @ ( F @ A3 ) @ C ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % order_le_less_subst2
% 0.26/0.59 thf(fact_297_order__less__le__subst1,axiom,
% 0.26/0.59 ! [A3: set_val,F: set_val > set_val,B3: set_val,C: set_val] :
% 0.26/0.59 ( ( ord_less_set_val @ A3 @ ( F @ B3 ) )
% 0.26/0.59 => ( ( ord_less_eq_set_val @ B3 @ C )
% 0.26/0.59 => ( ! [X2: set_val,Y3: set_val] :
% 0.26/0.59 ( ( ord_less_eq_set_val @ X2 @ Y3 )
% 0.26/0.59 => ( ord_less_eq_set_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.26/0.59 => ( ord_less_set_val @ A3 @ ( F @ C ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % order_less_le_subst1
% 0.26/0.59 thf(fact_298_le__neq__trans,axiom,
% 0.26/0.59 ! [A3: set_val,B3: set_val] :
% 0.26/0.59 ( ( ord_less_eq_set_val @ A3 @ B3 )
% 0.26/0.59 => ( ( A3 != B3 )
% 0.26/0.59 => ( ord_less_set_val @ A3 @ B3 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % le_neq_trans
% 0.26/0.59 thf(fact_299_antisym__conv1,axiom,
% 0.26/0.59 ! [X: set_val,Y2: set_val] :
% 0.26/0.59 ( ~ ( ord_less_set_val @ X @ Y2 )
% 0.26/0.59 => ( ( ord_less_eq_set_val @ X @ Y2 )
% 0.26/0.59 = ( X = Y2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % antisym_conv1
% 0.26/0.59 thf(fact_300_antisym__conv2,axiom,
% 0.26/0.59 ! [X: set_val,Y2: set_val] :
% 0.26/0.59 ( ( ord_less_eq_set_val @ X @ Y2 )
% 0.26/0.59 => ( ( ~ ( ord_less_set_val @ X @ Y2 ) )
% 0.26/0.59 = ( X = Y2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % antisym_conv2
% 0.26/0.59 thf(fact_301_less__imp__le,axiom,
% 0.26/0.59 ! [X: set_val,Y2: set_val] :
% 0.26/0.59 ( ( ord_less_set_val @ X @ Y2 )
% 0.26/0.59 => ( ord_less_eq_set_val @ X @ Y2 ) ) ).
% 0.26/0.59
% 0.26/0.59 % less_imp_le
% 0.26/0.59 thf(fact_302_le__less__trans,axiom,
% 0.26/0.59 ! [X: set_val,Y2: set_val,Z2: set_val] :
% 0.26/0.59 ( ( ord_less_eq_set_val @ X @ Y2 )
% 0.26/0.59 => ( ( ord_less_set_val @ Y2 @ Z2 )
% 0.26/0.59 => ( ord_less_set_val @ X @ Z2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % le_less_trans
% 0.26/0.59 thf(fact_303_less__le__trans,axiom,
% 0.26/0.59 ! [X: set_val,Y2: set_val,Z2: set_val] :
% 0.26/0.59 ( ( ord_less_set_val @ X @ Y2 )
% 0.26/0.59 => ( ( ord_less_eq_set_val @ Y2 @ Z2 )
% 0.26/0.59 => ( ord_less_set_val @ X @ Z2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % less_le_trans
% 0.26/0.59 thf(fact_304_le__imp__less__or__eq,axiom,
% 0.26/0.59 ! [X: set_val,Y2: set_val] :
% 0.26/0.59 ( ( ord_less_eq_set_val @ X @ Y2 )
% 0.26/0.59 => ( ( ord_less_set_val @ X @ Y2 )
% 0.26/0.59 | ( X = Y2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % le_imp_less_or_eq
% 0.26/0.59 thf(fact_305_less__le__not__le,axiom,
% 0.26/0.59 ( ord_less_set_val
% 0.26/0.59 = ( ^ [X3: set_val,Y4: set_val] :
% 0.26/0.59 ( ( ord_less_eq_set_val @ X3 @ Y4 )
% 0.26/0.59 & ~ ( ord_less_eq_set_val @ Y4 @ X3 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % less_le_not_le
% 0.26/0.59 thf(fact_306_order_Ostrict__trans1,axiom,
% 0.26/0.59 ! [A3: set_val,B3: set_val,C: set_val] :
% 0.26/0.59 ( ( ord_less_eq_set_val @ A3 @ B3 )
% 0.26/0.59 => ( ( ord_less_set_val @ B3 @ C )
% 0.26/0.59 => ( ord_less_set_val @ A3 @ C ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % order.strict_trans1
% 0.26/0.59 thf(fact_307_order_Ostrict__trans2,axiom,
% 0.26/0.59 ! [A3: set_val,B3: set_val,C: set_val] :
% 0.26/0.59 ( ( ord_less_set_val @ A3 @ B3 )
% 0.26/0.59 => ( ( ord_less_eq_set_val @ B3 @ C )
% 0.26/0.59 => ( ord_less_set_val @ A3 @ C ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % order.strict_trans2
% 0.26/0.59 thf(fact_308_order_Oorder__iff__strict,axiom,
% 0.26/0.59 ( ord_less_eq_set_val
% 0.26/0.59 = ( ^ [A4: set_val,B4: set_val] :
% 0.26/0.59 ( ( ord_less_set_val @ A4 @ B4 )
% 0.26/0.59 | ( A4 = B4 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % order.order_iff_strict
% 0.26/0.59 thf(fact_309_order_Ostrict__iff__order,axiom,
% 0.26/0.59 ( ord_less_set_val
% 0.26/0.59 = ( ^ [A4: set_val,B4: set_val] :
% 0.26/0.59 ( ( ord_less_eq_set_val @ A4 @ B4 )
% 0.26/0.59 & ( A4 != B4 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % order.strict_iff_order
% 0.26/0.59 thf(fact_310_dual__order_Ostrict__trans1,axiom,
% 0.26/0.59 ! [B3: set_val,A3: set_val,C: set_val] :
% 0.26/0.59 ( ( ord_less_eq_set_val @ B3 @ A3 )
% 0.26/0.59 => ( ( ord_less_set_val @ C @ B3 )
% 0.26/0.59 => ( ord_less_set_val @ C @ A3 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % dual_order.strict_trans1
% 0.26/0.59 thf(fact_311_dual__order_Ostrict__trans2,axiom,
% 0.26/0.59 ! [B3: set_val,A3: set_val,C: set_val] :
% 0.26/0.59 ( ( ord_less_set_val @ B3 @ A3 )
% 0.26/0.59 => ( ( ord_less_eq_set_val @ C @ B3 )
% 0.26/0.59 => ( ord_less_set_val @ C @ A3 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % dual_order.strict_trans2
% 0.26/0.59 thf(fact_312_order_Ostrict__implies__order,axiom,
% 0.26/0.59 ! [A3: set_val,B3: set_val] :
% 0.26/0.59 ( ( ord_less_set_val @ A3 @ B3 )
% 0.26/0.59 => ( ord_less_eq_set_val @ A3 @ B3 ) ) ).
% 0.26/0.59
% 0.26/0.59 % order.strict_implies_order
% 0.26/0.59 thf(fact_313_dual__order_Oorder__iff__strict,axiom,
% 0.26/0.59 ( ord_less_eq_set_val
% 0.26/0.59 = ( ^ [B4: set_val,A4: set_val] :
% 0.26/0.59 ( ( ord_less_set_val @ B4 @ A4 )
% 0.26/0.59 | ( A4 = B4 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % dual_order.order_iff_strict
% 0.26/0.59 thf(fact_314_dual__order_Ostrict__iff__order,axiom,
% 0.26/0.59 ( ord_less_set_val
% 0.26/0.59 = ( ^ [B4: set_val,A4: set_val] :
% 0.26/0.59 ( ( ord_less_eq_set_val @ B4 @ A4 )
% 0.26/0.59 & ( A4 != B4 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % dual_order.strict_iff_order
% 0.26/0.59 thf(fact_315_dual__order_Ostrict__implies__order,axiom,
% 0.26/0.59 ! [B3: set_val,A3: set_val] :
% 0.26/0.59 ( ( ord_less_set_val @ B3 @ A3 )
% 0.26/0.59 => ( ord_less_eq_set_val @ B3 @ A3 ) ) ).
% 0.26/0.59
% 0.26/0.59 % dual_order.strict_implies_order
% 0.26/0.59 thf(fact_316_order_Onot__eq__order__implies__strict,axiom,
% 0.26/0.59 ! [A3: set_val,B3: set_val] :
% 0.26/0.59 ( ( A3 != B3 )
% 0.26/0.59 => ( ( ord_less_eq_set_val @ A3 @ B3 )
% 0.26/0.59 => ( ord_less_set_val @ A3 @ B3 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % order.not_eq_order_implies_strict
% 0.26/0.59 thf(fact_317_psubsetE,axiom,
% 0.26/0.59 ! [A: set_val,B: set_val] :
% 0.26/0.59 ( ( ord_less_set_val @ A @ B )
% 0.26/0.59 => ~ ( ( ord_less_eq_set_val @ A @ B )
% 0.26/0.59 => ( ord_less_eq_set_val @ B @ A ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % psubsetE
% 0.26/0.59 thf(fact_318_psubset__eq,axiom,
% 0.26/0.59 ( ord_less_set_val
% 0.26/0.59 = ( ^ [A2: set_val,B2: set_val] :
% 0.26/0.59 ( ( ord_less_eq_set_val @ A2 @ B2 )
% 0.26/0.59 & ( A2 != B2 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % psubset_eq
% 0.26/0.59 thf(fact_319_psubset__imp__subset,axiom,
% 0.26/0.59 ! [A: set_val,B: set_val] :
% 0.26/0.59 ( ( ord_less_set_val @ A @ B )
% 0.26/0.59 => ( ord_less_eq_set_val @ A @ B ) ) ).
% 0.26/0.59
% 0.26/0.59 % psubset_imp_subset
% 0.26/0.59 thf(fact_320_psubset__subset__trans,axiom,
% 0.26/0.59 ! [A: set_val,B: set_val,C2: set_val] :
% 0.26/0.59 ( ( ord_less_set_val @ A @ B )
% 0.26/0.59 => ( ( ord_less_eq_set_val @ B @ C2 )
% 0.26/0.59 => ( ord_less_set_val @ A @ C2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % psubset_subset_trans
% 0.26/0.59 thf(fact_321_subset__not__subset__eq,axiom,
% 0.26/0.59 ( ord_less_set_val
% 0.26/0.59 = ( ^ [A2: set_val,B2: set_val] :
% 0.26/0.59 ( ( ord_less_eq_set_val @ A2 @ B2 )
% 0.26/0.59 & ~ ( ord_less_eq_set_val @ B2 @ A2 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % subset_not_subset_eq
% 0.26/0.59 thf(fact_322_subset__psubset__trans,axiom,
% 0.26/0.59 ! [A: set_val,B: set_val,C2: set_val] :
% 0.26/0.59 ( ( ord_less_eq_set_val @ A @ B )
% 0.26/0.59 => ( ( ord_less_set_val @ B @ C2 )
% 0.26/0.59 => ( ord_less_set_val @ A @ C2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % subset_psubset_trans
% 0.26/0.59 thf(fact_323_subset__iff__psubset__eq,axiom,
% 0.26/0.59 ( ord_less_eq_set_val
% 0.26/0.59 = ( ^ [A2: set_val,B2: set_val] :
% 0.26/0.59 ( ( ord_less_set_val @ A2 @ B2 )
% 0.26/0.59 | ( A2 = B2 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % subset_iff_psubset_eq
% 0.26/0.59 thf(fact_324_compl__le__compl__iff,axiom,
% 0.26/0.59 ! [X: set_val,Y2: set_val] :
% 0.26/0.59 ( ( ord_less_eq_set_val @ ( uminus1961393973et_val @ X ) @ ( uminus1961393973et_val @ Y2 ) )
% 0.26/0.59 = ( ord_less_eq_set_val @ Y2 @ X ) ) ).
% 0.26/0.59
% 0.26/0.59 % compl_le_compl_iff
% 0.26/0.59 thf(fact_325_compl__mono,axiom,
% 0.26/0.59 ! [X: set_val,Y2: set_val] :
% 0.26/0.59 ( ( ord_less_eq_set_val @ X @ Y2 )
% 0.26/0.59 => ( ord_less_eq_set_val @ ( uminus1961393973et_val @ Y2 ) @ ( uminus1961393973et_val @ X ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % compl_mono
% 0.26/0.59 thf(fact_326_compl__le__swap1,axiom,
% 0.26/0.59 ! [Y2: set_val,X: set_val] :
% 0.26/0.59 ( ( ord_less_eq_set_val @ Y2 @ ( uminus1961393973et_val @ X ) )
% 0.26/0.59 => ( ord_less_eq_set_val @ X @ ( uminus1961393973et_val @ Y2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % compl_le_swap1
% 0.26/0.59 thf(fact_327_compl__le__swap2,axiom,
% 0.26/0.59 ! [Y2: set_val,X: set_val] :
% 0.26/0.59 ( ( ord_less_eq_set_val @ ( uminus1961393973et_val @ Y2 ) @ X )
% 0.26/0.59 => ( ord_less_eq_set_val @ ( uminus1961393973et_val @ X ) @ Y2 ) ) ).
% 0.26/0.59
% 0.26/0.59 % compl_le_swap2
% 0.26/0.59 thf(fact_328_psubsetD,axiom,
% 0.26/0.59 ! [A: set_val,B: set_val,C: val] :
% 0.26/0.59 ( ( ord_less_set_val @ A @ B )
% 0.26/0.59 => ( ( member_val @ C @ A )
% 0.26/0.59 => ( member_val @ C @ B ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % psubsetD
% 0.26/0.59 thf(fact_329_UnCI,axiom,
% 0.26/0.59 ! [C: val,B: set_val,A: set_val] :
% 0.26/0.59 ( ( ~ ( member_val @ C @ B )
% 0.26/0.59 => ( member_val @ C @ A ) )
% 0.26/0.59 => ( member_val @ C @ ( sup_sup_set_val @ A @ B ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % UnCI
% 0.26/0.59 thf(fact_330_Un__iff,axiom,
% 0.26/0.59 ! [C: val,A: set_val,B: set_val] :
% 0.26/0.59 ( ( member_val @ C @ ( sup_sup_set_val @ A @ B ) )
% 0.26/0.59 = ( ( member_val @ C @ A )
% 0.26/0.59 | ( member_val @ C @ B ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Un_iff
% 0.26/0.59 thf(fact_331_le__sup__iff,axiom,
% 0.26/0.59 ! [X: set_val,Y2: set_val,Z2: set_val] :
% 0.26/0.59 ( ( ord_less_eq_set_val @ ( sup_sup_set_val @ X @ Y2 ) @ Z2 )
% 0.26/0.59 = ( ( ord_less_eq_set_val @ X @ Z2 )
% 0.26/0.59 & ( ord_less_eq_set_val @ Y2 @ Z2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % le_sup_iff
% 0.26/0.59 thf(fact_332_sup_Obounded__iff,axiom,
% 0.26/0.59 ! [B3: set_val,C: set_val,A3: set_val] :
% 0.26/0.59 ( ( ord_less_eq_set_val @ ( sup_sup_set_val @ B3 @ C ) @ A3 )
% 0.26/0.59 = ( ( ord_less_eq_set_val @ B3 @ A3 )
% 0.26/0.59 & ( ord_less_eq_set_val @ C @ A3 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % sup.bounded_iff
% 0.26/0.59 thf(fact_333_Un__subset__iff,axiom,
% 0.26/0.59 ! [A: set_val,B: set_val,C2: set_val] :
% 0.26/0.59 ( ( ord_less_eq_set_val @ ( sup_sup_set_val @ A @ B ) @ C2 )
% 0.26/0.59 = ( ( ord_less_eq_set_val @ A @ C2 )
% 0.26/0.59 & ( ord_less_eq_set_val @ B @ C2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Un_subset_iff
% 0.26/0.59 thf(fact_334_greaterThanLessThan__iff,axiom,
% 0.26/0.59 ! [I: val,L: val,U: val] :
% 0.26/0.59 ( ( member_val @ I @ ( set_or2126567818an_val @ L @ U ) )
% 0.26/0.59 = ( ( ord_less_val @ L @ I )
% 0.26/0.59 & ( ord_less_val @ I @ U ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % greaterThanLessThan_iff
% 0.26/0.59 thf(fact_335_sup_OcoboundedI2,axiom,
% 0.26/0.59 ! [C: set_val,B3: set_val,A3: set_val] :
% 0.26/0.59 ( ( ord_less_eq_set_val @ C @ B3 )
% 0.26/0.59 => ( ord_less_eq_set_val @ C @ ( sup_sup_set_val @ A3 @ B3 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % sup.coboundedI2
% 0.26/0.59 thf(fact_336_sup_OcoboundedI1,axiom,
% 0.26/0.59 ! [C: set_val,A3: set_val,B3: set_val] :
% 0.26/0.59 ( ( ord_less_eq_set_val @ C @ A3 )
% 0.26/0.59 => ( ord_less_eq_set_val @ C @ ( sup_sup_set_val @ A3 @ B3 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % sup.coboundedI1
% 0.26/0.59 thf(fact_337_sup_Oabsorb__iff2,axiom,
% 0.26/0.59 ( ord_less_eq_set_val
% 0.26/0.59 = ( ^ [A4: set_val,B4: set_val] :
% 0.26/0.59 ( ( sup_sup_set_val @ A4 @ B4 )
% 0.26/0.59 = B4 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % sup.absorb_iff2
% 0.26/0.59 thf(fact_338_sup_Oabsorb__iff1,axiom,
% 0.26/0.59 ( ord_less_eq_set_val
% 0.26/0.59 = ( ^ [B4: set_val,A4: set_val] :
% 0.26/0.59 ( ( sup_sup_set_val @ A4 @ B4 )
% 0.26/0.59 = A4 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % sup.absorb_iff1
% 0.26/0.59 thf(fact_339_sup_Ocobounded2,axiom,
% 0.26/0.59 ! [B3: set_val,A3: set_val] : ( ord_less_eq_set_val @ B3 @ ( sup_sup_set_val @ A3 @ B3 ) ) ).
% 0.26/0.59
% 0.26/0.59 % sup.cobounded2
% 0.26/0.59 thf(fact_340_sup_Ocobounded1,axiom,
% 0.26/0.59 ! [A3: set_val,B3: set_val] : ( ord_less_eq_set_val @ A3 @ ( sup_sup_set_val @ A3 @ B3 ) ) ).
% 0.26/0.59
% 0.26/0.59 % sup.cobounded1
% 0.26/0.59 thf(fact_341_sup_Oorder__iff,axiom,
% 0.26/0.59 ( ord_less_eq_set_val
% 0.26/0.59 = ( ^ [B4: set_val,A4: set_val] :
% 0.26/0.59 ( A4
% 0.26/0.59 = ( sup_sup_set_val @ A4 @ B4 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % sup.order_iff
% 0.26/0.59 thf(fact_342_sup_OboundedI,axiom,
% 0.26/0.59 ! [B3: set_val,A3: set_val,C: set_val] :
% 0.26/0.59 ( ( ord_less_eq_set_val @ B3 @ A3 )
% 0.26/0.59 => ( ( ord_less_eq_set_val @ C @ A3 )
% 0.26/0.59 => ( ord_less_eq_set_val @ ( sup_sup_set_val @ B3 @ C ) @ A3 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % sup.boundedI
% 0.26/0.59 thf(fact_343_sup_OboundedE,axiom,
% 0.26/0.59 ! [B3: set_val,C: set_val,A3: set_val] :
% 0.26/0.59 ( ( ord_less_eq_set_val @ ( sup_sup_set_val @ B3 @ C ) @ A3 )
% 0.26/0.59 => ~ ( ( ord_less_eq_set_val @ B3 @ A3 )
% 0.26/0.59 => ~ ( ord_less_eq_set_val @ C @ A3 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % sup.boundedE
% 0.26/0.59 thf(fact_344_sup__absorb2,axiom,
% 0.26/0.59 ! [X: set_val,Y2: set_val] :
% 0.26/0.59 ( ( ord_less_eq_set_val @ X @ Y2 )
% 0.26/0.59 => ( ( sup_sup_set_val @ X @ Y2 )
% 0.26/0.59 = Y2 ) ) ).
% 0.26/0.59
% 0.26/0.59 % sup_absorb2
% 0.26/0.59 thf(fact_345_sup__absorb1,axiom,
% 0.26/0.59 ! [Y2: set_val,X: set_val] :
% 0.26/0.59 ( ( ord_less_eq_set_val @ Y2 @ X )
% 0.26/0.59 => ( ( sup_sup_set_val @ X @ Y2 )
% 0.26/0.59 = X ) ) ).
% 0.26/0.59
% 0.26/0.59 % sup_absorb1
% 0.26/0.59 thf(fact_346_sup_Oabsorb2,axiom,
% 0.26/0.59 ! [A3: set_val,B3: set_val] :
% 0.26/0.59 ( ( ord_less_eq_set_val @ A3 @ B3 )
% 0.26/0.59 => ( ( sup_sup_set_val @ A3 @ B3 )
% 0.26/0.59 = B3 ) ) ).
% 0.26/0.59
% 0.26/0.59 % sup.absorb2
% 0.26/0.59 thf(fact_347_sup_Oabsorb1,axiom,
% 0.26/0.59 ! [B3: set_val,A3: set_val] :
% 0.26/0.59 ( ( ord_less_eq_set_val @ B3 @ A3 )
% 0.26/0.59 => ( ( sup_sup_set_val @ A3 @ B3 )
% 0.26/0.59 = A3 ) ) ).
% 0.26/0.59
% 0.26/0.59 % sup.absorb1
% 0.26/0.59 thf(fact_348_sup__unique,axiom,
% 0.26/0.59 ! [F: set_val > set_val > set_val,X: set_val,Y2: set_val] :
% 0.26/0.59 ( ! [X2: set_val,Y3: set_val] : ( ord_less_eq_set_val @ X2 @ ( F @ X2 @ Y3 ) )
% 0.26/0.59 => ( ! [X2: set_val,Y3: set_val] : ( ord_less_eq_set_val @ Y3 @ ( F @ X2 @ Y3 ) )
% 0.26/0.59 => ( ! [X2: set_val,Y3: set_val,Z3: set_val] :
% 0.26/0.59 ( ( ord_less_eq_set_val @ Y3 @ X2 )
% 0.26/0.59 => ( ( ord_less_eq_set_val @ Z3 @ X2 )
% 0.26/0.59 => ( ord_less_eq_set_val @ ( F @ Y3 @ Z3 ) @ X2 ) ) )
% 0.26/0.59 => ( ( sup_sup_set_val @ X @ Y2 )
% 0.26/0.59 = ( F @ X @ Y2 ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % sup_unique
% 0.26/0.59 thf(fact_349_sup_OorderI,axiom,
% 0.26/0.59 ! [A3: set_val,B3: set_val] :
% 0.26/0.59 ( ( A3
% 0.26/0.59 = ( sup_sup_set_val @ A3 @ B3 ) )
% 0.26/0.59 => ( ord_less_eq_set_val @ B3 @ A3 ) ) ).
% 0.26/0.59
% 0.26/0.59 % sup.orderI
% 0.26/0.67
% 0.26/0.67 % Helper facts (9)
% 0.26/0.67 thf(help_If_2_1_If_001tf__val_T,axiom,
% 0.26/0.67 ! [X: val,Y2: val] :
% 0.26/0.67 ( ( if_val @ $false @ X @ Y2 )
% 0.26/0.67 = Y2 ) ).
% 0.26/0.67
% 0.26/0.67 thf(help_If_1_1_If_001tf__val_T,axiom,
% 0.26/0.67 ! [X: val,Y2: val] :
% 0.26/0.67 ( ( if_val @ $true @ X @ Y2 )
% 0.26/0.67 = X ) ).
% 0.26/0.67
% 0.26/0.67 thf(help_If_2_1_If_001t__Set__Oset_Itf__val_J_T,axiom,
% 0.26/0.67 ! [X: set_val,Y2: set_val] :
% 0.26/0.67 ( ( if_set_val @ $false @ X @ Y2 )
% 0.26/0.67 = Y2 ) ).
% 0.26/0.67
% 0.26/0.67 thf(help_If_1_1_If_001t__Set__Oset_Itf__val_J_T,axiom,
% 0.26/0.67 ! [X: set_val,Y2: set_val] :
% 0.26/0.67 ( ( if_set_val @ $true @ X @ Y2 )
% 0.26/0.67 = X ) ).
% 0.26/0.67
% 0.26/0.67 thf(help_If_2_1_If_001_062_I_Eo_Mt__Set__Oset_Itf__val_J_J_T,axiom,
% 0.26/0.67 ! [X: $o > set_val,Y2: $o > set_val] :
% 0.26/0.67 ( ( if_o_set_val @ $false @ X @ Y2 )
% 0.26/0.67 = Y2 ) ).
% 0.26/0.67
% 0.26/0.67 thf(help_If_1_1_If_001_062_I_Eo_Mt__Set__Oset_Itf__val_J_J_T,axiom,
% 0.26/0.67 ! [X: $o > set_val,Y2: $o > set_val] :
% 0.26/0.67 ( ( if_o_set_val @ $true @ X @ Y2 )
% 0.26/0.67 = X ) ).
% 0.26/0.67
% 0.26/0.67 thf(help_If_3_1_If_001t__Set__Oset_It__Set__Oset_Itf__val_J_J_T,axiom,
% 0.26/0.67 ! [P: $o] :
% 0.26/0.67 ( ( P = $true )
% 0.26/0.67 | ( P = $false ) ) ).
% 0.26/0.67
% 0.26/0.67 thf(help_If_2_1_If_001t__Set__Oset_It__Set__Oset_Itf__val_J_J_T,axiom,
% 0.26/0.67 ! [X: set_set_val,Y2: set_set_val] :
% 0.26/0.67 ( ( if_set_set_val @ $false @ X @ Y2 )
% 0.26/0.67 = Y2 ) ).
% 0.26/0.67
% 0.26/0.67 thf(help_If_1_1_If_001t__Set__Oset_It__Set__Oset_Itf__val_J_J_T,axiom,
% 0.26/0.67 ! [X: set_set_val,Y2: set_set_val] :
% 0.26/0.67 ( ( if_set_set_val @ $true @ X @ Y2 )
% 0.26/0.67 = X ) ).
% 0.26/0.67
% 0.26/0.67 % Conjectures (1)
% 0.26/0.67 thf(conj_0,conjecture,
% 0.26/0.67 ord_less_eq_set_val @ scc @ p ).
% 0.26/0.67
% 0.26/0.67 %------------------------------------------------------------------------------
% 0.26/0.67 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.ljPqlPmDHj/cvc5---1.0.5_27339.p...
% 0.26/0.67 (declare-sort $$unsorted 0)
% 0.26/0.67 (declare-sort tptp.set_set_set_val 0)
% 0.26/0.67 (declare-sort tptp.set_set_val 0)
% 0.26/0.67 (declare-sort tptp.set_val 0)
% 0.26/0.67 (declare-sort tptp.val 0)
% 0.26/0.67 (declare-fun tptp.uminus1961393973et_val (tptp.set_val) tptp.set_val)
% 0.26/0.67 (declare-fun tptp.if_o_set_val (Bool (-> Bool tptp.set_val) (-> Bool tptp.set_val) Bool) tptp.set_val)
% 0.26/0.67 (declare-fun tptp.if_set_set_val (Bool tptp.set_set_val tptp.set_set_val) tptp.set_set_val)
% 0.26/0.67 (declare-fun tptp.if_set_val (Bool tptp.set_val tptp.set_val) tptp.set_val)
% 0.26/0.67 (declare-fun tptp.if_val (Bool tptp.val tptp.val) tptp.val)
% 0.26/0.67 (declare-fun tptp.sup_sup_set_val (tptp.set_val tptp.set_val) tptp.set_val)
% 0.26/0.67 (declare-fun tptp.ord_less_set_set_val (tptp.set_set_val tptp.set_set_val) Bool)
% 0.26/0.67 (declare-fun tptp.ord_less_set_val (tptp.set_val tptp.set_val) Bool)
% 0.26/0.67 (declare-fun tptp.ord_less_val (tptp.val tptp.val) Bool)
% 0.26/0.67 (declare-fun tptp.ord_le1441829300et_val ((-> Bool Bool tptp.set_val) (-> Bool Bool tptp.set_val)) Bool)
% 0.26/0.67 (declare-fun tptp.ord_le936627147et_val ((-> Bool tptp.set_set_val) (-> Bool tptp.set_set_val)) Bool)
% 0.26/0.67 (declare-fun tptp.ord_le994826475et_val ((-> Bool tptp.set_val) (-> Bool tptp.set_val)) Bool)
% 0.26/0.67 (declare-fun tptp.ord_less_eq_o_val ((-> Bool tptp.val) (-> Bool tptp.val)) Bool)
% 0.26/0.67 (declare-fun tptp.ord_le1135847966et_val (tptp.set_set_set_val tptp.set_set_set_val) Bool)
% 0.26/0.67 (declare-fun tptp.ord_le1742111550et_val (tptp.set_set_val tptp.set_set_val) Bool)
% 0.26/0.67 (declare-fun tptp.ord_less_eq_set_val (tptp.set_val tptp.set_val) Bool)
% 0.26/0.67 (declare-fun tptp.ord_less_eq_val (tptp.val tptp.val) Bool)
% 0.26/0.67 (declare-fun tptp.order_985126002et_val ((-> (-> Bool tptp.set_val) Bool) Bool) tptp.set_val)
% 0.26/0.67 (declare-fun tptp.order_544136439et_val ((-> tptp.set_set_val Bool)) tptp.set_set_val)
% 0.26/0.67 (declare-fun tptp.order_1960465943et_val ((-> tptp.set_val Bool)) tptp.set_val)
% 0.26/0.67 (declare-fun tptp.order_Greatest_val ((-> tptp.val Bool)) tptp.val)
% 0.26/0.67 (declare-fun tptp.order_23236447al_val ((-> (-> Bool tptp.set_val) tptp.val)) Bool)
% 0.26/0.67 (declare-fun tptp.order_650823122et_val ((-> tptp.set_set_val tptp.set_val)) Bool)
% 0.26/0.67 (declare-fun tptp.order_1520822002al_val ((-> tptp.set_set_val tptp.val)) Bool)
% 0.26/0.67 (declare-fun tptp.order_1957703570et_val ((-> tptp.set_val tptp.set_set_val)) Bool)
% 0.26/0.67 (declare-fun tptp.order_1719375026et_val ((-> tptp.set_val tptp.set_val)) Bool)
% 0.26/0.67 (declare-fun tptp.order_1375876562al_val ((-> tptp.set_val tptp.val)) Bool)
% 0.26/0.67 (declare-fun tptp.order_255079095et_val ((-> tptp.val Bool tptp.set_val)) Bool)
% 0.26/0.67 (declare-fun tptp.order_1945059954et_val ((-> tptp.val tptp.set_set_val)) Bool)
% 0.26/0.67 (declare-fun tptp.order_1484138386et_val ((-> tptp.val tptp.set_val)) Bool)
% 0.26/0.67 (declare-fun tptp.order_1689798834al_val ((-> tptp.val tptp.val)) Bool)
% 0.26/0.67 (declare-fun tptp.order_1205732848et_val ((-> tptp.val Bool tptp.set_val)) Bool)
% 0.26/0.67 (declare-fun tptp.order_68692473et_val ((-> tptp.val tptp.set_set_val)) Bool)
% 0.26/0.67 (declare-fun tptp.order_99134233et_val ((-> tptp.val tptp.set_val)) Bool)
% 0.26/0.67 (declare-fun tptp.order_1139042361al_val ((-> tptp.val tptp.val)) Bool)
% 0.26/0.67 (declare-fun tptp.refine1593386065et_val ((-> Bool tptp.set_val) (-> Bool tptp.set_val)) Bool)
% 0.26/0.67 (declare-fun tptp.refine1034950713et_val (tptp.set_set_val tptp.set_set_val) Bool)
% 0.26/0.67 (declare-fun tptp.refine654574649et_val (tptp.set_val tptp.set_val) Bool)
% 0.26/0.67 (declare-fun tptp.refine2021912633al_val (tptp.val tptp.val) Bool)
% 0.26/0.67 (declare-fun tptp.refine511606705et_val ((-> Bool tptp.set_val) (-> Bool tptp.set_val)) Bool)
% 0.26/0.67 (declare-fun tptp.refine1908789496et_val (tptp.set_set_val tptp.set_set_val) Bool)
% 0.26/0.67 (declare-fun tptp.refine1893322264et_val (tptp.set_val tptp.set_val) Bool)
% 0.26/0.67 (declare-fun tptp.refine403244856MP_val (tptp.val tptp.val) Bool)
% 0.26/0.67 (declare-fun tptp.refine1924899106et_val ((-> (-> Bool tptp.set_val) Bool tptp.set_val) (-> (-> Bool tptp.set_val) Bool tptp.set_val)) Bool)
% 0.26/0.67 (declare-fun tptp.refine1169396807et_val ((-> (-> Bool tptp.set_val) tptp.set_set_val) (-> tptp.set_set_val Bool tptp.set_val)) Bool)
% 0.26/0.67 (declare-fun tptp.refine1948536167et_val ((-> (-> Bool tptp.set_val) tptp.set_val) (-> tptp.set_val Bool tptp.set_val)) Bool)
% 0.26/0.67 (declare-fun tptp.refine86398879et_val ((-> tptp.set_set_val Bool tptp.set_val) (-> (-> Bool tptp.set_val) tptp.set_set_val)) Bool)
% 0.26/0.67 (declare-fun tptp.refine855985034et_val ((-> tptp.set_set_val tptp.set_set_val) (-> tptp.set_set_val tptp.set_set_val)) Bool)
% 0.26/0.67 (declare-fun tptp.refine8163498et_val ((-> tptp.set_set_val tptp.set_val) (-> tptp.set_val tptp.set_set_val)) Bool)
% 0.26/0.67 (declare-fun tptp.refine51544255et_val ((-> tptp.set_val Bool tptp.set_val) (-> (-> Bool tptp.set_val) tptp.set_val)) Bool)
% 0.26/0.67 (declare-fun tptp.refine1315043946et_val ((-> tptp.set_val tptp.set_set_val) (-> tptp.set_set_val tptp.set_val)) Bool)
% 0.26/0.67 (declare-fun tptp.refine1929691018et_val ((-> tptp.set_val tptp.set_val) (-> tptp.set_val tptp.set_val)) Bool)
% 0.26/0.67 (declare-fun tptp.refine2057434761et_val ((-> tptp.set_val tptp.set_val)) Bool)
% 0.26/0.67 (declare-fun tptp.refine16560100et_val ((-> (-> Bool tptp.set_val) (-> Bool tptp.set_val) Bool)) Bool)
% 0.26/0.67 (declare-fun tptp.refine1506227973et_val ((-> tptp.set_set_val tptp.set_set_val Bool)) Bool)
% 0.26/0.67 (declare-fun tptp.refine275900453et_val ((-> tptp.set_val tptp.set_val Bool)) Bool)
% 0.26/0.67 (declare-fun tptp.refine67622213oc_val ((-> tptp.val tptp.val Bool)) Bool)
% 0.26/0.67 (declare-fun tptp.collect_set_val ((-> tptp.set_val Bool)) tptp.set_set_val)
% 0.26/0.67 (declare-fun tptp.collect_val ((-> tptp.val Bool)) tptp.set_val)
% 0.26/0.67 (declare-fun tptp.set_or1554624499et_val (tptp.set_val tptp.set_val) tptp.set_set_val)
% 0.26/0.67 (declare-fun tptp.set_or18208019st_val (tptp.val tptp.val) tptp.set_val)
% 0.26/0.67 (declare-fun tptp.set_or1337784553et_val (tptp.set_set_val) tptp.set_set_set_val)
% 0.26/0.67 (declare-fun tptp.set_or650197513et_val (tptp.set_val) tptp.set_set_val)
% 0.26/0.67 (declare-fun tptp.set_ord_atLeast_val (tptp.val) tptp.set_val)
% 0.26/0.67 (declare-fun tptp.set_or867701765et_val (tptp.set_val) tptp.set_set_val)
% 0.26/0.67 (declare-fun tptp.set_ord_atMost_val (tptp.val) tptp.set_val)
% 0.26/0.67 (declare-fun tptp.set_or2126567818an_val (tptp.val tptp.val) tptp.set_val)
% 0.26/0.67 (declare-fun tptp.set_or1288365508an_val (tptp.val) tptp.set_val)
% 0.26/0.67 (declare-fun tptp.set_ord_lessThan_val (tptp.val) tptp.set_val)
% 0.26/0.67 (declare-fun tptp.member_set_val (tptp.set_val tptp.set_set_val) Bool)
% 0.26/0.67 (declare-fun tptp.member_val (tptp.val tptp.set_val) Bool)
% 0.26/0.67 (declare-fun tptp.p () tptp.set_val)
% 0.26/0.67 (declare-fun tptp.scc () tptp.set_val)
% 0.26/0.67 (assert (forall ((X tptp.val)) (let ((_let_1 (@ tptp.member_val X))) (=> (@ _let_1 tptp.scc) (@ _let_1 tptp.p)))))
% 0.26/0.67 (assert (forall ((A tptp.set_set_val) (B tptp.set_set_val)) (=> (forall ((X2 tptp.set_val)) (let ((_let_1 (@ tptp.member_set_val X2))) (=> (@ _let_1 A) (@ _let_1 B)))) (@ (@ tptp.ord_le1742111550et_val A) B))))
% 0.26/0.67 (assert (forall ((A tptp.set_val) (B tptp.set_val)) (=> (forall ((X2 tptp.val)) (let ((_let_1 (@ tptp.member_val X2))) (=> (@ _let_1 A) (@ _let_1 B)))) (@ (@ tptp.ord_less_eq_set_val A) B))))
% 0.26/0.67 (assert (forall ((A tptp.set_set_val) (B tptp.set_set_val)) (=> (@ (@ tptp.ord_le1742111550et_val A) B) (=> (@ (@ tptp.ord_le1742111550et_val B) A) (= A B)))))
% 0.26/0.67 (assert (forall ((A tptp.set_val) (B tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val A) B) (=> (@ (@ tptp.ord_less_eq_set_val B) A) (= A B)))))
% 0.26/0.67 (assert (forall ((X (-> Bool tptp.set_val))) (@ (@ tptp.ord_le994826475et_val X) X)))
% 0.26/0.67 (assert (forall ((X tptp.val)) (@ (@ tptp.ord_less_eq_val X) X)))
% 0.26/0.67 (assert (forall ((X tptp.set_set_val)) (@ (@ tptp.ord_le1742111550et_val X) X)))
% 0.26/0.67 (assert (forall ((X tptp.set_val)) (@ (@ tptp.ord_less_eq_set_val X) X)))
% 0.26/0.67 (assert (forall ((R tptp.set_set_val) (R2 tptp.set_set_val)) (let ((_let_1 (@ (@ tptp.ord_le1742111550et_val R) R2))) (=> _let_1 _let_1))))
% 0.26/0.67 (assert (forall ((R tptp.set_val) (R2 tptp.set_val)) (let ((_let_1 (@ (@ tptp.ord_less_eq_set_val R) R2))) (=> _let_1 _let_1))))
% 0.26/0.67 (assert (forall ((A tptp.set_set_val) (B tptp.set_set_val) (X tptp.set_val)) (let ((_let_1 (@ tptp.member_set_val X))) (=> (@ (@ tptp.ord_le1742111550et_val A) B) (=> (@ _let_1 A) (@ _let_1 B))))))
% 0.26/0.67 (assert (forall ((A tptp.set_val) (B tptp.set_val) (X tptp.val)) (let ((_let_1 (@ tptp.member_val X))) (=> (@ (@ tptp.ord_less_eq_set_val A) B) (=> (@ _let_1 A) (@ _let_1 B))))))
% 0.26/0.67 (assert (forall ((A tptp.set_set_val) (B tptp.set_set_val) (C tptp.set_val)) (let ((_let_1 (@ tptp.member_set_val C))) (=> (@ (@ tptp.ord_le1742111550et_val A) B) (=> (@ _let_1 A) (@ _let_1 B))))))
% 0.26/0.67 (assert (forall ((A tptp.set_val) (B tptp.set_val) (C tptp.val)) (let ((_let_1 (@ tptp.member_val C))) (=> (@ (@ tptp.ord_less_eq_set_val A) B) (=> (@ _let_1 A) (@ _let_1 B))))))
% 0.26/0.67 (assert (forall ((A tptp.set_set_val) (B tptp.set_set_val)) (=> (= A B) (not (=> (@ (@ tptp.ord_le1742111550et_val A) B) (not (@ (@ tptp.ord_le1742111550et_val B) A)))))))
% 0.26/0.67 (assert (forall ((A tptp.set_val) (B tptp.set_val)) (=> (= A B) (not (=> (@ (@ tptp.ord_less_eq_set_val A) B) (not (@ (@ tptp.ord_less_eq_set_val B) A)))))))
% 0.26/0.67 (assert (= tptp.ord_le1742111550et_val (lambda ((A2 tptp.set_set_val) (B2 tptp.set_set_val)) (forall ((X3 tptp.set_val)) (let ((_let_1 (@ tptp.member_set_val X3))) (=> (@ _let_1 A2) (@ _let_1 B2)))))))
% 0.26/0.67 (assert (= tptp.ord_less_eq_set_val (lambda ((A2 tptp.set_val) (B2 tptp.set_val)) (forall ((X3 tptp.val)) (let ((_let_1 (@ tptp.member_val X3))) (=> (@ _let_1 A2) (@ _let_1 B2)))))))
% 0.26/0.67 (assert (forall ((A tptp.set_set_val) (B tptp.set_set_val)) (=> (= A B) (@ (@ tptp.ord_le1742111550et_val A) B))))
% 0.26/0.67 (assert (forall ((A tptp.set_val) (B tptp.set_val)) (=> (= A B) (@ (@ tptp.ord_less_eq_set_val A) B))))
% 0.26/0.67 (assert (forall ((A tptp.set_set_val) (B tptp.set_set_val)) (=> (= A B) (@ (@ tptp.ord_le1742111550et_val B) A))))
% 0.26/0.67 (assert (forall ((A tptp.set_val) (B tptp.set_val)) (=> (= A B) (@ (@ tptp.ord_less_eq_set_val B) A))))
% 0.26/0.67 (assert (= tptp.ord_le1742111550et_val (lambda ((A2 tptp.set_set_val) (B2 tptp.set_set_val)) (forall ((T tptp.set_val)) (let ((_let_1 (@ tptp.member_set_val T))) (=> (@ _let_1 A2) (@ _let_1 B2)))))))
% 0.26/0.67 (assert (= tptp.ord_less_eq_set_val (lambda ((A2 tptp.set_val) (B2 tptp.set_val)) (forall ((T tptp.val)) (let ((_let_1 (@ tptp.member_val T))) (=> (@ _let_1 A2) (@ _let_1 B2)))))))
% 0.26/0.67 (assert (forall ((A tptp.set_set_val)) (@ (@ tptp.ord_le1742111550et_val A) A)))
% 0.26/0.67 (assert (forall ((A tptp.set_val)) (@ (@ tptp.ord_less_eq_set_val A) A)))
% 0.26/0.67 (assert (forall ((T2 (-> Bool tptp.set_val)) (T3 (-> Bool tptp.set_val)) (E (-> Bool tptp.set_val)) (E2 (-> Bool tptp.set_val)) (B3 Bool)) (let ((_let_1 (@ tptp.if_o_set_val B3))) (=> (@ (@ tptp.ord_le994826475et_val T2) T3) (=> (@ (@ tptp.ord_le994826475et_val E) E2) (@ (@ tptp.ord_le994826475et_val (@ (@ _let_1 T2) E)) (@ (@ _let_1 T3) E2)))))))
% 0.26/0.67 (assert (forall ((T2 tptp.val) (T3 tptp.val) (E tptp.val) (E2 tptp.val) (B3 Bool)) (let ((_let_1 (@ tptp.if_val B3))) (=> (@ (@ tptp.ord_less_eq_val T2) T3) (=> (@ (@ tptp.ord_less_eq_val E) E2) (@ (@ tptp.ord_less_eq_val (@ (@ _let_1 T2) E)) (@ (@ _let_1 T3) E2)))))))
% 0.26/0.67 (assert (forall ((T2 tptp.set_set_val) (T3 tptp.set_set_val) (E tptp.set_set_val) (E2 tptp.set_set_val) (B3 Bool)) (let ((_let_1 (@ tptp.if_set_set_val B3))) (=> (@ (@ tptp.ord_le1742111550et_val T2) T3) (=> (@ (@ tptp.ord_le1742111550et_val E) E2) (@ (@ tptp.ord_le1742111550et_val (@ (@ _let_1 T2) E)) (@ (@ _let_1 T3) E2)))))))
% 0.26/0.67 (assert (forall ((T2 tptp.set_val) (T3 tptp.set_val) (E tptp.set_val) (E2 tptp.set_val) (B3 Bool)) (let ((_let_1 (@ tptp.if_set_val B3))) (=> (@ (@ tptp.ord_less_eq_set_val T2) T3) (=> (@ (@ tptp.ord_less_eq_set_val E) E2) (@ (@ tptp.ord_less_eq_set_val (@ (@ _let_1 T2) E)) (@ (@ _let_1 T3) E2)))))))
% 0.26/0.67 (assert (forall ((P (-> tptp.set_val Bool)) (Q (-> tptp.set_val Bool))) (= (@ (@ tptp.ord_le1742111550et_val (@ tptp.collect_set_val P)) (@ tptp.collect_set_val Q)) (forall ((X3 tptp.set_val)) (=> (@ P X3) (@ Q X3))))))
% 0.26/0.67 (assert (forall ((P (-> tptp.val Bool)) (Q (-> tptp.val Bool))) (= (@ (@ tptp.ord_less_eq_set_val (@ tptp.collect_val P)) (@ tptp.collect_val Q)) (forall ((X3 tptp.val)) (=> (@ P X3) (@ Q X3))))))
% 0.26/0.67 (assert (= (lambda ((Y tptp.set_set_val) (Z tptp.set_set_val)) (= Y Z)) (lambda ((A2 tptp.set_set_val) (B2 tptp.set_set_val)) (and (@ (@ tptp.ord_le1742111550et_val A2) B2) (@ (@ tptp.ord_le1742111550et_val B2) A2)))))
% 0.26/0.67 (assert (= (lambda ((Y tptp.set_val) (Z tptp.set_val)) (= Y Z)) (lambda ((A2 tptp.set_val) (B2 tptp.set_val)) (and (@ (@ tptp.ord_less_eq_set_val A2) B2) (@ (@ tptp.ord_less_eq_set_val B2) A2)))))
% 0.26/0.67 (assert (forall ((A tptp.set_set_val) (B tptp.set_set_val) (C2 tptp.set_set_val)) (let ((_let_1 (@ tptp.ord_le1742111550et_val A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_le1742111550et_val B) C2) (@ _let_1 C2))))))
% 0.26/0.67 (assert (forall ((A tptp.set_val) (B tptp.set_val) (C2 tptp.set_val)) (let ((_let_1 (@ tptp.ord_less_eq_set_val A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_set_val B) C2) (@ _let_1 C2))))))
% 0.26/0.67 (assert (forall ((P (-> tptp.set_val Bool)) (Q (-> tptp.set_val Bool))) (=> (forall ((X2 tptp.set_val)) (=> (@ P X2) (@ Q X2))) (@ (@ tptp.ord_le1742111550et_val (@ tptp.collect_set_val P)) (@ tptp.collect_set_val Q)))))
% 0.26/0.67 (assert (forall ((P (-> tptp.val Bool)) (Q (-> tptp.val Bool))) (=> (forall ((X2 tptp.val)) (=> (@ P X2) (@ Q X2))) (@ (@ tptp.ord_less_eq_set_val (@ tptp.collect_val P)) (@ tptp.collect_val Q)))))
% 0.26/0.67 (assert (forall ((S tptp.set_set_val) (P (-> tptp.set_val Bool))) (= (@ (@ tptp.ord_le1742111550et_val S) (@ tptp.collect_set_val P)) (forall ((X3 tptp.set_val)) (=> (@ (@ tptp.member_set_val X3) S) (@ P X3))))))
% 0.26/0.67 (assert (forall ((S tptp.set_val) (P (-> tptp.val Bool))) (= (@ (@ tptp.ord_less_eq_set_val S) (@ tptp.collect_val P)) (forall ((X3 tptp.val)) (=> (@ (@ tptp.member_val X3) S) (@ P X3))))))
% 0.26/0.67 (assert (forall ((B3 (-> Bool tptp.set_val)) (A3 (-> Bool tptp.set_val))) (=> (@ (@ tptp.ord_le994826475et_val B3) A3) (=> (@ (@ tptp.ord_le994826475et_val A3) B3) (= A3 B3)))))
% 0.26/0.67 (assert (forall ((B3 tptp.val) (A3 tptp.val)) (=> (@ (@ tptp.ord_less_eq_val B3) A3) (=> (@ (@ tptp.ord_less_eq_val A3) B3) (= A3 B3)))))
% 0.26/0.67 (assert (forall ((B3 tptp.set_set_val) (A3 tptp.set_set_val)) (=> (@ (@ tptp.ord_le1742111550et_val B3) A3) (=> (@ (@ tptp.ord_le1742111550et_val A3) B3) (= A3 B3)))))
% 0.26/0.67 (assert (forall ((B3 tptp.set_val) (A3 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val B3) A3) (=> (@ (@ tptp.ord_less_eq_set_val A3) B3) (= A3 B3)))))
% 0.26/0.67 (assert (= (lambda ((Y (-> Bool tptp.set_val)) (Z (-> Bool tptp.set_val))) (= Y Z)) (lambda ((A4 (-> Bool tptp.set_val)) (B4 (-> Bool tptp.set_val))) (and (@ (@ tptp.ord_le994826475et_val B4) A4) (@ (@ tptp.ord_le994826475et_val A4) B4)))))
% 0.26/0.67 (assert (= (lambda ((Y tptp.val) (Z tptp.val)) (= Y Z)) (lambda ((A4 tptp.val) (B4 tptp.val)) (and (@ (@ tptp.ord_less_eq_val B4) A4) (@ (@ tptp.ord_less_eq_val A4) B4)))))
% 0.26/0.67 (assert (= (lambda ((Y tptp.set_set_val) (Z tptp.set_set_val)) (= Y Z)) (lambda ((A4 tptp.set_set_val) (B4 tptp.set_set_val)) (and (@ (@ tptp.ord_le1742111550et_val B4) A4) (@ (@ tptp.ord_le1742111550et_val A4) B4)))))
% 0.26/0.67 (assert (= (lambda ((Y tptp.set_val) (Z tptp.set_val)) (= Y Z)) (lambda ((A4 tptp.set_val) (B4 tptp.set_val)) (and (@ (@ tptp.ord_less_eq_set_val B4) A4) (@ (@ tptp.ord_less_eq_set_val A4) B4)))))
% 0.26/0.67 (assert (forall ((B3 (-> Bool tptp.set_val)) (A3 (-> Bool tptp.set_val)) (C (-> Bool tptp.set_val))) (let ((_let_1 (@ tptp.ord_le994826475et_val C))) (=> (@ (@ tptp.ord_le994826475et_val B3) A3) (=> (@ _let_1 B3) (@ _let_1 A3))))))
% 0.26/0.67 (assert (forall ((B3 tptp.val) (A3 tptp.val) (C tptp.val)) (let ((_let_1 (@ tptp.ord_less_eq_val C))) (=> (@ (@ tptp.ord_less_eq_val B3) A3) (=> (@ _let_1 B3) (@ _let_1 A3))))))
% 0.26/0.67 (assert (forall ((B3 tptp.set_set_val) (A3 tptp.set_set_val) (C tptp.set_set_val)) (let ((_let_1 (@ tptp.ord_le1742111550et_val C))) (=> (@ (@ tptp.ord_le1742111550et_val B3) A3) (=> (@ _let_1 B3) (@ _let_1 A3))))))
% 0.26/0.67 (assert (forall ((B3 tptp.set_val) (A3 tptp.set_val) (C tptp.set_val)) (let ((_let_1 (@ tptp.ord_less_eq_set_val C))) (=> (@ (@ tptp.ord_less_eq_set_val B3) A3) (=> (@ _let_1 B3) (@ _let_1 A3))))))
% 0.26/0.67 (assert (forall ((P (-> tptp.val tptp.val Bool)) (A3 tptp.val) (B3 tptp.val)) (=> (forall ((A5 tptp.val) (B5 tptp.val)) (=> (@ (@ tptp.ord_less_eq_val A5) B5) (@ (@ P A5) B5))) (=> (forall ((A5 tptp.val) (B5 tptp.val)) (=> (@ (@ P B5) A5) (@ (@ P A5) B5))) (@ (@ P A3) B3)))))
% 0.26/0.67 (assert (forall ((A3 (-> Bool tptp.set_val))) (@ (@ tptp.ord_le994826475et_val A3) A3)))
% 0.26/0.67 (assert (forall ((A3 tptp.val)) (@ (@ tptp.ord_less_eq_val A3) A3)))
% 0.26/0.67 (assert (forall ((A3 tptp.set_set_val)) (@ (@ tptp.ord_le1742111550et_val A3) A3)))
% 0.26/0.67 (assert (forall ((A3 tptp.set_val)) (@ (@ tptp.ord_less_eq_set_val A3) A3)))
% 0.26/0.67 (assert (forall ((X (-> Bool tptp.set_val)) (Y2 (-> Bool tptp.set_val)) (Z2 (-> Bool tptp.set_val))) (let ((_let_1 (@ tptp.ord_le994826475et_val X))) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_le994826475et_val Y2) Z2) (@ _let_1 Z2))))))
% 0.26/0.67 (assert (forall ((X tptp.val) (Y2 tptp.val) (Z2 tptp.val)) (let ((_let_1 (@ tptp.ord_less_eq_val X))) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_eq_val Y2) Z2) (@ _let_1 Z2))))))
% 0.26/0.67 (assert (forall ((X tptp.set_set_val) (Y2 tptp.set_set_val) (Z2 tptp.set_set_val)) (let ((_let_1 (@ tptp.ord_le1742111550et_val X))) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_le1742111550et_val Y2) Z2) (@ _let_1 Z2))))))
% 0.26/0.67 (assert (forall ((X tptp.set_val) (Y2 tptp.set_val) (Z2 tptp.set_val)) (let ((_let_1 (@ tptp.ord_less_eq_set_val X))) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_eq_set_val Y2) Z2) (@ _let_1 Z2))))))
% 0.26/0.67 (assert (forall ((A3 (-> Bool tptp.set_val)) (B3 (-> Bool tptp.set_val))) (=> (@ (@ tptp.ord_le994826475et_val A3) B3) (=> (@ (@ tptp.ord_le994826475et_val B3) A3) (= A3 B3)))))
% 0.26/0.67 (assert (forall ((A3 tptp.val) (B3 tptp.val)) (=> (@ (@ tptp.ord_less_eq_val A3) B3) (=> (@ (@ tptp.ord_less_eq_val B3) A3) (= A3 B3)))))
% 0.26/0.67 (assert (forall ((A3 tptp.set_set_val) (B3 tptp.set_set_val)) (=> (@ (@ tptp.ord_le1742111550et_val A3) B3) (=> (@ (@ tptp.ord_le1742111550et_val B3) A3) (= A3 B3)))))
% 0.26/0.67 (assert (forall ((A3 tptp.set_val) (B3 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val A3) B3) (=> (@ (@ tptp.ord_less_eq_set_val B3) A3) (= A3 B3)))))
% 0.26/0.67 (assert (forall ((A3 (-> Bool tptp.set_val)) (B3 (-> Bool tptp.set_val)) (C (-> Bool tptp.set_val))) (let ((_let_1 (@ tptp.ord_le994826475et_val A3))) (=> (@ _let_1 B3) (=> (= B3 C) (@ _let_1 C))))))
% 0.26/0.67 (assert (forall ((A3 tptp.val) (B3 tptp.val) (C tptp.val)) (let ((_let_1 (@ tptp.ord_less_eq_val A3))) (=> (@ _let_1 B3) (=> (= B3 C) (@ _let_1 C))))))
% 0.26/0.67 (assert (forall ((A3 tptp.set_set_val) (B3 tptp.set_set_val) (C tptp.set_set_val)) (let ((_let_1 (@ tptp.ord_le1742111550et_val A3))) (=> (@ _let_1 B3) (=> (= B3 C) (@ _let_1 C))))))
% 0.26/0.67 (assert (forall ((A3 tptp.set_val) (B3 tptp.set_val) (C tptp.set_val)) (let ((_let_1 (@ tptp.ord_less_eq_set_val A3))) (=> (@ _let_1 B3) (=> (= B3 C) (@ _let_1 C))))))
% 0.26/0.67 (assert (forall ((F (-> Bool tptp.set_val)) (G (-> Bool tptp.set_val)) (X Bool)) (=> (@ (@ tptp.ord_le994826475et_val F) G) (@ (@ tptp.ord_less_eq_set_val (@ F X)) (@ G X)))))
% 0.26/0.67 (assert (forall ((F (-> Bool tptp.set_val)) (G (-> Bool tptp.set_val)) (X Bool)) (=> (@ (@ tptp.ord_le994826475et_val F) G) (@ (@ tptp.ord_less_eq_set_val (@ F X)) (@ G X)))))
% 0.26/0.67 (assert (forall ((F (-> Bool tptp.set_val)) (G (-> Bool tptp.set_val))) (=> (forall ((X2 Bool)) (@ (@ tptp.ord_less_eq_set_val (@ F X2)) (@ G X2))) (@ (@ tptp.ord_le994826475et_val F) G))))
% 0.26/0.67 (assert (= tptp.ord_le994826475et_val (lambda ((F2 (-> Bool tptp.set_val)) (G2 (-> Bool tptp.set_val))) (forall ((X3 Bool)) (@ (@ tptp.ord_less_eq_set_val (@ F2 X3)) (@ G2 X3))))))
% 0.26/0.67 (assert (forall ((A3 tptp.set_val) (F (-> tptp.set_val tptp.set_val)) (B3 tptp.set_val) (C tptp.set_val)) (let ((_let_1 (@ tptp.ord_less_eq_set_val A3))) (=> (@ _let_1 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_set_val B3) C) (=> (forall ((X2 tptp.set_val) (Y3 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val X2) Y3) (@ (@ tptp.ord_less_eq_set_val (@ F X2)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 0.26/0.67 (assert (forall ((A3 tptp.val) (F (-> tptp.val tptp.val)) (B3 tptp.val) (C tptp.val)) (let ((_let_1 (@ tptp.ord_less_eq_val A3))) (=> (@ _let_1 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_val B3) C) (=> (forall ((X2 tptp.val) (Y3 tptp.val)) (=> (@ (@ tptp.ord_less_eq_val X2) Y3) (@ (@ tptp.ord_less_eq_val (@ F X2)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 0.26/0.67 (assert (forall ((A3 tptp.set_val) (F (-> tptp.val tptp.set_val)) (B3 tptp.val) (C tptp.val)) (let ((_let_1 (@ tptp.ord_less_eq_set_val A3))) (=> (@ _let_1 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_val B3) C) (=> (forall ((X2 tptp.val) (Y3 tptp.val)) (=> (@ (@ tptp.ord_less_eq_val X2) Y3) (@ (@ tptp.ord_less_eq_set_val (@ F X2)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 0.26/0.67 (assert (forall ((A3 tptp.val) (F (-> tptp.set_val tptp.val)) (B3 tptp.set_val) (C tptp.set_val)) (let ((_let_1 (@ tptp.ord_less_eq_val A3))) (=> (@ _let_1 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_set_val B3) C) (=> (forall ((X2 tptp.set_val) (Y3 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val X2) Y3) (@ (@ tptp.ord_less_eq_val (@ F X2)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 0.26/0.67 (assert (forall ((A3 tptp.val) (F (-> tptp.set_set_val tptp.val)) (B3 tptp.set_set_val) (C tptp.set_set_val)) (let ((_let_1 (@ tptp.ord_less_eq_val A3))) (=> (@ _let_1 (@ F B3)) (=> (@ (@ tptp.ord_le1742111550et_val B3) C) (=> (forall ((X2 tptp.set_set_val) (Y3 tptp.set_set_val)) (=> (@ (@ tptp.ord_le1742111550et_val X2) Y3) (@ (@ tptp.ord_less_eq_val (@ F X2)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 0.26/0.67 (assert (forall ((A3 tptp.set_set_val) (F (-> tptp.val tptp.set_set_val)) (B3 tptp.val) (C tptp.val)) (let ((_let_1 (@ tptp.ord_le1742111550et_val A3))) (=> (@ _let_1 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_val B3) C) (=> (forall ((X2 tptp.val) (Y3 tptp.val)) (=> (@ (@ tptp.ord_less_eq_val X2) Y3) (@ (@ tptp.ord_le1742111550et_val (@ F X2)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 0.26/0.67 (assert (forall ((A3 tptp.set_val) (F (-> tptp.set_set_val tptp.set_val)) (B3 tptp.set_set_val) (C tptp.set_set_val)) (let ((_let_1 (@ tptp.ord_less_eq_set_val A3))) (=> (@ _let_1 (@ F B3)) (=> (@ (@ tptp.ord_le1742111550et_val B3) C) (=> (forall ((X2 tptp.set_set_val) (Y3 tptp.set_set_val)) (=> (@ (@ tptp.ord_le1742111550et_val X2) Y3) (@ (@ tptp.ord_less_eq_set_val (@ F X2)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 0.26/0.67 (assert (forall ((A3 (-> Bool tptp.set_val)) (F (-> tptp.val Bool tptp.set_val)) (B3 tptp.val) (C tptp.val)) (let ((_let_1 (@ tptp.ord_le994826475et_val A3))) (=> (@ _let_1 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_val B3) C) (=> (forall ((X2 tptp.val) (Y3 tptp.val)) (=> (@ (@ tptp.ord_less_eq_val X2) Y3) (@ (@ tptp.ord_le994826475et_val (@ F X2)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 0.26/0.67 (assert (forall ((A3 tptp.val) (F (-> (-> Bool tptp.set_val) tptp.val)) (B3 (-> Bool tptp.set_val)) (C (-> Bool tptp.set_val))) (let ((_let_1 (@ tptp.ord_less_eq_val A3))) (=> (@ _let_1 (@ F B3)) (=> (@ (@ tptp.ord_le994826475et_val B3) C) (=> (forall ((X2 (-> Bool tptp.set_val)) (Y3 (-> Bool tptp.set_val))) (=> (@ (@ tptp.ord_le994826475et_val X2) Y3) (@ (@ tptp.ord_less_eq_val (@ F X2)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 0.26/0.67 (assert (forall ((A3 tptp.set_set_val) (F (-> tptp.set_val tptp.set_set_val)) (B3 tptp.set_val) (C tptp.set_val)) (let ((_let_1 (@ tptp.ord_le1742111550et_val A3))) (=> (@ _let_1 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_set_val B3) C) (=> (forall ((X2 tptp.set_val) (Y3 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val X2) Y3) (@ (@ tptp.ord_le1742111550et_val (@ F X2)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 0.26/0.67 (assert (forall ((A3 tptp.set_val) (B3 tptp.set_val) (F (-> tptp.set_val tptp.set_val)) (C tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val A3) B3) (=> (@ (@ tptp.ord_less_eq_set_val (@ F B3)) C) (=> (forall ((X2 tptp.set_val) (Y3 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val X2) Y3) (@ (@ tptp.ord_less_eq_set_val (@ F X2)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_set_val (@ F A3)) C))))))
% 0.26/0.67 (assert (forall ((A3 tptp.val) (B3 tptp.val) (F (-> tptp.val tptp.val)) (C tptp.val)) (=> (@ (@ tptp.ord_less_eq_val A3) B3) (=> (@ (@ tptp.ord_less_eq_val (@ F B3)) C) (=> (forall ((X2 tptp.val) (Y3 tptp.val)) (=> (@ (@ tptp.ord_less_eq_val X2) Y3) (@ (@ tptp.ord_less_eq_val (@ F X2)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_val (@ F A3)) C))))))
% 0.26/0.67 (assert (forall ((A3 tptp.set_val) (B3 tptp.set_val) (F (-> tptp.set_val tptp.val)) (C tptp.val)) (=> (@ (@ tptp.ord_less_eq_set_val A3) B3) (=> (@ (@ tptp.ord_less_eq_val (@ F B3)) C) (=> (forall ((X2 tptp.set_val) (Y3 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val X2) Y3) (@ (@ tptp.ord_less_eq_val (@ F X2)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_val (@ F A3)) C))))))
% 0.26/0.67 (assert (forall ((A3 tptp.val) (B3 tptp.val) (F (-> tptp.val tptp.set_val)) (C tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_val A3) B3) (=> (@ (@ tptp.ord_less_eq_set_val (@ F B3)) C) (=> (forall ((X2 tptp.val) (Y3 tptp.val)) (=> (@ (@ tptp.ord_less_eq_val X2) Y3) (@ (@ tptp.ord_less_eq_set_val (@ F X2)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_set_val (@ F A3)) C))))))
% 0.26/0.67 (assert (forall ((A3 tptp.val) (B3 tptp.val) (F (-> tptp.val tptp.set_set_val)) (C tptp.set_set_val)) (=> (@ (@ tptp.ord_less_eq_val A3) B3) (=> (@ (@ tptp.ord_le1742111550et_val (@ F B3)) C) (=> (forall ((X2 tptp.val) (Y3 tptp.val)) (=> (@ (@ tptp.ord_less_eq_val X2) Y3) (@ (@ tptp.ord_le1742111550et_val (@ F X2)) (@ F Y3)))) (@ (@ tptp.ord_le1742111550et_val (@ F A3)) C))))))
% 0.26/0.67 (assert (forall ((A3 tptp.set_set_val) (B3 tptp.set_set_val) (F (-> tptp.set_set_val tptp.val)) (C tptp.val)) (=> (@ (@ tptp.ord_le1742111550et_val A3) B3) (=> (@ (@ tptp.ord_less_eq_val (@ F B3)) C) (=> (forall ((X2 tptp.set_set_val) (Y3 tptp.set_set_val)) (=> (@ (@ tptp.ord_le1742111550et_val X2) Y3) (@ (@ tptp.ord_less_eq_val (@ F X2)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_val (@ F A3)) C))))))
% 0.26/0.67 (assert (forall ((A3 tptp.set_val) (B3 tptp.set_val) (F (-> tptp.set_val tptp.set_set_val)) (C tptp.set_set_val)) (=> (@ (@ tptp.ord_less_eq_set_val A3) B3) (=> (@ (@ tptp.ord_le1742111550et_val (@ F B3)) C) (=> (forall ((X2 tptp.set_val) (Y3 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val X2) Y3) (@ (@ tptp.ord_le1742111550et_val (@ F X2)) (@ F Y3)))) (@ (@ tptp.ord_le1742111550et_val (@ F A3)) C))))))
% 0.26/0.67 (assert (forall ((A3 (-> Bool tptp.set_val)) (B3 (-> Bool tptp.set_val)) (F (-> (-> Bool tptp.set_val) tptp.val)) (C tptp.val)) (=> (@ (@ tptp.ord_le994826475et_val A3) B3) (=> (@ (@ tptp.ord_less_eq_val (@ F B3)) C) (=> (forall ((X2 (-> Bool tptp.set_val)) (Y3 (-> Bool tptp.set_val))) (=> (@ (@ tptp.ord_le994826475et_val X2) Y3) (@ (@ tptp.ord_less_eq_val (@ F X2)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_val (@ F A3)) C))))))
% 0.26/0.67 (assert (forall ((A3 tptp.val) (B3 tptp.val) (F (-> tptp.val Bool tptp.set_val)) (C (-> Bool tptp.set_val))) (=> (@ (@ tptp.ord_less_eq_val A3) B3) (=> (@ (@ tptp.ord_le994826475et_val (@ F B3)) C) (=> (forall ((X2 tptp.val) (Y3 tptp.val)) (=> (@ (@ tptp.ord_less_eq_val X2) Y3) (@ (@ tptp.ord_le994826475et_val (@ F X2)) (@ F Y3)))) (@ (@ tptp.ord_le994826475et_val (@ F A3)) C))))))
% 0.26/0.67 (assert (forall ((A3 tptp.set_set_val) (B3 tptp.set_set_val) (F (-> tptp.set_set_val tptp.set_val)) (C tptp.set_val)) (=> (@ (@ tptp.ord_le1742111550et_val A3) B3) (=> (@ (@ tptp.ord_less_eq_set_val (@ F B3)) C) (=> (forall ((X2 tptp.set_set_val) (Y3 tptp.set_set_val)) (=> (@ (@ tptp.ord_le1742111550et_val X2) Y3) (@ (@ tptp.ord_less_eq_set_val (@ F X2)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_set_val (@ F A3)) C))))))
% 0.26/0.67 (assert (forall ((A3 (-> Bool tptp.set_val)) (B3 (-> Bool tptp.set_val)) (C (-> Bool tptp.set_val)) (D (-> Bool tptp.set_val))) (=> (= A3 B3) (=> (@ (@ tptp.ord_le994826475et_val B3) C) (=> (= C D) (@ (@ tptp.ord_le994826475et_val A3) D))))))
% 0.26/0.67 (assert (forall ((A3 tptp.val) (B3 tptp.val) (C tptp.val) (D tptp.val)) (=> (= A3 B3) (=> (@ (@ tptp.ord_less_eq_val B3) C) (=> (= C D) (@ (@ tptp.ord_less_eq_val A3) D))))))
% 0.26/0.67 (assert (forall ((A3 tptp.set_set_val) (B3 tptp.set_set_val) (C tptp.set_set_val) (D tptp.set_set_val)) (=> (= A3 B3) (=> (@ (@ tptp.ord_le1742111550et_val B3) C) (=> (= C D) (@ (@ tptp.ord_le1742111550et_val A3) D))))))
% 0.26/0.67 (assert (forall ((A3 tptp.set_val) (B3 tptp.set_val) (C tptp.set_val) (D tptp.set_val)) (=> (= A3 B3) (=> (@ (@ tptp.ord_less_eq_set_val B3) C) (=> (= C D) (@ (@ tptp.ord_less_eq_set_val A3) D))))))
% 0.26/0.67 (assert (forall ((A3 tptp.set_val) (F (-> tptp.set_val tptp.set_val)) (B3 tptp.set_val) (C tptp.set_val)) (=> (= A3 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_set_val B3) C) (=> (forall ((X2 tptp.set_val) (Y3 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val X2) Y3) (@ (@ tptp.ord_less_eq_set_val (@ F X2)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_set_val A3) (@ F C)))))))
% 0.26/0.67 (assert (forall ((A3 tptp.val) (F (-> tptp.val tptp.val)) (B3 tptp.val) (C tptp.val)) (=> (= A3 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_val B3) C) (=> (forall ((X2 tptp.val) (Y3 tptp.val)) (=> (@ (@ tptp.ord_less_eq_val X2) Y3) (@ (@ tptp.ord_less_eq_val (@ F X2)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_val A3) (@ F C)))))))
% 0.26/0.67 (assert (forall ((A3 tptp.val) (F (-> tptp.set_val tptp.val)) (B3 tptp.set_val) (C tptp.set_val)) (=> (= A3 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_set_val B3) C) (=> (forall ((X2 tptp.set_val) (Y3 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val X2) Y3) (@ (@ tptp.ord_less_eq_val (@ F X2)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_val A3) (@ F C)))))))
% 0.26/0.67 (assert (forall ((A3 tptp.set_val) (F (-> tptp.val tptp.set_val)) (B3 tptp.val) (C tptp.val)) (=> (= A3 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_val B3) C) (=> (forall ((X2 tptp.val) (Y3 tptp.val)) (=> (@ (@ tptp.ord_less_eq_val X2) Y3) (@ (@ tptp.ord_less_eq_set_val (@ F X2)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_set_val A3) (@ F C)))))))
% 0.26/0.67 (assert (forall ((A3 tptp.set_set_val) (F (-> tptp.val tptp.set_set_val)) (B3 tptp.val) (C tptp.val)) (=> (= A3 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_val B3) C) (=> (forall ((X2 tptp.val) (Y3 tptp.val)) (=> (@ (@ tptp.ord_less_eq_val X2) Y3) (@ (@ tptp.ord_le1742111550et_val (@ F X2)) (@ F Y3)))) (@ (@ tptp.ord_le1742111550et_val A3) (@ F C)))))))
% 0.26/0.67 (assert (forall ((A3 tptp.val) (F (-> tptp.set_set_val tptp.val)) (B3 tptp.set_set_val) (C tptp.set_set_val)) (=> (= A3 (@ F B3)) (=> (@ (@ tptp.ord_le1742111550et_val B3) C) (=> (forall ((X2 tptp.set_set_val) (Y3 tptp.set_set_val)) (=> (@ (@ tptp.ord_le1742111550et_val X2) Y3) (@ (@ tptp.ord_less_eq_val (@ F X2)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_val A3) (@ F C)))))))
% 0.26/0.67 (assert (forall ((A3 tptp.set_set_val) (F (-> tptp.set_val tptp.set_set_val)) (B3 tptp.set_val) (C tptp.set_val)) (=> (= A3 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_set_val B3) C) (=> (forall ((X2 tptp.set_val) (Y3 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val X2) Y3) (@ (@ tptp.ord_le1742111550et_val (@ F X2)) (@ F Y3)))) (@ (@ tptp.ord_le1742111550et_val A3) (@ F C)))))))
% 0.26/0.67 (assert (forall ((A3 tptp.val) (F (-> (-> Bool tptp.set_val) tptp.val)) (B3 (-> Bool tptp.set_val)) (C (-> Bool tptp.set_val))) (=> (= A3 (@ F B3)) (=> (@ (@ tptp.ord_le994826475et_val B3) C) (=> (forall ((X2 (-> Bool tptp.set_val)) (Y3 (-> Bool tptp.set_val))) (=> (@ (@ tptp.ord_le994826475et_val X2) Y3) (@ (@ tptp.ord_less_eq_val (@ F X2)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_val A3) (@ F C)))))))
% 0.26/0.67 (assert (forall ((A3 (-> Bool tptp.set_val)) (F (-> tptp.val Bool tptp.set_val)) (B3 tptp.val) (C tptp.val)) (=> (= A3 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_val B3) C) (=> (forall ((X2 tptp.val) (Y3 tptp.val)) (=> (@ (@ tptp.ord_less_eq_val X2) Y3) (@ (@ tptp.ord_le994826475et_val (@ F X2)) (@ F Y3)))) (@ (@ tptp.ord_le994826475et_val A3) (@ F C)))))))
% 0.26/0.67 (assert (forall ((A3 tptp.set_val) (F (-> tptp.set_set_val tptp.set_val)) (B3 tptp.set_set_val) (C tptp.set_set_val)) (=> (= A3 (@ F B3)) (=> (@ (@ tptp.ord_le1742111550et_val B3) C) (=> (forall ((X2 tptp.set_set_val) (Y3 tptp.set_set_val)) (=> (@ (@ tptp.ord_le1742111550et_val X2) Y3) (@ (@ tptp.ord_less_eq_set_val (@ F X2)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_set_val A3) (@ F C)))))))
% 0.26/0.67 (assert (forall ((A3 tptp.set_val) (B3 tptp.set_val) (F (-> tptp.set_val tptp.set_val)) (C tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val A3) B3) (=> (= (@ F B3) C) (=> (forall ((X2 tptp.set_val) (Y3 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val X2) Y3) (@ (@ tptp.ord_less_eq_set_val (@ F X2)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_set_val (@ F A3)) C))))))
% 0.26/0.67 (assert (forall ((A3 tptp.val) (B3 tptp.val) (F (-> tptp.val tptp.val)) (C tptp.val)) (=> (@ (@ tptp.ord_less_eq_val A3) B3) (=> (= (@ F B3) C) (=> (forall ((X2 tptp.val) (Y3 tptp.val)) (=> (@ (@ tptp.ord_less_eq_val X2) Y3) (@ (@ tptp.ord_less_eq_val (@ F X2)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_val (@ F A3)) C))))))
% 0.26/0.67 (assert (forall ((A3 tptp.set_val) (B3 tptp.set_val) (F (-> tptp.set_val tptp.val)) (C tptp.val)) (=> (@ (@ tptp.ord_less_eq_set_val A3) B3) (=> (= (@ F B3) C) (=> (forall ((X2 tptp.set_val) (Y3 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val X2) Y3) (@ (@ tptp.ord_less_eq_val (@ F X2)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_val (@ F A3)) C))))))
% 0.26/0.67 (assert (forall ((A3 tptp.val) (B3 tptp.val) (F (-> tptp.val tptp.set_val)) (C tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_val A3) B3) (=> (= (@ F B3) C) (=> (forall ((X2 tptp.val) (Y3 tptp.val)) (=> (@ (@ tptp.ord_less_eq_val X2) Y3) (@ (@ tptp.ord_less_eq_set_val (@ F X2)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_set_val (@ F A3)) C))))))
% 0.26/0.67 (assert (forall ((A3 tptp.val) (B3 tptp.val) (F (-> tptp.val tptp.set_set_val)) (C tptp.set_set_val)) (=> (@ (@ tptp.ord_less_eq_val A3) B3) (=> (= (@ F B3) C) (=> (forall ((X2 tptp.val) (Y3 tptp.val)) (=> (@ (@ tptp.ord_less_eq_val X2) Y3) (@ (@ tptp.ord_le1742111550et_val (@ F X2)) (@ F Y3)))) (@ (@ tptp.ord_le1742111550et_val (@ F A3)) C))))))
% 0.26/0.67 (assert (forall ((A3 tptp.set_set_val) (B3 tptp.set_set_val) (F (-> tptp.set_set_val tptp.val)) (C tptp.val)) (=> (@ (@ tptp.ord_le1742111550et_val A3) B3) (=> (= (@ F B3) C) (=> (forall ((X2 tptp.set_set_val) (Y3 tptp.set_set_val)) (=> (@ (@ tptp.ord_le1742111550et_val X2) Y3) (@ (@ tptp.ord_less_eq_val (@ F X2)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_val (@ F A3)) C))))))
% 0.26/0.67 (assert (forall ((A3 tptp.set_val) (B3 tptp.set_val) (F (-> tptp.set_val tptp.set_set_val)) (C tptp.set_set_val)) (=> (@ (@ tptp.ord_less_eq_set_val A3) B3) (=> (= (@ F B3) C) (=> (forall ((X2 tptp.set_val) (Y3 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val X2) Y3) (@ (@ tptp.ord_le1742111550et_val (@ F X2)) (@ F Y3)))) (@ (@ tptp.ord_le1742111550et_val (@ F A3)) C))))))
% 0.26/0.67 (assert (forall ((A3 (-> Bool tptp.set_val)) (B3 (-> Bool tptp.set_val)) (F (-> (-> Bool tptp.set_val) tptp.val)) (C tptp.val)) (=> (@ (@ tptp.ord_le994826475et_val A3) B3) (=> (= (@ F B3) C) (=> (forall ((X2 (-> Bool tptp.set_val)) (Y3 (-> Bool tptp.set_val))) (=> (@ (@ tptp.ord_le994826475et_val X2) Y3) (@ (@ tptp.ord_less_eq_val (@ F X2)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_val (@ F A3)) C))))))
% 0.26/0.67 (assert (forall ((A3 tptp.val) (B3 tptp.val) (F (-> tptp.val Bool tptp.set_val)) (C (-> Bool tptp.set_val))) (=> (@ (@ tptp.ord_less_eq_val A3) B3) (=> (= (@ F B3) C) (=> (forall ((X2 tptp.val) (Y3 tptp.val)) (=> (@ (@ tptp.ord_less_eq_val X2) Y3) (@ (@ tptp.ord_le994826475et_val (@ F X2)) (@ F Y3)))) (@ (@ tptp.ord_le994826475et_val (@ F A3)) C))))))
% 0.26/0.67 (assert (forall ((A3 tptp.set_set_val) (B3 tptp.set_set_val) (F (-> tptp.set_set_val tptp.set_val)) (C tptp.set_val)) (=> (@ (@ tptp.ord_le1742111550et_val A3) B3) (=> (= (@ F B3) C) (=> (forall ((X2 tptp.set_set_val) (Y3 tptp.set_set_val)) (=> (@ (@ tptp.ord_le1742111550et_val X2) Y3) (@ (@ tptp.ord_less_eq_set_val (@ F X2)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_set_val (@ F A3)) C))))))
% 0.26/0.67 (assert (= (lambda ((Y (-> Bool tptp.set_val)) (Z (-> Bool tptp.set_val))) (= Y Z)) (lambda ((X3 (-> Bool tptp.set_val)) (Y4 (-> Bool tptp.set_val))) (and (@ (@ tptp.ord_le994826475et_val X3) Y4) (@ (@ tptp.ord_le994826475et_val Y4) X3)))))
% 0.26/0.67 (assert (= (lambda ((Y tptp.val) (Z tptp.val)) (= Y Z)) (lambda ((X3 tptp.val) (Y4 tptp.val)) (and (@ (@ tptp.ord_less_eq_val X3) Y4) (@ (@ tptp.ord_less_eq_val Y4) X3)))))
% 0.26/0.67 (assert (= (lambda ((Y tptp.set_set_val) (Z tptp.set_set_val)) (= Y Z)) (lambda ((X3 tptp.set_set_val) (Y4 tptp.set_set_val)) (and (@ (@ tptp.ord_le1742111550et_val X3) Y4) (@ (@ tptp.ord_le1742111550et_val Y4) X3)))))
% 0.26/0.67 (assert (= (lambda ((Y tptp.set_val) (Z tptp.set_val)) (= Y Z)) (lambda ((X3 tptp.set_val) (Y4 tptp.set_val)) (and (@ (@ tptp.ord_less_eq_set_val X3) Y4) (@ (@ tptp.ord_less_eq_set_val Y4) X3)))))
% 0.26/0.67 (assert (forall ((X (-> Bool tptp.set_val)) (Y2 (-> Bool tptp.set_val))) (=> (@ (@ tptp.ord_le994826475et_val X) Y2) (=> (@ (@ tptp.ord_le994826475et_val Y2) X) (= X Y2)))))
% 0.26/0.67 (assert (forall ((X tptp.val) (Y2 tptp.val)) (=> (@ (@ tptp.ord_less_eq_val X) Y2) (=> (@ (@ tptp.ord_less_eq_val Y2) X) (= X Y2)))))
% 0.26/0.67 (assert (forall ((X tptp.set_set_val) (Y2 tptp.set_set_val)) (=> (@ (@ tptp.ord_le1742111550et_val X) Y2) (=> (@ (@ tptp.ord_le1742111550et_val Y2) X) (= X Y2)))))
% 0.26/0.67 (assert (forall ((X tptp.set_val) (Y2 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val X) Y2) (=> (@ (@ tptp.ord_less_eq_set_val Y2) X) (= X Y2)))))
% 0.26/0.67 (assert (forall ((X tptp.val) (Y2 tptp.val)) (or (@ (@ tptp.ord_less_eq_val X) Y2) (@ (@ tptp.ord_less_eq_val Y2) X))))
% 0.26/0.67 (assert (forall ((X (-> Bool tptp.set_val)) (Y2 (-> Bool tptp.set_val))) (=> (= X Y2) (@ (@ tptp.ord_le994826475et_val X) Y2))))
% 0.26/0.67 (assert (forall ((X tptp.val) (Y2 tptp.val)) (=> (= X Y2) (@ (@ tptp.ord_less_eq_val X) Y2))))
% 0.26/0.67 (assert (forall ((X tptp.set_set_val) (Y2 tptp.set_set_val)) (=> (= X Y2) (@ (@ tptp.ord_le1742111550et_val X) Y2))))
% 0.26/0.67 (assert (forall ((X tptp.set_val) (Y2 tptp.set_val)) (=> (= X Y2) (@ (@ tptp.ord_less_eq_set_val X) Y2))))
% 0.26/0.67 (assert (forall ((X tptp.val) (Y2 tptp.val)) (=> (not (@ (@ tptp.ord_less_eq_val X) Y2)) (@ (@ tptp.ord_less_eq_val Y2) X))))
% 0.26/0.67 (assert (forall ((A3 (-> Bool tptp.set_val)) (B3 (-> Bool tptp.set_val)) (C (-> Bool tptp.set_val))) (let ((_let_1 (@ tptp.ord_le994826475et_val A3))) (=> (@ _let_1 B3) (=> (@ (@ tptp.ord_le994826475et_val B3) C) (@ _let_1 C))))))
% 0.26/0.67 (assert (forall ((A3 tptp.val) (B3 tptp.val) (C tptp.val)) (let ((_let_1 (@ tptp.ord_less_eq_val A3))) (=> (@ _let_1 B3) (=> (@ (@ tptp.ord_less_eq_val B3) C) (@ _let_1 C))))))
% 0.26/0.67 (assert (forall ((A3 tptp.set_set_val) (B3 tptp.set_set_val) (C tptp.set_set_val)) (let ((_let_1 (@ tptp.ord_le1742111550et_val A3))) (=> (@ _let_1 B3) (=> (@ (@ tptp.ord_le1742111550et_val B3) C) (@ _let_1 C))))))
% 0.26/0.67 (assert (forall ((A3 tptp.set_val) (B3 tptp.set_val) (C tptp.set_val)) (let ((_let_1 (@ tptp.ord_less_eq_set_val A3))) (=> (@ _let_1 B3) (=> (@ (@ tptp.ord_less_eq_set_val B3) C) (@ _let_1 C))))))
% 0.26/0.67 (assert (forall ((A3 tptp.set_val) (P (-> tptp.set_val Bool))) (= (@ (@ tptp.member_set_val A3) (@ tptp.collect_set_val P)) (@ P A3))))
% 0.26/0.67 (assert (forall ((A3 tptp.val) (P (-> tptp.val Bool))) (= (@ (@ tptp.member_val A3) (@ tptp.collect_val P)) (@ P A3))))
% 0.26/0.67 (assert (forall ((A tptp.set_set_val)) (= (@ tptp.collect_set_val (lambda ((X3 tptp.set_val)) (@ (@ tptp.member_set_val X3) A))) A)))
% 0.26/0.67 (assert (forall ((A tptp.set_val)) (= (@ tptp.collect_val (lambda ((X3 tptp.val)) (@ (@ tptp.member_val X3) A))) A)))
% 0.26/0.67 (assert (forall ((P (-> tptp.val Bool)) (Q (-> tptp.val Bool))) (=> (forall ((X2 tptp.val)) (= (@ P X2) (@ Q X2))) (= (@ tptp.collect_val P) (@ tptp.collect_val Q)))))
% 0.26/0.67 (assert (forall ((X tptp.val) (Y2 tptp.val) (Z2 tptp.val)) (let ((_let_1 (@ tptp.ord_less_eq_val X))) (let ((_let_2 (@ _let_1 Y2))) (let ((_let_3 (@ tptp.ord_less_eq_val Z2))) (let ((_let_4 (@ _let_3 X))) (let ((_let_5 (@ tptp.ord_less_eq_val Y2))) (let ((_let_6 (@ _let_5 Z2))) (let ((_let_7 (@ _let_5 X))) (let ((_let_8 (@ _let_3 Y2))) (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)))))))))))))))))))
% 0.26/0.67 (assert (forall ((Y2 (-> Bool tptp.set_val)) (X (-> Bool tptp.set_val))) (=> (@ (@ tptp.ord_le994826475et_val Y2) X) (= (@ (@ tptp.ord_le994826475et_val X) Y2) (= X Y2)))))
% 0.26/0.67 (assert (forall ((Y2 tptp.val) (X tptp.val)) (=> (@ (@ tptp.ord_less_eq_val Y2) X) (= (@ (@ tptp.ord_less_eq_val X) Y2) (= X Y2)))))
% 0.26/0.67 (assert (forall ((Y2 tptp.set_set_val) (X tptp.set_set_val)) (=> (@ (@ tptp.ord_le1742111550et_val Y2) X) (= (@ (@ tptp.ord_le1742111550et_val X) Y2) (= X Y2)))))
% 0.26/0.67 (assert (forall ((Y2 tptp.set_val) (X tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val Y2) X) (= (@ (@ tptp.ord_less_eq_set_val X) Y2) (= X Y2)))))
% 0.26/0.67 (assert (= (lambda ((Y (-> Bool tptp.set_val)) (Z (-> Bool tptp.set_val))) (= Y Z)) (lambda ((A4 (-> Bool tptp.set_val)) (B4 (-> Bool tptp.set_val))) (and (@ (@ tptp.ord_le994826475et_val A4) B4) (@ (@ tptp.ord_le994826475et_val B4) A4)))))
% 0.26/0.67 (assert (= (lambda ((Y tptp.val) (Z tptp.val)) (= Y Z)) (lambda ((A4 tptp.val) (B4 tptp.val)) (and (@ (@ tptp.ord_less_eq_val A4) B4) (@ (@ tptp.ord_less_eq_val B4) A4)))))
% 0.26/0.67 (assert (= (lambda ((Y tptp.set_set_val) (Z tptp.set_set_val)) (= Y Z)) (lambda ((A4 tptp.set_set_val) (B4 tptp.set_set_val)) (and (@ (@ tptp.ord_le1742111550et_val A4) B4) (@ (@ tptp.ord_le1742111550et_val B4) A4)))))
% 0.26/0.67 (assert (= (lambda ((Y tptp.set_val) (Z tptp.set_val)) (= Y Z)) (lambda ((A4 tptp.set_val) (B4 tptp.set_val)) (and (@ (@ tptp.ord_less_eq_set_val A4) B4) (@ (@ tptp.ord_less_eq_set_val B4) A4)))))
% 0.26/0.67 (assert (forall ((A3 (-> Bool tptp.set_val)) (B3 (-> Bool tptp.set_val)) (C (-> Bool tptp.set_val))) (=> (= A3 B3) (=> (@ (@ tptp.ord_le994826475et_val B3) C) (@ (@ tptp.ord_le994826475et_val A3) C)))))
% 0.26/0.67 (assert (forall ((A3 tptp.val) (B3 tptp.val) (C tptp.val)) (=> (= A3 B3) (=> (@ (@ tptp.ord_less_eq_val B3) C) (@ (@ tptp.ord_less_eq_val A3) C)))))
% 0.26/0.67 (assert (forall ((A3 tptp.set_set_val) (B3 tptp.set_set_val) (C tptp.set_set_val)) (=> (= A3 B3) (=> (@ (@ tptp.ord_le1742111550et_val B3) C) (@ (@ tptp.ord_le1742111550et_val A3) C)))))
% 0.26/0.67 (assert (forall ((A3 tptp.set_val) (B3 tptp.set_val) (C tptp.set_val)) (=> (= A3 B3) (=> (@ (@ tptp.ord_less_eq_set_val B3) C) (@ (@ tptp.ord_less_eq_set_val A3) C)))))
% 0.26/0.67 (assert (forall ((P (-> (-> Bool tptp.set_val) Bool)) (X (-> Bool tptp.set_val)) (Q (-> (-> Bool tptp.set_val) Bool))) (=> (@ P X) (=> (forall ((Y3 (-> Bool tptp.set_val))) (=> (@ P Y3) (@ (@ tptp.ord_le994826475et_val Y3) X))) (=> (forall ((X2 (-> Bool tptp.set_val))) (=> (@ P X2) (=> (forall ((Y5 (-> Bool tptp.set_val))) (=> (@ P Y5) (@ (@ tptp.ord_le994826475et_val Y5) X2))) (@ Q X2)))) (@ Q (@ tptp.order_985126002et_val P)))))))
% 0.26/0.67 (assert (forall ((P (-> tptp.val Bool)) (X tptp.val) (Q (-> tptp.val Bool))) (=> (@ P X) (=> (forall ((Y3 tptp.val)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_val Y3) X))) (=> (forall ((X2 tptp.val)) (=> (@ P X2) (=> (forall ((Y5 tptp.val)) (=> (@ P Y5) (@ (@ tptp.ord_less_eq_val Y5) X2))) (@ Q X2)))) (@ Q (@ tptp.order_Greatest_val P)))))))
% 0.26/0.67 (assert (forall ((P (-> tptp.set_set_val Bool)) (X tptp.set_set_val) (Q (-> tptp.set_set_val Bool))) (=> (@ P X) (=> (forall ((Y3 tptp.set_set_val)) (=> (@ P Y3) (@ (@ tptp.ord_le1742111550et_val Y3) X))) (=> (forall ((X2 tptp.set_set_val)) (=> (@ P X2) (=> (forall ((Y5 tptp.set_set_val)) (=> (@ P Y5) (@ (@ tptp.ord_le1742111550et_val Y5) X2))) (@ Q X2)))) (@ Q (@ tptp.order_544136439et_val P)))))))
% 0.26/0.67 (assert (forall ((P (-> tptp.set_val Bool)) (X tptp.set_val) (Q (-> tptp.set_val Bool))) (=> (@ P X) (=> (forall ((Y3 tptp.set_val)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_set_val Y3) X))) (=> (forall ((X2 tptp.set_val)) (=> (@ P X2) (=> (forall ((Y5 tptp.set_val)) (=> (@ P Y5) (@ (@ tptp.ord_less_eq_set_val Y5) X2))) (@ Q X2)))) (@ Q (@ tptp.order_1960465943et_val P)))))))
% 0.26/0.67 (assert (forall ((P (-> (-> Bool tptp.set_val) Bool)) (X (-> Bool tptp.set_val))) (=> (@ P X) (=> (forall ((Y3 (-> Bool tptp.set_val))) (=> (@ P Y3) (@ (@ tptp.ord_le994826475et_val Y3) X))) (= (@ tptp.order_985126002et_val P) X)))))
% 0.26/0.67 (assert (forall ((P (-> tptp.val Bool)) (X tptp.val)) (=> (@ P X) (=> (forall ((Y3 tptp.val)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_val Y3) X))) (= (@ tptp.order_Greatest_val P) X)))))
% 0.26/0.67 (assert (forall ((P (-> tptp.set_set_val Bool)) (X tptp.set_set_val)) (=> (@ P X) (=> (forall ((Y3 tptp.set_set_val)) (=> (@ P Y3) (@ (@ tptp.ord_le1742111550et_val Y3) X))) (= (@ tptp.order_544136439et_val P) X)))))
% 0.26/0.67 (assert (forall ((P (-> tptp.set_val Bool)) (X tptp.set_val)) (=> (@ P X) (=> (forall ((Y3 tptp.set_val)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_set_val Y3) X))) (= (@ tptp.order_1960465943et_val P) X)))))
% 0.26/0.67 (assert (forall ((B3 Bool) (M1 (-> Bool tptp.set_val)) (M12 (-> Bool tptp.set_val)) (M2 (-> Bool tptp.set_val)) (M22 (-> Bool tptp.set_val))) (let ((_let_1 (@ tptp.if_o_set_val B3))) (=> (=> B3 (@ (@ tptp.ord_le994826475et_val M1) M12)) (=> (=> (not B3) (@ (@ tptp.ord_le994826475et_val M2) M22)) (@ (@ tptp.ord_le994826475et_val (@ (@ _let_1 M1) M2)) (@ (@ _let_1 M12) M22)))))))
% 0.26/0.67 (assert (forall ((B3 Bool) (M1 tptp.val) (M12 tptp.val) (M2 tptp.val) (M22 tptp.val)) (let ((_let_1 (@ tptp.if_val B3))) (=> (=> B3 (@ (@ tptp.ord_less_eq_val M1) M12)) (=> (=> (not B3) (@ (@ tptp.ord_less_eq_val M2) M22)) (@ (@ tptp.ord_less_eq_val (@ (@ _let_1 M1) M2)) (@ (@ _let_1 M12) M22)))))))
% 0.26/0.67 (assert (forall ((B3 Bool) (M1 tptp.set_set_val) (M12 tptp.set_set_val) (M2 tptp.set_set_val) (M22 tptp.set_set_val)) (let ((_let_1 (@ tptp.if_set_set_val B3))) (=> (=> B3 (@ (@ tptp.ord_le1742111550et_val M1) M12)) (=> (=> (not B3) (@ (@ tptp.ord_le1742111550et_val M2) M22)) (@ (@ tptp.ord_le1742111550et_val (@ (@ _let_1 M1) M2)) (@ (@ _let_1 M12) M22)))))))
% 0.26/0.67 (assert (forall ((B3 Bool) (M1 tptp.set_val) (M12 tptp.set_val) (M2 tptp.set_val) (M22 tptp.set_val)) (let ((_let_1 (@ tptp.if_set_val B3))) (=> (=> B3 (@ (@ tptp.ord_less_eq_set_val M1) M12)) (=> (=> (not B3) (@ (@ tptp.ord_less_eq_set_val M2) M22)) (@ (@ tptp.ord_less_eq_set_val (@ (@ _let_1 M1) M2)) (@ (@ _let_1 M12) M22)))))))
% 0.26/0.67 (assert (forall ((B3 Bool) (T2 (-> Bool tptp.set_val)) (M (-> Bool tptp.set_val)) (E (-> Bool tptp.set_val))) (=> (=> B3 (@ (@ tptp.ord_le994826475et_val T2) M)) (=> (=> (not B3) (@ (@ tptp.ord_le994826475et_val E) M)) (@ (@ tptp.ord_le994826475et_val (@ (@ (@ tptp.if_o_set_val B3) T2) E)) M)))))
% 0.26/0.67 (assert (forall ((B3 Bool) (T2 tptp.val) (M tptp.val) (E tptp.val)) (=> (=> B3 (@ (@ tptp.ord_less_eq_val T2) M)) (=> (=> (not B3) (@ (@ tptp.ord_less_eq_val E) M)) (@ (@ tptp.ord_less_eq_val (@ (@ (@ tptp.if_val B3) T2) E)) M)))))
% 0.26/0.67 (assert (forall ((B3 Bool) (T2 tptp.set_set_val) (M tptp.set_set_val) (E tptp.set_set_val)) (=> (=> B3 (@ (@ tptp.ord_le1742111550et_val T2) M)) (=> (=> (not B3) (@ (@ tptp.ord_le1742111550et_val E) M)) (@ (@ tptp.ord_le1742111550et_val (@ (@ (@ tptp.if_set_set_val B3) T2) E)) M)))))
% 0.26/0.67 (assert (forall ((B3 Bool) (T2 tptp.set_val) (M tptp.set_val) (E tptp.set_val)) (=> (=> B3 (@ (@ tptp.ord_less_eq_set_val T2) M)) (=> (=> (not B3) (@ (@ tptp.ord_less_eq_set_val E) M)) (@ (@ tptp.ord_less_eq_set_val (@ (@ (@ tptp.if_set_val B3) T2) E)) M)))))
% 0.26/0.67 (assert (forall ((A3 tptp.val) (B3 tptp.val)) (or (= A3 B3) (not (@ (@ tptp.ord_less_eq_val A3) B3)) (not (@ (@ tptp.ord_less_eq_val B3) A3)))))
% 0.26/0.67 (assert (= tptp.ord_le1441829300et_val (lambda ((X4 (-> Bool Bool tptp.set_val)) (Y6 (-> Bool Bool tptp.set_val))) (and (@ (@ tptp.ord_le994826475et_val (@ X4 false)) (@ Y6 false)) (@ (@ tptp.ord_le994826475et_val (@ X4 true)) (@ Y6 true))))))
% 0.26/0.67 (assert (= tptp.ord_less_eq_o_val (lambda ((X4 (-> Bool tptp.val)) (Y6 (-> Bool tptp.val))) (and (@ (@ tptp.ord_less_eq_val (@ X4 false)) (@ Y6 false)) (@ (@ tptp.ord_less_eq_val (@ X4 true)) (@ Y6 true))))))
% 0.26/0.67 (assert (= tptp.ord_le936627147et_val (lambda ((X4 (-> Bool tptp.set_set_val)) (Y6 (-> Bool tptp.set_set_val))) (and (@ (@ tptp.ord_le1742111550et_val (@ X4 false)) (@ Y6 false)) (@ (@ tptp.ord_le1742111550et_val (@ X4 true)) (@ Y6 true))))))
% 0.26/0.67 (assert (= tptp.ord_le994826475et_val (lambda ((X4 (-> Bool tptp.set_val)) (Y6 (-> Bool tptp.set_val))) (and (@ (@ tptp.ord_less_eq_set_val (@ X4 false)) (@ Y6 false)) (@ (@ tptp.ord_less_eq_set_val (@ X4 true)) (@ Y6 true))))))
% 0.26/0.67 (assert (forall ((F (-> tptp.set_val tptp.set_val)) (X tptp.set_val) (Y2 tptp.set_val)) (=> (@ tptp.order_1719375026et_val F) (=> (@ (@ tptp.ord_less_eq_set_val X) Y2) (@ (@ tptp.ord_less_eq_set_val (@ F Y2)) (@ F X))))))
% 0.26/0.67 (assert (forall ((F (-> tptp.val tptp.val)) (X tptp.val) (Y2 tptp.val)) (=> (@ tptp.order_1689798834al_val F) (=> (@ (@ tptp.ord_less_eq_val X) Y2) (@ (@ tptp.ord_less_eq_val (@ F Y2)) (@ F X))))))
% 0.26/0.67 (assert (forall ((F (-> tptp.set_val tptp.val)) (X tptp.set_val) (Y2 tptp.set_val)) (=> (@ tptp.order_1375876562al_val F) (=> (@ (@ tptp.ord_less_eq_set_val X) Y2) (@ (@ tptp.ord_less_eq_val (@ F Y2)) (@ F X))))))
% 0.26/0.67 (assert (forall ((F (-> tptp.val tptp.set_val)) (X tptp.val) (Y2 tptp.val)) (=> (@ tptp.order_1484138386et_val F) (=> (@ (@ tptp.ord_less_eq_val X) Y2) (@ (@ tptp.ord_less_eq_set_val (@ F Y2)) (@ F X))))))
% 0.26/0.67 (assert (forall ((F (-> tptp.val tptp.set_set_val)) (X tptp.val) (Y2 tptp.val)) (=> (@ tptp.order_1945059954et_val F) (=> (@ (@ tptp.ord_less_eq_val X) Y2) (@ (@ tptp.ord_le1742111550et_val (@ F Y2)) (@ F X))))))
% 0.26/0.67 (assert (forall ((F (-> tptp.set_set_val tptp.val)) (X tptp.set_set_val) (Y2 tptp.set_set_val)) (=> (@ tptp.order_1520822002al_val F) (=> (@ (@ tptp.ord_le1742111550et_val X) Y2) (@ (@ tptp.ord_less_eq_val (@ F Y2)) (@ F X))))))
% 0.26/0.67 (assert (forall ((F (-> tptp.set_val tptp.set_set_val)) (X tptp.set_val) (Y2 tptp.set_val)) (=> (@ tptp.order_1957703570et_val F) (=> (@ (@ tptp.ord_less_eq_set_val X) Y2) (@ (@ tptp.ord_le1742111550et_val (@ F Y2)) (@ F X))))))
% 0.26/0.67 (assert (forall ((F (-> (-> Bool tptp.set_val) tptp.val)) (X (-> Bool tptp.set_val)) (Y2 (-> Bool tptp.set_val))) (=> (@ tptp.order_23236447al_val F) (=> (@ (@ tptp.ord_le994826475et_val X) Y2) (@ (@ tptp.ord_less_eq_val (@ F Y2)) (@ F X))))))
% 0.26/0.67 (assert (forall ((F (-> tptp.val Bool tptp.set_val)) (X tptp.val) (Y2 tptp.val)) (=> (@ tptp.order_255079095et_val F) (=> (@ (@ tptp.ord_less_eq_val X) Y2) (@ (@ tptp.ord_le994826475et_val (@ F Y2)) (@ F X))))))
% 0.26/0.67 (assert (forall ((F (-> tptp.set_set_val tptp.set_val)) (X tptp.set_set_val) (Y2 tptp.set_set_val)) (=> (@ tptp.order_650823122et_val F) (=> (@ (@ tptp.ord_le1742111550et_val X) Y2) (@ (@ tptp.ord_less_eq_set_val (@ F Y2)) (@ F X))))))
% 0.26/0.67 (assert (forall ((F (-> tptp.set_val tptp.set_val)) (X tptp.set_val) (Y2 tptp.set_val)) (=> (@ tptp.order_1719375026et_val F) (=> (@ (@ tptp.ord_less_eq_set_val X) Y2) (@ (@ tptp.ord_less_eq_set_val (@ F Y2)) (@ F X))))))
% 0.26/0.67 (assert (forall ((F (-> tptp.val tptp.val)) (X tptp.val) (Y2 tptp.val)) (=> (@ tptp.order_1689798834al_val F) (=> (@ (@ tptp.ord_less_eq_val X) Y2) (@ (@ tptp.ord_less_eq_val (@ F Y2)) (@ F X))))))
% 0.26/0.67 (assert (forall ((F (-> tptp.set_val tptp.val)) (X tptp.set_val) (Y2 tptp.set_val)) (=> (@ tptp.order_1375876562al_val F) (=> (@ (@ tptp.ord_less_eq_set_val X) Y2) (@ (@ tptp.ord_less_eq_val (@ F Y2)) (@ F X))))))
% 0.26/0.67 (assert (forall ((F (-> tptp.val tptp.set_val)) (X tptp.val) (Y2 tptp.val)) (=> (@ tptp.order_1484138386et_val F) (=> (@ (@ tptp.ord_less_eq_val X) Y2) (@ (@ tptp.ord_less_eq_set_val (@ F Y2)) (@ F X))))))
% 0.26/0.67 (assert (forall ((F (-> tptp.val tptp.set_set_val)) (X tptp.val) (Y2 tptp.val)) (=> (@ tptp.order_1945059954et_val F) (=> (@ (@ tptp.ord_less_eq_val X) Y2) (@ (@ tptp.ord_le1742111550et_val (@ F Y2)) (@ F X))))))
% 0.26/0.67 (assert (forall ((F (-> tptp.set_set_val tptp.val)) (X tptp.set_set_val) (Y2 tptp.set_set_val)) (=> (@ tptp.order_1520822002al_val F) (=> (@ (@ tptp.ord_le1742111550et_val X) Y2) (@ (@ tptp.ord_less_eq_val (@ F Y2)) (@ F X))))))
% 0.26/0.67 (assert (forall ((F (-> tptp.set_val tptp.set_set_val)) (X tptp.set_val) (Y2 tptp.set_val)) (=> (@ tptp.order_1957703570et_val F) (=> (@ (@ tptp.ord_less_eq_set_val X) Y2) (@ (@ tptp.ord_le1742111550et_val (@ F Y2)) (@ F X))))))
% 0.26/0.67 (assert (forall ((F (-> (-> Bool tptp.set_val) tptp.val)) (X (-> Bool tptp.set_val)) (Y2 (-> Bool tptp.set_val))) (=> (@ tptp.order_23236447al_val F) (=> (@ (@ tptp.ord_le994826475et_val X) Y2) (@ (@ tptp.ord_less_eq_val (@ F Y2)) (@ F X))))))
% 0.26/0.67 (assert (forall ((F (-> tptp.val Bool tptp.set_val)) (X tptp.val) (Y2 tptp.val)) (=> (@ tptp.order_255079095et_val F) (=> (@ (@ tptp.ord_less_eq_val X) Y2) (@ (@ tptp.ord_le994826475et_val (@ F Y2)) (@ F X))))))
% 0.26/0.67 (assert (forall ((F (-> tptp.set_set_val tptp.set_val)) (X tptp.set_set_val) (Y2 tptp.set_set_val)) (=> (@ tptp.order_650823122et_val F) (=> (@ (@ tptp.ord_le1742111550et_val X) Y2) (@ (@ tptp.ord_less_eq_set_val (@ F Y2)) (@ F X))))))
% 0.26/0.67 (assert (= tptp.order_1719375026et_val (lambda ((F2 (-> tptp.set_val tptp.set_val))) (forall ((X3 tptp.set_val) (Y4 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val X3) Y4) (@ (@ tptp.ord_less_eq_set_val (@ F2 Y4)) (@ F2 X3)))))))
% 0.26/0.67 (assert (= tptp.order_1689798834al_val (lambda ((F2 (-> tptp.val tptp.val))) (forall ((X3 tptp.val) (Y4 tptp.val)) (=> (@ (@ tptp.ord_less_eq_val X3) Y4) (@ (@ tptp.ord_less_eq_val (@ F2 Y4)) (@ F2 X3)))))))
% 0.26/0.67 (assert (= tptp.order_1375876562al_val (lambda ((F2 (-> tptp.set_val tptp.val))) (forall ((X3 tptp.set_val) (Y4 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val X3) Y4) (@ (@ tptp.ord_less_eq_val (@ F2 Y4)) (@ F2 X3)))))))
% 0.26/0.67 (assert (= tptp.order_1484138386et_val (lambda ((F2 (-> tptp.val tptp.set_val))) (forall ((X3 tptp.val) (Y4 tptp.val)) (=> (@ (@ tptp.ord_less_eq_val X3) Y4) (@ (@ tptp.ord_less_eq_set_val (@ F2 Y4)) (@ F2 X3)))))))
% 0.26/0.67 (assert (= tptp.order_1945059954et_val (lambda ((F2 (-> tptp.val tptp.set_set_val))) (forall ((X3 tptp.val) (Y4 tptp.val)) (=> (@ (@ tptp.ord_less_eq_val X3) Y4) (@ (@ tptp.ord_le1742111550et_val (@ F2 Y4)) (@ F2 X3)))))))
% 0.26/0.67 (assert (= tptp.order_1520822002al_val (lambda ((F2 (-> tptp.set_set_val tptp.val))) (forall ((X3 tptp.set_set_val) (Y4 tptp.set_set_val)) (=> (@ (@ tptp.ord_le1742111550et_val X3) Y4) (@ (@ tptp.ord_less_eq_val (@ F2 Y4)) (@ F2 X3)))))))
% 0.26/0.67 (assert (= tptp.order_1957703570et_val (lambda ((F2 (-> tptp.set_val tptp.set_set_val))) (forall ((X3 tptp.set_val) (Y4 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val X3) Y4) (@ (@ tptp.ord_le1742111550et_val (@ F2 Y4)) (@ F2 X3)))))))
% 0.26/0.67 (assert (= tptp.order_23236447al_val (lambda ((F2 (-> (-> Bool tptp.set_val) tptp.val))) (forall ((X3 (-> Bool tptp.set_val)) (Y4 (-> Bool tptp.set_val))) (=> (@ (@ tptp.ord_le994826475et_val X3) Y4) (@ (@ tptp.ord_less_eq_val (@ F2 Y4)) (@ F2 X3)))))))
% 0.26/0.67 (assert (= tptp.order_255079095et_val (lambda ((F2 (-> tptp.val Bool tptp.set_val))) (forall ((X3 tptp.val) (Y4 tptp.val)) (=> (@ (@ tptp.ord_less_eq_val X3) Y4) (@ (@ tptp.ord_le994826475et_val (@ F2 Y4)) (@ F2 X3)))))))
% 0.26/0.67 (assert (= tptp.order_650823122et_val (lambda ((F2 (-> tptp.set_set_val tptp.set_val))) (forall ((X3 tptp.set_set_val) (Y4 tptp.set_set_val)) (=> (@ (@ tptp.ord_le1742111550et_val X3) Y4) (@ (@ tptp.ord_less_eq_set_val (@ F2 Y4)) (@ F2 X3)))))))
% 0.26/0.67 (assert (forall ((F (-> tptp.set_val tptp.set_val))) (=> (forall ((X2 tptp.set_val) (Y3 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val X2) Y3) (@ (@ tptp.ord_less_eq_set_val (@ F Y3)) (@ F X2)))) (@ tptp.order_1719375026et_val F))))
% 0.26/0.67 (assert (forall ((F (-> tptp.val tptp.val))) (=> (forall ((X2 tptp.val) (Y3 tptp.val)) (=> (@ (@ tptp.ord_less_eq_val X2) Y3) (@ (@ tptp.ord_less_eq_val (@ F Y3)) (@ F X2)))) (@ tptp.order_1689798834al_val F))))
% 0.26/0.67 (assert (forall ((F (-> tptp.set_val tptp.val))) (=> (forall ((X2 tptp.set_val) (Y3 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val X2) Y3) (@ (@ tptp.ord_less_eq_val (@ F Y3)) (@ F X2)))) (@ tptp.order_1375876562al_val F))))
% 0.26/0.67 (assert (forall ((F (-> tptp.val tptp.set_val))) (=> (forall ((X2 tptp.val) (Y3 tptp.val)) (=> (@ (@ tptp.ord_less_eq_val X2) Y3) (@ (@ tptp.ord_less_eq_set_val (@ F Y3)) (@ F X2)))) (@ tptp.order_1484138386et_val F))))
% 0.26/0.67 (assert (forall ((F (-> tptp.val tptp.set_set_val))) (=> (forall ((X2 tptp.val) (Y3 tptp.val)) (=> (@ (@ tptp.ord_less_eq_val X2) Y3) (@ (@ tptp.ord_le1742111550et_val (@ F Y3)) (@ F X2)))) (@ tptp.order_1945059954et_val F))))
% 0.26/0.67 (assert (forall ((F (-> tptp.set_set_val tptp.val))) (=> (forall ((X2 tptp.set_set_val) (Y3 tptp.set_set_val)) (=> (@ (@ tptp.ord_le1742111550et_val X2) Y3) (@ (@ tptp.ord_less_eq_val (@ F Y3)) (@ F X2)))) (@ tptp.order_1520822002al_val F))))
% 0.26/0.67 (assert (forall ((F (-> tptp.set_val tptp.set_set_val))) (=> (forall ((X2 tptp.set_val) (Y3 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val X2) Y3) (@ (@ tptp.ord_le1742111550et_val (@ F Y3)) (@ F X2)))) (@ tptp.order_1957703570et_val F))))
% 0.26/0.67 (assert (forall ((F (-> (-> Bool tptp.set_val) tptp.val))) (=> (forall ((X2 (-> Bool tptp.set_val)) (Y3 (-> Bool tptp.set_val))) (=> (@ (@ tptp.ord_le994826475et_val X2) Y3) (@ (@ tptp.ord_less_eq_val (@ F Y3)) (@ F X2)))) (@ tptp.order_23236447al_val F))))
% 0.26/0.67 (assert (forall ((F (-> tptp.val Bool tptp.set_val))) (=> (forall ((X2 tptp.val) (Y3 tptp.val)) (=> (@ (@ tptp.ord_less_eq_val X2) Y3) (@ (@ tptp.ord_le994826475et_val (@ F Y3)) (@ F X2)))) (@ tptp.order_255079095et_val F))))
% 0.26/0.67 (assert (forall ((F (-> tptp.set_set_val tptp.set_val))) (=> (forall ((X2 tptp.set_set_val) (Y3 tptp.set_set_val)) (=> (@ (@ tptp.ord_le1742111550et_val X2) Y3) (@ (@ tptp.ord_less_eq_set_val (@ F Y3)) (@ F X2)))) (@ tptp.order_650823122et_val F))))
% 0.26/0.67 (assert (@ tptp.refine16560100et_val tptp.ord_le994826475et_val))
% 0.26/0.67 (assert (@ tptp.refine67622213oc_val tptp.ord_less_eq_val))
% 0.26/0.67 (assert (@ tptp.refine1506227973et_val tptp.ord_le1742111550et_val))
% 0.26/0.67 (assert (@ tptp.refine275900453et_val tptp.ord_less_eq_set_val))
% 0.26/0.67 (assert (forall ((Alpha (-> tptp.set_val tptp.set_val)) (Gamma (-> tptp.set_val tptp.set_val)) (X tptp.set_val)) (=> (@ (@ tptp.refine1929691018et_val Alpha) Gamma) (@ (@ tptp.ord_less_eq_set_val X) (@ Gamma (@ Alpha X))))))
% 0.26/0.67 (assert (forall ((Alpha (-> tptp.set_val tptp.set_val)) (Gamma (-> tptp.set_val tptp.set_val)) (X tptp.set_val)) (=> (@ (@ tptp.refine1929691018et_val Alpha) Gamma) (@ (@ tptp.ord_less_eq_set_val (@ Alpha (@ Gamma X))) X))))
% 0.26/0.67 (assert (forall ((Alpha (-> tptp.set_val Bool tptp.set_val)) (Gamma (-> (-> Bool tptp.set_val) tptp.set_val)) (C tptp.set_val) (A3 (-> Bool tptp.set_val))) (=> (@ (@ tptp.refine51544255et_val Alpha) Gamma) (= (@ (@ tptp.ord_less_eq_set_val C) (@ Gamma A3)) (@ (@ tptp.ord_le994826475et_val (@ Alpha C)) A3)))))
% 0.26/0.67 (assert (forall ((Alpha (-> tptp.set_val tptp.set_set_val)) (Gamma (-> tptp.set_set_val tptp.set_val)) (C tptp.set_val) (A3 tptp.set_set_val)) (=> (@ (@ tptp.refine1315043946et_val Alpha) Gamma) (= (@ (@ tptp.ord_less_eq_set_val C) (@ Gamma A3)) (@ (@ tptp.ord_le1742111550et_val (@ Alpha C)) A3)))))
% 0.26/0.67 (assert (forall ((Alpha (-> (-> Bool tptp.set_val) tptp.set_val)) (Gamma (-> tptp.set_val Bool tptp.set_val)) (C (-> Bool tptp.set_val)) (A3 tptp.set_val)) (=> (@ (@ tptp.refine1948536167et_val Alpha) Gamma) (= (@ (@ tptp.ord_le994826475et_val C) (@ Gamma A3)) (@ (@ tptp.ord_less_eq_set_val (@ Alpha C)) A3)))))
% 0.26/0.67 (assert (forall ((Alpha (-> (-> Bool tptp.set_val) Bool tptp.set_val)) (Gamma (-> (-> Bool tptp.set_val) Bool tptp.set_val)) (C (-> Bool tptp.set_val)) (A3 (-> Bool tptp.set_val))) (=> (@ (@ tptp.refine1924899106et_val Alpha) Gamma) (= (@ (@ tptp.ord_le994826475et_val C) (@ Gamma A3)) (@ (@ tptp.ord_le994826475et_val (@ Alpha C)) A3)))))
% 0.26/0.67 (assert (forall ((Alpha (-> (-> Bool tptp.set_val) tptp.set_set_val)) (Gamma (-> tptp.set_set_val Bool tptp.set_val)) (C (-> Bool tptp.set_val)) (A3 tptp.set_set_val)) (=> (@ (@ tptp.refine1169396807et_val Alpha) Gamma) (= (@ (@ tptp.ord_le994826475et_val C) (@ Gamma A3)) (@ (@ tptp.ord_le1742111550et_val (@ Alpha C)) A3)))))
% 0.26/0.67 (assert (forall ((Alpha (-> tptp.set_set_val tptp.set_val)) (Gamma (-> tptp.set_val tptp.set_set_val)) (C tptp.set_set_val) (A3 tptp.set_val)) (=> (@ (@ tptp.refine8163498et_val Alpha) Gamma) (= (@ (@ tptp.ord_le1742111550et_val C) (@ Gamma A3)) (@ (@ tptp.ord_less_eq_set_val (@ Alpha C)) A3)))))
% 0.26/0.67 (assert (forall ((Alpha (-> tptp.set_set_val Bool tptp.set_val)) (Gamma (-> (-> Bool tptp.set_val) tptp.set_set_val)) (C tptp.set_set_val) (A3 (-> Bool tptp.set_val))) (=> (@ (@ tptp.refine86398879et_val Alpha) Gamma) (= (@ (@ tptp.ord_le1742111550et_val C) (@ Gamma A3)) (@ (@ tptp.ord_le994826475et_val (@ Alpha C)) A3)))))
% 0.26/0.67 (assert (forall ((Alpha (-> tptp.set_set_val tptp.set_set_val)) (Gamma (-> tptp.set_set_val tptp.set_set_val)) (C tptp.set_set_val) (A3 tptp.set_set_val)) (=> (@ (@ tptp.refine855985034et_val Alpha) Gamma) (= (@ (@ tptp.ord_le1742111550et_val C) (@ Gamma A3)) (@ (@ tptp.ord_le1742111550et_val (@ Alpha C)) A3)))))
% 0.26/0.67 (assert (forall ((Alpha (-> tptp.set_val tptp.set_val)) (Gamma (-> tptp.set_val tptp.set_val)) (C tptp.set_val) (A3 tptp.set_val)) (=> (@ (@ tptp.refine1929691018et_val Alpha) Gamma) (= (@ (@ tptp.ord_less_eq_set_val C) (@ Gamma A3)) (@ (@ tptp.ord_less_eq_set_val (@ Alpha C)) A3)))))
% 0.26/0.67 (assert (forall ((Gamma (-> (-> Bool tptp.set_val) tptp.set_val)) (Alpha (-> tptp.set_val Bool tptp.set_val))) (=> (forall ((C3 tptp.set_val) (A5 (-> Bool tptp.set_val))) (= (@ (@ tptp.ord_less_eq_set_val C3) (@ Gamma A5)) (@ (@ tptp.ord_le994826475et_val (@ Alpha C3)) A5))) (@ (@ tptp.refine51544255et_val Alpha) Gamma))))
% 0.26/0.67 (assert (forall ((Gamma (-> tptp.set_set_val tptp.set_val)) (Alpha (-> tptp.set_val tptp.set_set_val))) (=> (forall ((C3 tptp.set_val) (A5 tptp.set_set_val)) (= (@ (@ tptp.ord_less_eq_set_val C3) (@ Gamma A5)) (@ (@ tptp.ord_le1742111550et_val (@ Alpha C3)) A5))) (@ (@ tptp.refine1315043946et_val Alpha) Gamma))))
% 0.26/0.67 (assert (forall ((Gamma (-> tptp.set_val Bool tptp.set_val)) (Alpha (-> (-> Bool tptp.set_val) tptp.set_val))) (=> (forall ((C3 (-> Bool tptp.set_val)) (A5 tptp.set_val)) (= (@ (@ tptp.ord_le994826475et_val C3) (@ Gamma A5)) (@ (@ tptp.ord_less_eq_set_val (@ Alpha C3)) A5))) (@ (@ tptp.refine1948536167et_val Alpha) Gamma))))
% 0.26/0.67 (assert (forall ((Gamma (-> (-> Bool tptp.set_val) Bool tptp.set_val)) (Alpha (-> (-> Bool tptp.set_val) Bool tptp.set_val))) (=> (forall ((C3 (-> Bool tptp.set_val)) (A5 (-> Bool tptp.set_val))) (= (@ (@ tptp.ord_le994826475et_val C3) (@ Gamma A5)) (@ (@ tptp.ord_le994826475et_val (@ Alpha C3)) A5))) (@ (@ tptp.refine1924899106et_val Alpha) Gamma))))
% 0.26/0.67 (assert (forall ((Gamma (-> tptp.set_set_val Bool tptp.set_val)) (Alpha (-> (-> Bool tptp.set_val) tptp.set_set_val))) (=> (forall ((C3 (-> Bool tptp.set_val)) (A5 tptp.set_set_val)) (= (@ (@ tptp.ord_le994826475et_val C3) (@ Gamma A5)) (@ (@ tptp.ord_le1742111550et_val (@ Alpha C3)) A5))) (@ (@ tptp.refine1169396807et_val Alpha) Gamma))))
% 0.26/0.67 (assert (forall ((Gamma (-> tptp.set_val tptp.set_set_val)) (Alpha (-> tptp.set_set_val tptp.set_val))) (=> (forall ((C3 tptp.set_set_val) (A5 tptp.set_val)) (= (@ (@ tptp.ord_le1742111550et_val C3) (@ Gamma A5)) (@ (@ tptp.ord_less_eq_set_val (@ Alpha C3)) A5))) (@ (@ tptp.refine8163498et_val Alpha) Gamma))))
% 0.26/0.67 (assert (forall ((Gamma (-> (-> Bool tptp.set_val) tptp.set_set_val)) (Alpha (-> tptp.set_set_val Bool tptp.set_val))) (=> (forall ((C3 tptp.set_set_val) (A5 (-> Bool tptp.set_val))) (= (@ (@ tptp.ord_le1742111550et_val C3) (@ Gamma A5)) (@ (@ tptp.ord_le994826475et_val (@ Alpha C3)) A5))) (@ (@ tptp.refine86398879et_val Alpha) Gamma))))
% 0.26/0.67 (assert (forall ((Gamma (-> tptp.set_set_val tptp.set_set_val)) (Alpha (-> tptp.set_set_val tptp.set_set_val))) (=> (forall ((C3 tptp.set_set_val) (A5 tptp.set_set_val)) (= (@ (@ tptp.ord_le1742111550et_val C3) (@ Gamma A5)) (@ (@ tptp.ord_le1742111550et_val (@ Alpha C3)) A5))) (@ (@ tptp.refine855985034et_val Alpha) Gamma))))
% 0.26/0.67 (assert (forall ((Gamma (-> tptp.set_val tptp.set_val)) (Alpha (-> tptp.set_val tptp.set_val))) (=> (forall ((C3 tptp.set_val) (A5 tptp.set_val)) (= (@ (@ tptp.ord_less_eq_set_val C3) (@ Gamma A5)) (@ (@ tptp.ord_less_eq_set_val (@ Alpha C3)) A5))) (@ (@ tptp.refine1929691018et_val Alpha) Gamma))))
% 0.26/0.67 (assert (= tptp.refine51544255et_val (lambda ((Alpha2 (-> tptp.set_val Bool tptp.set_val)) (Gamma2 (-> (-> Bool tptp.set_val) tptp.set_val))) (forall ((C4 tptp.set_val) (A4 (-> Bool tptp.set_val))) (= (@ (@ tptp.ord_less_eq_set_val C4) (@ Gamma2 A4)) (@ (@ tptp.ord_le994826475et_val (@ Alpha2 C4)) A4))))))
% 0.26/0.67 (assert (= tptp.refine1315043946et_val (lambda ((Alpha2 (-> tptp.set_val tptp.set_set_val)) (Gamma2 (-> tptp.set_set_val tptp.set_val))) (forall ((C4 tptp.set_val) (A4 tptp.set_set_val)) (= (@ (@ tptp.ord_less_eq_set_val C4) (@ Gamma2 A4)) (@ (@ tptp.ord_le1742111550et_val (@ Alpha2 C4)) A4))))))
% 0.26/0.67 (assert (= tptp.refine1948536167et_val (lambda ((Alpha2 (-> (-> Bool tptp.set_val) tptp.set_val)) (Gamma2 (-> tptp.set_val Bool tptp.set_val))) (forall ((C4 (-> Bool tptp.set_val)) (A4 tptp.set_val)) (= (@ (@ tptp.ord_le994826475et_val C4) (@ Gamma2 A4)) (@ (@ tptp.ord_less_eq_set_val (@ Alpha2 C4)) A4))))))
% 0.26/0.67 (assert (= tptp.refine1924899106et_val (lambda ((Alpha2 (-> (-> Bool tptp.set_val) Bool tptp.set_val)) (Gamma2 (-> (-> Bool tptp.set_val) Bool tptp.set_val))) (forall ((C4 (-> Bool tptp.set_val)) (A4 (-> Bool tptp.set_val))) (= (@ (@ tptp.ord_le994826475et_val C4) (@ Gamma2 A4)) (@ (@ tptp.ord_le994826475et_val (@ Alpha2 C4)) A4))))))
% 0.26/0.67 (assert (= tptp.refine1169396807et_val (lambda ((Alpha2 (-> (-> Bool tptp.set_val) tptp.set_set_val)) (Gamma2 (-> tptp.set_set_val Bool tptp.set_val))) (forall ((C4 (-> Bool tptp.set_val)) (A4 tptp.set_set_val)) (= (@ (@ tptp.ord_le994826475et_val C4) (@ Gamma2 A4)) (@ (@ tptp.ord_le1742111550et_val (@ Alpha2 C4)) A4))))))
% 0.26/0.67 (assert (= tptp.refine8163498et_val (lambda ((Alpha2 (-> tptp.set_set_val tptp.set_val)) (Gamma2 (-> tptp.set_val tptp.set_set_val))) (forall ((C4 tptp.set_set_val) (A4 tptp.set_val)) (= (@ (@ tptp.ord_le1742111550et_val C4) (@ Gamma2 A4)) (@ (@ tptp.ord_less_eq_set_val (@ Alpha2 C4)) A4))))))
% 0.26/0.67 (assert (= tptp.refine86398879et_val (lambda ((Alpha2 (-> tptp.set_set_val Bool tptp.set_val)) (Gamma2 (-> (-> Bool tptp.set_val) tptp.set_set_val))) (forall ((C4 tptp.set_set_val) (A4 (-> Bool tptp.set_val))) (= (@ (@ tptp.ord_le1742111550et_val C4) (@ Gamma2 A4)) (@ (@ tptp.ord_le994826475et_val (@ Alpha2 C4)) A4))))))
% 0.26/0.67 (assert (= tptp.refine855985034et_val (lambda ((Alpha2 (-> tptp.set_set_val tptp.set_set_val)) (Gamma2 (-> tptp.set_set_val tptp.set_set_val))) (forall ((C4 tptp.set_set_val) (A4 tptp.set_set_val)) (= (@ (@ tptp.ord_le1742111550et_val C4) (@ Gamma2 A4)) (@ (@ tptp.ord_le1742111550et_val (@ Alpha2 C4)) A4))))))
% 0.26/0.67 (assert (= tptp.refine1929691018et_val (lambda ((Alpha2 (-> tptp.set_val tptp.set_val)) (Gamma2 (-> tptp.set_val tptp.set_val))) (forall ((C4 tptp.set_val) (A4 tptp.set_val)) (= (@ (@ tptp.ord_less_eq_set_val C4) (@ Gamma2 A4)) (@ (@ tptp.ord_less_eq_set_val (@ Alpha2 C4)) A4))))))
% 0.26/0.67 (assert (= tptp.refine275900453et_val (lambda ((Le (-> tptp.set_val tptp.set_val Bool))) (forall ((X3 tptp.set_val)) (@ (@ Le X3) X3)))))
% 0.26/0.67 (assert (forall ((Le2 (-> tptp.set_val tptp.set_val Bool)) (X tptp.set_val)) (=> (@ tptp.refine275900453et_val Le2) (@ (@ Le2 X) X))))
% 0.26/0.67 (assert (forall ((Le2 (-> tptp.set_val tptp.set_val Bool))) (=> (forall ((X2 tptp.set_val)) (@ (@ Le2 X2) X2)) (@ tptp.refine275900453et_val Le2))))
% 0.26/0.67 (assert (forall ((Le2 (-> tptp.set_val tptp.set_val Bool)) (T2 tptp.set_val) (T3 tptp.set_val) (E tptp.set_val) (E2 tptp.set_val) (B3 Bool)) (let ((_let_1 (@ tptp.if_set_val B3))) (=> (@ tptp.refine275900453et_val Le2) (=> (@ (@ Le2 T2) T3) (=> (@ (@ Le2 E) E2) (@ (@ Le2 (@ (@ _let_1 T2) E)) (@ (@ _let_1 T3) E2))))))))
% 0.26/0.67 (assert (forall ((Alpha (-> tptp.set_val tptp.set_val)) (Gamma (-> tptp.set_val tptp.set_val))) (=> (@ (@ tptp.refine1929691018et_val Alpha) Gamma) (@ tptp.refine2057434761et_val Alpha))))
% 0.26/0.67 (assert (forall ((F (-> tptp.val tptp.set_val)) (X tptp.val) (Y2 tptp.val)) (=> (@ tptp.order_99134233et_val F) (= (@ (@ tptp.ord_less_eq_set_val (@ F X)) (@ F Y2)) (@ (@ tptp.ord_less_eq_val X) Y2)))))
% 0.26/0.67 (assert (forall ((F (-> tptp.val Bool tptp.set_val)) (X tptp.val) (Y2 tptp.val)) (=> (@ tptp.order_1205732848et_val F) (= (@ (@ tptp.ord_le994826475et_val (@ F X)) (@ F Y2)) (@ (@ tptp.ord_less_eq_val X) Y2)))))
% 0.26/0.67 (assert (forall ((F (-> tptp.val tptp.val)) (X tptp.val) (Y2 tptp.val)) (=> (@ tptp.order_1139042361al_val F) (= (@ (@ tptp.ord_less_eq_val (@ F X)) (@ F Y2)) (@ (@ tptp.ord_less_eq_val X) Y2)))))
% 0.26/0.67 (assert (forall ((F (-> tptp.val tptp.set_set_val)) (X tptp.val) (Y2 tptp.val)) (=> (@ tptp.order_68692473et_val F) (= (@ (@ tptp.ord_le1742111550et_val (@ F X)) (@ F Y2)) (@ (@ tptp.ord_less_eq_val X) Y2)))))
% 0.26/0.67 (assert (forall ((X tptp.val) (Y2 tptp.val)) (= (@ (@ tptp.ord_less_eq_set_val (@ tptp.set_or1288365508an_val X)) (@ tptp.set_or1288365508an_val Y2)) (@ (@ tptp.ord_less_eq_val Y2) X))))
% 0.26/0.67 (assert (forall ((D (-> Bool tptp.set_val)) (C (-> Bool tptp.set_val)) (A3 (-> Bool tptp.set_val))) (=> (@ (@ tptp.refine1593386065et_val D) C) (=> (@ (@ tptp.ord_le994826475et_val C) A3) (=> (@ (@ tptp.refine511606705et_val C) D) (@ (@ tptp.ord_le994826475et_val D) A3))))))
% 0.26/0.67 (assert (forall ((D tptp.val) (C tptp.val) (A3 tptp.val)) (=> (@ (@ tptp.refine2021912633al_val D) C) (=> (@ (@ tptp.ord_less_eq_val C) A3) (=> (@ (@ tptp.refine403244856MP_val C) D) (@ (@ tptp.ord_less_eq_val D) A3))))))
% 0.26/0.67 (assert (forall ((D tptp.set_set_val) (C tptp.set_set_val) (A3 tptp.set_set_val)) (=> (@ (@ tptp.refine1034950713et_val D) C) (=> (@ (@ tptp.ord_le1742111550et_val C) A3) (=> (@ (@ tptp.refine1908789496et_val C) D) (@ (@ tptp.ord_le1742111550et_val D) A3))))))
% 0.26/0.67 (assert (forall ((D tptp.set_val) (C tptp.set_val) (A3 tptp.set_val)) (=> (@ (@ tptp.refine654574649et_val D) C) (=> (@ (@ tptp.ord_less_eq_set_val C) A3) (=> (@ (@ tptp.refine1893322264et_val C) D) (@ (@ tptp.ord_less_eq_set_val D) A3))))))
% 0.26/0.67 (assert (forall ((X tptp.val) (Y2 tptp.val)) (= (@ (@ tptp.ord_less_eq_set_val (@ tptp.set_ord_lessThan_val X)) (@ tptp.set_ord_lessThan_val Y2)) (@ (@ tptp.ord_less_eq_val X) Y2))))
% 0.26/0.67 (assert (forall ((X tptp.set_set_val) (Y2 tptp.set_set_val)) (= (@ (@ tptp.ord_le1135847966et_val (@ tptp.set_or1337784553et_val X)) (@ tptp.set_or1337784553et_val Y2)) (@ (@ tptp.ord_le1742111550et_val Y2) X))))
% 0.26/0.67 (assert (forall ((X tptp.set_val) (Y2 tptp.set_val)) (= (@ (@ tptp.ord_le1742111550et_val (@ tptp.set_or650197513et_val X)) (@ tptp.set_or650197513et_val Y2)) (@ (@ tptp.ord_less_eq_set_val Y2) X))))
% 0.26/0.67 (assert (forall ((X tptp.val) (Y2 tptp.val)) (= (@ (@ tptp.ord_less_eq_set_val (@ tptp.set_ord_atLeast_val X)) (@ tptp.set_ord_atLeast_val Y2)) (@ (@ tptp.ord_less_eq_val Y2) X))))
% 0.26/0.67 (assert (forall ((I tptp.val) (K tptp.val)) (= (@ (@ tptp.member_val I) (@ tptp.set_ord_atLeast_val K)) (@ (@ tptp.ord_less_eq_val K) I))))
% 0.26/0.67 (assert (forall ((I tptp.set_val) (K tptp.set_val)) (= (@ (@ tptp.member_set_val I) (@ tptp.set_or650197513et_val K)) (@ (@ tptp.ord_less_eq_set_val K) I))))
% 0.26/0.67 (assert (forall ((A3 tptp.val)) (@ (@ tptp.ord_less_eq_set_val (@ tptp.set_or1288365508an_val A3)) (@ tptp.set_ord_atLeast_val A3))))
% 0.26/0.67 (assert (forall ((A3 tptp.val) (B3 tptp.val)) (= (@ (@ tptp.ord_less_eq_set_val (@ tptp.set_ord_atLeast_val A3)) (@ tptp.set_or1288365508an_val B3)) (@ (@ tptp.ord_less_val B3) A3))))
% 0.26/0.67 (assert (forall ((L tptp.set_val) (H tptp.set_val) (L2 tptp.set_val)) (= (@ (@ tptp.ord_le1742111550et_val (@ (@ tptp.set_or1554624499et_val L) H)) (@ tptp.set_or650197513et_val L2)) (or (not (@ (@ tptp.ord_less_eq_set_val L) H)) (@ (@ tptp.ord_less_eq_set_val L2) L)))))
% 0.26/0.67 (assert (forall ((L tptp.val) (H tptp.val) (L2 tptp.val)) (= (@ (@ tptp.ord_less_eq_set_val (@ (@ tptp.set_or18208019st_val L) H)) (@ tptp.set_ord_atLeast_val L2)) (or (not (@ (@ tptp.ord_less_eq_val L) H)) (@ (@ tptp.ord_less_eq_val L2) L)))))
% 0.26/0.67 (assert (forall ((X tptp.set_val) (Y2 tptp.set_val)) (= (@ (@ tptp.ord_le1742111550et_val (@ tptp.set_or867701765et_val X)) (@ tptp.set_or867701765et_val Y2)) (@ (@ tptp.ord_less_eq_set_val X) Y2))))
% 0.26/0.67 (assert (forall ((X tptp.val) (Y2 tptp.val)) (= (@ (@ tptp.ord_less_eq_set_val (@ tptp.set_ord_atMost_val X)) (@ tptp.set_ord_atMost_val Y2)) (@ (@ tptp.ord_less_eq_val X) Y2))))
% 0.26/0.67 (assert (forall ((A tptp.set_val) (B tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_set_val A) B)))))
% 0.26/0.67 (assert (forall ((C tptp.val) (A tptp.set_val)) (let ((_let_1 (@ tptp.member_val C))) (=> (not (@ _let_1 A)) (@ _let_1 (@ tptp.uminus1961393973et_val A))))))
% 0.26/0.67 (assert (forall ((C tptp.val) (A tptp.set_val)) (let ((_let_1 (@ tptp.member_val C))) (= (@ _let_1 (@ tptp.uminus1961393973et_val A)) (not (@ _let_1 A))))))
% 0.26/0.67 (assert (forall ((I tptp.val) (L tptp.val) (U tptp.val)) (= (@ (@ tptp.member_val I) (@ (@ tptp.set_or18208019st_val L) U)) (and (@ (@ tptp.ord_less_eq_val L) I) (@ (@ tptp.ord_less_eq_val I) U)))))
% 0.26/0.67 (assert (forall ((I tptp.set_val) (L tptp.set_val) (U tptp.set_val)) (= (@ (@ tptp.member_set_val I) (@ (@ tptp.set_or1554624499et_val L) U)) (and (@ (@ tptp.ord_less_eq_set_val L) I) (@ (@ tptp.ord_less_eq_set_val I) U)))))
% 0.26/0.67 (assert (forall ((L tptp.set_val) (H tptp.set_val) (L2 tptp.set_val) (H2 tptp.set_val)) (= (= (@ (@ tptp.set_or1554624499et_val L) H) (@ (@ tptp.set_or1554624499et_val L2) H2)) (or (and (= L L2) (= H H2)) (and (not (@ (@ tptp.ord_less_eq_set_val L) H)) (not (@ (@ tptp.ord_less_eq_set_val L2) H2)))))))
% 0.26/0.67 (assert (forall ((I tptp.val) (K tptp.val)) (= (@ (@ tptp.member_val I) (@ tptp.set_ord_atMost_val K)) (@ (@ tptp.ord_less_eq_val I) K))))
% 0.26/0.67 (assert (forall ((I tptp.set_val) (K tptp.set_val)) (= (@ (@ tptp.member_set_val I) (@ tptp.set_or867701765et_val K)) (@ (@ tptp.ord_less_eq_set_val I) K))))
% 0.26/0.67 (assert (forall ((I tptp.val) (K tptp.val)) (= (@ (@ tptp.member_val I) (@ tptp.set_ord_lessThan_val K)) (@ (@ tptp.ord_less_val I) K))))
% 0.26/0.67 (assert (forall ((A tptp.set_val) (B tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val A) B) (@ (@ tptp.ord_less_eq_set_val (@ tptp.uminus1961393973et_val B)) (@ tptp.uminus1961393973et_val A)))))
% 0.26/0.67 (assert (forall ((A tptp.set_val) (B tptp.set_val)) (= (@ (@ tptp.ord_less_eq_set_val (@ tptp.uminus1961393973et_val A)) (@ tptp.uminus1961393973et_val B)) (@ (@ tptp.ord_less_eq_set_val B) A))))
% 0.26/0.67 (assert (forall ((I tptp.val) (K tptp.val)) (= (@ (@ tptp.member_val I) (@ tptp.set_or1288365508an_val K)) (@ (@ tptp.ord_less_val K) I))))
% 0.26/0.67 (assert (forall ((A3 tptp.set_val) (B3 tptp.set_val) (C tptp.set_val) (D tptp.set_val)) (= (@ (@ tptp.ord_le1742111550et_val (@ (@ tptp.set_or1554624499et_val A3) B3)) (@ (@ tptp.set_or1554624499et_val C) D)) (or (not (@ (@ tptp.ord_less_eq_set_val A3) B3)) (and (@ (@ tptp.ord_less_eq_set_val C) A3) (@ (@ tptp.ord_less_eq_set_val B3) D))))))
% 0.26/0.67 (assert (forall ((A3 tptp.val) (B3 tptp.val) (C tptp.val) (D tptp.val)) (= (@ (@ tptp.ord_less_eq_set_val (@ (@ tptp.set_or18208019st_val A3) B3)) (@ (@ tptp.set_or18208019st_val C) D)) (or (not (@ (@ tptp.ord_less_eq_val A3) B3)) (and (@ (@ tptp.ord_less_eq_val C) A3) (@ (@ tptp.ord_less_eq_val B3) D))))))
% 0.26/0.67 (assert (forall ((L tptp.set_val) (H tptp.set_val) (H2 tptp.set_val)) (= (@ (@ tptp.ord_le1742111550et_val (@ (@ tptp.set_or1554624499et_val L) H)) (@ tptp.set_or867701765et_val H2)) (or (not (@ (@ tptp.ord_less_eq_set_val L) H)) (@ (@ tptp.ord_less_eq_set_val H) H2)))))
% 0.26/0.67 (assert (forall ((L tptp.val) (H tptp.val) (H2 tptp.val)) (= (@ (@ tptp.ord_less_eq_set_val (@ (@ tptp.set_or18208019st_val L) H)) (@ tptp.set_ord_atMost_val H2)) (or (not (@ (@ tptp.ord_less_eq_val L) H)) (@ (@ tptp.ord_less_eq_val H) H2)))))
% 0.26/0.67 (assert (forall ((A3 tptp.set_val) (B3 tptp.set_val) (C tptp.set_val) (D tptp.set_val)) (let ((_let_1 (@ tptp.ord_less_eq_set_val C))) (= (@ (@ tptp.ord_less_set_set_val (@ (@ tptp.set_or1554624499et_val A3) B3)) (@ (@ tptp.set_or1554624499et_val C) D)) (and (or (not (@ (@ tptp.ord_less_eq_set_val A3) B3)) (and (@ _let_1 A3) (@ (@ tptp.ord_less_eq_set_val B3) D) (or (@ (@ tptp.ord_less_set_val C) A3) (@ (@ tptp.ord_less_set_val B3) D)))) (@ _let_1 D))))))
% 0.26/0.67 (assert (forall ((C tptp.val) (A tptp.set_val)) (let ((_let_1 (@ tptp.member_val C))) (=> (@ _let_1 (@ tptp.uminus1961393973et_val A)) (not (@ _let_1 A))))))
% 0.26/0.67 (assert (forall ((A3 tptp.val) (B3 tptp.val)) (= (@ (@ tptp.ord_less_eq_set_val (@ tptp.set_ord_atMost_val A3)) (@ tptp.set_ord_lessThan_val B3)) (@ (@ tptp.ord_less_val A3) B3))))
% 0.26/0.67 (assert (forall ((Y2 tptp.set_val) (X tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val Y2) X) (not (@ (@ tptp.ord_less_set_val X) Y2)))))
% 0.26/0.67 (assert (= tptp.ord_less_eq_set_val (lambda ((X3 tptp.set_val) (Y4 tptp.set_val)) (or (@ (@ tptp.ord_less_set_val X3) Y4) (= X3 Y4)))))
% 0.26/0.67 (assert (= tptp.ord_less_set_val (lambda ((X3 tptp.set_val) (Y4 tptp.set_val)) (and (@ (@ tptp.ord_less_eq_set_val X3) Y4) (not (= X3 Y4))))))
% 0.26/0.67 (assert (forall ((A3 tptp.set_val) (B3 tptp.set_val) (F (-> tptp.set_val tptp.set_val)) (C tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val A3) B3) (=> (@ (@ tptp.ord_less_set_val (@ F B3)) C) (=> (forall ((X2 tptp.set_val) (Y3 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val X2) Y3) (@ (@ tptp.ord_less_eq_set_val (@ F X2)) (@ F Y3)))) (@ (@ tptp.ord_less_set_val (@ F A3)) C))))))
% 0.26/0.67 (assert (forall ((A3 tptp.set_val) (F (-> tptp.set_val tptp.set_val)) (B3 tptp.set_val) (C tptp.set_val)) (let ((_let_1 (@ tptp.ord_less_set_val A3))) (=> (@ _let_1 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_set_val B3) C) (=> (forall ((X2 tptp.set_val) (Y3 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val X2) Y3) (@ (@ tptp.ord_less_eq_set_val (@ F X2)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 0.26/0.67 (assert (forall ((A3 tptp.set_val) (B3 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val A3) B3) (=> (not (= A3 B3)) (@ (@ tptp.ord_less_set_val A3) B3)))))
% 0.26/0.67 (assert (forall ((X tptp.set_val) (Y2 tptp.set_val)) (=> (not (@ (@ tptp.ord_less_set_val X) Y2)) (= (@ (@ tptp.ord_less_eq_set_val X) Y2) (= X Y2)))))
% 0.26/0.67 (assert (forall ((X tptp.set_val) (Y2 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val X) Y2) (= (not (@ (@ tptp.ord_less_set_val X) Y2)) (= X Y2)))))
% 0.26/0.67 (assert (forall ((X tptp.set_val) (Y2 tptp.set_val)) (=> (@ (@ tptp.ord_less_set_val X) Y2) (@ (@ tptp.ord_less_eq_set_val X) Y2))))
% 0.26/0.67 (assert (forall ((X tptp.set_val) (Y2 tptp.set_val) (Z2 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val X) Y2) (=> (@ (@ tptp.ord_less_set_val Y2) Z2) (@ (@ tptp.ord_less_set_val X) Z2)))))
% 0.26/0.67 (assert (forall ((X tptp.set_val) (Y2 tptp.set_val) (Z2 tptp.set_val)) (let ((_let_1 (@ tptp.ord_less_set_val X))) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_eq_set_val Y2) Z2) (@ _let_1 Z2))))))
% 0.26/0.67 (assert (forall ((X tptp.set_val) (Y2 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val X) Y2) (or (@ (@ tptp.ord_less_set_val X) Y2) (= X Y2)))))
% 0.26/0.67 (assert (= tptp.ord_less_set_val (lambda ((X3 tptp.set_val) (Y4 tptp.set_val)) (and (@ (@ tptp.ord_less_eq_set_val X3) Y4) (not (@ (@ tptp.ord_less_eq_set_val Y4) X3))))))
% 0.26/0.67 (assert (forall ((A3 tptp.set_val) (B3 tptp.set_val) (C tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val A3) B3) (=> (@ (@ tptp.ord_less_set_val B3) C) (@ (@ tptp.ord_less_set_val A3) C)))))
% 0.26/0.67 (assert (forall ((A3 tptp.set_val) (B3 tptp.set_val) (C tptp.set_val)) (let ((_let_1 (@ tptp.ord_less_set_val A3))) (=> (@ _let_1 B3) (=> (@ (@ tptp.ord_less_eq_set_val B3) C) (@ _let_1 C))))))
% 0.26/0.67 (assert (= tptp.ord_less_eq_set_val (lambda ((A4 tptp.set_val) (B4 tptp.set_val)) (or (@ (@ tptp.ord_less_set_val A4) B4) (= A4 B4)))))
% 0.26/0.67 (assert (= tptp.ord_less_set_val (lambda ((A4 tptp.set_val) (B4 tptp.set_val)) (and (@ (@ tptp.ord_less_eq_set_val A4) B4) (not (= A4 B4))))))
% 0.26/0.67 (assert (forall ((B3 tptp.set_val) (A3 tptp.set_val) (C tptp.set_val)) (let ((_let_1 (@ tptp.ord_less_set_val C))) (=> (@ (@ tptp.ord_less_eq_set_val B3) A3) (=> (@ _let_1 B3) (@ _let_1 A3))))))
% 0.26/0.67 (assert (forall ((B3 tptp.set_val) (A3 tptp.set_val) (C tptp.set_val)) (=> (@ (@ tptp.ord_less_set_val B3) A3) (=> (@ (@ tptp.ord_less_eq_set_val C) B3) (@ (@ tptp.ord_less_set_val C) A3)))))
% 0.26/0.67 (assert (forall ((A3 tptp.set_val) (B3 tptp.set_val)) (=> (@ (@ tptp.ord_less_set_val A3) B3) (@ (@ tptp.ord_less_eq_set_val A3) B3))))
% 0.26/0.67 (assert (= tptp.ord_less_eq_set_val (lambda ((B4 tptp.set_val) (A4 tptp.set_val)) (or (@ (@ tptp.ord_less_set_val B4) A4) (= A4 B4)))))
% 0.26/0.67 (assert (= tptp.ord_less_set_val (lambda ((B4 tptp.set_val) (A4 tptp.set_val)) (and (@ (@ tptp.ord_less_eq_set_val B4) A4) (not (= A4 B4))))))
% 0.26/0.67 (assert (forall ((B3 tptp.set_val) (A3 tptp.set_val)) (=> (@ (@ tptp.ord_less_set_val B3) A3) (@ (@ tptp.ord_less_eq_set_val B3) A3))))
% 0.26/0.67 (assert (forall ((A3 tptp.set_val) (B3 tptp.set_val)) (=> (not (= A3 B3)) (=> (@ (@ tptp.ord_less_eq_set_val A3) B3) (@ (@ tptp.ord_less_set_val A3) B3)))))
% 0.26/0.67 (assert (forall ((A tptp.set_val) (B tptp.set_val)) (=> (@ (@ tptp.ord_less_set_val A) B) (not (=> (@ (@ tptp.ord_less_eq_set_val A) B) (@ (@ tptp.ord_less_eq_set_val B) A))))))
% 0.26/0.67 (assert (= tptp.ord_less_set_val (lambda ((A2 tptp.set_val) (B2 tptp.set_val)) (and (@ (@ tptp.ord_less_eq_set_val A2) B2) (not (= A2 B2))))))
% 0.26/0.67 (assert (forall ((A tptp.set_val) (B tptp.set_val)) (=> (@ (@ tptp.ord_less_set_val A) B) (@ (@ tptp.ord_less_eq_set_val A) B))))
% 0.26/0.67 (assert (forall ((A tptp.set_val) (B tptp.set_val) (C2 tptp.set_val)) (let ((_let_1 (@ tptp.ord_less_set_val A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_set_val B) C2) (@ _let_1 C2))))))
% 0.26/0.67 (assert (= tptp.ord_less_set_val (lambda ((A2 tptp.set_val) (B2 tptp.set_val)) (and (@ (@ tptp.ord_less_eq_set_val A2) B2) (not (@ (@ tptp.ord_less_eq_set_val B2) A2))))))
% 0.26/0.67 (assert (forall ((A tptp.set_val) (B tptp.set_val) (C2 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val A) B) (=> (@ (@ tptp.ord_less_set_val B) C2) (@ (@ tptp.ord_less_set_val A) C2)))))
% 0.26/0.67 (assert (= tptp.ord_less_eq_set_val (lambda ((A2 tptp.set_val) (B2 tptp.set_val)) (or (@ (@ tptp.ord_less_set_val A2) B2) (= A2 B2)))))
% 0.26/0.67 (assert (forall ((X tptp.set_val) (Y2 tptp.set_val)) (= (@ (@ tptp.ord_less_eq_set_val (@ tptp.uminus1961393973et_val X)) (@ tptp.uminus1961393973et_val Y2)) (@ (@ tptp.ord_less_eq_set_val Y2) X))))
% 0.26/0.67 (assert (forall ((X tptp.set_val) (Y2 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val X) Y2) (@ (@ tptp.ord_less_eq_set_val (@ tptp.uminus1961393973et_val Y2)) (@ tptp.uminus1961393973et_val X)))))
% 0.26/0.67 (assert (forall ((Y2 tptp.set_val) (X tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val Y2) (@ tptp.uminus1961393973et_val X)) (@ (@ tptp.ord_less_eq_set_val X) (@ tptp.uminus1961393973et_val Y2)))))
% 0.26/0.67 (assert (forall ((Y2 tptp.set_val) (X tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val (@ tptp.uminus1961393973et_val Y2)) X) (@ (@ tptp.ord_less_eq_set_val (@ tptp.uminus1961393973et_val X)) Y2))))
% 0.26/0.67 (assert (forall ((A tptp.set_val) (B tptp.set_val) (C tptp.val)) (let ((_let_1 (@ tptp.member_val C))) (=> (@ (@ tptp.ord_less_set_val A) B) (=> (@ _let_1 A) (@ _let_1 B))))))
% 0.26/0.67 (assert (forall ((C tptp.val) (B tptp.set_val) (A tptp.set_val)) (let ((_let_1 (@ tptp.member_val C))) (=> (=> (not (@ _let_1 B)) (@ _let_1 A)) (@ _let_1 (@ (@ tptp.sup_sup_set_val A) B))))))
% 0.26/0.67 (assert (forall ((C tptp.val) (A tptp.set_val) (B tptp.set_val)) (let ((_let_1 (@ tptp.member_val C))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_val A) B)) (or (@ _let_1 A) (@ _let_1 B))))))
% 0.26/0.67 (assert (forall ((X tptp.set_val) (Y2 tptp.set_val) (Z2 tptp.set_val)) (= (@ (@ tptp.ord_less_eq_set_val (@ (@ tptp.sup_sup_set_val X) Y2)) Z2) (and (@ (@ tptp.ord_less_eq_set_val X) Z2) (@ (@ tptp.ord_less_eq_set_val Y2) Z2)))))
% 0.26/0.67 (assert (forall ((B3 tptp.set_val) (C tptp.set_val) (A3 tptp.set_val)) (= (@ (@ tptp.ord_less_eq_set_val (@ (@ tptp.sup_sup_set_val B3) C)) A3) (and (@ (@ tptp.ord_less_eq_set_val B3) A3) (@ (@ tptp.ord_less_eq_set_val C) A3)))))
% 0.26/0.67 (assert (forall ((A tptp.set_val) (B tptp.set_val) (C2 tptp.set_val)) (= (@ (@ tptp.ord_less_eq_set_val (@ (@ tptp.sup_sup_set_val A) B)) C2) (and (@ (@ tptp.ord_less_eq_set_val A) C2) (@ (@ tptp.ord_less_eq_set_val B) C2)))))
% 0.26/0.67 (assert (forall ((I tptp.val) (L tptp.val) (U tptp.val)) (= (@ (@ tptp.member_val I) (@ (@ tptp.set_or2126567818an_val L) U)) (and (@ (@ tptp.ord_less_val L) I) (@ (@ tptp.ord_less_val I) U)))))
% 0.26/0.67 (assert (forall ((C tptp.set_val) (B3 tptp.set_val) (A3 tptp.set_val)) (let ((_let_1 (@ tptp.ord_less_eq_set_val C))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.sup_sup_set_val A3) B3))))))
% 0.26/0.67 (assert (forall ((C tptp.set_val) (A3 tptp.set_val) (B3 tptp.set_val)) (let ((_let_1 (@ tptp.ord_less_eq_set_val C))) (=> (@ _let_1 A3) (@ _let_1 (@ (@ tptp.sup_sup_set_val A3) B3))))))
% 0.26/0.67 (assert (= tptp.ord_less_eq_set_val (lambda ((A4 tptp.set_val) (B4 tptp.set_val)) (= (@ (@ tptp.sup_sup_set_val A4) B4) B4))))
% 0.26/0.67 (assert (= tptp.ord_less_eq_set_val (lambda ((B4 tptp.set_val) (A4 tptp.set_val)) (= (@ (@ tptp.sup_sup_set_val A4) B4) A4))))
% 0.26/0.67 (assert (forall ((B3 tptp.set_val) (A3 tptp.set_val)) (@ (@ tptp.ord_less_eq_set_val B3) (@ (@ tptp.sup_sup_set_val A3) B3))))
% 0.26/0.67 (assert (forall ((A3 tptp.set_val) (B3 tptp.set_val)) (@ (@ tptp.ord_less_eq_set_val A3) (@ (@ tptp.sup_sup_set_val A3) B3))))
% 0.26/0.67 (assert (= tptp.ord_less_eq_set_val (lambda ((B4 tptp.set_val) (A4 tptp.set_val)) (= A4 (@ (@ tptp.sup_sup_set_val A4) B4)))))
% 0.26/0.67 (assert (forall ((B3 tptp.set_val) (A3 tptp.set_val) (C tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val B3) A3) (=> (@ (@ tptp.ord_less_eq_set_val C) A3) (@ (@ tptp.ord_less_eq_set_val (@ (@ tptp.sup_sup_set_val B3) C)) A3)))))
% 0.26/0.67 (assert (forall ((B3 tptp.set_val) (C tptp.set_val) (A3 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val (@ (@ tptp.sup_sup_set_val B3) C)) A3) (not (=> (@ (@ tptp.ord_less_eq_set_val B3) A3) (not (@ (@ tptp.ord_less_eq_set_val C) A3)))))))
% 0.26/0.67 (assert (forall ((X tptp.set_val) (Y2 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val X) Y2) (= (@ (@ tptp.sup_sup_set_val X) Y2) Y2))))
% 0.26/0.67 (assert (forall ((Y2 tptp.set_val) (X tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val Y2) X) (= (@ (@ tptp.sup_sup_set_val X) Y2) X))))
% 0.26/0.67 (assert (forall ((A3 tptp.set_val) (B3 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val A3) B3) (= (@ (@ tptp.sup_sup_set_val A3) B3) B3))))
% 0.83/1.05 (assert (forall ((B3 tptp.set_val) (A3 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val B3) A3) (= (@ (@ tptp.sup_sup_set_val A3) B3) A3))))
% 0.83/1.05 (assert (forall ((F (-> tptp.set_val tptp.set_val tptp.set_val)) (X tptp.set_val) (Y2 tptp.set_val)) (=> (forall ((X2 tptp.set_val) (Y3 tptp.set_val)) (@ (@ tptp.ord_less_eq_set_val X2) (@ (@ F X2) Y3))) (=> (forall ((X2 tptp.set_val) (Y3 tptp.set_val)) (@ (@ tptp.ord_less_eq_set_val Y3) (@ (@ F X2) Y3))) (=> (forall ((X2 tptp.set_val) (Y3 tptp.set_val) (Z3 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val Y3) X2) (=> (@ (@ tptp.ord_less_eq_set_val Z3) X2) (@ (@ tptp.ord_less_eq_set_val (@ (@ F Y3) Z3)) X2)))) (= (@ (@ tptp.sup_sup_set_val X) Y2) (@ (@ F X) Y2)))))))
% 0.83/1.05 (assert (forall ((A3 tptp.set_val) (B3 tptp.set_val)) (=> (= A3 (@ (@ tptp.sup_sup_set_val A3) B3)) (@ (@ tptp.ord_less_eq_set_val B3) A3))))
% 0.83/1.05 (assert (forall ((X tptp.val) (Y2 tptp.val)) (= (@ (@ (@ tptp.if_val false) X) Y2) Y2)))
% 0.83/1.05 (assert (forall ((X tptp.val) (Y2 tptp.val)) (= (@ (@ (@ tptp.if_val true) X) Y2) X)))
% 0.83/1.05 (assert (forall ((X tptp.set_val) (Y2 tptp.set_val)) (= (@ (@ (@ tptp.if_set_val false) X) Y2) Y2)))
% 0.83/1.05 (assert (forall ((X tptp.set_val) (Y2 tptp.set_val)) (= (@ (@ (@ tptp.if_set_val true) X) Y2) X)))
% 0.83/1.05 (assert (forall ((X (-> Bool tptp.set_val)) (Y2 (-> Bool tptp.set_val))) (= (@ (@ (@ tptp.if_o_set_val false) X) Y2) Y2)))
% 0.83/1.05 (assert (forall ((X (-> Bool tptp.set_val)) (Y2 (-> Bool tptp.set_val))) (= (@ (@ (@ tptp.if_o_set_val true) X) Y2) X)))
% 0.83/1.05 (assert (forall ((P Bool)) (or (= P true) (= P false))))
% 0.83/1.05 (assert (forall ((X tptp.set_set_val) (Y2 tptp.set_set_val)) (= (@ (@ (@ tptp.if_set_set_val false) X) Y2) Y2)))
% 0.83/1.05 (assert (forall ((X tptp.set_set_val) (Y2 tptp.set_set_val)) (= (@ (@ (@ tptp.if_set_set_val true) X) Y2) X)))
% 0.83/1.05 (assert (not (@ (@ tptp.ord_less_eq_set_val tptp.scc) tptp.p)))
% 0.83/1.05 (set-info :filename cvc5---1.0.5_27339)
% 0.83/1.05 (check-sat-assuming ( true ))
% 0.83/1.05 ------- get file name : TPTP file name is ITP079^1
% 0.83/1.05 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_27339.smt2...
% 0.83/1.05 --- Run --ho-elim --full-saturate-quant at 10...
% 0.83/1.05 % SZS status Theorem for ITP079^1
% 0.83/1.05 % SZS output start Proof for ITP079^1
% 0.83/1.05 (
% 0.83/1.05 (let ((_let_1 (not (@ (@ tptp.ord_less_eq_set_val tptp.scc) tptp.p)))) (let ((_let_2 (= tptp.ord_less_set_val (lambda ((X3 tptp.set_val) (Y4 tptp.set_val)) (and (@ (@ tptp.ord_less_eq_set_val X3) Y4) (not (= X3 Y4))))))) (let ((_let_3 (= tptp.refine275900453et_val (lambda ((Le (-> tptp.set_val tptp.set_val Bool))) (forall ((X3 tptp.set_val)) (@ (@ Le X3) X3)))))) (let ((_let_4 (= tptp.refine1929691018et_val (lambda ((Alpha2 (-> tptp.set_val tptp.set_val)) (Gamma2 (-> tptp.set_val tptp.set_val))) (forall ((C4 tptp.set_val) (A4 tptp.set_val)) (= (@ (@ tptp.ord_less_eq_set_val C4) (@ Gamma2 A4)) (@ (@ tptp.ord_less_eq_set_val (@ Alpha2 C4)) A4))))))) (let ((_let_5 (= tptp.refine855985034et_val (lambda ((Alpha2 (-> tptp.set_set_val tptp.set_set_val)) (Gamma2 (-> tptp.set_set_val tptp.set_set_val))) (forall ((C4 tptp.set_set_val) (A4 tptp.set_set_val)) (= (@ (@ tptp.ord_le1742111550et_val C4) (@ Gamma2 A4)) (@ (@ tptp.ord_le1742111550et_val (@ Alpha2 C4)) A4))))))) (let ((_let_6 (= tptp.refine86398879et_val (lambda ((Alpha2 (-> tptp.set_set_val Bool tptp.set_val)) (Gamma2 (-> (-> Bool tptp.set_val) tptp.set_set_val))) (forall ((C4 tptp.set_set_val) (A4 (-> Bool tptp.set_val))) (= (@ (@ tptp.ord_le1742111550et_val C4) (@ Gamma2 A4)) (@ (@ tptp.ord_le994826475et_val (@ Alpha2 C4)) A4))))))) (let ((_let_7 (= tptp.refine8163498et_val (lambda ((Alpha2 (-> tptp.set_set_val tptp.set_val)) (Gamma2 (-> tptp.set_val tptp.set_set_val))) (forall ((C4 tptp.set_set_val) (A4 tptp.set_val)) (= (@ (@ tptp.ord_le1742111550et_val C4) (@ Gamma2 A4)) (@ (@ tptp.ord_less_eq_set_val (@ Alpha2 C4)) A4))))))) (let ((_let_8 (= tptp.refine1169396807et_val (lambda ((Alpha2 (-> (-> Bool tptp.set_val) tptp.set_set_val)) (Gamma2 (-> tptp.set_set_val Bool tptp.set_val))) (forall ((C4 (-> Bool tptp.set_val)) (A4 tptp.set_set_val)) (= (@ (@ tptp.ord_le994826475et_val C4) (@ Gamma2 A4)) (@ (@ tptp.ord_le1742111550et_val (@ Alpha2 C4)) A4))))))) (let ((_let_9 (= tptp.refine1924899106et_val (lambda ((Alpha2 (-> (-> Bool tptp.set_val) Bool tptp.set_val)) (Gamma2 (-> (-> Bool tptp.set_val) Bool tptp.set_val))) (forall ((C4 (-> Bool tptp.set_val)) (A4 (-> Bool tptp.set_val))) (= (@ (@ tptp.ord_le994826475et_val C4) (@ Gamma2 A4)) (@ (@ tptp.ord_le994826475et_val (@ Alpha2 C4)) A4))))))) (let ((_let_10 (= tptp.refine1948536167et_val (lambda ((Alpha2 (-> (-> Bool tptp.set_val) tptp.set_val)) (Gamma2 (-> tptp.set_val Bool tptp.set_val))) (forall ((C4 (-> Bool tptp.set_val)) (A4 tptp.set_val)) (= (@ (@ tptp.ord_le994826475et_val C4) (@ Gamma2 A4)) (@ (@ tptp.ord_less_eq_set_val (@ Alpha2 C4)) A4))))))) (let ((_let_11 (= tptp.refine1315043946et_val (lambda ((Alpha2 (-> tptp.set_val tptp.set_set_val)) (Gamma2 (-> tptp.set_set_val tptp.set_val))) (forall ((C4 tptp.set_val) (A4 tptp.set_set_val)) (= (@ (@ tptp.ord_less_eq_set_val C4) (@ Gamma2 A4)) (@ (@ tptp.ord_le1742111550et_val (@ Alpha2 C4)) A4))))))) (let ((_let_12 (= tptp.refine51544255et_val (lambda ((Alpha2 (-> tptp.set_val Bool tptp.set_val)) (Gamma2 (-> (-> Bool tptp.set_val) tptp.set_val))) (forall ((C4 tptp.set_val) (A4 (-> Bool tptp.set_val))) (= (@ (@ tptp.ord_less_eq_set_val C4) (@ Gamma2 A4)) (@ (@ tptp.ord_le994826475et_val (@ Alpha2 C4)) A4))))))) (let ((_let_13 (= tptp.order_650823122et_val (lambda ((F2 (-> tptp.set_set_val tptp.set_val))) (forall ((X3 tptp.set_set_val) (Y4 tptp.set_set_val)) (=> (@ (@ tptp.ord_le1742111550et_val X3) Y4) (@ (@ tptp.ord_less_eq_set_val (@ F2 Y4)) (@ F2 X3)))))))) (let ((_let_14 (= tptp.order_255079095et_val (lambda ((F2 (-> tptp.val Bool tptp.set_val))) (forall ((X3 tptp.val) (Y4 tptp.val)) (=> (@ (@ tptp.ord_less_eq_val X3) Y4) (@ (@ tptp.ord_le994826475et_val (@ F2 Y4)) (@ F2 X3)))))))) (let ((_let_15 (= tptp.order_23236447al_val (lambda ((F2 (-> (-> Bool tptp.set_val) tptp.val))) (forall ((X3 (-> Bool tptp.set_val)) (Y4 (-> Bool tptp.set_val))) (=> (@ (@ tptp.ord_le994826475et_val X3) Y4) (@ (@ tptp.ord_less_eq_val (@ F2 Y4)) (@ F2 X3)))))))) (let ((_let_16 (= tptp.order_1957703570et_val (lambda ((F2 (-> tptp.set_val tptp.set_set_val))) (forall ((X3 tptp.set_val) (Y4 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val X3) Y4) (@ (@ tptp.ord_le1742111550et_val (@ F2 Y4)) (@ F2 X3)))))))) (let ((_let_17 (= tptp.order_1520822002al_val (lambda ((F2 (-> tptp.set_set_val tptp.val))) (forall ((X3 tptp.set_set_val) (Y4 tptp.set_set_val)) (=> (@ (@ tptp.ord_le1742111550et_val X3) Y4) (@ (@ tptp.ord_less_eq_val (@ F2 Y4)) (@ F2 X3)))))))) (let ((_let_18 (= tptp.order_1945059954et_val (lambda ((F2 (-> tptp.val tptp.set_set_val))) (forall ((X3 tptp.val) (Y4 tptp.val)) (=> (@ (@ tptp.ord_less_eq_val X3) Y4) (@ (@ tptp.ord_le1742111550et_val (@ F2 Y4)) (@ F2 X3)))))))) (let ((_let_19 (= tptp.order_1484138386et_val (lambda ((F2 (-> tptp.val tptp.set_val))) (forall ((X3 tptp.val) (Y4 tptp.val)) (=> (@ (@ tptp.ord_less_eq_val X3) Y4) (@ (@ tptp.ord_less_eq_set_val (@ F2 Y4)) (@ F2 X3)))))))) (let ((_let_20 (= tptp.order_1375876562al_val (lambda ((F2 (-> tptp.set_val tptp.val))) (forall ((X3 tptp.set_val) (Y4 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val X3) Y4) (@ (@ tptp.ord_less_eq_val (@ F2 Y4)) (@ F2 X3)))))))) (let ((_let_21 (= tptp.order_1689798834al_val (lambda ((F2 (-> tptp.val tptp.val))) (forall ((X3 tptp.val) (Y4 tptp.val)) (=> (@ (@ tptp.ord_less_eq_val X3) Y4) (@ (@ tptp.ord_less_eq_val (@ F2 Y4)) (@ F2 X3)))))))) (let ((_let_22 (= tptp.order_1719375026et_val (lambda ((F2 (-> tptp.set_val tptp.set_val))) (forall ((X3 tptp.set_val) (Y4 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val X3) Y4) (@ (@ tptp.ord_less_eq_set_val (@ F2 Y4)) (@ F2 X3)))))))) (let ((_let_23 (= tptp.ord_le936627147et_val (lambda ((X4 (-> Bool tptp.set_set_val)) (Y6 (-> Bool tptp.set_set_val))) (and (@ (@ tptp.ord_le1742111550et_val (@ X4 false)) (@ Y6 false)) (@ (@ tptp.ord_le1742111550et_val (@ X4 true)) (@ Y6 true))))))) (let ((_let_24 (= tptp.ord_less_eq_o_val (lambda ((X4 (-> Bool tptp.val)) (Y6 (-> Bool tptp.val))) (and (@ (@ tptp.ord_less_eq_val (@ X4 false)) (@ Y6 false)) (@ (@ tptp.ord_less_eq_val (@ X4 true)) (@ Y6 true))))))) (let ((_let_25 (= tptp.ord_le1441829300et_val (lambda ((X4 (-> Bool Bool tptp.set_val)) (Y6 (-> Bool Bool tptp.set_val))) (and (@ (@ tptp.ord_le994826475et_val (@ X4 false)) (@ Y6 false)) (@ (@ tptp.ord_le994826475et_val (@ X4 true)) (@ Y6 true))))))) (let ((_let_26 (= tptp.ord_le994826475et_val (lambda ((F2 (-> Bool tptp.set_val)) (G2 (-> Bool tptp.set_val))) (forall ((X3 Bool)) (@ (@ tptp.ord_less_eq_set_val (@ F2 X3)) (@ G2 X3))))))) (let ((_let_27 (= tptp.ord_less_eq_set_val (lambda ((A2 tptp.set_val) (B2 tptp.set_val)) (forall ((X3 tptp.val)) (let ((_let_1 (@ tptp.member_val X3))) (=> (@ _let_1 A2) (@ _let_1 B2)))))))) (let ((_let_28 (= tptp.ord_le1742111550et_val (lambda ((A2 tptp.set_set_val) (B2 tptp.set_set_val)) (forall ((X3 tptp.set_val)) (let ((_let_1 (@ tptp.member_set_val X3))) (=> (@ _let_1 A2) (@ _let_1 B2)))))))) (let ((_let_29 (forall ((X tptp.val)) (let ((_let_1 (@ tptp.member_val X))) (=> (@ _let_1 tptp.scc) (@ _let_1 tptp.p)))))) (let ((_let_30 (forall ((X3 tptp.val)) (let ((_let_1 (ho_61 k_60 X3))) (or (not (ho_53 _let_1 tptp.scc)) (ho_53 _let_1 tptp.p)))))) (let ((_let_31 (forall ((X tptp.val)) (let ((_let_1 (ho_61 k_60 X))) (or (not (ho_53 _let_1 tptp.scc)) (ho_53 _let_1 tptp.p)))))) (let ((_let_32 (forall ((u |u_(-> _u_(-> tptp.val Bool)_ tptp.set_val)|) (e tptp.set_val) (i |u_(-> tptp.val Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.val Bool)_ tptp.set_val)|)) (not (forall ((ii |u_(-> tptp.val Bool)|)) (= (ho_136 v ii) (ite (= i ii) e (ho_136 u ii)))))))))) (let ((_let_33 (forall ((x |u_(-> _u_(-> tptp.val Bool)_ tptp.set_val)|) (y |u_(-> _u_(-> tptp.val Bool)_ tptp.set_val)|)) (or (not (forall ((z |u_(-> tptp.val Bool)|)) (= (ho_136 x z) (ho_136 y z)))) (= x y))))) (let ((_let_34 (forall ((u |u_(-> Bool tptp.set_set_val tptp.set_set_val tptp.set_set_val)|) (e |u_(-> tptp.set_set_val tptp.set_set_val tptp.set_set_val)|) (i Bool)) (not (forall ((v |u_(-> Bool tptp.set_set_val tptp.set_set_val tptp.set_set_val)|)) (not (forall ((ii Bool)) (= (ho_128 v ii) (ite (= i ii) e (ho_128 u ii)))))))))) (let ((_let_35 (forall ((x |u_(-> Bool tptp.set_set_val tptp.set_set_val tptp.set_set_val)|) (y |u_(-> Bool tptp.set_set_val tptp.set_set_val tptp.set_set_val)|)) (or (not (forall ((z Bool)) (= (ho_128 x z) (ho_128 y z)))) (= x y))))) (let ((_let_36 (forall ((u |u_(-> tptp.val Bool tptp.set_val)|) (e |u_(-> Bool tptp.set_val)|) (i tptp.val)) (not (forall ((v |u_(-> tptp.val Bool tptp.set_val)|)) (not (forall ((ii tptp.val)) (= (ho_142 v ii) (ite (= i ii) e (ho_142 u ii)))))))))) (let ((_let_37 (forall ((x |u_(-> tptp.val Bool tptp.set_val)|) (y |u_(-> tptp.val Bool tptp.set_val)|)) (or (not (forall ((z tptp.val)) (= (ho_142 x z) (ho_142 y z)))) (= x y))))) (let ((_let_38 (forall ((u |u_(-> Bool tptp.set_val tptp.set_val tptp.set_val)|) (e |u_(-> tptp.set_val tptp.set_val tptp.set_val)|) (i Bool)) (not (forall ((v |u_(-> Bool tptp.set_val tptp.set_val tptp.set_val)|)) (not (forall ((ii Bool)) (= (ho_132 v ii) (ite (= i ii) e (ho_132 u ii)))))))))) (let ((_let_39 (forall ((x |u_(-> Bool tptp.set_val tptp.set_val tptp.set_val)|) (y |u_(-> Bool tptp.set_val tptp.set_val tptp.set_val)|)) (or (not (forall ((z Bool)) (= (ho_132 x z) (ho_132 y z)))) (= x y))))) (let ((_let_40 (forall ((u |u_(-> tptp.set_val tptp.set_val tptp.set_set_val)|) (e |u_(-> tptp.set_val tptp.set_set_val)|) (i tptp.set_val)) (not (forall ((v |u_(-> tptp.set_val tptp.set_val tptp.set_set_val)|)) (not (forall ((ii tptp.set_val)) (= (ho_192 v ii) (ite (= i ii) e (ho_192 u ii)))))))))) (let ((_let_41 (forall ((x |u_(-> tptp.set_val tptp.set_val tptp.set_set_val)|) (y |u_(-> tptp.set_val tptp.set_val tptp.set_set_val)|)) (or (not (forall ((z tptp.set_val)) (= (ho_192 x z) (ho_192 y z)))) (= x y))))) (let ((_let_42 (forall ((u |u_(-> _u_(-> tptp.set_val Bool)_ tptp.set_set_val)|) (e tptp.set_set_val) (i |u_(-> tptp.set_val Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.set_val Bool)_ tptp.set_set_val)|)) (not (forall ((ii |u_(-> tptp.set_val Bool)|)) (= (ho_134 v ii) (ite (= i ii) e (ho_134 u ii)))))))))) (let ((_let_43 (forall ((x |u_(-> _u_(-> tptp.set_val Bool)_ tptp.set_set_val)|) (y |u_(-> _u_(-> tptp.set_val Bool)_ tptp.set_set_val)|)) (or (not (forall ((z |u_(-> tptp.set_val Bool)|)) (= (ho_134 x z) (ho_134 y z)))) (= x y))))) (let ((_let_44 (forall ((u |u_(-> Bool _u_(-> Bool tptp.set_val)_ _u_(-> Bool tptp.set_val)_ Bool tptp.set_val)|) (e |u_(-> _u_(-> Bool tptp.set_val)_ _u_(-> Bool tptp.set_val)_ Bool tptp.set_val)|) (i Bool)) (not (forall ((v |u_(-> Bool _u_(-> Bool tptp.set_val)_ _u_(-> Bool tptp.set_val)_ Bool tptp.set_val)|)) (not (forall ((ii Bool)) (= (ho_120 v ii) (ite (= i ii) e (ho_120 u ii)))))))))) (let ((_let_45 (forall ((x |u_(-> Bool _u_(-> Bool tptp.set_val)_ _u_(-> Bool tptp.set_val)_ Bool tptp.set_val)|) (y |u_(-> Bool _u_(-> Bool tptp.set_val)_ _u_(-> Bool tptp.set_val)_ Bool tptp.set_val)|)) (or (not (forall ((z Bool)) (= (ho_120 x z) (ho_120 y z)))) (= x y))))) (let ((_let_46 (forall ((u |u_(-> tptp.set_set_val tptp.set_set_val tptp.set_set_val)|) (e |u_(-> tptp.set_set_val tptp.set_set_val)|) (i tptp.set_set_val)) (not (forall ((v |u_(-> tptp.set_set_val tptp.set_set_val tptp.set_set_val)|)) (not (forall ((ii tptp.set_set_val)) (= (ho_129 v ii) (ite (= i ii) e (ho_129 u ii)))))))))) (let ((_let_47 (forall ((x |u_(-> tptp.set_set_val tptp.set_set_val tptp.set_set_val)|) (y |u_(-> tptp.set_set_val tptp.set_set_val tptp.set_set_val)|)) (or (not (forall ((z tptp.set_set_val)) (= (ho_129 x z) (ho_129 y z)))) (= x y))))) (let ((_let_48 (forall ((u |u_(-> tptp.set_val Bool tptp.set_val)|) (e |u_(-> Bool tptp.set_val)|) (i tptp.set_val)) (not (forall ((v |u_(-> tptp.set_val Bool tptp.set_val)|)) (not (forall ((ii tptp.set_val)) (= (ho_160 v ii) (ite (= i ii) e (ho_160 u ii)))))))))) (let ((_let_49 (forall ((x |u_(-> tptp.set_val Bool tptp.set_val)|) (y |u_(-> tptp.set_val Bool tptp.set_val)|)) (or (not (forall ((z tptp.set_val)) (= (ho_160 x z) (ho_160 y z)))) (= x y))))) (let ((_let_50 (forall ((u |u_(-> tptp.set_set_val tptp.set_set_val)|) (e tptp.set_set_val) (i tptp.set_set_val)) (not (forall ((v |u_(-> tptp.set_set_val tptp.set_set_val)|)) (not (forall ((ii tptp.set_set_val)) (= (ho_130 v ii) (ite (= i ii) e (ho_130 u ii)))))))))) (let ((_let_51 (forall ((x |u_(-> tptp.set_set_val tptp.set_set_val)|) (y |u_(-> tptp.set_set_val tptp.set_set_val)|)) (or (not (forall ((z tptp.set_set_val)) (= (ho_130 x z) (ho_130 y z)))) (= x y))))) (let ((_let_52 (forall ((u |u_(-> _u_(-> tptp.set_val Bool)_ tptp.set_val)|) (e tptp.set_val) (i |u_(-> tptp.set_val Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.set_val Bool)_ tptp.set_val)|)) (not (forall ((ii |u_(-> tptp.set_val Bool)|)) (= (ho_152 v ii) (ite (= i ii) e (ho_152 u ii)))))))))) (let ((_let_53 (forall ((x |u_(-> _u_(-> tptp.set_val Bool)_ tptp.set_val)|) (y |u_(-> _u_(-> tptp.set_val Bool)_ tptp.set_val)|)) (or (not (forall ((z |u_(-> tptp.set_val Bool)|)) (= (ho_152 x z) (ho_152 y z)))) (= x y))))) (let ((_let_54 (forall ((u |u_(-> tptp.val tptp.val tptp.val)|) (e |u_(-> tptp.val tptp.val)|) (i tptp.val)) (not (forall ((v |u_(-> tptp.val tptp.val tptp.val)|)) (not (forall ((ii tptp.val)) (= (ho_125 v ii) (ite (= i ii) e (ho_125 u ii)))))))))) (let ((_let_55 (forall ((x |u_(-> tptp.val tptp.val tptp.val)|) (y |u_(-> tptp.val tptp.val tptp.val)|)) (or (not (forall ((z tptp.val)) (= (ho_125 x z) (ho_125 y z)))) (= x y))))) (let ((_let_56 (forall ((u |u_(-> tptp.set_val tptp.val)|) (e tptp.val) (i tptp.set_val)) (not (forall ((v |u_(-> tptp.set_val tptp.val)|)) (not (forall ((ii tptp.set_val)) (= (ho_138 v ii) (ite (= i ii) e (ho_138 u ii)))))))))) (let ((_let_57 (forall ((x |u_(-> tptp.set_val tptp.val)|) (y |u_(-> tptp.set_val tptp.val)|)) (or (not (forall ((z tptp.set_val)) (= (ho_138 x z) (ho_138 y z)))) (= x y))))) (let ((_let_58 (forall ((u |u_(-> Bool tptp.set_val)|) (e tptp.set_val) (i Bool)) (not (forall ((v |u_(-> Bool tptp.set_val)|)) (not (forall ((ii Bool)) (= (ho_71 v ii) (ite (= i ii) e (ho_71 u ii)))))))))) (let ((_let_59 (forall ((x |u_(-> Bool tptp.set_val)|) (y |u_(-> Bool tptp.set_val)|)) (or (not (forall ((z Bool)) (= (ho_71 x z) (ho_71 y z)))) (= x y))))) (let ((_let_60 (forall ((u |u_(-> _u_(-> Bool tptp.set_val)_ Bool tptp.set_val)|) (e |u_(-> Bool tptp.set_val)|) (i |u_(-> Bool tptp.set_val)|)) (not (forall ((v |u_(-> _u_(-> Bool tptp.set_val)_ Bool tptp.set_val)|)) (not (forall ((ii |u_(-> Bool tptp.set_val)|)) (= (ho_122 v ii) (ite (= i ii) e (ho_122 u ii)))))))))) (let ((_let_61 (forall ((x |u_(-> _u_(-> Bool tptp.set_val)_ Bool tptp.set_val)|) (y |u_(-> _u_(-> Bool tptp.set_val)_ Bool tptp.set_val)|)) (or (not (forall ((z |u_(-> Bool tptp.set_val)|)) (= (ho_122 x z) (ho_122 y z)))) (= x y))))) (let ((_let_62 (forall ((u |u_(-> tptp.set_set_val tptp.set_val Bool)|) (e |u_(-> tptp.set_val Bool)|) (i tptp.set_set_val)) (not (forall ((v |u_(-> tptp.set_set_val tptp.set_val Bool)|)) (not (forall ((ii tptp.set_set_val)) (= (ho_94 v ii) (ite (= i ii) e (ho_94 u ii)))))))))) (let ((_let_63 (forall ((x |u_(-> tptp.set_set_val tptp.set_val Bool)|) (y |u_(-> tptp.set_set_val tptp.set_val Bool)|)) (or (not (forall ((z tptp.set_set_val)) (= (ho_94 x z) (ho_94 y z)))) (= x y))))) (let ((_let_64 (forall ((u |u_(-> Bool tptp.val tptp.val tptp.val)|) (e |u_(-> tptp.val tptp.val tptp.val)|) (i Bool)) (not (forall ((v |u_(-> Bool tptp.val tptp.val tptp.val)|)) (not (forall ((ii Bool)) (= (ho_124 v ii) (ite (= i ii) e (ho_124 u ii)))))))))) (let ((_let_65 (forall ((x |u_(-> Bool tptp.val tptp.val tptp.val)|) (y |u_(-> Bool tptp.val tptp.val tptp.val)|)) (or (not (forall ((z Bool)) (= (ho_124 x z) (ho_124 y z)))) (= x y))))) (let ((_let_66 (forall ((u |u_(-> _u_(-> tptp.val tptp.set_set_val)_ Bool)|) (e Bool) (i |u_(-> tptp.val tptp.set_set_val)|)) (not (forall ((v |u_(-> _u_(-> tptp.val tptp.set_set_val)_ Bool)|)) (not (forall ((ii |u_(-> tptp.val tptp.set_set_val)|)) (= (ho_172 v ii) (ite (= i ii) e (ho_172 u ii)))))))))) (let ((_let_67 (forall ((x |u_(-> _u_(-> tptp.val tptp.set_set_val)_ Bool)|) (y |u_(-> _u_(-> tptp.val tptp.set_set_val)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.val tptp.set_set_val)|)) (= (ho_172 x z) (ho_172 y z)))) (= x y))))) (let ((_let_68 (forall ((u |u_(-> tptp.val tptp.val tptp.set_val)|) (e |u_(-> tptp.val tptp.set_val)|) (i tptp.val)) (not (forall ((v |u_(-> tptp.val tptp.val tptp.set_val)|)) (not (forall ((ii tptp.val)) (= (ho_194 v ii) (ite (= i ii) e (ho_194 u ii)))))))))) (let ((_let_69 (forall ((x |u_(-> tptp.val tptp.val tptp.set_val)|) (y |u_(-> tptp.val tptp.val tptp.set_val)|)) (or (not (forall ((z tptp.val)) (= (ho_194 x z) (ho_194 y z)))) (= x y))))) (let ((_let_70 (forall ((u |u_(-> tptp.set_val tptp.val Bool)|) (e |u_(-> tptp.val Bool)|) (i tptp.set_val)) (not (forall ((v |u_(-> tptp.set_val tptp.val Bool)|)) (not (forall ((ii tptp.set_val)) (= (ho_92 v ii) (ite (= i ii) e (ho_92 u ii)))))))))) (let ((_let_71 (forall ((x |u_(-> tptp.set_val tptp.val Bool)|) (y |u_(-> tptp.set_val tptp.val Bool)|)) (or (not (forall ((z tptp.set_val)) (= (ho_92 x z) (ho_92 y z)))) (= x y))))) (let ((_let_72 (forall ((u |u_(-> tptp.set_val tptp.set_set_val Bool)|) (e |u_(-> tptp.set_set_val Bool)|) (i tptp.set_val)) (not (forall ((v |u_(-> tptp.set_val tptp.set_set_val Bool)|)) (not (forall ((ii tptp.set_val)) (= (ho_83 v ii) (ite (= i ii) e (ho_83 u ii)))))))))) (let ((_let_73 (forall ((x |u_(-> tptp.set_val tptp.set_set_val Bool)|) (y |u_(-> tptp.set_val tptp.set_set_val Bool)|)) (or (not (forall ((z tptp.set_val)) (= (ho_83 x z) (ho_83 y z)))) (= x y))))) (let ((_let_74 (forall ((u |u_(-> tptp.val tptp.set_val)|) (e tptp.set_val) (i tptp.val)) (not (forall ((v |u_(-> tptp.val tptp.set_val)|)) (not (forall ((ii tptp.val)) (= (ho_137 v ii) (ite (= i ii) e (ho_137 u ii)))))))))) (let ((_let_75 (forall ((x |u_(-> tptp.val tptp.set_val)|) (y |u_(-> tptp.val tptp.set_val)|)) (or (not (forall ((z tptp.val)) (= (ho_137 x z) (ho_137 y z)))) (= x y))))) (let ((_let_76 (forall ((u |u_(-> tptp.set_val tptp.set_val tptp.set_val)|) (e |u_(-> tptp.set_val tptp.set_val)|) (i tptp.set_val)) (not (forall ((v |u_(-> tptp.set_val tptp.set_val tptp.set_val)|)) (not (forall ((ii tptp.set_val)) (= (ho_55 v ii) (ite (= i ii) e (ho_55 u ii)))))))))) (let ((_let_77 (forall ((x |u_(-> tptp.set_val tptp.set_val tptp.set_val)|) (y |u_(-> tptp.set_val tptp.set_val tptp.set_val)|)) (or (not (forall ((z tptp.set_val)) (= (ho_55 x z) (ho_55 y z)))) (= x y))))) (let ((_let_78 (forall ((u |u_(-> tptp.set_set_val tptp.set_set_set_val)|) (e tptp.set_set_set_val) (i tptp.set_set_val)) (not (forall ((v |u_(-> tptp.set_set_val tptp.set_set_set_val)|)) (not (forall ((ii tptp.set_set_val)) (= (ho_184 v ii) (ite (= i ii) e (ho_184 u ii)))))))))) (let ((_let_79 (forall ((x |u_(-> tptp.set_set_val tptp.set_set_set_val)|) (y |u_(-> tptp.set_set_val tptp.set_set_set_val)|)) (or (not (forall ((z tptp.set_set_val)) (= (ho_184 x z) (ho_184 y z)))) (= x y))))) (let ((_let_80 (forall ((u |u_(-> tptp.set_val Bool)|) (e Bool) (i tptp.set_val)) (not (forall ((v |u_(-> tptp.set_val Bool)|)) (not (forall ((ii tptp.set_val)) (= (ho_53 v ii) (ite (= i ii) e (ho_53 u ii)))))))))) (let ((_let_81 (forall ((x |u_(-> tptp.set_val Bool)|) (y |u_(-> tptp.set_val Bool)|)) (or (not (forall ((z tptp.set_val)) (= (ho_53 x z) (ho_53 y z)))) (= x y))))) (let ((_let_82 (forall ((u |u_(-> tptp.set_val tptp.set_val)|) (e tptp.set_val) (i tptp.set_val)) (not (forall ((v |u_(-> tptp.set_val tptp.set_val)|)) (not (forall ((ii tptp.set_val)) (= (ho_56 v ii) (ite (= i ii) e (ho_56 u ii)))))))))) (let ((_let_83 (forall ((x |u_(-> tptp.set_val tptp.set_val)|) (y |u_(-> tptp.set_val tptp.set_val)|)) (or (not (forall ((z tptp.set_val)) (= (ho_56 x z) (ho_56 y z)))) (= x y))))) (let ((_let_84 (forall ((u |u_(-> _u_(-> tptp.set_val tptp.set_val)_ Bool)|) (e Bool) (i |u_(-> tptp.set_val tptp.set_val)|)) (not (forall ((v |u_(-> _u_(-> tptp.set_val tptp.set_val)_ Bool)|)) (not (forall ((ii |u_(-> tptp.set_val tptp.set_val)|)) (= (ho_164 v ii) (ite (= i ii) e (ho_164 u ii)))))))))) (let ((_let_85 (forall ((x |u_(-> _u_(-> tptp.set_val tptp.set_val)_ Bool)|) (y |u_(-> _u_(-> tptp.set_val tptp.set_val)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.set_val tptp.set_val)|)) (= (ho_164 x z) (ho_164 y z)))) (= x y))))) (let ((_let_86 (forall ((u |u_(-> tptp.set_set_val tptp.set_set_val Bool)|) (e |u_(-> tptp.set_set_val Bool)|) (i tptp.set_set_val)) (not (forall ((v |u_(-> tptp.set_set_val tptp.set_set_val Bool)|)) (not (forall ((ii tptp.set_set_val)) (= (ho_79 v ii) (ite (= i ii) e (ho_79 u ii)))))))))) (let ((_let_87 (forall ((x |u_(-> tptp.set_set_val tptp.set_set_val Bool)|) (y |u_(-> tptp.set_set_val tptp.set_set_val Bool)|)) (or (not (forall ((z tptp.set_set_val)) (= (ho_79 x z) (ho_79 y z)))) (= x y))))) (let ((_let_88 (forall ((u |u_(-> tptp.val tptp.set_val Bool)|) (e |u_(-> tptp.set_val Bool)|) (i tptp.val)) (not (forall ((v |u_(-> tptp.val tptp.set_val Bool)|)) (not (forall ((ii tptp.val)) (= (ho_61 v ii) (ite (= i ii) e (ho_61 u ii)))))))))) (let ((_let_89 (forall ((x |u_(-> tptp.val tptp.set_val Bool)|) (y |u_(-> tptp.val tptp.set_val Bool)|)) (or (not (forall ((z tptp.val)) (= (ho_61 x z) (ho_61 y z)))) (= x y))))) (let ((_let_90 (forall ((u |u_(-> _u_(-> Bool tptp.set_val)_ _u_(-> Bool tptp.set_val)_ Bool tptp.set_val)|) (e |u_(-> _u_(-> Bool tptp.set_val)_ Bool tptp.set_val)|) (i |u_(-> Bool tptp.set_val)|)) (not (forall ((v |u_(-> _u_(-> Bool tptp.set_val)_ _u_(-> Bool tptp.set_val)_ Bool tptp.set_val)|)) (not (forall ((ii |u_(-> Bool tptp.set_val)|)) (= (ho_121 v ii) (ite (= i ii) e (ho_121 u ii)))))))))) (let ((_let_91 (forall ((x |u_(-> _u_(-> Bool tptp.set_val)_ _u_(-> Bool tptp.set_val)_ Bool tptp.set_val)|) (y |u_(-> _u_(-> Bool tptp.set_val)_ _u_(-> Bool tptp.set_val)_ Bool tptp.set_val)|)) (or (not (forall ((z |u_(-> Bool tptp.set_val)|)) (= (ho_121 x z) (ho_121 y z)))) (= x y))))) (let ((_let_92 (forall ((u |u_(-> _u_(-> _u_(-> Bool tptp.set_val)_ _u_(-> Bool tptp.set_val)_ Bool)_ Bool)|) (e Bool) (i |u_(-> _u_(-> Bool tptp.set_val)_ _u_(-> Bool tptp.set_val)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> Bool tptp.set_val)_ _u_(-> Bool tptp.set_val)_ Bool)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> Bool tptp.set_val)_ _u_(-> Bool tptp.set_val)_ Bool)|)) (= (ho_154 v ii) (ite (= i ii) e (ho_154 u ii)))))))))) (let ((_let_93 (forall ((x |u_(-> _u_(-> _u_(-> Bool tptp.set_val)_ _u_(-> Bool tptp.set_val)_ Bool)_ Bool)|) (y |u_(-> _u_(-> _u_(-> Bool tptp.set_val)_ _u_(-> Bool tptp.set_val)_ Bool)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> Bool tptp.set_val)_ _u_(-> Bool tptp.set_val)_ Bool)|)) (= (ho_154 x z) (ho_154 y z)))) (= x y))))) (let ((_let_94 (forall ((u |u_(-> _u_(-> Bool tptp.set_val)_ Bool)|) (e Bool) (i |u_(-> Bool tptp.set_val)|)) (not (forall ((v |u_(-> _u_(-> Bool tptp.set_val)_ Bool)|)) (not (forall ((ii |u_(-> Bool tptp.set_val)|)) (= (ho_74 v ii) (ite (= i ii) e (ho_74 u ii)))))))))) (let ((_let_95 (forall ((x |u_(-> _u_(-> Bool tptp.set_val)_ Bool)|) (y |u_(-> _u_(-> Bool tptp.set_val)_ Bool)|)) (or (not (forall ((z |u_(-> Bool tptp.set_val)|)) (= (ho_74 x z) (ho_74 y z)))) (= x y))))) (let ((_let_96 (forall ((u |u_(-> _u_(-> Bool tptp.set_val)_ _u_(-> Bool tptp.set_val)_ Bool)|) (e |u_(-> _u_(-> Bool tptp.set_val)_ Bool)|) (i |u_(-> Bool tptp.set_val)|)) (not (forall ((v |u_(-> _u_(-> Bool tptp.set_val)_ _u_(-> Bool tptp.set_val)_ Bool)|)) (not (forall ((ii |u_(-> Bool tptp.set_val)|)) (= (ho_73 v ii) (ite (= i ii) e (ho_73 u ii)))))))))) (let ((_let_97 (forall ((x |u_(-> _u_(-> Bool tptp.set_val)_ _u_(-> Bool tptp.set_val)_ Bool)|) (y |u_(-> _u_(-> Bool tptp.set_val)_ _u_(-> Bool tptp.set_val)_ Bool)|)) (or (not (forall ((z |u_(-> Bool tptp.set_val)|)) (= (ho_73 x z) (ho_73 y z)))) (= x y))))) (let ((_let_98 (forall ((u |u_(-> tptp.set_set_val Bool)|) (e Bool) (i tptp.set_set_val)) (not (forall ((v |u_(-> tptp.set_set_val Bool)|)) (not (forall ((ii tptp.set_set_val)) (= (ho_80 v ii) (ite (= i ii) e (ho_80 u ii)))))))))) (let ((_let_99 (forall ((x |u_(-> tptp.set_set_val Bool)|) (y |u_(-> tptp.set_set_val Bool)|)) (or (not (forall ((z tptp.set_set_val)) (= (ho_80 x z) (ho_80 y z)))) (= x y))))) (let ((_let_100 (forall ((u |u_(-> tptp.val tptp.val)|) (e tptp.val) (i tptp.val)) (not (forall ((v |u_(-> tptp.val tptp.val)|)) (not (forall ((ii tptp.val)) (= (ho_126 v ii) (ite (= i ii) e (ho_126 u ii)))))))))) (let ((_let_101 (forall ((x |u_(-> tptp.val tptp.val)|) (y |u_(-> tptp.val tptp.val)|)) (or (not (forall ((z tptp.val)) (= (ho_126 x z) (ho_126 y z)))) (= x y))))) (let ((_let_102 (forall ((u |u_(-> tptp.set_val tptp.set_val Bool)|) (e |u_(-> tptp.set_val Bool)|) (i tptp.set_val)) (not (forall ((v |u_(-> tptp.set_val tptp.set_val Bool)|)) (not (forall ((ii tptp.set_val)) (= (ho_52 v ii) (ite (= i ii) e (ho_52 u ii)))))))))) (let ((_let_103 (forall ((x |u_(-> tptp.set_val tptp.set_val Bool)|) (y |u_(-> tptp.set_val tptp.set_val Bool)|)) (or (not (forall ((z tptp.set_val)) (= (ho_52 x z) (ho_52 y z)))) (= x y))))) (let ((_let_104 (forall ((u |u_(-> _u_(-> tptp.val tptp.val)_ Bool)|) (e Bool) (i |u_(-> tptp.val tptp.val)|)) (not (forall ((v |u_(-> _u_(-> tptp.val tptp.val)_ Bool)|)) (not (forall ((ii |u_(-> tptp.val tptp.val)|)) (= (ho_170 v ii) (ite (= i ii) e (ho_170 u ii)))))))))) (let ((_let_105 (forall ((x |u_(-> _u_(-> tptp.val tptp.val)_ Bool)|) (y |u_(-> _u_(-> tptp.val tptp.val)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.val tptp.val)|)) (= (ho_170 x z) (ho_170 y z)))) (= x y))))) (let ((_let_106 (forall ((u |u_(-> tptp.val Bool)|) (e Bool) (i tptp.val)) (not (forall ((v |u_(-> tptp.val Bool)|)) (not (forall ((ii tptp.val)) (= (ho_86 v ii) (ite (= i ii) e (ho_86 u ii)))))))))) (let ((_let_107 (forall ((x |u_(-> tptp.val Bool)|) (y |u_(-> tptp.val Bool)|)) (or (not (forall ((z tptp.val)) (= (ho_86 x z) (ho_86 y z)))) (= x y))))) (let ((_let_108 (forall ((u |u_(-> tptp.val tptp.val Bool)|) (e |u_(-> tptp.val Bool)|) (i tptp.val)) (not (forall ((v |u_(-> tptp.val tptp.val Bool)|)) (not (forall ((ii tptp.val)) (= (ho_85 v ii) (ite (= i ii) e (ho_85 u ii)))))))))) (let ((_let_109 (forall ((x |u_(-> tptp.val tptp.val Bool)|) (y |u_(-> tptp.val tptp.val Bool)|)) (or (not (forall ((z tptp.val)) (= (ho_85 x z) (ho_85 y z)))) (= x y))))) (let ((_let_110 (forall ((u |u_(-> tptp.set_set_val tptp.val)|) (e tptp.val) (i tptp.set_set_val)) (not (forall ((v |u_(-> tptp.set_set_val tptp.val)|)) (not (forall ((ii tptp.set_set_val)) (= (ho_139 v ii) (ite (= i ii) e (ho_139 u ii)))))))))) (let ((_let_111 (forall ((x |u_(-> tptp.set_set_val tptp.val)|) (y |u_(-> tptp.set_set_val tptp.val)|)) (or (not (forall ((z tptp.set_set_val)) (= (ho_139 x z) (ho_139 y z)))) (= x y))))) (let ((_let_112 (forall ((u |u_(-> tptp.val tptp.set_set_val)|) (e tptp.set_set_val) (i tptp.val)) (not (forall ((v |u_(-> tptp.val tptp.set_set_val)|)) (not (forall ((ii tptp.val)) (= (ho_140 v ii) (ite (= i ii) e (ho_140 u ii)))))))))) (let ((_let_113 (forall ((x |u_(-> tptp.val tptp.set_set_val)|) (y |u_(-> tptp.val tptp.set_set_val)|)) (or (not (forall ((z tptp.val)) (= (ho_140 x z) (ho_140 y z)))) (= x y))))) (let ((_let_114 (forall ((u |u_(-> tptp.set_set_val tptp.set_val)|) (e tptp.set_val) (i tptp.set_set_val)) (not (forall ((v |u_(-> tptp.set_set_val tptp.set_val)|)) (not (forall ((ii tptp.set_set_val)) (= (ho_141 v ii) (ite (= i ii) e (ho_141 u ii)))))))))) (let ((_let_115 (forall ((x |u_(-> tptp.set_set_val tptp.set_val)|) (y |u_(-> tptp.set_set_val tptp.set_val)|)) (or (not (forall ((z tptp.set_set_val)) (= (ho_141 x z) (ho_141 y z)))) (= x y))))) (let ((_let_116 (forall ((u |u_(-> _u_(-> Bool tptp.set_val)_ tptp.val)|) (e tptp.val) (i |u_(-> Bool tptp.set_val)|)) (not (forall ((v |u_(-> _u_(-> Bool tptp.set_val)_ tptp.val)|)) (not (forall ((ii |u_(-> Bool tptp.set_val)|)) (= (ho_143 v ii) (ite (= i ii) e (ho_143 u ii)))))))))) (let ((_let_117 (forall ((x |u_(-> _u_(-> Bool tptp.set_val)_ tptp.val)|) (y |u_(-> _u_(-> Bool tptp.set_val)_ tptp.val)|)) (or (not (forall ((z |u_(-> Bool tptp.set_val)|)) (= (ho_143 x z) (ho_143 y z)))) (= x y))))) (let ((_let_118 (forall ((u |u_(-> tptp.set_val tptp.set_set_val)|) (e tptp.set_set_val) (i tptp.set_val)) (not (forall ((v |u_(-> tptp.set_val tptp.set_set_val)|)) (not (forall ((ii tptp.set_val)) (= (ho_144 v ii) (ite (= i ii) e (ho_144 u ii)))))))))) (let ((_let_119 (forall ((x |u_(-> tptp.set_val tptp.set_set_val)|) (y |u_(-> tptp.set_val tptp.set_set_val)|)) (or (not (forall ((z tptp.set_val)) (= (ho_144 x z) (ho_144 y z)))) (= x y))))) (let ((_let_120 (forall ((u |u_(-> _u_(-> tptp.set_set_val tptp.set_set_val Bool)_ Bool)|) (e Bool) (i |u_(-> tptp.set_set_val tptp.set_set_val Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.set_set_val tptp.set_set_val Bool)_ Bool)|)) (not (forall ((ii |u_(-> tptp.set_set_val tptp.set_set_val Bool)|)) (= (ho_158 v ii) (ite (= i ii) e (ho_158 u ii)))))))))) (let ((_let_121 (forall ((x |u_(-> _u_(-> tptp.set_set_val tptp.set_set_val Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.set_set_val tptp.set_set_val Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.set_set_val tptp.set_set_val Bool)|)) (= (ho_158 x z) (ho_158 y z)))) (= x y))))) (let ((_let_122 (forall ((u |u_(-> _u_(-> _u_(-> Bool tptp.set_val)_ Bool)_ Bool tptp.set_val)|) (e |u_(-> Bool tptp.set_val)|) (i |u_(-> _u_(-> Bool tptp.set_val)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> Bool tptp.set_val)_ Bool)_ Bool tptp.set_val)|)) (not (forall ((ii |u_(-> _u_(-> Bool tptp.set_val)_ Bool)|)) (= (ho_146 v ii) (ite (= i ii) e (ho_146 u ii)))))))))) (let ((_let_123 (forall ((x |u_(-> _u_(-> _u_(-> Bool tptp.set_val)_ Bool)_ Bool tptp.set_val)|) (y |u_(-> _u_(-> _u_(-> Bool tptp.set_val)_ Bool)_ Bool tptp.set_val)|)) (or (not (forall ((z |u_(-> _u_(-> Bool tptp.set_val)_ Bool)|)) (= (ho_146 x z) (ho_146 y z)))) (= x y))))) (let ((_let_124 (forall ((u |u_(-> _u_(-> Bool tptp.set_val)_ tptp.set_val)|) (e tptp.set_val) (i |u_(-> Bool tptp.set_val)|)) (not (forall ((v |u_(-> _u_(-> Bool tptp.set_val)_ tptp.set_val)|)) (not (forall ((ii |u_(-> Bool tptp.set_val)|)) (= (ho_159 v ii) (ite (= i ii) e (ho_159 u ii)))))))))) (let ((_let_125 (forall ((x |u_(-> _u_(-> Bool tptp.set_val)_ tptp.set_val)|) (y |u_(-> _u_(-> Bool tptp.set_val)_ tptp.set_val)|)) (or (not (forall ((z |u_(-> Bool tptp.set_val)|)) (= (ho_159 x z) (ho_159 y z)))) (= x y))))) (let ((_let_126 (forall ((u |u_(-> _u_(-> tptp.val Bool)_ tptp.val)|) (e tptp.val) (i |u_(-> tptp.val Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.val Bool)_ tptp.val)|)) (not (forall ((ii |u_(-> tptp.val Bool)|)) (= (ho_148 v ii) (ite (= i ii) e (ho_148 u ii)))))))))) (let ((_let_127 (forall ((x |u_(-> _u_(-> tptp.val Bool)_ tptp.val)|) (y |u_(-> _u_(-> tptp.val Bool)_ tptp.val)|)) (or (not (forall ((z |u_(-> tptp.val Bool)|)) (= (ho_148 x z) (ho_148 y z)))) (= x y))))) (let ((_let_128 (forall ((u |u_(-> _u_(-> tptp.set_set_val Bool)_ tptp.set_set_val)|) (e tptp.set_set_val) (i |u_(-> tptp.set_set_val Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.set_set_val Bool)_ tptp.set_set_val)|)) (not (forall ((ii |u_(-> tptp.set_set_val Bool)|)) (= (ho_150 v ii) (ite (= i ii) e (ho_150 u ii)))))))))) (let ((_let_129 (forall ((x |u_(-> _u_(-> tptp.set_set_val Bool)_ tptp.set_set_val)|) (y |u_(-> _u_(-> tptp.set_set_val Bool)_ tptp.set_set_val)|)) (or (not (forall ((z |u_(-> tptp.set_set_val Bool)|)) (= (ho_150 x z) (ho_150 y z)))) (= x y))))) (let ((_let_130 (forall ((u |u_(-> _u_(-> tptp.val tptp.val Bool)_ Bool)|) (e Bool) (i |u_(-> tptp.val tptp.val Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.val tptp.val Bool)_ Bool)|)) (not (forall ((ii |u_(-> tptp.val tptp.val Bool)|)) (= (ho_156 v ii) (ite (= i ii) e (ho_156 u ii)))))))))) (let ((_let_131 (forall ((x |u_(-> _u_(-> tptp.val tptp.val Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.val tptp.val Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.val tptp.val Bool)|)) (= (ho_156 x z) (ho_156 y z)))) (= x y))))) (let ((_let_132 (forall ((u |u_(-> tptp.set_set_val Bool tptp.set_val)|) (e |u_(-> Bool tptp.set_val)|) (i tptp.set_set_val)) (not (forall ((v |u_(-> tptp.set_set_val Bool tptp.set_val)|)) (not (forall ((ii tptp.set_set_val)) (= (ho_161 v ii) (ite (= i ii) e (ho_161 u ii)))))))))) (let ((_let_133 (forall ((x |u_(-> tptp.set_set_val Bool tptp.set_val)|) (y |u_(-> tptp.set_set_val Bool tptp.set_val)|)) (or (not (forall ((z tptp.set_set_val)) (= (ho_161 x z) (ho_161 y z)))) (= x y))))) (let ((_let_134 (forall ((u |u_(-> _u_(-> Bool tptp.set_val)_ tptp.set_set_val)|) (e tptp.set_set_val) (i |u_(-> Bool tptp.set_val)|)) (not (forall ((v |u_(-> _u_(-> Bool tptp.set_val)_ tptp.set_set_val)|)) (not (forall ((ii |u_(-> Bool tptp.set_val)|)) (= (ho_162 v ii) (ite (= i ii) e (ho_162 u ii)))))))))) (let ((_let_135 (forall ((x |u_(-> _u_(-> Bool tptp.set_val)_ tptp.set_set_val)|) (y |u_(-> _u_(-> Bool tptp.set_val)_ tptp.set_set_val)|)) (or (not (forall ((z |u_(-> Bool tptp.set_val)|)) (= (ho_162 x z) (ho_162 y z)))) (= x y))))) (let ((_let_136 (forall ((u |u_(-> _u_(-> tptp.val tptp.set_val)_ Bool)|) (e Bool) (i |u_(-> tptp.val tptp.set_val)|)) (not (forall ((v |u_(-> _u_(-> tptp.val tptp.set_val)_ Bool)|)) (not (forall ((ii |u_(-> tptp.val tptp.set_val)|)) (= (ho_166 v ii) (ite (= i ii) e (ho_166 u ii)))))))))) (let ((_let_137 (forall ((x |u_(-> _u_(-> tptp.val tptp.set_val)_ Bool)|) (y |u_(-> _u_(-> tptp.val tptp.set_val)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.val tptp.set_val)|)) (= (ho_166 x z) (ho_166 y z)))) (= x y))))) (let ((_let_138 (forall ((u |u_(-> _u_(-> tptp.val Bool tptp.set_val)_ Bool)|) (e Bool) (i |u_(-> tptp.val Bool tptp.set_val)|)) (not (forall ((v |u_(-> _u_(-> tptp.val Bool tptp.set_val)_ Bool)|)) (not (forall ((ii |u_(-> tptp.val Bool tptp.set_val)|)) (= (ho_168 v ii) (ite (= i ii) e (ho_168 u ii)))))))))) (let ((_let_139 (forall ((x |u_(-> _u_(-> tptp.val Bool tptp.set_val)_ Bool)|) (y |u_(-> _u_(-> tptp.val Bool tptp.set_val)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.val Bool tptp.set_val)|)) (= (ho_168 x z) (ho_168 y z)))) (= x y))))) (let ((_let_140 (forall ((u |u_(-> tptp.set_set_set_val Bool)|) (e Bool) (i tptp.set_set_set_val)) (not (forall ((v |u_(-> tptp.set_set_set_val Bool)|)) (not (forall ((ii tptp.set_set_set_val)) (= (ho_187 v ii) (ite (= i ii) e (ho_187 u ii)))))))))) (let ((_let_141 (forall ((x |u_(-> tptp.set_set_set_val Bool)|) (y |u_(-> tptp.set_set_set_val Bool)|)) (or (not (forall ((z tptp.set_set_set_val)) (= (ho_187 x z) (ho_187 y z)))) (= x y))))) (let ((_let_142 (forall ((u |u_(-> tptp.set_set_set_val tptp.set_set_set_val Bool)|) (e |u_(-> tptp.set_set_set_val Bool)|) (i tptp.set_set_set_val)) (not (forall ((v |u_(-> tptp.set_set_set_val tptp.set_set_set_val Bool)|)) (not (forall ((ii tptp.set_set_set_val)) (= (ho_186 v ii) (ite (= i ii) e (ho_186 u ii)))))))))) (let ((_let_143 (forall ((x |u_(-> tptp.set_set_set_val tptp.set_set_set_val Bool)|) (y |u_(-> tptp.set_set_set_val tptp.set_set_set_val Bool)|)) (or (not (forall ((z tptp.set_set_set_val)) (= (ho_186 x z) (ho_186 y z)))) (= x y))))) (let ((_let_144 (forall ((BOUND_VARIABLE_21585 tptp.set_val) (BOUND_VARIABLE_21586 tptp.set_val)) (= (ho_53 (ho_52 k_51 BOUND_VARIABLE_21585) BOUND_VARIABLE_21586) (= BOUND_VARIABLE_21586 (ho_56 (ho_55 k_54 BOUND_VARIABLE_21586) BOUND_VARIABLE_21585)))))) (let ((_let_145 (forall ((BOUND_VARIABLE_21576 tptp.set_val) (BOUND_VARIABLE_21577 tptp.set_val)) (= (ho_53 (ho_52 k_57 BOUND_VARIABLE_21576) BOUND_VARIABLE_21577) (= BOUND_VARIABLE_21577 (ho_56 (ho_55 k_54 BOUND_VARIABLE_21577) BOUND_VARIABLE_21576)))))) (let ((_let_146 (forall ((BOUND_VARIABLE_21567 tptp.set_val) (BOUND_VARIABLE_21568 tptp.set_val)) (= (ho_53 (ho_52 k_58 BOUND_VARIABLE_21567) BOUND_VARIABLE_21568) (= BOUND_VARIABLE_21568 (ho_56 (ho_55 k_54 BOUND_VARIABLE_21567) BOUND_VARIABLE_21568)))))) (let ((_let_147 (forall ((BOUND_VARIABLE_21552 tptp.set_val) (BOUND_VARIABLE_21553 tptp.set_val)) (let ((_let_1 (= BOUND_VARIABLE_21552 BOUND_VARIABLE_21553))) (= (ho_53 (ho_52 k_59 BOUND_VARIABLE_21552) BOUND_VARIABLE_21553) (or (and (forall ((X3 tptp.val)) (let ((_let_1 (ho_61 k_60 X3))) (or (not (ho_53 _let_1 BOUND_VARIABLE_21552)) (ho_53 _let_1 BOUND_VARIABLE_21553)))) (not _let_1)) _let_1)))))) (let ((_let_148 (forall ((BOUND_VARIABLE_21536 tptp.set_val) (BOUND_VARIABLE_21537 tptp.set_val)) (= (ho_53 (ho_52 k_62 BOUND_VARIABLE_21536) BOUND_VARIABLE_21537) (and (forall ((X3 tptp.val)) (let ((_let_1 (ho_61 k_60 X3))) (or (not (ho_53 _let_1 BOUND_VARIABLE_21536)) (ho_53 _let_1 BOUND_VARIABLE_21537)))) (not (forall ((X3 tptp.val)) (let ((_let_1 (ho_61 k_60 X3))) (or (not (ho_53 _let_1 BOUND_VARIABLE_21537)) (ho_53 _let_1 BOUND_VARIABLE_21536)))))))))) (let ((_let_149 (forall ((BOUND_VARIABLE_21522 tptp.set_val) (BOUND_VARIABLE_21523 tptp.set_val)) (= (ho_53 (ho_52 k_63 BOUND_VARIABLE_21522) BOUND_VARIABLE_21523) (and (forall ((X3 tptp.val)) (let ((_let_1 (ho_61 k_60 X3))) (or (not (ho_53 _let_1 BOUND_VARIABLE_21522)) (ho_53 _let_1 BOUND_VARIABLE_21523)))) (not (= BOUND_VARIABLE_21522 BOUND_VARIABLE_21523))))))) (let ((_let_150 (forall ((BOUND_VARIABLE_21508 tptp.set_val) (BOUND_VARIABLE_21509 tptp.set_val)) (= (ho_53 (ho_52 k_64 BOUND_VARIABLE_21508) BOUND_VARIABLE_21509) (and (forall ((X3 tptp.val)) (let ((_let_1 (ho_61 k_60 X3))) (or (not (ho_53 _let_1 BOUND_VARIABLE_21508)) (ho_53 _let_1 BOUND_VARIABLE_21509)))) (not (= BOUND_VARIABLE_21508 BOUND_VARIABLE_21509))))))) (let ((_let_151 (forall ((BOUND_VARIABLE_21493 tptp.set_val) (BOUND_VARIABLE_21494 tptp.set_val)) (let ((_let_1 (= BOUND_VARIABLE_21493 BOUND_VARIABLE_21494))) (= (ho_53 (ho_52 k_65 BOUND_VARIABLE_21493) BOUND_VARIABLE_21494) (or (and (forall ((X3 tptp.val)) (let ((_let_1 (ho_61 k_60 X3))) (or (not (ho_53 _let_1 BOUND_VARIABLE_21493)) (ho_53 _let_1 BOUND_VARIABLE_21494)))) (not _let_1)) _let_1)))))) (let ((_let_152 (forall ((BOUND_VARIABLE_21479 tptp.set_val) (BOUND_VARIABLE_21480 tptp.set_val)) (= (ho_53 (ho_52 k_66 BOUND_VARIABLE_21479) BOUND_VARIABLE_21480) (and (forall ((X3 tptp.val)) (let ((_let_1 (ho_61 k_60 X3))) (or (not (ho_53 _let_1 BOUND_VARIABLE_21479)) (ho_53 _let_1 BOUND_VARIABLE_21480)))) (not (= BOUND_VARIABLE_21479 BOUND_VARIABLE_21480))))))) (let ((_let_153 (forall ((BOUND_VARIABLE_21464 tptp.set_val) (BOUND_VARIABLE_21465 tptp.set_val)) (let ((_let_1 (= BOUND_VARIABLE_21464 BOUND_VARIABLE_21465))) (= (ho_53 (ho_52 k_67 BOUND_VARIABLE_21464) BOUND_VARIABLE_21465) (or (and (forall ((X3 tptp.val)) (let ((_let_1 (ho_61 k_60 X3))) (or (not (ho_53 _let_1 BOUND_VARIABLE_21464)) (ho_53 _let_1 BOUND_VARIABLE_21465)))) (not _let_1)) _let_1)))))) (let ((_let_154 (forall ((BOUND_VARIABLE_21450 tptp.set_val) (BOUND_VARIABLE_21451 tptp.set_val)) (= (ho_53 (ho_52 k_68 BOUND_VARIABLE_21450) BOUND_VARIABLE_21451) (and (forall ((X3 tptp.val)) (let ((_let_1 (ho_61 k_60 X3))) (or (not (ho_53 _let_1 BOUND_VARIABLE_21450)) (ho_53 _let_1 BOUND_VARIABLE_21451)))) (not (= BOUND_VARIABLE_21450 BOUND_VARIABLE_21451))))))) (let ((_let_155 (forall ((BOUND_VARIABLE_21434 tptp.set_val) (BOUND_VARIABLE_21435 tptp.set_val)) (= (ho_53 (ho_52 k_69 BOUND_VARIABLE_21434) BOUND_VARIABLE_21435) (and (forall ((X3 tptp.val)) (let ((_let_1 (ho_61 k_60 X3))) (or (not (ho_53 _let_1 BOUND_VARIABLE_21434)) (ho_53 _let_1 BOUND_VARIABLE_21435)))) (not (forall ((X3 tptp.val)) (let ((_let_1 (ho_61 k_60 X3))) (or (not (ho_53 _let_1 BOUND_VARIABLE_21435)) (ho_53 _let_1 BOUND_VARIABLE_21434)))))))))) (let ((_let_156 (forall ((BOUND_VARIABLE_21419 tptp.set_val) (BOUND_VARIABLE_21420 tptp.set_val)) (let ((_let_1 (= BOUND_VARIABLE_21419 BOUND_VARIABLE_21420))) (= (ho_53 (ho_52 k_70 BOUND_VARIABLE_21419) BOUND_VARIABLE_21420) (or (and (forall ((X3 tptp.val)) (let ((_let_1 (ho_61 k_60 X3))) (or (not (ho_53 _let_1 BOUND_VARIABLE_21419)) (ho_53 _let_1 BOUND_VARIABLE_21420)))) (not _let_1)) _let_1)))))) (let ((_let_157 (forall ((BOUND_VARIABLE_21892 |u_(-> Bool tptp.set_val)|) (BOUND_VARIABLE_21889 |u_(-> Bool tptp.set_val)|)) (= (ho_74 (ho_73 k_72 BOUND_VARIABLE_21892) BOUND_VARIABLE_21889) (forall ((X3 Bool) (X3 tptp.val)) (let ((_let_1 (ho_61 k_60 X3))) (or (not (ho_53 _let_1 (ho_71 BOUND_VARIABLE_21892 X3))) (ho_53 _let_1 (ho_71 BOUND_VARIABLE_21889 X3))))))))) (let ((_let_158 (forall ((BOUND_VARIABLE_21917 |u_(-> Bool tptp.set_val)|) (BOUND_VARIABLE_21916 |u_(-> Bool tptp.set_val)|)) (= (ho_74 (ho_73 k_75 BOUND_VARIABLE_21917) BOUND_VARIABLE_21916) (and (forall ((X3 tptp.val)) (let ((_let_1 (ho_61 k_60 X3))) (or (not (ho_53 _let_1 (ho_71 BOUND_VARIABLE_21917 false))) (ho_53 _let_1 (ho_71 BOUND_VARIABLE_21916 false))))) (forall ((X3 tptp.val)) (let ((_let_1 (ho_61 k_60 X3))) (or (not (ho_53 _let_1 (ho_71 BOUND_VARIABLE_21917 true))) (ho_53 _let_1 (ho_71 BOUND_VARIABLE_21916 true)))))))))) (let ((_let_159 (forall ((BOUND_VARIABLE_21378 tptp.set_val) (BOUND_VARIABLE_21379 tptp.set_val)) (= (= BOUND_VARIABLE_21378 BOUND_VARIABLE_21379) (ho_53 (ho_52 k_76 BOUND_VARIABLE_21378) BOUND_VARIABLE_21379))))) (let ((_let_160 (forall ((BOUND_VARIABLE_21363 tptp.set_val) (BOUND_VARIABLE_21364 tptp.set_val)) (= (ho_53 (ho_52 k_77 BOUND_VARIABLE_21363) BOUND_VARIABLE_21364) (and (forall ((X3 tptp.val)) (let ((_let_1 (ho_61 k_60 X3))) (or (not (ho_53 _let_1 BOUND_VARIABLE_21363)) (ho_53 _let_1 BOUND_VARIABLE_21364)))) (forall ((X3 tptp.val)) (let ((_let_1 (ho_61 k_60 X3))) (or (not (ho_53 _let_1 BOUND_VARIABLE_21364)) (ho_53 _let_1 BOUND_VARIABLE_21363))))))))) (let ((_let_161 (forall ((BOUND_VARIABLE_21356 tptp.set_set_val) (BOUND_VARIABLE_21357 tptp.set_set_val)) (= (= BOUND_VARIABLE_21356 BOUND_VARIABLE_21357) (ho_80 (ho_79 k_78 BOUND_VARIABLE_21356) BOUND_VARIABLE_21357))))) (let ((_let_162 (forall ((BOUND_VARIABLE_21341 tptp.set_set_val) (BOUND_VARIABLE_21342 tptp.set_set_val)) (= (ho_80 (ho_79 k_81 BOUND_VARIABLE_21341) BOUND_VARIABLE_21342) (and (forall ((X3 tptp.set_val)) (let ((_let_1 (ho_83 k_82 X3))) (or (not (ho_80 _let_1 BOUND_VARIABLE_21341)) (ho_80 _let_1 BOUND_VARIABLE_21342)))) (forall ((X3 tptp.set_val)) (let ((_let_1 (ho_83 k_82 X3))) (or (not (ho_80 _let_1 BOUND_VARIABLE_21342)) (ho_80 _let_1 BOUND_VARIABLE_21341))))))))) (let ((_let_163 (forall ((BOUND_VARIABLE_21334 tptp.val) (BOUND_VARIABLE_21335 tptp.val)) (= (= BOUND_VARIABLE_21334 BOUND_VARIABLE_21335) (ho_86 (ho_85 k_84 BOUND_VARIABLE_21334) BOUND_VARIABLE_21335))))) (let ((_let_164 (forall ((BOUND_VARIABLE_21323 tptp.val) (BOUND_VARIABLE_21324 tptp.val)) (= (ho_86 (ho_85 k_87 BOUND_VARIABLE_21323) BOUND_VARIABLE_21324) (and (ho_86 (ho_85 k_88 BOUND_VARIABLE_21323) BOUND_VARIABLE_21324) (ho_86 (ho_85 k_88 BOUND_VARIABLE_21324) BOUND_VARIABLE_21323)))))) (let ((_let_165 (forall ((BOUND_VARIABLE_22025 |u_(-> Bool tptp.set_val)|) (BOUND_VARIABLE_22024 |u_(-> Bool tptp.set_val)|)) (= (ho_74 (ho_73 k_89 BOUND_VARIABLE_22025) BOUND_VARIABLE_22024) (= BOUND_VARIABLE_22024 BOUND_VARIABLE_22025))))) (let ((_let_166 (forall ((BOUND_VARIABLE_22036 |u_(-> Bool tptp.set_val)|) (BOUND_VARIABLE_22035 |u_(-> Bool tptp.set_val)|)) (= (ho_74 (ho_73 k_90 BOUND_VARIABLE_22036) BOUND_VARIABLE_22035) (and (forall ((X3 Bool) (X3 tptp.val)) (let ((_let_1 (ho_61 k_60 X3))) (or (not (ho_53 _let_1 (ho_71 BOUND_VARIABLE_22036 X3))) (ho_53 _let_1 (ho_71 BOUND_VARIABLE_22035 X3))))) (forall ((X3 Bool) (X3 tptp.val)) (let ((_let_1 (ho_61 k_60 X3))) (or (not (ho_53 _let_1 (ho_71 BOUND_VARIABLE_22035 X3))) (ho_53 _let_1 (ho_71 BOUND_VARIABLE_22036 X3)))))))))) (let ((_let_167 (forall ((BOUND_VARIABLE_21291 tptp.set_val) (BOUND_VARIABLE_21292 tptp.val)) (= (ho_86 (ho_92 k_91 BOUND_VARIABLE_21291) BOUND_VARIABLE_21292) (ho_53 (ho_61 k_60 BOUND_VARIABLE_21292) BOUND_VARIABLE_21291))))) (let ((_let_168 (forall ((BOUND_VARIABLE_21283 tptp.set_set_val) (BOUND_VARIABLE_21284 tptp.set_val)) (= (ho_53 (ho_94 k_93 BOUND_VARIABLE_21283) BOUND_VARIABLE_21284) (ho_80 (ho_83 k_82 BOUND_VARIABLE_21284) BOUND_VARIABLE_21283))))) (let ((_let_169 (forall ((BOUND_VARIABLE_21276 tptp.set_val) (BOUND_VARIABLE_21277 tptp.set_val)) (= (= BOUND_VARIABLE_21276 BOUND_VARIABLE_21277) (ho_53 (ho_52 k_95 BOUND_VARIABLE_21276) BOUND_VARIABLE_21277))))) (let ((_let_170 (forall ((BOUND_VARIABLE_21261 tptp.set_val) (BOUND_VARIABLE_21262 tptp.set_val)) (= (ho_53 (ho_52 k_96 BOUND_VARIABLE_21261) BOUND_VARIABLE_21262) (and (forall ((X3 tptp.val)) (let ((_let_1 (ho_61 k_60 X3))) (or (not (ho_53 _let_1 BOUND_VARIABLE_21261)) (ho_53 _let_1 BOUND_VARIABLE_21262)))) (forall ((X3 tptp.val)) (let ((_let_1 (ho_61 k_60 X3))) (or (not (ho_53 _let_1 BOUND_VARIABLE_21262)) (ho_53 _let_1 BOUND_VARIABLE_21261))))))))) (let ((_let_171 (forall ((BOUND_VARIABLE_21254 tptp.set_set_val) (BOUND_VARIABLE_21255 tptp.set_set_val)) (= (= BOUND_VARIABLE_21254 BOUND_VARIABLE_21255) (ho_80 (ho_79 k_97 BOUND_VARIABLE_21254) BOUND_VARIABLE_21255))))) (let ((_let_172 (forall ((BOUND_VARIABLE_21239 tptp.set_set_val) (BOUND_VARIABLE_21240 tptp.set_set_val)) (= (ho_80 (ho_79 k_98 BOUND_VARIABLE_21239) BOUND_VARIABLE_21240) (and (forall ((X3 tptp.set_val)) (let ((_let_1 (ho_83 k_82 X3))) (or (not (ho_80 _let_1 BOUND_VARIABLE_21239)) (ho_80 _let_1 BOUND_VARIABLE_21240)))) (forall ((X3 tptp.set_val)) (let ((_let_1 (ho_83 k_82 X3))) (or (not (ho_80 _let_1 BOUND_VARIABLE_21240)) (ho_80 _let_1 BOUND_VARIABLE_21239))))))))) (let ((_let_173 (forall ((BOUND_VARIABLE_21232 tptp.val) (BOUND_VARIABLE_21233 tptp.val)) (= (= BOUND_VARIABLE_21232 BOUND_VARIABLE_21233) (ho_86 (ho_85 k_99 BOUND_VARIABLE_21232) BOUND_VARIABLE_21233))))) (let ((_let_174 (forall ((BOUND_VARIABLE_21221 tptp.val) (BOUND_VARIABLE_21222 tptp.val)) (= (ho_86 (ho_85 k_100 BOUND_VARIABLE_21221) BOUND_VARIABLE_21222) (and (ho_86 (ho_85 k_88 BOUND_VARIABLE_21221) BOUND_VARIABLE_21222) (ho_86 (ho_85 k_88 BOUND_VARIABLE_21222) BOUND_VARIABLE_21221)))))) (let ((_let_175 (forall ((BOUND_VARIABLE_22146 |u_(-> Bool tptp.set_val)|) (BOUND_VARIABLE_22145 |u_(-> Bool tptp.set_val)|)) (= (ho_74 (ho_73 k_101 BOUND_VARIABLE_22146) BOUND_VARIABLE_22145) (= BOUND_VARIABLE_22145 BOUND_VARIABLE_22146))))) (let ((_let_176 (forall ((BOUND_VARIABLE_22157 |u_(-> Bool tptp.set_val)|) (BOUND_VARIABLE_22156 |u_(-> Bool tptp.set_val)|)) (= (ho_74 (ho_73 k_102 BOUND_VARIABLE_22157) BOUND_VARIABLE_22156) (and (forall ((X3 Bool) (X3 tptp.val)) (let ((_let_1 (ho_61 k_60 X3))) (or (not (ho_53 _let_1 (ho_71 BOUND_VARIABLE_22157 X3))) (ho_53 _let_1 (ho_71 BOUND_VARIABLE_22156 X3))))) (forall ((X3 Bool) (X3 tptp.val)) (let ((_let_1 (ho_61 k_60 X3))) (or (not (ho_53 _let_1 (ho_71 BOUND_VARIABLE_22156 X3))) (ho_53 _let_1 (ho_71 BOUND_VARIABLE_22157 X3)))))))))) (let ((_let_177 (forall ((BOUND_VARIABLE_21190 tptp.set_val) (BOUND_VARIABLE_21191 tptp.set_val)) (= (= BOUND_VARIABLE_21190 BOUND_VARIABLE_21191) (ho_53 (ho_52 k_103 BOUND_VARIABLE_21190) BOUND_VARIABLE_21191))))) (let ((_let_178 (forall ((BOUND_VARIABLE_21175 tptp.set_val) (BOUND_VARIABLE_21176 tptp.set_val)) (= (ho_53 (ho_52 k_104 BOUND_VARIABLE_21175) BOUND_VARIABLE_21176) (and (forall ((X3 tptp.val)) (let ((_let_1 (ho_61 k_60 X3))) (or (not (ho_53 _let_1 BOUND_VARIABLE_21176)) (ho_53 _let_1 BOUND_VARIABLE_21175)))) (forall ((X3 tptp.val)) (let ((_let_1 (ho_61 k_60 X3))) (or (not (ho_53 _let_1 BOUND_VARIABLE_21175)) (ho_53 _let_1 BOUND_VARIABLE_21176))))))))) (let ((_let_179 (forall ((BOUND_VARIABLE_21168 tptp.set_set_val) (BOUND_VARIABLE_21169 tptp.set_set_val)) (= (= BOUND_VARIABLE_21168 BOUND_VARIABLE_21169) (ho_80 (ho_79 k_105 BOUND_VARIABLE_21168) BOUND_VARIABLE_21169))))) (let ((_let_180 (forall ((BOUND_VARIABLE_21153 tptp.set_set_val) (BOUND_VARIABLE_21154 tptp.set_set_val)) (= (ho_80 (ho_79 k_106 BOUND_VARIABLE_21153) BOUND_VARIABLE_21154) (and (forall ((X3 tptp.set_val)) (let ((_let_1 (ho_83 k_82 X3))) (or (not (ho_80 _let_1 BOUND_VARIABLE_21154)) (ho_80 _let_1 BOUND_VARIABLE_21153)))) (forall ((X3 tptp.set_val)) (let ((_let_1 (ho_83 k_82 X3))) (or (not (ho_80 _let_1 BOUND_VARIABLE_21153)) (ho_80 _let_1 BOUND_VARIABLE_21154))))))))) (let ((_let_181 (forall ((BOUND_VARIABLE_21146 tptp.val) (BOUND_VARIABLE_21147 tptp.val)) (= (= BOUND_VARIABLE_21146 BOUND_VARIABLE_21147) (ho_86 (ho_85 k_107 BOUND_VARIABLE_21146) BOUND_VARIABLE_21147))))) (let ((_let_182 (forall ((BOUND_VARIABLE_21135 tptp.val) (BOUND_VARIABLE_21136 tptp.val)) (= (ho_86 (ho_85 k_108 BOUND_VARIABLE_21135) BOUND_VARIABLE_21136) (and (ho_86 (ho_85 k_88 BOUND_VARIABLE_21136) BOUND_VARIABLE_21135) (ho_86 (ho_85 k_88 BOUND_VARIABLE_21135) BOUND_VARIABLE_21136)))))) (let ((_let_183 (forall ((BOUND_VARIABLE_22243 |u_(-> Bool tptp.set_val)|) (BOUND_VARIABLE_22242 |u_(-> Bool tptp.set_val)|)) (= (ho_74 (ho_73 k_109 BOUND_VARIABLE_22243) BOUND_VARIABLE_22242) (= BOUND_VARIABLE_22242 BOUND_VARIABLE_22243))))) (let ((_let_184 (forall ((BOUND_VARIABLE_22254 |u_(-> Bool tptp.set_val)|) (BOUND_VARIABLE_22253 |u_(-> Bool tptp.set_val)|)) (= (ho_74 (ho_73 k_110 BOUND_VARIABLE_22254) BOUND_VARIABLE_22253) (and (forall ((X3 Bool) (X3 tptp.val)) (let ((_let_1 (ho_61 k_60 X3))) (or (not (ho_53 _let_1 (ho_71 BOUND_VARIABLE_22253 X3))) (ho_53 _let_1 (ho_71 BOUND_VARIABLE_22254 X3))))) (forall ((X3 Bool) (X3 tptp.val)) (let ((_let_1 (ho_61 k_60 X3))) (or (not (ho_53 _let_1 (ho_71 BOUND_VARIABLE_22254 X3))) (ho_53 _let_1 (ho_71 BOUND_VARIABLE_22253 X3)))))))))) (let ((_let_185 (forall ((BOUND_VARIABLE_21104 tptp.set_val) (BOUND_VARIABLE_21105 tptp.set_val)) (= (= BOUND_VARIABLE_21104 BOUND_VARIABLE_21105) (ho_53 (ho_52 k_111 BOUND_VARIABLE_21104) BOUND_VARIABLE_21105))))) (let ((_let_186 (forall ((BOUND_VARIABLE_21089 tptp.set_val) (BOUND_VARIABLE_21090 tptp.set_val)) (= (ho_53 (ho_52 k_112 BOUND_VARIABLE_21089) BOUND_VARIABLE_21090) (and (forall ((X3 tptp.val)) (let ((_let_1 (ho_61 k_60 X3))) (or (not (ho_53 _let_1 BOUND_VARIABLE_21089)) (ho_53 _let_1 BOUND_VARIABLE_21090)))) (forall ((X3 tptp.val)) (let ((_let_1 (ho_61 k_60 X3))) (or (not (ho_53 _let_1 BOUND_VARIABLE_21090)) (ho_53 _let_1 BOUND_VARIABLE_21089))))))))) (let ((_let_187 (forall ((BOUND_VARIABLE_21082 tptp.set_set_val) (BOUND_VARIABLE_21083 tptp.set_set_val)) (= (= BOUND_VARIABLE_21082 BOUND_VARIABLE_21083) (ho_80 (ho_79 k_113 BOUND_VARIABLE_21082) BOUND_VARIABLE_21083))))) (let ((_let_188 (forall ((BOUND_VARIABLE_21067 tptp.set_set_val) (BOUND_VARIABLE_21068 tptp.set_set_val)) (= (ho_80 (ho_79 k_114 BOUND_VARIABLE_21067) BOUND_VARIABLE_21068) (and (forall ((X3 tptp.set_val)) (let ((_let_1 (ho_83 k_82 X3))) (or (not (ho_80 _let_1 BOUND_VARIABLE_21067)) (ho_80 _let_1 BOUND_VARIABLE_21068)))) (forall ((X3 tptp.set_val)) (let ((_let_1 (ho_83 k_82 X3))) (or (not (ho_80 _let_1 BOUND_VARIABLE_21068)) (ho_80 _let_1 BOUND_VARIABLE_21067))))))))) (let ((_let_189 (forall ((BOUND_VARIABLE_21056 tptp.set_val) (BOUND_VARIABLE_21057 tptp.set_val)) (= (ho_53 (ho_52 k_115 BOUND_VARIABLE_21056) BOUND_VARIABLE_21057) (forall ((X3 tptp.val)) (let ((_let_1 (ho_61 k_60 X3))) (or (not (ho_53 _let_1 BOUND_VARIABLE_21056)) (ho_53 _let_1 BOUND_VARIABLE_21057)))))))) (let ((_let_190 (forall ((BOUND_VARIABLE_21045 tptp.set_val) (BOUND_VARIABLE_21046 tptp.set_val)) (= (ho_53 (ho_52 k_116 BOUND_VARIABLE_21045) BOUND_VARIABLE_21046) (forall ((T tptp.val)) (let ((_let_1 (ho_61 k_60 T))) (or (not (ho_53 _let_1 BOUND_VARIABLE_21045)) (ho_53 _let_1 BOUND_VARIABLE_21046)))))))) (let ((_let_191 (forall ((BOUND_VARIABLE_21034 tptp.set_set_val) (BOUND_VARIABLE_21035 tptp.set_set_val)) (= (ho_80 (ho_79 k_117 BOUND_VARIABLE_21034) BOUND_VARIABLE_21035) (forall ((X3 tptp.set_val)) (let ((_let_1 (ho_83 k_82 X3))) (or (not (ho_80 _let_1 BOUND_VARIABLE_21034)) (ho_80 _let_1 BOUND_VARIABLE_21035)))))))) (let ((_let_192 (forall ((BOUND_VARIABLE_21023 tptp.set_set_val) (BOUND_VARIABLE_21024 tptp.set_set_val)) (= (ho_80 (ho_79 k_118 BOUND_VARIABLE_21023) BOUND_VARIABLE_21024) (forall ((T tptp.set_val)) (let ((_let_1 (ho_83 k_82 T))) (or (not (ho_80 _let_1 BOUND_VARIABLE_21023)) (ho_80 _let_1 BOUND_VARIABLE_21024)))))))) (let ((_let_193 (forall ((BOUND_VARIABLE_21585 tptp.set_val) (BOUND_VARIABLE_21586 tptp.set_val)) (= (= BOUND_VARIABLE_21586 (@ (@ tptp.sup_sup_set_val BOUND_VARIABLE_21586) BOUND_VARIABLE_21585)) (ll_50 BOUND_VARIABLE_21585 BOUND_VARIABLE_21586))))) (let ((_let_194 (forall ((BOUND_VARIABLE_21576 tptp.set_val) (BOUND_VARIABLE_21577 tptp.set_val)) (= (= BOUND_VARIABLE_21577 (@ (@ tptp.sup_sup_set_val BOUND_VARIABLE_21577) BOUND_VARIABLE_21576)) (ll_49 BOUND_VARIABLE_21576 BOUND_VARIABLE_21577))))) (let ((_let_195 (forall ((BOUND_VARIABLE_21567 tptp.set_val) (BOUND_VARIABLE_21568 tptp.set_val)) (= (= BOUND_VARIABLE_21568 (@ (@ tptp.sup_sup_set_val BOUND_VARIABLE_21567) BOUND_VARIABLE_21568)) (ll_48 BOUND_VARIABLE_21567 BOUND_VARIABLE_21568))))) (let ((_let_196 (forall ((BOUND_VARIABLE_21552 tptp.set_val) (BOUND_VARIABLE_21553 tptp.set_val)) (let ((_let_1 (= BOUND_VARIABLE_21552 BOUND_VARIABLE_21553))) (= (or (and (forall ((X3 tptp.val)) (let ((_let_1 (@ tptp.member_val X3))) (or (not (@ _let_1 BOUND_VARIABLE_21552)) (@ _let_1 BOUND_VARIABLE_21553)))) (not _let_1)) _let_1) (ll_47 BOUND_VARIABLE_21552 BOUND_VARIABLE_21553)))))) (let ((_let_197 (forall ((BOUND_VARIABLE_21536 tptp.set_val) (BOUND_VARIABLE_21537 tptp.set_val)) (= (and (forall ((X3 tptp.val)) (let ((_let_1 (@ tptp.member_val X3))) (or (not (@ _let_1 BOUND_VARIABLE_21536)) (@ _let_1 BOUND_VARIABLE_21537)))) (not (forall ((X3 tptp.val)) (let ((_let_1 (@ tptp.member_val X3))) (or (not (@ _let_1 BOUND_VARIABLE_21537)) (@ _let_1 BOUND_VARIABLE_21536)))))) (ll_46 BOUND_VARIABLE_21536 BOUND_VARIABLE_21537))))) (let ((_let_198 (forall ((BOUND_VARIABLE_21522 tptp.set_val) (BOUND_VARIABLE_21523 tptp.set_val)) (= (and (forall ((X3 tptp.val)) (let ((_let_1 (@ tptp.member_val X3))) (or (not (@ _let_1 BOUND_VARIABLE_21522)) (@ _let_1 BOUND_VARIABLE_21523)))) (not (= BOUND_VARIABLE_21522 BOUND_VARIABLE_21523))) (ll_45 BOUND_VARIABLE_21522 BOUND_VARIABLE_21523))))) (let ((_let_199 (forall ((BOUND_VARIABLE_21508 tptp.set_val) (BOUND_VARIABLE_21509 tptp.set_val)) (= (and (forall ((X3 tptp.val)) (let ((_let_1 (@ tptp.member_val X3))) (or (not (@ _let_1 BOUND_VARIABLE_21508)) (@ _let_1 BOUND_VARIABLE_21509)))) (not (= BOUND_VARIABLE_21508 BOUND_VARIABLE_21509))) (ll_44 BOUND_VARIABLE_21508 BOUND_VARIABLE_21509))))) (let ((_let_200 (forall ((BOUND_VARIABLE_21493 tptp.set_val) (BOUND_VARIABLE_21494 tptp.set_val)) (let ((_let_1 (= BOUND_VARIABLE_21493 BOUND_VARIABLE_21494))) (= (or (and (forall ((X3 tptp.val)) (let ((_let_1 (@ tptp.member_val X3))) (or (not (@ _let_1 BOUND_VARIABLE_21493)) (@ _let_1 BOUND_VARIABLE_21494)))) (not _let_1)) _let_1) (ll_43 BOUND_VARIABLE_21493 BOUND_VARIABLE_21494)))))) (let ((_let_201 (forall ((BOUND_VARIABLE_21479 tptp.set_val) (BOUND_VARIABLE_21480 tptp.set_val)) (= (and (forall ((X3 tptp.val)) (let ((_let_1 (@ tptp.member_val X3))) (or (not (@ _let_1 BOUND_VARIABLE_21479)) (@ _let_1 BOUND_VARIABLE_21480)))) (not (= BOUND_VARIABLE_21479 BOUND_VARIABLE_21480))) (ll_42 BOUND_VARIABLE_21479 BOUND_VARIABLE_21480))))) (let ((_let_202 (forall ((BOUND_VARIABLE_21464 tptp.set_val) (BOUND_VARIABLE_21465 tptp.set_val)) (let ((_let_1 (= BOUND_VARIABLE_21464 BOUND_VARIABLE_21465))) (= (or (and (forall ((X3 tptp.val)) (let ((_let_1 (@ tptp.member_val X3))) (or (not (@ _let_1 BOUND_VARIABLE_21464)) (@ _let_1 BOUND_VARIABLE_21465)))) (not _let_1)) _let_1) (ll_41 BOUND_VARIABLE_21464 BOUND_VARIABLE_21465)))))) (let ((_let_203 (forall ((BOUND_VARIABLE_21450 tptp.set_val) (BOUND_VARIABLE_21451 tptp.set_val)) (= (and (forall ((X3 tptp.val)) (let ((_let_1 (@ tptp.member_val X3))) (or (not (@ _let_1 BOUND_VARIABLE_21450)) (@ _let_1 BOUND_VARIABLE_21451)))) (not (= BOUND_VARIABLE_21450 BOUND_VARIABLE_21451))) (ll_40 BOUND_VARIABLE_21450 BOUND_VARIABLE_21451))))) (let ((_let_204 (forall ((BOUND_VARIABLE_21434 tptp.set_val) (BOUND_VARIABLE_21435 tptp.set_val)) (= (and (forall ((X3 tptp.val)) (let ((_let_1 (@ tptp.member_val X3))) (or (not (@ _let_1 BOUND_VARIABLE_21434)) (@ _let_1 BOUND_VARIABLE_21435)))) (not (forall ((X3 tptp.val)) (let ((_let_1 (@ tptp.member_val X3))) (or (not (@ _let_1 BOUND_VARIABLE_21435)) (@ _let_1 BOUND_VARIABLE_21434)))))) (ll_39 BOUND_VARIABLE_21434 BOUND_VARIABLE_21435))))) (let ((_let_205 (forall ((BOUND_VARIABLE_21419 tptp.set_val) (BOUND_VARIABLE_21420 tptp.set_val)) (let ((_let_1 (= BOUND_VARIABLE_21419 BOUND_VARIABLE_21420))) (= (or (and (forall ((X3 tptp.val)) (let ((_let_1 (@ tptp.member_val X3))) (or (not (@ _let_1 BOUND_VARIABLE_21419)) (@ _let_1 BOUND_VARIABLE_21420)))) (not _let_1)) _let_1) (ll_38 BOUND_VARIABLE_21419 BOUND_VARIABLE_21420)))))) (let ((_let_206 (forall ((BOUND_VARIABLE_21406 (-> Bool tptp.set_val)) (BOUND_VARIABLE_21407 (-> Bool tptp.set_val))) (= (forall ((X3 Bool) (X3 tptp.val)) (let ((_let_1 (@ tptp.member_val X3))) (or (not (@ _let_1 (@ BOUND_VARIABLE_21406 X3))) (@ _let_1 (@ BOUND_VARIABLE_21407 X3))))) (ll_37 BOUND_VARIABLE_21406 BOUND_VARIABLE_21407))))) (let ((_let_207 (forall ((BOUND_VARIABLE_21385 (-> Bool tptp.set_val)) (BOUND_VARIABLE_21386 (-> Bool tptp.set_val))) (= (and (forall ((X3 tptp.val)) (let ((_let_1 (@ tptp.member_val X3))) (or (not (@ _let_1 (@ BOUND_VARIABLE_21385 false))) (@ _let_1 (@ BOUND_VARIABLE_21386 false))))) (forall ((X3 tptp.val)) (let ((_let_1 (@ tptp.member_val X3))) (or (not (@ _let_1 (@ BOUND_VARIABLE_21385 true))) (@ _let_1 (@ BOUND_VARIABLE_21386 true)))))) (ll_36 BOUND_VARIABLE_21385 BOUND_VARIABLE_21386))))) (let ((_let_208 (forall ((BOUND_VARIABLE_21378 tptp.set_val) (BOUND_VARIABLE_21379 tptp.set_val)) (= (= BOUND_VARIABLE_21378 BOUND_VARIABLE_21379) (ll_35 BOUND_VARIABLE_21378 BOUND_VARIABLE_21379))))) (let ((_let_209 (forall ((BOUND_VARIABLE_21363 tptp.set_val) (BOUND_VARIABLE_21364 tptp.set_val)) (= (and (forall ((X3 tptp.val)) (let ((_let_1 (@ tptp.member_val X3))) (or (not (@ _let_1 BOUND_VARIABLE_21363)) (@ _let_1 BOUND_VARIABLE_21364)))) (forall ((X3 tptp.val)) (let ((_let_1 (@ tptp.member_val X3))) (or (not (@ 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((_let_213 (forall ((BOUND_VARIABLE_21323 tptp.val) (BOUND_VARIABLE_21324 tptp.val)) (= (and (@ (@ tptp.ord_less_eq_val BOUND_VARIABLE_21323) BOUND_VARIABLE_21324) (@ (@ tptp.ord_less_eq_val BOUND_VARIABLE_21324) BOUND_VARIABLE_21323)) (ll_30 BOUND_VARIABLE_21323 BOUND_VARIABLE_21324))))) (let ((_let_214 (forall ((BOUND_VARIABLE_21316 (-> Bool tptp.set_val)) (BOUND_VARIABLE_21317 (-> Bool tptp.set_val))) (= (= BOUND_VARIABLE_21316 BOUND_VARIABLE_21317) (ll_29 BOUND_VARIABLE_21316 BOUND_VARIABLE_21317))))) (let ((_let_215 (forall ((BOUND_VARIABLE_21299 (-> Bool tptp.set_val)) (BOUND_VARIABLE_21300 (-> Bool tptp.set_val))) (= (and (forall ((X3 Bool) (X3 tptp.val)) (let ((_let_1 (@ tptp.member_val X3))) (or (not (@ _let_1 (@ BOUND_VARIABLE_21299 X3))) (@ _let_1 (@ BOUND_VARIABLE_21300 X3))))) (forall ((X3 Bool) (X3 tptp.val)) (let ((_let_1 (@ tptp.member_val X3))) (or (not (@ _let_1 (@ BOUND_VARIABLE_21300 X3))) (@ _let_1 (@ BOUND_VARIABLE_21299 X3)))))) (ll_28 BOUND_VARIABLE_21299 BOUND_VARIABLE_21300))))) (let ((_let_216 (forall ((BOUND_VARIABLE_21291 tptp.set_val) (BOUND_VARIABLE_21292 tptp.val)) (= (@ (@ tptp.member_val BOUND_VARIABLE_21292) BOUND_VARIABLE_21291) (ll_27 BOUND_VARIABLE_21291 BOUND_VARIABLE_21292))))) (let ((_let_217 (forall ((BOUND_VARIABLE_21283 tptp.set_set_val) (BOUND_VARIABLE_21284 tptp.set_val)) (= (@ (@ tptp.member_set_val BOUND_VARIABLE_21284) BOUND_VARIABLE_21283) (ll_26 BOUND_VARIABLE_21283 BOUND_VARIABLE_21284))))) (let ((_let_218 (forall ((BOUND_VARIABLE_21276 tptp.set_val) (BOUND_VARIABLE_21277 tptp.set_val)) (= (= BOUND_VARIABLE_21276 BOUND_VARIABLE_21277) (ll_25 BOUND_VARIABLE_21276 BOUND_VARIABLE_21277))))) (let ((_let_219 (forall ((BOUND_VARIABLE_21261 tptp.set_val) (BOUND_VARIABLE_21262 tptp.set_val)) (= (and (forall ((X3 tptp.val)) (let ((_let_1 (@ tptp.member_val X3))) (or (not (@ _let_1 BOUND_VARIABLE_21261)) (@ _let_1 BOUND_VARIABLE_21262)))) (forall ((X3 tptp.val)) (let ((_let_1 (@ tptp.member_val X3))) (or (not (@ _let_1 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(forall ((BOUND_VARIABLE_21221 tptp.val) (BOUND_VARIABLE_21222 tptp.val)) (= (and (@ (@ tptp.ord_less_eq_val BOUND_VARIABLE_21221) BOUND_VARIABLE_21222) (@ (@ tptp.ord_less_eq_val BOUND_VARIABLE_21222) BOUND_VARIABLE_21221)) (ll_20 BOUND_VARIABLE_21221 BOUND_VARIABLE_21222))))) (let ((_let_224 (forall ((BOUND_VARIABLE_21214 (-> Bool tptp.set_val)) (BOUND_VARIABLE_21215 (-> Bool tptp.set_val))) (= (= BOUND_VARIABLE_21214 BOUND_VARIABLE_21215) (ll_19 BOUND_VARIABLE_21214 BOUND_VARIABLE_21215))))) (let ((_let_225 (forall ((BOUND_VARIABLE_21197 (-> Bool tptp.set_val)) (BOUND_VARIABLE_21198 (-> Bool tptp.set_val))) (= (and (forall ((X3 Bool) (X3 tptp.val)) (let ((_let_1 (@ tptp.member_val X3))) (or (not (@ _let_1 (@ BOUND_VARIABLE_21197 X3))) (@ _let_1 (@ BOUND_VARIABLE_21198 X3))))) (forall ((X3 Bool) (X3 tptp.val)) (let ((_let_1 (@ tptp.member_val X3))) (or (not (@ _let_1 (@ BOUND_VARIABLE_21198 X3))) (@ _let_1 (@ BOUND_VARIABLE_21197 X3)))))) (ll_18 BOUND_VARIABLE_21197 BOUND_VARIABLE_21198))))) (let ((_let_226 (forall ((BOUND_VARIABLE_21190 tptp.set_val) (BOUND_VARIABLE_21191 tptp.set_val)) (= (= BOUND_VARIABLE_21190 BOUND_VARIABLE_21191) (ll_17 BOUND_VARIABLE_21190 BOUND_VARIABLE_21191))))) (let ((_let_227 (forall ((BOUND_VARIABLE_21175 tptp.set_val) (BOUND_VARIABLE_21176 tptp.set_val)) (= (and (forall ((X3 tptp.val)) (let ((_let_1 (@ tptp.member_val X3))) (or (not (@ _let_1 BOUND_VARIABLE_21176)) (@ _let_1 BOUND_VARIABLE_21175)))) (forall ((X3 tptp.val)) (let ((_let_1 (@ tptp.member_val X3))) (or (not (@ _let_1 BOUND_VARIABLE_21175)) (@ _let_1 BOUND_VARIABLE_21176))))) (ll_16 BOUND_VARIABLE_21175 BOUND_VARIABLE_21176))))) (let ((_let_228 (forall ((BOUND_VARIABLE_21168 tptp.set_set_val) (BOUND_VARIABLE_21169 tptp.set_set_val)) (= (= BOUND_VARIABLE_21168 BOUND_VARIABLE_21169) (ll_15 BOUND_VARIABLE_21168 BOUND_VARIABLE_21169))))) (let ((_let_229 (forall ((BOUND_VARIABLE_21153 tptp.set_set_val) (BOUND_VARIABLE_21154 tptp.set_set_val)) (= (and (forall ((X3 tptp.set_val)) (let ((_let_1 (@ tptp.member_set_val X3))) (or (not (@ _let_1 BOUND_VARIABLE_21154)) (@ _let_1 BOUND_VARIABLE_21153)))) (forall ((X3 tptp.set_val)) (let ((_let_1 (@ tptp.member_set_val X3))) (or (not (@ _let_1 BOUND_VARIABLE_21153)) (@ _let_1 BOUND_VARIABLE_21154))))) (ll_14 BOUND_VARIABLE_21153 BOUND_VARIABLE_21154))))) (let ((_let_230 (forall ((BOUND_VARIABLE_21146 tptp.val) (BOUND_VARIABLE_21147 tptp.val)) (= (= BOUND_VARIABLE_21146 BOUND_VARIABLE_21147) (ll_13 BOUND_VARIABLE_21146 BOUND_VARIABLE_21147))))) (let ((_let_231 (forall ((BOUND_VARIABLE_21135 tptp.val) (BOUND_VARIABLE_21136 tptp.val)) (= (and (@ (@ tptp.ord_less_eq_val BOUND_VARIABLE_21136) BOUND_VARIABLE_21135) (@ (@ tptp.ord_less_eq_val BOUND_VARIABLE_21135) BOUND_VARIABLE_21136)) (ll_12 BOUND_VARIABLE_21135 BOUND_VARIABLE_21136))))) (let ((_let_232 (forall ((BOUND_VARIABLE_21128 (-> Bool tptp.set_val)) (BOUND_VARIABLE_21129 (-> Bool tptp.set_val))) (= (= BOUND_VARIABLE_21128 BOUND_VARIABLE_21129) (ll_11 BOUND_VARIABLE_21128 BOUND_VARIABLE_21129))))) (let ((_let_233 (forall ((BOUND_VARIABLE_21111 (-> Bool tptp.set_val)) (BOUND_VARIABLE_21112 (-> Bool tptp.set_val))) (= (and (forall ((X3 Bool) (X3 tptp.val)) (let ((_let_1 (@ tptp.member_val X3))) (or (not (@ _let_1 (@ BOUND_VARIABLE_21112 X3))) (@ _let_1 (@ BOUND_VARIABLE_21111 X3))))) (forall ((X3 Bool) (X3 tptp.val)) (let ((_let_1 (@ tptp.member_val X3))) (or (not (@ _let_1 (@ BOUND_VARIABLE_21111 X3))) (@ _let_1 (@ BOUND_VARIABLE_21112 X3)))))) (ll_10 BOUND_VARIABLE_21111 BOUND_VARIABLE_21112))))) (let ((_let_234 (forall ((BOUND_VARIABLE_21104 tptp.set_val) (BOUND_VARIABLE_21105 tptp.set_val)) (= (= BOUND_VARIABLE_21104 BOUND_VARIABLE_21105) (ll_9 BOUND_VARIABLE_21104 BOUND_VARIABLE_21105))))) (let ((_let_235 (forall ((BOUND_VARIABLE_21089 tptp.set_val) (BOUND_VARIABLE_21090 tptp.set_val)) (= (and (forall ((X3 tptp.val)) (let ((_let_1 (@ tptp.member_val X3))) (or (not (@ _let_1 BOUND_VARIABLE_21089)) (@ _let_1 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((X3 tptp.val)) (let ((_let_1 (@ tptp.member_val X3))) (or (not (@ _let_1 BOUND_VARIABLE_21056)) (@ _let_1 BOUND_VARIABLE_21057)))) (ll_5 BOUND_VARIABLE_21056 BOUND_VARIABLE_21057))))) (let ((_let_239 (forall ((BOUND_VARIABLE_21045 tptp.set_val) (BOUND_VARIABLE_21046 tptp.set_val)) (= (forall ((T tptp.val)) (let ((_let_1 (@ tptp.member_val T))) (or (not (@ _let_1 BOUND_VARIABLE_21045)) (@ _let_1 BOUND_VARIABLE_21046)))) (ll_4 BOUND_VARIABLE_21045 BOUND_VARIABLE_21046))))) (let ((_let_240 (forall ((BOUND_VARIABLE_21034 tptp.set_set_val) (BOUND_VARIABLE_21035 tptp.set_set_val)) (= (forall ((X3 tptp.set_val)) (let ((_let_1 (@ tptp.member_set_val X3))) (or (not (@ _let_1 BOUND_VARIABLE_21034)) (@ _let_1 BOUND_VARIABLE_21035)))) (ll_3 BOUND_VARIABLE_21034 BOUND_VARIABLE_21035))))) (let ((_let_241 (forall ((BOUND_VARIABLE_21023 tptp.set_set_val) (BOUND_VARIABLE_21024 tptp.set_set_val)) (= (forall ((T tptp.set_val)) (let ((_let_1 (@ tptp.member_set_val T))) (or (not (@ _let_1 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(AND_INTRO _let_244 _let_243) :args (_let_26 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_246 (EQ_RESOLVE (ASSUME :args (_let_25)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_245 _let_244 _let_243) :args (_let_25 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_247 (ASSUME :args (_let_24)))) (let ((_let_248 (EQ_RESOLVE (ASSUME :args (_let_23)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_247 _let_246 _let_245 _let_244 _let_243) :args (_let_23 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_249 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_22)) (MACRO_SR_EQ_INTRO :args (_let_22 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_248 _let_247 _let_246 _let_245 _let_244 _let_243) :args ((= tptp.order_1719375026et_val (lambda ((F2 (-> tptp.set_val tptp.set_val))) (forall ((X3 tptp.set_val) (Y4 tptp.set_val)) (or (not (@ (@ tptp.ord_less_eq_set_val X3) Y4)) (@ (@ tptp.ord_less_eq_set_val (@ F2 Y4)) (@ F2 X3)))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_250 (EQ_RESOLVE (ASSUME :args (_let_21)) (MACRO_SR_EQ_INTRO :args (_let_21 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_251 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_20)) (MACRO_SR_EQ_INTRO :args (_let_20 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243) :args ((= tptp.order_1375876562al_val (lambda ((F2 (-> tptp.set_val tptp.val))) (forall ((X3 tptp.set_val) (Y4 tptp.set_val)) (or (not (@ (@ tptp.ord_less_eq_set_val X3) Y4)) (@ (@ tptp.ord_less_eq_val (@ F2 Y4)) (@ F2 X3)))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_252 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_19)) (MACRO_SR_EQ_INTRO :args (_let_19 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243) :args ((= tptp.order_1484138386et_val (lambda ((F2 (-> tptp.val tptp.set_val))) (forall ((X3 tptp.val) (Y4 tptp.val)) (or (not (@ (@ tptp.ord_less_eq_val X3) Y4)) (@ (@ tptp.ord_less_eq_set_val (@ F2 Y4)) (@ F2 X3)))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_253 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243) :args ((= tptp.order_1945059954et_val (lambda ((F2 (-> tptp.val tptp.set_set_val))) (forall ((X3 tptp.val) (Y4 tptp.val)) (or (not (@ (@ tptp.ord_less_eq_val X3) Y4)) (@ (@ tptp.ord_le1742111550et_val (@ F2 Y4)) (@ F2 X3)))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_254 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243) :args ((= tptp.order_1520822002al_val (lambda ((F2 (-> tptp.set_set_val tptp.val))) (forall ((X3 tptp.set_set_val) (Y4 tptp.set_set_val)) (or (not (@ (@ tptp.ord_le1742111550et_val X3) Y4)) (@ (@ tptp.ord_less_eq_val (@ F2 Y4)) (@ F2 X3)))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_255 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243) :args ((= tptp.order_1957703570et_val (lambda ((F2 (-> tptp.set_val tptp.set_set_val))) (forall ((X3 tptp.set_val) (Y4 tptp.set_val)) (or (not (@ (@ tptp.ord_less_eq_set_val X3) Y4)) (@ (@ tptp.ord_le1742111550et_val (@ F2 Y4)) (@ F2 X3)))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_256 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243) :args ((= tptp.order_23236447al_val (lambda ((F2 (-> (-> Bool tptp.set_val) tptp.val))) (forall ((X3 (-> Bool tptp.set_val)) (Y4 (-> Bool tptp.set_val))) (or (not (@ (@ tptp.ord_le994826475et_val X3) Y4)) (@ (@ tptp.ord_less_eq_val (@ F2 Y4)) (@ F2 X3)))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_257 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243) :args ((= tptp.order_255079095et_val (lambda ((F2 (-> tptp.val Bool tptp.set_val))) (forall ((X3 tptp.val) (Y4 tptp.val)) (or (not (@ (@ tptp.ord_less_eq_val X3) Y4)) (@ (@ tptp.ord_le994826475et_val (@ F2 Y4)) (@ F2 X3)))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_258 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243) :args ((= tptp.order_650823122et_val (lambda ((F2 (-> tptp.set_set_val tptp.set_val))) (forall ((X3 tptp.set_set_val) (Y4 tptp.set_set_val)) (or (not (@ (@ tptp.ord_le1742111550et_val X3) Y4)) (@ (@ tptp.ord_less_eq_set_val (@ F2 Y4)) (@ F2 X3)))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_259 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243) :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_260 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243) :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_261 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243) :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_262 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243) :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_263 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243) :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_264 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243) :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_265 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243) :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_266 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243) :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_267 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243) :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_268 (ASSUME :args (_let_3)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (MACRO_SR_EQ_INTRO (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243) :args (_let_2 SB_DEFAULT SBA_FIXPOINT))) _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243) :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (forall ((X3 tptp.val)) (let ((_let_1 (@ tptp.member_val X3))) (or (not (@ _let_1 tptp.scc)) (@ _let_1 tptp.p))))) (not _let_30)))))) (MACRO_RESOLUTION_TRUST (REORDERING (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_31 (= X X3)))) :args ((or _let_30 (not _let_31)))) (AND_ELIM (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_29)) (MACRO_SR_EQ_INTRO :args (_let_29 SB_DEFAULT SBA_FIXPOINT))) (PREPROCESS :args ((and _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193)))) :args (_let_242)) (PREPROCESS :args ((= _let_242 (and _let_31 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _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))))) (PREPROCESS :args ((and _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 _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 _let_43 _let_42 _let_41 _let_40 _let_39 _let_38 _let_37 _let_36 _let_35 _let_34 _let_33 _let_32)))) :args ((and _let_31 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _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 _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 _let_43 _let_42 _let_41 _let_40 _let_39 _let_38 _let_37 _let_36 _let_35 _let_34 _let_33 _let_32))) :args (0)) :args (_let_30 false _let_31)) :args (false false _let_30)) :args (_let_29 (forall ((A tptp.set_set_val) (B tptp.set_set_val)) (=> (forall ((X2 tptp.set_val)) (let ((_let_1 (@ tptp.member_set_val X2))) (=> (@ _let_1 A) (@ _let_1 B)))) (@ (@ tptp.ord_le1742111550et_val A) B))) (forall ((A tptp.set_val) (B tptp.set_val)) (=> (forall 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((A tptp.set_set_val) (B tptp.set_set_val)) (=> (= A B) (@ (@ tptp.ord_le1742111550et_val A) B))) (forall ((A tptp.set_val) (B tptp.set_val)) (=> (= A B) (@ (@ tptp.ord_less_eq_set_val A) B))) (forall ((A tptp.set_set_val) (B tptp.set_set_val)) (=> (= A B) (@ (@ tptp.ord_le1742111550et_val B) A))) (forall ((A tptp.set_val) (B tptp.set_val)) (=> (= A B) (@ (@ tptp.ord_less_eq_set_val B) A))) (= tptp.ord_le1742111550et_val (lambda ((A2 tptp.set_set_val) (B2 tptp.set_set_val)) (forall ((T tptp.set_val)) (let ((_let_1 (@ tptp.member_set_val T))) (=> (@ _let_1 A2) (@ _let_1 B2)))))) (= tptp.ord_less_eq_set_val (lambda ((A2 tptp.set_val) (B2 tptp.set_val)) (forall ((T tptp.val)) (let ((_let_1 (@ tptp.member_val T))) (=> (@ _let_1 A2) (@ _let_1 B2)))))) (forall ((A tptp.set_set_val)) (@ (@ tptp.ord_le1742111550et_val A) A)) (forall ((A tptp.set_val)) (@ (@ tptp.ord_less_eq_set_val A) A)) (forall ((T2 (-> Bool tptp.set_val)) (T3 (-> Bool tptp.set_val)) (E (-> Bool tptp.set_val)) (E2 (-> Bool 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tptp.collect_val P)) (forall ((X3 tptp.val)) (=> (@ (@ tptp.member_val X3) S) (@ P X3))))) (forall ((B3 (-> Bool tptp.set_val)) (A3 (-> Bool tptp.set_val))) (=> (@ (@ tptp.ord_le994826475et_val B3) A3) (=> (@ (@ tptp.ord_le994826475et_val A3) B3) (= A3 B3)))) (forall ((B3 tptp.val) (A3 tptp.val)) (=> (@ (@ tptp.ord_less_eq_val B3) A3) (=> (@ (@ tptp.ord_less_eq_val A3) B3) (= A3 B3)))) (forall ((B3 tptp.set_set_val) (A3 tptp.set_set_val)) (=> (@ (@ tptp.ord_le1742111550et_val B3) A3) (=> (@ (@ tptp.ord_le1742111550et_val A3) B3) (= A3 B3)))) (forall ((B3 tptp.set_val) (A3 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val B3) A3) (=> (@ (@ tptp.ord_less_eq_set_val A3) B3) (= A3 B3)))) (= (lambda ((Y (-> Bool tptp.set_val)) (Z (-> Bool tptp.set_val))) (= Y Z)) (lambda ((A4 (-> Bool tptp.set_val)) (B4 (-> Bool tptp.set_val))) (and (@ (@ tptp.ord_le994826475et_val B4) A4) (@ (@ tptp.ord_le994826475et_val A4) B4)))) (= (lambda ((Y tptp.val) (Z tptp.val)) (= Y Z)) (lambda ((A4 tptp.val) (B4 tptp.val)) (and (@ (@ tptp.ord_less_eq_val B4) A4) (@ (@ tptp.ord_less_eq_val A4) B4)))) (= (lambda ((Y tptp.set_set_val) (Z tptp.set_set_val)) (= Y Z)) (lambda ((A4 tptp.set_set_val) (B4 tptp.set_set_val)) (and (@ (@ tptp.ord_le1742111550et_val B4) A4) (@ (@ tptp.ord_le1742111550et_val A4) B4)))) (= (lambda ((Y tptp.set_val) (Z tptp.set_val)) (= Y Z)) (lambda ((A4 tptp.set_val) (B4 tptp.set_val)) (and (@ (@ tptp.ord_less_eq_set_val B4) A4) (@ (@ tptp.ord_less_eq_set_val A4) B4)))) (forall ((B3 (-> Bool tptp.set_val)) (A3 (-> Bool tptp.set_val)) (C (-> Bool tptp.set_val))) (let ((_let_1 (@ tptp.ord_le994826475et_val C))) (=> (@ (@ tptp.ord_le994826475et_val B3) A3) (=> (@ _let_1 B3) (@ _let_1 A3))))) (forall ((B3 tptp.val) (A3 tptp.val) (C tptp.val)) (let ((_let_1 (@ tptp.ord_less_eq_val C))) (=> (@ (@ tptp.ord_less_eq_val B3) A3) (=> (@ _let_1 B3) (@ _let_1 A3))))) (forall ((B3 tptp.set_set_val) (A3 tptp.set_set_val) (C tptp.set_set_val)) (let ((_let_1 (@ tptp.ord_le1742111550et_val C))) (=> (@ (@ tptp.ord_le1742111550et_val B3) A3) (=> (@ _let_1 B3) (@ _let_1 A3))))) (forall ((B3 tptp.set_val) (A3 tptp.set_val) (C tptp.set_val)) (let ((_let_1 (@ tptp.ord_less_eq_set_val C))) (=> (@ (@ tptp.ord_less_eq_set_val B3) A3) (=> (@ _let_1 B3) (@ _let_1 A3))))) (forall ((P (-> tptp.val tptp.val Bool)) (A3 tptp.val) (B3 tptp.val)) (=> (forall ((A5 tptp.val) (B5 tptp.val)) (=> (@ (@ tptp.ord_less_eq_val A5) B5) (@ (@ P A5) B5))) (=> (forall ((A5 tptp.val) (B5 tptp.val)) (=> (@ (@ P B5) A5) (@ (@ P A5) B5))) (@ (@ P A3) B3)))) (forall ((A3 (-> Bool tptp.set_val))) (@ (@ tptp.ord_le994826475et_val A3) A3)) (forall ((A3 tptp.val)) (@ (@ tptp.ord_less_eq_val A3) A3)) (forall ((A3 tptp.set_set_val)) (@ (@ tptp.ord_le1742111550et_val A3) A3)) (forall ((A3 tptp.set_val)) (@ (@ tptp.ord_less_eq_set_val A3) A3)) (forall ((X (-> Bool tptp.set_val)) (Y2 (-> Bool tptp.set_val)) (Z2 (-> Bool tptp.set_val))) (let ((_let_1 (@ tptp.ord_le994826475et_val X))) (=> (@ _let_1 Y2) (=> (@ (@ 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tptp.ord_le1742111550et_val A3) B3) (=> (@ (@ tptp.ord_le1742111550et_val B3) A3) (= A3 B3)))) (forall ((A3 tptp.set_val) (B3 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val A3) B3) (=> (@ (@ tptp.ord_less_eq_set_val B3) A3) (= A3 B3)))) (forall ((A3 (-> Bool tptp.set_val)) (B3 (-> Bool tptp.set_val)) (C (-> Bool tptp.set_val))) (let ((_let_1 (@ tptp.ord_le994826475et_val A3))) (=> (@ _let_1 B3) (=> (= B3 C) (@ _let_1 C))))) (forall ((A3 tptp.val) (B3 tptp.val) (C tptp.val)) (let ((_let_1 (@ tptp.ord_less_eq_val A3))) (=> (@ _let_1 B3) (=> (= B3 C) (@ _let_1 C))))) (forall ((A3 tptp.set_set_val) (B3 tptp.set_set_val) (C tptp.set_set_val)) (let ((_let_1 (@ tptp.ord_le1742111550et_val A3))) (=> (@ _let_1 B3) (=> (= B3 C) (@ _let_1 C))))) (forall ((A3 tptp.set_val) (B3 tptp.set_val) (C tptp.set_val)) (let ((_let_1 (@ tptp.ord_less_eq_set_val A3))) (=> (@ _let_1 B3) (=> (= B3 C) (@ _let_1 C))))) (forall ((F (-> Bool tptp.set_val)) (G (-> Bool tptp.set_val)) (X Bool)) (=> (@ (@ tptp.ord_le994826475et_val F) G) (@ (@ tptp.ord_less_eq_set_val (@ F X)) (@ G X)))) (forall ((F (-> Bool tptp.set_val)) (G (-> Bool tptp.set_val)) (X Bool)) (=> (@ (@ tptp.ord_le994826475et_val F) G) (@ (@ tptp.ord_less_eq_set_val (@ F X)) (@ G X)))) (forall ((F (-> Bool tptp.set_val)) (G (-> Bool tptp.set_val))) (=> (forall ((X2 Bool)) (@ (@ tptp.ord_less_eq_set_val (@ F X2)) (@ G X2))) (@ (@ tptp.ord_le994826475et_val F) G))) _let_26 (forall ((A3 tptp.set_val) (F (-> tptp.set_val tptp.set_val)) (B3 tptp.set_val) (C tptp.set_val)) (let ((_let_1 (@ tptp.ord_less_eq_set_val A3))) (=> (@ _let_1 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_set_val B3) C) (=> (forall ((X2 tptp.set_val) (Y3 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val X2) Y3) (@ (@ tptp.ord_less_eq_set_val (@ F X2)) (@ F Y3)))) (@ _let_1 (@ F C))))))) (forall ((A3 tptp.val) (F (-> tptp.val tptp.val)) (B3 tptp.val) (C tptp.val)) (let ((_let_1 (@ tptp.ord_less_eq_val A3))) (=> (@ _let_1 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_val B3) C) (=> (forall ((X2 tptp.val) (Y3 tptp.val)) (=> (@ (@ tptp.ord_less_eq_val X2) Y3) (@ (@ tptp.ord_less_eq_val (@ F X2)) (@ F Y3)))) (@ _let_1 (@ F C))))))) (forall ((A3 tptp.set_val) (F (-> tptp.val tptp.set_val)) (B3 tptp.val) (C tptp.val)) (let ((_let_1 (@ tptp.ord_less_eq_set_val A3))) (=> (@ _let_1 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_val B3) C) (=> (forall ((X2 tptp.val) (Y3 tptp.val)) (=> (@ (@ tptp.ord_less_eq_val X2) Y3) (@ (@ tptp.ord_less_eq_set_val (@ F X2)) (@ F Y3)))) (@ _let_1 (@ F C))))))) (forall ((A3 tptp.val) (F (-> tptp.set_val tptp.val)) (B3 tptp.set_val) (C tptp.set_val)) (let ((_let_1 (@ tptp.ord_less_eq_val A3))) (=> (@ _let_1 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_set_val B3) C) (=> (forall ((X2 tptp.set_val) (Y3 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val X2) Y3) (@ (@ tptp.ord_less_eq_val (@ F X2)) (@ F Y3)))) (@ _let_1 (@ F C))))))) (forall ((A3 tptp.val) (F (-> tptp.set_set_val tptp.val)) (B3 tptp.set_set_val) (C tptp.set_set_val)) (let ((_let_1 (@ tptp.ord_less_eq_val A3))) (=> (@ _let_1 (@ F B3)) (=> (@ (@ tptp.ord_le1742111550et_val B3) C) (=> (forall ((X2 tptp.set_set_val) (Y3 tptp.set_set_val)) (=> (@ (@ tptp.ord_le1742111550et_val X2) Y3) (@ (@ tptp.ord_less_eq_val (@ F X2)) (@ F Y3)))) (@ _let_1 (@ F C))))))) (forall ((A3 tptp.set_set_val) (F (-> tptp.val tptp.set_set_val)) (B3 tptp.val) (C tptp.val)) (let ((_let_1 (@ tptp.ord_le1742111550et_val A3))) (=> (@ _let_1 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_val B3) C) (=> (forall ((X2 tptp.val) (Y3 tptp.val)) (=> (@ (@ tptp.ord_less_eq_val X2) Y3) (@ (@ tptp.ord_le1742111550et_val (@ F X2)) (@ F Y3)))) (@ _let_1 (@ F C))))))) (forall ((A3 tptp.set_val) (F (-> tptp.set_set_val tptp.set_val)) (B3 tptp.set_set_val) (C tptp.set_set_val)) (let ((_let_1 (@ tptp.ord_less_eq_set_val A3))) (=> (@ _let_1 (@ F B3)) (=> (@ (@ tptp.ord_le1742111550et_val B3) C) (=> (forall ((X2 tptp.set_set_val) (Y3 tptp.set_set_val)) (=> (@ (@ tptp.ord_le1742111550et_val X2) Y3) (@ (@ tptp.ord_less_eq_set_val (@ F X2)) (@ F Y3)))) (@ _let_1 (@ F C))))))) (forall ((A3 (-> Bool tptp.set_val)) (F (-> tptp.val Bool tptp.set_val)) (B3 tptp.val) (C tptp.val)) (let ((_let_1 (@ tptp.ord_le994826475et_val A3))) (=> (@ _let_1 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_val B3) C) (=> (forall ((X2 tptp.val) (Y3 tptp.val)) (=> (@ (@ tptp.ord_less_eq_val X2) Y3) (@ (@ tptp.ord_le994826475et_val (@ F X2)) (@ F Y3)))) (@ _let_1 (@ F C))))))) (forall ((A3 tptp.val) (F (-> (-> Bool tptp.set_val) tptp.val)) (B3 (-> Bool tptp.set_val)) (C (-> Bool tptp.set_val))) (let ((_let_1 (@ tptp.ord_less_eq_val A3))) (=> (@ _let_1 (@ F B3)) (=> (@ (@ tptp.ord_le994826475et_val B3) C) (=> (forall ((X2 (-> Bool tptp.set_val)) (Y3 (-> Bool tptp.set_val))) (=> (@ (@ tptp.ord_le994826475et_val X2) Y3) (@ (@ tptp.ord_less_eq_val (@ F X2)) (@ F Y3)))) (@ _let_1 (@ F C))))))) (forall ((A3 tptp.set_set_val) (F (-> tptp.set_val tptp.set_set_val)) (B3 tptp.set_val) (C tptp.set_val)) (let ((_let_1 (@ tptp.ord_le1742111550et_val A3))) (=> (@ _let_1 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_set_val B3) C) (=> (forall ((X2 tptp.set_val) (Y3 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val X2) Y3) (@ (@ tptp.ord_le1742111550et_val (@ F X2)) (@ F Y3)))) (@ _let_1 (@ F C))))))) (forall ((A3 tptp.set_val) (B3 tptp.set_val) (F (-> tptp.set_val tptp.set_val)) (C tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val A3) B3) (=> (@ (@ tptp.ord_less_eq_set_val (@ F B3)) C) (=> (forall ((X2 tptp.set_val) (Y3 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val X2) Y3) (@ (@ tptp.ord_less_eq_set_val (@ F X2)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_set_val (@ F A3)) C))))) (forall ((A3 tptp.val) (B3 tptp.val) (F (-> tptp.val tptp.val)) (C tptp.val)) (=> (@ (@ tptp.ord_less_eq_val A3) B3) (=> (@ (@ tptp.ord_less_eq_val (@ F B3)) C) (=> (forall ((X2 tptp.val) (Y3 tptp.val)) (=> (@ (@ tptp.ord_less_eq_val X2) Y3) (@ (@ tptp.ord_less_eq_val (@ F X2)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_val (@ F A3)) C))))) (forall ((A3 tptp.set_val) (B3 tptp.set_val) (F (-> tptp.set_val tptp.val)) (C tptp.val)) (=> (@ (@ tptp.ord_less_eq_set_val A3) B3) (=> (@ (@ tptp.ord_less_eq_val (@ F B3)) C) (=> (forall ((X2 tptp.set_val) (Y3 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val X2) Y3) (@ (@ tptp.ord_less_eq_val (@ F X2)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_val (@ F A3)) C))))) (forall ((A3 tptp.val) (B3 tptp.val) (F (-> tptp.val tptp.set_val)) (C tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_val A3) B3) (=> (@ (@ tptp.ord_less_eq_set_val (@ F B3)) C) (=> (forall ((X2 tptp.val) (Y3 tptp.val)) (=> (@ (@ tptp.ord_less_eq_val X2) Y3) (@ (@ tptp.ord_less_eq_set_val (@ F X2)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_set_val (@ F A3)) C))))) (forall ((A3 tptp.val) (B3 tptp.val) (F (-> tptp.val tptp.set_set_val)) (C tptp.set_set_val)) (=> (@ (@ tptp.ord_less_eq_val A3) B3) (=> (@ (@ tptp.ord_le1742111550et_val (@ F B3)) C) (=> (forall ((X2 tptp.val) (Y3 tptp.val)) (=> (@ (@ tptp.ord_less_eq_val X2) Y3) (@ (@ tptp.ord_le1742111550et_val (@ F X2)) (@ F Y3)))) (@ (@ tptp.ord_le1742111550et_val (@ F A3)) C))))) (forall ((A3 tptp.set_set_val) (B3 tptp.set_set_val) (F (-> tptp.set_set_val tptp.val)) (C tptp.val)) (=> (@ (@ tptp.ord_le1742111550et_val A3) B3) (=> (@ (@ tptp.ord_less_eq_val (@ F B3)) C) (=> (forall ((X2 tptp.set_set_val) (Y3 tptp.set_set_val)) (=> (@ (@ tptp.ord_le1742111550et_val X2) Y3) (@ (@ tptp.ord_less_eq_val (@ F X2)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_val (@ F A3)) C))))) (forall ((A3 tptp.set_val) (B3 tptp.set_val) (F (-> tptp.set_val tptp.set_set_val)) (C tptp.set_set_val)) (=> (@ (@ tptp.ord_less_eq_set_val A3) B3) (=> (@ (@ tptp.ord_le1742111550et_val (@ F B3)) C) (=> (forall ((X2 tptp.set_val) (Y3 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val X2) Y3) (@ (@ tptp.ord_le1742111550et_val (@ F X2)) (@ F Y3)))) (@ (@ tptp.ord_le1742111550et_val (@ F A3)) C))))) (forall ((A3 (-> Bool tptp.set_val)) (B3 (-> Bool tptp.set_val)) (F (-> (-> Bool tptp.set_val) tptp.val)) (C tptp.val)) (=> (@ (@ tptp.ord_le994826475et_val A3) B3) (=> (@ (@ tptp.ord_less_eq_val (@ F B3)) C) (=> (forall ((X2 (-> Bool tptp.set_val)) (Y3 (-> Bool tptp.set_val))) (=> (@ (@ tptp.ord_le994826475et_val X2) Y3) (@ (@ tptp.ord_less_eq_val (@ F X2)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_val (@ F A3)) C))))) (forall ((A3 tptp.val) (B3 tptp.val) (F (-> tptp.val Bool tptp.set_val)) (C (-> Bool tptp.set_val))) (=> (@ (@ tptp.ord_less_eq_val A3) B3) (=> (@ (@ tptp.ord_le994826475et_val (@ F B3)) C) (=> (forall ((X2 tptp.val) (Y3 tptp.val)) (=> (@ (@ tptp.ord_less_eq_val X2) Y3) (@ (@ tptp.ord_le994826475et_val (@ F X2)) (@ F Y3)))) (@ (@ tptp.ord_le994826475et_val (@ F A3)) C))))) (forall ((A3 tptp.set_set_val) (B3 tptp.set_set_val) (F (-> tptp.set_set_val tptp.set_val)) (C tptp.set_val)) (=> (@ (@ tptp.ord_le1742111550et_val A3) B3) (=> (@ (@ tptp.ord_less_eq_set_val (@ F B3)) C) (=> (forall ((X2 tptp.set_set_val) (Y3 tptp.set_set_val)) (=> (@ (@ tptp.ord_le1742111550et_val X2) Y3) (@ (@ 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(= A3 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_set_val B3) C) (=> (forall ((X2 tptp.set_val) (Y3 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val X2) Y3) (@ (@ tptp.ord_less_eq_set_val (@ F X2)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_set_val A3) (@ F C)))))) (forall ((A3 tptp.val) (F (-> tptp.val tptp.val)) (B3 tptp.val) (C tptp.val)) (=> (= A3 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_val B3) C) (=> (forall ((X2 tptp.val) (Y3 tptp.val)) (=> (@ (@ tptp.ord_less_eq_val X2) Y3) (@ (@ tptp.ord_less_eq_val (@ F X2)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_val A3) (@ F C)))))) (forall ((A3 tptp.val) (F (-> tptp.set_val tptp.val)) (B3 tptp.set_val) (C tptp.set_val)) (=> (= A3 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_set_val B3) C) (=> (forall ((X2 tptp.set_val) (Y3 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val X2) Y3) (@ (@ tptp.ord_less_eq_val (@ F X2)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_val A3) (@ F C)))))) (forall ((A3 tptp.set_val) (F (-> tptp.val tptp.set_val)) (B3 tptp.val) (C tptp.val)) (=> (= A3 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_val B3) C) (=> (forall ((X2 tptp.val) (Y3 tptp.val)) (=> (@ (@ tptp.ord_less_eq_val X2) Y3) (@ (@ tptp.ord_less_eq_set_val (@ F X2)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_set_val A3) (@ F C)))))) (forall ((A3 tptp.set_set_val) (F (-> tptp.val tptp.set_set_val)) (B3 tptp.val) (C tptp.val)) (=> (= A3 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_val B3) C) (=> (forall ((X2 tptp.val) (Y3 tptp.val)) (=> (@ (@ tptp.ord_less_eq_val X2) Y3) (@ (@ tptp.ord_le1742111550et_val (@ F X2)) (@ F Y3)))) (@ (@ tptp.ord_le1742111550et_val A3) (@ F C)))))) (forall ((A3 tptp.val) (F (-> tptp.set_set_val tptp.val)) (B3 tptp.set_set_val) (C tptp.set_set_val)) (=> (= A3 (@ F B3)) (=> (@ (@ tptp.ord_le1742111550et_val B3) C) (=> (forall ((X2 tptp.set_set_val) (Y3 tptp.set_set_val)) (=> (@ (@ tptp.ord_le1742111550et_val X2) Y3) (@ (@ tptp.ord_less_eq_val (@ F X2)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_val A3) (@ F C)))))) (forall ((A3 tptp.set_set_val) (F (-> tptp.set_val tptp.set_set_val)) (B3 tptp.set_val) (C tptp.set_val)) (=> (= A3 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_set_val B3) C) (=> (forall ((X2 tptp.set_val) (Y3 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val X2) Y3) (@ (@ tptp.ord_le1742111550et_val (@ F X2)) (@ F Y3)))) (@ (@ tptp.ord_le1742111550et_val A3) (@ F C)))))) (forall ((A3 tptp.val) (F (-> (-> Bool tptp.set_val) tptp.val)) (B3 (-> Bool tptp.set_val)) (C (-> Bool tptp.set_val))) (=> (= A3 (@ F B3)) (=> (@ (@ tptp.ord_le994826475et_val B3) C) (=> (forall ((X2 (-> Bool tptp.set_val)) (Y3 (-> Bool tptp.set_val))) (=> (@ (@ tptp.ord_le994826475et_val X2) Y3) (@ (@ tptp.ord_less_eq_val (@ F X2)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_val A3) (@ F C)))))) (forall ((A3 (-> Bool tptp.set_val)) (F (-> tptp.val Bool tptp.set_val)) (B3 tptp.val) (C tptp.val)) (=> (= A3 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_val B3) C) (=> (forall ((X2 tptp.val) (Y3 tptp.val)) (=> (@ (@ tptp.ord_less_eq_val X2) Y3) (@ (@ tptp.ord_le994826475et_val (@ F X2)) (@ F Y3)))) (@ (@ 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(=> (= (@ F B3) C) (=> (forall ((X2 (-> Bool tptp.set_val)) (Y3 (-> Bool tptp.set_val))) (=> (@ (@ tptp.ord_le994826475et_val X2) Y3) (@ (@ tptp.ord_less_eq_val (@ F X2)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_val (@ F A3)) C))))) (forall ((A3 tptp.val) (B3 tptp.val) (F (-> tptp.val Bool tptp.set_val)) (C (-> Bool tptp.set_val))) (=> (@ (@ tptp.ord_less_eq_val A3) B3) (=> (= (@ F B3) C) (=> (forall ((X2 tptp.val) (Y3 tptp.val)) (=> (@ (@ tptp.ord_less_eq_val X2) Y3) (@ (@ tptp.ord_le994826475et_val (@ F X2)) (@ F Y3)))) (@ (@ tptp.ord_le994826475et_val (@ F A3)) C))))) (forall ((A3 tptp.set_set_val) (B3 tptp.set_set_val) (F (-> tptp.set_set_val tptp.set_val)) (C tptp.set_val)) (=> (@ (@ tptp.ord_le1742111550et_val A3) B3) (=> (= (@ F B3) C) (=> (forall ((X2 tptp.set_set_val) (Y3 tptp.set_set_val)) (=> (@ (@ tptp.ord_le1742111550et_val X2) Y3) (@ (@ tptp.ord_less_eq_set_val (@ F X2)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_set_val (@ F A3)) C))))) (= (lambda ((Y (-> Bool tptp.set_val)) (Z (-> 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(forall ((P (-> (-> Bool tptp.set_val) Bool)) (X (-> Bool tptp.set_val)) (Q (-> (-> Bool tptp.set_val) Bool))) (=> (@ P X) (=> (forall ((Y3 (-> Bool tptp.set_val))) (=> (@ P Y3) (@ (@ tptp.ord_le994826475et_val Y3) X))) (=> (forall ((X2 (-> Bool tptp.set_val))) (=> (@ P X2) (=> (forall ((Y5 (-> Bool tptp.set_val))) (=> (@ P Y5) (@ (@ tptp.ord_le994826475et_val Y5) X2))) (@ Q X2)))) (@ Q (@ tptp.order_985126002et_val P)))))) (forall ((P (-> tptp.val Bool)) (X tptp.val) (Q (-> tptp.val Bool))) (=> (@ P X) (=> (forall ((Y3 tptp.val)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_val Y3) X))) (=> (forall ((X2 tptp.val)) (=> (@ P X2) (=> (forall ((Y5 tptp.val)) (=> (@ P Y5) (@ (@ tptp.ord_less_eq_val Y5) X2))) (@ Q X2)))) (@ Q (@ tptp.order_Greatest_val P)))))) (forall ((P (-> tptp.set_set_val Bool)) (X tptp.set_set_val) (Q (-> tptp.set_set_val Bool))) (=> (@ P X) (=> (forall ((Y3 tptp.set_set_val)) (=> (@ P Y3) (@ (@ tptp.ord_le1742111550et_val Y3) X))) (=> (forall ((X2 tptp.set_set_val)) (=> (@ P X2) (=> (forall ((Y5 tptp.set_set_val)) (=> (@ P Y5) (@ (@ tptp.ord_le1742111550et_val Y5) X2))) (@ Q X2)))) (@ Q (@ tptp.order_544136439et_val P)))))) (forall ((P (-> tptp.set_val Bool)) (X tptp.set_val) (Q (-> tptp.set_val Bool))) (=> (@ P X) (=> (forall ((Y3 tptp.set_val)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_set_val Y3) X))) (=> (forall ((X2 tptp.set_val)) (=> (@ P X2) (=> (forall ((Y5 tptp.set_val)) (=> (@ P Y5) (@ (@ tptp.ord_less_eq_set_val Y5) X2))) (@ Q X2)))) (@ Q (@ tptp.order_1960465943et_val P)))))) (forall ((P (-> (-> Bool tptp.set_val) Bool)) (X (-> Bool tptp.set_val))) (=> (@ P X) (=> (forall ((Y3 (-> Bool tptp.set_val))) (=> (@ P Y3) (@ (@ tptp.ord_le994826475et_val Y3) X))) (= (@ tptp.order_985126002et_val P) X)))) (forall ((P (-> tptp.val Bool)) (X tptp.val)) (=> (@ P X) (=> (forall ((Y3 tptp.val)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_val Y3) X))) (= (@ tptp.order_Greatest_val P) X)))) (forall ((P (-> tptp.set_set_val Bool)) (X tptp.set_set_val)) (=> (@ P X) (=> (forall ((Y3 tptp.set_set_val)) (=> (@ P Y3) (@ (@ tptp.ord_le1742111550et_val Y3) X))) (= (@ tptp.order_544136439et_val P) X)))) (forall ((P (-> tptp.set_val Bool)) (X tptp.set_val)) (=> (@ P X) (=> (forall ((Y3 tptp.set_val)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_set_val Y3) X))) (= (@ tptp.order_1960465943et_val P) X)))) (forall ((B3 Bool) (M1 (-> Bool tptp.set_val)) (M12 (-> Bool tptp.set_val)) (M2 (-> Bool tptp.set_val)) (M22 (-> Bool tptp.set_val))) (let ((_let_1 (@ tptp.if_o_set_val B3))) (=> (=> B3 (@ (@ tptp.ord_le994826475et_val M1) M12)) (=> (=> (not B3) (@ (@ tptp.ord_le994826475et_val M2) M22)) (@ (@ tptp.ord_le994826475et_val (@ (@ _let_1 M1) M2)) (@ (@ _let_1 M12) M22)))))) (forall ((B3 Bool) (M1 tptp.val) (M12 tptp.val) (M2 tptp.val) (M22 tptp.val)) (let ((_let_1 (@ tptp.if_val B3))) (=> (=> B3 (@ (@ tptp.ord_less_eq_val M1) M12)) (=> (=> (not B3) (@ (@ tptp.ord_less_eq_val M2) M22)) (@ (@ tptp.ord_less_eq_val (@ (@ _let_1 M1) M2)) (@ (@ _let_1 M12) M22)))))) (forall ((B3 Bool) (M1 tptp.set_set_val) (M12 tptp.set_set_val) (M2 tptp.set_set_val) (M22 tptp.set_set_val)) (let ((_let_1 (@ tptp.if_set_set_val B3))) (=> (=> B3 (@ (@ tptp.ord_le1742111550et_val M1) M12)) (=> (=> (not B3) (@ (@ tptp.ord_le1742111550et_val M2) M22)) (@ (@ tptp.ord_le1742111550et_val (@ (@ _let_1 M1) M2)) (@ (@ _let_1 M12) M22)))))) (forall ((B3 Bool) (M1 tptp.set_val) (M12 tptp.set_val) (M2 tptp.set_val) (M22 tptp.set_val)) (let ((_let_1 (@ tptp.if_set_val B3))) (=> (=> B3 (@ (@ tptp.ord_less_eq_set_val M1) M12)) (=> (=> (not B3) (@ (@ tptp.ord_less_eq_set_val M2) M22)) (@ (@ tptp.ord_less_eq_set_val (@ (@ _let_1 M1) M2)) (@ (@ _let_1 M12) M22)))))) (forall ((B3 Bool) (T2 (-> Bool tptp.set_val)) (M (-> Bool tptp.set_val)) (E (-> Bool tptp.set_val))) (=> (=> B3 (@ (@ tptp.ord_le994826475et_val T2) M)) (=> (=> (not B3) (@ (@ tptp.ord_le994826475et_val E) M)) (@ (@ tptp.ord_le994826475et_val (@ (@ (@ tptp.if_o_set_val B3) T2) E)) M)))) (forall ((B3 Bool) (T2 tptp.val) (M tptp.val) (E tptp.val)) (=> (=> B3 (@ (@ tptp.ord_less_eq_val T2) M)) (=> (=> (not B3) (@ (@ tptp.ord_less_eq_val E) M)) (@ (@ tptp.ord_less_eq_val (@ (@ (@ tptp.if_val B3) T2) E)) M)))) (forall ((B3 Bool) (T2 tptp.set_set_val) (M tptp.set_set_val) (E tptp.set_set_val)) (=> (=> B3 (@ (@ tptp.ord_le1742111550et_val T2) M)) (=> (=> (not B3) (@ (@ tptp.ord_le1742111550et_val E) M)) (@ (@ tptp.ord_le1742111550et_val (@ (@ (@ tptp.if_set_set_val B3) T2) E)) M)))) (forall ((B3 Bool) (T2 tptp.set_val) (M tptp.set_val) (E tptp.set_val)) (=> (=> B3 (@ (@ tptp.ord_less_eq_set_val T2) M)) (=> (=> (not B3) (@ (@ tptp.ord_less_eq_set_val E) M)) (@ (@ tptp.ord_less_eq_set_val (@ (@ (@ tptp.if_set_val B3) T2) E)) M)))) (forall ((A3 tptp.val) (B3 tptp.val)) (or (= A3 B3) (not (@ (@ tptp.ord_less_eq_val A3) B3)) (not (@ (@ tptp.ord_less_eq_val B3) A3)))) _let_25 _let_24 _let_23 (= tptp.ord_le994826475et_val (lambda ((X4 (-> Bool tptp.set_val)) (Y6 (-> Bool tptp.set_val))) (and (@ (@ tptp.ord_less_eq_set_val (@ X4 false)) (@ Y6 false)) (@ (@ tptp.ord_less_eq_set_val (@ X4 true)) (@ Y6 true))))) (forall ((F (-> tptp.set_val tptp.set_val)) (X tptp.set_val) (Y2 tptp.set_val)) (=> (@ tptp.order_1719375026et_val F) (=> (@ (@ tptp.ord_less_eq_set_val X) Y2) (@ (@ tptp.ord_less_eq_set_val (@ F Y2)) (@ F X))))) (forall ((F (-> tptp.val tptp.val)) (X tptp.val) (Y2 tptp.val)) (=> (@ tptp.order_1689798834al_val F) (=> (@ (@ tptp.ord_less_eq_val X) Y2) (@ (@ tptp.ord_less_eq_val (@ F Y2)) (@ F X))))) (forall ((F (-> tptp.set_val tptp.val)) (X tptp.set_val) (Y2 tptp.set_val)) (=> (@ tptp.order_1375876562al_val F) (=> (@ (@ tptp.ord_less_eq_set_val X) Y2) (@ (@ tptp.ord_less_eq_val (@ F Y2)) (@ F X))))) (forall ((F (-> tptp.val tptp.set_val)) (X tptp.val) (Y2 tptp.val)) (=> (@ tptp.order_1484138386et_val F) (=> (@ (@ tptp.ord_less_eq_val X) Y2) (@ (@ tptp.ord_less_eq_set_val (@ F Y2)) (@ F X))))) (forall ((F (-> tptp.val tptp.set_set_val)) (X tptp.val) (Y2 tptp.val)) (=> (@ tptp.order_1945059954et_val F) (=> (@ (@ tptp.ord_less_eq_val X) Y2) (@ (@ tptp.ord_le1742111550et_val (@ F Y2)) (@ F X))))) (forall ((F (-> tptp.set_set_val tptp.val)) (X tptp.set_set_val) (Y2 tptp.set_set_val)) (=> (@ tptp.order_1520822002al_val F) (=> (@ (@ tptp.ord_le1742111550et_val X) Y2) (@ (@ tptp.ord_less_eq_val (@ F Y2)) (@ F X))))) (forall ((F (-> tptp.set_val tptp.set_set_val)) (X tptp.set_val) (Y2 tptp.set_val)) (=> (@ tptp.order_1957703570et_val F) (=> (@ (@ tptp.ord_less_eq_set_val X) Y2) (@ (@ tptp.ord_le1742111550et_val (@ F Y2)) (@ F X))))) (forall ((F (-> (-> Bool tptp.set_val) tptp.val)) (X (-> Bool tptp.set_val)) (Y2 (-> Bool tptp.set_val))) (=> (@ tptp.order_23236447al_val F) (=> (@ (@ tptp.ord_le994826475et_val X) Y2) (@ (@ tptp.ord_less_eq_val (@ F Y2)) (@ F X))))) (forall ((F (-> tptp.val Bool tptp.set_val)) (X tptp.val) (Y2 tptp.val)) (=> (@ tptp.order_255079095et_val F) (=> (@ (@ tptp.ord_less_eq_val X) Y2) (@ (@ tptp.ord_le994826475et_val (@ F Y2)) (@ F X))))) (forall ((F (-> tptp.set_set_val tptp.set_val)) (X tptp.set_set_val) (Y2 tptp.set_set_val)) (=> (@ tptp.order_650823122et_val F) (=> (@ (@ tptp.ord_le1742111550et_val X) Y2) (@ (@ tptp.ord_less_eq_set_val (@ F Y2)) (@ F X))))) (forall ((F (-> tptp.set_val tptp.set_val)) (X tptp.set_val) (Y2 tptp.set_val)) (=> (@ tptp.order_1719375026et_val F) (=> (@ (@ tptp.ord_less_eq_set_val X) Y2) (@ (@ tptp.ord_less_eq_set_val (@ F Y2)) (@ F X))))) (forall ((F (-> tptp.val tptp.val)) (X tptp.val) (Y2 tptp.val)) (=> (@ tptp.order_1689798834al_val F) (=> (@ (@ tptp.ord_less_eq_val X) Y2) (@ (@ tptp.ord_less_eq_val (@ F Y2)) (@ F X))))) (forall ((F (-> tptp.set_val tptp.val)) (X tptp.set_val) (Y2 tptp.set_val)) (=> (@ tptp.order_1375876562al_val F) (=> (@ (@ tptp.ord_less_eq_set_val X) Y2) (@ (@ tptp.ord_less_eq_val (@ F Y2)) (@ F X))))) (forall ((F (-> tptp.val tptp.set_val)) (X tptp.val) (Y2 tptp.val)) (=> (@ tptp.order_1484138386et_val F) (=> (@ (@ tptp.ord_less_eq_val X) Y2) (@ (@ tptp.ord_less_eq_set_val (@ F Y2)) (@ F X))))) (forall ((F (-> tptp.val tptp.set_set_val)) (X tptp.val) (Y2 tptp.val)) (=> (@ tptp.order_1945059954et_val F) (=> (@ (@ tptp.ord_less_eq_val X) Y2) (@ (@ tptp.ord_le1742111550et_val (@ F Y2)) (@ F X))))) (forall ((F (-> tptp.set_set_val tptp.val)) (X tptp.set_set_val) (Y2 tptp.set_set_val)) (=> (@ tptp.order_1520822002al_val F) (=> (@ (@ tptp.ord_le1742111550et_val X) Y2) (@ (@ tptp.ord_less_eq_val (@ F Y2)) (@ F X))))) (forall ((F (-> tptp.set_val tptp.set_set_val)) (X tptp.set_val) (Y2 tptp.set_val)) (=> (@ tptp.order_1957703570et_val F) (=> (@ (@ tptp.ord_less_eq_set_val X) Y2) (@ (@ tptp.ord_le1742111550et_val (@ F Y2)) (@ F X))))) (forall ((F (-> (-> Bool tptp.set_val) tptp.val)) (X (-> Bool tptp.set_val)) (Y2 (-> Bool tptp.set_val))) (=> (@ tptp.order_23236447al_val F) (=> (@ (@ tptp.ord_le994826475et_val X) Y2) (@ (@ tptp.ord_less_eq_val (@ F Y2)) (@ F X))))) (forall ((F (-> tptp.val Bool tptp.set_val)) (X tptp.val) (Y2 tptp.val)) (=> (@ tptp.order_255079095et_val F) (=> (@ (@ tptp.ord_less_eq_val X) Y2) (@ (@ tptp.ord_le994826475et_val (@ F Y2)) (@ F X))))) (forall ((F (-> tptp.set_set_val tptp.set_val)) (X tptp.set_set_val) (Y2 tptp.set_set_val)) (=> (@ tptp.order_650823122et_val F) (=> (@ (@ tptp.ord_le1742111550et_val X) Y2) (@ (@ tptp.ord_less_eq_set_val (@ F Y2)) (@ F X))))) _let_22 _let_21 _let_20 _let_19 _let_18 _let_17 _let_16 _let_15 _let_14 _let_13 (forall ((F (-> tptp.set_val tptp.set_val))) (=> (forall ((X2 tptp.set_val) (Y3 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val X2) Y3) (@ (@ tptp.ord_less_eq_set_val (@ F Y3)) (@ F X2)))) (@ tptp.order_1719375026et_val F))) (forall ((F (-> tptp.val tptp.val))) (=> (forall ((X2 tptp.val) (Y3 tptp.val)) (=> (@ (@ tptp.ord_less_eq_val X2) Y3) (@ (@ tptp.ord_less_eq_val (@ F Y3)) (@ F X2)))) (@ tptp.order_1689798834al_val F))) (forall ((F (-> tptp.set_val tptp.val))) (=> (forall ((X2 tptp.set_val) (Y3 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val X2) Y3) (@ (@ 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tptp.set_val)) (=> (@ (@ tptp.refine1929691018et_val Alpha) Gamma) (@ (@ tptp.ord_less_eq_set_val X) (@ Gamma (@ Alpha X))))) (forall ((Alpha (-> tptp.set_val tptp.set_val)) (Gamma (-> tptp.set_val tptp.set_val)) (X tptp.set_val)) (=> (@ (@ tptp.refine1929691018et_val Alpha) Gamma) (@ (@ tptp.ord_less_eq_set_val (@ Alpha (@ Gamma X))) X))) (forall ((Alpha (-> tptp.set_val Bool tptp.set_val)) (Gamma (-> (-> Bool tptp.set_val) tptp.set_val)) (C tptp.set_val) (A3 (-> Bool tptp.set_val))) (=> (@ (@ tptp.refine51544255et_val Alpha) Gamma) (= (@ (@ tptp.ord_less_eq_set_val C) (@ Gamma A3)) (@ (@ tptp.ord_le994826475et_val (@ Alpha C)) A3)))) (forall ((Alpha (-> tptp.set_val tptp.set_set_val)) (Gamma (-> tptp.set_set_val tptp.set_val)) (C tptp.set_val) (A3 tptp.set_set_val)) (=> (@ (@ tptp.refine1315043946et_val Alpha) Gamma) (= (@ (@ tptp.ord_less_eq_set_val C) (@ Gamma A3)) (@ (@ tptp.ord_le1742111550et_val (@ Alpha C)) A3)))) (forall ((Alpha (-> (-> Bool tptp.set_val) tptp.set_val)) (Gamma (-> tptp.set_val Bool tptp.set_val)) (C (-> Bool tptp.set_val)) (A3 tptp.set_val)) (=> (@ (@ tptp.refine1948536167et_val Alpha) Gamma) (= (@ (@ tptp.ord_le994826475et_val C) (@ Gamma A3)) (@ (@ tptp.ord_less_eq_set_val (@ Alpha C)) A3)))) (forall ((Alpha (-> (-> Bool tptp.set_val) Bool tptp.set_val)) (Gamma (-> (-> Bool tptp.set_val) Bool tptp.set_val)) (C (-> Bool tptp.set_val)) (A3 (-> Bool tptp.set_val))) (=> (@ (@ tptp.refine1924899106et_val Alpha) Gamma) (= (@ (@ tptp.ord_le994826475et_val C) (@ Gamma A3)) (@ (@ tptp.ord_le994826475et_val (@ Alpha C)) A3)))) (forall ((Alpha (-> (-> Bool tptp.set_val) tptp.set_set_val)) (Gamma (-> tptp.set_set_val Bool tptp.set_val)) (C (-> Bool tptp.set_val)) (A3 tptp.set_set_val)) (=> (@ (@ tptp.refine1169396807et_val Alpha) Gamma) (= (@ (@ tptp.ord_le994826475et_val C) (@ Gamma A3)) (@ (@ tptp.ord_le1742111550et_val (@ Alpha C)) A3)))) (forall ((Alpha (-> tptp.set_set_val tptp.set_val)) (Gamma (-> tptp.set_val tptp.set_set_val)) (C tptp.set_set_val) (A3 tptp.set_val)) (=> (@ (@ tptp.refine8163498et_val Alpha) Gamma) (= (@ (@ tptp.ord_le1742111550et_val C) (@ Gamma A3)) (@ (@ tptp.ord_less_eq_set_val (@ Alpha C)) A3)))) (forall ((Alpha (-> tptp.set_set_val Bool tptp.set_val)) (Gamma (-> (-> Bool tptp.set_val) tptp.set_set_val)) (C tptp.set_set_val) (A3 (-> Bool tptp.set_val))) (=> (@ (@ tptp.refine86398879et_val Alpha) Gamma) (= (@ (@ tptp.ord_le1742111550et_val C) (@ Gamma A3)) (@ (@ tptp.ord_le994826475et_val (@ Alpha C)) A3)))) (forall ((Alpha (-> tptp.set_set_val tptp.set_set_val)) (Gamma (-> tptp.set_set_val tptp.set_set_val)) (C tptp.set_set_val) (A3 tptp.set_set_val)) (=> (@ (@ tptp.refine855985034et_val Alpha) Gamma) (= (@ (@ tptp.ord_le1742111550et_val C) (@ Gamma A3)) (@ (@ tptp.ord_le1742111550et_val (@ Alpha C)) A3)))) (forall ((Alpha (-> tptp.set_val tptp.set_val)) (Gamma (-> tptp.set_val tptp.set_val)) (C tptp.set_val) (A3 tptp.set_val)) (=> (@ (@ tptp.refine1929691018et_val Alpha) Gamma) (= (@ (@ tptp.ord_less_eq_set_val C) (@ Gamma A3)) (@ (@ tptp.ord_less_eq_set_val (@ Alpha C)) A3)))) (forall ((Gamma (-> (-> Bool tptp.set_val) tptp.set_val)) (Alpha (-> tptp.set_val Bool tptp.set_val))) (=> (forall ((C3 tptp.set_val) (A5 (-> Bool tptp.set_val))) (= (@ (@ tptp.ord_less_eq_set_val C3) (@ Gamma A5)) (@ (@ tptp.ord_le994826475et_val (@ Alpha C3)) A5))) (@ (@ tptp.refine51544255et_val Alpha) Gamma))) (forall ((Gamma (-> tptp.set_set_val tptp.set_val)) (Alpha (-> tptp.set_val tptp.set_set_val))) (=> (forall ((C3 tptp.set_val) (A5 tptp.set_set_val)) (= (@ (@ tptp.ord_less_eq_set_val C3) (@ Gamma A5)) (@ (@ tptp.ord_le1742111550et_val (@ Alpha C3)) A5))) (@ (@ tptp.refine1315043946et_val Alpha) Gamma))) (forall ((Gamma (-> tptp.set_val Bool tptp.set_val)) (Alpha (-> (-> Bool tptp.set_val) tptp.set_val))) (=> (forall ((C3 (-> Bool tptp.set_val)) (A5 tptp.set_val)) (= (@ (@ tptp.ord_le994826475et_val C3) (@ Gamma A5)) (@ (@ tptp.ord_less_eq_set_val (@ Alpha C3)) A5))) (@ (@ tptp.refine1948536167et_val Alpha) Gamma))) (forall ((Gamma (-> (-> Bool tptp.set_val) Bool tptp.set_val)) (Alpha (-> (-> Bool tptp.set_val) Bool tptp.set_val))) (=> (forall ((C3 (-> Bool tptp.set_val)) (A5 (-> Bool tptp.set_val))) (= (@ (@ tptp.ord_le994826475et_val C3) (@ Gamma A5)) (@ (@ tptp.ord_le994826475et_val (@ Alpha C3)) A5))) (@ (@ tptp.refine1924899106et_val Alpha) Gamma))) (forall ((Gamma (-> tptp.set_set_val Bool tptp.set_val)) (Alpha (-> (-> Bool tptp.set_val) tptp.set_set_val))) (=> (forall ((C3 (-> Bool tptp.set_val)) (A5 tptp.set_set_val)) (= (@ (@ tptp.ord_le994826475et_val C3) (@ Gamma A5)) (@ (@ tptp.ord_le1742111550et_val (@ Alpha C3)) A5))) (@ (@ tptp.refine1169396807et_val Alpha) Gamma))) (forall ((Gamma (-> tptp.set_val tptp.set_set_val)) (Alpha (-> tptp.set_set_val tptp.set_val))) (=> (forall ((C3 tptp.set_set_val) (A5 tptp.set_val)) (= (@ (@ tptp.ord_le1742111550et_val C3) (@ Gamma A5)) (@ (@ tptp.ord_less_eq_set_val (@ Alpha C3)) A5))) (@ (@ tptp.refine8163498et_val Alpha) Gamma))) (forall ((Gamma (-> (-> Bool tptp.set_val) tptp.set_set_val)) (Alpha (-> tptp.set_set_val Bool tptp.set_val))) (=> (forall ((C3 tptp.set_set_val) (A5 (-> Bool tptp.set_val))) (= (@ (@ tptp.ord_le1742111550et_val C3) (@ Gamma A5)) (@ (@ tptp.ord_le994826475et_val (@ Alpha C3)) A5))) (@ (@ tptp.refine86398879et_val Alpha) Gamma))) (forall ((Gamma (-> tptp.set_set_val tptp.set_set_val)) (Alpha (-> tptp.set_set_val tptp.set_set_val))) (=> (forall ((C3 tptp.set_set_val) (A5 tptp.set_set_val)) (= (@ (@ tptp.ord_le1742111550et_val C3) (@ Gamma A5)) (@ (@ tptp.ord_le1742111550et_val (@ Alpha C3)) A5))) (@ (@ tptp.refine855985034et_val Alpha) Gamma))) (forall ((Gamma (-> tptp.set_val tptp.set_val)) (Alpha (-> tptp.set_val tptp.set_val))) (=> (forall ((C3 tptp.set_val) (A5 tptp.set_val)) (= (@ (@ tptp.ord_less_eq_set_val C3) (@ Gamma A5)) (@ (@ tptp.ord_less_eq_set_val (@ Alpha C3)) A5))) (@ (@ tptp.refine1929691018et_val Alpha) Gamma))) _let_12 _let_11 _let_10 _let_9 _let_8 _let_7 _let_6 _let_5 _let_4 _let_3 (forall ((Le2 (-> tptp.set_val tptp.set_val Bool)) (X tptp.set_val)) (=> (@ tptp.refine275900453et_val Le2) (@ (@ Le2 X) X))) (forall ((Le2 (-> tptp.set_val tptp.set_val Bool))) (=> (forall ((X2 tptp.set_val)) (@ (@ Le2 X2) X2)) (@ tptp.refine275900453et_val Le2))) (forall ((Le2 (-> tptp.set_val tptp.set_val Bool)) (T2 tptp.set_val) (T3 tptp.set_val) (E tptp.set_val) (E2 tptp.set_val) (B3 Bool)) (let ((_let_1 (@ tptp.if_set_val B3))) (=> (@ tptp.refine275900453et_val Le2) (=> (@ (@ Le2 T2) T3) (=> (@ (@ Le2 E) E2) (@ (@ Le2 (@ (@ _let_1 T2) E)) (@ (@ _let_1 T3) E2))))))) (forall ((Alpha (-> tptp.set_val tptp.set_val)) (Gamma (-> tptp.set_val tptp.set_val))) (=> (@ (@ tptp.refine1929691018et_val Alpha) Gamma) (@ tptp.refine2057434761et_val Alpha))) (forall ((F (-> tptp.val tptp.set_val)) (X tptp.val) (Y2 tptp.val)) (=> (@ tptp.order_99134233et_val F) (= (@ (@ tptp.ord_less_eq_set_val (@ F X)) (@ F Y2)) (@ (@ tptp.ord_less_eq_val X) Y2)))) (forall ((F (-> tptp.val Bool tptp.set_val)) (X tptp.val) (Y2 tptp.val)) (=> (@ tptp.order_1205732848et_val F) (= (@ (@ tptp.ord_le994826475et_val (@ F X)) (@ F Y2)) (@ (@ tptp.ord_less_eq_val X) Y2)))) (forall ((F (-> tptp.val tptp.val)) (X tptp.val) (Y2 tptp.val)) (=> (@ tptp.order_1139042361al_val F) (= (@ (@ tptp.ord_less_eq_val (@ F X)) (@ F Y2)) (@ (@ tptp.ord_less_eq_val X) Y2)))) (forall ((F (-> tptp.val tptp.set_set_val)) (X tptp.val) (Y2 tptp.val)) (=> (@ tptp.order_68692473et_val F) (= (@ (@ tptp.ord_le1742111550et_val (@ F X)) (@ F Y2)) (@ (@ tptp.ord_less_eq_val X) Y2)))) (forall ((X tptp.val) (Y2 tptp.val)) (= (@ (@ tptp.ord_less_eq_set_val (@ tptp.set_or1288365508an_val X)) (@ tptp.set_or1288365508an_val Y2)) (@ (@ tptp.ord_less_eq_val Y2) X))) (forall ((D (-> Bool tptp.set_val)) (C (-> Bool tptp.set_val)) (A3 (-> Bool tptp.set_val))) (=> (@ (@ tptp.refine1593386065et_val D) C) (=> (@ (@ tptp.ord_le994826475et_val C) A3) (=> (@ (@ tptp.refine511606705et_val C) D) (@ (@ tptp.ord_le994826475et_val D) A3))))) (forall ((D tptp.val) (C tptp.val) (A3 tptp.val)) (=> (@ (@ tptp.refine2021912633al_val D) C) (=> (@ (@ tptp.ord_less_eq_val C) A3) (=> (@ (@ tptp.refine403244856MP_val C) D) (@ (@ tptp.ord_less_eq_val D) A3))))) (forall ((D tptp.set_set_val) (C tptp.set_set_val) (A3 tptp.set_set_val)) (=> (@ (@ tptp.refine1034950713et_val D) C) (=> (@ (@ tptp.ord_le1742111550et_val C) A3) (=> (@ (@ tptp.refine1908789496et_val C) D) (@ (@ tptp.ord_le1742111550et_val D) A3))))) (forall ((D tptp.set_val) (C tptp.set_val) (A3 tptp.set_val)) (=> (@ (@ tptp.refine654574649et_val D) C) (=> (@ (@ tptp.ord_less_eq_set_val C) A3) (=> (@ (@ tptp.refine1893322264et_val C) D) (@ (@ tptp.ord_less_eq_set_val D) A3))))) (forall ((X tptp.val) (Y2 tptp.val)) (= (@ (@ tptp.ord_less_eq_set_val (@ tptp.set_ord_lessThan_val X)) (@ tptp.set_ord_lessThan_val Y2)) (@ (@ tptp.ord_less_eq_val X) Y2))) (forall ((X tptp.set_set_val) (Y2 tptp.set_set_val)) (= (@ (@ tptp.ord_le1135847966et_val (@ tptp.set_or1337784553et_val X)) (@ tptp.set_or1337784553et_val Y2)) (@ (@ tptp.ord_le1742111550et_val Y2) X))) (forall ((X tptp.set_val) (Y2 tptp.set_val)) (= (@ (@ tptp.ord_le1742111550et_val (@ tptp.set_or650197513et_val X)) (@ tptp.set_or650197513et_val Y2)) (@ (@ tptp.ord_less_eq_set_val Y2) X))) (forall ((X tptp.val) (Y2 tptp.val)) (= (@ (@ tptp.ord_less_eq_set_val (@ tptp.set_ord_atLeast_val X)) (@ tptp.set_ord_atLeast_val Y2)) (@ (@ tptp.ord_less_eq_val Y2) X))) (forall ((I tptp.val) (K tptp.val)) (= (@ (@ tptp.member_val I) (@ tptp.set_ord_atLeast_val K)) (@ (@ tptp.ord_less_eq_val K) I))) (forall ((I tptp.set_val) (K tptp.set_val)) (= (@ (@ tptp.member_set_val I) (@ tptp.set_or650197513et_val K)) (@ (@ tptp.ord_less_eq_set_val K) I))) (forall ((A3 tptp.val)) (@ (@ tptp.ord_less_eq_set_val (@ tptp.set_or1288365508an_val A3)) (@ tptp.set_ord_atLeast_val A3))) (forall ((A3 tptp.val) (B3 tptp.val)) (= (@ (@ tptp.ord_less_eq_set_val (@ tptp.set_ord_atLeast_val A3)) (@ tptp.set_or1288365508an_val B3)) (@ (@ tptp.ord_less_val B3) A3))) (forall ((L tptp.set_val) (H tptp.set_val) (L2 tptp.set_val)) (= (@ (@ tptp.ord_le1742111550et_val (@ (@ tptp.set_or1554624499et_val L) H)) (@ tptp.set_or650197513et_val L2)) (or (not (@ (@ tptp.ord_less_eq_set_val L) H)) (@ (@ tptp.ord_less_eq_set_val L2) L)))) (forall ((L tptp.val) (H tptp.val) (L2 tptp.val)) (= (@ (@ tptp.ord_less_eq_set_val (@ (@ tptp.set_or18208019st_val L) H)) (@ tptp.set_ord_atLeast_val L2)) (or (not (@ (@ tptp.ord_less_eq_val L) H)) (@ (@ tptp.ord_less_eq_val L2) L)))) (forall ((X tptp.set_val) (Y2 tptp.set_val)) (= (@ (@ tptp.ord_le1742111550et_val (@ tptp.set_or867701765et_val X)) (@ tptp.set_or867701765et_val Y2)) (@ (@ tptp.ord_less_eq_set_val X) Y2))) (forall ((X tptp.val) (Y2 tptp.val)) (= (@ (@ tptp.ord_less_eq_set_val (@ tptp.set_ord_atMost_val X)) (@ tptp.set_ord_atMost_val Y2)) (@ (@ tptp.ord_less_eq_val X) Y2))) (forall ((A tptp.set_val) (B tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_set_val A) B)))) (forall ((C tptp.val) (A tptp.set_val)) (let ((_let_1 (@ tptp.member_val C))) (=> (not (@ _let_1 A)) (@ _let_1 (@ tptp.uminus1961393973et_val A))))) (forall ((C tptp.val) (A tptp.set_val)) (let ((_let_1 (@ tptp.member_val C))) (= (@ _let_1 (@ tptp.uminus1961393973et_val A)) (not (@ _let_1 A))))) (forall ((I tptp.val) (L tptp.val) (U tptp.val)) (= (@ (@ tptp.member_val I) (@ (@ tptp.set_or18208019st_val L) U)) (and (@ (@ tptp.ord_less_eq_val L) I) (@ (@ tptp.ord_less_eq_val I) U)))) (forall ((I tptp.set_val) (L tptp.set_val) (U tptp.set_val)) (= (@ (@ tptp.member_set_val I) (@ (@ tptp.set_or1554624499et_val L) U)) (and (@ (@ tptp.ord_less_eq_set_val L) I) (@ (@ tptp.ord_less_eq_set_val I) U)))) (forall ((L tptp.set_val) (H tptp.set_val) (L2 tptp.set_val) (H2 tptp.set_val)) (= (= (@ (@ tptp.set_or1554624499et_val L) H) (@ (@ tptp.set_or1554624499et_val L2) H2)) (or (and (= L L2) (= H H2)) (and (not (@ (@ tptp.ord_less_eq_set_val L) H)) (not (@ (@ tptp.ord_less_eq_set_val L2) H2)))))) (forall ((I tptp.val) (K tptp.val)) (= (@ (@ tptp.member_val I) (@ tptp.set_ord_atMost_val K)) (@ (@ tptp.ord_less_eq_val I) K))) (forall ((I tptp.set_val) (K tptp.set_val)) (= (@ (@ tptp.member_set_val I) (@ tptp.set_or867701765et_val K)) (@ (@ tptp.ord_less_eq_set_val I) K))) (forall ((I tptp.val) (K tptp.val)) (= (@ (@ tptp.member_val I) (@ tptp.set_ord_lessThan_val K)) (@ (@ tptp.ord_less_val I) K))) (forall ((A tptp.set_val) (B tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val A) B) (@ (@ tptp.ord_less_eq_set_val (@ tptp.uminus1961393973et_val B)) (@ tptp.uminus1961393973et_val A)))) (forall ((A tptp.set_val) (B tptp.set_val)) (= (@ (@ tptp.ord_less_eq_set_val (@ tptp.uminus1961393973et_val A)) (@ tptp.uminus1961393973et_val B)) (@ (@ tptp.ord_less_eq_set_val B) A))) (forall ((I tptp.val) (K tptp.val)) (= (@ (@ tptp.member_val I) (@ tptp.set_or1288365508an_val K)) (@ (@ tptp.ord_less_val K) I))) (forall ((A3 tptp.set_val) (B3 tptp.set_val) (C tptp.set_val) (D tptp.set_val)) (= (@ (@ tptp.ord_le1742111550et_val (@ (@ tptp.set_or1554624499et_val A3) B3)) (@ (@ tptp.set_or1554624499et_val C) D)) (or (not (@ (@ tptp.ord_less_eq_set_val A3) B3)) (and (@ (@ tptp.ord_less_eq_set_val C) A3) (@ (@ tptp.ord_less_eq_set_val B3) D))))) (forall ((A3 tptp.val) (B3 tptp.val) (C tptp.val) (D tptp.val)) (= (@ (@ tptp.ord_less_eq_set_val (@ (@ tptp.set_or18208019st_val A3) B3)) (@ (@ tptp.set_or18208019st_val C) D)) (or (not (@ (@ tptp.ord_less_eq_val A3) B3)) (and (@ (@ tptp.ord_less_eq_val C) A3) (@ (@ tptp.ord_less_eq_val B3) D))))) (forall ((L tptp.set_val) (H tptp.set_val) (H2 tptp.set_val)) (= (@ (@ tptp.ord_le1742111550et_val (@ (@ tptp.set_or1554624499et_val L) H)) (@ tptp.set_or867701765et_val H2)) (or (not (@ (@ tptp.ord_less_eq_set_val L) H)) (@ (@ tptp.ord_less_eq_set_val H) H2)))) (forall ((L tptp.val) (H tptp.val) (H2 tptp.val)) (= (@ (@ tptp.ord_less_eq_set_val (@ (@ tptp.set_or18208019st_val L) H)) (@ tptp.set_ord_atMost_val H2)) (or (not (@ (@ tptp.ord_less_eq_val L) H)) (@ (@ tptp.ord_less_eq_val H) H2)))) (forall ((A3 tptp.set_val) (B3 tptp.set_val) (C tptp.set_val) (D tptp.set_val)) (let ((_let_1 (@ tptp.ord_less_eq_set_val C))) (= (@ (@ tptp.ord_less_set_set_val (@ (@ tptp.set_or1554624499et_val A3) B3)) (@ (@ tptp.set_or1554624499et_val C) D)) (and (or (not (@ (@ tptp.ord_less_eq_set_val A3) B3)) (and (@ _let_1 A3) (@ (@ tptp.ord_less_eq_set_val B3) D) (or (@ (@ tptp.ord_less_set_val C) A3) (@ (@ tptp.ord_less_set_val B3) D)))) (@ _let_1 D))))) (forall ((C tptp.val) (A tptp.set_val)) (let ((_let_1 (@ tptp.member_val C))) (=> (@ _let_1 (@ tptp.uminus1961393973et_val A)) (not (@ _let_1 A))))) (forall ((A3 tptp.val) (B3 tptp.val)) (= (@ (@ tptp.ord_less_eq_set_val (@ tptp.set_ord_atMost_val A3)) (@ tptp.set_ord_lessThan_val B3)) (@ (@ tptp.ord_less_val A3) B3))) (forall ((Y2 tptp.set_val) (X tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val Y2) X) (not (@ (@ tptp.ord_less_set_val X) Y2)))) (= tptp.ord_less_eq_set_val (lambda ((X3 tptp.set_val) (Y4 tptp.set_val)) (or (@ (@ tptp.ord_less_set_val X3) Y4) (= X3 Y4)))) _let_2 (forall ((A3 tptp.set_val) (B3 tptp.set_val) (F (-> tptp.set_val tptp.set_val)) (C tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val A3) B3) (=> (@ (@ tptp.ord_less_set_val (@ F B3)) C) (=> (forall ((X2 tptp.set_val) (Y3 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val X2) Y3) (@ (@ tptp.ord_less_eq_set_val (@ F X2)) (@ F Y3)))) (@ (@ tptp.ord_less_set_val (@ F A3)) C))))) (forall ((A3 tptp.set_val) (F (-> tptp.set_val tptp.set_val)) (B3 tptp.set_val) (C tptp.set_val)) (let ((_let_1 (@ tptp.ord_less_set_val A3))) (=> (@ _let_1 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_set_val B3) C) (=> (forall ((X2 tptp.set_val) (Y3 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val X2) Y3) (@ (@ tptp.ord_less_eq_set_val (@ F X2)) (@ F Y3)))) (@ _let_1 (@ F C))))))) (forall ((A3 tptp.set_val) (B3 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val A3) B3) (=> (not (= A3 B3)) (@ (@ tptp.ord_less_set_val A3) B3)))) (forall ((X tptp.set_val) (Y2 tptp.set_val)) (=> (not (@ (@ tptp.ord_less_set_val X) Y2)) (= (@ (@ tptp.ord_less_eq_set_val X) Y2) (= X Y2)))) (forall ((X tptp.set_val) (Y2 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val X) Y2) (= (not (@ (@ tptp.ord_less_set_val X) Y2)) (= X Y2)))) (forall ((X tptp.set_val) (Y2 tptp.set_val)) (=> (@ (@ tptp.ord_less_set_val X) Y2) (@ (@ tptp.ord_less_eq_set_val X) Y2))) (forall ((X tptp.set_val) (Y2 tptp.set_val) (Z2 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val X) Y2) (=> (@ (@ tptp.ord_less_set_val Y2) Z2) (@ (@ tptp.ord_less_set_val X) Z2)))) (forall ((X tptp.set_val) (Y2 tptp.set_val) (Z2 tptp.set_val)) (let ((_let_1 (@ tptp.ord_less_set_val X))) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_eq_set_val Y2) Z2) (@ _let_1 Z2))))) (forall ((X tptp.set_val) (Y2 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val X) Y2) (or (@ (@ tptp.ord_less_set_val X) Y2) (= X Y2)))) (= tptp.ord_less_set_val (lambda ((X3 tptp.set_val) (Y4 tptp.set_val)) (and (@ (@ tptp.ord_less_eq_set_val X3) Y4) (not (@ (@ tptp.ord_less_eq_set_val Y4) X3))))) (forall ((A3 tptp.set_val) (B3 tptp.set_val) (C tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val A3) B3) (=> (@ (@ tptp.ord_less_set_val B3) C) (@ (@ tptp.ord_less_set_val A3) C)))) (forall ((A3 tptp.set_val) (B3 tptp.set_val) (C tptp.set_val)) (let ((_let_1 (@ tptp.ord_less_set_val A3))) (=> (@ _let_1 B3) (=> (@ (@ tptp.ord_less_eq_set_val B3) C) (@ _let_1 C))))) (= tptp.ord_less_eq_set_val (lambda ((A4 tptp.set_val) (B4 tptp.set_val)) (or (@ (@ tptp.ord_less_set_val A4) B4) (= A4 B4)))) (= tptp.ord_less_set_val (lambda ((A4 tptp.set_val) (B4 tptp.set_val)) (and (@ (@ tptp.ord_less_eq_set_val A4) B4) (not (= A4 B4))))) (forall ((B3 tptp.set_val) (A3 tptp.set_val) (C tptp.set_val)) (let ((_let_1 (@ tptp.ord_less_set_val C))) (=> (@ (@ tptp.ord_less_eq_set_val B3) A3) (=> (@ _let_1 B3) (@ _let_1 A3))))) (forall ((B3 tptp.set_val) (A3 tptp.set_val) (C tptp.set_val)) (=> (@ (@ tptp.ord_less_set_val B3) A3) (=> (@ (@ tptp.ord_less_eq_set_val C) B3) (@ (@ tptp.ord_less_set_val C) A3)))) (forall ((A3 tptp.set_val) (B3 tptp.set_val)) (=> (@ (@ tptp.ord_less_set_val A3) B3) (@ (@ tptp.ord_less_eq_set_val A3) B3))) (= tptp.ord_less_eq_set_val (lambda ((B4 tptp.set_val) (A4 tptp.set_val)) (or (@ (@ tptp.ord_less_set_val B4) A4) (= A4 B4)))) (= tptp.ord_less_set_val (lambda ((B4 tptp.set_val) (A4 tptp.set_val)) (and (@ (@ tptp.ord_less_eq_set_val B4) A4) (not (= A4 B4))))) (forall ((B3 tptp.set_val) (A3 tptp.set_val)) (=> (@ (@ tptp.ord_less_set_val B3) A3) (@ (@ tptp.ord_less_eq_set_val B3) A3))) (forall ((A3 tptp.set_val) (B3 tptp.set_val)) (=> (not (= A3 B3)) (=> (@ (@ tptp.ord_less_eq_set_val A3) B3) (@ (@ tptp.ord_less_set_val A3) B3)))) (forall ((A tptp.set_val) (B tptp.set_val)) (=> (@ (@ tptp.ord_less_set_val A) B) (not (=> (@ (@ tptp.ord_less_eq_set_val A) B) (@ (@ tptp.ord_less_eq_set_val B) A))))) (= tptp.ord_less_set_val (lambda ((A2 tptp.set_val) (B2 tptp.set_val)) (and (@ (@ tptp.ord_less_eq_set_val A2) B2) (not (= A2 B2))))) (forall ((A tptp.set_val) (B tptp.set_val)) (=> (@ (@ tptp.ord_less_set_val A) B) (@ (@ tptp.ord_less_eq_set_val A) B))) (forall ((A tptp.set_val) (B tptp.set_val) (C2 tptp.set_val)) (let ((_let_1 (@ tptp.ord_less_set_val A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_set_val B) C2) (@ _let_1 C2))))) (= tptp.ord_less_set_val (lambda ((A2 tptp.set_val) (B2 tptp.set_val)) (and (@ (@ tptp.ord_less_eq_set_val A2) B2) (not (@ (@ tptp.ord_less_eq_set_val B2) A2))))) (forall ((A tptp.set_val) (B tptp.set_val) (C2 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val A) B) (=> (@ (@ tptp.ord_less_set_val B) C2) (@ (@ tptp.ord_less_set_val A) C2)))) (= tptp.ord_less_eq_set_val (lambda ((A2 tptp.set_val) (B2 tptp.set_val)) (or (@ (@ tptp.ord_less_set_val A2) B2) (= A2 B2)))) (forall ((X tptp.set_val) (Y2 tptp.set_val)) (= (@ (@ tptp.ord_less_eq_set_val (@ tptp.uminus1961393973et_val X)) (@ tptp.uminus1961393973et_val Y2)) (@ (@ tptp.ord_less_eq_set_val Y2) X))) (forall ((X tptp.set_val) (Y2 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val X) Y2) (@ (@ tptp.ord_less_eq_set_val (@ tptp.uminus1961393973et_val Y2)) (@ tptp.uminus1961393973et_val X)))) (forall ((Y2 tptp.set_val) (X tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val Y2) (@ tptp.uminus1961393973et_val X)) (@ (@ tptp.ord_less_eq_set_val X) (@ tptp.uminus1961393973et_val Y2)))) (forall ((Y2 tptp.set_val) (X tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val (@ tptp.uminus1961393973et_val Y2)) X) (@ (@ tptp.ord_less_eq_set_val (@ tptp.uminus1961393973et_val X)) Y2))) (forall ((A tptp.set_val) (B tptp.set_val) (C tptp.val)) (let ((_let_1 (@ tptp.member_val C))) (=> (@ (@ tptp.ord_less_set_val A) B) (=> (@ _let_1 A) (@ _let_1 B))))) (forall ((C tptp.val) (B tptp.set_val) (A tptp.set_val)) (let ((_let_1 (@ tptp.member_val C))) (=> (=> (not (@ _let_1 B)) (@ _let_1 A)) (@ _let_1 (@ (@ tptp.sup_sup_set_val A) B))))) (forall ((C tptp.val) (A tptp.set_val) (B tptp.set_val)) (let ((_let_1 (@ tptp.member_val C))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_val A) B)) (or (@ _let_1 A) (@ _let_1 B))))) (forall ((X tptp.set_val) (Y2 tptp.set_val) (Z2 tptp.set_val)) (= (@ (@ tptp.ord_less_eq_set_val (@ (@ tptp.sup_sup_set_val X) Y2)) Z2) (and (@ (@ tptp.ord_less_eq_set_val X) Z2) (@ (@ tptp.ord_less_eq_set_val Y2) Z2)))) (forall ((B3 tptp.set_val) (C tptp.set_val) (A3 tptp.set_val)) (= (@ (@ tptp.ord_less_eq_set_val (@ (@ tptp.sup_sup_set_val B3) C)) A3) (and (@ (@ tptp.ord_less_eq_set_val B3) A3) (@ (@ tptp.ord_less_eq_set_val C) A3)))) (forall ((A tptp.set_val) (B tptp.set_val) (C2 tptp.set_val)) (= (@ (@ tptp.ord_less_eq_set_val (@ (@ tptp.sup_sup_set_val A) B)) C2) (and (@ (@ tptp.ord_less_eq_set_val A) C2) (@ (@ tptp.ord_less_eq_set_val B) C2)))) (forall ((I tptp.val) (L tptp.val) (U tptp.val)) (= (@ (@ tptp.member_val I) (@ (@ tptp.set_or2126567818an_val L) U)) (and (@ (@ tptp.ord_less_val L) I) (@ (@ tptp.ord_less_val I) U)))) (forall ((C tptp.set_val) (B3 tptp.set_val) (A3 tptp.set_val)) (let ((_let_1 (@ tptp.ord_less_eq_set_val C))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.sup_sup_set_val A3) B3))))) (forall ((C tptp.set_val) (A3 tptp.set_val) (B3 tptp.set_val)) (let ((_let_1 (@ tptp.ord_less_eq_set_val C))) (=> (@ _let_1 A3) (@ _let_1 (@ (@ tptp.sup_sup_set_val A3) B3))))) (= tptp.ord_less_eq_set_val (lambda ((A4 tptp.set_val) (B4 tptp.set_val)) (= (@ (@ tptp.sup_sup_set_val A4) B4) B4))) (= tptp.ord_less_eq_set_val (lambda ((B4 tptp.set_val) (A4 tptp.set_val)) (= (@ (@ tptp.sup_sup_set_val A4) B4) A4))) (forall ((B3 tptp.set_val) (A3 tptp.set_val)) (@ (@ tptp.ord_less_eq_set_val B3) (@ (@ tptp.sup_sup_set_val A3) B3))) (forall ((A3 tptp.set_val) (B3 tptp.set_val)) (@ (@ tptp.ord_less_eq_set_val A3) (@ (@ tptp.sup_sup_set_val A3) B3))) (= tptp.ord_less_eq_set_val (lambda ((B4 tptp.set_val) (A4 tptp.set_val)) (= A4 (@ (@ tptp.sup_sup_set_val A4) B4)))) (forall ((B3 tptp.set_val) (A3 tptp.set_val) (C tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val B3) A3) (=> (@ (@ tptp.ord_less_eq_set_val C) A3) (@ (@ tptp.ord_less_eq_set_val (@ (@ tptp.sup_sup_set_val B3) C)) A3)))) (forall ((B3 tptp.set_val) (C tptp.set_val) (A3 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val (@ (@ tptp.sup_sup_set_val B3) C)) A3) (not (=> (@ (@ tptp.ord_less_eq_set_val B3) A3) (not (@ (@ tptp.ord_less_eq_set_val C) A3)))))) (forall ((X tptp.set_val) (Y2 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val X) Y2) (= (@ (@ tptp.sup_sup_set_val X) Y2) Y2))) (forall ((Y2 tptp.set_val) (X tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val Y2) X) (= (@ (@ tptp.sup_sup_set_val X) Y2) X))) (forall ((A3 tptp.set_val) (B3 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val A3) B3) (= (@ (@ tptp.sup_sup_set_val A3) B3) B3))) (forall ((B3 tptp.set_val) (A3 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val B3) A3) (= (@ (@ tptp.sup_sup_set_val A3) B3) A3))) (forall ((F (-> tptp.set_val tptp.set_val tptp.set_val)) (X tptp.set_val) (Y2 tptp.set_val)) (=> (forall ((X2 tptp.set_val) (Y3 tptp.set_val)) (@ (@ tptp.ord_less_eq_set_val X2) (@ (@ F X2) Y3))) (=> (forall ((X2 tptp.set_val) (Y3 tptp.set_val)) (@ (@ tptp.ord_less_eq_set_val Y3) (@ (@ F X2) Y3))) (=> (forall ((X2 tptp.set_val) (Y3 tptp.set_val) (Z3 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val Y3) X2) (=> (@ (@ tptp.ord_less_eq_set_val Z3) X2) (@ (@ tptp.ord_less_eq_set_val (@ (@ F Y3) Z3)) X2)))) (= (@ (@ tptp.sup_sup_set_val X) Y2) (@ (@ F X) Y2)))))) (forall ((A3 tptp.set_val) (B3 tptp.set_val)) (=> (= A3 (@ (@ tptp.sup_sup_set_val A3) B3)) (@ (@ tptp.ord_less_eq_set_val B3) A3))) (forall ((X tptp.val) (Y2 tptp.val)) (= (@ (@ (@ tptp.if_val false) X) Y2) Y2)) (forall ((X tptp.val) (Y2 tptp.val)) (= (@ (@ (@ tptp.if_val true) X) Y2) X)) (forall ((X tptp.set_val) (Y2 tptp.set_val)) (= (@ (@ (@ tptp.if_set_val false) X) Y2) Y2)) (forall ((X tptp.set_val) (Y2 tptp.set_val)) (= (@ (@ (@ tptp.if_set_val true) X) Y2) X)) (forall ((X (-> Bool tptp.set_val)) (Y2 (-> Bool tptp.set_val))) (= (@ (@ (@ tptp.if_o_set_val false) X) Y2) Y2)) (forall ((X (-> Bool tptp.set_val)) (Y2 (-> Bool tptp.set_val))) (= (@ (@ (@ tptp.if_o_set_val true) X) Y2) X)) (forall ((P Bool)) (or (= P true) (= P false))) (forall ((X tptp.set_set_val) (Y2 tptp.set_set_val)) (= (@ (@ (@ tptp.if_set_set_val false) X) Y2) Y2)) (forall ((X tptp.set_set_val) (Y2 tptp.set_set_val)) (= (@ (@ (@ tptp.if_set_set_val true) X) Y2) X)) _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.83/1.06 )
% 0.83/1.06 % SZS output end Proof for ITP079^1
% 0.83/1.06 % cvc5---1.0.5 exiting
% 0.83/1.06 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------