TSTP Solution File: ITP093^1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP093^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n016.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 03:18:11 EDT 2023
% Result : Timeout 299.81s 300.23s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.17 % Problem : ITP093^1 : TPTP v8.1.2. Released v7.5.0.
% 0.12/0.18 % Command : do_cvc5 %s %d
% 0.19/0.39 % Computer : n016.cluster.edu
% 0.19/0.39 % Model : x86_64 x86_64
% 0.19/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.39 % Memory : 8042.1875MB
% 0.19/0.39 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.39 % CPULimit : 300
% 0.19/0.39 % WCLimit : 300
% 0.19/0.39 % DateTime : Sun Aug 27 13:57:43 EDT 2023
% 0.19/0.40 % CPUTime :
% 0.26/0.58 %----Proving TH0
% 0.26/0.58 %------------------------------------------------------------------------------
% 0.26/0.58 % File : ITP093^1 : TPTP v8.1.2. Released v7.5.0.
% 0.26/0.58 % Domain : Interactive Theorem Proving
% 0.26/0.58 % Problem : Sledgehammer Kuratowski problem prob_43__5514550_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 : Kuratowski/prob_43__5514550_1 [Des21]
% 0.26/0.58
% 0.26/0.58 % Status : Theorem
% 0.26/0.58 % Rating : 0.31 v8.1.0, 0.36 v7.5.0
% 0.26/0.58 % Syntax : Number of formulae : 493 ( 113 unt; 138 typ; 0 def)
% 0.26/0.58 % Number of atoms : 1236 ( 234 equ; 0 cnn)
% 0.26/0.58 % Maximal formula atoms : 12 ( 3 avg)
% 0.26/0.58 % Number of connectives : 3205 ( 91 ~; 31 |; 122 &;2361 @)
% 0.26/0.58 % ( 0 <=>; 600 =>; 0 <=; 0 <~>)
% 0.26/0.58 % Maximal formula depth : 16 ( 7 avg)
% 0.26/0.58 % Number of types : 32 ( 31 usr)
% 0.26/0.58 % Number of type conns : 337 ( 337 >; 0 *; 0 +; 0 <<)
% 0.26/0.58 % Number of symbols : 108 ( 107 usr; 6 con; 0-3 aty)
% 0.26/0.58 % Number of variables : 1153 ( 214 ^; 904 !; 35 ?;1153 :)
% 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 15:44:24.363
% 0.26/0.58 %------------------------------------------------------------------------------
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% 0.26/0.58 = ( ^ [G: pair_p1593840546t_unit] :
% 0.26/0.58 ( ( finite1664988688od_a_a @ ( pair_p1652294923t_unit @ G ) )
% 0.26/0.58 & ( finite256329232od_a_a @ ( pair_p1559300324t_unit @ G ) ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % pair_fin_digraph_axioms_def
% 0.26/0.58 thf(fact_4_pair__fin__digraph__axioms__def,axiom,
% 0.26/0.58 ( pair_p504738056od_a_a
% 0.26/0.58 = ( ^ [G: pair_p1765063010t_unit] :
% 0.26/0.58 ( ( finite179568208od_a_a @ ( pair_p447552203t_unit @ G ) )
% 0.26/0.58 & ( finite1664988688od_a_a @ ( pair_p1783210148t_unit @ G ) ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % pair_fin_digraph_axioms_def
% 0.26/0.58 thf(fact_5_pair__fin__digraph__axioms__def,axiom,
% 0.26/0.58 ( pair_p1027063983ms_nat
% 0.26/0.58 = ( ^ [G: pair_p1914262621t_unit] :
% 0.26/0.58 ( ( finite_finite_nat @ ( pair_p1677060310t_unit @ G ) )
% 0.26/0.58 & ( finite772653738at_nat @ ( pair_p715279805t_unit @ G ) ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % pair_fin_digraph_axioms_def
% 0.26/0.58 thf(fact_6_pair__fin__digraph__axioms__def,axiom,
% 0.26/0.58 ( pair_p1864019935ioms_a
% 0.26/0.58 = ( ^ [G: pair_p125712459t_unit] :
% 0.26/0.58 ( ( finite_finite_a @ ( pair_p1047056820t_unit @ G ) )
% 0.26/0.58 & ( finite179568208od_a_a @ ( pair_p133601421t_unit @ G ) ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % pair_fin_digraph_axioms_def
% 0.26/0.58 thf(fact_7_pair__fin__digraph__axioms_Ointro,axiom,
% 0.26/0.58 ! [G2: pair_p2041852168t_unit] :
% 0.26/0.58 ( ( finite772653738at_nat @ ( pair_p210955889t_unit @ G2 ) )
% 0.26/0.58 => ( ( finite48957584at_nat @ ( pair_p806300874t_unit @ G2 ) )
% 0.26/0.58 => ( pair_p56914274at_nat @ G2 ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % pair_fin_digraph_axioms.intro
% 0.26/0.58 thf(fact_8_pair__fin__digraph__axioms_Ointro,axiom,
% 0.26/0.58 ! [G2: pair_p1593840546t_unit] :
% 0.26/0.58 ( ( finite1664988688od_a_a @ ( pair_p1652294923t_unit @ G2 ) )
% 0.26/0.58 => ( ( finite256329232od_a_a @ ( pair_p1559300324t_unit @ G2 ) )
% 0.26/0.58 => ( pair_p1906342088od_a_a @ G2 ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % pair_fin_digraph_axioms.intro
% 0.26/0.58 thf(fact_9_pair__fin__digraph__axioms_Ointro,axiom,
% 0.26/0.58 ! [G2: pair_p1765063010t_unit] :
% 0.26/0.58 ( ( finite179568208od_a_a @ ( pair_p447552203t_unit @ G2 ) )
% 0.26/0.58 => ( ( finite1664988688od_a_a @ ( pair_p1783210148t_unit @ G2 ) )
% 0.26/0.58 => ( pair_p504738056od_a_a @ G2 ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % pair_fin_digraph_axioms.intro
% 0.26/0.58 thf(fact_10_pair__fin__digraph__axioms_Ointro,axiom,
% 0.26/0.58 ! [G2: pair_p1914262621t_unit] :
% 0.26/0.58 ( ( finite_finite_nat @ ( pair_p1677060310t_unit @ G2 ) )
% 0.26/0.58 => ( ( finite772653738at_nat @ ( pair_p715279805t_unit @ G2 ) )
% 0.26/0.58 => ( pair_p1027063983ms_nat @ G2 ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % pair_fin_digraph_axioms.intro
% 0.26/0.58 thf(fact_11_pair__fin__digraph__axioms_Ointro,axiom,
% 0.26/0.58 ! [G2: pair_p125712459t_unit] :
% 0.26/0.58 ( ( finite_finite_a @ ( pair_p1047056820t_unit @ G2 ) )
% 0.26/0.58 => ( ( finite179568208od_a_a @ ( pair_p133601421t_unit @ G2 ) )
% 0.26/0.58 => ( pair_p1864019935ioms_a @ G2 ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % pair_fin_digraph_axioms.intro
% 0.26/0.58 thf(fact_12_pair__fin__digraph_Opair__finite__arcs,axiom,
% 0.26/0.58 ! [G2: pair_p1914262621t_unit] :
% 0.26/0.58 ( ( pair_p128415500ph_nat @ G2 )
% 0.26/0.58 => ( finite772653738at_nat @ ( pair_p715279805t_unit @ G2 ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % pair_fin_digraph.pair_finite_arcs
% 0.26/0.58 thf(fact_13_pair__fin__digraph_Opair__finite__arcs,axiom,
% 0.26/0.58 ! [G2: pair_p1765063010t_unit] :
% 0.26/0.58 ( ( pair_p374947051od_a_a @ G2 )
% 0.26/0.58 => ( finite1664988688od_a_a @ ( pair_p1783210148t_unit @ G2 ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % pair_fin_digraph.pair_finite_arcs
% 0.26/0.58 thf(fact_14_pair__fin__digraph_Opair__finite__arcs,axiom,
% 0.26/0.58 ! [G2: pair_p125712459t_unit] :
% 0.26/0.58 ( ( pair_p1802376898raph_a @ G2 )
% 0.26/0.58 => ( finite179568208od_a_a @ ( pair_p133601421t_unit @ G2 ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % pair_fin_digraph.pair_finite_arcs
% 0.26/0.58 thf(fact_15_finite__subset,axiom,
% 0.26/0.58 ! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
% 0.26/0.58 ( ( ord_le841296385at_nat @ A @ B )
% 0.26/0.58 => ( ( finite772653738at_nat @ B )
% 0.26/0.58 => ( finite772653738at_nat @ A ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % finite_subset
% 0.26/0.58 thf(fact_16_finite__subset,axiom,
% 0.26/0.58 ! [A: set_Pr1948701895od_a_a,B: set_Pr1948701895od_a_a] :
% 0.26/0.58 ( ( ord_le456379495od_a_a @ A @ B )
% 0.26/0.58 => ( ( finite1664988688od_a_a @ B )
% 0.26/0.58 => ( finite1664988688od_a_a @ A ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % finite_subset
% 0.26/0.58 thf(fact_17_finite__subset,axiom,
% 0.26/0.58 ! [A: set_a,B: set_a] :
% 0.26/0.58 ( ( ord_less_eq_set_a @ A @ B )
% 0.26/0.58 => ( ( finite_finite_a @ B )
% 0.26/0.58 => ( finite_finite_a @ A ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % finite_subset
% 0.26/0.58 thf(fact_18_finite__subset,axiom,
% 0.26/0.58 ! [A: set_nat,B: set_nat] :
% 0.26/0.58 ( ( ord_less_eq_set_nat @ A @ B )
% 0.26/0.58 => ( ( finite_finite_nat @ B )
% 0.26/0.58 => ( finite_finite_nat @ A ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % finite_subset
% 0.26/0.58 thf(fact_19_finite__subset,axiom,
% 0.26/0.58 ! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
% 0.26/0.58 ( ( ord_le1824328871od_a_a @ A @ B )
% 0.26/0.58 => ( ( finite179568208od_a_a @ B )
% 0.26/0.58 => ( finite179568208od_a_a @ A ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % finite_subset
% 0.26/0.58 thf(fact_20_infinite__super,axiom,
% 0.26/0.58 ! [S: set_Pr1986765409at_nat,T: set_Pr1986765409at_nat] :
% 0.26/0.58 ( ( ord_le841296385at_nat @ S @ T )
% 0.26/0.58 => ( ~ ( finite772653738at_nat @ S )
% 0.26/0.58 => ~ ( finite772653738at_nat @ T ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % infinite_super
% 0.26/0.58 thf(fact_21_infinite__super,axiom,
% 0.26/0.58 ! [S: set_Pr1948701895od_a_a,T: set_Pr1948701895od_a_a] :
% 0.26/0.58 ( ( ord_le456379495od_a_a @ S @ T )
% 0.26/0.58 => ( ~ ( finite1664988688od_a_a @ S )
% 0.26/0.58 => ~ ( finite1664988688od_a_a @ T ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % infinite_super
% 0.26/0.58 thf(fact_22_infinite__super,axiom,
% 0.26/0.58 ! [S: set_a,T: set_a] :
% 0.26/0.58 ( ( ord_less_eq_set_a @ S @ T )
% 0.26/0.58 => ( ~ ( finite_finite_a @ S )
% 0.26/0.58 => ~ ( finite_finite_a @ T ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % infinite_super
% 0.26/0.58 thf(fact_23_infinite__super,axiom,
% 0.26/0.58 ! [S: set_nat,T: set_nat] :
% 0.26/0.58 ( ( ord_less_eq_set_nat @ S @ T )
% 0.26/0.58 => ( ~ ( finite_finite_nat @ S )
% 0.26/0.58 => ~ ( finite_finite_nat @ T ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % infinite_super
% 0.26/0.58 thf(fact_24_infinite__super,axiom,
% 0.26/0.58 ! [S: set_Product_prod_a_a,T: set_Product_prod_a_a] :
% 0.26/0.58 ( ( ord_le1824328871od_a_a @ S @ T )
% 0.26/0.58 => ( ~ ( finite179568208od_a_a @ S )
% 0.26/0.58 => ~ ( finite179568208od_a_a @ T ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % infinite_super
% 0.26/0.58 thf(fact_25_rev__finite__subset,axiom,
% 0.26/0.58 ! [B: set_Pr1986765409at_nat,A: set_Pr1986765409at_nat] :
% 0.26/0.58 ( ( finite772653738at_nat @ B )
% 0.26/0.58 => ( ( ord_le841296385at_nat @ A @ B )
% 0.26/0.58 => ( finite772653738at_nat @ A ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % rev_finite_subset
% 0.26/0.58 thf(fact_26_rev__finite__subset,axiom,
% 0.26/0.58 ! [B: set_Pr1948701895od_a_a,A: set_Pr1948701895od_a_a] :
% 0.26/0.58 ( ( finite1664988688od_a_a @ B )
% 0.26/0.58 => ( ( ord_le456379495od_a_a @ A @ B )
% 0.26/0.58 => ( finite1664988688od_a_a @ A ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % rev_finite_subset
% 0.26/0.58 thf(fact_27_rev__finite__subset,axiom,
% 0.26/0.58 ! [B: set_Product_prod_a_a,A: set_Product_prod_a_a] :
% 0.26/0.58 ( ( finite179568208od_a_a @ B )
% 0.26/0.58 => ( ( ord_le1824328871od_a_a @ A @ B )
% 0.26/0.58 => ( finite179568208od_a_a @ A ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % rev_finite_subset
% 0.26/0.58 thf(fact_28_rev__finite__subset,axiom,
% 0.26/0.58 ! [B: set_nat,A: set_nat] :
% 0.26/0.58 ( ( finite_finite_nat @ B )
% 0.26/0.58 => ( ( ord_less_eq_set_nat @ A @ B )
% 0.26/0.58 => ( finite_finite_nat @ A ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % rev_finite_subset
% 0.26/0.58 thf(fact_29_rev__finite__subset,axiom,
% 0.26/0.58 ! [B: set_a,A: set_a] :
% 0.26/0.58 ( ( finite_finite_a @ B )
% 0.26/0.58 => ( ( ord_less_eq_set_a @ A @ B )
% 0.26/0.58 => ( finite_finite_a @ A ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % rev_finite_subset
% 0.26/0.58 thf(fact_30_finite__has__maximal2,axiom,
% 0.26/0.58 ! [A: set_se1596668135od_a_a,A2: set_Product_prod_a_a] :
% 0.26/0.58 ( ( finite1145471536od_a_a @ A )
% 0.26/0.58 => ( ( member1838126896od_a_a @ A2 @ A )
% 0.26/0.58 => ? [X: set_Product_prod_a_a] :
% 0.26/0.58 ( ( member1838126896od_a_a @ X @ A )
% 0.26/0.58 & ( ord_le1824328871od_a_a @ A2 @ X )
% 0.26/0.58 & ! [Xa: set_Product_prod_a_a] :
% 0.26/0.58 ( ( member1838126896od_a_a @ Xa @ A )
% 0.26/0.58 => ( ( ord_le1824328871od_a_a @ X @ Xa )
% 0.26/0.58 => ( X = Xa ) ) ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % finite_has_maximal2
% 0.26/0.58 thf(fact_31_finite__has__maximal2,axiom,
% 0.26/0.58 ! [A: set_nat,A2: nat] :
% 0.26/0.58 ( ( finite_finite_nat @ A )
% 0.26/0.58 => ( ( member_nat @ A2 @ A )
% 0.26/0.58 => ? [X: nat] :
% 0.26/0.58 ( ( member_nat @ X @ A )
% 0.26/0.58 & ( ord_less_eq_nat @ A2 @ X )
% 0.26/0.58 & ! [Xa: nat] :
% 0.26/0.58 ( ( member_nat @ Xa @ A )
% 0.26/0.58 => ( ( ord_less_eq_nat @ X @ Xa )
% 0.26/0.58 => ( X = Xa ) ) ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % finite_has_maximal2
% 0.26/0.58 thf(fact_32_finite__has__maximal2,axiom,
% 0.26/0.58 ! [A: set_set_nat,A2: set_nat] :
% 0.26/0.58 ( ( finite2012248349et_nat @ A )
% 0.26/0.58 => ( ( member_set_nat @ A2 @ A )
% 0.26/0.58 => ? [X: set_nat] :
% 0.26/0.58 ( ( member_set_nat @ X @ A )
% 0.26/0.58 & ( ord_less_eq_set_nat @ A2 @ X )
% 0.26/0.58 & ! [Xa: set_nat] :
% 0.26/0.58 ( ( member_set_nat @ Xa @ A )
% 0.26/0.58 => ( ( ord_less_eq_set_nat @ X @ Xa )
% 0.26/0.58 => ( X = Xa ) ) ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % finite_has_maximal2
% 0.26/0.58 thf(fact_33_finite__has__maximal2,axiom,
% 0.26/0.58 ! [A: set_set_a,A2: set_a] :
% 0.26/0.58 ( ( finite_finite_set_a @ A )
% 0.26/0.58 => ( ( member_set_a @ A2 @ A )
% 0.26/0.58 => ? [X: set_a] :
% 0.26/0.58 ( ( member_set_a @ X @ A )
% 0.26/0.58 & ( ord_less_eq_set_a @ A2 @ X )
% 0.26/0.58 & ! [Xa: set_a] :
% 0.26/0.58 ( ( member_set_a @ Xa @ A )
% 0.26/0.58 => ( ( ord_less_eq_set_a @ X @ Xa )
% 0.26/0.58 => ( X = Xa ) ) ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % finite_has_maximal2
% 0.26/0.58 thf(fact_34_finite__Collect__conjI,axiom,
% 0.26/0.58 ! [P: product_prod_a_a > $o,Q: product_prod_a_a > $o] :
% 0.26/0.58 ( ( ( finite179568208od_a_a @ ( collec645855634od_a_a @ P ) )
% 0.26/0.58 | ( finite179568208od_a_a @ ( collec645855634od_a_a @ Q ) ) )
% 0.26/0.58 => ( finite179568208od_a_a
% 0.26/0.58 @ ( collec645855634od_a_a
% 0.26/0.58 @ ^ [X2: product_prod_a_a] :
% 0.26/0.58 ( ( P @ X2 )
% 0.26/0.58 & ( Q @ X2 ) ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % finite_Collect_conjI
% 0.26/0.58 thf(fact_35_finite__Collect__conjI,axiom,
% 0.26/0.58 ! [P: a > $o,Q: a > $o] :
% 0.26/0.58 ( ( ( finite_finite_a @ ( collect_a @ P ) )
% 0.26/0.58 | ( finite_finite_a @ ( collect_a @ Q ) ) )
% 0.26/0.58 => ( finite_finite_a
% 0.26/0.58 @ ( collect_a
% 0.26/0.58 @ ^ [X2: a] :
% 0.26/0.58 ( ( P @ X2 )
% 0.26/0.58 & ( Q @ X2 ) ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % finite_Collect_conjI
% 0.26/0.58 thf(fact_36_finite__Collect__conjI,axiom,
% 0.26/0.58 ! [P: nat > $o,Q: nat > $o] :
% 0.26/0.58 ( ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 0.26/0.58 | ( finite_finite_nat @ ( collect_nat @ Q ) ) )
% 0.26/0.58 => ( finite_finite_nat
% 0.26/0.58 @ ( collect_nat
% 0.26/0.58 @ ^ [X2: nat] :
% 0.26/0.58 ( ( P @ X2 )
% 0.26/0.58 & ( Q @ X2 ) ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % finite_Collect_conjI
% 0.26/0.58 thf(fact_37_finite__Collect__conjI,axiom,
% 0.26/0.58 ! [P: product_prod_nat_nat > $o,Q: product_prod_nat_nat > $o] :
% 0.26/0.58 ( ( ( finite772653738at_nat @ ( collec7649004at_nat @ P ) )
% 0.26/0.58 | ( finite772653738at_nat @ ( collec7649004at_nat @ Q ) ) )
% 0.26/0.58 => ( finite772653738at_nat
% 0.26/0.58 @ ( collec7649004at_nat
% 0.26/0.58 @ ^ [X2: product_prod_nat_nat] :
% 0.26/0.58 ( ( P @ X2 )
% 0.26/0.58 & ( Q @ X2 ) ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % finite_Collect_conjI
% 0.26/0.58 thf(fact_38_finite__Collect__conjI,axiom,
% 0.26/0.58 ! [P: produc1572603623od_a_a > $o,Q: produc1572603623od_a_a > $o] :
% 0.26/0.58 ( ( ( finite1664988688od_a_a @ ( collec1635618130od_a_a @ P ) )
% 0.26/0.58 | ( finite1664988688od_a_a @ ( collec1635618130od_a_a @ Q ) ) )
% 0.26/0.58 => ( finite1664988688od_a_a
% 0.26/0.58 @ ( collec1635618130od_a_a
% 0.26/0.58 @ ^ [X2: produc1572603623od_a_a] :
% 0.26/0.58 ( ( P @ X2 )
% 0.26/0.58 & ( Q @ X2 ) ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % finite_Collect_conjI
% 0.26/0.58 thf(fact_39_finite__Collect__disjI,axiom,
% 0.26/0.58 ! [P: product_prod_a_a > $o,Q: product_prod_a_a > $o] :
% 0.26/0.58 ( ( finite179568208od_a_a
% 0.26/0.58 @ ( collec645855634od_a_a
% 0.26/0.58 @ ^ [X2: product_prod_a_a] :
% 0.26/0.58 ( ( P @ X2 )
% 0.26/0.58 | ( Q @ X2 ) ) ) )
% 0.26/0.58 = ( ( finite179568208od_a_a @ ( collec645855634od_a_a @ P ) )
% 0.26/0.58 & ( finite179568208od_a_a @ ( collec645855634od_a_a @ Q ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % finite_Collect_disjI
% 0.26/0.58 thf(fact_40_finite__Collect__disjI,axiom,
% 0.26/0.58 ! [P: a > $o,Q: a > $o] :
% 0.26/0.58 ( ( finite_finite_a
% 0.26/0.58 @ ( collect_a
% 0.26/0.58 @ ^ [X2: a] :
% 0.26/0.58 ( ( P @ X2 )
% 0.26/0.58 | ( Q @ X2 ) ) ) )
% 0.26/0.58 = ( ( finite_finite_a @ ( collect_a @ P ) )
% 0.26/0.58 & ( finite_finite_a @ ( collect_a @ Q ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % finite_Collect_disjI
% 0.26/0.58 thf(fact_41_finite__Collect__disjI,axiom,
% 0.26/0.58 ! [P: nat > $o,Q: nat > $o] :
% 0.26/0.58 ( ( finite_finite_nat
% 0.26/0.58 @ ( collect_nat
% 0.26/0.58 @ ^ [X2: nat] :
% 0.26/0.58 ( ( P @ X2 )
% 0.26/0.58 | ( Q @ X2 ) ) ) )
% 0.26/0.58 = ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 0.26/0.58 & ( finite_finite_nat @ ( collect_nat @ Q ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % finite_Collect_disjI
% 0.26/0.58 thf(fact_42_finite__Collect__disjI,axiom,
% 0.26/0.58 ! [P: product_prod_nat_nat > $o,Q: product_prod_nat_nat > $o] :
% 0.26/0.58 ( ( finite772653738at_nat
% 0.26/0.58 @ ( collec7649004at_nat
% 0.26/0.58 @ ^ [X2: product_prod_nat_nat] :
% 0.26/0.58 ( ( P @ X2 )
% 0.26/0.58 | ( Q @ X2 ) ) ) )
% 0.26/0.58 = ( ( finite772653738at_nat @ ( collec7649004at_nat @ P ) )
% 0.26/0.58 & ( finite772653738at_nat @ ( collec7649004at_nat @ Q ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % finite_Collect_disjI
% 0.26/0.58 thf(fact_43_finite__Collect__disjI,axiom,
% 0.26/0.58 ! [P: produc1572603623od_a_a > $o,Q: produc1572603623od_a_a > $o] :
% 0.26/0.58 ( ( finite1664988688od_a_a
% 0.26/0.58 @ ( collec1635618130od_a_a
% 0.26/0.58 @ ^ [X2: produc1572603623od_a_a] :
% 0.26/0.58 ( ( P @ X2 )
% 0.26/0.58 | ( Q @ X2 ) ) ) )
% 0.26/0.58 = ( ( finite1664988688od_a_a @ ( collec1635618130od_a_a @ P ) )
% 0.26/0.58 & ( finite1664988688od_a_a @ ( collec1635618130od_a_a @ Q ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % finite_Collect_disjI
% 0.26/0.58 thf(fact_44_finite__Collect__subsets,axiom,
% 0.26/0.58 ! [A: set_Pr1986765409at_nat] :
% 0.26/0.58 ( ( finite772653738at_nat @ A )
% 0.26/0.58 => ( finite1457549322at_nat
% 0.26/0.58 @ ( collec1606769740at_nat
% 0.26/0.58 @ ^ [B2: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ B2 @ A ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % finite_Collect_subsets
% 0.26/0.58 thf(fact_45_finite__Collect__subsets,axiom,
% 0.26/0.58 ! [A: set_Pr1948701895od_a_a] :
% 0.26/0.58 ( ( finite1664988688od_a_a @ A )
% 0.26/0.58 => ( finite323969008od_a_a
% 0.26/0.58 @ ( collec453062450od_a_a
% 0.26/0.58 @ ^ [B2: set_Pr1948701895od_a_a] : ( ord_le456379495od_a_a @ B2 @ A ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % finite_Collect_subsets
% 0.26/0.58 thf(fact_46_finite__Collect__subsets,axiom,
% 0.26/0.58 ! [A: set_Product_prod_a_a] :
% 0.26/0.58 ( ( finite179568208od_a_a @ A )
% 0.26/0.58 => ( finite1145471536od_a_a
% 0.26/0.58 @ ( collec183727474od_a_a
% 0.26/0.58 @ ^ [B2: set_Product_prod_a_a] : ( ord_le1824328871od_a_a @ B2 @ A ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % finite_Collect_subsets
% 0.26/0.58 thf(fact_47_finite__Collect__subsets,axiom,
% 0.26/0.58 ! [A: set_nat] :
% 0.26/0.58 ( ( finite_finite_nat @ A )
% 0.26/0.58 => ( finite2012248349et_nat
% 0.26/0.58 @ ( collect_set_nat
% 0.26/0.58 @ ^ [B2: set_nat] : ( ord_less_eq_set_nat @ B2 @ A ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % finite_Collect_subsets
% 0.26/0.58 thf(fact_48_finite__Collect__subsets,axiom,
% 0.26/0.58 ! [A: set_a] :
% 0.26/0.58 ( ( finite_finite_a @ A )
% 0.26/0.58 => ( finite_finite_set_a
% 0.26/0.58 @ ( collect_set_a
% 0.26/0.58 @ ^ [B2: set_a] : ( ord_less_eq_set_a @ B2 @ A ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % finite_Collect_subsets
% 0.26/0.58 thf(fact_49_finite__SigmaI,axiom,
% 0.26/0.58 ! [A: set_a,B: a > set_nat] :
% 0.26/0.58 ( ( finite_finite_a @ A )
% 0.26/0.58 => ( ! [A3: a] :
% 0.26/0.58 ( ( member_a @ A3 @ A )
% 0.26/0.58 => ( finite_finite_nat @ ( B @ A3 ) ) )
% 0.26/0.58 => ( finite1743148308_a_nat @ ( product_Sigma_a_nat @ A @ B ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % finite_SigmaI
% 0.26/0.58 thf(fact_50_finite__SigmaI,axiom,
% 0.26/0.58 ! [A: set_nat,B: nat > set_a] :
% 0.26/0.58 ( ( finite_finite_nat @ A )
% 0.26/0.58 => ( ! [A3: nat] :
% 0.26/0.58 ( ( member_nat @ A3 @ A )
% 0.26/0.58 => ( finite_finite_a @ ( B @ A3 ) ) )
% 0.26/0.58 => ( finite1808550458_nat_a @ ( product_Sigma_nat_a @ A @ B ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % finite_SigmaI
% 0.26/0.58 thf(fact_51_finite__SigmaI,axiom,
% 0.26/0.58 ! [A: set_nat,B: nat > set_nat] :
% 0.26/0.58 ( ( finite_finite_nat @ A )
% 0.26/0.58 => ( ! [A3: nat] :
% 0.26/0.58 ( ( member_nat @ A3 @ A )
% 0.26/0.58 => ( finite_finite_nat @ ( B @ A3 ) ) )
% 0.26/0.58 => ( finite772653738at_nat @ ( produc45129834at_nat @ A @ B ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % finite_SigmaI
% 0.26/0.58 thf(fact_52_finite__SigmaI,axiom,
% 0.26/0.58 ! [A: set_a,B: a > set_a] :
% 0.26/0.58 ( ( finite_finite_a @ A )
% 0.26/0.58 => ( ! [A3: a] :
% 0.26/0.58 ( ( member_a @ A3 @ A )
% 0.26/0.58 => ( finite_finite_a @ ( B @ A3 ) ) )
% 0.26/0.58 => ( finite179568208od_a_a @ ( product_Sigma_a_a @ A @ B ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % finite_SigmaI
% 0.26/0.58 thf(fact_53_finite__SigmaI,axiom,
% 0.26/0.58 ! [A: set_Product_prod_a_a,B: product_prod_a_a > set_a] :
% 0.26/0.58 ( ( finite179568208od_a_a @ A )
% 0.26/0.58 => ( ! [A3: product_prod_a_a] :
% 0.26/0.58 ( ( member449909584od_a_a @ A3 @ A )
% 0.26/0.58 => ( finite_finite_a @ ( B @ A3 ) ) )
% 0.26/0.58 => ( finite1919032935_a_a_a @ ( produc1282482655_a_a_a @ A @ B ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % finite_SigmaI
% 0.26/0.58 thf(fact_54_finite__SigmaI,axiom,
% 0.26/0.58 ! [A: set_Product_prod_a_a,B: product_prod_a_a > set_nat] :
% 0.26/0.58 ( ( finite179568208od_a_a @ A )
% 0.26/0.58 => ( ! [A3: product_prod_a_a] :
% 0.26/0.58 ( ( member449909584od_a_a @ A3 @ A )
% 0.26/0.58 => ( finite_finite_nat @ ( B @ A3 ) ) )
% 0.26/0.58 => ( finite1837575485_a_nat @ ( produc931712687_a_nat @ A @ B ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % finite_SigmaI
% 0.26/0.58 thf(fact_55_finite__SigmaI,axiom,
% 0.26/0.58 ! [A: set_a,B: a > set_Product_prod_a_a] :
% 0.26/0.58 ( ( finite_finite_a @ A )
% 0.26/0.58 => ( ! [A3: a] :
% 0.26/0.58 ( ( member_a @ A3 @ A )
% 0.26/0.58 => ( finite179568208od_a_a @ ( B @ A3 ) ) )
% 0.26/0.58 => ( finite676513017od_a_a @ ( produc520147185od_a_a @ A @ B ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % finite_SigmaI
% 0.26/0.58 thf(fact_56_finite__SigmaI,axiom,
% 0.26/0.58 ! [A: set_a,B: a > set_Pr1986765409at_nat] :
% 0.26/0.58 ( ( finite_finite_a @ A )
% 0.26/0.58 => ( ! [A3: a] :
% 0.26/0.58 ( ( member_a @ A3 @ A )
% 0.26/0.58 => ( finite772653738at_nat @ ( B @ A3 ) ) )
% 0.26/0.58 => ( finite942416723at_nat @ ( produc292491723at_nat @ A @ B ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % finite_SigmaI
% 0.26/0.58 thf(fact_57_finite__SigmaI,axiom,
% 0.26/0.58 ! [A: set_nat,B: nat > set_Product_prod_a_a] :
% 0.26/0.58 ( ( finite_finite_nat @ A )
% 0.26/0.58 => ( ! [A3: nat] :
% 0.26/0.58 ( ( member_nat @ A3 @ A )
% 0.26/0.58 => ( finite179568208od_a_a @ ( B @ A3 ) ) )
% 0.26/0.58 => ( finite1297454819od_a_a @ ( produc1182842125od_a_a @ A @ B ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % finite_SigmaI
% 0.26/0.58 thf(fact_58_finite__SigmaI,axiom,
% 0.26/0.58 ! [A: set_nat,B: nat > set_Pr1986765409at_nat] :
% 0.26/0.58 ( ( finite_finite_nat @ A )
% 0.26/0.58 => ( ! [A3: nat] :
% 0.26/0.58 ( ( member_nat @ A3 @ A )
% 0.26/0.58 => ( finite772653738at_nat @ ( B @ A3 ) ) )
% 0.26/0.58 => ( finite277291581at_nat @ ( produc894163943at_nat @ A @ B ) ) ) ) ).
% 0.26/0.58
% 0.26/0.58 % finite_SigmaI
% 0.26/0.58 thf(fact_59_pair__fin__digraph_Oaxioms_I2_J,axiom,
% 0.26/0.58 ! [G2: pair_p125712459t_unit] :
% 0.26/0.58 ( ( pair_p1802376898raph_a @ G2 )
% 0.26/0.58 => ( pair_p1864019935ioms_a @ G2 ) ) ).
% 0.26/0.58
% 0.26/0.58 % pair_fin_digraph.axioms(2)
% 0.26/0.58 thf(fact_60_pair__fin__digraph_Oaxioms_I2_J,axiom,
% 0.26/0.58 ! [G2: pair_p1914262621t_unit] :
% 0.26/0.58 ( ( pair_p128415500ph_nat @ G2 )
% 0.26/0.58 => ( pair_p1027063983ms_nat @ G2 ) ) ).
% 0.26/0.58
% 0.26/0.58 % pair_fin_digraph.axioms(2)
% 0.26/0.58 thf(fact_61_pair__fin__digraph_Oaxioms_I2_J,axiom,
% 0.26/0.58 ! [G2: pair_p1765063010t_unit] :
% 0.26/0.58 ( ( pair_p374947051od_a_a @ G2 )
% 0.26/0.58 => ( pair_p504738056od_a_a @ G2 ) ) ).
% 0.26/0.58
% 0.26/0.58 % pair_fin_digraph.axioms(2)
% 0.26/0.58 thf(fact_62_not__finite__existsD,axiom,
% 0.26/0.58 ! [P: product_prod_a_a > $o] :
% 0.26/0.58 ( ~ ( finite179568208od_a_a @ ( collec645855634od_a_a @ P ) )
% 0.26/0.58 => ? [X_1: product_prod_a_a] : ( P @ X_1 ) ) ).
% 0.26/0.58
% 0.26/0.58 % not_finite_existsD
% 0.26/0.58 thf(fact_63_not__finite__existsD,axiom,
% 0.26/0.58 ! [P: a > $o] :
% 0.26/0.58 ( ~ ( finite_finite_a @ ( collect_a @ P ) )
% 0.26/0.58 => ? [X_1: a] : ( P @ X_1 ) ) ).
% 0.26/0.58
% 0.26/0.58 % not_finite_existsD
% 0.26/0.58 thf(fact_64_not__finite__existsD,axiom,
% 0.26/0.58 ! [P: nat > $o] :
% 0.26/0.58 ( ~ ( finite_finite_nat @ ( collect_nat @ P ) )
% 0.26/0.58 => ? [X_1: nat] : ( P @ X_1 ) ) ).
% 0.26/0.58
% 0.26/0.58 % not_finite_existsD
% 0.26/0.58 thf(fact_65_not__finite__existsD,axiom,
% 0.26/0.58 ! [P: product_prod_nat_nat > $o] :
% 0.26/0.58 ( ~ ( finite772653738at_nat @ ( collec7649004at_nat @ P ) )
% 0.26/0.58 => ? [X_1: product_prod_nat_nat] : ( P @ X_1 ) ) ).
% 0.26/0.58
% 0.26/0.58 % not_finite_existsD
% 0.26/0.58 thf(fact_66_not__finite__existsD,axiom,
% 0.26/0.58 ! [P: produc1572603623od_a_a > $o] :
% 0.26/0.58 ( ~ ( finite1664988688od_a_a @ ( collec1635618130od_a_a @ P ) )
% 0.26/0.58 => ? [X_1: produc1572603623od_a_a] : ( P @ X_1 ) ) ).
% 0.26/0.58
% 0.26/0.58 % not_finite_existsD
% 0.26/0.58 thf(fact_67_pigeonhole__infinite__rel,axiom,
% 0.26/0.58 ! [A: set_a,B: set_a,R: a > a > $o] :
% 0.26/0.58 ( ~ ( finite_finite_a @ A )
% 0.26/0.58 => ( ( finite_finite_a @ B )
% 0.26/0.58 => ( ! [X: a] :
% 0.26/0.58 ( ( member_a @ X @ A )
% 0.26/0.58 => ? [Xa: a] :
% 0.26/0.58 ( ( member_a @ Xa @ B )
% 0.26/0.58 & ( R @ X @ Xa ) ) )
% 0.26/0.59 => ? [X: a] :
% 0.26/0.59 ( ( member_a @ X @ B )
% 0.26/0.59 & ~ ( finite_finite_a
% 0.26/0.59 @ ( collect_a
% 0.26/0.59 @ ^ [A4: a] :
% 0.26/0.59 ( ( member_a @ A4 @ A )
% 0.26/0.59 & ( R @ A4 @ X ) ) ) ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % pigeonhole_infinite_rel
% 0.26/0.59 thf(fact_68_pigeonhole__infinite__rel,axiom,
% 0.26/0.59 ! [A: set_a,B: set_nat,R: a > nat > $o] :
% 0.26/0.59 ( ~ ( finite_finite_a @ A )
% 0.26/0.59 => ( ( finite_finite_nat @ B )
% 0.26/0.59 => ( ! [X: a] :
% 0.26/0.59 ( ( member_a @ X @ A )
% 0.26/0.59 => ? [Xa: nat] :
% 0.26/0.59 ( ( member_nat @ Xa @ B )
% 0.26/0.59 & ( R @ X @ Xa ) ) )
% 0.26/0.59 => ? [X: nat] :
% 0.26/0.59 ( ( member_nat @ X @ B )
% 0.26/0.59 & ~ ( finite_finite_a
% 0.26/0.59 @ ( collect_a
% 0.26/0.59 @ ^ [A4: a] :
% 0.26/0.59 ( ( member_a @ A4 @ A )
% 0.26/0.59 & ( R @ A4 @ X ) ) ) ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % pigeonhole_infinite_rel
% 0.26/0.59 thf(fact_69_pigeonhole__infinite__rel,axiom,
% 0.26/0.59 ! [A: set_nat,B: set_a,R: nat > a > $o] :
% 0.26/0.59 ( ~ ( finite_finite_nat @ A )
% 0.26/0.59 => ( ( finite_finite_a @ B )
% 0.26/0.59 => ( ! [X: nat] :
% 0.26/0.59 ( ( member_nat @ X @ A )
% 0.26/0.59 => ? [Xa: a] :
% 0.26/0.59 ( ( member_a @ Xa @ B )
% 0.26/0.59 & ( R @ X @ Xa ) ) )
% 0.26/0.59 => ? [X: a] :
% 0.26/0.59 ( ( member_a @ X @ B )
% 0.26/0.59 & ~ ( finite_finite_nat
% 0.26/0.59 @ ( collect_nat
% 0.26/0.59 @ ^ [A4: nat] :
% 0.26/0.59 ( ( member_nat @ A4 @ A )
% 0.26/0.59 & ( R @ A4 @ X ) ) ) ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % pigeonhole_infinite_rel
% 0.26/0.59 thf(fact_70_pigeonhole__infinite__rel,axiom,
% 0.26/0.59 ! [A: set_nat,B: set_nat,R: nat > nat > $o] :
% 0.26/0.59 ( ~ ( finite_finite_nat @ A )
% 0.26/0.59 => ( ( finite_finite_nat @ B )
% 0.26/0.59 => ( ! [X: nat] :
% 0.26/0.59 ( ( member_nat @ X @ A )
% 0.26/0.59 => ? [Xa: nat] :
% 0.26/0.59 ( ( member_nat @ Xa @ B )
% 0.26/0.59 & ( R @ X @ Xa ) ) )
% 0.26/0.59 => ? [X: nat] :
% 0.26/0.59 ( ( member_nat @ X @ B )
% 0.26/0.59 & ~ ( finite_finite_nat
% 0.26/0.59 @ ( collect_nat
% 0.26/0.59 @ ^ [A4: nat] :
% 0.26/0.59 ( ( member_nat @ A4 @ A )
% 0.26/0.59 & ( R @ A4 @ X ) ) ) ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % pigeonhole_infinite_rel
% 0.26/0.59 thf(fact_71_pigeonhole__infinite__rel,axiom,
% 0.26/0.59 ! [A: set_Product_prod_a_a,B: set_a,R: product_prod_a_a > a > $o] :
% 0.26/0.59 ( ~ ( finite179568208od_a_a @ A )
% 0.26/0.59 => ( ( finite_finite_a @ B )
% 0.26/0.59 => ( ! [X: product_prod_a_a] :
% 0.26/0.59 ( ( member449909584od_a_a @ X @ A )
% 0.26/0.59 => ? [Xa: a] :
% 0.26/0.59 ( ( member_a @ Xa @ B )
% 0.26/0.59 & ( R @ X @ Xa ) ) )
% 0.26/0.59 => ? [X: a] :
% 0.26/0.59 ( ( member_a @ X @ B )
% 0.26/0.59 & ~ ( finite179568208od_a_a
% 0.26/0.59 @ ( collec645855634od_a_a
% 0.26/0.59 @ ^ [A4: product_prod_a_a] :
% 0.26/0.59 ( ( member449909584od_a_a @ A4 @ A )
% 0.26/0.59 & ( R @ A4 @ X ) ) ) ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % pigeonhole_infinite_rel
% 0.26/0.59 thf(fact_72_pigeonhole__infinite__rel,axiom,
% 0.26/0.59 ! [A: set_Product_prod_a_a,B: set_nat,R: product_prod_a_a > nat > $o] :
% 0.26/0.59 ( ~ ( finite179568208od_a_a @ A )
% 0.26/0.59 => ( ( finite_finite_nat @ B )
% 0.26/0.59 => ( ! [X: product_prod_a_a] :
% 0.26/0.59 ( ( member449909584od_a_a @ X @ A )
% 0.26/0.59 => ? [Xa: nat] :
% 0.26/0.59 ( ( member_nat @ Xa @ B )
% 0.26/0.59 & ( R @ X @ Xa ) ) )
% 0.26/0.59 => ? [X: nat] :
% 0.26/0.59 ( ( member_nat @ X @ B )
% 0.26/0.59 & ~ ( finite179568208od_a_a
% 0.26/0.59 @ ( collec645855634od_a_a
% 0.26/0.59 @ ^ [A4: product_prod_a_a] :
% 0.26/0.59 ( ( member449909584od_a_a @ A4 @ A )
% 0.26/0.59 & ( R @ A4 @ X ) ) ) ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % pigeonhole_infinite_rel
% 0.26/0.59 thf(fact_73_pigeonhole__infinite__rel,axiom,
% 0.26/0.59 ! [A: set_a,B: set_Product_prod_a_a,R: a > product_prod_a_a > $o] :
% 0.26/0.59 ( ~ ( finite_finite_a @ A )
% 0.26/0.59 => ( ( finite179568208od_a_a @ B )
% 0.26/0.59 => ( ! [X: a] :
% 0.26/0.59 ( ( member_a @ X @ A )
% 0.26/0.59 => ? [Xa: product_prod_a_a] :
% 0.26/0.59 ( ( member449909584od_a_a @ Xa @ B )
% 0.26/0.59 & ( R @ X @ Xa ) ) )
% 0.26/0.59 => ? [X: product_prod_a_a] :
% 0.26/0.59 ( ( member449909584od_a_a @ X @ B )
% 0.26/0.59 & ~ ( finite_finite_a
% 0.26/0.59 @ ( collect_a
% 0.26/0.59 @ ^ [A4: a] :
% 0.26/0.59 ( ( member_a @ A4 @ A )
% 0.26/0.59 & ( R @ A4 @ X ) ) ) ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % pigeonhole_infinite_rel
% 0.26/0.59 thf(fact_74_pigeonhole__infinite__rel,axiom,
% 0.26/0.59 ! [A: set_a,B: set_Pr1986765409at_nat,R: a > product_prod_nat_nat > $o] :
% 0.26/0.59 ( ~ ( finite_finite_a @ A )
% 0.26/0.59 => ( ( finite772653738at_nat @ B )
% 0.26/0.59 => ( ! [X: a] :
% 0.26/0.59 ( ( member_a @ X @ A )
% 0.26/0.59 => ? [Xa: product_prod_nat_nat] :
% 0.26/0.59 ( ( member701585322at_nat @ Xa @ B )
% 0.26/0.59 & ( R @ X @ Xa ) ) )
% 0.26/0.59 => ? [X: product_prod_nat_nat] :
% 0.26/0.59 ( ( member701585322at_nat @ X @ B )
% 0.26/0.59 & ~ ( finite_finite_a
% 0.26/0.59 @ ( collect_a
% 0.26/0.59 @ ^ [A4: a] :
% 0.26/0.59 ( ( member_a @ A4 @ A )
% 0.26/0.59 & ( R @ A4 @ X ) ) ) ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % pigeonhole_infinite_rel
% 0.26/0.59 thf(fact_75_pigeonhole__infinite__rel,axiom,
% 0.26/0.59 ! [A: set_nat,B: set_Product_prod_a_a,R: nat > product_prod_a_a > $o] :
% 0.26/0.59 ( ~ ( finite_finite_nat @ A )
% 0.26/0.59 => ( ( finite179568208od_a_a @ B )
% 0.26/0.59 => ( ! [X: nat] :
% 0.26/0.59 ( ( member_nat @ X @ A )
% 0.26/0.59 => ? [Xa: product_prod_a_a] :
% 0.26/0.59 ( ( member449909584od_a_a @ Xa @ B )
% 0.26/0.59 & ( R @ X @ Xa ) ) )
% 0.26/0.59 => ? [X: product_prod_a_a] :
% 0.26/0.59 ( ( member449909584od_a_a @ X @ B )
% 0.26/0.59 & ~ ( finite_finite_nat
% 0.26/0.59 @ ( collect_nat
% 0.26/0.59 @ ^ [A4: nat] :
% 0.26/0.59 ( ( member_nat @ A4 @ A )
% 0.26/0.59 & ( R @ A4 @ X ) ) ) ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % pigeonhole_infinite_rel
% 0.26/0.59 thf(fact_76_pigeonhole__infinite__rel,axiom,
% 0.26/0.59 ! [A: set_nat,B: set_Pr1986765409at_nat,R: nat > product_prod_nat_nat > $o] :
% 0.26/0.59 ( ~ ( finite_finite_nat @ A )
% 0.26/0.59 => ( ( finite772653738at_nat @ B )
% 0.26/0.59 => ( ! [X: nat] :
% 0.26/0.59 ( ( member_nat @ X @ A )
% 0.26/0.59 => ? [Xa: product_prod_nat_nat] :
% 0.26/0.59 ( ( member701585322at_nat @ Xa @ B )
% 0.26/0.59 & ( R @ X @ Xa ) ) )
% 0.26/0.59 => ? [X: product_prod_nat_nat] :
% 0.26/0.59 ( ( member701585322at_nat @ X @ B )
% 0.26/0.59 & ~ ( finite_finite_nat
% 0.26/0.59 @ ( collect_nat
% 0.26/0.59 @ ^ [A4: nat] :
% 0.26/0.59 ( ( member_nat @ A4 @ A )
% 0.26/0.59 & ( R @ A4 @ X ) ) ) ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % pigeonhole_infinite_rel
% 0.26/0.59 thf(fact_77_pair__fin__digraph_Opair__fin__digraph,axiom,
% 0.26/0.59 ! [G2: pair_p125712459t_unit] :
% 0.26/0.59 ( ( pair_p1802376898raph_a @ G2 )
% 0.26/0.59 => ( pair_p1802376898raph_a @ G2 ) ) ).
% 0.26/0.59
% 0.26/0.59 % pair_fin_digraph.pair_fin_digraph
% 0.26/0.59 thf(fact_78_finite__cartesian__product,axiom,
% 0.26/0.59 ! [A: set_a,B: set_nat] :
% 0.26/0.59 ( ( finite_finite_a @ A )
% 0.26/0.59 => ( ( finite_finite_nat @ B )
% 0.26/0.59 => ( finite1743148308_a_nat
% 0.26/0.59 @ ( product_Sigma_a_nat @ A
% 0.26/0.59 @ ^ [Uu: a] : B ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % finite_cartesian_product
% 0.26/0.59 thf(fact_79_finite__cartesian__product,axiom,
% 0.26/0.59 ! [A: set_nat,B: set_a] :
% 0.26/0.59 ( ( finite_finite_nat @ A )
% 0.26/0.59 => ( ( finite_finite_a @ B )
% 0.26/0.59 => ( finite1808550458_nat_a
% 0.26/0.59 @ ( product_Sigma_nat_a @ A
% 0.26/0.59 @ ^ [Uu: nat] : B ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % finite_cartesian_product
% 0.26/0.59 thf(fact_80_finite__cartesian__product,axiom,
% 0.26/0.59 ! [A: set_nat,B: set_nat] :
% 0.26/0.59 ( ( finite_finite_nat @ A )
% 0.26/0.59 => ( ( finite_finite_nat @ B )
% 0.26/0.59 => ( finite772653738at_nat
% 0.26/0.59 @ ( produc45129834at_nat @ A
% 0.26/0.59 @ ^ [Uu: nat] : B ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % finite_cartesian_product
% 0.26/0.59 thf(fact_81_finite__cartesian__product,axiom,
% 0.26/0.59 ! [A: set_a,B: set_a] :
% 0.26/0.59 ( ( finite_finite_a @ A )
% 0.26/0.59 => ( ( finite_finite_a @ B )
% 0.26/0.59 => ( finite179568208od_a_a
% 0.26/0.59 @ ( product_Sigma_a_a @ A
% 0.26/0.59 @ ^ [Uu: a] : B ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % finite_cartesian_product
% 0.26/0.59 thf(fact_82_finite__cartesian__product,axiom,
% 0.26/0.59 ! [A: set_Product_prod_a_a,B: set_a] :
% 0.26/0.59 ( ( finite179568208od_a_a @ A )
% 0.26/0.59 => ( ( finite_finite_a @ B )
% 0.26/0.59 => ( finite1919032935_a_a_a
% 0.26/0.59 @ ( produc1282482655_a_a_a @ A
% 0.26/0.59 @ ^ [Uu: product_prod_a_a] : B ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % finite_cartesian_product
% 0.26/0.59 thf(fact_83_finite__cartesian__product,axiom,
% 0.26/0.59 ! [A: set_Product_prod_a_a,B: set_nat] :
% 0.26/0.59 ( ( finite179568208od_a_a @ A )
% 0.26/0.59 => ( ( finite_finite_nat @ B )
% 0.26/0.59 => ( finite1837575485_a_nat
% 0.26/0.59 @ ( produc931712687_a_nat @ A
% 0.26/0.59 @ ^ [Uu: product_prod_a_a] : B ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % finite_cartesian_product
% 0.26/0.59 thf(fact_84_finite__cartesian__product,axiom,
% 0.26/0.59 ! [A: set_a,B: set_Product_prod_a_a] :
% 0.26/0.59 ( ( finite_finite_a @ A )
% 0.26/0.59 => ( ( finite179568208od_a_a @ B )
% 0.26/0.59 => ( finite676513017od_a_a
% 0.26/0.59 @ ( produc520147185od_a_a @ A
% 0.26/0.59 @ ^ [Uu: a] : B ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % finite_cartesian_product
% 0.26/0.59 thf(fact_85_finite__cartesian__product,axiom,
% 0.26/0.59 ! [A: set_a,B: set_Pr1986765409at_nat] :
% 0.26/0.59 ( ( finite_finite_a @ A )
% 0.26/0.59 => ( ( finite772653738at_nat @ B )
% 0.26/0.59 => ( finite942416723at_nat
% 0.26/0.59 @ ( produc292491723at_nat @ A
% 0.26/0.59 @ ^ [Uu: a] : B ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % finite_cartesian_product
% 0.26/0.59 thf(fact_86_finite__cartesian__product,axiom,
% 0.26/0.59 ! [A: set_nat,B: set_Product_prod_a_a] :
% 0.26/0.59 ( ( finite_finite_nat @ A )
% 0.26/0.59 => ( ( finite179568208od_a_a @ B )
% 0.26/0.59 => ( finite1297454819od_a_a
% 0.26/0.59 @ ( produc1182842125od_a_a @ A
% 0.26/0.59 @ ^ [Uu: nat] : B ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % finite_cartesian_product
% 0.26/0.59 thf(fact_87_finite__cartesian__product,axiom,
% 0.26/0.59 ! [A: set_nat,B: set_Pr1986765409at_nat] :
% 0.26/0.59 ( ( finite_finite_nat @ A )
% 0.26/0.59 => ( ( finite772653738at_nat @ B )
% 0.26/0.59 => ( finite277291581at_nat
% 0.26/0.59 @ ( produc894163943at_nat @ A
% 0.26/0.59 @ ^ [Uu: nat] : B ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % finite_cartesian_product
% 0.26/0.59 thf(fact_88_pair__fin__digraph_Opair__finite__verts,axiom,
% 0.26/0.59 ! [G2: pair_p2041852168t_unit] :
% 0.26/0.59 ( ( pair_p752841413at_nat @ G2 )
% 0.26/0.59 => ( finite772653738at_nat @ ( pair_p210955889t_unit @ G2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % pair_fin_digraph.pair_finite_verts
% 0.26/0.59 thf(fact_89_pair__fin__digraph_Opair__finite__verts,axiom,
% 0.26/0.59 ! [G2: pair_p1593840546t_unit] :
% 0.26/0.59 ( ( pair_p159207083od_a_a @ G2 )
% 0.26/0.59 => ( finite1664988688od_a_a @ ( pair_p1652294923t_unit @ G2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % pair_fin_digraph.pair_finite_verts
% 0.26/0.59 thf(fact_90_pair__fin__digraph_Opair__finite__verts,axiom,
% 0.26/0.59 ! [G2: pair_p125712459t_unit] :
% 0.26/0.59 ( ( pair_p1802376898raph_a @ G2 )
% 0.26/0.59 => ( finite_finite_a @ ( pair_p1047056820t_unit @ G2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % pair_fin_digraph.pair_finite_verts
% 0.26/0.59 thf(fact_91_pair__fin__digraph_Opair__finite__verts,axiom,
% 0.26/0.59 ! [G2: pair_p1914262621t_unit] :
% 0.26/0.59 ( ( pair_p128415500ph_nat @ G2 )
% 0.26/0.59 => ( finite_finite_nat @ ( pair_p1677060310t_unit @ G2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % pair_fin_digraph.pair_finite_verts
% 0.26/0.59 thf(fact_92_pair__fin__digraph_Opair__finite__verts,axiom,
% 0.26/0.59 ! [G2: pair_p1765063010t_unit] :
% 0.26/0.59 ( ( pair_p374947051od_a_a @ G2 )
% 0.26/0.59 => ( finite179568208od_a_a @ ( pair_p447552203t_unit @ G2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % pair_fin_digraph.pair_finite_verts
% 0.26/0.59 thf(fact_93_finite__has__minimal2,axiom,
% 0.26/0.59 ! [A: set_se1596668135od_a_a,A2: set_Product_prod_a_a] :
% 0.26/0.59 ( ( finite1145471536od_a_a @ A )
% 0.26/0.59 => ( ( member1838126896od_a_a @ A2 @ A )
% 0.26/0.59 => ? [X: set_Product_prod_a_a] :
% 0.26/0.59 ( ( member1838126896od_a_a @ X @ A )
% 0.26/0.59 & ( ord_le1824328871od_a_a @ X @ A2 )
% 0.26/0.59 & ! [Xa: set_Product_prod_a_a] :
% 0.26/0.59 ( ( member1838126896od_a_a @ Xa @ A )
% 0.26/0.59 => ( ( ord_le1824328871od_a_a @ Xa @ X )
% 0.26/0.59 => ( X = Xa ) ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % finite_has_minimal2
% 0.26/0.59 thf(fact_94_finite__has__minimal2,axiom,
% 0.26/0.59 ! [A: set_nat,A2: nat] :
% 0.26/0.59 ( ( finite_finite_nat @ A )
% 0.26/0.59 => ( ( member_nat @ A2 @ A )
% 0.26/0.59 => ? [X: nat] :
% 0.26/0.59 ( ( member_nat @ X @ A )
% 0.26/0.59 & ( ord_less_eq_nat @ X @ A2 )
% 0.26/0.59 & ! [Xa: nat] :
% 0.26/0.59 ( ( member_nat @ Xa @ A )
% 0.26/0.59 => ( ( ord_less_eq_nat @ Xa @ X )
% 0.26/0.59 => ( X = Xa ) ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % finite_has_minimal2
% 0.26/0.59 thf(fact_95_finite__has__minimal2,axiom,
% 0.26/0.59 ! [A: set_set_nat,A2: set_nat] :
% 0.26/0.59 ( ( finite2012248349et_nat @ A )
% 0.26/0.59 => ( ( member_set_nat @ A2 @ A )
% 0.26/0.59 => ? [X: set_nat] :
% 0.26/0.59 ( ( member_set_nat @ X @ A )
% 0.26/0.59 & ( ord_less_eq_set_nat @ X @ A2 )
% 0.26/0.59 & ! [Xa: set_nat] :
% 0.26/0.59 ( ( member_set_nat @ Xa @ A )
% 0.26/0.59 => ( ( ord_less_eq_set_nat @ Xa @ X )
% 0.26/0.59 => ( X = Xa ) ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % finite_has_minimal2
% 0.26/0.59 thf(fact_96_finite__has__minimal2,axiom,
% 0.26/0.59 ! [A: set_set_a,A2: set_a] :
% 0.26/0.59 ( ( finite_finite_set_a @ A )
% 0.26/0.59 => ( ( member_set_a @ A2 @ A )
% 0.26/0.59 => ? [X: set_a] :
% 0.26/0.59 ( ( member_set_a @ X @ A )
% 0.26/0.59 & ( ord_less_eq_set_a @ X @ A2 )
% 0.26/0.59 & ! [Xa: set_a] :
% 0.26/0.59 ( ( member_set_a @ Xa @ A )
% 0.26/0.59 => ( ( ord_less_eq_set_a @ Xa @ X )
% 0.26/0.59 => ( X = Xa ) ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % finite_has_minimal2
% 0.26/0.59 thf(fact_97_infinite__cartesian__product,axiom,
% 0.26/0.59 ! [A: set_a,B: set_nat] :
% 0.26/0.59 ( ~ ( finite_finite_a @ A )
% 0.26/0.59 => ( ~ ( finite_finite_nat @ B )
% 0.26/0.59 => ~ ( finite1743148308_a_nat
% 0.26/0.59 @ ( product_Sigma_a_nat @ A
% 0.26/0.59 @ ^ [Uu: a] : B ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % infinite_cartesian_product
% 0.26/0.59 thf(fact_98_infinite__cartesian__product,axiom,
% 0.26/0.59 ! [A: set_nat,B: set_a] :
% 0.26/0.59 ( ~ ( finite_finite_nat @ A )
% 0.26/0.59 => ( ~ ( finite_finite_a @ B )
% 0.26/0.59 => ~ ( finite1808550458_nat_a
% 0.26/0.59 @ ( product_Sigma_nat_a @ A
% 0.26/0.59 @ ^ [Uu: nat] : B ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % infinite_cartesian_product
% 0.26/0.59 thf(fact_99_infinite__cartesian__product,axiom,
% 0.26/0.59 ! [A: set_nat,B: set_nat] :
% 0.26/0.59 ( ~ ( finite_finite_nat @ A )
% 0.26/0.59 => ( ~ ( finite_finite_nat @ B )
% 0.26/0.59 => ~ ( finite772653738at_nat
% 0.26/0.59 @ ( produc45129834at_nat @ A
% 0.26/0.59 @ ^ [Uu: nat] : B ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % infinite_cartesian_product
% 0.26/0.59 thf(fact_100_infinite__cartesian__product,axiom,
% 0.26/0.59 ! [A: set_a,B: set_a] :
% 0.26/0.59 ( ~ ( finite_finite_a @ A )
% 0.26/0.59 => ( ~ ( finite_finite_a @ B )
% 0.26/0.59 => ~ ( finite179568208od_a_a
% 0.26/0.59 @ ( product_Sigma_a_a @ A
% 0.26/0.59 @ ^ [Uu: a] : B ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % infinite_cartesian_product
% 0.26/0.59 thf(fact_101_infinite__cartesian__product,axiom,
% 0.26/0.59 ! [A: set_Product_prod_a_a,B: set_a] :
% 0.26/0.59 ( ~ ( finite179568208od_a_a @ A )
% 0.26/0.59 => ( ~ ( finite_finite_a @ B )
% 0.26/0.59 => ~ ( finite1919032935_a_a_a
% 0.26/0.59 @ ( produc1282482655_a_a_a @ A
% 0.26/0.59 @ ^ [Uu: product_prod_a_a] : B ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % infinite_cartesian_product
% 0.26/0.59 thf(fact_102_infinite__cartesian__product,axiom,
% 0.26/0.59 ! [A: set_Product_prod_a_a,B: set_nat] :
% 0.26/0.59 ( ~ ( finite179568208od_a_a @ A )
% 0.26/0.59 => ( ~ ( finite_finite_nat @ B )
% 0.26/0.59 => ~ ( finite1837575485_a_nat
% 0.26/0.59 @ ( produc931712687_a_nat @ A
% 0.26/0.59 @ ^ [Uu: product_prod_a_a] : B ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % infinite_cartesian_product
% 0.26/0.59 thf(fact_103_infinite__cartesian__product,axiom,
% 0.26/0.59 ! [A: set_a,B: set_Product_prod_a_a] :
% 0.26/0.59 ( ~ ( finite_finite_a @ A )
% 0.26/0.59 => ( ~ ( finite179568208od_a_a @ B )
% 0.26/0.59 => ~ ( finite676513017od_a_a
% 0.26/0.59 @ ( produc520147185od_a_a @ A
% 0.26/0.59 @ ^ [Uu: a] : B ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % infinite_cartesian_product
% 0.26/0.59 thf(fact_104_infinite__cartesian__product,axiom,
% 0.26/0.59 ! [A: set_a,B: set_Pr1986765409at_nat] :
% 0.26/0.59 ( ~ ( finite_finite_a @ A )
% 0.26/0.59 => ( ~ ( finite772653738at_nat @ B )
% 0.26/0.59 => ~ ( finite942416723at_nat
% 0.26/0.59 @ ( produc292491723at_nat @ A
% 0.26/0.59 @ ^ [Uu: a] : B ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % infinite_cartesian_product
% 0.26/0.59 thf(fact_105_infinite__cartesian__product,axiom,
% 0.26/0.59 ! [A: set_nat,B: set_Product_prod_a_a] :
% 0.26/0.59 ( ~ ( finite_finite_nat @ A )
% 0.26/0.59 => ( ~ ( finite179568208od_a_a @ B )
% 0.26/0.59 => ~ ( finite1297454819od_a_a
% 0.26/0.59 @ ( produc1182842125od_a_a @ A
% 0.26/0.59 @ ^ [Uu: nat] : B ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % infinite_cartesian_product
% 0.26/0.59 thf(fact_106_infinite__cartesian__product,axiom,
% 0.26/0.59 ! [A: set_nat,B: set_Pr1986765409at_nat] :
% 0.26/0.59 ( ~ ( finite_finite_nat @ A )
% 0.26/0.59 => ( ~ ( finite772653738at_nat @ B )
% 0.26/0.59 => ~ ( finite277291581at_nat
% 0.26/0.59 @ ( produc894163943at_nat @ A
% 0.26/0.59 @ ^ [Uu: nat] : B ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % infinite_cartesian_product
% 0.26/0.59 thf(fact_107_Times__subset__cancel2,axiom,
% 0.26/0.59 ! [X3: product_prod_a_a,C: set_Product_prod_a_a,A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
% 0.26/0.59 ( ( member449909584od_a_a @ X3 @ C )
% 0.26/0.59 => ( ( ord_le456379495od_a_a
% 0.26/0.59 @ ( produc304751368od_a_a @ A
% 0.26/0.59 @ ^ [Uu: product_prod_a_a] : C )
% 0.26/0.59 @ ( produc304751368od_a_a @ B
% 0.26/0.59 @ ^ [Uu: product_prod_a_a] : C ) )
% 0.26/0.59 = ( ord_le1824328871od_a_a @ A @ B ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Times_subset_cancel2
% 0.26/0.59 thf(fact_108_Times__subset__cancel2,axiom,
% 0.26/0.59 ! [X3: nat,C: set_nat,A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
% 0.26/0.59 ( ( member_nat @ X3 @ C )
% 0.26/0.59 => ( ( ord_le492294332_a_nat
% 0.26/0.59 @ ( produc931712687_a_nat @ A
% 0.26/0.59 @ ^ [Uu: product_prod_a_a] : C )
% 0.26/0.59 @ ( produc931712687_a_nat @ B
% 0.26/0.59 @ ^ [Uu: product_prod_a_a] : C ) )
% 0.26/0.59 = ( ord_le1824328871od_a_a @ A @ B ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Times_subset_cancel2
% 0.26/0.59 thf(fact_109_Times__subset__cancel2,axiom,
% 0.26/0.59 ! [X3: product_prod_a_a,C: set_Product_prod_a_a,A: set_nat,B: set_nat] :
% 0.26/0.59 ( ( member449909584od_a_a @ X3 @ C )
% 0.26/0.59 => ( ( ord_le2084554594od_a_a
% 0.26/0.59 @ ( produc1182842125od_a_a @ A
% 0.26/0.59 @ ^ [Uu: nat] : C )
% 0.26/0.59 @ ( produc1182842125od_a_a @ B
% 0.26/0.59 @ ^ [Uu: nat] : C ) )
% 0.26/0.59 = ( ord_less_eq_set_nat @ A @ B ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Times_subset_cancel2
% 0.26/0.59 thf(fact_110_Times__subset__cancel2,axiom,
% 0.26/0.59 ! [X3: nat,C: set_nat,A: set_nat,B: set_nat] :
% 0.26/0.59 ( ( member_nat @ X3 @ C )
% 0.26/0.59 => ( ( ord_le841296385at_nat
% 0.26/0.59 @ ( produc45129834at_nat @ A
% 0.26/0.59 @ ^ [Uu: nat] : C )
% 0.26/0.59 @ ( produc45129834at_nat @ B
% 0.26/0.59 @ ^ [Uu: nat] : C ) )
% 0.26/0.59 = ( ord_less_eq_set_nat @ A @ B ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Times_subset_cancel2
% 0.26/0.59 thf(fact_111_Times__subset__cancel2,axiom,
% 0.26/0.59 ! [X3: product_prod_a_a,C: set_Product_prod_a_a,A: set_a,B: set_a] :
% 0.26/0.59 ( ( member449909584od_a_a @ X3 @ C )
% 0.26/0.59 => ( ( ord_le1816232656od_a_a
% 0.26/0.59 @ ( produc520147185od_a_a @ A
% 0.26/0.59 @ ^ [Uu: a] : C )
% 0.26/0.59 @ ( produc520147185od_a_a @ B
% 0.26/0.59 @ ^ [Uu: a] : C ) )
% 0.26/0.59 = ( ord_less_eq_set_a @ A @ B ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Times_subset_cancel2
% 0.26/0.59 thf(fact_112_Times__subset__cancel2,axiom,
% 0.26/0.59 ! [X3: nat,C: set_nat,A: set_a,B: set_a] :
% 0.26/0.59 ( ( member_nat @ X3 @ C )
% 0.26/0.59 => ( ( ord_le2073555219_a_nat
% 0.26/0.59 @ ( product_Sigma_a_nat @ A
% 0.26/0.59 @ ^ [Uu: a] : C )
% 0.26/0.59 @ ( product_Sigma_a_nat @ B
% 0.26/0.59 @ ^ [Uu: a] : C ) )
% 0.26/0.59 = ( ord_less_eq_set_a @ A @ B ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Times_subset_cancel2
% 0.26/0.59 thf(fact_113_Times__subset__cancel2,axiom,
% 0.26/0.59 ! [X3: a,C: set_a,A: set_a,B: set_a] :
% 0.26/0.59 ( ( member_a @ X3 @ C )
% 0.26/0.59 => ( ( ord_le1824328871od_a_a
% 0.26/0.59 @ ( product_Sigma_a_a @ A
% 0.26/0.59 @ ^ [Uu: a] : C )
% 0.26/0.59 @ ( product_Sigma_a_a @ B
% 0.26/0.59 @ ^ [Uu: a] : C ) )
% 0.26/0.59 = ( ord_less_eq_set_a @ A @ B ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Times_subset_cancel2
% 0.26/0.59 thf(fact_114_Sigma__mono,axiom,
% 0.26/0.59 ! [A: set_Product_prod_a_a,C: set_Product_prod_a_a,B: product_prod_a_a > set_Product_prod_a_a,D: product_prod_a_a > set_Product_prod_a_a] :
% 0.26/0.59 ( ( ord_le1824328871od_a_a @ A @ C )
% 0.26/0.59 => ( ! [X: product_prod_a_a] :
% 0.26/0.59 ( ( member449909584od_a_a @ X @ A )
% 0.26/0.59 => ( ord_le1824328871od_a_a @ ( B @ X ) @ ( D @ X ) ) )
% 0.26/0.59 => ( ord_le456379495od_a_a @ ( produc304751368od_a_a @ A @ B ) @ ( produc304751368od_a_a @ C @ D ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Sigma_mono
% 0.26/0.59 thf(fact_115_Sigma__mono,axiom,
% 0.26/0.59 ! [A: set_Product_prod_a_a,C: set_Product_prod_a_a,B: product_prod_a_a > set_nat,D: product_prod_a_a > set_nat] :
% 0.26/0.59 ( ( ord_le1824328871od_a_a @ A @ C )
% 0.26/0.59 => ( ! [X: product_prod_a_a] :
% 0.26/0.59 ( ( member449909584od_a_a @ X @ A )
% 0.26/0.59 => ( ord_less_eq_set_nat @ ( B @ X ) @ ( D @ X ) ) )
% 0.26/0.59 => ( ord_le492294332_a_nat @ ( produc931712687_a_nat @ A @ B ) @ ( produc931712687_a_nat @ C @ D ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Sigma_mono
% 0.26/0.59 thf(fact_116_Sigma__mono,axiom,
% 0.26/0.59 ! [A: set_Product_prod_a_a,C: set_Product_prod_a_a,B: product_prod_a_a > set_a,D: product_prod_a_a > set_a] :
% 0.26/0.59 ( ( ord_le1824328871od_a_a @ A @ C )
% 0.26/0.59 => ( ! [X: product_prod_a_a] :
% 0.26/0.59 ( ( member449909584od_a_a @ X @ A )
% 0.26/0.59 => ( ord_less_eq_set_a @ ( B @ X ) @ ( D @ X ) ) )
% 0.26/0.59 => ( ord_le677315902_a_a_a @ ( produc1282482655_a_a_a @ A @ B ) @ ( produc1282482655_a_a_a @ C @ D ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Sigma_mono
% 0.26/0.59 thf(fact_117_Sigma__mono,axiom,
% 0.26/0.59 ! [A: set_nat,C: set_nat,B: nat > set_Product_prod_a_a,D: nat > set_Product_prod_a_a] :
% 0.26/0.59 ( ( ord_less_eq_set_nat @ A @ C )
% 0.26/0.59 => ( ! [X: nat] :
% 0.26/0.59 ( ( member_nat @ X @ A )
% 0.26/0.59 => ( ord_le1824328871od_a_a @ ( B @ X ) @ ( D @ X ) ) )
% 0.26/0.59 => ( ord_le2084554594od_a_a @ ( produc1182842125od_a_a @ A @ B ) @ ( produc1182842125od_a_a @ C @ D ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Sigma_mono
% 0.26/0.59 thf(fact_118_Sigma__mono,axiom,
% 0.26/0.59 ! [A: set_nat,C: set_nat,B: nat > set_nat,D: nat > set_nat] :
% 0.26/0.59 ( ( ord_less_eq_set_nat @ A @ C )
% 0.26/0.59 => ( ! [X: nat] :
% 0.26/0.59 ( ( member_nat @ X @ A )
% 0.26/0.59 => ( ord_less_eq_set_nat @ ( B @ X ) @ ( D @ X ) ) )
% 0.26/0.59 => ( ord_le841296385at_nat @ ( produc45129834at_nat @ A @ B ) @ ( produc45129834at_nat @ C @ D ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Sigma_mono
% 0.26/0.59 thf(fact_119_Sigma__mono,axiom,
% 0.26/0.59 ! [A: set_nat,C: set_nat,B: nat > set_a,D: nat > set_a] :
% 0.26/0.59 ( ( ord_less_eq_set_nat @ A @ C )
% 0.26/0.59 => ( ! [X: nat] :
% 0.26/0.59 ( ( member_nat @ X @ A )
% 0.26/0.59 => ( ord_less_eq_set_a @ ( B @ X ) @ ( D @ X ) ) )
% 0.26/0.59 => ( ord_le344568633_nat_a @ ( product_Sigma_nat_a @ A @ B ) @ ( product_Sigma_nat_a @ C @ D ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Sigma_mono
% 0.26/0.59 thf(fact_120_Sigma__mono,axiom,
% 0.26/0.59 ! [A: set_a,C: set_a,B: a > set_Product_prod_a_a,D: a > set_Product_prod_a_a] :
% 0.26/0.59 ( ( ord_less_eq_set_a @ A @ C )
% 0.26/0.59 => ( ! [X: a] :
% 0.26/0.59 ( ( member_a @ X @ A )
% 0.26/0.59 => ( ord_le1824328871od_a_a @ ( B @ X ) @ ( D @ X ) ) )
% 0.26/0.59 => ( ord_le1816232656od_a_a @ ( produc520147185od_a_a @ A @ B ) @ ( produc520147185od_a_a @ C @ D ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Sigma_mono
% 0.26/0.59 thf(fact_121_Sigma__mono,axiom,
% 0.26/0.59 ! [A: set_a,C: set_a,B: a > set_nat,D: a > set_nat] :
% 0.26/0.59 ( ( ord_less_eq_set_a @ A @ C )
% 0.26/0.59 => ( ! [X: a] :
% 0.26/0.59 ( ( member_a @ X @ A )
% 0.26/0.59 => ( ord_less_eq_set_nat @ ( B @ X ) @ ( D @ X ) ) )
% 0.26/0.59 => ( ord_le2073555219_a_nat @ ( product_Sigma_a_nat @ A @ B ) @ ( product_Sigma_a_nat @ C @ D ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Sigma_mono
% 0.26/0.59 thf(fact_122_Sigma__mono,axiom,
% 0.26/0.59 ! [A: set_a,C: set_a,B: a > set_a,D: a > set_a] :
% 0.26/0.59 ( ( ord_less_eq_set_a @ A @ C )
% 0.26/0.59 => ( ! [X: a] :
% 0.26/0.59 ( ( member_a @ X @ A )
% 0.26/0.59 => ( ord_less_eq_set_a @ ( B @ X ) @ ( D @ X ) ) )
% 0.26/0.59 => ( ord_le1824328871od_a_a @ ( product_Sigma_a_a @ A @ B ) @ ( product_Sigma_a_a @ C @ D ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Sigma_mono
% 0.26/0.59 thf(fact_123_subsetI,axiom,
% 0.26/0.59 ! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
% 0.26/0.59 ( ! [X: product_prod_a_a] :
% 0.26/0.59 ( ( member449909584od_a_a @ X @ A )
% 0.26/0.59 => ( member449909584od_a_a @ X @ B ) )
% 0.26/0.59 => ( ord_le1824328871od_a_a @ A @ B ) ) ).
% 0.26/0.59
% 0.26/0.59 % subsetI
% 0.26/0.59 thf(fact_124_subsetI,axiom,
% 0.26/0.59 ! [A: set_nat,B: set_nat] :
% 0.26/0.59 ( ! [X: nat] :
% 0.26/0.59 ( ( member_nat @ X @ A )
% 0.26/0.59 => ( member_nat @ X @ B ) )
% 0.26/0.59 => ( ord_less_eq_set_nat @ A @ B ) ) ).
% 0.26/0.59
% 0.26/0.59 % subsetI
% 0.26/0.59 thf(fact_125_subsetI,axiom,
% 0.26/0.59 ! [A: set_a,B: set_a] :
% 0.26/0.59 ( ! [X: a] :
% 0.26/0.59 ( ( member_a @ X @ A )
% 0.26/0.59 => ( member_a @ X @ B ) )
% 0.26/0.59 => ( ord_less_eq_set_a @ A @ B ) ) ).
% 0.26/0.59
% 0.26/0.59 % subsetI
% 0.26/0.59 thf(fact_126_subset__antisym,axiom,
% 0.26/0.59 ! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
% 0.26/0.59 ( ( ord_le1824328871od_a_a @ A @ B )
% 0.26/0.59 => ( ( ord_le1824328871od_a_a @ B @ A )
% 0.26/0.59 => ( A = B ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % subset_antisym
% 0.26/0.59 thf(fact_127_subset__antisym,axiom,
% 0.26/0.59 ! [A: set_nat,B: set_nat] :
% 0.26/0.59 ( ( ord_less_eq_set_nat @ A @ B )
% 0.26/0.59 => ( ( ord_less_eq_set_nat @ B @ A )
% 0.26/0.59 => ( A = B ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % subset_antisym
% 0.26/0.59 thf(fact_128_subset__antisym,axiom,
% 0.26/0.59 ! [A: set_a,B: set_a] :
% 0.26/0.59 ( ( ord_less_eq_set_a @ A @ B )
% 0.26/0.59 => ( ( ord_less_eq_set_a @ B @ A )
% 0.26/0.59 => ( A = B ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % subset_antisym
% 0.26/0.59 thf(fact_129_order__refl,axiom,
% 0.26/0.59 ! [X3: set_Product_prod_a_a] : ( ord_le1824328871od_a_a @ X3 @ X3 ) ).
% 0.26/0.59
% 0.26/0.59 % order_refl
% 0.26/0.59 thf(fact_130_order__refl,axiom,
% 0.26/0.59 ! [X3: nat] : ( ord_less_eq_nat @ X3 @ X3 ) ).
% 0.26/0.59
% 0.26/0.59 % order_refl
% 0.26/0.59 thf(fact_131_order__refl,axiom,
% 0.26/0.59 ! [X3: set_nat] : ( ord_less_eq_set_nat @ X3 @ X3 ) ).
% 0.26/0.59
% 0.26/0.59 % order_refl
% 0.26/0.59 thf(fact_132_order__refl,axiom,
% 0.26/0.59 ! [X3: set_a] : ( ord_less_eq_set_a @ X3 @ X3 ) ).
% 0.26/0.59
% 0.26/0.59 % order_refl
% 0.26/0.59 thf(fact_133_pair__pre__digraph_Oequality,axiom,
% 0.26/0.59 ! [R2: pair_p125712459t_unit,R3: pair_p125712459t_unit] :
% 0.26/0.59 ( ( ( pair_p1047056820t_unit @ R2 )
% 0.26/0.59 = ( pair_p1047056820t_unit @ R3 ) )
% 0.26/0.59 => ( ( ( pair_p133601421t_unit @ R2 )
% 0.26/0.59 = ( pair_p133601421t_unit @ R3 ) )
% 0.26/0.59 => ( ( ( pair_p1896222615t_unit @ R2 )
% 0.26/0.59 = ( pair_p1896222615t_unit @ R3 ) )
% 0.26/0.59 => ( R2 = R3 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % pair_pre_digraph.equality
% 0.26/0.59 thf(fact_134_pair__pre__digraph_Oequality,axiom,
% 0.26/0.59 ! [R2: pair_p1914262621t_unit,R3: pair_p1914262621t_unit] :
% 0.26/0.59 ( ( ( pair_p1677060310t_unit @ R2 )
% 0.26/0.59 = ( pair_p1677060310t_unit @ R3 ) )
% 0.26/0.59 => ( ( ( pair_p715279805t_unit @ R2 )
% 0.26/0.59 = ( pair_p715279805t_unit @ R3 ) )
% 0.26/0.59 => ( ( ( pair_p69470259t_unit @ R2 )
% 0.26/0.59 = ( pair_p69470259t_unit @ R3 ) )
% 0.26/0.59 => ( R2 = R3 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % pair_pre_digraph.equality
% 0.26/0.59 thf(fact_135_pair__pre__digraph_Oequality,axiom,
% 0.26/0.59 ! [R2: pair_p1765063010t_unit,R3: pair_p1765063010t_unit] :
% 0.26/0.59 ( ( ( pair_p447552203t_unit @ R2 )
% 0.26/0.59 = ( pair_p447552203t_unit @ R3 ) )
% 0.26/0.59 => ( ( ( pair_p1783210148t_unit @ R2 )
% 0.26/0.59 = ( pair_p1783210148t_unit @ R3 ) )
% 0.26/0.59 => ( ( ( pair_p1984658862t_unit @ R2 )
% 0.26/0.59 = ( pair_p1984658862t_unit @ R3 ) )
% 0.26/0.59 => ( R2 = R3 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % pair_pre_digraph.equality
% 0.26/0.59 thf(fact_136_Sigma__cong,axiom,
% 0.26/0.59 ! [A: set_a,B: set_a,C: a > set_a,D: a > set_a] :
% 0.26/0.59 ( ( A = B )
% 0.26/0.59 => ( ! [X: a] :
% 0.26/0.59 ( ( member_a @ X @ B )
% 0.26/0.59 => ( ( C @ X )
% 0.26/0.59 = ( D @ X ) ) )
% 0.26/0.59 => ( ( product_Sigma_a_a @ A @ C )
% 0.26/0.59 = ( product_Sigma_a_a @ B @ D ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Sigma_cong
% 0.26/0.59 thf(fact_137_Times__eq__cancel2,axiom,
% 0.26/0.59 ! [X3: a,C: set_a,A: set_a,B: set_a] :
% 0.26/0.59 ( ( member_a @ X3 @ C )
% 0.26/0.59 => ( ( ( product_Sigma_a_a @ A
% 0.26/0.59 @ ^ [Uu: a] : C )
% 0.26/0.59 = ( product_Sigma_a_a @ B
% 0.26/0.59 @ ^ [Uu: a] : C ) )
% 0.26/0.59 = ( A = B ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Times_eq_cancel2
% 0.26/0.59 thf(fact_138_Collect__subset,axiom,
% 0.26/0.59 ! [A: set_Product_prod_a_a,P: product_prod_a_a > $o] :
% 0.26/0.59 ( ord_le1824328871od_a_a
% 0.26/0.59 @ ( collec645855634od_a_a
% 0.26/0.59 @ ^ [X2: product_prod_a_a] :
% 0.26/0.59 ( ( member449909584od_a_a @ X2 @ A )
% 0.26/0.59 & ( P @ X2 ) ) )
% 0.26/0.59 @ A ) ).
% 0.26/0.59
% 0.26/0.59 % Collect_subset
% 0.26/0.59 thf(fact_139_Collect__subset,axiom,
% 0.26/0.59 ! [A: set_nat,P: nat > $o] :
% 0.26/0.59 ( ord_less_eq_set_nat
% 0.26/0.59 @ ( collect_nat
% 0.26/0.59 @ ^ [X2: nat] :
% 0.26/0.59 ( ( member_nat @ X2 @ A )
% 0.26/0.59 & ( P @ X2 ) ) )
% 0.26/0.59 @ A ) ).
% 0.26/0.59
% 0.26/0.59 % Collect_subset
% 0.26/0.59 thf(fact_140_Collect__subset,axiom,
% 0.26/0.59 ! [A: set_a,P: a > $o] :
% 0.26/0.59 ( ord_less_eq_set_a
% 0.26/0.59 @ ( collect_a
% 0.26/0.59 @ ^ [X2: a] :
% 0.26/0.59 ( ( member_a @ X2 @ A )
% 0.26/0.59 & ( P @ X2 ) ) )
% 0.26/0.59 @ A ) ).
% 0.26/0.59
% 0.26/0.59 % Collect_subset
% 0.26/0.59 thf(fact_141_less__eq__set__def,axiom,
% 0.26/0.59 ( ord_le1824328871od_a_a
% 0.26/0.59 = ( ^ [A5: set_Product_prod_a_a,B2: set_Product_prod_a_a] :
% 0.26/0.59 ( ord_le1347718902_a_a_o
% 0.26/0.59 @ ^ [X2: product_prod_a_a] : ( member449909584od_a_a @ X2 @ A5 )
% 0.26/0.59 @ ^ [X2: product_prod_a_a] : ( member449909584od_a_a @ X2 @ B2 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % less_eq_set_def
% 0.26/0.59 thf(fact_142_less__eq__set__def,axiom,
% 0.26/0.59 ( ord_less_eq_set_nat
% 0.26/0.59 = ( ^ [A5: set_nat,B2: set_nat] :
% 0.26/0.59 ( ord_less_eq_nat_o
% 0.26/0.59 @ ^ [X2: nat] : ( member_nat @ X2 @ A5 )
% 0.26/0.59 @ ^ [X2: nat] : ( member_nat @ X2 @ B2 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % less_eq_set_def
% 0.26/0.59 thf(fact_143_less__eq__set__def,axiom,
% 0.26/0.59 ( ord_less_eq_set_a
% 0.26/0.59 = ( ^ [A5: set_a,B2: set_a] :
% 0.26/0.59 ( ord_less_eq_a_o
% 0.26/0.59 @ ^ [X2: a] : ( member_a @ X2 @ A5 )
% 0.26/0.59 @ ^ [X2: a] : ( member_a @ X2 @ B2 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % less_eq_set_def
% 0.26/0.59 thf(fact_144_dual__order_Oantisym,axiom,
% 0.26/0.59 ! [B3: set_Product_prod_a_a,A2: set_Product_prod_a_a] :
% 0.26/0.59 ( ( ord_le1824328871od_a_a @ B3 @ A2 )
% 0.26/0.59 => ( ( ord_le1824328871od_a_a @ A2 @ B3 )
% 0.26/0.59 => ( A2 = B3 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % dual_order.antisym
% 0.26/0.59 thf(fact_145_dual__order_Oantisym,axiom,
% 0.26/0.59 ! [B3: nat,A2: nat] :
% 0.26/0.59 ( ( ord_less_eq_nat @ B3 @ A2 )
% 0.26/0.59 => ( ( ord_less_eq_nat @ A2 @ B3 )
% 0.26/0.59 => ( A2 = B3 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % dual_order.antisym
% 0.26/0.59 thf(fact_146_dual__order_Oantisym,axiom,
% 0.26/0.59 ! [B3: set_nat,A2: set_nat] :
% 0.26/0.59 ( ( ord_less_eq_set_nat @ B3 @ A2 )
% 0.26/0.59 => ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 0.26/0.59 => ( A2 = B3 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % dual_order.antisym
% 0.26/0.59 thf(fact_147_dual__order_Oantisym,axiom,
% 0.26/0.59 ! [B3: set_a,A2: set_a] :
% 0.26/0.59 ( ( ord_less_eq_set_a @ B3 @ A2 )
% 0.26/0.59 => ( ( ord_less_eq_set_a @ A2 @ B3 )
% 0.26/0.59 => ( A2 = B3 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % dual_order.antisym
% 0.26/0.59 thf(fact_148_dual__order_Oeq__iff,axiom,
% 0.26/0.59 ( ( ^ [Y: set_Product_prod_a_a,Z: set_Product_prod_a_a] : ( Y = Z ) )
% 0.26/0.59 = ( ^ [A4: set_Product_prod_a_a,B4: set_Product_prod_a_a] :
% 0.26/0.59 ( ( ord_le1824328871od_a_a @ B4 @ A4 )
% 0.26/0.59 & ( ord_le1824328871od_a_a @ A4 @ B4 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % dual_order.eq_iff
% 0.26/0.59 thf(fact_149_dual__order_Oeq__iff,axiom,
% 0.26/0.59 ( ( ^ [Y: nat,Z: nat] : ( Y = Z ) )
% 0.26/0.59 = ( ^ [A4: nat,B4: nat] :
% 0.26/0.59 ( ( ord_less_eq_nat @ B4 @ A4 )
% 0.26/0.59 & ( ord_less_eq_nat @ A4 @ B4 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % dual_order.eq_iff
% 0.26/0.59 thf(fact_150_dual__order_Oeq__iff,axiom,
% 0.26/0.59 ( ( ^ [Y: set_nat,Z: set_nat] : ( Y = Z ) )
% 0.26/0.59 = ( ^ [A4: set_nat,B4: set_nat] :
% 0.26/0.59 ( ( ord_less_eq_set_nat @ B4 @ A4 )
% 0.26/0.59 & ( ord_less_eq_set_nat @ A4 @ B4 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % dual_order.eq_iff
% 0.26/0.59 thf(fact_151_dual__order_Oeq__iff,axiom,
% 0.26/0.59 ( ( ^ [Y: set_a,Z: set_a] : ( Y = Z ) )
% 0.26/0.59 = ( ^ [A4: set_a,B4: set_a] :
% 0.26/0.59 ( ( ord_less_eq_set_a @ B4 @ A4 )
% 0.26/0.59 & ( ord_less_eq_set_a @ A4 @ B4 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % dual_order.eq_iff
% 0.26/0.59 thf(fact_152_dual__order_Otrans,axiom,
% 0.26/0.59 ! [B3: set_Product_prod_a_a,A2: set_Product_prod_a_a,C2: set_Product_prod_a_a] :
% 0.26/0.59 ( ( ord_le1824328871od_a_a @ B3 @ A2 )
% 0.26/0.59 => ( ( ord_le1824328871od_a_a @ C2 @ B3 )
% 0.26/0.59 => ( ord_le1824328871od_a_a @ C2 @ A2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % dual_order.trans
% 0.26/0.59 thf(fact_153_dual__order_Otrans,axiom,
% 0.26/0.59 ! [B3: nat,A2: nat,C2: nat] :
% 0.26/0.59 ( ( ord_less_eq_nat @ B3 @ A2 )
% 0.26/0.59 => ( ( ord_less_eq_nat @ C2 @ B3 )
% 0.26/0.59 => ( ord_less_eq_nat @ C2 @ A2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % dual_order.trans
% 0.26/0.59 thf(fact_154_dual__order_Otrans,axiom,
% 0.26/0.59 ! [B3: set_nat,A2: set_nat,C2: set_nat] :
% 0.26/0.59 ( ( ord_less_eq_set_nat @ B3 @ A2 )
% 0.26/0.59 => ( ( ord_less_eq_set_nat @ C2 @ B3 )
% 0.26/0.59 => ( ord_less_eq_set_nat @ C2 @ A2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % dual_order.trans
% 0.26/0.59 thf(fact_155_dual__order_Otrans,axiom,
% 0.26/0.59 ! [B3: set_a,A2: set_a,C2: set_a] :
% 0.26/0.59 ( ( ord_less_eq_set_a @ B3 @ A2 )
% 0.26/0.59 => ( ( ord_less_eq_set_a @ C2 @ B3 )
% 0.26/0.59 => ( ord_less_eq_set_a @ C2 @ A2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % dual_order.trans
% 0.26/0.59 thf(fact_156_linorder__wlog,axiom,
% 0.26/0.59 ! [P: nat > nat > $o,A2: nat,B3: nat] :
% 0.26/0.59 ( ! [A3: nat,B5: nat] :
% 0.26/0.59 ( ( ord_less_eq_nat @ A3 @ B5 )
% 0.26/0.59 => ( P @ A3 @ B5 ) )
% 0.26/0.59 => ( ! [A3: nat,B5: nat] :
% 0.26/0.59 ( ( P @ B5 @ A3 )
% 0.26/0.59 => ( P @ A3 @ B5 ) )
% 0.26/0.59 => ( P @ A2 @ B3 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % linorder_wlog
% 0.26/0.59 thf(fact_157_dual__order_Orefl,axiom,
% 0.26/0.59 ! [A2: set_Product_prod_a_a] : ( ord_le1824328871od_a_a @ A2 @ A2 ) ).
% 0.26/0.59
% 0.26/0.59 % dual_order.refl
% 0.26/0.59 thf(fact_158_dual__order_Orefl,axiom,
% 0.26/0.59 ! [A2: nat] : ( ord_less_eq_nat @ A2 @ A2 ) ).
% 0.26/0.59
% 0.26/0.59 % dual_order.refl
% 0.26/0.59 thf(fact_159_dual__order_Orefl,axiom,
% 0.26/0.59 ! [A2: set_nat] : ( ord_less_eq_set_nat @ A2 @ A2 ) ).
% 0.26/0.59
% 0.26/0.59 % dual_order.refl
% 0.26/0.59 thf(fact_160_dual__order_Orefl,axiom,
% 0.26/0.59 ! [A2: set_a] : ( ord_less_eq_set_a @ A2 @ A2 ) ).
% 0.26/0.59
% 0.26/0.59 % dual_order.refl
% 0.26/0.59 thf(fact_161_order__trans,axiom,
% 0.26/0.59 ! [X3: set_Product_prod_a_a,Y2: set_Product_prod_a_a,Z2: set_Product_prod_a_a] :
% 0.26/0.59 ( ( ord_le1824328871od_a_a @ X3 @ Y2 )
% 0.26/0.59 => ( ( ord_le1824328871od_a_a @ Y2 @ Z2 )
% 0.26/0.59 => ( ord_le1824328871od_a_a @ X3 @ Z2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % order_trans
% 0.26/0.59 thf(fact_162_order__trans,axiom,
% 0.26/0.59 ! [X3: nat,Y2: nat,Z2: nat] :
% 0.26/0.59 ( ( ord_less_eq_nat @ X3 @ Y2 )
% 0.26/0.59 => ( ( ord_less_eq_nat @ Y2 @ Z2 )
% 0.26/0.59 => ( ord_less_eq_nat @ X3 @ Z2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % order_trans
% 0.26/0.59 thf(fact_163_order__trans,axiom,
% 0.26/0.59 ! [X3: set_nat,Y2: set_nat,Z2: set_nat] :
% 0.26/0.59 ( ( ord_less_eq_set_nat @ X3 @ Y2 )
% 0.26/0.59 => ( ( ord_less_eq_set_nat @ Y2 @ Z2 )
% 0.26/0.59 => ( ord_less_eq_set_nat @ X3 @ Z2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % order_trans
% 0.26/0.59 thf(fact_164_order__trans,axiom,
% 0.26/0.59 ! [X3: set_a,Y2: set_a,Z2: set_a] :
% 0.26/0.59 ( ( ord_less_eq_set_a @ X3 @ Y2 )
% 0.26/0.59 => ( ( ord_less_eq_set_a @ Y2 @ Z2 )
% 0.26/0.59 => ( ord_less_eq_set_a @ X3 @ Z2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % order_trans
% 0.26/0.59 thf(fact_165_order__class_Oorder_Oantisym,axiom,
% 0.26/0.59 ! [A2: set_Product_prod_a_a,B3: set_Product_prod_a_a] :
% 0.26/0.59 ( ( ord_le1824328871od_a_a @ A2 @ B3 )
% 0.26/0.59 => ( ( ord_le1824328871od_a_a @ B3 @ A2 )
% 0.26/0.59 => ( A2 = B3 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % order_class.order.antisym
% 0.26/0.59 thf(fact_166_order__class_Oorder_Oantisym,axiom,
% 0.26/0.59 ! [A2: nat,B3: nat] :
% 0.26/0.59 ( ( ord_less_eq_nat @ A2 @ B3 )
% 0.26/0.59 => ( ( ord_less_eq_nat @ B3 @ A2 )
% 0.26/0.59 => ( A2 = B3 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % order_class.order.antisym
% 0.26/0.59 thf(fact_167_order__class_Oorder_Oantisym,axiom,
% 0.26/0.59 ! [A2: set_nat,B3: set_nat] :
% 0.26/0.59 ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 0.26/0.59 => ( ( ord_less_eq_set_nat @ B3 @ A2 )
% 0.26/0.59 => ( A2 = B3 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % order_class.order.antisym
% 0.26/0.59 thf(fact_168_order__class_Oorder_Oantisym,axiom,
% 0.26/0.59 ! [A2: set_a,B3: set_a] :
% 0.26/0.59 ( ( ord_less_eq_set_a @ A2 @ B3 )
% 0.26/0.59 => ( ( ord_less_eq_set_a @ B3 @ A2 )
% 0.26/0.59 => ( A2 = B3 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % order_class.order.antisym
% 0.26/0.59 thf(fact_169_ord__le__eq__trans,axiom,
% 0.26/0.59 ! [A2: set_Product_prod_a_a,B3: set_Product_prod_a_a,C2: set_Product_prod_a_a] :
% 0.26/0.59 ( ( ord_le1824328871od_a_a @ A2 @ B3 )
% 0.26/0.59 => ( ( B3 = C2 )
% 0.26/0.59 => ( ord_le1824328871od_a_a @ A2 @ C2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % ord_le_eq_trans
% 0.26/0.59 thf(fact_170_ord__le__eq__trans,axiom,
% 0.26/0.59 ! [A2: nat,B3: nat,C2: nat] :
% 0.26/0.59 ( ( ord_less_eq_nat @ A2 @ B3 )
% 0.26/0.59 => ( ( B3 = C2 )
% 0.26/0.59 => ( ord_less_eq_nat @ A2 @ C2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % ord_le_eq_trans
% 0.26/0.59 thf(fact_171_ord__le__eq__trans,axiom,
% 0.26/0.59 ! [A2: set_nat,B3: set_nat,C2: set_nat] :
% 0.26/0.59 ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 0.26/0.59 => ( ( B3 = C2 )
% 0.26/0.59 => ( ord_less_eq_set_nat @ A2 @ C2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % ord_le_eq_trans
% 0.26/0.59 thf(fact_172_ord__le__eq__trans,axiom,
% 0.26/0.59 ! [A2: set_a,B3: set_a,C2: set_a] :
% 0.26/0.59 ( ( ord_less_eq_set_a @ A2 @ B3 )
% 0.26/0.59 => ( ( B3 = C2 )
% 0.26/0.59 => ( ord_less_eq_set_a @ A2 @ C2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % ord_le_eq_trans
% 0.26/0.59 thf(fact_173_mem__Collect__eq,axiom,
% 0.26/0.59 ! [A2: product_prod_a_a,P: product_prod_a_a > $o] :
% 0.26/0.59 ( ( member449909584od_a_a @ A2 @ ( collec645855634od_a_a @ P ) )
% 0.26/0.59 = ( P @ A2 ) ) ).
% 0.26/0.59
% 0.26/0.59 % mem_Collect_eq
% 0.26/0.59 thf(fact_174_mem__Collect__eq,axiom,
% 0.26/0.59 ! [A2: nat,P: nat > $o] :
% 0.26/0.59 ( ( member_nat @ A2 @ ( collect_nat @ P ) )
% 0.26/0.59 = ( P @ A2 ) ) ).
% 0.26/0.59
% 0.26/0.59 % mem_Collect_eq
% 0.26/0.59 thf(fact_175_Collect__mem__eq,axiom,
% 0.26/0.59 ! [A: set_Product_prod_a_a] :
% 0.26/0.59 ( ( collec645855634od_a_a
% 0.26/0.59 @ ^ [X2: product_prod_a_a] : ( member449909584od_a_a @ X2 @ A ) )
% 0.26/0.59 = A ) ).
% 0.26/0.59
% 0.26/0.59 % Collect_mem_eq
% 0.26/0.59 thf(fact_176_Collect__mem__eq,axiom,
% 0.26/0.59 ! [A: set_nat] :
% 0.26/0.59 ( ( collect_nat
% 0.26/0.59 @ ^ [X2: nat] : ( member_nat @ X2 @ A ) )
% 0.26/0.59 = A ) ).
% 0.26/0.59
% 0.26/0.59 % Collect_mem_eq
% 0.26/0.59 thf(fact_177_Collect__cong,axiom,
% 0.26/0.59 ! [P: product_prod_a_a > $o,Q: product_prod_a_a > $o] :
% 0.26/0.59 ( ! [X: product_prod_a_a] :
% 0.26/0.59 ( ( P @ X )
% 0.26/0.59 = ( Q @ X ) )
% 0.26/0.59 => ( ( collec645855634od_a_a @ P )
% 0.26/0.59 = ( collec645855634od_a_a @ Q ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Collect_cong
% 0.26/0.59 thf(fact_178_Collect__cong,axiom,
% 0.26/0.59 ! [P: nat > $o,Q: nat > $o] :
% 0.26/0.59 ( ! [X: nat] :
% 0.26/0.59 ( ( P @ X )
% 0.26/0.59 = ( Q @ X ) )
% 0.26/0.59 => ( ( collect_nat @ P )
% 0.26/0.59 = ( collect_nat @ Q ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Collect_cong
% 0.26/0.59 thf(fact_179_ord__eq__le__trans,axiom,
% 0.26/0.59 ! [A2: set_Product_prod_a_a,B3: set_Product_prod_a_a,C2: set_Product_prod_a_a] :
% 0.26/0.59 ( ( A2 = B3 )
% 0.26/0.59 => ( ( ord_le1824328871od_a_a @ B3 @ C2 )
% 0.26/0.59 => ( ord_le1824328871od_a_a @ A2 @ C2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % ord_eq_le_trans
% 0.26/0.59 thf(fact_180_ord__eq__le__trans,axiom,
% 0.26/0.59 ! [A2: nat,B3: nat,C2: nat] :
% 0.26/0.59 ( ( A2 = B3 )
% 0.26/0.59 => ( ( ord_less_eq_nat @ B3 @ C2 )
% 0.26/0.59 => ( ord_less_eq_nat @ A2 @ C2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % ord_eq_le_trans
% 0.26/0.59 thf(fact_181_ord__eq__le__trans,axiom,
% 0.26/0.59 ! [A2: set_nat,B3: set_nat,C2: set_nat] :
% 0.26/0.59 ( ( A2 = B3 )
% 0.26/0.59 => ( ( ord_less_eq_set_nat @ B3 @ C2 )
% 0.26/0.59 => ( ord_less_eq_set_nat @ A2 @ C2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % ord_eq_le_trans
% 0.26/0.59 thf(fact_182_ord__eq__le__trans,axiom,
% 0.26/0.59 ! [A2: set_a,B3: set_a,C2: set_a] :
% 0.26/0.59 ( ( A2 = B3 )
% 0.26/0.59 => ( ( ord_less_eq_set_a @ B3 @ C2 )
% 0.26/0.59 => ( ord_less_eq_set_a @ A2 @ C2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % ord_eq_le_trans
% 0.26/0.59 thf(fact_183_order__class_Oorder_Oeq__iff,axiom,
% 0.26/0.59 ( ( ^ [Y: set_Product_prod_a_a,Z: set_Product_prod_a_a] : ( Y = Z ) )
% 0.26/0.59 = ( ^ [A4: set_Product_prod_a_a,B4: set_Product_prod_a_a] :
% 0.26/0.59 ( ( ord_le1824328871od_a_a @ A4 @ B4 )
% 0.26/0.59 & ( ord_le1824328871od_a_a @ B4 @ A4 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % order_class.order.eq_iff
% 0.26/0.59 thf(fact_184_order__class_Oorder_Oeq__iff,axiom,
% 0.26/0.59 ( ( ^ [Y: nat,Z: nat] : ( Y = Z ) )
% 0.26/0.59 = ( ^ [A4: nat,B4: nat] :
% 0.26/0.59 ( ( ord_less_eq_nat @ A4 @ B4 )
% 0.26/0.59 & ( ord_less_eq_nat @ B4 @ A4 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % order_class.order.eq_iff
% 0.26/0.59 thf(fact_185_order__class_Oorder_Oeq__iff,axiom,
% 0.26/0.59 ( ( ^ [Y: set_nat,Z: set_nat] : ( Y = Z ) )
% 0.26/0.59 = ( ^ [A4: set_nat,B4: set_nat] :
% 0.26/0.59 ( ( ord_less_eq_set_nat @ A4 @ B4 )
% 0.26/0.59 & ( ord_less_eq_set_nat @ B4 @ A4 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % order_class.order.eq_iff
% 0.26/0.59 thf(fact_186_order__class_Oorder_Oeq__iff,axiom,
% 0.26/0.59 ( ( ^ [Y: set_a,Z: set_a] : ( Y = Z ) )
% 0.26/0.59 = ( ^ [A4: set_a,B4: set_a] :
% 0.26/0.59 ( ( ord_less_eq_set_a @ A4 @ B4 )
% 0.26/0.59 & ( ord_less_eq_set_a @ B4 @ A4 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % order_class.order.eq_iff
% 0.26/0.59 thf(fact_187_antisym__conv,axiom,
% 0.26/0.59 ! [Y2: set_Product_prod_a_a,X3: set_Product_prod_a_a] :
% 0.26/0.59 ( ( ord_le1824328871od_a_a @ Y2 @ X3 )
% 0.26/0.59 => ( ( ord_le1824328871od_a_a @ X3 @ Y2 )
% 0.26/0.59 = ( X3 = Y2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % antisym_conv
% 0.26/0.59 thf(fact_188_antisym__conv,axiom,
% 0.26/0.59 ! [Y2: nat,X3: nat] :
% 0.26/0.59 ( ( ord_less_eq_nat @ Y2 @ X3 )
% 0.26/0.59 => ( ( ord_less_eq_nat @ X3 @ Y2 )
% 0.26/0.59 = ( X3 = Y2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % antisym_conv
% 0.26/0.59 thf(fact_189_antisym__conv,axiom,
% 0.26/0.59 ! [Y2: set_nat,X3: set_nat] :
% 0.26/0.59 ( ( ord_less_eq_set_nat @ Y2 @ X3 )
% 0.26/0.59 => ( ( ord_less_eq_set_nat @ X3 @ Y2 )
% 0.26/0.59 = ( X3 = Y2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % antisym_conv
% 0.26/0.59 thf(fact_190_antisym__conv,axiom,
% 0.26/0.59 ! [Y2: set_a,X3: set_a] :
% 0.26/0.59 ( ( ord_less_eq_set_a @ Y2 @ X3 )
% 0.26/0.59 => ( ( ord_less_eq_set_a @ X3 @ Y2 )
% 0.26/0.59 = ( X3 = Y2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % antisym_conv
% 0.26/0.59 thf(fact_191_le__cases3,axiom,
% 0.26/0.59 ! [X3: nat,Y2: nat,Z2: nat] :
% 0.26/0.59 ( ( ( ord_less_eq_nat @ X3 @ Y2 )
% 0.26/0.59 => ~ ( ord_less_eq_nat @ Y2 @ Z2 ) )
% 0.26/0.59 => ( ( ( ord_less_eq_nat @ Y2 @ X3 )
% 0.26/0.59 => ~ ( ord_less_eq_nat @ X3 @ Z2 ) )
% 0.26/0.59 => ( ( ( ord_less_eq_nat @ X3 @ Z2 )
% 0.26/0.59 => ~ ( ord_less_eq_nat @ Z2 @ Y2 ) )
% 0.26/0.59 => ( ( ( ord_less_eq_nat @ Z2 @ Y2 )
% 0.26/0.59 => ~ ( ord_less_eq_nat @ Y2 @ X3 ) )
% 0.26/0.59 => ( ( ( ord_less_eq_nat @ Y2 @ Z2 )
% 0.26/0.59 => ~ ( ord_less_eq_nat @ Z2 @ X3 ) )
% 0.26/0.59 => ~ ( ( ord_less_eq_nat @ Z2 @ X3 )
% 0.26/0.59 => ~ ( ord_less_eq_nat @ X3 @ Y2 ) ) ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % le_cases3
% 0.26/0.59 thf(fact_192_order_Otrans,axiom,
% 0.26/0.59 ! [A2: set_Product_prod_a_a,B3: set_Product_prod_a_a,C2: set_Product_prod_a_a] :
% 0.26/0.59 ( ( ord_le1824328871od_a_a @ A2 @ B3 )
% 0.26/0.59 => ( ( ord_le1824328871od_a_a @ B3 @ C2 )
% 0.26/0.59 => ( ord_le1824328871od_a_a @ A2 @ C2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % order.trans
% 0.26/0.59 thf(fact_193_order_Otrans,axiom,
% 0.26/0.59 ! [A2: nat,B3: nat,C2: nat] :
% 0.26/0.59 ( ( ord_less_eq_nat @ A2 @ B3 )
% 0.26/0.59 => ( ( ord_less_eq_nat @ B3 @ C2 )
% 0.26/0.59 => ( ord_less_eq_nat @ A2 @ C2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % order.trans
% 0.26/0.59 thf(fact_194_order_Otrans,axiom,
% 0.26/0.59 ! [A2: set_nat,B3: set_nat,C2: set_nat] :
% 0.26/0.59 ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 0.26/0.59 => ( ( ord_less_eq_set_nat @ B3 @ C2 )
% 0.26/0.59 => ( ord_less_eq_set_nat @ A2 @ C2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % order.trans
% 0.26/0.59 thf(fact_195_order_Otrans,axiom,
% 0.26/0.59 ! [A2: set_a,B3: set_a,C2: set_a] :
% 0.26/0.59 ( ( ord_less_eq_set_a @ A2 @ B3 )
% 0.26/0.59 => ( ( ord_less_eq_set_a @ B3 @ C2 )
% 0.26/0.59 => ( ord_less_eq_set_a @ A2 @ C2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % order.trans
% 0.26/0.59 thf(fact_196_le__cases,axiom,
% 0.26/0.59 ! [X3: nat,Y2: nat] :
% 0.26/0.59 ( ~ ( ord_less_eq_nat @ X3 @ Y2 )
% 0.26/0.59 => ( ord_less_eq_nat @ Y2 @ X3 ) ) ).
% 0.26/0.59
% 0.26/0.59 % le_cases
% 0.26/0.59 thf(fact_197_eq__refl,axiom,
% 0.26/0.59 ! [X3: set_Product_prod_a_a,Y2: set_Product_prod_a_a] :
% 0.26/0.59 ( ( X3 = Y2 )
% 0.26/0.59 => ( ord_le1824328871od_a_a @ X3 @ Y2 ) ) ).
% 0.26/0.59
% 0.26/0.59 % eq_refl
% 0.26/0.59 thf(fact_198_eq__refl,axiom,
% 0.26/0.59 ! [X3: nat,Y2: nat] :
% 0.26/0.59 ( ( X3 = Y2 )
% 0.26/0.59 => ( ord_less_eq_nat @ X3 @ Y2 ) ) ).
% 0.26/0.59
% 0.26/0.59 % eq_refl
% 0.26/0.59 thf(fact_199_eq__refl,axiom,
% 0.26/0.59 ! [X3: set_nat,Y2: set_nat] :
% 0.26/0.59 ( ( X3 = Y2 )
% 0.26/0.59 => ( ord_less_eq_set_nat @ X3 @ Y2 ) ) ).
% 0.26/0.59
% 0.26/0.59 % eq_refl
% 0.26/0.59 thf(fact_200_eq__refl,axiom,
% 0.26/0.59 ! [X3: set_a,Y2: set_a] :
% 0.26/0.59 ( ( X3 = Y2 )
% 0.26/0.59 => ( ord_less_eq_set_a @ X3 @ Y2 ) ) ).
% 0.26/0.59
% 0.26/0.59 % eq_refl
% 0.26/0.59 thf(fact_201_linear,axiom,
% 0.26/0.59 ! [X3: nat,Y2: nat] :
% 0.26/0.59 ( ( ord_less_eq_nat @ X3 @ Y2 )
% 0.26/0.59 | ( ord_less_eq_nat @ Y2 @ X3 ) ) ).
% 0.26/0.59
% 0.26/0.59 % linear
% 0.26/0.59 thf(fact_202_antisym,axiom,
% 0.26/0.59 ! [X3: set_Product_prod_a_a,Y2: set_Product_prod_a_a] :
% 0.26/0.59 ( ( ord_le1824328871od_a_a @ X3 @ Y2 )
% 0.26/0.59 => ( ( ord_le1824328871od_a_a @ Y2 @ X3 )
% 0.26/0.59 => ( X3 = Y2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % antisym
% 0.26/0.59 thf(fact_203_antisym,axiom,
% 0.26/0.59 ! [X3: nat,Y2: nat] :
% 0.26/0.59 ( ( ord_less_eq_nat @ X3 @ Y2 )
% 0.26/0.59 => ( ( ord_less_eq_nat @ Y2 @ X3 )
% 0.26/0.59 => ( X3 = Y2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % antisym
% 0.26/0.59 thf(fact_204_antisym,axiom,
% 0.26/0.59 ! [X3: set_nat,Y2: set_nat] :
% 0.26/0.59 ( ( ord_less_eq_set_nat @ X3 @ Y2 )
% 0.26/0.59 => ( ( ord_less_eq_set_nat @ Y2 @ X3 )
% 0.26/0.59 => ( X3 = Y2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % antisym
% 0.26/0.59 thf(fact_205_antisym,axiom,
% 0.26/0.59 ! [X3: set_a,Y2: set_a] :
% 0.26/0.59 ( ( ord_less_eq_set_a @ X3 @ Y2 )
% 0.26/0.59 => ( ( ord_less_eq_set_a @ Y2 @ X3 )
% 0.26/0.59 => ( X3 = Y2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % antisym
% 0.26/0.59 thf(fact_206_eq__iff,axiom,
% 0.26/0.59 ( ( ^ [Y: set_Product_prod_a_a,Z: set_Product_prod_a_a] : ( Y = Z ) )
% 0.26/0.59 = ( ^ [X2: set_Product_prod_a_a,Y3: set_Product_prod_a_a] :
% 0.26/0.59 ( ( ord_le1824328871od_a_a @ X2 @ Y3 )
% 0.26/0.59 & ( ord_le1824328871od_a_a @ Y3 @ X2 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % eq_iff
% 0.26/0.59 thf(fact_207_eq__iff,axiom,
% 0.26/0.59 ( ( ^ [Y: nat,Z: nat] : ( Y = Z ) )
% 0.26/0.59 = ( ^ [X2: nat,Y3: nat] :
% 0.26/0.59 ( ( ord_less_eq_nat @ X2 @ Y3 )
% 0.26/0.59 & ( ord_less_eq_nat @ Y3 @ X2 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % eq_iff
% 0.26/0.59 thf(fact_208_eq__iff,axiom,
% 0.26/0.59 ( ( ^ [Y: set_nat,Z: set_nat] : ( Y = Z ) )
% 0.26/0.59 = ( ^ [X2: set_nat,Y3: set_nat] :
% 0.26/0.59 ( ( ord_less_eq_set_nat @ X2 @ Y3 )
% 0.26/0.59 & ( ord_less_eq_set_nat @ Y3 @ X2 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % eq_iff
% 0.26/0.59 thf(fact_209_eq__iff,axiom,
% 0.26/0.59 ( ( ^ [Y: set_a,Z: set_a] : ( Y = Z ) )
% 0.26/0.59 = ( ^ [X2: set_a,Y3: set_a] :
% 0.26/0.59 ( ( ord_less_eq_set_a @ X2 @ Y3 )
% 0.26/0.59 & ( ord_less_eq_set_a @ Y3 @ X2 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % eq_iff
% 0.26/0.59 thf(fact_210_ord__le__eq__subst,axiom,
% 0.26/0.59 ! [A2: nat,B3: nat,F: nat > nat,C2: nat] :
% 0.26/0.59 ( ( ord_less_eq_nat @ A2 @ B3 )
% 0.26/0.59 => ( ( ( F @ B3 )
% 0.26/0.59 = C2 )
% 0.26/0.59 => ( ! [X: nat,Y4: nat] :
% 0.26/0.59 ( ( ord_less_eq_nat @ X @ Y4 )
% 0.26/0.59 => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.26/0.59 => ( ord_less_eq_nat @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % ord_le_eq_subst
% 0.26/0.59 thf(fact_211_ord__le__eq__subst,axiom,
% 0.26/0.59 ! [A2: nat,B3: nat,F: nat > set_nat,C2: set_nat] :
% 0.26/0.59 ( ( ord_less_eq_nat @ A2 @ B3 )
% 0.26/0.59 => ( ( ( F @ B3 )
% 0.26/0.59 = C2 )
% 0.26/0.59 => ( ! [X: nat,Y4: nat] :
% 0.26/0.59 ( ( ord_less_eq_nat @ X @ Y4 )
% 0.26/0.59 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.26/0.59 => ( ord_less_eq_set_nat @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % ord_le_eq_subst
% 0.26/0.59 thf(fact_212_ord__le__eq__subst,axiom,
% 0.26/0.59 ! [A2: nat,B3: nat,F: nat > set_a,C2: set_a] :
% 0.26/0.59 ( ( ord_less_eq_nat @ A2 @ B3 )
% 0.26/0.59 => ( ( ( F @ B3 )
% 0.26/0.59 = C2 )
% 0.26/0.59 => ( ! [X: nat,Y4: nat] :
% 0.26/0.59 ( ( ord_less_eq_nat @ X @ Y4 )
% 0.26/0.59 => ( ord_less_eq_set_a @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.26/0.59 => ( ord_less_eq_set_a @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % ord_le_eq_subst
% 0.26/0.59 thf(fact_213_ord__le__eq__subst,axiom,
% 0.26/0.59 ! [A2: set_nat,B3: set_nat,F: set_nat > nat,C2: nat] :
% 0.26/0.59 ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 0.26/0.59 => ( ( ( F @ B3 )
% 0.26/0.59 = C2 )
% 0.26/0.59 => ( ! [X: set_nat,Y4: set_nat] :
% 0.26/0.59 ( ( ord_less_eq_set_nat @ X @ Y4 )
% 0.26/0.59 => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.26/0.59 => ( ord_less_eq_nat @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % ord_le_eq_subst
% 0.26/0.59 thf(fact_214_ord__le__eq__subst,axiom,
% 0.26/0.59 ! [A2: set_a,B3: set_a,F: set_a > nat,C2: nat] :
% 0.26/0.59 ( ( ord_less_eq_set_a @ A2 @ B3 )
% 0.26/0.59 => ( ( ( F @ B3 )
% 0.26/0.59 = C2 )
% 0.26/0.59 => ( ! [X: set_a,Y4: set_a] :
% 0.26/0.59 ( ( ord_less_eq_set_a @ X @ Y4 )
% 0.26/0.59 => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.26/0.59 => ( ord_less_eq_nat @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % ord_le_eq_subst
% 0.26/0.59 thf(fact_215_ord__le__eq__subst,axiom,
% 0.26/0.59 ! [A2: set_nat,B3: set_nat,F: set_nat > set_nat,C2: set_nat] :
% 0.26/0.59 ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 0.26/0.59 => ( ( ( F @ B3 )
% 0.26/0.59 = C2 )
% 0.26/0.59 => ( ! [X: set_nat,Y4: set_nat] :
% 0.26/0.59 ( ( ord_less_eq_set_nat @ X @ Y4 )
% 0.26/0.59 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.26/0.59 => ( ord_less_eq_set_nat @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % ord_le_eq_subst
% 0.26/0.59 thf(fact_216_ord__le__eq__subst,axiom,
% 0.26/0.59 ! [A2: set_nat,B3: set_nat,F: set_nat > set_a,C2: set_a] :
% 0.26/0.59 ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 0.26/0.59 => ( ( ( F @ B3 )
% 0.26/0.59 = C2 )
% 0.26/0.59 => ( ! [X: set_nat,Y4: set_nat] :
% 0.26/0.59 ( ( ord_less_eq_set_nat @ X @ Y4 )
% 0.26/0.59 => ( ord_less_eq_set_a @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.26/0.59 => ( ord_less_eq_set_a @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % ord_le_eq_subst
% 0.26/0.59 thf(fact_217_ord__le__eq__subst,axiom,
% 0.26/0.59 ! [A2: set_a,B3: set_a,F: set_a > set_nat,C2: set_nat] :
% 0.26/0.59 ( ( ord_less_eq_set_a @ A2 @ B3 )
% 0.26/0.59 => ( ( ( F @ B3 )
% 0.26/0.59 = C2 )
% 0.26/0.59 => ( ! [X: set_a,Y4: set_a] :
% 0.26/0.59 ( ( ord_less_eq_set_a @ X @ Y4 )
% 0.26/0.59 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.26/0.59 => ( ord_less_eq_set_nat @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % ord_le_eq_subst
% 0.26/0.59 thf(fact_218_ord__le__eq__subst,axiom,
% 0.26/0.59 ! [A2: set_a,B3: set_a,F: set_a > set_a,C2: set_a] :
% 0.26/0.59 ( ( ord_less_eq_set_a @ A2 @ B3 )
% 0.26/0.59 => ( ( ( F @ B3 )
% 0.26/0.59 = C2 )
% 0.26/0.59 => ( ! [X: set_a,Y4: set_a] :
% 0.26/0.59 ( ( ord_less_eq_set_a @ X @ Y4 )
% 0.26/0.59 => ( ord_less_eq_set_a @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.26/0.59 => ( ord_less_eq_set_a @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % ord_le_eq_subst
% 0.26/0.59 thf(fact_219_ord__le__eq__subst,axiom,
% 0.26/0.59 ! [A2: set_Product_prod_a_a,B3: set_Product_prod_a_a,F: set_Product_prod_a_a > nat,C2: nat] :
% 0.26/0.59 ( ( ord_le1824328871od_a_a @ A2 @ B3 )
% 0.26/0.59 => ( ( ( F @ B3 )
% 0.26/0.59 = C2 )
% 0.26/0.59 => ( ! [X: set_Product_prod_a_a,Y4: set_Product_prod_a_a] :
% 0.26/0.59 ( ( ord_le1824328871od_a_a @ X @ Y4 )
% 0.26/0.59 => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.26/0.59 => ( ord_less_eq_nat @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % ord_le_eq_subst
% 0.26/0.59 thf(fact_220_ord__eq__le__subst,axiom,
% 0.26/0.59 ! [A2: nat,F: nat > nat,B3: nat,C2: nat] :
% 0.26/0.59 ( ( A2
% 0.26/0.59 = ( F @ B3 ) )
% 0.26/0.59 => ( ( ord_less_eq_nat @ B3 @ C2 )
% 0.26/0.59 => ( ! [X: nat,Y4: nat] :
% 0.26/0.59 ( ( ord_less_eq_nat @ X @ Y4 )
% 0.26/0.59 => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.26/0.59 => ( ord_less_eq_nat @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % ord_eq_le_subst
% 0.26/0.59 thf(fact_221_ord__eq__le__subst,axiom,
% 0.26/0.59 ! [A2: set_nat,F: nat > set_nat,B3: nat,C2: nat] :
% 0.26/0.59 ( ( A2
% 0.26/0.59 = ( F @ B3 ) )
% 0.26/0.59 => ( ( ord_less_eq_nat @ B3 @ C2 )
% 0.26/0.59 => ( ! [X: nat,Y4: nat] :
% 0.26/0.59 ( ( ord_less_eq_nat @ X @ Y4 )
% 0.26/0.59 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.26/0.59 => ( ord_less_eq_set_nat @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % ord_eq_le_subst
% 0.26/0.59 thf(fact_222_ord__eq__le__subst,axiom,
% 0.26/0.59 ! [A2: set_a,F: nat > set_a,B3: nat,C2: nat] :
% 0.26/0.59 ( ( A2
% 0.26/0.59 = ( F @ B3 ) )
% 0.26/0.59 => ( ( ord_less_eq_nat @ B3 @ C2 )
% 0.26/0.59 => ( ! [X: nat,Y4: nat] :
% 0.26/0.59 ( ( ord_less_eq_nat @ X @ Y4 )
% 0.26/0.59 => ( ord_less_eq_set_a @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.26/0.59 => ( ord_less_eq_set_a @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % ord_eq_le_subst
% 0.26/0.59 thf(fact_223_ord__eq__le__subst,axiom,
% 0.26/0.59 ! [A2: nat,F: set_nat > nat,B3: set_nat,C2: set_nat] :
% 0.26/0.59 ( ( A2
% 0.26/0.59 = ( F @ B3 ) )
% 0.26/0.59 => ( ( ord_less_eq_set_nat @ B3 @ C2 )
% 0.26/0.59 => ( ! [X: set_nat,Y4: set_nat] :
% 0.26/0.59 ( ( ord_less_eq_set_nat @ X @ Y4 )
% 0.26/0.59 => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.26/0.59 => ( ord_less_eq_nat @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % ord_eq_le_subst
% 0.26/0.59 thf(fact_224_ord__eq__le__subst,axiom,
% 0.26/0.59 ! [A2: nat,F: set_a > nat,B3: set_a,C2: set_a] :
% 0.26/0.59 ( ( A2
% 0.26/0.59 = ( F @ B3 ) )
% 0.26/0.59 => ( ( ord_less_eq_set_a @ B3 @ C2 )
% 0.26/0.59 => ( ! [X: set_a,Y4: set_a] :
% 0.26/0.59 ( ( ord_less_eq_set_a @ X @ Y4 )
% 0.26/0.59 => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.26/0.59 => ( ord_less_eq_nat @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % ord_eq_le_subst
% 0.26/0.59 thf(fact_225_ord__eq__le__subst,axiom,
% 0.26/0.59 ! [A2: set_nat,F: set_nat > set_nat,B3: set_nat,C2: set_nat] :
% 0.26/0.59 ( ( A2
% 0.26/0.59 = ( F @ B3 ) )
% 0.26/0.59 => ( ( ord_less_eq_set_nat @ B3 @ C2 )
% 0.26/0.59 => ( ! [X: set_nat,Y4: set_nat] :
% 0.26/0.59 ( ( ord_less_eq_set_nat @ X @ Y4 )
% 0.26/0.59 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.26/0.59 => ( ord_less_eq_set_nat @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % ord_eq_le_subst
% 0.26/0.59 thf(fact_226_ord__eq__le__subst,axiom,
% 0.26/0.59 ! [A2: set_a,F: set_nat > set_a,B3: set_nat,C2: set_nat] :
% 0.26/0.59 ( ( A2
% 0.26/0.59 = ( F @ B3 ) )
% 0.26/0.59 => ( ( ord_less_eq_set_nat @ B3 @ C2 )
% 0.26/0.59 => ( ! [X: set_nat,Y4: set_nat] :
% 0.26/0.59 ( ( ord_less_eq_set_nat @ X @ Y4 )
% 0.26/0.59 => ( ord_less_eq_set_a @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.26/0.59 => ( ord_less_eq_set_a @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % ord_eq_le_subst
% 0.26/0.59 thf(fact_227_ord__eq__le__subst,axiom,
% 0.26/0.59 ! [A2: set_nat,F: set_a > set_nat,B3: set_a,C2: set_a] :
% 0.26/0.59 ( ( A2
% 0.26/0.59 = ( F @ B3 ) )
% 0.26/0.59 => ( ( ord_less_eq_set_a @ B3 @ C2 )
% 0.26/0.59 => ( ! [X: set_a,Y4: set_a] :
% 0.26/0.59 ( ( ord_less_eq_set_a @ X @ Y4 )
% 0.26/0.59 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.26/0.59 => ( ord_less_eq_set_nat @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % ord_eq_le_subst
% 0.26/0.59 thf(fact_228_ord__eq__le__subst,axiom,
% 0.26/0.59 ! [A2: set_a,F: set_a > set_a,B3: set_a,C2: set_a] :
% 0.26/0.59 ( ( A2
% 0.26/0.59 = ( F @ B3 ) )
% 0.26/0.59 => ( ( ord_less_eq_set_a @ B3 @ C2 )
% 0.26/0.59 => ( ! [X: set_a,Y4: set_a] :
% 0.26/0.59 ( ( ord_less_eq_set_a @ X @ Y4 )
% 0.26/0.59 => ( ord_less_eq_set_a @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.26/0.59 => ( ord_less_eq_set_a @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % ord_eq_le_subst
% 0.26/0.59 thf(fact_229_ord__eq__le__subst,axiom,
% 0.26/0.59 ! [A2: nat,F: set_Product_prod_a_a > nat,B3: set_Product_prod_a_a,C2: set_Product_prod_a_a] :
% 0.26/0.59 ( ( A2
% 0.26/0.59 = ( F @ B3 ) )
% 0.26/0.59 => ( ( ord_le1824328871od_a_a @ B3 @ C2 )
% 0.26/0.59 => ( ! [X: set_Product_prod_a_a,Y4: set_Product_prod_a_a] :
% 0.26/0.59 ( ( ord_le1824328871od_a_a @ X @ Y4 )
% 0.26/0.59 => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.26/0.59 => ( ord_less_eq_nat @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % ord_eq_le_subst
% 0.26/0.59 thf(fact_230_order__subst2,axiom,
% 0.26/0.59 ! [A2: nat,B3: nat,F: nat > nat,C2: nat] :
% 0.26/0.59 ( ( ord_less_eq_nat @ A2 @ B3 )
% 0.26/0.59 => ( ( ord_less_eq_nat @ ( F @ B3 ) @ C2 )
% 0.26/0.59 => ( ! [X: nat,Y4: nat] :
% 0.26/0.59 ( ( ord_less_eq_nat @ X @ Y4 )
% 0.26/0.59 => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.26/0.59 => ( ord_less_eq_nat @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % order_subst2
% 0.26/0.59 thf(fact_231_order__subst2,axiom,
% 0.26/0.59 ! [A2: nat,B3: nat,F: nat > set_nat,C2: set_nat] :
% 0.26/0.59 ( ( ord_less_eq_nat @ A2 @ B3 )
% 0.26/0.59 => ( ( ord_less_eq_set_nat @ ( F @ B3 ) @ C2 )
% 0.26/0.59 => ( ! [X: nat,Y4: nat] :
% 0.26/0.59 ( ( ord_less_eq_nat @ X @ Y4 )
% 0.26/0.59 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.26/0.59 => ( ord_less_eq_set_nat @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % order_subst2
% 0.26/0.59 thf(fact_232_order__subst2,axiom,
% 0.26/0.59 ! [A2: nat,B3: nat,F: nat > set_a,C2: set_a] :
% 0.26/0.59 ( ( ord_less_eq_nat @ A2 @ B3 )
% 0.26/0.59 => ( ( ord_less_eq_set_a @ ( F @ B3 ) @ C2 )
% 0.26/0.59 => ( ! [X: nat,Y4: nat] :
% 0.26/0.59 ( ( ord_less_eq_nat @ X @ Y4 )
% 0.26/0.59 => ( ord_less_eq_set_a @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.26/0.59 => ( ord_less_eq_set_a @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % order_subst2
% 0.26/0.59 thf(fact_233_order__subst2,axiom,
% 0.26/0.59 ! [A2: set_nat,B3: set_nat,F: set_nat > nat,C2: nat] :
% 0.26/0.59 ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 0.26/0.59 => ( ( ord_less_eq_nat @ ( F @ B3 ) @ C2 )
% 0.26/0.59 => ( ! [X: set_nat,Y4: set_nat] :
% 0.26/0.59 ( ( ord_less_eq_set_nat @ X @ Y4 )
% 0.26/0.59 => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.26/0.59 => ( ord_less_eq_nat @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % order_subst2
% 0.26/0.59 thf(fact_234_order__subst2,axiom,
% 0.26/0.59 ! [A2: set_a,B3: set_a,F: set_a > nat,C2: nat] :
% 0.26/0.59 ( ( ord_less_eq_set_a @ A2 @ B3 )
% 0.26/0.59 => ( ( ord_less_eq_nat @ ( F @ B3 ) @ C2 )
% 0.26/0.59 => ( ! [X: set_a,Y4: set_a] :
% 0.26/0.59 ( ( ord_less_eq_set_a @ X @ Y4 )
% 0.26/0.59 => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.26/0.59 => ( ord_less_eq_nat @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % order_subst2
% 0.26/0.59 thf(fact_235_order__subst2,axiom,
% 0.26/0.59 ! [A2: set_nat,B3: set_nat,F: set_nat > set_nat,C2: set_nat] :
% 0.26/0.59 ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 0.26/0.59 => ( ( ord_less_eq_set_nat @ ( F @ B3 ) @ C2 )
% 0.26/0.59 => ( ! [X: set_nat,Y4: set_nat] :
% 0.26/0.59 ( ( ord_less_eq_set_nat @ X @ Y4 )
% 0.26/0.59 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.26/0.59 => ( ord_less_eq_set_nat @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % order_subst2
% 0.26/0.59 thf(fact_236_order__subst2,axiom,
% 0.26/0.59 ! [A2: set_nat,B3: set_nat,F: set_nat > set_a,C2: set_a] :
% 0.26/0.59 ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 0.26/0.59 => ( ( ord_less_eq_set_a @ ( F @ B3 ) @ C2 )
% 0.26/0.59 => ( ! [X: set_nat,Y4: set_nat] :
% 0.26/0.59 ( ( ord_less_eq_set_nat @ X @ Y4 )
% 0.26/0.59 => ( ord_less_eq_set_a @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.26/0.59 => ( ord_less_eq_set_a @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % order_subst2
% 0.26/0.59 thf(fact_237_order__subst2,axiom,
% 0.26/0.59 ! [A2: set_a,B3: set_a,F: set_a > set_nat,C2: set_nat] :
% 0.26/0.59 ( ( ord_less_eq_set_a @ A2 @ B3 )
% 0.26/0.59 => ( ( ord_less_eq_set_nat @ ( F @ B3 ) @ C2 )
% 0.26/0.59 => ( ! [X: set_a,Y4: set_a] :
% 0.26/0.59 ( ( ord_less_eq_set_a @ X @ Y4 )
% 0.26/0.59 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.26/0.59 => ( ord_less_eq_set_nat @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % order_subst2
% 0.26/0.59 thf(fact_238_order__subst2,axiom,
% 0.26/0.59 ! [A2: set_a,B3: set_a,F: set_a > set_a,C2: set_a] :
% 0.26/0.59 ( ( ord_less_eq_set_a @ A2 @ B3 )
% 0.26/0.59 => ( ( ord_less_eq_set_a @ ( F @ B3 ) @ C2 )
% 0.26/0.59 => ( ! [X: set_a,Y4: set_a] :
% 0.26/0.59 ( ( ord_less_eq_set_a @ X @ Y4 )
% 0.26/0.59 => ( ord_less_eq_set_a @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.26/0.59 => ( ord_less_eq_set_a @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % order_subst2
% 0.26/0.59 thf(fact_239_order__subst2,axiom,
% 0.26/0.59 ! [A2: set_Product_prod_a_a,B3: set_Product_prod_a_a,F: set_Product_prod_a_a > nat,C2: nat] :
% 0.26/0.59 ( ( ord_le1824328871od_a_a @ A2 @ B3 )
% 0.26/0.59 => ( ( ord_less_eq_nat @ ( F @ B3 ) @ C2 )
% 0.26/0.59 => ( ! [X: set_Product_prod_a_a,Y4: set_Product_prod_a_a] :
% 0.26/0.59 ( ( ord_le1824328871od_a_a @ X @ Y4 )
% 0.26/0.59 => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.26/0.59 => ( ord_less_eq_nat @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % order_subst2
% 0.26/0.59 thf(fact_240_order__subst1,axiom,
% 0.26/0.59 ! [A2: nat,F: nat > nat,B3: nat,C2: nat] :
% 0.26/0.59 ( ( ord_less_eq_nat @ A2 @ ( F @ B3 ) )
% 0.26/0.59 => ( ( ord_less_eq_nat @ B3 @ C2 )
% 0.26/0.59 => ( ! [X: nat,Y4: nat] :
% 0.26/0.59 ( ( ord_less_eq_nat @ X @ Y4 )
% 0.26/0.59 => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.26/0.59 => ( ord_less_eq_nat @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % order_subst1
% 0.26/0.59 thf(fact_241_order__subst1,axiom,
% 0.26/0.59 ! [A2: nat,F: set_nat > nat,B3: set_nat,C2: set_nat] :
% 0.26/0.59 ( ( ord_less_eq_nat @ A2 @ ( F @ B3 ) )
% 0.26/0.59 => ( ( ord_less_eq_set_nat @ B3 @ C2 )
% 0.26/0.59 => ( ! [X: set_nat,Y4: set_nat] :
% 0.26/0.59 ( ( ord_less_eq_set_nat @ X @ Y4 )
% 0.26/0.59 => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.26/0.59 => ( ord_less_eq_nat @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % order_subst1
% 0.26/0.59 thf(fact_242_order__subst1,axiom,
% 0.26/0.59 ! [A2: nat,F: set_a > nat,B3: set_a,C2: set_a] :
% 0.26/0.59 ( ( ord_less_eq_nat @ A2 @ ( F @ B3 ) )
% 0.26/0.59 => ( ( ord_less_eq_set_a @ B3 @ C2 )
% 0.26/0.59 => ( ! [X: set_a,Y4: set_a] :
% 0.26/0.59 ( ( ord_less_eq_set_a @ X @ Y4 )
% 0.26/0.59 => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.26/0.59 => ( ord_less_eq_nat @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % order_subst1
% 0.26/0.59 thf(fact_243_order__subst1,axiom,
% 0.26/0.59 ! [A2: set_nat,F: nat > set_nat,B3: nat,C2: nat] :
% 0.26/0.59 ( ( ord_less_eq_set_nat @ A2 @ ( F @ B3 ) )
% 0.26/0.59 => ( ( ord_less_eq_nat @ B3 @ C2 )
% 0.26/0.59 => ( ! [X: nat,Y4: nat] :
% 0.26/0.59 ( ( ord_less_eq_nat @ X @ Y4 )
% 0.26/0.59 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.26/0.59 => ( ord_less_eq_set_nat @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % order_subst1
% 0.26/0.59 thf(fact_244_order__subst1,axiom,
% 0.26/0.59 ! [A2: set_a,F: nat > set_a,B3: nat,C2: nat] :
% 0.26/0.59 ( ( ord_less_eq_set_a @ A2 @ ( F @ B3 ) )
% 0.26/0.59 => ( ( ord_less_eq_nat @ B3 @ C2 )
% 0.26/0.59 => ( ! [X: nat,Y4: nat] :
% 0.26/0.59 ( ( ord_less_eq_nat @ X @ Y4 )
% 0.26/0.59 => ( ord_less_eq_set_a @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.26/0.59 => ( ord_less_eq_set_a @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % order_subst1
% 0.26/0.59 thf(fact_245_order__subst1,axiom,
% 0.26/0.59 ! [A2: set_nat,F: set_nat > set_nat,B3: set_nat,C2: set_nat] :
% 0.26/0.59 ( ( ord_less_eq_set_nat @ A2 @ ( F @ B3 ) )
% 0.26/0.59 => ( ( ord_less_eq_set_nat @ B3 @ C2 )
% 0.26/0.59 => ( ! [X: set_nat,Y4: set_nat] :
% 0.26/0.59 ( ( ord_less_eq_set_nat @ X @ Y4 )
% 0.26/0.59 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.26/0.59 => ( ord_less_eq_set_nat @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % order_subst1
% 0.26/0.59 thf(fact_246_order__subst1,axiom,
% 0.26/0.59 ! [A2: set_nat,F: set_a > set_nat,B3: set_a,C2: set_a] :
% 0.26/0.59 ( ( ord_less_eq_set_nat @ A2 @ ( F @ B3 ) )
% 0.26/0.59 => ( ( ord_less_eq_set_a @ B3 @ C2 )
% 0.26/0.59 => ( ! [X: set_a,Y4: set_a] :
% 0.26/0.59 ( ( ord_less_eq_set_a @ X @ Y4 )
% 0.26/0.59 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.26/0.59 => ( ord_less_eq_set_nat @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % order_subst1
% 0.26/0.59 thf(fact_247_order__subst1,axiom,
% 0.26/0.59 ! [A2: set_a,F: set_nat > set_a,B3: set_nat,C2: set_nat] :
% 0.26/0.59 ( ( ord_less_eq_set_a @ A2 @ ( F @ B3 ) )
% 0.26/0.59 => ( ( ord_less_eq_set_nat @ B3 @ C2 )
% 0.26/0.59 => ( ! [X: set_nat,Y4: set_nat] :
% 0.26/0.59 ( ( ord_less_eq_set_nat @ X @ Y4 )
% 0.26/0.59 => ( ord_less_eq_set_a @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.26/0.59 => ( ord_less_eq_set_a @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % order_subst1
% 0.26/0.59 thf(fact_248_order__subst1,axiom,
% 0.26/0.59 ! [A2: set_a,F: set_a > set_a,B3: set_a,C2: set_a] :
% 0.26/0.59 ( ( ord_less_eq_set_a @ A2 @ ( F @ B3 ) )
% 0.26/0.59 => ( ( ord_less_eq_set_a @ B3 @ C2 )
% 0.26/0.59 => ( ! [X: set_a,Y4: set_a] :
% 0.26/0.59 ( ( ord_less_eq_set_a @ X @ Y4 )
% 0.26/0.59 => ( ord_less_eq_set_a @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.26/0.59 => ( ord_less_eq_set_a @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % order_subst1
% 0.26/0.59 thf(fact_249_order__subst1,axiom,
% 0.26/0.59 ! [A2: set_Product_prod_a_a,F: nat > set_Product_prod_a_a,B3: nat,C2: nat] :
% 0.26/0.59 ( ( ord_le1824328871od_a_a @ A2 @ ( F @ B3 ) )
% 0.26/0.59 => ( ( ord_less_eq_nat @ B3 @ C2 )
% 0.26/0.59 => ( ! [X: nat,Y4: nat] :
% 0.26/0.59 ( ( ord_less_eq_nat @ X @ Y4 )
% 0.26/0.59 => ( ord_le1824328871od_a_a @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.26/0.59 => ( ord_le1824328871od_a_a @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % order_subst1
% 0.26/0.59 thf(fact_250_Collect__mono__iff,axiom,
% 0.26/0.59 ! [P: product_prod_a_a > $o,Q: product_prod_a_a > $o] :
% 0.26/0.59 ( ( ord_le1824328871od_a_a @ ( collec645855634od_a_a @ P ) @ ( collec645855634od_a_a @ Q ) )
% 0.26/0.59 = ( ! [X2: product_prod_a_a] :
% 0.26/0.59 ( ( P @ X2 )
% 0.26/0.59 => ( Q @ X2 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Collect_mono_iff
% 0.26/0.59 thf(fact_251_Collect__mono__iff,axiom,
% 0.26/0.59 ! [P: nat > $o,Q: nat > $o] :
% 0.26/0.59 ( ( ord_less_eq_set_nat @ ( collect_nat @ P ) @ ( collect_nat @ Q ) )
% 0.26/0.59 = ( ! [X2: nat] :
% 0.26/0.59 ( ( P @ X2 )
% 0.26/0.59 => ( Q @ X2 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Collect_mono_iff
% 0.26/0.59 thf(fact_252_Collect__mono__iff,axiom,
% 0.26/0.59 ! [P: a > $o,Q: a > $o] :
% 0.26/0.59 ( ( ord_less_eq_set_a @ ( collect_a @ P ) @ ( collect_a @ Q ) )
% 0.26/0.59 = ( ! [X2: a] :
% 0.26/0.59 ( ( P @ X2 )
% 0.26/0.59 => ( Q @ X2 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Collect_mono_iff
% 0.26/0.59 thf(fact_253_set__eq__subset,axiom,
% 0.26/0.59 ( ( ^ [Y: set_Product_prod_a_a,Z: set_Product_prod_a_a] : ( Y = Z ) )
% 0.26/0.59 = ( ^ [A5: set_Product_prod_a_a,B2: set_Product_prod_a_a] :
% 0.26/0.59 ( ( ord_le1824328871od_a_a @ A5 @ B2 )
% 0.26/0.59 & ( ord_le1824328871od_a_a @ B2 @ A5 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % set_eq_subset
% 0.26/0.59 thf(fact_254_set__eq__subset,axiom,
% 0.26/0.59 ( ( ^ [Y: set_nat,Z: set_nat] : ( Y = Z ) )
% 0.26/0.59 = ( ^ [A5: set_nat,B2: set_nat] :
% 0.26/0.59 ( ( ord_less_eq_set_nat @ A5 @ B2 )
% 0.26/0.59 & ( ord_less_eq_set_nat @ B2 @ A5 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % set_eq_subset
% 0.26/0.59 thf(fact_255_set__eq__subset,axiom,
% 0.26/0.59 ( ( ^ [Y: set_a,Z: set_a] : ( Y = Z ) )
% 0.26/0.59 = ( ^ [A5: set_a,B2: set_a] :
% 0.26/0.59 ( ( ord_less_eq_set_a @ A5 @ B2 )
% 0.26/0.59 & ( ord_less_eq_set_a @ B2 @ A5 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % set_eq_subset
% 0.26/0.59 thf(fact_256_subset__trans,axiom,
% 0.26/0.59 ! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: set_Product_prod_a_a] :
% 0.26/0.59 ( ( ord_le1824328871od_a_a @ A @ B )
% 0.26/0.59 => ( ( ord_le1824328871od_a_a @ B @ C )
% 0.26/0.59 => ( ord_le1824328871od_a_a @ A @ C ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % subset_trans
% 0.26/0.59 thf(fact_257_subset__trans,axiom,
% 0.26/0.59 ! [A: set_nat,B: set_nat,C: set_nat] :
% 0.26/0.59 ( ( ord_less_eq_set_nat @ A @ B )
% 0.26/0.59 => ( ( ord_less_eq_set_nat @ B @ C )
% 0.26/0.59 => ( ord_less_eq_set_nat @ A @ C ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % subset_trans
% 0.26/0.59 thf(fact_258_subset__trans,axiom,
% 0.26/0.59 ! [A: set_a,B: set_a,C: set_a] :
% 0.26/0.59 ( ( ord_less_eq_set_a @ A @ B )
% 0.26/0.59 => ( ( ord_less_eq_set_a @ B @ C )
% 0.26/0.59 => ( ord_less_eq_set_a @ A @ C ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % subset_trans
% 0.26/0.59 thf(fact_259_Collect__mono,axiom,
% 0.26/0.59 ! [P: product_prod_a_a > $o,Q: product_prod_a_a > $o] :
% 0.26/0.59 ( ! [X: product_prod_a_a] :
% 0.26/0.59 ( ( P @ X )
% 0.26/0.59 => ( Q @ X ) )
% 0.26/0.59 => ( ord_le1824328871od_a_a @ ( collec645855634od_a_a @ P ) @ ( collec645855634od_a_a @ Q ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Collect_mono
% 0.26/0.59 thf(fact_260_Collect__mono,axiom,
% 0.26/0.59 ! [P: nat > $o,Q: nat > $o] :
% 0.26/0.59 ( ! [X: nat] :
% 0.26/0.59 ( ( P @ X )
% 0.26/0.59 => ( Q @ X ) )
% 0.26/0.59 => ( ord_less_eq_set_nat @ ( collect_nat @ P ) @ ( collect_nat @ Q ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Collect_mono
% 0.26/0.59 thf(fact_261_Collect__mono,axiom,
% 0.26/0.59 ! [P: a > $o,Q: a > $o] :
% 0.26/0.59 ( ! [X: a] :
% 0.26/0.59 ( ( P @ X )
% 0.26/0.59 => ( Q @ X ) )
% 0.26/0.59 => ( ord_less_eq_set_a @ ( collect_a @ P ) @ ( collect_a @ Q ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Collect_mono
% 0.26/0.59 thf(fact_262_subset__refl,axiom,
% 0.26/0.59 ! [A: set_Product_prod_a_a] : ( ord_le1824328871od_a_a @ A @ A ) ).
% 0.26/0.59
% 0.26/0.59 % subset_refl
% 0.26/0.59 thf(fact_263_subset__refl,axiom,
% 0.26/0.59 ! [A: set_nat] : ( ord_less_eq_set_nat @ A @ A ) ).
% 0.26/0.59
% 0.26/0.59 % subset_refl
% 0.26/0.59 thf(fact_264_subset__refl,axiom,
% 0.26/0.59 ! [A: set_a] : ( ord_less_eq_set_a @ A @ A ) ).
% 0.26/0.59
% 0.26/0.59 % subset_refl
% 0.26/0.59 thf(fact_265_subset__iff,axiom,
% 0.26/0.59 ( ord_le1824328871od_a_a
% 0.26/0.59 = ( ^ [A5: set_Product_prod_a_a,B2: set_Product_prod_a_a] :
% 0.26/0.59 ! [T2: product_prod_a_a] :
% 0.26/0.59 ( ( member449909584od_a_a @ T2 @ A5 )
% 0.26/0.59 => ( member449909584od_a_a @ T2 @ B2 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % subset_iff
% 0.26/0.59 thf(fact_266_subset__iff,axiom,
% 0.26/0.59 ( ord_less_eq_set_nat
% 0.26/0.59 = ( ^ [A5: set_nat,B2: set_nat] :
% 0.26/0.59 ! [T2: nat] :
% 0.26/0.59 ( ( member_nat @ T2 @ A5 )
% 0.26/0.59 => ( member_nat @ T2 @ B2 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % subset_iff
% 0.26/0.59 thf(fact_267_subset__iff,axiom,
% 0.26/0.59 ( ord_less_eq_set_a
% 0.26/0.59 = ( ^ [A5: set_a,B2: set_a] :
% 0.26/0.59 ! [T2: a] :
% 0.26/0.59 ( ( member_a @ T2 @ A5 )
% 0.26/0.59 => ( member_a @ T2 @ B2 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % subset_iff
% 0.26/0.59 thf(fact_268_equalityD2,axiom,
% 0.26/0.59 ! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
% 0.26/0.59 ( ( A = B )
% 0.26/0.59 => ( ord_le1824328871od_a_a @ B @ A ) ) ).
% 0.26/0.59
% 0.26/0.59 % equalityD2
% 0.26/0.59 thf(fact_269_equalityD2,axiom,
% 0.26/0.59 ! [A: set_nat,B: set_nat] :
% 0.26/0.59 ( ( A = B )
% 0.26/0.59 => ( ord_less_eq_set_nat @ B @ A ) ) ).
% 0.26/0.59
% 0.26/0.59 % equalityD2
% 0.26/0.59 thf(fact_270_equalityD2,axiom,
% 0.26/0.59 ! [A: set_a,B: set_a] :
% 0.26/0.59 ( ( A = B )
% 0.26/0.59 => ( ord_less_eq_set_a @ B @ A ) ) ).
% 0.26/0.59
% 0.26/0.59 % equalityD2
% 0.26/0.59 thf(fact_271_equalityD1,axiom,
% 0.26/0.59 ! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
% 0.26/0.59 ( ( A = B )
% 0.26/0.59 => ( ord_le1824328871od_a_a @ A @ B ) ) ).
% 0.26/0.59
% 0.26/0.59 % equalityD1
% 0.26/0.59 thf(fact_272_equalityD1,axiom,
% 0.26/0.59 ! [A: set_nat,B: set_nat] :
% 0.26/0.59 ( ( A = B )
% 0.26/0.59 => ( ord_less_eq_set_nat @ A @ B ) ) ).
% 0.26/0.59
% 0.26/0.59 % equalityD1
% 0.26/0.59 thf(fact_273_equalityD1,axiom,
% 0.26/0.59 ! [A: set_a,B: set_a] :
% 0.26/0.59 ( ( A = B )
% 0.26/0.59 => ( ord_less_eq_set_a @ A @ B ) ) ).
% 0.26/0.59
% 0.26/0.59 % equalityD1
% 0.26/0.59 thf(fact_274_subset__eq,axiom,
% 0.26/0.59 ( ord_le1824328871od_a_a
% 0.26/0.59 = ( ^ [A5: set_Product_prod_a_a,B2: set_Product_prod_a_a] :
% 0.26/0.59 ! [X2: product_prod_a_a] :
% 0.26/0.59 ( ( member449909584od_a_a @ X2 @ A5 )
% 0.26/0.59 => ( member449909584od_a_a @ X2 @ B2 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % subset_eq
% 0.26/0.59 thf(fact_275_subset__eq,axiom,
% 0.26/0.59 ( ord_less_eq_set_nat
% 0.26/0.59 = ( ^ [A5: set_nat,B2: set_nat] :
% 0.26/0.59 ! [X2: nat] :
% 0.26/0.59 ( ( member_nat @ X2 @ A5 )
% 0.26/0.59 => ( member_nat @ X2 @ B2 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % subset_eq
% 0.26/0.59 thf(fact_276_subset__eq,axiom,
% 0.26/0.59 ( ord_less_eq_set_a
% 0.26/0.59 = ( ^ [A5: set_a,B2: set_a] :
% 0.26/0.59 ! [X2: a] :
% 0.26/0.59 ( ( member_a @ X2 @ A5 )
% 0.26/0.59 => ( member_a @ X2 @ B2 ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % subset_eq
% 0.26/0.59 thf(fact_277_equalityE,axiom,
% 0.26/0.59 ! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
% 0.26/0.59 ( ( A = B )
% 0.26/0.59 => ~ ( ( ord_le1824328871od_a_a @ A @ B )
% 0.26/0.59 => ~ ( ord_le1824328871od_a_a @ B @ A ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % equalityE
% 0.26/0.59 thf(fact_278_equalityE,axiom,
% 0.26/0.59 ! [A: set_nat,B: set_nat] :
% 0.26/0.59 ( ( A = B )
% 0.26/0.59 => ~ ( ( ord_less_eq_set_nat @ A @ B )
% 0.26/0.59 => ~ ( ord_less_eq_set_nat @ B @ A ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % equalityE
% 0.26/0.59 thf(fact_279_equalityE,axiom,
% 0.26/0.59 ! [A: set_a,B: set_a] :
% 0.26/0.59 ( ( A = B )
% 0.26/0.59 => ~ ( ( ord_less_eq_set_a @ A @ B )
% 0.26/0.59 => ~ ( ord_less_eq_set_a @ B @ A ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % equalityE
% 0.26/0.59 thf(fact_280_subsetD,axiom,
% 0.26/0.59 ! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C2: product_prod_a_a] :
% 0.26/0.59 ( ( ord_le1824328871od_a_a @ A @ B )
% 0.26/0.59 => ( ( member449909584od_a_a @ C2 @ A )
% 0.26/0.59 => ( member449909584od_a_a @ C2 @ B ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % subsetD
% 0.26/0.59 thf(fact_281_subsetD,axiom,
% 0.26/0.59 ! [A: set_nat,B: set_nat,C2: nat] :
% 0.26/0.59 ( ( ord_less_eq_set_nat @ A @ B )
% 0.26/0.59 => ( ( member_nat @ C2 @ A )
% 0.26/0.59 => ( member_nat @ C2 @ B ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % subsetD
% 0.26/0.59 thf(fact_282_subsetD,axiom,
% 0.26/0.59 ! [A: set_a,B: set_a,C2: a] :
% 0.26/0.59 ( ( ord_less_eq_set_a @ A @ B )
% 0.26/0.59 => ( ( member_a @ C2 @ A )
% 0.26/0.59 => ( member_a @ C2 @ B ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % subsetD
% 0.26/0.59 thf(fact_283_in__mono,axiom,
% 0.26/0.59 ! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,X3: product_prod_a_a] :
% 0.26/0.59 ( ( ord_le1824328871od_a_a @ A @ B )
% 0.26/0.59 => ( ( member449909584od_a_a @ X3 @ A )
% 0.26/0.59 => ( member449909584od_a_a @ X3 @ B ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % in_mono
% 0.26/0.59 thf(fact_284_in__mono,axiom,
% 0.26/0.59 ! [A: set_nat,B: set_nat,X3: nat] :
% 0.26/0.59 ( ( ord_less_eq_set_nat @ A @ B )
% 0.26/0.59 => ( ( member_nat @ X3 @ A )
% 0.26/0.59 => ( member_nat @ X3 @ B ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % in_mono
% 0.26/0.59 thf(fact_285_in__mono,axiom,
% 0.26/0.59 ! [A: set_a,B: set_a,X3: a] :
% 0.26/0.59 ( ( ord_less_eq_set_a @ A @ B )
% 0.26/0.59 => ( ( member_a @ X3 @ A )
% 0.26/0.59 => ( member_a @ X3 @ B ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % in_mono
% 0.26/0.59 thf(fact_286_pred__subset__eq,axiom,
% 0.26/0.59 ! [R: set_Product_prod_a_a,S: set_Product_prod_a_a] :
% 0.26/0.59 ( ( ord_le1347718902_a_a_o
% 0.26/0.59 @ ^ [X2: product_prod_a_a] : ( member449909584od_a_a @ X2 @ R )
% 0.26/0.59 @ ^ [X2: product_prod_a_a] : ( member449909584od_a_a @ X2 @ S ) )
% 0.26/0.59 = ( ord_le1824328871od_a_a @ R @ S ) ) ).
% 0.26/0.59
% 0.26/0.59 % pred_subset_eq
% 0.26/0.59 thf(fact_287_pred__subset__eq,axiom,
% 0.26/0.59 ! [R: set_nat,S: set_nat] :
% 0.26/0.59 ( ( ord_less_eq_nat_o
% 0.26/0.59 @ ^ [X2: nat] : ( member_nat @ X2 @ R )
% 0.26/0.59 @ ^ [X2: nat] : ( member_nat @ X2 @ S ) )
% 0.26/0.59 = ( ord_less_eq_set_nat @ R @ S ) ) ).
% 0.26/0.59
% 0.26/0.59 % pred_subset_eq
% 0.26/0.59 thf(fact_288_pred__subset__eq,axiom,
% 0.26/0.59 ! [R: set_a,S: set_a] :
% 0.26/0.59 ( ( ord_less_eq_a_o
% 0.26/0.59 @ ^ [X2: a] : ( member_a @ X2 @ R )
% 0.26/0.59 @ ^ [X2: a] : ( member_a @ X2 @ S ) )
% 0.26/0.59 = ( ord_less_eq_set_a @ R @ S ) ) ).
% 0.26/0.59
% 0.26/0.59 % pred_subset_eq
% 0.26/0.59 thf(fact_289_pair__pre__digraph_Osurjective,axiom,
% 0.26/0.59 ! [R2: pair_p125712459t_unit] :
% 0.26/0.59 ( R2
% 0.26/0.59 = ( pair_p1621517565t_unit @ ( pair_p1047056820t_unit @ R2 ) @ ( pair_p133601421t_unit @ R2 ) @ ( pair_p1896222615t_unit @ R2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % pair_pre_digraph.surjective
% 0.26/0.59 thf(fact_290_pair__pre__digraph_Osurjective,axiom,
% 0.26/0.59 ! [R2: pair_p1914262621t_unit] :
% 0.26/0.59 ( R2
% 0.26/0.59 = ( pair_p1167410509t_unit @ ( pair_p1677060310t_unit @ R2 ) @ ( pair_p715279805t_unit @ R2 ) @ ( pair_p69470259t_unit @ R2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % pair_pre_digraph.surjective
% 0.26/0.59 thf(fact_291_pair__pre__digraph_Osurjective,axiom,
% 0.26/0.59 ! [R2: pair_p1765063010t_unit] :
% 0.26/0.59 ( R2
% 0.26/0.59 = ( pair_p398687508t_unit @ ( pair_p447552203t_unit @ R2 ) @ ( pair_p1783210148t_unit @ R2 ) @ ( pair_p1984658862t_unit @ R2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % pair_pre_digraph.surjective
% 0.26/0.59 thf(fact_292_member__product,axiom,
% 0.26/0.59 ! [X3: product_prod_a_a,A: set_a,B: set_a] :
% 0.26/0.59 ( ( member449909584od_a_a @ X3 @ ( product_product_a_a @ A @ B ) )
% 0.26/0.59 = ( member449909584od_a_a @ X3
% 0.26/0.59 @ ( product_Sigma_a_a @ A
% 0.26/0.59 @ ^ [Uu: a] : B ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % member_product
% 0.26/0.59 thf(fact_293_Product__Type_Oproduct__def,axiom,
% 0.26/0.59 ( product_product_a_a
% 0.26/0.59 = ( ^ [A5: set_a,B2: set_a] :
% 0.26/0.59 ( product_Sigma_a_a @ A5
% 0.26/0.59 @ ^ [Uu: a] : B2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Product_Type.product_def
% 0.26/0.59 thf(fact_294_subset__Collect__iff,axiom,
% 0.26/0.59 ! [B: set_Product_prod_a_a,A: set_Product_prod_a_a,P: product_prod_a_a > $o] :
% 0.26/0.59 ( ( ord_le1824328871od_a_a @ B @ A )
% 0.26/0.59 => ( ( ord_le1824328871od_a_a @ B
% 0.26/0.59 @ ( collec645855634od_a_a
% 0.26/0.59 @ ^ [X2: product_prod_a_a] :
% 0.26/0.59 ( ( member449909584od_a_a @ X2 @ A )
% 0.26/0.59 & ( P @ X2 ) ) ) )
% 0.26/0.59 = ( ! [X2: product_prod_a_a] :
% 0.26/0.59 ( ( member449909584od_a_a @ X2 @ B )
% 0.26/0.59 => ( P @ X2 ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % subset_Collect_iff
% 0.26/0.59 thf(fact_295_subset__Collect__iff,axiom,
% 0.26/0.59 ! [B: set_nat,A: set_nat,P: nat > $o] :
% 0.26/0.59 ( ( ord_less_eq_set_nat @ B @ A )
% 0.26/0.59 => ( ( ord_less_eq_set_nat @ B
% 0.26/0.59 @ ( collect_nat
% 0.26/0.59 @ ^ [X2: nat] :
% 0.26/0.59 ( ( member_nat @ X2 @ A )
% 0.26/0.59 & ( P @ X2 ) ) ) )
% 0.26/0.59 = ( ! [X2: nat] :
% 0.26/0.59 ( ( member_nat @ X2 @ B )
% 0.26/0.59 => ( P @ X2 ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % subset_Collect_iff
% 0.26/0.59 thf(fact_296_subset__Collect__iff,axiom,
% 0.26/0.59 ! [B: set_a,A: set_a,P: a > $o] :
% 0.26/0.59 ( ( ord_less_eq_set_a @ B @ A )
% 0.26/0.59 => ( ( ord_less_eq_set_a @ B
% 0.26/0.59 @ ( collect_a
% 0.26/0.59 @ ^ [X2: a] :
% 0.26/0.59 ( ( member_a @ X2 @ A )
% 0.26/0.59 & ( P @ X2 ) ) ) )
% 0.26/0.59 = ( ! [X2: a] :
% 0.26/0.59 ( ( member_a @ X2 @ B )
% 0.26/0.59 => ( P @ X2 ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % subset_Collect_iff
% 0.26/0.59 thf(fact_297_subset__CollectI,axiom,
% 0.26/0.59 ! [B: set_Product_prod_a_a,A: set_Product_prod_a_a,Q: product_prod_a_a > $o,P: product_prod_a_a > $o] :
% 0.26/0.59 ( ( ord_le1824328871od_a_a @ B @ A )
% 0.26/0.59 => ( ! [X: product_prod_a_a] :
% 0.26/0.59 ( ( member449909584od_a_a @ X @ B )
% 0.26/0.59 => ( ( Q @ X )
% 0.26/0.59 => ( P @ X ) ) )
% 0.26/0.59 => ( ord_le1824328871od_a_a
% 0.26/0.59 @ ( collec645855634od_a_a
% 0.26/0.59 @ ^ [X2: product_prod_a_a] :
% 0.26/0.59 ( ( member449909584od_a_a @ X2 @ B )
% 0.26/0.59 & ( Q @ X2 ) ) )
% 0.26/0.59 @ ( collec645855634od_a_a
% 0.26/0.59 @ ^ [X2: product_prod_a_a] :
% 0.26/0.59 ( ( member449909584od_a_a @ X2 @ A )
% 0.26/0.59 & ( P @ X2 ) ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % subset_CollectI
% 0.26/0.59 thf(fact_298_subset__CollectI,axiom,
% 0.26/0.59 ! [B: set_nat,A: set_nat,Q: nat > $o,P: nat > $o] :
% 0.26/0.59 ( ( ord_less_eq_set_nat @ B @ A )
% 0.26/0.59 => ( ! [X: nat] :
% 0.26/0.59 ( ( member_nat @ X @ B )
% 0.26/0.59 => ( ( Q @ X )
% 0.26/0.59 => ( P @ X ) ) )
% 0.26/0.59 => ( ord_less_eq_set_nat
% 0.26/0.59 @ ( collect_nat
% 0.26/0.59 @ ^ [X2: nat] :
% 0.26/0.59 ( ( member_nat @ X2 @ B )
% 0.26/0.59 & ( Q @ X2 ) ) )
% 0.26/0.59 @ ( collect_nat
% 0.26/0.59 @ ^ [X2: nat] :
% 0.26/0.59 ( ( member_nat @ X2 @ A )
% 0.26/0.59 & ( P @ X2 ) ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % subset_CollectI
% 0.26/0.59 thf(fact_299_subset__CollectI,axiom,
% 0.26/0.59 ! [B: set_a,A: set_a,Q: a > $o,P: a > $o] :
% 0.26/0.59 ( ( ord_less_eq_set_a @ B @ A )
% 0.26/0.59 => ( ! [X: a] :
% 0.26/0.59 ( ( member_a @ X @ B )
% 0.26/0.59 => ( ( Q @ X )
% 0.26/0.59 => ( P @ X ) ) )
% 0.26/0.59 => ( ord_less_eq_set_a
% 0.26/0.59 @ ( collect_a
% 0.26/0.59 @ ^ [X2: a] :
% 0.26/0.59 ( ( member_a @ X2 @ B )
% 0.26/0.59 & ( Q @ X2 ) ) )
% 0.26/0.59 @ ( collect_a
% 0.26/0.59 @ ^ [X2: a] :
% 0.26/0.59 ( ( member_a @ X2 @ A )
% 0.26/0.59 & ( P @ X2 ) ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % subset_CollectI
% 0.26/0.59 thf(fact_300_Collect__restrict,axiom,
% 0.26/0.59 ! [X4: set_Product_prod_a_a,P: product_prod_a_a > $o] :
% 0.26/0.59 ( ord_le1824328871od_a_a
% 0.26/0.59 @ ( collec645855634od_a_a
% 0.26/0.59 @ ^ [X2: product_prod_a_a] :
% 0.26/0.59 ( ( member449909584od_a_a @ X2 @ X4 )
% 0.26/0.59 & ( P @ X2 ) ) )
% 0.26/0.59 @ X4 ) ).
% 0.26/0.59
% 0.26/0.59 % Collect_restrict
% 0.26/0.59 thf(fact_301_Collect__restrict,axiom,
% 0.26/0.59 ! [X4: set_nat,P: nat > $o] :
% 0.26/0.59 ( ord_less_eq_set_nat
% 0.26/0.59 @ ( collect_nat
% 0.26/0.59 @ ^ [X2: nat] :
% 0.26/0.59 ( ( member_nat @ X2 @ X4 )
% 0.26/0.59 & ( P @ X2 ) ) )
% 0.26/0.59 @ X4 ) ).
% 0.26/0.59
% 0.26/0.59 % Collect_restrict
% 0.26/0.59 thf(fact_302_Collect__restrict,axiom,
% 0.26/0.59 ! [X4: set_a,P: a > $o] :
% 0.26/0.59 ( ord_less_eq_set_a
% 0.26/0.59 @ ( collect_a
% 0.26/0.59 @ ^ [X2: a] :
% 0.26/0.59 ( ( member_a @ X2 @ X4 )
% 0.26/0.59 & ( P @ X2 ) ) )
% 0.26/0.59 @ X4 ) ).
% 0.26/0.59
% 0.26/0.59 % Collect_restrict
% 0.26/0.59 thf(fact_303_prop__restrict,axiom,
% 0.26/0.59 ! [X3: product_prod_a_a,Z3: set_Product_prod_a_a,X4: set_Product_prod_a_a,P: product_prod_a_a > $o] :
% 0.26/0.59 ( ( member449909584od_a_a @ X3 @ Z3 )
% 0.26/0.59 => ( ( ord_le1824328871od_a_a @ Z3
% 0.26/0.59 @ ( collec645855634od_a_a
% 0.26/0.59 @ ^ [X2: product_prod_a_a] :
% 0.26/0.59 ( ( member449909584od_a_a @ X2 @ X4 )
% 0.26/0.59 & ( P @ X2 ) ) ) )
% 0.26/0.59 => ( P @ X3 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % prop_restrict
% 0.26/0.59 thf(fact_304_prop__restrict,axiom,
% 0.26/0.59 ! [X3: nat,Z3: set_nat,X4: set_nat,P: nat > $o] :
% 0.26/0.59 ( ( member_nat @ X3 @ Z3 )
% 0.26/0.59 => ( ( ord_less_eq_set_nat @ Z3
% 0.26/0.59 @ ( collect_nat
% 0.26/0.59 @ ^ [X2: nat] :
% 0.26/0.59 ( ( member_nat @ X2 @ X4 )
% 0.26/0.59 & ( P @ X2 ) ) ) )
% 0.26/0.59 => ( P @ X3 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % prop_restrict
% 0.26/0.59 thf(fact_305_prop__restrict,axiom,
% 0.26/0.59 ! [X3: a,Z3: set_a,X4: set_a,P: a > $o] :
% 0.26/0.59 ( ( member_a @ X3 @ Z3 )
% 0.26/0.59 => ( ( ord_less_eq_set_a @ Z3
% 0.26/0.59 @ ( collect_a
% 0.26/0.59 @ ^ [X2: a] :
% 0.26/0.59 ( ( member_a @ X2 @ X4 )
% 0.26/0.59 & ( P @ X2 ) ) ) )
% 0.26/0.59 => ( P @ X3 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % prop_restrict
% 0.26/0.59 thf(fact_306_conj__subset__def,axiom,
% 0.26/0.59 ! [A: set_Product_prod_a_a,P: product_prod_a_a > $o,Q: product_prod_a_a > $o] :
% 0.26/0.59 ( ( ord_le1824328871od_a_a @ A
% 0.26/0.59 @ ( collec645855634od_a_a
% 0.26/0.59 @ ^ [X2: product_prod_a_a] :
% 0.26/0.59 ( ( P @ X2 )
% 0.26/0.59 & ( Q @ X2 ) ) ) )
% 0.26/0.59 = ( ( ord_le1824328871od_a_a @ A @ ( collec645855634od_a_a @ P ) )
% 0.26/0.59 & ( ord_le1824328871od_a_a @ A @ ( collec645855634od_a_a @ Q ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % conj_subset_def
% 0.26/0.59 thf(fact_307_conj__subset__def,axiom,
% 0.26/0.59 ! [A: set_nat,P: nat > $o,Q: nat > $o] :
% 0.26/0.59 ( ( ord_less_eq_set_nat @ A
% 0.26/0.59 @ ( collect_nat
% 0.26/0.59 @ ^ [X2: nat] :
% 0.26/0.59 ( ( P @ X2 )
% 0.26/0.59 & ( Q @ X2 ) ) ) )
% 0.26/0.59 = ( ( ord_less_eq_set_nat @ A @ ( collect_nat @ P ) )
% 0.26/0.59 & ( ord_less_eq_set_nat @ A @ ( collect_nat @ Q ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % conj_subset_def
% 0.26/0.59 thf(fact_308_conj__subset__def,axiom,
% 0.26/0.59 ! [A: set_a,P: a > $o,Q: a > $o] :
% 0.26/0.59 ( ( ord_less_eq_set_a @ A
% 0.26/0.59 @ ( collect_a
% 0.26/0.59 @ ^ [X2: a] :
% 0.26/0.59 ( ( P @ X2 )
% 0.26/0.59 & ( Q @ X2 ) ) ) )
% 0.26/0.59 = ( ( ord_less_eq_set_a @ A @ ( collect_a @ P ) )
% 0.26/0.59 & ( ord_less_eq_set_a @ A @ ( collect_a @ Q ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % conj_subset_def
% 0.26/0.59 thf(fact_309_pair__pre__digraph_Oselect__convs_I2_J,axiom,
% 0.26/0.59 ! [Pverts: set_a,Parcs: set_Product_prod_a_a,More: product_unit] :
% 0.26/0.59 ( ( pair_p133601421t_unit @ ( pair_p1621517565t_unit @ Pverts @ Parcs @ More ) )
% 0.26/0.59 = Parcs ) ).
% 0.26/0.59
% 0.26/0.59 % pair_pre_digraph.select_convs(2)
% 0.26/0.59 thf(fact_310_pair__pre__digraph_Oselect__convs_I2_J,axiom,
% 0.26/0.59 ! [Pverts: set_nat,Parcs: set_Pr1986765409at_nat,More: product_unit] :
% 0.26/0.59 ( ( pair_p715279805t_unit @ ( pair_p1167410509t_unit @ Pverts @ Parcs @ More ) )
% 0.26/0.59 = Parcs ) ).
% 0.26/0.59
% 0.26/0.59 % pair_pre_digraph.select_convs(2)
% 0.26/0.59 thf(fact_311_pair__pre__digraph_Oselect__convs_I2_J,axiom,
% 0.26/0.59 ! [Pverts: set_Product_prod_a_a,Parcs: set_Pr1948701895od_a_a,More: product_unit] :
% 0.26/0.59 ( ( pair_p1783210148t_unit @ ( pair_p398687508t_unit @ Pverts @ Parcs @ More ) )
% 0.26/0.59 = Parcs ) ).
% 0.26/0.59
% 0.26/0.59 % pair_pre_digraph.select_convs(2)
% 0.26/0.59 thf(fact_312_pair__pre__digraph_Oselect__convs_I1_J,axiom,
% 0.26/0.59 ! [Pverts: set_a,Parcs: set_Product_prod_a_a,More: product_unit] :
% 0.26/0.59 ( ( pair_p1047056820t_unit @ ( pair_p1621517565t_unit @ Pverts @ Parcs @ More ) )
% 0.26/0.59 = Pverts ) ).
% 0.26/0.59
% 0.26/0.59 % pair_pre_digraph.select_convs(1)
% 0.26/0.59 thf(fact_313_pair__pre__digraph_Oselect__convs_I1_J,axiom,
% 0.26/0.59 ! [Pverts: set_nat,Parcs: set_Pr1986765409at_nat,More: product_unit] :
% 0.26/0.59 ( ( pair_p1677060310t_unit @ ( pair_p1167410509t_unit @ Pverts @ Parcs @ More ) )
% 0.26/0.59 = Pverts ) ).
% 0.26/0.59
% 0.26/0.59 % pair_pre_digraph.select_convs(1)
% 0.26/0.59 thf(fact_314_pair__pre__digraph_Oselect__convs_I1_J,axiom,
% 0.26/0.59 ! [Pverts: set_Product_prod_a_a,Parcs: set_Pr1948701895od_a_a,More: product_unit] :
% 0.26/0.59 ( ( pair_p447552203t_unit @ ( pair_p398687508t_unit @ Pverts @ Parcs @ More ) )
% 0.26/0.59 = Pverts ) ).
% 0.26/0.59
% 0.26/0.59 % pair_pre_digraph.select_convs(1)
% 0.26/0.59 thf(fact_315_Fpow__def,axiom,
% 0.26/0.59 ( finite361944167at_nat
% 0.26/0.59 = ( ^ [A5: set_Pr1986765409at_nat] :
% 0.26/0.59 ( collec1606769740at_nat
% 0.26/0.59 @ ^ [X5: set_Pr1986765409at_nat] :
% 0.26/0.59 ( ( ord_le841296385at_nat @ X5 @ A5 )
% 0.26/0.59 & ( finite772653738at_nat @ X5 ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Fpow_def
% 0.26/0.59 thf(fact_316_Fpow__def,axiom,
% 0.26/0.59 ( finite702915405od_a_a
% 0.26/0.59 = ( ^ [A5: set_Pr1948701895od_a_a] :
% 0.26/0.59 ( collec453062450od_a_a
% 0.26/0.59 @ ^ [X5: set_Pr1948701895od_a_a] :
% 0.26/0.59 ( ( ord_le456379495od_a_a @ X5 @ A5 )
% 0.26/0.59 & ( finite1664988688od_a_a @ X5 ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Fpow_def
% 0.26/0.59 thf(fact_317_Fpow__def,axiom,
% 0.26/0.59 ( finite351630733od_a_a
% 0.26/0.59 = ( ^ [A5: set_Product_prod_a_a] :
% 0.26/0.59 ( collec183727474od_a_a
% 0.26/0.59 @ ^ [X5: set_Product_prod_a_a] :
% 0.26/0.59 ( ( ord_le1824328871od_a_a @ X5 @ A5 )
% 0.26/0.59 & ( finite179568208od_a_a @ X5 ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Fpow_def
% 0.26/0.59 thf(fact_318_Fpow__def,axiom,
% 0.26/0.59 ( finite_Fpow_nat
% 0.26/0.59 = ( ^ [A5: set_nat] :
% 0.26/0.59 ( collect_set_nat
% 0.26/0.59 @ ^ [X5: set_nat] :
% 0.26/0.59 ( ( ord_less_eq_set_nat @ X5 @ A5 )
% 0.26/0.59 & ( finite_finite_nat @ X5 ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Fpow_def
% 0.26/0.59 thf(fact_319_Fpow__def,axiom,
% 0.26/0.59 ( finite_Fpow_a
% 0.26/0.59 = ( ^ [A5: set_a] :
% 0.26/0.59 ( collect_set_a
% 0.26/0.59 @ ^ [X5: set_a] :
% 0.26/0.59 ( ( ord_less_eq_set_a @ X5 @ A5 )
% 0.26/0.59 & ( finite_finite_a @ X5 ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Fpow_def
% 0.26/0.59 thf(fact_320_pair__fin__digraph__def,axiom,
% 0.26/0.59 ( pair_p1802376898raph_a
% 0.26/0.59 = ( ^ [G: pair_p125712459t_unit] :
% 0.26/0.59 ( ( pair_p68905728raph_a @ G )
% 0.26/0.59 & ( pair_p1864019935ioms_a @ G ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % pair_fin_digraph_def
% 0.26/0.59 thf(fact_321_pair__fin__digraph__def,axiom,
% 0.26/0.59 ( pair_p128415500ph_nat
% 0.26/0.59 = ( ^ [G: pair_p1914262621t_unit] :
% 0.26/0.59 ( ( pair_p1515597646ph_nat @ G )
% 0.26/0.59 & ( pair_p1027063983ms_nat @ G ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % pair_fin_digraph_def
% 0.26/0.59 thf(fact_322_pair__fin__digraph__def,axiom,
% 0.26/0.59 ( pair_p374947051od_a_a
% 0.26/0.59 = ( ^ [G: pair_p1765063010t_unit] :
% 0.26/0.59 ( ( pair_p646030121od_a_a @ G )
% 0.26/0.59 & ( pair_p504738056od_a_a @ G ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % pair_fin_digraph_def
% 0.26/0.59 thf(fact_323_pair__fin__digraph_Ointro,axiom,
% 0.26/0.59 ! [G2: pair_p125712459t_unit] :
% 0.26/0.59 ( ( pair_p68905728raph_a @ G2 )
% 0.26/0.59 => ( ( pair_p1864019935ioms_a @ G2 )
% 0.26/0.59 => ( pair_p1802376898raph_a @ G2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % pair_fin_digraph.intro
% 0.26/0.59 thf(fact_324_pair__fin__digraph_Ointro,axiom,
% 0.26/0.59 ! [G2: pair_p1914262621t_unit] :
% 0.26/0.59 ( ( pair_p1515597646ph_nat @ G2 )
% 0.26/0.59 => ( ( pair_p1027063983ms_nat @ G2 )
% 0.26/0.59 => ( pair_p128415500ph_nat @ G2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % pair_fin_digraph.intro
% 0.26/0.59 thf(fact_325_pair__fin__digraph_Ointro,axiom,
% 0.26/0.59 ! [G2: pair_p1765063010t_unit] :
% 0.26/0.59 ( ( pair_p646030121od_a_a @ G2 )
% 0.26/0.59 => ( ( pair_p504738056od_a_a @ G2 )
% 0.26/0.59 => ( pair_p374947051od_a_a @ G2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % pair_fin_digraph.intro
% 0.26/0.59 thf(fact_326_finite__cartesian__product__iff,axiom,
% 0.26/0.59 ! [A: set_a,B: set_nat] :
% 0.26/0.59 ( ( finite1743148308_a_nat
% 0.26/0.59 @ ( product_Sigma_a_nat @ A
% 0.26/0.59 @ ^ [Uu: a] : B ) )
% 0.26/0.59 = ( ( A = bot_bot_set_a )
% 0.26/0.59 | ( B = bot_bot_set_nat )
% 0.26/0.59 | ( ( finite_finite_a @ A )
% 0.26/0.59 & ( finite_finite_nat @ B ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % finite_cartesian_product_iff
% 0.26/0.59 thf(fact_327_finite__cartesian__product__iff,axiom,
% 0.26/0.59 ! [A: set_nat,B: set_a] :
% 0.26/0.59 ( ( finite1808550458_nat_a
% 0.26/0.59 @ ( product_Sigma_nat_a @ A
% 0.26/0.59 @ ^ [Uu: nat] : B ) )
% 0.26/0.59 = ( ( A = bot_bot_set_nat )
% 0.26/0.59 | ( B = bot_bot_set_a )
% 0.26/0.59 | ( ( finite_finite_nat @ A )
% 0.26/0.59 & ( finite_finite_a @ B ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % finite_cartesian_product_iff
% 0.26/0.59 thf(fact_328_finite__cartesian__product__iff,axiom,
% 0.26/0.59 ! [A: set_nat,B: set_nat] :
% 0.26/0.59 ( ( finite772653738at_nat
% 0.26/0.59 @ ( produc45129834at_nat @ A
% 0.26/0.59 @ ^ [Uu: nat] : B ) )
% 0.26/0.59 = ( ( A = bot_bot_set_nat )
% 0.26/0.59 | ( B = bot_bot_set_nat )
% 0.26/0.59 | ( ( finite_finite_nat @ A )
% 0.26/0.59 & ( finite_finite_nat @ B ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % finite_cartesian_product_iff
% 0.26/0.59 thf(fact_329_finite__cartesian__product__iff,axiom,
% 0.26/0.59 ! [A: set_a,B: set_a] :
% 0.26/0.59 ( ( finite179568208od_a_a
% 0.26/0.59 @ ( product_Sigma_a_a @ A
% 0.26/0.59 @ ^ [Uu: a] : B ) )
% 0.26/0.59 = ( ( A = bot_bot_set_a )
% 0.26/0.59 | ( B = bot_bot_set_a )
% 0.26/0.59 | ( ( finite_finite_a @ A )
% 0.26/0.59 & ( finite_finite_a @ B ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % finite_cartesian_product_iff
% 0.26/0.59 thf(fact_330_finite__cartesian__product__iff,axiom,
% 0.26/0.59 ! [A: set_Product_prod_a_a,B: set_a] :
% 0.26/0.59 ( ( finite1919032935_a_a_a
% 0.26/0.59 @ ( produc1282482655_a_a_a @ A
% 0.26/0.59 @ ^ [Uu: product_prod_a_a] : B ) )
% 0.26/0.59 = ( ( A = bot_bo2131659635od_a_a )
% 0.26/0.59 | ( B = bot_bot_set_a )
% 0.26/0.59 | ( ( finite179568208od_a_a @ A )
% 0.26/0.59 & ( finite_finite_a @ B ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % finite_cartesian_product_iff
% 0.26/0.59 thf(fact_331_finite__cartesian__product__iff,axiom,
% 0.26/0.59 ! [A: set_Product_prod_a_a,B: set_nat] :
% 0.26/0.59 ( ( finite1837575485_a_nat
% 0.26/0.59 @ ( produc931712687_a_nat @ A
% 0.26/0.59 @ ^ [Uu: product_prod_a_a] : B ) )
% 0.26/0.59 = ( ( A = bot_bo2131659635od_a_a )
% 0.26/0.59 | ( B = bot_bot_set_nat )
% 0.26/0.59 | ( ( finite179568208od_a_a @ A )
% 0.26/0.59 & ( finite_finite_nat @ B ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % finite_cartesian_product_iff
% 0.26/0.59 thf(fact_332_finite__cartesian__product__iff,axiom,
% 0.26/0.59 ! [A: set_a,B: set_Product_prod_a_a] :
% 0.26/0.59 ( ( finite676513017od_a_a
% 0.26/0.59 @ ( produc520147185od_a_a @ A
% 0.26/0.59 @ ^ [Uu: a] : B ) )
% 0.26/0.59 = ( ( A = bot_bot_set_a )
% 0.26/0.59 | ( B = bot_bo2131659635od_a_a )
% 0.26/0.59 | ( ( finite_finite_a @ A )
% 0.26/0.59 & ( finite179568208od_a_a @ B ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % finite_cartesian_product_iff
% 0.26/0.59 thf(fact_333_finite__cartesian__product__iff,axiom,
% 0.26/0.59 ! [A: set_a,B: set_Pr1986765409at_nat] :
% 0.26/0.59 ( ( finite942416723at_nat
% 0.26/0.59 @ ( produc292491723at_nat @ A
% 0.26/0.59 @ ^ [Uu: a] : B ) )
% 0.26/0.59 = ( ( A = bot_bot_set_a )
% 0.26/0.59 | ( B = bot_bo2130386637at_nat )
% 0.26/0.59 | ( ( finite_finite_a @ A )
% 0.26/0.59 & ( finite772653738at_nat @ B ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % finite_cartesian_product_iff
% 0.26/0.59 thf(fact_334_finite__cartesian__product__iff,axiom,
% 0.26/0.59 ! [A: set_nat,B: set_Product_prod_a_a] :
% 0.26/0.59 ( ( finite1297454819od_a_a
% 0.26/0.59 @ ( produc1182842125od_a_a @ A
% 0.26/0.59 @ ^ [Uu: nat] : B ) )
% 0.26/0.59 = ( ( A = bot_bot_set_nat )
% 0.26/0.59 | ( B = bot_bo2131659635od_a_a )
% 0.26/0.59 | ( ( finite_finite_nat @ A )
% 0.26/0.59 & ( finite179568208od_a_a @ B ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % finite_cartesian_product_iff
% 0.26/0.59 thf(fact_335_finite__cartesian__product__iff,axiom,
% 0.26/0.59 ! [A: set_nat,B: set_Pr1986765409at_nat] :
% 0.26/0.59 ( ( finite277291581at_nat
% 0.26/0.59 @ ( produc894163943at_nat @ A
% 0.26/0.59 @ ^ [Uu: nat] : B ) )
% 0.26/0.59 = ( ( A = bot_bot_set_nat )
% 0.26/0.59 | ( B = bot_bo2130386637at_nat )
% 0.26/0.59 | ( ( finite_finite_nat @ A )
% 0.26/0.59 & ( finite772653738at_nat @ B ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % finite_cartesian_product_iff
% 0.26/0.59 thf(fact_336_empty__iff,axiom,
% 0.26/0.59 ! [C2: product_prod_a_a] :
% 0.26/0.59 ~ ( member449909584od_a_a @ C2 @ bot_bo2131659635od_a_a ) ).
% 0.26/0.59
% 0.26/0.59 % empty_iff
% 0.26/0.59 thf(fact_337_empty__iff,axiom,
% 0.26/0.59 ! [C2: nat] :
% 0.26/0.59 ~ ( member_nat @ C2 @ bot_bot_set_nat ) ).
% 0.26/0.59
% 0.26/0.59 % empty_iff
% 0.26/0.59 thf(fact_338_all__not__in__conv,axiom,
% 0.26/0.59 ! [A: set_Product_prod_a_a] :
% 0.26/0.59 ( ( ! [X2: product_prod_a_a] :
% 0.26/0.59 ~ ( member449909584od_a_a @ X2 @ A ) )
% 0.26/0.59 = ( A = bot_bo2131659635od_a_a ) ) ).
% 0.26/0.59
% 0.26/0.59 % all_not_in_conv
% 0.26/0.59 thf(fact_339_all__not__in__conv,axiom,
% 0.26/0.59 ! [A: set_nat] :
% 0.26/0.59 ( ( ! [X2: nat] :
% 0.26/0.59 ~ ( member_nat @ X2 @ A ) )
% 0.26/0.59 = ( A = bot_bot_set_nat ) ) ).
% 0.26/0.59
% 0.26/0.59 % all_not_in_conv
% 0.26/0.59 thf(fact_340_Collect__empty__eq,axiom,
% 0.26/0.59 ! [P: product_prod_a_a > $o] :
% 0.26/0.59 ( ( ( collec645855634od_a_a @ P )
% 0.26/0.59 = bot_bo2131659635od_a_a )
% 0.26/0.59 = ( ! [X2: product_prod_a_a] :
% 0.26/0.59 ~ ( P @ X2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Collect_empty_eq
% 0.26/0.59 thf(fact_341_Collect__empty__eq,axiom,
% 0.26/0.59 ! [P: nat > $o] :
% 0.26/0.59 ( ( ( collect_nat @ P )
% 0.26/0.59 = bot_bot_set_nat )
% 0.26/0.59 = ( ! [X2: nat] :
% 0.26/0.59 ~ ( P @ X2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % Collect_empty_eq
% 0.26/0.59 thf(fact_342_empty__Collect__eq,axiom,
% 0.26/0.59 ! [P: product_prod_a_a > $o] :
% 0.26/0.59 ( ( bot_bo2131659635od_a_a
% 0.26/0.59 = ( collec645855634od_a_a @ P ) )
% 0.26/0.59 = ( ! [X2: product_prod_a_a] :
% 0.26/0.59 ~ ( P @ X2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % empty_Collect_eq
% 0.26/0.59 thf(fact_343_empty__Collect__eq,axiom,
% 0.26/0.59 ! [P: nat > $o] :
% 0.26/0.59 ( ( bot_bot_set_nat
% 0.26/0.59 = ( collect_nat @ P ) )
% 0.26/0.59 = ( ! [X2: nat] :
% 0.26/0.59 ~ ( P @ X2 ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % empty_Collect_eq
% 0.26/0.59 thf(fact_344_empty__subsetI,axiom,
% 0.26/0.59 ! [A: set_Product_prod_a_a] : ( ord_le1824328871od_a_a @ bot_bo2131659635od_a_a @ A ) ).
% 0.26/0.59
% 0.26/0.59 % empty_subsetI
% 0.26/0.59 thf(fact_345_empty__subsetI,axiom,
% 0.26/0.59 ! [A: set_nat] : ( ord_less_eq_set_nat @ bot_bot_set_nat @ A ) ).
% 0.26/0.59
% 0.26/0.59 % empty_subsetI
% 0.26/0.59 thf(fact_346_empty__subsetI,axiom,
% 0.26/0.59 ! [A: set_a] : ( ord_less_eq_set_a @ bot_bot_set_a @ A ) ).
% 0.26/0.59
% 0.26/0.59 % empty_subsetI
% 0.26/0.59 thf(fact_347_subset__empty,axiom,
% 0.26/0.59 ! [A: set_a] :
% 0.26/0.59 ( ( ord_less_eq_set_a @ A @ bot_bot_set_a )
% 0.26/0.59 = ( A = bot_bot_set_a ) ) ).
% 0.26/0.59
% 0.26/0.59 % subset_empty
% 0.26/0.59 thf(fact_348_calculation,axiom,
% 0.26/0.59 ( ( finite_finite_a @ ( pair_p1047056820t_unit @ g ) )
% 0.26/0.59 & ( ( finite_card_a @ ( pair_p1047056820t_unit @ g ) )
% 0.26/0.59 = n )
% 0.26/0.59 & ( ( pair_p133601421t_unit @ g )
% 0.26/0.59 = ( collec645855634od_a_a
% 0.26/0.59 @ ( produc1833107820_a_a_o
% 0.26/0.59 @ ^ [U: a,V: a] :
% 0.26/0.59 ( ( member449909584od_a_a @ ( product_Pair_a_a @ U @ V )
% 0.26/0.59 @ ( product_Sigma_a_a @ ( pair_p1047056820t_unit @ g )
% 0.26/0.59 @ ^ [Uu: a] : ( pair_p1047056820t_unit @ g ) ) )
% 0.26/0.59 & ( U != V ) ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % calculation
% 0.26/0.59 thf(fact_349_finite__Collect__le__nat,axiom,
% 0.26/0.59 ! [K: nat] :
% 0.26/0.59 ( finite_finite_nat
% 0.26/0.59 @ ( collect_nat
% 0.26/0.59 @ ^ [N: nat] : ( ord_less_eq_nat @ N @ K ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % finite_Collect_le_nat
% 0.26/0.59 thf(fact_350_finite__nat__set__iff__bounded__le,axiom,
% 0.26/0.59 ( finite_finite_nat
% 0.26/0.59 = ( ^ [N2: set_nat] :
% 0.26/0.59 ? [M: nat] :
% 0.26/0.59 ! [X2: nat] :
% 0.26/0.59 ( ( member_nat @ X2 @ N2 )
% 0.26/0.59 => ( ord_less_eq_nat @ X2 @ M ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % finite_nat_set_iff_bounded_le
% 0.26/0.59 thf(fact_351_infinite__nat__iff__unbounded__le,axiom,
% 0.26/0.59 ! [S: set_nat] :
% 0.26/0.59 ( ( ~ ( finite_finite_nat @ S ) )
% 0.26/0.59 = ( ! [M: nat] :
% 0.26/0.59 ? [N: nat] :
% 0.26/0.59 ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.59 & ( member_nat @ N @ S ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % infinite_nat_iff_unbounded_le
% 0.26/0.59 thf(fact_352_bounded__Max__nat,axiom,
% 0.26/0.59 ! [P: nat > $o,X3: nat,M2: nat] :
% 0.26/0.59 ( ( P @ X3 )
% 0.26/0.59 => ( ! [X: nat] :
% 0.26/0.59 ( ( P @ X )
% 0.26/0.59 => ( ord_less_eq_nat @ X @ M2 ) )
% 0.26/0.59 => ~ ! [M3: nat] :
% 0.26/0.59 ( ( P @ M3 )
% 0.26/0.59 => ~ ! [X6: nat] :
% 0.26/0.59 ( ( P @ X6 )
% 0.26/0.59 => ( ord_less_eq_nat @ X6 @ M3 ) ) ) ) ) ).
% 0.26/0.59
% 0.26/0.59 % bounded_Max_nat
% 0.26/0.59 thf(fact_353_finite__less__ub,axiom,
% 0.26/0.59 ! [F: nat > nat,U2: nat] :
% 0.26/0.59 ( ! [N3: nat] : ( ord_less_eq_nat @ N3 @ ( F @ N3 ) )
% 0.26/0.68 => ( finite_finite_nat
% 0.26/0.68 @ ( collect_nat
% 0.26/0.68 @ ^ [N: nat] : ( ord_less_eq_nat @ ( F @ N ) @ U2 ) ) ) ) ).
% 0.26/0.68
% 0.26/0.68 % finite_less_ub
% 0.26/0.68
% 0.26/0.68 % Conjectures (1)
% 0.26/0.68 thf(conj_0,conjecture,
% 0.26/0.68 finite179568208od_a_a @ ( pair_p133601421t_unit @ g ) ).
% 0.26/0.68
% 0.26/0.68 %------------------------------------------------------------------------------
% 0.26/0.68 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.5XOAeiifJn/cvc5---1.0.5_21782.p...
% 0.26/0.68 (declare-sort $$unsorted 0)
% 0.26/0.68 (declare-sort tptp.set_Pr1295299783od_a_a 0)
% 0.26/0.68 (declare-sort tptp.pair_p1593840546t_unit 0)
% 0.26/0.68 (declare-sort tptp.pair_p2041852168t_unit 0)
% 0.26/0.68 (declare-sort tptp.set_Pr1490359111at_nat 0)
% 0.26/0.68 (declare-sort tptp.pair_p1765063010t_unit 0)
% 0.26/0.68 (declare-sort tptp.set_se958357159od_a_a 0)
% 0.26/0.68 (declare-sort tptp.set_Pr1948701895od_a_a 0)
% 0.26/0.68 (declare-sort tptp.pair_p1914262621t_unit 0)
% 0.26/0.68 (declare-sort tptp.set_Pr1746169692at_nat 0)
% 0.26/0.68 (declare-sort tptp.produc1572603623od_a_a 0)
% 0.26/0.68 (declare-sort tptp.pair_p125712459t_unit 0)
% 0.26/0.68 (declare-sort tptp.set_Pr7688842at_nat 0)
% 0.26/0.68 (declare-sort tptp.set_Pr894832732_a_nat 0)
% 0.26/0.68 (declare-sort tptp.set_Pr339609346od_a_a 0)
% 0.26/0.68 (declare-sort tptp.set_Pr681306928od_a_a 0)
% 0.26/0.68 (declare-sort tptp.set_Pr1689873822_a_a_a 0)
% 0.26/0.68 (declare-sort tptp.set_se1612935105at_nat 0)
% 0.26/0.68 (declare-sort tptp.set_se1596668135od_a_a 0)
% 0.26/0.68 (declare-sort tptp.set_Pr1986765409at_nat 0)
% 0.26/0.68 (declare-sort tptp.set_Pr548851891_a_nat 0)
% 0.26/0.68 (declare-sort tptp.set_Pr967348953_nat_a 0)
% 0.26/0.68 (declare-sort tptp.set_Product_prod_a_a 0)
% 0.26/0.68 (declare-sort tptp.product_prod_nat_nat 0)
% 0.26/0.68 (declare-sort tptp.set_set_nat 0)
% 0.26/0.68 (declare-sort tptp.product_prod_a_a 0)
% 0.26/0.68 (declare-sort tptp.set_set_a 0)
% 0.26/0.68 (declare-sort tptp.set_nat 0)
% 0.26/0.68 (declare-sort tptp.product_unit 0)
% 0.26/0.68 (declare-sort tptp.set_a 0)
% 0.26/0.68 (declare-sort tptp.nat 0)
% 0.26/0.68 (declare-sort tptp.a 0)
% 0.26/0.68 (declare-fun tptp.finite_Fpow_nat (tptp.set_nat) tptp.set_set_nat)
% 0.26/0.68 (declare-fun tptp.finite361944167at_nat (tptp.set_Pr1986765409at_nat) tptp.set_se1612935105at_nat)
% 0.26/0.68 (declare-fun tptp.finite702915405od_a_a (tptp.set_Pr1948701895od_a_a) tptp.set_se958357159od_a_a)
% 0.26/0.68 (declare-fun tptp.finite351630733od_a_a (tptp.set_Product_prod_a_a) tptp.set_se1596668135od_a_a)
% 0.26/0.68 (declare-fun tptp.finite_Fpow_a (tptp.set_a) tptp.set_set_a)
% 0.26/0.68 (declare-fun tptp.finite_card_a (tptp.set_a) tptp.nat)
% 0.26/0.68 (declare-fun tptp.finite_finite_nat (tptp.set_nat) Bool)
% 0.26/0.68 (declare-fun tptp.finite772653738at_nat (tptp.set_Pr1986765409at_nat) Bool)
% 0.26/0.68 (declare-fun tptp.finite277291581at_nat (tptp.set_Pr1746169692at_nat) Bool)
% 0.26/0.68 (declare-fun tptp.finite1297454819od_a_a (tptp.set_Pr339609346od_a_a) Bool)
% 0.26/0.68 (declare-fun tptp.finite1808550458_nat_a (tptp.set_Pr967348953_nat_a) Bool)
% 0.26/0.68 (declare-fun tptp.finite48957584at_nat (tptp.set_Pr1490359111at_nat) Bool)
% 0.26/0.68 (declare-fun tptp.finite256329232od_a_a (tptp.set_Pr1295299783od_a_a) Bool)
% 0.26/0.68 (declare-fun tptp.finite1837575485_a_nat (tptp.set_Pr894832732_a_nat) Bool)
% 0.26/0.68 (declare-fun tptp.finite1664988688od_a_a (tptp.set_Pr1948701895od_a_a) Bool)
% 0.26/0.68 (declare-fun tptp.finite1919032935_a_a_a (tptp.set_Pr1689873822_a_a_a) Bool)
% 0.26/0.68 (declare-fun tptp.finite1743148308_a_nat (tptp.set_Pr548851891_a_nat) Bool)
% 0.26/0.68 (declare-fun tptp.finite942416723at_nat (tptp.set_Pr7688842at_nat) Bool)
% 0.26/0.68 (declare-fun tptp.finite676513017od_a_a (tptp.set_Pr681306928od_a_a) Bool)
% 0.26/0.68 (declare-fun tptp.finite179568208od_a_a (tptp.set_Product_prod_a_a) Bool)
% 0.26/0.68 (declare-fun tptp.finite2012248349et_nat (tptp.set_set_nat) Bool)
% 0.26/0.68 (declare-fun tptp.finite1457549322at_nat (tptp.set_se1612935105at_nat) Bool)
% 0.26/0.68 (declare-fun tptp.finite323969008od_a_a (tptp.set_se958357159od_a_a) Bool)
% 0.26/0.68 (declare-fun tptp.finite1145471536od_a_a (tptp.set_se1596668135od_a_a) Bool)
% 0.26/0.68 (declare-fun tptp.finite_finite_set_a (tptp.set_set_a) Bool)
% 0.26/0.68 (declare-fun tptp.finite_finite_a (tptp.set_a) Bool)
% 0.26/0.68 (declare-fun tptp.bot_bot_set_nat () tptp.set_nat)
% 0.26/0.68 (declare-fun tptp.bot_bo2130386637at_nat () tptp.set_Pr1986765409at_nat)
% 0.26/0.68 (declare-fun tptp.bot_bo2131659635od_a_a () tptp.set_Product_prod_a_a)
% 0.26/0.68 (declare-fun tptp.bot_bot_set_a () tptp.set_a)
% 0.26/0.68 (declare-fun tptp.ord_less_eq_nat_o ((-> tptp.nat Bool) (-> tptp.nat Bool)) Bool)
% 0.26/0.68 (declare-fun tptp.ord_le1347718902_a_a_o ((-> tptp.product_prod_a_a Bool) (-> tptp.product_prod_a_a Bool)) Bool)
% 0.26/0.68 (declare-fun tptp.ord_less_eq_a_o ((-> tptp.a Bool) (-> tptp.a Bool)) Bool)
% 0.26/0.68 (declare-fun tptp.ord_less_eq_nat (tptp.nat tptp.nat) Bool)
% 0.26/0.68 (declare-fun tptp.ord_less_eq_set_nat (tptp.set_nat tptp.set_nat) Bool)
% 0.26/0.68 (declare-fun tptp.ord_le841296385at_nat (tptp.set_Pr1986765409at_nat tptp.set_Pr1986765409at_nat) Bool)
% 0.26/0.68 (declare-fun tptp.ord_le2084554594od_a_a (tptp.set_Pr339609346od_a_a tptp.set_Pr339609346od_a_a) Bool)
% 0.26/0.68 (declare-fun tptp.ord_le344568633_nat_a (tptp.set_Pr967348953_nat_a tptp.set_Pr967348953_nat_a) Bool)
% 0.26/0.68 (declare-fun tptp.ord_le492294332_a_nat (tptp.set_Pr894832732_a_nat tptp.set_Pr894832732_a_nat) Bool)
% 0.26/0.68 (declare-fun tptp.ord_le456379495od_a_a (tptp.set_Pr1948701895od_a_a tptp.set_Pr1948701895od_a_a) Bool)
% 0.26/0.68 (declare-fun tptp.ord_le677315902_a_a_a (tptp.set_Pr1689873822_a_a_a tptp.set_Pr1689873822_a_a_a) Bool)
% 0.26/0.68 (declare-fun tptp.ord_le2073555219_a_nat (tptp.set_Pr548851891_a_nat tptp.set_Pr548851891_a_nat) Bool)
% 0.26/0.68 (declare-fun tptp.ord_le1816232656od_a_a (tptp.set_Pr681306928od_a_a tptp.set_Pr681306928od_a_a) Bool)
% 0.26/0.68 (declare-fun tptp.ord_le1824328871od_a_a (tptp.set_Product_prod_a_a tptp.set_Product_prod_a_a) Bool)
% 0.26/0.68 (declare-fun tptp.ord_less_eq_set_a (tptp.set_a tptp.set_a) Bool)
% 0.26/0.68 (declare-fun tptp.pair_p128415500ph_nat (tptp.pair_p1914262621t_unit) Bool)
% 0.26/0.68 (declare-fun tptp.pair_p752841413at_nat (tptp.pair_p2041852168t_unit) Bool)
% 0.26/0.68 (declare-fun tptp.pair_p159207083od_a_a (tptp.pair_p1593840546t_unit) Bool)
% 0.26/0.68 (declare-fun tptp.pair_p374947051od_a_a (tptp.pair_p1765063010t_unit) Bool)
% 0.26/0.68 (declare-fun tptp.pair_p1802376898raph_a (tptp.pair_p125712459t_unit) Bool)
% 0.26/0.68 (declare-fun tptp.pair_p1027063983ms_nat (tptp.pair_p1914262621t_unit) Bool)
% 0.26/0.68 (declare-fun tptp.pair_p56914274at_nat (tptp.pair_p2041852168t_unit) Bool)
% 0.26/0.68 (declare-fun tptp.pair_p1906342088od_a_a (tptp.pair_p1593840546t_unit) Bool)
% 0.26/0.68 (declare-fun tptp.pair_p504738056od_a_a (tptp.pair_p1765063010t_unit) Bool)
% 0.26/0.68 (declare-fun tptp.pair_p1864019935ioms_a (tptp.pair_p125712459t_unit) Bool)
% 0.26/0.68 (declare-fun tptp.pair_p69470259t_unit (tptp.pair_p1914262621t_unit) tptp.product_unit)
% 0.26/0.68 (declare-fun tptp.pair_p1984658862t_unit (tptp.pair_p1765063010t_unit) tptp.product_unit)
% 0.26/0.68 (declare-fun tptp.pair_p1896222615t_unit (tptp.pair_p125712459t_unit) tptp.product_unit)
% 0.26/0.68 (declare-fun tptp.pair_p1167410509t_unit (tptp.set_nat tptp.set_Pr1986765409at_nat tptp.product_unit) tptp.pair_p1914262621t_unit)
% 0.26/0.68 (declare-fun tptp.pair_p398687508t_unit (tptp.set_Product_prod_a_a tptp.set_Pr1948701895od_a_a tptp.product_unit) tptp.pair_p1765063010t_unit)
% 0.26/0.68 (declare-fun tptp.pair_p1621517565t_unit (tptp.set_a tptp.set_Product_prod_a_a tptp.product_unit) tptp.pair_p125712459t_unit)
% 0.26/0.68 (declare-fun tptp.pair_p715279805t_unit (tptp.pair_p1914262621t_unit) tptp.set_Pr1986765409at_nat)
% 0.26/0.68 (declare-fun tptp.pair_p806300874t_unit (tptp.pair_p2041852168t_unit) tptp.set_Pr1490359111at_nat)
% 0.26/0.68 (declare-fun tptp.pair_p1559300324t_unit (tptp.pair_p1593840546t_unit) tptp.set_Pr1295299783od_a_a)
% 0.26/0.68 (declare-fun tptp.pair_p1783210148t_unit (tptp.pair_p1765063010t_unit) tptp.set_Pr1948701895od_a_a)
% 0.26/0.68 (declare-fun tptp.pair_p133601421t_unit (tptp.pair_p125712459t_unit) tptp.set_Product_prod_a_a)
% 0.26/0.68 (declare-fun tptp.pair_p1677060310t_unit (tptp.pair_p1914262621t_unit) tptp.set_nat)
% 0.26/0.68 (declare-fun tptp.pair_p210955889t_unit (tptp.pair_p2041852168t_unit) tptp.set_Pr1986765409at_nat)
% 0.26/0.68 (declare-fun tptp.pair_p1652294923t_unit (tptp.pair_p1593840546t_unit) tptp.set_Pr1948701895od_a_a)
% 0.26/0.68 (declare-fun tptp.pair_p447552203t_unit (tptp.pair_p1765063010t_unit) tptp.set_Product_prod_a_a)
% 0.26/0.68 (declare-fun tptp.pair_p1047056820t_unit (tptp.pair_p125712459t_unit) tptp.set_a)
% 0.26/0.68 (declare-fun tptp.pair_p1515597646ph_nat (tptp.pair_p1914262621t_unit) Bool)
% 0.26/0.68 (declare-fun tptp.pair_p646030121od_a_a (tptp.pair_p1765063010t_unit) Bool)
% 0.26/0.68 (declare-fun tptp.pair_p68905728raph_a (tptp.pair_p125712459t_unit) Bool)
% 0.26/0.68 (declare-fun tptp.product_Pair_a_a (tptp.a tptp.a) tptp.product_prod_a_a)
% 0.26/0.68 (declare-fun tptp.produc45129834at_nat (tptp.set_nat (-> tptp.nat tptp.set_nat)) tptp.set_Pr1986765409at_nat)
% 0.26/0.68 (declare-fun tptp.produc894163943at_nat (tptp.set_nat (-> tptp.nat tptp.set_Pr1986765409at_nat)) tptp.set_Pr1746169692at_nat)
% 0.26/0.68 (declare-fun tptp.produc1182842125od_a_a (tptp.set_nat (-> tptp.nat tptp.set_Product_prod_a_a)) tptp.set_Pr339609346od_a_a)
% 0.26/0.68 (declare-fun tptp.product_Sigma_nat_a (tptp.set_nat (-> tptp.nat tptp.set_a)) tptp.set_Pr967348953_nat_a)
% 0.26/0.68 (declare-fun tptp.produc931712687_a_nat (tptp.set_Product_prod_a_a (-> tptp.product_prod_a_a tptp.set_nat)) tptp.set_Pr894832732_a_nat)
% 0.26/0.68 (declare-fun tptp.produc304751368od_a_a (tptp.set_Product_prod_a_a (-> tptp.product_prod_a_a tptp.set_Product_prod_a_a)) tptp.set_Pr1948701895od_a_a)
% 0.26/0.68 (declare-fun tptp.produc1282482655_a_a_a (tptp.set_Product_prod_a_a (-> tptp.product_prod_a_a tptp.set_a)) tptp.set_Pr1689873822_a_a_a)
% 0.26/0.68 (declare-fun tptp.product_Sigma_a_nat (tptp.set_a (-> tptp.a tptp.set_nat)) tptp.set_Pr548851891_a_nat)
% 0.26/0.68 (declare-fun tptp.produc292491723at_nat (tptp.set_a (-> tptp.a tptp.set_Pr1986765409at_nat)) tptp.set_Pr7688842at_nat)
% 0.26/0.68 (declare-fun tptp.produc520147185od_a_a (tptp.set_a (-> tptp.a tptp.set_Product_prod_a_a)) tptp.set_Pr681306928od_a_a)
% 0.26/0.68 (declare-fun tptp.product_Sigma_a_a (tptp.set_a (-> tptp.a tptp.set_a)) tptp.set_Product_prod_a_a)
% 0.26/0.68 (declare-fun tptp.produc1833107820_a_a_o ((-> tptp.a tptp.a Bool) tptp.product_prod_a_a) Bool)
% 0.26/0.68 (declare-fun tptp.product_product_a_a (tptp.set_a tptp.set_a) tptp.set_Product_prod_a_a)
% 0.26/0.68 (declare-fun tptp.collect_nat ((-> tptp.nat Bool)) tptp.set_nat)
% 0.26/0.68 (declare-fun tptp.collec7649004at_nat ((-> tptp.product_prod_nat_nat Bool)) tptp.set_Pr1986765409at_nat)
% 0.26/0.68 (declare-fun tptp.collec1635618130od_a_a ((-> tptp.produc1572603623od_a_a Bool)) tptp.set_Pr1948701895od_a_a)
% 0.26/0.68 (declare-fun tptp.collec645855634od_a_a ((-> tptp.product_prod_a_a Bool)) tptp.set_Product_prod_a_a)
% 0.26/0.68 (declare-fun tptp.collect_set_nat ((-> tptp.set_nat Bool)) tptp.set_set_nat)
% 0.26/0.68 (declare-fun tptp.collec1606769740at_nat ((-> tptp.set_Pr1986765409at_nat Bool)) tptp.set_se1612935105at_nat)
% 0.26/0.68 (declare-fun tptp.collec453062450od_a_a ((-> tptp.set_Pr1948701895od_a_a Bool)) tptp.set_se958357159od_a_a)
% 0.26/0.68 (declare-fun tptp.collec183727474od_a_a ((-> tptp.set_Product_prod_a_a Bool)) tptp.set_se1596668135od_a_a)
% 0.26/0.68 (declare-fun tptp.collect_set_a ((-> tptp.set_a Bool)) tptp.set_set_a)
% 0.26/0.68 (declare-fun tptp.collect_a ((-> tptp.a Bool)) tptp.set_a)
% 0.26/0.68 (declare-fun tptp.member_nat (tptp.nat tptp.set_nat) Bool)
% 0.26/0.68 (declare-fun tptp.member701585322at_nat (tptp.product_prod_nat_nat tptp.set_Pr1986765409at_nat) Bool)
% 0.26/0.68 (declare-fun tptp.member449909584od_a_a (tptp.product_prod_a_a tptp.set_Product_prod_a_a) Bool)
% 0.26/0.68 (declare-fun tptp.member_set_nat (tptp.set_nat tptp.set_set_nat) Bool)
% 0.26/0.68 (declare-fun tptp.member1838126896od_a_a (tptp.set_Product_prod_a_a tptp.set_se1596668135od_a_a) Bool)
% 0.26/0.68 (declare-fun tptp.member_set_a (tptp.set_a tptp.set_set_a) Bool)
% 0.26/0.68 (declare-fun tptp.member_a (tptp.a tptp.set_a) Bool)
% 0.26/0.68 (declare-fun tptp.g () tptp.pair_p125712459t_unit)
% 0.26/0.68 (declare-fun tptp.n () tptp.nat)
% 0.26/0.68 (assert (@ tptp.finite179568208od_a_a (@ (@ tptp.product_Sigma_a_a (@ tptp.pair_p1047056820t_unit tptp.g)) (lambda ((Uu tptp.a)) (@ tptp.pair_p1047056820t_unit tptp.g)))))
% 0.26/0.68 (assert (@ (@ tptp.ord_le1824328871od_a_a (@ tptp.pair_p133601421t_unit tptp.g)) (@ (@ tptp.product_Sigma_a_a (@ tptp.pair_p1047056820t_unit tptp.g)) (lambda ((Uu tptp.a)) (@ tptp.pair_p1047056820t_unit tptp.g)))))
% 0.26/0.68 (assert (= tptp.pair_p56914274at_nat (lambda ((G tptp.pair_p2041852168t_unit)) (and (@ tptp.finite772653738at_nat (@ tptp.pair_p210955889t_unit G)) (@ tptp.finite48957584at_nat (@ tptp.pair_p806300874t_unit G))))))
% 0.26/0.68 (assert (= tptp.pair_p1906342088od_a_a (lambda ((G tptp.pair_p1593840546t_unit)) (and (@ tptp.finite1664988688od_a_a (@ tptp.pair_p1652294923t_unit G)) (@ tptp.finite256329232od_a_a (@ tptp.pair_p1559300324t_unit G))))))
% 0.26/0.68 (assert (= tptp.pair_p504738056od_a_a (lambda ((G tptp.pair_p1765063010t_unit)) (and (@ tptp.finite179568208od_a_a (@ tptp.pair_p447552203t_unit G)) (@ tptp.finite1664988688od_a_a (@ tptp.pair_p1783210148t_unit G))))))
% 0.26/0.68 (assert (= tptp.pair_p1027063983ms_nat (lambda ((G tptp.pair_p1914262621t_unit)) (and (@ tptp.finite_finite_nat (@ tptp.pair_p1677060310t_unit G)) (@ tptp.finite772653738at_nat (@ tptp.pair_p715279805t_unit G))))))
% 0.26/0.68 (assert (= tptp.pair_p1864019935ioms_a (lambda ((G tptp.pair_p125712459t_unit)) (and (@ tptp.finite_finite_a (@ tptp.pair_p1047056820t_unit G)) (@ tptp.finite179568208od_a_a (@ tptp.pair_p133601421t_unit G))))))
% 0.26/0.68 (assert (forall ((G2 tptp.pair_p2041852168t_unit)) (=> (@ tptp.finite772653738at_nat (@ tptp.pair_p210955889t_unit G2)) (=> (@ tptp.finite48957584at_nat (@ tptp.pair_p806300874t_unit G2)) (@ tptp.pair_p56914274at_nat G2)))))
% 0.26/0.68 (assert (forall ((G2 tptp.pair_p1593840546t_unit)) (=> (@ tptp.finite1664988688od_a_a (@ tptp.pair_p1652294923t_unit G2)) (=> (@ tptp.finite256329232od_a_a (@ tptp.pair_p1559300324t_unit G2)) (@ tptp.pair_p1906342088od_a_a G2)))))
% 0.26/0.68 (assert (forall ((G2 tptp.pair_p1765063010t_unit)) (=> (@ tptp.finite179568208od_a_a (@ tptp.pair_p447552203t_unit G2)) (=> (@ tptp.finite1664988688od_a_a (@ tptp.pair_p1783210148t_unit G2)) (@ tptp.pair_p504738056od_a_a G2)))))
% 0.26/0.68 (assert (forall ((G2 tptp.pair_p1914262621t_unit)) (=> (@ tptp.finite_finite_nat (@ tptp.pair_p1677060310t_unit G2)) (=> (@ tptp.finite772653738at_nat (@ tptp.pair_p715279805t_unit G2)) (@ tptp.pair_p1027063983ms_nat G2)))))
% 0.26/0.68 (assert (forall ((G2 tptp.pair_p125712459t_unit)) (=> (@ tptp.finite_finite_a (@ tptp.pair_p1047056820t_unit G2)) (=> (@ tptp.finite179568208od_a_a (@ tptp.pair_p133601421t_unit G2)) (@ tptp.pair_p1864019935ioms_a G2)))))
% 0.26/0.68 (assert (forall ((G2 tptp.pair_p1914262621t_unit)) (=> (@ tptp.pair_p128415500ph_nat G2) (@ tptp.finite772653738at_nat (@ tptp.pair_p715279805t_unit G2)))))
% 0.26/0.68 (assert (forall ((G2 tptp.pair_p1765063010t_unit)) (=> (@ tptp.pair_p374947051od_a_a G2) (@ tptp.finite1664988688od_a_a (@ tptp.pair_p1783210148t_unit G2)))))
% 0.26/0.68 (assert (forall ((G2 tptp.pair_p125712459t_unit)) (=> (@ tptp.pair_p1802376898raph_a G2) (@ tptp.finite179568208od_a_a (@ tptp.pair_p133601421t_unit G2)))))
% 0.26/0.68 (assert (forall ((A tptp.set_Pr1986765409at_nat) (B tptp.set_Pr1986765409at_nat)) (=> (@ (@ tptp.ord_le841296385at_nat A) B) (=> (@ tptp.finite772653738at_nat B) (@ tptp.finite772653738at_nat A)))))
% 0.26/0.68 (assert (forall ((A tptp.set_Pr1948701895od_a_a) (B tptp.set_Pr1948701895od_a_a)) (=> (@ (@ tptp.ord_le456379495od_a_a A) B) (=> (@ tptp.finite1664988688od_a_a B) (@ tptp.finite1664988688od_a_a A)))))
% 0.26/0.68 (assert (forall ((A tptp.set_a) (B tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a A) B) (=> (@ tptp.finite_finite_a B) (@ tptp.finite_finite_a A)))))
% 0.26/0.68 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (=> (@ tptp.finite_finite_nat B) (@ tptp.finite_finite_nat A)))))
% 0.26/0.68 (assert (forall ((A tptp.set_Product_prod_a_a) (B tptp.set_Product_prod_a_a)) (=> (@ (@ tptp.ord_le1824328871od_a_a A) B) (=> (@ tptp.finite179568208od_a_a B) (@ tptp.finite179568208od_a_a A)))))
% 0.26/0.68 (assert (forall ((S tptp.set_Pr1986765409at_nat) (T tptp.set_Pr1986765409at_nat)) (=> (@ (@ tptp.ord_le841296385at_nat S) T) (=> (not (@ tptp.finite772653738at_nat S)) (not (@ tptp.finite772653738at_nat T))))))
% 0.26/0.68 (assert (forall ((S tptp.set_Pr1948701895od_a_a) (T tptp.set_Pr1948701895od_a_a)) (=> (@ (@ tptp.ord_le456379495od_a_a S) T) (=> (not (@ tptp.finite1664988688od_a_a S)) (not (@ tptp.finite1664988688od_a_a T))))))
% 0.26/0.68 (assert (forall ((S tptp.set_a) (T tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a S) T) (=> (not (@ tptp.finite_finite_a S)) (not (@ tptp.finite_finite_a T))))))
% 0.26/0.68 (assert (forall ((S tptp.set_nat) (T tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat S) T) (=> (not (@ tptp.finite_finite_nat S)) (not (@ tptp.finite_finite_nat T))))))
% 0.26/0.68 (assert (forall ((S tptp.set_Product_prod_a_a) (T tptp.set_Product_prod_a_a)) (=> (@ (@ tptp.ord_le1824328871od_a_a S) T) (=> (not (@ tptp.finite179568208od_a_a S)) (not (@ tptp.finite179568208od_a_a T))))))
% 0.26/0.68 (assert (forall ((B tptp.set_Pr1986765409at_nat) (A tptp.set_Pr1986765409at_nat)) (=> (@ tptp.finite772653738at_nat B) (=> (@ (@ tptp.ord_le841296385at_nat A) B) (@ tptp.finite772653738at_nat A)))))
% 0.26/0.68 (assert (forall ((B tptp.set_Pr1948701895od_a_a) (A tptp.set_Pr1948701895od_a_a)) (=> (@ tptp.finite1664988688od_a_a B) (=> (@ (@ tptp.ord_le456379495od_a_a A) B) (@ tptp.finite1664988688od_a_a A)))))
% 0.26/0.68 (assert (forall ((B tptp.set_Product_prod_a_a) (A tptp.set_Product_prod_a_a)) (=> (@ tptp.finite179568208od_a_a B) (=> (@ (@ tptp.ord_le1824328871od_a_a A) B) (@ tptp.finite179568208od_a_a A)))))
% 0.26/0.68 (assert (forall ((B tptp.set_nat) (A tptp.set_nat)) (=> (@ tptp.finite_finite_nat B) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (@ tptp.finite_finite_nat A)))))
% 0.26/0.68 (assert (forall ((B tptp.set_a) (A tptp.set_a)) (=> (@ tptp.finite_finite_a B) (=> (@ (@ tptp.ord_less_eq_set_a A) B) (@ tptp.finite_finite_a A)))))
% 0.26/0.68 (assert (forall ((A tptp.set_se1596668135od_a_a) (A2 tptp.set_Product_prod_a_a)) (=> (@ tptp.finite1145471536od_a_a A) (=> (@ (@ tptp.member1838126896od_a_a A2) A) (exists ((X tptp.set_Product_prod_a_a)) (and (@ (@ tptp.member1838126896od_a_a X) A) (@ (@ tptp.ord_le1824328871od_a_a A2) X) (forall ((Xa tptp.set_Product_prod_a_a)) (=> (@ (@ tptp.member1838126896od_a_a Xa) A) (=> (@ (@ tptp.ord_le1824328871od_a_a X) Xa) (= X Xa))))))))))
% 0.26/0.68 (assert (forall ((A tptp.set_nat) (A2 tptp.nat)) (=> (@ tptp.finite_finite_nat A) (=> (@ (@ tptp.member_nat A2) A) (exists ((X tptp.nat)) (and (@ (@ tptp.member_nat X) A) (@ (@ tptp.ord_less_eq_nat A2) X) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.member_nat Xa) A) (=> (@ (@ tptp.ord_less_eq_nat X) Xa) (= X Xa))))))))))
% 0.26/0.68 (assert (forall ((A tptp.set_set_nat) (A2 tptp.set_nat)) (=> (@ tptp.finite2012248349et_nat A) (=> (@ (@ tptp.member_set_nat A2) A) (exists ((X tptp.set_nat)) (and (@ (@ tptp.member_set_nat X) A) (@ (@ tptp.ord_less_eq_set_nat A2) X) (forall ((Xa tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Xa) A) (=> (@ (@ tptp.ord_less_eq_set_nat X) Xa) (= X Xa))))))))))
% 0.26/0.68 (assert (forall ((A tptp.set_set_a) (A2 tptp.set_a)) (=> (@ tptp.finite_finite_set_a A) (=> (@ (@ tptp.member_set_a A2) A) (exists ((X tptp.set_a)) (and (@ (@ tptp.member_set_a X) A) (@ (@ tptp.ord_less_eq_set_a A2) X) (forall ((Xa tptp.set_a)) (=> (@ (@ tptp.member_set_a Xa) A) (=> (@ (@ tptp.ord_less_eq_set_a X) Xa) (= X Xa))))))))))
% 0.26/0.68 (assert (forall ((P (-> tptp.product_prod_a_a Bool)) (Q (-> tptp.product_prod_a_a Bool))) (=> (or (@ tptp.finite179568208od_a_a (@ tptp.collec645855634od_a_a P)) (@ tptp.finite179568208od_a_a (@ tptp.collec645855634od_a_a Q))) (@ tptp.finite179568208od_a_a (@ tptp.collec645855634od_a_a (lambda ((X2 tptp.product_prod_a_a)) (and (@ P X2) (@ Q X2))))))))
% 0.26/0.68 (assert (forall ((P (-> tptp.a Bool)) (Q (-> tptp.a Bool))) (=> (or (@ tptp.finite_finite_a (@ tptp.collect_a P)) (@ tptp.finite_finite_a (@ tptp.collect_a Q))) (@ tptp.finite_finite_a (@ tptp.collect_a (lambda ((X2 tptp.a)) (and (@ P X2) (@ Q X2))))))))
% 0.26/0.68 (assert (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (=> (or (@ tptp.finite_finite_nat (@ tptp.collect_nat P)) (@ tptp.finite_finite_nat (@ tptp.collect_nat Q))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (and (@ P X2) (@ Q X2))))))))
% 0.26/0.68 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool)) (Q (-> tptp.product_prod_nat_nat Bool))) (=> (or (@ tptp.finite772653738at_nat (@ tptp.collec7649004at_nat P)) (@ tptp.finite772653738at_nat (@ tptp.collec7649004at_nat Q))) (@ tptp.finite772653738at_nat (@ tptp.collec7649004at_nat (lambda ((X2 tptp.product_prod_nat_nat)) (and (@ P X2) (@ Q X2))))))))
% 0.26/0.68 (assert (forall ((P (-> tptp.produc1572603623od_a_a Bool)) (Q (-> tptp.produc1572603623od_a_a Bool))) (=> (or (@ tptp.finite1664988688od_a_a (@ tptp.collec1635618130od_a_a P)) (@ tptp.finite1664988688od_a_a (@ tptp.collec1635618130od_a_a Q))) (@ tptp.finite1664988688od_a_a (@ tptp.collec1635618130od_a_a (lambda ((X2 tptp.produc1572603623od_a_a)) (and (@ P X2) (@ Q X2))))))))
% 0.26/0.68 (assert (forall ((P (-> tptp.product_prod_a_a Bool)) (Q (-> tptp.product_prod_a_a Bool))) (= (@ tptp.finite179568208od_a_a (@ tptp.collec645855634od_a_a (lambda ((X2 tptp.product_prod_a_a)) (or (@ P X2) (@ Q X2))))) (and (@ tptp.finite179568208od_a_a (@ tptp.collec645855634od_a_a P)) (@ tptp.finite179568208od_a_a (@ tptp.collec645855634od_a_a Q))))))
% 0.26/0.68 (assert (forall ((P (-> tptp.a Bool)) (Q (-> tptp.a Bool))) (= (@ tptp.finite_finite_a (@ tptp.collect_a (lambda ((X2 tptp.a)) (or (@ P X2) (@ Q X2))))) (and (@ tptp.finite_finite_a (@ tptp.collect_a P)) (@ tptp.finite_finite_a (@ tptp.collect_a Q))))))
% 0.26/0.68 (assert (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (= (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (or (@ P X2) (@ Q X2))))) (and (@ tptp.finite_finite_nat (@ tptp.collect_nat P)) (@ tptp.finite_finite_nat (@ tptp.collect_nat Q))))))
% 0.26/0.68 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool)) (Q (-> tptp.product_prod_nat_nat Bool))) (= (@ tptp.finite772653738at_nat (@ tptp.collec7649004at_nat (lambda ((X2 tptp.product_prod_nat_nat)) (or (@ P X2) (@ Q X2))))) (and (@ tptp.finite772653738at_nat (@ tptp.collec7649004at_nat P)) (@ tptp.finite772653738at_nat (@ tptp.collec7649004at_nat Q))))))
% 0.26/0.68 (assert (forall ((P (-> tptp.produc1572603623od_a_a Bool)) (Q (-> tptp.produc1572603623od_a_a Bool))) (= (@ tptp.finite1664988688od_a_a (@ tptp.collec1635618130od_a_a (lambda ((X2 tptp.produc1572603623od_a_a)) (or (@ P X2) (@ Q X2))))) (and (@ tptp.finite1664988688od_a_a (@ tptp.collec1635618130od_a_a P)) (@ tptp.finite1664988688od_a_a (@ tptp.collec1635618130od_a_a Q))))))
% 0.26/0.68 (assert (forall ((A tptp.set_Pr1986765409at_nat)) (=> (@ tptp.finite772653738at_nat A) (@ tptp.finite1457549322at_nat (@ tptp.collec1606769740at_nat (lambda ((B2 tptp.set_Pr1986765409at_nat)) (@ (@ tptp.ord_le841296385at_nat B2) A)))))))
% 0.26/0.68 (assert (forall ((A tptp.set_Pr1948701895od_a_a)) (=> (@ tptp.finite1664988688od_a_a A) (@ tptp.finite323969008od_a_a (@ tptp.collec453062450od_a_a (lambda ((B2 tptp.set_Pr1948701895od_a_a)) (@ (@ tptp.ord_le456379495od_a_a B2) A)))))))
% 0.26/0.68 (assert (forall ((A tptp.set_Product_prod_a_a)) (=> (@ tptp.finite179568208od_a_a A) (@ tptp.finite1145471536od_a_a (@ tptp.collec183727474od_a_a (lambda ((B2 tptp.set_Product_prod_a_a)) (@ (@ tptp.ord_le1824328871od_a_a B2) A)))))))
% 0.26/0.68 (assert (forall ((A tptp.set_nat)) (=> (@ tptp.finite_finite_nat A) (@ tptp.finite2012248349et_nat (@ tptp.collect_set_nat (lambda ((B2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat B2) A)))))))
% 0.26/0.68 (assert (forall ((A tptp.set_a)) (=> (@ tptp.finite_finite_a A) (@ tptp.finite_finite_set_a (@ tptp.collect_set_a (lambda ((B2 tptp.set_a)) (@ (@ tptp.ord_less_eq_set_a B2) A)))))))
% 0.26/0.68 (assert (forall ((A tptp.set_a) (B (-> tptp.a tptp.set_nat))) (=> (@ tptp.finite_finite_a A) (=> (forall ((A3 tptp.a)) (=> (@ (@ tptp.member_a A3) A) (@ tptp.finite_finite_nat (@ B A3)))) (@ tptp.finite1743148308_a_nat (@ (@ tptp.product_Sigma_a_nat A) B))))))
% 0.26/0.68 (assert (forall ((A tptp.set_nat) (B (-> tptp.nat tptp.set_a))) (=> (@ tptp.finite_finite_nat A) (=> (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) A) (@ tptp.finite_finite_a (@ B A3)))) (@ tptp.finite1808550458_nat_a (@ (@ tptp.product_Sigma_nat_a A) B))))))
% 0.26/0.68 (assert (forall ((A tptp.set_nat) (B (-> tptp.nat tptp.set_nat))) (=> (@ tptp.finite_finite_nat A) (=> (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) A) (@ tptp.finite_finite_nat (@ B A3)))) (@ tptp.finite772653738at_nat (@ (@ tptp.produc45129834at_nat A) B))))))
% 0.26/0.68 (assert (forall ((A tptp.set_a) (B (-> tptp.a tptp.set_a))) (=> (@ tptp.finite_finite_a A) (=> (forall ((A3 tptp.a)) (=> (@ (@ tptp.member_a A3) A) (@ tptp.finite_finite_a (@ B A3)))) (@ tptp.finite179568208od_a_a (@ (@ tptp.product_Sigma_a_a A) B))))))
% 0.26/0.68 (assert (forall ((A tptp.set_Product_prod_a_a) (B (-> tptp.product_prod_a_a tptp.set_a))) (=> (@ tptp.finite179568208od_a_a A) (=> (forall ((A3 tptp.product_prod_a_a)) (=> (@ (@ tptp.member449909584od_a_a A3) A) (@ tptp.finite_finite_a (@ B A3)))) (@ tptp.finite1919032935_a_a_a (@ (@ tptp.produc1282482655_a_a_a A) B))))))
% 0.26/0.68 (assert (forall ((A tptp.set_Product_prod_a_a) (B (-> tptp.product_prod_a_a tptp.set_nat))) (=> (@ tptp.finite179568208od_a_a A) (=> (forall ((A3 tptp.product_prod_a_a)) (=> (@ (@ tptp.member449909584od_a_a A3) A) (@ tptp.finite_finite_nat (@ B A3)))) (@ tptp.finite1837575485_a_nat (@ (@ tptp.produc931712687_a_nat A) B))))))
% 0.26/0.68 (assert (forall ((A tptp.set_a) (B (-> tptp.a tptp.set_Product_prod_a_a))) (=> (@ tptp.finite_finite_a A) (=> (forall ((A3 tptp.a)) (=> (@ (@ tptp.member_a A3) A) (@ tptp.finite179568208od_a_a (@ B A3)))) (@ tptp.finite676513017od_a_a (@ (@ tptp.produc520147185od_a_a A) B))))))
% 0.26/0.68 (assert (forall ((A tptp.set_a) (B (-> tptp.a tptp.set_Pr1986765409at_nat))) (=> (@ tptp.finite_finite_a A) (=> (forall ((A3 tptp.a)) (=> (@ (@ tptp.member_a A3) A) (@ tptp.finite772653738at_nat (@ B A3)))) (@ tptp.finite942416723at_nat (@ (@ tptp.produc292491723at_nat A) B))))))
% 0.26/0.68 (assert (forall ((A tptp.set_nat) (B (-> tptp.nat tptp.set_Product_prod_a_a))) (=> (@ tptp.finite_finite_nat A) (=> (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) A) (@ tptp.finite179568208od_a_a (@ B A3)))) (@ tptp.finite1297454819od_a_a (@ (@ tptp.produc1182842125od_a_a A) B))))))
% 0.26/0.68 (assert (forall ((A tptp.set_nat) (B (-> tptp.nat tptp.set_Pr1986765409at_nat))) (=> (@ tptp.finite_finite_nat A) (=> (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) A) (@ tptp.finite772653738at_nat (@ B A3)))) (@ tptp.finite277291581at_nat (@ (@ tptp.produc894163943at_nat A) B))))))
% 0.26/0.68 (assert (forall ((G2 tptp.pair_p125712459t_unit)) (=> (@ tptp.pair_p1802376898raph_a G2) (@ tptp.pair_p1864019935ioms_a G2))))
% 0.26/0.68 (assert (forall ((G2 tptp.pair_p1914262621t_unit)) (=> (@ tptp.pair_p128415500ph_nat G2) (@ tptp.pair_p1027063983ms_nat G2))))
% 0.26/0.68 (assert (forall ((G2 tptp.pair_p1765063010t_unit)) (=> (@ tptp.pair_p374947051od_a_a G2) (@ tptp.pair_p504738056od_a_a G2))))
% 0.26/0.68 (assert (forall ((P (-> tptp.product_prod_a_a Bool))) (=> (not (@ tptp.finite179568208od_a_a (@ tptp.collec645855634od_a_a P))) (exists ((X_1 tptp.product_prod_a_a)) (@ P X_1)))))
% 0.26/0.68 (assert (forall ((P (-> tptp.a Bool))) (=> (not (@ tptp.finite_finite_a (@ tptp.collect_a P))) (exists ((X_1 tptp.a)) (@ P X_1)))))
% 0.26/0.68 (assert (forall ((P (-> tptp.nat Bool))) (=> (not (@ tptp.finite_finite_nat (@ tptp.collect_nat P))) (exists ((X_1 tptp.nat)) (@ P X_1)))))
% 0.26/0.68 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool))) (=> (not (@ tptp.finite772653738at_nat (@ tptp.collec7649004at_nat P))) (exists ((X_1 tptp.product_prod_nat_nat)) (@ P X_1)))))
% 0.26/0.68 (assert (forall ((P (-> tptp.produc1572603623od_a_a Bool))) (=> (not (@ tptp.finite1664988688od_a_a (@ tptp.collec1635618130od_a_a P))) (exists ((X_1 tptp.produc1572603623od_a_a)) (@ P X_1)))))
% 0.26/0.68 (assert (forall ((A tptp.set_a) (B tptp.set_a) (R (-> tptp.a tptp.a Bool))) (=> (not (@ tptp.finite_finite_a A)) (=> (@ tptp.finite_finite_a B) (=> (forall ((X tptp.a)) (=> (@ (@ tptp.member_a X) A) (exists ((Xa tptp.a)) (and (@ (@ tptp.member_a Xa) B) (@ (@ R X) Xa))))) (exists ((X tptp.a)) (and (@ (@ tptp.member_a X) B) (not (@ tptp.finite_finite_a (@ tptp.collect_a (lambda ((A4 tptp.a)) (and (@ (@ tptp.member_a A4) A) (@ (@ R A4) X)))))))))))))
% 0.26/0.68 (assert (forall ((A tptp.set_a) (B tptp.set_nat) (R (-> tptp.a tptp.nat Bool))) (=> (not (@ tptp.finite_finite_a A)) (=> (@ tptp.finite_finite_nat B) (=> (forall ((X tptp.a)) (=> (@ (@ tptp.member_a X) A) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) B) (@ (@ R X) Xa))))) (exists ((X tptp.nat)) (and (@ (@ tptp.member_nat X) B) (not (@ tptp.finite_finite_a (@ tptp.collect_a (lambda ((A4 tptp.a)) (and (@ (@ tptp.member_a A4) A) (@ (@ R A4) X)))))))))))))
% 0.26/0.68 (assert (forall ((A tptp.set_nat) (B tptp.set_a) (R (-> tptp.nat tptp.a Bool))) (=> (not (@ tptp.finite_finite_nat A)) (=> (@ tptp.finite_finite_a B) (=> (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) A) (exists ((Xa tptp.a)) (and (@ (@ tptp.member_a Xa) B) (@ (@ R X) Xa))))) (exists ((X tptp.a)) (and (@ (@ tptp.member_a X) B) (not (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((A4 tptp.nat)) (and (@ (@ tptp.member_nat A4) A) (@ (@ R A4) X)))))))))))))
% 0.26/0.68 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (R (-> tptp.nat tptp.nat Bool))) (=> (not (@ tptp.finite_finite_nat A)) (=> (@ tptp.finite_finite_nat B) (=> (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) A) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) B) (@ (@ R X) Xa))))) (exists ((X tptp.nat)) (and (@ (@ tptp.member_nat X) B) (not (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((A4 tptp.nat)) (and (@ (@ tptp.member_nat A4) A) (@ (@ R A4) X)))))))))))))
% 0.26/0.68 (assert (forall ((A tptp.set_Product_prod_a_a) (B tptp.set_a) (R (-> tptp.product_prod_a_a tptp.a Bool))) (=> (not (@ tptp.finite179568208od_a_a A)) (=> (@ tptp.finite_finite_a B) (=> (forall ((X tptp.product_prod_a_a)) (=> (@ (@ tptp.member449909584od_a_a X) A) (exists ((Xa tptp.a)) (and (@ (@ tptp.member_a Xa) B) (@ (@ R X) Xa))))) (exists ((X tptp.a)) (and (@ (@ tptp.member_a X) B) (not (@ tptp.finite179568208od_a_a (@ tptp.collec645855634od_a_a (lambda ((A4 tptp.product_prod_a_a)) (and (@ (@ tptp.member449909584od_a_a A4) A) (@ (@ R A4) X)))))))))))))
% 0.26/0.68 (assert (forall ((A tptp.set_Product_prod_a_a) (B tptp.set_nat) (R (-> tptp.product_prod_a_a tptp.nat Bool))) (=> (not (@ tptp.finite179568208od_a_a A)) (=> (@ tptp.finite_finite_nat B) (=> (forall ((X tptp.product_prod_a_a)) (=> (@ (@ tptp.member449909584od_a_a X) A) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) B) (@ (@ R X) Xa))))) (exists ((X tptp.nat)) (and (@ (@ tptp.member_nat X) B) (not (@ tptp.finite179568208od_a_a (@ tptp.collec645855634od_a_a (lambda ((A4 tptp.product_prod_a_a)) (and (@ (@ tptp.member449909584od_a_a A4) A) (@ (@ R A4) X)))))))))))))
% 0.26/0.68 (assert (forall ((A tptp.set_a) (B tptp.set_Product_prod_a_a) (R (-> tptp.a tptp.product_prod_a_a Bool))) (=> (not (@ tptp.finite_finite_a A)) (=> (@ tptp.finite179568208od_a_a B) (=> (forall ((X tptp.a)) (=> (@ (@ tptp.member_a X) A) (exists ((Xa tptp.product_prod_a_a)) (and (@ (@ tptp.member449909584od_a_a Xa) B) (@ (@ R X) Xa))))) (exists ((X tptp.product_prod_a_a)) (and (@ (@ tptp.member449909584od_a_a X) B) (not (@ tptp.finite_finite_a (@ tptp.collect_a (lambda ((A4 tptp.a)) (and (@ (@ tptp.member_a A4) A) (@ (@ R A4) X)))))))))))))
% 0.26/0.68 (assert (forall ((A tptp.set_a) (B tptp.set_Pr1986765409at_nat) (R (-> tptp.a tptp.product_prod_nat_nat Bool))) (=> (not (@ tptp.finite_finite_a A)) (=> (@ tptp.finite772653738at_nat B) (=> (forall ((X tptp.a)) (=> (@ (@ tptp.member_a X) A) (exists ((Xa tptp.product_prod_nat_nat)) (and (@ (@ tptp.member701585322at_nat Xa) B) (@ (@ R X) Xa))))) (exists ((X tptp.product_prod_nat_nat)) (and (@ (@ tptp.member701585322at_nat X) B) (not (@ tptp.finite_finite_a (@ tptp.collect_a (lambda ((A4 tptp.a)) (and (@ (@ tptp.member_a A4) A) (@ (@ R A4) X)))))))))))))
% 0.26/0.68 (assert (forall ((A tptp.set_nat) (B tptp.set_Product_prod_a_a) (R (-> tptp.nat tptp.product_prod_a_a Bool))) (=> (not (@ tptp.finite_finite_nat A)) (=> (@ tptp.finite179568208od_a_a B) (=> (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) A) (exists ((Xa tptp.product_prod_a_a)) (and (@ (@ tptp.member449909584od_a_a Xa) B) (@ (@ R X) Xa))))) (exists ((X tptp.product_prod_a_a)) (and (@ (@ tptp.member449909584od_a_a X) B) (not (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((A4 tptp.nat)) (and (@ (@ tptp.member_nat A4) A) (@ (@ R A4) X)))))))))))))
% 0.26/0.68 (assert (forall ((A tptp.set_nat) (B tptp.set_Pr1986765409at_nat) (R (-> tptp.nat tptp.product_prod_nat_nat Bool))) (=> (not (@ tptp.finite_finite_nat A)) (=> (@ tptp.finite772653738at_nat B) (=> (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) A) (exists ((Xa tptp.product_prod_nat_nat)) (and (@ (@ tptp.member701585322at_nat Xa) B) (@ (@ R X) Xa))))) (exists ((X tptp.product_prod_nat_nat)) (and (@ (@ tptp.member701585322at_nat X) B) (not (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((A4 tptp.nat)) (and (@ (@ tptp.member_nat A4) A) (@ (@ R A4) X)))))))))))))
% 0.26/0.68 (assert (forall ((G2 tptp.pair_p125712459t_unit)) (let ((_let_1 (@ tptp.pair_p1802376898raph_a G2))) (=> _let_1 _let_1))))
% 0.26/0.68 (assert (forall ((A tptp.set_a) (B tptp.set_nat)) (=> (@ tptp.finite_finite_a A) (=> (@ tptp.finite_finite_nat B) (@ tptp.finite1743148308_a_nat (@ (@ tptp.product_Sigma_a_nat A) (lambda ((Uu tptp.a)) B)))))))
% 0.26/0.68 (assert (forall ((A tptp.set_nat) (B tptp.set_a)) (=> (@ tptp.finite_finite_nat A) (=> (@ tptp.finite_finite_a B) (@ tptp.finite1808550458_nat_a (@ (@ tptp.product_Sigma_nat_a A) (lambda ((Uu tptp.nat)) B)))))))
% 0.26/0.68 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (@ tptp.finite_finite_nat A) (=> (@ tptp.finite_finite_nat B) (@ tptp.finite772653738at_nat (@ (@ tptp.produc45129834at_nat A) (lambda ((Uu tptp.nat)) B)))))))
% 0.26/0.68 (assert (forall ((A tptp.set_a) (B tptp.set_a)) (=> (@ tptp.finite_finite_a A) (=> (@ tptp.finite_finite_a B) (@ tptp.finite179568208od_a_a (@ (@ tptp.product_Sigma_a_a A) (lambda ((Uu tptp.a)) B)))))))
% 0.26/0.68 (assert (forall ((A tptp.set_Product_prod_a_a) (B tptp.set_a)) (=> (@ tptp.finite179568208od_a_a A) (=> (@ tptp.finite_finite_a B) (@ tptp.finite1919032935_a_a_a (@ (@ tptp.produc1282482655_a_a_a A) (lambda ((Uu tptp.product_prod_a_a)) B)))))))
% 0.26/0.68 (assert (forall ((A tptp.set_Product_prod_a_a) (B tptp.set_nat)) (=> (@ tptp.finite179568208od_a_a A) (=> (@ tptp.finite_finite_nat B) (@ tptp.finite1837575485_a_nat (@ (@ tptp.produc931712687_a_nat A) (lambda ((Uu tptp.product_prod_a_a)) B)))))))
% 0.26/0.68 (assert (forall ((A tptp.set_a) (B tptp.set_Product_prod_a_a)) (=> (@ tptp.finite_finite_a A) (=> (@ tptp.finite179568208od_a_a B) (@ tptp.finite676513017od_a_a (@ (@ tptp.produc520147185od_a_a A) (lambda ((Uu tptp.a)) B)))))))
% 0.26/0.68 (assert (forall ((A tptp.set_a) (B tptp.set_Pr1986765409at_nat)) (=> (@ tptp.finite_finite_a A) (=> (@ tptp.finite772653738at_nat B) (@ tptp.finite942416723at_nat (@ (@ tptp.produc292491723at_nat A) (lambda ((Uu tptp.a)) B)))))))
% 0.26/0.68 (assert (forall ((A tptp.set_nat) (B tptp.set_Product_prod_a_a)) (=> (@ tptp.finite_finite_nat A) (=> (@ tptp.finite179568208od_a_a B) (@ tptp.finite1297454819od_a_a (@ (@ tptp.produc1182842125od_a_a A) (lambda ((Uu tptp.nat)) B)))))))
% 0.26/0.68 (assert (forall ((A tptp.set_nat) (B tptp.set_Pr1986765409at_nat)) (=> (@ tptp.finite_finite_nat A) (=> (@ tptp.finite772653738at_nat B) (@ tptp.finite277291581at_nat (@ (@ tptp.produc894163943at_nat A) (lambda ((Uu tptp.nat)) B)))))))
% 0.26/0.68 (assert (forall ((G2 tptp.pair_p2041852168t_unit)) (=> (@ tptp.pair_p752841413at_nat G2) (@ tptp.finite772653738at_nat (@ tptp.pair_p210955889t_unit G2)))))
% 0.26/0.68 (assert (forall ((G2 tptp.pair_p1593840546t_unit)) (=> (@ tptp.pair_p159207083od_a_a G2) (@ tptp.finite1664988688od_a_a (@ tptp.pair_p1652294923t_unit G2)))))
% 0.26/0.68 (assert (forall ((G2 tptp.pair_p125712459t_unit)) (=> (@ tptp.pair_p1802376898raph_a G2) (@ tptp.finite_finite_a (@ tptp.pair_p1047056820t_unit G2)))))
% 0.26/0.68 (assert (forall ((G2 tptp.pair_p1914262621t_unit)) (=> (@ tptp.pair_p128415500ph_nat G2) (@ tptp.finite_finite_nat (@ tptp.pair_p1677060310t_unit G2)))))
% 0.26/0.68 (assert (forall ((G2 tptp.pair_p1765063010t_unit)) (=> (@ tptp.pair_p374947051od_a_a G2) (@ tptp.finite179568208od_a_a (@ tptp.pair_p447552203t_unit G2)))))
% 0.26/0.68 (assert (forall ((A tptp.set_se1596668135od_a_a) (A2 tptp.set_Product_prod_a_a)) (=> (@ tptp.finite1145471536od_a_a A) (=> (@ (@ tptp.member1838126896od_a_a A2) A) (exists ((X tptp.set_Product_prod_a_a)) (and (@ (@ tptp.member1838126896od_a_a X) A) (@ (@ tptp.ord_le1824328871od_a_a X) A2) (forall ((Xa tptp.set_Product_prod_a_a)) (=> (@ (@ tptp.member1838126896od_a_a Xa) A) (=> (@ (@ tptp.ord_le1824328871od_a_a Xa) X) (= X Xa))))))))))
% 0.26/0.68 (assert (forall ((A tptp.set_nat) (A2 tptp.nat)) (=> (@ tptp.finite_finite_nat A) (=> (@ (@ tptp.member_nat A2) A) (exists ((X tptp.nat)) (and (@ (@ tptp.member_nat X) A) (@ (@ tptp.ord_less_eq_nat X) A2) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.member_nat Xa) A) (=> (@ (@ tptp.ord_less_eq_nat Xa) X) (= X Xa))))))))))
% 0.26/0.68 (assert (forall ((A tptp.set_set_nat) (A2 tptp.set_nat)) (=> (@ tptp.finite2012248349et_nat A) (=> (@ (@ tptp.member_set_nat A2) A) (exists ((X tptp.set_nat)) (and (@ (@ tptp.member_set_nat X) A) (@ (@ tptp.ord_less_eq_set_nat X) A2) (forall ((Xa tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Xa) A) (=> (@ (@ tptp.ord_less_eq_set_nat Xa) X) (= X Xa))))))))))
% 0.26/0.68 (assert (forall ((A tptp.set_set_a) (A2 tptp.set_a)) (=> (@ tptp.finite_finite_set_a A) (=> (@ (@ tptp.member_set_a A2) A) (exists ((X tptp.set_a)) (and (@ (@ tptp.member_set_a X) A) (@ (@ tptp.ord_less_eq_set_a X) A2) (forall ((Xa tptp.set_a)) (=> (@ (@ tptp.member_set_a Xa) A) (=> (@ (@ tptp.ord_less_eq_set_a Xa) X) (= X Xa))))))))))
% 0.26/0.68 (assert (forall ((A tptp.set_a) (B tptp.set_nat)) (=> (not (@ tptp.finite_finite_a A)) (=> (not (@ tptp.finite_finite_nat B)) (not (@ tptp.finite1743148308_a_nat (@ (@ tptp.product_Sigma_a_nat A) (lambda ((Uu tptp.a)) B))))))))
% 0.26/0.68 (assert (forall ((A tptp.set_nat) (B tptp.set_a)) (=> (not (@ tptp.finite_finite_nat A)) (=> (not (@ tptp.finite_finite_a B)) (not (@ tptp.finite1808550458_nat_a (@ (@ tptp.product_Sigma_nat_a A) (lambda ((Uu tptp.nat)) B))))))))
% 0.26/0.68 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (not (@ tptp.finite_finite_nat A)) (=> (not (@ tptp.finite_finite_nat B)) (not (@ tptp.finite772653738at_nat (@ (@ tptp.produc45129834at_nat A) (lambda ((Uu tptp.nat)) B))))))))
% 0.26/0.68 (assert (forall ((A tptp.set_a) (B tptp.set_a)) (=> (not (@ tptp.finite_finite_a A)) (=> (not (@ tptp.finite_finite_a B)) (not (@ tptp.finite179568208od_a_a (@ (@ tptp.product_Sigma_a_a A) (lambda ((Uu tptp.a)) B))))))))
% 0.26/0.68 (assert (forall ((A tptp.set_Product_prod_a_a) (B tptp.set_a)) (=> (not (@ tptp.finite179568208od_a_a A)) (=> (not (@ tptp.finite_finite_a B)) (not (@ tptp.finite1919032935_a_a_a (@ (@ tptp.produc1282482655_a_a_a A) (lambda ((Uu tptp.product_prod_a_a)) B))))))))
% 0.26/0.68 (assert (forall ((A tptp.set_Product_prod_a_a) (B tptp.set_nat)) (=> (not (@ tptp.finite179568208od_a_a A)) (=> (not (@ tptp.finite_finite_nat B)) (not (@ tptp.finite1837575485_a_nat (@ (@ tptp.produc931712687_a_nat A) (lambda ((Uu tptp.product_prod_a_a)) B))))))))
% 0.26/0.68 (assert (forall ((A tptp.set_a) (B tptp.set_Product_prod_a_a)) (=> (not (@ tptp.finite_finite_a A)) (=> (not (@ tptp.finite179568208od_a_a B)) (not (@ tptp.finite676513017od_a_a (@ (@ tptp.produc520147185od_a_a A) (lambda ((Uu tptp.a)) B))))))))
% 0.26/0.68 (assert (forall ((A tptp.set_a) (B tptp.set_Pr1986765409at_nat)) (=> (not (@ tptp.finite_finite_a A)) (=> (not (@ tptp.finite772653738at_nat B)) (not (@ tptp.finite942416723at_nat (@ (@ tptp.produc292491723at_nat A) (lambda ((Uu tptp.a)) B))))))))
% 0.26/0.68 (assert (forall ((A tptp.set_nat) (B tptp.set_Product_prod_a_a)) (=> (not (@ tptp.finite_finite_nat A)) (=> (not (@ tptp.finite179568208od_a_a B)) (not (@ tptp.finite1297454819od_a_a (@ (@ tptp.produc1182842125od_a_a A) (lambda ((Uu tptp.nat)) B))))))))
% 0.26/0.68 (assert (forall ((A tptp.set_nat) (B tptp.set_Pr1986765409at_nat)) (=> (not (@ tptp.finite_finite_nat A)) (=> (not (@ tptp.finite772653738at_nat B)) (not (@ tptp.finite277291581at_nat (@ (@ tptp.produc894163943at_nat A) (lambda ((Uu tptp.nat)) B))))))))
% 0.26/0.68 (assert (forall ((X3 tptp.product_prod_a_a) (C tptp.set_Product_prod_a_a) (A tptp.set_Product_prod_a_a) (B tptp.set_Product_prod_a_a)) (=> (@ (@ tptp.member449909584od_a_a X3) C) (= (@ (@ tptp.ord_le456379495od_a_a (@ (@ tptp.produc304751368od_a_a A) (lambda ((Uu tptp.product_prod_a_a)) C))) (@ (@ tptp.produc304751368od_a_a B) (lambda ((Uu tptp.product_prod_a_a)) C))) (@ (@ tptp.ord_le1824328871od_a_a A) B)))))
% 0.26/0.68 (assert (forall ((X3 tptp.nat) (C tptp.set_nat) (A tptp.set_Product_prod_a_a) (B tptp.set_Product_prod_a_a)) (=> (@ (@ tptp.member_nat X3) C) (= (@ (@ tptp.ord_le492294332_a_nat (@ (@ tptp.produc931712687_a_nat A) (lambda ((Uu tptp.product_prod_a_a)) C))) (@ (@ tptp.produc931712687_a_nat B) (lambda ((Uu tptp.product_prod_a_a)) C))) (@ (@ tptp.ord_le1824328871od_a_a A) B)))))
% 0.26/0.68 (assert (forall ((X3 tptp.product_prod_a_a) (C tptp.set_Product_prod_a_a) (A tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.member449909584od_a_a X3) C) (= (@ (@ tptp.ord_le2084554594od_a_a (@ (@ tptp.produc1182842125od_a_a A) (lambda ((Uu tptp.nat)) C))) (@ (@ tptp.produc1182842125od_a_a B) (lambda ((Uu tptp.nat)) C))) (@ (@ tptp.ord_less_eq_set_nat A) B)))))
% 0.26/0.68 (assert (forall ((X3 tptp.nat) (C tptp.set_nat) (A tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.member_nat X3) C) (= (@ (@ tptp.ord_le841296385at_nat (@ (@ tptp.produc45129834at_nat A) (lambda ((Uu tptp.nat)) C))) (@ (@ tptp.produc45129834at_nat B) (lambda ((Uu tptp.nat)) C))) (@ (@ tptp.ord_less_eq_set_nat A) B)))))
% 0.26/0.68 (assert (forall ((X3 tptp.product_prod_a_a) (C tptp.set_Product_prod_a_a) (A tptp.set_a) (B tptp.set_a)) (=> (@ (@ tptp.member449909584od_a_a X3) C) (= (@ (@ tptp.ord_le1816232656od_a_a (@ (@ tptp.produc520147185od_a_a A) (lambda ((Uu tptp.a)) C))) (@ (@ tptp.produc520147185od_a_a B) (lambda ((Uu tptp.a)) C))) (@ (@ tptp.ord_less_eq_set_a A) B)))))
% 0.26/0.68 (assert (forall ((X3 tptp.nat) (C tptp.set_nat) (A tptp.set_a) (B tptp.set_a)) (=> (@ (@ tptp.member_nat X3) C) (= (@ (@ tptp.ord_le2073555219_a_nat (@ (@ tptp.product_Sigma_a_nat A) (lambda ((Uu tptp.a)) C))) (@ (@ tptp.product_Sigma_a_nat B) (lambda ((Uu tptp.a)) C))) (@ (@ tptp.ord_less_eq_set_a A) B)))))
% 0.26/0.68 (assert (forall ((X3 tptp.a) (C tptp.set_a) (A tptp.set_a) (B tptp.set_a)) (=> (@ (@ tptp.member_a X3) C) (= (@ (@ tptp.ord_le1824328871od_a_a (@ (@ tptp.product_Sigma_a_a A) (lambda ((Uu tptp.a)) C))) (@ (@ tptp.product_Sigma_a_a B) (lambda ((Uu tptp.a)) C))) (@ (@ tptp.ord_less_eq_set_a A) B)))))
% 0.26/0.68 (assert (forall ((A tptp.set_Product_prod_a_a) (C tptp.set_Product_prod_a_a) (B (-> tptp.product_prod_a_a tptp.set_Product_prod_a_a)) (D (-> tptp.product_prod_a_a tptp.set_Product_prod_a_a))) (=> (@ (@ tptp.ord_le1824328871od_a_a A) C) (=> (forall ((X tptp.product_prod_a_a)) (=> (@ (@ tptp.member449909584od_a_a X) A) (@ (@ tptp.ord_le1824328871od_a_a (@ B X)) (@ D X)))) (@ (@ tptp.ord_le456379495od_a_a (@ (@ tptp.produc304751368od_a_a A) B)) (@ (@ tptp.produc304751368od_a_a C) D))))))
% 0.26/0.68 (assert (forall ((A tptp.set_Product_prod_a_a) (C tptp.set_Product_prod_a_a) (B (-> tptp.product_prod_a_a tptp.set_nat)) (D (-> tptp.product_prod_a_a tptp.set_nat))) (=> (@ (@ tptp.ord_le1824328871od_a_a A) C) (=> (forall ((X tptp.product_prod_a_a)) (=> (@ (@ tptp.member449909584od_a_a X) A) (@ (@ tptp.ord_less_eq_set_nat (@ B X)) (@ D X)))) (@ (@ tptp.ord_le492294332_a_nat (@ (@ tptp.produc931712687_a_nat A) B)) (@ (@ tptp.produc931712687_a_nat C) D))))))
% 0.26/0.68 (assert (forall ((A tptp.set_Product_prod_a_a) (C tptp.set_Product_prod_a_a) (B (-> tptp.product_prod_a_a tptp.set_a)) (D (-> tptp.product_prod_a_a tptp.set_a))) (=> (@ (@ tptp.ord_le1824328871od_a_a A) C) (=> (forall ((X tptp.product_prod_a_a)) (=> (@ (@ tptp.member449909584od_a_a X) A) (@ (@ tptp.ord_less_eq_set_a (@ B X)) (@ D X)))) (@ (@ tptp.ord_le677315902_a_a_a (@ (@ tptp.produc1282482655_a_a_a A) B)) (@ (@ tptp.produc1282482655_a_a_a C) D))))))
% 0.26/0.68 (assert (forall ((A tptp.set_nat) (C tptp.set_nat) (B (-> tptp.nat tptp.set_Product_prod_a_a)) (D (-> tptp.nat tptp.set_Product_prod_a_a))) (=> (@ (@ tptp.ord_less_eq_set_nat A) C) (=> (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) A) (@ (@ tptp.ord_le1824328871od_a_a (@ B X)) (@ D X)))) (@ (@ tptp.ord_le2084554594od_a_a (@ (@ tptp.produc1182842125od_a_a A) B)) (@ (@ tptp.produc1182842125od_a_a C) D))))))
% 0.26/0.68 (assert (forall ((A tptp.set_nat) (C tptp.set_nat) (B (-> tptp.nat tptp.set_nat)) (D (-> tptp.nat tptp.set_nat))) (=> (@ (@ tptp.ord_less_eq_set_nat A) C) (=> (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) A) (@ (@ tptp.ord_less_eq_set_nat (@ B X)) (@ D X)))) (@ (@ tptp.ord_le841296385at_nat (@ (@ tptp.produc45129834at_nat A) B)) (@ (@ tptp.produc45129834at_nat C) D))))))
% 0.26/0.68 (assert (forall ((A tptp.set_nat) (C tptp.set_nat) (B (-> tptp.nat tptp.set_a)) (D (-> tptp.nat tptp.set_a))) (=> (@ (@ tptp.ord_less_eq_set_nat A) C) (=> (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) A) (@ (@ tptp.ord_less_eq_set_a (@ B X)) (@ D X)))) (@ (@ tptp.ord_le344568633_nat_a (@ (@ tptp.product_Sigma_nat_a A) B)) (@ (@ tptp.product_Sigma_nat_a C) D))))))
% 0.26/0.68 (assert (forall ((A tptp.set_a) (C tptp.set_a) (B (-> tptp.a tptp.set_Product_prod_a_a)) (D (-> tptp.a tptp.set_Product_prod_a_a))) (=> (@ (@ tptp.ord_less_eq_set_a A) C) (=> (forall ((X tptp.a)) (=> (@ (@ tptp.member_a X) A) (@ (@ tptp.ord_le1824328871od_a_a (@ B X)) (@ D X)))) (@ (@ tptp.ord_le1816232656od_a_a (@ (@ tptp.produc520147185od_a_a A) B)) (@ (@ tptp.produc520147185od_a_a C) D))))))
% 0.26/0.68 (assert (forall ((A tptp.set_a) (C tptp.set_a) (B (-> tptp.a tptp.set_nat)) (D (-> tptp.a tptp.set_nat))) (=> (@ (@ tptp.ord_less_eq_set_a A) C) (=> (forall ((X tptp.a)) (=> (@ (@ tptp.member_a X) A) (@ (@ tptp.ord_less_eq_set_nat (@ B X)) (@ D X)))) (@ (@ tptp.ord_le2073555219_a_nat (@ (@ tptp.product_Sigma_a_nat A) B)) (@ (@ tptp.product_Sigma_a_nat C) D))))))
% 0.26/0.68 (assert (forall ((A tptp.set_a) (C tptp.set_a) (B (-> tptp.a tptp.set_a)) (D (-> tptp.a tptp.set_a))) (=> (@ (@ tptp.ord_less_eq_set_a A) C) (=> (forall ((X tptp.a)) (=> (@ (@ tptp.member_a X) A) (@ (@ tptp.ord_less_eq_set_a (@ B X)) (@ D X)))) (@ (@ tptp.ord_le1824328871od_a_a (@ (@ tptp.product_Sigma_a_a A) B)) (@ (@ tptp.product_Sigma_a_a C) D))))))
% 0.26/0.68 (assert (forall ((A tptp.set_Product_prod_a_a) (B tptp.set_Product_prod_a_a)) (=> (forall ((X tptp.product_prod_a_a)) (let ((_let_1 (@ tptp.member449909584od_a_a X))) (=> (@ _let_1 A) (@ _let_1 B)))) (@ (@ tptp.ord_le1824328871od_a_a A) B))))
% 0.26/0.68 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.member_nat X))) (=> (@ _let_1 A) (@ _let_1 B)))) (@ (@ tptp.ord_less_eq_set_nat A) B))))
% 0.26/0.68 (assert (forall ((A tptp.set_a) (B tptp.set_a)) (=> (forall ((X tptp.a)) (let ((_let_1 (@ tptp.member_a X))) (=> (@ _let_1 A) (@ _let_1 B)))) (@ (@ tptp.ord_less_eq_set_a A) B))))
% 0.26/0.68 (assert (forall ((A tptp.set_Product_prod_a_a) (B tptp.set_Product_prod_a_a)) (=> (@ (@ tptp.ord_le1824328871od_a_a A) B) (=> (@ (@ tptp.ord_le1824328871od_a_a B) A) (= A B)))))
% 0.26/0.68 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (=> (@ (@ tptp.ord_less_eq_set_nat B) A) (= A B)))))
% 0.26/0.68 (assert (forall ((A tptp.set_a) (B tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a A) B) (=> (@ (@ tptp.ord_less_eq_set_a B) A) (= A B)))))
% 0.26/0.68 (assert (forall ((X3 tptp.set_Product_prod_a_a)) (@ (@ tptp.ord_le1824328871od_a_a X3) X3)))
% 0.26/0.68 (assert (forall ((X3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat X3) X3)))
% 0.26/0.68 (assert (forall ((X3 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat X3) X3)))
% 0.26/0.68 (assert (forall ((X3 tptp.set_a)) (@ (@ tptp.ord_less_eq_set_a X3) X3)))
% 0.26/0.68 (assert (forall ((R2 tptp.pair_p125712459t_unit) (R3 tptp.pair_p125712459t_unit)) (=> (= (@ tptp.pair_p1047056820t_unit R2) (@ tptp.pair_p1047056820t_unit R3)) (=> (= (@ tptp.pair_p133601421t_unit R2) (@ tptp.pair_p133601421t_unit R3)) (=> (= (@ tptp.pair_p1896222615t_unit R2) (@ tptp.pair_p1896222615t_unit R3)) (= R2 R3))))))
% 0.26/0.68 (assert (forall ((R2 tptp.pair_p1914262621t_unit) (R3 tptp.pair_p1914262621t_unit)) (=> (= (@ tptp.pair_p1677060310t_unit R2) (@ tptp.pair_p1677060310t_unit R3)) (=> (= (@ tptp.pair_p715279805t_unit R2) (@ tptp.pair_p715279805t_unit R3)) (=> (= (@ tptp.pair_p69470259t_unit R2) (@ tptp.pair_p69470259t_unit R3)) (= R2 R3))))))
% 0.26/0.68 (assert (forall ((R2 tptp.pair_p1765063010t_unit) (R3 tptp.pair_p1765063010t_unit)) (=> (= (@ tptp.pair_p447552203t_unit R2) (@ tptp.pair_p447552203t_unit R3)) (=> (= (@ tptp.pair_p1783210148t_unit R2) (@ tptp.pair_p1783210148t_unit R3)) (=> (= (@ tptp.pair_p1984658862t_unit R2) (@ tptp.pair_p1984658862t_unit R3)) (= R2 R3))))))
% 0.26/0.68 (assert (forall ((A tptp.set_a) (B tptp.set_a) (C (-> tptp.a tptp.set_a)) (D (-> tptp.a tptp.set_a))) (=> (= A B) (=> (forall ((X tptp.a)) (=> (@ (@ tptp.member_a X) B) (= (@ C X) (@ D X)))) (= (@ (@ tptp.product_Sigma_a_a A) C) (@ (@ tptp.product_Sigma_a_a B) D))))))
% 0.26/0.68 (assert (forall ((X3 tptp.a) (C tptp.set_a) (A tptp.set_a) (B tptp.set_a)) (=> (@ (@ tptp.member_a X3) C) (= (= (@ (@ tptp.product_Sigma_a_a A) (lambda ((Uu tptp.a)) C)) (@ (@ tptp.product_Sigma_a_a B) (lambda ((Uu tptp.a)) C))) (= A B)))))
% 0.26/0.68 (assert (forall ((A tptp.set_Product_prod_a_a) (P (-> tptp.product_prod_a_a Bool))) (@ (@ tptp.ord_le1824328871od_a_a (@ tptp.collec645855634od_a_a (lambda ((X2 tptp.product_prod_a_a)) (and (@ (@ tptp.member449909584od_a_a X2) A) (@ P X2))))) A)))
% 0.26/0.68 (assert (forall ((A tptp.set_nat) (P (-> tptp.nat Bool))) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) A) (@ P X2))))) A)))
% 0.26/0.68 (assert (forall ((A tptp.set_a) (P (-> tptp.a Bool))) (@ (@ tptp.ord_less_eq_set_a (@ tptp.collect_a (lambda ((X2 tptp.a)) (and (@ (@ tptp.member_a X2) A) (@ P X2))))) A)))
% 0.26/0.68 (assert (= tptp.ord_le1824328871od_a_a (lambda ((A5 tptp.set_Product_prod_a_a) (B2 tptp.set_Product_prod_a_a)) (@ (@ tptp.ord_le1347718902_a_a_o (lambda ((X2 tptp.product_prod_a_a)) (@ (@ tptp.member449909584od_a_a X2) A5))) (lambda ((X2 tptp.product_prod_a_a)) (@ (@ tptp.member449909584od_a_a X2) B2))))))
% 0.26/0.68 (assert (= tptp.ord_less_eq_set_nat (lambda ((A5 tptp.set_nat) (B2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_nat_o (lambda ((X2 tptp.nat)) (@ (@ tptp.member_nat X2) A5))) (lambda ((X2 tptp.nat)) (@ (@ tptp.member_nat X2) B2))))))
% 0.26/0.68 (assert (= tptp.ord_less_eq_set_a (lambda ((A5 tptp.set_a) (B2 tptp.set_a)) (@ (@ tptp.ord_less_eq_a_o (lambda ((X2 tptp.a)) (@ (@ tptp.member_a X2) A5))) (lambda ((X2 tptp.a)) (@ (@ tptp.member_a X2) B2))))))
% 0.26/0.68 (assert (forall ((B3 tptp.set_Product_prod_a_a) (A2 tptp.set_Product_prod_a_a)) (=> (@ (@ tptp.ord_le1824328871od_a_a B3) A2) (=> (@ (@ tptp.ord_le1824328871od_a_a A2) B3) (= A2 B3)))))
% 0.26/0.68 (assert (forall ((B3 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B3) A2) (=> (@ (@ tptp.ord_less_eq_nat A2) B3) (= A2 B3)))))
% 0.26/0.68 (assert (forall ((B3 tptp.set_nat) (A2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B3) A2) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B3) (= A2 B3)))))
% 0.26/0.68 (assert (forall ((B3 tptp.set_a) (A2 tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a B3) A2) (=> (@ (@ tptp.ord_less_eq_set_a A2) B3) (= A2 B3)))))
% 0.26/0.68 (assert (= (lambda ((Y tptp.set_Product_prod_a_a) (Z tptp.set_Product_prod_a_a)) (= Y Z)) (lambda ((A4 tptp.set_Product_prod_a_a) (B4 tptp.set_Product_prod_a_a)) (and (@ (@ tptp.ord_le1824328871od_a_a B4) A4) (@ (@ tptp.ord_le1824328871od_a_a A4) B4)))))
% 0.26/0.68 (assert (= (lambda ((Y tptp.nat) (Z tptp.nat)) (= Y Z)) (lambda ((A4 tptp.nat) (B4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B4) A4) (@ (@ tptp.ord_less_eq_nat A4) B4)))))
% 0.26/0.68 (assert (= (lambda ((Y tptp.set_nat) (Z tptp.set_nat)) (= Y Z)) (lambda ((A4 tptp.set_nat) (B4 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat B4) A4) (@ (@ tptp.ord_less_eq_set_nat A4) B4)))))
% 0.26/0.68 (assert (= (lambda ((Y tptp.set_a) (Z tptp.set_a)) (= Y Z)) (lambda ((A4 tptp.set_a) (B4 tptp.set_a)) (and (@ (@ tptp.ord_less_eq_set_a B4) A4) (@ (@ tptp.ord_less_eq_set_a A4) B4)))))
% 0.26/0.68 (assert (forall ((B3 tptp.set_Product_prod_a_a) (A2 tptp.set_Product_prod_a_a) (C2 tptp.set_Product_prod_a_a)) (let ((_let_1 (@ tptp.ord_le1824328871od_a_a C2))) (=> (@ (@ tptp.ord_le1824328871od_a_a B3) A2) (=> (@ _let_1 B3) (@ _let_1 A2))))))
% 0.26/0.68 (assert (forall ((B3 tptp.nat) (A2 tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C2))) (=> (@ (@ tptp.ord_less_eq_nat B3) A2) (=> (@ _let_1 B3) (@ _let_1 A2))))))
% 0.26/0.68 (assert (forall ((B3 tptp.set_nat) (A2 tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat C2))) (=> (@ (@ tptp.ord_less_eq_set_nat B3) A2) (=> (@ _let_1 B3) (@ _let_1 A2))))))
% 0.26/0.68 (assert (forall ((B3 tptp.set_a) (A2 tptp.set_a) (C2 tptp.set_a)) (let ((_let_1 (@ tptp.ord_less_eq_set_a C2))) (=> (@ (@ tptp.ord_less_eq_set_a B3) A2) (=> (@ _let_1 B3) (@ _let_1 A2))))))
% 0.26/0.68 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A2 tptp.nat) (B3 tptp.nat)) (=> (forall ((A3 tptp.nat) (B5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A3) B5) (@ (@ P A3) B5))) (=> (forall ((A3 tptp.nat) (B5 tptp.nat)) (=> (@ (@ P B5) A3) (@ (@ P A3) B5))) (@ (@ P A2) B3)))))
% 0.26/0.68 (assert (forall ((A2 tptp.set_Product_prod_a_a)) (@ (@ tptp.ord_le1824328871od_a_a A2) A2)))
% 0.26/0.68 (assert (forall ((A2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat A2) A2)))
% 0.26/0.68 (assert (forall ((A2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat A2) A2)))
% 0.26/0.68 (assert (forall ((A2 tptp.set_a)) (@ (@ tptp.ord_less_eq_set_a A2) A2)))
% 0.26/0.68 (assert (forall ((X3 tptp.set_Product_prod_a_a) (Y2 tptp.set_Product_prod_a_a) (Z2 tptp.set_Product_prod_a_a)) (let ((_let_1 (@ tptp.ord_le1824328871od_a_a X3))) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_le1824328871od_a_a Y2) Z2) (@ _let_1 Z2))))))
% 0.26/0.68 (assert (forall ((X3 tptp.nat) (Y2 tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X3))) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_eq_nat Y2) Z2) (@ _let_1 Z2))))))
% 0.26/0.68 (assert (forall ((X3 tptp.set_nat) (Y2 tptp.set_nat) (Z2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat X3))) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_eq_set_nat Y2) Z2) (@ _let_1 Z2))))))
% 0.26/0.68 (assert (forall ((X3 tptp.set_a) (Y2 tptp.set_a) (Z2 tptp.set_a)) (let ((_let_1 (@ tptp.ord_less_eq_set_a X3))) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_eq_set_a Y2) Z2) (@ _let_1 Z2))))))
% 0.26/0.68 (assert (forall ((A2 tptp.set_Product_prod_a_a) (B3 tptp.set_Product_prod_a_a)) (=> (@ (@ tptp.ord_le1824328871od_a_a A2) B3) (=> (@ (@ tptp.ord_le1824328871od_a_a B3) A2) (= A2 B3)))))
% 0.26/0.68 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B3) (=> (@ (@ tptp.ord_less_eq_nat B3) A2) (= A2 B3)))))
% 0.26/0.68 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B3) (=> (@ (@ tptp.ord_less_eq_set_nat B3) A2) (= A2 B3)))))
% 0.26/0.68 (assert (forall ((A2 tptp.set_a) (B3 tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a A2) B3) (=> (@ (@ tptp.ord_less_eq_set_a B3) A2) (= A2 B3)))))
% 0.26/0.68 (assert (forall ((A2 tptp.set_Product_prod_a_a) (B3 tptp.set_Product_prod_a_a) (C2 tptp.set_Product_prod_a_a)) (let ((_let_1 (@ tptp.ord_le1824328871od_a_a A2))) (=> (@ _let_1 B3) (=> (= B3 C2) (@ _let_1 C2))))))
% 0.26/0.68 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A2))) (=> (@ _let_1 B3) (=> (= B3 C2) (@ _let_1 C2))))))
% 0.26/0.68 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A2))) (=> (@ _let_1 B3) (=> (= B3 C2) (@ _let_1 C2))))))
% 0.26/0.68 (assert (forall ((A2 tptp.set_a) (B3 tptp.set_a) (C2 tptp.set_a)) (let ((_let_1 (@ tptp.ord_less_eq_set_a A2))) (=> (@ _let_1 B3) (=> (= B3 C2) (@ _let_1 C2))))))
% 0.26/0.68 (assert (forall ((A2 tptp.product_prod_a_a) (P (-> tptp.product_prod_a_a Bool))) (= (@ (@ tptp.member449909584od_a_a A2) (@ tptp.collec645855634od_a_a P)) (@ P A2))))
% 0.26/0.68 (assert (forall ((A2 tptp.nat) (P (-> tptp.nat Bool))) (= (@ (@ tptp.member_nat A2) (@ tptp.collect_nat P)) (@ P A2))))
% 0.26/0.68 (assert (forall ((A tptp.set_Product_prod_a_a)) (= (@ tptp.collec645855634od_a_a (lambda ((X2 tptp.product_prod_a_a)) (@ (@ tptp.member449909584od_a_a X2) A))) A)))
% 0.26/0.68 (assert (forall ((A tptp.set_nat)) (= (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.member_nat X2) A))) A)))
% 0.26/0.68 (assert (forall ((P (-> tptp.product_prod_a_a Bool)) (Q (-> tptp.product_prod_a_a Bool))) (=> (forall ((X tptp.product_prod_a_a)) (= (@ P X) (@ Q X))) (= (@ tptp.collec645855634od_a_a P) (@ tptp.collec645855634od_a_a Q)))))
% 0.26/0.68 (assert (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (=> (forall ((X tptp.nat)) (= (@ P X) (@ Q X))) (= (@ tptp.collect_nat P) (@ tptp.collect_nat Q)))))
% 0.26/0.68 (assert (forall ((A2 tptp.set_Product_prod_a_a) (B3 tptp.set_Product_prod_a_a) (C2 tptp.set_Product_prod_a_a)) (=> (= A2 B3) (=> (@ (@ tptp.ord_le1824328871od_a_a B3) C2) (@ (@ tptp.ord_le1824328871od_a_a A2) C2)))))
% 0.26/0.68 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (C2 tptp.nat)) (=> (= A2 B3) (=> (@ (@ tptp.ord_less_eq_nat B3) C2) (@ (@ tptp.ord_less_eq_nat A2) C2)))))
% 0.26/0.68 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat) (C2 tptp.set_nat)) (=> (= A2 B3) (=> (@ (@ tptp.ord_less_eq_set_nat B3) C2) (@ (@ tptp.ord_less_eq_set_nat A2) C2)))))
% 0.26/0.68 (assert (forall ((A2 tptp.set_a) (B3 tptp.set_a) (C2 tptp.set_a)) (=> (= A2 B3) (=> (@ (@ tptp.ord_less_eq_set_a B3) C2) (@ (@ tptp.ord_less_eq_set_a A2) C2)))))
% 0.26/0.68 (assert (= (lambda ((Y tptp.set_Product_prod_a_a) (Z tptp.set_Product_prod_a_a)) (= Y Z)) (lambda ((A4 tptp.set_Product_prod_a_a) (B4 tptp.set_Product_prod_a_a)) (and (@ (@ tptp.ord_le1824328871od_a_a A4) B4) (@ (@ tptp.ord_le1824328871od_a_a B4) A4)))))
% 0.26/0.68 (assert (= (lambda ((Y tptp.nat) (Z tptp.nat)) (= Y Z)) (lambda ((A4 tptp.nat) (B4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A4) B4) (@ (@ tptp.ord_less_eq_nat B4) A4)))))
% 0.26/0.68 (assert (= (lambda ((Y tptp.set_nat) (Z tptp.set_nat)) (= Y Z)) (lambda ((A4 tptp.set_nat) (B4 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A4) B4) (@ (@ tptp.ord_less_eq_set_nat B4) A4)))))
% 0.26/0.68 (assert (= (lambda ((Y tptp.set_a) (Z tptp.set_a)) (= Y Z)) (lambda ((A4 tptp.set_a) (B4 tptp.set_a)) (and (@ (@ tptp.ord_less_eq_set_a A4) B4) (@ (@ tptp.ord_less_eq_set_a B4) A4)))))
% 0.26/0.68 (assert (forall ((Y2 tptp.set_Product_prod_a_a) (X3 tptp.set_Product_prod_a_a)) (=> (@ (@ tptp.ord_le1824328871od_a_a Y2) X3) (= (@ (@ tptp.ord_le1824328871od_a_a X3) Y2) (= X3 Y2)))))
% 0.26/0.68 (assert (forall ((Y2 tptp.nat) (X3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y2) X3) (= (@ (@ tptp.ord_less_eq_nat X3) Y2) (= X3 Y2)))))
% 0.26/0.68 (assert (forall ((Y2 tptp.set_nat) (X3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y2) X3) (= (@ (@ tptp.ord_less_eq_set_nat X3) Y2) (= X3 Y2)))))
% 0.26/0.68 (assert (forall ((Y2 tptp.set_a) (X3 tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a Y2) X3) (= (@ (@ tptp.ord_less_eq_set_a X3) Y2) (= X3 Y2)))))
% 0.26/0.68 (assert (forall ((X3 tptp.nat) (Y2 tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X3))) (let ((_let_2 (@ _let_1 Y2))) (let ((_let_3 (@ tptp.ord_less_eq_nat Z2))) (let ((_let_4 (@ _let_3 X3))) (let ((_let_5 (@ tptp.ord_less_eq_nat Y2))) (let ((_let_6 (@ _let_5 Z2))) (let ((_let_7 (@ _let_5 X3))) (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)))))))))))))))))))
% 0.26/0.68 (assert (forall ((A2 tptp.set_Product_prod_a_a) (B3 tptp.set_Product_prod_a_a) (C2 tptp.set_Product_prod_a_a)) (let ((_let_1 (@ tptp.ord_le1824328871od_a_a A2))) (=> (@ _let_1 B3) (=> (@ (@ tptp.ord_le1824328871od_a_a B3) C2) (@ _let_1 C2))))))
% 0.26/0.68 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A2))) (=> (@ _let_1 B3) (=> (@ (@ tptp.ord_less_eq_nat B3) C2) (@ _let_1 C2))))))
% 0.26/0.68 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A2))) (=> (@ _let_1 B3) (=> (@ (@ tptp.ord_less_eq_set_nat B3) C2) (@ _let_1 C2))))))
% 0.26/0.68 (assert (forall ((A2 tptp.set_a) (B3 tptp.set_a) (C2 tptp.set_a)) (let ((_let_1 (@ tptp.ord_less_eq_set_a A2))) (=> (@ _let_1 B3) (=> (@ (@ tptp.ord_less_eq_set_a B3) C2) (@ _let_1 C2))))))
% 0.26/0.68 (assert (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat X3) Y2)) (@ (@ tptp.ord_less_eq_nat Y2) X3))))
% 0.26/0.68 (assert (forall ((X3 tptp.set_Product_prod_a_a) (Y2 tptp.set_Product_prod_a_a)) (=> (= X3 Y2) (@ (@ tptp.ord_le1824328871od_a_a X3) Y2))))
% 0.26/0.68 (assert (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (= X3 Y2) (@ (@ tptp.ord_less_eq_nat X3) Y2))))
% 0.26/0.68 (assert (forall ((X3 tptp.set_nat) (Y2 tptp.set_nat)) (=> (= X3 Y2) (@ (@ tptp.ord_less_eq_set_nat X3) Y2))))
% 0.26/0.68 (assert (forall ((X3 tptp.set_a) (Y2 tptp.set_a)) (=> (= X3 Y2) (@ (@ tptp.ord_less_eq_set_a X3) Y2))))
% 0.26/0.68 (assert (forall ((X3 tptp.nat) (Y2 tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_nat Y2) X3))))
% 0.26/0.68 (assert (forall ((X3 tptp.set_Product_prod_a_a) (Y2 tptp.set_Product_prod_a_a)) (=> (@ (@ tptp.ord_le1824328871od_a_a X3) Y2) (=> (@ (@ tptp.ord_le1824328871od_a_a Y2) X3) (= X3 Y2)))))
% 0.26/0.68 (assert (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (=> (@ (@ tptp.ord_less_eq_nat Y2) X3) (= X3 Y2)))))
% 0.26/0.68 (assert (forall ((X3 tptp.set_nat) (Y2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X3) Y2) (=> (@ (@ tptp.ord_less_eq_set_nat Y2) X3) (= X3 Y2)))))
% 0.26/0.68 (assert (forall ((X3 tptp.set_a) (Y2 tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a X3) Y2) (=> (@ (@ tptp.ord_less_eq_set_a Y2) X3) (= X3 Y2)))))
% 0.26/0.68 (assert (= (lambda ((Y tptp.set_Product_prod_a_a) (Z tptp.set_Product_prod_a_a)) (= Y Z)) (lambda ((X2 tptp.set_Product_prod_a_a) (Y3 tptp.set_Product_prod_a_a)) (and (@ (@ tptp.ord_le1824328871od_a_a X2) Y3) (@ (@ tptp.ord_le1824328871od_a_a Y3) X2)))))
% 0.26/0.68 (assert (= (lambda ((Y tptp.nat) (Z tptp.nat)) (= Y Z)) (lambda ((X2 tptp.nat) (Y3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X2) Y3) (@ (@ tptp.ord_less_eq_nat Y3) X2)))))
% 0.26/0.68 (assert (= (lambda ((Y tptp.set_nat) (Z tptp.set_nat)) (= Y Z)) (lambda ((X2 tptp.set_nat) (Y3 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat X2) Y3) (@ (@ tptp.ord_less_eq_set_nat Y3) X2)))))
% 0.26/0.68 (assert (= (lambda ((Y tptp.set_a) (Z tptp.set_a)) (= Y Z)) (lambda ((X2 tptp.set_a) (Y3 tptp.set_a)) (and (@ (@ tptp.ord_less_eq_set_a X2) Y3) (@ (@ tptp.ord_less_eq_set_a Y3) X2)))))
% 0.26/0.68 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (F (-> tptp.nat tptp.nat)) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B3) (=> (= (@ F B3) C2) (=> (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_nat (@ F A2)) C2))))))
% 0.26/0.68 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (F (-> tptp.nat tptp.set_nat)) (C2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B3) (=> (= (@ F B3) C2) (=> (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y4) (@ (@ tptp.ord_less_eq_set_nat (@ F X)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_set_nat (@ F A2)) C2))))))
% 0.26/0.68 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (F (-> tptp.nat tptp.set_a)) (C2 tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_nat A2) B3) (=> (= (@ F B3) C2) (=> (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y4) (@ (@ tptp.ord_less_eq_set_a (@ F X)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_set_a (@ F A2)) C2))))))
% 0.26/0.68 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat) (F (-> tptp.set_nat tptp.nat)) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B3) (=> (= (@ F B3) C2) (=> (forall ((X tptp.set_nat) (Y4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_nat (@ F A2)) C2))))))
% 0.26/0.68 (assert (forall ((A2 tptp.set_a) (B3 tptp.set_a) (F (-> tptp.set_a tptp.nat)) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_a A2) B3) (=> (= (@ F B3) C2) (=> (forall ((X tptp.set_a) (Y4 tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a X) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_nat (@ F A2)) C2))))))
% 0.26/0.68 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat) (F (-> tptp.set_nat tptp.set_nat)) (C2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B3) (=> (= (@ F B3) C2) (=> (forall ((X tptp.set_nat) (Y4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y4) (@ (@ tptp.ord_less_eq_set_nat (@ F X)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_set_nat (@ F A2)) C2))))))
% 0.26/0.68 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat) (F (-> tptp.set_nat tptp.set_a)) (C2 tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B3) (=> (= (@ F B3) C2) (=> (forall ((X tptp.set_nat) (Y4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y4) (@ (@ tptp.ord_less_eq_set_a (@ F X)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_set_a (@ F A2)) C2))))))
% 0.26/0.68 (assert (forall ((A2 tptp.set_a) (B3 tptp.set_a) (F (-> tptp.set_a tptp.set_nat)) (C2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_a A2) B3) (=> (= (@ F B3) C2) (=> (forall ((X tptp.set_a) (Y4 tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a X) Y4) (@ (@ tptp.ord_less_eq_set_nat (@ F X)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_set_nat (@ F A2)) C2))))))
% 0.26/0.68 (assert (forall ((A2 tptp.set_a) (B3 tptp.set_a) (F (-> tptp.set_a tptp.set_a)) (C2 tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a A2) B3) (=> (= (@ F B3) C2) (=> (forall ((X tptp.set_a) (Y4 tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a X) Y4) (@ (@ tptp.ord_less_eq_set_a (@ F X)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_set_a (@ F A2)) C2))))))
% 0.26/0.68 (assert (forall ((A2 tptp.set_Product_prod_a_a) (B3 tptp.set_Product_prod_a_a) (F (-> tptp.set_Product_prod_a_a tptp.nat)) (C2 tptp.nat)) (=> (@ (@ tptp.ord_le1824328871od_a_a A2) B3) (=> (= (@ F B3) C2) (=> (forall ((X tptp.set_Product_prod_a_a) (Y4 tptp.set_Product_prod_a_a)) (=> (@ (@ tptp.ord_le1824328871od_a_a X) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_nat (@ F A2)) C2))))))
% 0.26/0.68 (assert (forall ((A2 tptp.nat) (F (-> tptp.nat tptp.nat)) (B3 tptp.nat) (C2 tptp.nat)) (=> (= A2 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_nat B3) C2) (=> (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_nat A2) (@ F C2)))))))
% 0.26/0.68 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.set_nat)) (B3 tptp.nat) (C2 tptp.nat)) (=> (= A2 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_nat B3) C2) (=> (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y4) (@ (@ tptp.ord_less_eq_set_nat (@ F X)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_set_nat A2) (@ F C2)))))))
% 0.26/0.68 (assert (forall ((A2 tptp.set_a) (F (-> tptp.nat tptp.set_a)) (B3 tptp.nat) (C2 tptp.nat)) (=> (= A2 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_nat B3) C2) (=> (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y4) (@ (@ tptp.ord_less_eq_set_a (@ F X)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_set_a A2) (@ F C2)))))))
% 0.26/0.68 (assert (forall ((A2 tptp.nat) (F (-> tptp.set_nat tptp.nat)) (B3 tptp.set_nat) (C2 tptp.set_nat)) (=> (= A2 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_set_nat B3) C2) (=> (forall ((X tptp.set_nat) (Y4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_nat A2) (@ F C2)))))))
% 0.26/0.68 (assert (forall ((A2 tptp.nat) (F (-> tptp.set_a tptp.nat)) (B3 tptp.set_a) (C2 tptp.set_a)) (=> (= A2 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_set_a B3) C2) (=> (forall ((X tptp.set_a) (Y4 tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a X) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_nat A2) (@ F C2)))))))
% 0.26/0.68 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.set_nat tptp.set_nat)) (B3 tptp.set_nat) (C2 tptp.set_nat)) (=> (= A2 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_set_nat B3) C2) (=> (forall ((X tptp.set_nat) (Y4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y4) (@ (@ tptp.ord_less_eq_set_nat (@ F X)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_set_nat A2) (@ F C2)))))))
% 0.26/0.68 (assert (forall ((A2 tptp.set_a) (F (-> tptp.set_nat tptp.set_a)) (B3 tptp.set_nat) (C2 tptp.set_nat)) (=> (= A2 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_set_nat B3) C2) (=> (forall ((X tptp.set_nat) (Y4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y4) (@ (@ tptp.ord_less_eq_set_a (@ F X)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_set_a A2) (@ F C2)))))))
% 0.26/0.68 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.set_a tptp.set_nat)) (B3 tptp.set_a) (C2 tptp.set_a)) (=> (= A2 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_set_a B3) C2) (=> (forall ((X tptp.set_a) (Y4 tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a X) Y4) (@ (@ tptp.ord_less_eq_set_nat (@ F X)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_set_nat A2) (@ F C2)))))))
% 0.26/0.68 (assert (forall ((A2 tptp.set_a) (F (-> tptp.set_a tptp.set_a)) (B3 tptp.set_a) (C2 tptp.set_a)) (=> (= A2 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_set_a B3) C2) (=> (forall ((X tptp.set_a) (Y4 tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a X) Y4) (@ (@ tptp.ord_less_eq_set_a (@ F X)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_set_a A2) (@ F C2)))))))
% 0.26/0.68 (assert (forall ((A2 tptp.nat) (F (-> tptp.set_Product_prod_a_a tptp.nat)) (B3 tptp.set_Product_prod_a_a) (C2 tptp.set_Product_prod_a_a)) (=> (= A2 (@ F B3)) (=> (@ (@ tptp.ord_le1824328871od_a_a B3) C2) (=> (forall ((X tptp.set_Product_prod_a_a) (Y4 tptp.set_Product_prod_a_a)) (=> (@ (@ tptp.ord_le1824328871od_a_a X) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_nat A2) (@ F C2)))))))
% 0.26/0.68 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (F (-> tptp.nat tptp.nat)) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B3) (=> (@ (@ tptp.ord_less_eq_nat (@ F B3)) C2) (=> (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_nat (@ F A2)) C2))))))
% 0.26/0.68 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (F (-> tptp.nat tptp.set_nat)) (C2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B3) (=> (@ (@ tptp.ord_less_eq_set_nat (@ F B3)) C2) (=> (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y4) (@ (@ tptp.ord_less_eq_set_nat (@ F X)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_set_nat (@ F A2)) C2))))))
% 0.26/0.68 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (F (-> tptp.nat tptp.set_a)) (C2 tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_nat A2) B3) (=> (@ (@ tptp.ord_less_eq_set_a (@ F B3)) C2) (=> (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y4) (@ (@ tptp.ord_less_eq_set_a (@ F X)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_set_a (@ F A2)) C2))))))
% 0.26/0.68 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat) (F (-> tptp.set_nat tptp.nat)) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B3) (=> (@ (@ tptp.ord_less_eq_nat (@ F B3)) C2) (=> (forall ((X tptp.set_nat) (Y4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_nat (@ F A2)) C2))))))
% 0.26/0.68 (assert (forall ((A2 tptp.set_a) (B3 tptp.set_a) (F (-> tptp.set_a tptp.nat)) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_a A2) B3) (=> (@ (@ tptp.ord_less_eq_nat (@ F B3)) C2) (=> (forall ((X tptp.set_a) (Y4 tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a X) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_nat (@ F A2)) C2))))))
% 0.26/0.68 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat) (F (-> tptp.set_nat tptp.set_nat)) (C2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B3) (=> (@ (@ tptp.ord_less_eq_set_nat (@ F B3)) C2) (=> (forall ((X tptp.set_nat) (Y4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y4) (@ (@ tptp.ord_less_eq_set_nat (@ F X)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_set_nat (@ F A2)) C2))))))
% 0.26/0.68 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat) (F (-> tptp.set_nat tptp.set_a)) (C2 tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B3) (=> (@ (@ tptp.ord_less_eq_set_a (@ F B3)) C2) (=> (forall ((X tptp.set_nat) (Y4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y4) (@ (@ tptp.ord_less_eq_set_a (@ F X)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_set_a (@ F A2)) C2))))))
% 0.26/0.68 (assert (forall ((A2 tptp.set_a) (B3 tptp.set_a) (F (-> tptp.set_a tptp.set_nat)) (C2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_a A2) B3) (=> (@ (@ tptp.ord_less_eq_set_nat (@ F B3)) C2) (=> (forall ((X tptp.set_a) (Y4 tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a X) Y4) (@ (@ tptp.ord_less_eq_set_nat (@ F X)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_set_nat (@ F A2)) C2))))))
% 0.26/0.68 (assert (forall ((A2 tptp.set_a) (B3 tptp.set_a) (F (-> tptp.set_a tptp.set_a)) (C2 tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a A2) B3) (=> (@ (@ tptp.ord_less_eq_set_a (@ F B3)) C2) (=> (forall ((X tptp.set_a) (Y4 tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a X) Y4) (@ (@ tptp.ord_less_eq_set_a (@ F X)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_set_a (@ F A2)) C2))))))
% 0.26/0.68 (assert (forall ((A2 tptp.set_Product_prod_a_a) (B3 tptp.set_Product_prod_a_a) (F (-> tptp.set_Product_prod_a_a tptp.nat)) (C2 tptp.nat)) (=> (@ (@ tptp.ord_le1824328871od_a_a A2) B3) (=> (@ (@ tptp.ord_less_eq_nat (@ F B3)) C2) (=> (forall ((X tptp.set_Product_prod_a_a) (Y4 tptp.set_Product_prod_a_a)) (=> (@ (@ tptp.ord_le1824328871od_a_a X) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_nat (@ F A2)) C2))))))
% 0.26/0.68 (assert (forall ((A2 tptp.nat) (F (-> tptp.nat tptp.nat)) (B3 tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A2))) (=> (@ _let_1 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_nat B3) C2) (=> (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X)) (@ F Y4)))) (@ _let_1 (@ F C2))))))))
% 0.26/0.68 (assert (forall ((A2 tptp.nat) (F (-> tptp.set_nat tptp.nat)) (B3 tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A2))) (=> (@ _let_1 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_set_nat B3) C2) (=> (forall ((X tptp.set_nat) (Y4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X)) (@ F Y4)))) (@ _let_1 (@ F C2))))))))
% 0.26/0.68 (assert (forall ((A2 tptp.nat) (F (-> tptp.set_a tptp.nat)) (B3 tptp.set_a) (C2 tptp.set_a)) (let ((_let_1 (@ tptp.ord_less_eq_nat A2))) (=> (@ _let_1 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_set_a B3) C2) (=> (forall ((X tptp.set_a) (Y4 tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a X) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X)) (@ F Y4)))) (@ _let_1 (@ F C2))))))))
% 0.26/0.68 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.set_nat)) (B3 tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A2))) (=> (@ _let_1 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_nat B3) C2) (=> (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y4) (@ (@ tptp.ord_less_eq_set_nat (@ F X)) (@ F Y4)))) (@ _let_1 (@ F C2))))))))
% 0.26/0.68 (assert (forall ((A2 tptp.set_a) (F (-> tptp.nat tptp.set_a)) (B3 tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_a A2))) (=> (@ _let_1 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_nat B3) C2) (=> (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y4) (@ (@ tptp.ord_less_eq_set_a (@ F X)) (@ F Y4)))) (@ _let_1 (@ F C2))))))))
% 0.26/0.68 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.set_nat tptp.set_nat)) (B3 tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A2))) (=> (@ _let_1 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_set_nat B3) C2) (=> (forall ((X tptp.set_nat) (Y4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y4) (@ (@ tptp.ord_less_eq_set_nat (@ F X)) (@ F Y4)))) (@ _let_1 (@ F C2))))))))
% 0.26/0.68 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.set_a tptp.set_nat)) (B3 tptp.set_a) (C2 tptp.set_a)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A2))) (=> (@ _let_1 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_set_a B3) C2) (=> (forall ((X tptp.set_a) (Y4 tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a X) Y4) (@ (@ tptp.ord_less_eq_set_nat (@ F X)) (@ F Y4)))) (@ _let_1 (@ F C2))))))))
% 0.26/0.68 (assert (forall ((A2 tptp.set_a) (F (-> tptp.set_nat tptp.set_a)) (B3 tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_a A2))) (=> (@ _let_1 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_set_nat B3) C2) (=> (forall ((X tptp.set_nat) (Y4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y4) (@ (@ tptp.ord_less_eq_set_a (@ F X)) (@ F Y4)))) (@ _let_1 (@ F C2))))))))
% 0.26/0.68 (assert (forall ((A2 tptp.set_a) (F (-> tptp.set_a tptp.set_a)) (B3 tptp.set_a) (C2 tptp.set_a)) (let ((_let_1 (@ tptp.ord_less_eq_set_a A2))) (=> (@ _let_1 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_set_a B3) C2) (=> (forall ((X tptp.set_a) (Y4 tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a X) Y4) (@ (@ tptp.ord_less_eq_set_a (@ F X)) (@ F Y4)))) (@ _let_1 (@ F C2))))))))
% 0.26/0.68 (assert (forall ((A2 tptp.set_Product_prod_a_a) (F (-> tptp.nat tptp.set_Product_prod_a_a)) (B3 tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_le1824328871od_a_a A2))) (=> (@ _let_1 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_nat B3) C2) (=> (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y4) (@ (@ tptp.ord_le1824328871od_a_a (@ F X)) (@ F Y4)))) (@ _let_1 (@ F C2))))))))
% 0.26/0.68 (assert (forall ((P (-> tptp.product_prod_a_a Bool)) (Q (-> tptp.product_prod_a_a Bool))) (= (@ (@ tptp.ord_le1824328871od_a_a (@ tptp.collec645855634od_a_a P)) (@ tptp.collec645855634od_a_a Q)) (forall ((X2 tptp.product_prod_a_a)) (=> (@ P X2) (@ Q X2))))))
% 0.26/0.68 (assert (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat P)) (@ tptp.collect_nat Q)) (forall ((X2 tptp.nat)) (=> (@ P X2) (@ Q X2))))))
% 0.26/0.68 (assert (forall ((P (-> tptp.a Bool)) (Q (-> tptp.a Bool))) (= (@ (@ tptp.ord_less_eq_set_a (@ tptp.collect_a P)) (@ tptp.collect_a Q)) (forall ((X2 tptp.a)) (=> (@ P X2) (@ Q X2))))))
% 0.26/0.68 (assert (= (lambda ((Y tptp.set_Product_prod_a_a) (Z tptp.set_Product_prod_a_a)) (= Y Z)) (lambda ((A5 tptp.set_Product_prod_a_a) (B2 tptp.set_Product_prod_a_a)) (and (@ (@ tptp.ord_le1824328871od_a_a A5) B2) (@ (@ tptp.ord_le1824328871od_a_a B2) A5)))))
% 0.26/0.68 (assert (= (lambda ((Y tptp.set_nat) (Z tptp.set_nat)) (= Y Z)) (lambda ((A5 tptp.set_nat) (B2 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A5) B2) (@ (@ tptp.ord_less_eq_set_nat B2) A5)))))
% 0.26/0.68 (assert (= (lambda ((Y tptp.set_a) (Z tptp.set_a)) (= Y Z)) (lambda ((A5 tptp.set_a) (B2 tptp.set_a)) (and (@ (@ tptp.ord_less_eq_set_a A5) B2) (@ (@ tptp.ord_less_eq_set_a B2) A5)))))
% 0.26/0.68 (assert (forall ((A tptp.set_Product_prod_a_a) (B tptp.set_Product_prod_a_a) (C tptp.set_Product_prod_a_a)) (let ((_let_1 (@ tptp.ord_le1824328871od_a_a A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_le1824328871od_a_a B) C) (@ _let_1 C))))))
% 0.26/0.68 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_set_nat B) C) (@ _let_1 C))))))
% 0.26/0.68 (assert (forall ((A tptp.set_a) (B tptp.set_a) (C tptp.set_a)) (let ((_let_1 (@ tptp.ord_less_eq_set_a A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_set_a B) C) (@ _let_1 C))))))
% 0.26/0.68 (assert (forall ((P (-> tptp.product_prod_a_a Bool)) (Q (-> tptp.product_prod_a_a Bool))) (=> (forall ((X tptp.product_prod_a_a)) (=> (@ P X) (@ Q X))) (@ (@ tptp.ord_le1824328871od_a_a (@ tptp.collec645855634od_a_a P)) (@ tptp.collec645855634od_a_a Q)))))
% 0.26/0.68 (assert (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (=> (forall ((X tptp.nat)) (=> (@ P X) (@ Q X))) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat P)) (@ tptp.collect_nat Q)))))
% 0.26/0.68 (assert (forall ((P (-> tptp.a Bool)) (Q (-> tptp.a Bool))) (=> (forall ((X tptp.a)) (=> (@ P X) (@ Q X))) (@ (@ tptp.ord_less_eq_set_a (@ tptp.collect_a P)) (@ tptp.collect_a Q)))))
% 0.26/0.68 (assert (forall ((A tptp.set_Product_prod_a_a)) (@ (@ tptp.ord_le1824328871od_a_a A) A)))
% 0.26/0.68 (assert (forall ((A tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat A) A)))
% 0.26/0.68 (assert (forall ((A tptp.set_a)) (@ (@ tptp.ord_less_eq_set_a A) A)))
% 0.26/0.68 (assert (= tptp.ord_le1824328871od_a_a (lambda ((A5 tptp.set_Product_prod_a_a) (B2 tptp.set_Product_prod_a_a)) (forall ((T2 tptp.product_prod_a_a)) (let ((_let_1 (@ tptp.member449909584od_a_a T2))) (=> (@ _let_1 A5) (@ _let_1 B2)))))))
% 0.26/0.68 (assert (= tptp.ord_less_eq_set_nat (lambda ((A5 tptp.set_nat) (B2 tptp.set_nat)) (forall ((T2 tptp.nat)) (let ((_let_1 (@ tptp.member_nat T2))) (=> (@ _let_1 A5) (@ _let_1 B2)))))))
% 0.26/0.68 (assert (= tptp.ord_less_eq_set_a (lambda ((A5 tptp.set_a) (B2 tptp.set_a)) (forall ((T2 tptp.a)) (let ((_let_1 (@ tptp.member_a T2))) (=> (@ _let_1 A5) (@ _let_1 B2)))))))
% 0.26/0.68 (assert (forall ((A tptp.set_Product_prod_a_a) (B tptp.set_Product_prod_a_a)) (=> (= A B) (@ (@ tptp.ord_le1824328871od_a_a B) A))))
% 0.26/0.68 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (= A B) (@ (@ tptp.ord_less_eq_set_nat B) A))))
% 0.26/0.68 (assert (forall ((A tptp.set_a) (B tptp.set_a)) (=> (= A B) (@ (@ tptp.ord_less_eq_set_a B) A))))
% 0.26/0.68 (assert (forall ((A tptp.set_Product_prod_a_a) (B tptp.set_Product_prod_a_a)) (=> (= A B) (@ (@ tptp.ord_le1824328871od_a_a A) B))))
% 0.26/0.68 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (= A B) (@ (@ tptp.ord_less_eq_set_nat A) B))))
% 0.26/0.68 (assert (forall ((A tptp.set_a) (B tptp.set_a)) (=> (= A B) (@ (@ tptp.ord_less_eq_set_a A) B))))
% 0.26/0.68 (assert (= tptp.ord_le1824328871od_a_a (lambda ((A5 tptp.set_Product_prod_a_a) (B2 tptp.set_Product_prod_a_a)) (forall ((X2 tptp.product_prod_a_a)) (let ((_let_1 (@ tptp.member449909584od_a_a X2))) (=> (@ _let_1 A5) (@ _let_1 B2)))))))
% 0.26/0.68 (assert (= tptp.ord_less_eq_set_nat (lambda ((A5 tptp.set_nat) (B2 tptp.set_nat)) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X2))) (=> (@ _let_1 A5) (@ _let_1 B2)))))))
% 0.26/0.68 (assert (= tptp.ord_less_eq_set_a (lambda ((A5 tptp.set_a) (B2 tptp.set_a)) (forall ((X2 tptp.a)) (let ((_let_1 (@ tptp.member_a X2))) (=> (@ _let_1 A5) (@ _let_1 B2)))))))
% 0.26/0.68 (assert (forall ((A tptp.set_Product_prod_a_a) (B tptp.set_Product_prod_a_a)) (=> (= A B) (not (=> (@ (@ tptp.ord_le1824328871od_a_a A) B) (not (@ (@ tptp.ord_le1824328871od_a_a B) A)))))))
% 0.26/0.68 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (= A B) (not (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (not (@ (@ tptp.ord_less_eq_set_nat B) A)))))))
% 0.26/0.68 (assert (forall ((A tptp.set_a) (B tptp.set_a)) (=> (= A B) (not (=> (@ (@ tptp.ord_less_eq_set_a A) B) (not (@ (@ tptp.ord_less_eq_set_a B) A)))))))
% 0.26/0.68 (assert (forall ((A tptp.set_Product_prod_a_a) (B tptp.set_Product_prod_a_a) (C2 tptp.product_prod_a_a)) (let ((_let_1 (@ tptp.member449909584od_a_a C2))) (=> (@ (@ tptp.ord_le1824328871od_a_a A) B) (=> (@ _let_1 A) (@ _let_1 B))))))
% 0.26/0.68 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.member_nat C2))) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (=> (@ _let_1 A) (@ _let_1 B))))))
% 0.26/0.68 (assert (forall ((A tptp.set_a) (B tptp.set_a) (C2 tptp.a)) (let ((_let_1 (@ tptp.member_a C2))) (=> (@ (@ tptp.ord_less_eq_set_a A) B) (=> (@ _let_1 A) (@ _let_1 B))))))
% 0.26/0.68 (assert (forall ((A tptp.set_Product_prod_a_a) (B tptp.set_Product_prod_a_a) (X3 tptp.product_prod_a_a)) (let ((_let_1 (@ tptp.member449909584od_a_a X3))) (=> (@ (@ tptp.ord_le1824328871od_a_a A) B) (=> (@ _let_1 A) (@ _let_1 B))))))
% 0.26/0.68 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (X3 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X3))) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (=> (@ _let_1 A) (@ _let_1 B))))))
% 0.26/0.68 (assert (forall ((A tptp.set_a) (B tptp.set_a) (X3 tptp.a)) (let ((_let_1 (@ tptp.member_a X3))) (=> (@ (@ tptp.ord_less_eq_set_a A) B) (=> (@ _let_1 A) (@ _let_1 B))))))
% 0.26/0.68 (assert (forall ((R tptp.set_Product_prod_a_a) (S tptp.set_Product_prod_a_a)) (= (@ (@ tptp.ord_le1347718902_a_a_o (lambda ((X2 tptp.product_prod_a_a)) (@ (@ tptp.member449909584od_a_a X2) R))) (lambda ((X2 tptp.product_prod_a_a)) (@ (@ tptp.member449909584od_a_a X2) S))) (@ (@ tptp.ord_le1824328871od_a_a R) S))))
% 0.26/0.68 (assert (forall ((R tptp.set_nat) (S tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_nat_o (lambda ((X2 tptp.nat)) (@ (@ tptp.member_nat X2) R))) (lambda ((X2 tptp.nat)) (@ (@ tptp.member_nat X2) S))) (@ (@ tptp.ord_less_eq_set_nat R) S))))
% 0.26/0.68 (assert (forall ((R tptp.set_a) (S tptp.set_a)) (= (@ (@ tptp.ord_less_eq_a_o (lambda ((X2 tptp.a)) (@ (@ tptp.member_a X2) R))) (lambda ((X2 tptp.a)) (@ (@ tptp.member_a X2) S))) (@ (@ tptp.ord_less_eq_set_a R) S))))
% 0.26/0.68 (assert (forall ((R2 tptp.pair_p125712459t_unit)) (= R2 (@ (@ (@ tptp.pair_p1621517565t_unit (@ tptp.pair_p1047056820t_unit R2)) (@ tptp.pair_p133601421t_unit R2)) (@ tptp.pair_p1896222615t_unit R2)))))
% 0.26/0.68 (assert (forall ((R2 tptp.pair_p1914262621t_unit)) (= R2 (@ (@ (@ tptp.pair_p1167410509t_unit (@ tptp.pair_p1677060310t_unit R2)) (@ tptp.pair_p715279805t_unit R2)) (@ tptp.pair_p69470259t_unit R2)))))
% 0.26/0.68 (assert (forall ((R2 tptp.pair_p1765063010t_unit)) (= R2 (@ (@ (@ tptp.pair_p398687508t_unit (@ tptp.pair_p447552203t_unit R2)) (@ tptp.pair_p1783210148t_unit R2)) (@ tptp.pair_p1984658862t_unit R2)))))
% 0.26/0.68 (assert (forall ((X3 tptp.product_prod_a_a) (A tptp.set_a) (B tptp.set_a)) (let ((_let_1 (@ tptp.member449909584od_a_a X3))) (= (@ _let_1 (@ (@ tptp.product_product_a_a A) B)) (@ _let_1 (@ (@ tptp.product_Sigma_a_a A) (lambda ((Uu tptp.a)) B)))))))
% 0.26/0.68 (assert (= tptp.product_product_a_a (lambda ((A5 tptp.set_a) (B2 tptp.set_a)) (@ (@ tptp.product_Sigma_a_a A5) (lambda ((Uu tptp.a)) B2)))))
% 0.26/0.68 (assert (forall ((B tptp.set_Product_prod_a_a) (A tptp.set_Product_prod_a_a) (P (-> tptp.product_prod_a_a Bool))) (let ((_let_1 (@ tptp.ord_le1824328871od_a_a B))) (=> (@ _let_1 A) (= (@ _let_1 (@ tptp.collec645855634od_a_a (lambda ((X2 tptp.product_prod_a_a)) (and (@ (@ tptp.member449909584od_a_a X2) A) (@ P X2))))) (forall ((X2 tptp.product_prod_a_a)) (=> (@ (@ tptp.member449909584od_a_a X2) B) (@ P X2))))))))
% 0.26/0.68 (assert (forall ((B tptp.set_nat) (A tptp.set_nat) (P (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.ord_less_eq_set_nat B))) (=> (@ _let_1 A) (= (@ _let_1 (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) A) (@ P X2))))) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) B) (@ P X2))))))))
% 0.26/0.68 (assert (forall ((B tptp.set_a) (A tptp.set_a) (P (-> tptp.a Bool))) (let ((_let_1 (@ tptp.ord_less_eq_set_a B))) (=> (@ _let_1 A) (= (@ _let_1 (@ tptp.collect_a (lambda ((X2 tptp.a)) (and (@ (@ tptp.member_a X2) A) (@ P X2))))) (forall ((X2 tptp.a)) (=> (@ (@ tptp.member_a X2) B) (@ P X2))))))))
% 0.26/0.68 (assert (forall ((B tptp.set_Product_prod_a_a) (A tptp.set_Product_prod_a_a) (Q (-> tptp.product_prod_a_a Bool)) (P (-> tptp.product_prod_a_a Bool))) (=> (@ (@ tptp.ord_le1824328871od_a_a B) A) (=> (forall ((X tptp.product_prod_a_a)) (=> (@ (@ tptp.member449909584od_a_a X) B) (=> (@ Q X) (@ P X)))) (@ (@ tptp.ord_le1824328871od_a_a (@ tptp.collec645855634od_a_a (lambda ((X2 tptp.product_prod_a_a)) (and (@ (@ tptp.member449909584od_a_a X2) B) (@ Q X2))))) (@ tptp.collec645855634od_a_a (lambda ((X2 tptp.product_prod_a_a)) (and (@ (@ tptp.member449909584od_a_a X2) A) (@ P X2)))))))))
% 0.26/0.68 (assert (forall ((B tptp.set_nat) (A tptp.set_nat) (Q (-> tptp.nat Bool)) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_set_nat B) A) (=> (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) B) (=> (@ Q X) (@ P X)))) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) B) (@ Q X2))))) (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) A) (@ P X2)))))))))
% 0.26/0.68 (assert (forall ((B tptp.set_a) (A tptp.set_a) (Q (-> tptp.a Bool)) (P (-> tptp.a Bool))) (=> (@ (@ tptp.ord_less_eq_set_a B) A) (=> (forall ((X tptp.a)) (=> (@ (@ tptp.member_a X) B) (=> (@ Q X) (@ P X)))) (@ (@ tptp.ord_less_eq_set_a (@ tptp.collect_a (lambda ((X2 tptp.a)) (and (@ (@ tptp.member_a X2) B) (@ Q X2))))) (@ tptp.collect_a (lambda ((X2 tptp.a)) (and (@ (@ tptp.member_a X2) A) (@ P X2)))))))))
% 0.26/0.68 (assert (forall ((X4 tptp.set_Product_prod_a_a) (P (-> tptp.product_prod_a_a Bool))) (@ (@ tptp.ord_le1824328871od_a_a (@ tptp.collec645855634od_a_a (lambda ((X2 tptp.product_prod_a_a)) (and (@ (@ tptp.member449909584od_a_a X2) X4) (@ P X2))))) X4)))
% 0.26/0.68 (assert (forall ((X4 tptp.set_nat) (P (-> tptp.nat Bool))) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) X4) (@ P X2))))) X4)))
% 0.26/0.68 (assert (forall ((X4 tptp.set_a) (P (-> tptp.a Bool))) (@ (@ tptp.ord_less_eq_set_a (@ tptp.collect_a (lambda ((X2 tptp.a)) (and (@ (@ tptp.member_a X2) X4) (@ P X2))))) X4)))
% 0.26/0.68 (assert (forall ((X3 tptp.product_prod_a_a) (Z3 tptp.set_Product_prod_a_a) (X4 tptp.set_Product_prod_a_a) (P (-> tptp.product_prod_a_a Bool))) (=> (@ (@ tptp.member449909584od_a_a X3) Z3) (=> (@ (@ tptp.ord_le1824328871od_a_a Z3) (@ tptp.collec645855634od_a_a (lambda ((X2 tptp.product_prod_a_a)) (and (@ (@ tptp.member449909584od_a_a X2) X4) (@ P X2))))) (@ P X3)))))
% 0.26/0.68 (assert (forall ((X3 tptp.nat) (Z3 tptp.set_nat) (X4 tptp.set_nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.member_nat X3) Z3) (=> (@ (@ tptp.ord_less_eq_set_nat Z3) (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) X4) (@ P X2))))) (@ P X3)))))
% 0.26/0.68 (assert (forall ((X3 tptp.a) (Z3 tptp.set_a) (X4 tptp.set_a) (P (-> tptp.a Bool))) (=> (@ (@ tptp.member_a X3) Z3) (=> (@ (@ tptp.ord_less_eq_set_a Z3) (@ tptp.collect_a (lambda ((X2 tptp.a)) (and (@ (@ tptp.member_a X2) X4) (@ P X2))))) (@ P X3)))))
% 0.26/0.68 (assert (forall ((A tptp.set_Product_prod_a_a) (P (-> tptp.product_prod_a_a Bool)) (Q (-> tptp.product_prod_a_a Bool))) (let ((_let_1 (@ tptp.ord_le1824328871od_a_a A))) (= (@ _let_1 (@ tptp.collec645855634od_a_a (lambda ((X2 tptp.product_prod_a_a)) (and (@ P X2) (@ Q X2))))) (and (@ _let_1 (@ tptp.collec645855634od_a_a P)) (@ _let_1 (@ tptp.collec645855634od_a_a Q)))))))
% 0.26/0.68 (assert (forall ((A tptp.set_nat) (P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A))) (= (@ _let_1 (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (and (@ P X2) (@ Q X2))))) (and (@ _let_1 (@ tptp.collect_nat P)) (@ _let_1 (@ tptp.collect_nat Q)))))))
% 0.26/0.68 (assert (forall ((A tptp.set_a) (P (-> tptp.a Bool)) (Q (-> tptp.a Bool))) (let ((_let_1 (@ tptp.ord_less_eq_set_a A))) (= (@ _let_1 (@ tptp.collect_a (lambda ((X2 tptp.a)) (and (@ P X2) (@ Q X2))))) (and (@ _let_1 (@ tptp.collect_a P)) (@ _let_1 (@ tptp.collect_a Q)))))))
% 0.26/0.68 (assert (forall ((Pverts tptp.set_a) (Parcs tptp.set_Product_prod_a_a) (More tptp.product_unit)) (= (@ tptp.pair_p133601421t_unit (@ (@ (@ tptp.pair_p1621517565t_unit Pverts) Parcs) More)) Parcs)))
% 0.26/0.68 (assert (forall ((Pverts tptp.set_nat) (Parcs tptp.set_Pr1986765409at_nat) (More tptp.product_unit)) (= (@ tptp.pair_p715279805t_unit (@ (@ (@ tptp.pair_p1167410509t_unit Pverts) Parcs) More)) Parcs)))
% 0.26/0.68 (assert (forall ((Pverts tptp.set_Product_prod_a_a) (Parcs tptp.set_Pr1948701895od_a_a) (More tptp.product_unit)) (= (@ tptp.pair_p1783210148t_unit (@ (@ (@ tptp.pair_p398687508t_unit Pverts) Parcs) More)) Parcs)))
% 0.26/0.68 (assert (forall ((Pverts tptp.set_a) (Parcs tptp.set_Product_prod_a_a) (More tptp.product_unit)) (= (@ tptp.pair_p1047056820t_unit (@ (@ (@ tptp.pair_p1621517565t_unit Pverts) Parcs) More)) Pverts)))
% 0.26/0.68 (assert (forall ((Pverts tptp.set_nat) (Parcs tptp.set_Pr1986765409at_nat) (More tptp.product_unit)) (= (@ tptp.pair_p1677060310t_unit (@ (@ (@ tptp.pair_p1167410509t_unit Pverts) Parcs) More)) Pverts)))
% 0.26/0.68 (assert (forall ((Pverts tptp.set_Product_prod_a_a) (Parcs tptp.set_Pr1948701895od_a_a) (More tptp.product_unit)) (= (@ tptp.pair_p447552203t_unit (@ (@ (@ tptp.pair_p398687508t_unit Pverts) Parcs) More)) Pverts)))
% 0.26/0.68 (assert (= tptp.finite361944167at_nat (lambda ((A5 tptp.set_Pr1986765409at_nat)) (@ tptp.collec1606769740at_nat (lambda ((X5 tptp.set_Pr1986765409at_nat)) (and (@ (@ tptp.ord_le841296385at_nat X5) A5) (@ tptp.finite772653738at_nat X5)))))))
% 0.26/0.68 (assert (= tptp.finite702915405od_a_a (lambda ((A5 tptp.set_Pr1948701895od_a_a)) (@ tptp.collec453062450od_a_a (lambda ((X5 tptp.set_Pr1948701895od_a_a)) (and (@ (@ tptp.ord_le456379495od_a_a X5) A5) (@ tptp.finite1664988688od_a_a X5)))))))
% 0.26/0.68 (assert (= tptp.finite351630733od_a_a (lambda ((A5 tptp.set_Product_prod_a_a)) (@ tptp.collec183727474od_a_a (lambda ((X5 tptp.set_Product_prod_a_a)) (and (@ (@ tptp.ord_le1824328871od_a_a X5) A5) (@ tptp.finite179568208od_a_a X5)))))))
% 0.26/0.68 (assert (= tptp.finite_Fpow_nat (lambda ((A5 tptp.set_nat)) (@ tptp.collect_set_nat (lambda ((X5 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat X5) A5) (@ tptp.finite_finite_nat X5)))))))
% 0.26/0.68 (assert (= tptp.finite_Fpow_a (lambda ((A5 tptp.set_a)) (@ tptp.collect_set_a (lambda ((X5 tptp.set_a)) (and (@ (@ tptp.ord_less_eq_set_a X5) A5) (@ tptp.finite_finite_a X5)))))))
% 0.26/0.68 (assert (= tptp.pair_p1802376898raph_a (lambda ((G tptp.pair_p125712459t_unit)) (and (@ tptp.pair_p68905728raph_a G) (@ tptp.pair_p1864019935ioms_a G)))))
% 0.26/0.68 (assert (= tptp.pair_p128415500ph_nat (lambda ((G tptp.pair_p1914262621t_unit)) (and (@ tptp.pair_p1515597646ph_nat G) (@ tptp.pair_p1027063983ms_nat G)))))
% 0.26/0.68 (assert (= tptp.pair_p374947051od_a_a (lambda ((G tptp.pair_p1765063010t_unit)) (and (@ tptp.pair_p646030121od_a_a G) (@ tptp.pair_p504738056od_a_a G)))))
% 0.26/0.68 (assert (forall ((G2 tptp.pair_p125712459t_unit)) (=> (@ tptp.pair_p68905728raph_a G2) (=> (@ tptp.pair_p1864019935ioms_a G2) (@ tptp.pair_p1802376898raph_a G2)))))
% 0.26/0.68 (assert (forall ((G2 tptp.pair_p1914262621t_unit)) (=> (@ tptp.pair_p1515597646ph_nat G2) (=> (@ tptp.pair_p1027063983ms_nat G2) (@ tptp.pair_p128415500ph_nat G2)))))
% 0.26/0.68 (assert (forall ((G2 tptp.pair_p1765063010t_unit)) (=> (@ tptp.pair_p646030121od_a_a G2) (=> (@ tptp.pair_p504738056od_a_a G2) (@ tptp.pair_p374947051od_a_a G2)))))
% 0.26/0.68 (assert (forall ((A tptp.set_a) (B tptp.set_nat)) (= (@ tptp.finite1743148308_a_nat (@ (@ tptp.product_Sigma_a_nat A) (lambda ((Uu tptp.a)) B))) (or (= A tptp.bot_bot_set_a) (= B tptp.bot_bot_set_nat) (and (@ tptp.finite_finite_a A) (@ tptp.finite_finite_nat B))))))
% 0.26/0.68 (assert (forall ((A tptp.set_nat) (B tptp.set_a)) (= (@ tptp.finite1808550458_nat_a (@ (@ tptp.product_Sigma_nat_a A) (lambda ((Uu tptp.nat)) B))) (or (= A tptp.bot_bot_set_nat) (= B tptp.bot_bot_set_a) (and (@ tptp.finite_finite_nat A) (@ tptp.finite_finite_a B))))))
% 0.26/0.68 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (= (@ tptp.finite772653738at_nat (@ (@ tptp.produc45129834at_nat A) (lambda ((Uu tptp.nat)) B))) (or (= A tptp.bot_bot_set_nat) (= B tptp.bot_bot_set_nat) (and (@ tptp.finite_finite_nat A) (@ tptp.finite_finite_nat B))))))
% 0.26/0.68 (assert (forall ((A tptp.set_a) (B tptp.set_a)) (= (@ tptp.finite179568208od_a_a (@ (@ tptp.product_Sigma_a_a A) (lambda ((Uu tptp.a)) B))) (or (= A tptp.bot_bot_set_a) (= B tptp.bot_bot_set_a) (and (@ tptp.finite_finite_a A) (@ tptp.finite_finite_a B))))))
% 0.26/0.68 (assert (forall ((A tptp.set_Product_prod_a_a) (B tptp.set_a)) (= (@ tptp.finite1919032935_a_a_a (@ (@ tptp.produc1282482655_a_a_a A) (lambda ((Uu tptp.product_prod_a_a)) B))) (or (= A tptp.bot_bo2131659635od_a_a) (= B tptp.bot_bot_set_a) (and (@ tptp.finite179568208od_a_a A) (@ tptp.finite_finite_a B))))))
% 0.26/0.68 (assert (forall ((A tptp.set_Product_prod_a_a) (B tptp.set_nat)) (= (@ tptp.finite1837575485_a_nat (@ (@ tptp.produc931712687_a_nat A) (lambda ((Uu tptp.product_prod_a_a)) B))) (or (= A tptp.bot_bo2131659635od_a_a) (= B tptp.bot_bot_set_nat) (and (@ tptp.finite179568208od_a_a A) (@ tptp.finite_finite_nat B))))))
% 0.26/0.68 (assert (forall ((A tptp.set_a) (B tptp.set_Product_prod_a_a)) (= (@ tptp.finite676513017od_a_a (@ (@ tptp.produc520147185od_a_a A) (lambda ((Uu tptp.a)) B))) (or (= A tptp.bot_bot_set_a) (= B tptp.bot_bo2131659635od_a_a) (and (@ tptp.finite_finite_a A) (@ tptp.finite179568208od_a_a B))))))
% 0.26/0.68 (assert (forall ((A tptp.set_a) (B tptp.set_Pr1986765409at_nat)) (= (@ tptp.finite942416723at_nat (@ (@ tptp.produc292491723at_nat A) (lambda ((Uu tptp.a)) B))) (or (= A tptp.bot_bot_set_a) (= B tptp.bot_bo2130386637at_nat) (and (@ tptp.finite_finite_a A) (@ tptp.finite772653738at_nat B))))))
% 0.26/0.68 (assert (forall ((A tptp.set_nat) (B tptp.set_Product_prod_a_a)) (= (@ tptp.finite1297454819od_a_a (@ (@ tptp.produc1182842125od_a_a A) (lambda ((Uu tptp.nat)) B))) (or (= A tptp.bot_bot_set_nat) (= B tptp.bot_bo2131659635od_a_a) (and (@ tptp.finite_finite_nat A) (@ tptp.finite179568208od_a_a B))))))
% 41.44/41.63 (assert (forall ((A tptp.set_nat) (B tptp.set_Pr1986765409at_nat)) (= (@ tptp.finite277291581at_nat (@ (@ tptp.produc894163943at_nat A) (lambda ((Uu tptp.nat)) B))) (or (= A tptp.bot_bot_set_nat) (= B tptp.bot_bo2130386637at_nat) (and (@ tptp.finite_finite_nat A) (@ tptp.finite772653738at_nat B))))))
% 41.44/41.63 (assert (forall ((C2 tptp.product_prod_a_a)) (not (@ (@ tptp.member449909584od_a_a C2) tptp.bot_bo2131659635od_a_a))))
% 41.44/41.63 (assert (forall ((C2 tptp.nat)) (not (@ (@ tptp.member_nat C2) tptp.bot_bot_set_nat))))
% 41.44/41.63 (assert (forall ((A tptp.set_Product_prod_a_a)) (= (forall ((X2 tptp.product_prod_a_a)) (not (@ (@ tptp.member449909584od_a_a X2) A))) (= A tptp.bot_bo2131659635od_a_a))))
% 41.44/41.63 (assert (forall ((A tptp.set_nat)) (= (forall ((X2 tptp.nat)) (not (@ (@ tptp.member_nat X2) A))) (= A tptp.bot_bot_set_nat))))
% 41.44/41.63 (assert (forall ((P (-> tptp.product_prod_a_a Bool))) (= (= (@ tptp.collec645855634od_a_a P) tptp.bot_bo2131659635od_a_a) (forall ((X2 tptp.product_prod_a_a)) (not (@ P X2))))))
% 41.44/41.63 (assert (forall ((P (-> tptp.nat Bool))) (= (= (@ tptp.collect_nat P) tptp.bot_bot_set_nat) (forall ((X2 tptp.nat)) (not (@ P X2))))))
% 41.44/41.63 (assert (forall ((P (-> tptp.product_prod_a_a Bool))) (= (= tptp.bot_bo2131659635od_a_a (@ tptp.collec645855634od_a_a P)) (forall ((X2 tptp.product_prod_a_a)) (not (@ P X2))))))
% 41.44/41.63 (assert (forall ((P (-> tptp.nat Bool))) (= (= tptp.bot_bot_set_nat (@ tptp.collect_nat P)) (forall ((X2 tptp.nat)) (not (@ P X2))))))
% 41.44/41.63 (assert (forall ((A tptp.set_Product_prod_a_a)) (@ (@ tptp.ord_le1824328871od_a_a tptp.bot_bo2131659635od_a_a) A)))
% 41.44/41.63 (assert (forall ((A tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat tptp.bot_bot_set_nat) A)))
% 41.44/41.63 (assert (forall ((A tptp.set_a)) (@ (@ tptp.ord_less_eq_set_a tptp.bot_bot_set_a) A)))
% 41.44/41.63 (assert (forall ((A tptp.set_a)) (= (@ (@ tptp.ord_less_eq_set_a A) tptp.bot_bot_set_a) (= A tptp.bot_bot_set_a))))
% 41.44/41.63 (assert (let ((_let_1 (@ tptp.pair_p1047056820t_unit tptp.g))) (and (@ tptp.finite_finite_a _let_1) (= (@ tptp.finite_card_a _let_1) tptp.n) (= (@ tptp.pair_p133601421t_unit tptp.g) (@ tptp.collec645855634od_a_a (@ tptp.produc1833107820_a_a_o (lambda ((U tptp.a) (V tptp.a)) (and (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a U) V)) (@ (@ tptp.product_Sigma_a_a (@ tptp.pair_p1047056820t_unit tptp.g)) (lambda ((Uu tptp.a)) (@ tptp.pair_p1047056820t_unit tptp.g)))) (not (= U V))))))))))
% 41.44/41.63 (assert (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) K))))))
% 41.44/41.63 (assert (= tptp.finite_finite_nat (lambda ((N2 tptp.set_nat)) (exists ((M tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) N2) (@ (@ tptp.ord_less_eq_nat X2) M)))))))
% 41.44/41.63 (assert (forall ((S tptp.set_nat)) (= (not (@ tptp.finite_finite_nat S)) (forall ((M tptp.nat)) (exists ((N tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.member_nat N) S)))))))
% 41.44/41.63 (assert (forall ((P (-> tptp.nat Bool)) (X3 tptp.nat) (M2 tptp.nat)) (=> (@ P X3) (=> (forall ((X tptp.nat)) (=> (@ P X) (@ (@ tptp.ord_less_eq_nat X) M2))) (not (forall ((M3 tptp.nat)) (=> (@ P M3) (not (forall ((X6 tptp.nat)) (=> (@ P X6) (@ (@ tptp.ord_less_eq_nat X6) M3)))))))))))
% 41.44/41.63 (assert (forall ((F (-> tptp.nat tptp.nat)) (U2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N3) (@ F N3))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N)) U2)))))))
% 41.44/41.63 (assert (not (@ tptp.finite179568208od_a_a (@ tptp.pair_p133601421t_unit tptp.g))))
% 41.44/41.63 (set-info :filename cvc5---1.0.5_21782)
% 41.44/41.63 (check-sat-assuming ( true ))
% 41.44/41.63 ------- get file name : TPTP file name is ITP093^1
% 41.44/41.63 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_21782.smt2...
% 41.44/41.63 --- Run --ho-elim --full-saturate-quant at 10...
% 41.44/41.63 --- Run --ho-elim --no-e-matching --full-saturate-quant at 10...
% 41.44/41.63 --- Run --ho-elim --no-e-matching --enum-inst-sum --full-saturate-quant at 10...
% 41.44/41.63 --- Run --ho-elim --finite-model-find --uf-ss=no-minimal at 5...
% 41.44/41.63 --- Run --no-ho-matching --finite-model-find --uf-ss=no-minimal at 5...
% 41.44/41.63 --- Run --no-ho-matching --full-saturate-quant --e/export/starexec/sandbox2/solver/bin/do_THM_THF: line 35: 21916 Alarm clock ( read result; case "$result" in
% 299.81/300.23 unsat)
% 299.81/300.23 echo "% SZS status $unsatResult for $tptpfilename"; echo "% SZS output start Proof for $tptpfilename"; cat; echo "% SZS output end Proof for $tptpfilename"; exit 0
% 299.81/300.23 ;;
% 299.81/300.23 sat)
% 299.81/300.23 echo "% SZS status $satResult for $tptpfilename"; cat; exit 0
% 299.81/300.23 ;;
% 299.81/300.23 esac; exit 1 )
% 299.81/300.24 Alarm clock
% 299.81/300.24 % cvc5---1.0.5 exiting
% 299.81/300.24 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------