TSTP Solution File: ITP120^1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP120^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n011.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 03:18:24 EDT 2023
% Result : Theorem 0.90s 1.11s
% Output : Proof 0.95s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.15 % Problem : ITP120^1 : TPTP v8.1.2. Released v7.5.0.
% 0.12/0.16 % Command : do_cvc5 %s %d
% 0.16/0.37 % Computer : n011.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Sun Aug 27 14:12:55 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.22/0.53 %----Proving TH0
% 0.22/0.54 %------------------------------------------------------------------------------
% 0.22/0.54 % File : ITP120^1 : TPTP v8.1.2. Released v7.5.0.
% 0.22/0.54 % Domain : Interactive Theorem Proving
% 0.22/0.54 % Problem : Sledgehammer Modular_Distrib_Lattice problem prob_203__3262370_1
% 0.22/0.54 % Version : Especial.
% 0.22/0.54 % English :
% 0.22/0.54
% 0.22/0.54 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.22/0.54 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.22/0.54 % Source : [Des21]
% 0.22/0.54 % Names : Modular_Distrib_Lattice/prob_203__3262370_1 [Des21]
% 0.22/0.54
% 0.22/0.54 % Status : Theorem
% 0.22/0.54 % Rating : 0.54 v8.1.0, 0.45 v7.5.0
% 0.22/0.54 % Syntax : Number of formulae : 284 ( 138 unt; 34 typ; 0 def)
% 0.22/0.54 % Number of atoms : 592 ( 190 equ; 0 cnn)
% 0.22/0.54 % Maximal formula atoms : 7 ( 2 avg)
% 0.22/0.54 % Number of connectives : 1817 ( 14 ~; 1 |; 30 &;1556 @)
% 0.22/0.54 % ( 0 <=>; 216 =>; 0 <=; 0 <~>)
% 0.22/0.54 % Maximal formula depth : 16 ( 5 avg)
% 0.22/0.54 % Number of types : 3 ( 2 usr)
% 0.22/0.54 % Number of type conns : 184 ( 184 >; 0 *; 0 +; 0 <<)
% 0.22/0.54 % Number of symbols : 35 ( 32 usr; 5 con; 0-5 aty)
% 0.22/0.54 % Number of variables : 616 ( 40 ^; 570 !; 6 ?; 616 :)
% 0.22/0.54 % SPC : TH0_THM_EQU_NAR
% 0.22/0.54
% 0.22/0.54 % Comments : This file was generated by Sledgehammer 2021-02-23 15:44:17.242
% 0.22/0.54 %------------------------------------------------------------------------------
% 0.22/0.54 % Could-be-implicit typings (2)
% 0.22/0.54 thf(ty_n_t__Set__Oset_Itf__a_J,type,
% 0.22/0.54 set_a: $tType ).
% 0.22/0.54
% 0.22/0.54 thf(ty_n_tf__a,type,
% 0.22/0.54 a: $tType ).
% 0.22/0.54
% 0.22/0.54 % Explicit typings (32)
% 0.22/0.54 thf(sy_c_Conditionally__Complete__Lattices_Opreorder_Obdd__above_001tf__a,type,
% 0.22/0.54 condit1627435690bove_a: ( a > a > $o ) > set_a > $o ).
% 0.22/0.54
% 0.22/0.54 thf(sy_c_Conditionally__Complete__Lattices_Opreorder_Obdd__below_001tf__a,type,
% 0.22/0.54 condit1001553558elow_a: ( a > a > $o ) > set_a > $o ).
% 0.22/0.54
% 0.22/0.54 thf(sy_c_Finite__Set_Ocomp__fun__idem_001tf__a_001tf__a,type,
% 0.22/0.54 finite40241356em_a_a: ( a > a > a ) > $o ).
% 0.22/0.54
% 0.22/0.54 thf(sy_c_Finite__Set_Ofinite_001tf__a,type,
% 0.22/0.54 finite_finite_a: set_a > $o ).
% 0.22/0.54
% 0.22/0.54 thf(sy_c_Groups_Oabel__semigroup_001tf__a,type,
% 0.22/0.54 abel_semigroup_a: ( a > a > a ) > $o ).
% 0.22/0.54
% 0.22/0.54 thf(sy_c_Groups_Osemigroup_001tf__a,type,
% 0.22/0.54 semigroup_a: ( a > a > a ) > $o ).
% 0.22/0.54
% 0.22/0.54 thf(sy_c_If_001tf__a,type,
% 0.22/0.54 if_a: $o > a > a > a ).
% 0.22/0.54
% 0.22/0.54 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_Itf__a_J,type,
% 0.22/0.54 inf_inf_set_a: set_a > set_a > set_a ).
% 0.22/0.54
% 0.22/0.54 thf(sy_c_Lattices_Osemilattice_001tf__a,type,
% 0.22/0.54 semilattice_a: ( a > a > a ) > $o ).
% 0.22/0.54
% 0.22/0.54 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_Itf__a_J,type,
% 0.22/0.54 sup_sup_set_a: set_a > set_a > set_a ).
% 0.22/0.54
% 0.22/0.54 thf(sy_c_Lattices__Big_Osemilattice__set_001tf__a,type,
% 0.22/0.54 lattic1885654924_set_a: ( a > a > a ) > $o ).
% 0.22/0.54
% 0.22/0.54 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Oa__aux_001tf__a,type,
% 0.22/0.54 modula17988509_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
% 0.22/0.54
% 0.22/0.54 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Ob__aux_001tf__a,type,
% 0.22/0.54 modula1373251614_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
% 0.22/0.54
% 0.22/0.54 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Oc__aux_001tf__a,type,
% 0.22/0.54 modula581031071_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
% 0.22/0.54
% 0.22/0.54 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Od__aux_001tf__a,type,
% 0.22/0.54 modula1936294176_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
% 0.22/0.54
% 0.22/0.54 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Oe__aux_001tf__a,type,
% 0.22/0.54 modula1144073633_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
% 0.22/0.54
% 0.22/0.54 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Oincomp_001tf__a,type,
% 0.22/0.54 modula1727524044comp_a: ( a > a > $o ) > a > a > $o ).
% 0.22/0.54
% 0.22/0.54 thf(sy_c_Orderings_Oord_OLeast_001tf__a,type,
% 0.22/0.54 least_a: ( a > a > $o ) > ( a > $o ) > a ).
% 0.22/0.54
% 0.22/0.54 thf(sy_c_Orderings_Oord_Omax_001tf__a,type,
% 0.22/0.54 max_a: ( a > a > $o ) > a > a > a ).
% 0.22/0.54
% 0.22/0.54 thf(sy_c_Orderings_Oord_Omin_001tf__a,type,
% 0.22/0.54 min_a: ( a > a > $o ) > a > a > a ).
% 0.22/0.54
% 0.22/0.54 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__a_J,type,
% 0.22/0.54 ord_less_eq_set_a: set_a > set_a > $o ).
% 0.22/0.54
% 0.22/0.54 thf(sy_c_Orderings_Oorder_OGreatest_001tf__a,type,
% 0.22/0.54 greatest_a: ( a > a > $o ) > ( a > $o ) > a ).
% 0.22/0.54
% 0.22/0.54 thf(sy_c_Orderings_Oorder_Oantimono_001tf__a_001t__Set__Oset_Itf__a_J,type,
% 0.22/0.54 antimono_a_set_a: ( a > a > $o ) > ( a > set_a ) > $o ).
% 0.22/0.54
% 0.22/0.54 thf(sy_c_Orderings_Oorder_Omono_001tf__a_001t__Set__Oset_Itf__a_J,type,
% 0.22/0.54 mono_a_set_a: ( a > a > $o ) > ( a > set_a ) > $o ).
% 0.22/0.54
% 0.22/0.54 thf(sy_c_Set_OCollect_001tf__a,type,
% 0.22/0.54 collect_a: ( a > $o ) > set_a ).
% 0.22/0.54
% 0.22/0.54 thf(sy_c_member_001tf__a,type,
% 0.22/0.54 member_a: a > set_a > $o ).
% 0.22/0.54
% 0.22/0.54 thf(sy_v_a,type,
% 0.22/0.54 a2: a ).
% 0.22/0.54
% 0.22/0.54 thf(sy_v_b,type,
% 0.22/0.54 b: a ).
% 0.22/0.54
% 0.22/0.54 thf(sy_v_c,type,
% 0.22/0.54 c: a ).
% 0.22/0.54
% 0.22/0.54 thf(sy_v_inf,type,
% 0.22/0.54 inf: a > a > a ).
% 0.22/0.54
% 0.22/0.54 thf(sy_v_less__eq,type,
% 0.22/0.54 less_eq: a > a > $o ).
% 0.22/0.54
% 0.22/0.54 thf(sy_v_sup,type,
% 0.22/0.54 sup: a > a > a ).
% 0.22/0.54
% 0.22/0.54 % Relevant facts (245)
% 0.22/0.54 thf(fact_0_local_Oantisym,axiom,
% 0.22/0.54 ! [X: a,Y: a] :
% 0.22/0.54 ( ( less_eq @ X @ Y )
% 0.22/0.54 => ( ( less_eq @ Y @ X )
% 0.22/0.54 => ( X = Y ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.antisym
% 0.22/0.54 thf(fact_1_local_Oantisym__conv,axiom,
% 0.22/0.54 ! [Y: a,X: a] :
% 0.22/0.54 ( ( less_eq @ Y @ X )
% 0.22/0.54 => ( ( less_eq @ X @ Y )
% 0.22/0.54 = ( X = Y ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.antisym_conv
% 0.22/0.54 thf(fact_2_local_Odual__order_Oantisym,axiom,
% 0.22/0.54 ! [B: a,A: a] :
% 0.22/0.54 ( ( less_eq @ B @ A )
% 0.22/0.54 => ( ( less_eq @ A @ B )
% 0.22/0.54 => ( A = B ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.dual_order.antisym
% 0.22/0.54 thf(fact_3_local_Odual__order_Oeq__iff,axiom,
% 0.22/0.54 ( ( ^ [Y2: a,Z: a] : ( Y2 = Z ) )
% 0.22/0.54 = ( ^ [A2: a,B2: a] :
% 0.22/0.54 ( ( less_eq @ B2 @ A2 )
% 0.22/0.54 & ( less_eq @ A2 @ B2 ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.dual_order.eq_iff
% 0.22/0.54 thf(fact_4_local_Odual__order_Otrans,axiom,
% 0.22/0.54 ! [B: a,A: a,C: a] :
% 0.22/0.54 ( ( less_eq @ B @ A )
% 0.22/0.54 => ( ( less_eq @ C @ B )
% 0.22/0.54 => ( less_eq @ C @ A ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.dual_order.trans
% 0.22/0.54 thf(fact_5_local_Oeq__iff,axiom,
% 0.22/0.54 ( ( ^ [Y2: a,Z: a] : ( Y2 = Z ) )
% 0.22/0.54 = ( ^ [X2: a,Y3: a] :
% 0.22/0.54 ( ( less_eq @ X2 @ Y3 )
% 0.22/0.54 & ( less_eq @ Y3 @ X2 ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.eq_iff
% 0.22/0.54 thf(fact_6_local_Oeq__refl,axiom,
% 0.22/0.54 ! [X: a,Y: a] :
% 0.22/0.54 ( ( X = Y )
% 0.22/0.54 => ( less_eq @ X @ Y ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.eq_refl
% 0.22/0.54 thf(fact_7_local_Oord__eq__le__trans,axiom,
% 0.22/0.54 ! [A: a,B: a,C: a] :
% 0.22/0.54 ( ( A = B )
% 0.22/0.54 => ( ( less_eq @ B @ C )
% 0.22/0.54 => ( less_eq @ A @ C ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.ord_eq_le_trans
% 0.22/0.54 thf(fact_8_local_Oord__le__eq__trans,axiom,
% 0.22/0.54 ! [A: a,B: a,C: a] :
% 0.22/0.54 ( ( less_eq @ A @ B )
% 0.22/0.54 => ( ( B = C )
% 0.22/0.54 => ( less_eq @ A @ C ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.ord_le_eq_trans
% 0.22/0.54 thf(fact_9_local_Oorder_Oantisym,axiom,
% 0.22/0.54 ! [A: a,B: a] :
% 0.22/0.54 ( ( less_eq @ A @ B )
% 0.22/0.54 => ( ( less_eq @ B @ A )
% 0.22/0.54 => ( A = B ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.order.antisym
% 0.22/0.54 thf(fact_10_local_Oorder_Oeq__iff,axiom,
% 0.22/0.54 ( ( ^ [Y2: a,Z: a] : ( Y2 = Z ) )
% 0.22/0.54 = ( ^ [A2: a,B2: a] :
% 0.22/0.54 ( ( less_eq @ A2 @ B2 )
% 0.22/0.54 & ( less_eq @ B2 @ A2 ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.order.eq_iff
% 0.22/0.54 thf(fact_11_local_Oorder_Otrans,axiom,
% 0.22/0.54 ! [A: a,B: a,C: a] :
% 0.22/0.54 ( ( less_eq @ A @ B )
% 0.22/0.54 => ( ( less_eq @ B @ C )
% 0.22/0.54 => ( less_eq @ A @ C ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.order.trans
% 0.22/0.54 thf(fact_12_local_Oorder__trans,axiom,
% 0.22/0.54 ! [X: a,Y: a,Z2: a] :
% 0.22/0.54 ( ( less_eq @ X @ Y )
% 0.22/0.54 => ( ( less_eq @ Y @ Z2 )
% 0.22/0.54 => ( less_eq @ X @ Z2 ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.order_trans
% 0.22/0.54 thf(fact_13_local_Oinf_Oassoc,axiom,
% 0.22/0.54 ! [A: a,B: a,C: a] :
% 0.22/0.54 ( ( inf @ ( inf @ A @ B ) @ C )
% 0.22/0.54 = ( inf @ A @ ( inf @ B @ C ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.inf.assoc
% 0.22/0.54 thf(fact_14_local_Oinf_Ocommute,axiom,
% 0.22/0.54 ! [A: a,B: a] :
% 0.22/0.54 ( ( inf @ A @ B )
% 0.22/0.54 = ( inf @ B @ A ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.inf.commute
% 0.22/0.54 thf(fact_15_local_Oinf_Oleft__commute,axiom,
% 0.22/0.54 ! [B: a,A: a,C: a] :
% 0.22/0.54 ( ( inf @ B @ ( inf @ A @ C ) )
% 0.22/0.54 = ( inf @ A @ ( inf @ B @ C ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.inf.left_commute
% 0.22/0.54 thf(fact_16_local_Oinf__assoc,axiom,
% 0.22/0.54 ! [X: a,Y: a,Z2: a] :
% 0.22/0.54 ( ( inf @ ( inf @ X @ Y ) @ Z2 )
% 0.22/0.54 = ( inf @ X @ ( inf @ Y @ Z2 ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.inf_assoc
% 0.22/0.54 thf(fact_17_local_Oinf__commute,axiom,
% 0.22/0.54 ! [X: a,Y: a] :
% 0.22/0.54 ( ( inf @ X @ Y )
% 0.22/0.54 = ( inf @ Y @ X ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.inf_commute
% 0.22/0.54 thf(fact_18_local_Oinf__left__commute,axiom,
% 0.22/0.54 ! [X: a,Y: a,Z2: a] :
% 0.22/0.54 ( ( inf @ X @ ( inf @ Y @ Z2 ) )
% 0.22/0.54 = ( inf @ Y @ ( inf @ X @ Z2 ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.inf_left_commute
% 0.22/0.54 thf(fact_19_local_Osup_Oassoc,axiom,
% 0.22/0.54 ! [A: a,B: a,C: a] :
% 0.22/0.54 ( ( sup @ ( sup @ A @ B ) @ C )
% 0.22/0.54 = ( sup @ A @ ( sup @ B @ C ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.sup.assoc
% 0.22/0.54 thf(fact_20_local_Osup_Ocommute,axiom,
% 0.22/0.54 ! [A: a,B: a] :
% 0.22/0.54 ( ( sup @ A @ B )
% 0.22/0.54 = ( sup @ B @ A ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.sup.commute
% 0.22/0.54 thf(fact_21_local_Osup_Oleft__commute,axiom,
% 0.22/0.54 ! [B: a,A: a,C: a] :
% 0.22/0.54 ( ( sup @ B @ ( sup @ A @ C ) )
% 0.22/0.54 = ( sup @ A @ ( sup @ B @ C ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.sup.left_commute
% 0.22/0.54 thf(fact_22_local_Osup__assoc,axiom,
% 0.22/0.54 ! [X: a,Y: a,Z2: a] :
% 0.22/0.54 ( ( sup @ ( sup @ X @ Y ) @ Z2 )
% 0.22/0.54 = ( sup @ X @ ( sup @ Y @ Z2 ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.sup_assoc
% 0.22/0.54 thf(fact_23_local_Osup__commute,axiom,
% 0.22/0.54 ! [X: a,Y: a] :
% 0.22/0.54 ( ( sup @ X @ Y )
% 0.22/0.54 = ( sup @ Y @ X ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.sup_commute
% 0.22/0.54 thf(fact_24_local_Osup__left__commute,axiom,
% 0.22/0.54 ! [X: a,Y: a,Z2: a] :
% 0.22/0.54 ( ( sup @ X @ ( sup @ Y @ Z2 ) )
% 0.22/0.54 = ( sup @ Y @ ( sup @ X @ Z2 ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.sup_left_commute
% 0.22/0.54 thf(fact_25_local_Oinf_Oabsorb1,axiom,
% 0.22/0.54 ! [A: a,B: a] :
% 0.22/0.54 ( ( less_eq @ A @ B )
% 0.22/0.54 => ( ( inf @ A @ B )
% 0.22/0.54 = A ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.inf.absorb1
% 0.22/0.54 thf(fact_26_local_Oinf_Oabsorb2,axiom,
% 0.22/0.54 ! [B: a,A: a] :
% 0.22/0.54 ( ( less_eq @ B @ A )
% 0.22/0.54 => ( ( inf @ A @ B )
% 0.22/0.54 = B ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.inf.absorb2
% 0.22/0.54 thf(fact_27_local_Oinf_Oabsorb__iff1,axiom,
% 0.22/0.54 ! [A: a,B: a] :
% 0.22/0.54 ( ( less_eq @ A @ B )
% 0.22/0.54 = ( ( inf @ A @ B )
% 0.22/0.54 = A ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.inf.absorb_iff1
% 0.22/0.54 thf(fact_28_local_Oinf_Oabsorb__iff2,axiom,
% 0.22/0.54 ! [B: a,A: a] :
% 0.22/0.54 ( ( less_eq @ B @ A )
% 0.22/0.54 = ( ( inf @ A @ B )
% 0.22/0.54 = B ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.inf.absorb_iff2
% 0.22/0.54 thf(fact_29_local_Oinf_OboundedE,axiom,
% 0.22/0.54 ! [A: a,B: a,C: a] :
% 0.22/0.54 ( ( less_eq @ A @ ( inf @ B @ C ) )
% 0.22/0.54 => ~ ( ( less_eq @ A @ B )
% 0.22/0.54 => ~ ( less_eq @ A @ C ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.inf.boundedE
% 0.22/0.54 thf(fact_30_local_Oinf_OboundedI,axiom,
% 0.22/0.54 ! [A: a,B: a,C: a] :
% 0.22/0.54 ( ( less_eq @ A @ B )
% 0.22/0.54 => ( ( less_eq @ A @ C )
% 0.22/0.54 => ( less_eq @ A @ ( inf @ B @ C ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.inf.boundedI
% 0.22/0.54 thf(fact_31_local_Oinf_Ocobounded1,axiom,
% 0.22/0.54 ! [A: a,B: a] : ( less_eq @ ( inf @ A @ B ) @ A ) ).
% 0.22/0.54
% 0.22/0.54 % local.inf.cobounded1
% 0.22/0.54 thf(fact_32_local_Oinf_Ocobounded2,axiom,
% 0.22/0.54 ! [A: a,B: a] : ( less_eq @ ( inf @ A @ B ) @ B ) ).
% 0.22/0.54
% 0.22/0.54 % local.inf.cobounded2
% 0.22/0.54 thf(fact_33_local_Oinf_OcoboundedI1,axiom,
% 0.22/0.54 ! [A: a,C: a,B: a] :
% 0.22/0.54 ( ( less_eq @ A @ C )
% 0.22/0.54 => ( less_eq @ ( inf @ A @ B ) @ C ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.inf.coboundedI1
% 0.22/0.54 thf(fact_34_local_Oinf_OcoboundedI2,axiom,
% 0.22/0.54 ! [B: a,C: a,A: a] :
% 0.22/0.54 ( ( less_eq @ B @ C )
% 0.22/0.54 => ( less_eq @ ( inf @ A @ B ) @ C ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.inf.coboundedI2
% 0.22/0.54 thf(fact_35_local_Oinf_OorderE,axiom,
% 0.22/0.54 ! [A: a,B: a] :
% 0.22/0.54 ( ( less_eq @ A @ B )
% 0.22/0.54 => ( A
% 0.22/0.54 = ( inf @ A @ B ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.inf.orderE
% 0.22/0.54 thf(fact_36_local_Oinf_OorderI,axiom,
% 0.22/0.54 ! [A: a,B: a] :
% 0.22/0.54 ( ( A
% 0.22/0.54 = ( inf @ A @ B ) )
% 0.22/0.54 => ( less_eq @ A @ B ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.inf.orderI
% 0.22/0.54 thf(fact_37_local_Oinf_Oorder__iff,axiom,
% 0.22/0.54 ! [A: a,B: a] :
% 0.22/0.54 ( ( less_eq @ A @ B )
% 0.22/0.54 = ( A
% 0.22/0.54 = ( inf @ A @ B ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.inf.order_iff
% 0.22/0.54 thf(fact_38_local_Oinf__absorb1,axiom,
% 0.22/0.54 ! [X: a,Y: a] :
% 0.22/0.54 ( ( less_eq @ X @ Y )
% 0.22/0.54 => ( ( inf @ X @ Y )
% 0.22/0.54 = X ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.inf_absorb1
% 0.22/0.54 thf(fact_39_local_Oinf__absorb2,axiom,
% 0.22/0.54 ! [Y: a,X: a] :
% 0.22/0.54 ( ( less_eq @ Y @ X )
% 0.22/0.54 => ( ( inf @ X @ Y )
% 0.22/0.54 = Y ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.inf_absorb2
% 0.22/0.54 thf(fact_40_local_Oinf__greatest,axiom,
% 0.22/0.54 ! [X: a,Y: a,Z2: a] :
% 0.22/0.54 ( ( less_eq @ X @ Y )
% 0.22/0.54 => ( ( less_eq @ X @ Z2 )
% 0.22/0.54 => ( less_eq @ X @ ( inf @ Y @ Z2 ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.inf_greatest
% 0.22/0.54 thf(fact_41_local_Oinf__le1,axiom,
% 0.22/0.54 ! [X: a,Y: a] : ( less_eq @ ( inf @ X @ Y ) @ X ) ).
% 0.22/0.54
% 0.22/0.54 % local.inf_le1
% 0.22/0.54 thf(fact_42_local_Oinf__le2,axiom,
% 0.22/0.54 ! [X: a,Y: a] : ( less_eq @ ( inf @ X @ Y ) @ Y ) ).
% 0.22/0.54
% 0.22/0.54 % local.inf_le2
% 0.22/0.54 thf(fact_43_local_Oinf__mono,axiom,
% 0.22/0.54 ! [A: a,C: a,B: a,D: a] :
% 0.22/0.54 ( ( less_eq @ A @ C )
% 0.22/0.54 => ( ( less_eq @ B @ D )
% 0.22/0.54 => ( less_eq @ ( inf @ A @ B ) @ ( inf @ C @ D ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.inf_mono
% 0.22/0.54 thf(fact_44_local_Oinf__unique,axiom,
% 0.22/0.54 ! [F: a > a > a,X: a,Y: a] :
% 0.22/0.54 ( ! [X3: a,Y4: a] : ( less_eq @ ( F @ X3 @ Y4 ) @ X3 )
% 0.22/0.54 => ( ! [X3: a,Y4: a] : ( less_eq @ ( F @ X3 @ Y4 ) @ Y4 )
% 0.22/0.54 => ( ! [X3: a,Y4: a,Z3: a] :
% 0.22/0.54 ( ( less_eq @ X3 @ Y4 )
% 0.22/0.54 => ( ( less_eq @ X3 @ Z3 )
% 0.22/0.54 => ( less_eq @ X3 @ ( F @ Y4 @ Z3 ) ) ) )
% 0.22/0.54 => ( ( inf @ X @ Y )
% 0.22/0.54 = ( F @ X @ Y ) ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.inf_unique
% 0.22/0.54 thf(fact_45_mem__Collect__eq,axiom,
% 0.22/0.54 ! [A: a,P: a > $o] :
% 0.22/0.54 ( ( member_a @ A @ ( collect_a @ P ) )
% 0.22/0.54 = ( P @ A ) ) ).
% 0.22/0.54
% 0.22/0.54 % mem_Collect_eq
% 0.22/0.54 thf(fact_46_Collect__mem__eq,axiom,
% 0.22/0.54 ! [A3: set_a] :
% 0.22/0.54 ( ( collect_a
% 0.22/0.54 @ ^ [X2: a] : ( member_a @ X2 @ A3 ) )
% 0.22/0.54 = A3 ) ).
% 0.22/0.54
% 0.22/0.54 % Collect_mem_eq
% 0.22/0.54 thf(fact_47_Collect__cong,axiom,
% 0.22/0.54 ! [P: a > $o,Q: a > $o] :
% 0.22/0.54 ( ! [X3: a] :
% 0.22/0.54 ( ( P @ X3 )
% 0.22/0.54 = ( Q @ X3 ) )
% 0.22/0.54 => ( ( collect_a @ P )
% 0.22/0.54 = ( collect_a @ Q ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % Collect_cong
% 0.22/0.54 thf(fact_48_local_Ole__iff__inf,axiom,
% 0.22/0.54 ! [X: a,Y: a] :
% 0.22/0.54 ( ( less_eq @ X @ Y )
% 0.22/0.54 = ( ( inf @ X @ Y )
% 0.22/0.54 = X ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.le_iff_inf
% 0.22/0.54 thf(fact_49_local_Ole__infE,axiom,
% 0.22/0.54 ! [X: a,A: a,B: a] :
% 0.22/0.54 ( ( less_eq @ X @ ( inf @ A @ B ) )
% 0.22/0.54 => ~ ( ( less_eq @ X @ A )
% 0.22/0.54 => ~ ( less_eq @ X @ B ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.le_infE
% 0.22/0.54 thf(fact_50_local_Ole__infI,axiom,
% 0.22/0.54 ! [X: a,A: a,B: a] :
% 0.22/0.54 ( ( less_eq @ X @ A )
% 0.22/0.54 => ( ( less_eq @ X @ B )
% 0.22/0.54 => ( less_eq @ X @ ( inf @ A @ B ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.le_infI
% 0.22/0.54 thf(fact_51_local_Ole__infI1,axiom,
% 0.22/0.54 ! [A: a,X: a,B: a] :
% 0.22/0.54 ( ( less_eq @ A @ X )
% 0.22/0.54 => ( less_eq @ ( inf @ A @ B ) @ X ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.le_infI1
% 0.22/0.54 thf(fact_52_local_Ole__infI2,axiom,
% 0.22/0.54 ! [B: a,X: a,A: a] :
% 0.22/0.54 ( ( less_eq @ B @ X )
% 0.22/0.54 => ( less_eq @ ( inf @ A @ B ) @ X ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.le_infI2
% 0.22/0.54 thf(fact_53_local_Ole__iff__sup,axiom,
% 0.22/0.54 ! [X: a,Y: a] :
% 0.22/0.54 ( ( less_eq @ X @ Y )
% 0.22/0.54 = ( ( sup @ X @ Y )
% 0.22/0.54 = Y ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.le_iff_sup
% 0.22/0.54 thf(fact_54_local_Ole__supE,axiom,
% 0.22/0.54 ! [A: a,B: a,X: a] :
% 0.22/0.54 ( ( less_eq @ ( sup @ A @ B ) @ X )
% 0.22/0.54 => ~ ( ( less_eq @ A @ X )
% 0.22/0.54 => ~ ( less_eq @ B @ X ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.le_supE
% 0.22/0.54 thf(fact_55_local_Ole__supI,axiom,
% 0.22/0.54 ! [A: a,X: a,B: a] :
% 0.22/0.54 ( ( less_eq @ A @ X )
% 0.22/0.54 => ( ( less_eq @ B @ X )
% 0.22/0.54 => ( less_eq @ ( sup @ A @ B ) @ X ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.le_supI
% 0.22/0.54 thf(fact_56_local_Ole__supI1,axiom,
% 0.22/0.54 ! [X: a,A: a,B: a] :
% 0.22/0.54 ( ( less_eq @ X @ A )
% 0.22/0.54 => ( less_eq @ X @ ( sup @ A @ B ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.le_supI1
% 0.22/0.54 thf(fact_57_local_Ole__supI2,axiom,
% 0.22/0.54 ! [X: a,B: a,A: a] :
% 0.22/0.54 ( ( less_eq @ X @ B )
% 0.22/0.54 => ( less_eq @ X @ ( sup @ A @ B ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.le_supI2
% 0.22/0.54 thf(fact_58_local_Osup_Oabsorb1,axiom,
% 0.22/0.54 ! [B: a,A: a] :
% 0.22/0.54 ( ( less_eq @ B @ A )
% 0.22/0.54 => ( ( sup @ A @ B )
% 0.22/0.54 = A ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.sup.absorb1
% 0.22/0.54 thf(fact_59_local_Osup_Oabsorb2,axiom,
% 0.22/0.54 ! [A: a,B: a] :
% 0.22/0.54 ( ( less_eq @ A @ B )
% 0.22/0.54 => ( ( sup @ A @ B )
% 0.22/0.54 = B ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.sup.absorb2
% 0.22/0.54 thf(fact_60_local_Osup_Oabsorb__iff1,axiom,
% 0.22/0.54 ! [B: a,A: a] :
% 0.22/0.54 ( ( less_eq @ B @ A )
% 0.22/0.54 = ( ( sup @ A @ B )
% 0.22/0.54 = A ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.sup.absorb_iff1
% 0.22/0.54 thf(fact_61_local_Osup_Oabsorb__iff2,axiom,
% 0.22/0.54 ! [A: a,B: a] :
% 0.22/0.54 ( ( less_eq @ A @ B )
% 0.22/0.54 = ( ( sup @ A @ B )
% 0.22/0.54 = B ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.sup.absorb_iff2
% 0.22/0.54 thf(fact_62_local_Osup_OboundedE,axiom,
% 0.22/0.54 ! [B: a,C: a,A: a] :
% 0.22/0.54 ( ( less_eq @ ( sup @ B @ C ) @ A )
% 0.22/0.54 => ~ ( ( less_eq @ B @ A )
% 0.22/0.54 => ~ ( less_eq @ C @ A ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.sup.boundedE
% 0.22/0.54 thf(fact_63_local_Osup_OboundedI,axiom,
% 0.22/0.54 ! [B: a,A: a,C: a] :
% 0.22/0.54 ( ( less_eq @ B @ A )
% 0.22/0.54 => ( ( less_eq @ C @ A )
% 0.22/0.54 => ( less_eq @ ( sup @ B @ C ) @ A ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.sup.boundedI
% 0.22/0.54 thf(fact_64_local_Osup_Ocobounded1,axiom,
% 0.22/0.54 ! [A: a,B: a] : ( less_eq @ A @ ( sup @ A @ B ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.sup.cobounded1
% 0.22/0.54 thf(fact_65_local_Osup_Ocobounded2,axiom,
% 0.22/0.54 ! [B: a,A: a] : ( less_eq @ B @ ( sup @ A @ B ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.sup.cobounded2
% 0.22/0.54 thf(fact_66_local_Osup_OcoboundedI1,axiom,
% 0.22/0.54 ! [C: a,A: a,B: a] :
% 0.22/0.54 ( ( less_eq @ C @ A )
% 0.22/0.54 => ( less_eq @ C @ ( sup @ A @ B ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.sup.coboundedI1
% 0.22/0.54 thf(fact_67_local_Osup_OcoboundedI2,axiom,
% 0.22/0.54 ! [C: a,B: a,A: a] :
% 0.22/0.54 ( ( less_eq @ C @ B )
% 0.22/0.54 => ( less_eq @ C @ ( sup @ A @ B ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.sup.coboundedI2
% 0.22/0.54 thf(fact_68_local_Osup_Omono,axiom,
% 0.22/0.54 ! [C: a,A: a,D: a,B: a] :
% 0.22/0.54 ( ( less_eq @ C @ A )
% 0.22/0.54 => ( ( less_eq @ D @ B )
% 0.22/0.54 => ( less_eq @ ( sup @ C @ D ) @ ( sup @ A @ B ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.sup.mono
% 0.22/0.54 thf(fact_69_local_Osup_OorderE,axiom,
% 0.22/0.54 ! [B: a,A: a] :
% 0.22/0.54 ( ( less_eq @ B @ A )
% 0.22/0.54 => ( A
% 0.22/0.54 = ( sup @ A @ B ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.sup.orderE
% 0.22/0.54 thf(fact_70_local_Osup_OorderI,axiom,
% 0.22/0.54 ! [A: a,B: a] :
% 0.22/0.54 ( ( A
% 0.22/0.54 = ( sup @ A @ B ) )
% 0.22/0.54 => ( less_eq @ B @ A ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.sup.orderI
% 0.22/0.54 thf(fact_71_local_Osup_Oorder__iff,axiom,
% 0.22/0.54 ! [B: a,A: a] :
% 0.22/0.54 ( ( less_eq @ B @ A )
% 0.22/0.54 = ( A
% 0.22/0.54 = ( sup @ A @ B ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.sup.order_iff
% 0.22/0.54 thf(fact_72_local_Osup__absorb1,axiom,
% 0.22/0.54 ! [Y: a,X: a] :
% 0.22/0.54 ( ( less_eq @ Y @ X )
% 0.22/0.54 => ( ( sup @ X @ Y )
% 0.22/0.54 = X ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.sup_absorb1
% 0.22/0.54 thf(fact_73_local_Osup__absorb2,axiom,
% 0.22/0.54 ! [X: a,Y: a] :
% 0.22/0.54 ( ( less_eq @ X @ Y )
% 0.22/0.54 => ( ( sup @ X @ Y )
% 0.22/0.54 = Y ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.sup_absorb2
% 0.22/0.54 thf(fact_74_local_Osup__ge1,axiom,
% 0.22/0.54 ! [X: a,Y: a] : ( less_eq @ X @ ( sup @ X @ Y ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.sup_ge1
% 0.22/0.54 thf(fact_75_local_Osup__ge2,axiom,
% 0.22/0.54 ! [Y: a,X: a] : ( less_eq @ Y @ ( sup @ X @ Y ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.sup_ge2
% 0.22/0.54 thf(fact_76_local_Osup__least,axiom,
% 0.22/0.54 ! [Y: a,X: a,Z2: a] :
% 0.22/0.54 ( ( less_eq @ Y @ X )
% 0.22/0.54 => ( ( less_eq @ Z2 @ X )
% 0.22/0.54 => ( less_eq @ ( sup @ Y @ Z2 ) @ X ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.sup_least
% 0.22/0.54 thf(fact_77_local_Osup__mono,axiom,
% 0.22/0.54 ! [A: a,C: a,B: a,D: a] :
% 0.22/0.54 ( ( less_eq @ A @ C )
% 0.22/0.54 => ( ( less_eq @ B @ D )
% 0.22/0.54 => ( less_eq @ ( sup @ A @ B ) @ ( sup @ C @ D ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.sup_mono
% 0.22/0.54 thf(fact_78_local_Osup__unique,axiom,
% 0.22/0.54 ! [F: a > a > a,X: a,Y: a] :
% 0.22/0.54 ( ! [X3: a,Y4: a] : ( less_eq @ X3 @ ( F @ X3 @ Y4 ) )
% 0.22/0.54 => ( ! [X3: a,Y4: a] : ( less_eq @ Y4 @ ( F @ X3 @ Y4 ) )
% 0.22/0.54 => ( ! [X3: a,Y4: a,Z3: a] :
% 0.22/0.54 ( ( less_eq @ Y4 @ X3 )
% 0.22/0.54 => ( ( less_eq @ Z3 @ X3 )
% 0.22/0.54 => ( less_eq @ ( F @ Y4 @ Z3 ) @ X3 ) ) )
% 0.22/0.54 => ( ( sup @ X @ Y )
% 0.22/0.54 = ( F @ X @ Y ) ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.sup_unique
% 0.22/0.54 thf(fact_79_local_Odistrib__imp1,axiom,
% 0.22/0.54 ! [X: a,Y: a,Z2: a] :
% 0.22/0.54 ( ! [X3: a,Y4: a,Z3: a] :
% 0.22/0.54 ( ( inf @ X3 @ ( sup @ Y4 @ Z3 ) )
% 0.22/0.54 = ( sup @ ( inf @ X3 @ Y4 ) @ ( inf @ X3 @ Z3 ) ) )
% 0.22/0.54 => ( ( sup @ X @ ( inf @ Y @ Z2 ) )
% 0.22/0.54 = ( inf @ ( sup @ X @ Y ) @ ( sup @ X @ Z2 ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.distrib_imp1
% 0.22/0.54 thf(fact_80_local_Odistrib__imp2,axiom,
% 0.22/0.54 ! [X: a,Y: a,Z2: a] :
% 0.22/0.54 ( ! [X3: a,Y4: a,Z3: a] :
% 0.22/0.54 ( ( sup @ X3 @ ( inf @ Y4 @ Z3 ) )
% 0.22/0.54 = ( inf @ ( sup @ X3 @ Y4 ) @ ( sup @ X3 @ Z3 ) ) )
% 0.22/0.54 => ( ( inf @ X @ ( sup @ Y @ Z2 ) )
% 0.22/0.54 = ( sup @ ( inf @ X @ Y ) @ ( inf @ X @ Z2 ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.distrib_imp2
% 0.22/0.54 thf(fact_81_local_Oa__join__d,axiom,
% 0.22/0.54 ! [A: a,B: a,C: a] :
% 0.22/0.54 ( ( sup @ A @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) )
% 0.22/0.54 = ( sup @ A @ ( inf @ B @ C ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.a_join_d
% 0.22/0.54 thf(fact_82_a__meet__d,axiom,
% 0.22/0.54 ! [A: a,B: a,C: a] :
% 0.22/0.54 ( ( inf @ A @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) )
% 0.22/0.54 = ( sup @ ( inf @ A @ B ) @ ( inf @ C @ A ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % a_meet_d
% 0.22/0.54 thf(fact_83_local_Ob__join__d,axiom,
% 0.22/0.54 ! [B: a,A: a,C: a] :
% 0.22/0.54 ( ( sup @ B @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) )
% 0.22/0.54 = ( sup @ B @ ( inf @ C @ A ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.b_join_d
% 0.22/0.54 thf(fact_84_b__meet__d,axiom,
% 0.22/0.54 ! [B: a,A: a,C: a] :
% 0.22/0.54 ( ( inf @ B @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) )
% 0.22/0.54 = ( sup @ ( inf @ B @ C ) @ ( inf @ A @ B ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % b_meet_d
% 0.22/0.54 thf(fact_85_c__meet__d,axiom,
% 0.22/0.54 ! [C: a,A: a,B: a] :
% 0.22/0.54 ( ( inf @ C @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) )
% 0.22/0.54 = ( sup @ ( inf @ C @ A ) @ ( inf @ B @ C ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % c_meet_d
% 0.22/0.54 thf(fact_86_local_Od__aux__def,axiom,
% 0.22/0.54 ! [A: a,B: a,C: a] :
% 0.22/0.54 ( ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C )
% 0.22/0.54 = ( sup @ ( sup @ ( inf @ A @ B ) @ ( inf @ B @ C ) ) @ ( inf @ C @ A ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.d_aux_def
% 0.22/0.54 thf(fact_87_local_Od__b__c__a,axiom,
% 0.22/0.54 ! [B: a,C: a,A: a] :
% 0.22/0.54 ( ( modula1936294176_aux_a @ inf @ sup @ B @ C @ A )
% 0.22/0.54 = ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.d_b_c_a
% 0.22/0.54 thf(fact_88_local_Od__c__a__b,axiom,
% 0.22/0.54 ! [C: a,A: a,B: a] :
% 0.22/0.54 ( ( modula1936294176_aux_a @ inf @ sup @ C @ A @ B )
% 0.22/0.54 = ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.d_c_a_b
% 0.22/0.54 thf(fact_89_local_Oa__meet__e,axiom,
% 0.22/0.54 ! [A: a,B: a,C: a] :
% 0.22/0.54 ( ( inf @ A @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
% 0.22/0.54 = ( inf @ A @ ( sup @ B @ C ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.a_meet_e
% 0.22/0.54 thf(fact_90_local_Ob__meet__e,axiom,
% 0.22/0.54 ! [B: a,A: a,C: a] :
% 0.22/0.54 ( ( inf @ B @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
% 0.22/0.54 = ( inf @ B @ ( sup @ C @ A ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.b_meet_e
% 0.22/0.54 thf(fact_91_local_Oc__meet__e,axiom,
% 0.22/0.54 ! [C: a,A: a,B: a] :
% 0.22/0.54 ( ( inf @ C @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
% 0.22/0.54 = ( inf @ C @ ( sup @ A @ B ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.c_meet_e
% 0.22/0.54 thf(fact_92_local_Oe__aux__def,axiom,
% 0.22/0.54 ! [A: a,B: a,C: a] :
% 0.22/0.54 ( ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C )
% 0.22/0.54 = ( inf @ ( inf @ ( sup @ A @ B ) @ ( sup @ B @ C ) ) @ ( sup @ C @ A ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.e_aux_def
% 0.22/0.54 thf(fact_93_local_Oe__b__c__a,axiom,
% 0.22/0.54 ! [B: a,C: a,A: a] :
% 0.22/0.54 ( ( modula1144073633_aux_a @ inf @ sup @ B @ C @ A )
% 0.22/0.54 = ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.e_b_c_a
% 0.22/0.54 thf(fact_94_local_Oe__c__a__b,axiom,
% 0.22/0.54 ! [C: a,A: a,B: a] :
% 0.22/0.54 ( ( modula1144073633_aux_a @ inf @ sup @ C @ A @ B )
% 0.22/0.54 = ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.e_c_a_b
% 0.22/0.54 thf(fact_95_local_Odistrib__inf__le,axiom,
% 0.22/0.54 ! [X: a,Y: a,Z2: a] : ( less_eq @ ( sup @ ( inf @ X @ Y ) @ ( inf @ X @ Z2 ) ) @ ( inf @ X @ ( sup @ Y @ Z2 ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.distrib_inf_le
% 0.22/0.54 thf(fact_96_local_Odistrib__sup__le,axiom,
% 0.22/0.54 ! [X: a,Y: a,Z2: a] : ( less_eq @ ( sup @ X @ ( inf @ Y @ Z2 ) ) @ ( inf @ ( sup @ X @ Y ) @ ( sup @ X @ Z2 ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.distrib_sup_le
% 0.22/0.54 thf(fact_97_local_Omodular,axiom,
% 0.22/0.54 ! [X: a,Y: a,Z2: a] :
% 0.22/0.54 ( ( less_eq @ X @ Y )
% 0.22/0.54 => ( ( sup @ X @ ( inf @ Y @ Z2 ) )
% 0.22/0.54 = ( inf @ Y @ ( sup @ X @ Z2 ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.modular
% 0.22/0.54 thf(fact_98_local_Oincomp__def,axiom,
% 0.22/0.54 ! [X: a,Y: a] :
% 0.22/0.54 ( ( modula1727524044comp_a @ less_eq @ X @ Y )
% 0.22/0.54 = ( ~ ( less_eq @ X @ Y )
% 0.22/0.54 & ~ ( less_eq @ Y @ X ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.incomp_def
% 0.22/0.54 thf(fact_99_local_Oorder_Orefl,axiom,
% 0.22/0.54 ! [A: a] : ( less_eq @ A @ A ) ).
% 0.22/0.54
% 0.22/0.54 % local.order.refl
% 0.22/0.54 thf(fact_100_local_Oorder__refl,axiom,
% 0.22/0.54 ! [X: a] : ( less_eq @ X @ X ) ).
% 0.22/0.54
% 0.22/0.54 % local.order_refl
% 0.22/0.54 thf(fact_101_local_Oinf_Oidem,axiom,
% 0.22/0.54 ! [A: a] :
% 0.22/0.54 ( ( inf @ A @ A )
% 0.22/0.54 = A ) ).
% 0.22/0.54
% 0.22/0.54 % local.inf.idem
% 0.22/0.54 thf(fact_102_local_Oinf_Oleft__idem,axiom,
% 0.22/0.54 ! [A: a,B: a] :
% 0.22/0.54 ( ( inf @ A @ ( inf @ A @ B ) )
% 0.22/0.54 = ( inf @ A @ B ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.inf.left_idem
% 0.22/0.54 thf(fact_103_local_Oinf_Oright__idem,axiom,
% 0.22/0.54 ! [A: a,B: a] :
% 0.22/0.54 ( ( inf @ ( inf @ A @ B ) @ B )
% 0.22/0.54 = ( inf @ A @ B ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.inf.right_idem
% 0.22/0.54 thf(fact_104_local_Oinf__idem,axiom,
% 0.22/0.54 ! [X: a] :
% 0.22/0.54 ( ( inf @ X @ X )
% 0.22/0.54 = X ) ).
% 0.22/0.54
% 0.22/0.54 % local.inf_idem
% 0.22/0.54 thf(fact_105_local_Oinf__left__idem,axiom,
% 0.22/0.54 ! [X: a,Y: a] :
% 0.22/0.54 ( ( inf @ X @ ( inf @ X @ Y ) )
% 0.22/0.54 = ( inf @ X @ Y ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.inf_left_idem
% 0.22/0.54 thf(fact_106_local_Oinf__right__idem,axiom,
% 0.22/0.54 ! [X: a,Y: a] :
% 0.22/0.54 ( ( inf @ ( inf @ X @ Y ) @ Y )
% 0.22/0.54 = ( inf @ X @ Y ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.inf_right_idem
% 0.22/0.54 thf(fact_107_local_Osup_Oidem,axiom,
% 0.22/0.54 ! [A: a] :
% 0.22/0.54 ( ( sup @ A @ A )
% 0.22/0.54 = A ) ).
% 0.22/0.54
% 0.22/0.54 % local.sup.idem
% 0.22/0.54 thf(fact_108_local_Osup_Oleft__idem,axiom,
% 0.22/0.54 ! [A: a,B: a] :
% 0.22/0.54 ( ( sup @ A @ ( sup @ A @ B ) )
% 0.22/0.54 = ( sup @ A @ B ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.sup.left_idem
% 0.22/0.54 thf(fact_109_local_Osup_Oright__idem,axiom,
% 0.22/0.54 ! [A: a,B: a] :
% 0.22/0.54 ( ( sup @ ( sup @ A @ B ) @ B )
% 0.22/0.54 = ( sup @ A @ B ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.sup.right_idem
% 0.22/0.54 thf(fact_110_local_Osup__idem,axiom,
% 0.22/0.54 ! [X: a] :
% 0.22/0.54 ( ( sup @ X @ X )
% 0.22/0.54 = X ) ).
% 0.22/0.54
% 0.22/0.54 % local.sup_idem
% 0.22/0.54 thf(fact_111_local_Osup__left__idem,axiom,
% 0.22/0.54 ! [X: a,Y: a] :
% 0.22/0.54 ( ( sup @ X @ ( sup @ X @ Y ) )
% 0.22/0.54 = ( sup @ X @ Y ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.sup_left_idem
% 0.22/0.54 thf(fact_112_local_Oc__a,axiom,
% 0.22/0.54 ! [A: a,B: a,C: a] :
% 0.22/0.54 ( ( modula581031071_aux_a @ inf @ sup @ A @ B @ C )
% 0.22/0.54 = ( modula17988509_aux_a @ inf @ sup @ C @ A @ B ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.c_a
% 0.22/0.54 thf(fact_113_local_OGreatestI2__order,axiom,
% 0.22/0.54 ! [P: a > $o,X: a,Q: a > $o] :
% 0.22/0.54 ( ( P @ X )
% 0.22/0.54 => ( ! [Y4: a] :
% 0.22/0.54 ( ( P @ Y4 )
% 0.22/0.54 => ( less_eq @ Y4 @ X ) )
% 0.22/0.54 => ( ! [X3: a] :
% 0.22/0.54 ( ( P @ X3 )
% 0.22/0.54 => ( ! [Y5: a] :
% 0.22/0.54 ( ( P @ Y5 )
% 0.22/0.54 => ( less_eq @ Y5 @ X3 ) )
% 0.22/0.54 => ( Q @ X3 ) ) )
% 0.22/0.54 => ( Q @ ( greatest_a @ less_eq @ P ) ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.GreatestI2_order
% 0.22/0.54 thf(fact_114_local_OGreatest__equality,axiom,
% 0.22/0.54 ! [P: a > $o,X: a] :
% 0.22/0.54 ( ( P @ X )
% 0.22/0.54 => ( ! [Y4: a] :
% 0.22/0.54 ( ( P @ Y4 )
% 0.22/0.54 => ( less_eq @ Y4 @ X ) )
% 0.22/0.54 => ( ( greatest_a @ less_eq @ P )
% 0.22/0.54 = X ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.Greatest_equality
% 0.22/0.54 thf(fact_115_local_Omax__def,axiom,
% 0.22/0.54 ! [A: a,B: a] :
% 0.22/0.54 ( ( ( less_eq @ A @ B )
% 0.22/0.54 => ( ( max_a @ less_eq @ A @ B )
% 0.22/0.54 = B ) )
% 0.22/0.54 & ( ~ ( less_eq @ A @ B )
% 0.22/0.54 => ( ( max_a @ less_eq @ A @ B )
% 0.22/0.54 = A ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.max_def
% 0.22/0.54 thf(fact_116_local_Omin__def,axiom,
% 0.22/0.54 ! [A: a,B: a] :
% 0.22/0.54 ( ( ( less_eq @ A @ B )
% 0.22/0.54 => ( ( min_a @ less_eq @ A @ B )
% 0.22/0.54 = A ) )
% 0.22/0.54 & ( ~ ( less_eq @ A @ B )
% 0.22/0.54 => ( ( min_a @ less_eq @ A @ B )
% 0.22/0.54 = B ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.min_def
% 0.22/0.54 thf(fact_117_local_Oa__aux__def,axiom,
% 0.22/0.54 ! [A: a,B: a,C: a] :
% 0.22/0.54 ( ( modula17988509_aux_a @ inf @ sup @ A @ B @ C )
% 0.22/0.54 = ( sup @ ( inf @ A @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.a_aux_def
% 0.22/0.54 thf(fact_118_local_Oc__aux__def,axiom,
% 0.22/0.54 ! [A: a,B: a,C: a] :
% 0.22/0.54 ( ( modula581031071_aux_a @ inf @ sup @ A @ B @ C )
% 0.22/0.54 = ( sup @ ( inf @ C @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.c_aux_def
% 0.22/0.54 thf(fact_119_local_Oinf_Obounded__iff,axiom,
% 0.22/0.54 ! [A: a,B: a,C: a] :
% 0.22/0.54 ( ( less_eq @ A @ ( inf @ B @ C ) )
% 0.22/0.54 = ( ( less_eq @ A @ B )
% 0.22/0.54 & ( less_eq @ A @ C ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.inf.bounded_iff
% 0.22/0.54 thf(fact_120_local_Ole__inf__iff,axiom,
% 0.22/0.54 ! [X: a,Y: a,Z2: a] :
% 0.22/0.54 ( ( less_eq @ X @ ( inf @ Y @ Z2 ) )
% 0.22/0.54 = ( ( less_eq @ X @ Y )
% 0.22/0.54 & ( less_eq @ X @ Z2 ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.le_inf_iff
% 0.22/0.54 thf(fact_121_local_Ole__sup__iff,axiom,
% 0.22/0.54 ! [X: a,Y: a,Z2: a] :
% 0.22/0.54 ( ( less_eq @ ( sup @ X @ Y ) @ Z2 )
% 0.22/0.54 = ( ( less_eq @ X @ Z2 )
% 0.22/0.54 & ( less_eq @ Y @ Z2 ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.le_sup_iff
% 0.22/0.54 thf(fact_122_local_Osup_Obounded__iff,axiom,
% 0.22/0.54 ! [B: a,C: a,A: a] :
% 0.22/0.54 ( ( less_eq @ ( sup @ B @ C ) @ A )
% 0.22/0.54 = ( ( less_eq @ B @ A )
% 0.22/0.54 & ( less_eq @ C @ A ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.sup.bounded_iff
% 0.22/0.54 thf(fact_123_local_Oinf__sup__absorb,axiom,
% 0.22/0.54 ! [X: a,Y: a] :
% 0.22/0.54 ( ( inf @ X @ ( sup @ X @ Y ) )
% 0.22/0.54 = X ) ).
% 0.22/0.54
% 0.22/0.54 % local.inf_sup_absorb
% 0.22/0.54 thf(fact_124_local_Osup__inf__absorb,axiom,
% 0.22/0.54 ! [X: a,Y: a] :
% 0.22/0.54 ( ( sup @ X @ ( inf @ X @ Y ) )
% 0.22/0.54 = X ) ).
% 0.22/0.54
% 0.22/0.54 % local.sup_inf_absorb
% 0.22/0.54 thf(fact_125_local_Ob__a,axiom,
% 0.22/0.54 ! [A: a,B: a,C: a] :
% 0.22/0.54 ( ( modula1373251614_aux_a @ inf @ sup @ A @ B @ C )
% 0.22/0.54 = ( modula17988509_aux_a @ inf @ sup @ B @ C @ A ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.b_a
% 0.22/0.54 thf(fact_126_local_OLeast1I,axiom,
% 0.22/0.54 ! [P: a > $o] :
% 0.22/0.54 ( ? [X4: a] :
% 0.22/0.54 ( ( P @ X4 )
% 0.22/0.54 & ! [Y4: a] :
% 0.22/0.54 ( ( P @ Y4 )
% 0.22/0.54 => ( less_eq @ X4 @ Y4 ) )
% 0.22/0.54 & ! [Y4: a] :
% 0.22/0.54 ( ( ( P @ Y4 )
% 0.22/0.54 & ! [Ya: a] :
% 0.22/0.54 ( ( P @ Ya )
% 0.22/0.54 => ( less_eq @ Y4 @ Ya ) ) )
% 0.22/0.54 => ( Y4 = X4 ) ) )
% 0.22/0.54 => ( P @ ( least_a @ less_eq @ P ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.Least1I
% 0.22/0.54 thf(fact_127_local_OLeast1__le,axiom,
% 0.22/0.54 ! [P: a > $o,Z2: a] :
% 0.22/0.54 ( ? [X4: a] :
% 0.22/0.54 ( ( P @ X4 )
% 0.22/0.54 & ! [Y4: a] :
% 0.22/0.54 ( ( P @ Y4 )
% 0.22/0.54 => ( less_eq @ X4 @ Y4 ) )
% 0.22/0.54 & ! [Y4: a] :
% 0.22/0.54 ( ( ( P @ Y4 )
% 0.22/0.54 & ! [Ya: a] :
% 0.22/0.54 ( ( P @ Ya )
% 0.22/0.54 => ( less_eq @ Y4 @ Ya ) ) )
% 0.22/0.54 => ( Y4 = X4 ) ) )
% 0.22/0.54 => ( ( P @ Z2 )
% 0.22/0.54 => ( less_eq @ ( least_a @ less_eq @ P ) @ Z2 ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.Least1_le
% 0.22/0.54 thf(fact_128_local_OLeastI2__order,axiom,
% 0.22/0.54 ! [P: a > $o,X: a,Q: a > $o] :
% 0.22/0.54 ( ( P @ X )
% 0.22/0.54 => ( ! [Y4: a] :
% 0.22/0.54 ( ( P @ Y4 )
% 0.22/0.54 => ( less_eq @ X @ Y4 ) )
% 0.22/0.54 => ( ! [X3: a] :
% 0.22/0.54 ( ( P @ X3 )
% 0.22/0.54 => ( ! [Y5: a] :
% 0.22/0.54 ( ( P @ Y5 )
% 0.22/0.54 => ( less_eq @ X3 @ Y5 ) )
% 0.22/0.54 => ( Q @ X3 ) ) )
% 0.22/0.54 => ( Q @ ( least_a @ less_eq @ P ) ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.LeastI2_order
% 0.22/0.54 thf(fact_129_local_OLeast__equality,axiom,
% 0.22/0.54 ! [P: a > $o,X: a] :
% 0.22/0.54 ( ( P @ X )
% 0.22/0.54 => ( ! [Y4: a] :
% 0.22/0.54 ( ( P @ Y4 )
% 0.22/0.54 => ( less_eq @ X @ Y4 ) )
% 0.22/0.54 => ( ( least_a @ less_eq @ P )
% 0.22/0.54 = X ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.Least_equality
% 0.22/0.54 thf(fact_130_local_Ob__aux__def,axiom,
% 0.22/0.54 ! [A: a,B: a,C: a] :
% 0.22/0.54 ( ( modula1373251614_aux_a @ inf @ sup @ A @ B @ C )
% 0.22/0.54 = ( sup @ ( inf @ B @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.b_aux_def
% 0.22/0.54 thf(fact_131_a__meet__b__eq__d,axiom,
% 0.22/0.54 ! [A: a,B: a,C: a] :
% 0.22/0.54 ( ( less_eq @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
% 0.22/0.54 => ( ( inf @ ( modula17988509_aux_a @ inf @ sup @ A @ B @ C ) @ ( modula1373251614_aux_a @ inf @ sup @ A @ B @ C ) )
% 0.22/0.54 = ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % a_meet_b_eq_d
% 0.22/0.54 thf(fact_132_lattice_Oa__aux_Ocong,axiom,
% 0.22/0.54 modula17988509_aux_a = modula17988509_aux_a ).
% 0.22/0.54
% 0.22/0.54 % lattice.a_aux.cong
% 0.22/0.54 thf(fact_133_lattice_Oc__aux_Ocong,axiom,
% 0.22/0.54 modula581031071_aux_a = modula581031071_aux_a ).
% 0.22/0.54
% 0.22/0.54 % lattice.c_aux.cong
% 0.22/0.54 thf(fact_134_lattice_Od__aux_Ocong,axiom,
% 0.22/0.54 modula1936294176_aux_a = modula1936294176_aux_a ).
% 0.22/0.54
% 0.22/0.54 % lattice.d_aux.cong
% 0.22/0.54 thf(fact_135_lattice_Oe__aux_Ocong,axiom,
% 0.22/0.54 modula1144073633_aux_a = modula1144073633_aux_a ).
% 0.22/0.54
% 0.22/0.54 % lattice.e_aux.cong
% 0.22/0.54 thf(fact_136_local_Ocomp__fun__idem__sup,axiom,
% 0.22/0.54 finite40241356em_a_a @ sup ).
% 0.22/0.54
% 0.22/0.54 % local.comp_fun_idem_sup
% 0.22/0.54 thf(fact_137_local_Ocomp__fun__idem__inf,axiom,
% 0.22/0.54 finite40241356em_a_a @ inf ).
% 0.22/0.54
% 0.22/0.54 % local.comp_fun_idem_inf
% 0.22/0.54 thf(fact_138_local_Osup_Osemigroup__axioms,axiom,
% 0.22/0.54 semigroup_a @ sup ).
% 0.22/0.54
% 0.22/0.54 % local.sup.semigroup_axioms
% 0.22/0.54 thf(fact_139_local_Oinf_Osemigroup__axioms,axiom,
% 0.22/0.54 semigroup_a @ inf ).
% 0.22/0.54
% 0.22/0.54 % local.inf.semigroup_axioms
% 0.22/0.54 thf(fact_140_local_Osup_Osemilattice__axioms,axiom,
% 0.22/0.54 semilattice_a @ sup ).
% 0.22/0.54
% 0.22/0.54 % local.sup.semilattice_axioms
% 0.22/0.54 thf(fact_141_local_Oinf_Osemilattice__axioms,axiom,
% 0.22/0.54 semilattice_a @ inf ).
% 0.22/0.54
% 0.22/0.54 % local.inf.semilattice_axioms
% 0.22/0.54 thf(fact_142_local_Osup_Oabel__semigroup__axioms,axiom,
% 0.22/0.54 abel_semigroup_a @ sup ).
% 0.22/0.54
% 0.22/0.54 % local.sup.abel_semigroup_axioms
% 0.22/0.54 thf(fact_143_local_Oinf_Oabel__semigroup__axioms,axiom,
% 0.22/0.54 abel_semigroup_a @ inf ).
% 0.22/0.54
% 0.22/0.54 % local.inf.abel_semigroup_axioms
% 0.22/0.54 thf(fact_144_local_OSup__fin_Osemilattice__set__axioms,axiom,
% 0.22/0.54 lattic1885654924_set_a @ sup ).
% 0.22/0.54
% 0.22/0.54 % local.Sup_fin.semilattice_set_axioms
% 0.22/0.54 thf(fact_145_local_OInf__fin_Osemilattice__set__axioms,axiom,
% 0.22/0.54 lattic1885654924_set_a @ inf ).
% 0.22/0.54
% 0.22/0.54 % local.Inf_fin.semilattice_set_axioms
% 0.22/0.54 thf(fact_146_local_Obdd__above__def,axiom,
% 0.22/0.54 ! [A3: set_a] :
% 0.22/0.54 ( ( condit1627435690bove_a @ less_eq @ A3 )
% 0.22/0.54 = ( ? [M: a] :
% 0.22/0.54 ! [X2: a] :
% 0.22/0.54 ( ( member_a @ X2 @ A3 )
% 0.22/0.54 => ( less_eq @ X2 @ M ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.bdd_above_def
% 0.22/0.54 thf(fact_147_local_Obdd__below__def,axiom,
% 0.22/0.54 ! [A3: set_a] :
% 0.22/0.54 ( ( condit1001553558elow_a @ less_eq @ A3 )
% 0.22/0.54 = ( ? [M2: a] :
% 0.22/0.54 ! [X2: a] :
% 0.22/0.54 ( ( member_a @ X2 @ A3 )
% 0.22/0.54 => ( less_eq @ M2 @ X2 ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.bdd_below_def
% 0.22/0.54 thf(fact_148_local_Obdd__belowI,axiom,
% 0.22/0.54 ! [A3: set_a,M3: a] :
% 0.22/0.54 ( ! [X3: a] :
% 0.22/0.54 ( ( member_a @ X3 @ A3 )
% 0.22/0.54 => ( less_eq @ M3 @ X3 ) )
% 0.22/0.54 => ( condit1001553558elow_a @ less_eq @ A3 ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.bdd_belowI
% 0.22/0.54 thf(fact_149_local_Obdd__aboveI,axiom,
% 0.22/0.54 ! [A3: set_a,M4: a] :
% 0.22/0.54 ( ! [X3: a] :
% 0.22/0.54 ( ( member_a @ X3 @ A3 )
% 0.22/0.54 => ( less_eq @ X3 @ M4 ) )
% 0.22/0.54 => ( condit1627435690bove_a @ less_eq @ A3 ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.bdd_aboveI
% 0.22/0.54 thf(fact_150_lattice_Oincomp_Ocong,axiom,
% 0.22/0.54 modula1727524044comp_a = modula1727524044comp_a ).
% 0.22/0.54
% 0.22/0.54 % lattice.incomp.cong
% 0.22/0.54 thf(fact_151_lattice_Ob__aux_Ocong,axiom,
% 0.22/0.54 modula1373251614_aux_a = modula1373251614_aux_a ).
% 0.22/0.54
% 0.22/0.54 % lattice.b_aux.cong
% 0.22/0.54 thf(fact_152_abel__semigroup_Oaxioms_I1_J,axiom,
% 0.22/0.54 ! [F: a > a > a] :
% 0.22/0.54 ( ( abel_semigroup_a @ F )
% 0.22/0.54 => ( semigroup_a @ F ) ) ).
% 0.22/0.54
% 0.22/0.54 % abel_semigroup.axioms(1)
% 0.22/0.54 thf(fact_153_semilattice__set__def,axiom,
% 0.22/0.54 lattic1885654924_set_a = semilattice_a ).
% 0.22/0.54
% 0.22/0.54 % semilattice_set_def
% 0.22/0.54 thf(fact_154_semilattice__set_Ointro,axiom,
% 0.22/0.54 ! [F: a > a > a] :
% 0.22/0.54 ( ( semilattice_a @ F )
% 0.22/0.54 => ( lattic1885654924_set_a @ F ) ) ).
% 0.22/0.54
% 0.22/0.54 % semilattice_set.intro
% 0.22/0.54 thf(fact_155_abel__semigroup_Oleft__commute,axiom,
% 0.22/0.54 ! [F: a > a > a,B: a,A: a,C: a] :
% 0.22/0.54 ( ( abel_semigroup_a @ F )
% 0.22/0.54 => ( ( F @ B @ ( F @ A @ C ) )
% 0.22/0.54 = ( F @ A @ ( F @ B @ C ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % abel_semigroup.left_commute
% 0.22/0.54 thf(fact_156_abel__semigroup_Ocommute,axiom,
% 0.22/0.54 ! [F: a > a > a,A: a,B: a] :
% 0.22/0.54 ( ( abel_semigroup_a @ F )
% 0.22/0.54 => ( ( F @ A @ B )
% 0.22/0.54 = ( F @ B @ A ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % abel_semigroup.commute
% 0.22/0.54 thf(fact_157_semigroup_Ointro,axiom,
% 0.22/0.54 ! [F: a > a > a] :
% 0.22/0.54 ( ! [A4: a,B3: a,C2: a] :
% 0.22/0.54 ( ( F @ ( F @ A4 @ B3 ) @ C2 )
% 0.22/0.54 = ( F @ A4 @ ( F @ B3 @ C2 ) ) )
% 0.22/0.54 => ( semigroup_a @ F ) ) ).
% 0.22/0.54
% 0.22/0.54 % semigroup.intro
% 0.22/0.54 thf(fact_158_semigroup_Oassoc,axiom,
% 0.22/0.54 ! [F: a > a > a,A: a,B: a,C: a] :
% 0.22/0.54 ( ( semigroup_a @ F )
% 0.22/0.54 => ( ( F @ ( F @ A @ B ) @ C )
% 0.22/0.54 = ( F @ A @ ( F @ B @ C ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % semigroup.assoc
% 0.22/0.54 thf(fact_159_semigroup__def,axiom,
% 0.22/0.54 ( semigroup_a
% 0.22/0.54 = ( ^ [F2: a > a > a] :
% 0.22/0.54 ! [A2: a,B2: a,C3: a] :
% 0.22/0.54 ( ( F2 @ ( F2 @ A2 @ B2 ) @ C3 )
% 0.22/0.54 = ( F2 @ A2 @ ( F2 @ B2 @ C3 ) ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % semigroup_def
% 0.22/0.54 thf(fact_160_semilattice__set_Oaxioms,axiom,
% 0.22/0.54 ! [F: a > a > a] :
% 0.22/0.54 ( ( lattic1885654924_set_a @ F )
% 0.22/0.54 => ( semilattice_a @ F ) ) ).
% 0.22/0.54
% 0.22/0.54 % semilattice_set.axioms
% 0.22/0.54 thf(fact_161_semilattice_Oaxioms_I1_J,axiom,
% 0.22/0.54 ! [F: a > a > a] :
% 0.22/0.54 ( ( semilattice_a @ F )
% 0.22/0.54 => ( abel_semigroup_a @ F ) ) ).
% 0.22/0.54
% 0.22/0.54 % semilattice.axioms(1)
% 0.22/0.54 thf(fact_162_local_Obdd__above__mono,axiom,
% 0.22/0.54 ! [B4: set_a,A3: set_a] :
% 0.22/0.54 ( ( condit1627435690bove_a @ less_eq @ B4 )
% 0.22/0.54 => ( ( ord_less_eq_set_a @ A3 @ B4 )
% 0.22/0.54 => ( condit1627435690bove_a @ less_eq @ A3 ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.bdd_above_mono
% 0.22/0.54 thf(fact_163_local_Obdd__below__mono,axiom,
% 0.22/0.54 ! [B4: set_a,A3: set_a] :
% 0.22/0.54 ( ( condit1001553558elow_a @ less_eq @ B4 )
% 0.22/0.54 => ( ( ord_less_eq_set_a @ A3 @ B4 )
% 0.22/0.54 => ( condit1001553558elow_a @ less_eq @ A3 ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.bdd_below_mono
% 0.22/0.54 thf(fact_164_local_Oantimono__def,axiom,
% 0.22/0.54 ! [F: a > set_a] :
% 0.22/0.54 ( ( antimono_a_set_a @ less_eq @ F )
% 0.22/0.54 = ( ! [X2: a,Y3: a] :
% 0.22/0.54 ( ( less_eq @ X2 @ Y3 )
% 0.22/0.54 => ( ord_less_eq_set_a @ ( F @ Y3 ) @ ( F @ X2 ) ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.antimono_def
% 0.22/0.54 thf(fact_165_local_OantimonoI,axiom,
% 0.22/0.54 ! [F: a > set_a] :
% 0.22/0.54 ( ! [X3: a,Y4: a] :
% 0.22/0.54 ( ( less_eq @ X3 @ Y4 )
% 0.22/0.54 => ( ord_less_eq_set_a @ ( F @ Y4 ) @ ( F @ X3 ) ) )
% 0.22/0.54 => ( antimono_a_set_a @ less_eq @ F ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.antimonoI
% 0.22/0.54 thf(fact_166_local_OantimonoE,axiom,
% 0.22/0.54 ! [F: a > set_a,X: a,Y: a] :
% 0.22/0.54 ( ( antimono_a_set_a @ less_eq @ F )
% 0.22/0.54 => ( ( less_eq @ X @ Y )
% 0.22/0.54 => ( ord_less_eq_set_a @ ( F @ Y ) @ ( F @ X ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.antimonoE
% 0.22/0.54 thf(fact_167_local_OantimonoD,axiom,
% 0.22/0.54 ! [F: a > set_a,X: a,Y: a] :
% 0.22/0.54 ( ( antimono_a_set_a @ less_eq @ F )
% 0.22/0.54 => ( ( less_eq @ X @ Y )
% 0.22/0.54 => ( ord_less_eq_set_a @ ( F @ Y ) @ ( F @ X ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.antimonoD
% 0.22/0.54 thf(fact_168_local_OmonoD,axiom,
% 0.22/0.54 ! [F: a > set_a,X: a,Y: a] :
% 0.22/0.54 ( ( mono_a_set_a @ less_eq @ F )
% 0.22/0.54 => ( ( less_eq @ X @ Y )
% 0.22/0.54 => ( ord_less_eq_set_a @ ( F @ X ) @ ( F @ Y ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.monoD
% 0.22/0.54 thf(fact_169_local_OmonoE,axiom,
% 0.22/0.54 ! [F: a > set_a,X: a,Y: a] :
% 0.22/0.54 ( ( mono_a_set_a @ less_eq @ F )
% 0.22/0.54 => ( ( less_eq @ X @ Y )
% 0.22/0.54 => ( ord_less_eq_set_a @ ( F @ X ) @ ( F @ Y ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.monoE
% 0.22/0.54 thf(fact_170_local_OmonoI,axiom,
% 0.22/0.54 ! [F: a > set_a] :
% 0.22/0.54 ( ! [X3: a,Y4: a] :
% 0.22/0.54 ( ( less_eq @ X3 @ Y4 )
% 0.22/0.54 => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.22/0.54 => ( mono_a_set_a @ less_eq @ F ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.monoI
% 0.22/0.54 thf(fact_171_local_Omono__def,axiom,
% 0.22/0.54 ! [F: a > set_a] :
% 0.22/0.54 ( ( mono_a_set_a @ less_eq @ F )
% 0.22/0.54 = ( ! [X2: a,Y3: a] :
% 0.22/0.54 ( ( less_eq @ X2 @ Y3 )
% 0.22/0.54 => ( ord_less_eq_set_a @ ( F @ X2 ) @ ( F @ Y3 ) ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.mono_def
% 0.22/0.54 thf(fact_172_semilattice_Oidem,axiom,
% 0.22/0.54 ! [F: a > a > a,A: a] :
% 0.22/0.54 ( ( semilattice_a @ F )
% 0.22/0.54 => ( ( F @ A @ A )
% 0.22/0.54 = A ) ) ).
% 0.22/0.54
% 0.22/0.54 % semilattice.idem
% 0.22/0.54 thf(fact_173_semilattice_Oleft__idem,axiom,
% 0.22/0.54 ! [F: a > a > a,A: a,B: a] :
% 0.22/0.54 ( ( semilattice_a @ F )
% 0.22/0.54 => ( ( F @ A @ ( F @ A @ B ) )
% 0.22/0.54 = ( F @ A @ B ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % semilattice.left_idem
% 0.22/0.54 thf(fact_174_semilattice_Oright__idem,axiom,
% 0.22/0.54 ! [F: a > a > a,A: a,B: a] :
% 0.22/0.54 ( ( semilattice_a @ F )
% 0.22/0.54 => ( ( F @ ( F @ A @ B ) @ B )
% 0.22/0.54 = ( F @ A @ B ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % semilattice.right_idem
% 0.22/0.54 thf(fact_175_subsetI,axiom,
% 0.22/0.54 ! [A3: set_a,B4: set_a] :
% 0.22/0.54 ( ! [X3: a] :
% 0.22/0.54 ( ( member_a @ X3 @ A3 )
% 0.22/0.54 => ( member_a @ X3 @ B4 ) )
% 0.22/0.54 => ( ord_less_eq_set_a @ A3 @ B4 ) ) ).
% 0.22/0.54
% 0.22/0.54 % subsetI
% 0.22/0.54 thf(fact_176_subset__antisym,axiom,
% 0.22/0.54 ! [A3: set_a,B4: set_a] :
% 0.22/0.54 ( ( ord_less_eq_set_a @ A3 @ B4 )
% 0.22/0.54 => ( ( ord_less_eq_set_a @ B4 @ A3 )
% 0.22/0.54 => ( A3 = B4 ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % subset_antisym
% 0.22/0.54 thf(fact_177_preorder__class_Oorder__refl,axiom,
% 0.22/0.54 ! [X: set_a] : ( ord_less_eq_set_a @ X @ X ) ).
% 0.22/0.54
% 0.22/0.54 % preorder_class.order_refl
% 0.22/0.54 thf(fact_178_order_Oantimono_Ocong,axiom,
% 0.22/0.54 antimono_a_set_a = antimono_a_set_a ).
% 0.22/0.54
% 0.22/0.54 % order.antimono.cong
% 0.22/0.54 thf(fact_179_order_Omono_Ocong,axiom,
% 0.22/0.54 mono_a_set_a = mono_a_set_a ).
% 0.22/0.54
% 0.22/0.54 % order.mono.cong
% 0.22/0.54 thf(fact_180_order__class_Odual__order_Oantisym,axiom,
% 0.22/0.54 ! [B: set_a,A: set_a] :
% 0.22/0.54 ( ( ord_less_eq_set_a @ B @ A )
% 0.22/0.54 => ( ( ord_less_eq_set_a @ A @ B )
% 0.22/0.54 => ( A = B ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % order_class.dual_order.antisym
% 0.22/0.54 thf(fact_181_order__class_Odual__order_Oeq__iff,axiom,
% 0.22/0.54 ( ( ^ [Y2: set_a,Z: set_a] : ( Y2 = Z ) )
% 0.22/0.54 = ( ^ [A2: set_a,B2: set_a] :
% 0.22/0.54 ( ( ord_less_eq_set_a @ B2 @ A2 )
% 0.22/0.54 & ( ord_less_eq_set_a @ A2 @ B2 ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % order_class.dual_order.eq_iff
% 0.22/0.54 thf(fact_182_order__class_Odual__order_Otrans,axiom,
% 0.22/0.54 ! [B: set_a,A: set_a,C: set_a] :
% 0.22/0.54 ( ( ord_less_eq_set_a @ B @ A )
% 0.22/0.54 => ( ( ord_less_eq_set_a @ C @ B )
% 0.22/0.54 => ( ord_less_eq_set_a @ C @ A ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % order_class.dual_order.trans
% 0.22/0.54 thf(fact_183_order__class_Odual__order_Orefl,axiom,
% 0.22/0.54 ! [A: set_a] : ( ord_less_eq_set_a @ A @ A ) ).
% 0.22/0.54
% 0.22/0.54 % order_class.dual_order.refl
% 0.22/0.54 thf(fact_184_preorder__class_Oorder__trans,axiom,
% 0.22/0.54 ! [X: set_a,Y: set_a,Z2: set_a] :
% 0.22/0.54 ( ( ord_less_eq_set_a @ X @ Y )
% 0.22/0.54 => ( ( ord_less_eq_set_a @ Y @ Z2 )
% 0.22/0.54 => ( ord_less_eq_set_a @ X @ Z2 ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % preorder_class.order_trans
% 0.22/0.54 thf(fact_185_order__class_Oorder_Oantisym,axiom,
% 0.22/0.54 ! [A: set_a,B: set_a] :
% 0.22/0.54 ( ( ord_less_eq_set_a @ A @ B )
% 0.22/0.54 => ( ( ord_less_eq_set_a @ B @ A )
% 0.22/0.54 => ( A = B ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % order_class.order.antisym
% 0.22/0.54 thf(fact_186_ord__class_Oord__le__eq__trans,axiom,
% 0.22/0.54 ! [A: set_a,B: set_a,C: set_a] :
% 0.22/0.54 ( ( ord_less_eq_set_a @ A @ B )
% 0.22/0.54 => ( ( B = C )
% 0.22/0.54 => ( ord_less_eq_set_a @ A @ C ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % ord_class.ord_le_eq_trans
% 0.22/0.54 thf(fact_187_ord__class_Oord__eq__le__trans,axiom,
% 0.22/0.54 ! [A: set_a,B: set_a,C: set_a] :
% 0.22/0.54 ( ( A = B )
% 0.22/0.54 => ( ( ord_less_eq_set_a @ B @ C )
% 0.22/0.54 => ( ord_less_eq_set_a @ A @ C ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % ord_class.ord_eq_le_trans
% 0.22/0.54 thf(fact_188_order__class_Oorder_Oeq__iff,axiom,
% 0.22/0.54 ( ( ^ [Y2: set_a,Z: set_a] : ( Y2 = Z ) )
% 0.22/0.54 = ( ^ [A2: set_a,B2: set_a] :
% 0.22/0.54 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 0.22/0.54 & ( ord_less_eq_set_a @ B2 @ A2 ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % order_class.order.eq_iff
% 0.22/0.54 thf(fact_189_order__class_Oantisym__conv,axiom,
% 0.22/0.54 ! [Y: set_a,X: set_a] :
% 0.22/0.54 ( ( ord_less_eq_set_a @ Y @ X )
% 0.22/0.54 => ( ( ord_less_eq_set_a @ X @ Y )
% 0.22/0.54 = ( X = Y ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % order_class.antisym_conv
% 0.22/0.54 thf(fact_190_order__class_Oorder_Otrans,axiom,
% 0.22/0.54 ! [A: set_a,B: set_a,C: set_a] :
% 0.22/0.54 ( ( ord_less_eq_set_a @ A @ B )
% 0.22/0.54 => ( ( ord_less_eq_set_a @ B @ C )
% 0.22/0.54 => ( ord_less_eq_set_a @ A @ C ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % order_class.order.trans
% 0.22/0.54 thf(fact_191_preorder__class_Oeq__refl,axiom,
% 0.22/0.54 ! [X: set_a,Y: set_a] :
% 0.22/0.54 ( ( X = Y )
% 0.22/0.54 => ( ord_less_eq_set_a @ X @ Y ) ) ).
% 0.22/0.54
% 0.22/0.54 % preorder_class.eq_refl
% 0.22/0.54 thf(fact_192_order__class_Oantisym,axiom,
% 0.22/0.54 ! [X: set_a,Y: set_a] :
% 0.22/0.54 ( ( ord_less_eq_set_a @ X @ Y )
% 0.22/0.54 => ( ( ord_less_eq_set_a @ Y @ X )
% 0.22/0.54 => ( X = Y ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % order_class.antisym
% 0.22/0.54 thf(fact_193_order__class_Oeq__iff,axiom,
% 0.22/0.54 ( ( ^ [Y2: set_a,Z: set_a] : ( Y2 = Z ) )
% 0.22/0.54 = ( ^ [X2: set_a,Y3: set_a] :
% 0.22/0.54 ( ( ord_less_eq_set_a @ X2 @ Y3 )
% 0.22/0.54 & ( ord_less_eq_set_a @ Y3 @ X2 ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % order_class.eq_iff
% 0.22/0.54 thf(fact_194_ord__le__eq__subst,axiom,
% 0.22/0.54 ! [A: set_a,B: set_a,F: set_a > set_a,C: set_a] :
% 0.22/0.54 ( ( ord_less_eq_set_a @ A @ B )
% 0.22/0.54 => ( ( ( F @ B )
% 0.22/0.54 = C )
% 0.22/0.54 => ( ! [X3: set_a,Y4: set_a] :
% 0.22/0.54 ( ( ord_less_eq_set_a @ X3 @ Y4 )
% 0.22/0.54 => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.22/0.54 => ( ord_less_eq_set_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % ord_le_eq_subst
% 0.22/0.54 thf(fact_195_ord__eq__le__subst,axiom,
% 0.22/0.54 ! [A: set_a,F: set_a > set_a,B: set_a,C: set_a] :
% 0.22/0.54 ( ( A
% 0.22/0.54 = ( F @ B ) )
% 0.22/0.54 => ( ( ord_less_eq_set_a @ B @ C )
% 0.22/0.54 => ( ! [X3: set_a,Y4: set_a] :
% 0.22/0.54 ( ( ord_less_eq_set_a @ X3 @ Y4 )
% 0.22/0.54 => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.22/0.54 => ( ord_less_eq_set_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % ord_eq_le_subst
% 0.22/0.54 thf(fact_196_order__subst2,axiom,
% 0.22/0.54 ! [A: set_a,B: set_a,F: set_a > set_a,C: set_a] :
% 0.22/0.54 ( ( ord_less_eq_set_a @ A @ B )
% 0.22/0.54 => ( ( ord_less_eq_set_a @ ( F @ B ) @ C )
% 0.22/0.54 => ( ! [X3: set_a,Y4: set_a] :
% 0.22/0.54 ( ( ord_less_eq_set_a @ X3 @ Y4 )
% 0.22/0.54 => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.22/0.54 => ( ord_less_eq_set_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % order_subst2
% 0.22/0.54 thf(fact_197_order__subst1,axiom,
% 0.22/0.54 ! [A: set_a,F: set_a > set_a,B: set_a,C: set_a] :
% 0.22/0.54 ( ( ord_less_eq_set_a @ A @ ( F @ B ) )
% 0.22/0.54 => ( ( ord_less_eq_set_a @ B @ C )
% 0.22/0.54 => ( ! [X3: set_a,Y4: set_a] :
% 0.22/0.54 ( ( ord_less_eq_set_a @ X3 @ Y4 )
% 0.22/0.54 => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.22/0.54 => ( ord_less_eq_set_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % order_subst1
% 0.22/0.54 thf(fact_198_Collect__mono__iff,axiom,
% 0.22/0.54 ! [P: a > $o,Q: a > $o] :
% 0.22/0.54 ( ( ord_less_eq_set_a @ ( collect_a @ P ) @ ( collect_a @ Q ) )
% 0.22/0.54 = ( ! [X2: a] :
% 0.22/0.54 ( ( P @ X2 )
% 0.22/0.54 => ( Q @ X2 ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % Collect_mono_iff
% 0.22/0.54 thf(fact_199_set__eq__subset,axiom,
% 0.22/0.54 ( ( ^ [Y2: set_a,Z: set_a] : ( Y2 = Z ) )
% 0.22/0.54 = ( ^ [A5: set_a,B5: set_a] :
% 0.22/0.54 ( ( ord_less_eq_set_a @ A5 @ B5 )
% 0.22/0.54 & ( ord_less_eq_set_a @ B5 @ A5 ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % set_eq_subset
% 0.22/0.54 thf(fact_200_subset__trans,axiom,
% 0.22/0.54 ! [A3: set_a,B4: set_a,C4: set_a] :
% 0.22/0.54 ( ( ord_less_eq_set_a @ A3 @ B4 )
% 0.22/0.54 => ( ( ord_less_eq_set_a @ B4 @ C4 )
% 0.22/0.54 => ( ord_less_eq_set_a @ A3 @ C4 ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % subset_trans
% 0.22/0.54 thf(fact_201_Collect__mono,axiom,
% 0.22/0.54 ! [P: a > $o,Q: a > $o] :
% 0.22/0.54 ( ! [X3: a] :
% 0.22/0.54 ( ( P @ X3 )
% 0.22/0.54 => ( Q @ X3 ) )
% 0.22/0.54 => ( ord_less_eq_set_a @ ( collect_a @ P ) @ ( collect_a @ Q ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % Collect_mono
% 0.22/0.54 thf(fact_202_subset__refl,axiom,
% 0.22/0.54 ! [A3: set_a] : ( ord_less_eq_set_a @ A3 @ A3 ) ).
% 0.22/0.54
% 0.22/0.54 % subset_refl
% 0.22/0.54 thf(fact_203_subset__iff,axiom,
% 0.22/0.54 ( ord_less_eq_set_a
% 0.22/0.54 = ( ^ [A5: set_a,B5: set_a] :
% 0.22/0.54 ! [T: a] :
% 0.22/0.54 ( ( member_a @ T @ A5 )
% 0.22/0.54 => ( member_a @ T @ B5 ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % subset_iff
% 0.22/0.54 thf(fact_204_equalityD2,axiom,
% 0.22/0.54 ! [A3: set_a,B4: set_a] :
% 0.22/0.54 ( ( A3 = B4 )
% 0.22/0.54 => ( ord_less_eq_set_a @ B4 @ A3 ) ) ).
% 0.22/0.54
% 0.22/0.54 % equalityD2
% 0.22/0.54 thf(fact_205_equalityD1,axiom,
% 0.22/0.54 ! [A3: set_a,B4: set_a] :
% 0.22/0.54 ( ( A3 = B4 )
% 0.22/0.54 => ( ord_less_eq_set_a @ A3 @ B4 ) ) ).
% 0.22/0.54
% 0.22/0.54 % equalityD1
% 0.22/0.54 thf(fact_206_subset__eq,axiom,
% 0.22/0.54 ( ord_less_eq_set_a
% 0.22/0.54 = ( ^ [A5: set_a,B5: set_a] :
% 0.22/0.54 ! [X2: a] :
% 0.22/0.54 ( ( member_a @ X2 @ A5 )
% 0.22/0.54 => ( member_a @ X2 @ B5 ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % subset_eq
% 0.22/0.54 thf(fact_207_equalityE,axiom,
% 0.22/0.54 ! [A3: set_a,B4: set_a] :
% 0.22/0.54 ( ( A3 = B4 )
% 0.22/0.54 => ~ ( ( ord_less_eq_set_a @ A3 @ B4 )
% 0.22/0.54 => ~ ( ord_less_eq_set_a @ B4 @ A3 ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % equalityE
% 0.22/0.54 thf(fact_208_subsetD,axiom,
% 0.22/0.54 ! [A3: set_a,B4: set_a,C: a] :
% 0.22/0.54 ( ( ord_less_eq_set_a @ A3 @ B4 )
% 0.22/0.54 => ( ( member_a @ C @ A3 )
% 0.22/0.54 => ( member_a @ C @ B4 ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % subsetD
% 0.22/0.54 thf(fact_209_in__mono,axiom,
% 0.22/0.54 ! [A3: set_a,B4: set_a,X: a] :
% 0.22/0.54 ( ( ord_less_eq_set_a @ A3 @ B4 )
% 0.22/0.54 => ( ( member_a @ X @ A3 )
% 0.22/0.54 => ( member_a @ X @ B4 ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % in_mono
% 0.22/0.54 thf(fact_210_ord_OLeast_Ocong,axiom,
% 0.22/0.54 least_a = least_a ).
% 0.22/0.54
% 0.22/0.54 % ord.Least.cong
% 0.22/0.54 thf(fact_211_order_OGreatest_Ocong,axiom,
% 0.22/0.54 greatest_a = greatest_a ).
% 0.22/0.54
% 0.22/0.54 % order.Greatest.cong
% 0.22/0.54 thf(fact_212_ord_Omin_Ocong,axiom,
% 0.22/0.54 min_a = min_a ).
% 0.22/0.54
% 0.22/0.54 % ord.min.cong
% 0.22/0.54 thf(fact_213_ord_Omax_Ocong,axiom,
% 0.22/0.54 max_a = max_a ).
% 0.22/0.54
% 0.22/0.54 % ord.max.cong
% 0.22/0.54 thf(fact_214_ord_Omin__def,axiom,
% 0.22/0.54 ( min_a
% 0.22/0.54 = ( ^ [Less_eq: a > a > $o,A2: a,B2: a] : ( if_a @ ( Less_eq @ A2 @ B2 ) @ A2 @ B2 ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % ord.min_def
% 0.22/0.54 thf(fact_215_ord_Omax__def,axiom,
% 0.22/0.54 ( max_a
% 0.22/0.54 = ( ^ [Less_eq: a > a > $o,A2: a,B2: a] : ( if_a @ ( Less_eq @ A2 @ B2 ) @ B2 @ A2 ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % ord.max_def
% 0.22/0.54 thf(fact_216_local_Omono__inf,axiom,
% 0.22/0.54 ! [F: a > set_a,A3: a,B4: a] :
% 0.22/0.54 ( ( mono_a_set_a @ less_eq @ F )
% 0.22/0.54 => ( ord_less_eq_set_a @ ( F @ ( inf @ A3 @ B4 ) ) @ ( inf_inf_set_a @ ( F @ A3 ) @ ( F @ B4 ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.mono_inf
% 0.22/0.54 thf(fact_217_local_Omono__sup,axiom,
% 0.22/0.54 ! [F: a > set_a,A3: a,B4: a] :
% 0.22/0.54 ( ( mono_a_set_a @ less_eq @ F )
% 0.22/0.54 => ( ord_less_eq_set_a @ ( sup_sup_set_a @ ( F @ A3 ) @ ( F @ B4 ) ) @ ( F @ ( sup @ A3 @ B4 ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.mono_sup
% 0.22/0.54 thf(fact_218_local_Obdd__above__finite,axiom,
% 0.22/0.54 ! [A3: set_a] :
% 0.22/0.54 ( ( finite_finite_a @ A3 )
% 0.22/0.54 => ( condit1627435690bove_a @ less_eq @ A3 ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.bdd_above_finite
% 0.22/0.54 thf(fact_219_local_Ofinite__has__minimal2,axiom,
% 0.22/0.54 ! [A3: set_a,A: a] :
% 0.22/0.54 ( ( finite_finite_a @ A3 )
% 0.22/0.54 => ( ( member_a @ A @ A3 )
% 0.22/0.54 => ? [X3: a] :
% 0.22/0.54 ( ( member_a @ X3 @ A3 )
% 0.22/0.54 & ( less_eq @ X3 @ A )
% 0.22/0.54 & ! [Xa: a] :
% 0.22/0.54 ( ( member_a @ Xa @ A3 )
% 0.22/0.54 => ( ( less_eq @ Xa @ X3 )
% 0.22/0.54 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.finite_has_minimal2
% 0.22/0.54 thf(fact_220_local_Ofinite__has__maximal2,axiom,
% 0.22/0.54 ! [A3: set_a,A: a] :
% 0.22/0.54 ( ( finite_finite_a @ A3 )
% 0.22/0.54 => ( ( member_a @ A @ A3 )
% 0.22/0.54 => ? [X3: a] :
% 0.22/0.54 ( ( member_a @ X3 @ A3 )
% 0.22/0.54 & ( less_eq @ A @ X3 )
% 0.22/0.54 & ! [Xa: a] :
% 0.22/0.54 ( ( member_a @ Xa @ A3 )
% 0.22/0.54 => ( ( less_eq @ X3 @ Xa )
% 0.22/0.54 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.finite_has_maximal2
% 0.22/0.54 thf(fact_221_local_Obdd__below__Int2,axiom,
% 0.22/0.54 ! [B4: set_a,A3: set_a] :
% 0.22/0.54 ( ( condit1001553558elow_a @ less_eq @ B4 )
% 0.22/0.54 => ( condit1001553558elow_a @ less_eq @ ( inf_inf_set_a @ A3 @ B4 ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.bdd_below_Int2
% 0.22/0.54 thf(fact_222_local_Obdd__below__Int1,axiom,
% 0.22/0.54 ! [A3: set_a,B4: set_a] :
% 0.22/0.54 ( ( condit1001553558elow_a @ less_eq @ A3 )
% 0.22/0.54 => ( condit1001553558elow_a @ less_eq @ ( inf_inf_set_a @ A3 @ B4 ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.bdd_below_Int1
% 0.22/0.54 thf(fact_223_local_Obdd__above__Int2,axiom,
% 0.22/0.54 ! [B4: set_a,A3: set_a] :
% 0.22/0.54 ( ( condit1627435690bove_a @ less_eq @ B4 )
% 0.22/0.54 => ( condit1627435690bove_a @ less_eq @ ( inf_inf_set_a @ A3 @ B4 ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.bdd_above_Int2
% 0.22/0.54 thf(fact_224_local_Obdd__above__Int1,axiom,
% 0.22/0.54 ! [A3: set_a,B4: set_a] :
% 0.22/0.54 ( ( condit1627435690bove_a @ less_eq @ A3 )
% 0.22/0.54 => ( condit1627435690bove_a @ less_eq @ ( inf_inf_set_a @ A3 @ B4 ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.bdd_above_Int1
% 0.22/0.54 thf(fact_225_local_Obdd__below__finite,axiom,
% 0.22/0.54 ! [A3: set_a] :
% 0.22/0.54 ( ( finite_finite_a @ A3 )
% 0.22/0.54 => ( condit1001553558elow_a @ less_eq @ A3 ) ) ).
% 0.22/0.54
% 0.22/0.54 % local.bdd_below_finite
% 0.22/0.54 thf(fact_226_Un__subset__iff,axiom,
% 0.22/0.54 ! [A3: set_a,B4: set_a,C4: set_a] :
% 0.22/0.54 ( ( ord_less_eq_set_a @ ( sup_sup_set_a @ A3 @ B4 ) @ C4 )
% 0.22/0.54 = ( ( ord_less_eq_set_a @ A3 @ C4 )
% 0.22/0.54 & ( ord_less_eq_set_a @ B4 @ C4 ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % Un_subset_iff
% 0.22/0.54 thf(fact_227_Int__subset__iff,axiom,
% 0.22/0.54 ! [C4: set_a,A3: set_a,B4: set_a] :
% 0.22/0.54 ( ( ord_less_eq_set_a @ C4 @ ( inf_inf_set_a @ A3 @ B4 ) )
% 0.22/0.54 = ( ( ord_less_eq_set_a @ C4 @ A3 )
% 0.22/0.54 & ( ord_less_eq_set_a @ C4 @ B4 ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % Int_subset_iff
% 0.22/0.54 thf(fact_228_semilattice__inf__class_Oinf__right__idem,axiom,
% 0.22/0.54 ! [X: set_a,Y: set_a] :
% 0.22/0.54 ( ( inf_inf_set_a @ ( inf_inf_set_a @ X @ Y ) @ Y )
% 0.22/0.54 = ( inf_inf_set_a @ X @ Y ) ) ).
% 0.22/0.54
% 0.22/0.54 % semilattice_inf_class.inf_right_idem
% 0.22/0.54 thf(fact_229_semilattice__inf__class_Oinf_Oright__idem,axiom,
% 0.22/0.54 ! [A: set_a,B: set_a] :
% 0.22/0.54 ( ( inf_inf_set_a @ ( inf_inf_set_a @ A @ B ) @ B )
% 0.22/0.54 = ( inf_inf_set_a @ A @ B ) ) ).
% 0.22/0.54
% 0.22/0.54 % semilattice_inf_class.inf.right_idem
% 0.22/0.54 thf(fact_230_semilattice__inf__class_Oinf__left__idem,axiom,
% 0.22/0.54 ! [X: set_a,Y: set_a] :
% 0.22/0.54 ( ( inf_inf_set_a @ X @ ( inf_inf_set_a @ X @ Y ) )
% 0.22/0.54 = ( inf_inf_set_a @ X @ Y ) ) ).
% 0.22/0.54
% 0.22/0.54 % semilattice_inf_class.inf_left_idem
% 0.22/0.54 thf(fact_231_semilattice__inf__class_Oinf_Oleft__idem,axiom,
% 0.22/0.54 ! [A: set_a,B: set_a] :
% 0.22/0.54 ( ( inf_inf_set_a @ A @ ( inf_inf_set_a @ A @ B ) )
% 0.22/0.54 = ( inf_inf_set_a @ A @ B ) ) ).
% 0.22/0.54
% 0.22/0.54 % semilattice_inf_class.inf.left_idem
% 0.22/0.54 thf(fact_232_semilattice__inf__class_Oinf__idem,axiom,
% 0.22/0.54 ! [X: set_a] :
% 0.22/0.54 ( ( inf_inf_set_a @ X @ X )
% 0.22/0.54 = X ) ).
% 0.22/0.54
% 0.22/0.54 % semilattice_inf_class.inf_idem
% 0.22/0.54 thf(fact_233_semilattice__inf__class_Oinf_Oidem,axiom,
% 0.22/0.54 ! [A: set_a] :
% 0.22/0.54 ( ( inf_inf_set_a @ A @ A )
% 0.22/0.54 = A ) ).
% 0.22/0.54
% 0.22/0.54 % semilattice_inf_class.inf.idem
% 0.22/0.54 thf(fact_234_semilattice__sup__class_Osup_Oright__idem,axiom,
% 0.22/0.54 ! [A: set_a,B: set_a] :
% 0.22/0.54 ( ( sup_sup_set_a @ ( sup_sup_set_a @ A @ B ) @ B )
% 0.22/0.54 = ( sup_sup_set_a @ A @ B ) ) ).
% 0.22/0.54
% 0.22/0.54 % semilattice_sup_class.sup.right_idem
% 0.22/0.54 thf(fact_235_semilattice__sup__class_Osup__left__idem,axiom,
% 0.22/0.54 ! [X: set_a,Y: set_a] :
% 0.22/0.54 ( ( sup_sup_set_a @ X @ ( sup_sup_set_a @ X @ Y ) )
% 0.22/0.54 = ( sup_sup_set_a @ X @ Y ) ) ).
% 0.22/0.54
% 0.22/0.54 % semilattice_sup_class.sup_left_idem
% 0.22/0.54 thf(fact_236_semilattice__sup__class_Osup_Oleft__idem,axiom,
% 0.22/0.54 ! [A: set_a,B: set_a] :
% 0.22/0.54 ( ( sup_sup_set_a @ A @ ( sup_sup_set_a @ A @ B ) )
% 0.22/0.54 = ( sup_sup_set_a @ A @ B ) ) ).
% 0.22/0.54
% 0.22/0.54 % semilattice_sup_class.sup.left_idem
% 0.22/0.54 thf(fact_237_semilattice__sup__class_Osup__idem,axiom,
% 0.22/0.54 ! [X: set_a] :
% 0.22/0.54 ( ( sup_sup_set_a @ X @ X )
% 0.22/0.54 = X ) ).
% 0.22/0.54
% 0.22/0.54 % semilattice_sup_class.sup_idem
% 0.22/0.54 thf(fact_238_semilattice__sup__class_Osup_Oidem,axiom,
% 0.22/0.54 ! [A: set_a] :
% 0.22/0.54 ( ( sup_sup_set_a @ A @ A )
% 0.22/0.54 = A ) ).
% 0.22/0.54
% 0.22/0.54 % semilattice_sup_class.sup.idem
% 0.22/0.54 thf(fact_239_semilattice__inf__class_Ole__inf__iff,axiom,
% 0.22/0.54 ! [X: set_a,Y: set_a,Z2: set_a] :
% 0.22/0.54 ( ( ord_less_eq_set_a @ X @ ( inf_inf_set_a @ Y @ Z2 ) )
% 0.22/0.54 = ( ( ord_less_eq_set_a @ X @ Y )
% 0.22/0.54 & ( ord_less_eq_set_a @ X @ Z2 ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % semilattice_inf_class.le_inf_iff
% 0.22/0.54 thf(fact_240_semilattice__inf__class_Oinf_Obounded__iff,axiom,
% 0.22/0.54 ! [A: set_a,B: set_a,C: set_a] :
% 0.22/0.54 ( ( ord_less_eq_set_a @ A @ ( inf_inf_set_a @ B @ C ) )
% 0.22/0.54 = ( ( ord_less_eq_set_a @ A @ B )
% 0.22/0.54 & ( ord_less_eq_set_a @ A @ C ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % semilattice_inf_class.inf.bounded_iff
% 0.22/0.54 thf(fact_241_semilattice__sup__class_Ole__sup__iff,axiom,
% 0.22/0.54 ! [X: set_a,Y: set_a,Z2: set_a] :
% 0.22/0.54 ( ( ord_less_eq_set_a @ ( sup_sup_set_a @ X @ Y ) @ Z2 )
% 0.22/0.54 = ( ( ord_less_eq_set_a @ X @ Z2 )
% 0.22/0.54 & ( ord_less_eq_set_a @ Y @ Z2 ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % semilattice_sup_class.le_sup_iff
% 0.22/0.54 thf(fact_242_semilattice__sup__class_Osup_Obounded__iff,axiom,
% 0.22/0.54 ! [B: set_a,C: set_a,A: set_a] :
% 0.22/0.54 ( ( ord_less_eq_set_a @ ( sup_sup_set_a @ B @ C ) @ A )
% 0.22/0.54 = ( ( ord_less_eq_set_a @ B @ A )
% 0.22/0.54 & ( ord_less_eq_set_a @ C @ A ) ) ) ).
% 0.22/0.54
% 0.22/0.54 % semilattice_sup_class.sup.bounded_iff
% 0.22/0.54 thf(fact_243_lattice__class_Osup__inf__absorb,axiom,
% 0.22/0.54 ! [X: set_a,Y: set_a] :
% 0.22/0.54 ( ( sup_sup_set_a @ X @ ( inf_inf_set_a @ X @ Y ) )
% 0.22/0.54 = X ) ).
% 0.22/0.54
% 0.22/0.54 % lattice_class.sup_inf_absorb
% 0.22/0.54 thf(fact_244_lattice__class_Oinf__sup__absorb,axiom,
% 0.22/0.54 ! [X: set_a,Y: set_a] :
% 0.22/0.54 ( ( inf_inf_set_a @ X @ ( sup_sup_set_a @ X @ Y ) )
% 0.22/0.54 = X ) ).
% 0.22/0.54
% 0.22/0.54 % lattice_class.inf_sup_absorb
% 0.22/0.54
% 0.22/0.54 % Helper facts (3)
% 0.22/0.54 thf(help_If_3_1_If_001tf__a_T,axiom,
% 0.22/0.54 ! [P: $o] :
% 0.22/0.54 ( ( P = $true )
% 0.22/0.54 | ( P = $false ) ) ).
% 0.22/0.54
% 0.22/0.54 thf(help_If_2_1_If_001tf__a_T,axiom,
% 0.22/0.54 ! [X: a,Y: a] :
% 0.22/0.54 ( ( if_a @ $false @ X @ Y )
% 0.22/0.54 = Y ) ).
% 0.22/0.54
% 0.22/0.54 thf(help_If_1_1_If_001tf__a_T,axiom,
% 0.22/0.54 ! [X: a,Y: a] :
% 0.22/0.54 ( ( if_a @ $true @ X @ Y )
% 0.22/0.54 = X ) ).
% 0.22/0.54
% 0.22/0.54 % Conjectures (2)
% 0.22/0.54 thf(conj_0,hypothesis,
% 0.22/0.54 less_eq @ ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c ) @ ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ) ).
% 0.22/0.54
% 0.22/0.54 thf(conj_1,conjecture,
% 0.22/0.54 ( ( inf @ ( modula17988509_aux_a @ inf @ sup @ b @ c @ a2 ) @ ( modula581031071_aux_a @ inf @ sup @ a2 @ b @ c ) )
% 0.22/0.58 = ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c ) ) ).
% 0.22/0.58
% 0.22/0.58 %------------------------------------------------------------------------------
% 0.22/0.58 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.9P2JiMTWXK/cvc5---1.0.5_29300.p...
% 0.22/0.58 (declare-sort $$unsorted 0)
% 0.22/0.58 (declare-sort tptp.set_a 0)
% 0.22/0.58 (declare-sort tptp.a 0)
% 0.22/0.58 (declare-fun tptp.condit1627435690bove_a ((-> tptp.a tptp.a Bool) tptp.set_a) Bool)
% 0.22/0.58 (declare-fun tptp.condit1001553558elow_a ((-> tptp.a tptp.a Bool) tptp.set_a) Bool)
% 0.22/0.58 (declare-fun tptp.finite40241356em_a_a ((-> tptp.a tptp.a tptp.a)) Bool)
% 0.22/0.58 (declare-fun tptp.finite_finite_a (tptp.set_a) Bool)
% 0.22/0.58 (declare-fun tptp.abel_semigroup_a ((-> tptp.a tptp.a tptp.a)) Bool)
% 0.22/0.58 (declare-fun tptp.semigroup_a ((-> tptp.a tptp.a tptp.a)) Bool)
% 0.22/0.58 (declare-fun tptp.if_a (Bool tptp.a tptp.a) tptp.a)
% 0.22/0.58 (declare-fun tptp.inf_inf_set_a (tptp.set_a tptp.set_a) tptp.set_a)
% 0.22/0.58 (declare-fun tptp.semilattice_a ((-> tptp.a tptp.a tptp.a)) Bool)
% 0.22/0.58 (declare-fun tptp.sup_sup_set_a (tptp.set_a tptp.set_a) tptp.set_a)
% 0.22/0.58 (declare-fun tptp.lattic1885654924_set_a ((-> tptp.a tptp.a tptp.a)) Bool)
% 0.22/0.58 (declare-fun tptp.modula17988509_aux_a ((-> tptp.a tptp.a tptp.a) (-> tptp.a tptp.a tptp.a) tptp.a tptp.a tptp.a) tptp.a)
% 0.22/0.58 (declare-fun tptp.modula1373251614_aux_a ((-> tptp.a tptp.a tptp.a) (-> tptp.a tptp.a tptp.a) tptp.a tptp.a tptp.a) tptp.a)
% 0.22/0.58 (declare-fun tptp.modula581031071_aux_a ((-> tptp.a tptp.a tptp.a) (-> tptp.a tptp.a tptp.a) tptp.a tptp.a tptp.a) tptp.a)
% 0.22/0.58 (declare-fun tptp.modula1936294176_aux_a ((-> tptp.a tptp.a tptp.a) (-> tptp.a tptp.a tptp.a) tptp.a tptp.a tptp.a) tptp.a)
% 0.22/0.58 (declare-fun tptp.modula1144073633_aux_a ((-> tptp.a tptp.a tptp.a) (-> tptp.a tptp.a tptp.a) tptp.a tptp.a tptp.a) tptp.a)
% 0.22/0.58 (declare-fun tptp.modula1727524044comp_a ((-> tptp.a tptp.a Bool) tptp.a tptp.a) Bool)
% 0.22/0.58 (declare-fun tptp.least_a ((-> tptp.a tptp.a Bool) (-> tptp.a Bool)) tptp.a)
% 0.22/0.58 (declare-fun tptp.max_a ((-> tptp.a tptp.a Bool) tptp.a tptp.a) tptp.a)
% 0.22/0.58 (declare-fun tptp.min_a ((-> tptp.a tptp.a Bool) tptp.a tptp.a) tptp.a)
% 0.22/0.58 (declare-fun tptp.ord_less_eq_set_a (tptp.set_a tptp.set_a) Bool)
% 0.22/0.58 (declare-fun tptp.greatest_a ((-> tptp.a tptp.a Bool) (-> tptp.a Bool)) tptp.a)
% 0.22/0.58 (declare-fun tptp.antimono_a_set_a ((-> tptp.a tptp.a Bool) (-> tptp.a tptp.set_a)) Bool)
% 0.22/0.58 (declare-fun tptp.mono_a_set_a ((-> tptp.a tptp.a Bool) (-> tptp.a tptp.set_a)) Bool)
% 0.22/0.58 (declare-fun tptp.collect_a ((-> tptp.a Bool)) tptp.set_a)
% 0.22/0.58 (declare-fun tptp.member_a (tptp.a tptp.set_a) Bool)
% 0.22/0.58 (declare-fun tptp.a2 () tptp.a)
% 0.22/0.58 (declare-fun tptp.b () tptp.a)
% 0.22/0.58 (declare-fun tptp.c () tptp.a)
% 0.22/0.58 (declare-fun tptp.inf (tptp.a tptp.a) tptp.a)
% 0.22/0.58 (declare-fun tptp.less_eq (tptp.a tptp.a) Bool)
% 0.22/0.58 (declare-fun tptp.sup (tptp.a tptp.a) tptp.a)
% 0.22/0.58 (assert (forall ((X tptp.a) (Y tptp.a)) (=> (@ (@ tptp.less_eq X) Y) (=> (@ (@ tptp.less_eq Y) X) (= X Y)))))
% 0.22/0.58 (assert (forall ((Y tptp.a) (X tptp.a)) (=> (@ (@ tptp.less_eq Y) X) (= (@ (@ tptp.less_eq X) Y) (= X Y)))))
% 0.22/0.58 (assert (forall ((B tptp.a) (A tptp.a)) (=> (@ (@ tptp.less_eq B) A) (=> (@ (@ tptp.less_eq A) B) (= A B)))))
% 0.22/0.58 (assert (= (lambda ((Y2 tptp.a) (Z tptp.a)) (= Y2 Z)) (lambda ((A2 tptp.a) (B2 tptp.a)) (and (@ (@ tptp.less_eq B2) A2) (@ (@ tptp.less_eq A2) B2)))))
% 0.22/0.58 (assert (forall ((B tptp.a) (A tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.less_eq C))) (=> (@ (@ tptp.less_eq B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 0.22/0.58 (assert (= (lambda ((Y2 tptp.a) (Z tptp.a)) (= Y2 Z)) (lambda ((X2 tptp.a) (Y3 tptp.a)) (and (@ (@ tptp.less_eq X2) Y3) (@ (@ tptp.less_eq Y3) X2)))))
% 0.22/0.58 (assert (forall ((X tptp.a) (Y tptp.a)) (=> (= X Y) (@ (@ tptp.less_eq X) Y))))
% 0.22/0.58 (assert (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (=> (= A B) (=> (@ (@ tptp.less_eq B) C) (@ (@ tptp.less_eq A) C)))))
% 0.22/0.58 (assert (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.less_eq A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 0.22/0.58 (assert (forall ((A tptp.a) (B tptp.a)) (=> (@ (@ tptp.less_eq A) B) (=> (@ (@ tptp.less_eq B) A) (= A B)))))
% 0.22/0.58 (assert (= (lambda ((Y2 tptp.a) (Z tptp.a)) (= Y2 Z)) (lambda ((A2 tptp.a) (B2 tptp.a)) (and (@ (@ tptp.less_eq A2) B2) (@ (@ tptp.less_eq B2) A2)))))
% 0.22/0.58 (assert (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.less_eq A))) (=> (@ _let_1 B) (=> (@ (@ tptp.less_eq B) C) (@ _let_1 C))))))
% 0.22/0.58 (assert (forall ((X tptp.a) (Y tptp.a) (Z2 tptp.a)) (let ((_let_1 (@ tptp.less_eq X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.less_eq Y) Z2) (@ _let_1 Z2))))))
% 0.22/0.58 (assert (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.inf A))) (= (@ (@ tptp.inf (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.inf B) C))))))
% 0.22/0.58 (assert (forall ((A tptp.a) (B tptp.a)) (= (@ (@ tptp.inf A) B) (@ (@ tptp.inf B) A))))
% 0.22/0.58 (assert (forall ((B tptp.a) (A tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.inf B))) (let ((_let_2 (@ tptp.inf A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 0.22/0.58 (assert (forall ((X tptp.a) (Y tptp.a) (Z2 tptp.a)) (let ((_let_1 (@ tptp.inf X))) (= (@ (@ tptp.inf (@ _let_1 Y)) Z2) (@ _let_1 (@ (@ tptp.inf Y) Z2))))))
% 0.22/0.58 (assert (forall ((X tptp.a) (Y tptp.a)) (= (@ (@ tptp.inf X) Y) (@ (@ tptp.inf Y) X))))
% 0.22/0.58 (assert (forall ((X tptp.a) (Y tptp.a) (Z2 tptp.a)) (let ((_let_1 (@ tptp.inf X))) (let ((_let_2 (@ tptp.inf Y))) (= (@ _let_1 (@ _let_2 Z2)) (@ _let_2 (@ _let_1 Z2)))))))
% 0.22/0.58 (assert (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.sup A))) (= (@ (@ tptp.sup (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.sup B) C))))))
% 0.22/0.58 (assert (forall ((A tptp.a) (B tptp.a)) (= (@ (@ tptp.sup A) B) (@ (@ tptp.sup B) A))))
% 0.22/0.58 (assert (forall ((B tptp.a) (A tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.sup B))) (let ((_let_2 (@ tptp.sup A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 0.22/0.58 (assert (forall ((X tptp.a) (Y tptp.a) (Z2 tptp.a)) (let ((_let_1 (@ tptp.sup X))) (= (@ (@ tptp.sup (@ _let_1 Y)) Z2) (@ _let_1 (@ (@ tptp.sup Y) Z2))))))
% 0.22/0.58 (assert (forall ((X tptp.a) (Y tptp.a)) (= (@ (@ tptp.sup X) Y) (@ (@ tptp.sup Y) X))))
% 0.22/0.58 (assert (forall ((X tptp.a) (Y tptp.a) (Z2 tptp.a)) (let ((_let_1 (@ tptp.sup X))) (let ((_let_2 (@ tptp.sup Y))) (= (@ _let_1 (@ _let_2 Z2)) (@ _let_2 (@ _let_1 Z2)))))))
% 0.22/0.58 (assert (forall ((A tptp.a) (B tptp.a)) (=> (@ (@ tptp.less_eq A) B) (= (@ (@ tptp.inf A) B) A))))
% 0.22/0.58 (assert (forall ((B tptp.a) (A tptp.a)) (=> (@ (@ tptp.less_eq B) A) (= (@ (@ tptp.inf A) B) B))))
% 0.22/0.58 (assert (forall ((A tptp.a) (B tptp.a)) (= (@ (@ tptp.less_eq A) B) (= (@ (@ tptp.inf A) B) A))))
% 0.22/0.58 (assert (forall ((B tptp.a) (A tptp.a)) (= (@ (@ tptp.less_eq B) A) (= (@ (@ tptp.inf A) B) B))))
% 0.22/0.58 (assert (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.less_eq A))) (=> (@ _let_1 (@ (@ tptp.inf B) C)) (not (=> (@ _let_1 B) (not (@ _let_1 C))))))))
% 0.22/0.58 (assert (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.less_eq A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.inf B) C)))))))
% 0.22/0.58 (assert (forall ((A tptp.a) (B tptp.a)) (@ (@ tptp.less_eq (@ (@ tptp.inf A) B)) A)))
% 0.22/0.58 (assert (forall ((A tptp.a) (B tptp.a)) (@ (@ tptp.less_eq (@ (@ tptp.inf A) B)) B)))
% 0.22/0.58 (assert (forall ((A tptp.a) (C tptp.a) (B tptp.a)) (=> (@ (@ tptp.less_eq A) C) (@ (@ tptp.less_eq (@ (@ tptp.inf A) B)) C))))
% 0.22/0.58 (assert (forall ((B tptp.a) (C tptp.a) (A tptp.a)) (=> (@ (@ tptp.less_eq B) C) (@ (@ tptp.less_eq (@ (@ tptp.inf A) B)) C))))
% 0.22/0.58 (assert (forall ((A tptp.a) (B tptp.a)) (=> (@ (@ tptp.less_eq A) B) (= A (@ (@ tptp.inf A) B)))))
% 0.22/0.58 (assert (forall ((A tptp.a) (B tptp.a)) (=> (= A (@ (@ tptp.inf A) B)) (@ (@ tptp.less_eq A) B))))
% 0.22/0.58 (assert (forall ((A tptp.a) (B tptp.a)) (= (@ (@ tptp.less_eq A) B) (= A (@ (@ tptp.inf A) B)))))
% 0.22/0.58 (assert (forall ((X tptp.a) (Y tptp.a)) (=> (@ (@ tptp.less_eq X) Y) (= (@ (@ tptp.inf X) Y) X))))
% 0.22/0.58 (assert (forall ((Y tptp.a) (X tptp.a)) (=> (@ (@ tptp.less_eq Y) X) (= (@ (@ tptp.inf X) Y) Y))))
% 0.22/0.58 (assert (forall ((X tptp.a) (Y tptp.a) (Z2 tptp.a)) (let ((_let_1 (@ tptp.less_eq X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z2) (@ _let_1 (@ (@ tptp.inf Y) Z2)))))))
% 0.22/0.58 (assert (forall ((X tptp.a) (Y tptp.a)) (@ (@ tptp.less_eq (@ (@ tptp.inf X) Y)) X)))
% 0.22/0.58 (assert (forall ((X tptp.a) (Y tptp.a)) (@ (@ tptp.less_eq (@ (@ tptp.inf X) Y)) Y)))
% 0.22/0.58 (assert (forall ((A tptp.a) (C tptp.a) (B tptp.a) (D tptp.a)) (=> (@ (@ tptp.less_eq A) C) (=> (@ (@ tptp.less_eq B) D) (@ (@ tptp.less_eq (@ (@ tptp.inf A) B)) (@ (@ tptp.inf C) D))))))
% 0.22/0.58 (assert (forall ((F (-> tptp.a tptp.a tptp.a)) (X tptp.a) (Y tptp.a)) (=> (forall ((X3 tptp.a) (Y4 tptp.a)) (@ (@ tptp.less_eq (@ (@ F X3) Y4)) X3)) (=> (forall ((X3 tptp.a) (Y4 tptp.a)) (@ (@ tptp.less_eq (@ (@ F X3) Y4)) Y4)) (=> (forall ((X3 tptp.a) (Y4 tptp.a) (Z3 tptp.a)) (let ((_let_1 (@ tptp.less_eq X3))) (=> (@ _let_1 Y4) (=> (@ _let_1 Z3) (@ _let_1 (@ (@ F Y4) Z3)))))) (= (@ (@ tptp.inf X) Y) (@ (@ F X) Y)))))))
% 0.22/0.58 (assert (forall ((A tptp.a) (P (-> tptp.a Bool))) (= (@ (@ tptp.member_a A) (@ tptp.collect_a P)) (@ P A))))
% 0.22/0.58 (assert (forall ((A3 tptp.set_a)) (= (@ tptp.collect_a (lambda ((X2 tptp.a)) (@ (@ tptp.member_a X2) A3))) A3)))
% 0.22/0.58 (assert (forall ((P (-> tptp.a Bool)) (Q (-> tptp.a Bool))) (=> (forall ((X3 tptp.a)) (= (@ P X3) (@ Q X3))) (= (@ tptp.collect_a P) (@ tptp.collect_a Q)))))
% 0.22/0.58 (assert (forall ((X tptp.a) (Y tptp.a)) (= (@ (@ tptp.less_eq X) Y) (= (@ (@ tptp.inf X) Y) X))))
% 0.22/0.58 (assert (forall ((X tptp.a) (A tptp.a) (B tptp.a)) (let ((_let_1 (@ tptp.less_eq X))) (=> (@ _let_1 (@ (@ tptp.inf A) B)) (not (=> (@ _let_1 A) (not (@ _let_1 B))))))))
% 0.22/0.58 (assert (forall ((X tptp.a) (A tptp.a) (B tptp.a)) (let ((_let_1 (@ tptp.less_eq X))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.inf A) B)))))))
% 0.22/0.58 (assert (forall ((A tptp.a) (X tptp.a) (B tptp.a)) (=> (@ (@ tptp.less_eq A) X) (@ (@ tptp.less_eq (@ (@ tptp.inf A) B)) X))))
% 0.22/0.58 (assert (forall ((B tptp.a) (X tptp.a) (A tptp.a)) (=> (@ (@ tptp.less_eq B) X) (@ (@ tptp.less_eq (@ (@ tptp.inf A) B)) X))))
% 0.22/0.58 (assert (forall ((X tptp.a) (Y tptp.a)) (= (@ (@ tptp.less_eq X) Y) (= (@ (@ tptp.sup X) Y) Y))))
% 0.22/0.58 (assert (forall ((A tptp.a) (B tptp.a) (X tptp.a)) (=> (@ (@ tptp.less_eq (@ (@ tptp.sup A) B)) X) (not (=> (@ (@ tptp.less_eq A) X) (not (@ (@ tptp.less_eq B) X)))))))
% 0.22/0.58 (assert (forall ((A tptp.a) (X tptp.a) (B tptp.a)) (=> (@ (@ tptp.less_eq A) X) (=> (@ (@ tptp.less_eq B) X) (@ (@ tptp.less_eq (@ (@ tptp.sup A) B)) X)))))
% 0.22/0.58 (assert (forall ((X tptp.a) (A tptp.a) (B tptp.a)) (let ((_let_1 (@ tptp.less_eq X))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup A) B))))))
% 0.22/0.58 (assert (forall ((X tptp.a) (B tptp.a) (A tptp.a)) (let ((_let_1 (@ tptp.less_eq X))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup A) B))))))
% 0.22/0.58 (assert (forall ((B tptp.a) (A tptp.a)) (=> (@ (@ tptp.less_eq B) A) (= (@ (@ tptp.sup A) B) A))))
% 0.22/0.58 (assert (forall ((A tptp.a) (B tptp.a)) (=> (@ (@ tptp.less_eq A) B) (= (@ (@ tptp.sup A) B) B))))
% 0.22/0.58 (assert (forall ((B tptp.a) (A tptp.a)) (= (@ (@ tptp.less_eq B) A) (= (@ (@ tptp.sup A) B) A))))
% 0.22/0.58 (assert (forall ((A tptp.a) (B tptp.a)) (= (@ (@ tptp.less_eq A) B) (= (@ (@ tptp.sup A) B) B))))
% 0.22/0.58 (assert (forall ((B tptp.a) (C tptp.a) (A tptp.a)) (=> (@ (@ tptp.less_eq (@ (@ tptp.sup B) C)) A) (not (=> (@ (@ tptp.less_eq B) A) (not (@ (@ tptp.less_eq C) A)))))))
% 0.22/0.58 (assert (forall ((B tptp.a) (A tptp.a) (C tptp.a)) (=> (@ (@ tptp.less_eq B) A) (=> (@ (@ tptp.less_eq C) A) (@ (@ tptp.less_eq (@ (@ tptp.sup B) C)) A)))))
% 0.22/0.58 (assert (forall ((A tptp.a) (B tptp.a)) (@ (@ tptp.less_eq A) (@ (@ tptp.sup A) B))))
% 0.22/0.58 (assert (forall ((B tptp.a) (A tptp.a)) (@ (@ tptp.less_eq B) (@ (@ tptp.sup A) B))))
% 0.22/0.58 (assert (forall ((C tptp.a) (A tptp.a) (B tptp.a)) (let ((_let_1 (@ tptp.less_eq C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup A) B))))))
% 0.22/0.58 (assert (forall ((C tptp.a) (B tptp.a) (A tptp.a)) (let ((_let_1 (@ tptp.less_eq C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup A) B))))))
% 0.22/0.58 (assert (forall ((C tptp.a) (A tptp.a) (D tptp.a) (B tptp.a)) (=> (@ (@ tptp.less_eq C) A) (=> (@ (@ tptp.less_eq D) B) (@ (@ tptp.less_eq (@ (@ tptp.sup C) D)) (@ (@ tptp.sup A) B))))))
% 0.22/0.58 (assert (forall ((B tptp.a) (A tptp.a)) (=> (@ (@ tptp.less_eq B) A) (= A (@ (@ tptp.sup A) B)))))
% 0.22/0.58 (assert (forall ((A tptp.a) (B tptp.a)) (=> (= A (@ (@ tptp.sup A) B)) (@ (@ tptp.less_eq B) A))))
% 0.22/0.58 (assert (forall ((B tptp.a) (A tptp.a)) (= (@ (@ tptp.less_eq B) A) (= A (@ (@ tptp.sup A) B)))))
% 0.22/0.58 (assert (forall ((Y tptp.a) (X tptp.a)) (=> (@ (@ tptp.less_eq Y) X) (= (@ (@ tptp.sup X) Y) X))))
% 0.22/0.58 (assert (forall ((X tptp.a) (Y tptp.a)) (=> (@ (@ tptp.less_eq X) Y) (= (@ (@ tptp.sup X) Y) Y))))
% 0.22/0.58 (assert (forall ((X tptp.a) (Y tptp.a)) (@ (@ tptp.less_eq X) (@ (@ tptp.sup X) Y))))
% 0.22/0.58 (assert (forall ((Y tptp.a) (X tptp.a)) (@ (@ tptp.less_eq Y) (@ (@ tptp.sup X) Y))))
% 0.22/0.58 (assert (forall ((Y tptp.a) (X tptp.a) (Z2 tptp.a)) (=> (@ (@ tptp.less_eq Y) X) (=> (@ (@ tptp.less_eq Z2) X) (@ (@ tptp.less_eq (@ (@ tptp.sup Y) Z2)) X)))))
% 0.22/0.58 (assert (forall ((A tptp.a) (C tptp.a) (B tptp.a) (D tptp.a)) (=> (@ (@ tptp.less_eq A) C) (=> (@ (@ tptp.less_eq B) D) (@ (@ tptp.less_eq (@ (@ tptp.sup A) B)) (@ (@ tptp.sup C) D))))))
% 0.22/0.58 (assert (forall ((F (-> tptp.a tptp.a tptp.a)) (X tptp.a) (Y tptp.a)) (=> (forall ((X3 tptp.a) (Y4 tptp.a)) (@ (@ tptp.less_eq X3) (@ (@ F X3) Y4))) (=> (forall ((X3 tptp.a) (Y4 tptp.a)) (@ (@ tptp.less_eq Y4) (@ (@ F X3) Y4))) (=> (forall ((X3 tptp.a) (Y4 tptp.a) (Z3 tptp.a)) (=> (@ (@ tptp.less_eq Y4) X3) (=> (@ (@ tptp.less_eq Z3) X3) (@ (@ tptp.less_eq (@ (@ F Y4) Z3)) X3)))) (= (@ (@ tptp.sup X) Y) (@ (@ F X) Y)))))))
% 0.22/0.58 (assert (forall ((X tptp.a) (Y tptp.a) (Z2 tptp.a)) (let ((_let_1 (@ tptp.sup X))) (=> (forall ((X3 tptp.a) (Y4 tptp.a) (Z3 tptp.a)) (let ((_let_1 (@ tptp.inf X3))) (= (@ _let_1 (@ (@ tptp.sup Y4) Z3)) (@ (@ tptp.sup (@ _let_1 Y4)) (@ _let_1 Z3))))) (= (@ _let_1 (@ (@ tptp.inf Y) Z2)) (@ (@ tptp.inf (@ _let_1 Y)) (@ _let_1 Z2)))))))
% 0.22/0.58 (assert (forall ((X tptp.a) (Y tptp.a) (Z2 tptp.a)) (let ((_let_1 (@ tptp.inf X))) (=> (forall ((X3 tptp.a) (Y4 tptp.a) (Z3 tptp.a)) (let ((_let_1 (@ tptp.sup X3))) (= (@ _let_1 (@ (@ tptp.inf Y4) Z3)) (@ (@ tptp.inf (@ _let_1 Y4)) (@ _let_1 Z3))))) (= (@ _let_1 (@ (@ tptp.sup Y) Z2)) (@ (@ tptp.sup (@ _let_1 Y)) (@ _let_1 Z2)))))))
% 0.22/0.58 (assert (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.sup A))) (= (@ _let_1 (@ (@ (@ (@ (@ tptp.modula1936294176_aux_a tptp.inf) tptp.sup) A) B) C)) (@ _let_1 (@ (@ tptp.inf B) C))))))
% 0.22/0.58 (assert (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.inf A))) (= (@ _let_1 (@ (@ (@ (@ (@ tptp.modula1936294176_aux_a tptp.inf) tptp.sup) A) B) C)) (@ (@ tptp.sup (@ _let_1 B)) (@ (@ tptp.inf C) A))))))
% 0.22/0.58 (assert (forall ((B tptp.a) (A tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.sup B))) (= (@ _let_1 (@ (@ (@ (@ (@ tptp.modula1936294176_aux_a tptp.inf) tptp.sup) A) B) C)) (@ _let_1 (@ (@ tptp.inf C) A))))))
% 0.22/0.58 (assert (forall ((B tptp.a) (A tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.inf B))) (= (@ _let_1 (@ (@ (@ (@ (@ tptp.modula1936294176_aux_a tptp.inf) tptp.sup) A) B) C)) (@ (@ tptp.sup (@ _let_1 C)) (@ (@ tptp.inf A) B))))))
% 0.22/0.58 (assert (forall ((C tptp.a) (A tptp.a) (B tptp.a)) (let ((_let_1 (@ tptp.inf C))) (= (@ _let_1 (@ (@ (@ (@ (@ tptp.modula1936294176_aux_a tptp.inf) tptp.sup) A) B) C)) (@ (@ tptp.sup (@ _let_1 A)) (@ (@ tptp.inf B) C))))))
% 0.22/0.58 (assert (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (= (@ (@ (@ (@ (@ tptp.modula1936294176_aux_a tptp.inf) tptp.sup) A) B) C) (@ (@ tptp.sup (@ (@ tptp.sup (@ (@ tptp.inf A) B)) (@ (@ tptp.inf B) C))) (@ (@ tptp.inf C) A)))))
% 0.22/0.58 (assert (forall ((B tptp.a) (C tptp.a) (A tptp.a)) (let ((_let_1 (@ (@ tptp.modula1936294176_aux_a tptp.inf) tptp.sup))) (= (@ (@ (@ _let_1 B) C) A) (@ (@ (@ _let_1 A) B) C)))))
% 0.22/0.58 (assert (forall ((C tptp.a) (A tptp.a) (B tptp.a)) (let ((_let_1 (@ (@ tptp.modula1936294176_aux_a tptp.inf) tptp.sup))) (= (@ (@ (@ _let_1 C) A) B) (@ (@ (@ _let_1 A) B) C)))))
% 0.22/0.58 (assert (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.inf A))) (= (@ _let_1 (@ (@ (@ (@ (@ tptp.modula1144073633_aux_a tptp.inf) tptp.sup) A) B) C)) (@ _let_1 (@ (@ tptp.sup B) C))))))
% 0.22/0.58 (assert (forall ((B tptp.a) (A tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.inf B))) (= (@ _let_1 (@ (@ (@ (@ (@ tptp.modula1144073633_aux_a tptp.inf) tptp.sup) A) B) C)) (@ _let_1 (@ (@ tptp.sup C) A))))))
% 0.22/0.58 (assert (forall ((C tptp.a) (A tptp.a) (B tptp.a)) (let ((_let_1 (@ tptp.inf C))) (= (@ _let_1 (@ (@ (@ (@ (@ tptp.modula1144073633_aux_a tptp.inf) tptp.sup) A) B) C)) (@ _let_1 (@ (@ tptp.sup A) B))))))
% 0.22/0.58 (assert (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (= (@ (@ (@ (@ (@ tptp.modula1144073633_aux_a tptp.inf) tptp.sup) A) B) C) (@ (@ tptp.inf (@ (@ tptp.inf (@ (@ tptp.sup A) B)) (@ (@ tptp.sup B) C))) (@ (@ tptp.sup C) A)))))
% 0.22/0.58 (assert (forall ((B tptp.a) (C tptp.a) (A tptp.a)) (let ((_let_1 (@ (@ tptp.modula1144073633_aux_a tptp.inf) tptp.sup))) (= (@ (@ (@ _let_1 B) C) A) (@ (@ (@ _let_1 A) B) C)))))
% 0.22/0.58 (assert (forall ((C tptp.a) (A tptp.a) (B tptp.a)) (let ((_let_1 (@ (@ tptp.modula1144073633_aux_a tptp.inf) tptp.sup))) (= (@ (@ (@ _let_1 C) A) B) (@ (@ (@ _let_1 A) B) C)))))
% 0.22/0.58 (assert (forall ((X tptp.a) (Y tptp.a) (Z2 tptp.a)) (let ((_let_1 (@ tptp.inf X))) (@ (@ tptp.less_eq (@ (@ tptp.sup (@ _let_1 Y)) (@ _let_1 Z2))) (@ _let_1 (@ (@ tptp.sup Y) Z2))))))
% 0.22/0.58 (assert (forall ((X tptp.a) (Y tptp.a) (Z2 tptp.a)) (let ((_let_1 (@ tptp.sup X))) (@ (@ tptp.less_eq (@ _let_1 (@ (@ tptp.inf Y) Z2))) (@ (@ tptp.inf (@ _let_1 Y)) (@ _let_1 Z2))))))
% 0.22/0.58 (assert (forall ((X tptp.a) (Y tptp.a) (Z2 tptp.a)) (let ((_let_1 (@ tptp.sup X))) (let ((_let_2 (@ tptp.inf Y))) (=> (@ (@ tptp.less_eq X) Y) (= (@ _let_1 (@ _let_2 Z2)) (@ _let_2 (@ _let_1 Z2))))))))
% 0.22/0.58 (assert (forall ((X tptp.a) (Y tptp.a)) (= (@ (@ (@ tptp.modula1727524044comp_a tptp.less_eq) X) Y) (and (not (@ (@ tptp.less_eq X) Y)) (not (@ (@ tptp.less_eq Y) X))))))
% 0.22/0.58 (assert (forall ((A tptp.a)) (@ (@ tptp.less_eq A) A)))
% 0.22/0.58 (assert (forall ((X tptp.a)) (@ (@ tptp.less_eq X) X)))
% 0.22/0.58 (assert (forall ((A tptp.a)) (= (@ (@ tptp.inf A) A) A)))
% 0.22/0.58 (assert (forall ((A tptp.a) (B tptp.a)) (let ((_let_1 (@ tptp.inf A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 0.22/0.58 (assert (forall ((A tptp.a) (B tptp.a)) (let ((_let_1 (@ (@ tptp.inf A) B))) (= (@ (@ tptp.inf _let_1) B) _let_1))))
% 0.22/0.58 (assert (forall ((X tptp.a)) (= (@ (@ tptp.inf X) X) X)))
% 0.22/0.58 (assert (forall ((X tptp.a) (Y tptp.a)) (let ((_let_1 (@ tptp.inf X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))))
% 0.22/0.58 (assert (forall ((X tptp.a) (Y tptp.a)) (let ((_let_1 (@ (@ tptp.inf X) Y))) (= (@ (@ tptp.inf _let_1) Y) _let_1))))
% 0.22/0.58 (assert (forall ((A tptp.a)) (= (@ (@ tptp.sup A) A) A)))
% 0.22/0.58 (assert (forall ((A tptp.a) (B tptp.a)) (let ((_let_1 (@ tptp.sup A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 0.22/0.58 (assert (forall ((A tptp.a) (B tptp.a)) (let ((_let_1 (@ (@ tptp.sup A) B))) (= (@ (@ tptp.sup _let_1) B) _let_1))))
% 0.22/0.58 (assert (forall ((X tptp.a)) (= (@ (@ tptp.sup X) X) X)))
% 0.22/0.58 (assert (forall ((X tptp.a) (Y tptp.a)) (let ((_let_1 (@ tptp.sup X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))))
% 0.22/0.58 (assert (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (= (@ (@ (@ (@ (@ tptp.modula581031071_aux_a tptp.inf) tptp.sup) A) B) C) (@ (@ (@ (@ (@ tptp.modula17988509_aux_a tptp.inf) tptp.sup) C) A) B))))
% 0.22/0.58 (assert (forall ((P (-> tptp.a Bool)) (X tptp.a) (Q (-> tptp.a Bool))) (=> (@ P X) (=> (forall ((Y4 tptp.a)) (=> (@ P Y4) (@ (@ tptp.less_eq Y4) X))) (=> (forall ((X3 tptp.a)) (=> (@ P X3) (=> (forall ((Y5 tptp.a)) (=> (@ P Y5) (@ (@ tptp.less_eq Y5) X3))) (@ Q X3)))) (@ Q (@ (@ tptp.greatest_a tptp.less_eq) P)))))))
% 0.22/0.58 (assert (forall ((P (-> tptp.a Bool)) (X tptp.a)) (=> (@ P X) (=> (forall ((Y4 tptp.a)) (=> (@ P Y4) (@ (@ tptp.less_eq Y4) X))) (= (@ (@ tptp.greatest_a tptp.less_eq) P) X)))))
% 0.22/0.58 (assert (forall ((A tptp.a) (B tptp.a)) (let ((_let_1 (@ (@ (@ tptp.max_a tptp.less_eq) A) B))) (let ((_let_2 (@ (@ tptp.less_eq A) B))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 A)))))))
% 0.22/0.58 (assert (forall ((A tptp.a) (B tptp.a)) (let ((_let_1 (@ (@ (@ tptp.min_a tptp.less_eq) A) B))) (let ((_let_2 (@ (@ tptp.less_eq A) B))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 B)))))))
% 0.22/0.58 (assert (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (= (@ (@ (@ (@ (@ tptp.modula17988509_aux_a tptp.inf) tptp.sup) A) B) C) (@ (@ tptp.sup (@ (@ tptp.inf A) (@ (@ (@ (@ (@ tptp.modula1144073633_aux_a tptp.inf) tptp.sup) A) B) C))) (@ (@ (@ (@ (@ tptp.modula1936294176_aux_a tptp.inf) tptp.sup) A) B) C)))))
% 0.22/0.58 (assert (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (= (@ (@ (@ (@ (@ tptp.modula581031071_aux_a tptp.inf) tptp.sup) A) B) C) (@ (@ tptp.sup (@ (@ tptp.inf C) (@ (@ (@ (@ (@ tptp.modula1144073633_aux_a tptp.inf) tptp.sup) A) B) C))) (@ (@ (@ (@ (@ tptp.modula1936294176_aux_a tptp.inf) tptp.sup) A) B) C)))))
% 0.22/0.58 (assert (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.less_eq A))) (= (@ _let_1 (@ (@ tptp.inf B) C)) (and (@ _let_1 B) (@ _let_1 C))))))
% 0.22/0.58 (assert (forall ((X tptp.a) (Y tptp.a) (Z2 tptp.a)) (let ((_let_1 (@ tptp.less_eq X))) (= (@ _let_1 (@ (@ tptp.inf Y) Z2)) (and (@ _let_1 Y) (@ _let_1 Z2))))))
% 0.22/0.58 (assert (forall ((X tptp.a) (Y tptp.a) (Z2 tptp.a)) (= (@ (@ tptp.less_eq (@ (@ tptp.sup X) Y)) Z2) (and (@ (@ tptp.less_eq X) Z2) (@ (@ tptp.less_eq Y) Z2)))))
% 0.22/0.58 (assert (forall ((B tptp.a) (C tptp.a) (A tptp.a)) (= (@ (@ tptp.less_eq (@ (@ tptp.sup B) C)) A) (and (@ (@ tptp.less_eq B) A) (@ (@ tptp.less_eq C) A)))))
% 0.22/0.58 (assert (forall ((X tptp.a) (Y tptp.a)) (= (@ (@ tptp.inf X) (@ (@ tptp.sup X) Y)) X)))
% 0.22/0.58 (assert (forall ((X tptp.a) (Y tptp.a)) (= (@ (@ tptp.sup X) (@ (@ tptp.inf X) Y)) X)))
% 0.22/0.58 (assert (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (= (@ (@ (@ (@ (@ tptp.modula1373251614_aux_a tptp.inf) tptp.sup) A) B) C) (@ (@ (@ (@ (@ tptp.modula17988509_aux_a tptp.inf) tptp.sup) B) C) A))))
% 0.22/0.58 (assert (forall ((P (-> tptp.a Bool))) (=> (exists ((X4 tptp.a)) (and (@ P X4) (forall ((Y4 tptp.a)) (=> (@ P Y4) (@ (@ tptp.less_eq X4) Y4))) (forall ((Y4 tptp.a)) (=> (and (@ P Y4) (forall ((Ya tptp.a)) (=> (@ P Ya) (@ (@ tptp.less_eq Y4) Ya)))) (= Y4 X4))))) (@ P (@ (@ tptp.least_a tptp.less_eq) P)))))
% 0.22/0.58 (assert (forall ((P (-> tptp.a Bool)) (Z2 tptp.a)) (=> (exists ((X4 tptp.a)) (and (@ P X4) (forall ((Y4 tptp.a)) (=> (@ P Y4) (@ (@ tptp.less_eq X4) Y4))) (forall ((Y4 tptp.a)) (=> (and (@ P Y4) (forall ((Ya tptp.a)) (=> (@ P Ya) (@ (@ tptp.less_eq Y4) Ya)))) (= Y4 X4))))) (=> (@ P Z2) (@ (@ tptp.less_eq (@ (@ tptp.least_a tptp.less_eq) P)) Z2)))))
% 0.22/0.58 (assert (forall ((P (-> tptp.a Bool)) (X tptp.a) (Q (-> tptp.a Bool))) (=> (@ P X) (=> (forall ((Y4 tptp.a)) (=> (@ P Y4) (@ (@ tptp.less_eq X) Y4))) (=> (forall ((X3 tptp.a)) (=> (@ P X3) (=> (forall ((Y5 tptp.a)) (=> (@ P Y5) (@ (@ tptp.less_eq X3) Y5))) (@ Q X3)))) (@ Q (@ (@ tptp.least_a tptp.less_eq) P)))))))
% 0.22/0.58 (assert (forall ((P (-> tptp.a Bool)) (X tptp.a)) (=> (@ P X) (=> (forall ((Y4 tptp.a)) (=> (@ P Y4) (@ (@ tptp.less_eq X) Y4))) (= (@ (@ tptp.least_a tptp.less_eq) P) X)))))
% 0.22/0.58 (assert (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (= (@ (@ (@ (@ (@ tptp.modula1373251614_aux_a tptp.inf) tptp.sup) A) B) C) (@ (@ tptp.sup (@ (@ tptp.inf B) (@ (@ (@ (@ (@ tptp.modula1144073633_aux_a tptp.inf) tptp.sup) A) B) C))) (@ (@ (@ (@ (@ tptp.modula1936294176_aux_a tptp.inf) tptp.sup) A) B) C)))))
% 0.22/0.58 (assert (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ (@ (@ (@ (@ tptp.modula1936294176_aux_a tptp.inf) tptp.sup) A) B) C))) (=> (@ (@ tptp.less_eq _let_1) (@ (@ (@ (@ (@ tptp.modula1144073633_aux_a tptp.inf) tptp.sup) A) B) C)) (= (@ (@ tptp.inf (@ (@ (@ (@ (@ tptp.modula17988509_aux_a tptp.inf) tptp.sup) A) B) C)) (@ (@ (@ (@ (@ tptp.modula1373251614_aux_a tptp.inf) tptp.sup) A) B) C)) _let_1)))))
% 0.22/0.58 (assert (= tptp.modula17988509_aux_a tptp.modula17988509_aux_a))
% 0.22/0.58 (assert (= tptp.modula581031071_aux_a tptp.modula581031071_aux_a))
% 0.22/0.58 (assert (= tptp.modula1936294176_aux_a tptp.modula1936294176_aux_a))
% 0.22/0.58 (assert (= tptp.modula1144073633_aux_a tptp.modula1144073633_aux_a))
% 0.22/0.58 (assert (@ tptp.finite40241356em_a_a tptp.sup))
% 0.22/0.58 (assert (@ tptp.finite40241356em_a_a tptp.inf))
% 0.22/0.58 (assert (@ tptp.semigroup_a tptp.sup))
% 0.22/0.58 (assert (@ tptp.semigroup_a tptp.inf))
% 0.22/0.58 (assert (@ tptp.semilattice_a tptp.sup))
% 0.22/0.58 (assert (@ tptp.semilattice_a tptp.inf))
% 0.22/0.58 (assert (@ tptp.abel_semigroup_a tptp.sup))
% 0.22/0.58 (assert (@ tptp.abel_semigroup_a tptp.inf))
% 0.22/0.58 (assert (@ tptp.lattic1885654924_set_a tptp.sup))
% 0.22/0.58 (assert (@ tptp.lattic1885654924_set_a tptp.inf))
% 0.22/0.58 (assert (forall ((A3 tptp.set_a)) (= (@ (@ tptp.condit1627435690bove_a tptp.less_eq) A3) (exists ((M tptp.a)) (forall ((X2 tptp.a)) (=> (@ (@ tptp.member_a X2) A3) (@ (@ tptp.less_eq X2) M)))))))
% 0.22/0.58 (assert (forall ((A3 tptp.set_a)) (= (@ (@ tptp.condit1001553558elow_a tptp.less_eq) A3) (exists ((M2 tptp.a)) (forall ((X2 tptp.a)) (=> (@ (@ tptp.member_a X2) A3) (@ (@ tptp.less_eq M2) X2)))))))
% 0.22/0.58 (assert (forall ((A3 tptp.set_a) (M3 tptp.a)) (=> (forall ((X3 tptp.a)) (=> (@ (@ tptp.member_a X3) A3) (@ (@ tptp.less_eq M3) X3))) (@ (@ tptp.condit1001553558elow_a tptp.less_eq) A3))))
% 0.22/0.58 (assert (forall ((A3 tptp.set_a) (M4 tptp.a)) (=> (forall ((X3 tptp.a)) (=> (@ (@ tptp.member_a X3) A3) (@ (@ tptp.less_eq X3) M4))) (@ (@ tptp.condit1627435690bove_a tptp.less_eq) A3))))
% 0.22/0.58 (assert (= tptp.modula1727524044comp_a tptp.modula1727524044comp_a))
% 0.22/0.58 (assert (= tptp.modula1373251614_aux_a tptp.modula1373251614_aux_a))
% 0.22/0.58 (assert (forall ((F (-> tptp.a tptp.a tptp.a))) (=> (@ tptp.abel_semigroup_a F) (@ tptp.semigroup_a F))))
% 0.22/0.58 (assert (= tptp.lattic1885654924_set_a tptp.semilattice_a))
% 0.22/0.58 (assert (forall ((F (-> tptp.a tptp.a tptp.a))) (=> (@ tptp.semilattice_a F) (@ tptp.lattic1885654924_set_a F))))
% 0.22/0.58 (assert (forall ((F (-> tptp.a tptp.a tptp.a)) (B tptp.a) (A tptp.a) (C tptp.a)) (let ((_let_1 (@ F B))) (let ((_let_2 (@ F A))) (=> (@ tptp.abel_semigroup_a F) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C))))))))
% 0.22/0.58 (assert (forall ((F (-> tptp.a tptp.a tptp.a)) (A tptp.a) (B tptp.a)) (=> (@ tptp.abel_semigroup_a F) (= (@ (@ F A) B) (@ (@ F B) A)))))
% 0.22/0.58 (assert (forall ((F (-> tptp.a tptp.a tptp.a))) (=> (forall ((A4 tptp.a) (B3 tptp.a) (C2 tptp.a)) (let ((_let_1 (@ F A4))) (= (@ (@ F (@ _let_1 B3)) C2) (@ _let_1 (@ (@ F B3) C2))))) (@ tptp.semigroup_a F))))
% 0.22/0.58 (assert (forall ((F (-> tptp.a tptp.a tptp.a)) (A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ F A))) (=> (@ tptp.semigroup_a F) (= (@ (@ F (@ _let_1 B)) C) (@ _let_1 (@ (@ F B) C)))))))
% 0.22/0.58 (assert (= tptp.semigroup_a (lambda ((F2 (-> tptp.a tptp.a tptp.a))) (forall ((A2 tptp.a) (B2 tptp.a) (C3 tptp.a)) (let ((_let_1 (@ F2 A2))) (= (@ (@ F2 (@ _let_1 B2)) C3) (@ _let_1 (@ (@ F2 B2) C3))))))))
% 0.22/0.58 (assert (forall ((F (-> tptp.a tptp.a tptp.a))) (=> (@ tptp.lattic1885654924_set_a F) (@ tptp.semilattice_a F))))
% 0.22/0.58 (assert (forall ((F (-> tptp.a tptp.a tptp.a))) (=> (@ tptp.semilattice_a F) (@ tptp.abel_semigroup_a F))))
% 0.22/0.58 (assert (forall ((B4 tptp.set_a) (A3 tptp.set_a)) (let ((_let_1 (@ tptp.condit1627435690bove_a tptp.less_eq))) (=> (@ _let_1 B4) (=> (@ (@ tptp.ord_less_eq_set_a A3) B4) (@ _let_1 A3))))))
% 0.22/0.58 (assert (forall ((B4 tptp.set_a) (A3 tptp.set_a)) (let ((_let_1 (@ tptp.condit1001553558elow_a tptp.less_eq))) (=> (@ _let_1 B4) (=> (@ (@ tptp.ord_less_eq_set_a A3) B4) (@ _let_1 A3))))))
% 0.22/0.58 (assert (forall ((F (-> tptp.a tptp.set_a))) (= (@ (@ tptp.antimono_a_set_a tptp.less_eq) F) (forall ((X2 tptp.a) (Y3 tptp.a)) (=> (@ (@ tptp.less_eq X2) Y3) (@ (@ tptp.ord_less_eq_set_a (@ F Y3)) (@ F X2)))))))
% 0.22/0.58 (assert (forall ((F (-> tptp.a tptp.set_a))) (=> (forall ((X3 tptp.a) (Y4 tptp.a)) (=> (@ (@ tptp.less_eq X3) Y4) (@ (@ tptp.ord_less_eq_set_a (@ F Y4)) (@ F X3)))) (@ (@ tptp.antimono_a_set_a tptp.less_eq) F))))
% 0.22/0.58 (assert (forall ((F (-> tptp.a tptp.set_a)) (X tptp.a) (Y tptp.a)) (=> (@ (@ tptp.antimono_a_set_a tptp.less_eq) F) (=> (@ (@ tptp.less_eq X) Y) (@ (@ tptp.ord_less_eq_set_a (@ F Y)) (@ F X))))))
% 0.22/0.58 (assert (forall ((F (-> tptp.a tptp.set_a)) (X tptp.a) (Y tptp.a)) (=> (@ (@ tptp.antimono_a_set_a tptp.less_eq) F) (=> (@ (@ tptp.less_eq X) Y) (@ (@ tptp.ord_less_eq_set_a (@ F Y)) (@ F X))))))
% 0.22/0.58 (assert (forall ((F (-> tptp.a tptp.set_a)) (X tptp.a) (Y tptp.a)) (=> (@ (@ tptp.mono_a_set_a tptp.less_eq) F) (=> (@ (@ tptp.less_eq X) Y) (@ (@ tptp.ord_less_eq_set_a (@ F X)) (@ F Y))))))
% 0.22/0.58 (assert (forall ((F (-> tptp.a tptp.set_a)) (X tptp.a) (Y tptp.a)) (=> (@ (@ tptp.mono_a_set_a tptp.less_eq) F) (=> (@ (@ tptp.less_eq X) Y) (@ (@ tptp.ord_less_eq_set_a (@ F X)) (@ F Y))))))
% 0.22/0.58 (assert (forall ((F (-> tptp.a tptp.set_a))) (=> (forall ((X3 tptp.a) (Y4 tptp.a)) (=> (@ (@ tptp.less_eq X3) Y4) (@ (@ tptp.ord_less_eq_set_a (@ F X3)) (@ F Y4)))) (@ (@ tptp.mono_a_set_a tptp.less_eq) F))))
% 0.22/0.58 (assert (forall ((F (-> tptp.a tptp.set_a))) (= (@ (@ tptp.mono_a_set_a tptp.less_eq) F) (forall ((X2 tptp.a) (Y3 tptp.a)) (=> (@ (@ tptp.less_eq X2) Y3) (@ (@ tptp.ord_less_eq_set_a (@ F X2)) (@ F Y3)))))))
% 0.22/0.58 (assert (forall ((F (-> tptp.a tptp.a tptp.a)) (A tptp.a)) (=> (@ tptp.semilattice_a F) (= (@ (@ F A) A) A))))
% 0.22/0.58 (assert (forall ((F (-> tptp.a tptp.a tptp.a)) (A tptp.a) (B tptp.a)) (let ((_let_1 (@ F A))) (let ((_let_2 (@ _let_1 B))) (=> (@ tptp.semilattice_a F) (= (@ _let_1 _let_2) _let_2))))))
% 0.22/0.59 (assert (forall ((F (-> tptp.a tptp.a tptp.a)) (A tptp.a) (B tptp.a)) (let ((_let_1 (@ (@ F A) B))) (=> (@ tptp.semilattice_a F) (= (@ (@ F _let_1) B) _let_1)))))
% 0.22/0.59 (assert (forall ((A3 tptp.set_a) (B4 tptp.set_a)) (=> (forall ((X3 tptp.a)) (let ((_let_1 (@ tptp.member_a X3))) (=> (@ _let_1 A3) (@ _let_1 B4)))) (@ (@ tptp.ord_less_eq_set_a A3) B4))))
% 0.22/0.59 (assert (forall ((A3 tptp.set_a) (B4 tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a A3) B4) (=> (@ (@ tptp.ord_less_eq_set_a B4) A3) (= A3 B4)))))
% 0.22/0.59 (assert (forall ((X tptp.set_a)) (@ (@ tptp.ord_less_eq_set_a X) X)))
% 0.22/0.59 (assert (= tptp.antimono_a_set_a tptp.antimono_a_set_a))
% 0.22/0.59 (assert (= tptp.mono_a_set_a tptp.mono_a_set_a))
% 0.22/0.59 (assert (forall ((B tptp.set_a) (A tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a B) A) (=> (@ (@ tptp.ord_less_eq_set_a A) B) (= A B)))))
% 0.22/0.59 (assert (= (lambda ((Y2 tptp.set_a) (Z tptp.set_a)) (= Y2 Z)) (lambda ((A2 tptp.set_a) (B2 tptp.set_a)) (and (@ (@ tptp.ord_less_eq_set_a B2) A2) (@ (@ tptp.ord_less_eq_set_a A2) B2)))))
% 0.22/0.59 (assert (forall ((B tptp.set_a) (A tptp.set_a) (C tptp.set_a)) (let ((_let_1 (@ tptp.ord_less_eq_set_a C))) (=> (@ (@ tptp.ord_less_eq_set_a B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 0.22/0.59 (assert (forall ((A tptp.set_a)) (@ (@ tptp.ord_less_eq_set_a A) A)))
% 0.22/0.59 (assert (forall ((X tptp.set_a) (Y tptp.set_a) (Z2 tptp.set_a)) (let ((_let_1 (@ tptp.ord_less_eq_set_a X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_set_a Y) Z2) (@ _let_1 Z2))))))
% 0.22/0.59 (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)))))
% 0.22/0.59 (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) (=> (= B C) (@ _let_1 C))))))
% 0.22/0.59 (assert (forall ((A tptp.set_a) (B tptp.set_a) (C tptp.set_a)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_set_a B) C) (@ (@ tptp.ord_less_eq_set_a A) C)))))
% 0.22/0.59 (assert (= (lambda ((Y2 tptp.set_a) (Z tptp.set_a)) (= Y2 Z)) (lambda ((A2 tptp.set_a) (B2 tptp.set_a)) (and (@ (@ tptp.ord_less_eq_set_a A2) B2) (@ (@ tptp.ord_less_eq_set_a B2) A2)))))
% 0.22/0.59 (assert (forall ((Y tptp.set_a) (X tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a Y) X) (= (@ (@ tptp.ord_less_eq_set_a X) Y) (= X Y)))))
% 0.22/0.59 (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))))))
% 0.22/0.59 (assert (forall ((X tptp.set_a) (Y tptp.set_a)) (=> (= X Y) (@ (@ tptp.ord_less_eq_set_a X) Y))))
% 0.22/0.59 (assert (forall ((X tptp.set_a) (Y tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a X) Y) (=> (@ (@ tptp.ord_less_eq_set_a Y) X) (= X Y)))))
% 0.22/0.59 (assert (= (lambda ((Y2 tptp.set_a) (Z tptp.set_a)) (= Y2 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)))))
% 0.22/0.59 (assert (forall ((A tptp.set_a) (B tptp.set_a) (F (-> tptp.set_a tptp.set_a)) (C tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.set_a) (Y4 tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a X3) Y4) (@ (@ tptp.ord_less_eq_set_a (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_set_a (@ F A)) C))))))
% 0.22/0.59 (assert (forall ((A tptp.set_a) (F (-> tptp.set_a tptp.set_a)) (B tptp.set_a) (C tptp.set_a)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_set_a B) C) (=> (forall ((X3 tptp.set_a) (Y4 tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a X3) Y4) (@ (@ tptp.ord_less_eq_set_a (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_set_a A) (@ F C)))))))
% 0.22/0.59 (assert (forall ((A tptp.set_a) (B tptp.set_a) (F (-> tptp.set_a tptp.set_a)) (C tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a A) B) (=> (@ (@ tptp.ord_less_eq_set_a (@ F B)) C) (=> (forall ((X3 tptp.set_a) (Y4 tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a X3) Y4) (@ (@ tptp.ord_less_eq_set_a (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_set_a (@ F A)) C))))))
% 0.22/0.59 (assert (forall ((A tptp.set_a) (F (-> tptp.set_a tptp.set_a)) (B tptp.set_a) (C tptp.set_a)) (let ((_let_1 (@ tptp.ord_less_eq_set_a A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_set_a B) C) (=> (forall ((X3 tptp.set_a) (Y4 tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a X3) Y4) (@ (@ tptp.ord_less_eq_set_a (@ F X3)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 0.22/0.59 (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))))))
% 0.22/0.59 (assert (= (lambda ((Y2 tptp.set_a) (Z tptp.set_a)) (= Y2 Z)) (lambda ((A5 tptp.set_a) (B5 tptp.set_a)) (and (@ (@ tptp.ord_less_eq_set_a A5) B5) (@ (@ tptp.ord_less_eq_set_a B5) A5)))))
% 0.22/0.59 (assert (forall ((A3 tptp.set_a) (B4 tptp.set_a) (C4 tptp.set_a)) (let ((_let_1 (@ tptp.ord_less_eq_set_a A3))) (=> (@ _let_1 B4) (=> (@ (@ tptp.ord_less_eq_set_a B4) C4) (@ _let_1 C4))))))
% 0.22/0.59 (assert (forall ((P (-> tptp.a Bool)) (Q (-> tptp.a Bool))) (=> (forall ((X3 tptp.a)) (=> (@ P X3) (@ Q X3))) (@ (@ tptp.ord_less_eq_set_a (@ tptp.collect_a P)) (@ tptp.collect_a Q)))))
% 0.22/0.59 (assert (forall ((A3 tptp.set_a)) (@ (@ tptp.ord_less_eq_set_a A3) A3)))
% 0.22/0.59 (assert (= tptp.ord_less_eq_set_a (lambda ((A5 tptp.set_a) (B5 tptp.set_a)) (forall ((T tptp.a)) (let ((_let_1 (@ tptp.member_a T))) (=> (@ _let_1 A5) (@ _let_1 B5)))))))
% 0.22/0.59 (assert (forall ((A3 tptp.set_a) (B4 tptp.set_a)) (=> (= A3 B4) (@ (@ tptp.ord_less_eq_set_a B4) A3))))
% 0.22/0.59 (assert (forall ((A3 tptp.set_a) (B4 tptp.set_a)) (=> (= A3 B4) (@ (@ tptp.ord_less_eq_set_a A3) B4))))
% 0.22/0.59 (assert (= tptp.ord_less_eq_set_a (lambda ((A5 tptp.set_a) (B5 tptp.set_a)) (forall ((X2 tptp.a)) (let ((_let_1 (@ tptp.member_a X2))) (=> (@ _let_1 A5) (@ _let_1 B5)))))))
% 0.22/0.59 (assert (forall ((A3 tptp.set_a) (B4 tptp.set_a)) (=> (= A3 B4) (not (=> (@ (@ tptp.ord_less_eq_set_a A3) B4) (not (@ (@ tptp.ord_less_eq_set_a B4) A3)))))))
% 0.22/0.59 (assert (forall ((A3 tptp.set_a) (B4 tptp.set_a) (C tptp.a)) (let ((_let_1 (@ tptp.member_a C))) (=> (@ (@ tptp.ord_less_eq_set_a A3) B4) (=> (@ _let_1 A3) (@ _let_1 B4))))))
% 0.22/0.59 (assert (forall ((A3 tptp.set_a) (B4 tptp.set_a) (X tptp.a)) (let ((_let_1 (@ tptp.member_a X))) (=> (@ (@ tptp.ord_less_eq_set_a A3) B4) (=> (@ _let_1 A3) (@ _let_1 B4))))))
% 0.22/0.59 (assert (= tptp.least_a tptp.least_a))
% 0.22/0.59 (assert (= tptp.greatest_a tptp.greatest_a))
% 0.22/0.59 (assert (= tptp.min_a tptp.min_a))
% 0.22/0.59 (assert (= tptp.max_a tptp.max_a))
% 0.22/0.59 (assert (= tptp.min_a (lambda ((Less_eq (-> tptp.a tptp.a Bool)) (A2 tptp.a) (B2 tptp.a)) (@ (@ (@ tptp.if_a (@ (@ Less_eq A2) B2)) A2) B2))))
% 0.22/0.59 (assert (= tptp.max_a (lambda ((Less_eq (-> tptp.a tptp.a Bool)) (A2 tptp.a) (B2 tptp.a)) (@ (@ (@ tptp.if_a (@ (@ Less_eq A2) B2)) B2) A2))))
% 0.22/0.59 (assert (forall ((F (-> tptp.a tptp.set_a)) (A3 tptp.a) (B4 tptp.a)) (=> (@ (@ tptp.mono_a_set_a tptp.less_eq) F) (@ (@ tptp.ord_less_eq_set_a (@ F (@ (@ tptp.inf A3) B4))) (@ (@ tptp.inf_inf_set_a (@ F A3)) (@ F B4))))))
% 0.22/0.59 (assert (forall ((F (-> tptp.a tptp.set_a)) (A3 tptp.a) (B4 tptp.a)) (=> (@ (@ tptp.mono_a_set_a tptp.less_eq) F) (@ (@ tptp.ord_less_eq_set_a (@ (@ tptp.sup_sup_set_a (@ F A3)) (@ F B4))) (@ F (@ (@ tptp.sup A3) B4))))))
% 0.22/0.59 (assert (forall ((A3 tptp.set_a)) (=> (@ tptp.finite_finite_a A3) (@ (@ tptp.condit1627435690bove_a tptp.less_eq) A3))))
% 0.22/0.59 (assert (forall ((A3 tptp.set_a) (A tptp.a)) (=> (@ tptp.finite_finite_a A3) (=> (@ (@ tptp.member_a A) A3) (exists ((X3 tptp.a)) (and (@ (@ tptp.member_a X3) A3) (@ (@ tptp.less_eq X3) A) (forall ((Xa tptp.a)) (=> (@ (@ tptp.member_a Xa) A3) (=> (@ (@ tptp.less_eq Xa) X3) (= X3 Xa))))))))))
% 0.22/0.59 (assert (forall ((A3 tptp.set_a) (A tptp.a)) (=> (@ tptp.finite_finite_a A3) (=> (@ (@ tptp.member_a A) A3) (exists ((X3 tptp.a)) (and (@ (@ tptp.member_a X3) A3) (@ (@ tptp.less_eq A) X3) (forall ((Xa tptp.a)) (=> (@ (@ tptp.member_a Xa) A3) (=> (@ (@ tptp.less_eq X3) Xa) (= X3 Xa))))))))))
% 0.22/0.59 (assert (forall ((B4 tptp.set_a) (A3 tptp.set_a)) (let ((_let_1 (@ tptp.condit1001553558elow_a tptp.less_eq))) (=> (@ _let_1 B4) (@ _let_1 (@ (@ tptp.inf_inf_set_a A3) B4))))))
% 0.22/0.59 (assert (forall ((A3 tptp.set_a) (B4 tptp.set_a)) (let ((_let_1 (@ tptp.condit1001553558elow_a tptp.less_eq))) (=> (@ _let_1 A3) (@ _let_1 (@ (@ tptp.inf_inf_set_a A3) B4))))))
% 0.22/0.59 (assert (forall ((B4 tptp.set_a) (A3 tptp.set_a)) (let ((_let_1 (@ tptp.condit1627435690bove_a tptp.less_eq))) (=> (@ _let_1 B4) (@ _let_1 (@ (@ tptp.inf_inf_set_a A3) B4))))))
% 0.90/1.11 (assert (forall ((A3 tptp.set_a) (B4 tptp.set_a)) (let ((_let_1 (@ tptp.condit1627435690bove_a tptp.less_eq))) (=> (@ _let_1 A3) (@ _let_1 (@ (@ tptp.inf_inf_set_a A3) B4))))))
% 0.90/1.11 (assert (forall ((A3 tptp.set_a)) (=> (@ tptp.finite_finite_a A3) (@ (@ tptp.condit1001553558elow_a tptp.less_eq) A3))))
% 0.90/1.11 (assert (forall ((A3 tptp.set_a) (B4 tptp.set_a) (C4 tptp.set_a)) (= (@ (@ tptp.ord_less_eq_set_a (@ (@ tptp.sup_sup_set_a A3) B4)) C4) (and (@ (@ tptp.ord_less_eq_set_a A3) C4) (@ (@ tptp.ord_less_eq_set_a B4) C4)))))
% 0.90/1.11 (assert (forall ((C4 tptp.set_a) (A3 tptp.set_a) (B4 tptp.set_a)) (let ((_let_1 (@ tptp.ord_less_eq_set_a C4))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_a A3) B4)) (and (@ _let_1 A3) (@ _let_1 B4))))))
% 0.90/1.11 (assert (forall ((X tptp.set_a) (Y tptp.set_a)) (let ((_let_1 (@ (@ tptp.inf_inf_set_a X) Y))) (= (@ (@ tptp.inf_inf_set_a _let_1) Y) _let_1))))
% 0.90/1.11 (assert (forall ((A tptp.set_a) (B tptp.set_a)) (let ((_let_1 (@ (@ tptp.inf_inf_set_a A) B))) (= (@ (@ tptp.inf_inf_set_a _let_1) B) _let_1))))
% 0.90/1.11 (assert (forall ((X tptp.set_a) (Y tptp.set_a)) (let ((_let_1 (@ tptp.inf_inf_set_a X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))))
% 0.90/1.11 (assert (forall ((A tptp.set_a) (B tptp.set_a)) (let ((_let_1 (@ tptp.inf_inf_set_a A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 0.90/1.11 (assert (forall ((X tptp.set_a)) (= (@ (@ tptp.inf_inf_set_a X) X) X)))
% 0.90/1.11 (assert (forall ((A tptp.set_a)) (= (@ (@ tptp.inf_inf_set_a A) A) A)))
% 0.90/1.11 (assert (forall ((A tptp.set_a) (B tptp.set_a)) (let ((_let_1 (@ (@ tptp.sup_sup_set_a A) B))) (= (@ (@ tptp.sup_sup_set_a _let_1) B) _let_1))))
% 0.90/1.11 (assert (forall ((X tptp.set_a) (Y tptp.set_a)) (let ((_let_1 (@ tptp.sup_sup_set_a X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))))
% 0.90/1.11 (assert (forall ((A tptp.set_a) (B tptp.set_a)) (let ((_let_1 (@ tptp.sup_sup_set_a A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 0.90/1.11 (assert (forall ((X tptp.set_a)) (= (@ (@ tptp.sup_sup_set_a X) X) X)))
% 0.90/1.11 (assert (forall ((A tptp.set_a)) (= (@ (@ tptp.sup_sup_set_a A) A) A)))
% 0.90/1.11 (assert (forall ((X tptp.set_a) (Y tptp.set_a) (Z2 tptp.set_a)) (let ((_let_1 (@ tptp.ord_less_eq_set_a X))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_a Y) Z2)) (and (@ _let_1 Y) (@ _let_1 Z2))))))
% 0.90/1.11 (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 (@ (@ tptp.inf_inf_set_a B) C)) (and (@ _let_1 B) (@ _let_1 C))))))
% 0.90/1.11 (assert (forall ((X tptp.set_a) (Y tptp.set_a) (Z2 tptp.set_a)) (= (@ (@ tptp.ord_less_eq_set_a (@ (@ tptp.sup_sup_set_a X) Y)) Z2) (and (@ (@ tptp.ord_less_eq_set_a X) Z2) (@ (@ tptp.ord_less_eq_set_a Y) Z2)))))
% 0.90/1.11 (assert (forall ((B tptp.set_a) (C tptp.set_a) (A tptp.set_a)) (= (@ (@ tptp.ord_less_eq_set_a (@ (@ tptp.sup_sup_set_a B) C)) A) (and (@ (@ tptp.ord_less_eq_set_a B) A) (@ (@ tptp.ord_less_eq_set_a C) A)))))
% 0.90/1.11 (assert (forall ((X tptp.set_a) (Y tptp.set_a)) (= (@ (@ tptp.sup_sup_set_a X) (@ (@ tptp.inf_inf_set_a X) Y)) X)))
% 0.90/1.11 (assert (forall ((X tptp.set_a) (Y tptp.set_a)) (= (@ (@ tptp.inf_inf_set_a X) (@ (@ tptp.sup_sup_set_a X) Y)) X)))
% 0.90/1.11 (assert (forall ((P Bool)) (or (= P true) (= P false))))
% 0.90/1.11 (assert (forall ((X tptp.a) (Y tptp.a)) (= (@ (@ (@ tptp.if_a false) X) Y) Y)))
% 0.90/1.11 (assert (forall ((X tptp.a) (Y tptp.a)) (= (@ (@ (@ tptp.if_a true) X) Y) X)))
% 0.90/1.11 (assert (@ (@ tptp.less_eq (@ (@ (@ (@ (@ tptp.modula1936294176_aux_a tptp.inf) tptp.sup) tptp.a2) tptp.b) tptp.c)) (@ (@ (@ (@ (@ tptp.modula1144073633_aux_a tptp.inf) tptp.sup) tptp.a2) tptp.b) tptp.c)))
% 0.90/1.11 (assert (not (= (@ (@ tptp.inf (@ (@ (@ (@ (@ tptp.modula17988509_aux_a tptp.inf) tptp.sup) tptp.b) tptp.c) tptp.a2)) (@ (@ (@ (@ (@ tptp.modula581031071_aux_a tptp.inf) tptp.sup) tptp.a2) tptp.b) tptp.c)) (@ (@ (@ (@ (@ tptp.modula1936294176_aux_a tptp.inf) tptp.sup) tptp.a2) tptp.b) tptp.c))))
% 0.90/1.11 (set-info :filename cvc5---1.0.5_29300)
% 0.90/1.11 (check-sat-assuming ( true ))
% 0.90/1.11 ------- get file name : TPTP file name is ITP120^1
% 0.90/1.11 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_29300.smt2...
% 0.90/1.11 --- Run --ho-elim --full-saturate-quant at 10...
% 0.90/1.11 % SZS status Theorem for ITP120^1
% 0.90/1.12 % SZS output start Proof for ITP120^1
% 0.90/1.12 (
% 0.90/1.12 (let ((_let_1 (@ (@ (@ (@ (@ tptp.modula1936294176_aux_a tptp.inf) tptp.sup) tptp.a2) tptp.b) tptp.c))) (let ((_let_2 (@ (@ tptp.inf (@ (@ (@ (@ (@ tptp.modula17988509_aux_a tptp.inf) tptp.sup) tptp.b) tptp.c) tptp.a2)) (@ (@ (@ (@ (@ tptp.modula581031071_aux_a tptp.inf) tptp.sup) tptp.a2) tptp.b) tptp.c)))) (let ((_let_3 (not (= _let_2 _let_1)))) (let ((_let_4 (@ (@ tptp.less_eq _let_1) (@ (@ (@ (@ (@ tptp.modula1144073633_aux_a tptp.inf) tptp.sup) tptp.a2) tptp.b) tptp.c)))) (let ((_let_5 (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ (@ (@ (@ (@ tptp.modula1936294176_aux_a tptp.inf) tptp.sup) A) B) C))) (=> (@ (@ tptp.less_eq _let_1) (@ (@ (@ (@ (@ tptp.modula1144073633_aux_a tptp.inf) tptp.sup) A) B) C)) (= (@ (@ tptp.inf (@ (@ (@ (@ (@ tptp.modula17988509_aux_a tptp.inf) tptp.sup) A) B) C)) (@ (@ (@ (@ (@ tptp.modula1373251614_aux_a tptp.inf) tptp.sup) A) B) C)) _let_1)))))) (let ((_let_6 (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (= (@ (@ (@ (@ (@ tptp.modula1373251614_aux_a tptp.inf) tptp.sup) A) B) C) (@ (@ (@ (@ (@ tptp.modula17988509_aux_a tptp.inf) tptp.sup) B) C) A))))) (let ((_let_7 (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (= (@ (@ (@ (@ (@ tptp.modula581031071_aux_a tptp.inf) tptp.sup) A) B) C) (@ (@ (@ (@ (@ tptp.modula17988509_aux_a tptp.inf) tptp.sup) C) A) B))))) (let ((_let_8 (forall ((B tptp.a) (C tptp.a) (A tptp.a)) (let ((_let_1 (@ (@ tptp.modula1144073633_aux_a tptp.inf) tptp.sup))) (= (@ (@ (@ _let_1 B) C) A) (@ (@ (@ _let_1 A) B) C)))))) (let ((_let_9 (forall ((B tptp.a) (C tptp.a) (A tptp.a)) (let ((_let_1 (@ (@ tptp.modula1936294176_aux_a tptp.inf) tptp.sup))) (= (@ (@ (@ _let_1 B) C) A) (@ (@ (@ _let_1 A) B) C)))))) (let ((_let_10 (ho_52 (ho_51 k_58 k_44) k_47))) (let ((_let_11 (ho_46 (ho_45 (ho_53 _let_10 tptp.a2) tptp.b) tptp.c))) (let ((_let_12 (ho_52 (ho_51 k_57 k_44) k_47))) (let ((_let_13 (ho_45 k_44 (ho_46 (ho_45 (ho_53 _let_12 tptp.b) tptp.c) tptp.a2)))) (let ((_let_14 (ho_52 (ho_51 k_50 k_44) k_47))) (let ((_let_15 (ho_46 (ho_45 (ho_53 _let_14 tptp.a2) tptp.b) tptp.c))) (let ((_let_16 (= _let_15 (ho_46 _let_13 _let_11)))) (let ((_let_17 (ho_46 (ho_45 (ho_53 _let_14 tptp.b) tptp.c) tptp.a2))) (let ((_let_18 (= _let_15 _let_17))) (let ((_let_19 (ho_46 (ho_45 (ho_53 _let_12 tptp.c) tptp.a2) tptp.b))) (let ((_let_20 (= _let_11 _let_19))) (let ((_let_21 (ho_46 (ho_45 (ho_53 (ho_52 (ho_51 k_64 k_44) k_47) tptp.b) tptp.c) tptp.a2))) (let ((_let_22 (= _let_17 (ho_46 _let_13 _let_21)))) (let ((_let_23 (= _let_19 _let_21))) (let ((_let_24 (forall ((B tptp.a) (C tptp.a) (A tptp.a)) (let ((_let_1 (ho_52 (ho_51 k_50 k_44) k_47))) (= (ho_46 (ho_45 (ho_53 _let_1 A) B) C) (ho_46 (ho_45 (ho_53 _let_1 B) C) A)))))) (let ((_let_25 (EQ_RESOLVE (ASSUME :args (_let_9)) (PREPROCESS :args ((= _let_9 _let_24)))))) (let ((_let_26 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_25 :args (tptp.b tptp.c tptp.a2 QUANTIFIERS_INST_E_MATCHING ((ho_46 (ho_45 (ho_53 _let_14 A) B) C)))) :args (_let_24))) _let_25 :args (_let_18 false _let_24)))) (let ((_let_27 (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (= (ho_46 (ho_45 (ho_53 (ho_52 (ho_51 k_57 k_44) k_47) C) A) B) (ho_46 (ho_45 (ho_53 (ho_52 (ho_51 k_58 k_44) k_47) A) B) C))))) (let ((_let_28 (EQ_RESOLVE (ASSUME :args (_let_7)) (PREPROCESS :args ((= _let_7 _let_27)))))) (let ((_let_29 (ho_52 (ho_51 k_54 k_44) k_47))) (let ((_let_30 (ho_46 (ho_45 (ho_53 _let_29 tptp.b) tptp.c) tptp.a2))) (let ((_let_31 (ho_35 (ho_37 k_39 _let_17) _let_30))) (let ((_let_32 (not _let_31))) (let ((_let_33 (or _let_32 _let_22))) (let ((_let_34 (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (ho_46 (ho_45 (ho_53 (ho_52 (ho_51 k_50 k_44) k_47) A) B) C))) (or (not (ho_35 (ho_37 k_39 _let_1) (ho_46 (ho_45 (ho_53 (ho_52 (ho_51 k_54 k_44) k_47) A) B) C))) (= (ho_46 (ho_45 k_44 (ho_46 (ho_45 (ho_53 (ho_52 (ho_51 k_57 k_44) k_47) A) B) C)) (ho_46 (ho_45 (ho_53 (ho_52 (ho_51 k_64 k_44) k_47) A) B) C)) _let_1)))))) (let ((_let_35 (EQ_RESOLVE (ASSUME :args (_let_5)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ (@ (@ (@ (@ tptp.modula1936294176_aux_a tptp.inf) tptp.sup) A) B) C))) (or (not (@ (@ tptp.less_eq _let_1) (@ (@ (@ (@ (@ tptp.modula1144073633_aux_a tptp.inf) tptp.sup) A) B) C))) (= _let_1 (@ (@ tptp.inf (@ (@ (@ (@ (@ tptp.modula17988509_aux_a tptp.inf) tptp.sup) A) B) C)) (@ (@ (@ (@ (@ tptp.modula1373251614_aux_a tptp.inf) tptp.sup) A) B) C)))))) _let_34))))))) (let ((_let_36 (ho_46 (ho_45 (ho_53 _let_29 tptp.a2) tptp.b) tptp.c))) (let ((_let_37 (= _let_36 _let_30))) (let ((_let_38 (ho_35 (ho_37 k_39 _let_15) _let_36))) (let ((_let_39 (forall ((B tptp.a) (C tptp.a) (A tptp.a)) (let ((_let_1 (ho_52 (ho_51 k_54 k_44) k_47))) (= (ho_46 (ho_45 (ho_53 _let_1 A) B) C) (ho_46 (ho_45 (ho_53 _let_1 B) C) A)))))) (let ((_let_40 (EQ_RESOLVE (ASSUME :args (_let_8)) (PREPROCESS :args ((= _let_8 _let_39)))))) (let ((_let_41 (EQ_RESOLVE (ASSUME :args (_let_4)) (PREPROCESS :args ((= _let_4 _let_38)))))) (let ((_let_42 (not _let_18))) (let ((_let_43 (and _let_38 _let_18 _let_37))) (let ((_let_44 (_let_38 _let_18 _let_37))) (let ((_let_45 (ASSUME :args (_let_37)))) (let ((_let_46 (ASSUME :args (_let_18)))) (let ((_let_47 (SYMM (SYMM _let_46)))) (let ((_let_48 (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (= (ho_46 (ho_45 (ho_53 (ho_52 (ho_51 k_57 k_44) k_47) B) C) A) (ho_46 (ho_45 (ho_53 (ho_52 (ho_51 k_64 k_44) k_47) A) B) C))))) (let ((_let_49 (EQ_RESOLVE (ASSUME :args (_let_6)) (PREPROCESS :args ((= _let_6 _let_48)))))) (let ((_let_50 (and _let_18 _let_20 _let_22 _let_23))) (let ((_let_51 (ASSUME :args (_let_20)))) (let ((_let_52 (ASSUME :args (_let_23)))) (let ((_let_53 (ASSUME :args (_let_22)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_50)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_51 _let_52 _let_53 _let_46) (SCOPE (TRANS _let_47 (SYMM (SYMM _let_53)) (CONG (REFL :args (_let_13)) (TRANS (SYMM _let_52) (SYMM _let_51)) :args (APPLY_UF ho_46))) :args (_let_20 _let_23 _let_22 _let_18))) :args (_let_18 _let_20 _let_22 _let_23))) :args (true _let_50)) :args ((or _let_16 _let_42 (not _let_20) (not _let_22) (not _let_23)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_49 :args (tptp.b tptp.c tptp.a2 QUANTIFIERS_INST_CBQI_PROP)) :args (_let_48))) _let_49 :args (_let_23 false _let_48)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_33)) :args ((or _let_32 _let_22 (not _let_33)))) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_43)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_41 _let_46 _let_45) (SCOPE (TRUE_ELIM (TRANS (CONG (CONG (REFL :args (k_39)) (SYMM _let_47) :args (APPLY_UF ho_37)) (SYMM _let_45) :args (APPLY_UF ho_35)) (TRUE_INTRO _let_41))) :args _let_44)) :args _let_44)) :args (true _let_43)) :args ((or (not _let_38) _let_31 _let_42 (not _let_37)))) _let_41 _let_26 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_40 :args (tptp.b tptp.c tptp.a2 QUANTIFIERS_INST_E_MATCHING ((ho_46 (ho_45 (ho_53 _let_29 A) B) C)))) :args (_let_39))) _let_40 :args (_let_37 false _let_39)) :args (_let_31 false _let_38 false _let_18 false _let_37)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_35 :args (tptp.b tptp.c tptp.a2 QUANTIFIERS_INST_E_MATCHING ((ho_46 (ho_45 (ho_53 _let_12 A) B) C)))) :args (_let_34)))) _let_35 :args (_let_33 false _let_34)) :args (_let_22 false _let_31 false _let_33)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_28 :args (tptp.a2 tptp.b tptp.c QUANTIFIERS_INST_E_MATCHING ((ho_46 (ho_45 (ho_53 _let_10 A) B) C)))) :args (_let_27)))) _let_28 :args (_let_20 false _let_27)) _let_26 (EQ_RESOLVE (ASSUME :args (_let_3)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (= _let_1 _let_2)) (not _let_16)))))) :args (false false _let_23 false _let_22 false _let_20 false _let_18 true _let_16)) :args ((forall ((X tptp.a) (Y tptp.a)) (=> (@ (@ tptp.less_eq X) Y) (=> (@ (@ tptp.less_eq Y) X) (= X Y)))) (forall ((Y tptp.a) (X tptp.a)) (=> (@ (@ tptp.less_eq Y) X) (= (@ (@ tptp.less_eq X) Y) (= X Y)))) (forall ((B tptp.a) (A tptp.a)) (=> (@ (@ tptp.less_eq B) A) (=> (@ (@ tptp.less_eq A) B) (= A B)))) (= (lambda ((Y2 tptp.a) (Z tptp.a)) (= Y2 Z)) (lambda ((A2 tptp.a) (B2 tptp.a)) (and (@ (@ tptp.less_eq B2) A2) (@ (@ tptp.less_eq A2) B2)))) (forall ((B tptp.a) (A tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.less_eq C))) (=> (@ (@ tptp.less_eq B) A) (=> (@ _let_1 B) (@ _let_1 A))))) (= (lambda ((Y2 tptp.a) (Z tptp.a)) (= Y2 Z)) (lambda ((X2 tptp.a) (Y3 tptp.a)) (and (@ (@ tptp.less_eq X2) Y3) (@ (@ tptp.less_eq Y3) X2)))) (forall ((X tptp.a) (Y tptp.a)) (=> (= X Y) (@ (@ tptp.less_eq X) Y))) (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (=> (= A B) (=> (@ (@ tptp.less_eq B) C) (@ (@ tptp.less_eq A) C)))) (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.less_eq A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))) (forall ((A tptp.a) (B tptp.a)) (=> (@ (@ tptp.less_eq A) B) (=> (@ (@ tptp.less_eq B) A) (= A B)))) (= (lambda ((Y2 tptp.a) (Z tptp.a)) (= Y2 Z)) (lambda ((A2 tptp.a) (B2 tptp.a)) (and (@ (@ tptp.less_eq A2) B2) (@ (@ tptp.less_eq B2) A2)))) (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.less_eq A))) (=> (@ _let_1 B) (=> (@ (@ tptp.less_eq B) C) (@ _let_1 C))))) (forall ((X tptp.a) (Y tptp.a) (Z2 tptp.a)) (let ((_let_1 (@ tptp.less_eq X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.less_eq Y) Z2) (@ _let_1 Z2))))) (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.inf A))) (= (@ (@ tptp.inf (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.inf B) C))))) (forall ((A tptp.a) (B tptp.a)) (= (@ (@ tptp.inf A) B) (@ (@ tptp.inf B) A))) (forall ((B tptp.a) (A tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.inf B))) (let ((_let_2 (@ tptp.inf A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (forall ((X tptp.a) (Y tptp.a) (Z2 tptp.a)) (let ((_let_1 (@ tptp.inf X))) (= (@ (@ tptp.inf (@ _let_1 Y)) Z2) (@ _let_1 (@ (@ tptp.inf Y) Z2))))) (forall ((X tptp.a) (Y tptp.a)) (= (@ (@ tptp.inf X) Y) (@ (@ tptp.inf Y) X))) (forall ((X tptp.a) (Y tptp.a) (Z2 tptp.a)) (let ((_let_1 (@ tptp.inf X))) (let ((_let_2 (@ tptp.inf Y))) (= (@ _let_1 (@ _let_2 Z2)) (@ _let_2 (@ _let_1 Z2)))))) (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.sup A))) (= (@ (@ tptp.sup (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.sup B) C))))) (forall ((A tptp.a) (B tptp.a)) (= (@ (@ tptp.sup A) B) (@ (@ tptp.sup B) A))) (forall ((B tptp.a) (A tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.sup B))) (let ((_let_2 (@ tptp.sup A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (forall ((X tptp.a) (Y tptp.a) (Z2 tptp.a)) (let ((_let_1 (@ tptp.sup X))) (= (@ (@ tptp.sup (@ _let_1 Y)) Z2) (@ _let_1 (@ (@ tptp.sup Y) Z2))))) (forall ((X tptp.a) (Y tptp.a)) (= (@ (@ tptp.sup X) Y) (@ (@ tptp.sup Y) X))) (forall ((X tptp.a) (Y tptp.a) (Z2 tptp.a)) (let ((_let_1 (@ tptp.sup X))) (let ((_let_2 (@ tptp.sup Y))) (= (@ _let_1 (@ _let_2 Z2)) (@ _let_2 (@ _let_1 Z2)))))) (forall ((A tptp.a) (B tptp.a)) (=> (@ (@ tptp.less_eq A) B) (= (@ (@ tptp.inf A) B) A))) (forall ((B tptp.a) (A tptp.a)) (=> (@ (@ tptp.less_eq B) A) (= (@ (@ tptp.inf A) B) B))) (forall ((A tptp.a) (B tptp.a)) (= (@ (@ tptp.less_eq A) B) (= (@ (@ tptp.inf A) B) A))) (forall ((B tptp.a) (A tptp.a)) (= (@ (@ tptp.less_eq B) A) (= (@ (@ tptp.inf A) B) B))) (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.less_eq A))) (=> (@ _let_1 (@ (@ tptp.inf B) C)) (not (=> (@ _let_1 B) (not (@ _let_1 C))))))) (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.less_eq A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.inf B) C)))))) (forall ((A tptp.a) (B tptp.a)) (@ (@ tptp.less_eq (@ (@ tptp.inf A) B)) A)) (forall ((A tptp.a) (B tptp.a)) (@ (@ tptp.less_eq (@ (@ tptp.inf A) B)) B)) (forall ((A tptp.a) (C tptp.a) (B tptp.a)) (=> (@ (@ tptp.less_eq A) C) (@ (@ tptp.less_eq (@ (@ tptp.inf A) B)) C))) (forall ((B tptp.a) (C tptp.a) (A tptp.a)) (=> (@ (@ tptp.less_eq B) C) (@ (@ tptp.less_eq (@ (@ tptp.inf A) B)) C))) (forall ((A tptp.a) (B tptp.a)) (=> (@ (@ tptp.less_eq A) B) (= A (@ (@ tptp.inf A) B)))) (forall ((A tptp.a) (B tptp.a)) (=> (= A (@ (@ tptp.inf A) B)) (@ (@ tptp.less_eq A) B))) (forall ((A tptp.a) (B tptp.a)) (= (@ (@ tptp.less_eq A) B) (= A (@ (@ tptp.inf A) B)))) (forall ((X tptp.a) (Y tptp.a)) (=> (@ (@ tptp.less_eq X) Y) (= (@ (@ tptp.inf X) Y) X))) (forall ((Y tptp.a) (X tptp.a)) (=> (@ (@ tptp.less_eq Y) X) (= (@ (@ tptp.inf X) Y) Y))) (forall ((X tptp.a) (Y tptp.a) (Z2 tptp.a)) (let ((_let_1 (@ tptp.less_eq X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z2) (@ _let_1 (@ (@ tptp.inf Y) Z2)))))) (forall ((X tptp.a) (Y tptp.a)) (@ (@ tptp.less_eq (@ (@ tptp.inf X) Y)) X)) (forall ((X tptp.a) (Y tptp.a)) (@ (@ tptp.less_eq (@ (@ tptp.inf X) Y)) Y)) (forall ((A tptp.a) (C tptp.a) (B tptp.a) (D tptp.a)) (=> (@ (@ tptp.less_eq A) C) (=> (@ (@ tptp.less_eq B) D) (@ (@ tptp.less_eq (@ (@ tptp.inf A) B)) (@ (@ tptp.inf C) D))))) (forall ((F (-> tptp.a tptp.a tptp.a)) (X tptp.a) (Y tptp.a)) (=> (forall ((X3 tptp.a) (Y4 tptp.a)) (@ (@ tptp.less_eq (@ (@ F X3) Y4)) X3)) (=> (forall ((X3 tptp.a) (Y4 tptp.a)) (@ (@ tptp.less_eq (@ (@ F X3) Y4)) Y4)) (=> (forall ((X3 tptp.a) (Y4 tptp.a) (Z3 tptp.a)) (let ((_let_1 (@ tptp.less_eq X3))) (=> (@ _let_1 Y4) (=> (@ _let_1 Z3) (@ _let_1 (@ (@ F Y4) Z3)))))) (= (@ (@ tptp.inf X) Y) (@ (@ F X) Y)))))) (forall ((A tptp.a) (P (-> tptp.a Bool))) (= (@ (@ tptp.member_a A) (@ tptp.collect_a P)) (@ P A))) (forall ((A3 tptp.set_a)) (= (@ tptp.collect_a (lambda ((X2 tptp.a)) (@ (@ tptp.member_a X2) A3))) A3)) (forall ((P (-> tptp.a Bool)) (Q (-> tptp.a Bool))) (=> (forall ((X3 tptp.a)) (= (@ P X3) (@ Q X3))) (= (@ tptp.collect_a P) (@ tptp.collect_a Q)))) (forall ((X tptp.a) (Y tptp.a)) (= (@ (@ tptp.less_eq X) Y) (= (@ (@ tptp.inf X) Y) X))) (forall ((X tptp.a) (A tptp.a) (B tptp.a)) (let ((_let_1 (@ tptp.less_eq X))) (=> (@ _let_1 (@ (@ tptp.inf A) B)) (not (=> (@ _let_1 A) (not (@ _let_1 B))))))) (forall ((X tptp.a) (A tptp.a) (B tptp.a)) (let ((_let_1 (@ tptp.less_eq X))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.inf A) B)))))) (forall ((A tptp.a) (X tptp.a) (B tptp.a)) (=> (@ (@ tptp.less_eq A) X) (@ (@ tptp.less_eq (@ (@ tptp.inf A) B)) X))) (forall ((B tptp.a) (X tptp.a) (A tptp.a)) (=> (@ (@ tptp.less_eq B) X) (@ (@ tptp.less_eq (@ (@ tptp.inf A) B)) X))) (forall ((X tptp.a) (Y tptp.a)) (= (@ (@ tptp.less_eq X) Y) (= (@ (@ tptp.sup X) Y) Y))) (forall ((A tptp.a) (B tptp.a) (X tptp.a)) (=> (@ (@ tptp.less_eq (@ (@ tptp.sup A) B)) X) (not (=> (@ (@ tptp.less_eq A) X) (not (@ (@ tptp.less_eq B) X)))))) (forall ((A tptp.a) (X tptp.a) (B tptp.a)) (=> (@ (@ tptp.less_eq A) X) (=> (@ (@ tptp.less_eq B) X) (@ (@ tptp.less_eq (@ (@ tptp.sup A) B)) X)))) (forall ((X tptp.a) (A tptp.a) (B tptp.a)) (let ((_let_1 (@ tptp.less_eq X))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup A) B))))) (forall ((X tptp.a) (B tptp.a) (A tptp.a)) (let ((_let_1 (@ tptp.less_eq X))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup A) B))))) (forall ((B tptp.a) (A tptp.a)) (=> (@ (@ tptp.less_eq B) A) (= (@ (@ tptp.sup A) B) A))) (forall ((A tptp.a) (B tptp.a)) (=> (@ (@ tptp.less_eq A) B) (= (@ (@ tptp.sup A) B) B))) (forall ((B tptp.a) (A tptp.a)) (= (@ (@ tptp.less_eq B) A) (= (@ (@ tptp.sup A) B) A))) (forall ((A tptp.a) (B tptp.a)) (= (@ (@ tptp.less_eq A) B) (= (@ (@ tptp.sup A) B) B))) (forall ((B tptp.a) (C tptp.a) (A tptp.a)) (=> (@ (@ tptp.less_eq (@ (@ tptp.sup B) C)) A) (not (=> (@ (@ tptp.less_eq B) A) (not (@ (@ tptp.less_eq C) A)))))) (forall ((B tptp.a) (A tptp.a) (C tptp.a)) (=> (@ (@ tptp.less_eq B) A) (=> (@ (@ tptp.less_eq C) A) (@ (@ tptp.less_eq (@ (@ tptp.sup B) C)) A)))) (forall ((A tptp.a) (B tptp.a)) (@ (@ tptp.less_eq A) (@ (@ tptp.sup A) B))) (forall ((B tptp.a) (A tptp.a)) (@ (@ tptp.less_eq B) (@ (@ tptp.sup A) B))) (forall ((C tptp.a) (A tptp.a) (B tptp.a)) (let ((_let_1 (@ tptp.less_eq C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup A) B))))) (forall ((C tptp.a) (B tptp.a) (A tptp.a)) (let ((_let_1 (@ tptp.less_eq C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup A) B))))) (forall ((C tptp.a) (A tptp.a) (D tptp.a) (B tptp.a)) (=> (@ (@ tptp.less_eq C) A) (=> (@ (@ tptp.less_eq D) B) (@ (@ tptp.less_eq (@ (@ tptp.sup C) D)) (@ (@ tptp.sup A) B))))) (forall ((B tptp.a) (A tptp.a)) (=> (@ (@ tptp.less_eq B) A) (= A (@ (@ tptp.sup A) B)))) (forall ((A tptp.a) (B tptp.a)) (=> (= A (@ (@ tptp.sup A) B)) (@ (@ tptp.less_eq B) A))) (forall ((B tptp.a) (A tptp.a)) (= (@ (@ tptp.less_eq B) A) (= A (@ (@ tptp.sup A) B)))) (forall ((Y tptp.a) (X tptp.a)) (=> (@ (@ tptp.less_eq Y) X) (= (@ (@ tptp.sup X) Y) X))) (forall ((X tptp.a) (Y tptp.a)) (=> (@ (@ tptp.less_eq X) Y) (= (@ (@ tptp.sup X) Y) Y))) (forall ((X tptp.a) (Y tptp.a)) (@ (@ tptp.less_eq X) (@ (@ tptp.sup X) Y))) (forall ((Y tptp.a) (X tptp.a)) (@ (@ tptp.less_eq Y) (@ (@ tptp.sup X) Y))) (forall ((Y tptp.a) (X tptp.a) (Z2 tptp.a)) (=> (@ (@ tptp.less_eq Y) X) (=> (@ (@ tptp.less_eq Z2) X) (@ (@ tptp.less_eq (@ (@ tptp.sup Y) Z2)) X)))) (forall ((A tptp.a) (C tptp.a) (B tptp.a) (D tptp.a)) (=> (@ (@ tptp.less_eq A) C) (=> (@ (@ tptp.less_eq B) D) (@ (@ tptp.less_eq (@ (@ tptp.sup A) B)) (@ (@ tptp.sup C) D))))) (forall ((F (-> tptp.a tptp.a tptp.a)) (X tptp.a) (Y tptp.a)) (=> (forall ((X3 tptp.a) (Y4 tptp.a)) (@ (@ tptp.less_eq X3) (@ (@ F X3) Y4))) (=> (forall ((X3 tptp.a) (Y4 tptp.a)) (@ (@ tptp.less_eq Y4) (@ (@ F X3) Y4))) (=> (forall ((X3 tptp.a) (Y4 tptp.a) (Z3 tptp.a)) (=> (@ (@ tptp.less_eq Y4) X3) (=> (@ (@ tptp.less_eq Z3) X3) (@ (@ tptp.less_eq (@ (@ F Y4) Z3)) X3)))) (= (@ (@ tptp.sup X) Y) (@ (@ F X) Y)))))) (forall ((X tptp.a) (Y tptp.a) (Z2 tptp.a)) (let ((_let_1 (@ tptp.sup X))) (=> (forall ((X3 tptp.a) (Y4 tptp.a) (Z3 tptp.a)) (let ((_let_1 (@ tptp.inf X3))) (= (@ _let_1 (@ (@ tptp.sup Y4) Z3)) (@ (@ tptp.sup (@ _let_1 Y4)) (@ _let_1 Z3))))) (= (@ _let_1 (@ (@ tptp.inf Y) Z2)) (@ (@ tptp.inf (@ _let_1 Y)) (@ _let_1 Z2)))))) (forall ((X tptp.a) (Y tptp.a) (Z2 tptp.a)) (let ((_let_1 (@ tptp.inf X))) (=> (forall ((X3 tptp.a) (Y4 tptp.a) (Z3 tptp.a)) (let ((_let_1 (@ tptp.sup X3))) (= (@ _let_1 (@ (@ tptp.inf Y4) Z3)) (@ (@ tptp.inf (@ _let_1 Y4)) (@ _let_1 Z3))))) (= (@ _let_1 (@ (@ tptp.sup Y) Z2)) (@ (@ tptp.sup (@ _let_1 Y)) (@ _let_1 Z2)))))) (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.sup A))) (= (@ _let_1 (@ (@ (@ (@ (@ tptp.modula1936294176_aux_a tptp.inf) tptp.sup) A) B) C)) (@ _let_1 (@ (@ tptp.inf B) C))))) (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.inf A))) (= (@ _let_1 (@ (@ (@ (@ (@ tptp.modula1936294176_aux_a tptp.inf) tptp.sup) A) B) C)) (@ (@ tptp.sup (@ _let_1 B)) (@ (@ tptp.inf C) A))))) (forall ((B tptp.a) (A tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.sup B))) (= (@ _let_1 (@ (@ (@ (@ (@ tptp.modula1936294176_aux_a tptp.inf) tptp.sup) A) B) C)) (@ _let_1 (@ (@ tptp.inf C) A))))) (forall ((B tptp.a) (A tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.inf B))) (= (@ _let_1 (@ (@ (@ (@ (@ tptp.modula1936294176_aux_a tptp.inf) tptp.sup) A) B) C)) (@ (@ tptp.sup (@ _let_1 C)) (@ (@ tptp.inf A) B))))) (forall ((C tptp.a) (A tptp.a) (B tptp.a)) (let ((_let_1 (@ tptp.inf C))) (= (@ _let_1 (@ (@ (@ (@ (@ tptp.modula1936294176_aux_a tptp.inf) tptp.sup) A) B) C)) (@ (@ tptp.sup (@ _let_1 A)) (@ (@ tptp.inf B) C))))) (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (= (@ (@ (@ (@ (@ tptp.modula1936294176_aux_a tptp.inf) tptp.sup) A) B) C) (@ (@ tptp.sup (@ (@ tptp.sup (@ (@ tptp.inf A) B)) (@ (@ tptp.inf B) C))) (@ (@ tptp.inf C) A)))) _let_9 (forall ((C tptp.a) (A tptp.a) (B tptp.a)) (let ((_let_1 (@ (@ tptp.modula1936294176_aux_a tptp.inf) tptp.sup))) (= (@ (@ (@ _let_1 C) A) B) (@ (@ (@ _let_1 A) B) C)))) (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.inf A))) (= (@ _let_1 (@ (@ (@ (@ (@ tptp.modula1144073633_aux_a tptp.inf) tptp.sup) A) B) C)) (@ _let_1 (@ (@ tptp.sup B) C))))) (forall ((B tptp.a) (A tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.inf B))) (= (@ _let_1 (@ (@ (@ (@ (@ tptp.modula1144073633_aux_a tptp.inf) tptp.sup) A) B) C)) (@ _let_1 (@ (@ tptp.sup C) A))))) (forall ((C tptp.a) (A tptp.a) (B tptp.a)) (let ((_let_1 (@ tptp.inf C))) (= (@ _let_1 (@ (@ (@ (@ (@ tptp.modula1144073633_aux_a tptp.inf) tptp.sup) A) B) C)) (@ _let_1 (@ (@ tptp.sup A) B))))) (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (= (@ (@ (@ (@ (@ tptp.modula1144073633_aux_a tptp.inf) tptp.sup) A) B) C) (@ (@ tptp.inf (@ (@ tptp.inf (@ (@ tptp.sup A) B)) (@ (@ tptp.sup B) C))) (@ (@ tptp.sup C) A)))) _let_8 (forall ((C tptp.a) (A tptp.a) (B tptp.a)) (let ((_let_1 (@ (@ tptp.modula1144073633_aux_a tptp.inf) tptp.sup))) (= (@ (@ (@ _let_1 C) A) B) (@ (@ (@ _let_1 A) B) C)))) (forall ((X tptp.a) (Y tptp.a) (Z2 tptp.a)) (let ((_let_1 (@ tptp.inf X))) (@ (@ tptp.less_eq (@ (@ tptp.sup (@ _let_1 Y)) (@ _let_1 Z2))) (@ _let_1 (@ (@ tptp.sup Y) Z2))))) (forall ((X tptp.a) (Y tptp.a) (Z2 tptp.a)) (let ((_let_1 (@ tptp.sup X))) (@ (@ tptp.less_eq (@ _let_1 (@ (@ tptp.inf Y) Z2))) (@ (@ tptp.inf (@ _let_1 Y)) (@ _let_1 Z2))))) (forall ((X tptp.a) (Y tptp.a) (Z2 tptp.a)) (let ((_let_1 (@ tptp.sup X))) (let ((_let_2 (@ tptp.inf Y))) (=> (@ (@ tptp.less_eq X) Y) (= (@ _let_1 (@ _let_2 Z2)) (@ _let_2 (@ _let_1 Z2))))))) (forall ((X tptp.a) (Y tptp.a)) (= (@ (@ (@ tptp.modula1727524044comp_a tptp.less_eq) X) Y) (and (not (@ (@ tptp.less_eq X) Y)) (not (@ (@ tptp.less_eq Y) X))))) (forall ((A tptp.a)) (@ (@ tptp.less_eq A) A)) (forall ((X tptp.a)) (@ (@ tptp.less_eq X) X)) (forall ((A tptp.a)) (= (@ (@ tptp.inf A) A) A)) (forall ((A tptp.a) (B tptp.a)) (let ((_let_1 (@ tptp.inf A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))) (forall ((A tptp.a) (B tptp.a)) (let ((_let_1 (@ (@ tptp.inf A) B))) (= (@ (@ tptp.inf _let_1) B) _let_1))) (forall ((X tptp.a)) (= (@ (@ tptp.inf X) X) X)) (forall ((X tptp.a) (Y tptp.a)) (let ((_let_1 (@ tptp.inf X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))) (forall ((X tptp.a) (Y tptp.a)) (let ((_let_1 (@ (@ tptp.inf X) Y))) (= (@ (@ tptp.inf _let_1) Y) _let_1))) (forall ((A tptp.a)) (= (@ (@ tptp.sup A) A) A)) (forall ((A tptp.a) (B tptp.a)) (let ((_let_1 (@ tptp.sup A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))) (forall ((A tptp.a) (B tptp.a)) (let ((_let_1 (@ (@ tptp.sup A) B))) (= (@ (@ tptp.sup _let_1) B) _let_1))) (forall ((X tptp.a)) (= (@ (@ tptp.sup X) X) X)) (forall ((X tptp.a) (Y tptp.a)) (let ((_let_1 (@ tptp.sup X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))) _let_7 (forall ((P (-> tptp.a Bool)) (X tptp.a) (Q (-> tptp.a Bool))) (=> (@ P X) (=> (forall ((Y4 tptp.a)) (=> (@ P Y4) (@ (@ tptp.less_eq Y4) X))) (=> (forall ((X3 tptp.a)) (=> (@ P X3) (=> (forall ((Y5 tptp.a)) (=> (@ P Y5) (@ (@ tptp.less_eq Y5) X3))) (@ Q X3)))) (@ Q (@ (@ tptp.greatest_a tptp.less_eq) P)))))) (forall ((P (-> tptp.a Bool)) (X tptp.a)) (=> (@ P X) (=> (forall ((Y4 tptp.a)) (=> (@ P Y4) (@ (@ tptp.less_eq Y4) X))) (= (@ (@ tptp.greatest_a tptp.less_eq) P) X)))) (forall ((A tptp.a) (B tptp.a)) (let ((_let_1 (@ (@ (@ tptp.max_a tptp.less_eq) A) B))) (let ((_let_2 (@ (@ tptp.less_eq A) B))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 A)))))) (forall ((A tptp.a) (B tptp.a)) (let ((_let_1 (@ (@ (@ tptp.min_a tptp.less_eq) A) B))) (let ((_let_2 (@ (@ tptp.less_eq A) B))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 B)))))) (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (= (@ (@ (@ (@ (@ tptp.modula17988509_aux_a tptp.inf) tptp.sup) A) B) C) (@ (@ tptp.sup (@ (@ tptp.inf A) (@ (@ (@ (@ (@ tptp.modula1144073633_aux_a tptp.inf) tptp.sup) A) B) C))) (@ (@ (@ (@ (@ tptp.modula1936294176_aux_a tptp.inf) tptp.sup) A) B) C)))) (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (= (@ (@ (@ (@ (@ tptp.modula581031071_aux_a tptp.inf) tptp.sup) A) B) C) (@ (@ tptp.sup (@ (@ tptp.inf C) (@ (@ (@ (@ (@ tptp.modula1144073633_aux_a tptp.inf) tptp.sup) A) B) C))) (@ (@ (@ (@ (@ tptp.modula1936294176_aux_a tptp.inf) tptp.sup) A) B) C)))) (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.less_eq A))) (= (@ _let_1 (@ (@ tptp.inf B) C)) (and (@ _let_1 B) (@ _let_1 C))))) (forall ((X tptp.a) (Y tptp.a) (Z2 tptp.a)) (let ((_let_1 (@ tptp.less_eq X))) (= (@ _let_1 (@ (@ tptp.inf Y) Z2)) (and (@ _let_1 Y) (@ _let_1 Z2))))) (forall ((X tptp.a) (Y tptp.a) (Z2 tptp.a)) (= (@ (@ tptp.less_eq (@ (@ tptp.sup X) Y)) Z2) (and (@ (@ tptp.less_eq X) Z2) (@ (@ tptp.less_eq Y) Z2)))) (forall ((B tptp.a) (C tptp.a) (A tptp.a)) (= (@ (@ tptp.less_eq (@ (@ tptp.sup B) C)) A) (and (@ (@ tptp.less_eq B) A) (@ (@ tptp.less_eq C) A)))) (forall ((X tptp.a) (Y tptp.a)) (= (@ (@ tptp.inf X) (@ (@ tptp.sup X) Y)) X)) (forall ((X tptp.a) (Y tptp.a)) (= (@ (@ tptp.sup X) (@ (@ tptp.inf X) Y)) X)) _let_6 (forall ((P (-> tptp.a Bool))) (=> (exists ((X4 tptp.a)) (and (@ P X4) (forall ((Y4 tptp.a)) (=> (@ P Y4) (@ (@ tptp.less_eq X4) Y4))) (forall ((Y4 tptp.a)) (=> (and (@ P Y4) (forall ((Ya tptp.a)) (=> (@ P Ya) (@ (@ tptp.less_eq Y4) Ya)))) (= Y4 X4))))) (@ P (@ (@ tptp.least_a tptp.less_eq) P)))) (forall ((P (-> tptp.a Bool)) (Z2 tptp.a)) (=> (exists ((X4 tptp.a)) (and (@ P X4) (forall ((Y4 tptp.a)) (=> (@ P Y4) (@ (@ tptp.less_eq X4) Y4))) (forall ((Y4 tptp.a)) (=> (and (@ P Y4) (forall ((Ya tptp.a)) (=> (@ P Ya) (@ (@ tptp.less_eq Y4) Ya)))) (= Y4 X4))))) (=> (@ P Z2) (@ (@ tptp.less_eq (@ (@ tptp.least_a tptp.less_eq) P)) Z2)))) (forall ((P (-> tptp.a Bool)) (X tptp.a) (Q (-> tptp.a Bool))) (=> (@ P X) (=> (forall ((Y4 tptp.a)) (=> (@ P Y4) (@ (@ tptp.less_eq X) Y4))) (=> (forall ((X3 tptp.a)) (=> (@ P X3) (=> (forall ((Y5 tptp.a)) (=> (@ P Y5) (@ (@ tptp.less_eq X3) Y5))) (@ Q X3)))) (@ Q (@ (@ tptp.least_a tptp.less_eq) P)))))) (forall ((P (-> tptp.a Bool)) (X tptp.a)) (=> (@ P X) (=> (forall ((Y4 tptp.a)) (=> (@ P Y4) (@ (@ tptp.less_eq X) Y4))) (= (@ (@ tptp.least_a tptp.less_eq) P) X)))) (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (= (@ (@ (@ (@ (@ tptp.modula1373251614_aux_a tptp.inf) tptp.sup) A) B) C) (@ (@ tptp.sup (@ (@ tptp.inf B) (@ (@ (@ (@ (@ tptp.modula1144073633_aux_a tptp.inf) tptp.sup) A) B) C))) (@ (@ (@ (@ (@ tptp.modula1936294176_aux_a tptp.inf) tptp.sup) A) B) C)))) _let_5 (= tptp.modula17988509_aux_a tptp.modula17988509_aux_a) (= tptp.modula581031071_aux_a tptp.modula581031071_aux_a) (= tptp.modula1936294176_aux_a tptp.modula1936294176_aux_a) (= tptp.modula1144073633_aux_a tptp.modula1144073633_aux_a) (@ tptp.finite40241356em_a_a tptp.sup) (@ tptp.finite40241356em_a_a tptp.inf) (@ tptp.semigroup_a tptp.sup) (@ tptp.semigroup_a tptp.inf) (@ tptp.semilattice_a tptp.sup) (@ tptp.semilattice_a tptp.inf) (@ tptp.abel_semigroup_a tptp.sup) (@ tptp.abel_semigroup_a tptp.inf) (@ tptp.lattic1885654924_set_a tptp.sup) (@ tptp.lattic1885654924_set_a tptp.inf) (forall ((A3 tptp.set_a)) (= (@ (@ tptp.condit1627435690bove_a tptp.less_eq) A3) (exists ((M tptp.a)) (forall ((X2 tptp.a)) (=> (@ (@ tptp.member_a X2) A3) (@ (@ tptp.less_eq X2) M)))))) (forall ((A3 tptp.set_a)) (= (@ (@ tptp.condit1001553558elow_a tptp.less_eq) A3) (exists ((M2 tptp.a)) (forall ((X2 tptp.a)) (=> (@ (@ tptp.member_a X2) A3) (@ (@ tptp.less_eq M2) X2)))))) (forall ((A3 tptp.set_a) (M3 tptp.a)) (=> (forall ((X3 tptp.a)) (=> (@ (@ tptp.member_a X3) A3) (@ (@ tptp.less_eq M3) X3))) (@ (@ tptp.condit1001553558elow_a tptp.less_eq) A3))) (forall ((A3 tptp.set_a) (M4 tptp.a)) (=> (forall ((X3 tptp.a)) (=> (@ (@ tptp.member_a X3) A3) (@ (@ tptp.less_eq X3) M4))) (@ (@ tptp.condit1627435690bove_a tptp.less_eq) A3))) (= tptp.modula1727524044comp_a tptp.modula1727524044comp_a) (= tptp.modula1373251614_aux_a tptp.modula1373251614_aux_a) (forall ((F (-> tptp.a tptp.a tptp.a))) (=> (@ tptp.abel_semigroup_a F) (@ tptp.semigroup_a F))) (= tptp.lattic1885654924_set_a tptp.semilattice_a) (forall ((F (-> tptp.a tptp.a tptp.a))) (=> (@ tptp.semilattice_a F) (@ tptp.lattic1885654924_set_a F))) (forall ((F (-> tptp.a tptp.a tptp.a)) (B tptp.a) (A tptp.a) (C tptp.a)) (let ((_let_1 (@ F B))) (let ((_let_2 (@ F A))) (=> (@ tptp.abel_semigroup_a F) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C))))))) (forall ((F (-> tptp.a tptp.a tptp.a)) (A tptp.a) (B tptp.a)) (=> (@ tptp.abel_semigroup_a F) (= (@ (@ F A) B) (@ (@ F B) A)))) (forall ((F (-> tptp.a tptp.a tptp.a))) (=> (forall ((A4 tptp.a) (B3 tptp.a) (C2 tptp.a)) (let ((_let_1 (@ F A4))) (= (@ (@ F (@ _let_1 B3)) C2) (@ _let_1 (@ (@ F B3) C2))))) (@ tptp.semigroup_a F))) (forall ((F (-> tptp.a tptp.a tptp.a)) (A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ F A))) (=> (@ tptp.semigroup_a F) (= (@ (@ F (@ _let_1 B)) C) (@ _let_1 (@ (@ F B) C)))))) (= tptp.semigroup_a (lambda ((F2 (-> tptp.a tptp.a tptp.a))) (forall ((A2 tptp.a) (B2 tptp.a) (C3 tptp.a)) (let ((_let_1 (@ F2 A2))) (= (@ (@ F2 (@ _let_1 B2)) C3) (@ _let_1 (@ (@ F2 B2) C3))))))) (forall ((F (-> tptp.a tptp.a tptp.a))) (=> (@ tptp.lattic1885654924_set_a F) (@ tptp.semilattice_a F))) (forall ((F (-> tptp.a tptp.a tptp.a))) (=> (@ tptp.semilattice_a F) (@ tptp.abel_semigroup_a F))) (forall ((B4 tptp.set_a) (A3 tptp.set_a)) (let ((_let_1 (@ tptp.condit1627435690bove_a tptp.less_eq))) (=> (@ _let_1 B4) (=> (@ (@ tptp.ord_less_eq_set_a A3) B4) (@ _let_1 A3))))) (forall ((B4 tptp.set_a) (A3 tptp.set_a)) (let ((_let_1 (@ tptp.condit1001553558elow_a tptp.less_eq))) (=> (@ _let_1 B4) (=> (@ (@ tptp.ord_less_eq_set_a A3) B4) (@ _let_1 A3))))) (forall ((F (-> tptp.a tptp.set_a))) (= (@ (@ tptp.antimono_a_set_a tptp.less_eq) F) (forall ((X2 tptp.a) (Y3 tptp.a)) (=> (@ (@ tptp.less_eq X2) Y3) (@ (@ tptp.ord_less_eq_set_a (@ F Y3)) (@ F X2)))))) (forall ((F (-> tptp.a tptp.set_a))) (=> (forall ((X3 tptp.a) (Y4 tptp.a)) (=> (@ (@ tptp.less_eq X3) Y4) (@ (@ tptp.ord_less_eq_set_a (@ F Y4)) (@ F X3)))) (@ (@ tptp.antimono_a_set_a tptp.less_eq) F))) (forall ((F (-> tptp.a tptp.set_a)) (X tptp.a) (Y tptp.a)) (=> (@ (@ tptp.antimono_a_set_a tptp.less_eq) F) (=> (@ (@ tptp.less_eq X) Y) (@ (@ tptp.ord_less_eq_set_a (@ F Y)) (@ F X))))) (forall ((F (-> tptp.a tptp.set_a)) (X tptp.a) (Y tptp.a)) (=> (@ (@ tptp.antimono_a_set_a tptp.less_eq) F) (=> (@ (@ tptp.less_eq X) Y) (@ (@ tptp.ord_less_eq_set_a (@ F Y)) (@ F X))))) (forall ((F (-> tptp.a tptp.set_a)) (X tptp.a) (Y tptp.a)) (=> (@ (@ tptp.mono_a_set_a tptp.less_eq) F) (=> (@ (@ tptp.less_eq X) Y) (@ (@ tptp.ord_less_eq_set_a (@ F X)) (@ F Y))))) (forall ((F (-> tptp.a tptp.set_a)) (X tptp.a) (Y tptp.a)) (=> (@ (@ tptp.mono_a_set_a tptp.less_eq) F) (=> (@ (@ tptp.less_eq X) Y) (@ (@ tptp.ord_less_eq_set_a (@ F X)) (@ F Y))))) (forall ((F (-> tptp.a tptp.set_a))) (=> (forall ((X3 tptp.a) (Y4 tptp.a)) (=> (@ (@ tptp.less_eq X3) Y4) (@ (@ tptp.ord_less_eq_set_a (@ F X3)) (@ F Y4)))) (@ (@ tptp.mono_a_set_a tptp.less_eq) F))) (forall ((F (-> tptp.a tptp.set_a))) (= (@ (@ tptp.mono_a_set_a tptp.less_eq) F) (forall ((X2 tptp.a) (Y3 tptp.a)) (=> (@ (@ tptp.less_eq X2) Y3) (@ (@ tptp.ord_less_eq_set_a (@ F X2)) (@ F Y3)))))) (forall ((F (-> tptp.a tptp.a tptp.a)) (A tptp.a)) (=> (@ tptp.semilattice_a F) (= (@ (@ F A) A) A))) (forall ((F (-> tptp.a tptp.a tptp.a)) (A tptp.a) (B tptp.a)) (let ((_let_1 (@ F A))) (let ((_let_2 (@ _let_1 B))) (=> (@ tptp.semilattice_a F) (= (@ _let_1 _let_2) _let_2))))) (forall ((F (-> tptp.a tptp.a tptp.a)) (A tptp.a) (B tptp.a)) (let ((_let_1 (@ (@ F A) B))) (=> (@ tptp.semilattice_a F) (= (@ (@ F _let_1) B) _let_1)))) (forall ((A3 tptp.set_a) (B4 tptp.set_a)) (=> (forall ((X3 tptp.a)) (let ((_let_1 (@ tptp.member_a X3))) (=> (@ _let_1 A3) (@ _let_1 B4)))) (@ (@ tptp.ord_less_eq_set_a A3) B4))) (forall ((A3 tptp.set_a) (B4 tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a A3) B4) (=> (@ (@ tptp.ord_less_eq_set_a B4) A3) (= A3 B4)))) (forall ((X tptp.set_a)) (@ (@ tptp.ord_less_eq_set_a X) X)) (= tptp.antimono_a_set_a tptp.antimono_a_set_a) (= tptp.mono_a_set_a tptp.mono_a_set_a) (forall ((B tptp.set_a) (A tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a B) A) (=> (@ (@ tptp.ord_less_eq_set_a A) B) (= A B)))) (= (lambda ((Y2 tptp.set_a) (Z tptp.set_a)) (= Y2 Z)) (lambda ((A2 tptp.set_a) (B2 tptp.set_a)) (and (@ (@ tptp.ord_less_eq_set_a B2) A2) (@ (@ tptp.ord_less_eq_set_a A2) B2)))) (forall ((B tptp.set_a) (A tptp.set_a) (C tptp.set_a)) (let ((_let_1 (@ tptp.ord_less_eq_set_a C))) (=> (@ (@ tptp.ord_less_eq_set_a B) A) (=> (@ _let_1 B) (@ _let_1 A))))) (forall ((A tptp.set_a)) (@ (@ tptp.ord_less_eq_set_a A) A)) (forall ((X tptp.set_a) (Y tptp.set_a) (Z2 tptp.set_a)) (let ((_let_1 (@ tptp.ord_less_eq_set_a X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_set_a Y) Z2) (@ _let_1 Z2))))) (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)))) (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) (=> (= B C) (@ _let_1 C))))) (forall ((A tptp.set_a) (B tptp.set_a) (C tptp.set_a)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_set_a B) C) (@ (@ tptp.ord_less_eq_set_a A) C)))) (= (lambda ((Y2 tptp.set_a) (Z tptp.set_a)) (= Y2 Z)) (lambda ((A2 tptp.set_a) (B2 tptp.set_a)) (and (@ (@ tptp.ord_less_eq_set_a A2) B2) (@ (@ tptp.ord_less_eq_set_a B2) A2)))) (forall ((Y tptp.set_a) (X tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a Y) X) (= (@ (@ tptp.ord_less_eq_set_a X) Y) (= X Y)))) (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))))) (forall ((X tptp.set_a) (Y tptp.set_a)) (=> (= X Y) (@ (@ tptp.ord_less_eq_set_a X) Y))) (forall ((X tptp.set_a) (Y tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a X) Y) (=> (@ (@ tptp.ord_less_eq_set_a Y) X) (= X Y)))) (= (lambda ((Y2 tptp.set_a) (Z tptp.set_a)) (= Y2 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)))) (forall ((A tptp.set_a) (B tptp.set_a) (F (-> tptp.set_a tptp.set_a)) (C tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.set_a) (Y4 tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a X3) Y4) (@ (@ tptp.ord_less_eq_set_a (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_set_a (@ F A)) C))))) (forall ((A tptp.set_a) (F (-> tptp.set_a tptp.set_a)) (B tptp.set_a) (C tptp.set_a)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_set_a B) C) (=> (forall ((X3 tptp.set_a) (Y4 tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a X3) Y4) (@ (@ tptp.ord_less_eq_set_a (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_set_a A) (@ F C)))))) (forall ((A tptp.set_a) (B tptp.set_a) (F (-> tptp.set_a tptp.set_a)) (C tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a A) B) (=> (@ (@ tptp.ord_less_eq_set_a (@ F B)) C) (=> (forall ((X3 tptp.set_a) (Y4 tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a X3) Y4) (@ (@ tptp.ord_less_eq_set_a (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_set_a (@ F A)) C))))) (forall ((A tptp.set_a) (F (-> tptp.set_a tptp.set_a)) (B tptp.set_a) (C tptp.set_a)) (let ((_let_1 (@ tptp.ord_less_eq_set_a A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_set_a B) C) (=> (forall ((X3 tptp.set_a) (Y4 tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_set_a X3) Y4) (@ (@ tptp.ord_less_eq_set_a (@ F X3)) (@ F Y4)))) (@ _let_1 (@ F C))))))) (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))))) (= (lambda ((Y2 tptp.set_a) (Z tptp.set_a)) (= Y2 Z)) (lambda ((A5 tptp.set_a) (B5 tptp.set_a)) (and (@ (@ tptp.ord_less_eq_set_a A5) B5) (@ (@ tptp.ord_less_eq_set_a B5) A5)))) (forall ((A3 tptp.set_a) (B4 tptp.set_a) (C4 tptp.set_a)) (let ((_let_1 (@ tptp.ord_less_eq_set_a A3))) (=> (@ _let_1 B4) (=> (@ (@ tptp.ord_less_eq_set_a B4) C4) (@ _let_1 C4))))) (forall ((P (-> tptp.a Bool)) (Q (-> tptp.a Bool))) (=> (forall ((X3 tptp.a)) (=> (@ P X3) (@ Q X3))) (@ (@ tptp.ord_less_eq_set_a (@ tptp.collect_a P)) (@ tptp.collect_a Q)))) (forall ((A3 tptp.set_a)) (@ (@ tptp.ord_less_eq_set_a A3) A3)) (= tptp.ord_less_eq_set_a (lambda ((A5 tptp.set_a) (B5 tptp.set_a)) (forall ((T tptp.a)) (let ((_let_1 (@ tptp.member_a T))) (=> (@ _let_1 A5) (@ _let_1 B5)))))) (forall ((A3 tptp.set_a) (B4 tptp.set_a)) (=> (= A3 B4) (@ (@ tptp.ord_less_eq_set_a B4) A3))) (forall ((A3 tptp.set_a) (B4 tptp.set_a)) (=> (= A3 B4) (@ (@ tptp.ord_less_eq_set_a A3) B4))) (= tptp.ord_less_eq_set_a (lambda ((A5 tptp.set_a) (B5 tptp.set_a)) (forall ((X2 tptp.a)) (let ((_let_1 (@ tptp.member_a X2))) (=> (@ _let_1 A5) (@ _let_1 B5)))))) (forall ((A3 tptp.set_a) (B4 tptp.set_a)) (=> (= A3 B4) (not (=> (@ (@ tptp.ord_less_eq_set_a A3) B4) (not (@ (@ tptp.ord_less_eq_set_a B4) A3)))))) (forall ((A3 tptp.set_a) (B4 tptp.set_a) (C tptp.a)) (let ((_let_1 (@ tptp.member_a C))) (=> (@ (@ tptp.ord_less_eq_set_a A3) B4) (=> (@ _let_1 A3) (@ _let_1 B4))))) (forall ((A3 tptp.set_a) (B4 tptp.set_a) (X tptp.a)) (let ((_let_1 (@ tptp.member_a X))) (=> (@ (@ tptp.ord_less_eq_set_a A3) B4) (=> (@ _let_1 A3) (@ _let_1 B4))))) (= tptp.least_a tptp.least_a) (= tptp.greatest_a tptp.greatest_a) (= tptp.min_a tptp.min_a) (= tptp.max_a tptp.max_a) (= tptp.min_a (lambda ((Less_eq (-> tptp.a tptp.a Bool)) (A2 tptp.a) (B2 tptp.a)) (@ (@ (@ tptp.if_a (@ (@ Less_eq A2) B2)) A2) B2))) (= tptp.max_a (lambda ((Less_eq (-> tptp.a tptp.a Bool)) (A2 tptp.a) (B2 tptp.a)) (@ (@ (@ tptp.if_a (@ (@ Less_eq A2) B2)) B2) A2))) (forall ((F (-> tptp.a tptp.set_a)) (A3 tptp.a) (B4 tptp.a)) (=> (@ (@ tptp.mono_a_set_a tptp.less_eq) F) (@ (@ tptp.ord_less_eq_set_a (@ F (@ (@ tptp.inf A3) B4))) (@ (@ tptp.inf_inf_set_a (@ F A3)) (@ F B4))))) (forall ((F (-> tptp.a tptp.set_a)) (A3 tptp.a) (B4 tptp.a)) (=> (@ (@ tptp.mono_a_set_a tptp.less_eq) F) (@ (@ tptp.ord_less_eq_set_a (@ (@ tptp.sup_sup_set_a (@ F A3)) (@ F B4))) (@ F (@ (@ tptp.sup A3) B4))))) (forall ((A3 tptp.set_a)) (=> (@ tptp.finite_finite_a A3) (@ (@ tptp.condit1627435690bove_a tptp.less_eq) A3))) (forall ((A3 tptp.set_a) (A tptp.a)) (=> (@ tptp.finite_finite_a A3) (=> (@ (@ tptp.member_a A) A3) (exists ((X3 tptp.a)) (and (@ (@ tptp.member_a X3) A3) (@ (@ tptp.less_eq X3) A) (forall ((Xa tptp.a)) (=> (@ (@ tptp.member_a Xa) A3) (=> (@ (@ tptp.less_eq Xa) X3) (= X3 Xa))))))))) (forall ((A3 tptp.set_a) (A tptp.a)) (=> (@ tptp.finite_finite_a A3) (=> (@ (@ tptp.member_a A) A3) (exists ((X3 tptp.a)) (and (@ (@ tptp.member_a X3) A3) (@ (@ tptp.less_eq A) X3) (forall ((Xa tptp.a)) (=> (@ (@ tptp.member_a Xa) A3) (=> (@ (@ tptp.less_eq X3) Xa) (= X3 Xa))))))))) (forall ((B4 tptp.set_a) (A3 tptp.set_a)) (let ((_let_1 (@ tptp.condit1001553558elow_a tptp.less_eq))) (=> (@ _let_1 B4) (@ _let_1 (@ (@ tptp.inf_inf_set_a A3) B4))))) (forall ((A3 tptp.set_a) (B4 tptp.set_a)) (let ((_let_1 (@ tptp.condit1001553558elow_a tptp.less_eq))) (=> (@ _let_1 A3) (@ _let_1 (@ (@ tptp.inf_inf_set_a A3) B4))))) (forall ((B4 tptp.set_a) (A3 tptp.set_a)) (let ((_let_1 (@ tptp.condit1627435690bove_a tptp.less_eq))) (=> (@ _let_1 B4) (@ _let_1 (@ (@ tptp.inf_inf_set_a A3) B4))))) (forall ((A3 tptp.set_a) (B4 tptp.set_a)) (let ((_let_1 (@ tptp.condit1627435690bove_a tptp.less_eq))) (=> (@ _let_1 A3) (@ _let_1 (@ (@ tptp.inf_inf_set_a A3) B4))))) (forall ((A3 tptp.set_a)) (=> (@ tptp.finite_finite_a A3) (@ (@ tptp.condit1001553558elow_a tptp.less_eq) A3))) (forall ((A3 tptp.set_a) (B4 tptp.set_a) (C4 tptp.set_a)) (= (@ (@ tptp.ord_less_eq_set_a (@ (@ tptp.sup_sup_set_a A3) B4)) C4) (and (@ (@ tptp.ord_less_eq_set_a A3) C4) (@ (@ tptp.ord_less_eq_set_a B4) C4)))) (forall ((C4 tptp.set_a) (A3 tptp.set_a) (B4 tptp.set_a)) (let ((_let_1 (@ tptp.ord_less_eq_set_a C4))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_a A3) B4)) (and (@ _let_1 A3) (@ _let_1 B4))))) (forall ((X tptp.set_a) (Y tptp.set_a)) (let ((_let_1 (@ (@ tptp.inf_inf_set_a X) Y))) (= (@ (@ tptp.inf_inf_set_a _let_1) Y) _let_1))) (forall ((A tptp.set_a) (B tptp.set_a)) (let ((_let_1 (@ (@ tptp.inf_inf_set_a A) B))) (= (@ (@ tptp.inf_inf_set_a _let_1) B) _let_1))) (forall ((X tptp.set_a) (Y tptp.set_a)) (let ((_let_1 (@ tptp.inf_inf_set_a X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))) (forall ((A tptp.set_a) (B tptp.set_a)) (let ((_let_1 (@ tptp.inf_inf_set_a A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))) (forall ((X tptp.set_a)) (= (@ (@ tptp.inf_inf_set_a X) X) X)) (forall ((A tptp.set_a)) (= (@ (@ tptp.inf_inf_set_a A) A) A)) (forall ((A tptp.set_a) (B tptp.set_a)) (let ((_let_1 (@ (@ tptp.sup_sup_set_a A) B))) (= (@ (@ tptp.sup_sup_set_a _let_1) B) _let_1))) (forall ((X tptp.set_a) (Y tptp.set_a)) (let ((_let_1 (@ tptp.sup_sup_set_a X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))) (forall ((A tptp.set_a) (B tptp.set_a)) (let ((_let_1 (@ tptp.sup_sup_set_a A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))) (forall ((X tptp.set_a)) (= (@ (@ tptp.sup_sup_set_a X) X) X)) (forall ((A tptp.set_a)) (= (@ (@ tptp.sup_sup_set_a A) A) A)) (forall ((X tptp.set_a) (Y tptp.set_a) (Z2 tptp.set_a)) (let ((_let_1 (@ tptp.ord_less_eq_set_a X))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_a Y) Z2)) (and (@ _let_1 Y) (@ _let_1 Z2))))) (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 (@ (@ tptp.inf_inf_set_a B) C)) (and (@ _let_1 B) (@ _let_1 C))))) (forall ((X tptp.set_a) (Y tptp.set_a) (Z2 tptp.set_a)) (= (@ (@ tptp.ord_less_eq_set_a (@ (@ tptp.sup_sup_set_a X) Y)) Z2) (and (@ (@ tptp.ord_less_eq_set_a X) Z2) (@ (@ tptp.ord_less_eq_set_a Y) Z2)))) (forall ((B tptp.set_a) (C tptp.set_a) (A tptp.set_a)) (= (@ (@ tptp.ord_less_eq_set_a (@ (@ tptp.sup_sup_set_a B) C)) A) (and (@ (@ tptp.ord_less_eq_set_a B) A) (@ (@ tptp.ord_less_eq_set_a C) A)))) (forall ((X tptp.set_a) (Y tptp.set_a)) (= (@ (@ tptp.sup_sup_set_a X) (@ (@ tptp.inf_inf_set_a X) Y)) X)) (forall ((X tptp.set_a) (Y tptp.set_a)) (= (@ (@ tptp.inf_inf_set_a X) (@ (@ tptp.sup_sup_set_a X) Y)) X)) (forall ((P Bool)) (or (= P true) (= P false))) (forall ((X tptp.a) (Y tptp.a)) (= (@ (@ (@ tptp.if_a false) X) Y) Y)) (forall ((X tptp.a) (Y tptp.a)) (= (@ (@ (@ tptp.if_a true) X) Y) X)) _let_4 _let_3 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.95/1.12 )
% 0.95/1.12 % SZS output end Proof for ITP120^1
% 0.95/1.12 % cvc5---1.0.5 exiting
% 0.95/1.13 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------