%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP073^2 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n027.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 : Wed Feb 25 08:55:20 AM UTC 2026
% Result : Theorem 141.08s 21.38s
% Output : Refutation 141.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ITP073^2 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n027.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 08:25:22 EST 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.28/0.45 ---- Original DTF file ---
% 0.28/0.45 thf(spec,logic,$$dhol).
% 0.28/0.45 %------------------------------------------------------------------------------
% 0.28/0.45 % File : ITP073^2 : TPTP v9.2.1. Released v7.5.0.
% 0.28/0.45 % Domain : Interactive Theorem Proving
% 0.28/0.45 % Problem : Sledgehammer HF problem prob_473__5331678_1
% 0.28/0.45 % Version : Especial.
% 0.28/0.45 % English :
% 0.28/0.45
% 0.28/0.45 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.28/0.45 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.28/0.45 % Source : [Des21]
% 0.28/0.45 % Names : HF/prob_473__5331678_1 [Des21]
% 0.28/0.45
% 0.28/0.45 % Status : Theorem
% 0.28/0.45 % Rating : 0.33 v9.0.0, 0.67 v8.1.0, 0.50 v7.5.0
% 0.28/0.45 % Syntax : Number of formulae : 324 ( 67 unt; 43 typ; 0 def)
% 0.28/0.45 % Number of atoms : 977 ( 194 equ; 0 cnn)
% 0.28/0.45 % Maximal formula atoms : 13 ( 3 avg)
% 0.28/0.45 % Number of connectives : 3417 ( 95 ~; 21 |; 81 &;2637 @)
% 0.28/0.45 % ( 0 <=>; 583 =>; 0 <=; 0 <~>)
% 0.28/0.45 % Maximal formula depth : 21 ( 9 avg)
% 0.28/0.45 % Number of types : 3 ( 2 usr)
% 0.28/0.45 % Number of type conns : 259 ( 259 >; 0 *; 0 +; 0 <<)
% 0.28/0.45 % Number of symbols : 44 ( 41 usr; 4 con; 0-4 aty)
% 0.28/0.45 % Number of variables : 1111 ( 51 ^; 961 !; 66 ?;1111 :)
% 0.28/0.45 % ( 33 !>; 0 ?*; 0 @-; 0 @+)
% 0.28/0.45 % SPC : TH1_THM_EQU_NAR
% 0.28/0.45
% 0.28/0.45 % Comments : This file was generated by Sledgehammer 2021-02-23 16:22:11.962
% 0.28/0.45 %------------------------------------------------------------------------------
% 0.28/0.45 % Could-be-implicit typings (3)
% 0.28/0.45 thf(ty_t_HF__Mirabelle__fsbjehakzm_Ohf,type,
% 0.28/0.45 hF_Mirabelle_hf: $tType ).
% 0.28/0.45
% 0.28/0.45 thf(ty_t_Set_Oset,type,
% 0.28/0.45 set: $tType > $tType ).
% 0.28/0.45
% 0.28/0.45 thf(ty_t_Nat_Onat,type,
% 0.28/0.45 nat: $tType ).
% 0.28/0.45
% 0.28/0.45 % Explicit typings (40)
% 0.28/0.45 thf(sy_cl_HOL_Otype,type,
% 0.28/0.45 type:
% 0.28/0.45 !>[A: $tType] : $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_cl_Orderings_Oord,type,
% 0.28/0.45 ord:
% 0.28/0.45 !>[A: $tType] : $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_cl_Orderings_Oorder,type,
% 0.28/0.45 order:
% 0.28/0.45 !>[A: $tType] : $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_cl_Orderings_Ono__bot,type,
% 0.28/0.45 no_bot:
% 0.28/0.45 !>[A: $tType] : $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_cl_Orderings_Ono__top,type,
% 0.28/0.45 no_top:
% 0.28/0.45 !>[A: $tType] : $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_cl_Finite__Set_Ofinite,type,
% 0.28/0.45 finite_finite:
% 0.28/0.45 !>[A: $tType] : $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_cl_Orderings_Olinorder,type,
% 0.28/0.45 linorder:
% 0.28/0.45 !>[A: $tType] : $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_cl_Orderings_Opreorder,type,
% 0.28/0.45 preorder:
% 0.28/0.45 !>[A: $tType] : $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_cl_Orderings_Owellorder,type,
% 0.28/0.45 wellorder:
% 0.28/0.45 !>[A: $tType] : $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_cl_Orderings_Odense__order,type,
% 0.28/0.45 dense_order:
% 0.28/0.45 !>[A: $tType] : $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_cl_Rings_Olinordered__idom,type,
% 0.28/0.45 linordered_idom:
% 0.28/0.45 !>[A: $tType] : $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_cl_Fields_Olinordered__field,type,
% 0.28/0.45 linordered_field:
% 0.28/0.45 !>[A: $tType] : $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_cl_Orderings_Odense__linorder,type,
% 0.28/0.45 dense_linorder:
% 0.28/0.45 !>[A: $tType] : $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add,type,
% 0.28/0.45 canoni770627133id_add:
% 0.28/0.45 !>[A: $tType] : $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_cl_Conditionally__Complete__Lattices_Olinear__continuum,type,
% 0.28/0.45 condit1656338222tinuum:
% 0.28/0.45 !>[A: $tType] : $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_cl_Conditionally__Complete__Lattices_Oconditionally__complete__linorder,type,
% 0.28/0.45 condit1037483654norder:
% 0.28/0.45 !>[A: $tType] : $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Finite__Set_OFpow,type,
% 0.28/0.45 finite_Fpow:
% 0.28/0.45 !>[A: $tType] : ( ( set @ A ) > ( set @ ( set @ A ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Finite__Set_Ocard,type,
% 0.28/0.45 finite_card:
% 0.28/0.45 !>[B: $tType] : ( ( set @ B ) > nat ) ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Finite__Set_Ofinite,type,
% 0.28/0.45 finite_finite2:
% 0.28/0.45 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Fun_Oinj__on,type,
% 0.28/0.45 inj_on:
% 0.28/0.45 !>[A: $tType,B: $tType] : ( ( A > B ) > ( set @ A ) > $o ) ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Groups_Ozero__class_Ozero,type,
% 0.28/0.45 zero_zero:
% 0.28/0.45 !>[A: $tType] : A ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_HF__Mirabelle__fsbjehakzm_OHCollect,type,
% 0.28/0.45 hF_Mir1687042746ollect: ( hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf > hF_Mirabelle_hf ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_HF__Mirabelle__fsbjehakzm_OHF,type,
% 0.28/0.45 hF_Mirabelle_HF: ( set @ hF_Mirabelle_hf ) > hF_Mirabelle_hf ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_HF__Mirabelle__fsbjehakzm_OHUnion,type,
% 0.28/0.45 hF_Mirabelle_HUnion: hF_Mirabelle_hf > hF_Mirabelle_hf ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_HF__Mirabelle__fsbjehakzm_OPrimReplace,type,
% 0.28/0.45 hF_Mir569462966eplace: hF_Mirabelle_hf > ( hF_Mirabelle_hf > hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_HF__Mirabelle__fsbjehakzm_ORepFun,type,
% 0.28/0.45 hF_Mirabelle_RepFun: hF_Mirabelle_hf > ( hF_Mirabelle_hf > hF_Mirabelle_hf ) > hF_Mirabelle_hf ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_HF__Mirabelle__fsbjehakzm_OReplace,type,
% 0.28/0.45 hF_Mirabelle_Replace: hF_Mirabelle_hf > ( hF_Mirabelle_hf > hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_HF__Mirabelle__fsbjehakzm_Ohfset,type,
% 0.28/0.45 hF_Mirabelle_hfset: hF_Mirabelle_hf > ( set @ hF_Mirabelle_hf ) ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_HF__Mirabelle__fsbjehakzm_Ohmem,type,
% 0.28/0.45 hF_Mirabelle_hmem: hF_Mirabelle_hf > hF_Mirabelle_hf > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Orderings_Oord__class_Oless,type,
% 0.28/0.45 ord_less:
% 0.28/0.45 !>[A: $tType] : ( A > A > $o ) ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.28/0.45 ord_less_eq:
% 0.28/0.45 !>[A: $tType] : ( A > A > $o ) ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Orderings_Oorder__class_OGreatest,type,
% 0.28/0.45 order_Greatest:
% 0.28/0.45 !>[A: $tType] : ( ( A > $o ) > A ) ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Orderings_Oorder__class_Oantimono,type,
% 0.28/0.45 order_antimono:
% 0.28/0.45 !>[A: $tType,B: $tType] : ( ( A > B ) > $o ) ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Orderings_Oordering,type,
% 0.28/0.45 ordering:
% 0.28/0.45 !>[A: $tType] : ( ( A > A > $o ) > ( A > A > $o ) > $o ) ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Set_OCollect,type,
% 0.28/0.45 collect:
% 0.28/0.45 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Set_Oimage,type,
% 0.28/0.45 image:
% 0.28/0.45 !>[A: $tType,B: $tType] : ( ( A > B ) > ( set @ A ) > ( set @ B ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan,type,
% 0.28/0.45 set_or578182835ssThan:
% 0.28/0.45 !>[A: $tType] : ( A > A > ( set @ A ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_member,type,
% 0.28/0.45 member:
% 0.28/0.45 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.28/0.45
% 0.28/0.45 thf(sy_v_A,type,
% 0.28/0.45 a: hF_Mirabelle_hf ).
% 0.28/0.45
% 0.28/0.45 thf(sy_v_B,type,
% 0.28/0.45 b: hF_Mirabelle_hf ).
% 0.28/0.45
% 0.28/0.45 % Relevant facts (255)
% 0.28/0.45 thf(fact_0_hf__equalityI,axiom,
% 0.28/0.45 ! [A2: hF_Mirabelle_hf,B2: hF_Mirabelle_hf] :
% 0.28/0.45 ( ! [X: hF_Mirabelle_hf] :
% 0.28/0.45 ( ( hF_Mirabelle_hmem @ X @ A2 )
% 0.28/0.45 = ( hF_Mirabelle_hmem @ X @ B2 ) )
% 0.28/0.45 => ( A2 = B2 ) ) ).
% 0.28/0.45
% 0.28/0.45 % hf_equalityI
% 0.28/0.45 thf(fact_1_hf__ext,axiom,
% 0.28/0.45 ( ( ^ [Y: hF_Mirabelle_hf,Z: hF_Mirabelle_hf] : ( Y = Z ) )
% 0.28/0.45 = ( ^ [A3: hF_Mirabelle_hf,B3: hF_Mirabelle_hf] :
% 0.28/0.45 ! [X2: hF_Mirabelle_hf] :
% 0.28/0.45 ( ( hF_Mirabelle_hmem @ X2 @ A3 )
% 0.28/0.45 = ( hF_Mirabelle_hmem @ X2 @ B3 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % hf_ext
% 0.28/0.45 thf(fact_2_replacement,axiom,
% 0.28/0.45 ! [X3: hF_Mirabelle_hf,R: hF_Mirabelle_hf > hF_Mirabelle_hf > $o] :
% 0.28/0.45 ( ! [U: hF_Mirabelle_hf,V: hF_Mirabelle_hf,V2: hF_Mirabelle_hf] :
% 0.28/0.45 ( ( hF_Mirabelle_hmem @ U @ X3 )
% 0.28/0.45 => ( ( R @ U @ V )
% 0.28/0.45 => ( ( R @ U @ V2 )
% 0.28/0.45 => ( V2 = V ) ) ) )
% 0.28/0.45 => ? [Z2: hF_Mirabelle_hf] :
% 0.28/0.45 ! [V3: hF_Mirabelle_hf] :
% 0.28/0.45 ( ( hF_Mirabelle_hmem @ V3 @ Z2 )
% 0.28/0.45 = ( ? [U2: hF_Mirabelle_hf] :
% 0.28/0.45 ( ( hF_Mirabelle_hmem @ U2 @ X3 )
% 0.28/0.45 & ( R @ U2 @ V3 ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % replacement
% 0.28/0.45 thf(fact_3_binary__union,axiom,
% 0.28/0.45 ! [X3: hF_Mirabelle_hf,Y2: hF_Mirabelle_hf] :
% 0.28/0.45 ? [Z2: hF_Mirabelle_hf] :
% 0.28/0.45 ! [U3: hF_Mirabelle_hf] :
% 0.28/0.45 ( ( hF_Mirabelle_hmem @ U3 @ Z2 )
% 0.28/0.45 = ( ( hF_Mirabelle_hmem @ U3 @ X3 )
% 0.28/0.45 | ( hF_Mirabelle_hmem @ U3 @ Y2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % binary_union
% 0.28/0.45 thf(fact_4_union__of__set,axiom,
% 0.28/0.45 ! [X3: hF_Mirabelle_hf] :
% 0.28/0.45 ? [Z2: hF_Mirabelle_hf] :
% 0.28/0.45 ! [U3: hF_Mirabelle_hf] :
% 0.28/0.45 ( ( hF_Mirabelle_hmem @ U3 @ Z2 )
% 0.28/0.45 = ( ? [Y3: hF_Mirabelle_hf] :
% 0.28/0.45 ( ( hF_Mirabelle_hmem @ Y3 @ X3 )
% 0.28/0.45 & ( hF_Mirabelle_hmem @ U3 @ Y3 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % union_of_set
% 0.28/0.45 thf(fact_5_comprehension,axiom,
% 0.28/0.45 ! [X3: hF_Mirabelle_hf,P: hF_Mirabelle_hf > $o] :
% 0.28/0.45 ? [Z2: hF_Mirabelle_hf] :
% 0.28/0.45 ! [U3: hF_Mirabelle_hf] :
% 0.28/0.45 ( ( hF_Mirabelle_hmem @ U3 @ Z2 )
% 0.28/0.45 = ( ( hF_Mirabelle_hmem @ U3 @ X3 )
% 0.28/0.45 & ( P @ U3 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % comprehension
% 0.28/0.45 thf(fact_6_less__eq__hf__def,axiom,
% 0.28/0.45 ( ( ord_less_eq @ hF_Mirabelle_hf )
% 0.28/0.45 = ( ^ [A4: hF_Mirabelle_hf,B4: hF_Mirabelle_hf] :
% 0.28/0.45 ! [X2: hF_Mirabelle_hf] :
% 0.28/0.45 ( ( hF_Mirabelle_hmem @ X2 @ A4 )
% 0.28/0.45 => ( hF_Mirabelle_hmem @ X2 @ B4 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % less_eq_hf_def
% 0.28/0.45 thf(fact_7_replacement__fun,axiom,
% 0.28/0.45 ! [X3: hF_Mirabelle_hf,F: hF_Mirabelle_hf > hF_Mirabelle_hf] :
% 0.28/0.45 ? [Z2: hF_Mirabelle_hf] :
% 0.28/0.45 ! [V3: hF_Mirabelle_hf] :
% 0.28/0.45 ( ( hF_Mirabelle_hmem @ V3 @ Z2 )
% 0.28/0.45 = ( ? [U2: hF_Mirabelle_hf] :
% 0.28/0.45 ( ( hF_Mirabelle_hmem @ U2 @ X3 )
% 0.28/0.45 & ( V3
% 0.28/0.45 = ( F @ U2 ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % replacement_fun
% 0.28/0.45 thf(fact_8_order__refl,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( preorder @ A )
% 0.28/0.45 => ! [X3: A] : ( ord_less_eq @ A @ X3 @ X3 ) ) ).
% 0.28/0.45
% 0.28/0.45 % order_refl
% 0.28/0.45 thf(fact_9_PrimReplace__iff,axiom,
% 0.28/0.45 ! [A5: hF_Mirabelle_hf,R: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,V4: hF_Mirabelle_hf] :
% 0.28/0.45 ( ! [U: hF_Mirabelle_hf,V: hF_Mirabelle_hf,V2: hF_Mirabelle_hf] :
% 0.28/0.45 ( ( hF_Mirabelle_hmem @ U @ A5 )
% 0.28/0.45 => ( ( R @ U @ V )
% 0.28/0.45 => ( ( R @ U @ V2 )
% 0.28/0.45 => ( V2 = V ) ) ) )
% 0.28/0.45 => ( ( hF_Mirabelle_hmem @ V4 @ ( hF_Mir569462966eplace @ A5 @ R ) )
% 0.28/0.45 = ( ? [U2: hF_Mirabelle_hf] :
% 0.28/0.45 ( ( hF_Mirabelle_hmem @ U2 @ A5 )
% 0.28/0.45 & ( R @ U2 @ V4 ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % PrimReplace_iff
% 0.28/0.45 thf(fact_10_HCollect__iff,axiom,
% 0.28/0.45 ! [X3: hF_Mirabelle_hf,P: hF_Mirabelle_hf > $o,A5: hF_Mirabelle_hf] :
% 0.28/0.45 ( ( hF_Mirabelle_hmem @ X3 @ ( hF_Mir1687042746ollect @ P @ A5 ) )
% 0.28/0.45 = ( ( P @ X3 )
% 0.28/0.45 & ( hF_Mirabelle_hmem @ X3 @ A5 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % HCollect_iff
% 0.28/0.45 thf(fact_11_HUnion__iff,axiom,
% 0.28/0.45 ! [X3: hF_Mirabelle_hf,A5: hF_Mirabelle_hf] :
% 0.28/0.45 ( ( hF_Mirabelle_hmem @ X3 @ ( hF_Mirabelle_HUnion @ A5 ) )
% 0.28/0.45 = ( ? [Y3: hF_Mirabelle_hf] :
% 0.28/0.45 ( ( hF_Mirabelle_hmem @ Y3 @ A5 )
% 0.28/0.45 & ( hF_Mirabelle_hmem @ X3 @ Y3 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % HUnion_iff
% 0.28/0.45 thf(fact_12_Replace__iff,axiom,
% 0.28/0.45 ! [V4: hF_Mirabelle_hf,A5: hF_Mirabelle_hf,R: hF_Mirabelle_hf > hF_Mirabelle_hf > $o] :
% 0.28/0.45 ( ( hF_Mirabelle_hmem @ V4 @ ( hF_Mirabelle_Replace @ A5 @ R ) )
% 0.28/0.45 = ( ? [U2: hF_Mirabelle_hf] :
% 0.28/0.45 ( ( hF_Mirabelle_hmem @ U2 @ A5 )
% 0.28/0.45 & ( R @ U2 @ V4 )
% 0.28/0.45 & ! [Y3: hF_Mirabelle_hf] :
% 0.28/0.45 ( ( R @ U2 @ Y3 )
% 0.28/0.45 => ( Y3 = V4 ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % Replace_iff
% 0.28/0.45 thf(fact_13_le__funD,axiom,
% 0.28/0.45 ! [B: $tType,A: $tType] :
% 0.28/0.45 ( ( ord @ B )
% 0.28/0.45 => ! [F: A > B,G: A > B,X3: A] :
% 0.28/0.45 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 0.28/0.45 => ( ord_less_eq @ B @ ( F @ X3 ) @ ( G @ X3 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % le_funD
% 0.28/0.45 thf(fact_14_le__funE,axiom,
% 0.28/0.45 ! [B: $tType,A: $tType] :
% 0.28/0.45 ( ( ord @ B )
% 0.28/0.45 => ! [F: A > B,G: A > B,X3: A] :
% 0.28/0.45 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 0.28/0.45 => ( ord_less_eq @ B @ ( F @ X3 ) @ ( G @ X3 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % le_funE
% 0.28/0.45 thf(fact_15_le__funI,axiom,
% 0.28/0.45 ! [B: $tType,A: $tType] :
% 0.28/0.45 ( ( ord @ B )
% 0.28/0.45 => ! [F: A > B,G: A > B] :
% 0.28/0.45 ( ! [X: A] : ( ord_less_eq @ B @ ( F @ X ) @ ( G @ X ) )
% 0.28/0.45 => ( ord_less_eq @ ( A > B ) @ F @ G ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % le_funI
% 0.28/0.45 thf(fact_16_le__fun__def,axiom,
% 0.28/0.45 ! [B: $tType,A: $tType] :
% 0.28/0.45 ( ( ord @ B )
% 0.28/0.45 => ( ( ord_less_eq @ ( A > B ) )
% 0.28/0.45 = ( ^ [F2: A > B,G2: A > B] :
% 0.28/0.45 ! [X2: A] : ( ord_less_eq @ B @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % le_fun_def
% 0.28/0.45 thf(fact_17_order__subst1,axiom,
% 0.28/0.45 ! [A: $tType,B: $tType] :
% 0.28/0.45 ( ( ( order @ B )
% 0.28/0.45 & ( order @ A ) )
% 0.28/0.45 => ! [A2: A,F: B > A,B2: B,C: B] :
% 0.28/0.45 ( ( ord_less_eq @ A @ A2 @ ( F @ B2 ) )
% 0.28/0.45 => ( ( ord_less_eq @ B @ B2 @ C )
% 0.28/0.45 => ( ! [X: B,Y4: B] :
% 0.28/0.45 ( ( ord_less_eq @ B @ X @ Y4 )
% 0.28/0.45 => ( ord_less_eq @ A @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.28/0.45 => ( ord_less_eq @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % order_subst1
% 0.28/0.45 thf(fact_18_order__subst2,axiom,
% 0.28/0.45 ! [A: $tType,C2: $tType] :
% 0.28/0.45 ( ( ( order @ C2 )
% 0.28/0.45 & ( order @ A ) )
% 0.28/0.45 => ! [A2: A,B2: A,F: A > C2,C: C2] :
% 0.28/0.45 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.28/0.45 => ( ( ord_less_eq @ C2 @ ( F @ B2 ) @ C )
% 0.28/0.45 => ( ! [X: A,Y4: A] :
% 0.28/0.45 ( ( ord_less_eq @ A @ X @ Y4 )
% 0.28/0.45 => ( ord_less_eq @ C2 @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.28/0.45 => ( ord_less_eq @ C2 @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % order_subst2
% 0.28/0.45 thf(fact_19_verit__la__disequality,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( linorder @ A )
% 0.28/0.45 => ! [A2: A,B2: A] :
% 0.28/0.45 ( ( A2 = B2 )
% 0.28/0.45 | ~ ( ord_less_eq @ A @ A2 @ B2 )
% 0.28/0.45 | ~ ( ord_less_eq @ A @ B2 @ A2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % verit_la_disequality
% 0.28/0.45 thf(fact_20_Replace__cong,axiom,
% 0.28/0.45 ! [A5: hF_Mirabelle_hf,B5: hF_Mirabelle_hf,P: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,Q: hF_Mirabelle_hf > hF_Mirabelle_hf > $o] :
% 0.28/0.45 ( ( A5 = B5 )
% 0.28/0.45 => ( ! [X: hF_Mirabelle_hf,Y4: hF_Mirabelle_hf] :
% 0.28/0.45 ( ( hF_Mirabelle_hmem @ X @ B5 )
% 0.28/0.45 => ( ( P @ X @ Y4 )
% 0.28/0.45 = ( Q @ X @ Y4 ) ) )
% 0.28/0.45 => ( ( hF_Mirabelle_Replace @ A5 @ P )
% 0.28/0.45 = ( hF_Mirabelle_Replace @ B5 @ Q ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % Replace_cong
% 0.28/0.45 thf(fact_21_dual__order_Oantisym,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( order @ A )
% 0.28/0.45 => ! [B2: A,A2: A] :
% 0.28/0.45 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.28/0.45 => ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.28/0.45 => ( A2 = B2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % dual_order.antisym
% 0.28/0.45 thf(fact_22_dual__order_Oeq__iff,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( order @ A )
% 0.28/0.45 => ( ( ^ [Y: A,Z: A] : ( Y = Z ) )
% 0.28/0.45 = ( ^ [A3: A,B3: A] :
% 0.28/0.45 ( ( ord_less_eq @ A @ B3 @ A3 )
% 0.28/0.45 & ( ord_less_eq @ A @ A3 @ B3 ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % dual_order.eq_iff
% 0.28/0.45 thf(fact_23_dual__order_Otrans,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( order @ A )
% 0.28/0.45 => ! [B2: A,A2: A,C: A] :
% 0.28/0.45 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.28/0.45 => ( ( ord_less_eq @ A @ C @ B2 )
% 0.28/0.45 => ( ord_less_eq @ A @ C @ A2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % dual_order.trans
% 0.28/0.45 thf(fact_24_linorder__wlog,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( linorder @ A )
% 0.28/0.45 => ! [P: A > A > $o,A2: A,B2: A] :
% 0.28/0.45 ( ! [A6: A,B6: A] :
% 0.28/0.45 ( ( ord_less_eq @ A @ A6 @ B6 )
% 0.28/0.45 => ( P @ A6 @ B6 ) )
% 0.28/0.45 => ( ! [A6: A,B6: A] :
% 0.28/0.45 ( ( P @ B6 @ A6 )
% 0.28/0.45 => ( P @ A6 @ B6 ) )
% 0.28/0.45 => ( P @ A2 @ B2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % linorder_wlog
% 0.28/0.45 thf(fact_25_dual__order_Orefl,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( order @ A )
% 0.28/0.45 => ! [A2: A] : ( ord_less_eq @ A @ A2 @ A2 ) ) ).
% 0.28/0.45
% 0.28/0.45 % dual_order.refl
% 0.28/0.45 thf(fact_26_order__trans,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( preorder @ A )
% 0.28/0.45 => ! [X3: A,Y2: A,Z3: A] :
% 0.28/0.45 ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.28/0.45 => ( ( ord_less_eq @ A @ Y2 @ Z3 )
% 0.28/0.45 => ( ord_less_eq @ A @ X3 @ Z3 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % order_trans
% 0.28/0.45 thf(fact_27_order__class_Oorder_Oantisym,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( order @ A )
% 0.28/0.45 => ! [A2: A,B2: A] :
% 0.28/0.45 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.28/0.45 => ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.28/0.45 => ( A2 = B2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % order_class.order.antisym
% 0.28/0.45 thf(fact_28_ord__le__eq__trans,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( ord @ A )
% 0.28/0.45 => ! [A2: A,B2: A,C: A] :
% 0.28/0.45 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.28/0.45 => ( ( B2 = C )
% 0.28/0.45 => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % ord_le_eq_trans
% 0.28/0.45 thf(fact_29_ord__eq__le__trans,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( ord @ A )
% 0.28/0.45 => ! [A2: A,B2: A,C: A] :
% 0.28/0.45 ( ( A2 = B2 )
% 0.28/0.45 => ( ( ord_less_eq @ A @ B2 @ C )
% 0.28/0.45 => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % ord_eq_le_trans
% 0.28/0.45 thf(fact_30_order__class_Oorder_Oeq__iff,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( order @ A )
% 0.28/0.45 => ( ( ^ [Y: A,Z: A] : ( Y = Z ) )
% 0.28/0.45 = ( ^ [A3: A,B3: A] :
% 0.28/0.45 ( ( ord_less_eq @ A @ A3 @ B3 )
% 0.28/0.45 & ( ord_less_eq @ A @ B3 @ A3 ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % order_class.order.eq_iff
% 0.28/0.45 thf(fact_31_antisym__conv,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( order @ A )
% 0.28/0.45 => ! [Y2: A,X3: A] :
% 0.28/0.45 ( ( ord_less_eq @ A @ Y2 @ X3 )
% 0.28/0.45 => ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.28/0.45 = ( X3 = Y2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % antisym_conv
% 0.28/0.45 thf(fact_32_le__cases3,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( linorder @ A )
% 0.28/0.45 => ! [X3: A,Y2: A,Z3: A] :
% 0.28/0.45 ( ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.28/0.45 => ~ ( ord_less_eq @ A @ Y2 @ Z3 ) )
% 0.28/0.45 => ( ( ( ord_less_eq @ A @ Y2 @ X3 )
% 0.28/0.45 => ~ ( ord_less_eq @ A @ X3 @ Z3 ) )
% 0.28/0.45 => ( ( ( ord_less_eq @ A @ X3 @ Z3 )
% 0.28/0.45 => ~ ( ord_less_eq @ A @ Z3 @ Y2 ) )
% 0.28/0.45 => ( ( ( ord_less_eq @ A @ Z3 @ Y2 )
% 0.28/0.45 => ~ ( ord_less_eq @ A @ Y2 @ X3 ) )
% 0.28/0.45 => ( ( ( ord_less_eq @ A @ Y2 @ Z3 )
% 0.28/0.45 => ~ ( ord_less_eq @ A @ Z3 @ X3 ) )
% 0.28/0.45 => ~ ( ( ord_less_eq @ A @ Z3 @ X3 )
% 0.28/0.45 => ~ ( ord_less_eq @ A @ X3 @ Y2 ) ) ) ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % le_cases3
% 0.28/0.45 thf(fact_33_order_Otrans,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( order @ A )
% 0.28/0.45 => ! [A2: A,B2: A,C: A] :
% 0.28/0.45 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.28/0.45 => ( ( ord_less_eq @ A @ B2 @ C )
% 0.28/0.45 => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % order.trans
% 0.28/0.45 thf(fact_34_le__cases,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( linorder @ A )
% 0.28/0.45 => ! [X3: A,Y2: A] :
% 0.28/0.45 ( ~ ( ord_less_eq @ A @ X3 @ Y2 )
% 0.28/0.45 => ( ord_less_eq @ A @ Y2 @ X3 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % le_cases
% 0.28/0.45 thf(fact_35_eq__refl,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( preorder @ A )
% 0.28/0.45 => ! [X3: A,Y2: A] :
% 0.28/0.45 ( ( X3 = Y2 )
% 0.28/0.45 => ( ord_less_eq @ A @ X3 @ Y2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % eq_refl
% 0.28/0.45 thf(fact_36_linear,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( linorder @ A )
% 0.28/0.45 => ! [X3: A,Y2: A] :
% 0.28/0.45 ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.28/0.45 | ( ord_less_eq @ A @ Y2 @ X3 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % linear
% 0.28/0.45 thf(fact_37_antisym,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( order @ A )
% 0.28/0.45 => ! [X3: A,Y2: A] :
% 0.28/0.45 ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.28/0.45 => ( ( ord_less_eq @ A @ Y2 @ X3 )
% 0.28/0.45 => ( X3 = Y2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % antisym
% 0.28/0.45 thf(fact_38_eq__iff,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( order @ A )
% 0.28/0.45 => ( ( ^ [Y: A,Z: A] : ( Y = Z ) )
% 0.28/0.45 = ( ^ [X2: A,Y3: A] :
% 0.28/0.45 ( ( ord_less_eq @ A @ X2 @ Y3 )
% 0.28/0.45 & ( ord_less_eq @ A @ Y3 @ X2 ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % eq_iff
% 0.28/0.45 thf(fact_39_ord__le__eq__subst,axiom,
% 0.28/0.45 ! [A: $tType,B: $tType] :
% 0.28/0.45 ( ( ( ord @ B )
% 0.28/0.45 & ( ord @ A ) )
% 0.28/0.45 => ! [A2: A,B2: A,F: A > B,C: B] :
% 0.28/0.45 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.28/0.45 => ( ( ( F @ B2 )
% 0.28/0.45 = C )
% 0.28/0.45 => ( ! [X: A,Y4: A] :
% 0.28/0.45 ( ( ord_less_eq @ A @ X @ Y4 )
% 0.28/0.45 => ( ord_less_eq @ B @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.28/0.45 => ( ord_less_eq @ B @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % ord_le_eq_subst
% 0.28/0.45 thf(fact_40_ord__eq__le__subst,axiom,
% 0.28/0.45 ! [A: $tType,B: $tType] :
% 0.28/0.45 ( ( ( ord @ B )
% 0.28/0.45 & ( ord @ A ) )
% 0.28/0.45 => ! [A2: A,F: B > A,B2: B,C: B] :
% 0.28/0.45 ( ( A2
% 0.28/0.45 = ( F @ B2 ) )
% 0.28/0.45 => ( ( ord_less_eq @ B @ B2 @ C )
% 0.28/0.45 => ( ! [X: B,Y4: B] :
% 0.28/0.45 ( ( ord_less_eq @ B @ X @ Y4 )
% 0.28/0.45 => ( ord_less_eq @ A @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.28/0.45 => ( ord_less_eq @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % ord_eq_le_subst
% 0.28/0.45 thf(fact_41_Greatest__equality,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( order @ A )
% 0.28/0.45 => ! [P: A > $o,X3: A] :
% 0.28/0.45 ( ( P @ X3 )
% 0.28/0.45 => ( ! [Y4: A] :
% 0.28/0.45 ( ( P @ Y4 )
% 0.28/0.45 => ( ord_less_eq @ A @ Y4 @ X3 ) )
% 0.28/0.45 => ( ( order_Greatest @ A @ P )
% 0.28/0.45 = X3 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % Greatest_equality
% 0.28/0.45 thf(fact_42_GreatestI2__order,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( order @ A )
% 0.28/0.45 => ! [P: A > $o,X3: A,Q: A > $o] :
% 0.28/0.45 ( ( P @ X3 )
% 0.28/0.45 => ( ! [Y4: A] :
% 0.28/0.45 ( ( P @ Y4 )
% 0.28/0.45 => ( ord_less_eq @ A @ Y4 @ X3 ) )
% 0.28/0.45 => ( ! [X: A] :
% 0.28/0.45 ( ( P @ X )
% 0.28/0.45 => ( ! [Y5: A] :
% 0.28/0.45 ( ( P @ Y5 )
% 0.28/0.45 => ( ord_less_eq @ A @ Y5 @ X ) )
% 0.28/0.45 => ( Q @ X ) ) )
% 0.28/0.45 => ( Q @ ( order_Greatest @ A @ P ) ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % GreatestI2_order
% 0.28/0.45 thf(fact_43_le__rel__bool__arg__iff,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( ord @ A )
% 0.28/0.45 => ( ( ord_less_eq @ ( $o > A ) )
% 0.28/0.45 = ( ^ [X4: $o > A,Y6: $o > A] :
% 0.28/0.45 ( ( ord_less_eq @ A @ ( X4 @ $false ) @ ( Y6 @ $false ) )
% 0.28/0.45 & ( ord_less_eq @ A @ ( X4 @ $true ) @ ( Y6 @ $true ) ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % le_rel_bool_arg_iff
% 0.28/0.45 thf(fact_44_hmem__def,axiom,
% 0.28/0.45 ( hF_Mirabelle_hmem
% 0.28/0.45 = ( ^ [A3: hF_Mirabelle_hf,B3: hF_Mirabelle_hf] : ( member @ hF_Mirabelle_hf @ A3 @ ( hF_Mirabelle_hfset @ B3 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % hmem_def
% 0.28/0.45 thf(fact_45_mem__Collect__eq,axiom,
% 0.28/0.45 ! [A: $tType,A2: A,P: A > $o] :
% 0.28/0.45 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 0.28/0.45 = ( P @ A2 ) ) ).
% 0.28/0.45
% 0.28/0.45 % mem_Collect_eq
% 0.28/0.45 thf(fact_46_Collect__mem__eq,axiom,
% 0.28/0.45 ! [A: $tType,A5: set @ A] :
% 0.28/0.45 ( ( collect @ A
% 0.28/0.45 @ ^ [X2: A] : ( member @ A @ X2 @ A5 ) )
% 0.28/0.45 = A5 ) ).
% 0.28/0.45
% 0.28/0.45 % Collect_mem_eq
% 0.28/0.45 thf(fact_47_Collect__cong,axiom,
% 0.28/0.45 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.28/0.45 ( ! [X: A] :
% 0.28/0.45 ( ( P @ X )
% 0.28/0.45 = ( Q @ X ) )
% 0.28/0.45 => ( ( collect @ A @ P )
% 0.28/0.45 = ( collect @ A @ Q ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % Collect_cong
% 0.28/0.45 thf(fact_48_ext,axiom,
% 0.28/0.45 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.28/0.45 ( ! [X: A] :
% 0.28/0.45 ( ( F @ X )
% 0.28/0.45 = ( G @ X ) )
% 0.28/0.45 => ( F = G ) ) ).
% 0.28/0.45
% 0.28/0.45 % ext
% 0.28/0.45 thf(fact_49_RepFun__iff,axiom,
% 0.28/0.45 ! [V4: hF_Mirabelle_hf,A5: hF_Mirabelle_hf,F: hF_Mirabelle_hf > hF_Mirabelle_hf] :
% 0.28/0.45 ( ( hF_Mirabelle_hmem @ V4 @ ( hF_Mirabelle_RepFun @ A5 @ F ) )
% 0.28/0.45 = ( ? [U2: hF_Mirabelle_hf] :
% 0.28/0.45 ( ( hF_Mirabelle_hmem @ U2 @ A5 )
% 0.28/0.45 & ( V4
% 0.28/0.45 = ( F @ U2 ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % RepFun_iff
% 0.28/0.45 thf(fact_50_less__hf__def,axiom,
% 0.28/0.45 ( ( ord_less @ hF_Mirabelle_hf )
% 0.28/0.45 = ( ^ [A4: hF_Mirabelle_hf,B4: hF_Mirabelle_hf] :
% 0.28/0.45 ( ( ord_less_eq @ hF_Mirabelle_hf @ A4 @ B4 )
% 0.28/0.45 & ( A4 != B4 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % less_hf_def
% 0.28/0.45 thf(fact_51_antimono__def,axiom,
% 0.28/0.45 ! [B: $tType,A: $tType] :
% 0.28/0.45 ( ( ( order @ A )
% 0.28/0.45 & ( order @ B ) )
% 0.28/0.45 => ( ( order_antimono @ A @ B )
% 0.28/0.45 = ( ^ [F2: A > B] :
% 0.28/0.45 ! [X2: A,Y3: A] :
% 0.28/0.45 ( ( ord_less_eq @ A @ X2 @ Y3 )
% 0.28/0.45 => ( ord_less_eq @ B @ ( F2 @ Y3 ) @ ( F2 @ X2 ) ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % antimono_def
% 0.28/0.45 thf(fact_52_antimonoI,axiom,
% 0.28/0.45 ! [B: $tType,A: $tType] :
% 0.28/0.45 ( ( ( order @ A )
% 0.28/0.45 & ( order @ B ) )
% 0.28/0.45 => ! [F: A > B] :
% 0.28/0.45 ( ! [X: A,Y4: A] :
% 0.28/0.45 ( ( ord_less_eq @ A @ X @ Y4 )
% 0.28/0.45 => ( ord_less_eq @ B @ ( F @ Y4 ) @ ( F @ X ) ) )
% 0.28/0.45 => ( order_antimono @ A @ B @ F ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % antimonoI
% 0.28/0.45 thf(fact_53_antimonoE,axiom,
% 0.28/0.45 ! [B: $tType,A: $tType] :
% 0.28/0.45 ( ( ( order @ A )
% 0.28/0.45 & ( order @ B ) )
% 0.28/0.45 => ! [F: A > B,X3: A,Y2: A] :
% 0.28/0.45 ( ( order_antimono @ A @ B @ F )
% 0.28/0.45 => ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.28/0.45 => ( ord_less_eq @ B @ ( F @ Y2 ) @ ( F @ X3 ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % antimonoE
% 0.28/0.45 thf(fact_54_antimonoD,axiom,
% 0.28/0.45 ! [B: $tType,A: $tType] :
% 0.28/0.45 ( ( ( order @ A )
% 0.28/0.45 & ( order @ B ) )
% 0.28/0.45 => ! [F: A > B,X3: A,Y2: A] :
% 0.28/0.45 ( ( order_antimono @ A @ B @ F )
% 0.28/0.45 => ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.28/0.45 => ( ord_less_eq @ B @ ( F @ Y2 ) @ ( F @ X3 ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % antimonoD
% 0.28/0.45 thf(fact_55_verit__comp__simplify1_I1_J,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( order @ A )
% 0.28/0.45 => ! [A2: A] :
% 0.28/0.45 ~ ( ord_less @ A @ A2 @ A2 ) ) ).
% 0.28/0.45
% 0.28/0.45 % verit_comp_simplify1(1)
% 0.28/0.45 thf(fact_56_ord__eq__less__subst,axiom,
% 0.28/0.45 ! [A: $tType,B: $tType] :
% 0.28/0.45 ( ( ( ord @ B )
% 0.28/0.45 & ( ord @ A ) )
% 0.28/0.45 => ! [A2: A,F: B > A,B2: B,C: B] :
% 0.28/0.45 ( ( A2
% 0.28/0.45 = ( F @ B2 ) )
% 0.28/0.45 => ( ( ord_less @ B @ B2 @ C )
% 0.28/0.45 => ( ! [X: B,Y4: B] :
% 0.28/0.45 ( ( ord_less @ B @ X @ Y4 )
% 0.28/0.45 => ( ord_less @ A @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.28/0.45 => ( ord_less @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % ord_eq_less_subst
% 0.28/0.45 thf(fact_57_ord__less__eq__subst,axiom,
% 0.28/0.45 ! [A: $tType,B: $tType] :
% 0.28/0.45 ( ( ( ord @ B )
% 0.28/0.45 & ( ord @ A ) )
% 0.28/0.45 => ! [A2: A,B2: A,F: A > B,C: B] :
% 0.28/0.45 ( ( ord_less @ A @ A2 @ B2 )
% 0.28/0.45 => ( ( ( F @ B2 )
% 0.28/0.45 = C )
% 0.28/0.45 => ( ! [X: A,Y4: A] :
% 0.28/0.45 ( ( ord_less @ A @ X @ Y4 )
% 0.28/0.45 => ( ord_less @ B @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.28/0.45 => ( ord_less @ B @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % ord_less_eq_subst
% 0.28/0.45 thf(fact_58_order__less__subst1,axiom,
% 0.28/0.45 ! [A: $tType,B: $tType] :
% 0.28/0.45 ( ( ( order @ B )
% 0.28/0.45 & ( order @ A ) )
% 0.28/0.45 => ! [A2: A,F: B > A,B2: B,C: B] :
% 0.28/0.45 ( ( ord_less @ A @ A2 @ ( F @ B2 ) )
% 0.28/0.45 => ( ( ord_less @ B @ B2 @ C )
% 0.28/0.45 => ( ! [X: B,Y4: B] :
% 0.28/0.45 ( ( ord_less @ B @ X @ Y4 )
% 0.28/0.45 => ( ord_less @ A @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.28/0.45 => ( ord_less @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % order_less_subst1
% 0.28/0.45 thf(fact_59_order__less__subst2,axiom,
% 0.28/0.45 ! [A: $tType,C2: $tType] :
% 0.28/0.45 ( ( ( order @ C2 )
% 0.28/0.45 & ( order @ A ) )
% 0.28/0.45 => ! [A2: A,B2: A,F: A > C2,C: C2] :
% 0.28/0.45 ( ( ord_less @ A @ A2 @ B2 )
% 0.28/0.45 => ( ( ord_less @ C2 @ ( F @ B2 ) @ C )
% 0.28/0.45 => ( ! [X: A,Y4: A] :
% 0.28/0.45 ( ( ord_less @ A @ X @ Y4 )
% 0.28/0.45 => ( ord_less @ C2 @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.28/0.45 => ( ord_less @ C2 @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % order_less_subst2
% 0.28/0.45 thf(fact_60_lt__ex,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( no_bot @ A )
% 0.28/0.45 => ! [X3: A] :
% 0.28/0.45 ? [Y4: A] : ( ord_less @ A @ Y4 @ X3 ) ) ).
% 0.28/0.45
% 0.28/0.45 % lt_ex
% 0.28/0.45 thf(fact_61_gt__ex,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( no_top @ A )
% 0.28/0.45 => ! [X3: A] :
% 0.28/0.45 ? [X_1: A] : ( ord_less @ A @ X3 @ X_1 ) ) ).
% 0.28/0.45
% 0.28/0.45 % gt_ex
% 0.28/0.45 thf(fact_62_neqE,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( linorder @ A )
% 0.28/0.45 => ! [X3: A,Y2: A] :
% 0.28/0.45 ( ( X3 != Y2 )
% 0.28/0.45 => ( ~ ( ord_less @ A @ X3 @ Y2 )
% 0.28/0.45 => ( ord_less @ A @ Y2 @ X3 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % neqE
% 0.28/0.45 thf(fact_63_neq__iff,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( linorder @ A )
% 0.28/0.45 => ! [X3: A,Y2: A] :
% 0.28/0.45 ( ( X3 != Y2 )
% 0.28/0.45 = ( ( ord_less @ A @ X3 @ Y2 )
% 0.28/0.45 | ( ord_less @ A @ Y2 @ X3 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % neq_iff
% 0.28/0.45 thf(fact_64_order_Oasym,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( order @ A )
% 0.28/0.45 => ! [A2: A,B2: A] :
% 0.28/0.45 ( ( ord_less @ A @ A2 @ B2 )
% 0.28/0.45 => ~ ( ord_less @ A @ B2 @ A2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % order.asym
% 0.28/0.45 thf(fact_65_dense,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( dense_order @ A )
% 0.28/0.45 => ! [X3: A,Y2: A] :
% 0.28/0.45 ( ( ord_less @ A @ X3 @ Y2 )
% 0.28/0.45 => ? [Z2: A] :
% 0.28/0.45 ( ( ord_less @ A @ X3 @ Z2 )
% 0.28/0.45 & ( ord_less @ A @ Z2 @ Y2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % dense
% 0.28/0.45 thf(fact_66_less__imp__neq,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( order @ A )
% 0.28/0.45 => ! [X3: A,Y2: A] :
% 0.28/0.45 ( ( ord_less @ A @ X3 @ Y2 )
% 0.28/0.45 => ( X3 != Y2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % less_imp_neq
% 0.28/0.45 thf(fact_67_less__asym,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( preorder @ A )
% 0.28/0.45 => ! [X3: A,Y2: A] :
% 0.28/0.45 ( ( ord_less @ A @ X3 @ Y2 )
% 0.28/0.45 => ~ ( ord_less @ A @ Y2 @ X3 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % less_asym
% 0.28/0.45 thf(fact_68_less__asym_H,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( preorder @ A )
% 0.28/0.45 => ! [A2: A,B2: A] :
% 0.28/0.45 ( ( ord_less @ A @ A2 @ B2 )
% 0.28/0.45 => ~ ( ord_less @ A @ B2 @ A2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % less_asym'
% 0.28/0.45 thf(fact_69_less__trans,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( preorder @ A )
% 0.28/0.45 => ! [X3: A,Y2: A,Z3: A] :
% 0.28/0.45 ( ( ord_less @ A @ X3 @ Y2 )
% 0.28/0.45 => ( ( ord_less @ A @ Y2 @ Z3 )
% 0.28/0.45 => ( ord_less @ A @ X3 @ Z3 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % less_trans
% 0.28/0.45 thf(fact_70_less__linear,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( linorder @ A )
% 0.28/0.45 => ! [X3: A,Y2: A] :
% 0.28/0.45 ( ( ord_less @ A @ X3 @ Y2 )
% 0.28/0.45 | ( X3 = Y2 )
% 0.28/0.45 | ( ord_less @ A @ Y2 @ X3 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % less_linear
% 0.28/0.45 thf(fact_71_less__irrefl,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( preorder @ A )
% 0.28/0.45 => ! [X3: A] :
% 0.28/0.45 ~ ( ord_less @ A @ X3 @ X3 ) ) ).
% 0.28/0.45
% 0.28/0.45 % less_irrefl
% 0.28/0.45 thf(fact_72_ord__eq__less__trans,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( ord @ A )
% 0.28/0.45 => ! [A2: A,B2: A,C: A] :
% 0.28/0.45 ( ( A2 = B2 )
% 0.28/0.45 => ( ( ord_less @ A @ B2 @ C )
% 0.28/0.45 => ( ord_less @ A @ A2 @ C ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % ord_eq_less_trans
% 0.28/0.45 thf(fact_73_ord__less__eq__trans,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( ord @ A )
% 0.28/0.45 => ! [A2: A,B2: A,C: A] :
% 0.28/0.45 ( ( ord_less @ A @ A2 @ B2 )
% 0.28/0.45 => ( ( B2 = C )
% 0.28/0.45 => ( ord_less @ A @ A2 @ C ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % ord_less_eq_trans
% 0.28/0.45 thf(fact_74_dual__order_Oasym,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( order @ A )
% 0.28/0.45 => ! [B2: A,A2: A] :
% 0.28/0.45 ( ( ord_less @ A @ B2 @ A2 )
% 0.28/0.45 => ~ ( ord_less @ A @ A2 @ B2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % dual_order.asym
% 0.28/0.45 thf(fact_75_less__imp__not__eq,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( order @ A )
% 0.28/0.45 => ! [X3: A,Y2: A] :
% 0.28/0.45 ( ( ord_less @ A @ X3 @ Y2 )
% 0.28/0.45 => ( X3 != Y2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % less_imp_not_eq
% 0.28/0.45 thf(fact_76_less__not__sym,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( preorder @ A )
% 0.28/0.45 => ! [X3: A,Y2: A] :
% 0.28/0.45 ( ( ord_less @ A @ X3 @ Y2 )
% 0.28/0.45 => ~ ( ord_less @ A @ Y2 @ X3 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % less_not_sym
% 0.28/0.45 thf(fact_77_less__induct,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( wellorder @ A )
% 0.28/0.45 => ! [P: A > $o,A2: A] :
% 0.28/0.45 ( ! [X: A] :
% 0.28/0.45 ( ! [Y5: A] :
% 0.28/0.45 ( ( ord_less @ A @ Y5 @ X )
% 0.28/0.45 => ( P @ Y5 ) )
% 0.28/0.45 => ( P @ X ) )
% 0.28/0.45 => ( P @ A2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % less_induct
% 0.28/0.45 thf(fact_78_antisym__conv3,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( linorder @ A )
% 0.28/0.45 => ! [Y2: A,X3: A] :
% 0.28/0.45 ( ~ ( ord_less @ A @ Y2 @ X3 )
% 0.28/0.45 => ( ( ~ ( ord_less @ A @ X3 @ Y2 ) )
% 0.28/0.45 = ( X3 = Y2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % antisym_conv3
% 0.28/0.45 thf(fact_79_less__imp__not__eq2,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( order @ A )
% 0.28/0.45 => ! [X3: A,Y2: A] :
% 0.28/0.45 ( ( ord_less @ A @ X3 @ Y2 )
% 0.28/0.45 => ( Y2 != X3 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % less_imp_not_eq2
% 0.28/0.45 thf(fact_80_less__imp__triv,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( preorder @ A )
% 0.28/0.45 => ! [X3: A,Y2: A,P: $o] :
% 0.28/0.45 ( ( ord_less @ A @ X3 @ Y2 )
% 0.28/0.45 => ( ( ord_less @ A @ Y2 @ X3 )
% 0.28/0.45 => P ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % less_imp_triv
% 0.28/0.45 thf(fact_81_linorder__cases,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( linorder @ A )
% 0.28/0.45 => ! [X3: A,Y2: A] :
% 0.28/0.45 ( ~ ( ord_less @ A @ X3 @ Y2 )
% 0.28/0.45 => ( ( X3 != Y2 )
% 0.28/0.45 => ( ord_less @ A @ Y2 @ X3 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % linorder_cases
% 0.28/0.45 thf(fact_82_dual__order_Oirrefl,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( order @ A )
% 0.28/0.45 => ! [A2: A] :
% 0.28/0.45 ~ ( ord_less @ A @ A2 @ A2 ) ) ).
% 0.28/0.45
% 0.28/0.45 % dual_order.irrefl
% 0.28/0.45 thf(fact_83_order_Ostrict__trans,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( order @ A )
% 0.28/0.45 => ! [A2: A,B2: A,C: A] :
% 0.28/0.45 ( ( ord_less @ A @ A2 @ B2 )
% 0.28/0.45 => ( ( ord_less @ A @ B2 @ C )
% 0.28/0.45 => ( ord_less @ A @ A2 @ C ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % order.strict_trans
% 0.28/0.45 thf(fact_84_less__imp__not__less,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( preorder @ A )
% 0.28/0.45 => ! [X3: A,Y2: A] :
% 0.28/0.45 ( ( ord_less @ A @ X3 @ Y2 )
% 0.28/0.45 => ~ ( ord_less @ A @ Y2 @ X3 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % less_imp_not_less
% 0.28/0.45 thf(fact_85_exists__least__iff,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( wellorder @ A )
% 0.28/0.45 => ( ( ^ [P2: A > $o] :
% 0.28/0.45 ? [X5: A] : ( P2 @ X5 ) )
% 0.28/0.45 = ( ^ [P3: A > $o] :
% 0.28/0.45 ? [N: A] :
% 0.28/0.45 ( ( P3 @ N )
% 0.28/0.45 & ! [M: A] :
% 0.28/0.45 ( ( ord_less @ A @ M @ N )
% 0.28/0.45 => ~ ( P3 @ M ) ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % exists_least_iff
% 0.28/0.45 thf(fact_86_linorder__less__wlog,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( linorder @ A )
% 0.28/0.45 => ! [P: A > A > $o,A2: A,B2: A] :
% 0.28/0.45 ( ! [A6: A,B6: A] :
% 0.28/0.45 ( ( ord_less @ A @ A6 @ B6 )
% 0.28/0.45 => ( P @ A6 @ B6 ) )
% 0.28/0.45 => ( ! [A6: A] : ( P @ A6 @ A6 )
% 0.28/0.45 => ( ! [A6: A,B6: A] :
% 0.28/0.45 ( ( P @ B6 @ A6 )
% 0.28/0.45 => ( P @ A6 @ B6 ) )
% 0.28/0.45 => ( P @ A2 @ B2 ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % linorder_less_wlog
% 0.28/0.45 thf(fact_87_dual__order_Ostrict__trans,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( order @ A )
% 0.28/0.45 => ! [B2: A,A2: A,C: A] :
% 0.28/0.45 ( ( ord_less @ A @ B2 @ A2 )
% 0.28/0.45 => ( ( ord_less @ A @ C @ B2 )
% 0.28/0.45 => ( ord_less @ A @ C @ A2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % dual_order.strict_trans
% 0.28/0.45 thf(fact_88_not__less__iff__gr__or__eq,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( linorder @ A )
% 0.28/0.45 => ! [X3: A,Y2: A] :
% 0.28/0.45 ( ( ~ ( ord_less @ A @ X3 @ Y2 ) )
% 0.28/0.45 = ( ( ord_less @ A @ Y2 @ X3 )
% 0.28/0.45 | ( X3 = Y2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % not_less_iff_gr_or_eq
% 0.28/0.45 thf(fact_89_order_Ostrict__implies__not__eq,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( order @ A )
% 0.28/0.45 => ! [A2: A,B2: A] :
% 0.28/0.45 ( ( ord_less @ A @ A2 @ B2 )
% 0.28/0.45 => ( A2 != B2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % order.strict_implies_not_eq
% 0.28/0.45 thf(fact_90_dual__order_Ostrict__implies__not__eq,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( order @ A )
% 0.28/0.45 => ! [B2: A,A2: A] :
% 0.28/0.45 ( ( ord_less @ A @ B2 @ A2 )
% 0.28/0.45 => ( A2 != B2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % dual_order.strict_implies_not_eq
% 0.28/0.45 thf(fact_91_verit__comp__simplify1_I3_J,axiom,
% 0.28/0.45 ! [B: $tType] :
% 0.28/0.45 ( ( linorder @ B )
% 0.28/0.45 => ! [B7: B,A7: B] :
% 0.28/0.45 ( ( ~ ( ord_less_eq @ B @ B7 @ A7 ) )
% 0.28/0.45 = ( ord_less @ B @ A7 @ B7 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % verit_comp_simplify1(3)
% 0.28/0.45 thf(fact_92_leD,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( order @ A )
% 0.28/0.45 => ! [Y2: A,X3: A] :
% 0.28/0.45 ( ( ord_less_eq @ A @ Y2 @ X3 )
% 0.28/0.45 => ~ ( ord_less @ A @ X3 @ Y2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % leD
% 0.28/0.45 thf(fact_93_leI,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( linorder @ A )
% 0.28/0.45 => ! [X3: A,Y2: A] :
% 0.28/0.45 ( ~ ( ord_less @ A @ X3 @ Y2 )
% 0.28/0.45 => ( ord_less_eq @ A @ Y2 @ X3 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % leI
% 0.28/0.45 thf(fact_94_le__less,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( order @ A )
% 0.28/0.45 => ( ( ord_less_eq @ A )
% 0.28/0.45 = ( ^ [X2: A,Y3: A] :
% 0.28/0.45 ( ( ord_less @ A @ X2 @ Y3 )
% 0.28/0.45 | ( X2 = Y3 ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % le_less
% 0.28/0.45 thf(fact_95_less__le,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( order @ A )
% 0.28/0.45 => ( ( ord_less @ A )
% 0.28/0.45 = ( ^ [X2: A,Y3: A] :
% 0.28/0.45 ( ( ord_less_eq @ A @ X2 @ Y3 )
% 0.28/0.45 & ( X2 != Y3 ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % less_le
% 0.28/0.45 thf(fact_96_order__le__less__subst1,axiom,
% 0.28/0.45 ! [A: $tType,B: $tType] :
% 0.28/0.45 ( ( ( order @ B )
% 0.28/0.45 & ( order @ A ) )
% 0.28/0.45 => ! [A2: A,F: B > A,B2: B,C: B] :
% 0.28/0.45 ( ( ord_less_eq @ A @ A2 @ ( F @ B2 ) )
% 0.28/0.45 => ( ( ord_less @ B @ B2 @ C )
% 0.28/0.45 => ( ! [X: B,Y4: B] :
% 0.28/0.45 ( ( ord_less @ B @ X @ Y4 )
% 0.28/0.45 => ( ord_less @ A @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.28/0.45 => ( ord_less @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % order_le_less_subst1
% 0.28/0.45 thf(fact_97_order__le__less__subst2,axiom,
% 0.28/0.45 ! [A: $tType,C2: $tType] :
% 0.28/0.45 ( ( ( order @ C2 )
% 0.28/0.45 & ( order @ A ) )
% 0.28/0.45 => ! [A2: A,B2: A,F: A > C2,C: C2] :
% 0.28/0.45 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.28/0.45 => ( ( ord_less @ C2 @ ( F @ B2 ) @ C )
% 0.28/0.45 => ( ! [X: A,Y4: A] :
% 0.28/0.45 ( ( ord_less_eq @ A @ X @ Y4 )
% 0.28/0.45 => ( ord_less_eq @ C2 @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.28/0.45 => ( ord_less @ C2 @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % order_le_less_subst2
% 0.28/0.45 thf(fact_98_order__less__le__subst1,axiom,
% 0.28/0.45 ! [A: $tType,B: $tType] :
% 0.28/0.45 ( ( ( order @ B )
% 0.28/0.45 & ( order @ A ) )
% 0.28/0.45 => ! [A2: A,F: B > A,B2: B,C: B] :
% 0.28/0.45 ( ( ord_less @ A @ A2 @ ( F @ B2 ) )
% 0.28/0.45 => ( ( ord_less_eq @ B @ B2 @ C )
% 0.28/0.45 => ( ! [X: B,Y4: B] :
% 0.28/0.45 ( ( ord_less_eq @ B @ X @ Y4 )
% 0.28/0.45 => ( ord_less_eq @ A @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.28/0.45 => ( ord_less @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % order_less_le_subst1
% 0.28/0.45 thf(fact_99_order__less__le__subst2,axiom,
% 0.28/0.45 ! [A: $tType,C2: $tType] :
% 0.28/0.45 ( ( ( order @ C2 )
% 0.28/0.45 & ( order @ A ) )
% 0.28/0.45 => ! [A2: A,B2: A,F: A > C2,C: C2] :
% 0.28/0.45 ( ( ord_less @ A @ A2 @ B2 )
% 0.28/0.45 => ( ( ord_less_eq @ C2 @ ( F @ B2 ) @ C )
% 0.28/0.45 => ( ! [X: A,Y4: A] :
% 0.28/0.45 ( ( ord_less @ A @ X @ Y4 )
% 0.28/0.45 => ( ord_less @ C2 @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.28/0.45 => ( ord_less @ C2 @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % order_less_le_subst2
% 0.28/0.45 thf(fact_100_not__le,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( linorder @ A )
% 0.28/0.45 => ! [X3: A,Y2: A] :
% 0.28/0.45 ( ( ~ ( ord_less_eq @ A @ X3 @ Y2 ) )
% 0.28/0.45 = ( ord_less @ A @ Y2 @ X3 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % not_le
% 0.28/0.45 thf(fact_101_not__less,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( linorder @ A )
% 0.28/0.45 => ! [X3: A,Y2: A] :
% 0.28/0.45 ( ( ~ ( ord_less @ A @ X3 @ Y2 ) )
% 0.28/0.45 = ( ord_less_eq @ A @ Y2 @ X3 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % not_less
% 0.28/0.45 thf(fact_102_le__neq__trans,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( order @ A )
% 0.28/0.45 => ! [A2: A,B2: A] :
% 0.28/0.45 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.28/0.45 => ( ( A2 != B2 )
% 0.28/0.45 => ( ord_less @ A @ A2 @ B2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % le_neq_trans
% 0.28/0.45 thf(fact_103_antisym__conv1,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( order @ A )
% 0.28/0.45 => ! [X3: A,Y2: A] :
% 0.28/0.45 ( ~ ( ord_less @ A @ X3 @ Y2 )
% 0.28/0.45 => ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.28/0.45 = ( X3 = Y2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % antisym_conv1
% 0.28/0.45 thf(fact_104_antisym__conv2,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( order @ A )
% 0.28/0.45 => ! [X3: A,Y2: A] :
% 0.28/0.45 ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.28/0.45 => ( ( ~ ( ord_less @ A @ X3 @ Y2 ) )
% 0.28/0.45 = ( X3 = Y2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % antisym_conv2
% 0.28/0.45 thf(fact_105_less__imp__le,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( preorder @ A )
% 0.28/0.45 => ! [X3: A,Y2: A] :
% 0.28/0.45 ( ( ord_less @ A @ X3 @ Y2 )
% 0.28/0.45 => ( ord_less_eq @ A @ X3 @ Y2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % less_imp_le
% 0.28/0.45 thf(fact_106_le__less__trans,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( preorder @ A )
% 0.28/0.45 => ! [X3: A,Y2: A,Z3: A] :
% 0.28/0.45 ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.28/0.45 => ( ( ord_less @ A @ Y2 @ Z3 )
% 0.28/0.45 => ( ord_less @ A @ X3 @ Z3 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % le_less_trans
% 0.28/0.45 thf(fact_107_less__le__trans,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( preorder @ A )
% 0.28/0.45 => ! [X3: A,Y2: A,Z3: A] :
% 0.28/0.45 ( ( ord_less @ A @ X3 @ Y2 )
% 0.28/0.45 => ( ( ord_less_eq @ A @ Y2 @ Z3 )
% 0.28/0.45 => ( ord_less @ A @ X3 @ Z3 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % less_le_trans
% 0.28/0.45 thf(fact_108_dense__ge,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( dense_linorder @ A )
% 0.28/0.45 => ! [Z3: A,Y2: A] :
% 0.28/0.45 ( ! [X: A] :
% 0.28/0.45 ( ( ord_less @ A @ Z3 @ X )
% 0.28/0.45 => ( ord_less_eq @ A @ Y2 @ X ) )
% 0.28/0.45 => ( ord_less_eq @ A @ Y2 @ Z3 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % dense_ge
% 0.28/0.45 thf(fact_109_dense__le,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( dense_linorder @ A )
% 0.28/0.45 => ! [Y2: A,Z3: A] :
% 0.28/0.45 ( ! [X: A] :
% 0.28/0.45 ( ( ord_less @ A @ X @ Y2 )
% 0.28/0.45 => ( ord_less_eq @ A @ X @ Z3 ) )
% 0.28/0.45 => ( ord_less_eq @ A @ Y2 @ Z3 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % dense_le
% 0.28/0.45 thf(fact_110_le__less__linear,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( linorder @ A )
% 0.28/0.45 => ! [X3: A,Y2: A] :
% 0.28/0.45 ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.28/0.45 | ( ord_less @ A @ Y2 @ X3 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % le_less_linear
% 0.28/0.45 thf(fact_111_le__imp__less__or__eq,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( order @ A )
% 0.28/0.45 => ! [X3: A,Y2: A] :
% 0.28/0.45 ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.28/0.45 => ( ( ord_less @ A @ X3 @ Y2 )
% 0.28/0.45 | ( X3 = Y2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % le_imp_less_or_eq
% 0.28/0.45 thf(fact_112_less__le__not__le,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( preorder @ A )
% 0.28/0.45 => ( ( ord_less @ A )
% 0.28/0.45 = ( ^ [X2: A,Y3: A] :
% 0.28/0.45 ( ( ord_less_eq @ A @ X2 @ Y3 )
% 0.28/0.45 & ~ ( ord_less_eq @ A @ Y3 @ X2 ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % less_le_not_le
% 0.28/0.45 thf(fact_113_not__le__imp__less,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( linorder @ A )
% 0.28/0.45 => ! [Y2: A,X3: A] :
% 0.28/0.45 ( ~ ( ord_less_eq @ A @ Y2 @ X3 )
% 0.28/0.45 => ( ord_less @ A @ X3 @ Y2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % not_le_imp_less
% 0.28/0.45 thf(fact_114_order_Ostrict__trans1,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( order @ A )
% 0.28/0.45 => ! [A2: A,B2: A,C: A] :
% 0.28/0.45 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.28/0.45 => ( ( ord_less @ A @ B2 @ C )
% 0.28/0.45 => ( ord_less @ A @ A2 @ C ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % order.strict_trans1
% 0.28/0.45 thf(fact_115_order_Ostrict__trans2,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( order @ A )
% 0.28/0.45 => ! [A2: A,B2: A,C: A] :
% 0.28/0.45 ( ( ord_less @ A @ A2 @ B2 )
% 0.28/0.45 => ( ( ord_less_eq @ A @ B2 @ C )
% 0.28/0.45 => ( ord_less @ A @ A2 @ C ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % order.strict_trans2
% 0.28/0.45 thf(fact_116_order_Oorder__iff__strict,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( order @ A )
% 0.28/0.45 => ( ( ord_less_eq @ A )
% 0.28/0.45 = ( ^ [A3: A,B3: A] :
% 0.28/0.45 ( ( ord_less @ A @ A3 @ B3 )
% 0.28/0.45 | ( A3 = B3 ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % order.order_iff_strict
% 0.28/0.45 thf(fact_117_order_Ostrict__iff__order,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( order @ A )
% 0.28/0.45 => ( ( ord_less @ A )
% 0.28/0.45 = ( ^ [A3: A,B3: A] :
% 0.28/0.45 ( ( ord_less_eq @ A @ A3 @ B3 )
% 0.28/0.45 & ( A3 != B3 ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % order.strict_iff_order
% 0.28/0.45 thf(fact_118_dual__order_Ostrict__trans1,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( order @ A )
% 0.28/0.45 => ! [B2: A,A2: A,C: A] :
% 0.28/0.45 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.28/0.45 => ( ( ord_less @ A @ C @ B2 )
% 0.28/0.45 => ( ord_less @ A @ C @ A2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % dual_order.strict_trans1
% 0.28/0.45 thf(fact_119_dual__order_Ostrict__trans2,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( order @ A )
% 0.28/0.45 => ! [B2: A,A2: A,C: A] :
% 0.28/0.45 ( ( ord_less @ A @ B2 @ A2 )
% 0.28/0.45 => ( ( ord_less_eq @ A @ C @ B2 )
% 0.28/0.45 => ( ord_less @ A @ C @ A2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % dual_order.strict_trans2
% 0.28/0.45 thf(fact_120_dense__ge__bounded,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( dense_linorder @ A )
% 0.28/0.45 => ! [Z3: A,X3: A,Y2: A] :
% 0.28/0.45 ( ( ord_less @ A @ Z3 @ X3 )
% 0.28/0.45 => ( ! [W: A] :
% 0.28/0.45 ( ( ord_less @ A @ Z3 @ W )
% 0.28/0.45 => ( ( ord_less @ A @ W @ X3 )
% 0.28/0.45 => ( ord_less_eq @ A @ Y2 @ W ) ) )
% 0.28/0.45 => ( ord_less_eq @ A @ Y2 @ Z3 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % dense_ge_bounded
% 0.28/0.45 thf(fact_121_dense__le__bounded,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( dense_linorder @ A )
% 0.28/0.45 => ! [X3: A,Y2: A,Z3: A] :
% 0.28/0.45 ( ( ord_less @ A @ X3 @ Y2 )
% 0.28/0.45 => ( ! [W: A] :
% 0.28/0.45 ( ( ord_less @ A @ X3 @ W )
% 0.28/0.45 => ( ( ord_less @ A @ W @ Y2 )
% 0.28/0.45 => ( ord_less_eq @ A @ W @ Z3 ) ) )
% 0.28/0.45 => ( ord_less_eq @ A @ Y2 @ Z3 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % dense_le_bounded
% 0.28/0.45 thf(fact_122_order_Ostrict__implies__order,axiom,
% 0.28/0.45 ! [A: $tType] :
% 0.28/0.45 ( ( order @ A )
% 0.28/0.46 => ! [A2: A,B2: A] :
% 0.28/0.46 ( ( ord_less @ A @ A2 @ B2 )
% 0.28/0.46 => ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % order.strict_implies_order
% 0.28/0.46 thf(fact_123_dual__order_Oorder__iff__strict,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( order @ A )
% 0.28/0.46 => ( ( ord_less_eq @ A )
% 0.28/0.46 = ( ^ [B3: A,A3: A] :
% 0.28/0.46 ( ( ord_less @ A @ B3 @ A3 )
% 0.28/0.46 | ( A3 = B3 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % dual_order.order_iff_strict
% 0.28/0.46 thf(fact_124_dual__order_Ostrict__iff__order,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( order @ A )
% 0.28/0.46 => ( ( ord_less @ A )
% 0.28/0.46 = ( ^ [B3: A,A3: A] :
% 0.28/0.46 ( ( ord_less_eq @ A @ B3 @ A3 )
% 0.28/0.46 & ( A3 != B3 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % dual_order.strict_iff_order
% 0.28/0.46 thf(fact_125_dual__order_Ostrict__implies__order,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( order @ A )
% 0.28/0.46 => ! [B2: A,A2: A] :
% 0.28/0.46 ( ( ord_less @ A @ B2 @ A2 )
% 0.28/0.46 => ( ord_less_eq @ A @ B2 @ A2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % dual_order.strict_implies_order
% 0.28/0.46 thf(fact_126_order_Onot__eq__order__implies__strict,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( order @ A )
% 0.28/0.46 => ! [A2: A,B2: A] :
% 0.28/0.46 ( ( A2 != B2 )
% 0.28/0.46 => ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.28/0.46 => ( ord_less @ A @ A2 @ B2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % order.not_eq_order_implies_strict
% 0.28/0.46 thf(fact_127_RepFun__cong,axiom,
% 0.28/0.46 ! [A5: hF_Mirabelle_hf,B5: hF_Mirabelle_hf,F: hF_Mirabelle_hf > hF_Mirabelle_hf,G: hF_Mirabelle_hf > hF_Mirabelle_hf] :
% 0.28/0.46 ( ( A5 = B5 )
% 0.28/0.46 => ( ! [X: hF_Mirabelle_hf] :
% 0.28/0.46 ( ( hF_Mirabelle_hmem @ X @ B5 )
% 0.28/0.46 => ( ( F @ X )
% 0.28/0.46 = ( G @ X ) ) )
% 0.28/0.46 => ( ( hF_Mirabelle_RepFun @ A5 @ F )
% 0.28/0.46 = ( hF_Mirabelle_RepFun @ B5 @ G ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % RepFun_cong
% 0.28/0.46 thf(fact_128_minf_I8_J,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( linorder @ A )
% 0.28/0.46 => ! [T: A] :
% 0.28/0.46 ? [Z2: A] :
% 0.28/0.46 ! [X6: A] :
% 0.28/0.46 ( ( ord_less @ A @ X6 @ Z2 )
% 0.28/0.46 => ~ ( ord_less_eq @ A @ T @ X6 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % minf(8)
% 0.28/0.46 thf(fact_129_minf_I6_J,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( linorder @ A )
% 0.28/0.46 => ! [T: A] :
% 0.28/0.46 ? [Z2: A] :
% 0.28/0.46 ! [X6: A] :
% 0.28/0.46 ( ( ord_less @ A @ X6 @ Z2 )
% 0.28/0.46 => ( ord_less_eq @ A @ X6 @ T ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % minf(6)
% 0.28/0.46 thf(fact_130_pinf_I8_J,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( linorder @ A )
% 0.28/0.46 => ! [T: A] :
% 0.28/0.46 ? [Z2: A] :
% 0.28/0.46 ! [X6: A] :
% 0.28/0.46 ( ( ord_less @ A @ Z2 @ X6 )
% 0.28/0.46 => ( ord_less_eq @ A @ T @ X6 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % pinf(8)
% 0.28/0.46 thf(fact_131_pinf_I6_J,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( linorder @ A )
% 0.28/0.46 => ! [T: A] :
% 0.28/0.46 ? [Z2: A] :
% 0.28/0.46 ! [X6: A] :
% 0.28/0.46 ( ( ord_less @ A @ Z2 @ X6 )
% 0.28/0.46 => ~ ( ord_less_eq @ A @ X6 @ T ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % pinf(6)
% 0.28/0.46 thf(fact_132_complete__interval,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( condit1037483654norder @ A )
% 0.28/0.46 => ! [A2: A,B2: A,P: A > $o] :
% 0.28/0.46 ( ( ord_less @ A @ A2 @ B2 )
% 0.28/0.46 => ( ( P @ A2 )
% 0.28/0.46 => ( ~ ( P @ B2 )
% 0.28/0.46 => ? [C3: A] :
% 0.28/0.46 ( ( ord_less_eq @ A @ A2 @ C3 )
% 0.28/0.46 & ( ord_less_eq @ A @ C3 @ B2 )
% 0.28/0.46 & ! [X6: A] :
% 0.28/0.46 ( ( ( ord_less_eq @ A @ A2 @ X6 )
% 0.28/0.46 & ( ord_less @ A @ X6 @ C3 ) )
% 0.28/0.46 => ( P @ X6 ) )
% 0.28/0.46 & ! [D: A] :
% 0.28/0.46 ( ! [X: A] :
% 0.28/0.46 ( ( ( ord_less_eq @ A @ A2 @ X )
% 0.28/0.46 & ( ord_less @ A @ X @ D ) )
% 0.28/0.46 => ( P @ X ) )
% 0.28/0.46 => ( ord_less_eq @ A @ D @ C3 ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % complete_interval
% 0.28/0.46 thf(fact_133_HF__hfset,axiom,
% 0.28/0.46 ! [A2: hF_Mirabelle_hf] :
% 0.28/0.46 ( ( hF_Mirabelle_HF @ ( hF_Mirabelle_hfset @ A2 ) )
% 0.28/0.46 = A2 ) ).
% 0.28/0.46
% 0.28/0.46 % HF_hfset
% 0.28/0.46 thf(fact_134_ex__gt__or__lt,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( condit1656338222tinuum @ A )
% 0.28/0.46 => ! [A2: A] :
% 0.28/0.46 ? [B6: A] :
% 0.28/0.46 ( ( ord_less @ A @ A2 @ B6 )
% 0.28/0.46 | ( ord_less @ A @ B6 @ A2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % ex_gt_or_lt
% 0.28/0.46 thf(fact_135_linorder__neqE__linordered__idom,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( linordered_idom @ A )
% 0.28/0.46 => ! [X3: A,Y2: A] :
% 0.28/0.46 ( ( X3 != Y2 )
% 0.28/0.46 => ( ~ ( ord_less @ A @ X3 @ Y2 )
% 0.28/0.46 => ( ord_less @ A @ Y2 @ X3 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % linorder_neqE_linordered_idom
% 0.28/0.46 thf(fact_136_less__fun__def,axiom,
% 0.28/0.46 ! [B: $tType,A: $tType] :
% 0.28/0.46 ( ( ord @ B )
% 0.28/0.46 => ( ( ord_less @ ( A > B ) )
% 0.28/0.46 = ( ^ [F2: A > B,G2: A > B] :
% 0.28/0.46 ( ( ord_less_eq @ ( A > B ) @ F2 @ G2 )
% 0.28/0.46 & ~ ( ord_less_eq @ ( A > B ) @ G2 @ F2 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % less_fun_def
% 0.28/0.46 thf(fact_137_minf_I11_J,axiom,
% 0.28/0.46 ! [C2: $tType,D2: $tType] :
% 0.28/0.46 ( ( ord @ C2 )
% 0.28/0.46 => ! [F3: D2] :
% 0.28/0.46 ? [Z2: C2] :
% 0.28/0.46 ! [X6: C2] :
% 0.28/0.46 ( ( ord_less @ C2 @ X6 @ Z2 )
% 0.28/0.46 => ( F3 = F3 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % minf(11)
% 0.28/0.46 thf(fact_138_minf_I7_J,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( linorder @ A )
% 0.28/0.46 => ! [T: A] :
% 0.28/0.46 ? [Z2: A] :
% 0.28/0.46 ! [X6: A] :
% 0.28/0.46 ( ( ord_less @ A @ X6 @ Z2 )
% 0.28/0.46 => ~ ( ord_less @ A @ T @ X6 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % minf(7)
% 0.28/0.46 thf(fact_139_minf_I5_J,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( linorder @ A )
% 0.28/0.46 => ! [T: A] :
% 0.28/0.46 ? [Z2: A] :
% 0.28/0.46 ! [X6: A] :
% 0.28/0.46 ( ( ord_less @ A @ X6 @ Z2 )
% 0.28/0.46 => ( ord_less @ A @ X6 @ T ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % minf(5)
% 0.28/0.46 thf(fact_140_minf_I4_J,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( linorder @ A )
% 0.28/0.46 => ! [T: A] :
% 0.28/0.46 ? [Z2: A] :
% 0.28/0.46 ! [X6: A] :
% 0.28/0.46 ( ( ord_less @ A @ X6 @ Z2 )
% 0.28/0.46 => ( X6 != T ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % minf(4)
% 0.28/0.46 thf(fact_141_minf_I3_J,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( linorder @ A )
% 0.28/0.46 => ! [T: A] :
% 0.28/0.46 ? [Z2: A] :
% 0.28/0.46 ! [X6: A] :
% 0.28/0.46 ( ( ord_less @ A @ X6 @ Z2 )
% 0.28/0.46 => ( X6 != T ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % minf(3)
% 0.28/0.46 thf(fact_142_minf_I2_J,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( linorder @ A )
% 0.28/0.46 => ! [P: A > $o,P4: A > $o,Q: A > $o,Q2: A > $o] :
% 0.28/0.46 ( ? [Z4: A] :
% 0.28/0.46 ! [X: A] :
% 0.28/0.46 ( ( ord_less @ A @ X @ Z4 )
% 0.28/0.46 => ( ( P @ X )
% 0.28/0.46 = ( P4 @ X ) ) )
% 0.28/0.46 => ( ? [Z4: A] :
% 0.28/0.46 ! [X: A] :
% 0.28/0.46 ( ( ord_less @ A @ X @ Z4 )
% 0.28/0.46 => ( ( Q @ X )
% 0.28/0.46 = ( Q2 @ X ) ) )
% 0.28/0.46 => ? [Z2: A] :
% 0.28/0.46 ! [X6: A] :
% 0.28/0.46 ( ( ord_less @ A @ X6 @ Z2 )
% 0.28/0.46 => ( ( ( P @ X6 )
% 0.28/0.46 | ( Q @ X6 ) )
% 0.28/0.46 = ( ( P4 @ X6 )
% 0.28/0.46 | ( Q2 @ X6 ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % minf(2)
% 0.28/0.46 thf(fact_143_minf_I1_J,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( linorder @ A )
% 0.28/0.46 => ! [P: A > $o,P4: A > $o,Q: A > $o,Q2: A > $o] :
% 0.28/0.46 ( ? [Z4: A] :
% 0.28/0.46 ! [X: A] :
% 0.28/0.46 ( ( ord_less @ A @ X @ Z4 )
% 0.28/0.46 => ( ( P @ X )
% 0.28/0.46 = ( P4 @ X ) ) )
% 0.28/0.46 => ( ? [Z4: A] :
% 0.28/0.46 ! [X: A] :
% 0.28/0.46 ( ( ord_less @ A @ X @ Z4 )
% 0.28/0.46 => ( ( Q @ X )
% 0.28/0.46 = ( Q2 @ X ) ) )
% 0.28/0.46 => ? [Z2: A] :
% 0.28/0.46 ! [X6: A] :
% 0.28/0.46 ( ( ord_less @ A @ X6 @ Z2 )
% 0.28/0.46 => ( ( ( P @ X6 )
% 0.28/0.46 & ( Q @ X6 ) )
% 0.28/0.46 = ( ( P4 @ X6 )
% 0.28/0.46 & ( Q2 @ X6 ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % minf(1)
% 0.28/0.46 thf(fact_144_pinf_I11_J,axiom,
% 0.28/0.46 ! [C2: $tType,D2: $tType] :
% 0.28/0.46 ( ( ord @ C2 )
% 0.28/0.46 => ! [F3: D2] :
% 0.28/0.46 ? [Z2: C2] :
% 0.28/0.46 ! [X6: C2] :
% 0.28/0.46 ( ( ord_less @ C2 @ Z2 @ X6 )
% 0.28/0.46 => ( F3 = F3 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % pinf(11)
% 0.28/0.46 thf(fact_145_pinf_I7_J,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( linorder @ A )
% 0.28/0.46 => ! [T: A] :
% 0.28/0.46 ? [Z2: A] :
% 0.28/0.46 ! [X6: A] :
% 0.28/0.46 ( ( ord_less @ A @ Z2 @ X6 )
% 0.28/0.46 => ( ord_less @ A @ T @ X6 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % pinf(7)
% 0.28/0.46 thf(fact_146_pinf_I5_J,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( linorder @ A )
% 0.28/0.46 => ! [T: A] :
% 0.28/0.46 ? [Z2: A] :
% 0.28/0.46 ! [X6: A] :
% 0.28/0.46 ( ( ord_less @ A @ Z2 @ X6 )
% 0.28/0.46 => ~ ( ord_less @ A @ X6 @ T ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % pinf(5)
% 0.28/0.46 thf(fact_147_pinf_I4_J,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( linorder @ A )
% 0.28/0.46 => ! [T: A] :
% 0.28/0.46 ? [Z2: A] :
% 0.28/0.46 ! [X6: A] :
% 0.28/0.46 ( ( ord_less @ A @ Z2 @ X6 )
% 0.28/0.46 => ( X6 != T ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % pinf(4)
% 0.28/0.46 thf(fact_148_pinf_I3_J,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( linorder @ A )
% 0.28/0.46 => ! [T: A] :
% 0.28/0.46 ? [Z2: A] :
% 0.28/0.46 ! [X6: A] :
% 0.28/0.46 ( ( ord_less @ A @ Z2 @ X6 )
% 0.28/0.46 => ( X6 != T ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % pinf(3)
% 0.28/0.46 thf(fact_149_pinf_I2_J,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( linorder @ A )
% 0.28/0.46 => ! [P: A > $o,P4: A > $o,Q: A > $o,Q2: A > $o] :
% 0.28/0.46 ( ? [Z4: A] :
% 0.28/0.46 ! [X: A] :
% 0.28/0.46 ( ( ord_less @ A @ Z4 @ X )
% 0.28/0.46 => ( ( P @ X )
% 0.28/0.46 = ( P4 @ X ) ) )
% 0.28/0.46 => ( ? [Z4: A] :
% 0.28/0.46 ! [X: A] :
% 0.28/0.46 ( ( ord_less @ A @ Z4 @ X )
% 0.28/0.46 => ( ( Q @ X )
% 0.28/0.46 = ( Q2 @ X ) ) )
% 0.28/0.46 => ? [Z2: A] :
% 0.28/0.46 ! [X6: A] :
% 0.28/0.46 ( ( ord_less @ A @ Z2 @ X6 )
% 0.28/0.46 => ( ( ( P @ X6 )
% 0.28/0.46 | ( Q @ X6 ) )
% 0.28/0.46 = ( ( P4 @ X6 )
% 0.28/0.46 | ( Q2 @ X6 ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % pinf(2)
% 0.28/0.46 thf(fact_150_pinf_I1_J,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( linorder @ A )
% 0.28/0.46 => ! [P: A > $o,P4: A > $o,Q: A > $o,Q2: A > $o] :
% 0.28/0.46 ( ? [Z4: A] :
% 0.28/0.46 ! [X: A] :
% 0.28/0.46 ( ( ord_less @ A @ Z4 @ X )
% 0.28/0.46 => ( ( P @ X )
% 0.28/0.46 = ( P4 @ X ) ) )
% 0.28/0.46 => ( ? [Z4: A] :
% 0.28/0.46 ! [X: A] :
% 0.28/0.46 ( ( ord_less @ A @ Z4 @ X )
% 0.28/0.46 => ( ( Q @ X )
% 0.28/0.46 = ( Q2 @ X ) ) )
% 0.28/0.46 => ? [Z2: A] :
% 0.28/0.46 ! [X6: A] :
% 0.28/0.46 ( ( ord_less @ A @ Z2 @ X6 )
% 0.28/0.46 => ( ( ( P @ X6 )
% 0.28/0.46 & ( Q @ X6 ) )
% 0.28/0.46 = ( ( P4 @ X6 )
% 0.28/0.46 & ( Q2 @ X6 ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % pinf(1)
% 0.28/0.46 thf(fact_151_hfset__HF,axiom,
% 0.28/0.46 ! [A5: set @ hF_Mirabelle_hf] :
% 0.28/0.46 ( ( finite_finite2 @ hF_Mirabelle_hf @ A5 )
% 0.28/0.46 => ( ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ A5 ) )
% 0.28/0.46 = A5 ) ) ).
% 0.28/0.46
% 0.28/0.46 % hfset_HF
% 0.28/0.46 thf(fact_152_hmem__HF__iff,axiom,
% 0.28/0.46 ! [X3: hF_Mirabelle_hf,A5: set @ hF_Mirabelle_hf] :
% 0.28/0.46 ( ( hF_Mirabelle_hmem @ X3 @ ( hF_Mirabelle_HF @ A5 ) )
% 0.28/0.46 = ( ( member @ hF_Mirabelle_hf @ X3 @ A5 )
% 0.28/0.46 & ( finite_finite2 @ hF_Mirabelle_hf @ A5 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % hmem_HF_iff
% 0.28/0.46 thf(fact_153_measure__induct,axiom,
% 0.28/0.46 ! [B: $tType,A: $tType] :
% 0.28/0.46 ( ( wellorder @ B )
% 0.28/0.46 => ! [F: A > B,P: A > $o,A2: A] :
% 0.28/0.46 ( ! [X: A] :
% 0.28/0.46 ( ! [Y5: A] :
% 0.28/0.46 ( ( ord_less @ B @ ( F @ Y5 ) @ ( F @ X ) )
% 0.28/0.46 => ( P @ Y5 ) )
% 0.28/0.46 => ( P @ X ) )
% 0.28/0.46 => ( P @ A2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % measure_induct
% 0.28/0.46 thf(fact_154_measure__induct__rule,axiom,
% 0.28/0.46 ! [B: $tType,A: $tType] :
% 0.28/0.46 ( ( wellorder @ B )
% 0.28/0.46 => ! [F: A > B,P: A > $o,A2: A] :
% 0.28/0.46 ( ! [X: A] :
% 0.28/0.46 ( ! [Y5: A] :
% 0.28/0.46 ( ( ord_less @ B @ ( F @ Y5 ) @ ( F @ X ) )
% 0.28/0.46 => ( P @ Y5 ) )
% 0.28/0.46 => ( P @ X ) )
% 0.28/0.46 => ( P @ A2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % measure_induct_rule
% 0.28/0.46 thf(fact_155_finite__hfset,axiom,
% 0.28/0.46 ! [A2: hF_Mirabelle_hf] : ( finite_finite2 @ hF_Mirabelle_hf @ ( hF_Mirabelle_hfset @ A2 ) ) ).
% 0.28/0.46
% 0.28/0.46 % finite_hfset
% 0.28/0.46 thf(fact_156_finite__code,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( finite_finite @ A )
% 0.28/0.46 => ( ( finite_finite2 @ A )
% 0.28/0.46 = ( ^ [A4: set @ A] : $true ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % finite_code
% 0.28/0.46 thf(fact_157_finite__has__minimal2,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( order @ A )
% 0.28/0.46 => ! [A5: set @ A,A2: A] :
% 0.28/0.46 ( ( finite_finite2 @ A @ A5 )
% 0.28/0.46 => ( ( member @ A @ A2 @ A5 )
% 0.28/0.46 => ? [X: A] :
% 0.28/0.46 ( ( member @ A @ X @ A5 )
% 0.28/0.46 & ( ord_less_eq @ A @ X @ A2 )
% 0.28/0.46 & ! [Xa: A] :
% 0.28/0.46 ( ( member @ A @ Xa @ A5 )
% 0.28/0.46 => ( ( ord_less_eq @ A @ Xa @ X )
% 0.28/0.46 => ( X = Xa ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % finite_has_minimal2
% 0.28/0.46 thf(fact_158_finite__has__maximal2,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( order @ A )
% 0.28/0.46 => ! [A5: set @ A,A2: A] :
% 0.28/0.46 ( ( finite_finite2 @ A @ A5 )
% 0.28/0.46 => ( ( member @ A @ A2 @ A5 )
% 0.28/0.46 => ? [X: A] :
% 0.28/0.46 ( ( member @ A @ X @ A5 )
% 0.28/0.46 & ( ord_less_eq @ A @ A2 @ X )
% 0.28/0.46 & ! [Xa: A] :
% 0.28/0.46 ( ( member @ A @ Xa @ A5 )
% 0.28/0.46 => ( ( ord_less_eq @ A @ X @ Xa )
% 0.28/0.46 => ( X = Xa ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % finite_has_maximal2
% 0.28/0.46 thf(fact_159_finite__subset,axiom,
% 0.28/0.46 ! [A: $tType,A5: set @ A,B5: set @ A] :
% 0.28/0.46 ( ( ord_less_eq @ ( set @ A ) @ A5 @ B5 )
% 0.28/0.46 => ( ( finite_finite2 @ A @ B5 )
% 0.28/0.46 => ( finite_finite2 @ A @ A5 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % finite_subset
% 0.28/0.46 thf(fact_160_infinite__super,axiom,
% 0.28/0.46 ! [A: $tType,S: set @ A,T2: set @ A] :
% 0.28/0.46 ( ( ord_less_eq @ ( set @ A ) @ S @ T2 )
% 0.28/0.46 => ( ~ ( finite_finite2 @ A @ S )
% 0.28/0.46 => ~ ( finite_finite2 @ A @ T2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % infinite_super
% 0.28/0.46 thf(fact_161_rev__finite__subset,axiom,
% 0.28/0.46 ! [A: $tType,B5: set @ A,A5: set @ A] :
% 0.28/0.46 ( ( finite_finite2 @ A @ B5 )
% 0.28/0.46 => ( ( ord_less_eq @ ( set @ A ) @ A5 @ B5 )
% 0.28/0.46 => ( finite_finite2 @ A @ A5 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % rev_finite_subset
% 0.28/0.46 thf(fact_162_finite__set__choice,axiom,
% 0.28/0.46 ! [B: $tType,A: $tType,A5: set @ A,P: A > B > $o] :
% 0.28/0.46 ( ( finite_finite2 @ A @ A5 )
% 0.28/0.46 => ( ! [X: A] :
% 0.28/0.46 ( ( member @ A @ X @ A5 )
% 0.28/0.46 => ? [X_12: B] : ( P @ X @ X_12 ) )
% 0.28/0.46 => ? [F4: A > B] :
% 0.28/0.46 ! [X6: A] :
% 0.28/0.46 ( ( member @ A @ X6 @ A5 )
% 0.28/0.46 => ( P @ X6 @ ( F4 @ X6 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % finite_set_choice
% 0.28/0.46 thf(fact_163_finite,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( finite_finite @ A )
% 0.28/0.46 => ! [A5: set @ A] : ( finite_finite2 @ A @ A5 ) ) ).
% 0.28/0.46
% 0.28/0.46 % finite
% 0.28/0.46 thf(fact_164_finite__psubset__induct,axiom,
% 0.28/0.46 ! [A: $tType,A5: set @ A,P: ( set @ A ) > $o] :
% 0.28/0.46 ( ( finite_finite2 @ A @ A5 )
% 0.28/0.46 => ( ! [A8: set @ A] :
% 0.28/0.46 ( ( finite_finite2 @ A @ A8 )
% 0.28/0.46 => ( ! [B8: set @ A] :
% 0.28/0.46 ( ( ord_less @ ( set @ A ) @ B8 @ A8 )
% 0.28/0.46 => ( P @ B8 ) )
% 0.28/0.46 => ( P @ A8 ) ) )
% 0.28/0.46 => ( P @ A5 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % finite_psubset_induct
% 0.28/0.46 thf(fact_165_dependent__wellorder__choice,axiom,
% 0.28/0.46 ! [B: $tType,A: $tType] :
% 0.28/0.46 ( ( wellorder @ A )
% 0.28/0.46 => ! [P: ( A > B ) > A > B > $o] :
% 0.28/0.46 ( ! [R2: B,F4: A > B,G3: A > B,X: A] :
% 0.28/0.46 ( ! [Y5: A] :
% 0.28/0.46 ( ( ord_less @ A @ Y5 @ X )
% 0.28/0.46 => ( ( F4 @ Y5 )
% 0.28/0.46 = ( G3 @ Y5 ) ) )
% 0.28/0.46 => ( ( P @ F4 @ X @ R2 )
% 0.28/0.46 = ( P @ G3 @ X @ R2 ) ) )
% 0.28/0.46 => ( ! [X: A,F4: A > B] :
% 0.28/0.46 ( ! [Y5: A] :
% 0.28/0.46 ( ( ord_less @ A @ Y5 @ X )
% 0.28/0.46 => ( P @ F4 @ Y5 @ ( F4 @ Y5 ) ) )
% 0.28/0.46 => ? [X_12: B] : ( P @ F4 @ X @ X_12 ) )
% 0.28/0.46 => ? [F4: A > B] :
% 0.28/0.46 ! [X6: A] : ( P @ F4 @ X6 @ ( F4 @ X6 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % dependent_wellorder_choice
% 0.28/0.46 thf(fact_166_linordered__field__no__lb,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( linordered_field @ A )
% 0.28/0.46 => ! [X6: A] :
% 0.28/0.46 ? [Y4: A] : ( ord_less @ A @ Y4 @ X6 ) ) ).
% 0.28/0.46
% 0.28/0.46 % linordered_field_no_lb
% 0.28/0.46 thf(fact_167_linordered__field__no__ub,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( linordered_field @ A )
% 0.28/0.46 => ! [X6: A] :
% 0.28/0.46 ? [X_1: A] : ( ord_less @ A @ X6 @ X_1 ) ) ).
% 0.28/0.46
% 0.28/0.46 % linordered_field_no_ub
% 0.28/0.46 thf(fact_168_card__psubset,axiom,
% 0.28/0.46 ! [A: $tType,B5: set @ A,A5: set @ A] :
% 0.28/0.46 ( ( finite_finite2 @ A @ B5 )
% 0.28/0.46 => ( ( ord_less_eq @ ( set @ A ) @ A5 @ B5 )
% 0.28/0.46 => ( ( ord_less @ nat @ ( finite_card @ A @ A5 ) @ ( finite_card @ A @ B5 ) )
% 0.28/0.46 => ( ord_less @ ( set @ A ) @ A5 @ B5 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % card_psubset
% 0.28/0.46 thf(fact_169_inj__on__HF,axiom,
% 0.28/0.46 inj_on @ ( set @ hF_Mirabelle_hf ) @ hF_Mirabelle_hf @ hF_Mirabelle_HF @ ( collect @ ( set @ hF_Mirabelle_hf ) @ ( finite_finite2 @ hF_Mirabelle_hf ) ) ).
% 0.28/0.46
% 0.28/0.46 % inj_on_HF
% 0.28/0.46 thf(fact_170_order_Oordering__axioms,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( order @ A )
% 0.28/0.46 => ( ordering @ A @ ( ord_less_eq @ A ) @ ( ord_less @ A ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % order.ordering_axioms
% 0.28/0.46 thf(fact_171_ordering_Onot__eq__order__implies__strict,axiom,
% 0.28/0.46 ! [A: $tType,Less_eq: A > A > $o,Less: A > A > $o,A2: A,B2: A] :
% 0.28/0.46 ( ( ordering @ A @ Less_eq @ Less )
% 0.28/0.46 => ( ( A2 != B2 )
% 0.28/0.46 => ( ( Less_eq @ A2 @ B2 )
% 0.28/0.46 => ( Less @ A2 @ B2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % ordering.not_eq_order_implies_strict
% 0.28/0.46 thf(fact_172_ordering_Ostrict__implies__not__eq,axiom,
% 0.28/0.46 ! [A: $tType,Less_eq: A > A > $o,Less: A > A > $o,A2: A,B2: A] :
% 0.28/0.46 ( ( ordering @ A @ Less_eq @ Less )
% 0.28/0.46 => ( ( Less @ A2 @ B2 )
% 0.28/0.46 => ( A2 != B2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % ordering.strict_implies_not_eq
% 0.28/0.46 thf(fact_173_ordering_Ostrict__implies__order,axiom,
% 0.28/0.46 ! [A: $tType,Less_eq: A > A > $o,Less: A > A > $o,A2: A,B2: A] :
% 0.28/0.46 ( ( ordering @ A @ Less_eq @ Less )
% 0.28/0.46 => ( ( Less @ A2 @ B2 )
% 0.28/0.46 => ( Less_eq @ A2 @ B2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % ordering.strict_implies_order
% 0.28/0.46 thf(fact_174_ordering_Ostrict__iff__order,axiom,
% 0.28/0.46 ! [A: $tType,Less_eq: A > A > $o,Less: A > A > $o,A2: A,B2: A] :
% 0.28/0.46 ( ( ordering @ A @ Less_eq @ Less )
% 0.28/0.46 => ( ( Less @ A2 @ B2 )
% 0.28/0.46 = ( ( Less_eq @ A2 @ B2 )
% 0.28/0.46 & ( A2 != B2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % ordering.strict_iff_order
% 0.28/0.46 thf(fact_175_ordering_Oorder__iff__strict,axiom,
% 0.28/0.46 ! [A: $tType,Less_eq: A > A > $o,Less: A > A > $o,A2: A,B2: A] :
% 0.28/0.46 ( ( ordering @ A @ Less_eq @ Less )
% 0.28/0.46 => ( ( Less_eq @ A2 @ B2 )
% 0.28/0.46 = ( ( Less @ A2 @ B2 )
% 0.28/0.46 | ( A2 = B2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % ordering.order_iff_strict
% 0.28/0.46 thf(fact_176_ordering_Ostrict__trans2,axiom,
% 0.28/0.46 ! [A: $tType,Less_eq: A > A > $o,Less: A > A > $o,A2: A,B2: A,C: A] :
% 0.28/0.46 ( ( ordering @ A @ Less_eq @ Less )
% 0.28/0.46 => ( ( Less @ A2 @ B2 )
% 0.28/0.46 => ( ( Less_eq @ B2 @ C )
% 0.28/0.46 => ( Less @ A2 @ C ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % ordering.strict_trans2
% 0.28/0.46 thf(fact_177_ordering_Ostrict__trans1,axiom,
% 0.28/0.46 ! [A: $tType,Less_eq: A > A > $o,Less: A > A > $o,A2: A,B2: A,C: A] :
% 0.28/0.46 ( ( ordering @ A @ Less_eq @ Less )
% 0.28/0.46 => ( ( Less_eq @ A2 @ B2 )
% 0.28/0.46 => ( ( Less @ B2 @ C )
% 0.28/0.46 => ( Less @ A2 @ C ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % ordering.strict_trans1
% 0.28/0.46 thf(fact_178_ordering_Ostrict__trans,axiom,
% 0.28/0.46 ! [A: $tType,Less_eq: A > A > $o,Less: A > A > $o,A2: A,B2: A,C: A] :
% 0.28/0.46 ( ( ordering @ A @ Less_eq @ Less )
% 0.28/0.46 => ( ( Less @ A2 @ B2 )
% 0.28/0.46 => ( ( Less @ B2 @ C )
% 0.28/0.46 => ( Less @ A2 @ C ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % ordering.strict_trans
% 0.28/0.46 thf(fact_179_ordering__strictI,axiom,
% 0.28/0.46 ! [A: $tType,Less_eq: A > A > $o,Less: A > A > $o] :
% 0.28/0.46 ( ! [A6: A,B6: A] :
% 0.28/0.46 ( ( Less_eq @ A6 @ B6 )
% 0.28/0.46 = ( ( Less @ A6 @ B6 )
% 0.28/0.46 | ( A6 = B6 ) ) )
% 0.28/0.46 => ( ! [A6: A,B6: A] :
% 0.28/0.46 ( ( Less @ A6 @ B6 )
% 0.28/0.46 => ~ ( Less @ B6 @ A6 ) )
% 0.28/0.46 => ( ! [A6: A] :
% 0.28/0.46 ~ ( Less @ A6 @ A6 )
% 0.28/0.46 => ( ! [A6: A,B6: A,C3: A] :
% 0.28/0.46 ( ( Less @ A6 @ B6 )
% 0.28/0.46 => ( ( Less @ B6 @ C3 )
% 0.28/0.46 => ( Less @ A6 @ C3 ) ) )
% 0.28/0.46 => ( ordering @ A @ Less_eq @ Less ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % ordering_strictI
% 0.28/0.46 thf(fact_180_ordering_Oantisym,axiom,
% 0.28/0.46 ! [A: $tType,Less_eq: A > A > $o,Less: A > A > $o,A2: A,B2: A] :
% 0.28/0.46 ( ( ordering @ A @ Less_eq @ Less )
% 0.28/0.46 => ( ( Less_eq @ A2 @ B2 )
% 0.28/0.46 => ( ( Less_eq @ B2 @ A2 )
% 0.28/0.46 => ( A2 = B2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % ordering.antisym
% 0.28/0.46 thf(fact_181_ordering_Oirrefl,axiom,
% 0.28/0.46 ! [A: $tType,Less_eq: A > A > $o,Less: A > A > $o,A2: A] :
% 0.28/0.46 ( ( ordering @ A @ Less_eq @ Less )
% 0.28/0.46 => ~ ( Less @ A2 @ A2 ) ) ).
% 0.28/0.46
% 0.28/0.46 % ordering.irrefl
% 0.28/0.46 thf(fact_182_ordering_Oeq__iff,axiom,
% 0.28/0.46 ! [A: $tType,Less_eq: A > A > $o,Less: A > A > $o,A2: A,B2: A] :
% 0.28/0.46 ( ( ordering @ A @ Less_eq @ Less )
% 0.28/0.46 => ( ( A2 = B2 )
% 0.28/0.46 = ( ( Less_eq @ A2 @ B2 )
% 0.28/0.46 & ( Less_eq @ B2 @ A2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % ordering.eq_iff
% 0.28/0.46 thf(fact_183_ordering_Otrans,axiom,
% 0.28/0.46 ! [A: $tType,Less_eq: A > A > $o,Less: A > A > $o,A2: A,B2: A,C: A] :
% 0.28/0.46 ( ( ordering @ A @ Less_eq @ Less )
% 0.28/0.46 => ( ( Less_eq @ A2 @ B2 )
% 0.28/0.46 => ( ( Less_eq @ B2 @ C )
% 0.28/0.46 => ( Less_eq @ A2 @ C ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % ordering.trans
% 0.28/0.46 thf(fact_184_ordering_Ointro,axiom,
% 0.28/0.46 ! [A: $tType,Less: A > A > $o,Less_eq: A > A > $o] :
% 0.28/0.46 ( ! [A6: A,B6: A] :
% 0.28/0.46 ( ( Less @ A6 @ B6 )
% 0.28/0.46 = ( ( Less_eq @ A6 @ B6 )
% 0.28/0.46 & ( A6 != B6 ) ) )
% 0.28/0.46 => ( ! [A6: A] : ( Less_eq @ A6 @ A6 )
% 0.28/0.46 => ( ! [A6: A,B6: A] :
% 0.28/0.46 ( ( Less_eq @ A6 @ B6 )
% 0.28/0.46 => ( ( Less_eq @ B6 @ A6 )
% 0.28/0.46 => ( A6 = B6 ) ) )
% 0.28/0.46 => ( ! [A6: A,B6: A,C3: A] :
% 0.28/0.46 ( ( Less_eq @ A6 @ B6 )
% 0.28/0.46 => ( ( Less_eq @ B6 @ C3 )
% 0.28/0.46 => ( Less_eq @ A6 @ C3 ) ) )
% 0.28/0.46 => ( ordering @ A @ Less_eq @ Less ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % ordering.intro
% 0.28/0.46 thf(fact_185_ordering_Orefl,axiom,
% 0.28/0.46 ! [A: $tType,Less_eq: A > A > $o,Less: A > A > $o,A2: A] :
% 0.28/0.46 ( ( ordering @ A @ Less_eq @ Less )
% 0.28/0.46 => ( Less_eq @ A2 @ A2 ) ) ).
% 0.28/0.46
% 0.28/0.46 % ordering.refl
% 0.28/0.46 thf(fact_186_ordering_Oasym,axiom,
% 0.28/0.46 ! [A: $tType,Less_eq: A > A > $o,Less: A > A > $o,A2: A,B2: A] :
% 0.28/0.46 ( ( ordering @ A @ Less_eq @ Less )
% 0.28/0.46 => ( ( Less @ A2 @ B2 )
% 0.28/0.46 => ~ ( Less @ B2 @ A2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % ordering.asym
% 0.28/0.46 thf(fact_187_ordering__def,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( ordering @ A )
% 0.28/0.46 = ( ^ [Less_eq2: A > A > $o,Less2: A > A > $o] :
% 0.28/0.46 ( ! [A3: A,B3: A] :
% 0.28/0.46 ( ( Less2 @ A3 @ B3 )
% 0.28/0.46 = ( ( Less_eq2 @ A3 @ B3 )
% 0.28/0.46 & ( A3 != B3 ) ) )
% 0.28/0.46 & ! [A3: A] : ( Less_eq2 @ A3 @ A3 )
% 0.28/0.46 & ! [A3: A,B3: A] :
% 0.28/0.46 ( ( Less_eq2 @ A3 @ B3 )
% 0.28/0.46 => ( ( Less_eq2 @ B3 @ A3 )
% 0.28/0.46 => ( A3 = B3 ) ) )
% 0.28/0.46 & ! [A3: A,B3: A,C4: A] :
% 0.28/0.46 ( ( Less_eq2 @ A3 @ B3 )
% 0.28/0.46 => ( ( Less_eq2 @ B3 @ C4 )
% 0.28/0.46 => ( Less_eq2 @ A3 @ C4 ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % ordering_def
% 0.28/0.46 thf(fact_188_card__mono,axiom,
% 0.28/0.46 ! [A: $tType,B5: set @ A,A5: set @ A] :
% 0.28/0.46 ( ( finite_finite2 @ A @ B5 )
% 0.28/0.46 => ( ( ord_less_eq @ ( set @ A ) @ A5 @ B5 )
% 0.28/0.46 => ( ord_less_eq @ nat @ ( finite_card @ A @ A5 ) @ ( finite_card @ A @ B5 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % card_mono
% 0.28/0.46 thf(fact_189_card__seteq,axiom,
% 0.28/0.46 ! [A: $tType,B5: set @ A,A5: set @ A] :
% 0.28/0.46 ( ( finite_finite2 @ A @ B5 )
% 0.28/0.46 => ( ( ord_less_eq @ ( set @ A ) @ A5 @ B5 )
% 0.28/0.46 => ( ( ord_less_eq @ nat @ ( finite_card @ A @ B5 ) @ ( finite_card @ A @ A5 ) )
% 0.28/0.46 => ( A5 = B5 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % card_seteq
% 0.28/0.46 thf(fact_190_card__subset__eq,axiom,
% 0.28/0.46 ! [A: $tType,B5: set @ A,A5: set @ A] :
% 0.28/0.46 ( ( finite_finite2 @ A @ B5 )
% 0.28/0.46 => ( ( ord_less_eq @ ( set @ A ) @ A5 @ B5 )
% 0.28/0.46 => ( ( ( finite_card @ A @ A5 )
% 0.28/0.46 = ( finite_card @ A @ B5 ) )
% 0.28/0.46 => ( A5 = B5 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % card_subset_eq
% 0.28/0.46 thf(fact_191_infinite__arbitrarily__large,axiom,
% 0.28/0.46 ! [A: $tType,A5: set @ A,N2: nat] :
% 0.28/0.46 ( ~ ( finite_finite2 @ A @ A5 )
% 0.28/0.46 => ? [B9: set @ A] :
% 0.28/0.46 ( ( finite_finite2 @ A @ B9 )
% 0.28/0.46 & ( ( finite_card @ A @ B9 )
% 0.28/0.46 = N2 )
% 0.28/0.46 & ( ord_less_eq @ ( set @ A ) @ B9 @ A5 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % infinite_arbitrarily_large
% 0.28/0.46 thf(fact_192_finite__if__finite__subsets__card__bdd,axiom,
% 0.28/0.46 ! [A: $tType,F3: set @ A,C5: nat] :
% 0.28/0.46 ( ! [G4: set @ A] :
% 0.28/0.46 ( ( ord_less_eq @ ( set @ A ) @ G4 @ F3 )
% 0.28/0.46 => ( ( finite_finite2 @ A @ G4 )
% 0.28/0.46 => ( ord_less_eq @ nat @ ( finite_card @ A @ G4 ) @ C5 ) ) )
% 0.28/0.46 => ( ( finite_finite2 @ A @ F3 )
% 0.28/0.46 & ( ord_less_eq @ nat @ ( finite_card @ A @ F3 ) @ C5 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % finite_if_finite_subsets_card_bdd
% 0.28/0.46 thf(fact_193_psubset__card__mono,axiom,
% 0.28/0.46 ! [A: $tType,B5: set @ A,A5: set @ A] :
% 0.28/0.46 ( ( finite_finite2 @ A @ B5 )
% 0.28/0.46 => ( ( ord_less @ ( set @ A ) @ A5 @ B5 )
% 0.28/0.46 => ( ord_less @ nat @ ( finite_card @ A @ A5 ) @ ( finite_card @ A @ B5 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % psubset_card_mono
% 0.28/0.46 thf(fact_194_obtain__subset__with__card__n,axiom,
% 0.28/0.46 ! [A: $tType,N2: nat,S: set @ A] :
% 0.28/0.46 ( ( ord_less_eq @ nat @ N2 @ ( finite_card @ A @ S ) )
% 0.28/0.46 => ~ ! [T3: set @ A] :
% 0.28/0.46 ( ( ord_less_eq @ ( set @ A ) @ T3 @ S )
% 0.28/0.46 => ( ( ( finite_card @ A @ T3 )
% 0.28/0.46 = N2 )
% 0.28/0.46 => ~ ( finite_finite2 @ A @ T3 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % obtain_subset_with_card_n
% 0.28/0.46 thf(fact_195_linorder__inj__onI,axiom,
% 0.28/0.46 ! [B: $tType,A: $tType] :
% 0.28/0.46 ( ( order @ A )
% 0.28/0.46 => ! [A5: set @ A,F: A > B] :
% 0.28/0.46 ( ! [X: A,Y4: A] :
% 0.28/0.46 ( ( ord_less @ A @ X @ Y4 )
% 0.28/0.46 => ( ( member @ A @ X @ A5 )
% 0.28/0.46 => ( ( member @ A @ Y4 @ A5 )
% 0.28/0.46 => ( ( F @ X )
% 0.28/0.46 != ( F @ Y4 ) ) ) ) )
% 0.28/0.46 => ( ! [X: A,Y4: A] :
% 0.28/0.46 ( ( member @ A @ X @ A5 )
% 0.28/0.46 => ( ( member @ A @ Y4 @ A5 )
% 0.28/0.46 => ( ( ord_less_eq @ A @ X @ Y4 )
% 0.28/0.46 | ( ord_less_eq @ A @ Y4 @ X ) ) ) )
% 0.28/0.46 => ( inj_on @ A @ B @ F @ A5 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % linorder_inj_onI
% 0.28/0.46 thf(fact_196_card__le__if__inj__on__rel,axiom,
% 0.28/0.46 ! [B: $tType,A: $tType,B5: set @ A,A5: set @ B,R3: B > A > $o] :
% 0.28/0.46 ( ( finite_finite2 @ A @ B5 )
% 0.28/0.46 => ( ! [A6: B] :
% 0.28/0.46 ( ( member @ B @ A6 @ A5 )
% 0.28/0.46 => ? [B10: A] :
% 0.28/0.46 ( ( member @ A @ B10 @ B5 )
% 0.28/0.46 & ( R3 @ A6 @ B10 ) ) )
% 0.28/0.46 => ( ! [A1: B,A22: B,B6: A] :
% 0.28/0.46 ( ( member @ B @ A1 @ A5 )
% 0.28/0.46 => ( ( member @ B @ A22 @ A5 )
% 0.28/0.46 => ( ( member @ A @ B6 @ B5 )
% 0.28/0.46 => ( ( R3 @ A1 @ B6 )
% 0.28/0.46 => ( ( R3 @ A22 @ B6 )
% 0.28/0.46 => ( A1 = A22 ) ) ) ) ) )
% 0.28/0.46 => ( ord_less_eq @ nat @ ( finite_card @ B @ A5 ) @ ( finite_card @ A @ B5 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % card_le_if_inj_on_rel
% 0.28/0.46 thf(fact_197_finite__nat__set__iff__bounded__le,axiom,
% 0.28/0.46 ( ( finite_finite2 @ nat )
% 0.28/0.46 = ( ^ [N3: set @ nat] :
% 0.28/0.46 ? [M: nat] :
% 0.28/0.46 ! [X2: nat] :
% 0.28/0.46 ( ( member @ nat @ X2 @ N3 )
% 0.28/0.46 => ( ord_less_eq @ nat @ X2 @ M ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % finite_nat_set_iff_bounded_le
% 0.28/0.46 thf(fact_198_bounded__nat__set__is__finite,axiom,
% 0.28/0.46 ! [N4: set @ nat,N2: nat] :
% 0.28/0.46 ( ! [X: nat] :
% 0.28/0.46 ( ( member @ nat @ X @ N4 )
% 0.28/0.46 => ( ord_less @ nat @ X @ N2 ) )
% 0.28/0.46 => ( finite_finite2 @ nat @ N4 ) ) ).
% 0.28/0.46
% 0.28/0.46 % bounded_nat_set_is_finite
% 0.28/0.46 thf(fact_199_finite__nat__set__iff__bounded,axiom,
% 0.28/0.46 ( ( finite_finite2 @ nat )
% 0.28/0.46 = ( ^ [N3: set @ nat] :
% 0.28/0.46 ? [M: nat] :
% 0.28/0.46 ! [X2: nat] :
% 0.28/0.46 ( ( member @ nat @ X2 @ N3 )
% 0.28/0.46 => ( ord_less @ nat @ X2 @ M ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % finite_nat_set_iff_bounded
% 0.28/0.46 thf(fact_200_card__le__inj,axiom,
% 0.28/0.46 ! [B: $tType,A: $tType,A5: set @ A,B5: set @ B] :
% 0.28/0.46 ( ( finite_finite2 @ A @ A5 )
% 0.28/0.46 => ( ( finite_finite2 @ B @ B5 )
% 0.28/0.46 => ( ( ord_less_eq @ nat @ ( finite_card @ A @ A5 ) @ ( finite_card @ B @ B5 ) )
% 0.28/0.46 => ? [F4: A > B] :
% 0.28/0.46 ( ( ord_less_eq @ ( set @ B ) @ ( image @ A @ B @ F4 @ A5 ) @ B5 )
% 0.28/0.46 & ( inj_on @ A @ B @ F4 @ A5 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % card_le_inj
% 0.28/0.46 thf(fact_201_card__inj__on__le,axiom,
% 0.28/0.46 ! [A: $tType,B: $tType,F: A > B,A5: set @ A,B5: set @ B] :
% 0.28/0.46 ( ( inj_on @ A @ B @ F @ A5 )
% 0.28/0.46 => ( ( ord_less_eq @ ( set @ B ) @ ( image @ A @ B @ F @ A5 ) @ B5 )
% 0.28/0.46 => ( ( finite_finite2 @ B @ B5 )
% 0.28/0.46 => ( ord_less_eq @ nat @ ( finite_card @ A @ A5 ) @ ( finite_card @ B @ B5 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % card_inj_on_le
% 0.28/0.46 thf(fact_202_finite__imageI,axiom,
% 0.28/0.46 ! [B: $tType,A: $tType,F3: set @ A,H: A > B] :
% 0.28/0.46 ( ( finite_finite2 @ A @ F3 )
% 0.28/0.46 => ( finite_finite2 @ B @ ( image @ A @ B @ H @ F3 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % finite_imageI
% 0.28/0.46 thf(fact_203_all__subset__image,axiom,
% 0.28/0.46 ! [A: $tType,B: $tType,F: B > A,A5: set @ B,P: ( set @ A ) > $o] :
% 0.28/0.46 ( ( ! [B4: set @ A] :
% 0.28/0.46 ( ( ord_less_eq @ ( set @ A ) @ B4 @ ( image @ B @ A @ F @ A5 ) )
% 0.28/0.46 => ( P @ B4 ) ) )
% 0.28/0.46 = ( ! [B4: set @ B] :
% 0.28/0.46 ( ( ord_less_eq @ ( set @ B ) @ B4 @ A5 )
% 0.28/0.46 => ( P @ ( image @ B @ A @ F @ B4 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % all_subset_image
% 0.28/0.46 thf(fact_204_all__finite__subset__image,axiom,
% 0.28/0.46 ! [A: $tType,B: $tType,F: B > A,A5: set @ B,P: ( set @ A ) > $o] :
% 0.28/0.46 ( ( ! [B4: set @ A] :
% 0.28/0.46 ( ( ( finite_finite2 @ A @ B4 )
% 0.28/0.46 & ( ord_less_eq @ ( set @ A ) @ B4 @ ( image @ B @ A @ F @ A5 ) ) )
% 0.28/0.46 => ( P @ B4 ) ) )
% 0.28/0.46 = ( ! [B4: set @ B] :
% 0.28/0.46 ( ( ( finite_finite2 @ B @ B4 )
% 0.28/0.46 & ( ord_less_eq @ ( set @ B ) @ B4 @ A5 ) )
% 0.28/0.46 => ( P @ ( image @ B @ A @ F @ B4 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % all_finite_subset_image
% 0.28/0.46 thf(fact_205_ex__finite__subset__image,axiom,
% 0.28/0.46 ! [A: $tType,B: $tType,F: B > A,A5: set @ B,P: ( set @ A ) > $o] :
% 0.28/0.46 ( ( ? [B4: set @ A] :
% 0.28/0.46 ( ( finite_finite2 @ A @ B4 )
% 0.28/0.46 & ( ord_less_eq @ ( set @ A ) @ B4 @ ( image @ B @ A @ F @ A5 ) )
% 0.28/0.46 & ( P @ B4 ) ) )
% 0.28/0.46 = ( ? [B4: set @ B] :
% 0.28/0.46 ( ( finite_finite2 @ B @ B4 )
% 0.28/0.46 & ( ord_less_eq @ ( set @ B ) @ B4 @ A5 )
% 0.28/0.46 & ( P @ ( image @ B @ A @ F @ B4 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % ex_finite_subset_image
% 0.28/0.46 thf(fact_206_finite__subset__image,axiom,
% 0.28/0.46 ! [A: $tType,B: $tType,B5: set @ A,F: B > A,A5: set @ B] :
% 0.28/0.46 ( ( finite_finite2 @ A @ B5 )
% 0.28/0.46 => ( ( ord_less_eq @ ( set @ A ) @ B5 @ ( image @ B @ A @ F @ A5 ) )
% 0.28/0.46 => ? [C6: set @ B] :
% 0.28/0.46 ( ( ord_less_eq @ ( set @ B ) @ C6 @ A5 )
% 0.28/0.46 & ( finite_finite2 @ B @ C6 )
% 0.28/0.46 & ( B5
% 0.28/0.46 = ( image @ B @ A @ F @ C6 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % finite_subset_image
% 0.28/0.46 thf(fact_207_finite__surj,axiom,
% 0.28/0.46 ! [A: $tType,B: $tType,A5: set @ A,B5: set @ B,F: A > B] :
% 0.28/0.46 ( ( finite_finite2 @ A @ A5 )
% 0.28/0.46 => ( ( ord_less_eq @ ( set @ B ) @ B5 @ ( image @ A @ B @ F @ A5 ) )
% 0.28/0.46 => ( finite_finite2 @ B @ B5 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % finite_surj
% 0.28/0.46 thf(fact_208_finite__image__iff,axiom,
% 0.28/0.46 ! [B: $tType,A: $tType,F: A > B,A5: set @ A] :
% 0.28/0.46 ( ( inj_on @ A @ B @ F @ A5 )
% 0.28/0.46 => ( ( finite_finite2 @ B @ ( image @ A @ B @ F @ A5 ) )
% 0.28/0.46 = ( finite_finite2 @ A @ A5 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % finite_image_iff
% 0.28/0.46 thf(fact_209_finite__imageD,axiom,
% 0.28/0.46 ! [A: $tType,B: $tType,F: B > A,A5: set @ B] :
% 0.28/0.46 ( ( finite_finite2 @ A @ ( image @ B @ A @ F @ A5 ) )
% 0.28/0.46 => ( ( inj_on @ B @ A @ F @ A5 )
% 0.28/0.46 => ( finite_finite2 @ B @ A5 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % finite_imageD
% 0.28/0.46 thf(fact_210_card__image,axiom,
% 0.28/0.46 ! [B: $tType,A: $tType,F: A > B,A5: set @ A] :
% 0.28/0.46 ( ( inj_on @ A @ B @ F @ A5 )
% 0.28/0.46 => ( ( finite_card @ B @ ( image @ A @ B @ F @ A5 ) )
% 0.28/0.46 = ( finite_card @ A @ A5 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % card_image
% 0.28/0.46 thf(fact_211_finite__surj__inj,axiom,
% 0.28/0.46 ! [A: $tType,A5: set @ A,F: A > A] :
% 0.28/0.46 ( ( finite_finite2 @ A @ A5 )
% 0.28/0.46 => ( ( ord_less_eq @ ( set @ A ) @ A5 @ ( image @ A @ A @ F @ A5 ) )
% 0.28/0.46 => ( inj_on @ A @ A @ F @ A5 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % finite_surj_inj
% 0.28/0.46 thf(fact_212_inj__on__finite,axiom,
% 0.28/0.46 ! [B: $tType,A: $tType,F: A > B,A5: set @ A,B5: set @ B] :
% 0.28/0.46 ( ( inj_on @ A @ B @ F @ A5 )
% 0.28/0.46 => ( ( ord_less_eq @ ( set @ B ) @ ( image @ A @ B @ F @ A5 ) @ B5 )
% 0.28/0.46 => ( ( finite_finite2 @ B @ B5 )
% 0.28/0.46 => ( finite_finite2 @ A @ A5 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % inj_on_finite
% 0.28/0.46 thf(fact_213_endo__inj__surj,axiom,
% 0.28/0.46 ! [A: $tType,A5: set @ A,F: A > A] :
% 0.28/0.46 ( ( finite_finite2 @ A @ A5 )
% 0.28/0.46 => ( ( ord_less_eq @ ( set @ A ) @ ( image @ A @ A @ F @ A5 ) @ A5 )
% 0.28/0.46 => ( ( inj_on @ A @ A @ F @ A5 )
% 0.28/0.46 => ( ( image @ A @ A @ F @ A5 )
% 0.28/0.46 = A5 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % endo_inj_surj
% 0.28/0.46 thf(fact_214_card__image__le,axiom,
% 0.28/0.46 ! [B: $tType,A: $tType,A5: set @ A,F: A > B] :
% 0.28/0.46 ( ( finite_finite2 @ A @ A5 )
% 0.28/0.46 => ( ord_less_eq @ nat @ ( finite_card @ B @ ( image @ A @ B @ F @ A5 ) ) @ ( finite_card @ A @ A5 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % card_image_le
% 0.28/0.46 thf(fact_215_eq__card__imp__inj__on,axiom,
% 0.28/0.46 ! [B: $tType,A: $tType,A5: set @ A,F: A > B] :
% 0.28/0.46 ( ( finite_finite2 @ A @ A5 )
% 0.28/0.46 => ( ( ( finite_card @ B @ ( image @ A @ B @ F @ A5 ) )
% 0.28/0.46 = ( finite_card @ A @ A5 ) )
% 0.28/0.46 => ( inj_on @ A @ B @ F @ A5 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % eq_card_imp_inj_on
% 0.28/0.46 thf(fact_216_inj__on__iff__eq__card,axiom,
% 0.28/0.46 ! [B: $tType,A: $tType,A5: set @ A,F: A > B] :
% 0.28/0.46 ( ( finite_finite2 @ A @ A5 )
% 0.28/0.46 => ( ( inj_on @ A @ B @ F @ A5 )
% 0.28/0.46 = ( ( finite_card @ B @ ( image @ A @ B @ F @ A5 ) )
% 0.28/0.46 = ( finite_card @ A @ A5 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % inj_on_iff_eq_card
% 0.28/0.46 thf(fact_217_pigeonhole,axiom,
% 0.28/0.46 ! [A: $tType,B: $tType,F: B > A,A5: set @ B] :
% 0.28/0.46 ( ( ord_less @ nat @ ( finite_card @ A @ ( image @ B @ A @ F @ A5 ) ) @ ( finite_card @ B @ A5 ) )
% 0.28/0.46 => ~ ( inj_on @ B @ A @ F @ A5 ) ) ).
% 0.28/0.46
% 0.28/0.46 % pigeonhole
% 0.28/0.46 thf(fact_218_surj__card__le,axiom,
% 0.28/0.46 ! [B: $tType,A: $tType,A5: set @ A,B5: set @ B,F: A > B] :
% 0.28/0.46 ( ( finite_finite2 @ A @ A5 )
% 0.28/0.46 => ( ( ord_less_eq @ ( set @ B ) @ B5 @ ( image @ A @ B @ F @ A5 ) )
% 0.28/0.46 => ( ord_less_eq @ nat @ ( finite_card @ B @ B5 ) @ ( finite_card @ A @ A5 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % surj_card_le
% 0.28/0.46 thf(fact_219_surjective__iff__injective__gen,axiom,
% 0.28/0.46 ! [B: $tType,A: $tType,S: set @ A,T2: set @ B,F: A > B] :
% 0.28/0.46 ( ( finite_finite2 @ A @ S )
% 0.28/0.46 => ( ( finite_finite2 @ B @ T2 )
% 0.28/0.46 => ( ( ( finite_card @ A @ S )
% 0.28/0.46 = ( finite_card @ B @ T2 ) )
% 0.28/0.46 => ( ( ord_less_eq @ ( set @ B ) @ ( image @ A @ B @ F @ S ) @ T2 )
% 0.28/0.46 => ( ( ! [X2: B] :
% 0.28/0.46 ( ( member @ B @ X2 @ T2 )
% 0.28/0.46 => ? [Y3: A] :
% 0.28/0.46 ( ( member @ A @ Y3 @ S )
% 0.28/0.46 & ( ( F @ Y3 )
% 0.28/0.46 = X2 ) ) ) )
% 0.28/0.46 = ( inj_on @ A @ B @ F @ S ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % surjective_iff_injective_gen
% 0.28/0.46 thf(fact_220_card__bij__eq,axiom,
% 0.28/0.46 ! [A: $tType,B: $tType,F: A > B,A5: set @ A,B5: set @ B,G: B > A] :
% 0.28/0.46 ( ( inj_on @ A @ B @ F @ A5 )
% 0.28/0.46 => ( ( ord_less_eq @ ( set @ B ) @ ( image @ A @ B @ F @ A5 ) @ B5 )
% 0.28/0.46 => ( ( inj_on @ B @ A @ G @ B5 )
% 0.28/0.46 => ( ( ord_less_eq @ ( set @ A ) @ ( image @ B @ A @ G @ B5 ) @ A5 )
% 0.28/0.46 => ( ( finite_finite2 @ A @ A5 )
% 0.28/0.46 => ( ( finite_finite2 @ B @ B5 )
% 0.28/0.46 => ( ( finite_card @ A @ A5 )
% 0.28/0.46 = ( finite_card @ B @ B5 ) ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % card_bij_eq
% 0.28/0.46 thf(fact_221_inj__on__iff__card__le,axiom,
% 0.28/0.46 ! [A: $tType,B: $tType,A5: set @ A,B5: set @ B] :
% 0.28/0.46 ( ( finite_finite2 @ A @ A5 )
% 0.28/0.46 => ( ( finite_finite2 @ B @ B5 )
% 0.28/0.46 => ( ( ? [F2: A > B] :
% 0.28/0.46 ( ( inj_on @ A @ B @ F2 @ A5 )
% 0.28/0.46 & ( ord_less_eq @ ( set @ B ) @ ( image @ A @ B @ F2 @ A5 ) @ B5 ) ) )
% 0.28/0.46 = ( ord_less_eq @ nat @ ( finite_card @ A @ A5 ) @ ( finite_card @ B @ B5 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % inj_on_iff_card_le
% 0.28/0.46 thf(fact_222_inj__on__image__Fpow,axiom,
% 0.28/0.46 ! [B: $tType,A: $tType,F: A > B,A5: set @ A] :
% 0.28/0.46 ( ( inj_on @ A @ B @ F @ A5 )
% 0.28/0.46 => ( inj_on @ ( set @ A ) @ ( set @ B ) @ ( image @ A @ B @ F ) @ ( finite_Fpow @ A @ A5 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % inj_on_image_Fpow
% 0.28/0.46 thf(fact_223_image__Fpow__mono,axiom,
% 0.28/0.46 ! [B: $tType,A: $tType,F: B > A,A5: set @ B,B5: set @ A] :
% 0.28/0.46 ( ( ord_less_eq @ ( set @ A ) @ ( image @ B @ A @ F @ A5 ) @ B5 )
% 0.28/0.46 => ( ord_less_eq @ ( set @ ( set @ A ) ) @ ( image @ ( set @ B ) @ ( set @ A ) @ ( image @ B @ A @ F ) @ ( finite_Fpow @ B @ A5 ) ) @ ( finite_Fpow @ A @ B5 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % image_Fpow_mono
% 0.28/0.46 thf(fact_224_Fpow__mono,axiom,
% 0.28/0.46 ! [A: $tType,A5: set @ A,B5: set @ A] :
% 0.28/0.46 ( ( ord_less_eq @ ( set @ A ) @ A5 @ B5 )
% 0.28/0.46 => ( ord_less_eq @ ( set @ ( set @ A ) ) @ ( finite_Fpow @ A @ A5 ) @ ( finite_Fpow @ A @ B5 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % Fpow_mono
% 0.28/0.46 thf(fact_225_card__ge__0__finite,axiom,
% 0.28/0.46 ! [A: $tType,A5: set @ A] :
% 0.28/0.46 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( finite_card @ A @ A5 ) )
% 0.28/0.46 => ( finite_finite2 @ A @ A5 ) ) ).
% 0.28/0.46
% 0.28/0.46 % card_ge_0_finite
% 0.28/0.46 thf(fact_226_greaterThanLessThan__subseteq__greaterThanLessThan,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( dense_linorder @ A )
% 0.28/0.46 => ! [A2: A,B2: A,C: A,D3: A] :
% 0.28/0.46 ( ( ord_less_eq @ ( set @ A ) @ ( set_or578182835ssThan @ A @ A2 @ B2 ) @ ( set_or578182835ssThan @ A @ C @ D3 ) )
% 0.28/0.46 = ( ( ord_less @ A @ A2 @ B2 )
% 0.28/0.46 => ( ( ord_less_eq @ A @ C @ A2 )
% 0.28/0.46 & ( ord_less_eq @ A @ B2 @ D3 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % greaterThanLessThan_subseteq_greaterThanLessThan
% 0.28/0.46 thf(fact_227_finite__greaterThanLessThan,axiom,
% 0.28/0.46 ! [L: nat,U4: nat] : ( finite_finite2 @ nat @ ( set_or578182835ssThan @ nat @ L @ U4 ) ) ).
% 0.28/0.46
% 0.28/0.46 % finite_greaterThanLessThan
% 0.28/0.46 thf(fact_228_bot__nat__0_Onot__eq__extremum,axiom,
% 0.28/0.46 ! [A2: nat] :
% 0.28/0.46 ( ( A2
% 0.28/0.46 != ( zero_zero @ nat ) )
% 0.28/0.46 = ( ord_less @ nat @ ( zero_zero @ nat ) @ A2 ) ) ).
% 0.28/0.46
% 0.28/0.46 % bot_nat_0.not_eq_extremum
% 0.28/0.46 thf(fact_229_less__nat__zero__code,axiom,
% 0.28/0.46 ! [N2: nat] :
% 0.28/0.46 ~ ( ord_less @ nat @ N2 @ ( zero_zero @ nat ) ) ).
% 0.28/0.46
% 0.28/0.46 % less_nat_zero_code
% 0.28/0.46 thf(fact_230_neq0__conv,axiom,
% 0.28/0.46 ! [N2: nat] :
% 0.28/0.46 ( ( N2
% 0.28/0.46 != ( zero_zero @ nat ) )
% 0.28/0.46 = ( ord_less @ nat @ ( zero_zero @ nat ) @ N2 ) ) ).
% 0.28/0.46
% 0.28/0.46 % neq0_conv
% 0.28/0.46 thf(fact_231_le0,axiom,
% 0.28/0.46 ! [N2: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ N2 ) ).
% 0.28/0.46
% 0.28/0.46 % le0
% 0.28/0.46 thf(fact_232_bot__nat__0_Oextremum,axiom,
% 0.28/0.46 ! [A2: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A2 ) ).
% 0.28/0.46
% 0.28/0.46 % bot_nat_0.extremum
% 0.28/0.46 thf(fact_233_greaterThanLessThan__iff,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( ord @ A )
% 0.28/0.46 => ! [I: A,L: A,U4: A] :
% 0.28/0.46 ( ( member @ A @ I @ ( set_or578182835ssThan @ A @ L @ U4 ) )
% 0.28/0.46 = ( ( ord_less @ A @ L @ I )
% 0.28/0.46 & ( ord_less @ A @ I @ U4 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % greaterThanLessThan_iff
% 0.28/0.46 thf(fact_234_card_Oinfinite,axiom,
% 0.28/0.46 ! [A: $tType,A5: set @ A] :
% 0.28/0.46 ( ~ ( finite_finite2 @ A @ A5 )
% 0.28/0.46 => ( ( finite_card @ A @ A5 )
% 0.28/0.46 = ( zero_zero @ nat ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % card.infinite
% 0.28/0.46 thf(fact_235_infinite__Ioo__iff,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( dense_linorder @ A )
% 0.28/0.46 => ! [A2: A,B2: A] :
% 0.28/0.46 ( ( ~ ( finite_finite2 @ A @ ( set_or578182835ssThan @ A @ A2 @ B2 ) ) )
% 0.28/0.46 = ( ord_less @ A @ A2 @ B2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % infinite_Ioo_iff
% 0.28/0.46 thf(fact_236_less__eq__nat_Osimps_I1_J,axiom,
% 0.28/0.46 ! [N2: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ N2 ) ).
% 0.28/0.46
% 0.28/0.46 % less_eq_nat.simps(1)
% 0.28/0.46 thf(fact_237_le__0__eq,axiom,
% 0.28/0.46 ! [N2: nat] :
% 0.28/0.46 ( ( ord_less_eq @ nat @ N2 @ ( zero_zero @ nat ) )
% 0.28/0.46 = ( N2
% 0.28/0.46 = ( zero_zero @ nat ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % le_0_eq
% 0.28/0.46 thf(fact_238_bot__nat__0_Oextremum__unique,axiom,
% 0.28/0.46 ! [A2: nat] :
% 0.28/0.46 ( ( ord_less_eq @ nat @ A2 @ ( zero_zero @ nat ) )
% 0.28/0.46 = ( A2
% 0.28/0.46 = ( zero_zero @ nat ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % bot_nat_0.extremum_unique
% 0.28/0.46 thf(fact_239_bot__nat__0_Oextremum__uniqueI,axiom,
% 0.28/0.46 ! [A2: nat] :
% 0.28/0.46 ( ( ord_less_eq @ nat @ A2 @ ( zero_zero @ nat ) )
% 0.28/0.46 => ( A2
% 0.28/0.46 = ( zero_zero @ nat ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % bot_nat_0.extremum_uniqueI
% 0.28/0.46 thf(fact_240_ex__least__nat__le,axiom,
% 0.28/0.46 ! [P: nat > $o,N2: nat] :
% 0.28/0.46 ( ( P @ N2 )
% 0.28/0.46 => ( ~ ( P @ ( zero_zero @ nat ) )
% 0.28/0.46 => ? [K: nat] :
% 0.28/0.46 ( ( ord_less_eq @ nat @ K @ N2 )
% 0.28/0.46 & ! [I2: nat] :
% 0.28/0.46 ( ( ord_less @ nat @ I2 @ K )
% 0.28/0.46 => ~ ( P @ I2 ) )
% 0.28/0.46 & ( P @ K ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % ex_least_nat_le
% 0.28/0.46 thf(fact_241_infinite__descent0__measure,axiom,
% 0.28/0.46 ! [A: $tType,V5: A > nat,P: A > $o,X3: A] :
% 0.28/0.46 ( ! [X: A] :
% 0.28/0.46 ( ( ( V5 @ X )
% 0.28/0.46 = ( zero_zero @ nat ) )
% 0.28/0.46 => ( P @ X ) )
% 0.28/0.46 => ( ! [X: A] :
% 0.28/0.46 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( V5 @ X ) )
% 0.28/0.46 => ( ~ ( P @ X )
% 0.28/0.46 => ? [Y5: A] :
% 0.28/0.46 ( ( ord_less @ nat @ ( V5 @ Y5 ) @ ( V5 @ X ) )
% 0.28/0.46 & ~ ( P @ Y5 ) ) ) )
% 0.28/0.46 => ( P @ X3 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % infinite_descent0_measure
% 0.28/0.46 thf(fact_242_bot__nat__0_Oextremum__strict,axiom,
% 0.28/0.46 ! [A2: nat] :
% 0.28/0.46 ~ ( ord_less @ nat @ A2 @ ( zero_zero @ nat ) ) ).
% 0.28/0.46
% 0.28/0.46 % bot_nat_0.extremum_strict
% 0.28/0.46 thf(fact_243_infinite__descent0,axiom,
% 0.28/0.46 ! [P: nat > $o,N2: nat] :
% 0.28/0.46 ( ( P @ ( zero_zero @ nat ) )
% 0.28/0.46 => ( ! [N5: nat] :
% 0.28/0.46 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N5 )
% 0.28/0.46 => ( ~ ( P @ N5 )
% 0.28/0.46 => ? [M2: nat] :
% 0.28/0.46 ( ( ord_less @ nat @ M2 @ N5 )
% 0.28/0.46 & ~ ( P @ M2 ) ) ) )
% 0.28/0.46 => ( P @ N2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % infinite_descent0
% 0.28/0.46 thf(fact_244_gr__implies__not0,axiom,
% 0.28/0.46 ! [M3: nat,N2: nat] :
% 0.28/0.46 ( ( ord_less @ nat @ M3 @ N2 )
% 0.28/0.46 => ( N2
% 0.28/0.46 != ( zero_zero @ nat ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % gr_implies_not0
% 0.28/0.46 thf(fact_245_less__zeroE,axiom,
% 0.28/0.46 ! [N2: nat] :
% 0.28/0.46 ~ ( ord_less @ nat @ N2 @ ( zero_zero @ nat ) ) ).
% 0.28/0.46
% 0.28/0.46 % less_zeroE
% 0.28/0.46 thf(fact_246_not__less0,axiom,
% 0.28/0.46 ! [N2: nat] :
% 0.28/0.46 ~ ( ord_less @ nat @ N2 @ ( zero_zero @ nat ) ) ).
% 0.28/0.46
% 0.28/0.46 % not_less0
% 0.28/0.46 thf(fact_247_not__gr0,axiom,
% 0.28/0.46 ! [N2: nat] :
% 0.28/0.46 ( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ N2 ) )
% 0.28/0.46 = ( N2
% 0.28/0.46 = ( zero_zero @ nat ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % not_gr0
% 0.28/0.46 thf(fact_248_gr0I,axiom,
% 0.28/0.46 ! [N2: nat] :
% 0.28/0.46 ( ( N2
% 0.28/0.46 != ( zero_zero @ nat ) )
% 0.28/0.46 => ( ord_less @ nat @ ( zero_zero @ nat ) @ N2 ) ) ).
% 0.28/0.46
% 0.28/0.46 % gr0I
% 0.28/0.46 thf(fact_249_infinite__Ioo,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( dense_linorder @ A )
% 0.28/0.46 => ! [A2: A,B2: A] :
% 0.28/0.46 ( ( ord_less @ A @ A2 @ B2 )
% 0.28/0.46 => ~ ( finite_finite2 @ A @ ( set_or578182835ssThan @ A @ A2 @ B2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % infinite_Ioo
% 0.28/0.46 thf(fact_250_not__gr__zero,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( canoni770627133id_add @ A )
% 0.28/0.46 => ! [N2: A] :
% 0.28/0.46 ( ( ~ ( ord_less @ A @ ( zero_zero @ A ) @ N2 ) )
% 0.28/0.46 = ( N2
% 0.28/0.46 = ( zero_zero @ A ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % not_gr_zero
% 0.28/0.46 thf(fact_251_le__zero__eq,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( canoni770627133id_add @ A )
% 0.28/0.46 => ! [N2: A] :
% 0.28/0.46 ( ( ord_less_eq @ A @ N2 @ ( zero_zero @ A ) )
% 0.28/0.46 = ( N2
% 0.28/0.46 = ( zero_zero @ A ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % le_zero_eq
% 0.28/0.46 thf(fact_252_RepFun__0,axiom,
% 0.28/0.46 ! [F: hF_Mirabelle_hf > hF_Mirabelle_hf] :
% 0.28/0.46 ( ( hF_Mirabelle_RepFun @ ( zero_zero @ hF_Mirabelle_hf ) @ F )
% 0.28/0.46 = ( zero_zero @ hF_Mirabelle_hf ) ) ).
% 0.28/0.46
% 0.28/0.46 % RepFun_0
% 0.28/0.46 thf(fact_253_HUnion__hempty,axiom,
% 0.28/0.46 ( ( hF_Mirabelle_HUnion @ ( zero_zero @ hF_Mirabelle_hf ) )
% 0.28/0.46 = ( zero_zero @ hF_Mirabelle_hf ) ) ).
% 0.28/0.46
% 0.28/0.46 % HUnion_hempty
% 0.28/0.46 thf(fact_254_Replace__0,axiom,
% 0.28/0.46 ! [R: hF_Mirabelle_hf > hF_Mirabelle_hf > $o] :
% 0.28/0.46 ( ( hF_Mirabelle_Replace @ ( zero_zero @ hF_Mirabelle_hf ) @ R )
% 0.28/0.46 = ( zero_zero @ hF_Mirabelle_hf ) ) ).
% 0.28/0.46
% 0.28/0.46 % Replace_0
% 0.28/0.46
% 0.28/0.46 % Type constructors (24)
% 0.28/0.46 thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.28/0.46 ! [A9: $tType,A10: $tType] :
% 0.28/0.46 ( ( preorder @ A10 )
% 0.28/0.46 => ( preorder @ ( A9 > A10 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(tcon_fun___Finite__Set_Ofinite,axiom,
% 0.28/0.46 ! [A9: $tType,A10: $tType] :
% 0.28/0.46 ( ( ( finite_finite @ A9 )
% 0.28/0.46 & ( finite_finite @ A10 ) )
% 0.28/0.46 => ( finite_finite @ ( A9 > A10 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.28/0.46 ! [A9: $tType,A10: $tType] :
% 0.28/0.46 ( ( order @ A10 )
% 0.28/0.46 => ( order @ ( A9 > A10 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(tcon_fun___Orderings_Oord,axiom,
% 0.28/0.46 ! [A9: $tType,A10: $tType] :
% 0.28/0.46 ( ( ord @ A10 )
% 0.28/0.46 => ( ord @ ( A9 > A10 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(tcon_Nat_Onat___Conditionally__Complete__Lattices_Oconditionally__complete__linorder,axiom,
% 0.28/0.46 condit1037483654norder @ nat ).
% 0.28/0.46
% 0.28/0.46 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add,axiom,
% 0.28/0.46 canoni770627133id_add @ nat ).
% 0.28/0.46
% 0.28/0.46 thf(tcon_Nat_Onat___Orderings_Owellorder,axiom,
% 0.28/0.46 wellorder @ nat ).
% 0.28/0.46
% 0.28/0.46 thf(tcon_Nat_Onat___Orderings_Opreorder_1,axiom,
% 0.28/0.46 preorder @ nat ).
% 0.28/0.46
% 0.28/0.46 thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 0.28/0.46 linorder @ nat ).
% 0.28/0.46
% 0.28/0.46 thf(tcon_Nat_Onat___Orderings_Ono__top,axiom,
% 0.28/0.46 no_top @ nat ).
% 0.28/0.46
% 0.28/0.46 thf(tcon_Nat_Onat___Orderings_Oorder_2,axiom,
% 0.28/0.46 order @ nat ).
% 0.28/0.46
% 0.28/0.46 thf(tcon_Nat_Onat___Orderings_Oord_3,axiom,
% 0.28/0.46 ord @ nat ).
% 0.28/0.46
% 0.28/0.46 thf(tcon_Set_Oset___Orderings_Opreorder_4,axiom,
% 0.28/0.46 ! [A9: $tType] : ( preorder @ ( set @ A9 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(tcon_Set_Oset___Finite__Set_Ofinite_5,axiom,
% 0.28/0.46 ! [A9: $tType] :
% 0.28/0.46 ( ( finite_finite @ A9 )
% 0.28/0.46 => ( finite_finite @ ( set @ A9 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(tcon_Set_Oset___Orderings_Oorder_6,axiom,
% 0.28/0.46 ! [A9: $tType] : ( order @ ( set @ A9 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(tcon_Set_Oset___Orderings_Oord_7,axiom,
% 0.28/0.46 ! [A9: $tType] : ( ord @ ( set @ A9 ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(tcon_HOL_Obool___Orderings_Opreorder_8,axiom,
% 0.28/0.46 preorder @ $o ).
% 0.28/0.46
% 0.28/0.46 thf(tcon_HOL_Obool___Orderings_Olinorder_9,axiom,
% 0.28/0.46 linorder @ $o ).
% 0.28/0.46
% 0.28/0.46 thf(tcon_HOL_Obool___Finite__Set_Ofinite_10,axiom,
% 0.28/0.46 finite_finite @ $o ).
% 0.28/0.46
% 0.28/0.46 thf(tcon_HOL_Obool___Orderings_Oorder_11,axiom,
% 0.28/0.46 order @ $o ).
% 0.28/0.46
% 0.28/0.46 thf(tcon_HOL_Obool___Orderings_Oord_12,axiom,
% 0.28/0.46 ord @ $o ).
% 0.28/0.46
% 0.28/0.46 thf(tcon_HF__Mirabelle__fsbjehakzm_Ohf___Orderings_Opreorder_13,axiom,
% 0.28/0.46 preorder @ hF_Mirabelle_hf ).
% 0.28/0.46
% 0.28/0.46 thf(tcon_HF__Mirabelle__fsbjehakzm_Ohf___Orderings_Oorder_14,axiom,
% 0.28/0.46 order @ hF_Mirabelle_hf ).
% 0.28/0.46
% 0.28/0.46 thf(tcon_HF__Mirabelle__fsbjehakzm_Ohf___Orderings_Oord_15,axiom,
% 0.28/0.46 ord @ hF_Mirabelle_hf ).
% 0.28/0.46
% 0.28/0.46 % Conjectures (2)
% 0.28/0.46 thf(conj_0,hypothesis,
% 0.28/0.46 ! [X6: hF_Mirabelle_hf] :
% 0.28/0.46 ( ( hF_Mirabelle_hmem @ X6 @ a )
% 0.28/0.46 => ( hF_Mirabelle_hmem @ X6 @ b ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(conj_1,conjecture,
% 0.28/0.46 ord_less_eq @ hF_Mirabelle_hf @ a @ b ).
% 0.28/0.46
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 ------------------------
% 0.29/1.50 ---- Embedded in THF ---
% 0.29/1.50 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.29/1.50 %%% Generated on Tue Feb 24 08:25:23 EST 2026
% 0.29/1.50 %%% using '$$dhol' embedding, version 1.3.0.
% 0.29/1.50 %%% Logic specification used:
% 0.29/1.50 %%% thf(spec, logic, $$dhol).
% 0.29/1.50
% 0.29/1.50 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.vTURPhR8yA/DTF2DTF14628.p
% 0.29/1.50 thf(ty_t_HF__Mirabelle__fsbjehakzm_Ohf, type, hF_Mirabelle_hf: $tType).
% 0.29/1.50 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 0.29/1.50 thf(ty_t_Nat_Onat, type, nat: $tType).
% 0.29/1.50 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: ($o))).
% 0.29/1.50 thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: ($o))).
% 0.29/1.50 thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: ($o))).
% 0.29/1.50 thf(sy_cl_Orderings_Ono__bot, type, no_bot: (!> [A:$tType]: ($o))).
% 0.29/1.50 thf(sy_cl_Orderings_Ono__top, type, no_top: (!> [A:$tType]: ($o))).
% 0.29/1.50 thf(sy_cl_Finite__Set_Ofinite, type, finite_finite: (!> [A:$tType]: ($o))).
% 0.29/1.50 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: ($o))).
% 0.29/1.50 thf(sy_cl_Orderings_Opreorder, type, preorder: (!> [A:$tType]: ($o))).
% 0.29/1.50 thf(sy_cl_Orderings_Owellorder, type, wellorder: (!> [A:$tType]: ($o))).
% 0.29/1.50 thf(sy_cl_Orderings_Odense__order, type, dense_order: (!> [A:$tType]: ($o))).
% 0.29/1.50 thf(sy_cl_Rings_Olinordered__idom, type, linordered_idom: (!> [A:$tType]: ($o))).
% 0.29/1.50 thf(sy_cl_Fields_Olinordered__field, type, linordered_field: (!> [A:$tType]: ($o))).
% 0.29/1.50 thf(sy_cl_Orderings_Odense__linorder, type, dense_linorder: (!> [A:$tType]: ($o))).
% 0.29/1.50 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add, type, canoni770627133id_add: (!> [A:$tType]: ($o))).
% 0.29/1.50 thf(sy_cl_Conditionally__Complete__Lattices_Olinear__continuum, type, condit1656338222tinuum: (!> [A:$tType]: ($o))).
% 0.29/1.50 thf(sy_cl_Conditionally__Complete__Lattices_Oconditionally__complete__linorder, type, condit1037483654norder: (!> [A:$tType]: ($o))).
% 0.29/1.50 thf(sy_c_Finite__Set_OFpow, type, finite_Fpow: (!> [A:$tType]: (((set @ A) > (set @ (set @ A)))))).
% 0.29/1.50 thf(sy_c_Finite__Set_Ocard, type, finite_card: (!> [B:$tType]: (((set @ B) > nat)))).
% 0.29/1.50 thf(sy_c_Finite__Set_Ofinite, type, finite_finite2: (!> [A:$tType]: (((set @ A) > $o)))).
% 0.29/1.50 thf(sy_c_Fun_Oinj__on, type, inj_on: (!> [A:$tType,B:$tType]: (((A > B) > ((set @ A) > $o))))).
% 0.29/1.50 thf(sy_c_Groups_Ozero__class_Ozero, type, zero_zero: (!> [A:$tType]: (A))).
% 0.29/1.50 thf(sy_c_HF__Mirabelle__fsbjehakzm_OHCollect, type, hF_Mir1687042746ollect: ((hF_Mirabelle_hf > $o) > (hF_Mirabelle_hf > hF_Mirabelle_hf))).
% 0.29/1.50 thf(sy_c_HF__Mirabelle__fsbjehakzm_OHF, type, hF_Mirabelle_HF: ((set @ hF_Mirabelle_hf) > hF_Mirabelle_hf)).
% 0.29/1.50 thf(sy_c_HF__Mirabelle__fsbjehakzm_OHUnion, type, hF_Mirabelle_HUnion: (hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.29/1.50 thf(sy_c_HF__Mirabelle__fsbjehakzm_OPrimReplace, type, hF_Mir569462966eplace: (hF_Mirabelle_hf > ((hF_Mirabelle_hf > (hF_Mirabelle_hf > $o)) > hF_Mirabelle_hf))).
% 0.29/1.50 thf(sy_c_HF__Mirabelle__fsbjehakzm_ORepFun, type, hF_Mirabelle_RepFun: (hF_Mirabelle_hf > ((hF_Mirabelle_hf > hF_Mirabelle_hf) > hF_Mirabelle_hf))).
% 0.29/1.50 thf(sy_c_HF__Mirabelle__fsbjehakzm_OReplace, type, hF_Mirabelle_Replace: (hF_Mirabelle_hf > ((hF_Mirabelle_hf > (hF_Mirabelle_hf > $o)) > hF_Mirabelle_hf))).
% 0.29/1.50 thf(sy_c_HF__Mirabelle__fsbjehakzm_Ohfset, type, hF_Mirabelle_hfset: (hF_Mirabelle_hf > (set @ hF_Mirabelle_hf))).
% 0.29/1.50 thf(sy_c_HF__Mirabelle__fsbjehakzm_Ohmem, type, hF_Mirabelle_hmem: (hF_Mirabelle_hf > (hF_Mirabelle_hf > $o))).
% 0.29/1.50 thf(sy_c_Orderings_Oord__class_Oless, type, ord_less: (!> [A:$tType]: ((A > (A > $o))))).
% 0.29/1.50 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 0.29/1.50 thf(sy_c_Orderings_Oorder__class_OGreatest, type, order_Greatest: (!> [A:$tType]: (((A > $o) > A)))).
% 0.29/1.50 thf(sy_c_Orderings_Oorder__class_Oantimono, type, order_antimono: (!> [A:$tType,B:$tType]: (((A > B) > $o)))).
% 0.29/1.50 thf(sy_c_Orderings_Oordering, type, ordering: (!> [A:$tType]: (((A > (A > $o)) > ((A > (A > $o)) > $o))))).
% 0.29/1.50 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 0.29/1.50 thf(sy_c_Set_Oimage, type, image: (!> [A:$tType,B:$tType]: (((A > B) > ((set @ A) > (set @ B)))))).
% 0.29/1.50 thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan, type, set_or578182835ssThan: (!> [A:$tType]: ((A > (A > (set @ A)))))).
% 0.29/1.50 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 0.29/1.50 thf(sy_v_A, type, a: hF_Mirabelle_hf).
% 0.29/1.50 thf(sy_v_B, type, b: hF_Mirabelle_hf).
% 0.29/1.50 thf(fact_0_hf__equalityI, axiom, (! [A2:hF_Mirabelle_hf,B2:hF_Mirabelle_hf]: (((! [X:hF_Mirabelle_hf]: ((((hF_Mirabelle_hmem @ X) @ A2) = ((hF_Mirabelle_hmem @ X) @ B2)))) => (A2 = B2))))).
% 0.29/1.50 thf(fact_1_hf__ext, axiom, ((^ [Y:hF_Mirabelle_hf,Z:hF_Mirabelle_hf]: ((Y = Z))) = (^ [A3:hF_Mirabelle_hf,B3:hF_Mirabelle_hf]: ((! [X2:hF_Mirabelle_hf]: ((((hF_Mirabelle_hmem @ X2) @ A3) = ((hF_Mirabelle_hmem @ X2) @ B3)))))))).
% 0.29/1.50 thf(fact_2_replacement, axiom, (! [X3:hF_Mirabelle_hf,R:(hF_Mirabelle_hf > (hF_Mirabelle_hf > $o))]: (((! [U:hF_Mirabelle_hf,V:hF_Mirabelle_hf,V2:hF_Mirabelle_hf]: ((((hF_Mirabelle_hmem @ U) @ X3) => (((R @ U) @ V) => (((R @ U) @ V2) => (V2 = V)))))) => (? [Z2:hF_Mirabelle_hf]: ((! [V3:hF_Mirabelle_hf]: ((((hF_Mirabelle_hmem @ V3) @ Z2) = (? [U2:hF_Mirabelle_hf]: ((((hF_Mirabelle_hmem @ U2) @ X3) & ((R @ U2) @ V3))))))))))))).
% 0.29/1.50 thf(fact_3_binary__union, axiom, (! [X3:hF_Mirabelle_hf,Y2:hF_Mirabelle_hf]: ((? [Z2:hF_Mirabelle_hf]: ((! [U3:hF_Mirabelle_hf]: ((((hF_Mirabelle_hmem @ U3) @ Z2) = (((hF_Mirabelle_hmem @ U3) @ X3) | ((hF_Mirabelle_hmem @ U3) @ Y2)))))))))).
% 0.29/1.50 thf(fact_4_union__of__set, axiom, (! [X3:hF_Mirabelle_hf]: ((? [Z2:hF_Mirabelle_hf]: ((! [U3:hF_Mirabelle_hf]: ((((hF_Mirabelle_hmem @ U3) @ Z2) = (? [Y3:hF_Mirabelle_hf]: ((((hF_Mirabelle_hmem @ Y3) @ X3) & ((hF_Mirabelle_hmem @ U3) @ Y3)))))))))))).
% 0.29/1.50 thf(fact_5_comprehension, axiom, (! [X3:hF_Mirabelle_hf,P:(hF_Mirabelle_hf > $o)]: ((? [Z2:hF_Mirabelle_hf]: ((! [U3:hF_Mirabelle_hf]: ((((hF_Mirabelle_hmem @ U3) @ Z2) = (((hF_Mirabelle_hmem @ U3) @ X3) & (P @ U3)))))))))).
% 0.29/1.50 thf(fact_6_less__eq__hf__def, axiom, ((ord_less_eq @ hF_Mirabelle_hf) = (^ [A4:hF_Mirabelle_hf,B4:hF_Mirabelle_hf]: ((! [X2:hF_Mirabelle_hf]: ((((hF_Mirabelle_hmem @ X2) @ A4) => ((hF_Mirabelle_hmem @ X2) @ B4)))))))).
% 0.29/1.50 thf(fact_7_replacement__fun, axiom, (! [X3:hF_Mirabelle_hf,F:(hF_Mirabelle_hf > hF_Mirabelle_hf)]: ((? [Z2:hF_Mirabelle_hf]: ((! [V3:hF_Mirabelle_hf]: ((((hF_Mirabelle_hmem @ V3) @ Z2) = (? [U2:hF_Mirabelle_hf]: ((((hF_Mirabelle_hmem @ U2) @ X3) & (V3 = (F @ U2))))))))))))).
% 0.29/1.50 thf(fact_8_order__refl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A]: ((((ord_less_eq @ A) @ X3) @ X3))))))).
% 0.29/1.50 thf(fact_9_PrimReplace__iff, axiom, (! [A5:hF_Mirabelle_hf,R:(hF_Mirabelle_hf > (hF_Mirabelle_hf > $o)),V4:hF_Mirabelle_hf]: (((! [U:hF_Mirabelle_hf,V:hF_Mirabelle_hf,V2:hF_Mirabelle_hf]: ((((hF_Mirabelle_hmem @ U) @ A5) => (((R @ U) @ V) => (((R @ U) @ V2) => (V2 = V)))))) => (((hF_Mirabelle_hmem @ V4) @ ((hF_Mir569462966eplace @ A5) @ R)) = (? [U2:hF_Mirabelle_hf]: ((((hF_Mirabelle_hmem @ U2) @ A5) & ((R @ U2) @ V4))))))))).
% 0.29/1.50 thf(fact_10_HCollect__iff, axiom, (! [X3:hF_Mirabelle_hf,P:(hF_Mirabelle_hf > $o),A5:hF_Mirabelle_hf]: ((((hF_Mirabelle_hmem @ X3) @ ((hF_Mir1687042746ollect @ P) @ A5)) = ((P @ X3) & ((hF_Mirabelle_hmem @ X3) @ A5)))))).
% 0.29/1.50 thf(fact_11_HUnion__iff, axiom, (! [X3:hF_Mirabelle_hf,A5:hF_Mirabelle_hf]: ((((hF_Mirabelle_hmem @ X3) @ (hF_Mirabelle_HUnion @ A5)) = (? [Y3:hF_Mirabelle_hf]: ((((hF_Mirabelle_hmem @ Y3) @ A5) & ((hF_Mirabelle_hmem @ X3) @ Y3)))))))).
% 0.29/1.50 thf(fact_12_Replace__iff, axiom, (! [V4:hF_Mirabelle_hf,A5:hF_Mirabelle_hf,R:(hF_Mirabelle_hf > (hF_Mirabelle_hf > $o))]: ((((hF_Mirabelle_hmem @ V4) @ ((hF_Mirabelle_Replace @ A5) @ R)) = (? [U2:hF_Mirabelle_hf]: ((((hF_Mirabelle_hmem @ U2) @ A5) & (((R @ U2) @ V4) & (! [Y3:hF_Mirabelle_hf]: ((((R @ U2) @ Y3) => (Y3 = V4)))))))))))).
% 0.29/1.50 thf(fact_13_le__funD, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F:(A > B),G:(A > B),X3:A]: (((((ord_less_eq @ (A > B)) @ F) @ G) => (((ord_less_eq @ B) @ (F @ X3)) @ (G @ X3))))))))).
% 0.29/1.50 thf(fact_14_le__funE, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F:(A > B),G:(A > B),X3:A]: (((((ord_less_eq @ (A > B)) @ F) @ G) => (((ord_less_eq @ B) @ (F @ X3)) @ (G @ X3))))))))).
% 0.29/1.50 thf(fact_15_le__funI, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F:(A > B),G:(A > B)]: (((! [X:A]: ((((ord_less_eq @ B) @ (F @ X)) @ (G @ X)))) => (((ord_less_eq @ (A > B)) @ F) @ G)))))))).
% 0.29/1.50 thf(fact_16_le__fun__def, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => ((ord_less_eq @ (A > B)) = (^ [F2:(A > B),G2:(A > B)]: ((! [X2:A]: ((((ord_less_eq @ B) @ (F2 @ X2)) @ (G2 @ X2))))))))))).
% 0.29/1.50 thf(fact_17_order__subst1, axiom, (! [A:$tType,B:$tType]: ((((order @ B) & (order @ A)) => (! [A2:A,F:(B > A),B2:B,C:B]: (((((ord_less_eq @ A) @ A2) @ (F @ B2)) => ((((ord_less_eq @ B) @ B2) @ C) => ((! [X:B,Y4:B]: (((((ord_less_eq @ B) @ X) @ Y4) => (((ord_less_eq @ A) @ (F @ X)) @ (F @ Y4))))) => (((ord_less_eq @ A) @ A2) @ (F @ C))))))))))).
% 0.29/1.50 thf(fact_18_order__subst2, axiom, (! [A:$tType,C2:$tType]: ((((order @ C2) & (order @ A)) => (! [A2:A,B2:A,F:(A > C2),C:C2]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ C2) @ (F @ B2)) @ C) => ((! [X:A,Y4:A]: (((((ord_less_eq @ A) @ X) @ Y4) => (((ord_less_eq @ C2) @ (F @ X)) @ (F @ Y4))))) => (((ord_less_eq @ C2) @ (F @ A2)) @ C)))))))))).
% 0.29/1.50 thf(fact_19_verit__la__disequality, axiom, (! [A:$tType]: (((linorder @ A) => (! [A2:A,B2:A]: (((A2 = B2) | ((~ ((((ord_less_eq @ A) @ A2) @ B2))) | (~ ((((ord_less_eq @ A) @ B2) @ A2))))))))))).
% 0.29/1.50 thf(fact_20_Replace__cong, axiom, (! [A5:hF_Mirabelle_hf,B5:hF_Mirabelle_hf,P:(hF_Mirabelle_hf > (hF_Mirabelle_hf > $o)),Q:(hF_Mirabelle_hf > (hF_Mirabelle_hf > $o))]: (((A5 = B5) => ((! [X:hF_Mirabelle_hf,Y4:hF_Mirabelle_hf]: ((((hF_Mirabelle_hmem @ X) @ B5) => (((P @ X) @ Y4) = ((Q @ X) @ Y4))))) => (((hF_Mirabelle_Replace @ A5) @ P) = ((hF_Mirabelle_Replace @ B5) @ Q))))))).
% 0.29/1.50 thf(fact_21_dual__order_Oantisym, axiom, (! [A:$tType]: (((order @ A) => (! [B2:A,A2:A]: (((((ord_less_eq @ A) @ B2) @ A2) => ((((ord_less_eq @ A) @ A2) @ B2) => (A2 = B2))))))))).
% 0.29/1.50 thf(fact_22_dual__order_Oeq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y:A,Z:A]: ((Y = Z))) = (^ [A3:A,B3:A]: (((((ord_less_eq @ A) @ B3) @ A3) & (((ord_less_eq @ A) @ A3) @ B3))))))))).
% 0.29/1.50 thf(fact_23_dual__order_Otrans, axiom, (! [A:$tType]: (((order @ A) => (! [B2:A,A2:A,C:A]: (((((ord_less_eq @ A) @ B2) @ A2) => ((((ord_less_eq @ A) @ C) @ B2) => (((ord_less_eq @ A) @ C) @ A2))))))))).
% 0.29/1.50 thf(fact_24_linorder__wlog, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:(A > (A > $o)),A2:A,B2:A]: (((! [A6:A,B6:A]: (((((ord_less_eq @ A) @ A6) @ B6) => ((P @ A6) @ B6)))) => ((! [A6:A,B6:A]: ((((P @ B6) @ A6) => ((P @ A6) @ B6)))) => ((P @ A2) @ B2))))))))).
% 0.29/1.50 thf(fact_25_dual__order_Orefl, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A]: ((((ord_less_eq @ A) @ A2) @ A2))))))).
% 0.29/1.50 thf(fact_26_order__trans, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A,Y2:A,Z3:A]: (((((ord_less_eq @ A) @ X3) @ Y2) => ((((ord_less_eq @ A) @ Y2) @ Z3) => (((ord_less_eq @ A) @ X3) @ Z3))))))))).
% 0.29/1.50 thf(fact_27_order__class_Oorder_Oantisym, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ B2) @ A2) => (A2 = B2))))))))).
% 0.29/1.50 thf(fact_28_ord__le__eq__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A2:A,B2:A,C:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((B2 = C) => (((ord_less_eq @ A) @ A2) @ C))))))))).
% 0.29/1.50 thf(fact_29_ord__eq__le__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A2:A,B2:A,C:A]: (((A2 = B2) => ((((ord_less_eq @ A) @ B2) @ C) => (((ord_less_eq @ A) @ A2) @ C))))))))).
% 0.29/1.50 thf(fact_30_order__class_Oorder_Oeq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y:A,Z:A]: ((Y = Z))) = (^ [A3:A,B3:A]: (((((ord_less_eq @ A) @ A3) @ B3) & (((ord_less_eq @ A) @ B3) @ A3))))))))).
% 0.29/1.50 thf(fact_31_antisym__conv, axiom, (! [A:$tType]: (((order @ A) => (! [Y2:A,X3:A]: (((((ord_less_eq @ A) @ Y2) @ X3) => ((((ord_less_eq @ A) @ X3) @ Y2) = (X3 = Y2))))))))).
% 0.29/1.50 thf(fact_32_le__cases3, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y2:A,Z3:A]: ((((((ord_less_eq @ A) @ X3) @ Y2) => (~ ((((ord_less_eq @ A) @ Y2) @ Z3)))) => (((((ord_less_eq @ A) @ Y2) @ X3) => (~ ((((ord_less_eq @ A) @ X3) @ Z3)))) => (((((ord_less_eq @ A) @ X3) @ Z3) => (~ ((((ord_less_eq @ A) @ Z3) @ Y2)))) => (((((ord_less_eq @ A) @ Z3) @ Y2) => (~ ((((ord_less_eq @ A) @ Y2) @ X3)))) => (((((ord_less_eq @ A) @ Y2) @ Z3) => (~ ((((ord_less_eq @ A) @ Z3) @ X3)))) => (~ (((((ord_less_eq @ A) @ Z3) @ X3) => (~ ((((ord_less_eq @ A) @ X3) @ Y2))))))))))))))))).
% 0.29/1.50 thf(fact_33_order_Otrans, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B2:A,C:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ B2) @ C) => (((ord_less_eq @ A) @ A2) @ C))))))))).
% 0.29/1.50 thf(fact_34_le__cases, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y2:A]: (((~ ((((ord_less_eq @ A) @ X3) @ Y2))) => (((ord_less_eq @ A) @ Y2) @ X3)))))))).
% 0.29/1.50 thf(fact_35_eq__refl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A,Y2:A]: (((X3 = Y2) => (((ord_less_eq @ A) @ X3) @ Y2)))))))).
% 0.29/1.50 thf(fact_36_linear, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y2:A]: (((((ord_less_eq @ A) @ X3) @ Y2) | (((ord_less_eq @ A) @ Y2) @ X3)))))))).
% 0.29/1.50 thf(fact_37_antisym, axiom, (! [A:$tType]: (((order @ A) => (! [X3:A,Y2:A]: (((((ord_less_eq @ A) @ X3) @ Y2) => ((((ord_less_eq @ A) @ Y2) @ X3) => (X3 = Y2))))))))).
% 0.29/1.50 thf(fact_38_eq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y:A,Z:A]: ((Y = Z))) = (^ [X2:A,Y3:A]: (((((ord_less_eq @ A) @ X2) @ Y3) & (((ord_less_eq @ A) @ Y3) @ X2))))))))).
% 0.29/1.50 thf(fact_39_ord__le__eq__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A2:A,B2:A,F:(A > B),C:B]: (((((ord_less_eq @ A) @ A2) @ B2) => (((F @ B2) = C) => ((! [X:A,Y4:A]: (((((ord_less_eq @ A) @ X) @ Y4) => (((ord_less_eq @ B) @ (F @ X)) @ (F @ Y4))))) => (((ord_less_eq @ B) @ (F @ A2)) @ C)))))))))).
% 0.29/1.50 thf(fact_40_ord__eq__le__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A2:A,F:(B > A),B2:B,C:B]: (((A2 = (F @ B2)) => ((((ord_less_eq @ B) @ B2) @ C) => ((! [X:B,Y4:B]: (((((ord_less_eq @ B) @ X) @ Y4) => (((ord_less_eq @ A) @ (F @ X)) @ (F @ Y4))))) => (((ord_less_eq @ A) @ A2) @ (F @ C))))))))))).
% 0.29/1.50 thf(fact_41_Greatest__equality, axiom, (! [A:$tType]: (((order @ A) => (! [P:(A > $o),X3:A]: (((P @ X3) => ((! [Y4:A]: (((P @ Y4) => (((ord_less_eq @ A) @ Y4) @ X3)))) => (((order_Greatest @ A) @ P) = X3))))))))).
% 0.29/1.50 thf(fact_42_GreatestI2__order, axiom, (! [A:$tType]: (((order @ A) => (! [P:(A > $o),X3:A,Q:(A > $o)]: (((P @ X3) => ((! [Y4:A]: (((P @ Y4) => (((ord_less_eq @ A) @ Y4) @ X3)))) => ((! [X:A]: (((P @ X) => ((! [Y5:A]: (((P @ Y5) => (((ord_less_eq @ A) @ Y5) @ X)))) => (Q @ X))))) => (Q @ ((order_Greatest @ A) @ P))))))))))).
% 0.29/1.50 thf(fact_43_le__rel__bool__arg__iff, axiom, (! [A:$tType]: (((ord @ A) => ((ord_less_eq @ ($o > A)) = (^ [X4:($o > A),Y6:($o > A)]: (((((ord_less_eq @ A) @ (X4 @ $false)) @ (Y6 @ $false)) & (((ord_less_eq @ A) @ (X4 @ $true)) @ (Y6 @ $true)))))))))).
% 0.29/1.50 thf(fact_44_hmem__def, axiom, (hF_Mirabelle_hmem = (^ [A3:hF_Mirabelle_hf,B3:hF_Mirabelle_hf]: ((((member @ hF_Mirabelle_hf) @ A3) @ (hF_Mirabelle_hfset @ B3)))))).
% 0.29/1.50 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P)) = (P @ A2))))).
% 0.29/1.50 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A5:(set @ A)]: ((((collect @ A) @ (^ [X2:A]: ((((member @ A) @ X2) @ A5)))) = A5)))).
% 0.29/1.50 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X:A]: (((P @ X) = (Q @ X)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 0.29/1.50 thf(fact_48_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G:(A > B)]: (((! [X:A]: (((F @ X) = (G @ X)))) => (F = G))))).
% 0.29/1.50 thf(fact_49_RepFun__iff, axiom, (! [V4:hF_Mirabelle_hf,A5:hF_Mirabelle_hf,F:(hF_Mirabelle_hf > hF_Mirabelle_hf)]: ((((hF_Mirabelle_hmem @ V4) @ ((hF_Mirabelle_RepFun @ A5) @ F)) = (? [U2:hF_Mirabelle_hf]: ((((hF_Mirabelle_hmem @ U2) @ A5) & (V4 = (F @ U2))))))))).
% 0.29/1.50 thf(fact_50_less__hf__def, axiom, ((ord_less @ hF_Mirabelle_hf) = (^ [A4:hF_Mirabelle_hf,B4:hF_Mirabelle_hf]: (((((ord_less_eq @ hF_Mirabelle_hf) @ A4) @ B4) & (A4 != B4)))))).
% 0.29/1.50 thf(fact_51_antimono__def, axiom, (! [B:$tType,A:$tType]: ((((order @ A) & (order @ B)) => (((order_antimono @ A) @ B) = (^ [F2:(A > B)]: ((! [X2:A,Y3:A]: (((((ord_less_eq @ A) @ X2) @ Y3) => (((ord_less_eq @ B) @ (F2 @ Y3)) @ (F2 @ X2)))))))))))).
% 0.29/1.50 thf(fact_52_antimonoI, axiom, (! [B:$tType,A:$tType]: ((((order @ A) & (order @ B)) => (! [F:(A > B)]: (((! [X:A,Y4:A]: (((((ord_less_eq @ A) @ X) @ Y4) => (((ord_less_eq @ B) @ (F @ Y4)) @ (F @ X))))) => (((order_antimono @ A) @ B) @ F)))))))).
% 0.29/1.50 thf(fact_53_antimonoE, axiom, (! [B:$tType,A:$tType]: ((((order @ A) & (order @ B)) => (! [F:(A > B),X3:A,Y2:A]: (((((order_antimono @ A) @ B) @ F) => ((((ord_less_eq @ A) @ X3) @ Y2) => (((ord_less_eq @ B) @ (F @ Y2)) @ (F @ X3)))))))))).
% 0.29/1.50 thf(fact_54_antimonoD, axiom, (! [B:$tType,A:$tType]: ((((order @ A) & (order @ B)) => (! [F:(A > B),X3:A,Y2:A]: (((((order_antimono @ A) @ B) @ F) => ((((ord_less_eq @ A) @ X3) @ Y2) => (((ord_less_eq @ B) @ (F @ Y2)) @ (F @ X3)))))))))).
% 0.29/1.50 thf(fact_55_verit__comp__simplify1_I1_J, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A]: ((~ ((((ord_less @ A) @ A2) @ A2))))))))).
% 0.29/1.50 thf(fact_56_ord__eq__less__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A2:A,F:(B > A),B2:B,C:B]: (((A2 = (F @ B2)) => ((((ord_less @ B) @ B2) @ C) => ((! [X:B,Y4:B]: (((((ord_less @ B) @ X) @ Y4) => (((ord_less @ A) @ (F @ X)) @ (F @ Y4))))) => (((ord_less @ A) @ A2) @ (F @ C))))))))))).
% 0.29/1.50 thf(fact_57_ord__less__eq__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A2:A,B2:A,F:(A > B),C:B]: (((((ord_less @ A) @ A2) @ B2) => (((F @ B2) = C) => ((! [X:A,Y4:A]: (((((ord_less @ A) @ X) @ Y4) => (((ord_less @ B) @ (F @ X)) @ (F @ Y4))))) => (((ord_less @ B) @ (F @ A2)) @ C)))))))))).
% 0.29/1.50 thf(fact_58_order__less__subst1, axiom, (! [A:$tType,B:$tType]: ((((order @ B) & (order @ A)) => (! [A2:A,F:(B > A),B2:B,C:B]: (((((ord_less @ A) @ A2) @ (F @ B2)) => ((((ord_less @ B) @ B2) @ C) => ((! [X:B,Y4:B]: (((((ord_less @ B) @ X) @ Y4) => (((ord_less @ A) @ (F @ X)) @ (F @ Y4))))) => (((ord_less @ A) @ A2) @ (F @ C))))))))))).
% 0.29/1.50 thf(fact_59_order__less__subst2, axiom, (! [A:$tType,C2:$tType]: ((((order @ C2) & (order @ A)) => (! [A2:A,B2:A,F:(A > C2),C:C2]: (((((ord_less @ A) @ A2) @ B2) => ((((ord_less @ C2) @ (F @ B2)) @ C) => ((! [X:A,Y4:A]: (((((ord_less @ A) @ X) @ Y4) => (((ord_less @ C2) @ (F @ X)) @ (F @ Y4))))) => (((ord_less @ C2) @ (F @ A2)) @ C)))))))))).
% 0.29/1.50 thf(fact_60_lt__ex, axiom, (! [A:$tType]: (((no_bot @ A) => (! [X3:A]: ((? [Y4:A]: ((((ord_less @ A) @ Y4) @ X3))))))))).
% 0.29/1.50 thf(fact_61_gt__ex, axiom, (! [A:$tType]: (((no_top @ A) => (! [X3:A]: ((? [X_1:A]: ((((ord_less @ A) @ X3) @ X_1))))))))).
% 0.29/1.50 thf(fact_62_neqE, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y2:A]: (((X3 != Y2) => ((~ ((((ord_less @ A) @ X3) @ Y2))) => (((ord_less @ A) @ Y2) @ X3))))))))).
% 0.29/1.50 thf(fact_63_neq__iff, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y2:A]: (((X3 != Y2) = ((((ord_less @ A) @ X3) @ Y2) | (((ord_less @ A) @ Y2) @ X3))))))))).
% 0.29/1.50 thf(fact_64_order_Oasym, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B2:A]: (((((ord_less @ A) @ A2) @ B2) => (~ ((((ord_less @ A) @ B2) @ A2)))))))))).
% 0.29/1.50 thf(fact_65_dense, axiom, (! [A:$tType]: (((dense_order @ A) => (! [X3:A,Y2:A]: (((((ord_less @ A) @ X3) @ Y2) => (? [Z2:A]: (((((ord_less @ A) @ X3) @ Z2) & (((ord_less @ A) @ Z2) @ Y2))))))))))).
% 0.29/1.50 thf(fact_66_less__imp__neq, axiom, (! [A:$tType]: (((order @ A) => (! [X3:A,Y2:A]: (((((ord_less @ A) @ X3) @ Y2) => (X3 != Y2)))))))).
% 0.29/1.50 thf(fact_67_less__asym, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A,Y2:A]: (((((ord_less @ A) @ X3) @ Y2) => (~ ((((ord_less @ A) @ Y2) @ X3)))))))))).
% 0.29/1.50 thf(fact_68_less__asym_H, axiom, (! [A:$tType]: (((preorder @ A) => (! [A2:A,B2:A]: (((((ord_less @ A) @ A2) @ B2) => (~ ((((ord_less @ A) @ B2) @ A2)))))))))).
% 0.29/1.50 thf(fact_69_less__trans, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A,Y2:A,Z3:A]: (((((ord_less @ A) @ X3) @ Y2) => ((((ord_less @ A) @ Y2) @ Z3) => (((ord_less @ A) @ X3) @ Z3))))))))).
% 0.29/1.50 thf(fact_70_less__linear, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y2:A]: (((((ord_less @ A) @ X3) @ Y2) | ((X3 = Y2) | (((ord_less @ A) @ Y2) @ X3))))))))).
% 0.29/1.50 thf(fact_71_less__irrefl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A]: ((~ ((((ord_less @ A) @ X3) @ X3))))))))).
% 0.29/1.50 thf(fact_72_ord__eq__less__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A2:A,B2:A,C:A]: (((A2 = B2) => ((((ord_less @ A) @ B2) @ C) => (((ord_less @ A) @ A2) @ C))))))))).
% 0.29/1.50 thf(fact_73_ord__less__eq__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A2:A,B2:A,C:A]: (((((ord_less @ A) @ A2) @ B2) => ((B2 = C) => (((ord_less @ A) @ A2) @ C))))))))).
% 0.29/1.50 thf(fact_74_dual__order_Oasym, axiom, (! [A:$tType]: (((order @ A) => (! [B2:A,A2:A]: (((((ord_less @ A) @ B2) @ A2) => (~ ((((ord_less @ A) @ A2) @ B2)))))))))).
% 0.29/1.50 thf(fact_75_less__imp__not__eq, axiom, (! [A:$tType]: (((order @ A) => (! [X3:A,Y2:A]: (((((ord_less @ A) @ X3) @ Y2) => (X3 != Y2)))))))).
% 0.29/1.50 thf(fact_76_less__not__sym, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A,Y2:A]: (((((ord_less @ A) @ X3) @ Y2) => (~ ((((ord_less @ A) @ Y2) @ X3)))))))))).
% 0.29/1.50 thf(fact_77_less__induct, axiom, (! [A:$tType]: (((wellorder @ A) => (! [P:(A > $o),A2:A]: (((! [X:A]: (((! [Y5:A]: (((((ord_less @ A) @ Y5) @ X) => (P @ Y5)))) => (P @ X)))) => (P @ A2)))))))).
% 0.29/1.50 thf(fact_78_antisym__conv3, axiom, (! [A:$tType]: (((linorder @ A) => (! [Y2:A,X3:A]: (((~ ((((ord_less @ A) @ Y2) @ X3))) => ((~ ((((ord_less @ A) @ X3) @ Y2))) = (X3 = Y2))))))))).
% 0.29/1.50 thf(fact_79_less__imp__not__eq2, axiom, (! [A:$tType]: (((order @ A) => (! [X3:A,Y2:A]: (((((ord_less @ A) @ X3) @ Y2) => (Y2 != X3)))))))).
% 0.29/1.50 thf(fact_80_less__imp__triv, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A,Y2:A,P:$o]: (((((ord_less @ A) @ X3) @ Y2) => ((((ord_less @ A) @ Y2) @ X3) => P)))))))).
% 0.29/1.50 thf(fact_81_linorder__cases, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y2:A]: (((~ ((((ord_less @ A) @ X3) @ Y2))) => ((X3 != Y2) => (((ord_less @ A) @ Y2) @ X3))))))))).
% 0.29/1.50 thf(fact_82_dual__order_Oirrefl, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A]: ((~ ((((ord_less @ A) @ A2) @ A2))))))))).
% 0.29/1.50 thf(fact_83_order_Ostrict__trans, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B2:A,C:A]: (((((ord_less @ A) @ A2) @ B2) => ((((ord_less @ A) @ B2) @ C) => (((ord_less @ A) @ A2) @ C))))))))).
% 0.29/1.50 thf(fact_84_less__imp__not__less, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A,Y2:A]: (((((ord_less @ A) @ X3) @ Y2) => (~ ((((ord_less @ A) @ Y2) @ X3)))))))))).
% 0.29/1.50 thf(fact_85_exists__least__iff, axiom, (! [A:$tType]: (((wellorder @ A) => ((^ [P2:(A > $o)]: ((? [X5:A]: ((P2 @ X5))))) = (^ [P3:(A > $o)]: ((? [N:A]: (((P3 @ N) & (! [M:A]: (((((ord_less @ A) @ M) @ N) => (~ ((P3 @ M)))))))))))))))).
% 0.29/1.50 thf(fact_86_linorder__less__wlog, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:(A > (A > $o)),A2:A,B2:A]: (((! [A6:A,B6:A]: (((((ord_less @ A) @ A6) @ B6) => ((P @ A6) @ B6)))) => ((! [A6:A]: (((P @ A6) @ A6))) => ((! [A6:A,B6:A]: ((((P @ B6) @ A6) => ((P @ A6) @ B6)))) => ((P @ A2) @ B2)))))))))).
% 0.29/1.50 thf(fact_87_dual__order_Ostrict__trans, axiom, (! [A:$tType]: (((order @ A) => (! [B2:A,A2:A,C:A]: (((((ord_less @ A) @ B2) @ A2) => ((((ord_less @ A) @ C) @ B2) => (((ord_less @ A) @ C) @ A2))))))))).
% 0.29/1.50 thf(fact_88_not__less__iff__gr__or__eq, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y2:A]: (((~ ((((ord_less @ A) @ X3) @ Y2))) = ((((ord_less @ A) @ Y2) @ X3) | (X3 = Y2))))))))).
% 0.29/1.50 thf(fact_89_order_Ostrict__implies__not__eq, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B2:A]: (((((ord_less @ A) @ A2) @ B2) => (A2 != B2)))))))).
% 0.29/1.50 thf(fact_90_dual__order_Ostrict__implies__not__eq, axiom, (! [A:$tType]: (((order @ A) => (! [B2:A,A2:A]: (((((ord_less @ A) @ B2) @ A2) => (A2 != B2)))))))).
% 0.29/1.50 thf(fact_91_verit__comp__simplify1_I3_J, axiom, (! [B:$tType]: (((linorder @ B) => (! [B7:B,A7:B]: (((~ ((((ord_less_eq @ B) @ B7) @ A7))) = (((ord_less @ B) @ A7) @ B7)))))))).
% 0.29/1.50 thf(fact_92_leD, axiom, (! [A:$tType]: (((order @ A) => (! [Y2:A,X3:A]: (((((ord_less_eq @ A) @ Y2) @ X3) => (~ ((((ord_less @ A) @ X3) @ Y2)))))))))).
% 0.29/1.50 thf(fact_93_leI, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y2:A]: (((~ ((((ord_less @ A) @ X3) @ Y2))) => (((ord_less_eq @ A) @ Y2) @ X3)))))))).
% 0.29/1.50 thf(fact_94_le__less, axiom, (! [A:$tType]: (((order @ A) => ((ord_less_eq @ A) = (^ [X2:A,Y3:A]: (((((ord_less @ A) @ X2) @ Y3) | (X2 = Y3))))))))).
% 0.29/1.50 thf(fact_95_less__le, axiom, (! [A:$tType]: (((order @ A) => ((ord_less @ A) = (^ [X2:A,Y3:A]: (((((ord_less_eq @ A) @ X2) @ Y3) & (X2 != Y3))))))))).
% 0.29/1.50 thf(fact_96_order__le__less__subst1, axiom, (! [A:$tType,B:$tType]: ((((order @ B) & (order @ A)) => (! [A2:A,F:(B > A),B2:B,C:B]: (((((ord_less_eq @ A) @ A2) @ (F @ B2)) => ((((ord_less @ B) @ B2) @ C) => ((! [X:B,Y4:B]: (((((ord_less @ B) @ X) @ Y4) => (((ord_less @ A) @ (F @ X)) @ (F @ Y4))))) => (((ord_less @ A) @ A2) @ (F @ C))))))))))).
% 0.29/1.50 thf(fact_97_order__le__less__subst2, axiom, (! [A:$tType,C2:$tType]: ((((order @ C2) & (order @ A)) => (! [A2:A,B2:A,F:(A > C2),C:C2]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less @ C2) @ (F @ B2)) @ C) => ((! [X:A,Y4:A]: (((((ord_less_eq @ A) @ X) @ Y4) => (((ord_less_eq @ C2) @ (F @ X)) @ (F @ Y4))))) => (((ord_less @ C2) @ (F @ A2)) @ C)))))))))).
% 0.29/1.50 thf(fact_98_order__less__le__subst1, axiom, (! [A:$tType,B:$tType]: ((((order @ B) & (order @ A)) => (! [A2:A,F:(B > A),B2:B,C:B]: (((((ord_less @ A) @ A2) @ (F @ B2)) => ((((ord_less_eq @ B) @ B2) @ C) => ((! [X:B,Y4:B]: (((((ord_less_eq @ B) @ X) @ Y4) => (((ord_less_eq @ A) @ (F @ X)) @ (F @ Y4))))) => (((ord_less @ A) @ A2) @ (F @ C))))))))))).
% 0.29/1.50 thf(fact_99_order__less__le__subst2, axiom, (! [A:$tType,C2:$tType]: ((((order @ C2) & (order @ A)) => (! [A2:A,B2:A,F:(A > C2),C:C2]: (((((ord_less @ A) @ A2) @ B2) => ((((ord_less_eq @ C2) @ (F @ B2)) @ C) => ((! [X:A,Y4:A]: (((((ord_less @ A) @ X) @ Y4) => (((ord_less @ C2) @ (F @ X)) @ (F @ Y4))))) => (((ord_less @ C2) @ (F @ A2)) @ C)))))))))).
% 0.29/1.50 thf(fact_100_not__le, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y2:A]: (((~ ((((ord_less_eq @ A) @ X3) @ Y2))) = (((ord_less @ A) @ Y2) @ X3)))))))).
% 0.29/1.50 thf(fact_101_not__less, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y2:A]: (((~ ((((ord_less @ A) @ X3) @ Y2))) = (((ord_less_eq @ A) @ Y2) @ X3)))))))).
% 0.29/1.50 thf(fact_102_le__neq__trans, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((A2 != B2) => (((ord_less @ A) @ A2) @ B2))))))))).
% 0.29/1.50 thf(fact_103_antisym__conv1, axiom, (! [A:$tType]: (((order @ A) => (! [X3:A,Y2:A]: (((~ ((((ord_less @ A) @ X3) @ Y2))) => ((((ord_less_eq @ A) @ X3) @ Y2) = (X3 = Y2))))))))).
% 0.29/1.50 thf(fact_104_antisym__conv2, axiom, (! [A:$tType]: (((order @ A) => (! [X3:A,Y2:A]: (((((ord_less_eq @ A) @ X3) @ Y2) => ((~ ((((ord_less @ A) @ X3) @ Y2))) = (X3 = Y2))))))))).
% 0.29/1.50 thf(fact_105_less__imp__le, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A,Y2:A]: (((((ord_less @ A) @ X3) @ Y2) => (((ord_less_eq @ A) @ X3) @ Y2)))))))).
% 0.29/1.50 thf(fact_106_le__less__trans, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A,Y2:A,Z3:A]: (((((ord_less_eq @ A) @ X3) @ Y2) => ((((ord_less @ A) @ Y2) @ Z3) => (((ord_less @ A) @ X3) @ Z3))))))))).
% 0.29/1.50 thf(fact_107_less__le__trans, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A,Y2:A,Z3:A]: (((((ord_less @ A) @ X3) @ Y2) => ((((ord_less_eq @ A) @ Y2) @ Z3) => (((ord_less @ A) @ X3) @ Z3))))))))).
% 0.29/1.50 thf(fact_108_dense__ge, axiom, (! [A:$tType]: (((dense_linorder @ A) => (! [Z3:A,Y2:A]: (((! [X:A]: (((((ord_less @ A) @ Z3) @ X) => (((ord_less_eq @ A) @ Y2) @ X)))) => (((ord_less_eq @ A) @ Y2) @ Z3)))))))).
% 0.29/1.50 thf(fact_109_dense__le, axiom, (! [A:$tType]: (((dense_linorder @ A) => (! [Y2:A,Z3:A]: (((! [X:A]: (((((ord_less @ A) @ X) @ Y2) => (((ord_less_eq @ A) @ X) @ Z3)))) => (((ord_less_eq @ A) @ Y2) @ Z3)))))))).
% 0.29/1.50 thf(fact_110_le__less__linear, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y2:A]: (((((ord_less_eq @ A) @ X3) @ Y2) | (((ord_less @ A) @ Y2) @ X3)))))))).
% 0.29/1.50 thf(fact_111_le__imp__less__or__eq, axiom, (! [A:$tType]: (((order @ A) => (! [X3:A,Y2:A]: (((((ord_less_eq @ A) @ X3) @ Y2) => ((((ord_less @ A) @ X3) @ Y2) | (X3 = Y2))))))))).
% 0.29/1.50 thf(fact_112_less__le__not__le, axiom, (! [A:$tType]: (((preorder @ A) => ((ord_less @ A) = (^ [X2:A,Y3:A]: (((((ord_less_eq @ A) @ X2) @ Y3) & (~ ((((ord_less_eq @ A) @ Y3) @ X2))))))))))).
% 0.29/1.50 thf(fact_113_not__le__imp__less, axiom, (! [A:$tType]: (((linorder @ A) => (! [Y2:A,X3:A]: (((~ ((((ord_less_eq @ A) @ Y2) @ X3))) => (((ord_less @ A) @ X3) @ Y2)))))))).
% 0.29/1.50 thf(fact_114_order_Ostrict__trans1, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B2:A,C:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less @ A) @ B2) @ C) => (((ord_less @ A) @ A2) @ C))))))))).
% 0.29/1.50 thf(fact_115_order_Ostrict__trans2, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B2:A,C:A]: (((((ord_less @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ B2) @ C) => (((ord_less @ A) @ A2) @ C))))))))).
% 0.29/1.50 thf(fact_116_order_Oorder__iff__strict, axiom, (! [A:$tType]: (((order @ A) => ((ord_less_eq @ A) = (^ [A3:A,B3:A]: (((((ord_less @ A) @ A3) @ B3) | (A3 = B3))))))))).
% 0.29/1.50 thf(fact_117_order_Ostrict__iff__order, axiom, (! [A:$tType]: (((order @ A) => ((ord_less @ A) = (^ [A3:A,B3:A]: (((((ord_less_eq @ A) @ A3) @ B3) & (A3 != B3))))))))).
% 0.29/1.50 thf(fact_118_dual__order_Ostrict__trans1, axiom, (! [A:$tType]: (((order @ A) => (! [B2:A,A2:A,C:A]: (((((ord_less_eq @ A) @ B2) @ A2) => ((((ord_less @ A) @ C) @ B2) => (((ord_less @ A) @ C) @ A2))))))))).
% 0.29/1.50 thf(fact_119_dual__order_Ostrict__trans2, axiom, (! [A:$tType]: (((order @ A) => (! [B2:A,A2:A,C:A]: (((((ord_less @ A) @ B2) @ A2) => ((((ord_less_eq @ A) @ C) @ B2) => (((ord_less @ A) @ C) @ A2))))))))).
% 0.29/1.50 thf(fact_120_dense__ge__bounded, axiom, (! [A:$tType]: (((dense_linorder @ A) => (! [Z3:A,X3:A,Y2:A]: (((((ord_less @ A) @ Z3) @ X3) => ((! [W:A]: (((((ord_less @ A) @ Z3) @ W) => ((((ord_less @ A) @ W) @ X3) => (((ord_less_eq @ A) @ Y2) @ W))))) => (((ord_less_eq @ A) @ Y2) @ Z3))))))))).
% 0.29/1.50 thf(fact_121_dense__le__bounded, axiom, (! [A:$tType]: (((dense_linorder @ A) => (! [X3:A,Y2:A,Z3:A]: (((((ord_less @ A) @ X3) @ Y2) => ((! [W:A]: (((((ord_less @ A) @ X3) @ W) => ((((ord_less @ A) @ W) @ Y2) => (((ord_less_eq @ A) @ W) @ Z3))))) => (((ord_less_eq @ A) @ Y2) @ Z3))))))))).
% 0.29/1.50 thf(fact_122_order_Ostrict__implies__order, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B2:A]: (((((ord_less @ A) @ A2) @ B2) => (((ord_less_eq @ A) @ A2) @ B2)))))))).
% 0.29/1.50 thf(fact_123_dual__order_Oorder__iff__strict, axiom, (! [A:$tType]: (((order @ A) => ((ord_less_eq @ A) = (^ [B3:A,A3:A]: (((((ord_less @ A) @ B3) @ A3) | (A3 = B3))))))))).
% 0.29/1.50 thf(fact_124_dual__order_Ostrict__iff__order, axiom, (! [A:$tType]: (((order @ A) => ((ord_less @ A) = (^ [B3:A,A3:A]: (((((ord_less_eq @ A) @ B3) @ A3) & (A3 != B3))))))))).
% 0.29/1.50 thf(fact_125_dual__order_Ostrict__implies__order, axiom, (! [A:$tType]: (((order @ A) => (! [B2:A,A2:A]: (((((ord_less @ A) @ B2) @ A2) => (((ord_less_eq @ A) @ B2) @ A2)))))))).
% 0.29/1.50 thf(fact_126_order_Onot__eq__order__implies__strict, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B2:A]: (((A2 != B2) => ((((ord_less_eq @ A) @ A2) @ B2) => (((ord_less @ A) @ A2) @ B2))))))))).
% 0.29/1.50 thf(fact_127_RepFun__cong, axiom, (! [A5:hF_Mirabelle_hf,B5:hF_Mirabelle_hf,F:(hF_Mirabelle_hf > hF_Mirabelle_hf),G:(hF_Mirabelle_hf > hF_Mirabelle_hf)]: (((A5 = B5) => ((! [X:hF_Mirabelle_hf]: ((((hF_Mirabelle_hmem @ X) @ B5) => ((F @ X) = (G @ X))))) => (((hF_Mirabelle_RepFun @ A5) @ F) = ((hF_Mirabelle_RepFun @ B5) @ G))))))).
% 0.29/1.50 thf(fact_128_minf_I8_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [T:A]: ((? [Z2:A]: ((! [X6:A]: (((((ord_less @ A) @ X6) @ Z2) => (~ ((((ord_less_eq @ A) @ T) @ X6)))))))))))))).
% 0.29/1.50 thf(fact_129_minf_I6_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [T:A]: ((? [Z2:A]: ((! [X6:A]: (((((ord_less @ A) @ X6) @ Z2) => (((ord_less_eq @ A) @ X6) @ T)))))))))))).
% 0.29/1.50 thf(fact_130_pinf_I8_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [T:A]: ((? [Z2:A]: ((! [X6:A]: (((((ord_less @ A) @ Z2) @ X6) => (((ord_less_eq @ A) @ T) @ X6)))))))))))).
% 0.29/1.50 thf(fact_131_pinf_I6_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [T:A]: ((? [Z2:A]: ((! [X6:A]: (((((ord_less @ A) @ Z2) @ X6) => (~ ((((ord_less_eq @ A) @ X6) @ T)))))))))))))).
% 0.29/1.50 thf(fact_132_complete__interval, axiom, (! [A:$tType]: (((condit1037483654norder @ A) => (! [A2:A,B2:A,P:(A > $o)]: (((((ord_less @ A) @ A2) @ B2) => ((P @ A2) => ((~ ((P @ B2))) => (? [C3:A]: (((((ord_less_eq @ A) @ A2) @ C3) & ((((ord_less_eq @ A) @ C3) @ B2) & ((! [X6:A]: ((((((ord_less_eq @ A) @ A2) @ X6) & (((ord_less @ A) @ X6) @ C3)) => (P @ X6)))) & (! [D:A]: (((! [X:A]: ((((((ord_less_eq @ A) @ A2) @ X) & (((ord_less @ A) @ X) @ D)) => (P @ X)))) => (((ord_less_eq @ A) @ D) @ C3)))))))))))))))))).
% 0.29/1.50 thf(fact_133_HF__hfset, axiom, (! [A2:hF_Mirabelle_hf]: (((hF_Mirabelle_HF @ (hF_Mirabelle_hfset @ A2)) = A2)))).
% 0.29/1.50 thf(fact_134_ex__gt__or__lt, axiom, (! [A:$tType]: (((condit1656338222tinuum @ A) => (! [A2:A]: ((? [B6:A]: (((((ord_less @ A) @ A2) @ B6) | (((ord_less @ A) @ B6) @ A2)))))))))).
% 0.29/1.50 thf(fact_135_linorder__neqE__linordered__idom, axiom, (! [A:$tType]: (((linordered_idom @ A) => (! [X3:A,Y2:A]: (((X3 != Y2) => ((~ ((((ord_less @ A) @ X3) @ Y2))) => (((ord_less @ A) @ Y2) @ X3))))))))).
% 0.29/1.50 thf(fact_136_less__fun__def, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => ((ord_less @ (A > B)) = (^ [F2:(A > B),G2:(A > B)]: (((((ord_less_eq @ (A > B)) @ F2) @ G2) & (~ ((((ord_less_eq @ (A > B)) @ G2) @ F2))))))))))).
% 0.29/1.50 thf(fact_137_minf_I11_J, axiom, (! [C2:$tType,D2:$tType]: (((ord @ C2) => (! [F3:D2]: ((? [Z2:C2]: ((! [X6:C2]: (((((ord_less @ C2) @ X6) @ Z2) => (F3 = F3)))))))))))).
% 0.29/1.50 thf(fact_138_minf_I7_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [T:A]: ((? [Z2:A]: ((! [X6:A]: (((((ord_less @ A) @ X6) @ Z2) => (~ ((((ord_less @ A) @ T) @ X6)))))))))))))).
% 0.29/1.50 thf(fact_139_minf_I5_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [T:A]: ((? [Z2:A]: ((! [X6:A]: (((((ord_less @ A) @ X6) @ Z2) => (((ord_less @ A) @ X6) @ T)))))))))))).
% 0.29/1.50 thf(fact_140_minf_I4_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [T:A]: ((? [Z2:A]: ((! [X6:A]: (((((ord_less @ A) @ X6) @ Z2) => (X6 != T)))))))))))).
% 0.29/1.50 thf(fact_141_minf_I3_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [T:A]: ((? [Z2:A]: ((! [X6:A]: (((((ord_less @ A) @ X6) @ Z2) => (X6 != T)))))))))))).
% 0.29/1.50 thf(fact_142_minf_I2_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:(A > $o),P4:(A > $o),Q:(A > $o),Q2:(A > $o)]: (((? [Z4:A]: ((! [X:A]: (((((ord_less @ A) @ X) @ Z4) => ((P @ X) = (P4 @ X))))))) => ((? [Z4:A]: ((! [X:A]: (((((ord_less @ A) @ X) @ Z4) => ((Q @ X) = (Q2 @ X))))))) => (? [Z2:A]: ((! [X6:A]: (((((ord_less @ A) @ X6) @ Z2) => (((P @ X6) | (Q @ X6)) = ((P4 @ X6) | (Q2 @ X6)))))))))))))))).
% 0.29/1.50 thf(fact_143_minf_I1_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:(A > $o),P4:(A > $o),Q:(A > $o),Q2:(A > $o)]: (((? [Z4:A]: ((! [X:A]: (((((ord_less @ A) @ X) @ Z4) => ((P @ X) = (P4 @ X))))))) => ((? [Z4:A]: ((! [X:A]: (((((ord_less @ A) @ X) @ Z4) => ((Q @ X) = (Q2 @ X))))))) => (? [Z2:A]: ((! [X6:A]: (((((ord_less @ A) @ X6) @ Z2) => (((P @ X6) & (Q @ X6)) = ((P4 @ X6) & (Q2 @ X6)))))))))))))))).
% 0.29/1.50 thf(fact_144_pinf_I11_J, axiom, (! [C2:$tType,D2:$tType]: (((ord @ C2) => (! [F3:D2]: ((? [Z2:C2]: ((! [X6:C2]: (((((ord_less @ C2) @ Z2) @ X6) => (F3 = F3)))))))))))).
% 0.29/1.50 thf(fact_145_pinf_I7_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [T:A]: ((? [Z2:A]: ((! [X6:A]: (((((ord_less @ A) @ Z2) @ X6) => (((ord_less @ A) @ T) @ X6)))))))))))).
% 0.29/1.50 thf(fact_146_pinf_I5_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [T:A]: ((? [Z2:A]: ((! [X6:A]: (((((ord_less @ A) @ Z2) @ X6) => (~ ((((ord_less @ A) @ X6) @ T)))))))))))))).
% 0.29/1.50 thf(fact_147_pinf_I4_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [T:A]: ((? [Z2:A]: ((! [X6:A]: (((((ord_less @ A) @ Z2) @ X6) => (X6 != T)))))))))))).
% 0.29/1.50 thf(fact_148_pinf_I3_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [T:A]: ((? [Z2:A]: ((! [X6:A]: (((((ord_less @ A) @ Z2) @ X6) => (X6 != T)))))))))))).
% 0.29/1.50 thf(fact_149_pinf_I2_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:(A > $o),P4:(A > $o),Q:(A > $o),Q2:(A > $o)]: (((? [Z4:A]: ((! [X:A]: (((((ord_less @ A) @ Z4) @ X) => ((P @ X) = (P4 @ X))))))) => ((? [Z4:A]: ((! [X:A]: (((((ord_less @ A) @ Z4) @ X) => ((Q @ X) = (Q2 @ X))))))) => (? [Z2:A]: ((! [X6:A]: (((((ord_less @ A) @ Z2) @ X6) => (((P @ X6) | (Q @ X6)) = ((P4 @ X6) | (Q2 @ X6)))))))))))))))).
% 0.29/1.50 thf(fact_150_pinf_I1_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:(A > $o),P4:(A > $o),Q:(A > $o),Q2:(A > $o)]: (((? [Z4:A]: ((! [X:A]: (((((ord_less @ A) @ Z4) @ X) => ((P @ X) = (P4 @ X))))))) => ((? [Z4:A]: ((! [X:A]: (((((ord_less @ A) @ Z4) @ X) => ((Q @ X) = (Q2 @ X))))))) => (? [Z2:A]: ((! [X6:A]: (((((ord_less @ A) @ Z2) @ X6) => (((P @ X6) & (Q @ X6)) = ((P4 @ X6) & (Q2 @ X6)))))))))))))))).
% 0.29/1.50 thf(fact_151_hfset__HF, axiom, (! [A5:(set @ hF_Mirabelle_hf)]: ((((finite_finite2 @ hF_Mirabelle_hf) @ A5) => ((hF_Mirabelle_hfset @ (hF_Mirabelle_HF @ A5)) = A5))))).
% 0.29/1.50 thf(fact_152_hmem__HF__iff, axiom, (! [X3:hF_Mirabelle_hf,A5:(set @ hF_Mirabelle_hf)]: ((((hF_Mirabelle_hmem @ X3) @ (hF_Mirabelle_HF @ A5)) = ((((member @ hF_Mirabelle_hf) @ X3) @ A5) & ((finite_finite2 @ hF_Mirabelle_hf) @ A5)))))).
% 0.29/1.50 thf(fact_153_measure__induct, axiom, (! [B:$tType,A:$tType]: (((wellorder @ B) => (! [F:(A > B),P:(A > $o),A2:A]: (((! [X:A]: (((! [Y5:A]: (((((ord_less @ B) @ (F @ Y5)) @ (F @ X)) => (P @ Y5)))) => (P @ X)))) => (P @ A2)))))))).
% 0.29/1.50 thf(fact_154_measure__induct__rule, axiom, (! [B:$tType,A:$tType]: (((wellorder @ B) => (! [F:(A > B),P:(A > $o),A2:A]: (((! [X:A]: (((! [Y5:A]: (((((ord_less @ B) @ (F @ Y5)) @ (F @ X)) => (P @ Y5)))) => (P @ X)))) => (P @ A2)))))))).
% 0.29/1.50 thf(fact_155_finite__hfset, axiom, (! [A2:hF_Mirabelle_hf]: (((finite_finite2 @ hF_Mirabelle_hf) @ (hF_Mirabelle_hfset @ A2))))).
% 0.29/1.50 thf(fact_156_finite__code, axiom, (! [A:$tType]: (((finite_finite @ A) => ((finite_finite2 @ A) = (^ [A4:(set @ A)]: ($true))))))).
% 0.29/1.50 thf(fact_157_finite__has__minimal2, axiom, (! [A:$tType]: (((order @ A) => (! [A5:(set @ A),A2:A]: ((((finite_finite2 @ A) @ A5) => ((((member @ A) @ A2) @ A5) => (? [X:A]: (((((member @ A) @ X) @ A5) & ((((ord_less_eq @ A) @ X) @ A2) & (! [Xa:A]: (((((member @ A) @ Xa) @ A5) => ((((ord_less_eq @ A) @ Xa) @ X) => (X = Xa))))))))))))))))).
% 0.29/1.50 thf(fact_158_finite__has__maximal2, axiom, (! [A:$tType]: (((order @ A) => (! [A5:(set @ A),A2:A]: ((((finite_finite2 @ A) @ A5) => ((((member @ A) @ A2) @ A5) => (? [X:A]: (((((member @ A) @ X) @ A5) & ((((ord_less_eq @ A) @ A2) @ X) & (! [Xa:A]: (((((member @ A) @ Xa) @ A5) => ((((ord_less_eq @ A) @ X) @ Xa) => (X = Xa))))))))))))))))).
% 0.29/1.50 thf(fact_159_finite__subset, axiom, (! [A:$tType,A5:(set @ A),B5:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A5) @ B5) => (((finite_finite2 @ A) @ B5) => ((finite_finite2 @ A) @ A5)))))).
% 0.29/1.50 thf(fact_160_infinite__super, axiom, (! [A:$tType,S:(set @ A),T2:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ S) @ T2) => ((~ (((finite_finite2 @ A) @ S))) => (~ (((finite_finite2 @ A) @ T2)))))))).
% 0.29/1.50 thf(fact_161_rev__finite__subset, axiom, (! [A:$tType,B5:(set @ A),A5:(set @ A)]: ((((finite_finite2 @ A) @ B5) => ((((ord_less_eq @ (set @ A)) @ A5) @ B5) => ((finite_finite2 @ A) @ A5)))))).
% 0.29/1.50 thf(fact_162_finite__set__choice, axiom, (! [B:$tType,A:$tType,A5:(set @ A),P:(A > (B > $o))]: ((((finite_finite2 @ A) @ A5) => ((! [X:A]: (((((member @ A) @ X) @ A5) => (? [X_12:B]: (((P @ X) @ X_12)))))) => (? [F4:(A > B)]: ((! [X6:A]: (((((member @ A) @ X6) @ A5) => ((P @ X6) @ (F4 @ X6)))))))))))).
% 0.29/1.50 thf(fact_163_finite, axiom, (! [A:$tType]: (((finite_finite @ A) => (! [A5:(set @ A)]: (((finite_finite2 @ A) @ A5))))))).
% 0.29/1.50 thf(fact_164_finite__psubset__induct, axiom, (! [A:$tType,A5:(set @ A),P:((set @ A) > $o)]: ((((finite_finite2 @ A) @ A5) => ((! [A8:(set @ A)]: ((((finite_finite2 @ A) @ A8) => ((! [B8:(set @ A)]: (((((ord_less @ (set @ A)) @ B8) @ A8) => (P @ B8)))) => (P @ A8))))) => (P @ A5)))))).
% 0.29/1.50 thf(fact_165_dependent__wellorder__choice, axiom, (! [B:$tType,A:$tType]: (((wellorder @ A) => (! [P:((A > B) > (A > (B > $o)))]: (((! [R2:B,F4:(A > B),G3:(A > B),X:A]: (((! [Y5:A]: (((((ord_less @ A) @ Y5) @ X) => ((F4 @ Y5) = (G3 @ Y5))))) => ((((P @ F4) @ X) @ R2) = (((P @ G3) @ X) @ R2))))) => ((! [X:A,F4:(A > B)]: (((! [Y5:A]: (((((ord_less @ A) @ Y5) @ X) => (((P @ F4) @ Y5) @ (F4 @ Y5))))) => (? [X_12:B]: ((((P @ F4) @ X) @ X_12)))))) => (? [F4:(A > B)]: ((! [X6:A]: ((((P @ F4) @ X6) @ (F4 @ X6)))))))))))))).
% 0.29/1.50 thf(fact_166_linordered__field__no__lb, axiom, (! [A:$tType]: (((linordered_field @ A) => (! [X6:A]: ((? [Y4:A]: ((((ord_less @ A) @ Y4) @ X6))))))))).
% 0.29/1.50 thf(fact_167_linordered__field__no__ub, axiom, (! [A:$tType]: (((linordered_field @ A) => (! [X6:A]: ((? [X_1:A]: ((((ord_less @ A) @ X6) @ X_1))))))))).
% 0.29/1.50 thf(fact_168_card__psubset, axiom, (! [A:$tType,B5:(set @ A),A5:(set @ A)]: ((((finite_finite2 @ A) @ B5) => ((((ord_less_eq @ (set @ A)) @ A5) @ B5) => ((((ord_less @ nat) @ ((finite_card @ A) @ A5)) @ ((finite_card @ A) @ B5)) => (((ord_less @ (set @ A)) @ A5) @ B5))))))).
% 0.29/1.50 thf(fact_169_inj__on__HF, axiom, ((((inj_on @ (set @ hF_Mirabelle_hf)) @ hF_Mirabelle_hf) @ hF_Mirabelle_HF) @ ((collect @ (set @ hF_Mirabelle_hf)) @ (finite_finite2 @ hF_Mirabelle_hf)))).
% 0.29/1.50 thf(fact_170_order_Oordering__axioms, axiom, (! [A:$tType]: (((order @ A) => (((ordering @ A) @ (ord_less_eq @ A)) @ (ord_less @ A)))))).
% 0.29/1.50 thf(fact_171_ordering_Onot__eq__order__implies__strict, axiom, (! [A:$tType,Less_eq:(A > (A > $o)),Less:(A > (A > $o)),A2:A,B2:A]: (((((ordering @ A) @ Less_eq) @ Less) => ((A2 != B2) => (((Less_eq @ A2) @ B2) => ((Less @ A2) @ B2))))))).
% 0.29/1.50 thf(fact_172_ordering_Ostrict__implies__not__eq, axiom, (! [A:$tType,Less_eq:(A > (A > $o)),Less:(A > (A > $o)),A2:A,B2:A]: (((((ordering @ A) @ Less_eq) @ Less) => (((Less @ A2) @ B2) => (A2 != B2)))))).
% 0.29/1.50 thf(fact_173_ordering_Ostrict__implies__order, axiom, (! [A:$tType,Less_eq:(A > (A > $o)),Less:(A > (A > $o)),A2:A,B2:A]: (((((ordering @ A) @ Less_eq) @ Less) => (((Less @ A2) @ B2) => ((Less_eq @ A2) @ B2)))))).
% 0.29/1.50 thf(fact_174_ordering_Ostrict__iff__order, axiom, (! [A:$tType,Less_eq:(A > (A > $o)),Less:(A > (A > $o)),A2:A,B2:A]: (((((ordering @ A) @ Less_eq) @ Less) => (((Less @ A2) @ B2) = (((Less_eq @ A2) @ B2) & (A2 != B2))))))).
% 0.29/1.50 thf(fact_175_ordering_Oorder__iff__strict, axiom, (! [A:$tType,Less_eq:(A > (A > $o)),Less:(A > (A > $o)),A2:A,B2:A]: (((((ordering @ A) @ Less_eq) @ Less) => (((Less_eq @ A2) @ B2) = (((Less @ A2) @ B2) | (A2 = B2))))))).
% 0.29/1.50 thf(fact_176_ordering_Ostrict__trans2, axiom, (! [A:$tType,Less_eq:(A > (A > $o)),Less:(A > (A > $o)),A2:A,B2:A,C:A]: (((((ordering @ A) @ Less_eq) @ Less) => (((Less @ A2) @ B2) => (((Less_eq @ B2) @ C) => ((Less @ A2) @ C))))))).
% 0.29/1.50 thf(fact_177_ordering_Ostrict__trans1, axiom, (! [A:$tType,Less_eq:(A > (A > $o)),Less:(A > (A > $o)),A2:A,B2:A,C:A]: (((((ordering @ A) @ Less_eq) @ Less) => (((Less_eq @ A2) @ B2) => (((Less @ B2) @ C) => ((Less @ A2) @ C))))))).
% 0.29/1.50 thf(fact_178_ordering_Ostrict__trans, axiom, (! [A:$tType,Less_eq:(A > (A > $o)),Less:(A > (A > $o)),A2:A,B2:A,C:A]: (((((ordering @ A) @ Less_eq) @ Less) => (((Less @ A2) @ B2) => (((Less @ B2) @ C) => ((Less @ A2) @ C))))))).
% 0.29/1.50 thf(fact_179_ordering__strictI, axiom, (! [A:$tType,Less_eq:(A > (A > $o)),Less:(A > (A > $o))]: (((! [A6:A,B6:A]: ((((Less_eq @ A6) @ B6) = (((Less @ A6) @ B6) | (A6 = B6))))) => ((! [A6:A,B6:A]: ((((Less @ A6) @ B6) => (~ (((Less @ B6) @ A6)))))) => ((! [A6:A]: ((~ (((Less @ A6) @ A6))))) => ((! [A6:A,B6:A,C3:A]: ((((Less @ A6) @ B6) => (((Less @ B6) @ C3) => ((Less @ A6) @ C3))))) => (((ordering @ A) @ Less_eq) @ Less)))))))).
% 0.29/1.50 thf(fact_180_ordering_Oantisym, axiom, (! [A:$tType,Less_eq:(A > (A > $o)),Less:(A > (A > $o)),A2:A,B2:A]: (((((ordering @ A) @ Less_eq) @ Less) => (((Less_eq @ A2) @ B2) => (((Less_eq @ B2) @ A2) => (A2 = B2))))))).
% 0.29/1.50 thf(fact_181_ordering_Oirrefl, axiom, (! [A:$tType,Less_eq:(A > (A > $o)),Less:(A > (A > $o)),A2:A]: (((((ordering @ A) @ Less_eq) @ Less) => (~ (((Less @ A2) @ A2))))))).
% 0.29/1.50 thf(fact_182_ordering_Oeq__iff, axiom, (! [A:$tType,Less_eq:(A > (A > $o)),Less:(A > (A > $o)),A2:A,B2:A]: (((((ordering @ A) @ Less_eq) @ Less) => ((A2 = B2) = (((Less_eq @ A2) @ B2) & ((Less_eq @ B2) @ A2))))))).
% 0.29/1.50 thf(fact_183_ordering_Otrans, axiom, (! [A:$tType,Less_eq:(A > (A > $o)),Less:(A > (A > $o)),A2:A,B2:A,C:A]: (((((ordering @ A) @ Less_eq) @ Less) => (((Less_eq @ A2) @ B2) => (((Less_eq @ B2) @ C) => ((Less_eq @ A2) @ C))))))).
% 0.29/1.50 thf(fact_184_ordering_Ointro, axiom, (! [A:$tType,Less:(A > (A > $o)),Less_eq:(A > (A > $o))]: (((! [A6:A,B6:A]: ((((Less @ A6) @ B6) = (((Less_eq @ A6) @ B6) & (A6 != B6))))) => ((! [A6:A]: (((Less_eq @ A6) @ A6))) => ((! [A6:A,B6:A]: ((((Less_eq @ A6) @ B6) => (((Less_eq @ B6) @ A6) => (A6 = B6))))) => ((! [A6:A,B6:A,C3:A]: ((((Less_eq @ A6) @ B6) => (((Less_eq @ B6) @ C3) => ((Less_eq @ A6) @ C3))))) => (((ordering @ A) @ Less_eq) @ Less)))))))).
% 0.29/1.50 thf(fact_185_ordering_Orefl, axiom, (! [A:$tType,Less_eq:(A > (A > $o)),Less:(A > (A > $o)),A2:A]: (((((ordering @ A) @ Less_eq) @ Less) => ((Less_eq @ A2) @ A2))))).
% 0.29/1.50 thf(fact_186_ordering_Oasym, axiom, (! [A:$tType,Less_eq:(A > (A > $o)),Less:(A > (A > $o)),A2:A,B2:A]: (((((ordering @ A) @ Less_eq) @ Less) => (((Less @ A2) @ B2) => (~ (((Less @ B2) @ A2)))))))).
% 0.29/1.50 thf(fact_187_ordering__def, axiom, (! [A:$tType]: (((ordering @ A) = (^ [Less_eq2:(A > (A > $o)),Less2:(A > (A > $o))]: (((! [A3:A,B3:A]: ((((Less2 @ A3) @ B3) = (((Less_eq2 @ A3) @ B3) & (A3 != B3))))) & ((! [A3:A]: (((Less_eq2 @ A3) @ A3))) & ((! [A3:A,B3:A]: ((((Less_eq2 @ A3) @ B3) => (((Less_eq2 @ B3) @ A3) => (A3 = B3))))) & (! [A3:A,B3:A,C4:A]: ((((Less_eq2 @ A3) @ B3) => (((Less_eq2 @ B3) @ C4) => ((Less_eq2 @ A3) @ C4)))))))))))))).
% 0.29/1.50 thf(fact_188_card__mono, axiom, (! [A:$tType,B5:(set @ A),A5:(set @ A)]: ((((finite_finite2 @ A) @ B5) => ((((ord_less_eq @ (set @ A)) @ A5) @ B5) => (((ord_less_eq @ nat) @ ((finite_card @ A) @ A5)) @ ((finite_card @ A) @ B5))))))).
% 0.29/1.50 thf(fact_189_card__seteq, axiom, (! [A:$tType,B5:(set @ A),A5:(set @ A)]: ((((finite_finite2 @ A) @ B5) => ((((ord_less_eq @ (set @ A)) @ A5) @ B5) => ((((ord_less_eq @ nat) @ ((finite_card @ A) @ B5)) @ ((finite_card @ A) @ A5)) => (A5 = B5))))))).
% 0.29/1.50 thf(fact_190_card__subset__eq, axiom, (! [A:$tType,B5:(set @ A),A5:(set @ A)]: ((((finite_finite2 @ A) @ B5) => ((((ord_less_eq @ (set @ A)) @ A5) @ B5) => ((((finite_card @ A) @ A5) = ((finite_card @ A) @ B5)) => (A5 = B5))))))).
% 0.29/1.50 thf(fact_191_infinite__arbitrarily__large, axiom, (! [A:$tType,A5:(set @ A),N2:nat]: (((~ (((finite_finite2 @ A) @ A5))) => (? [B9:(set @ A)]: ((((finite_finite2 @ A) @ B9) & ((((finite_card @ A) @ B9) = N2) & (((ord_less_eq @ (set @ A)) @ B9) @ A5))))))))).
% 0.29/1.50 thf(fact_192_finite__if__finite__subsets__card__bdd, axiom, (! [A:$tType,F3:(set @ A),C5:nat]: (((! [G4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ G4) @ F3) => (((finite_finite2 @ A) @ G4) => (((ord_less_eq @ nat) @ ((finite_card @ A) @ G4)) @ C5))))) => (((finite_finite2 @ A) @ F3) & (((ord_less_eq @ nat) @ ((finite_card @ A) @ F3)) @ C5)))))).
% 0.29/1.50 thf(fact_193_psubset__card__mono, axiom, (! [A:$tType,B5:(set @ A),A5:(set @ A)]: ((((finite_finite2 @ A) @ B5) => ((((ord_less @ (set @ A)) @ A5) @ B5) => (((ord_less @ nat) @ ((finite_card @ A) @ A5)) @ ((finite_card @ A) @ B5))))))).
% 0.29/1.50 thf(fact_194_obtain__subset__with__card__n, axiom, (! [A:$tType,N2:nat,S:(set @ A)]: (((((ord_less_eq @ nat) @ N2) @ ((finite_card @ A) @ S)) => (~ ((! [T3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ T3) @ S) => ((((finite_card @ A) @ T3) = N2) => (~ (((finite_finite2 @ A) @ T3))))))))))))).
% 0.29/1.50 thf(fact_195_linorder__inj__onI, axiom, (! [B:$tType,A:$tType]: (((order @ A) => (! [A5:(set @ A),F:(A > B)]: (((! [X:A,Y4:A]: (((((ord_less @ A) @ X) @ Y4) => ((((member @ A) @ X) @ A5) => ((((member @ A) @ Y4) @ A5) => ((F @ X) != (F @ Y4))))))) => ((! [X:A,Y4:A]: (((((member @ A) @ X) @ A5) => ((((member @ A) @ Y4) @ A5) => ((((ord_less_eq @ A) @ X) @ Y4) | (((ord_less_eq @ A) @ Y4) @ X)))))) => ((((inj_on @ A) @ B) @ F) @ A5))))))))).
% 0.29/1.50 thf(fact_196_card__le__if__inj__on__rel, axiom, (! [B:$tType,A:$tType,B5:(set @ A),A5:(set @ B),R3:(B > (A > $o))]: ((((finite_finite2 @ A) @ B5) => ((! [A6:B]: (((((member @ B) @ A6) @ A5) => (? [B10:A]: (((((member @ A) @ B10) @ B5) & ((R3 @ A6) @ B10))))))) => ((! [A1:B,A22:B,B6:A]: (((((member @ B) @ A1) @ A5) => ((((member @ B) @ A22) @ A5) => ((((member @ A) @ B6) @ B5) => (((R3 @ A1) @ B6) => (((R3 @ A22) @ B6) => (A1 = A22)))))))) => (((ord_less_eq @ nat) @ ((finite_card @ B) @ A5)) @ ((finite_card @ A) @ B5)))))))).
% 0.29/1.50 thf(fact_197_finite__nat__set__iff__bounded__le, axiom, ((finite_finite2 @ nat) = (^ [N3:(set @ nat)]: ((? [M:nat]: ((! [X2:nat]: (((((member @ nat) @ X2) @ N3) => (((ord_less_eq @ nat) @ X2) @ M)))))))))).
% 0.29/1.50 thf(fact_198_bounded__nat__set__is__finite, axiom, (! [N4:(set @ nat),N2:nat]: (((! [X:nat]: (((((member @ nat) @ X) @ N4) => (((ord_less @ nat) @ X) @ N2)))) => ((finite_finite2 @ nat) @ N4))))).
% 0.29/1.50 thf(fact_199_finite__nat__set__iff__bounded, axiom, ((finite_finite2 @ nat) = (^ [N3:(set @ nat)]: ((? [M:nat]: ((! [X2:nat]: (((((member @ nat) @ X2) @ N3) => (((ord_less @ nat) @ X2) @ M)))))))))).
% 0.29/1.50 thf(fact_200_card__le__inj, axiom, (! [B:$tType,A:$tType,A5:(set @ A),B5:(set @ B)]: ((((finite_finite2 @ A) @ A5) => (((finite_finite2 @ B) @ B5) => ((((ord_less_eq @ nat) @ ((finite_card @ A) @ A5)) @ ((finite_card @ B) @ B5)) => (? [F4:(A > B)]: (((((ord_less_eq @ (set @ B)) @ ((((image @ A) @ B) @ F4) @ A5)) @ B5) & ((((inj_on @ A) @ B) @ F4) @ A5)))))))))).
% 0.29/1.50 thf(fact_201_card__inj__on__le, axiom, (! [A:$tType,B:$tType,F:(A > B),A5:(set @ A),B5:(set @ B)]: ((((((inj_on @ A) @ B) @ F) @ A5) => ((((ord_less_eq @ (set @ B)) @ ((((image @ A) @ B) @ F) @ A5)) @ B5) => (((finite_finite2 @ B) @ B5) => (((ord_less_eq @ nat) @ ((finite_card @ A) @ A5)) @ ((finite_card @ B) @ B5)))))))).
% 0.29/1.50 thf(fact_202_finite__imageI, axiom, (! [B:$tType,A:$tType,F3:(set @ A),H:(A > B)]: ((((finite_finite2 @ A) @ F3) => ((finite_finite2 @ B) @ ((((image @ A) @ B) @ H) @ F3)))))).
% 0.29/1.50 thf(fact_203_all__subset__image, axiom, (! [A:$tType,B:$tType,F:(B > A),A5:(set @ B),P:((set @ A) > $o)]: (((! [B4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ B4) @ ((((image @ B) @ A) @ F) @ A5)) => (P @ B4)))) = (! [B4:(set @ B)]: (((((ord_less_eq @ (set @ B)) @ B4) @ A5) => (P @ ((((image @ B) @ A) @ F) @ B4))))))))).
% 0.29/1.50 thf(fact_204_all__finite__subset__image, axiom, (! [A:$tType,B:$tType,F:(B > A),A5:(set @ B),P:((set @ A) > $o)]: (((! [B4:(set @ A)]: (((((finite_finite2 @ A) @ B4) & (((ord_less_eq @ (set @ A)) @ B4) @ ((((image @ B) @ A) @ F) @ A5))) => (P @ B4)))) = (! [B4:(set @ B)]: (((((finite_finite2 @ B) @ B4) & (((ord_less_eq @ (set @ B)) @ B4) @ A5)) => (P @ ((((image @ B) @ A) @ F) @ B4))))))))).
% 0.29/1.50 thf(fact_205_ex__finite__subset__image, axiom, (! [A:$tType,B:$tType,F:(B > A),A5:(set @ B),P:((set @ A) > $o)]: (((? [B4:(set @ A)]: ((((finite_finite2 @ A) @ B4) & ((((ord_less_eq @ (set @ A)) @ B4) @ ((((image @ B) @ A) @ F) @ A5)) & (P @ B4))))) = (? [B4:(set @ B)]: ((((finite_finite2 @ B) @ B4) & ((((ord_less_eq @ (set @ B)) @ B4) @ A5) & (P @ ((((image @ B) @ A) @ F) @ B4)))))))))).
% 0.29/1.50 thf(fact_206_finite__subset__image, axiom, (! [A:$tType,B:$tType,B5:(set @ A),F:(B > A),A5:(set @ B)]: ((((finite_finite2 @ A) @ B5) => ((((ord_less_eq @ (set @ A)) @ B5) @ ((((image @ B) @ A) @ F) @ A5)) => (? [C6:(set @ B)]: (((((ord_less_eq @ (set @ B)) @ C6) @ A5) & (((finite_finite2 @ B) @ C6) & (B5 = ((((image @ B) @ A) @ F) @ C6))))))))))).
% 0.29/1.50 thf(fact_207_finite__surj, axiom, (! [A:$tType,B:$tType,A5:(set @ A),B5:(set @ B),F:(A > B)]: ((((finite_finite2 @ A) @ A5) => ((((ord_less_eq @ (set @ B)) @ B5) @ ((((image @ A) @ B) @ F) @ A5)) => ((finite_finite2 @ B) @ B5)))))).
% 0.29/1.50 thf(fact_208_finite__image__iff, axiom, (! [B:$tType,A:$tType,F:(A > B),A5:(set @ A)]: ((((((inj_on @ A) @ B) @ F) @ A5) => (((finite_finite2 @ B) @ ((((image @ A) @ B) @ F) @ A5)) = ((finite_finite2 @ A) @ A5)))))).
% 0.29/1.50 thf(fact_209_finite__imageD, axiom, (! [A:$tType,B:$tType,F:(B > A),A5:(set @ B)]: ((((finite_finite2 @ A) @ ((((image @ B) @ A) @ F) @ A5)) => (((((inj_on @ B) @ A) @ F) @ A5) => ((finite_finite2 @ B) @ A5)))))).
% 0.29/1.50 thf(fact_210_card__image, axiom, (! [B:$tType,A:$tType,F:(A > B),A5:(set @ A)]: ((((((inj_on @ A) @ B) @ F) @ A5) => (((finite_card @ B) @ ((((image @ A) @ B) @ F) @ A5)) = ((finite_card @ A) @ A5)))))).
% 0.29/1.50 thf(fact_211_finite__surj__inj, axiom, (! [A:$tType,A5:(set @ A),F:(A > A)]: ((((finite_finite2 @ A) @ A5) => ((((ord_less_eq @ (set @ A)) @ A5) @ ((((image @ A) @ A) @ F) @ A5)) => ((((inj_on @ A) @ A) @ F) @ A5)))))).
% 0.29/1.50 thf(fact_212_inj__on__finite, axiom, (! [B:$tType,A:$tType,F:(A > B),A5:(set @ A),B5:(set @ B)]: ((((((inj_on @ A) @ B) @ F) @ A5) => ((((ord_less_eq @ (set @ B)) @ ((((image @ A) @ B) @ F) @ A5)) @ B5) => (((finite_finite2 @ B) @ B5) => ((finite_finite2 @ A) @ A5))))))).
% 0.29/1.50 thf(fact_213_endo__inj__surj, axiom, (! [A:$tType,A5:(set @ A),F:(A > A)]: ((((finite_finite2 @ A) @ A5) => ((((ord_less_eq @ (set @ A)) @ ((((image @ A) @ A) @ F) @ A5)) @ A5) => (((((inj_on @ A) @ A) @ F) @ A5) => (((((image @ A) @ A) @ F) @ A5) = A5))))))).
% 0.29/1.50 thf(fact_214_card__image__le, axiom, (! [B:$tType,A:$tType,A5:(set @ A),F:(A > B)]: ((((finite_finite2 @ A) @ A5) => (((ord_less_eq @ nat) @ ((finite_card @ B) @ ((((image @ A) @ B) @ F) @ A5))) @ ((finite_card @ A) @ A5)))))).
% 0.29/1.50 thf(fact_215_eq__card__imp__inj__on, axiom, (! [B:$tType,A:$tType,A5:(set @ A),F:(A > B)]: ((((finite_finite2 @ A) @ A5) => ((((finite_card @ B) @ ((((image @ A) @ B) @ F) @ A5)) = ((finite_card @ A) @ A5)) => ((((inj_on @ A) @ B) @ F) @ A5)))))).
% 0.29/1.50 thf(fact_216_inj__on__iff__eq__card, axiom, (! [B:$tType,A:$tType,A5:(set @ A),F:(A > B)]: ((((finite_finite2 @ A) @ A5) => (((((inj_on @ A) @ B) @ F) @ A5) = (((finite_card @ B) @ ((((image @ A) @ B) @ F) @ A5)) = ((finite_card @ A) @ A5))))))).
% 0.29/1.50 thf(fact_217_pigeonhole, axiom, (! [A:$tType,B:$tType,F:(B > A),A5:(set @ B)]: (((((ord_less @ nat) @ ((finite_card @ A) @ ((((image @ B) @ A) @ F) @ A5))) @ ((finite_card @ B) @ A5)) => (~ (((((inj_on @ B) @ A) @ F) @ A5))))))).
% 0.29/1.50 thf(fact_218_surj__card__le, axiom, (! [B:$tType,A:$tType,A5:(set @ A),B5:(set @ B),F:(A > B)]: ((((finite_finite2 @ A) @ A5) => ((((ord_less_eq @ (set @ B)) @ B5) @ ((((image @ A) @ B) @ F) @ A5)) => (((ord_less_eq @ nat) @ ((finite_card @ B) @ B5)) @ ((finite_card @ A) @ A5))))))).
% 0.29/1.50 thf(fact_219_surjective__iff__injective__gen, axiom, (! [B:$tType,A:$tType,S:(set @ A),T2:(set @ B),F:(A > B)]: ((((finite_finite2 @ A) @ S) => (((finite_finite2 @ B) @ T2) => ((((finite_card @ A) @ S) = ((finite_card @ B) @ T2)) => ((((ord_less_eq @ (set @ B)) @ ((((image @ A) @ B) @ F) @ S)) @ T2) => ((! [X2:B]: (((((member @ B) @ X2) @ T2) => (? [Y3:A]: (((((member @ A) @ Y3) @ S) & ((F @ Y3) = X2))))))) = ((((inj_on @ A) @ B) @ F) @ S))))))))).
% 0.29/1.50 thf(fact_220_card__bij__eq, axiom, (! [A:$tType,B:$tType,F:(A > B),A5:(set @ A),B5:(set @ B),G:(B > A)]: ((((((inj_on @ A) @ B) @ F) @ A5) => ((((ord_less_eq @ (set @ B)) @ ((((image @ A) @ B) @ F) @ A5)) @ B5) => (((((inj_on @ B) @ A) @ G) @ B5) => ((((ord_less_eq @ (set @ A)) @ ((((image @ B) @ A) @ G) @ B5)) @ A5) => (((finite_finite2 @ A) @ A5) => (((finite_finite2 @ B) @ B5) => (((finite_card @ A) @ A5) = ((finite_card @ B) @ B5))))))))))).
% 0.29/1.50 thf(fact_221_inj__on__iff__card__le, axiom, (! [A:$tType,B:$tType,A5:(set @ A),B5:(set @ B)]: ((((finite_finite2 @ A) @ A5) => (((finite_finite2 @ B) @ B5) => ((? [F2:(A > B)]: ((((((inj_on @ A) @ B) @ F2) @ A5) & (((ord_less_eq @ (set @ B)) @ ((((image @ A) @ B) @ F2) @ A5)) @ B5)))) = (((ord_less_eq @ nat) @ ((finite_card @ A) @ A5)) @ ((finite_card @ B) @ B5)))))))).
% 0.29/1.50 thf(fact_222_inj__on__image__Fpow, axiom, (! [B:$tType,A:$tType,F:(A > B),A5:(set @ A)]: ((((((inj_on @ A) @ B) @ F) @ A5) => ((((inj_on @ (set @ A)) @ (set @ B)) @ (((image @ A) @ B) @ F)) @ ((finite_Fpow @ A) @ A5)))))).
% 0.29/1.50 thf(fact_223_image__Fpow__mono, axiom, (! [B:$tType,A:$tType,F:(B > A),A5:(set @ B),B5:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ ((((image @ B) @ A) @ F) @ A5)) @ B5) => (((ord_less_eq @ (set @ (set @ A))) @ ((((image @ (set @ B)) @ (set @ A)) @ (((image @ B) @ A) @ F)) @ ((finite_Fpow @ B) @ A5))) @ ((finite_Fpow @ A) @ B5)))))).
% 0.29/1.50 thf(fact_224_Fpow__mono, axiom, (! [A:$tType,A5:(set @ A),B5:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A5) @ B5) => (((ord_less_eq @ (set @ (set @ A))) @ ((finite_Fpow @ A) @ A5)) @ ((finite_Fpow @ A) @ B5)))))).
% 0.29/1.50 thf(fact_225_card__ge__0__finite, axiom, (! [A:$tType,A5:(set @ A)]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ ((finite_card @ A) @ A5)) => ((finite_finite2 @ A) @ A5))))).
% 0.29/1.50 thf(fact_226_greaterThanLessThan__subseteq__greaterThanLessThan, axiom, (! [A:$tType]: (((dense_linorder @ A) => (! [A2:A,B2:A,C:A,D3:A]: (((((ord_less_eq @ (set @ A)) @ (((set_or578182835ssThan @ A) @ A2) @ B2)) @ (((set_or578182835ssThan @ A) @ C) @ D3)) = ((((ord_less @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ C) @ A2) & (((ord_less_eq @ A) @ B2) @ D3)))))))))).
% 0.29/1.50 thf(fact_227_finite__greaterThanLessThan, axiom, (! [L:nat,U4:nat]: (((finite_finite2 @ nat) @ (((set_or578182835ssThan @ nat) @ L) @ U4))))).
% 0.29/1.50 thf(fact_228_bot__nat__0_Onot__eq__extremum, axiom, (! [A2:nat]: (((A2 != (zero_zero @ nat)) = (((ord_less @ nat) @ (zero_zero @ nat)) @ A2))))).
% 0.29/1.50 thf(fact_229_less__nat__zero__code, axiom, (! [N2:nat]: ((~ ((((ord_less @ nat) @ N2) @ (zero_zero @ nat))))))).
% 0.29/1.50 thf(fact_230_neq0__conv, axiom, (! [N2:nat]: (((N2 != (zero_zero @ nat)) = (((ord_less @ nat) @ (zero_zero @ nat)) @ N2))))).
% 0.29/1.50 thf(fact_231_le0, axiom, (! [N2:nat]: ((((ord_less_eq @ nat) @ (zero_zero @ nat)) @ N2)))).
% 0.29/1.50 thf(fact_232_bot__nat__0_Oextremum, axiom, (! [A2:nat]: ((((ord_less_eq @ nat) @ (zero_zero @ nat)) @ A2)))).
% 0.29/1.50 thf(fact_233_greaterThanLessThan__iff, axiom, (! [A:$tType]: (((ord @ A) => (! [I:A,L:A,U4:A]: (((((member @ A) @ I) @ (((set_or578182835ssThan @ A) @ L) @ U4)) = ((((ord_less @ A) @ L) @ I) & (((ord_less @ A) @ I) @ U4))))))))).
% 0.29/1.50 thf(fact_234_card_Oinfinite, axiom, (! [A:$tType,A5:(set @ A)]: (((~ (((finite_finite2 @ A) @ A5))) => (((finite_card @ A) @ A5) = (zero_zero @ nat)))))).
% 0.29/1.50 thf(fact_235_infinite__Ioo__iff, axiom, (! [A:$tType]: (((dense_linorder @ A) => (! [A2:A,B2:A]: (((~ (((finite_finite2 @ A) @ (((set_or578182835ssThan @ A) @ A2) @ B2)))) = (((ord_less @ A) @ A2) @ B2)))))))).
% 0.29/1.50 thf(fact_236_less__eq__nat_Osimps_I1_J, axiom, (! [N2:nat]: ((((ord_less_eq @ nat) @ (zero_zero @ nat)) @ N2)))).
% 0.29/1.50 thf(fact_237_le__0__eq, axiom, (! [N2:nat]: (((((ord_less_eq @ nat) @ N2) @ (zero_zero @ nat)) = (N2 = (zero_zero @ nat)))))).
% 0.29/1.50 thf(fact_238_bot__nat__0_Oextremum__unique, axiom, (! [A2:nat]: (((((ord_less_eq @ nat) @ A2) @ (zero_zero @ nat)) = (A2 = (zero_zero @ nat)))))).
% 0.29/1.50 thf(fact_239_bot__nat__0_Oextremum__uniqueI, axiom, (! [A2:nat]: (((((ord_less_eq @ nat) @ A2) @ (zero_zero @ nat)) => (A2 = (zero_zero @ nat)))))).
% 0.29/1.50 thf(fact_240_ex__least__nat__le, axiom, (! [P:(nat > $o),N2:nat]: (((P @ N2) => ((~ ((P @ (zero_zero @ nat)))) => (? [K:nat]: (((((ord_less_eq @ nat) @ K) @ N2) & ((! [I2:nat]: (((((ord_less @ nat) @ I2) @ K) => (~ ((P @ I2)))))) & (P @ K)))))))))).
% 0.29/1.50 thf(fact_241_infinite__descent0__measure, axiom, (! [A:$tType,V5:(A > nat),P:(A > $o),X3:A]: (((! [X:A]: ((((V5 @ X) = (zero_zero @ nat)) => (P @ X)))) => ((! [X:A]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ (V5 @ X)) => ((~ ((P @ X))) => (? [Y5:A]: (((((ord_less @ nat) @ (V5 @ Y5)) @ (V5 @ X)) & (~ ((P @ Y5)))))))))) => (P @ X3)))))).
% 0.29/1.50 thf(fact_242_bot__nat__0_Oextremum__strict, axiom, (! [A2:nat]: ((~ ((((ord_less @ nat) @ A2) @ (zero_zero @ nat))))))).
% 0.29/1.50 thf(fact_243_infinite__descent0, axiom, (! [P:(nat > $o),N2:nat]: (((P @ (zero_zero @ nat)) => ((! [N5:nat]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ N5) => ((~ ((P @ N5))) => (? [M2:nat]: (((((ord_less @ nat) @ M2) @ N5) & (~ ((P @ M2)))))))))) => (P @ N2)))))).
% 0.29/1.50 thf(fact_244_gr__implies__not0, axiom, (! [M3:nat,N2:nat]: (((((ord_less @ nat) @ M3) @ N2) => (N2 != (zero_zero @ nat)))))).
% 0.29/1.50 thf(fact_245_less__zeroE, axiom, (! [N2:nat]: ((~ ((((ord_less @ nat) @ N2) @ (zero_zero @ nat))))))).
% 0.29/1.50 thf(fact_246_not__less0, axiom, (! [N2:nat]: ((~ ((((ord_less @ nat) @ N2) @ (zero_zero @ nat))))))).
% 0.29/1.50 thf(fact_247_not__gr0, axiom, (! [N2:nat]: (((~ ((((ord_less @ nat) @ (zero_zero @ nat)) @ N2))) = (N2 = (zero_zero @ nat)))))).
% 0.29/1.50 thf(fact_248_gr0I, axiom, (! [N2:nat]: (((N2 != (zero_zero @ nat)) => (((ord_less @ nat) @ (zero_zero @ nat)) @ N2))))).
% 0.29/1.50 thf(fact_249_infinite__Ioo, axiom, (! [A:$tType]: (((dense_linorder @ A) => (! [A2:A,B2:A]: (((((ord_less @ A) @ A2) @ B2) => (~ (((finite_finite2 @ A) @ (((set_or578182835ssThan @ A) @ A2) @ B2))))))))))).
% 0.29/1.50 thf(fact_250_not__gr__zero, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [N2:A]: (((~ ((((ord_less @ A) @ (zero_zero @ A)) @ N2))) = (N2 = (zero_zero @ A))))))))).
% 0.29/1.50 thf(fact_251_le__zero__eq, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [N2:A]: (((((ord_less_eq @ A) @ N2) @ (zero_zero @ A)) = (N2 = (zero_zero @ A))))))))).
% 0.29/1.50 thf(fact_252_RepFun__0, axiom, (! [F:(hF_Mirabelle_hf > hF_Mirabelle_hf)]: ((((hF_Mirabelle_RepFun @ (zero_zero @ hF_Mirabelle_hf)) @ F) = (zero_zero @ hF_Mirabelle_hf))))).
% 0.29/1.50 thf(fact_253_HUnion__hempty, axiom, ((hF_Mirabelle_HUnion @ (zero_zero @ hF_Mirabelle_hf)) = (zero_zero @ hF_Mirabelle_hf))).
% 0.29/1.50 thf(fact_254_Replace__0, axiom, (! [R:(hF_Mirabelle_hf > (hF_Mirabelle_hf > $o))]: ((((hF_Mirabelle_Replace @ (zero_zero @ hF_Mirabelle_hf)) @ R) = (zero_zero @ hF_Mirabelle_hf))))).
% 0.29/1.50 thf(tcon_fun___Orderings_Opreorder, axiom, (! [A9:$tType,A10:$tType]: (((preorder @ A10) => (preorder @ (A9 > A10)))))).
% 0.29/1.50 thf(tcon_fun___Finite__Set_Ofinite, axiom, (! [A9:$tType,A10:$tType]: ((((finite_finite @ A9) & (finite_finite @ A10)) => (finite_finite @ (A9 > A10)))))).
% 0.29/1.50 thf(tcon_fun___Orderings_Oorder, axiom, (! [A9:$tType,A10:$tType]: (((order @ A10) => (order @ (A9 > A10)))))).
% 0.29/1.50 thf(tcon_fun___Orderings_Oord, axiom, (! [A9:$tType,A10:$tType]: (((ord @ A10) => (ord @ (A9 > A10)))))).
% 0.29/1.50 thf(tcon_Nat_Onat___Conditionally__Complete__Lattices_Oconditionally__complete__linorder, axiom, (condit1037483654norder @ nat)).
% 0.29/1.50 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add, axiom, (canoni770627133id_add @ nat)).
% 0.29/1.50 thf(tcon_Nat_Onat___Orderings_Owellorder, axiom, (wellorder @ nat)).
% 0.29/1.50 thf(tcon_Nat_Onat___Orderings_Opreorder_1, axiom, (preorder @ nat)).
% 0.29/1.50 thf(tcon_Nat_Onat___Orderings_Olinorder, axiom, (linorder @ nat)).
% 0.29/1.50 thf(tcon_Nat_Onat___Orderings_Ono__top, axiom, (no_top @ nat)).
% 0.29/1.50 thf(tcon_Nat_Onat___Orderings_Oorder_2, axiom, (order @ nat)).
% 0.29/1.50 thf(tcon_Nat_Onat___Orderings_Oord_3, axiom, (ord @ nat)).
% 0.29/1.50 thf(tcon_Set_Oset___Orderings_Opreorder_4, axiom, (! [A9:$tType]: ((preorder @ (set @ A9))))).
% 0.29/1.50 thf(tcon_Set_Oset___Finite__Set_Ofinite_5, axiom, (! [A9:$tType]: (((finite_finite @ A9) => (finite_finite @ (set @ A9)))))).
% 0.29/1.50 thf(tcon_Set_Oset___Orderings_Oorder_6, axiom, (! [A9:$tType]: ((order @ (set @ A9))))).
% 0.29/1.50 thf(tcon_Set_Oset___Orderings_Oord_7, axiom, (! [A9:$tType]: ((ord @ (set @ A9))))).
% 0.29/1.50 thf(tcon_HOL_Obool___Orderings_Opreorder_8, axiom, (preorder @ $o)).
% 0.29/1.50 thf(tcon_HOL_Obool___Orderings_Olinorder_9, axiom, (linorder @ $o)).
% 0.29/1.50 thf(tcon_HOL_Obool___Finite__Set_Ofinite_10, axiom, (finite_finite @ $o)).
% 0.29/1.50 thf(tcon_HOL_Obool___Orderings_Oorder_11, axiom, (order @ $o)).
% 0.29/1.50 thf(tcon_HOL_Obool___Orderings_Oord_12, axiom, (ord @ $o)).
% 0.29/1.50 thf(tcon_HF__Mirabelle__fsbjehakzm_Ohf___Orderings_Opreorder_13, axiom, (preorder @ hF_Mirabelle_hf)).
% 0.29/1.50 thf(tcon_HF__Mirabelle__fsbjehakzm_Ohf___Orderings_Oorder_14, axiom, (order @ hF_Mirabelle_hf)).
% 0.29/1.50 thf(tcon_HF__Mirabelle__fsbjehakzm_Ohf___Orderings_Oord_15, axiom, (ord @ hF_Mirabelle_hf)).
% 0.29/1.50 thf(conj_0, hypothesis, (! [X6:hF_Mirabelle_hf]: ((((hF_Mirabelle_hmem @ X6) @ a) => ((hF_Mirabelle_hmem @ X6) @ b))))).
% 0.29/1.50 thf(conj_1, conjecture, (((ord_less_eq @ hF_Mirabelle_hf) @ a) @ b)).
% 0.29/1.50 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.vTURPhR8yA/DTF2DTF14628.p
% 0.29/1.50 ------------------------
% 0.29/1.52 ---- Cleaned THF ---
% 0.29/1.52 thf(ty_t_HF__Mirabelle__fsbjehakzm_Ohf,type,
% 0.29/1.52 hF_Mirabelle_hf: $tType ).
% 0.29/1.52
% 0.29/1.52 thf(ty_t_Set_Oset,type,
% 0.29/1.52 set: $tType > $tType ).
% 0.29/1.52
% 0.29/1.52 thf(ty_t_Nat_Onat,type,
% 0.29/1.52 nat: $tType ).
% 0.29/1.52
% 0.29/1.52 thf(sy_cl_HOL_Otype,type,
% 0.29/1.52 type:
% 0.29/1.52 !>[A: $tType] : $o ).
% 0.29/1.52
% 0.29/1.52 thf(sy_cl_Orderings_Oord,type,
% 0.29/1.52 ord:
% 0.29/1.52 !>[A: $tType] : $o ).
% 0.29/1.52
% 0.29/1.52 thf(sy_cl_Orderings_Oorder,type,
% 0.29/1.52 order:
% 0.29/1.52 !>[A: $tType] : $o ).
% 0.29/1.52
% 0.29/1.52 thf(sy_cl_Orderings_Ono__bot,type,
% 0.29/1.52 no_bot:
% 0.29/1.52 !>[A: $tType] : $o ).
% 0.29/1.52
% 0.29/1.52 thf(sy_cl_Orderings_Ono__top,type,
% 0.29/1.52 no_top:
% 0.29/1.52 !>[A: $tType] : $o ).
% 0.29/1.52
% 0.29/1.52 thf(sy_cl_Finite__Set_Ofinite,type,
% 0.29/1.52 finite_finite:
% 0.29/1.52 !>[A: $tType] : $o ).
% 0.29/1.52
% 0.29/1.52 thf(sy_cl_Orderings_Olinorder,type,
% 0.29/1.52 linorder:
% 0.29/1.52 !>[A: $tType] : $o ).
% 0.29/1.52
% 0.29/1.52 thf(sy_cl_Orderings_Opreorder,type,
% 0.29/1.52 preorder:
% 0.29/1.52 !>[A: $tType] : $o ).
% 0.29/1.52
% 0.29/1.52 thf(sy_cl_Orderings_Owellorder,type,
% 0.29/1.52 wellorder:
% 0.29/1.52 !>[A: $tType] : $o ).
% 0.29/1.52
% 0.29/1.52 thf(sy_cl_Orderings_Odense__order,type,
% 0.29/1.52 dense_order:
% 0.29/1.52 !>[A: $tType] : $o ).
% 0.29/1.52
% 0.29/1.52 thf(sy_cl_Rings_Olinordered__idom,type,
% 0.29/1.52 linordered_idom:
% 0.29/1.52 !>[A: $tType] : $o ).
% 0.29/1.52
% 0.29/1.52 thf(sy_cl_Fields_Olinordered__field,type,
% 0.29/1.52 linordered_field:
% 0.29/1.52 !>[A: $tType] : $o ).
% 0.29/1.52
% 0.29/1.52 thf(sy_cl_Orderings_Odense__linorder,type,
% 0.29/1.52 dense_linorder:
% 0.29/1.52 !>[A: $tType] : $o ).
% 0.29/1.52
% 0.29/1.52 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add,type,
% 0.29/1.52 canoni770627133id_add:
% 0.29/1.52 !>[A: $tType] : $o ).
% 0.29/1.52
% 0.29/1.52 thf(sy_cl_Conditionally__Complete__Lattices_Olinear__continuum,type,
% 0.29/1.52 condit1656338222tinuum:
% 0.29/1.52 !>[A: $tType] : $o ).
% 0.29/1.52
% 0.29/1.52 thf(sy_cl_Conditionally__Complete__Lattices_Oconditionally__complete__linorder,type,
% 0.29/1.52 condit1037483654norder:
% 0.29/1.52 !>[A: $tType] : $o ).
% 0.29/1.52
% 0.29/1.52 thf(sy_c_Finite__Set_OFpow,type,
% 0.29/1.52 finite_Fpow:
% 0.29/1.52 !>[A: $tType] : ( ( set @ A ) > ( set @ ( set @ A ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(sy_c_Finite__Set_Ocard,type,
% 0.29/1.52 finite_card:
% 0.29/1.52 !>[B: $tType] : ( ( set @ B ) > nat ) ).
% 0.29/1.52
% 0.29/1.52 thf(sy_c_Finite__Set_Ofinite,type,
% 0.29/1.52 finite_finite2:
% 0.29/1.52 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 0.29/1.52
% 0.29/1.52 thf(sy_c_Fun_Oinj__on,type,
% 0.29/1.52 inj_on:
% 0.29/1.52 !>[A: $tType,B: $tType] : ( ( A > B ) > ( set @ A ) > $o ) ).
% 0.29/1.52
% 0.29/1.52 thf(sy_c_Groups_Ozero__class_Ozero,type,
% 0.29/1.52 zero_zero:
% 0.29/1.52 !>[A: $tType] : A ).
% 0.29/1.52
% 0.29/1.52 thf(sy_c_HF__Mirabelle__fsbjehakzm_OHCollect,type,
% 0.29/1.52 hF_Mir1687042746ollect: ( hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf > hF_Mirabelle_hf ).
% 0.29/1.52
% 0.29/1.52 thf(sy_c_HF__Mirabelle__fsbjehakzm_OHF,type,
% 0.29/1.52 hF_Mirabelle_HF: ( set @ hF_Mirabelle_hf ) > hF_Mirabelle_hf ).
% 0.29/1.52
% 0.29/1.52 thf(sy_c_HF__Mirabelle__fsbjehakzm_OHUnion,type,
% 0.29/1.52 hF_Mirabelle_HUnion: hF_Mirabelle_hf > hF_Mirabelle_hf ).
% 0.29/1.52
% 0.29/1.52 thf(sy_c_HF__Mirabelle__fsbjehakzm_OPrimReplace,type,
% 0.29/1.52 hF_Mir569462966eplace: hF_Mirabelle_hf > ( hF_Mirabelle_hf > hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf ).
% 0.29/1.52
% 0.29/1.52 thf(sy_c_HF__Mirabelle__fsbjehakzm_ORepFun,type,
% 0.29/1.52 hF_Mirabelle_RepFun: hF_Mirabelle_hf > ( hF_Mirabelle_hf > hF_Mirabelle_hf ) > hF_Mirabelle_hf ).
% 0.29/1.52
% 0.29/1.52 thf(sy_c_HF__Mirabelle__fsbjehakzm_OReplace,type,
% 0.29/1.52 hF_Mirabelle_Replace: hF_Mirabelle_hf > ( hF_Mirabelle_hf > hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf ).
% 0.29/1.52
% 0.29/1.52 thf(sy_c_HF__Mirabelle__fsbjehakzm_Ohfset,type,
% 0.29/1.52 hF_Mirabelle_hfset: hF_Mirabelle_hf > ( set @ hF_Mirabelle_hf ) ).
% 0.29/1.52
% 0.29/1.52 thf(sy_c_HF__Mirabelle__fsbjehakzm_Ohmem,type,
% 0.29/1.52 hF_Mirabelle_hmem: hF_Mirabelle_hf > hF_Mirabelle_hf > $o ).
% 0.29/1.52
% 0.29/1.52 thf(sy_c_Orderings_Oord__class_Oless,type,
% 0.29/1.52 ord_less:
% 0.29/1.52 !>[A: $tType] : ( A > A > $o ) ).
% 0.29/1.52
% 0.29/1.52 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.29/1.52 ord_less_eq:
% 0.29/1.52 !>[A: $tType] : ( A > A > $o ) ).
% 0.29/1.52
% 0.29/1.52 thf(sy_c_Orderings_Oorder__class_OGreatest,type,
% 0.29/1.52 order_Greatest:
% 0.29/1.52 !>[A: $tType] : ( ( A > $o ) > A ) ).
% 0.29/1.52
% 0.29/1.52 thf(sy_c_Orderings_Oorder__class_Oantimono,type,
% 0.29/1.52 order_antimono:
% 0.29/1.52 !>[A: $tType,B: $tType] : ( ( A > B ) > $o ) ).
% 0.29/1.52
% 0.29/1.52 thf(sy_c_Orderings_Oordering,type,
% 0.29/1.52 ordering:
% 0.29/1.52 !>[A: $tType] : ( ( A > A > $o ) > ( A > A > $o ) > $o ) ).
% 0.29/1.52
% 0.29/1.52 thf(sy_c_Set_OCollect,type,
% 0.29/1.52 collect:
% 0.29/1.52 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(sy_c_Set_Oimage,type,
% 0.29/1.52 image:
% 0.29/1.52 !>[A: $tType,B: $tType] : ( ( A > B ) > ( set @ A ) > ( set @ B ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan,type,
% 0.29/1.52 set_or578182835ssThan:
% 0.29/1.52 !>[A: $tType] : ( A > A > ( set @ A ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(sy_c_member,type,
% 0.29/1.52 member:
% 0.29/1.52 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.29/1.52
% 0.29/1.52 thf(sy_v_A,type,
% 0.29/1.52 a: hF_Mirabelle_hf ).
% 0.29/1.52
% 0.29/1.52 thf(sy_v_B,type,
% 0.29/1.52 b: hF_Mirabelle_hf ).
% 0.29/1.52
% 0.29/1.52 thf(fact_0_hf__equalityI,axiom,
% 0.29/1.52 ! [A2: hF_Mirabelle_hf,B2: hF_Mirabelle_hf] :
% 0.29/1.52 ( ! [X: hF_Mirabelle_hf] :
% 0.29/1.52 ( ( hF_Mirabelle_hmem @ X @ A2 )
% 0.29/1.52 = ( hF_Mirabelle_hmem @ X @ B2 ) )
% 0.29/1.52 => ( A2 = B2 ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_1_hf__ext,axiom,
% 0.29/1.52 ( ( ^ [Y: hF_Mirabelle_hf,Z: hF_Mirabelle_hf] : ( Y = Z ) )
% 0.29/1.52 = ( ^ [A3: hF_Mirabelle_hf,B3: hF_Mirabelle_hf] :
% 0.29/1.52 ! [X2: hF_Mirabelle_hf] :
% 0.29/1.52 ( ( hF_Mirabelle_hmem @ X2 @ A3 )
% 0.29/1.52 = ( hF_Mirabelle_hmem @ X2 @ B3 ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_2_replacement,axiom,
% 0.29/1.52 ! [X3: hF_Mirabelle_hf,R: hF_Mirabelle_hf > hF_Mirabelle_hf > $o] :
% 0.29/1.52 ( ! [U: hF_Mirabelle_hf,V: hF_Mirabelle_hf,V2: hF_Mirabelle_hf] :
% 0.29/1.52 ( ( hF_Mirabelle_hmem @ U @ X3 )
% 0.29/1.52 => ( ( R @ U @ V )
% 0.29/1.52 => ( ( R @ U @ V2 )
% 0.29/1.52 => ( V2 = V ) ) ) )
% 0.29/1.52 => ? [Z2: hF_Mirabelle_hf] :
% 0.29/1.52 ! [V3: hF_Mirabelle_hf] :
% 0.29/1.52 ( ( hF_Mirabelle_hmem @ V3 @ Z2 )
% 0.29/1.52 = ( ? [U2: hF_Mirabelle_hf] :
% 0.29/1.52 ( ( hF_Mirabelle_hmem @ U2 @ X3 )
% 0.29/1.52 & ( R @ U2 @ V3 ) ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_3_binary__union,axiom,
% 0.29/1.52 ! [X3: hF_Mirabelle_hf,Y2: hF_Mirabelle_hf] :
% 0.29/1.52 ? [Z2: hF_Mirabelle_hf] :
% 0.29/1.52 ! [U3: hF_Mirabelle_hf] :
% 0.29/1.52 ( ( hF_Mirabelle_hmem @ U3 @ Z2 )
% 0.29/1.52 = ( ( hF_Mirabelle_hmem @ U3 @ X3 )
% 0.29/1.52 | ( hF_Mirabelle_hmem @ U3 @ Y2 ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_4_union__of__set,axiom,
% 0.29/1.52 ! [X3: hF_Mirabelle_hf] :
% 0.29/1.52 ? [Z2: hF_Mirabelle_hf] :
% 0.29/1.52 ! [U3: hF_Mirabelle_hf] :
% 0.29/1.52 ( ( hF_Mirabelle_hmem @ U3 @ Z2 )
% 0.29/1.52 = ( ? [Y3: hF_Mirabelle_hf] :
% 0.29/1.52 ( ( hF_Mirabelle_hmem @ Y3 @ X3 )
% 0.29/1.52 & ( hF_Mirabelle_hmem @ U3 @ Y3 ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_5_comprehension,axiom,
% 0.29/1.52 ! [X3: hF_Mirabelle_hf,P: hF_Mirabelle_hf > $o] :
% 0.29/1.52 ? [Z2: hF_Mirabelle_hf] :
% 0.29/1.52 ! [U3: hF_Mirabelle_hf] :
% 0.29/1.52 ( ( hF_Mirabelle_hmem @ U3 @ Z2 )
% 0.29/1.52 = ( ( hF_Mirabelle_hmem @ U3 @ X3 )
% 0.29/1.52 & ( P @ U3 ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_6_less__eq__hf__def,axiom,
% 0.29/1.52 ( ( ord_less_eq @ hF_Mirabelle_hf )
% 0.29/1.52 = ( ^ [A4: hF_Mirabelle_hf,B4: hF_Mirabelle_hf] :
% 0.29/1.52 ! [X2: hF_Mirabelle_hf] :
% 0.29/1.52 ( ( hF_Mirabelle_hmem @ X2 @ A4 )
% 0.29/1.52 => ( hF_Mirabelle_hmem @ X2 @ B4 ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_7_replacement__fun,axiom,
% 0.29/1.52 ! [X3: hF_Mirabelle_hf,F: hF_Mirabelle_hf > hF_Mirabelle_hf] :
% 0.29/1.52 ? [Z2: hF_Mirabelle_hf] :
% 0.29/1.52 ! [V3: hF_Mirabelle_hf] :
% 0.29/1.52 ( ( hF_Mirabelle_hmem @ V3 @ Z2 )
% 0.29/1.52 = ( ? [U2: hF_Mirabelle_hf] :
% 0.29/1.52 ( ( hF_Mirabelle_hmem @ U2 @ X3 )
% 0.29/1.52 & ( V3
% 0.29/1.52 = ( F @ U2 ) ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_8_order__refl,axiom,
% 0.29/1.52 ! [A: $tType] :
% 0.29/1.52 ( ( preorder @ A )
% 0.29/1.52 => ! [X3: A] : ( ord_less_eq @ A @ X3 @ X3 ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_9_PrimReplace__iff,axiom,
% 0.29/1.52 ! [A5: hF_Mirabelle_hf,R: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,V4: hF_Mirabelle_hf] :
% 0.29/1.52 ( ! [U: hF_Mirabelle_hf,V: hF_Mirabelle_hf,V2: hF_Mirabelle_hf] :
% 0.29/1.52 ( ( hF_Mirabelle_hmem @ U @ A5 )
% 0.29/1.52 => ( ( R @ U @ V )
% 0.29/1.52 => ( ( R @ U @ V2 )
% 0.29/1.52 => ( V2 = V ) ) ) )
% 0.29/1.52 => ( ( hF_Mirabelle_hmem @ V4 @ ( hF_Mir569462966eplace @ A5 @ R ) )
% 0.29/1.52 = ( ? [U2: hF_Mirabelle_hf] :
% 0.29/1.52 ( ( hF_Mirabelle_hmem @ U2 @ A5 )
% 0.29/1.52 & ( R @ U2 @ V4 ) ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_10_HCollect__iff,axiom,
% 0.29/1.52 ! [X3: hF_Mirabelle_hf,P: hF_Mirabelle_hf > $o,A5: hF_Mirabelle_hf] :
% 0.29/1.52 ( ( hF_Mirabelle_hmem @ X3 @ ( hF_Mir1687042746ollect @ P @ A5 ) )
% 0.29/1.52 = ( ( P @ X3 )
% 0.29/1.52 & ( hF_Mirabelle_hmem @ X3 @ A5 ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_11_HUnion__iff,axiom,
% 0.29/1.52 ! [X3: hF_Mirabelle_hf,A5: hF_Mirabelle_hf] :
% 0.29/1.52 ( ( hF_Mirabelle_hmem @ X3 @ ( hF_Mirabelle_HUnion @ A5 ) )
% 0.29/1.52 = ( ? [Y3: hF_Mirabelle_hf] :
% 0.29/1.52 ( ( hF_Mirabelle_hmem @ Y3 @ A5 )
% 0.29/1.52 & ( hF_Mirabelle_hmem @ X3 @ Y3 ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_12_Replace__iff,axiom,
% 0.29/1.52 ! [V4: hF_Mirabelle_hf,A5: hF_Mirabelle_hf,R: hF_Mirabelle_hf > hF_Mirabelle_hf > $o] :
% 0.29/1.52 ( ( hF_Mirabelle_hmem @ V4 @ ( hF_Mirabelle_Replace @ A5 @ R ) )
% 0.29/1.52 = ( ? [U2: hF_Mirabelle_hf] :
% 0.29/1.52 ( ( hF_Mirabelle_hmem @ U2 @ A5 )
% 0.29/1.52 & ( R @ U2 @ V4 )
% 0.29/1.52 & ! [Y3: hF_Mirabelle_hf] :
% 0.29/1.52 ( ( R @ U2 @ Y3 )
% 0.29/1.52 => ( Y3 = V4 ) ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_13_le__funD,axiom,
% 0.29/1.52 ! [B: $tType,A: $tType] :
% 0.29/1.52 ( ( ord @ B )
% 0.29/1.52 => ! [F: A > B,G: A > B,X3: A] :
% 0.29/1.52 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 0.29/1.52 => ( ord_less_eq @ B @ ( F @ X3 ) @ ( G @ X3 ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_14_le__funE,axiom,
% 0.29/1.52 ! [B: $tType,A: $tType] :
% 0.29/1.52 ( ( ord @ B )
% 0.29/1.52 => ! [F: A > B,G: A > B,X3: A] :
% 0.29/1.52 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 0.29/1.52 => ( ord_less_eq @ B @ ( F @ X3 ) @ ( G @ X3 ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_15_le__funI,axiom,
% 0.29/1.52 ! [B: $tType,A: $tType] :
% 0.29/1.52 ( ( ord @ B )
% 0.29/1.52 => ! [F: A > B,G: A > B] :
% 0.29/1.52 ( ! [X: A] : ( ord_less_eq @ B @ ( F @ X ) @ ( G @ X ) )
% 0.29/1.52 => ( ord_less_eq @ ( A > B ) @ F @ G ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_16_le__fun__def,axiom,
% 0.29/1.52 ! [B: $tType,A: $tType] :
% 0.29/1.52 ( ( ord @ B )
% 0.29/1.52 => ( ( ord_less_eq @ ( A > B ) )
% 0.29/1.52 = ( ^ [F2: A > B,G2: A > B] :
% 0.29/1.52 ! [X2: A] : ( ord_less_eq @ B @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_17_order__subst1,axiom,
% 0.29/1.52 ! [A: $tType,B: $tType] :
% 0.29/1.52 ( ( ( order @ B )
% 0.29/1.52 & ( order @ A ) )
% 0.29/1.52 => ! [A2: A,F: B > A,B2: B,C: B] :
% 0.29/1.52 ( ( ord_less_eq @ A @ A2 @ ( F @ B2 ) )
% 0.29/1.52 => ( ( ord_less_eq @ B @ B2 @ C )
% 0.29/1.52 => ( ! [X: B,Y4: B] :
% 0.29/1.52 ( ( ord_less_eq @ B @ X @ Y4 )
% 0.29/1.52 => ( ord_less_eq @ A @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.29/1.52 => ( ord_less_eq @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_18_order__subst2,axiom,
% 0.29/1.52 ! [A: $tType,C2: $tType] :
% 0.29/1.52 ( ( ( order @ C2 )
% 0.29/1.52 & ( order @ A ) )
% 0.29/1.52 => ! [A2: A,B2: A,F: A > C2,C: C2] :
% 0.29/1.52 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.29/1.52 => ( ( ord_less_eq @ C2 @ ( F @ B2 ) @ C )
% 0.29/1.52 => ( ! [X: A,Y4: A] :
% 0.29/1.52 ( ( ord_less_eq @ A @ X @ Y4 )
% 0.29/1.52 => ( ord_less_eq @ C2 @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.29/1.52 => ( ord_less_eq @ C2 @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_19_verit__la__disequality,axiom,
% 0.29/1.52 ! [A: $tType] :
% 0.29/1.52 ( ( linorder @ A )
% 0.29/1.52 => ! [A2: A,B2: A] :
% 0.29/1.52 ( ( A2 = B2 )
% 0.29/1.52 | ~ ( ord_less_eq @ A @ A2 @ B2 )
% 0.29/1.52 | ~ ( ord_less_eq @ A @ B2 @ A2 ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_20_Replace__cong,axiom,
% 0.29/1.52 ! [A5: hF_Mirabelle_hf,B5: hF_Mirabelle_hf,P: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,Q: hF_Mirabelle_hf > hF_Mirabelle_hf > $o] :
% 0.29/1.52 ( ( A5 = B5 )
% 0.29/1.52 => ( ! [X: hF_Mirabelle_hf,Y4: hF_Mirabelle_hf] :
% 0.29/1.52 ( ( hF_Mirabelle_hmem @ X @ B5 )
% 0.29/1.52 => ( ( P @ X @ Y4 )
% 0.29/1.52 = ( Q @ X @ Y4 ) ) )
% 0.29/1.52 => ( ( hF_Mirabelle_Replace @ A5 @ P )
% 0.29/1.52 = ( hF_Mirabelle_Replace @ B5 @ Q ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_21_dual__order_Oantisym,axiom,
% 0.29/1.52 ! [A: $tType] :
% 0.29/1.52 ( ( order @ A )
% 0.29/1.52 => ! [B2: A,A2: A] :
% 0.29/1.52 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.29/1.52 => ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.29/1.52 => ( A2 = B2 ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_22_dual__order_Oeq__iff,axiom,
% 0.29/1.52 ! [A: $tType] :
% 0.29/1.52 ( ( order @ A )
% 0.29/1.52 => ( ( ^ [Y: A,Z: A] : ( Y = Z ) )
% 0.29/1.52 = ( ^ [A3: A,B3: A] :
% 0.29/1.52 ( ( ord_less_eq @ A @ B3 @ A3 )
% 0.29/1.52 & ( ord_less_eq @ A @ A3 @ B3 ) ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_23_dual__order_Otrans,axiom,
% 0.29/1.52 ! [A: $tType] :
% 0.29/1.52 ( ( order @ A )
% 0.29/1.52 => ! [B2: A,A2: A,C: A] :
% 0.29/1.52 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.29/1.52 => ( ( ord_less_eq @ A @ C @ B2 )
% 0.29/1.52 => ( ord_less_eq @ A @ C @ A2 ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_24_linorder__wlog,axiom,
% 0.29/1.52 ! [A: $tType] :
% 0.29/1.52 ( ( linorder @ A )
% 0.29/1.52 => ! [P: A > A > $o,A2: A,B2: A] :
% 0.29/1.52 ( ! [A6: A,B6: A] :
% 0.29/1.52 ( ( ord_less_eq @ A @ A6 @ B6 )
% 0.29/1.52 => ( P @ A6 @ B6 ) )
% 0.29/1.52 => ( ! [A6: A,B6: A] :
% 0.29/1.52 ( ( P @ B6 @ A6 )
% 0.29/1.52 => ( P @ A6 @ B6 ) )
% 0.29/1.52 => ( P @ A2 @ B2 ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_25_dual__order_Orefl,axiom,
% 0.29/1.52 ! [A: $tType] :
% 0.29/1.52 ( ( order @ A )
% 0.29/1.52 => ! [A2: A] : ( ord_less_eq @ A @ A2 @ A2 ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_26_order__trans,axiom,
% 0.29/1.52 ! [A: $tType] :
% 0.29/1.52 ( ( preorder @ A )
% 0.29/1.52 => ! [X3: A,Y2: A,Z3: A] :
% 0.29/1.52 ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.29/1.52 => ( ( ord_less_eq @ A @ Y2 @ Z3 )
% 0.29/1.52 => ( ord_less_eq @ A @ X3 @ Z3 ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_27_order__class_Oorder_Oantisym,axiom,
% 0.29/1.52 ! [A: $tType] :
% 0.29/1.52 ( ( order @ A )
% 0.29/1.52 => ! [A2: A,B2: A] :
% 0.29/1.52 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.29/1.52 => ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.29/1.52 => ( A2 = B2 ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_28_ord__le__eq__trans,axiom,
% 0.29/1.52 ! [A: $tType] :
% 0.29/1.52 ( ( ord @ A )
% 0.29/1.52 => ! [A2: A,B2: A,C: A] :
% 0.29/1.52 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.29/1.52 => ( ( B2 = C )
% 0.29/1.52 => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_29_ord__eq__le__trans,axiom,
% 0.29/1.52 ! [A: $tType] :
% 0.29/1.52 ( ( ord @ A )
% 0.29/1.52 => ! [A2: A,B2: A,C: A] :
% 0.29/1.52 ( ( A2 = B2 )
% 0.29/1.52 => ( ( ord_less_eq @ A @ B2 @ C )
% 0.29/1.52 => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_30_order__class_Oorder_Oeq__iff,axiom,
% 0.29/1.52 ! [A: $tType] :
% 0.29/1.52 ( ( order @ A )
% 0.29/1.52 => ( ( ^ [Y: A,Z: A] : ( Y = Z ) )
% 0.29/1.52 = ( ^ [A3: A,B3: A] :
% 0.29/1.52 ( ( ord_less_eq @ A @ A3 @ B3 )
% 0.29/1.52 & ( ord_less_eq @ A @ B3 @ A3 ) ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_31_antisym__conv,axiom,
% 0.29/1.52 ! [A: $tType] :
% 0.29/1.52 ( ( order @ A )
% 0.29/1.52 => ! [Y2: A,X3: A] :
% 0.29/1.52 ( ( ord_less_eq @ A @ Y2 @ X3 )
% 0.29/1.52 => ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.29/1.52 = ( X3 = Y2 ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_32_le__cases3,axiom,
% 0.29/1.52 ! [A: $tType] :
% 0.29/1.52 ( ( linorder @ A )
% 0.29/1.52 => ! [X3: A,Y2: A,Z3: A] :
% 0.29/1.52 ( ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.29/1.52 => ~ ( ord_less_eq @ A @ Y2 @ Z3 ) )
% 0.29/1.52 => ( ( ( ord_less_eq @ A @ Y2 @ X3 )
% 0.29/1.52 => ~ ( ord_less_eq @ A @ X3 @ Z3 ) )
% 0.29/1.52 => ( ( ( ord_less_eq @ A @ X3 @ Z3 )
% 0.29/1.52 => ~ ( ord_less_eq @ A @ Z3 @ Y2 ) )
% 0.29/1.52 => ( ( ( ord_less_eq @ A @ Z3 @ Y2 )
% 0.29/1.52 => ~ ( ord_less_eq @ A @ Y2 @ X3 ) )
% 0.29/1.52 => ( ( ( ord_less_eq @ A @ Y2 @ Z3 )
% 0.29/1.52 => ~ ( ord_less_eq @ A @ Z3 @ X3 ) )
% 0.29/1.52 => ~ ( ( ord_less_eq @ A @ Z3 @ X3 )
% 0.29/1.52 => ~ ( ord_less_eq @ A @ X3 @ Y2 ) ) ) ) ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_33_order_Otrans,axiom,
% 0.29/1.52 ! [A: $tType] :
% 0.29/1.52 ( ( order @ A )
% 0.29/1.52 => ! [A2: A,B2: A,C: A] :
% 0.29/1.52 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.29/1.52 => ( ( ord_less_eq @ A @ B2 @ C )
% 0.29/1.52 => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_34_le__cases,axiom,
% 0.29/1.52 ! [A: $tType] :
% 0.29/1.52 ( ( linorder @ A )
% 0.29/1.52 => ! [X3: A,Y2: A] :
% 0.29/1.52 ( ~ ( ord_less_eq @ A @ X3 @ Y2 )
% 0.29/1.52 => ( ord_less_eq @ A @ Y2 @ X3 ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_35_eq__refl,axiom,
% 0.29/1.52 ! [A: $tType] :
% 0.29/1.52 ( ( preorder @ A )
% 0.29/1.52 => ! [X3: A,Y2: A] :
% 0.29/1.52 ( ( X3 = Y2 )
% 0.29/1.52 => ( ord_less_eq @ A @ X3 @ Y2 ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_36_linear,axiom,
% 0.29/1.52 ! [A: $tType] :
% 0.29/1.52 ( ( linorder @ A )
% 0.29/1.52 => ! [X3: A,Y2: A] :
% 0.29/1.52 ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.29/1.52 | ( ord_less_eq @ A @ Y2 @ X3 ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_37_antisym,axiom,
% 0.29/1.52 ! [A: $tType] :
% 0.29/1.52 ( ( order @ A )
% 0.29/1.52 => ! [X3: A,Y2: A] :
% 0.29/1.52 ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.29/1.52 => ( ( ord_less_eq @ A @ Y2 @ X3 )
% 0.29/1.52 => ( X3 = Y2 ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_38_eq__iff,axiom,
% 0.29/1.52 ! [A: $tType] :
% 0.29/1.52 ( ( order @ A )
% 0.29/1.52 => ( ( ^ [Y: A,Z: A] : ( Y = Z ) )
% 0.29/1.52 = ( ^ [X2: A,Y3: A] :
% 0.29/1.52 ( ( ord_less_eq @ A @ X2 @ Y3 )
% 0.29/1.52 & ( ord_less_eq @ A @ Y3 @ X2 ) ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_39_ord__le__eq__subst,axiom,
% 0.29/1.52 ! [A: $tType,B: $tType] :
% 0.29/1.52 ( ( ( ord @ B )
% 0.29/1.52 & ( ord @ A ) )
% 0.29/1.52 => ! [A2: A,B2: A,F: A > B,C: B] :
% 0.29/1.52 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.29/1.52 => ( ( ( F @ B2 )
% 0.29/1.52 = C )
% 0.29/1.52 => ( ! [X: A,Y4: A] :
% 0.29/1.52 ( ( ord_less_eq @ A @ X @ Y4 )
% 0.29/1.52 => ( ord_less_eq @ B @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.29/1.52 => ( ord_less_eq @ B @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_40_ord__eq__le__subst,axiom,
% 0.29/1.52 ! [A: $tType,B: $tType] :
% 0.29/1.52 ( ( ( ord @ B )
% 0.29/1.52 & ( ord @ A ) )
% 0.29/1.52 => ! [A2: A,F: B > A,B2: B,C: B] :
% 0.29/1.52 ( ( A2
% 0.29/1.52 = ( F @ B2 ) )
% 0.29/1.52 => ( ( ord_less_eq @ B @ B2 @ C )
% 0.29/1.52 => ( ! [X: B,Y4: B] :
% 0.29/1.52 ( ( ord_less_eq @ B @ X @ Y4 )
% 0.29/1.52 => ( ord_less_eq @ A @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.29/1.52 => ( ord_less_eq @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_41_Greatest__equality,axiom,
% 0.29/1.52 ! [A: $tType] :
% 0.29/1.52 ( ( order @ A )
% 0.29/1.52 => ! [P: A > $o,X3: A] :
% 0.29/1.52 ( ( P @ X3 )
% 0.29/1.52 => ( ! [Y4: A] :
% 0.29/1.52 ( ( P @ Y4 )
% 0.29/1.52 => ( ord_less_eq @ A @ Y4 @ X3 ) )
% 0.29/1.52 => ( ( order_Greatest @ A @ P )
% 0.29/1.52 = X3 ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_42_GreatestI2__order,axiom,
% 0.29/1.52 ! [A: $tType] :
% 0.29/1.52 ( ( order @ A )
% 0.29/1.52 => ! [P: A > $o,X3: A,Q: A > $o] :
% 0.29/1.52 ( ( P @ X3 )
% 0.29/1.52 => ( ! [Y4: A] :
% 0.29/1.52 ( ( P @ Y4 )
% 0.29/1.52 => ( ord_less_eq @ A @ Y4 @ X3 ) )
% 0.29/1.52 => ( ! [X: A] :
% 0.29/1.52 ( ( P @ X )
% 0.29/1.52 => ( ! [Y5: A] :
% 0.29/1.52 ( ( P @ Y5 )
% 0.29/1.52 => ( ord_less_eq @ A @ Y5 @ X ) )
% 0.29/1.52 => ( Q @ X ) ) )
% 0.29/1.52 => ( Q @ ( order_Greatest @ A @ P ) ) ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_43_le__rel__bool__arg__iff,axiom,
% 0.29/1.52 ! [A: $tType] :
% 0.29/1.52 ( ( ord @ A )
% 0.29/1.52 => ( ( ord_less_eq @ ( $o > A ) )
% 0.29/1.52 = ( ^ [X4: $o > A,Y6: $o > A] :
% 0.29/1.52 ( ( ord_less_eq @ A @ ( X4 @ $false ) @ ( Y6 @ $false ) )
% 0.29/1.52 & ( ord_less_eq @ A @ ( X4 @ $true ) @ ( Y6 @ $true ) ) ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_44_hmem__def,axiom,
% 0.29/1.52 ( hF_Mirabelle_hmem
% 0.29/1.52 = ( ^ [A3: hF_Mirabelle_hf,B3: hF_Mirabelle_hf] : ( member @ hF_Mirabelle_hf @ A3 @ ( hF_Mirabelle_hfset @ B3 ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_45_mem__Collect__eq,axiom,
% 0.29/1.52 ! [A: $tType,A2: A,P: A > $o] :
% 0.29/1.52 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 0.29/1.52 = ( P @ A2 ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_46_Collect__mem__eq,axiom,
% 0.29/1.52 ! [A: $tType,A5: set @ A] :
% 0.29/1.52 ( ( collect @ A
% 0.29/1.52 @ ^ [X2: A] : ( member @ A @ X2 @ A5 ) )
% 0.29/1.52 = A5 ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_47_Collect__cong,axiom,
% 0.29/1.52 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.29/1.52 ( ! [X: A] :
% 0.29/1.52 ( ( P @ X )
% 0.29/1.52 = ( Q @ X ) )
% 0.29/1.52 => ( ( collect @ A @ P )
% 0.29/1.52 = ( collect @ A @ Q ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_48_ext,axiom,
% 0.29/1.52 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.29/1.52 ( ! [X: A] :
% 0.29/1.52 ( ( F @ X )
% 0.29/1.52 = ( G @ X ) )
% 0.29/1.52 => ( F = G ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_49_RepFun__iff,axiom,
% 0.29/1.52 ! [V4: hF_Mirabelle_hf,A5: hF_Mirabelle_hf,F: hF_Mirabelle_hf > hF_Mirabelle_hf] :
% 0.29/1.52 ( ( hF_Mirabelle_hmem @ V4 @ ( hF_Mirabelle_RepFun @ A5 @ F ) )
% 0.29/1.52 = ( ? [U2: hF_Mirabelle_hf] :
% 0.29/1.52 ( ( hF_Mirabelle_hmem @ U2 @ A5 )
% 0.29/1.52 & ( V4
% 0.29/1.52 = ( F @ U2 ) ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_50_less__hf__def,axiom,
% 0.29/1.52 ( ( ord_less @ hF_Mirabelle_hf )
% 0.29/1.52 = ( ^ [A4: hF_Mirabelle_hf,B4: hF_Mirabelle_hf] :
% 0.29/1.52 ( ( ord_less_eq @ hF_Mirabelle_hf @ A4 @ B4 )
% 0.29/1.52 & ( A4 != B4 ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_51_antimono__def,axiom,
% 0.29/1.52 ! [B: $tType,A: $tType] :
% 0.29/1.52 ( ( ( order @ A )
% 0.29/1.52 & ( order @ B ) )
% 0.29/1.52 => ( ( order_antimono @ A @ B )
% 0.29/1.52 = ( ^ [F2: A > B] :
% 0.29/1.52 ! [X2: A,Y3: A] :
% 0.29/1.52 ( ( ord_less_eq @ A @ X2 @ Y3 )
% 0.29/1.52 => ( ord_less_eq @ B @ ( F2 @ Y3 ) @ ( F2 @ X2 ) ) ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_52_antimonoI,axiom,
% 0.29/1.52 ! [B: $tType,A: $tType] :
% 0.29/1.52 ( ( ( order @ A )
% 0.29/1.52 & ( order @ B ) )
% 0.29/1.52 => ! [F: A > B] :
% 0.29/1.52 ( ! [X: A,Y4: A] :
% 0.29/1.52 ( ( ord_less_eq @ A @ X @ Y4 )
% 0.29/1.52 => ( ord_less_eq @ B @ ( F @ Y4 ) @ ( F @ X ) ) )
% 0.29/1.52 => ( order_antimono @ A @ B @ F ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_53_antimonoE,axiom,
% 0.29/1.52 ! [B: $tType,A: $tType] :
% 0.29/1.52 ( ( ( order @ A )
% 0.29/1.52 & ( order @ B ) )
% 0.29/1.52 => ! [F: A > B,X3: A,Y2: A] :
% 0.29/1.52 ( ( order_antimono @ A @ B @ F )
% 0.29/1.52 => ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.29/1.52 => ( ord_less_eq @ B @ ( F @ Y2 ) @ ( F @ X3 ) ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_54_antimonoD,axiom,
% 0.29/1.52 ! [B: $tType,A: $tType] :
% 0.29/1.52 ( ( ( order @ A )
% 0.29/1.52 & ( order @ B ) )
% 0.29/1.52 => ! [F: A > B,X3: A,Y2: A] :
% 0.29/1.52 ( ( order_antimono @ A @ B @ F )
% 0.29/1.52 => ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.29/1.52 => ( ord_less_eq @ B @ ( F @ Y2 ) @ ( F @ X3 ) ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_55_verit__comp__simplify1_I1_J,axiom,
% 0.29/1.52 ! [A: $tType] :
% 0.29/1.52 ( ( order @ A )
% 0.29/1.52 => ! [A2: A] :
% 0.29/1.52 ~ ( ord_less @ A @ A2 @ A2 ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_56_ord__eq__less__subst,axiom,
% 0.29/1.52 ! [A: $tType,B: $tType] :
% 0.29/1.52 ( ( ( ord @ B )
% 0.29/1.52 & ( ord @ A ) )
% 0.29/1.52 => ! [A2: A,F: B > A,B2: B,C: B] :
% 0.29/1.52 ( ( A2
% 0.29/1.52 = ( F @ B2 ) )
% 0.29/1.52 => ( ( ord_less @ B @ B2 @ C )
% 0.29/1.52 => ( ! [X: B,Y4: B] :
% 0.29/1.52 ( ( ord_less @ B @ X @ Y4 )
% 0.29/1.52 => ( ord_less @ A @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.29/1.52 => ( ord_less @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_57_ord__less__eq__subst,axiom,
% 0.29/1.52 ! [A: $tType,B: $tType] :
% 0.29/1.52 ( ( ( ord @ B )
% 0.29/1.52 & ( ord @ A ) )
% 0.29/1.52 => ! [A2: A,B2: A,F: A > B,C: B] :
% 0.29/1.52 ( ( ord_less @ A @ A2 @ B2 )
% 0.29/1.52 => ( ( ( F @ B2 )
% 0.29/1.52 = C )
% 0.29/1.52 => ( ! [X: A,Y4: A] :
% 0.29/1.52 ( ( ord_less @ A @ X @ Y4 )
% 0.29/1.52 => ( ord_less @ B @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.29/1.52 => ( ord_less @ B @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_58_order__less__subst1,axiom,
% 0.29/1.52 ! [A: $tType,B: $tType] :
% 0.29/1.52 ( ( ( order @ B )
% 0.29/1.52 & ( order @ A ) )
% 0.29/1.52 => ! [A2: A,F: B > A,B2: B,C: B] :
% 0.29/1.52 ( ( ord_less @ A @ A2 @ ( F @ B2 ) )
% 0.29/1.52 => ( ( ord_less @ B @ B2 @ C )
% 0.29/1.52 => ( ! [X: B,Y4: B] :
% 0.29/1.52 ( ( ord_less @ B @ X @ Y4 )
% 0.29/1.52 => ( ord_less @ A @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.29/1.52 => ( ord_less @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_59_order__less__subst2,axiom,
% 0.29/1.52 ! [A: $tType,C2: $tType] :
% 0.29/1.52 ( ( ( order @ C2 )
% 0.29/1.52 & ( order @ A ) )
% 0.29/1.52 => ! [A2: A,B2: A,F: A > C2,C: C2] :
% 0.29/1.52 ( ( ord_less @ A @ A2 @ B2 )
% 0.29/1.52 => ( ( ord_less @ C2 @ ( F @ B2 ) @ C )
% 0.29/1.52 => ( ! [X: A,Y4: A] :
% 0.29/1.52 ( ( ord_less @ A @ X @ Y4 )
% 0.29/1.52 => ( ord_less @ C2 @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.29/1.52 => ( ord_less @ C2 @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_60_lt__ex,axiom,
% 0.29/1.52 ! [A: $tType] :
% 0.29/1.52 ( ( no_bot @ A )
% 0.29/1.52 => ! [X3: A] :
% 0.29/1.52 ? [Y4: A] : ( ord_less @ A @ Y4 @ X3 ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_61_gt__ex,axiom,
% 0.29/1.52 ! [A: $tType] :
% 0.29/1.52 ( ( no_top @ A )
% 0.29/1.52 => ! [X3: A] :
% 0.29/1.52 ? [X_1: A] : ( ord_less @ A @ X3 @ X_1 ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_62_neqE,axiom,
% 0.29/1.52 ! [A: $tType] :
% 0.29/1.52 ( ( linorder @ A )
% 0.29/1.52 => ! [X3: A,Y2: A] :
% 0.29/1.52 ( ( X3 != Y2 )
% 0.29/1.52 => ( ~ ( ord_less @ A @ X3 @ Y2 )
% 0.29/1.52 => ( ord_less @ A @ Y2 @ X3 ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_63_neq__iff,axiom,
% 0.29/1.52 ! [A: $tType] :
% 0.29/1.52 ( ( linorder @ A )
% 0.29/1.52 => ! [X3: A,Y2: A] :
% 0.29/1.52 ( ( X3 != Y2 )
% 0.29/1.52 = ( ( ord_less @ A @ X3 @ Y2 )
% 0.29/1.52 | ( ord_less @ A @ Y2 @ X3 ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_64_order_Oasym,axiom,
% 0.29/1.52 ! [A: $tType] :
% 0.29/1.52 ( ( order @ A )
% 0.29/1.52 => ! [A2: A,B2: A] :
% 0.29/1.52 ( ( ord_less @ A @ A2 @ B2 )
% 0.29/1.52 => ~ ( ord_less @ A @ B2 @ A2 ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_65_dense,axiom,
% 0.29/1.52 ! [A: $tType] :
% 0.29/1.52 ( ( dense_order @ A )
% 0.29/1.52 => ! [X3: A,Y2: A] :
% 0.29/1.52 ( ( ord_less @ A @ X3 @ Y2 )
% 0.29/1.52 => ? [Z2: A] :
% 0.29/1.52 ( ( ord_less @ A @ X3 @ Z2 )
% 0.29/1.52 & ( ord_less @ A @ Z2 @ Y2 ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_66_less__imp__neq,axiom,
% 0.29/1.52 ! [A: $tType] :
% 0.29/1.52 ( ( order @ A )
% 0.29/1.52 => ! [X3: A,Y2: A] :
% 0.29/1.52 ( ( ord_less @ A @ X3 @ Y2 )
% 0.29/1.52 => ( X3 != Y2 ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_67_less__asym,axiom,
% 0.29/1.52 ! [A: $tType] :
% 0.29/1.52 ( ( preorder @ A )
% 0.29/1.52 => ! [X3: A,Y2: A] :
% 0.29/1.52 ( ( ord_less @ A @ X3 @ Y2 )
% 0.29/1.52 => ~ ( ord_less @ A @ Y2 @ X3 ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_68_less__asym_H,axiom,
% 0.29/1.52 ! [A: $tType] :
% 0.29/1.52 ( ( preorder @ A )
% 0.29/1.52 => ! [A2: A,B2: A] :
% 0.29/1.52 ( ( ord_less @ A @ A2 @ B2 )
% 0.29/1.52 => ~ ( ord_less @ A @ B2 @ A2 ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_69_less__trans,axiom,
% 0.29/1.52 ! [A: $tType] :
% 0.29/1.52 ( ( preorder @ A )
% 0.29/1.52 => ! [X3: A,Y2: A,Z3: A] :
% 0.29/1.52 ( ( ord_less @ A @ X3 @ Y2 )
% 0.29/1.52 => ( ( ord_less @ A @ Y2 @ Z3 )
% 0.29/1.52 => ( ord_less @ A @ X3 @ Z3 ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_70_less__linear,axiom,
% 0.29/1.52 ! [A: $tType] :
% 0.29/1.52 ( ( linorder @ A )
% 0.29/1.52 => ! [X3: A,Y2: A] :
% 0.29/1.52 ( ( ord_less @ A @ X3 @ Y2 )
% 0.29/1.52 | ( X3 = Y2 )
% 0.29/1.52 | ( ord_less @ A @ Y2 @ X3 ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_71_less__irrefl,axiom,
% 0.29/1.52 ! [A: $tType] :
% 0.29/1.52 ( ( preorder @ A )
% 0.29/1.52 => ! [X3: A] :
% 0.29/1.52 ~ ( ord_less @ A @ X3 @ X3 ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_72_ord__eq__less__trans,axiom,
% 0.29/1.52 ! [A: $tType] :
% 0.29/1.52 ( ( ord @ A )
% 0.29/1.52 => ! [A2: A,B2: A,C: A] :
% 0.29/1.52 ( ( A2 = B2 )
% 0.29/1.52 => ( ( ord_less @ A @ B2 @ C )
% 0.29/1.52 => ( ord_less @ A @ A2 @ C ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_73_ord__less__eq__trans,axiom,
% 0.29/1.52 ! [A: $tType] :
% 0.29/1.52 ( ( ord @ A )
% 0.29/1.52 => ! [A2: A,B2: A,C: A] :
% 0.29/1.52 ( ( ord_less @ A @ A2 @ B2 )
% 0.29/1.52 => ( ( B2 = C )
% 0.29/1.52 => ( ord_less @ A @ A2 @ C ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_74_dual__order_Oasym,axiom,
% 0.29/1.52 ! [A: $tType] :
% 0.29/1.52 ( ( order @ A )
% 0.29/1.52 => ! [B2: A,A2: A] :
% 0.29/1.52 ( ( ord_less @ A @ B2 @ A2 )
% 0.29/1.52 => ~ ( ord_less @ A @ A2 @ B2 ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_75_less__imp__not__eq,axiom,
% 0.29/1.52 ! [A: $tType] :
% 0.29/1.52 ( ( order @ A )
% 0.29/1.52 => ! [X3: A,Y2: A] :
% 0.29/1.52 ( ( ord_less @ A @ X3 @ Y2 )
% 0.29/1.52 => ( X3 != Y2 ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_76_less__not__sym,axiom,
% 0.29/1.52 ! [A: $tType] :
% 0.29/1.52 ( ( preorder @ A )
% 0.29/1.52 => ! [X3: A,Y2: A] :
% 0.29/1.52 ( ( ord_less @ A @ X3 @ Y2 )
% 0.29/1.52 => ~ ( ord_less @ A @ Y2 @ X3 ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_77_less__induct,axiom,
% 0.29/1.52 ! [A: $tType] :
% 0.29/1.52 ( ( wellorder @ A )
% 0.29/1.52 => ! [P: A > $o,A2: A] :
% 0.29/1.52 ( ! [X: A] :
% 0.29/1.52 ( ! [Y5: A] :
% 0.29/1.52 ( ( ord_less @ A @ Y5 @ X )
% 0.29/1.52 => ( P @ Y5 ) )
% 0.29/1.52 => ( P @ X ) )
% 0.29/1.52 => ( P @ A2 ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_78_antisym__conv3,axiom,
% 0.29/1.52 ! [A: $tType] :
% 0.29/1.52 ( ( linorder @ A )
% 0.29/1.52 => ! [Y2: A,X3: A] :
% 0.29/1.52 ( ~ ( ord_less @ A @ Y2 @ X3 )
% 0.29/1.52 => ( ( ~ ( ord_less @ A @ X3 @ Y2 ) )
% 0.29/1.52 = ( X3 = Y2 ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_79_less__imp__not__eq2,axiom,
% 0.29/1.52 ! [A: $tType] :
% 0.29/1.52 ( ( order @ A )
% 0.29/1.52 => ! [X3: A,Y2: A] :
% 0.29/1.52 ( ( ord_less @ A @ X3 @ Y2 )
% 0.29/1.52 => ( Y2 != X3 ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_80_less__imp__triv,axiom,
% 0.29/1.52 ! [A: $tType] :
% 0.29/1.52 ( ( preorder @ A )
% 0.29/1.52 => ! [X3: A,Y2: A,P: $o] :
% 0.29/1.52 ( ( ord_less @ A @ X3 @ Y2 )
% 0.29/1.52 => ( ( ord_less @ A @ Y2 @ X3 )
% 0.29/1.52 => P ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_81_linorder__cases,axiom,
% 0.29/1.52 ! [A: $tType] :
% 0.29/1.52 ( ( linorder @ A )
% 0.29/1.52 => ! [X3: A,Y2: A] :
% 0.29/1.52 ( ~ ( ord_less @ A @ X3 @ Y2 )
% 0.29/1.52 => ( ( X3 != Y2 )
% 0.29/1.52 => ( ord_less @ A @ Y2 @ X3 ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_82_dual__order_Oirrefl,axiom,
% 0.29/1.52 ! [A: $tType] :
% 0.29/1.52 ( ( order @ A )
% 0.29/1.52 => ! [A2: A] :
% 0.29/1.52 ~ ( ord_less @ A @ A2 @ A2 ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_83_order_Ostrict__trans,axiom,
% 0.29/1.52 ! [A: $tType] :
% 0.29/1.52 ( ( order @ A )
% 0.29/1.52 => ! [A2: A,B2: A,C: A] :
% 0.29/1.52 ( ( ord_less @ A @ A2 @ B2 )
% 0.29/1.52 => ( ( ord_less @ A @ B2 @ C )
% 0.29/1.52 => ( ord_less @ A @ A2 @ C ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_84_less__imp__not__less,axiom,
% 0.29/1.52 ! [A: $tType] :
% 0.29/1.52 ( ( preorder @ A )
% 0.29/1.52 => ! [X3: A,Y2: A] :
% 0.29/1.52 ( ( ord_less @ A @ X3 @ Y2 )
% 0.29/1.52 => ~ ( ord_less @ A @ Y2 @ X3 ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_85_exists__least__iff,axiom,
% 0.29/1.52 ! [A: $tType] :
% 0.29/1.52 ( ( wellorder @ A )
% 0.29/1.52 => ( ( ^ [P2: A > $o] :
% 0.29/1.52 ? [X5: A] : ( P2 @ X5 ) )
% 0.29/1.52 = ( ^ [P3: A > $o] :
% 0.29/1.52 ? [N: A] :
% 0.29/1.52 ( ( P3 @ N )
% 0.29/1.52 & ! [M: A] :
% 0.29/1.52 ( ( ord_less @ A @ M @ N )
% 0.29/1.52 => ~ ( P3 @ M ) ) ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_86_linorder__less__wlog,axiom,
% 0.29/1.52 ! [A: $tType] :
% 0.29/1.52 ( ( linorder @ A )
% 0.29/1.52 => ! [P: A > A > $o,A2: A,B2: A] :
% 0.29/1.52 ( ! [A6: A,B6: A] :
% 0.29/1.52 ( ( ord_less @ A @ A6 @ B6 )
% 0.29/1.52 => ( P @ A6 @ B6 ) )
% 0.29/1.52 => ( ! [A6: A] : ( P @ A6 @ A6 )
% 0.29/1.52 => ( ! [A6: A,B6: A] :
% 0.29/1.52 ( ( P @ B6 @ A6 )
% 0.29/1.52 => ( P @ A6 @ B6 ) )
% 0.29/1.52 => ( P @ A2 @ B2 ) ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_87_dual__order_Ostrict__trans,axiom,
% 0.29/1.52 ! [A: $tType] :
% 0.29/1.52 ( ( order @ A )
% 0.29/1.52 => ! [B2: A,A2: A,C: A] :
% 0.29/1.52 ( ( ord_less @ A @ B2 @ A2 )
% 0.29/1.52 => ( ( ord_less @ A @ C @ B2 )
% 0.29/1.52 => ( ord_less @ A @ C @ A2 ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_88_not__less__iff__gr__or__eq,axiom,
% 0.29/1.52 ! [A: $tType] :
% 0.29/1.52 ( ( linorder @ A )
% 0.29/1.52 => ! [X3: A,Y2: A] :
% 0.29/1.52 ( ( ~ ( ord_less @ A @ X3 @ Y2 ) )
% 0.29/1.52 = ( ( ord_less @ A @ Y2 @ X3 )
% 0.29/1.52 | ( X3 = Y2 ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_89_order_Ostrict__implies__not__eq,axiom,
% 0.29/1.52 ! [A: $tType] :
% 0.29/1.52 ( ( order @ A )
% 0.29/1.52 => ! [A2: A,B2: A] :
% 0.29/1.52 ( ( ord_less @ A @ A2 @ B2 )
% 0.29/1.52 => ( A2 != B2 ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_90_dual__order_Ostrict__implies__not__eq,axiom,
% 0.29/1.52 ! [A: $tType] :
% 0.29/1.52 ( ( order @ A )
% 0.29/1.52 => ! [B2: A,A2: A] :
% 0.29/1.52 ( ( ord_less @ A @ B2 @ A2 )
% 0.29/1.52 => ( A2 != B2 ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_91_verit__comp__simplify1_I3_J,axiom,
% 0.29/1.52 ! [B: $tType] :
% 0.29/1.52 ( ( linorder @ B )
% 0.29/1.52 => ! [B7: B,A7: B] :
% 0.29/1.52 ( ( ~ ( ord_less_eq @ B @ B7 @ A7 ) )
% 0.29/1.52 = ( ord_less @ B @ A7 @ B7 ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_92_leD,axiom,
% 0.29/1.52 ! [A: $tType] :
% 0.29/1.52 ( ( order @ A )
% 0.29/1.52 => ! [Y2: A,X3: A] :
% 0.29/1.52 ( ( ord_less_eq @ A @ Y2 @ X3 )
% 0.29/1.52 => ~ ( ord_less @ A @ X3 @ Y2 ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_93_leI,axiom,
% 0.29/1.52 ! [A: $tType] :
% 0.29/1.52 ( ( linorder @ A )
% 0.29/1.52 => ! [X3: A,Y2: A] :
% 0.29/1.52 ( ~ ( ord_less @ A @ X3 @ Y2 )
% 0.29/1.52 => ( ord_less_eq @ A @ Y2 @ X3 ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_94_le__less,axiom,
% 0.29/1.52 ! [A: $tType] :
% 0.29/1.52 ( ( order @ A )
% 0.29/1.52 => ( ( ord_less_eq @ A )
% 0.29/1.52 = ( ^ [X2: A,Y3: A] :
% 0.29/1.52 ( ( ord_less @ A @ X2 @ Y3 )
% 0.29/1.52 | ( X2 = Y3 ) ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_95_less__le,axiom,
% 0.29/1.52 ! [A: $tType] :
% 0.29/1.52 ( ( order @ A )
% 0.29/1.52 => ( ( ord_less @ A )
% 0.29/1.52 = ( ^ [X2: A,Y3: A] :
% 0.29/1.52 ( ( ord_less_eq @ A @ X2 @ Y3 )
% 0.29/1.52 & ( X2 != Y3 ) ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_96_order__le__less__subst1,axiom,
% 0.29/1.52 ! [A: $tType,B: $tType] :
% 0.29/1.52 ( ( ( order @ B )
% 0.29/1.52 & ( order @ A ) )
% 0.29/1.52 => ! [A2: A,F: B > A,B2: B,C: B] :
% 0.29/1.52 ( ( ord_less_eq @ A @ A2 @ ( F @ B2 ) )
% 0.29/1.52 => ( ( ord_less @ B @ B2 @ C )
% 0.29/1.52 => ( ! [X: B,Y4: B] :
% 0.29/1.52 ( ( ord_less @ B @ X @ Y4 )
% 0.29/1.52 => ( ord_less @ A @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.29/1.52 => ( ord_less @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_97_order__le__less__subst2,axiom,
% 0.29/1.52 ! [A: $tType,C2: $tType] :
% 0.29/1.52 ( ( ( order @ C2 )
% 0.29/1.52 & ( order @ A ) )
% 0.29/1.52 => ! [A2: A,B2: A,F: A > C2,C: C2] :
% 0.29/1.52 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.29/1.52 => ( ( ord_less @ C2 @ ( F @ B2 ) @ C )
% 0.29/1.52 => ( ! [X: A,Y4: A] :
% 0.29/1.52 ( ( ord_less_eq @ A @ X @ Y4 )
% 0.29/1.52 => ( ord_less_eq @ C2 @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.29/1.52 => ( ord_less @ C2 @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_98_order__less__le__subst1,axiom,
% 0.29/1.52 ! [A: $tType,B: $tType] :
% 0.29/1.52 ( ( ( order @ B )
% 0.29/1.52 & ( order @ A ) )
% 0.29/1.52 => ! [A2: A,F: B > A,B2: B,C: B] :
% 0.29/1.52 ( ( ord_less @ A @ A2 @ ( F @ B2 ) )
% 0.29/1.52 => ( ( ord_less_eq @ B @ B2 @ C )
% 0.29/1.52 => ( ! [X: B,Y4: B] :
% 0.29/1.52 ( ( ord_less_eq @ B @ X @ Y4 )
% 0.29/1.52 => ( ord_less_eq @ A @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.29/1.52 => ( ord_less @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_99_order__less__le__subst2,axiom,
% 0.29/1.52 ! [A: $tType,C2: $tType] :
% 0.29/1.52 ( ( ( order @ C2 )
% 0.29/1.52 & ( order @ A ) )
% 0.29/1.52 => ! [A2: A,B2: A,F: A > C2,C: C2] :
% 0.29/1.52 ( ( ord_less @ A @ A2 @ B2 )
% 0.29/1.52 => ( ( ord_less_eq @ C2 @ ( F @ B2 ) @ C )
% 0.29/1.52 => ( ! [X: A,Y4: A] :
% 0.29/1.52 ( ( ord_less @ A @ X @ Y4 )
% 0.29/1.52 => ( ord_less @ C2 @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.29/1.52 => ( ord_less @ C2 @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_100_not__le,axiom,
% 0.29/1.52 ! [A: $tType] :
% 0.29/1.52 ( ( linorder @ A )
% 0.29/1.52 => ! [X3: A,Y2: A] :
% 0.29/1.52 ( ( ~ ( ord_less_eq @ A @ X3 @ Y2 ) )
% 0.29/1.52 = ( ord_less @ A @ Y2 @ X3 ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_101_not__less,axiom,
% 0.29/1.52 ! [A: $tType] :
% 0.29/1.52 ( ( linorder @ A )
% 0.29/1.52 => ! [X3: A,Y2: A] :
% 0.29/1.52 ( ( ~ ( ord_less @ A @ X3 @ Y2 ) )
% 0.29/1.52 = ( ord_less_eq @ A @ Y2 @ X3 ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_102_le__neq__trans,axiom,
% 0.29/1.52 ! [A: $tType] :
% 0.29/1.52 ( ( order @ A )
% 0.29/1.52 => ! [A2: A,B2: A] :
% 0.29/1.52 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.29/1.52 => ( ( A2 != B2 )
% 0.29/1.52 => ( ord_less @ A @ A2 @ B2 ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_103_antisym__conv1,axiom,
% 0.29/1.52 ! [A: $tType] :
% 0.29/1.52 ( ( order @ A )
% 0.29/1.52 => ! [X3: A,Y2: A] :
% 0.29/1.52 ( ~ ( ord_less @ A @ X3 @ Y2 )
% 0.29/1.52 => ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.29/1.52 = ( X3 = Y2 ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_104_antisym__conv2,axiom,
% 0.29/1.52 ! [A: $tType] :
% 0.29/1.52 ( ( order @ A )
% 0.29/1.52 => ! [X3: A,Y2: A] :
% 0.29/1.52 ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.29/1.52 => ( ( ~ ( ord_less @ A @ X3 @ Y2 ) )
% 0.29/1.52 = ( X3 = Y2 ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_105_less__imp__le,axiom,
% 0.29/1.52 ! [A: $tType] :
% 0.29/1.52 ( ( preorder @ A )
% 0.29/1.52 => ! [X3: A,Y2: A] :
% 0.29/1.52 ( ( ord_less @ A @ X3 @ Y2 )
% 0.29/1.52 => ( ord_less_eq @ A @ X3 @ Y2 ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_106_le__less__trans,axiom,
% 0.29/1.52 ! [A: $tType] :
% 0.29/1.52 ( ( preorder @ A )
% 0.29/1.52 => ! [X3: A,Y2: A,Z3: A] :
% 0.29/1.52 ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.29/1.52 => ( ( ord_less @ A @ Y2 @ Z3 )
% 0.29/1.52 => ( ord_less @ A @ X3 @ Z3 ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_107_less__le__trans,axiom,
% 0.29/1.52 ! [A: $tType] :
% 0.29/1.52 ( ( preorder @ A )
% 0.29/1.52 => ! [X3: A,Y2: A,Z3: A] :
% 0.29/1.52 ( ( ord_less @ A @ X3 @ Y2 )
% 0.29/1.52 => ( ( ord_less_eq @ A @ Y2 @ Z3 )
% 0.29/1.52 => ( ord_less @ A @ X3 @ Z3 ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_108_dense__ge,axiom,
% 0.29/1.52 ! [A: $tType] :
% 0.29/1.52 ( ( dense_linorder @ A )
% 0.29/1.52 => ! [Z3: A,Y2: A] :
% 0.29/1.52 ( ! [X: A] :
% 0.29/1.52 ( ( ord_less @ A @ Z3 @ X )
% 0.29/1.53 => ( ord_less_eq @ A @ Y2 @ X ) )
% 0.29/1.53 => ( ord_less_eq @ A @ Y2 @ Z3 ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_109_dense__le,axiom,
% 0.29/1.53 ! [A: $tType] :
% 0.29/1.53 ( ( dense_linorder @ A )
% 0.29/1.53 => ! [Y2: A,Z3: A] :
% 0.29/1.53 ( ! [X: A] :
% 0.29/1.53 ( ( ord_less @ A @ X @ Y2 )
% 0.29/1.53 => ( ord_less_eq @ A @ X @ Z3 ) )
% 0.29/1.53 => ( ord_less_eq @ A @ Y2 @ Z3 ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_110_le__less__linear,axiom,
% 0.29/1.53 ! [A: $tType] :
% 0.29/1.53 ( ( linorder @ A )
% 0.29/1.53 => ! [X3: A,Y2: A] :
% 0.29/1.53 ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.29/1.53 | ( ord_less @ A @ Y2 @ X3 ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_111_le__imp__less__or__eq,axiom,
% 0.29/1.53 ! [A: $tType] :
% 0.29/1.53 ( ( order @ A )
% 0.29/1.53 => ! [X3: A,Y2: A] :
% 0.29/1.53 ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.29/1.53 => ( ( ord_less @ A @ X3 @ Y2 )
% 0.29/1.53 | ( X3 = Y2 ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_112_less__le__not__le,axiom,
% 0.29/1.53 ! [A: $tType] :
% 0.29/1.53 ( ( preorder @ A )
% 0.29/1.53 => ( ( ord_less @ A )
% 0.29/1.53 = ( ^ [X2: A,Y3: A] :
% 0.29/1.53 ( ( ord_less_eq @ A @ X2 @ Y3 )
% 0.29/1.53 & ~ ( ord_less_eq @ A @ Y3 @ X2 ) ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_113_not__le__imp__less,axiom,
% 0.29/1.53 ! [A: $tType] :
% 0.29/1.53 ( ( linorder @ A )
% 0.29/1.53 => ! [Y2: A,X3: A] :
% 0.29/1.53 ( ~ ( ord_less_eq @ A @ Y2 @ X3 )
% 0.29/1.53 => ( ord_less @ A @ X3 @ Y2 ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_114_order_Ostrict__trans1,axiom,
% 0.29/1.53 ! [A: $tType] :
% 0.29/1.53 ( ( order @ A )
% 0.29/1.53 => ! [A2: A,B2: A,C: A] :
% 0.29/1.53 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.29/1.53 => ( ( ord_less @ A @ B2 @ C )
% 0.29/1.53 => ( ord_less @ A @ A2 @ C ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_115_order_Ostrict__trans2,axiom,
% 0.29/1.53 ! [A: $tType] :
% 0.29/1.53 ( ( order @ A )
% 0.29/1.53 => ! [A2: A,B2: A,C: A] :
% 0.29/1.53 ( ( ord_less @ A @ A2 @ B2 )
% 0.29/1.53 => ( ( ord_less_eq @ A @ B2 @ C )
% 0.29/1.53 => ( ord_less @ A @ A2 @ C ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_116_order_Oorder__iff__strict,axiom,
% 0.29/1.53 ! [A: $tType] :
% 0.29/1.53 ( ( order @ A )
% 0.29/1.53 => ( ( ord_less_eq @ A )
% 0.29/1.53 = ( ^ [A3: A,B3: A] :
% 0.29/1.53 ( ( ord_less @ A @ A3 @ B3 )
% 0.29/1.53 | ( A3 = B3 ) ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_117_order_Ostrict__iff__order,axiom,
% 0.29/1.53 ! [A: $tType] :
% 0.29/1.53 ( ( order @ A )
% 0.29/1.53 => ( ( ord_less @ A )
% 0.29/1.53 = ( ^ [A3: A,B3: A] :
% 0.29/1.53 ( ( ord_less_eq @ A @ A3 @ B3 )
% 0.29/1.53 & ( A3 != B3 ) ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_118_dual__order_Ostrict__trans1,axiom,
% 0.29/1.53 ! [A: $tType] :
% 0.29/1.53 ( ( order @ A )
% 0.29/1.53 => ! [B2: A,A2: A,C: A] :
% 0.29/1.53 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.29/1.53 => ( ( ord_less @ A @ C @ B2 )
% 0.29/1.53 => ( ord_less @ A @ C @ A2 ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_119_dual__order_Ostrict__trans2,axiom,
% 0.29/1.53 ! [A: $tType] :
% 0.29/1.53 ( ( order @ A )
% 0.29/1.53 => ! [B2: A,A2: A,C: A] :
% 0.29/1.53 ( ( ord_less @ A @ B2 @ A2 )
% 0.29/1.53 => ( ( ord_less_eq @ A @ C @ B2 )
% 0.29/1.53 => ( ord_less @ A @ C @ A2 ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_120_dense__ge__bounded,axiom,
% 0.29/1.53 ! [A: $tType] :
% 0.29/1.53 ( ( dense_linorder @ A )
% 0.29/1.53 => ! [Z3: A,X3: A,Y2: A] :
% 0.29/1.53 ( ( ord_less @ A @ Z3 @ X3 )
% 0.29/1.53 => ( ! [W: A] :
% 0.29/1.53 ( ( ord_less @ A @ Z3 @ W )
% 0.29/1.53 => ( ( ord_less @ A @ W @ X3 )
% 0.29/1.53 => ( ord_less_eq @ A @ Y2 @ W ) ) )
% 0.29/1.53 => ( ord_less_eq @ A @ Y2 @ Z3 ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_121_dense__le__bounded,axiom,
% 0.29/1.53 ! [A: $tType] :
% 0.29/1.53 ( ( dense_linorder @ A )
% 0.29/1.53 => ! [X3: A,Y2: A,Z3: A] :
% 0.29/1.53 ( ( ord_less @ A @ X3 @ Y2 )
% 0.29/1.53 => ( ! [W: A] :
% 0.29/1.53 ( ( ord_less @ A @ X3 @ W )
% 0.29/1.53 => ( ( ord_less @ A @ W @ Y2 )
% 0.29/1.53 => ( ord_less_eq @ A @ W @ Z3 ) ) )
% 0.29/1.53 => ( ord_less_eq @ A @ Y2 @ Z3 ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_122_order_Ostrict__implies__order,axiom,
% 0.29/1.53 ! [A: $tType] :
% 0.29/1.53 ( ( order @ A )
% 0.29/1.53 => ! [A2: A,B2: A] :
% 0.29/1.53 ( ( ord_less @ A @ A2 @ B2 )
% 0.29/1.53 => ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_123_dual__order_Oorder__iff__strict,axiom,
% 0.29/1.53 ! [A: $tType] :
% 0.29/1.53 ( ( order @ A )
% 0.29/1.53 => ( ( ord_less_eq @ A )
% 0.29/1.53 = ( ^ [B3: A,A3: A] :
% 0.29/1.53 ( ( ord_less @ A @ B3 @ A3 )
% 0.29/1.53 | ( A3 = B3 ) ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_124_dual__order_Ostrict__iff__order,axiom,
% 0.29/1.53 ! [A: $tType] :
% 0.29/1.53 ( ( order @ A )
% 0.29/1.53 => ( ( ord_less @ A )
% 0.29/1.53 = ( ^ [B3: A,A3: A] :
% 0.29/1.53 ( ( ord_less_eq @ A @ B3 @ A3 )
% 0.29/1.53 & ( A3 != B3 ) ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_125_dual__order_Ostrict__implies__order,axiom,
% 0.29/1.53 ! [A: $tType] :
% 0.29/1.53 ( ( order @ A )
% 0.29/1.53 => ! [B2: A,A2: A] :
% 0.29/1.53 ( ( ord_less @ A @ B2 @ A2 )
% 0.29/1.53 => ( ord_less_eq @ A @ B2 @ A2 ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_126_order_Onot__eq__order__implies__strict,axiom,
% 0.29/1.53 ! [A: $tType] :
% 0.29/1.53 ( ( order @ A )
% 0.29/1.53 => ! [A2: A,B2: A] :
% 0.29/1.53 ( ( A2 != B2 )
% 0.29/1.53 => ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.29/1.53 => ( ord_less @ A @ A2 @ B2 ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_127_RepFun__cong,axiom,
% 0.29/1.53 ! [A5: hF_Mirabelle_hf,B5: hF_Mirabelle_hf,F: hF_Mirabelle_hf > hF_Mirabelle_hf,G: hF_Mirabelle_hf > hF_Mirabelle_hf] :
% 0.29/1.53 ( ( A5 = B5 )
% 0.29/1.53 => ( ! [X: hF_Mirabelle_hf] :
% 0.29/1.53 ( ( hF_Mirabelle_hmem @ X @ B5 )
% 0.29/1.53 => ( ( F @ X )
% 0.29/1.53 = ( G @ X ) ) )
% 0.29/1.53 => ( ( hF_Mirabelle_RepFun @ A5 @ F )
% 0.29/1.53 = ( hF_Mirabelle_RepFun @ B5 @ G ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_128_minf_I8_J,axiom,
% 0.29/1.53 ! [A: $tType] :
% 0.29/1.53 ( ( linorder @ A )
% 0.29/1.53 => ! [T: A] :
% 0.29/1.53 ? [Z2: A] :
% 0.29/1.53 ! [X6: A] :
% 0.29/1.53 ( ( ord_less @ A @ X6 @ Z2 )
% 0.29/1.53 => ~ ( ord_less_eq @ A @ T @ X6 ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_129_minf_I6_J,axiom,
% 0.29/1.53 ! [A: $tType] :
% 0.29/1.53 ( ( linorder @ A )
% 0.29/1.53 => ! [T: A] :
% 0.29/1.53 ? [Z2: A] :
% 0.29/1.53 ! [X6: A] :
% 0.29/1.53 ( ( ord_less @ A @ X6 @ Z2 )
% 0.29/1.53 => ( ord_less_eq @ A @ X6 @ T ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_130_pinf_I8_J,axiom,
% 0.29/1.53 ! [A: $tType] :
% 0.29/1.53 ( ( linorder @ A )
% 0.29/1.53 => ! [T: A] :
% 0.29/1.53 ? [Z2: A] :
% 0.29/1.53 ! [X6: A] :
% 0.29/1.53 ( ( ord_less @ A @ Z2 @ X6 )
% 0.29/1.53 => ( ord_less_eq @ A @ T @ X6 ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_131_pinf_I6_J,axiom,
% 0.29/1.53 ! [A: $tType] :
% 0.29/1.53 ( ( linorder @ A )
% 0.29/1.53 => ! [T: A] :
% 0.29/1.53 ? [Z2: A] :
% 0.29/1.53 ! [X6: A] :
% 0.29/1.53 ( ( ord_less @ A @ Z2 @ X6 )
% 0.29/1.53 => ~ ( ord_less_eq @ A @ X6 @ T ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_132_complete__interval,axiom,
% 0.29/1.53 ! [A: $tType] :
% 0.29/1.53 ( ( condit1037483654norder @ A )
% 0.29/1.53 => ! [A2: A,B2: A,P: A > $o] :
% 0.29/1.53 ( ( ord_less @ A @ A2 @ B2 )
% 0.29/1.53 => ( ( P @ A2 )
% 0.29/1.53 => ( ~ ( P @ B2 )
% 0.29/1.53 => ? [C3: A] :
% 0.29/1.53 ( ( ord_less_eq @ A @ A2 @ C3 )
% 0.29/1.53 & ( ord_less_eq @ A @ C3 @ B2 )
% 0.29/1.53 & ! [X6: A] :
% 0.29/1.53 ( ( ( ord_less_eq @ A @ A2 @ X6 )
% 0.29/1.53 & ( ord_less @ A @ X6 @ C3 ) )
% 0.29/1.53 => ( P @ X6 ) )
% 0.29/1.53 & ! [D: A] :
% 0.29/1.53 ( ! [X: A] :
% 0.29/1.53 ( ( ( ord_less_eq @ A @ A2 @ X )
% 0.29/1.53 & ( ord_less @ A @ X @ D ) )
% 0.29/1.53 => ( P @ X ) )
% 0.29/1.53 => ( ord_less_eq @ A @ D @ C3 ) ) ) ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_133_HF__hfset,axiom,
% 0.29/1.53 ! [A2: hF_Mirabelle_hf] :
% 0.29/1.53 ( ( hF_Mirabelle_HF @ ( hF_Mirabelle_hfset @ A2 ) )
% 0.29/1.53 = A2 ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_134_ex__gt__or__lt,axiom,
% 0.29/1.53 ! [A: $tType] :
% 0.29/1.53 ( ( condit1656338222tinuum @ A )
% 0.29/1.53 => ! [A2: A] :
% 0.29/1.53 ? [B6: A] :
% 0.29/1.53 ( ( ord_less @ A @ A2 @ B6 )
% 0.29/1.53 | ( ord_less @ A @ B6 @ A2 ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_135_linorder__neqE__linordered__idom,axiom,
% 0.29/1.53 ! [A: $tType] :
% 0.29/1.53 ( ( linordered_idom @ A )
% 0.29/1.53 => ! [X3: A,Y2: A] :
% 0.29/1.53 ( ( X3 != Y2 )
% 0.29/1.53 => ( ~ ( ord_less @ A @ X3 @ Y2 )
% 0.29/1.53 => ( ord_less @ A @ Y2 @ X3 ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_136_less__fun__def,axiom,
% 0.29/1.53 ! [B: $tType,A: $tType] :
% 0.29/1.53 ( ( ord @ B )
% 0.29/1.53 => ( ( ord_less @ ( A > B ) )
% 0.29/1.53 = ( ^ [F2: A > B,G2: A > B] :
% 0.29/1.53 ( ( ord_less_eq @ ( A > B ) @ F2 @ G2 )
% 0.29/1.53 & ~ ( ord_less_eq @ ( A > B ) @ G2 @ F2 ) ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_137_minf_I11_J,axiom,
% 0.29/1.53 ! [C2: $tType,D2: $tType] :
% 0.29/1.53 ( ( ord @ C2 )
% 0.29/1.53 => ! [F3: D2] :
% 0.29/1.53 ? [Z2: C2] :
% 0.29/1.53 ! [X6: C2] :
% 0.29/1.53 ( ( ord_less @ C2 @ X6 @ Z2 )
% 0.29/1.53 => ( F3 = F3 ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_138_minf_I7_J,axiom,
% 0.29/1.53 ! [A: $tType] :
% 0.29/1.53 ( ( linorder @ A )
% 0.29/1.53 => ! [T: A] :
% 0.29/1.53 ? [Z2: A] :
% 0.29/1.53 ! [X6: A] :
% 0.29/1.53 ( ( ord_less @ A @ X6 @ Z2 )
% 0.29/1.53 => ~ ( ord_less @ A @ T @ X6 ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_139_minf_I5_J,axiom,
% 0.29/1.53 ! [A: $tType] :
% 0.29/1.53 ( ( linorder @ A )
% 0.29/1.53 => ! [T: A] :
% 0.29/1.53 ? [Z2: A] :
% 0.29/1.53 ! [X6: A] :
% 0.29/1.53 ( ( ord_less @ A @ X6 @ Z2 )
% 0.29/1.53 => ( ord_less @ A @ X6 @ T ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_140_minf_I4_J,axiom,
% 0.29/1.53 ! [A: $tType] :
% 0.29/1.53 ( ( linorder @ A )
% 0.29/1.53 => ! [T: A] :
% 0.29/1.53 ? [Z2: A] :
% 0.29/1.53 ! [X6: A] :
% 0.29/1.53 ( ( ord_less @ A @ X6 @ Z2 )
% 0.29/1.53 => ( X6 != T ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_141_minf_I3_J,axiom,
% 0.29/1.53 ! [A: $tType] :
% 0.29/1.53 ( ( linorder @ A )
% 0.29/1.53 => ! [T: A] :
% 0.29/1.53 ? [Z2: A] :
% 0.29/1.53 ! [X6: A] :
% 0.29/1.53 ( ( ord_less @ A @ X6 @ Z2 )
% 0.29/1.53 => ( X6 != T ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_142_minf_I2_J,axiom,
% 0.29/1.53 ! [A: $tType] :
% 0.29/1.53 ( ( linorder @ A )
% 0.29/1.53 => ! [P: A > $o,P4: A > $o,Q: A > $o,Q2: A > $o] :
% 0.29/1.53 ( ? [Z4: A] :
% 0.29/1.53 ! [X: A] :
% 0.29/1.53 ( ( ord_less @ A @ X @ Z4 )
% 0.29/1.53 => ( ( P @ X )
% 0.29/1.53 = ( P4 @ X ) ) )
% 0.29/1.53 => ( ? [Z4: A] :
% 0.29/1.53 ! [X: A] :
% 0.29/1.53 ( ( ord_less @ A @ X @ Z4 )
% 0.29/1.53 => ( ( Q @ X )
% 0.29/1.53 = ( Q2 @ X ) ) )
% 0.29/1.53 => ? [Z2: A] :
% 0.29/1.53 ! [X6: A] :
% 0.29/1.53 ( ( ord_less @ A @ X6 @ Z2 )
% 0.29/1.53 => ( ( ( P @ X6 )
% 0.29/1.53 | ( Q @ X6 ) )
% 0.29/1.53 = ( ( P4 @ X6 )
% 0.29/1.53 | ( Q2 @ X6 ) ) ) ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_143_minf_I1_J,axiom,
% 0.29/1.53 ! [A: $tType] :
% 0.29/1.53 ( ( linorder @ A )
% 0.29/1.53 => ! [P: A > $o,P4: A > $o,Q: A > $o,Q2: A > $o] :
% 0.29/1.53 ( ? [Z4: A] :
% 0.29/1.53 ! [X: A] :
% 0.29/1.53 ( ( ord_less @ A @ X @ Z4 )
% 0.29/1.53 => ( ( P @ X )
% 0.29/1.53 = ( P4 @ X ) ) )
% 0.29/1.53 => ( ? [Z4: A] :
% 0.29/1.53 ! [X: A] :
% 0.29/1.53 ( ( ord_less @ A @ X @ Z4 )
% 0.29/1.53 => ( ( Q @ X )
% 0.29/1.53 = ( Q2 @ X ) ) )
% 0.29/1.53 => ? [Z2: A] :
% 0.29/1.53 ! [X6: A] :
% 0.29/1.53 ( ( ord_less @ A @ X6 @ Z2 )
% 0.29/1.53 => ( ( ( P @ X6 )
% 0.29/1.53 & ( Q @ X6 ) )
% 0.29/1.53 = ( ( P4 @ X6 )
% 0.29/1.53 & ( Q2 @ X6 ) ) ) ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_144_pinf_I11_J,axiom,
% 0.29/1.53 ! [C2: $tType,D2: $tType] :
% 0.29/1.53 ( ( ord @ C2 )
% 0.29/1.53 => ! [F3: D2] :
% 0.29/1.53 ? [Z2: C2] :
% 0.29/1.53 ! [X6: C2] :
% 0.29/1.53 ( ( ord_less @ C2 @ Z2 @ X6 )
% 0.29/1.53 => ( F3 = F3 ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_145_pinf_I7_J,axiom,
% 0.29/1.53 ! [A: $tType] :
% 0.29/1.53 ( ( linorder @ A )
% 0.29/1.53 => ! [T: A] :
% 0.29/1.53 ? [Z2: A] :
% 0.29/1.53 ! [X6: A] :
% 0.29/1.53 ( ( ord_less @ A @ Z2 @ X6 )
% 0.29/1.53 => ( ord_less @ A @ T @ X6 ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_146_pinf_I5_J,axiom,
% 0.29/1.53 ! [A: $tType] :
% 0.29/1.53 ( ( linorder @ A )
% 0.29/1.53 => ! [T: A] :
% 0.29/1.53 ? [Z2: A] :
% 0.29/1.53 ! [X6: A] :
% 0.29/1.53 ( ( ord_less @ A @ Z2 @ X6 )
% 0.29/1.53 => ~ ( ord_less @ A @ X6 @ T ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_147_pinf_I4_J,axiom,
% 0.29/1.53 ! [A: $tType] :
% 0.29/1.53 ( ( linorder @ A )
% 0.29/1.53 => ! [T: A] :
% 0.29/1.53 ? [Z2: A] :
% 0.29/1.53 ! [X6: A] :
% 0.29/1.53 ( ( ord_less @ A @ Z2 @ X6 )
% 0.29/1.53 => ( X6 != T ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_148_pinf_I3_J,axiom,
% 0.29/1.53 ! [A: $tType] :
% 0.29/1.53 ( ( linorder @ A )
% 0.29/1.53 => ! [T: A] :
% 0.29/1.53 ? [Z2: A] :
% 0.29/1.53 ! [X6: A] :
% 0.29/1.53 ( ( ord_less @ A @ Z2 @ X6 )
% 0.29/1.53 => ( X6 != T ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_149_pinf_I2_J,axiom,
% 0.29/1.53 ! [A: $tType] :
% 0.29/1.53 ( ( linorder @ A )
% 0.29/1.53 => ! [P: A > $o,P4: A > $o,Q: A > $o,Q2: A > $o] :
% 0.29/1.53 ( ? [Z4: A] :
% 0.29/1.53 ! [X: A] :
% 0.29/1.53 ( ( ord_less @ A @ Z4 @ X )
% 0.29/1.53 => ( ( P @ X )
% 0.29/1.53 = ( P4 @ X ) ) )
% 0.29/1.53 => ( ? [Z4: A] :
% 0.29/1.53 ! [X: A] :
% 0.29/1.53 ( ( ord_less @ A @ Z4 @ X )
% 0.29/1.53 => ( ( Q @ X )
% 0.29/1.53 = ( Q2 @ X ) ) )
% 0.29/1.53 => ? [Z2: A] :
% 0.29/1.53 ! [X6: A] :
% 0.29/1.53 ( ( ord_less @ A @ Z2 @ X6 )
% 0.29/1.53 => ( ( ( P @ X6 )
% 0.29/1.53 | ( Q @ X6 ) )
% 0.29/1.53 = ( ( P4 @ X6 )
% 0.29/1.53 | ( Q2 @ X6 ) ) ) ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_150_pinf_I1_J,axiom,
% 0.29/1.53 ! [A: $tType] :
% 0.29/1.53 ( ( linorder @ A )
% 0.29/1.53 => ! [P: A > $o,P4: A > $o,Q: A > $o,Q2: A > $o] :
% 0.29/1.53 ( ? [Z4: A] :
% 0.29/1.53 ! [X: A] :
% 0.29/1.53 ( ( ord_less @ A @ Z4 @ X )
% 0.29/1.53 => ( ( P @ X )
% 0.29/1.53 = ( P4 @ X ) ) )
% 0.29/1.53 => ( ? [Z4: A] :
% 0.29/1.53 ! [X: A] :
% 0.29/1.53 ( ( ord_less @ A @ Z4 @ X )
% 0.29/1.53 => ( ( Q @ X )
% 0.29/1.53 = ( Q2 @ X ) ) )
% 0.29/1.53 => ? [Z2: A] :
% 0.29/1.53 ! [X6: A] :
% 0.29/1.53 ( ( ord_less @ A @ Z2 @ X6 )
% 0.29/1.53 => ( ( ( P @ X6 )
% 0.29/1.53 & ( Q @ X6 ) )
% 0.29/1.53 = ( ( P4 @ X6 )
% 0.29/1.53 & ( Q2 @ X6 ) ) ) ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_151_hfset__HF,axiom,
% 0.29/1.53 ! [A5: set @ hF_Mirabelle_hf] :
% 0.29/1.53 ( ( finite_finite2 @ hF_Mirabelle_hf @ A5 )
% 0.29/1.53 => ( ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ A5 ) )
% 0.29/1.53 = A5 ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_152_hmem__HF__iff,axiom,
% 0.29/1.53 ! [X3: hF_Mirabelle_hf,A5: set @ hF_Mirabelle_hf] :
% 0.29/1.53 ( ( hF_Mirabelle_hmem @ X3 @ ( hF_Mirabelle_HF @ A5 ) )
% 0.29/1.53 = ( ( member @ hF_Mirabelle_hf @ X3 @ A5 )
% 0.29/1.53 & ( finite_finite2 @ hF_Mirabelle_hf @ A5 ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_153_measure__induct,axiom,
% 0.29/1.53 ! [B: $tType,A: $tType] :
% 0.29/1.53 ( ( wellorder @ B )
% 0.29/1.53 => ! [F: A > B,P: A > $o,A2: A] :
% 0.29/1.53 ( ! [X: A] :
% 0.29/1.53 ( ! [Y5: A] :
% 0.29/1.53 ( ( ord_less @ B @ ( F @ Y5 ) @ ( F @ X ) )
% 0.29/1.53 => ( P @ Y5 ) )
% 0.29/1.53 => ( P @ X ) )
% 0.29/1.53 => ( P @ A2 ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_154_measure__induct__rule,axiom,
% 0.29/1.53 ! [B: $tType,A: $tType] :
% 0.29/1.53 ( ( wellorder @ B )
% 0.29/1.53 => ! [F: A > B,P: A > $o,A2: A] :
% 0.29/1.53 ( ! [X: A] :
% 0.29/1.53 ( ! [Y5: A] :
% 0.29/1.53 ( ( ord_less @ B @ ( F @ Y5 ) @ ( F @ X ) )
% 0.29/1.53 => ( P @ Y5 ) )
% 0.29/1.53 => ( P @ X ) )
% 0.29/1.53 => ( P @ A2 ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_155_finite__hfset,axiom,
% 0.29/1.53 ! [A2: hF_Mirabelle_hf] : ( finite_finite2 @ hF_Mirabelle_hf @ ( hF_Mirabelle_hfset @ A2 ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_156_finite__code,axiom,
% 0.29/1.53 ! [A: $tType] :
% 0.29/1.53 ( ( finite_finite @ A )
% 0.29/1.53 => ( ( finite_finite2 @ A )
% 0.29/1.53 = ( ^ [A4: set @ A] : $true ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_157_finite__has__minimal2,axiom,
% 0.29/1.53 ! [A: $tType] :
% 0.29/1.53 ( ( order @ A )
% 0.29/1.53 => ! [A5: set @ A,A2: A] :
% 0.29/1.53 ( ( finite_finite2 @ A @ A5 )
% 0.29/1.53 => ( ( member @ A @ A2 @ A5 )
% 0.29/1.53 => ? [X: A] :
% 0.29/1.53 ( ( member @ A @ X @ A5 )
% 0.29/1.53 & ( ord_less_eq @ A @ X @ A2 )
% 0.29/1.53 & ! [Xa: A] :
% 0.29/1.53 ( ( member @ A @ Xa @ A5 )
% 0.29/1.53 => ( ( ord_less_eq @ A @ Xa @ X )
% 0.29/1.53 => ( X = Xa ) ) ) ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_158_finite__has__maximal2,axiom,
% 0.29/1.53 ! [A: $tType] :
% 0.29/1.53 ( ( order @ A )
% 0.29/1.53 => ! [A5: set @ A,A2: A] :
% 0.29/1.53 ( ( finite_finite2 @ A @ A5 )
% 0.29/1.53 => ( ( member @ A @ A2 @ A5 )
% 0.29/1.53 => ? [X: A] :
% 0.29/1.53 ( ( member @ A @ X @ A5 )
% 0.29/1.53 & ( ord_less_eq @ A @ A2 @ X )
% 0.29/1.53 & ! [Xa: A] :
% 0.29/1.53 ( ( member @ A @ Xa @ A5 )
% 0.29/1.53 => ( ( ord_less_eq @ A @ X @ Xa )
% 0.29/1.53 => ( X = Xa ) ) ) ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_159_finite__subset,axiom,
% 0.29/1.53 ! [A: $tType,A5: set @ A,B5: set @ A] :
% 0.29/1.53 ( ( ord_less_eq @ ( set @ A ) @ A5 @ B5 )
% 0.29/1.53 => ( ( finite_finite2 @ A @ B5 )
% 0.29/1.53 => ( finite_finite2 @ A @ A5 ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_160_infinite__super,axiom,
% 0.29/1.53 ! [A: $tType,S: set @ A,T2: set @ A] :
% 0.29/1.53 ( ( ord_less_eq @ ( set @ A ) @ S @ T2 )
% 0.29/1.53 => ( ~ ( finite_finite2 @ A @ S )
% 0.29/1.53 => ~ ( finite_finite2 @ A @ T2 ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_161_rev__finite__subset,axiom,
% 0.29/1.53 ! [A: $tType,B5: set @ A,A5: set @ A] :
% 0.29/1.53 ( ( finite_finite2 @ A @ B5 )
% 0.29/1.53 => ( ( ord_less_eq @ ( set @ A ) @ A5 @ B5 )
% 0.29/1.53 => ( finite_finite2 @ A @ A5 ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_162_finite__set__choice,axiom,
% 0.29/1.53 ! [B: $tType,A: $tType,A5: set @ A,P: A > B > $o] :
% 0.29/1.53 ( ( finite_finite2 @ A @ A5 )
% 0.29/1.53 => ( ! [X: A] :
% 0.29/1.53 ( ( member @ A @ X @ A5 )
% 0.29/1.53 => ? [X_12: B] : ( P @ X @ X_12 ) )
% 0.29/1.53 => ? [F4: A > B] :
% 0.29/1.53 ! [X6: A] :
% 0.29/1.53 ( ( member @ A @ X6 @ A5 )
% 0.29/1.53 => ( P @ X6 @ ( F4 @ X6 ) ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_163_finite,axiom,
% 0.29/1.53 ! [A: $tType] :
% 0.29/1.53 ( ( finite_finite @ A )
% 0.29/1.53 => ! [A5: set @ A] : ( finite_finite2 @ A @ A5 ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_164_finite__psubset__induct,axiom,
% 0.29/1.53 ! [A: $tType,A5: set @ A,P: ( set @ A ) > $o] :
% 0.29/1.53 ( ( finite_finite2 @ A @ A5 )
% 0.29/1.53 => ( ! [A8: set @ A] :
% 0.29/1.53 ( ( finite_finite2 @ A @ A8 )
% 0.29/1.53 => ( ! [B8: set @ A] :
% 0.29/1.53 ( ( ord_less @ ( set @ A ) @ B8 @ A8 )
% 0.29/1.53 => ( P @ B8 ) )
% 0.29/1.53 => ( P @ A8 ) ) )
% 0.29/1.53 => ( P @ A5 ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_165_dependent__wellorder__choice,axiom,
% 0.29/1.53 ! [B: $tType,A: $tType] :
% 0.29/1.53 ( ( wellorder @ A )
% 0.29/1.53 => ! [P: ( A > B ) > A > B > $o] :
% 0.29/1.53 ( ! [R2: B,F4: A > B,G3: A > B,X: A] :
% 0.29/1.53 ( ! [Y5: A] :
% 0.29/1.53 ( ( ord_less @ A @ Y5 @ X )
% 0.29/1.53 => ( ( F4 @ Y5 )
% 0.29/1.53 = ( G3 @ Y5 ) ) )
% 0.29/1.53 => ( ( P @ F4 @ X @ R2 )
% 0.29/1.53 = ( P @ G3 @ X @ R2 ) ) )
% 0.29/1.53 => ( ! [X: A,F4: A > B] :
% 0.29/1.53 ( ! [Y5: A] :
% 0.29/1.53 ( ( ord_less @ A @ Y5 @ X )
% 0.29/1.53 => ( P @ F4 @ Y5 @ ( F4 @ Y5 ) ) )
% 0.29/1.53 => ? [X_12: B] : ( P @ F4 @ X @ X_12 ) )
% 0.29/1.53 => ? [F4: A > B] :
% 0.29/1.53 ! [X6: A] : ( P @ F4 @ X6 @ ( F4 @ X6 ) ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_166_linordered__field__no__lb,axiom,
% 0.29/1.53 ! [A: $tType] :
% 0.29/1.53 ( ( linordered_field @ A )
% 0.29/1.53 => ! [X6: A] :
% 0.29/1.53 ? [Y4: A] : ( ord_less @ A @ Y4 @ X6 ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_167_linordered__field__no__ub,axiom,
% 0.29/1.53 ! [A: $tType] :
% 0.29/1.53 ( ( linordered_field @ A )
% 0.29/1.53 => ! [X6: A] :
% 0.29/1.53 ? [X_1: A] : ( ord_less @ A @ X6 @ X_1 ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_168_card__psubset,axiom,
% 0.29/1.53 ! [A: $tType,B5: set @ A,A5: set @ A] :
% 0.29/1.53 ( ( finite_finite2 @ A @ B5 )
% 0.29/1.53 => ( ( ord_less_eq @ ( set @ A ) @ A5 @ B5 )
% 0.29/1.53 => ( ( ord_less @ nat @ ( finite_card @ A @ A5 ) @ ( finite_card @ A @ B5 ) )
% 0.29/1.53 => ( ord_less @ ( set @ A ) @ A5 @ B5 ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_169_inj__on__HF,axiom,
% 0.29/1.53 inj_on @ ( set @ hF_Mirabelle_hf ) @ hF_Mirabelle_hf @ hF_Mirabelle_HF @ ( collect @ ( set @ hF_Mirabelle_hf ) @ ( finite_finite2 @ hF_Mirabelle_hf ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_170_order_Oordering__axioms,axiom,
% 0.29/1.53 ! [A: $tType] :
% 0.29/1.53 ( ( order @ A )
% 0.29/1.53 => ( ordering @ A @ ( ord_less_eq @ A ) @ ( ord_less @ A ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_171_ordering_Onot__eq__order__implies__strict,axiom,
% 0.29/1.53 ! [A: $tType,Less_eq: A > A > $o,Less: A > A > $o,A2: A,B2: A] :
% 0.29/1.53 ( ( ordering @ A @ Less_eq @ Less )
% 0.29/1.53 => ( ( A2 != B2 )
% 0.29/1.53 => ( ( Less_eq @ A2 @ B2 )
% 0.29/1.53 => ( Less @ A2 @ B2 ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_172_ordering_Ostrict__implies__not__eq,axiom,
% 0.29/1.53 ! [A: $tType,Less_eq: A > A > $o,Less: A > A > $o,A2: A,B2: A] :
% 0.29/1.53 ( ( ordering @ A @ Less_eq @ Less )
% 0.29/1.53 => ( ( Less @ A2 @ B2 )
% 0.29/1.53 => ( A2 != B2 ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_173_ordering_Ostrict__implies__order,axiom,
% 0.29/1.53 ! [A: $tType,Less_eq: A > A > $o,Less: A > A > $o,A2: A,B2: A] :
% 0.29/1.53 ( ( ordering @ A @ Less_eq @ Less )
% 0.29/1.53 => ( ( Less @ A2 @ B2 )
% 0.29/1.53 => ( Less_eq @ A2 @ B2 ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_174_ordering_Ostrict__iff__order,axiom,
% 0.29/1.53 ! [A: $tType,Less_eq: A > A > $o,Less: A > A > $o,A2: A,B2: A] :
% 0.29/1.53 ( ( ordering @ A @ Less_eq @ Less )
% 0.29/1.53 => ( ( Less @ A2 @ B2 )
% 0.29/1.53 = ( ( Less_eq @ A2 @ B2 )
% 0.29/1.53 & ( A2 != B2 ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_175_ordering_Oorder__iff__strict,axiom,
% 0.29/1.53 ! [A: $tType,Less_eq: A > A > $o,Less: A > A > $o,A2: A,B2: A] :
% 0.29/1.53 ( ( ordering @ A @ Less_eq @ Less )
% 0.29/1.53 => ( ( Less_eq @ A2 @ B2 )
% 0.29/1.53 = ( ( Less @ A2 @ B2 )
% 0.29/1.53 | ( A2 = B2 ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_176_ordering_Ostrict__trans2,axiom,
% 0.29/1.53 ! [A: $tType,Less_eq: A > A > $o,Less: A > A > $o,A2: A,B2: A,C: A] :
% 0.29/1.53 ( ( ordering @ A @ Less_eq @ Less )
% 0.29/1.53 => ( ( Less @ A2 @ B2 )
% 0.29/1.53 => ( ( Less_eq @ B2 @ C )
% 0.29/1.53 => ( Less @ A2 @ C ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_177_ordering_Ostrict__trans1,axiom,
% 0.29/1.53 ! [A: $tType,Less_eq: A > A > $o,Less: A > A > $o,A2: A,B2: A,C: A] :
% 0.29/1.53 ( ( ordering @ A @ Less_eq @ Less )
% 0.29/1.53 => ( ( Less_eq @ A2 @ B2 )
% 0.29/1.53 => ( ( Less @ B2 @ C )
% 0.29/1.53 => ( Less @ A2 @ C ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_178_ordering_Ostrict__trans,axiom,
% 0.29/1.53 ! [A: $tType,Less_eq: A > A > $o,Less: A > A > $o,A2: A,B2: A,C: A] :
% 0.29/1.53 ( ( ordering @ A @ Less_eq @ Less )
% 0.29/1.53 => ( ( Less @ A2 @ B2 )
% 0.29/1.53 => ( ( Less @ B2 @ C )
% 0.29/1.53 => ( Less @ A2 @ C ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_179_ordering__strictI,axiom,
% 0.29/1.53 ! [A: $tType,Less_eq: A > A > $o,Less: A > A > $o] :
% 0.29/1.53 ( ! [A6: A,B6: A] :
% 0.29/1.53 ( ( Less_eq @ A6 @ B6 )
% 0.29/1.53 = ( ( Less @ A6 @ B6 )
% 0.29/1.53 | ( A6 = B6 ) ) )
% 0.29/1.53 => ( ! [A6: A,B6: A] :
% 0.29/1.53 ( ( Less @ A6 @ B6 )
% 0.29/1.53 => ~ ( Less @ B6 @ A6 ) )
% 0.29/1.53 => ( ! [A6: A] :
% 0.29/1.53 ~ ( Less @ A6 @ A6 )
% 0.29/1.53 => ( ! [A6: A,B6: A,C3: A] :
% 0.29/1.53 ( ( Less @ A6 @ B6 )
% 0.29/1.53 => ( ( Less @ B6 @ C3 )
% 0.29/1.53 => ( Less @ A6 @ C3 ) ) )
% 0.29/1.53 => ( ordering @ A @ Less_eq @ Less ) ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_180_ordering_Oantisym,axiom,
% 0.29/1.53 ! [A: $tType,Less_eq: A > A > $o,Less: A > A > $o,A2: A,B2: A] :
% 0.29/1.53 ( ( ordering @ A @ Less_eq @ Less )
% 0.29/1.53 => ( ( Less_eq @ A2 @ B2 )
% 0.29/1.53 => ( ( Less_eq @ B2 @ A2 )
% 0.29/1.53 => ( A2 = B2 ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_181_ordering_Oirrefl,axiom,
% 0.29/1.53 ! [A: $tType,Less_eq: A > A > $o,Less: A > A > $o,A2: A] :
% 0.29/1.53 ( ( ordering @ A @ Less_eq @ Less )
% 0.29/1.53 => ~ ( Less @ A2 @ A2 ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_182_ordering_Oeq__iff,axiom,
% 0.29/1.53 ! [A: $tType,Less_eq: A > A > $o,Less: A > A > $o,A2: A,B2: A] :
% 0.29/1.53 ( ( ordering @ A @ Less_eq @ Less )
% 0.29/1.53 => ( ( A2 = B2 )
% 0.29/1.53 = ( ( Less_eq @ A2 @ B2 )
% 0.29/1.53 & ( Less_eq @ B2 @ A2 ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_183_ordering_Otrans,axiom,
% 0.29/1.53 ! [A: $tType,Less_eq: A > A > $o,Less: A > A > $o,A2: A,B2: A,C: A] :
% 0.29/1.53 ( ( ordering @ A @ Less_eq @ Less )
% 0.29/1.53 => ( ( Less_eq @ A2 @ B2 )
% 0.29/1.53 => ( ( Less_eq @ B2 @ C )
% 0.29/1.53 => ( Less_eq @ A2 @ C ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_184_ordering_Ointro,axiom,
% 0.29/1.53 ! [A: $tType,Less: A > A > $o,Less_eq: A > A > $o] :
% 0.29/1.53 ( ! [A6: A,B6: A] :
% 0.29/1.53 ( ( Less @ A6 @ B6 )
% 0.29/1.53 = ( ( Less_eq @ A6 @ B6 )
% 0.29/1.53 & ( A6 != B6 ) ) )
% 0.29/1.53 => ( ! [A6: A] : ( Less_eq @ A6 @ A6 )
% 0.29/1.53 => ( ! [A6: A,B6: A] :
% 0.29/1.53 ( ( Less_eq @ A6 @ B6 )
% 0.29/1.53 => ( ( Less_eq @ B6 @ A6 )
% 0.29/1.53 => ( A6 = B6 ) ) )
% 0.29/1.53 => ( ! [A6: A,B6: A,C3: A] :
% 0.29/1.53 ( ( Less_eq @ A6 @ B6 )
% 0.29/1.53 => ( ( Less_eq @ B6 @ C3 )
% 0.29/1.53 => ( Less_eq @ A6 @ C3 ) ) )
% 0.29/1.53 => ( ordering @ A @ Less_eq @ Less ) ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_185_ordering_Orefl,axiom,
% 0.29/1.53 ! [A: $tType,Less_eq: A > A > $o,Less: A > A > $o,A2: A] :
% 0.29/1.53 ( ( ordering @ A @ Less_eq @ Less )
% 0.29/1.53 => ( Less_eq @ A2 @ A2 ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_186_ordering_Oasym,axiom,
% 0.29/1.53 ! [A: $tType,Less_eq: A > A > $o,Less: A > A > $o,A2: A,B2: A] :
% 0.29/1.53 ( ( ordering @ A @ Less_eq @ Less )
% 0.29/1.53 => ( ( Less @ A2 @ B2 )
% 0.29/1.53 => ~ ( Less @ B2 @ A2 ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_187_ordering__def,axiom,
% 0.29/1.53 ! [A: $tType] :
% 0.29/1.53 ( ( ordering @ A )
% 0.29/1.53 = ( ^ [Less_eq2: A > A > $o,Less2: A > A > $o] :
% 0.29/1.53 ( ! [A3: A,B3: A] :
% 0.29/1.53 ( ( Less2 @ A3 @ B3 )
% 0.29/1.53 = ( ( Less_eq2 @ A3 @ B3 )
% 0.29/1.53 & ( A3 != B3 ) ) )
% 0.29/1.53 & ! [A3: A] : ( Less_eq2 @ A3 @ A3 )
% 0.29/1.53 & ! [A3: A,B3: A] :
% 0.29/1.53 ( ( Less_eq2 @ A3 @ B3 )
% 0.29/1.53 => ( ( Less_eq2 @ B3 @ A3 )
% 0.29/1.53 => ( A3 = B3 ) ) )
% 0.29/1.53 & ! [A3: A,B3: A,C4: A] :
% 0.29/1.53 ( ( Less_eq2 @ A3 @ B3 )
% 0.29/1.53 => ( ( Less_eq2 @ B3 @ C4 )
% 0.29/1.53 => ( Less_eq2 @ A3 @ C4 ) ) ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_188_card__mono,axiom,
% 0.29/1.53 ! [A: $tType,B5: set @ A,A5: set @ A] :
% 0.29/1.53 ( ( finite_finite2 @ A @ B5 )
% 0.29/1.53 => ( ( ord_less_eq @ ( set @ A ) @ A5 @ B5 )
% 0.29/1.53 => ( ord_less_eq @ nat @ ( finite_card @ A @ A5 ) @ ( finite_card @ A @ B5 ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_189_card__seteq,axiom,
% 0.29/1.53 ! [A: $tType,B5: set @ A,A5: set @ A] :
% 0.29/1.53 ( ( finite_finite2 @ A @ B5 )
% 0.29/1.53 => ( ( ord_less_eq @ ( set @ A ) @ A5 @ B5 )
% 0.29/1.53 => ( ( ord_less_eq @ nat @ ( finite_card @ A @ B5 ) @ ( finite_card @ A @ A5 ) )
% 0.29/1.53 => ( A5 = B5 ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_190_card__subset__eq,axiom,
% 0.29/1.53 ! [A: $tType,B5: set @ A,A5: set @ A] :
% 0.29/1.53 ( ( finite_finite2 @ A @ B5 )
% 0.29/1.53 => ( ( ord_less_eq @ ( set @ A ) @ A5 @ B5 )
% 0.29/1.53 => ( ( ( finite_card @ A @ A5 )
% 0.29/1.53 = ( finite_card @ A @ B5 ) )
% 0.29/1.53 => ( A5 = B5 ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_191_infinite__arbitrarily__large,axiom,
% 0.29/1.53 ! [A: $tType,A5: set @ A,N2: nat] :
% 0.29/1.53 ( ~ ( finite_finite2 @ A @ A5 )
% 0.29/1.53 => ? [B9: set @ A] :
% 0.29/1.53 ( ( finite_finite2 @ A @ B9 )
% 0.29/1.53 & ( ( finite_card @ A @ B9 )
% 0.29/1.53 = N2 )
% 0.29/1.53 & ( ord_less_eq @ ( set @ A ) @ B9 @ A5 ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_192_finite__if__finite__subsets__card__bdd,axiom,
% 0.29/1.53 ! [A: $tType,F3: set @ A,C5: nat] :
% 0.29/1.53 ( ! [G4: set @ A] :
% 0.29/1.53 ( ( ord_less_eq @ ( set @ A ) @ G4 @ F3 )
% 0.29/1.53 => ( ( finite_finite2 @ A @ G4 )
% 0.29/1.53 => ( ord_less_eq @ nat @ ( finite_card @ A @ G4 ) @ C5 ) ) )
% 0.29/1.53 => ( ( finite_finite2 @ A @ F3 )
% 0.29/1.53 & ( ord_less_eq @ nat @ ( finite_card @ A @ F3 ) @ C5 ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_193_psubset__card__mono,axiom,
% 0.29/1.53 ! [A: $tType,B5: set @ A,A5: set @ A] :
% 0.29/1.53 ( ( finite_finite2 @ A @ B5 )
% 0.29/1.53 => ( ( ord_less @ ( set @ A ) @ A5 @ B5 )
% 0.29/1.53 => ( ord_less @ nat @ ( finite_card @ A @ A5 ) @ ( finite_card @ A @ B5 ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_194_obtain__subset__with__card__n,axiom,
% 0.29/1.53 ! [A: $tType,N2: nat,S: set @ A] :
% 0.29/1.53 ( ( ord_less_eq @ nat @ N2 @ ( finite_card @ A @ S ) )
% 0.29/1.53 => ~ ! [T3: set @ A] :
% 0.29/1.53 ( ( ord_less_eq @ ( set @ A ) @ T3 @ S )
% 0.29/1.53 => ( ( ( finite_card @ A @ T3 )
% 0.29/1.53 = N2 )
% 0.29/1.53 => ~ ( finite_finite2 @ A @ T3 ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_195_linorder__inj__onI,axiom,
% 0.29/1.53 ! [B: $tType,A: $tType] :
% 0.29/1.53 ( ( order @ A )
% 0.29/1.53 => ! [A5: set @ A,F: A > B] :
% 0.29/1.53 ( ! [X: A,Y4: A] :
% 0.29/1.53 ( ( ord_less @ A @ X @ Y4 )
% 0.29/1.53 => ( ( member @ A @ X @ A5 )
% 0.29/1.53 => ( ( member @ A @ Y4 @ A5 )
% 0.29/1.53 => ( ( F @ X )
% 0.29/1.53 != ( F @ Y4 ) ) ) ) )
% 0.29/1.53 => ( ! [X: A,Y4: A] :
% 0.29/1.53 ( ( member @ A @ X @ A5 )
% 0.29/1.53 => ( ( member @ A @ Y4 @ A5 )
% 0.29/1.53 => ( ( ord_less_eq @ A @ X @ Y4 )
% 0.29/1.53 | ( ord_less_eq @ A @ Y4 @ X ) ) ) )
% 0.29/1.53 => ( inj_on @ A @ B @ F @ A5 ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_196_card__le__if__inj__on__rel,axiom,
% 0.29/1.53 ! [B: $tType,A: $tType,B5: set @ A,A5: set @ B,R3: B > A > $o] :
% 0.29/1.53 ( ( finite_finite2 @ A @ B5 )
% 0.29/1.53 => ( ! [A6: B] :
% 0.29/1.53 ( ( member @ B @ A6 @ A5 )
% 0.29/1.53 => ? [B10: A] :
% 0.29/1.53 ( ( member @ A @ B10 @ B5 )
% 0.29/1.53 & ( R3 @ A6 @ B10 ) ) )
% 0.29/1.53 => ( ! [A1: B,A22: B,B6: A] :
% 0.29/1.53 ( ( member @ B @ A1 @ A5 )
% 0.29/1.53 => ( ( member @ B @ A22 @ A5 )
% 0.29/1.53 => ( ( member @ A @ B6 @ B5 )
% 0.29/1.53 => ( ( R3 @ A1 @ B6 )
% 0.29/1.53 => ( ( R3 @ A22 @ B6 )
% 0.29/1.53 => ( A1 = A22 ) ) ) ) ) )
% 0.29/1.53 => ( ord_less_eq @ nat @ ( finite_card @ B @ A5 ) @ ( finite_card @ A @ B5 ) ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_197_finite__nat__set__iff__bounded__le,axiom,
% 0.29/1.53 ( ( finite_finite2 @ nat )
% 0.29/1.53 = ( ^ [N3: set @ nat] :
% 0.29/1.53 ? [M: nat] :
% 0.29/1.53 ! [X2: nat] :
% 0.29/1.53 ( ( member @ nat @ X2 @ N3 )
% 0.29/1.53 => ( ord_less_eq @ nat @ X2 @ M ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_198_bounded__nat__set__is__finite,axiom,
% 0.29/1.53 ! [N4: set @ nat,N2: nat] :
% 0.29/1.53 ( ! [X: nat] :
% 0.29/1.53 ( ( member @ nat @ X @ N4 )
% 0.29/1.53 => ( ord_less @ nat @ X @ N2 ) )
% 0.29/1.53 => ( finite_finite2 @ nat @ N4 ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_199_finite__nat__set__iff__bounded,axiom,
% 0.29/1.53 ( ( finite_finite2 @ nat )
% 0.29/1.53 = ( ^ [N3: set @ nat] :
% 0.29/1.53 ? [M: nat] :
% 0.29/1.53 ! [X2: nat] :
% 0.29/1.53 ( ( member @ nat @ X2 @ N3 )
% 0.29/1.53 => ( ord_less @ nat @ X2 @ M ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_200_card__le__inj,axiom,
% 0.29/1.53 ! [B: $tType,A: $tType,A5: set @ A,B5: set @ B] :
% 0.29/1.53 ( ( finite_finite2 @ A @ A5 )
% 0.29/1.53 => ( ( finite_finite2 @ B @ B5 )
% 0.29/1.53 => ( ( ord_less_eq @ nat @ ( finite_card @ A @ A5 ) @ ( finite_card @ B @ B5 ) )
% 0.29/1.53 => ? [F4: A > B] :
% 0.29/1.53 ( ( ord_less_eq @ ( set @ B ) @ ( image @ A @ B @ F4 @ A5 ) @ B5 )
% 0.29/1.53 & ( inj_on @ A @ B @ F4 @ A5 ) ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_201_card__inj__on__le,axiom,
% 0.29/1.53 ! [A: $tType,B: $tType,F: A > B,A5: set @ A,B5: set @ B] :
% 0.29/1.53 ( ( inj_on @ A @ B @ F @ A5 )
% 0.29/1.53 => ( ( ord_less_eq @ ( set @ B ) @ ( image @ A @ B @ F @ A5 ) @ B5 )
% 0.29/1.53 => ( ( finite_finite2 @ B @ B5 )
% 0.29/1.53 => ( ord_less_eq @ nat @ ( finite_card @ A @ A5 ) @ ( finite_card @ B @ B5 ) ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_202_finite__imageI,axiom,
% 0.29/1.53 ! [B: $tType,A: $tType,F3: set @ A,H: A > B] :
% 0.29/1.53 ( ( finite_finite2 @ A @ F3 )
% 0.29/1.53 => ( finite_finite2 @ B @ ( image @ A @ B @ H @ F3 ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_203_all__subset__image,axiom,
% 0.29/1.53 ! [A: $tType,B: $tType,F: B > A,A5: set @ B,P: ( set @ A ) > $o] :
% 0.29/1.53 ( ( ! [B4: set @ A] :
% 0.29/1.53 ( ( ord_less_eq @ ( set @ A ) @ B4 @ ( image @ B @ A @ F @ A5 ) )
% 0.29/1.53 => ( P @ B4 ) ) )
% 0.29/1.53 = ( ! [B4: set @ B] :
% 0.29/1.53 ( ( ord_less_eq @ ( set @ B ) @ B4 @ A5 )
% 0.29/1.53 => ( P @ ( image @ B @ A @ F @ B4 ) ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_204_all__finite__subset__image,axiom,
% 0.29/1.53 ! [A: $tType,B: $tType,F: B > A,A5: set @ B,P: ( set @ A ) > $o] :
% 0.29/1.53 ( ( ! [B4: set @ A] :
% 0.29/1.53 ( ( ( finite_finite2 @ A @ B4 )
% 0.29/1.53 & ( ord_less_eq @ ( set @ A ) @ B4 @ ( image @ B @ A @ F @ A5 ) ) )
% 0.29/1.53 => ( P @ B4 ) ) )
% 0.29/1.53 = ( ! [B4: set @ B] :
% 0.29/1.53 ( ( ( finite_finite2 @ B @ B4 )
% 0.29/1.53 & ( ord_less_eq @ ( set @ B ) @ B4 @ A5 ) )
% 0.29/1.53 => ( P @ ( image @ B @ A @ F @ B4 ) ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_205_ex__finite__subset__image,axiom,
% 0.29/1.53 ! [A: $tType,B: $tType,F: B > A,A5: set @ B,P: ( set @ A ) > $o] :
% 0.29/1.53 ( ( ? [B4: set @ A] :
% 0.29/1.53 ( ( finite_finite2 @ A @ B4 )
% 0.29/1.53 & ( ord_less_eq @ ( set @ A ) @ B4 @ ( image @ B @ A @ F @ A5 ) )
% 0.29/1.53 & ( P @ B4 ) ) )
% 0.29/1.53 = ( ? [B4: set @ B] :
% 0.29/1.53 ( ( finite_finite2 @ B @ B4 )
% 0.29/1.53 & ( ord_less_eq @ ( set @ B ) @ B4 @ A5 )
% 0.29/1.53 & ( P @ ( image @ B @ A @ F @ B4 ) ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_206_finite__subset__image,axiom,
% 0.29/1.53 ! [A: $tType,B: $tType,B5: set @ A,F: B > A,A5: set @ B] :
% 0.29/1.53 ( ( finite_finite2 @ A @ B5 )
% 0.29/1.53 => ( ( ord_less_eq @ ( set @ A ) @ B5 @ ( image @ B @ A @ F @ A5 ) )
% 0.29/1.53 => ? [C6: set @ B] :
% 0.29/1.53 ( ( ord_less_eq @ ( set @ B ) @ C6 @ A5 )
% 0.29/1.53 & ( finite_finite2 @ B @ C6 )
% 0.29/1.53 & ( B5
% 0.29/1.53 = ( image @ B @ A @ F @ C6 ) ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_207_finite__surj,axiom,
% 0.29/1.53 ! [A: $tType,B: $tType,A5: set @ A,B5: set @ B,F: A > B] :
% 0.29/1.53 ( ( finite_finite2 @ A @ A5 )
% 0.29/1.53 => ( ( ord_less_eq @ ( set @ B ) @ B5 @ ( image @ A @ B @ F @ A5 ) )
% 0.29/1.53 => ( finite_finite2 @ B @ B5 ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_208_finite__image__iff,axiom,
% 0.29/1.53 ! [B: $tType,A: $tType,F: A > B,A5: set @ A] :
% 0.29/1.53 ( ( inj_on @ A @ B @ F @ A5 )
% 0.29/1.53 => ( ( finite_finite2 @ B @ ( image @ A @ B @ F @ A5 ) )
% 0.29/1.53 = ( finite_finite2 @ A @ A5 ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_209_finite__imageD,axiom,
% 0.29/1.53 ! [A: $tType,B: $tType,F: B > A,A5: set @ B] :
% 0.29/1.53 ( ( finite_finite2 @ A @ ( image @ B @ A @ F @ A5 ) )
% 0.29/1.53 => ( ( inj_on @ B @ A @ F @ A5 )
% 0.29/1.53 => ( finite_finite2 @ B @ A5 ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_210_card__image,axiom,
% 0.29/1.53 ! [B: $tType,A: $tType,F: A > B,A5: set @ A] :
% 0.29/1.53 ( ( inj_on @ A @ B @ F @ A5 )
% 0.29/1.53 => ( ( finite_card @ B @ ( image @ A @ B @ F @ A5 ) )
% 0.29/1.53 = ( finite_card @ A @ A5 ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_211_finite__surj__inj,axiom,
% 0.29/1.53 ! [A: $tType,A5: set @ A,F: A > A] :
% 0.29/1.53 ( ( finite_finite2 @ A @ A5 )
% 0.29/1.53 => ( ( ord_less_eq @ ( set @ A ) @ A5 @ ( image @ A @ A @ F @ A5 ) )
% 0.29/1.53 => ( inj_on @ A @ A @ F @ A5 ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_212_inj__on__finite,axiom,
% 0.29/1.53 ! [B: $tType,A: $tType,F: A > B,A5: set @ A,B5: set @ B] :
% 0.29/1.53 ( ( inj_on @ A @ B @ F @ A5 )
% 0.29/1.53 => ( ( ord_less_eq @ ( set @ B ) @ ( image @ A @ B @ F @ A5 ) @ B5 )
% 0.29/1.53 => ( ( finite_finite2 @ B @ B5 )
% 0.29/1.53 => ( finite_finite2 @ A @ A5 ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_213_endo__inj__surj,axiom,
% 0.29/1.53 ! [A: $tType,A5: set @ A,F: A > A] :
% 0.29/1.53 ( ( finite_finite2 @ A @ A5 )
% 0.29/1.53 => ( ( ord_less_eq @ ( set @ A ) @ ( image @ A @ A @ F @ A5 ) @ A5 )
% 0.29/1.53 => ( ( inj_on @ A @ A @ F @ A5 )
% 0.29/1.53 => ( ( image @ A @ A @ F @ A5 )
% 0.29/1.53 = A5 ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_214_card__image__le,axiom,
% 0.29/1.53 ! [B: $tType,A: $tType,A5: set @ A,F: A > B] :
% 0.29/1.53 ( ( finite_finite2 @ A @ A5 )
% 0.29/1.53 => ( ord_less_eq @ nat @ ( finite_card @ B @ ( image @ A @ B @ F @ A5 ) ) @ ( finite_card @ A @ A5 ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_215_eq__card__imp__inj__on,axiom,
% 0.29/1.53 ! [B: $tType,A: $tType,A5: set @ A,F: A > B] :
% 0.29/1.53 ( ( finite_finite2 @ A @ A5 )
% 0.29/1.53 => ( ( ( finite_card @ B @ ( image @ A @ B @ F @ A5 ) )
% 0.29/1.53 = ( finite_card @ A @ A5 ) )
% 0.29/1.53 => ( inj_on @ A @ B @ F @ A5 ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_216_inj__on__iff__eq__card,axiom,
% 0.29/1.53 ! [B: $tType,A: $tType,A5: set @ A,F: A > B] :
% 0.29/1.53 ( ( finite_finite2 @ A @ A5 )
% 0.29/1.53 => ( ( inj_on @ A @ B @ F @ A5 )
% 0.29/1.53 = ( ( finite_card @ B @ ( image @ A @ B @ F @ A5 ) )
% 0.29/1.53 = ( finite_card @ A @ A5 ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_217_pigeonhole,axiom,
% 0.29/1.53 ! [A: $tType,B: $tType,F: B > A,A5: set @ B] :
% 0.29/1.53 ( ( ord_less @ nat @ ( finite_card @ A @ ( image @ B @ A @ F @ A5 ) ) @ ( finite_card @ B @ A5 ) )
% 0.29/1.53 => ~ ( inj_on @ B @ A @ F @ A5 ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_218_surj__card__le,axiom,
% 0.29/1.53 ! [B: $tType,A: $tType,A5: set @ A,B5: set @ B,F: A > B] :
% 0.29/1.53 ( ( finite_finite2 @ A @ A5 )
% 0.29/1.53 => ( ( ord_less_eq @ ( set @ B ) @ B5 @ ( image @ A @ B @ F @ A5 ) )
% 0.29/1.53 => ( ord_less_eq @ nat @ ( finite_card @ B @ B5 ) @ ( finite_card @ A @ A5 ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_219_surjective__iff__injective__gen,axiom,
% 0.29/1.53 ! [B: $tType,A: $tType,S: set @ A,T2: set @ B,F: A > B] :
% 0.29/1.53 ( ( finite_finite2 @ A @ S )
% 0.29/1.53 => ( ( finite_finite2 @ B @ T2 )
% 0.29/1.53 => ( ( ( finite_card @ A @ S )
% 0.29/1.53 = ( finite_card @ B @ T2 ) )
% 0.29/1.53 => ( ( ord_less_eq @ ( set @ B ) @ ( image @ A @ B @ F @ S ) @ T2 )
% 0.29/1.53 => ( ( ! [X2: B] :
% 0.29/1.53 ( ( member @ B @ X2 @ T2 )
% 0.29/1.53 => ? [Y3: A] :
% 0.29/1.53 ( ( member @ A @ Y3 @ S )
% 0.29/1.53 & ( ( F @ Y3 )
% 0.29/1.53 = X2 ) ) ) )
% 0.29/1.53 = ( inj_on @ A @ B @ F @ S ) ) ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_220_card__bij__eq,axiom,
% 0.29/1.53 ! [A: $tType,B: $tType,F: A > B,A5: set @ A,B5: set @ B,G: B > A] :
% 0.29/1.53 ( ( inj_on @ A @ B @ F @ A5 )
% 0.29/1.53 => ( ( ord_less_eq @ ( set @ B ) @ ( image @ A @ B @ F @ A5 ) @ B5 )
% 0.29/1.53 => ( ( inj_on @ B @ A @ G @ B5 )
% 0.29/1.53 => ( ( ord_less_eq @ ( set @ A ) @ ( image @ B @ A @ G @ B5 ) @ A5 )
% 0.29/1.53 => ( ( finite_finite2 @ A @ A5 )
% 0.29/1.53 => ( ( finite_finite2 @ B @ B5 )
% 0.29/1.53 => ( ( finite_card @ A @ A5 )
% 0.29/1.53 = ( finite_card @ B @ B5 ) ) ) ) ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_221_inj__on__iff__card__le,axiom,
% 0.29/1.53 ! [A: $tType,B: $tType,A5: set @ A,B5: set @ B] :
% 0.29/1.53 ( ( finite_finite2 @ A @ A5 )
% 0.29/1.53 => ( ( finite_finite2 @ B @ B5 )
% 0.29/1.53 => ( ( ? [F2: A > B] :
% 0.29/1.53 ( ( inj_on @ A @ B @ F2 @ A5 )
% 0.29/1.53 & ( ord_less_eq @ ( set @ B ) @ ( image @ A @ B @ F2 @ A5 ) @ B5 ) ) )
% 0.29/1.53 = ( ord_less_eq @ nat @ ( finite_card @ A @ A5 ) @ ( finite_card @ B @ B5 ) ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_222_inj__on__image__Fpow,axiom,
% 0.29/1.53 ! [B: $tType,A: $tType,F: A > B,A5: set @ A] :
% 0.29/1.53 ( ( inj_on @ A @ B @ F @ A5 )
% 0.29/1.53 => ( inj_on @ ( set @ A ) @ ( set @ B ) @ ( image @ A @ B @ F ) @ ( finite_Fpow @ A @ A5 ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_223_image__Fpow__mono,axiom,
% 0.29/1.53 ! [B: $tType,A: $tType,F: B > A,A5: set @ B,B5: set @ A] :
% 0.29/1.53 ( ( ord_less_eq @ ( set @ A ) @ ( image @ B @ A @ F @ A5 ) @ B5 )
% 0.29/1.53 => ( ord_less_eq @ ( set @ ( set @ A ) ) @ ( image @ ( set @ B ) @ ( set @ A ) @ ( image @ B @ A @ F ) @ ( finite_Fpow @ B @ A5 ) ) @ ( finite_Fpow @ A @ B5 ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_224_Fpow__mono,axiom,
% 0.29/1.53 ! [A: $tType,A5: set @ A,B5: set @ A] :
% 0.29/1.53 ( ( ord_less_eq @ ( set @ A ) @ A5 @ B5 )
% 0.29/1.53 => ( ord_less_eq @ ( set @ ( set @ A ) ) @ ( finite_Fpow @ A @ A5 ) @ ( finite_Fpow @ A @ B5 ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_225_card__ge__0__finite,axiom,
% 0.29/1.53 ! [A: $tType,A5: set @ A] :
% 0.29/1.53 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( finite_card @ A @ A5 ) )
% 0.29/1.53 => ( finite_finite2 @ A @ A5 ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_226_greaterThanLessThan__subseteq__greaterThanLessThan,axiom,
% 0.29/1.53 ! [A: $tType] :
% 0.29/1.53 ( ( dense_linorder @ A )
% 0.29/1.53 => ! [A2: A,B2: A,C: A,D3: A] :
% 0.29/1.53 ( ( ord_less_eq @ ( set @ A ) @ ( set_or578182835ssThan @ A @ A2 @ B2 ) @ ( set_or578182835ssThan @ A @ C @ D3 ) )
% 0.29/1.53 = ( ( ord_less @ A @ A2 @ B2 )
% 0.29/1.53 => ( ( ord_less_eq @ A @ C @ A2 )
% 0.29/1.53 & ( ord_less_eq @ A @ B2 @ D3 ) ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_227_finite__greaterThanLessThan,axiom,
% 0.29/1.53 ! [L: nat,U4: nat] : ( finite_finite2 @ nat @ ( set_or578182835ssThan @ nat @ L @ U4 ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_228_bot__nat__0_Onot__eq__extremum,axiom,
% 0.29/1.53 ! [A2: nat] :
% 0.29/1.53 ( ( A2
% 0.29/1.53 != ( zero_zero @ nat ) )
% 0.29/1.53 = ( ord_less @ nat @ ( zero_zero @ nat ) @ A2 ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_229_less__nat__zero__code,axiom,
% 0.29/1.53 ! [N2: nat] :
% 0.29/1.53 ~ ( ord_less @ nat @ N2 @ ( zero_zero @ nat ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_230_neq0__conv,axiom,
% 0.29/1.53 ! [N2: nat] :
% 0.29/1.53 ( ( N2
% 0.29/1.53 != ( zero_zero @ nat ) )
% 0.29/1.53 = ( ord_less @ nat @ ( zero_zero @ nat ) @ N2 ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_231_le0,axiom,
% 0.29/1.53 ! [N2: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ N2 ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_232_bot__nat__0_Oextremum,axiom,
% 0.29/1.53 ! [A2: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A2 ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_233_greaterThanLessThan__iff,axiom,
% 0.29/1.53 ! [A: $tType] :
% 0.29/1.53 ( ( ord @ A )
% 0.29/1.53 => ! [I: A,L: A,U4: A] :
% 0.29/1.53 ( ( member @ A @ I @ ( set_or578182835ssThan @ A @ L @ U4 ) )
% 0.29/1.53 = ( ( ord_less @ A @ L @ I )
% 0.29/1.53 & ( ord_less @ A @ I @ U4 ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_234_card_Oinfinite,axiom,
% 0.29/1.53 ! [A: $tType,A5: set @ A] :
% 0.29/1.53 ( ~ ( finite_finite2 @ A @ A5 )
% 0.29/1.53 => ( ( finite_card @ A @ A5 )
% 0.29/1.53 = ( zero_zero @ nat ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_235_infinite__Ioo__iff,axiom,
% 0.29/1.53 ! [A: $tType] :
% 0.29/1.53 ( ( dense_linorder @ A )
% 0.29/1.53 => ! [A2: A,B2: A] :
% 0.29/1.53 ( ( ~ ( finite_finite2 @ A @ ( set_or578182835ssThan @ A @ A2 @ B2 ) ) )
% 0.29/1.53 = ( ord_less @ A @ A2 @ B2 ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_236_less__eq__nat_Osimps_I1_J,axiom,
% 0.29/1.53 ! [N2: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ N2 ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_237_le__0__eq,axiom,
% 0.29/1.53 ! [N2: nat] :
% 0.29/1.53 ( ( ord_less_eq @ nat @ N2 @ ( zero_zero @ nat ) )
% 0.29/1.53 = ( N2
% 0.29/1.53 = ( zero_zero @ nat ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_238_bot__nat__0_Oextremum__unique,axiom,
% 0.29/1.53 ! [A2: nat] :
% 0.29/1.53 ( ( ord_less_eq @ nat @ A2 @ ( zero_zero @ nat ) )
% 0.29/1.53 = ( A2
% 0.29/1.53 = ( zero_zero @ nat ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_239_bot__nat__0_Oextremum__uniqueI,axiom,
% 0.29/1.53 ! [A2: nat] :
% 0.29/1.53 ( ( ord_less_eq @ nat @ A2 @ ( zero_zero @ nat ) )
% 0.29/1.53 => ( A2
% 0.29/1.53 = ( zero_zero @ nat ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_240_ex__least__nat__le,axiom,
% 0.29/1.53 ! [P: nat > $o,N2: nat] :
% 0.29/1.53 ( ( P @ N2 )
% 0.29/1.53 => ( ~ ( P @ ( zero_zero @ nat ) )
% 0.29/1.53 => ? [K: nat] :
% 0.29/1.53 ( ( ord_less_eq @ nat @ K @ N2 )
% 0.29/1.53 & ! [I2: nat] :
% 0.29/1.53 ( ( ord_less @ nat @ I2 @ K )
% 0.29/1.53 => ~ ( P @ I2 ) )
% 0.29/1.53 & ( P @ K ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_241_infinite__descent0__measure,axiom,
% 0.29/1.53 ! [A: $tType,V5: A > nat,P: A > $o,X3: A] :
% 0.29/1.53 ( ! [X: A] :
% 0.29/1.53 ( ( ( V5 @ X )
% 0.29/1.53 = ( zero_zero @ nat ) )
% 0.29/1.53 => ( P @ X ) )
% 0.29/1.53 => ( ! [X: A] :
% 0.29/1.53 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( V5 @ X ) )
% 0.29/1.53 => ( ~ ( P @ X )
% 0.29/1.53 => ? [Y5: A] :
% 0.29/1.53 ( ( ord_less @ nat @ ( V5 @ Y5 ) @ ( V5 @ X ) )
% 0.29/1.53 & ~ ( P @ Y5 ) ) ) )
% 0.29/1.53 => ( P @ X3 ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_242_bot__nat__0_Oextremum__strict,axiom,
% 0.29/1.53 ! [A2: nat] :
% 0.29/1.53 ~ ( ord_less @ nat @ A2 @ ( zero_zero @ nat ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_243_infinite__descent0,axiom,
% 0.29/1.53 ! [P: nat > $o,N2: nat] :
% 0.29/1.53 ( ( P @ ( zero_zero @ nat ) )
% 0.29/1.53 => ( ! [N5: nat] :
% 0.29/1.53 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N5 )
% 0.29/1.53 => ( ~ ( P @ N5 )
% 0.29/1.53 => ? [M2: nat] :
% 0.29/1.53 ( ( ord_less @ nat @ M2 @ N5 )
% 0.29/1.53 & ~ ( P @ M2 ) ) ) )
% 0.29/1.53 => ( P @ N2 ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_244_gr__implies__not0,axiom,
% 0.29/1.53 ! [M3: nat,N2: nat] :
% 0.29/1.53 ( ( ord_less @ nat @ M3 @ N2 )
% 0.29/1.53 => ( N2
% 0.29/1.53 != ( zero_zero @ nat ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_245_less__zeroE,axiom,
% 0.29/1.53 ! [N2: nat] :
% 0.29/1.53 ~ ( ord_less @ nat @ N2 @ ( zero_zero @ nat ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_246_not__less0,axiom,
% 0.29/1.53 ! [N2: nat] :
% 0.29/1.53 ~ ( ord_less @ nat @ N2 @ ( zero_zero @ nat ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_247_not__gr0,axiom,
% 0.29/1.53 ! [N2: nat] :
% 0.29/1.53 ( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ N2 ) )
% 0.29/1.53 = ( N2
% 0.29/1.53 = ( zero_zero @ nat ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_248_gr0I,axiom,
% 0.29/1.53 ! [N2: nat] :
% 0.29/1.53 ( ( N2
% 0.29/1.53 != ( zero_zero @ nat ) )
% 0.29/1.53 => ( ord_less @ nat @ ( zero_zero @ nat ) @ N2 ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_249_infinite__Ioo,axiom,
% 0.29/1.53 ! [A: $tType] :
% 0.29/1.53 ( ( dense_linorder @ A )
% 0.29/1.53 => ! [A2: A,B2: A] :
% 0.29/1.53 ( ( ord_less @ A @ A2 @ B2 )
% 0.29/1.53 => ~ ( finite_finite2 @ A @ ( set_or578182835ssThan @ A @ A2 @ B2 ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_250_not__gr__zero,axiom,
% 0.29/1.53 ! [A: $tType] :
% 0.29/1.53 ( ( canoni770627133id_add @ A )
% 0.29/1.53 => ! [N2: A] :
% 0.29/1.53 ( ( ~ ( ord_less @ A @ ( zero_zero @ A ) @ N2 ) )
% 0.29/1.53 = ( N2
% 0.29/1.53 = ( zero_zero @ A ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_251_le__zero__eq,axiom,
% 0.29/1.53 ! [A: $tType] :
% 0.29/1.53 ( ( canoni770627133id_add @ A )
% 0.29/1.53 => ! [N2: A] :
% 0.29/1.53 ( ( ord_less_eq @ A @ N2 @ ( zero_zero @ A ) )
% 0.29/1.53 = ( N2
% 0.29/1.53 = ( zero_zero @ A ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_252_RepFun__0,axiom,
% 0.29/1.53 ! [F: hF_Mirabelle_hf > hF_Mirabelle_hf] :
% 0.29/1.53 ( ( hF_Mirabelle_RepFun @ ( zero_zero @ hF_Mirabelle_hf ) @ F )
% 0.29/1.53 = ( zero_zero @ hF_Mirabelle_hf ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_253_HUnion__hempty,axiom,
% 0.29/1.53 ( ( hF_Mirabelle_HUnion @ ( zero_zero @ hF_Mirabelle_hf ) )
% 0.29/1.53 = ( zero_zero @ hF_Mirabelle_hf ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_254_Replace__0,axiom,
% 0.29/1.53 ! [R: hF_Mirabelle_hf > hF_Mirabelle_hf > $o] :
% 0.29/1.53 ( ( hF_Mirabelle_Replace @ ( zero_zero @ hF_Mirabelle_hf ) @ R )
% 0.29/1.53 = ( zero_zero @ hF_Mirabelle_hf ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.29/1.53 ! [A9: $tType,A10: $tType] :
% 0.29/1.53 ( ( preorder @ A10 )
% 0.29/1.53 => ( preorder @ ( A9 > A10 ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(tcon_fun___Finite__Set_Ofinite,axiom,
% 0.29/1.53 ! [A9: $tType,A10: $tType] :
% 0.29/1.53 ( ( ( finite_finite @ A9 )
% 0.29/1.53 & ( finite_finite @ A10 ) )
% 0.29/1.53 => ( finite_finite @ ( A9 > A10 ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.29/1.53 ! [A9: $tType,A10: $tType] :
% 0.29/1.53 ( ( order @ A10 )
% 0.29/1.53 => ( order @ ( A9 > A10 ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(tcon_fun___Orderings_Oord,axiom,
% 0.29/1.53 ! [A9: $tType,A10: $tType] :
% 0.29/1.53 ( ( ord @ A10 )
% 0.29/1.53 => ( ord @ ( A9 > A10 ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(tcon_Nat_Onat___Conditionally__Complete__Lattices_Oconditionally__complete__linorder,axiom,
% 0.29/1.53 condit1037483654norder @ nat ).
% 0.29/1.53
% 0.29/1.53 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add,axiom,
% 0.29/1.53 canoni770627133id_add @ nat ).
% 0.29/1.53
% 0.29/1.53 thf(tcon_Nat_Onat___Orderings_Owellorder,axiom,
% 0.29/1.53 wellorder @ nat ).
% 0.29/1.53
% 0.29/1.53 thf(tcon_Nat_Onat___Orderings_Opreorder_1,axiom,
% 0.29/1.53 preorder @ nat ).
% 0.29/1.53
% 0.29/1.53 thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 0.29/1.53 linorder @ nat ).
% 0.29/1.53
% 0.29/1.53 thf(tcon_Nat_Onat___Orderings_Ono__top,axiom,
% 0.29/1.53 no_top @ nat ).
% 0.29/1.53
% 0.29/1.53 thf(tcon_Nat_Onat___Orderings_Oorder_2,axiom,
% 0.29/1.53 order @ nat ).
% 0.29/1.53
% 0.29/1.53 thf(tcon_Nat_Onat___Orderings_Oord_3,axiom,
% 0.29/1.53 ord @ nat ).
% 0.29/1.53
% 0.29/1.53 thf(tcon_Set_Oset___Orderings_Opreorder_4,axiom,
% 0.29/1.53 ! [A9: $tType] : ( preorder @ ( set @ A9 ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(tcon_Set_Oset___Finite__Set_Ofinite_5,axiom,
% 0.29/1.53 ! [A9: $tType] :
% 0.29/1.53 ( ( finite_finite @ A9 )
% 0.29/1.53 => ( finite_finite @ ( set @ A9 ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(tcon_Set_Oset___Orderings_Oorder_6,axiom,
% 0.29/1.53 ! [A9: $tType] : ( order @ ( set @ A9 ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(tcon_Set_Oset___Orderings_Oord_7,axiom,
% 0.29/1.53 ! [A9: $tType] : ( ord @ ( set @ A9 ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(tcon_HOL_Obool___Orderings_Opreorder_8,axiom,
% 0.29/1.53 preorder @ $o ).
% 0.29/1.53
% 0.29/1.53 thf(tcon_HOL_Obool___Orderings_Olinorder_9,axiom,
% 0.29/1.53 linorder @ $o ).
% 0.29/1.53
% 0.29/1.53 thf(tcon_HOL_Obool___Finite__Set_Ofinite_10,axiom,
% 0.29/1.53 finite_finite @ $o ).
% 0.29/1.53
% 0.29/1.53 thf(tcon_HOL_Obool___Orderings_Oorder_11,axiom,
% 0.29/1.53 order @ $o ).
% 0.29/1.53
% 0.29/1.53 thf(tcon_HOL_Obool___Orderings_Oord_12,axiom,
% 0.29/1.53 ord @ $o ).
% 0.29/1.53
% 0.29/1.53 thf(tcon_HF__Mirabelle__fsbjehakzm_Ohf___Orderings_Opreorder_13,axiom,
% 0.29/1.53 preorder @ hF_Mirabelle_hf ).
% 0.29/1.53
% 0.29/1.53 thf(tcon_HF__Mirabelle__fsbjehakzm_Ohf___Orderings_Oorder_14,axiom,
% 0.29/1.53 order @ hF_Mirabelle_hf ).
% 0.29/1.53
% 0.29/1.53 thf(tcon_HF__Mirabelle__fsbjehakzm_Ohf___Orderings_Oord_15,axiom,
% 0.29/1.53 ord @ hF_Mirabelle_hf ).
% 0.29/1.53
% 0.29/1.53 thf(conj_0,hypothesis,
% 0.29/1.53 ! [X6: hF_Mirabelle_hf] :
% 0.29/1.53 ( ( hF_Mirabelle_hmem @ X6 @ a )
% 0.29/1.53 => ( hF_Mirabelle_hmem @ X6 @ b ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(conj_1,conjecture,
% 0.29/1.53 ord_less_eq @ hF_Mirabelle_hf @ a @ b ).
% 0.29/1.53 ------------------------
% 0.29/1.55 % (14728)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_14628 for (2999ds/4Mi)
% 0.29/1.55 % (14727)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_14628 for (2999ds/183Mi)
% 0.29/1.55 % (14729)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_14628 for (2999ds/27Mi)
% 0.29/1.56 % (14731)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_14628 for (2999ds/2Mi)
% 0.29/1.56 % (14728)Instruction limit reached!
% 0.29/1.56 % (14728)------------------------------
% 0.29/1.56 % (14728)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.29/1.56 % (14728)Termination reason: Unknown
% 0.29/1.56 % (14728)Termination phase: shuffling
% 0.29/1.56
% 0.29/1.56 % (14728)Memory used [KB]: 1407
% 0.29/1.56 % (14728)Time elapsed: 0.003 s
% 0.29/1.56 % (14728)Instructions burned: 5 (million)
% 0.29/1.56 % (14728)------------------------------
% 0.29/1.56 % (14728)------------------------------
% 0.29/1.56 % (14731)Instruction limit reached!
% 0.29/1.56 % (14731)------------------------------
% 0.29/1.56 % (14731)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.29/1.56 % (14731)Termination reason: Unknown
% 0.29/1.56 % (14731)Termination phase: shuffling
% 0.29/1.56
% 0.29/1.56 % (14731)Memory used [KB]: 1407
% 0.29/1.56 % (14731)Time elapsed: 0.002 s
% 0.29/1.56 % (14731)Instructions burned: 3 (million)
% 0.29/1.56 % (14731)------------------------------
% 0.29/1.56 % (14731)------------------------------
% 0.29/1.56 % (14730)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_14628 for (2999ds/2Mi)
% 0.29/1.56 % (14732)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_14628 for (2999ds/275Mi)
% 0.29/1.56 % (14733)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_14628 for (2999ds/18Mi)
% 0.29/1.56 % (14729)Instruction limit reached!
% 0.29/1.56 % (14729)------------------------------
% 0.29/1.56 % (14729)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.29/1.56 % (14729)Termination reason: Unknown
% 0.29/1.56 % (14729)Termination phase: Property scanning
% 0.29/1.56
% 0.29/1.56 % (14729)Memory used [KB]: 1918
% 0.29/1.56 % (14729)Time elapsed: 0.010 s
% 0.29/1.56 % (14729)Instructions burned: 27 (million)
% 0.29/1.56 % (14729)------------------------------
% 0.29/1.56 % (14729)------------------------------
% 0.29/1.56 % (14730)Instruction limit reached!
% 0.29/1.56 % (14730)------------------------------
% 0.29/1.56 % (14730)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.29/1.56 % (14730)Termination reason: Unknown
% 0.29/1.56 % (14730)Termination phase: shuffling
% 0.29/1.56
% 0.29/1.56 % (14730)Memory used [KB]: 1407
% 0.29/1.56 % (14730)Time elapsed: 0.004 s
% 0.29/1.56 % (14730)Instructions burned: 3 (million)
% 0.29/1.56 % (14730)------------------------------
% 0.29/1.56 % (14730)------------------------------
% 0.29/1.57 % (14734)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_14628 for (2999ds/3Mi)
% 0.29/1.57 % (14734)Instruction limit reached!
% 0.29/1.57 % (14734)------------------------------
% 0.29/1.57 % (14734)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.29/1.57 % (14735)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_14628 for (2999ds/37Mi)
% 0.29/1.57 % (14734)Termination reason: Unknown
% 0.29/1.57 % (14734)Termination phase: shuffling
% 0.29/1.57
% 0.29/1.57 % (14734)Memory used [KB]: 1407
% 0.29/1.57 % (14734)Time elapsed: 0.002 s
% 0.29/1.57 % (14734)Instructions burned: 3 (million)
% 0.29/1.57 % (14734)------------------------------
% 0.29/1.57 % (14734)------------------------------
% 0.29/1.57 % (14736)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_14628 for (2999ds/15Mi)
% 0.29/1.57 % (14733)Instruction limit reached!
% 0.29/1.57 % (14733)------------------------------
% 0.29/1.57 % (14733)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.29/1.57 % (14733)Termination reason: Unknown
% 0.29/1.57 % (14733)Termination phase: shuffling
% 0.29/1.57
% 0.29/1.57 % (14733)Memory used [KB]: 1791
% 0.29/1.57 % (14733)Time elapsed: 0.014 s
% 0.29/1.57 % (14733)Instructions burned: 19 (million)
% 0.29/1.57 % (14733)------------------------------
% 0.29/1.57 % (14733)------------------------------
% 0.29/1.58 % (14738)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_14628 for (2999ds/1041Mi)
% 0.29/1.58 % (14736)Instruction limit reached!
% 0.29/1.58 % (14736)------------------------------
% 0.29/1.58 % (14736)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.29/1.58 % (14736)Termination reason: Unknown
% 0.29/1.58 % (14736)Termination phase: shuffling
% 0.29/1.58
% 0.29/1.58 % (14736)Memory used [KB]: 1791
% 0.29/1.58 % (14736)Time elapsed: 0.006 s
% 0.29/1.58 % (14736)Instructions burned: 15 (million)
% 0.29/1.58 % (14736)------------------------------
% 0.29/1.58 % (14736)------------------------------
% 0.29/1.58 % (14735)Instruction limit reached!
% 0.29/1.58 % (14735)------------------------------
% 0.29/1.58 % (14735)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.29/1.58 % (14735)Termination reason: Unknown
% 0.29/1.58 % (14735)Termination phase: shuffling
% 0.29/1.58
% 0.29/1.58 % (14735)Memory used [KB]: 2174
% 0.29/1.58 % (14735)Time elapsed: 0.013 s
% 0.29/1.58 % (14735)Instructions burned: 38 (million)
% 0.29/1.58 % (14735)------------------------------
% 0.29/1.58 % (14735)------------------------------
% 0.29/1.58 % (14737)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_14628 for (2999ds/3Mi)
% 0.29/1.58 % (14737)Instruction limit reached!
% 0.29/1.58 % (14737)------------------------------
% 0.29/1.58 % (14737)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.29/1.58 % (14737)Termination reason: Unknown
% 0.29/1.58 % (14737)Termination phase: shuffling
% 0.29/1.58
% 0.29/1.58 % (14737)Memory used [KB]: 1407
% 0.29/1.58 % (14737)Time elapsed: 0.003 s
% 0.29/1.58 % (14737)Instructions burned: 3 (million)
% 0.29/1.58 % (14737)------------------------------
% 0.29/1.58 % (14737)------------------------------
% 0.29/1.59 % (14740)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_14628 for (2999ds/16Mi)
% 0.29/1.59 % (14741)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_14628 for (2999ds/3Mi)
% 0.29/1.59 % (14741)Instruction limit reached!
% 0.29/1.59 % (14741)------------------------------
% 0.29/1.59 % (14741)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.29/1.59 % (14741)Termination reason: Unknown
% 0.29/1.59 % (14741)Termination phase: shuffling
% 0.29/1.59
% 0.29/1.59 % (14741)Memory used [KB]: 1407
% 0.29/1.59 % (14741)Time elapsed: 0.003 s
% 0.29/1.59 % (14741)Instructions burned: 3 (million)
% 0.29/1.59 % (14741)------------------------------
% 0.29/1.59 % (14741)------------------------------
% 0.29/1.59 % (14740)Instruction limit reached!
% 0.29/1.59 % (14740)------------------------------
% 0.29/1.59 % (14740)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.29/1.59 % (14740)Termination reason: Unknown
% 0.29/1.59 % (14740)Termination phase: shuffling
% 0.29/1.59
% 0.29/1.59 % (14740)Memory used [KB]: 1791
% 0.29/1.59 % (14740)Time elapsed: 0.006 s
% 0.29/1.59 % (14740)Instructions burned: 16 (million)
% 0.29/1.59 % (14740)------------------------------
% 0.29/1.59 % (14740)------------------------------
% 0.29/1.59 % (14739)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_14628 for (2999ds/7Mi)
% 0.29/1.59 % (14742)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_14628 for (2999ds/3Mi)
% 0.29/1.59 % (14742)Instruction limit reached!
% 0.29/1.59 % (14742)------------------------------
% 0.29/1.59 % (14742)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.29/1.59 % (14742)Termination reason: Unknown
% 0.29/1.59 % (14742)Termination phase: shuffling
% 0.29/1.59
% 0.29/1.59 % (14742)Memory used [KB]: 1407
% 0.29/1.59 % (14742)Time elapsed: 0.003 s
% 0.29/1.59 % (14742)Instructions burned: 5 (million)
% 0.29/1.59 % (14742)------------------------------
% 0.29/1.59 % (14742)------------------------------
% 2.85/1.60 % (14739)Instruction limit reached!
% 2.85/1.60 % (14739)------------------------------
% 2.85/1.60 % (14739)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.60 % (14739)Termination reason: Unknown
% 2.85/1.60 % (14739)Termination phase: shuffling
% 2.85/1.60
% 2.85/1.60 % (14739)Memory used [KB]: 1535
% 2.85/1.60 % (14739)Time elapsed: 0.006 s
% 2.85/1.60 % (14739)Instructions burned: 7 (million)
% 2.85/1.60 % (14739)------------------------------
% 2.85/1.60 % (14739)------------------------------
% 2.85/1.60 % (14743)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_14628 for (2999ds/7Mi)
% 2.85/1.60 % (14744)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_14628 for (2999ds/3Mi)
% 2.85/1.60 % (14744)Instruction limit reached!
% 2.85/1.60 % (14744)------------------------------
% 2.85/1.60 % (14744)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.60 % (14744)Termination reason: Unknown
% 2.85/1.60 % (14744)Termination phase: shuffling
% 2.85/1.60
% 2.85/1.60 % (14744)Memory used [KB]: 1407
% 2.85/1.60 % (14744)Time elapsed: 0.002 s
% 2.85/1.60 % (14744)Instructions burned: 4 (million)
% 2.85/1.60 % (14744)------------------------------
% 2.85/1.60 % (14744)------------------------------
% 2.85/1.60 % (14743)Instruction limit reached!
% 2.85/1.60 % (14743)------------------------------
% 2.85/1.60 % (14743)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.60 % (14743)Termination reason: Unknown
% 2.85/1.60 % (14743)Termination phase: shuffling
% 2.85/1.60
% 2.85/1.60 % (14743)Memory used [KB]: 1535
% 2.85/1.60 % (14743)Time elapsed: 0.005 s
% 2.85/1.60 % (14743)Instructions burned: 9 (million)
% 2.85/1.60 % (14743)------------------------------
% 2.85/1.60 % (14743)------------------------------
% 2.85/1.60 % (14745)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_14628 for (2999ds/4Mi)
% 2.85/1.61 % (14745)Instruction limit reached!
% 2.85/1.61 % (14745)------------------------------
% 2.85/1.61 % (14745)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.61 % (14745)Termination reason: Unknown
% 2.85/1.61 % (14745)Termination phase: shuffling
% 2.85/1.61
% 2.85/1.61 % (14745)Memory used [KB]: 1535
% 2.85/1.61 % (14745)Time elapsed: 0.003 s
% 2.85/1.61 % (14727)Instruction limit reached!
% 2.85/1.61 % (14727)------------------------------
% 2.85/1.61 % (14727)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.61 % (14727)Termination reason: Unknown
% 2.85/1.61 % (14727)Termination phase: Saturation
% 2.85/1.61
% 2.85/1.61 % (14727)Memory used [KB]: 7419
% 2.85/1.61 % (14727)Time elapsed: 0.053 s
% 2.85/1.61 % (14727)Instructions burned: 186 (million)
% 2.85/1.61 % (14727)------------------------------
% 2.85/1.61 % (14727)------------------------------
% 2.85/1.61 % (14745)Instructions burned: 6 (million)
% 2.85/1.61 % (14745)------------------------------
% 2.85/1.61 % (14745)------------------------------
% 2.85/1.61 % (14747)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_14628 for (2999ds/710Mi)
% 2.85/1.61 % (14748)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_14628 for (2999ds/6Mi)
% 2.85/1.61 % (14746)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_14628 for (2999ds/18Mi)
% 2.85/1.62 % (14748)Instruction limit reached!
% 2.85/1.62 % (14748)------------------------------
% 2.85/1.62 % (14748)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.62 % (14748)Termination reason: Unknown
% 2.85/1.62 % (14748)Termination phase: shuffling
% 2.85/1.62
% 2.85/1.62 % (14748)Memory used [KB]: 1535
% 2.85/1.62 % (14748)Time elapsed: 0.004 s
% 2.85/1.62 % (14748)Instructions burned: 6 (million)
% 2.85/1.62 % (14748)------------------------------
% 2.85/1.62 % (14748)------------------------------
% 2.85/1.62 % (14749)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_14628 for (2999ds/902Mi)
% 2.85/1.62 % (14750)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_14628 for (2999ds/21Mi)
% 2.85/1.62 % (14750)Instruction limit reached!
% 2.85/1.62 % (14750)------------------------------
% 2.85/1.62 % (14750)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.62 % (14750)Termination reason: Unknown
% 2.85/1.62 % (14750)Termination phase: shuffling
% 2.85/1.62
% 2.85/1.62 % (14750)Memory used [KB]: 1918
% 2.85/1.62 % (14750)Time elapsed: 0.008 s
% 2.85/1.62 % (14750)Instructions burned: 21 (million)
% 2.85/1.62 % (14750)------------------------------
% 2.85/1.62 % (14750)------------------------------
% 2.85/1.63 % (14746)Instruction limit reached!
% 2.85/1.63 % (14746)------------------------------
% 2.85/1.63 % (14746)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.63 % (14746)Termination reason: Unknown
% 2.85/1.63 % (14746)Termination phase: shuffling
% 2.85/1.63
% 2.85/1.63 % (14746)Memory used [KB]: 1791
% 2.85/1.63 % (14746)Time elapsed: 0.013 s
% 2.85/1.63 % (14746)Instructions burned: 18 (million)
% 2.85/1.63 % (14746)------------------------------
% 2.85/1.63 % (14746)------------------------------
% 2.85/1.63 % (14751)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_14628 for (2999ds/5Mi)
% 2.85/1.63 % (14751)Instruction limit reached!
% 2.85/1.63 % (14751)------------------------------
% 2.85/1.63 % (14751)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.63 % (14751)Termination reason: Unknown
% 2.85/1.63 % (14751)Termination phase: shuffling
% 2.85/1.63
% 2.85/1.63 % (14751)Memory used [KB]: 1535
% 2.85/1.63 % (14751)Time elapsed: 0.004 s
% 2.85/1.63 % (14751)Instructions burned: 7 (million)
% 2.85/1.63 % (14751)------------------------------
% 2.85/1.63 % (14751)------------------------------
% 2.85/1.63 % (14752)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_14628 for (2999ds/6Mi)
% 2.85/1.63 % (14752)Instruction limit reached!
% 2.85/1.63 % (14752)------------------------------
% 2.85/1.63 % (14752)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.63 % (14752)Termination reason: Unknown
% 2.85/1.63 % (14752)Termination phase: shuffling
% 2.85/1.63
% 2.85/1.63 % (14752)Memory used [KB]: 1535
% 2.85/1.63 % (14752)Time elapsed: 0.003 s
% 2.85/1.63 % (14752)Instructions burned: 8 (million)
% 2.85/1.63 % (14752)------------------------------
% 2.85/1.63 % (14752)------------------------------
% 2.85/1.64 % (14754)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_14628 for (2998ds/779Mi)
% 2.85/1.64 % (14753)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_14628 for (2998ds/377Mi)
% 2.85/1.64 % (14755)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_14628 for (2998ds/19Mi)
% 2.85/1.65 % (14755)Instruction limit reached!
% 2.85/1.65 % (14755)------------------------------
% 2.85/1.65 % (14755)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.65 % (14755)Termination reason: Unknown
% 2.85/1.65 % (14755)Termination phase: shuffling
% 2.85/1.65
% 2.85/1.65 % (14755)Memory used [KB]: 1791
% 2.85/1.65 % (14755)Time elapsed: 0.007 s
% 2.85/1.65 % (14755)Instructions burned: 22 (million)
% 2.85/1.65 % (14755)------------------------------
% 2.85/1.65 % (14755)------------------------------
% 2.85/1.66 % (14756)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_14628 for (2998ds/879Mi)
% 2.85/1.70 % (14732)Instruction limit reached!
% 2.85/1.70 % (14732)------------------------------
% 2.85/1.70 % (14732)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.70 % (14732)Termination reason: Unknown
% 2.85/1.70 % (14732)Termination phase: Saturation
% 2.85/1.70
% 2.85/1.70 % (14732)Memory used [KB]: 6780
% 2.85/1.70 % (14732)Time elapsed: 0.139 s
% 2.85/1.70 % (14732)Instructions burned: 275 (million)
% 2.85/1.70 % (14732)------------------------------
% 2.85/1.70 % (14732)------------------------------
% 2.85/1.71 % (14757)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_14628 for (2998ds/17Mi)
% 2.85/1.72 % (14757)Instruction limit reached!
% 2.85/1.72 % (14757)------------------------------
% 2.85/1.72 % (14757)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.72 % (14757)Termination reason: Unknown
% 2.85/1.72 % (14757)Termination phase: shuffling
% 2.85/1.72
% 2.85/1.72 % (14757)Memory used [KB]: 1791
% 2.85/1.72 % (14757)Time elapsed: 0.007 s
% 2.85/1.72 % (14757)Instructions burned: 17 (million)
% 2.85/1.72 % (14757)------------------------------
% 2.85/1.72 % (14757)------------------------------
% 2.85/1.73 % (14758)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_14628 for (2998ds/3Mi)
% 2.85/1.73 % (14758)Instruction limit reached!
% 2.85/1.73 % (14758)------------------------------
% 2.85/1.73 % (14758)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.73 % (14758)Termination reason: Unknown
% 2.85/1.73 % (14758)Termination phase: shuffling
% 2.85/1.73
% 2.85/1.73 % (14758)Memory used [KB]: 1407
% 2.85/1.73 % (14758)Time elapsed: 0.003 s
% 2.85/1.73 % (14758)Instructions burned: 3 (million)
% 2.85/1.73 % (14758)------------------------------
% 2.85/1.73 % (14758)------------------------------
% 2.85/1.74 % (14759)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_14628 for (2997ds/30Mi)
% 2.85/1.75 % (14759)Instruction limit reached!
% 2.85/1.75 % (14759)------------------------------
% 2.85/1.75 % (14759)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.75 % (14759)Termination reason: Unknown
% 2.85/1.75 % (14759)Termination phase: Property scanning
% 2.85/1.75
% 2.85/1.75 % (14759)Memory used [KB]: 1918
% 2.85/1.75 % (14759)Time elapsed: 0.012 s
% 2.85/1.75 % (14759)Instructions burned: 30 (million)
% 2.85/1.75 % (14759)------------------------------
% 2.85/1.75 % (14759)------------------------------
% 2.85/1.76 % (14760)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_14628 for (2997ds/127Mi)
% 2.85/1.76 % (14753)Instruction limit reached!
% 2.85/1.76 % (14753)------------------------------
% 2.85/1.76 % (14753)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.76 % (14753)Termination reason: Unknown
% 2.85/1.76 % (14753)Termination phase: Saturation
% 2.85/1.76
% 2.85/1.76 % (14753)Memory used [KB]: 8187
% 2.85/1.76 % (14753)Time elapsed: 0.122 s
% 2.85/1.76 % (14753)Instructions burned: 379 (million)
% 2.85/1.76 % (14753)------------------------------
% 2.85/1.76 % (14753)------------------------------
% 2.85/1.77 % (14761)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_14628 for (2997ds/100Mi)
% 2.85/1.80 % (14760)Instruction limit reached!
% 2.85/1.80 % (14760)------------------------------
% 2.85/1.80 % (14760)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.80 % (14760)Termination reason: Unknown
% 2.85/1.80 % (14760)Termination phase: Saturation
% 2.85/1.80
% 2.85/1.80 % (14760)Memory used [KB]: 7036
% 2.85/1.80 % (14760)Time elapsed: 0.041 s
% 2.85/1.80 % (14760)Instructions burned: 129 (million)
% 2.85/1.80 % (14760)------------------------------
% 2.85/1.80 % (14760)------------------------------
% 2.85/1.80 % (14761)Instruction limit reached!
% 2.85/1.80 % (14761)------------------------------
% 2.85/1.80 % (14761)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.80 % (14761)Termination reason: Unknown
% 2.85/1.80 % (14761)Termination phase: Property scanning
% 2.85/1.80
% 2.85/1.80 % (14761)Memory used [KB]: 2430
% 2.85/1.80 % (14761)Time elapsed: 0.031 s
% 2.85/1.80 % (14761)Instructions burned: 101 (million)
% 2.85/1.80 % (14761)------------------------------
% 2.85/1.80 % (14761)------------------------------
% 2.85/1.81 % (14762)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_14628 for (2997ds/3Mi)
% 2.85/1.81 % (14762)Instruction limit reached!
% 2.85/1.81 % (14762)------------------------------
% 2.85/1.81 % (14762)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.81 % (14762)Termination reason: Unknown
% 2.85/1.81 % (14762)Termination phase: shuffling
% 2.85/1.81
% 2.85/1.81 % (14762)Memory used [KB]: 1407
% 2.85/1.81 % (14762)Time elapsed: 0.003 s
% 2.85/1.81 % (14762)Instructions burned: 4 (million)
% 2.85/1.81 % (14762)------------------------------
% 2.85/1.81 % (14762)------------------------------
% 2.85/1.81 % (14763)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_14628 for (2997ds/20Mi)
% 2.85/1.82 % (14764)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_14628 for (2997ds/86Mi)
% 2.85/1.82 % (14763)Instruction limit reached!
% 2.85/1.82 % (14763)------------------------------
% 2.85/1.82 % (14763)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.82 % (14763)Termination reason: Unknown
% 2.85/1.82 % (14763)Termination phase: shuffling
% 2.85/1.82
% 2.85/1.82 % (14763)Memory used [KB]: 1791
% 2.85/1.82 % (14763)Time elapsed: 0.009 s
% 2.85/1.82 % (14763)Instructions burned: 20 (million)
% 2.85/1.82 % (14763)------------------------------
% 2.85/1.82 % (14763)------------------------------
% 2.85/1.82 % (14747)Instruction limit reached!
% 2.85/1.82 % (14747)------------------------------
% 2.85/1.82 % (14747)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.82 % (14747)Termination reason: Unknown
% 2.85/1.82 % (14747)Termination phase: Saturation
% 2.85/1.82
% 2.85/1.82 % (14747)Memory used [KB]: 8059
% 2.85/1.82 % (14747)Time elapsed: 0.232 s
% 2.85/1.82 % (14747)Instructions burned: 710 (million)
% 2.85/1.82 % (14747)------------------------------
% 2.85/1.82 % (14747)------------------------------
% 2.85/1.83 % (14765)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_14628 for (2997ds/107Mi)
% 2.85/1.83 % (14766)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_14628 for (2997ds/39Mi)
% 2.85/1.84 % (14766)Instruction limit reached!
% 2.85/1.84 % (14766)------------------------------
% 2.85/1.84 % (14766)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.84 % (14766)Termination reason: Unknown
% 2.85/1.84 % (14766)Termination phase: shuffling
% 2.85/1.84
% 2.85/1.84 % (14766)Memory used [KB]: 2174
% 2.85/1.84 % (14766)Time elapsed: 0.012 s
% 2.85/1.84 % (14766)Instructions burned: 40 (million)
% 2.85/1.84 % (14766)------------------------------
% 2.85/1.84 % (14766)------------------------------
% 2.85/1.85 % (14764)Instruction limit reached!
% 2.85/1.85 % (14764)------------------------------
% 2.85/1.85 % (14764)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.85 % (14764)Termination reason: Unknown
% 2.85/1.85 % (14764)Termination phase: Property scanning
% 2.85/1.85
% 2.85/1.85 % (14764)Memory used [KB]: 2558
% 2.85/1.85 % (14764)Time elapsed: 0.029 s
% 2.85/1.85 % (14764)Instructions burned: 87 (million)
% 2.85/1.85 % (14764)------------------------------
% 2.85/1.85 % (14764)------------------------------
% 2.85/1.85 % (14767)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_14628 for (2996ds/448Mi)
% 2.85/1.86 % (14768)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_14628 for (2996ds/46Mi)
% 2.85/1.86 % (14765)Instruction limit reached!
% 2.85/1.86 % (14765)------------------------------
% 2.85/1.86 % (14765)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.86 % (14765)Termination reason: Unknown
% 2.85/1.86 % (14765)Termination phase: Saturation
% 2.85/1.86
% 2.85/1.86 % (14765)Memory used [KB]: 7036
% 2.85/1.86 % (14765)Time elapsed: 0.036 s
% 2.85/1.86 % (14765)Instructions burned: 107 (million)
% 2.85/1.86 % (14765)------------------------------
% 2.85/1.86 % (14765)------------------------------
% 2.85/1.87 % (14768)Instruction limit reached!
% 2.85/1.87 % (14768)------------------------------
% 2.85/1.87 % (14768)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.87 % (14768)Termination reason: Unknown
% 2.85/1.87 % (14768)Termination phase: Preprocessing 3
% 2.85/1.87
% 2.85/1.87 % (14768)Memory used [KB]: 2174
% 2.85/1.87 % (14768)Time elapsed: 0.018 s
% 2.85/1.87 % (14768)Instructions burned: 48 (million)
% 2.85/1.87 % (14768)------------------------------
% 2.85/1.87 % (14768)------------------------------
% 2.85/1.87 % (14769)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_14628 for (2996ds/98Mi)
% 2.85/1.88 % (14738)Instruction limit reached!
% 2.85/1.88 % (14738)------------------------------
% 2.85/1.88 % (14738)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.88 % (14738)Termination reason: Unknown
% 2.85/1.88 % (14738)Termination phase: Saturation
% 2.85/1.88
% 2.85/1.88 % (14738)Memory used [KB]: 9722
% 2.85/1.88 % (14738)Time elapsed: 0.301 s
% 2.85/1.88 % (14738)Instructions burned: 1042 (million)
% 2.85/1.88 % (14738)------------------------------
% 2.85/1.88 % (14738)------------------------------
% 2.85/1.88 % (14754)Instruction limit reached!
% 2.85/1.88 % (14754)------------------------------
% 2.85/1.88 % (14754)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.88 % (14754)Termination reason: Unknown
% 2.85/1.88 % (14754)Termination phase: Saturation
% 2.85/1.88
% 2.85/1.88 % (14754)Memory used [KB]: 9210
% 2.85/1.88 % (14754)Time elapsed: 0.241 s
% 2.85/1.88 % (14754)Instructions burned: 780 (million)
% 2.85/1.88 % (14754)------------------------------
% 2.85/1.88 % (14754)------------------------------
% 2.85/1.88 % (14749)Instruction limit reached!
% 2.85/1.88 % (14749)------------------------------
% 2.85/1.88 % (14749)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.88 % (14749)Termination reason: Unknown
% 2.85/1.88 % (14749)Termination phase: Saturation
% 2.85/1.88
% 2.85/1.88 % (14749)Memory used [KB]: 9978
% 2.85/1.88 % (14749)Time elapsed: 0.292 s
% 2.85/1.88 % (14749)Instructions burned: 902 (million)
% 2.85/1.88 % (14749)------------------------------
% 2.85/1.88 % (14749)------------------------------
% 2.85/1.88 % (14770)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_14628 for (2996ds/507Mi)
% 2.85/1.89 % (14771)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_14628 for (2996ds/149Mi)
% 2.85/1.89 % (14772)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_14628 for (2996ds/39Mi)
% 2.85/1.89 % (14773)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_14628 for (2996ds/6Mi)
% 2.85/1.89 % (14773)Instruction limit reached!
% 2.85/1.89 % (14773)------------------------------
% 2.85/1.89 % (14773)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.89 % (14773)Termination reason: Unknown
% 2.85/1.89 % (14773)Termination phase: shuffling
% 2.85/1.89
% 2.85/1.89 % (14773)Memory used [KB]: 1407
% 2.85/1.89 % (14773)Time elapsed: 0.003 s
% 2.85/1.89 % (14773)Instructions burned: 7 (million)
% 2.85/1.89 % (14773)------------------------------
% 2.85/1.89 % (14773)------------------------------
% 2.85/1.90 % (14772)Instruction limit reached!
% 2.85/1.90 % (14772)------------------------------
% 2.85/1.90 % (14772)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.90 % (14772)Termination reason: Unknown
% 2.85/1.90 % (14772)Termination phase: Preprocessing 3
% 2.85/1.90
% 2.85/1.90 % (14772)Memory used [KB]: 2174
% 2.85/1.90 % (14772)Time elapsed: 0.013 s
% 2.85/1.90 % (14772)Instructions burned: 39 (million)
% 2.85/1.90 % (14772)------------------------------
% 2.85/1.90 % (14772)------------------------------
% 2.85/1.90 % (14774)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_14628 for (2996ds/1087Mi)
% 2.85/1.90 % (14769)Instruction limit reached!
% 2.85/1.90 % (14769)------------------------------
% 2.85/1.90 % (14769)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.90 % (14769)Termination reason: Unknown
% 2.85/1.90 % (14769)Termination phase: Property scanning
% 2.85/1.90
% 2.85/1.90 % (14769)Memory used [KB]: 2430
% 2.85/1.90 % (14769)Time elapsed: 0.029 s
% 2.85/1.90 % (14769)Instructions burned: 98 (million)
% 2.85/1.90 % (14769)------------------------------
% 2.85/1.90 % (14769)------------------------------
% 2.85/1.91 % (14775)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_14628 for (2996ds/47Mi)
% 2.85/1.91 % (14776)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_14628 for (2996ds/44Mi)
% 2.85/1.92 % (14775)Instruction limit reached!
% 2.85/1.92 % (14775)------------------------------
% 2.85/1.92 % (14775)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.92 % (14775)Termination reason: Unknown
% 2.85/1.92 % (14775)Termination phase: Preprocessing 3
% 2.85/1.92
% 2.85/1.92 % (14775)Memory used [KB]: 2302
% 2.85/1.92 % (14775)Time elapsed: 0.016 s
% 2.85/1.92 % (14775)Instructions burned: 49 (million)
% 2.85/1.92 % (14775)------------------------------
% 2.85/1.92 % (14775)------------------------------
% 2.85/1.93 % (14756)Instruction limit reached!
% 2.85/1.93 % (14756)------------------------------
% 2.85/1.93 % (14756)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.93 % (14756)Termination reason: Unknown
% 2.85/1.93 % (14756)Termination phase: Saturation
% 2.85/1.93
% 2.85/1.93 % (14756)Memory used [KB]: 7803
% 2.85/1.93 % (14756)Time elapsed: 0.268 s
% 2.85/1.93 % (14756)Instructions burned: 880 (million)
% 2.85/1.93 % (14756)------------------------------
% 2.85/1.93 % (14756)------------------------------
% 2.85/1.93 % (14776)Instruction limit reached!
% 2.85/1.93 % (14776)------------------------------
% 2.85/1.93 % (14776)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.93 % (14776)Termination reason: Unknown
% 2.85/1.93 % (14776)Termination phase: Property scanning
% 2.85/1.93
% 2.85/1.93 % (14776)Memory used [KB]: 2174
% 2.85/1.93 % (14776)Time elapsed: 0.015 s
% 2.85/1.93 % (14776)Instructions burned: 44 (million)
% 2.85/1.93 % (14776)------------------------------
% 2.85/1.93 % (14776)------------------------------
% 2.85/1.93 % (14771)Instruction limit reached!
% 2.85/1.93 % (14771)------------------------------
% 2.85/1.93 % (14771)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.93 % (14771)Termination reason: Unknown
% 2.85/1.93 % (14771)Termination phase: Saturation
% 2.85/1.93
% 2.85/1.93 % (14771)Memory used [KB]: 7291
% 2.85/1.93 % (14771)Time elapsed: 0.042 s
% 2.85/1.93 % (14771)Instructions burned: 151 (million)
% 2.85/1.93 % (14771)------------------------------
% 2.85/1.93 % (14771)------------------------------
% 2.85/1.93 % (14777)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_14628 for (2996ds/432Mi)
% 2.85/1.94 % (14778)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_14628 for (2996ds/62Mi)
% 2.85/1.94 % (14780)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_14628 for (2996ds/96Mi)
% 2.85/1.94 % (14779)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_14628 for (2996ds/31Mi)
% 2.85/1.95 % (14779)Instruction limit reached!
% 2.85/1.95 % (14779)------------------------------
% 2.85/1.95 % (14779)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.95 % (14779)Termination reason: Unknown
% 2.85/1.95 % (14779)Termination phase: Property scanning
% 2.85/1.95
% 2.85/1.95 % (14779)Memory used [KB]: 1918
% 2.85/1.95 % (14779)Time elapsed: 0.012 s
% 2.85/1.95 % (14779)Instructions burned: 31 (million)
% 2.85/1.95 % (14779)------------------------------
% 2.85/1.95 % (14779)------------------------------
% 2.85/1.95 % (14778)Instruction limit reached!
% 2.85/1.95 % (14778)------------------------------
% 2.85/1.95 % (14778)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.95 % (14778)Termination reason: Unknown
% 2.85/1.95 % (14778)Termination phase: Property scanning
% 2.85/1.95
% 2.85/1.95 % (14778)Memory used [KB]: 2174
% 2.85/1.95 % (14778)Time elapsed: 0.017 s
% 2.85/1.95 % (14778)Instructions burned: 62 (million)
% 2.85/1.95 % (14778)------------------------------
% 2.85/1.95 % (14778)------------------------------
% 2.85/1.96 % (14781)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_14628 for (2995ds/453Mi)
% 2.85/1.96 % (14782)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_14628 for (2995ds/71Mi)
% 2.85/1.96 % (14780)Instruction limit reached!
% 2.85/1.96 % (14780)------------------------------
% 2.85/1.96 % (14780)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.96 % (14780)Termination reason: Unknown
% 2.85/1.96 % (14780)Termination phase: Property scanning
% 2.85/1.96
% 2.85/1.96 % (14780)Memory used [KB]: 2430
% 2.85/1.96 % (14780)Time elapsed: 0.028 s
% 2.85/1.96 % (14780)Instructions burned: 96 (million)
% 2.85/1.96 % (14780)------------------------------
% 2.85/1.96 % (14780)------------------------------
% 2.85/1.97 % (14783)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_14628 for (2995ds/83Mi)
% 2.85/1.98 % (14767)Instruction limit reached!
% 2.85/1.98 % (14767)------------------------------
% 2.85/1.98 % (14767)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.98 % (14767)Termination reason: Unknown
% 2.85/1.98 % (14767)Termination phase: Saturation
% 2.85/1.98
% 2.85/1.98 % (14767)Memory used [KB]: 8059
% 2.85/1.98 % (14767)Time elapsed: 0.131 s
% 2.85/1.98 % (14767)Instructions burned: 450 (million)
% 2.85/1.98 % (14767)------------------------------
% 2.85/1.98 % (14767)------------------------------
% 2.85/1.98 % (14782)Instruction limit reached!
% 2.85/1.98 % (14782)------------------------------
% 2.85/1.98 % (14782)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.98 % (14782)Termination reason: Unknown
% 2.85/1.98 % (14782)Termination phase: Function definition elimination
% 2.85/1.98
% 2.85/1.98 % (14782)Memory used [KB]: 2430
% 2.85/1.98 % (14782)Time elapsed: 0.022 s
% 2.85/1.98 % (14782)Instructions burned: 74 (million)
% 2.85/1.98 % (14782)------------------------------
% 2.85/1.98 % (14782)------------------------------
% 2.85/1.99 % (14784)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_14628 for (2995ds/11Mi)
% 2.85/1.99 % (14785)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_14628 for (2995ds/41Mi)
% 2.85/1.99 % (14784)Instruction limit reached!
% 2.85/1.99 % (14784)------------------------------
% 2.85/1.99 % (14784)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.99 % (14784)Termination reason: Unknown
% 2.85/1.99 % (14784)Termination phase: shuffling
% 2.85/1.99
% 2.85/1.99 % (14784)Memory used [KB]: 1663
% 2.85/1.99 % (14784)Time elapsed: 0.004 s
% 2.85/1.99 % (14784)Instructions burned: 11 (million)
% 2.85/1.99 % (14784)------------------------------
% 2.85/1.99 % (14784)------------------------------
% 2.85/2.00 % (14783)Instruction limit reached!
% 2.85/2.00 % (14783)------------------------------
% 2.85/2.00 % (14783)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/2.00 % (14783)Termination reason: Unknown
% 2.85/2.00 % (14783)Termination phase: Saturation
% 2.85/2.00
% 2.85/2.00 % (14783)Memory used [KB]: 6780
% 2.85/2.00 % (14783)Time elapsed: 0.050 s
% 2.85/2.00 % (14783)Instructions burned: 83 (million)
% 2.85/2.00 % (14783)------------------------------
% 2.85/2.00 % (14783)------------------------------
% 2.85/2.00 % (14785)Instruction limit reached!
% 2.85/2.00 % (14785)------------------------------
% 2.85/2.00 % (14785)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/2.00 % (14785)Termination reason: Unknown
% 2.85/2.00 % (14785)Termination phase: shuffling
% 2.85/2.00
% 2.85/2.00 % (14785)Memory used [KB]: 2174
% 2.85/2.00 % (14785)Time elapsed: 0.012 s
% 2.85/2.00 % (14785)Instructions burned: 41 (million)
% 2.85/2.00 % (14785)------------------------------
% 2.85/2.00 % (14785)------------------------------
% 2.85/2.01 % (14786)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_14628 for (2995ds/6Mi)
% 2.85/2.01 % (14787)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_14628 for (2995ds/150Mi)
% 2.85/2.01 % (14786)Instruction limit reached!
% 2.85/2.01 % (14786)------------------------------
% 2.85/2.01 % (14786)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/2.01 % (14786)Termination reason: Unknown
% 2.85/2.01 % (14786)Termination phase: shuffling
% 2.85/2.01
% 2.85/2.01 % (14786)Memory used [KB]: 1535
% 2.85/2.01 % (14786)Time elapsed: 0.003 s
% 2.85/2.01 % (14786)Instructions burned: 6 (million)
% 2.85/2.01 % (14786)------------------------------
% 2.85/2.01 % (14786)------------------------------
% 6.02/2.02 % (14788)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_14628 for (2995ds/343Mi)
% 6.02/2.02 % (14789)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_14628 for (2995ds/109Mi)
% 6.02/2.05 % (14787)Instruction limit reached!
% 6.02/2.05 % (14787)------------------------------
% 6.02/2.05 % (14787)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.02/2.05 % (14787)Termination reason: Unknown
% 6.02/2.05 % (14787)Termination phase: Property scanning
% 6.02/2.05
% 6.02/2.05 % (14787)Memory used [KB]: 2686
% 6.02/2.05 % (14787)Time elapsed: 0.043 s
% 6.02/2.05 % (14787)Instructions burned: 152 (million)
% 6.02/2.05 % (14787)------------------------------
% 6.02/2.05 % (14787)------------------------------
% 6.02/2.05 % (14770)Instruction limit reached!
% 6.02/2.05 % (14770)------------------------------
% 6.02/2.05 % (14770)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.02/2.05 % (14770)Termination reason: Unknown
% 6.02/2.05 % (14770)Termination phase: Saturation
% 6.02/2.05
% 6.02/2.05 % (14770)Memory used [KB]: 8443
% 6.02/2.05 % (14770)Time elapsed: 0.170 s
% 6.02/2.05 % (14770)Instructions burned: 508 (million)
% 6.02/2.05 % (14770)------------------------------
% 6.02/2.05 % (14770)------------------------------
% 6.02/2.05 % (14789)Instruction limit reached!
% 6.02/2.05 % (14789)------------------------------
% 6.02/2.05 % (14789)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.02/2.05 % (14789)Termination reason: Unknown
% 6.02/2.05 % (14789)Termination phase: Saturation
% 6.02/2.05
% 6.02/2.05 % (14789)Memory used [KB]: 6908
% 6.02/2.05 % (14789)Time elapsed: 0.033 s
% 6.02/2.05 % (14789)Instructions burned: 112 (million)
% 6.02/2.05 % (14789)------------------------------
% 6.02/2.05 % (14789)------------------------------
% 6.02/2.06 % (14777)Instruction limit reached!
% 6.02/2.06 % (14777)------------------------------
% 6.02/2.06 % (14777)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.02/2.06 % (14777)Termination reason: Unknown
% 6.02/2.06 % (14777)Termination phase: Saturation
% 6.02/2.06
% 6.02/2.06 % (14777)Memory used [KB]: 3709
% 6.02/2.06 % (14777)Time elapsed: 0.126 s
% 6.02/2.06 % (14777)Instructions burned: 432 (million)
% 6.02/2.06 % (14777)------------------------------
% 6.02/2.06 % (14777)------------------------------
% 6.02/2.06 % (14790)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_14628 for (2994ds/253Mi)
% 6.02/2.06 % (14791)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_14628 for (2994ds/140Mi)
% 6.02/2.06 % (14792)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_14628 for (2994ds/614Mi)
% 6.02/2.07 % (14793)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_14628 for (2994ds/202Mi)
% 6.02/2.09 % (14781)Instruction limit reached!
% 6.02/2.09 % (14781)------------------------------
% 6.02/2.09 % (14781)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.02/2.09 % (14781)Termination reason: Unknown
% 6.02/2.09 % (14781)Termination phase: Saturation
% 6.02/2.09
% 6.02/2.09 % (14781)Memory used [KB]: 7803
% 6.02/2.09 % (14781)Time elapsed: 0.155 s
% 6.02/2.09 % (14781)Instructions burned: 454 (million)
% 6.02/2.09 % (14781)------------------------------
% 6.02/2.09 % (14781)------------------------------
% 6.02/2.10 % (14794)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_14628 for (2994ds/339Mi)
% 6.02/2.10 % (14791)Instruction limit reached!
% 6.02/2.10 % (14791)------------------------------
% 6.02/2.10 % (14791)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.02/2.10 % (14791)Termination reason: Unknown
% 6.02/2.10 % (14791)Termination phase: Saturation
% 6.02/2.10
% 6.02/2.10 % (14791)Memory used [KB]: 6908
% 6.02/2.10 % (14791)Time elapsed: 0.044 s
% 6.02/2.10 % (14791)Instructions burned: 140 (million)
% 6.02/2.10 % (14791)------------------------------
% 6.02/2.10 % (14791)------------------------------
% 6.48/2.11 % (14795)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on DTF2THF_14628 for (2994ds/283Mi)
% 6.48/2.12 % (14788)Instruction limit reached!
% 6.48/2.12 % (14788)------------------------------
% 6.48/2.12 % (14788)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.48/2.12 % (14788)Termination reason: Unknown
% 6.48/2.12 % (14788)Termination phase: Saturation
% 6.48/2.12
% 6.48/2.12 % (14788)Memory used [KB]: 7547
% 6.48/2.12 % (14788)Time elapsed: 0.105 s
% 6.48/2.12 % (14788)Instructions burned: 345 (million)
% 6.48/2.12 % (14788)------------------------------
% 6.48/2.12 % (14788)------------------------------
% 6.48/2.13 % (14793)Instruction limit reached!
% 6.48/2.13 % (14793)------------------------------
% 6.48/2.13 % (14793)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.48/2.13 % (14793)Termination reason: Unknown
% 6.48/2.13 % (14793)Termination phase: Saturation
% 6.48/2.13
% 6.48/2.13 % (14793)Memory used [KB]: 7164
% 6.48/2.13 % (14793)Time elapsed: 0.064 s
% 6.48/2.13 % (14793)Instructions burned: 203 (million)
% 6.48/2.13 % (14793)------------------------------
% 6.48/2.13 % (14793)------------------------------
% 6.48/2.13 % (14796)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_14628 for (2993ds/134Mi)
% 6.48/2.14 % (14790)Instruction limit reached!
% 6.48/2.14 % (14790)------------------------------
% 6.48/2.14 % (14790)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.48/2.14 % (14790)Termination reason: Unknown
% 6.48/2.14 % (14790)Termination phase: Saturation
% 6.48/2.14
% 6.48/2.14 % (14790)Memory used [KB]: 7036
% 6.48/2.14 % (14790)Time elapsed: 0.080 s
% 6.48/2.14 % (14790)Instructions burned: 254 (million)
% 6.48/2.14 % (14790)------------------------------
% 6.48/2.14 % (14790)------------------------------
% 6.48/2.14 % (14797)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_14628 for (2993ds/298Mi)
% 6.48/2.15 % (14798)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_14628 for (2993ds/192Mi)
% 6.48/2.17 % (14796)Instruction limit reached!
% 6.48/2.17 % (14796)------------------------------
% 6.48/2.17 % (14796)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.48/2.17 % (14796)Termination reason: Unknown
% 6.48/2.17 % (14796)Termination phase: Saturation
% 6.48/2.17
% 6.48/2.17 % (14796)Memory used [KB]: 7164
% 6.48/2.17 % (14796)Time elapsed: 0.038 s
% 6.48/2.17 % (14796)Instructions burned: 134 (million)
% 6.48/2.17 % (14796)------------------------------
% 6.48/2.17 % (14796)------------------------------
% 6.48/2.18 % (14799)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_14628 for (2993ds/258Mi)
% 6.48/2.20 % (14795)Instruction limit reached!
% 6.48/2.20 % (14795)------------------------------
% 6.48/2.20 % (14795)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.48/2.20 % (14795)Termination reason: Unknown
% 6.48/2.20 % (14795)Termination phase: Saturation
% 6.48/2.20
% 6.48/2.20 % (14795)Memory used [KB]: 7547
% 6.48/2.20 % (14795)Time elapsed: 0.083 s
% 6.48/2.20 % (14795)Instructions burned: 285 (million)
% 6.48/2.20 % (14795)------------------------------
% 6.48/2.20 % (14795)------------------------------
% 6.89/2.20 % (14794)Instruction limit reached!
% 6.89/2.20 % (14794)------------------------------
% 6.89/2.20 % (14794)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.89/2.20 % (14794)Termination reason: Unknown
% 6.89/2.20 % (14794)Termination phase: Saturation
% 6.89/2.20
% 6.89/2.20 % (14794)Memory used [KB]: 7803
% 6.89/2.20 % (14794)Time elapsed: 0.099 s
% 6.89/2.20 % (14794)Instructions burned: 341 (million)
% 6.89/2.20 % (14794)------------------------------
% 6.89/2.20 % (14794)------------------------------
% 6.89/2.20 % (14798)Instruction limit reached!
% 6.89/2.20 % (14798)------------------------------
% 6.89/2.20 % (14798)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.89/2.20 % (14798)Termination reason: Unknown
% 6.89/2.20 % (14798)Termination phase: Saturation
% 6.89/2.20
% 6.89/2.20 % (14798)Memory used [KB]: 3454
% 6.89/2.20 % (14798)Time elapsed: 0.058 s
% 6.89/2.20 % (14798)Instructions burned: 194 (million)
% 6.89/2.20 % (14798)------------------------------
% 6.89/2.20 % (14798)------------------------------
% 6.89/2.21 % (14800)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_14628 for (2993ds/90Mi)
% 6.89/2.21 % (14801)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_14628 for (2993ds/231Mi)
% 6.89/2.21 % (14802)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on DTF2THF_14628 for (2993ds/458Mi)
% 6.89/2.22 % (14797)Instruction limit reached!
% 6.89/2.22 % (14797)------------------------------
% 6.89/2.22 % (14797)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.89/2.22 % (14797)Termination reason: Unknown
% 6.89/2.22 % (14797)Termination phase: Saturation
% 6.89/2.22
% 6.89/2.22 % (14797)Memory used [KB]: 7803
% 6.89/2.22 % (14797)Time elapsed: 0.082 s
% 6.89/2.22 % (14797)Instructions burned: 299 (million)
% 6.89/2.22 % (14797)------------------------------
% 6.89/2.22 % (14797)------------------------------
% 6.89/2.23 % (14803)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_14628 for (2993ds/31Mi)
% 6.89/2.23 % (14800)Instruction limit reached!
% 6.89/2.23 % (14800)------------------------------
% 6.89/2.23 % (14800)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.89/2.23 % (14800)Termination reason: Unknown
% 6.89/2.23 % (14800)Termination phase: Property scanning
% 6.89/2.23
% 6.89/2.23 % (14800)Memory used [KB]: 2430
% 6.89/2.23 % (14800)Time elapsed: 0.027 s
% 6.89/2.23 % (14800)Instructions burned: 92 (million)
% 6.89/2.23 % (14800)------------------------------
% 6.89/2.23 % (14800)------------------------------
% 6.89/2.24 % (14774)Instruction limit reached!
% 6.89/2.24 % (14774)------------------------------
% 6.89/2.24 % (14774)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.89/2.24 % (14774)Termination reason: Unknown
% 6.89/2.24 % (14774)Termination phase: Saturation
% 6.89/2.24
% 6.89/2.24 % (14774)Memory used [KB]: 8187
% 6.89/2.24 % (14774)Time elapsed: 0.352 s
% 6.89/2.24 % (14774)Instructions burned: 1090 (million)
% 6.89/2.24 % (14774)------------------------------
% 6.89/2.24 % (14774)------------------------------
% 6.89/2.24 % (14792)Instruction limit reached!
% 6.89/2.24 % (14792)------------------------------
% 6.89/2.24 % (14792)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.89/2.24 % (14792)Termination reason: Unknown
% 6.89/2.24 % (14792)Termination phase: Saturation
% 6.89/2.24
% 6.89/2.24 % (14792)Memory used [KB]: 8699
% 6.89/2.24 % (14792)Time elapsed: 0.178 s
% 6.89/2.24 % (14792)Instructions burned: 616 (million)
% 6.89/2.24 % (14792)------------------------------
% 6.89/2.24 % (14792)------------------------------
% 6.89/2.24 % (14803)Instruction limit reached!
% 6.89/2.24 % (14803)------------------------------
% 6.89/2.24 % (14803)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.89/2.24 % (14803)Termination reason: Unknown
% 6.89/2.24 % (14803)Termination phase: Property scanning
% 6.89/2.24
% 6.89/2.24 % (14803)Memory used [KB]: 1918
% 6.89/2.24 % (14803)Time elapsed: 0.011 s
% 6.89/2.24 % (14803)Instructions burned: 33 (million)
% 6.89/2.24 % (14803)------------------------------
% 6.89/2.24 % (14803)------------------------------
% 6.89/2.24 % (14804)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on DTF2THF_14628 for (2992ds/297Mi)
% 6.89/2.25 % (14805)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on DTF2THF_14628 for (2992ds/987Mi)
% 6.89/2.25 % (14806)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on DTF2THF_14628 for (2992ds/182Mi)
% 6.89/2.25 % (14807)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on DTF2THF_14628 for (2992ds/182Mi)
% 6.89/2.26 % (14799)Instruction limit reached!
% 6.89/2.26 % (14799)------------------------------
% 6.89/2.26 % (14799)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.89/2.26 % (14799)Termination reason: Unknown
% 6.89/2.26 % (14799)Termination phase: Saturation
% 6.89/2.26
% 6.89/2.26 % (14799)Memory used [KB]: 7547
% 6.89/2.26 % (14799)Time elapsed: 0.078 s
% 6.89/2.26 % (14799)Instructions burned: 258 (million)
% 6.89/2.26 % (14799)------------------------------
% 6.89/2.26 % (14799)------------------------------
% 6.89/2.27 % (14801)Instruction limit reached!
% 6.89/2.27 % (14801)------------------------------
% 6.89/2.27 % (14801)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.89/2.27 % (14801)Termination reason: Unknown
% 6.89/2.27 % (14801)Termination phase: Saturation
% 6.89/2.27
% 6.89/2.27 % (14801)Memory used [KB]: 7036
% 6.89/2.27 % (14801)Time elapsed: 0.061 s
% 6.89/2.27 % (14801)Instructions burned: 234 (million)
% 6.89/2.27 % (14801)------------------------------
% 6.89/2.27 % (14801)------------------------------
% 6.89/2.27 % (14808)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on DTF2THF_14628 for (2992ds/154Mi)
% 6.89/2.28 % (14809)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on DTF2THF_14628 for (2992ds/79Mi)
% 7.69/2.30 % (14809)Instruction limit reached!
% 7.69/2.30 % (14809)------------------------------
% 7.69/2.30 % (14809)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.69/2.30 % (14809)Termination reason: Unknown
% 7.69/2.30 % (14809)Termination phase: Property scanning
% 7.69/2.30
% 7.69/2.30 % (14809)Memory used [KB]: 2558
% 7.69/2.30 % (14809)Time elapsed: 0.025 s
% 7.69/2.30 % (14809)Instructions burned: 80 (million)
% 7.69/2.30 % (14809)------------------------------
% 7.69/2.30 % (14809)------------------------------
% 7.69/2.30 % (14806)Instruction limit reached!
% 7.69/2.30 % (14806)------------------------------
% 7.69/2.30 % (14806)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.69/2.30 % (14806)Termination reason: Unknown
% 7.69/2.30 % (14806)Termination phase: Saturation
% 7.69/2.30
% 7.69/2.30 % (14806)Memory used [KB]: 7291
% 7.69/2.30 % (14806)Time elapsed: 0.052 s
% 7.69/2.30 % (14806)Instructions burned: 185 (million)
% 7.69/2.30 % (14806)------------------------------
% 7.69/2.30 % (14806)------------------------------
% 7.69/2.30 % (14807)Instruction limit reached!
% 7.69/2.30 % (14807)------------------------------
% 7.69/2.30 % (14807)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.69/2.30 % (14807)Termination reason: Unknown
% 7.69/2.30 % (14807)Termination phase: Saturation
% 7.69/2.30
% 7.69/2.30 % (14807)Memory used [KB]: 7419
% 7.69/2.30 % (14807)Time elapsed: 0.056 s
% 7.69/2.30 % (14807)Instructions burned: 182 (million)
% 7.69/2.30 % (14807)------------------------------
% 7.69/2.30 % (14807)------------------------------
% 7.69/2.31 % (14808)Instruction limit reached!
% 7.69/2.31 % (14808)------------------------------
% 7.69/2.31 % (14808)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.69/2.31 % (14808)Termination reason: Unknown
% 7.69/2.31 % (14808)Termination phase: Saturation
% 7.69/2.31
% 7.69/2.31 % (14808)Memory used [KB]: 2558
% 7.69/2.31 % (14808)Time elapsed: 0.041 s
% 7.69/2.31 % (14808)Instructions burned: 155 (million)
% 7.69/2.31 % (14808)------------------------------
% 7.69/2.31 % (14808)------------------------------
% 7.69/2.31 % (14810)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on DTF2THF_14628 for (2992ds/216Mi)
% 7.69/2.31 % (14811)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_14628 for (2992ds/114Mi)
% 7.69/2.31 % (14812)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on DTF2THF_14628 for (2992ds/922Mi)
% 7.69/2.32 % (14813)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on DTF2THF_14628 for (2992ds/182Mi)
% 7.69/2.33 % (14804)Instruction limit reached!
% 7.69/2.33 % (14804)------------------------------
% 7.69/2.33 % (14804)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.69/2.33 % (14804)Termination reason: Unknown
% 7.69/2.33 % (14804)Termination phase: Saturation
% 7.69/2.33
% 7.69/2.33 % (14804)Memory used [KB]: 7675
% 7.69/2.33 % (14804)Time elapsed: 0.088 s
% 7.69/2.33 % (14804)Instructions burned: 299 (million)
% 7.69/2.33 % (14804)------------------------------
% 7.69/2.33 % (14804)------------------------------
% 7.69/2.34 % (14814)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on DTF2THF_14628 for (2992ds/164Mi)
% 7.69/2.34 % (14811)Instruction limit reached!
% 7.69/2.34 % (14811)------------------------------
% 7.69/2.34 % (14811)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.69/2.34 % (14811)Termination reason: Unknown
% 7.69/2.34 % (14811)Termination phase: Saturation
% 7.69/2.34
% 7.69/2.34 % (14811)Memory used [KB]: 7036
% 7.69/2.34 % (14811)Time elapsed: 0.033 s
% 7.69/2.34 % (14811)Instructions burned: 115 (million)
% 7.69/2.34 % (14811)------------------------------
% 7.69/2.34 % (14811)------------------------------
% 7.69/2.35 % (14815)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on DTF2THF_14628 for (2991ds/50Mi)
% 7.69/2.36 % (14813)Instruction limit reached!
% 7.69/2.36 % (14813)------------------------------
% 7.69/2.36 % (14813)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.69/2.36 % (14815)Instruction limit reached!
% 7.69/2.36 % (14815)------------------------------
% 7.69/2.36 % (14815)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.69/2.36 % (14815)Termination reason: Unknown
% 7.69/2.36 % (14815)Termination phase: Property scanning
% 7.69/2.36
% 7.69/2.36 % (14815)Memory used [KB]: 2174
% 7.69/2.36 % (14815)Time elapsed: 0.015 s
% 7.69/2.36 % (14815)Instructions burned: 51 (million)
% 7.69/2.36 % (14815)------------------------------
% 7.69/2.36 % (14815)------------------------------
% 7.69/2.36 % (14813)Termination reason: Unknown
% 7.69/2.36 % (14813)Termination phase: Saturation
% 7.69/2.36
% 7.69/2.36 % (14813)Memory used [KB]: 7036
% 7.69/2.36 % (14813)Time elapsed: 0.049 s
% 7.69/2.36 % (14813)Instructions burned: 183 (million)
% 7.69/2.36 % (14813)------------------------------
% 7.69/2.36 % (14813)------------------------------
% 7.69/2.37 % (14810)Instruction limit reached!
% 7.69/2.37 % (14810)------------------------------
% 7.69/2.37 % (14810)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.69/2.37 % (14810)Termination reason: Unknown
% 7.69/2.37 % (14810)Termination phase: Saturation
% 7.69/2.37
% 7.69/2.37 % (14810)Memory used [KB]: 7419
% 7.69/2.37 % (14810)Time elapsed: 0.060 s
% 7.69/2.37 % (14810)Instructions burned: 219 (million)
% 7.69/2.37 % (14810)------------------------------
% 7.69/2.37 % (14810)------------------------------
% 7.69/2.37 % (14816)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_14628 for (2991ds/368Mi)
% 7.69/2.37 % (14817)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on DTF2THF_14628 for (2991ds/1021Mi)
% 7.69/2.38 % (14818)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on DTF2THF_14628 for (2991ds/267Mi)
% 7.69/2.38 % (14802)Instruction limit reached!
% 7.69/2.38 % (14802)------------------------------
% 7.69/2.38 % (14802)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.69/2.38 % (14802)Termination reason: Unknown
% 7.69/2.38 % (14802)Termination phase: Saturation
% 7.69/2.38
% 7.69/2.38 % (14802)Memory used [KB]: 8699
% 7.69/2.38 % (14802)Time elapsed: 0.169 s
% 7.69/2.38 % (14802)Instructions burned: 458 (million)
% 7.69/2.38 % (14802)------------------------------
% 7.69/2.38 % (14802)------------------------------
% 7.69/2.38 % (14814)Instruction limit reached!
% 7.69/2.38 % (14814)------------------------------
% 7.69/2.38 % (14814)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.69/2.38 % (14814)Termination reason: Unknown
% 7.69/2.38 % (14814)Termination phase: Saturation
% 7.69/2.38
% 7.69/2.38 % (14814)Memory used [KB]: 2430
% 7.69/2.38 % (14814)Time elapsed: 0.047 s
% 7.69/2.38 % (14814)Instructions burned: 167 (million)
% 7.69/2.38 % (14814)------------------------------
% 7.69/2.38 % (14814)------------------------------
% 7.69/2.39 % (14820)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_14628 for (2991ds/26Mi)
% 8.41/2.40 % (14819)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on DTF2THF_14628 for (2991ds/204Mi)
% 8.41/2.40 % (14820)Instruction limit reached!
% 8.41/2.40 % (14820)------------------------------
% 8.41/2.40 % (14820)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.41/2.40 % (14820)Termination reason: Unknown
% 8.41/2.40 % (14820)Termination phase: shuffling
% 8.41/2.40
% 8.41/2.40 % (14820)Memory used [KB]: 2046
% 8.41/2.40 % (14820)Time elapsed: 0.009 s
% 8.41/2.40 % (14820)Instructions burned: 29 (million)
% 8.41/2.40 % (14820)------------------------------
% 8.41/2.40 % (14820)------------------------------
% 8.41/2.41 % (14821)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on DTF2THF_14628 for (2991ds/53Mi)
% 8.41/2.43 % (14821)Instruction limit reached!
% 8.41/2.43 % (14821)------------------------------
% 8.41/2.43 % (14821)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.41/2.43 % (14821)Termination reason: Unknown
% 8.41/2.43 % (14821)Termination phase: Property scanning
% 8.41/2.43
% 8.41/2.43 % (14821)Memory used [KB]: 2174
% 8.41/2.43 % (14821)Time elapsed: 0.016 s
% 8.41/2.43 % (14821)Instructions burned: 56 (million)
% 8.41/2.43 % (14821)------------------------------
% 8.41/2.43 % (14821)------------------------------
% 8.41/2.43 % (14822)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on DTF2THF_14628 for (2991ds/4436Mi)
% 8.41/2.45 % (14818)Instruction limit reached!
% 8.41/2.45 % (14818)------------------------------
% 8.41/2.45 % (14818)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.41/2.45 % (14818)Termination reason: Unknown
% 8.41/2.45 % (14818)Termination phase: Saturation
% 8.41/2.45
% 8.41/2.45 % (14818)Memory used [KB]: 7547
% 8.41/2.45 % (14818)Time elapsed: 0.077 s
% 8.41/2.45 % (14818)Instructions burned: 267 (million)
% 8.41/2.45 % (14818)------------------------------
% 8.41/2.45 % (14818)------------------------------
% 8.41/2.46 % (14823)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on DTF2THF_14628 for (2990ds/1539Mi)
% 8.41/2.48 % (14816)Instruction limit reached!
% 8.41/2.48 % (14816)------------------------------
% 8.41/2.48 % (14816)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.41/2.48 % (14816)Termination reason: Unknown
% 8.41/2.48 % (14816)Termination phase: Saturation
% 8.41/2.48
% 8.41/2.48 % (14816)Memory used [KB]: 8059
% 8.41/2.48 % (14816)Time elapsed: 0.104 s
% 8.41/2.48 % (14816)Instructions burned: 369 (million)
% 8.41/2.48 % (14816)------------------------------
% 8.41/2.48 % (14816)------------------------------
% 8.41/2.48 % (14819)Instruction limit reached!
% 8.41/2.48 % (14819)------------------------------
% 8.41/2.48 % (14819)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.41/2.48 % (14819)Termination reason: Unknown
% 8.41/2.48 % (14819)Termination phase: Saturation
% 8.41/2.48
% 8.41/2.48 % (14819)Memory used [KB]: 7419
% 8.41/2.48 % (14819)Time elapsed: 0.087 s
% 8.41/2.48 % (14819)Instructions burned: 204 (million)
% 8.41/2.48 % (14819)------------------------------
% 8.41/2.48 % (14819)------------------------------
% 8.41/2.49 % (14824)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=408:si=on:rtra=on_0 on DTF2THF_14628 for (2990ds/408Mi)
% 8.75/2.50 % (14825)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=5205:si=on:rtra=on_0 on DTF2THF_14628 for (2990ds/5205Mi)
% 8.75/2.54 % (14805)Instruction limit reached!
% 8.75/2.54 % (14805)------------------------------
% 8.75/2.54 % (14805)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.75/2.54 % (14805)Termination reason: Unknown
% 8.75/2.54 % (14805)Termination phase: Saturation
% 8.75/2.54
% 8.75/2.54 % (14805)Memory used [KB]: 9978
% 8.75/2.54 % (14805)Time elapsed: 0.297 s
% 8.75/2.54 % (14805)Instructions burned: 990 (million)
% 8.75/2.54 % (14805)------------------------------
% 8.75/2.54 % (14805)------------------------------
% 8.75/2.55 % (14826)dis+1010_1:4_au=on:av=off:cbe=off:nwc=10.0:s2a=on:s2at=3.0:sd=2:ss=axioms:st=5.0:i=1913:si=on:rtra=on_0 on DTF2THF_14628 for (2989ds/1913Mi)
% 8.75/2.59 % (14812)Instruction limit reached!
% 8.75/2.59 % (14812)------------------------------
% 8.75/2.59 % (14812)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.75/2.59 % (14812)Termination reason: Unknown
% 8.75/2.59 % (14812)Termination phase: Saturation
% 8.75/2.59
% 8.75/2.59 % (14812)Memory used [KB]: 8059
% 8.75/2.59 % (14812)Time elapsed: 0.278 s
% 8.75/2.59 % (14812)Instructions burned: 923 (million)
% 8.75/2.59 % (14812)------------------------------
% 8.75/2.59 % (14812)------------------------------
% 9.35/2.60 % (14827)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on DTF2THF_14628 for (2989ds/4350Mi)
% 9.35/2.60 % (14824)Instruction limit reached!
% 9.35/2.60 % (14824)------------------------------
% 9.35/2.60 % (14824)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.35/2.60 % (14824)Termination reason: Unknown
% 9.35/2.60 % (14824)Termination phase: Saturation
% 9.35/2.60
% 9.35/2.60 % (14824)Memory used [KB]: 8571
% 9.35/2.60 % (14824)Time elapsed: 0.119 s
% 9.35/2.60 % (14824)Instructions burned: 408 (million)
% 9.35/2.60 % (14824)------------------------------
% 9.35/2.60 % (14824)------------------------------
% 9.35/2.61 % (14828)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_14628 for (2989ds/68Mi)
% 9.35/2.64 % (14828)Instruction limit reached!
% 9.35/2.64 % (14828)------------------------------
% 9.35/2.64 % (14828)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.35/2.64 % (14828)Termination reason: Unknown
% 9.35/2.64 % (14828)Termination phase: Property scanning
% 9.35/2.64
% 9.35/2.64 % (14828)Memory used [KB]: 2430
% 9.35/2.64 % (14828)Time elapsed: 0.022 s
% 9.35/2.64 % (14828)Instructions burned: 70 (million)
% 9.35/2.64 % (14828)------------------------------
% 9.35/2.64 % (14828)------------------------------
% 9.35/2.64 % (14829)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on DTF2THF_14628 for (2989ds/358Mi)
% 9.35/2.68 % (14817)Instruction limit reached!
% 9.35/2.68 % (14817)------------------------------
% 9.35/2.68 % (14817)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.35/2.68 % (14817)Termination reason: Unknown
% 9.35/2.68 % (14817)Termination phase: Saturation
% 9.35/2.68
% 9.35/2.68 % (14817)Memory used [KB]: 10106
% 9.35/2.68 % (14817)Time elapsed: 0.302 s
% 9.35/2.68 % (14817)Instructions burned: 1022 (million)
% 9.35/2.68 % (14817)------------------------------
% 9.35/2.68 % (14817)------------------------------
% 9.35/2.69 % (14830)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_14628 for (2988ds/31Mi)
% 9.35/2.70 % (14830)Instruction limit reached!
% 9.35/2.70 % (14830)------------------------------
% 9.35/2.70 % (14830)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.35/2.70 % (14830)Termination reason: Unknown
% 9.35/2.70 % (14830)Termination phase: Property scanning
% 9.35/2.70
% 9.35/2.70 % (14830)Memory used [KB]: 1918
% 9.35/2.70 % (14830)Time elapsed: 0.011 s
% 9.35/2.70 % (14830)Instructions burned: 32 (million)
% 9.35/2.70 % (14830)------------------------------
% 9.35/2.70 % (14830)------------------------------
% 9.84/2.70 % (14831)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_14628 for (2988ds/279Mi)
% 9.84/2.73 % (14831)Refutation not found, incomplete strategy
% 9.84/2.73 % (14831)------------------------------
% 9.84/2.73 % (14831)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.84/2.73 % (14831)Termination reason: Refutation not found, incomplete strategy
% 9.84/2.73
% 9.84/2.73
% 9.84/2.73 % (14831)Memory used [KB]: 6908
% 9.84/2.73 % (14831)Time elapsed: 0.028 s
% 9.84/2.73 % (14831)Instructions burned: 101 (million)
% 9.84/2.73 % (14831)------------------------------
% 9.84/2.73 % (14831)------------------------------
% 9.84/2.74 % (14832)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_14628 for (2988ds/258Mi)
% 9.84/2.75 % (14829)Instruction limit reached!
% 9.84/2.75 % (14829)------------------------------
% 9.84/2.75 % (14829)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.84/2.75 % (14829)Termination reason: Unknown
% 9.84/2.75 % (14829)Termination phase: Saturation
% 9.84/2.75
% 9.84/2.75 % (14829)Memory used [KB]: 7547
% 9.84/2.75 % (14829)Time elapsed: 0.133 s
% 9.84/2.75 % (14829)Instructions burned: 360 (million)
% 9.84/2.75 % (14829)------------------------------
% 9.84/2.75 % (14829)------------------------------
% 9.84/2.76 % (14833)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_14628 for (2987ds/26Mi)
% 9.84/2.77 % (14833)Instruction limit reached!
% 9.84/2.77 % (14833)------------------------------
% 9.84/2.77 % (14833)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.84/2.77 % (14833)Termination reason: Unknown
% 9.84/2.77 % (14833)Termination phase: shuffling
% 9.84/2.77
% 9.84/2.77 % (14833)Memory used [KB]: 2046
% 9.84/2.77 % (14833)Time elapsed: 0.009 s
% 9.84/2.77 % (14833)Instructions burned: 28 (million)
% 9.84/2.77 % (14833)------------------------------
% 9.84/2.77 % (14833)------------------------------
% 9.84/2.78 % (14834)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=995:si=on:rtra=on_0 on DTF2THF_14628 for (2987ds/995Mi)
% 10.01/2.82 % (14832)Instruction limit reached!
% 10.01/2.82 % (14832)------------------------------
% 10.01/2.82 % (14832)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.01/2.82 % (14832)Termination reason: Unknown
% 10.01/2.82 % (14832)Termination phase: Saturation
% 10.01/2.82
% 10.01/2.82 % (14832)Memory used [KB]: 7675
% 10.01/2.82 % (14832)Time elapsed: 0.077 s
% 10.01/2.82 % (14832)Instructions burned: 261 (million)
% 10.01/2.82 % (14832)------------------------------
% 10.01/2.82 % (14832)------------------------------
% 10.01/2.83 % (14835)dis+10_1:8_amm=sco:cbe=off:hflw=5:hfsq=on:hfsqc=14:hfsql=off:hfsqr=4,1:hud=5:ile=on:lma=on:nm=2:ntd=on:prag=on:sac=on:sp=frequency:i=373:si=on:rtra=on_0 on DTF2THF_14628 for (2987ds/373Mi)
% 10.10/2.91 % (14823)Instruction limit reached!
% 10.10/2.91 % (14823)------------------------------
% 10.10/2.91 % (14823)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.10/2.91 % (14823)Termination reason: Unknown
% 10.10/2.91 % (14823)Termination phase: Saturation
% 10.10/2.91
% 10.10/2.91 % (14823)Memory used [KB]: 11385
% 10.10/2.91 % (14823)Time elapsed: 0.450 s
% 10.10/2.91 % (14823)Instructions burned: 1541 (million)
% 10.10/2.91 % (14823)------------------------------
% 10.10/2.91 % (14823)------------------------------
% 10.10/2.92 % (14836)lrs+1010_1:128_au=on:cnfonf=lazy_pi_sigma_gen:hflw=4:hfsq=on:hfsqc=20:hfsql=off:i=253:si=on:rtra=on_0 on DTF2THF_14628 for (2986ds/253Mi)
% 10.10/2.93 % (14835)Instruction limit reached!
% 10.10/2.93 % (14835)------------------------------
% 10.10/2.93 % (14835)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.10/2.93 % (14835)Termination reason: Unknown
% 10.10/2.93 % (14835)Termination phase: Saturation
% 10.10/2.93
% 10.10/2.93 % (14835)Memory used [KB]: 8315
% 10.10/2.93 % (14835)Time elapsed: 0.106 s
% 10.10/2.93 % (14835)Instructions burned: 375 (million)
% 10.10/2.93 % (14835)------------------------------
% 10.10/2.93 % (14835)------------------------------
% 10.10/2.94 % (14837)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=832:si=on:rtra=on_0 on DTF2THF_14628 for (2985ds/832Mi)
% 10.10/2.99 % (14836)Instruction limit reached!
% 10.10/2.99 % (14836)------------------------------
% 10.10/2.99 % (14836)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.10/2.99 % (14836)Termination reason: Unknown
% 10.10/2.99 % (14836)Termination phase: Saturation
% 10.10/2.99
% 10.10/2.99 % (14836)Memory used [KB]: 7419
% 10.10/2.99 % (14836)Time elapsed: 0.070 s
% 10.10/2.99 % (14836)Instructions burned: 253 (million)
% 10.10/2.99 % (14836)------------------------------
% 10.10/2.99 % (14836)------------------------------
% 10.10/3.00 % (14838)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=668:si=on:rtra=on_0 on DTF2THF_14628 for (2985ds/668Mi)
% 12.98/3.08 % (14834)Instruction limit reached!
% 12.98/3.08 % (14834)------------------------------
% 12.98/3.08 % (14834)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.98/3.08 % (14834)Termination reason: Unknown
% 12.98/3.08 % (14834)Termination phase: Saturation
% 12.98/3.08
% 12.98/3.08 % (14834)Memory used [KB]: 9466
% 12.98/3.08 % (14834)Time elapsed: 0.294 s
% 12.98/3.08 % (14834)Instructions burned: 997 (million)
% 12.98/3.08 % (14834)------------------------------
% 12.98/3.08 % (14834)------------------------------
% 12.98/3.09 % (14839)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=40:si=on:rtra=on_0 on DTF2THF_14628 for (2984ds/40Mi)
% 12.98/3.10 % (14839)Instruction limit reached!
% 12.98/3.10 % (14839)------------------------------
% 12.98/3.10 % (14839)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.98/3.10 % (14839)Termination reason: Unknown
% 12.98/3.10 % (14839)Termination phase: Property scanning
% 12.98/3.10
% 12.98/3.10 % (14839)Memory used [KB]: 2174
% 12.98/3.10 % (14839)Time elapsed: 0.013 s
% 12.98/3.10 % (14839)Instructions burned: 42 (million)
% 12.98/3.10 % (14839)------------------------------
% 12.98/3.10 % (14839)------------------------------
% 12.98/3.11 % (14840)lrs+1010_1:1_cnfonf=lazy_pi_sigma_gen:fd=off:ntd=on:sd=1:sgt=32:sos=on:ss=axioms:i=294:si=on:rtra=on_0 on DTF2THF_14628 for (2984ds/294Mi)
% 13.70/3.13 % (14840)Refutation not found, incomplete strategy
% 13.70/3.13 % (14840)------------------------------
% 13.70/3.13 % (14840)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.70/3.13 % (14840)Termination reason: Refutation not found, incomplete strategy
% 13.70/3.13
% 13.70/3.13
% 13.70/3.13 % (14840)Memory used [KB]: 6780
% 13.70/3.13 % (14840)Time elapsed: 0.025 s
% 13.70/3.13 % (14840)Instructions burned: 90 (million)
% 13.70/3.13 % (14840)------------------------------
% 13.70/3.13 % (14840)------------------------------
% 13.70/3.14 % (14826)Instruction limit reached!
% 13.70/3.14 % (14826)------------------------------
% 13.70/3.14 % (14826)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.70/3.14 % (14826)Termination reason: Unknown
% 13.70/3.14 % (14826)Termination phase: Saturation
% 13.70/3.14
% 13.70/3.14 % (14826)Memory used [KB]: 4989
% 13.70/3.14 % (14826)Time elapsed: 0.590 s
% 13.70/3.14 % (14826)Instructions burned: 1913 (million)
% 13.70/3.14 % (14826)------------------------------
% 13.70/3.14 % (14826)------------------------------
% 13.70/3.14 % (14841)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on DTF2THF_14628 for (2983ds/187Mi)
% 13.70/3.15 % (14842)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_14628 for (2983ds/371Mi)
% 13.70/3.20 % (14841)Instruction limit reached!
% 13.70/3.20 % (14841)------------------------------
% 13.70/3.20 % (14841)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.70/3.20 % (14841)Termination reason: Unknown
% 13.70/3.20 % (14841)Termination phase: Saturation
% 13.70/3.20
% 13.70/3.20 % (14841)Memory used [KB]: 7419
% 13.70/3.20 % (14841)Time elapsed: 0.053 s
% 13.70/3.20 % (14841)Instructions burned: 187 (million)
% 13.70/3.20 % (14841)------------------------------
% 13.70/3.20 % (14841)------------------------------
% 13.70/3.20 % (14838)Instruction limit reached!
% 13.70/3.20 % (14838)------------------------------
% 13.70/3.20 % (14838)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.70/3.20 % (14838)Termination reason: Unknown
% 13.70/3.20 % (14838)Termination phase: Saturation
% 13.70/3.20
% 13.70/3.20 % (14838)Memory used [KB]: 13688
% 13.70/3.20 % (14838)Time elapsed: 0.197 s
% 13.70/3.20 % (14838)Instructions burned: 668 (million)
% 13.70/3.20 % (14838)------------------------------
% 13.70/3.20 % (14838)------------------------------
% 14.20/3.20 % (14837)Instruction limit reached!
% 14.20/3.20 % (14837)------------------------------
% 14.20/3.20 % (14837)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.20/3.20 % (14837)Termination reason: Unknown
% 14.20/3.20 % (14837)Termination phase: Saturation
% 14.20/3.20
% 14.20/3.20 % (14837)Memory used [KB]: 8571
% 14.20/3.20 % (14837)Time elapsed: 0.259 s
% 14.20/3.20 % (14837)Instructions burned: 832 (million)
% 14.20/3.20 % (14837)------------------------------
% 14.20/3.20 % (14837)------------------------------
% 14.20/3.21 % (14843)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_14628 for (2983ds/1827Mi)
% 14.20/3.21 % (14844)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=70:si=on:rtra=on_0 on DTF2THF_14628 for (2983ds/70Mi)
% 14.20/3.21 % (14845)lrs+10_1:20_bd=off:cnfonf=lazy_not_be_gen:fe=axiom:hud=10:ins=1:nm=20:prag=on:sos=on:i=316:si=on:rtra=on_0 on DTF2THF_14628 for (2983ds/316Mi)
% 14.20/3.23 % (14844)Instruction limit reached!
% 14.20/3.23 % (14844)------------------------------
% 14.20/3.23 % (14844)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.20/3.23 % (14844)Termination reason: Unknown
% 14.20/3.23 % (14844)Termination phase: Preprocessing 1
% 14.20/3.23
% 14.20/3.23 % (14844)Memory used [KB]: 2302
% 14.20/3.23 % (14844)Time elapsed: 0.020 s
% 14.20/3.23 % (14844)Instructions burned: 72 (million)
% 14.20/3.23 % (14844)------------------------------
% 14.20/3.23 % (14844)------------------------------
% 14.20/3.23 % (14846)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=932:si=on:rtra=on_0 on DTF2THF_14628 for (2982ds/932Mi)
% 14.20/3.26 % (14842)Instruction limit reached!
% 14.20/3.26 % (14842)------------------------------
% 14.20/3.26 % (14842)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.20/3.26 % (14842)Termination reason: Unknown
% 14.20/3.26 % (14842)Termination phase: Saturation
% 14.20/3.26
% 14.20/3.26 % (14842)Memory used [KB]: 7675
% 14.20/3.26 % (14842)Time elapsed: 0.114 s
% 14.20/3.26 % (14842)Instructions burned: 371 (million)
% 14.20/3.26 % (14842)------------------------------
% 14.20/3.26 % (14842)------------------------------
% 14.20/3.27 % (14845)Refutation not found, incomplete strategy
% 14.20/3.27 % (14845)------------------------------
% 14.20/3.27 % (14845)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.20/3.27 % (14845)Termination reason: Refutation not found, incomplete strategy
% 14.20/3.27
% 14.20/3.27
% 14.20/3.27 % (14845)Memory used [KB]: 7547
% 14.20/3.27 % (14845)Time elapsed: 0.059 s
% 14.20/3.27 % (14845)Instructions burned: 214 (million)
% 14.20/3.27 % (14845)------------------------------
% 14.20/3.27 % (14845)------------------------------
% 14.20/3.27 % (14847)lrs+1010_1:128_au=on:bd=preordered:cnfonf=lazy_pi_sigma_gen:plsq=on:plsqc=1:plsqr=32,1:sos=all:sp=occurrence:i=4714:si=on:rtra=on_0 on DTF2THF_14628 for (2982ds/4714Mi)
% 14.20/3.28 % (14848)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=8250:si=on:rtra=on_0 on DTF2THF_14628 for (2982ds/8250Mi)
% 14.79/3.34 % (14847)Refutation not found, incomplete strategy
% 14.79/3.34 % (14847)------------------------------
% 14.79/3.34 % (14847)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.79/3.34 % (14847)Termination reason: Refutation not found, incomplete strategy
% 14.79/3.34
% 14.79/3.34
% 14.79/3.34 % (14847)Memory used [KB]: 7803
% 14.79/3.34 % (14847)Time elapsed: 0.068 s
% 14.79/3.34 % (14847)Instructions burned: 246 (million)
% 14.79/3.34 % (14847)------------------------------
% 14.79/3.34 % (14847)------------------------------
% 14.79/3.35 % (14849)lrs+1002_1:1_apa=on:cnfonf=off:fd=off:flr=on:hud=1:lcm=reverse:prag=on:sd=1:sos=on:ss=axioms:i=770:si=on:rtra=on_0 on DTF2THF_14628 for (2981ds/770Mi)
% 15.17/3.48 % (14849)Refutation not found, incomplete strategy
% 15.17/3.48 % (14849)------------------------------
% 15.17/3.48 % (14849)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.17/3.48 % (14849)Termination reason: Refutation not found, incomplete strategy
% 15.17/3.48
% 15.17/3.48
% 15.17/3.48 % (14849)Memory used [KB]: 7291
% 15.17/3.48 % (14849)Time elapsed: 0.126 s
% 15.17/3.48 % (14849)Instructions burned: 416 (million)
% 15.17/3.48 % (14849)------------------------------
% 15.17/3.48 % (14849)------------------------------
% 15.17/3.49 % (14850)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_14628 for (2980ds/794Mi)
% 15.61/3.50 % (14846)Instruction limit reached!
% 15.61/3.50 % (14846)------------------------------
% 15.61/3.50 % (14846)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.61/3.50 % (14846)Termination reason: Unknown
% 15.61/3.50 % (14846)Termination phase: Saturation
% 15.61/3.50
% 15.61/3.50 % (14846)Memory used [KB]: 10106
% 15.61/3.50 % (14846)Time elapsed: 0.265 s
% 15.61/3.50 % (14846)Instructions burned: 932 (million)
% 15.61/3.50 % (14846)------------------------------
% 15.61/3.50 % (14846)------------------------------
% 15.61/3.51 % (14851)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_14628 for (2980ds/464Mi)
% 16.18/3.64 % (14851)Instruction limit reached!
% 16.18/3.64 % (14851)------------------------------
% 16.18/3.64 % (14851)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.18/3.64 % (14851)Termination reason: Unknown
% 16.18/3.64 % (14851)Termination phase: Saturation
% 16.18/3.64
% 16.18/3.64 % (14851)Memory used [KB]: 7547
% 16.18/3.64 % (14851)Time elapsed: 0.130 s
% 16.18/3.64 % (14851)Instructions burned: 464 (million)
% 16.18/3.64 % (14851)------------------------------
% 16.18/3.64 % (14851)------------------------------
% 16.18/3.65 % (14852)ott+21_1:3_avsq=on:bd=off:cnfonf=lazy_gen:fe=off:hud=10:ixr=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=1376:si=on:rtra=on_0 on DTF2THF_14628 for (2978ds/1376Mi)
% 16.61/3.72 % (14850)Instruction limit reached!
% 16.61/3.72 % (14850)------------------------------
% 16.61/3.72 % (14850)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.61/3.72 % (14850)Termination reason: Unknown
% 16.61/3.72 % (14850)Termination phase: Saturation
% 16.61/3.72
% 16.61/3.72 % (14850)Memory used [KB]: 5373
% 16.61/3.72 % (14850)Time elapsed: 0.234 s
% 16.61/3.72 % (14850)Instructions burned: 794 (million)
% 16.61/3.72 % (14850)------------------------------
% 16.61/3.72 % (14850)------------------------------
% 16.61/3.73 % (14853)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_14628 for (2978ds/906Mi)
% 16.61/3.75 % (14822)Instruction limit reached!
% 16.61/3.75 % (14822)------------------------------
% 16.61/3.75 % (14822)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.61/3.75 % (14822)Termination reason: Unknown
% 16.61/3.75 % (14822)Termination phase: Saturation
% 16.61/3.75
% 16.61/3.75 % (14822)Memory used [KB]: 11001
% 16.61/3.75 % (14822)Time elapsed: 1.321 s
% 16.61/3.75 % (14822)Instructions burned: 4437 (million)
% 16.61/3.75 % (14822)------------------------------
% 16.61/3.75 % (14822)------------------------------
% 16.61/3.76 % (14854)lrs+1002_1:16_bd=off:e2e=on:fde=unused:kws=precedence:sac=on:sos=on:ss=axioms:i=434:si=on:rtra=on_0 on DTF2THF_14628 for (2977ds/434Mi)
% 16.61/3.77 % (14843)Instruction limit reached!
% 16.61/3.77 % (14843)------------------------------
% 16.61/3.77 % (14843)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.61/3.77 % (14843)Termination reason: Unknown
% 16.61/3.77 % (14843)Termination phase: Saturation
% 16.61/3.77
% 16.61/3.77 % (14843)Memory used [KB]: 11641
% 16.61/3.77 % (14843)Time elapsed: 0.567 s
% 16.61/3.77 % (14843)Instructions burned: 1829 (million)
% 16.61/3.77 % (14843)------------------------------
% 16.61/3.77 % (14843)------------------------------
% 16.61/3.78 % (14855)lrs+10_5:4_cnfonf=conj_eager:fe=axiom:hflw=5:hfsq=on:hfsqc=10:hfsql=off:hud=10:plsq=on:sgt=5:spb=goal_then_units:ss=axioms:i=865:si=on:rtra=on_0 on DTF2THF_14628 for (2977ds/865Mi)
% 17.70/3.86 % (14827)Instruction limit reached!
% 17.70/3.86 % (14827)------------------------------
% 17.70/3.86 % (14827)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.70/3.86 % (14827)Termination reason: Unknown
% 17.70/3.86 % (14827)Termination phase: Saturation
% 17.70/3.86
% 17.70/3.86 % (14827)Memory used [KB]: 12281
% 17.70/3.86 % (14827)Time elapsed: 1.271 s
% 17.70/3.86 % (14827)Instructions burned: 4350 (million)
% 17.70/3.86 % (14827)------------------------------
% 17.70/3.86 % (14827)------------------------------
% 17.70/3.87 % (14856)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=593:si=on:rtra=on_0 on DTF2THF_14628 for (2976ds/593Mi)
% 17.70/3.90 % (14854)Instruction limit reached!
% 17.70/3.90 % (14854)------------------------------
% 17.70/3.90 % (14854)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.70/3.90 % (14854)Termination reason: Unknown
% 17.70/3.90 % (14854)Termination phase: Saturation
% 17.70/3.90
% 17.70/3.90 % (14854)Memory used [KB]: 7291
% 17.70/3.90 % (14854)Time elapsed: 0.132 s
% 17.70/3.90 % (14854)Instructions burned: 434 (million)
% 17.70/3.90 % (14854)------------------------------
% 17.70/3.90 % (14854)------------------------------
% 17.88/3.91 % (14857)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_14628 for (2976ds/443Mi)
% 19.97/4.03 % (14853)Instruction limit reached!
% 19.97/4.03 % (14853)------------------------------
% 19.97/4.03 % (14853)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.97/4.03 % (14853)Termination reason: Unknown
% 19.97/4.03 % (14853)Termination phase: Saturation
% 19.97/4.03
% 19.97/4.03 % (14853)Memory used [KB]: 12281
% 19.97/4.03 % (14853)Time elapsed: 0.300 s
% 19.97/4.03 % (14853)Instructions burned: 906 (million)
% 19.97/4.03 % (14853)------------------------------
% 19.97/4.03 % (14853)------------------------------
% 19.97/4.03 % (14825)Instruction limit reached!
% 19.97/4.03 % (14825)------------------------------
% 19.97/4.03 % (14825)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.97/4.03 % (14825)Termination reason: Unknown
% 19.97/4.03 % (14825)Termination phase: Saturation
% 19.97/4.03
% 19.97/4.03 % (14825)Memory used [KB]: 16119
% 19.97/4.03 % (14825)Time elapsed: 1.546 s
% 19.97/4.03 % (14825)Instructions burned: 5208 (million)
% 19.97/4.03 % (14825)------------------------------
% 19.97/4.03 % (14825)------------------------------
% 19.97/4.04 % (14857)Instruction limit reached!
% 19.97/4.04 % (14857)------------------------------
% 19.97/4.04 % (14857)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.97/4.04 % (14857)Termination reason: Unknown
% 19.97/4.04 % (14855)Instruction limit reached!
% 19.97/4.04 % (14855)------------------------------
% 19.97/4.04 % (14855)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.97/4.04 % (14855)Termination reason: Unknown
% 19.97/4.04 % (14855)Termination phase: Saturation
% 19.97/4.04
% 19.97/4.04 % (14855)Memory used [KB]: 8187
% 19.97/4.04 % (14855)Time elapsed: 0.256 s
% 19.97/4.04 % (14855)Instructions burned: 867 (million)
% 19.97/4.04 % (14855)------------------------------
% 19.97/4.04 % (14855)------------------------------
% 19.97/4.04 % (14857)Termination phase: Saturation
% 19.97/4.04
% 19.97/4.04 % (14857)Memory used [KB]: 8187
% 19.97/4.04 % (14857)Time elapsed: 0.132 s
% 19.97/4.04 % (14857)Instructions burned: 445 (million)
% 19.97/4.04 % (14857)------------------------------
% 19.97/4.04 % (14857)------------------------------
% 19.97/4.04 % (14856)Instruction limit reached!
% 19.97/4.04 % (14856)------------------------------
% 19.97/4.04 % (14856)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.97/4.04 % (14856)Termination reason: Unknown
% 19.97/4.04 % (14856)Termination phase: Saturation
% 19.97/4.04
% 19.97/4.04 % (14856)Memory used [KB]: 9466
% 19.97/4.04 % (14856)Time elapsed: 0.170 s
% 19.97/4.04 % (14856)Instructions burned: 595 (million)
% 19.97/4.04 % (14856)------------------------------
% 19.97/4.04 % (14856)------------------------------
% 19.97/4.04 % (14858)dis+10_1:1_atotf=0.1:cbe=off:sd=3:ss=axioms:st=2.0:i=594:si=on:rtra=on_0 on DTF2THF_14628 for (2975ds/594Mi)
% 19.97/4.04 % (14859)ott+10_1:1024_anc=none:bd=off:e2e=on:fde=none:fsr=off:hud=10:ixr=off:nm=4:nwc=5.0:spb=goal:i=327:si=on:rtra=on_0 on DTF2THF_14628 for (2975ds/327Mi)
% 19.97/4.05 % (14860)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=5411:si=on:rtra=on_0 on DTF2THF_14628 for (2974ds/5411Mi)
% 19.97/4.05 % (14861)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=1762:si=on:rtra=on_0 on DTF2THF_14628 for (2974ds/1762Mi)
% 19.97/4.05 % (14862)dis+1003_1:64_cha=on:cnfonf=lazy_gen:hud=9:nwc=8.0:prag=on:i=96:si=on:rtra=on_0 on DTF2THF_14628 for (2974ds/96Mi)
% 19.97/4.06 % (14852)Instruction limit reached!
% 19.97/4.06 % (14852)------------------------------
% 19.97/4.06 % (14852)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.97/4.06 % (14852)Termination reason: Unknown
% 19.97/4.06 % (14852)Termination phase: Saturation
% 19.97/4.06
% 19.97/4.06 % (14852)Memory used [KB]: 13688
% 19.97/4.06 % (14852)Time elapsed: 0.409 s
% 19.97/4.06 % (14852)Instructions burned: 1377 (million)
% 19.97/4.06 % (14852)------------------------------
% 19.97/4.06 % (14852)------------------------------
% 19.97/4.07 % (14862)Instruction limit reached!
% 19.97/4.07 % (14862)------------------------------
% 19.97/4.07 % (14862)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.97/4.07 % (14862)Termination reason: Unknown
% 19.97/4.07 % (14862)Termination phase: Property scanning
% 19.97/4.07
% 19.97/4.07 % (14862)Memory used [KB]: 2430
% 19.97/4.07 % (14862)Time elapsed: 0.027 s
% 19.97/4.07 % (14862)Instructions burned: 98 (million)
% 19.97/4.07 % (14862)------------------------------
% 19.97/4.07 % (14862)------------------------------
% 19.97/4.07 % (14863)lrs+21_1:1_hud=5:kws=inv_frequency:nm=16:nwc=2.0:prag=on:sos=on:ss=axioms:i=503:si=on:rtra=on_0 on DTF2THF_14628 for (2974ds/503Mi)
% 19.97/4.08 % (14864)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_14628 for (2974ds/90Mi)
% 19.97/4.11 % (14864)Instruction limit reached!
% 19.97/4.11 % (14864)------------------------------
% 19.97/4.11 % (14864)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.97/4.11 % (14864)Termination reason: Unknown
% 19.97/4.11 % (14864)Termination phase: Property scanning
% 19.97/4.11
% 19.97/4.11 % (14864)Memory used [KB]: 2558
% 19.97/4.11 % (14864)Time elapsed: 0.027 s
% 19.97/4.11 % (14864)Instructions burned: 92 (million)
% 19.97/4.11 % (14864)------------------------------
% 19.97/4.11 % (14864)------------------------------
% 20.38/4.12 % (14865)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_14628 for (2974ds/593Mi)
% 20.38/4.14 % (14859)Instruction limit reached!
% 20.38/4.14 % (14859)------------------------------
% 20.38/4.14 % (14859)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.38/4.14 % (14859)Termination reason: Unknown
% 20.38/4.14 % (14859)Termination phase: Saturation
% 20.38/4.14
% 20.38/4.14 % (14859)Memory used [KB]: 7803
% 20.38/4.14 % (14859)Time elapsed: 0.101 s
% 20.38/4.14 % (14859)Instructions burned: 327 (million)
% 20.38/4.14 % (14859)------------------------------
% 20.38/4.14 % (14859)------------------------------
% 20.38/4.15 % (14866)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=1512:si=on:rtra=on_0 on DTF2THF_14628 for (2973ds/1512Mi)
% 20.56/4.22 % (14858)Instruction limit reached!
% 20.56/4.22 % (14858)------------------------------
% 20.56/4.22 % (14858)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.56/4.22 % (14858)Termination reason: Unknown
% 20.56/4.22 % (14858)Termination phase: Saturation
% 20.56/4.22
% 20.56/4.22 % (14858)Memory used [KB]: 8571
% 20.56/4.22 % (14858)Time elapsed: 0.185 s
% 20.56/4.22 % (14858)Instructions burned: 595 (million)
% 20.56/4.22 % (14858)------------------------------
% 20.56/4.22 % (14858)------------------------------
% 20.56/4.23 % (14867)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_14628 for (2973ds/569Mi)
% 20.56/4.24 % (14863)Instruction limit reached!
% 20.56/4.24 % (14863)------------------------------
% 20.56/4.24 % (14863)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.56/4.24 % (14863)Termination reason: Unknown
% 20.56/4.24 % (14863)Termination phase: Saturation
% 20.56/4.24
% 20.56/4.24 % (14863)Memory used [KB]: 7675
% 20.56/4.24 % (14863)Time elapsed: 0.162 s
% 20.56/4.24 % (14863)Instructions burned: 505 (million)
% 20.56/4.24 % (14863)------------------------------
% 20.56/4.24 % (14863)------------------------------
% 20.56/4.24 % (14868)ott+1002_1:1_bd=off:cnfonf=off:e2e=on:fd=off:fe=axiom:hud=5:prag=on:sos=on:i=501:si=on:rtra=on_0 on DTF2THF_14628 for (2973ds/501Mi)
% 20.56/4.29 % (14865)Instruction limit reached!
% 20.56/4.29 % (14865)------------------------------
% 20.56/4.29 % (14865)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.56/4.29 % (14865)Termination reason: Unknown
% 20.56/4.29 % (14865)Termination phase: Saturation
% 20.56/4.29
% 20.56/4.29 % (14865)Memory used [KB]: 9083
% 20.56/4.29 % (14865)Time elapsed: 0.169 s
% 20.56/4.29 % (14865)Instructions burned: 595 (million)
% 20.56/4.29 % (14865)------------------------------
% 20.56/4.29 % (14865)------------------------------
% 20.56/4.30 % (14869)lrs+1010_1:3_cnfonf=conj_eager:fsr=off:prag=on:sd=4:sgt=10:ss=axioms:i=562:si=on:rtra=on_0 on DTF2THF_14628 for (2972ds/562Mi)
% 21.20/4.39 % (14868)Instruction limit reached!
% 21.20/4.39 % (14868)------------------------------
% 21.20/4.39 % (14868)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.20/4.39 % (14868)Termination reason: Unknown
% 21.20/4.39 % (14868)Termination phase: Saturation
% 21.20/4.39
% 21.20/4.39 % (14868)Memory used [KB]: 8699
% 21.20/4.39 % (14868)Time elapsed: 0.151 s
% 21.20/4.39 % (14868)Instructions burned: 503 (million)
% 21.20/4.39 % (14868)------------------------------
% 21.20/4.39 % (14868)------------------------------
% 21.20/4.40 % (14867)Instruction limit reached!
% 21.20/4.40 % (14867)------------------------------
% 21.20/4.40 % (14867)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.46/4.40 % (14867)Termination reason: Unknown
% 21.46/4.40 % (14867)Termination phase: Saturation
% 21.46/4.40
% 21.46/4.40 % (14867)Memory used [KB]: 8699
% 21.46/4.40 % (14867)Time elapsed: 0.165 s
% 21.46/4.40 % (14867)Instructions burned: 571 (million)
% 21.46/4.40 % (14867)------------------------------
% 21.46/4.40 % (14867)------------------------------
% 21.46/4.41 % (14870)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_14628 for (2971ds/406Mi)
% 21.46/4.41 % (14871)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_14628 for (2971ds/582Mi)
% 21.46/4.47 % (14869)Instruction limit reached!
% 21.46/4.47 % (14869)------------------------------
% 21.46/4.47 % (14869)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.46/4.47 % (14869)Termination reason: Unknown
% 21.46/4.47 % (14869)Termination phase: Saturation
% 21.46/4.47
% 21.46/4.47 % (14869)Memory used [KB]: 7547
% 21.46/4.47 % (14869)Time elapsed: 0.192 s
% 21.46/4.47 % (14869)Instructions burned: 564 (million)
% 21.46/4.47 % (14869)------------------------------
% 21.46/4.47 % (14869)------------------------------
% 21.46/4.48 % (14872)lrs+2_1:1_au=on:bd=off:bsr=unit_only:sd=2:sgt=32:sos=all:ss=axioms:i=456:si=on:rtra=on_0 on DTF2THF_14628 for (2970ds/456Mi)
% 21.92/4.53 % (14870)Instruction limit reached!
% 21.92/4.53 % (14870)------------------------------
% 21.92/4.53 % (14870)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.92/4.53 % (14870)Termination reason: Unknown
% 21.92/4.53 % (14870)Termination phase: Saturation
% 21.92/4.53
% 21.92/4.53 % (14870)Memory used [KB]: 8059
% 21.92/4.53 % (14870)Time elapsed: 0.149 s
% 21.92/4.53 % (14870)Instructions burned: 407 (million)
% 21.92/4.53 % (14870)------------------------------
% 21.92/4.53 % (14870)------------------------------
% 21.92/4.54 % (14873)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_14628 for (2970ds/393Mi)
% 21.92/4.56 % (14861)Instruction limit reached!
% 21.92/4.56 % (14861)------------------------------
% 21.92/4.56 % (14861)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.92/4.56 % (14861)Termination reason: Unknown
% 21.92/4.56 % (14861)Termination phase: Saturation
% 21.92/4.56
% 21.92/4.56 % (14861)Memory used [KB]: 11641
% 21.92/4.56 % (14861)Time elapsed: 0.515 s
% 21.92/4.56 % (14861)Instructions burned: 1762 (million)
% 21.92/4.56 % (14861)------------------------------
% 21.92/4.56 % (14861)------------------------------
% 21.92/4.57 % (14874)lrs+1010_1:6_au=on:cnfonf=conj_eager:nwc=10.0:pe=on:prag=on:s2a=on:ss=axioms:st=1.5:i=1335:si=on:rtra=on_0 on DTF2THF_14628 for (2969ds/1335Mi)
% 21.92/4.58 % (14871)Instruction limit reached!
% 21.92/4.58 % (14871)------------------------------
% 21.92/4.58 % (14871)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.92/4.58 % (14871)Termination reason: Unknown
% 21.92/4.58 % (14871)Termination phase: Saturation
% 21.92/4.58
% 21.92/4.58 % (14871)Memory used [KB]: 9338
% 21.92/4.58 % (14871)Time elapsed: 0.194 s
% 21.92/4.58 % (14871)Instructions burned: 582 (million)
% 21.92/4.58 % (14871)------------------------------
% 21.92/4.58 % (14871)------------------------------
% 21.92/4.59 % (14875)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=3373:si=on:rtra=on_0 on DTF2THF_14628 for (2969ds/3373Mi)
% 22.86/4.61 % (14872)Instruction limit reached!
% 22.86/4.61 % (14872)------------------------------
% 22.86/4.61 % (14872)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.86/4.61 % (14872)Termination reason: Unknown
% 22.86/4.61 % (14872)Termination phase: Saturation
% 22.86/4.61
% 22.86/4.61 % (14872)Memory used [KB]: 8059
% 22.86/4.61 % (14872)Time elapsed: 0.160 s
% 22.86/4.61 % (14872)Instructions burned: 458 (million)
% 22.86/4.61 % (14872)------------------------------
% 22.86/4.61 % (14872)------------------------------
% 22.86/4.62 % (14866)Instruction limit reached!
% 22.86/4.62 % (14866)------------------------------
% 22.86/4.62 % (14866)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.86/4.62 % (14866)Termination reason: Unknown
% 22.86/4.62 % (14866)Termination phase: Saturation
% 22.86/4.62
% 22.86/4.62 % (14866)Memory used [KB]: 9338
% 22.86/4.62 % (14866)Time elapsed: 0.470 s
% 22.86/4.62 % (14866)Instructions burned: 1512 (million)
% 22.86/4.62 % (14866)------------------------------
% 22.86/4.62 % (14866)------------------------------
% 22.86/4.62 % (14876)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_14628 for (2969ds/474Mi)
% 22.86/4.63 % (14877)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_14628 for (2969ds/157Mi)
% 22.86/4.65 % (14873)Instruction limit reached!
% 22.86/4.65 % (14873)------------------------------
% 22.86/4.65 % (14873)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.86/4.65 % (14873)Termination reason: Unknown
% 22.86/4.65 % (14873)Termination phase: Saturation
% 22.86/4.65
% 22.86/4.65 % (14873)Memory used [KB]: 7675
% 22.86/4.65 % (14873)Time elapsed: 0.113 s
% 22.86/4.65 % (14873)Instructions burned: 393 (million)
% 22.86/4.65 % (14873)------------------------------
% 22.86/4.65 % (14873)------------------------------
% 22.86/4.66 % (14878)dis+1010_1:1_amm=off:cs=on:kws=precedence:nwc=10.0:piset=all:s2a=on:sac=on:sp=unary_frequency:spb=goal:ss=axioms:st=3.0:i=590:si=on:rtra=on_0 on DTF2THF_14628 for (2968ds/590Mi)
% 22.86/4.67 % (14877)Instruction limit reached!
% 22.86/4.67 % (14877)------------------------------
% 22.86/4.67 % (14877)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.86/4.67 % (14877)Termination reason: Unknown
% 22.86/4.67 % (14877)Termination phase: Saturation
% 22.86/4.67
% 22.86/4.67 % (14877)Memory used [KB]: 6908
% 22.86/4.67 % (14877)Time elapsed: 0.042 s
% 22.86/4.67 % (14877)Instructions burned: 159 (million)
% 22.86/4.67 % (14877)------------------------------
% 22.86/4.67 % (14877)------------------------------
% 22.86/4.68 % (14879)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_14628 for (2968ds/104Mi)
% 23.75/4.71 % (14879)Instruction limit reached!
% 23.75/4.71 % (14879)------------------------------
% 23.75/4.71 % (14879)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.75/4.71 % (14879)Termination reason: Unknown
% 23.75/4.71 % (14879)Termination phase: Saturation
% 23.75/4.71
% 23.75/4.71 % (14879)Memory used [KB]: 2558
% 23.75/4.71 % (14879)Time elapsed: 0.031 s
% 23.75/4.71 % (14879)Instructions burned: 107 (million)
% 23.75/4.71 % (14879)------------------------------
% 23.75/4.71 % (14879)------------------------------
% 23.75/4.72 % (14880)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_14628 for (2968ds/414Mi)
% 23.75/4.76 % (14876)Instruction limit reached!
% 23.75/4.76 % (14876)------------------------------
% 23.75/4.76 % (14876)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.75/4.76 % (14876)Termination reason: Unknown
% 23.75/4.76 % (14876)Termination phase: Saturation
% 23.75/4.76
% 23.75/4.76 % (14876)Memory used [KB]: 8699
% 23.75/4.76 % (14876)Time elapsed: 0.141 s
% 23.75/4.76 % (14876)Instructions burned: 476 (million)
% 23.75/4.76 % (14876)------------------------------
% 23.75/4.76 % (14876)------------------------------
% 23.75/4.77 % (14881)dis+10_1:1_av=off:bsd=on:bsr=unit_only:fd=off:hud=8:nm=16:prag=on:i=715:si=on:rtra=on_0 on DTF2THF_14628 for (2967ds/715Mi)
% 24.04/4.84 % (14878)Instruction limit reached!
% 24.04/4.84 % (14878)------------------------------
% 24.04/4.84 % (14878)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.04/4.84 % (14878)Termination reason: Unknown
% 24.04/4.84 % (14878)Termination phase: Saturation
% 24.04/4.84
% 24.04/4.84 % (14878)Memory used [KB]: 8571
% 24.04/4.84 % (14878)Time elapsed: 0.174 s
% 24.04/4.84 % (14878)Instructions burned: 593 (million)
% 24.04/4.84 % (14878)------------------------------
% 24.04/4.84 % (14878)------------------------------
% 24.04/4.84 % (14880)Instruction limit reached!
% 24.04/4.84 % (14880)------------------------------
% 24.04/4.84 % (14880)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.04/4.84 % (14880)Termination reason: Unknown
% 24.04/4.84 % (14880)Termination phase: Saturation
% 24.04/4.84
% 24.04/4.84 % (14880)Memory used [KB]: 7675
% 24.04/4.84 % (14880)Time elapsed: 0.118 s
% 24.04/4.84 % (14880)Instructions burned: 415 (million)
% 24.04/4.84 % (14880)------------------------------
% 24.04/4.84 % (14880)------------------------------
% 24.04/4.85 % (14882)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=961:si=on:rtra=on_0 on DTF2THF_14628 for (2966ds/961Mi)
% 24.04/4.85 % (14883)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=1213:si=on:rtra=on_0 on DTF2THF_14628 for (2966ds/1213Mi)
% 24.45/4.96 % (14874)Instruction limit reached!
% 24.45/4.96 % (14874)------------------------------
% 24.45/4.96 % (14874)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.45/4.96 % (14874)Termination reason: Unknown
% 24.45/4.96 % (14874)Termination phase: Saturation
% 24.45/4.96
% 24.45/4.96 % (14874)Memory used [KB]: 9338
% 24.45/4.96 % (14874)Time elapsed: 0.395 s
% 24.45/4.96 % (14874)Instructions burned: 1337 (million)
% 24.45/4.96 % (14874)------------------------------
% 24.45/4.96 % (14874)------------------------------
% 24.45/4.97 % (14884)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_14628 for (2965ds/1979Mi)
% 24.45/4.98 % (14881)Instruction limit reached!
% 24.45/4.98 % (14881)------------------------------
% 24.45/4.98 % (14881)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.45/4.98 % (14881)Termination reason: Unknown
% 24.45/4.98 % (14881)Termination phase: Saturation
% 24.45/4.98
% 24.45/4.98 % (14881)Memory used [KB]: 5117
% 24.45/4.98 % (14881)Time elapsed: 0.210 s
% 24.45/4.98 % (14881)Instructions burned: 716 (million)
% 24.45/4.98 % (14881)------------------------------
% 24.45/4.98 % (14881)------------------------------
% 24.45/4.99 % (14885)dis+1002_1:1_amm=off:au=on:bsd=on:cbe=off:cnfonf=lazy_gen:sp=unary_frequency:i=481:si=on:rtra=on_0 on DTF2THF_14628 for (2965ds/481Mi)
% 27.69/5.14 % (14885)Instruction limit reached!
% 27.69/5.14 % (14885)------------------------------
% 27.69/5.14 % (14885)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.69/5.14 % (14885)Termination reason: Unknown
% 27.69/5.14 % (14885)Termination phase: Saturation
% 27.69/5.14
% 27.69/5.14 % (14885)Memory used [KB]: 8059
% 27.69/5.14 % (14885)Time elapsed: 0.150 s
% 27.69/5.14 % (14885)Instructions burned: 483 (million)
% 27.69/5.14 % (14885)------------------------------
% 27.69/5.14 % (14885)------------------------------
% 27.69/5.14 % (14882)Instruction limit reached!
% 27.69/5.14 % (14882)------------------------------
% 27.69/5.14 % (14882)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.69/5.14 % (14882)Termination reason: Unknown
% 27.69/5.14 % (14882)Termination phase: Saturation
% 27.69/5.14
% 27.69/5.14 % (14882)Memory used [KB]: 8443
% 27.69/5.14 % (14882)Time elapsed: 0.298 s
% 27.69/5.14 % (14882)Instructions burned: 962 (million)
% 27.69/5.14 % (14882)------------------------------
% 27.69/5.14 % (14882)------------------------------
% 27.69/5.15 % (14886)dis+10_8:1_apa=on:cnfonf=off:e2e=on:plsq=on:plsqc=1:plsqr=32,1:ss=axioms:i=783:si=on:rtra=on_0 on DTF2THF_14628 for (2963ds/783Mi)
% 27.69/5.15 % (14887)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=432:si=on:rtra=on_0 on DTF2THF_14628 for (2963ds/432Mi)
% 28.18/5.24 % (14883)Instruction limit reached!
% 28.18/5.24 % (14883)------------------------------
% 28.18/5.24 % (14883)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.18/5.24 % (14883)Termination reason: Unknown
% 28.18/5.24 % (14883)Termination phase: Saturation
% 28.18/5.24
% 28.18/5.24 % (14883)Memory used [KB]: 9850
% 28.18/5.24 % (14883)Time elapsed: 0.393 s
% 28.18/5.24 % (14883)Instructions burned: 1216 (million)
% 28.18/5.24 % (14883)------------------------------
% 28.18/5.24 % (14883)------------------------------
% 28.18/5.25 % (14888)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=1670:si=on:rtra=on_0 on DTF2THF_14628 for (2962ds/1670Mi)
% 28.18/5.28 % (14887)Instruction limit reached!
% 28.18/5.28 % (14887)------------------------------
% 28.18/5.28 % (14887)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.18/5.28 % (14887)Termination reason: Unknown
% 28.18/5.28 % (14887)Termination phase: Saturation
% 28.18/5.28
% 28.18/5.28 % (14887)Memory used [KB]: 7419
% 28.18/5.28 % (14887)Time elapsed: 0.132 s
% 28.18/5.28 % (14887)Instructions burned: 434 (million)
% 28.18/5.28 % (14887)------------------------------
% 28.18/5.28 % (14887)------------------------------
% 28.18/5.29 % (14889)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_14628 for (2962ds/90Mi)
% 28.76/5.32 % (14889)Instruction limit reached!
% 28.76/5.32 % (14889)------------------------------
% 28.76/5.32 % (14889)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.76/5.32 % (14889)Termination reason: Unknown
% 28.76/5.32 % (14889)Termination phase: Property scanning
% 28.76/5.32
% 28.76/5.32 % (14889)Memory used [KB]: 2430
% 28.76/5.32 % (14889)Time elapsed: 0.027 s
% 28.76/5.32 % (14889)Instructions burned: 90 (million)
% 28.76/5.32 % (14889)------------------------------
% 28.76/5.32 % (14889)------------------------------
% 28.76/5.33 % (14890)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_14628 for (2962ds/346Mi)
% 28.76/5.39 % (14886)Instruction limit reached!
% 28.76/5.39 % (14886)------------------------------
% 28.76/5.39 % (14886)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.76/5.39 % (14886)Termination reason: Unknown
% 28.76/5.39 % (14886)Termination phase: Saturation
% 28.76/5.39
% 28.76/5.39 % (14886)Memory used [KB]: 8059
% 28.76/5.39 % (14886)Time elapsed: 0.237 s
% 28.76/5.39 % (14886)Instructions burned: 785 (million)
% 28.76/5.39 % (14886)------------------------------
% 28.76/5.39 % (14886)------------------------------
% 28.76/5.40 % (14891)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=401:si=on:rtra=on_0 on DTF2THF_14628 for (2961ds/401Mi)
% 29.44/5.43 % (14890)Instruction limit reached!
% 29.44/5.43 % (14890)------------------------------
% 29.44/5.43 % (14890)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.44/5.43 % (14890)Termination reason: Unknown
% 29.44/5.43 % (14890)Termination phase: Saturation
% 29.44/5.43
% 29.44/5.43 % (14890)Memory used [KB]: 7803
% 29.44/5.43 % (14890)Time elapsed: 0.103 s
% 29.44/5.43 % (14890)Instructions burned: 348 (million)
% 29.44/5.43 % (14890)------------------------------
% 29.44/5.43 % (14890)------------------------------
% 29.44/5.44 % (14892)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on DTF2THF_14628 for (2960ds/6454Mi)
% 29.44/5.46 % (14860)Refutation not found, non-redundant clauses discarded% (14860)------------------------------
% 29.44/5.46 % (14860)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.44/5.46 % (14860)Termination reason: Refutation not found, non-redundant clauses discarded
% 29.44/5.46
% 29.44/5.46 % (14860)Memory used [KB]: 8699
% 29.44/5.46 % (14860)Time elapsed: 1.421 s
% 29.44/5.46 % (14860)Instructions burned: 5193 (million)
% 29.44/5.46 % (14860)------------------------------
% 29.44/5.46 % (14860)------------------------------
% 29.44/5.47 % (14893)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:kws=arity:prag=on:i=283:si=on:rtra=on_0 on DTF2THF_14628 for (2960ds/283Mi)
% 29.92/5.51 % (14891)Instruction limit reached!
% 29.92/5.51 % (14891)------------------------------
% 29.92/5.51 % (14891)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.92/5.51 % (14891)Termination reason: Unknown
% 29.92/5.51 % (14891)Termination phase: Saturation
% 29.92/5.51
% 29.92/5.51 % (14891)Memory used [KB]: 8059
% 29.92/5.51 % (14891)Time elapsed: 0.112 s
% 29.92/5.51 % (14891)Instructions burned: 401 (million)
% 29.92/5.51 % (14891)------------------------------
% 29.92/5.51 % (14891)------------------------------
% 29.92/5.52 % (14894)ott+10_1:1_aac=none:apa=on:au=on:cnfonf=off:ntd=on:nwc=12.0:sos=on:i=865:si=on:rtra=on_0 on DTF2THF_14628 for (2960ds/865Mi)
% 29.92/5.55 % (14893)Instruction limit reached!
% 29.92/5.55 % (14893)------------------------------
% 29.92/5.55 % (14893)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.92/5.55 % (14893)Termination reason: Unknown
% 29.92/5.55 % (14893)Termination phase: Saturation
% 29.92/5.55
% 29.92/5.55 % (14893)Memory used [KB]: 7675
% 29.92/5.55 % (14893)Time elapsed: 0.080 s
% 29.92/5.55 % (14893)Instructions burned: 283 (million)
% 29.92/5.55 % (14893)------------------------------
% 29.92/5.55 % (14893)------------------------------
% 29.92/5.56 % (14895)lrs+1002_3:4_au=on:av=off:cnfonf=off:fd=off:fsr=off:ins=2:sd=1:sos=on:ss=axioms:i=4528:si=on:rtra=on_0 on DTF2THF_14628 for (2959ds/4528Mi)
% 29.92/5.56 % (14884)Instruction limit reached!
% 29.92/5.56 % (14884)------------------------------
% 29.92/5.56 % (14884)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.92/5.56 % (14884)Termination reason: Unknown
% 29.92/5.56 % (14884)Termination phase: Saturation
% 29.92/5.56
% 29.92/5.56 % (14884)Memory used [KB]: 9338
% 29.92/5.56 % (14884)Time elapsed: 0.588 s
% 29.92/5.56 % (14884)Instructions burned: 1979 (million)
% 29.92/5.56 % (14884)------------------------------
% 29.92/5.56 % (14884)------------------------------
% 29.92/5.57 % (14896)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=1001:si=on:rtra=on_0 on DTF2THF_14628 for (2959ds/1001Mi)
% 30.41/5.60 % (14875)Instruction limit reached!
% 30.41/5.60 % (14875)------------------------------
% 30.41/5.60 % (14875)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.41/5.60 % (14875)Termination reason: Unknown
% 30.41/5.60 % (14875)Termination phase: Saturation
% 30.41/5.60
% 30.41/5.60 % (14875)Memory used [KB]: 14583
% 30.41/5.60 % (14875)Time elapsed: 1.018 s
% 30.41/5.60 % (14875)Instructions burned: 3374 (million)
% 30.41/5.60 % (14875)------------------------------
% 30.41/5.60 % (14875)------------------------------
% 30.41/5.61 % (14897)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on DTF2THF_14628 for (2959ds/102Mi)
% 30.41/5.64 % (14897)Instruction limit reached!
% 30.41/5.64 % (14897)------------------------------
% 30.41/5.64 % (14897)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.41/5.64 % (14897)Termination reason: Unknown
% 30.41/5.64 % (14897)Termination phase: Property scanning
% 30.41/5.64
% 30.41/5.64 % (14897)Memory used [KB]: 2430
% 30.41/5.64 % (14897)Time elapsed: 0.029 s
% 30.41/5.64 % (14897)Instructions burned: 106 (million)
% 30.41/5.64 % (14897)------------------------------
% 30.41/5.64 % (14897)------------------------------
% 30.41/5.65 % (14898)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on DTF2THF_14628 for (2958ds/952Mi)
% 30.56/5.76 % (14888)Instruction limit reached!
% 30.56/5.76 % (14888)------------------------------
% 30.56/5.76 % (14888)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.56/5.76 % (14888)Termination reason: Unknown
% 30.56/5.76 % (14888)Termination phase: Saturation
% 30.56/5.76
% 30.56/5.76 % (14888)Memory used [KB]: 10234
% 30.56/5.76 % (14888)Time elapsed: 0.509 s
% 30.56/5.76 % (14888)Instructions burned: 1670 (million)
% 30.56/5.76 % (14888)------------------------------
% 30.56/5.76 % (14888)------------------------------
% 30.56/5.77 % (14899)lrs+1010_1:1024_add=large:c=on:cbe=off:cnfonf=lazy_gen:fde=none:nm=30:piset=and:sac=on:uhcvi=on:i=578:si=on:rtra=on_0 on DTF2THF_14628 for (2957ds/578Mi)
% 30.56/5.79 % (14894)Instruction limit reached!
% 30.56/5.79 % (14894)------------------------------
% 30.56/5.79 % (14894)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.56/5.79 % (14894)Termination reason: Unknown
% 30.56/5.79 % (14894)Termination phase: Saturation
% 30.56/5.79
% 30.56/5.79 % (14894)Memory used [KB]: 9466
% 30.56/5.79 % (14894)Time elapsed: 0.274 s
% 30.56/5.79 % (14894)Instructions burned: 865 (million)
% 30.56/5.79 % (14894)------------------------------
% 30.56/5.79 % (14894)------------------------------
% 31.46/5.80 % (14900)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on DTF2THF_14628 for (2957ds/643Mi)
% 31.46/5.81 % (14848)Instruction limit reached!
% 31.46/5.81 % (14848)------------------------------
% 31.46/5.81 % (14848)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.46/5.81 % (14848)Termination reason: Unknown
% 31.46/5.81 % (14848)Termination phase: Saturation
% 31.46/5.81
% 31.46/5.81 % (14848)Memory used [KB]: 14328
% 31.46/5.81 % (14848)Time elapsed: 2.532 s
% 31.46/5.81 % (14848)Instructions burned: 8251 (million)
% 31.46/5.81 % (14848)------------------------------
% 31.46/5.81 % (14848)------------------------------
% 31.46/5.82 % (14909)lrs+1010_1:1_cnfonf=off:ntd=on:nwc=3.0:s2a=on:sp=const_frequency:i=865:si=on:rtra=on_0 on DTF2THF_14628 for (2957ds/865Mi)
% 31.46/5.87 % (14896)Instruction limit reached!
% 31.46/5.87 % (14896)------------------------------
% 31.46/5.87 % (14896)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.46/5.87 % (14896)Termination reason: Unknown
% 31.46/5.87 % (14896)Termination phase: Saturation
% 31.46/5.87
% 31.46/5.87 % (14896)Memory used [KB]: 10490
% 31.46/5.87 % (14896)Time elapsed: 0.303 s
% 31.46/5.87 % (14896)Instructions burned: 1001 (million)
% 31.46/5.87 % (14896)------------------------------
% 31.46/5.87 % (14896)------------------------------
% 31.46/5.88 % (14942)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on DTF2THF_14628 for (2956ds/1174Mi)
% 31.80/5.93 % (14898)Instruction limit reached!
% 31.80/5.93 % (14898)------------------------------
% 31.80/5.93 % (14898)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.80/5.93 % (14898)Termination reason: Unknown
% 31.80/5.93 % (14898)Termination phase: Saturation
% 31.80/5.93
% 31.80/5.93 % (14898)Memory used [KB]: 9722
% 31.80/5.93 % (14898)Time elapsed: 0.278 s
% 31.80/5.93 % (14898)Instructions burned: 952 (million)
% 31.80/5.93 % (14898)------------------------------
% 31.80/5.93 % (14898)------------------------------
% 31.80/5.94 % (14899)Instruction limit reached!
% 31.80/5.94 % (14899)------------------------------
% 31.80/5.94 % (14899)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.80/5.94 % (14899)Termination reason: Unknown
% 31.80/5.94 % (14899)Termination phase: Saturation
% 31.80/5.94
% 31.80/5.94 % (14899)Memory used [KB]: 9083
% 31.80/5.94 % (14899)Time elapsed: 0.172 s
% 31.80/5.94 % (14899)Instructions burned: 578 (million)
% 31.80/5.94 % (14899)------------------------------
% 31.80/5.94 % (14899)------------------------------
% 31.80/5.94 % (14964)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=644:si=on:rtra=on_0 on DTF2THF_14628 for (2956ds/644Mi)
% 31.80/5.95 % (14970)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on DTF2THF_14628 for (2955ds/1201Mi)
% 31.80/5.99 % (14900)Instruction limit reached!
% 31.80/5.99 % (14900)------------------------------
% 31.80/5.99 % (14900)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.80/5.99 % (14900)Termination reason: Unknown
% 31.80/5.99 % (14900)Termination phase: Saturation
% 31.80/5.99
% 31.80/5.99 % (14900)Memory used [KB]: 9466
% 31.80/5.99 % (14900)Time elapsed: 0.194 s
% 31.80/5.99 % (14900)Instructions burned: 645 (million)
% 31.80/5.99 % (14900)------------------------------
% 31.80/5.99 % (14900)------------------------------
% 31.80/6.00 % (14996)lrs+1666_1:64_cnfonf=lazy_simp:hud=5:plsq=on:plsql=on:plsqr=152565,524288:tnu=2:i=1046:si=on:rtra=on_0 on DTF2THF_14628 for (2955ds/1046Mi)
% 34.03/6.09 % (14909)Instruction limit reached!
% 34.03/6.09 % (14909)------------------------------
% 34.03/6.09 % (14909)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.03/6.09 % (14909)Termination reason: Unknown
% 34.03/6.09 % (14909)Termination phase: Saturation
% 34.03/6.09
% 34.03/6.09 % (14909)Memory used [KB]: 9466
% 34.03/6.09 % (14909)Time elapsed: 0.270 s
% 34.03/6.09 % (14909)Instructions burned: 865 (million)
% 34.03/6.09 % (14909)------------------------------
% 34.03/6.09 % (14909)------------------------------
% 34.03/6.10 % (15046)lrs+1010_1:1_c=on:cnfonf=lazy_simp:fsr=off:hud=5:kws=arity:nm=32:plsq=on:plsqc=1:plsqr=642,29:prag=on:i=222:si=on:rtra=on_0 on DTF2THF_14628 for (2954ds/222Mi)
% 34.73/6.15 % (14964)Instruction limit reached!
% 34.73/6.15 % (14964)------------------------------
% 34.73/6.15 % (14964)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.73/6.15 % (14964)Termination reason: Unknown
% 34.73/6.15 % (14964)Termination phase: Saturation
% 34.73/6.15
% 34.73/6.15 % (14964)Memory used [KB]: 8955
% 34.73/6.15 % (14964)Time elapsed: 0.210 s
% 34.73/6.15 % (14964)Instructions burned: 644 (million)
% 34.73/6.15 % (14964)------------------------------
% 34.73/6.15 % (14964)------------------------------
% 34.73/6.16 % (15073)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_14628 for (2953ds/68Mi)
% 34.73/6.16 % (15046)Instruction limit reached!
% 34.73/6.16 % (15046)------------------------------
% 34.73/6.16 % (15046)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.73/6.16 % (15046)Termination reason: Unknown
% 34.73/6.16 % (15046)Termination phase: Saturation
% 34.73/6.16
% 34.73/6.16 % (15046)Memory used [KB]: 7291
% 34.73/6.16 % (15046)Time elapsed: 0.064 s
% 34.73/6.16 % (15046)Instructions burned: 224 (million)
% 34.73/6.16 % (15046)------------------------------
% 34.73/6.16 % (15046)------------------------------
% 34.73/6.17 % (15078)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=454:si=on:rtra=on_0 on DTF2THF_14628 for (2953ds/454Mi)
% 34.73/6.18 % (15073)Instruction limit reached!
% 34.73/6.18 % (15073)------------------------------
% 34.73/6.18 % (15073)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.73/6.18 % (15073)Termination reason: Unknown
% 34.73/6.18 % (15073)Termination phase: Property scanning
% 34.73/6.18
% 34.73/6.18 % (15073)Memory used [KB]: 2430
% 34.73/6.18 % (15073)Time elapsed: 0.022 s
% 34.73/6.18 % (15073)Instructions burned: 70 (million)
% 34.73/6.18 % (15073)------------------------------
% 34.73/6.18 % (15073)------------------------------
% 34.73/6.19 % (15083)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on DTF2THF_14628 for (2953ds/360Mi)
% 35.25/6.24 % (14942)Instruction limit reached!
% 35.25/6.24 % (14942)------------------------------
% 35.25/6.24 % (14942)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.25/6.24 % (14942)Termination reason: Unknown
% 35.25/6.24 % (14942)Termination phase: Saturation
% 35.25/6.24
% 35.25/6.24 % (14942)Memory used [KB]: 10106
% 35.25/6.24 % (14942)Time elapsed: 0.362 s
% 35.25/6.24 % (14942)Instructions burned: 1175 (million)
% 35.25/6.24 % (14942)------------------------------
% 35.25/6.24 % (14942)------------------------------
% 35.25/6.25 % (15114)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_14628 for (2952ds/157Mi)
% 35.25/6.29 % (15083)Instruction limit reached!
% 35.25/6.29 % (15083)------------------------------
% 35.25/6.29 % (15083)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.25/6.29 % (15083)Termination reason: Unknown
% 35.25/6.29 % (15083)Termination phase: Saturation
% 35.25/6.29
% 35.25/6.29 % (15083)Memory used [KB]: 7931
% 35.25/6.29 % (15083)Time elapsed: 0.103 s
% 35.25/6.29 % (15083)Instructions burned: 363 (million)
% 35.25/6.29 % (15083)------------------------------
% 35.25/6.29 % (15083)------------------------------
% 35.25/6.29 % (15114)Instruction limit reached!
% 35.25/6.29 % (15114)------------------------------
% 35.25/6.29 % (15114)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.25/6.29 % (15114)Termination reason: Unknown
% 35.25/6.29 % (15114)Termination phase: Saturation
% 35.25/6.29
% 35.25/6.29 % (15114)Memory used [KB]: 6908
% 35.25/6.29 % (15114)Time elapsed: 0.042 s
% 35.25/6.29 % (15114)Instructions burned: 157 (million)
% 35.25/6.29 % (15114)------------------------------
% 35.25/6.29 % (15114)------------------------------
% 35.86/6.30 % (15140)ott+1004_1:24_anc=none:cbe=off:cnfonf=lazy_not_gen:fe=off:piset=not:prag=on:rp=on:i=5061:si=on:rtra=on_0 on DTF2THF_14628 for (2952ds/5061Mi)
% 35.86/6.30 % (15078)Instruction limit reached!
% 35.86/6.30 % (15078)------------------------------
% 35.86/6.30 % (15078)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.86/6.30 % (15078)Termination reason: Unknown
% 35.86/6.30 % (15078)Termination phase: Saturation
% 35.86/6.30
% 35.86/6.30 % (15078)Memory used [KB]: 12537
% 35.86/6.30 % (15078)Time elapsed: 0.133 s
% 35.86/6.30 % (15078)Instructions burned: 454 (million)
% 35.86/6.30 % (15078)------------------------------
% 35.86/6.30 % (15078)------------------------------
% 35.86/6.30 % (14970)Instruction limit reached!
% 35.86/6.30 % (14970)------------------------------
% 35.86/6.30 % (14970)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.86/6.30 % (14970)Termination reason: Unknown
% 35.86/6.30 % (14970)Termination phase: Saturation
% 35.86/6.30
% 35.86/6.30 % (14970)Memory used [KB]: 9722
% 35.86/6.30 % (14970)Time elapsed: 0.358 s
% 35.86/6.30 % (14970)Instructions burned: 1202 (million)
% 35.86/6.30 % (14970)------------------------------
% 35.86/6.30 % (14970)------------------------------
% 35.86/6.30 % (15141)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=2401:si=on:rtra=on_0 on DTF2THF_14628 for (2952ds/2401Mi)
% 35.86/6.31 % (15142)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=5798:si=on:rtra=on_0 on DTF2THF_14628 for (2952ds/5798Mi)
% 35.86/6.31 % (15143)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_14628 for (2952ds/346Mi)
% 35.86/6.32 % (14996)Instruction limit reached!
% 35.86/6.32 % (14996)------------------------------
% 35.86/6.32 % (14996)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.86/6.32 % (14996)Termination reason: Unknown
% 35.86/6.32 % (14996)Termination phase: Saturation
% 35.86/6.32
% 35.86/6.32 % (14996)Memory used [KB]: 8955
% 35.86/6.32 % (14996)Time elapsed: 0.315 s
% 35.86/6.32 % (14996)Instructions burned: 1048 (million)
% 35.86/6.32 % (14996)------------------------------
% 35.86/6.32 % (14996)------------------------------
% 35.86/6.33 % (15144)lrs+1002_1:1_av=off:bd=off:bet=on:e2e=on:fde=unused:fe=off:plsq=on:prag=on:sos=on:i=1321:si=on:rtra=on_0 on DTF2THF_14628 for (2952ds/1321Mi)
% 36.24/6.42 % (15143)Instruction limit reached!
% 36.24/6.42 % (15143)------------------------------
% 36.24/6.42 % (15143)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.24/6.42 % (15143)Termination reason: Unknown
% 36.24/6.42 % (15143)Termination phase: Saturation
% 36.24/6.42
% 36.24/6.42 % (15143)Memory used [KB]: 7803
% 36.24/6.42 % (15143)Time elapsed: 0.107 s
% 36.24/6.42 % (15143)Instructions burned: 348 (million)
% 36.24/6.42 % (15143)------------------------------
% 36.24/6.42 % (15143)------------------------------
% 36.24/6.43 % (15145)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:i=1312:si=on:rtra=on_0 on DTF2THF_14628 for (2951ds/1312Mi)
% 36.95/6.72 % (15144)Instruction limit reached!
% 36.95/6.72 % (15144)------------------------------
% 36.95/6.72 % (15144)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.95/6.72 % (15144)Termination reason: Unknown
% 36.95/6.72 % (15144)Termination phase: Saturation
% 36.95/6.72
% 36.95/6.72 % (15144)Memory used [KB]: 5756
% 36.95/6.72 % (15144)Time elapsed: 0.399 s
% 36.95/6.72 % (15144)Instructions burned: 1322 (million)
% 36.95/6.72 % (15144)------------------------------
% 36.95/6.72 % (15144)------------------------------
% 36.95/6.73 % (15146)ott+2_8:1_add=large:c=on:cnfonf=off:e2e=on:er=filter:hud=5:plsq=on:plsqr=1,1:ss=axioms:i=672:si=on:rtra=on_0 on DTF2THF_14628 for (2948ds/672Mi)
% 37.58/6.82 % (15145)Instruction limit reached!
% 37.58/6.82 % (15145)------------------------------
% 37.58/6.82 % (15145)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.58/6.82 % (15145)Termination reason: Unknown
% 37.58/6.82 % (15145)Termination phase: Saturation
% 37.58/6.82
% 37.58/6.82 % (15145)Memory used [KB]: 9594
% 37.58/6.82 % (15145)Time elapsed: 0.394 s
% 37.58/6.82 % (15145)Instructions burned: 1314 (million)
% 37.58/6.82 % (15145)------------------------------
% 37.58/6.82 % (15145)------------------------------
% 37.58/6.83 % (15147)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=1897:si=on:rtra=on_0 on DTF2THF_14628 for (2947ds/1897Mi)
% 38.19/6.91 % (14895)Instruction limit reached!
% 38.19/6.91 % (14895)------------------------------
% 38.19/6.91 % (14895)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.19/6.91 % (14895)Termination reason: Unknown
% 38.19/6.91 % (14895)Termination phase: Saturation
% 38.19/6.91
% 38.19/6.91 % (14895)Memory used [KB]: 10746
% 38.19/6.91 % (14895)Time elapsed: 1.354 s
% 38.19/6.91 % (14895)Instructions burned: 4530 (million)
% 38.19/6.91 % (14895)------------------------------
% 38.19/6.91 % (14895)------------------------------
% 38.19/6.92 % (15148)lrs+10_1:40_av=off:fde=unused:ntd=on:plsq=on:plsqc=2:plsqr=411915,1048576:sp=unary_frequency:tgt=full:i=1202:si=on:rtra=on_0 on DTF2THF_14628 for (2946ds/1202Mi)
% 38.19/6.94 % (15146)Instruction limit reached!
% 38.19/6.94 % (15146)------------------------------
% 38.19/6.94 % (15146)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.19/6.94 % (15146)Termination reason: Unknown
% 38.19/6.94 % (15146)Termination phase: Saturation
% 38.19/6.94
% 38.19/6.94 % (15146)Memory used [KB]: 8955
% 38.19/6.94 % (15146)Time elapsed: 0.203 s
% 38.19/6.94 % (15146)Instructions burned: 675 (million)
% 38.19/6.94 % (15146)------------------------------
% 38.19/6.94 % (15146)------------------------------
% 38.19/6.94 % (15149)dis+21_1:1_au=on:cnfonf=lazy_pi_sigma_gen:hfsq=on:hfsqc=40:hfsqr=8,1:ntd=on:sos=on:sp=occurrence:ss=axioms:i=1493:si=on:rtra=on_0 on DTF2THF_14628 for (2945ds/1493Mi)
% 38.19/6.97 % (15149)Refutation not found, incomplete strategy
% 38.19/6.97 % (15149)------------------------------
% 38.19/6.97 % (15149)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.19/6.97 % (15149)Termination reason: Refutation not found, incomplete strategy
% 38.19/6.97
% 38.19/6.97
% 38.19/6.97 % (15149)Memory used [KB]: 6908
% 38.19/6.97 % (15149)Time elapsed: 0.029 s
% 38.19/6.97 % (15149)Instructions burned: 104 (million)
% 38.19/6.97 % (15149)------------------------------
% 38.19/6.97 % (15149)------------------------------
% 38.19/6.98 % (15150)dis+1010_3:1_av=off:fde=unused:hud=10:nwc=10.0:s2a=on:ss=axioms:i=7679:si=on:rtra=on_0 on DTF2THF_14628 for (2945ds/7679Mi)
% 41.06/7.03 % (15141)Instruction limit reached!
% 41.06/7.03 % (15141)------------------------------
% 41.06/7.03 % (15141)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.06/7.03 % (15141)Termination reason: Unknown
% 41.06/7.03 % (15141)Termination phase: Saturation
% 41.06/7.03
% 41.06/7.03 % (15141)Memory used [KB]: 6524
% 41.06/7.03 % (15141)Time elapsed: 0.732 s
% 41.06/7.03 % (15141)Instructions burned: 2401 (million)
% 41.06/7.03 % (15141)------------------------------
% 41.06/7.03 % (15141)------------------------------
% 41.06/7.05 % (15151)lrs+2_1:1024_anc=all:cnfonf=off:cs=on:e2e=on:nm=20:s2at=1.5:slsq=on:slsqr=1,2:spb=goal:i=340:si=on:rtra=on_0 on DTF2THF_14628 for (2945ds/340Mi)
% 41.70/7.14 % (15151)Instruction limit reached!
% 41.70/7.14 % (15151)------------------------------
% 41.70/7.14 % (15151)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.70/7.14 % (15151)Termination reason: Unknown
% 41.70/7.14 % (15151)Termination phase: Saturation
% 41.70/7.14
% 41.70/7.14 % (15151)Memory used [KB]: 7419
% 41.70/7.14 % (15151)Time elapsed: 0.096 s
% 41.70/7.14 % (15151)Instructions burned: 340 (million)
% 41.70/7.14 % (15151)------------------------------
% 41.70/7.14 % (15151)------------------------------
% 41.70/7.15 % (15152)dis+1002_1:1_acc=model:au=on:nwc=5.0:sd=5:ss=axioms:st=2.5:i=3672:si=on:rtra=on_0 on DTF2THF_14628 for (2943ds/3672Mi)
% 42.26/7.29 % (15148)Instruction limit reached!
% 42.26/7.29 % (15148)------------------------------
% 42.26/7.29 % (15148)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.26/7.29 % (15148)Termination reason: Unknown
% 42.26/7.29 % (15148)Termination phase: Saturation
% 42.26/7.29
% 42.26/7.29 % (15148)Memory used [KB]: 4605
% 42.26/7.29 % (15148)Time elapsed: 0.372 s
% 42.26/7.29 % (15148)Instructions burned: 1203 (million)
% 42.26/7.29 % (15148)------------------------------
% 42.26/7.29 % (15148)------------------------------
% 42.85/7.30 % (15153)dis-1002_3:1_acc=model:bd=off:bsd=on:bsdmm=1:cnfonf=lazy_not_be_gen:fd=off:fe=off:ntd=on:nwc=10.0:piset=equals:plsq=on:plsqc=1:plsqr=32,1:sp=const_max:uhcvi=on:i=1535:si=on:rtra=on_0 on DTF2THF_14628 for (2942ds/1535Mi)
% 42.85/7.33 % (14892)Refutation not found, non-redundant clauses discarded% (14892)------------------------------
% 42.85/7.33 % (14892)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.85/7.33 % (14892)Termination reason: Refutation not found, non-redundant clauses discarded
% 42.85/7.33
% 42.85/7.33 % (14892)Memory used [KB]: 9850
% 42.85/7.33 % (14892)Time elapsed: 1.887 s
% 42.85/7.33 % (14892)Instructions burned: 6156 (million)
% 42.85/7.33 % (14892)------------------------------
% 42.85/7.33 % (14892)------------------------------
% 42.85/7.34 % (15154)dis+10_16:1_hud=1:plsq=on:plsqc=1:plsqr=32,1:prag=on:sd=1:sgt=64:ss=axioms:i=4637:si=on:rtra=on_0 on DTF2THF_14628 for (2941ds/4637Mi)
% 43.29/7.43 % (15147)Instruction limit reached!
% 43.29/7.43 % (15147)------------------------------
% 43.29/7.43 % (15147)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.29/7.43 % (15147)Termination reason: Unknown
% 43.29/7.43 % (15147)Termination phase: Saturation
% 43.29/7.43
% 43.29/7.43 % (15147)Memory used [KB]: 9594
% 43.29/7.43 % (15147)Time elapsed: 0.600 s
% 43.29/7.43 % (15147)Instructions burned: 1898 (million)
% 43.29/7.43 % (15147)------------------------------
% 43.29/7.43 % (15147)------------------------------
% 43.29/7.44 % (15155)lrs+10_1:1_fde=unused:prag=on:sd=2:sgt=32:ss=axioms:i=3174:si=on:rtra=on_0 on DTF2THF_14628 for (2940ds/3174Mi)
% 44.24/7.76 % (15153)Instruction limit reached!
% 44.24/7.76 % (15153)------------------------------
% 44.24/7.76 % (15153)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.24/7.76 % (15153)Termination reason: Unknown
% 44.24/7.76 % (15153)Termination phase: Saturation
% 44.24/7.76
% 44.24/7.76 % (15153)Memory used [KB]: 12153
% 44.24/7.76 % (15153)Time elapsed: 0.459 s
% 44.24/7.76 % (15153)Instructions burned: 1535 (million)
% 44.24/7.76 % (15153)------------------------------
% 44.24/7.76 % (15153)------------------------------
% 44.24/7.77 % (15156)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_14628 for (2937ds/307Mi)
% 45.00/7.85 % (15156)Instruction limit reached!
% 45.00/7.85 % (15156)------------------------------
% 45.00/7.85 % (15156)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 45.00/7.85 % (15156)Termination reason: Unknown
% 45.00/7.85 % (15156)Termination phase: Saturation
% 45.00/7.85
% 45.00/7.85 % (15156)Memory used [KB]: 7419
% 45.00/7.85 % (15156)Time elapsed: 0.085 s
% 45.00/7.85 % (15156)Instructions burned: 308 (million)
% 45.00/7.85 % (15156)------------------------------
% 45.00/7.85 % (15156)------------------------------
% 45.00/7.86 % (15157)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=3619:si=on:rtra=on_0 on DTF2THF_14628 for (2936ds/3619Mi)
% 45.00/7.88 % (15140)Instruction limit reached!
% 45.00/7.88 % (15140)------------------------------
% 45.00/7.88 % (15140)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 45.00/7.88 % (15140)Termination reason: Unknown
% 45.00/7.88 % (15140)Termination phase: Saturation
% 45.00/7.88
% 45.00/7.88 % (15140)Memory used [KB]: 18549
% 45.00/7.88 % (15140)Time elapsed: 1.583 s
% 45.00/7.88 % (15140)Instructions burned: 5064 (million)
% 45.00/7.88 % (15140)------------------------------
% 45.00/7.88 % (15140)------------------------------
% 45.00/7.89 % (15158)lrs+1002_1:1_au=on:cbe=off:fde=none:ins=1:sp=const_max:i=2325:si=on:rtra=on_0 on DTF2THF_14628 for (2936ds/2325Mi)
% 48.07/8.08 % (15142)Instruction limit reached!
% 48.07/8.08 % (15142)------------------------------
% 48.07/8.08 % (15142)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.07/8.08 % (15142)Termination reason: Unknown
% 48.07/8.08 % (15142)Termination phase: Saturation
% 48.07/8.08
% 48.07/8.08 % (15142)Memory used [KB]: 10490
% 48.07/8.08 % (15142)Time elapsed: 1.767 s
% 48.07/8.08 % (15142)Instructions burned: 5800 (million)
% 48.07/8.08 % (15142)------------------------------
% 48.07/8.08 % (15142)------------------------------
% 48.07/8.09 % (15159)dis+1002_1:1_au=on:sac=on:sd=5:slsq=on:slsqr=1,4:ss=axioms:st=2.0:i=2341:si=on:rtra=on_0 on DTF2THF_14628 for (2934ds/2341Mi)
% 49.80/8.30 % (15152)Instruction limit reached!
% 49.80/8.30 % (15152)------------------------------
% 49.80/8.30 % (15152)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.80/8.30 % (15152)Termination reason: Unknown
% 49.80/8.30 % (15152)Termination phase: Saturation
% 49.80/8.30
% 49.80/8.30 % (15152)Memory used [KB]: 12409
% 49.80/8.30 % (15152)Time elapsed: 1.154 s
% 49.80/8.30 % (15152)Instructions burned: 3674 (million)
% 49.80/8.30 % (15152)------------------------------
% 49.80/8.30 % (15152)------------------------------
% 49.80/8.31 % (15160)lrs+1010_1:16_apa=on:bsd=on:cnfonf=off:hud=10:sac=on:sos=on:ss=axioms:i=7257:si=on:rtra=on_0 on DTF2THF_14628 for (2932ds/7257Mi)
% 49.80/8.33 % (15160)Refutation not found, incomplete strategy
% 49.80/8.33 % (15160)------------------------------
% 49.80/8.33 % (15160)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.80/8.33 % (15160)Termination reason: Refutation not found, incomplete strategy
% 49.80/8.33
% 49.80/8.33
% 49.80/8.33 % (15160)Memory used [KB]: 6780
% 49.80/8.33 % (15160)Time elapsed: 0.023 s
% 49.80/8.33 % (15160)Instructions burned: 73 (million)
% 49.80/8.33 % (15160)------------------------------
% 49.80/8.33 % (15160)------------------------------
% 49.80/8.34 % (15161)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=3710:si=on:rtra=on_0 on DTF2THF_14628 for (2932ds/3710Mi)
% 50.35/8.43 % (15155)Instruction limit reached!
% 50.35/8.43 % (15155)------------------------------
% 50.35/8.43 % (15155)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.35/8.43 % (15155)Termination reason: Unknown
% 50.35/8.43 % (15155)Termination phase: Saturation
% 50.35/8.43
% 50.35/8.43 % (15155)Memory used [KB]: 12920
% 50.35/8.43 % (15155)Time elapsed: 0.986 s
% 50.35/8.43 % (15155)Instructions burned: 3177 (million)
% 50.35/8.43 % (15155)------------------------------
% 50.35/8.43 % (15155)------------------------------
% 50.35/8.44 % (15162)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=326:si=on:rtra=on_0 on DTF2THF_14628 for (2931ds/326Mi)
% 50.79/8.54 % (15162)Instruction limit reached!
% 50.79/8.54 % (15162)------------------------------
% 50.79/8.54 % (15162)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.79/8.54 % (15162)Termination reason: Unknown
% 50.79/8.54 % (15162)Termination phase: Saturation
% 50.79/8.54
% 50.79/8.54 % (15162)Memory used [KB]: 7291
% 50.79/8.54 % (15162)Time elapsed: 0.124 s
% 50.79/8.54 % (15162)Instructions burned: 326 (million)
% 50.79/8.54 % (15162)------------------------------
% 50.79/8.54 % (15162)------------------------------
% 50.79/8.55 % (15163)lrs+1010_1:64_au=on:c=on:e2e=on:flr=on:hfsq=on:hfsql=off:hfsqr=4,1:ins=1:ntd=on:sp=occurrence:i=1100:si=on:rtra=on_0 on DTF2THF_14628 for (2929ds/1100Mi)
% 50.79/8.58 % (15158)Refutation not found, non-redundant clauses discarded% (15158)------------------------------
% 50.79/8.58 % (15158)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.79/8.58 % (15158)Termination reason: Refutation not found, non-redundant clauses discarded
% 50.79/8.58
% 50.79/8.58 % (15158)Memory used [KB]: 12025
% 50.79/8.58 % (15158)Time elapsed: 0.685 s
% 50.79/8.58 % (15158)Instructions burned: 2208 (million)
% 50.79/8.58 % (15158)------------------------------
% 50.79/8.58 % (15158)------------------------------
% 50.79/8.59 % (15164)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_14628 for (2929ds/406Mi)
% 51.29/8.67 % (15154)Instruction limit reached!
% 51.29/8.67 % (15154)------------------------------
% 51.29/8.67 % (15154)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.29/8.67 % (15154)Termination reason: Unknown
% 51.29/8.67 % (15154)Termination phase: Saturation
% 51.29/8.67
% 51.29/8.67 % (15154)Memory used [KB]: 9210
% 51.29/8.67 % (15154)Time elapsed: 1.334 s
% 51.29/8.67 % (15154)Instructions burned: 4638 (million)
% 51.29/8.67 % (15154)------------------------------
% 51.29/8.67 % (15154)------------------------------
% 51.29/8.68 % (15165)dis+1010_1:1_aac=none:bd=preordered:e2e=on:fde=none:fe=axiom:nm=16:nwc=10.0:prag=on:i=1871:si=on:rtra=on_0 on DTF2THF_14628 for (2928ds/1871Mi)
% 51.57/8.71 % (15164)Instruction limit reached!
% 51.57/8.71 % (15164)------------------------------
% 51.57/8.71 % (15164)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.57/8.71 % (15164)Termination reason: Unknown
% 51.57/8.71 % (15164)Termination phase: Saturation
% 51.57/8.71
% 51.57/8.71 % (15164)Memory used [KB]: 8187
% 51.57/8.71 % (15164)Time elapsed: 0.127 s
% 51.57/8.71 % (15164)Instructions burned: 406 (million)
% 51.57/8.71 % (15164)------------------------------
% 51.57/8.71 % (15164)------------------------------
% 51.57/8.72 % (15166)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1194:si=on:rtra=on_0 on DTF2THF_14628 for (2928ds/1194Mi)
% 51.91/8.82 % (15159)Instruction limit reached!
% 51.91/8.82 % (15159)------------------------------
% 51.91/8.82 % (15159)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.91/8.82 % (15159)Termination reason: Unknown
% 51.91/8.82 % (15159)Termination phase: Saturation
% 51.91/8.82
% 51.91/8.82 % (15159)Memory used [KB]: 9722
% 51.91/8.82 % (15159)Time elapsed: 0.735 s
% 51.91/8.82 % (15159)Instructions burned: 2342 (million)
% 51.91/8.82 % (15159)------------------------------
% 51.91/8.82 % (15159)------------------------------
% 51.91/8.83 % (15167)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_14628 for (2926ds/474Mi)
% 51.91/8.88 % (15163)Instruction limit reached!
% 51.91/8.88 % (15163)------------------------------
% 51.91/8.88 % (15163)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.91/8.88 % (15163)Termination reason: Unknown
% 51.91/8.88 % (15163)Termination phase: Saturation
% 51.91/8.88
% 51.91/8.88 % (15163)Memory used [KB]: 11257
% 51.91/8.88 % (15163)Time elapsed: 0.337 s
% 51.91/8.88 % (15163)Instructions burned: 1102 (million)
% 51.91/8.88 % (15163)------------------------------
% 51.91/8.88 % (15163)------------------------------
% 51.91/8.89 % (15168)dis+1010_1:1_au=on:cnfonf=lazy_gen:ins=3:plsq=on:plsqc=1:plsqr=15142123,262144:sp=reverse_arity:i=3115:si=on:rtra=on_0 on DTF2THF_14628 for (2926ds/3115Mi)
% 53.21/8.94 % (15157)Instruction limit reached!
% 53.21/8.94 % (15157)------------------------------
% 53.21/8.94 % (15157)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 53.21/8.94 % (15157)Termination reason: Unknown
% 53.21/8.94 % (15157)Termination phase: Saturation
% 53.21/8.94
% 53.21/8.94 % (15157)Memory used [KB]: 15479
% 53.21/8.94 % (15157)Time elapsed: 1.079 s
% 53.21/8.94 % (15157)Instructions burned: 3621 (million)
% 53.21/8.94 % (15157)------------------------------
% 53.21/8.94 % (15157)------------------------------
% 53.21/8.95 % (15169)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=831:si=on:rtra=on_0 on DTF2THF_14628 for (2925ds/831Mi)
% 53.21/8.97 % (15167)Instruction limit reached!
% 53.21/8.97 % (15167)------------------------------
% 53.21/8.97 % (15167)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 53.21/8.97 % (15167)Termination reason: Unknown
% 53.21/8.97 % (15167)Termination phase: Saturation
% 53.21/8.97
% 53.21/8.97 % (15167)Memory used [KB]: 8699
% 53.21/8.97 % (15167)Time elapsed: 0.142 s
% 53.21/8.97 % (15167)Instructions burned: 474 (million)
% 53.21/8.97 % (15167)------------------------------
% 53.21/8.97 % (15167)------------------------------
% 53.21/8.98 % (15170)dis+1666_14:1_cnfonf=lazy_gen:fe=off:hud=10:piset=all_but_not_eq:prag=on:sp=const_max:i=1188:si=on:rtra=on_0 on DTF2THF_14628 for (2925ds/1188Mi)
% 55.10/9.08 % (15166)Instruction limit reached!
% 55.10/9.08 % (15166)------------------------------
% 55.10/9.08 % (15166)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.10/9.08 % (15166)Termination reason: Unknown
% 55.10/9.08 % (15166)Termination phase: Saturation
% 55.10/9.08
% 55.10/9.08 % (15166)Memory used [KB]: 10362
% 55.10/9.08 % (15166)Time elapsed: 0.358 s
% 55.10/9.08 % (15166)Instructions burned: 1195 (million)
% 55.10/9.08 % (15166)------------------------------
% 55.10/9.08 % (15166)------------------------------
% 55.10/9.09 % (15171)ott+1010_1:20_cnfonf=lazy_pi_sigma_gen:fe=axiom:plsq=on:plsqc=2:plsqr=32,1:sac=on:sos=all:i=2868:si=on:rtra=on_0 on DTF2THF_14628 for (2924ds/2868Mi)
% 55.78/9.16 % (15171)Refutation not found, incomplete strategy
% 55.78/9.16 % (15171)------------------------------
% 55.78/9.16 % (15171)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.78/9.16 % (15171)Termination reason: Refutation not found, incomplete strategy
% 55.78/9.16
% 55.78/9.16
% 55.78/9.16 % (15171)Memory used [KB]: 7931
% 55.78/9.16 % (15171)Time elapsed: 0.076 s
% 55.78/9.16 % (15171)Instructions burned: 262 (million)
% 55.78/9.16 % (15171)------------------------------
% 55.78/9.16 % (15171)------------------------------
% 55.78/9.17 % (15172)dis+10_1:4_atotf=0.1:avsq=on:bsr=unit_only:e2e=on:sd=1:sp=const_max:ss=axioms:i=1516:si=on:rtra=on_0 on DTF2THF_14628 for (2923ds/1516Mi)
% 56.31/9.20 % (15169)Instruction limit reached!
% 56.31/9.20 % (15169)------------------------------
% 56.31/9.20 % (15169)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.31/9.20 % (15169)Termination reason: Unknown
% 56.31/9.20 % (15169)Termination phase: Saturation
% 56.31/9.20
% 56.31/9.20 % (15169)Memory used [KB]: 9338
% 56.31/9.20 % (15169)Time elapsed: 0.251 s
% 56.31/9.20 % (15169)Instructions burned: 833 (million)
% 56.31/9.20 % (15169)------------------------------
% 56.31/9.20 % (15169)------------------------------
% 56.31/9.21 % (15173)lrs+1002_1:20_afp=1000:au=on:bsd=on:cnfonf=lazy_not_gen_be_off:sos=all:sp=const_max:i=2321:si=on:rtra=on_0 on DTF2THF_14628 for (2923ds/2321Mi)
% 56.31/9.26 % (15165)Instruction limit reached!
% 56.31/9.26 % (15165)------------------------------
% 56.31/9.26 % (15165)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.31/9.26 % (15165)Termination reason: Unknown
% 56.31/9.26 % (15165)Termination phase: Saturation
% 56.31/9.26
% 56.31/9.26 % (15165)Memory used [KB]: 13816
% 56.31/9.26 % (15165)Time elapsed: 0.585 s
% 56.31/9.26 % (15165)Instructions burned: 1873 (million)
% 56.31/9.26 % (15165)------------------------------
% 56.31/9.26 % (15165)------------------------------
% 56.31/9.27 % (15174)dis+1010_1:1_au=on:bd=off:bsd=on:ixr=off:sp=const_max:i=2812:si=on:rtra=on_0 on DTF2THF_14628 for (2922ds/2812Mi)
% 56.31/9.28 % (15173)Refutation not found, incomplete strategy
% 56.31/9.28 % (15173)------------------------------
% 56.31/9.28 % (15173)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.31/9.28 % (15173)Termination reason: Refutation not found, incomplete strategy
% 56.31/9.28
% 56.31/9.28
% 56.31/9.28 % (15173)Memory used [KB]: 7803
% 56.31/9.28 % (15173)Time elapsed: 0.068 s
% 56.31/9.28 % (15173)Instructions burned: 248 (million)
% 56.31/9.28 % (15173)------------------------------
% 56.31/9.28 % (15173)------------------------------
% 56.31/9.29 % (15175)dis+1002_8:1_bd=off:sd=1:sgt=16:ss=axioms:i=4604:si=on:rtra=on_0 on DTF2THF_14628 for (2922ds/4604Mi)
% 56.87/9.30 % (15150)Instruction limit reached!
% 56.87/9.30 % (15150)------------------------------
% 56.87/9.30 % (15150)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.87/9.30 % (15150)Termination reason: Unknown
% 56.87/9.30 % (15150)Termination phase: Saturation
% 56.87/9.30
% 56.87/9.30 % (15150)Memory used [KB]: 15095
% 56.87/9.30 % (15150)Time elapsed: 2.321 s
% 56.87/9.30 % (15150)Instructions burned: 7681 (million)
% 56.87/9.30 % (15150)------------------------------
% 56.87/9.30 % (15150)------------------------------
% 56.87/9.31 % (15176)ott+1002_1:4_c=on:chr=on:cnfonf=lazy_not_be_gen:hud=10:nm=10:piset=all_but_not_eq:rp=on:spb=goal:uhcvi=on:i=2678:si=on:rtra=on_0 on DTF2THF_14628 for (2922ds/2678Mi)
% 56.87/9.35 % (15170)Instruction limit reached!
% 56.87/9.35 % (15170)------------------------------
% 56.87/9.35 % (15170)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.87/9.35 % (15170)Termination reason: Unknown
% 56.87/9.35 % (15170)Termination phase: Saturation
% 56.87/9.35
% 56.87/9.35 % (15170)Memory used [KB]: 9722
% 56.87/9.35 % (15170)Time elapsed: 0.366 s
% 56.87/9.35 % (15170)Instructions burned: 1189 (million)
% 56.87/9.35 % (15170)------------------------------
% 56.87/9.35 % (15170)------------------------------
% 56.87/9.36 % (15177)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on DTF2THF_14628 for (2921ds/643Mi)
% 57.15/9.40 % (15161)Instruction limit reached!
% 57.15/9.40 % (15161)------------------------------
% 57.15/9.40 % (15161)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.15/9.40 % (15161)Termination reason: Unknown
% 57.15/9.40 % (15161)Termination phase: Saturation
% 57.15/9.40
% 57.15/9.40 % (15161)Memory used [KB]: 14200
% 57.15/9.40 % (15161)Time elapsed: 1.079 s
% 57.15/9.40 % (15161)Instructions burned: 3710 (million)
% 57.15/9.40 % (15161)------------------------------
% 57.15/9.40 % (15161)------------------------------
% 57.15/9.41 % (15178)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=458:si=on:rtra=on_0 on DTF2THF_14628 for (2921ds/458Mi)
% 57.27/9.54 % (15178)Instruction limit reached!
% 57.27/9.54 % (15178)------------------------------
% 57.27/9.54 % (15178)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.27/9.54 % (15178)Termination reason: Unknown
% 57.27/9.54 % (15178)Termination phase: Saturation
% 57.27/9.54
% 57.27/9.54 % (15178)Memory used [KB]: 7803
% 57.27/9.54 % (15178)Time elapsed: 0.133 s
% 57.27/9.54 % (15178)Instructions burned: 459 (million)
% 57.27/9.54 % (15178)------------------------------
% 57.27/9.54 % (15178)------------------------------
% 57.27/9.55 % (15177)Instruction limit reached!
% 57.27/9.55 % (15177)------------------------------
% 57.27/9.55 % (15177)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.27/9.55 % (15177)Termination reason: Unknown
% 57.27/9.55 % (15177)Termination phase: Saturation
% 57.27/9.55
% 57.27/9.55 % (15177)Memory used [KB]: 9466
% 57.27/9.55 % (15177)Time elapsed: 0.215 s
% 57.27/9.55 % (15177)Instructions burned: 645 (million)
% 57.27/9.55 % (15177)------------------------------
% 57.27/9.55 % (15177)------------------------------
% 57.27/9.55 % (15179)lrs+1010_1:1_anc=all_dependent:apa=on:au=on:bd=off:c=on:cnfonf=off:ntd=on:i=2546:si=on:rtra=on_0 on DTF2THF_14628 for (2919ds/2546Mi)
% 57.27/9.56 % (15180)dis+21_1:1_acc=model:au=on:cnfonf=lazy_gen:ins=2:plsq=on:plsqc=1:plsqr=32,1:i=1432:si=on:rtra=on_0 on DTF2THF_14628 for (2919ds/1432Mi)
% 57.73/9.63 % (15172)Instruction limit reached!
% 57.73/9.63 % (15172)------------------------------
% 57.73/9.63 % (15172)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.73/9.63 % (15172)Termination reason: Unknown
% 57.73/9.63 % (15172)Termination phase: Saturation
% 57.73/9.63
% 57.73/9.63 % (15172)Memory used [KB]: 9338
% 57.73/9.63 % (15172)Time elapsed: 0.453 s
% 57.73/9.63 % (15172)Instructions burned: 1518 (million)
% 57.73/9.63 % (15172)------------------------------
% 57.73/9.63 % (15172)------------------------------
% 57.73/9.64 % (15181)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=386:si=on:rtra=on_0 on DTF2THF_14628 for (2919ds/386Mi)
% 58.28/9.74 % (15181)Instruction limit reached!
% 58.28/9.74 % (15181)------------------------------
% 58.28/9.74 % (15181)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.28/9.74 % (15181)Termination reason: Unknown
% 58.28/9.74 % (15181)Termination phase: Saturation
% 58.28/9.74
% 58.28/9.74 % (15181)Memory used [KB]: 8059
% 58.28/9.74 % (15181)Time elapsed: 0.108 s
% 58.28/9.74 % (15181)Instructions burned: 388 (million)
% 58.28/9.74 % (15181)------------------------------
% 58.28/9.74 % (15181)------------------------------
% 58.28/9.75 % (15182)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on DTF2THF_14628 for (2917ds/360Mi)
% 58.50/9.80 % (15168)Instruction limit reached!
% 58.50/9.80 % (15168)------------------------------
% 58.50/9.80 % (15168)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.50/9.80 % (15168)Termination reason: Unknown
% 58.50/9.80 % (15168)Termination phase: Saturation
% 58.50/9.80
% 58.50/9.80 % (15168)Memory used [KB]: 14711
% 58.50/9.80 % (15168)Time elapsed: 0.908 s
% 58.50/9.80 % (15168)Instructions burned: 3117 (million)
% 58.50/9.80 % (15168)------------------------------
% 58.50/9.80 % (15168)------------------------------
% 58.50/9.81 % (15183)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=5446:si=on:rtra=on_0 on DTF2THF_14628 for (2917ds/5446Mi)
% 58.50/9.85 % (15182)Instruction limit reached!
% 58.50/9.85 % (15182)------------------------------
% 58.50/9.85 % (15182)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.50/9.85 % (15182)Termination reason: Unknown
% 58.50/9.85 % (15182)Termination phase: Saturation
% 58.50/9.85
% 58.50/9.85 % (15182)Memory used [KB]: 7931
% 58.50/9.85 % (15182)Time elapsed: 0.102 s
% 58.50/9.85 % (15182)Instructions burned: 360 (million)
% 58.50/9.85 % (15182)------------------------------
% 58.50/9.85 % (15182)------------------------------
% 58.50/9.86 % (15184)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=2573:si=on:rtra=on_0 on DTF2THF_14628 for (2916ds/2573Mi)
% 58.63/9.93 % (15180)Instruction limit reached!
% 58.63/9.93 % (15180)------------------------------
% 58.63/9.93 % (15180)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.63/9.93 % (15180)Termination reason: Unknown
% 58.63/9.93 % (15180)Termination phase: Saturation
% 58.63/9.93
% 58.63/9.93 % (15180)Memory used [KB]: 10874
% 58.63/9.93 % (15180)Time elapsed: 0.395 s
% 58.63/9.93 % (15180)Instructions burned: 1436 (million)
% 58.63/9.93 % (15180)------------------------------
% 58.63/9.93 % (15180)------------------------------
% 58.63/9.94 % (15185)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=2655:si=on:rtra=on_0 on DTF2THF_14628 for (2915ds/2655Mi)
% 62.84/10.15 % (15176)Instruction limit reached!
% 62.84/10.15 % (15176)------------------------------
% 62.84/10.15 % (15176)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 62.84/10.15 % (15176)Termination reason: Unknown
% 62.84/10.15 % (15176)Termination phase: Saturation
% 62.84/10.15
% 62.84/10.15 % (15176)Memory used [KB]: 12153
% 62.84/10.15 % (15176)Time elapsed: 0.855 s
% 62.84/10.15 % (15176)Instructions burned: 2678 (million)
% 62.84/10.15 % (15176)------------------------------
% 62.84/10.15 % (15176)------------------------------
% 62.84/10.16 % (15186)dis+1002_16:1_apa=on:au=on:av=off:cnfonf=off:e2e=on:nm=0:nwc=10.0:i=2781:si=on:rtra=on_0 on DTF2THF_14628 for (2913ds/2781Mi)
% 62.84/10.16 % (15174)Instruction limit reached!
% 62.84/10.16 % (15174)------------------------------
% 62.84/10.16 % (15174)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 62.84/10.16 % (15174)Termination reason: Unknown
% 62.84/10.16 % (15174)Termination phase: Saturation
% 62.84/10.16
% 62.84/10.16 % (15174)Memory used [KB]: 13304
% 62.84/10.16 % (15174)Time elapsed: 0.907 s
% 62.84/10.16 % (15174)Instructions burned: 2813 (million)
% 62.84/10.16 % (15174)------------------------------
% 62.84/10.16 % (15174)------------------------------
% 62.84/10.17 % (15187)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_14628 for (2913ds/307Mi)
% 63.28/10.25 % (15187)Instruction limit reached!
% 63.28/10.25 % (15187)------------------------------
% 63.28/10.25 % (15187)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.28/10.25 % (15187)Termination reason: Unknown
% 63.28/10.25 % (15187)Termination phase: Saturation
% 63.28/10.25
% 63.28/10.25 % (15187)Memory used [KB]: 7419
% 63.28/10.25 % (15187)Time elapsed: 0.086 s
% 63.28/10.25 % (15187)Instructions burned: 310 (million)
% 63.28/10.25 % (15187)------------------------------
% 63.28/10.25 % (15187)------------------------------
% 63.28/10.26 % (15188)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=1548:si=on:rtra=on_0 on DTF2THF_14628 for (2912ds/1548Mi)
% 63.88/10.32 % (15179)Refutation not found, non-redundant clauses discarded% (15179)------------------------------
% 63.88/10.32 % (15179)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.88/10.32 % (15179)Termination reason: Refutation not found, non-redundant clauses discarded
% 63.88/10.32
% 63.88/10.32 % (15179)Memory used [KB]: 11769
% 63.88/10.32 % (15179)Time elapsed: 0.786 s
% 63.88/10.32 % (15179)Instructions burned: 2447 (million)
% 63.88/10.32 % (15179)------------------------------
% 63.88/10.32 % (15179)------------------------------
% 63.88/10.33 % (15189)lrs+10_1:3_alpa=true:hud=3:ins=1:ntd=on:plsq=on:plsqc=1:plsqr=32,1:prag=on:s2a=on:s2agt=10:i=5214:si=on:rtra=on_0 on DTF2THF_14628 for (2912ds/5214Mi)
% 65.11/10.62 % (15184)Instruction limit reached!
% 65.11/10.62 % (15184)------------------------------
% 65.11/10.62 % (15184)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 65.11/10.62 % (15184)Termination reason: Unknown
% 65.11/10.62 % (15184)Termination phase: Saturation
% 65.11/10.62
% 65.11/10.62 % (15184)Memory used [KB]: 13560
% 65.11/10.62 % (15184)Time elapsed: 0.762 s
% 65.11/10.62 % (15184)Instructions burned: 2574 (million)
% 65.11/10.62 % (15184)------------------------------
% 65.11/10.62 % (15184)------------------------------
% 65.11/10.64 % (15190)dis+21_1:1_aac=none:bsr=on:nwc=3.0:s2a=on:i=3201:si=on:rtra=on_0 on DTF2THF_14628 for (2908ds/3201Mi)
% 65.11/10.66 % (15175)Instruction limit reached!
% 65.11/10.66 % (15175)------------------------------
% 65.11/10.66 % (15175)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 65.11/10.66 % (15175)Termination reason: Unknown
% 65.11/10.66 % (15175)Termination phase: Saturation
% 65.11/10.66
% 65.11/10.66 % (15175)Memory used [KB]: 11129
% 65.11/10.66 % (15175)Time elapsed: 1.391 s
% 65.11/10.66 % (15175)Instructions burned: 4604 (million)
% 65.11/10.66 % (15175)------------------------------
% 65.11/10.66 % (15175)------------------------------
% 65.11/10.67 % (15191)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=454:si=on:rtra=on_0 on DTF2THF_14628 for (2908ds/454Mi)
% 65.43/10.72 % (15185)Instruction limit reached!
% 65.43/10.72 % (15185)------------------------------
% 65.43/10.72 % (15185)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 65.43/10.72 % (15185)Termination reason: Unknown
% 65.43/10.72 % (15185)Termination phase: Saturation
% 65.43/10.72
% 65.43/10.72 % (15185)Memory used [KB]: 14583
% 65.43/10.72 % (15185)Time elapsed: 0.777 s
% 65.43/10.72 % (15185)Instructions burned: 2657 (million)
% 65.43/10.72 % (15185)------------------------------
% 65.43/10.72 % (15185)------------------------------
% 65.43/10.73 % (15192)lrs+1002_1:32_au=on:ins=2:nm=16:ntd=on:piset=all_but_not_eq:sp=occurrence:i=3049:si=on:rtra=on_0 on DTF2THF_14628 for (2908ds/3049Mi)
% 65.43/10.75 % (15188)Instruction limit reached!
% 65.43/10.75 % (15188)------------------------------
% 65.43/10.75 % (15188)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 65.43/10.75 % (15188)Termination reason: Unknown
% 65.43/10.75 % (15188)Termination phase: Saturation
% 65.43/10.75
% 65.43/10.75 % (15188)Memory used [KB]: 9594
% 65.43/10.75 % (15188)Time elapsed: 0.486 s
% 65.43/10.75 % (15188)Instructions burned: 1550 (million)
% 65.43/10.75 % (15188)------------------------------
% 65.43/10.75 % (15188)------------------------------
% 65.43/10.76 % (15193)lrs+1010_1:1_bd=preordered:cnfonf=off:e2e=on:kws=inv_precedence:lwlo=on:sd=2:ss=axioms:i=7311:si=on:rtra=on_0 on DTF2THF_14628 for (2907ds/7311Mi)
% 66.06/10.80 % (15191)Instruction limit reached!
% 66.06/10.80 % (15191)------------------------------
% 66.06/10.80 % (15191)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 66.06/10.80 % (15191)Termination reason: Unknown
% 66.06/10.80 % (15191)Termination phase: Saturation
% 66.06/10.80
% 66.06/10.80 % (15191)Memory used [KB]: 12537
% 66.06/10.80 % (15191)Time elapsed: 0.133 s
% 66.06/10.80 % (15191)Instructions burned: 455 (million)
% 66.06/10.80 % (15191)------------------------------
% 66.06/10.80 % (15191)------------------------------
% 66.06/10.81 % (15194)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=6804:si=on:rtra=on_0 on DTF2THF_14628 for (2907ds/6804Mi)
% 69.14/11.03 % (15186)Instruction limit reached!
% 69.14/11.03 % (15186)------------------------------
% 69.14/11.03 % (15186)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 69.14/11.03 % (15186)Termination reason: Unknown
% 69.14/11.03 % (15186)Termination phase: Saturation
% 69.14/11.03
% 69.14/11.03 % (15186)Memory used [KB]: 6652
% 69.14/11.03 % (15186)Time elapsed: 0.874 s
% 69.14/11.03 % (15186)Instructions burned: 2783 (million)
% 69.14/11.03 % (15186)------------------------------
% 69.14/11.03 % (15186)------------------------------
% 69.14/11.04 % (15195)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1683:si=on:rtra=on_0 on DTF2THF_14628 for (2905ds/1683Mi)
% 72.04/11.57 % (15183)Instruction limit reached!
% 72.04/11.57 % (15183)------------------------------
% 72.04/11.57 % (15183)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 72.04/11.57 % (15183)Termination reason: Unknown
% 72.04/11.57 % (15183)Termination phase: Saturation
% 72.04/11.57
% 72.04/11.57 % (15183)Memory used [KB]: 19701
% 72.04/11.57 % (15183)Time elapsed: 1.757 s
% 72.04/11.57 % (15183)Instructions burned: 5446 (million)
% 72.04/11.57 % (15183)------------------------------
% 72.04/11.57 % (15183)------------------------------
% 72.04/11.57 % (15195)Instruction limit reached!
% 72.04/11.57 % (15195)------------------------------
% 72.04/11.57 % (15195)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 72.04/11.57 % (15195)Termination reason: Unknown
% 72.04/11.57 % (15195)Termination phase: Saturation
% 72.04/11.57
% 72.04/11.57 % (15195)Memory used [KB]: 11257
% 72.04/11.57 % (15195)Time elapsed: 0.534 s
% 72.04/11.57 % (15195)Instructions burned: 1683 (million)
% 72.04/11.57 % (15195)------------------------------
% 72.04/11.57 % (15195)------------------------------
% 72.04/11.58 % (15196)lrs+10_8:1_au=on:av=off:bd=off:cs=on:e2e=on:hfsq=on:hfsqc=50:hfsql=off:nm=0:i=4688:si=on:rtra=on_0 on DTF2THF_14628 for (2899ds/4688Mi)
% 72.04/11.58 % (15197)dis-1_1:1_amm=off:au=on:cbe=off:spb=intro:i=2207:si=on:rtra=on_0 on DTF2THF_14628 for (2899ds/2207Mi)
% 73.15/11.60 % (15190)Instruction limit reached!
% 73.15/11.60 % (15190)------------------------------
% 73.15/11.60 % (15190)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 73.15/11.60 % (15190)Termination reason: Unknown
% 73.15/11.60 % (15190)Termination phase: Saturation
% 73.15/11.60
% 73.15/11.60 % (15190)Memory used [KB]: 11897
% 73.15/11.60 % (15190)Time elapsed: 0.968 s
% 73.15/11.60 % (15190)Instructions burned: 3202 (million)
% 73.15/11.60 % (15190)------------------------------
% 73.15/11.60 % (15190)------------------------------
% 73.15/11.61 % (15198)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=8216:si=on:rtra=on_0 on DTF2THF_14628 for (2899ds/8216Mi)
% 73.15/11.64 % (15192)Instruction limit reached!
% 73.15/11.64 % (15192)------------------------------
% 73.15/11.64 % (15192)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 73.15/11.64 % (15192)Termination reason: Unknown
% 73.15/11.64 % (15192)Termination phase: Saturation
% 73.15/11.64
% 73.15/11.64 % (15192)Memory used [KB]: 11257
% 73.15/11.64 % (15192)Time elapsed: 0.916 s
% 73.15/11.64 % (15192)Instructions burned: 3049 (million)
% 73.15/11.64 % (15192)------------------------------
% 73.15/11.64 % (15192)------------------------------
% 73.15/11.65 % (15199)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=430:si=on:rtra=on_0 on DTF2THF_14628 for (2898ds/430Mi)
% 73.52/11.78 % (15199)Instruction limit reached!
% 73.52/11.78 % (15199)------------------------------
% 73.52/11.78 % (15199)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 73.52/11.78 % (15199)Termination reason: Unknown
% 73.52/11.78 % (15199)Termination phase: Saturation
% 73.52/11.78
% 73.52/11.78 % (15199)Memory used [KB]: 7675
% 73.52/11.78 % (15199)Time elapsed: 0.122 s
% 73.52/11.78 % (15199)Instructions burned: 432 (million)
% 73.52/11.78 % (15199)------------------------------
% 73.52/11.78 % (15199)------------------------------
% 73.52/11.79 % (15200)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=2012:si=on:rtra=on_0 on DTF2THF_14628 for (2897ds/2012Mi)
% 74.27/11.94 % (15189)Instruction limit reached!
% 74.27/11.94 % (15189)------------------------------
% 74.27/11.94 % (15189)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 74.27/11.94 % (15189)Termination reason: Unknown
% 74.27/11.94 % (15189)Termination phase: Saturation
% 74.27/11.94
% 74.27/11.94 % (15189)Memory used [KB]: 13048
% 74.27/11.94 % (15189)Time elapsed: 1.618 s
% 74.27/11.94 % (15189)Instructions burned: 5215 (million)
% 74.27/11.94 % (15189)------------------------------
% 74.27/11.94 % (15189)------------------------------
% 74.27/11.95 % (15201)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=631:si=on:rtra=on_0 on DTF2THF_14628 for (2895ds/631Mi)
% 76.87/12.15 % (15201)Instruction limit reached!
% 76.87/12.15 % (15201)------------------------------
% 76.87/12.15 % (15201)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 76.87/12.15 % (15201)Termination reason: Unknown
% 76.87/12.15 % (15201)Termination phase: Saturation
% 76.87/12.15
% 76.87/12.15 % (15201)Memory used [KB]: 8955
% 76.87/12.15 % (15201)Time elapsed: 0.200 s
% 76.87/12.15 % (15201)Instructions burned: 633 (million)
% 76.87/12.15 % (15201)------------------------------
% 76.87/12.15 % (15201)------------------------------
% 76.87/12.16 % (15202)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=8785:si=on:rtra=on_0 on DTF2THF_14628 for (2893ds/8785Mi)
% 77.36/12.28 % (15197)Instruction limit reached!
% 77.36/12.28 % (15197)------------------------------
% 77.36/12.28 % (15197)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 77.36/12.28 % (15197)Termination reason: Unknown
% 77.36/12.28 % (15197)Termination phase: Saturation
% 77.36/12.28
% 77.36/12.28 % (15197)Memory used [KB]: 12665
% 77.36/12.28 % (15197)Time elapsed: 0.702 s
% 77.36/12.28 % (15197)Instructions burned: 2207 (million)
% 77.36/12.28 % (15197)------------------------------
% 77.36/12.28 % (15197)------------------------------
% 77.96/12.30 % (15203)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=739:si=on:rtra=on_0 on DTF2THF_14628 for (2892ds/739Mi)
% 78.45/12.41 % (15200)Instruction limit reached!
% 78.45/12.41 % (15200)------------------------------
% 78.45/12.41 % (15200)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 78.45/12.41 % (15200)Termination reason: Unknown
% 78.45/12.41 % (15200)Termination phase: Saturation
% 78.45/12.41
% 78.45/12.41 % (15200)Memory used [KB]: 18805
% 78.45/12.41 % (15200)Time elapsed: 0.625 s
% 78.45/12.41 % (15200)Instructions burned: 2014 (million)
% 78.45/12.41 % (15200)------------------------------
% 78.45/12.41 % (15200)------------------------------
% 78.45/12.42 % (15204)dis+1002_1:1024_fe=off:hud=5:prag=on:i=5473:si=on:rtra=on_0 on DTF2THF_14628 for (2891ds/5473Mi)
% 79.26/12.60 % (15203)Instruction limit reached!
% 79.26/12.60 % (15203)------------------------------
% 79.26/12.60 % (15203)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 79.26/12.60 % (15203)Termination reason: Unknown
% 79.26/12.60 % (15203)Termination phase: Saturation
% 79.26/12.60
% 79.26/12.60 % (15203)Memory used [KB]: 9210
% 79.26/12.60 % (15203)Time elapsed: 0.298 s
% 79.26/12.60 % (15203)Instructions burned: 739 (million)
% 79.26/12.60 % (15203)------------------------------
% 79.26/12.60 % (15203)------------------------------
% 79.26/12.61 % (15205)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=43570:si=on:rtra=on_0 on DTF2THF_14628 for (2889ds/43570Mi)
% 80.39/12.86 % (15194)Instruction limit reached!
% 80.39/12.86 % (15194)------------------------------
% 80.39/12.86 % (15194)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 80.39/12.86 % (15194)Termination reason: Unknown
% 80.39/12.86 % (15194)Termination phase: Saturation
% 80.39/12.86
% 80.39/12.86 % (15194)Memory used [KB]: 19829
% 80.39/12.86 % (15194)Time elapsed: 2.053 s
% 80.39/12.86 % (15194)Instructions burned: 6804 (million)
% 80.39/12.86 % (15194)------------------------------
% 80.39/12.86 % (15194)------------------------------
% 80.39/12.87 % (15206)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=8382:si=on:rtra=on_0 on DTF2THF_14628 for (2886ds/8382Mi)
% 80.77/12.94 % (15196)Instruction limit reached!
% 80.77/12.94 % (15196)------------------------------
% 80.77/12.94 % (15196)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 80.77/12.94 % (15196)Termination reason: Unknown
% 80.77/12.94 % (15196)Termination phase: Saturation
% 80.77/12.94
% 80.77/12.94 % (15196)Memory used [KB]: 14583
% 80.77/12.94 % (15196)Time elapsed: 1.363 s
% 80.77/12.94 % (15196)Instructions burned: 4690 (million)
% 80.77/12.94 % (15196)------------------------------
% 80.77/12.94 % (15196)------------------------------
% 80.77/12.95 % (15207)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=407:si=on:rtra=on_0 on DTF2THF_14628 for (2885ds/407Mi)
% 80.77/12.99 % (15193)Instruction limit reached!
% 80.77/12.99 % (15193)------------------------------
% 80.77/12.99 % (15193)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 80.77/12.99 % (15193)Termination reason: Unknown
% 80.77/12.99 % (15193)Termination phase: Saturation
% 80.77/12.99
% 80.77/12.99 % (15193)Memory used [KB]: 19189
% 80.77/12.99 % (15193)Time elapsed: 2.231 s
% 80.77/12.99 % (15193)Instructions burned: 7313 (million)
% 80.77/12.99 % (15193)------------------------------
% 80.77/12.99 % (15193)------------------------------
% 80.77/13.00 % (15208)lrs+10_1:50_cbe=off:cnfonf=lazy_pi_sigma_gen:fe=off:hud=5:plsq=on:plsqr=1,32:sos=all:i=2971:si=on:rtra=on_0 on DTF2THF_14628 for (2885ds/2971Mi)
% 83.08/13.06 % (15207)Instruction limit reached!
% 83.08/13.06 % (15207)------------------------------
% 83.08/13.06 % (15207)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 83.08/13.06 % (15207)Termination reason: Unknown
% 83.08/13.06 % (15207)Termination phase: Saturation
% 83.08/13.06
% 83.08/13.06 % (15207)Memory used [KB]: 8571
% 83.08/13.06 % (15207)Time elapsed: 0.115 s
% 83.08/13.06 % (15207)Instructions burned: 408 (million)
% 83.08/13.06 % (15207)------------------------------
% 83.08/13.06 % (15207)------------------------------
% 83.08/13.07 % (15208)Refutation not found, incomplete strategy
% 83.08/13.07 % (15208)------------------------------
% 83.08/13.07 % (15208)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 83.08/13.07 % (15208)Termination reason: Refutation not found, incomplete strategy
% 83.08/13.07
% 83.08/13.07
% 83.08/13.07 % (15208)Memory used [KB]: 7931
% 83.08/13.07 % (15208)Time elapsed: 0.073 s
% 83.08/13.07 % (15208)Instructions burned: 265 (million)
% 83.08/13.07 % (15208)------------------------------
% 83.08/13.07 % (15208)------------------------------
% 83.08/13.07 % (15209)lrs+1002_1:1_aac=none:bd=off:e2e=on:fde=none:fe=off:piset=or:prag=on:rawr=on:sos=on:updr=off:i=9822:si=on:rtra=on_0 on DTF2THF_14628 for (2884ds/9822Mi)
% 83.08/13.08 % (15210)dis+10_5:1_av=off:ntd=on:s2a=on:s2at=3.0:sgt=16:sp=unary_frequency:ss=axioms:i=8425:si=on:rtra=on_0 on DTF2THF_14628 for (2884ds/8425Mi)
% 90.90/14.14 % (15204)Instruction limit reached!
% 90.90/14.14 % (15204)------------------------------
% 90.90/14.14 % (15204)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 90.90/14.14 % (15204)Termination reason: Unknown
% 90.90/14.14 % (15204)Termination phase: Saturation
% 90.90/14.14
% 90.90/14.14 % (15204)Memory used [KB]: 15735
% 90.90/14.14 % (15204)Time elapsed: 1.720 s
% 90.90/14.14 % (15204)Instructions burned: 5476 (million)
% 90.90/14.14 % (15204)------------------------------
% 90.90/14.14 % (15204)------------------------------
% 90.90/14.15 % (15211)lrs+30_1:1_aac=none:au=on:cbe=off:cs=on:nm=2:rawr=on:sos=on:i=3107:si=on:rtra=on_0 on DTF2THF_14628 for (2873ds/3107Mi)
% 90.90/14.16 % (15198)Instruction limit reached!
% 90.90/14.16 % (15198)------------------------------
% 90.90/14.16 % (15198)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 90.90/14.16 % (15198)Termination reason: Unknown
% 90.90/14.16 % (15198)Termination phase: Saturation
% 90.90/14.16
% 90.90/14.16 % (15198)Memory used [KB]: 13432
% 90.90/14.16 % (15198)Time elapsed: 2.549 s
% 90.90/14.16 % (15198)Instructions burned: 8217 (million)
% 90.90/14.16 % (15198)------------------------------
% 90.90/14.16 % (15198)------------------------------
% 90.90/14.17 % (15212)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=7967:si=on:rtra=on_0 on DTF2THF_14628 for (2873ds/7967Mi)
% 91.35/14.24 % (15212)Refutation not found, incomplete strategy
% 91.35/14.24 % (15212)------------------------------
% 91.35/14.24 % (15212)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 91.35/14.24 % (15212)Termination reason: Refutation not found, incomplete strategy
% 91.35/14.24
% 91.35/14.24
% 91.35/14.24 % (15212)Memory used [KB]: 7675
% 91.35/14.24 % (15212)Time elapsed: 0.066 s
% 91.35/14.24 % (15212)Instructions burned: 239 (million)
% 91.35/14.24 % (15212)------------------------------
% 91.35/14.24 % (15212)------------------------------
% 91.35/14.25 % (15214)lrs+1010_10:959_abs=on:acc=on:bd=off:ccuc=small_ones:cha=on:cnfonf=lazy_simp:fd=preordered:fe=off:hud=3:ile=on:kws=inv_frequency:nm=2:piset=and:sd=5:sp=frequency:spb=goal_then_units:ss=axioms:st=4.5:i=3629:si=on:rtra=on_0 on DTF2THF_14628 for (2872ds/3629Mi)
% 94.44/14.86 % (15202)Instruction limit reached!
% 94.44/14.86 % (15202)------------------------------
% 94.44/14.86 % (15202)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 94.44/14.86 % (15202)Termination reason: Unknown
% 94.44/14.86 % (15202)Termination phase: Saturation
% 94.44/14.86
% 94.44/14.86 % (15202)Memory used [KB]: 20980
% 94.44/14.86 % (15202)Time elapsed: 2.701 s
% 94.44/14.86 % (15202)Instructions burned: 8786 (million)
% 94.44/14.86 % (15202)------------------------------
% 94.44/14.86 % (15202)------------------------------
% 94.44/14.87 % (15437)lrs+1010_1:1024_au=on:fe=axiom:lwlo=on:nm=0:ntd=on:nwc=10.0:spb=non_intro:uhcvi=on:i=939:si=on:rtra=on_0 on DTF2THF_14628 for (2866ds/939Mi)
% 97.27/15.08 % (15211)Instruction limit reached!
% 97.27/15.08 % (15211)------------------------------
% 97.27/15.08 % (15211)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 97.27/15.08 % (15211)Termination reason: Unknown
% 97.27/15.08 % (15211)Termination phase: Saturation
% 97.27/15.08
% 97.27/15.08 % (15211)Memory used [KB]: 10746
% 97.27/15.08 % (15211)Time elapsed: 0.933 s
% 97.27/15.08 % (15211)Instructions burned: 3109 (million)
% 97.27/15.08 % (15211)------------------------------
% 97.27/15.08 % (15211)------------------------------
% 97.27/15.09 % (15542)dis+1666_14:1_cnfonf=lazy_gen:fe=off:hud=10:piset=all_but_not_eq:prag=on:sp=const_max:i=1188:si=on:rtra=on_0 on DTF2THF_14628 for (2864ds/1188Mi)
% 97.97/15.15 % (15437)Instruction limit reached!
% 97.97/15.15 % (15437)------------------------------
% 97.97/15.15 % (15437)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 97.97/15.15 % (15437)Termination reason: Unknown
% 97.97/15.15 % (15437)Termination phase: Saturation
% 97.97/15.15
% 97.97/15.15 % (15437)Memory used [KB]: 9466
% 97.97/15.15 % (15437)Time elapsed: 0.281 s
% 97.97/15.15 % (15437)Instructions burned: 942 (million)
% 97.97/15.15 % (15437)------------------------------
% 97.97/15.15 % (15437)------------------------------
% 97.97/15.16 % (15581)dis+21_3:2_avsq=on:cbe=off:e2e=on:flr=on:ile=on:nwc=5.0:piset=or:rawr=on:sp=occurrence:i=3205:si=on:rtra=on_0 on DTF2THF_14628 for (2863ds/3205Mi)
% 98.81/15.36 % (15214)Instruction limit reached!
% 98.81/15.36 % (15214)------------------------------
% 98.81/15.36 % (15214)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 98.81/15.36 % (15214)Termination reason: Unknown
% 98.81/15.36 % (15214)Termination phase: Saturation
% 98.81/15.36
% 98.81/15.36 % (15214)Memory used [KB]: 11129
% 98.81/15.36 % (15214)Time elapsed: 1.112 s
% 98.81/15.36 % (15214)Instructions burned: 3630 (million)
% 98.81/15.36 % (15214)------------------------------
% 98.81/15.36 % (15214)------------------------------
% 98.81/15.37 % (15601)lrs+1010_1:1_cnfonf=off:ntd=on:nwc=3.0:s2a=on:sp=const_frequency:i=865:si=on:rtra=on_0 on DTF2THF_14628 for (2861ds/865Mi)
% 99.29/15.46 % (15206)Instruction limit reached!
% 99.29/15.46 % (15206)------------------------------
% 99.29/15.46 % (15206)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 99.29/15.46 % (15206)Termination reason: Unknown
% 99.29/15.46 % (15206)Termination phase: Saturation
% 99.29/15.46
% 99.29/15.46 % (15206)Memory used [KB]: 24690
% 99.29/15.46 % (15206)Time elapsed: 2.587 s
% 99.29/15.46 % (15206)Instructions burned: 8382 (million)
% 99.29/15.46 % (15206)------------------------------
% 99.29/15.46 % (15206)------------------------------
% 99.29/15.46 % (15542)Instruction limit reached!
% 99.29/15.46 % (15542)------------------------------
% 99.29/15.46 % (15542)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 99.29/15.46 % (15542)Termination reason: Unknown
% 99.29/15.46 % (15542)Termination phase: Saturation
% 99.29/15.46
% 99.29/15.46 % (15542)Memory used [KB]: 9722
% 99.29/15.46 % (15542)Time elapsed: 0.372 s
% 99.29/15.46 % (15542)Instructions burned: 1188 (million)
% 99.29/15.46 % (15542)------------------------------
% 99.29/15.46 % (15542)------------------------------
% 99.29/15.47 % (15676)ott+1002_1:1_au=on:bd=off:cbe=off:cha=on:cnfonf=lazy_pi_sigma_gen:fd=off:fe=off:ntd=on:sp=const_frequency:i=7469:si=on:rtra=on_0 on DTF2THF_14628 for (2860ds/7469Mi)
% 99.29/15.47 % (15677)dis+10_1:10_bd=preordered:e2e=on:fde=none:fe=axiom:hud=3:kws=precedence:nwc=3.0:prag=on:sp=const_max:tgt=full:i=4165:si=on:rtra=on_0 on DTF2THF_14628 for (2860ds/4165Mi)
% 100.33/15.61 % (15210)Instruction limit reached!
% 100.33/15.61 % (15210)------------------------------
% 100.33/15.61 % (15210)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 100.33/15.61 % (15210)Termination reason: Unknown
% 100.33/15.61 % (15210)Termination phase: Saturation
% 100.33/15.61
% 100.33/15.61 % (15210)Memory used [KB]: 12281
% 100.33/15.61 % (15210)Time elapsed: 2.546 s
% 100.33/15.61 % (15210)Instructions burned: 8427 (million)
% 100.33/15.61 % (15210)------------------------------
% 100.33/15.61 % (15210)------------------------------
% 100.33/15.61 % (15601)Refutation not found, non-redundant clauses discarded% (15601)------------------------------
% 100.33/15.61 % (15601)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 100.33/15.61 % (15601)Termination reason: Refutation not found, non-redundant clauses discarded
% 100.33/15.61
% 100.33/15.61 % (15601)Memory used [KB]: 8699
% 100.33/15.61 % (15601)Time elapsed: 0.242 s
% 100.33/15.61 % (15601)Instructions burned: 759 (million)
% 100.33/15.61 % (15601)------------------------------
% 100.33/15.61 % (15601)------------------------------
% 100.33/15.62 % (15695)dis+1002_1:1_au=on:bsr=unit_only:cbe=off:fe=off:fsr=off:nm=10:nwc=6.0:plsq=on:plsqc=1:plsqr=32,1:sos=all:i=2635:si=on:rtra=on_0 on DTF2THF_14628 for (2859ds/2635Mi)
% 100.33/15.62 % (15694)dis+1010_1:1_au=on:avsq=on:cnfonf=lazy_simp:fsr=off:ntd=on:nwc=10.0:sp=reverse_frequency:ss=axioms:st=1.5:i=13468:si=on:rtra=on_0 on DTF2THF_14628 for (2859ds/13468Mi)
% 104.14/16.09 % (15209)Instruction limit reached!
% 104.14/16.09 % (15209)------------------------------
% 104.14/16.09 % (15209)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 104.14/16.09 % (15209)Termination reason: Unknown
% 104.14/16.09 % (15209)Termination phase: Saturation
% 104.14/16.09
% 104.14/16.09 % (15209)Memory used [KB]: 20852
% 104.14/16.09 % (15209)Time elapsed: 3.042 s
% 104.14/16.09 % (15209)Instructions burned: 9824 (million)
% 104.14/16.09 % (15209)------------------------------
% 104.14/16.09 % (15209)------------------------------
% 104.14/16.11 % (15697)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=631:si=on:rtra=on_0 on DTF2THF_14628 for (2854ds/631Mi)
% 104.87/16.18 % (15581)Instruction limit reached!
% 104.87/16.18 % (15581)------------------------------
% 104.87/16.18 % (15581)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 104.87/16.18 % (15581)Termination reason: Unknown
% 104.87/16.18 % (15581)Termination phase: Saturation
% 104.87/16.18
% 104.87/16.18 % (15581)Memory used [KB]: 14839
% 104.87/16.18 % (15581)Time elapsed: 1.012 s
% 104.87/16.18 % (15581)Instructions burned: 3205 (million)
% 104.87/16.18 % (15581)------------------------------
% 104.87/16.18 % (15581)------------------------------
% 104.87/16.19 % (15699)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=15557:si=on:rtra=on_0 on DTF2THF_14628 for (2853ds/15557Mi)
% 105.35/16.29 % (15697)Instruction limit reached!
% 105.35/16.29 % (15697)------------------------------
% 105.35/16.29 % (15697)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 105.35/16.29 % (15697)Termination reason: Unknown
% 105.35/16.29 % (15697)Termination phase: Saturation
% 105.35/16.29
% 105.35/16.29 % (15697)Memory used [KB]: 9466
% 105.35/16.29 % (15697)Time elapsed: 0.190 s
% 105.35/16.29 % (15697)Instructions burned: 633 (million)
% 105.35/16.29 % (15697)------------------------------
% 105.35/16.29 % (15697)------------------------------
% 106.05/16.30 % (15700)dis+1002_1:1_au=on:sac=on:sd=5:slsq=on:slsqr=1,4:ss=axioms:st=2.0:i=2142:si=on:rtra=on_0 on DTF2THF_14628 for (2852ds/2142Mi)
% 107.05/16.54 % (15695)Instruction limit reached!
% 107.05/16.54 % (15695)------------------------------
% 107.05/16.54 % (15695)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 107.05/16.54 % (15695)Termination reason: Unknown
% 107.05/16.54 % (15695)Termination phase: Saturation
% 107.05/16.54
% 107.05/16.54 % (15695)Memory used [KB]: 12665
% 107.05/16.54 % (15695)Time elapsed: 0.924 s
% 107.05/16.54 % (15695)Instructions burned: 2636 (million)
% 107.05/16.54 % (15695)------------------------------
% 107.05/16.54 % (15695)------------------------------
% 107.05/16.55 % (15726)dis+1002_1:1_aac=none:au=on:bd=off:cnfonf=conj_eager:nwc=5.0:sgt=5:sp=reverse_arity:ss=axioms:i=5624:si=on:rtra=on_0 on DTF2THF_14628 for (2849ds/5624Mi)
% 108.70/16.94 % (15677)Instruction limit reached!
% 108.70/16.94 % (15677)------------------------------
% 108.70/16.94 % (15677)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 108.70/16.94 % (15677)Termination reason: Unknown
% 108.70/16.94 % (15677)Termination phase: Saturation
% 108.70/16.94
% 108.70/16.94 % (15677)Memory used [KB]: 22643
% 108.70/16.94 % (15677)Time elapsed: 1.470 s
% 108.70/16.94 % (15677)Instructions burned: 4166 (million)
% 108.70/16.94 % (15677)------------------------------
% 108.70/16.94 % (15677)------------------------------
% 108.70/16.95 % (15852)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=1665:si=on:rtra=on_0 on DTF2THF_14628 for (2845ds/1665Mi)
% 108.70/17.00 % (15700)Instruction limit reached!
% 108.70/17.00 % (15700)------------------------------
% 108.70/17.00 % (15700)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 108.70/17.00 % (15700)Termination reason: Unknown
% 108.70/17.00 % (15700)Termination phase: Saturation
% 108.70/17.00
% 108.70/17.00 % (15700)Memory used [KB]: 9338
% 108.70/17.00 % (15700)Time elapsed: 0.698 s
% 108.70/17.00 % (15700)Instructions burned: 2142 (million)
% 108.70/17.00 % (15700)------------------------------
% 108.70/17.00 % (15700)------------------------------
% 108.70/17.01 % (15878)dis+1002_1:1_av=off:prag=on:sd=1:sos=on:sp=occurrence:ss=axioms:i=64912:si=on:rtra=on_0 on DTF2THF_14628 for (2845ds/64912Mi)
% 113.49/17.47 % (15852)Instruction limit reached!
% 113.49/17.47 % (15852)------------------------------
% 113.49/17.47 % (15852)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 113.49/17.47 % (15852)Termination reason: Unknown
% 113.49/17.47 % (15852)Termination phase: Saturation
% 113.49/17.47
% 113.49/17.47 % (15852)Memory used [KB]: 10234
% 113.49/17.47 % (15852)Time elapsed: 0.515 s
% 113.49/17.47 % (15852)Instructions burned: 1667 (million)
% 113.49/17.47 % (15852)------------------------------
% 113.49/17.47 % (15852)------------------------------
% 113.49/17.48 % (15960)lrs+10_1:32_atotf=0.1:avsq=on:bsr=on:cnfonf=lazy_gen:fde=unused:i=7801:si=on:rtra=on_0 on DTF2THF_14628 for (2840ds/7801Mi)
% 116.07/17.95 % (15676)Instruction limit reached!
% 116.07/17.95 % (15676)------------------------------
% 116.07/17.95 % (15676)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 116.07/17.95 % (15676)Termination reason: Unknown
% 116.07/17.95 % (15676)Termination phase: Saturation
% 116.07/17.95
% 116.07/17.95 % (15676)Memory used [KB]: 15095
% 116.07/17.95 % (15676)Time elapsed: 2.492 s
% 116.07/17.95 % (15676)Instructions burned: 7471 (million)
% 116.07/17.95 % (15676)------------------------------
% 116.07/17.95 % (15676)------------------------------
% 116.07/17.96 % (15961)ott+2_1:1_au=on:hfsq=on:hfsqc=5:hfsql=off:nwc=5.0:sd=3:ss=axioms:st=5.0:i=15194:si=on:rtra=on_0 on DTF2THF_14628 for (2835ds/15194Mi)
% 119.48/18.26 % (15726)Instruction limit reached!
% 119.48/18.26 % (15726)------------------------------
% 119.48/18.26 % (15726)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 119.48/18.26 % (15726)Termination reason: Unknown
% 119.48/18.26 % (15726)Termination phase: Saturation
% 119.48/18.26
% 119.48/18.26 % (15726)Memory used [KB]: 10234
% 119.48/18.26 % (15726)Time elapsed: 1.704 s
% 119.48/18.26 % (15726)Instructions burned: 5625 (million)
% 119.48/18.26 % (15726)------------------------------
% 119.48/18.26 % (15726)------------------------------
% 119.48/18.27 % (15962)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=6753:si=on:rtra=on_0 on DTF2THF_14628 for (2832ds/6753Mi)
% 131.42/19.99 % (15960)Instruction limit reached!
% 131.42/19.99 % (15960)------------------------------
% 131.42/19.99 % (15960)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 131.42/19.99 % (15960)Termination reason: Unknown
% 131.42/19.99 % (15960)Termination phase: Saturation
% 131.42/19.99
% 131.42/19.99 % (15960)Memory used [KB]: 41577
% 131.42/19.99 % (15960)Time elapsed: 2.520 s
% 131.42/19.99 % (15960)Instructions burned: 7802 (million)
% 131.42/19.99 % (15960)------------------------------
% 131.42/19.99 % (15960)------------------------------
% 131.42/20.01 % (15963)lrs+1002_1:28_bd=off:cnfonf=lazy_simp:plsq=on:plsqr=1,1:prag=on:i=1003:si=on:rtra=on_0 on DTF2THF_14628 for (2815ds/1003Mi)
% 132.27/20.05 % (15694)Instruction limit reached!
% 132.27/20.05 % (15694)------------------------------
% 132.27/20.05 % (15694)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 132.27/20.05 % (15694)Termination reason: Unknown
% 132.27/20.05 % (15694)Termination phase: Saturation
% 132.27/20.05
% 132.27/20.05 % (15694)Memory used [KB]: 19445
% 132.27/20.05 % (15694)Time elapsed: 4.430 s
% 132.27/20.05 % (15694)Instructions burned: 13469 (million)
% 132.27/20.05 % (15694)------------------------------
% 132.27/20.05 % (15694)------------------------------
% 132.27/20.06 % (15964)ott-21_5:4_atotf=0.3:e2e=on:hud=15:ins=1:plsq=on:plsqc=1:plsqr=32,1:sp=unary_frequency:tnu=2:i=13018:si=on:rtra=on_0 on DTF2THF_14628 for (2814ds/13018Mi)
% 133.69/20.31 % (15963)Instruction limit reached!
% 133.69/20.31 % (15963)------------------------------
% 133.69/20.31 % (15963)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 133.69/20.31 % (15963)Termination reason: Unknown
% 133.69/20.31 % (15963)Termination phase: Saturation
% 133.69/20.31
% 133.69/20.31 % (15963)Memory used [KB]: 7931
% 133.69/20.31 % (15963)Time elapsed: 0.305 s
% 133.69/20.31 % (15963)Instructions burned: 1005 (million)
% 133.69/20.31 % (15963)------------------------------
% 133.69/20.31 % (15963)------------------------------
% 133.69/20.32 % (15965)dis+10_1:4_atotf=0.1:avsq=on:bsr=unit_only:e2e=on:sd=1:sp=const_max:ss=axioms:i=1267:si=on:rtra=on_0 on DTF2THF_14628 for (2812ds/1267Mi)
% 133.69/20.37 % (15962)Instruction limit reached!
% 133.69/20.37 % (15962)------------------------------
% 133.69/20.37 % (15962)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 133.69/20.37 % (15962)Termination reason: Unknown
% 133.69/20.37 % (15962)Termination phase: Saturation
% 133.69/20.37
% 133.69/20.37 % (15962)Memory used [KB]: 12281
% 133.69/20.37 % (15962)Time elapsed: 2.103 s
% 133.69/20.37 % (15962)Instructions burned: 6754 (million)
% 133.69/20.37 % (15962)------------------------------
% 133.69/20.37 % (15962)------------------------------
% 133.69/20.38 % (15966)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=2570:si=on:rtra=on_0 on DTF2THF_14628 for (2811ds/2570Mi)
% 135.29/20.70 % (15965)Instruction limit reached!
% 135.29/20.70 % (15965)------------------------------
% 135.29/20.70 % (15965)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 135.29/20.70 % (15965)Termination reason: Unknown
% 135.29/20.70 % (15965)Termination phase: Saturation
% 135.29/20.70
% 135.29/20.70 % (15965)Memory used [KB]: 9083
% 135.29/20.70 % (15965)Time elapsed: 0.376 s
% 135.29/20.70 % (15965)Instructions burned: 1270 (million)
% 135.29/20.70 % (15965)------------------------------
% 135.29/20.70 % (15965)------------------------------
% 136.07/20.71 % (15967)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=13163:si=on:rtra=on_0 on DTF2THF_14628 for (2808ds/13163Mi)
% 136.48/20.85 % (15699)Instruction limit reached!
% 136.48/20.85 % (15699)------------------------------
% 136.48/20.85 % (15699)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 136.48/20.85 % (15699)Termination reason: Unknown
% 136.48/20.85 % (15699)Termination phase: Saturation
% 136.48/20.85
% 136.48/20.85 % (15699)Memory used [KB]: 29423
% 136.48/20.85 % (15699)Time elapsed: 4.661 s
% 136.48/20.85 % (15699)Instructions burned: 15560 (million)
% 136.48/20.85 % (15699)------------------------------
% 136.48/20.85 % (15699)------------------------------
% 136.48/20.86 % (15968)lrs+1666_1:1_au=on:s2a=on:sd=2:ss=axioms:st=5.0:i=5087:si=on:rtra=on_0 on DTF2THF_14628 for (2806ds/5087Mi)
% 140.02/21.13 % (15966)Instruction limit reached!
% 140.02/21.13 % (15966)------------------------------
% 140.02/21.13 % (15966)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 140.02/21.13 % (15966)Termination reason: Unknown
% 140.02/21.13 % (15966)Termination phase: Saturation
% 140.02/21.13
% 140.02/21.13 % (15966)Memory used [KB]: 14583
% 140.02/21.13 % (15966)Time elapsed: 0.754 s
% 140.02/21.13 % (15966)Instructions burned: 2572 (million)
% 140.02/21.13 % (15966)------------------------------
% 140.02/21.13 % (15966)------------------------------
% 140.02/21.14 % (15969)lrs+1002_1:1_aac=none:au=on:bd=off:cnfonf=lazy_pi_sigma_gen:s2a=on:sac=on:sd=1:sgt=20:ss=axioms:i=10380:si=on:rtra=on_0 on DTF2THF_14628 for (2804ds/10380Mi)
% 141.08/21.38 % (15969)First to succeed.
% 141.08/21.38 % (15969)Refutation found. Thanks to Tanya!
% 141.08/21.38 % SZS status Theorem for DTF2THF_14628
% 141.08/21.38 % SZS output start Proof for DTF2THF_14628
% 141.08/21.38 thf(type_def_5, type, set: ($tType) > $tType).
% 141.08/21.38 thf(type_def_7, type, nat: $tType).
% 141.08/21.38 thf(type_def_8, type, hF_Mirabelle_hf: $tType).
% 141.08/21.38 thf(func_def_0, type, hF_Mirabelle_hf: $tType).
% 141.08/21.38 thf(func_def_1, type, set: ($tType) > $tType).
% 141.08/21.38 thf(func_def_2, type, nat: $tType).
% 141.08/21.38 thf(func_def_3, type, type: !>[X0: $tType]:($o)).
% 141.08/21.38 thf(func_def_4, type, ord: !>[X0: $tType]:($o)).
% 141.08/21.38 thf(func_def_5, type, order: !>[X0: $tType]:($o)).
% 141.08/21.38 thf(func_def_6, type, no_bot: !>[X0: $tType]:($o)).
% 141.08/21.38 thf(func_def_7, type, no_top: !>[X0: $tType]:($o)).
% 141.08/21.38 thf(func_def_8, type, finite_finite: !>[X0: $tType]:($o)).
% 141.08/21.38 thf(func_def_9, type, linorder: !>[X0: $tType]:($o)).
% 141.08/21.38 thf(func_def_10, type, preorder: !>[X0: $tType]:($o)).
% 141.08/21.38 thf(func_def_11, type, wellorder: !>[X0: $tType]:($o)).
% 141.08/21.38 thf(func_def_12, type, dense_order: !>[X0: $tType]:($o)).
% 141.08/21.38 thf(func_def_13, type, linordered_idom: !>[X0: $tType]:($o)).
% 141.08/21.38 thf(func_def_14, type, linordered_field: !>[X0: $tType]:($o)).
% 141.08/21.38 thf(func_def_15, type, dense_linorder: !>[X0: $tType]:($o)).
% 141.08/21.38 thf(func_def_16, type, canoni770627133id_add: !>[X0: $tType]:($o)).
% 141.08/21.38 thf(func_def_17, type, condit1656338222tinuum: !>[X0: $tType]:($o)).
% 141.08/21.38 thf(func_def_18, type, condit1037483654norder: !>[X0: $tType]:($o)).
% 141.08/21.38 thf(func_def_19, type, finite_Fpow: !>[X0: $tType]:(set @ X0 > set @ set @ X0)).
% 141.08/21.38 thf(func_def_20, type, finite_card: !>[X0: $tType]:(set @ X0 > nat)).
% 141.08/21.38 thf(func_def_21, type, finite_finite2: !>[X0: $tType]:(set @ X0 > $o)).
% 141.08/21.38 thf(func_def_22, type, inj_on: !>[X0: $tType, X1: $tType]:((X0 > X1) > set @ X0 > $o)).
% 141.08/21.38 thf(func_def_23, type, zero_zero: !>[X0: $tType]:(X0)).
% 141.08/21.38 thf(func_def_24, type, hF_Mir1687042746ollect: (hF_Mirabelle_hf > $o) > hF_Mirabelle_hf > hF_Mirabelle_hf).
% 141.08/21.38 thf(func_def_25, type, hF_Mirabelle_HF: set @ hF_Mirabelle_hf > hF_Mirabelle_hf).
% 141.08/21.38 thf(func_def_26, type, hF_Mirabelle_HUnion: hF_Mirabelle_hf > hF_Mirabelle_hf).
% 141.08/21.38 thf(func_def_27, type, hF_Mir569462966eplace: hF_Mirabelle_hf > (hF_Mirabelle_hf > hF_Mirabelle_hf > $o) > hF_Mirabelle_hf).
% 141.08/21.38 thf(func_def_28, type, hF_Mirabelle_RepFun: hF_Mirabelle_hf > (hF_Mirabelle_hf > hF_Mirabelle_hf) > hF_Mirabelle_hf).
% 141.08/21.38 thf(func_def_29, type, hF_Mirabelle_Replace: hF_Mirabelle_hf > (hF_Mirabelle_hf > hF_Mirabelle_hf > $o) > hF_Mirabelle_hf).
% 141.08/21.38 thf(func_def_30, type, hF_Mirabelle_hfset: hF_Mirabelle_hf > set @ hF_Mirabelle_hf).
% 141.08/21.38 thf(func_def_31, type, hF_Mirabelle_hmem: hF_Mirabelle_hf > hF_Mirabelle_hf > $o).
% 141.08/21.38 thf(func_def_32, type, ord_less: !>[X0: $tType]:(X0 > X0 > $o)).
% 141.08/21.38 thf(func_def_33, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 141.08/21.38 thf(func_def_34, type, order_Greatest: !>[X0: $tType]:((X0 > $o) > X0)).
% 141.08/21.38 thf(func_def_35, type, order_antimono: !>[X0: $tType, X1: $tType]:((X0 > X1) > $o)).
% 141.08/21.38 thf(func_def_36, type, ordering: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > $o)).
% 141.08/21.38 thf(func_def_37, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 141.08/21.38 thf(func_def_38, type, image: !>[X0: $tType, X1: $tType]:((X0 > X1) > set @ X0 > set @ X1)).
% 141.08/21.38 thf(func_def_39, type, set_or578182835ssThan: !>[X0: $tType]:(X0 > X0 > set @ X0)).
% 141.08/21.38 thf(func_def_40, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 141.08/21.38 thf(func_def_41, type, a: hF_Mirabelle_hf).
% 141.08/21.38 thf(func_def_42, type, b: hF_Mirabelle_hf).
% 141.08/21.38 thf(func_def_61, type, ph1: !>[X0: $tType]:(X0)).
% 141.08/21.38 thf(func_def_62, type, sK2: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf).
% 141.08/21.38 thf(func_def_63, type, sK3: (hF_Mirabelle_hf > $o) > hF_Mirabelle_hf > hF_Mirabelle_hf).
% 141.08/21.38 thf(func_def_64, type, sK4: hF_Mirabelle_hf > hF_Mirabelle_hf).
% 141.08/21.38 thf(func_def_65, type, sK5: (hF_Mirabelle_hf > hF_Mirabelle_hf) > hF_Mirabelle_hf > hF_Mirabelle_hf).
% 141.08/21.38 thf(func_def_66, type, sK6: (hF_Mirabelle_hf > hF_Mirabelle_hf > $o) > hF_Mirabelle_hf > hF_Mirabelle_hf).
% 141.08/21.38 thf(func_def_67, type, sK7: (hF_Mirabelle_hf > hF_Mirabelle_hf > $o) > hF_Mirabelle_hf > hF_Mirabelle_hf).
% 141.08/21.38 thf(func_def_68, type, sK8: (hF_Mirabelle_hf > hF_Mirabelle_hf > $o) > hF_Mirabelle_hf > hF_Mirabelle_hf).
% 141.08/21.38 thf(func_def_69, type, sK9: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf).
% 141.08/21.38 thf(func_def_70, type, sK10: hF_Mirabelle_hf > (hF_Mirabelle_hf > hF_Mirabelle_hf) > hF_Mirabelle_hf > hF_Mirabelle_hf).
% 141.08/21.38 thf(func_def_71, type, sK11: (hF_Mirabelle_hf > hF_Mirabelle_hf > $o) > hF_Mirabelle_hf > hF_Mirabelle_hf).
% 141.08/21.38 thf(func_def_72, type, sK12: hF_Mirabelle_hf > (hF_Mirabelle_hf > hF_Mirabelle_hf > $o) > hF_Mirabelle_hf > hF_Mirabelle_hf).
% 141.08/21.38 thf(func_def_73, type, sK13: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf).
% 141.08/21.38 thf(f2535,plain,(
% 141.08/21.38 $false),
% 141.08/21.38 inference(trivial_inequality_removal,[status(thm)],[f2534])).
% 141.08/21.38 thf(f2534,plain,(
% 141.08/21.38 ($false = $true)),
% 141.08/21.38 inference(forward_demodulation,[status(thm)],[f2533,f900])).
% 141.08/21.38 thf(f900,plain,(
% 141.08/21.38 ((ord_less_eq @ hF_Mirabelle_hf @ a @ b) = $false)),
% 141.08/21.38 inference(not_proxy_clausification,[status(thm)],[f851])).
% 141.08/21.38 thf(f851,plain,(
% 141.08/21.38 ((~ (ord_less_eq @ hF_Mirabelle_hf @ a @ b)) = $true)),
% 141.08/21.38 inference(cnf_transformation,[status(thm)],[f385])).
% 141.08/21.38 thf(f385,plain,(
% 141.08/21.38 ((~ (ord_less_eq @ hF_Mirabelle_hf @ a @ b)) = $true)),
% 141.08/21.38 inference(fool_elimination,[status(thm)],[f384])).
% 141.08/21.38 thf(f384,plain,(
% 141.08/21.38 ~(ord_less_eq @ hF_Mirabelle_hf @ a @ b)),
% 141.08/21.38 inference(rectify,[status(thm)],[f282])).
% 141.08/21.38 thf(f282,negated_conjecture,(
% 141.08/21.38 ~(ord_less_eq @ hF_Mirabelle_hf @ a @ b)),
% 141.08/21.38 inference(negated_conjecture,[status(cth)],[f281])).
% 141.08/21.38 thf(f281,conjecture,(
% 141.08/21.38 (ord_less_eq @ hF_Mirabelle_hf @ a @ b)),
% 141.08/21.38 file('/export/starexec/sandbox/tmp/tmp.vTURPhR8yA/DTF2THF_14628.p',conj_1)).
% 141.08/21.38 thf(f2533,plain,(
% 141.08/21.38 ((ord_less_eq @ hF_Mirabelle_hf @ a @ b) = $true)),
% 141.08/21.38 inference(trivial_inequality_removal,[status(thm)],[f2529])).
% 141.08/21.38 thf(f2529,plain,(
% 141.08/21.38 ($false = $true) | ((ord_less_eq @ hF_Mirabelle_hf @ a @ b) = $true)),
% 141.08/21.38 inference(superposition,[status(thm)],[f1105,f894])).
% 141.08/21.38 thf(f894,plain,(
% 141.08/21.38 ((!! @ hF_Mirabelle_hf @ (^[Y0 : hF_Mirabelle_hf]: ((member @ hF_Mirabelle_hf @ Y0 @ (hF_Mirabelle_hfset @ a)) => (member @ hF_Mirabelle_hf @ Y0 @ (hF_Mirabelle_hfset @ b))))) = $true)),
% 141.08/21.38 inference(beta_eta_normalization,[status(thm)],[f882])).
% 141.08/21.38 thf(f882,plain,(
% 141.08/21.38 ((!! @ hF_Mirabelle_hf @ (^[Y0 : hF_Mirabelle_hf]: (((^[Y1 : hF_Mirabelle_hf]: ((^[Y2 : hF_Mirabelle_hf]: (member @ hF_Mirabelle_hf @ Y1 @ (hF_Mirabelle_hfset @ Y2))))) @ Y0 @ a) => ((^[Y1 : hF_Mirabelle_hf]: ((^[Y2 : hF_Mirabelle_hf]: (member @ hF_Mirabelle_hf @ Y1 @ (hF_Mirabelle_hfset @ Y2))))) @ Y0 @ b)))) = $true)),
% 141.08/21.38 inference(definition_unfolding,[status(thm)],[f864,f865,f865])).
% 141.08/21.38 thf(f865,plain,(
% 141.08/21.38 (hF_Mirabelle_hmem = (^[Y0 : hF_Mirabelle_hf]: ((^[Y1 : hF_Mirabelle_hf]: (member @ hF_Mirabelle_hf @ Y0 @ (hF_Mirabelle_hfset @ Y1))))))),
% 141.08/21.38 inference(cnf_transformation,[status(thm)],[f655])).
% 141.08/21.38 thf(f655,plain,(
% 141.08/21.38 (hF_Mirabelle_hmem = (^[Y0 : hF_Mirabelle_hf]: ((^[Y1 : hF_Mirabelle_hf]: (member @ hF_Mirabelle_hf @ Y0 @ (hF_Mirabelle_hfset @ Y1))))))),
% 141.08/21.38 inference(fool_elimination,[status(thm)],[f654])).
% 141.08/21.38 thf(f654,plain,(
% 141.08/21.38 ((^[X0 : hF_Mirabelle_hf, X1 : hF_Mirabelle_hf] : (member @ hF_Mirabelle_hf @ X0 @ (hF_Mirabelle_hfset @ X1))) = hF_Mirabelle_hmem)),
% 141.08/21.38 inference(rectify,[status(thm)],[f45])).
% 141.08/21.38 thf(f45,axiom,(
% 141.08/21.38 ((^[X7 : hF_Mirabelle_hf, X8 : hF_Mirabelle_hf] : (member @ hF_Mirabelle_hf @ X7 @ (hF_Mirabelle_hfset @ X8))) = hF_Mirabelle_hmem)),
% 141.08/21.38 file('/export/starexec/sandbox/tmp/tmp.vTURPhR8yA/DTF2THF_14628.p',fact_44_hmem__def)).
% 141.08/21.38 thf(f864,plain,(
% 141.08/21.38 ((!! @ hF_Mirabelle_hf @ (^[Y0 : hF_Mirabelle_hf]: ((hF_Mirabelle_hmem @ Y0 @ a) => (hF_Mirabelle_hmem @ Y0 @ b)))) = $true)),
% 141.08/21.38 inference(cnf_transformation,[status(thm)],[f816])).
% 141.08/21.38 thf(f816,plain,(
% 141.08/21.38 ((!! @ hF_Mirabelle_hf @ (^[Y0 : hF_Mirabelle_hf]: ((hF_Mirabelle_hmem @ Y0 @ a) => (hF_Mirabelle_hmem @ Y0 @ b)))) = $true)),
% 141.08/21.38 inference(fool_elimination,[status(thm)],[f815])).
% 141.08/21.38 thf(f815,plain,(
% 141.08/21.38 ! [X0 : hF_Mirabelle_hf] : ((hF_Mirabelle_hmem @ X0 @ a) => (hF_Mirabelle_hmem @ X0 @ b))),
% 141.08/21.38 inference(rectify,[status(thm)],[f280])).
% 141.08/21.38 thf(f280,axiom,(
% 141.08/21.38 ! [X51 : hF_Mirabelle_hf] : ((hF_Mirabelle_hmem @ X51 @ a) => (hF_Mirabelle_hmem @ X51 @ b))),
% 141.08/21.38 file('/export/starexec/sandbox/tmp/tmp.vTURPhR8yA/DTF2THF_14628.p',conj_0)).
% 141.08/21.38 thf(f1105,plain,(
% 141.08/21.38 ( ! [X2 : hF_Mirabelle_hf,X1 : hF_Mirabelle_hf] : (($false = (!! @ hF_Mirabelle_hf @ (^[Y0 : hF_Mirabelle_hf]: ((member @ hF_Mirabelle_hf @ Y0 @ (hF_Mirabelle_hfset @ X1)) => (member @ hF_Mirabelle_hf @ Y0 @ (hF_Mirabelle_hfset @ X2)))))) | ((ord_less_eq @ hF_Mirabelle_hf @ X1 @ X2) = $true)) )),
% 141.08/21.38 inference(binary_proxy_clausification,[status(thm)],[f1104])).
% 141.08/21.38 thf(f1104,plain,(
% 141.08/21.38 ( ! [X2 : hF_Mirabelle_hf,X1 : hF_Mirabelle_hf] : (((ord_less_eq @ hF_Mirabelle_hf @ X1 @ X2) = (!! @ hF_Mirabelle_hf @ (^[Y0 : hF_Mirabelle_hf]: ((member @ hF_Mirabelle_hf @ Y0 @ (hF_Mirabelle_hfset @ X1)) => (member @ hF_Mirabelle_hf @ Y0 @ (hF_Mirabelle_hfset @ X2))))))) )),
% 141.08/21.38 inference(beta_eta_normalization,[status(thm)],[f1103])).
% 141.08/21.38 thf(f1103,plain,(
% 141.08/21.38 ( ! [X2 : hF_Mirabelle_hf,X1 : hF_Mirabelle_hf] : ((((^[Y0 : hF_Mirabelle_hf]: (!! @ hF_Mirabelle_hf @ (^[Y1 : hF_Mirabelle_hf]: ((member @ hF_Mirabelle_hf @ Y1 @ (hF_Mirabelle_hfset @ X1)) => (member @ hF_Mirabelle_hf @ Y1 @ (hF_Mirabelle_hfset @ Y0)))))) @ X2) = (ord_less_eq @ hF_Mirabelle_hf @ X1 @ X2))) )),
% 141.08/21.38 inference(argument_congruence,[status(thm)],[f907])).
% 141.08/21.38 thf(f907,plain,(
% 141.08/21.38 ( ! [X1 : hF_Mirabelle_hf] : (((ord_less_eq @ hF_Mirabelle_hf @ X1) = (^[Y0 : hF_Mirabelle_hf]: (!! @ hF_Mirabelle_hf @ (^[Y1 : hF_Mirabelle_hf]: ((member @ hF_Mirabelle_hf @ Y1 @ (hF_Mirabelle_hfset @ X1)) => (member @ hF_Mirabelle_hf @ Y1 @ (hF_Mirabelle_hfset @ Y0)))))))) )),
% 141.08/21.38 inference(beta_eta_normalization,[status(thm)],[f906])).
% 141.08/21.38 thf(f906,plain,(
% 141.08/21.38 ( ! [X1 : hF_Mirabelle_hf] : ((((^[Y0 : hF_Mirabelle_hf]: ((^[Y1 : hF_Mirabelle_hf]: (!! @ hF_Mirabelle_hf @ (^[Y2 : hF_Mirabelle_hf]: ((member @ hF_Mirabelle_hf @ Y2 @ (hF_Mirabelle_hfset @ Y0)) => (member @ hF_Mirabelle_hf @ Y2 @ (hF_Mirabelle_hfset @ Y1)))))))) @ X1) = (ord_less_eq @ hF_Mirabelle_hf @ X1))) )),
% 141.08/21.38 inference(argument_congruence,[status(thm)],[f887])).
% 141.08/21.38 thf(f887,plain,(
% 141.08/21.38 (ord_less_eq @ hF_Mirabelle_hf = (^[Y0 : hF_Mirabelle_hf]: ((^[Y1 : hF_Mirabelle_hf]: (!! @ hF_Mirabelle_hf @ (^[Y2 : hF_Mirabelle_hf]: ((member @ hF_Mirabelle_hf @ Y2 @ (hF_Mirabelle_hfset @ Y0)) => (member @ hF_Mirabelle_hf @ Y2 @ (hF_Mirabelle_hfset @ Y1)))))))))),
% 141.08/21.38 inference(beta_eta_normalization,[status(thm)],[f871])).
% 141.08/21.38 thf(f871,plain,(
% 141.08/21.38 (ord_less_eq @ hF_Mirabelle_hf = (^[Y0 : hF_Mirabelle_hf]: ((^[Y1 : hF_Mirabelle_hf]: (!! @ hF_Mirabelle_hf @ (^[Y2 : hF_Mirabelle_hf]: (((^[Y3 : hF_Mirabelle_hf]: ((^[Y4 : hF_Mirabelle_hf]: (member @ hF_Mirabelle_hf @ Y3 @ (hF_Mirabelle_hfset @ Y4))))) @ Y2 @ Y0) => ((^[Y3 : hF_Mirabelle_hf]: ((^[Y4 : hF_Mirabelle_hf]: (member @ hF_Mirabelle_hf @ Y3 @ (hF_Mirabelle_hfset @ Y4))))) @ Y2 @ Y1))))))))),
% 141.08/21.38 inference(definition_unfolding,[status(thm)],[f850,f865,f865])).
% 141.08/21.38 thf(f850,plain,(
% 141.08/21.38 (ord_less_eq @ hF_Mirabelle_hf = (^[Y0 : hF_Mirabelle_hf]: ((^[Y1 : hF_Mirabelle_hf]: (!! @ hF_Mirabelle_hf @ (^[Y2 : hF_Mirabelle_hf]: ((hF_Mirabelle_hmem @ Y2 @ Y0) => (hF_Mirabelle_hmem @ Y2 @ Y1))))))))),
% 141.08/21.38 inference(cnf_transformation,[status(thm)],[f461])).
% 141.08/21.38 thf(f461,plain,(
% 141.08/21.38 (ord_less_eq @ hF_Mirabelle_hf = (^[Y0 : hF_Mirabelle_hf]: ((^[Y1 : hF_Mirabelle_hf]: (!! @ hF_Mirabelle_hf @ (^[Y2 : hF_Mirabelle_hf]: ((hF_Mirabelle_hmem @ Y2 @ Y0) => (hF_Mirabelle_hmem @ Y2 @ Y1))))))))),
% 141.08/21.38 inference(fool_elimination,[status(thm)],[f460])).
% 141.08/21.38 thf(f460,plain,(
% 141.08/21.38 ((^[X0 : hF_Mirabelle_hf, X1 : hF_Mirabelle_hf] : (! [X2 : hF_Mirabelle_hf] : ((hF_Mirabelle_hmem @ X2 @ X0) => (hF_Mirabelle_hmem @ X2 @ X1)))) = ord_less_eq @ hF_Mirabelle_hf)),
% 141.08/21.38 inference(rectify,[status(thm)],[f7])).
% 141.08/21.38 thf(f7,axiom,(
% 141.08/21.38 ((^[X22 : hF_Mirabelle_hf, X23 : hF_Mirabelle_hf] : (! [X9 : hF_Mirabelle_hf] : ((hF_Mirabelle_hmem @ X9 @ X22) => (hF_Mirabelle_hmem @ X9 @ X23)))) = ord_less_eq @ hF_Mirabelle_hf)),
% 141.08/21.38 file('/export/starexec/sandbox/tmp/tmp.vTURPhR8yA/DTF2THF_14628.p',fact_6_less__eq__hf__def)).
% 141.08/21.38 % SZS output end Proof for DTF2THF_14628
% 141.08/21.38 % (15969)------------------------------
% 141.08/21.38 % (15969)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 141.08/21.38 % (15969)Termination reason: Refutation
% 141.08/21.38
% 141.08/21.38 % (15969)Memory used [KB]: 7547
% 141.08/21.38 % (15969)Time elapsed: 0.240 s
% 141.08/21.38 % (15969)Instructions burned: 809 (million)
% 141.08/21.38 % (15969)------------------------------
% 141.08/21.38 % (15969)------------------------------
% 141.08/21.38 % (14726)Success in time 19.849 s
%------------------------------------------------------------------------------