Leo-III---1.8.0.THM-Ref.s

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%------------------------------------------------------------------------------
% File     : Leo-III---1.8.0
% Problem  : DAT170^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39

% Computer : n017.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed Sep 30 07:48:04 AM UTC 2026

% Result   : Theorem 189.03s 62.56s
% Output   : Refutation 180.72s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   84
%            Number of leaves      :  300
% Syntax   : Number of formulae    : 1068 ( 252 unt;   0 typ;   5 def)
%            Number of atoms       : 3562 ( 982 equ;   4 cnn)
%            Maximal formula atoms :   13 (   3 avg)
%            Number of connectives : 14164 ( 763   ~; 582   |;  75   &;12002   @)
%                                         (   0 <=>; 742  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   59 (  11 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  : 7353 (7353   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   73 (  68 usr;  10 con; 0-6 aty)
%            Number of variables   : 6227 ( 203   ^;6004   !;  15   ?;6227   :)
%                                         (   0  !>;   0  ?*;   0  @-;   5  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(nat_type,type,
    nat: $tType ).

thf(a_type,type,
    a: $tType ).

thf(ring_decl,type,
    ring: 
      !>[TA: $tType] : ( ( itself @ TA ) > $o ) ).

thf(zero_decl,type,
    zero: 
      !>[TA: $tType] : ( ( itself @ TA ) > $o ) ).

thf(ord_decl,type,
    ord: 
      !>[TA: $tType] : ( ( itself @ TA ) > $o ) ).

thf(semiring_decl,type,
    semiring: 
      !>[TA: $tType] : ( ( itself @ TA ) > $o ) ).

thf(order_decl,type,
    order: 
      !>[TA: $tType] : ( ( itself @ TA ) > $o ) ).

thf(mult_zero_decl,type,
    mult_zero: 
      !>[TA: $tType] : ( ( itself @ TA ) > $o ) ).

thf(group_add_decl,type,
    group_add: 
      !>[TA: $tType] : ( ( itself @ TA ) > $o ) ).

thf(monoid_add_decl,type,
    monoid_add: 
      !>[TA: $tType] : ( ( itself @ TA ) > $o ) ).

thf(linorder_decl,type,
    linorder: 
      !>[TA: $tType] : ( ( itself @ TA ) > $o ) ).

thf(preorder_decl,type,
    preorder: 
      !>[TA: $tType] : ( ( itself @ TA ) > $o ) ).

thf(ordered_ring_decl,type,
    ordered_ring: 
      !>[TA: $tType] : ( ( itself @ TA ) > $o ) ).

thf(comm_semiring_decl,type,
    comm_semiring: 
      !>[TA: $tType] : ( ( itself @ TA ) > $o ) ).

thf(semigroup_add_decl,type,
    semigroup_add: 
      !>[TA: $tType] : ( ( itself @ TA ) > $o ) ).

thf(semigroup_mult_decl,type,
    semigroup_mult: 
      !>[TA: $tType] : ( ( itself @ TA ) > $o ) ).

thf(comm_semiring_1_decl,type,
    comm_semiring_1: 
      !>[TA: $tType] : ( ( itself @ TA ) > $o ) ).

thf(linordered_ring_decl,type,
    linordered_ring: 
      !>[TA: $tType] : ( ( itself @ TA ) > $o ) ).

thf(comm_monoid_add_decl,type,
    comm_monoid_add: 
      !>[TA: $tType] : ( ( itself @ TA ) > $o ) ).

thf(ordered_semiring_decl,type,
    ordered_semiring: 
      !>[TA: $tType] : ( ( itself @ TA ) > $o ) ).

thf(linordered_field_decl,type,
    linordered_field: 
      !>[TA: $tType] : ( ( itself @ TA ) > $o ) ).

thf(ab_semigroup_add_decl,type,
    ab_semigroup_add: 
      !>[TA: $tType] : ( ( itself @ TA ) > $o ) ).

thf(ab_semigroup_mult_decl,type,
    ab_semigroup_mult: 
      !>[TA: $tType] : ( ( itself @ TA ) > $o ) ).

thf(ordered_semiring_0_decl,type,
    ordered_semiring_0: 
      !>[TA: $tType] : ( ( itself @ TA ) > $o ) ).

thf(cancel_semigroup_add_decl,type,
    cancel_semigroup_add: 
      !>[TA: $tType] : ( ( itself @ TA ) > $o ) ).

thf(ordere1490568538miring_decl,type,
    ordere1490568538miring: 
      !>[TA: $tType] : ( ( itself @ TA ) > $o ) ).

thf(linord581940658strict_decl,type,
    linord581940658strict: 
      !>[TA: $tType] : ( ( itself @ TA ) > $o ) ).

thf(cancel1352612707id_add_decl,type,
    cancel1352612707id_add: 
      !>[TA: $tType] : ( ( itself @ TA ) > $o ) ).

thf(linord219039673up_add_decl,type,
    linord219039673up_add: 
      !>[TA: $tType] : ( ( itself @ TA ) > $o ) ).

thf(ordere216010020id_add_decl,type,
    ordere216010020id_add: 
      !>[TA: $tType] : ( ( itself @ TA ) > $o ) ).

thf(ordere779506340up_add_decl,type,
    ordere779506340up_add: 
      !>[TA: $tType] : ( ( itself @ TA ) > $o ) ).

thf(semiri1193490041visors_decl,type,
    semiri1193490041visors: 
      !>[TA: $tType] : ( ( itself @ TA ) > $o ) ).

thf(canoni770627133id_add_decl,type,
    canoni770627133id_add: 
      !>[TA: $tType] : ( ( itself @ TA ) > $o ) ).

thf(ordere236663937imp_le_decl,type,
    ordere236663937imp_le: 
      !>[TA: $tType] : ( ( itself @ TA ) > $o ) ).

thf(semiri1923998003cancel_decl,type,
    semiri1923998003cancel: 
      !>[TA: $tType] : ( ( itself @ TA ) > $o ) ).

thf(ordere516151231imp_le_decl,type,
    ordere516151231imp_le: 
      !>[TA: $tType] : ( ( itself @ TA ) > $o ) ).

thf(semiri456707255roduct_decl,type,
    semiri456707255roduct: 
      !>[TA: $tType] : ( ( itself @ TA ) > $o ) ).

thf(plus_plus_decl,type,
    plus_plus: 
      !>[TA: $tType] : ( TA > TA > TA ) ).

thf(times_times_decl,type,
    times_times: 
      !>[TA: $tType] : ( TA > TA > TA ) ).

thf(zero_zero_decl,type,
    zero_zero: 
      !>[TA: $tType] : TA ).

thf(huffma505251170phabet_decl,type,
    huffma505251170phabet: 
      !>[TA: $tType] : ( ( huffma16452318e_tree @ TA ) > ( set @ TA ) ) ).

thf(huffma787811817Weight_decl,type,
    huffma787811817Weight: 
      !>[TA: $tType] : ( ( huffma16452318e_tree @ TA ) > nat ) ).

thf(huffma1050891809istent_decl,type,
    huffma1050891809istent: 
      !>[TA: $tType] : ( ( huffma16452318e_tree @ TA ) > $o ) ).

thf(huffma636208924e_cost_decl,type,
    huffma636208924e_cost: 
      !>[TA: $tType] : ( ( huffma16452318e_tree @ TA ) > nat ) ).

thf(huffma223349076_depth_decl,type,
    huffma223349076_depth: 
      !>[TA: $tType] : ( ( huffma16452318e_tree @ TA ) > TA > nat ) ).

thf(huffma854352999e_freq_decl,type,
    huffma854352999e_freq: 
      !>[TA: $tType] : ( ( huffma16452318e_tree @ TA ) > TA > nat ) ).

thf(huffma1554076246height_decl,type,
    huffma1554076246height: 
      !>[TA: $tType] : ( ( huffma16452318e_tree @ TA ) > nat ) ).

thf(huffma936049440ptimum_decl,type,
    huffma936049440ptimum: 
      !>[TA: $tType] : ( ( huffma16452318e_tree @ TA ) > $o ) ).

thf(huffma943100115ibling_decl,type,
    huffma943100115ibling: 
      !>[TA: $tType] : ( ( huffma16452318e_tree @ TA ) > TA > TA ) ).

thf(huffma2094459102Leaves_decl,type,
    huffma2094459102Leaves: 
      !>[TA: $tType] : ( ( huffma16452318e_tree @ TA ) > nat > TA > nat > TA > ( huffma16452318e_tree @ TA ) ) ).

thf(huffma469337550apSyms_decl,type,
    huffma469337550apSyms: 
      !>[TA: $tType] : ( ( huffma16452318e_tree @ TA ) > TA > TA > ( huffma16452318e_tree @ TA ) ) ).

thf(huffma453905539eTrees_decl,type,
    huffma453905539eTrees: 
      !>[TA: $tType] : ( ( huffma16452318e_tree @ TA ) > ( huffma16452318e_tree @ TA ) > ( huffma16452318e_tree @ TA ) ) ).

thf(huffma691733767weight_decl,type,
    huffma691733767weight: 
      !>[TA: $tType] : ( ( huffma16452318e_tree @ TA ) > nat ) ).

thf(if_decl,type,
    if: 
      !>[TA: $tType] : ( $o > TA > TA > TA ) ).

thf(ord_less_decl,type,
    ord_less: 
      !>[TA: $tType] : ( TA > TA > $o ) ).

thf(ord_less_eq_decl,type,
    ord_less_eq: 
      !>[TA: $tType] : ( TA > TA > $o ) ).

thf(type2_decl,type,
    type2: 
      !>[TA: $tType] : ( itself @ TA ) ).

thf(collect_decl,type,
    collect: 
      !>[TA: $tType] : ( ( TA > $o ) > ( set @ TA ) ) ).

thf(member_decl,type,
    member: 
      !>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).

thf(a2_decl,type,
    a2: a ).

thf(b_decl,type,
    b: a ).

thf(t_decl,type,
    t: huffma16452318e_tree @ a ).

thf(sk1_decl,type,
    sk1: 
      !>[TA: $tType] : ( ( TA > $o ) > ( TA > $o ) > TA ) ).

thf(sk2_decl,type,
    sk2: 
      !>[TA: $tType,TB: $tType] : ( TB > TB > ( TB > TA ) > TA > TB ) ).

thf(sk3_decl,type,
    sk3: 
      !>[TA: $tType,TB: $tType] : ( TB > TB > ( TB > TA ) > TA > TB ) ).

thf(sk4_decl,type,
    sk4: 
      !>[TA: $tType] : ( TA > TA ) ).

thf(sk5_decl,type,
    sk5: 
      !>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( TB > TA ) > TB ) ).

thf(sk1_def,definition,
    ( sk1
    = ( ^ [TA: $tType,A: TA > $o,B: TA > $o] :
        @+[C: TA] :
          ( ( B @ C )
         != ( A @ C ) ) ) ) ).

thf(sk2_def,definition,
    ( sk2
    = ( ^ [TA: $tType,TB: $tType,A: TB,B: TB,C: TB > TA,D: TA] :
        @+[E: TB] :
          ~ ! [F: TB] :
              ( ( ord_less_eq @ TB @ E @ F )
             => ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) ) ) ) ).

thf(sk3_def,definition,
    ( sk3
    = ( ^ [TA: $tType,TB: $tType,A: TB,B: TB,C: TB > TA,D: TA] :
        @+[E: TB] :
          ~ ( ( ord_less_eq @ TB @ ( sk2 @ TB @ TA @ A @ B @ C @ D ) @ E )
           => ( ord_less_eq @ TA @ ( C @ ( sk2 @ TB @ TA @ A @ B @ C @ D ) ) @ ( C @ E ) ) ) ) ) ).

thf(sk4_def,definition,
    ( sk4
    = ( ^ [TA: $tType,A: TA] :
        @+[B: TA] : ( ord_less @ TA @ B @ A ) ) ) ).

thf(sk5_def,definition,
    ( sk5
    = ( ^ [TA: $tType,TB: $tType,A: TB > TA,B: TB > TA] :
        @+[C: TB] :
          ~ ( ord_less_eq @ TA @ ( B @ C ) @ ( A @ C ) ) ) ) ).

thf(188,axiom,
    semigroup_mult @ nat @ ( type2 @ nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Osemigroup__mult) ).

thf(809,plain,
    semigroup_mult @ nat @ ( type2 @ nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(266,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq @ nat @ A @ B )
     => ( ord_less_eq @ nat @ ( times_times @ nat @ C @ A ) @ ( times_times @ nat @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_mult__le__mono2) ).

thf(1024,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq @ nat @ A @ B )
     => ( ord_less_eq @ nat @ ( times_times @ nat @ C @ A ) @ ( times_times @ nat @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(169,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq @ nat @ A @ B )
     => ( ord_less_eq @ nat @ A @ ( plus_plus @ nat @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_trans__le__add2) ).

thf(760,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq @ nat @ A @ B )
     => ( ord_less_eq @ nat @ A @ ( plus_plus @ nat @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(22,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ~ ( ord_less_eq @ TA @ A @ B )
         => ( ord_less_eq @ TA @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_le__cases) ).

thf(347,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ~ ( ord_less_eq @ TA @ A @ B )
         => ( ord_less_eq @ TA @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(204,axiom,
    ! [TA: $tType] :
      ( ( linordered_ring @ TA @ ( type2 @ TA ) )
     => ! [A: TA] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( times_times @ TA @ A @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_zero__le__square) ).

thf(846,plain,
    ! [TA: $tType] :
      ( ( linordered_ring @ TA @ ( type2 @ TA ) )
     => ! [A: TA] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( times_times @ TA @ A @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(24,axiom,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ TA ) )
     => ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_dual__order_Orefl) ).

thf(351,plain,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ TA ) )
     => ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(352,plain,
    ! [TA: $tType,A: TA] :
      ( ~ ( order @ TA @ ( type2 @ TA ) )
      | ( ord_less_eq @ TA @ A @ A ) ),
    inference(cnf,[status(esa)],[351]) ).

thf(64,axiom,
    ! [TA: $tType] :
      ( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
          = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_semiring__normalization__rules_I5_J) ).

thf(479,plain,
    ! [TA: $tType] :
      ( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
          = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(1,conjecture,
    ( ( plus_plus @ nat @ ( huffma636208924e_cost @ a @ ( huffma469337550apSyms @ a @ t @ a2 @ b ) ) @ ( plus_plus @ nat @ ( times_times @ nat @ ( huffma854352999e_freq @ a @ t @ a2 ) @ ( huffma223349076_depth @ a @ t @ a2 ) ) @ ( times_times @ nat @ ( huffma854352999e_freq @ a @ t @ b ) @ ( huffma223349076_depth @ a @ t @ b ) ) ) )
    = ( plus_plus @ nat @ ( huffma636208924e_cost @ a @ t ) @ ( plus_plus @ nat @ ( times_times @ nat @ ( huffma854352999e_freq @ a @ t @ a2 ) @ ( huffma223349076_depth @ a @ t @ b ) ) @ ( times_times @ nat @ ( huffma854352999e_freq @ a @ t @ b ) @ ( huffma223349076_depth @ a @ t @ a2 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

thf(2,negated_conjecture,
    ( ( plus_plus @ nat @ ( huffma636208924e_cost @ a @ ( huffma469337550apSyms @ a @ t @ a2 @ b ) ) @ ( plus_plus @ nat @ ( times_times @ nat @ ( huffma854352999e_freq @ a @ t @ a2 ) @ ( huffma223349076_depth @ a @ t @ a2 ) ) @ ( times_times @ nat @ ( huffma854352999e_freq @ a @ t @ b ) @ ( huffma223349076_depth @ a @ t @ b ) ) ) )
   != ( plus_plus @ nat @ ( huffma636208924e_cost @ a @ t ) @ ( plus_plus @ nat @ ( times_times @ nat @ ( huffma854352999e_freq @ a @ t @ a2 ) @ ( huffma223349076_depth @ a @ t @ b ) ) @ ( times_times @ nat @ ( huffma854352999e_freq @ a @ t @ b ) @ ( huffma223349076_depth @ a @ t @ a2 ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(297,plain,
    ( ( plus_plus @ nat @ ( huffma636208924e_cost @ a @ ( huffma469337550apSyms @ a @ t @ a2 @ b ) ) @ ( plus_plus @ nat @ ( times_times @ nat @ ( huffma854352999e_freq @ a @ t @ a2 ) @ ( huffma223349076_depth @ a @ t @ a2 ) ) @ ( times_times @ nat @ ( huffma854352999e_freq @ a @ t @ b ) @ ( huffma223349076_depth @ a @ t @ b ) ) ) )
   != ( plus_plus @ nat @ ( huffma636208924e_cost @ a @ t ) @ ( plus_plus @ nat @ ( times_times @ nat @ ( huffma854352999e_freq @ a @ t @ a2 ) @ ( huffma223349076_depth @ a @ t @ b ) ) @ ( times_times @ nat @ ( huffma854352999e_freq @ a @ t @ b ) @ ( huffma223349076_depth @ a @ t @ a2 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(298,plain,
    ( ( plus_plus @ nat @ ( huffma636208924e_cost @ a @ ( huffma469337550apSyms @ a @ t @ a2 @ b ) ) @ ( plus_plus @ nat @ ( times_times @ nat @ ( huffma854352999e_freq @ a @ t @ a2 ) @ ( huffma223349076_depth @ a @ t @ a2 ) ) @ ( times_times @ nat @ ( huffma854352999e_freq @ a @ t @ b ) @ ( huffma223349076_depth @ a @ t @ b ) ) ) )
   != ( plus_plus @ nat @ ( huffma636208924e_cost @ a @ t ) @ ( plus_plus @ nat @ ( times_times @ nat @ ( huffma854352999e_freq @ a @ t @ a2 ) @ ( huffma223349076_depth @ a @ t @ b ) ) @ ( times_times @ nat @ ( huffma854352999e_freq @ a @ t @ b ) @ ( huffma223349076_depth @ a @ t @ a2 ) ) ) ) ),
    inference(lifteq,[status(thm)],[297]) ).

thf(1102,plain,
    ( ( ( huffma636208924e_cost @ a @ ( huffma469337550apSyms @ a @ t @ a2 @ b ) )
     != ( huffma636208924e_cost @ a @ t ) )
    | ( ( plus_plus @ nat @ ( times_times @ nat @ ( huffma854352999e_freq @ a @ t @ a2 ) @ ( huffma223349076_depth @ a @ t @ a2 ) ) @ ( times_times @ nat @ ( huffma854352999e_freq @ a @ t @ b ) @ ( huffma223349076_depth @ a @ t @ b ) ) )
     != ( plus_plus @ nat @ ( times_times @ nat @ ( huffma854352999e_freq @ a @ t @ a2 ) @ ( huffma223349076_depth @ a @ t @ b ) ) @ ( times_times @ nat @ ( huffma854352999e_freq @ a @ t @ b ) @ ( huffma223349076_depth @ a @ t @ a2 ) ) ) ) ),
    inference(simp,[status(thm)],[298]) ).

thf(1105,plain,
    ( ( ( huffma469337550apSyms @ a @ t @ a2 @ b )
     != t )
    | ( ( times_times @ nat @ ( huffma854352999e_freq @ a @ t @ a2 ) @ ( huffma223349076_depth @ a @ t @ b ) )
     != ( times_times @ nat @ ( huffma854352999e_freq @ a @ t @ a2 ) @ ( huffma223349076_depth @ a @ t @ a2 ) ) )
    | ( ( times_times @ nat @ ( huffma854352999e_freq @ a @ t @ b ) @ ( huffma223349076_depth @ a @ t @ b ) )
     != ( times_times @ nat @ ( huffma854352999e_freq @ a @ t @ b ) @ ( huffma223349076_depth @ a @ t @ a2 ) ) ) ),
    inference(simp,[status(thm)],[1102]) ).

thf(228,axiom,
    ! [TA: $tType] :
      ( ( ordere1490568538miring @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ C )
           => ( ord_less_eq @ TA @ ( times_times @ TA @ C @ A ) @ ( times_times @ TA @ C @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_ordered__comm__semiring__class_Ocomm__mult__left__mono) ).

thf(909,plain,
    ! [TA: $tType] :
      ( ( ordere1490568538miring @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ C )
           => ( ord_less_eq @ TA @ ( times_times @ TA @ C @ A ) @ ( times_times @ TA @ C @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(17,axiom,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ord_less_eq @ TA @ B @ A )
            = ( B = A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_antisym__conv) ).

thf(333,plain,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ord_less_eq @ TA @ B @ A )
            = ( B = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(96,axiom,
    preorder @ nat @ ( type2 @ nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Opreorder_1) ).

thf(567,plain,
    preorder @ nat @ ( type2 @ nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(11,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( preorder @ TA @ ( type2 @ TA ) )
     => ( preorder @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Opreorder) ).

thf(319,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( preorder @ TA @ ( type2 @ TA ) )
     => ( preorder @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(320,plain,
    ! [TA: $tType,TB: $tType] :
      ( ~ ( preorder @ TB @ ( type2 @ TB ) )
      | ( preorder @ ( TA > TB ) @ ( type2 @ ( TA > TB ) ) ) ),
    inference(cnf,[status(esa)],[319]) ).

thf(2888,plain,
    ! [TA: $tType,TB: $tType] :
      ( ~ $true
      | ( preorder @ ( TA > TB ) @ ( type2 @ ( TA > TB ) ) )
      | ( ( preorder @ nat @ ( type2 @ nat ) )
       != ( preorder @ TB @ ( type2 @ TB ) ) ) ),
    inference(paramod_ordered,[status(thm)],[567,320]) ).

thf(2889,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( preorder @ ( TA > TB ) @ ( type2 @ ( TA > TB ) ) )
      | ( ( preorder @ nat @ ( type2 @ nat ) )
       != ( preorder @ TB @ ( type2 @ TB ) ) ) ),
    inference(simp,[status(thm)],[2888]) ).

thf(2890,plain,
    ! [TA: $tType] : ( preorder @ ( TA > nat ) @ ( type2 @ ( TA > nat ) ) ),
    inference(pattern_uni,[status(thm)],[2889:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( nat ))]]) ).

thf(2954,plain,
    ! [TA: $tType,TB: $tType,TC: $tType] :
      ( ~ $true
      | ( preorder @ ( TB > TC ) @ ( type2 @ ( TB > TC ) ) )
      | ( ( preorder @ ( TA > nat ) @ ( type2 @ ( TA > nat ) ) )
       != ( preorder @ TC @ ( type2 @ TC ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2890,320]) ).

thf(2955,plain,
    ! [TA: $tType,TB: $tType,TC: $tType] :
      ( ( preorder @ ( TB > TC ) @ ( type2 @ ( TB > TC ) ) )
      | ( ( preorder @ ( TA > nat ) @ ( type2 @ ( TA > nat ) ) )
       != ( preorder @ TC @ ( type2 @ TC ) ) ) ),
    inference(simp,[status(thm)],[2954]) ).

thf(2956,plain,
    ! [TA: $tType,TB: $tType] : ( preorder @ ( TB > TA > nat ) @ ( type2 @ ( TB > TA > nat ) ) ),
    inference(pattern_uni,[status(thm)],[2955:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TA > nat ))]]) ).

thf(3086,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] :
      ( ~ $true
      | ( preorder @ ( TC > TD ) @ ( type2 @ ( TC > TD ) ) )
      | ( ( preorder @ ( TB > TA > nat ) @ ( type2 @ ( TB > TA > nat ) ) )
       != ( preorder @ TD @ ( type2 @ TD ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2956,320]) ).

thf(3087,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] :
      ( ( preorder @ ( TC > TD ) @ ( type2 @ ( TC > TD ) ) )
      | ( ( preorder @ ( TB > TA > nat ) @ ( type2 @ ( TB > TA > nat ) ) )
       != ( preorder @ TD @ ( type2 @ TD ) ) ) ),
    inference(simp,[status(thm)],[3086]) ).

thf(3088,plain,
    ! [TA: $tType,TB: $tType,TC: $tType] : ( preorder @ ( TC > TB > TA > nat ) @ ( type2 @ ( TC > TB > TA > nat ) ) ),
    inference(pattern_uni,[status(thm)],[3087:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TB > TA > nat ))]]) ).

thf(3152,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType] :
      ( ~ $true
      | ( preorder @ ( TD > TE ) @ ( type2 @ ( TD > TE ) ) )
      | ( ( preorder @ ( TC > TB > TA > nat ) @ ( type2 @ ( TC > TB > TA > nat ) ) )
       != ( preorder @ TE @ ( type2 @ TE ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3088,320]) ).

thf(3153,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType] :
      ( ( preorder @ ( TD > TE ) @ ( type2 @ ( TD > TE ) ) )
      | ( ( preorder @ ( TC > TB > TA > nat ) @ ( type2 @ ( TC > TB > TA > nat ) ) )
       != ( preorder @ TE @ ( type2 @ TE ) ) ) ),
    inference(simp,[status(thm)],[3152]) ).

thf(3154,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] : ( preorder @ ( TD > TC > TB > TA > nat ) @ ( type2 @ ( TD > TC > TB > TA > nat ) ) ),
    inference(pattern_uni,[status(thm)],[3153:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TC > TB > TA > nat ))]]) ).

thf(3256,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType] :
      ( ~ $true
      | ( preorder @ ( TE > TF ) @ ( type2 @ ( TE > TF ) ) )
      | ( ( preorder @ ( TD > TC > TB > TA > nat ) @ ( type2 @ ( TD > TC > TB > TA > nat ) ) )
       != ( preorder @ TF @ ( type2 @ TF ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3154,320]) ).

thf(3257,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType] :
      ( ( preorder @ ( TE > TF ) @ ( type2 @ ( TE > TF ) ) )
      | ( ( preorder @ ( TD > TC > TB > TA > nat ) @ ( type2 @ ( TD > TC > TB > TA > nat ) ) )
       != ( preorder @ TF @ ( type2 @ TF ) ) ) ),
    inference(simp,[status(thm)],[3256]) ).

thf(3258,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType] : ( preorder @ ( TE > TD > TC > TB > TA > nat ) @ ( type2 @ ( TE > TD > TC > TB > TA > nat ) ) ),
    inference(pattern_uni,[status(thm)],[3257:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TD > TC > TB > TA > nat ))]]) ).

thf(3347,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType] :
      ( ~ $true
      | ( preorder @ ( TF > TG ) @ ( type2 @ ( TF > TG ) ) )
      | ( ( preorder @ ( TE > TD > TC > TB > TA > nat ) @ ( type2 @ ( TE > TD > TC > TB > TA > nat ) ) )
       != ( preorder @ TG @ ( type2 @ TG ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3258,320]) ).

thf(3348,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType] :
      ( ( preorder @ ( TF > TG ) @ ( type2 @ ( TF > TG ) ) )
      | ( ( preorder @ ( TE > TD > TC > TB > TA > nat ) @ ( type2 @ ( TE > TD > TC > TB > TA > nat ) ) )
       != ( preorder @ TG @ ( type2 @ TG ) ) ) ),
    inference(simp,[status(thm)],[3347]) ).

thf(3349,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType] : ( preorder @ ( TF > TE > TD > TC > TB > TA > nat ) @ ( type2 @ ( TF > TE > TD > TC > TB > TA > nat ) ) ),
    inference(pattern_uni,[status(thm)],[3348:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TE > TD > TC > TB > TA > nat ))]]) ).

thf(5345,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType] :
      ( ~ $true
      | ( preorder @ ( TG > TH ) @ ( type2 @ ( TG > TH ) ) )
      | ( ( preorder @ ( TF > TE > TD > TC > TB > TA > nat ) @ ( type2 @ ( TF > TE > TD > TC > TB > TA > nat ) ) )
       != ( preorder @ TH @ ( type2 @ TH ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3349,320]) ).

thf(5346,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType] :
      ( ( preorder @ ( TG > TH ) @ ( type2 @ ( TG > TH ) ) )
      | ( ( preorder @ ( TF > TE > TD > TC > TB > TA > nat ) @ ( type2 @ ( TF > TE > TD > TC > TB > TA > nat ) ) )
       != ( preorder @ TH @ ( type2 @ TH ) ) ) ),
    inference(simp,[status(thm)],[5345]) ).

thf(5347,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType] : ( preorder @ ( TG > TF > TE > TD > TC > TB > TA > nat ) @ ( type2 @ ( TG > TF > TE > TD > TC > TB > TA > nat ) ) ),
    inference(pattern_uni,[status(thm)],[5346:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TF > TE > TD > TC > TB > TA > nat ))]]) ).

thf(5740,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType] :
      ( ~ $true
      | ( preorder @ ( TH > TI ) @ ( type2 @ ( TH > TI ) ) )
      | ( ( preorder @ ( TG > TF > TE > TD > TC > TB > TA > nat ) @ ( type2 @ ( TG > TF > TE > TD > TC > TB > TA > nat ) ) )
       != ( preorder @ TI @ ( type2 @ TI ) ) ) ),
    inference(paramod_ordered,[status(thm)],[5347,320]) ).

thf(5741,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType] :
      ( ( preorder @ ( TH > TI ) @ ( type2 @ ( TH > TI ) ) )
      | ( ( preorder @ ( TG > TF > TE > TD > TC > TB > TA > nat ) @ ( type2 @ ( TG > TF > TE > TD > TC > TB > TA > nat ) ) )
       != ( preorder @ TI @ ( type2 @ TI ) ) ) ),
    inference(simp,[status(thm)],[5740]) ).

thf(5742,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType] : ( preorder @ ( TH > TG > TF > TE > TD > TC > TB > TA > nat ) @ ( type2 @ ( TH > TG > TF > TE > TD > TC > TB > TA > nat ) ) ),
    inference(pattern_uni,[status(thm)],[5741:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TG > TF > TE > TD > TC > TB > TA > nat ))]]) ).

thf(5830,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType] :
      ( ~ $true
      | ( preorder @ ( TI > TJ ) @ ( type2 @ ( TI > TJ ) ) )
      | ( ( preorder @ ( TH > TG > TF > TE > TD > TC > TB > TA > nat ) @ ( type2 @ ( TH > TG > TF > TE > TD > TC > TB > TA > nat ) ) )
       != ( preorder @ TJ @ ( type2 @ TJ ) ) ) ),
    inference(paramod_ordered,[status(thm)],[5742,320]) ).

thf(5831,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType] :
      ( ( preorder @ ( TI > TJ ) @ ( type2 @ ( TI > TJ ) ) )
      | ( ( preorder @ ( TH > TG > TF > TE > TD > TC > TB > TA > nat ) @ ( type2 @ ( TH > TG > TF > TE > TD > TC > TB > TA > nat ) ) )
       != ( preorder @ TJ @ ( type2 @ TJ ) ) ) ),
    inference(simp,[status(thm)],[5830]) ).

thf(5832,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType] : ( preorder @ ( TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) @ ( type2 @ ( TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ) ),
    inference(pattern_uni,[status(thm)],[5831:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TH > TG > TF > TE > TD > TC > TB > TA > nat ))]]) ).

thf(6021,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType] :
      ( ~ $true
      | ( preorder @ ( TJ > TK ) @ ( type2 @ ( TJ > TK ) ) )
      | ( ( preorder @ ( TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) @ ( type2 @ ( TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ) )
       != ( preorder @ TK @ ( type2 @ TK ) ) ) ),
    inference(paramod_ordered,[status(thm)],[5832,320]) ).

thf(6022,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType] :
      ( ( preorder @ ( TJ > TK ) @ ( type2 @ ( TJ > TK ) ) )
      | ( ( preorder @ ( TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) @ ( type2 @ ( TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ) )
       != ( preorder @ TK @ ( type2 @ TK ) ) ) ),
    inference(simp,[status(thm)],[6021]) ).

thf(6023,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType] : ( preorder @ ( TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) @ ( type2 @ ( TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ) ),
    inference(pattern_uni,[status(thm)],[6022:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ))]]) ).

thf(6193,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType] :
      ( ~ $true
      | ( preorder @ ( TK > TL ) @ ( type2 @ ( TK > TL ) ) )
      | ( ( preorder @ ( TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) @ ( type2 @ ( TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ) )
       != ( preorder @ TL @ ( type2 @ TL ) ) ) ),
    inference(paramod_ordered,[status(thm)],[6023,320]) ).

thf(6194,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType] :
      ( ( preorder @ ( TK > TL ) @ ( type2 @ ( TK > TL ) ) )
      | ( ( preorder @ ( TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) @ ( type2 @ ( TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ) )
       != ( preorder @ TL @ ( type2 @ TL ) ) ) ),
    inference(simp,[status(thm)],[6193]) ).

thf(6195,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType] : ( preorder @ ( TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) @ ( type2 @ ( TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ) ),
    inference(pattern_uni,[status(thm)],[6194:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ))]]) ).

thf(6408,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType] :
      ( ~ $true
      | ( preorder @ ( TL > TM ) @ ( type2 @ ( TL > TM ) ) )
      | ( ( preorder @ ( TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) @ ( type2 @ ( TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ) )
       != ( preorder @ TM @ ( type2 @ TM ) ) ) ),
    inference(paramod_ordered,[status(thm)],[6195,320]) ).

thf(6409,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType] :
      ( ( preorder @ ( TL > TM ) @ ( type2 @ ( TL > TM ) ) )
      | ( ( preorder @ ( TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) @ ( type2 @ ( TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ) )
       != ( preorder @ TM @ ( type2 @ TM ) ) ) ),
    inference(simp,[status(thm)],[6408]) ).

thf(6410,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType] : ( preorder @ ( TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) @ ( type2 @ ( TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ) ),
    inference(pattern_uni,[status(thm)],[6409:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ))]]) ).

thf(6772,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType] :
      ( ~ $true
      | ( preorder @ ( TM > TN ) @ ( type2 @ ( TM > TN ) ) )
      | ( ( preorder @ ( TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) @ ( type2 @ ( TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ) )
       != ( preorder @ TN @ ( type2 @ TN ) ) ) ),
    inference(paramod_ordered,[status(thm)],[6410,320]) ).

thf(6773,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType] :
      ( ( preorder @ ( TM > TN ) @ ( type2 @ ( TM > TN ) ) )
      | ( ( preorder @ ( TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) @ ( type2 @ ( TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ) )
       != ( preorder @ TN @ ( type2 @ TN ) ) ) ),
    inference(simp,[status(thm)],[6772]) ).

thf(6774,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType] : ( preorder @ ( TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) @ ( type2 @ ( TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ) ),
    inference(pattern_uni,[status(thm)],[6773:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ))]]) ).

thf(6871,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType] :
      ( ~ $true
      | ( preorder @ ( TN > TO ) @ ( type2 @ ( TN > TO ) ) )
      | ( ( preorder @ ( TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) @ ( type2 @ ( TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ) )
       != ( preorder @ TO @ ( type2 @ TO ) ) ) ),
    inference(paramod_ordered,[status(thm)],[6774,320]) ).

thf(6872,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType] :
      ( ( preorder @ ( TN > TO ) @ ( type2 @ ( TN > TO ) ) )
      | ( ( preorder @ ( TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) @ ( type2 @ ( TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ) )
       != ( preorder @ TO @ ( type2 @ TO ) ) ) ),
    inference(simp,[status(thm)],[6871]) ).

thf(6873,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType] : ( preorder @ ( TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) @ ( type2 @ ( TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ) ),
    inference(pattern_uni,[status(thm)],[6872:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ))]]) ).

thf(7197,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType] :
      ( ~ $true
      | ( preorder @ ( TO > TP ) @ ( type2 @ ( TO > TP ) ) )
      | ( ( preorder @ ( TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) @ ( type2 @ ( TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ) )
       != ( preorder @ TP @ ( type2 @ TP ) ) ) ),
    inference(paramod_ordered,[status(thm)],[6873,320]) ).

thf(7198,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType] :
      ( ( preorder @ ( TO > TP ) @ ( type2 @ ( TO > TP ) ) )
      | ( ( preorder @ ( TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) @ ( type2 @ ( TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ) )
       != ( preorder @ TP @ ( type2 @ TP ) ) ) ),
    inference(simp,[status(thm)],[7197]) ).

thf(7199,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType] : ( preorder @ ( TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) @ ( type2 @ ( TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ) ),
    inference(pattern_uni,[status(thm)],[7198:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ))]]) ).

thf(7355,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType] :
      ( ~ $true
      | ( preorder @ ( TP > TQ ) @ ( type2 @ ( TP > TQ ) ) )
      | ( ( preorder @ ( TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) @ ( type2 @ ( TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ) )
       != ( preorder @ TQ @ ( type2 @ TQ ) ) ) ),
    inference(paramod_ordered,[status(thm)],[7199,320]) ).

thf(7356,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType] :
      ( ( preorder @ ( TP > TQ ) @ ( type2 @ ( TP > TQ ) ) )
      | ( ( preorder @ ( TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) @ ( type2 @ ( TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ) )
       != ( preorder @ TQ @ ( type2 @ TQ ) ) ) ),
    inference(simp,[status(thm)],[7355]) ).

thf(7357,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType] : ( preorder @ ( TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) @ ( type2 @ ( TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ) ),
    inference(pattern_uni,[status(thm)],[7356:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ))]]) ).

thf(8337,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType] :
      ( ~ $true
      | ( preorder @ ( TQ > TR ) @ ( type2 @ ( TQ > TR ) ) )
      | ( ( preorder @ ( TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) @ ( type2 @ ( TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ) )
       != ( preorder @ TR @ ( type2 @ TR ) ) ) ),
    inference(paramod_ordered,[status(thm)],[7357,320]) ).

thf(8338,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType] :
      ( ( preorder @ ( TQ > TR ) @ ( type2 @ ( TQ > TR ) ) )
      | ( ( preorder @ ( TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) @ ( type2 @ ( TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ) )
       != ( preorder @ TR @ ( type2 @ TR ) ) ) ),
    inference(simp,[status(thm)],[8337]) ).

thf(8339,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType] : ( preorder @ ( TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) @ ( type2 @ ( TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ) ),
    inference(pattern_uni,[status(thm)],[8338:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ))]]) ).

thf(8782,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType] :
      ( ~ $true
      | ( preorder @ ( TR > TS ) @ ( type2 @ ( TR > TS ) ) )
      | ( ( preorder @ ( TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) @ ( type2 @ ( TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ) )
       != ( preorder @ TS @ ( type2 @ TS ) ) ) ),
    inference(paramod_ordered,[status(thm)],[8339,320]) ).

thf(8783,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType] :
      ( ( preorder @ ( TR > TS ) @ ( type2 @ ( TR > TS ) ) )
      | ( ( preorder @ ( TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) @ ( type2 @ ( TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ) )
       != ( preorder @ TS @ ( type2 @ TS ) ) ) ),
    inference(simp,[status(thm)],[8782]) ).

thf(8784,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType] : ( preorder @ ( TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) @ ( type2 @ ( TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ) ),
    inference(pattern_uni,[status(thm)],[8783:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ))]]) ).

thf(79,axiom,
    ! [TA: $tType] :
      ( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ C )
          = ( times_times @ TA @ ( times_times @ TA @ A @ C ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_semiring__normalization__rules_I16_J) ).

thf(518,plain,
    ! [TA: $tType] :
      ( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ C )
          = ( times_times @ TA @ ( times_times @ TA @ A @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(290,axiom,
    ( ( ord_less_eq @ nat )
    = ( ^ [A: nat,B: nat] :
        ? [C: nat] :
          ( B
          = ( plus_plus @ nat @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_nat__le__iff__add) ).

thf(1082,plain,
    ( ( ord_less_eq @ nat )
    = ( ^ [A: nat,B: nat] :
        ? [C: nat] :
          ( B
          = ( plus_plus @ nat @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(1083,plain,
    ( ( ord_less_eq @ nat )
    = ( ^ [A: nat,B: nat] :
        ? [C: nat] :
          ( B
          = ( plus_plus @ nat @ A @ C ) ) ) ),
    inference(lifteq,[status(thm)],[1082]) ).

thf(61,axiom,
    ! [TA: $tType] : ( order @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oorder_5) ).

thf(468,plain,
    ! [TA: $tType] : ( order @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(15,axiom,
    preorder @ $o @ ( type2 @ $o ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Opreorder_7) ).

thf(329,plain,
    preorder @ $o @ ( type2 @ $o ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(2885,plain,
    ! [TA: $tType,TB: $tType] :
      ( ~ $true
      | ( preorder @ ( TA > TB ) @ ( type2 @ ( TA > TB ) ) )
      | ( ( preorder @ $o @ ( type2 @ $o ) )
       != ( preorder @ TB @ ( type2 @ TB ) ) ) ),
    inference(paramod_ordered,[status(thm)],[329,320]) ).

thf(2886,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( preorder @ ( TA > TB ) @ ( type2 @ ( TA > TB ) ) )
      | ( ( preorder @ $o @ ( type2 @ $o ) )
       != ( preorder @ TB @ ( type2 @ TB ) ) ) ),
    inference(simp,[status(thm)],[2885]) ).

thf(2887,plain,
    ! [TA: $tType] : ( preorder @ ( TA > $o ) @ ( type2 @ ( TA > $o ) ) ),
    inference(pattern_uni,[status(thm)],[2886:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( $o ))]]) ).

thf(2932,plain,
    ! [TA: $tType,TB: $tType,TC: $tType] :
      ( ~ $true
      | ( preorder @ ( TB > TC ) @ ( type2 @ ( TB > TC ) ) )
      | ( ( preorder @ ( TA > $o ) @ ( type2 @ ( TA > $o ) ) )
       != ( preorder @ TC @ ( type2 @ TC ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2887,320]) ).

thf(2933,plain,
    ! [TA: $tType,TB: $tType,TC: $tType] :
      ( ( preorder @ ( TB > TC ) @ ( type2 @ ( TB > TC ) ) )
      | ( ( preorder @ ( TA > $o ) @ ( type2 @ ( TA > $o ) ) )
       != ( preorder @ TC @ ( type2 @ TC ) ) ) ),
    inference(simp,[status(thm)],[2932]) ).

thf(2934,plain,
    ! [TA: $tType,TB: $tType] : ( preorder @ ( TB > TA > $o ) @ ( type2 @ ( TB > TA > $o ) ) ),
    inference(pattern_uni,[status(thm)],[2933:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TA > $o ))]]) ).

thf(3024,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] :
      ( ~ $true
      | ( preorder @ ( TC > TD ) @ ( type2 @ ( TC > TD ) ) )
      | ( ( preorder @ ( TB > TA > $o ) @ ( type2 @ ( TB > TA > $o ) ) )
       != ( preorder @ TD @ ( type2 @ TD ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2934,320]) ).

thf(3025,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] :
      ( ( preorder @ ( TC > TD ) @ ( type2 @ ( TC > TD ) ) )
      | ( ( preorder @ ( TB > TA > $o ) @ ( type2 @ ( TB > TA > $o ) ) )
       != ( preorder @ TD @ ( type2 @ TD ) ) ) ),
    inference(simp,[status(thm)],[3024]) ).

thf(3026,plain,
    ! [TA: $tType,TB: $tType,TC: $tType] : ( preorder @ ( TC > TB > TA > $o ) @ ( type2 @ ( TC > TB > TA > $o ) ) ),
    inference(pattern_uni,[status(thm)],[3025:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TB > TA > $o ))]]) ).

thf(3130,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType] :
      ( ~ $true
      | ( preorder @ ( TD > TE ) @ ( type2 @ ( TD > TE ) ) )
      | ( ( preorder @ ( TC > TB > TA > $o ) @ ( type2 @ ( TC > TB > TA > $o ) ) )
       != ( preorder @ TE @ ( type2 @ TE ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3026,320]) ).

thf(3131,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType] :
      ( ( preorder @ ( TD > TE ) @ ( type2 @ ( TD > TE ) ) )
      | ( ( preorder @ ( TC > TB > TA > $o ) @ ( type2 @ ( TC > TB > TA > $o ) ) )
       != ( preorder @ TE @ ( type2 @ TE ) ) ) ),
    inference(simp,[status(thm)],[3130]) ).

thf(3132,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] : ( preorder @ ( TD > TC > TB > TA > $o ) @ ( type2 @ ( TD > TC > TB > TA > $o ) ) ),
    inference(pattern_uni,[status(thm)],[3131:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TC > TB > TA > $o ))]]) ).

thf(3234,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType] :
      ( ~ $true
      | ( preorder @ ( TE > TF ) @ ( type2 @ ( TE > TF ) ) )
      | ( ( preorder @ ( TD > TC > TB > TA > $o ) @ ( type2 @ ( TD > TC > TB > TA > $o ) ) )
       != ( preorder @ TF @ ( type2 @ TF ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3132,320]) ).

thf(3235,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType] :
      ( ( preorder @ ( TE > TF ) @ ( type2 @ ( TE > TF ) ) )
      | ( ( preorder @ ( TD > TC > TB > TA > $o ) @ ( type2 @ ( TD > TC > TB > TA > $o ) ) )
       != ( preorder @ TF @ ( type2 @ TF ) ) ) ),
    inference(simp,[status(thm)],[3234]) ).

thf(3236,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType] : ( preorder @ ( TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TE > TD > TC > TB > TA > $o ) ) ),
    inference(pattern_uni,[status(thm)],[3235:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TD > TC > TB > TA > $o ))]]) ).

thf(3300,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType] :
      ( ~ $true
      | ( preorder @ ( TF > TG ) @ ( type2 @ ( TF > TG ) ) )
      | ( ( preorder @ ( TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TE > TD > TC > TB > TA > $o ) ) )
       != ( preorder @ TG @ ( type2 @ TG ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3236,320]) ).

thf(3301,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType] :
      ( ( preorder @ ( TF > TG ) @ ( type2 @ ( TF > TG ) ) )
      | ( ( preorder @ ( TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TE > TD > TC > TB > TA > $o ) ) )
       != ( preorder @ TG @ ( type2 @ TG ) ) ) ),
    inference(simp,[status(thm)],[3300]) ).

thf(3302,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType] : ( preorder @ ( TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TF > TE > TD > TC > TB > TA > $o ) ) ),
    inference(pattern_uni,[status(thm)],[3301:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TE > TD > TC > TB > TA > $o ))]]) ).

thf(5315,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType] :
      ( ~ $true
      | ( preorder @ ( TG > TH ) @ ( type2 @ ( TG > TH ) ) )
      | ( ( preorder @ ( TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TF > TE > TD > TC > TB > TA > $o ) ) )
       != ( preorder @ TH @ ( type2 @ TH ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3302,320]) ).

thf(5316,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType] :
      ( ( preorder @ ( TG > TH ) @ ( type2 @ ( TG > TH ) ) )
      | ( ( preorder @ ( TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TF > TE > TD > TC > TB > TA > $o ) ) )
       != ( preorder @ TH @ ( type2 @ TH ) ) ) ),
    inference(simp,[status(thm)],[5315]) ).

thf(5317,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType] : ( preorder @ ( TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TG > TF > TE > TD > TC > TB > TA > $o ) ) ),
    inference(pattern_uni,[status(thm)],[5316:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TF > TE > TD > TC > TB > TA > $o ))]]) ).

thf(5475,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType] :
      ( ~ $true
      | ( preorder @ ( TH > TI ) @ ( type2 @ ( TH > TI ) ) )
      | ( ( preorder @ ( TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TG > TF > TE > TD > TC > TB > TA > $o ) ) )
       != ( preorder @ TI @ ( type2 @ TI ) ) ) ),
    inference(paramod_ordered,[status(thm)],[5317,320]) ).

thf(5476,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType] :
      ( ( preorder @ ( TH > TI ) @ ( type2 @ ( TH > TI ) ) )
      | ( ( preorder @ ( TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TG > TF > TE > TD > TC > TB > TA > $o ) ) )
       != ( preorder @ TI @ ( type2 @ TI ) ) ) ),
    inference(simp,[status(thm)],[5475]) ).

thf(5477,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType] : ( preorder @ ( TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) ),
    inference(pattern_uni,[status(thm)],[5476:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TG > TF > TE > TD > TC > TB > TA > $o ))]]) ).

thf(5800,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType] :
      ( ~ $true
      | ( preorder @ ( TI > TJ ) @ ( type2 @ ( TI > TJ ) ) )
      | ( ( preorder @ ( TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) )
       != ( preorder @ TJ @ ( type2 @ TJ ) ) ) ),
    inference(paramod_ordered,[status(thm)],[5477,320]) ).

thf(5801,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType] :
      ( ( preorder @ ( TI > TJ ) @ ( type2 @ ( TI > TJ ) ) )
      | ( ( preorder @ ( TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) )
       != ( preorder @ TJ @ ( type2 @ TJ ) ) ) ),
    inference(simp,[status(thm)],[5800]) ).

thf(5802,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType] : ( preorder @ ( TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) ),
    inference(pattern_uni,[status(thm)],[5801:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TH > TG > TF > TE > TD > TC > TB > TA > $o ))]]) ).

thf(5991,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType] :
      ( ~ $true
      | ( preorder @ ( TJ > TK ) @ ( type2 @ ( TJ > TK ) ) )
      | ( ( preorder @ ( TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) )
       != ( preorder @ TK @ ( type2 @ TK ) ) ) ),
    inference(paramod_ordered,[status(thm)],[5802,320]) ).

thf(5992,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType] :
      ( ( preorder @ ( TJ > TK ) @ ( type2 @ ( TJ > TK ) ) )
      | ( ( preorder @ ( TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) )
       != ( preorder @ TK @ ( type2 @ TK ) ) ) ),
    inference(simp,[status(thm)],[5991]) ).

thf(5993,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType] : ( preorder @ ( TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) ),
    inference(pattern_uni,[status(thm)],[5992:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ))]]) ).

thf(6081,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType] :
      ( ~ $true
      | ( preorder @ ( TK > TL ) @ ( type2 @ ( TK > TL ) ) )
      | ( ( preorder @ ( TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) )
       != ( preorder @ TL @ ( type2 @ TL ) ) ) ),
    inference(paramod_ordered,[status(thm)],[5993,320]) ).

thf(6082,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType] :
      ( ( preorder @ ( TK > TL ) @ ( type2 @ ( TK > TL ) ) )
      | ( ( preorder @ ( TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) )
       != ( preorder @ TL @ ( type2 @ TL ) ) ) ),
    inference(simp,[status(thm)],[6081]) ).

thf(6083,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType] : ( preorder @ ( TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) ),
    inference(pattern_uni,[status(thm)],[6082:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ))]]) ).

thf(6378,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType] :
      ( ~ $true
      | ( preorder @ ( TL > TM ) @ ( type2 @ ( TL > TM ) ) )
      | ( ( preorder @ ( TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) )
       != ( preorder @ TM @ ( type2 @ TM ) ) ) ),
    inference(paramod_ordered,[status(thm)],[6083,320]) ).

thf(6379,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType] :
      ( ( preorder @ ( TL > TM ) @ ( type2 @ ( TL > TM ) ) )
      | ( ( preorder @ ( TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) )
       != ( preorder @ TM @ ( type2 @ TM ) ) ) ),
    inference(simp,[status(thm)],[6378]) ).

thf(6380,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType] : ( preorder @ ( TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) ),
    inference(pattern_uni,[status(thm)],[6379:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ))]]) ).

thf(6537,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType] :
      ( ~ $true
      | ( preorder @ ( TM > TN ) @ ( type2 @ ( TM > TN ) ) )
      | ( ( preorder @ ( TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) )
       != ( preorder @ TN @ ( type2 @ TN ) ) ) ),
    inference(paramod_ordered,[status(thm)],[6380,320]) ).

thf(6538,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType] :
      ( ( preorder @ ( TM > TN ) @ ( type2 @ ( TM > TN ) ) )
      | ( ( preorder @ ( TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) )
       != ( preorder @ TN @ ( type2 @ TN ) ) ) ),
    inference(simp,[status(thm)],[6537]) ).

thf(6539,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType] : ( preorder @ ( TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) ),
    inference(pattern_uni,[status(thm)],[6538:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ))]]) ).

thf(6838,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType] :
      ( ~ $true
      | ( preorder @ ( TN > TO ) @ ( type2 @ ( TN > TO ) ) )
      | ( ( preorder @ ( TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) )
       != ( preorder @ TO @ ( type2 @ TO ) ) ) ),
    inference(paramod_ordered,[status(thm)],[6539,320]) ).

thf(6839,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType] :
      ( ( preorder @ ( TN > TO ) @ ( type2 @ ( TN > TO ) ) )
      | ( ( preorder @ ( TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) )
       != ( preorder @ TO @ ( type2 @ TO ) ) ) ),
    inference(simp,[status(thm)],[6838]) ).

thf(6840,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType] : ( preorder @ ( TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) ),
    inference(pattern_uni,[status(thm)],[6839:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ))]]) ).

thf(7164,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType] :
      ( ~ $true
      | ( preorder @ ( TO > TP ) @ ( type2 @ ( TO > TP ) ) )
      | ( ( preorder @ ( TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) )
       != ( preorder @ TP @ ( type2 @ TP ) ) ) ),
    inference(paramod_ordered,[status(thm)],[6840,320]) ).

thf(7165,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType] :
      ( ( preorder @ ( TO > TP ) @ ( type2 @ ( TO > TP ) ) )
      | ( ( preorder @ ( TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) )
       != ( preorder @ TP @ ( type2 @ TP ) ) ) ),
    inference(simp,[status(thm)],[7164]) ).

thf(7166,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType] : ( preorder @ ( TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) ),
    inference(pattern_uni,[status(thm)],[7165:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ))]]) ).

thf(7263,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType] :
      ( ~ $true
      | ( preorder @ ( TP > TQ ) @ ( type2 @ ( TP > TQ ) ) )
      | ( ( preorder @ ( TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) )
       != ( preorder @ TQ @ ( type2 @ TQ ) ) ) ),
    inference(paramod_ordered,[status(thm)],[7166,320]) ).

thf(7264,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType] :
      ( ( preorder @ ( TP > TQ ) @ ( type2 @ ( TP > TQ ) ) )
      | ( ( preorder @ ( TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) )
       != ( preorder @ TQ @ ( type2 @ TQ ) ) ) ),
    inference(simp,[status(thm)],[7263]) ).

thf(7265,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType] : ( preorder @ ( TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) ),
    inference(pattern_uni,[status(thm)],[7264:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ))]]) ).

thf(8298,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType] :
      ( ~ $true
      | ( preorder @ ( TQ > TR ) @ ( type2 @ ( TQ > TR ) ) )
      | ( ( preorder @ ( TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) )
       != ( preorder @ TR @ ( type2 @ TR ) ) ) ),
    inference(paramod_ordered,[status(thm)],[7265,320]) ).

thf(8299,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType] :
      ( ( preorder @ ( TQ > TR ) @ ( type2 @ ( TQ > TR ) ) )
      | ( ( preorder @ ( TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) )
       != ( preorder @ TR @ ( type2 @ TR ) ) ) ),
    inference(simp,[status(thm)],[8298]) ).

thf(8300,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType] : ( preorder @ ( TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) ),
    inference(pattern_uni,[status(thm)],[8299:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ))]]) ).

thf(8487,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType] :
      ( ~ $true
      | ( preorder @ ( TR > TS ) @ ( type2 @ ( TR > TS ) ) )
      | ( ( preorder @ ( TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) )
       != ( preorder @ TS @ ( type2 @ TS ) ) ) ),
    inference(paramod_ordered,[status(thm)],[8300,320]) ).

thf(8488,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType] :
      ( ( preorder @ ( TR > TS ) @ ( type2 @ ( TR > TS ) ) )
      | ( ( preorder @ ( TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) )
       != ( preorder @ TS @ ( type2 @ TS ) ) ) ),
    inference(simp,[status(thm)],[8487]) ).

thf(8489,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType] : ( preorder @ ( TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) ),
    inference(pattern_uni,[status(thm)],[8488:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ))]]) ).

thf(8860,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType] :
      ( ~ $true
      | ( preorder @ ( TS > TT ) @ ( type2 @ ( TS > TT ) ) )
      | ( ( preorder @ ( TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) )
       != ( preorder @ TT @ ( type2 @ TT ) ) ) ),
    inference(paramod_ordered,[status(thm)],[8489,320]) ).

thf(8861,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType] :
      ( ( preorder @ ( TS > TT ) @ ( type2 @ ( TS > TT ) ) )
      | ( ( preorder @ ( TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) )
       != ( preorder @ TT @ ( type2 @ TT ) ) ) ),
    inference(simp,[status(thm)],[8860]) ).

thf(8862,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType] : ( preorder @ ( TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) ),
    inference(pattern_uni,[status(thm)],[8861:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ))]]) ).

thf(9107,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType] :
      ( ~ $true
      | ( preorder @ ( TT > TU ) @ ( type2 @ ( TT > TU ) ) )
      | ( ( preorder @ ( TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) )
       != ( preorder @ TU @ ( type2 @ TU ) ) ) ),
    inference(paramod_ordered,[status(thm)],[8862,320]) ).

thf(9108,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType] :
      ( ( preorder @ ( TT > TU ) @ ( type2 @ ( TT > TU ) ) )
      | ( ( preorder @ ( TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) )
       != ( preorder @ TU @ ( type2 @ TU ) ) ) ),
    inference(simp,[status(thm)],[9107]) ).

thf(9109,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType] : ( preorder @ ( TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) ),
    inference(pattern_uni,[status(thm)],[9108:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ))]]) ).

thf(9224,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType] :
      ( ~ $true
      | ( preorder @ ( TU > TV ) @ ( type2 @ ( TU > TV ) ) )
      | ( ( preorder @ ( TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) )
       != ( preorder @ TV @ ( type2 @ TV ) ) ) ),
    inference(paramod_ordered,[status(thm)],[9109,320]) ).

thf(9225,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType] :
      ( ( preorder @ ( TU > TV ) @ ( type2 @ ( TU > TV ) ) )
      | ( ( preorder @ ( TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) )
       != ( preorder @ TV @ ( type2 @ TV ) ) ) ),
    inference(simp,[status(thm)],[9224]) ).

thf(9226,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType] : ( preorder @ ( TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) ),
    inference(pattern_uni,[status(thm)],[9225:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ))]]) ).

thf(9622,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType] :
      ( ~ $true
      | ( preorder @ ( TV > TW ) @ ( type2 @ ( TV > TW ) ) )
      | ( ( preorder @ ( TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) )
       != ( preorder @ TW @ ( type2 @ TW ) ) ) ),
    inference(paramod_ordered,[status(thm)],[9226,320]) ).

thf(9623,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType] :
      ( ( preorder @ ( TV > TW ) @ ( type2 @ ( TV > TW ) ) )
      | ( ( preorder @ ( TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) )
       != ( preorder @ TW @ ( type2 @ TW ) ) ) ),
    inference(simp,[status(thm)],[9622]) ).

thf(9624,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType] : ( preorder @ ( TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) ),
    inference(pattern_uni,[status(thm)],[9623:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ))]]) ).

thf(11037,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType] :
      ( ~ $true
      | ( preorder @ ( TW > TX ) @ ( type2 @ ( TW > TX ) ) )
      | ( ( preorder @ ( TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) )
       != ( preorder @ TX @ ( type2 @ TX ) ) ) ),
    inference(paramod_ordered,[status(thm)],[9624,320]) ).

thf(11038,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType] :
      ( ( preorder @ ( TW > TX ) @ ( type2 @ ( TW > TX ) ) )
      | ( ( preorder @ ( TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) )
       != ( preorder @ TX @ ( type2 @ TX ) ) ) ),
    inference(simp,[status(thm)],[11037]) ).

thf(11039,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType] : ( preorder @ ( TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) ),
    inference(pattern_uni,[status(thm)],[11038:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ))]]) ).

thf(11689,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType] :
      ( ~ $true
      | ( preorder @ ( TX > TY ) @ ( type2 @ ( TX > TY ) ) )
      | ( ( preorder @ ( TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) )
       != ( preorder @ TY @ ( type2 @ TY ) ) ) ),
    inference(paramod_ordered,[status(thm)],[11039,320]) ).

thf(11690,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType] :
      ( ( preorder @ ( TX > TY ) @ ( type2 @ ( TX > TY ) ) )
      | ( ( preorder @ ( TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) )
       != ( preorder @ TY @ ( type2 @ TY ) ) ) ),
    inference(simp,[status(thm)],[11689]) ).

thf(11691,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType] : ( preorder @ ( TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) ),
    inference(pattern_uni,[status(thm)],[11690:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ))]]) ).

thf(12381,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType] :
      ( ~ $true
      | ( preorder @ ( TY > TZ ) @ ( type2 @ ( TY > TZ ) ) )
      | ( ( preorder @ ( TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) )
       != ( preorder @ TZ @ ( type2 @ TZ ) ) ) ),
    inference(paramod_ordered,[status(thm)],[11691,320]) ).

thf(12382,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType] :
      ( ( preorder @ ( TY > TZ ) @ ( type2 @ ( TY > TZ ) ) )
      | ( ( preorder @ ( TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) )
       != ( preorder @ TZ @ ( type2 @ TZ ) ) ) ),
    inference(simp,[status(thm)],[12381]) ).

thf(12383,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType] : ( preorder @ ( TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) ),
    inference(pattern_uni,[status(thm)],[12382:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ))]]) ).

thf(240,axiom,
    ! [TA: $tType] :
      ( ( semiring @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA,D: TA] :
          ( ( plus_plus @ TA @ ( times_times @ TA @ A @ B ) @ ( plus_plus @ TA @ ( times_times @ TA @ C @ B ) @ D ) )
          = ( plus_plus @ TA @ ( times_times @ TA @ ( plus_plus @ TA @ A @ C ) @ B ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_combine__common__factor) ).

thf(941,plain,
    ! [TA: $tType] :
      ( ( semiring @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA,D: TA] :
          ( ( plus_plus @ TA @ ( times_times @ TA @ A @ B ) @ ( plus_plus @ TA @ ( times_times @ TA @ C @ B ) @ D ) )
          = ( plus_plus @ TA @ ( times_times @ TA @ ( plus_plus @ TA @ A @ C ) @ B ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(12,axiom,
    ! [TA: $tType] :
      ( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
          = ( A
           != ( zero_zero @ TA ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_zero__less__iff__neq__zero) ).

thf(321,plain,
    ! [TA: $tType] :
      ( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
          = ( A
           != ( zero_zero @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(322,plain,
    ! [TA: $tType,A: TA] :
      ( ~ ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
      | ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
        = ( A
         != ( zero_zero @ TA ) ) ) ),
    inference(cnf,[status(esa)],[321]) ).

thf(323,plain,
    ! [TA: $tType,A: TA] :
      ( ( ( A
         != ( zero_zero @ TA ) )
        = ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) )
      | ~ ( canoni770627133id_add @ TA @ ( type2 @ TA ) ) ),
    inference(lifteq,[status(thm)],[322]) ).

thf(3044,plain,
    ! [TA: $tType,A: TA] :
      ( ~ ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
      | ( A
       != ( zero_zero @ TA ) )
      | ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ),
    inference(bool_ext,[status(thm)],[323]) ).

thf(3070,plain,
    ! [TA: $tType,A: TA] :
      ( ~ ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
      | ( A
       != ( zero_zero @ TA ) )
      | ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ),
    inference(cnf,[status(esa)],[3044]) ).

thf(3071,plain,
    ! [TA: $tType,A: TA] :
      ( ( A
       != ( zero_zero @ TA ) )
      | ~ ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
      | ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ),
    inference(lifteq,[status(thm)],[3070]) ).

thf(3072,plain,
    ! [TA: $tType] :
      ( ~ ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
      | ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ ( zero_zero @ TA ) ) ),
    inference(simp,[status(thm)],[3071]) ).

thf(157,axiom,
    ! [A: nat] : ( ord_less_eq @ nat @ A @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_le__refl) ).

thf(730,plain,
    ! [A: nat] : ( ord_less_eq @ nat @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(284,axiom,
    ! [TA: $tType] :
      ( ( linord581940658strict @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( times_times @ TA @ A @ B ) )
          = ( ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
              & ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B ) )
            | ( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
              & ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_zero__le__mult__iff) ).

thf(1068,plain,
    ! [TA: $tType] :
      ( ( linord581940658strict @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( times_times @ TA @ A @ B ) )
          = ( ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
              & ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B ) )
            | ( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
              & ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(20,axiom,
    ord @ $o @ ( type2 @ $o ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oord_10) ).

thf(342,plain,
    ord @ $o @ ( type2 @ $o ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(9,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ord @ TB @ ( type2 @ TB ) )
     => ( ( ord_less_eq @ ( TA > TB ) )
        = ( ^ [A: TA > TB,B: TA > TB] :
            ! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_le__fun__def) ).

thf(314,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ord @ TB @ ( type2 @ TB ) )
     => ( ( ord_less_eq @ ( TA > TB ) )
        = ( ^ [A: TA > TB,B: TA > TB] :
            ! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(315,plain,
    ! [TA: $tType,TB: $tType] :
      ( ~ ( ord @ TA @ ( type2 @ TA ) )
      | ( ( ord_less_eq @ ( TB > TA ) )
        = ( ^ [A: TB > TA,B: TB > TA] :
            ! [C: TB] : ( ord_less_eq @ TA @ ( A @ C ) @ ( B @ C ) ) ) ) ),
    inference(cnf,[status(esa)],[314]) ).

thf(316,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( ord_less_eq @ ( TB > TA ) )
        = ( ^ [A: TB > TA,B: TB > TA] :
            ! [C: TB] : ( ord_less_eq @ TA @ ( A @ C ) @ ( B @ C ) ) ) )
      | ~ ( ord @ TA @ ( type2 @ TA ) ) ),
    inference(lifteq,[status(thm)],[315]) ).

thf(2377,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( ord_less_eq @ ( TB > TA ) )
        = ( ^ [A: TB > TA,B: TB > TA] :
            ! [C: TB] : ( ord_less_eq @ TA @ ( A @ C ) @ ( B @ C ) ) ) )
      | ~ $true
      | ( ( ord @ $o @ ( type2 @ $o ) )
       != ( ord @ TA @ ( type2 @ TA ) ) ) ),
    inference(paramod_ordered,[status(thm)],[342,316]) ).

thf(2378,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( ord_less_eq @ ( TB > TA ) )
        = ( ^ [A: TB > TA,B: TB > TA] :
            ! [C: TB] : ( ord_less_eq @ TA @ ( A @ C ) @ ( B @ C ) ) ) )
      | ( ( ord @ $o @ ( type2 @ $o ) )
       != ( ord @ TA @ ( type2 @ TA ) ) ) ),
    inference(simp,[status(thm)],[2377]) ).

thf(2379,plain,
    ! [TB: $tType] :
      ( ( ord_less_eq @ ( TB > $o ) )
      = ( ^ [A: TB > $o,B: TB > $o] :
          ! [C: TB] : ( ord_less_eq @ $o @ ( A @ C ) @ ( B @ C ) ) ) ),
    inference(pattern_uni,[status(thm)],[2378:[bind_type(TA,$thf( $o ))]]) ).

thf(2395,plain,
    ! [TA: $tType] :
      ( ( ord_less_eq @ ( TA > $o ) )
      = ( ^ [A: TA > $o,B: TA > $o] :
          ! [C: TA] : ( ord_less_eq @ $o @ ( A @ C ) @ ( B @ C ) ) ) ),
    inference(simp,[status(thm)],[2379]) ).

thf(7,axiom,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ord_less_eq @ TA @ C @ A )
           => ( ord_less_eq @ TA @ C @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_dual__order_Otrans) ).

thf(308,plain,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ord_less_eq @ TA @ C @ A )
           => ( ord_less_eq @ TA @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(286,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( plus_plus @ nat @ ( times_times @ nat @ A @ B ) @ ( plus_plus @ nat @ ( times_times @ nat @ C @ B ) @ D ) )
      = ( plus_plus @ nat @ ( times_times @ nat @ ( plus_plus @ nat @ A @ C ) @ B ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_left__add__mult__distrib) ).

thf(1073,plain,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( plus_plus @ nat @ ( times_times @ nat @ A @ B ) @ ( plus_plus @ nat @ ( times_times @ nat @ C @ B ) @ D ) )
      = ( plus_plus @ nat @ ( times_times @ nat @ ( plus_plus @ nat @ A @ C ) @ B ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(215,axiom,
    ! [TA: $tType] :
      ( ( ordere216010020id_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
         => ( ( ord_less_eq @ TA @ B @ C )
           => ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_add__decreasing) ).

thf(873,plain,
    ! [TA: $tType] :
      ( ( ordere216010020id_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
         => ( ( ord_less_eq @ TA @ B @ C )
           => ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(1112,plain,
    ( ( ( huffma469337550apSyms @ a @ t @ a2 @ b )
     != t )
    | ( ( times_times @ nat @ ( huffma854352999e_freq @ a @ t @ a2 ) @ ( huffma223349076_depth @ a @ t @ b ) )
     != ( times_times @ nat @ ( huffma854352999e_freq @ a @ t @ a2 ) @ ( huffma223349076_depth @ a @ t @ a2 ) ) )
    | ( ( times_times @ nat @ ( huffma854352999e_freq @ a @ t @ b ) @ ( huffma223349076_depth @ a @ t @ b ) )
     != ( times_times @ nat @ ( huffma854352999e_freq @ a @ t @ a2 ) @ ( huffma223349076_depth @ a @ t @ b ) ) )
    | ( ( times_times @ nat @ ( huffma854352999e_freq @ a @ t @ b ) @ ( huffma223349076_depth @ a @ t @ a2 ) )
     != ( times_times @ nat @ ( huffma854352999e_freq @ a @ t @ a2 ) @ ( huffma223349076_depth @ a @ t @ a2 ) ) ) ),
    inference(eqfactor_ordered,[status(thm)],[1105]) ).

thf(1119,plain,
    ( ( ( huffma469337550apSyms @ a @ t @ a2 @ b )
     != t )
    | ( ( times_times @ nat @ ( huffma854352999e_freq @ a @ t @ a2 ) @ ( huffma223349076_depth @ a @ t @ b ) )
     != ( times_times @ nat @ ( huffma854352999e_freq @ a @ t @ a2 ) @ ( huffma223349076_depth @ a @ t @ a2 ) ) )
    | ( ( huffma854352999e_freq @ a @ t @ b )
     != ( huffma854352999e_freq @ a @ t @ a2 ) )
    | ( ( huffma223349076_depth @ a @ t @ b )
     != ( huffma223349076_depth @ a @ t @ b ) )
    | ( ( huffma854352999e_freq @ a @ t @ b )
     != ( huffma854352999e_freq @ a @ t @ a2 ) )
    | ( ( huffma223349076_depth @ a @ t @ a2 )
     != ( huffma223349076_depth @ a @ t @ a2 ) ) ),
    inference(simp,[status(thm)],[1112]) ).

thf(1142,plain,
    ( ( ( huffma469337550apSyms @ a @ t @ a2 @ b )
     != t )
    | ( ( times_times @ nat @ ( huffma854352999e_freq @ a @ t @ a2 ) @ ( huffma223349076_depth @ a @ t @ b ) )
     != ( times_times @ nat @ ( huffma854352999e_freq @ a @ t @ a2 ) @ ( huffma223349076_depth @ a @ t @ a2 ) ) )
    | ( ( huffma854352999e_freq @ a @ t @ b )
     != ( huffma854352999e_freq @ a @ t @ a2 ) ) ),
    inference(simp,[status(thm)],[1119]) ).

thf(76,axiom,
    canoni770627133id_add @ nat @ ( type2 @ nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add) ).

thf(511,plain,
    canoni770627133id_add @ nat @ ( type2 @ nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(108,axiom,
    ! [TA: $tType] :
      ( ( ordere516151231imp_le @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ ( plus_plus @ TA @ B @ A ) )
          = ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_le__add__same__cancel2) ).

thf(597,plain,
    ! [TA: $tType] :
      ( ( ordere516151231imp_le @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ ( plus_plus @ TA @ B @ A ) )
          = ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(211,axiom,
    ! [TA: $tType] :
      ( ( monoid_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
          = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_add_Oleft__neutral) ).

thf(861,plain,
    ! [TA: $tType] :
      ( ( monoid_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
          = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(112,axiom,
    ! [TA: $tType] :
      ( ( linordered_field @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( times_times @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
          = ( plus_plus @ TA @ ( times_times @ TA @ A @ C ) @ ( times_times @ TA @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_linordered__field__class_Osign__simps_I35_J) ).

thf(614,plain,
    ! [TA: $tType] :
      ( ( linordered_field @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( times_times @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
          = ( plus_plus @ TA @ ( times_times @ TA @ A @ C ) @ ( times_times @ TA @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(135,axiom,
    cancel_semigroup_add @ nat @ ( type2 @ nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocancel__semigroup__add) ).

thf(677,plain,
    cancel_semigroup_add @ nat @ ( type2 @ nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(151,axiom,
    ! [TA: $tType] :
      ( ( ordere216010020id_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
         => ( ( ord_less_eq @ TA @ B @ C )
           => ( ord_less_eq @ TA @ B @ ( plus_plus @ TA @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_add__increasing) ).

thf(715,plain,
    ! [TA: $tType] :
      ( ( ordere216010020id_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
         => ( ( ord_less_eq @ TA @ B @ C )
           => ( ord_less_eq @ TA @ B @ ( plus_plus @ TA @ A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(144,axiom,
    ! [TA: $tType] :
      ( ( ordered_ring @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ord_less_eq @ TA @ C @ ( zero_zero @ TA ) )
           => ( ord_less_eq @ TA @ ( times_times @ TA @ B @ C ) @ ( times_times @ TA @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_mult__right__mono__neg) ).

thf(698,plain,
    ! [TA: $tType] :
      ( ( ordered_ring @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ord_less_eq @ TA @ C @ ( zero_zero @ TA ) )
           => ( ord_less_eq @ TA @ ( times_times @ TA @ B @ C ) @ ( times_times @ TA @ A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(164,axiom,
    linorder @ nat @ ( type2 @ nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Olinorder) ).

thf(747,plain,
    linorder @ nat @ ( type2 @ nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(87,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( times_times @ nat @ A @ B )
        = ( times_times @ nat @ C @ B ) )
      = ( ( A = C )
        | ( B
          = ( zero_zero @ nat ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_mult__cancel2) ).

thf(538,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( times_times @ nat @ A @ B )
        = ( times_times @ nat @ C @ B ) )
      = ( ( A = C )
        | ( B
          = ( zero_zero @ nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(132,axiom,
    ! [TA: $tType] :
      ( ( ordere236663937imp_le @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
         => ( ord_less_eq @ TA @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_add__le__imp__le__left) ).

thf(670,plain,
    ! [TA: $tType] :
      ( ( ordere236663937imp_le @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
         => ( ord_less_eq @ TA @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(260,axiom,
    ! [TA: $tType] :
      ( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA,D: TA] :
          ( ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ C @ D ) )
          = ( times_times @ TA @ C @ ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_semiring__normalization__rules_I15_J) ).

thf(1001,plain,
    ! [TA: $tType] :
      ( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA,D: TA] :
          ( ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ C @ D ) )
          = ( times_times @ TA @ C @ ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(48,axiom,
    ! [TA: $tType] : ( preorder @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Opreorder_4) ).

thf(416,plain,
    ! [TA: $tType] : ( preorder @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(417,plain,
    ! [TA: $tType] : ( preorder @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
    inference(cnf,[status(esa)],[416]) ).

thf(2877,plain,
    ! [TA: $tType,TB: $tType,TC: $tType] :
      ( ~ $true
      | ( preorder @ ( TB > TC ) @ ( type2 @ ( TB > TC ) ) )
      | ( ( preorder @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) )
       != ( preorder @ TC @ ( type2 @ TC ) ) ) ),
    inference(paramod_ordered,[status(thm)],[417,320]) ).

thf(2878,plain,
    ! [TA: $tType,TB: $tType,TC: $tType] :
      ( ( preorder @ ( TB > TC ) @ ( type2 @ ( TB > TC ) ) )
      | ( ( preorder @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) )
       != ( preorder @ TC @ ( type2 @ TC ) ) ) ),
    inference(simp,[status(thm)],[2877]) ).

thf(2879,plain,
    ! [TA: $tType,TB: $tType] : ( preorder @ ( TB > ( set @ TA ) ) @ ( type2 @ ( TB > ( set @ TA ) ) ) ),
    inference(pattern_uni,[status(thm)],[2878:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( set @ TA ))]]) ).

thf(2910,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] :
      ( ~ $true
      | ( preorder @ ( TC > TD ) @ ( type2 @ ( TC > TD ) ) )
      | ( ( preorder @ ( TB > ( set @ TA ) ) @ ( type2 @ ( TB > ( set @ TA ) ) ) )
       != ( preorder @ TD @ ( type2 @ TD ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2879,320]) ).

thf(2911,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] :
      ( ( preorder @ ( TC > TD ) @ ( type2 @ ( TC > TD ) ) )
      | ( ( preorder @ ( TB > ( set @ TA ) ) @ ( type2 @ ( TB > ( set @ TA ) ) ) )
       != ( preorder @ TD @ ( type2 @ TD ) ) ) ),
    inference(simp,[status(thm)],[2910]) ).

thf(2912,plain,
    ! [TA: $tType,TB: $tType,TC: $tType] : ( preorder @ ( TC > TB > ( set @ TA ) ) @ ( type2 @ ( TC > TB > ( set @ TA ) ) ) ),
    inference(pattern_uni,[status(thm)],[2911:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TB > ( set @ TA ) ))]]) ).

thf(2976,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType] :
      ( ~ $true
      | ( preorder @ ( TD > TE ) @ ( type2 @ ( TD > TE ) ) )
      | ( ( preorder @ ( TC > TB > ( set @ TA ) ) @ ( type2 @ ( TC > TB > ( set @ TA ) ) ) )
       != ( preorder @ TE @ ( type2 @ TE ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2912,320]) ).

thf(2977,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType] :
      ( ( preorder @ ( TD > TE ) @ ( type2 @ ( TD > TE ) ) )
      | ( ( preorder @ ( TC > TB > ( set @ TA ) ) @ ( type2 @ ( TC > TB > ( set @ TA ) ) ) )
       != ( preorder @ TE @ ( type2 @ TE ) ) ) ),
    inference(simp,[status(thm)],[2976]) ).

thf(2978,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] : ( preorder @ ( TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TD > TC > TB > ( set @ TA ) ) ) ),
    inference(pattern_uni,[status(thm)],[2977:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TC > TB > ( set @ TA ) ))]]) ).

thf(3108,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType] :
      ( ~ $true
      | ( preorder @ ( TE > TF ) @ ( type2 @ ( TE > TF ) ) )
      | ( ( preorder @ ( TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TD > TC > TB > ( set @ TA ) ) ) )
       != ( preorder @ TF @ ( type2 @ TF ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2978,320]) ).

thf(3109,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType] :
      ( ( preorder @ ( TE > TF ) @ ( type2 @ ( TE > TF ) ) )
      | ( ( preorder @ ( TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TD > TC > TB > ( set @ TA ) ) ) )
       != ( preorder @ TF @ ( type2 @ TF ) ) ) ),
    inference(simp,[status(thm)],[3108]) ).

thf(3110,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType] : ( preorder @ ( TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TE > TD > TC > TB > ( set @ TA ) ) ) ),
    inference(pattern_uni,[status(thm)],[3109:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TD > TC > TB > ( set @ TA ) ))]]) ).

thf(3188,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType] :
      ( ~ $true
      | ( preorder @ ( TF > TG ) @ ( type2 @ ( TF > TG ) ) )
      | ( ( preorder @ ( TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TE > TD > TC > TB > ( set @ TA ) ) ) )
       != ( preorder @ TG @ ( type2 @ TG ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3110,320]) ).

thf(3189,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType] :
      ( ( preorder @ ( TF > TG ) @ ( type2 @ ( TF > TG ) ) )
      | ( ( preorder @ ( TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TE > TD > TC > TB > ( set @ TA ) ) ) )
       != ( preorder @ TG @ ( type2 @ TG ) ) ) ),
    inference(simp,[status(thm)],[3188]) ).

thf(3190,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType] : ( preorder @ ( TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TF > TE > TD > TC > TB > ( set @ TA ) ) ) ),
    inference(pattern_uni,[status(thm)],[3189:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TE > TD > TC > TB > ( set @ TA ) ))]]) ).

thf(3278,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType] :
      ( ~ $true
      | ( preorder @ ( TG > TH ) @ ( type2 @ ( TG > TH ) ) )
      | ( ( preorder @ ( TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TF > TE > TD > TC > TB > ( set @ TA ) ) ) )
       != ( preorder @ TH @ ( type2 @ TH ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3190,320]) ).

thf(3279,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType] :
      ( ( preorder @ ( TG > TH ) @ ( type2 @ ( TG > TH ) ) )
      | ( ( preorder @ ( TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TF > TE > TD > TC > TB > ( set @ TA ) ) ) )
       != ( preorder @ TH @ ( type2 @ TH ) ) ) ),
    inference(simp,[status(thm)],[3278]) ).

thf(3280,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType] : ( preorder @ ( TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) ),
    inference(pattern_uni,[status(thm)],[3279:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TF > TE > TD > TC > TB > ( set @ TA ) ))]]) ).

thf(5288,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType] :
      ( ~ $true
      | ( preorder @ ( TH > TI ) @ ( type2 @ ( TH > TI ) ) )
      | ( ( preorder @ ( TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) )
       != ( preorder @ TI @ ( type2 @ TI ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3280,320]) ).

thf(5289,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType] :
      ( ( preorder @ ( TH > TI ) @ ( type2 @ ( TH > TI ) ) )
      | ( ( preorder @ ( TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) )
       != ( preorder @ TI @ ( type2 @ TI ) ) ) ),
    inference(simp,[status(thm)],[5288]) ).

thf(5290,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType] : ( preorder @ ( TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) ),
    inference(pattern_uni,[status(thm)],[5289:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TG > TF > TE > TD > TC > TB > ( set @ TA ) ))]]) ).

thf(5375,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType] :
      ( ~ $true
      | ( preorder @ ( TI > TJ ) @ ( type2 @ ( TI > TJ ) ) )
      | ( ( preorder @ ( TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) )
       != ( preorder @ TJ @ ( type2 @ TJ ) ) ) ),
    inference(paramod_ordered,[status(thm)],[5290,320]) ).

thf(5376,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType] :
      ( ( preorder @ ( TI > TJ ) @ ( type2 @ ( TI > TJ ) ) )
      | ( ( preorder @ ( TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) )
       != ( preorder @ TJ @ ( type2 @ TJ ) ) ) ),
    inference(simp,[status(thm)],[5375]) ).

thf(5377,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType] : ( preorder @ ( TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) ),
    inference(pattern_uni,[status(thm)],[5376:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ))]]) ).

thf(5770,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType] :
      ( ~ $true
      | ( preorder @ ( TJ > TK ) @ ( type2 @ ( TJ > TK ) ) )
      | ( ( preorder @ ( TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) )
       != ( preorder @ TK @ ( type2 @ TK ) ) ) ),
    inference(paramod_ordered,[status(thm)],[5377,320]) ).

thf(5771,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType] :
      ( ( preorder @ ( TJ > TK ) @ ( type2 @ ( TJ > TK ) ) )
      | ( ( preorder @ ( TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) )
       != ( preorder @ TK @ ( type2 @ TK ) ) ) ),
    inference(simp,[status(thm)],[5770]) ).

thf(5772,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType] : ( preorder @ ( TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) ),
    inference(pattern_uni,[status(thm)],[5771:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ))]]) ).

thf(5919,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType] :
      ( ~ $true
      | ( preorder @ ( TK > TL ) @ ( type2 @ ( TK > TL ) ) )
      | ( ( preorder @ ( TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) )
       != ( preorder @ TL @ ( type2 @ TL ) ) ) ),
    inference(paramod_ordered,[status(thm)],[5772,320]) ).

thf(5920,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType] :
      ( ( preorder @ ( TK > TL ) @ ( type2 @ ( TK > TL ) ) )
      | ( ( preorder @ ( TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) )
       != ( preorder @ TL @ ( type2 @ TL ) ) ) ),
    inference(simp,[status(thm)],[5919]) ).

thf(5921,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType] : ( preorder @ ( TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) ),
    inference(pattern_uni,[status(thm)],[5920:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ))]]) ).

thf(3,axiom,
    ! [TA: $tType,A: TA > $o,B: TA > $o] :
      ( ! [C: TA] :
          ( ( A @ C )
          = ( B @ C ) )
     => ( ( collect @ TA @ A )
        = ( collect @ TA @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_Collect__cong) ).

thf(299,plain,
    ! [TA: $tType,A: TA > $o,B: TA > $o] :
      ( ! [C: TA] :
          ( ( A @ C )
          = ( B @ C ) )
     => ( ( collect @ TA @ A )
        = ( collect @ TA @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(300,plain,
    ! [TA: $tType,B: TA > $o,A: TA > $o] :
      ( ( ( A @ ( sk1 @ TA @ B @ A ) )
       != ( B @ ( sk1 @ TA @ B @ A ) ) )
      | ( ( collect @ TA @ A )
        = ( collect @ TA @ B ) ) ),
    inference(cnf,[status(esa)],[299]) ).

thf(301,plain,
    ! [TA: $tType,B: TA > $o,A: TA > $o] :
      ( ( ( A @ ( sk1 @ TA @ B @ A ) )
       != ( B @ ( sk1 @ TA @ B @ A ) ) )
      | ( ( collect @ TA @ A )
        = ( collect @ TA @ B ) ) ),
    inference(lifteq,[status(thm)],[300]) ).

thf(196,axiom,
    member @ a @ b @ ( huffma505251170phabet @ a @ t ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_assms_I3_J) ).

thf(829,plain,
    member @ a @ b @ ( huffma505251170phabet @ a @ t ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(44,axiom,
    ! [TA: $tType] : ( ord @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oord_6) ).

thf(404,plain,
    ! [TA: $tType] : ( ord @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(201,axiom,
    ! [TA: $tType] :
      ( ( ordered_semiring_0 @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
         => ( ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) )
           => ( ord_less_eq @ TA @ ( times_times @ TA @ B @ A ) @ ( zero_zero @ TA ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_mult__nonneg__nonpos2) ).

thf(841,plain,
    ! [TA: $tType] :
      ( ( ordered_semiring_0 @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
         => ( ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) )
           => ( ord_less_eq @ TA @ ( times_times @ TA @ B @ A ) @ ( zero_zero @ TA ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(252,axiom,
    ! [TA: $tType] :
      ( ( ordere516151231imp_le @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ B )
          = ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_add__less__same__cancel2) ).

thf(973,plain,
    ! [TA: $tType] :
      ( ( ordere516151231imp_le @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ B )
          = ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(220,axiom,
    ! [TA: $tType] :
      ( ( linordered_field @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
          = ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_linordered__field__class_Osign__simps_I26_J) ).

thf(885,plain,
    ! [TA: $tType] :
      ( ( linordered_field @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
          = ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(8899,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType] :
      ( ~ $true
      | ( preorder @ ( TS > TT ) @ ( type2 @ ( TS > TT ) ) )
      | ( ( preorder @ ( TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) @ ( type2 @ ( TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ) )
       != ( preorder @ TT @ ( type2 @ TT ) ) ) ),
    inference(paramod_ordered,[status(thm)],[8784,320]) ).

thf(8900,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType] :
      ( ( preorder @ ( TS > TT ) @ ( type2 @ ( TS > TT ) ) )
      | ( ( preorder @ ( TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) @ ( type2 @ ( TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ) )
       != ( preorder @ TT @ ( type2 @ TT ) ) ) ),
    inference(simp,[status(thm)],[8899]) ).

thf(8901,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType] : ( preorder @ ( TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) @ ( type2 @ ( TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ) ),
    inference(pattern_uni,[status(thm)],[8900:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ))]]) ).

thf(9146,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType] :
      ( ~ $true
      | ( preorder @ ( TT > TU ) @ ( type2 @ ( TT > TU ) ) )
      | ( ( preorder @ ( TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) @ ( type2 @ ( TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ) )
       != ( preorder @ TU @ ( type2 @ TU ) ) ) ),
    inference(paramod_ordered,[status(thm)],[8901,320]) ).

thf(9147,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType] :
      ( ( preorder @ ( TT > TU ) @ ( type2 @ ( TT > TU ) ) )
      | ( ( preorder @ ( TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) @ ( type2 @ ( TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ) )
       != ( preorder @ TU @ ( type2 @ TU ) ) ) ),
    inference(simp,[status(thm)],[9146]) ).

thf(9148,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType] : ( preorder @ ( TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) @ ( type2 @ ( TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ) ),
    inference(pattern_uni,[status(thm)],[9147:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ))]]) ).

thf(9302,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType] :
      ( ~ $true
      | ( preorder @ ( TU > TV ) @ ( type2 @ ( TU > TV ) ) )
      | ( ( preorder @ ( TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) @ ( type2 @ ( TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ) )
       != ( preorder @ TV @ ( type2 @ TV ) ) ) ),
    inference(paramod_ordered,[status(thm)],[9148,320]) ).

thf(9303,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType] :
      ( ( preorder @ ( TU > TV ) @ ( type2 @ ( TU > TV ) ) )
      | ( ( preorder @ ( TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) @ ( type2 @ ( TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ) )
       != ( preorder @ TV @ ( type2 @ TV ) ) ) ),
    inference(simp,[status(thm)],[9302]) ).

thf(9304,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType] : ( preorder @ ( TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) @ ( type2 @ ( TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ) ),
    inference(pattern_uni,[status(thm)],[9303:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ))]]) ).

thf(9661,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType] :
      ( ~ $true
      | ( preorder @ ( TV > TW ) @ ( type2 @ ( TV > TW ) ) )
      | ( ( preorder @ ( TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) @ ( type2 @ ( TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ) )
       != ( preorder @ TW @ ( type2 @ TW ) ) ) ),
    inference(paramod_ordered,[status(thm)],[9304,320]) ).

thf(9662,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType] :
      ( ( preorder @ ( TV > TW ) @ ( type2 @ ( TV > TW ) ) )
      | ( ( preorder @ ( TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) @ ( type2 @ ( TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ) )
       != ( preorder @ TW @ ( type2 @ TW ) ) ) ),
    inference(simp,[status(thm)],[9661]) ).

thf(9663,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType] : ( preorder @ ( TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) @ ( type2 @ ( TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ) ),
    inference(pattern_uni,[status(thm)],[9662:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ))]]) ).

thf(11082,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType] :
      ( ~ $true
      | ( preorder @ ( TW > TX ) @ ( type2 @ ( TW > TX ) ) )
      | ( ( preorder @ ( TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) @ ( type2 @ ( TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ) )
       != ( preorder @ TX @ ( type2 @ TX ) ) ) ),
    inference(paramod_ordered,[status(thm)],[9663,320]) ).

thf(11083,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType] :
      ( ( preorder @ ( TW > TX ) @ ( type2 @ ( TW > TX ) ) )
      | ( ( preorder @ ( TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) @ ( type2 @ ( TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ) )
       != ( preorder @ TX @ ( type2 @ TX ) ) ) ),
    inference(simp,[status(thm)],[11082]) ).

thf(11084,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType] : ( preorder @ ( TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) @ ( type2 @ ( TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ) ),
    inference(pattern_uni,[status(thm)],[11083:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ))]]) ).

thf(11736,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType] :
      ( ~ $true
      | ( preorder @ ( TX > TY ) @ ( type2 @ ( TX > TY ) ) )
      | ( ( preorder @ ( TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) @ ( type2 @ ( TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ) )
       != ( preorder @ TY @ ( type2 @ TY ) ) ) ),
    inference(paramod_ordered,[status(thm)],[11084,320]) ).

thf(11737,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType] :
      ( ( preorder @ ( TX > TY ) @ ( type2 @ ( TX > TY ) ) )
      | ( ( preorder @ ( TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) @ ( type2 @ ( TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ) )
       != ( preorder @ TY @ ( type2 @ TY ) ) ) ),
    inference(simp,[status(thm)],[11736]) ).

thf(11738,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType] : ( preorder @ ( TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) @ ( type2 @ ( TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ) ),
    inference(pattern_uni,[status(thm)],[11737:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ))]]) ).

thf(12427,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType] :
      ( ~ $true
      | ( preorder @ ( TY > TZ ) @ ( type2 @ ( TY > TZ ) ) )
      | ( ( preorder @ ( TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) @ ( type2 @ ( TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ) )
       != ( preorder @ TZ @ ( type2 @ TZ ) ) ) ),
    inference(paramod_ordered,[status(thm)],[11738,320]) ).

thf(12428,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType] :
      ( ( preorder @ ( TY > TZ ) @ ( type2 @ ( TY > TZ ) ) )
      | ( ( preorder @ ( TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) @ ( type2 @ ( TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ) )
       != ( preorder @ TZ @ ( type2 @ TZ ) ) ) ),
    inference(simp,[status(thm)],[12427]) ).

thf(12429,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType] : ( preorder @ ( TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) @ ( type2 @ ( TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ) ),
    inference(pattern_uni,[status(thm)],[12428:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ))]]) ).

thf(13037,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType] :
      ( ~ $true
      | ( preorder @ ( TZ > TZA ) @ ( type2 @ ( TZ > TZA ) ) )
      | ( ( preorder @ ( TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) @ ( type2 @ ( TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ) )
       != ( preorder @ TZA @ ( type2 @ TZA ) ) ) ),
    inference(paramod_ordered,[status(thm)],[12429,320]) ).

thf(13038,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType] :
      ( ( preorder @ ( TZ > TZA ) @ ( type2 @ ( TZ > TZA ) ) )
      | ( ( preorder @ ( TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) @ ( type2 @ ( TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ) )
       != ( preorder @ TZA @ ( type2 @ TZA ) ) ) ),
    inference(simp,[status(thm)],[13037]) ).

thf(13039,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType] : ( preorder @ ( TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) @ ( type2 @ ( TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ) ),
    inference(pattern_uni,[status(thm)],[13038:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ))]]) ).

thf(126,axiom,
    ! [TA: $tType] :
      ( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( times_times @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
          = ( plus_plus @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_semiring__normalization__rules_I34_J) ).

thf(651,plain,
    ! [TA: $tType] :
      ( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( times_times @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
          = ( plus_plus @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(39,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( order @ TA @ ( type2 @ TA ) )
        & ( order @ TB @ ( type2 @ TB ) ) )
     => ! [A: TB,B: TB,C: TB > TA,D: TA] :
          ( ( ord_less_eq @ TB @ A @ B )
         => ( ( ord_less_eq @ TA @ ( C @ B ) @ D )
           => ( ! [E: TB,F: TB] :
                  ( ( ord_less_eq @ TB @ E @ F )
                 => ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
             => ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_order__subst2) ).

thf(389,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( order @ TA @ ( type2 @ TA ) )
        & ( order @ TB @ ( type2 @ TB ) ) )
     => ! [A: TB,B: TB,C: TB > TA,D: TA] :
          ( ( ord_less_eq @ TB @ A @ B )
         => ( ( ord_less_eq @ TA @ ( C @ B ) @ D )
           => ( ! [E: TB,F: TB] :
                  ( ( ord_less_eq @ TB @ E @ F )
                 => ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
             => ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(16,axiom,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ord_less_eq @ TA @ B @ A )
           => ( B = A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_dual__order_Oantisym) ).

thf(330,plain,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ord_less_eq @ TA @ B @ A )
           => ( B = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(331,plain,
    ! [TA: $tType,B: TA,A: TA] :
      ( ~ ( order @ TA @ ( type2 @ TA ) )
      | ~ ( ord_less_eq @ TA @ A @ B )
      | ~ ( ord_less_eq @ TA @ B @ A )
      | ( B = A ) ),
    inference(cnf,[status(esa)],[330]) ).

thf(332,plain,
    ! [TA: $tType,B: TA,A: TA] :
      ( ( B = A )
      | ~ ( order @ TA @ ( type2 @ TA ) )
      | ~ ( ord_less_eq @ TA @ A @ B )
      | ~ ( ord_less_eq @ TA @ B @ A ) ),
    inference(lifteq,[status(thm)],[331]) ).

thf(1111,plain,
    ( ( ( huffma469337550apSyms @ a @ t @ a2 @ b )
     != t )
    | ( ( huffma854352999e_freq @ a @ t @ a2 )
     != ( huffma854352999e_freq @ a @ t @ a2 ) )
    | ( ( huffma223349076_depth @ a @ t @ b )
     != ( huffma223349076_depth @ a @ t @ a2 ) )
    | ( ( huffma854352999e_freq @ a @ t @ b )
     != ( huffma854352999e_freq @ a @ t @ b ) )
    | ( ( huffma223349076_depth @ a @ t @ b )
     != ( huffma223349076_depth @ a @ t @ a2 ) ) ),
    inference(simp,[status(thm)],[1105]) ).

thf(1136,plain,
    ( ( ( huffma469337550apSyms @ a @ t @ a2 @ b )
     != t )
    | ( ( huffma223349076_depth @ a @ t @ b )
     != ( huffma223349076_depth @ a @ t @ a2 ) ) ),
    inference(simp,[status(thm)],[1111]) ).

thf(1143,plain,
    ( ( ( huffma469337550apSyms @ a @ t @ a2 @ b )
     != t )
    | ( t != t )
    | ( b != a2 ) ),
    inference(simp,[status(thm)],[1136]) ).

thf(1144,plain,
    ( ( ( huffma469337550apSyms @ a @ t @ a2 @ b )
     != t )
    | ( b != a2 ) ),
    inference(simp,[status(thm)],[1143]) ).

thf(4399,plain,
    ! [B: a,A: a] :
      ( ~ ( order @ a @ ( type2 @ a ) )
      | ~ ( ord_less_eq @ a @ A @ B )
      | ~ ( ord_less_eq @ a @ B @ A )
      | ( ( huffma469337550apSyms @ a @ t @ a2 @ b )
       != t )
      | ( A != a2 )
      | ( B != b ) ),
    inference(paramod_ordered,[status(thm)],[332,1144]) ).

thf(4400,plain,
    ! [A: a] :
      ( ~ ( order @ a @ ( type2 @ a ) )
      | ~ ( ord_less_eq @ a @ A @ b )
      | ~ ( ord_less_eq @ a @ b @ A )
      | ( ( huffma469337550apSyms @ a @ t @ a2 @ b )
       != t )
      | ( A != a2 ) ),
    inference(pattern_uni,[status(thm)],[4399:[bind(A,$thf( A )),bind(B,$thf( b ))]]) ).

thf(4943,plain,
    ( ~ ( order @ a @ ( type2 @ a ) )
    | ~ ( ord_less_eq @ a @ a2 @ b )
    | ~ ( ord_less_eq @ a @ b @ a2 )
    | ( ( huffma469337550apSyms @ a @ t @ a2 @ b )
     != t ) ),
    inference(simp,[status(thm)],[4400]) ).

thf(5580,plain,
    ( ~ ( order @ a @ ( type2 @ a ) )
    | ~ ( ord_less_eq @ a @ a2 @ b )
    | ( ( huffma469337550apSyms @ a @ t @ a2 @ b )
     != t )
    | ( ( ord_less_eq @ a @ b @ a2 )
     != ( ord_less_eq @ a @ a2 @ b ) )
    | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[4943]) ).

thf(5585,plain,
    ( ~ ( order @ a @ ( type2 @ a ) )
    | ~ ( ord_less_eq @ a @ a2 @ b )
    | ( ( huffma469337550apSyms @ a @ t @ a2 @ b )
     != t )
    | ( ( ord_less_eq @ a @ b @ a2 )
     != ( ord_less_eq @ a @ a2 @ b ) ) ),
    inference(simp,[status(thm)],[5580]) ).

thf(5,axiom,
    ! [TA: $tType,A: TA,B: TA > $o] :
      ( ( member @ TA @ A @ ( collect @ TA @ B ) )
      = ( B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_mem__Collect__eq) ).

thf(303,plain,
    ! [TA: $tType,A: TA,B: TA > $o] :
      ( ( member @ TA @ A @ ( collect @ TA @ B ) )
      = ( B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(304,plain,
    ! [TA: $tType,B: TA > $o,A: TA] :
      ( ( member @ TA @ A @ ( collect @ TA @ B ) )
      = ( B @ A ) ),
    inference(cnf,[status(esa)],[303]) ).

thf(305,plain,
    ! [TA: $tType,B: TA > $o,A: TA] :
      ( ( member @ TA @ A @ ( collect @ TA @ B ) )
      = ( B @ A ) ),
    inference(lifteq,[status(thm)],[304]) ).

thf(10,axiom,
    ! [TA: $tType] :
      ( ( linordered_field @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
        ? [B: TA] : ( ord_less @ TA @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_linordered__field__no__lb) ).

thf(317,plain,
    ! [TA: $tType] :
      ( ( linordered_field @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
        ? [B: TA] : ( ord_less @ TA @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(318,plain,
    ! [TA: $tType,A: TA] :
      ( ~ ( linordered_field @ TA @ ( type2 @ TA ) )
      | ( ord_less @ TA @ ( sk4 @ TA @ A ) @ A ) ),
    inference(cnf,[status(esa)],[317]) ).

thf(13,axiom,
    ! [TA: $tType] :
      ( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ~ ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_not__less__zero) ).

thf(324,plain,
    ! [TA: $tType] :
      ( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ~ ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(325,plain,
    ! [TA: $tType,A: TA] :
      ( ~ ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
      | ~ ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ),
    inference(cnf,[status(esa)],[324]) ).

thf(2624,plain,
    ! [TA: $tType,TB: $tType,B: TB,A: TA] :
      ( ~ ( linordered_field @ TA @ ( type2 @ TA ) )
      | ~ ( canoni770627133id_add @ TB @ ( type2 @ TB ) )
      | ~ $true
      | ( ( ord_less @ TA @ ( sk4 @ TA @ A ) @ A )
       != ( ord_less @ TB @ B @ ( zero_zero @ TB ) ) ) ),
    inference(paramod_ordered,[status(thm)],[318,325]) ).

thf(2625,plain,
    ! [TA: $tType,TB: $tType,B: TB,A: TA] :
      ( ~ ( linordered_field @ TA @ ( type2 @ TA ) )
      | ~ ( canoni770627133id_add @ TB @ ( type2 @ TB ) )
      | ( ( ord_less @ TA @ ( sk4 @ TA @ A ) @ A )
       != ( ord_less @ TB @ B @ ( zero_zero @ TB ) ) ) ),
    inference(simp,[status(thm)],[2624]) ).

thf(2626,plain,
    ! [TB: $tType] :
      ( ~ ( linordered_field @ TB @ ( type2 @ TB ) )
      | ~ ( canoni770627133id_add @ TB @ ( type2 @ TB ) ) ),
    inference(pattern_uni,[status(thm)],[2625:[bind(A,$thf( zero_zero @ TB )),bind(B,$thf( sk4 @ TB @ ( zero_zero @ TB ) )),bind_type(TA,$thf( TB ))]]) ).

thf(2646,plain,
    ! [TA: $tType] :
      ( ~ ( linordered_field @ TA @ ( type2 @ TA ) )
      | ~ ( canoni770627133id_add @ TA @ ( type2 @ TA ) ) ),
    inference(simp,[status(thm)],[2626]) ).

thf(2733,plain,
    ! [TA: $tType,TB: $tType,B: TA > $o,A: TA] :
      ( ~ ( member @ TA @ A @ ( collect @ TA @ B ) )
      | ~ ( canoni770627133id_add @ TB @ ( type2 @ TB ) )
      | ( ( B @ A )
       != ( linordered_field @ TB @ ( type2 @ TB ) ) ) ),
    inference(paramod_ordered,[status(thm)],[305,2646]) ).

thf(2735,plain,
    ! [TA: $tType,TB: $tType,A: TA] :
      ( ~ ( member @ TA @ A
          @ ( collect @ TA
            @ ^ [B: TA] : ( linordered_field @ TB @ ( type2 @ TB ) ) ) )
      | ~ ( canoni770627133id_add @ TB @ ( type2 @ TB ) ) ),
    inference(pre_uni,[status(thm)],[2733:[bind(A,$thf( A )),bind(B,$thf( ^ [C: TA] : ( linordered_field @ TB @ ( type2 @ TB ) ) ))]]) ).

thf(33,axiom,
    ! [TA: $tType] :
      ( ( preorder @ TA @ ( type2 @ TA ) )
     => ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_order__refl) ).

thf(372,plain,
    ! [TA: $tType] :
      ( ( preorder @ TA @ ( type2 @ TA ) )
     => ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(6051,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType] :
      ( ~ $true
      | ( preorder @ ( TL > TM ) @ ( type2 @ ( TL > TM ) ) )
      | ( ( preorder @ ( TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) )
       != ( preorder @ TM @ ( type2 @ TM ) ) ) ),
    inference(paramod_ordered,[status(thm)],[5921,320]) ).

thf(6052,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType] :
      ( ( preorder @ ( TL > TM ) @ ( type2 @ ( TL > TM ) ) )
      | ( ( preorder @ ( TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) )
       != ( preorder @ TM @ ( type2 @ TM ) ) ) ),
    inference(simp,[status(thm)],[6051]) ).

thf(6053,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType] : ( preorder @ ( TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) ),
    inference(pattern_uni,[status(thm)],[6052:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ))]]) ).

thf(6348,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType] :
      ( ~ $true
      | ( preorder @ ( TM > TN ) @ ( type2 @ ( TM > TN ) ) )
      | ( ( preorder @ ( TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) )
       != ( preorder @ TN @ ( type2 @ TN ) ) ) ),
    inference(paramod_ordered,[status(thm)],[6053,320]) ).

thf(6349,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType] :
      ( ( preorder @ ( TM > TN ) @ ( type2 @ ( TM > TN ) ) )
      | ( ( preorder @ ( TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) )
       != ( preorder @ TN @ ( type2 @ TN ) ) ) ),
    inference(simp,[status(thm)],[6348]) ).

thf(6350,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType] : ( preorder @ ( TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) ),
    inference(pattern_uni,[status(thm)],[6349:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ))]]) ).

thf(27,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ord @ TB @ ( type2 @ TB ) )
     => ! [A: TA > TB,B: TA > TB,C: TA] :
          ( ( ord_less_eq @ ( TA > TB ) @ A @ B )
         => ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_le__funD) ).

thf(357,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ord @ TB @ ( type2 @ TB ) )
     => ! [A: TA > TB,B: TA > TB,C: TA] :
          ( ( ord_less_eq @ ( TA > TB ) @ A @ B )
         => ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(280,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( ord_less_eq @ nat @ A @ B )
     => ( ( ord_less_eq @ nat @ C @ D )
       => ( ord_less_eq @ nat @ ( times_times @ nat @ A @ C ) @ ( times_times @ nat @ B @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_mult__le__mono) ).

thf(1059,plain,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( ord_less_eq @ nat @ A @ B )
     => ( ( ord_less_eq @ nat @ C @ D )
       => ( ord_less_eq @ nat @ ( times_times @ nat @ A @ C ) @ ( times_times @ nat @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(104,axiom,
    ! [TA: $tType] :
      ( ( group_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ( plus_plus @ TA @ A @ B )
            = ( plus_plus @ TA @ A @ C ) )
          = ( B = C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_add_Oleft__cancel) ).

thf(587,plain,
    ! [TA: $tType] :
      ( ( group_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ( plus_plus @ TA @ A @ B )
            = ( plus_plus @ TA @ A @ C ) )
          = ( B = C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(200,axiom,
    ! [TA: $tType] :
      ( ( linordered_field @ TA @ ( type2 @ TA ) )
     => ( ( plus_plus @ TA )
        = ( ^ [A: TA,B: TA] : ( plus_plus @ TA @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_linordered__field__class_Osign__simps_I27_J) ).

thf(838,plain,
    ! [TA: $tType] :
      ( ( linordered_field @ TA @ ( type2 @ TA ) )
     => ( ( plus_plus @ TA )
        = ( ^ [A: TA,B: TA] : ( plus_plus @ TA @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(146,axiom,
    ! [A: nat] :
      ( ( times_times @ nat @ ( zero_zero @ nat ) @ A )
      = ( zero_zero @ nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_mult__0) ).

thf(702,plain,
    ! [A: nat] :
      ( ( times_times @ nat @ ( zero_zero @ nat ) @ A )
      = ( zero_zero @ nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(166,axiom,
    ! [TA: $tType] :
      ( ( comm_semiring @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( times_times @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
          = ( plus_plus @ TA @ ( times_times @ TA @ A @ C ) @ ( times_times @ TA @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_comm__semiring__class_Odistrib) ).

thf(751,plain,
    ! [TA: $tType] :
      ( ( comm_semiring @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( times_times @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
          = ( plus_plus @ TA @ ( times_times @ TA @ A @ C ) @ ( times_times @ TA @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(207,axiom,
    semigroup_add @ nat @ ( type2 @ nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Osemigroup__add) ).

thf(853,plain,
    semigroup_add @ nat @ ( type2 @ nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(292,axiom,
    ! [TA: $tType] :
      ( ( linordered_ring @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ ( times_times @ TA @ A @ A ) @ ( times_times @ TA @ B @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_sum__squares__ge__zero) ).

thf(1087,plain,
    ! [TA: $tType] :
      ( ( linordered_ring @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ ( times_times @ TA @ A @ A ) @ ( times_times @ TA @ B @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(1145,plain,
    ! [TA: $tType,A: TA] :
      ( ~ $true
      | ~ ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
      | ( ( canoni770627133id_add @ nat @ ( type2 @ nat ) )
       != ( canoni770627133id_add @ TA @ ( type2 @ TA ) ) ) ),
    inference(paramod_ordered,[status(thm)],[511,325]) ).

thf(1146,plain,
    ! [TA: $tType,A: TA] :
      ( ~ ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
      | ( ( canoni770627133id_add @ nat @ ( type2 @ nat ) )
       != ( canoni770627133id_add @ TA @ ( type2 @ TA ) ) ) ),
    inference(simp,[status(thm)],[1145]) ).

thf(1147,plain,
    ! [A: nat] :
      ~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
    inference(pattern_uni,[status(thm)],[1146:[bind_type(TA,$thf( nat ))]]) ).

thf(173,axiom,
    ! [TA: $tType] :
      ( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ( plus_plus @ TA @ A @ B )
            = ( zero_zero @ TA ) )
          = ( ( A
              = ( zero_zero @ TA ) )
            & ( B
              = ( zero_zero @ TA ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_add__eq__0__iff__both__eq__0) ).

thf(770,plain,
    ! [TA: $tType] :
      ( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ( plus_plus @ TA @ A @ B )
            = ( zero_zero @ TA ) )
          = ( ( A
              = ( zero_zero @ TA ) )
            & ( B
              = ( zero_zero @ TA ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(58,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ( ord_less_eq @ TA @ A @ B )
           => ~ ( ord_less_eq @ TA @ B @ C ) )
         => ( ( ( ord_less_eq @ TA @ B @ A )
             => ~ ( ord_less_eq @ TA @ A @ C ) )
           => ( ( ( ord_less_eq @ TA @ A @ C )
               => ~ ( ord_less_eq @ TA @ C @ B ) )
             => ( ( ( ord_less_eq @ TA @ C @ B )
                 => ~ ( ord_less_eq @ TA @ B @ A ) )
               => ( ( ( ord_less_eq @ TA @ B @ C )
                   => ~ ( ord_less_eq @ TA @ C @ A ) )
                 => ~ ( ( ord_less_eq @ TA @ C @ A )
                     => ~ ( ord_less_eq @ TA @ A @ B ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_le__cases3) ).

thf(448,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ( ord_less_eq @ TA @ A @ B )
           => ~ ( ord_less_eq @ TA @ B @ C ) )
         => ( ( ( ord_less_eq @ TA @ B @ A )
             => ~ ( ord_less_eq @ TA @ A @ C ) )
           => ( ( ( ord_less_eq @ TA @ A @ C )
               => ~ ( ord_less_eq @ TA @ C @ B ) )
             => ( ( ( ord_less_eq @ TA @ C @ B )
                 => ~ ( ord_less_eq @ TA @ B @ A ) )
               => ( ( ( ord_less_eq @ TA @ B @ C )
                   => ~ ( ord_less_eq @ TA @ C @ A ) )
                 => ~ ( ( ord_less_eq @ TA @ C @ A )
                     => ~ ( ord_less_eq @ TA @ A @ B ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(3176,plain,
    ! [TA: $tType,TB: $tType,B: TA > $o,A: TA] :
      ( ~ ( member @ TA @ A @ ( collect @ TA @ B ) )
      | ~ ( ord_less @ TB @ ( zero_zero @ TB ) @ ( zero_zero @ TB ) )
      | ( ( B @ A )
       != ( canoni770627133id_add @ TB @ ( type2 @ TB ) ) ) ),
    inference(paramod_ordered,[status(thm)],[305,3072]) ).

thf(3180,plain,
    ! [TA: $tType,TB: $tType,A: TA] :
      ( ~ ( member @ TA @ A
          @ ( collect @ TA
            @ ^ [B: TA] : ( canoni770627133id_add @ TB @ ( type2 @ TB ) ) ) )
      | ~ ( ord_less @ TB @ ( zero_zero @ TB ) @ ( zero_zero @ TB ) ) ),
    inference(pre_uni,[status(thm)],[3176:[bind(A,$thf( A )),bind(B,$thf( ^ [C: TA] : ( canoni770627133id_add @ TB @ ( type2 @ TB ) ) ))]]) ).

thf(50,axiom,
    ! [TA: $tType,A: TA,B: TA] :
      ( ( if @ TA @ $true @ A @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_T) ).

thf(421,plain,
    ! [TA: $tType,A: TA,B: TA] :
      ( ( if @ TA @ $true @ A @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(214,axiom,
    ! [TA: $tType] :
      ( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA,D: TA] :
          ( ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ C @ D ) )
          = ( times_times @ TA @ ( times_times @ TA @ A @ C ) @ ( times_times @ TA @ B @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_semiring__normalization__rules_I13_J) ).

thf(870,plain,
    ! [TA: $tType] :
      ( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA,D: TA] :
          ( ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ C @ D ) )
          = ( times_times @ TA @ ( times_times @ TA @ A @ C ) @ ( times_times @ TA @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(69,axiom,
    ! [TA: $tType] :
      ( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( times_times @ TA @ A @ ( times_times @ TA @ B @ C ) )
          = ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_semiring__normalization__rules_I18_J) ).

thf(492,plain,
    ! [TA: $tType] :
      ( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( times_times @ TA @ A @ ( times_times @ TA @ B @ C ) )
          = ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(25,axiom,
    ! [TA: $tType,A: TA,B: huffma16452318e_tree @ TA] :
      ( ( member @ TA @ A @ ( huffma505251170phabet @ TA @ B ) )
     => ( member @ TA @ ( huffma943100115ibling @ TA @ B @ A ) @ ( huffma505251170phabet @ TA @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_in__alphabet__imp__sibling__in__alphabet) ).

thf(353,plain,
    ! [TA: $tType,A: TA,B: huffma16452318e_tree @ TA] :
      ( ( member @ TA @ A @ ( huffma505251170phabet @ TA @ B ) )
     => ( member @ TA @ ( huffma943100115ibling @ TA @ B @ A ) @ ( huffma505251170phabet @ TA @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(193,axiom,
    ! [TA: $tType] :
      ( ( semiri1193490041visors @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ( times_times @ TA @ A @ B )
            = ( zero_zero @ TA ) )
          = ( ( A
              = ( zero_zero @ TA ) )
            | ( B
              = ( zero_zero @ TA ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_mult__eq__0__iff) ).

thf(821,plain,
    ! [TA: $tType] :
      ( ( semiri1193490041visors @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ( times_times @ TA @ A @ B )
            = ( zero_zero @ TA ) )
          = ( ( A
              = ( zero_zero @ TA ) )
            | ( B
              = ( zero_zero @ TA ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(234,axiom,
    ! [TA: $tType] :
      ( ( ordered_ring @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
         => ( ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) )
           => ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( times_times @ TA @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_mult__nonpos__nonpos) ).

thf(924,plain,
    ! [TA: $tType] :
      ( ( ordered_ring @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
         => ( ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) )
           => ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( times_times @ TA @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(273,axiom,
    ! [TA: $tType] :
      ( ( ordere779506340up_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ord_less_eq @ TA @ ( plus_plus @ TA @ C @ A ) @ ( plus_plus @ TA @ C @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_add__left__mono) ).

thf(1040,plain,
    ! [TA: $tType] :
      ( ( ordere779506340up_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ord_less_eq @ TA @ ( plus_plus @ TA @ C @ A ) @ ( plus_plus @ TA @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(123,axiom,
    comm_semiring_1 @ nat @ ( type2 @ nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Ocomm__semiring__1) ).

thf(646,plain,
    comm_semiring_1 @ nat @ ( type2 @ nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(66,axiom,
    ! [TA: $tType] :
      ( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
          = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_semiring__normalization__rules_I6_J) ).

thf(485,plain,
    ! [TA: $tType] :
      ( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
          = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(348,plain,
    ! [TA: $tType,B: TA,A: TA] :
      ( ~ ( linorder @ TA @ ( type2 @ TA ) )
      | ( ord_less_eq @ TA @ A @ B )
      | ( ord_less_eq @ TA @ B @ A ) ),
    inference(cnf,[status(esa)],[347]) ).

thf(99,axiom,
    ! [TA: $tType] :
      ( ( ordered_semiring_0 @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
         => ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B )
           => ( ord_less_eq @ TA @ ( times_times @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_mult__nonpos__nonneg) ).

thf(574,plain,
    ! [TA: $tType] :
      ( ( ordered_semiring_0 @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
         => ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B )
           => ( ord_less_eq @ TA @ ( times_times @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(6438,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType] :
      ( ~ $true
      | ( preorder @ ( TN > TO ) @ ( type2 @ ( TN > TO ) ) )
      | ( ( preorder @ ( TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) )
       != ( preorder @ TO @ ( type2 @ TO ) ) ) ),
    inference(paramod_ordered,[status(thm)],[6350,320]) ).

thf(6439,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType] :
      ( ( preorder @ ( TN > TO ) @ ( type2 @ ( TN > TO ) ) )
      | ( ( preorder @ ( TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) )
       != ( preorder @ TO @ ( type2 @ TO ) ) ) ),
    inference(simp,[status(thm)],[6438]) ).

thf(6440,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType] : ( preorder @ ( TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) ),
    inference(pattern_uni,[status(thm)],[6439:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ))]]) ).

thf(6805,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType] :
      ( ~ $true
      | ( preorder @ ( TO > TP ) @ ( type2 @ ( TO > TP ) ) )
      | ( ( preorder @ ( TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) )
       != ( preorder @ TP @ ( type2 @ TP ) ) ) ),
    inference(paramod_ordered,[status(thm)],[6440,320]) ).

thf(6806,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType] :
      ( ( preorder @ ( TO > TP ) @ ( type2 @ ( TO > TP ) ) )
      | ( ( preorder @ ( TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) )
       != ( preorder @ TP @ ( type2 @ TP ) ) ) ),
    inference(simp,[status(thm)],[6805]) ).

thf(6807,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType] : ( preorder @ ( TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) ),
    inference(pattern_uni,[status(thm)],[6806:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ))]]) ).

thf(6956,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType] :
      ( ~ $true
      | ( preorder @ ( TP > TQ ) @ ( type2 @ ( TP > TQ ) ) )
      | ( ( preorder @ ( TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) )
       != ( preorder @ TQ @ ( type2 @ TQ ) ) ) ),
    inference(paramod_ordered,[status(thm)],[6807,320]) ).

thf(6957,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType] :
      ( ( preorder @ ( TP > TQ ) @ ( type2 @ ( TP > TQ ) ) )
      | ( ( preorder @ ( TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) )
       != ( preorder @ TQ @ ( type2 @ TQ ) ) ) ),
    inference(simp,[status(thm)],[6956]) ).

thf(6958,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType] : ( preorder @ ( TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) ),
    inference(pattern_uni,[status(thm)],[6957:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ))]]) ).

thf(7230,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType] :
      ( ~ $true
      | ( preorder @ ( TQ > TR ) @ ( type2 @ ( TQ > TR ) ) )
      | ( ( preorder @ ( TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) )
       != ( preorder @ TR @ ( type2 @ TR ) ) ) ),
    inference(paramod_ordered,[status(thm)],[6958,320]) ).

thf(7231,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType] :
      ( ( preorder @ ( TQ > TR ) @ ( type2 @ ( TQ > TR ) ) )
      | ( ( preorder @ ( TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) )
       != ( preorder @ TR @ ( type2 @ TR ) ) ) ),
    inference(simp,[status(thm)],[7230]) ).

thf(7232,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType] : ( preorder @ ( TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) ),
    inference(pattern_uni,[status(thm)],[7231:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ))]]) ).

thf(8259,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType] :
      ( ~ $true
      | ( preorder @ ( TR > TS ) @ ( type2 @ ( TR > TS ) ) )
      | ( ( preorder @ ( TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) )
       != ( preorder @ TS @ ( type2 @ TS ) ) ) ),
    inference(paramod_ordered,[status(thm)],[7232,320]) ).

thf(8260,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType] :
      ( ( preorder @ ( TR > TS ) @ ( type2 @ ( TR > TS ) ) )
      | ( ( preorder @ ( TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) )
       != ( preorder @ TS @ ( type2 @ TS ) ) ) ),
    inference(simp,[status(thm)],[8259]) ).

thf(8261,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType] : ( preorder @ ( TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) ),
    inference(pattern_uni,[status(thm)],[8260:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ))]]) ).

thf(8376,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType] :
      ( ~ $true
      | ( preorder @ ( TS > TT ) @ ( type2 @ ( TS > TT ) ) )
      | ( ( preorder @ ( TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) )
       != ( preorder @ TT @ ( type2 @ TT ) ) ) ),
    inference(paramod_ordered,[status(thm)],[8261,320]) ).

thf(8377,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType] :
      ( ( preorder @ ( TS > TT ) @ ( type2 @ ( TS > TT ) ) )
      | ( ( preorder @ ( TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) )
       != ( preorder @ TT @ ( type2 @ TT ) ) ) ),
    inference(simp,[status(thm)],[8376]) ).

thf(8378,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType] : ( preorder @ ( TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) ),
    inference(pattern_uni,[status(thm)],[8377:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ))]]) ).

thf(8821,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType] :
      ( ~ $true
      | ( preorder @ ( TT > TU ) @ ( type2 @ ( TT > TU ) ) )
      | ( ( preorder @ ( TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) )
       != ( preorder @ TU @ ( type2 @ TU ) ) ) ),
    inference(paramod_ordered,[status(thm)],[8378,320]) ).

thf(8822,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType] :
      ( ( preorder @ ( TT > TU ) @ ( type2 @ ( TT > TU ) ) )
      | ( ( preorder @ ( TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) )
       != ( preorder @ TU @ ( type2 @ TU ) ) ) ),
    inference(simp,[status(thm)],[8821]) ).

thf(8823,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType] : ( preorder @ ( TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) ),
    inference(pattern_uni,[status(thm)],[8822:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ))]]) ).

thf(41,axiom,
    ! [TA: $tType,A: huffma16452318e_tree @ TA,B: nat,C: TA,D: nat,E: TA] :
      ( ( huffma1554076246height @ TA @ ( huffma2094459102Leaves @ TA @ A @ B @ C @ D @ E ) )
      = ( huffma1554076246height @ TA @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_height__swapLeaves) ).

thf(396,plain,
    ! [TA: $tType,A: huffma16452318e_tree @ TA,B: nat,C: TA,D: nat,E: TA] :
      ( ( huffma1554076246height @ TA @ ( huffma2094459102Leaves @ TA @ A @ B @ C @ D @ E ) )
      = ( huffma1554076246height @ TA @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(129,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( times_times @ nat @ ( plus_plus @ nat @ A @ B ) @ C )
      = ( plus_plus @ nat @ ( times_times @ nat @ A @ C ) @ ( times_times @ nat @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_add__mult__distrib) ).

thf(660,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( times_times @ nat @ ( plus_plus @ nat @ A @ B ) @ C )
      = ( plus_plus @ nat @ ( times_times @ nat @ A @ C ) @ ( times_times @ nat @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(1104,plain,
    ( ( ( huffma636208924e_cost @ a @ ( huffma469337550apSyms @ a @ t @ a2 @ b ) )
     != ( huffma636208924e_cost @ a @ t ) )
    | ( ( times_times @ nat @ ( huffma854352999e_freq @ a @ t @ a2 ) @ ( huffma223349076_depth @ a @ t @ b ) )
     != ( times_times @ nat @ ( huffma854352999e_freq @ a @ t @ a2 ) @ ( huffma223349076_depth @ a @ t @ a2 ) ) )
    | ( ( times_times @ nat @ ( huffma854352999e_freq @ a @ t @ b ) @ ( huffma223349076_depth @ a @ t @ b ) )
     != ( times_times @ nat @ ( huffma854352999e_freq @ a @ t @ b ) @ ( huffma223349076_depth @ a @ t @ a2 ) ) ) ),
    inference(simp,[status(thm)],[1102]) ).

thf(74,axiom,
    ordere779506340up_add @ nat @ ( type2 @ nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add) ).

thf(507,plain,
    ordere779506340up_add @ nat @ ( type2 @ nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(34,axiom,
    order @ $o @ ( type2 @ $o ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder_9) ).

thf(374,plain,
    order @ $o @ ( type2 @ $o ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(26,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( order @ TA @ ( type2 @ TA ) )
     => ( order @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oorder) ).

thf(355,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( order @ TA @ ( type2 @ TA ) )
     => ( order @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(356,plain,
    ! [TA: $tType,TB: $tType] :
      ( ~ ( order @ TB @ ( type2 @ TB ) )
      | ( order @ ( TA > TB ) @ ( type2 @ ( TA > TB ) ) ) ),
    inference(cnf,[status(esa)],[355]) ).

thf(9520,plain,
    ! [TA: $tType,TB: $tType] :
      ( ~ $true
      | ( order @ ( TA > TB ) @ ( type2 @ ( TA > TB ) ) )
      | ( ( order @ $o @ ( type2 @ $o ) )
       != ( order @ TB @ ( type2 @ TB ) ) ) ),
    inference(paramod_ordered,[status(thm)],[374,356]) ).

thf(9521,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( order @ ( TA > TB ) @ ( type2 @ ( TA > TB ) ) )
      | ( ( order @ $o @ ( type2 @ $o ) )
       != ( order @ TB @ ( type2 @ TB ) ) ) ),
    inference(simp,[status(thm)],[9520]) ).

thf(9522,plain,
    ! [TA: $tType] : ( order @ ( TA > $o ) @ ( type2 @ ( TA > $o ) ) ),
    inference(pattern_uni,[status(thm)],[9521:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( $o ))]]) ).

thf(9713,plain,
    ! [TA: $tType,TB: $tType,TC: $tType] :
      ( ~ $true
      | ( order @ ( TB > TC ) @ ( type2 @ ( TB > TC ) ) )
      | ( ( order @ ( TA > $o ) @ ( type2 @ ( TA > $o ) ) )
       != ( order @ TC @ ( type2 @ TC ) ) ) ),
    inference(paramod_ordered,[status(thm)],[9522,356]) ).

thf(9714,plain,
    ! [TA: $tType,TB: $tType,TC: $tType] :
      ( ( order @ ( TB > TC ) @ ( type2 @ ( TB > TC ) ) )
      | ( ( order @ ( TA > $o ) @ ( type2 @ ( TA > $o ) ) )
       != ( order @ TC @ ( type2 @ TC ) ) ) ),
    inference(simp,[status(thm)],[9713]) ).

thf(9715,plain,
    ! [TA: $tType,TB: $tType] : ( order @ ( TB > TA > $o ) @ ( type2 @ ( TB > TA > $o ) ) ),
    inference(pattern_uni,[status(thm)],[9714:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TA > $o ))]]) ).

thf(11142,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] :
      ( ~ $true
      | ( order @ ( TC > TD ) @ ( type2 @ ( TC > TD ) ) )
      | ( ( order @ ( TB > TA > $o ) @ ( type2 @ ( TB > TA > $o ) ) )
       != ( order @ TD @ ( type2 @ TD ) ) ) ),
    inference(paramod_ordered,[status(thm)],[9715,356]) ).

thf(11143,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] :
      ( ( order @ ( TC > TD ) @ ( type2 @ ( TC > TD ) ) )
      | ( ( order @ ( TB > TA > $o ) @ ( type2 @ ( TB > TA > $o ) ) )
       != ( order @ TD @ ( type2 @ TD ) ) ) ),
    inference(simp,[status(thm)],[11142]) ).

thf(11144,plain,
    ! [TA: $tType,TB: $tType,TC: $tType] : ( order @ ( TC > TB > TA > $o ) @ ( type2 @ ( TC > TB > TA > $o ) ) ),
    inference(pattern_uni,[status(thm)],[11143:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TB > TA > $o ))]]) ).

thf(12088,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType] :
      ( ~ $true
      | ( order @ ( TD > TE ) @ ( type2 @ ( TD > TE ) ) )
      | ( ( order @ ( TC > TB > TA > $o ) @ ( type2 @ ( TC > TB > TA > $o ) ) )
       != ( order @ TE @ ( type2 @ TE ) ) ) ),
    inference(paramod_ordered,[status(thm)],[11144,356]) ).

thf(12089,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType] :
      ( ( order @ ( TD > TE ) @ ( type2 @ ( TD > TE ) ) )
      | ( ( order @ ( TC > TB > TA > $o ) @ ( type2 @ ( TC > TB > TA > $o ) ) )
       != ( order @ TE @ ( type2 @ TE ) ) ) ),
    inference(simp,[status(thm)],[12088]) ).

thf(12090,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] : ( order @ ( TD > TC > TB > TA > $o ) @ ( type2 @ ( TD > TC > TB > TA > $o ) ) ),
    inference(pattern_uni,[status(thm)],[12089:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TC > TB > TA > $o ))]]) ).

thf(255,axiom,
    ! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA,C: TA,D: nat,E: nat] :
      ( ( huffma1050891809istent @ TA @ A )
     => ( ( B != C )
       => ( ( ( member @ TA @ B @ ( huffma505251170phabet @ TA @ A ) )
           => ( ( ( member @ TA @ C @ ( huffma505251170phabet @ TA @ A ) )
               => ( ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma636208924e_cost @ TA @ ( huffma2094459102Leaves @ TA @ A @ D @ B @ E @ C ) ) @ ( times_times @ nat @ ( huffma854352999e_freq @ TA @ A @ B ) @ ( huffma223349076_depth @ TA @ A @ B ) ) ) @ ( times_times @ nat @ ( huffma854352999e_freq @ TA @ A @ C ) @ ( huffma223349076_depth @ TA @ A @ C ) ) )
                  = ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma636208924e_cost @ TA @ A ) @ ( times_times @ nat @ D @ ( huffma223349076_depth @ TA @ A @ C ) ) ) @ ( times_times @ nat @ E @ ( huffma223349076_depth @ TA @ A @ B ) ) ) ) )
              & ( ~ ( member @ TA @ C @ ( huffma505251170phabet @ TA @ A ) )
               => ( ( plus_plus @ nat @ ( huffma636208924e_cost @ TA @ ( huffma2094459102Leaves @ TA @ A @ D @ B @ E @ C ) ) @ ( times_times @ nat @ ( huffma854352999e_freq @ TA @ A @ B ) @ ( huffma223349076_depth @ TA @ A @ B ) ) )
                  = ( plus_plus @ nat @ ( huffma636208924e_cost @ TA @ A ) @ ( times_times @ nat @ E @ ( huffma223349076_depth @ TA @ A @ B ) ) ) ) ) ) )
          & ( ~ ( member @ TA @ B @ ( huffma505251170phabet @ TA @ A ) )
           => ( ( ( member @ TA @ C @ ( huffma505251170phabet @ TA @ A ) )
               => ( ( plus_plus @ nat @ ( huffma636208924e_cost @ TA @ ( huffma2094459102Leaves @ TA @ A @ D @ B @ E @ C ) ) @ ( times_times @ nat @ ( huffma854352999e_freq @ TA @ A @ C ) @ ( huffma223349076_depth @ TA @ A @ C ) ) )
                  = ( plus_plus @ nat @ ( huffma636208924e_cost @ TA @ A ) @ ( times_times @ nat @ D @ ( huffma223349076_depth @ TA @ A @ C ) ) ) ) )
              & ( ~ ( member @ TA @ C @ ( huffma505251170phabet @ TA @ A ) )
               => ( ( huffma636208924e_cost @ TA @ ( huffma2094459102Leaves @ TA @ A @ D @ B @ E @ C ) )
                  = ( huffma636208924e_cost @ TA @ A ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_cost__swapLeaves) ).

thf(981,plain,
    ! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA,C: TA,D: nat,E: nat] :
      ( ( huffma1050891809istent @ TA @ A )
     => ( ( B != C )
       => ( ( ( member @ TA @ B @ ( huffma505251170phabet @ TA @ A ) )
           => ( ( ( member @ TA @ C @ ( huffma505251170phabet @ TA @ A ) )
               => ( ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma636208924e_cost @ TA @ ( huffma2094459102Leaves @ TA @ A @ D @ B @ E @ C ) ) @ ( times_times @ nat @ ( huffma854352999e_freq @ TA @ A @ B ) @ ( huffma223349076_depth @ TA @ A @ B ) ) ) @ ( times_times @ nat @ ( huffma854352999e_freq @ TA @ A @ C ) @ ( huffma223349076_depth @ TA @ A @ C ) ) )
                  = ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma636208924e_cost @ TA @ A ) @ ( times_times @ nat @ D @ ( huffma223349076_depth @ TA @ A @ C ) ) ) @ ( times_times @ nat @ E @ ( huffma223349076_depth @ TA @ A @ B ) ) ) ) )
              & ( ~ ( member @ TA @ C @ ( huffma505251170phabet @ TA @ A ) )
               => ( ( plus_plus @ nat @ ( huffma636208924e_cost @ TA @ ( huffma2094459102Leaves @ TA @ A @ D @ B @ E @ C ) ) @ ( times_times @ nat @ ( huffma854352999e_freq @ TA @ A @ B ) @ ( huffma223349076_depth @ TA @ A @ B ) ) )
                  = ( plus_plus @ nat @ ( huffma636208924e_cost @ TA @ A ) @ ( times_times @ nat @ E @ ( huffma223349076_depth @ TA @ A @ B ) ) ) ) ) ) )
          & ( ~ ( member @ TA @ B @ ( huffma505251170phabet @ TA @ A ) )
           => ( ( ( member @ TA @ C @ ( huffma505251170phabet @ TA @ A ) )
               => ( ( plus_plus @ nat @ ( huffma636208924e_cost @ TA @ ( huffma2094459102Leaves @ TA @ A @ D @ B @ E @ C ) ) @ ( times_times @ nat @ ( huffma854352999e_freq @ TA @ A @ C ) @ ( huffma223349076_depth @ TA @ A @ C ) ) )
                  = ( plus_plus @ nat @ ( huffma636208924e_cost @ TA @ A ) @ ( times_times @ nat @ D @ ( huffma223349076_depth @ TA @ A @ C ) ) ) ) )
              & ( ~ ( member @ TA @ C @ ( huffma505251170phabet @ TA @ A ) )
               => ( ( huffma636208924e_cost @ TA @ ( huffma2094459102Leaves @ TA @ A @ D @ B @ E @ C ) )
                  = ( huffma636208924e_cost @ TA @ A ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(171,axiom,
    member @ a @ a2 @ ( huffma505251170phabet @ a @ t ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_assms_I2_J) ).

thf(766,plain,
    member @ a @ a2 @ ( huffma505251170phabet @ a @ t ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(119,axiom,
    ! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA] :
      ( ( ( huffma1554076246height @ TA @ A )
        = ( zero_zero @ nat ) )
     => ( ( huffma943100115ibling @ TA @ A @ B )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_height__0__imp__sibling__id) ).

thf(634,plain,
    ! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA] :
      ( ( ( huffma1554076246height @ TA @ A )
        = ( zero_zero @ nat ) )
     => ( ( huffma943100115ibling @ TA @ A @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(8975,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType] :
      ( ~ $true
      | ( preorder @ ( TU > TV ) @ ( type2 @ ( TU > TV ) ) )
      | ( ( preorder @ ( TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) )
       != ( preorder @ TV @ ( type2 @ TV ) ) ) ),
    inference(paramod_ordered,[status(thm)],[8823,320]) ).

thf(8976,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType] :
      ( ( preorder @ ( TU > TV ) @ ( type2 @ ( TU > TV ) ) )
      | ( ( preorder @ ( TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) )
       != ( preorder @ TV @ ( type2 @ TV ) ) ) ),
    inference(simp,[status(thm)],[8975]) ).

thf(8977,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType] : ( preorder @ ( TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) ),
    inference(pattern_uni,[status(thm)],[8976:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ))]]) ).

thf(217,axiom,
    ! [TA: $tType] :
      ( ( linordered_field @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( times_times @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
          = ( plus_plus @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_linordered__field__class_Osign__simps_I36_J) ).

thf(877,plain,
    ! [TA: $tType] :
      ( ( linordered_field @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( times_times @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
          = ( plus_plus @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(142,axiom,
    ! [TA: $tType] :
      ( ( ordere236663937imp_le @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
          = ( ord_less_eq @ TA @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_add__le__cancel__left) ).

thf(692,plain,
    ! [TA: $tType] :
      ( ( ordere236663937imp_le @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
          = ( ord_less_eq @ TA @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(9185,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType] :
      ( ~ $true
      | ( preorder @ ( TV > TW ) @ ( type2 @ ( TV > TW ) ) )
      | ( ( preorder @ ( TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) )
       != ( preorder @ TW @ ( type2 @ TW ) ) ) ),
    inference(paramod_ordered,[status(thm)],[8977,320]) ).

thf(9186,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType] :
      ( ( preorder @ ( TV > TW ) @ ( type2 @ ( TV > TW ) ) )
      | ( ( preorder @ ( TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) )
       != ( preorder @ TW @ ( type2 @ TW ) ) ) ),
    inference(simp,[status(thm)],[9185]) ).

thf(9187,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType] : ( preorder @ ( TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) ),
    inference(pattern_uni,[status(thm)],[9186:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ))]]) ).

thf(259,axiom,
    ! [TA: $tType] :
      ( ( monoid_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
          = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_add_Oright__neutral) ).

thf(998,plain,
    ! [TA: $tType] :
      ( ( monoid_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
          = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(83,axiom,
    ! [TA: $tType] :
      ( ( cancel_semigroup_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ( plus_plus @ TA @ A @ B )
            = ( plus_plus @ TA @ A @ C ) )
          = ( B = C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_add__left__cancel) ).

thf(527,plain,
    ! [TA: $tType] :
      ( ( cancel_semigroup_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ( plus_plus @ TA @ A @ B )
            = ( plus_plus @ TA @ A @ C ) )
          = ( B = C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(8,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( order @ TA @ ( type2 @ TA ) )
        & ( order @ TB @ ( type2 @ TB ) ) )
     => ! [A: TB,B: TA > TB,C: TA,D: TA] :
          ( ( ord_less_eq @ TB @ A @ ( B @ C ) )
         => ( ( ord_less_eq @ TA @ C @ D )
           => ( ! [E: TA,F: TA] :
                  ( ( ord_less_eq @ TA @ E @ F )
                 => ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
             => ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_order__subst1) ).

thf(310,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( order @ TA @ ( type2 @ TA ) )
        & ( order @ TB @ ( type2 @ TB ) ) )
     => ! [A: TB,B: TA > TB,C: TA,D: TA] :
          ( ( ord_less_eq @ TB @ A @ ( B @ C ) )
         => ( ( ord_less_eq @ TA @ C @ D )
           => ( ! [E: TA,F: TA] :
                  ( ( ord_less_eq @ TA @ E @ F )
                 => ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
             => ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(311,plain,
    ! [TA: $tType,TB: $tType,D: TB,C: TB,B: TB > TA,A: TA] :
      ( ( ~ ( order @ TB @ ( type2 @ TB ) )
        | ~ ( order @ TA @ ( type2 @ TA ) )
        | ~ ( ord_less_eq @ TA @ A @ ( B @ C ) )
        | ~ ( ord_less_eq @ TB @ C @ D )
        | ( ord_less_eq @ TB @ ( sk2 @ TB @ TA @ D @ C @ B @ A ) @ ( sk3 @ TB @ TA @ D @ C @ B @ A ) )
        | ( ord_less_eq @ TA @ A @ ( B @ D ) ) )
      & ( ~ ( order @ TB @ ( type2 @ TB ) )
        | ~ ( order @ TA @ ( type2 @ TA ) )
        | ~ ( ord_less_eq @ TA @ A @ ( B @ C ) )
        | ~ ( ord_less_eq @ TB @ C @ D )
        | ~ ( ord_less_eq @ TA @ ( B @ ( sk2 @ TB @ TA @ D @ C @ B @ A ) ) @ ( B @ ( sk3 @ TB @ TA @ D @ C @ B @ A ) ) )
        | ( ord_less_eq @ TA @ A @ ( B @ D ) ) ) ),
    inference(cnf,[status(esa)],[310]) ).

thf(312,plain,
    ! [TA: $tType,TB: $tType,D: TB,C: TB,B: TB > TA,A: TA] :
      ( ~ ( order @ TB @ ( type2 @ TB ) )
      | ~ ( order @ TA @ ( type2 @ TA ) )
      | ~ ( ord_less_eq @ TA @ A @ ( B @ C ) )
      | ~ ( ord_less_eq @ TB @ C @ D )
      | ( ord_less_eq @ TB @ ( sk2 @ TB @ TA @ D @ C @ B @ A ) @ ( sk3 @ TB @ TA @ D @ C @ B @ A ) )
      | ( ord_less_eq @ TA @ A @ ( B @ D ) ) ),
    inference(cnfConj,[status(thm)],[311]) ).

thf(6,axiom,
    ! [TA: $tType,A: huffma16452318e_tree @ TA,B: nat,C: TA,D: nat,E: TA] :
      ( ( huffma1050891809istent @ TA @ A )
     => ( huffma1050891809istent @ TA @ ( huffma2094459102Leaves @ TA @ A @ B @ C @ D @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_consistent__swapLeaves) ).

thf(306,plain,
    ! [TA: $tType,A: huffma16452318e_tree @ TA,B: nat,C: TA,D: nat,E: TA] :
      ( ( huffma1050891809istent @ TA @ A )
     => ( huffma1050891809istent @ TA @ ( huffma2094459102Leaves @ TA @ A @ B @ C @ D @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(307,plain,
    ! [TA: $tType,E: TA,D: nat,C: TA,B: nat,A: huffma16452318e_tree @ TA] :
      ( ~ ( huffma1050891809istent @ TA @ A )
      | ( huffma1050891809istent @ TA @ ( huffma2094459102Leaves @ TA @ A @ B @ C @ D @ E ) ) ),
    inference(cnf,[status(esa)],[306]) ).

thf(136,axiom,
    ! [TA: $tType] :
      ( ( linord219039673up_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ A ) @ ( zero_zero @ TA ) )
          = ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_double__add__le__zero__iff__single__add__le__zero) ).

thf(678,plain,
    ! [TA: $tType] :
      ( ( linord219039673up_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ A ) @ ( zero_zero @ TA ) )
          = ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(181,axiom,
    ! [TA: $tType] :
      ( ( semiri1923998003cancel @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ( times_times @ TA @ A @ B )
            = ( times_times @ TA @ C @ B ) )
          = ( ( B
              = ( zero_zero @ TA ) )
            | ( A = C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_mult__cancel__right) ).

thf(793,plain,
    ! [TA: $tType] :
      ( ( semiri1923998003cancel @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ( times_times @ TA @ A @ B )
            = ( times_times @ TA @ C @ B ) )
          = ( ( B
              = ( zero_zero @ TA ) )
            | ( A = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(189,axiom,
    ! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA] :
      ( ( huffma1050891809istent @ TA @ A )
     => ( ( huffma223349076_depth @ TA @ A @ ( huffma943100115ibling @ TA @ A @ B ) )
        = ( huffma223349076_depth @ TA @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_depth__sibling) ).

thf(810,plain,
    ! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA] :
      ( ( huffma1050891809istent @ TA @ A )
     => ( ( huffma223349076_depth @ TA @ A @ ( huffma943100115ibling @ TA @ A @ B ) )
        = ( huffma223349076_depth @ TA @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(37,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ TA ) )
     => ! [A: TA > TA > $o,B: TA,C: TA] :
          ( ! [D: TA,E: TA] :
              ( ( ord_less_eq @ TA @ D @ E )
             => ( A @ D @ E ) )
         => ( ! [D: TA,E: TA] :
                ( ( A @ E @ D )
               => ( A @ D @ E ) )
           => ( A @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_linorder__wlog) ).

thf(381,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ TA ) )
     => ! [A: TA > TA > $o,B: TA,C: TA] :
          ( ! [D: TA,E: TA] :
              ( ( ord_less_eq @ TA @ D @ E )
             => ( A @ D @ E ) )
         => ( ! [D: TA,E: TA] :
                ( ( A @ E @ D )
               => ( A @ D @ E ) )
           => ( A @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(12487,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType] :
      ( ~ $true
      | ( order @ ( TE > TF ) @ ( type2 @ ( TE > TF ) ) )
      | ( ( order @ ( TD > TC > TB > TA > $o ) @ ( type2 @ ( TD > TC > TB > TA > $o ) ) )
       != ( order @ TF @ ( type2 @ TF ) ) ) ),
    inference(paramod_ordered,[status(thm)],[12090,356]) ).

thf(12488,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType] :
      ( ( order @ ( TE > TF ) @ ( type2 @ ( TE > TF ) ) )
      | ( ( order @ ( TD > TC > TB > TA > $o ) @ ( type2 @ ( TD > TC > TB > TA > $o ) ) )
       != ( order @ TF @ ( type2 @ TF ) ) ) ),
    inference(simp,[status(thm)],[12487]) ).

thf(12489,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType] : ( order @ ( TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TE > TD > TC > TB > TA > $o ) ) ),
    inference(pattern_uni,[status(thm)],[12488:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TD > TC > TB > TA > $o ))]]) ).

thf(283,axiom,
    ordere216010020id_add @ nat @ ( type2 @ nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__comm__monoid__add) ).

thf(1067,plain,
    ordere216010020id_add @ nat @ ( type2 @ nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(77,axiom,
    ! [TA: $tType] :
      ( ( ordere516151231imp_le @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ ( plus_plus @ TA @ A @ B ) )
          = ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_le__add__same__cancel1) ).

thf(512,plain,
    ! [TA: $tType] :
      ( ( ordere516151231imp_le @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ ( plus_plus @ TA @ A @ B ) )
          = ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(54,axiom,
    ! [TA: $tType] :
      ( ( linordered_field @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
        ? [B: TA] : ( ord_less @ TA @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_linordered__field__no__ub) ).

thf(439,plain,
    ! [TA: $tType] :
      ( ( linordered_field @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
        ? [B: TA] : ( ord_less @ TA @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(223,axiom,
    ! [TA: $tType] :
      ( ( semiri456707255roduct @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA,D: TA] :
          ( ( ( plus_plus @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ C @ D ) )
            = ( plus_plus @ TA @ ( times_times @ TA @ A @ D ) @ ( times_times @ TA @ C @ B ) ) )
          = ( ( A = C )
            | ( B = D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_crossproduct__eq) ).

thf(894,plain,
    ! [TA: $tType] :
      ( ( semiri456707255roduct @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA,D: TA] :
          ( ( ( plus_plus @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ C @ D ) )
            = ( plus_plus @ TA @ ( times_times @ TA @ A @ D ) @ ( times_times @ TA @ C @ B ) ) )
          = ( ( A = C )
            | ( B = D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(274,axiom,
    ! [TA: $tType,A: huffma16452318e_tree @ TA] :
      ( ( ( huffma1554076246height @ TA @ A )
        = ( zero_zero @ nat ) )
     => ( ( huffma636208924e_cost @ TA @ A )
        = ( zero_zero @ nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_height__0__imp__cost__0) ).

thf(1042,plain,
    ! [TA: $tType,A: huffma16452318e_tree @ TA] :
      ( ( ( huffma1554076246height @ TA @ A )
        = ( zero_zero @ nat ) )
     => ( ( huffma636208924e_cost @ TA @ A )
        = ( zero_zero @ nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(4,axiom,
    ! [A: $o] :
      ( ( A = $true )
      | ( A = $false ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_3_1_T) ).

thf(302,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(23,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ord @ TB @ ( type2 @ TB ) )
     => ! [A: TA > TB,B: TA > TB] :
          ( ! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) )
         => ( ord_less_eq @ ( TA > TB ) @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_le__funI) ).

thf(349,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ord @ TB @ ( type2 @ TB ) )
     => ! [A: TA > TB,B: TA > TB] :
          ( ! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) )
         => ( ord_less_eq @ ( TA > TB ) @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(9583,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType] :
      ( ~ $true
      | ( preorder @ ( TW > TX ) @ ( type2 @ ( TW > TX ) ) )
      | ( ( preorder @ ( TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) )
       != ( preorder @ TX @ ( type2 @ TX ) ) ) ),
    inference(paramod_ordered,[status(thm)],[9187,320]) ).

thf(9584,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType] :
      ( ( preorder @ ( TW > TX ) @ ( type2 @ ( TW > TX ) ) )
      | ( ( preorder @ ( TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) )
       != ( preorder @ TX @ ( type2 @ TX ) ) ) ),
    inference(simp,[status(thm)],[9583]) ).

thf(9585,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType] : ( preorder @ ( TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) ),
    inference(pattern_uni,[status(thm)],[9584:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ))]]) ).

thf(10992,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType] :
      ( ~ $true
      | ( preorder @ ( TX > TY ) @ ( type2 @ ( TX > TY ) ) )
      | ( ( preorder @ ( TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) )
       != ( preorder @ TY @ ( type2 @ TY ) ) ) ),
    inference(paramod_ordered,[status(thm)],[9585,320]) ).

thf(10993,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType] :
      ( ( preorder @ ( TX > TY ) @ ( type2 @ ( TX > TY ) ) )
      | ( ( preorder @ ( TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) )
       != ( preorder @ TY @ ( type2 @ TY ) ) ) ),
    inference(simp,[status(thm)],[10992]) ).

thf(10994,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType] : ( preorder @ ( TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) ),
    inference(pattern_uni,[status(thm)],[10993:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ))]]) ).

thf(11644,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType] :
      ( ~ $true
      | ( preorder @ ( TY > TZ ) @ ( type2 @ ( TY > TZ ) ) )
      | ( ( preorder @ ( TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) )
       != ( preorder @ TZ @ ( type2 @ TZ ) ) ) ),
    inference(paramod_ordered,[status(thm)],[10994,320]) ).

thf(11645,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType] :
      ( ( preorder @ ( TY > TZ ) @ ( type2 @ ( TY > TZ ) ) )
      | ( ( preorder @ ( TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) )
       != ( preorder @ TZ @ ( type2 @ TZ ) ) ) ),
    inference(simp,[status(thm)],[11644]) ).

thf(11646,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType] : ( preorder @ ( TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) ),
    inference(pattern_uni,[status(thm)],[11645:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ))]]) ).

thf(12334,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType] :
      ( ~ $true
      | ( preorder @ ( TZ > TZA ) @ ( type2 @ ( TZ > TZA ) ) )
      | ( ( preorder @ ( TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) )
       != ( preorder @ TZA @ ( type2 @ TZA ) ) ) ),
    inference(paramod_ordered,[status(thm)],[11646,320]) ).

thf(12335,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType] :
      ( ( preorder @ ( TZ > TZA ) @ ( type2 @ ( TZ > TZA ) ) )
      | ( ( preorder @ ( TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) )
       != ( preorder @ TZA @ ( type2 @ TZA ) ) ) ),
    inference(simp,[status(thm)],[12334]) ).

thf(12336,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType] : ( preorder @ ( TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) ),
    inference(pattern_uni,[status(thm)],[12335:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ))]]) ).

thf(12735,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType] :
      ( ~ $true
      | ( preorder @ ( TZA > TZB ) @ ( type2 @ ( TZA > TZB ) ) )
      | ( ( preorder @ ( TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) )
       != ( preorder @ TZB @ ( type2 @ TZB ) ) ) ),
    inference(paramod_ordered,[status(thm)],[12336,320]) ).

thf(12736,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType] :
      ( ( preorder @ ( TZA > TZB ) @ ( type2 @ ( TZA > TZB ) ) )
      | ( ( preorder @ ( TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) )
       != ( preorder @ TZB @ ( type2 @ TZB ) ) ) ),
    inference(simp,[status(thm)],[12735]) ).

thf(12737,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType] : ( preorder @ ( TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) ),
    inference(pattern_uni,[status(thm)],[12736:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ))]]) ).

thf(51,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( ord @ TA @ ( type2 @ TA ) )
        & ( ord @ TB @ ( type2 @ TB ) ) )
     => ! [A: TB,B: TB,C: TB > TA,D: TA] :
          ( ( ord_less_eq @ TB @ A @ B )
         => ( ( ( C @ B )
              = D )
           => ( ! [E: TB,F: TB] :
                  ( ( ord_less_eq @ TB @ E @ F )
                 => ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
             => ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_ord__le__eq__subst) ).

thf(424,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( ord @ TA @ ( type2 @ TA ) )
        & ( ord @ TB @ ( type2 @ TB ) ) )
     => ! [A: TB,B: TB,C: TB > TA,D: TA] :
          ( ( ord_less_eq @ TB @ A @ B )
         => ( ( ( C @ B )
              = D )
           => ( ! [E: TB,F: TB] :
                  ( ( ord_less_eq @ TB @ E @ F )
                 => ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
             => ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(117,axiom,
    ! [TA: $tType] :
      ( ( ab_semigroup_mult @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ C )
          = ( times_times @ TA @ A @ ( times_times @ TA @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_ab__semigroup__mult__class_Omult__ac_I1_J) ).

thf(630,plain,
    ! [TA: $tType] :
      ( ( ab_semigroup_mult @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ C )
          = ( times_times @ TA @ A @ ( times_times @ TA @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(405,plain,
    ! [TA: $tType] : ( ord @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
    inference(cnf,[status(esa)],[404]) ).

thf(2380,plain,
    ! [TA: $tType,TB: $tType,TC: $tType] :
      ( ( ( ord_less_eq @ ( TC > TB ) )
        = ( ^ [A: TC > TB,B: TC > TB] :
            ! [C: TC] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) )
      | ~ $true
      | ( ( ord @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) )
       != ( ord @ TB @ ( type2 @ TB ) ) ) ),
    inference(paramod_ordered,[status(thm)],[405,316]) ).

thf(2381,plain,
    ! [TA: $tType,TB: $tType,TC: $tType] :
      ( ( ( ord_less_eq @ ( TC > TB ) )
        = ( ^ [A: TC > TB,B: TC > TB] :
            ! [C: TC] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) )
      | ( ( ord @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) )
       != ( ord @ TB @ ( type2 @ TB ) ) ) ),
    inference(simp,[status(thm)],[2380]) ).

thf(2382,plain,
    ! [TA: $tType,TC: $tType] :
      ( ( ord_less_eq @ ( TC > ( set @ TA ) ) )
      = ( ^ [A: TC > ( set @ TA ),B: TC > ( set @ TA )] :
          ! [C: TC] : ( ord_less_eq @ ( set @ TA ) @ ( A @ C ) @ ( B @ C ) ) ) ),
    inference(pattern_uni,[status(thm)],[2381:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( set @ TA ))]]) ).

thf(2396,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ord_less_eq @ ( TB > ( set @ TA ) ) )
      = ( ^ [A: TB > ( set @ TA ),B: TB > ( set @ TA )] :
          ! [C: TB] : ( ord_less_eq @ ( set @ TA ) @ ( A @ C ) @ ( B @ C ) ) ) ),
    inference(simp,[status(thm)],[2382]) ).

thf(94,axiom,
    ! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA] :
      ( ( huffma1050891809istent @ TA @ A )
     => ( ( huffma469337550apSyms @ TA @ A @ B @ B )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_swapSyms__id) ).

thf(561,plain,
    ! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA] :
      ( ( huffma1050891809istent @ TA @ A )
     => ( ( huffma469337550apSyms @ TA @ A @ B @ B )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(140,axiom,
    order @ nat @ ( type2 @ nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Oorder_2) ).

thf(688,plain,
    order @ nat @ ( type2 @ nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(9526,plain,
    ! [TA: $tType,TB: $tType] :
      ( ~ $true
      | ( order @ ( TA > TB ) @ ( type2 @ ( TA > TB ) ) )
      | ( ( order @ nat @ ( type2 @ nat ) )
       != ( order @ TB @ ( type2 @ TB ) ) ) ),
    inference(paramod_ordered,[status(thm)],[688,356]) ).

thf(9527,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( order @ ( TA > TB ) @ ( type2 @ ( TA > TB ) ) )
      | ( ( order @ nat @ ( type2 @ nat ) )
       != ( order @ TB @ ( type2 @ TB ) ) ) ),
    inference(simp,[status(thm)],[9526]) ).

thf(9528,plain,
    ! [TA: $tType] : ( order @ ( TA > nat ) @ ( type2 @ ( TA > nat ) ) ),
    inference(pattern_uni,[status(thm)],[9527:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( nat ))]]) ).

thf(9791,plain,
    ! [TA: $tType,TB: $tType,TC: $tType] :
      ( ~ $true
      | ( order @ ( TB > TC ) @ ( type2 @ ( TB > TC ) ) )
      | ( ( order @ ( TA > nat ) @ ( type2 @ ( TA > nat ) ) )
       != ( order @ TC @ ( type2 @ TC ) ) ) ),
    inference(paramod_ordered,[status(thm)],[9528,356]) ).

thf(9792,plain,
    ! [TA: $tType,TB: $tType,TC: $tType] :
      ( ( order @ ( TB > TC ) @ ( type2 @ ( TB > TC ) ) )
      | ( ( order @ ( TA > nat ) @ ( type2 @ ( TA > nat ) ) )
       != ( order @ TC @ ( type2 @ TC ) ) ) ),
    inference(simp,[status(thm)],[9791]) ).

thf(9793,plain,
    ! [TA: $tType,TB: $tType] : ( order @ ( TB > TA > nat ) @ ( type2 @ ( TB > TA > nat ) ) ),
    inference(pattern_uni,[status(thm)],[9792:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TA > nat ))]]) ).

thf(11487,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] :
      ( ~ $true
      | ( order @ ( TC > TD ) @ ( type2 @ ( TC > TD ) ) )
      | ( ( order @ ( TB > TA > nat ) @ ( type2 @ ( TB > TA > nat ) ) )
       != ( order @ TD @ ( type2 @ TD ) ) ) ),
    inference(paramod_ordered,[status(thm)],[9793,356]) ).

thf(11488,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] :
      ( ( order @ ( TC > TD ) @ ( type2 @ ( TC > TD ) ) )
      | ( ( order @ ( TB > TA > nat ) @ ( type2 @ ( TB > TA > nat ) ) )
       != ( order @ TD @ ( type2 @ TD ) ) ) ),
    inference(simp,[status(thm)],[11487]) ).

thf(11489,plain,
    ! [TA: $tType,TB: $tType,TC: $tType] : ( order @ ( TC > TB > TA > nat ) @ ( type2 @ ( TC > TB > TA > nat ) ) ),
    inference(pattern_uni,[status(thm)],[11488:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TB > TA > nat ))]]) ).

thf(12175,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType] :
      ( ~ $true
      | ( order @ ( TD > TE ) @ ( type2 @ ( TD > TE ) ) )
      | ( ( order @ ( TC > TB > TA > nat ) @ ( type2 @ ( TC > TB > TA > nat ) ) )
       != ( order @ TE @ ( type2 @ TE ) ) ) ),
    inference(paramod_ordered,[status(thm)],[11489,356]) ).

thf(12176,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType] :
      ( ( order @ ( TD > TE ) @ ( type2 @ ( TD > TE ) ) )
      | ( ( order @ ( TC > TB > TA > nat ) @ ( type2 @ ( TC > TB > TA > nat ) ) )
       != ( order @ TE @ ( type2 @ TE ) ) ) ),
    inference(simp,[status(thm)],[12175]) ).

thf(12177,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] : ( order @ ( TD > TC > TB > TA > nat ) @ ( type2 @ ( TD > TC > TB > TA > nat ) ) ),
    inference(pattern_uni,[status(thm)],[12176:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TC > TB > TA > nat ))]]) ).

thf(12574,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType] :
      ( ~ $true
      | ( order @ ( TE > TF ) @ ( type2 @ ( TE > TF ) ) )
      | ( ( order @ ( TD > TC > TB > TA > nat ) @ ( type2 @ ( TD > TC > TB > TA > nat ) ) )
       != ( order @ TF @ ( type2 @ TF ) ) ) ),
    inference(paramod_ordered,[status(thm)],[12177,356]) ).

thf(12575,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType] :
      ( ( order @ ( TE > TF ) @ ( type2 @ ( TE > TF ) ) )
      | ( ( order @ ( TD > TC > TB > TA > nat ) @ ( type2 @ ( TD > TC > TB > TA > nat ) ) )
       != ( order @ TF @ ( type2 @ TF ) ) ) ),
    inference(simp,[status(thm)],[12574]) ).

thf(12576,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType] : ( order @ ( TE > TD > TC > TB > TA > nat ) @ ( type2 @ ( TE > TD > TC > TB > TA > nat ) ) ),
    inference(pattern_uni,[status(thm)],[12575:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TD > TC > TB > TA > nat ))]]) ).

thf(358,plain,
    ! [TA: $tType,TB: $tType,C: TB,B: TB > TA,A: TB > TA] :
      ( ~ ( ord @ TA @ ( type2 @ TA ) )
      | ~ ( ord_less_eq @ ( TB > TA ) @ A @ B )
      | ( ord_less_eq @ TA @ ( A @ C ) @ ( B @ C ) ) ),
    inference(cnf,[status(esa)],[357]) ).

thf(10028,plain,
    ! [TA: $tType,TB: $tType,C: TB,B: TB > TA,A: TB > TA] :
      ( ~ ( ord @ TA @ ( type2 @ TA ) )
      | ~ ( ord_less_eq @ ( TB > TA ) @ A @ B )
      | ~ ( order @ a @ ( type2 @ a ) )
      | ~ ( ord_less_eq @ a @ a2 @ b )
      | ~ $true
      | ( ( huffma469337550apSyms @ a @ t @ a2 @ b )
       != t )
      | ( ( ord_less_eq @ TA @ ( A @ C ) @ ( B @ C ) )
       != ( ord_less_eq @ a @ b @ a2 ) ) ),
    inference(paramod_ordered,[status(thm)],[358,4943]) ).

thf(10029,plain,
    ! [TA: $tType,TB: $tType,C: TB,B: TB > TA,A: TB > TA] :
      ( ~ ( ord @ TA @ ( type2 @ TA ) )
      | ~ ( ord_less_eq @ ( TB > TA ) @ A @ B )
      | ~ ( order @ a @ ( type2 @ a ) )
      | ~ ( ord_less_eq @ a @ a2 @ b )
      | ( ( huffma469337550apSyms @ a @ t @ a2 @ b )
       != t )
      | ( ( ord_less_eq @ TA @ ( A @ C ) @ ( B @ C ) )
       != ( ord_less_eq @ a @ b @ a2 ) ) ),
    inference(simp,[status(thm)],[10028]) ).

thf(10321,plain,
    ! [TB: $tType] :
      ( ~ ( ord @ a @ ( type2 @ a ) )
      | ~ ( ord_less_eq @ ( TB > a )
          @ ^ [A: TB] : b
          @ ^ [A: TB] : a2 )
      | ~ ( order @ a @ ( type2 @ a ) )
      | ~ ( ord_less_eq @ a @ a2 @ b )
      | ( ( huffma469337550apSyms @ a @ t @ a2 @ b )
       != t ) ),
    inference(pre_uni,[status(thm)],[10029:[bind(A,$thf( ^ [D: TB] : b )),bind(B,$thf( ^ [D: TB] : a2 )),bind_type(TA,$thf( a ))]]) ).

thf(10657,plain,
    ! [TA: $tType] :
      ( ~ ( ord @ a @ ( type2 @ a ) )
      | ~ ( ord_less_eq @ ( TA > a )
          @ ^ [A: TA] : b
          @ ^ [A: TA] : a2 )
      | ~ ( order @ a @ ( type2 @ a ) )
      | ~ ( ord_less_eq @ a @ a2 @ b )
      | ( ( huffma469337550apSyms @ a @ t @ a2 @ b )
       != t ) ),
    inference(simp,[status(thm)],[10321]) ).

thf(1221,plain,
    ! [TA: $tType,C: nat,B: TA > $o,A: TA] :
      ( ~ ( member @ TA @ A @ ( collect @ TA @ B ) )
      | ( ( B @ A )
       != ( ord_less @ nat @ C @ ( zero_zero @ nat ) ) ) ),
    inference(paramod_ordered,[status(thm)],[305,1147]) ).

thf(1222,plain,
    ! [TA: $tType,B: TA > nat,A: TA] :
      ~ ( member @ TA @ A
        @ ( collect @ TA
          @ ^ [C: TA] : ( ord_less @ nat @ ( B @ C ) @ ( zero_zero @ nat ) ) ) ),
    inference(pre_uni,[status(thm)],[1221:[bind(A,$thf( A )),bind(B,$thf( ^ [E: TA] : ( ord_less @ nat @ ( D @ E ) @ ( zero_zero @ nat ) ) )),bind(C,$thf( D @ A ))]]) ).

thf(1223,plain,
    ! [TA: $tType,B: TA > nat,A: TA] :
      ~ ( member @ TA @ A
        @ ( collect @ TA
          @ ^ [C: TA] : ( ord_less @ nat @ ( B @ C ) @ ( zero_zero @ nat ) ) ) ),
    inference(simp,[status(thm)],[1222]) ).

thf(1224,plain,
    ! [TA: $tType,A: TA] :
      ~ ( member @ TA @ A
        @ ( collect @ TA
          @ ^ [B: TA] : $false ) ),
    inference(rewrite,[status(thm)],[1223,1147]) ).

thf(1228,plain,
    ! [TA: $tType,TB: $tType,C: TB,B: TA > $o,A: TA] :
      ( ~ ( member @ TB @ C
          @ ( collect @ TB
            @ ^ [D: TB] : ( member @ TA @ A @ ( collect @ TA @ B ) ) ) )
      | ( B @ A ) ),
    inference(paramod_ordered,[status(thm)],[305,1224]) ).

thf(1233,plain,
    ! [TA: $tType,TB: $tType,B: TB,A: TA] :
      ~ ( member @ TB @ B
        @ ( collect @ TB
          @ ^ [C: TB] :
              ( member @ TA @ A
              @ ( collect @ TA
                @ ^ [D: TA] : $false ) ) ) ),
    inference(pre_uni,[status(thm)],[1228:[bind(A,$thf( A )),bind(B,$thf( ^ [D: TA] : $false ))]]) ).

thf(1236,plain,
    ! [TA: $tType,TB: $tType,B: TB,A: TA] :
      ~ ( member @ TB @ B
        @ ( collect @ TB
          @ ^ [C: TB] :
              ( member @ TA @ A
              @ ( collect @ TA
                @ ^ [D: TA] : $false ) ) ) ),
    inference(simp,[status(thm)],[1233]) ).

thf(1272,plain,
    ! [TB: $tType,A: TB] :
      ~ ( member @ TB @ A
        @ ( collect @ TB
          @ ^ [B: TB] : $false ) ),
    inference(rewrite,[status(thm)],[1236,1224]) ).

thf(1277,plain,
    ! [TA: $tType,TC: $tType,C: TC,B: TA > $o,A: TA] :
      ( ~ ( member @ TC @ C
          @ ( collect @ TC
            @ ^ [D: TC] : ( member @ TA @ A @ ( collect @ TA @ B ) ) ) )
      | ( B @ A ) ),
    inference(paramod_ordered,[status(thm)],[305,1272]) ).

thf(1282,plain,
    ! [TA: $tType,TC: $tType,B: TC,A: TA] :
      ~ ( member @ TC @ B
        @ ( collect @ TC
          @ ^ [C: TC] :
              ( member @ TA @ A
              @ ( collect @ TA
                @ ^ [D: TA] : $false ) ) ) ),
    inference(pre_uni,[status(thm)],[1277:[bind(A,$thf( (@) )),bind(B,$thf( ^ [D: TA] : $false ))]]) ).

thf(1285,plain,
    ! [TA: $tType,TB: $tType,B: TB,A: TA] :
      ~ ( member @ TB @ B
        @ ( collect @ TB
          @ ^ [C: TB] :
              ( member @ TA @ A
              @ ( collect @ TA
                @ ^ [D: TA] : $false ) ) ) ),
    inference(simp,[status(thm)],[1282]) ).

thf(1227,plain,
    ! [TA: $tType,TB: $tType,C: TB,B: TA > $o,A: TA] :
      ( ~ ( member @ TA @ A @ ( collect @ TA @ B ) )
      | ( ( B @ A )
       != ( member @ TB @ C
          @ ( collect @ TB
            @ ^ [D: TB] : $false ) ) ) ),
    inference(paramod_ordered,[status(thm)],[305,1224]) ).

thf(1234,plain,
    ! [TA: $tType,TB: $tType,B: TA > TB,A: TA] :
      ~ ( member @ TA @ A
        @ ( collect @ TA
          @ ^ [C: TA] :
              ( member @ TB @ ( B @ C )
              @ ( collect @ TB
                @ ^ [D: TB] : $false ) ) ) ),
    inference(pre_uni,[status(thm)],[1227:[bind(A,$thf( A )),bind(B,$thf( ^ [E: TA] : ( member @ TB @ ( D @ E ) @ ( collect @ TB @ ^ [F: TB] : $false ) ) )),bind(C,$thf( D @ A ))]]) ).

thf(1237,plain,
    ! [TA: $tType,TB: $tType,B: TA > TB,A: TA] :
      ~ ( member @ TA @ A
        @ ( collect @ TA
          @ ^ [C: TA] :
              ( member @ TB @ ( B @ C )
              @ ( collect @ TB
                @ ^ [D: TB] : $false ) ) ) ),
    inference(simp,[status(thm)],[1234]) ).

thf(1288,plain,
    ! [TA: $tType,A: TA] :
      ~ ( member @ TA @ A
        @ ( collect @ TA
          @ ^ [B: TA] : $false ) ),
    inference(rewrite,[status(thm)],[1237,1272]) ).

thf(1365,plain,
    ! [TB: $tType,A: TB] :
      ~ ( member @ TB @ A
        @ ( collect @ TB
          @ ^ [B: TB] : $false ) ),
    inference(rewrite,[status(thm)],[1285,1288]) ).

thf(1370,plain,
    ! [TA: $tType,TC: $tType,C: TC,B: TA > $o,A: TA] :
      ( ~ ( member @ TC @ C
          @ ( collect @ TC
            @ ^ [D: TC] : ( member @ TA @ A @ ( collect @ TA @ B ) ) ) )
      | ( B @ A ) ),
    inference(paramod_ordered,[status(thm)],[305,1365]) ).

thf(1376,plain,
    ! [TA: $tType,TC: $tType,B: TC,A: TA] :
      ~ ( member @ TC @ B
        @ ( collect @ TC
          @ ^ [C: TC] :
              ( member @ TA @ A
              @ ( collect @ TA
                @ ^ [D: TA] : $false ) ) ) ),
    inference(pre_uni,[status(thm)],[1370:[bind(A,$thf( (@) )),bind(B,$thf( ^ [D: TA] : $false ))]]) ).

thf(1377,plain,
    ! [TA: $tType,TB: $tType,B: TB,A: TA] :
      ~ ( member @ TB @ B
        @ ( collect @ TB
          @ ^ [C: TB] :
              ( member @ TA @ A
              @ ( collect @ TA
                @ ^ [D: TA] : $false ) ) ) ),
    inference(simp,[status(thm)],[1376]) ).

thf(1296,plain,
    ! [TA: $tType,TB: $tType,C: TB,B: TA > $o,A: TA] :
      ( ~ ( member @ TA @ A @ ( collect @ TA @ B ) )
      | ( ( B @ A )
       != ( member @ TB @ C
          @ ( collect @ TB
            @ ^ [D: TB] : $false ) ) ) ),
    inference(paramod_ordered,[status(thm)],[305,1288]) ).

thf(1299,plain,
    ! [TA: $tType,TB: $tType,B: TA > TB,A: TA] :
      ~ ( member @ TA @ A
        @ ( collect @ TA
          @ ^ [C: TA] :
              ( member @ TB @ ( B @ C )
              @ ( collect @ TB
                @ ^ [D: TB] : $false ) ) ) ),
    inference(pre_uni,[status(thm)],[1296:[bind(A,$thf( A )),bind(B,$thf( ^ [E: TA] : ( member @ TB @ ( D @ E ) @ ( collect @ TB @ ^ [F: TB] : $false ) ) )),bind(C,$thf( D @ A ))]]) ).

thf(1301,plain,
    ! [TA: $tType,TB: $tType,B: TA > TB,A: TA] :
      ~ ( member @ TA @ A
        @ ( collect @ TA
          @ ^ [C: TA] :
              ( member @ TB @ ( B @ C )
              @ ( collect @ TB
                @ ^ [D: TB] : $false ) ) ) ),
    inference(simp,[status(thm)],[1299]) ).

thf(1297,plain,
    ! [TA: $tType,TB: $tType,C: TB,B: TA > $o,A: TA] :
      ( ~ ( member @ TB @ C
          @ ( collect @ TB
            @ ^ [D: TB] : ( member @ TA @ A @ ( collect @ TA @ B ) ) ) )
      | ( B @ A ) ),
    inference(paramod_ordered,[status(thm)],[305,1288]) ).

thf(1298,plain,
    ! [TA: $tType,TB: $tType,B: TB,A: TA] :
      ~ ( member @ TB @ B
        @ ( collect @ TB
          @ ^ [C: TB] :
              ( member @ TA @ A
              @ ( collect @ TA
                @ ^ [D: TA] : $false ) ) ) ),
    inference(pre_uni,[status(thm)],[1297:[bind(A,$thf( A )),bind(B,$thf( ^ [D: TA] : $false ))]]) ).

thf(1300,plain,
    ! [TA: $tType,TB: $tType,B: TB,A: TA] :
      ~ ( member @ TB @ B
        @ ( collect @ TB
          @ ^ [C: TB] :
              ( member @ TA @ A
              @ ( collect @ TA
                @ ^ [D: TA] : $false ) ) ) ),
    inference(simp,[status(thm)],[1298]) ).

thf(1276,plain,
    ! [TA: $tType,TC: $tType,C: TC,B: TA > $o,A: TA] :
      ( ~ ( member @ TA @ A @ ( collect @ TA @ B ) )
      | ( ( B @ A )
       != ( member @ TC @ C
          @ ( collect @ TC
            @ ^ [D: TC] : $false ) ) ) ),
    inference(paramod_ordered,[status(thm)],[305,1272]) ).

thf(1283,plain,
    ! [TA: $tType,TC: $tType,B: TA > TC,A: TA] :
      ~ ( member @ TA @ A
        @ ( collect @ TA
          @ ^ [C: TA] :
              ( member @ TC @ ( B @ C )
              @ ( collect @ TC
                @ ^ [D: TC] : $false ) ) ) ),
    inference(pre_uni,[status(thm)],[1276:[bind(A,$thf( (@) )),bind(B,$thf( ^ [E: TA] : ( member @ TC @ ( D @ E ) @ ( collect @ TC @ ^ [F: TC] : $false ) ) )),bind(C,$thf( D @ (@) ))]]) ).

thf(1286,plain,
    ! [TA: $tType,TB: $tType,B: TA > TB,A: TA] :
      ~ ( member @ TA @ A
        @ ( collect @ TA
          @ ^ [C: TA] :
              ( member @ TB @ ( B @ C )
              @ ( collect @ TB
                @ ^ [D: TB] : $false ) ) ) ),
    inference(simp,[status(thm)],[1283]) ).

thf(1738,plain,
    ! [TA: $tType,A: TA] :
      ~ ( member @ TA @ A
        @ ( collect @ TA
          @ ^ [B: TA] : $false ) ),
    inference(rewrite,[status(thm)],[1286,1365]) ).

thf(1754,plain,
    ! [TB: $tType,A: TB] :
      ~ ( member @ TB @ A
        @ ( collect @ TB
          @ ^ [B: TB] : $false ) ),
    inference(rewrite,[status(thm)],[1300,1738]) ).

thf(2310,plain,
    ! [TA: $tType,A: TA] :
      ~ ( member @ TA @ A
        @ ( collect @ TA
          @ ^ [B: TA] : $false ) ),
    inference(rewrite,[status(thm)],[1301,1754]) ).

thf(2326,plain,
    ! [TB: $tType,A: TB] :
      ~ ( member @ TB @ A
        @ ( collect @ TB
          @ ^ [B: TB] : $false ) ),
    inference(rewrite,[status(thm)],[1377,2310]) ).

thf(2330,plain,
    ! [TA: $tType,TC: $tType,C: TC,B: TA > $o,A: TA] :
      ( ~ ( member @ TA @ A @ ( collect @ TA @ B ) )
      | ( ( B @ A )
       != ( member @ TC @ C
          @ ( collect @ TC
            @ ^ [D: TC] : $false ) ) ) ),
    inference(paramod_ordered,[status(thm)],[305,2326]) ).

thf(2337,plain,
    ! [TA: $tType,TC: $tType,B: TA > TC,A: TA] :
      ~ ( member @ TA @ A
        @ ( collect @ TA
          @ ^ [C: TA] :
              ( member @ TC @ ( B @ C )
              @ ( collect @ TC
                @ ^ [D: TC] : $false ) ) ) ),
    inference(pre_uni,[status(thm)],[2330:[bind(A,$thf( (@) )),bind(B,$thf( ^ [E: TA] : ( member @ TC @ ( D @ E ) @ ( collect @ TC @ ^ [F: TC] : $false ) ) )),bind(C,$thf( D @ (@) ))]]) ).

thf(2339,plain,
    ! [TA: $tType,TB: $tType,B: TA > TB,A: TA] :
      ~ ( member @ TA @ A
        @ ( collect @ TA
          @ ^ [C: TA] :
              ( member @ TB @ ( B @ C )
              @ ( collect @ TB
                @ ^ [D: TB] : $false ) ) ) ),
    inference(simp,[status(thm)],[2337]) ).

thf(2315,plain,
    ! [TA: $tType,TB: $tType,C: TB,B: TA > $o,A: TA] :
      ( ~ ( member @ TB @ C
          @ ( collect @ TB
            @ ^ [D: TB] : ( member @ TA @ A @ ( collect @ TA @ B ) ) ) )
      | ( B @ A ) ),
    inference(paramod_ordered,[status(thm)],[305,2310]) ).

thf(2321,plain,
    ! [TA: $tType,TB: $tType,B: TB,A: TA] :
      ~ ( member @ TB @ B
        @ ( collect @ TB
          @ ^ [C: TB] :
              ( member @ TA @ A
              @ ( collect @ TA
                @ ^ [D: TA] : $false ) ) ) ),
    inference(pre_uni,[status(thm)],[2315:[bind(A,$thf( A )),bind(B,$thf( ^ [D: TA] : $false ))]]) ).

thf(2323,plain,
    ! [TA: $tType,TB: $tType,B: TB,A: TA] :
      ~ ( member @ TB @ B
        @ ( collect @ TB
          @ ^ [C: TB] :
              ( member @ TA @ A
              @ ( collect @ TA
                @ ^ [D: TA] : $false ) ) ) ),
    inference(simp,[status(thm)],[2321]) ).

thf(1758,plain,
    ! [TA: $tType,TC: $tType,C: TC,B: TA > $o,A: TA] :
      ( ~ ( member @ TA @ A @ ( collect @ TA @ B ) )
      | ( ( B @ A )
       != ( member @ TC @ C
          @ ( collect @ TC
            @ ^ [D: TC] : $false ) ) ) ),
    inference(paramod_ordered,[status(thm)],[305,1754]) ).

thf(1765,plain,
    ! [TA: $tType,TC: $tType,B: TA > TC,A: TA] :
      ~ ( member @ TA @ A
        @ ( collect @ TA
          @ ^ [C: TA] :
              ( member @ TC @ ( B @ C )
              @ ( collect @ TC
                @ ^ [D: TC] : $false ) ) ) ),
    inference(pre_uni,[status(thm)],[1758:[bind(A,$thf( (@) )),bind(B,$thf( ^ [E: TA] : ( member @ TC @ ( D @ E ) @ ( collect @ TC @ ^ [F: TC] : $false ) ) )),bind(C,$thf( D @ (@) ))]]) ).

thf(1769,plain,
    ! [TA: $tType,TB: $tType,B: TA > TB,A: TA] :
      ~ ( member @ TA @ A
        @ ( collect @ TA
          @ ^ [C: TA] :
              ( member @ TB @ ( B @ C )
              @ ( collect @ TB
                @ ^ [D: TB] : $false ) ) ) ),
    inference(simp,[status(thm)],[1765]) ).

thf(1759,plain,
    ! [TA: $tType,TC: $tType,C: TC,B: TA > $o,A: TA] :
      ( ~ ( member @ TC @ C
          @ ( collect @ TC
            @ ^ [D: TC] : ( member @ TA @ A @ ( collect @ TA @ B ) ) ) )
      | ( B @ A ) ),
    inference(paramod_ordered,[status(thm)],[305,1754]) ).

thf(1764,plain,
    ! [TA: $tType,TC: $tType,B: TC,A: TA] :
      ~ ( member @ TC @ B
        @ ( collect @ TC
          @ ^ [C: TC] :
              ( member @ TA @ A
              @ ( collect @ TA
                @ ^ [D: TA] : $false ) ) ) ),
    inference(pre_uni,[status(thm)],[1759:[bind(A,$thf( (@) )),bind(B,$thf( ^ [D: TA] : $false ))]]) ).

thf(1768,plain,
    ! [TA: $tType,TB: $tType,B: TB,A: TA] :
      ~ ( member @ TB @ B
        @ ( collect @ TB
          @ ^ [C: TB] :
              ( member @ TA @ A
              @ ( collect @ TA
                @ ^ [D: TA] : $false ) ) ) ),
    inference(simp,[status(thm)],[1764]) ).

thf(2621,plain,
    ! [TA: $tType,B: nat,A: TA] :
      ( ~ ( linordered_field @ TA @ ( type2 @ TA ) )
      | ~ $true
      | ( ( ord_less @ TA @ ( sk4 @ TA @ A ) @ A )
       != ( ord_less @ nat @ B @ ( zero_zero @ nat ) ) ) ),
    inference(paramod_ordered,[status(thm)],[318,1147]) ).

thf(2622,plain,
    ! [TA: $tType,B: nat,A: TA] :
      ( ~ ( linordered_field @ TA @ ( type2 @ TA ) )
      | ( ( ord_less @ TA @ ( sk4 @ TA @ A ) @ A )
       != ( ord_less @ nat @ B @ ( zero_zero @ nat ) ) ) ),
    inference(simp,[status(thm)],[2621]) ).

thf(2623,plain,
    ~ ( linordered_field @ nat @ ( type2 @ nat ) ),
    inference(pattern_uni,[status(thm)],[2622:[bind(A,$thf( zero_zero @ nat )),bind(B,$thf( sk4 @ nat @ ( zero_zero @ nat ) )),bind_type(TA,$thf( nat ))]]) ).

thf(2655,plain,
    ! [TA: $tType,B: TA > $o,A: TA] :
      ( ~ ( member @ TA @ A @ ( collect @ TA @ B ) )
      | ( ( B @ A )
       != ( linordered_field @ nat @ ( type2 @ nat ) ) ) ),
    inference(paramod_ordered,[status(thm)],[305,2623]) ).

thf(2656,plain,
    ! [TA: $tType,A: TA] :
      ~ ( member @ TA @ A
        @ ( collect @ TA
          @ ^ [B: TA] : ( linordered_field @ nat @ ( type2 @ nat ) ) ) ),
    inference(pre_uni,[status(thm)],[2655:[bind(A,$thf( A )),bind(B,$thf( ^ [C: TA] : ( linordered_field @ nat @ ( type2 @ nat ) ) ))]]) ).

thf(2737,plain,
    ! [TA: $tType,A: TA] :
      ~ ( member @ TA @ A
        @ ( collect @ TA
          @ ^ [B: TA] : $false ) ),
    inference(rewrite,[status(thm)],[2656,2623]) ).

thf(8415,plain,
    ! [TB: $tType,A: TB] :
      ~ ( member @ TB @ A
        @ ( collect @ TB
          @ ^ [B: TB] : $false ) ),
    inference(rewrite,[status(thm)],[1768,2737]) ).

thf(8451,plain,
    ! [TA: $tType,A: TA] :
      ~ ( member @ TA @ A
        @ ( collect @ TA
          @ ^ [B: TA] : $false ) ),
    inference(rewrite,[status(thm)],[1769,8415]) ).

thf(8939,plain,
    ! [TB: $tType,A: TB] :
      ~ ( member @ TB @ A
        @ ( collect @ TB
          @ ^ [B: TB] : $false ) ),
    inference(rewrite,[status(thm)],[2323,8451]) ).

thf(9264,plain,
    ! [TA: $tType,A: TA] :
      ~ ( member @ TA @ A
        @ ( collect @ TA
          @ ^ [B: TA] : $false ) ),
    inference(rewrite,[status(thm)],[2339,8939]) ).

thf(29,axiom,
    ! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA,C: TA,D: nat,E: nat] :
      ( ( huffma1050891809istent @ TA @ A )
     => ( ( ( huffma943100115ibling @ TA @ A @ B )
         != B )
       => ( ( C != B )
         => ( ( huffma943100115ibling @ TA @ ( huffma2094459102Leaves @ TA @ A @ D @ C @ E @ ( huffma943100115ibling @ TA @ A @ B ) ) @ C )
            = B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_sibling__swapLeaves__sibling) ).

thf(361,plain,
    ! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA,C: TA,D: nat,E: nat] :
      ( ( huffma1050891809istent @ TA @ A )
     => ( ( ( huffma943100115ibling @ TA @ A @ B )
         != B )
       => ( ( C != B )
         => ( ( huffma943100115ibling @ TA @ ( huffma2094459102Leaves @ TA @ A @ D @ C @ E @ ( huffma943100115ibling @ TA @ A @ B ) ) @ C )
            = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(53,axiom,
    ! [TA: $tType] :
      ( ( ord @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( A = B )
         => ( ( ord_less_eq @ TA @ B @ C )
           => ( ord_less_eq @ TA @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_ord__eq__le__trans) ).

thf(435,plain,
    ! [TA: $tType] :
      ( ( ord @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( A = B )
         => ( ( ord_less_eq @ TA @ B @ C )
           => ( ord_less_eq @ TA @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(2805,plain,
    ( ( ( huffma636208924e_cost @ a @ ( huffma469337550apSyms @ a @ t @ a2 @ b ) )
     != ( huffma636208924e_cost @ a @ t ) )
    | ( ( huffma854352999e_freq @ a @ t @ a2 )
     != ( huffma854352999e_freq @ a @ t @ a2 ) )
    | ( ( huffma223349076_depth @ a @ t @ b )
     != ( huffma223349076_depth @ a @ t @ a2 ) )
    | ( ( huffma854352999e_freq @ a @ t @ b )
     != ( huffma854352999e_freq @ a @ t @ b ) )
    | ( ( huffma223349076_depth @ a @ t @ b )
     != ( huffma223349076_depth @ a @ t @ a2 ) ) ),
    inference(simp,[status(thm)],[1104]) ).

thf(2863,plain,
    ( ( ( huffma636208924e_cost @ a @ ( huffma469337550apSyms @ a @ t @ a2 @ b ) )
     != ( huffma636208924e_cost @ a @ t ) )
    | ( ( huffma223349076_depth @ a @ t @ b )
     != ( huffma223349076_depth @ a @ t @ a2 ) ) ),
    inference(simp,[status(thm)],[2805]) ).

thf(2870,plain,
    ( ( ( huffma636208924e_cost @ a @ ( huffma469337550apSyms @ a @ t @ a2 @ b ) )
     != ( huffma636208924e_cost @ a @ t ) )
    | ( t != t )
    | ( b != a2 ) ),
    inference(simp,[status(thm)],[2863]) ).

thf(2872,plain,
    ( ( ( huffma636208924e_cost @ a @ ( huffma469337550apSyms @ a @ t @ a2 @ b ) )
     != ( huffma636208924e_cost @ a @ t ) )
    | ( b != a2 ) ),
    inference(simp,[status(thm)],[2870]) ).

thf(197,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq @ nat @ A @ B )
     => ( ord_less_eq @ nat @ ( plus_plus @ nat @ A @ C ) @ ( plus_plus @ nat @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_add__le__mono1) ).

thf(830,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq @ nat @ A @ B )
     => ( ord_less_eq @ nat @ ( plus_plus @ nat @ A @ C ) @ ( plus_plus @ nat @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(10026,plain,
    ! [TA: $tType,TB: $tType,C: TB,B: TB > TA,A: TB > TA] :
      ( ~ ( ord @ TA @ ( type2 @ TA ) )
      | ~ ( ord_less_eq @ ( TB > TA ) @ A @ B )
      | ~ ( order @ a @ ( type2 @ a ) )
      | ~ $true
      | ~ ( ord_less_eq @ a @ b @ a2 )
      | ( ( huffma469337550apSyms @ a @ t @ a2 @ b )
       != t )
      | ( ( ord_less_eq @ TA @ ( A @ C ) @ ( B @ C ) )
       != ( ord_less_eq @ a @ a2 @ b ) ) ),
    inference(paramod_ordered,[status(thm)],[358,4943]) ).

thf(10027,plain,
    ! [TA: $tType,TB: $tType,C: TB,B: TB > TA,A: TB > TA] :
      ( ~ ( ord @ TA @ ( type2 @ TA ) )
      | ~ ( ord_less_eq @ ( TB > TA ) @ A @ B )
      | ~ ( order @ a @ ( type2 @ a ) )
      | ~ ( ord_less_eq @ a @ b @ a2 )
      | ( ( huffma469337550apSyms @ a @ t @ a2 @ b )
       != t )
      | ( ( ord_less_eq @ TA @ ( A @ C ) @ ( B @ C ) )
       != ( ord_less_eq @ a @ a2 @ b ) ) ),
    inference(simp,[status(thm)],[10026]) ).

thf(10466,plain,
    ! [TB: $tType] :
      ( ~ ( ord @ a @ ( type2 @ a ) )
      | ~ ( ord_less_eq @ ( TB > a )
          @ ^ [A: TB] : a2
          @ ^ [A: TB] : b )
      | ~ ( order @ a @ ( type2 @ a ) )
      | ~ ( ord_less_eq @ a @ b @ a2 )
      | ( ( huffma469337550apSyms @ a @ t @ a2 @ b )
       != t ) ),
    inference(pre_uni,[status(thm)],[10027:[bind(A,$thf( ^ [D: TB] : a2 )),bind(B,$thf( ^ [D: TB] : b )),bind_type(TA,$thf( a ))]]) ).

thf(10794,plain,
    ! [TA: $tType] :
      ( ~ ( ord @ a @ ( type2 @ a ) )
      | ~ ( ord_less_eq @ ( TA > a )
          @ ^ [A: TA] : a2
          @ ^ [A: TA] : b )
      | ~ ( order @ a @ ( type2 @ a ) )
      | ~ ( ord_less_eq @ a @ b @ a2 )
      | ( ( huffma469337550apSyms @ a @ t @ a2 @ b )
       != t ) ),
    inference(simp,[status(thm)],[10466]) ).

thf(13431,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType] :
      ( ~ $true
      | ( preorder @ ( TZB > TZC ) @ ( type2 @ ( TZB > TZC ) ) )
      | ( ( preorder @ ( TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) )
       != ( preorder @ TZC @ ( type2 @ TZC ) ) ) ),
    inference(paramod_ordered,[status(thm)],[12737,320]) ).

thf(13432,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType] :
      ( ( preorder @ ( TZB > TZC ) @ ( type2 @ ( TZB > TZC ) ) )
      | ( ( preorder @ ( TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) )
       != ( preorder @ TZC @ ( type2 @ TZC ) ) ) ),
    inference(simp,[status(thm)],[13431]) ).

thf(13433,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType] : ( preorder @ ( TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) ),
    inference(pattern_uni,[status(thm)],[13432:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ))]]) ).

thf(267,axiom,
    huffma1050891809istent @ a @ t,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_assms_I1_J) ).

thf(1027,plain,
    huffma1050891809istent @ a @ t,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(168,axiom,
    ! [TA: $tType] :
      ( ( linord581940658strict @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ ( times_times @ TA @ A @ B ) @ ( zero_zero @ TA ) )
          = ( ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
              & ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) ) )
            | ( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
              & ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_mult__le__0__iff) ).

thf(757,plain,
    ! [TA: $tType] :
      ( ( linord581940658strict @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ ( times_times @ TA @ A @ B ) @ ( zero_zero @ TA ) )
          = ( ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
              & ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) ) )
            | ( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
              & ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(138,axiom,
    ! [TA: $tType] :
      ( ( linordered_field @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
          = ( plus_plus @ TA @ B @ ( plus_plus @ TA @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_linordered__field__class_Osign__simps_I28_J) ).

thf(682,plain,
    ! [TA: $tType] :
      ( ( linordered_field @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
          = ( plus_plus @ TA @ B @ ( plus_plus @ TA @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(162,axiom,
    ! [TA: $tType] :
      ( ( ordere779506340up_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA,D: TA] :
          ( ( ( ord_less_eq @ TA @ A @ B )
            & ( ord_less_eq @ TA @ C @ D ) )
         => ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_add__mono__thms__linordered__semiring_I1_J) ).

thf(742,plain,
    ! [TA: $tType] :
      ( ( ordere779506340up_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA,D: TA] :
          ( ( ( ord_less_eq @ TA @ A @ B )
            & ( ord_less_eq @ TA @ C @ D ) )
         => ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(293,axiom,
    ! [TA: $tType] :
      ( ( ordered_semiring_0 @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
              & ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) ) )
            | ( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
              & ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B ) ) )
         => ( ord_less_eq @ TA @ ( times_times @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_split__mult__neg__le) ).

thf(1089,plain,
    ! [TA: $tType] :
      ( ( ordered_semiring_0 @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
              & ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) ) )
            | ( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
              & ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B ) ) )
         => ( ord_less_eq @ TA @ ( times_times @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(469,plain,
    ! [TA: $tType] : ( order @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
    inference(cnf,[status(esa)],[468]) ).

thf(9549,plain,
    ! [TA: $tType,TB: $tType,TC: $tType] :
      ( ~ $true
      | ( order @ ( TB > TC ) @ ( type2 @ ( TB > TC ) ) )
      | ( ( order @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) )
       != ( order @ TC @ ( type2 @ TC ) ) ) ),
    inference(paramod_ordered,[status(thm)],[469,356]) ).

thf(9550,plain,
    ! [TA: $tType,TB: $tType,TC: $tType] :
      ( ( order @ ( TB > TC ) @ ( type2 @ ( TB > TC ) ) )
      | ( ( order @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) )
       != ( order @ TC @ ( type2 @ TC ) ) ) ),
    inference(simp,[status(thm)],[9549]) ).

thf(9551,plain,
    ! [TA: $tType,TB: $tType] : ( order @ ( TB > ( set @ TA ) ) @ ( type2 @ ( TB > ( set @ TA ) ) ) ),
    inference(pattern_uni,[status(thm)],[9550:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( set @ TA ))]]) ).

thf(10923,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] :
      ( ~ $true
      | ( order @ ( TC > TD ) @ ( type2 @ ( TC > TD ) ) )
      | ( ( order @ ( TB > ( set @ TA ) ) @ ( type2 @ ( TB > ( set @ TA ) ) ) )
       != ( order @ TD @ ( type2 @ TD ) ) ) ),
    inference(paramod_ordered,[status(thm)],[9551,356]) ).

thf(10924,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] :
      ( ( order @ ( TC > TD ) @ ( type2 @ ( TC > TD ) ) )
      | ( ( order @ ( TB > ( set @ TA ) ) @ ( type2 @ ( TB > ( set @ TA ) ) ) )
       != ( order @ TD @ ( type2 @ TD ) ) ) ),
    inference(simp,[status(thm)],[10923]) ).

thf(10925,plain,
    ! [TA: $tType,TB: $tType,TC: $tType] : ( order @ ( TC > TB > ( set @ TA ) ) @ ( type2 @ ( TC > TB > ( set @ TA ) ) ) ),
    inference(pattern_uni,[status(thm)],[10924:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TB > ( set @ TA ) ))]]) ).

thf(11572,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType] :
      ( ~ $true
      | ( order @ ( TD > TE ) @ ( type2 @ ( TD > TE ) ) )
      | ( ( order @ ( TC > TB > ( set @ TA ) ) @ ( type2 @ ( TC > TB > ( set @ TA ) ) ) )
       != ( order @ TE @ ( type2 @ TE ) ) ) ),
    inference(paramod_ordered,[status(thm)],[10925,356]) ).

thf(11573,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType] :
      ( ( order @ ( TD > TE ) @ ( type2 @ ( TD > TE ) ) )
      | ( ( order @ ( TC > TB > ( set @ TA ) ) @ ( type2 @ ( TC > TB > ( set @ TA ) ) ) )
       != ( order @ TE @ ( type2 @ TE ) ) ) ),
    inference(simp,[status(thm)],[11572]) ).

thf(11574,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] : ( order @ ( TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TD > TC > TB > ( set @ TA ) ) ) ),
    inference(pattern_uni,[status(thm)],[11573:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TC > TB > ( set @ TA ) ))]]) ).

thf(12262,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType] :
      ( ~ $true
      | ( order @ ( TE > TF ) @ ( type2 @ ( TE > TF ) ) )
      | ( ( order @ ( TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TD > TC > TB > ( set @ TA ) ) ) )
       != ( order @ TF @ ( type2 @ TF ) ) ) ),
    inference(paramod_ordered,[status(thm)],[11574,356]) ).

thf(12263,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType] :
      ( ( order @ ( TE > TF ) @ ( type2 @ ( TE > TF ) ) )
      | ( ( order @ ( TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TD > TC > TB > ( set @ TA ) ) ) )
       != ( order @ TF @ ( type2 @ TF ) ) ) ),
    inference(simp,[status(thm)],[12262]) ).

thf(12264,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType] : ( order @ ( TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TE > TD > TC > TB > ( set @ TA ) ) ) ),
    inference(pattern_uni,[status(thm)],[12263:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TD > TC > TB > ( set @ TA ) ))]]) ).

thf(263,axiom,
    ! [TA: $tType] :
      ( ( ordere779506340up_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA,D: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ord_less_eq @ TA @ C @ D )
           => ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_add__mono) ).

thf(1017,plain,
    ! [TA: $tType] :
      ( ( ordere779506340up_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA,D: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ord_less_eq @ TA @ C @ D )
           => ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(43,axiom,
    linorder @ $o @ ( type2 @ $o ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Olinorder_8) ).

thf(403,plain,
    linorder @ $o @ ( type2 @ $o ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(3179,plain,
    ! [TA: $tType,B: TA > $o,A: TA] :
      ( ~ ( canoni770627133id_add @ $o @ ( type2 @ $o ) )
      | ~ ( ord_less @ $o @ ( zero_zero @ $o ) @ ( member @ TA @ A @ ( collect @ TA @ B ) ) )
      | ( ( B @ A )
       != ( zero_zero @ $o ) ) ),
    inference(paramod_ordered,[status(thm)],[305,3072]) ).

thf(3181,plain,
    ! [TA: $tType,A: TA] :
      ( ~ ( canoni770627133id_add @ $o @ ( type2 @ $o ) )
      | ~ ( ord_less @ $o @ ( zero_zero @ $o )
          @ ( member @ TA @ A
            @ ( collect @ TA
              @ ^ [B: TA] : ( zero_zero @ $o ) ) ) ) ),
    inference(pre_uni,[status(thm)],[3179:[bind(A,$thf( A )),bind(B,$thf( ^ [C: TA] : ( zero_zero @ $o ) ))]]) ).

thf(5888,plain,
    ! [TA: $tType,TB: $tType,C: TB,B: TA > $o,A: TA] :
      ( ~ ( canoni770627133id_add @ $o @ ( type2 @ $o ) )
      | ~ ( ord_less @ $o @ ( zero_zero @ $o ) @ ( B @ A ) )
      | ( ( member @ TA @ A @ ( collect @ TA @ B ) )
       != ( member @ TB @ C
          @ ( collect @ TB
            @ ^ [D: TB] : ( zero_zero @ $o ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[305,3181]) ).

thf(5889,plain,
    ( ~ ( canoni770627133id_add @ $o @ ( type2 @ $o ) )
    | ~ ( ord_less @ $o @ ( zero_zero @ $o ) @ ( zero_zero @ $o ) ) ),
    inference(pattern_uni,[status(thm)],[5888:[bind(A,$thf( A )),bind(B,$thf( ^ [D: TB] : ( zero_zero @ $o ) )),bind(C,$thf( A )),bind_type(TA,$thf( TB ))]]) ).

thf(6122,plain,
    ! [TA: $tType,B: TA > $o,A: TA] :
      ( ~ ( canoni770627133id_add @ $o @ ( type2 @ $o ) )
      | ~ ( member @ TA @ A @ ( collect @ TA @ B ) )
      | ( ( B @ A )
       != ( ord_less @ $o @ ( zero_zero @ $o ) @ ( zero_zero @ $o ) ) ) ),
    inference(paramod_ordered,[status(thm)],[305,5889]) ).

thf(6128,plain,
    ! [TA: $tType,A: TA] :
      ( ~ ( canoni770627133id_add @ $o @ ( type2 @ $o ) )
      | ~ ( member @ TA @ A
          @ ( collect @ TA
            @ ^ [B: TA] : ( ord_less @ $o @ ( zero_zero @ $o ) @ ( zero_zero @ $o ) ) ) ) ),
    inference(pre_uni,[status(thm)],[6122:[bind(A,$thf( A )),bind(B,$thf( ^ [C: TA] : ( ord_less @ $o @ ( zero_zero @ $o ) @ ( zero_zero @ $o ) ) ))]]) ).

thf(209,axiom,
    comm_monoid_add @ nat @ ( type2 @ nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocomm__monoid__add) ).

thf(857,plain,
    comm_monoid_add @ nat @ ( type2 @ nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(295,axiom,
    ! [TA: $tType] :
      ( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( times_times @ TA @ A @ ( zero_zero @ TA ) )
          = ( zero_zero @ TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_semiring__normalization__rules_I10_J) ).

thf(1096,plain,
    ! [TA: $tType] :
      ( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( times_times @ TA @ A @ ( zero_zero @ TA ) )
          = ( zero_zero @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(106,axiom,
    ord_less_eq @ nat @ ( huffma223349076_depth @ a @ t @ a2 ) @ ( huffma223349076_depth @ a @ t @ b ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_assms_I5_J) ).

thf(593,plain,
    ord_less_eq @ nat @ ( huffma223349076_depth @ a @ t @ a2 ) @ ( huffma223349076_depth @ a @ t @ b ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(14,axiom,
    ! [TA: $tType,A: TA,B: TA] :
      ( ( if @ TA @ $false @ A @ B )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_T) ).

thf(326,plain,
    ! [TA: $tType,A: TA,B: TA] :
      ( ( if @ TA @ $false @ A @ B )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(327,plain,
    ! [TA: $tType,B: TA,A: TA] :
      ( ( if @ TA @ $false @ A @ B )
      = B ),
    inference(cnf,[status(esa)],[326]) ).

thf(328,plain,
    ! [TA: $tType,B: TA,A: TA] :
      ( ( if @ TA @ $false @ A @ B )
      = B ),
    inference(lifteq,[status(thm)],[327]) ).

thf(67,axiom,
    ordered_semiring_0 @ nat @ ( type2 @ nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Oordered__semiring__0) ).

thf(488,plain,
    ordered_semiring_0 @ nat @ ( type2 @ nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(19,axiom,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ord_less_eq @ TA @ B @ A )
           => ( A = B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_antisym) ).

thf(339,plain,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ord_less_eq @ TA @ B @ A )
           => ( A = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(13188,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType] :
      ( ~ $true
      | ( order @ ( TF > TG ) @ ( type2 @ ( TF > TG ) ) )
      | ( ( order @ ( TE > TD > TC > TB > TA > nat ) @ ( type2 @ ( TE > TD > TC > TB > TA > nat ) ) )
       != ( order @ TG @ ( type2 @ TG ) ) ) ),
    inference(paramod_ordered,[status(thm)],[12576,356]) ).

thf(13189,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType] :
      ( ( order @ ( TF > TG ) @ ( type2 @ ( TF > TG ) ) )
      | ( ( order @ ( TE > TD > TC > TB > TA > nat ) @ ( type2 @ ( TE > TD > TC > TB > TA > nat ) ) )
       != ( order @ TG @ ( type2 @ TG ) ) ) ),
    inference(simp,[status(thm)],[13188]) ).

thf(13190,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType] : ( order @ ( TF > TE > TD > TC > TB > TA > nat ) @ ( type2 @ ( TF > TE > TD > TC > TB > TA > nat ) ) ),
    inference(pattern_uni,[status(thm)],[13189:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TE > TD > TC > TB > TA > nat ))]]) ).

thf(82,axiom,
    ab_semigroup_add @ nat @ ( type2 @ nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oab__semigroup__add) ).

thf(526,plain,
    ab_semigroup_add @ nat @ ( type2 @ nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(120,axiom,
    ! [TA: $tType] :
      ( ( ab_semigroup_add @ TA @ ( type2 @ TA ) )
     => ( ( plus_plus @ TA )
        = ( ^ [A: TA,B: TA] : ( plus_plus @ TA @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_add_Ocommute) ).

thf(637,plain,
    ! [TA: $tType] :
      ( ( ab_semigroup_add @ TA @ ( type2 @ TA ) )
     => ( ( plus_plus @ TA )
        = ( ^ [A: TA,B: TA] : ( plus_plus @ TA @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(68,axiom,
    ! [TA: $tType] :
      ( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
     => ( ( plus_plus @ TA )
        = ( ^ [A: TA,B: TA] : ( plus_plus @ TA @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_semiring__normalization__rules_I24_J) ).

thf(489,plain,
    ! [TA: $tType] :
      ( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
     => ( ( plus_plus @ TA )
        = ( ^ [A: TA,B: TA] : ( plus_plus @ TA @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(268,axiom,
    ! [TA: $tType] :
      ( ( ordere216010020id_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
         => ( ( ord_less_eq @ TA @ B @ C )
           => ( ord_less_eq @ TA @ B @ ( plus_plus @ TA @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_add__increasing2) ).

thf(1028,plain,
    ! [TA: $tType] :
      ( ( ordere216010020id_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
         => ( ( ord_less_eq @ TA @ B @ C )
           => ( ord_less_eq @ TA @ B @ ( plus_plus @ TA @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(105,axiom,
    ! [TA: $tType] :
      ( ( ordere216010020id_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
         => ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B )
           => ( ( ( plus_plus @ TA @ A @ B )
                = ( zero_zero @ TA ) )
              = ( ( A
                  = ( zero_zero @ TA ) )
                & ( B
                  = ( zero_zero @ TA ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_add__nonneg__eq__0__iff) ).

thf(590,plain,
    ! [TA: $tType] :
      ( ( ordere216010020id_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
         => ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B )
           => ( ( ( plus_plus @ TA @ A @ B )
                = ( zero_zero @ TA ) )
              = ( ( A
                  = ( zero_zero @ TA ) )
                & ( B
                  = ( zero_zero @ TA ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(251,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less @ nat @ ( plus_plus @ nat @ A @ B ) @ ( plus_plus @ nat @ A @ C ) )
      = ( ord_less @ nat @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_nat__add__left__cancel__less) ).

thf(970,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less @ nat @ ( plus_plus @ nat @ A @ B ) @ ( plus_plus @ nat @ A @ C ) )
      = ( ord_less @ nat @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(40,axiom,
    ! [TA: $tType] :
      ( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
          = ( A
            = ( zero_zero @ TA ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_le__zero__eq) ).

thf(393,plain,
    ! [TA: $tType] :
      ( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
          = ( A
            = ( zero_zero @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(296,axiom,
    ! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA,C: TA,D: TA,E: nat,F: nat] :
      ( ( huffma1050891809istent @ TA @ A )
     => ( ( B != C )
       => ( ( B != D )
         => ( ( huffma223349076_depth @ TA @ ( huffma2094459102Leaves @ TA @ A @ E @ C @ F @ D ) @ B )
            = ( huffma223349076_depth @ TA @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_depth__swapLeaves__neither) ).

thf(1099,plain,
    ! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA,C: TA,D: TA,E: nat,F: nat] :
      ( ( huffma1050891809istent @ TA @ A )
     => ( ( B != C )
       => ( ( B != D )
         => ( ( huffma223349076_depth @ TA @ ( huffma2094459102Leaves @ TA @ A @ E @ C @ F @ D ) @ B )
            = ( huffma223349076_depth @ TA @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(78,axiom,
    ! [TA: $tType] :
      ( ( semiring @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( times_times @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
          = ( plus_plus @ TA @ ( times_times @ TA @ A @ C ) @ ( times_times @ TA @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_distrib__right) ).

thf(515,plain,
    ! [TA: $tType] :
      ( ( semiring @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( times_times @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
          = ( plus_plus @ TA @ ( times_times @ TA @ A @ C ) @ ( times_times @ TA @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(12992,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType] :
      ( ~ $true
      | ( preorder @ ( TZ > TZA ) @ ( type2 @ ( TZ > TZA ) ) )
      | ( ( preorder @ ( TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) )
       != ( preorder @ TZA @ ( type2 @ TZA ) ) ) ),
    inference(paramod_ordered,[status(thm)],[12383,320]) ).

thf(12993,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType] :
      ( ( preorder @ ( TZ > TZA ) @ ( type2 @ ( TZ > TZA ) ) )
      | ( ( preorder @ ( TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) )
       != ( preorder @ TZA @ ( type2 @ TZA ) ) ) ),
    inference(simp,[status(thm)],[12992]) ).

thf(12994,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType] : ( preorder @ ( TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) ),
    inference(pattern_uni,[status(thm)],[12993:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ))]]) ).

thf(160,axiom,
    zero @ nat @ ( type2 @ nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ozero) ).

thf(738,plain,
    zero @ nat @ ( type2 @ nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(127,axiom,
    ! [TA: $tType] :
      ( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
          = ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_semiring__normalization__rules_I21_J) ).

thf(654,plain,
    ! [TA: $tType] :
      ( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
          = ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(277,axiom,
    ! [TA: $tType] :
      ( ( cancel1352612707id_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( A
            = ( plus_plus @ TA @ B @ A ) )
          = ( B
            = ( zero_zero @ TA ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_add__cancel__right__left) ).

thf(1050,plain,
    ! [TA: $tType] :
      ( ( cancel1352612707id_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( A
            = ( plus_plus @ TA @ B @ A ) )
          = ( B
            = ( zero_zero @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(229,axiom,
    ordere516151231imp_le @ nat @ ( type2 @ nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__ab__semigroup__monoid__add__imp__le) ).

thf(911,plain,
    ordere516151231imp_le @ nat @ ( type2 @ nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(176,axiom,
    ! [A: nat,B: nat] : ( ord_less_eq @ nat @ A @ ( plus_plus @ nat @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_le__add2) ).

thf(779,plain,
    ! [A: nat,B: nat] : ( ord_less_eq @ nat @ A @ ( plus_plus @ nat @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(32,axiom,
    ! [TA: $tType] :
      ( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) )
          = ( A
            = ( zero_zero @ TA ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_not__gr__zero) ).

thf(369,plain,
    ! [TA: $tType] :
      ( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) )
          = ( A
            = ( zero_zero @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(370,plain,
    ! [TA: $tType,A: TA] :
      ( ~ ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
      | ( ( ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) )
        = ( A
          = ( zero_zero @ TA ) ) ) ),
    inference(cnf,[status(esa)],[369]) ).

thf(371,plain,
    ! [TA: $tType,A: TA] :
      ( ( ( ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) )
        = ( A
          = ( zero_zero @ TA ) ) )
      | ~ ( canoni770627133id_add @ TA @ ( type2 @ TA ) ) ),
    inference(lifteq,[status(thm)],[370]) ).

thf(73,axiom,
    ! [TA: $tType] :
      ( ( ordere779506340up_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA,D: TA] :
          ( ( ( A = B )
            & ( ord_less_eq @ TA @ C @ D ) )
         => ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_add__mono__thms__linordered__semiring_I2_J) ).

thf(503,plain,
    ! [TA: $tType] :
      ( ( ordere779506340up_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA,D: TA] :
          ( ( ( A = B )
            & ( ord_less_eq @ TA @ C @ D ) )
         => ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(124,axiom,
    ! [TA: $tType] :
      ( ( ordere216010020id_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
         => ( ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) )
           => ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_add__nonpos__nonpos) ).

thf(647,plain,
    ! [TA: $tType] :
      ( ( ordere216010020id_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
         => ( ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) )
           => ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(21,axiom,
    ! [TA: $tType] :
      ( ( preorder @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( A = B )
         => ( ord_less_eq @ TA @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_eq__refl) ).

thf(343,plain,
    ! [TA: $tType] :
      ( ( preorder @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( A = B )
         => ( ord_less_eq @ TA @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(186,axiom,
    ! [TA: $tType,A: TA,B: huffma16452318e_tree @ TA,C: TA] :
      ( ( member @ TA @ A @ ( huffma505251170phabet @ TA @ B ) )
     => ( ( member @ TA @ C @ ( huffma505251170phabet @ TA @ B ) )
       => ( ( huffma505251170phabet @ TA @ ( huffma469337550apSyms @ TA @ B @ A @ C ) )
          = ( huffma505251170phabet @ TA @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_alphabet__swapSyms) ).

thf(805,plain,
    ! [TA: $tType,A: TA,B: huffma16452318e_tree @ TA,C: TA] :
      ( ( member @ TA @ A @ ( huffma505251170phabet @ TA @ B ) )
     => ( ( member @ TA @ C @ ( huffma505251170phabet @ TA @ B ) )
       => ( ( huffma505251170phabet @ TA @ ( huffma469337550apSyms @ TA @ B @ A @ C ) )
          = ( huffma505251170phabet @ TA @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(233,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq @ nat @ A @ B )
     => ( ( ord_less_eq @ nat @ B @ A )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_le__antisym) ).

thf(921,plain,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq @ nat @ A @ B )
     => ( ( ord_less_eq @ nat @ B @ A )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(88,axiom,
    ! [A: nat,B: nat] :
      ( ( A = B )
     => ( ord_less_eq @ nat @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_eq__imp__le) ).

thf(541,plain,
    ! [A: nat,B: nat] :
      ( ( A = B )
     => ( ord_less_eq @ nat @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(128,axiom,
    ! [TA: $tType] :
      ( ( linordered_field @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( times_times @ TA @ A @ ( times_times @ TA @ B @ C ) )
          = ( times_times @ TA @ B @ ( times_times @ TA @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_linordered__field__class_Osign__simps_I25_J) ).

thf(657,plain,
    ! [TA: $tType] :
      ( ( linordered_field @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( times_times @ TA @ A @ ( times_times @ TA @ B @ C ) )
          = ( times_times @ TA @ B @ ( times_times @ TA @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(134,axiom,
    ! [TA: $tType] :
      ( ( cancel1352612707id_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ( plus_plus @ TA @ A @ B )
            = A )
          = ( B
            = ( zero_zero @ TA ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_add__cancel__left__right) ).

thf(674,plain,
    ! [TA: $tType] :
      ( ( cancel1352612707id_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ( plus_plus @ TA @ A @ B )
            = A )
          = ( B
            = ( zero_zero @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(84,axiom,
    ! [TA: $tType] :
      ( ( ordered_semiring_0 @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
         => ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B )
           => ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( times_times @ TA @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_mult__nonneg__nonneg) ).

thf(530,plain,
    ! [TA: $tType] :
      ( ( ordered_semiring_0 @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
         => ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B )
           => ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( times_times @ TA @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(174,axiom,
    ! [TA: $tType] :
      ( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
          = ( plus_plus @ TA @ B @ ( plus_plus @ TA @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_semiring__normalization__rules_I22_J) ).

thf(773,plain,
    ! [TA: $tType] :
      ( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
          = ( plus_plus @ TA @ B @ ( plus_plus @ TA @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(221,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( times_times @ nat @ A @ B ) )
      = ( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
        & ( ord_less @ nat @ ( zero_zero @ nat ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_nat__0__less__mult__iff) ).

thf(888,plain,
    ! [A: nat,B: nat] :
      ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( times_times @ nat @ A @ B ) )
      = ( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
        & ( ord_less @ nat @ ( zero_zero @ nat ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(235,axiom,
    ! [TA: $tType] :
      ( ( huffma469337550apSyms @ TA )
      = ( ^ [A: huffma16452318e_tree @ TA,B: TA,C: TA] : ( huffma2094459102Leaves @ TA @ A @ ( huffma854352999e_freq @ TA @ A @ B ) @ B @ ( huffma854352999e_freq @ TA @ A @ C ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_swapSyms__def) ).

thf(926,plain,
    ! [TA: $tType] :
      ( ( huffma469337550apSyms @ TA )
      = ( ^ [A: huffma16452318e_tree @ TA,B: TA,C: TA] : ( huffma2094459102Leaves @ TA @ A @ ( huffma854352999e_freq @ TA @ A @ B ) @ B @ ( huffma854352999e_freq @ TA @ A @ C ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(239,axiom,
    ! [TA: $tType,A: huffma16452318e_tree @ TA,B: huffma16452318e_tree @ TA] :
      ( ( huffma854352999e_freq @ TA @ ( huffma453905539eTrees @ TA @ A @ B ) )
      = ( ^ [C: TA] : ( plus_plus @ nat @ ( huffma854352999e_freq @ TA @ A @ C ) @ ( huffma854352999e_freq @ TA @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_freq__uniteTrees) ).

thf(938,plain,
    ! [TA: $tType,A: huffma16452318e_tree @ TA,B: huffma16452318e_tree @ TA] :
      ( ( huffma854352999e_freq @ TA @ ( huffma453905539eTrees @ TA @ A @ B ) )
      = ( ^ [C: TA] : ( plus_plus @ nat @ ( huffma854352999e_freq @ TA @ A @ C ) @ ( huffma854352999e_freq @ TA @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(118,axiom,
    mult_zero @ nat @ ( type2 @ nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Omult__zero) ).

thf(633,plain,
    mult_zero @ nat @ ( type2 @ nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(28,axiom,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ord_less_eq @ TA @ B @ C )
           => ( ord_less_eq @ TA @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_order_Otrans) ).

thf(359,plain,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ord_less_eq @ TA @ B @ C )
           => ( ord_less_eq @ TA @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(360,plain,
    ! [TA: $tType,C: TA,B: TA,A: TA] :
      ( ~ ( order @ TA @ ( type2 @ TA ) )
      | ~ ( ord_less_eq @ TA @ A @ B )
      | ~ ( ord_less_eq @ TA @ B @ C )
      | ( ord_less_eq @ TA @ A @ C ) ),
    inference(cnf,[status(esa)],[359]) ).

thf(75,axiom,
    ! [TA: $tType] :
      ( ( ring @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( times_times @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
          = ( plus_plus @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_ring__class_Oring__distribs_I1_J) ).

thf(508,plain,
    ! [TA: $tType] :
      ( ( ring @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( times_times @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
          = ( plus_plus @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(3177,plain,
    ! [TA: $tType,TB: $tType,B: TA > $o,A: TA] :
      ( ~ ( canoni770627133id_add @ TB @ ( type2 @ TB ) )
      | ~ ( member @ TA @ A @ ( collect @ TA @ B ) )
      | ( ( B @ A )
       != ( ord_less @ TB @ ( zero_zero @ TB ) @ ( zero_zero @ TB ) ) ) ),
    inference(paramod_ordered,[status(thm)],[305,3072]) ).

thf(3183,plain,
    ! [TA: $tType,TB: $tType,A: TA] :
      ( ~ ( canoni770627133id_add @ TB @ ( type2 @ TB ) )
      | ~ ( member @ TA @ A
          @ ( collect @ TA
            @ ^ [B: TA] : ( ord_less @ TB @ ( zero_zero @ TB ) @ ( zero_zero @ TB ) ) ) ) ),
    inference(pre_uni,[status(thm)],[3177:[bind(A,$thf( A )),bind(B,$thf( ^ [C: TA] : ( ord_less @ TB @ ( zero_zero @ TB ) @ ( zero_zero @ TB ) ) ))]]) ).

thf(93,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( ord_less_eq @ nat @ A @ B )
     => ( ( ord_less_eq @ nat @ C @ D )
       => ( ord_less_eq @ nat @ ( plus_plus @ nat @ A @ C ) @ ( plus_plus @ nat @ B @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_add__le__mono) ).

thf(558,plain,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( ord_less_eq @ nat @ A @ B )
     => ( ( ord_less_eq @ nat @ C @ D )
       => ( ord_less_eq @ nat @ ( plus_plus @ nat @ A @ C ) @ ( plus_plus @ nat @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(285,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq @ nat @ ( plus_plus @ nat @ A @ B ) @ C )
     => ( ord_less_eq @ nat @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_add__leD1) ).

thf(1071,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq @ nat @ ( plus_plus @ nat @ A @ B ) @ C )
     => ( ord_less_eq @ nat @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(227,axiom,
    ! [TA: $tType] :
      ( ( linord581940658strict @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ ( plus_plus @ TA @ ( times_times @ TA @ A @ A ) @ ( times_times @ TA @ B @ B ) ) @ ( zero_zero @ TA ) )
          = ( ( A
              = ( zero_zero @ TA ) )
            & ( B
              = ( zero_zero @ TA ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_sum__squares__le__zero__iff) ).

thf(906,plain,
    ! [TA: $tType] :
      ( ( linord581940658strict @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ ( plus_plus @ TA @ ( times_times @ TA @ A @ A ) @ ( times_times @ TA @ B @ B ) ) @ ( zero_zero @ TA ) )
          = ( ( A
              = ( zero_zero @ TA ) )
            & ( B
              = ( zero_zero @ TA ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(1103,plain,
    ( ( ( huffma469337550apSyms @ a @ t @ a2 @ b )
     != t )
    | ( ( plus_plus @ nat @ ( times_times @ nat @ ( huffma854352999e_freq @ a @ t @ a2 ) @ ( huffma223349076_depth @ a @ t @ a2 ) ) @ ( times_times @ nat @ ( huffma854352999e_freq @ a @ t @ b ) @ ( huffma223349076_depth @ a @ t @ b ) ) )
     != ( plus_plus @ nat @ ( times_times @ nat @ ( huffma854352999e_freq @ a @ t @ a2 ) @ ( huffma223349076_depth @ a @ t @ b ) ) @ ( times_times @ nat @ ( huffma854352999e_freq @ a @ t @ b ) @ ( huffma223349076_depth @ a @ t @ a2 ) ) ) ) ),
    inference(simp,[status(thm)],[1102]) ).

thf(194,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( times_times @ nat @ A @ B )
        = ( times_times @ nat @ A @ C ) )
      = ( ( A
          = ( zero_zero @ nat ) )
        | ( B = C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_nat__mult__eq__cancel__disj) ).

thf(824,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( times_times @ nat @ A @ B )
        = ( times_times @ nat @ A @ C ) )
      = ( ( A
          = ( zero_zero @ nat ) )
        | ( B = C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(141,axiom,
    ! [TA: $tType] :
      ( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
          = ( plus_plus @ TA @ ( plus_plus @ TA @ A @ C ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_semiring__normalization__rules_I23_J) ).

thf(689,plain,
    ! [TA: $tType] :
      ( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
          = ( plus_plus @ TA @ ( plus_plus @ TA @ A @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(56,axiom,
    ! [TA: $tType,A: huffma16452318e_tree @ TA] :
    ? [B: TA] : ( member @ TA @ B @ ( huffma505251170phabet @ TA @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_exists__in__alphabet) ).

thf(444,plain,
    ! [TA: $tType,A: huffma16452318e_tree @ TA] :
    ? [B: TA] : ( member @ TA @ B @ ( huffma505251170phabet @ TA @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(35,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ord @ TB @ ( type2 @ TB ) )
     => ! [A: TA > TB,B: TA > TB,C: TA] :
          ( ( ord_less_eq @ ( TA > TB ) @ A @ B )
         => ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_le__funE) ).

thf(375,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ord @ TB @ ( type2 @ TB ) )
     => ! [A: TA > TB,B: TA > TB,C: TA] :
          ( ( ord_less_eq @ ( TA > TB ) @ A @ B )
         => ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(192,axiom,
    ! [A: nat,B: nat] : ( ord_less_eq @ nat @ A @ ( plus_plus @ nat @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_le__add1) ).

thf(819,plain,
    ! [A: nat,B: nat] : ( ord_less_eq @ nat @ A @ ( plus_plus @ nat @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(262,axiom,
    ! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA,C: TA,D: nat,E: nat] :
      ( ( huffma1050891809istent @ TA @ A )
     => ( ( B != C )
       => ( ( ( member @ TA @ B @ ( huffma505251170phabet @ TA @ A ) )
           => ( ( ( member @ TA @ C @ ( huffma505251170phabet @ TA @ A ) )
               => ( ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma691733767weight @ TA @ ( huffma2094459102Leaves @ TA @ A @ D @ B @ E @ C ) ) @ ( huffma854352999e_freq @ TA @ A @ B ) ) @ ( huffma854352999e_freq @ TA @ A @ C ) )
                  = ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma691733767weight @ TA @ A ) @ D ) @ E ) ) )
              & ( ~ ( member @ TA @ C @ ( huffma505251170phabet @ TA @ A ) )
               => ( ( plus_plus @ nat @ ( huffma691733767weight @ TA @ ( huffma2094459102Leaves @ TA @ A @ D @ B @ E @ C ) ) @ ( huffma854352999e_freq @ TA @ A @ B ) )
                  = ( plus_plus @ nat @ ( huffma691733767weight @ TA @ A ) @ E ) ) ) ) )
          & ( ~ ( member @ TA @ B @ ( huffma505251170phabet @ TA @ A ) )
           => ( ( ( member @ TA @ C @ ( huffma505251170phabet @ TA @ A ) )
               => ( ( plus_plus @ nat @ ( huffma691733767weight @ TA @ ( huffma2094459102Leaves @ TA @ A @ D @ B @ E @ C ) ) @ ( huffma854352999e_freq @ TA @ A @ C ) )
                  = ( plus_plus @ nat @ ( huffma691733767weight @ TA @ A ) @ D ) ) )
              & ( ~ ( member @ TA @ C @ ( huffma505251170phabet @ TA @ A ) )
               => ( ( huffma691733767weight @ TA @ ( huffma2094459102Leaves @ TA @ A @ D @ B @ E @ C ) )
                  = ( huffma691733767weight @ TA @ A ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_weight__swapLeaves) ).

thf(1007,plain,
    ! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA,C: TA,D: nat,E: nat] :
      ( ( huffma1050891809istent @ TA @ A )
     => ( ( B != C )
       => ( ( ( member @ TA @ B @ ( huffma505251170phabet @ TA @ A ) )
           => ( ( ( member @ TA @ C @ ( huffma505251170phabet @ TA @ A ) )
               => ( ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma691733767weight @ TA @ ( huffma2094459102Leaves @ TA @ A @ D @ B @ E @ C ) ) @ ( huffma854352999e_freq @ TA @ A @ B ) ) @ ( huffma854352999e_freq @ TA @ A @ C ) )
                  = ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma691733767weight @ TA @ A ) @ D ) @ E ) ) )
              & ( ~ ( member @ TA @ C @ ( huffma505251170phabet @ TA @ A ) )
               => ( ( plus_plus @ nat @ ( huffma691733767weight @ TA @ ( huffma2094459102Leaves @ TA @ A @ D @ B @ E @ C ) ) @ ( huffma854352999e_freq @ TA @ A @ B ) )
                  = ( plus_plus @ nat @ ( huffma691733767weight @ TA @ A ) @ E ) ) ) ) )
          & ( ~ ( member @ TA @ B @ ( huffma505251170phabet @ TA @ A ) )
           => ( ( ( member @ TA @ C @ ( huffma505251170phabet @ TA @ A ) )
               => ( ( plus_plus @ nat @ ( huffma691733767weight @ TA @ ( huffma2094459102Leaves @ TA @ A @ D @ B @ E @ C ) ) @ ( huffma854352999e_freq @ TA @ A @ C ) )
                  = ( plus_plus @ nat @ ( huffma691733767weight @ TA @ A ) @ D ) ) )
              & ( ~ ( member @ TA @ C @ ( huffma505251170phabet @ TA @ A ) )
               => ( ( huffma691733767weight @ TA @ ( huffma2094459102Leaves @ TA @ A @ D @ B @ E @ C ) )
                  = ( huffma691733767weight @ TA @ A ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(158,axiom,
    ! [TA: $tType] :
      ( ( ordere216010020id_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
         => ( ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) )
           => ( ( ( plus_plus @ TA @ A @ B )
                = ( zero_zero @ TA ) )
              = ( ( A
                  = ( zero_zero @ TA ) )
                & ( B
                  = ( zero_zero @ TA ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_add__nonpos__eq__0__iff) ).

thf(732,plain,
    ! [TA: $tType] :
      ( ( ordere216010020id_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
         => ( ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) )
           => ( ( ( plus_plus @ TA @ A @ B )
                = ( zero_zero @ TA ) )
              = ( ( A
                  = ( zero_zero @ TA ) )
                & ( B
                  = ( zero_zero @ TA ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(202,axiom,
    comm_semiring @ nat @ ( type2 @ nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Ocomm__semiring) ).

thf(843,plain,
    comm_semiring @ nat @ ( type2 @ nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(247,axiom,
    ! [TA: $tType,A: huffma16452318e_tree @ TA] :
      ( ( huffma1050891809istent @ TA @ A )
     => ? [B: TA] :
          ( ( member @ TA @ B @ ( huffma505251170phabet @ TA @ A ) )
          & ( ( huffma223349076_depth @ TA @ A @ B )
            = ( huffma1554076246height @ TA @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_exists__at__height) ).

thf(958,plain,
    ! [TA: $tType,A: huffma16452318e_tree @ TA] :
      ( ( huffma1050891809istent @ TA @ A )
     => ? [B: TA] :
          ( ( member @ TA @ B @ ( huffma505251170phabet @ TA @ A ) )
          & ( ( huffma223349076_depth @ TA @ A @ B )
            = ( huffma1554076246height @ TA @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(89,axiom,
    ! [TA: $tType] :
      ( ( ordered_ring @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
              & ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B ) )
            | ( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
              & ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) ) ) )
         => ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( times_times @ TA @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_split__mult__pos__le) ).

thf(545,plain,
    ! [TA: $tType] :
      ( ( ordered_ring @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
              & ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B ) )
            | ( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
              & ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) ) ) )
         => ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( times_times @ TA @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(47,axiom,
    ! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA] :
      ( ( huffma1050891809istent @ TA @ A )
     => ( ( huffma943100115ibling @ TA @ A @ ( huffma943100115ibling @ TA @ A @ B ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_sibling__sibling__id) ).

thf(413,plain,
    ! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA] :
      ( ( huffma1050891809istent @ TA @ A )
     => ( ( huffma943100115ibling @ TA @ A @ ( huffma943100115ibling @ TA @ A @ B ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(103,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( times_times @ nat @ A @ B )
        = ( times_times @ nat @ A @ C ) )
      = ( ( B = C )
        | ( A
          = ( zero_zero @ nat ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_mult__cancel1) ).

thf(584,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( times_times @ nat @ A @ B )
        = ( times_times @ nat @ A @ C ) )
      = ( ( B = C )
        | ( A
          = ( zero_zero @ nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(216,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq @ nat @ A @ B )
      | ( ord_less_eq @ nat @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_nat__le__linear) ).

thf(875,plain,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq @ nat @ A @ B )
      | ( ord_less_eq @ nat @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(149,axiom,
    cancel1352612707id_add @ nat @ ( type2 @ nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocancel__comm__monoid__add) ).

thf(711,plain,
    cancel1352612707id_add @ nat @ ( type2 @ nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(12661,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType] :
      ( ~ $true
      | ( order @ ( TF > TG ) @ ( type2 @ ( TF > TG ) ) )
      | ( ( order @ ( TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TE > TD > TC > TB > ( set @ TA ) ) ) )
       != ( order @ TG @ ( type2 @ TG ) ) ) ),
    inference(paramod_ordered,[status(thm)],[12264,356]) ).

thf(12662,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType] :
      ( ( order @ ( TF > TG ) @ ( type2 @ ( TF > TG ) ) )
      | ( ( order @ ( TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TE > TD > TC > TB > ( set @ TA ) ) ) )
       != ( order @ TG @ ( type2 @ TG ) ) ) ),
    inference(simp,[status(thm)],[12661]) ).

thf(12663,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType] : ( order @ ( TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TF > TE > TD > TC > TB > ( set @ TA ) ) ) ),
    inference(pattern_uni,[status(thm)],[12662:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TE > TD > TC > TB > ( set @ TA ) ))]]) ).

thf(13279,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType] :
      ( ~ $true
      | ( order @ ( TG > TH ) @ ( type2 @ ( TG > TH ) ) )
      | ( ( order @ ( TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TF > TE > TD > TC > TB > ( set @ TA ) ) ) )
       != ( order @ TH @ ( type2 @ TH ) ) ) ),
    inference(paramod_ordered,[status(thm)],[12663,356]) ).

thf(13280,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType] :
      ( ( order @ ( TG > TH ) @ ( type2 @ ( TG > TH ) ) )
      | ( ( order @ ( TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TF > TE > TD > TC > TB > ( set @ TA ) ) ) )
       != ( order @ TH @ ( type2 @ TH ) ) ) ),
    inference(simp,[status(thm)],[13279]) ).

thf(13281,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType] : ( order @ ( TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) ),
    inference(pattern_uni,[status(thm)],[13280:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TF > TE > TD > TC > TB > ( set @ TA ) ))]]) ).

thf(101,axiom,
    ord @ nat @ ( type2 @ nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Oord_3) ).

thf(579,plain,
    ord @ nat @ ( type2 @ nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(313,plain,
    ! [TA: $tType,TB: $tType,D: TB,C: TB,B: TB > TA,A: TA] :
      ( ~ ( order @ TB @ ( type2 @ TB ) )
      | ~ ( order @ TA @ ( type2 @ TA ) )
      | ~ ( ord_less_eq @ TA @ A @ ( B @ C ) )
      | ~ ( ord_less_eq @ TB @ C @ D )
      | ~ ( ord_less_eq @ TA @ ( B @ ( sk2 @ TB @ TA @ D @ C @ B @ A ) ) @ ( B @ ( sk3 @ TB @ TA @ D @ C @ B @ A ) ) )
      | ( ord_less_eq @ TA @ A @ ( B @ D ) ) ),
    inference(cnfConj,[status(thm)],[311]) ).

thf(71,axiom,
    ! [TA: $tType] :
      ( ( ordere236663937imp_le @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
          = ( ord_less_eq @ TA @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_add__le__cancel__right) ).

thf(498,plain,
    ! [TA: $tType] :
      ( ( ordere236663937imp_le @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
          = ( ord_less_eq @ TA @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(334,plain,
    ! [TA: $tType,B: TA,A: TA] :
      ( ~ ( order @ TA @ ( type2 @ TA ) )
      | ~ ( ord_less_eq @ TA @ A @ B )
      | ( ( ord_less_eq @ TA @ B @ A )
        = ( B = A ) ) ),
    inference(cnf,[status(esa)],[333]) ).

thf(335,plain,
    ! [TA: $tType,B: TA,A: TA] :
      ( ( ( ord_less_eq @ TA @ B @ A )
        = ( B = A ) )
      | ~ ( order @ TA @ ( type2 @ TA ) )
      | ~ ( ord_less_eq @ TA @ A @ B ) ),
    inference(lifteq,[status(thm)],[334]) ).

thf(242,axiom,
    ! [TA: $tType] :
      ( ( ordere516151231imp_le @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ A )
          = ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_add__le__same__cancel1) ).

thf(947,plain,
    ! [TA: $tType] :
      ( ( ordere516151231imp_le @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ A )
          = ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(350,plain,
    ! [TA: $tType,TB: $tType,B: TB > TA,A: TB > TA] :
      ( ~ ( ord @ TA @ ( type2 @ TA ) )
      | ~ ( ord_less_eq @ TA @ ( A @ ( sk5 @ TB @ TA @ B @ A ) ) @ ( B @ ( sk5 @ TB @ TA @ B @ A ) ) )
      | ( ord_less_eq @ ( TB > TA ) @ A @ B ) ),
    inference(cnf,[status(esa)],[349]) ).

thf(133,axiom,
    ! [TA: $tType] :
      ( ( ordered_ring @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ord_less_eq @ TA @ C @ ( zero_zero @ TA ) )
           => ( ord_less_eq @ TA @ ( times_times @ TA @ C @ B ) @ ( times_times @ TA @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_mult__left__mono__neg) ).

thf(672,plain,
    ! [TA: $tType] :
      ( ( ordered_ring @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ord_less_eq @ TA @ C @ ( zero_zero @ TA ) )
           => ( ord_less_eq @ TA @ ( times_times @ TA @ C @ B ) @ ( times_times @ TA @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(111,axiom,
    ! [TA: $tType] :
      ( ( ordere516151231imp_le @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ ( plus_plus @ TA @ B @ A ) )
          = ( ord_less @ TA @ ( zero_zero @ TA ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_less__add__same__cancel2) ).

thf(611,plain,
    ! [TA: $tType] :
      ( ( ordere516151231imp_le @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ ( plus_plus @ TA @ B @ A ) )
          = ( ord_less @ TA @ ( zero_zero @ TA ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(179,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq @ nat @ A @ B )
     => ( ( ord_less_eq @ nat @ B @ C )
       => ( ord_less_eq @ nat @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_le__trans) ).

thf(787,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq @ nat @ A @ B )
     => ( ( ord_less_eq @ nat @ B @ C )
       => ( ord_less_eq @ nat @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(254,axiom,
    ! [A: nat] : ( ord_less_eq @ nat @ A @ ( times_times @ nat @ A @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_le__square) ).

thf(979,plain,
    ! [A: nat] : ( ord_less_eq @ nat @ A @ ( times_times @ nat @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(137,axiom,
    ab_semigroup_mult @ nat @ ( type2 @ nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oab__semigroup__mult) ).

thf(681,plain,
    ab_semigroup_mult @ nat @ ( type2 @ nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(178,axiom,
    ! [TA: $tType] :
      ( ( ring @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( times_times @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
          = ( plus_plus @ TA @ ( times_times @ TA @ A @ C ) @ ( times_times @ TA @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_ring__class_Oring__distribs_I2_J) ).

thf(784,plain,
    ! [TA: $tType] :
      ( ( ring @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( times_times @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
          = ( plus_plus @ TA @ ( times_times @ TA @ A @ C ) @ ( times_times @ TA @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(276,axiom,
    ! [TA: $tType] :
      ( ( ordered_semiring_0 @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
         => ( ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) )
           => ( ord_less_eq @ TA @ ( times_times @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_mult__nonneg__nonpos) ).

thf(1048,plain,
    ! [TA: $tType] :
      ( ( ordered_semiring_0 @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
         => ( ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) )
           => ( ord_less_eq @ TA @ ( times_times @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(36,axiom,
    ! [TA: $tType] :
      ( ( ord @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( B = C )
           => ( ord_less_eq @ TA @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_ord__le__eq__trans) ).

thf(377,plain,
    ! [TA: $tType] :
      ( ( ord @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( B = C )
           => ( ord_less_eq @ TA @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(3178,plain,
    ! [TA: $tType,B: TA > $o,A: TA] :
      ( ~ ( canoni770627133id_add @ $o @ ( type2 @ $o ) )
      | ~ ( ord_less @ $o @ ( member @ TA @ A @ ( collect @ TA @ B ) ) @ ( zero_zero @ $o ) )
      | ( ( B @ A )
       != ( zero_zero @ $o ) ) ),
    inference(paramod_ordered,[status(thm)],[305,3072]) ).

thf(3182,plain,
    ! [TA: $tType,A: TA] :
      ( ~ ( canoni770627133id_add @ $o @ ( type2 @ $o ) )
      | ~ ( ord_less @ $o
          @ ( member @ TA @ A
            @ ( collect @ TA
              @ ^ [B: TA] : ( zero_zero @ $o ) ) )
          @ ( zero_zero @ $o ) ) ),
    inference(pre_uni,[status(thm)],[3178:[bind(A,$thf( A )),bind(B,$thf( ^ [C: TA] : ( zero_zero @ $o ) ))]]) ).

thf(225,axiom,
    ! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA,C: TA,D: nat,E: nat] :
      ( ( huffma1050891809istent @ TA @ A )
     => ( ( B != C )
       => ( ( huffma854352999e_freq @ TA @ ( huffma2094459102Leaves @ TA @ A @ D @ B @ E @ C ) )
          = ( ^ [F: TA] : ( if @ nat @ ( F = B ) @ ( if @ nat @ ( member @ TA @ C @ ( huffma505251170phabet @ TA @ A ) ) @ D @ ( zero_zero @ nat ) ) @ ( if @ nat @ ( F = C ) @ ( if @ nat @ ( member @ TA @ B @ ( huffma505251170phabet @ TA @ A ) ) @ E @ ( zero_zero @ nat ) ) @ ( huffma854352999e_freq @ TA @ A @ F ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_freq__swapLeaves) ).

thf(900,plain,
    ! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA,C: TA,D: nat,E: nat] :
      ( ( huffma1050891809istent @ TA @ A )
     => ( ( B != C )
       => ( ( huffma854352999e_freq @ TA @ ( huffma2094459102Leaves @ TA @ A @ D @ B @ E @ C ) )
          = ( ^ [F: TA] : ( if @ nat @ ( F = B ) @ ( if @ nat @ ( member @ TA @ C @ ( huffma505251170phabet @ TA @ A ) ) @ D @ ( zero_zero @ nat ) ) @ ( if @ nat @ ( F = C ) @ ( if @ nat @ ( member @ TA @ B @ ( huffma505251170phabet @ TA @ A ) ) @ E @ ( zero_zero @ nat ) ) @ ( huffma854352999e_freq @ TA @ A @ F ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(45,axiom,
    ! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA,C: TA] :
      ( ( huffma1050891809istent @ TA @ A )
     => ( ( ( huffma943100115ibling @ TA @ A @ B )
          = C )
       => ( ( huffma943100115ibling @ TA @ A @ C )
          = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_sibling__reciprocal) ).

thf(406,plain,
    ! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA,C: TA] :
      ( ( huffma1050891809istent @ TA @ A )
     => ( ( ( huffma943100115ibling @ TA @ A @ B )
          = C )
       => ( ( huffma943100115ibling @ TA @ A @ C )
          = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(218,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq @ nat @ A @ B )
     => ( ord_less_eq @ nat @ ( times_times @ nat @ A @ C ) @ ( times_times @ nat @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_mult__le__mono1) ).

thf(880,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq @ nat @ A @ B )
     => ( ord_less_eq @ nat @ ( times_times @ nat @ A @ C ) @ ( times_times @ nat @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(125,axiom,
    ! [TA: $tType] :
      ( ( ordere216010020id_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
         => ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B )
           => ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_add__nonneg__nonneg) ).

thf(649,plain,
    ! [TA: $tType] :
      ( ( ordere216010020id_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
         => ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B )
           => ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(38,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ord @ TA @ ( type2 @ TA ) )
     => ( ord @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oord) ).

thf(387,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ord @ TA @ ( type2 @ TA ) )
     => ( ord @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(289,axiom,
    ! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA] : ( ord_less_eq @ nat @ ( huffma223349076_depth @ TA @ A @ B ) @ ( huffma1554076246height @ TA @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_depth__le__height) ).

thf(1080,plain,
    ! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA] : ( ord_less_eq @ nat @ ( huffma223349076_depth @ TA @ A @ B ) @ ( huffma1554076246height @ TA @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(86,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq @ nat @ ( times_times @ nat @ A @ B ) @ ( times_times @ nat @ C @ B ) )
      = ( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
       => ( ord_less_eq @ nat @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_mult__le__cancel2) ).

thf(535,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq @ nat @ ( times_times @ nat @ A @ B ) @ ( times_times @ nat @ C @ B ) )
      = ( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
       => ( ord_less_eq @ nat @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(191,axiom,
    ! [A: nat] :
      ( ( times_times @ nat @ A @ ( zero_zero @ nat ) )
      = ( zero_zero @ nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_mult__0__right) ).

thf(816,plain,
    ! [A: nat] :
      ( ( times_times @ nat @ A @ ( zero_zero @ nat ) )
      = ( zero_zero @ nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(107,axiom,
    ! [TA: $tType] :
      ( ( mult_zero @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( times_times @ TA @ ( zero_zero @ TA ) @ A )
          = ( zero_zero @ TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_mult__zero__left) ).

thf(594,plain,
    ! [TA: $tType] :
      ( ( mult_zero @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( times_times @ TA @ ( zero_zero @ TA ) @ A )
          = ( zero_zero @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(249,axiom,
    ! [TA: $tType] :
      ( ( semiri1923998003cancel @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( A
           != ( zero_zero @ TA ) )
         => ( ( ( times_times @ TA @ B @ A )
              = ( times_times @ TA @ C @ A ) )
            = ( B = C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_mult__right__cancel) ).

thf(964,plain,
    ! [TA: $tType] :
      ( ( semiri1923998003cancel @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( A
           != ( zero_zero @ TA ) )
         => ( ( ( times_times @ TA @ B @ A )
              = ( times_times @ TA @ C @ A ) )
            = ( B = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(231,axiom,
    ! [TA: $tType] :
      ( ( mult_zero @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( times_times @ TA @ A @ ( zero_zero @ TA ) )
          = ( zero_zero @ TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_mult__zero__right) ).

thf(915,plain,
    ! [TA: $tType] :
      ( ( mult_zero @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( times_times @ TA @ A @ ( zero_zero @ TA ) )
          = ( zero_zero @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(237,axiom,
    ! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA,C: TA] :
      ( ( huffma1050891809istent @ TA @ A )
     => ( ( member @ TA @ B @ ( huffma505251170phabet @ TA @ A ) )
       => ( ( member @ TA @ C @ ( huffma505251170phabet @ TA @ A ) )
         => ( ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma636208924e_cost @ TA @ ( huffma469337550apSyms @ TA @ A @ B @ C ) ) @ ( times_times @ nat @ ( huffma854352999e_freq @ TA @ A @ B ) @ ( huffma223349076_depth @ TA @ A @ B ) ) ) @ ( times_times @ nat @ ( huffma854352999e_freq @ TA @ A @ C ) @ ( huffma223349076_depth @ TA @ A @ C ) ) )
            = ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma636208924e_cost @ TA @ A ) @ ( times_times @ nat @ ( huffma854352999e_freq @ TA @ A @ B ) @ ( huffma223349076_depth @ TA @ A @ C ) ) ) @ ( times_times @ nat @ ( huffma854352999e_freq @ TA @ A @ C ) @ ( huffma223349076_depth @ TA @ A @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_cost__swapSyms) ).

thf(932,plain,
    ! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA,C: TA] :
      ( ( huffma1050891809istent @ TA @ A )
     => ( ( member @ TA @ B @ ( huffma505251170phabet @ TA @ A ) )
       => ( ( member @ TA @ C @ ( huffma505251170phabet @ TA @ A ) )
         => ( ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma636208924e_cost @ TA @ ( huffma469337550apSyms @ TA @ A @ B @ C ) ) @ ( times_times @ nat @ ( huffma854352999e_freq @ TA @ A @ B ) @ ( huffma223349076_depth @ TA @ A @ B ) ) ) @ ( times_times @ nat @ ( huffma854352999e_freq @ TA @ A @ C ) @ ( huffma223349076_depth @ TA @ A @ C ) ) )
            = ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma636208924e_cost @ TA @ A ) @ ( times_times @ nat @ ( huffma854352999e_freq @ TA @ A @ B ) @ ( huffma223349076_depth @ TA @ A @ C ) ) ) @ ( times_times @ nat @ ( huffma854352999e_freq @ TA @ A @ C ) @ ( huffma223349076_depth @ TA @ A @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(210,axiom,
    ! [TA: $tType] :
      ( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
     => ( ( times_times @ TA )
        = ( ^ [A: TA,B: TA] : ( times_times @ TA @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_semiring__normalization__rules_I7_J) ).

thf(858,plain,
    ! [TA: $tType] :
      ( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
     => ( ( times_times @ TA )
        = ( ^ [A: TA,B: TA] : ( times_times @ TA @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(31,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
          | ( ord_less_eq @ TA @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_linear) ).

thf(367,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
          | ( ord_less_eq @ TA @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(91,axiom,
    ! [TA: $tType] :
      ( ( semiri456707255roduct @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA,D: TA,E: TA] :
          ( ( A
           != ( zero_zero @ TA ) )
         => ( ( ( B = C )
              & ( D != E ) )
           => ( ( plus_plus @ TA @ B @ ( times_times @ TA @ A @ D ) )
             != ( plus_plus @ TA @ C @ ( times_times @ TA @ A @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_add__scale__eq__noteq) ).

thf(552,plain,
    ! [TA: $tType] :
      ( ( semiri456707255roduct @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA,D: TA,E: TA] :
          ( ( A
           != ( zero_zero @ TA ) )
         => ( ( ( B = C )
              & ( D != E ) )
           => ( ( plus_plus @ TA @ B @ ( times_times @ TA @ A @ D ) )
             != ( plus_plus @ TA @ C @ ( times_times @ TA @ A @ E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(183,axiom,
    semiri1193490041visors @ nat @ ( type2 @ nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Osemiring__no__zero__divisors) ).

thf(799,plain,
    semiri1193490041visors @ nat @ ( type2 @ nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(155,axiom,
    semiring @ nat @ ( type2 @ nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Osemiring) ).

thf(726,plain,
    semiring @ nat @ ( type2 @ nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(205,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq @ nat @ A @ B )
     => ( ord_less_eq @ nat @ A @ ( plus_plus @ nat @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_trans__le__add1) ).

thf(848,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq @ nat @ A @ B )
     => ( ord_less_eq @ nat @ A @ ( plus_plus @ nat @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(145,axiom,
    ! [TA: $tType] :
      ( ( ordered_semiring @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA,D: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ord_less_eq @ TA @ C @ D )
           => ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B )
             => ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ C )
               => ( ord_less_eq @ TA @ ( times_times @ TA @ A @ C ) @ ( times_times @ TA @ B @ D ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_mult__mono) ).

thf(700,plain,
    ! [TA: $tType] :
      ( ( ordered_semiring @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA,D: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ord_less_eq @ TA @ C @ D )
           => ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B )
             => ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ C )
               => ( ord_less_eq @ TA @ ( times_times @ TA @ A @ C ) @ ( times_times @ TA @ B @ D ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(265,axiom,
    ! [TA: $tType] :
      ( ( ordered_semiring @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA,D: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ord_less_eq @ TA @ C @ D )
           => ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
             => ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ C )
               => ( ord_less_eq @ TA @ ( times_times @ TA @ A @ C ) @ ( times_times @ TA @ B @ D ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_mult__mono_H) ).

thf(1022,plain,
    ! [TA: $tType] :
      ( ( ordered_semiring @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA,D: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ord_less_eq @ TA @ C @ D )
           => ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
             => ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ C )
               => ( ord_less_eq @ TA @ ( times_times @ TA @ A @ C ) @ ( times_times @ TA @ B @ D ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(143,axiom,
    ! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA] :
      ( ( huffma1050891809istent @ TA @ A )
     => ( ( huffma2094459102Leaves @ TA @ A @ ( huffma854352999e_freq @ TA @ A @ B ) @ B @ ( huffma854352999e_freq @ TA @ A @ B ) @ B )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_swapLeaves__id) ).

thf(695,plain,
    ! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA] :
      ( ( huffma1050891809istent @ TA @ A )
     => ( ( huffma2094459102Leaves @ TA @ A @ ( huffma854352999e_freq @ TA @ A @ B ) @ B @ ( huffma854352999e_freq @ TA @ A @ B ) @ B )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(219,axiom,
    ! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA,C: TA] :
      ( ( huffma1050891809istent @ TA @ A )
     => ( huffma1050891809istent @ TA @ ( huffma469337550apSyms @ TA @ A @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_consistent__swapSyms) ).

thf(883,plain,
    ! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA,C: TA] :
      ( ( huffma1050891809istent @ TA @ A )
     => ( huffma1050891809istent @ TA @ ( huffma469337550apSyms @ TA @ A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(110,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less @ nat @ ( times_times @ nat @ A @ B ) @ ( times_times @ nat @ C @ B ) )
      = ( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
        & ( ord_less @ nat @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_mult__less__cancel2) ).

thf(608,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less @ nat @ ( times_times @ nat @ A @ B ) @ ( times_times @ nat @ C @ B ) )
      = ( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
        & ( ord_less @ nat @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(230,axiom,
    ! [TA: $tType] :
      ( ( group_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
          = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_add_Ogroup__left__neutral) ).

thf(912,plain,
    ! [TA: $tType] :
      ( ( group_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
          = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(139,axiom,
    ! [TA: $tType] :
      ( ( ordere516151231imp_le @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ A )
          = ( ord_less @ TA @ B @ ( zero_zero @ TA ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_add__less__same__cancel1) ).

thf(685,plain,
    ! [TA: $tType] :
      ( ( ordere516151231imp_le @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ A )
          = ( ord_less @ TA @ B @ ( zero_zero @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(80,axiom,
    ! [A: nat] :
      ( ( plus_plus @ nat @ A @ ( zero_zero @ nat ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_Nat_Oadd__0__right) ).

thf(521,plain,
    ! [A: nat] :
      ( ( plus_plus @ nat @ A @ ( zero_zero @ nat ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(42,axiom,
    ! [TA: $tType] :
      ( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ( B
           != ( zero_zero @ TA ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_gr__implies__not__zero) ).

thf(399,plain,
    ! [TA: $tType] :
      ( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ( B
           != ( zero_zero @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(195,axiom,
    ! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_le0) ).

thf(827,plain,
    ! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(206,axiom,
    ! [TA: $tType] :
      ( ( ordered_semiring @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ C )
           => ( ord_less_eq @ TA @ ( times_times @ TA @ C @ A ) @ ( times_times @ TA @ C @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_mult__left__mono) ).

thf(851,plain,
    ! [TA: $tType] :
      ( ( ordered_semiring @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ C )
           => ( ord_less_eq @ TA @ ( times_times @ TA @ C @ A ) @ ( times_times @ TA @ C @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(271,axiom,
    ! [TA: $tType] :
      ( ( semigroup_mult @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ C )
          = ( times_times @ TA @ A @ ( times_times @ TA @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_mult_Oassoc) ).

thf(1034,plain,
    ! [TA: $tType] :
      ( ( semigroup_mult @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ C )
          = ( times_times @ TA @ A @ ( times_times @ TA @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(241,axiom,
    ! [TA: $tType] :
      ( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( times_times @ TA @ A @ ( times_times @ TA @ B @ C ) )
          = ( times_times @ TA @ B @ ( times_times @ TA @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_semiring__normalization__rules_I19_J) ).

thf(944,plain,
    ! [TA: $tType] :
      ( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( times_times @ TA @ A @ ( times_times @ TA @ B @ C ) )
          = ( times_times @ TA @ B @ ( times_times @ TA @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(130,axiom,
    ! [TA: $tType] :
      ( ( ordere779506340up_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA,D: TA] :
          ( ( ( A = B )
            & ( C = D ) )
         => ( ( plus_plus @ TA @ A @ C )
            = ( plus_plus @ TA @ B @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_add__mono__thms__linordered__semiring_I4_J) ).

thf(663,plain,
    ! [TA: $tType] :
      ( ( ordere779506340up_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA,D: TA] :
          ( ( ( A = B )
            & ( C = D ) )
         => ( ( plus_plus @ TA @ A @ C )
            = ( plus_plus @ TA @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(113,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( plus_plus @ nat @ A @ B ) )
      = ( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
        | ( ord_less @ nat @ ( zero_zero @ nat ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_add__gr__0) ).

thf(617,plain,
    ! [A: nat,B: nat] :
      ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( plus_plus @ nat @ A @ B ) )
      = ( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
        | ( ord_less @ nat @ ( zero_zero @ nat ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(167,axiom,
    ! [TA: $tType] :
      ( ( group_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ( plus_plus @ TA @ A @ B )
            = ( plus_plus @ TA @ C @ B ) )
          = ( A = C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_add_Oright__cancel) ).

thf(754,plain,
    ! [TA: $tType] :
      ( ( group_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ( plus_plus @ TA @ A @ B )
            = ( plus_plus @ TA @ C @ B ) )
          = ( A = C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(287,axiom,
    semiri1923998003cancel @ nat @ ( type2 @ nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Osemiring__no__zero__divisors__cancel) ).

thf(1076,plain,
    semiri1923998003cancel @ nat @ ( type2 @ nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(175,axiom,
    ! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA] :
      ( ( huffma1050891809istent @ TA @ A )
     => ( ( ( huffma223349076_depth @ TA @ A @ B )
          = ( huffma1554076246height @ TA @ A ) )
       => ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( huffma1554076246height @ TA @ A ) )
         => ( ( member @ TA @ B @ ( huffma505251170phabet @ TA @ A ) )
           => ( ( huffma943100115ibling @ TA @ A @ B )
             != B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_depth__height__imp__sibling__ne) ).

thf(776,plain,
    ! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA] :
      ( ( huffma1050891809istent @ TA @ A )
     => ( ( ( huffma223349076_depth @ TA @ A @ B )
          = ( huffma1554076246height @ TA @ A ) )
       => ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( huffma1554076246height @ TA @ A ) )
         => ( ( member @ TA @ B @ ( huffma505251170phabet @ TA @ A ) )
           => ( ( huffma943100115ibling @ TA @ A @ B )
             != B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(150,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( plus_plus @ nat @ A @ B )
        = ( plus_plus @ nat @ A @ C ) )
      = ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_nat__add__left__cancel) ).

thf(712,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( plus_plus @ nat @ A @ B )
        = ( plus_plus @ nat @ A @ C ) )
      = ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(102,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq @ nat @ ( plus_plus @ nat @ A @ B ) @ C )
     => ~ ( ( ord_less_eq @ nat @ A @ C )
         => ~ ( ord_less_eq @ nat @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_add__leE) ).

thf(580,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq @ nat @ ( plus_plus @ nat @ A @ B ) @ C )
     => ~ ( ( ord_less_eq @ nat @ A @ C )
         => ~ ( ord_less_eq @ nat @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(121,axiom,
    ! [TA: $tType] :
      ( ( ordere516151231imp_le @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ B )
          = ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_add__le__same__cancel2) ).

thf(640,plain,
    ! [TA: $tType] :
      ( ( ordere516151231imp_le @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ B )
          = ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(147,axiom,
    ! [A: nat,B: nat] :
      ( ( ( times_times @ nat @ A @ B )
        = ( zero_zero @ nat ) )
      = ( ( A
          = ( zero_zero @ nat ) )
        | ( B
          = ( zero_zero @ nat ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_mult__is__0) ).

thf(705,plain,
    ! [A: nat,B: nat] :
      ( ( ( times_times @ nat @ A @ B )
        = ( zero_zero @ nat ) )
      = ( ( A
          = ( zero_zero @ nat ) )
        | ( B
          = ( zero_zero @ nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(13521,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType] :
      ( ~ $true
      | ( preorder @ ( TZA > TZB ) @ ( type2 @ ( TZA > TZB ) ) )
      | ( ( preorder @ ( TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) @ ( type2 @ ( TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ) )
       != ( preorder @ TZB @ ( type2 @ TZB ) ) ) ),
    inference(paramod_ordered,[status(thm)],[13039,320]) ).

thf(13522,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType] :
      ( ( preorder @ ( TZA > TZB ) @ ( type2 @ ( TZA > TZB ) ) )
      | ( ( preorder @ ( TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) @ ( type2 @ ( TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ) )
       != ( preorder @ TZB @ ( type2 @ TZB ) ) ) ),
    inference(simp,[status(thm)],[13521]) ).

thf(13523,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType] : ( preorder @ ( TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) @ ( type2 @ ( TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ) ),
    inference(pattern_uni,[status(thm)],[13522:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ))]]) ).

thf(245,axiom,
    ordere1490568538miring @ nat @ ( type2 @ nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Oordered__comm__semiring) ).

thf(954,plain,
    ordere1490568538miring @ nat @ ( type2 @ nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(161,axiom,
    ! [TA: $tType] :
      ( ( semiri1923998003cancel @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( A
           != ( zero_zero @ TA ) )
         => ( ( ( times_times @ TA @ A @ B )
              = ( times_times @ TA @ A @ C ) )
            = ( B = C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_mult__left__cancel) ).

thf(739,plain,
    ! [TA: $tType] :
      ( ( semiri1923998003cancel @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( A
           != ( zero_zero @ TA ) )
         => ( ( ( times_times @ TA @ A @ B )
              = ( times_times @ TA @ A @ C ) )
            = ( B = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(278,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( plus_plus @ nat @ A @ B )
        = ( plus_plus @ nat @ C @ B ) )
      = ( A = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_nat__add__right__cancel) ).

thf(1053,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( plus_plus @ nat @ A @ B )
        = ( plus_plus @ nat @ C @ B ) )
      = ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(55,axiom,
    ! [TA: $tType,A: set @ TA] :
      ( ( collect @ TA
        @ ^ [B: TA] : ( member @ TA @ B @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_Collect__mem__eq) ).

thf(441,plain,
    ! [TA: $tType,A: set @ TA] :
      ( ( collect @ TA
        @ ^ [B: TA] : ( member @ TA @ B @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(152,axiom,
    ! [A: nat,B: nat] :
      ( ( ( plus_plus @ nat @ A @ B )
        = ( zero_zero @ nat ) )
      = ( ( A
          = ( zero_zero @ nat ) )
        & ( B
          = ( zero_zero @ nat ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_add__is__0) ).

thf(717,plain,
    ! [A: nat,B: nat] :
      ( ( ( plus_plus @ nat @ A @ B )
        = ( zero_zero @ nat ) )
      = ( ( A
          = ( zero_zero @ nat ) )
        & ( B
          = ( zero_zero @ nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(59,axiom,
    ! [TA: $tType] :
      ( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_zero__le) ).

thf(463,plain,
    ! [TA: $tType] :
      ( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(6121,plain,
    ! [TA: $tType,B: TA > $o,A: TA] :
      ( ~ ( member @ TA @ A @ ( collect @ TA @ B ) )
      | ~ ( ord_less @ $o @ ( zero_zero @ $o ) @ ( zero_zero @ $o ) )
      | ( ( B @ A )
       != ( canoni770627133id_add @ $o @ ( type2 @ $o ) ) ) ),
    inference(paramod_ordered,[status(thm)],[305,5889]) ).

thf(6125,plain,
    ! [TA: $tType,A: TA] :
      ( ~ ( member @ TA @ A
          @ ( collect @ TA
            @ ^ [B: TA] : ( canoni770627133id_add @ $o @ ( type2 @ $o ) ) ) )
      | ~ ( ord_less @ $o @ ( zero_zero @ $o ) @ ( zero_zero @ $o ) ) ),
    inference(pre_uni,[status(thm)],[6121:[bind(A,$thf( A )),bind(B,$thf( ^ [C: TA] : ( canoni770627133id_add @ $o @ ( type2 @ $o ) ) ))]]) ).

thf(18,axiom,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ TA ) )
     => ( ( (=) @ TA )
        = ( ^ [A: TA,B: TA] :
              ( ( ord_less_eq @ TA @ A @ B )
              & ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_eq__iff) ).

thf(336,plain,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ TA ) )
     => ( ( (=) @ TA )
        = ( ^ [A: TA,B: TA] :
              ( ( ord_less_eq @ TA @ A @ B )
              & ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(337,plain,
    ! [TA: $tType] :
      ( ~ ( order @ TA @ ( type2 @ TA ) )
      | ( ( (=) @ TA )
        = ( ^ [A: TA,B: TA] :
              ( ( ord_less_eq @ TA @ A @ B )
              & ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
    inference(cnf,[status(esa)],[336]) ).

thf(338,plain,
    ! [TA: $tType] :
      ( ( ( ^ [A: TA,B: TA] :
              ( ( ord_less_eq @ TA @ A @ B )
              & ( ord_less_eq @ TA @ B @ A ) ) )
        = ( (=) @ TA ) )
      | ~ ( order @ TA @ ( type2 @ TA ) ) ),
    inference(lifteq,[status(thm)],[337]) ).

thf(122,axiom,
    ! [TA: $tType] :
      ( ( cancel_semigroup_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ( plus_plus @ TA @ A @ B )
            = ( plus_plus @ TA @ C @ B ) )
         => ( A = C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_add__right__imp__eq) ).

thf(643,plain,
    ! [TA: $tType] :
      ( ( cancel_semigroup_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ( plus_plus @ TA @ A @ B )
            = ( plus_plus @ TA @ C @ B ) )
         => ( A = C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(62,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( ord @ TA @ ( type2 @ TA ) )
        & ( ord @ TB @ ( type2 @ TB ) ) )
     => ! [A: TB,B: TA > TB,C: TA,D: TA] :
          ( ( A
            = ( B @ C ) )
         => ( ( ord_less_eq @ TA @ C @ D )
           => ( ! [E: TA,F: TA] :
                  ( ( ord_less_eq @ TA @ E @ F )
                 => ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
             => ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_ord__eq__le__subst) ).

thf(470,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( ord @ TA @ ( type2 @ TA ) )
        & ( ord @ TB @ ( type2 @ TB ) ) )
     => ! [A: TB,B: TA > TB,C: TA,D: TA] :
          ( ( A
            = ( B @ C ) )
         => ( ( ord_less_eq @ TA @ C @ D )
           => ( ! [E: TA,F: TA] :
                  ( ( ord_less_eq @ TA @ E @ F )
                 => ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
             => ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(100,axiom,
    ! [TA: $tType] :
      ( ( ordere236663937imp_le @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
          = ( ord_less @ TA @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_add__less__cancel__right) ).

thf(576,plain,
    ! [TA: $tType] :
      ( ( ordere236663937imp_le @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
          = ( ord_less @ TA @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(244,axiom,
    ! [TA: $tType] :
      ( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( plus_plus @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ C @ B ) )
          = ( times_times @ TA @ ( plus_plus @ TA @ A @ C ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_semiring__normalization__rules_I1_J) ).

thf(951,plain,
    ! [TA: $tType] :
      ( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( plus_plus @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ C @ B ) )
          = ( times_times @ TA @ ( plus_plus @ TA @ A @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(187,axiom,
    semiri456707255roduct @ nat @ ( type2 @ nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).

thf(808,plain,
    semiri456707255roduct @ nat @ ( type2 @ nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(163,axiom,
    ! [TA: $tType] :
      ( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
          = ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_semiring__normalization__rules_I25_J) ).

thf(744,plain,
    ! [TA: $tType] :
      ( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
          = ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(109,axiom,
    ! [TA: $tType] :
      ( ( mult_zero @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ( times_times @ TA @ A @ B )
           != ( zero_zero @ TA ) )
         => ( ( A
             != ( zero_zero @ TA ) )
            & ( B
             != ( zero_zero @ TA ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_mult__not__zero) ).

thf(600,plain,
    ! [TA: $tType] :
      ( ( mult_zero @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ( times_times @ TA @ A @ B )
           != ( zero_zero @ TA ) )
         => ( ( A
             != ( zero_zero @ TA ) )
            & ( B
             != ( zero_zero @ TA ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(212,axiom,
    ! [TA: $tType] :
      ( ( linord219039673up_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( ( zero_zero @ TA )
            = ( plus_plus @ TA @ A @ A ) )
          = ( A
            = ( zero_zero @ TA ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_double__zero__sym) ).

thf(864,plain,
    ! [TA: $tType] :
      ( ( linord219039673up_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( ( zero_zero @ TA )
            = ( plus_plus @ TA @ A @ A ) )
          = ( A
            = ( zero_zero @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(156,axiom,
    ! [TA: $tType] :
      ( ( ab_semigroup_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
          = ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_ab__semigroup__add__class_Oadd__ac_I1_J) ).

thf(727,plain,
    ! [TA: $tType] :
      ( ( ab_semigroup_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
          = ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(256,axiom,
    monoid_add @ nat @ ( type2 @ nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Omonoid__add) ).

thf(991,plain,
    monoid_add @ nat @ ( type2 @ nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(57,axiom,
    ! [TA: $tType] :
      ( ( preorder @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ord_less_eq @ TA @ B @ C )
           => ( ord_less_eq @ TA @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_order__trans) ).

thf(446,plain,
    ! [TA: $tType] :
      ( ( preorder @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ord_less_eq @ TA @ B @ C )
           => ( ord_less_eq @ TA @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(98,axiom,
    ! [TA: $tType] :
      ( ( semiri1193490041visors @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ( times_times @ TA @ A @ B )
            = ( zero_zero @ TA ) )
         => ( ( A
              = ( zero_zero @ TA ) )
            | ( B
              = ( zero_zero @ TA ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_divisors__zero) ).

thf(571,plain,
    ! [TA: $tType] :
      ( ( semiri1193490041visors @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ( times_times @ TA @ A @ B )
            = ( zero_zero @ TA ) )
         => ( ( A
              = ( zero_zero @ TA ) )
            | ( B
              = ( zero_zero @ TA ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(60,axiom,
    ! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA] :
      ( ( ( huffma943100115ibling @ TA @ A @ B )
       != B )
     => ( member @ TA @ ( huffma943100115ibling @ TA @ A @ B ) @ ( huffma505251170phabet @ TA @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_sibling__ne__imp__sibling__in__alphabet) ).

thf(465,plain,
    ! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA] :
      ( ( ( huffma943100115ibling @ TA @ A @ B )
       != B )
     => ( member @ TA @ ( huffma943100115ibling @ TA @ A @ B ) @ ( huffma505251170phabet @ TA @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(116,axiom,
    ! [TA: $tType] :
      ( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
     => ( ( ord_less_eq @ TA )
        = ( ^ [A: TA,B: TA] :
            ? [C: TA] :
              ( B
              = ( plus_plus @ TA @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_le__iff__add) ).

thf(627,plain,
    ! [TA: $tType] :
      ( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
     => ( ( ord_less_eq @ TA )
        = ( ^ [A: TA,B: TA] :
            ? [C: TA] :
              ( B
              = ( plus_plus @ TA @ A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(291,axiom,
    ! [TA: $tType] :
      ( ( ab_semigroup_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
          = ( plus_plus @ TA @ B @ ( plus_plus @ TA @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_add_Oleft__commute) ).

thf(1084,plain,
    ! [TA: $tType] :
      ( ( ab_semigroup_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
          = ( plus_plus @ TA @ B @ ( plus_plus @ TA @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(65,axiom,
    ! [TA: $tType] :
      ( ( semiri1923998003cancel @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ( times_times @ TA @ A @ B )
            = ( times_times @ TA @ A @ C ) )
          = ( ( A
              = ( zero_zero @ TA ) )
            | ( B = C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_mult__cancel__left) ).

thf(482,plain,
    ! [TA: $tType] :
      ( ( semiri1923998003cancel @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ( times_times @ TA @ A @ B )
            = ( times_times @ TA @ A @ C ) )
          = ( ( A
              = ( zero_zero @ TA ) )
            | ( B = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(81,axiom,
    ! [A: nat] : ( ord_less_eq @ nat @ A @ ( times_times @ nat @ A @ ( times_times @ nat @ A @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_le__cube) ).

thf(524,plain,
    ! [A: nat] : ( ord_less_eq @ nat @ A @ ( times_times @ nat @ A @ ( times_times @ nat @ A @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(70,axiom,
    ! [TA: $tType] :
      ( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( times_times @ TA @ ( zero_zero @ TA ) @ A )
          = ( zero_zero @ TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_semiring__normalization__rules_I9_J) ).

thf(495,plain,
    ! [TA: $tType] :
      ( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( times_times @ TA @ ( zero_zero @ TA ) @ A )
          = ( zero_zero @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(222,axiom,
    ! [A: nat] :
      ( ( A
       != ( zero_zero @ nat ) )
      = ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_neq0__conv) ).

thf(891,plain,
    ! [A: nat] :
      ( ( A
       != ( zero_zero @ nat ) )
      = ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(203,axiom,
    ! [TA: $tType] :
      ( ( ordere216010020id_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
         => ( ( ord_less_eq @ TA @ B @ C )
           => ( ord_less_eq @ TA @ ( plus_plus @ TA @ B @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_add__decreasing2) ).

thf(844,plain,
    ! [TA: $tType] :
      ( ( ordere216010020id_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
         => ( ( ord_less_eq @ TA @ B @ C )
           => ( ord_less_eq @ TA @ ( plus_plus @ TA @ B @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(362,plain,
    ! [TA: $tType,E: nat,D: nat,C: TA,B: TA,A: huffma16452318e_tree @ TA] :
      ( ~ ( huffma1050891809istent @ TA @ A )
      | ( ( huffma943100115ibling @ TA @ A @ B )
        = B )
      | ( C = B )
      | ( ( huffma943100115ibling @ TA @ ( huffma2094459102Leaves @ TA @ A @ D @ C @ E @ ( huffma943100115ibling @ TA @ A @ B ) ) @ C )
        = B ) ),
    inference(cnf,[status(esa)],[361]) ).

thf(363,plain,
    ! [TA: $tType,E: nat,D: nat,C: TA,B: TA,A: huffma16452318e_tree @ TA] :
      ( ( ( huffma943100115ibling @ TA @ A @ B )
        = B )
      | ( C = B )
      | ( ( huffma943100115ibling @ TA @ ( huffma2094459102Leaves @ TA @ A @ D @ C @ E @ ( huffma943100115ibling @ TA @ A @ B ) ) @ C )
        = B )
      | ~ ( huffma1050891809istent @ TA @ A ) ),
    inference(lifteq,[status(thm)],[362]) ).

thf(92,axiom,
    ! [TA: $tType] :
      ( ( ordere236663937imp_le @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
         => ( ord_less_eq @ TA @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_add__le__imp__le__right) ).

thf(556,plain,
    ! [TA: $tType] :
      ( ( ordere236663937imp_le @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
         => ( ord_less_eq @ TA @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(253,axiom,
    ! [TA: $tType] :
      ( ( linordered_field @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ C )
          = ( times_times @ TA @ A @ ( times_times @ TA @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_linordered__field__class_Osign__simps_I23_J) ).

thf(976,plain,
    ! [TA: $tType] :
      ( ( linordered_field @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ C )
          = ( times_times @ TA @ A @ ( times_times @ TA @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(226,axiom,
    ! [TA: $tType] :
      ( ( linord581940658strict @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ( plus_plus @ TA @ ( times_times @ TA @ A @ A ) @ ( times_times @ TA @ B @ B ) )
            = ( zero_zero @ TA ) )
          = ( ( A
              = ( zero_zero @ TA ) )
            & ( B
              = ( zero_zero @ TA ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_sum__squares__eq__zero__iff) ).

thf(903,plain,
    ! [TA: $tType] :
      ( ( linord581940658strict @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ( plus_plus @ TA @ ( times_times @ TA @ A @ A ) @ ( times_times @ TA @ B @ B ) )
            = ( zero_zero @ TA ) )
          = ( ( A
              = ( zero_zero @ TA ) )
            & ( B
              = ( zero_zero @ TA ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(3989,plain,
    ! [B: a,A: a] :
      ( ~ ( order @ a @ ( type2 @ a ) )
      | ~ ( ord_less_eq @ a @ A @ B )
      | ~ ( ord_less_eq @ a @ B @ A )
      | ( ( huffma636208924e_cost @ a @ ( huffma469337550apSyms @ a @ t @ a2 @ b ) )
       != ( huffma636208924e_cost @ a @ t ) )
      | ( A != a2 )
      | ( B != b ) ),
    inference(paramod_ordered,[status(thm)],[332,2872]) ).

thf(3990,plain,
    ! [A: a] :
      ( ~ ( order @ a @ ( type2 @ a ) )
      | ~ ( ord_less_eq @ a @ A @ b )
      | ~ ( ord_less_eq @ a @ b @ A )
      | ( ( huffma636208924e_cost @ a @ ( huffma469337550apSyms @ a @ t @ a2 @ b ) )
       != ( huffma636208924e_cost @ a @ t ) )
      | ( A != a2 ) ),
    inference(pattern_uni,[status(thm)],[3989:[bind(A,$thf( A )),bind(B,$thf( b ))]]) ).

thf(5258,plain,
    ( ~ ( order @ a @ ( type2 @ a ) )
    | ~ ( ord_less_eq @ a @ a2 @ b )
    | ~ ( ord_less_eq @ a @ b @ a2 )
    | ( ( huffma636208924e_cost @ a @ ( huffma469337550apSyms @ a @ t @ a2 @ b ) )
     != ( huffma636208924e_cost @ a @ t ) ) ),
    inference(simp,[status(thm)],[3990]) ).

thf(190,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( ord_less_eq @ nat @ A @ B )
     => ( ( ord_less_eq @ nat @ C @ D )
       => ( ord_less_eq @ nat @ ( plus_plus @ nat @ ( times_times @ nat @ A @ D ) @ ( times_times @ nat @ B @ C ) ) @ ( plus_plus @ nat @ ( times_times @ nat @ A @ C ) @ ( times_times @ nat @ B @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_le__le__imp__sum__mult__le__sum__mult) ).

thf(813,plain,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( ord_less_eq @ nat @ A @ B )
     => ( ( ord_less_eq @ nat @ C @ D )
       => ( ord_less_eq @ nat @ ( plus_plus @ nat @ ( times_times @ nat @ A @ D ) @ ( times_times @ nat @ B @ C ) ) @ ( plus_plus @ nat @ ( times_times @ nat @ A @ C ) @ ( times_times @ nat @ B @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(248,axiom,
    ordered_semiring @ nat @ ( type2 @ nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Oordered__semiring) ).

thf(963,plain,
    ordered_semiring @ nat @ ( type2 @ nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(165,axiom,
    ! [TA: $tType] :
      ( ( ordere236663937imp_le @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
          = ( ord_less @ TA @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_add__less__cancel__left) ).

thf(748,plain,
    ! [TA: $tType] :
      ( ( ordere236663937imp_le @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
          = ( ord_less @ TA @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(49,axiom,
    ! [TA: $tType,A: TA,B: huffma16452318e_tree @ TA] :
      ( ~ ( member @ TA @ A @ ( huffma505251170phabet @ TA @ B ) )
     => ( ( huffma943100115ibling @ TA @ B @ A )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_notin__alphabet__imp__sibling__id) ).

thf(418,plain,
    ! [TA: $tType,A: TA,B: huffma16452318e_tree @ TA] :
      ( ~ ( member @ TA @ A @ ( huffma505251170phabet @ TA @ B ) )
     => ( ( huffma943100115ibling @ TA @ B @ A )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(177,axiom,
    ! [TA: $tType] :
      ( ( semigroup_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
          = ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_add_Oassoc) ).

thf(781,plain,
    ! [TA: $tType] :
      ( ( semigroup_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
          = ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(2368,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( ord_less_eq @ ( TB > TA ) )
        = ( ^ [A: TB > TA,B: TB > TA] :
            ! [C: TB] : ( ord_less_eq @ TA @ ( A @ C ) @ ( B @ C ) ) ) )
      | ~ $true
      | ( ( ord @ nat @ ( type2 @ nat ) )
       != ( ord @ TA @ ( type2 @ TA ) ) ) ),
    inference(paramod_ordered,[status(thm)],[579,316]) ).

thf(2369,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( ord_less_eq @ ( TB > TA ) )
        = ( ^ [A: TB > TA,B: TB > TA] :
            ! [C: TB] : ( ord_less_eq @ TA @ ( A @ C ) @ ( B @ C ) ) ) )
      | ( ( ord @ nat @ ( type2 @ nat ) )
       != ( ord @ TA @ ( type2 @ TA ) ) ) ),
    inference(simp,[status(thm)],[2368]) ).

thf(2370,plain,
    ! [TB: $tType] :
      ( ( ord_less_eq @ ( TB > nat ) )
      = ( ^ [A: TB > nat,B: TB > nat] :
          ! [C: TB] : ( ord_less_eq @ nat @ ( A @ C ) @ ( B @ C ) ) ) ),
    inference(pattern_uni,[status(thm)],[2369:[bind_type(TA,$thf( nat ))]]) ).

thf(2394,plain,
    ! [TA: $tType] :
      ( ( ord_less_eq @ ( TA > nat ) )
      = ( ^ [A: TA > nat,B: TA > nat] :
          ! [C: TA] : ( ord_less_eq @ nat @ ( A @ C ) @ ( B @ C ) ) ) ),
    inference(simp,[status(thm)],[2370]) ).

thf(281,axiom,
    ! [TA: $tType] :
      ( ( linord219039673up_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( ord_less @ TA @ ( plus_plus @ TA @ A @ A ) @ ( zero_zero @ TA ) )
          = ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_double__add__less__zero__iff__single__add__less__zero) ).

thf(1062,plain,
    ! [TA: $tType] :
      ( ( linord219039673up_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( ord_less @ TA @ ( plus_plus @ TA @ A @ A ) @ ( zero_zero @ TA ) )
          = ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(258,axiom,
    ! [TA: $tType] :
      ( ( semiri456707255roduct @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA,D: TA] :
          ( ( ( A != B )
            & ( C != D ) )
          = ( ( plus_plus @ TA @ ( times_times @ TA @ A @ C ) @ ( times_times @ TA @ B @ D ) )
           != ( plus_plus @ TA @ ( times_times @ TA @ A @ D ) @ ( times_times @ TA @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_crossproduct__noteq) ).

thf(995,plain,
    ! [TA: $tType] :
      ( ( semiri456707255roduct @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA,D: TA] :
          ( ( ( A != B )
            & ( C != D ) )
          = ( ( plus_plus @ TA @ ( times_times @ TA @ A @ C ) @ ( times_times @ TA @ B @ D ) )
           != ( plus_plus @ TA @ ( times_times @ TA @ A @ D ) @ ( times_times @ TA @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(97,axiom,
    ! [TA: $tType] :
      ( ( semiring @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( times_times @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
          = ( plus_plus @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_distrib__left) ).

thf(568,plain,
    ! [TA: $tType] :
      ( ( semiring @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( times_times @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
          = ( plus_plus @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(131,axiom,
    ! [TA: $tType] :
      ( ( linord219039673up_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ A @ A ) )
          = ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_zero__le__double__add__iff__zero__le__single__add) ).

thf(667,plain,
    ! [TA: $tType] :
      ( ( linord219039673up_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ A @ A ) )
          = ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(236,axiom,
    ! [TA: $tType] :
      ( ( ordere516151231imp_le @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ ( plus_plus @ TA @ A @ B ) )
          = ( ord_less @ TA @ ( zero_zero @ TA ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_less__add__same__cancel1) ).

thf(929,plain,
    ! [TA: $tType] :
      ( ( ordere516151231imp_le @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ ( plus_plus @ TA @ A @ B ) )
          = ( ord_less @ TA @ ( zero_zero @ TA ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(170,axiom,
    ! [TA: $tType] :
      ( ( cancel1352612707id_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( A
            = ( plus_plus @ TA @ A @ B ) )
          = ( B
            = ( zero_zero @ TA ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_add__cancel__right__right) ).

thf(763,plain,
    ! [TA: $tType] :
      ( ( cancel1352612707id_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( A
            = ( plus_plus @ TA @ A @ B ) )
          = ( B
            = ( zero_zero @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(344,plain,
    ! [TA: $tType,B: TA,A: TA] :
      ( ~ ( preorder @ TA @ ( type2 @ TA ) )
      | ( A != B )
      | ( ord_less_eq @ TA @ A @ B ) ),
    inference(cnf,[status(esa)],[343]) ).

thf(345,plain,
    ! [TA: $tType,B: TA,A: TA] :
      ( ( A != B )
      | ~ ( preorder @ TA @ ( type2 @ TA ) )
      | ( ord_less_eq @ TA @ A @ B ) ),
    inference(lifteq,[status(thm)],[344]) ).

thf(346,plain,
    ! [TA: $tType,A: TA] :
      ( ~ ( preorder @ TA @ ( type2 @ TA ) )
      | ( ord_less_eq @ TA @ A @ A ) ),
    inference(simp,[status(thm)],[345]) ).

thf(90,axiom,
    ! [TA: $tType] :
      ( ( ab_semigroup_mult @ TA @ ( type2 @ TA ) )
     => ( ( times_times @ TA )
        = ( ^ [A: TA,B: TA] : ( times_times @ TA @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_mult_Ocommute) ).

thf(549,plain,
    ! [TA: $tType] :
      ( ( ab_semigroup_mult @ TA @ ( type2 @ TA ) )
     => ( ( times_times @ TA )
        = ( ^ [A: TA,B: TA] : ( times_times @ TA @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(275,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( times_times @ nat @ A @ ( plus_plus @ nat @ B @ C ) )
      = ( plus_plus @ nat @ ( times_times @ nat @ A @ B ) @ ( times_times @ nat @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_add__mult__distrib2) ).

thf(1045,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( times_times @ nat @ A @ ( plus_plus @ nat @ B @ C ) )
      = ( plus_plus @ nat @ ( times_times @ nat @ A @ B ) @ ( times_times @ nat @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(184,axiom,
    ! [TA: $tType] :
      ( ( linordered_field @ TA @ ( type2 @ TA ) )
     => ( ( times_times @ TA )
        = ( ^ [A: TA,B: TA] : ( times_times @ TA @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_linordered__field__class_Osign__simps_I24_J) ).

thf(800,plain,
    ! [TA: $tType] :
      ( ( linordered_field @ TA @ ( type2 @ TA ) )
     => ( ( times_times @ TA )
        = ( ^ [A: TA,B: TA] : ( times_times @ TA @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(269,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq @ nat @ ( plus_plus @ nat @ A @ B ) @ ( plus_plus @ nat @ A @ C ) )
      = ( ord_less_eq @ nat @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_nat__add__left__cancel__le) ).

thf(1030,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq @ nat @ ( plus_plus @ nat @ A @ B ) @ ( plus_plus @ nat @ A @ C ) )
      = ( ord_less_eq @ nat @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(288,axiom,
    ! [TA: $tType] :
      ( ( ab_semigroup_mult @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( times_times @ TA @ A @ ( times_times @ TA @ B @ C ) )
          = ( times_times @ TA @ B @ ( times_times @ TA @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_mult_Oleft__commute) ).

thf(1077,plain,
    ! [TA: $tType] :
      ( ( ab_semigroup_mult @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( times_times @ TA @ A @ ( times_times @ TA @ B @ C ) )
          = ( times_times @ TA @ B @ ( times_times @ TA @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(63,axiom,
    ord_less_eq @ nat @ ( huffma854352999e_freq @ a @ t @ a2 ) @ ( huffma854352999e_freq @ a @ t @ b ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_assms_I4_J) ).

thf(478,plain,
    ord_less_eq @ nat @ ( huffma854352999e_freq @ a @ t @ a2 ) @ ( huffma854352999e_freq @ a @ t @ b ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(114,axiom,
    ! [TA: $tType] :
      ( ( ordere779506340up_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA,D: TA] :
          ( ( ( ord_less_eq @ TA @ A @ B )
            & ( C = D ) )
         => ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_add__mono__thms__linordered__semiring_I3_J) ).

thf(620,plain,
    ! [TA: $tType] :
      ( ( ordere779506340up_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA,D: TA] :
          ( ( ( ord_less_eq @ TA @ A @ B )
            & ( C = D ) )
         => ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(52,axiom,
    ! [TA: $tType,A: TA,B: huffma16452318e_tree @ TA,C: nat,D: nat] :
      ( ~ ( member @ TA @ A @ ( huffma505251170phabet @ TA @ B ) )
     => ( ( huffma2094459102Leaves @ TA @ B @ C @ A @ D @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_swapLeaves__id__when__notin__alphabet) ).

thf(432,plain,
    ! [TA: $tType,A: TA,B: huffma16452318e_tree @ TA,C: nat,D: nat] :
      ( ~ ( member @ TA @ A @ ( huffma505251170phabet @ TA @ B ) )
     => ( ( huffma2094459102Leaves @ TA @ B @ C @ A @ D @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(213,axiom,
    ! [TA: $tType] :
      ( ( comm_monoid_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
          = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_add_Ocomm__neutral) ).

thf(867,plain,
    ! [TA: $tType] :
      ( ( comm_monoid_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
          = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(159,axiom,
    ! [A: nat] :
      ( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
      = ( A
        = ( zero_zero @ nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_le__0__eq) ).

thf(735,plain,
    ! [A: nat] :
      ( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
      = ( A
        = ( zero_zero @ nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(198,axiom,
    ! [TA: $tType] :
      ( ( ordered_semiring @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ C )
           => ( ord_less_eq @ TA @ ( times_times @ TA @ A @ C ) @ ( times_times @ TA @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_mult__right__mono) ).

thf(833,plain,
    ! [TA: $tType] :
      ( ( ordered_semiring @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ C )
           => ( ord_less_eq @ TA @ ( times_times @ TA @ A @ C ) @ ( times_times @ TA @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(46,axiom,
    ! [TA: $tType] :
      ( ( zero @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( ( zero_zero @ TA )
            = A )
          = ( A
            = ( zero_zero @ TA ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_zero__reorient) ).

thf(410,plain,
    ! [TA: $tType] :
      ( ( zero @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( ( zero_zero @ TA )
            = A )
          = ( A
            = ( zero_zero @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(250,axiom,
    ! [TA: $tType] :
      ( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA,D: TA] :
          ( ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ C @ D ) )
          = ( times_times @ TA @ A @ ( times_times @ TA @ B @ ( times_times @ TA @ C @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_semiring__normalization__rules_I14_J) ).

thf(967,plain,
    ! [TA: $tType] :
      ( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA,D: TA] :
          ( ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ C @ D ) )
          = ( times_times @ TA @ A @ ( times_times @ TA @ B @ ( times_times @ TA @ C @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(243,axiom,
    ordere236663937imp_le @ nat @ ( type2 @ nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le) ).

thf(950,plain,
    ordere236663937imp_le @ nat @ ( type2 @ nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(199,axiom,
    ! [TA: $tType] :
      ( ( linord219039673up_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ A @ A ) )
          = ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_zero__less__double__add__iff__zero__less__single__add) ).

thf(835,plain,
    ! [TA: $tType] :
      ( ( linord219039673up_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ A @ A ) )
          = ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(2734,plain,
    ! [TA: $tType,TB: $tType,B: TA > $o,A: TA] :
      ( ~ ( linordered_field @ TB @ ( type2 @ TB ) )
      | ~ ( member @ TA @ A @ ( collect @ TA @ B ) )
      | ( ( B @ A )
       != ( canoni770627133id_add @ TB @ ( type2 @ TB ) ) ) ),
    inference(paramod_ordered,[status(thm)],[305,2646]) ).

thf(2736,plain,
    ! [TA: $tType,TB: $tType,A: TA] :
      ( ~ ( linordered_field @ TB @ ( type2 @ TB ) )
      | ~ ( member @ TA @ A
          @ ( collect @ TA
            @ ^ [B: TA] : ( canoni770627133id_add @ TB @ ( type2 @ TB ) ) ) ) ),
    inference(pre_uni,[status(thm)],[2734:[bind(A,$thf( A )),bind(B,$thf( ^ [C: TA] : ( canoni770627133id_add @ TB @ ( type2 @ TB ) ) ))]]) ).

thf(208,axiom,
    ! [TA: $tType,A: TA,B: huffma16452318e_tree @ TA] :
      ( ~ ( member @ TA @ A @ ( huffma505251170phabet @ TA @ B ) )
     => ( ( huffma854352999e_freq @ TA @ B @ A )
        = ( zero_zero @ nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_notin__alphabet__imp__freq__0) ).

thf(854,plain,
    ! [TA: $tType,A: TA,B: huffma16452318e_tree @ TA] :
      ( ~ ( member @ TA @ A @ ( huffma505251170phabet @ TA @ B ) )
     => ( ( huffma854352999e_freq @ TA @ B @ A )
        = ( zero_zero @ nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(180,axiom,
    ! [TA: $tType] :
      ( ( cancel_semigroup_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ( plus_plus @ TA @ A @ B )
            = ( plus_plus @ TA @ C @ B ) )
          = ( A = C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_add__right__cancel) ).

thf(790,plain,
    ! [TA: $tType] :
      ( ( cancel_semigroup_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ( plus_plus @ TA @ A @ B )
            = ( plus_plus @ TA @ C @ B ) )
          = ( A = C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(95,axiom,
    ! [TA: $tType] :
      ( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ C )
          = ( times_times @ TA @ A @ ( times_times @ TA @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_semiring__normalization__rules_I17_J) ).

thf(564,plain,
    ! [TA: $tType] :
      ( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ C )
          = ( times_times @ TA @ A @ ( times_times @ TA @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(232,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less @ nat @ ( times_times @ nat @ A @ B ) @ ( times_times @ nat @ A @ C ) )
      = ( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
        & ( ord_less @ nat @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_nat__mult__less__cancel__disj) ).

thf(918,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less @ nat @ ( times_times @ nat @ A @ B ) @ ( times_times @ nat @ A @ C ) )
      = ( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
        & ( ord_less @ nat @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(279,axiom,
    ! [TA: $tType] :
      ( ( cancel_semigroup_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ( plus_plus @ TA @ A @ B )
            = ( plus_plus @ TA @ A @ C ) )
         => ( B = C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_add__left__imp__eq) ).

thf(1056,plain,
    ! [TA: $tType] :
      ( ( cancel_semigroup_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ( plus_plus @ TA @ A @ B )
            = ( plus_plus @ TA @ A @ C ) )
         => ( B = C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(270,axiom,
    ord_less_eq @ nat @ ( plus_plus @ nat @ ( times_times @ nat @ ( huffma854352999e_freq @ a @ t @ a2 ) @ ( huffma223349076_depth @ a @ t @ b ) ) @ ( times_times @ nat @ ( huffma854352999e_freq @ a @ t @ b ) @ ( huffma223349076_depth @ a @ t @ a2 ) ) ) @ ( plus_plus @ nat @ ( times_times @ nat @ ( huffma854352999e_freq @ a @ t @ a2 ) @ ( huffma223349076_depth @ a @ t @ a2 ) ) @ ( times_times @ nat @ ( huffma854352999e_freq @ a @ t @ b ) @ ( huffma223349076_depth @ a @ t @ b ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7__092_060open_062freq_At_Aa_A_K_Adepth_At_Ab_A_L_Afreq_At_Ab_A_K_Adepth_At_Aa_A_092_060le_062_Afreq_At_Aa_A_K_Adepth_At_Aa_A_L_Afreq_At_Ab_A_K_Adepth_At_Ab_092_060close_062) ).

thf(1033,plain,
    ord_less_eq @ nat @ ( plus_plus @ nat @ ( times_times @ nat @ ( huffma854352999e_freq @ a @ t @ a2 ) @ ( huffma223349076_depth @ a @ t @ b ) ) @ ( times_times @ nat @ ( huffma854352999e_freq @ a @ t @ b ) @ ( huffma223349076_depth @ a @ t @ a2 ) ) ) @ ( plus_plus @ nat @ ( times_times @ nat @ ( huffma854352999e_freq @ a @ t @ a2 ) @ ( huffma223349076_depth @ a @ t @ a2 ) ) @ ( times_times @ nat @ ( huffma854352999e_freq @ a @ t @ b ) @ ( huffma223349076_depth @ a @ t @ b ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(153,axiom,
    ! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA,C: TA,D: TA] :
      ( ( huffma1050891809istent @ TA @ A )
     => ( ( B != C )
       => ( ( B != D )
         => ( ( huffma223349076_depth @ TA @ ( huffma469337550apSyms @ TA @ A @ C @ D ) @ B )
            = ( huffma223349076_depth @ TA @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_depth__swapSyms__neither) ).

thf(720,plain,
    ! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA,C: TA,D: TA] :
      ( ( huffma1050891809istent @ TA @ A )
     => ( ( B != C )
       => ( ( B != D )
         => ( ( huffma223349076_depth @ TA @ ( huffma469337550apSyms @ TA @ A @ C @ D ) @ B )
            = ( huffma223349076_depth @ TA @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(246,axiom,
    ! [TA: $tType] :
      ( ( huffma936049440ptimum @ TA )
      = ( ^ [A: huffma16452318e_tree @ TA] :
          ! [B: huffma16452318e_tree @ TA] :
            ( ( huffma1050891809istent @ TA @ B )
           => ( ( ( huffma505251170phabet @ TA @ A )
                = ( huffma505251170phabet @ TA @ B ) )
             => ( ( ( huffma854352999e_freq @ TA @ A )
                  = ( huffma854352999e_freq @ TA @ B ) )
               => ( ord_less_eq @ nat @ ( huffma636208924e_cost @ TA @ A ) @ ( huffma636208924e_cost @ TA @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_optimum__def) ).

thf(955,plain,
    ! [TA: $tType] :
      ( ( huffma936049440ptimum @ TA )
      = ( ^ [A: huffma16452318e_tree @ TA] :
          ! [B: huffma16452318e_tree @ TA] :
            ( ( huffma1050891809istent @ TA @ B )
           => ( ( ( huffma505251170phabet @ TA @ A )
                = ( huffma505251170phabet @ TA @ B ) )
             => ( ( ( huffma854352999e_freq @ TA @ A )
                  = ( huffma854352999e_freq @ TA @ B ) )
               => ( ord_less_eq @ nat @ ( huffma636208924e_cost @ TA @ A ) @ ( huffma636208924e_cost @ TA @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(182,axiom,
    ! [TA: $tType,A: huffma16452318e_tree @ TA] :
      ( ( ( huffma1554076246height @ TA @ A )
        = ( zero_zero @ nat ) )
     => ( ( huffma787811817Weight @ TA @ A )
        = ( huffma691733767weight @ TA @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_height__0__imp__cachedWeight__eq__weight) ).

thf(796,plain,
    ! [TA: $tType,A: huffma16452318e_tree @ TA] :
      ( ( ( huffma1554076246height @ TA @ A )
        = ( zero_zero @ nat ) )
     => ( ( huffma787811817Weight @ TA @ A )
        = ( huffma691733767weight @ TA @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(927,plain,
    ! [TA: $tType] :
      ( ( huffma469337550apSyms @ TA )
      = ( ^ [A: huffma16452318e_tree @ TA,B: TA,C: TA] : ( huffma2094459102Leaves @ TA @ A @ ( huffma854352999e_freq @ TA @ A @ B ) @ B @ ( huffma854352999e_freq @ TA @ A @ C ) @ C ) ) ),
    inference(cnf,[status(esa)],[926]) ).

thf(928,plain,
    ! [TA: $tType] :
      ( ( huffma469337550apSyms @ TA )
      = ( ^ [A: huffma16452318e_tree @ TA,B: TA,C: TA] : ( huffma2094459102Leaves @ TA @ A @ ( huffma854352999e_freq @ TA @ A @ B ) @ B @ ( huffma854352999e_freq @ TA @ A @ C ) @ C ) ) ),
    inference(lifteq,[status(thm)],[927]) ).

thf(13099,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType] :
      ( ~ $true
      | ( order @ ( TF > TG ) @ ( type2 @ ( TF > TG ) ) )
      | ( ( order @ ( TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TE > TD > TC > TB > TA > $o ) ) )
       != ( order @ TG @ ( type2 @ TG ) ) ) ),
    inference(paramod_ordered,[status(thm)],[12489,356]) ).

thf(13100,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType] :
      ( ( order @ ( TF > TG ) @ ( type2 @ ( TF > TG ) ) )
      | ( ( order @ ( TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TE > TD > TC > TB > TA > $o ) ) )
       != ( order @ TG @ ( type2 @ TG ) ) ) ),
    inference(simp,[status(thm)],[13099]) ).

thf(13101,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType] : ( order @ ( TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TF > TE > TD > TC > TB > TA > $o ) ) ),
    inference(pattern_uni,[status(thm)],[13100:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TE > TD > TC > TB > TA > $o ))]]) ).

thf(224,axiom,
    ! [TA: $tType] :
      ( ( semiri456707255roduct @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( A
            = ( plus_plus @ TA @ A @ B ) )
          = ( B
            = ( zero_zero @ TA ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_add__0__iff) ).

thf(897,plain,
    ! [TA: $tType] :
      ( ( semiri456707255roduct @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( A
            = ( plus_plus @ TA @ A @ B ) )
          = ( B
            = ( zero_zero @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(172,axiom,
    ! [TA: $tType] :
      ( ( linord219039673up_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( ( plus_plus @ TA @ A @ A )
            = ( zero_zero @ TA ) )
          = ( A
            = ( zero_zero @ TA ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_double__zero) ).

thf(767,plain,
    ! [TA: $tType] :
      ( ( linord219039673up_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( ( plus_plus @ TA @ A @ A )
            = ( zero_zero @ TA ) )
          = ( A
            = ( zero_zero @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(85,axiom,
    ! [TA: $tType] :
      ( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA,D: TA] :
          ( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ D ) )
          = ( plus_plus @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_semiring__normalization__rules_I20_J) ).

thf(532,plain,
    ! [TA: $tType] :
      ( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA,D: TA] :
          ( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ D ) )
          = ( plus_plus @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(282,axiom,
    ! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_less__eq__nat_Osimps_I1_J) ).

thf(1065,plain,
    ! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(264,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq @ nat @ A @ B )
     => ? [C: nat] :
          ( B
          = ( plus_plus @ nat @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_le__Suc__ex) ).

thf(1019,plain,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq @ nat @ A @ B )
     => ? [C: nat] :
          ( B
          = ( plus_plus @ nat @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(257,axiom,
    ! [A: nat,B: nat] :
      ( ( ( plus_plus @ nat @ A @ B )
        = A )
     => ( B
        = ( zero_zero @ nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_add__eq__self__zero) ).

thf(992,plain,
    ! [A: nat,B: nat] :
      ( ( ( plus_plus @ nat @ A @ B )
        = A )
     => ( B
        = ( zero_zero @ nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(154,axiom,
    ! [TA: $tType] :
      ( ( cancel1352612707id_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ( plus_plus @ TA @ A @ B )
            = B )
          = ( A
            = ( zero_zero @ TA ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_add__cancel__left__left) ).

thf(723,plain,
    ! [TA: $tType] :
      ( ( cancel1352612707id_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ( plus_plus @ TA @ A @ B )
            = B )
          = ( A
            = ( zero_zero @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(261,axiom,
    ! [TA: $tType] :
      ( ( comm_monoid_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
          = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_comm__monoid__add__class_Oadd__0) ).

thf(1004,plain,
    ! [TA: $tType] :
      ( ( comm_monoid_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
          = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(72,axiom,
    ! [TA: $tType] :
      ( ( ordere779506340up_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_add__right__mono) ).

thf(501,plain,
    ! [TA: $tType] :
      ( ( ordere779506340up_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(294,axiom,
    ! [A: nat] :
      ( ( plus_plus @ nat @ ( zero_zero @ nat ) @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_plus__nat_Oadd__0) ).

thf(1093,plain,
    ! [A: nat] :
      ( ( plus_plus @ nat @ ( zero_zero @ nat ) @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(115,axiom,
    ! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA,C: TA] :
      ( ( huffma1050891809istent @ TA @ A )
     => ( ( member @ TA @ B @ ( huffma505251170phabet @ TA @ A ) )
       => ( ( member @ TA @ C @ ( huffma505251170phabet @ TA @ A ) )
         => ( ( huffma854352999e_freq @ TA @ ( huffma469337550apSyms @ TA @ A @ B @ C ) )
            = ( huffma854352999e_freq @ TA @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_freq__swapSyms) ).

thf(624,plain,
    ! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA,C: TA] :
      ( ( huffma1050891809istent @ TA @ A )
     => ( ( member @ TA @ B @ ( huffma505251170phabet @ TA @ A ) )
       => ( ( member @ TA @ C @ ( huffma505251170phabet @ TA @ A ) )
         => ( ( huffma854352999e_freq @ TA @ ( huffma469337550apSyms @ TA @ A @ B @ C ) )
            = ( huffma854352999e_freq @ TA @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(185,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq @ nat @ ( plus_plus @ nat @ A @ B ) @ C )
     => ( ord_less_eq @ nat @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_add__leD2) ).

thf(803,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq @ nat @ ( plus_plus @ nat @ A @ B ) @ C )
     => ( ord_less_eq @ nat @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(354,plain,
    ! [TA: $tType,B: huffma16452318e_tree @ TA,A: TA] :
      ( ~ ( member @ TA @ A @ ( huffma505251170phabet @ TA @ B ) )
      | ( member @ TA @ ( huffma943100115ibling @ TA @ B @ A ) @ ( huffma505251170phabet @ TA @ B ) ) ),
    inference(cnf,[status(esa)],[353]) ).

thf(238,axiom,
    ! [TA: $tType] :
      ( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( times_times @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
          = ( plus_plus @ TA @ ( times_times @ TA @ A @ C ) @ ( times_times @ TA @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_semiring__normalization__rules_I8_J) ).

thf(935,plain,
    ! [TA: $tType] :
      ( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( times_times @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
          = ( plus_plus @ TA @ ( times_times @ TA @ A @ C ) @ ( times_times @ TA @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(309,plain,
    ! [TA: $tType,C: TA,B: TA,A: TA] :
      ( ~ ( order @ TA @ ( type2 @ TA ) )
      | ~ ( ord_less_eq @ TA @ A @ B )
      | ~ ( ord_less_eq @ TA @ C @ A )
      | ( ord_less_eq @ TA @ C @ B ) ),
    inference(cnf,[status(esa)],[308]) ).

thf(272,axiom,
    ! [TA: $tType] :
      ( ( semiri1193490041visors @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( A
           != ( zero_zero @ TA ) )
         => ( ( B
             != ( zero_zero @ TA ) )
           => ( ( times_times @ TA @ A @ B )
             != ( zero_zero @ TA ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_no__zero__divisors) ).

thf(1037,plain,
    ! [TA: $tType] :
      ( ( semiri1193490041visors @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( A
           != ( zero_zero @ TA ) )
         => ( ( B
             != ( zero_zero @ TA ) )
           => ( ( times_times @ TA @ A @ B )
             != ( zero_zero @ TA ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(13476,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType] :
      ( ~ $true
      | ( preorder @ ( TZA > TZB ) @ ( type2 @ ( TZA > TZB ) ) )
      | ( ( preorder @ ( TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) )
       != ( preorder @ TZB @ ( type2 @ TZB ) ) ) ),
    inference(paramod_ordered,[status(thm)],[12994,320]) ).

thf(13477,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType] :
      ( ( preorder @ ( TZA > TZB ) @ ( type2 @ ( TZA > TZB ) ) )
      | ( ( preorder @ ( TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) )
       != ( preorder @ TZB @ ( type2 @ TZB ) ) ) ),
    inference(simp,[status(thm)],[13476]) ).

thf(13478,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType] : ( preorder @ ( TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) ),
    inference(pattern_uni,[status(thm)],[13477:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ))]]) ).

thf(30,axiom,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ord_less_eq @ TA @ B @ A )
           => ( A = B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_order__class_Oorder_Oantisym) ).

thf(364,plain,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ord_less_eq @ TA @ B @ A )
           => ( A = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(4391,plain,
    ! [B: huffma16452318e_tree @ a,A: huffma16452318e_tree @ a] :
      ( ~ ( order @ ( huffma16452318e_tree @ a ) @ ( type2 @ ( huffma16452318e_tree @ a ) ) )
      | ~ ( ord_less_eq @ ( huffma16452318e_tree @ a ) @ A @ B )
      | ~ ( ord_less_eq @ ( huffma16452318e_tree @ a ) @ B @ A )
      | ( A != t )
      | ( b != a2 )
      | ( B
       != ( huffma469337550apSyms @ a @ t @ a2 @ b ) ) ),
    inference(paramod_ordered,[status(thm)],[332,1144]) ).

thf(4392,plain,
    ! [A: huffma16452318e_tree @ a] :
      ( ~ ( order @ ( huffma16452318e_tree @ a ) @ ( type2 @ ( huffma16452318e_tree @ a ) ) )
      | ~ ( ord_less_eq @ ( huffma16452318e_tree @ a ) @ A @ ( huffma469337550apSyms @ a @ t @ a2 @ b ) )
      | ~ ( ord_less_eq @ ( huffma16452318e_tree @ a ) @ ( huffma469337550apSyms @ a @ t @ a2 @ b ) @ A )
      | ( A != t )
      | ( b != a2 ) ),
    inference(pattern_uni,[status(thm)],[4391:[bind(A,$thf( A )),bind(B,$thf( huffma469337550apSyms @ a @ t @ a2 @ b ))]]) ).

thf(4940,plain,
    ( ~ ( order @ ( huffma16452318e_tree @ a ) @ ( type2 @ ( huffma16452318e_tree @ a ) ) )
    | ~ ( ord_less_eq @ ( huffma16452318e_tree @ a ) @ t @ ( huffma469337550apSyms @ a @ t @ a2 @ b ) )
    | ~ ( ord_less_eq @ ( huffma16452318e_tree @ a ) @ ( huffma469337550apSyms @ a @ t @ a2 @ b ) @ t )
    | ( b != a2 ) ),
    inference(simp,[status(thm)],[4392]) ).

thf(148,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq @ nat @ ( times_times @ nat @ A @ B ) @ ( times_times @ nat @ A @ C ) )
      = ( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
       => ( ord_less_eq @ nat @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_nat__mult__le__cancel__disj) ).

thf(708,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq @ nat @ ( times_times @ nat @ A @ B ) @ ( times_times @ nat @ A @ C ) )
      = ( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
       => ( ord_less_eq @ nat @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(31953,plain,
    $false,
    inference(e,[status(thm)],[809,1024,760,347,846,352,479,1105,909,333,8784,518,1083,468,12383,941,3072,730,1068,2395,308,1073,873,1142,511,597,861,614,677,715,698,747,538,670,3236,1001,5921,301,829,404,841,417,973,885,3088,320,9148,13039,651,389,5585,2735,372,6350,3280,357,1059,6873,587,838,702,751,853,1087,1147,770,416,325,448,316,3180,3258,5802,421,870,492,6840,11691,353,821,9304,924,1040,321,6410,646,485,1136,348,574,8823,5772,396,660,1104,507,12090,981,766,8261,634,8977,877,692,9187,998,527,312,307,678,793,2646,810,381,7357,12489,1067,512,439,894,9522,1042,302,349,12737,424,630,3154,2890,2396,561,12576,10657,297,9264,361,435,3349,329,2872,830,10794,13433,11646,1027,757,682,5993,324,742,1089,12264,317,1017,6195,8339,403,356,5889,6128,857,1096,9624,6958,593,328,488,339,13190,526,637,489,11574,1028,1082,590,6539,2978,970,393,1099,515,12994,738,12429,654,1050,911,779,371,503,5317,647,343,805,921,541,657,674,3190,530,773,888,9226,926,938,11084,633,360,508,3183,558,1071,8378,9793,906,298,6053,1103,824,689,444,375,819,1007,732,843,958,9663,9585,545,413,584,4943,875,711,13281,579,12663,6774,313,8862,498,8300,335,947,3302,350,672,611,787,979,681,784,1048,377,567,1144,303,3182,900,406,318,7265,880,649,387,1080,535,816,323,594,964,915,330,932,858,367,552,799,726,848,700,1022,9528,12336,695,3110,10925,883,608,306,299,7232,912,685,521,399,5742,827,5377,851,1102,1034,944,663,374,617,342,355,754,6440,6083,1076,11738,776,712,580,640,705,13523,954,739,7166,2863,9715,310,1053,10994,441,717,3026,463,6125,338,359,643,470,576,951,808,9109,744,336,5347,600,864,727,314,991,446,571,5832,465,627,1084,482,524,495,891,844,363,556,976,688,903,5258,813,963,319,748,351,6023,418,781,2394,1062,11039,995,2934,3181,568,2912,667,929,763,346,549,2623,1045,800,1030,2956,1077,478,620,9551,432,405,867,8489,735,833,410,967,950,835,8901,2736,854,5477,3132,790,564,305,326,7199,918,5290,358,1056,1033,6380,720,955,796,928,12177,13101,897,767,532,1065,332,1019,992,723,1004,11489,501,369,1093,624,11144,6807,2879,803,469,354,935,2887,309,1037,13478,364,4940,708]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : DAT170^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.07  % Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.09/0.21  % Computer : n017.cluster.edu
% 0.09/0.21  % Model    : x86_64 x86_64
% 0.09/0.21  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21  % Memory   : 8046.5625MB
% 0.09/0.21  % OS       : Linux 6.8.0-71-generic
% 0.09/0.21  % CPULimit : 300
% 0.09/0.21  % WCLimit  : 300
% 0.09/0.21  % DateTime : Tue Sep 29 18:00:22 UTC 2026
% 0.09/0.21  % CPUTime  : 
% 0.09/0.21  Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.85/0.78  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 2.17/1.19  % [INFO] 	 Parsing done (409ms). 
% 2.37/1.20  % [INFO] 	 Running in sequential loop mode. 
% 3.12/1.41  % [INFO] 	 eprover registered as external prover. 
% 3.12/1.42  % [INFO] 	 Scanning for conjecture ... 
% 3.49/1.52  % [INFO] 	 Found a conjecture (or negated_conjecture) and 295 axioms. Running axiom selection ... 
% 3.87/1.61  % [INFO] 	 Axiom selection finished. Selected 294 axioms (removed 1 axioms). 
% 4.66/1.86  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 5.06/1.90  % [INFO] 	 Type checking passed. 
% 5.06/1.90  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 189.03/62.56  % External prover 'e' found a proof!
% 189.03/62.56  % [INFO] 	 Killing All external provers ... 
% 189.03/62.56  % Time passed: 62210ms (effective reasoning time: 61357ms)
% 189.03/62.56  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 189.03/62.56  % Axioms used in derivation (294): fact_181_divisors__zero, fact_194_add__decreasing, fact_196_add__decreasing2, fact_132_freq__swapLeaves, fact_224_linordered__field__class_Osign__simps_I28_J, fact_232_not__gr__zero, fact_78_distrib__right, fact_183_semiring__normalization__rules_I9_J, fact_189_nat__mult__eq__cancel__disj, tcon_HOL_Obool___Orderings_Opreorder_7, fact_206_mult__left__mono__neg, fact_42_le__add2, fact_66_mult_Ocommute, tcon_Nat_Onat___Orderings_Oorder_2, fact_124_ring__class_Oring__distribs_I2_J, fact_110_semiring__normalization__rules_I24_J, fact_8_alphabet__swapSyms, fact_195_add__increasing, fact_77_combine__common__factor, fact_96_le__cases, fact_167_height__0__imp__cost__0, fact_234_add__less__cancel__left, tcon_Nat_Onat___Orderings_Olinorder, fact_229_height__0__imp__cachedWeight__eq__weight, fact_75_crossproduct__noteq, fact_122_semiring__normalization__rules_I7_J, fact_227_linordered__field__class_Osign__simps_I25_J, fact_117_semiring__normalization__rules_I17_J, fact_217_zero__le__mult__iff, fact_28_add__right__mono, fact_236_nat__add__left__cancel__less, fact_27_le__iff__add, fact_91_ord__le__eq__trans, fact_215_mult__nonpos__nonneg, fact_58_add_Oleft__commute, tcon_Nat_Onat___Groups_Ocancel__comm__monoid__add, fact_102_ord__eq__le__subst, fact_166_height__0__imp__sibling__id, fact_44_add__leE, fact_23_le__antisym, fact_138_add__cancel__left__right, fact_158_height__swapLeaves, fact_12_add__left__cancel, fact_184_semiring__normalization__rules_I10_J, tcon_Nat_Onat___Groups_Oordered__ab__semigroup__monoid__add__imp__le, fact_134_sibling__swapLeaves__sibling, fact_157_sibling__sibling__id, tcon_Nat_Onat___Rings_Osemiring__no__zero__divisors, tcon_fun___Orderings_Oord, fact_231_depth__height__imp__sibling__ne, fact_155_mult__is__0, fact_128_semiring__normalization__rules_I1_J, fact_40_add__leD2, fact_34_nat__le__iff__add, fact_163_double__add__le__zero__iff__single__add__le__zero, fact_201_add__nonpos__eq__0__iff, fact_41_add__leD1, fact_56_add__right__imp__eq, fact_208_mult__left__mono, fact_70_nat__add__left__cancel, fact_242_zero__less__double__add__iff__zero__less__single__add, tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add, fact_250_linordered__field__no__ub, fact_76_crossproduct__eq, fact_121_semiring__normalization__rules_I13_J, fact_26_add__le__imp__le__left, tcon_Nat_Onat___Rings_Oordered__semiring, tcon_HOL_Obool___Orderings_Oorder_9, fact_151_le0, tcon_Nat_Onat___Groups_Ocomm__monoid__add, fact_88_dual__order_Orefl, fact_239_less__add__same__cancel1, fact_22_eq__imp__le, fact_51_mult__le__mono, fact_87_linorder__wlog, fact_199_add__nonpos__nonpos, fact_106_le__funI, fact_152_mult__cancel2, fact_108_le__funD, fact_253_not__less__zero, tcon_Nat_Onat___Groups_Ocancel__semigroup__add, fact_186_plus__nat_Oadd__0, fact_90_order__class_Oorder_Oantisym, fact_71_optimum__def, fact_73_order__refl, fact_154_mult__0__right, fact_19_nat__add__left__cancel__le, fact_230_sum__squares__eq__zero__iff, fact_111_semiring__normalization__rules_I23_J, fact_164_zero__le__double__add__iff__zero__le__single__add, fact_11_consistent__swapSyms, fact_62_add_Oassoc, fact_37_add__le__mono1, fact_220_depth__le__height, fact_216_mult__nonneg__nonpos2, tcon_Nat_Onat___Groups_Oab__semigroup__mult, fact_46_Collect__mem__eq, fact_148_mult__zero__left, fact_15_add__mult__distrib2, fact_81_swapLeaves__id__when__notin__alphabet, fact_143_add_Oleft__neutral, fact_9_cost__swapSyms, fact_92_ord__eq__le__trans, tcon_Nat_Onat___Groups_Omonoid__add, fact_237_add__less__same__cancel1, fact_213_mult__nonneg__nonneg, fact_109_semiring__normalization__rules_I25_J, fact_7__092_060open_062freq_At_Aa_A_K_Adepth_At_Ab_A_L_Afreq_At_Ab_A_K_Adepth_At_Aa_A_092_060le_062_Afreq_At_Aa_A_K_Adepth_At_Aa_A_L_Afreq_At_Ab_A_K_Adepth_At_Ab_092_060close_062, help_If_1_1_T, fact_240_less__add__same__cancel2, fact_169_zero__reorient, fact_176_semiring__normalization__rules_I5_J, fact_57_add__left__imp__eq, fact_84_consistent__swapLeaves, fact_150_add__is__0, fact_209_mult__right__mono__neg, fact_165_notin__alphabet__imp__freq__0, tcon_Nat_Onat___Rings_Osemiring__no__zero__divisors__cancel, fact_89_order__trans, fact_114_semiring__normalization__rules_I20_J, fact_13_add__right__cancel, tcon_Set_Oset___Orderings_Oord_6, fact_248_mult__le__cancel2, fact_200_add__nonneg__eq__0__iff, fact_35_trans__le__add2, fact_5_depth__swapSyms__neither, fact_191_sibling__ne__imp__sibling__in__alphabet, fact_211_mult__le__0__iff, fact_68_ab__semigroup__mult__class_Omult__ac_I1_J, fact_243_add__gr__0, fact_168_depth__sibling, fact_116_semiring__normalization__rules_I18_J, fact_17_add__le__cancel__right, fact_38_add__le__mono, fact_55_le__le__imp__sum__mult__le__sum__mult, fact_83_depth__swapLeaves__neither, fact_223_linordered__field__class_Osign__simps_I27_J, fact_204_zero__le__square, tcon_Nat_Onat___Groups_Ozero, fact_120_semiring__normalization__rules_I14_J, fact_210_mult__right__mono, tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le, fact_180_no__zero__divisors, fact_67_mult_Oassoc, fact_129_weight__swapLeaves, tcon_HOL_Obool___Orderings_Oord_10, fact_95_order_Otrans, fact_45_mem__Collect__eq, fact_53_le__cube, fact_31_add__mono__thms__linordered__semiring_I1_J, fact_207_mult__nonpos__nonpos, fact_61_add_Oleft__cancel, fact_247_nat__mult__le__cancel__disj, fact_49_mult__le__mono2, fact_36_trans__le__add1, fact_18_add__le__cancel__left, fact_21_le__trans, fact_3_assms_I5_J, fact_197_add__increasing2, fact_202_mult__mono, fact_221_sum__squares__ge__zero, tcon_Nat_Onat___Rings_Ocomm__semiring, fact_156_notin__alphabet__imp__sibling__id, fact_113_semiring__normalization__rules_I21_J, fact_60_add_Oright__cancel, fact_188_le__0__eq, fact_160_add__le__same__cancel2, fact_6_swapSyms__id, fact_54_exists__in__alphabet, fact_238_add__less__same__cancel2, tcon_Nat_Onat___Orderings_Oord_3, fact_153_mult__cancel1, fact_139_add__cancel__left__left, fact_161_le__add__same__cancel1, fact_24_nat__le__linear, fact_177_semiring__normalization__rules_I6_J, fact_104_order__subst1, fact_179_mult__left__cancel, fact_214_mult__nonneg__nonpos, fact_112_semiring__normalization__rules_I22_J, tcon_Nat_Onat___Rings_Omult__zero, fact_162_le__add__same__cancel2, fact_103_order__subst2, fact_64_ab__semigroup__add__class_Oadd__ac_I1_J, fact_30_add__mono, fact_185_add__eq__self__zero, tcon_Nat_Onat___Rings_Osemiring, fact_47_Collect__cong, tcon_Nat_Onat___Rings_Oordered__semiring__0, fact_63_add__mono__thms__linordered__semiring_I4_J, help_If_3_1_T, help_If_2_1_T, fact_100_eq__iff, fact_137_add__cancel__right__left, fact_50_mult__le__mono1, fact_140_double__zero__sym, fact_43_le__add1, fact_39_le__Suc__ex, fact_97_eq__refl, tcon_Set_Oset___Orderings_Opreorder_4, fact_159_add__le__same__cancel1, fact_149_Nat_Oadd__0__right, fact_1_assms_I3_J, fact_245_nat__0__less__mult__iff, fact_2_assms_I2_J, fact_203_mult__mono_H, fact_190_mult__0, fact_251_zero__less__iff__neq__zero, fact_145_mult__cancel__left, fact_192_in__alphabet__imp__sibling__in__alphabet, fact_125_ring__class_Oring__distribs_I1_J, tcon_Nat_Onat___Rings_Ocomm__semiring__1, fact_147_mult__zero__right, fact_233_add__less__cancel__right, fact_33_add__mono__thms__linordered__semiring_I3_J, fact_182_mult__not__zero, tcon_fun___Orderings_Opreorder, fact_119_semiring__normalization__rules_I15_J, tcon_Set_Oset___Orderings_Oorder_5, fact_171_add__eq__0__iff__both__eq__0, fact_29_add__left__mono, tcon_Nat_Onat___Orderings_Opreorder_1, fact_80_comm__semiring__class_Odistrib, fact_226_linordered__field__class_Osign__simps_I24_J, fact_205_split__mult__pos__le, fact_14_add__mult__distrib, fact_105_le__fun__def, fact_65_mult_Oleft__commute, fact_246_nat__mult__less__cancel__disj, tcon_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, fact_136_add__cancel__right__right, tcon_HOL_Obool___Orderings_Olinorder_8, fact_175_add__0__iff, fact_93_antisym__conv, fact_32_add__mono__thms__linordered__semiring_I2_J, fact_218_ordered__comm__semiring__class_Ocomm__mult__left__mono, fact_82_swapLeaves__id, fact_79_distrib__left, fact_172_add_Ogroup__left__neutral, fact_133_exists__at__height, fact_174_comm__monoid__add__class_Oadd__0, fact_135_le__zero__eq, fact_118_semiring__normalization__rules_I16_J, fact_249_linordered__field__no__lb, fact_170_zero__le, fact_142_add_Oright__neutral, fact_85_dual__order_Oantisym, tcon_Nat_Onat___Rings_Oordered__comm__semiring, tcon_fun___Orderings_Oorder, tcon_Nat_Onat___Groups_Osemigroup__add, fact_228_sum__squares__le__zero__iff, fact_146_mult__eq__0__iff, fact_52_le__square, fact_99_antisym, fact_131_linordered__field__class_Osign__simps_I35_J, fact_241_double__add__less__zero__iff__single__add__less__zero, tcon_Nat_Onat___Groups_Osemigroup__mult, fact_198_add__nonneg__nonneg, fact_115_semiring__normalization__rules_I19_J, fact_244_mult__less__cancel2, fact_173_add_Ocomm__neutral, tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add, fact_123_swapSyms__def, fact_212_split__mult__neg__le, fact_94_le__cases3, fact_0_assms_I1_J, fact_225_linordered__field__class_Osign__simps_I23_J, fact_252_gr__implies__not__zero, fact_74_freq__uniteTrees, tcon_Nat_Onat___Groups_Oab__semigroup__add, fact_86_dual__order_Otrans, fact_98_linear, fact_219_add__scale__eq__noteq, fact_4_assms_I4_J, fact_10_freq__swapSyms, fact_141_double__zero, fact_235_neq0__conv, fact_25_add__le__imp__le__right, fact_69_nat__add__right__cancel, fact_130_linordered__field__class_Osign__simps_I36_J, fact_16_left__add__mult__distrib, fact_101_ord__le__eq__subst, fact_59_add_Ocommute, fact_20_le__refl, fact_178_mult__right__cancel, fact_144_mult__cancel__right, fact_72_cost__swapLeaves, fact_107_le__funE, tcon_Nat_Onat___Groups_Oordered__comm__monoid__add, fact_193_sibling__reciprocal, fact_187_less__eq__nat_Osimps_I1_J, fact_126_semiring__normalization__rules_I34_J, fact_127_semiring__normalization__rules_I8_J, fact_222_linordered__field__class_Osign__simps_I26_J
% 189.03/62.56  % No. of inferences in proof: 1063
% 189.03/62.56  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 62210 ms resp. 61357 ms w/o parsing
% 180.72/62.97  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 180.72/62.99  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------