Leo-III---1.8.0.UNS-Ref.s

%------------------------------------------------------------------------------
% File     : Leo-III---1.8.0
% Problem  : SET839-1 : TPTP v9.3.1. Released v3.2.0.
% 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 : n007.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 : Sun Sep 27 08:31:05 AM UTC 2026

% Result   : Unsatisfiable 75.54s 28.46s
% Output   : Refutation 75.02s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   25
%            Number of leaves      :  307
% Syntax   : Number of formulae    : 1122 ( 325 unt;   0 typ;   7 def)
%            Number of atoms       : 2523 (1094 equ;   0 cnn)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives : 12446 (1541   ~;1218   |;   0   &;9687   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   32 (  32   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  122 ( 119 usr;  15 con; 0-6 aty)
%            Number of variables   : 2719 (   0   ^;2705   !;   7   ?;2719   :)
%                                         (   0  !>;   0  ?*;   0  @-;   7  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(c_lessequals_decl,type,
    c_lessequals: $i > $i > $i > $o ).

thf(v_S_decl,type,
    v_S: $i ).

thf(c_insert_decl,type,
    c_insert: $i > $i > $i > $i ).

thf(c_emptyset_decl,type,
    c_emptyset: $i ).

thf(tc_set_decl,type,
    tc_set: $i > $i ).

thf(t_a_decl,type,
    t_a: $i ).

thf(c_in_decl,type,
    c_in: $i > $i > $i > $o ).

thf(c_Pair_decl,type,
    c_Pair: $i > $i > $i > $i > $i ).

thf(c_List_Olist_OCons_decl,type,
    c_List_Olist_OCons: $i > $i > $i > $i ).

thf(tc_List_Olist_decl,type,
    tc_List_Olist: $i > $i ).

thf(c_List_Olistrel_decl,type,
    c_List_Olistrel: $i > $i > $i ).

thf(tc_prod_decl,type,
    tc_prod: $i > $i > $i ).

thf(c_Main_Olistrel__Cons2__1_decl,type,
    c_Main_Olistrel__Cons2__1: $i > $i > $i > $i > $i > $i ).

thf(c_Main_Olistrel__Cons2__2_decl,type,
    c_Main_Olistrel__Cons2__2: $i > $i > $i > $i > $i > $i ).

thf(c_Main_Olistrel__Cons1__1_decl,type,
    c_Main_Olistrel__Cons1__1: $i > $i > $i > $i > $i > $i ).

thf(c_Main_Olistrel__Cons1__2_decl,type,
    c_Main_Olistrel__Cons1__2: $i > $i > $i > $i > $i > $i ).

thf(c_Divides_Oop_Advd_decl,type,
    c_Divides_Oop_Advd: $i > $i > $i > $o ).

thf(c_0_decl,type,
    c_0: $i ).

thf(tc_IntDef_Oint_decl,type,
    tc_IntDef_Oint: $i ).

thf(c_append_decl,type,
    c_append: $i > $i > $i > $i ).

thf(c_List_Olist_ONil_decl,type,
    c_List_Olist_ONil: $i ).

thf(c_less_decl,type,
    c_less: $i > $i > $i > $o ).

thf(tc_nat_decl,type,
    tc_nat: $i ).

thf(c_Suc_decl,type,
    c_Suc: $i > $i ).

thf(c_plus_decl,type,
    c_plus: $i > $i > $i > $i ).

thf(c_Nat_Osize_decl,type,
    c_Nat_Osize: $i > $i > $i ).

thf(class_Finite__Set_Ofinite_decl,type,
    class_Finite__Set_Ofinite: $i > $o ).

thf(tc_fun_decl,type,
    tc_fun: $i > $i > $i ).

thf(class_HOL_Ominus_decl,type,
    class_HOL_Ominus: $i > $o ).

thf(class_Orderings_Oord_decl,type,
    class_Orderings_Oord: $i > $o ).

thf(c_SetInterval_OlessThan_decl,type,
    c_SetInterval_OlessThan: $i > $i > $i ).

thf(c_List_Olists_decl,type,
    c_List_Olists: $i > $i > $i ).

thf(c_Datatype__Universe_OScons_decl,type,
    c_Datatype__Universe_OScons: $i > $i > $i > $i > $i ).

thf(class_Orderings_Oorder_decl,type,
    class_Orderings_Oorder: $i > $o ).

thf(c_Wellfounded__Recursion_Owf_decl,type,
    c_Wellfounded__Recursion_Owf: $i > $i > $o ).

thf(c_Wellfounded__Relations_Olex__prod_decl,type,
    c_Wellfounded__Relations_Olex__prod: $i > $i > $i > $i > $i ).

thf(class_Orderings_Olinorder_decl,type,
    class_Orderings_Olinorder: $i > $o ).

thf(c_SetInterval_OatLeast_decl,type,
    c_SetInterval_OatLeast: $i > $i > $i ).

thf(c_Relation_Orel__comp_decl,type,
    c_Relation_Orel__comp: $i > $i > $i > $i > $i > $i ).

thf(c_uminus_decl,type,
    c_uminus: $i > $i > $i ).

thf(tc_bool_decl,type,
    tc_bool: $i ).

thf(class_Nat_Opower_decl,type,
    class_Nat_Opower: $i > $o ).

thf(tc_Datatype_Ooption_decl,type,
    tc_Datatype_Ooption: $i > $i ).

thf(c_SetInterval_OgreaterThan_decl,type,
    c_SetInterval_OgreaterThan: $i > $i > $i ).

thf(c_List_Oset_decl,type,
    c_List_Oset: $i > $i > $i ).

thf(tc_Datatype__Universe_Onode_decl,type,
    tc_Datatype__Universe_Onode: $i > $i > $i ).

thf(c_Datatype__Universe_OIn1_decl,type,
    c_Datatype__Universe_OIn1: $i > $i > $i > $i ).

thf(c_Datatype__Universe_Odsum_decl,type,
    c_Datatype__Universe_Odsum: $i > $i > $i > $i > $i ).

thf(c_Relation_OId_decl,type,
    c_Relation_OId: $i ).

thf(c_Datatype__Universe_Odprod_decl,type,
    c_Datatype__Universe_Odprod: $i > $i > $i > $i > $i ).

thf(c_Datatype__Universe_OIn0_decl,type,
    c_Datatype__Universe_OIn0: $i > $i > $i > $i ).

thf(c_Sum__Type_OInr_decl,type,
    c_Sum__Type_OInr: $i > $i > $i > $i ).

thf(c_Sum__Type_OInl_decl,type,
    c_Sum__Type_OInl: $i > $i > $i > $i ).

thf(c_Relation_Oconverse_decl,type,
    c_Relation_Oconverse: $i > $i > $i > $i ).

thf(tc_sum_decl,type,
    tc_sum: $i > $i > $i ).

thf(c_Transitive__Closure_Otrancl_decl,type,
    c_Transitive__Closure_Otrancl: $i > $i > $i ).

thf(c_Transitive__Closure_Ortrancl_decl,type,
    c_Transitive__Closure_Ortrancl: $i > $i > $i ).

thf(c_IntDef_Oint_decl,type,
    c_IntDef_Oint: $i > $i ).

thf(c_Wellfounded__Relations_Oless__than_decl,type,
    c_Wellfounded__Relations_Oless__than: $i ).

thf(tc_Product__Type_Ounit_decl,type,
    tc_Product__Type_Ounit: $i ).

thf(c_Relation_OImage_decl,type,
    c_Relation_OImage: $i > $i > $i > $i > $i ).

thf(c_Main_OImageE__1_decl,type,
    c_Main_OImageE__1: $i > $i > $i > $i > $i > $i ).

thf(c_List_Olex_decl,type,
    c_List_Olex: $i > $i > $i ).

thf(c_Sum__Type_OPlus_decl,type,
    c_Sum__Type_OPlus: $i > $i > $i > $i > $i ).

thf(c_Main_OPlusE__1_decl,type,
    c_Main_OPlusE__1: $i > $i > $i > $i > $i ).

thf(c_Main_OPlusE__2_decl,type,
    c_Main_OPlusE__2: $i > $i > $i > $i > $i ).

thf(c_Relation_Odiag_decl,type,
    c_Relation_Odiag: $i > $i > $i ).

thf(c_List_Olenlex_decl,type,
    c_List_Olenlex: $i > $i > $i ).

thf(c_Datatype_Ooption_OSome_decl,type,
    c_Datatype_Ooption_OSome: $i > $i > $i ).

thf(c_SetInterval_OatMost_decl,type,
    c_SetInterval_OatMost: $i > $i > $i ).

thf(c_Wellfounded__Recursion_Oacyclic_decl,type,
    c_Wellfounded__Recursion_Oacyclic: $i > $i > $o ).

thf(c_Relation_ORange_decl,type,
    c_Relation_ORange: $i > $i > $i > $i ).

thf(c_Main_ORangeE__1_decl,type,
    c_Main_ORangeE__1: $i > $i > $i > $i > $i ).

thf(c_Union_decl,type,
    c_Union: $i > $i > $i ).

thf(c_Main_OUnionE__1_decl,type,
    c_Main_OUnionE__1: $i > $i > $i > $i ).

thf(c_Datatype__Universe_Ousum_decl,type,
    c_Datatype__Universe_Ousum: $i > $i > $i > $i > $i ).

thf(c_Main_OusumE__2_decl,type,
    c_Main_OusumE__2: $i > $i > $i > $i > $i ).

thf(c_Main_OusumE__1_decl,type,
    c_Main_OusumE__1: $i > $i > $i > $i > $i ).

thf(c_Finite__Set_OFinites_decl,type,
    c_Finite__Set_OFinites: $i ).

thf(c_SetInterval_OgreaterThanAtMost_decl,type,
    c_SetInterval_OgreaterThanAtMost: $i > $i > $i > $i ).

thf(c_SetInterval_OatLeastAtMost_decl,type,
    c_SetInterval_OatLeastAtMost: $i > $i > $i > $i ).

thf(c_Main_OsubsetI__1_decl,type,
    c_Main_OsubsetI__1: $i > $i > $i > $i ).

thf(c_union_decl,type,
    c_union: $i > $i > $i > $i ).

thf(c_minus_decl,type,
    c_minus: $i > $i > $i > $i ).

thf(c_Main_OconverseE__1_decl,type,
    c_Main_OconverseE__1: $i > $i > $i > $i > $i ).

thf(c_Main_OconverseE__2_decl,type,
    c_Main_OconverseE__2: $i > $i > $i > $i > $i ).

thf(c_SetInterval_OatLeastLessThan_decl,type,
    c_SetInterval_OatLeastLessThan: $i > $i > $i > $i ).

thf(c_Pow_decl,type,
    c_Pow: $i > $i > $i ).

thf(c_Equiv__Relations_Oquotient_decl,type,
    c_Equiv__Relations_Oquotient: $i > $i > $i > $i ).

thf(c_Main_Oin__listsI__1_decl,type,
    c_Main_Oin__listsI__1: $i > $i > $i > $i ).

thf(c_UNIV_decl,type,
    c_UNIV: $i ).

thf(c_Datatype_Oo2s_decl,type,
    c_Datatype_Oo2s: $i > $i > $i ).

thf(c_Datatype__Universe_Ouprod_decl,type,
    c_Datatype__Universe_Ouprod: $i > $i > $i > $i > $i ).

thf(c_Main_OuprodE__1_decl,type,
    c_Main_OuprodE__1: $i > $i > $i > $i > $i > $i ).

thf(c_Main_OuprodE__2_decl,type,
    c_Main_OuprodE__2: $i > $i > $i > $i > $i > $i ).

thf(c_inter_decl,type,
    c_inter: $i > $i > $i > $i ).

thf(c_Infinite__Set_Oatmost__one_decl,type,
    c_Infinite__Set_Oatmost__one: $i > $i > $o ).

thf(c_Main_Orel__compE__1_decl,type,
    c_Main_Orel__compE__1: $i > $i > $i > $i > $i > $i > $i ).

thf(c_Main_Orel__compE__3_decl,type,
    c_Main_Orel__compE__3: $i > $i > $i > $i > $i > $i > $i ).

thf(c_Main_OdprodE__1_decl,type,
    c_Main_OdprodE__1: $i > $i > $i > $i > $i > $i ).

thf(c_Main_OdprodE__3_decl,type,
    c_Main_OdprodE__3: $i > $i > $i > $i > $i > $i ).

thf(c_Main_Ofinite__Union__1_decl,type,
    c_Main_Ofinite__Union__1: $i > $i > $i ).

thf(c_Main_OdiagE__1_decl,type,
    c_Main_OdiagE__1: $i > $i > $i > $i ).

thf(c_Main_OdprodE__2_decl,type,
    c_Main_OdprodE__2: $i > $i > $i > $i > $i > $i ).

thf(c_Main_OdprodE__4_decl,type,
    c_Main_OdprodE__4: $i > $i > $i > $i > $i > $i ).

thf(c_Main_Orel__compE__2_decl,type,
    c_Main_Orel__compE__2: $i > $i > $i > $i > $i > $i > $i ).

thf(c_SetInterval_OgreaterThanLessThan_decl,type,
    c_SetInterval_OgreaterThanLessThan: $i > $i > $i > $i ).

thf(c_Main_OIdE__1_decl,type,
    c_Main_OIdE__1: $i > $i > $i ).

thf(c_Inter_decl,type,
    c_Inter: $i > $i > $i ).

thf(c_Relation_ODomain_decl,type,
    c_Relation_ODomain: $i > $i > $i > $i ).

thf(c_Main_OInterI__1_decl,type,
    c_Main_OInterI__1: $i > $i > $i > $i ).

thf(c_Main_ODomainE__1_decl,type,
    c_Main_ODomainE__1: $i > $i > $i > $i > $i ).

thf(sk1_decl,type,
    sk1: $i > $i > $i > $i ).

thf(sk2_decl,type,
    sk2: $i > $i > $i > $i ).

thf(sk3_decl,type,
    sk3: $i > $i > $i > $i ).

thf(sk4_decl,type,
    sk4: $i > $i > $i > $i ).

thf(sk6_decl,type,
    sk6: $i > $i ).

thf(sk7_decl,type,
    sk7: $i > $i ).

thf(sk12_decl,type,
    sk12: $i > $i > $i ).

thf(sk1_def,definition,
    ( sk1
    = ( @+[A: $i > $i > $i > $i] :
        ! [B: $i,C: $i,D: $i] :
          ( ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( D @ ( C @ A ) ) )
          = B ) ) ) ).

thf(sk2_def,definition,
    ( sk2
    = ( @+[A: $i > $i > $i > $i] :
        ! [B: $i,C: $i,D: $i] :
          ( ( D @ ( C @ ( B @ c_append ) ) @ ( D @ ( B @ A ) ) )
          = C ) ) ) ).

thf(sk3_def,definition,
    ( sk3
    = ( @+[A: $i > $i > $i > $i] :
        ! [B: $i,C: $i,D: $i] :
          ( ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( D @ ( B @ A ) ) )
          = C ) ) ) ).

thf(sk4_def,definition,
    ( sk4
    = ( @+[A: $i > $i > $i > $i] :
        ! [B: $i,C: $i,D: $i] :
          ( ( D @ ( C @ ( B @ c_append ) ) @ ( D @ ( C @ A ) ) )
          = B ) ) ) ).

thf(sk6_def,definition,
    ( sk6
    = ( @+[A: $i > $i] :
        ! [B: $i] :
          ( ( B @ c_IntDef_Oint @ A )
          = B ) ) ) ).

thf(sk7_def,definition,
    ( sk7
    = ( @+[A: $i > $i] :
        ! [B: $i] :
          ( ( B @ c_Suc @ A )
          = B ) ) ) ).

thf(sk12_def,definition,
    ( sk12
    = ( @+[A: $i > $i > $i] :
        ! [B: $i,C: $i] :
          ( ( C @ ( B @ c_Datatype_Ooption_OSome ) @ ( C @ A ) )
          = B ) ) ) ).

thf(146,axiom,
    tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Wellfounded__Recursion_Owf ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Owf__less__than_0) ).

thf(645,plain,
    tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Wellfounded__Recursion_Owf ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(140,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = F )
      | ( ( D @ ( C @ ( B @ ( A @ c_Datatype__Universe_OScons ) ) ) )
       != ( D @ ( C @ ( F @ ( E @ c_Datatype__Universe_OScons ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__Scons__eq__iff1_1) ).

thf(629,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = F )
      | ( ( D @ ( C @ ( B @ ( A @ c_Datatype__Universe_OScons ) ) ) )
       != ( D @ ( C @ ( F @ ( E @ c_Datatype__Universe_OScons ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(6,axiom,
    ! [A: $i] :
      ( ( A = c_0 )
      | ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__left__iff1_0) ).

thf(313,plain,
    ! [A: $i] :
      ( ( A = c_0 )
      | ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(314,plain,
    ! [A: $i] :
      ( ( A = c_0 )
      | ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(cnf,[status(esa)],[313]) ).

thf(315,plain,
    ! [A: $i] :
      ( ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) )
      | ( A = c_0 ) ),
    inference(lifteq,[status(thm)],[314]) ).

thf(18,axiom,
    ! [A: $i] :
      ( ( A = c_0 )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oneq0__conv__iff1_0) ).

thf(348,plain,
    ! [A: $i] :
      ( ( A = c_0 )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(349,plain,
    ! [A: $i] :
      ( ( A = c_0 )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(cnf,[status(esa)],[348]) ).

thf(350,plain,
    ! [A: $i] :
      ( ( tc_nat @ ( A @ ( c_0 @ c_less ) ) )
      | ( A = c_0 ) ),
    inference(lifteq,[status(thm)],[349]) ).

thf(71,axiom,
    ! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( c_0 @ c_less ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ozero__less__Suc_0) ).

thf(471,plain,
    ! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( c_0 @ c_less ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(64,axiom,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__add__less2__iff1_0) ).

thf(459,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(460,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
    inference(polarity_switch,[status(thm)],[459]) ).

thf(6451,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_nat @ ( A @ c_Suc @ ( c_0 @ c_less ) ) )
       != ( tc_nat @ ( C @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_less ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[471,460]) ).

thf(6452,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( A @ c_Suc @ ( c_0 @ c_less ) ) )
     != ( tc_nat @ ( C @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_less ) ) ) ),
    inference(simp,[status(thm)],[6451]) ).

thf(6495,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat != tc_nat )
      | ( ( A @ c_Suc )
       != C )
      | ( ( tc_nat @ ( C @ ( B @ c_plus ) ) )
       != c_0 ) ),
    inference(simp,[status(thm)],[6452]) ).

thf(6521,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( A @ c_Suc @ ( B @ c_plus ) ) )
     != c_0 ),
    inference(simp,[status(thm)],[6495]) ).

thf(6702,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( tc_nat @ ( B @ c_Suc @ ( C @ c_plus ) ) ) )
      | ( c_0 != c_0 )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(paramod_ordered,[status(thm)],[350,6521]) ).

thf(6703,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( tc_nat @ ( B @ c_Suc @ ( C @ c_plus ) ) ) )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(simp,[status(thm)],[6702]) ).

thf(6704,plain,
    ! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) ),
    inference(pattern_uni,[status(thm)],[6703:[bind(A,$thf( tc_nat @ ( G @ c_Suc @ ( D @ c_plus ) ) )),bind(B,$thf( G )),bind(C,$thf( D ))]]) ).

thf(6722,plain,
    ! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) ),
    inference(simp,[status(thm)],[6704]) ).

thf(78,axiom,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__add__less1__iff1_0) ).

thf(483,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(484,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
    inference(polarity_switch,[status(thm)],[483]) ).

thf(7629,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_nat @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
       != ( tc_nat @ ( C @ ( tc_nat @ ( D @ ( C @ c_plus ) ) @ c_less ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[6722,484]) ).

thf(7630,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
     != ( tc_nat @ ( C @ ( tc_nat @ ( D @ ( C @ c_plus ) ) @ c_less ) ) ) ),
    inference(simp,[status(thm)],[7629]) ).

thf(7643,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_nat != tc_nat )
      | ( ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) )
       != C )
      | ( ( tc_nat @ ( D @ ( C @ c_plus ) ) )
       != c_0 ) ),
    inference(simp,[status(thm)],[7630]) ).

thf(7665,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) @ c_plus ) ) )
     != c_0 ),
    inference(simp,[status(thm)],[7643]) ).

thf(9256,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
       != ( tc_nat @ ( D @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ c_plus ) ) ) )
      | ( c_0 != c_0 )
      | ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(paramod_ordered,[status(thm)],[315,7665]) ).

thf(9257,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
       != ( tc_nat @ ( D @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ c_plus ) ) ) )
      | ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(simp,[status(thm)],[9256]) ).

thf(9258,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( tc_IntDef_Oint @ ( tc_nat @ ( A @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
    inference(pattern_uni,[status(thm)],[9257:[bind(A,$thf( tc_nat @ ( F @ ( tc_nat @ ( K @ c_Suc @ ( H @ c_plus ) ) @ c_plus ) ) )),bind(B,$thf( H )),bind(C,$thf( K )),bind(D,$thf( F ))]]) ).

thf(9273,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( tc_IntDef_Oint @ ( tc_nat @ ( A @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
    inference(simp,[status(thm)],[9258]) ).

thf(269,axiom,
    ! [B: $i,A: $i] : ( B @ ( c_UNIV @ ( A @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUNIV__I_0) ).

thf(898,plain,
    ! [B: $i,A: $i] : ( B @ ( c_UNIV @ ( A @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(2,negated_conjecture,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) )
      | ~ ( t_a @ tc_set @ ( v_S @ ( B @ c_in ) ) )
      | ( t_a @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).

thf(302,plain,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) )
      | ~ ( t_a @ tc_set @ ( v_S @ ( B @ c_in ) ) )
      | ( t_a @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(304,plain,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) )
      | ~ ( t_a @ tc_set @ ( v_S @ ( B @ c_in ) ) )
      | ( t_a @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(cnf,[status(esa)],[302]) ).

thf(965,plain,
    ! [B: $i,A: $i] :
      ( ~ $true
      | ( ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) )
       != ( t_a @ tc_set @ ( v_S @ ( B @ c_in ) ) ) )
      | ~ ( t_a @ tc_set @ ( v_S @ ( B @ c_in ) ) )
      | ( t_a @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(eqfactor_ordered,[status(thm)],[304]) ).

thf(967,plain,
    ! [A: $i] :
      ( ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) )
      | ( t_a @ tc_set @ ( A @ ( A @ c_lessequals ) ) ) ),
    inference(pattern_uni,[status(thm)],[965:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).

thf(2045,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
       != ( t_a @ tc_set @ ( v_S @ ( C @ c_in ) ) ) )
      | ~ $true
      | ( t_a @ tc_set @ ( C @ ( C @ c_lessequals ) ) ) ),
    inference(paramod_ordered,[status(thm)],[898,967]) ).

thf(2046,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
       != ( t_a @ tc_set @ ( v_S @ ( C @ c_in ) ) ) )
      | ( t_a @ tc_set @ ( C @ ( C @ c_lessequals ) ) ) ),
    inference(simp,[status(thm)],[2045]) ).

thf(2054,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
       != ( t_a @ tc_set ) )
      | ( c_UNIV != v_S )
      | ( A != C )
      | ( t_a @ tc_set @ ( C @ ( C @ c_lessequals ) ) ) ),
    inference(simp,[status(thm)],[2046]) ).

thf(2072,plain,
    ! [A: $i] :
      ( ( c_UNIV != v_S )
      | ( t_a @ tc_set @ ( A @ ( A @ c_lessequals ) ) ) ),
    inference(simp,[status(thm)],[2054]) ).

thf(76,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olistrel ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( A @ ( c_List_Olist_ONil @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Nil1_0) ).

thf(479,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olistrel ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( A @ ( c_List_Olist_ONil @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(13,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_List_Olist_ONil )
      | ( A
       != ( C @ ( A @ ( B @ c_append ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oself__append__conv2__iff1_0) ).

thf(333,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_List_Olist_ONil )
      | ( A
       != ( C @ ( A @ ( B @ c_append ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(122,axiom,
    tc_nat @ class_Orderings_Oorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_3) ).

thf(582,plain,
    tc_nat @ class_Orderings_Oorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(2558,plain,
    ! [A: $i] :
      ( ( A != tc_nat )
      | ( c_0 @ class_Orderings_Oorder )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(paramod_ordered,[status(thm)],[350,582]) ).

thf(2559,plain,
    ( ( c_0 @ class_Orderings_Oorder )
    | ( tc_nat @ ( tc_nat @ ( c_0 @ c_less ) ) ) ),
    inference(pattern_uni,[status(thm)],[2558:[bind(A,$thf( tc_nat ))]]) ).

thf(290,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( C @ ( A @ c_Datatype_Ooption_OSome ) ) )
      | ~ ( C @ ( C @ ( B @ c_Datatype_Oo2s ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Oelem__o2s__iff1_0) ).

thf(941,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( C @ ( A @ c_Datatype_Ooption_OSome ) ) )
      | ~ ( C @ ( C @ ( B @ c_Datatype_Oo2s ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(105,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Suc )
       != ( B @ c_Suc ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__Suc__eq__iff1_0) ).

thf(538,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Suc )
       != ( B @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(539,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Suc )
       != ( B @ c_Suc ) ) ),
    inference(cnf,[status(esa)],[538]) ).

thf(540,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Suc )
       != ( B @ c_Suc ) ) ),
    inference(lifteq,[status(thm)],[539]) ).

thf(541,plain,
    ? [A: $i > $i] :
    ! [B: $i] :
      ( ( B @ c_Suc @ A )
      = B ),
    inference(detectInverse,[status(thm)],[540]) ).

thf(542,plain,
    ! [A: $i] :
      ( ( A @ c_Suc @ sk7 )
      = A ),
    inference(cnf,[status(esa)],[541]) ).

thf(2331,plain,
    ! [A: $i] :
      ( ( A @ c_Suc @ sk7 )
      = A ),
    inference(lifteq,[status(thm)],[542]) ).

thf(156,axiom,
    ! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanAtMost_0) ).

thf(666,plain,
    ! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(6733,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_nat @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
       != ( tc_nat @ ( D @ ( tc_nat @ ( D @ ( C @ c_plus ) ) @ c_less ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[6722,460]) ).

thf(6734,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
     != ( tc_nat @ ( D @ ( tc_nat @ ( D @ ( C @ c_plus ) ) @ c_less ) ) ) ),
    inference(simp,[status(thm)],[6733]) ).

thf(6780,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_nat != tc_nat )
      | ( ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) )
       != D )
      | ( ( tc_nat @ ( D @ ( C @ c_plus ) ) )
       != c_0 ) ),
    inference(simp,[status(thm)],[6734]) ).

thf(6802,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) @ ( C @ c_plus ) ) )
     != c_0 ),
    inference(simp,[status(thm)],[6780]) ).

thf(9201,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
       != ( tc_nat @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ ( D @ c_plus ) ) ) )
      | ( c_0 != c_0 )
      | ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(paramod_ordered,[status(thm)],[315,6802]) ).

thf(9202,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
       != ( tc_nat @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ ( D @ c_plus ) ) ) )
      | ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(simp,[status(thm)],[9201]) ).

thf(9203,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( tc_IntDef_Oint @ ( tc_nat @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ ( A @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
    inference(pattern_uni,[status(thm)],[9202:[bind(A,$thf( tc_nat @ ( tc_nat @ ( K @ c_Suc @ ( H @ c_plus ) ) @ ( E @ c_plus ) ) )),bind(B,$thf( H )),bind(C,$thf( K )),bind(D,$thf( E ))]]) ).

thf(9222,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( tc_IntDef_Oint @ ( tc_nat @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ ( A @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
    inference(simp,[status(thm)],[9203]) ).

thf(19,axiom,
    ( ( tc_nat @ ( c_0 @ ( c_0 @ c_plus ) ) )
    = c_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0__iff2_0) ).

thf(351,plain,
    ( ( tc_nat @ ( c_0 @ ( c_0 @ c_plus ) ) )
    = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(352,plain,
    ( ( tc_nat @ ( c_0 @ ( c_0 @ c_plus ) ) )
    = c_0 ),
    inference(lifteq,[status(thm)],[351]) ).

thf(300,axiom,
    ! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanLessThan_0) ).

thf(962,plain,
    ! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(69,axiom,
    tc_nat @ class_Nat_Opower,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_12) ).

thf(468,plain,
    tc_nat @ class_Nat_Opower,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(41,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
     != c_List_Olist_ONil ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Odistinct__2__iff1_0) ).

thf(408,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
     != c_List_Olist_ONil ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(51,axiom,
    ! [A: $i] :
      ( ( A = c_0 )
      | ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__0__left__iff__iff1_0) ).

thf(427,plain,
    ! [A: $i] :
      ( ( A = c_0 )
      | ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(428,plain,
    ! [A: $i] :
      ( ( A = c_0 )
      | ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(cnf,[status(esa)],[427]) ).

thf(429,plain,
    ! [A: $i] :
      ( ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) )
      | ( A = c_0 ) ),
    inference(lifteq,[status(thm)],[428]) ).

thf(1,negated_conjecture,
    ! [A: $i] :
      ~ ( t_a @ tc_set @ tc_set @ ( t_a @ tc_set @ ( c_emptyset @ ( A @ c_insert ) ) @ ( v_S @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(301,plain,
    ! [A: $i] :
      ~ ( t_a @ tc_set @ tc_set @ ( t_a @ tc_set @ ( c_emptyset @ ( A @ c_insert ) ) @ ( v_S @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(303,plain,
    ! [A: $i] :
      ~ ( t_a @ tc_set @ tc_set @ ( t_a @ tc_set @ ( c_emptyset @ ( A @ c_insert ) ) @ ( v_S @ c_lessequals ) ) ),
    inference(polarity_switch,[status(thm)],[301]) ).

thf(963,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( t_a @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
       != ( t_a @ tc_set @ tc_set @ ( t_a @ tc_set @ ( c_emptyset @ ( C @ c_insert ) ) @ ( v_S @ c_lessequals ) ) ) )
      | ~ $true
      | ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) )
      | ~ ( t_a @ tc_set @ ( v_S @ ( B @ c_in ) ) ) ),
    inference(paramod_ordered,[status(thm)],[304,303]) ).

thf(964,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( t_a @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
       != ( t_a @ tc_set @ tc_set @ ( t_a @ tc_set @ ( c_emptyset @ ( C @ c_insert ) ) @ ( v_S @ c_lessequals ) ) ) )
      | ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) )
      | ~ ( t_a @ tc_set @ ( v_S @ ( B @ c_in ) ) ) ),
    inference(simp,[status(thm)],[963]) ).

thf(966,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( t_a @ tc_set @ tc_set )
       != ( t_a @ tc_set ) )
      | ( B
       != ( t_a @ tc_set @ ( c_emptyset @ ( C @ c_insert ) ) ) )
      | ( A != v_S )
      | ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) )
      | ~ ( t_a @ tc_set @ ( v_S @ ( B @ c_in ) ) ) ),
    inference(simp,[status(thm)],[964]) ).

thf(968,plain,
    ! [A: $i] :
      ( ( ( t_a @ tc_set @ tc_set )
       != ( t_a @ tc_set ) )
      | ~ ( t_a @ tc_set @ ( v_S @ ( v_S @ c_in ) ) )
      | ~ ( t_a @ tc_set @ ( v_S @ ( t_a @ tc_set @ ( c_emptyset @ ( A @ c_insert ) ) @ c_in ) ) ) ),
    inference(simp,[status(thm)],[966]) ).

thf(972,plain,
    ! [A: $i] :
      ( ( ( t_a @ tc_set )
       != t_a )
      | ~ ( t_a @ tc_set @ ( v_S @ ( v_S @ c_in ) ) )
      | ~ ( t_a @ tc_set @ ( v_S @ ( t_a @ tc_set @ ( c_emptyset @ ( A @ c_insert ) ) @ c_in ) ) ) ),
    inference(simp,[status(thm)],[968]) ).

thf(2047,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
       != ( t_a @ tc_set @ ( v_S @ ( t_a @ tc_set @ ( c_emptyset @ ( C @ c_insert ) ) @ c_in ) ) ) )
      | ( ( t_a @ tc_set )
       != t_a )
      | ~ ( t_a @ tc_set @ ( v_S @ ( v_S @ c_in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[898,972]) ).

thf(2048,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
       != ( t_a @ tc_set @ ( v_S @ ( t_a @ tc_set @ ( c_emptyset @ ( C @ c_insert ) ) @ c_in ) ) ) )
      | ( ( t_a @ tc_set )
       != t_a )
      | ~ ( t_a @ tc_set @ ( v_S @ ( v_S @ c_in ) ) ) ),
    inference(simp,[status(thm)],[2047]) ).

thf(2062,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
       != ( t_a @ tc_set ) )
      | ( c_UNIV != v_S )
      | ( A
       != ( t_a @ tc_set @ ( c_emptyset @ ( C @ c_insert ) ) ) )
      | ( ( t_a @ tc_set )
       != t_a )
      | ~ ( t_a @ tc_set @ ( v_S @ ( v_S @ c_in ) ) ) ),
    inference(simp,[status(thm)],[2048]) ).

thf(2079,plain,
    ( ( c_UNIV != v_S )
    | ( ( t_a @ tc_set )
     != t_a )
    | ~ ( t_a @ tc_set @ ( v_S @ ( v_S @ c_in ) ) ) ),
    inference(simp,[status(thm)],[2062]) ).

thf(3409,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
       != ( t_a @ tc_set @ ( v_S @ ( v_S @ c_in ) ) ) )
      | ( c_UNIV != v_S )
      | ( ( t_a @ tc_set )
       != t_a )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[898,2079]) ).

thf(3410,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
       != ( t_a @ tc_set @ ( v_S @ ( v_S @ c_in ) ) ) )
      | ( c_UNIV != v_S )
      | ( ( t_a @ tc_set )
       != t_a ) ),
    inference(simp,[status(thm)],[3409]) ).

thf(3438,plain,
    ! [B: $i,A: $i] :
      ( ( B
       != ( t_a @ tc_set ) )
      | ( c_UNIV != v_S )
      | ( A != v_S )
      | ( c_UNIV != v_S )
      | ( ( t_a @ tc_set )
       != t_a ) ),
    inference(simp,[status(thm)],[3410]) ).

thf(3443,plain,
    ( ( c_UNIV != v_S )
    | ( ( t_a @ tc_set )
     != t_a ) ),
    inference(simp,[status(thm)],[3438]) ).

thf(3489,plain,
    ! [A: $i] :
      ( ( A != c_UNIV )
      | ( c_0 != v_S )
      | ( ( t_a @ tc_set )
       != t_a )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(paramod_ordered,[status(thm)],[350,3443]) ).

thf(3490,plain,
    ( ( c_0 != v_S )
    | ( ( t_a @ tc_set )
     != t_a )
    | ( tc_nat @ ( c_UNIV @ ( c_0 @ c_less ) ) ) ),
    inference(pattern_uni,[status(thm)],[3489:[bind(A,$thf( c_UNIV ))]]) ).

thf(117,axiom,
    ! [A: $i] :
      ~ ( tc_nat @ ( A @ ( A @ c_less ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__irrefl_0) ).

thf(574,plain,
    ! [A: $i] :
      ~ ( tc_nat @ ( A @ ( A @ c_less ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(575,plain,
    ! [A: $i] :
      ~ ( tc_nat @ ( A @ ( A @ c_less ) ) ),
    inference(polarity_switch,[status(thm)],[574]) ).

thf(3862,plain,
    ! [A: $i] :
      ( ( ( tc_nat @ ( c_UNIV @ ( c_0 @ c_less ) ) )
       != ( tc_nat @ ( A @ ( A @ c_less ) ) ) )
      | ~ $true
      | ( c_0 != v_S )
      | ( ( t_a @ tc_set )
       != t_a ) ),
    inference(paramod_ordered,[status(thm)],[3490,575]) ).

thf(3863,plain,
    ! [A: $i] :
      ( ( ( tc_nat @ ( c_UNIV @ ( c_0 @ c_less ) ) )
       != ( tc_nat @ ( A @ ( A @ c_less ) ) ) )
      | ( c_0 != v_S )
      | ( ( t_a @ tc_set )
       != t_a ) ),
    inference(simp,[status(thm)],[3862]) ).

thf(3866,plain,
    ! [A: $i] :
      ( ( tc_nat != tc_nat )
      | ( c_UNIV != A )
      | ( c_0 != A )
      | ( c_0 != v_S )
      | ( ( t_a @ tc_set )
       != t_a ) ),
    inference(simp,[status(thm)],[3863]) ).

thf(3871,plain,
    ( ( c_UNIV != c_0 )
    | ( c_0 != v_S )
    | ( ( t_a @ tc_set )
     != t_a ) ),
    inference(simp,[status(thm)],[3866]) ).

thf(12632,plain,
    ! [A: $i] :
      ( ( A != c_UNIV )
      | ( c_0 != c_0 )
      | ( c_0 != v_S )
      | ( ( t_a @ tc_set )
       != t_a )
      | ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(paramod_ordered,[status(thm)],[429,3871]) ).

thf(12633,plain,
    ! [A: $i] :
      ( ( A != c_UNIV )
      | ( c_0 != v_S )
      | ( ( t_a @ tc_set )
       != t_a )
      | ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(simp,[status(thm)],[12632]) ).

thf(12634,plain,
    ( ( c_0 != v_S )
    | ( ( t_a @ tc_set )
     != t_a )
    | ~ ( tc_nat @ ( c_UNIV @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(pattern_uni,[status(thm)],[12633:[bind(A,$thf( c_UNIV ))]]) ).

thf(166,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_set @ ( D @ ( B @ c_minus ) ) @ ( A @ c_in ) ) )
      | ( C @ ( D @ ( A @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiffI_0) ).

thf(683,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_set @ ( D @ ( B @ c_minus ) ) @ ( A @ c_in ) ) )
      | ( C @ ( D @ ( A @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(190,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = A )
      | ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
       != ( B @ ( D @ ( C @ c_insert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq__iff1_0) ).

thf(730,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = A )
      | ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
       != ( B @ ( D @ ( C @ c_insert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(40,axiom,
    ! [A: $i] : ( tc_IntDef_Oint @ ( c_0 @ ( A @ c_Divides_Oop_Advd ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__right_0) ).

thf(407,plain,
    ! [A: $i] : ( tc_IntDef_Oint @ ( c_0 @ ( A @ c_Divides_Oop_Advd ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(182,axiom,
    ~ ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Infinite__Set_Onat__not__finite_0) ).

thf(713,plain,
    ~ ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(714,plain,
    ~ ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ),
    inference(polarity_switch,[status(thm)],[713]) ).

thf(2031,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
       != ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[898,714]) ).

thf(2032,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
     != ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
    inference(simp,[status(thm)],[2031]) ).

thf(2057,plain,
    ! [B: $i,A: $i] :
      ( ( B
       != ( tc_nat @ tc_set ) )
      | ( c_UNIV != c_Finite__Set_OFinites )
      | ( A != c_UNIV ) ),
    inference(simp,[status(thm)],[2032]) ).

thf(2075,plain,
    c_UNIV != c_Finite__Set_OFinites,
    inference(simp,[status(thm)],[2057]) ).

thf(2087,plain,
    ! [A: $i] :
      ( ( A != c_UNIV )
      | ( c_Finite__Set_OFinites != c_0 )
      | ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(paramod_ordered,[status(thm)],[315,2075]) ).

thf(2088,plain,
    ( ( c_Finite__Set_OFinites != c_0 )
    | ~ ( tc_IntDef_Oint @ ( c_UNIV @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(pattern_uni,[status(thm)],[2087:[bind(A,$thf( c_UNIV ))]]) ).

thf(2356,plain,
    ! [A: $i] :
      ( ( ( tc_IntDef_Oint @ ( c_0 @ ( A @ c_Divides_Oop_Advd ) ) )
       != ( tc_IntDef_Oint @ ( c_UNIV @ ( c_0 @ c_Divides_Oop_Advd ) ) ) )
      | ( c_Finite__Set_OFinites != c_0 )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[407,2088]) ).

thf(2357,plain,
    ! [A: $i] :
      ( ( ( tc_IntDef_Oint @ ( c_0 @ ( A @ c_Divides_Oop_Advd ) ) )
       != ( tc_IntDef_Oint @ ( c_UNIV @ ( c_0 @ c_Divides_Oop_Advd ) ) ) )
      | ( c_Finite__Set_OFinites != c_0 ) ),
    inference(simp,[status(thm)],[2356]) ).

thf(2375,plain,
    ! [A: $i] :
      ( ( tc_IntDef_Oint != tc_IntDef_Oint )
      | ( c_UNIV != c_0 )
      | ( A != c_0 )
      | ( c_Finite__Set_OFinites != c_0 ) ),
    inference(simp,[status(thm)],[2357]) ).

thf(2378,plain,
    ( ( c_UNIV != c_0 )
    | ( c_Finite__Set_OFinites != c_0 ) ),
    inference(simp,[status(thm)],[2375]) ).

thf(2379,plain,
    ! [A: $i] :
      ( ( A != c_Finite__Set_OFinites )
      | ( c_UNIV != c_0 )
      | ( c_0 != c_0 )
      | ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(paramod_ordered,[status(thm)],[315,2378]) ).

thf(2380,plain,
    ! [A: $i] :
      ( ( A != c_Finite__Set_OFinites )
      | ( c_UNIV != c_0 )
      | ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(simp,[status(thm)],[2379]) ).

thf(2381,plain,
    ( ( c_UNIV != c_0 )
    | ~ ( tc_IntDef_Oint @ ( c_Finite__Set_OFinites @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(pattern_uni,[status(thm)],[2380:[bind(A,$thf( c_Finite__Set_OFinites ))]]) ).

thf(284,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsingletonI_0) ).

thf(928,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(296,axiom,
    ! [B: $i,A: $i] :
      ~ ( B @ ( c_emptyset @ ( A @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OemptyE_0) ).

thf(953,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ ( c_emptyset @ ( A @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(954,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ ( c_emptyset @ ( A @ c_in ) ) ),
    inference(polarity_switch,[status(thm)],[953]) ).

thf(9660,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
       != ( D @ ( c_emptyset @ ( C @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[928,954]) ).

thf(9661,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
     != ( D @ ( c_emptyset @ ( C @ c_in ) ) ) ),
    inference(simp,[status(thm)],[9660]) ).

thf(9683,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B != D )
      | ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
       != c_emptyset )
      | ( A != C ) ),
    inference(simp,[status(thm)],[9661]) ).

thf(9704,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
     != c_emptyset ),
    inference(simp,[status(thm)],[9683]) ).

thf(4,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D
        = ( C @ ( C @ ( B @ ( A @ ( D @ ( E @ c_Main_Olistrel__Cons1__2 ) ) ) ) @ ( C @ ( B @ ( A @ ( D @ ( E @ c_Main_Olistrel__Cons1__1 ) ) ) ) @ c_List_Olist_OCons ) ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( E @ c_List_Olistrel ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Cons1_0) ).

thf(308,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D
        = ( C @ ( C @ ( B @ ( A @ ( D @ ( E @ c_Main_Olistrel__Cons1__2 ) ) ) ) @ ( C @ ( B @ ( A @ ( D @ ( E @ c_Main_Olistrel__Cons1__1 ) ) ) ) @ c_List_Olist_OCons ) ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( E @ c_List_Olistrel ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(7587,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_nat @ ( A @ c_Suc @ ( c_0 @ c_less ) ) )
       != ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_less ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[471,484]) ).

thf(7588,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( A @ c_Suc @ ( c_0 @ c_less ) ) )
     != ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_less ) ) ) ),
    inference(simp,[status(thm)],[7587]) ).

thf(7632,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat != tc_nat )
      | ( ( A @ c_Suc )
       != B )
      | ( ( tc_nat @ ( C @ ( B @ c_plus ) ) )
       != c_0 ) ),
    inference(simp,[status(thm)],[7588]) ).

thf(7654,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_Suc @ c_plus ) ) )
     != c_0 ),
    inference(simp,[status(thm)],[7632]) ).

thf(12824,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( tc_nat @ ( C @ ( B @ c_Suc @ c_plus ) ) ) )
      | ( c_0 != c_0 )
      | ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(paramod_ordered,[status(thm)],[429,7654]) ).

thf(12825,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( tc_nat @ ( C @ ( B @ c_Suc @ c_plus ) ) ) )
      | ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(simp,[status(thm)],[12824]) ).

thf(12826,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_Suc @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
    inference(pattern_uni,[status(thm)],[12825:[bind(A,$thf( tc_nat @ ( E @ ( G @ c_Suc @ c_plus ) ) )),bind(B,$thf( G )),bind(C,$thf( E ))]]) ).

thf(13672,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_Suc @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
    inference(simp,[status(thm)],[12826]) ).

thf(60,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( B @ c_less ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__irrefl__iff1_0) ).

thf(449,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( B @ c_less ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(163,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( C @ ( E @ ( D @ ( A @ ( C @ c_Main_OusumE__2 ) ) ) @ c_in ) ) )
      | ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( E @ ( D @ ( A @ ( B @ c_Main_OusumE__1 ) ) ) @ c_in ) ) )
      | ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ousum ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OusumE_3) ).

thf(677,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( C @ ( E @ ( D @ ( A @ ( C @ c_Main_OusumE__2 ) ) ) @ c_in ) ) )
      | ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( E @ ( D @ ( A @ ( B @ c_Main_OusumE__1 ) ) ) @ c_in ) ) )
      | ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ousum ) ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(251,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( E @ ( D @ ( E @ ( D @ ( A @ ( C @ c_Main_OusumE__2 ) ) ) @ c_Datatype__Universe_OIn1 ) ) ) )
      | ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( E @ ( D @ ( A @ ( B @ c_Main_OusumE__1 ) ) ) @ c_in ) ) )
      | ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ousum ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OusumE_2) ).

thf(861,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( E @ ( D @ ( E @ ( D @ ( A @ ( C @ c_Main_OusumE__2 ) ) ) @ c_Datatype__Universe_OIn1 ) ) ) )
      | ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( E @ ( D @ ( A @ ( B @ c_Main_OusumE__1 ) ) ) @ c_in ) ) )
      | ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ousum ) ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(130,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Datatype_Ooption_OSome ) )
       != ( B @ ( C @ c_Datatype_Ooption_OSome ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Ooption_Oinject__iff1_0) ).

thf(600,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Datatype_Ooption_OSome ) )
       != ( B @ ( C @ c_Datatype_Ooption_OSome ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(601,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Datatype_Ooption_OSome ) )
       != ( B @ ( C @ c_Datatype_Ooption_OSome ) ) ) ),
    inference(cnf,[status(esa)],[600]) ).

thf(602,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Datatype_Ooption_OSome ) )
       != ( B @ ( C @ c_Datatype_Ooption_OSome ) ) ) ),
    inference(lifteq,[status(thm)],[601]) ).

thf(603,plain,
    ? [A: $i > $i > $i] :
    ! [B: $i,C: $i] :
      ( ( C @ ( B @ c_Datatype_Ooption_OSome ) @ ( C @ A ) )
      = B ),
    inference(detectInverse,[status(thm)],[602]) ).

thf(604,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Datatype_Ooption_OSome ) @ ( B @ sk12 ) )
      = A ),
    inference(cnf,[status(esa)],[603]) ).

thf(9621,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Datatype_Ooption_OSome ) @ ( B @ sk12 ) )
      = A ),
    inference(lifteq,[status(thm)],[604]) ).

thf(96,axiom,
    tc_IntDef_Oint @ class_HOL_Ominus,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_0) ).

thf(519,plain,
    tc_IntDef_Oint @ class_HOL_Ominus,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(2511,plain,
    ! [A: $i] :
      ( ( A != tc_IntDef_Oint )
      | ( c_0 @ class_HOL_Ominus )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(paramod_ordered,[status(thm)],[350,519]) ).

thf(2512,plain,
    ( ( c_0 @ class_HOL_Ominus )
    | ( tc_nat @ ( tc_IntDef_Oint @ ( c_0 @ c_less ) ) ) ),
    inference(pattern_uni,[status(thm)],[2511:[bind(A,$thf( tc_IntDef_Oint ))]]) ).

thf(259,axiom,
    ! [A: $i] : ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OemptyI_0) ).

thf(878,plain,
    ! [A: $i] : ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(57,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( C @ ( D @ ( A @ c_List_Olist_OCons ) ) @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( D @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olists_OCons_0) ).

thf(440,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( C @ ( D @ ( A @ c_List_Olist_OCons ) ) @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( D @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(151,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_Main_OUnionE__1 ) ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( C @ ( B @ c_Union ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnionE_1) ).

thf(655,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_Main_OUnionE__1 ) ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( C @ ( B @ c_Union ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(2180,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) )
       != ( C @ ( c_emptyset @ ( B @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[878,954]) ).

thf(2181,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) )
     != ( C @ ( c_emptyset @ ( B @ c_in ) ) ) ),
    inference(simp,[status(thm)],[2180]) ).

thf(2193,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ tc_set )
       != C )
      | ( c_Finite__Set_OFinites != c_emptyset )
      | ( c_emptyset != B ) ),
    inference(simp,[status(thm)],[2181]) ).

thf(2195,plain,
    c_Finite__Set_OFinites != c_emptyset,
    inference(simp,[status(thm)],[2193]) ).

thf(31,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv__iff1_0) ).

thf(383,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(384,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != c_List_Olist_ONil ) ),
    inference(cnf,[status(esa)],[383]) ).

thf(385,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != c_List_Olist_ONil ) ),
    inference(lifteq,[status(thm)],[384]) ).

thf(7909,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( tc_nat @ ( C @ ( B @ c_Suc @ c_plus ) ) ) )
      | ( c_0 != c_0 )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(paramod_ordered,[status(thm)],[350,7654]) ).

thf(7910,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( tc_nat @ ( C @ ( B @ c_Suc @ c_plus ) ) ) )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(simp,[status(thm)],[7909]) ).

thf(7911,plain,
    ! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_Suc @ c_plus ) ) @ ( c_0 @ c_less ) ) ),
    inference(pattern_uni,[status(thm)],[7910:[bind(A,$thf( tc_nat @ ( E @ ( G @ c_Suc @ c_plus ) ) )),bind(B,$thf( G )),bind(C,$thf( E ))]]) ).

thf(7933,plain,
    ! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_Suc @ c_plus ) ) @ ( c_0 @ c_less ) ) ),
    inference(simp,[status(thm)],[7911]) ).

thf(32,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_plus ) ) @ ( c_0 @ c_less ) ) )
      | ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0__iff2_1) ).

thf(386,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_plus ) ) @ ( c_0 @ c_less ) ) )
      | ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(387,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_plus ) ) @ ( c_0 @ c_less ) ) )
      | ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(cnf,[status(esa)],[386]) ).

thf(8226,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_Suc @ c_plus ) ) @ ( c_0 @ c_less ) ) )
       != ( tc_nat @ ( C @ ( c_0 @ c_less ) ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( D @ c_plus ) ) @ ( c_0 @ c_less ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[7933,387]) ).

thf(8227,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_Suc @ c_plus ) ) @ ( c_0 @ c_less ) ) )
       != ( tc_nat @ ( C @ ( c_0 @ c_less ) ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( D @ c_plus ) ) @ ( c_0 @ c_less ) ) ) ),
    inference(simp,[status(thm)],[8226]) ).

thf(8228,plain,
    ! [C: $i,B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_Suc @ c_plus ) ) @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) ),
    inference(pattern_uni,[status(thm)],[8227:[bind(A,$thf( F )),bind(B,$thf( H )),bind(C,$thf( tc_nat @ ( F @ ( H @ c_Suc @ c_plus ) ) )),bind(D,$thf( D ))]]) ).

thf(8277,plain,
    ! [C: $i,B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_Suc @ c_plus ) ) @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) ),
    inference(simp,[status(thm)],[8228]) ).

thf(10404,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_nat @ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_Suc @ c_plus ) ) @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
       != ( tc_nat @ ( D @ ( D @ c_less ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[8277,575]) ).

thf(10405,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_Suc @ c_plus ) ) @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
     != ( tc_nat @ ( D @ ( D @ c_less ) ) ) ),
    inference(simp,[status(thm)],[10404]) ).

thf(10408,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_nat != tc_nat )
      | ( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_Suc @ c_plus ) ) @ ( A @ c_plus ) ) )
       != D )
      | ( c_0 != D ) ),
    inference(simp,[status(thm)],[10405]) ).

thf(10433,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_Suc @ c_plus ) ) @ ( A @ c_plus ) ) )
     != c_0 ),
    inference(simp,[status(thm)],[10408]) ).

thf(108,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Advd ) ) )
      | ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_uminus ) @ ( A @ c_Divides_Oop_Advd ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Odvd__zminus__iff__iff1_0) ).

thf(550,plain,
    ! [B: $i,A: $i] :
      ( ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Advd ) ) )
      | ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_uminus ) @ ( A @ c_Divides_Oop_Advd ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(50,axiom,
    ! [A: $i] : ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole0_0) ).

thf(426,plain,
    ! [A: $i] : ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(1678,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
       != ( t_a @ tc_set @ tc_set @ ( t_a @ tc_set @ ( c_emptyset @ ( B @ c_insert ) ) @ ( v_S @ c_lessequals ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[426,303]) ).

thf(1679,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
     != ( t_a @ tc_set @ tc_set @ ( t_a @ tc_set @ ( c_emptyset @ ( B @ c_insert ) ) @ ( v_S @ c_lessequals ) ) ) ),
    inference(simp,[status(thm)],[1678]) ).

thf(1686,plain,
    ! [B: $i,A: $i] :
      ( ( ( t_a @ tc_set @ tc_set )
       != tc_nat )
      | ( A
       != ( t_a @ tc_set @ ( c_emptyset @ ( B @ c_insert ) ) ) )
      | ( c_0 != v_S ) ),
    inference(simp,[status(thm)],[1679]) ).

thf(1689,plain,
    ( ( ( t_a @ tc_set @ tc_set )
     != tc_nat )
    | ( c_0 != v_S ) ),
    inference(simp,[status(thm)],[1686]) ).

thf(1708,plain,
    ! [A: $i] :
      ( ( A
       != ( t_a @ tc_set @ tc_set ) )
      | ( tc_nat != c_0 )
      | ( c_0 != v_S )
      | ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(paramod_ordered,[status(thm)],[315,1689]) ).

thf(1709,plain,
    ( ( tc_nat != c_0 )
    | ( c_0 != v_S )
    | ~ ( tc_IntDef_Oint @ ( t_a @ tc_set @ tc_set @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(pattern_uni,[status(thm)],[1708:[bind(A,$thf( t_a @ tc_set @ tc_set ))]]) ).

thf(1981,plain,
    ! [A: $i] :
      ( ( ( tc_IntDef_Oint @ ( c_0 @ ( A @ c_Divides_Oop_Advd ) ) )
       != ( tc_IntDef_Oint @ ( t_a @ tc_set @ tc_set @ ( c_0 @ c_Divides_Oop_Advd ) ) ) )
      | ( tc_nat != c_0 )
      | ( c_0 != v_S )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[407,1709]) ).

thf(1982,plain,
    ! [A: $i] :
      ( ( ( tc_IntDef_Oint @ ( c_0 @ ( A @ c_Divides_Oop_Advd ) ) )
       != ( tc_IntDef_Oint @ ( t_a @ tc_set @ tc_set @ ( c_0 @ c_Divides_Oop_Advd ) ) ) )
      | ( tc_nat != c_0 )
      | ( c_0 != v_S ) ),
    inference(simp,[status(thm)],[1981]) ).

thf(2005,plain,
    ! [A: $i] :
      ( ( tc_IntDef_Oint != tc_IntDef_Oint )
      | ( ( t_a @ tc_set @ tc_set )
       != c_0 )
      | ( A != c_0 )
      | ( tc_nat != c_0 )
      | ( c_0 != v_S ) ),
    inference(simp,[status(thm)],[1982]) ).

thf(2009,plain,
    ( ( ( t_a @ tc_set @ tc_set )
     != c_0 )
    | ( tc_nat != c_0 )
    | ( c_0 != v_S ) ),
    inference(simp,[status(thm)],[2005]) ).

thf(2916,plain,
    ! [A: $i] :
      ( ( A
       != ( t_a @ tc_set @ tc_set ) )
      | ( c_0 != c_0 )
      | ( tc_nat != c_0 )
      | ( c_0 != v_S )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(paramod_ordered,[status(thm)],[350,2009]) ).

thf(2917,plain,
    ! [A: $i] :
      ( ( A
       != ( t_a @ tc_set @ tc_set ) )
      | ( tc_nat != c_0 )
      | ( c_0 != v_S )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(simp,[status(thm)],[2916]) ).

thf(2918,plain,
    ( ( tc_nat != c_0 )
    | ( c_0 != v_S )
    | ( tc_nat @ ( t_a @ tc_set @ tc_set @ ( c_0 @ c_less ) ) ) ),
    inference(pattern_uni,[status(thm)],[2917:[bind(A,$thf( t_a @ tc_set @ tc_set ))]]) ).

thf(221,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( C @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__4 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__2 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Odprod ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_1) ).

thf(797,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( C @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__4 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__2 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Odprod ) ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(183,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__le__mono__iff1_0) ).

thf(715,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(20,axiom,
    ! [A: $i] :
      ( ( A = c_0 )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq__iff1_0) ).

thf(353,plain,
    ! [A: $i] :
      ( ( A = c_0 )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(354,plain,
    ! [A: $i] :
      ( ( A = c_0 )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(cnf,[status(esa)],[353]) ).

thf(355,plain,
    ! [A: $i] :
      ( ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) )
      | ( A = c_0 ) ),
    inference(lifteq,[status(thm)],[354]) ).

thf(6709,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( tc_nat @ ( B @ c_Suc @ ( C @ c_plus ) ) ) )
      | ( c_0 != c_0 )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(paramod_ordered,[status(thm)],[355,6521]) ).

thf(6710,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( tc_nat @ ( B @ c_Suc @ ( C @ c_plus ) ) ) )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(simp,[status(thm)],[6709]) ).

thf(6711,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( c_0 @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) @ c_lessequals ) ) ),
    inference(pattern_uni,[status(thm)],[6710:[bind(A,$thf( tc_nat @ ( G @ c_Suc @ ( D @ c_plus ) ) )),bind(B,$thf( G )),bind(C,$thf( D ))]]) ).

thf(6727,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( c_0 @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) @ c_lessequals ) ) ),
    inference(simp,[status(thm)],[6711]) ).

thf(72,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_less ) ) )
      | ~ ( A @ ( A @ ( C @ c_SetInterval_OgreaterThan ) @ ( B @ c_in ) ) )
      | ~ ( A @ class_Orderings_Oord ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__iff__iff1_0) ).

thf(472,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_less ) ) )
      | ~ ( A @ ( A @ ( C @ c_SetInterval_OgreaterThan ) @ ( B @ c_in ) ) )
      | ~ ( A @ class_Orderings_Oord ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(229,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__3 ) ) ) ) ) @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__2 ) ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( E @ ( F @ tc_prod ) @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Orel__compE_0) ).

thf(814,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__3 ) ) ) ) ) @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__2 ) ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( E @ ( F @ tc_prod ) @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(174,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OatMost ) @ ( A @ ( B @ c_SetInterval_OatMost ) @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__subset__iff__iff1_0) ).

thf(698,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OatMost ) @ ( A @ ( B @ c_SetInterval_OatMost ) @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(16,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( C @ ( C @ ( c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) )
       != ( C @ ( C @ ( c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_append ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend1__eq__conv__iff1_1) ).

thf(340,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( C @ ( C @ ( c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) )
       != ( C @ ( C @ ( c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_append ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(12814,plain,
    ! [A: $i] :
      ( ( A != c_Finite__Set_OFinites )
      | ( c_UNIV != c_0 )
      | ( c_0 != c_0 )
      | ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(paramod_ordered,[status(thm)],[429,2378]) ).

thf(12815,plain,
    ! [A: $i] :
      ( ( A != c_Finite__Set_OFinites )
      | ( c_UNIV != c_0 )
      | ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(simp,[status(thm)],[12814]) ).

thf(12816,plain,
    ( ( c_UNIV != c_0 )
    | ~ ( tc_nat @ ( c_Finite__Set_OFinites @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(pattern_uni,[status(thm)],[12815:[bind(A,$thf( c_Finite__Set_OFinites ))]]) ).

thf(159,axiom,
    ! [B: $i,A: $i] : ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanAtMost__int_0) ).

thf(670,plain,
    ! [B: $i,A: $i] : ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(198,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ~ ( B @ ( A @ ( D @ c_in ) ) )
      | ~ ( B @ ( A @ ( C @ c_in ) ) )
      | ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Infinite__Set_Oatmost__one__unique_0) ).

thf(747,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ~ ( B @ ( A @ ( D @ c_in ) ) )
      | ~ ( B @ ( A @ ( C @ c_in ) ) )
      | ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(277,axiom,
    ! [A: $i] :
      ( ~ ( A @ class_Finite__Set_Ofinite )
      | ( A @ tc_set @ class_Finite__Set_Ofinite ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_3) ).

thf(913,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Finite__Set_Ofinite )
      | ( A @ tc_set @ class_Finite__Set_Ofinite ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(45,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
      | ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0__iff2_0) ).

thf(417,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
      | ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(263,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ tc_prod ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( C @ ( D @ c_Pair ) ) ) @ c_in ) ) )
      | ( B @ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( D @ ( C @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Oacyclic ) )
      | ~ ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert__iff2_0) ).

thf(885,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ tc_prod ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( C @ ( D @ c_Pair ) ) ) @ c_in ) ) )
      | ( B @ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( D @ ( C @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Oacyclic ) )
      | ~ ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(46,axiom,
    tc_IntDef_Oint @ ( c_0 @ ( c_0 @ c_Divides_Oop_Advd ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__left__iff2_0) ).

thf(419,plain,
    tc_IntDef_Oint @ ( c_0 @ ( c_0 @ c_Divides_Oop_Advd ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(231,axiom,
    c_UNIV != c_emptyset,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUNIV__not__empty__iff1_0) ).

thf(819,plain,
    c_UNIV != c_emptyset,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(820,plain,
    c_UNIV != c_emptyset,
    inference(polarity_switch,[status(thm)],[819]) ).

thf(821,plain,
    c_UNIV != c_emptyset,
    inference(lifteq,[status(thm)],[820]) ).

thf(1231,plain,
    ! [A: $i] :
      ( ( A != c_UNIV )
      | ( c_0 != c_emptyset )
      | ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(paramod_ordered,[status(thm)],[315,821]) ).

thf(1232,plain,
    ( ( c_0 != c_emptyset )
    | ~ ( tc_IntDef_Oint @ ( c_UNIV @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(pattern_uni,[status(thm)],[1231:[bind(A,$thf( c_UNIV ))]]) ).

thf(1508,plain,
    ( ( ( tc_IntDef_Oint @ ( c_UNIV @ ( c_0 @ c_Divides_Oop_Advd ) ) )
     != ( tc_IntDef_Oint @ ( c_0 @ ( c_0 @ c_Divides_Oop_Advd ) ) ) )
    | ( c_0 != c_emptyset )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[419,1232]) ).

thf(1509,plain,
    ( ( ( tc_IntDef_Oint @ ( c_UNIV @ ( c_0 @ c_Divides_Oop_Advd ) ) )
     != ( tc_IntDef_Oint @ ( c_0 @ ( c_0 @ c_Divides_Oop_Advd ) ) ) )
    | ( c_0 != c_emptyset ) ),
    inference(simp,[status(thm)],[1508]) ).

thf(1523,plain,
    ( ( tc_IntDef_Oint != tc_IntDef_Oint )
    | ( c_UNIV != c_0 )
    | ( c_0 != c_0 )
    | ( c_0 != c_emptyset ) ),
    inference(simp,[status(thm)],[1509]) ).

thf(1526,plain,
    ( ( c_UNIV != c_0 )
    | ( c_0 != c_emptyset ) ),
    inference(simp,[status(thm)],[1523]) ).

thf(1701,plain,
    ! [A: $i] :
      ( ( c_0 != c_0 )
      | ( c_UNIV != c_0 )
      | ( A != c_emptyset )
      | ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(paramod_ordered,[status(thm)],[315,1526]) ).

thf(1702,plain,
    ! [A: $i] :
      ( ( c_UNIV != c_0 )
      | ( A != c_emptyset )
      | ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(pattern_uni,[status(thm)],[1701:[]]) ).

thf(1703,plain,
    ( ( c_UNIV != c_0 )
    | ~ ( tc_IntDef_Oint @ ( c_emptyset @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(simp,[status(thm)],[1702]) ).

thf(2530,plain,
    ! [A: $i] :
      ( ( A != c_Wellfounded__Relations_Oless__than )
      | ( tc_nat @ ( c_0 @ c_Wellfounded__Recursion_Owf ) )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(paramod_ordered,[status(thm)],[350,645]) ).

thf(2531,plain,
    ( ( tc_nat @ ( c_0 @ c_Wellfounded__Recursion_Owf ) )
    | ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ ( c_0 @ c_less ) ) ) ),
    inference(pattern_uni,[status(thm)],[2530:[bind(A,$thf( c_Wellfounded__Relations_Oless__than ))]]) ).

thf(149,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) )
      | ~ ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Wellfounded__Recursion_Oacyclic ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse__iff1_0) ).

thf(651,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) )
      | ~ ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Wellfounded__Recursion_Oacyclic ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(236,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ~ ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OgreaterThan ) @ ( A @ ( B @ c_SetInterval_OgreaterThan ) @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__subset__iff__iff1_0) ).

thf(829,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ~ ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OgreaterThan ) @ ( A @ ( B @ c_SetInterval_OgreaterThan ) @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(38,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_List_Olist_ONil )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__self__conv__iff1_0) ).

thf(402,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_List_Olist_ONil )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(403,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_List_Olist_ONil )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != A ) ),
    inference(cnf,[status(esa)],[402]) ).

thf(404,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_List_Olist_ONil )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != A ) ),
    inference(lifteq,[status(thm)],[403]) ).

thf(185,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( B @ ( A @ c_in ) ) )
      | ( D @ ( C @ ( A @ c_in ) ) )
      | ~ ( D @ ( D @ ( C @ ( B @ c_union ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnE_0) ).

thf(719,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( B @ ( A @ c_in ) ) )
      | ( D @ ( C @ ( A @ c_in ) ) )
      | ~ ( D @ ( D @ ( C @ ( B @ c_union ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(241,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ tc_set @ ( A @ ( B @ c_SetInterval_OatLeast ) @ ( A @ ( C @ c_SetInterval_OatLeast ) @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__subset__iff__iff2_0) ).

thf(838,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ tc_set @ ( A @ ( B @ c_SetInterval_OatLeast ) @ ( A @ ( C @ c_SetInterval_OatLeast ) @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(279,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ( C @ tc_set @ ( B @ ( A @ c_less ) ) )
      | ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OpsubsetI_0) ).

thf(917,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ( C @ tc_set @ ( B @ ( A @ c_less ) ) )
      | ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(223,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( F @ tc_prod ) @ ( C @ ( D @ ( F @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__2 ) ) ) ) ) @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__1 ) ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( E @ ( F @ tc_prod ) @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Orel__compE_1) ).

thf(802,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( F @ tc_prod ) @ ( C @ ( D @ ( F @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__2 ) ) ) ) ) @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__1 ) ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( E @ ( F @ tc_prod ) @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(27,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__self__conv2__iff1_0) ).

thf(372,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(3494,plain,
    ! [A: $i] :
      ( ( A != c_UNIV )
      | ( c_0 != v_S )
      | ( ( t_a @ tc_set )
       != t_a )
      | ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(paramod_ordered,[status(thm)],[315,3443]) ).

thf(3495,plain,
    ( ( c_0 != v_S )
    | ( ( t_a @ tc_set )
     != t_a )
    | ~ ( tc_IntDef_Oint @ ( c_UNIV @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(pattern_uni,[status(thm)],[3494:[bind(A,$thf( c_UNIV ))]]) ).

thf(67,axiom,
    tc_bool @ class_Finite__Set_Ofinite,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool_0) ).

thf(465,plain,
    tc_bool @ class_Finite__Set_Ofinite,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(2896,plain,
    ! [A: $i] :
      ( ( A != tc_bool )
      | ( c_0 @ class_Finite__Set_Ofinite )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(paramod_ordered,[status(thm)],[350,465]) ).

thf(2897,plain,
    ( ( c_0 @ class_Finite__Set_Ofinite )
    | ( tc_nat @ ( tc_bool @ ( c_0 @ c_less ) ) ) ),
    inference(pattern_uni,[status(thm)],[2896:[bind(A,$thf( tc_bool ))]]) ).

thf(12817,plain,
    ! [A: $i] :
      ( ( A != c_UNIV )
      | ( c_0 != c_0 )
      | ( c_Finite__Set_OFinites != c_0 )
      | ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(paramod_ordered,[status(thm)],[429,2378]) ).

thf(12818,plain,
    ! [A: $i] :
      ( ( A != c_UNIV )
      | ( c_Finite__Set_OFinites != c_0 )
      | ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(simp,[status(thm)],[12817]) ).

thf(12819,plain,
    ( ( c_Finite__Set_OFinites != c_0 )
    | ~ ( tc_nat @ ( c_UNIV @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(pattern_uni,[status(thm)],[12818:[bind(A,$thf( c_UNIV ))]]) ).

thf(271,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ ( E @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) )
      | ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ODomainI_0) ).

thf(902,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ ( E @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) )
      | ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(248,axiom,
    ! [A: $i] :
      ( ( A @ ( c_List_Olist_ONil @ c_List_Oset ) )
      = c_emptyset ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__empty__iff2_0) ).

thf(853,plain,
    ! [A: $i] :
      ( ( A @ ( c_List_Olist_ONil @ c_List_Oset ) )
      = c_emptyset ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(1710,plain,
    ! [A: $i] :
      ( ( A
       != ( t_a @ tc_set ) )
      | ( ( c_0 @ tc_set )
       != tc_nat )
      | ( c_0 != v_S )
      | ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(paramod_ordered,[status(thm)],[315,1689]) ).

thf(1711,plain,
    ( ( ( c_0 @ tc_set )
     != tc_nat )
    | ( c_0 != v_S )
    | ~ ( tc_IntDef_Oint @ ( t_a @ tc_set @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(pattern_uni,[status(thm)],[1710:[bind(A,$thf( t_a @ tc_set ))]]) ).

thf(2241,plain,
    ! [A: $i] :
      ( ( ( tc_IntDef_Oint @ ( c_0 @ ( A @ c_Divides_Oop_Advd ) ) )
       != ( tc_IntDef_Oint @ ( t_a @ tc_set @ ( c_0 @ c_Divides_Oop_Advd ) ) ) )
      | ( ( c_0 @ tc_set )
       != tc_nat )
      | ( c_0 != v_S )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[407,1711]) ).

thf(2242,plain,
    ! [A: $i] :
      ( ( ( tc_IntDef_Oint @ ( c_0 @ ( A @ c_Divides_Oop_Advd ) ) )
       != ( tc_IntDef_Oint @ ( t_a @ tc_set @ ( c_0 @ c_Divides_Oop_Advd ) ) ) )
      | ( ( c_0 @ tc_set )
       != tc_nat )
      | ( c_0 != v_S ) ),
    inference(simp,[status(thm)],[2241]) ).

thf(2266,plain,
    ! [A: $i] :
      ( ( tc_IntDef_Oint != tc_IntDef_Oint )
      | ( ( t_a @ tc_set )
       != c_0 )
      | ( A != c_0 )
      | ( ( c_0 @ tc_set )
       != tc_nat )
      | ( c_0 != v_S ) ),
    inference(simp,[status(thm)],[2242]) ).

thf(2270,plain,
    ( ( ( t_a @ tc_set )
     != c_0 )
    | ( ( c_0 @ tc_set )
     != tc_nat )
    | ( c_0 != v_S ) ),
    inference(simp,[status(thm)],[2266]) ).

thf(2399,plain,
    ! [A: $i] :
      ( ( c_0 != c_0 )
      | ( ( t_a @ tc_set )
       != c_0 )
      | ( ( c_0 @ tc_set )
       != tc_nat )
      | ( A != v_S )
      | ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(paramod_ordered,[status(thm)],[315,2270]) ).

thf(2400,plain,
    ! [A: $i] :
      ( ( ( t_a @ tc_set )
       != c_0 )
      | ( ( c_0 @ tc_set )
       != tc_nat )
      | ( A != v_S )
      | ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(pattern_uni,[status(thm)],[2399:[]]) ).

thf(2403,plain,
    ( ( ( t_a @ tc_set )
     != c_0 )
    | ( ( c_0 @ tc_set )
     != tc_nat )
    | ~ ( tc_IntDef_Oint @ ( v_S @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(simp,[status(thm)],[2400]) ).

thf(120,axiom,
    ! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_less ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OlessI_0) ).

thf(580,plain,
    ! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_less ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(6477,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_nat @ ( A @ c_Suc @ ( A @ c_less ) ) )
       != ( tc_nat @ ( C @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_less ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[580,460]) ).

thf(6478,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( A @ c_Suc @ ( A @ c_less ) ) )
     != ( tc_nat @ ( C @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_less ) ) ) ),
    inference(simp,[status(thm)],[6477]) ).

thf(6498,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat != tc_nat )
      | ( ( A @ c_Suc )
       != C )
      | ( A
       != ( tc_nat @ ( C @ ( B @ c_plus ) ) ) ) ),
    inference(simp,[status(thm)],[6478]) ).

thf(6502,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_Suc )
     != B ),
    inference(simp,[status(thm)],[6498]) ).

thf(10,axiom,
    ! [B: $i,A: $i] :
      ( A
      = ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oself__append__conv__iff2_0) ).

thf(325,plain,
    ! [B: $i,A: $i] :
      ( A
      = ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(8,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__self__conv__iff2_0) ).

thf(321,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(322,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) )
      = A ),
    inference(lifteq,[status(thm)],[321]) ).

thf(34,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != ( C @ ( B @ ( D @ c_append ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__same__eq__iff1_0) ).

thf(391,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != ( C @ ( B @ ( D @ c_append ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(392,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != ( C @ ( B @ ( D @ c_append ) ) ) ) ),
    inference(cnf,[status(esa)],[391]) ).

thf(393,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != ( C @ ( B @ ( D @ c_append ) ) ) ) ),
    inference(lifteq,[status(thm)],[392]) ).

thf(394,plain,
    ? [A: $i > $i > $i > $i] :
    ! [B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( B @ c_append ) ) @ ( D @ ( C @ A ) ) )
      = B ),
    inference(detectInverse,[status(thm)],[393]) ).

thf(395,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_append ) ) @ ( C @ ( B @ sk4 ) ) )
      = A ),
    inference(cnf,[status(esa)],[394]) ).

thf(8599,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_append ) ) @ ( C @ ( B @ sk4 ) ) )
      = A ),
    inference(lifteq,[status(thm)],[395]) ).

thf(8614,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) )
       != ( E @ ( D @ ( C @ c_append ) ) ) )
      | ( ( A @ ( E @ ( D @ sk4 ) ) )
        = C ) ),
    inference(paramod_ordered,[status(thm)],[322,8599]) ).

thf(8615,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( c_List_Olist_ONil @ sk4 ) ) )
      = A ),
    inference(pattern_uni,[status(thm)],[8614:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( c_List_Olist_ONil )),bind(E,$thf( B ))]]) ).

thf(7,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
       != ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Oinject__iff1_0) ).

thf(316,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
       != ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(2532,plain,
    ! [A: $i] :
      ( ( A != tc_nat )
      | ( c_0 @ ( c_Wellfounded__Relations_Oless__than @ c_Wellfounded__Recursion_Owf ) )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(paramod_ordered,[status(thm)],[350,645]) ).

thf(2533,plain,
    ( ( c_0 @ ( c_Wellfounded__Relations_Oless__than @ c_Wellfounded__Recursion_Owf ) )
    | ( tc_nat @ ( tc_nat @ ( c_0 @ c_less ) ) ) ),
    inference(pattern_uni,[status(thm)],[2532:[bind(A,$thf( tc_nat ))]]) ).

thf(3486,plain,
    ! [A: $i] :
      ( ( A
       != ( t_a @ tc_set ) )
      | ( c_UNIV != v_S )
      | ( c_0 != t_a )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(paramod_ordered,[status(thm)],[350,3443]) ).

thf(3487,plain,
    ( ( c_UNIV != v_S )
    | ( c_0 != t_a )
    | ( tc_nat @ ( t_a @ tc_set @ ( c_0 @ c_less ) ) ) ),
    inference(pattern_uni,[status(thm)],[3486:[bind(A,$thf( t_a @ tc_set ))]]) ).

thf(9,axiom,
    ! [A: $i] :
      ~ ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__less0__iff1_0) ).

thf(323,plain,
    ! [A: $i] :
      ~ ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(324,plain,
    ! [A: $i] :
      ~ ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ),
    inference(polarity_switch,[status(thm)],[323]) ).

thf(3558,plain,
    ! [A: $i] :
      ( ( ( tc_nat @ ( t_a @ tc_set @ ( c_0 @ c_less ) ) )
       != ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ) )
      | ~ $true
      | ( c_UNIV != v_S )
      | ( c_0 != t_a ) ),
    inference(paramod_ordered,[status(thm)],[3487,324]) ).

thf(3559,plain,
    ! [A: $i] :
      ( ( ( tc_nat @ ( t_a @ tc_set @ ( c_0 @ c_less ) ) )
       != ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ) )
      | ( c_UNIV != v_S )
      | ( c_0 != t_a ) ),
    inference(simp,[status(thm)],[3558]) ).

thf(3594,plain,
    ! [A: $i] :
      ( ( tc_nat != tc_nat )
      | ( ( t_a @ tc_set )
       != c_0 )
      | ( c_0 != A )
      | ( c_UNIV != v_S )
      | ( c_0 != t_a ) ),
    inference(simp,[status(thm)],[3559]) ).

thf(3598,plain,
    ( ( ( t_a @ tc_set )
     != c_0 )
    | ( c_UNIV != v_S )
    | ( c_0 != t_a ) ),
    inference(simp,[status(thm)],[3594]) ).

thf(4490,plain,
    ! [A: $i] :
      ( ( A
       != ( t_a @ tc_set ) )
      | ( c_0 != c_0 )
      | ( c_UNIV != v_S )
      | ( c_0 != t_a )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(paramod_ordered,[status(thm)],[355,3598]) ).

thf(4491,plain,
    ! [A: $i] :
      ( ( A
       != ( t_a @ tc_set ) )
      | ( c_UNIV != v_S )
      | ( c_0 != t_a )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(simp,[status(thm)],[4490]) ).

thf(4492,plain,
    ( ( c_UNIV != v_S )
    | ( c_0 != t_a )
    | ~ ( tc_nat @ ( c_0 @ ( t_a @ tc_set @ c_lessequals ) ) ) ),
    inference(pattern_uni,[status(thm)],[4491:[bind(A,$thf( t_a @ tc_set ))]]) ).

thf(132,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Oless__than__iff__iff2_0) ).

thf(606,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(169,axiom,
    ! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastLessThan_0) ).

thf(689,plain,
    ! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(5247,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ c_in ) ) )
       != ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[689,714]) ).

thf(5248,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ c_in ) ) )
     != ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
    inference(simp,[status(thm)],[5247]) ).

thf(5315,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ tc_set )
       != ( tc_nat @ tc_set ) )
      | ( c_Finite__Set_OFinites != c_Finite__Set_OFinites )
      | ( ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) )
       != c_UNIV ) ),
    inference(simp,[status(thm)],[5248]) ).

thf(5323,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) )
     != c_UNIV ),
    inference(simp,[status(thm)],[5315]) ).

thf(261,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ ( D @ c_in ) ) )
      | ~ ( C @ ( C @ ( B @ c_Inter ) @ ( D @ c_in ) ) )
      | ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInterD_0) ).

thf(881,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ ( D @ c_in ) ) )
      | ~ ( C @ ( C @ ( B @ c_Inter ) @ ( D @ c_in ) ) )
      | ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(44,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__self__conv2__iff2_0) ).

thf(415,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(416,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) )
      = A ),
    inference(lifteq,[status(thm)],[415]) ).

thf(282,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl_Or__into__trancl_0) ).

thf(924,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(217,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( C @ ( A @ c_inter ) ) @ c_in ) ) )
      | ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_0) ).

thf(789,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( C @ ( A @ c_inter ) ) @ c_in ) ) )
      | ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(127,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olenlex ) @ c_Wellfounded__Recursion_Owf ) )
      | ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Owf__lenlex_0) ).

thf(591,plain,
    ! [B: $i,A: $i] :
      ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olenlex ) @ c_Wellfounded__Recursion_Owf ) )
      | ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(147,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olistrel ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Nil2_0) ).

thf(646,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olistrel ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(79,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( C @ ( C @ tc_prod ) @ ( c_Relation_OId @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Opair__in__Id__conv__iff1_0) ).

thf(485,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( C @ ( C @ tc_prod ) @ ( c_Relation_OId @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(93,axiom,
    tc_IntDef_Oint @ class_Orderings_Oord,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_5) ).

thf(514,plain,
    tc_IntDef_Oint @ class_Orderings_Oord,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(2539,plain,
    ! [A: $i] :
      ( ( A != tc_nat )
      | ( c_0 @ class_Nat_Opower )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(paramod_ordered,[status(thm)],[350,468]) ).

thf(2540,plain,
    ( ( c_0 @ class_Nat_Opower )
    | ( tc_nat @ ( tc_nat @ ( c_0 @ c_less ) ) ) ),
    inference(pattern_uni,[status(thm)],[2539:[bind(A,$thf( tc_nat ))]]) ).

thf(225,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) )
      | ~ ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_union ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un__iff1_1) ).

thf(806,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) )
      | ~ ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_union ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(82,axiom,
    ! [B: $i,A: $i] : ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olists ) @ ( c_List_Olist_ONil @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olists_ONil_0) ).

thf(493,plain,
    ! [B: $i,A: $i] : ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olists ) @ ( c_List_Olist_ONil @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(9022,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olists ) @ ( c_List_Olist_ONil @ c_in ) ) )
       != ( D @ ( c_emptyset @ ( C @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[493,954]) ).

thf(9023,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olists ) @ ( c_List_Olist_ONil @ c_in ) ) )
     != ( D @ ( c_emptyset @ ( C @ c_in ) ) ) ),
    inference(simp,[status(thm)],[9022]) ).

thf(9056,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ tc_List_Olist )
       != D )
      | ( ( B @ ( A @ c_List_Olists ) )
       != c_emptyset )
      | ( c_List_Olist_ONil != C ) ),
    inference(simp,[status(thm)],[9023]) ).

thf(9071,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_List_Olists ) )
     != c_emptyset ),
    inference(simp,[status(thm)],[9056]) ).

thf(7923,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( tc_nat @ ( C @ ( B @ c_Suc @ c_plus ) ) ) )
      | ( c_0 != c_0 )
      | ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(paramod_ordered,[status(thm)],[315,7654]) ).

thf(7924,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( tc_nat @ ( C @ ( B @ c_Suc @ c_plus ) ) ) )
      | ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(simp,[status(thm)],[7923]) ).

thf(7925,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_IntDef_Oint @ ( tc_nat @ ( A @ ( B @ c_Suc @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
    inference(pattern_uni,[status(thm)],[7924:[bind(A,$thf( tc_nat @ ( E @ ( G @ c_Suc @ c_plus ) ) )),bind(B,$thf( G )),bind(C,$thf( E ))]]) ).

thf(7931,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_IntDef_Oint @ ( tc_nat @ ( A @ ( B @ c_Suc @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
    inference(simp,[status(thm)],[7925]) ).

thf(141,axiom,
    ! [A: $i] :
      ( ( A = c_0 )
      | ~ ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_less ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__Suc0__iff1_0) ).

thf(634,plain,
    ! [A: $i] :
      ( ( A = c_0 )
      | ~ ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_less ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(171,axiom,
    ! [B: $i,A: $i] : ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastLessThan__int_0) ).

thf(692,plain,
    ! [B: $i,A: $i] : ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(192,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ ( E @ c_Datatype__Universe_Ousum ) ) ) @ ( D @ ( C @ ( A @ c_Datatype__Universe_OIn1 ) ) @ c_in ) ) )
      | ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Ousum__In1I_0) ).

thf(734,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ ( E @ c_Datatype__Universe_Ousum ) ) ) @ ( D @ ( C @ ( A @ c_Datatype__Universe_OIn1 ) ) @ c_in ) ) )
      | ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(210,axiom,
    ! [A: $i] :
      ( ( A @ ( c_emptyset @ ( c_emptyset @ c_union ) ) )
      = c_emptyset ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty__iff2_0) ).

thf(774,plain,
    ! [A: $i] :
      ( ( A @ ( c_emptyset @ ( c_emptyset @ c_union ) ) )
      = c_emptyset ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(153,axiom,
    ! [A: $i] : ( A @ tc_set @ class_Orderings_Oord ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_1) ).

thf(660,plain,
    ! [A: $i] : ( A @ tc_set @ class_Orderings_Oord ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(42,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ tc_prod ) @ ( E @ ( D @ ( D @ ( B @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ ( E @ c_List_Olistrel ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Cons2_2) ).

thf(411,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ tc_prod ) @ ( E @ ( D @ ( D @ ( B @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ ( E @ c_List_Olistrel ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(289,axiom,
    ! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( c_emptyset @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__subsetI_0) ).

thf(940,plain,
    ! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( c_emptyset @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(2423,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ tc_set @ ( A @ ( c_emptyset @ c_lessequals ) ) )
       != ( t_a @ tc_set @ tc_set @ ( t_a @ tc_set @ ( c_emptyset @ ( C @ c_insert ) ) @ ( v_S @ c_lessequals ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[940,303]) ).

thf(2424,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ tc_set @ ( A @ ( c_emptyset @ c_lessequals ) ) )
     != ( t_a @ tc_set @ tc_set @ ( t_a @ tc_set @ ( c_emptyset @ ( C @ c_insert ) ) @ ( v_S @ c_lessequals ) ) ) ),
    inference(simp,[status(thm)],[2423]) ).

thf(2428,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ tc_set )
       != ( t_a @ tc_set @ tc_set ) )
      | ( A
       != ( t_a @ tc_set @ ( c_emptyset @ ( C @ c_insert ) ) ) )
      | ( c_emptyset != v_S ) ),
    inference(simp,[status(thm)],[2424]) ).

thf(2430,plain,
    ! [A: $i] :
      ( ( ( A @ tc_set )
       != ( t_a @ tc_set @ tc_set ) )
      | ( c_emptyset != v_S ) ),
    inference(simp,[status(thm)],[2428]) ).

thf(3206,plain,
    ! [A: $i] :
      ( ( A
       != ( t_a @ tc_set ) )
      | ( c_emptyset != v_S ) ),
    inference(simp,[status(thm)],[2430]) ).

thf(3226,plain,
    c_emptyset != v_S,
    inference(simp,[status(thm)],[3206]) ).

thf(178,axiom,
    ! [A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atMost_0) ).

thf(706,plain,
    ! [A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(1923,plain,
    ! [A: $i] :
      ( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_in ) ) )
       != ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[706,714]) ).

thf(1924,plain,
    ! [A: $i] :
      ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_in ) ) )
     != ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
    inference(simp,[status(thm)],[1923]) ).

thf(1952,plain,
    ! [A: $i] :
      ( ( ( tc_nat @ tc_set )
       != ( tc_nat @ tc_set ) )
      | ( c_Finite__Set_OFinites != c_Finite__Set_OFinites )
      | ( ( tc_nat @ ( A @ c_SetInterval_OatMost ) )
       != c_UNIV ) ),
    inference(simp,[status(thm)],[1924]) ).

thf(1975,plain,
    ! [A: $i] :
      ( ( tc_nat @ ( A @ c_SetInterval_OatMost ) )
     != c_UNIV ),
    inference(simp,[status(thm)],[1952]) ).

thf(35,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( E @ c_List_Olistrel ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ ( D @ ( E @ c_Main_Olistrel__Cons1__2 ) ) ) ) @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( E @ c_List_Olistrel ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Cons1_1) ).

thf(396,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( E @ c_List_Olistrel ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ ( D @ ( E @ c_Main_Olistrel__Cons1__2 ) ) ) ) @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( E @ c_List_Olistrel ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(397,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( E @ c_List_Olistrel ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ ( D @ ( E @ c_Main_Olistrel__Cons1__2 ) ) ) ) @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( E @ c_List_Olistrel ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(cnf,[status(esa)],[396]) ).

thf(168,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( D @ c_union ) ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnCI_0) ).

thf(687,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( D @ c_union ) ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(253,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__le__mono__iff2_0) ).

thf(866,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(7916,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( tc_nat @ ( C @ ( B @ c_Suc @ c_plus ) ) ) )
      | ( c_0 != c_0 )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(paramod_ordered,[status(thm)],[355,7654]) ).

thf(7917,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( tc_nat @ ( C @ ( B @ c_Suc @ c_plus ) ) ) )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(simp,[status(thm)],[7916]) ).

thf(7918,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( c_0 @ ( tc_nat @ ( A @ ( B @ c_Suc @ c_plus ) ) @ c_lessequals ) ) ),
    inference(pattern_uni,[status(thm)],[7917:[bind(A,$thf( tc_nat @ ( E @ ( G @ c_Suc @ c_plus ) ) )),bind(B,$thf( G )),bind(C,$thf( E ))]]) ).

thf(7936,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( c_0 @ ( tc_nat @ ( A @ ( B @ c_Suc @ c_plus ) ) @ c_lessequals ) ) ),
    inference(simp,[status(thm)],[7918]) ).

thf(5,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_prod ) @ ( E @ ( C @ ( C @ ( C @ ( B @ ( A @ ( D @ ( E @ c_Main_Olistrel__Cons1__1 ) ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( E @ c_List_Olistrel ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Cons1_2) ).

thf(311,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_prod ) @ ( E @ ( C @ ( C @ ( C @ ( B @ ( A @ ( D @ ( E @ c_Main_Olistrel__Cons1__1 ) ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( E @ c_List_Olistrel ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(312,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_prod ) @ ( E @ ( C @ ( C @ ( C @ ( B @ ( A @ ( D @ ( E @ c_Main_Olistrel__Cons1__1 ) ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( E @ c_List_Olistrel ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(cnf,[status(esa)],[311]) ).

thf(3491,plain,
    ! [A: $i] :
      ( ( A
       != ( t_a @ tc_set ) )
      | ( c_UNIV != v_S )
      | ( c_0 != t_a )
      | ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(paramod_ordered,[status(thm)],[315,3443]) ).

thf(3492,plain,
    ( ( c_UNIV != v_S )
    | ( c_0 != t_a )
    | ~ ( tc_IntDef_Oint @ ( t_a @ tc_set @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(pattern_uni,[status(thm)],[3491:[bind(A,$thf( t_a @ tc_set ))]]) ).

thf(3,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( D @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__2 ) ) ) ) @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__1 ) ) ) ) @ c_List_Olist_OCons ) ) ) )
      | ~ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ ( E @ c_List_Olistrel ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Cons2_0) ).

thf(305,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( D @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__2 ) ) ) ) @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__1 ) ) ) ) @ c_List_Olist_OCons ) ) ) )
      | ~ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ ( E @ c_List_Olistrel ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(306,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( D @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__2 ) ) ) ) @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__1 ) ) ) ) @ c_List_Olist_OCons ) ) ) )
      | ~ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ ( E @ c_List_Olistrel ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(cnf,[status(esa)],[305]) ).

thf(307,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ ( E @ c_List_Olistrel ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( ( D @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__2 ) ) ) ) @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__1 ) ) ) ) @ c_List_Olist_OCons ) ) )
        = A ) ),
    inference(lifteq,[status(thm)],[306]) ).

thf(280,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ tc_sum ) @ ( D @ ( C @ ( E @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( D @ ( C @ ( A @ c_Sum__Type_OInl ) ) @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInlI_0) ).

thf(920,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ tc_sum ) @ ( D @ ( C @ ( E @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( D @ ( C @ ( A @ c_Sum__Type_OInl ) ) @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(154,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ tc_set @ ( A @ c_uminus ) )
       != ( B @ tc_set @ ( C @ c_uminus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__eq__Compl__iff__iff1_0) ).

thf(661,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ tc_set @ ( A @ c_uminus ) )
       != ( B @ tc_set @ ( C @ c_uminus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(204,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( B @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__3 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Odprod ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_2) ).

thf(761,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( B @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__3 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Odprod ) ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(227,axiom,
    ! [A: $i] :
      ( c_emptyset
      = ( A @ ( c_List_Olist_ONil @ c_List_Oset ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__empty2__iff2_0) ).

thf(810,plain,
    ! [A: $i] :
      ( c_emptyset
      = ( A @ ( c_List_Olist_ONil @ c_List_Oset ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(30,axiom,
    ! [A: $i] :
      ( c_List_Olist_ONil
      = ( A @ ( c_List_Olist_ONil @ ( c_List_Olist_ONil @ c_append ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv__iff2_0) ).

thf(381,plain,
    ! [A: $i] :
      ( c_List_Olist_ONil
      = ( A @ ( c_List_Olist_ONil @ ( c_List_Olist_ONil @ c_append ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(24,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( c_0 @ c_less ) ) )
      | ( tc_nat @ ( B @ ( c_0 @ c_less ) ) )
      | ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0__iff1_0) ).

thf(366,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( c_0 @ c_less ) ) )
      | ( tc_nat @ ( B @ ( c_0 @ c_less ) ) )
      | ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(317,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
       != ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
    inference(cnf,[status(esa)],[316]) ).

thf(318,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
       != ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
    inference(lifteq,[status(thm)],[317]) ).

thf(319,plain,
    ? [A: $i > $i > $i > $i] :
    ! [B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( D @ ( C @ A ) ) )
      = B ),
    inference(detectInverse,[status(thm)],[318]) ).

thf(320,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( C @ ( B @ sk1 ) ) )
      = A ),
    inference(cnf,[status(esa)],[319]) ).

thf(1736,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( C @ ( B @ sk1 ) ) )
      = A ),
    inference(lifteq,[status(thm)],[320]) ).

thf(92,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ c_Wellfounded__Recursion_Owf ) )
      | ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Owf ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert__iff1_0) ).

thf(512,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ c_Wellfounded__Recursion_Owf ) )
      | ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Owf ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(56,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( C @ c_SetInterval_OlessThan ) @ ( B @ c_in ) ) )
      | ~ ( A @ ( C @ ( B @ c_less ) ) )
      | ~ ( A @ class_Orderings_Oord ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__iff__iff2_0) ).

thf(438,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( C @ c_SetInterval_OlessThan ) @ ( B @ c_in ) ) )
      | ~ ( A @ ( C @ ( B @ c_less ) ) )
      | ~ ( A @ class_Orderings_Oord ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(439,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( C @ c_SetInterval_OlessThan ) @ ( B @ c_in ) ) )
      | ~ ( A @ ( C @ ( B @ c_less ) ) )
      | ~ ( A @ class_Orderings_Oord ) ),
    inference(cnf,[status(esa)],[438]) ).

thf(77,axiom,
    tc_IntDef_Oint @ class_Nat_Opower,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_62) ).

thf(482,plain,
    tc_IntDef_Oint @ class_Nat_Opower,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(2909,plain,
    ! [A: $i] :
      ( ( A != tc_IntDef_Oint )
      | ( c_0 @ class_Nat_Opower )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(paramod_ordered,[status(thm)],[350,482]) ).

thf(2910,plain,
    ( ( c_0 @ class_Nat_Opower )
    | ( tc_nat @ ( tc_IntDef_Oint @ ( c_0 @ c_less ) ) ) ),
    inference(pattern_uni,[status(thm)],[2909:[bind(A,$thf( tc_IntDef_Oint ))]]) ).

thf(6716,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( tc_nat @ ( B @ c_Suc @ ( C @ c_plus ) ) ) )
      | ( c_0 != c_0 )
      | ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(paramod_ordered,[status(thm)],[315,6521]) ).

thf(6717,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( tc_nat @ ( B @ c_Suc @ ( C @ c_plus ) ) ) )
      | ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(simp,[status(thm)],[6716]) ).

thf(6718,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_IntDef_Oint @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
    inference(pattern_uni,[status(thm)],[6717:[bind(A,$thf( tc_nat @ ( G @ c_Suc @ ( D @ c_plus ) ) )),bind(B,$thf( G )),bind(C,$thf( D ))]]) ).

thf(6731,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_IntDef_Oint @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
    inference(simp,[status(thm)],[6718]) ).

thf(219,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( C @ ( A @ ( B @ c_Main_OdiagE__1 ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_Odiag ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OdiagE_1) ).

thf(793,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( C @ ( A @ ( B @ c_Main_OdiagE__1 ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_Odiag ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(275,axiom,
    ! [B: $i,A: $i] : ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastAtMost__int_0) ).

thf(910,plain,
    ! [B: $i,A: $i] : ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(55,axiom,
    tc_nat @ class_HOL_Ominus,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_9) ).

thf(437,plain,
    tc_nat @ class_HOL_Ominus,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(2968,plain,
    ! [A: $i] :
      ( ( A != tc_nat )
      | ( c_0 @ class_HOL_Ominus )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(paramod_ordered,[status(thm)],[350,437]) ).

thf(2969,plain,
    ( ( c_0 @ class_HOL_Ominus )
    | ( tc_nat @ ( tc_nat @ ( c_0 @ c_less ) ) ) ),
    inference(pattern_uni,[status(thm)],[2968:[bind(A,$thf( tc_nat ))]]) ).

thf(48,axiom,
    ! [B: $i,A: $i] :
      ( ( A = c_0 )
      | ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
       != c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0__iff1_0) ).

thf(422,plain,
    ! [B: $i,A: $i] :
      ( ( A = c_0 )
      | ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
       != c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(423,plain,
    ! [B: $i,A: $i] :
      ( ( A = c_0 )
      | ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
       != c_0 ) ),
    inference(cnf,[status(esa)],[422]) ).

thf(424,plain,
    ! [B: $i,A: $i] :
      ( ( A = c_0 )
      | ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
       != c_0 ) ),
    inference(lifteq,[status(thm)],[423]) ).

thf(298,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( B @ ( C @ ( B @ ( A @ c_Main_OInterI__1 ) ) @ c_in ) ) )
      | ( C @ ( C @ ( B @ c_Inter ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInterI_0) ).

thf(957,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( B @ ( C @ ( B @ ( A @ c_Main_OInterI__1 ) ) @ c_in ) ) )
      | ( C @ ( C @ ( B @ c_Inter ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(267,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( C @ ( D @ ( E @ ( A @ ( C @ c_Main_OPlusE__2 ) ) ) @ c_in ) ) )
      | ( D @ ( B @ ( E @ ( D @ ( A @ ( B @ c_Main_OPlusE__1 ) ) ) @ c_in ) ) )
      | ~ ( E @ ( D @ tc_sum ) @ ( E @ ( D @ ( C @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_3) ).

thf(894,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( C @ ( D @ ( E @ ( A @ ( C @ c_Main_OPlusE__2 ) ) ) @ c_in ) ) )
      | ( D @ ( B @ ( E @ ( D @ ( A @ ( B @ c_Main_OPlusE__1 ) ) ) @ c_in ) ) )
      | ~ ( E @ ( D @ tc_sum ) @ ( E @ ( D @ ( C @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(234,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( c_emptyset @ ( B @ c_insert ) ) )
        = ( C @ ( A @ ( B @ c_insert ) ) ) )
      | ~ ( C @ tc_set @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq__iff2_0) ).

thf(825,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( c_emptyset @ ( B @ c_insert ) ) )
        = ( C @ ( A @ ( B @ c_insert ) ) ) )
      | ~ ( C @ tc_set @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(7849,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_nat @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
       != ( tc_nat @ ( C @ ( c_0 @ c_less ) ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( D @ c_plus ) ) @ ( c_0 @ c_less ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[6722,387]) ).

thf(7850,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_nat @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
       != ( tc_nat @ ( C @ ( c_0 @ c_less ) ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( D @ c_plus ) ) @ ( c_0 @ c_less ) ) ) ),
    inference(simp,[status(thm)],[7849]) ).

thf(7851,plain,
    ! [C: $i,B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) ),
    inference(pattern_uni,[status(thm)],[7850:[bind(A,$thf( E )),bind(B,$thf( H )),bind(C,$thf( tc_nat @ ( H @ c_Suc @ ( E @ c_plus ) ) )),bind(D,$thf( D ))]]) ).

thf(7870,plain,
    ! [C: $i,B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) ),
    inference(simp,[status(thm)],[7851]) ).

thf(13333,plain,
    ! [A: $i] :
      ( ( A
       != ( t_a @ tc_set ) )
      | ( c_0 != c_0 )
      | ( c_UNIV != v_S )
      | ( c_0 != t_a )
      | ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(paramod_ordered,[status(thm)],[429,3598]) ).

thf(13334,plain,
    ! [A: $i] :
      ( ( A
       != ( t_a @ tc_set ) )
      | ( c_UNIV != v_S )
      | ( c_0 != t_a )
      | ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(simp,[status(thm)],[13333]) ).

thf(13335,plain,
    ( ( c_UNIV != v_S )
    | ( c_0 != t_a )
    | ~ ( tc_nat @ ( t_a @ tc_set @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(pattern_uni,[status(thm)],[13334:[bind(A,$thf( t_a @ tc_set ))]]) ).

thf(212,axiom,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertCI_1) ).

thf(778,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(172,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_emptyset )
      | ( ( C @ ( B @ ( A @ c_union ) ) )
       != c_emptyset ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty__iff1_1) ).

thf(693,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_emptyset )
      | ( ( C @ ( B @ ( A @ c_union ) ) )
       != c_emptyset ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(9190,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
       != ( tc_nat @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ ( D @ c_plus ) ) ) )
      | ( c_0 != c_0 )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(paramod_ordered,[status(thm)],[355,6802]) ).

thf(9191,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
       != ( tc_nat @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ ( D @ c_plus ) ) ) )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(simp,[status(thm)],[9190]) ).

thf(9192,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( tc_nat @ ( c_0 @ ( tc_nat @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ ( A @ c_plus ) ) @ c_lessequals ) ) ),
    inference(pattern_uni,[status(thm)],[9191:[bind(A,$thf( tc_nat @ ( tc_nat @ ( K @ c_Suc @ ( H @ c_plus ) ) @ ( E @ c_plus ) ) )),bind(B,$thf( H )),bind(C,$thf( K )),bind(D,$thf( E ))]]) ).

thf(9217,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( tc_nat @ ( c_0 @ ( tc_nat @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ ( A @ c_plus ) ) @ c_lessequals ) ) ),
    inference(simp,[status(thm)],[9192]) ).

thf(22,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
       != ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Oinject__iff1_1) ).

thf(359,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
       != ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(360,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
       != ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
    inference(cnf,[status(esa)],[359]) ).

thf(361,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
       != ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
    inference(lifteq,[status(thm)],[360]) ).

thf(260,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( C @ tc_set @ ( C @ ( B @ c_Pow ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OPow__iff__iff1_0) ).

thf(879,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( C @ tc_set @ ( C @ ( B @ c_Pow ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(11,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_List_Olist_ONil )
      | ( c_List_Olist_ONil
       != ( C @ ( B @ ( A @ c_append ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv__iff1_1) ).

thf(327,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_List_Olist_ONil )
      | ( c_List_Olist_ONil
       != ( C @ ( B @ ( A @ c_append ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(328,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_List_Olist_ONil )
      | ( c_List_Olist_ONil
       != ( C @ ( B @ ( A @ c_append ) ) ) ) ),
    inference(cnf,[status(esa)],[327]) ).

thf(329,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_List_Olist_ONil )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != c_List_Olist_ONil ) ),
    inference(lifteq,[status(thm)],[328]) ).

thf(265,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Oacyclic ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert__iff1_1) ).

thf(889,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Oacyclic ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(202,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__1 ) ) ) ) @ c_in ) ) )
      | ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ouprod ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_2) ).

thf(757,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__1 ) ) ) ) @ c_in ) ) )
      | ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ouprod ) ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(63,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( B @ c_SetInterval_OatLeast ) )
       != ( A @ ( C @ c_SetInterval_OatLeast ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__eq__iff__iff1_0) ).

thf(456,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( B @ c_SetInterval_OatLeast ) )
       != ( A @ ( C @ c_SetInterval_OatLeast ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(245,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = A )
      | ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
      | ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).

thf(847,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = A )
      | ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
      | ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(4278,plain,
    ! [A: $i] :
      ( ( A != c_Finite__Set_OFinites )
      | ( c_UNIV != c_0 )
      | ( c_0 != c_0 )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(paramod_ordered,[status(thm)],[355,2378]) ).

thf(4279,plain,
    ! [A: $i] :
      ( ( A != c_Finite__Set_OFinites )
      | ( c_UNIV != c_0 )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(simp,[status(thm)],[4278]) ).

thf(4280,plain,
    ( ( c_UNIV != c_0 )
    | ~ ( tc_nat @ ( c_0 @ ( c_Finite__Set_OFinites @ c_lessequals ) ) ) ),
    inference(pattern_uni,[status(thm)],[4279:[bind(A,$thf( c_Finite__Set_OFinites ))]]) ).

thf(123,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Oorder_0) ).

thf(583,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(2199,plain,
    ! [A: $i] :
      ( ( A != c_Finite__Set_OFinites )
      | ( c_0 != c_emptyset )
      | ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(paramod_ordered,[status(thm)],[315,2195]) ).

thf(2200,plain,
    ( ( c_0 != c_emptyset )
    | ~ ( tc_IntDef_Oint @ ( c_Finite__Set_OFinites @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(pattern_uni,[status(thm)],[2199:[bind(A,$thf( c_Finite__Set_OFinites ))]]) ).

thf(98,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Sum__Type_OInl ) ) )
     != ( B @ ( C @ ( D @ c_Sum__Type_OInr ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInl__not__Inr__iff1_0) ).

thf(522,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Sum__Type_OInl ) ) )
     != ( B @ ( C @ ( D @ c_Sum__Type_OInr ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(65,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( G @ tc_prod ) @ ( G @ ( D @ ( C @ ( H @ ( E @ c_Relation_Orel__comp ) ) ) ) @ ( D @ ( G @ ( B @ ( F @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( G @ tc_prod ) @ ( H @ ( C @ ( G @ ( A @ ( F @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Orel__compI_0) ).

thf(461,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( G @ tc_prod ) @ ( G @ ( D @ ( C @ ( H @ ( E @ c_Relation_Orel__comp ) ) ) ) @ ( D @ ( G @ ( B @ ( F @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( G @ tc_prod ) @ ( H @ ( C @ ( G @ ( A @ ( F @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(4484,plain,
    ! [A: $i] :
      ( ( c_0 != c_0 )
      | ( ( t_a @ tc_set @ tc_set )
       != tc_nat )
      | ( A != v_S )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(paramod_ordered,[status(thm)],[355,1689]) ).

thf(4485,plain,
    ! [A: $i] :
      ( ( ( t_a @ tc_set @ tc_set )
       != tc_nat )
      | ( A != v_S )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(pattern_uni,[status(thm)],[4484:[]]) ).

thf(4746,plain,
    ( ( ( t_a @ tc_set @ tc_set )
     != tc_nat )
    | ~ ( tc_nat @ ( c_0 @ ( v_S @ c_lessequals ) ) ) ),
    inference(simp,[status(thm)],[4485]) ).

thf(293,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OComplD__dest_0) ).

thf(948,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(136,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn0 ) ) )
       != ( C @ ( B @ ( D @ c_Datatype__Universe_OIn0 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn0__eq__iff1_0) ).

thf(615,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn0 ) ) )
       != ( C @ ( B @ ( D @ c_Datatype__Universe_OIn0 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(36,axiom,
    ! [A: $i] : ( tc_nat @ ( c_0 @ ( A @ c_Divides_Oop_Advd ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__0__right_0) ).

thf(398,plain,
    ! [A: $i] : ( tc_nat @ ( c_0 @ ( A @ c_Divides_Oop_Advd ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(11988,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( tc_nat @ ( C @ ( B @ c_plus ) ) ) )
      | ( ( c_0 @ c_Suc )
       != C )
      | ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(paramod_ordered,[status(thm)],[429,6502]) ).

thf(11989,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_0 @ c_Suc )
       != B )
      | ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(pattern_uni,[status(thm)],[11988:[bind(A,$thf( tc_nat @ ( E @ ( D @ c_plus ) ) )),bind(B,$thf( D )),bind(C,$thf( E ))]]) ).

thf(13932,plain,
    ! [A: $i] :
      ~ ( tc_nat @ ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
    inference(simp,[status(thm)],[11989]) ).

thf(14789,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ ( c_0 @ ( A @ c_Divides_Oop_Advd ) ) )
       != ( tc_nat @ ( tc_nat @ ( c_0 @ c_Suc @ ( B @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[398,13932]) ).

thf(14790,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( c_0 @ ( A @ c_Divides_Oop_Advd ) ) )
     != ( tc_nat @ ( tc_nat @ ( c_0 @ c_Suc @ ( B @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(simp,[status(thm)],[14789]) ).

thf(14840,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat != tc_nat )
      | ( ( tc_nat @ ( c_0 @ c_Suc @ ( B @ c_plus ) ) )
       != c_0 )
      | ( A != c_0 ) ),
    inference(simp,[status(thm)],[14790]) ).

thf(14866,plain,
    ! [A: $i] :
      ( ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_plus ) ) )
     != c_0 ),
    inference(simp,[status(thm)],[14840]) ).

thf(74,axiom,
    tc_IntDef_Oint @ class_Orderings_Olinorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_35) ).

thf(476,plain,
    tc_IntDef_Oint @ class_Orderings_Olinorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(2691,plain,
    ! [A: $i] :
      ( ( A != tc_IntDef_Oint )
      | ( c_0 @ class_Orderings_Olinorder )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(paramod_ordered,[status(thm)],[350,476]) ).

thf(2692,plain,
    ( ( c_0 @ class_Orderings_Olinorder )
    | ( tc_nat @ ( tc_IntDef_Oint @ ( c_0 @ c_less ) ) ) ),
    inference(pattern_uni,[status(thm)],[2691:[bind(A,$thf( tc_IntDef_Oint ))]]) ).

thf(33,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( c_List_Olist_ONil
       != ( C @ ( B @ ( A @ c_append ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv__iff1_0) ).

thf(388,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( c_List_Olist_ONil
       != ( C @ ( B @ ( A @ c_append ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(21,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( c_List_Olist_ONil
     != ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Odistinct__1__iff1_0) ).

thf(356,plain,
    ! [C: $i,B: $i,A: $i] :
      ( c_List_Olist_ONil
     != ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(128,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ c_SetInterval_OgreaterThan ) @ ( C @ c_in ) ) )
      | ~ ( A @ ( C @ ( B @ c_less ) ) )
      | ~ ( A @ class_Orderings_Oord ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__iff__iff2_0) ).

thf(593,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ c_SetInterval_OgreaterThan ) @ ( C @ c_in ) ) )
      | ~ ( A @ ( C @ ( B @ c_less ) ) )
      | ~ ( A @ class_Orderings_Oord ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(255,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( C @ ( c_emptyset @ ( D @ c_insert ) ) @ ( B @ c_lessequals ) ) )
      | ( ( C @ ( B @ ( A @ c_insert ) ) )
       != ( C @ ( c_emptyset @ ( D @ c_insert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H__iff1_1) ).

thf(869,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( C @ ( c_emptyset @ ( D @ c_insert ) ) @ ( B @ c_lessequals ) ) )
      | ( ( C @ ( B @ ( A @ c_insert ) ) )
       != ( C @ ( c_emptyset @ ( D @ c_insert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(134,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( B @ c_SetInterval_OatMost ) )
       != ( A @ ( C @ c_SetInterval_OatMost ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__eq__iff__iff1_0) ).

thf(610,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( B @ c_SetInterval_OatMost ) )
       != ( A @ ( C @ c_SetInterval_OatMost ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(47,axiom,
    ~ ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oneq0__conv__iff2_0) ).

thf(420,plain,
    ~ ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(85,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_3) ).

thf(499,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(196,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( B @ ( A @ c_in ) ) )
      | ~ ( D @ ( D @ ( C @ ( B @ c_inter ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OIntE_1) ).

thf(742,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( B @ ( A @ c_in ) ) )
      | ~ ( D @ ( D @ ( C @ ( B @ c_inter ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(119,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olex ) @ c_Wellfounded__Recursion_Owf ) )
      | ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Owf__lex_0) ).

thf(578,plain,
    ! [B: $i,A: $i] :
      ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olex ) @ c_Wellfounded__Recursion_Owf ) )
      | ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(257,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_set @ ( B @ ( D @ c_minus ) ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiffE_0) ).

thf(874,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_set @ ( B @ ( D @ c_minus ) ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(2155,plain,
    ! [A: $i] :
      ( ( A != tc_nat )
      | ( ( t_a @ tc_set @ tc_set )
       != c_0 )
      | ( c_0 != c_0 )
      | ( c_0 != v_S )
      | ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(paramod_ordered,[status(thm)],[315,2009]) ).

thf(2156,plain,
    ! [A: $i] :
      ( ( A != tc_nat )
      | ( ( t_a @ tc_set @ tc_set )
       != c_0 )
      | ( c_0 != v_S )
      | ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(simp,[status(thm)],[2155]) ).

thf(2157,plain,
    ( ( ( t_a @ tc_set @ tc_set )
     != c_0 )
    | ( c_0 != v_S )
    | ~ ( tc_IntDef_Oint @ ( tc_nat @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(pattern_uni,[status(thm)],[2156:[bind(A,$thf( tc_nat ))]]) ).

thf(80,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( D @ ( C @ ( E @ ( H @ c_Datatype__Universe_Odprod ) ) ) @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ ( G @ c_Datatype__Universe_OScons ) ) ) @ ( D @ ( C @ ( A @ ( F @ c_Datatype__Universe_OScons ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( H @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( G @ ( F @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodI_0) ).

thf(488,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( D @ ( C @ ( E @ ( H @ c_Datatype__Universe_Odprod ) ) ) @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ ( G @ c_Datatype__Universe_OScons ) ) ) @ ( D @ ( C @ ( A @ ( F @ c_Datatype__Universe_OScons ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( H @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( G @ ( F @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(15,axiom,
    ! [A: $i] : ( tc_nat @ ( A @ ( c_0 @ c_Suc @ c_Divides_Oop_Advd ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__1__left_0) ).

thf(339,plain,
    ! [A: $i] : ( tc_nat @ ( A @ ( c_0 @ c_Suc @ c_Divides_Oop_Advd ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(3620,plain,
    ! [A: $i] :
      ( ( c_0 != c_0 )
      | ( ( t_a @ tc_set )
       != c_0 )
      | ( c_UNIV != v_S )
      | ( A != t_a )
      | ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(paramod_ordered,[status(thm)],[315,3598]) ).

thf(3621,plain,
    ! [A: $i] :
      ( ( ( t_a @ tc_set )
       != c_0 )
      | ( c_UNIV != v_S )
      | ( A != t_a )
      | ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(pattern_uni,[status(thm)],[3620:[]]) ).

thf(3622,plain,
    ( ( ( t_a @ tc_set )
     != c_0 )
    | ( c_UNIV != v_S )
    | ~ ( tc_IntDef_Oint @ ( t_a @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(simp,[status(thm)],[3621]) ).

thf(200,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ~ ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OatLeast ) @ ( A @ ( B @ c_SetInterval_OatLeast ) @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__subset__iff__iff1_0) ).

thf(753,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ~ ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OatLeast ) @ ( A @ ( B @ c_SetInterval_OatLeast ) @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(14,axiom,
    ! [A: $i] :
      ( ( A @ c_Suc )
     != c_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__not__Zero__iff1_0) ).

thf(336,plain,
    ! [A: $i] :
      ( ( A @ c_Suc )
     != c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(337,plain,
    ! [A: $i] :
      ( ( A @ c_Suc )
     != c_0 ),
    inference(polarity_switch,[status(thm)],[336]) ).

thf(338,plain,
    ! [A: $i] :
      ( ( A @ c_Suc )
     != c_0 ),
    inference(lifteq,[status(thm)],[337]) ).

thf(1379,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( B @ c_Suc ) )
      | ( c_0 != c_0 )
      | ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(paramod_ordered,[status(thm)],[315,338]) ).

thf(1380,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( B @ c_Suc ) )
      | ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(simp,[status(thm)],[1379]) ).

thf(1381,plain,
    ! [A: $i] :
      ~ ( tc_IntDef_Oint @ ( A @ c_Suc @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
    inference(pattern_uni,[status(thm)],[1380:[bind(A,$thf( C @ c_Suc )),bind(B,$thf( C ))]]) ).

thf(1424,plain,
    ! [A: $i] :
      ~ ( tc_IntDef_Oint @ ( A @ c_Suc @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
    inference(simp,[status(thm)],[1381]) ).

thf(100,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_less ) ) )
      | ~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Oless__than__iff__iff1_0) ).

thf(526,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_less ) ) )
      | ~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(142,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( A @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_append ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv__iff1_0) ).

thf(637,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( A @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_append ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(4411,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( B @ c_Suc ) )
      | ( c_0 != c_0 )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(paramod_ordered,[status(thm)],[355,338]) ).

thf(4412,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( B @ c_Suc ) )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(simp,[status(thm)],[4411]) ).

thf(4413,plain,
    ! [A: $i] :
      ~ ( tc_nat @ ( c_0 @ ( A @ c_Suc @ c_lessequals ) ) ),
    inference(pattern_uni,[status(thm)],[4412:[bind(A,$thf( C @ c_Suc )),bind(B,$thf( C ))]]) ).

thf(4721,plain,
    ! [A: $i] :
      ~ ( tc_nat @ ( c_0 @ ( A @ c_Suc @ c_lessequals ) ) ),
    inference(simp,[status(thm)],[4413]) ).

thf(104,axiom,
    tc_Product__Type_Ounit @ class_Finite__Set_Ofinite,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Product____Type__Ounit_0) ).

thf(537,plain,
    tc_Product__Type_Ounit @ class_Finite__Set_Ofinite,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(2440,plain,
    ! [A: $i] :
      ( ( ( tc_IntDef_Oint @ ( c_0 @ ( A @ c_Divides_Oop_Advd ) ) )
       != ( tc_IntDef_Oint @ ( c_Finite__Set_OFinites @ ( c_0 @ c_Divides_Oop_Advd ) ) ) )
      | ( c_0 != c_emptyset )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[407,2200]) ).

thf(2441,plain,
    ! [A: $i] :
      ( ( ( tc_IntDef_Oint @ ( c_0 @ ( A @ c_Divides_Oop_Advd ) ) )
       != ( tc_IntDef_Oint @ ( c_Finite__Set_OFinites @ ( c_0 @ c_Divides_Oop_Advd ) ) ) )
      | ( c_0 != c_emptyset ) ),
    inference(simp,[status(thm)],[2440]) ).

thf(2458,plain,
    ! [A: $i] :
      ( ( tc_IntDef_Oint != tc_IntDef_Oint )
      | ( c_Finite__Set_OFinites != c_0 )
      | ( A != c_0 )
      | ( c_0 != c_emptyset ) ),
    inference(simp,[status(thm)],[2441]) ).

thf(2462,plain,
    ( ( c_Finite__Set_OFinites != c_0 )
    | ( c_0 != c_emptyset ) ),
    inference(simp,[status(thm)],[2458]) ).

thf(2470,plain,
    ! [A: $i] :
      ( ( c_0 != c_0 )
      | ( c_Finite__Set_OFinites != c_0 )
      | ( A != c_emptyset )
      | ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(paramod_ordered,[status(thm)],[315,2462]) ).

thf(2471,plain,
    ! [A: $i] :
      ( ( c_Finite__Set_OFinites != c_0 )
      | ( A != c_emptyset )
      | ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(pattern_uni,[status(thm)],[2470:[]]) ).

thf(2472,plain,
    ( ( c_Finite__Set_OFinites != c_0 )
    | ~ ( tc_IntDef_Oint @ ( c_emptyset @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(simp,[status(thm)],[2471]) ).

thf(164,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( C @ ( B @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).

thf(679,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( C @ ( B @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(94,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ class_Finite__Set_Ofinite )
      | ~ ( B @ class_Finite__Set_Ofinite )
      | ( B @ ( A @ tc_sum ) @ class_Finite__Set_Ofinite ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_sum_0) ).

thf(515,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ class_Finite__Set_Ofinite )
      | ~ ( B @ class_Finite__Set_Ofinite )
      | ( B @ ( A @ tc_sum ) @ class_Finite__Set_Ofinite ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(276,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ c_SetInterval_OatLeast ) @ ( C @ c_in ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oord ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__iff__iff2_0) ).

thf(911,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ c_SetInterval_OatLeast ) @ ( C @ c_in ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oord ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(186,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ tc_set @ ( C @ ( B @ ( D @ c_insert ) ) @ ( A @ c_minus ) ) @ c_in ) ) )
      | ~ ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ tc_set @ ( B @ ( A @ c_minus ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff__insert__iff2_0) ).

thf(721,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ tc_set @ ( C @ ( B @ ( D @ c_insert ) ) @ ( A @ c_minus ) ) @ c_in ) ) )
      | ~ ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ tc_set @ ( B @ ( A @ c_minus ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(6260,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) @ c_in ) ) )
       != ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[962,714]) ).

thf(6261,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) @ c_in ) ) )
     != ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
    inference(simp,[status(thm)],[6260]) ).

thf(6326,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ tc_set )
       != ( tc_nat @ tc_set ) )
      | ( c_Finite__Set_OFinites != c_Finite__Set_OFinites )
      | ( ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) )
       != c_UNIV ) ),
    inference(simp,[status(thm)],[6261]) ).

thf(6346,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) )
     != c_UNIV ),
    inference(simp,[status(thm)],[6326]) ).

thf(115,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( D @ ( E @ ( D @ ( E @ ( A @ ( C @ c_Main_OPlusE__2 ) ) ) @ c_Sum__Type_OInr ) ) ) )
      | ( A
        = ( E @ ( D @ ( E @ ( D @ ( A @ ( B @ c_Main_OPlusE__1 ) ) ) @ c_Sum__Type_OInl ) ) ) )
      | ~ ( E @ ( D @ tc_sum ) @ ( E @ ( D @ ( C @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_0) ).

thf(569,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( D @ ( E @ ( D @ ( E @ ( A @ ( C @ c_Main_OPlusE__2 ) ) ) @ c_Sum__Type_OInr ) ) ) )
      | ( A
        = ( E @ ( D @ ( E @ ( D @ ( A @ ( B @ c_Main_OPlusE__1 ) ) ) @ c_Sum__Type_OInl ) ) ) )
      | ~ ( E @ ( D @ tc_sum ) @ ( E @ ( D @ ( C @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(1713,plain,
    ! [A: $i] :
      ( ( c_0 != c_0 )
      | ( ( t_a @ tc_set @ tc_set )
       != tc_nat )
      | ( A != v_S )
      | ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(paramod_ordered,[status(thm)],[315,1689]) ).

thf(1714,plain,
    ! [A: $i] :
      ( ( ( t_a @ tc_set @ tc_set )
       != tc_nat )
      | ( A != v_S )
      | ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(pattern_uni,[status(thm)],[1713:[]]) ).

thf(1715,plain,
    ( ( ( t_a @ tc_set @ tc_set )
     != tc_nat )
    | ~ ( tc_IntDef_Oint @ ( v_S @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(simp,[status(thm)],[1714]) ).

thf(213,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( C @ c_SetInterval_OatMost ) @ ( B @ c_in ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oord ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__iff__iff2_0) ).

thf(779,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( C @ c_SetInterval_OatMost ) @ ( B @ c_in ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oord ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(26,axiom,
    tc_nat @ ( c_0 @ ( c_0 @ c_lessequals ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq__iff2_0) ).

thf(371,plain,
    tc_nat @ ( c_0 @ ( c_0 @ c_lessequals ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(131,axiom,
    ! [B: $i,A: $i] : ( B @ ( A @ tc_fun ) @ class_Nat_Opower ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun_1) ).

thf(605,plain,
    ! [B: $i,A: $i] : ( B @ ( A @ tc_fun ) @ class_Nat_Opower ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(2368,plain,
    ! [A: $i] :
      ( ( A != c_Finite__Set_OFinites )
      | ( c_0 != c_0 )
      | ~ ( tc_IntDef_Oint @ ( c_UNIV @ ( c_0 @ c_Divides_Oop_Advd ) ) )
      | ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(paramod_ordered,[status(thm)],[315,2088]) ).

thf(2369,plain,
    ! [A: $i] :
      ( ( A != c_Finite__Set_OFinites )
      | ~ ( tc_IntDef_Oint @ ( c_UNIV @ ( c_0 @ c_Divides_Oop_Advd ) ) )
      | ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(simp,[status(thm)],[2368]) ).

thf(2370,plain,
    ( ~ ( tc_IntDef_Oint @ ( c_UNIV @ ( c_0 @ c_Divides_Oop_Advd ) ) )
    | ~ ( tc_IntDef_Oint @ ( c_Finite__Set_OFinites @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(pattern_uni,[status(thm)],[2369:[bind(A,$thf( c_Finite__Set_OFinites ))]]) ).

thf(138,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_Sum__Type_OInl ) ) )
       != ( C @ ( B @ ( D @ c_Sum__Type_OInl ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInl__eq__iff1_0) ).

thf(622,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_Sum__Type_OInl ) ) )
       != ( C @ ( B @ ( D @ c_Sum__Type_OInl ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(240,axiom,
    ! [B: $i,A: $i] : ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanLessThan__int_0) ).

thf(837,plain,
    ! [B: $i,A: $i] : ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(17,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != ( C @ ( D @ ( A @ c_append ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Osame__append__eq__iff1_0) ).

thf(343,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != ( C @ ( D @ ( A @ c_append ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(218,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( c_emptyset @ c_Equiv__Relations_Oquotient ) ) )
      = c_emptyset ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Equiv__Relations_Oquotient__is__empty__iff2_0) ).

thf(791,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( c_emptyset @ c_Equiv__Relations_Oquotient ) ) )
      = c_emptyset ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(792,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( c_emptyset @ c_Equiv__Relations_Oquotient ) ) )
      = c_emptyset ),
    inference(lifteq,[status(thm)],[791]) ).

thf(288,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ c_Inter ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( C @ ( B @ ( A @ c_Main_OInterI__1 ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInterI_1) ).

thf(938,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ c_Inter ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( C @ ( B @ ( A @ c_Main_OInterI__1 ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(89,axiom,
    tc_nat @ class_Orderings_Oord,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_2) ).

thf(508,plain,
    tc_nat @ class_Orderings_Oord,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(9646,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
       != ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[928,714]) ).

thf(9647,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
     != ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
    inference(simp,[status(thm)],[9646]) ).

thf(9697,plain,
    ! [B: $i,A: $i] :
      ( ( B
       != ( tc_nat @ tc_set ) )
      | ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
       != c_Finite__Set_OFinites )
      | ( A != c_UNIV ) ),
    inference(simp,[status(thm)],[9647]) ).

thf(9716,plain,
    ( ( tc_nat @ tc_set @ ( c_emptyset @ ( c_UNIV @ c_insert ) ) )
   != c_Finite__Set_OFinites ),
    inference(simp,[status(thm)],[9697]) ).

thf(152,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( E @ ( D @ ( E @ ( D @ ( A @ ( B @ c_Main_OusumE__1 ) ) ) @ c_Datatype__Universe_OIn0 ) ) ) )
      | ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( C @ ( E @ ( D @ ( A @ ( C @ c_Main_OusumE__2 ) ) ) @ c_in ) ) )
      | ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ousum ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OusumE_1) ).

thf(657,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( E @ ( D @ ( E @ ( D @ ( A @ ( B @ c_Main_OusumE__1 ) ) ) @ c_Datatype__Universe_OIn0 ) ) ) )
      | ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( C @ ( E @ ( D @ ( A @ ( C @ c_Main_OusumE__2 ) ) ) @ c_in ) ) )
      | ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ousum ) ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(111,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( B @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_append ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv__iff1_1) ).

thf(558,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( B @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_append ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(2913,plain,
    ! [A: $i] :
      ( ( A != tc_nat )
      | ( ( t_a @ tc_set @ tc_set )
       != c_0 )
      | ( c_0 != c_0 )
      | ( c_0 != v_S )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(paramod_ordered,[status(thm)],[350,2009]) ).

thf(2914,plain,
    ! [A: $i] :
      ( ( A != tc_nat )
      | ( ( t_a @ tc_set @ tc_set )
       != c_0 )
      | ( c_0 != v_S )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(simp,[status(thm)],[2913]) ).

thf(2915,plain,
    ( ( ( t_a @ tc_set @ tc_set )
     != c_0 )
    | ( c_0 != v_S )
    | ( tc_nat @ ( tc_nat @ ( c_0 @ c_less ) ) ) ),
    inference(pattern_uni,[status(thm)],[2914:[bind(A,$thf( tc_nat ))]]) ).

thf(102,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( C @ ( A @ ( D @ c_append ) ) @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( D @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv__iff2_0) ).

thf(530,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( C @ ( A @ ( D @ c_append ) ) @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( D @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(125,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn0 ) ) )
     != ( C @ ( B @ ( D @ c_Datatype__Universe_OIn1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn0__not__In1__iff1_0) ).

thf(586,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn0 ) ) )
     != ( C @ ( B @ ( D @ c_Datatype__Universe_OIn1 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(283,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( E @ ( B @ c_Datatype__Universe_Ousum ) ) ) @ ( D @ ( C @ ( A @ c_Datatype__Universe_OIn0 ) ) @ c_in ) ) )
      | ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Ousum__In0I_0) ).

thf(926,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( E @ ( B @ c_Datatype__Universe_Ousum ) ) ) @ ( D @ ( C @ ( A @ c_Datatype__Universe_OIn0 ) ) @ c_in ) ) )
      | ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(344,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != ( C @ ( D @ ( A @ c_append ) ) ) ) ),
    inference(cnf,[status(esa)],[343]) ).

thf(345,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != ( C @ ( D @ ( A @ c_append ) ) ) ) ),
    inference(lifteq,[status(thm)],[344]) ).

thf(346,plain,
    ? [A: $i > $i > $i > $i] :
    ! [B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( B @ c_append ) ) @ ( D @ ( B @ A ) ) )
      = C ),
    inference(detectInverse,[status(thm)],[345]) ).

thf(347,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_append ) ) @ ( C @ ( A @ sk2 ) ) )
      = B ),
    inference(cnf,[status(esa)],[346]) ).

thf(3624,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_append ) ) @ ( C @ ( A @ sk2 ) ) )
      = B ),
    inference(lifteq,[status(thm)],[347]) ).

thf(4624,plain,
    ! [A: $i] :
      ( ( A != c_UNIV )
      | ( c_0 != v_S )
      | ( ( t_a @ tc_set )
       != t_a )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(paramod_ordered,[status(thm)],[355,3443]) ).

thf(4625,plain,
    ( ( c_0 != v_S )
    | ( ( t_a @ tc_set )
     != t_a )
    | ~ ( tc_nat @ ( c_0 @ ( c_UNIV @ c_lessequals ) ) ) ),
    inference(pattern_uni,[status(thm)],[4624:[bind(A,$thf( c_UNIV ))]]) ).

thf(206,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OlessThan ) @ ( A @ ( B @ c_SetInterval_OlessThan ) @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__subset__iff__iff1_0) ).

thf(765,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OlessThan ) @ ( A @ ( B @ c_SetInterval_OlessThan ) @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(109,axiom,
    tc_nat @ ( c_0 @ c_Suc @ ( c_0 @ c_less ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__Suc0__iff2_0) ).

thf(552,plain,
    tc_nat @ ( c_0 @ c_Suc @ ( c_0 @ c_less ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(1051,plain,
    ! [A: $i] :
      ( ( ( tc_nat @ ( c_0 @ c_Suc @ ( c_0 @ c_less ) ) )
       != ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[552,324]) ).

thf(1052,plain,
    ! [A: $i] :
      ( ( tc_nat @ ( c_0 @ c_Suc @ ( c_0 @ c_less ) ) )
     != ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ) ),
    inference(simp,[status(thm)],[1051]) ).

thf(1053,plain,
    ! [A: $i] :
      ( ( tc_nat != tc_nat )
      | ( ( c_0 @ c_Suc )
       != c_0 )
      | ( c_0 != A ) ),
    inference(simp,[status(thm)],[1052]) ).

thf(1054,plain,
    ( ( c_0 @ c_Suc )
   != c_0 ),
    inference(simp,[status(thm)],[1053]) ).

thf(273,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ ( C @ c_inter ) ) @ c_in ) ) )
      | ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_1) ).

thf(906,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ ( C @ c_inter ) ) @ c_in ) ) )
      | ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(199,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( E @ ( F @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__3 ) ) ) ) ) @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__1 ) ) ) ) ) @ c_Pair ) ) ) ) )
      | ~ ( E @ ( F @ tc_prod ) @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Orel__compE_2) ).

thf(750,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( E @ ( F @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__3 ) ) ) ) ) @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__1 ) ) ) ) ) @ c_Pair ) ) ) ) )
      | ~ ( E @ ( F @ tc_prod ) @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(52,axiom,
    ! [B: $i,A: $i] :
      ( A
      = ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oself__append__conv2__iff2_0) ).

thf(430,plain,
    ! [B: $i,A: $i] :
      ( A
      = ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(233,axiom,
    ! [A: $i] : ( A @ tc_set @ class_HOL_Ominus ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_0) ).

thf(824,plain,
    ! [A: $i] : ( A @ tc_set @ class_HOL_Ominus ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(4016,plain,
    ! [A: $i] :
      ( ( A != c_UNIV )
      | ( c_0 != c_emptyset )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(paramod_ordered,[status(thm)],[355,821]) ).

thf(4017,plain,
    ( ( c_0 != c_emptyset )
    | ~ ( tc_nat @ ( c_0 @ ( c_UNIV @ c_lessequals ) ) ) ),
    inference(pattern_uni,[status(thm)],[4016:[bind(A,$thf( c_UNIV ))]]) ).

thf(2728,plain,
    ! [A: $i] :
      ( ( A != tc_nat )
      | ( c_0 @ class_Orderings_Oord )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(paramod_ordered,[status(thm)],[350,508]) ).

thf(2729,plain,
    ( ( c_0 @ class_Orderings_Oord )
    | ( tc_nat @ ( tc_nat @ ( c_0 @ c_less ) ) ) ),
    inference(pattern_uni,[status(thm)],[2728:[bind(A,$thf( tc_nat ))]]) ).

thf(412,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ tc_prod ) @ ( E @ ( D @ ( D @ ( B @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ ( E @ c_List_Olistrel ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(cnf,[status(esa)],[411]) ).

thf(11836,plain,
    ! [A: $i] :
      ( ( A != c_Finite__Set_OFinites )
      | ( c_0 != c_emptyset )
      | ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(paramod_ordered,[status(thm)],[429,2195]) ).

thf(11837,plain,
    ( ( c_0 != c_emptyset )
    | ~ ( tc_nat @ ( c_Finite__Set_OFinites @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(pattern_uni,[status(thm)],[11836:[bind(A,$thf( c_Finite__Set_OFinites ))]]) ).

thf(49,axiom,
    tc_nat @ ( c_0 @ ( c_0 @ c_Divides_Oop_Advd ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__0__left__iff__iff2_0) ).

thf(425,plain,
    tc_nat @ ( c_0 @ ( c_0 @ c_Divides_Oop_Advd ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(235,axiom,
    ! [A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OlessThan ) @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__lessThan_0) ).

thf(828,plain,
    ! [A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OlessThan ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(2097,plain,
    ! [A: $i] :
      ( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OlessThan ) @ c_in ) ) )
       != ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[828,714]) ).

thf(2098,plain,
    ! [A: $i] :
      ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OlessThan ) @ c_in ) ) )
     != ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
    inference(simp,[status(thm)],[2097]) ).

thf(2131,plain,
    ! [A: $i] :
      ( ( ( tc_nat @ tc_set )
       != ( tc_nat @ tc_set ) )
      | ( c_Finite__Set_OFinites != c_Finite__Set_OFinites )
      | ( ( tc_nat @ ( A @ c_SetInterval_OlessThan ) )
       != c_UNIV ) ),
    inference(simp,[status(thm)],[2098]) ).

thf(2149,plain,
    ! [A: $i] :
      ( ( tc_nat @ ( A @ c_SetInterval_OlessThan ) )
     != c_UNIV ),
    inference(simp,[status(thm)],[2131]) ).

thf(28,axiom,
    ! [B: $i,A: $i] :
      ( ( B = c_0 )
      | ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
       != c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0__iff1_1) ).

thf(375,plain,
    ! [B: $i,A: $i] :
      ( ( B = c_0 )
      | ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
       != c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(191,axiom,
    ! [A: $i] : ( A @ ( c_emptyset @ c_Wellfounded__Recursion_Owf ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__empty_0) ).

thf(733,plain,
    ! [A: $i] : ( A @ ( c_emptyset @ c_Wellfounded__Recursion_Owf ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(3635,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) )
       != ( E @ ( D @ ( C @ c_append ) ) ) )
      | ( ( A @ ( E @ ( C @ sk2 ) ) )
        = D ) ),
    inference(paramod_ordered,[status(thm)],[322,3624]) ).

thf(3636,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ sk2 ) ) )
      = c_List_Olist_ONil ),
    inference(pattern_uni,[status(thm)],[3635:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( c_List_Olist_ONil )),bind(E,$thf( B ))]]) ).

thf(4281,plain,
    ! [A: $i] :
      ( ( A != c_UNIV )
      | ( c_0 != c_0 )
      | ( c_Finite__Set_OFinites != c_0 )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(paramod_ordered,[status(thm)],[355,2378]) ).

thf(4282,plain,
    ! [A: $i] :
      ( ( A != c_UNIV )
      | ( c_Finite__Set_OFinites != c_0 )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(simp,[status(thm)],[4281]) ).

thf(4283,plain,
    ( ( c_Finite__Set_OFinites != c_0 )
    | ~ ( tc_nat @ ( c_0 @ ( c_UNIV @ c_lessequals ) ) ) ),
    inference(pattern_uni,[status(thm)],[4282:[bind(A,$thf( c_UNIV ))]]) ).

thf(243,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( C @ tc_set @ ( B @ ( A @ c_less ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OpsubsetE_1) ).

thf(843,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( C @ tc_set @ ( B @ ( A @ c_less ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(181,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( A @ c_List_Olists ) @ ( B @ c_in ) ) )
      | ~ ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_Oin__listsI__1 ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oin__listsI_1) ).

thf(711,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( A @ c_List_Olists ) @ ( B @ c_in ) ) )
      | ~ ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_Oin__listsI__1 ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(107,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = F )
      | ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
       != ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq__iff1_1) ).

thf(545,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = F )
      | ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
       != ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(43,axiom,
    ! [A: $i] :
      ( ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Nat_Osize ) )
      = c_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__0__conv__iff2_0) ).

thf(413,plain,
    ! [A: $i] :
      ( ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Nat_Osize ) )
      = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(113,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_less ) ) )
      | ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__less__eq__iff2_0) ).

thf(562,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_less ) ) )
      | ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(272,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( D @ c_Union ) @ ( A @ c_in ) ) )
      | ~ ( C @ tc_set @ ( D @ ( B @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnionI_0) ).

thf(904,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( D @ c_Union ) @ ( A @ c_in ) ) )
      | ~ ( C @ tc_set @ ( D @ ( B @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(9245,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
       != ( tc_nat @ ( D @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ c_plus ) ) ) )
      | ( c_0 != c_0 )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(paramod_ordered,[status(thm)],[355,7665]) ).

thf(9246,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
       != ( tc_nat @ ( D @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ c_plus ) ) ) )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(simp,[status(thm)],[9245]) ).

thf(9247,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( tc_nat @ ( c_0 @ ( tc_nat @ ( A @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ c_plus ) ) @ c_lessequals ) ) ),
    inference(pattern_uni,[status(thm)],[9246:[bind(A,$thf( tc_nat @ ( F @ ( tc_nat @ ( K @ c_Suc @ ( H @ c_plus ) ) @ c_plus ) ) )),bind(B,$thf( H )),bind(C,$thf( K )),bind(D,$thf( F ))]]) ).

thf(9285,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( tc_nat @ ( c_0 @ ( tc_nat @ ( A @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ c_plus ) ) @ c_lessequals ) ) ),
    inference(simp,[status(thm)],[9247]) ).

thf(116,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( B @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_OlistsE_0) ).

thf(572,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( B @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(334,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_List_Olist_ONil )
      | ( A
       != ( C @ ( A @ ( B @ c_append ) ) ) ) ),
    inference(cnf,[status(esa)],[333]) ).

thf(335,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_List_Olist_ONil )
      | ( ( C @ ( A @ ( B @ c_append ) ) )
       != A ) ),
    inference(lifteq,[status(thm)],[334]) ).

thf(2164,plain,
    ! [A: $i] :
      ( ( c_0 != c_0 )
      | ( ( t_a @ tc_set @ tc_set )
       != c_0 )
      | ( tc_nat != c_0 )
      | ( A != v_S )
      | ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(paramod_ordered,[status(thm)],[315,2009]) ).

thf(2165,plain,
    ! [A: $i] :
      ( ( ( t_a @ tc_set @ tc_set )
       != c_0 )
      | ( tc_nat != c_0 )
      | ( A != v_S )
      | ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(pattern_uni,[status(thm)],[2164:[]]) ).

thf(2166,plain,
    ( ( ( t_a @ tc_set @ tc_set )
     != c_0 )
    | ( tc_nat != c_0 )
    | ~ ( tc_IntDef_Oint @ ( v_S @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(simp,[status(thm)],[2165]) ).

thf(224,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) )
      | ~ ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Pow ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff__iff1_0) ).

thf(804,plain,
    ! [B: $i,A: $i] :
      ( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) )
      | ~ ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Pow ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(177,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( B @ ( A @ c_in ) ) )
      | ~ ( D @ ( D @ tc_set @ ( C @ ( B @ c_minus ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiffE_1) ).

thf(704,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( B @ ( A @ c_in ) ) )
      | ~ ( D @ ( D @ tc_set @ ( C @ ( B @ c_minus ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(144,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ c_Wellfounded__Recursion_Oacyclic ) )
      | ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Oacyclic ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert__iff1_0) ).

thf(641,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ c_Wellfounded__Recursion_Oacyclic ) )
      | ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Oacyclic ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(8600,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) )
       != ( E @ ( D @ ( C @ c_append ) ) ) )
      | ( ( A @ ( E @ ( D @ sk4 ) ) )
        = C ) ),
    inference(paramod_ordered,[status(thm)],[416,8599]) ).

thf(8601,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ sk4 ) ) )
      = c_List_Olist_ONil ),
    inference(pattern_uni,[status(thm)],[8600:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( c_List_Olist_ONil )),bind(D,$thf( A )),bind(E,$thf( B ))]]) ).

thf(68,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_less ) ) )
      | ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_less ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__less__eq__iff1_0) ).

thf(466,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_less ) ) )
      | ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_less ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(973,plain,
    ! [A: $i] :
      ( ~ $true
      | ( ( t_a @ tc_set @ ( v_S @ ( t_a @ tc_set @ ( c_emptyset @ ( A @ c_insert ) ) @ c_in ) ) )
       != ( t_a @ tc_set @ ( v_S @ ( v_S @ c_in ) ) ) )
      | ( ( t_a @ tc_set @ tc_set )
       != ( t_a @ tc_set ) )
      | ~ ( t_a @ tc_set @ ( v_S @ ( v_S @ c_in ) ) ) ),
    inference(eqfactor_ordered,[status(thm)],[968]) ).

thf(977,plain,
    ! [A: $i] :
      ( ( ( t_a @ tc_set )
       != ( t_a @ tc_set ) )
      | ( v_S != v_S )
      | ( ( t_a @ tc_set @ ( c_emptyset @ ( A @ c_insert ) ) )
       != v_S )
      | ( ( t_a @ tc_set )
       != t_a )
      | ~ ( t_a @ tc_set @ ( v_S @ ( v_S @ c_in ) ) ) ),
    inference(simp,[status(thm)],[973]) ).

thf(979,plain,
    ! [A: $i] :
      ( ( ( t_a @ tc_set @ ( c_emptyset @ ( A @ c_insert ) ) )
       != v_S )
      | ( ( t_a @ tc_set )
       != t_a )
      | ~ ( t_a @ tc_set @ ( v_S @ ( v_S @ c_in ) ) ) ),
    inference(simp,[status(thm)],[977]) ).

thf(39,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ class_Finite__Set_Ofinite )
      | ~ ( B @ class_Finite__Set_Ofinite )
      | ( B @ ( A @ tc_fun ) @ class_Finite__Set_Ofinite ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun_0) ).

thf(405,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ class_Finite__Set_Ofinite )
      | ~ ( B @ class_Finite__Set_Ofinite )
      | ( B @ ( A @ tc_fun ) @ class_Finite__Set_Ofinite ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(406,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ class_Finite__Set_Ofinite )
      | ~ ( B @ class_Finite__Set_Ofinite )
      | ( B @ ( A @ tc_fun ) @ class_Finite__Set_Ofinite ) ),
    inference(cnf,[status(esa)],[405]) ).

thf(165,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) )
      | ~ ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_union ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un__iff1_0) ).

thf(681,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) )
      | ~ ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_union ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(2931,plain,
    ! [A: $i] :
      ( ( c_0 != c_0 )
      | ( ( t_a @ tc_set @ tc_set )
       != tc_nat )
      | ( A != v_S )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(paramod_ordered,[status(thm)],[350,1689]) ).

thf(2932,plain,
    ! [A: $i] :
      ( ( ( t_a @ tc_set @ tc_set )
       != tc_nat )
      | ( A != v_S )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(pattern_uni,[status(thm)],[2931:[]]) ).

thf(3155,plain,
    ( ( ( t_a @ tc_set @ tc_set )
     != tc_nat )
    | ( tc_nat @ ( v_S @ ( c_0 @ c_less ) ) ) ),
    inference(simp,[status(thm)],[2932]) ).

thf(215,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( E @ c_Relation_ORange ) ) @ ( B @ c_in ) ) )
      | ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ORangeI_0) ).

thf(784,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( E @ c_Relation_ORange ) ) @ ( B @ c_in ) ) )
      | ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(1520,plain,
    ! [A: $i] :
      ( ( c_0 != c_0 )
      | ( A != c_emptyset )
      | ~ ( tc_IntDef_Oint @ ( c_UNIV @ ( c_0 @ c_Divides_Oop_Advd ) ) )
      | ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(paramod_ordered,[status(thm)],[315,1232]) ).

thf(1521,plain,
    ! [A: $i] :
      ( ( A != c_emptyset )
      | ~ ( tc_IntDef_Oint @ ( c_UNIV @ ( c_0 @ c_Divides_Oop_Advd ) ) )
      | ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(pattern_uni,[status(thm)],[1520:[]]) ).

thf(1524,plain,
    ( ~ ( tc_IntDef_Oint @ ( c_UNIV @ ( c_0 @ c_Divides_Oop_Advd ) ) )
    | ~ ( tc_IntDef_Oint @ ( c_emptyset @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(simp,[status(thm)],[1521]) ).

thf(193,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ ( B @ ( A @ c_Datatype_Ooption_OSome ) @ c_Datatype_Oo2s ) @ ( A @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Oelem__o2s__iff2_0) ).

thf(736,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ ( B @ ( A @ c_Datatype_Ooption_OSome ) @ c_Datatype_Oo2s ) @ ( A @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(376,plain,
    ! [B: $i,A: $i] :
      ( ( B = c_0 )
      | ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
       != c_0 ) ),
    inference(cnf,[status(esa)],[375]) ).

thf(377,plain,
    ! [B: $i,A: $i] :
      ( ( B = c_0 )
      | ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
       != c_0 ) ),
    inference(lifteq,[status(thm)],[376]) ).

thf(61,axiom,
    ! [B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__greater__0__conv__iff2_0) ).

thf(451,plain,
    ! [B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(237,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( C @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__2 ) ) ) ) @ c_in ) ) )
      | ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ouprod ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_1) ).

thf(831,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( C @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__2 ) ) ) ) @ c_in ) ) )
      | ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ouprod ) ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(194,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( E @ ( D @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__2 ) ) ) ) @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__1 ) ) ) ) @ c_Datatype__Universe_OScons ) ) ) ) )
      | ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ouprod ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_0) ).

thf(737,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( E @ ( D @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__2 ) ) ) ) @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__1 ) ) ) ) @ c_Datatype__Universe_OScons ) ) ) ) )
      | ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ouprod ) ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(90,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( c_Relation_OId @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OIdI_0) ).

thf(509,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( c_Relation_OId @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(148,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_IntDef_Oint @ ( B @ ( tc_IntDef_Oint @ ( A @ c_uminus ) @ c_Divides_Oop_Advd ) ) )
      | ~ ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Advd ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozminus__dvd__iff__iff2_0) ).

thf(649,plain,
    ! [B: $i,A: $i] :
      ( ( tc_IntDef_Oint @ ( B @ ( tc_IntDef_Oint @ ( A @ c_uminus ) @ c_Divides_Oop_Advd ) ) )
      | ~ ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Advd ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(5070,plain,
    ! [A: $i] :
      ( ( c_0 != c_0 )
      | ( c_UNIV != c_0 )
      | ( A != v_S )
      | ( ( t_a @ tc_set )
       != t_a )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(paramod_ordered,[status(thm)],[350,3871]) ).

thf(5071,plain,
    ! [A: $i] :
      ( ( c_UNIV != c_0 )
      | ( A != v_S )
      | ( ( t_a @ tc_set )
       != t_a )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(pattern_uni,[status(thm)],[5070:[]]) ).

thf(5093,plain,
    ( ( c_UNIV != c_0 )
    | ( ( t_a @ tc_set )
     != t_a )
    | ( tc_nat @ ( v_S @ ( c_0 @ c_less ) ) ) ),
    inference(simp,[status(thm)],[5071]) ).

thf(54,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_List_Olist_ONil )
      | ( A
       != ( C @ ( B @ ( A @ c_append ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oself__append__conv__iff1_0) ).

thf(434,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_List_Olist_ONil )
      | ( A
       != ( C @ ( B @ ( A @ c_append ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(75,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( D @ ( C @ ( E @ ( F @ c_Datatype__Universe_Odsum ) ) ) @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ c_Datatype__Universe_OIn1 ) ) @ ( D @ ( C @ ( A @ c_Datatype__Universe_OIn1 ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Odsum__In1I_0) ).

thf(477,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( D @ ( C @ ( E @ ( F @ c_Datatype__Universe_Odsum ) ) ) @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ c_Datatype__Universe_OIn1 ) ) @ ( D @ ( C @ ( A @ c_Datatype__Universe_OIn1 ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(83,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( B @ c_SetInterval_OlessThan ) )
       != ( A @ ( C @ c_SetInterval_OlessThan ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__eq__iff__iff1_0) ).

thf(494,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( B @ c_SetInterval_OlessThan ) )
       != ( A @ ( C @ c_SetInterval_OlessThan ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(230,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( D @ ( E @ ( D @ ( E @ ( A @ ( C @ c_Main_OPlusE__2 ) ) ) @ c_Sum__Type_OInr ) ) ) )
      | ( D @ ( B @ ( E @ ( D @ ( A @ ( B @ c_Main_OPlusE__1 ) ) ) @ c_in ) ) )
      | ~ ( E @ ( D @ tc_sum ) @ ( E @ ( D @ ( C @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_2) ).

thf(816,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( D @ ( E @ ( D @ ( E @ ( A @ ( C @ c_Main_OPlusE__2 ) ) ) @ c_Sum__Type_OInr ) ) ) )
      | ( D @ ( B @ ( E @ ( D @ ( A @ ( B @ c_Main_OPlusE__1 ) ) ) @ c_in ) ) )
      | ~ ( E @ ( D @ tc_sum ) @ ( E @ ( D @ ( C @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(124,axiom,
    tc_IntDef_Oint @ class_Orderings_Oorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_31) ).

thf(585,plain,
    tc_IntDef_Oint @ class_Orderings_Oorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(2873,plain,
    ! [A: $i] :
      ( ( A != tc_IntDef_Oint )
      | ( c_0 @ class_Orderings_Oorder )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(paramod_ordered,[status(thm)],[350,585]) ).

thf(2874,plain,
    ( ( c_0 @ class_Orderings_Oorder )
    | ( tc_nat @ ( tc_IntDef_Oint @ ( c_0 @ c_less ) ) ) ),
    inference(pattern_uni,[status(thm)],[2873:[bind(A,$thf( tc_IntDef_Oint ))]]) ).

thf(278,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OlessThan ) @ ( A @ ( B @ c_SetInterval_OlessThan ) @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__subset__iff__iff2_0) ).

thf(915,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OlessThan ) @ ( A @ ( B @ c_SetInterval_OlessThan ) @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(208,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OComplI_0) ).

thf(769,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(286,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ( D @ ( C @ ( A @ c_in ) ) )
      | ~ ( D @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertE_0) ).

thf(932,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ( D @ ( C @ ( A @ c_in ) ) )
      | ~ ( D @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(2577,plain,
    ! [A: $i] :
      ( ( A != tc_IntDef_Oint )
      | ( c_0 @ class_Orderings_Oord )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(paramod_ordered,[status(thm)],[350,514]) ).

thf(2578,plain,
    ( ( c_0 @ class_Orderings_Oord )
    | ( tc_nat @ ( tc_IntDef_Oint @ ( c_0 @ c_less ) ) ) ),
    inference(pattern_uni,[status(thm)],[2577:[bind(A,$thf( tc_IntDef_Oint ))]]) ).

thf(811,plain,
    ! [A: $i] :
      ( ( A @ ( c_List_Olist_ONil @ c_List_Oset ) )
      = c_emptyset ),
    inference(lifteq,[status(thm)],[810]) ).

thf(250,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
       != ( B @ ( c_emptyset @ ( C @ c_insert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__inject__dest_0) ).

thf(858,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
       != ( B @ ( c_emptyset @ ( C @ c_insert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(367,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( c_0 @ c_less ) ) )
      | ( tc_nat @ ( B @ ( c_0 @ c_less ) ) )
      | ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) ) ),
    inference(cnf,[status(esa)],[366]) ).

thf(222,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ tc_set @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( D @ c_lessequals ) ) )
      | ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
       != ( B @ ( D @ ( C @ c_insert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq__iff1_1) ).

thf(799,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ tc_set @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( D @ c_lessequals ) ) )
      | ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
       != ( B @ ( D @ ( C @ c_insert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(188,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) )
      | ~ ( B @ ( C @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__converse__iff1_0) ).

thf(726,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) )
      | ~ ( B @ ( C @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(175,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_emptyset )
      | ( ( C @ ( B @ ( A @ c_Equiv__Relations_Oquotient ) ) )
       != c_emptyset ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Equiv__Relations_Oquotient__is__empty__iff1_0) ).

thf(700,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_emptyset )
      | ( ( C @ ( B @ ( A @ c_Equiv__Relations_Oquotient ) ) )
       != c_emptyset ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(97,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( A @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_OlistsE_1) ).

thf(520,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( A @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(2552,plain,
    ! [A: $i] :
      ( ( A != tc_nat )
      | ( ( c_0 @ ( c_0 @ ( c_0 @ c_plus ) ) )
        = c_0 )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(paramod_ordered,[status(thm)],[350,352]) ).

thf(2553,plain,
    ( ( ( c_0 @ ( c_0 @ ( c_0 @ c_plus ) ) )
      = c_0 )
    | ( tc_nat @ ( tc_nat @ ( c_0 @ c_less ) ) ) ),
    inference(pattern_uni,[status(thm)],[2552:[bind(A,$thf( tc_nat ))]]) ).

thf(158,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oaxioms__1_0) ).

thf(668,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(2456,plain,
    ! [A: $i] :
      ( ( c_0 != c_0 )
      | ( A != c_emptyset )
      | ~ ( tc_IntDef_Oint @ ( c_Finite__Set_OFinites @ ( c_0 @ c_Divides_Oop_Advd ) ) )
      | ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(paramod_ordered,[status(thm)],[315,2200]) ).

thf(2457,plain,
    ! [A: $i] :
      ( ( A != c_emptyset )
      | ~ ( tc_IntDef_Oint @ ( c_Finite__Set_OFinites @ ( c_0 @ c_Divides_Oop_Advd ) ) )
      | ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(pattern_uni,[status(thm)],[2456:[]]) ).

thf(2461,plain,
    ( ~ ( tc_IntDef_Oint @ ( c_Finite__Set_OFinites @ ( c_0 @ c_Divides_Oop_Advd ) ) )
    | ~ ( tc_IntDef_Oint @ ( c_emptyset @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(simp,[status(thm)],[2457]) ).

thf(12,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( C @ ( c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) )
       != ( C @ ( C @ ( c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_append ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend1__eq__conv__iff1_0) ).

thf(330,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( C @ ( c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) )
       != ( C @ ( C @ ( c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_append ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(167,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__2 ) ) ) @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( D @ tc_prod ) @ ( D @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OconverseE_0) ).

thf(685,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__2 ) ) ) @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( D @ tc_prod ) @ ( D @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(37,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_List_Olist_ONil )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv__iff1_1) ).

thf(399,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_List_Olist_ONil )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(299,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_insert ) ) )
       != ( C @ ( c_emptyset @ ( D @ c_insert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H__iff1_0) ).

thf(959,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_insert ) ) )
       != ( C @ ( c_emptyset @ ( D @ c_insert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(5080,plain,
    ! [A: $i] :
      ( ( c_0 != c_0 )
      | ( c_UNIV != c_0 )
      | ( A != v_S )
      | ( ( t_a @ tc_set )
       != t_a )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(paramod_ordered,[status(thm)],[355,3871]) ).

thf(5081,plain,
    ! [A: $i] :
      ( ( c_UNIV != c_0 )
      | ( A != v_S )
      | ( ( t_a @ tc_set )
       != t_a )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(pattern_uni,[status(thm)],[5080:[]]) ).

thf(5094,plain,
    ( ( c_UNIV != c_0 )
    | ( ( t_a @ tc_set )
     != t_a )
    | ~ ( tc_nat @ ( c_0 @ ( v_S @ c_lessequals ) ) ) ),
    inference(simp,[status(thm)],[5081]) ).

thf(254,axiom,
    ! [B: $i,A: $i] : ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_List_Oset ) @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ofinite__set_0) ).

thf(868,plain,
    ! [B: $i,A: $i] : ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_List_Oset ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(262,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( C @ tc_set @ ( A @ c_uminus ) @ ( C @ tc_set @ ( B @ c_uminus ) @ c_lessequals ) ) )
      | ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff__iff2_0) ).

thf(883,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( C @ tc_set @ ( A @ c_uminus ) @ ( C @ tc_set @ ( B @ c_uminus ) @ c_lessequals ) ) )
      | ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(133,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( E @ ( C @ ( B @ ( F @ c_Relation_OImage ) ) ) @ ( D @ c_in ) ) )
      | ~ ( E @ ( C @ tc_prod ) @ ( F @ ( E @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImageI_0) ).

thf(608,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( E @ ( C @ ( B @ ( F @ c_Relation_OImage ) ) ) @ ( D @ c_in ) ) )
      | ~ ( E @ ( C @ tc_prod ) @ ( F @ ( E @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(86,axiom,
    tc_nat @ class_Orderings_Olinorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_7) ).

thf(501,plain,
    tc_nat @ class_Orderings_Olinorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(3015,plain,
    ! [A: $i] :
      ( ( A != tc_nat )
      | ( c_0 @ class_Orderings_Olinorder )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(paramod_ordered,[status(thm)],[350,501]) ).

thf(3016,plain,
    ( ( c_0 @ class_Orderings_Olinorder )
    | ( tc_nat @ ( tc_nat @ ( c_0 @ c_less ) ) ) ),
    inference(pattern_uni,[status(thm)],[3015:[bind(A,$thf( tc_nat ))]]) ).

thf(247,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OatMost ) @ ( A @ ( B @ c_SetInterval_OatMost ) @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__subset__iff__iff2_0) ).

thf(851,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OatMost ) @ ( A @ ( B @ c_SetInterval_OatMost ) @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(150,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( A @ ( C @ ( D @ ( B @ ( A @ c_Main_ORangeE__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ ( D @ ( C @ ( B @ c_Relation_ORange ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ORangeE_0) ).

thf(653,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( A @ ( C @ ( D @ ( B @ ( A @ c_Main_ORangeE__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ ( D @ ( C @ ( B @ c_Relation_ORange ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(281,axiom,
    ! [B: $i,A: $i] :
      ~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Onot__psubset__empty__iff1_0) ).

thf(922,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(6735,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_nat @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
       != ( tc_nat @ ( c_0 @ ( C @ c_less ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[6722,324]) ).

thf(6736,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
     != ( tc_nat @ ( c_0 @ ( C @ c_less ) ) ) ),
    inference(simp,[status(thm)],[6735]) ).

thf(6784,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat != tc_nat )
      | ( ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) )
       != c_0 )
      | ( c_0 != C ) ),
    inference(simp,[status(thm)],[6736]) ).

thf(6785,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) )
     != c_0 ),
    inference(simp,[status(thm)],[6784]) ).

thf(88,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( B @ c_SetInterval_OgreaterThan ) )
       != ( A @ ( C @ c_SetInterval_OgreaterThan ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__eq__iff__iff1_0) ).

thf(505,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( B @ c_SetInterval_OgreaterThan ) )
       != ( A @ ( C @ c_SetInterval_OgreaterThan ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(126,axiom,
    ! [A: $i] :
      ~ ( tc_nat @ ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__greater__0__conv__iff1_0) ).

thf(589,plain,
    ! [A: $i] :
      ~ ( tc_nat @ ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(291,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( D @ ( B @ c_union ) ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnCI_1) ).

thf(944,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( D @ ( B @ c_union ) ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(220,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( A @ c_in ) ) )
      | ~ ( D @ ( D @ ( C @ ( B @ c_inter ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OIntE_0) ).

thf(795,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( A @ c_in ) ) )
      | ~ ( D @ ( D @ ( C @ ( B @ c_inter ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(373,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != B ) ),
    inference(cnf,[status(esa)],[372]) ).

thf(374,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != B ) ),
    inference(lifteq,[status(thm)],[373]) ).

thf(228,axiom,
    ! [B: $i,A: $i] :
      ( c_emptyset
      = ( B @ ( A @ ( c_emptyset @ c_Equiv__Relations_Oquotient ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Equiv__Relations_Oquotient__is__empty2__iff2_0) ).

thf(812,plain,
    ! [B: $i,A: $i] :
      ( c_emptyset
      = ( B @ ( A @ ( c_emptyset @ c_Equiv__Relations_Oquotient ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(341,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( C @ ( C @ ( c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) )
       != ( C @ ( C @ ( c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_append ) ) ) ) ),
    inference(cnf,[status(esa)],[340]) ).

thf(342,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( C @ ( C @ ( c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) )
       != ( C @ ( C @ ( c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_append ) ) ) ) ),
    inference(lifteq,[status(thm)],[341]) ).

thf(110,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = E )
      | ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
       != ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq__iff1_0) ).

thf(553,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = E )
      | ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
       != ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(81,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn1 ) ) )
     != ( C @ ( B @ ( D @ c_Datatype__Universe_OIn0 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn1__not__In0__iff1_0) ).

thf(490,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn1 ) ) )
     != ( C @ ( B @ ( D @ c_Datatype__Universe_OIn0 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(162,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( A @ ( C @ c_SetInterval_OatLeast ) @ ( B @ c_in ) ) )
      | ~ ( A @ class_Orderings_Oord ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__iff__iff1_0) ).

thf(675,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( A @ ( C @ c_SetInterval_OatLeast ) @ ( B @ c_in ) ) )
      | ~ ( A @ class_Orderings_Oord ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(4501,plain,
    ! [A: $i] :
      ( ( c_0 != c_0 )
      | ( c_Finite__Set_OFinites != c_0 )
      | ( A != c_emptyset )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(paramod_ordered,[status(thm)],[355,2462]) ).

thf(4502,plain,
    ! [A: $i] :
      ( ( c_Finite__Set_OFinites != c_0 )
      | ( A != c_emptyset )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(pattern_uni,[status(thm)],[4501:[]]) ).

thf(4749,plain,
    ( ( c_Finite__Set_OFinites != c_0 )
    | ~ ( tc_nat @ ( c_0 @ ( c_emptyset @ c_lessequals ) ) ) ),
    inference(simp,[status(thm)],[4502]) ).

thf(211,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( E @ ( E @ ( D @ ( D @ ( c_emptyset @ ( C @ c_insert ) ) @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImage__singleton__iff__iff1_0) ).

thf(776,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( E @ ( E @ ( D @ ( D @ ( c_emptyset @ ( C @ c_insert ) ) @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(170,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( A @ c_in ) ) )
      | ~ ( C @ tc_set @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).

thf(690,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( A @ c_in ) ) )
      | ~ ( C @ tc_set @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(256,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ ( F @ c_Datatype__Universe_Ouprod ) ) ) @ ( D @ ( C @ ( A @ ( E @ c_Datatype__Universe_OScons ) ) ) @ c_in ) ) )
      | ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( F @ ( E @ c_in ) ) )
      | ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodI_0) ).

thf(872,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ ( F @ c_Datatype__Universe_Ouprod ) ) ) @ ( D @ ( C @ ( A @ ( E @ c_Datatype__Universe_OScons ) ) ) @ c_in ) ) )
      | ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( F @ ( E @ c_in ) ) )
      | ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(179,axiom,
    ! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( B @ c_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_IntDef_Oint @ c_uminus ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onegative__zle_0) ).

thf(707,plain,
    ! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( B @ c_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_IntDef_Oint @ c_uminus ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(264,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( A @ ( C @ c_SetInterval_OatMost ) @ ( B @ c_in ) ) )
      | ~ ( A @ class_Orderings_Oord ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__iff__iff1_0) ).

thf(887,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( A @ ( C @ c_SetInterval_OatMost ) @ ( B @ c_in ) ) )
      | ~ ( A @ class_Orderings_Oord ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(414,plain,
    ! [A: $i] :
      ( ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Nat_Osize ) )
      = c_0 ),
    inference(lifteq,[status(thm)],[413]) ).

thf(309,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D
        = ( C @ ( C @ ( B @ ( A @ ( D @ ( E @ c_Main_Olistrel__Cons1__2 ) ) ) ) @ ( C @ ( B @ ( A @ ( D @ ( E @ c_Main_Olistrel__Cons1__1 ) ) ) ) @ c_List_Olist_OCons ) ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( E @ c_List_Olistrel ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(cnf,[status(esa)],[308]) ).

thf(310,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( E @ c_List_Olistrel ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( ( C @ ( C @ ( B @ ( A @ ( D @ ( E @ c_Main_Olistrel__Cons1__2 ) ) ) ) @ ( C @ ( B @ ( A @ ( D @ ( E @ c_Main_Olistrel__Cons1__1 ) ) ) ) @ c_List_Olist_OCons ) ) )
        = D ) ),
    inference(lifteq,[status(thm)],[309]) ).

thf(99,axiom,
    ! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( B @ c_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Suc @ c_IntDef_Oint @ c_uminus ) @ c_less ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onegative__zless_0) ).

thf(525,plain,
    ! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( B @ c_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Suc @ c_IntDef_Oint @ c_uminus ) @ c_less ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(9797,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_nat @ ( tc_nat @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
       != ( tc_nat @ ( c_0 @ ( D @ c_less ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[7870,324]) ).

thf(9798,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
     != ( tc_nat @ ( c_0 @ ( D @ c_less ) ) ) ),
    inference(simp,[status(thm)],[9797]) ).

thf(9868,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_nat != tc_nat )
      | ( ( tc_nat @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ ( A @ c_plus ) ) )
       != c_0 )
      | ( c_0 != D ) ),
    inference(simp,[status(thm)],[9798]) ).

thf(9879,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ ( A @ c_plus ) ) )
     != c_0 ),
    inference(simp,[status(thm)],[9868]) ).

thf(249,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( E @ ( D @ ( E @ ( D @ ( A @ ( B @ c_Main_OPlusE__1 ) ) ) @ c_Sum__Type_OInl ) ) ) )
      | ( E @ ( C @ ( D @ ( E @ ( A @ ( C @ c_Main_OPlusE__2 ) ) ) @ c_in ) ) )
      | ~ ( E @ ( D @ tc_sum ) @ ( E @ ( D @ ( C @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_1) ).

thf(855,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( E @ ( D @ ( E @ ( D @ ( A @ ( B @ c_Main_OPlusE__1 ) ) ) @ c_Sum__Type_OInl ) ) ) )
      | ( E @ ( C @ ( D @ ( E @ ( A @ ( C @ c_Main_OPlusE__2 ) ) ) @ c_in ) ) )
      | ~ ( E @ ( D @ tc_sum ) @ ( E @ ( D @ ( C @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(10988,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_IntDef_Oint @ ( c_0 @ ( A @ c_Divides_Oop_Advd ) ) )
       != ( tc_IntDef_Oint @ ( tc_nat @ ( B @ ( tc_nat @ ( D @ c_Suc @ ( C @ c_plus ) ) @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[407,9273]) ).

thf(10989,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_IntDef_Oint @ ( c_0 @ ( A @ c_Divides_Oop_Advd ) ) )
     != ( tc_IntDef_Oint @ ( tc_nat @ ( B @ ( tc_nat @ ( D @ c_Suc @ ( C @ c_plus ) ) @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(simp,[status(thm)],[10988]) ).

thf(11045,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_IntDef_Oint != tc_IntDef_Oint )
      | ( ( tc_nat @ ( B @ ( tc_nat @ ( D @ c_Suc @ ( C @ c_plus ) ) @ c_plus ) ) )
       != c_0 )
      | ( A != c_0 ) ),
    inference(simp,[status(thm)],[10989]) ).

thf(11066,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ c_plus ) ) )
     != c_0 ),
    inference(simp,[status(thm)],[11045]) ).

thf(161,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_in ) ) )
      | ~ ( C @ ( B @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__converse__iff2_0) ).

thf(673,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_in ) ) )
      | ~ ( C @ ( B @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(441,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( C @ ( D @ ( A @ c_List_Olist_OCons ) ) @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( D @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(cnf,[status(esa)],[440]) ).

thf(184,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Or__into__rtrancl_0) ).

thf(717,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(87,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Sum__Type_OInr ) ) )
     != ( B @ ( C @ ( D @ c_Sum__Type_OInl ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInr__not__Inl__iff1_0) ).

thf(502,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Sum__Type_OInr ) ) )
     != ( B @ ( C @ ( D @ c_Sum__Type_OInl ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(66,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_uminus ) @ ( A @ c_Divides_Oop_Advd ) ) )
      | ~ ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Advd ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Odvd__zminus__iff__iff2_0) ).

thf(463,plain,
    ! [B: $i,A: $i] :
      ( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_uminus ) @ ( A @ c_Divides_Oop_Advd ) ) )
      | ~ ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Advd ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(118,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_Odiag ) @ ( C @ ( C @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OdiagI_0) ).

thf(576,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_Odiag ) @ ( C @ ( C @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(3610,plain,
    ! [A: $i] :
      ( ( c_0 != c_0 )
      | ( ( t_a @ tc_set )
       != c_0 )
      | ( c_UNIV != v_S )
      | ( A != t_a )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(paramod_ordered,[status(thm)],[350,3598]) ).

thf(3611,plain,
    ! [A: $i] :
      ( ( ( t_a @ tc_set )
       != c_0 )
      | ( c_UNIV != v_S )
      | ( A != t_a )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(pattern_uni,[status(thm)],[3610:[]]) ).

thf(3623,plain,
    ( ( ( t_a @ tc_set )
     != c_0 )
    | ( c_UNIV != v_S )
    | ( tc_nat @ ( t_a @ ( c_0 @ c_less ) ) ) ),
    inference(simp,[status(thm)],[3611]) ).

thf(145,axiom,
    ! [C: $i,B: $i,A: $i] :
      ~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olex ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil2__notin__lex__iff1_0) ).

thf(643,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olex ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(25,axiom,
    ! [B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) )
       != c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__0__conv__iff1_0) ).

thf(368,plain,
    ! [B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) )
       != c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(369,plain,
    ! [B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) )
       != c_0 ) ),
    inference(cnf,[status(esa)],[368]) ).

thf(370,plain,
    ! [B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) )
       != c_0 ) ),
    inference(lifteq,[status(thm)],[369]) ).

thf(242,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( B @ ( B @ ( B @ ( A @ c_Main_OIdE__1 ) @ ( B @ ( A @ c_Main_OIdE__1 ) @ c_Pair ) ) ) ) )
      | ~ ( B @ ( B @ tc_prod ) @ ( c_Relation_OId @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OIdE_0) ).

thf(840,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( B @ ( B @ ( B @ ( A @ c_Main_OIdE__1 ) @ ( B @ ( A @ c_Main_OIdE__1 ) @ c_Pair ) ) ) ) )
      | ~ ( B @ ( B @ tc_prod ) @ ( c_Relation_OId @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(7617,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_nat @ ( A @ c_Suc @ ( A @ c_less ) ) )
       != ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_less ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[580,484]) ).

thf(7618,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( A @ c_Suc @ ( A @ c_less ) ) )
     != ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_less ) ) ) ),
    inference(simp,[status(thm)],[7617]) ).

thf(7645,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat != tc_nat )
      | ( ( A @ c_Suc )
       != B )
      | ( A
       != ( tc_nat @ ( C @ ( B @ c_plus ) ) ) ) ),
    inference(simp,[status(thm)],[7618]) ).

thf(7667,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_Suc )
     != A ),
    inference(simp,[status(thm)],[7645]) ).

thf(295,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( B @ ( C @ ( B @ ( A @ c_Main_OUnionE__1 ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ ( B @ c_Union ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnionE_0) ).

thf(951,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( B @ ( C @ ( B @ ( A @ c_Main_OUnionE__1 ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ ( B @ c_Union ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(226,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( E @ ( D @ ( B @ ( A @ ( C @ c_Main_OImageE__1 ) ) ) ) @ c_in ) ) )
      | ~ ( E @ ( E @ ( D @ ( C @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImageE_0) ).

thf(808,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( E @ ( D @ ( B @ ( A @ ( C @ c_Main_OImageE__1 ) ) ) ) @ c_in ) ) )
      | ~ ( E @ ( E @ ( D @ ( C @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(197,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( C @ ( D @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__1 ) ) ) @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__2 ) ) ) @ c_Pair ) ) ) ) )
      | ~ ( C @ ( D @ tc_prod ) @ ( D @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OconverseE_1) ).

thf(744,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( C @ ( D @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__1 ) ) ) @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__2 ) ) ) @ c_Pair ) ) ) ) )
      | ~ ( C @ ( D @ tc_prod ) @ ( D @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(176,axiom,
    ! [A: $i] : ( A @ tc_set @ class_Nat_Opower ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_4) ).

thf(703,plain,
    ! [A: $i] : ( A @ tc_set @ class_Nat_Opower ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(135,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Wellfounded__Recursion_Oacyclic ) )
      | ~ ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse__iff2_0) ).

thf(613,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Wellfounded__Recursion_Oacyclic ) )
      | ~ ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(252,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ tc_prod ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( C @ ( D @ c_Pair ) ) ) @ c_in ) ) )
      | ( B @ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( D @ ( C @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Owf ) )
      | ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert__iff2_0) ).

thf(864,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ tc_prod ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( C @ ( D @ c_Pair ) ) ) @ c_in ) ) )
      | ( B @ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( D @ ( C @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Owf ) )
      | ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(4494,plain,
    ! [A: $i] :
      ( ( c_0 != c_0 )
      | ( ( t_a @ tc_set )
       != c_0 )
      | ( c_UNIV != v_S )
      | ( A != t_a )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(paramod_ordered,[status(thm)],[355,3598]) ).

thf(4495,plain,
    ! [A: $i] :
      ( ( ( t_a @ tc_set )
       != c_0 )
      | ( c_UNIV != v_S )
      | ( A != t_a )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(pattern_uni,[status(thm)],[4494:[]]) ).

thf(4748,plain,
    ( ( ( t_a @ tc_set )
     != c_0 )
    | ( c_UNIV != v_S )
    | ~ ( tc_nat @ ( c_0 @ ( t_a @ c_lessequals ) ) ) ),
    inference(simp,[status(thm)],[4495]) ).

thf(976,plain,
    ! [A: $i] :
      ( ( ( t_a @ tc_set )
       != ( t_a @ tc_set ) )
      | ( v_S != v_S )
      | ( ( t_a @ tc_set @ ( c_emptyset @ ( A @ c_insert ) ) )
       != v_S )
      | ( ( t_a @ tc_set @ tc_set )
       != ( t_a @ tc_set ) )
      | ~ ( t_a @ tc_set @ ( v_S @ ( v_S @ c_in ) ) ) ),
    inference(simp,[status(thm)],[973]) ).

thf(978,plain,
    ! [A: $i] :
      ( ( ( t_a @ tc_set @ ( c_emptyset @ ( A @ c_insert ) ) )
       != v_S )
      | ( ( t_a @ tc_set @ tc_set )
       != ( t_a @ tc_set ) )
      | ~ ( t_a @ tc_set @ ( v_S @ ( v_S @ c_in ) ) ) ),
    inference(simp,[status(thm)],[976]) ).

thf(12053,plain,
    ! [A: $i] :
      ( ( A != c_UNIV )
      | ( c_0 != c_emptyset )
      | ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(paramod_ordered,[status(thm)],[429,821]) ).

thf(12054,plain,
    ( ( c_0 != c_emptyset )
    | ~ ( tc_nat @ ( c_UNIV @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(pattern_uni,[status(thm)],[12053:[bind(A,$thf( c_UNIV ))]]) ).

thf(129,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn1 ) ) )
       != ( C @ ( B @ ( D @ c_Datatype__Universe_OIn1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn1__eq__iff1_0) ).

thf(595,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn1 ) ) )
       != ( C @ ( B @ ( D @ c_Datatype__Universe_OIn1 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(84,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( D @ ( C @ ( F @ ( E @ c_Datatype__Universe_Odsum ) ) ) @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ c_Datatype__Universe_OIn0 ) ) @ ( D @ ( C @ ( A @ c_Datatype__Universe_OIn0 ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Odsum__In0I_0) ).

thf(497,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( D @ ( C @ ( F @ ( E @ c_Datatype__Universe_Odsum ) ) ) @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ c_Datatype__Universe_OIn0 ) ) @ ( D @ ( C @ ( A @ c_Datatype__Universe_OIn0 ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(258,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Owf ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert__iff1_1) ).

thf(876,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Owf ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(244,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ tc_set @ ( A @ ( B @ c_SetInterval_OgreaterThan ) @ ( A @ ( C @ c_SetInterval_OgreaterThan ) @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__subset__iff__iff2_0) ).

thf(845,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ tc_set @ ( A @ ( B @ c_SetInterval_OgreaterThan ) @ ( A @ ( C @ c_SetInterval_OgreaterThan ) @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(9234,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
       != ( tc_nat @ ( D @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ c_plus ) ) ) )
      | ( c_0 != c_0 )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(paramod_ordered,[status(thm)],[350,7665]) ).

thf(9235,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
       != ( tc_nat @ ( D @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ c_plus ) ) ) )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(simp,[status(thm)],[9234]) ).

thf(9236,plain,
    ! [C: $i,B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ c_plus ) ) @ ( c_0 @ c_less ) ) ),
    inference(pattern_uni,[status(thm)],[9235:[bind(A,$thf( tc_nat @ ( F @ ( tc_nat @ ( K @ c_Suc @ ( H @ c_plus ) ) @ c_plus ) ) )),bind(B,$thf( H )),bind(C,$thf( K )),bind(D,$thf( F ))]]) ).

thf(9279,plain,
    ! [C: $i,B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ c_plus ) ) @ ( c_0 @ c_less ) ) ),
    inference(simp,[status(thm)],[9236]) ).

thf(139,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_4) ).

thf(627,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(160,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
      | ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).

thf(671,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
      | ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(121,axiom,
    ! [C: $i,B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl_Ortrancl__refl_0) ).

thf(581,plain,
    ! [C: $i,B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(203,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( A @ c_List_Oset ) @ ( C @ ( A @ ( B @ c_Main_Oin__listsI__1 ) ) @ c_in ) ) )
      | ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oin__listsI_0) ).

thf(759,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( A @ c_List_Oset ) @ ( C @ ( A @ ( B @ c_Main_Oin__listsI__1 ) ) @ c_in ) ) )
      | ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(266,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__4 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__3 ) ) ) ) @ c_Datatype__Universe_OScons ) ) ) @ ( E @ ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__2 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__1 ) ) ) ) @ c_Datatype__Universe_OScons ) ) ) @ c_Pair ) ) ) ) )
      | ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Odprod ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_0) ).

thf(891,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__4 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__3 ) ) ) ) @ c_Datatype__Universe_OScons ) ) ) @ ( E @ ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__2 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__1 ) ) ) ) @ c_Datatype__Universe_OScons ) ) ) @ c_Pair ) ) ) ) )
      | ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Odprod ) ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(209,axiom,
    ! [B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( B @ ( A @ c_List_Oset ) )
       != c_emptyset ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__empty__iff1_0) ).

thf(771,plain,
    ! [B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( B @ ( A @ c_List_Oset ) )
       != c_emptyset ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(4023,plain,
    ! [A: $i] :
      ( ( c_0 != c_0 )
      | ( c_UNIV != c_0 )
      | ( A != c_emptyset )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(paramod_ordered,[status(thm)],[355,1526]) ).

thf(4024,plain,
    ! [A: $i] :
      ( ( c_UNIV != c_0 )
      | ( A != c_emptyset )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(pattern_uni,[status(thm)],[4023:[]]) ).

thf(4763,plain,
    ( ( c_UNIV != c_0 )
    | ~ ( tc_nat @ ( c_0 @ ( c_emptyset @ c_lessequals ) ) ) ),
    inference(simp,[status(thm)],[4024]) ).

thf(95,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__into__rtrancl_0) ).

thf(517,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(268,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( D @ c_insert ) ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertCI_0) ).

thf(896,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( D @ c_insert ) ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(292,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Main_ODomainE__1 ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ODomainE_0) ).

thf(946,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Main_ODomainE__1 ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(3683,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) @ c_in ) ) )
       != ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[666,714]) ).

thf(3684,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) @ c_in ) ) )
     != ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
    inference(simp,[status(thm)],[3683]) ).

thf(3739,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ tc_set )
       != ( tc_nat @ tc_set ) )
      | ( c_Finite__Set_OFinites != c_Finite__Set_OFinites )
      | ( ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) )
       != c_UNIV ) ),
    inference(simp,[status(thm)],[3684]) ).

thf(3748,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) )
     != c_UNIV ),
    inference(simp,[status(thm)],[3739]) ).

thf(157,axiom,
    ! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastAtMost_0) ).

thf(667,plain,
    ! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(4932,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) @ c_in ) ) )
       != ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[667,714]) ).

thf(4933,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) @ c_in ) ) )
     != ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
    inference(simp,[status(thm)],[4932]) ).

thf(5001,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ tc_set )
       != ( tc_nat @ tc_set ) )
      | ( c_Finite__Set_OFinites != c_Finite__Set_OFinites )
      | ( ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) )
       != c_UNIV ) ),
    inference(simp,[status(thm)],[4933]) ).

thf(5010,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) )
     != c_UNIV ),
    inference(simp,[status(thm)],[5001]) ).

thf(214,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( C @ ( C @ ( C @ ( A @ ( B @ c_Main_OdiagE__1 ) ) @ ( C @ ( A @ ( B @ c_Main_OdiagE__1 ) ) @ c_Pair ) ) ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_Odiag ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OdiagE_0) ).

thf(781,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( C @ ( C @ ( C @ ( A @ ( B @ c_Main_OdiagE__1 ) ) @ ( C @ ( A @ ( B @ c_Main_OdiagE__1 ) ) @ c_Pair ) ) ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_Odiag ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(7938,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_IntDef_Oint @ ( c_0 @ ( A @ c_Divides_Oop_Advd ) ) )
       != ( tc_IntDef_Oint @ ( tc_nat @ ( B @ ( C @ c_Suc @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[407,7931]) ).

thf(7939,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_IntDef_Oint @ ( c_0 @ ( A @ c_Divides_Oop_Advd ) ) )
     != ( tc_IntDef_Oint @ ( tc_nat @ ( B @ ( C @ c_Suc @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(simp,[status(thm)],[7938]) ).

thf(7983,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_IntDef_Oint != tc_IntDef_Oint )
      | ( ( tc_nat @ ( B @ ( C @ c_Suc @ c_plus ) ) )
       != c_0 )
      | ( A != c_0 ) ),
    inference(simp,[status(thm)],[7939]) ).

thf(7996,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( B @ c_Suc @ c_plus ) ) )
     != c_0 ),
    inference(simp,[status(thm)],[7983]) ).

thf(418,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
      | ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(cnf,[status(esa)],[417]) ).

thf(216,axiom,
    ! [B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( c_emptyset
       != ( B @ ( A @ c_List_Oset ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__empty2__iff1_0) ).

thf(786,plain,
    ! [B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( c_emptyset
       != ( B @ ( A @ c_List_Oset ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(285,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( A @ ( B @ c_insert ) ) )
        = ( C @ ( c_emptyset @ ( B @ c_insert ) ) ) )
      | ~ ( C @ tc_set @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H__iff2_0) ).

thf(929,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( A @ ( B @ c_insert ) ) )
        = ( C @ ( c_emptyset @ ( B @ c_insert ) ) ) )
      | ~ ( C @ tc_set @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(205,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Union ) @ c_in ) ) )
      | ( B @ tc_set @ ( A @ ( B @ ( A @ c_Main_Ofinite__Union__1 ) @ c_in ) ) )
      | ~ ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Union_0) ).

thf(763,plain,
    ! [B: $i,A: $i] :
      ( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Union ) @ c_in ) ) )
      | ( B @ tc_set @ ( A @ ( B @ ( A @ c_Main_Ofinite__Union__1 ) @ c_in ) ) )
      | ~ ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(270,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_emptyset )
      | ( ( C @ ( B @ ( A @ c_union ) ) )
       != c_emptyset ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty__iff1_0) ).

thf(899,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_emptyset )
      | ( ( C @ ( B @ ( A @ c_union ) ) )
       != c_emptyset ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(8208,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_Suc @ c_plus ) ) @ ( c_0 @ c_less ) ) )
       != ( tc_nat @ ( D @ ( tc_nat @ ( D @ ( C @ c_plus ) ) @ c_less ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[7933,460]) ).

thf(8209,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_Suc @ c_plus ) ) @ ( c_0 @ c_less ) ) )
     != ( tc_nat @ ( D @ ( tc_nat @ ( D @ ( C @ c_plus ) ) @ c_less ) ) ) ),
    inference(simp,[status(thm)],[8208]) ).

thf(8261,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_nat != tc_nat )
      | ( ( tc_nat @ ( A @ ( B @ c_Suc @ c_plus ) ) )
       != D )
      | ( ( tc_nat @ ( D @ ( C @ c_plus ) ) )
       != c_0 ) ),
    inference(simp,[status(thm)],[8209]) ).

thf(8267,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_Suc @ c_plus ) ) @ ( C @ c_plus ) ) )
     != c_0 ),
    inference(simp,[status(thm)],[8261]) ).

thf(13299,plain,
    ! [A: $i] :
      ( ( c_0 != c_0 )
      | ( ( t_a @ tc_set @ tc_set )
       != tc_nat )
      | ( A != v_S )
      | ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(paramod_ordered,[status(thm)],[429,1689]) ).

thf(13300,plain,
    ! [A: $i] :
      ( ( ( t_a @ tc_set @ tc_set )
       != tc_nat )
      | ( A != v_S )
      | ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(pattern_uni,[status(thm)],[13299:[]]) ).

thf(13793,plain,
    ( ( ( t_a @ tc_set @ tc_set )
     != tc_nat )
    | ~ ( tc_nat @ ( v_S @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(simp,[status(thm)],[13300]) ).

thf(29,axiom,
    ! [A: $i] :
      ( c_0
     != ( A @ c_Suc ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OZero__not__Suc__iff1_0) ).

thf(378,plain,
    ! [A: $i] :
      ( c_0
     != ( A @ c_Suc ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(53,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ ( E @ c_List_Olistrel ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( C @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__2 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ ( E @ c_List_Olistrel ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Cons2_1) ).

thf(432,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ ( E @ c_List_Olistrel ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( C @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__2 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ ( E @ c_List_Olistrel ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(433,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ ( E @ c_List_Olistrel ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( C @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__2 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ ( E @ c_List_Olistrel ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(cnf,[status(esa)],[432]) ).

thf(91,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ tc_prod ) @ ( E @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ ( C @ tc_prod ) @ ( C @ ( D @ ( E @ c_Relation_Oconverse ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Oconverse__iff__iff1_0) ).

thf(510,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ tc_prod ) @ ( E @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ ( C @ tc_prod ) @ ( C @ ( D @ ( E @ c_Relation_Oconverse ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(137,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_less ) ) )
      | ~ ( A @ ( A @ ( C @ c_SetInterval_OlessThan ) @ ( B @ c_in ) ) )
      | ~ ( A @ class_Orderings_Oord ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__iff__iff1_0) ).

thf(620,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_less ) ) )
      | ~ ( A @ ( A @ ( C @ c_SetInterval_OlessThan ) @ ( B @ c_in ) ) )
      | ~ ( A @ class_Orderings_Oord ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(9522,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
       != ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_Suc @ c_plus ) ) @ ( D @ c_plus ) ) ) )
      | ( c_0 != c_0 )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(paramod_ordered,[status(thm)],[355,8267]) ).

thf(9523,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
       != ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_Suc @ c_plus ) ) @ ( D @ c_plus ) ) ) )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(simp,[status(thm)],[9522]) ).

thf(9524,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( tc_nat @ ( c_0 @ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_Suc @ c_plus ) ) @ ( A @ c_plus ) ) @ c_lessequals ) ) ),
    inference(pattern_uni,[status(thm)],[9523:[bind(A,$thf( tc_nat @ ( tc_nat @ ( I @ ( K @ c_Suc @ c_plus ) ) @ ( E @ c_plus ) ) )),bind(B,$thf( I )),bind(C,$thf( K )),bind(D,$thf( E ))]]) ).

thf(9551,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( tc_nat @ ( c_0 @ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_Suc @ c_plus ) ) @ ( A @ c_plus ) ) @ c_lessequals ) ) ),
    inference(simp,[status(thm)],[9524]) ).

thf(59,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ class_Finite__Set_Ofinite )
      | ~ ( B @ class_Finite__Set_Ofinite )
      | ( B @ ( A @ tc_prod ) @ class_Finite__Set_Ofinite ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_prod_0) ).

thf(447,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ class_Finite__Set_Ofinite )
      | ~ ( B @ class_Finite__Set_Ofinite )
      | ( B @ ( A @ tc_prod ) @ class_Finite__Set_Ofinite ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(238,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( C @ ( c_emptyset @ ( A @ c_insert ) ) @ ( E @ c_Relation_OImage ) ) ) @ ( B @ c_in ) ) )
      | ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImage__singleton__iff__iff2_0) ).

thf(833,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( C @ ( c_emptyset @ ( A @ c_insert ) ) @ ( E @ c_Relation_OImage ) ) ) @ ( B @ c_in ) ) )
      | ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(294,axiom,
    ! [A: $i] : ( A @ tc_set @ class_Orderings_Oorder ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_2) ).

thf(950,plain,
    ! [A: $i] : ( A @ tc_set @ class_Orderings_Oorder ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(239,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( D @ c_inter ) ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( D @ ( A @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OIntI_0) ).

thf(835,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( D @ c_inter ) ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( D @ ( A @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(114,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_Sum__Type_OInr ) ) )
       != ( C @ ( B @ ( D @ c_Sum__Type_OInr ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInr__eq__iff1_0) ).

thf(564,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_Sum__Type_OInr ) ) )
       != ( C @ ( B @ ( D @ c_Sum__Type_OInr ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(5090,plain,
    ! [A: $i] :
      ( ( c_0 != c_0 )
      | ( c_UNIV != c_0 )
      | ( A != v_S )
      | ( ( t_a @ tc_set )
       != t_a )
      | ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(paramod_ordered,[status(thm)],[315,3871]) ).

thf(5091,plain,
    ! [A: $i] :
      ( ( c_UNIV != c_0 )
      | ( A != v_S )
      | ( ( t_a @ tc_set )
       != t_a )
      | ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(pattern_uni,[status(thm)],[5090:[]]) ).

thf(5092,plain,
    ( ( c_UNIV != c_0 )
    | ( ( t_a @ tc_set )
     != t_a )
    | ~ ( tc_IntDef_Oint @ ( v_S @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(simp,[status(thm)],[5091]) ).

thf(357,plain,
    ! [C: $i,B: $i,A: $i] :
      ( c_List_Olist_ONil
     != ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) ) ),
    inference(polarity_switch,[status(thm)],[356]) ).

thf(358,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
     != c_List_Olist_ONil ),
    inference(lifteq,[status(thm)],[357]) ).

thf(3874,plain,
    ! [A: $i] :
      ( ( A != c_Finite__Set_OFinites )
      | ( c_0 != c_emptyset )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(paramod_ordered,[status(thm)],[355,2195]) ).

thf(3875,plain,
    ( ( c_0 != c_emptyset )
    | ~ ( tc_nat @ ( c_0 @ ( c_Finite__Set_OFinites @ c_lessequals ) ) ) ),
    inference(pattern_uni,[status(thm)],[3874:[bind(A,$thf( c_Finite__Set_OFinites ))]]) ).

thf(155,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ ( C @ c_insert ) ) @ c_in ) ) )
      | ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OinsertI_0) ).

thf(664,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ ( C @ c_insert ) ) @ c_in ) ) )
      | ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(103,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_IntDef_Oint )
       != ( B @ c_IntDef_Oint ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__int__eq__iff1_0) ).

thf(532,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_IntDef_Oint )
       != ( B @ c_IntDef_Oint ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(173,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Pow ) @ c_in ) ) )
      | ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff__iff2_0) ).

thf(696,plain,
    ! [B: $i,A: $i] :
      ( ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Pow ) @ c_in ) ) )
      | ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(297,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ ( C @ c_union ) ) @ c_in ) ) )
      | ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ c_in ) ) )
      | ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un__iff2_0) ).

thf(955,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ ( C @ c_union ) ) @ c_in ) ) )
      | ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ c_in ) ) )
      | ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(73,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( D @ c_in ) ) )
      | ~ ( C @ ( C @ ( A @ c_List_Oset ) @ ( D @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oin__listsD__dest_0) ).

thf(474,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( D @ c_in ) ) )
      | ~ ( C @ ( C @ ( A @ c_List_Oset ) @ ( D @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(207,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( C @ ( B @ c_Pow ) @ ( A @ c_in ) ) )
      | ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OPow__iff__iff2_0) ).

thf(767,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( C @ ( B @ c_Pow ) @ ( A @ c_in ) ) )
      | ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(8212,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_Suc @ c_plus ) ) @ ( c_0 @ c_less ) ) )
       != ( tc_nat @ ( C @ ( tc_nat @ ( D @ ( C @ c_plus ) ) @ c_less ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[7933,484]) ).

thf(8213,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_Suc @ c_plus ) ) @ ( c_0 @ c_less ) ) )
     != ( tc_nat @ ( C @ ( tc_nat @ ( D @ ( C @ c_plus ) ) @ c_less ) ) ) ),
    inference(simp,[status(thm)],[8212]) ).

thf(8262,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_nat != tc_nat )
      | ( ( tc_nat @ ( A @ ( B @ c_Suc @ c_plus ) ) )
       != C )
      | ( ( tc_nat @ ( D @ ( C @ c_plus ) ) )
       != c_0 ) ),
    inference(simp,[status(thm)],[8213]) ).

thf(8268,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ ( tc_nat @ ( A @ ( B @ c_Suc @ c_plus ) ) @ c_plus ) ) )
     != c_0 ),
    inference(simp,[status(thm)],[8262]) ).

thf(533,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_IntDef_Oint )
       != ( B @ c_IntDef_Oint ) ) ),
    inference(cnf,[status(esa)],[532]) ).

thf(534,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_IntDef_Oint )
       != ( B @ c_IntDef_Oint ) ) ),
    inference(lifteq,[status(thm)],[533]) ).

thf(535,plain,
    ? [A: $i > $i] :
    ! [B: $i] :
      ( ( B @ c_IntDef_Oint @ A )
      = B ),
    inference(detectInverse,[status(thm)],[534]) ).

thf(536,plain,
    ! [A: $i] :
      ( ( A @ c_IntDef_Oint @ sk6 )
      = A ),
    inference(cnf,[status(esa)],[535]) ).

thf(2223,plain,
    ! [A: $i] :
      ( ( A @ c_IntDef_Oint @ sk6 )
      = A ),
    inference(lifteq,[status(thm)],[536]) ).

thf(331,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( C @ ( c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) )
       != ( C @ ( C @ ( c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_append ) ) ) ) ),
    inference(cnf,[status(esa)],[330]) ).

thf(332,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( C @ ( c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) )
       != ( C @ ( C @ ( c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_append ) ) ) ) ),
    inference(lifteq,[status(thm)],[331]) ).

thf(101,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Advd ) ) )
      | ~ ( tc_IntDef_Oint @ ( B @ ( tc_IntDef_Oint @ ( A @ c_uminus ) @ c_Divides_Oop_Advd ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozminus__dvd__iff__iff1_0) ).

thf(528,plain,
    ! [B: $i,A: $i] :
      ( ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Advd ) ) )
      | ~ ( tc_IntDef_Oint @ ( B @ ( tc_IntDef_Oint @ ( A @ c_uminus ) @ c_Divides_Oop_Advd ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(274,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Union ) @ c_in ) ) )
      | ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Main_Ofinite__Union__1 ) @ c_in ) ) )
      | ~ ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Union_1) ).

thf(908,plain,
    ! [B: $i,A: $i] :
      ( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Union ) @ c_in ) ) )
      | ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Main_Ofinite__Union__1 ) @ c_in ) ) )
      | ~ ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(187,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsingletonD__dest_0) ).

thf(723,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(232,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
      | ~ ( C @ tc_set @ ( B @ ( A @ c_less ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OpsubsetE_0) ).

thf(822,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
      | ~ ( C @ tc_set @ ( B @ ( A @ c_less ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(246,axiom,
    ! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).

thf(850,plain,
    ! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(58,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = E )
      | ( ( D @ ( C @ ( B @ ( A @ c_Datatype__Universe_OScons ) ) ) )
       != ( D @ ( C @ ( F @ ( E @ c_Datatype__Universe_OScons ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__Scons__eq__iff1_0) ).

thf(442,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = E )
      | ( ( D @ ( C @ ( B @ ( A @ c_Datatype__Universe_OScons ) ) ) )
       != ( D @ ( C @ ( F @ ( E @ c_Datatype__Universe_OScons ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(12951,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) ) )
      | ( c_0 != c_0 )
      | ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(paramod_ordered,[status(thm)],[429,6785]) ).

thf(12952,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) ) )
      | ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(simp,[status(thm)],[12951]) ).

thf(12953,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
    inference(pattern_uni,[status(thm)],[12952:[bind(A,$thf( tc_nat @ ( G @ c_Suc @ ( D @ c_plus ) ) )),bind(B,$thf( D )),bind(C,$thf( G ))]]) ).

thf(13697,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
    inference(simp,[status(thm)],[12953]) ).

thf(189,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( D @ tc_set @ ( C @ ( A @ c_minus ) ) @ c_in ) ) )
      | ~ ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( D @ tc_set @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_minus ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff__insert__iff1_0) ).

thf(728,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( D @ tc_set @ ( C @ ( A @ c_minus ) ) @ c_in ) ) )
      | ~ ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( D @ tc_set @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_minus ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(195,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ tc_set @ ( A @ ( C @ c_lessequals ) ) )
      | ~ ( B @ tc_set @ ( B @ tc_set @ ( C @ c_uminus ) @ ( B @ tc_set @ ( A @ c_uminus ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff__iff1_0) ).

thf(740,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ tc_set @ ( A @ ( C @ c_lessequals ) ) )
      | ~ ( B @ tc_set @ ( B @ tc_set @ ( C @ c_uminus ) @ ( B @ tc_set @ ( A @ c_uminus ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(3958,plain,
    ! [A: $i] :
      ( ( A != c_UNIV )
      | ( c_0 != c_0 )
      | ~ ( tc_IntDef_Oint @ ( c_Finite__Set_OFinites @ ( c_0 @ c_Divides_Oop_Advd ) ) )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(paramod_ordered,[status(thm)],[355,2381]) ).

thf(3959,plain,
    ! [A: $i] :
      ( ( A != c_UNIV )
      | ~ ( tc_IntDef_Oint @ ( c_Finite__Set_OFinites @ ( c_0 @ c_Divides_Oop_Advd ) ) )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(simp,[status(thm)],[3958]) ).

thf(3960,plain,
    ( ~ ( tc_IntDef_Oint @ ( c_Finite__Set_OFinites @ ( c_0 @ c_Divides_Oop_Advd ) ) )
    | ~ ( tc_nat @ ( c_0 @ ( c_UNIV @ c_lessequals ) ) ) ),
    inference(pattern_uni,[status(thm)],[3959:[bind(A,$thf( c_UNIV ))]]) ).

thf(13136,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( tc_nat @ ( C @ ( B @ c_plus ) ) ) )
      | ( ( c_0 @ c_Suc )
       != B )
      | ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(paramod_ordered,[status(thm)],[429,7667]) ).

thf(13137,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_0 @ c_Suc )
       != A )
      | ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(pattern_uni,[status(thm)],[13136:[bind(A,$thf( tc_nat @ ( E @ ( D @ c_plus ) ) )),bind(B,$thf( D )),bind(C,$thf( E ))]]) ).

thf(13757,plain,
    ! [A: $i] :
      ~ ( tc_nat @ ( tc_nat @ ( A @ ( c_0 @ c_Suc @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
    inference(simp,[status(thm)],[13137]) ).

thf(14170,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ ( c_0 @ ( A @ c_Divides_Oop_Advd ) ) )
       != ( tc_nat @ ( tc_nat @ ( B @ ( c_0 @ c_Suc @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[398,13757]) ).

thf(14171,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( c_0 @ ( A @ c_Divides_Oop_Advd ) ) )
     != ( tc_nat @ ( tc_nat @ ( B @ ( c_0 @ c_Suc @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(simp,[status(thm)],[14170]) ).

thf(14223,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat != tc_nat )
      | ( ( tc_nat @ ( B @ ( c_0 @ c_Suc @ c_plus ) ) )
       != c_0 )
      | ( A != c_0 ) ),
    inference(simp,[status(thm)],[14171]) ).

thf(14237,plain,
    ! [A: $i] :
      ( ( tc_nat @ ( A @ ( c_0 @ c_Suc @ c_plus ) ) )
     != c_0 ),
    inference(simp,[status(thm)],[14223]) ).

thf(3625,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) )
       != ( E @ ( D @ ( C @ c_append ) ) ) )
      | ( ( A @ ( E @ ( C @ sk2 ) ) )
        = D ) ),
    inference(paramod_ordered,[status(thm)],[416,3624]) ).

thf(3626,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( c_List_Olist_ONil @ sk2 ) ) )
      = A ),
    inference(pattern_uni,[status(thm)],[3625:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( c_List_Olist_ONil )),bind(D,$thf( A )),bind(E,$thf( B ))]]) ).

thf(287,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_emptyset )
      | ( c_emptyset
       != ( C @ ( B @ ( A @ c_Equiv__Relations_Oquotient ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Equiv__Relations_Oquotient__is__empty2__iff1_0) ).

thf(935,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_emptyset )
      | ( c_emptyset
       != ( C @ ( B @ ( A @ c_Equiv__Relations_Oquotient ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(923,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ),
    inference(polarity_switch,[status(thm)],[922]) ).

thf(13142,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( B @ c_Suc ) )
      | ( c_0 != c_0 )
      | ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(paramod_ordered,[status(thm)],[429,338]) ).

thf(13143,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( B @ c_Suc ) )
      | ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(simp,[status(thm)],[13142]) ).

thf(13144,plain,
    ! [A: $i] :
      ~ ( tc_nat @ ( A @ c_Suc @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
    inference(pattern_uni,[status(thm)],[13143:[bind(A,$thf( C @ c_Suc )),bind(B,$thf( C ))]]) ).

thf(13760,plain,
    ! [A: $i] :
      ~ ( tc_nat @ ( A @ c_Suc @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
    inference(simp,[status(thm)],[13144]) ).

thf(2689,plain,
    ! [A: $i] :
      ( ( A != tc_Product__Type_Ounit )
      | ( c_0 @ class_Finite__Set_Ofinite )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(paramod_ordered,[status(thm)],[350,537]) ).

thf(2690,plain,
    ( ( c_0 @ class_Finite__Set_Ofinite )
    | ( tc_nat @ ( tc_Product__Type_Ounit @ ( c_0 @ c_less ) ) ) ),
    inference(pattern_uni,[status(thm)],[2689:[bind(A,$thf( tc_Product__Type_Ounit ))]]) ).

thf(106,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( E @ ( D @ ( B @ ( A @ ( C @ c_Main_OImageE__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( E @ ( E @ ( D @ ( C @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImageE_1) ).

thf(543,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( E @ ( D @ ( B @ ( A @ ( C @ c_Main_OImageE__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( E @ ( E @ ( D @ ( C @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(362,plain,
    ? [A: $i > $i > $i > $i] :
    ! [B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( D @ ( B @ A ) ) )
      = C ),
    inference(detectInverse,[status(thm)],[361]) ).

thf(363,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( C @ ( A @ sk3 ) ) )
      = B ),
    inference(cnf,[status(esa)],[362]) ).

thf(5569,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( C @ ( A @ sk3 ) ) )
      = B ),
    inference(lifteq,[status(thm)],[363]) ).

thf(143,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ tc_prod ) @ ( D @ ( C @ ( E @ c_Relation_Oconverse ) ) @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Oconverse__iff__iff2_0) ).

thf(639,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ tc_prod ) @ ( D @ ( C @ ( E @ c_Relation_Oconverse ) ) @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(201,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ tc_sum ) @ ( C @ ( D @ ( B @ ( E @ c_Sum__Type_OPlus ) ) ) @ ( D @ ( C @ ( A @ c_Sum__Type_OInr ) ) @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInrI_0) ).

thf(755,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ tc_sum ) @ ( C @ ( D @ ( B @ ( E @ c_Sum__Type_OPlus ) ) ) @ ( D @ ( C @ ( A @ c_Sum__Type_OInr ) ) @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(2344,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ ( A @ c_Suc @ ( A @ c_less ) ) )
       != ( tc_nat @ ( B @ ( B @ c_less ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[580,575]) ).

thf(2345,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( A @ c_Suc @ ( A @ c_less ) ) )
     != ( tc_nat @ ( B @ ( B @ c_less ) ) ) ),
    inference(simp,[status(thm)],[2344]) ).

thf(2347,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat != tc_nat )
      | ( ( A @ c_Suc )
       != B )
      | ( A != B ) ),
    inference(simp,[status(thm)],[2345]) ).

thf(2351,plain,
    ! [A: $i] :
      ( ( A @ c_Suc )
     != A ),
    inference(simp,[status(thm)],[2347]) ).

thf(62,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( D @ tc_prod ) @ ( B @ ( D @ ( A @ ( C @ c_Wellfounded__Relations_Olex__prod ) ) ) @ c_Wellfounded__Recursion_Owf ) )
      | ~ ( D @ ( C @ c_Wellfounded__Recursion_Owf ) )
      | ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Owf__lex__prod_0) ).

thf(454,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( D @ tc_prod ) @ ( B @ ( D @ ( A @ ( C @ c_Wellfounded__Relations_Olex__prod ) ) ) @ c_Wellfounded__Recursion_Owf ) )
      | ~ ( D @ ( C @ c_Wellfounded__Recursion_Owf ) )
      | ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(180,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( E @ ( D @ ( E @ ( D @ ( A @ ( C @ c_Main_OusumE__2 ) ) ) @ c_Datatype__Universe_OIn1 ) ) ) )
      | ( A
        = ( E @ ( D @ ( E @ ( D @ ( A @ ( B @ c_Main_OusumE__1 ) ) ) @ c_Datatype__Universe_OIn0 ) ) ) )
      | ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ousum ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OusumE_0) ).

thf(708,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( E @ ( D @ ( E @ ( D @ ( A @ ( C @ c_Main_OusumE__2 ) ) ) @ c_Datatype__Universe_OIn1 ) ) ) )
      | ( A
        = ( E @ ( D @ ( E @ ( D @ ( A @ ( B @ c_Main_OusumE__1 ) ) ) @ c_Datatype__Universe_OIn0 ) ) ) )
      | ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ousum ) ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(70,axiom,
    ! [A: $i] :
      ( ~ ( A @ class_Finite__Set_Ofinite )
      | ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Datatype__Ooption_0) ).

thf(469,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Finite__Set_Ofinite )
      | ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(775,plain,
    ! [A: $i] :
      ( ( A @ ( c_emptyset @ ( c_emptyset @ c_union ) ) )
      = c_emptyset ),
    inference(lifteq,[status(thm)],[774]) ).

thf(112,axiom,
    ! [C: $i,B: $i,A: $i] :
      ~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olex ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( A @ ( c_List_Olist_ONil @ c_Pair ) ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__notin__lex__iff1_0) ).

thf(560,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olex ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( A @ ( c_List_Olist_ONil @ c_Pair ) ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(23,axiom,
    ! [A: $i] :
      ( ( A @ ( c_List_Olist_ONil @ ( c_List_Olist_ONil @ c_append ) ) )
      = c_List_Olist_ONil ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv__iff2_0) ).

thf(364,plain,
    ! [A: $i] :
      ( ( A @ ( c_List_Olist_ONil @ ( c_List_Olist_ONil @ c_append ) ) )
      = c_List_Olist_ONil ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(23284,plain,
    $false,
    inference(e,[status(thm)],[645,629,9273,2072,479,333,2559,941,2331,666,9222,352,962,468,408,12634,683,730,2381,9704,308,13672,449,677,861,9621,2512,582,878,440,655,2195,385,10433,550,2918,797,715,6727,472,814,698,340,538,12816,670,747,913,898,417,885,301,1703,2531,651,829,404,1709,719,838,917,802,372,3495,2897,12819,7665,460,902,853,2403,6502,325,8615,316,2533,1232,4492,606,5323,881,416,924,789,591,646,485,514,2540,806,353,821,9071,321,348,574,7931,634,692,734,774,660,411,3226,1975,397,687,866,7936,396,1526,312,3492,307,920,661,761,810,381,366,1736,714,512,439,2910,6731,793,910,302,2969,424,429,957,894,825,7870,13335,778,407,693,9217,361,879,329,889,493,757,456,324,847,4280,484,583,2200,522,461,4746,948,615,14866,2692,388,356,593,869,610,420,499,519,742,578,874,2157,471,488,339,3622,753,476,1424,526,637,706,4721,537,2472,679,393,8599,515,911,721,6346,569,1715,779,371,605,2370,622,837,343,792,938,508,311,9716,657,398,558,2915,530,953,586,926,3624,4625,765,1054,906,750,430,824,689,4017,2729,412,11837,425,3871,2149,375,733,819,402,3636,4283,843,711,545,413,562,904,391,9285,572,313,713,335,2166,804,704,350,641,8601,3487,466,979,406,681,3155,784,419,1524,736,377,451,303,2378,831,7933,737,318,509,649,5093,434,477,494,816,323,483,7654,2874,915,769,6802,932,2578,811,387,345,858,367,552,799,726,700,520,2553,668,2461,330,685,2075,399,959,5094,868,883,608,3016,851,653,922,6785,3490,505,438,426,589,944,795,374,812,342,355,553,968,490,675,4749,776,690,872,707,887,414,327,954,310,525,9879,580,855,1711,11066,673,791,441,717,502,463,338,576,3623,359,643,585,370,840,7667,951,808,744,336,703,613,864,4748,600,978,386,12054,595,497,876,845,465,9279,627,2088,671,581,759,891,368,771,482,4763,517,896,304,946,3748,5010,781,7996,351,418,786,2009,1689,929,6521,763,383,899,8267,13793,378,433,510,667,3598,2462,620,9551,447,315,432,405,422,833,967,950,835,564,305,5092,358,3875,437,664,8277,828,532,696,955,474,767,8268,2223,928,415,332,575,427,528,459,908,723,822,850,442,2270,501,13697,728,740,3960,322,14237,3626,935,923,13760,2690,543,5569,639,755,2351,454,708,972,469,940,775,560,3443,6722,364]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SET839-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.08  % 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
% 0.15/0.41  % Computer : n007.cluster.edu
% 0.15/0.41  % Model    : x86_64 x86_64
% 0.15/0.41  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41  % Memory   : 8046.5625MB
% 0.15/0.41  % OS       : Linux 6.8.0-71-generic
% 0.15/0.41  % CPULimit : 300
% 0.15/0.41  % WCLimit  : 300
% 0.15/0.41  % DateTime : Sat Sep 26 08:18:09 UTC 2026
% 0.15/0.41  % CPUTime  : 
% 0.15/0.41  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
% 0.94/1.27  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 2.03/1.85  % [INFO] 	 Parsing done (568ms). 
% 2.03/1.87  % [INFO] 	 Running in sequential loop mode. 
% 3.17/2.52  % [INFO] 	 eprover registered as external prover. 
% 3.17/2.54  % [INFO] 	 Scanning for conjecture ... 
% 3.73/2.84  % [INFO] 	 Found a conjecture (or negated_conjecture) and 1357 axioms. Running axiom selection ... 
% 4.12/3.18  % [INFO] 	 Axiom selection finished. Selected 298 axioms (removed 1059 axioms). 
% 5.30/3.52  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 5.30/3.54  % [INFO] 	 Type checking passed. 
% 5.30/3.56  % [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 ... 
% 75.54/28.44  % External prover 'e' found a proof!
% 75.54/28.44  % [INFO] 	 Killing All external provers ... 
% 75.54/28.45  % Time passed: 27789ms (effective reasoning time: 26577ms)
% 75.54/28.46  % Axioms used in derivation (298): cls_List_Olistrel__Cons1_0, cls_Finite__Set_Ofinite__converse__iff1_0, cls_IntDiv_Ozdvd__0__right_0, cls_Finite__Set_Ofinite__Union_0, cls_Datatype__Universe_Ousum__In1I_0, cls_Datatype__Universe_OuprodI_0, cls_Nat_Ole__0__eq__iff1_0, cls_SetInterval_OgreaterThan__subset__iff__iff1_0, cls_List_Ofinite__set_0, cls_Finite__Set_Ofinite__Un__iff1_1, cls_Datatype__Universe_OdprodE_0, cls_SetInterval_OlessThan__iff__iff2_0, cls_List_Oset__empty2__iff2_0, cls_List_Oappend__in__lists__conv__iff2_0, cls_Datatype__Universe_Odsum__In0I_0, cls_List_Oset__empty2__iff1_0, cls_List_ONil__notin__lex__iff1_0, cls_Relation_OImageI_0, cls_List_Olistrel__Cons2_1, cls_SetInterval_OatLeast__subset__iff__iff2_0, cls_Set_OsubsetI_1, cls_Sum__Type_OInr__not__Inl__iff1_0, clsarity_prod_0, cls_List_Olists_ONil_0, cls_Set_OInterD_0, cls_List_ONil__is__append__conv__iff2_0, cls_SetInterval_OgreaterThan__iff__iff2_0, clsarity_nat_7, cls_Sum__Type_OInr__eq__iff1_0, cls_Set_OemptyE_0, cls_Set_OUNIV__not__empty__iff1_0, cls_Wellfounded__Recursion_Oacyclic__insert__iff2_0, cls_Wellfounded__Recursion_Owf__insert__iff1_0, cls_Finite__Set_OFinites_OemptyI_0, cls_Wellfounded__Recursion_Oacyclic__converse__iff1_0, cls_List_Oappend__self__conv2__iff1_0, cls_Relation_OImageE_0, cls_Datatype__Universe_Ousum__In0I_0, cls_IntDiv_Ozdvd__0__left__iff2_0, clsrel_Orderings_Olinorder_4, cls_Nat_Oless__Suc0__iff1_0, cls_Set_Osingleton__insert__inj__eq__iff1_1, cls_Datatype__Universe_OusumE_2, cls_Datatype_Ooption_Oinject__iff1_0, cls_Transitive__Closure_Otrancl_Or__into__trancl_0, cls_Set_Osingleton__inject__dest_0, cls_Set_Osingleton__insert__inj__eq_H__iff1_1, cls_Set_OUnionE_1, cls_Nat_Oadd__is__0__iff1_1, clsarity_sum_0, cls_Nat_Oless__irrefl_0, cls_IntDiv_Ozminus__dvd__iff__iff1_0, clsarity_set_2, cls_Nat_Onot__less0__iff1_0, cls_Finite__Set_OFinites_OinsertI_0, cls_Wellfounded__Relations_Owf__lex__prod_0, cls_List_Olistrel__Nil1_0, clsarity_nat_3, cls_Datatype__Universe_OIn1__eq__iff1_0, cls_Set_OComplI_0, cls_Relation_OconverseE_1, cls_Finite__Set_Ofinite__Int_0, cls_Nat_Oadd__gr__0__iff2_0, cls_SetInterval_Ofinite__atLeastLessThan__int_0, cls_Nat_Oneq0__conv__iff2_0, cls_Sum__Type_OPlusE_0, cls_Nat_Oadd__is__0__iff2_0, cls_List_ONil__is__append__conv__iff1_0, cls_Relation_Orel__compE_0, cls_Finite__Set_Ofinite__Pow__iff__iff1_0, cls_Wellfounded__Recursion_Oacyclic__insert__iff1_1, cls_Sum__Type_OInlI_0, clsarity_IntDef__Oint_0, cls_Infinite__Set_Onat__not__finite_0, cls_Set_OpsubsetI_0, cls_Relation_Oconverse__iff__iff2_0, cls_Set_Osubset__refl_0, cls_List_Olist_Oinject__iff1_0, cls_Relation_ORangeE_0, cls_SetInterval_OlessThan__iff__iff1_0, cls_Set_OInterI_1, cls_Nat_OSuc__Suc__eq__iff1_0, cls_List_Oset__empty__iff2_0, cls_Set_OUnCI_1, cls_Product__Type_OPair__eq__iff1_0, cls_Set_OinsertCI_0, cls_SetInterval_Ofinite__greaterThanAtMost_0, clsarity_IntDef__Oint_35, cls_Set_Osingleton__insert__inj__eq_H__iff2_0, cls_Set_OPow__iff__iff2_0, cls_List_Oappend__in__lists__conv__iff1_0, cls_Finite__Set_Ofinite__converse__iff2_0, cls_SetInterval_OatMost__iff__iff2_0, cls_SetInterval_Ofinite__greaterThanAtMost__int_0, cls_Nat_Ole__0__eq__iff2_0, cls_Datatype__Universe_OIn0__not__In1__iff1_0, cls_Relation_OdiagI_0, cls_Set_OCompl__subset__Compl__iff__iff2_0, cls_Datatype__Universe_OdprodE_1, cls_Set_OUNIV__I_0, cls_Set_OCompl__eq__Compl__iff__iff1_0, cls_Set_OsubsetI_0, cls_Sum__Type_OPlusE_3, cls_Finite__Set_Ofinite__Diff__insert__iff1_0, cls_List_OlistsE_0, cls_List_Olength__0__conv__iff2_0, cls_Divides_Odvd__0__left__iff__iff2_0, cls_Finite__Set_Ofinite__Un__iff1_0, cls_List_Oself__append__conv__iff2_0, cls_Relation_ODomainI_0, cls_Set_OinsertE_0, cls_Set_Onot__psubset__empty__iff1_0, cls_Set_OUnE_0, cls_SetInterval_OlessThan__subset__iff__iff2_0, cls_List_Owf__lex_0, cls_SetInterval_OatMost__eq__iff__iff1_0, cls_List_Olistrel__Cons2_0, cls_SetInterval_OgreaterThan__subset__iff__iff2_0, cls_Datatype__Universe_OusumE_1, cls_Set_OComplD__dest_0, cls_Set_OUn__empty__iff1_1, cls_Relation_Orel__compE_2, cls_Nat_OZero__not__Suc__iff1_0, cls_Relation_OImageE_1, cls_Relation_OdiagE_0, cls_Set_OsingletonD__dest_0, clsarity_set_3, cls_SetInterval_Ofinite__atLeastAtMost_0, cls_SetInterval_OatMost__subset__iff__iff2_0, cls_SetInterval_OatLeast__subset__iff__iff1_0, cls_SetInterval_Ofinite__atLeastLessThan_0, cls_Set_OUn__empty__iff1_0, cls_Transitive__Closure_Ortrancl_Ortrancl__refl_0, cls_Wellfounded__Recursion_Owf__insert__iff2_0, cls_Set_Oempty__subsetI_0, cls_Finite__Set_Ofinite__Int_1, cls_Relation_OIdI_0, cls_SetInterval_OlessThan__eq__iff__iff1_0, clsarity_IntDef__Oint_31, cls_List_Oappend__is__Nil__conv__iff2_0, cls_SetInterval_Ofinite__atLeastAtMost__int_0, cls_Nat_OSuc__less__eq__iff2_0, cls_Divides_Odvd__0__left__iff__iff1_0, cls_SetInterval_Ofinite__lessThan_0, cls_List_Olength__greater__0__conv__iff1_0, cls_List_Oappend1__eq__conv__iff1_1, cls_Set_OsubsetD_0, cls_Product__Type_OPair__eq__iff1_1, cls_Nat_Oadd__gr__0__iff2_1, cls_List_Osame__append__eq__iff1_0, cls_Set_OsingletonI_0, cls_Nat_Oless__Suc0__iff2_0, cls_Wellfounded__Relations_Oless__than__iff__iff1_0, cls_Set_Osubset__antisym_0, cls_Wellfounded__Recursion_Oacyclic__insert__iff1_0, cls_List_Oself__append__conv__iff1_0, cls_SetInterval_OatLeast__iff__iff2_0, cls_Nat_Ozero__less__Suc_0, cls_List_Oin__listsI_1, cls_SetInterval_OatMost__subset__iff__iff1_0, cls_Datatype_Oelem__o2s__iff1_0, cls_Relation_OconverseE_0, cls_List_Olength__greater__0__conv__iff2_0, cls_Datatype__Universe_OuprodE_2, clsrel_Orderings_Oorder_0, cls_SetInterval_Ofinite__greaterThanLessThan__int_0, cls_Relation_Oconverse__iff__iff1_0, cls_Datatype__Universe_OIn1__not__In0__iff1_0, cls_Datatype__Universe_OScons__Scons__eq__iff1_0, cls_List_Olist_Oinject__iff1_1, cls_Datatype__Universe_OuprodE_0, cls_Equiv__Relations_Oquotient__is__empty__iff2_0, cls_Set_ODiffE_0, cls_Datatype__Universe_OusumE_0, cls_SetInterval_OatMost__iff__iff1_0, cls_Datatype_Oelem__o2s__iff2_0, cls_SetInterval_OgreaterThan__eq__iff__iff1_0, cls_Sum__Type_OInl__not__Inr__iff1_0, cls_Infinite__Set_Oatmost__one__unique_0, clsarity_set_1, cls_Datatype__Universe_OdprodE_2, cls_Relation_ORangeI_0, cls_List_Oset__empty__iff1_0, cls_Nat_OSuc__le__mono__iff1_0, cls_List_Oself__append__conv2__iff2_0, cls_Set_OIntE_1, cls_Relation_Opair__in__Id__conv__iff1_0, cls_Nat_Onot__add__less1__iff1_0, cls_Set_OIntI_0, cls_Finite__Set_Ofinite__Union_1, cls_Sum__Type_OPlusE_2, cls_Set_Osingleton__insert__inj__eq__iff2_0, cls_IntDiv_Ozdvd__0__left__iff1_0, cls_Wellfounded__Relations_Oless__than__iff__iff2_0, cls_Equiv__Relations_Oquotient__is__empty__iff1_0, cls_Nat_Oadd__gr__0__iff1_0, cls_Divides_Odvd__0__right_0, cls_IntDef_Oint__int__eq__iff1_0, cls_IntDiv_Odvd__zminus__iff__iff1_0, cls_Wellfounded__Recursion_Owf__empty_0, cls_Wellfounded__Relations_Owf__less__than_0, cls_List_Olist_Odistinct__2__iff1_0, cls_Transitive__Closure_Or__into__rtrancl_0, cls_Finite__Set_Ofinite__Diff__insert__iff2_0, cls_Datatype__Universe_OdprodI_0, cls_SetInterval_Ofinite__greaterThanLessThan_0, clsarity_fun_1, cls_List_Olistrel__Cons1_2, cls_List_OlistsE_1, cls_List_Oappend__self__conv2__iff2_0, clsarity_nat_12, cls_Nat_OSuc__le__mono__iff2_0, cls_IntDiv_Odvd__zminus__iff__iff2_0, cls_List_Oappend__self__conv__iff2_0, cls_SetInterval_OgreaterThan__iff__iff1_0, cls_List_Oappend__same__eq__iff1_0, cls_Equiv__Relations_Oquotient__is__empty2__iff1_0, clsarity_IntDef__Oint_5, cls_Set_OCompl__subset__Compl__iff__iff1_0, cls_Set_ODiffI_0, cls_Orderings_Oorder__less__irrefl__iff1_0, cls_Sum__Type_OInrI_0, cls_Datatype__Universe_Odsum__In1I_0, clsarity_IntDef__Oint_62, cls_Set_OUn__empty__iff2_0, cls_Datatype__Universe_OuprodE_1, cls_Set_OpsubsetE_0, cls_Set_OUnionI_0, cls_Datatype__Universe_OScons__Scons__eq__iff1_1, cls_List_Olistrel__Nil2_0, cls_Relation_Orel__compI_0, cls_Finite__Set_Ofinite__Pow__iff__iff2_0, cls_List_Oappend__is__Nil__conv__iff1_0, cls_Datatype__Universe_OIn0__eq__iff1_0, cls_Wellfounded__Recursion_Oacyclic__converse__iff2_0, cls_Nat_OSuc__less__eq__iff1_0, cls_Relation_OdiagE_1, clsarity_nat_9, cls_Relation_OImage__singleton__iff__iff1_0, cls_List_ONil2__notin__lex__iff1_0, cls_List_Oself__append__conv2__iff1_0, cls_Nat_Oneq0__conv__iff1_0, cls_List_Olist_Odistinct__1__iff1_0, clsarity_bool_0, cls_List_Olistrel__Cons1_1, cls_Nat_Oadd__is__0__iff1_0, cls_Set_OInterI_0, cls_List_Olistrel__Cons2_2, cls_SetInterval_OatLeast__eq__iff__iff1_0, cls_Orderings_Oorder__class_Oaxioms__1_0, clsarity_Product____Type__Ounit_0, cls_IntDef_Onegative__zle_0, cls_Sum__Type_OPlusE_1, cls_Set_OUnionE_0, cls_Relation_ODomainE_0, clsrel_Orderings_Olinorder_3, cls_List_Oin__listsI_0, cls_Divides_Odvd__1__left_0, cls_SetInterval_OatLeast__iff__iff1_0, cls_Wellfounded__Recursion_Owf__insert__iff1_1, cls_List_Oappend1__eq__conv__iff1_0, clsarity_set_0, clsarity_Datatype__Ooption_0, cls_Nat_OSuc__not__Zero__iff1_0, cls_List_Oin__listsD__dest_0, cls_Set_OPow__iff__iff1_0, cls_Nat_Ole0_0, cls_Set_Osingleton__insert__inj__eq__iff1_0, cls_Sum__Type_OInl__eq__iff1_0, cls_Set_Osingleton__insert__inj__eq_H__iff1_0, cls_Relation_OImage__singleton__iff__iff2_0, cls_Datatype__Universe_OusumE_3, cls_List_Olength__0__conv__iff1_0, cls_List_Owf__lenlex_0, clsarity_fun_0, cls_Relation_OIdE_0, clsarity_nat_2, cls_Set_OpsubsetE_1, cls_Nat_OlessI_0, cls_SetInterval_Ofinite__atMost_0, cls_Equiv__Relations_Oquotient__is__empty2__iff2_0, cls_Set_OIntE_0, cls_Relation_Orel__compE_1, clsarity_set_4, cls_List_Oappend__is__Nil__conv__iff1_1, cls_Finite__Set_Ofinite__Un__iff2_0, cls_Nat_Onot__add__less2__iff1_0, cls_Set_OinsertCI_1, cls_Set_ODiffE_1, cls_IntDef_Onegative__zless_0, cls_List_ONil__is__append__conv__iff1_1, cls_Transitive__Closure_Otrancl__into__rtrancl_0, cls_List_Oappend__self__conv__iff1_0, cls_IntDiv_Ozminus__dvd__iff__iff2_0, cls_Set_OUnCI_0, cls_List_Olists_OCons_0, cls_List_Oappend__in__lists__conv__iff1_1, cls_SetInterval_OlessThan__subset__iff__iff1_0
% 75.54/28.46  % No. of inferences in proof: 1115
% 75.54/28.46  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 27789 ms resp. 26577 ms w/o parsing
% 75.02/29.07  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 75.02/29.09  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------