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

%------------------------------------------------------------------------------
% File     : Leo-III---1.8.0
% Problem  : SWV263-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39

% Computer : n009.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 08:58:37 AM UTC 2026

% Result   : Unsatisfiable 11.15s 8.92s
% Output   : Refutation 12.06s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :  297
% Syntax   : Number of formulae    :  595 ( 173 unt;   0 typ;   0 def)
%            Number of atoms       : 1127 ( 282 equ;   0 cnn)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives : 7074 ( 542   ~; 532   |;   0   &;6000   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (   9 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  112 ( 110 usr;  16 con; 0-6 aty)
%            Number of variables   : 1688 (   0   ^;1688   !;   0   ?;1688   :)

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

thf(v_G_decl,type,
    v_G: $i ).

thf(v_H_decl,type,
    v_H: $i ).

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

thf(tc_Message_Omsg_decl,type,
    tc_Message_Omsg: $i ).

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

thf(v_X_decl,type,
    v_X: $i ).

thf(c_Message_Oparts_decl,type,
    c_Message_Oparts: $i > $i ).

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

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

thf(c_0_decl,type,
    c_0: $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_Wellfounded__Recursion_Owf_decl,type,
    c_Wellfounded__Recursion_Owf: $i > $i > $o ).

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

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

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

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

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

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

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

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

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

thf(c_List_Olex_decl,type,
    c_List_Olex: $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(tc_IntDef_Oint_decl,type,
    tc_IntDef_Oint: $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(class_Orderings_Olinorder_decl,type,
    class_Orderings_Olinorder: $i > $o ).

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

thf(c_Message_Omsg_OCrypt_decl,type,
    c_Message_Omsg_OCrypt: $i > $i > $i ).

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

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

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

thf(c_Message_Omsg_OMPair_decl,type,
    c_Message_Omsg_OMPair: $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(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_UNIV_decl,type,
    c_UNIV: $i ).

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

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

thf(c_Main_OImageE__1_decl,type,
    c_Main_OImageE__1: $i > $i > $i > $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_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_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_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_Main_Oin__listsI__1_decl,type,
    c_Main_Oin__listsI__1: $i > $i > $i > $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(264,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/sandbox2/benchmark/theBenchmark.p',cls_Set_OInterD_0) ).

thf(892,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)],[264]) ).

thf(77,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/sandbox2/benchmark/theBenchmark.p',cls_List_Oin__listsD__dest_0) ).

thf(479,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)],[77]) ).

thf(140,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/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert__iff2_0) ).

thf(628,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)],[140]) ).

thf(70,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/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Odvd__zminus__iff__iff2_0) ).

thf(468,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)],[70]) ).

thf(288,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/sandbox2/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)],[288]) ).

thf(110,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/sandbox2/benchmark/theBenchmark.p',cls_List_OlistsE_1) ).

thf(555,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)],[110]) ).

thf(78,axiom,
    tc_IntDef_Oint @ class_Orderings_Olinorder,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_35) ).

thf(481,plain,
    tc_IntDef_Oint @ class_Orderings_Olinorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(121,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/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq__iff1_1) ).

thf(582,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)],[121]) ).

thf(34,axiom,
    ! [B: $i,A: $i] :
      ( ( B = c_0 )
      | ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
       != c_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0__iff1_1) ).

thf(379,plain,
    ! [B: $i,A: $i] :
      ( ( B = c_0 )
      | ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
       != c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(249,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( C @ tc_set @ ( B @ ( A @ c_less ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OpsubsetE_1) ).

thf(861,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)],[249]) ).

thf(255,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/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_1) ).

thf(873,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)],[255]) ).

thf(63,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/sandbox2/benchmark/theBenchmark.p',clsarity_prod_0) ).

thf(449,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)],[63]) ).

thf(60,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/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__iff__iff2_0) ).

thf(440,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)],[60]) ).

thf(91,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/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Odsum__In0I_0) ).

thf(511,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)],[91]) ).

thf(36,axiom,
    ! [A: $i] :
      ( c_List_Olist_ONil
      = ( A @ ( c_List_Olist_ONil @ ( c_List_Olist_ONil @ c_append ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv__iff2_0) ).

thf(385,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)],[36]) ).

thf(175,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/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastAtMost_0) ).

thf(715,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)],[175]) ).

thf(166,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/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozminus__dvd__iff__iff2_0) ).

thf(698,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)],[166]) ).

thf(193,axiom,
    ! [A: $i] : ( A @ tc_set @ class_Nat_Opower ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_4) ).

thf(747,plain,
    ! [A: $i] : ( A @ tc_set @ class_Nat_Opower ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(103,axiom,
    tc_IntDef_Oint @ class_Orderings_Oord,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_5) ).

thf(538,plain,
    tc_IntDef_Oint @ class_Orderings_Oord,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(283,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( B @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts_OSnd_0) ).

thf(930,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( B @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(267,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/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_0) ).

thf(898,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)],[267]) ).

thf(172,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ tc_set @ ( A @ c_uminus ) )
       != ( B @ tc_set @ ( C @ c_uminus ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__eq__Compl__iff__iff1_0) ).

thf(709,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)],[172]) ).

thf(51,axiom,
    ! [B: $i,A: $i] :
      ( ( A = c_0 )
      | ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
       != c_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0__iff1_0) ).

thf(417,plain,
    ! [B: $i,A: $i] :
      ( ( A = c_0 )
      | ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
       != c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(260,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/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodI_0) ).

thf(885,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)],[260]) ).

thf(58,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_List_Olist_ONil )
      | ( A
       != ( C @ ( B @ ( A @ c_append ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oself__append__conv__iff1_0) ).

thf(436,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)],[58]) ).

thf(148,axiom,
    ! [B: $i,A: $i] :
      ~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Onot__psubset__empty__iff1_0) ).

thf(651,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(233,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/sandbox2/benchmark/theBenchmark.p',cls_Relation_Orel__compE_1) ).

thf(829,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)],[233]) ).

thf(44,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/sandbox2/benchmark/theBenchmark.p',clsarity_fun_0) ).

thf(404,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)],[44]) ).

thf(11,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/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Nil2_0) ).

thf(320,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)],[11]) ).

thf(115,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/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv__iff2_0) ).

thf(565,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)],[115]) ).

thf(118,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_IntDef_Oint )
       != ( B @ c_IntDef_Oint ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__int__eq__iff1_0) ).

thf(570,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_IntDef_Oint )
       != ( B @ c_IntDef_Oint ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(178,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/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).

thf(719,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)],[178]) ).

thf(31,axiom,
    ! [A: $i] :
      ( ( A @ ( c_List_Olist_ONil @ ( c_List_Olist_ONil @ c_append ) ) )
      = c_List_Olist_ONil ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv__iff2_0) ).

thf(372,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)],[31]) ).

thf(122,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/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Odvd__zminus__iff__iff1_0) ).

thf(587,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)],[122]) ).

thf(277,axiom,
    ! [A: $i] :
      ( ~ ( A @ class_Finite__Set_Ofinite )
      | ( A @ tc_set @ class_Finite__Set_Ofinite ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_3) ).

thf(917,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(196,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/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onegative__zle_0) ).

thf(751,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)],[196]) ).

thf(220,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/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Union_0) ).

thf(802,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)],[220]) ).

thf(21,axiom,
    ! [A: $i] : ( tc_nat @ ( A @ ( c_0 @ c_Suc @ c_Divides_Oop_Advd ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__1__left_0) ).

thf(344,plain,
    ! [A: $i] : ( tc_nat @ ( A @ ( c_0 @ c_Suc @ c_Divides_Oop_Advd ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(245,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/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanLessThan__int_0) ).

thf(853,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)],[245]) ).

thf(253,axiom,
    ! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).

thf(870,plain,
    ! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(130,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_less ) ) )
      | ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__less__eq__iff2_0) ).

thf(606,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)],[130]) ).

thf(14,axiom,
    ! [A: $i] :
      ~ ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__less0__iff1_0) ).

thf(325,plain,
    ! [A: $i] :
      ~ ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(258,axiom,
    ! [B: $i,A: $i] : ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_List_Oset ) @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ofinite__set_0) ).

thf(881,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)],[258]) ).

thf(50,axiom,
    tc_IntDef_Oint @ ( c_0 @ ( c_0 @ c_Divides_Oop_Advd ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__left__iff2_0) ).

thf(416,plain,
    tc_IntDef_Oint @ ( c_0 @ ( c_0 @ c_Divides_Oop_Advd ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

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/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInlI_0) ).

thf(924,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(84,axiom,
    ! [B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( B @ ( A @ c_List_Oset ) )
       != c_emptyset ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__empty__iff1_0) ).

thf(492,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)],[84]) ).

thf(214,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/sandbox2/benchmark/theBenchmark.p',cls_Relation_Orel__compE_2) ).

thf(789,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)],[214]) ).

thf(33,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__self__conv2__iff1_0) ).

thf(376,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)],[33]) ).

thf(147,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Datatype_Ooption_OSome ) )
       != ( B @ ( C @ c_Datatype_Ooption_OSome ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Ooption_Oinject__iff1_0) ).

thf(646,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)],[147]) ).

thf(81,axiom,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__add__less1__iff1_0) ).

thf(485,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(23,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != ( C @ ( D @ ( A @ c_append ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osame__append__eq__iff1_0) ).

thf(348,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)],[23]) ).

thf(222,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/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__iff__iff2_0) ).

thf(806,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)],[222]) ).

thf(24,axiom,
    ! [A: $i] :
      ( ( A = c_0 )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oneq0__conv__iff1_0) ).

thf(353,plain,
    ! [A: $i] :
      ( ( A = c_0 )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(270,axiom,
    ! [B: $i,A: $i] : ( B @ ( c_UNIV @ ( A @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUNIV__I_0) ).

thf(905,plain,
    ! [B: $i,A: $i] : ( B @ ( c_UNIV @ ( A @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(128,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/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__notin__lex__iff1_0) ).

thf(602,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)],[128]) ).

thf(164,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsingletonD__dest_0) ).

thf(692,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)],[164]) ).

thf(65,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/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__eq__iff__iff1_0) ).

thf(453,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)],[65]) ).

thf(41,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_List_Olist_ONil )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv__iff1_1) ).

thf(396,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)],[41]) ).

thf(55,axiom,
    tc_nat @ ( c_0 @ ( c_0 @ c_lessequals ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq__iff2_0) ).

thf(428,plain,
    tc_nat @ ( c_0 @ ( c_0 @ c_lessequals ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(243,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/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__subset__iff__iff1_0) ).

thf(849,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)],[243]) ).

thf(97,axiom,
    tc_nat @ class_Orderings_Oord,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_2) ).

thf(527,plain,
    tc_nat @ class_Orderings_Oord,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(8,axiom,
    tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Wellfounded__Recursion_Owf ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Owf__less__than_0) ).

thf(312,plain,
    tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Wellfounded__Recursion_Owf ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(6,axiom,
    ~ ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oneq0__conv__iff2_0) ).

thf(307,plain,
    ~ ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(59,axiom,
    tc_nat @ class_HOL_Ominus,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_9) ).

thf(439,plain,
    tc_nat @ class_HOL_Ominus,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(107,axiom,
    tc_IntDef_Oint @ class_HOL_Ominus,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_0) ).

thf(546,plain,
    tc_IntDef_Oint @ class_HOL_Ominus,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(201,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/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Or__into__rtrancl_0) ).

thf(761,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)],[201]) ).

thf(224,axiom,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OinsertCI_1) ).

thf(810,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(101,axiom,
    ! [A: $i] :
      ( c_emptyset
      = ( A @ ( c_List_Olist_ONil @ c_List_Oset ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__empty2__iff2_0) ).

thf(534,plain,
    ! [A: $i] :
      ( c_emptyset
      = ( A @ ( c_List_Olist_ONil @ c_List_Oset ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(174,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/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanAtMost_0) ).

thf(714,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)],[174]) ).

thf(218,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/sandbox2/benchmark/theBenchmark.p',cls_List_Oin__listsI_0) ).

thf(798,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)],[218]) ).

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/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_1) ).

thf(910,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(4,axiom,
    ! [B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) )
       != c_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__0__conv__iff1_0) ).

thf(302,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)],[4]) ).

thf(229,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/sandbox2/benchmark/theBenchmark.p',cls_Set_OIntE_0) ).

thf(820,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)],[229]) ).

thf(113,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/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Oless__than__iff__iff1_0) ).

thf(561,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)],[113]) ).

thf(39,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( c_List_Olist_ONil
       != ( C @ ( B @ ( A @ c_append ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv__iff1_0) ).

thf(392,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)],[39]) ).

thf(56,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != ( C @ ( B @ ( D @ c_append ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__same__eq__iff1_0) ).

thf(429,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)],[56]) ).

thf(183,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/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un__iff1_0) ).

thf(729,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)],[183]) ).

thf(296,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/sandbox2/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)],[296]) ).

thf(265,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/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff__iff2_0) ).

thf(894,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)],[265]) ).

thf(46,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
     != c_List_Olist_ONil ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Odistinct__2__iff1_0) ).

thf(407,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)],[46]) ).

thf(141,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Oorder_0) ).

thf(630,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(80,axiom,
    tc_IntDef_Oint @ class_Nat_Opower,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_62) ).

thf(484,plain,
    tc_IntDef_Oint @ class_Nat_Opower,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(27,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( c_List_Olist_ONil
     != ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Odistinct__1__iff1_0) ).

thf(361,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)],[27]) ).

thf(257,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__le__mono__iff2_0) ).

thf(879,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)],[257]) ).

thf(16,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_List_Olist_ONil )
      | ( c_List_Olist_ONil
       != ( C @ ( B @ ( A @ c_append ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv__iff1_1) ).

thf(329,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)],[16]) ).

thf(262,axiom,
    ! [A: $i] : ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OemptyI_0) ).

thf(889,plain,
    ! [A: $i] : ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(67,axiom,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__add__less2__iff1_0) ).

thf(461,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(199,axiom,
    ~ ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Infinite__Set_Onat__not__finite_0) ).

thf(757,plain,
    ~ ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(13,axiom,
    ! [A: $i] : ( A @ ( c_emptyset @ c_Wellfounded__Recursion_Owf ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__empty_0) ).

thf(324,plain,
    ! [A: $i] : ( A @ ( c_emptyset @ c_Wellfounded__Recursion_Owf ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(66,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
       != ( D @ ( C @ c_Message_Omsg_OCrypt ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__7__iff1_0) ).

thf(456,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
       != ( D @ ( C @ c_Message_Omsg_OCrypt ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(239,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
      | ~ ( C @ tc_set @ ( B @ ( A @ c_less ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OpsubsetE_0) ).

thf(842,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)],[239]) ).

thf(291,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/sandbox2/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)],[291]) ).

thf(181,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/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OusumE_3) ).

thf(725,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)],[181]) ).

thf(25,axiom,
    ( ( tc_nat @ ( c_0 @ ( c_0 @ c_plus ) ) )
    = c_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0__iff2_0) ).

thf(356,plain,
    ( ( tc_nat @ ( c_0 @ ( c_0 @ c_plus ) ) )
    = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(87,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/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn1__not__In0__iff1_0) ).

thf(499,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)],[87]) ).

thf(95,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
       != ( D @ ( C @ c_Message_Omsg_OMPair ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__6__iff1_1) ).

thf(519,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
       != ( D @ ( C @ c_Message_Omsg_OMPair ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(190,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/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastLessThan__int_0) ).

thf(742,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)],[190]) ).

thf(212,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/sandbox2/benchmark/theBenchmark.p',cls_Relation_OconverseE_1) ).

thf(783,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)],[212]) ).

thf(52,axiom,
    ! [A: $i] :
      ( ( A = c_0 )
      | ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__left__iff1_0) ).

thf(420,plain,
    ! [A: $i] :
      ( ( A = c_0 )
      | ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(72,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_less ) ) )
      | ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_less ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__less__eq__iff1_0) ).

thf(471,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)],[72]) ).

thf(156,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/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInl__eq__iff1_0) ).

thf(669,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)],[156]) ).

thf(124,axiom,
    ! [A: $i] :
      ( ( A @ ( c_List_Olist_ONil @ c_List_Oset ) )
      = c_emptyset ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__empty__iff2_0) ).

thf(590,plain,
    ! [A: $i] :
      ( ( A @ ( c_List_Olist_ONil @ c_List_Oset ) )
      = c_emptyset ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(108,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
       != ( D @ ( C @ c_Message_Omsg_OMPair ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__6__iff1_0) ).

thf(547,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
       != ( D @ ( C @ c_Message_Omsg_OMPair ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(268,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/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_3) ).

thf(901,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)],[268]) ).

thf(161,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/sandbox2/benchmark/theBenchmark.p',cls_Relation_Oconverse__iff__iff2_0) ).

thf(686,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)],[161]) ).

thf(75,axiom,
    ! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( c_0 @ c_less ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ozero__less__Suc_0) ).

thf(476,plain,
    ! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( c_0 @ c_less ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(168,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/sandbox2/benchmark/theBenchmark.p',cls_Relation_ORangeE_0) ).

thf(701,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)],[168]) ).

thf(93,axiom,
    tc_nat @ class_Orderings_Olinorder,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_7) ).

thf(515,plain,
    tc_nat @ class_Orderings_Olinorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(188,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts_OInj_0) ).

thf(738,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(150,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/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Oless__than__iff__iff2_0) ).

thf(654,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)],[150]) ).

thf(179,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/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__converse__iff2_0) ).

thf(721,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)],[179]) ).

thf(210,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/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff__iff1_0) ).

thf(779,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)],[210]) ).

thf(30,axiom,
    ! [A: $i] : ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole0_0) ).

thf(371,plain,
    ! [A: $i] : ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(89,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
       != ( D @ ( C @ c_Message_Omsg_OCrypt ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__7__iff1_1) ).

thf(503,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
       != ( D @ ( C @ c_Message_Omsg_OCrypt ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(136,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/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert__iff1_1) ).

thf(622,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)],[136]) ).

thf(237,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/sandbox2/benchmark/theBenchmark.p',cls_Relation_Orel__compE_0) ).

thf(837,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)],[237]) ).

thf(215,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/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__subset__iff__iff1_0) ).

thf(792,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)],[215]) ).

thf(286,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/sandbox2/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)],[286]) ).

thf(90,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/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__eq__iff__iff1_0) ).

thf(508,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)],[90]) ).

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/sandbox2/benchmark/theBenchmark.p',cls_Set_OpsubsetI_0) ).

thf(921,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(105,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/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__into__rtrancl_0) ).

thf(541,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)],[105]) ).

thf(152,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/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImageI_0) ).

thf(657,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)],[152]) ).

thf(203,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/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff__insert__iff2_0) ).

thf(765,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)],[203]) ).

thf(157,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_4) ).

thf(674,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(294,axiom,
    ! [B: $i,A: $i] :
      ~ ( B @ ( c_emptyset @ ( A @ c_in ) ) ),
    file('/export/starexec/sandbox2/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)],[294]) ).

thf(281,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/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl_Or__into__trancl_0) ).

thf(926,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)],[281]) ).

thf(207,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts_OFst_0) ).

thf(773,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(216,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/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInrI_0) ).

thf(794,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)],[216]) ).

thf(154,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/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn0__eq__iff1_0) ).

thf(662,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)],[154]) ).

thf(177,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/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanAtMost__int_0) ).

thf(718,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)],[177]) ).

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/sandbox2/benchmark/theBenchmark.p',cls_Relation_ODomainI_0) ).

thf(906,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(1,negated_conjecture,
    tc_Message_Omsg @ tc_set @ ( v_H @ ( v_G @ c_lessequals ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(298,plain,
    tc_Message_Omsg @ tc_set @ ( v_H @ ( v_G @ c_lessequals ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(48,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__self__conv2__iff2_0) ).

thf(412,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(195,axiom,
    ! [A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atMost_0) ).

thf(750,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)],[195]) ).

thf(134,axiom,
    ! [A: $i] :
      ~ ( tc_nat @ ( A @ ( A @ c_less ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__irrefl_0) ).

thf(618,plain,
    ! [A: $i] :
      ~ ( tc_nat @ ( A @ ( A @ c_less ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(92,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_3) ).

thf(513,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(231,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/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq__iff1_1) ).

thf(824,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)],[231]) ).

thf(247,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/sandbox2/benchmark/theBenchmark.p',cls_Set_OIntI_0) ).

thf(856,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)],[247]) ).

thf(192,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/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__subset__iff__iff1_0) ).

thf(745,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)],[192]) ).

thf(62,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/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__Scons__eq__iff1_0) ).

thf(444,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)],[62]) ).

thf(185,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/sandbox2/benchmark/theBenchmark.p',cls_Relation_OconverseE_0) ).

thf(733,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)],[185]) ).

thf(53,axiom,
    ! [A: $i] :
      ( ( A = c_0 )
      | ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__0__left__iff__iff1_0) ).

thf(423,plain,
    ! [A: $i] :
      ( ( A = c_0 )
      | ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(43,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/sandbox2/benchmark/theBenchmark.p',cls_List_Owf__lex_0) ).

thf(402,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)],[43]) ).

thf(191,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/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff__iff2_0) ).

thf(743,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)],[191]) ).

thf(146,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/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn1__eq__iff1_0) ).

thf(641,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)],[146]) ).

thf(35,axiom,
    ! [A: $i] :
      ( c_0
     != ( A @ c_Suc ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OZero__not__Suc__iff1_0) ).

thf(382,plain,
    ! [A: $i] :
      ( c_0
     != ( A @ c_Suc ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(9,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/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Oinject__iff1_0) ).

thf(313,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)],[9]) ).

thf(69,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/sandbox2/benchmark/theBenchmark.p',cls_Relation_Orel__compI_0) ).

thf(466,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)],[69]) ).

thf(18,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_List_Olist_ONil )
      | ( A
       != ( C @ ( A @ ( B @ c_append ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oself__append__conv2__iff1_0) ).

thf(335,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)],[18]) ).

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/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__subset__iff__iff2_0) ).

thf(919,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(221,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/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__subset__iff__iff1_0) ).

thf(804,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)],[221]) ).

thf(129,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/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert__iff2_0) ).

thf(604,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)],[129]) ).

thf(45,axiom,
    ! [A: $i] : ( tc_IntDef_Oint @ ( c_0 @ ( A @ c_Divides_Oop_Advd ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__right_0) ).

thf(406,plain,
    ! [A: $i] : ( tc_IntDef_Oint @ ( c_0 @ ( A @ c_Divides_Oop_Advd ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(234,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/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff__iff1_0) ).

thf(831,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)],[234]) ).

thf(159,axiom,
    ! [A: $i] :
      ( ( A = c_0 )
      | ~ ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_less ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__Suc0__iff1_0) ).

thf(681,plain,
    ! [A: $i] :
      ( ( A = c_0 )
      | ~ ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_less ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(57,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/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse__iff2_0) ).

thf(434,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)],[57]) ).

thf(133,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/sandbox2/benchmark/theBenchmark.p',cls_List_OlistsE_0) ).

thf(616,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)],[133]) ).

thf(250,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( B @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts_OBody_0) ).

thf(863,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( B @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(64,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( B @ c_less ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__irrefl__iff1_0) ).

thf(451,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( B @ c_less ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(116,axiom,
    tc_Product__Type_Ounit @ class_Finite__Set_Ofinite,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Product____Type__Ounit_0) ).

thf(567,plain,
    tc_Product__Type_Ounit @ class_Finite__Set_Ofinite,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(187,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/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastLessThan_0) ).

thf(737,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)],[187]) ).

thf(10,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__self__conv__iff2_0) ).

thf(318,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(263,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/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__iff__iff1_0) ).

thf(890,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)],[263]) ).

thf(76,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/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__iff__iff1_0) ).

thf(477,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)],[76]) ).

thf(227,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/sandbox2/benchmark/theBenchmark.p',cls_Relation_ORangeI_0) ).

thf(816,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)],[227]) ).

thf(12,axiom,
    tc_nat @ ( c_0 @ ( c_0 @ c_Divides_Oop_Advd ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__0__left__iff__iff2_0) ).

thf(323,plain,
    tc_nat @ ( c_0 @ ( c_0 @ c_Divides_Oop_Advd ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(205,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/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff__insert__iff1_0) ).

thf(769,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)],[205]) ).

thf(284,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/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H__iff2_0) ).

thf(932,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)],[284]) ).

thf(225,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/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__iff__iff2_0) ).

thf(811,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)],[225]) ).

thf(37,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv__iff1_0) ).

thf(387,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)],[37]) ).

thf(22,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/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend1__eq__conv__iff1_1) ).

thf(345,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)],[22]) ).

thf(248,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/sandbox2/benchmark/theBenchmark.p',cls_Relation_OIdE_0) ).

thf(858,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)],[248]) ).

thf(109,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/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H__iff1_0) ).

thf(552,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)],[109]) ).

thf(242,axiom,
    ! [A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OlessThan ) @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__lessThan_0) ).

thf(848,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)],[242]) ).

thf(167,axiom,
    ! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_less ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OlessI_0) ).

thf(700,plain,
    ! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_less ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(138,axiom,
    tc_nat @ class_Orderings_Oorder,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_3) ).

thf(626,plain,
    tc_nat @ class_Orderings_Oorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

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/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__iff__iff2_0) ).

thf(915,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(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/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Union_1) ).

thf(912,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(42,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_List_Olist_ONil )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__self__conv__iff1_0) ).

thf(399,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)],[42]) ).

thf(297,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/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanLessThan_0) ).

thf(959,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)],[297]) ).

thf(232,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/sandbox2/benchmark/theBenchmark.p',cls_Relation_OdiagE_1) ).

thf(827,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)],[232]) ).

thf(131,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/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInr__eq__iff1_0) ).

thf(608,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)],[131]) ).

thf(114,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/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozminus__dvd__iff__iff1_0) ).

thf(563,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)],[114]) ).

thf(2,negated_conjecture,
    tc_Message_Omsg @ ( v_G @ ( v_X @ c_in ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).

thf(299,plain,
    tc_Message_Omsg @ ( v_G @ ( v_X @ c_in ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(244,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/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_1) ).

thf(851,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)],[244]) ).

thf(149,axiom,
    ! [B: $i,A: $i] : ( B @ ( A @ tc_fun ) @ class_Nat_Opower ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_1) ).

thf(653,plain,
    ! [B: $i,A: $i] : ( B @ ( A @ tc_fun ) @ class_Nat_Opower ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(144,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/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn0__not__In1__iff1_0) ).

thf(636,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)],[144]) ).

thf(165,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/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq__iff1_0) ).

thf(695,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)],[165]) ).

thf(73,axiom,
    tc_nat @ class_Nat_Opower,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_12) ).

thf(473,plain,
    tc_nat @ class_Nat_Opower,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(83,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/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodI_0) ).

thf(490,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)],[83]) ).

thf(54,axiom,
    ! [B: $i,A: $i] :
      ( A
      = ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oself__append__conv2__iff2_0) ).

thf(426,plain,
    ! [B: $i,A: $i] :
      ( A
      = ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(123,axiom,
    tc_nat @ ( c_0 @ c_Suc @ ( c_0 @ c_less ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__Suc0__iff2_0) ).

thf(589,plain,
    tc_nat @ ( c_0 @ c_Suc @ ( c_0 @ c_less ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(32,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/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0__iff1_0) ).

thf(374,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)],[32]) ).

thf(82,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/sandbox2/benchmark/theBenchmark.p',cls_Relation_Opair__in__Id__conv__iff1_0) ).

thf(487,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)],[82]) ).

thf(94,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/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__eq__iff__iff1_0) ).

thf(516,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)],[94]) ).

thf(99,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( c_Relation_OId @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OIdI_0) ).

thf(531,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)],[99]) ).

thf(289,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/sandbox2/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)],[289]) ).

thf(209,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/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_0) ).

thf(776,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)],[209]) ).

thf(120,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/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImageE_1) ).

thf(580,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)],[120]) ).

thf(163,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/sandbox2/benchmark/theBenchmark.p',cls_List_ONil2__notin__lex__iff1_0) ).

thf(690,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)],[163]) ).

thf(170,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/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OusumE_1) ).

thf(705,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)],[170]) ).

thf(261,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/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiffE_0) ).

thf(887,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)],[261]) ).

thf(49,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/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0__iff2_0) ).

thf(414,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)],[49]) ).

thf(15,axiom,
    ! [B: $i,A: $i] :
      ( A
      = ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oself__append__conv__iff2_0) ).

thf(327,plain,
    ! [B: $i,A: $i] :
      ( A
      = ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(173,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/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OinsertI_0) ).

thf(712,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)],[173]) ).

thf(111,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/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInl__not__Inr__iff1_0) ).

thf(557,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)],[111]) ).

thf(88,axiom,
    ! [B: $i,A: $i] : ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olists ) @ ( c_List_Olist_ONil @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olists_ONil_0) ).

thf(502,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)],[88]) ).

thf(68,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_emptyset )
      | ( ( C @ ( B @ ( A @ c_union ) ) )
       != c_emptyset ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty__iff1_1) ).

thf(463,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)],[68]) ).

thf(19,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/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Nil1_0) ).

thf(338,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)],[19]) ).

thf(71,axiom,
    tc_bool @ class_Finite__Set_Ofinite,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool_0) ).

thf(470,plain,
    tc_bool @ class_Finite__Set_Ofinite,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(293,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/sandbox2/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)],[293]) ).

thf(223,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/sandbox2/benchmark/theBenchmark.p',cls_Set_OComplI_0) ).

thf(808,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)],[223]) ).

thf(169,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/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnionE_1) ).

thf(703,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)],[169]) ).

thf(151,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsingletonI_0) ).

thf(656,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(132,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/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_0) ).

thf(613,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)],[132]) ).

thf(127,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/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv__iff1_1) ).

thf(600,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)],[127]) ).

thf(182,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/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).

thf(727,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)],[182]) ).

thf(126,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/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq__iff1_0) ).

thf(595,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)],[126]) ).

thf(86,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/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImage__singleton__iff__iff1_0) ).

thf(497,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)],[86]) ).

thf(256,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/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OusumE_2) ).

thf(876,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)],[256]) ).

thf(241,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/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq__iff2_0) ).

thf(845,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)],[241]) ).

thf(139,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/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl_Ortrancl__refl_0) ).

thf(627,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)],[139]) ).

thf(104,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/sandbox2/benchmark/theBenchmark.p',clsarity_sum_0) ).

thf(539,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)],[104]) ).

thf(79,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/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Odsum__In1I_0) ).

thf(482,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)],[79]) ).

thf(96,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/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInr__not__Inl__iff1_0) ).

thf(524,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)],[96]) ).

thf(85,axiom,
    ! [A: $i] :
      ( ( A @ ( c_emptyset @ ( c_emptyset @ c_union ) ) )
      = c_emptyset ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty__iff2_0) ).

thf(495,plain,
    ! [A: $i] :
      ( ( A @ ( c_emptyset @ ( c_emptyset @ c_union ) ) )
      = c_emptyset ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(200,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__le__mono__iff1_0) ).

thf(759,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)],[200]) ).

thf(240,axiom,
    ! [A: $i] : ( A @ tc_set @ class_HOL_Ominus ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_0) ).

thf(844,plain,
    ! [A: $i] : ( A @ tc_set @ class_HOL_Ominus ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(206,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/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Ousum__In1I_0) ).

thf(771,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)],[206]) ).

thf(162,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/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert__iff1_0) ).

thf(688,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)],[162]) ).

thf(269,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/sandbox2/benchmark/theBenchmark.p',cls_Set_OinsertCI_0) ).

thf(903,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)],[269]) ).

thf(226,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/sandbox2/benchmark/theBenchmark.p',cls_Relation_OdiagE_0) ).

thf(813,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)],[226]) ).

thf(290,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/sandbox2/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)],[290]) ).

thf(38,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/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0__iff2_1) ).

thf(390,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)],[38]) ).

thf(142,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_emptyset )
      | ( ( C @ ( B @ ( A @ c_union ) ) )
       != c_emptyset ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty__iff1_0) ).

thf(632,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)],[142]) ).

thf(211,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/sandbox2/benchmark/theBenchmark.p',cls_Set_OIntE_1) ).

thf(781,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)],[211]) ).

thf(266,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/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__iff__iff1_0) ).

thf(896,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)],[266]) ).

thf(194,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/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiffE_1) ).

thf(748,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)],[194]) ).

thf(184,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/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiffI_0) ).

thf(731,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)],[184]) ).

thf(213,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/sandbox2/benchmark/theBenchmark.p',cls_Infinite__Set_Oatmost__one__unique_0) ).

thf(786,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)],[213]) ).

thf(117,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/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImage__singleton__iff__iff2_0) ).

thf(568,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)],[117]) ).

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/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastAtMost__int_0) ).

thf(914,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(155,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/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__iff__iff1_0) ).

thf(667,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)],[155]) ).

thf(202,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/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnE_0) ).

thf(763,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)],[202]) ).

thf(160,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/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv__iff1_0) ).

thf(684,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)],[160]) ).

thf(102,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/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert__iff1_0) ).

thf(536,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)],[102]) ).

thf(176,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oaxioms__1_0) ).

thf(716,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(219,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/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_2) ).

thf(800,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)],[219]) ).

thf(3,negated_conjecture,
    ~ ( tc_Message_Omsg @ ( v_H @ c_Message_Oparts @ ( v_X @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).

thf(300,plain,
    ~ ( tc_Message_Omsg @ ( v_H @ c_Message_Oparts @ ( v_X @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(135,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/sandbox2/benchmark/theBenchmark.p',cls_Relation_OdiagI_0) ).

thf(620,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)],[135]) ).

thf(197,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/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OusumE_0) ).

thf(752,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)],[197]) ).

thf(228,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/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_0) ).

thf(818,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)],[228]) ).

thf(246,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/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__subset__iff__iff2_0) ).

thf(854,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)],[246]) ).

thf(252,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/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).

thf(867,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)],[252]) ).

thf(251,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/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__subset__iff__iff2_0) ).

thf(865,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)],[251]) ).

thf(186,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/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnCI_0) ).

thf(735,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)],[186]) ).

thf(235,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/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un__iff1_1) ).

thf(833,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)],[235]) ).

thf(47,axiom,
    ! [A: $i] :
      ~ ( tc_nat @ ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__greater__0__conv__iff1_0) ).

thf(410,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)],[47]) ).

thf(292,axiom,
    ! [A: $i] : ( A @ tc_set @ class_Orderings_Oorder ),
    file('/export/starexec/sandbox2/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)],[292]) ).

thf(236,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/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImageE_0) ).

thf(835,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)],[236]) ).

thf(5,axiom,
    ! [A: $i] :
      ( ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Nat_Osize ) )
      = c_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__0__conv__iff2_0) ).

thf(305,plain,
    ! [A: $i] :
      ( ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Nat_Osize ) )
      = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(20,axiom,
    ! [A: $i] :
      ( ( A @ c_Suc )
     != c_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__not__Zero__iff1_0) ).

thf(341,plain,
    ! [A: $i] :
      ( ( A @ c_Suc )
     != c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(26,axiom,
    ! [A: $i] :
      ( ( A = c_0 )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq__iff1_0) ).

thf(358,plain,
    ! [A: $i] :
      ( ( A = c_0 )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(143,axiom,
    tc_IntDef_Oint @ class_Orderings_Oorder,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_31) ).

thf(635,plain,
    tc_IntDef_Oint @ class_Orderings_Oorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(100,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/sandbox2/benchmark/theBenchmark.p',cls_Relation_Oconverse__iff__iff1_0) ).

thf(532,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)],[100]) ).

thf(295,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/sandbox2/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)],[295]) ).

thf(217,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/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_2) ).

thf(796,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)],[217]) ).

thf(282,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/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Ousum__In0I_0) ).

thf(928,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)],[282]) ).

thf(74,axiom,
    ! [A: $i] :
      ( ~ ( A @ class_Finite__Set_Ofinite )
      | ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Datatype__Ooption_0) ).

thf(474,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Finite__Set_Ofinite )
      | ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(204,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/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__converse__iff1_0) ).

thf(767,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)],[204]) ).

thf(189,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/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).

thf(740,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)],[189]) ).

thf(17,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/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend1__eq__conv__iff1_0) ).

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(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(119,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Suc )
       != ( B @ c_Suc ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__Suc__eq__iff1_0) ).

thf(575,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Suc )
       != ( B @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(98,axiom,
    ! [B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( c_emptyset
       != ( B @ ( A @ c_List_Oset ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__empty2__iff1_0) ).

thf(528,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)],[98]) ).

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/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnionI_0) ).

thf(908,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(180,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/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__iff__iff1_0) ).

thf(723,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)],[180]) ).

thf(230,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/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_1) ).

thf(822,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)],[230]) ).

thf(61,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/sandbox2/benchmark/theBenchmark.p',cls_List_Olists_OCons_0) ).

thf(442,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)],[61]) ).

thf(254,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/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__subset__iff__iff2_0) ).

thf(871,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)],[254]) ).

thf(29,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/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse__iff1_0) ).

thf(369,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)],[29]) ).

thf(40,axiom,
    ! [A: $i] : ( tc_nat @ ( c_0 @ ( A @ c_Divides_Oop_Advd ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__0__right_0) ).

thf(395,plain,
    ! [A: $i] : ( tc_nat @ ( c_0 @ ( A @ c_Divides_Oop_Advd ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(137,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/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert__iff1_1) ).

thf(624,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)],[137]) ).

thf(238,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/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_2) ).

thf(839,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)],[238]) ).

thf(287,axiom,
    ! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( c_emptyset @ c_lessequals ) ) ),
    file('/export/starexec/sandbox2/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)],[287]) ).

thf(285,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/sandbox2/benchmark/theBenchmark.p',cls_Set_OinsertE_0) ).

thf(935,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)],[285]) ).

thf(106,axiom,
    c_UNIV != c_emptyset,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUNIV__not__empty__iff1_0) ).

thf(543,plain,
    c_UNIV != c_emptyset,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(145,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/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__iff__iff2_0) ).

thf(639,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)],[145]) ).

thf(125,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
       != ( B @ ( c_emptyset @ ( C @ c_insert ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__inject__dest_0) ).

thf(592,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)],[125]) ).

thf(28,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/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Oinject__iff1_1) ).

thf(364,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)],[28]) ).

thf(171,axiom,
    ! [A: $i] : ( A @ tc_set @ class_Orderings_Oord ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_1) ).

thf(708,plain,
    ! [A: $i] : ( A @ tc_set @ class_Orderings_Oord ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(259,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/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H__iff1_1) ).

thf(882,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)],[259]) ).

thf(7,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/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__greater__0__conv__iff2_0) ).

thf(309,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)],[7]) ).

thf(153,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/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__eq__iff__iff1_0) ).

thf(659,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)],[153]) ).

thf(208,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ ( B @ ( A @ c_Datatype_Ooption_OSome ) @ c_Datatype_Oo2s ) @ ( A @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Oelem__o2s__iff2_0) ).

thf(775,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)],[208]) ).

thf(112,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/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onegative__zless_0) ).

thf(560,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)],[112]) ).

thf(198,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/sandbox2/benchmark/theBenchmark.p',cls_List_Oin__listsI_1) ).

thf(755,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)],[198]) ).

thf(158,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/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__Scons__eq__iff1_1) ).

thf(676,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)],[158]) ).

thf(964,plain,
    $false,
    inference(e,[status(thm)],[892,479,628,468,941,555,481,582,379,861,873,449,440,511,385,715,698,747,538,930,898,709,417,885,436,651,829,404,320,565,570,719,372,587,917,751,802,344,853,870,606,325,881,416,924,492,789,376,646,485,348,806,353,905,602,692,453,396,428,849,527,312,307,439,546,761,810,534,714,798,910,302,820,561,392,429,729,957,894,407,630,484,361,879,329,889,461,757,324,456,842,948,725,356,499,519,742,783,420,471,669,590,547,901,686,476,701,515,738,654,721,779,371,503,622,837,792,938,508,921,541,657,765,674,953,926,773,794,662,718,906,298,412,750,618,513,824,856,745,444,733,423,402,743,641,382,313,466,335,919,804,604,406,831,681,434,616,863,451,567,737,318,890,477,816,323,769,932,811,387,345,858,552,848,700,626,915,912,399,959,827,608,563,299,851,653,636,695,473,490,426,589,374,487,516,531,944,776,580,690,705,887,414,327,712,557,502,463,338,470,951,808,703,656,613,600,727,595,497,876,845,627,539,482,524,495,759,844,771,688,903,813,946,390,632,781,896,748,731,786,568,914,667,763,684,536,716,800,300,620,752,818,854,867,865,735,833,410,950,835,305,341,358,635,532,955,796,928,474,767,740,332,575,528,908,723,822,442,871,369,395,624,839,940,935,543,639,592,364,708,882,309,659,775,560,755,676]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SWV263-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.08  % Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.14/5.40  % Computer : n009.cluster.edu
% 0.14/5.40  % Model    : x86_64 x86_64
% 0.14/5.40  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/5.40  % Memory   : 8046.5625MB
% 0.14/5.40  % OS       : Linux 6.8.0-71-generic
% 0.14/5.40  % CPULimit : 300
% 0.14/5.40  % WCLimit  : 300
% 0.14/5.40  % DateTime : Sat Sep 26 13:24:50 UTC 2026
% 0.14/5.41  % CPUTime  : 
% 0.14/5.41  Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.17/5.99  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.80/6.40  % [INFO] 	 Parsing done (403ms). 
% 1.80/6.41  % [INFO] 	 Running in sequential loop mode. 
% 3.07/6.79  % [INFO] 	 eprover registered as external prover. 
% 3.07/6.80  % [INFO] 	 Scanning for conjecture ... 
% 3.49/6.98  % [INFO] 	 Found a conjecture (or negated_conjecture) and 1377 axioms. Running axiom selection ... 
% 4.33/7.18  % [INFO] 	 Axiom selection finished. Selected 294 axioms (removed 1083 axioms). 
% 5.08/7.35  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 5.08/7.37  % [INFO] 	 Type checking passed. 
% 5.08/7.37  % [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 ... 
% 11.15/8.91  % External prover 'e' found a proof!
% 11.15/8.91  % [INFO] 	 Killing All external provers ... 
% 11.15/8.91  % Time passed: 3364ms (effective reasoning time: 2493ms)
% 11.15/8.92  % Axioms used in derivation (294): cls_Message_Omsg_Oinject__7__iff1_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_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_Finite__Set_OFinites_OinsertI_0, cls_Nat_Oless__irrefl_0, cls_IntDiv_Ozminus__dvd__iff__iff1_0, clsarity_set_2, cls_Nat_Onot__less0__iff1_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_Message_Omsg_Oinject__7__iff1_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_Message_Oparts_OInj_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_SetInterval_OatMost__eq__iff__iff1_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_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_Message_Oparts_OSnd_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_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_Nat_Oadd__gr__0__iff1_0, cls_Divides_Odvd__0__right_0, cls_IntDef_Oint__int__eq__iff1_0, cls_Wellfounded__Relations_Oless__than__iff__iff2_0, cls_Message_Omsg_Oinject__6__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_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, 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_Set_OInterI_0, cls_List_Olist_Odistinct__1__iff1_0, clsarity_bool_0, cls_Nat_Oadd__is__0__iff1_0, 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_Message_Oparts_OFst_0, cls_Sum__Type_OPlusE_1, cls_Set_OUnionE_0, cls_Message_Omsg_Oinject__6__iff1_1, 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, clsarity_fun_0, cls_Relation_OIdE_0, clsarity_nat_2, cls_Set_OpsubsetE_1, cls_Message_Oparts_OBody_0, cls_Nat_OlessI_0, cls_SetInterval_Ofinite__atMost_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
% 11.15/8.92  % No. of inferences in proof: 595
% 11.15/8.92  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3364 ms resp. 2493 ms w/o parsing
% 12.06/9.15  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 12.06/9.16  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------