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

%------------------------------------------------------------------------------
% File     : Leo-III---1.8.0
% Problem  : COM011-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39

% Computer : n004.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 06:57:52 AM UTC 2026

% Result   : Unsatisfiable 47.03s 25.99s
% Output   : Refutation 47.98s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :  184
% Syntax   : Number of formulae    :  369 (  87 unt;   0 typ;   0 def)
%            Number of atoms       :  709 ( 204 equ;   0 cnn)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives : 5358 ( 344   ~; 340   |;   0   &;4674   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (  10 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   85 (  83 usr;  11 con; 0-6 aty)
%            Number of variables   : 1280 (   0   ^;1280   !;   0   ?;1280   :)

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

thf(v_F_decl,type,
    v_F: $i ).

thf(c_UNITY_Oconstrains_decl,type,
    c_UNITY_Oconstrains: $i > $i > $i > $i ).

thf(v_A_decl,type,
    v_A: $i ).

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

thf(v_B_decl,type,
    v_B: $i ).

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

thf(tc_UNITY_Oprogram_decl,type,
    tc_UNITY_Oprogram: $i > $i ).

thf(c_WFair_Otransient_decl,type,
    c_WFair_Otransient: $i > $i > $i ).

thf(c_WFair_OleadsTo_decl,type,
    c_WFair_OleadsTo: $i > $i > $i > $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_List_Olist_ONil_decl,type,
    c_List_Olist_ONil: $i ).

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

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

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

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

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

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

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

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

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

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

thf(c_Datatype__Universe_OScons_decl,type,
    c_Datatype__Universe_OScons: $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__2_decl,type,
    c_Main_OdprodE__2: $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_OdprodE__4_decl,type,
    c_Main_OdprodE__4: $i > $i > $i > $i > $i > $i ).

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

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

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

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

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

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

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

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

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

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

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

thf(c_UNITY_OActs_decl,type,
    c_UNITY_OActs: $i > $i > $i ).

thf(c_UNITY_OAllowedActs_decl,type,
    c_UNITY_OAllowedActs: $i > $i > $i ).

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

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

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

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

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

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_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(tc_sum_decl,type,
    tc_sum: $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__Universe_Ouprod_decl,type,
    c_Datatype__Universe_Ouprod: $i > $i > $i > $i > $i ).

thf(c_Datatype_Ooption_OSome_decl,type,
    c_Datatype_Ooption_OSome: $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_Main_OsubsetI__1_decl,type,
    c_Main_OsubsetI__1: $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_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_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_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_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_Orel__compE__2_decl,type,
    c_Main_Orel__compE__2: $i > $i > $i > $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_WFair_Oensures_decl,type,
    c_WFair_Oensures: $i > $i > $i > $i ).

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

thf(88,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( B @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_OlistsE_0) ).

thf(414,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)],[88]) ).

thf(70,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Sum__Type_OInl ) ) )
     != ( B @ ( C @ ( D @ c_Sum__Type_OInr ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInl__not__Inr__iff1_0) ).

thf(365,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)],[70]) ).

thf(62,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ tc_prod ) @ ( E @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ ( C @ tc_prod ) @ ( C @ ( D @ ( E @ c_Relation_Oconverse ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Oconverse__iff__iff1_0) ).

thf(347,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)],[62]) ).

thf(154,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( B @ ( B @ ( B @ ( A @ c_Main_OIdE__1 ) @ ( B @ ( A @ c_Main_OIdE__1 ) @ c_Pair ) ) ) ) )
      | ~ ( B @ ( B @ tc_prod ) @ ( c_Relation_OId @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OIdE_0) ).

thf(555,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)],[154]) ).

thf(56,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Sum__Type_OInr ) ) )
     != ( B @ ( C @ ( D @ c_Sum__Type_OInl ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInr__not__Inl__iff1_0) ).

thf(333,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)],[56]) ).

thf(24,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn0 ) ) )
       != ( C @ ( B @ ( D @ c_Datatype__Universe_OIn0 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn0__eq__iff1_0) ).

thf(249,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)],[24]) ).

thf(86,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( C @ ( c_emptyset @ ( D @ c_insert ) ) @ ( B @ c_lessequals ) ) )
      | ( ( C @ ( B @ ( A @ c_insert ) ) )
       != ( C @ ( c_emptyset @ ( D @ c_insert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H__iff1_1) ).

thf(408,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)],[86]) ).

thf(139,axiom,
    ! [C: $i,B: $i,A: $i] : ( C @ tc_UNITY_Oprogram @ ( C @ ( B @ ( c_emptyset @ c_UNITY_Oconstrains ) ) @ ( A @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNITY_Oconstrains__empty_0) ).

thf(523,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ tc_UNITY_Oprogram @ ( C @ ( B @ ( c_emptyset @ c_UNITY_Oconstrains ) ) @ ( A @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(33,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__4 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__3 ) ) ) ) @ c_Datatype__Universe_OScons ) ) ) @ ( E @ ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__2 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__1 ) ) ) ) @ c_Datatype__Universe_OScons ) ) ) @ c_Pair ) ) ) ) )
      | ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Odprod ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_0) ).

thf(276,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)],[33]) ).

thf(23,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Wellfounded__Recursion_Oacyclic ) )
      | ~ ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse__iff2_0) ).

thf(247,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)],[23]) ).

thf(134,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ~ ( B @ ( A @ ( D @ c_in ) ) )
      | ~ ( B @ ( A @ ( C @ c_in ) ) )
      | ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Infinite__Set_Oatmost__one__unique_0) ).

thf(511,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)],[134]) ).

thf(183,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( E @ ( D @ ( E @ ( D @ ( A @ ( B @ c_Main_OPlusE__1 ) ) ) @ c_Sum__Type_OInl ) ) ) )
      | ( E @ ( C @ ( D @ ( E @ ( A @ ( C @ c_Main_OPlusE__2 ) ) ) @ c_in ) ) )
      | ~ ( E @ ( D @ tc_sum ) @ ( E @ ( D @ ( C @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_1) ).

thf(614,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)],[183]) ).

thf(31,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != ( C @ ( B @ ( D @ c_append ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__same__eq__iff1_0) ).

thf(269,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)],[31]) ).

thf(9,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_List_Olist_ONil )
      | ( c_List_Olist_ONil
       != ( C @ ( B @ ( A @ c_append ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv__iff1_1) ).

thf(202,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)],[9]) ).

thf(175,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ tc_UNITY_Oprogram @ ( D @ ( C @ ( B @ c_WFair_OleadsTo ) ) @ ( A @ c_in ) ) )
      | ~ ( D @ tc_UNITY_Oprogram @ ( D @ ( C @ ( B @ c_WFair_Oensures ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WFair_OleadsTo__Basis_0) ).

thf(597,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ tc_UNITY_Oprogram @ ( D @ ( C @ ( B @ c_WFair_OleadsTo ) ) @ ( A @ c_in ) ) )
      | ~ ( D @ tc_UNITY_Oprogram @ ( D @ ( C @ ( B @ c_WFair_Oensures ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(77,axiom,
    ! [A: $i] :
      ( ( A @ ( c_List_Olist_ONil @ c_List_Oset ) )
      = c_emptyset ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__empty__iff2_0) ).

thf(385,plain,
    ! [A: $i] :
      ( ( A @ ( c_List_Olist_ONil @ c_List_Oset ) )
      = c_emptyset ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(129,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( B @ ( A @ c_in ) ) )
      | ( D @ ( C @ ( A @ c_in ) ) )
      | ~ ( D @ ( D @ ( C @ ( B @ c_union ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnE_0) ).

thf(500,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)],[129]) ).

thf(1,negated_conjecture,
    t_a @ tc_UNITY_Oprogram @ ( t_a @ ( t_a @ ( v_B @ ( v_A @ c_union ) ) @ ( v_A @ c_UNITY_Oconstrains ) ) @ ( v_F @ c_in ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(185,plain,
    t_a @ tc_UNITY_Oprogram @ ( t_a @ ( t_a @ ( v_B @ ( v_A @ c_union ) ) @ ( v_A @ c_UNITY_Oconstrains ) ) @ ( v_F @ c_in ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(26,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) )
      | ~ ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Wellfounded__Recursion_Oacyclic ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse__iff1_0) ).

thf(257,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)],[26]) ).

thf(61,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ tc_set @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( D @ c_lessequals ) ) )
      | ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
       != ( B @ ( D @ ( C @ c_insert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq__iff1_1) ).

thf(344,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)],[61]) ).

thf(67,axiom,
    c_UNIV != c_emptyset,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUNIV__not__empty__iff1_0) ).

thf(357,plain,
    c_UNIV != c_emptyset,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(6,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olistrel ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Nil2_0) ).

thf(196,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)],[6]) ).

thf(156,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_set @ ( B @ ( D @ c_minus ) ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiffE_0) ).

thf(559,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)],[156]) ).

thf(4,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
       != ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Oinject__iff1_0) ).

thf(189,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)],[4]) ).

thf(35,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_List_Olist_ONil )
      | ( A
       != ( C @ ( B @ ( A @ c_append ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oself__append__conv__iff1_0) ).

thf(284,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)],[35]) ).

thf(89,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_Odiag ) @ ( C @ ( C @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OdiagI_0) ).

thf(416,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)],[89]) ).

thf(37,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( C @ ( D @ ( A @ c_List_Olist_OCons ) ) @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( D @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olists_OCons_0) ).

thf(289,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)],[37]) ).

thf(104,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( A @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_append ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv__iff1_0) ).

thf(448,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)],[104]) ).

thf(125,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( D @ c_union ) ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnCI_0) ).

thf(492,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)],[125]) ).

thf(103,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = F )
      | ( ( D @ ( C @ ( B @ ( A @ c_Datatype__Universe_OScons ) ) ) )
       != ( D @ ( C @ ( F @ ( E @ c_Datatype__Universe_OScons ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__Scons__eq__iff1_1) ).

thf(443,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)],[103]) ).

thf(51,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( C @ ( C @ tc_prod ) @ ( c_Relation_OId @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Opair__in__Id__conv__iff1_0) ).

thf(321,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)],[51]) ).

thf(12,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( C @ ( C @ ( c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) )
       != ( C @ ( C @ ( c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_append ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend1__eq__conv__iff1_1) ).

thf(211,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)],[12]) ).

thf(20,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_List_Olist_ONil )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__self__conv__iff1_0) ).

thf(238,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)],[20]) ).

thf(135,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( E @ ( F @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__3 ) ) ) ) ) @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__1 ) ) ) ) ) @ c_Pair ) ) ) ) )
      | ~ ( E @ ( F @ tc_prod ) @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Orel__compE_2) ).

thf(514,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)],[135]) ).

thf(164,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( D @ c_Union ) @ ( A @ c_in ) ) )
      | ~ ( C @ tc_set @ ( D @ ( B @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnionI_0) ).

thf(574,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)],[164]) ).

thf(65,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ c_Wellfounded__Recursion_Owf ) )
      | ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Owf ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert__iff1_0) ).

thf(353,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)],[65]) ).

thf(119,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
      | ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).

thf(480,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)],[119]) ).

thf(81,axiom,
    ! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).

thf(397,plain,
    ! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(39,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = E )
      | ( ( D @ ( C @ ( B @ ( A @ c_Datatype__Universe_OScons ) ) ) )
       != ( D @ ( C @ ( F @ ( E @ c_Datatype__Universe_OScons ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__Scons__eq__iff1_0) ).

thf(293,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)],[39]) ).

thf(107,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ c_Wellfounded__Recursion_Oacyclic ) )
      | ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Oacyclic ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert__iff1_0) ).

thf(453,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)],[107]) ).

thf(87,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( D @ ( E @ ( D @ ( E @ ( A @ ( C @ c_Main_OPlusE__2 ) ) ) @ c_Sum__Type_OInr ) ) ) )
      | ( A
        = ( E @ ( D @ ( E @ ( D @ ( A @ ( B @ c_Main_OPlusE__1 ) ) ) @ c_Sum__Type_OInl ) ) ) )
      | ~ ( E @ ( D @ tc_sum ) @ ( E @ ( D @ ( C @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_0) ).

thf(411,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)],[87]) ).

thf(97,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ tc_prod ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( C @ ( D @ c_Pair ) ) ) @ c_in ) ) )
      | ( B @ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( D @ ( C @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Oacyclic ) )
      | ~ ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert__iff2_0) ).

thf(428,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)],[97]) ).

thf(142,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( C @ ( C @ ( C @ ( A @ ( B @ c_Main_OdiagE__1 ) ) @ ( C @ ( A @ ( B @ c_Main_OdiagE__1 ) ) @ c_Pair ) ) ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_Odiag ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OdiagE_0) ).

thf(527,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)],[142]) ).

thf(106,axiom,
    ! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( c_emptyset @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__subsetI_0) ).

thf(452,plain,
    ! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( c_emptyset @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(76,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = F )
      | ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
       != ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq__iff1_1) ).

thf(380,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)],[76]) ).

thf(42,axiom,
    ~ ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Infinite__Set_Onat__not__finite_0) ).

thf(302,plain,
    ~ ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(63,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) )
      | ~ ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Pow ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff__iff1_0) ).

thf(349,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)],[63]) ).

thf(157,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ ( D @ c_in ) ) )
      | ~ ( C @ ( C @ ( B @ c_Inter ) @ ( D @ c_in ) ) )
      | ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInterD_0) ).

thf(561,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)],[157]) ).

thf(85,axiom,
    ! [B: $i,A: $i] : ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_List_Oset ) @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ofinite__set_0) ).

thf(407,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)],[85]) ).

thf(114,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( D @ ( C @ ( F @ ( E @ c_Datatype__Universe_Odsum ) ) ) @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ c_Datatype__Universe_OIn0 ) ) @ ( D @ ( C @ ( A @ c_Datatype__Universe_OIn0 ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Odsum__In0I_0) ).

thf(467,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)],[114]) ).

thf(101,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( A @ ( B @ c_insert ) ) )
        = ( C @ ( c_emptyset @ ( B @ c_insert ) ) ) )
      | ~ ( C @ tc_set @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H__iff2_0) ).

thf(435,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)],[101]) ).

thf(169,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ( D @ ( C @ ( A @ c_in ) ) )
      | ~ ( D @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertE_0) ).

thf(583,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)],[169]) ).

thf(111,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = A )
      | ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
       != ( B @ ( D @ ( C @ c_insert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq__iff1_0) ).

thf(461,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)],[111]) ).

thf(152,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( C @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__2 ) ) ) ) @ c_in ) ) )
      | ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ouprod ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_1) ).

thf(551,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)],[152]) ).

thf(52,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( D @ ( C @ ( E @ ( H @ c_Datatype__Universe_Odprod ) ) ) @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ ( G @ c_Datatype__Universe_OScons ) ) ) @ ( D @ ( C @ ( A @ ( F @ c_Datatype__Universe_OScons ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( H @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( G @ ( F @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodI_0) ).

thf(324,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)],[52]) ).

thf(17,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv__iff1_0) ).

thf(229,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)],[17]) ).

thf(160,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( D @ c_insert ) ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertCI_0) ).

thf(566,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)],[160]) ).

thf(121,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) )
      | ~ ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_union ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un__iff1_0) ).

thf(484,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)],[121]) ).

thf(49,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ tc_prod ) @ tc_set @ ( B @ ( A @ c_UNITY_OActs ) @ ( c_Relation_OId @ c_insert ) ) )
      = ( B @ ( A @ c_UNITY_OActs ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNITY_Oinsert__Id__Acts_0) ).

thf(317,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ tc_prod ) @ tc_set @ ( B @ ( A @ c_UNITY_OActs ) @ ( c_Relation_OId @ c_insert ) ) )
      = ( B @ ( A @ c_UNITY_OActs ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(173,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( D @ ( B @ c_union ) ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnCI_1) ).

thf(593,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)],[173]) ).

thf(181,axiom,
    ! [A: $i] :
      ( ( A @ ( c_emptyset @ ( c_emptyset @ c_union ) ) )
      = c_emptyset ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty__iff2_0) ).

thf(610,plain,
    ! [A: $i] :
      ( ( A @ ( c_emptyset @ ( c_emptyset @ c_union ) ) )
      = c_emptyset ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(91,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Owf ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert__iff1_1) ).

thf(420,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)],[91]) ).

thf(137,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__1 ) ) ) ) @ c_in ) ) )
      | ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ouprod ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_2) ).

thf(519,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)],[137]) ).

thf(166,axiom,
    ! [B: $i,A: $i] : ( B @ tc_UNITY_Oprogram @ ( B @ ( c_emptyset @ ( c_emptyset @ c_UNITY_Oconstrains ) ) @ ( A @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNITY_Oconstrains__empty2__iff2_0) ).

thf(578,plain,
    ! [B: $i,A: $i] : ( B @ tc_UNITY_Oprogram @ ( B @ ( c_emptyset @ ( c_emptyset @ c_UNITY_Oconstrains ) ) @ ( A @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(123,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_UNITY_Oprogram @ ( C @ ( D @ c_WFair_Otransient ) @ ( A @ c_in ) ) )
      | ~ ( C @ tc_set @ ( B @ ( D @ c_lessequals ) ) )
      | ~ ( C @ tc_UNITY_Oprogram @ ( C @ ( B @ c_WFair_Otransient ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WFair_Otransient__strengthen_0) ).

thf(488,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_UNITY_Oprogram @ ( C @ ( D @ c_WFair_Otransient ) @ ( A @ c_in ) ) )
      | ~ ( C @ tc_set @ ( B @ ( D @ c_lessequals ) ) )
      | ~ ( C @ tc_UNITY_Oprogram @ ( C @ ( B @ c_WFair_Otransient ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(58,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( C @ ( A @ c_inter ) ) @ c_in ) ) )
      | ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_0) ).

thf(339,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)],[58]) ).

thf(146,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( F @ tc_prod ) @ ( C @ ( D @ ( F @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__2 ) ) ) ) ) @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__1 ) ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( E @ ( F @ tc_prod ) @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Orel__compE_1) ).

thf(537,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)],[146]) ).

thf(117,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( A @ ( C @ ( D @ ( B @ ( A @ c_Main_ORangeE__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ ( D @ ( C @ ( B @ c_Relation_ORange ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ORangeE_0) ).

thf(476,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)],[117]) ).

thf(141,axiom,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertCI_1) ).

thf(526,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(172,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( C @ ( A @ c_Datatype_Ooption_OSome ) ) )
      | ~ ( C @ ( C @ ( B @ c_Datatype_Oo2s ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Oelem__o2s__iff1_0) ).

thf(590,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)],[172]) ).

thf(54,axiom,
    ! [B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( B @ ( A @ c_List_Oset ) )
       != c_emptyset ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__empty__iff1_0) ).

thf(328,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)],[54]) ).

thf(116,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Datatype_Ooption_OSome ) )
       != ( B @ ( C @ c_Datatype_Ooption_OSome ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Ooption_Oinject__iff1_0) ).

thf(471,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)],[116]) ).

thf(109,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_in ) ) )
      | ~ ( C @ ( B @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__converse__iff2_0) ).

thf(457,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)],[109]) ).

thf(162,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_emptyset )
      | ( ( C @ ( B @ ( A @ c_union ) ) )
       != c_emptyset ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty__iff1_0) ).

thf(569,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)],[162]) ).

thf(72,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( C @ ( A @ ( D @ c_append ) ) @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( D @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv__iff2_0) ).

thf(371,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)],[72]) ).

thf(131,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( E @ ( D @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__2 ) ) ) ) @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__1 ) ) ) ) @ c_Datatype__Universe_OScons ) ) ) ) )
      | ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ouprod ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_0) ).

thf(503,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)],[131]) ).

thf(179,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_emptyset )
      | ( ( C @ ( B @ ( A @ c_union ) ) )
       != c_emptyset ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty__iff1_1) ).

thf(605,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)],[179]) ).

thf(60,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( c_Relation_OId @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OIdI_0) ).

thf(343,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)],[60]) ).

thf(22,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
     != c_List_Olist_ONil ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Odistinct__2__iff1_0) ).

thf(244,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)],[22]) ).

thf(30,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__self__conv2__iff1_0) ).

thf(266,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)],[30]) ).

thf(68,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_insert ) ) )
       != ( C @ ( c_emptyset @ ( D @ c_insert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H__iff1_0) ).

thf(360,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)],[68]) ).

thf(10,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( C @ ( c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) )
       != ( C @ ( C @ ( c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_append ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend1__eq__conv__iff1_0) ).

thf(205,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)],[10]) ).

thf(133,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( C @ ( D @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__1 ) ) ) @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__2 ) ) ) @ c_Pair ) ) ) ) )
      | ~ ( C @ ( D @ tc_prod ) @ ( D @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OconverseE_1) ).

thf(508,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)],[133]) ).

thf(46,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( D @ tc_set @ ( C @ ( A @ c_minus ) ) @ c_in ) ) )
      | ~ ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( D @ tc_set @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_minus ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff__insert__iff1_0) ).

thf(311,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)],[46]) ).

thf(148,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( E @ ( D @ ( B @ ( A @ ( C @ c_Main_OImageE__1 ) ) ) ) @ c_in ) ) )
      | ~ ( E @ ( E @ ( D @ ( C @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImageE_0) ).

thf(541,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)],[148]) ).

thf(82,axiom,
    ! [C: $i,B: $i,A: $i] :
      ~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olex ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( A @ ( c_List_Olist_ONil @ c_Pair ) ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__notin__lex__iff1_0) ).

thf(398,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)],[82]) ).

thf(155,axiom,
    ! [B: $i,A: $i] : ( B @ tc_UNITY_Oprogram @ ( B @ ( c_UNIV @ ( c_UNIV @ c_UNITY_Oconstrains ) ) @ ( A @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNITY_Oconstrains__UNIV__iff2_0) ).

thf(558,plain,
    ! [B: $i,A: $i] : ( B @ tc_UNITY_Oprogram @ ( B @ ( c_UNIV @ ( c_UNIV @ c_UNITY_Oconstrains ) ) @ ( A @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(143,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( A @ c_in ) ) )
      | ~ ( D @ ( D @ ( C @ ( B @ c_inter ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OIntE_0) ).

thf(530,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)],[143]) ).

thf(170,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ c_Inter ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( C @ ( B @ ( A @ c_Main_OInterI__1 ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInterI_1) ).

thf(586,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)],[170]) ).

thf(40,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Pow ) @ c_in ) ) )
      | ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff__iff2_0) ).

thf(298,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)],[40]) ).

thf(94,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ tc_set @ ( B @ ( A @ c_UNITY_OAllowedActs ) @ ( c_Relation_OId @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNITY_OId__in__AllowedActs_0) ).

thf(425,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ tc_set @ ( B @ ( A @ c_UNITY_OAllowedActs ) @ ( c_Relation_OId @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(98,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Oacyclic ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert__iff1_1) ).

thf(430,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)],[98]) ).

thf(29,axiom,
    ! [A: $i] :
      ( ( A @ ( c_List_Olist_ONil @ ( c_List_Olist_ONil @ c_append ) ) )
      = c_List_Olist_ONil ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv__iff2_0) ).

thf(264,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)],[29]) ).

thf(34,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn1 ) ) )
       != ( C @ ( B @ ( D @ c_Datatype__Universe_OIn1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn1__eq__iff1_0) ).

thf(279,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)],[34]) ).

thf(74,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( E @ ( D @ ( B @ ( A @ ( C @ c_Main_OImageE__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( E @ ( E @ ( D @ ( C @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImageE_1) ).

thf(375,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)],[74]) ).

thf(177,axiom,
    ! [B: $i,A: $i] :
      ~ ( B @ ( c_emptyset @ ( A @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OemptyE_0) ).

thf(601,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ ( c_emptyset @ ( A @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(93,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( C @ tc_set @ ( C @ ( B @ c_Pow ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OPow__iff__iff1_0) ).

thf(423,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)],[93]) ).

thf(84,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_Sum__Type_OInr ) ) )
       != ( C @ ( B @ ( D @ c_Sum__Type_OInr ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInr__eq__iff1_0) ).

thf(402,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)],[84]) ).

thf(150,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( D @ ( E @ ( D @ ( E @ ( A @ ( C @ c_Main_OPlusE__2 ) ) ) @ c_Sum__Type_OInr ) ) ) )
      | ( D @ ( B @ ( E @ ( D @ ( A @ ( B @ c_Main_OPlusE__1 ) ) ) @ c_in ) ) )
      | ~ ( E @ ( D @ tc_sum ) @ ( E @ ( D @ ( C @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_2) ).

thf(545,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)],[150]) ).

thf(27,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn1 ) ) )
     != ( C @ ( B @ ( D @ c_Datatype__Universe_OIn0 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn1__not__In0__iff1_0) ).

thf(259,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)],[27]) ).

thf(167,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ tc_sum ) @ ( D @ ( C @ ( E @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( D @ ( C @ ( A @ c_Sum__Type_OInl ) ) @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInlI_0) ).

thf(579,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)],[167]) ).

thf(38,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ ( C @ c_insert ) ) @ c_in ) ) )
      | ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OinsertI_0) ).

thf(291,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)],[38]) ).

thf(163,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ ( E @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) )
      | ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ODomainI_0) ).

thf(572,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)],[163]) ).

thf(47,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( D @ ( C @ ( E @ ( F @ c_Datatype__Universe_Odsum ) ) ) @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ c_Datatype__Universe_OIn1 ) ) @ ( D @ ( C @ ( A @ c_Datatype__Universe_OIn1 ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Odsum__In1I_0) ).

thf(313,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)],[47]) ).

thf(128,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Or__into__rtrancl_0) ).

thf(498,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)],[128]) ).

thf(113,axiom,
    ! [B: $i,A: $i] : ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olists ) @ ( c_List_Olist_ONil @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olists_ONil_0) ).

thf(466,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)],[113]) ).

thf(3,negated_conjecture,
    ~ ( t_a @ tc_UNITY_Oprogram @ ( t_a @ ( v_B @ ( v_A @ c_WFair_OleadsTo ) ) @ ( v_F @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).

thf(187,plain,
    ~ ( t_a @ tc_UNITY_Oprogram @ ( t_a @ ( v_B @ ( v_A @ c_WFair_OleadsTo ) ) @ ( v_F @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(14,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( c_List_Olist_ONil
     != ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Odistinct__1__iff1_0) ).

thf(219,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)],[14]) ).

thf(32,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olex ) @ c_Wellfounded__Recursion_Owf ) )
      | ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Owf__lex_0) ).

thf(274,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)],[32]) ).

thf(75,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = A )
      | ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
      | ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).

thf(377,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)],[75]) ).

thf(11,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_List_Olist_ONil )
      | ( A
       != ( C @ ( A @ ( B @ c_append ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oself__append__conv2__iff1_0) ).

thf(208,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)],[11]) ).

thf(176,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( B @ ( C @ ( B @ ( A @ c_Main_OUnionE__1 ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ ( B @ c_Union ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnionE_0) ).

thf(599,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)],[176]) ).

thf(78,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
       != ( B @ ( c_emptyset @ ( C @ c_insert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__inject__dest_0) ).

thf(387,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)],[78]) ).

thf(126,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( B @ ( A @ c_in ) ) )
      | ~ ( D @ ( D @ tc_set @ ( C @ ( B @ c_minus ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiffE_1) ).

thf(494,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)],[126]) ).

thf(145,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( C @ ( A @ ( B @ c_Main_OdiagE__1 ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_Odiag ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OdiagE_1) ).

thf(535,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)],[145]) ).

thf(138,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( A @ c_List_Oset ) @ ( C @ ( A @ ( B @ c_Main_Oin__listsI__1 ) ) @ c_in ) ) )
      | ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oin__listsI_0) ).

thf(521,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)],[138]) ).

thf(108,axiom,
    ! [C: $i,B: $i,A: $i] :
      ~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olex ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil2__notin__lex__iff1_0) ).

thf(455,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)],[108]) ).

thf(180,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( B @ ( C @ ( B @ ( A @ c_Main_OInterI__1 ) ) @ c_in ) ) )
      | ( C @ ( C @ ( B @ c_Inter ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInterI_0) ).

thf(608,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)],[180]) ).

thf(44,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsingletonD__dest_0) ).

thf(306,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)],[44]) ).

thf(158,axiom,
    ! [C: $i,B: $i,A: $i] : ( C @ tc_UNITY_Oprogram @ ( C @ ( c_UNIV @ ( B @ c_UNITY_Oconstrains ) ) @ ( A @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNITY_Oconstrains__UNIV2_0) ).

thf(563,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ tc_UNITY_Oprogram @ ( C @ ( c_UNIV @ ( B @ c_UNITY_Oconstrains ) ) @ ( A @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(102,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_Sum__Type_OInl ) ) )
       != ( C @ ( B @ ( D @ c_Sum__Type_OInl ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInl__eq__iff1_0) ).

thf(438,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)],[102]) ).

thf(21,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn0 ) ) )
     != ( C @ ( B @ ( D @ c_Datatype__Universe_OIn1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn0__not__In1__iff1_0) ).

thf(241,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)],[21]) ).

thf(124,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__2 ) ) ) @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( D @ tc_prod ) @ ( D @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OconverseE_0) ).

thf(490,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)],[124]) ).

thf(95,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ tc_set @ ( B @ ( A @ c_UNITY_OActs ) @ ( c_Relation_OId @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNITY_OId__in__Acts_0) ).

thf(426,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ tc_set @ ( B @ ( A @ c_UNITY_OActs ) @ ( c_Relation_OId @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(151,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_UNIV )
      | ~ ( C @ tc_UNITY_Oprogram @ ( C @ ( B @ ( c_UNIV @ c_UNITY_Oconstrains ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNITY_Oconstrains__UNIV__iff1_0) ).

thf(548,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_UNIV )
      | ~ ( C @ tc_UNITY_Oprogram @ ( C @ ( B @ ( c_UNIV @ c_UNITY_Oconstrains ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(184,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ tc_UNITY_Oprogram @ ( D @ ( C @ ( E @ c_UNITY_Oconstrains ) ) @ ( A @ c_in ) ) )
      | ~ ( D @ tc_set @ ( B @ ( E @ c_lessequals ) ) )
      | ~ ( D @ tc_UNITY_Oprogram @ ( D @ ( C @ ( B @ c_UNITY_Oconstrains ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNITY_Oconstrains__weaken__L_0) ).

thf(617,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ tc_UNITY_Oprogram @ ( D @ ( C @ ( E @ c_UNITY_Oconstrains ) ) @ ( A @ c_in ) ) )
      | ~ ( D @ tc_set @ ( B @ ( E @ c_lessequals ) ) )
      | ~ ( D @ tc_UNITY_Oprogram @ ( D @ ( C @ ( B @ c_UNITY_Oconstrains ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(66,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__into__rtrancl_0) ).

thf(355,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)],[66]) ).

thf(153,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( D @ c_inter ) ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( D @ ( A @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OIntI_0) ).

thf(553,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)],[153]) ).

thf(5,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__self__conv__iff2_0) ).

thf(194,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(7,axiom,
    ! [A: $i] : ( A @ ( c_emptyset @ c_Wellfounded__Recursion_Owf ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__empty_0) ).

thf(199,plain,
    ! [A: $i] : ( A @ ( c_emptyset @ c_Wellfounded__Recursion_Owf ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(55,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( E @ ( E @ ( D @ ( D @ ( c_emptyset @ ( C @ c_insert ) ) @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImage__singleton__iff__iff1_0) ).

thf(331,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)],[55]) ).

thf(130,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ ( B @ ( A @ c_Datatype_Ooption_OSome ) @ c_Datatype_Oo2s ) @ ( A @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Oelem__o2s__iff2_0) ).

thf(502,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)],[130]) ).

thf(165,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Union ) @ c_in ) ) )
      | ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Main_Ofinite__Union__1 ) @ c_in ) ) )
      | ~ ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Union_1) ).

thf(576,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)],[165]) ).

thf(57,axiom,
    ! [B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( c_emptyset
       != ( B @ ( A @ c_List_Oset ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__empty2__iff1_0) ).

thf(336,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)],[57]) ).

thf(174,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Main_ODomainE__1 ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ODomainE_0) ).

thf(595,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)],[174]) ).

thf(182,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( E @ c_Relation_ORange ) ) @ ( B @ c_in ) ) )
      | ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ORangeI_0) ).

thf(612,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)],[182]) ).

thf(105,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ tc_prod ) @ ( D @ ( C @ ( E @ c_Relation_Oconverse ) ) @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Oconverse__iff__iff2_0) ).

thf(450,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)],[105]) ).

thf(69,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( A @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_OlistsE_1) ).

thf(363,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)],[69]) ).

thf(147,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) )
      | ~ ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_union ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un__iff1_1) ).

thf(539,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)],[147]) ).

thf(120,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( C @ ( B @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).

thf(482,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)],[120]) ).

thf(71,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( c_emptyset @ ( B @ c_insert ) ) )
        = ( C @ ( A @ ( B @ c_insert ) ) ) )
      | ~ ( C @ tc_set @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq__iff2_0) ).

thf(368,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)],[71]) ).

thf(140,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Union ) @ c_in ) ) )
      | ( B @ tc_set @ ( A @ ( B @ ( A @ c_Main_Ofinite__Union__1 ) @ c_in ) ) )
      | ~ ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Union_0) ).

thf(524,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)],[140]) ).

thf(168,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl_Or__into__trancl_0) ).

thf(581,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)],[168]) ).

thf(171,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ tc_UNITY_Oprogram @ ( D @ ( C @ ( B @ c_WFair_Oensures ) ) @ ( A @ c_in ) ) )
      | ~ ( D @ tc_UNITY_Oprogram @ ( D @ ( D @ tc_set @ ( C @ ( B @ c_minus ) ) @ c_WFair_Otransient ) @ ( A @ c_in ) ) )
      | ~ ( D @ tc_UNITY_Oprogram @ ( D @ ( D @ ( C @ ( B @ c_union ) ) @ ( D @ tc_set @ ( C @ ( B @ c_minus ) ) @ c_UNITY_Oconstrains ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WFair_OensuresI_0) ).

thf(588,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ tc_UNITY_Oprogram @ ( D @ ( C @ ( B @ c_WFair_Oensures ) ) @ ( A @ c_in ) ) )
      | ~ ( D @ tc_UNITY_Oprogram @ ( D @ ( D @ tc_set @ ( C @ ( B @ c_minus ) ) @ c_WFair_Otransient ) @ ( A @ c_in ) ) )
      | ~ ( D @ tc_UNITY_Oprogram @ ( D @ ( D @ ( C @ ( B @ c_union ) ) @ ( D @ tc_set @ ( C @ ( B @ c_minus ) ) @ c_UNITY_Oconstrains ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(136,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ tc_sum ) @ ( C @ ( D @ ( B @ ( E @ c_Sum__Type_OPlus ) ) ) @ ( D @ ( C @ ( A @ c_Sum__Type_OInr ) ) @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInrI_0) ).

thf(517,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)],[136]) ).

thf(50,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ tc_prod ) @ tc_set @ ( B @ ( A @ c_UNITY_OAllowedActs ) @ ( c_Relation_OId @ c_insert ) ) )
      = ( B @ ( A @ c_UNITY_OAllowedActs ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNITY_Oinsert__Id__AllowedActs_0) ).

thf(319,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ tc_prod ) @ tc_set @ ( B @ ( A @ c_UNITY_OAllowedActs ) @ ( c_Relation_OId @ c_insert ) ) )
      = ( B @ ( A @ c_UNITY_OAllowedActs ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(43,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ tc_set @ ( C @ ( B @ ( D @ c_insert ) ) @ ( A @ c_minus ) ) @ c_in ) ) )
      | ~ ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ tc_set @ ( B @ ( A @ c_minus ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff__insert__iff2_0) ).

thf(304,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)],[43]) ).

thf(64,axiom,
    ! [A: $i] :
      ( c_emptyset
      = ( A @ ( c_List_Olist_ONil @ c_List_Oset ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__empty2__iff2_0) ).

thf(351,plain,
    ! [A: $i] :
      ( c_emptyset
      = ( A @ ( c_List_Olist_ONil @ c_List_Oset ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(79,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = E )
      | ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
       != ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq__iff1_0) ).

thf(390,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)],[79]) ).

thf(2,negated_conjecture,
    t_a @ tc_UNITY_Oprogram @ ( t_a @ ( v_A @ c_WFair_Otransient ) @ ( v_F @ c_in ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).

thf(186,plain,
    t_a @ tc_UNITY_Oprogram @ ( t_a @ ( v_A @ c_WFair_Otransient ) @ ( v_F @ c_in ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(90,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ ( F @ c_Datatype__Universe_Ouprod ) ) ) @ ( D @ ( C @ ( A @ ( E @ c_Datatype__Universe_OScons ) ) ) @ c_in ) ) )
      | ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( F @ ( E @ c_in ) ) )
      | ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodI_0) ).

thf(418,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)],[90]) ).

thf(161,axiom,
    ! [B: $i,A: $i] : ( B @ ( c_UNIV @ ( A @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUNIV__I_0) ).

thf(568,plain,
    ! [B: $i,A: $i] : ( B @ ( c_UNIV @ ( A @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(19,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_List_Olist_ONil )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv__iff1_1) ).

thf(235,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)],[19]) ).

thf(100,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( E @ ( C @ ( B @ ( F @ c_Relation_OImage ) ) ) @ ( D @ c_in ) ) )
      | ~ ( E @ ( C @ tc_prod ) @ ( F @ ( E @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImageI_0) ).

thf(433,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)],[100]) ).

thf(118,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_Main_OUnionE__1 ) ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( C @ ( B @ c_Union ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnionE_1) ).

thf(478,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)],[118]) ).

thf(13,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != ( C @ ( D @ ( A @ c_append ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Osame__append__eq__iff1_0) ).

thf(214,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)],[13]) ).

thf(36,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__self__conv2__iff2_0) ).

thf(287,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(41,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( G @ tc_prod ) @ ( G @ ( D @ ( C @ ( H @ ( E @ c_Relation_Orel__comp ) ) ) ) @ ( D @ ( G @ ( B @ ( F @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( G @ tc_prod ) @ ( H @ ( C @ ( G @ ( A @ ( F @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Orel__compI_0) ).

thf(300,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)],[41]) ).

thf(48,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( D @ c_in ) ) )
      | ~ ( C @ ( C @ ( A @ c_List_Oset ) @ ( D @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oin__listsD__dest_0) ).

thf(315,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)],[48]) ).

thf(99,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsingletonI_0) ).

thf(432,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(28,axiom,
    ! [B: $i,A: $i] :
      ( A
      = ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oself__append__conv2__iff2_0) ).

thf(262,plain,
    ! [B: $i,A: $i] :
      ( A
      = ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(92,axiom,
    ! [A: $i] : ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OemptyI_0) ).

thf(422,plain,
    ! [A: $i] : ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(73,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( C @ ( c_emptyset @ ( A @ c_insert ) ) @ ( E @ c_Relation_OImage ) ) ) @ ( B @ c_in ) ) )
      | ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImage__singleton__iff__iff2_0) ).

thf(373,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)],[73]) ).

thf(178,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ ( C @ c_union ) ) @ c_in ) ) )
      | ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ c_in ) ) )
      | ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un__iff2_0) ).

thf(603,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)],[178]) ).

thf(159,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( C @ ( D @ ( E @ ( A @ ( C @ c_Main_OPlusE__2 ) ) ) @ c_in ) ) )
      | ( D @ ( B @ ( E @ ( D @ ( A @ ( B @ c_Main_OPlusE__1 ) ) ) @ c_in ) ) )
      | ~ ( E @ ( D @ tc_sum ) @ ( E @ ( D @ ( C @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_3) ).

thf(564,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)],[159]) ).

thf(53,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( B @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__3 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Odprod ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_2) ).

thf(326,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)],[53]) ).

thf(59,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( C @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__4 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__2 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Odprod ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_1) ).

thf(341,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)],[59]) ).

thf(132,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( B @ ( A @ c_in ) ) )
      | ~ ( D @ ( D @ ( C @ ( B @ c_inter ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OIntE_1) ).

thf(506,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)],[132]) ).

thf(83,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ tc_prod ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( C @ ( D @ c_Pair ) ) ) @ c_in ) ) )
      | ( B @ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( D @ ( C @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Owf ) )
      | ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert__iff2_0) ).

thf(400,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)],[83]) ).

thf(144,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_emptyset )
      | ~ ( C @ tc_UNITY_Oprogram @ ( C @ ( c_emptyset @ ( B @ c_UNITY_Oconstrains ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNITY_Oconstrains__empty2__iff1_0) ).

thf(532,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_emptyset )
      | ~ ( C @ tc_UNITY_Oprogram @ ( C @ ( c_emptyset @ ( B @ c_UNITY_Oconstrains ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(80,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( B @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_append ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv__iff1_1) ).

thf(395,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)],[80]) ).

thf(112,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( C @ ( B @ c_Pow ) @ ( A @ c_in ) ) )
      | ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OPow__iff__iff2_0) ).

thf(464,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)],[112]) ).

thf(96,axiom,
    ! [C: $i,B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl_Ortrancl__refl_0) ).

thf(427,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)],[96]) ).

thf(110,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( A @ c_in ) ) )
      | ~ ( C @ tc_set @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).

thf(459,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)],[110]) ).

thf(8,axiom,
    ! [B: $i,A: $i] :
      ( A
      = ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oself__append__conv__iff2_0) ).

thf(200,plain,
    ! [B: $i,A: $i] :
      ( A
      = ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(122,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_set @ ( D @ ( B @ c_minus ) ) @ ( A @ c_in ) ) )
      | ( C @ ( D @ ( A @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiffI_0) ).

thf(486,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)],[122]) ).

thf(115,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ ( C @ c_inter ) ) @ c_in ) ) )
      | ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_1) ).

thf(469,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)],[115]) ).

thf(45,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) )
      | ~ ( B @ ( C @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__converse__iff1_0) ).

thf(309,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)],[45]) ).

thf(149,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__3 ) ) ) ) ) @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__2 ) ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( E @ ( F @ tc_prod ) @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Orel__compE_0) ).

thf(543,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)],[149]) ).

thf(15,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
       != ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Oinject__iff1_1) ).

thf(222,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)],[15]) ).

thf(127,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( A @ c_List_Olists ) @ ( B @ c_in ) ) )
      | ~ ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_Oin__listsI__1 ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oin__listsI_1) ).

thf(496,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)],[127]) ).

thf(18,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( c_List_Olist_ONil
       != ( C @ ( B @ ( A @ c_append ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv__iff1_0) ).

thf(232,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)],[18]) ).

thf(25,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olistrel ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( A @ ( c_List_Olist_ONil @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Nil1_0) ).

thf(254,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)],[25]) ).

thf(16,axiom,
    ! [A: $i] :
      ( c_List_Olist_ONil
      = ( A @ ( c_List_Olist_ONil @ ( c_List_Olist_ONil @ c_append ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv__iff2_0) ).

thf(227,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)],[16]) ).

thf(10385,plain,
    $false,
    inference(e,[status(thm)],[414,365,347,555,333,249,408,523,276,247,511,614,269,202,597,385,500,185,257,344,357,196,559,189,284,416,289,448,492,443,321,211,238,514,574,353,480,397,293,453,411,428,527,452,380,302,349,561,407,467,435,583,461,551,324,229,566,484,317,593,610,420,519,578,488,339,537,476,526,590,328,471,457,569,371,503,605,343,244,266,360,205,508,311,541,398,558,530,586,298,425,430,264,279,375,601,423,402,545,259,579,291,572,313,498,466,187,219,274,377,208,599,387,494,535,521,455,608,306,563,438,241,490,426,548,617,355,553,194,199,331,502,576,336,595,612,450,363,539,482,368,524,581,588,517,319,304,351,390,186,418,568,235,433,478,214,287,300,315,432,262,422,373,603,564,326,341,506,400,532,395,464,427,459,200,486,469,309,543,222,496,232,254,227]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : COM011-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07  % Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.13/15.42  % Computer : n004.cluster.edu
% 0.13/15.42  % Model    : x86_64 x86_64
% 0.13/15.42  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/15.42  % Memory   : 8046.5625MB
% 0.13/15.42  % OS       : Linux 6.8.0-71-generic
% 0.13/15.42  % CPULimit : 300
% 0.13/15.42  % WCLimit  : 300
% 0.13/15.42  % DateTime : Sat Sep 26 23:21:08 UTC 2026
% 0.13/15.42  % CPUTime  : 
% 0.13/15.42  Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.18/16.00  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 2.33/16.40  % [INFO] 	 Parsing done (404ms). 
% 2.33/16.42  % [INFO] 	 Running in sequential loop mode. 
% 3.14/16.80  % [INFO] 	 eprover registered as external prover. 
% 3.14/16.81  % [INFO] 	 Scanning for conjecture ... 
% 3.34/16.99  % [INFO] 	 Found a conjecture (or negated_conjecture) and 1371 axioms. Running axiom selection ... 
% 4.20/17.17  % [INFO] 	 Axiom selection finished. Selected 181 axioms (removed 1190 axioms). 
% 4.93/17.34  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 4.93/17.36  % [INFO] 	 Type checking passed. 
% 4.93/17.37  % [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 ... 
% 47.03/25.98  % External prover 'e' found a proof!
% 47.03/25.98  % [INFO] 	 Killing All external provers ... 
% 47.03/25.98  % Time passed: 10415ms (effective reasoning time: 9555ms)
% 47.03/25.98  % Axioms used in derivation (181): cls_WFair_OensuresI_0, cls_Relation_OIdE_0, cls_Finite__Set_Ofinite__converse__iff1_0, cls_List_Ofinite__set_0, cls_Finite__Set_Ofinite__Union_0, cls_List_Oset__empty2__iff2_0, cls_Datatype__Universe_OuprodI_0, cls_Finite__Set_Ofinite__Un__iff1_1, cls_Datatype__Universe_OdprodE_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_Set_OsubsetI_1, cls_Sum__Type_OInr__not__Inl__iff1_0, cls_List_Olists_ONil_0, cls_Set_OInterD_0, cls_List_ONil__is__append__conv__iff2_0, 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_Set_Osingleton__insert__inj__eq__iff1_1, 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_UNITY_Oconstrains__weaken__L_0, cls_Set_OUnionE_1, cls_Finite__Set_OFinites_OinsertI_0, cls_List_Olistrel__Nil1_0, cls_Datatype__Universe_OIn1__eq__iff1_0, cls_Relation_OconverseE_1, cls_Sum__Type_OPlusE_0, cls_Finite__Set_Ofinite__Int_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, cls_Infinite__Set_Onat__not__finite_0, cls_UNITY_Oconstrains__UNIV__iff1_0, cls_Relation_Oconverse__iff__iff2_0, cls_Set_Osubset__refl_0, cls_List_Olist_Oinject__iff1_0, cls_Relation_ORangeE_0, cls_Set_OInterI_1, cls_List_Oset__empty__iff2_0, cls_Set_OUnCI_1, cls_Product__Type_OPair__eq__iff1_0, cls_Set_OinsertCI_0, cls_Set_Osingleton__insert__inj__eq_H__iff2_0, cls_Set_OPow__iff__iff2_0, cls_List_Oappend__in__lists__conv__iff1_0, cls_Finite__Set_Ofinite__converse__iff2_0, cls_Relation_OdiagI_0, cls_Datatype__Universe_OIn0__not__In1__iff1_0, cls_Datatype__Universe_OdprodE_1, cls_Set_OUNIV__I_0, cls_Set_OsubsetI_0, cls_Sum__Type_OPlusE_3, cls_Finite__Set_Ofinite__Diff__insert__iff1_0, cls_List_OlistsE_0, cls_Finite__Set_Ofinite__Un__iff1_0, cls_List_Oself__append__conv__iff2_0, cls_Relation_ODomainI_0, cls_Set_OinsertE_0, cls_Set_OUnE_0, cls_List_Owf__lex_0, cls_UNITY_Oconstrains__empty_0, cls_Set_OUn__empty__iff1_1, cls_Relation_Orel__compE_2, cls_Relation_OImageE_1, cls_Relation_OdiagE_0, cls_Set_OsingletonD__dest_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_List_Oappend__is__Nil__conv__iff2_0, cls_Relation_OIdI_0, cls_List_Oappend1__eq__conv__iff1_1, cls_Set_OsubsetD_0, cls_Product__Type_OPair__eq__iff1_1, cls_List_Oin__listsI_1, cls_List_Osame__append__eq__iff1_0, cls_Set_OsingletonI_0, cls_Set_Osubset__antisym_0, cls_Wellfounded__Recursion_Oacyclic__insert__iff1_0, cls_UNITY_OId__in__AllowedActs_0, cls_List_Oself__append__conv__iff1_0, cls_Datatype_Oelem__o2s__iff1_0, cls_Datatype__Universe_OuprodE_2, cls_Relation_Oconverse__iff__iff1_0, cls_Relation_OconverseE_0, cls_Datatype__Universe_OIn1__not__In0__iff1_0, cls_Datatype__Universe_OScons__Scons__eq__iff1_0, cls_Datatype_Oelem__o2s__iff2_0, cls_List_Olist_Oinject__iff1_1, cls_Datatype__Universe_OuprodE_0, cls_Set_ODiffE_0, cls_Sum__Type_OInl__not__Inr__iff1_0, cls_Infinite__Set_Oatmost__one__unique_0, cls_Datatype__Universe_OdprodE_2, cls_Relation_ORangeI_0, cls_List_Oset__empty__iff1_0, cls_List_Oself__append__conv2__iff2_0, cls_Set_OIntE_1, cls_Relation_Opair__in__Id__conv__iff1_0, cls_Set_OIntI_0, cls_Finite__Set_Ofinite__Union_1, cls_UNITY_OId__in__Acts_0, cls_Sum__Type_OPlusE_2, cls_Set_Osingleton__insert__inj__eq__iff2_0, cls_Wellfounded__Recursion_Owf__empty_0, cls_List_Olist_Odistinct__2__iff1_0, cls_Transitive__Closure_Or__into__rtrancl_0, cls_Finite__Set_Ofinite__Diff__insert__iff2_0, cls_WFair_Otransient__strengthen_0, cls_Datatype__Universe_OdprodI_0, cls_List_OlistsE_1, cls_List_Oappend__self__conv2__iff2_0, cls_List_Oappend__self__conv__iff2_0, cls_Set_OUn__empty__iff2_0, cls_List_Oappend__same__eq__iff1_0, cls_Set_ODiffI_0, cls_Sum__Type_OInrI_0, cls_UNITY_Oconstrains__empty2__iff1_0, cls_Datatype__Universe_Odsum__In1I_0, cls_Datatype__Universe_OuprodE_1, cls_UNITY_Oinsert__Id__AllowedActs_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_Relation_OdiagE_1, cls_UNITY_Oconstrains__UNIV2_0, cls_Relation_OImage__singleton__iff__iff1_0, cls_UNITY_Oconstrains__empty2__iff2_0, cls_List_ONil2__notin__lex__iff1_0, cls_List_Oself__append__conv2__iff1_0, cls_Set_OInterI_0, cls_List_Olist_Odistinct__1__iff1_0, cls_UNITY_Oconstrains__UNIV__iff2_0, cls_Relation_ODomainE_0, cls_List_Oin__listsI_0, cls_Sum__Type_OPlusE_1, cls_Wellfounded__Recursion_Owf__insert__iff1_1, cls_Set_OUnionE_0, cls_List_Oappend1__eq__conv__iff1_0, cls_List_Oin__listsD__dest_0, cls_Set_OPow__iff__iff1_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_WFair_OleadsTo__Basis_0, cls_Set_OIntE_0, cls_List_Oappend__is__Nil__conv__iff1_1, cls_Finite__Set_Ofinite__Un__iff2_0, cls_UNITY_Oinsert__Id__Acts_0, cls_Relation_Orel__compE_1, cls_List_Oappend__in__lists__conv__iff1_1, cls_Set_OinsertCI_1, cls_Set_ODiffE_1, cls_List_ONil__is__append__conv__iff1_1, cls_Transitive__Closure_Otrancl__into__rtrancl_0, cls_List_Oappend__self__conv__iff1_0, cls_Set_OUnCI_0, cls_List_Olists_OCons_0
% 47.03/25.98  % No. of inferences in proof: 369
% 47.03/25.99  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 10415 ms resp. 9555 ms w/o parsing
% 47.98/26.13  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 47.98/26.14  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------