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

%------------------------------------------------------------------------------
% File     : Leo-III---1.8.0
% Problem  : LAT259-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39

% Computer : n006.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 07:46:50 AM UTC 2026

% Result   : Unsatisfiable 15.34s 5.39s
% Output   : Refutation 16.33s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :  167
% Syntax   : Number of formulae    :  335 ( 139 unt;   0 typ;   0 def)
%            Number of atoms       :  579 ( 192 equ;   0 cnn)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives : 5014 ( 254   ~; 244   |;   0   &;4516   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (  10 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   79 (  77 usr;  16 con; 0-6 aty)
%            Number of variables   : 1066 (   0   ^;1066   !;   0   ?;1066   :)

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

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

thf(v_a_decl,type,
    v_a: $i ).

thf(v_b_decl,type,
    v_b: $i ).

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

thf(v_r_decl,type,
    v_r: $i ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(c_Tarski_OPartialOrder_decl,type,
    c_Tarski_OPartialOrder: $i ).

thf(tc_Tarski_Opotype_Opotype__ext__type_decl,type,
    tc_Tarski_Opotype_Opotype__ext__type: $i > $i > $i ).

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

thf(c_Relation_Oantisym_decl,type,
    c_Relation_Oantisym: $i > $i > $o ).

thf(c_Tarski_Opotype_Oorder_decl,type,
    c_Tarski_Opotype_Oorder: $i > $i > $i > $i ).

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

thf(c_List_Onth_decl,type,
    c_List_Onth: $i > $i > $i > $i ).

thf(c_List_Ozip_decl,type,
    c_List_Ozip: $i > $i > $i > $i > $i ).

thf(c_Relation_Orefl_decl,type,
    c_Relation_Orefl: $i > $i > $i > $o ).

thf(c_Tarski_Opotype_Opset_decl,type,
    c_Tarski_Opotype_Opset: $i > $i > $i > $i ).

thf(c_Relation_Otrans_decl,type,
    c_Relation_Otrans: $i > $i > $o ).

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

thf(c_List_Olexord_decl,type,
    c_List_Olexord: $i > $i > $i ).

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

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

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

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

thf(c_IntDef_Ointrel_decl,type,
    c_IntDef_Ointrel: $i ).

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

thf(c_fst_decl,type,
    c_fst: $i > $i > $i > $i ).

thf(c_snd_decl,type,
    c_snd: $i > $i > $i > $i ).

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

thf(c_Set_Ocontents_decl,type,
    c_Set_Ocontents: $i > $i > $i ).

thf(c_List_Olistset_decl,type,
    c_List_Olistset: $i > $i > $i ).

thf(c_IntDef_OInteg_decl,type,
    c_IntDef_OInteg: $i ).

thf(c_Main_Oantisym__def__1_decl,type,
    c_Main_Oantisym__def__1: $i > $i > $i ).

thf(c_Main_Oantisym__def__2_decl,type,
    c_Main_Oantisym__def__2: $i > $i > $i ).

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

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

thf(v_cl_decl,type,
    v_cl: $i ).

thf(c_Main_Olexord__Nil__left__1_decl,type,
    c_Main_Olexord__Nil__left__1: $i > $i > $i ).

thf(c_Main_Olexord__Nil__left__2_decl,type,
    c_Main_Olexord__Nil__left__2: $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_OdiagE__1_decl,type,
    c_Main_OdiagE__1: $i > $i > $i > $i ).

thf(c_Main_Osurj__pair__1_decl,type,
    c_Main_Osurj__pair__1: $i > $i > $i > $i ).

thf(c_Main_Osurj__pair__2_decl,type,
    c_Main_Osurj__pair__2: $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_Oall__not__in__conv__1_decl,type,
    c_Main_Oall__not__in__conv__1: $i > $i > $i ).

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

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

thf(89,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Relation_ODomain ) ) )
      = ( B @ ( B @ ( A @ c_Relation_ODomain ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__domain_0) ).

thf(365,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Relation_ODomain ) ) )
      = ( B @ ( B @ ( A @ c_Relation_ODomain ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(139,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ tc_prod ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( C @ ( D @ c_Pair ) ) ) @ c_in ) ) )
      | ( B @ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( D @ ( C @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Owf ) )
      | ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert_2) ).

thf(479,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)],[139]) ).

thf(38,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( tc_Product__Type_Ounit @ ( B @ ( A @ c_Tarski_Opotype_Oorder ) ) @ c_Relation_Oantisym ) )
      | ~ ( tc_Product__Type_Ounit @ ( B @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OPartialOrder @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_OPartialOrder__iff_1) ).

thf(249,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( tc_Product__Type_Ounit @ ( B @ ( A @ c_Tarski_Opotype_Oorder ) ) @ c_Relation_Oantisym ) )
      | ~ ( tc_Product__Type_Ounit @ ( B @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OPartialOrder @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(134,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__3 ) ) ) ) ) @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__2 ) ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( E @ ( F @ tc_prod ) @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Orel__compE_0) ).

thf(468,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)],[134]) ).

thf(31,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( F @ c_List_Olex ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( E @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( F @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( F @ c_List_Olex ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_OCons__in__lex_1) ).

thf(234,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( F @ c_List_Olex ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( E @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( F @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( F @ c_List_Olex ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(140,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Oacyclic ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert_1) ).

thf(481,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)],[140]) ).

thf(3,negated_conjecture,
    v_a != v_b,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).

thf(170,plain,
    v_a != v_b,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(126,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( C @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__not__refl_0) ).

thf(449,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( C @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(37,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Relation_Orel__comp ) ) ) ) )
      = ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl__idemp__self__comp_0) ).

thf(247,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Relation_Orel__comp ) ) ) ) )
      = ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(96,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ ( c_Relation_OId @ c_Relation_OImage ) ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImage__Id_0) ).

thf(379,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ ( c_Relation_OId @ c_Relation_OImage ) ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(164,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( E @ c_Relation_ORange ) ) @ ( B @ c_in ) ) )
      | ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ORangeI_0) ).

thf(533,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)],[164]) ).

thf(148,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_Odiag ) @ ( C @ ( C @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OdiagI_0) ).

thf(500,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)],[148]) ).

thf(136,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( F @ c_List_Olexord ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( E @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( F @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( F @ c_List_Olexord ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olexord__cons__cons_1) ).

thf(472,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( F @ c_List_Olexord ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( E @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( F @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( F @ c_List_Olexord ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(167,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( E @ ( C @ ( B @ ( F @ c_Relation_OImage ) ) ) @ ( D @ c_in ) ) )
      | ~ ( E @ ( C @ tc_prod ) @ ( F @ ( E @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImageI_0) ).

thf(538,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)],[167]) ).

thf(108,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
       != ( tc_nat @ ( B @ ( C @ c_plus ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__right__cancel_0) ).

thf(404,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
       != ( tc_nat @ ( B @ ( C @ c_plus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(8,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ tc_List_Olist @ ( B @ c_Nat_Osize ) )
        = ( C @ tc_List_Olist @ ( E @ c_Nat_Osize ) ) )
      | ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( F @ c_List_Olex ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( E @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( F @ c_List_Olex ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_OCons__in__lex_3) ).

thf(185,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ tc_List_Olist @ ( B @ c_Nat_Osize ) )
        = ( C @ tc_List_Olist @ ( E @ c_Nat_Osize ) ) )
      | ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( F @ c_List_Olex ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( E @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( F @ c_List_Olex ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(114,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( D @ tc_prod ) @ ( B @ ( D @ ( A @ ( C @ c_Wellfounded__Relations_Olex__prod ) ) ) @ c_Wellfounded__Recursion_Owf ) )
      | ~ ( D @ ( C @ c_Wellfounded__Recursion_Owf ) )
      | ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Owf__lex__prod_0) ).

thf(417,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( D @ tc_prod ) @ ( B @ ( D @ ( A @ ( C @ c_Wellfounded__Relations_Olex__prod ) ) ) @ c_Wellfounded__Recursion_Owf ) )
      | ~ ( D @ ( C @ c_Wellfounded__Recursion_Owf ) )
      | ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(56,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( tc_Product__Type_Ounit @ ( B @ ( A @ c_Tarski_Opotype_Oorder ) ) @ c_Relation_Otrans ) )
      | ~ ( tc_Product__Type_Ounit @ ( B @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OPartialOrder @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_OPartialOrder__iff_2) ).

thf(288,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( tc_Product__Type_Ounit @ ( B @ ( A @ c_Tarski_Opotype_Oorder ) ) @ c_Relation_Otrans ) )
      | ~ ( tc_Product__Type_Ounit @ ( B @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OPartialOrder @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(62,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( B @ ( A @ ( c_Relation_OId @ c_Relation_Orel__comp ) ) ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OId__O__R_0) ).

thf(301,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( B @ ( A @ ( c_Relation_OId @ c_Relation_Orel__comp ) ) ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(122,axiom,
    ( v_r
    = ( tc_Product__Type_Ounit @ ( t_a @ ( v_cl @ c_Tarski_Opotype_Oorder ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Or_A_61_61_Aorder_Acl_0) ).

thf(436,plain,
    ( v_r
    = ( tc_Product__Type_Ounit @ ( t_a @ ( v_cl @ c_Tarski_Opotype_Oorder ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(150,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_snd ) ) )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_Osnd__conv_0) ).

thf(504,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_snd ) ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(80,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ tc_prod ) @ ( c_Relation_OId @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_union ) ) )
      = ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Oreflcl__trancl_0) ).

thf(344,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ tc_prod ) @ ( c_Relation_OId @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_union ) ) )
      = ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(13,axiom,
    ! [A: $i] :
      ( ~ ( A @ class_Finite__Set_Ofinite )
      | ( A @ tc_set @ class_Finite__Set_Ofinite ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_3) ).

thf(196,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Finite__Set_Ofinite )
      | ( A @ tc_set @ class_Finite__Set_Ofinite ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(116,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ c_Wellfounded__Recursion_Oacyclic ) )
      | ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Oacyclic ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert_0) ).

thf(421,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)],[116]) ).

thf(54,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( B @ ( c_Relation_OId @ ( A @ c_Relation_Orel__comp ) ) ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OR__O__Id_0) ).

thf(284,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( B @ ( c_Relation_OId @ ( A @ c_Relation_Orel__comp ) ) ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(28,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( C @ ( D @ ( A @ c_List_Olist_OCons ) ) @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( D @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olists_OCons_0) ).

thf(228,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)],[28]) ).

thf(69,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ( D @ ( C @ ( A @ c_in ) ) )
      | ~ ( D @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_0) ).

thf(316,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)],[69]) ).

thf(43,axiom,
    ! [C: $i,B: $i,A: $i] :
      ~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olex ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( A @ ( c_List_Olist_ONil @ c_Pair ) ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__notin__lex_0) ).

thf(261,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)],[43]) ).

thf(22,axiom,
    ! [A: $i] :
      ( ( A @ ( c_emptyset @ ( c_emptyset @ c_union ) ) )
      = c_emptyset ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty_2) ).

thf(216,plain,
    ! [A: $i] :
      ( ( A @ ( c_emptyset @ ( c_emptyset @ c_union ) ) )
      = c_emptyset ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(145,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Owf ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert_1) ).

thf(492,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)],[145]) ).

thf(6,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_emptyset )
      | ( ( C @ ( B @ ( A @ c_union ) ) )
       != c_emptyset ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty_0) ).

thf(179,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)],[6]) ).

thf(71,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
       != ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Oinject_0) ).

thf(321,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)],[71]) ).

thf(95,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( c_emptyset
     != ( C @ ( B @ ( A @ c_insert ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__not__insert_0) ).

thf(376,plain,
    ! [C: $i,B: $i,A: $i] :
      ( c_emptyset
     != ( C @ ( B @ ( A @ c_insert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(84,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = A )
      | ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
       != ( B @ ( D @ ( C @ c_insert ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_0) ).

thf(353,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)],[84]) ).

thf(111,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Oless__than__iff_1) ).

thf(411,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(119,axiom,
    ( v_A
    = ( tc_Product__Type_Ounit @ ( t_a @ ( v_cl @ c_Tarski_Opotype_Opset ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_OA_A_61_61_Apset_Acl_0) ).

thf(428,plain,
    ( v_A
    = ( tc_Product__Type_Ounit @ ( t_a @ ( v_cl @ c_Tarski_Opotype_Opset ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(45,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olistrel ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Nil2_0) ).

thf(265,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)],[45]) ).

thf(161,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( G @ tc_prod ) @ ( G @ ( D @ ( C @ ( H @ ( E @ c_Relation_Orel__comp ) ) ) ) @ ( D @ ( G @ ( B @ ( F @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( G @ tc_prod ) @ ( H @ ( C @ ( G @ ( A @ ( F @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Orel__compI_0) ).

thf(527,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)],[161]) ).

thf(67,axiom,
    ! [C: $i,B: $i,A: $i] :
      ~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olex ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil2__notin__lex_0) ).

thf(312,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)],[67]) ).

thf(65,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( E @ ( E @ ( D @ ( D @ ( c_emptyset @ ( C @ c_insert ) ) @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImage__singleton__iff_0) ).

thf(307,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)],[65]) ).

thf(58,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ tc_prod ) @ ( c_IntDef_Ointrel @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_emptyset @ ( A @ c_insert ) ) @ ( c_IntDef_Ointrel @ c_Relation_OImage ) ) ) )
       != ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_emptyset @ ( B @ c_insert ) ) @ ( c_IntDef_Ointrel @ c_Relation_OImage ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oequiv__intrel__iff_0) ).

thf(292,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ tc_prod ) @ ( c_IntDef_Ointrel @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_emptyset @ ( A @ c_insert ) ) @ ( c_IntDef_Ointrel @ c_Relation_OImage ) ) ) )
       != ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_emptyset @ ( B @ c_insert ) ) @ ( c_IntDef_Ointrel @ c_Relation_OImage ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(162,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ c_Wellfounded__Recursion_Owf ) )
      | ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Owf ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert_0) ).

thf(529,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)],[162]) ).

thf(97,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ c_Set_Ocontents ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Ocontents__eq_0) ).

thf(381,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ c_Set_Ocontents ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(24,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( c_emptyset @ c_union ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty__left_0) ).

thf(220,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( c_emptyset @ c_union ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(82,axiom,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__add__less2_0) ).

thf(349,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(60,axiom,
    ! [B: $i,A: $i] : ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olists ) @ ( c_List_Olist_ONil @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olists_ONil_0) ).

thf(297,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)],[60]) ).

thf(50,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) )
      | ~ ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Wellfounded__Recursion_Oacyclic ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse_0) ).

thf(275,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)],[50]) ).

thf(11,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( D @ c_union ) ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__iff_2) ).

thf(192,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)],[11]) ).

thf(109,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( tc_Product__Type_Ounit @ ( B @ ( A @ c_Tarski_Opotype_Oorder ) ) @ ( tc_Product__Type_Ounit @ ( B @ ( A @ c_Tarski_Opotype_Opset ) ) @ c_Relation_Orefl ) ) )
      | ~ ( tc_Product__Type_Ounit @ ( B @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OPartialOrder @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_OPartialOrder__iff_0) ).

thf(407,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( tc_Product__Type_Ounit @ ( B @ ( A @ c_Tarski_Opotype_Oorder ) ) @ ( tc_Product__Type_Ounit @ ( B @ ( A @ c_Tarski_Opotype_Opset ) ) @ c_Relation_Orefl ) ) )
      | ~ ( tc_Product__Type_Ounit @ ( B @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OPartialOrder @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(74,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_plus ) ) @ ( tc_nat @ ( A @ ( C @ c_plus ) ) @ c_less ) ) )
      | ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__less_1) ).

thf(329,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_plus ) ) @ ( tc_nat @ ( A @ ( C @ c_plus ) ) @ c_less ) ) )
      | ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(26,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ ( E @ c_List_Olistrel ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( C @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__2 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ ( E @ c_List_Olistrel ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Cons2_1) ).

thf(224,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ ( E @ c_List_Olistrel ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( C @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__2 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ ( E @ c_List_Olistrel ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(157,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( D @ c_List_Olexord ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ ( B @ ( E @ c_List_Olist_OCons ) ) @ ( C @ ( A @ ( E @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( D @ c_List_Olexord ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olexord__cons__cons_3) ).

thf(519,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( D @ c_List_Olexord ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ ( B @ ( E @ c_List_Olist_OCons ) ) @ ( C @ ( A @ ( E @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( D @ c_List_Olexord ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(107,axiom,
    tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_Otrans ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Otrans__less__than_0) ).

thf(403,plain,
    tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_Otrans ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(9,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ ( B @ ( A @ c_insert ) ) @ c_union ) ) )
      = ( C @ ( C @ ( D @ ( B @ c_union ) ) @ ( A @ c_insert ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__insert__left_0) ).

thf(188,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ ( B @ ( A @ c_insert ) ) @ c_union ) ) )
      = ( C @ ( C @ ( D @ ( B @ c_union ) ) @ ( A @ c_insert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(100,axiom,
    ! [A: $i] :
      ( ( A @ ( c_List_Olist_ONil @ c_List_Olistset ) )
      = ( A @ tc_List_Olist @ ( c_emptyset @ ( c_List_Olist_ONil @ c_insert ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistset_Osimps__1_0) ).

thf(388,plain,
    ! [A: $i] :
      ( ( A @ ( c_List_Olist_ONil @ c_List_Olistset ) )
      = ( A @ tc_List_Olist @ ( c_emptyset @ ( c_List_Olist_ONil @ c_insert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(85,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( B @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_OlistsE_0) ).

thf(356,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)],[85]) ).

thf(2,negated_conjecture,
    t_a @ ( t_a @ tc_prod ) @ ( v_r @ ( t_a @ ( t_a @ ( v_a @ ( v_b @ c_Pair ) ) ) @ c_in ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).

thf(169,plain,
    t_a @ ( t_a @ tc_prod ) @ ( v_r @ ( t_a @ ( t_a @ ( v_a @ ( v_b @ c_Pair ) ) ) @ c_in ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(143,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( B @ ( A @ c_Main_Oantisym__def__2 ) @ ( B @ ( A @ c_Main_Oantisym__def__1 ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( B @ ( A @ c_Relation_Oantisym ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Oantisym__def_1) ).

thf(488,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( B @ ( A @ c_Main_Oantisym__def__2 ) @ ( B @ ( A @ c_Main_Oantisym__def__1 ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( B @ ( A @ c_Relation_Oantisym ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(138,axiom,
    ! [B: $i,A: $i] :
      ( ( A = c_emptyset )
      | ( B @ ( A @ ( B @ ( A @ c_Main_Oall__not__in__conv__1 ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oall__not__in__conv_0) ).

thf(476,plain,
    ! [B: $i,A: $i] :
      ( ( A = c_emptyset )
      | ( B @ ( A @ ( B @ ( A @ c_Main_Oall__not__in__conv__1 ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(20,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( D @ ( B @ c_union ) ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__iff_1) ).

thf(212,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)],[20]) ).

thf(73,axiom,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_1) ).

thf(328,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(41,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( E @ tc_prod ) @ ( A @ ( C @ ( E @ ( B @ ( D @ c_List_Ozip ) ) ) @ c_List_Onth ) ) )
        = ( C @ ( E @ ( C @ ( A @ ( B @ c_List_Onth ) ) @ ( E @ ( A @ ( D @ c_List_Onth ) ) @ c_Pair ) ) ) ) )
      | ~ ( tc_nat @ ( E @ tc_List_Olist @ ( D @ c_Nat_Osize ) @ ( A @ c_less ) ) )
      | ~ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize ) @ ( A @ c_less ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__zip_0) ).

thf(256,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( E @ tc_prod ) @ ( A @ ( C @ ( E @ ( B @ ( D @ c_List_Ozip ) ) ) @ c_List_Onth ) ) )
        = ( C @ ( E @ ( C @ ( A @ ( B @ c_List_Onth ) ) @ ( E @ ( A @ ( D @ c_List_Onth ) ) @ c_Pair ) ) ) ) )
      | ~ ( tc_nat @ ( E @ tc_List_Olist @ ( D @ c_Nat_Osize ) @ ( A @ c_less ) ) )
      | ~ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize ) @ ( A @ c_less ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(103,axiom,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__add__less1_0) ).

thf(393,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(155,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Main_ODomainE__1 ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ODomainE_0) ).

thf(515,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)],[155]) ).

thf(129,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( B @ ( A @ c_Main_Oantisym__def__1 ) @ ( B @ ( A @ c_Main_Oantisym__def__2 ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( B @ ( A @ c_Relation_Oantisym ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Oantisym__def_2) ).

thf(457,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( B @ ( A @ c_Main_Oantisym__def__1 ) @ ( B @ ( A @ c_Main_Oantisym__def__2 ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( B @ ( A @ c_Relation_Oantisym ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(4,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( D @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__2 ) ) ) ) @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__1 ) ) ) ) @ c_List_Olist_OCons ) ) ) )
      | ~ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ ( E @ c_List_Olistrel ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Cons2_0) ).

thf(173,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( D @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__2 ) ) ) ) @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__1 ) ) ) ) @ c_List_Olist_OCons ) ) ) )
      | ~ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ ( E @ c_List_Olistrel ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(92,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olenlex ) @ c_Wellfounded__Recursion_Owf ) )
      | ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Owf__lenlex_0) ).

thf(371,plain,
    ! [B: $i,A: $i] :
      ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olenlex ) @ c_Wellfounded__Recursion_Owf ) )
      | ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(35,axiom,
    ! [A: $i] :
      ( ( A @ ( c_emptyset @ c_Transitive__Closure_Ortrancl ) )
      = c_Relation_OId ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl__empty_0) ).

thf(244,plain,
    ! [A: $i] :
      ( ( A @ ( c_emptyset @ c_Transitive__Closure_Ortrancl ) )
      = c_Relation_OId ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(87,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
     != B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ox2_A_D_At1_A_61_At1_A_61_61_AFalse_0) ).

thf(360,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
     != B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(17,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_emptyset )
      | ( ( C @ ( B @ ( A @ c_union ) ) )
       != c_emptyset ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty_1) ).

thf(205,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)],[17]) ).

thf(152,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ ( E @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) )
      | ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ODomainI_0) ).

thf(508,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)],[152]) ).

thf(105,axiom,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_emptyset @ ( A @ c_insert ) ) @ ( c_IntDef_Ointrel @ c_Relation_OImage ) ) ) )
        = ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_emptyset @ ( B @ c_insert ) ) @ ( c_IntDef_Ointrel @ c_Relation_OImage ) ) ) ) )
      | ~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ tc_prod ) @ ( c_IntDef_Ointrel @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oequiv__intrel__iff_1) ).

thf(398,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_emptyset @ ( A @ c_insert ) ) @ ( c_IntDef_Ointrel @ c_Relation_OImage ) ) ) )
        = ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_emptyset @ ( B @ c_insert ) ) @ ( c_IntDef_Ointrel @ c_Relation_OImage ) ) ) ) )
      | ~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ tc_prod ) @ ( c_IntDef_Ointrel @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(61,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_insert ) ) )
       != ( C @ ( c_emptyset @ ( D @ c_insert ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H_0) ).

thf(298,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)],[61]) ).

thf(52,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( D @ c_insert ) ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_2) ).

thf(279,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)],[52]) ).

thf(125,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = E )
      | ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
       != ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq_0) ).

thf(444,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)],[125]) ).

thf(154,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_less ) ) )
      | ~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Oless__than__iff_0) ).

thf(513,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_less ) ) )
      | ~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(120,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( B @ ( B @ ( A @ c_Main_Olexord__Nil__left__2 ) @ ( B @ ( A @ c_Main_Olexord__Nil__left__1 ) @ c_List_Olist_OCons ) ) ) )
      | ~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olexord ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( A @ ( c_List_Olist_ONil @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olexord__Nil__left_0) ).

thf(430,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( B @ ( B @ ( A @ c_Main_Olexord__Nil__left__2 ) @ ( B @ ( A @ c_Main_Olexord__Nil__left__1 ) @ c_List_Olist_OCons ) ) ) )
      | ~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olexord ) @ ( 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)],[120]) ).

thf(5,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D
        = ( C @ ( C @ ( B @ ( A @ ( D @ ( E @ c_Main_Olistrel__Cons1__2 ) ) ) ) @ ( C @ ( B @ ( A @ ( D @ ( E @ c_Main_Olistrel__Cons1__1 ) ) ) ) @ c_List_Olist_OCons ) ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( E @ c_List_Olistrel ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Cons1_0) ).

thf(176,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D
        = ( C @ ( C @ ( B @ ( A @ ( D @ ( E @ c_Main_Olistrel__Cons1__2 ) ) ) ) @ ( C @ ( B @ ( A @ ( D @ ( E @ c_Main_Olistrel__Cons1__1 ) ) ) ) @ c_List_Olist_OCons ) ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( E @ c_List_Olistrel ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(117,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( C @ ( C @ tc_prod ) @ ( F @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( F @ c_List_Olexord ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olexord__cons__cons_0) ).

thf(423,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( C @ ( C @ tc_prod ) @ ( F @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( F @ c_List_Olexord ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(55,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( c_emptyset @ c_Relation_ODomain ) ) )
      = c_emptyset ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ODomain__empty_0) ).

thf(286,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( c_emptyset @ c_Relation_ODomain ) ) )
      = c_emptyset ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(53,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olistrel ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( A @ ( c_List_Olist_ONil @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Nil1_0) ).

thf(281,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)],[53]) ).

thf(42,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Product__Type_Ounit @ ( B @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OPartialOrder @ ( A @ c_in ) ) )
      | ~ ( B @ ( tc_Product__Type_Ounit @ ( B @ ( A @ c_Tarski_Opotype_Oorder ) ) @ c_Relation_Otrans ) )
      | ~ ( B @ ( tc_Product__Type_Ounit @ ( B @ ( A @ c_Tarski_Opotype_Oorder ) ) @ ( tc_Product__Type_Ounit @ ( B @ ( A @ c_Tarski_Opotype_Opset ) ) @ c_Relation_Orefl ) ) )
      | ~ ( B @ ( tc_Product__Type_Ounit @ ( B @ ( A @ c_Tarski_Opotype_Oorder ) ) @ c_Relation_Oantisym ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_OPartialOrder__iff_3) ).

thf(259,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Product__Type_Ounit @ ( B @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OPartialOrder @ ( A @ c_in ) ) )
      | ~ ( B @ ( tc_Product__Type_Ounit @ ( B @ ( A @ c_Tarski_Opotype_Oorder ) ) @ c_Relation_Otrans ) )
      | ~ ( B @ ( tc_Product__Type_Ounit @ ( B @ ( A @ c_Tarski_Opotype_Oorder ) ) @ ( tc_Product__Type_Ounit @ ( B @ ( A @ c_Tarski_Opotype_Opset ) ) @ c_Relation_Orefl ) ) )
      | ~ ( B @ ( tc_Product__Type_Ounit @ ( B @ ( A @ c_Tarski_Opotype_Oorder ) ) @ c_Relation_Oantisym ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(112,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ class_Finite__Set_Ofinite )
      | ~ ( B @ class_Finite__Set_Ofinite )
      | ( B @ ( A @ tc_prod ) @ class_Finite__Set_Ofinite ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_prod_0) ).

thf(413,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ class_Finite__Set_Ofinite )
      | ~ ( B @ class_Finite__Set_Ofinite )
      | ( B @ ( A @ tc_prod ) @ class_Finite__Set_Ofinite ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(102,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( A @ c_Relation_Odiag ) @ c_Relation_ORange ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ORange__diag_0) ).

thf(391,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( A @ c_Relation_Odiag ) @ c_Relation_ORange ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(133,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( F @ tc_prod ) @ ( C @ ( D @ ( F @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__2 ) ) ) ) ) @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__1 ) ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( E @ ( F @ tc_prod ) @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Orel__compE_1) ).

thf(466,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)],[133]) ).

thf(77,axiom,
    ! [A: $i] :
      ( ( A @ ( A @ ( c_Relation_OId @ c_Relation_Oconverse ) ) )
      = c_Relation_OId ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Oconverse__Id_0) ).

thf(335,plain,
    ! [A: $i] :
      ( ( A @ ( A @ ( c_Relation_OId @ c_Relation_Oconverse ) ) )
      = c_Relation_OId ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(32,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( A
     != ( C @ ( A @ ( B @ c_List_Olist_OCons ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onot__Cons__self_0) ).

thf(236,plain,
    ! [C: $i,B: $i,A: $i] :
      ( A
     != ( C @ ( A @ ( B @ c_List_Olist_OCons ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(49,axiom,
    ! [A: $i] : ( A @ ( c_emptyset @ c_Wellfounded__Recursion_Owf ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__empty_0) ).

thf(274,plain,
    ! [A: $i] : ( A @ ( c_emptyset @ c_Wellfounded__Recursion_Owf ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(115,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__2 ) ) ) @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( D @ tc_prod ) @ ( D @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OconverseE_0) ).

thf(419,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)],[115]) ).

thf(29,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Oconverse ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Oconverse__converse_0) ).

thf(230,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Oconverse ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(127,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( C @ ( C @ tc_prod ) @ ( c_Relation_OId @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Opair__in__Id__conv_0) ).

thf(451,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)],[127]) ).

thf(63,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ tc_prod ) @ ( c_Relation_OId @ ( A @ c_union ) ) @ c_Transitive__Closure_Otrancl ) )
      = ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__reflcl_0) ).

thf(303,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ tc_prod ) @ ( c_Relation_OId @ ( A @ c_union ) ) @ c_Transitive__Closure_Otrancl ) )
      = ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(47,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( D @ c_List_Olexord ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( c_List_Olist_ONil @ c_Pair ) ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olexord__Nil__left_1) ).

thf(271,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( D @ c_List_Olexord ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( c_List_Olist_ONil @ c_Pair ) ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(18,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_union ) ) )
      = ( D @ ( D @ ( C @ ( A @ c_union ) ) @ ( B @ c_insert ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__insert__right_0) ).

thf(208,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_union ) ) )
      = ( D @ ( D @ ( C @ ( A @ c_union ) ) @ ( B @ c_insert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(146,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( c_Relation_OId @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Opair__in__Id__conv_1) ).

thf(494,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)],[146]) ).

thf(90,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( c_emptyset @ ( A @ c_Relation_OImage ) ) ) )
      = c_emptyset ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImage__empty_0) ).

thf(367,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( c_emptyset @ ( A @ c_Relation_OImage ) ) ) )
      = c_emptyset ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(165,axiom,
    ! [C: $i,B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl_Ortrancl__refl_0) ).

thf(535,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)],[165]) ).

thf(141,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( B @ ( B @ ( B @ ( A @ c_Main_OIdE__1 ) @ ( B @ ( A @ c_Main_OIdE__1 ) @ c_Pair ) ) ) ) )
      | ~ ( B @ ( B @ tc_prod ) @ ( c_Relation_OId @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OIdE_0) ).

thf(483,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)],[141]) ).

thf(39,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsingletonD__dest_0) ).

thf(251,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)],[39]) ).

thf(14,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( A @ c_union ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__absorb_0) ).

thf(198,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( A @ c_union ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(131,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( A
      = ( C @ ( B @ ( C @ ( B @ ( A @ c_Main_Osurj__pair__2 ) ) @ ( C @ ( B @ ( A @ c_Main_Osurj__pair__1 ) ) @ c_Pair ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_Osurj__pair_0) ).

thf(462,plain,
    ! [C: $i,B: $i,A: $i] :
      ( A
      = ( C @ ( B @ ( C @ ( B @ ( A @ c_Main_Osurj__pair__2 ) ) @ ( C @ ( B @ ( A @ c_Main_Osurj__pair__1 ) ) @ c_Pair ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(158,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ tc_prod ) @ ( c_IntDef_Ointrel @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_Pair ) ) ) @ ( tc_nat @ ( tc_nat @ ( D @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
       != ( tc_nat @ ( D @ ( C @ c_plus ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ointrel__iff_1) ).

thf(521,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ tc_prod ) @ ( c_IntDef_Ointrel @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_Pair ) ) ) @ ( tc_nat @ ( tc_nat @ ( D @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
       != ( tc_nat @ ( D @ ( C @ c_plus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(27,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_insert ) ) )
      = ( C @ ( B @ ( A @ c_insert ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__absorb2_0) ).

thf(226,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_insert ) ) )
      = ( C @ ( B @ ( A @ c_insert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(123,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ~ ( B @ ( A @ ( D @ c_in ) ) )
      | ~ ( B @ ( A @ ( C @ c_in ) ) )
      | ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Infinite__Set_Oatmost__one__unique_0) ).

thf(438,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)],[123]) ).

thf(34,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
     != c_List_Olist_ONil ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Odistinct__2_0) ).

thf(241,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)],[34]) ).

thf(144,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( C @ ( F @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Ozip ) ) ) )
      = ( F @ ( C @ tc_prod ) @ ( F @ ( C @ ( E @ ( B @ c_List_Ozip ) ) ) @ ( F @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_List_Olist_OCons ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ozip__Cons__Cons_0) ).

thf(490,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( C @ ( F @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Ozip ) ) ) )
      = ( F @ ( C @ tc_prod ) @ ( F @ ( C @ ( E @ ( B @ c_List_Ozip ) ) ) @ ( F @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_List_Olist_OCons ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(118,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ tc_prod ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( C @ ( D @ c_Pair ) ) ) @ c_in ) ) )
      | ( B @ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( D @ ( C @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Oacyclic ) )
      | ~ ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert_2) ).

thf(426,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)],[118]) ).

thf(163,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Or__into__rtrancl_0) ).

thf(531,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)],[163]) ).

thf(94,axiom,
    ! [A: $i] :
      ( ( A @ ( c_emptyset @ c_Transitive__Closure_Otrancl ) )
      = c_emptyset ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__empty_0) ).

thf(374,plain,
    ! [A: $i] :
      ( ( A @ ( c_emptyset @ c_Transitive__Closure_Otrancl ) )
      = c_emptyset ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(79,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( A @ c_Relation_Odiag ) @ c_Relation_ODomain ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ODomain__diag_0) ).

thf(342,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( A @ c_Relation_Odiag ) @ c_Relation_ODomain ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(12,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ tc_prod ) @ ( E @ ( D @ ( D @ ( B @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ ( E @ c_List_Olistrel ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Cons2_2) ).

thf(194,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ tc_prod ) @ ( E @ ( D @ ( D @ ( B @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ ( E @ c_List_Olistrel ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(160,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( D @ c_List_Olexord ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ ( F @ ( B @ c_List_Olist_OCons ) ) @ ( C @ ( E @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olexord__cons__cons_2) ).

thf(525,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( D @ c_List_Olexord ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ ( F @ ( B @ c_List_Olist_OCons ) ) @ ( C @ ( E @ ( A @ c_List_Olist_OCons ) ) @ 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)],[160]) ).

thf(59,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( D @ c_List_Olex ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ ( B @ ( E @ c_List_Olist_OCons ) ) @ ( C @ ( A @ ( E @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( D @ c_List_Olex ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_OCons__in__lex_5) ).

thf(295,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( D @ c_List_Olex ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ ( B @ ( E @ c_List_Olist_OCons ) ) @ ( C @ ( A @ ( E @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( D @ c_List_Olex ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(110,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( A @ ( C @ ( D @ ( B @ ( A @ c_Main_ORangeE__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ ( D @ ( C @ ( B @ c_Relation_ORange ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ORangeE_0) ).

thf(409,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)],[110]) ).

thf(44,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ ( B @ c_less ) ) )
      | ~ ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_plus ) ) @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__less_0) ).

thf(263,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ ( B @ c_less ) ) )
      | ~ ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_plus ) ) @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(7,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( D @ c_List_Olex ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ ( F @ ( B @ c_List_Olist_OCons ) ) @ ( C @ ( E @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( ( C @ tc_List_Olist @ ( E @ c_Nat_Osize ) )
       != ( C @ tc_List_Olist @ ( F @ c_Nat_Osize ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_OCons__in__lex_4) ).

thf(182,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( D @ c_List_Olex ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ ( F @ ( B @ c_List_Olist_OCons ) ) @ ( C @ ( E @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( ( C @ tc_List_Olist @ ( E @ c_Nat_Osize ) )
       != ( C @ tc_List_Olist @ ( F @ c_Nat_Osize ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(75,axiom,
    tc_Product__Type_Ounit @ class_Finite__Set_Ofinite,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Product____Type__Ounit_0) ).

thf(331,plain,
    tc_Product__Type_Ounit @ class_Finite__Set_Ofinite,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(124,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( E @ ( F @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__3 ) ) ) ) ) @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__1 ) ) ) ) ) @ c_Pair ) ) ) ) )
      | ~ ( E @ ( F @ tc_prod ) @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Orel__compE_2) ).

thf(441,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)],[124]) ).

thf(149,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_fst ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_Ofst__conv_0) ).

thf(502,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_fst ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(135,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__into__rtrancl_0) ).

thf(470,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)],[135]) ).

thf(99,axiom,
    ! [B: $i,A: $i] :
      ~ ( B @ ( c_emptyset @ ( A @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__iff_0) ).

thf(386,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ ( c_emptyset @ ( A @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(68,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( E @ ( D @ ( B @ ( A @ ( C @ c_Main_OImageE__1 ) ) ) ) @ c_in ) ) )
      | ~ ( E @ ( E @ ( D @ ( C @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImageE_0) ).

thf(314,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)],[68]) ).

thf(88,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( C @ ( B @ ( A @ c_snd ) ) @ ( C @ ( B @ ( A @ c_fst ) ) @ c_Pair ) ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_Opair__collapse_0) ).

thf(363,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( C @ ( B @ ( A @ c_snd ) ) @ ( C @ ( B @ ( A @ c_fst ) ) @ c_Pair ) ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(16,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_prod ) @ ( E @ ( C @ ( C @ ( C @ ( B @ ( A @ ( D @ ( E @ c_Main_Olistrel__Cons1__1 ) ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( E @ c_List_Olistrel ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Cons1_2) ).

thf(203,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_prod ) @ ( E @ ( C @ ( C @ ( C @ ( B @ ( A @ ( D @ ( E @ c_Main_Olistrel__Cons1__1 ) ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( E @ c_List_Olistrel ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(159,axiom,
    tc_Product__Type_Ounit @ ( t_a @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OPartialOrder @ ( v_cl @ c_in ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Ocl_A_58_APartialOrder_0) ).

thf(524,plain,
    tc_Product__Type_Ounit @ ( t_a @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OPartialOrder @ ( v_cl @ c_in ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(147,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = F )
      | ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
       != ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq_1) ).

thf(495,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)],[147]) ).

thf(23,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( E @ c_List_Olistrel ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ ( D @ ( E @ c_Main_Olistrel__Cons1__2 ) ) ) ) @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( E @ c_List_Olistrel ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Cons1_1) ).

thf(218,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( E @ c_List_Olistrel ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ ( D @ ( E @ c_Main_Olistrel__Cons1__2 ) ) ) ) @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( E @ c_List_Olistrel ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(156,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ tc_prod ) @ ( D @ ( C @ ( E @ c_Relation_Oconverse ) ) @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Oconverse__iff_1) ).

thf(517,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)],[156]) ).

thf(70,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( A @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_OlistsE_1) ).

thf(319,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)],[70]) ).

thf(83,axiom,
    ! [A: $i] :
      ( ( A @ ( c_emptyset @ c_Relation_Odiag ) )
      = c_emptyset ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Odiag__empty_0) ).

thf(351,plain,
    ! [A: $i] :
      ( ( A @ ( c_emptyset @ c_Relation_Odiag ) )
      = c_emptyset ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(101,axiom,
    ! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ tc_prod ) @ tc_set @ ( c_IntDef_OInteg @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_emptyset @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ ( c_IntDef_Ointrel @ c_Relation_OImage ) ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ointrel_A_96_96_A_123_Ix1_M_Ay1_J_125_A_58_AInteg_A_61_61_ATrue_0) ).

thf(390,plain,
    ! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ tc_prod ) @ tc_set @ ( c_IntDef_OInteg @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_emptyset @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ ( c_IntDef_Ointrel @ c_Relation_OImage ) ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(106,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ tc_prod ) @ ( c_Relation_OId @ ( A @ c_union ) ) @ c_Transitive__Closure_Ortrancl ) )
      = ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl__reflcl_0) ).

thf(401,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ tc_prod ) @ ( c_Relation_OId @ ( A @ c_union ) ) @ c_Transitive__Closure_Ortrancl ) )
      = ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(57,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Wellfounded__Recursion_Oacyclic ) )
      | ~ ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse_1) ).

thf(290,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Wellfounded__Recursion_Oacyclic ) )
      | ~ ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(36,axiom,
    tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Wellfounded__Recursion_Owf ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Owf__less__than_0) ).

thf(246,plain,
    tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Wellfounded__Recursion_Owf ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(48,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( c_emptyset @ ( c_List_Olist_ONil @ c_insert ) ) @ ( B @ ( A @ c_List_Olistrel ) @ c_Relation_OImage ) ) ) )
      = ( B @ tc_List_Olist @ ( c_emptyset @ ( c_List_Olist_ONil @ c_insert ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Nil_0) ).

thf(272,plain,
    ! [B: $i,A: $i] :
      ( ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( c_emptyset @ ( c_List_Olist_ONil @ c_insert ) ) @ ( B @ ( A @ c_List_Olistrel ) @ c_Relation_OImage ) ) ) )
      = ( B @ tc_List_Olist @ ( c_emptyset @ ( c_List_Olist_ONil @ c_insert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(98,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( C @ ( C @ tc_prod ) @ ( F @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( F @ c_List_Olex ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_OCons__in__lex_0) ).

thf(383,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( C @ ( C @ tc_prod ) @ ( F @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( F @ c_List_Olex ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(81,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
       != ( B @ ( c_emptyset @ ( C @ c_insert ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__inject__dest_0) ).

thf(346,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)],[81]) ).

thf(166,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl_Or__into__trancl_0) ).

thf(536,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)],[166]) ).

thf(21,axiom,
    ! [B: $i,A: $i] :
      ~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Onot__psubset__empty_0) ).

thf(214,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(121,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( C @ ( D @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__1 ) ) ) @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__2 ) ) ) @ c_Pair ) ) ) ) )
      | ~ ( C @ ( D @ tc_prod ) @ ( D @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OconverseE_1) ).

thf(433,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)],[121]) ).

thf(153,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D = C )
      | ~ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( C @ ( D @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( D @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( B @ ( A @ c_Relation_Oantisym ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Oantisym__def_0) ).

thf(510,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D = C )
      | ~ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( C @ ( D @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( D @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( B @ ( A @ c_Relation_Oantisym ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(1,negated_conjecture,
    t_a @ ( t_a @ tc_prod ) @ ( v_r @ ( t_a @ ( t_a @ ( v_b @ ( v_a @ c_Pair ) ) ) @ c_in ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(168,plain,
    t_a @ ( t_a @ tc_prod ) @ ( v_r @ ( t_a @ ( t_a @ ( v_b @ ( v_a @ c_Pair ) ) ) @ c_in ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(10,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( B @ ( A @ c_in ) ) )
      | ( D @ ( C @ ( A @ c_in ) ) )
      | ~ ( D @ ( D @ ( C @ ( B @ c_union ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__iff_0) ).

thf(190,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)],[10]) ).

thf(93,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsingletonI_0) ).

thf(373,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(64,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( C @ ( c_emptyset @ ( A @ c_insert ) ) @ ( E @ c_Relation_OImage ) ) ) @ ( B @ c_in ) ) )
      | ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImage__singleton__iff_1) ).

thf(305,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)],[64]) ).

thf(19,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( c_emptyset @ ( A @ c_union ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty__right_0) ).

thf(210,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( c_emptyset @ ( A @ c_union ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(72,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ ( c_List_Olist_ONil @ c_List_Ozip ) ) ) )
      = c_List_Olist_ONil ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ozip__Nil_0) ).

thf(326,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ ( c_List_Olist_ONil @ c_List_Ozip ) ) ) )
      = c_List_Olist_ONil ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(33,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( c_emptyset @ c_Relation_ORange ) ) )
      = c_emptyset ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ORange__empty_0) ).

thf(239,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( c_emptyset @ c_Relation_ORange ) ) )
      = c_emptyset ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(86,axiom,
    ! [A: $i] :
      ~ ( tc_nat @ ( A @ ( A @ c_less ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__irrefl_0) ).

thf(358,plain,
    ! [A: $i] :
      ~ ( tc_nat @ ( A @ ( A @ c_less ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(137,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ tc_prod ) @ ( E @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ ( C @ tc_prod ) @ ( C @ ( D @ ( E @ c_Relation_Oconverse ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Oconverse__iff_0) ).

thf(474,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)],[137]) ).

thf(113,axiom,
    ! [C: $i,B: $i,A: $i] :
      ~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olexord ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olexord__Nil__right_0) ).

thf(415,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olexord ) @ ( 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)],[113]) ).

thf(151,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( D @ tc_prod ) @ ( B @ ( D @ ( A @ ( C @ c_Wellfounded__Relations_Olex__prod ) ) ) @ c_Relation_Otrans ) )
      | ~ ( D @ ( C @ c_Relation_Otrans ) )
      | ~ ( B @ ( A @ c_Relation_Otrans ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Otrans__lex__prod_0) ).

thf(506,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( D @ tc_prod ) @ ( B @ ( D @ ( A @ ( C @ c_Wellfounded__Relations_Olex__prod ) ) ) @ c_Relation_Otrans ) )
      | ~ ( D @ ( C @ c_Relation_Otrans ) )
      | ~ ( B @ ( A @ c_Relation_Otrans ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(46,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_insert ) ) )
     != c_emptyset ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__not__empty_0) ).

thf(268,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_insert ) ) )
     != c_emptyset ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(104,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Relation_Oantisym ) )
      | ( ( B @ ( A @ c_Main_Oantisym__def__1 ) )
       != ( B @ ( A @ c_Main_Oantisym__def__2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Oantisym__def_3) ).

thf(395,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Relation_Oantisym ) )
      | ( ( B @ ( A @ c_Main_Oantisym__def__1 ) )
       != ( B @ ( A @ c_Main_Oantisym__def__2 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(132,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( C @ ( A @ ( B @ c_Main_OdiagE__1 ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_Odiag ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OdiagE_1) ).

thf(464,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)],[132]) ).

thf(76,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
       != ( tc_nat @ ( C @ ( A @ c_plus ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel_0) ).

thf(332,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
       != ( tc_nat @ ( C @ ( A @ c_plus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(130,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( C @ ( C @ ( C @ ( A @ ( B @ c_Main_OdiagE__1 ) ) @ ( C @ ( A @ ( B @ c_Main_OdiagE__1 ) ) @ c_Pair ) ) ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_Odiag ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OdiagE_0) ).

thf(459,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)],[130]) ).

thf(15,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ tc_List_Olist @ ( B @ c_Nat_Osize ) )
        = ( C @ tc_List_Olist @ ( E @ c_Nat_Osize ) ) )
      | ( A = D )
      | ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( F @ c_List_Olex ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_OCons__in__lex_2) ).

thf(200,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ tc_List_Olist @ ( B @ c_Nat_Osize ) )
        = ( C @ tc_List_Olist @ ( E @ c_Nat_Osize ) ) )
      | ( A = D )
      | ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( F @ c_List_Olex ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(51,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( A @ c_Relation_Odiag ) @ c_Relation_Oconverse ) ) )
      = ( B @ ( A @ c_Relation_Odiag ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Oconverse__diag_0) ).

thf(277,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( A @ c_Relation_Odiag ) @ c_Relation_Oconverse ) ) )
      = ( B @ ( A @ c_Relation_Odiag ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(91,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( c_List_Olist_ONil @ ( A @ c_List_Ozip ) ) ) )
      = c_List_Olist_ONil ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ozip_Osimps__1_0) ).

thf(369,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( c_List_Olist_ONil @ ( A @ c_List_Ozip ) ) ) )
      = c_List_Olist_ONil ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(40,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Relation_ORange ) ) )
      = ( B @ ( B @ ( A @ c_Relation_ORange ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__range_0) ).

thf(254,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Relation_ORange ) ) )
      = ( B @ ( B @ ( A @ c_Relation_ORange ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(142,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( E @ ( D @ ( B @ ( A @ ( C @ c_Main_OImageE__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( E @ ( E @ ( D @ ( C @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImageE_1) ).

thf(486,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)],[142]) ).

thf(78,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
       != ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Oinject_1) ).

thf(337,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)],[78]) ).

thf(66,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( c_List_Olist_ONil
     != ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Odistinct__1_0) ).

thf(309,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)],[66]) ).

thf(25,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olex ) @ c_Wellfounded__Recursion_Owf ) )
      | ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Owf__lex_0) ).

thf(222,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)],[25]) ).

thf(128,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_nat @ ( D @ ( A @ c_plus ) ) )
        = ( tc_nat @ ( B @ ( C @ c_plus ) ) ) )
      | ~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ tc_prod ) @ ( c_IntDef_Ointrel @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ ( D @ ( C @ c_Pair ) ) ) @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ointrel__iff_0) ).

thf(454,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_nat @ ( D @ ( A @ c_plus ) ) )
        = ( tc_nat @ ( B @ ( C @ c_plus ) ) ) )
      | ~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ tc_prod ) @ ( c_IntDef_Ointrel @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ ( D @ ( C @ c_Pair ) ) ) @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(30,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Transitive__Closure_Ortrancl ) )
      = ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl__idemp_0) ).

thf(232,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Transitive__Closure_Ortrancl ) )
      = ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(552,plain,
    $false,
    inference(e,[status(thm)],[365,479,249,468,234,481,170,449,247,379,533,500,472,538,404,185,417,288,301,436,504,344,196,421,284,228,316,261,216,492,179,321,376,353,411,428,265,527,312,307,292,529,381,220,349,297,275,192,407,329,224,519,403,188,388,356,169,488,476,212,328,256,393,515,457,173,371,244,360,205,508,398,298,279,444,513,430,176,423,286,281,259,413,391,466,335,236,274,419,230,451,303,271,208,494,367,535,483,251,198,462,521,226,438,241,490,426,531,374,342,194,525,295,409,263,182,331,441,502,470,386,314,363,203,524,495,218,517,319,351,390,401,290,246,272,383,346,536,214,433,510,168,190,373,305,210,326,239,358,474,415,506,268,395,464,332,459,200,277,369,254,486,337,309,222,454,232]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05  % Problem  : LAT259-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.13  % Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.23/0.50  % Computer : n006.cluster.edu
% 0.23/0.50  % Model    : x86_64 x86_64
% 0.23/0.50  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.50  % Memory   : 8046.5625MB
% 0.23/0.50  % OS       : Linux 6.8.0-71-generic
% 0.23/0.50  % CPULimit : 300
% 0.23/0.50  % WCLimit  : 300
% 0.23/0.50  % DateTime : Fri Sep 25 20:21:00 UTC 2026
% 0.23/0.50  % CPUTime  : 
% 0.23/0.50  Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.96/1.02  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 4.18/1.81  % [INFO] 	 Parsing done (783ms). 
% 4.18/1.84  % [INFO] 	 Running in sequential loop mode. 
% 5.63/2.42  % [INFO] 	 eprover registered as external prover. 
% 5.63/2.43  % [INFO] 	 Scanning for conjecture ... 
% 7.38/2.90  % [INFO] 	 Found a conjecture (or negated_conjecture) and 2747 axioms. Running axiom selection ... 
% 9.08/3.35  % [INFO] 	 Axiom selection finished. Selected 164 axioms (removed 2583 axioms). 
% 9.74/3.57  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 9.74/3.60  % [INFO] 	 Type checking passed. 
% 9.91/3.60  % [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 ... 
% 15.34/5.39  % External prover 'e' found a proof!
% 15.34/5.39  % [INFO] 	 Killing All external provers ... 
% 15.34/5.39  % Time passed: 4731ms (effective reasoning time: 3541ms)
% 15.34/5.39  % Axioms used in derivation (164): cls_List_Olistrel__Cons1_0, cls_Relation_ODomain__empty_0, cls_Transitive__Closure_Otrancl__range_0, cls_Nat_Onat__add__left__cancel__less_1, cls_Set_Osingleton__insert__inj__eq_0, cls_List_Olists_ONil_0, cls_List_Onth__zip_0, cls_Relation_OImageI_0, cls_List_Olistrel__Cons2_1, cls_Relation_ODomain__diag_0, cls_List_OCons__in__lex_1, cls_Relation_ORange__diag_0, cls_List_Olexord__cons__cons_2, cls_Nat_Onat__add__right__cancel_0, clsarity_prod_0, cls_Wellfounded__Recursion_Owf__insert_0, cls_Product__Type_Ofst__conv_0, cls_IntDef_Ointrel_A_96_96_A_123_Ix1_M_Ay1_J_125_A_58_AInteg_A_61_61_ATrue_0, cls_Transitive__Closure_Otrancl_Or__into__trancl_0, cls_Set_Osingleton__inject__dest_0, cls_Relation_OImageE_0, cls_Transitive__Closure_Ortrancl__reflcl_0, cls_List_Olexord__Nil__left_0, cls_Wellfounded__Relations_Owf__lex__prod_0, cls_Nat_Oless__irrefl_0, cls_List_Olistrel__Nil1_0, cls_Transitive__Closure_Ortrancl__idemp_0, cls_List_Olist_Oinject_1, cls_Relation_Oconverse__converse_0, cls_Relation_OconverseE_1, cls_Set_Osingleton__insert__inj__eq_H_0, cls_Product__Type_Osurj__pair_0, cls_Relation_Orel__compE_0, cls_Relation_Opair__in__Id__conv_0, cls_Relation_ORangeE_0, cls_List_OCons__in__lex_0, cls_Relation_Oantisym__def_3, cls_Nat_Onat__add__left__cancel__less_0, cls_List_OCons__in__lex_5, cls_Wellfounded__Recursion_Oacyclic__converse_1, cls_Relation_OdiagI_0, cls_IntDef_Ointrel__iff_1, cls_Transitive__Closure_Ortrancl__empty_0, cls_List_OlistsE_0, cls_Tarski_OPartialOrder__iff_0, cls_Relation_Oantisym__def_2, cls_List_Olistrel__Cons2_0, cls_Relation_ODomainI_0, cls_List_Olexord__cons__cons_1, cls_Tarski_OA_A_61_61_Apset_Acl_0, cls_Set_OUn__iff_0, cls_List_Owf__lex_0, cls_Set_OUn__empty_1, cls_Relation_OImage__Id_0, cls_Wellfounded__Recursion_Oacyclic__insert_1, cls_Relation_Orel__compE_2, cls_Set_Oinsert__iff_2, cls_List_ONil2__notin__lex_0, cls_Relation_OImageE_1, cls_Relation_OdiagE_0, cls_Set_OsingletonD__dest_0, clsarity_set_3, cls_Relation_OImage__singleton__iff_1, cls_Set_Oinsert__not__empty_0, cls_Transitive__Closure_Ortrancl_Ortrancl__refl_0, cls_Transitive__Closure_Otrancl__empty_0, cls_List_OCons__in__lex_4, cls_Relation_Oconverse__iff_1, cls_List_ONil__notin__lex_0, cls_List_Ox2_A_D_At1_A_61_At1_A_61_61_AFalse_0, cls_List_Olist_Oinject_0, cls_Set_Oempty__iff_0, cls_Wellfounded__Recursion_Owf__not__refl_0, cls_Tarski_Ocl_A_58_APartialOrder_0, cls_Set_OsingletonI_0, cls_Relation_ORange__empty_0, cls_List_Ozip_Osimps__1_0, cls_Relation_OImage__empty_0, cls_Relation_OconverseE_0, cls_Set_Oall__not__in__conv_0, cls_Set_Oinsert__iff_1, cls_Relation_Oconverse__diag_0, cls_Relation_ORangeI_0, cls_Relation_OId__O__R_0, cls_Infinite__Set_Oatmost__one__unique_0, cls_Relation_Opair__in__Id__conv_1, cls_Wellfounded__Relations_Otrans__less__than_0, cls_IntDef_Ointrel__iff_0, cls_Tarski_Or_A_61_61_Aorder_Acl_0, cls_Set_OUn__insert__left_0, cls_Wellfounded__Recursion_Oacyclic__converse_0, cls_Wellfounded__Recursion_Owf__insert_2, cls_Set_OUn__insert__right_0, cls_Nat_Onot__add__less1_0, cls_Relation_OR__O__Id_0, cls_List_Olist_Odistinct__2_0, cls_List_Olistrel__Nil_0, cls_IntDef_Oequiv__intrel__iff_0, cls_Product__Type_OPair__eq_1, cls_Wellfounded__Recursion_Owf__empty_0, cls_Wellfounded__Relations_Owf__less__than_0, cls_Transitive__Closure_Or__into__rtrancl_0, cls_List_OCons__in__lex_3, cls_Relation_Oconverse__iff_0, cls_Tarski_OPartialOrder__iff_2, cls_List_Olistrel__Cons1_2, cls_List_OlistsE_1, cls_Relation_OImage__singleton__iff_0, cls_List_Onot__Cons__self_0, cls_Set_OUn__iff_1, cls_Wellfounded__Recursion_Oacyclic__insert_2, cls_Tarski_OPartialOrder__iff_1, cls_Relation_Orel__compI_0, cls_List_Olist_Odistinct__1_0, cls_Set_Oempty__not__insert_0, cls_Wellfounded__Relations_Oless__than__iff_1, cls_Nat_Onot__add__less2_0, cls_List_Olistrel__Nil2_0, cls_Transitive__Closure_Otrancl__domain_0, cls_List_Olexord__Nil__right_0, cls_Relation_OdiagE_1, cls_Wellfounded__Relations_Otrans__lex__prod_0, cls_Relation_Odiag__empty_0, cls_Set_OUn__empty__left_0, cls_Set_OUn__empty__right_0, cls_Transitive__Closure_Otrancl__reflcl_0, cls_Wellfounded__Recursion_Owf__insert_1, cls_List_Olistrel__Cons2_2, cls_List_Olistrel__Cons1_1, cls_Set_Ocontents__eq_0, cls_List_Ozip__Nil_0, cls_Relation_ODomainE_0, cls_List_Olexord__cons__cons_3, cls_IntDef_Oequiv__intrel__iff_1, cls_Relation_Oantisym__def_0, cls_Nat_Onat__add__left__cancel_0, clsarity_Product____Type__Ounit_0, cls_List_Olistset_Osimps__1_0, cls_Product__Type_OPair__eq_0, cls_List_Olexord__Nil__left_1, cls_Transitive__Closure_Oreflcl__trancl_0, cls_List_Ozip__Cons__Cons_0, cls_List_Olexord__cons__cons_0, cls_List_OCons__in__lex_2, cls_Transitive__Closure_Ortrancl__idemp__self__comp_0, cls_Product__Type_Osnd__conv_0, cls_Set_OUn__empty_0, cls_Set_Oinsert__absorb2_0, cls_Set_Onot__psubset__empty_0, cls_Set_Oinsert__iff_0, cls_Wellfounded__Recursion_Oacyclic__insert_0, cls_Set_OUn__empty_2, cls_List_Owf__lenlex_0, cls_Relation_OIdE_0, cls_Set_OUn__iff_2, cls_Relation_Oantisym__def_1, cls_Relation_Orel__compE_1, cls_Product__Type_Opair__collapse_0, cls_Wellfounded__Relations_Oless__than__iff_0, cls_Set_OUn__absorb_0, cls_List_Olists_OCons_0, cls_Tarski_OPartialOrder__iff_3, cls_Transitive__Closure_Otrancl__into__rtrancl_0, cls_Relation_Oconverse__Id_0
% 15.34/5.39  % No. of inferences in proof: 335
% 15.34/5.39  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4731 ms resp. 3541 ms w/o parsing
% 16.33/5.56  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 16.33/5.57  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------